LMFDB - Embedded newform 108.6.h.a.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.87383 + 2.87155i) q^{2} +(15.5084 - 27.9909i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(-89.9985 - 51.9607i) q^{7} +(4.79147 + 180.956i) q^{8} +O(q^{10})$	\(q+(-4.87383 + 2.87155i) q^{2} +(15.5084 - 27.9909i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(-89.9985 - 51.9607i) q^{7} +(4.79147 + 180.956i) q^{8} +(225.745 - 399.094i) q^{10} +(-214.271 + 371.129i) q^{11} +(42.9574 + 74.4044i) q^{13} +(587.845 - 5.18738i) q^{14} +(-542.976 - 868.190i) q^{16} -1509.75i q^{17} +1224.53i q^{19} +(45.7731 + 2593.36i) q^{20} +(-21.3913 - 2424.11i) q^{22} +(-1530.14 - 2650.27i) q^{23} +(1722.45 - 2983.38i) q^{25} +(-423.023 - 239.280i) q^{26} +(-2850.16 + 1713.31i) q^{28} +(4347.44 + 2510.00i) q^{29} +(3400.78 - 1963.44i) q^{31} +(5139.42 + 2672.23i) q^{32} +(4335.30 + 7358.24i) q^{34} +8423.34 q^{35} +13035.3 q^{37} +(-3516.29 - 5968.14i) q^{38} +(-7670.03 - 12508.1i) q^{40} +(15071.6 - 8701.62i) q^{41} +(5754.33 + 3322.27i) q^{43} +(7065.19 + 11753.3i) q^{44} +(15068.0 + 8523.13i) q^{46} +(-10068.4 + 17438.9i) q^{47} +(-3003.68 - 5202.52i) q^{49} +(171.957 + 19486.6i) q^{50} +(2748.85 - 48.5176i) q^{52} -18043.0i q^{53} -34735.5i q^{55} +(8971.37 - 16534.7i) q^{56} +(-28396.3 + 250.580i) q^{58} +(-14736.4 - 25524.2i) q^{59} +(-11989.0 + 20765.6i) q^{61} +(-10936.7 + 19335.0i) q^{62} +(-32722.1 + 1734.09i) q^{64} +(-6030.85 - 3481.91i) q^{65} +(348.663 - 201.301i) q^{67} +(-42259.1 - 23413.8i) q^{68} +(-41054.0 + 24188.0i) q^{70} -36645.5 q^{71} +58635.9 q^{73} +(-63531.8 + 37431.5i) q^{74} +(34275.6 + 18990.5i) q^{76} +(38568.2 - 22267.4i) q^{77} +(-39354.5 - 22721.3i) q^{79} +(73300.1 + 38937.7i) q^{80} +(-48469.5 + 85689.1i) q^{82} +(27253.7 - 47204.9i) q^{83} +(61186.2 + 105978. i) q^{85} +(-37585.7 + 331.671i) q^{86} +(-68184.6 - 36995.4i) q^{88} +45338.5i q^{89} -8928.39i q^{91} +(-97913.4 + 1728.19i) q^{92} +(-1005.15 - 113906. i) q^{94} +(-49627.1 - 85956.6i) q^{95} +(41820.0 - 72434.3i) q^{97} +(29578.7 + 16731.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−4.87383	+	2.87155i	−0.861580	+	0.507622i
$2$	−4.87383	+	2.87155i	−0.861580	+	0.507622i
$3$		0			0
$3$		0			0
$4$	15.5084	−	27.9909i	0.484639	−	0.874714i
$5$	−70.1957	+	40.5275i	−1.25570	+	0.724978i	−0.972235	−	0.234005i	$-0.924817\pi$
$5$	−70.1957	+	40.5275i	−1.25570	+	0.724978i	−0.283463	+	0.958983i	$0.591483\pi$
$6$		0			0
$7$	−89.9985	−	51.9607i	−0.694209	−	0.400802i	0.110978	−	0.993823i	$-0.464602\pi$
$7$	−89.9985	−	51.9607i	−0.694209	−	0.400802i	−0.805187	+	0.593021i	$0.797935\pi$
$8$	4.79147	+	180.956i	0.0264694	+	0.999650i
$9$		0			0
$10$	225.745	−	399.094i	0.713869	−	1.26205i
$11$	−214.271	+	371.129i	−0.533927	+	0.924789i	0.465287	+	0.885160i	$0.345951\pi$
$11$	−214.271	+	371.129i	−0.533927	+	0.924789i	−0.999214	+	0.0396293i	$0.987382\pi$
$12$		0			0
$13$	42.9574	+	74.4044i	0.0704985	+	0.122107i	0.899120	−	0.437702i	$-0.144208\pi$
$13$	42.9574	+	74.4044i	0.0704985	+	0.122107i	−0.828621	+	0.559809i	$0.810874\pi$
$14$	587.845	−	5.18738i	0.801573	−	0.00707339i
$15$		0			0
$16$	−542.976	−	868.190i	−0.530250	−	0.847841i
$17$		−	1509.75i		−	1.26701i	−0.773737	−	0.633507i	$-0.781615\pi$
$17$		−	1509.75i		−	1.26701i	0.773737	−	0.633507i	$-0.218385\pi$
$18$		0			0
$19$			1224.53i			0.778189i	0.921198	+	0.389094i	$0.127212\pi$
$19$			1224.53i			0.778189i	−0.921198	+	0.389094i	$0.872788\pi$
$20$	45.7731	+	2593.36i	0.0255880	+	1.44973i
$21$		0			0
$22$	−21.3913	−	2424.11i	−0.00942280	−	1.06781i
$23$	−1530.14	−	2650.27i	−0.603129	−	1.04465i	−0.992344	−	0.123503i	$-0.960587\pi$
$23$	−1530.14	−	2650.27i	−0.603129	−	1.04465i	0.389215	−	0.921147i	$-0.372746\pi$
$24$		0			0
$25$	1722.45	−	2983.38i	0.551186	−	0.954681i
$26$	−423.023	−	239.280i	−0.122724	−	0.0694183i
$27$		0			0
$28$	−2850.16	+	1713.31i	−0.687028	+	0.412990i
$29$	4347.44	+	2510.00i	0.959929	+	0.554215i	0.896151	−	0.443749i	$-0.146352\pi$
$29$	4347.44	+	2510.00i	0.959929	+	0.554215i	0.0637776	+	0.997964i	$0.479685\pi$
$30$		0			0
$31$	3400.78	−	1963.44i	0.635587	−	0.366956i	−0.147326	−	0.989088i	$-0.547067\pi$
$31$	3400.78	−	1963.44i	0.635587	−	0.366956i	0.782913	+	0.622132i	$0.213733\pi$
$32$	5139.42	+	2672.23i	0.887236	+	0.461316i
$33$		0			0
$34$	4335.30	+	7358.24i	0.643165	+	1.09163i
$35$	8423.34			1.16229
$36$		0			0
$37$	13035.3			1.56537			0.782684	−	0.622419i	$-0.213850\pi$
$37$	13035.3			1.56537			0.782684	+	0.622419i	$0.213850\pi$
$38$	−3516.29	−	5968.14i	−0.395026	−	0.670471i
$39$		0			0
$40$	−7670.03	−	12508.1i	−0.757961	−	1.23607i
$41$	15071.6	−	8701.62i	1.40024	−	0.808426i	0.405819	−	0.913954i	$-0.366986\pi$
$41$	15071.6	−	8701.62i	1.40024	−	0.808426i	0.994416	+	0.105527i	$0.0336531\pi$
$42$		0			0
$43$	5754.33	+	3322.27i	0.474596	+	0.274008i	0.718162	−	0.695876i	$-0.244984\pi$
$43$	5754.33	+	3322.27i	0.474596	+	0.274008i	−0.243566	+	0.969884i	$0.578317\pi$
$44$	7065.19	+	11753.3i	0.550164	+	0.915223i
$45$		0			0
$46$	15068.0	+	8523.13i	1.04993	+	0.593888i
$47$	−10068.4	+	17438.9i	−0.664836	+	1.15153i	0.314494	+	0.949260i	$0.398165\pi$
$47$	−10068.4	+	17438.9i	−0.664836	+	1.15153i	−0.979330	+	0.202270i	$0.935168\pi$
$48$		0			0
$49$	−3003.68	−	5202.52i	−0.178716	−	0.309545i
$50$	171.957	+	19486.6i	0.00972738	+	1.10233i
$51$		0			0
$52$	2748.85	−	48.5176i	0.140975	−	0.00248823i
$53$		−	18043.0i		−	0.882304i	−0.897432	−	0.441152i	$-0.854570\pi$
$53$		−	18043.0i		−	0.882304i	0.897432	−	0.441152i	$-0.145430\pi$
$54$		0			0
$55$		−	34735.5i		−	1.54834i
$56$	8971.37	−	16534.7i	0.382286	−	0.704575i
$57$		0			0
$58$	−28396.3	+	250.580i	−1.10839	+	0.00978084i
$59$	−14736.4	−	25524.2i	−0.551140	−	0.954602i	−0.998193	−	0.0600943i	$-0.980860\pi$
$59$	−14736.4	−	25524.2i	−0.551140	−	0.954602i	0.447053	−	0.894507i	$-0.352473\pi$
$60$		0			0
$61$	−11989.0	+	20765.6i	−0.412533	+	0.714528i	−0.995166	−	0.0982073i	$-0.968689\pi$
$61$	−11989.0	+	20765.6i	−0.412533	+	0.714528i	0.582633	+	0.812735i	$0.302023\pi$
$62$	−10936.7	+	19335.0i	−0.361334	+	0.638800i
$63$		0			0
$64$	−32722.1	+	1734.09i	−0.998599	+	0.0529203i
$65$	−6030.85	−	3481.91i	−0.177050	−	0.102220i
$66$		0			0
$67$	348.663	−	201.301i	0.00948897	−	0.00547846i	−0.495248	−	0.868752i	$-0.664923\pi$
$67$	348.663	−	201.301i	0.00948897	−	0.00547846i	0.504737	+	0.863273i	$0.331589\pi$
$68$	−42259.1	−	23413.8i	−1.10828	−	0.614044i
$69$		0			0
$70$	−41054.0	+	24188.0i	−1.00141	+	0.590004i
$71$	−36645.5			−0.862730			−0.431365	−	0.902178i	$-0.641968\pi$
$71$	−36645.5			−0.862730			−0.431365	+	0.902178i	$0.641968\pi$
$72$		0			0
$73$	58635.9			1.28782			0.643911	−	0.765100i	$-0.277311\pi$
$73$	58635.9			1.28782			0.643911	+	0.765100i	$0.277311\pi$
$74$	−63531.8	+	37431.5i	−1.34869	+	0.794616i
$75$		0			0
$76$	34275.6	+	18990.5i	0.680693	+	0.377141i
$77$	38568.2	−	22267.4i	0.741314	−	0.427998i
$78$		0			0
$79$	−39354.5	−	22721.3i	−0.709457	−	0.409605i	0.101403	−	0.994845i	$-0.467667\pi$
$79$	−39354.5	−	22721.3i	−0.709457	−	0.409605i	−0.810860	+	0.585240i	$0.801000\pi$
$80$	73300.1	+	38937.7i	1.28050	+	0.680213i
$81$		0			0
$82$	−48469.5	+	85689.1i	−0.796039	+	1.40731i
$83$	27253.7	−	47204.9i	0.434241	−	0.752128i	−0.562992	−	0.826462i	$-0.690350\pi$
$83$	27253.7	−	47204.9i	0.434241	−	0.752128i	0.997233	+	0.0743344i	$0.0236832\pi$
$84$		0			0
$85$	61186.2	+	105978.i	0.918557	+	1.59099i
$86$	−37585.7	+	331.671i	−0.547995	+	0.00483572i
$87$		0			0
$88$	−68184.6	−	36995.4i	−0.938598	−	0.509261i
$89$			45338.5i			0.606726i	0.952875	+	0.303363i	$0.0981094\pi$
$89$			45338.5i			0.606726i	−0.952875	+	0.303363i	$0.901891\pi$
$90$		0			0
$91$		−	8928.39i		−	0.113024i
$92$	−97913.4	+	1728.19i	−1.20607	+	0.0212873i
$93$		0			0
$94$	−1005.15	−	113906.i	−0.0117331	−	1.32962i
$95$	−49627.1	−	85956.6i	−0.564169	−	0.977170i
$96$		0			0
$97$	41820.0	−	72434.3i	0.451289	−	0.781655i	−0.547178	−	0.837016i	$-0.684298\pi$
$97$	41820.0	−	72434.3i	0.451289	−	0.781655i	0.998466	+	0.0553615i	$0.0176311\pi$
$98$	29578.7	+	16731.0i	0.311110	+	0.175977i
$99$		0			0
$100$	−56794.7	−	94480.6i	−0.567947	−	0.944806i
$101$	−107672.	−	62164.7i	−1.05027	−	0.606374i	−0.127545	−	0.991833i	$-0.540710\pi$
$101$	−107672.	−	62164.7i	−1.05027	−	0.606374i	−0.922725	+	0.385459i	$0.874043\pi$
$102$		0			0
$103$	−57893.0	+	33424.5i	−0.537691	+	0.310436i	−0.744143	−	0.668021i	$-0.767142\pi$
$103$	−57893.0	+	33424.5i	−0.537691	+	0.310436i	0.206452	+	0.978457i	$0.433808\pi$
$104$	−13258.1	+	8129.91i	−0.120198	+	0.0737059i
$105$		0			0
$106$	51811.2	+	87938.4i	0.447877	+	0.760175i
$107$	144038.			1.21624			0.608119	−	0.793846i	$-0.291924\pi$
$107$	144038.			1.21624			0.608119	+	0.793846i	$0.291924\pi$
$108$		0			0
$109$	−137855.			−1.11136			−0.555680	−	0.831396i	$-0.687542\pi$
$109$	−137855.			−1.11136			−0.555680	+	0.831396i	$0.687542\pi$
$110$	99744.6	+	169295.i	0.785973	+	1.33402i
$111$		0			0
$112$	3755.33	+	106349.i	0.0282881	+	0.801104i
$113$	24697.0	−	14258.8i	0.181948	−	0.105048i	−0.406259	−	0.913758i	$-0.633167\pi$
$113$	24697.0	−	14258.8i	0.181948	−	0.105048i	0.588208	+	0.808710i	$0.299834\pi$
$114$		0			0
$115$	214818.	+	124025.i	1.51470	+	0.874511i
$116$	137679.	−	82762.5i	0.949999	−	0.571069i
$117$		0			0
$118$	145117.	+	82084.4i	0.959428	+	0.542695i
$119$	−78447.4	+	135875.i	−0.507821	+	0.879573i
$120$		0			0
$121$	−11298.8	−	19570.0i	−0.0701565	−	0.121515i
$122$	−1196.90	−	135635.i	−0.00728042	−	0.825034i
$123$		0			0
$124$	−2217.58	−	125641.i	−0.0129517	−	0.733798i
$125$			25930.3i			0.148434i
$126$		0			0
$127$		−	74540.3i		−	0.410093i	−0.978752	−	0.205046i	$-0.934266\pi$
$127$		−	74540.3i		−	0.410093i	0.978752	−	0.205046i	$-0.0657345\pi$
$128$	154502.	−	102415.i	0.833509	−	0.552506i
$129$		0			0
$130$	39391.8	−	347.609i	0.204431	−	0.00180398i
$131$	66965.9	+	115988.i	0.340938	+	0.590522i	0.984607	−	0.174782i	$-0.0559221\pi$
$131$	66965.9	+	115988.i	0.340938	+	0.590522i	−0.643669	+	0.765304i	$0.722589\pi$
$132$		0			0
$133$	63627.3	−	110206.i	0.311899	−	0.540226i
$134$	−1121.28	+	1982.31i	−0.00539451	+	0.00953694i
$135$		0			0
$136$	273197.	−	7233.90i	1.26657	−	0.0335371i
$137$	143212.	+	82683.3i	0.651894	+	0.376371i	0.789182	−	0.614160i	$-0.210505\pi$
$137$	143212.	+	82683.3i	0.651894	+	0.376371i	−0.137287	+	0.990531i	$0.543838\pi$
$138$		0			0
$139$	−105373.	+	60837.0i	−0.462585	+	0.267074i	−0.713131	−	0.701031i	$-0.752723\pi$
$139$	−105373.	+	60837.0i	−0.462585	+	0.267074i	0.250546	+	0.968105i	$0.419390\pi$
$140$	130633.	−	235777.i	0.563291	−	1.01667i
$141$		0			0
$142$	178604.	−	105229.i	0.743311	−	0.437941i
$143$	−36818.2			−0.150564
$144$		0			0
$145$	−406896.			−1.60717
$146$	−285781.	+	168376.i	−1.10956	+	0.653728i
$147$		0			0
$148$	202157.	−	364869.i	0.758639	−	1.36925i
$149$	60786.2	−	35094.9i	0.224305	−	0.129503i	−0.383637	−	0.923484i	$-0.625329\pi$
$149$	60786.2	−	35094.9i	0.224305	−	0.129503i	0.607942	+	0.793981i	$0.291995\pi$
$150$		0			0
$151$	−31118.1	−	17966.1i	−0.111064	−	0.0641225i	0.443439	−	0.896304i	$-0.353758\pi$
$151$	−31118.1	−	17966.1i	−0.111064	−	0.0641225i	−0.554503	+	0.832182i	$0.687092\pi$
$152$	−221586.	+	5867.29i	−0.777916	+	0.0205982i
$153$		0			0
$154$	−124033.	+	219278.i	−0.421440	+	0.745062i
$155$	−159147.	+	275651.i	−0.532070	+	0.921573i
$156$		0			0
$157$	−84404.3	−	146193.i	−0.273285	−	0.473343i	0.696416	−	0.717638i	$-0.254777\pi$
$157$	−84404.3	−	146193.i	−0.273285	−	0.473343i	−0.969701	+	0.244295i	$0.921443\pi$
$158$	257052.	−	2268.33i	0.819179	−	0.00722876i
$159$		0			0
$160$	−469064.	+	20708.9i	−1.44854	+	0.0639525i
$161$			318028.i			0.966941i
$162$		0			0
$163$		−	325623.i		−	0.959943i	−0.877284	−	0.479972i	$-0.840647\pi$
$163$		−	325623.i		−	0.959943i	0.877284	−	0.479972i	$-0.159353\pi$
$164$	−9827.91	−	556817.i	−0.0285333	−	1.61660i
$165$		0			0
$166$	2720.82	+	308329.i	0.00766353	+	0.868449i
$167$	106712.	+	184831.i	0.296090	+	0.512843i	0.975238	−	0.221158i	$-0.0709838\pi$
$167$	106712.	+	184831.i	0.296090	+	0.512843i	−0.679148	+	0.734002i	$0.737650\pi$
$168$		0			0
$169$	181956.	−	315157.i	0.490060	−	0.848809i
$170$	−602531.	−	340818.i	−1.59903	−	0.904482i
$171$		0			0
$172$	182234.	−	109546.i	0.469686	−	0.282341i
$173$	27550.4	+	15906.2i	0.0699862	+	0.0404066i	0.534585	−	0.845115i	$-0.320468\pi$
$173$	27550.4	+	15906.2i	0.0699862	+	0.0404066i	−0.464599	+	0.885521i	$0.653801\pi$
$174$		0			0
$175$	−310037.	+	179000.i	−0.765276	+	0.441832i
$176$	438554.	−	15485.9i	1.06719	−	0.0376839i
$177$		0			0
$178$	−130192.	−	220972.i	−0.307988	−	0.522742i
$179$	475398.			1.10898			0.554491	−	0.832189i	$-0.312913\pi$
$179$	475398.			1.10898			0.554491	+	0.832189i	$0.312913\pi$
$180$		0			0
$181$	4695.48			0.0106533			0.00532664	−	0.999986i	$-0.498304\pi$
$181$	4695.48			0.0106533			0.00532664	+	0.999986i	$0.498304\pi$
$182$	25638.3	+	43515.5i	0.0573734	+	0.0973789i
$183$		0			0
$184$	472251.	−	289586.i	1.02832	−	0.630569i
$185$	−915021.	+	528288.i	−1.96563	+	1.13486i
$186$		0			0
$187$	560310.	+	323495.i	1.17172	+	0.676493i
$188$	331986.	+	552273.i	0.685054	+	1.13962i
$189$		0			0
$190$	488702.	+	276431.i	0.982110	+	0.555525i
$191$	302770.	−	524412.i	0.600522	−	1.04013i	−0.392220	−	0.919871i	$-0.628293\pi$
$191$	302770.	−	524412.i	0.600522	−	1.04013i	0.992742	−	0.120263i	$-0.0383738\pi$
$192$		0			0
$193$	46694.6	+	80877.5i	0.0902347	+	0.156291i	0.907610	−	0.419815i	$-0.137905\pi$
$193$	46694.6	+	80877.5i	0.0902347	+	0.156291i	−0.817375	+	0.576106i	$0.804572\pi$
$194$	4175.00	+	473121.i	0.00796439	+	0.902542i
$195$		0			0
$196$	−192205.	+	3392.45i	−0.357376	+	0.00630774i
$197$		−	466419.i		−	0.856270i	−0.903715	−	0.428135i	$-0.859171\pi$
$197$		−	466419.i		−	0.856270i	0.903715	−	0.428135i	$-0.140829\pi$
$198$		0			0
$199$			625885.i			1.12037i	0.828367	+	0.560185i	$0.189270\pi$
$199$			625885.i			1.12037i	−0.828367	+	0.560185i	$0.810730\pi$
$200$	548113.	+	297394.i	0.968936	+	0.525723i
$201$		0			0
$202$	703286.	−	6206.07i	1.21270	−	0.0107013i
$203$	−260842.	−	451792.i	−0.444261	−	0.769482i
$204$		0			0
$205$	−705309.	+	1.22163e6i	−1.17218	+	2.03028i
$206$	186181.	−	329148.i	0.305679	−	0.540409i
$207$		0			0
$208$	41272.3	−	77695.0i	0.0661455	−	0.124519i
$209$	−454457.	−	262381.i	−0.719660	−	0.415496i
$210$		0			0
$211$	−756200.	+	436592.i	−1.16931	+	0.675103i	−0.953518	−	0.301336i	$-0.902567\pi$
$211$	−756200.	+	436592.i	−1.16931	+	0.675103i	−0.215794	+	0.976439i	$0.569234\pi$
$212$	−505038.	−	279818.i	−0.771764	−	0.427599i
$213$		0			0
$214$	−702018.	+	413613.i	−1.04789	+	0.617390i
$215$	−538572.			−0.794599
$216$		0			0
$217$	−408088.			−0.588307
$218$	671880.	−	395856.i	0.957525	−	0.564151i
$219$		0			0
$220$	−972276.	−	538694.i	−1.35436	−	0.750387i
$221$	112332.	−	64854.8i	0.154711	−	0.0893226i
$222$		0			0
$223$	419169.	+	242007.i	0.564452	+	0.325886i	0.754930	−	0.655805i	$-0.227671\pi$
$223$	419169.	+	242007.i	0.564452	+	0.325886i	−0.190479	+	0.981691i	$0.561004\pi$
$224$	−323689.	−	507544.i	−0.431031	−	0.675856i
$225$		0			0
$226$	−79424.2	+	140414.i	−0.103438	+	0.182868i
$227$	117910.	−	204225.i	0.151874	−	0.263054i	−0.780042	−	0.625727i	$-0.784802\pi$
$227$	117910.	−	204225.i	0.151874	−	0.263054i	0.931917	+	0.362673i	$0.118136\pi$
$228$		0			0
$229$	124091.	+	214932.i	0.156369	+	0.270840i	0.933557	−	0.358429i	$-0.116688\pi$
$229$	124091.	+	214932.i	0.156369	+	0.270840i	−0.777187	+	0.629269i	$0.783354\pi$
$230$	−1.40313e6	+	12381.8i	−1.74895	+	0.0154334i
$231$		0			0
$232$	−433368.	+	798722.i	−0.528612	+	0.974262i
$233$			340275.i			0.410620i	0.978697	+	0.205310i	$0.0658202\pi$
$233$			340275.i			0.410620i	−0.978697	+	0.205310i	$0.934180\pi$
$234$		0			0
$235$		−	1.63218e6i		−	1.92797i
$236$	−942983.	+	16643.8i	−1.10211	+	0.0194524i
$237$		0			0
$238$	−7831.62	−	887496.i	−0.00896208	−	1.01560i
$239$	303908.	+	526384.i	0.344149	+	0.596084i	0.985199	−	0.171415i	$-0.0548340\pi$
$239$	303908.	+	526384.i	0.344149	+	0.596084i	−0.641049	+	0.767500i	$0.721501\pi$
$240$		0			0
$241$	756653.	−	1.31056e6i	0.839179	−	1.45350i	−0.0514039	−	0.998678i	$-0.516370\pi$
$241$	756653.	−	1.31056e6i	0.839179	−	1.45350i	0.890582	−	0.454822i	$-0.150297\pi$
$242$	111265.	+	62936.1i	0.122129	+	0.0690815i
$243$		0			0
$244$	395315.	+	657624.i	0.425078	+	0.707137i
$245$	421690.	+	243463.i	0.448826	+	0.259130i
$246$		0			0
$247$	−91110.3	+	52602.6i	−0.0950223	+	0.0548611i
$248$	371592.	+	605984.i	0.383651	+	0.625651i
$249$		0			0
$250$	−74460.0	−	126380.i	−0.0753482	−	0.127887i
$251$	−1.13311e6			−1.13524			−0.567622	−	0.823289i	$-0.692136\pi$
$251$	−1.13311e6			−1.13524			−0.567622	+	0.823289i	$0.692136\pi$
$252$		0			0
$253$	1.31146e6			1.28811
$254$	214046.	+	363297.i	0.208172	+	0.353327i
$255$		0			0
$256$	−458930.	+	942812.i	−0.437670	+	0.899136i
$257$	928992.	−	536354.i	0.877362	−	0.506545i	0.00757446	−	0.999971i	$-0.497589\pi$
$257$	928992.	−	536354.i	0.877362	−	0.506545i	0.869788	+	0.493426i	$0.164256\pi$
$258$		0			0
$259$	−1.17316e6	−	677323.i	−1.08669	−	0.627403i
$260$	−190991.	+	114810.i	−0.175218	+	0.105328i
$261$		0			0
$262$	−659446.	−	373012.i	−0.593507	−	0.335714i
$263$	341490.	−	591477.i	0.304430	−	0.527289i	−0.672704	−	0.739912i	$-0.734867\pi$
$263$	341490.	−	591477.i	0.304430	−	0.527289i	0.977134	+	0.212623i	$0.0682006\pi$
$264$		0			0
$265$	731236.	+	1.26654e6i	0.639651	+	1.10791i
$266$	6352.09	+	719833.i	0.00550443	+	0.623775i
$267$		0			0
$268$	−227.356	−	12881.2i	−0.000193361	−	0.0109552i
$269$		−	931829.i		−	0.785155i	−0.919719	−	0.392577i	$-0.871583\pi$
$269$		−	931829.i		−	0.785155i	0.919719	−	0.392577i	$-0.128417\pi$
$270$		0			0
$271$		−	1.76382e6i		−	1.45892i	−0.684023	−	0.729460i	$-0.739771\pi$
$271$		−	1.76382e6i		−	1.45892i	0.684023	−	0.729460i	$-0.260229\pi$
$272$	−1.31074e6	+	819755.i	−1.07423	+	0.671834i
$273$		0			0
$274$	−935419.	+	8254.50i	−0.752713	+	0.00664224i
$275$	738145.	+	1.27850e6i	0.588586	+	1.01946i
$276$		0			0
$277$	309348.	−	535806.i	0.242241	−	0.419573i	−0.719111	−	0.694895i	$-0.755451\pi$
$277$	309348.	−	535806.i	0.242241	−	0.419573i	0.961352	+	0.275321i	$0.0887843\pi$
$278$	338873.	−	599092.i	0.262981	−	0.464924i
$279$		0			0
$280$	40360.2	+	1.52425e6i	0.0307651	+	1.16188i
$281$	1.58185e6	+	913279.i	1.19508	+	0.689982i	0.959455	−	0.281861i	$-0.0909518\pi$
$281$	1.58185e6	+	913279.i	1.19508	+	0.689982i	0.235628	+	0.971843i	$0.424285\pi$
$282$		0			0
$283$	1.63561e6	−	944320.i	1.21399	−	0.700895i	0.250361	−	0.968153i	$-0.419451\pi$
$283$	1.63561e6	−	944320.i	1.21399	−	0.700895i	0.963625	+	0.267258i	$0.0861174\pi$
$284$	−568315.	+	1.02574e6i	−0.418113	+	0.754642i
$285$		0			0
$286$	179445.	−	105725.i	0.129723	−	0.0764298i
$287$	−1.80857e6			−1.29607
$288$		0			0
$289$	−859473.			−0.605324
$290$	1.98314e6	−	1.16842e6i	1.38471	−	0.815838i
$291$		0			0
$292$	909351.	−	1.64127e6i	0.624129	−	1.12648i
$293$	965146.	−	557227.i	0.656786	−	0.379196i	−0.134265	−	0.990945i	$-0.542867\pi$
$293$	965146.	−	557227.i	0.656786	−	0.379196i	0.791051	+	0.611750i	$0.209534\pi$
$294$		0			0
$295$	2.06886e6	+	1.19446e6i	1.38413	+	0.799128i
$296$	62458.3	+	2.35881e6i	0.0414344	+	1.56482i
$297$		0			0
$298$	−195485.	+	345597.i	−0.127518	+	0.225439i
$299$	131461.	−	227698.i	0.0850394	−	0.147293i
$300$		0			0
$301$	−345254.	−	597998.i	−0.219646	−	0.380438i
$302$	203255.	−	1793.60i	0.128240	−	0.00113164i
$303$		0			0
$304$	1.06312e6	−	664890.i	0.659780	−	0.412634i
$305$		−	1.94354e6i		−	1.19631i
$306$		0			0
$307$			1.64394e6i			0.995497i	0.867321	+	0.497749i	$0.165840\pi$
$307$			1.64394e6i			0.995497i	−0.867321	+	0.497749i	$0.834160\pi$
$308$	−25149.5	−	1.42489e6i	−0.0151061	−	0.855863i
$309$		0			0
$310$	−15888.1	−	1.80047e6i	−0.00939003	−	1.06410i
$311$	−363235.	−	629141.i	−0.212954	−	0.368848i	0.739683	−	0.672955i	$-0.234975\pi$
$311$	−363235.	−	629141.i	−0.212954	−	0.368848i	−0.952638	+	0.304107i	$0.901642\pi$
$312$		0			0
$313$	702457.	−	1.21669e6i	0.405284	−	0.701972i	−0.589071	−	0.808081i	$-0.700506\pi$
$313$	702457.	−	1.21669e6i	0.405284	−	0.701972i	0.994354	+	0.106110i	$0.0338394\pi$
$314$	831171.	+	470147.i	0.475736	+	0.269097i
$315$		0			0
$316$	−1.24632e6	+	749193.i	−0.702118	+	0.422062i
$317$	−1.21701e6	−	702639.i	−0.680213	−	0.392721i	0.119722	−	0.992807i	$-0.461800\pi$
$317$	−1.21701e6	−	702639.i	−0.680213	−	0.392721i	−0.799935	+	0.600086i	$0.795133\pi$
$318$		0			0
$319$	−1.86306e6	+	1.07564e6i	−1.02506	+	0.591821i
$320$	2.22667e6	−	1.44787e6i	1.21557	−	0.790414i
$321$		0			0
$322$	−913231.	−	1.55001e6i	−0.490841	−	0.833097i
$323$	1.84873e6			0.985976
$324$		0			0
$325$	295969.			0.155431
$326$	935040.	+	1.58703e6i	0.487289	+	0.827068i
$327$		0			0
$328$	1.64682e6	+	2.68561e6i	0.845206	+	1.37835i
$329$	1.81228e6	−	1.04632e6i	0.923071	−	0.532935i
$330$		0			0
$331$	214028.	+	123569.i	0.107374	+	0.0619926i	0.552725	−	0.833363i	$-0.313588\pi$
$331$	214028.	+	123569.i	0.107374	+	0.0619926i	−0.445351	+	0.895356i	$0.646921\pi$
$332$	−898642.	−	1.49493e6i	−0.447447	−	0.744347i
$333$		0			0
$334$	−1.05085e6	−	594407.i	−0.515436	−	0.291553i
$335$	−16316.4	+	28260.9i	−0.00794352	+	0.0137586i
$336$		0			0
$337$	1.07901e6	+	1.86890e6i	0.517549	+	0.896421i	0.999792	+	0.0203835i	$0.00648871\pi$
$337$	1.07901e6	+	1.86890e6i	0.517549	+	0.896421i	−0.482244	+	0.876037i	$0.660178\pi$
$338$	18165.1	+	2.05851e6i	0.00864863	+	0.980082i
$339$		0			0
$340$	3.91531e6	−	69105.8i	1.83683	−	0.0324203i
$341$			1.68284e6i			0.783712i
$342$		0			0
$343$			2.37090e6i			1.08812i
$344$	−573612.	+	1.05720e6i	−0.261350	+	0.481682i
$345$		0			0
$346$	−179951.	+	1587.96i	−0.0808100	+	0.000713099i
$347$	−804114.	−	1.39277e6i	−0.358504	−	0.620947i	0.629207	−	0.777237i	$-0.283380\pi$
$347$	−804114.	−	1.39277e6i	−0.358504	−	0.620947i	−0.987711	+	0.156291i	$0.950046\pi$
$348$		0			0
$349$	233867.	−	405070.i	0.102779	−	0.178019i	−0.810049	−	0.586362i	$-0.800560\pi$
$349$	233867.	−	405070.i	0.102779	−	0.178019i	0.912829	+	0.408343i	$0.133893\pi$
$350$	997061.	−	1.76270e6i	0.435062	−	0.769145i
$351$		0			0
$352$	−2.09297e6	+	1.33480e6i	−0.900339	+	0.574197i
$353$	−397710.	−	229618.i	−0.169875	−	0.0980773i	0.412652	−	0.910889i	$-0.364603\pi$
$353$	−397710.	−	229618.i	−0.169875	−	0.0980773i	−0.582527	+	0.812811i	$0.697936\pi$
$354$		0			0
$355$	2.57236e6	−	1.48515e6i	1.08333	−	0.625460i
$356$	1.26906e6	+	703130.i	0.530712	+	0.294043i
$357$		0			0
$358$	−2.31701e6	+	1.36513e6i	−0.955477	+	0.562945i
$359$	2.21493e6			0.907037			0.453518	−	0.891247i	$-0.350169\pi$
$359$	2.21493e6			0.907037			0.453518	+	0.891247i	$0.350169\pi$
$360$		0			0
$361$	976629.			0.394423
$362$	−22885.0	+	13483.3i	−0.00917864	+	0.00540784i
$363$		0			0
$364$	−249913.	−	138465.i	−0.0988635	−	0.0547757i
$365$	−4.11598e6	+	2.37636e6i	−1.61712	+	0.933643i
$366$		0			0
$367$	−2.54558e6	−	1.46969e6i	−0.986555	−	0.569588i	−0.0823124	−	0.996607i	$-0.526231\pi$
$367$	−2.54558e6	−	1.46969e6i	−0.986555	−	0.569588i	−0.904243	+	0.427019i	$0.859564\pi$
$368$	−1.47011e6	+	2.76748e6i	−0.565889	+	1.06528i
$369$		0			0
$370$	2.94266e6	−	5.20231e6i	1.11747	−	1.97557i
$371$	−937525.	+	1.62384e6i	−0.353629	+	0.612504i
$372$		0			0
$373$	−830424.	−	1.43834e6i	−0.309049	−	0.535289i	0.669105	−	0.743168i	$-0.266678\pi$
$373$	−830424.	−	1.43834e6i	−0.309049	−	0.535289i	−0.978155	+	0.207878i	$0.933344\pi$
$374$	−3.65978e6	+	32295.4i	−1.35293	+	0.0119388i
$375$		0			0
$376$	−3.20392e6	−	1.73837e6i	−1.16872	−	0.634123i
$377$			431292.i			0.156285i
$378$		0			0
$379$		−	4.69152e6i		−	1.67770i	−0.544360	−	0.838852i	$-0.683227\pi$
$379$		−	4.69152e6i		−	1.67770i	0.544360	−	0.838852i	$-0.316773\pi$
$380$	−3.17564e6	+	56050.5i	−1.12816	+	0.0199123i
$381$		0			0
$382$	30226.3	+	3.42531e6i	0.0105981	+	1.20100i
$383$	−2.64821e6	−	4.58683e6i	−0.922476	−	1.59777i	−0.795571	−	0.605860i	$-0.792829\pi$
$383$	−2.64821e6	−	4.58683e6i	−0.922476	−	1.59777i	−0.126904	−	0.991915i	$-0.540504\pi$
$384$		0			0
$385$	−1.80488e6	+	3.12614e6i	−0.620578	+	1.07487i
$386$	−459825.	−	260097.i	−0.157081	−	0.0888521i
$387$		0			0
$388$	−1.37894e6	−	2.29392e6i	−0.465013	−	0.773569i
$389$	1.59537e6	+	921088.i	0.534549	+	0.308622i	0.742867	−	0.669439i	$-0.233465\pi$
$389$	1.59537e6	+	921088.i	0.534549	+	0.308622i	−0.208318	+	0.978061i	$0.566799\pi$
$390$		0			0
$391$	−4.00124e6	+	2.31011e6i	−1.32359	+	0.764173i
$392$	927034.	−	568461.i	0.304706	−	0.186847i
$393$		0			0
$394$	1.33934e6	+	2.27325e6i	0.434662	+	0.737744i
$395$	3.68335e6			1.18782
$396$		0			0
$397$	75711.5			0.0241094			0.0120547	−	0.999927i	$-0.496163\pi$
$397$	75711.5			0.0241094			0.0120547	+	0.999927i	$0.496163\pi$
$398$	−1.79726e6	−	3.05046e6i	−0.568725	−	0.965288i
$399$		0			0
$400$	−3.52539e6	+	124486.i	−1.10168	+	0.0389019i
$401$	−2.92456e6	+	1.68849e6i	−0.908237	+	0.524371i	−0.879863	−	0.475227i	$-0.842366\pi$
$401$	−2.92456e6	+	1.68849e6i	−0.908237	+	0.524371i	−0.0283735	+	0.999597i	$0.509033\pi$
$402$		0			0
$403$	292178.	+	168689.i	0.0896158	+	0.0517397i
$404$	−3.40988e6	+	2.04977e6i	−1.03941	+	0.624814i
$405$		0			0
$406$	2.56864e6	+	1.45294e6i	0.773373	+	0.437454i
$407$	−2.79309e6	+	4.83777e6i	−0.835793	+	1.44764i
$408$		0			0
$409$	−1.75008e6	−	3.03123e6i	−0.517310	−	0.896007i	−0.999798	−	0.0201041i	$-0.993600\pi$
$409$	−1.75008e6	−	3.03123e6i	−0.517310	−	0.896007i	0.482488	−	0.875902i	$-0.339733\pi$
$410$	−70413.0	−	7.97935e6i	−0.0206868	−	2.34427i
$411$		0			0
$412$	37750.8	+	2.13884e6i	0.0109568	+	0.620776i
$413$			3.06285e6i			0.883591i
$414$		0			0
$415$			4.41810e6i			1.25926i
$416$	21950.6	+	497188.i	0.00621888	+	0.140860i
$417$		0			0
$418$	2.96839e6	−	26194.2i	0.830960	−	0.00733271i
$419$	2.65830e6	+	4.60430e6i	0.739721	+	1.28123i	0.952621	+	0.304161i	$0.0983760\pi$
$419$	2.65830e6	+	4.60430e6i	0.739721	+	1.28123i	−0.212899	+	0.977074i	$0.568291\pi$
$420$		0			0
$421$	−2.59023e6	+	4.48640e6i	−0.712250	+	1.23365i	0.251761	+	0.967790i	$0.418990\pi$
$421$	−2.59023e6	+	4.48640e6i	−0.712250	+	1.23365i	−0.964011	+	0.265864i	$0.914343\pi$
$422$	2.43190e6	−	4.29934e6i	0.664758	−	1.17522i
$423$		0			0
$424$	3.26498e6	−	86452.4i	0.881995	−	0.0233541i
$425$	−4.50414e6	−	2.60047e6i	−1.20959	−	0.698360i
$426$		0			0
$427$	2.15799e6	−	1.24591e6i	0.572768	−	0.330688i
$428$	2.23381e6	−	4.03176e6i	0.589437	−	1.06386i
$429$		0			0
$430$	2.62491e6	−	1.54654e6i	0.684610	−	0.403356i
$431$	−5.72244e6			−1.48384			−0.741922	−	0.670486i	$-0.766086\pi$
$431$	−5.72244e6			−1.48384			−0.741922	+	0.670486i	$0.766086\pi$
$432$		0			0
$433$	−6.17405e6			−1.58252			−0.791262	−	0.611478i	$-0.790575\pi$
$433$	−6.17405e6			−1.58252			−0.791262	+	0.611478i	$0.790575\pi$
$434$	1.98895e6	−	1.17184e6i	0.506873	−	0.298638i
$435$		0			0
$436$	−2.13791e6	+	3.85867e6i	−0.538609	+	0.972123i
$437$	3.24533e6	−	1.87369e6i	0.812935	−	0.469348i
$438$		0			0
$439$	−5.02340e6	−	2.90026e6i	−1.24405	−	0.718251i	−0.274131	−	0.961692i	$-0.588390\pi$
$439$	−5.02340e6	−	2.90026e6i	−1.24405	−	0.718251i	−0.969915	+	0.243442i	$0.921723\pi$
$440$	6.28559e6	−	166434.i	1.54780	−	0.0409837i
$441$		0			0
$442$	−361252.	+	638657.i	−0.0879539	+	0.155493i
$443$	2.08981e6	−	3.61966e6i	0.505939	−	0.876312i	−0.494037	−	0.869441i	$-0.664479\pi$
$443$	2.08981e6	−	3.61966e6i	0.505939	−	0.876312i	0.999976	−	0.00687158i	$-0.00218731\pi$
$444$		0			0
$445$	−1.83746e6	−	3.18257e6i	−0.439863	−	0.761864i
$446$	−2.73789e6	+	24160.2i	−0.651747	+	0.00575127i
$447$		0			0
$448$	3.03504e6	+	1.54420e6i	0.714447	+	0.363503i
$449$			970936.i			0.227287i	0.993522	+	0.113644i	$0.0362522\pi$
$449$			970936.i			0.227287i	−0.993522	+	0.113644i	$0.963748\pi$
$450$		0			0
$451$			7.45802e6i			1.72656i
$452$	−16104.4	−	912423.i	−0.00370765	−	0.210063i
$453$		0			0
$454$	11771.2	+	1.33394e6i	0.00268029	+	0.303737i
$455$	361845.	+	626734.i	0.0819397	+	0.141924i
$456$		0			0
$457$	−1.03810e6	+	1.79803e6i	−0.232513	+	0.402724i	−0.958547	−	0.284935i	$-0.908028\pi$
$457$	−1.03810e6	+	1.79803e6i	−0.232513	+	0.402724i	0.726034	+	0.687659i	$0.241361\pi$
$458$	−1.22199e6	−	691209.i	−0.272209	−	0.153973i
$459$		0			0
$460$	6.80306e6	−	4.08950e6i	1.49903	−	0.901105i
$461$	−2.52767e6	−	1.45935e6i	−0.553947	−	0.319821i	0.196766	−	0.980451i	$-0.436956\pi$
$461$	−2.52767e6	−	1.45935e6i	−0.553947	−	0.319821i	−0.750712	+	0.660629i	$0.770290\pi$
$462$		0			0
$463$	5.02987e6	−	2.90400e6i	1.09045	−	0.629569i	0.156751	−	0.987638i	$-0.449898\pi$
$463$	5.02987e6	−	2.90400e6i	1.09045	−	0.629569i	0.933695	+	0.358069i	$0.116565\pi$
$464$	−181404.	−	5.13727e6i	−0.0391158	−	1.10774i
$465$		0			0
$466$	−977114.	−	1.65844e6i	−0.208440	−	0.353781i
$467$	8.31962e6			1.76527			0.882636	−	0.470058i	$-0.155767\pi$
$467$	8.31962e6			1.76527			0.882636	+	0.470058i	$0.155767\pi$
$468$		0			0
$469$	−41838.9			−0.00878311
$470$	4.68689e6	+	7.95498e6i	0.978678	+	1.66110i
$471$		0			0
$472$	4.54815e6	−	2.78894e6i	0.939679	−	0.576214i
$473$	−2.46598e6	+	1.42373e6i	−0.506799	+	0.292601i
$474$		0			0
$475$	3.65323e6	+	2.10919e6i	0.742922	+	0.428926i
$476$	2.58666e6	+	4.30302e6i	0.523265	+	0.870474i
$477$		0			0
$478$	−2.99273e6	−	1.69282e6i	−0.599098	−	0.338876i
$479$	−57304.6	+	99254.5i	−0.0114117	+	0.0197657i	−0.871675	−	0.490085i	$-0.836966\pi$
$479$	−57304.6	+	99254.5i	−0.0114117	+	0.0197657i	0.860263	+	0.509850i	$0.170299\pi$
$480$		0			0
$481$	559963.	+	969884.i	0.110356	+	0.191142i
$482$	75538.8	+	8.56022e6i	0.0148099	+	1.67829i
$483$		0			0
$484$	−723009.	+	12761.2i	−0.140291	+	0.00247616i
$485$			6.77943e6i			1.30870i
$486$		0			0
$487$			2.72517e6i			0.520681i	0.965517	+	0.260340i	$0.0838348\pi$
$487$			2.72517e6i			0.520681i	−0.965517	+	0.260340i	$0.916165\pi$
$488$	−3.81510e6	−	2.06998e6i	−0.725197	−	0.393475i
$489$		0			0
$490$	−2.75436e6	+	24305.6i	−0.518240	+	0.00457315i
$491$	2.94851e6	+	5.10696e6i	0.551948	+	0.956002i	0.998134	+	0.0610621i	$0.0194488\pi$
$491$	2.94851e6	+	5.10696e6i	0.551948	+	0.956002i	−0.446186	+	0.894940i	$0.647218\pi$
$492$		0			0
$493$	3.78946e6	−	6.56353e6i	0.702198	−	1.21624i
$494$	293006.	−	518004.i	0.0540205	−	0.0955027i
$495$		0			0
$496$	−3.55119e6	−	1.88642e6i	−0.648141	−	0.344298i
$497$	3.29804e6	+	1.90413e6i	0.598915	+	0.345784i
$498$		0			0
$499$	6.34312e6	−	3.66220e6i	1.14039	−	0.658402i	0.193860	−	0.981029i	$-0.437899\pi$
$499$	6.34312e6	−	3.66220e6i	1.14039	−	0.658402i	0.946526	+	0.322627i	$0.104566\pi$
$500$	725811.	+	402138.i	0.129837	+	0.0719367i
$501$		0			0
$502$	5.52260e6	−	3.25379e6i	0.978103	−	0.576275i
$503$	−5.80816e6			−1.02357			−0.511786	−	0.859113i	$-0.671016\pi$
$503$	−5.80816e6			−1.02357			−0.511786	+	0.859113i	$0.671016\pi$
$504$		0			0
$505$	1.00775e7			1.75843
$506$	−6.39181e6	+	3.76591e6i	−1.10981	+	0.653873i
$507$		0			0
$508$	−2.08645e6	−	1.15600e6i	−0.358714	−	0.198747i
$509$	3.70500e6	−	2.13908e6i	0.633861	−	0.365960i	−0.148385	−	0.988930i	$-0.547407\pi$
$509$	3.70500e6	−	2.13908e6i	0.633861	−	0.365960i	0.782246	+	0.622970i	$0.214074\pi$
$510$		0			0
$511$	−5.27714e6	−	3.04676e6i	−0.894018	−	0.516162i
$512$	−470581.	−	5.91295e6i	−0.0793340	−	0.996848i
$513$		0			0
$514$	−2.98758e6	+	5.28174e6i	−0.498784	+	0.881798i
$515$	2.70922e6	−	4.69251e6i	0.450119	−	0.779628i
$516$		0			0
$517$	−4.31472e6	−	7.47332e6i	−0.709948	−	1.22967i
$518$	7.66274e6	−	67619.0i	1.25476	−	0.0110725i
$519$		0			0
$520$	601176.	−	1.10800e6i	0.0974975	−	0.179693i
$521$		−	6.07298e6i		−	0.980184i	−0.871671	−	0.490092i	$-0.836963\pi$
$521$		−	6.07298e6i		−	0.980184i	0.871671	−	0.490092i	$-0.163037\pi$
$522$		0			0
$523$		−	525817.i		−	0.0840583i	−0.999116	−	0.0420291i	$-0.986618\pi$
$523$		−	525817.i		−	0.0840583i	0.999116	−	0.0420291i	$-0.0133822\pi$
$524$	4.28515e6	−	75633.5i	0.681770	−	0.0120333i
$525$		0			0
$526$	34091.8	+	3.86336e6i	0.00537262	+	0.608837i
$527$	−2.96430e6	−	5.13432e6i	−0.464939	−	0.805297i
$528$		0			0
$529$	−1.46446e6	+	2.53652e6i	−0.227530	+	0.394093i
$530$	−7.20085e6	−	4.07312e6i	−1.11351	−	0.629850i
$531$		0			0
$532$	−2.09799e6	−	3.49010e6i	−0.321384	−	0.534637i
$533$	1.29488e6	+	747598.i	0.197429	+	0.113986i
$534$		0			0
$535$	−1.01109e7	+	5.83751e6i	−1.52723	+	0.881746i
$536$	38097.2	+	62128.1i	0.00572771	+	0.00934063i
$537$		0			0
$538$	2.67579e6	+	4.54158e6i	0.398562	+	0.676474i
$539$	2.57440e6			0.381685
$540$		0			0
$541$	1.11917e7			1.64400			0.822000	−	0.569488i	$-0.192858\pi$
$541$	1.11917e7			1.64400			0.822000	+	0.569488i	$0.192858\pi$
$542$	5.06490e6	+	8.59657e6i	0.740581	+	1.25698i
$543$		0			0
$544$	4.03438e6	−	7.75921e6i	0.584494	−	1.12414i
$545$	9.67679e6	−	5.58690e6i	1.39553	−	0.805711i
$546$		0			0
$547$	−776917.	−	448553.i	−0.111021	−	0.0640982i	0.443461	−	0.896294i	$-0.353750\pi$
$547$	−776917.	−	448553.i	−0.111021	−	0.0640982i	−0.554482	+	0.832195i	$0.687084\pi$
$548$	4.53537e6	−	2.72633e6i	0.645151	−	0.387817i
$549$		0			0
$550$	−7.26888e6	−	4.11160e6i	−1.02461	−	0.579567i
$551$	−3.07356e6	+	5.32357e6i	−0.431284	+	0.747006i
$552$		0			0
$553$	2.36123e6	+	4.08977e6i	0.328341	+	0.568704i
$554$	30883.0	+	3.49973e6i	0.00427509	+	0.484463i
$555$		0			0
$556$	68711.4	+	3.89296e6i	0.00942631	+	0.534064i
$557$		−	2.91603e6i		−	0.398249i	−0.979974	−	0.199124i	$-0.936190\pi$
$557$		−	2.91603e6i		−	0.398249i	0.979974	−	0.199124i	$-0.0638098\pi$
$558$		0			0
$559$			570864.i			0.0772686i
$560$	−4.57367e6	−	7.31306e6i	−0.616304	−	0.985437i
$561$		0			0
$562$	−1.03322e7	+	91175.1i	−1.37991	+	0.0121769i
$563$	−1.88482e6	−	3.26460e6i	−0.250610	−	0.434070i	0.713084	−	0.701079i	$-0.247298\pi$
$563$	−1.88482e6	−	3.26460e6i	−0.250610	−	0.434070i	−0.963694	+	0.267009i	$0.913965\pi$
$564$		0			0
$565$	−1.15575e6	+	2.00182e6i	−0.152315	+	0.263817i
$566$	−5.26003e6	+	9.29918e6i	−0.690156	+	1.22012i
$567$		0			0
$568$	−175586.	−	6.63122e6i	−0.0228359	−	0.862428i
$569$	578222.	+	333836.i	0.0748710	+	0.0432268i	0.536968	−	0.843603i	$-0.319570\pi$
$569$	578222.	+	333836.i	0.0748710	+	0.0432268i	−0.462097	+	0.886829i	$0.652903\pi$
$570$		0			0
$571$	5.54218e6	−	3.19978e6i	0.711361	−	0.410704i	−0.100204	−	0.994967i	$-0.531949\pi$
$571$	5.54218e6	−	3.19978e6i	0.711361	−	0.410704i	0.811565	+	0.584262i	$0.198616\pi$
$572$	−570992.	+	1.03057e6i	−0.0729693	+	0.131701i
$573$		0			0
$574$	8.81465e6	−	5.19339e6i	1.11667	−	0.657917i
$575$	−1.05424e7			−1.32974
$576$		0			0
$577$	−8.64788e6			−1.08136			−0.540680	−	0.841229i	$-0.681833\pi$
$577$	−8.64788e6			−1.08136			−0.540680	+	0.841229i	$0.681833\pi$
$578$	4.18893e6	−	2.46802e6i	0.521535	−	0.307276i
$579$		0			0
$580$	−6.31032e6	+	1.13894e7i	−0.778899	+	1.40582i
$581$	−4.90560e6	+	2.83225e6i	−0.602908	+	0.348089i
$582$		0			0
$583$	6.69626e6	+	3.86609e6i	0.815945	+	0.471086i
$584$	280952.	+	1.06105e7i	0.0340879	+	1.28737i
$585$		0			0
$586$	−3.10385e6	+	5.48729e6i	−0.373385	+	0.660107i
$587$	−358200.	+	620420.i	−0.0429072	+	0.0743175i	−0.886681	−	0.462381i	$-0.846995\pi$
$587$	−358200.	+	620420.i	−0.0429072	+	0.0743175i	0.843774	+	0.536698i	$0.180329\pi$
$588$		0			0
$589$	2.40429e6	+	4.16436e6i	0.285561	+	0.494606i
$590$	−1.35132e7	+	119246.i	−1.59819	+	0.0141031i
$591$		0			0
$592$	−7.07785e6	−	1.13171e7i	−0.830037	−	1.32718i
$593$		−	6.55369e6i		−	0.765331i	−0.923887	−	0.382665i	$-0.875006\pi$
$593$		−	6.55369e6i		−	0.765331i	0.923887	−	0.382665i	$-0.124994\pi$
$594$		0			0
$595$		−	1.27171e7i		−	1.47264i
$596$	−39637.4	−	2.24572e6i	−0.00457077	−	0.258965i
$597$		0			0
$598$	13124.1	+	1.48726e6i	0.00150078	+	0.170072i
$599$	−1.04139e6	−	1.80373e6i	−0.118589	−	0.205402i	0.800620	−	0.599173i	$-0.204504\pi$
$599$	−1.04139e6	−	1.80373e6i	−0.118589	−	0.205402i	−0.919209	+	0.393771i	$0.871170\pi$
$600$		0			0
$601$	392578.	−	679965.i	0.0443343	−	0.0767893i	−0.843007	−	0.537903i	$-0.819217\pi$
$601$	392578.	−	679965.i	0.0443343	−	0.0767893i	0.887341	+	0.461114i	$0.152550\pi$
$602$	3.39989e6	+	1.92313e6i	0.382361	+	0.216280i
$603$		0			0
$604$	−985480.	+	592398.i	−0.109915	+	0.0660725i
$605$	1.58625e6	+	915822.i	0.176191	+	0.101724i
$606$		0			0
$607$	8.67650e6	−	5.00938e6i	0.955812	−	0.551838i	0.0609306	−	0.998142i	$-0.480593\pi$
$607$	8.67650e6	−	5.00938e6i	0.955812	−	0.551838i	0.894882	+	0.446304i	$0.147260\pi$
$608$	−3.27222e6	+	6.29336e6i	−0.358991	+	0.690437i
$609$		0			0
$610$	5.58096e6	+	9.47247e6i	0.607273	+	1.03072i
$611$	−1.73005e6			−0.187480
$612$		0			0
$613$	−4.81550e6			−0.517595			−0.258797	−	0.965932i	$-0.583326\pi$
$613$	−4.81550e6			−0.517595			−0.258797	+	0.965932i	$0.583326\pi$
$614$	−4.72065e6	−	8.01229e6i	−0.505337	−	0.857700i
$615$		0			0
$616$	4.21421e6	+	6.87245e6i	0.447470	+	0.729726i
$617$	−8.76037e6	+	5.05780e6i	−0.926423	+	0.534871i	−0.885678	−	0.464299i	$-0.846306\pi$
$617$	−8.76037e6	+	5.05780e6i	−0.926423	+	0.534871i	−0.0407445	+	0.999170i	$0.512973\pi$
$618$		0			0
$619$	−1.10769e7	−	6.39527e6i	−1.16196	−	0.670860i	−0.210190	−	0.977661i	$-0.567408\pi$
$619$	−1.10769e7	−	6.39527e6i	−1.16196	−	0.670860i	−0.951774	+	0.306800i	$0.900742\pi$
$620$	5.24757e6	+	8.72957e6i	0.548251	+	0.912040i
$621$		0			0
$622$	3.57695e6	+	2.02328e6i	0.370712	+	0.209691i
$623$	2.35582e6	−	4.08040e6i	0.243177	−	0.421195i
$624$		0			0
$625$	4.33178e6	+	7.50287e6i	0.443575	+	0.768294i
$626$	70128.2	+	7.94709e6i	0.00715248	+	0.810536i
$627$		0			0
$628$	−5.40103e6	+	95329.1i	−0.546484	+	0.00964554i
$629$		−	1.96800e7i		−	1.98334i
$630$		0			0
$631$			1.13313e7i			1.13294i	0.824082	+	0.566471i	$0.191692\pi$
$631$			1.13313e7i			1.13294i	−0.824082	+	0.566471i	$0.808308\pi$
$632$	3.92299e6	−	7.23029e6i	0.390683	−	0.720051i
$633$		0			0
$634$	7.94915e6	−	70146.4i	0.785412	−	0.00693078i
$635$	3.02093e6	+	5.23241e6i	0.297308	+	0.514953i
$636$		0			0
$637$	258060.	−	446974.i	0.0251984	−	0.0436449i
$638$	5.99151e6	−	1.05924e7i	0.582753	−	1.03025i
$639$		0			0
$640$	−6.69479e6	+	1.34507e7i	−0.646081	+	1.29806i
$641$	1.30074e7	+	7.50980e6i	1.25039	+	0.721910i	0.971186	−	0.238323i	$-0.0765976\pi$
$641$	1.30074e7	+	7.50980e6i	1.25039	+	0.721910i	0.279200	+	0.960233i	$0.409931\pi$
$642$		0			0
$643$	2.31540e6	−	1.33680e6i	0.220851	−	0.127508i	−0.385493	−	0.922711i	$-0.625969\pi$
$643$	2.31540e6	−	1.33680e6i	0.220851	−	0.127508i	0.606344	+	0.795202i	$0.292635\pi$
$644$	8.90186e6	+	4.93211e6i	0.845797	+	0.468617i
$645$		0			0
$646$	−9.01038e6	+	5.30870e6i	−0.849497	+	0.500503i
$647$	1.55764e7			1.46288			0.731438	−	0.681908i	$-0.238850\pi$
$647$	1.55764e7			1.46288			0.731438	+	0.681908i	$0.238850\pi$
$648$		0			0
$649$	1.26303e7			1.17707
$650$	−1.44250e6	+	849888.i	−0.133916	+	0.0789003i
$651$		0			0
$652$	−9.11446e6	−	5.04990e6i	−0.839676	−	0.465226i
$653$	−415132.	+	239677.i	−0.0380981	+	0.0219959i	−0.518928	−	0.854818i	$-0.673669\pi$
$653$	−415132.	+	239677.i	−0.0380981	+	0.0219959i	0.480830	+	0.876814i	$0.340335\pi$
$654$		0			0
$655$	−9.40143e6	−	5.42792e6i	−0.856230	−	0.494345i
$656$	−1.57382e7	−	8.36027e6i	−1.42789	−	0.758509i
$657$		0			0
$658$	−5.82818e6	+	1.03036e7i	−0.524769	+	0.927737i
$659$	155358.	−	269087.i	0.0139354	−	0.0241368i	−0.858974	−	0.512020i	$-0.828897\pi$
$659$	155358.	−	269087.i	0.0139354	−	0.0241368i	0.872909	+	0.487883i	$0.162231\pi$
$660$		0			0
$661$	1.04750e7	+	1.81433e7i	0.932505	+	1.61515i	0.779023	+	0.626995i	$0.215715\pi$
$661$	1.04750e7	+	1.81433e7i	0.932505	+	1.61515i	0.153482	+	0.988151i	$0.450951\pi$
$662$	−1.39797e6	+	12336.2i	−0.123980	+	0.00109405i
$663$		0			0
$664$	8.67259e6	+	4.70555e6i	0.763358	+	0.414181i
$665$			1.03146e7i			0.904481i
$666$		0			0
$667$		−	1.53625e7i		−	1.33705i
$668$	6.82853e6	−	120525.i	0.592088	−	0.0104505i
$669$		0			0
$670$	−1628.91	−	184592.i	−0.000140188	−	0.0158864i
$671$	−5.13780e6	−	8.89893e6i	−0.440525	−	0.763012i
$672$		0			0
$673$	6.73764e6	−	1.16699e7i	0.573417	−	0.993187i	−0.422795	−	0.906225i	$-0.638951\pi$
$673$	6.73764e6	−	1.16699e7i	0.573417	−	0.993187i	0.996212	−	0.0869616i	$-0.0277157\pi$
$674$	−1.06256e7	−	6.01028e6i	−0.900953	−	0.509619i
$675$		0			0
$676$	−5.99965e6	−	9.98069e6i	−0.504963	−	0.840028i
$677$	−3.38026e6	−	1.95159e6i	−0.283451	−	0.163650i	0.351534	−	0.936175i	$-0.385660\pi$
$677$	−3.38026e6	−	1.95159e6i	−0.283451	−	0.163650i	−0.634985	+	0.772525i	$0.718994\pi$
$678$		0			0
$679$	−7.52747e6	+	4.34599e6i	−0.626577	+	0.361755i
$680$	−1.88841e7	+	1.15798e7i	−1.56612	+	0.960347i
$681$		0			0
$682$	−4.83235e6	−	8.20187e6i	−0.397830	−	0.675230i
$683$	−1.55558e7			−1.27597			−0.637985	−	0.770048i	$-0.720232\pi$
$683$	−1.55558e7			−1.27597			−0.637985	+	0.770048i	$0.720232\pi$
$684$		0			0
$685$	−1.34038e7			−1.09144
$686$	−6.80814e6	−	1.15554e7i	−0.552355	−	0.937504i
$687$		0			0
$688$	−240109.	−	6.79976e6i	−0.0193391	−	0.547675i
$689$	1.34248e6	−	775080.i	0.107736	−	0.0622011i
$690$		0			0
$691$	9.52435e6	+	5.49889e6i	0.758823	+	0.438107i	0.828873	−	0.559437i	$-0.188983\pi$
$691$	9.52435e6	+	5.49889e6i	0.758823	+	0.438107i	−0.0700501	+	0.997543i	$0.522316\pi$
$692$	872493.	−	524478.i	0.0692622	−	0.0416353i
$693$		0			0
$694$	7.91850e6	+	4.47905e6i	0.624086	+	0.353010i
$695$	4.93114e6	−	8.54099e6i	0.387245	−	0.670728i
$696$		0			0
$697$	−1.31372e7	−	2.27543e7i	−1.02429	−	1.77412i
$698$	23347.6	+	2.64580e6i	0.00181386	+	0.205551i
$699$		0			0
$700$	202169.	+	1.14542e7i	0.0155944	+	0.883527i
$701$			1.51787e7i			1.16665i	0.812239	+	0.583324i	$0.198248\pi$
$701$			1.51787e7i			1.16665i	−0.812239	+	0.583324i	$0.801752\pi$
$702$		0			0
$703$			1.59621e7i			1.21815i
$704$	6.36783e6	−	1.25157e7i	0.484239	−	0.951749i
$705$		0			0
$706$	2.59773e6	−	22923.4i	0.196147	−	0.00173088i
$707$	6.46024e6	+	1.11895e7i	0.486071	+	0.841900i
$708$		0			0
$709$	−6.34771e6	+	1.09946e7i	−0.474244	+	0.821414i	−0.999565	−	0.0294896i	$-0.990612\pi$
$709$	−6.34771e6	+	1.09946e7i	−0.474244	+	0.821414i	0.525321	+	0.850904i	$0.323945\pi$
$710$	−8.27255e6	+	1.46250e7i	−0.615876	+	1.08881i
$711$		0			0
$712$	−8.20427e6	+	217238.i	−0.606513	+	0.0160597i
$713$	−1.04073e7	−	6.00867e6i	−0.766682	−	0.442644i
$714$		0			0
$715$	2.58447e6	−	1.49215e6i	0.189063	−	0.109156i
$716$	7.37269e6	−	1.33068e7i	0.537456	−	0.970043i
$717$		0			0
$718$	−1.07952e7	+	6.36029e6i	−0.781484	+	0.460432i
$719$	−1.30901e7			−0.944324			−0.472162	−	0.881512i	$-0.656526\pi$
$719$	−1.30901e7			−0.944324			−0.472162	+	0.881512i	$0.656526\pi$
$720$		0			0
$721$	6.94705e6			0.497693
$722$	−4.75993e6	+	2.80444e6i	−0.339826	+	0.200218i
$723$		0			0
$724$	72819.5	−	131430.i	0.00516299	−	0.00931857i
$725$	1.49766e7	−	8.64672e6i	1.05820	−	0.610951i
$726$		0			0
$727$	6.63075e6	+	3.82826e6i	0.465293	+	0.268637i	0.714267	−	0.699873i	$-0.246760\pi$
$727$	6.63075e6	+	3.82826e6i	0.465293	+	0.268637i	−0.248974	+	0.968510i	$0.580093\pi$
$728$	1.61564e6	−	42780.1i	0.112984	−	0.00299167i
$729$		0			0
$730$	1.32368e7	−	2.34012e7i	0.919337	−	1.62529i
$731$	5.01578e6	−	8.68758e6i	0.347172	−	0.601319i
$732$		0			0
$733$	9.24808e6	+	1.60181e7i	0.635757	+	1.10116i	0.986354	+	0.164638i	$0.0526455\pi$
$733$	9.24808e6	+	1.60181e7i	0.635757	+	1.10116i	−0.350597	+	0.936527i	$0.614021\pi$
$734$	1.66270e7	−	146723.i	1.13913	−	0.0100521i
$735$		0			0
$736$	−781875.	−	1.77097e7i	−0.0532038	−	1.20508i
$737$			172532.i			0.0117004i
$738$		0			0
$739$		−	3.75594e6i		−	0.252992i	−0.991967	−	0.126496i	$-0.959627\pi$
$739$		−	3.75594e6i		−	0.252992i	0.991967	−	0.126496i	$-0.0403732\pi$
$740$	596666.	+	3.38052e7i	0.0400546	+	2.26936i
$741$		0			0
$742$	−93595.7	−	1.06065e7i	−0.00624088	−	0.707231i
$743$	22492.7	+	38958.6i	0.00149476	+	0.00258899i	0.866772	−	0.498705i	$-0.166191\pi$
$743$	22492.7	+	38958.6i	0.00149476	+	0.00258899i	−0.865277	+	0.501294i	$0.832858\pi$
$744$		0			0
$745$	−2.84462e6	+	4.92702e6i	−0.187773	+	0.325232i
$746$	8.17760e6	+	4.62561e6i	0.537996	+	0.304314i
$747$		0			0
$748$	1.77444e7	−	1.06666e7i	1.15960	−	0.697066i
$749$	−1.29632e7	−	7.48433e6i	−0.844324	−	0.487471i
$750$		0			0
$751$	−2.26479e7	+	1.30757e7i	−1.46530	+	0.845993i	−0.999248	−	0.0387633i	$-0.987658\pi$
$751$	−2.26479e7	+	1.30757e7i	−1.46530	+	0.845993i	−0.466054	+	0.884756i	$0.654325\pi$
$752$	2.06072e7	−	727667.i	1.32884	−	0.0469232i
$753$		0			0
$754$	−1.23848e6	−	2.10204e6i	−0.0793339	−	0.134652i
$755$	2.91248e6			0.185950
$756$		0			0
$757$	−8.60555e6			−0.545807			−0.272903	−	0.962041i	$-0.587984\pi$
$757$	−8.60555e6			−0.545807			−0.272903	+	0.962041i	$0.587984\pi$
$758$	1.34719e7	+	2.28657e7i	0.851640	+	1.44548i
$759$		0			0
$760$	1.53166e7	−	9.39217e6i	0.961894	−	0.589837i
$761$	−2.15910e7	+	1.24656e7i	−1.35148	+	0.780280i	−0.988458	−	0.151498i	$-0.951590\pi$
$761$	−2.15910e7	+	1.24656e7i	−1.35148	+	0.780280i	−0.363027	+	0.931779i	$0.618257\pi$
$762$		0			0
$763$	1.24067e7	+	7.16302e6i	0.771516	+	0.445435i
$764$	−9.98326e6	−	1.66076e7i	−0.618784	−	1.02937i
$765$		0			0
$766$	2.60782e7	+	1.47510e7i	1.60585	+	0.908341i
$767$	1.26608e6	−	2.19291e6i	0.0777090	−	0.134596i
$768$		0			0
$769$	−1.62777e7	−	2.81939e7i	−0.992610	−	1.71925i	−0.601398	−	0.798950i	$-0.705389\pi$
$769$	−1.62777e7	−	2.81939e7i	−0.992610	−	1.71925i	−0.391212	−	0.920300i	$-0.627944\pi$
$770$	−180186.	−	2.04191e7i	−0.0109520	−	1.24111i
$771$		0			0
$772$	2.98799e6	−	52738.5i	0.180441	−	0.00318482i
$773$		−	1.64551e6i		−	0.0990493i	−0.998773	−	0.0495246i	$-0.984229\pi$
$773$		−	1.64551e6i		−	0.0990493i	0.998773	−	0.0495246i	$-0.0157706\pi$
$774$		0			0
$775$		−	1.35278e7i		−	0.809044i
$776$	1.33078e7	+	7.22050e6i	0.793326	+	0.430441i
$777$		0			0
$778$	−1.04205e7	+	91954.7i	−0.617220	+	0.00544659i
$779$	1.06554e7	+	1.84557e7i	0.629108	+	1.08965i
$780$		0			0
$781$	7.85208e6	−	1.36002e7i	0.460635	−	0.797843i
$782$	1.28677e7	−	2.27488e7i	0.752464	−	1.33028i
$783$		0			0
$784$	−2.88585e6	+	5.43260e6i	−0.167681	+	0.315659i
$785$	1.18496e7	+	6.84139e6i	0.686326	+	0.396251i
$786$		0			0
$787$	−1.68858e7	+	9.74900e6i	−0.971816	+	0.561078i	−0.899789	−	0.436325i	$-0.856280\pi$
$787$	−1.68858e7	+	9.74900e6i	−0.971816	+	0.561078i	−0.0720264	+	0.997403i	$0.522947\pi$
$788$	−1.30555e7	−	7.23343e6i	−0.748991	−	0.414982i
$789$		0			0
$790$	−1.79520e7	+	1.05769e7i	−1.02340	+	0.602964i
$791$	−2.96359e6			−0.168414
$792$		0			0
$793$	−2.06007e6			−0.116332
$794$	−369005.	+	217409.i	−0.0207721	+	0.0122385i
$795$		0			0
$796$	1.75190e7	+	9.70650e6i	0.980004	+	0.542975i
$797$	318483.	−	183876.i	0.0177599	−	0.0102537i	−0.491094	−	0.871107i	$-0.663403\pi$
$797$	318483.	−	183876.i	0.0177599	−	0.0102537i	0.508854	+	0.860853i	$0.330069\pi$
$798$		0			0
$799$	2.63283e7	+	1.52007e7i	1.45900	+	0.842356i
$800$	1.68247e7	−	1.07300e7i	0.929441	−	0.592757i
$801$		0			0
$802$	9.40521e6	−	1.66274e7i	0.516336	−	0.912829i
$803$	−1.25640e7	+	2.17614e7i	−0.687604	+	1.19096i
$804$		0			0
$805$	−1.28889e7	−	2.23242e7i	−0.701011	−	1.21419i
$806$	−1.90842e6	+	16840.7i	−0.103475	+	0.000913108i
$807$		0			0
$808$	1.07332e7	−	1.97818e7i	0.578361	−	1.06595i
$809$		−	5.76347e6i		−	0.309609i	−0.987945	−	0.154804i	$-0.950525\pi$
$809$		−	5.76347e6i		−	0.309609i	0.987945	−	0.154804i	$-0.0494747\pi$
$810$		0			0
$811$			819789.i			0.0437673i	0.999761	+	0.0218837i	$0.00696634\pi$
$811$			819789.i			0.0437673i	−0.999761	+	0.0218837i	$0.993034\pi$
$812$	−1.66913e7	+	294604.i	−0.888383	+	0.0156801i
$813$		0			0
$814$	−278842.	−	3.15990e7i	−0.0147502	−	1.67152i
$815$	1.31967e7	+	2.28573e7i	0.695938	+	1.20540i
$816$		0			0
$817$	−4.06821e6	+	7.04635e6i	−0.213230	+	0.369325i
$818$	1.72339e7	+	9.74827e6i	0.900536	+	0.509383i
$819$		0			0
$820$	2.32563e7	+	3.86878e7i	1.20783	+	2.00928i
$821$	631565.	+	364634.i	0.0327009	+	0.0188799i	0.516261	−	0.856431i	$-0.327323\pi$
$821$	631565.	+	364634.i	0.0327009	+	0.0188799i	−0.483560	+	0.875311i	$0.660657\pi$
$822$		0			0
$823$	1.52844e7	−	8.82447e6i	0.786592	−	0.454139i	−0.0521692	−	0.998638i	$-0.516614\pi$
$823$	1.52844e7	−	8.82447e6i	0.786592	−	0.454139i	0.838762	+	0.544499i	$0.183280\pi$
$824$	−6.32576e6	−	1.03159e7i	−0.324560	−	0.529286i
$825$		0			0
$826$	−8.79513e6	−	1.49278e7i	−0.448531	−	0.761284i
$827$	2.90788e7			1.47847			0.739236	−	0.673447i	$-0.235187\pi$
$827$	2.90788e7			1.47847			0.739236	+	0.673447i	$0.235187\pi$
$828$		0			0
$829$	−1.37334e7			−0.694051			−0.347026	−	0.937856i	$-0.612808\pi$
$829$	−1.37334e7			−0.694051			−0.347026	+	0.937856i	$0.612808\pi$
$830$	−1.26868e7	−	2.15331e7i	−0.639229	−	1.08495i
$831$		0			0
$832$	−1.53468e6	−	2.36018e6i	−0.0768616	−	0.118205i
$833$	−7.85448e6	+	4.53478e6i	−0.392197	+	0.226435i
$834$		0			0
$835$	−1.49815e7	−	8.64958e6i	−0.743600	−	0.429318i
$836$	−1.43922e7	+	8.65153e6i	−0.712216	+	0.428131i
$837$		0			0
$838$	−2.61775e7	−	1.48072e7i	−1.28771	−	0.728387i
$839$	−5.44148e6	+	9.42491e6i	−0.266877	+	0.462245i	−0.968054	−	0.250743i	$-0.919325\pi$
$839$	−5.44148e6	+	9.42491e6i	−0.266877	+	0.462245i	0.701176	+	0.712988i	$0.252659\pi$
$840$		0			0
$841$	2.34460e6	+	4.06097e6i	0.114309	+	0.197989i
$842$	−258589.	−	2.93039e7i	−0.0125699	−	1.42444i
$843$		0			0
$844$	493102.	+	2.79376e7i	0.0238276	+	1.35000i
$845$			2.94969e7i			1.42113i
$846$		0			0
$847$			2.34837e6i			0.112475i
$848$	−1.56647e7	+	9.79690e6i	−0.748054	+	0.467842i
$849$		0			0
$850$	2.94198e7	−	259612.i	1.39667	−	0.0123247i
$851$	−1.99458e7	−	3.45471e7i	−0.944119	−	1.63526i
$852$		0			0
$853$	1.39626e6	−	2.41839e6i	0.0657043	−	0.113803i	−0.831302	−	0.555821i	$-0.812404\pi$
$853$	1.39626e6	−	2.41839e6i	0.0657043	−	0.113803i	0.897006	+	0.442018i	$0.145737\pi$
$854$	−6.93996e6	+	1.22691e7i	−0.325621	+	0.575664i
$855$		0			0
$856$	690156.	+	2.60646e7i	0.0321931	+	1.21581i
$857$	2.22286e7	+	1.28337e7i	1.03386	+	0.596898i	0.918087	−	0.396378i	$-0.129733\pi$
$857$	2.22286e7	+	1.28337e7i	1.03386	+	0.596898i	0.115770	+	0.993276i	$0.463066\pi$
$858$		0			0
$859$	4.15701e6	−	2.40005e6i	0.192220	−	0.110978i	−0.400802	−	0.916165i	$-0.631268\pi$
$859$	4.15701e6	−	2.40005e6i	0.192220	−	0.110978i	0.593021	+	0.805187i	$0.297935\pi$
$860$	−8.35242e6	+	1.50751e7i	−0.385094	+	0.695047i
$861$		0			0
$862$	2.78902e7	−	1.64323e7i	1.27845	−	0.753233i
$863$	2.59610e7			1.18658			0.593288	−	0.804991i	$-0.297830\pi$
$863$	2.59610e7			1.18658			0.593288	+	0.804991i	$0.297830\pi$
$864$		0			0
$865$	−2.57856e6			−0.117175
$866$	3.00913e7	−	1.77291e7i	1.36347	−	0.803324i
$867$		0			0
$868$	−6.32880e6	+	1.14227e7i	−0.285117	+	0.514600i
$869$	1.68651e7	−	9.73705e6i	0.757597	−	0.437399i
$870$		0			0
$871$	29955.3	+	17294.7i	0.00133792	+	0.000772446i
$872$	−660526.	−	2.49456e7i	−0.0294170	−	1.11097i
$873$		0			0
$874$	−1.04368e7	+	1.84512e7i	−0.462157	+	0.817045i
$875$	1.34735e6	−	2.33369e6i	0.0594924	−	0.103044i
$876$		0			0
$877$	1.75890e7	+	3.04651e7i	0.772222	+	1.33753i	0.936343	+	0.351088i	$0.114188\pi$
$877$	1.75890e7	+	3.04651e7i	0.772222	+	1.33753i	−0.164120	+	0.986440i	$0.552478\pi$
$878$	3.28114e7	−	289541.i	1.43645	−	0.0126758i
$879$		0			0
$880$	−3.01570e7	+	1.88605e7i	−1.31275	+	0.821008i
$881$			1.34812e7i			0.585177i	0.956238	+	0.292588i	$0.0945166\pi$
$881$			1.34812e7i			0.585177i	−0.956238	+	0.292588i	$0.905483\pi$
$882$		0			0
$883$		−	1.27557e7i		−	0.550557i	−0.961364	−	0.275279i	$-0.911230\pi$
$883$		−	1.27557e7i		−	0.550557i	0.961364	−	0.275279i	$-0.0887701\pi$
$884$	−73249.2	−	4.15006e6i	−0.00315262	−	0.178617i
$885$		0			0
$886$	208632.	+	2.36426e7i	0.00892886	+	1.01184i
$887$	−9.47111e6	−	1.64044e7i	−0.404196	−	0.700088i	0.590032	−	0.807380i	$-0.299115\pi$
$887$	−9.47111e6	−	1.64044e7i	−0.404196	−	0.700088i	−0.994228	+	0.107292i	$0.965782\pi$
$888$		0			0
$889$	−3.87317e6	+	6.70852e6i	−0.164366	+	0.284690i
$890$	1.80943e7	+	1.02350e7i	0.765716	+	0.433123i
$891$		0			0
$892$	1.32746e7	−	7.97973e6i	0.558613	−	0.335797i
$893$	−2.13545e7	−	1.23290e7i	−0.896107	−	0.517368i
$894$		0			0
$895$	−3.33709e7	+	1.92667e7i	−1.39255	+	0.803988i
$896$	−1.92265e7	+	1.18912e6i	−0.800075	+	0.0494829i
$897$		0			0
$898$	−2.78809e6	−	4.73218e6i	−0.115376	−	0.195826i
$899$	1.97130e7			0.813491
$900$		0			0
$901$	−2.72403e7			−1.11789
$902$	−2.14161e7	−	3.63491e7i	−0.876442	−	1.48757i
$903$		0			0
$904$	2.69855e6	+	4.40075e6i	0.109827	+	0.179104i
$905$	−329602.	+	190296.i	−0.0133773	+	0.00772339i
$906$		0			0
$907$	3.65444e7	+	2.10989e7i	1.47504	+	0.851613i	0.999604	−	0.0281382i	$-0.00895786\pi$
$907$	3.65444e7	+	2.10989e7i	1.47504	+	0.851613i	0.475434	+	0.879752i	$0.342291\pi$
$908$	−3.88785e6	−	6.46761e6i	−0.156493	−	0.260333i
$909$		0			0
$910$	−3.56327e6	−	2.01554e6i	−0.142641	−	0.0806841i
$911$	−1.29463e7	+	2.24236e7i	−0.516831	+	0.895177i	0.482978	+	0.875632i	$0.339555\pi$
$911$	−1.29463e7	+	2.24236e7i	−0.516831	+	0.895177i	−0.999809	+	0.0195449i	$0.993778\pi$
$912$		0			0
$913$	1.16794e7	+	2.02293e7i	0.463706	+	0.803163i
$914$	−103636.	−	1.17443e7i	−0.00410341	−	0.465008i
$915$		0			0
$916$	7.94059e6	−	140153.i	0.312690	−	0.00551903i
$917$		−	1.39184e7i		−	0.546594i
$918$		0			0
$919$		−	3.59722e7i		−	1.40501i	−0.711681	−	0.702503i	$-0.752066\pi$
$919$		−	3.59722e7i		−	1.40501i	0.711681	−	0.702503i	$-0.247934\pi$
$920$	−2.14138e7	+	3.94668e7i	−0.834111	+	1.53731i
$921$		0			0
$922$	1.65100e7	−	145691.i	0.639618	−	0.00564424i
$923$	−1.57420e6	−	2.72659e6i	−0.0608212	−	0.105345i
$924$		0			0
$925$	2.24527e7	−	3.88892e7i	0.862809	−	1.49443i
$926$	−1.61758e7	+	2.85971e7i	−0.619923	+	1.09596i
$927$		0			0
$928$	1.56360e7	+	2.45173e7i	0.596015	+	0.934550i
$929$	−3.28939e7	−	1.89913e7i	−1.25048	−	0.721964i	−0.279273	−	0.960212i	$-0.590094\pi$
$929$	−3.28939e7	−	1.89913e7i	−1.25048	−	0.721964i	−0.971204	+	0.238248i	$0.923427\pi$
$930$		0			0
$931$	6.37063e6	−	3.67809e6i	0.240884	−	0.139075i
$932$	9.52458e6	+	5.27713e6i	0.359175	+	0.199002i
$933$		0			0
$934$	−4.05484e7	+	2.38902e7i	−1.52092	+	0.896091i
$935$	−5.24417e7			−1.96177
$936$		0			0
$937$	−1.87349e7			−0.697111			−0.348555	−	0.937288i	$-0.613328\pi$
$937$	−1.87349e7			−0.697111			−0.348555	+	0.937288i	$0.613328\pi$
$938$	203916.	−	120142.i	0.00756735	−	0.00445850i
$939$		0			0
$940$	−4.56862e7	−	2.53126e7i	−1.68642	−	0.934367i
$941$	−1.73547e7	+	1.00197e7i	−0.638915	+	0.368878i	−0.784196	−	0.620513i	$-0.786925\pi$
$941$	−1.73547e7	+	1.00197e7i	−0.638915	+	0.368878i	0.145281	+	0.989390i	$0.453591\pi$
$942$		0			0
$943$	−4.61233e7	−	2.66293e7i	−1.68905	−	0.975171i
$944$	−1.41583e7	+	2.66530e7i	−0.517109	+	0.973456i
$945$		0			0
$946$	7.93044e6	−	1.40202e7i	0.288117	−	0.509361i
$947$	1.05215e7	−	1.82237e7i	0.381243	−	0.660332i	−0.609997	−	0.792404i	$-0.708829\pi$
$947$	1.05215e7	−	1.82237e7i	0.381243	−	0.660332i	0.991240	+	0.132071i	$0.0421628\pi$
$948$		0			0
$949$	2.51885e6	+	4.36277e6i	0.0907896	+	0.157252i
$950$	−2.38619e7	+	210567.i	−0.857819	+	0.00756973i
$951$		0			0
$952$	−2.49632e7	−	1.35445e7i	−0.892706	−	0.484362i
$953$			3.31281e6i			0.118158i	0.998253	+	0.0590792i	$0.0188164\pi$
$953$			3.31281e6i			0.118158i	−0.998253	+	0.0590792i	$0.981184\pi$
$954$		0			0
$955$			4.90820e7i			1.74146i
$956$	1.94471e7	−	343244.i	0.688192	−	0.0121467i
$957$		0			0
$958$	−5720.87	−	648302.i	−0.000201395	−	0.0228225i
$959$	−8.59256e6	−	1.48828e7i	−0.301701	−	0.522561i
$960$		0			0
$961$	−6.60435e6	+	1.14391e7i	−0.230686	+	0.399560i
$962$	−5.51423e6	−	3.11909e6i	−0.192109	−	0.108665i
$963$		0			0
$964$	−2.49492e7	−	4.15042e7i	−0.864698	−	1.43846i
$965$	−6.55552e6	−	3.78483e6i	−0.226615	−	0.130836i
$966$		0			0
$967$	1.14131e7	−	6.58936e6i	0.392498	−	0.226609i	−0.290744	−	0.956801i	$-0.593903\pi$
$967$	1.14131e7	−	6.58936e6i	0.392498	−	0.226609i	0.683242	+	0.730192i	$0.260569\pi$
$968$	3.48718e6	−	2.13835e6i	0.119615	−	0.0733483i
$969$		0			0
$970$	−1.94675e7	−	3.30418e7i	−0.664324	−	1.12755i
$971$	5.16587e6			0.175831			0.0879155	−	0.996128i	$-0.471979\pi$
$971$	5.16587e6			0.175831			0.0879155	+	0.996128i	$0.471979\pi$
$972$		0			0
$973$	1.26445e7			0.428174
$974$	−7.82545e6	−	1.32820e7i	−0.264309	−	0.448608i
$975$		0			0
$976$	2.45382e7	−	866476.i	0.824552	−	0.0291160i
$977$	−1.37911e6	+	796228.i	−0.0462234	+	0.0266871i	−0.522934	−	0.852373i	$-0.675162\pi$
$977$	−1.37911e6	+	796228.i	−0.0462234	+	0.0266871i	0.476710	+	0.879060i	$0.341829\pi$
$978$		0			0
$979$	−1.68264e7	−	9.71474e6i	−0.561093	−	0.323947i
$980$	1.33545e7	−	8.02773e6i	0.444183	−	0.267010i
$981$		0			0
$982$	−2.90354e7	−	1.64237e7i	−0.960836	−	0.543491i
$983$	−7.65007e6	+	1.32503e7i	−0.252512	+	0.437363i	−0.964217	−	0.265115i	$-0.914590\pi$
$983$	−7.65007e6	+	1.32503e7i	−0.252512	+	0.437363i	0.711705	+	0.702478i	$0.247923\pi$
$984$		0			0
$985$	1.89028e7	+	3.27406e7i	0.620776	+	1.07522i
$986$	378312.	+	4.28711e7i	0.0123925	+	1.40434i
$987$		0			0
$988$	59411.2	+	3.36604e6i	0.00193631	+	0.109705i
$989$		−	2.03341e7i		−	0.661049i
$990$		0			0
$991$		−	4.54893e7i		−	1.47138i	−0.677317	−	0.735691i	$-0.736858\pi$
$991$		−	4.54893e7i		−	1.47138i	0.677317	−	0.735691i	$-0.263142\pi$
$992$	2.27248e7	−	1.00329e6i	0.733198	−	0.0323703i
$993$		0			0
$994$	−2.15419e7	+	190094.i	−0.691541	+	0.00610243i
$995$	−2.53655e7	−	4.39344e7i	−0.812244	−	1.40685i
$996$		0			0
$997$	−1.16700e7	+	2.02131e7i	−0.371821	+	0.644013i	−0.989846	−	0.142146i	$-0.954600\pi$
$997$	−1.16700e7	+	2.02131e7i	−0.371821	+	0.644013i	0.618025	+	0.786159i	$0.287933\pi$
$998$	−2.03991e7	+	3.60635e7i	−0.648314	+	1.14615i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.5		56
3.2	odd	2		36.6.h.a.11.24	yes	56
4.3	odd	2	inner	108.6.h.a.35.15		56
9.4	even	3		36.6.h.a.23.14	yes	56
9.5	odd	6	inner	108.6.h.a.71.15		56
12.11	even	2		36.6.h.a.11.14	✓	56
36.23	even	6	inner	108.6.h.a.71.5		56
36.31	odd	6		36.6.h.a.23.24	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.14	✓	56	12.11	even	2
36.6.h.a.11.24	yes	56	3.2	odd	2
36.6.h.a.23.14	yes	56	9.4	even	3
36.6.h.a.23.24	yes	56	36.31	odd	6
108.6.h.a.35.5		56	1.1	even	1	trivial
108.6.h.a.35.15		56	4.3	odd	2	inner
108.6.h.a.71.5		56	36.23	even	6	inner
108.6.h.a.71.15		56	9.5	odd	6	inner

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.87383 + 2.87155i) q^{2} +(15.5084 - 27.9909i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(-89.9985 - 51.9607i) q^{7} +(4.79147 + 180.956i) q^{8} +O(q^{10})\)	\(q+(-4.87383 + 2.87155i) q^{2} +(15.5084 - 27.9909i) q^{4} +(-70.1957 + 40.5275i) q^{5} +(-89.9985 - 51.9607i) q^{7} +(4.79147 + 180.956i) q^{8} +(225.745 - 399.094i) q^{10} +(-214.271 + 371.129i) q^{11} +(42.9574 + 74.4044i) q^{13} +(587.845 - 5.18738i) q^{14} +(-542.976 - 868.190i) q^{16} -1509.75i q^{17} +1224.53i q^{19} +(45.7731 + 2593.36i) q^{20} +(-21.3913 - 2424.11i) q^{22} +(-1530.14 - 2650.27i) q^{23} +(1722.45 - 2983.38i) q^{25} +(-423.023 - 239.280i) q^{26} +(-2850.16 + 1713.31i) q^{28} +(4347.44 + 2510.00i) q^{29} +(3400.78 - 1963.44i) q^{31} +(5139.42 + 2672.23i) q^{32} +(4335.30 + 7358.24i) q^{34} +8423.34 q^{35} +13035.3 q^{37} +(-3516.29 - 5968.14i) q^{38} +(-7670.03 - 12508.1i) q^{40} +(15071.6 - 8701.62i) q^{41} +(5754.33 + 3322.27i) q^{43} +(7065.19 + 11753.3i) q^{44} +(15068.0 + 8523.13i) q^{46} +(-10068.4 + 17438.9i) q^{47} +(-3003.68 - 5202.52i) q^{49} +(171.957 + 19486.6i) q^{50} +(2748.85 - 48.5176i) q^{52} -18043.0i q^{53} -34735.5i q^{55} +(8971.37 - 16534.7i) q^{56} +(-28396.3 + 250.580i) q^{58} +(-14736.4 - 25524.2i) q^{59} +(-11989.0 + 20765.6i) q^{61} +(-10936.7 + 19335.0i) q^{62} +(-32722.1 + 1734.09i) q^{64} +(-6030.85 - 3481.91i) q^{65} +(348.663 - 201.301i) q^{67} +(-42259.1 - 23413.8i) q^{68} +(-41054.0 + 24188.0i) q^{70} -36645.5 q^{71} +58635.9 q^{73} +(-63531.8 + 37431.5i) q^{74} +(34275.6 + 18990.5i) q^{76} +(38568.2 - 22267.4i) q^{77} +(-39354.5 - 22721.3i) q^{79} +(73300.1 + 38937.7i) q^{80} +(-48469.5 + 85689.1i) q^{82} +(27253.7 - 47204.9i) q^{83} +(61186.2 + 105978. i) q^{85} +(-37585.7 + 331.671i) q^{86} +(-68184.6 - 36995.4i) q^{88} +45338.5i q^{89} -8928.39i q^{91} +(-97913.4 + 1728.19i) q^{92} +(-1005.15 - 113906. i) q^{94} +(-49627.1 - 85956.6i) q^{95} +(41820.0 - 72434.3i) q^{97} +(29578.7 + 16731.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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