LMFDB - Embedded newform 198.6.f.a.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, 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("198.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 1266x^{4} + 37016x^{2} + 436921 $ x^8 + x^6 + 1266x^4 + 37016x^2 + 436921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$-1.24383 - 3.82812i$ of defining polynomial
Character	$\chi$	$=$	198.91
Dual form			198.6.f.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 + 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(32.9084 + 23.9094i) q^{5} +(2.26170 - 6.96081i) q^{7} +(19.7771 + 60.8676i) q^{8} +O(q^{10})$	\(q+(-3.23607 + 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(32.9084 + 23.9094i) q^{5} +(2.26170 - 6.96081i) q^{7} +(19.7771 + 60.8676i) q^{8} -162.708 q^{10} +(400.203 + 29.8071i) q^{11} +(-237.143 + 172.295i) q^{13} +(9.04681 + 27.8432i) q^{14} +(-207.108 - 150.473i) q^{16} +(314.363 + 228.398i) q^{17} +(-70.6910 - 217.565i) q^{19} +(526.535 - 382.550i) q^{20} +(-1365.17 + 844.476i) q^{22} +1299.46 q^{23} +(-454.372 - 1398.41i) q^{25} +(362.323 - 1115.11i) q^{26} +(-94.7394 - 68.8322i) q^{28} +(-496.394 + 1527.74i) q^{29} +(2922.35 - 2123.21i) q^{31} +1024.00 q^{32} -1554.29 q^{34} +(240.857 - 174.993i) q^{35} +(2018.51 - 6212.34i) q^{37} +(740.286 + 537.849i) q^{38} +(-804.473 + 2475.91i) q^{40} +(2453.92 + 7552.40i) q^{41} +8779.75 q^{43} +(2432.28 - 5942.48i) q^{44} +(-4205.14 + 3055.21i) q^{46} +(4868.56 + 14983.9i) q^{47} +(13553.8 + 9847.42i) q^{49} +(4758.25 + 3457.07i) q^{50} +(1449.29 + 4460.46i) q^{52} +(-17784.1 + 12920.9i) q^{53} +(12457.4 + 10549.5i) q^{55} +468.418 q^{56} +(-1985.58 - 6110.98i) q^{58} +(-8330.81 + 25639.6i) q^{59} +(27878.3 + 20254.7i) q^{61} +(-4464.96 + 13741.7i) q^{62} +(-3313.73 + 2407.57i) q^{64} -11923.5 q^{65} -7617.73 q^{67} +(5029.80 - 3654.36i) q^{68} +(-367.997 + 1132.58i) q^{70} +(29759.3 + 21621.4i) q^{71} +(-12060.5 + 37118.4i) q^{73} +(8074.04 + 24849.4i) q^{74} -3660.18 q^{76} +(1112.62 - 2718.32i) q^{77} +(-67158.1 + 48793.2i) q^{79} +(-3217.89 - 9903.66i) q^{80} +(-25697.8 - 18670.6i) q^{82} +(68519.7 + 49782.4i) q^{83} +(4884.33 + 15032.4i) q^{85} +(-28411.9 + 20642.4i) q^{86} +(6100.57 + 24948.9i) q^{88} +100231. q^{89} +(662.962 + 2040.39i) q^{91} +(6424.88 - 19773.7i) q^{92} +(-50984.2 - 37042.2i) q^{94} +(2875.50 - 8849.88i) q^{95} +(-21403.4 + 15550.5i) q^{97} -67013.7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 32 q^{4} - 118 q^{5} + 2 q^{7} - 128 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 - 32 * q^4 - 118 * q^5 + 2 * q^7 - 128 * q^8	$ 8 q - 8 q^{2} - 32 q^{4} - 118 q^{5} + 2 q^{7} - 128 q^{8} - 112 q^{10} + 550 q^{11} + 958 q^{13} + 8 q^{14} - 512 q^{16} + 2600 q^{17} - 2336 q^{19} - 1888 q^{20} + 3064 q^{23} + 3988 q^{25} - 2808 q^{26} - 3488 q^{28} - 1572 q^{29} + 6188 q^{31} + 8192 q^{32} - 20240 q^{34} - 23722 q^{35} + 25114 q^{37} + 18696 q^{38} + 8448 q^{40} + 11914 q^{41} + 5528 q^{43} - 8800 q^{44} + 13576 q^{46} - 4354 q^{47} - 820 q^{49} - 25048 q^{50} - 11232 q^{52} - 18200 q^{53} - 44440 q^{55} + 27648 q^{56} - 6288 q^{58} - 98072 q^{59} - 10418 q^{61} - 23208 q^{62} - 8192 q^{64} - 99228 q^{65} + 76988 q^{67} + 41600 q^{68} + 58432 q^{70} + 84262 q^{71} - 72668 q^{73} + 100456 q^{74} - 74816 q^{76} - 132902 q^{77} - 192754 q^{79} + 33792 q^{80} - 26024 q^{82} + 106918 q^{83} - 219410 q^{85} - 169288 q^{86} + 49280 q^{88} - 128160 q^{89} - 37642 q^{91} - 78816 q^{92} + 35184 q^{94} + 90446 q^{95} + 45470 q^{97} - 331840 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 32 * q^4 - 118 * q^5 + 2 * q^7 - 128 * q^8 - 112 * q^10 + 550 * q^11 + 958 * q^13 + 8 * q^14 - 512 * q^16 + 2600 * q^17 - 2336 * q^19 - 1888 * q^20 + 3064 * q^23 + 3988 * q^25 - 2808 * q^26 - 3488 * q^28 - 1572 * q^29 + 6188 * q^31 + 8192 * q^32 - 20240 * q^34 - 23722 * q^35 + 25114 * q^37 + 18696 * q^38 + 8448 * q^40 + 11914 * q^41 + 5528 * q^43 - 8800 * q^44 + 13576 * q^46 - 4354 * q^47 - 820 * q^49 - 25048 * q^50 - 11232 * q^52 - 18200 * q^53 - 44440 * q^55 + 27648 * q^56 - 6288 * q^58 - 98072 * q^59 - 10418 * q^61 - 23208 * q^62 - 8192 * q^64 - 99228 * q^65 + 76988 * q^67 + 41600 * q^68 + 58432 * q^70 + 84262 * q^71 - 72668 * q^73 + 100456 * q^74 - 74816 * q^76 - 132902 * q^77 - 192754 * q^79 + 33792 * q^80 - 26024 * q^82 + 106918 * q^83 - 219410 * q^85 - 169288 * q^86 + 49280 * q^88 - 128160 * q^89 - 37642 * q^91 - 78816 * q^92 + 35184 * q^94 + 90446 * q^95 + 45470 * q^97 - 331840 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$2$	−3.23607	+	2.35114i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	32.9084	+	23.9094i	0.588684	+	0.427704i	0.841844	−	0.539721i	$-0.181470\pi$
$5$	32.9084	+	23.9094i	0.588684	+	0.427704i	−0.253161	+	0.967424i	$0.581470\pi$
$6$		0			0
$7$	2.26170	−	6.96081i	0.0174458	−	0.0536926i	−0.941955	−	0.335740i	$-0.891014\pi$
$7$	2.26170	−	6.96081i	0.0174458	−	0.0536926i	0.959400	+	0.282048i	$0.0910136\pi$
$8$	19.7771	+	60.8676i	0.109254	+	0.336249i
$9$		0			0
$10$	−162.708			−0.514528
$11$	400.203	+	29.8071i	0.997238	+	0.0742741i
$11$	400.203	+	29.8071i	0.997238	+	0.0742741i
$12$		0			0
$13$	−237.143	+	172.295i	−0.389182	+	0.282757i	−0.765120	−	0.643888i	$-0.777320\pi$
$13$	−237.143	+	172.295i	−0.389182	+	0.282757i	0.375938	+	0.926645i	$0.377320\pi$
$14$	9.04681	+	27.8432i	0.0123360	+	0.0379664i
$15$		0			0
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	314.363	+	228.398i	0.263820	+	0.191677i	0.711830	−	0.702352i	$-0.247867\pi$
$17$	314.363	+	228.398i	0.263820	+	0.191677i	−0.448009	+	0.894029i	$0.647867\pi$
$18$		0			0
$19$	−70.6910	−	217.565i	−0.0449242	−	0.138262i	0.926079	−	0.377331i	$-0.123158\pi$
$19$	−70.6910	−	217.565i	−0.0449242	−	0.138262i	−0.971003	+	0.239068i	$0.923158\pi$
$20$	526.535	−	382.550i	0.294342	−	0.213852i
$21$		0			0
$22$	−1365.17	+	844.476i	−0.601352	+	0.371990i
$23$	1299.46			0.512204			0.256102	−	0.966650i	$-0.417562\pi$
$23$	1299.46			0.512204			0.256102	+	0.966650i	$0.417562\pi$
$24$		0			0
$25$	−454.372	−	1398.41i	−0.145399	−	0.447492i
$26$	362.323	−	1115.11i	0.105114	−	0.323509i
$27$		0			0
$28$	−94.7394	−	68.8322i	−0.0228368	−	0.0165919i
$29$	−496.394	+	1527.74i	−0.109605	+	0.337330i	−0.990784	−	0.135453i	$-0.956751\pi$
$29$	−496.394	+	1527.74i	−0.109605	+	0.337330i	0.881178	+	0.472784i	$0.156751\pi$
$30$		0			0
$31$	2922.35	−	2123.21i	0.546171	−	0.396816i	−0.280201	−	0.959941i	$-0.590401\pi$
$31$	2922.35	−	2123.21i	0.546171	−	0.396816i	0.826372	+	0.563125i	$0.190401\pi$
$32$	1024.00			0.176777
$33$		0			0
$34$	−1554.29			−0.230588
$35$	240.857	−	174.993i	0.0332346	−	0.0241463i
$36$		0			0
$37$	2018.51	−	6212.34i	0.242397	−	0.746020i	−0.753657	−	0.657268i	$-0.771712\pi$
$37$	2018.51	−	6212.34i	0.242397	−	0.746020i	0.996054	−	0.0887525i	$-0.0282880\pi$
$38$	740.286	+	537.849i	0.0831650	+	0.0604229i
$39$		0			0
$40$	−804.473	+	2475.91i	−0.0794990	+	0.244673i
$41$	2453.92	+	7552.40i	0.227982	+	0.701658i	0.997975	+	0.0636052i	$0.0202598\pi$
$41$	2453.92	+	7552.40i	0.227982	+	0.701658i	−0.769993	+	0.638053i	$0.779740\pi$
$42$		0			0
$43$	8779.75			0.724121			0.362061	−	0.932155i	$-0.382073\pi$
$43$	8779.75			0.724121			0.362061	+	0.932155i	$0.382073\pi$
$44$	2432.28	−	5942.48i	0.189401	−	0.462739i
$45$		0			0
$46$	−4205.14	+	3055.21i	−0.293012	+	0.212886i
$47$	4868.56	+	14983.9i	0.321481	+	0.989417i	0.973004	+	0.230788i	$0.0741305\pi$
$47$	4868.56	+	14983.9i	0.321481	+	0.989417i	−0.651523	+	0.758629i	$0.725869\pi$
$48$		0			0
$49$	13553.8	+	9847.42i	0.806438	+	0.585912i
$50$	4758.25	+	3457.07i	0.269167	+	0.195561i
$51$		0			0
$52$	1449.29	+	4460.46i	0.0743271	+	0.228755i
$53$	−17784.1	+	12920.9i	−0.869644	+	0.631833i	−0.930491	−	0.366314i	$-0.880620\pi$
$53$	−17784.1	+	12920.9i	−0.869644	+	0.631833i	0.0608475	+	0.998147i	$0.480620\pi$
$54$		0			0
$55$	12457.4	+	10549.5i	0.555290	+	0.470246i
$56$	468.418			0.0199601
$57$		0			0
$58$	−1985.58	−	6110.98i	−0.0775027	−	0.238529i
$59$	−8330.81	+	25639.6i	−0.311571	+	0.958917i	0.665572	+	0.746334i	$0.268188\pi$
$59$	−8330.81	+	25639.6i	−0.311571	+	0.958917i	−0.977143	+	0.212583i	$0.931812\pi$
$60$		0			0
$61$	27878.3	+	20254.7i	0.959270	+	0.696951i	0.952981	−	0.303030i	$-0.0979981\pi$
$61$	27878.3	+	20254.7i	0.959270	+	0.696951i	0.00628902	+	0.999980i	$0.497998\pi$
$62$	−4464.96	+	13741.7i	−0.147516	+	0.454007i
$63$		0			0
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	−11923.5			−0.350041
$66$		0			0
$67$	−7617.73			−0.207319			−0.103659	−	0.994613i	$-0.533055\pi$
$67$	−7617.73			−0.207319			−0.103659	+	0.994613i	$0.533055\pi$
$68$	5029.80	−	3654.36i	0.131910	−	0.0958384i
$69$		0			0
$70$	−367.997	+	1132.58i	−0.00897635	+	0.0276264i
$71$	29759.3	+	21621.4i	0.700610	+	0.509023i	0.880131	−	0.474731i	$-0.157455\pi$
$71$	29759.3	+	21621.4i	0.700610	+	0.509023i	−0.179521	+	0.983754i	$0.557455\pi$
$72$		0			0
$73$	−12060.5	+	37118.4i	−0.264886	+	0.815235i	0.726834	+	0.686813i	$0.240991\pi$
$73$	−12060.5	+	37118.4i	−0.264886	+	0.815235i	−0.991720	+	0.128421i	$0.959009\pi$
$74$	8074.04	+	24849.4i	0.171400	+	0.527516i
$75$		0			0
$76$	−3660.18			−0.0726889
$77$	1112.62	−	2718.32i	0.0213856	−	0.0522485i
$78$		0			0
$79$	−67158.1	+	48793.2i	−1.21068	+	0.879614i	−0.995293	−	0.0969143i	$-0.969103\pi$
$79$	−67158.1	+	48793.2i	−1.21068	+	0.879614i	−0.215391	+	0.976528i	$0.569103\pi$
$80$	−3217.89	−	9903.66i	−0.0562143	−	0.173010i
$81$		0			0
$82$	−25697.8	−	18670.6i	−0.422048	−	0.306636i
$83$	68519.7	+	49782.4i	1.09174	+	0.793197i	0.979693	−	0.200506i	$-0.0642585\pi$
$83$	68519.7	+	49782.4i	1.09174	+	0.793197i	0.112049	+	0.993703i	$0.464259\pi$
$84$		0			0
$85$	4884.33	+	15032.4i	0.0733259	+	0.225674i
$86$	−28411.9	+	20642.4i	−0.414242	+	0.300964i
$87$		0			0
$88$	6100.57	+	24948.9i	0.0839776	+	0.343435i
$89$	100231.			1.34131			0.670653	−	0.741771i	$-0.266014\pi$
$89$	100231.			1.34131			0.670653	+	0.741771i	$0.266014\pi$
$90$		0			0
$91$	662.962	+	2040.39i	0.00839238	+	0.0258291i
$92$	6424.88	−	19773.7i	0.0791398	−	0.243567i
$93$		0			0
$94$	−50984.2	−	37042.2i	−0.595136	−	0.432391i
$95$	2875.50	−	8849.88i	0.0326892	−	0.100607i
$96$		0			0
$97$	−21403.4	+	15550.5i	−0.230969	+	0.167809i	−0.697250	−	0.716828i	$-0.745593\pi$
$97$	−21403.4	+	15550.5i	−0.230969	+	0.167809i	0.466281	+	0.884636i	$0.345593\pi$
$98$	−67013.7			−0.704853
$99$		0			0
$100$	−23526.1			−0.235261
$101$	87776.6	−	63773.4i	0.856200	−	0.622066i	−0.0706484	−	0.997501i	$-0.522507\pi$
$101$	87776.6	−	63773.4i	0.856200	−	0.622066i	0.926849	+	0.375435i	$0.122507\pi$
$102$		0			0
$103$	11253.7	−	34635.3i	0.104521	−	0.321681i	−0.885097	−	0.465407i	$-0.845908\pi$
$103$	11253.7	−	34635.3i	0.104521	−	0.321681i	0.989618	+	0.143725i	$0.0459081\pi$
$104$	−15177.2	−	11026.9i	−0.137597	−	0.0999697i
$105$		0			0
$106$	27171.6	−	83625.7i	0.234883	−	0.722895i
$107$	33046.4	+	101706.i	0.279038	+	0.858792i	0.988123	+	0.153668i	$0.0491087\pi$
$107$	33046.4	+	101706.i	0.279038	+	0.858792i	−0.709084	+	0.705124i	$0.750891\pi$
$108$		0			0
$109$	116482.			0.939056			0.469528	−	0.882918i	$-0.344424\pi$
$109$	116482.			0.939056			0.469528	+	0.882918i	$0.344424\pi$
$110$	−65116.3	−	4849.85i	−0.513107	−	0.0382161i
$111$		0			0
$112$	−1515.83	+	1101.32i	−0.0114184	+	0.00829596i
$113$	−45834.1	−	141063.i	−0.337670	−	1.03924i	−0.965392	−	0.260804i	$-0.916012\pi$
$113$	−45834.1	−	141063.i	−0.337670	−	1.03924i	0.627722	−	0.778438i	$-0.283988\pi$
$114$		0			0
$115$	42763.1	+	31069.2i	0.301526	+	0.219071i
$116$	20793.2	+	15107.2i	0.143475	+	0.104241i
$117$		0			0
$118$	−33323.2	−	102558.i	−0.220314	−	0.678057i
$119$	2300.83	−	1671.65i	0.0148942	−	0.0108213i
$120$		0			0
$121$	159274.	+	23857.8i	0.988967	+	0.148138i
$122$	−137838.			−0.838433
$123$		0			0
$124$	−17859.8	−	54966.9i	−0.104309	−	0.321031i
$125$	57763.4	−	177778.i	0.330657	−	1.01766i
$126$		0			0
$127$	94436.1	+	68611.8i	0.519552	+	0.377476i	0.816435	−	0.577437i	$-0.195947\pi$
$127$	94436.1	+	68611.8i	0.519552	+	0.377476i	−0.296883	+	0.954914i	$0.595947\pi$
$128$	5062.93	−	15582.1i	0.0273135	−	0.0840623i
$129$		0			0
$130$	38585.1	−	28033.7i	0.200245	−	0.145487i
$131$	−305439.			−1.55506			−0.777528	−	0.628849i	$-0.783526\pi$
$131$	−305439.			−1.55506			−0.777528	+	0.628849i	$0.783526\pi$
$132$		0			0
$133$	−1674.31			−0.00820741
$134$	24651.5	−	17910.4i	0.118599	−	0.0861673i
$135$		0			0
$136$	−7684.85	+	23651.5i	−0.0356277	+	0.109651i
$137$	−224538.	−	163137.i	−1.02209	−	0.742591i	−0.0553792	−	0.998465i	$-0.517637\pi$
$137$	−224538.	−	163137.i	−1.02209	−	0.742591i	−0.966710	+	0.255874i	$0.917637\pi$
$138$		0			0
$139$	69675.1	−	214438.i	0.305873	−	0.941379i	−0.673478	−	0.739208i	$-0.735200\pi$
$139$	69675.1	−	214438.i	0.305873	−	0.941379i	0.979350	−	0.202171i	$-0.0647998\pi$
$140$	−1471.99	−	4530.32i	−0.00634724	−	0.0195348i
$141$		0			0
$142$	−147138.			−0.612356
$143$	−100041.	+	61884.3i	−0.409108	+	0.253070i
$144$		0			0
$145$	−52862.9	+	38407.2i	−0.208800	+	0.151702i
$146$	−48242.1	−	148474.i	−0.187303	−	0.576458i
$147$		0			0
$148$	−84552.5	−	61431.0i	−0.317301	−	0.230533i
$149$	−75591.2	−	54920.2i	−0.278937	−	0.202659i	0.439517	−	0.898234i	$-0.355150\pi$
$149$	−75591.2	−	54920.2i	−0.278937	−	0.202659i	−0.718454	+	0.695575i	$0.755150\pi$
$150$		0			0
$151$	−98819.4	−	304135.i	−0.352695	−	1.08548i	−0.957334	−	0.288984i	$-0.906682\pi$
$151$	−98819.4	−	304135.i	−0.352695	−	1.08548i	0.604639	−	0.796500i	$-0.293318\pi$
$152$	11844.6	−	8605.59i	0.0415825	−	0.0302115i
$153$		0			0
$154$	2790.64	+	11412.6i	0.00948204	+	0.0387778i
$155$	146935.			0.491242
$156$		0			0
$157$	−107315.	−	330280.i	−0.347464	−	1.06938i	−0.960251	−	0.279136i	$-0.909952\pi$
$157$	−107315.	−	330280.i	−0.347464	−	1.06938i	0.612787	−	0.790248i	$-0.290048\pi$
$158$	102608.	−	315796.i	0.326995	−	1.00639i
$159$		0			0
$160$	33698.2	+	24483.2i	0.104066	+	0.0756080i
$161$	2938.99	−	9045.28i	0.00893580	−	0.0275016i
$162$		0			0
$163$	55992.4	−	40680.9i	0.165067	−	0.119928i	−0.502185	−	0.864760i	$-0.667470\pi$
$163$	55992.4	−	40680.9i	0.165067	−	0.119928i	0.667252	+	0.744832i	$0.267470\pi$
$164$	127057.			0.368883
$165$		0			0
$166$	−338780.			−0.954217
$167$	96617.2	−	70196.5i	0.268079	−	0.194771i	−0.445622	−	0.895221i	$-0.647017\pi$
$167$	96617.2	−	70196.5i	0.268079	−	0.194771i	0.713701	+	0.700450i	$0.247017\pi$
$168$		0			0
$169$	−88184.4	+	271404.i	−0.237506	+	0.730969i
$170$	−51149.3	−	37162.2i	−0.135743	−	0.0986231i
$171$		0			0
$172$	43409.5	−	133601.i	0.111883	−	0.344340i
$173$	60330.2	+	185677.i	0.153257	+	0.471676i	0.997980	−	0.0635275i	$-0.0202351\pi$
$173$	60330.2	+	185677.i	0.153257	+	0.471676i	−0.844723	+	0.535203i	$0.820235\pi$
$174$		0			0
$175$	−10761.7			−0.0265636
$176$	−78400.3	−	66393.1i	−0.190781	−	0.161563i
$177$		0			0
$178$	−324355.	+	235658.i	−0.767309	+	0.557483i
$179$	168321.	+	518040.i	0.392651	+	1.20846i	0.930776	+	0.365591i	$0.119133\pi$
$179$	168321.	+	518040.i	0.392651	+	1.20846i	−0.538125	+	0.842865i	$0.680867\pi$
$180$		0			0
$181$	249369.	+	181177.i	0.565779	+	0.411062i	0.833569	−	0.552415i	$-0.186294\pi$
$181$	249369.	+	181177.i	0.565779	+	0.411062i	−0.267791	+	0.963477i	$0.586294\pi$
$182$	−6942.63	−	5044.12i	−0.0155362	−	0.0112877i
$183$		0			0
$184$	25699.5	+	79094.9i	0.0559603	+	0.172228i
$185$	214959.	−	156177.i	0.461771	−	0.335496i
$186$		0			0
$187$	119001.	+	100776.i	0.248855	+	0.210742i
$188$	252080.			0.520168
$189$		0			0
$190$	11502.0	+	35399.5i	0.0231148	+	0.0711399i
$191$	222773.	−	685623.i	0.441854	−	1.35989i	−0.444044	−	0.896005i	$-0.646457\pi$
$191$	222773.	−	685623.i	0.441854	−	1.35989i	0.885898	−	0.463880i	$-0.153543\pi$
$192$		0			0
$193$	587809.	+	427068.i	1.13591	+	0.825285i	0.986544	−	0.163497i	$-0.0522774\pi$
$193$	587809.	+	427068.i	1.13591	+	0.825285i	0.149364	+	0.988782i	$0.452277\pi$
$194$	32701.5	−	100645.i	0.0623826	−	0.191994i
$195$		0			0
$196$	216861.	−	157559.i	0.403219	−	0.292956i
$197$	−564606.			−1.03653			−0.518263	−	0.855221i	$-0.673421\pi$
$197$	−564606.			−1.03653			−0.518263	+	0.855221i	$0.673421\pi$
$198$		0			0
$199$	−715563.			−1.28090			−0.640450	−	0.768000i	$-0.721252\pi$
$199$	−715563.			−1.28090			−0.640450	+	0.768000i	$0.721252\pi$
$200$	76132.0	−	55313.1i	0.134584	−	0.0977807i
$201$		0			0
$202$	−134111.	+	412750.i	−0.231252	+	0.711720i
$203$	9511.63	+	6910.61i	0.0162000	+	0.0117700i
$204$		0			0
$205$	−99818.3	+	307209.i	−0.165892	+	0.510563i
$206$	45014.8	+	138541.i	0.0739073	+	0.227463i
$207$		0			0
$208$	75040.1			0.120264
$209$	−21805.8	−	89177.1i	−0.0345308	−	0.141217i
$210$		0			0
$211$	−100956.	+	73349.0i	−0.156109	+	0.113420i	−0.663098	−	0.748533i	$-0.730759\pi$
$211$	−100956.	+	73349.0i	−0.156109	+	0.113420i	0.506989	+	0.861953i	$0.330759\pi$
$212$	108687.	+	334503.i	0.166087	+	0.511164i
$213$		0			0
$214$	−346066.	−	251432.i	−0.516564	−	0.375306i
$215$	288928.	+	209918.i	0.426278	+	0.309709i
$216$		0			0
$217$	−8169.79	−	25144.0i	−0.0117777	−	0.0362481i
$218$	−376943.	+	273865.i	−0.537198	+	0.390297i
$219$		0			0
$220$	222123.	−	137403.i	0.309412	−	0.191399i
$221$	−113901.			−0.156872
$222$		0			0
$223$	−286019.	−	880275.i	−0.385152	−	1.18538i	−0.936370	−	0.351015i	$-0.885837\pi$
$223$	−286019.	−	880275.i	−0.385152	−	1.18538i	0.551218	−	0.834361i	$-0.314163\pi$
$224$	2315.98	−	7127.87i	0.00308401	−	0.00949160i
$225$		0			0
$226$	479981.	+	348727.i	0.625105	+	0.454165i
$227$	−245384.	+	755213.i	−0.316068	+	0.972758i	0.659244	+	0.751929i	$0.270876\pi$
$227$	−245384.	+	755213.i	−0.316068	+	0.972758i	−0.975312	+	0.220829i	$0.929124\pi$
$228$		0			0
$229$	213716.	−	155274.i	0.269307	−	0.195663i	−0.444933	−	0.895564i	$-0.646772\pi$
$229$	213716.	−	155274.i	0.269307	−	0.195663i	0.714240	+	0.699901i	$0.246772\pi$
$230$	−211432.			−0.263543
$231$		0			0
$232$	−102807.			−0.125402
$233$	−545824.	+	396565.i	−0.658663	+	0.478546i	−0.866211	−	0.499678i	$-0.833452\pi$
$233$	−545824.	+	396565.i	−0.658663	+	0.478546i	0.207548	+	0.978225i	$0.433452\pi$
$234$		0			0
$235$	−198038.	+	609500.i	−0.233927	+	0.719952i
$236$	348965.	+	253538.i	0.407852	+	0.296322i
$237$		0			0
$238$	−3515.35	+	10819.1i	−0.00402278	+	0.0123808i
$239$	294682.	+	906938.i	0.333702	+	1.02703i	0.967358	+	0.253414i	$0.0815535\pi$
$239$	294682.	+	906938.i	0.333702	+	1.02703i	−0.633656	+	0.773615i	$0.718446\pi$
$240$		0			0
$241$	326720.			0.362354			0.181177	−	0.983451i	$-0.442009\pi$
$241$	326720.			0.362354			0.181177	+	0.983451i	$0.442009\pi$
$242$	−571515.	+	297271.i	−0.627320	+	0.326297i
$243$		0			0
$244$	446052.	−	324076.i	0.479635	−	0.348475i
$245$	210589.	+	648126.i	0.224140	+	0.689833i
$246$		0			0
$247$	54249.1	+	39414.3i	0.0565784	+	0.0411066i
$248$	187031.	+	135886.i	0.193101	+	0.140296i
$249$		0			0
$250$	231054.	+	711110.i	0.233810	+	0.719593i
$251$	509224.	−	369973.i	0.510181	−	0.370668i	−0.302711	−	0.953082i	$-0.597892\pi$
$251$	509224.	−	369973.i	0.510181	−	0.370668i	0.812892	+	0.582414i	$0.197892\pi$
$252$		0			0
$253$	520047.	+	38733.0i	0.510789	+	0.0380435i
$254$	−466918.			−0.454105
$255$		0			0
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	543920.	−	1.67401e6i	0.513691	−	1.58098i	−0.271960	−	0.962309i	$-0.587672\pi$
$257$	543920.	−	1.67401e6i	0.513691	−	1.58098i	0.785651	−	0.618670i	$-0.212328\pi$
$258$		0			0
$259$	−38677.6	−	28100.9i	−0.0358270	−	0.0260298i
$260$	−58952.8	+	181438.i	−0.0540843	+	0.166454i
$261$		0			0
$262$	988420.	−	718129.i	0.889587	−	0.646323i
$263$	−1.14387e6			−1.01974			−0.509868	−	0.860253i	$-0.670306\pi$
$263$	−1.14387e6			−1.01974			−0.509868	+	0.860253i	$0.670306\pi$
$264$		0			0
$265$	−894175.			−0.782182
$266$	5418.17	−	3936.53i	0.00469514	−	0.00341122i
$267$		0			0
$268$	−37664.1	+	115918.i	−0.0320325	+	0.0985859i
$269$	1.31960e6	+	958742.i	1.11189	+	0.807832i	0.982960	−	0.183822i	$-0.0588470\pi$
$269$	1.31960e6	+	958742.i	1.11189	+	0.807832i	0.128926	+	0.991654i	$0.458847\pi$
$270$		0			0
$271$	−529074.	+	1.62832e6i	−0.437616	+	1.34684i	0.452765	+	0.891630i	$0.350438\pi$
$271$	−529074.	+	1.62832e6i	−0.437616	+	1.34684i	−0.890382	+	0.455215i	$0.849562\pi$
$272$	−30739.4	−	94606.2i	−0.0251926	−	0.0775349i
$273$		0			0
$274$	1.11018e6			0.893339
$275$	−140159.	−	573193.i	−0.111760	−	0.457056i
$276$		0			0
$277$	848820.	−	616704.i	0.664686	−	0.482922i	−0.203556	−	0.979063i	$-0.565250\pi$
$277$	848820.	−	616704.i	0.664686	−	0.482922i	0.868242	+	0.496141i	$0.165250\pi$
$278$	278700.	+	857752.i	0.216285	+	0.665656i
$279$		0			0
$280$	15414.9	+	11199.6i	0.0117502	+	0.00853701i
$281$	−383375.	−	278538.i	−0.289639	−	0.210435i	0.433471	−	0.901167i	$-0.357288\pi$
$281$	−383375.	−	278538.i	−0.289639	−	0.210435i	−0.723111	+	0.690732i	$0.757288\pi$
$282$		0			0
$283$	−260414.	−	801472.i	−0.193285	−	0.594870i	−0.999992	−	0.00391907i	$-0.998753\pi$
$283$	−260414.	−	801472.i	−0.193285	−	0.594870i	0.806707	−	0.590951i	$-0.201247\pi$
$284$	476149.	−	345942.i	0.350305	−	0.254512i
$285$		0			0
$286$	178241.	−	435473.i	0.128852	−	0.314808i
$287$	58120.9			0.0416512
$288$		0			0
$289$	−392102.	−	1.20676e6i	−0.276156	−	0.849920i
$290$	80767.4	−	248576.i	0.0563950	−	0.173566i
$291$		0			0
$292$	505197.	+	367047.i	0.346740	+	0.251921i
$293$	−83684.4	+	257554.i	−0.0569476	+	0.175267i	−0.975484	−	0.220069i	$-0.929372\pi$
$293$	−83684.4	+	257554.i	−0.0569476	+	0.175267i	0.918537	+	0.395336i	$0.129372\pi$
$294$		0			0
$295$	−887180.	+	644574.i	−0.593549	+	0.431239i
$296$	418050.			0.277332
$297$		0			0
$298$	373744.			0.243800
$299$	−308158.	+	223890.i	−0.199340	+	0.144829i
$300$		0			0
$301$	19857.2	−	61114.2i	0.0126329	−	0.0388799i
$302$	1.03485e6	+	751862.i	0.652920	+	0.474374i
$303$		0			0
$304$	−18096.9	+	55696.5i	−0.0112310	+	0.0345656i
$305$	433151.	+	1.33310e6i	0.266618	+	0.820567i
$306$		0			0
$307$	846543.			0.512629			0.256314	−	0.966593i	$-0.417492\pi$
$307$	846543.			0.512629			0.256314	+	0.966593i	$0.417492\pi$
$308$	−35863.3	−	30370.8i	−0.0215414	−	0.0182423i
$309$		0			0
$310$	−475491.	+	345464.i	−0.281020	+	0.204173i
$311$	−190401.	−	585993.i	−0.111627	−	0.343551i	0.879602	−	0.475710i	$-0.157809\pi$
$311$	−190401.	−	585993.i	−0.111627	−	0.343551i	−0.991229	+	0.132159i	$0.957809\pi$
$312$		0			0
$313$	−1.81420e6	−	1.31810e6i	−1.04671	−	0.760477i	−0.0751233	−	0.997174i	$-0.523935\pi$
$313$	−1.81420e6	−	1.31810e6i	−1.04671	−	0.760477i	−0.971583	+	0.236697i	$0.923935\pi$
$314$	1.12381e6	+	816498.i	0.643236	+	0.467338i
$315$		0			0
$316$	410434.	+	1.26319e6i	0.231220	+	0.711622i
$317$	1.55124e6	−	1.12704e6i	0.867022	−	0.629928i	−0.0627642	−	0.998028i	$-0.519992\pi$
$317$	1.55124e6	−	1.12704e6i	0.867022	−	0.629928i	0.929786	+	0.368100i	$0.119992\pi$
$318$		0			0
$319$	−244196.	+	596612.i	−0.134357	+	0.328258i
$320$	−166613.			−0.0909566
$321$		0			0
$322$	11756.0	+	36181.1i	0.00631856	+	0.0194465i
$323$	27468.7	−	84539.8i	0.0146498	−	0.0450874i
$324$		0			0
$325$	348691.	+	253339.i	0.183118	+	0.133043i
$326$	−85548.8	+	263292.i	−0.0445831	+	0.137213i
$327$		0			0
$328$	−411165.	+	298729.i	−0.211024	+	0.153318i
$329$	115311.			0.0587329
$330$		0			0
$331$	−3.32999e6			−1.67060			−0.835302	−	0.549791i	$-0.814707\pi$
$331$	−3.32999e6			−1.67060			−0.835302	+	0.549791i	$0.814707\pi$
$332$	1.09631e6	−	796519.i	0.545871	−	0.396598i
$333$		0			0
$334$	−147618.	+	454321.i	−0.0724058	+	0.222842i
$335$	−250687.	−	182135.i	−0.122045	−	0.0886710i
$336$		0			0
$337$	−490380.	+	1.50924e6i	−0.235211	+	0.723906i	0.761882	+	0.647716i	$0.224276\pi$
$337$	−490380.	+	1.50924e6i	−0.235211	+	0.723906i	−0.997093	+	0.0761901i	$0.975724\pi$
$338$	−352737.	−	1.08561e6i	−0.167942	−	0.516873i
$339$		0			0
$340$	252896.			0.118644
$341$	1.23282e6	−	762610.i	0.574136	−	0.355154i
$342$		0			0
$343$	198719.	−	144377.i	0.0912017	−	0.0662619i
$344$	173638.	+	534403.i	0.0791131	+	0.243485i
$345$		0			0
$346$	−631786.	−	459019.i	−0.283713	−	0.206130i
$347$	−2.88095e6	−	2.09313e6i	−1.28444	−	0.933197i	−0.284758	−	0.958599i	$-0.591913\pi$
$347$	−2.88095e6	−	2.09313e6i	−1.28444	−	0.933197i	−0.999677	+	0.0254023i	$0.991913\pi$
$348$		0			0
$349$	−1.23211e6	−	3.79206e6i	−0.541486	−	1.66652i	−0.729201	−	0.684299i	$-0.760108\pi$
$349$	−1.23211e6	−	3.79206e6i	−0.541486	−	1.66652i	0.187715	−	0.982224i	$-0.439892\pi$
$350$	34825.7	−	25302.4i	0.0151960	−	0.0110406i
$351$		0			0
$352$	409808.	+	30522.4i	0.176288	+	0.0131299i
$353$	−1.92980e6			−0.824279			−0.412140	−	0.911121i	$-0.635218\pi$
$353$	−1.92980e6			−0.824279			−0.412140	+	0.911121i	$0.635218\pi$
$354$		0			0
$355$	462377.	+	1.42305e6i	0.194727	+	0.599307i
$356$	495570.	−	1.52521e6i	0.207243	−	0.637829i
$357$		0			0
$358$	−1.76268e6	−	1.28067e6i	−0.726887	−	0.528115i
$359$	−867556.	+	2.67006e6i	−0.355272	+	1.09342i	0.600579	+	0.799565i	$0.294937\pi$
$359$	−867556.	+	2.67006e6i	−0.355272	+	1.09342i	−0.955851	+	0.293851i	$0.905063\pi$
$360$		0			0
$361$	1.96087e6	−	1.42465e6i	0.791919	−	0.575363i
$362$	−1.23295e6			−0.494509
$363$		0			0
$364$	34326.3			0.0135792
$365$	−1.28437e6	+	933150.i	−0.504613	+	0.366623i
$366$		0			0
$367$	395658.	−	1.21771e6i	0.153340	−	0.471931i	−0.844649	−	0.535320i	$-0.820191\pi$
$367$	395658.	−	1.21771e6i	0.153340	−	0.471931i	0.997989	+	0.0633893i	$0.0201910\pi$
$368$	−269129.	−	195533.i	−0.103595	−	0.0752665i
$369$		0			0
$370$	−328428.	+	1.01080e6i	−0.124720	+	0.383849i
$371$	49717.5	+	153015.i	0.0187532	+	0.0577163i
$372$		0			0
$373$	−222284.			−0.0827251			−0.0413625	−	0.999144i	$-0.513170\pi$
$373$	−222284.			−0.0827251			−0.0413625	+	0.999144i	$0.513170\pi$
$374$	−622033.	−	46328.9i	−0.229951	−	0.0171267i
$375$		0			0
$376$	−815747.	+	592675.i	−0.297568	+	0.216196i
$377$	−145506.	−	447820.i	−0.0527262	−	0.162275i
$378$		0			0
$379$	2.83641e6	+	2.06077e6i	1.01431	+	0.736940i	0.965109	−	0.261848i	$-0.0843321\pi$
$379$	2.83641e6	+	2.06077e6i	1.01431	+	0.736940i	0.0492024	+	0.998789i	$0.484332\pi$
$380$	−120451.	−	87512.4i	−0.0427907	−	0.0310893i
$381$		0			0
$382$	891090.	+	2.74249e6i	0.312438	+	0.961584i
$383$	467465.	−	339633.i	0.162837	−	0.118308i	−0.503383	−	0.864064i	$-0.667911\pi$
$383$	467465.	−	339633.i	0.162837	−	0.118308i	0.666219	+	0.745756i	$0.267911\pi$
$384$		0			0
$385$	101608.	−	62853.6i	0.0349362	−	0.0216112i
$386$	−2.90629e6			−0.992820
$387$		0			0
$388$	130806.	+	402580.i	0.0441112	+	0.135760i
$389$	−29596.8	+	91089.6i	−0.00991678	+	0.0305207i	−0.955892	−	0.293717i	$-0.905108\pi$
$389$	−29596.8	+	91089.6i	−0.00991678	+	0.0305207i	0.945976	+	0.324238i	$0.105108\pi$
$390$		0			0
$391$	408501.	+	296793.i	0.135130	+	0.0981776i
$392$	−331334.	+	1.01974e6i	−0.108906	+	0.335178i
$393$		0			0
$394$	1.82710e6	−	1.32747e6i	0.592956	−	0.430808i
$395$	−3.37668e6			−1.08892
$396$		0			0
$397$	582870.			0.185607			0.0928037	−	0.995684i	$-0.470417\pi$
$397$	582870.			0.185607			0.0928037	+	0.995684i	$0.470417\pi$
$398$	2.31561e6	−	1.68239e6i	0.732753	−	0.532376i
$399$		0			0
$400$	−116319.	+	357994.i	−0.0363498	+	0.111873i
$401$	−1.96448e6	−	1.42728e6i	−0.610081	−	0.443250i	0.239362	−	0.970930i	$-0.423062\pi$
$401$	−1.96448e6	−	1.42728e6i	−0.610081	−	0.443250i	−0.849443	+	0.527680i	$0.823062\pi$
$402$		0			0
$403$	−327198.	+	1.00701e6i	−0.100357	+	0.308867i
$404$	−536443.	−	1.65100e6i	−0.163520	−	0.503262i
$405$		0			0
$406$	−47028.1			−0.0141593
$407$	992986.	−	2.42603e6i	0.297137	−	0.725956i
$408$		0			0
$409$	4.55484e6	−	3.30929e6i	1.34637	−	0.978196i	0.347188	−	0.937796i	$-0.387137\pi$
$409$	4.55484e6	−	3.30929e6i	1.34637	−	0.978196i	0.999184	−	0.0404007i	$-0.0128634\pi$
$410$	−399273.	−	1.22884e6i	−0.117303	−	0.361023i
$411$		0			0
$412$	−471401.	−	342493.i	−0.136819	−	0.0994050i
$413$	159630.	+	115978.i	0.0460511	+	0.0334581i
$414$		0			0
$415$	1.06461e6	+	3.27652e6i	0.303437	+	0.933884i
$416$	−242835.	+	176430.i	−0.0687983	+	0.0499849i
$417$		0			0
$418$	280233.	+	237315.i	0.0784474	+	0.0664330i
$419$	−2.54707e6			−0.708770			−0.354385	−	0.935100i	$-0.615310\pi$
$419$	−2.54707e6			−0.708770			−0.354385	+	0.935100i	$0.615310\pi$
$420$		0			0
$421$	−850534.	−	2.61767e6i	−0.233876	−	0.719797i	−0.997268	−	0.0738620i	$-0.976468\pi$
$421$	−850534.	−	2.61767e6i	−0.233876	−	0.719797i	0.763392	−	0.645935i	$-0.223532\pi$
$422$	154247.	−	474725.i	0.0421635	−	0.129766i
$423$		0			0
$424$	−1.13818e6	−	826936.i	−0.307466	−	0.223387i
$425$	176557.	−	543386.i	0.0474147	−	0.145927i
$426$		0			0
$427$	204042.	−	148245.i	0.0541563	−	0.0393469i
$428$	1.71104e6			0.451494
$429$		0			0
$430$	−1.42854e6			−0.372581
$431$	2.21696e6	−	1.61072e6i	0.574864	−	0.417663i	−0.262005	−	0.965067i	$-0.584384\pi$
$431$	2.21696e6	−	1.61072e6i	0.574864	−	0.417663i	0.836869	+	0.547403i	$0.184384\pi$
$432$		0			0
$433$	1.83568e6	−	5.64964e6i	0.470519	−	1.44811i	−0.381388	−	0.924415i	$-0.624554\pi$
$433$	1.83568e6	−	5.64964e6i	0.470519	−	1.44811i	0.851907	−	0.523693i	$-0.175446\pi$
$434$	85555.1	+	62159.4i	0.0218033	+	0.0158410i
$435$		0			0
$436$	575917.	−	1.77249e6i	0.145092	−	0.446548i
$437$	−91860.1	−	282716.i	−0.0230103	−	0.0708186i
$438$		0			0
$439$	−6.75442e6			−1.67273			−0.836367	−	0.548170i	$-0.815325\pi$
$439$	−6.75442e6			−1.67273			−0.836367	+	0.548170i	$0.815325\pi$
$440$	−395752.	+	966890.i	−0.0974522	+	0.238092i
$441$		0			0
$442$	368590.	−	267797.i	0.0897405	−	0.0652003i
$443$	−700997.	−	2.15745e6i	−0.169710	−	0.522313i	0.829643	−	0.558295i	$-0.188544\pi$
$443$	−700997.	−	2.15745e6i	−0.169710	−	0.522313i	−0.999352	+	0.0359819i	$0.988544\pi$
$444$		0			0
$445$	3.29845e6	+	2.39646e6i	0.789604	+	0.573681i
$446$	2.99523e6	+	2.17616e6i	0.713005	+	0.518028i
$447$		0			0
$448$	9263.94	+	28511.5i	0.00218072	+	0.00671158i
$449$	3.46391e6	−	2.51668e6i	0.810869	−	0.589131i	−0.103213	−	0.994659i	$-0.532912\pi$
$449$	3.46391e6	−	2.51668e6i	0.810869	−	0.589131i	0.914083	+	0.405528i	$0.132912\pi$
$450$		0			0
$451$	756953.	+	3.09564e6i	0.175238	+	0.716653i
$452$	−2.37316e6			−0.546362
$453$		0			0
$454$	−981535.	−	3.02085e6i	−0.223494	−	0.687844i
$455$	−26967.3	+	82996.9i	−0.00610674	+	0.0187946i
$456$		0			0
$457$	−3.59138e6	−	2.60929e6i	−0.804399	−	0.584430i	0.107803	−	0.994172i	$-0.465619\pi$
$457$	−3.59138e6	−	2.60929e6i	−0.804399	−	0.584430i	−0.912201	+	0.409742i	$0.865619\pi$
$458$	−326529.	+	1.00495e6i	−0.0727375	+	0.223863i
$459$		0			0
$460$	684210.	−	497108.i	0.150763	−	0.109536i
$461$	7.30546e6			1.60101			0.800507	−	0.599323i	$-0.204564\pi$
$461$	7.30546e6			1.60101			0.800507	+	0.599323i	$0.204564\pi$
$462$		0			0
$463$	−9.08647e6			−1.96989			−0.984947	−	0.172858i	$-0.944700\pi$
$463$	−9.08647e6			−1.96989			−0.984947	+	0.172858i	$0.944700\pi$
$464$	332692.	−	241715.i	0.0717376	−	0.0521204i
$465$		0			0
$466$	833945.	−	2.56662e6i	0.177899	−	0.547516i
$467$	−4.02133e6	−	2.92166e6i	−0.853252	−	0.619924i	0.0727890	−	0.997347i	$-0.476810\pi$
$467$	−4.02133e6	−	2.92166e6i	−0.853252	−	0.619924i	−0.926041	+	0.377424i	$0.876810\pi$
$468$		0			0
$469$	−17229.0	+	53025.6i	−0.00361684	+	0.0111315i
$470$	−792154.	−	2.43800e6i	−0.165411	−	0.509083i
$471$		0			0
$472$	−1.72538e6			−0.356475
$473$	3.51369e6	+	261699.i	0.722121	+	0.0537834i
$474$		0			0
$475$	−272125.	+	197711.i	−0.0553395	+	0.0402065i
$476$	−14061.4	−	43276.6i	−0.00284454	−	0.00875458i
$477$		0			0
$478$	−3.08595e6	−	2.24207e6i	−0.617759	−	0.448828i
$479$	6.02683e6	+	4.37875e6i	1.20019	+	0.871989i	0.994303	−	0.106587i	$-0.0339923\pi$
$479$	6.02683e6	+	4.37875e6i	1.20019	+	0.871989i	0.205886	+	0.978576i	$0.433992\pi$
$480$		0			0
$481$	591676.	+	1.82099e6i	0.116606	+	0.358877i
$482$	−1.05729e6	+	768164.i	−0.207289	+	0.150604i
$483$		0			0
$484$	1.15054e6	−	2.30570e6i	0.223248	−	0.447393i
$485$	−1.07616e6			−0.207740
$486$		0			0
$487$	2.76264e6	+	8.50254e6i	0.527840	+	1.62452i	0.758631	+	0.651521i	$0.225869\pi$
$487$	2.76264e6	+	8.50254e6i	0.527840	+	1.62452i	−0.230791	+	0.973003i	$0.574131\pi$
$488$	−681507.	+	2.09746e6i	−0.129545	+	0.398699i
$489$		0			0
$490$	−2.20532e6	−	1.60226e6i	−0.414935	−	0.301468i
$491$	−1.15978e6	+	3.56944e6i	−0.217106	+	0.668185i	0.781891	+	0.623415i	$0.214255\pi$
$491$	−1.15978e6	+	3.56944e6i	−0.217106	+	0.668185i	−0.998997	+	0.0447696i	$0.985745\pi$
$492$		0			0
$493$	−504981.	+	366890.i	−0.0935746	+	0.0679859i
$494$	−268222.			−0.0494513
$495$		0			0
$496$	−924730.			−0.168776
$497$	217809.	−	158247.i	0.0395535	−	0.0287373i
$498$		0			0
$499$	1.97049e6	−	6.06454e6i	0.354261	−	1.09030i	−0.602176	−	0.798363i	$-0.705700\pi$
$499$	1.97049e6	−	6.06454e6i	0.354261	−	1.09030i	0.956437	−	0.291939i	$-0.0943003\pi$
$500$	−2.41963e6	−	1.75796e6i	−0.432836	−	0.314474i
$501$		0			0
$502$	−778024.	+	2.39451e6i	−0.137795	+	0.424090i
$503$	966145.	+	2.97349e6i	0.170264	+	0.524018i	0.999386	−	0.0350499i	$-0.0111590\pi$
$503$	966145.	+	2.97349e6i	0.170264	+	0.524018i	−0.829122	+	0.559068i	$0.811159\pi$
$504$		0			0
$505$	4.41337e6			0.770091
$506$	−1.77398e6	+	1.09736e6i	−0.308015	+	0.190534i
$507$		0			0
$508$	1.51098e6	−	1.09779e6i	0.259776	−	0.188738i
$509$	265311.	+	816544.i	0.0453901	+	0.139696i	0.971183	−	0.238334i	$-0.0766014\pi$
$509$	265311.	+	816544.i	0.0453901	+	0.139696i	−0.925793	+	0.378031i	$0.876601\pi$
$510$		0			0
$511$	231097.	+	167902.i	0.0391509	+	0.0284448i
$512$	−212079.	−	154084.i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	2.17568e6	+	6.69605e6i	0.363235	+	1.11792i
$515$	1.19845e6	−	870724.i	0.199114	−	0.144665i
$516$		0			0
$517$	1.50179e6	+	6.14171e6i	0.247105	+	1.01056i
$518$	191233.			0.0313139
$519$		0			0
$520$	−235811.	−	725753.i	−0.0382434	−	0.117701i
$521$	−1.20653e6	+	3.71333e6i	−0.194735	+	0.599334i	0.805244	+	0.592943i	$0.202034\pi$
$521$	−1.20653e6	+	3.71333e6i	−0.194735	+	0.599334i	−0.999980	+	0.00639068i	$0.997966\pi$
$522$		0			0
$523$	587786.	+	427052.i	0.0939648	+	0.0682694i	0.633776	−	0.773517i	$-0.281504\pi$
$523$	587786.	+	427052.i	0.0939648	+	0.0682694i	−0.539811	+	0.841786i	$0.681504\pi$
$524$	−1.51017e6	+	4.64783e6i	−0.240269	+	0.739473i
$525$		0			0
$526$	3.70164e6	−	2.68940e6i	0.583351	−	0.423829i
$527$	1.40362e6			0.220152
$528$		0			0
$529$	−4.74775e6			−0.737647
$530$	2.89361e6	−	2.10233e6i	0.447456	−	0.325096i
$531$		0			0
$532$	−8278.23	+	25477.8i	−0.00126811	+	0.00390285i
$533$	−1.88317e6	−	1.36820e6i	−0.287125	−	0.208609i
$534$		0			0
$535$	−1.34423e6	+	4.13711e6i	−0.203043	+	0.624902i
$536$	−150657.	−	463673.i	−0.0226504	−	0.0697108i
$537$		0			0
$538$	−6.52444e6			−0.971824
$539$	5.13075e6	+	4.34497e6i	0.760693	+	0.644191i
$540$		0			0
$541$	1.05109e7	−	7.63662e6i	1.54400	−	1.12178i	0.596235	−	0.802810i	$-0.296663\pi$
$541$	1.05109e7	−	7.63662e6i	1.54400	−	1.12178i	0.947764	−	0.318971i	$-0.103337\pi$
$542$	−2.11630e6	−	6.51329e6i	−0.309441	−	0.952363i
$543$		0			0
$544$	321907.	+	233879.i	0.0466373	+	0.0338840i
$545$	3.83323e6	+	2.78500e6i	0.552807	+	0.401638i
$546$		0			0
$547$	3.93766e6	+	1.21189e7i	0.562691	+	1.73179i	0.674714	+	0.738080i	$0.264267\pi$
$547$	3.93766e6	+	1.21189e7i	0.562691	+	1.73179i	−0.112022	+	0.993706i	$0.535733\pi$
$548$	−3.59261e6	+	2.61019e6i	−0.511045	+	0.371296i
$549$		0			0
$550$	1.80122e6	+	1.52536e6i	0.253898	+	0.215013i
$551$	367474.			0.0515641
$552$		0			0
$553$	187749.	+	577831.i	0.0261074	+	0.0803503i
$554$	−1.29688e6	+	3.99139e6i	−0.179525	+	0.552523i
$555$		0			0
$556$	−2.91859e6	−	2.12048e6i	−0.400392	−	0.290902i
$557$	1.77671e6	−	5.46817e6i	0.242650	−	0.746799i	−0.753364	−	0.657603i	$-0.771570\pi$
$557$	1.77671e6	−	5.46817e6i	0.242650	−	0.746799i	0.996014	−	0.0891957i	$-0.0284297\pi$
$558$		0			0
$559$	−2.08206e6	+	1.51270e6i	−0.281815	+	0.204750i
$560$	−76215.3			−0.0102700
$561$		0			0
$562$	1.89551e6			0.253154
$563$	−1.00175e7	+	7.27817e6i	−1.33196	+	0.967724i	−0.332259	+	0.943188i	$0.607811\pi$
$563$	−1.00175e7	+	7.27817e6i	−1.33196	+	0.967724i	−0.999699	+	0.0245355i	$0.992189\pi$
$564$		0			0
$565$	1.86440e6	−	5.73802e6i	0.245707	−	0.756207i
$566$	2.72709e6	+	1.98135e6i	0.357815	+	0.259968i
$567$		0			0
$568$	−727490.	+	2.23898e6i	−0.0946142	+	0.291193i
$569$	2.95314e6	+	9.08884e6i	0.382388	+	1.17687i	0.938358	+	0.345666i	$0.112347\pi$
$569$	2.95314e6	+	9.08884e6i	0.382388	+	1.17687i	−0.555970	+	0.831202i	$0.687653\pi$
$570$		0			0
$571$	8.93838e6			1.14728			0.573639	−	0.819108i	$-0.305531\pi$
$571$	8.93838e6			1.14728			0.573639	+	0.819108i	$0.305531\pi$
$572$	447058.	+	1.82829e6i	0.0571312	+	0.233644i
$573$		0			0
$574$	−188083.	+	136650.i	−0.0238270	+	0.0173113i
$575$	−590438.	−	1.81718e6i	−0.0744740	−	0.229207i
$576$		0			0
$577$	1.25573e7	+	9.12344e6i	1.57021	+	1.14083i	0.926954	+	0.375176i	$0.122418\pi$
$577$	1.25573e7	+	9.12344e6i	1.57021	+	1.14083i	0.643258	+	0.765650i	$0.277582\pi$
$578$	4.10614e6	+	2.98329e6i	0.511228	+	0.371429i
$579$		0			0
$580$	323069.	+	994305.i	0.0398773	+	0.122730i
$581$	501497.	−	364359.i	0.0616351	−	0.0447805i
$582$		0			0
$583$	−7.50237e6	+	4.64089e6i	−0.914171	+	0.565496i
$584$	−2.49783e6			−0.303062
$585$		0			0
$586$	−334737.	−	1.03022e6i	−0.0402680	−	0.123932i
$587$	−2.27801e6	+	7.01101e6i	−0.272873	+	0.839818i	0.716901	+	0.697175i	$0.245560\pi$
$587$	−2.27801e6	+	7.01101e6i	−0.272873	+	0.839818i	−0.989774	+	0.142643i	$0.954440\pi$
$588$		0			0
$589$	−668521.	−	485709.i	−0.0794011	−	0.0576883i
$590$	1.35549e6	−	4.17177e6i	0.160312	−	0.493390i
$591$		0			0
$592$	−1.35284e6	+	982896.i	−0.158651	+	0.115267i
$593$	1.79629e6			0.209768			0.104884	−	0.994484i	$-0.466553\pi$
$593$	1.79629e6			0.209768			0.104884	+	0.994484i	$0.466553\pi$
$594$		0			0
$595$	115685.			0.0133962
$596$	−1.20946e6	+	878724.i	−0.139468	+	0.101330i
$597$		0			0
$598$	470823.	−	1.44905e6i	0.0538400	−	0.165702i
$599$	4.62549e6	+	3.36061e6i	0.526733	+	0.382694i	0.819134	−	0.573602i	$-0.194454\pi$
$599$	4.62549e6	+	3.36061e6i	0.526733	+	0.382694i	−0.292402	+	0.956296i	$0.594454\pi$
$600$		0			0
$601$	877296.	−	2.70004e6i	0.0990741	−	0.304919i	−0.889220	−	0.457480i	$-0.848752\pi$
$601$	877296.	−	2.70004e6i	0.0990741	−	0.304919i	0.988294	+	0.152561i	$0.0487522\pi$
$602$	79428.8	+	244457.i	0.00893278	+	0.0274923i
$603$		0			0
$604$	−5.11658e6			−0.570673
$605$	4.67103e6	+	4.59326e6i	0.518829	+	0.510191i
$606$		0			0
$607$	−366568.	+	266327.i	−0.0403815	+	0.0293389i	−0.607793	−	0.794096i	$-0.707945\pi$
$607$	−366568.	+	266327.i	−0.0403815	+	0.0293389i	0.567411	+	0.823434i	$0.307945\pi$
$608$	−72387.6	−	222786.i	−0.00794155	−	0.0244416i
$609$		0			0
$610$	−4.53602e6	−	3.29561e6i	−0.493572	−	0.358601i
$611$	−3.73619e6	−	2.71450e6i	−0.404879	−	0.294162i
$612$		0			0
$613$	4.06511e6	+	1.25111e7i	0.436940	+	1.34476i	0.891086	+	0.453835i	$0.149944\pi$
$613$	4.06511e6	+	1.25111e7i	0.436940	+	1.34476i	−0.454146	+	0.890927i	$0.650056\pi$
$614$	−2.73947e6	+	1.99034e6i	−0.293255	+	0.213062i
$615$		0			0
$616$	187462.	+	13962.1i	0.0199050	+	0.00148252i
$617$	−1.41516e7			−1.49656			−0.748278	−	0.663386i	$-0.769119\pi$
$617$	−1.41516e7			−1.49656			−0.748278	+	0.663386i	$0.769119\pi$
$618$		0			0
$619$	−3.94813e6	−	1.21511e7i	−0.414156	−	1.27464i	−0.913003	−	0.407952i	$-0.866243\pi$
$619$	−3.94813e6	−	1.21511e7i	−0.414156	−	1.27464i	0.498847	−	0.866690i	$-0.333757\pi$
$620$	726485.	−	2.23589e6i	0.0759010	−	0.233599i
$621$		0			0
$622$	1.99390e6	+	1.44865e6i	0.206646	+	0.150137i
$623$	226693.	−	697690.i	0.0234001	−	0.0720182i
$624$		0			0
$625$	2.43407e6	−	1.76845e6i	0.249249	−	0.181090i
$626$	8.96991e6			0.914855
$627$		0			0
$628$	−5.55644e6			−0.562209
$629$	2.05343e6	−	1.49190e6i	0.206944	−	0.150354i
$630$		0			0
$631$	2.68381e6	−	8.25992e6i	0.268336	−	0.825853i	−0.722570	−	0.691297i	$-0.757039\pi$
$631$	2.68381e6	−	8.25992e6i	0.268336	−	0.825853i	0.990906	−	0.134555i	$-0.0429605\pi$
$632$	−4.29812e6	−	3.12277e6i	−0.428041	−	0.310990i
$633$		0			0
$634$	−2.37008e6	+	7.29436e6i	−0.234175	+	0.720715i
$635$	1.46728e6	+	4.51581e6i	0.144403	+	0.444428i
$636$		0			0
$637$	−4.91085e6			−0.479522
$638$	−612484.	−	2.50482e6i	−0.0595721	−	0.243626i
$639$		0			0
$640$	539171.	−	391731.i	0.0520328	−	0.0378040i
$641$	−2.39826e6	−	7.38108e6i	−0.230542	−	0.709537i	−0.997682	−	0.0680559i	$-0.978320\pi$
$641$	−2.39826e6	−	7.38108e6i	−0.230542	−	0.709537i	0.767139	−	0.641481i	$-0.221680\pi$
$642$		0			0
$643$	−2.57845e6	−	1.87335e6i	−0.245941	−	0.178686i	0.457985	−	0.888960i	$-0.348571\pi$
$643$	−2.57845e6	−	1.87335e6i	−0.245941	−	0.178686i	−0.703926	+	0.710273i	$0.748571\pi$
$644$	−123110.	−	89444.6i	−0.0116971	−	0.00849845i
$645$		0			0
$646$	109875.	+	338159.i	0.0103590	+	0.0318816i
$647$	4.50620e6	−	3.27395e6i	0.423204	−	0.307476i	−0.355722	−	0.934592i	$-0.615765\pi$
$647$	4.50620e6	−	3.27395e6i	0.423204	−	0.307476i	0.778926	+	0.627116i	$0.215765\pi$
$648$		0			0
$649$	−4.09826e6	+	1.00127e7i	−0.381933	+	0.933127i
$650$	−1.72402e6			−0.160051
$651$		0			0
$652$	−342195.	−	1.05317e6i	−0.0315250	−	0.0970240i
$653$	497175.	−	1.53015e6i	0.0456274	−	0.140427i	−0.925647	−	0.378387i	$-0.876479\pi$
$653$	497175.	−	1.53015e6i	0.0456274	−	0.140427i	0.971275	+	0.237960i	$0.0764788\pi$
$654$		0			0
$655$	−1.00515e7	−	7.30284e6i	−0.915435	−	0.665103i
$656$	628205.	−	1.93341e6i	0.0569956	−	0.175414i
$657$		0			0
$658$	−373155.	+	271113.i	−0.0335988	+	0.0244110i
$659$	−3.00868e6			−0.269875			−0.134937	−	0.990854i	$-0.543083\pi$
$659$	−3.00868e6			−0.269875			−0.134937	+	0.990854i	$0.543083\pi$
$660$		0			0
$661$	1.10088e6			0.0980025			0.0490013	−	0.998799i	$-0.484396\pi$
$661$	1.10088e6			0.0980025			0.0490013	+	0.998799i	$0.484396\pi$
$662$	1.07761e7	−	7.82929e6i	0.955688	−	0.694348i
$663$		0			0
$664$	−1.67502e6	+	5.15518e6i	−0.147435	+	0.453757i
$665$	−55098.8	−	40031.6i	−0.00483157	−	0.00351034i
$666$		0			0
$667$	−645044.	+	1.98524e6i	−0.0561403	+	0.172782i
$668$	−590472.	−	1.81729e6i	−0.0511986	−	0.157573i
$669$		0			0
$670$	1.23947e6			0.106671
$671$	1.05532e7	+	8.93698e6i	0.904855	+	0.766274i
$672$		0			0
$673$	3.80191e6	−	2.76225e6i	0.323567	−	0.235085i	−0.414129	−	0.910218i	$-0.635914\pi$
$673$	3.80191e6	−	2.76225e6i	0.323567	−	0.235085i	0.737696	+	0.675133i	$0.235914\pi$
$674$	−1.96152e6	−	6.03694e6i	−0.166319	−	0.511879i
$675$		0			0
$676$	3.69391e6	+	2.68379e6i	0.310900	+	0.225882i
$677$	−9.99734e6	−	7.26349e6i	−0.838326	−	0.609079i	0.0835768	−	0.996501i	$-0.473366\pi$
$677$	−9.99734e6	−	7.26349e6i	−0.838326	−	0.609079i	−0.921902	+	0.387422i	$0.873366\pi$
$678$		0			0
$679$	59835.8	+	184156.i	0.00498066	+	0.0153289i
$680$	−818389.	+	594595.i	−0.0678715	+	0.0493116i
$681$		0			0
$682$	−2.19649e6	+	5.36640e6i	−0.180829	+	0.441796i
$683$	−1.41910e7			−1.16403			−0.582013	−	0.813180i	$-0.697735\pi$
$683$	−1.41910e7			−1.16403			−0.582013	+	0.813180i	$0.697735\pi$
$684$		0			0
$685$	−3.48871e6	−	1.07371e7i	−0.284078	−	0.874303i
$686$	−303615.	+	934431.i	−0.0246327	+	0.0758118i
$687$		0			0
$688$	−1.81836e6	−	1.32112e6i	−0.146457	−	0.106407i
$689$	1.99117e6	−	6.12820e6i	0.159794	−	0.491796i
$690$		0			0
$691$	8.08912e6	−	5.87709e6i	0.644475	−	0.468239i	−0.216910	−	0.976192i	$-0.569598\pi$
$691$	8.08912e6	−	5.87709e6i	0.644475	−	0.468239i	0.861385	+	0.507953i	$0.169598\pi$
$692$	3.12372e6			0.247975
$693$		0			0
$694$	1.42442e7			1.12264
$695$	7.41997e6	−	5.39092e6i	0.582693	−	0.423352i
$696$		0			0
$697$	−953530.	+	2.93466e6i	−0.0743451	+	0.228811i
$698$	1.29029e7	+	9.37448e6i	1.00242	+	0.728297i
$699$		0			0
$700$	−53209.0	+	163760.i	−0.00410431	+	0.0126318i
$701$	−2.77434e6	−	8.53855e6i	−0.213238	−	0.656280i	−0.999274	−	0.0380987i	$-0.987870\pi$
$701$	−2.77434e6	−	8.53855e6i	−0.213238	−	0.656280i	0.786036	−	0.618181i	$-0.212130\pi$
$702$		0			0
$703$	−1.49428e6			−0.114036
$704$	−1.39793e6	+	864744.i	−0.106305	+	0.0657591i
$705$		0			0
$706$	6.24495e6	−	4.53722e6i	0.471538	−	0.342593i
$707$	−245390.	−	755232.i	−0.0184632	−	0.0568240i
$708$		0			0
$709$	−1.47029e7	−	1.06823e7i	−1.09847	−	0.798085i	−0.117660	−	0.993054i	$-0.537539\pi$
$709$	−1.47029e7	−	1.06823e7i	−1.09847	−	0.798085i	−0.980809	+	0.194969i	$0.937539\pi$
$710$	−4.84208e6	−	3.51798e6i	−0.360484	−	0.261907i
$711$		0			0
$712$	1.98228e6	+	6.10083e6i	0.146543	+	0.451013i
$713$	3.79748e6	−	2.75903e6i	0.279751	−	0.203251i
$714$		0			0
$715$	−4.77181e6	−	355403.i	−0.349074	−	0.0259990i
$716$	8.71519e6			0.635323
$717$		0			0
$718$	−3.47022e6	−	1.06803e7i	−0.251216	−	0.773162i
$719$	1.43829e6	−	4.42662e6i	0.103759	−	0.319337i	−0.885678	−	0.464300i	$-0.846306\pi$
$719$	1.43829e6	−	4.42662e6i	0.103759	−	0.319337i	0.989437	+	0.144962i	$0.0463061\pi$
$720$		0			0
$721$	−215637.	−	156670.i	−0.0154485	−	0.0112240i
$722$	−2.99594e6	+	9.22056e6i	−0.213890	+	0.658285i
$723$		0			0
$724$	3.98991e6	−	2.89884e6i	0.282889	−	0.205531i
$725$	2.36197e6			0.166889
$726$		0			0
$727$	−2.56156e7			−1.79750			−0.898750	−	0.438462i	$-0.855523\pi$
$727$	−2.56156e7			−1.79750			−0.898750	+	0.438462i	$0.855523\pi$
$728$	−111082.	+	80705.9i	−0.00776811	+	0.00564386i
$729$		0			0
$730$	1.96234e6	−	6.03947e6i	0.136291	−	0.419461i
$731$	2.76003e6	+	2.00528e6i	0.191038	+	0.138797i
$732$		0			0
$733$	−487332.	+	1.49985e6i	−0.0335016	+	0.103107i	−0.966409	−	0.257009i	$-0.917263\pi$
$733$	−487332.	+	1.49985e6i	−0.0335016	+	0.103107i	0.932907	+	0.360116i	$0.117263\pi$
$734$	1.58263e6	+	4.87084e6i	0.108427	+	0.333705i
$735$		0			0
$736$	1.33065e6			0.0905457
$737$	−3.04864e6	−	227062.i	−0.206746	−	0.0153984i
$738$		0			0
$739$	5.71819e6	−	4.15451e6i	0.385166	−	0.279839i	−0.378306	−	0.925681i	$-0.623493\pi$
$739$	5.71819e6	−	4.15451e6i	0.385166	−	0.279839i	0.763472	+	0.645841i	$0.223493\pi$
$740$	−1.31371e6	−	4.04319e6i	−0.0881903	−	0.271422i
$741$		0			0
$742$	−520648.	−	378273.i	−0.0347164	−	0.0252229i
$743$	−2.20967e7	−	1.60542e7i	−1.46844	−	1.06688i	−0.981063	−	0.193691i	$-0.937954\pi$
$743$	−2.20967e7	−	1.60542e7i	−1.46844	−	1.06688i	−0.487376	−	0.873192i	$-0.662046\pi$
$744$		0			0
$745$	−1.17448e6	−	3.61468e6i	−0.0775273	−	0.238604i
$746$	719328.	−	522622.i	0.0473238	−	0.0343828i
$747$		0			0
$748$	2.12187e6	−	1.31256e6i	0.138664	−	0.0857762i
$749$	782698.			0.0509788
$750$		0			0
$751$	−6.91476e6	−	2.12814e7i	−0.447380	−	1.37690i	−0.879852	−	0.475248i	$-0.842358\pi$
$751$	−6.91476e6	−	2.12814e7i	−0.447380	−	1.37690i	0.432472	−	0.901648i	$-0.357642\pi$
$752$	1.24635e6	−	3.83587e6i	0.0803703	−	0.247354i
$753$		0			0
$754$	1.52375e6	+	1.10707e6i	0.0976083	+	0.0709166i
$755$	4.01968e6	−	1.23713e7i	0.256640	−	0.789856i
$756$		0			0
$757$	1.08001e7	−	7.84670e6i	0.684994	−	0.497677i	−0.190017	−	0.981781i	$-0.560854\pi$
$757$	1.08001e7	−	7.84670e6i	0.684994	−	0.497677i	0.875011	+	0.484104i	$0.160854\pi$
$758$	−1.40240e7			−0.886541
$759$		0			0
$760$	595540.			0.0374005
$761$	−2.71892e6	+	1.97541e6i	−0.170190	+	0.123651i	−0.669620	−	0.742704i	$-0.733543\pi$
$761$	−2.71892e6	+	1.97541e6i	−0.170190	+	0.123651i	0.499430	+	0.866355i	$0.333543\pi$
$762$		0			0
$763$	263447.	−	810806.i	0.0163826	−	0.0504203i
$764$	−9.33162e6	−	6.77982e6i	−0.578394	−	0.420228i
$765$		0			0
$766$	−714223.	+	2.19815e6i	−0.0439806	+	0.135359i
$767$	−2.44197e6	−	7.51561e6i	−0.149883	−	0.461292i
$768$		0			0
$769$	162618.			0.00991637			0.00495818	−	0.999988i	$-0.498422\pi$
$769$	162618.			0.00991637			0.00495818	+	0.999988i	$0.498422\pi$
$770$	−181033.	+	442293.i	−0.0110035	+	0.0268833i
$771$		0			0
$772$	9.40495e6	−	6.83309e6i	0.567954	−	0.412643i
$773$	−5.68253e6	−	1.74890e7i	−0.342053	−	1.05273i	−0.963143	−	0.268991i	$-0.913310\pi$
$773$	−5.68253e6	−	1.74890e7i	−0.342053	−	1.05273i	0.621090	−	0.783739i	$-0.286690\pi$
$774$		0			0
$775$	−4.29697e6	−	3.12193e6i	−0.256985	−	0.186711i
$776$	−1.36982e6	−	995232.i	−0.0816599	−	0.0593294i
$777$		0			0
$778$	−118387.	−	364358.i	−0.00701222	−	0.0215814i
$779$	1.46966e6	−	1.06777e6i	0.0867710	−	0.0630428i
$780$		0			0
$781$	1.12653e7	+	9.53998e6i	0.660868	+	0.559654i
$782$	−2.01974e6			−0.118108
$783$		0			0
$784$	−1.32534e6	−	4.07897e6i	−0.0770080	−	0.237006i
$785$	4.36524e6	−	1.34348e7i	0.252833	−	0.778140i
$786$		0			0
$787$	7.97896e6	+	5.79705e6i	0.459208	+	0.333634i	0.793220	−	0.608935i	$-0.208403\pi$
$787$	7.97896e6	+	5.79705e6i	0.459208	+	0.333634i	−0.334013	+	0.942569i	$0.608403\pi$
$788$	−2.79157e6	+	8.59156e6i	−0.160152	+	0.492897i
$789$		0			0
$790$	1.09272e7	−	7.93906e6i	0.622931	−	0.452586i
$791$	−1.08557e6			−0.0616905
$792$		0			0
$793$	−1.01009e7			−0.570398
$794$	−1.88621e6	+	1.37041e6i	−0.106179	+	0.0771435i
$795$		0			0
$796$	−3.53794e6	+	1.08886e7i	−0.197910	+	0.609104i
$797$	3.23633e6	+	2.35133e6i	0.180471	+	0.131120i	0.674353	−	0.738409i	$-0.264423\pi$
$797$	3.23633e6	+	2.35133e6i	0.180471	+	0.131120i	−0.493882	+	0.869529i	$0.664423\pi$
$798$		0			0
$799$	−1.89179e6	+	5.82234e6i	−0.104835	+	0.322649i
$800$	−465277.	−	1.43198e6i	−0.0257032	−	0.0791062i
$801$		0			0
$802$	9.71295e6			0.533231
$803$	−5.93305e6	+	1.44954e7i	−0.324705	+	0.793309i
$804$		0			0
$805$	312984.	−	227396.i	0.0170229	−	0.0123678i
$806$	−1.30879e6	−	4.02805e6i	−0.0709632	−	0.218402i
$807$		0			0
$808$	5.61770e6	+	4.08150e6i	0.302712	+	0.219933i
$809$	−1.69609e7	−	1.23228e7i	−0.911127	−	0.661972i	0.0301730	−	0.999545i	$-0.490394\pi$
$809$	−1.69609e7	−	1.23228e7i	−0.911127	−	0.661972i	−0.941300	+	0.337573i	$0.890394\pi$
$810$		0			0
$811$	4.34338e6	+	1.33676e7i	0.231887	+	0.713674i	0.997519	+	0.0703958i	$0.0224262\pi$
$811$	4.34338e6	+	1.33676e7i	0.231887	+	0.713674i	−0.765632	+	0.643278i	$0.777574\pi$
$812$	152186.	−	110570.i	0.00810000	−	0.00588499i
$813$		0			0
$814$	2.49057e6	+	1.01855e7i	0.131746	+	0.538790i
$815$	2.81528e6			0.148466
$816$		0			0
$817$	−620650.	−	1.91016e6i	−0.0325306	−	0.100119i
$818$	−6.95918e6	+	2.14181e7i	−0.363643	+	1.11918i
$819$		0			0
$820$	4.18125e6	+	3.03785e6i	0.217156	+	0.157773i
$821$	3.37105e6	−	1.03750e7i	0.174545	−	0.537194i	−0.825068	−	0.565034i	$-0.808863\pi$
$821$	3.37105e6	−	1.03750e7i	0.174545	−	0.537194i	0.999612	+	0.0278405i	$0.00886305\pi$
$822$		0			0
$823$	1.06493e6	−	773719.i	0.0548053	−	0.0398184i	−0.560045	−	0.828462i	$-0.689216\pi$
$823$	1.06493e6	−	773719.i	0.0548053	−	0.0398184i	0.614851	+	0.788644i	$0.289216\pi$
$824$	2.33073e6			0.119584
$825$		0			0
$826$	−789256.			−0.0402502
$827$	−8.05048e6	+	5.84901e6i	−0.409315	+	0.297385i	−0.773325	−	0.634010i	$-0.781408\pi$
$827$	−8.05048e6	+	5.84901e6i	−0.409315	+	0.297385i	0.364009	+	0.931395i	$0.381408\pi$
$828$		0			0
$829$	−3.38685e6	+	1.04236e7i	−0.171163	+	0.526785i	−0.999437	−	0.0335376i	$-0.989323\pi$
$829$	−3.38685e6	+	1.04236e7i	−0.171163	+	0.526785i	0.828275	+	0.560322i	$0.189323\pi$
$830$	−1.11487e7	−	8.10001e6i	−0.561732	−	0.408122i
$831$		0			0
$832$	371018.	−	1.14188e6i	0.0185818	−	0.0571888i
$833$	2.01168e6	+	6.19132e6i	0.100449	+	0.309151i
$834$		0			0
$835$	4.85787e6			0.241118
$836$	−1.46481e6	−	109099.i	−0.0724881	−	0.00539890i
$837$		0			0
$838$	8.24249e6	−	5.98852e6i	0.405460	−	0.294584i
$839$	5.50619e6	+	1.69463e7i	0.270052	+	0.831133i	0.990486	+	0.137611i	$0.0439422\pi$
$839$	5.50619e6	+	1.69463e7i	0.270052	+	0.831133i	−0.720435	+	0.693523i	$0.756058\pi$
$840$		0			0
$841$	1.45063e7	+	1.05394e7i	0.707238	+	0.513839i
$842$	8.90690e6	+	6.47124e6i	0.432959	+	0.314563i
$843$		0			0
$844$	616990.	+	1.89890e6i	0.0298141	+	0.0917584i
$845$	−9.39109e6	+	6.82303e6i	−0.452454	+	0.328727i
$846$		0			0
$847$	526300.	−	1.05472e6i	0.0252072	−	0.0505158i
$848$	5.62747e6			0.268735
$849$		0			0
$850$	706228.	+	2.17355e6i	0.0335272	+	0.103186i
$851$	2.62297e6	−	8.07268e6i	0.124157	−	0.382115i
$852$		0			0
$853$	−2.45877e7	−	1.78640e7i	−1.15703	−	0.840634i	−0.167634	−	0.985849i	$-0.553613\pi$
$853$	−2.45877e7	−	1.78640e7i	−1.15703	−	0.840634i	−0.989400	+	0.145215i	$0.953613\pi$
$854$	−311748.	+	959461.i	−0.0146271	+	0.0450176i
$855$		0			0
$856$	−5.53705e6	+	4.02291e6i	−0.258282	+	0.187653i
$857$	1.70541e7			0.793191			0.396595	−	0.917994i	$-0.370192\pi$
$857$	1.70541e7			0.793191			0.396595	+	0.917994i	$0.370192\pi$
$858$		0			0
$859$	−3.63315e7			−1.67996			−0.839982	−	0.542614i	$-0.817435\pi$
$859$	−3.63315e7			−1.67996			−0.839982	+	0.542614i	$0.817435\pi$
$860$	4.62284e6	−	3.35869e6i	0.213139	−	0.154855i
$861$		0			0
$862$	−3.38722e6	+	1.04248e7i	−0.155265	+	0.477858i
$863$	2.39948e7	+	1.74333e7i	1.09671	+	0.796804i	0.980519	−	0.196423i	$-0.0629325\pi$
$863$	2.39948e7	+	1.74333e7i	1.09671	+	0.796804i	0.116188	+	0.993227i	$0.462933\pi$
$864$		0			0
$865$	−2.45405e6	+	7.55280e6i	−0.111518	+	0.343216i
$866$	7.34272e6	+	2.25986e7i	0.332707	+	1.02397i
$867$		0			0
$868$	−423008.			−0.0190568
$869$	−2.83313e7	+	1.75254e7i	−1.27267	+	0.787261i
$870$		0			0
$871$	1.80649e6	−	1.31249e6i	0.0806847	−	0.0586209i
$872$	2.30367e6	+	7.08996e6i	0.102596	+	0.315757i
$873$		0			0
$874$	961971.	+	698913.i	0.0425974	+	0.0309488i
$875$	−1.10683e6	−	804160.i	−0.0488721	−	0.0355077i
$876$		0			0
$877$	−3.82087e6	−	1.17594e7i	−0.167750	−	0.516282i	0.831478	−	0.555557i	$-0.187495\pi$
$877$	−3.82087e6	−	1.17594e7i	−0.167750	−	0.516282i	−0.999228	+	0.0392754i	$0.987495\pi$
$878$	2.18578e7	−	1.58806e7i	0.956907	−	0.695233i
$879$		0			0
$880$	−992612.	−	4.05939e6i	−0.0432089	−	0.176707i
$881$	2.81617e7			1.22242			0.611208	−	0.791470i	$-0.290684\pi$
$881$	2.81617e7			1.22242			0.611208	+	0.791470i	$0.290684\pi$
$882$		0			0
$883$	2.33357e6	+	7.18200e6i	0.100721	+	0.309987i	0.988702	−	0.149892i	$-0.0478927\pi$
$883$	2.33357e6	+	7.18200e6i	0.100721	+	0.309987i	−0.887981	+	0.459879i	$0.847893\pi$
$884$	−563156.	+	1.73322e6i	−0.0242381	+	0.0745971i
$885$		0			0
$886$	7.34093e6	+	5.33350e6i	0.314172	+	0.228259i
$887$	−6.85902e6	+	2.11099e7i	−0.292720	+	0.900901i	0.691257	+	0.722609i	$0.257057\pi$
$887$	−6.85902e6	+	2.11099e7i	−0.292720	+	0.900901i	−0.983978	+	0.178292i	$0.942943\pi$
$888$		0			0
$889$	691180.	−	502172.i	0.0293317	−	0.0213107i
$890$	−1.63084e7			−0.690140
$891$		0			0
$892$	−1.48092e7			−0.623189
$893$	2.91580e6	−	2.11845e6i	0.122357	−	0.0888976i
$894$		0			0
$895$	−6.84682e6	+	2.10723e7i	−0.285714	+	0.879336i
$896$	−97013.2	−	70484.2i	−0.00403702	−	0.00293307i
$897$		0			0
$898$	−5.29239e6	+	1.62883e7i	−0.219008	+	0.674038i
$899$	1.79309e6	+	5.51856e6i	0.0739950	+	0.227733i
$900$		0			0
$901$	−8.54175e6			−0.350538
$902$	−9.72784e6	−	8.23799e6i	−0.398107	−	0.337136i
$903$		0			0
$904$	7.67970e6	−	5.57963e6i	0.312553	−	0.227083i
$905$	3.87451e6	+	1.19245e7i	0.157252	+	0.483971i
$906$		0			0
$907$	3.33407e6	+	2.42234e6i	0.134572	+	0.0977726i	0.653035	−	0.757328i	$-0.273495\pi$
$907$	3.33407e6	+	2.42234e6i	0.134572	+	0.0977726i	−0.518463	+	0.855100i	$0.673495\pi$
$908$	1.02788e7	+	7.46796e6i	0.413739	+	0.300599i
$909$		0			0
$910$	−107869.	−	331988.i	−0.00431812	−	0.0132898i
$911$	1.33460e7	−	9.69647e6i	0.532791	−	0.387095i	−0.288610	−	0.957447i	$-0.593193\pi$
$911$	1.33460e7	−	9.69647e6i	0.532791	−	0.387095i	0.821401	+	0.570352i	$0.193193\pi$
$912$		0			0
$913$	2.59379e7	+	2.19655e7i	1.02981	+	0.872094i
$914$	1.77568e7			0.703070
$915$		0			0
$916$	−1.30612e6	−	4.01981e6i	−0.0514331	−	0.158295i
$917$	−690812.	+	2.12610e6i	−0.0271292	+	0.0834950i
$918$		0			0
$919$	−1.47173e7	−	1.06928e7i	−0.574830	−	0.417639i	0.262026	−	0.965061i	$-0.415609\pi$
$919$	−1.47173e7	−	1.06928e7i	−0.574830	−	0.417639i	−0.836857	+	0.547422i	$0.815609\pi$
$920$	−1.04538e6	+	3.21735e6i	−0.0407197	+	0.125322i
$921$		0			0
$922$	−2.36410e7	+	1.71762e7i	−0.915879	+	0.665425i
$923$	−1.07825e7			−0.416595
$924$		0			0
$925$	−9.60457e6			−0.369083
$926$	2.94044e7	−	2.13636e7i	1.12690	−	0.818741i
$927$		0			0
$928$	−508308.	+	1.56441e6i	−0.0193757	+	0.0596322i
$929$	2.88921e7	+	2.09914e7i	1.09835	+	0.797997i	0.980790	−	0.195069i	$-0.0624930\pi$
$929$	2.88921e7	+	2.09914e7i	1.09835	+	0.797997i	0.117559	+	0.993066i	$0.462493\pi$
$930$		0			0
$931$	1.18432e6	−	3.64495e6i	0.0447810	−	0.137822i
$932$	3.33578e6	+	1.02665e7i	0.125793	+	0.387152i
$933$		0			0
$934$	1.98825e7			0.745769
$935$	1.50665e6	+	6.16161e6i	0.0563616	+	0.230497i
$936$		0			0
$937$	−1.18894e7	+	8.63817e6i	−0.442396	+	0.321420i	−0.786586	−	0.617480i	$-0.788154\pi$
$937$	−1.18894e7	+	8.63817e6i	−0.442396	+	0.321420i	0.344190	+	0.938900i	$0.388154\pi$
$938$	−68916.2	−	212102.i	−0.00255749	−	0.00787115i
$939$		0			0
$940$	8.29554e6	+	6.02706e6i	0.306214	+	0.222478i
$941$	−2.37149e7	−	1.72299e7i	−0.873066	−	0.634320i	0.0583416	−	0.998297i	$-0.481419\pi$
$941$	−2.37149e7	−	1.72299e7i	−0.873066	−	0.634320i	−0.931408	+	0.363977i	$0.881419\pi$
$942$		0			0
$943$	3.18877e6	+	9.81403e6i	0.116774	+	0.359392i
$944$	5.58345e6	−	4.05661e6i	0.203926	−	0.148161i
$945$		0			0
$946$	−1.19858e7	+	7.41429e6i	−0.435451	+	0.269366i
$947$	5.18061e6			0.187718			0.0938590	−	0.995586i	$-0.470080\pi$
$947$	5.18061e6			0.187718			0.0938590	+	0.995586i	$0.470080\pi$
$948$		0			0
$949$	−3.53524e6	−	1.08804e7i	−0.127425	−	0.392173i
$950$	415770.	−	1.27961e6i	0.0149467	−	0.0460011i
$951$		0			0
$952$	147253.	+	106986.i	0.00526589	+	0.00382589i
$953$	−5.82547e6	+	1.79290e7i	−0.207778	+	0.639474i	0.791810	+	0.610767i	$0.209139\pi$
$953$	−5.82547e6	+	1.79290e7i	−0.207778	+	0.639474i	−0.999588	+	0.0287069i	$0.990861\pi$
$954$		0			0
$955$	2.37239e7	−	1.72364e7i	0.841740	−	0.611560i
$956$	1.52578e7			0.539941
$957$		0			0
$958$	−2.97983e7			−1.04900
$959$	−1.64340e6	+	1.19400e6i	−0.0577028	+	0.0419235i
$960$		0			0
$961$	−4.81478e6	+	1.48184e7i	−0.168178	+	0.517597i
$962$	−6.19612e6	−	4.50174e6i	−0.215865	−	0.156835i
$963$		0			0
$964$	1.61539e6	−	4.97166e6i	0.0559867	−	0.172309i
$965$	9.13293e6	+	2.81083e7i	0.315713	+	0.971664i
$966$		0			0
$967$	4.49195e7			1.54479			0.772394	−	0.635143i	$-0.219059\pi$
$967$	4.49195e7			1.54479			0.772394	+	0.635143i	$0.219059\pi$
$968$	1.69781e6	+	1.01665e7i	0.0582373	+	0.348724i
$969$		0			0
$970$	3.48251e6	−	2.53019e6i	0.118840	−	0.0863424i
$971$	5.69460e6	+	1.75262e7i	0.193827	+	0.596539i	0.999988	+	0.00484290i	$0.00154155\pi$
$971$	5.69460e6	+	1.75262e7i	0.193827	+	0.596539i	−0.806161	+	0.591696i	$0.798458\pi$
$972$		0			0
$973$	−1.33508e6	−	969990.i	−0.0452089	−	0.0328462i
$974$	−2.89308e7	−	2.10194e7i	−0.977153	−	0.709943i
$975$		0			0
$976$	−2.72603e6	−	8.38985e6i	−0.0916021	−	0.281922i
$977$	−3.08862e7	+	2.24402e7i	−1.03521	+	0.752124i	−0.969345	−	0.245704i	$-0.920981\pi$
$977$	−3.08862e7	+	2.24402e7i	−1.03521	+	0.752124i	−0.0658656	+	0.997829i	$0.520981\pi$
$978$		0			0
$979$	4.01128e7	+	2.98760e6i	1.33760	+	0.0996242i
$980$	1.09037e7			0.362667
$981$		0			0
$982$	−4.63913e6	−	1.42778e7i	−0.153517	−	0.472478i
$983$	8.02051e6	−	2.46846e7i	0.264739	−	0.814783i	−0.727014	−	0.686622i	$-0.759093\pi$
$983$	8.02051e6	−	2.46846e7i	0.264739	−	0.814783i	0.991753	−	0.128161i	$-0.0409073\pi$
$984$		0			0
$985$	−1.85803e7	−	1.34994e7i	−0.610186	−	0.443326i
$986$	771542.	−	2.37456e6i	0.0252736	−	0.0777842i
$987$		0			0
$988$	867986.	−	630629.i	0.0282892	−	0.0205533i
$989$	1.14089e7			0.370898
$990$		0			0
$991$	2.01145e7			0.650617			0.325309	−	0.945608i	$-0.394532\pi$
$991$	2.01145e7			0.650617			0.325309	+	0.945608i	$0.394532\pi$
$992$	2.99249e6	−	2.17417e6i	0.0965503	−	0.0701479i
$993$		0			0
$994$	−332782.	+	1.02420e6i	−0.0106830	+	0.0328790i
$995$	−2.35480e7	−	1.71086e7i	−0.754044	−	0.547845i
$996$		0			0
$997$	1.33156e7	−	4.09812e7i	0.424251	−	1.30571i	−0.479460	−	0.877564i	$-0.659167\pi$
$997$	1.33156e7	−	4.09812e7i	0.424251	−	1.30571i	0.903710	−	0.428145i	$-0.140833\pi$
$998$	7.88196e6	+	2.42582e7i	0.250500	+	0.770960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.a.91.2		8
3.2	odd	2		66.6.e.b.25.1	✓	8
11.4	even	5	inner	198.6.f.a.37.2		8
33.2	even	10		726.6.a.bd.1.3		4
33.20	odd	10		726.6.a.ba.1.3		4
33.26	odd	10		66.6.e.b.37.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.b.25.1	✓	8	3.2	odd	2
66.6.e.b.37.1	yes	8	33.26	odd	10
198.6.f.a.37.2		8	11.4	even	5	inner
198.6.f.a.91.2		8	1.1	even	1	trivial
726.6.a.ba.1.3		4	33.20	odd	10
726.6.a.bd.1.3		4	33.2	even	10

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 + 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(32.9084 + 23.9094i) q^{5} +(2.26170 - 6.96081i) q^{7} +(19.7771 + 60.8676i) q^{8} +O(q^{10})\)	\(q+(-3.23607 + 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(32.9084 + 23.9094i) q^{5} +(2.26170 - 6.96081i) q^{7} +(19.7771 + 60.8676i) q^{8} -162.708 q^{10} +(400.203 + 29.8071i) q^{11} +(-237.143 + 172.295i) q^{13} +(9.04681 + 27.8432i) q^{14} +(-207.108 - 150.473i) q^{16} +(314.363 + 228.398i) q^{17} +(-70.6910 - 217.565i) q^{19} +(526.535 - 382.550i) q^{20} +(-1365.17 + 844.476i) q^{22} +1299.46 q^{23} +(-454.372 - 1398.41i) q^{25} +(362.323 - 1115.11i) q^{26} +(-94.7394 - 68.8322i) q^{28} +(-496.394 + 1527.74i) q^{29} +(2922.35 - 2123.21i) q^{31} +1024.00 q^{32} -1554.29 q^{34} +(240.857 - 174.993i) q^{35} +(2018.51 - 6212.34i) q^{37} +(740.286 + 537.849i) q^{38} +(-804.473 + 2475.91i) q^{40} +(2453.92 + 7552.40i) q^{41} +8779.75 q^{43} +(2432.28 - 5942.48i) q^{44} +(-4205.14 + 3055.21i) q^{46} +(4868.56 + 14983.9i) q^{47} +(13553.8 + 9847.42i) q^{49} +(4758.25 + 3457.07i) q^{50} +(1449.29 + 4460.46i) q^{52} +(-17784.1 + 12920.9i) q^{53} +(12457.4 + 10549.5i) q^{55} +468.418 q^{56} +(-1985.58 - 6110.98i) q^{58} +(-8330.81 + 25639.6i) q^{59} +(27878.3 + 20254.7i) q^{61} +(-4464.96 + 13741.7i) q^{62} +(-3313.73 + 2407.57i) q^{64} -11923.5 q^{65} -7617.73 q^{67} +(5029.80 - 3654.36i) q^{68} +(-367.997 + 1132.58i) q^{70} +(29759.3 + 21621.4i) q^{71} +(-12060.5 + 37118.4i) q^{73} +(8074.04 + 24849.4i) q^{74} -3660.18 q^{76} +(1112.62 - 2718.32i) q^{77} +(-67158.1 + 48793.2i) q^{79} +(-3217.89 - 9903.66i) q^{80} +(-25697.8 - 18670.6i) q^{82} +(68519.7 + 49782.4i) q^{83} +(4884.33 + 15032.4i) q^{85} +(-28411.9 + 20642.4i) q^{86} +(6100.57 + 24948.9i) q^{88} +100231. q^{89} +(662.962 + 2040.39i) q^{91} +(6424.88 - 19773.7i) q^{92} +(-50984.2 - 37042.2i) q^{94} +(2875.50 - 8849.88i) q^{95} +(-21403.4 + 15550.5i) q^{97} -67013.7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 32 q^{4} - 118 q^{5} + 2 q^{7} - 128 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 - 32 * q^4 - 118 * q^5 + 2 * q^7 - 128 * q^8	\( 8 q - 8 q^{2} - 32 q^{4} - 118 q^{5} + 2 q^{7} - 128 q^{8} - 112 q^{10} + 550 q^{11} + 958 q^{13} + 8 q^{14} - 512 q^{16} + 2600 q^{17} - 2336 q^{19} - 1888 q^{20} + 3064 q^{23} + 3988 q^{25} - 2808 q^{26} - 3488 q^{28} - 1572 q^{29} + 6188 q^{31} + 8192 q^{32} - 20240 q^{34} - 23722 q^{35} + 25114 q^{37} + 18696 q^{38} + 8448 q^{40} + 11914 q^{41} + 5528 q^{43} - 8800 q^{44} + 13576 q^{46} - 4354 q^{47} - 820 q^{49} - 25048 q^{50} - 11232 q^{52} - 18200 q^{53} - 44440 q^{55} + 27648 q^{56} - 6288 q^{58} - 98072 q^{59} - 10418 q^{61} - 23208 q^{62} - 8192 q^{64} - 99228 q^{65} + 76988 q^{67} + 41600 q^{68} + 58432 q^{70} + 84262 q^{71} - 72668 q^{73} + 100456 q^{74} - 74816 q^{76} - 132902 q^{77} - 192754 q^{79} + 33792 q^{80} - 26024 q^{82} + 106918 q^{83} - 219410 q^{85} - 169288 q^{86} + 49280 q^{88} - 128160 q^{89} - 37642 q^{91} - 78816 q^{92} + 35184 q^{94} + 90446 q^{95} + 45470 q^{97} - 331840 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 32 * q^4 - 118 * q^5 + 2 * q^7 - 128 * q^8 - 112 * q^10 + 550 * q^11 + 958 * q^13 + 8 * q^14 - 512 * q^16 + 2600 * q^17 - 2336 * q^19 - 1888 * q^20 + 3064 * q^23 + 3988 * q^25 - 2808 * q^26 - 3488 * q^28 - 1572 * q^29 + 6188 * q^31 + 8192 * q^32 - 20240 * q^34 - 23722 * q^35 + 25114 * q^37 + 18696 * q^38 + 8448 * q^40 + 11914 * q^41 + 5528 * q^43 - 8800 * q^44 + 13576 * q^46 - 4354 * q^47 - 820 * q^49 - 25048 * q^50 - 11232 * q^52 - 18200 * q^53 - 44440 * q^55 + 27648 * q^56 - 6288 * q^58 - 98072 * q^59 - 10418 * q^61 - 23208 * q^62 - 8192 * q^64 - 99228 * q^65 + 76988 * q^67 + 41600 * q^68 + 58432 * q^70 + 84262 * q^71 - 72668 * q^73 + 100456 * q^74 - 74816 * q^76 - 132902 * q^77 - 192754 * q^79 + 33792 * q^80 - 26024 * q^82 + 106918 * q^83 - 219410 * q^85 - 169288 * q^86 + 49280 * q^88 - 128160 * q^89 - 37642 * q^91 - 78816 * q^92 + 35184 * q^94 + 90446 * q^95 + 45470 * q^97 - 331840 * q^98

Introduction

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