LMFDB - Embedded newform 198.6.f.g.163.3

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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32717 x^{18} - 175765 x^{17} + 429989344 x^{16} + 5846276963 x^{15} + \cdots + 29\!\cdots\!01 $ x^20 - 3x^19 - 32717x^18 - 175765x^17 + 429989344x^16 + 5846276963x^15 - 2895568160445x^14 - 61486624057387x^13 + 10571261221333419x^12 + 294539949044070726x^11 - 20572959391661926036x^10 - 692661753702996624264x^9 + 20344799403272690812036x^8 + 835601227125892021783426x^7 - 8238304884590821296664394x^6 - 499725651021814750309330328x^5 - 404520969181668980873288047x^4 + 120964284575575042907998183609x^3 + 816183701186375238030969243281x^2 - 2633638927157539958891566472415*x + 2936565356795086268881959852401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.3
Root			$-24.7410 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	198.163
Dual form			198.6.f.g.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 - 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-7.80522 - 24.0220i) q^{5} +(84.3699 + 61.2983i) q^{7} +(-51.7771 + 37.6183i) q^{8} +O(q^{10})$	\(q+(1.23607 - 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-7.80522 - 24.0220i) q^{5} +(84.3699 + 61.2983i) q^{7} +(-51.7771 + 37.6183i) q^{8} -101.033 q^{10} +(-301.085 + 265.328i) q^{11} +(144.607 - 445.053i) q^{13} +(337.480 - 245.193i) q^{14} +(79.1084 + 243.470i) q^{16} +(524.197 + 1613.31i) q^{17} +(-1738.26 + 1262.92i) q^{19} +(-124.884 + 384.352i) q^{20} +(637.205 + 1473.36i) q^{22} -2081.60 q^{23} +(2012.04 - 1461.83i) q^{25} +(-1514.34 - 1100.23i) q^{26} +(-515.623 - 1586.92i) q^{28} +(4306.01 + 3128.50i) q^{29} +(193.781 - 596.396i) q^{31} +1024.00 q^{32} +6785.35 q^{34} +(813.983 - 2505.18i) q^{35} +(13226.2 + 9609.43i) q^{37} +(2655.82 + 8173.78i) q^{38} +(1307.80 + 950.170i) q^{40} +(-15642.2 + 11364.7i) q^{41} +17161.7 q^{43} +(6392.62 - 602.899i) q^{44} +(-2573.00 + 7918.89i) q^{46} +(2406.06 - 1748.10i) q^{47} +(-1832.85 - 5640.94i) q^{49} +(-3074.13 - 9461.19i) q^{50} +(-6057.36 + 4400.93i) q^{52} +(2697.68 - 8302.59i) q^{53} +(8723.74 + 5161.73i) q^{55} -6674.36 q^{56} +(17224.1 - 12514.0i) q^{58} +(6645.71 + 4828.39i) q^{59} +(15891.2 + 48908.2i) q^{61} +(-2029.30 - 1474.37i) q^{62} +(1265.73 - 3895.53i) q^{64} -11819.8 q^{65} +6447.54 q^{67} +(8387.15 - 25813.0i) q^{68} +(-8524.14 - 6193.15i) q^{70} +(7859.33 + 24188.5i) q^{71} +(40450.5 + 29389.0i) q^{73} +(52905.0 - 38437.7i) q^{74} +34377.7 q^{76} +(-41666.7 + 3929.65i) q^{77} +(4821.55 - 14839.2i) q^{79} +(5231.19 - 3800.68i) q^{80} +(23899.2 + 73554.2i) q^{82} +(-27816.4 - 85610.0i) q^{83} +(34663.5 - 25184.5i) q^{85} +(21213.1 - 65287.1i) q^{86} +(5608.15 - 25064.2i) q^{88} +523.362 q^{89} +(39481.5 - 28685.0i) q^{91} +(26944.9 + 19576.6i) q^{92} +(-3676.13 - 11314.0i) q^{94} +(43905.3 + 31899.1i) q^{95} +(-4439.21 + 13662.5i) q^{97} -23724.9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8	$ 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8} + 552 q^{10} + 60 q^{11} - 420 q^{13} - 1568 q^{14} - 1280 q^{16} + 712 q^{17} - 898 q^{19} - 1792 q^{20} + 2020 q^{22} + 1180 q^{23} - 1079 q^{25} - 2880 q^{26} + 4688 q^{28} + 517 q^{29} - 5551 q^{31} + 20480 q^{32} - 6992 q^{34} + 14325 q^{35} - 7584 q^{37} - 1832 q^{38} + 2752 q^{40} - 16868 q^{41} - 704 q^{43} + 8080 q^{44} - 11400 q^{46} - 38866 q^{47} - 22573 q^{49} - 5416 q^{50} - 11520 q^{52} - 97517 q^{53} + 14404 q^{55} + 12672 q^{56} + 2068 q^{58} - 52682 q^{59} + 73874 q^{61} + 21136 q^{62} - 20480 q^{64} + 236352 q^{65} - 267432 q^{67} + 11392 q^{68} - 67660 q^{70} + 20588 q^{71} + 97257 q^{73} - 30336 q^{74} + 43392 q^{76} + 100582 q^{77} + 37498 q^{79} + 11008 q^{80} - 3672 q^{82} - 140952 q^{83} - 158376 q^{85} - 75136 q^{86} - 63040 q^{88} + 168796 q^{89} + 173196 q^{91} + 36160 q^{92} + 45376 q^{94} - 518002 q^{95} - 225802 q^{97} + 396808 q^{98}+O(q^{100}) $ 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8 + 552 * q^10 + 60 * q^11 - 420 * q^13 - 1568 * q^14 - 1280 * q^16 + 712 * q^17 - 898 * q^19 - 1792 * q^20 + 2020 * q^22 + 1180 * q^23 - 1079 * q^25 - 2880 * q^26 + 4688 * q^28 + 517 * q^29 - 5551 * q^31 + 20480 * q^32 - 6992 * q^34 + 14325 * q^35 - 7584 * q^37 - 1832 * q^38 + 2752 * q^40 - 16868 * q^41 - 704 * q^43 + 8080 * q^44 - 11400 * q^46 - 38866 * q^47 - 22573 * q^49 - 5416 * q^50 - 11520 * q^52 - 97517 * q^53 + 14404 * q^55 + 12672 * q^56 + 2068 * q^58 - 52682 * q^59 + 73874 * q^61 + 21136 * q^62 - 20480 * q^64 + 236352 * q^65 - 267432 * q^67 + 11392 * q^68 - 67660 * q^70 + 20588 * q^71 + 97257 * q^73 - 30336 * q^74 + 43392 * q^76 + 100582 * q^77 + 37498 * q^79 + 11008 * q^80 - 3672 * q^82 - 140952 * q^83 - 158376 * q^85 - 75136 * q^86 - 63040 * q^88 + 168796 * q^89 + 173196 * q^91 + 36160 * q^92 + 45376 * q^94 - 518002 * q^95 - 225802 * q^97 + 396808 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−7.80522	−	24.0220i	−0.139624	−	0.429719i	0.856657	−	0.515887i	$-0.172538\pi$
$5$	−7.80522	−	24.0220i	−0.139624	−	0.429719i	−0.996281	+	0.0861686i	$0.972538\pi$
$6$		0			0
$7$	84.3699	+	61.2983i	0.650792	+	0.472828i	0.863541	−	0.504279i	$-0.168242\pi$
$7$	84.3699	+	61.2983i	0.650792	+	0.472828i	−0.212749	+	0.977107i	$0.568242\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$		0			0
$10$	−101.033			−0.319494
$11$	−301.085	+	265.328i	−0.750253	+	0.661151i
$11$	−301.085	+	265.328i	−0.750253	+	0.661151i
$12$		0			0
$13$	144.607	−	445.053i	0.237318	−	0.730388i	−0.759488	−	0.650521i	$-0.774550\pi$
$13$	144.607	−	445.053i	0.237318	−	0.730388i	0.996806	−	0.0798669i	$-0.0254495\pi$
$14$	337.480	−	245.193i	0.460180	−	0.334340i
$15$		0			0
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	524.197	+	1613.31i	0.439918	+	1.35393i	0.887962	+	0.459918i	$0.152121\pi$
$17$	524.197	+	1613.31i	0.439918	+	1.35393i	−0.448043	+	0.894012i	$0.647879\pi$
$18$		0			0
$19$	−1738.26	+	1262.92i	−1.10466	+	0.802585i	−0.981815	−	0.189840i	$-0.939203\pi$
$19$	−1738.26	+	1262.92i	−1.10466	+	0.802585i	−0.122849	+	0.992425i	$0.539203\pi$
$20$	−124.884	+	384.352i	−0.0698120	+	0.214859i
$21$		0			0
$22$	637.205	+	1473.36i	0.280687	+	0.649011i
$23$	−2081.60			−0.820500			−0.410250	−	0.911973i	$-0.634559\pi$
$23$	−2081.60			−0.820500			−0.410250	+	0.911973i	$0.634559\pi$
$24$		0			0
$25$	2012.04	−	1461.83i	0.643854	−	0.467787i
$26$	−1514.34	−	1100.23i	−0.439329	−	0.319191i
$27$		0			0
$28$	−515.623	−	1586.92i	−0.124290	−	0.382526i
$29$	4306.01	+	3128.50i	0.950781	+	0.690783i	0.950991	−	0.309217i	$-0.100067\pi$
$29$	4306.01	+	3128.50i	0.950781	+	0.690783i	−0.000210423		1.00000i	$0.500067\pi$
$30$		0			0
$31$	193.781	−	596.396i	0.0362165	−	0.111463i	−0.931314	−	0.364217i	$-0.881337\pi$
$31$	193.781	−	596.396i	0.0362165	−	0.111463i	0.967530	+	0.252755i	$0.0813365\pi$
$32$	1024.00			0.176777
$33$		0			0
$34$	6785.35			1.00664
$35$	813.983	−	2505.18i	0.112317	−	0.345676i
$36$		0			0
$37$	13226.2	+	9609.43i	1.58830	+	1.15397i	0.906317	+	0.422598i	$0.138882\pi$
$37$	13226.2	+	9609.43i	1.58830	+	1.15397i	0.681982	+	0.731369i	$0.261118\pi$
$38$	2655.82	+	8173.78i	0.298359	+	0.918256i
$39$		0			0
$40$	1307.80	+	950.170i	0.129238	+	0.0938969i
$41$	−15642.2	+	11364.7i	−1.45325	+	1.05585i	−0.468187	+	0.883630i	$0.655093\pi$
$41$	−15642.2	+	11364.7i	−1.45325	+	1.05585i	−0.985059	+	0.172216i	$0.944907\pi$
$42$		0			0
$43$	17161.7			1.41543			0.707717	−	0.706496i	$-0.249725\pi$
$43$	17161.7			1.41543			0.707717	+	0.706496i	$0.249725\pi$
$44$	6392.62	−	602.899i	0.497791	−	0.0469475i
$45$		0			0
$46$	−2573.00	+	7918.89i	−0.179286	+	0.551785i
$47$	2406.06	−	1748.10i	0.158877	−	0.115431i	−0.505506	−	0.862823i	$-0.668694\pi$
$47$	2406.06	−	1748.10i	0.158877	−	0.115431i	0.664383	+	0.747392i	$0.268694\pi$
$48$		0			0
$49$	−1832.85	−	5640.94i	−0.109053	−	0.335630i
$50$	−3074.13	−	9461.19i	−0.173899	−	0.535206i
$51$		0			0
$52$	−6057.36	+	4400.93i	−0.310653	+	0.225702i
$53$	2697.68	−	8302.59i	0.131917	−	0.405998i	−0.863181	−	0.504895i	$-0.831531\pi$
$53$	2697.68	−	8302.59i	0.131917	−	0.405998i	0.995098	+	0.0988966i	$0.0315313\pi$
$54$		0			0
$55$	8723.74	+	5161.73i	0.388862	+	0.230085i
$56$	−6674.36			−0.284407
$57$		0			0
$58$	17224.1	−	12514.0i	0.672304	−	0.488457i
$59$	6645.71	+	4828.39i	0.248549	+	0.180581i	0.705083	−	0.709124i	$-0.250910\pi$
$59$	6645.71	+	4828.39i	0.248549	+	0.180581i	−0.456535	+	0.889706i	$0.650910\pi$
$60$		0			0
$61$	15891.2	+	48908.2i	0.546806	+	1.68289i	0.716658	+	0.697425i	$0.245671\pi$
$61$	15891.2	+	48908.2i	0.546806	+	1.68289i	−0.169852	+	0.985470i	$0.554329\pi$
$62$	−2029.30	−	1474.37i	−0.0670450	−	0.0487111i
$63$		0			0
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−11819.8			−0.346997
$66$		0			0
$67$	6447.54			0.175472			0.0877358	−	0.996144i	$-0.472037\pi$
$67$	6447.54			0.175472			0.0877358	+	0.996144i	$0.472037\pi$
$68$	8387.15	−	25813.0i	0.219959	−	0.676965i
$69$		0			0
$70$	−8524.14	−	6193.15i	−0.207924	−	0.151066i
$71$	7859.33	+	24188.5i	0.185029	+	0.569461i	0.999949	−	0.0101130i	$-0.00321912\pi$
$71$	7859.33	+	24188.5i	0.185029	+	0.569461i	−0.814920	+	0.579574i	$0.803219\pi$
$72$		0			0
$73$	40450.5	+	29389.0i	0.888416	+	0.645472i	0.935465	−	0.353420i	$-0.114982\pi$
$73$	40450.5	+	29389.0i	0.888416	+	0.645472i	−0.0470484	+	0.998893i	$0.514982\pi$
$74$	52905.0	−	38437.7i	1.12310	−	0.815978i
$75$		0			0
$76$	34377.7			0.682720
$77$	−41666.7	+	3929.65i	−0.800870	+	0.0755314i
$78$		0			0
$79$	4821.55	−	14839.2i	0.0869199	−	0.267512i	−0.898144	−	0.439702i	$-0.855084\pi$
$79$	4821.55	−	14839.2i	0.0869199	−	0.267512i	0.985064	+	0.172190i	$0.0550842\pi$
$80$	5231.19	−	3800.68i	0.0913851	−	0.0663952i
$81$		0			0
$82$	23899.2	+	73554.2i	0.392508	+	1.20802i
$83$	−27816.4	−	85610.0i	−0.443206	−	1.36405i	−0.884439	−	0.466655i	$-0.845459\pi$
$83$	−27816.4	−	85610.0i	−0.443206	−	1.36405i	0.441233	−	0.897392i	$-0.354541\pi$
$84$		0			0
$85$	34663.5	−	25184.5i	0.520385	−	0.378082i
$86$	21213.1	−	65287.1i	0.309284	−	0.951878i
$87$		0			0
$88$	5608.15	−	25064.2i	0.0771992	−	0.345022i
$89$	523.362			0.00700370			0.00350185	−	0.999994i	$-0.498885\pi$
$89$	523.362			0.00700370			0.00350185	+	0.999994i	$0.498885\pi$
$90$		0			0
$91$	39481.5	−	28685.0i	0.499793	−	0.363121i
$92$	26944.9	+	19576.6i	0.331899	+	0.241139i
$93$		0			0
$94$	−3676.13	−	11314.0i	−0.0429112	−	0.132067i
$95$	43905.3	+	31899.1i	0.499123	+	0.362634i
$96$		0			0
$97$	−4439.21	+	13662.5i	−0.0479046	+	0.147435i	−0.972148	−	0.234370i	$-0.924697\pi$
$97$	−4439.21	+	13662.5i	−0.0479046	+	0.147435i	0.924243	+	0.381805i	$0.124697\pi$
$98$	−23724.9			−0.249540
$99$		0			0
$100$	−39792.4			−0.397924
$101$	−47893.7	+	147402.i	−0.467170	+	1.43780i	0.389062	+	0.921212i	$0.372799\pi$
$101$	−47893.7	+	147402.i	−0.467170	+	1.43780i	−0.856232	+	0.516591i	$0.827201\pi$
$102$		0			0
$103$	39954.0	+	29028.3i	0.371079	+	0.269605i	0.757658	−	0.652651i	$-0.226343\pi$
$103$	39954.0	+	29028.3i	0.371079	+	0.269605i	−0.386579	+	0.922256i	$0.626343\pi$
$104$	9254.82	+	28483.4i	0.0839044	+	0.258231i
$105$		0			0
$106$	−28250.4	−	20525.1i	−0.244208	−	0.177428i
$107$	−113439.	+	82418.1i	−0.957860	+	0.695926i	−0.952653	−	0.304060i	$-0.901658\pi$
$107$	−113439.	+	82418.1i	−0.957860	+	0.695926i	−0.00520732	+	0.999986i	$0.501658\pi$
$108$		0			0
$109$	−195870.			−1.57907			−0.789535	−	0.613706i	$-0.789678\pi$
$109$	−195870.			−1.57907			−0.789535	+	0.613706i	$0.789678\pi$
$110$	30419.5	−	26806.8i	0.239701	−	0.211234i
$111$		0			0
$112$	−8249.97	+	25390.8i	−0.0621452	+	0.191263i
$113$	73700.8	−	53546.7i	0.542970	−	0.394491i	−0.282217	−	0.959351i	$-0.591070\pi$
$113$	73700.8	−	53546.7i	0.542970	−	0.394491i	0.825187	+	0.564860i	$0.191070\pi$
$114$		0			0
$115$	16247.4	+	50004.3i	0.114562	+	0.352584i
$116$	−26316.0	−	80992.4i	−0.181583	−	0.558855i
$117$		0			0
$118$	26582.9	−	19313.6i	0.175750	−	0.127690i
$119$	−54666.9	+	168247.i	−0.353881	+	1.08913i
$120$		0			0
$121$	20253.5	−	159772.i	0.125758	−	0.992061i
$122$	205700.			1.25123
$123$		0			0
$124$	−8117.19	+	5897.48i	−0.0474080	+	0.0344439i
$125$	−114678.	−	83318.4i	−0.656455	−	0.476942i
$126$		0			0
$127$	−10257.7	−	31570.1i	−0.0564342	−	0.173687i	0.918866	−	0.394569i	$-0.129106\pi$
$127$	−10257.7	−	31570.1i	−0.0564342	−	0.173687i	−0.975300	+	0.220883i	$0.929106\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−14610.0	+	44965.0i	−0.0758215	+	0.233355i
$131$	−241031.			−1.22714			−0.613572	−	0.789639i	$-0.710268\pi$
$131$	−241031.			−1.22714			−0.613572	+	0.789639i	$0.710268\pi$
$132$		0			0
$133$	−224071.			−1.09839
$134$	7969.60	−	24527.9i	0.0383420	−	0.118004i
$135$		0			0
$136$	−87831.4	−	63813.2i	−0.407195	−	0.295844i
$137$	69490.5	+	213870.i	0.316318	+	0.973527i	0.975208	+	0.221288i	$0.0710261\pi$
$137$	69490.5	+	213870.i	0.316318	+	0.973527i	−0.658890	+	0.752239i	$0.728974\pi$
$138$		0			0
$139$	−278562.	−	202387.i	−1.22288	−	0.888477i	−0.226548	−	0.974000i	$-0.572744\pi$
$139$	−278562.	−	202387.i	−1.22288	−	0.888477i	−0.996336	+	0.0855227i	$0.972744\pi$
$140$	−34096.5	+	24772.6i	−0.147025	+	0.106820i
$141$		0			0
$142$	101733.			0.423392
$143$	74546.1	+	172367.i	0.304849	+	0.704878i
$144$		0			0
$145$	41543.5	−	127858.i	0.164090	−	0.505018i
$146$	161802.	−	117556.i	0.628205	−	0.456418i
$147$		0			0
$148$	−80831.6	−	248774.i	−0.303338	−	0.933579i
$149$	84963.8	+	261492.i	0.313522	+	0.964922i	0.976359	+	0.216157i	$0.0693524\pi$
$149$	84963.8	+	261492.i	0.313522	+	0.964922i	−0.662837	+	0.748764i	$0.730648\pi$
$150$		0			0
$151$	−379003.	+	275362.i	−1.35270	+	0.982792i	−0.353826	+	0.935311i	$0.615119\pi$
$151$	−379003.	+	275362.i	−1.35270	+	0.982792i	−0.998872	+	0.0474811i	$0.984881\pi$
$152$	42493.1	−	130780.i	0.149180	−	0.459128i
$153$		0			0
$154$	−36553.5	+	163367.i	−0.124202	+	0.555088i
$155$	−15839.1			−0.0529544
$156$		0			0
$157$	−180347.	+	131030.i	−0.583928	+	0.424248i	−0.840138	−	0.542373i	$-0.817526\pi$
$157$	−180347.	+	131030.i	−0.583928	+	0.424248i	0.256210	+	0.966621i	$0.417526\pi$
$158$	−50492.0	−	36684.6i	−0.160909	−	0.116907i
$159$		0			0
$160$	−7992.55	−	24598.5i	−0.0246823	−	0.0759642i
$161$	−175625.	−	127599.i	−0.533975	−	0.387956i
$162$		0			0
$163$	112949.	−	347620.i	0.332975	−	1.02479i	−0.634735	−	0.772730i	$-0.718891\pi$
$163$	112949.	−	347620.i	0.332975	−	1.02479i	0.967711	−	0.252063i	$-0.0811092\pi$
$164$	309358.			0.898155
$165$		0			0
$166$	−360063.			−1.01416
$167$	29048.8	−	89402.9i	0.0806003	−	0.248062i	−0.902634	−	0.430409i	$-0.858369\pi$
$167$	29048.8	−	89402.9i	0.0806003	−	0.248062i	0.983234	+	0.182347i	$0.0583694\pi$
$168$		0			0
$169$	123221.	+	89525.2i	0.331870	+	0.241117i
$170$	−52961.1	−	162998.i	−0.140551	−	0.432572i
$171$		0			0
$172$	−222146.	−	161399.i	−0.572555	−	0.415986i
$173$	−65763.8	+	47780.2i	−0.167060	+	0.121376i	−0.668174	−	0.744005i	$-0.732924\pi$
$173$	−65763.8	+	47780.2i	−0.167060	+	0.121376i	0.501114	+	0.865381i	$0.332924\pi$
$174$		0			0
$175$	259364.			0.640198
$176$	−88417.8	−	52315.7i	−0.215158	−	0.127306i
$177$		0			0
$178$	646.911	−	1990.99i	0.00153036	−	0.00470998i
$179$	−273739.	+	198883.i	−0.638564	+	0.463944i	−0.859356	−	0.511377i	$-0.829136\pi$
$179$	−273739.	+	198883.i	−0.638564	+	0.463944i	0.220793	+	0.975321i	$0.429136\pi$
$180$		0			0
$181$	33971.5	+	104554.i	0.0770759	+	0.237215i	0.982170	−	0.187997i	$-0.0601995\pi$
$181$	33971.5	+	104554.i	0.0770759	+	0.237215i	−0.905094	+	0.425212i	$0.860200\pi$
$182$	−60322.3	−	185653.i	−0.134989	−	0.415455i
$183$		0			0
$184$	107779.	−	78306.3i	0.234688	−	0.170511i
$185$	127604.	−	392725.i	0.274116	−	0.843643i
$186$		0			0
$187$	−585884.	−	346660.i	−1.22520	−	0.724937i
$188$	−47584.8			−0.0981915
$189$		0			0
$190$	175621.	−	127596.i	0.352933	−	0.256421i
$191$	−453887.	−	329768.i	−0.900253	−	0.654072i	0.0382779	−	0.999267i	$-0.487813\pi$
$191$	−453887.	−	329768.i	−0.900253	−	0.654072i	−0.938531	+	0.345195i	$0.887813\pi$
$192$		0			0
$193$	−77948.4	−	239900.i	−0.150631	−	0.463594i	0.847061	−	0.531495i	$-0.178370\pi$
$193$	−77948.4	−	239900.i	−0.150631	−	0.463594i	−0.997692	+	0.0679013i	$0.978370\pi$
$194$	46488.1	+	33775.6i	0.0886823	+	0.0644315i
$195$		0			0
$196$	−29325.6	+	90255.0i	−0.0545264	+	0.167815i
$197$	497050.			0.912503			0.456252	−	0.889851i	$-0.349192\pi$
$197$	497050.			0.912503			0.456252	+	0.889851i	$0.349192\pi$
$198$		0			0
$199$	351226.			0.628715			0.314358	−	0.949305i	$-0.398211\pi$
$199$	351226.			0.628715			0.314358	+	0.949305i	$0.398211\pi$
$200$	−49186.1	+	151379.i	−0.0869495	+	0.267603i
$201$		0			0
$202$	501550.	+	364397.i	0.864839	+	0.628343i
$203$	171526.	+	527903.i	0.292139	+	0.899113i
$204$		0			0
$205$	395095.	+	287053.i	0.656624	+	0.477065i
$206$	159816.	−	116113.i	0.262393	−	0.190639i
$207$		0			0
$208$	119797.			0.191994
$209$	188276.	−	841453.i	0.298147	−	1.33249i
$210$		0			0
$211$	−64851.7	+	199593.i	−0.100280	+	0.308631i	−0.988594	−	0.150607i	$-0.951877\pi$
$211$	−64851.7	+	199593.i	−0.100280	+	0.308631i	0.888314	+	0.459237i	$0.151877\pi$
$212$	−113002.	+	82100.6i	−0.172681	+	0.125460i
$213$		0			0
$214$	173319.	+	533421.i	0.258709	+	0.796225i
$215$	−133951.	−	412259.i	−0.197629	−	0.608239i
$216$		0			0
$217$	52907.3	−	38439.4i	0.0762722	−	0.0554150i
$218$	−242108.	+	745133.i	−0.345039	+	1.06192i
$219$		0			0
$220$	−64378.6	−	148858.i	−0.0896778	−	0.207355i
$221$	793812.			1.09329
$222$		0			0
$223$	63835.7	−	46379.3i	0.0859610	−	0.0624543i	−0.543975	−	0.839102i	$-0.683081\pi$
$223$	63835.7	−	46379.3i	0.0859610	−	0.0624543i	0.629936	+	0.776647i	$0.283081\pi$
$224$	86394.8	+	62769.5i	0.115045	+	0.0835850i
$225$		0			0
$226$	−112605.	−	346562.i	−0.146651	−	0.451346i
$227$	−501817.	−	364592.i	−0.646370	−	0.469615i	0.215663	−	0.976468i	$-0.430809\pi$
$227$	−501817.	−	364592.i	−0.646370	−	0.469615i	−0.862033	+	0.506853i	$0.830809\pi$
$228$		0			0
$229$	−63059.3	+	194077.i	−0.0794622	+	0.244559i	−0.982894	−	0.184172i	$-0.941039\pi$
$229$	−63059.3	+	194077.i	−0.0794622	+	0.244559i	0.903432	+	0.428732i	$0.141039\pi$
$230$	210311.			0.262145
$231$		0			0
$232$	−340642.			−0.415507
$233$	−68920.6	+	212116.i	−0.0831686	+	0.255967i	−0.983990	−	0.178223i	$-0.942965\pi$
$233$	−68920.6	+	212116.i	−0.0831686	+	0.255967i	0.900822	+	0.434189i	$0.142965\pi$
$234$		0			0
$235$	−60772.7	−	44154.0i	−0.0717859	−	0.0521555i
$236$	−40615.0	−	125000.i	−0.0474686	−	0.146093i
$237$		0			0
$238$	572479.	+	415930.i	0.655114	+	0.475969i
$239$	−60702.8	+	44103.2i	−0.0687407	+	0.0499431i	−0.621625	−	0.783315i	$-0.713527\pi$
$239$	−60702.8	+	44103.2i	−0.0687407	+	0.0499431i	0.552884	+	0.833258i	$0.313527\pi$
$240$		0			0
$241$	510379.			0.566044			0.283022	−	0.959113i	$-0.408663\pi$
$241$	510379.			0.566044			0.283022	+	0.959113i	$0.408663\pi$
$242$	−582776.	−	274538.i	−0.639680	−	0.301346i
$243$		0			0
$244$	254260.	−	782531.i	0.273403	−	0.841447i
$245$	−121201.	+	88057.5i	−0.129000	+	0.0937241i
$246$		0			0
$247$	310702.	+	956244.i	0.324043	+	0.997301i
$248$	12402.0	+	38169.3i	0.0128045	+	0.0394081i
$249$		0			0
$250$	−458712.	+	333274.i	−0.464184	+	0.337249i
$251$	55270.7	−	170106.i	0.0553746	−	0.170426i	−0.919544	−	0.392987i	$-0.871442\pi$
$251$	55270.7	−	170106.i	0.0553746	−	0.170426i	0.974919	+	0.222561i	$0.0714418\pi$
$252$		0			0
$253$	626740.	−	552307.i	0.615582	−	0.542475i
$254$	−132779.			−0.129135
$255$		0			0
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	171271.	+	124435.i	0.161752	+	0.117520i	0.665717	−	0.746204i	$-0.268126\pi$
$257$	171271.	+	124435.i	0.161752	+	0.117520i	−0.503965	+	0.863724i	$0.668126\pi$
$258$		0			0
$259$	526855.	+	1.62149e6i	0.488025	+	1.50199i
$260$	152998.	+	111160.i	0.140363	+	0.101980i
$261$		0			0
$262$	−297931.	+	916938.i	−0.268141	+	0.825252i
$263$	1.84873e6			1.64811			0.824053	−	0.566513i	$-0.191708\pi$
$263$	1.84873e6			1.64811			0.824053	+	0.566513i	$0.191708\pi$
$264$		0			0
$265$	−220501.			−0.192884
$266$	−276967.	+	852418.i	−0.240007	+	0.738667i
$267$		0			0
$268$	−83458.7	−	60636.3i	−0.0709798	−	0.0515698i
$269$	−292017.	−	898737.i	−0.246053	−	0.757272i	−0.995462	−	0.0951647i	$-0.969662\pi$
$269$	−292017.	−	898737.i	−0.246053	−	0.757272i	0.749409	−	0.662107i	$-0.230338\pi$
$270$		0			0
$271$	1.31810e6	+	957657.i	1.09025	+	0.792112i	0.979441	−	0.201730i	$-0.0646562\pi$
$271$	1.31810e6	+	957657.i	1.09025	+	0.792112i	0.110808	+	0.993842i	$0.464656\pi$
$272$	−351325.	+	255253.i	−0.287930	+	0.209194i
$273$		0			0
$274$	899504.			0.723814
$275$	−217931.	+	973987.i	−0.173775	+	0.776643i
$276$		0			0
$277$	642268.	−	1.97670e6i	0.502941	−	1.54789i	−0.301265	−	0.953540i	$-0.597409\pi$
$277$	642268.	−	1.97670e6i	0.502941	−	1.54789i	0.804205	−	0.594351i	$-0.202591\pi$
$278$	−1.11425e6	+	809549.i	−0.864710	+	0.628248i
$279$		0			0
$280$	52094.9	+	160332.i	0.0397100	+	0.122215i
$281$	606152.	+	1.86554e6i	0.457948	+	1.40942i	0.867639	+	0.497194i	$0.165636\pi$
$281$	606152.	+	1.86554e6i	0.457948	+	1.40942i	−0.409692	+	0.912224i	$0.634364\pi$
$282$		0			0
$283$	1.06550e6	−	774133.i	0.790840	−	0.574579i	−0.117373	−	0.993088i	$-0.537447\pi$
$283$	1.06550e6	−	774133.i	0.790840	−	0.574579i	0.908213	+	0.418509i	$0.137447\pi$
$284$	125749.	−	387017.i	0.0925145	−	0.284730i
$285$		0			0
$286$	747867.	−	70532.7i	0.540642	−	0.0509888i
$287$	−2.01637e6			−1.44500
$288$		0			0
$289$	−1.17930e6	+	856815.i	−0.830580	+	0.603451i
$290$	−435049.	−	316082.i	−0.303769	−	0.220701i
$291$		0			0
$292$	−247211.	−	760838.i	−0.169672	−	0.522198i
$293$	854365.	+	620733.i	0.581399	+	0.422411i	0.839228	−	0.543779i	$-0.183007\pi$
$293$	854365.	+	620733.i	0.581399	+	0.422411i	−0.257829	+	0.966191i	$0.583007\pi$
$294$		0			0
$295$	64116.4	−	197330.i	0.0428957	−	0.132019i
$296$	−1.04631e6			−0.694112
$297$		0			0
$298$	1.09979e6			0.717415
$299$	−301014.	+	926425.i	−0.194719	+	0.599284i
$300$		0			0
$301$	1.44793e6	+	1.05199e6i	0.921154	+	0.669258i
$302$	579066.	+	1.78218e6i	0.365351	+	1.12444i
$303$		0			0
$304$	−444994.	−	323307.i	−0.276166	−	0.200646i
$305$	1.05084e6	−	763478.i	0.646824	−	0.469945i
$306$		0			0
$307$	2.33319e6			1.41288			0.706439	−	0.707774i	$-0.250301\pi$
$307$	2.33319e6			1.41288			0.706439	+	0.707774i	$0.250301\pi$
$308$	576301.	+	340990.i	0.346157	+	0.204817i
$309$		0			0
$310$	−19578.2	+	60255.6i	−0.0115710	+	0.0356117i
$311$	2.36568e6	−	1.71877e6i	1.38693	−	1.00766i	0.390736	−	0.920503i	$-0.372221\pi$
$311$	2.36568e6	−	1.71877e6i	1.38693	−	1.00766i	0.996194	−	0.0871609i	$-0.0277794\pi$
$312$		0			0
$313$	544677.	+	1.67634e6i	0.314252	+	0.967168i	0.976061	+	0.217496i	$0.0697889\pi$
$313$	544677.	+	1.67634e6i	0.314252	+	0.967168i	−0.661809	+	0.749672i	$0.730211\pi$
$314$	275545.	+	848041.i	0.157714	+	0.485392i
$315$		0			0
$316$	−201968.	+	146738.i	−0.113780	+	0.0826657i
$317$	844582.	−	2.59936e6i	0.472056	−	1.45284i	−0.377831	−	0.925875i	$-0.623330\pi$
$317$	844582.	−	2.59936e6i	0.472056	−	1.45284i	0.849887	−	0.526965i	$-0.176670\pi$
$318$		0			0
$319$	−2.12656e6	+	200559.i	−1.17004	+	0.110348i
$320$	−103458.			−0.0564791
$321$		0			0
$322$	−702499.	+	510396.i	−0.377578	+	0.274326i
$323$	−2.94867e6	−	2.14233e6i	−1.57261	−	1.14256i
$324$		0			0
$325$	−359640.	−	1.10686e6i	−0.188868	−	0.581277i
$326$	−1.18281e6	−	859365.i	−0.616414	−	0.447851i
$327$		0			0
$328$	382387.	−	1.17687e6i	0.196254	−	0.604008i
$329$	310155.			0.157975
$330$		0			0
$331$	−3.61380e6			−1.81298			−0.906491	−	0.422225i	$-0.861249\pi$
$331$	−3.61380e6			−1.81298			−0.906491	+	0.422225i	$0.861249\pi$
$332$	−445062.	+	1.36976e6i	−0.221603	+	0.682024i
$333$		0			0
$334$	−304203.	−	221016.i	−0.149210	−	0.108407i
$335$	−50324.5	−	154883.i	−0.0245001	−	0.0754034i
$336$		0			0
$337$	−714622.	−	519203.i	−0.342769	−	0.249036i	0.403060	−	0.915173i	$-0.367947\pi$
$337$	−714622.	−	519203.i	−0.342769	−	0.249036i	−0.745829	+	0.666137i	$0.767947\pi$
$338$	492884.	−	358101.i	0.234667	−	0.170496i
$339$		0			0
$340$	−685543.			−0.321616
$341$	99895.8	+	230981.i	0.0465223	+	0.107570i
$342$		0			0
$343$	732772.	−	2.25524e6i	0.336305	−	1.03504i
$344$	−888584.	+	645594.i	−0.404858	+	0.294146i
$345$		0			0
$346$	100478.	+	309240.i	0.0451212	+	0.138869i
$347$	−291962.	−	898566.i	−0.130167	−	0.400614i	0.864640	−	0.502393i	$-0.167547\pi$
$347$	−291962.	−	898566.i	−0.130167	−	0.400614i	−0.994807	+	0.101778i	$0.967547\pi$
$348$		0			0
$349$	−3.43399e6	+	2.49494e6i	−1.50916	+	1.09647i	−0.542610	+	0.839985i	$0.682564\pi$
$349$	−3.43399e6	+	2.49494e6i	−1.50916	+	1.09647i	−0.966549	+	0.256484i	$0.917436\pi$
$350$	320591.	−	986679.i	0.139888	−	0.430532i
$351$		0			0
$352$	−308311.	+	271695.i	−0.132627	+	0.116876i
$353$	2.88012e6			1.23019			0.615097	−	0.788451i	$-0.289117\pi$
$353$	2.88012e6			1.23019			0.615097	+	0.788451i	$0.289117\pi$
$354$		0			0
$355$	519713.	−	377594.i	0.218873	−	0.159021i
$356$	−6774.54	−	4921.99i	−0.00283306	−	0.00205834i
$357$		0			0
$358$	418236.	+	1.28720e6i	0.172470	+	0.530809i
$359$	131847.	+	95792.2i	0.0539924	+	0.0392278i	0.614454	−	0.788953i	$-0.289376\pi$
$359$	131847.	+	95792.2i	0.0539924	+	0.0392278i	−0.560462	+	0.828180i	$0.689376\pi$
$360$		0			0
$361$	661420.	−	2.03564e6i	0.267122	−	0.822116i
$362$	439736.			0.176368
$363$		0			0
$364$	−780829.			−0.308889
$365$	390257.	−	1.20109e6i	0.153327	−	0.471892i
$366$		0			0
$367$	−2.44064e6	−	1.77323e6i	−0.945887	−	0.687227i	0.00394389	−	0.999992i	$-0.498745\pi$
$367$	−2.44064e6	−	1.77323e6i	−0.945887	−	0.687227i	−0.949830	+	0.312765i	$0.898745\pi$
$368$	−164672.	−	506809.i	−0.0633871	−	0.195085i
$369$		0			0
$370$	−1.33629e6	−	970869.i	−0.507452	−	0.368686i
$371$	736538.	−	535126.i	0.277818	−	0.201847i
$372$		0			0
$373$	−612407.			−0.227913			−0.113956	−	0.993486i	$-0.536352\pi$
$373$	−612407.			−0.227913			−0.113956	+	0.993486i	$0.536352\pi$
$374$	−2.04297e6	+	1.80034e6i	−0.755235	+	0.665542i
$375$		0			0
$376$	−58818.1	+	181023.i	−0.0214556	+	0.0660336i
$377$	2.01503e6	−	1.46400e6i	0.730177	−	0.530504i
$378$		0			0
$379$	−116909.	−	359810.i	−0.0418072	−	0.128669i	0.927974	−	0.372644i	$-0.121549\pi$
$379$	−116909.	−	359810.i	−0.0418072	−	0.128669i	−0.969782	+	0.243974i	$0.921549\pi$
$380$	−268325.	−	825820.i	−0.0953241	−	0.293377i
$381$		0			0
$382$	−1.81555e6	+	1.31907e6i	−0.636575	+	0.462499i
$383$	123953.	−	381488.i	0.0431777	−	0.132887i	−0.927144	−	0.374706i	$-0.877744\pi$
$383$	123953.	−	381488.i	0.0431777	−	0.132887i	0.970322	+	0.241818i	$0.0777438\pi$
$384$		0			0
$385$	419616.	+	970245.i	0.144278	+	0.333603i
$386$	−1.00899e6			−0.344680
$387$		0			0
$388$	185952.	−	135102.i	0.0627079	−	0.0455599i
$389$	−550388.	−	399880.i	−0.184414	−	0.133985i	0.491748	−	0.870738i	$-0.336358\pi$
$389$	−550388.	−	399880.i	−0.184414	−	0.133985i	−0.676162	+	0.736753i	$0.736358\pi$
$390$		0			0
$391$	−1.09117e6	−	3.35828e6i	−0.360953	−	1.11090i
$392$	307102.	+	223123.i	0.100941	+	0.0733379i
$393$		0			0
$394$	614388.	−	1.89089e6i	0.199389	−	0.613657i
$395$	−394101.			−0.127091
$396$		0			0
$397$	−456946.			−0.145509			−0.0727543	−	0.997350i	$-0.523179\pi$
$397$	−456946.			−0.145509			−0.0727543	+	0.997350i	$0.523179\pi$
$398$	434139.	−	1.33614e6i	0.137379	−	0.422810i
$399$		0			0
$400$	515083.	+	374230.i	0.160963	+	0.116947i
$401$	609884.	+	1.87703e6i	0.189403	+	0.582922i	0.999996	−	0.00268738i	$-0.000855420\pi$
$401$	609884.	+	1.87703e6i	0.189403	+	0.582922i	−0.810594	+	0.585609i	$0.800855\pi$
$402$		0			0
$403$	−237406.	−	172486.i	−0.0728164	−	0.0529042i
$404$	2.00620e6	−	1.45759e6i	0.611534	−	0.444305i
$405$		0			0
$406$	2.22028e6			0.668487
$407$	−6.53187e6	+	616032.i	−1.95457	+	0.184339i
$408$		0			0
$409$	1.21553e6	−	3.74100e6i	0.359299	−	1.10581i	−0.594176	−	0.804335i	$-0.702522\pi$
$409$	1.21553e6	−	3.74100e6i	0.359299	−	1.10581i	0.953475	−	0.301473i	$-0.0974784\pi$
$410$	1.58038e6	−	1.14821e6i	0.464303	−	0.337336i
$411$		0			0
$412$	−244177.	−	751499.i	−0.0708699	−	0.218115i
$413$	264726.	+	814742.i	0.0763697	+	0.235042i
$414$		0			0
$415$	−1.83941e6	+	1.33641e6i	−0.524274	+	0.380908i
$416$	148077.	−	455735.i	0.0419522	−	0.129116i
$417$		0			0
$418$	−2.96836e6	−	1.75634e6i	−0.830951	−	0.491663i
$419$	−5.31518e6			−1.47905			−0.739524	−	0.673130i	$-0.764950\pi$
$419$	−5.31518e6			−1.47905			−0.739524	+	0.673130i	$0.764950\pi$
$420$		0			0
$421$	−3.09529e6	+	2.24886e6i	−0.851131	+	0.618383i	−0.925458	−	0.378851i	$-0.876319\pi$
$421$	−3.09529e6	+	2.24886e6i	−0.851131	+	0.618383i	0.0743263	+	0.997234i	$0.476319\pi$
$422$	679136.	+	493421.i	0.185642	+	0.134877i
$423$		0			0
$424$	172651.	+	531366.i	0.0466396	+	0.143542i
$425$	3.41310e6	+	2.47976e6i	0.916594	+	0.665944i
$426$		0			0
$427$	−1.65725e6	+	5.10048e6i	−0.439863	+	1.35376i
$428$	2.24349e6			0.591990
$429$		0			0
$430$	−1.73390e6			−0.452223
$431$	−1.98117e6	+	6.09740e6i	−0.513721	+	1.58107i	0.271875	+	0.962333i	$0.412356\pi$
$431$	−1.98117e6	+	6.09740e6i	−0.513721	+	1.58107i	−0.785596	+	0.618740i	$0.787644\pi$
$432$		0			0
$433$	−1.54665e6	−	1.12371e6i	−0.396435	−	0.288027i	0.371652	−	0.928372i	$-0.378791\pi$
$433$	−1.54665e6	−	1.12371e6i	−0.396435	−	0.288027i	−0.768087	+	0.640345i	$0.778791\pi$
$434$	−80835.2	−	248785.i	−0.0206004	−	0.0634016i
$435$		0			0
$436$	2.53539e6	+	1.84207e6i	0.638747	+	0.464077i
$437$	3.61836e6	−	2.62890e6i	0.906376	−	0.658521i
$438$		0			0
$439$	−620608.			−0.153694			−0.0768468	−	0.997043i	$-0.524485\pi$
$439$	−620608.			−0.153694			−0.0768468	+	0.997043i	$0.524485\pi$
$440$	−645865.	+	60912.6i	−0.159041	+	0.0149995i
$441$		0			0
$442$	981206.	−	3.01984e6i	0.238894	−	0.735239i
$443$	−3.76642e6	+	2.73646e6i	−0.911841	+	0.662491i	−0.941480	−	0.337069i	$-0.890564\pi$
$443$	−3.76642e6	+	2.73646e6i	−0.911841	+	0.662491i	0.0296389	+	0.999561i	$0.490564\pi$
$444$		0			0
$445$	−4084.96	−	12572.2i	−0.000977884	−	0.00300962i
$446$	−97532.2	−	300173.i	−0.0232173	−	0.0714554i
$447$		0			0
$448$	345579.	−	251078.i	0.0813491	−	0.0591036i
$449$	2.07284e6	−	6.37956e6i	0.485234	−	1.49340i	−0.346408	−	0.938084i	$-0.612599\pi$
$449$	2.07284e6	−	6.37956e6i	0.485234	−	1.49340i	0.831642	−	0.555312i	$-0.187401\pi$
$450$		0			0
$451$	1.69426e6	−	7.57207e6i	0.392229	−	1.75297i
$452$	−1.45759e6			−0.335574
$453$		0			0
$454$	−2.00727e6	+	1.45837e6i	−0.457053	+	0.332068i
$455$	−997232.	−	724531.i	−0.225823	−	0.164070i
$456$		0			0
$457$	142929.	+	439889.i	0.0320132	+	0.0985264i	0.965786	−	0.259339i	$-0.0835047\pi$
$457$	142929.	+	439889.i	0.0320132	+	0.0985264i	−0.933773	+	0.357865i	$0.883505\pi$
$458$	660365.	+	479784.i	0.147103	+	0.106876i
$459$		0			0
$460$	259958.	−	800069.i	0.0572808	−	0.176292i
$461$	5.86516e6			1.28537			0.642684	−	0.766131i	$-0.277821\pi$
$461$	5.86516e6			1.28537			0.642684	+	0.766131i	$0.277821\pi$
$462$		0			0
$463$	−2.17059e6			−0.470570			−0.235285	−	0.971926i	$-0.575602\pi$
$463$	−2.17059e6			−0.470570			−0.235285	+	0.971926i	$0.575602\pi$
$464$	−421056.	+	1.29588e6i	−0.0907915	+	0.279428i
$465$		0			0
$466$	721746.	+	524379.i	0.153964	+	0.111861i
$467$	2.20750e6	+	6.79400e6i	0.468392	+	1.44156i	0.854666	+	0.519178i	$0.173762\pi$
$467$	2.20750e6	+	6.79400e6i	0.468392	+	1.44156i	−0.386275	+	0.922384i	$0.626238\pi$
$468$		0			0
$469$	543978.	+	395223.i	0.114196	+	0.0829680i
$470$	−243091.	+	176616.i	−0.0507603	+	0.0368795i
$471$		0			0
$472$	−525731.			−0.108620
$473$	−5.16714e6	+	4.55348e6i	−1.06193	+	0.935816i
$474$		0			0
$475$	−1.65127e6	+	5.08209e6i	−0.335803	+	1.03349i
$476$	2.28992e6	−	1.66372e6i	0.463236	−	0.336561i
$477$		0			0
$478$	92745.7	+	285442.i	0.0185662	+	0.0571410i
$479$	1.70845e6	+	5.25808e6i	0.340224	+	1.04710i	0.964091	+	0.265571i	$0.0855604\pi$
$479$	1.70845e6	+	5.25808e6i	0.340224	+	1.04710i	−0.623868	+	0.781530i	$0.714440\pi$
$480$		0			0
$481$	6.18931e6	−	4.49680e6i	1.21978	−	0.886219i
$482$	630863.	−	1.94160e6i	0.123685	−	0.380664i
$483$		0			0
$484$	−1.76476e6	+	1.87766e6i	−0.342430	+	0.364338i
$485$	362850.			0.0700442
$486$		0			0
$487$	5.81282e6	−	4.22326e6i	1.11062	−	0.806911i	0.127857	−	0.991793i	$-0.459190\pi$
$487$	5.81282e6	−	4.22326e6i	1.11062	−	0.806911i	0.982761	+	0.184881i	$0.0591900\pi$
$488$	−2.66264e6	−	1.93452e6i	−0.506131	−	0.367726i
$489$		0			0
$490$	185178.	+	569920.i	0.0348417	+	0.107232i
$491$	−7.93318e6	−	5.76380e6i	−1.48506	−	1.07896i	−0.975882	−	0.218297i	$-0.929950\pi$
$491$	−7.93318e6	−	5.76380e6i	−1.48506	−	1.07896i	−0.509177	−	0.860662i	$-0.670050\pi$
$492$		0			0
$493$	−2.79005e6	+	8.58690e6i	−0.517005	+	1.59118i
$494$	4.02182e6			0.741489
$495$		0			0
$496$	160534.			0.0292997
$497$	−819626.	+	2.52255e6i	−0.148842	+	0.458088i
$498$		0			0
$499$	5.51201e6	+	4.00471e6i	0.990966	+	0.719979i	0.960132	−	0.279546i	$-0.0901838\pi$
$499$	5.51201e6	+	4.00471e6i	0.990966	+	0.719979i	0.0308336	+	0.999525i	$0.490184\pi$
$500$	700849.	+	2.15699e6i	0.125372	+	0.385854i
$501$		0			0
$502$	−578803.	−	420525.i	−0.102511	−	0.0744787i
$503$	−2.32373e6	+	1.68829e6i	−0.409511	+	0.297527i	−0.773404	−	0.633914i	$-0.781447\pi$
$503$	−2.32373e6	+	1.68829e6i	−0.409511	+	0.297527i	0.363893	+	0.931441i	$0.381447\pi$
$504$		0			0
$505$	3.91471e6			0.683079
$506$	−1.32641e6	−	3.06695e6i	−0.230304	−	0.532513i
$507$		0			0
$508$	−164124.	+	505121.i	−0.0282171	+	0.0868433i
$509$	343499.	−	249567.i	0.0587667	−	0.0426965i	−0.558014	−	0.829831i	$-0.688437\pi$
$509$	343499.	−	249567.i	0.0587667	−	0.0426965i	0.616781	+	0.787135i	$0.288437\pi$
$510$		0			0
$511$	1.61131e6	+	4.95909e6i	0.272977	+	0.840137i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$		0			0
$514$	685082.	−	497741.i	0.114376	−	0.0830990i
$515$	385467.	−	1.18635e6i	0.0640427	−	0.197103i
$516$		0			0
$517$	−260608.	+	1.16472e6i	−0.0428807	+	0.191644i
$518$	6.81976e6			1.11672
$519$		0			0
$520$	611993.	−	444639.i	0.0992517	−	0.0721106i
$521$	−6.83389e6	−	4.96511e6i	−1.10300	−	0.801373i	−0.121449	−	0.992598i	$-0.538754\pi$
$521$	−6.83389e6	−	4.96511e6i	−1.10300	−	0.801373i	−0.981546	+	0.191224i	$0.938754\pi$
$522$		0			0
$523$	213221.	+	656226.i	0.0340860	+	0.104906i	0.966652	−	0.256094i	$-0.0824356\pi$
$523$	213221.	+	656226.i	0.0340860	+	0.104906i	−0.932566	+	0.361000i	$0.882436\pi$
$524$	3.11998e6	+	2.26680e6i	0.496390	+	0.360648i
$525$		0			0
$526$	2.28516e6	−	7.03300e6i	0.360124	−	1.10835i
$527$	1.06375e6			0.166845
$528$		0			0
$529$	−2.10327e6			−0.326780
$530$	−272554.	+	838835.i	−0.0421466	+	0.129714i
$531$		0			0
$532$	2.90044e6	+	2.10729e6i	0.444309	+	0.322809i
$533$	2.79595e6	+	8.60505e6i	0.426296	+	1.31200i
$534$		0			0
$535$	2.86526e6	+	2.08173e6i	0.432793	+	0.314442i
$536$	−333835.	+	242545.i	−0.0501903	+	0.0364654i
$537$		0			0
$538$	−3.77995e6			−0.563029
$539$	2.04854e6	+	1.21210e6i	0.303719	+	0.179707i
$540$		0			0
$541$	1.10787e6	−	3.40967e6i	0.162740	−	0.500863i	−0.836122	−	0.548543i	$-0.815183\pi$
$541$	1.10787e6	−	3.40967e6i	0.162740	−	0.500863i	0.998863	+	0.0476800i	$0.0151828\pi$
$542$	5.27241e6	−	3.83063e6i	0.770922	−	0.560108i
$543$		0			0
$544$	536778.	+	1.65203e6i	0.0777673	+	0.239343i
$545$	1.52881e6	+	4.70518e6i	0.220476	+	0.678555i
$546$		0			0
$547$	−1.33357e6	+	968898.i	−0.190567	+	0.138455i	−0.678978	−	0.734159i	$-0.737577\pi$
$547$	−1.33357e6	+	968898.i	−0.190567	+	0.138455i	0.488411	+	0.872614i	$0.337577\pi$
$548$	1.11185e6	−	3.42192e6i	0.158159	−	0.486764i
$549$		0			0
$550$	3.43589e6	+	2.03297e6i	0.484320	+	0.286566i
$551$	−1.14360e7			−1.60471
$552$		0			0
$553$	1.31641e6	−	956430.i	0.183054	−	0.132997i
$554$	−6.72591e6	−	4.88666e6i	−0.931058	−	0.676454i
$555$		0			0
$556$	1.70242e6	+	5.23951e6i	0.233550	+	0.718793i
$557$	−84226.8	−	61194.3i	−0.0115030	−	0.00835744i	0.582019	−	0.813175i	$-0.302263\pi$
$557$	−84226.8	−	61194.3i	−0.0115030	−	0.00835744i	−0.593522	+	0.804818i	$0.702263\pi$
$558$		0			0
$559$	2.48170e6	−	7.63788e6i	0.335907	−	1.03382i
$560$	674330.			0.0908663
$561$		0			0
$562$	7.84620e6			1.04790
$563$	−2.09071e6	+	6.43455e6i	−0.277986	+	0.855553i	0.710428	+	0.703770i	$0.248501\pi$
$563$	−2.09071e6	+	6.43455e6i	−0.277986	+	0.855553i	−0.988414	+	0.151783i	$0.951499\pi$
$564$		0			0
$565$	−1.86155e6	−	1.35250e6i	−0.245332	−	0.178244i
$566$	−1.62794e6	−	5.01029e6i	−0.213598	−	0.657389i
$567$		0			0
$568$	−1.31686e6	−	956758.i	−0.171266	−	0.124432i
$569$	7.28794e6	−	5.29500e6i	0.943678	−	0.685622i	−0.00562491	−	0.999984i	$-0.501790\pi$
$569$	7.28794e6	−	5.29500e6i	0.943678	−	0.685622i	0.949303	+	0.314362i	$0.101790\pi$
$570$		0			0
$571$	4.29670e6			0.551499			0.275750	−	0.961229i	$-0.411074\pi$
$571$	4.29670e6			0.551499			0.275750	+	0.961229i	$0.411074\pi$
$572$	656093.	−	2.93224e6i	0.0838446	−	0.374722i
$573$		0			0
$574$	−2.49238e6	+	7.67074e6i	−0.315743	+	0.971757i
$575$	−4.18828e6	+	3.04296e6i	−0.528282	+	0.383819i
$576$		0			0
$577$	3.17454e6	+	9.77024e6i	0.396955	+	1.22170i	0.927428	+	0.374001i	$0.122014\pi$
$577$	3.17454e6	+	9.77024e6i	0.396955	+	1.22170i	−0.530473	+	0.847702i	$0.677986\pi$
$578$	1.80182e6	+	5.54542e6i	0.224332	+	0.690423i
$579$		0			0
$580$	−1.74020e6	+	1.26433e6i	−0.214797	+	0.156059i
$581$	2.90089e6	−	8.92801e6i	0.356525	−	1.09727i
$582$		0			0
$583$	1.39068e6	+	3.21556e6i	0.169455	+	0.391818i
$584$	−3.19997e6			−0.388252
$585$		0			0
$586$	3.41746e6	−	2.48293e6i	0.411111	−	0.298690i
$587$	−1.05522e7	−	7.66660e6i	−1.26400	−	0.918348i	−0.265051	−	0.964234i	$-0.585389\pi$
$587$	−1.05522e7	−	7.66660e6i	−1.26400	−	0.918348i	−0.998947	+	0.0458864i	$0.985389\pi$
$588$		0			0
$589$	416358.	+	1.28142e6i	0.0494514	+	0.152196i
$590$	−671436.	−	487827.i	−0.0794098	−	0.0576946i
$591$		0			0
$592$	−1.29331e6	+	3.98039e6i	−0.151669	+	0.466789i
$593$	1.54858e7			1.80842			0.904208	−	0.427093i	$-0.140462\pi$
$593$	1.54858e7			1.80842			0.904208	+	0.427093i	$0.140462\pi$
$594$		0			0
$595$	4.46833e6			0.517431
$596$	1.35942e6	−	4.18386e6i	0.156761	−	0.482461i
$597$		0			0
$598$	3.15226e6	+	2.29025e6i	0.360470	+	0.261897i
$599$	−2.96126e6	−	9.11383e6i	−0.337217	−	1.03785i	−0.965620	−	0.259959i	$-0.916291\pi$
$599$	−2.96126e6	−	9.11383e6i	−0.337217	−	1.03785i	0.628402	−	0.777888i	$-0.283709\pi$
$600$		0			0
$601$	1.07860e6	+	783652.i	0.121808	+	0.0884987i	0.647021	−	0.762472i	$-0.276014\pi$
$601$	1.07860e6	+	783652.i	0.121808	+	0.0884987i	−0.525213	+	0.850971i	$0.676014\pi$
$602$	5.79173e6	−	4.20794e6i	0.651354	−	0.473237i
$603$		0			0
$604$	7.49558e6			0.836013
$605$	−3.99614e6	+	760529.i	−0.443866	+	0.0844749i
$606$		0			0
$607$	−1.45982e6	+	4.49285e6i	−0.160815	+	0.494937i	−0.998704	−	0.0509038i	$-0.983790\pi$
$607$	−1.45982e6	+	4.49285e6i	−0.160815	+	0.494937i	0.837889	+	0.545841i	$0.183790\pi$
$608$	−1.77998e6	+	1.29323e6i	−0.195279	+	0.141878i
$609$		0			0
$610$	−1.60554e6	−	4.94133e6i	−0.174701	−	0.537675i
$611$	−430067.	−	1.32361e6i	−0.0466051	−	0.143436i
$612$		0			0
$613$	1.14800e7	−	8.34070e6i	1.23393	−	0.896502i	0.236751	−	0.971570i	$-0.423917\pi$
$613$	1.14800e7	−	8.34070e6i	1.23393	−	0.896502i	0.997178	+	0.0750679i	$0.0239173\pi$
$614$	2.88398e6	−	8.87599e6i	0.308725	−	0.950158i
$615$		0			0
$616$	2.00955e6	−	1.77089e6i	0.213377	−	0.188036i
$617$	1.04163e7			1.10154			0.550769	−	0.834657i	$-0.314334\pi$
$617$	1.04163e7			1.10154			0.550769	+	0.834657i	$0.314334\pi$
$618$		0			0
$619$	−4.34082e6	+	3.15379e6i	−0.455350	+	0.330831i	−0.791704	−	0.610904i	$-0.790806\pi$
$619$	−4.34082e6	+	3.15379e6i	−0.455350	+	0.330831i	0.336354	+	0.941735i	$0.390806\pi$
$620$	205026.	+	148960.i	0.0214205	+	0.0155629i
$621$		0			0
$622$	−3.61443e6	−	1.11241e7i	−0.374597	−	1.15289i
$623$	44156.0	+	32081.2i	0.00455795	+	0.00331155i
$624$		0			0
$625$	1.29528e6	−	3.98645e6i	0.132636	−	0.408212i
$626$	7.05045e6			0.719086
$627$		0			0
$628$	3.56673e6			0.360887
$629$	−8.56985e6	+	2.63753e7i	−0.863668	+	2.65810i
$630$		0			0
$631$	9.52352e6	+	6.91925e6i	0.952191	+	0.691808i	0.951324	−	0.308192i	$-0.0997239\pi$
$631$	9.52352e6	+	6.91925e6i	0.952191	+	0.691808i	0.000867307		1.00000i	$0.499724\pi$
$632$	308579.	+	949710.i	0.0307308	+	0.0945798i
$633$		0			0
$634$	−8.84458e6	−	6.42596e6i	−0.873885	−	0.634914i
$635$	−678312.	+	492823.i	−0.0667568	+	0.0485016i
$636$		0			0
$637$	−2.77556e6			−0.271020
$638$	−1.86559e6	+	8.33780e6i	−0.181454	+	0.810961i
$639$		0			0
$640$	−127881.	+	393576.i	−0.0123411	+	0.0379821i
$641$	6.47350e6	−	4.70327e6i	0.622292	−	0.452121i	−0.231430	−	0.972852i	$-0.574340\pi$
$641$	6.47350e6	−	4.70327e6i	0.622292	−	0.452121i	0.853721	+	0.520730i	$0.174340\pi$
$642$		0			0
$643$	−4.59546e6	−	1.41434e7i	−0.438330	−	1.34904i	−0.889635	−	0.456672i	$-0.849041\pi$
$643$	−4.59546e6	−	1.41434e7i	−0.438330	−	1.34904i	0.451305	−	0.892370i	$-0.350959\pi$
$644$	1.07332e6	+	3.30335e6i	0.101980	+	0.313863i
$645$		0			0
$646$	−1.17947e7	+	8.56933e6i	−1.11200	+	0.807915i
$647$	1.57748e6	−	4.85497e6i	0.148150	−	0.455959i	−0.849252	−	0.527987i	$-0.822947\pi$
$647$	1.57748e6	−	4.85497e6i	0.148150	−	0.455959i	0.997403	+	0.0720276i	$0.0229470\pi$
$648$		0			0
$649$	−3.28203e6	+	309534.i	−0.305866	+	0.0288467i
$650$	−4.65528e6			−0.432177
$651$		0			0
$652$	−4.73126e6	+	3.43746e6i	−0.435871	+	0.316678i
$653$	−1.19042e7	−	8.64893e6i	−1.09249	−	0.793742i	−0.112674	−	0.993632i	$-0.535942\pi$
$653$	−1.19042e7	−	8.64893e6i	−1.09249	−	0.793742i	−0.979818	+	0.199890i	$0.935942\pi$
$654$		0			0
$655$	1.88130e6	+	5.79006e6i	0.171339	+	0.527326i
$656$	−4.00441e6	−	2.90938e6i	−0.363312	−	0.263961i
$657$		0			0
$658$	383372.	−	1.17990e6i	0.0345188	−	0.106238i
$659$	1.52006e7			1.36347			0.681736	−	0.731599i	$-0.261225\pi$
$659$	1.52006e7			1.36347			0.681736	+	0.731599i	$0.261225\pi$
$660$		0			0
$661$	−985356.			−0.0877182			−0.0438591	−	0.999038i	$-0.513965\pi$
$661$	−985356.			−0.0877182			−0.0438591	+	0.999038i	$0.513965\pi$
$662$	−4.46690e6	+	1.37477e7i	−0.396151	+	1.21923i
$663$		0			0
$664$	4.66075e6	+	3.38623e6i	0.410238	+	0.298055i
$665$	1.74893e6	+	5.38264e6i	0.153362	+	0.471999i
$666$		0			0
$667$	−8.96342e6	−	6.51231e6i	−0.780116	−	0.566787i
$668$	−1.21681e6	+	884065.i	−0.105507	+	0.0766554i
$669$		0			0
$670$	−651414.			−0.0560622
$671$	−1.77613e7	−	1.05091e7i	−1.52289	−	0.901075i
$672$		0			0
$673$	−3.39533e6	+	1.04497e7i	−0.288964	+	0.889341i	0.696218	+	0.717830i	$0.254865\pi$
$673$	−3.39533e6	+	1.04497e7i	−0.288964	+	0.889341i	−0.985182	+	0.171510i	$0.945135\pi$
$674$	−2.85849e6	+	2.07681e6i	−0.242374	+	0.176095i
$675$		0			0
$676$	−753059.	−	2.31768e6i	−0.0633815	−	0.195068i
$677$	−2.95074e6	−	9.08145e6i	−0.247434	−	0.761524i	−0.995227	−	0.0975911i	$-0.968886\pi$
$677$	−2.95074e6	−	9.08145e6i	−0.247434	−	0.761524i	0.747793	−	0.663932i	$-0.231114\pi$
$678$		0			0
$679$	−1.21202e6	+	880587.i	−0.100887	+	0.0732990i
$680$	−847378.	+	2.60796e6i	−0.0702756	+	0.216286i
$681$		0			0
$682$	1.00218e6	−	94517.6i	0.0825061	−	0.00778129i
$683$	2.33727e7			1.91716			0.958579	−	0.284827i	$-0.0919361\pi$
$683$	2.33727e7			1.91716			0.958579	+	0.284827i	$0.0919361\pi$
$684$		0			0
$685$	4.59519e6	−	3.33860e6i	0.374177	−	0.271856i
$686$	−7.67369e6	−	5.57526e6i	−0.622578	−	0.452330i
$687$		0			0
$688$	1.35764e6	+	4.17837e6i	0.109348	+	0.336540i
$689$	−3.30500e6	−	2.40122e6i	−0.265230	−	0.192701i
$690$		0			0
$691$	−4.04777e6	+	1.24578e7i	−0.322493	+	0.992533i	0.650066	+	0.759878i	$0.274741\pi$
$691$	−4.04777e6	+	1.24578e7i	−0.322493	+	0.992533i	−0.972559	+	0.232655i	$0.925259\pi$
$692$	1.30062e6			0.103248
$693$		0			0
$694$	−3.77923e6			−0.297855
$695$	−2.68751e6	+	8.27130e6i	−0.211051	+	0.649549i
$696$		0			0
$697$	−2.65345e7	−	1.92784e7i	−2.06885	−	1.50311i
$698$	5.24666e6	+	1.61476e7i	0.407610	+	1.25449i
$699$		0			0
$700$	−3.35728e6	−	2.43920e6i	−0.258966	−	0.188150i
$701$	9.27946e6	−	6.74192e6i	0.713227	−	0.518190i	−0.170986	−	0.985273i	$-0.554695\pi$
$701$	9.27946e6	−	6.74192e6i	0.713227	−	0.518190i	0.884213	+	0.467084i	$0.154695\pi$
$702$		0			0
$703$	−3.51265e7			−2.68069
$704$	652498.	+	1.50872e6i	0.0496189	+	0.114730i
$705$		0			0
$706$	3.56002e6	−	1.09566e7i	0.268807	−	0.827304i
$707$	−1.30763e7	+	9.50047e6i	−0.983865	+	0.714820i
$708$		0			0
$709$	−4.22514e6	−	1.30037e7i	−0.315665	−	0.971516i	−0.975480	−	0.220088i	$-0.929366\pi$
$709$	−4.22514e6	−	1.30037e7i	−0.315665	−	0.971516i	0.659815	−	0.751428i	$-0.270634\pi$
$710$	−794051.	−	2.44384e6i	−0.0591157	−	0.181939i
$711$		0			0
$712$	−27098.2	+	19688.0i	−0.00200327	+	0.00145546i
$713$	−403375.	+	1.24146e6i	−0.0297156	+	0.0914553i
$714$		0			0
$715$	3.55875e6	−	3.13611e6i	0.260335	−	0.229417i
$716$	5.41376e6			0.394654
$717$		0			0
$718$	527387.	−	383169.i	0.0381784	−	0.0277382i
$719$	−1.28855e7	−	9.36188e6i	−0.929565	−	0.675369i	0.0163211	−	0.999867i	$-0.494805\pi$
$719$	−1.28855e7	−	9.36188e6i	−0.929565	−	0.675369i	−0.945886	+	0.324498i	$0.894805\pi$
$720$		0			0
$721$	1.59153e6	+	4.89822e6i	0.114019	+	0.350914i
$722$	−6.92648e6	−	5.03238e6i	−0.494504	−	0.359278i
$723$		0			0
$724$	543544.	−	1.67286e6i	0.0385379	−	0.118608i
$725$	1.32372e7			0.935303
$726$		0			0
$727$	−1.09989e7			−0.771815			−0.385907	−	0.922538i	$-0.626112\pi$
$727$	−1.09989e7			−0.771815			−0.385907	+	0.922538i	$0.626112\pi$
$728$	−965157.	+	2.97045e6i	−0.0674947	+	0.207727i
$729$		0			0
$730$	−4.08683e6	−	2.96925e6i	−0.283844	−	0.206225i
$731$	8.99612e6	+	2.76872e7i	0.622676	+	1.91640i
$732$		0			0
$733$	1.76367e7	+	1.28138e7i	1.21243	+	0.880883i	0.995449	−	0.0952923i	$-0.0303786\pi$
$733$	1.76367e7	+	1.28138e7i	1.21243	+	0.880883i	0.216982	+	0.976176i	$0.430379\pi$
$734$	−9.76257e6	+	7.09292e6i	−0.668843	+	0.485943i
$735$		0			0
$736$	−2.13156e6			−0.145045
$737$	−1.94126e6	+	1.71071e6i	−0.131648	+	0.116013i
$738$		0			0
$739$	−820710.	+	2.52588e6i	−0.0552813	+	0.170138i	−0.974885	−	0.222709i	$-0.928510\pi$
$739$	−820710.	+	2.52588e6i	−0.0552813	+	0.170138i	0.919604	+	0.392848i	$0.128510\pi$
$740$	−5.34514e6	+	3.88347e6i	−0.358823	+	0.260700i
$741$		0			0
$742$	−1.12533e6	−	3.46341e6i	−0.0750361	−	0.230937i
$743$	4.88726e6	+	1.50414e7i	0.324783	+	0.999579i	0.971538	+	0.236882i	$0.0761254\pi$
$743$	4.88726e6	+	1.50414e7i	0.324783	+	0.999579i	−0.646755	+	0.762697i	$0.723875\pi$
$744$		0			0
$745$	5.61839e6	−	4.08200e6i	0.370869	−	0.269452i
$746$	−756977.	+	2.32974e6i	−0.0498007	+	0.153271i
$747$		0			0
$748$	4.32365e6	+	9.99725e6i	0.282551	+	0.653321i
$749$	−1.46229e7			−0.952422
$750$		0			0
$751$	1.86618e7	−	1.35586e7i	1.20741	−	0.877235i	0.212417	−	0.977179i	$-0.431866\pi$
$751$	1.86618e7	−	1.35586e7i	1.20741	−	0.877235i	0.994993	+	0.0999443i	$0.0318665\pi$
$752$	615951.	+	447514.i	0.0397193	+	0.0288578i
$753$		0			0
$754$	−3.07869e6	−	9.47523e6i	−0.197214	−	0.606962i
$755$	9.57295e6	+	6.95516e6i	0.611193	+	0.444058i
$756$		0			0
$757$	425290.	−	1.30891e6i	0.0269740	−	0.0830175i	−0.936663	−	0.350231i	$-0.886103\pi$
$757$	425290.	−	1.30891e6i	0.0269740	−	0.0830175i	0.963637	+	0.267214i	$0.0861030\pi$
$758$	−1.51331e6			−0.0956651
$759$		0			0
$760$	−3.47327e6			−0.218125
$761$	34696.5	−	106785.i	0.00217182	−	0.00668418i	−0.949965	−	0.312357i	$-0.898881\pi$
$761$	34696.5	−	106785.i	0.00217182	−	0.00668418i	0.952137	+	0.305673i	$0.0988814\pi$
$762$		0			0
$763$	−1.65255e7	−	1.20065e7i	−1.02765	−	0.746629i
$764$	2.77391e6	+	8.53722e6i	0.171933	+	0.529155i
$765$		0			0
$766$	−1.29805e6	−	943090.i	−0.0799319	−	0.0580739i
$767$	3.10991e6	−	2.25948e6i	0.190879	−	0.138682i
$768$		0			0
$769$	−1.44858e7			−0.883334			−0.441667	−	0.897179i	$-0.645613\pi$
$769$	−1.44858e7			−0.883334			−0.441667	+	0.897179i	$0.645613\pi$
$770$	4.20970e6	−	397024.i	0.255873	−	0.0241318i
$771$		0			0
$772$	−1.24717e6	+	3.83841e6i	−0.0753154	+	0.231797i
$773$	2.53862e7	−	1.84441e7i	1.52809	−	1.11022i	0.570797	−	0.821091i	$-0.306634\pi$
$773$	2.53862e7	−	1.84441e7i	1.52809	−	1.11022i	0.957290	−	0.289129i	$-0.0933657\pi$
$774$		0			0
$775$	−481937.	−	1.48325e6i	−0.0288228	−	0.0887074i
$776$	−284110.	−	874400.i	−0.0169368	−	0.0521262i
$777$		0			0
$778$	−2.20155e6	+	1.59952e6i	−0.130401	+	0.0947416i
$779$	1.28375e7	−	3.95097e7i	0.757942	−	2.33271i
$780$		0			0
$781$	−8.78421e6	−	5.19751e6i	−0.515318	−	0.304907i
$782$	−1.41244e7			−0.825949
$783$		0			0
$784$	1.22841e6	−	892490.i	0.0713760	−	0.0518577i
$785$	4.55524e6	+	3.30957e6i	0.263838	+	0.191689i
$786$		0			0
$787$	−1.24279e6	−	3.82492e6i	−0.0715255	−	0.220133i	0.908903	−	0.417007i	$-0.136921\pi$
$787$	−1.24279e6	−	3.82492e6i	−0.0715255	−	0.220133i	−0.980429	+	0.196874i	$0.936921\pi$
$788$	−6.43395e6	−	4.67454e6i	−0.369115	−	0.268178i
$789$		0			0
$790$	−487135.	+	1.49925e6i	−0.0277704	+	0.0854685i
$791$	9.50045e6			0.539887
$792$		0			0
$793$	2.40647e7			1.35893
$794$	−564817.	+	1.73833e6i	−0.0317948	+	0.0978544i
$795$		0			0
$796$	−4.54637e6	−	3.30313e6i	−0.254321	−	0.184775i
$797$	−2.89427e6	−	8.90764e6i	−0.161396	−	0.496726i	0.837357	−	0.546657i	$-0.184100\pi$
$797$	−2.89427e6	−	8.90764e6i	−0.161396	−	0.496726i	−0.998753	+	0.0499311i	$0.984100\pi$
$798$		0			0
$799$	4.08148e6	+	2.96537e6i	0.226178	+	0.164328i
$800$	2.06033e6	−	1.49692e6i	0.113818	−	0.0826939i
$801$		0			0
$802$	7.89450e6			0.433400
$803$	−1.99767e7	+	1.88404e6i	−1.09329	+	0.103110i
$804$		0			0
$805$	−1.69439e6	+	5.21480e6i	−0.0921560	+	0.283627i
$806$	−949624.	+	689942.i	−0.0514889	+	0.0374089i
$807$		0			0
$808$	−3.06520e6	−	9.43371e6i	−0.165170	−	0.508340i
$809$	−1.30781e6	−	4.02504e6i	−0.0702546	−	0.216221i	0.909765	−	0.415125i	$-0.136262\pi$
$809$	−1.30781e6	−	4.02504e6i	−0.0702546	−	0.216221i	−0.980019	+	0.198903i	$0.936262\pi$
$810$		0			0
$811$	2.47254e7	−	1.79640e7i	1.32005	−	0.959074i	0.320120	−	0.947377i	$-0.396277\pi$
$811$	2.47254e7	−	1.79640e7i	1.32005	−	0.959074i	0.999932	−	0.0116971i	$-0.00372339\pi$
$812$	2.74442e6	−	8.44645e6i	0.146070	−	0.449556i
$813$		0			0
$814$	−5.73031e6	+	2.56102e7i	−0.303122	+	1.35473i
$815$	−9.23213e6			−0.486864
$816$		0			0
$817$	−2.98315e7	+	2.16738e7i	−1.56358	+	1.13601i
$818$	−1.27292e7	−	9.24827e6i	−0.665145	−	0.483256i
$819$		0			0
$820$	−2.41461e6	−	7.43139e6i	−0.125404	−	0.385954i
$821$	−3.50196e6	−	2.54433e6i	−0.181323	−	0.131739i	0.493421	−	0.869791i	$-0.335746\pi$
$821$	−3.50196e6	−	2.54433e6i	−0.181323	−	0.131739i	−0.674744	+	0.738051i	$0.735746\pi$
$822$		0			0
$823$	−4.07659e6	+	1.25465e7i	−0.209796	+	0.645686i	0.789686	+	0.613511i	$0.210243\pi$
$823$	−4.07659e6	+	1.25465e7i	−0.209796	+	0.645686i	−0.999482	+	0.0321750i	$0.989757\pi$
$824$	−3.16069e6			−0.162168
$825$		0			0
$826$	3.42668e6			0.174753
$827$	2.02884e6	−	6.24413e6i	0.103153	−	0.317474i	−0.886139	−	0.463419i	$-0.846622\pi$
$827$	2.02884e6	−	6.24413e6i	0.103153	−	0.317474i	0.989293	+	0.145945i	$0.0466224\pi$
$828$		0			0
$829$	−1.96402e7	−	1.42694e7i	−0.992567	−	0.721142i	−0.0320852	−	0.999485i	$-0.510215\pi$
$829$	−1.96402e7	−	1.42694e7i	−0.992567	−	0.721142i	−0.960482	+	0.278343i	$0.910215\pi$
$830$	2.81037e6	+	8.64943e6i	0.141602	+	0.435805i
$831$		0			0
$832$	−1.55068e6	−	1.12664e6i	−0.0776632	−	0.0564256i
$833$	8.13981e6	−	5.91392e6i	0.406445	−	0.295300i
$834$		0			0
$835$	−2.37437e6			−0.117851
$836$	−1.03506e7	+	9.12134e6i	−0.512212	+	0.451381i
$837$		0			0
$838$	−6.56992e6	+	2.02201e7i	−0.323184	+	0.994658i
$839$	2.02828e7	−	1.47363e7i	0.994770	−	0.722742i	0.0338092	−	0.999428i	$-0.489236\pi$
$839$	2.02828e7	−	1.47363e7i	0.994770	−	0.722742i	0.960960	+	0.276686i	$0.0892361\pi$
$840$		0			0
$841$	2.41594e6	+	7.43550e6i	0.117787	+	0.362510i
$842$	4.72919e6	+	1.45549e7i	0.229883	+	0.707506i
$843$		0			0
$844$	2.71654e6	−	1.97368e6i	0.131269	−	0.0953722i
$845$	1.18881e6	−	3.65878e6i	0.0572757	−	0.176276i
$846$		0			0
$847$	1.15026e7	−	1.22385e7i	0.550917	−	0.586164i
$848$	2.23485e6			0.106723
$849$		0			0
$850$	1.36524e7	−	9.91906e6i	0.648130	−	0.470894i
$851$	−2.75318e7	−	2.00030e7i	−1.30320	−	0.946830i
$852$		0			0
$853$	−2.32831e6	−	7.16580e6i	−0.109564	−	0.337203i	0.881210	−	0.472724i	$-0.156729\pi$
$853$	−2.32831e6	−	7.16580e6i	−0.109564	−	0.337203i	−0.990775	+	0.135521i	$0.956729\pi$
$854$	1.73549e7	+	1.26091e7i	0.814288	+	0.591615i
$855$		0			0
$856$	2.77310e6	−	8.53474e6i	0.129355	−	0.398112i
$857$	1.52614e7			0.709812			0.354906	−	0.934902i	$-0.384513\pi$
$857$	1.52614e7			0.709812			0.354906	+	0.934902i	$0.384513\pi$
$858$		0			0
$859$	1.23887e7			0.572855			0.286427	−	0.958102i	$-0.407532\pi$
$859$	1.23887e7			0.572855			0.286427	+	0.958102i	$0.407532\pi$
$860$	−2.14322e6	+	6.59614e6i	−0.0988143	+	0.304119i
$861$		0			0
$862$	2.07470e7	+	1.50736e7i	0.951016	+	0.690954i
$863$	6.87320e6	+	2.11535e7i	0.314147	+	0.966844i	0.976104	+	0.217302i	$0.0697258\pi$
$863$	6.87320e6	+	2.11535e7i	0.314147	+	0.966844i	−0.661958	+	0.749541i	$0.730274\pi$
$864$		0			0
$865$	1.66108e6	+	1.20684e6i	0.0754830	+	0.0548416i
$866$	−6.18660e6	+	4.49483e6i	−0.280322	+	0.203666i
$867$		0			0
$868$	−1.04635e6			−0.0471388
$869$	2.48556e6	+	5.74716e6i	0.111654	+	0.258169i
$870$		0			0
$871$	932357.	−	2.86950e6i	0.0416425	−	0.128162i
$872$	1.01416e7	−	7.36828e6i	0.451662	−	0.328152i
$873$		0			0
$874$	−5.52837e6	−	1.70146e7i	−0.244804	−	0.753429i
$875$	−4.56809e6	−	1.40591e7i	−0.201704	−	0.620781i
$876$		0			0
$877$	−2.49267e7	+	1.81103e7i	−1.09437	+	0.795109i	−0.980133	−	0.198344i	$-0.936444\pi$
$877$	−2.49267e7	+	1.81103e7i	−1.09437	+	0.795109i	−0.114242	+	0.993453i	$0.536444\pi$
$878$	−767113.	+	2.36093e6i	−0.0335833	+	0.103359i
$879$		0			0
$880$	−566607.	+	2.53231e6i	−0.0246647	+	0.110233i
$881$	1.15457e7			0.501164			0.250582	−	0.968095i	$-0.419378\pi$
$881$	1.15457e7			0.501164			0.250582	+	0.968095i	$0.419378\pi$
$882$		0			0
$883$	−7.61834e6	+	5.53505e6i	−0.328820	+	0.238902i	−0.739930	−	0.672684i	$-0.765141\pi$
$883$	−7.61834e6	+	5.53505e6i	−0.328820	+	0.238902i	0.411110	+	0.911586i	$0.365141\pi$
$884$	−1.02753e7	−	7.46546e6i	−0.442247	−	0.321311i
$885$		0			0
$886$	5.75457e6	+	1.77108e7i	0.246280	+	0.757971i
$887$	−5.19522e6	−	3.77455e6i	−0.221715	−	0.161085i	0.471383	−	0.881928i	$-0.343755\pi$
$887$	−5.19522e6	−	3.77455e6i	−0.221715	−	0.161085i	−0.693098	+	0.720843i	$0.743755\pi$
$888$		0			0
$889$	1.06975e6	−	3.29235e6i	0.0453970	−	0.139718i
$890$	−52876.8			−0.00223764
$891$		0			0
$892$	−1.26248e6			−0.0531268
$893$	−1.97464e6	+	6.07731e6i	−0.0828626	+	0.255025i
$894$		0			0
$895$	6.91416e6	+	5.02343e6i	0.288524	+	0.209625i
$896$	−527998.	−	1.62501e6i	−0.0219716	−	0.0676217i
$897$		0			0
$898$	−2.17071e7	−	1.57711e7i	−0.898279	−	0.652638i
$899$	2.70025e6	−	1.96184e6i	0.111431	−	0.0809591i
$900$		0			0
$901$	1.48088e7			0.607726
$902$	−2.67117e7	−	1.58050e7i	−1.09316	−	0.646810i
$903$		0			0
$904$	−1.80168e6	+	5.54499e6i	−0.0733256	+	0.225673i
$905$	2.24643e6	−	1.63213e6i	0.0911741	−	0.0662419i
$906$		0			0
$907$	4.63893e6	+	1.42772e7i	0.187240	+	0.576267i	0.999980	−	0.00636064i	$-0.00202467\pi$
$907$	4.63893e6	+	1.42772e7i	0.187240	+	0.576267i	−0.812739	+	0.582627i	$0.802025\pi$
$908$	3.06684e6	+	9.43875e6i	0.123446	+	0.379927i
$909$		0			0
$910$	−3.98893e6	+	2.89813e6i	−0.159681	+	0.116015i
$911$	8.81694e6	−	2.71357e7i	0.351983	−	1.08329i	−0.605755	−	0.795651i	$-0.707129\pi$
$911$	8.81694e6	−	2.71357e7i	0.351983	−	1.08329i	0.957738	−	0.287641i	$-0.0928711\pi$
$912$		0			0
$913$	3.10898e7	+	1.83955e7i	1.23436	+	0.730354i
$914$	1.85011e6			0.0732540
$915$		0			0
$916$	2.64146e6	−	1.91913e6i	0.104017	−	0.0755730i
$917$	−2.03358e7	−	1.47748e7i	−0.798616	−	0.580228i
$918$		0			0
$919$	1.19247e7	+	3.67006e7i	0.465758	+	1.43346i	0.858027	+	0.513605i	$0.171690\pi$
$919$	1.19247e7	+	3.67006e7i	0.465758	+	1.43346i	−0.392269	+	0.919851i	$0.628310\pi$
$920$	−2.72232e6	−	1.97788e6i	−0.106040	−	0.0770425i
$921$		0			0
$922$	7.24973e6	−	2.23124e7i	0.280863	−	0.864408i
$923$	1.19017e7			0.459838
$924$		0			0
$925$	4.06592e7			1.56244
$926$	−2.68299e6	+	8.25740e6i	−0.102823	+	0.316458i
$927$		0			0
$928$	4.40936e6	+	3.20359e6i	0.168076	+	0.122114i
$929$	9.45612e6	+	2.91029e7i	0.359479	+	1.10636i	0.953367	+	0.301815i	$0.0975924\pi$
$929$	9.45612e6	+	2.91029e7i	0.359479	+	1.10636i	−0.593887	+	0.804548i	$0.702408\pi$
$930$		0			0
$931$	1.03100e7	+	7.49066e6i	0.389838	+	0.283234i
$932$	2.88698e6	−	2.09752e6i	0.108869	−	0.0790980i
$933$		0			0
$934$	2.85745e7			1.07180
$935$	−3.75452e6	+	1.67799e7i	−0.140451	+	0.627711i
$936$		0			0
$937$	181783.	−	559470.i	0.00676400	−	0.0208175i	−0.947618	−	0.319407i	$-0.896516\pi$
$937$	181783.	−	559470.i	0.00676400	−	0.0208175i	0.954382	+	0.298590i	$0.0965162\pi$
$938$	2.17591e6	−	1.58089e6i	0.0807485	−	0.0586672i
$939$		0			0
$940$	371410.	+	1.14308e6i	0.0137099	+	0.0421947i
$941$	−2.78264e6	−	8.56408e6i	−0.102443	−	0.315287i	0.886679	−	0.462386i	$-0.153007\pi$
$941$	−2.78264e6	−	8.56408e6i	−0.102443	−	0.315287i	−0.989122	+	0.147099i	$0.953007\pi$
$942$		0			0
$943$	3.25609e7	−	2.36569e7i	1.19239	−	0.866321i
$944$	−649840.	+	2.00000e6i	−0.0237343	+	0.0730466i
$945$		0			0
$946$	1.09355e7	+	2.52854e7i	0.397294	+	0.918632i
$947$	1.61542e7			0.585344			0.292672	−	0.956213i	$-0.405456\pi$
$947$	1.61542e7			0.585344			0.292672	+	0.956213i	$0.405456\pi$
$948$		0			0
$949$	1.89291e7	−	1.37528e7i	0.682282	−	0.495707i
$950$	1.72923e7	+	1.25636e7i	0.621648	+	0.451654i
$951$		0			0
$952$	−3.49868e6	−	1.07678e7i	−0.125116	−	0.385067i
$953$	−2.68998e7	−	1.95439e7i	−0.959439	−	0.697073i	−0.00641861	−	0.999979i	$-0.502043\pi$
$953$	−2.68998e7	−	1.95439e7i	−0.959439	−	0.697073i	−0.953020	+	0.302906i	$0.902043\pi$
$954$		0			0
$955$	−4.37901e6	+	1.34772e7i	−0.155370	+	0.478180i
$956$	1.20053e6			0.0424841
$957$		0			0
$958$	2.21147e7			0.778515
$959$	−7.24695e6	+	2.23038e7i	−0.254454	+	0.783128i
$960$		0			0
$961$	2.28433e7	+	1.65967e7i	0.797905	+	0.579712i
$962$	−9.45643e6	−	2.91039e7i	−0.329450	−	1.01394i
$963$		0			0
$964$	−6.60649e6	−	4.79989e6i	−0.228970	−	0.166356i
$965$	−5.15448e6	+	3.74495e6i	−0.178183	+	0.129458i
$966$		0			0
$967$	−4.11872e7			−1.41643			−0.708217	−	0.705995i	$-0.750500\pi$
$967$	−4.11872e7			−1.41643			−0.708217	+	0.705995i	$0.750500\pi$
$968$	4.96169e6	+	9.03445e6i	0.170193	+	0.309894i
$969$		0			0
$970$	448507.	−	1.38036e6i	0.0153052	−	0.0471046i
$971$	−1.01875e7	+	7.40164e6i	−0.346752	+	0.251930i	−0.747505	−	0.664256i	$-0.768748\pi$
$971$	−1.01875e7	+	7.40164e6i	−0.346752	+	0.251930i	0.400753	+	0.916186i	$0.368748\pi$
$972$		0			0
$973$	−1.10963e7	−	3.41508e7i	−0.375746	−	1.15643i
$974$	−8.88121e6	−	2.73335e7i	−0.299968	−	0.923206i
$975$		0			0
$976$	−1.06506e7	+	7.73809e6i	−0.357889	+	0.260021i
$977$	754731.	−	2.32282e6i	0.0252962	−	0.0778538i	−0.937611	−	0.347685i	$-0.886968\pi$
$977$	754731.	−	2.32282e6i	0.0252962	−	0.0778538i	0.962908	+	0.269831i	$0.0869679\pi$
$978$		0			0
$979$	−157577.	+	138862.i	−0.00525454	+	0.00463050i
$980$	2.39700e6			0.0797265
$981$		0			0
$982$	−3.17327e7	+	2.30552e7i	−1.05010	+	0.762939i
$983$	4.16285e7	+	3.02449e7i	1.37406	+	0.998316i	0.997407	+	0.0719633i	$0.0229264\pi$
$983$	4.16285e7	+	3.02449e7i	1.37406	+	0.998316i	0.376657	+	0.926353i	$0.377074\pi$
$984$		0			0
$985$	−3.87958e6	−	1.19401e7i	−0.127407	−	0.392120i
$986$	2.92178e7	+	2.12280e7i	0.957095	+	0.695370i
$987$		0			0
$988$	4.97124e6	−	1.52999e7i	0.162021	−	0.498650i
$989$	−3.57239e7			−1.16136
$990$		0			0
$991$	1.02761e7			0.332388			0.166194	−	0.986093i	$-0.446852\pi$
$991$	1.02761e7			0.332388			0.166194	+	0.986093i	$0.446852\pi$
$992$	198431.	−	610709.i	0.00640223	−	0.0197040i
$993$		0			0
$994$	8.58323e6	+	6.23608e6i	0.275540	+	0.200192i
$995$	−2.74140e6	−	8.43715e6i	−0.0877838	−	0.270171i
$996$		0			0
$997$	4.65020e7	+	3.37857e7i	1.48161	+	1.07645i	0.977034	+	0.213085i	$0.0683510\pi$
$997$	4.65020e7	+	3.37857e7i	1.48161	+	1.07645i	0.504576	+	0.863368i	$0.331649\pi$
$998$	2.20480e7	−	1.60188e7i	0.700719	−	0.509102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.g.163.3	✓	20
3.2	odd	2		198.6.f.h.163.3	yes	20
11.5	even	5	inner	198.6.f.g.181.3	yes	20
33.5	odd	10		198.6.f.h.181.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.f.g.163.3	✓	20	1.1	even	1	trivial
198.6.f.g.181.3	yes	20	11.5	even	5	inner
198.6.f.h.163.3	yes	20	3.2	odd	2
198.6.f.h.181.3	yes	20	33.5	odd	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)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-7.80522 - 24.0220i) q^{5} +(84.3699 + 61.2983i) q^{7} +(-51.7771 + 37.6183i) q^{8} +O(q^{10})\)	\(q+(1.23607 - 3.80423i) q^{2} +(-12.9443 - 9.40456i) q^{4} +(-7.80522 - 24.0220i) q^{5} +(84.3699 + 61.2983i) q^{7} +(-51.7771 + 37.6183i) q^{8} -101.033 q^{10} +(-301.085 + 265.328i) q^{11} +(144.607 - 445.053i) q^{13} +(337.480 - 245.193i) q^{14} +(79.1084 + 243.470i) q^{16} +(524.197 + 1613.31i) q^{17} +(-1738.26 + 1262.92i) q^{19} +(-124.884 + 384.352i) q^{20} +(637.205 + 1473.36i) q^{22} -2081.60 q^{23} +(2012.04 - 1461.83i) q^{25} +(-1514.34 - 1100.23i) q^{26} +(-515.623 - 1586.92i) q^{28} +(4306.01 + 3128.50i) q^{29} +(193.781 - 596.396i) q^{31} +1024.00 q^{32} +6785.35 q^{34} +(813.983 - 2505.18i) q^{35} +(13226.2 + 9609.43i) q^{37} +(2655.82 + 8173.78i) q^{38} +(1307.80 + 950.170i) q^{40} +(-15642.2 + 11364.7i) q^{41} +17161.7 q^{43} +(6392.62 - 602.899i) q^{44} +(-2573.00 + 7918.89i) q^{46} +(2406.06 - 1748.10i) q^{47} +(-1832.85 - 5640.94i) q^{49} +(-3074.13 - 9461.19i) q^{50} +(-6057.36 + 4400.93i) q^{52} +(2697.68 - 8302.59i) q^{53} +(8723.74 + 5161.73i) q^{55} -6674.36 q^{56} +(17224.1 - 12514.0i) q^{58} +(6645.71 + 4828.39i) q^{59} +(15891.2 + 48908.2i) q^{61} +(-2029.30 - 1474.37i) q^{62} +(1265.73 - 3895.53i) q^{64} -11819.8 q^{65} +6447.54 q^{67} +(8387.15 - 25813.0i) q^{68} +(-8524.14 - 6193.15i) q^{70} +(7859.33 + 24188.5i) q^{71} +(40450.5 + 29389.0i) q^{73} +(52905.0 - 38437.7i) q^{74} +34377.7 q^{76} +(-41666.7 + 3929.65i) q^{77} +(4821.55 - 14839.2i) q^{79} +(5231.19 - 3800.68i) q^{80} +(23899.2 + 73554.2i) q^{82} +(-27816.4 - 85610.0i) q^{83} +(34663.5 - 25184.5i) q^{85} +(21213.1 - 65287.1i) q^{86} +(5608.15 - 25064.2i) q^{88} +523.362 q^{89} +(39481.5 - 28685.0i) q^{91} +(26944.9 + 19576.6i) q^{92} +(-3676.13 - 11314.0i) q^{94} +(43905.3 + 31899.1i) q^{95} +(-4439.21 + 13662.5i) q^{97} -23724.9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8	\( 20 q - 20 q^{2} - 80 q^{4} - 112 q^{5} - 392 q^{7} - 320 q^{8} + 552 q^{10} + 60 q^{11} - 420 q^{13} - 1568 q^{14} - 1280 q^{16} + 712 q^{17} - 898 q^{19} - 1792 q^{20} + 2020 q^{22} + 1180 q^{23} - 1079 q^{25} - 2880 q^{26} + 4688 q^{28} + 517 q^{29} - 5551 q^{31} + 20480 q^{32} - 6992 q^{34} + 14325 q^{35} - 7584 q^{37} - 1832 q^{38} + 2752 q^{40} - 16868 q^{41} - 704 q^{43} + 8080 q^{44} - 11400 q^{46} - 38866 q^{47} - 22573 q^{49} - 5416 q^{50} - 11520 q^{52} - 97517 q^{53} + 14404 q^{55} + 12672 q^{56} + 2068 q^{58} - 52682 q^{59} + 73874 q^{61} + 21136 q^{62} - 20480 q^{64} + 236352 q^{65} - 267432 q^{67} + 11392 q^{68} - 67660 q^{70} + 20588 q^{71} + 97257 q^{73} - 30336 q^{74} + 43392 q^{76} + 100582 q^{77} + 37498 q^{79} + 11008 q^{80} - 3672 q^{82} - 140952 q^{83} - 158376 q^{85} - 75136 q^{86} - 63040 q^{88} + 168796 q^{89} + 173196 q^{91} + 36160 q^{92} + 45376 q^{94} - 518002 q^{95} - 225802 q^{97} + 396808 q^{98}+O(q^{100}) \) 20 * q - 20 * q^2 - 80 * q^4 - 112 * q^5 - 392 * q^7 - 320 * q^8 + 552 * q^10 + 60 * q^11 - 420 * q^13 - 1568 * q^14 - 1280 * q^16 + 712 * q^17 - 898 * q^19 - 1792 * q^20 + 2020 * q^22 + 1180 * q^23 - 1079 * q^25 - 2880 * q^26 + 4688 * q^28 + 517 * q^29 - 5551 * q^31 + 20480 * q^32 - 6992 * q^34 + 14325 * q^35 - 7584 * q^37 - 1832 * q^38 + 2752 * q^40 - 16868 * q^41 - 704 * q^43 + 8080 * q^44 - 11400 * q^46 - 38866 * q^47 - 22573 * q^49 - 5416 * q^50 - 11520 * q^52 - 97517 * q^53 + 14404 * q^55 + 12672 * q^56 + 2068 * q^58 - 52682 * q^59 + 73874 * q^61 + 21136 * q^62 - 20480 * q^64 + 236352 * q^65 - 267432 * q^67 + 11392 * q^68 - 67660 * q^70 + 20588 * q^71 + 97257 * q^73 - 30336 * q^74 + 43392 * q^76 + 100582 * q^77 + 37498 * q^79 + 11008 * q^80 - 3672 * q^82 - 140952 * q^83 - 158376 * q^85 - 75136 * q^86 - 63040 * q^88 + 168796 * q^89 + 173196 * q^91 + 36160 * q^92 + 45376 * q^94 - 518002 * q^95 - 225802 * q^97 + 396808 * q^98

Introduction

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