LMFDB - Embedded newform 198.6.f.h.37.4

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			37.4
Root			$28.0249 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	198.37
Dual form			198.6.f.h.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(34.0128 - 24.7118i) q^{5} +(58.4057 + 179.754i) q^{7} +(-19.7771 + 60.8676i) q^{8} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(34.0128 - 24.7118i) q^{5} +(58.4057 + 179.754i) q^{7} +(-19.7771 + 60.8676i) q^{8} +168.169 q^{10} +(-393.972 + 76.3995i) q^{11} +(193.036 + 140.249i) q^{13} +(-233.623 + 719.016i) q^{14} +(-207.108 + 150.473i) q^{16} +(-9.75136 + 7.08478i) q^{17} +(1.49370 - 4.59712i) q^{19} +(544.205 + 395.388i) q^{20} +(-1454.55 - 679.050i) q^{22} +898.471 q^{23} +(-419.477 + 1291.02i) q^{25} +(294.932 + 907.708i) q^{26} +(-2446.53 + 1777.51i) q^{28} +(623.128 + 1917.79i) q^{29} +(-95.7702 - 69.5811i) q^{31} -1024.00 q^{32} -48.2134 q^{34} +(6428.58 + 4670.64i) q^{35} +(3978.56 + 12244.7i) q^{37} +(15.6422 - 11.3647i) q^{38} +(831.471 + 2559.01i) q^{40} +(-3914.36 + 12047.2i) q^{41} -14084.2 q^{43} +(-3110.47 - 5617.30i) q^{44} +(2907.51 + 2112.43i) q^{46} +(2125.46 - 6541.50i) q^{47} +(-15303.2 + 11118.4i) q^{49} +(-4392.82 + 3191.57i) q^{50} +(-1179.73 + 3630.83i) q^{52} +(-5958.77 - 4329.30i) q^{53} +(-11512.1 + 12334.3i) q^{55} -12096.3 q^{56} +(-2492.51 + 7671.17i) q^{58} +(-2337.50 - 7194.07i) q^{59} +(-19619.5 + 14254.4i) q^{61} +(-146.324 - 450.338i) q^{62} +(-3313.73 - 2407.57i) q^{64} +10031.5 q^{65} -11275.9 q^{67} +(-156.022 - 113.356i) q^{68} +(9822.00 + 30229.0i) q^{70} +(53676.5 - 38998.3i) q^{71} +(27410.8 + 84361.9i) q^{73} +(-15914.2 + 48979.0i) q^{74} +77.3393 q^{76} +(-36743.3 - 66356.0i) q^{77} +(11511.9 + 8363.90i) q^{79} +(-3325.89 + 10236.0i) q^{80} +(-40991.7 + 29782.2i) q^{82} +(96212.9 - 69902.8i) q^{83} +(-156.594 + 481.947i) q^{85} +(-45577.4 - 33113.9i) q^{86} +(3141.37 - 25491.1i) q^{88} -27768.9 q^{89} +(-13935.9 + 42890.2i) q^{91} +(4442.28 + 13671.9i) q^{92} +(22258.1 - 16171.5i) q^{94} +(-62.7982 - 193.273i) q^{95} +(-87906.6 - 63867.9i) q^{97} -75663.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

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

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
$5$	34.0128	−	24.7118i	0.608440	−	0.442057i	−0.240425	−	0.970668i	$-0.577287\pi$
$5$	34.0128	−	24.7118i	0.608440	−	0.442057i	0.848865	+	0.528610i	$0.177287\pi$
$6$		0			0
$7$	58.4057	+	179.754i	0.450516	+	1.38654i	0.876320	+	0.481729i	$0.159991\pi$
$7$	58.4057	+	179.754i	0.450516	+	1.38654i	−0.425805	+	0.904815i	$0.640009\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$		0			0
$10$	168.169			0.531796
$11$	−393.972	+	76.3995i	−0.981712	+	0.190374i
$11$	−393.972	+	76.3995i	−0.981712	+	0.190374i
$12$		0			0
$13$	193.036	+	140.249i	0.316795	+	0.230165i	0.734807	−	0.678276i	$-0.237273\pi$
$13$	193.036	+	140.249i	0.316795	+	0.230165i	−0.418011	+	0.908442i	$0.637273\pi$
$14$	−233.623	+	719.016i	−0.318563	+	0.980435i
$15$		0			0
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−9.75136	+	7.08478i	−0.00818357	+	0.00594571i	−0.591870	−	0.806034i	$-0.701610\pi$
$17$	−9.75136	+	7.08478i	−0.00818357	+	0.00594571i	0.583686	+	0.811980i	$0.301610\pi$
$18$		0			0
$19$	1.49370	−	4.59712i	0.000949245	−	0.00292148i	−0.950581	−	0.310477i	$-0.899511\pi$
$19$	1.49370	−	4.59712i	0.000949245	−	0.00292148i	0.951530	+	0.307556i	$0.0995111\pi$
$20$	544.205	+	395.388i	0.304220	+	0.221029i
$21$		0			0
$22$	−1454.55	−	679.050i	−0.640724	−	0.299120i
$23$	898.471			0.354148			0.177074	−	0.984198i	$-0.443337\pi$
$23$	898.471			0.354148			0.177074	+	0.984198i	$0.443337\pi$
$24$		0			0
$25$	−419.477	+	1291.02i	−0.134233	+	0.413126i
$26$	294.932	+	907.708i	0.0855635	+	0.263337i
$27$		0			0
$28$	−2446.53	+	1777.51i	−0.589732	+	0.428466i
$29$	623.128	+	1917.79i	0.137589	+	0.423454i	0.995984	−	0.0895350i	$-0.0285381\pi$
$29$	623.128	+	1917.79i	0.137589	+	0.423454i	−0.858395	+	0.512989i	$0.828538\pi$
$30$		0			0
$31$	−95.7702	−	69.5811i	−0.0178989	−	0.0130043i	0.578800	−	0.815470i	$-0.303521\pi$
$31$	−95.7702	−	69.5811i	−0.0178989	−	0.0130043i	−0.596699	+	0.802465i	$0.703521\pi$
$32$	−1024.00			−0.176777
$33$		0			0
$34$	−48.2134			−0.00715271
$35$	6428.58	+	4670.64i	0.887044	+	0.644475i
$36$		0			0
$37$	3978.56	+	12244.7i	0.477773	+	1.47043i	0.842181	+	0.539195i	$0.181271\pi$
$37$	3978.56	+	12244.7i	0.477773	+	1.47043i	−0.364408	+	0.931239i	$0.618729\pi$
$38$	15.6422	−	11.3647i	0.00175727	−	0.00127673i
$39$		0			0
$40$	831.471	+	2559.01i	0.0821670	+	0.252884i
$41$	−3914.36	+	12047.2i	−0.363665	+	1.11925i	0.587148	+	0.809479i	$0.300251\pi$
$41$	−3914.36	+	12047.2i	−0.363665	+	1.11925i	−0.950813	+	0.309766i	$0.899749\pi$
$42$		0			0
$43$	−14084.2			−1.16161			−0.580805	−	0.814043i	$-0.697262\pi$
$43$	−14084.2			−1.16161			−0.580805	+	0.814043i	$0.697262\pi$
$44$	−3110.47	−	5617.30i	−0.242211	−	0.437417i
$45$		0			0
$46$	2907.51	+	2112.43i	0.202594	+	0.147193i
$47$	2125.46	−	6541.50i	0.140349	−	0.431950i	−0.856035	−	0.516918i	$-0.827079\pi$
$47$	2125.46	−	6541.50i	0.140349	−	0.431950i	0.996384	+	0.0849688i	$0.0270791\pi$
$48$		0			0
$49$	−15303.2	+	11118.4i	−0.910524	+	0.661534i
$50$	−4392.82	+	3191.57i	−0.248496	+	0.180543i
$51$		0			0
$52$	−1179.73	+	3630.83i	−0.0605025	+	0.186208i
$53$	−5958.77	−	4329.30i	−0.291385	−	0.211704i	0.432483	−	0.901642i	$-0.357638\pi$
$53$	−5958.77	−	4329.30i	−0.291385	−	0.211704i	−0.723868	+	0.689938i	$0.757638\pi$
$54$		0			0
$55$	−11512.1	+	12334.3i	−0.513156	+	0.549804i
$56$	−12096.3			−0.515445
$57$		0			0
$58$	−2492.51	+	7671.17i	−0.0972898	+	0.299427i
$59$	−2337.50	−	7194.07i	−0.0874220	−	0.269057i	0.897783	−	0.440439i	$-0.145177\pi$
$59$	−2337.50	−	7194.07i	−0.0874220	−	0.269057i	−0.985205	+	0.171381i	$0.945177\pi$
$60$		0			0
$61$	−19619.5	+	14254.4i	−0.675093	+	0.490484i	−0.871726	−	0.489993i	$-0.836999\pi$
$61$	−19619.5	+	14254.4i	−0.675093	+	0.490484i	0.196633	+	0.980477i	$0.436999\pi$
$62$	−146.324	−	450.338i	−0.00483432	−	0.0148785i
$63$		0			0
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	10031.5			0.294497
$66$		0			0
$67$	−11275.9			−0.306877			−0.153439	−	0.988158i	$-0.549035\pi$
$67$	−11275.9			−0.306877			−0.153439	+	0.988158i	$0.549035\pi$
$68$	−156.022	−	113.356i	−0.00409179	−	0.00297286i
$69$		0			0
$70$	9822.00	+	30229.0i	0.239582	+	0.737358i
$71$	53676.5	−	38998.3i	1.26368	−	0.918120i	0.264751	−	0.964317i	$-0.414710\pi$
$71$	53676.5	−	38998.3i	1.26368	−	0.918120i	0.998932	+	0.0461969i	$0.0147102\pi$
$72$		0			0
$73$	27410.8	+	84361.9i	0.602026	+	1.85285i	0.516070	+	0.856546i	$0.327394\pi$
$73$	27410.8	+	84361.9i	0.602026	+	1.85285i	0.0859559	+	0.996299i	$0.472606\pi$
$74$	−15914.2	+	48979.0i	−0.337837	+	1.03975i
$75$		0			0
$76$	77.3393			0.00153591
$77$	−36743.3	−	66356.0i	−0.706239	−	1.27542i
$78$		0			0
$79$	11511.9	+	8363.90i	0.207530	+	0.150779i	0.686695	−	0.726945i	$-0.259061\pi$
$79$	11511.9	+	8363.90i	0.207530	+	0.150779i	−0.479166	+	0.877725i	$0.659061\pi$
$80$	−3325.89	+	10236.0i	−0.0581008	+	0.178816i
$81$		0			0
$82$	−40991.7	+	29782.2i	−0.673227	+	0.489128i
$83$	96212.9	−	69902.8i	1.53299	−	1.11378i	0.578436	−	0.815728i	$-0.303663\pi$
$83$	96212.9	−	69902.8i	1.53299	−	1.11378i	0.954550	−	0.298051i	$-0.0963366\pi$
$84$		0			0
$85$	−156.594	+	481.947i	−0.00235086	+	0.00723522i
$86$	−45577.4	−	33113.9i	−0.664513	−	0.482797i
$87$		0			0
$88$	3141.37	−	25491.1i	0.0432427	−	0.350899i
$89$	−27768.9			−0.371607			−0.185804	−	0.982587i	$-0.559489\pi$
$89$	−27768.9			−0.371607			−0.185804	+	0.982587i	$0.559489\pi$
$90$		0			0
$91$	−13935.9	+	42890.2i	−0.176413	+	0.542944i
$92$	4442.28	+	13671.9i	0.0547188	+	0.168407i
$93$		0			0
$94$	22258.1	−	16171.5i	0.259818	−	0.188769i
$95$	−62.7982	−	193.273i	−0.000713901	−	0.00219716i
$96$		0			0
$97$	−87906.6	−	63867.9i	−0.948620	−	0.689213i	0.00185991	−	0.999998i	$-0.499408\pi$
$97$	−87906.6	−	63867.9i	−0.948620	−	0.689213i	−0.950480	+	0.310785i	$0.899408\pi$
$98$	−75663.0			−0.795827
$99$		0			0
$100$	−21719.3			−0.217193
$101$	103573.	+	75250.5i	1.01029	+	0.734017i	0.964269	−	0.264924i	$-0.0853467\pi$
$101$	103573.	+	75250.5i	1.01029	+	0.734017i	0.0460183	+	0.998941i	$0.485347\pi$
$102$		0			0
$103$	−24583.2	−	75659.4i	−0.228321	−	0.702700i	−0.997937	−	0.0641933i	$-0.979553\pi$
$103$	−24583.2	−	75659.4i	−0.228321	−	0.702700i	0.769616	−	0.638506i	$-0.220447\pi$
$104$	−12354.3	+	8975.91i	−0.112004	+	0.0813757i
$105$		0			0
$106$	−9104.20	−	28019.8i	−0.0787004	−	0.242215i
$107$	−30755.4	+	94655.4i	−0.259694	+	0.799256i	0.733174	+	0.680041i	$0.238038\pi$
$107$	−30755.4	+	94655.4i	−0.259694	+	0.799256i	−0.992868	+	0.119216i	$0.961962\pi$
$108$		0			0
$109$	6732.58			0.0542769			0.0271385	−	0.999632i	$-0.491360\pi$
$109$	6732.58			0.0542769			0.0271385	+	0.999632i	$0.491360\pi$
$110$	−66253.8	+	12848.0i	−0.522070	+	0.101240i
$111$		0			0
$112$	−39144.4	−	28440.1i	−0.294866	−	0.214233i
$113$	2391.22	−	7359.41i	0.0176166	−	0.0542184i	−0.941862	−	0.336001i	$-0.890926\pi$
$113$	2391.22	−	7359.41i	0.0176166	−	0.0542184i	0.959478	+	0.281782i	$0.0909256\pi$
$114$		0			0
$115$	30559.5	−	22202.8i	0.215477	−	0.156554i
$116$	−26101.9	+	18964.2i	−0.180106	+	0.130855i
$117$		0			0
$118$	9349.98	−	28776.3i	0.0618167	−	0.190252i
$119$	−1843.05	−	1339.06i	−0.0119308	−	0.00866825i
$120$		0			0
$121$	149377.	−	60198.5i	0.927515	−	0.373786i
$122$	−97004.2			−0.590053
$123$		0			0
$124$	585.295	−	1801.35i	0.00341838	−	0.0105207i
$125$	58234.9	+	179229.i	0.333356	+	1.02596i
$126$		0			0
$127$	221328.	−	160805.i	1.21767	−	0.884685i	0.221761	−	0.975101i	$-0.428820\pi$
$127$	221328.	−	160805.i	1.21767	−	0.884685i	0.995904	+	0.0904156i	$0.0288195\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	32462.5	+	23585.4i	0.168470	+	0.122401i
$131$	188029.			0.957296			0.478648	−	0.878007i	$-0.341127\pi$
$131$	188029.			0.957296			0.478648	+	0.878007i	$0.341127\pi$
$132$		0			0
$133$	913.592			0.00447841
$134$	−36489.6	−	26511.3i	−0.175553	−	0.127547i
$135$		0			0
$136$	−238.380	−	733.659i	−0.00110515	−	0.00340131i
$137$	224750.	−	163291.i	1.02306	−	0.743293i	0.0561483	−	0.998422i	$-0.482118\pi$
$137$	224750.	−	163291.i	1.02306	−	0.743293i	0.966907	+	0.255129i	$0.0821180\pi$
$138$		0			0
$139$	57980.6	+	178446.i	0.254534	+	0.783374i	0.993921	+	0.110094i	$0.0351152\pi$
$139$	57980.6	+	178446.i	0.254534	+	0.783374i	−0.739387	+	0.673280i	$0.764885\pi$
$140$	−39288.0	+	120916.i	−0.169410	+	0.521391i
$141$		0			0
$142$	265391.			1.10450
$143$	−86765.6	−	40506.2i	−0.354819	−	0.165646i
$144$		0			0
$145$	68586.3	+	49830.9i	0.270905	+	0.196824i
$146$	−109643.	+	337448.i	−0.425697	+	1.31016i
$147$		0			0
$148$	−166656.	+	121083.i	−0.625413	+	0.454389i
$149$	226305.	−	164420.i	0.835082	−	0.606723i	−0.0859105	−	0.996303i	$-0.527380\pi$
$149$	226305.	−	164420.i	0.835082	−	0.606723i	0.920993	+	0.389580i	$0.127380\pi$
$150$		0			0
$151$	127177.	−	391409.i	0.453905	−	1.39698i	−0.418511	−	0.908212i	$-0.637448\pi$
$151$	127177.	−	391409.i	0.453905	−	1.39698i	0.872416	−	0.488764i	$-0.162552\pi$
$152$	250.275	+	181.835i	0.000878635	+	0.000638366i
$153$		0			0
$154$	37108.3	−	301121.i	0.126087	−	1.02315i
$155$	−4976.89			−0.0166390
$156$		0			0
$157$	48564.0	−	149465.i	0.157241	−	0.483938i	−0.841140	−	0.540817i	$-0.818115\pi$
$157$	48564.0	−	149465.i	0.157241	−	0.483938i	0.998381	+	0.0568794i	$0.0181151\pi$
$158$	17588.7	+	54132.3i	0.0560519	+	0.172510i
$159$		0			0
$160$	−34829.1	+	25304.8i	−0.107558	+	0.0781454i
$161$	52475.8	+	161504.i	0.159549	+	0.491041i
$162$		0			0
$163$	−393856.	−	286153.i	−1.16110	−	0.843586i	−0.171180	−	0.985240i	$-0.554758\pi$
$163$	−393856.	−	286153.i	−1.16110	−	0.843586i	−0.989916	+	0.141654i	$0.954758\pi$
$164$	−202674.			−0.588422
$165$		0			0
$166$	475703.			1.33988
$167$	−336641.	−	244584.i	−0.934061	−	0.678635i	0.0129225	−	0.999917i	$-0.495887\pi$
$167$	−336641.	−	244584.i	−0.934061	−	0.678635i	−0.946984	+	0.321281i	$0.895887\pi$
$168$		0			0
$169$	−97142.8	−	298975.i	−0.261634	−	0.805226i
$170$	−1639.87	+	1191.44i	−0.00435199	+	0.00316191i
$171$		0			0
$172$	−69636.0	−	214318.i	−0.179479	−	0.552379i
$173$	167536.	−	515624.i	0.425592	−	1.30984i	−0.476834	−	0.878994i	$-0.658216\pi$
$173$	167536.	−	515624.i	0.425592	−	1.30984i	0.902426	−	0.430845i	$-0.141784\pi$
$174$		0			0
$175$	−256566.			−0.633291
$176$	70098.9	−	75105.2i	0.170581	−	0.182763i
$177$		0			0
$178$	−89862.1	−	65288.7i	−0.212582	−	0.154450i
$179$	−61771.2	+	190112.i	−0.144097	+	0.443483i	−0.996894	−	0.0787588i	$-0.974904\pi$
$179$	−61771.2	+	190112.i	−0.144097	+	0.443483i	0.852797	+	0.522242i	$0.174904\pi$
$180$		0			0
$181$	482893.	−	350843.i	1.09561	−	0.796005i	0.115270	−	0.993334i	$-0.463227\pi$
$181$	482893.	−	350843.i	1.09561	−	0.796005i	0.980337	+	0.197329i	$0.0632268\pi$
$182$	−145938.	+	106031.i	−0.326581	+	0.237275i
$183$		0			0
$184$	−17769.1	+	54687.8i	−0.0386920	+	0.119082i
$185$	437911.	+	318161.i	0.940712	+	0.683468i
$186$		0			0
$187$	3300.49	−	3536.21i	0.00690200	−	0.00739492i
$188$	110050.			0.227089
$189$		0			0
$190$	251.193	−	773.092i	0.000504805	−	0.00155363i
$191$	−179856.	−	553539.i	−0.356731	−	1.09790i	−0.954999	−	0.296609i	$-0.904144\pi$
$191$	−179856.	−	553539.i	−0.356731	−	1.09790i	0.598268	−	0.801296i	$-0.295856\pi$
$192$		0			0
$193$	−448329.	+	325730.i	−0.866369	+	0.629454i	−0.929610	−	0.368544i	$-0.879856\pi$
$193$	−448329.	+	325730.i	−0.866369	+	0.629454i	0.0632409	+	0.997998i	$0.479856\pi$
$194$	−134309.	−	413362.i	−0.256214	−	0.788544i
$195$		0			0
$196$	−244851.	−	177894.i	−0.455262	−	0.330767i
$197$	−30535.0			−0.0560573			−0.0280287	−	0.999607i	$-0.508923\pi$
$197$	−30535.0			−0.0560573			−0.0280287	+	0.999607i	$0.508923\pi$
$198$		0			0
$199$	428082.			0.766292			0.383146	−	0.923688i	$-0.374841\pi$
$199$	428082.			0.766292			0.383146	+	0.923688i	$0.374841\pi$
$200$	−70285.2	−	51065.2i	−0.124248	−	0.0902713i
$201$		0			0
$202$	158246.	+	487032.i	0.272869	+	0.839806i
$203$	−308337.	+	224020.i	−0.525152	+	0.381545i
$204$		0			0
$205$	164568.	+	506489.i	0.273502	+	0.841754i
$206$	98332.9	−	302638.i	0.161447	−	0.496884i
$207$		0			0
$208$	−61082.9			−0.0978952
$209$	−237.257	+	1925.26i	−0.000375711	+	0.00304876i
$210$		0			0
$211$	579168.	+	420790.i	0.895568	+	0.650668i	0.937324	−	0.348460i	$-0.113295\pi$
$211$	579168.	+	420790.i	0.895568	+	0.650668i	−0.0417561	+	0.999128i	$0.513295\pi$
$212$	36416.8	−	112079.i	0.0556496	−	0.171272i
$213$		0			0
$214$	−322075.	+	234001.i	−0.480753	+	0.349288i
$215$	−479043.	+	348045.i	−0.706770	+	0.513498i
$216$		0			0
$217$	6913.97	−	21279.0i	0.00996732	−	0.0306762i
$218$	21787.1	+	15829.2i	0.0310497	+	0.0225589i
$219$		0			0
$220$	−244609.	−	114195.i	−0.340734	−	0.159071i
$221$	−2875.99			−0.00396102
$222$		0			0
$223$	−280158.	+	862236.i	−0.377260	+	1.16109i	0.564682	+	0.825309i	$0.308999\pi$
$223$	−280158.	+	862236.i	−0.377260	+	1.16109i	−0.941942	+	0.335777i	$0.891001\pi$
$224$	−59807.4	−	184068.i	−0.0796406	−	0.245109i
$225$		0			0
$226$	25041.1	−	18193.5i	0.0326124	−	0.0236943i
$227$	64423.9	+	198276.i	0.0829817	+	0.255391i	0.983936	−	0.178523i	$-0.0571319\pi$
$227$	64423.9	+	198276.i	0.0829817	+	0.255391i	−0.900954	+	0.433915i	$0.857132\pi$
$228$		0			0
$229$	−12837.8	−	9327.21i	−0.0161771	−	0.0117534i	0.579667	−	0.814853i	$-0.303183\pi$
$229$	−12837.8	−	9327.21i	−0.0161771	−	0.0117534i	−0.595844	+	0.803100i	$0.703183\pi$
$230$	151095.			0.188334
$231$		0			0
$232$	−129055.			−0.157418
$233$	−23878.8	−	17349.0i	−0.0288153	−	0.0209355i	0.573284	−	0.819356i	$-0.305669\pi$
$233$	−23878.8	−	17349.0i	−0.0288153	−	0.0209355i	−0.602100	+	0.798421i	$0.705669\pi$
$234$		0			0
$235$	−89359.1	−	275019.i	−0.105553	−	0.324858i
$236$	97914.3	−	71138.9i	0.114437	−	0.0831433i
$237$		0			0
$238$	−2815.93	−	8666.56i	−0.00322241	−	0.00991754i
$239$	512113.	−	1.57612e6i	0.579924	−	1.78482i	−0.0388378	−	0.999246i	$-0.512366\pi$
$239$	512113.	−	1.57612e6i	0.579924	−	1.78482i	0.618762	−	0.785578i	$-0.287634\pi$
$240$		0			0
$241$	−397579.			−0.440942			−0.220471	−	0.975394i	$-0.570759\pi$
$241$	−397579.			−0.440942			−0.220471	+	0.975394i	$0.570759\pi$
$242$	624930.	+	156400.i	0.685951	+	0.171672i
$243$		0			0
$244$	−313912.	−	228071.i	−0.337547	−	0.245242i
$245$	−245749.	+	756337.i	−0.261563	+	0.805007i
$246$		0			0
$247$	933.077	−	677.920i	0.000973139	−	0.000707027i
$248$	6129.29	−	4453.19i	0.00632821	−	0.00459772i
$249$		0			0
$250$	−232940.	+	716915.i	−0.235718	+	0.725467i
$251$	928397.	+	674520.i	0.930142	+	0.675788i	0.946028	−	0.324086i	$-0.105057\pi$
$251$	928397.	+	674520.i	0.930142	+	0.675788i	−0.0158855	+	0.999874i	$0.505057\pi$
$252$		0			0
$253$	−353972.	+	68642.7i	−0.347671	+	0.0674206i
$254$	1.09431e6			1.06428
$255$		0			0
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	137035.	+	421751.i	0.129419	+	0.398312i	0.994680	−	0.103010i	$-0.0328473\pi$
$257$	137035.	+	421751.i	0.129419	+	0.398312i	−0.865261	+	0.501322i	$0.832847\pi$
$258$		0			0
$259$	−1.96867e6	+	1.43033e6i	−1.82358	+	1.32491i
$260$	49598.3	+	152648.i	0.0455023	+	0.140042i
$261$		0			0
$262$	608474.	+	442083.i	0.547632	+	0.397878i
$263$	−1.02639e6			−0.915002			−0.457501	−	0.889209i	$-0.651255\pi$
$263$	−1.02639e6			−0.915002			−0.457501	+	0.889209i	$0.651255\pi$
$264$		0			0
$265$	−309659.			−0.270875
$266$	2956.45	+	2147.98i	0.00256192	+	0.00186135i
$267$		0			0
$268$	−55751.2	−	171585.i	−0.0474152	−	0.145929i
$269$	−1.48598e6	+	1.07963e6i	−1.25208	+	0.909693i	−0.998341	−	0.0575789i	$-0.981662\pi$
$269$	−1.48598e6	+	1.07963e6i	−1.25208	+	0.909693i	−0.253744	+	0.967272i	$0.581662\pi$
$270$		0			0
$271$	382219.	+	1.17635e6i	0.316147	+	0.972999i	0.975280	+	0.220973i	$0.0709233\pi$
$271$	382219.	+	1.17635e6i	0.316147	+	0.972999i	−0.659133	+	0.752026i	$0.729077\pi$
$272$	953.520	−	2934.63i	0.000781462	−	0.00240509i
$273$		0			0
$274$	1.11123e6			0.894183
$275$	66629.3	−	540673.i	0.0531292	−	0.431125i
$276$		0			0
$277$	306798.	+	222902.i	0.240244	+	0.174548i	0.701392	−	0.712776i	$-0.252562\pi$
$277$	306798.	+	222902.i	0.240244	+	0.174548i	−0.461148	+	0.887323i	$0.652562\pi$
$278$	−231922.	+	713783.i	−0.179983	+	0.553929i
$279$		0			0
$280$	−411429.	+	298921.i	−0.313617	+	0.227856i
$281$	−801666.	+	582445.i	−0.605659	+	0.440037i	−0.847883	−	0.530184i	$-0.822123\pi$
$281$	−801666.	+	582445.i	−0.605659	+	0.440037i	0.242224	+	0.970220i	$0.422123\pi$
$282$		0			0
$283$	−230824.	+	710402.i	−0.171322	+	0.527276i	−0.999446	−	0.0332686i	$-0.989408\pi$
$283$	−230824.	+	710402.i	−0.171322	+	0.527276i	0.828124	+	0.560545i	$0.189408\pi$
$284$	858824.	+	623972.i	0.631842	+	0.459060i
$285$		0			0
$286$	−185543.	−	335079.i	−0.134131	−	0.242232i
$287$	−2.39415e6			−1.71572
$288$		0			0
$289$	−438715.	+	1.35023e6i	−0.308985	+	0.950959i
$290$	104791.	+	322512.i	0.0731690	+	0.225191i
$291$		0			0
$292$	−1.14820e6	+	834216.i	−0.788062	+	0.572561i
$293$	281175.	+	865369.i	0.191341	+	0.588887i	1.00000		0.000609350i	$0.000193962\pi$
$293$	281175.	+	865369.i	0.191341	+	0.588887i	−0.808659	+	0.588278i	$0.799806\pi$
$294$		0			0
$295$	−257283.	−	186927.i	−0.172130	−	0.125060i
$296$	−823993.			−0.546631
$297$		0			0
$298$	1.11892e6			0.729888
$299$	173437.	+	126009.i	0.112192	+	0.0815125i
$300$		0			0
$301$	−822596.	−	2.53169e6i	−0.523324	−	1.61062i
$302$	1.33181e6	−	967617.i	0.840282	−	0.610501i
$303$		0			0
$304$	382.386	+	1176.86i	0.000237311	+	0.000730369i
$305$	−315063.	+	969665.i	−0.193932	+	0.596860i
$306$		0			0
$307$	1.98222e6			1.20035			0.600174	−	0.799870i	$-0.295098\pi$
$307$	1.98222e6			1.20035			0.600174	+	0.799870i	$0.295098\pi$
$308$	828063.	−	887202.i	0.497378	−	0.532900i
$309$		0			0
$310$	−16105.5	−	11701.4i	−0.00951856	−	0.00691564i
$311$	225356.	−	693574.i	0.132120	−	0.406623i	−0.863011	−	0.505185i	$-0.831424\pi$
$311$	225356.	−	693574.i	0.132120	−	0.406623i	0.995131	+	0.0985619i	$0.0314242\pi$
$312$		0			0
$313$	−263866.	+	191710.i	−0.152238	+	0.110607i	−0.661297	−	0.750125i	$-0.729994\pi$
$313$	−263866.	+	191710.i	−0.152238	+	0.110607i	0.509059	+	0.860732i	$0.329994\pi$
$314$	508569.	−	369497.i	0.291089	−	0.211489i
$315$		0			0
$316$	−70354.6	+	216529.i	−0.0396346	+	0.121983i
$317$	564096.	+	409840.i	0.315286	+	0.229069i	0.734161	−	0.678975i	$-0.237576\pi$
$317$	564096.	+	409840.i	0.315286	+	0.229069i	−0.418875	+	0.908044i	$0.637576\pi$
$318$		0			0
$319$	−392013.	−	707950.i	−0.215687	−	0.389516i
$320$	−172205.			−0.0940091
$321$		0			0
$322$	−209903.	+	646015.i	−0.112818	+	0.347219i
$323$	18.0040	+	55.4107i	9.60204e−6	+	2.95521e-5i
$324$		0			0
$325$	−262038.	+	190381.i	−0.137612	+	0.0999807i
$326$	−601758.	−	1.85202e6i	−0.313601	−	0.965166i
$327$		0			0
$328$	−655868.	−	476516.i	−0.336614	−	0.244564i
$329$	1.30000e6			0.662147
$330$		0			0
$331$	215285.			0.108005			0.0540024	−	0.998541i	$-0.482802\pi$
$331$	215285.			0.108005			0.0540024	+	0.998541i	$0.482802\pi$
$332$	1.53941e6	+	1.11844e6i	0.766493	+	0.556890i
$333$		0			0
$334$	−514341.	−	1.58298e6i	−0.252281	−	0.776442i
$335$	−383526.	+	278648.i	−0.186716	+	0.135657i
$336$		0			0
$337$	−410818.	−	1.26437e6i	−0.197049	−	0.606455i	−0.999947	−	0.0103379i	$-0.996709\pi$
$337$	−410818.	−	1.26437e6i	−0.197049	−	0.606455i	0.802897	−	0.596117i	$-0.203291\pi$
$338$	388571.	−	1.19590e6i	0.185003	−	0.569381i
$339$		0			0
$340$	−8107.98			−0.00380378
$341$	43046.8	+	20096.2i	0.0200472	+	0.00935899i
$342$		0			0
$343$	−322446.	−	234271.i	−0.147987	−	0.107519i
$344$	278544.	−	857271.i	0.126911	−	0.390591i
$345$		0			0
$346$	1.75446e6	−	1.27469e6i	0.787869	−	0.572420i
$347$	−593519.	+	431216.i	−0.264613	+	0.192252i	−0.712178	−	0.701999i	$-0.752291\pi$
$347$	−593519.	+	431216.i	−0.264613	+	0.192252i	0.447565	+	0.894251i	$0.352291\pi$
$348$		0			0
$349$	−302116.	+	929817.i	−0.132773	+	0.408633i	−0.995237	−	0.0974851i	$-0.968920\pi$
$349$	−302116.	+	929817.i	−0.132773	+	0.408633i	0.862464	+	0.506119i	$0.168920\pi$
$350$	−830264.	−	603222.i	−0.362282	−	0.263213i
$351$		0			0
$352$	403428.	−	78233.1i	0.173544	−	0.0336538i
$353$	−3.29601e6			−1.40783			−0.703917	−	0.710283i	$-0.748567\pi$
$353$	−3.29601e6			−1.40783			−0.703917	+	0.710283i	$0.748567\pi$
$354$		0			0
$355$	861973.	−	2.65288e6i	0.363014	−	1.11724i
$356$	−137297.	−	422557.i	−0.0574165	−	0.176710i
$357$		0			0
$358$	−646876.	+	469983.i	−0.266756	+	0.193809i
$359$	−1.08625e6	−	3.34314e6i	−0.444831	−	1.36905i	−0.882669	−	0.469995i	$-0.844256\pi$
$359$	−1.08625e6	−	3.34314e6i	−0.444831	−	1.36905i	0.437838	−	0.899054i	$-0.355744\pi$
$360$		0			0
$361$	2.00319e6	+	1.45540e6i	0.809009	+	0.587780i
$362$	2.38756e6			0.957596
$363$		0			0
$364$	−721559.			−0.285443
$365$	3.01705e6	+	2.19202e6i	1.18536	+	0.861215i
$366$		0			0
$367$	−348883.	−	1.07375e6i	−0.135212	−	0.416139i	0.860411	−	0.509600i	$-0.170207\pi$
$367$	−348883.	−	1.07375e6i	−0.135212	−	0.416139i	−0.995623	+	0.0934617i	$0.970207\pi$
$368$	−186081.	+	135196.i	−0.0716278	+	0.0520407i
$369$		0			0
$370$	669069.	+	2.05918e6i	0.254078	+	0.781971i
$371$	430184.	−	1.32397e6i	0.162263	−	0.499394i
$372$		0			0
$373$	4.32936e6			1.61121			0.805604	−	0.592455i	$-0.201841\pi$
$373$	4.32936e6			1.61121			0.805604	+	0.592455i	$0.201841\pi$
$374$	18994.7	−	3683.48i	0.00702189	−	0.00136169i
$375$		0			0
$376$	356130.	+	258744.i	0.129909	+	0.0943844i
$377$	−148682.	+	457595.i	−0.0538770	+	0.165816i
$378$		0			0
$379$	1.66830e6	−	1.21209e6i	0.596591	−	0.433449i	−0.248076	−	0.968740i	$-0.579798\pi$
$379$	1.66830e6	−	1.21209e6i	0.596591	−	0.433449i	0.844667	+	0.535292i	$0.179798\pi$
$380$	2630.53	−	1911.19i	0.000934509	−	0.000678961i
$381$		0			0
$382$	719423.	−	2.21415e6i	0.252247	−	0.776336i
$383$	−3.36350e6	−	2.44373e6i	−1.17164	−	0.851248i	−0.180437	−	0.983586i	$-0.557751\pi$
$383$	−3.36350e6	−	2.44373e6i	−1.17164	−	0.851248i	−0.991205	+	0.132339i	$0.957751\pi$
$384$		0			0
$385$	−2.88952e6	−	1.34896e6i	−0.993513	−	0.463818i
$386$	−2.21666e6			−0.757235
$387$		0			0
$388$	537238.	−	1.65345e6i	0.181170	−	0.557585i
$389$	835632.	+	2.57181e6i	0.279989	+	0.861718i	0.987856	+	0.155372i	$0.0496576\pi$
$389$	835632.	+	2.57181e6i	0.279989	+	0.861718i	−0.707867	+	0.706346i	$0.750342\pi$
$390$		0			0
$391$	−8761.31	+	6365.47i	−0.00289819	+	0.00210566i
$392$	−374099.	−	1.15136e6i	−0.122962	−	0.378438i
$393$		0			0
$394$	−98813.3	−	71792.1i	−0.0320682	−	0.0232989i
$395$	598240.			0.192922
$396$		0			0
$397$	5.35980e6			1.70676			0.853380	−	0.521289i	$-0.174549\pi$
$397$	5.35980e6			1.70676			0.853380	+	0.521289i	$0.174549\pi$
$398$	1.38530e6	+	1.00648e6i	0.438366	+	0.318492i
$399$		0			0
$400$	−107386.	−	330501.i	−0.0335582	−	0.103282i
$401$	3.72914e6	−	2.70938e6i	1.15810	−	0.841412i	0.168567	−	0.985690i	$-0.446086\pi$
$401$	3.72914e6	−	2.70938e6i	1.15810	−	0.841412i	0.989537	+	0.144278i	$0.0460860\pi$
$402$		0			0
$403$	−8728.40	−	26863.3i	−0.00267715	−	0.00823941i
$404$	−632985.	+	1.94813e6i	−0.192948	+	0.593832i
$405$		0			0
$406$	−1.52450e6			−0.459000
$407$	−2.50293e6	−	4.52013e6i	−0.748968	−	1.35259i
$408$		0			0
$409$	1.20702e6	+	876950.i	0.356784	+	0.259219i	0.751710	−	0.659494i	$-0.229230\pi$
$409$	1.20702e6	+	876950.i	0.356784	+	0.259219i	−0.394925	+	0.918713i	$0.629230\pi$
$410$	−658273.	+	2.02595e6i	−0.193395	+	0.595210i
$411$		0			0
$412$	1.02976e6	−	748161.i	0.298876	−	0.217146i
$413$	1.15664e6	−	840349.i	0.333675	−	0.242429i
$414$		0			0
$415$	1.54505e6	−	4.75518e6i	0.440375	−	1.35534i
$416$	−197668.	−	143614.i	−0.0560020	−	0.0406879i
$417$		0			0
$418$	−5294.33	+	5672.44i	−0.00148208	+	0.00158792i
$419$	−6.36326e6			−1.77070			−0.885349	−	0.464928i	$-0.846080\pi$
$419$	−6.36326e6			−1.77070			−0.885349	+	0.464928i	$0.846080\pi$
$420$		0			0
$421$	161777.	−	497898.i	0.0444847	−	0.136910i	−0.926347	−	0.376670i	$-0.877069\pi$
$421$	161777.	−	497898.i	0.0444847	−	0.136910i	0.970832	+	0.239761i	$0.0770689\pi$
$422$	884890.	+	2.72341e6i	0.241885	+	0.744444i
$423$		0			0
$424$	381362.	−	277075.i	0.103020	−	0.0748485i
$425$	−5056.11	−	15561.1i	−0.00135783	−	0.00417896i
$426$		0			0
$427$	−3.70818e6	−	2.69415e6i	−0.984218	−	0.715076i
$428$	−1.59243e6			−0.420194
$429$		0			0
$430$	−2.36852e6			−0.617740
$431$	3.51305e6	+	2.55238e6i	0.910943	+	0.661839i	0.941253	−	0.337701i	$-0.109649\pi$
$431$	3.51305e6	+	2.55238e6i	0.910943	+	0.661839i	−0.0303100	+	0.999541i	$0.509649\pi$
$432$		0			0
$433$	−984251.	−	3.02921e6i	−0.252282	−	0.776444i	−0.994353	−	0.106123i	$-0.966156\pi$
$433$	−984251.	−	3.02921e6i	−0.252282	−	0.776444i	0.742071	−	0.670321i	$-0.233844\pi$
$434$	72404.0	−	52604.6i	0.0184518	−	0.0134060i
$435$		0			0
$436$	33287.7	+	102449.i	0.00838624	+	0.0258102i
$437$	1342.04	−	4130.38i	0.000336173	−	0.00103463i
$438$		0			0
$439$	−2.59024e6			−0.641474			−0.320737	−	0.947168i	$-0.603931\pi$
$439$	−2.59024e6			−0.641474			−0.320737	+	0.947168i	$0.603931\pi$
$440$	−523083.	−	944653.i	−0.128807	−	0.232617i
$441$		0			0
$442$	−9306.90	−	6761.86i	−0.00226594	−	0.00164631i
$443$	−759776.	+	2.33835e6i	−0.183940	+	0.566109i	−0.999928	−	0.0119590i	$-0.996193\pi$
$443$	−759776.	+	2.33835e6i	−0.183940	+	0.566109i	0.815988	+	0.578068i	$0.196193\pi$
$444$		0			0
$445$	−944499.	+	686219.i	−0.226101	+	0.164272i
$446$	−2.93385e6	+	2.13157e6i	−0.698394	+	0.507413i
$447$		0			0
$448$	239230.	−	736273.i	0.0563144	−	0.173318i
$449$	4.44382e6	+	3.22863e6i	1.04026	+	0.755792i	0.970336	−	0.241761i	$-0.0777250\pi$
$449$	4.44382e6	+	3.22863e6i	1.04026	+	0.755792i	0.0699220	+	0.997552i	$0.477725\pi$
$450$		0			0
$451$	621753.	−	5.04530e6i	0.143938	−	1.16801i
$452$	123810.			0.0285043
$453$		0			0
$454$	−257696.	+	793106.i	−0.0586769	+	0.180589i
$455$	585895.	+	1.80320e6i	0.132676	+	0.408333i
$456$		0			0
$457$	−5.69434e6	+	4.13718e6i	−1.27542	+	0.926646i	−0.999404	−	0.0345076i	$-0.989014\pi$
$457$	−5.69434e6	+	4.13718e6i	−1.27542	+	0.926646i	−0.276014	+	0.961154i	$0.589014\pi$
$458$	−19614.4	−	60367.0i	−0.00436930	−	0.0134473i
$459$		0			0
$460$	488952.	+	355245.i	0.107739	+	0.0782768i
$461$	7.38105e6			1.61758			0.808790	−	0.588097i	$-0.200123\pi$
$461$	7.38105e6			1.61758			0.808790	+	0.588097i	$0.200123\pi$
$462$		0			0
$463$	6.30006e6			1.36582			0.682908	−	0.730504i	$-0.260715\pi$
$463$	6.30006e6			1.36582			0.682908	+	0.730504i	$0.260715\pi$
$464$	−417631.	−	303427.i	−0.0900529	−	0.0654273i
$465$		0			0
$466$	−36483.6	−	112285.i	−0.00778274	−	0.0239528i
$467$	1.46437e6	−	1.06393e6i	0.310713	−	0.225746i	−0.421489	−	0.906833i	$-0.638492\pi$
$467$	1.46437e6	−	1.06393e6i	0.310713	−	0.225746i	0.732202	+	0.681087i	$0.238492\pi$
$468$		0			0
$469$	−658577.	−	2.02689e6i	−0.138253	−	0.425499i
$470$	357436.	−	1.10008e6i	0.0746370	−	0.229709i
$471$		0			0
$472$	484115.			0.100022
$473$	5.54878e6	−	1.07602e6i	1.14037	−	0.221141i
$474$		0			0
$475$	5308.40	+	3856.78i	0.00107952	+	0.000784316i
$476$	11263.7	−	34666.2i	0.00227858	−	0.00701276i
$477$		0			0
$478$	5.36292e6	−	3.89639e6i	1.07357	−	0.779997i
$479$	−5.10967e6	+	3.71239e6i	−1.01755	+	0.739290i	−0.965778	−	0.259369i	$-0.916485\pi$
$479$	−5.10967e6	+	3.71239e6i	−1.01755	+	0.739290i	−0.0517673	+	0.998659i	$0.516485\pi$
$480$		0			0
$481$	−949305.	+	2.92166e6i	−0.187087	+	0.575794i
$482$	−1.28659e6	−	934765.i	−0.252246	−	0.183267i
$483$		0			0
$484$	1.65460e6	+	1.97542e6i	0.321055	+	0.383307i
$485$	−4.56824e6			−0.881850
$486$		0			0
$487$	−1.67562e6	+	5.15704e6i	−0.320150	+	0.985321i	0.653432	+	0.756985i	$0.273329\pi$
$487$	−1.67562e6	+	5.15704e6i	−0.320150	+	0.985321i	−0.973582	+	0.228336i	$0.926671\pi$
$488$	−479615.	−	1.47610e6i	−0.0911682	−	0.280587i
$489$		0			0
$490$	−2.57351e6	+	1.86977e6i	−0.484213	+	0.351801i
$491$	−1.50217e6	−	4.62319e6i	−0.281199	−	0.865443i	−0.987512	−	0.157543i	$-0.949643\pi$
$491$	−1.50217e6	−	4.62319e6i	−0.281199	−	0.865443i	0.706313	−	0.707900i	$-0.250357\pi$
$492$		0			0
$493$	−19663.5	−	14286.4i	−0.00364370	−	0.00264731i
$494$	4613.38			0.000850555
$495$		0			0
$496$	30304.9			0.00553106
$497$	1.01451e7	+	7.37085e6i	1.84232	+	1.33853i
$498$		0			0
$499$	2.57950e6	+	7.93889e6i	0.463750	+	1.42728i	0.860547	+	0.509370i	$0.170122\pi$
$499$	2.57950e6	+	7.93889e6i	0.463750	+	1.42728i	−0.396797	+	0.917906i	$0.629878\pi$
$500$	−2.43938e6	+	1.77231e6i	−0.436369	+	0.317041i
$501$		0			0
$502$	1.41846e6	+	4.36558e6i	0.251223	+	0.773184i
$503$	2.45836e6	−	7.56607e6i	0.433238	−	1.33337i	−0.461644	−	0.887065i	$-0.652740\pi$
$503$	2.45836e6	−	7.56607e6i	0.433238	−	1.33337i	0.894882	−	0.446303i	$-0.147260\pi$
$504$		0			0
$505$	5.38240e6			0.939177
$506$	−1.30687e6	−	610107.i	−0.226911	−	0.105933i
$507$		0			0
$508$	3.54125e6	+	2.57287e6i	0.608833	+	0.442343i
$509$	−1.60837e6	+	4.95006e6i	−0.275164	+	0.846869i	0.714011	+	0.700134i	$0.246876\pi$
$509$	−1.60837e6	+	4.95006e6i	−0.275164	+	0.846869i	−0.989176	+	0.146735i	$0.953124\pi$
$510$		0			0
$511$	−1.35634e7	+	9.85442e6i	−2.29783	+	1.66947i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$		0			0
$514$	−548141.	+	1.68700e6i	−0.0915133	+	0.281649i
$515$	−2.70582e6	−	1.96589e6i	−0.449553	−	0.326619i
$516$		0			0
$517$	−337606.	+	2.73956e6i	−0.0555500	+	0.450769i
$518$	−9.73366e6			−1.59387
$519$		0			0
$520$	−198393.	+	610592.i	−0.0321750	+	0.0990245i
$521$	1.79470e6	+	5.52352e6i	0.289666	+	0.891501i	0.984961	+	0.172777i	$0.0552739\pi$
$521$	1.79470e6	+	5.52352e6i	0.289666	+	0.891501i	−0.695295	+	0.718725i	$0.744726\pi$
$522$		0			0
$523$	8.96814e6	−	6.51573e6i	1.43367	−	1.04162i	0.444347	−	0.895855i	$-0.353436\pi$
$523$	8.96814e6	−	6.51573e6i	1.43367	−	1.04162i	0.989319	−	0.145765i	$-0.0465642\pi$
$524$	929666.	+	2.86122e6i	0.147910	+	0.455222i
$525$		0			0
$526$	−3.32146e6	−	2.41318e6i	−0.523437	−	0.380299i
$527$	1426.86			0.000223797
$528$		0			0
$529$	−5.62909e6			−0.874580
$530$	−1.00208e6	−	728053.i	−0.154957	−	0.112583i
$531$		0			0
$532$	4517.05	+	13902.0i	0.000691952	+	0.00212961i
$533$	−2.44521e6	+	1.77655e6i	−0.372819	+	0.270869i
$534$		0			0
$535$	1.29302e6	+	3.97952e6i	0.195309	+	0.601099i
$536$	223005.	−	686338.i	0.0335276	−	0.103187i
$537$		0			0
$538$	−7.34711e6			−1.09436
$539$	5.17958e6	−	5.54950e6i	0.767932	−	0.822776i
$540$		0			0
$541$	−2.09508e6	−	1.52217e6i	−0.307757	−	0.223598i	0.423177	−	0.906047i	$-0.360915\pi$
$541$	−2.09508e6	−	1.52217e6i	−0.307757	−	0.223598i	−0.730933	+	0.682449i	$0.760915\pi$
$542$	−1.52887e6	+	4.70539e6i	−0.223549	+	0.688014i
$543$		0			0
$544$	9985.40	−	7254.81i	0.00144667	−	0.00105106i
$545$	228994.	−	166374.i	0.0330242	−	0.0239935i
$546$		0			0
$547$	−1.71011e6	+	5.26319e6i	−0.244375	+	0.752109i	0.751364	+	0.659888i	$0.229396\pi$
$547$	−1.71011e6	+	5.26319e6i	−0.244375	+	0.752109i	−0.995739	+	0.0922204i	$0.970604\pi$
$548$	3.59601e6	+	2.61265e6i	0.511528	+	0.371647i
$549$		0			0
$550$	1.48682e6	−	1.59300e6i	0.209580	−	0.224548i
$551$	9747.09			0.00136772
$552$		0			0
$553$	−831085.	+	2.55782e6i	−0.115567	+	0.355677i
$554$	468746.	+	1.44265e6i	0.0648878	+	0.199704i
$555$		0			0
$556$	−2.42872e6	+	1.76457e6i	−0.333189	+	0.242076i
$557$	−3.06511e6	−	9.43343e6i	−0.418608	−	1.28834i	−0.908984	−	0.416832i	$-0.863140\pi$
$557$	−3.06511e6	−	9.43343e6i	−0.418608	−	1.28834i	0.490375	−	0.871511i	$-0.336860\pi$
$558$		0			0
$559$	−2.71875e6	−	1.97529e6i	−0.367993	−	0.267363i
$560$	−2.03422e6			−0.274112
$561$		0			0
$562$	−3.96366e6			−0.529365
$563$	−2.79156e6	−	2.02819e6i	−0.371173	−	0.269673i	0.386524	−	0.922279i	$-0.373676\pi$
$563$	−2.79156e6	−	2.02819e6i	−0.371173	−	0.269673i	−0.757697	+	0.652606i	$0.773676\pi$
$564$		0			0
$565$	−100532.	−	309405.i	−0.0132490	−	0.0407762i
$566$	−2.41722e6	+	1.75621e6i	−0.317157	+	0.230428i
$567$		0			0
$568$	1.31217e6	+	4.03843e6i	0.170655	+	0.525221i
$569$	4.63990e6	−	1.42802e7i	0.600798	−	1.84907i	0.0773566	−	0.997003i	$-0.475352\pi$
$569$	4.63990e6	−	1.42802e7i	0.600798	−	1.84907i	0.523441	−	0.852062i	$-0.324648\pi$
$570$		0			0
$571$	−6.57535e6			−0.843974			−0.421987	−	0.906602i	$-0.638667\pi$
$571$	−6.57535e6			−0.843974			−0.421987	+	0.906602i	$0.638667\pi$
$572$	187387.	−	1.52058e6i	0.0239469	−	0.194320i
$573$		0			0
$574$	−7.74763e6	−	5.62898e6i	−0.981497	−	0.713099i
$575$	−376888.	+	1.15994e6i	−0.0475382	+	0.146308i
$576$		0			0
$577$	383500.	−	278629.i	0.0479541	−	0.0348407i	−0.563550	−	0.826082i	$-0.690565\pi$
$577$	383500.	−	278629.i	0.0479541	−	0.0348407i	0.611504	+	0.791241i	$0.290565\pi$
$578$	−4.59428e6	+	3.33794e6i	−0.572003	+	0.415584i
$579$		0			0
$580$	−419162.	+	1.29005e6i	−0.0517383	+	0.159234i
$581$	1.81847e7	+	1.32119e7i	2.23494	+	1.62378i
$582$		0			0
$583$	2.67835e6	+	1.25038e6i	0.326359	+	0.152360i
$584$	−5.67701e6			−0.688792
$585$		0			0
$586$	−1.12470e6	+	3.46148e6i	−0.135299	+	0.416406i
$587$	−5.04862e6	−	1.55381e7i	−0.604753	−	1.86124i	−0.498482	−	0.866900i	$-0.666109\pi$
$587$	−5.04862e6	−	1.55381e7i	−0.604753	−	1.86124i	−0.106270	−	0.994337i	$-0.533891\pi$
$588$		0			0
$589$	−462.925	+	336.334i	−5.49822e−5	+	3.99469e-5i
$590$	−393093.	−	1.20982e6i	−0.0464907	−	0.143084i
$591$		0			0
$592$	−2.66650e6	−	1.93732e6i	−0.312707	−	0.227195i
$593$	−1.17690e7			−1.37437			−0.687183	−	0.726484i	$-0.741153\pi$
$593$	−1.17690e7			−1.37437			−0.687183	+	0.726484i	$0.741153\pi$
$594$		0			0
$595$	−95777.9			−0.0110911
$596$	3.62089e6	+	2.63073e6i	0.417541	+	0.303361i
$597$		0			0
$598$	264988.	+	815548.i	0.0303021	+	0.0932603i
$599$	1.76885e6	−	1.28514e6i	0.201430	−	0.146347i	−0.482498	−	0.875897i	$-0.660270\pi$
$599$	1.76885e6	−	1.28514e6i	0.201430	−	0.146347i	0.683928	+	0.729550i	$0.260270\pi$
$600$		0			0
$601$	−1.91019e6	−	5.87896e6i	−0.215720	−	0.663918i	−0.999102	−	0.0423769i	$-0.986507\pi$
$601$	−1.91019e6	−	5.87896e6i	−0.215720	−	0.663918i	0.783382	−	0.621541i	$-0.213493\pi$
$602$	3.29038e6	−	1.01268e7i	0.370046	−	1.13888i
$603$		0			0
$604$	6.58483e6			0.734433
$605$	3.59313e6	−	5.73890e6i	0.399102	−	0.637441i
$606$		0			0
$607$	7.58928e6	+	5.51394e6i	0.836044	+	0.607421i	0.921263	−	0.388941i	$-0.127159\pi$
$607$	7.58928e6	+	5.51394e6i	0.836044	+	0.607421i	−0.0852190	+	0.996362i	$0.527159\pi$
$608$	−1529.55	+	4707.46i	−0.000167804	+	0.000516449i
$609$		0			0
$610$	−3.29939e6	+	2.39714e6i	−0.359012	+	0.260837i
$611$	1.32773e6	−	964650.i	0.143882	−	0.104536i
$612$		0			0
$613$	−953820.	+	2.93556e6i	−0.102522	+	0.315529i	−0.989141	−	0.146971i	$-0.953048\pi$
$613$	−953820.	+	2.93556e6i	−0.102522	+	0.315529i	0.886619	+	0.462500i	$0.153048\pi$
$614$	6.41461e6	+	4.66049e6i	0.686672	+	0.498897i
$615$		0			0
$616$	4.76561e6	−	924151.i	0.506018	−	0.0981276i
$617$	−2.64413e6			−0.279621			−0.139810	−	0.990178i	$-0.544649\pi$
$617$	−2.64413e6			−0.279621			−0.139810	+	0.990178i	$0.544649\pi$
$618$		0			0
$619$	−3.68512e6	+	1.13416e7i	−0.386567	+	1.18973i	0.548769	+	0.835974i	$0.315097\pi$
$619$	−3.68512e6	+	1.13416e7i	−0.386567	+	1.18973i	−0.935337	+	0.353759i	$0.884903\pi$
$620$	−24607.1	−	75732.8i	−0.00257087	−	0.00791234i
$621$		0			0
$622$	2.35996e6	−	1.71461e6i	0.244584	−	0.177701i
$623$	−1.62186e6	−	4.99158e6i	−0.167415	−	0.515250i
$624$		0			0
$625$	2.97789e6	+	2.16357e6i	0.304936	+	0.221549i
$626$	−1.30462e6			−0.133061
$627$		0			0
$628$	2.51450e6			0.254421
$629$	−125548.	−	91215.8i	−0.0126527	−	0.00919271i
$630$		0			0
$631$	−1.19752e6	−	3.68558e6i	−0.119732	−	0.368496i	0.873173	−	0.487411i	$-0.162059\pi$
$631$	−1.19752e6	−	3.68558e6i	−0.119732	−	0.368496i	−0.992904	+	0.118915i	$0.962059\pi$
$632$	−736763.	+	535290.i	−0.0733728	+	0.0533085i
$633$		0			0
$634$	861862.	+	2.65254e6i	0.0851559	+	0.262083i
$635$	3.55424e6	−	1.09388e7i	0.349794	−	1.07656i
$636$		0			0
$637$	−4.51340e6			−0.440712
$638$	395908.	−	3.21265e6i	0.0385072	−	0.312473i
$639$		0			0
$640$	−557266.	−	404877.i	−0.0537790	−	0.0390727i
$641$	−5.10551e6	+	1.57131e7i	−0.490788	+	1.51049i	0.332631	+	0.943057i	$0.392064\pi$
$641$	−5.10551e6	+	1.57131e7i	−0.490788	+	1.51049i	−0.823419	+	0.567433i	$0.807936\pi$
$642$		0			0
$643$	−2.16182e6	+	1.57065e6i	−0.206201	+	0.149814i	−0.686093	−	0.727514i	$-0.740676\pi$
$643$	−2.16182e6	+	1.57065e6i	−0.206201	+	0.149814i	0.479892	+	0.877328i	$0.340676\pi$
$644$	−2.19813e6	+	1.59704e6i	−0.208852	+	0.151740i
$645$		0			0
$646$	−72.0162	+	221.643i	−6.78967e−6	+	2.08965e-5i
$647$	1.19258e7	+	8.66459e6i	1.12002	+	0.813743i	0.984212	−	0.176992i	$-0.0566367\pi$
$647$	1.19258e7	+	8.66459e6i	1.12002	+	0.813743i	0.135809	+	0.990735i	$0.456637\pi$
$648$		0			0
$649$	1.47053e6	+	2.65568e6i	0.137045	+	0.247494i
$650$	−1.29558e6			−0.120277
$651$		0			0
$652$	2.40703e6	−	7.40808e6i	0.221750	−	0.682475i
$653$	5.68293e6	+	1.74903e7i	0.521542	+	1.60514i	0.771054	+	0.636769i	$0.219730\pi$
$653$	5.68293e6	+	1.74903e7i	0.521542	+	1.60514i	−0.249512	+	0.968372i	$0.580270\pi$
$654$		0			0
$655$	6.39539e6	−	4.64653e6i	0.582457	−	0.423180i
$656$	−1.00208e6	−	3.08407e6i	−0.0909162	−	0.279811i
$657$		0			0
$658$	4.20689e6	+	3.05649e6i	0.378788	+	0.275206i
$659$	−3.50408e6			−0.314312			−0.157156	−	0.987574i	$-0.550233\pi$
$659$	−3.50408e6			−0.314312			−0.157156	+	0.987574i	$0.550233\pi$
$660$		0			0
$661$	−1.14260e6			−0.101716			−0.0508581	−	0.998706i	$-0.516196\pi$
$661$	−1.14260e6			−0.101716			−0.0508581	+	0.998706i	$0.516196\pi$
$662$	696676.	+	506165.i	0.0617854	+	0.0448897i
$663$		0			0
$664$	2.35200e6	+	7.23872e6i	0.207023	+	0.637150i
$665$	31073.9	−	22576.5i	0.00272484	−	0.00197971i
$666$		0			0
$667$	559862.	+	1.72308e6i	0.0487267	+	0.149965i
$668$	2.05736e6	−	6.33192e6i	0.178390	−	0.549027i
$669$		0			0
$670$	−1.89626e6			−0.163196
$671$	6.64052e6	−	7.11476e6i	0.569371	−	0.610034i
$672$		0			0
$673$	624082.	+	453422.i	0.0531134	+	0.0385892i	0.614025	−	0.789286i	$-0.289549\pi$
$673$	624082.	+	453422.i	0.0531134	+	0.0385892i	−0.560912	+	0.827876i	$0.689549\pi$
$674$	1.64327e6	−	5.05747e6i	0.139335	−	0.428829i
$675$		0			0
$676$	4.06917e6	−	2.95642e6i	0.342483	−	0.248828i
$677$	−1.61655e7	+	1.17449e7i	−1.35556	+	0.984869i	−0.356842	+	0.934165i	$0.616146\pi$
$677$	−1.61655e7	+	1.17449e7i	−1.35556	+	0.984869i	−0.998714	+	0.0507038i	$0.983854\pi$
$678$		0			0
$679$	6.34628e6	−	1.95318e7i	0.528256	−	1.62581i
$680$	−26238.0	−	19063.0i	−0.00217600	−	0.00158095i
$681$		0			0
$682$	92053.1	+	166242.i	0.00757840	+	0.0136861i
$683$	−2.03706e7			−1.67090			−0.835452	−	0.549563i	$-0.814794\pi$
$683$	−2.03706e7			−1.67090			−0.835452	+	0.549563i	$0.814794\pi$
$684$		0			0
$685$	3.60919e6	−	1.11080e7i	0.293889	−	0.904498i
$686$	−492654.	−	1.51623e6i	−0.0399698	−	0.123014i
$687$		0			0
$688$	2.91695e6	−	2.11929e6i	0.234941	−	0.170694i
$689$	−543077.	−	1.67142e6i	−0.0435826	−	0.134133i
$690$		0			0
$691$	−1.06499e7	−	7.73760e6i	−0.848496	−	0.616469i	0.0762348	−	0.997090i	$-0.475710\pi$
$691$	−1.06499e7	−	7.73760e6i	−0.848496	−	0.616469i	−0.924731	+	0.380621i	$0.875710\pi$
$692$	8.67454e6			0.688623
$693$		0			0
$694$	−2.93452e6			−0.231280
$695$	6.38179e6	+	4.63664e6i	0.501165	+	0.364118i
$696$		0			0
$697$	−47181.2	−	145209.i	−0.00367863	−	0.0113217i
$698$	−3.16380e6	+	2.29863e6i	−0.245793	+	0.178579i
$699$		0			0
$700$	−1.26853e6	−	3.90414e6i	−0.0978489	−	0.301148i
$701$	2.18868e6	−	6.73605e6i	0.168223	−	0.517738i	−0.831036	−	0.556219i	$-0.812252\pi$
$701$	2.18868e6	−	6.73605e6i	0.168223	−	0.517738i	0.999259	+	0.0384803i	$0.0122517\pi$
$702$		0			0
$703$	62233.4			0.00474936
$704$	1.48946e6	+	695348.i	0.113265	+	0.0528774i
$705$		0			0
$706$	−1.06661e7	−	7.74937e6i	−0.805367	−	0.585133i
$707$	−7.47732e6	+	2.30128e7i	−0.562597	+	1.73149i
$708$		0			0
$709$	8.81580e6	−	6.40505e6i	0.658637	−	0.478528i	−0.207566	−	0.978221i	$-0.566554\pi$
$709$	8.81580e6	−	6.40505e6i	0.658637	−	0.478528i	0.866202	+	0.499694i	$0.166554\pi$
$710$	9.02670e6	−	6.55828e6i	0.672022	−	0.488252i
$711$		0			0
$712$	549188.	−	1.69023e6i	0.0405996	−	0.124953i
$713$	−86046.7	−	62516.6i	−0.00633885	−	0.00460544i
$714$		0			0
$715$	−3.95212e6	+	766399.i	−0.289111	+	0.0560647i
$716$	−3.19833e6			−0.233153
$717$		0			0
$718$	4.34501e6	−	1.33726e7i	0.314543	−	0.968063i
$719$	2.15981e6	+	6.64721e6i	0.155809	+	0.479532i	0.998242	−	0.0592699i	$-0.0188773\pi$
$719$	2.15981e6	+	6.64721e6i	0.155809	+	0.479532i	−0.842433	+	0.538802i	$0.818877\pi$
$720$		0			0
$721$	1.21643e7	−	8.83787e6i	0.871462	−	0.633154i
$722$	3.06060e6	+	9.41955e6i	0.218506	+	0.672492i
$723$		0			0
$724$	7.72629e6	+	5.61348e6i	0.547803	+	0.398002i
$725$	−2.73729e6			−0.193409
$726$		0			0
$727$	−6.65621e6			−0.467080			−0.233540	−	0.972347i	$-0.575031\pi$
$727$	−6.65621e6			−0.467080			−0.233540	+	0.972347i	$0.575031\pi$
$728$	−2.33502e6	−	1.69649e6i	−0.163291	−	0.118638i
$729$		0			0
$730$	4.60964e6	+	1.41870e7i	0.320155	+	0.985335i
$731$	137340.	−	99783.3i	0.00950613	−	0.00690661i
$732$		0			0
$733$	−4.98869e6	−	1.53536e7i	−0.342947	−	1.05548i	−0.962674	−	0.270664i	$-0.912757\pi$
$733$	−4.98869e6	−	1.53536e7i	−0.342947	−	1.05548i	0.619727	−	0.784817i	$-0.287243\pi$
$734$	1.39553e6	−	4.29500e6i	0.0956091	−	0.294255i
$735$		0			0
$736$	−920034.			−0.0626050
$737$	4.44240e6	−	861474.i	0.301265	−	0.0584216i
$738$		0			0
$739$	1.18655e7	+	8.62082e6i	0.799238	+	0.580681i	0.910691	−	0.413089i	$-0.135550\pi$
$739$	1.18655e7	+	8.62082e6i	0.799238	+	0.580681i	−0.111452	+	0.993770i	$0.535550\pi$
$740$	−2.67628e6	+	8.23673e6i	−0.179660	+	0.552937i
$741$		0			0
$742$	4.50494e6	−	3.27303e6i	0.300386	−	0.218243i
$743$	−1.37473e7	+	9.98798e6i	−0.913576	+	0.663752i	−0.941917	−	0.335846i	$-0.890978\pi$
$743$	−1.37473e7	+	9.98798e6i	−0.913576	+	0.663752i	0.0283406	+	0.999598i	$0.490978\pi$
$744$		0			0
$745$	3.63416e6	−	1.11848e7i	0.239891	−	0.738308i
$746$	1.40101e7	+	1.01789e7i	0.921710	+	0.669661i
$747$		0			0
$748$	70128.6	+	32739.3i	0.00458291	+	0.00213952i
$749$	−1.88110e7			−1.22520
$750$		0			0
$751$	6.08314e6	−	1.87220e7i	0.393575	−	1.21130i	−0.536490	−	0.843906i	$-0.680250\pi$
$751$	6.08314e6	−	1.87220e7i	0.393575	−	1.21130i	0.930066	−	0.367393i	$-0.119750\pi$
$752$	544119.	+	1.67463e6i	0.0350872	+	0.107987i
$753$		0			0
$754$	−1.55701e6	+	1.13124e6i	−0.0997387	+	0.0724644i
$755$	−5.34678e6	−	1.64557e7i	−0.341369	−	1.05063i
$756$		0			0
$757$	2.19421e7	+	1.59418e7i	1.39167	+	1.01111i	0.995679	+	0.0928578i	$0.0296002\pi$
$757$	2.19421e7	+	1.59418e7i	1.39167	+	1.01111i	0.395995	+	0.918253i	$0.370400\pi$
$758$	8.24854e6			0.521439
$759$		0			0
$760$	13006.0			0.000816791
$761$	1.22810e7	+	8.92267e6i	0.768727	+	0.558513i	0.901575	−	0.432623i	$-0.142412\pi$
$761$	1.22810e7	+	8.92267e6i	0.768727	+	0.558513i	−0.132847	+	0.991137i	$0.542412\pi$
$762$		0			0
$763$	393221.	+	1.21021e6i	0.0244526	+	0.0752573i
$764$	7.53389e6	−	5.47369e6i	0.466967	−	0.339271i
$765$		0			0
$766$	−5.13898e6	−	1.58161e7i	−0.316450	−	0.973932i
$767$	557738.	−	1.71654e6i	0.0342328	−	0.105358i
$768$		0			0
$769$	−8.44714e6			−0.515103			−0.257551	−	0.966265i	$-0.582916\pi$
$769$	−8.44714e6			−0.515103			−0.257551	+	0.966265i	$0.582916\pi$
$770$	−6.17907e6	−	1.11590e7i	−0.375575	−	0.678263i
$771$		0			0
$772$	−7.17326e6	−	5.21168e6i	−0.433185	−	0.314727i
$773$	−5.34034e6	+	1.64359e7i	−0.321455	+	0.989337i	0.651560	+	0.758597i	$0.274115\pi$
$773$	−5.34034e6	+	1.64359e7i	−0.321455	+	0.989337i	−0.973015	+	0.230740i	$0.925885\pi$
$774$		0			0
$775$	130004.	−	94453.4i	0.00777503	−	0.00564889i
$776$	5.62603e6	−	4.08755e6i	0.335388	−	0.243674i
$777$		0			0
$778$	−3.34253e6	+	1.02872e7i	−0.197982	+	0.609326i
$779$	49535.5	+	35989.6i	0.00292464	+	0.00212488i
$780$		0			0
$781$	−1.81676e7	+	1.94651e7i	−1.06579	+	1.14190i
$782$	−43318.3			−0.00253311
$783$		0			0
$784$	1.49639e6	−	4.60543e6i	0.0869473	−	0.267596i
$785$	−2.04174e6	−	6.28382e6i	−0.118257	−	0.363956i
$786$		0			0
$787$	2.23424e7	−	1.62327e7i	1.28586	−	0.934229i	0.286143	−	0.958187i	$-0.407627\pi$
$787$	2.23424e7	−	1.62327e7i	1.28586	−	0.934229i	0.999713	+	0.0239574i	$0.00762661\pi$
$788$	−150973.	−	464648.i	−0.00866133	−	0.0266568i
$789$		0			0
$790$	1.93594e6	+	1.40655e6i	0.110363	+	0.0801837i
$791$	1.46254e6			0.0831128
$792$		0			0
$793$	−5.78642e6			−0.326759
$794$	1.73447e7	+	1.26017e7i	0.976372	+	0.709376i
$795$		0			0
$796$	2.11655e6	+	6.51408e6i	0.118399	+	0.364394i
$797$	9.52505e6	−	6.92036e6i	0.531155	−	0.385907i	−0.289634	−	0.957137i	$-0.593534\pi$
$797$	9.52505e6	−	6.92036e6i	0.531155	−	0.385907i	0.820790	+	0.571230i	$0.193534\pi$
$798$		0			0
$799$	25619.0	+	78847.0i	0.00141969	+	0.00436937i
$800$	429545.	−	1.32200e6i	0.0237292	−	0.0730310i
$801$		0			0
$802$	1.84379e7			1.01222
$803$	−1.72443e7	−	3.11421e7i	−0.943750	−	1.70435i
$804$		0			0
$805$	5.77589e6	+	4.19643e6i	0.314144	+	0.228239i
$806$	34913.6	−	107453.i	0.00189303	−	0.00582614i
$807$		0			0
$808$	−6.62870e6	+	4.81603e6i	−0.357191	+	0.259514i
$809$	2.43793e7	−	1.77126e7i	1.30963	−	0.951503i	0.309632	−	0.950856i	$-0.399794\pi$
$809$	2.43793e7	−	1.77126e7i	1.30963	−	0.951503i	1.00000		0.000647009i	$-0.000205950\pi$
$810$		0			0
$811$	1.46608e6	−	4.51213e6i	0.0782719	−	0.240896i	−0.904263	−	0.426977i	$-0.859579\pi$
$811$	1.46608e6	−	4.51213e6i	0.0782719	−	0.240896i	0.982534	+	0.186081i	$0.0595786\pi$
$812$	−4.93339e6	−	3.58432e6i	−0.262576	−	0.190773i
$813$		0			0
$814$	2.52780e6	−	2.05122e7i	0.133715	−	1.08505i
$815$	−2.04675e7			−1.07937
$816$		0			0
$817$	−21037.5	+	64746.8i	−0.00110265	+	0.00339362i
$818$	1.84416e6	+	5.67574e6i	0.0963641	+	0.296578i
$819$		0			0
$820$	−6.89352e6	+	5.00844e6i	−0.358019	+	0.260116i
$821$	−2.45150e6	−	7.54493e6i	−0.126933	−	0.390659i	0.867316	−	0.497759i	$-0.165843\pi$
$821$	−2.45150e6	−	7.54493e6i	−0.126933	−	0.390659i	−0.994248	+	0.107100i	$0.965843\pi$
$822$		0			0
$823$	−7.31444e6	−	5.31425e6i	−0.376427	−	0.273491i	0.383444	−	0.923564i	$-0.374738\pi$
$823$	−7.31444e6	−	5.31425e6i	−0.376427	−	0.273491i	−0.759871	+	0.650074i	$0.774738\pi$
$824$	5.09139e6			0.261227
$825$		0			0
$826$	5.71875e6			0.291643
$827$	1.00484e7	+	7.30061e6i	0.510898	+	0.371189i	0.813164	−	0.582034i	$-0.197743\pi$
$827$	1.00484e7	+	7.30061e6i	0.510898	+	0.371189i	−0.302266	+	0.953224i	$0.597743\pi$
$828$		0			0
$829$	−7.66355e6	−	2.35860e7i	−0.387297	−	1.19198i	−0.934800	−	0.355173i	$-0.884422\pi$
$829$	−7.66355e6	−	2.35860e7i	−0.387297	−	1.19198i	0.547504	−	0.836803i	$-0.315578\pi$
$830$	1.61800e7	−	1.17555e7i	0.815235	−	0.592303i
$831$		0			0
$832$	−302010.	−	929493.i	−0.0151256	−	0.0465519i
$833$	70455.3	−	216839.i	0.00351804	−	0.0108274i
$834$		0			0
$835$	−1.74942e7			−0.868316
$836$	−30469.5	+	5908.68i	−0.00150782	+	0.000292398i
$837$		0			0
$838$	−2.05919e7	−	1.49609e7i	−1.01295	−	0.735950i
$839$	−8.28089e6	+	2.54860e7i	−0.406137	+	1.24996i	0.513806	+	0.857907i	$0.328235\pi$
$839$	−8.28089e6	+	2.54860e7i	−0.406137	+	1.24996i	−0.919942	+	0.392053i	$0.871765\pi$
$840$		0			0
$841$	1.33042e7	−	9.66609e6i	0.648634	−	0.471260i
$842$	1.69415e6	−	1.23087e6i	0.0823514	−	0.0598318i
$843$		0			0
$844$	−3.53956e6	+	1.08936e7i	−0.171038	+	0.526401i
$845$	−1.06923e7	−	7.76840e6i	−0.515144	−	0.374274i
$846$		0			0
$847$	1.95454e7	+	2.33352e7i	0.936130	+	1.11764i
$848$	1.88556e6			0.0900429
$849$		0			0
$850$	20224.4	−	62244.4i	0.000960128	−	0.00295497i
$851$	3.57462e6	+	1.10015e7i	0.169202	+	0.520751i
$852$		0			0
$853$	−1.08252e7	+	7.86494e6i	−0.509403	+	0.370103i	−0.812597	−	0.582826i	$-0.801947\pi$
$853$	−1.08252e7	+	7.86494e6i	−0.509403	+	0.370103i	0.303194	+	0.952929i	$0.401947\pi$
$854$	−5.66560e6	−	1.74369e7i	−0.265828	−	0.818135i
$855$		0			0
$856$	−5.15320e6	−	3.74402e6i	−0.240377	−	0.174644i
$857$	4.26416e6			0.198327			0.0991634	−	0.995071i	$-0.468383\pi$
$857$	4.26416e6			0.198327			0.0991634	+	0.995071i	$0.468383\pi$
$858$		0			0
$859$	−6.34671e6			−0.293471			−0.146736	−	0.989176i	$-0.546877\pi$
$859$	−6.34671e6			−0.293471			−0.146736	+	0.989176i	$0.546877\pi$
$860$	−7.66468e6	−	5.56872e6i	−0.353385	−	0.256749i
$861$		0			0
$862$	5.36747e6	+	1.65194e7i	0.246037	+	0.757225i
$863$	2.01914e6	−	1.46699e6i	0.0922869	−	0.0670504i	−0.540685	−	0.841225i	$-0.681835\pi$
$863$	2.01914e6	−	1.46699e6i	0.0922869	−	0.0670504i	0.632972	+	0.774175i	$0.281835\pi$
$864$		0			0
$865$	−7.04359e6	−	2.16779e7i	−0.320076	−	0.985094i
$866$	3.93701e6	−	1.21169e7i	0.178390	−	0.549029i
$867$		0			0
$868$	357985.			0.0161275
$869$	−5.17438e6	−	2.41564e6i	−0.232439	−	0.108513i
$870$		0			0
$871$	−2.17665e6	−	1.58143e6i	−0.0972174	−	0.0706325i
$872$	−133151.	+	409796.i	−0.00592997	+	0.0182506i
$873$		0			0
$874$	14054.0	−	10210.9i	0.000622333	−	0.000452151i
$875$	−2.88158e7	+	2.09359e7i	−1.27236	+	0.924426i
$876$		0			0
$877$	−9.03649e6	+	2.78115e7i	−0.396735	+	1.22103i	0.530866	+	0.847456i	$0.321867\pi$
$877$	−9.03649e6	+	2.78115e7i	−0.396735	+	1.22103i	−0.927602	+	0.373570i	$0.878133\pi$
$878$	−8.38220e6	−	6.09002e6i	−0.366962	−	0.266614i
$879$		0			0
$880$	528280.	−	4.28680e6i	0.0229963	−	0.186607i
$881$	−3.76845e7			−1.63577			−0.817887	−	0.575379i	$-0.804855\pi$
$881$	−3.76845e7			−1.63577			−0.817887	+	0.575379i	$0.804855\pi$
$882$		0			0
$883$	−6.94030e6	+	2.13600e7i	−0.299555	+	0.921935i	0.682099	+	0.731260i	$0.261068\pi$
$883$	−6.94030e6	+	2.13600e7i	−0.299555	+	0.921935i	−0.981653	+	0.190675i	$0.938932\pi$
$884$	−14219.7	−	43763.7i	−0.000612011	−	0.00188358i
$885$		0			0
$886$	−7.95648e6	+	5.78072e6i	−0.340515	+	0.247399i
$887$	1.76942e6	+	5.44572e6i	0.0755132	+	0.232406i	0.981687	−	0.190499i	$-0.0610106\pi$
$887$	1.76942e6	+	5.44572e6i	0.0755132	+	0.232406i	−0.906174	+	0.422905i	$0.861011\pi$
$888$		0			0
$889$	4.18321e7	+	3.03928e7i	1.77523	+	1.28978i
$890$	−4.66986e6			−0.197619
$891$		0			0
$892$	−1.45057e7			−0.610419
$893$	−26897.3	−	19542.0i	−0.00112870	−	0.000820052i
$894$		0			0
$895$	2.59699e6	+	7.99273e6i	0.108371	+	0.333532i
$896$	2.50524e6	−	1.82017e6i	0.104251	−	0.0757428i
$897$		0			0
$898$	6.78956e6	+	2.08961e7i	0.280964	+	0.864718i
$899$	73765.0	−	227025.i	0.00304404	−	0.00936860i
$900$		0			0
$901$	88778.3			0.00364330
$902$	1.38743e7	−	1.48651e7i	0.567797	−	0.608348i
$903$		0			0
$904$	400658.	+	291095.i	0.0163062	+	0.0118472i
$905$	7.75463e6	−	2.38663e7i	0.314731	−	0.968642i
$906$		0			0
$907$	−1.59930e7	+	1.16196e7i	−0.645522	+	0.469000i	−0.861743	−	0.507345i	$-0.830627\pi$
$907$	−1.59930e7	+	1.16196e7i	−0.645522	+	0.469000i	0.216221	+	0.976345i	$0.430627\pi$
$908$	−2.69862e6	+	1.96066e6i	−0.108624	+	0.0789203i
$909$		0			0
$910$	−2.34358e6	+	7.21279e6i	−0.0938158	+	0.288735i
$911$	−1.46335e7	−	1.06319e7i	−0.584189	−	0.424438i	0.256043	−	0.966665i	$-0.417581\pi$
$911$	−1.46335e7	−	1.06319e7i	−0.584189	−	0.424438i	−0.840232	+	0.542227i	$0.817581\pi$
$912$		0			0
$913$	−3.25647e7	+	3.48904e7i	−1.29291	+	1.38525i
$914$	−2.81544e7			−1.11476
$915$		0			0
$916$	78457.6	−	241468.i	0.00308956	−	0.00950869i
$917$	1.09820e7	+	3.37990e7i	0.431277	+	1.32733i
$918$		0			0
$919$	1.35593e7	−	9.85142e6i	0.529601	−	0.384778i	−0.290607	−	0.956842i	$-0.593857\pi$
$919$	1.35593e7	−	9.85142e6i	0.529601	−	0.384778i	0.820209	+	0.572065i	$0.193857\pi$
$920$	747053.	+	2.29919e6i	0.0290992	+	0.0895582i
$921$		0			0
$922$	2.38856e7	+	1.73539e7i	0.925355	+	0.672310i
$923$	1.58309e7			0.611649
$924$		0			0
$925$	−1.74771e7			−0.671607
$926$	2.03874e7	+	1.48123e7i	0.781331	+	0.567670i
$927$		0			0
$928$	−638083.	−	1.96382e6i	−0.0243225	−	0.0748568i
$929$	6.98849e6	−	5.07744e6i	0.265671	−	0.193021i	−0.446972	−	0.894548i	$-0.647498\pi$
$929$	6.98849e6	−	5.07744e6i	0.265671	−	0.193021i	0.712643	+	0.701526i	$0.247498\pi$
$930$		0			0
$931$	28254.4	+	86958.1i	0.00106835	+	0.00328803i
$932$	145934.	−	449140.i	0.00550323	−	0.0169372i
$933$		0			0
$934$	7.24026e6			0.271573
$935$	24873.2	−	201837.i	0.000930471	−	0.00755044i
$936$		0			0
$937$	1.93485e7	+	1.40575e7i	0.719942	+	0.523069i	0.886366	−	0.462986i	$-0.153222\pi$
$937$	1.93485e7	+	1.40575e7i	0.719942	+	0.523069i	−0.166423	+	0.986054i	$0.553222\pi$
$938$	2.63431e6	−	8.10757e6i	0.0977597	−	0.300873i
$939$		0			0
$940$	3.74312e6	−	2.71954e6i	0.138170	−	0.100386i
$941$	2.26978e7	−	1.64909e7i	0.835622	−	0.607115i	−0.0855221	−	0.996336i	$-0.527256\pi$
$941$	2.26978e7	−	1.64909e7i	0.835622	−	0.607115i	0.921144	+	0.389221i	$0.127256\pi$
$942$		0			0
$943$	−3.51694e6	+	1.08240e7i	−0.128791	+	0.396378i
$944$	1.56663e6	+	1.13822e6i	0.0572185	+	0.0415716i
$945$		0			0
$946$	2.04861e7	+	9.56387e6i	0.744272	+	0.347461i
$947$	1.42181e7			0.515189			0.257595	−	0.966253i	$-0.417070\pi$
$947$	1.42181e7			0.515189			0.257595	+	0.966253i	$0.417070\pi$
$948$		0			0
$949$	−6.54036e6	+	2.01292e7i	−0.235742	+	0.725538i
$950$	8110.52	+	24961.6i	0.000291568	+	0.000897353i
$951$		0			0
$952$	117955.	−	85699.6i	0.00421818	−	0.00306469i
$953$	−1.28053e7	−	3.94106e7i	−0.456727	−	1.40566i	−0.869095	−	0.494645i	$-0.835298\pi$
$953$	−1.28053e7	−	3.94106e7i	−0.456727	−	1.40566i	0.412368	−	0.911017i	$-0.364702\pi$
$954$		0			0
$955$	−1.97963e7	−	1.43829e7i	−0.702386	−	0.510313i
$956$	2.65157e7			0.938337
$957$		0			0
$958$	−2.52636e7			−0.889367
$959$	4.24789e7	+	3.08627e7i	1.49151	+	1.08365i
$960$		0			0
$961$	−8.84256e6	−	2.72146e7i	−0.308866	−	0.950591i
$962$	−9.94125e6	+	7.22274e6i	−0.346340	+	0.251631i
$963$		0			0
$964$	−1.96574e6	−	6.04993e6i	−0.0681293	−	0.209680i
$965$	−7.19956e6	+	2.21580e7i	−0.248879	+	0.765970i
$966$		0			0
$967$	−1.65136e7			−0.567905			−0.283952	−	0.958838i	$-0.591646\pi$
$967$	−1.65136e7			−0.567905			−0.283952	+	0.958838i	$0.591646\pi$
$968$	709895.	+	1.02828e7i	0.0243504	+	0.352714i
$969$		0			0
$970$	−1.47831e7	−	1.07406e7i	−0.504472	−	0.366521i
$971$	1.99157e6	−	6.12942e6i	0.0677871	−	0.208627i	−0.911425	−	0.411466i	$-0.865017\pi$
$971$	1.99157e6	−	6.12942e6i	0.0677871	−	0.208627i	0.979212	+	0.202839i	$0.0650168\pi$
$972$		0			0
$973$	−2.86900e7	+	2.08445e7i	−0.971512	+	0.705845i
$974$	−1.75474e7	+	1.27489e7i	−0.592672	+	0.430601i
$975$		0			0
$976$	1.91846e6	−	5.90442e6i	0.0644657	−	0.198405i
$977$	2.59341e7	+	1.88422e7i	0.869229	+	0.631532i	0.930380	−	0.366597i	$-0.119477\pi$
$977$	2.59341e7	+	1.88422e7i	0.869229	+	0.631532i	−0.0611511	+	0.998129i	$0.519477\pi$
$978$		0			0
$979$	1.09402e7	−	2.12153e6i	0.364811	−	0.0707445i
$980$	−1.27241e7			−0.423217
$981$		0			0
$982$	6.00867e6	−	1.84928e7i	0.198838	−	0.611960i
$983$	−5.62412e6	−	1.73093e7i	−0.185640	−	0.571340i	0.814319	−	0.580417i	$-0.197111\pi$
$983$	−5.62412e6	−	1.73093e7i	−0.185640	−	0.571340i	−0.999959	+	0.00907730i	$0.997111\pi$
$984$		0			0
$985$	−1.03858e6	+	754573.i	−0.0341075	+	0.0247805i
$986$	−30043.1	−	92463.2i	−0.000984131	−	0.00302884i
$987$		0			0
$988$	14929.2	+	10846.7i	0.000486569	+	0.000353513i
$989$	−1.26542e7			−0.411382
$990$		0			0
$991$	−3.35520e7			−1.08526			−0.542631	−	0.839971i	$-0.682572\pi$
$991$	−3.35520e7			−1.08526			−0.542631	+	0.839971i	$0.682572\pi$
$992$	98068.7	+	71251.1i	0.00316411	+	0.00229886i
$993$		0			0
$994$	1.55003e7	+	4.77052e7i	0.497594	+	1.53144i
$995$	1.45603e7	−	1.05787e7i	0.466243	−	0.338745i
$996$		0			0
$997$	−6.91421e6	−	2.12798e7i	−0.220295	−	0.677999i	−0.998735	−	0.0502797i	$-0.983989\pi$
$997$	−6.91421e6	−	2.12798e7i	−0.220295	−	0.677999i	0.778440	−	0.627719i	$-0.216011\pi$
$998$	−1.03180e7	+	3.17555e7i	−0.327921	+	1.00924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.f.h.37.4	yes	20
3.2	odd	2		198.6.f.g.37.2	✓	20
11.3	even	5	inner	198.6.f.h.91.4	yes	20
33.14	odd	10		198.6.f.g.91.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.f.g.37.2	✓	20	3.2	odd	2
198.6.f.g.91.2	yes	20	33.14	odd	10
198.6.f.h.37.4	yes	20	1.1	even	1	trivial
198.6.f.h.91.4	yes	20	11.3	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(34.0128 - 24.7118i) q^{5} +(58.4057 + 179.754i) q^{7} +(-19.7771 + 60.8676i) q^{8} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(4.94427 + 15.2169i) q^{4} +(34.0128 - 24.7118i) q^{5} +(58.4057 + 179.754i) q^{7} +(-19.7771 + 60.8676i) q^{8} +168.169 q^{10} +(-393.972 + 76.3995i) q^{11} +(193.036 + 140.249i) q^{13} +(-233.623 + 719.016i) q^{14} +(-207.108 + 150.473i) q^{16} +(-9.75136 + 7.08478i) q^{17} +(1.49370 - 4.59712i) q^{19} +(544.205 + 395.388i) q^{20} +(-1454.55 - 679.050i) q^{22} +898.471 q^{23} +(-419.477 + 1291.02i) q^{25} +(294.932 + 907.708i) q^{26} +(-2446.53 + 1777.51i) q^{28} +(623.128 + 1917.79i) q^{29} +(-95.7702 - 69.5811i) q^{31} -1024.00 q^{32} -48.2134 q^{34} +(6428.58 + 4670.64i) q^{35} +(3978.56 + 12244.7i) q^{37} +(15.6422 - 11.3647i) q^{38} +(831.471 + 2559.01i) q^{40} +(-3914.36 + 12047.2i) q^{41} -14084.2 q^{43} +(-3110.47 - 5617.30i) q^{44} +(2907.51 + 2112.43i) q^{46} +(2125.46 - 6541.50i) q^{47} +(-15303.2 + 11118.4i) q^{49} +(-4392.82 + 3191.57i) q^{50} +(-1179.73 + 3630.83i) q^{52} +(-5958.77 - 4329.30i) q^{53} +(-11512.1 + 12334.3i) q^{55} -12096.3 q^{56} +(-2492.51 + 7671.17i) q^{58} +(-2337.50 - 7194.07i) q^{59} +(-19619.5 + 14254.4i) q^{61} +(-146.324 - 450.338i) q^{62} +(-3313.73 - 2407.57i) q^{64} +10031.5 q^{65} -11275.9 q^{67} +(-156.022 - 113.356i) q^{68} +(9822.00 + 30229.0i) q^{70} +(53676.5 - 38998.3i) q^{71} +(27410.8 + 84361.9i) q^{73} +(-15914.2 + 48979.0i) q^{74} +77.3393 q^{76} +(-36743.3 - 66356.0i) q^{77} +(11511.9 + 8363.90i) q^{79} +(-3325.89 + 10236.0i) q^{80} +(-40991.7 + 29782.2i) q^{82} +(96212.9 - 69902.8i) q^{83} +(-156.594 + 481.947i) q^{85} +(-45577.4 - 33113.9i) q^{86} +(3141.37 - 25491.1i) q^{88} -27768.9 q^{89} +(-13935.9 + 42890.2i) q^{91} +(4442.28 + 13671.9i) q^{92} +(22258.1 - 16171.5i) q^{94} +(-62.7982 - 193.273i) q^{95} +(-87906.6 - 63867.9i) q^{97} -75663.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 80 q^{4} + 112 q^{5} - 392 q^{7} + 320 q^{8}+O(q^{10}) \) 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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