LMFDB - Embedded newform 198.6.f.f.91.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 1398 x^{10} - 6935 x^{9} + 711771 x^{8} - 2805540 x^{7} + 164334057 x^{6} + \cdots + 1097661271355 $ x^12 - 6x^11 + 1398x^10 - 6935x^9 + 711771x^8 - 2805540x^7 + 164334057x^6 - 483211842x^5 + 16770266011x^4 - 32738438245x^3 + 562246043505x^2 - 545956894175*x + 1097661271355
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 11 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.3
Root			$0.500000 - 7.59531i$ of defining polynomial
Character	$\chi$	$=$	198.91
Dual form			198.6.f.f.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 - 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(85.4776 + 62.1031i) q^{5} +(-3.56142 + 10.9609i) q^{7} +(-19.7771 - 60.8676i) q^{8} +O(q^{10})$	\(q+(3.23607 - 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(85.4776 + 62.1031i) q^{5} +(-3.56142 + 10.9609i) q^{7} +(-19.7771 - 60.8676i) q^{8} +422.624 q^{10} +(-58.1348 - 397.079i) q^{11} +(452.874 - 329.032i) q^{13} +(14.2457 + 43.8437i) q^{14} +(-207.108 - 150.473i) q^{16} +(55.4487 + 40.2858i) q^{17} +(690.180 + 2124.16i) q^{19} +(1367.64 - 993.650i) q^{20} +(-1121.72 - 1148.29i) q^{22} +2603.36 q^{23} +(2483.95 + 7644.80i) q^{25} +(691.930 - 2129.54i) q^{26} +(149.183 + 108.388i) q^{28} +(302.907 - 932.251i) q^{29} +(-3925.25 + 2851.86i) q^{31} -1024.00 q^{32} +274.153 q^{34} +(-985.129 + 715.738i) q^{35} +(3145.88 - 9682.02i) q^{37} +(7227.66 + 5251.20i) q^{38} +(2089.57 - 6431.04i) q^{40} +(3080.27 + 9480.09i) q^{41} +11137.8 q^{43} +(-6329.74 - 1078.63i) q^{44} +(8424.64 - 6120.86i) q^{46} +(-5814.26 - 17894.5i) q^{47} +(13489.7 + 9800.83i) q^{49} +(26012.2 + 18899.0i) q^{50} +(-2767.72 - 8518.16i) q^{52} +(27744.6 - 20157.6i) q^{53} +(19690.6 - 37551.7i) q^{55} +737.600 q^{56} +(-1211.63 - 3729.00i) q^{58} +(-3996.24 + 12299.2i) q^{59} +(-6907.52 - 5018.61i) q^{61} +(-5997.25 + 18457.6i) q^{62} +(-3313.73 + 2407.57i) q^{64} +59144.5 q^{65} -33452.6 q^{67} +(887.179 - 644.573i) q^{68} +(-1505.14 + 4632.35i) q^{70} +(2071.45 + 1504.99i) q^{71} +(-20597.5 + 63392.5i) q^{73} +(-12583.5 - 38728.1i) q^{74} +35735.5 q^{76} +(4559.39 + 776.951i) q^{77} +(-56515.0 + 41060.6i) q^{79} +(-8358.28 - 25724.1i) q^{80} +(32257.0 + 23436.1i) q^{82} +(-77029.5 - 55965.2i) q^{83} +(2237.75 + 6887.07i) q^{85} +(36042.8 - 26186.6i) q^{86} +(-23019.5 + 11391.6i) q^{88} +33456.2 q^{89} +(1993.62 + 6135.74i) q^{91} +(12871.7 - 39615.0i) q^{92} +(-60887.7 - 44237.5i) q^{94} +(-72921.8 + 224430. i) q^{95} +(16335.6 - 11868.5i) q^{97} +66696.7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} - 48 q^{4} + 118 q^{5} + 216 q^{7} + 192 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 - 48 * q^4 + 118 * q^5 + 216 * q^7 + 192 * q^8	$ 12 q + 12 q^{2} - 48 q^{4} + 118 q^{5} + 216 q^{7} + 192 q^{8} + 328 q^{10} + 814 q^{11} + 1130 q^{13} - 864 q^{14} - 768 q^{16} + 2256 q^{17} - 3018 q^{19} + 1888 q^{20} - 916 q^{22} + 5076 q^{23} - 3707 q^{25} + 4320 q^{26} - 944 q^{28} - 15311 q^{29} - 16989 q^{31} - 12288 q^{32} - 16944 q^{34} - 897 q^{35} + 4326 q^{37} - 12008 q^{38} + 4928 q^{40} - 18536 q^{41} + 14020 q^{43} - 11696 q^{44} - 6664 q^{46} - 75246 q^{47} + 94655 q^{49} + 10128 q^{50} - 17280 q^{52} + 33303 q^{53} + 24050 q^{55} + 20096 q^{56} + 61244 q^{58} - 29940 q^{59} - 78908 q^{61} + 23296 q^{62} - 12288 q^{64} - 123664 q^{65} - 73388 q^{67} + 36096 q^{68} - 9372 q^{70} - 140764 q^{71} - 242111 q^{73} - 17304 q^{74} + 512 q^{76} - 83852 q^{77} - 161870 q^{79} - 19712 q^{80} + 38264 q^{82} + 31192 q^{83} - 35038 q^{85} - 119000 q^{86} + 57664 q^{88} + 75180 q^{89} - 76956 q^{91} - 67264 q^{92} - 311696 q^{94} + 390998 q^{95} - 6508 q^{97} + 58520 q^{98}+O(q^{100}) $ 12 * q + 12 * q^2 - 48 * q^4 + 118 * q^5 + 216 * q^7 + 192 * q^8 + 328 * q^10 + 814 * q^11 + 1130 * q^13 - 864 * q^14 - 768 * q^16 + 2256 * q^17 - 3018 * q^19 + 1888 * q^20 - 916 * q^22 + 5076 * q^23 - 3707 * q^25 + 4320 * q^26 - 944 * q^28 - 15311 * q^29 - 16989 * q^31 - 12288 * q^32 - 16944 * q^34 - 897 * q^35 + 4326 * q^37 - 12008 * q^38 + 4928 * q^40 - 18536 * q^41 + 14020 * q^43 - 11696 * q^44 - 6664 * q^46 - 75246 * q^47 + 94655 * q^49 + 10128 * q^50 - 17280 * q^52 + 33303 * q^53 + 24050 * q^55 + 20096 * q^56 + 61244 * q^58 - 29940 * q^59 - 78908 * q^61 + 23296 * q^62 - 12288 * q^64 - 123664 * q^65 - 73388 * q^67 + 36096 * q^68 - 9372 * q^70 - 140764 * q^71 - 242111 * q^73 - 17304 * q^74 + 512 * q^76 - 83852 * q^77 - 161870 * q^79 - 19712 * q^80 + 38264 * q^82 + 31192 * q^83 - 35038 * q^85 - 119000 * q^86 + 57664 * q^88 + 75180 * q^89 - 76956 * q^91 - 67264 * q^92 - 311696 * q^94 + 390998 * q^95 - 6508 * q^97 + 58520 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$2$	3.23607	−	2.35114i	0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	85.4776	+	62.1031i	1.52907	+	1.11093i	0.956753	+	0.290902i	$0.0939552\pi$
$5$	85.4776	+	62.1031i	1.52907	+	1.11093i	0.572317	+	0.820033i	$0.306045\pi$
$6$		0			0
$7$	−3.56142	+	10.9609i	−0.0274712	+	0.0845477i	−0.963852	−	0.266438i	$-0.914153\pi$
$7$	−3.56142	+	10.9609i	−0.0274712	+	0.0845477i	0.936381	+	0.350985i	$0.114153\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$		0			0
$10$	422.624			1.33646
$11$	−58.1348	−	397.079i	−0.144862	−	0.989452i
$11$	−58.1348	−	397.079i	−0.144862	−	0.989452i
$12$		0			0
$13$	452.874	−	329.032i	0.743223	−	0.539983i	−0.150496	−	0.988611i	$-0.548087\pi$
$13$	452.874	−	329.032i	0.743223	−	0.539983i	0.893719	+	0.448628i	$0.148087\pi$
$14$	14.2457	+	43.8437i	0.0194251	+	0.0597843i
$15$		0			0
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	55.4487	+	40.2858i	0.0465339	+	0.0338088i	0.610809	−	0.791778i	$-0.290844\pi$
$17$	55.4487	+	40.2858i	0.0465339	+	0.0338088i	−0.564275	+	0.825587i	$0.690844\pi$
$18$		0			0
$19$	690.180	+	2124.16i	0.438610	+	1.34990i	0.889342	+	0.457243i	$0.151163\pi$
$19$	690.180	+	2124.16i	0.438610	+	1.34990i	−0.450732	+	0.892659i	$0.648837\pi$
$20$	1367.64	−	993.650i	0.764535	−	0.555467i
$21$		0			0
$22$	−1121.72	−	1148.29i	−0.494113	−	0.505819i
$23$	2603.36			1.02616			0.513079	−	0.858341i	$-0.328505\pi$
$23$	2603.36			1.02616			0.513079	+	0.858341i	$0.328505\pi$
$24$		0			0
$25$	2483.95	+	7644.80i	0.794862	+	2.44634i
$26$	691.930	−	2129.54i	0.200738	−	0.617807i
$27$		0			0
$28$	149.183	+	108.388i	0.0359603	+	0.0261267i
$29$	302.907	−	932.251i	0.0668827	−	0.205844i	−0.912030	−	0.410124i	$-0.865485\pi$
$29$	302.907	−	932.251i	0.0668827	−	0.205844i	0.978912	+	0.204280i	$0.0654854\pi$
$30$		0			0
$31$	−3925.25	+	2851.86i	−0.733607	+	0.532997i	−0.890702	−	0.454587i	$-0.849787\pi$
$31$	−3925.25	+	2851.86i	−0.733607	+	0.532997i	0.157096	+	0.987583i	$0.449787\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	274.153			0.0406721
$35$	−985.129	+	715.738i	−0.135932	+	0.0987606i
$36$		0			0
$37$	3145.88	−	9682.02i	0.377779	−	1.16268i	−0.563806	−	0.825908i	$-0.690663\pi$
$37$	3145.88	−	9682.02i	0.377779	−	1.16268i	0.941585	−	0.336777i	$-0.109337\pi$
$38$	7227.66	+	5251.20i	0.811968	+	0.589929i
$39$		0			0
$40$	2089.57	−	6431.04i	0.206494	−	0.635523i
$41$	3080.27	+	9480.09i	0.286173	+	0.880750i	0.986045	+	0.166482i	$0.0532406\pi$
$41$	3080.27	+	9480.09i	0.286173	+	0.880750i	−0.699871	+	0.714269i	$0.746759\pi$
$42$		0			0
$43$	11137.8			0.918607			0.459304	−	0.888279i	$-0.348099\pi$
$43$	11137.8			0.918607			0.459304	+	0.888279i	$0.348099\pi$
$44$	−6329.74	−	1078.63i	−0.492895	−	0.0839927i
$45$		0			0
$46$	8424.64	−	6120.86i	0.587025	−	0.426499i
$47$	−5814.26	−	17894.5i	−0.383928	−	1.18161i	−0.937255	−	0.348645i	$-0.886642\pi$
$47$	−5814.26	−	17894.5i	−0.383928	−	1.18161i	0.553327	−	0.832964i	$-0.313358\pi$
$48$		0			0
$49$	13489.7	+	9800.83i	0.802623	+	0.583140i
$50$	26012.2	+	18899.0i	1.47147	+	1.06909i
$51$		0			0
$52$	−2767.72	−	8518.16i	−0.141943	−	0.436855i
$53$	27744.6	−	20157.6i	1.35672	−	0.985712i	0.358071	−	0.933695i	$-0.383435\pi$
$53$	27744.6	−	20157.6i	1.35672	−	0.985712i	0.998646	−	0.0520179i	$-0.0165653\pi$
$54$		0			0
$55$	19690.6	−	37551.7i	0.877712	−	1.67387i
$56$	737.600			0.0314304
$57$		0			0
$58$	−1211.63	−	3729.00i	−0.0472932	−	0.145554i
$59$	−3996.24	+	12299.2i	−0.149459	+	0.459987i	−0.997557	−	0.0698514i	$-0.977747\pi$
$59$	−3996.24	+	12299.2i	−0.149459	+	0.459987i	0.848099	+	0.529839i	$0.177747\pi$
$60$		0			0
$61$	−6907.52	−	5018.61i	−0.237683	−	0.172687i	0.462568	−	0.886584i	$-0.346928\pi$
$61$	−6907.52	−	5018.61i	−0.237683	−	0.172687i	−0.700250	+	0.713897i	$0.746928\pi$
$62$	−5997.25	+	18457.6i	−0.198140	+	0.609814i
$63$		0			0
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	59144.5			1.73632
$66$		0			0
$67$	−33452.6			−0.910421			−0.455211	−	0.890384i	$-0.650436\pi$
$67$	−33452.6			−0.910421			−0.455211	+	0.890384i	$0.650436\pi$
$68$	887.179	−	644.573i	0.0232669	−	0.0169044i
$69$		0			0
$70$	−1505.14	+	4632.35i	−0.0367141	+	0.112994i
$71$	2071.45	+	1504.99i	0.0487672	+	0.0354315i	0.611902	−	0.790934i	$-0.290405\pi$
$71$	2071.45	+	1504.99i	0.0487672	+	0.0354315i	−0.563135	+	0.826365i	$0.690405\pi$
$72$		0			0
$73$	−20597.5	+	63392.5i	−0.452384	+	1.39229i	0.421796	+	0.906691i	$0.361400\pi$
$73$	−20597.5	+	63392.5i	−0.452384	+	1.39229i	−0.874180	+	0.485603i	$0.838600\pi$
$74$	−12583.5	−	38728.1i	−0.267130	−	0.822142i
$75$		0			0
$76$	35735.5			0.709686
$77$	4559.39	+	776.951i	0.0876354	+	0.0149337i
$78$		0			0
$79$	−56515.0	+	41060.6i	−1.01882	+	0.740214i	−0.966040	−	0.258392i	$-0.916807\pi$
$79$	−56515.0	+	41060.6i	−1.01882	+	0.740214i	−0.0527769	+	0.998606i	$0.516807\pi$
$80$	−8358.28	−	25724.1i	−0.146013	−	0.449382i
$81$		0			0
$82$	32257.0	+	23436.1i	0.529772	+	0.384902i
$83$	−77029.5	−	55965.2i	−1.22733	−	0.891708i	−0.230644	−	0.973038i	$-0.574083\pi$
$83$	−77029.5	−	55965.2i	−1.22733	−	0.891708i	−0.996687	+	0.0813300i	$0.974083\pi$
$84$		0			0
$85$	2237.75	+	6887.07i	0.0335941	+	0.103392i
$86$	36042.8	−	26186.6i	0.525500	−	0.381798i
$87$		0			0
$88$	−23019.5	+	11391.6i	−0.316876	+	0.156811i
$89$	33456.2			0.447715			0.223857	−	0.974622i	$-0.428135\pi$
$89$	33456.2			0.447715			0.223857	+	0.974622i	$0.428135\pi$
$90$		0			0
$91$	1993.62	+	6135.74i	0.0252371	+	0.0776718i
$92$	12871.7	−	39615.0i	0.158550	−	0.487967i
$93$		0			0
$94$	−60887.7	−	44237.5i	−0.710739	−	0.516382i
$95$	−72921.8	+	224430.i	−0.828988	+	2.55136i
$96$		0			0
$97$	16335.6	−	11868.5i	0.176281	−	0.128075i	−0.496146	−	0.868239i	$-0.665252\pi$
$97$	16335.6	−	11868.5i	0.176281	−	0.128075i	0.672427	+	0.740164i	$0.265252\pi$
$98$	66696.7			0.701519
$99$		0			0
$100$	128611.			1.28611
$101$	112891.	−	82020.3i	1.10118	−	0.800051i	0.119925	−	0.992783i	$-0.461735\pi$
$101$	112891.	−	82020.3i	1.10118	−	0.800051i	0.981252	+	0.192732i	$0.0617347\pi$
$102$		0			0
$103$	34829.3	−	107194.i	0.323483	−	0.995579i	−0.648638	−	0.761097i	$-0.724661\pi$
$103$	34829.3	−	107194.i	0.323483	−	0.995579i	0.972121	−	0.234481i	$-0.0753391\pi$
$104$	−28983.9	−	21058.1i	−0.262769	−	0.190913i
$105$		0			0
$106$	42390.0	−	130463.i	0.366437	−	1.12778i
$107$	−55048.0	−	169420.i	−0.464817	−	1.43056i	−0.859213	−	0.511618i	$-0.829046\pi$
$107$	−55048.0	−	169420.i	−0.464817	−	1.43056i	0.394396	−	0.918940i	$-0.370954\pi$
$108$		0			0
$109$	−145904.			−1.17625			−0.588126	−	0.808769i	$-0.700134\pi$
$109$	−145904.			−1.17625			−0.588126	+	0.808769i	$0.700134\pi$
$110$	−24569.2	−	167815.i	−0.193602	−	1.32236i
$111$		0			0
$112$	2386.92	−	1734.20i	0.0179801	−	0.0130633i
$113$	45758.8	+	140831.i	0.337115	+	1.03753i	0.965671	+	0.259769i	$0.0836464\pi$
$113$	45758.8	+	140831.i	0.337115	+	1.03753i	−0.628556	+	0.777765i	$0.716354\pi$
$114$		0			0
$115$	222529.	+	161677.i	1.56907	+	1.13999i
$116$	−12688.3	−	9218.60i	−0.0875506	−	0.0636092i
$117$		0			0
$118$	15985.0	+	49196.7i	0.105683	+	0.325260i
$119$	−639.046	+	464.294i	−0.00413680	+	0.00300556i
$120$		0			0
$121$	−154292.	+	46168.2i	−0.958030	+	0.286668i
$122$	−34152.7			−0.207742
$123$		0			0
$124$	23989.0	+	73830.6i	0.140106	+	0.431203i
$125$	−160414.	+	493704.i	−0.918265	+	2.82613i
$126$		0			0
$127$	−199945.	−	145269.i	−1.10002	−	0.799213i	−0.118958	−	0.992899i	$-0.537956\pi$
$127$	−199945.	−	145269.i	−1.10002	−	0.799213i	−0.981063	+	0.193687i	$0.937956\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	191396.	−	139057.i	0.993284	−	0.721663i
$131$	35559.9			0.181043			0.0905217	−	0.995894i	$-0.471147\pi$
$131$	35559.9			0.181043			0.0905217	+	0.995894i	$0.471147\pi$
$132$		0			0
$133$	−25740.7			−0.126180
$134$	−108255.	+	78651.7i	−0.520817	+	0.378396i
$135$		0			0
$136$	1355.49	−	4171.77i	0.00628418	−	0.0193407i
$137$	26147.9	+	18997.6i	0.119024	+	0.0864762i	0.645705	−	0.763587i	$-0.276564\pi$
$137$	26147.9	+	18997.6i	0.119024	+	0.0864762i	−0.526681	+	0.850063i	$0.676564\pi$
$138$		0			0
$139$	−78235.8	+	240785.i	−0.343454	+	1.05704i	0.618952	+	0.785429i	$0.287557\pi$
$139$	−78235.8	+	240785.i	−0.343454	+	1.05704i	−0.962406	+	0.271614i	$0.912443\pi$
$140$	6020.57	+	18529.4i	0.0259608	+	0.0798990i
$141$		0			0
$142$	10241.8			0.0426241
$143$	−156979.	−	160698.i	−0.641952	−	0.657160i
$144$		0			0
$145$	83787.4	−	60875.1i	0.330947	−	0.240447i
$146$	82389.9	+	253570.i	0.319883	+	0.984500i
$147$		0			0
$148$	−131776.	−	95741.1i	−0.494519	−	0.359289i
$149$	−63163.4	−	45890.9i	−0.233077	−	0.169340i	0.465116	−	0.885250i	$-0.346012\pi$
$149$	−63163.4	−	45890.9i	−0.233077	−	0.169340i	−0.698193	+	0.715909i	$0.746012\pi$
$150$		0			0
$151$	−41095.7	−	126480.i	−0.146674	−	0.451417i	0.850548	−	0.525897i	$-0.176270\pi$
$151$	−41095.7	−	126480.i	−0.146674	−	0.451417i	−0.997223	+	0.0744798i	$0.976270\pi$
$152$	115643.	−	84019.2i	0.405984	−	0.294965i
$153$		0			0
$154$	16581.2	−	8205.50i	0.0563397	−	0.0278807i
$155$	−512631.			−1.71386
$156$		0			0
$157$	154857.	+	476602.i	0.501399	+	1.54315i	0.806742	+	0.590904i	$0.201229\pi$
$157$	154857.	+	476602.i	0.501399	+	1.54315i	−0.305344	+	0.952242i	$0.598771\pi$
$158$	−86347.3	+	265750.i	−0.275173	+	0.846896i
$159$		0			0
$160$	−87529.1	−	63593.6i	−0.270304	−	0.196387i
$161$	−9271.65	+	28535.2i	−0.0281898	+	0.0867593i
$162$		0			0
$163$	−172809.	+	125553.i	−0.509446	+	0.370134i	−0.812613	−	0.582803i	$-0.801956\pi$
$163$	−172809.	+	125553.i	−0.509446	+	0.370134i	0.303167	+	0.952937i	$0.401956\pi$
$164$	159487.			0.463038
$165$		0			0
$166$	−380855.			−1.07273
$167$	−346164.	+	251503.i	−0.960485	+	0.697833i	−0.953263	−	0.302140i	$-0.902299\pi$
$167$	−346164.	+	251503.i	−0.960485	+	0.697833i	−0.00722195	+	0.999974i	$0.502299\pi$
$168$		0			0
$169$	−17903.2	+	55100.5i	−0.0482186	+	0.148402i
$170$	23434.0	+	17025.8i	0.0621905	+	0.0451840i
$171$		0			0
$172$	55068.5	−	169483.i	0.141933	−	0.436824i
$173$	−167884.	−	516694.i	−0.426476	−	1.31256i	−0.901574	−	0.432625i	$-0.857588\pi$
$173$	−167884.	−	516694.i	−0.426476	−	1.31256i	0.475099	−	0.879933i	$-0.342412\pi$
$174$		0			0
$175$	−92640.4			−0.228668
$176$	−47709.4	+	90986.0i	−0.116097	+	0.221408i
$177$		0			0
$178$	108267.	−	78660.2i	0.256120	−	0.186082i
$179$	−217604.	−	669717.i	−0.507616	−	1.56228i	−0.796328	−	0.604864i	$-0.793227\pi$
$179$	−217604.	−	669717.i	−0.507616	−	1.56228i	0.288713	−	0.957416i	$-0.406773\pi$
$180$		0			0
$181$	−268707.	−	195227.i	−0.609653	−	0.442939i	0.239639	−	0.970862i	$-0.422971\pi$
$181$	−268707.	−	195227.i	−0.609653	−	0.442939i	−0.849292	+	0.527923i	$0.822971\pi$
$182$	20877.5	+	15168.4i	0.0467196	+	0.0339438i
$183$		0			0
$184$	−51486.8	−	158460.i	−0.112112	−	0.345045i
$185$	870186.	−	632227.i	1.86932	−	1.35814i
$186$		0			0
$187$	12773.1	−	24359.5i	0.0267112	−	0.0509406i
$188$	−301046.			−0.621209
$189$		0			0
$190$	291687.	+	897720.i	0.586183	+	1.80409i
$191$	−120001.	+	369324.i	−0.238012	+	0.732527i	0.758695	+	0.651446i	$0.225837\pi$
$191$	−120001.	+	369324.i	−0.238012	+	0.732527i	−0.996708	+	0.0810810i	$0.974163\pi$
$192$		0			0
$193$	−371998.	−	270273.i	−0.718865	−	0.522286i	0.167156	−	0.985930i	$-0.446542\pi$
$193$	−371998.	−	270273.i	−0.718865	−	0.522286i	−0.886021	+	0.463644i	$0.846542\pi$
$194$	24958.5	−	76814.5i	0.0476118	−	0.146534i
$195$		0			0
$196$	215835.	−	156813.i	0.401312	−	0.291570i
$197$	−667771.			−1.22592			−0.612960	−	0.790114i	$-0.710021\pi$
$197$	−667771.			−1.22592			−0.612960	+	0.790114i	$0.710021\pi$
$198$		0			0
$199$	657383.			1.17675			0.588377	−	0.808586i	$-0.299767\pi$
$199$	657383.			1.17675			0.588377	+	0.808586i	$0.299767\pi$
$200$	416195.	−	302384.i	0.735736	−	0.534544i
$201$		0			0
$202$	172482.	−	530846.i	0.297418	−	0.915357i
$203$	9139.55	+	6640.27i	0.0155663	+	0.0113096i
$204$		0			0
$205$	−325449.	+	1.00163e6i	−0.540877	+	1.66465i
$206$	−139317.	−	428774.i	−0.228737	−	0.703980i
$207$		0			0
$208$	−143304.			−0.229668
$209$	803333.	−	397543.i	1.27213	−	0.629533i
$210$		0			0
$211$	240905.	−	175028.i	0.372511	−	0.270645i	−0.385740	−	0.922607i	$-0.626054\pi$
$211$	240905.	−	175028.i	0.372511	−	0.270645i	0.758251	+	0.651962i	$0.226054\pi$
$212$	−169560.	−	521852.i	−0.259110	−	0.797458i
$213$		0			0
$214$	−576470.	−	418830.i	−0.860482	−	0.625177i
$215$	952036.	+	691695.i	1.40461	+	1.02051i
$216$		0			0
$217$	−17279.6	−	53181.1i	−0.0249106	−	0.0766669i
$218$	−472155.	+	343040.i	−0.672888	+	0.488882i
$219$		0			0
$220$	−474065.	−	485295.i	−0.660360	−	0.676004i
$221$	38366.6			0.0528412
$222$		0			0
$223$	36138.3	+	111222.i	0.0486638	+	0.149772i	0.972436	−	0.233172i	$-0.0749104\pi$
$223$	36138.3	+	111222.i	0.0486638	+	0.149772i	−0.923772	+	0.382943i	$0.874910\pi$
$224$	3646.89	−	11224.0i	0.00485627	−	0.0149461i
$225$		0			0
$226$	479192.	+	348153.i	0.624077	+	0.453419i
$227$	−278724.	+	857824.i	−0.359013	+	1.10493i	0.594634	+	0.803997i	$0.297297\pi$
$227$	−278724.	+	857824.i	−0.359013	+	1.10493i	−0.953646	+	0.300930i	$0.902703\pi$
$228$		0			0
$229$	−454315.	+	330079.i	−0.572490	+	0.415939i	−0.836009	−	0.548716i	$-0.815117\pi$
$229$	−454315.	+	330079.i	−0.572490	+	0.415939i	0.263519	+	0.964654i	$0.415117\pi$
$230$	1.10024e6			1.37142
$231$		0			0
$232$	−62734.5			−0.0765220
$233$	−1.11398e6	+	809352.i	−1.34427	+	0.976670i	−0.344996	+	0.938604i	$0.612120\pi$
$233$	−1.11398e6	+	809352.i	−1.34427	+	0.976670i	−0.999275	+	0.0380658i	$0.987880\pi$
$234$		0			0
$235$	614312.	−	1.89066e6i	0.725637	−	2.23328i
$236$	167397.	+	121621.i	0.195644	+	0.142144i
$237$		0			0
$238$	−976.375	+	3004.97i	−0.00111731	+	0.00343873i
$239$	78866.3	+	242725.i	0.0893093	+	0.274866i	0.985729	−	0.168341i	$-0.0538409\pi$
$239$	78866.3	+	242725.i	0.0893093	+	0.274866i	−0.896420	+	0.443206i	$0.853841\pi$
$240$		0			0
$241$	−1.26774e6			−1.40600			−0.703002	−	0.711188i	$-0.748157\pi$
$241$	−1.26774e6			−1.40600			−0.703002	+	0.711188i	$0.748157\pi$
$242$	−390750.	+	512165.i	−0.428905	+	0.562175i
$243$		0			0
$244$	−110520.	+	80297.7i	−0.118841	+	0.0863433i
$245$	544404.	+	1.67550e6i	0.579437	+	1.78332i
$246$		0			0
$247$	1.01148e6	+	734883.i	1.05491	+	0.766436i
$248$	251216.	+	182519.i	0.259369	+	0.188443i
$249$		0			0
$250$	641657.	+	1.97482e6i	0.649311	+	1.99837i
$251$	2142.19	−	1556.39i	0.00214622	−	0.00155932i	−0.586712	−	0.809796i	$-0.699578\pi$
$251$	2142.19	−	1556.39i	0.00214622	−	0.00155932i	0.588858	+	0.808237i	$0.299578\pi$
$252$		0			0
$253$	−151346.	−	1.03374e6i	−0.148651	−	1.01533i
$254$	−988583.			−0.961454
$255$		0			0
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	485901.	−	1.49545e6i	0.458897	−	1.41234i	−0.407602	−	0.913159i	$-0.633635\pi$
$257$	485901.	−	1.49545e6i	0.458897	−	1.41234i	0.866499	−	0.499179i	$-0.166365\pi$
$258$		0			0
$259$	94920.1	+	68963.5i	0.0879242	+	0.0638807i
$260$	292426.	−	899996.i	0.268277	−	0.825671i
$261$		0			0
$262$	115074.	−	83606.4i	0.103568	−	0.0752465i
$263$	1.43211e6			1.27669			0.638347	−	0.769749i	$-0.279619\pi$
$263$	1.43211e6			1.27669			0.638347	+	0.769749i	$0.279619\pi$
$264$		0			0
$265$	3.62340e6			3.16958
$266$	−83298.7	+	60520.1i	−0.0721829	+	0.0524439i
$267$		0			0
$268$	−165399.	+	509044.i	−0.140668	+	0.432931i
$269$	−183948.	−	133646.i	−0.154993	−	0.112609i	0.507586	−	0.861601i	$-0.330538\pi$
$269$	−183948.	−	133646.i	−0.154993	−	0.112609i	−0.662579	+	0.748992i	$0.730538\pi$
$270$		0			0
$271$	365362.	−	1.12447e6i	0.302204	−	0.930087i	−0.678502	−	0.734598i	$-0.737371\pi$
$271$	365362.	−	1.12447e6i	0.302204	−	0.930087i	0.980706	−	0.195489i	$-0.0626293\pi$
$272$	−5421.96	−	16687.1i	−0.00444359	−	0.0136760i
$273$		0			0
$274$	129282.			0.104031
$275$	2.89118e6	−	1.43075e6i	2.30539	−	1.14086i
$276$		0			0
$277$	792864.	−	576050.i	0.620868	−	0.451087i	−0.232356	−	0.972631i	$-0.574644\pi$
$277$	792864.	−	576050.i	0.620868	−	0.451087i	0.853225	+	0.521543i	$0.174644\pi$
$278$	312943.	+	963140.i	0.242859	+	0.747442i
$279$		0			0
$280$	63048.2	+	45807.2i	0.0480593	+	0.0349172i
$281$	754890.	+	548460.i	0.570319	+	0.414361i	0.835221	−	0.549914i	$-0.185340\pi$
$281$	754890.	+	548460.i	0.570319	+	0.414361i	−0.264902	+	0.964275i	$0.585340\pi$
$282$		0			0
$283$	−283677.	−	873067.i	−0.210551	−	0.648010i	−0.999440	−	0.0334734i	$-0.989343\pi$
$283$	−283677.	−	873067.i	−0.210551	−	0.648010i	0.788888	−	0.614536i	$-0.210657\pi$
$284$	33143.2	−	24079.9i	0.0243836	−	0.0177157i
$285$		0			0
$286$	−885820.	−	150950.i	−0.640369	−	0.109123i
$287$	−114881.			−0.0823270
$288$		0			0
$289$	−437308.	−	1.34590e6i	−0.307995	−	0.947910i
$290$	128016.	−	393992.i	0.0893858	−	0.275101i
$291$		0			0
$292$	862798.	+	626860.i	0.592178	+	0.430242i
$293$	627104.	−	1.93003e6i	0.426747	−	1.31339i	−0.474564	−	0.880221i	$-0.657394\pi$
$293$	627104.	−	1.93003e6i	0.426747	−	1.31339i	0.901311	−	0.433172i	$-0.142606\pi$
$294$		0			0
$295$	−1.10541e6	+	803124.i	−0.739548	+	0.537313i
$296$	−651538.			−0.432226
$297$		0			0
$298$	−312297.			−0.203717
$299$	1.17899e6	−	856588.i	0.762664	−	0.554108i
$300$		0			0
$301$	−39666.5	+	122081.i	−0.0252353	+	0.0776662i
$302$	−430360.	−	312675.i	−0.271528	−	0.197277i
$303$		0			0
$304$	176686.	−	543784.i	0.109652	−	0.337476i
$305$	−278767.	−	857957.i	−0.171590	−	0.528100i
$306$		0			0
$307$	13269.5			0.00803539			0.00401770	−	0.999992i	$-0.498721\pi$
$307$	13269.5			0.00803539			0.00401770	+	0.999992i	$0.498721\pi$
$308$	34365.7	−	65538.3i	0.0206418	−	0.0393657i
$309$		0			0
$310$	−1.65891e6	+	1.20527e6i	−0.980433	+	0.712326i
$311$	−747091.	−	2.29931e6i	−0.437998	−	1.34802i	−0.889983	−	0.455995i	$-0.849284\pi$
$311$	−747091.	−	2.29931e6i	−0.437998	−	1.34802i	0.451984	−	0.892026i	$-0.350716\pi$
$312$		0			0
$313$	1.01652e6	+	738547.i	0.586484	+	0.426106i	0.841056	−	0.540948i	$-0.181935\pi$
$313$	1.01652e6	+	738547.i	0.586484	+	0.426106i	−0.254572	+	0.967054i	$0.581935\pi$
$314$	1.62169e6	+	1.17823e6i	0.928204	+	0.674380i
$315$		0			0
$316$	345389.	+	1.06300e6i	0.194577	+	0.598846i
$317$	−2.72262e6	+	1.97810e6i	−1.52174	+	1.10561i	−0.561117	+	0.827737i	$0.689628\pi$
$317$	−2.72262e6	+	1.97810e6i	−1.52174	+	1.10561i	−0.960619	+	0.277869i	$0.910372\pi$
$318$		0			0
$319$	−387786.	−	66081.5i	−0.213361	−	0.0363582i
$320$	−432767.			−0.236254
$321$		0			0
$322$	37086.6	+	114141.i	0.0199332	+	0.0613481i
$323$	−47303.8	+	145586.i	−0.0252284	+	0.0776451i
$324$		0			0
$325$	3.64030e6	+	2.64483e6i	1.91174	+	1.38896i
$326$	−264029.	+	812598.i	−0.137597	+	0.423479i
$327$		0			0
$328$	516112.	−	374977.i	0.264886	−	0.192451i
$329$	216847.			0.110449
$330$		0			0
$331$	−3.28145e6			−1.64625			−0.823126	−	0.567859i	$-0.807772\pi$
$331$	−3.28145e6			−1.64625			−0.823126	+	0.567859i	$0.807772\pi$
$332$	−1.23247e6	+	895443.i	−0.613666	+	0.445854i
$333$		0			0
$334$	−528892.	+	1.62776e6i	−0.259418	+	0.798407i
$335$	−2.85944e6	−	2.07751e6i	−1.39210	−	1.01142i
$336$		0			0
$337$	−59898.0	+	184347.i	−0.0287301	+	0.0884223i	−0.964393	−	0.264472i	$-0.914802\pi$
$337$	−59898.0	+	184347.i	−0.0287301	+	0.0884223i	0.935663	+	0.352894i	$0.114802\pi$
$338$	71613.0	+	220402.i	0.0340957	+	0.104936i
$339$		0			0
$340$	115864.			0.0543565
$341$	1.36061e6	+	1.39284e6i	0.633646	+	0.648658i
$342$		0			0
$343$	−312176.	+	226809.i	−0.143273	+	0.104094i
$344$	−220274.	−	677934.i	−0.100362	−	0.308881i
$345$		0			0
$346$	−1.75810e6	−	1.27734e6i	−0.789504	−	0.573608i
$347$	739385.	+	537195.i	0.329645	+	0.239501i	0.740280	−	0.672299i	$-0.234693\pi$
$347$	739385.	+	537195.i	0.329645	+	0.239501i	−0.410635	+	0.911800i	$0.634693\pi$
$348$		0			0
$349$	−84239.1	−	259261.i	−0.0370212	−	0.113939i	0.930838	−	0.365432i	$-0.119079\pi$
$349$	−84239.1	−	259261.i	−0.0370212	−	0.113939i	−0.967859	+	0.251492i	$0.919079\pi$
$350$	−299791.	+	217811.i	−0.130812	+	0.0950405i
$351$		0			0
$352$	59530.1	+	406608.i	0.0256082	+	0.174912i
$353$	1.89477e6			0.809317			0.404659	−	0.914468i	$-0.367390\pi$
$353$	1.89477e6			0.809317			0.404659	+	0.914468i	$0.367390\pi$
$354$		0			0
$355$	83597.5	+	257287.i	0.0352065	+	0.108354i
$356$	165417.	−	509100.i	0.0691758	−	0.212901i
$357$		0			0
$358$	−2.27878e6	−	1.65563e6i	−0.939713	−	0.682741i
$359$	−200588.	+	617346.i	−0.0821426	+	0.252809i	−0.983690	−	0.179871i	$-0.942432\pi$
$359$	−200588.	+	617346.i	−0.0821426	+	0.252809i	0.901548	+	0.432680i	$0.142432\pi$
$360$		0			0
$361$	−2.03248e6	+	1.47669e6i	−0.820841	+	0.596376i
$362$	−1.32856e6			−0.532857
$363$		0			0
$364$	103224.			0.0408345
$365$	−5.69749e6	+	4.13947e6i	−2.23847	+	1.62635i
$366$		0			0
$367$	899442.	−	2.76820e6i	0.348584	−	1.07283i	−0.611052	−	0.791590i	$-0.709254\pi$
$367$	899442.	−	2.76820e6i	0.348584	−	1.07283i	0.959637	−	0.281242i	$-0.0907464\pi$
$368$	−539177.	−	391735.i	−0.207545	−	0.150790i
$369$		0			0
$370$	1.32953e6	−	4.09186e6i	0.504885	−	1.55388i
$371$	122136.	+	375896.i	0.0460691	+	0.141786i
$372$		0			0
$373$	−3.07104e6			−1.14291			−0.571457	−	0.820632i	$-0.693622\pi$
$373$	−3.07104e6			−1.14291			−0.571457	+	0.820632i	$0.693622\pi$
$374$	−15937.9	−	108860.i	−0.00589184	−	0.0402431i
$375$		0			0
$376$	−974204.	+	707800.i	−0.355370	+	0.258191i
$377$	−169562.	−	521858.i	−0.0614434	−	0.189103i
$378$		0			0
$379$	−1.55584e6	−	1.13039e6i	−0.556375	−	0.404230i	0.273755	−	0.961799i	$-0.411734\pi$
$379$	−1.55584e6	−	1.13039e6i	−0.556375	−	0.404230i	−0.830131	+	0.557569i	$0.811734\pi$
$380$	3.05459e6	+	2.21929e6i	1.08516	+	0.788414i
$381$		0			0
$382$	480002.	+	1.47729e6i	0.168300	+	0.517975i
$383$	−305914.	+	222260.i	−0.106562	+	0.0774218i	−0.639790	−	0.768550i	$-0.720979\pi$
$383$	−305914.	+	222260.i	−0.106562	+	0.0774218i	0.533228	+	0.845971i	$0.320979\pi$
$384$		0			0
$385$	341474.	+	349564.i	0.117410	+	0.120192i
$386$	−1.83926e6			−0.628311
$387$		0			0
$388$	−99834.1	−	307258.i	−0.0336666	−	0.103615i
$389$	604571.	−	1.86068e6i	0.202569	−	0.623443i	−0.797235	−	0.603668i	$-0.793705\pi$
$389$	604571.	−	1.86068e6i	0.202569	−	0.623443i	0.999804	−	0.0197748i	$-0.00629492\pi$
$390$		0			0
$391$	144353.	+	104878.i	0.0477511	+	0.0346932i
$392$	329767.	−	1.01492e6i	0.108391	−	0.333592i
$393$		0			0
$394$	−2.16095e6	+	1.57002e6i	−0.701302	+	0.509526i
$395$	−7.38076e6			−2.38017
$396$		0			0
$397$	3.93029e6			1.25155			0.625776	−	0.780003i	$-0.284783\pi$
$397$	3.93029e6			1.25155			0.625776	+	0.780003i	$0.284783\pi$
$398$	2.12734e6	−	1.54560e6i	0.673176	−	0.489091i
$399$		0			0
$400$	635890.	−	1.95707e6i	0.198716	−	0.611584i
$401$	1.93782e6	+	1.40791e6i	0.601801	+	0.437234i	0.846518	−	0.532361i	$-0.178695\pi$
$401$	1.93782e6	+	1.40791e6i	0.601801	+	0.437234i	−0.244717	+	0.969595i	$0.578695\pi$
$402$		0			0
$403$	−839290.	+	2.58307e6i	−0.257424	+	0.792270i
$404$	−689930.	−	2.12339e6i	−0.210306	−	0.647255i
$405$		0			0
$406$	45188.4			0.0136054
$407$	−4.02741e6	−	686298.i	−1.20515	−	0.205365i
$408$		0			0
$409$	2.05161e6	−	1.49058e6i	0.606438	−	0.440603i	−0.241720	−	0.970346i	$-0.577712\pi$
$409$	2.05161e6	−	1.49058e6i	0.606438	−	0.440603i	0.848158	+	0.529743i	$0.177712\pi$
$410$	1.30180e6	+	4.00652e6i	0.382458	+	1.17708i
$411$		0			0
$412$	−1.45895e6	−	1.05999e6i	−0.423445	−	0.307651i
$413$	−120578.	−	87605.0i	−0.0347850	−	0.0252728i
$414$		0			0
$415$	−3.10868e6	−	9.56754e6i	−0.886046	−	2.72697i
$416$	−463743.	+	336929.i	−0.131384	+	0.0954564i
$417$		0			0
$418$	1.66496e6	−	3.17523e6i	0.466083	−	0.888861i
$419$	2.07782e6			0.578194			0.289097	−	0.957300i	$-0.406645\pi$
$419$	2.07782e6			0.578194			0.289097	+	0.957300i	$0.406645\pi$
$420$		0			0
$421$	1.72026e6	+	5.29443e6i	0.473031	+	1.45584i	0.848595	+	0.529044i	$0.177449\pi$
$421$	1.72026e6	+	5.29443e6i	0.473031	+	1.45584i	−0.375563	+	0.926797i	$0.622551\pi$
$422$	368070.	−	1.13280e6i	0.100612	−	0.309651i
$423$		0			0
$424$	−1.77566e6	−	1.29009e6i	−0.479672	−	0.348502i
$425$	−170246.	+	523962.i	−0.0457197	+	0.140711i
$426$		0			0
$427$	79609.1	−	57839.4i	0.0211297	−	0.0153516i
$428$	−2.85022e6			−0.752089
$429$		0			0
$430$	4.70712e6			1.22768
$431$	1.18300e6	−	859500.i	0.306755	−	0.222871i	−0.423748	−	0.905780i	$-0.639286\pi$
$431$	1.18300e6	−	859500.i	0.306755	−	0.222871i	0.730503	+	0.682910i	$0.239286\pi$
$432$		0			0
$433$	−759042.	+	2.33609e6i	−0.194557	+	0.598784i	0.805425	+	0.592698i	$0.201937\pi$
$433$	−759042.	+	2.33609e6i	−0.194557	+	0.598784i	−0.999981	+	0.00608592i	$0.998063\pi$
$434$	−180954.	−	131471.i	−0.0461152	−	0.0335046i
$435$		0			0
$436$	−721388.	+	2.22020e6i	−0.181741	+	0.559341i
$437$	1.79679e6	+	5.52994e6i	0.450083	+	1.38521i
$438$		0			0
$439$	−5.94174e6			−1.47147			−0.735737	−	0.677268i	$-0.763164\pi$
$439$	−5.94174e6			−1.47147			−0.735737	+	0.677268i	$0.763164\pi$
$440$	−2.67510e6	−	455856.i	−0.658732	−	0.112253i
$441$		0			0
$442$	124157.	−	90205.3i	0.0302284	−	0.0219622i
$443$	−695672.	−	2.14106e6i	−0.168421	−	0.518346i	0.830851	−	0.556494i	$-0.187854\pi$
$443$	−695672.	−	2.14106e6i	−0.168421	−	0.518346i	−0.999272	+	0.0381488i	$0.987854\pi$
$444$		0			0
$445$	2.85976e6	+	2.07773e6i	0.684587	+	0.497382i
$446$	378446.	+	274957.i	0.0900879	+	0.0654527i
$447$		0			0
$448$	−14587.6	−	44895.9i	−0.00343390	−	0.0105685i
$449$	3.03376e6	−	2.20415e6i	0.710174	−	0.515972i	−0.173056	−	0.984912i	$-0.555364\pi$
$449$	3.03376e6	−	2.20415e6i	0.710174	−	0.515972i	0.883230	+	0.468940i	$0.155364\pi$
$450$		0			0
$451$	3.58527e6	−	1.77423e6i	0.830005	−	0.410742i
$452$	2.36926e6			0.545464
$453$		0			0
$454$	1.11490e6	+	3.43130e6i	0.253860	+	0.781301i
$455$	−210638.	+	648278.i	−0.0476990	+	0.146802i
$456$		0			0
$457$	3.92255e6	+	2.84990e6i	0.878573	+	0.638320i	0.932874	−	0.360204i	$-0.117293\pi$
$457$	3.92255e6	+	2.84990e6i	0.878573	+	0.638320i	−0.0543007	+	0.998525i	$0.517293\pi$
$458$	−694131.	+	2.13632e6i	−0.154624	+	0.475885i
$459$		0			0
$460$	3.56046e6	−	2.58683e6i	0.784534	−	0.569997i
$461$	−2.78963e6			−0.611357			−0.305678	−	0.952135i	$-0.598883\pi$
$461$	−2.78963e6			−0.611357			−0.305678	+	0.952135i	$0.598883\pi$
$462$		0			0
$463$	−3.04658e6			−0.660481			−0.330241	−	0.943897i	$-0.607130\pi$
$463$	−3.04658e6			−0.660481			−0.330241	+	0.943897i	$0.607130\pi$
$464$	−203013.	+	147498.i	−0.0437753	+	0.0318046i
$465$		0			0
$466$	−1.70201e6	+	5.23824e6i	−0.363075	+	1.11743i
$467$	−2.76877e6	−	2.01163e6i	−0.587482	−	0.426831i	0.253932	−	0.967222i	$-0.418276\pi$
$467$	−2.76877e6	−	2.01163e6i	−0.587482	−	0.426831i	−0.841414	+	0.540391i	$0.818276\pi$
$468$		0			0
$469$	119139.	−	366671.i	0.0250104	−	0.0769740i
$470$	−2.45725e6	−	7.56264e6i	−0.513103	−	1.57917i
$471$		0			0
$472$	827655.			0.170999
$473$	−647497.	−	4.42260e6i	−0.133071	−	0.908918i
$474$		0			0
$475$	−1.45244e7	+	1.05526e7i	−2.95368	+	2.14597i
$476$	3905.50	+	12019.9i	0.000790059	+	0.00243155i
$477$		0			0
$478$	825899.	+	600050.i	0.165332	+	0.120121i
$479$	4.14877e6	+	3.01426e6i	0.826190	+	0.600262i	0.918479	−	0.395470i	$-0.129418\pi$
$479$	4.14877e6	+	3.01426e6i	0.826190	+	0.600262i	−0.0922885	+	0.995732i	$0.529418\pi$
$480$		0			0
$481$	−1.76101e6	−	5.41983e6i	−0.347056	−	1.06813i
$482$	−4.10248e6	+	2.98063e6i	−0.804320	+	0.584373i
$483$		0			0
$484$	−60323.0	+	2.57611e6i	−0.0117050	+	0.499863i
$485$	2.13340e6			0.411829
$486$		0			0
$487$	422018.	+	1.29884e6i	0.0806322	+	0.248160i	0.983244	−	0.182296i	$-0.0583528\pi$
$487$	422018.	+	1.29884e6i	0.0806322	+	0.248160i	−0.902612	+	0.430456i	$0.858353\pi$
$488$	−168860.	+	519698.i	−0.0320979	+	0.0987873i
$489$		0			0
$490$	5.70107e6	+	4.14207e6i	1.07267	+	0.779341i
$491$	203675.	−	626847.i	0.0381271	−	0.117343i	−0.930181	−	0.367100i	$-0.880351\pi$
$491$	203675.	−	626847.i	0.0381271	−	0.117343i	0.968309	+	0.249757i	$0.0803507\pi$
$492$		0			0
$493$	54352.3	−	39489.2i	0.0100716	−	0.00731748i
$494$	5.00103e6			0.922024
$495$		0			0
$496$	1.24208e6			0.226697
$497$	−23873.4	+	17345.0i	−0.00433534	+	0.00314981i
$498$		0			0
$499$	−486433.	+	1.49709e6i	−0.0874523	+	0.269151i	−0.985213	−	0.171332i	$-0.945193\pi$
$499$	−486433.	+	1.49709e6i	−0.0874523	+	0.269151i	0.897761	+	0.440483i	$0.145193\pi$
$500$	6.71952e6	+	4.88202e6i	1.20202	+	0.873321i
$501$		0			0
$502$	3272.98	−	10073.2i	0.000579674	−	0.00178405i
$503$	40265.6	+	123925.i	0.00709602	+	0.0218393i	0.954542	−	0.298077i	$-0.0963452\pi$
$503$	40265.6	+	123925.i	0.00709602	+	0.0218393i	−0.947446	+	0.319916i	$0.896345\pi$
$504$		0			0
$505$	1.47434e7			2.57258
$506$	−2.92023e6	−	2.98941e6i	−0.507038	−	0.519050i
$507$		0			0
$508$	−3.19912e6	+	2.32430e6i	−0.550011	+	0.399606i
$509$	3.29693e6	+	1.01469e7i	0.564047	+	1.73596i	0.670765	+	0.741670i	$0.265966\pi$
$509$	3.29693e6	+	1.01469e7i	0.564047	+	1.73596i	−0.106717	+	0.994289i	$0.534034\pi$
$510$		0			0
$511$	−621484.	−	451534.i	−0.105288	−	0.0764960i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$		0			0
$514$	−1.94360e6	−	5.98179e6i	−0.324489	−	0.998674i
$515$	9.63418e6	−	6.99964e6i	1.60065	−	1.16294i
$516$		0			0
$517$	−6.76749e6	+	3.34901e6i	−1.11353	+	0.551049i
$518$	469311.			0.0768486
$519$		0			0
$520$	−1.16971e6	−	3.59998e6i	−0.189700	−	0.583838i
$521$	−343303.	+	1.05658e6i	−0.0554094	+	0.170533i	−0.974931	−	0.222506i	$-0.928576\pi$
$521$	−343303.	+	1.05658e6i	−0.0554094	+	0.170533i	0.919522	+	0.393039i	$0.128576\pi$
$522$		0			0
$523$	5.87097e6	+	4.26551e6i	0.938546	+	0.681894i	0.948070	−	0.318061i	$-0.103032\pi$
$523$	5.87097e6	+	4.26551e6i	0.938546	+	0.681894i	−0.00952394	+	0.999955i	$0.503032\pi$
$524$	175818.	−	541112.i	0.0279727	−	0.0860912i
$525$		0			0
$526$	4.63440e6	−	3.36709e6i	0.730347	−	0.530628i
$527$	−332540.			−0.0521576
$528$		0			0
$529$	341129.			0.0530004
$530$	1.17256e7	−	8.51912e6i	1.81319	−	1.31736i
$531$		0			0
$532$	−127269.	+	391694.i	−0.0194959	+	0.0600023i
$533$	4.51423e6	+	3.27978e6i	0.688280	+	0.500065i
$534$		0			0
$535$	5.81615e6	−	1.79003e7i	0.878519	−	2.70380i
$536$	661594.	+	2.03618e6i	0.0994672	+	0.306128i
$537$		0			0
$538$	−909487.			−0.135469
$539$	3.10748e6	−	5.92624e6i	0.460719	−	0.878632i
$540$		0			0
$541$	−5.11753e6	+	3.71810e6i	−0.751739	+	0.546171i	−0.896366	−	0.443316i	$-0.853802\pi$
$541$	−5.11753e6	+	3.71810e6i	−0.751739	+	0.546171i	0.144626	+	0.989486i	$0.453802\pi$
$542$	−1.46145e6	−	4.49787e6i	−0.213690	−	0.657671i
$543$		0			0
$544$	−56779.5	−	41252.7i	−0.00822610	−	0.00597661i
$545$	−1.24715e7	−	9.06108e6i	−1.79857	−	1.30674i
$546$		0			0
$547$	−1.40319e6	−	4.31858e6i	−0.200516	−	0.617124i	−0.999868	−	0.0162611i	$-0.994824\pi$
$547$	−1.40319e6	−	4.31858e6i	−0.200516	−	0.617124i	0.799352	−	0.600863i	$-0.205176\pi$
$548$	418366.	−	303961.i	0.0595121	−	0.0432381i
$549$		0			0
$550$	5.99216e6	−	1.14276e7i	0.844650	−	1.61082i
$551$	2.18931e6			0.307204
$552$		0			0
$553$	−248788.	−	765691.i	−0.0345952	−	0.106473i
$554$	1.21139e6	−	3.72827e6i	0.167691	−	0.516099i
$555$		0			0
$556$	3.27718e6	+	2.38101e6i	0.449587	+	0.326644i
$557$	−1.02283e6	+	3.14796e6i	−0.139690	+	0.429923i	−0.996290	−	0.0860586i	$-0.972573\pi$
$557$	−1.02283e6	+	3.14796e6i	−0.139690	+	0.429923i	0.856600	+	0.515982i	$0.172573\pi$
$558$		0			0
$559$	5.04404e6	−	3.66471e6i	0.682730	−	0.496032i
$560$	311728.			0.0420054
$561$		0			0
$562$	3.73238e6			0.498477
$563$	−4.22834e6	+	3.07207e6i	−0.562211	+	0.408470i	−0.832267	−	0.554374i	$-0.812958\pi$
$563$	−4.22834e6	+	3.07207e6i	−0.562211	+	0.408470i	0.270056	+	0.962844i	$0.412958\pi$
$564$		0			0
$565$	−4.83469e6	+	1.48797e7i	−0.637159	+	1.96097i
$566$	−2.97070e6	−	2.15834e6i	−0.389779	−	0.283191i
$567$		0			0
$568$	50638.2	−	155848.i	0.00658579	−	0.0202690i
$569$	3.52074e6	+	1.08357e7i	0.455882	+	1.40306i	0.870096	+	0.492882i	$0.164057\pi$
$569$	3.52074e6	+	1.08357e7i	0.455882	+	1.40306i	−0.414214	+	0.910180i	$0.635943\pi$
$570$		0			0
$571$	8.62013e6			1.10643			0.553214	−	0.833039i	$-0.313401\pi$
$571$	8.62013e6			1.10643			0.553214	+	0.833039i	$0.313401\pi$
$572$	−3.22148e6	+	1.59420e6i	−0.411685	+	0.203729i
$573$		0			0
$574$	−371762.	+	270101.i	−0.0470961	+	0.0342173i
$575$	6.46660e6	+	1.99021e7i	0.815655	+	2.51033i
$576$		0			0
$577$	3.50001e6	+	2.54291e6i	0.437653	+	0.317974i	0.784702	−	0.619873i	$-0.212816\pi$
$577$	3.50001e6	+	2.54291e6i	0.437653	+	0.317974i	−0.347049	+	0.937847i	$0.612816\pi$
$578$	−4.57955e6	−	3.32724e6i	−0.570169	−	0.414252i
$579$		0			0
$580$	−512063.	−	1.57597e6i	−0.0632053	−	0.194526i
$581$	887764.	−	644998.i	0.109108	−	0.0792717i
$582$		0			0
$583$	−9.61710e6	−	9.84493e6i	−1.17185	−	1.19961i
$584$	4.26591e6			0.517582
$585$		0			0
$586$	−2.50842e6	−	7.72011e6i	−0.301756	−	0.928709i
$587$	−537359.	+	1.65382e6i	−0.0643678	+	0.198104i	−0.978068	−	0.208285i	$-0.933212\pi$
$587$	−537359.	+	1.65382e6i	−0.0643678	+	0.198104i	0.913700	+	0.406388i	$0.133212\pi$
$588$		0			0
$589$	−8.76693e6	−	6.36955e6i	−1.04126	−	0.756520i
$590$	−1.68891e6	+	5.19793e6i	−0.199745	+	0.614753i
$591$		0			0
$592$	−2.10842e6	+	1.53186e6i	−0.247260	+	0.179645i
$593$	1.24209e7			1.45050			0.725249	−	0.688486i	$-0.241724\pi$
$593$	1.24209e7			1.45050			0.725249	+	0.688486i	$0.241724\pi$
$594$		0			0
$595$	−83458.2			−0.00966444
$596$	−1.01061e6	+	734254.i	−0.116539	+	0.0846702i
$597$		0			0
$598$	1.80134e6	−	5.54396e6i	0.205988	−	0.633967i
$599$	3.15878e6	+	2.29498e6i	0.359709	+	0.261344i	0.752931	−	0.658100i	$-0.228639\pi$
$599$	3.15878e6	+	2.29498e6i	0.359709	+	0.261344i	−0.393222	+	0.919444i	$0.628639\pi$
$600$		0			0
$601$	−652526.	+	2.00827e6i	−0.0736906	+	0.226796i	−0.981117	−	0.193414i	$-0.938044\pi$
$601$	−652526.	+	2.00827e6i	−0.0736906	+	0.226796i	0.907427	+	0.420211i	$0.138044\pi$
$602$	158666.	+	488324.i	0.0178440	+	0.0549183i
$603$		0			0
$604$	−2.12782e6			−0.237324
$605$	−1.60557e7	−	5.63565e6i	−1.78336	−	0.625973i
$606$		0			0
$607$	2.76292e6	−	2.00738e6i	0.304367	−	0.221135i	−0.425109	−	0.905142i	$-0.639764\pi$
$607$	2.76292e6	−	2.00738e6i	0.304367	−	0.221135i	0.729476	+	0.684007i	$0.239764\pi$
$608$	−706745.	−	2.17514e6i	−0.0775360	−	0.238631i
$609$		0			0
$610$	−2.91929e6	−	2.12099e6i	−0.317652	−	0.230788i
$611$	−8.52098e6	−	6.19085e6i	−0.923393	−	0.670884i
$612$		0			0
$613$	−2.82066e6	−	8.68111e6i	−0.303180	−	0.933091i	−0.980350	−	0.197265i	$-0.936794\pi$
$613$	−2.82066e6	−	8.68111e6i	−0.303180	−	0.933091i	0.677170	−	0.735826i	$-0.263206\pi$
$614$	42940.9	−	31198.4i	0.00459674	−	0.00333973i
$615$		0			0
$616$	−42880.2	−	292885.i	−0.00455308	−	0.0310989i
$617$	2.48735e6			0.263042			0.131521	−	0.991313i	$-0.458014\pi$
$617$	2.48735e6			0.263042			0.131521	+	0.991313i	$0.458014\pi$
$618$		0			0
$619$	3.96095e6	+	1.21906e7i	0.415502	+	1.27878i	0.911801	+	0.410632i	$0.134692\pi$
$619$	3.96095e6	+	1.21906e7i	0.415502	+	1.27878i	−0.496299	+	0.868152i	$0.665308\pi$
$620$	−2.53459e6	+	7.80065e6i	−0.264806	+	0.814989i
$621$		0			0
$622$	−7.82364e6	−	5.68421e6i	−0.810836	−	0.589107i
$623$	−119152.	+	366711.i	−0.0122993	+	0.0378533i
$624$		0			0
$625$	−2.40503e7	+	1.74736e7i	−2.46276	+	1.78930i
$626$	5.02596e6			0.512606
$627$		0			0
$628$	8.01807e6			0.811280
$629$	564483.	−	410121.i	0.0568885	−	0.0413319i
$630$		0			0
$631$	−1.63017e6	+	5.01714e6i	−0.162989	+	0.501629i	−0.998882	−	0.0472629i	$-0.984950\pi$
$631$	−1.63017e6	+	5.01714e6i	−0.162989	+	0.501629i	0.835893	+	0.548892i	$0.184950\pi$
$632$	3.61696e6	+	2.62788e6i	0.360206	+	0.261705i
$633$		0			0
$634$	−4.15980e6	+	1.28025e7i	−0.411007	+	1.26495i
$635$	−8.06919e6	−	2.48344e7i	−0.794137	−	2.44410i
$636$		0			0
$637$	9.33392e6			0.911413
$638$	−1.41027e6	+	697896.i	−0.137167	+	0.0678795i
$639$		0			0
$640$	−1.40046e6	+	1.01750e6i	−0.135152	+	0.0981936i
$641$	−300710.	−	925489.i	−0.0289070	−	0.0889665i	0.935562	−	0.353162i	$-0.114894\pi$
$641$	−300710.	−	925489.i	−0.0289070	−	0.0889665i	−0.964469	+	0.264196i	$0.914894\pi$
$642$		0			0
$643$	2.35377e6	+	1.71011e6i	0.224511	+	0.163116i	0.694355	−	0.719633i	$-0.255690\pi$
$643$	2.35377e6	+	1.71011e6i	0.224511	+	0.163116i	−0.469844	+	0.882749i	$0.655690\pi$
$644$	388376.	+	282172.i	0.0369009	+	0.0268101i
$645$		0			0
$646$	189215.	+	582345.i	0.0178392	+	0.0549034i
$647$	−559482.	+	406488.i	−0.0525443	+	0.0381757i	−0.613747	−	0.789502i	$-0.710339\pi$
$647$	−559482.	+	406488.i	−0.0525443	+	0.0381757i	0.561203	+	0.827678i	$0.310339\pi$
$648$		0			0
$649$	5.11606e6	+	871812.i	0.476786	+	0.0812477i
$650$	1.79986e7			1.67092
$651$		0			0
$652$	1.05612e6	+	3.25039e6i	0.0972955	+	0.299445i
$653$	5.68218e6	−	1.74879e7i	0.521473	−	1.60493i	−0.249714	−	0.968320i	$-0.580337\pi$
$653$	5.68218e6	−	1.74879e7i	0.521473	−	1.60493i	0.771187	−	0.636609i	$-0.219663\pi$
$654$		0			0
$655$	3.03958e6	+	2.20838e6i	0.276828	+	0.201127i
$656$	788549.	−	2.42690e6i	0.0715433	−	0.220188i
$657$		0			0
$658$	701731.	−	509837.i	0.0631838	−	0.0459057i
$659$	−1.31342e7			−1.17813			−0.589063	−	0.808087i	$-0.700503\pi$
$659$	−1.31342e7			−1.17813			−0.589063	+	0.808087i	$0.700503\pi$
$660$		0			0
$661$	1.45689e7			1.29695			0.648474	−	0.761236i	$-0.275407\pi$
$661$	1.45689e7			1.29695			0.648474	+	0.761236i	$0.275407\pi$
$662$	−1.06190e7	+	7.71516e6i	−0.941757	+	0.684226i
$663$		0			0
$664$	−1.88305e6	+	5.79543e6i	−0.165745	+	0.510112i
$665$	−2.20026e6	−	1.59858e6i	−0.192939	−	0.140178i
$666$		0			0
$667$	788574.	−	2.42698e6i	0.0686322	−	0.211228i
$668$	2.11557e6	+	6.51104e6i	0.183436	+	0.564559i
$669$		0			0
$670$	−1.41379e7			−1.21674
$671$	−1.59121e6	+	3.03458e6i	−0.136434	+	0.260191i
$672$		0			0
$673$	−2.78560e6	+	2.02385e6i	−0.237072	+	0.172243i	−0.699978	−	0.714165i	$-0.746807\pi$
$673$	−2.78560e6	+	2.02385e6i	−0.237072	+	0.172243i	0.462906	+	0.886408i	$0.346807\pi$
$674$	239592.	+	737388.i	0.0203153	+	0.0625240i
$675$		0			0
$676$	749941.	+	544864.i	0.0631190	+	0.0458586i
$677$	8.45795e6	+	6.14506e6i	0.709240	+	0.515293i	0.882928	−	0.469508i	$-0.155569\pi$
$677$	8.45795e6	+	6.14506e6i	0.709240	+	0.515293i	−0.173688	+	0.984801i	$0.555569\pi$
$678$		0			0
$679$	71911.7	+	221322.i	0.00598584	+	0.0184225i
$680$	374944.	−	272413.i	0.0310952	−	0.0225920i
$681$		0			0
$682$	7.67778e6	+	1.30835e6i	0.632084	+	0.107712i
$683$	2.17238e7			1.78190			0.890951	−	0.454099i	$-0.150039\pi$
$683$	2.17238e7			1.78190			0.890951	+	0.454099i	$0.150039\pi$
$684$		0			0
$685$	1.05525e6	+	3.24773e6i	0.0859270	+	0.264456i
$686$	−476962.	+	1.46794e6i	−0.0386967	+	0.119096i
$687$		0			0
$688$	−2.30674e6	−	1.67594e6i	−0.185792	−	0.134986i
$689$	5.93230e6	−	1.82577e7i	0.476075	−	1.46521i
$690$		0			0
$691$	−9.19499e6	+	6.68055e6i	−0.732582	+	0.532252i	−0.890379	−	0.455219i	$-0.849561\pi$
$691$	−9.19499e6	+	6.68055e6i	−0.732582	+	0.532252i	0.157797	+	0.987472i	$0.449561\pi$
$692$	−8.69255e6			−0.690052
$693$		0			0
$694$	3.65572e6			0.288121
$695$	−2.16409e7	+	1.57230e7i	−1.69947	+	1.23474i
$696$		0			0
$697$	−211117.	+	649750.i	−0.0164604	+	0.0506599i
$698$	−882163.	−	640929.i	−0.0685347	−	0.0497934i
$699$		0			0
$700$	−458039.	+	1.40970e6i	−0.0353311	+	0.108738i
$701$	−1.81493e6	−	5.58577e6i	−0.139497	−	0.429327i	0.856766	−	0.515706i	$-0.172470\pi$
$701$	−1.81493e6	−	5.58577e6i	−0.139497	−	0.429327i	−0.996262	+	0.0863791i	$0.972470\pi$
$702$		0			0
$703$	2.27373e7			1.73521
$704$	1.14864e6	+	1.17585e6i	0.0873476	+	0.0894169i
$705$		0			0
$706$	6.13159e6	−	4.45486e6i	0.462979	−	0.336374i
$707$	496965.	+	1.52950e6i	0.0373919	+	0.115080i
$708$		0			0
$709$	−6.53454e6	−	4.74762e6i	−0.488202	−	0.354699i	0.316290	−	0.948662i	$-0.397563\pi$
$709$	−6.53454e6	−	4.74762e6i	−0.488202	−	0.354699i	−0.804492	+	0.593963i	$0.797563\pi$
$710$	875444.	+	636047.i	0.0651752	+	0.0473526i
$711$		0			0
$712$	−661666.	−	2.03640e6i	−0.0489146	−	0.150544i
$713$	−1.02188e7	+	7.42442e6i	−0.752797	+	0.546939i
$714$		0			0
$715$	−3.43836e6	−	2.34850e7i	−0.251528	−	1.71801i
$716$	−1.12669e7			−0.821339
$717$		0			0
$718$	802352.	+	2.46938e6i	0.0580836	+	0.178763i
$719$	661619.	−	2.03625e6i	0.0477294	−	0.146896i	−0.924351	−	0.381542i	$-0.875393\pi$
$719$	661619.	−	2.03625e6i	0.0477294	−	0.146896i	0.972081	+	0.234646i	$0.0753931\pi$
$720$		0			0
$721$	1.05090e6	+	763522.i	0.0752874	+	0.0546995i
$722$	−3.10536e6	+	9.55732e6i	−0.221702	+	0.682328i
$723$		0			0
$724$	−4.29932e6	+	3.12364e6i	−0.304827	+	0.221470i
$725$	7.87927e6			0.556725
$726$		0			0
$727$	−546966.			−0.0383817			−0.0191908	−	0.999816i	$-0.506109\pi$
$727$	−546966.			−0.0383817			−0.0191908	+	0.999816i	$0.506109\pi$
$728$	334040.	−	242694.i	0.0233598	−	0.0169719i
$729$		0			0
$730$	−8.70500e6	+	2.67912e7i	−0.604591	+	1.86074i
$731$	617579.	+	448697.i	0.0427463	+	0.0310570i
$732$		0			0
$733$	5.78296e6	−	1.77981e7i	0.397549	−	1.22353i	−0.529410	−	0.848366i	$-0.677587\pi$
$733$	5.78296e6	−	1.77981e7i	0.397549	−	1.22353i	0.926959	−	0.375163i	$-0.122413\pi$
$734$	−3.59777e6	−	1.10728e7i	−0.246486	−	0.758607i
$735$		0			0
$736$	−2.66584e6			−0.181401
$737$	1.94476e6	+	1.32833e7i	0.131886	+	0.900818i
$738$		0			0
$739$	4.21107e6	−	3.05952e6i	0.283649	−	0.206083i	−0.436858	−	0.899530i	$-0.643909\pi$
$739$	4.21107e6	−	3.05952e6i	0.283649	−	0.206083i	0.720507	+	0.693447i	$0.243909\pi$
$740$	−5.31810e6	−	1.63674e7i	−0.357008	−	1.09876i
$741$		0			0
$742$	1.27903e6	+	929267.i	0.0852844	+	0.0619628i
$743$	−9.82911e6	−	7.14127e6i	−0.653194	−	0.474573i	0.211164	−	0.977451i	$-0.432275\pi$
$743$	−9.82911e6	−	7.14127e6i	−0.653194	−	0.474573i	−0.864358	+	0.502877i	$0.832275\pi$
$744$		0			0
$745$	−2.54909e6	−	7.84528e6i	−0.168265	−	0.517867i
$746$	−9.93810e6	+	7.22045e6i	−0.653817	+	0.475026i
$747$		0			0
$748$	−307522.	−	314808.i	−0.0200966	−	0.0205727i
$749$	2.05305e6			0.133720
$750$		0			0
$751$	5.75469e6	+	1.77111e7i	0.372325	+	1.14590i	0.945266	+	0.326302i	$0.105803\pi$
$751$	5.75469e6	+	1.77111e7i	0.372325	+	1.14590i	−0.572941	+	0.819597i	$0.694197\pi$
$752$	−1.48845e6	+	4.58098e6i	−0.0959820	+	0.295402i
$753$		0			0
$754$	−1.77568e6	−	1.29010e6i	−0.113746	−	0.0826411i
$755$	4.34202e6	−	1.33634e7i	0.277220	−	0.853194i
$756$		0			0
$757$	1.48216e7	−	1.07685e7i	0.940059	−	0.682993i	−0.00837558	−	0.999965i	$-0.502666\pi$
$757$	1.48216e7	−	1.07685e7i	0.940059	−	0.682993i	0.948435	+	0.316972i	$0.102666\pi$
$758$	−7.69251e6			−0.486290
$759$		0			0
$760$	1.51027e7			0.948464
$761$	−4.63788e6	+	3.36962e6i	−0.290307	+	0.210921i	−0.723401	−	0.690428i	$-0.757422\pi$
$761$	−4.63788e6	+	3.36962e6i	−0.290307	+	0.210921i	0.433093	+	0.901349i	$0.357422\pi$
$762$		0			0
$763$	519624.	−	1.59924e6i	0.0323131	−	0.0994494i
$764$	5.02665e6	+	3.65207e6i	0.311562	+	0.226363i
$765$		0			0
$766$	−467395.	+	1.43849e6i	−0.0287814	+	0.0885801i
$767$	2.23703e6	+	6.88486e6i	0.137304	+	0.422578i
$768$		0			0
$769$	−2.75654e7			−1.68092			−0.840462	−	0.541871i	$-0.817716\pi$
$769$	−2.75654e7			−1.68092			−0.840462	+	0.541871i	$0.817716\pi$
$770$	1.92691e6	+	328359.i	0.117121	+	0.0199582i
$771$		0			0
$772$	−5.95197e6	+	4.32436e6i	−0.359433	+	0.261143i
$773$	−447676.	−	1.37781e6i	−0.0269473	−	0.0829352i	0.936678	−	0.350191i	$-0.113883\pi$
$773$	−447676.	−	1.37781e6i	−0.0269473	−	0.0829352i	−0.963626	+	0.267256i	$0.913883\pi$
$774$		0			0
$775$	−3.15520e7	−	2.29239e7i	−1.88700	−	1.37099i
$776$	−1.04548e6	−	759583.i	−0.0623247	−	0.0452815i
$777$		0			0
$778$	−2.41828e6	−	7.44271e6i	−0.143238	−	0.440841i
$779$	−1.80113e7	+	1.30859e7i	−1.06341	+	0.772612i
$780$		0			0
$781$	477178.	−	910020.i	0.0279932	−	0.0533855i
$782$	713720.			0.0417360
$783$		0			0
$784$	−1.31907e6	−	4.05967e6i	−0.0766437	−	0.235885i
$785$	−1.63616e7	+	5.03559e7i	−0.947660	+	2.91660i
$786$		0			0
$787$	2.14847e7	+	1.56096e7i	1.23650	+	0.898368i	0.997360	−	0.0726177i	$-0.0231353\pi$
$787$	2.14847e7	+	1.56096e7i	1.23650	+	0.898368i	0.239138	+	0.970986i	$0.423135\pi$
$788$	−3.30164e6	+	1.01614e7i	−0.189415	+	0.582960i
$789$		0			0
$790$	−2.38846e7	+	1.73532e7i	−1.36160	+	0.989263i
$791$	−1.70660e6			−0.0969821
$792$		0			0
$793$	−4.77952e6			−0.269899
$794$	1.27187e7	−	9.24067e6i	0.715964	−	0.520179i
$795$		0			0
$796$	3.25028e6	−	1.00033e7i	0.181819	−	0.559580i
$797$	2.73282e6	+	1.98551e6i	0.152393	+	0.110720i	0.661369	−	0.750061i	$-0.269976\pi$
$797$	2.73282e6	+	1.98551e6i	0.152393	+	0.110720i	−0.508976	+	0.860781i	$0.669976\pi$
$798$		0			0
$799$	398500.	−	1.22646e6i	0.0220832	−	0.0679650i
$800$	−2.54356e6	−	7.82827e6i	−0.140513	−	0.432455i
$801$		0			0
$802$	9.58112e6			0.525993
$803$	2.63692e7	+	4.49350e6i	1.44314	+	0.245921i
$804$		0			0
$805$	−2.56464e6	+	1.86332e6i	−0.139488	+	0.101344i
$806$	3.35716e6	+	1.03323e7i	0.182026	+	0.560220i
$807$		0			0
$808$	−7.22504e6	−	5.24930e6i	−0.389325	−	0.282861i
$809$	−8.37654e6	−	6.08591e6i	−0.449980	−	0.326930i	0.339608	−	0.940567i	$-0.389706\pi$
$809$	−8.37654e6	−	6.08591e6i	−0.449980	−	0.326930i	−0.789588	+	0.613637i	$0.789706\pi$
$810$		0			0
$811$	−4.34535e6	−	1.33736e7i	−0.231992	−	0.713997i	−0.997506	−	0.0705782i	$-0.977516\pi$
$811$	−4.34535e6	−	1.33736e7i	−0.231992	−	0.713997i	0.765515	−	0.643418i	$-0.222484\pi$
$812$	146233.	−	106244.i	0.00778314	−	0.00565478i
$813$		0			0
$814$	−1.46465e7	+	7.24810e6i	−0.774773	+	0.383410i
$815$	−2.25686e7			−1.19017
$816$		0			0
$817$	7.68712e6	+	2.36585e7i	0.402910	+	1.24003i
$818$	3.13458e6	−	9.64725e6i	0.163793	−	0.504104i
$819$		0			0
$820$	1.36326e7	+	9.90466e6i	0.708017	+	0.514405i
$821$	8.40439e6	−	2.58661e7i	0.435159	−	1.33928i	−0.457764	−	0.889074i	$-0.651350\pi$
$821$	8.40439e6	−	2.58661e7i	0.435159	−	1.33928i	0.892923	−	0.450209i	$-0.148650\pi$
$822$		0			0
$823$	4.96057e6	−	3.60406e6i	0.255289	−	0.185478i	−0.452779	−	0.891623i	$-0.649567\pi$
$823$	4.96057e6	−	3.60406e6i	0.255289	−	0.185478i	0.708067	+	0.706145i	$0.249567\pi$
$824$	−7.21344e6			−0.370104
$825$		0			0
$826$	−596170.			−0.0304032
$827$	−8.82041e6	+	6.40840e6i	−0.448461	+	0.325826i	−0.788988	−	0.614409i	$-0.789395\pi$
$827$	−8.82041e6	+	6.40840e6i	−0.448461	+	0.325826i	0.340527	+	0.940235i	$0.389395\pi$
$828$		0			0
$829$	−2.07927e6	+	6.39934e6i	−0.105081	+	0.323406i	−0.989749	−	0.142814i	$-0.954385\pi$
$829$	−2.07927e6	+	6.39934e6i	−0.105081	+	0.323406i	0.884668	+	0.466221i	$0.154385\pi$
$830$	−3.25545e7	−	2.36523e7i	−1.64027	−	1.19173i
$831$		0			0
$832$	−708536.	+	2.18065e6i	−0.0354857	+	0.109214i
$833$	353151.	+	1.08689e6i	0.0176339	+	0.0542715i
$834$		0			0
$835$	−4.52084e7			−2.24390
$836$	−2.07748e6	−	1.41898e7i	−0.102807	−	0.702200i
$837$		0			0
$838$	6.72397e6	−	4.88525e6i	0.330762	−	0.240313i
$839$	7.20967e6	+	2.21891e7i	0.353599	+	1.08826i	0.956818	+	0.290689i	$0.0938844\pi$
$839$	7.20967e6	+	2.21891e7i	0.353599	+	1.08826i	−0.603219	+	0.797576i	$0.706116\pi$
$840$		0			0
$841$	1.58165e7	+	1.14914e7i	0.771119	+	0.560250i
$842$	1.80148e7	+	1.30885e7i	0.875689	+	0.636226i
$843$		0			0
$844$	−1.47228e6	−	4.53121e6i	−0.0711433	−	0.218957i
$845$	−4.95224e6	+	3.59801e6i	−0.238594	+	0.173349i
$846$		0			0
$847$	43451.4	−	1.85560e6i	0.00208111	−	0.0888744i
$848$	−8.77933e6			−0.419249
$849$		0			0
$850$	680982.	+	2.09585e6i	0.0323287	+	0.0994976i
$851$	8.18985e6	−	2.52058e7i	0.387661	−	1.19310i
$852$		0			0
$853$	−2.20245e7	−	1.60017e7i	−1.03642	−	0.753000i	−0.0668326	−	0.997764i	$-0.521289\pi$
$853$	−2.20245e7	−	1.60017e7i	−1.03642	−	0.753000i	−0.969583	+	0.244765i	$0.921289\pi$
$854$	121632.	−	374345.i	0.00570693	−	0.0175641i
$855$		0			0
$856$	−9.22351e6	+	6.70128e6i	−0.430241	+	0.312589i
$857$	2.42787e7			1.12921			0.564603	−	0.825363i	$-0.309029\pi$
$857$	2.42787e7			1.12921			0.564603	+	0.825363i	$0.309029\pi$
$858$		0			0
$859$	3.87873e7			1.79352			0.896760	−	0.442518i	$-0.145915\pi$
$859$	3.87873e7			1.79352			0.896760	+	0.442518i	$0.145915\pi$
$860$	1.52326e7	−	1.10671e7i	0.702307	−	0.510256i
$861$		0			0
$862$	1.80746e6	−	5.56280e6i	0.0828517	−	0.254991i
$863$	−5.83529e6	−	4.23959e6i	−0.266708	−	0.193775i	0.446391	−	0.894838i	$-0.352709\pi$
$863$	−5.83529e6	−	4.23959e6i	−0.266708	−	0.193775i	−0.713099	+	0.701063i	$0.752709\pi$
$864$		0			0
$865$	1.77380e7	−	5.45919e7i	0.806054	−	2.48078i
$866$	3.03617e6	+	9.34437e6i	0.137572	+	0.423404i
$867$		0			0
$868$	−894686.			−0.0403062
$869$	1.95898e7	+	2.00539e7i	0.879994	+	0.900841i
$870$		0			0
$871$	−1.51498e7	+	1.10070e7i	−0.676646	+	0.491612i
$872$	2.88555e6	+	8.88082e6i	0.128510	+	0.395514i
$873$		0			0
$874$	1.88162e7	+	1.36708e7i	0.833207	+	0.605360i
$875$	−4.84015e6	−	3.51657e6i	−0.213717	−	0.155274i
$876$		0			0
$877$	6.76367e6	+	2.08164e7i	0.296950	+	0.913919i	0.982559	+	0.185949i	$0.0595359\pi$
$877$	6.76367e6	+	2.08164e7i	0.296950	+	0.913919i	−0.685609	+	0.727970i	$0.740464\pi$
$878$	−1.92279e7	+	1.39699e7i	−0.841773	+	0.611584i
$879$		0			0
$880$	−9.72860e6	+	4.81436e6i	−0.423490	+	0.209571i
$881$	1.90647e7			0.827543			0.413771	−	0.910381i	$-0.364211\pi$
$881$	1.90647e7			0.827543			0.413771	+	0.910381i	$0.364211\pi$
$882$		0			0
$883$	−7.77272e6	−	2.39220e7i	−0.335484	−	1.03251i	−0.966483	−	0.256730i	$-0.917355\pi$
$883$	−7.77272e6	−	2.39220e7i	−0.335484	−	1.03251i	0.631000	−	0.775783i	$-0.282645\pi$
$884$	189695.	−	583821.i	0.00816442	−	0.0251275i
$885$		0			0
$886$	−7.28518e6	−	5.29299e6i	−0.311785	−	0.226525i
$887$	1.44699e7	−	4.45337e7i	0.617527	−	1.90055i	0.270237	−	0.962794i	$-0.412898\pi$
$887$	1.44699e7	−	4.45337e7i	0.617527	−	1.90055i	0.347290	−	0.937758i	$-0.387102\pi$
$888$		0			0
$889$	2.30437e6	−	1.67422e6i	0.0977905	−	0.0710490i
$890$	1.41394e7			0.598351
$891$		0			0
$892$	1.87114e6			0.0787397
$893$	3.39977e7	−	2.47008e7i	1.42666	−	1.03653i
$894$		0			0
$895$	2.29912e7	−	7.07597e7i	0.959411	−	2.95276i
$896$	−152763.	−	110989.i	−0.00635694	−	0.00461859i
$897$		0			0
$898$	4.63517e6	−	1.42656e7i	0.191811	−	0.590335i
$899$	1.46967e6	+	4.52317e6i	0.0606484	+	0.186657i
$900$		0			0
$901$	2.35047e6			0.0964591
$902$	7.43071e6	−	1.41710e7i	0.304098	−	0.579942i
$903$		0			0
$904$	7.66707e6	−	5.57045e6i	0.312039	−	0.226709i
$905$	−1.08442e7	−	3.33751e7i	−0.440126	−	1.35457i
$906$		0			0
$907$	1.63907e7	+	1.19086e7i	0.661577	+	0.480664i	0.867195	−	0.497969i	$-0.165921\pi$
$907$	1.63907e7	+	1.19086e7i	0.661577	+	0.480664i	−0.205618	+	0.978632i	$0.565921\pi$
$908$	1.16753e7	+	8.48263e6i	0.469954	+	0.341441i
$909$		0			0
$910$	842553.	+	2.59311e6i	0.0337283	+	0.103805i
$911$	−1.92370e7	+	1.39765e7i	−0.767963	+	0.557958i	−0.901342	−	0.433107i	$-0.857417\pi$
$911$	−1.92370e7	+	1.39765e7i	−0.767963	+	0.557958i	0.133379	+	0.991065i	$0.457417\pi$
$912$		0			0
$913$	−1.77445e7	+	3.38403e7i	−0.704509	+	1.34356i
$914$	1.93941e7			0.767901
$915$		0			0
$916$	2.77653e6	+	8.54527e6i	0.109336	+	0.336501i
$917$	−126644.	+	389769.i	−0.00497348	+	0.0153068i
$918$		0			0
$919$	3.21413e7	+	2.33520e7i	1.25538	+	0.912087i	0.998521	−	0.0543621i	$-0.0173125\pi$
$919$	3.21413e7	+	2.33520e7i	1.25538	+	0.912087i	0.256859	+	0.966449i	$0.417313\pi$
$920$	5.43990e6	−	1.67423e7i	0.211895	−	0.652147i
$921$		0			0
$922$	−9.02744e6	+	6.55882e6i	−0.349734	+	0.254096i
$923$	1.43330e6			0.0553773
$924$		0			0
$925$	8.18313e7			3.14460
$926$	−9.85895e6	+	7.16294e6i	−0.377836	+	0.274514i
$927$		0			0
$928$	−310176.	+	954625.i	−0.0118233	+	0.0363884i
$929$	−1.74240e7	−	1.26593e7i	−0.662383	−	0.481249i	0.205084	−	0.978744i	$-0.434253\pi$
$929$	−1.74240e7	−	1.26593e7i	−0.662383	−	0.481249i	−0.867467	+	0.497495i	$0.834253\pi$
$930$		0			0
$931$	−1.15082e7	+	3.54186e7i	−0.435144	+	1.33923i
$932$	6.80803e6	+	2.09530e7i	0.256733	+	0.790143i
$933$		0			0
$934$	−1.36896e7			−0.513478
$935$	2.60462e6	−	1.28894e6i	0.0974350	−	0.0482174i
$936$		0			0
$937$	−3.86210e7	+	2.80598e7i	−1.43706	+	1.04408i	−0.448412	+	0.893827i	$0.648010\pi$
$937$	−3.86210e7	+	2.80598e7i	−1.43706	+	1.04408i	−0.988647	+	0.150258i	$0.951990\pi$
$938$	−476554.	−	1.46668e6i	−0.0176850	−	0.0544289i
$939$		0			0
$940$	−2.57326e7	−	1.86959e7i	−0.949871	−	0.690122i
$941$	1.02799e7	+	7.46881e6i	0.378457	+	0.274965i	0.760709	−	0.649093i	$-0.224851\pi$
$941$	1.02799e7	+	7.46881e6i	0.378457	+	0.274965i	−0.382252	+	0.924058i	$0.624851\pi$
$942$		0			0
$943$	8.01904e6	+	2.46801e7i	0.293659	+	0.903789i
$944$	2.67835e6	−	1.94593e6i	0.0978221	−	0.0710719i
$945$		0			0
$946$	−1.24935e7	−	1.27895e7i	−0.453896	−	0.464649i
$947$	645614.			0.0233936			0.0116968	−	0.999932i	$-0.496277\pi$
$947$	645614.			0.0233936			0.0116968	+	0.999932i	$0.496277\pi$
$948$		0			0
$949$	1.15301e7	+	3.54860e7i	0.415593	+	1.27906i
$950$	−2.21913e7	+	6.82977e7i	−0.797762	+	2.45526i
$951$		0			0
$952$	40898.9	+	29714.8i	0.00146258	+	0.00106263i
$953$	446166.	−	1.37316e6i	0.0159134	−	0.0489766i	−0.942784	−	0.333403i	$-0.891803\pi$
$953$	446166.	−	1.37316e6i	0.0159134	−	0.0489766i	0.958698	+	0.284426i	$0.0918031\pi$
$954$		0			0
$955$	−3.31935e7	+	2.41165e7i	−1.17773	+	0.855669i
$956$	4.08347e6			0.144505
$957$		0			0
$958$	2.05126e7			0.722117
$959$	−301354.	+	218947.i	−0.0105811	+	0.00768762i
$960$		0			0
$961$	−1.57241e6	+	4.83937e6i	−0.0549233	+	0.169037i
$962$	−1.84415e7	−	1.33986e7i	−0.642480	−	0.466789i
$963$		0			0
$964$	−6.26804e6	+	1.92910e7i	−0.217240	+	0.668595i
$965$	−1.50127e7	−	4.62045e7i	−0.518970	−	1.59722i
$966$		0			0
$967$	6.85751e6			0.235831			0.117915	−	0.993024i	$-0.462379\pi$
$967$	6.85751e6			0.235831			0.117915	+	0.993024i	$0.462379\pi$
$968$	5.86159e6	+	8.47829e6i	0.201061	+	0.290817i
$969$		0			0
$970$	6.90381e6	−	5.01591e6i	0.235591	−	0.171167i
$971$	−1.56971e7	−	4.83107e7i	−0.534283	−	1.64436i	−0.745192	−	0.666850i	$-0.767642\pi$
$971$	−1.56971e7	−	4.83107e7i	−0.534283	−	1.64436i	0.210909	−	0.977506i	$-0.432358\pi$
$972$		0			0
$973$	−2.36060e6	−	1.71507e6i	−0.0799355	−	0.0580765i
$974$	4.41943e6	+	3.21090e6i	0.149269	+	0.108450i
$975$		0			0
$976$	675440.	+	2.07879e6i	0.0226967	+	0.0698532i
$977$	−1.25239e7	+	9.09916e6i	−0.419763	+	0.304976i	−0.777542	−	0.628830i	$-0.783534\pi$
$977$	−1.25239e7	+	9.09916e6i	−0.419763	+	0.304976i	0.357779	+	0.933806i	$0.383534\pi$
$978$		0			0
$979$	−1.94497e6	−	1.32847e7i	−0.0648569	−	0.442992i
$980$	2.81877e7			0.937549
$981$		0			0
$982$	−814700.	−	2.50739e6i	−0.0269600	−	0.0829742i
$983$	9.19390e6	−	2.82959e7i	0.303470	−	0.933985i	−0.676773	−	0.736191i	$-0.736622\pi$
$983$	9.19390e6	−	2.82959e7i	0.303470	−	0.933985i	0.980244	−	0.197794i	$-0.0633777\pi$
$984$		0			0
$985$	−5.70795e7	−	4.14707e7i	−1.87452	−	1.36192i
$986$	83042.9	−	255580.i	0.00272026	−	0.00837210i
$987$		0			0
$988$	1.61837e7	−	1.17581e7i	0.527455	−	0.383218i
$989$	2.89958e7			0.942636
$990$		0			0
$991$	−2.33246e7			−0.754450			−0.377225	−	0.926122i	$-0.623122\pi$
$991$	−2.33246e7			−0.754450			−0.377225	+	0.926122i	$0.623122\pi$
$992$	4.01946e6	−	2.92031e6i	0.129685	−	0.0942214i
$993$		0			0
$994$	−36475.3	+	112260.i	−0.00117094	+	0.00360377i
$995$	5.61916e7	+	4.08256e7i	1.79934	+	1.30730i
$996$		0			0
$997$	1.22456e7	−	3.76882e7i	0.390160	−	1.20079i	−0.542506	−	0.840052i	$-0.682525\pi$
$997$	1.22456e7	−	3.76882e7i	0.390160	−	1.20079i	0.932667	−	0.360739i	$-0.117475\pi$
$998$	1.94573e6	+	5.98834e6i	0.0618381	+	0.190318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.f.91.3		12
3.2	odd	2		66.6.e.c.25.1	✓	12
11.4	even	5	inner	198.6.f.f.37.3		12
33.2	even	10		726.6.a.bf.1.6		6
33.20	odd	10		726.6.a.bh.1.6		6
33.26	odd	10		66.6.e.c.37.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.c.25.1	✓	12	3.2	odd	2
66.6.e.c.37.1	yes	12	33.26	odd	10
198.6.f.f.37.3		12	11.4	even	5	inner
198.6.f.f.91.3		12	1.1	even	1	trivial
726.6.a.bf.1.6		6	33.2	even	10
726.6.a.bh.1.6		6	33.20	odd	10

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(85.4776 + 62.1031i) q^{5} +(-3.56142 + 10.9609i) q^{7} +(-19.7771 - 60.8676i) q^{8} +O(q^{10})\)	\(q+(3.23607 - 2.35114i) q^{2} +(4.94427 - 15.2169i) q^{4} +(85.4776 + 62.1031i) q^{5} +(-3.56142 + 10.9609i) q^{7} +(-19.7771 - 60.8676i) q^{8} +422.624 q^{10} +(-58.1348 - 397.079i) q^{11} +(452.874 - 329.032i) q^{13} +(14.2457 + 43.8437i) q^{14} +(-207.108 - 150.473i) q^{16} +(55.4487 + 40.2858i) q^{17} +(690.180 + 2124.16i) q^{19} +(1367.64 - 993.650i) q^{20} +(-1121.72 - 1148.29i) q^{22} +2603.36 q^{23} +(2483.95 + 7644.80i) q^{25} +(691.930 - 2129.54i) q^{26} +(149.183 + 108.388i) q^{28} +(302.907 - 932.251i) q^{29} +(-3925.25 + 2851.86i) q^{31} -1024.00 q^{32} +274.153 q^{34} +(-985.129 + 715.738i) q^{35} +(3145.88 - 9682.02i) q^{37} +(7227.66 + 5251.20i) q^{38} +(2089.57 - 6431.04i) q^{40} +(3080.27 + 9480.09i) q^{41} +11137.8 q^{43} +(-6329.74 - 1078.63i) q^{44} +(8424.64 - 6120.86i) q^{46} +(-5814.26 - 17894.5i) q^{47} +(13489.7 + 9800.83i) q^{49} +(26012.2 + 18899.0i) q^{50} +(-2767.72 - 8518.16i) q^{52} +(27744.6 - 20157.6i) q^{53} +(19690.6 - 37551.7i) q^{55} +737.600 q^{56} +(-1211.63 - 3729.00i) q^{58} +(-3996.24 + 12299.2i) q^{59} +(-6907.52 - 5018.61i) q^{61} +(-5997.25 + 18457.6i) q^{62} +(-3313.73 + 2407.57i) q^{64} +59144.5 q^{65} -33452.6 q^{67} +(887.179 - 644.573i) q^{68} +(-1505.14 + 4632.35i) q^{70} +(2071.45 + 1504.99i) q^{71} +(-20597.5 + 63392.5i) q^{73} +(-12583.5 - 38728.1i) q^{74} +35735.5 q^{76} +(4559.39 + 776.951i) q^{77} +(-56515.0 + 41060.6i) q^{79} +(-8358.28 - 25724.1i) q^{80} +(32257.0 + 23436.1i) q^{82} +(-77029.5 - 55965.2i) q^{83} +(2237.75 + 6887.07i) q^{85} +(36042.8 - 26186.6i) q^{86} +(-23019.5 + 11391.6i) q^{88} +33456.2 q^{89} +(1993.62 + 6135.74i) q^{91} +(12871.7 - 39615.0i) q^{92} +(-60887.7 - 44237.5i) q^{94} +(-72921.8 + 224430. i) q^{95} +(16335.6 - 11868.5i) q^{97} +66696.7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 48 q^{4} + 118 q^{5} + 216 q^{7} + 192 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 - 48 * q^4 + 118 * q^5 + 216 * q^7 + 192 * q^8	\( 12 q + 12 q^{2} - 48 q^{4} + 118 q^{5} + 216 q^{7} + 192 q^{8} + 328 q^{10} + 814 q^{11} + 1130 q^{13} - 864 q^{14} - 768 q^{16} + 2256 q^{17} - 3018 q^{19} + 1888 q^{20} - 916 q^{22} + 5076 q^{23} - 3707 q^{25} + 4320 q^{26} - 944 q^{28} - 15311 q^{29} - 16989 q^{31} - 12288 q^{32} - 16944 q^{34} - 897 q^{35} + 4326 q^{37} - 12008 q^{38} + 4928 q^{40} - 18536 q^{41} + 14020 q^{43} - 11696 q^{44} - 6664 q^{46} - 75246 q^{47} + 94655 q^{49} + 10128 q^{50} - 17280 q^{52} + 33303 q^{53} + 24050 q^{55} + 20096 q^{56} + 61244 q^{58} - 29940 q^{59} - 78908 q^{61} + 23296 q^{62} - 12288 q^{64} - 123664 q^{65} - 73388 q^{67} + 36096 q^{68} - 9372 q^{70} - 140764 q^{71} - 242111 q^{73} - 17304 q^{74} + 512 q^{76} - 83852 q^{77} - 161870 q^{79} - 19712 q^{80} + 38264 q^{82} + 31192 q^{83} - 35038 q^{85} - 119000 q^{86} + 57664 q^{88} + 75180 q^{89} - 76956 q^{91} - 67264 q^{92} - 311696 q^{94} + 390998 q^{95} - 6508 q^{97} + 58520 q^{98}+O(q^{100}) \) 12 * q + 12 * q^2 - 48 * q^4 + 118 * q^5 + 216 * q^7 + 192 * q^8 + 328 * q^10 + 814 * q^11 + 1130 * q^13 - 864 * q^14 - 768 * q^16 + 2256 * q^17 - 3018 * q^19 + 1888 * q^20 - 916 * q^22 + 5076 * q^23 - 3707 * q^25 + 4320 * q^26 - 944 * q^28 - 15311 * q^29 - 16989 * q^31 - 12288 * q^32 - 16944 * q^34 - 897 * q^35 + 4326 * q^37 - 12008 * q^38 + 4928 * q^40 - 18536 * q^41 + 14020 * q^43 - 11696 * q^44 - 6664 * q^46 - 75246 * q^47 + 94655 * q^49 + 10128 * q^50 - 17280 * q^52 + 33303 * q^53 + 24050 * q^55 + 20096 * q^56 + 61244 * q^58 - 29940 * q^59 - 78908 * q^61 + 23296 * q^62 - 12288 * q^64 - 123664 * q^65 - 73388 * q^67 + 36096 * q^68 - 9372 * q^70 - 140764 * q^71 - 242111 * q^73 - 17304 * q^74 + 512 * q^76 - 83852 * q^77 - 161870 * q^79 - 19712 * q^80 + 38264 * q^82 + 31192 * q^83 - 35038 * q^85 - 119000 * q^86 + 57664 * q^88 + 75180 * q^89 - 76956 * q^91 - 67264 * q^92 - 311696 * q^94 + 390998 * q^95 - 6508 * q^97 + 58520 * q^98

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