LMFDB - Embedded newform 950.2.e.m.501.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.39075800976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 12x^{6} - 13x^{5} + 125x^{4} - 116x^{3} + 232x^{2} + 96x + 64 $ x^8 - x^7 + 12x^6 - 13x^5 + 125x^4 - 116x^3 + 232x^2 + 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.4
Root			$-1.63248 - 2.82754i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.m.201.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.63248 + 2.82754i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.63248 + 2.82754i) q^{6} -2.62013 q^{7} -1.00000 q^{8} +(-3.82998 + 6.63372i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.63248 + 2.82754i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.63248 + 2.82754i) q^{6} -2.62013 q^{7} -1.00000 q^{8} +(-3.82998 + 6.63372i) q^{9} +5.03983 q^{11} -3.26496 q^{12} +(-2.32241 + 4.02254i) q^{13} +(-1.31007 - 2.26910i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82998 + 3.16962i) q^{17} -7.65996 q^{18} +(0.697500 - 4.30273i) q^{19} +(-4.27731 - 7.40852i) q^{21} +(2.51991 + 4.36462i) q^{22} +(2.34233 - 4.05703i) q^{23} +(-1.63248 - 2.82754i) q^{24} -4.64483 q^{26} -15.2146 q^{27} +(1.31007 - 2.26910i) q^{28} +(4.01991 - 6.96270i) q^{29} -3.28009 q^{31} +(0.500000 - 0.866025i) q^{32} +(8.22742 + 14.2503i) q^{33} +(-1.82998 + 3.16962i) q^{34} +(-3.82998 - 6.63372i) q^{36} -5.75505 q^{37} +(4.07502 - 1.54731i) q^{38} -15.1652 q^{39} +(2.90735 + 5.03568i) q^{41} +(4.27731 - 7.40852i) q^{42} +(0.290150 + 0.502555i) q^{43} +(-2.51991 + 4.36462i) q^{44} +4.68466 q^{46} +(-2.31007 + 4.00115i) q^{47} +(1.63248 - 2.82754i) q^{48} -0.134919 q^{49} +(-5.97481 + 10.3487i) q^{51} +(-2.32241 - 4.02254i) q^{52} +(2.31007 - 4.00115i) q^{53} +(-7.60729 - 13.1762i) q^{54} +2.62013 q^{56} +(13.3048 - 5.05191i) q^{57} +8.03983 q^{58} +(1.88743 + 3.26913i) q^{59} +(-0.0650203 + 0.112618i) q^{61} +(-1.64004 - 2.84064i) q^{62} +(10.0350 - 17.3812i) q^{63} +1.00000 q^{64} +(-8.22742 + 14.2503i) q^{66} +(-0.189935 + 0.328977i) q^{67} -3.65996 q^{68} +15.2952 q^{69} +(4.56746 + 7.91107i) q^{71} +(3.82998 - 6.63372i) q^{72} +(4.25261 + 7.36574i) q^{73} +(-2.87752 - 4.98402i) q^{74} +(3.37752 + 2.75542i) q^{76} -13.2050 q^{77} +(-7.58259 - 13.1334i) q^{78} +(3.98237 + 6.89767i) q^{79} +(-13.3475 - 23.1186i) q^{81} +(-2.90735 + 5.03568i) q^{82} +7.86996 q^{83} +8.55462 q^{84} +(-0.290150 + 0.502555i) q^{86} +26.2497 q^{87} -5.03983 q^{88} +(4.14483 - 7.17905i) q^{89} +(6.08503 - 10.5396i) q^{91} +(2.34233 + 4.05703i) q^{92} +(-5.35468 - 9.27458i) q^{93} -4.62013 q^{94} +3.26496 q^{96} +(8.09494 + 14.0208i) q^{97} +(-0.0674593 - 0.116843i) q^{98} +(-19.3024 + 33.4328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} + q^{6} - 12 q^{7} - 8 q^{8} - 11 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 + q^6 - 12 * q^7 - 8 * q^8 - 11 * q^9	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} + q^{6} - 12 q^{7} - 8 q^{8} - 11 q^{9} + 10 q^{11} + 2 q^{12} - 9 q^{13} - 6 q^{14} - 4 q^{16} - 5 q^{17} - 22 q^{18} - q^{21} + 5 q^{22} - 6 q^{23} + q^{24} - 18 q^{26} - 16 q^{27} + 6 q^{28} + 17 q^{29} + 22 q^{31} + 4 q^{32} + 4 q^{33} + 5 q^{34} - 11 q^{36} + 8 q^{37} - 36 q^{39} + 7 q^{41} + q^{42} + 13 q^{43} - 5 q^{44} - 12 q^{46} - 14 q^{47} - q^{48} + 44 q^{49} - 9 q^{51} - 9 q^{52} + 14 q^{53} - 8 q^{54} + 12 q^{56} + 48 q^{57} + 34 q^{58} + 14 q^{59} - 9 q^{61} + 11 q^{62} + 45 q^{63} + 8 q^{64} - 4 q^{66} - 6 q^{67} + 10 q^{68} + 54 q^{69} + 14 q^{71} + 11 q^{72} + 11 q^{73} + 4 q^{74} + 10 q^{77} - 18 q^{78} - 17 q^{79} - 36 q^{81} - 7 q^{82} + 46 q^{83} + 2 q^{84} - 13 q^{86} + 2 q^{87} - 10 q^{88} + 14 q^{89} - 25 q^{91} - 6 q^{92} - 13 q^{93} - 28 q^{94} - 2 q^{96} + 17 q^{97} + 22 q^{98} - 60 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 + q^6 - 12 * q^7 - 8 * q^8 - 11 * q^9 + 10 * q^11 + 2 * q^12 - 9 * q^13 - 6 * q^14 - 4 * q^16 - 5 * q^17 - 22 * q^18 - q^21 + 5 * q^22 - 6 * q^23 + q^24 - 18 * q^26 - 16 * q^27 + 6 * q^28 + 17 * q^29 + 22 * q^31 + 4 * q^32 + 4 * q^33 + 5 * q^34 - 11 * q^36 + 8 * q^37 - 36 * q^39 + 7 * q^41 + q^42 + 13 * q^43 - 5 * q^44 - 12 * q^46 - 14 * q^47 - q^48 + 44 * q^49 - 9 * q^51 - 9 * q^52 + 14 * q^53 - 8 * q^54 + 12 * q^56 + 48 * q^57 + 34 * q^58 + 14 * q^59 - 9 * q^61 + 11 * q^62 + 45 * q^63 + 8 * q^64 - 4 * q^66 - 6 * q^67 + 10 * q^68 + 54 * q^69 + 14 * q^71 + 11 * q^72 + 11 * q^73 + 4 * q^74 + 10 * q^77 - 18 * q^78 - 17 * q^79 - 36 * q^81 - 7 * q^82 + 46 * q^83 + 2 * q^84 - 13 * q^86 + 2 * q^87 - 10 * q^88 + 14 * q^89 - 25 * q^91 - 6 * q^92 - 13 * q^93 - 28 * q^94 - 2 * q^96 + 17 * q^97 + 22 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.63248	+	2.82754i	0.942513	+	1.63248i	0.760657	+	0.649154i	$0.224877\pi$
$3$	1.63248	+	2.82754i	0.942513	+	1.63248i	0.181856	+	0.983325i	$0.441790\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.63248	+	2.82754i	−0.666457	+	1.15434i
$7$	−2.62013			−0.990316			−0.495158	−	0.868803i	$-0.664890\pi$
$7$	−2.62013			−0.990316			−0.495158	+	0.868803i	$0.664890\pi$
$8$	−1.00000			−0.353553
$9$	−3.82998	+	6.63372i	−1.27666	+	2.21124i
$10$		0			0
$11$	5.03983			1.51957			0.759783	−	0.650177i	$-0.225305\pi$
$11$	5.03983			1.51957			0.759783	+	0.650177i	$0.225305\pi$
$12$	−3.26496			−0.942513
$13$	−2.32241	+	4.02254i	−0.644122	+	1.11565i	0.340382	+	0.940287i	$0.389444\pi$
$13$	−2.32241	+	4.02254i	−0.644122	+	1.11565i	−0.984504	+	0.175365i	$0.943890\pi$
$14$	−1.31007	−	2.26910i	−0.350130	−	0.606442i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.82998	+	3.16962i	0.443835	+	0.768745i	0.997970	−	0.0636816i	$-0.0202842\pi$
$17$	1.82998	+	3.16962i	0.443835	+	0.768745i	−0.554135	+	0.832427i	$0.686951\pi$
$18$	−7.65996			−1.80547
$19$	0.697500	−	4.30273i	0.160017	−	0.987114i
$19$	0.697500	−	4.30273i	0.160017	−	0.987114i
$20$		0			0
$21$	−4.27731	−	7.40852i	−0.933385	−	1.61667i
$22$	2.51991	+	4.36462i	0.537248	+	0.930540i
$23$	2.34233	−	4.05703i	0.488409	−	0.845950i	−0.511502	−	0.859282i	$-0.670911\pi$
$23$	2.34233	−	4.05703i	0.488409	−	0.845950i	0.999911	+	0.0133324i	$0.00424395\pi$
$24$	−1.63248	−	2.82754i	−0.333229	−	0.577169i
$25$		0			0
$26$	−4.64483			−0.910926
$27$	−15.2146			−2.92805
$28$	1.31007	−	2.26910i	0.247579	−	0.428819i
$29$	4.01991	−	6.96270i	0.746479	−	1.29294i	−0.203021	−	0.979174i	$-0.565076\pi$
$29$	4.01991	−	6.96270i	0.746479	−	1.29294i	0.949500	−	0.313766i	$-0.101591\pi$
$30$		0			0
$31$	−3.28009			−0.589121			−0.294561	−	0.955633i	$-0.595173\pi$
$31$	−3.28009			−0.589121			−0.294561	+	0.955633i	$0.595173\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	8.22742	+	14.2503i	1.43221	+	2.48066i
$34$	−1.82998	+	3.16962i	−0.313839	+	0.543585i
$35$		0			0
$36$	−3.82998	−	6.63372i	−0.638330	−	1.10562i
$37$	−5.75505			−0.946124			−0.473062	−	0.881029i	$-0.656851\pi$
$37$	−5.75505			−0.946124			−0.473062	+	0.881029i	$0.656851\pi$
$38$	4.07502	−	1.54731i	0.661056	−	0.251007i
$39$	−15.1652			−2.42837
$40$		0			0
$41$	2.90735	+	5.03568i	0.454052	+	0.786441i	0.998633	−	0.0522673i	$-0.0166448\pi$
$41$	2.90735	+	5.03568i	0.454052	+	0.786441i	−0.544581	+	0.838708i	$0.683311\pi$
$42$	4.27731	−	7.40852i	0.660003	−	1.14316i
$43$	0.290150	+	0.502555i	0.0442475	+	0.0766390i	0.887301	−	0.461191i	$-0.152578\pi$
$43$	0.290150	+	0.502555i	0.0442475	+	0.0766390i	−0.843053	+	0.537830i	$0.819244\pi$
$44$	−2.51991	+	4.36462i	−0.379891	+	0.657991i
$45$		0			0
$46$	4.68466			0.690715
$47$	−2.31007	+	4.00115i	−0.336958	+	0.583628i	−0.983859	−	0.178946i	$-0.942731\pi$
$47$	−2.31007	+	4.00115i	−0.336958	+	0.583628i	0.646901	+	0.762574i	$0.276065\pi$
$48$	1.63248	−	2.82754i	0.235628	−	0.408120i
$49$	−0.134919			−0.0192741
$50$		0			0
$51$	−5.97481	+	10.3487i	−0.836641	+	1.44910i
$52$	−2.32241	−	4.02254i	−0.322061	−	0.557826i
$53$	2.31007	−	4.00115i	0.317312	−	0.549600i	−0.662614	−	0.748961i	$-0.730553\pi$
$53$	2.31007	−	4.00115i	0.317312	−	0.549600i	0.979926	+	0.199361i	$0.0638865\pi$
$54$	−7.60729	−	13.1762i	−1.03522	−	1.79306i
$55$		0			0
$56$	2.62013			0.350130
$57$	13.3048	−	5.05191i	1.76226	−	0.669142i
$58$	8.03983			1.05568
$59$	1.88743	+	3.26913i	0.245723	+	0.425605i	0.962335	−	0.271868i	$-0.0876413\pi$
$59$	1.88743	+	3.26913i	0.245723	+	0.425605i	−0.716612	+	0.697472i	$0.754308\pi$
$60$		0			0
$61$	−0.0650203	+	0.112618i	−0.00832500	+	0.0144193i	−0.870158	−	0.492773i	$-0.835983\pi$
$61$	−0.0650203	+	0.112618i	−0.00832500	+	0.0144193i	0.861833	+	0.507192i	$0.169317\pi$
$62$	−1.64004	−	2.84064i	−0.208286	−	0.360762i
$63$	10.0350	−	17.3812i	1.26430	−	2.18983i
$64$	1.00000			0.125000
$65$		0			0
$66$	−8.22742	+	14.2503i	−1.01273	+	1.75409i
$67$	−0.189935	+	0.328977i	−0.0232043	+	0.0401909i	−0.877394	−	0.479770i	$-0.840720\pi$
$67$	−0.189935	+	0.328977i	−0.0232043	+	0.0401909i	0.854190	+	0.519961i	$0.174053\pi$
$68$	−3.65996			−0.443835
$69$	15.2952			1.84133
$70$		0			0
$71$	4.56746	+	7.91107i	0.542058	+	0.938871i	0.998786	+	0.0492651i	$0.0156879\pi$
$71$	4.56746	+	7.91107i	0.542058	+	0.938871i	−0.456728	+	0.889606i	$0.650979\pi$
$72$	3.82998	−	6.63372i	0.451367	−	0.781791i
$73$	4.25261	+	7.36574i	0.497730	+	0.862094i	0.999997	−	0.00261883i	$-0.000833600\pi$
$73$	4.25261	+	7.36574i	0.497730	+	0.862094i	−0.502266	+	0.864713i	$0.667500\pi$
$74$	−2.87752	−	4.98402i	−0.334505	−	0.579380i
$75$		0			0
$76$	3.37752	+	2.75542i	0.387429	+	0.316068i
$77$	−13.2050			−1.50485
$78$	−7.58259	−	13.1334i	−0.858559	−	1.48707i
$79$	3.98237	+	6.89767i	0.448052	+	0.776049i	0.998259	−	0.0589793i	$-0.0187846\pi$
$79$	3.98237	+	6.89767i	0.448052	+	0.776049i	−0.550207	+	0.835028i	$0.685451\pi$
$80$		0			0
$81$	−13.3475	−	23.1186i	−1.48306	−	2.56874i
$82$	−2.90735	+	5.03568i	−0.321063	+	0.556098i
$83$	7.86996			0.863840			0.431920	−	0.901912i	$-0.357836\pi$
$83$	7.86996			0.863840			0.431920	+	0.901912i	$0.357836\pi$
$84$	8.55462			0.933385
$85$		0			0
$86$	−0.290150	+	0.502555i	−0.0312877	+	0.0541919i
$87$	26.2497			2.81426
$88$	−5.03983			−0.537248
$89$	4.14483	−	7.17905i	0.439351	−	0.760978i	−0.558289	−	0.829647i	$-0.688542\pi$
$89$	4.14483	−	7.17905i	0.439351	−	0.760978i	0.997640	+	0.0686686i	$0.0218751\pi$
$90$		0			0
$91$	6.08503	−	10.5396i	0.637884	−	1.10485i
$92$	2.34233	+	4.05703i	0.244205	+	0.422975i
$93$	−5.35468	−	9.27458i	−0.555254	−	0.961729i
$94$	−4.62013			−0.476530
$95$		0			0
$96$	3.26496			0.333229
$97$	8.09494	+	14.0208i	0.821917	+	1.42360i	0.904253	+	0.426997i	$0.140428\pi$
$97$	8.09494	+	14.0208i	0.821917	+	1.42360i	−0.0823367	+	0.996605i	$0.526238\pi$
$98$	−0.0674593	−	0.116843i	−0.00681442	−	0.0118029i
$99$	−19.3024	+	33.4328i	−1.93997	+	3.36012i
$100$		0			0
$101$	−4.23270	+	7.33124i	−0.421169	+	0.729486i	−0.996054	−	0.0887481i	$-0.971713\pi$
$101$	−4.23270	+	7.33124i	−0.421169	+	0.729486i	0.574885	+	0.818234i	$0.305047\pi$
$102$	−11.9496			−1.18319
$103$	11.8498			1.16760			0.583800	−	0.811898i	$-0.301565\pi$
$103$	11.8498			1.16760			0.583800	+	0.811898i	$0.301565\pi$
$104$	2.32241	−	4.02254i	0.227731	−	0.394443i
$105$		0			0
$106$	4.62013			0.448747
$107$	16.8100			1.62508			0.812542	−	0.582902i	$-0.198083\pi$
$107$	16.8100			1.62508			0.812542	+	0.582902i	$0.198083\pi$
$108$	7.60729	−	13.1762i	0.732012	−	1.26788i
$109$	−10.0023	−	17.3245i	−0.958045	−	1.65938i	−0.727240	−	0.686384i	$-0.759197\pi$
$109$	−10.0023	−	17.3245i	−0.958045	−	1.65938i	−0.230806	−	0.973000i	$-0.574136\pi$
$110$		0			0
$111$	−9.39500	−	16.2726i	−0.891734	−	1.54453i
$112$	1.31007	+	2.26910i	0.123790	+	0.214410i
$113$	−14.3505			−1.34998			−0.674990	−	0.737827i	$-0.735852\pi$
$113$	−14.3505			−1.34998			−0.674990	+	0.737827i	$0.735852\pi$
$114$	11.0275	+	8.99633i	1.03282	+	0.842583i
$115$		0			0
$116$	4.01991	+	6.96270i	0.373240	+	0.646470i
$117$	−17.7896	−	30.8125i	−1.64465	−	2.84862i
$118$	−1.88743	+	3.26913i	−0.173752	+	0.300948i
$119$	−4.79478	−	8.30481i	−0.439537	−	0.761301i
$120$		0			0
$121$	14.3999			1.30908
$122$	−0.130041			−0.0117733
$123$	−9.49238	+	16.4413i	−0.855899	+	1.48246i
$124$	1.64004	−	2.84064i	0.147280	−	0.255097i
$125$		0			0
$126$	20.0701			1.78799
$127$	−3.94254	+	6.82869i	−0.349844	+	0.605948i	−0.986222	−	0.165430i	$-0.947099\pi$
$127$	−3.94254	+	6.82869i	−0.349844	+	0.605948i	0.636377	+	0.771378i	$0.280432\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.947329	+	1.64082i	−0.0834077	+	0.144466i
$130$		0			0
$131$	−1.20228	−	2.08242i	−0.105044	−	0.181942i	0.808712	−	0.588205i	$-0.200165\pi$
$131$	−1.20228	−	2.08242i	−0.105044	−	0.181942i	−0.913756	+	0.406263i	$0.866832\pi$
$132$	−16.4548			−1.43221
$133$	−1.82754	+	11.2737i	−0.158468	+	0.977555i
$134$	−0.379870			−0.0328158
$135$		0			0
$136$	−1.82998	−	3.16962i	−0.156919	−	0.271792i
$137$	8.71751	−	15.0992i	0.744787	−	1.29001i	−0.205507	−	0.978656i	$-0.565884\pi$
$137$	8.71751	−	15.0992i	0.744787	−	1.29001i	0.950294	−	0.311353i	$-0.100782\pi$
$138$	7.64761	+	13.2460i	0.651008	+	1.12758i
$139$	−4.78487	+	8.28764i	−0.405848	+	0.702949i	−0.994420	−	0.105496i	$-0.966357\pi$
$139$	−4.78487	+	8.28764i	−0.405848	+	0.702949i	0.588572	+	0.808445i	$0.299690\pi$
$140$		0			0
$141$	−15.0845			−1.27035
$142$	−4.56746	+	7.91107i	−0.383293	+	0.663882i
$143$	−11.7046	+	20.2729i	−0.978786	+	1.69531i
$144$	7.65996			0.638330
$145$		0			0
$146$	−4.25261	+	7.36574i	−0.351948	+	0.609593i
$147$	−0.220252	−	0.381488i	−0.0181661	−	0.0314646i
$148$	2.87752	−	4.98402i	0.236531	−	0.409684i
$149$	8.56218	+	14.8301i	0.701441	+	1.21493i	0.967961	+	0.251102i	$0.0807931\pi$
$149$	8.56218	+	14.8301i	0.701441	+	1.21493i	−0.266519	+	0.963830i	$0.585874\pi$
$150$		0			0
$151$	−5.44440			−0.443059			−0.221529	−	0.975154i	$-0.571105\pi$
$151$	−5.44440			−0.443059			−0.221529	+	0.975154i	$0.571105\pi$
$152$	−0.697500	+	4.30273i	−0.0565747	+	0.348998i
$153$	−28.0351			−2.26651
$154$	−6.60250	−	11.4359i	−0.532045	−	0.921529i
$155$		0			0
$156$	7.58259	−	13.1334i	0.607093	−	1.05152i
$157$	−0.0123496	−	0.0213902i	−0.000985608	−	0.00170712i	0.865532	−	0.500853i	$-0.166980\pi$
$157$	−0.0123496	−	0.0213902i	−0.000985608	−	0.00170712i	−0.866518	+	0.499146i	$0.833647\pi$
$158$	−3.98237	+	6.89767i	−0.316821	+	0.548749i
$159$	15.0845			1.19628
$160$		0			0
$161$	−6.13721	+	10.6300i	−0.483680	+	0.837758i
$162$	13.3475	−	23.1186i	1.04868	−	1.81637i
$163$	10.8347			0.848640			0.424320	−	0.905512i	$-0.360513\pi$
$163$	10.8347			0.848640			0.424320	+	0.905512i	$0.360513\pi$
$164$	−5.81470			−0.454052
$165$		0			0
$166$	3.93498	+	6.81558i	0.305414	+	0.528992i
$167$	−3.14239	+	5.44278i	−0.243165	+	0.421175i	−0.961614	−	0.274405i	$-0.911519\pi$
$167$	−3.14239	+	5.44278i	−0.243165	+	0.421175i	0.718449	+	0.695580i	$0.244852\pi$
$168$	4.27731	+	7.40852i	0.330002	+	0.571579i
$169$	−4.28722	−	7.42568i	−0.329786	−	0.571206i
$170$		0			0
$171$	25.8717	+	21.1064i	1.97846	+	1.61405i
$172$	−0.580301			−0.0442475
$173$	−0.187589	−	0.324914i	−0.0142622	−	0.0247028i	0.858806	−	0.512301i	$-0.171207\pi$
$173$	−0.187589	−	0.324914i	−0.0142622	−	0.0247028i	−0.873068	+	0.487598i	$0.837873\pi$
$174$	13.1249	+	22.7329i	0.994993	+	1.72338i
$175$		0			0
$176$	−2.51991	−	4.36462i	−0.189946	−	0.328996i
$177$	−6.16240	+	10.6736i	−0.463194	+	0.802276i
$178$	8.28966			0.621336
$179$	−8.04940			−0.601640			−0.300820	−	0.953681i	$-0.597260\pi$
$179$	−8.04940			−0.601640			−0.300820	+	0.953681i	$0.597260\pi$
$180$		0			0
$181$	10.5251	−	18.2301i	0.782327	−	1.35503i	−0.148256	−	0.988949i	$-0.547366\pi$
$181$	10.5251	−	18.2301i	0.782327	−	1.35503i	0.930583	−	0.366081i	$-0.119301\pi$
$182$	12.1701			0.902105
$183$	−0.424577			−0.0313857
$184$	−2.34233	+	4.05703i	−0.172679	+	0.299088i
$185$		0			0
$186$	5.35468	−	9.27458i	0.392624	−	0.680045i
$187$	9.22278	+	15.9743i	0.674437	+	1.16816i
$188$	−2.31007	−	4.00115i	−0.168479	−	0.291814i
$189$	39.8642			2.89969
$190$		0			0
$191$	8.03983			0.581742			0.290871	−	0.956762i	$-0.406055\pi$
$191$	8.03983			0.581742			0.290871	+	0.956762i	$0.406055\pi$
$192$	1.63248	+	2.82754i	0.117814	+	0.204060i
$193$	−10.1224	−	17.5325i	−0.728628	−	1.26202i	−0.957463	−	0.288555i	$-0.906825\pi$
$193$	−10.1224	−	17.5325i	−0.728628	−	1.26202i	0.228836	−	0.973465i	$-0.426508\pi$
$194$	−8.09494	+	14.0208i	−0.581183	+	1.00664i
$195$		0			0
$196$	0.0674593	−	0.116843i	0.00481852	−	0.00834593i
$197$	2.92004			0.208044			0.104022	−	0.994575i	$-0.466829\pi$
$197$	2.92004			0.208044			0.104022	+	0.994575i	$0.466829\pi$
$198$	−38.6049			−2.74353
$199$	7.80244	−	13.5142i	0.553101	−	0.957998i	−0.444948	−	0.895556i	$-0.646778\pi$
$199$	7.80244	−	13.5142i	0.553101	−	0.957998i	0.998049	−	0.0624418i	$-0.0198888\pi$
$200$		0			0
$201$	−1.24026			−0.0874812
$202$	−8.46539			−0.595623
$203$	−10.5327	+	18.2432i	−0.739251	+	1.28042i
$204$	−5.97481	−	10.3487i	−0.418320	−	0.724552i
$205$		0			0
$206$	5.92492	+	10.2623i	0.412809	+	0.715006i
$207$	17.9421	+	31.0767i	1.24707	+	2.15998i
$208$	4.64483			0.322061
$209$	3.51528	−	21.6850i	0.243157	−	1.49998i
$210$		0			0
$211$	−0.572585	−	0.991747i	−0.0394184	−	0.0682747i	0.845643	−	0.533749i	$-0.179217\pi$
$211$	−0.572585	−	0.991747i	−0.0394184	−	0.0682747i	−0.885062	+	0.465474i	$0.845884\pi$
$212$	2.31007	+	4.00115i	0.158656	+	0.274800i
$213$	−14.9126	+	25.8293i	−1.02179	+	1.76980i
$214$	8.40500	+	14.5579i	0.574554	+	0.995157i
$215$		0			0
$216$	15.2146			1.03522
$217$	8.59426			0.583416
$218$	10.0023	−	17.3245i	0.677440	−	1.17336i
$219$	−13.8846	+	24.0488i	−0.938234	+	1.62507i
$220$		0			0
$221$	−16.9999			−1.14354
$222$	9.39500	−	16.2726i	0.630551	−	1.09215i
$223$	−7.66474	−	13.2757i	−0.513269	−	0.889008i	−0.999882	−	0.0153903i	$-0.995101\pi$
$223$	−7.66474	−	13.2757i	−0.513269	−	0.889008i	0.486612	−	0.873618i	$-0.338232\pi$
$224$	−1.31007	+	2.26910i	−0.0875324	+	0.151611i
$225$		0			0
$226$	−7.17524	−	12.4279i	−0.477290	−	0.826690i
$227$	−19.2850			−1.27999			−0.639994	−	0.768380i	$-0.721063\pi$
$227$	−19.2850			−1.27999			−0.639994	+	0.768380i	$0.721063\pi$
$228$	−2.27731	+	14.0482i	−0.150818	+	0.930368i
$229$	14.3752			0.949939			0.474969	−	0.880002i	$-0.342459\pi$
$229$	14.3752			0.949939			0.474969	+	0.880002i	$0.342459\pi$
$230$		0			0
$231$	−21.5569	−	37.3377i	−1.41834	−	2.45664i
$232$	−4.01991	+	6.96270i	−0.263920	+	0.457123i
$233$	−6.91272	−	11.9732i	−0.452867	−	0.784389i	0.545695	−	0.837984i	$-0.316266\pi$
$233$	−6.91272	−	11.9732i	−0.452867	−	0.784389i	−0.998563	+	0.0535944i	$0.982932\pi$
$234$	17.7896	−	30.8125i	1.16294	−	2.01428i
$235$		0			0
$236$	−3.77487			−0.245723
$237$	−13.0023	+	22.5206i	−0.844589	+	1.46287i
$238$	4.79478	−	8.30481i	0.310800	−	0.538321i
$239$	−14.9696			−0.968305			−0.484152	−	0.874984i	$-0.660872\pi$
$239$	−14.9696			−0.968305			−0.484152	+	0.874984i	$0.660872\pi$
$240$		0			0
$241$	9.66469	−	16.7397i	0.622557	−	1.07830i	−0.366451	−	0.930437i	$-0.619427\pi$
$241$	9.66469	−	16.7397i	0.622557	−	1.07830i	0.989008	−	0.147863i	$-0.0472395\pi$
$242$	7.19994	+	12.4707i	0.462830	+	0.801644i
$243$	20.7573	−	35.9528i	1.33158	−	2.30637i
$244$	−0.0650203	−	0.112618i	−0.00416250	−	0.00720966i
$245$		0			0
$246$	−18.9848			−1.21042
$247$	15.6880	+	12.7984i	0.998205	+	0.814346i
$248$	3.28009			0.208286
$249$	12.8475	+	22.2526i	0.814180	+	1.41020i
$250$		0			0
$251$	−5.16246	+	8.94164i	−0.325851	+	0.564391i	−0.981684	−	0.190515i	$-0.938984\pi$
$251$	−5.16246	+	8.94164i	−0.325851	+	0.564391i	0.655833	+	0.754906i	$0.272318\pi$
$252$	10.0350	+	17.3812i	0.632148	+	1.09491i
$253$	11.8049	−	20.4468i	0.742170	−	1.28548i
$254$	−7.88509			−0.494755
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.3846	−	24.9149i	0.897287	−	1.55415i	0.0663376	−	0.997797i	$-0.478869\pi$
$257$	14.3846	−	24.9149i	0.897287	−	1.55415i	0.830949	−	0.556349i	$-0.187798\pi$
$258$	−1.89466			−0.117956
$259$	15.0790			0.936962
$260$		0			0
$261$	30.7924	+	53.3340i	1.90600	+	3.30129i
$262$	1.20228	−	2.08242i	0.0742774	−	0.128652i
$263$	−4.56746	−	7.91107i	−0.281642	−	0.487818i	0.690148	−	0.723669i	$-0.257546\pi$
$263$	−4.56746	−	7.91107i	−0.281642	−	0.487818i	−0.971789	+	0.235851i	$0.924212\pi$
$264$	−8.22742	−	14.2503i	−0.506363	−	0.877046i
$265$		0			0
$266$	−10.6771	+	4.05416i	−0.654655	+	0.248577i
$267$	27.0654			1.65638
$268$	−0.189935	−	0.328977i	−0.0116021	−	0.0200955i
$269$	−8.45474	−	14.6440i	−0.515495	−	0.892863i	−0.999838	−	0.0179853i	$-0.994275\pi$
$269$	−8.45474	−	14.6440i	−0.515495	−	0.892863i	0.484343	−	0.874878i	$-0.339059\pi$
$270$		0			0
$271$	7.94483	+	13.7609i	0.482614	+	0.835912i	0.999801	−	0.0199603i	$-0.00635399\pi$
$271$	7.94483	+	13.7609i	0.482614	+	0.835912i	−0.517187	+	0.855873i	$0.673021\pi$
$272$	1.82998	−	3.16962i	0.110959	−	0.192186i
$273$	39.7347			2.40486
$274$	17.4350			1.05329
$275$		0			0
$276$	−7.64761	+	13.2460i	−0.460332	+	0.797318i
$277$	−11.4852			−0.690079			−0.345040	−	0.938588i	$-0.612135\pi$
$277$	−11.4852			−0.690079			−0.345040	+	0.938588i	$0.612135\pi$
$278$	−9.56975			−0.573955
$279$	12.5627	−	21.7592i	0.752108	−	1.30269i
$280$		0			0
$281$	7.14483	−	12.3752i	0.426225	−	0.738243i	−0.570309	−	0.821430i	$-0.693177\pi$
$281$	7.14483	−	12.3752i	0.426225	−	0.738243i	0.996534	+	0.0831872i	$0.0265099\pi$
$282$	−7.54227	−	13.0636i	−0.449136	−	0.777926i
$283$	1.58215	+	2.74037i	0.0940493	+	0.162898i	0.909211	−	0.416335i	$-0.136686\pi$
$283$	1.58215	+	2.74037i	0.0940493	+	0.162898i	−0.815162	+	0.579233i	$0.803352\pi$
$284$	−9.13492			−0.542058
$285$		0			0
$286$	−23.4091			−1.38421
$287$	−7.61763	−	13.1941i	−0.449655	−	0.778825i
$288$	3.82998	+	6.63372i	0.225684	+	0.390896i
$289$	1.80235	−	3.12176i	0.106021	−	0.183633i
$290$		0			0
$291$	−26.4296	+	45.7775i	−1.54933	+	2.68352i
$292$	−8.50522			−0.497730
$293$	−14.7094			−0.859330			−0.429665	−	0.902988i	$-0.641368\pi$
$293$	−14.7094			−0.859330			−0.429665	+	0.902988i	$0.641368\pi$
$294$	0.220252	−	0.381488i	0.0128454	−	0.0222488i
$295$		0			0
$296$	5.75505			0.334505
$297$	−76.6789			−4.44936
$298$	−8.56218	+	14.8301i	−0.495994	+	0.859087i
$299$	10.8797	+	18.8442i	0.629190	+	1.08979i
$300$		0			0
$301$	−0.760232	−	1.31676i	−0.0438190	−	0.0758968i
$302$	−2.72220	−	4.71499i	−0.156645	−	0.271317i
$303$	−27.6392			−1.58783
$304$	−4.07502	+	1.54731i	−0.233719	+	0.0887445i
$305$		0			0
$306$	−14.0176	−	24.2791i	−0.801331	−	1.38795i
$307$	−13.0727	−	22.6425i	−0.746097	−	1.29228i	−0.949680	−	0.313221i	$-0.898592\pi$
$307$	−13.0727	−	22.6425i	−0.746097	−	1.29228i	0.203583	−	0.979058i	$-0.434741\pi$
$308$	6.60250	−	11.4359i	0.376213	−	0.651619i
$309$	19.3446	+	33.5059i	1.10048	+	1.90608i
$310$		0			0
$311$	6.65039			0.377109			0.188555	−	0.982063i	$-0.439620\pi$
$311$	6.65039			0.377109			0.188555	+	0.982063i	$0.439620\pi$
$312$	15.1652			0.858559
$313$	−8.68988	+	15.0513i	−0.491181	+	0.850750i	−0.999948	−	0.0101536i	$-0.996768\pi$
$313$	−8.68988	+	15.0513i	−0.491181	+	0.850750i	0.508768	+	0.860904i	$0.330101\pi$
$314$	0.0123496	−	0.0213902i	0.000696930	−	0.00120712i
$315$		0			0
$316$	−7.96475			−0.448052
$317$	0.687647	−	1.19104i	0.0386221	−	0.0668954i	−0.846068	−	0.533075i	$-0.821036\pi$
$317$	0.687647	−	1.19104i	0.0386221	−	0.0668954i	0.884690	+	0.466179i	$0.154370\pi$
$318$	7.54227	+	13.0636i	0.422949	+	0.732570i
$319$	20.2597	−	35.0908i	1.13432	−	1.96471i
$320$		0			0
$321$	27.4420	+	47.5309i	1.53166	+	2.65292i
$322$	−12.2744			−0.684026
$323$	14.9144	−	5.66310i	0.829861	−	0.315103i
$324$	26.6951			1.48306
$325$		0			0
$326$	5.41735	+	9.38313i	0.300039	+	0.519684i
$327$	32.6571	−	56.5637i	1.80594	−	3.12798i
$328$	−2.90735	−	5.03568i	−0.160532	−	0.278049i
$329$	6.05267	−	10.4835i	0.333695	−	0.577976i
$330$		0			0
$331$	11.7399			0.645284			0.322642	−	0.946521i	$-0.395429\pi$
$331$	11.7399			0.645284			0.322642	+	0.946521i	$0.395429\pi$
$332$	−3.93498	+	6.81558i	−0.215960	+	0.374054i
$333$	22.0417	−	38.1774i	1.20788	−	2.09211i
$334$	−6.28478			−0.343888
$335$		0			0
$336$	−4.27731	+	7.40852i	−0.233346	+	0.404168i
$337$	6.44005	+	11.1545i	0.350812	+	0.607624i	0.986392	−	0.164411i	$-0.0525724\pi$
$337$	6.44005	+	11.1545i	0.350812	+	0.607624i	−0.635580	+	0.772035i	$0.719239\pi$
$338$	4.28722	−	7.42568i	0.233194	−	0.403904i
$339$	−23.4269	−	40.5765i	−1.27237	−	2.20381i
$340$		0			0
$341$	−16.5311			−0.895209
$342$	−5.34282	+	32.9587i	−0.288907	+	1.78220i
$343$	18.6944			1.00940
$344$	−0.290150	−	0.502555i	−0.0156439	−	0.0270960i
$345$		0			0
$346$	0.187589	−	0.324914i	0.0100849	−	0.0174675i
$347$	−2.46724	−	4.27339i	−0.132449	−	0.229408i	0.792171	−	0.610299i	$-0.208951\pi$
$347$	−2.46724	−	4.27339i	−0.132449	−	0.229408i	−0.924620	+	0.380891i	$0.875617\pi$
$348$	−13.1249	+	22.7329i	−0.703566	+	1.21861i
$349$	1.26594			0.0677644			0.0338822	−	0.999426i	$-0.489213\pi$
$349$	1.26594			0.0677644			0.0338822	+	0.999426i	$0.489213\pi$
$350$		0			0
$351$	35.3346	−	61.2012i	1.88602	−	3.26668i
$352$	2.51991	−	4.36462i	0.134312	−	0.232635i
$353$	2.16060			0.114997			0.0574986	−	0.998346i	$-0.481688\pi$
$353$	2.16060			0.114997			0.0574986	+	0.998346i	$0.481688\pi$
$354$	−12.3248			−0.655056
$355$		0			0
$356$	4.14483	+	7.17905i	0.219676	+	0.380489i
$357$	15.6548	−	27.1149i	0.828539	−	1.43507i
$358$	−4.02470	−	6.97098i	−0.212712	−	0.368428i
$359$	2.36981	+	4.10463i	0.125074	+	0.216634i	0.921762	−	0.387757i	$-0.126750\pi$
$359$	2.36981	+	4.10463i	0.125074	+	0.216634i	−0.796688	+	0.604391i	$0.793417\pi$
$360$		0			0
$361$	−18.0270	−	6.00231i	−0.948789	−	0.315911i
$362$	21.0503			1.10638
$363$	23.5075	+	40.7162i	1.23382	+	2.13705i
$364$	6.08503	+	10.5396i	0.318942	+	0.552424i
$365$		0			0
$366$	−0.212289	−	0.367695i	−0.0110965	−	0.0192197i
$367$	11.4472	−	19.8271i	0.597538	−	1.03497i	−0.395645	−	0.918403i	$-0.629479\pi$
$367$	11.4472	−	19.8271i	0.597538	−	1.03497i	0.993183	−	0.116563i	$-0.0371876\pi$
$368$	−4.68466			−0.244205
$369$	−44.5404			−2.31868
$370$		0			0
$371$	−6.05267	+	10.4835i	−0.314239	+	0.544278i
$372$	10.7094			0.555254
$373$	19.2393			0.996172			0.498086	−	0.867128i	$-0.334036\pi$
$373$	19.2393			0.996172			0.498086	+	0.867128i	$0.334036\pi$
$374$	−9.22278	+	15.9743i	−0.476899	+	0.826013i
$375$		0			0
$376$	2.31007	−	4.00115i	0.119133	−	0.206344i
$377$	18.6718	+	32.3405i	0.961647	+	1.66562i
$378$	19.9321	+	34.5234i	1.02520	+	1.77569i
$379$	−6.45953			−0.331804			−0.165902	−	0.986142i	$-0.553053\pi$
$379$	−6.45953			−0.331804			−0.165902	+	0.986142i	$0.553053\pi$
$380$		0			0
$381$	−25.7445			−1.31893
$382$	4.01991	+	6.96270i	0.205677	+	0.356243i
$383$	−4.56746	−	7.91107i	−0.233386	−	0.404237i	0.725416	−	0.688310i	$-0.241647\pi$
$383$	−4.56746	−	7.91107i	−0.233386	−	0.404237i	−0.958802	+	0.284074i	$0.908314\pi$
$384$	−1.63248	+	2.82754i	−0.0833071	+	0.144292i
$385$		0			0
$386$	10.1224	−	17.5325i	0.515218	−	0.892383i
$387$	−4.44508			−0.225956
$388$	−16.1899			−0.821917
$389$	13.3424	−	23.1098i	0.676488	−	1.17171i	−0.299544	−	0.954082i	$-0.596835\pi$
$389$	13.3424	−	23.1098i	0.676488	−	1.17171i	0.976032	−	0.217629i	$-0.0698321\pi$
$390$		0			0
$391$	17.1457			0.867093
$392$	0.134919			0.00681442
$393$	3.92541	−	6.79901i	0.198011	−	0.342965i
$394$	1.46002	+	2.52883i	0.0735548	+	0.127401i
$395$		0			0
$396$	−19.3024	−	33.4328i	−0.969984	−	1.68006i
$397$	7.37459	+	12.7732i	0.370120	+	0.641067i	0.989584	−	0.143958i	$-0.0459832\pi$
$397$	7.37459	+	12.7732i	0.370120	+	0.641067i	−0.619464	+	0.785025i	$0.712650\pi$
$398$	15.6049			0.782202
$399$	−34.8603	+	13.2367i	−1.74520	+	0.662662i
$400$		0			0
$401$	−5.82720	−	10.0930i	−0.290996	−	0.504021i	0.683049	−	0.730372i	$-0.260653\pi$
$401$	−5.82720	−	10.0930i	−0.290996	−	0.504021i	−0.974046	+	0.226352i	$0.927320\pi$
$402$	−0.620130	−	1.07410i	−0.0309293	−	0.0535711i
$403$	7.61773	−	13.1943i	0.379466	−	0.657254i
$404$	−4.23270	−	7.33124i	−0.210584	−	0.364743i
$405$		0			0
$406$	−21.0654			−1.04546
$407$	−29.0045			−1.43770
$408$	5.97481	−	10.3487i	0.295797	−	0.512336i
$409$	−19.7824	+	34.2641i	−0.978176	+	1.69425i	−0.309145	+	0.951015i	$0.600043\pi$
$409$	−19.7824	+	34.2641i	−0.978176	+	1.69425i	−0.669030	+	0.743235i	$0.733290\pi$
$410$		0			0
$411$	56.9246			2.80788
$412$	−5.92492	+	10.2623i	−0.291900	+	0.505585i
$413$	−4.94532	−	8.56555i	−0.243344	−	0.421483i
$414$	−17.9421	+	31.0767i	−0.881808	+	1.52734i
$415$		0			0
$416$	2.32241	+	4.02254i	0.113866	+	0.197221i
$417$	−31.2448			−1.53007
$418$	20.5374	−	7.79819i	1.00452	−	0.381422i
$419$	17.3292			0.846586			0.423293	−	0.905993i	$-0.360874\pi$
$419$	17.3292			0.846586			0.423293	+	0.905993i	$0.360874\pi$
$420$		0			0
$421$	−12.1652	−	21.0707i	−0.592895	−	1.02692i	−0.993840	−	0.110822i	$-0.964652\pi$
$421$	−12.1652	−	21.0707i	−0.592895	−	1.02692i	0.400946	−	0.916102i	$-0.368682\pi$
$422$	0.572585	−	0.991747i	0.0278730	−	0.0482775i
$423$	−17.6950	−	30.6486i	−0.860361	−	1.49019i
$424$	−2.31007	+	4.00115i	−0.112187	+	0.194313i
$425$		0			0
$426$	−29.8251			−1.44503
$427$	0.170362	−	0.295075i	0.00824438	−	0.0142797i
$428$	−8.40500	+	14.5579i	−0.406271	+	0.703682i
$429$	−76.4299			−3.69007
$430$		0			0
$431$	−14.1173	+	24.4519i	−0.680006	+	1.17781i	0.294972	+	0.955506i	$0.404690\pi$
$431$	−14.1173	+	24.4519i	−0.680006	+	1.17781i	−0.974978	+	0.222299i	$0.928644\pi$
$432$	7.60729	+	13.1762i	0.366006	+	0.633941i
$433$	−11.6899	+	20.2475i	−0.561780	+	0.973031i	0.435562	+	0.900159i	$0.356550\pi$
$433$	−11.6899	+	20.2475i	−0.561780	+	0.973031i	−0.997341	+	0.0728720i	$0.976784\pi$
$434$	4.29713	+	7.44285i	0.206269	+	0.357268i
$435$		0			0
$436$	20.0046			0.958045
$437$	−15.8225	−	12.9082i	−0.756895	−	0.617483i
$438$	−27.7692			−1.32686
$439$	−13.3775	−	23.1705i	−0.638472	−	1.10587i	−0.985768	−	0.168110i	$-0.946234\pi$
$439$	−13.3775	−	23.1705i	−0.638472	−	1.10587i	0.347297	−	0.937755i	$-0.387100\pi$
$440$		0			0
$441$	0.516736	−	0.895013i	0.0246065	−	0.0426197i
$442$	−8.49994	−	14.7223i	−0.404301	−	0.700270i
$443$	−8.84989	+	15.3285i	−0.420471	+	0.728277i	−0.995986	−	0.0895142i	$-0.971469\pi$
$443$	−8.84989	+	15.3285i	−0.420471	+	0.728277i	0.575514	+	0.817792i	$0.304802\pi$
$444$	18.7900			0.891734
$445$		0			0
$446$	7.66474	−	13.2757i	0.362936	−	0.628624i
$447$	−27.9552	+	48.4198i	−1.32223	+	2.29018i
$448$	−2.62013			−0.123790
$449$	28.3541			1.33811			0.669056	−	0.743212i	$-0.266699\pi$
$449$	28.3541			1.33811			0.669056	+	0.743212i	$0.266699\pi$
$450$		0			0
$451$	14.6525	+	25.3790i	0.689961	+	1.19505i
$452$	7.17524	−	12.4279i	0.337495	−	0.584558i
$453$	−8.88787	−	15.3942i	−0.417589	−	0.723285i
$454$	−9.64248	−	16.7013i	−0.452544	−	0.783830i
$455$		0			0
$456$	−13.3048	+	5.05191i	−0.623054	+	0.236578i
$457$	−11.5898			−0.542146			−0.271073	−	0.962559i	$-0.587378\pi$
$457$	−11.5898			−0.542146			−0.271073	+	0.962559i	$0.587378\pi$
$458$	7.18759	+	12.4493i	0.335854	+	0.581716i
$459$	−27.8424	−	48.2244i	−1.29957	−	2.25092i
$460$		0			0
$461$	−17.8899	−	30.9862i	−0.833214	−	1.44317i	−0.895476	−	0.445110i	$-0.853165\pi$
$461$	−17.8899	−	30.9862i	−0.833214	−	1.44317i	0.0622614	−	0.998060i	$-0.480169\pi$
$462$	21.5569	−	37.3377i	1.00292	−	1.73711i
$463$	−23.5039			−1.09232			−0.546160	−	0.837681i	$-0.683911\pi$
$463$	−23.5039			−1.09232			−0.546160	+	0.837681i	$0.683911\pi$
$464$	−8.03983			−0.373240
$465$		0			0
$466$	6.91272	−	11.9732i	0.320226	−	0.554647i
$467$	1.12047			0.0518492			0.0259246	−	0.999664i	$-0.491747\pi$
$467$	1.12047			0.0518492			0.0259246	+	0.999664i	$0.491747\pi$
$468$	35.5792			1.64465
$469$	0.497654	−	0.861963i	0.0229795	−	0.0398017i
$470$		0			0
$471$	0.0403210	−	0.0698381i	0.00185790	−	0.00321797i
$472$	−1.88743	−	3.26913i	−0.0868762	−	0.150474i
$473$	1.46231	+	2.53279i	0.0672370	+	0.116458i
$474$	−26.0046			−1.19443
$475$		0			0
$476$	9.58957			0.439537
$477$	17.6950	+	30.6486i	0.810199	+	1.40331i
$478$	−7.48481	−	12.9641i	−0.342347	−	0.592963i
$479$	−13.6547	+	23.6506i	−0.623898	+	1.08062i	0.364854	+	0.931065i	$0.381119\pi$
$479$	−13.6547	+	23.6506i	−0.623898	+	1.08062i	−0.988753	+	0.149559i	$0.952215\pi$
$480$		0			0
$481$	13.3656	−	23.1499i	0.609419	−	1.05555i
$482$	19.3294			0.880429
$483$	−40.0755			−1.82350
$484$	−7.19994	+	12.4707i	−0.327270	+	0.566848i
$485$		0			0
$486$	41.5147			1.88314
$487$	−6.32003			−0.286388			−0.143194	−	0.989695i	$-0.545737\pi$
$487$	−6.32003			−0.286388			−0.143194	+	0.989695i	$0.545737\pi$
$488$	0.0650203	−	0.112618i	0.00294333	−	0.00509800i
$489$	17.6874	+	30.6355i	0.799854	+	1.38539i
$490$		0			0
$491$	12.9025	+	22.3478i	0.582282	+	1.00854i	0.995208	+	0.0977776i	$0.0311734\pi$
$491$	12.9025	+	22.3478i	0.582282	+	1.00854i	−0.412926	+	0.910764i	$0.635493\pi$
$492$	−9.49238	−	16.4413i	−0.427949	−	0.741230i
$493$	29.4254			1.32526
$494$	−3.23977	+	19.9855i	−0.145764	+	0.899188i
$495$		0			0
$496$	1.64004	+	2.84064i	0.0736402	+	0.127549i
$497$	−11.9673	−	20.7280i	−0.536808	−	0.929779i
$498$	−12.8475	+	22.2526i	−0.575712	+	0.997163i
$499$	14.4572	+	25.0406i	0.647192	+	1.12097i	0.983790	+	0.179322i	$0.0573903\pi$
$499$	14.4572	+	25.0406i	0.647192	+	1.12097i	−0.336598	+	0.941648i	$0.609276\pi$
$500$		0			0
$501$	−20.5196			−0.916746
$502$	−10.3249			−0.460823
$503$	−0.575024	+	0.995971i	−0.0256391	+	0.0444082i	−0.878560	−	0.477632i	$-0.841495\pi$
$503$	−0.575024	+	0.995971i	−0.0256391	+	0.0444082i	0.852921	+	0.522040i	$0.174829\pi$
$504$	−10.0350	+	17.3812i	−0.446996	+	0.774220i
$505$		0			0
$506$	23.6099			1.04959
$507$	13.9976	−	24.2445i	0.621655	−	1.07674i
$508$	−3.94254	−	6.82869i	−0.174922	−	0.302974i
$509$	−20.3673	+	35.2772i	−0.902765	+	1.56364i	−0.0788760	+	0.996884i	$0.525133\pi$
$509$	−20.3673	+	35.2772i	−0.902765	+	1.56364i	−0.823889	+	0.566751i	$0.808200\pi$
$510$		0			0
$511$	−11.1424	−	19.2992i	−0.492910	−	0.853746i
$512$	−1.00000			−0.0441942
$513$	−10.6122	+	65.4642i	−0.468539	+	2.89032i
$514$	28.7692			1.26895
$515$		0			0
$516$	−0.947329	−	1.64082i	−0.0417038	−	0.0722332i
$517$	−11.6423	+	20.1651i	−0.512029	+	0.886861i
$518$	7.53949	+	13.0588i	0.331266	+	0.573770i
$519$	0.612472	−	1.06083i	0.0268845	−	0.0465654i
$520$		0			0
$521$	−11.4246			−0.500520			−0.250260	−	0.968179i	$-0.580516\pi$
$521$	−11.4246			−0.500520			−0.250260	+	0.968179i	$0.580516\pi$
$522$	−30.7924	+	53.3340i	−1.34775	+	2.33436i
$523$	−6.55696	+	11.3570i	−0.286716	+	0.496607i	−0.973024	−	0.230704i	$-0.925897\pi$
$523$	−6.55696	+	11.3570i	−0.286716	+	0.496607i	0.686308	+	0.727311i	$0.259230\pi$
$524$	2.40457			0.105044
$525$		0			0
$526$	4.56746	−	7.91107i	0.199151	−	0.344939i
$527$	−6.00250	−	10.3966i	−0.261473	−	0.452884i
$528$	8.22742	−	14.2503i	0.358052	−	0.620165i
$529$	0.526988	+	0.912769i	0.0229125	+	0.0396856i
$530$		0			0
$531$	−28.9153			−1.25482
$532$	−8.84955	−	7.21955i	−0.383677	−	0.313007i
$533$	−27.0083			−1.16986
$534$	13.5327	+	23.4393i	0.585617	+	1.01432i
$535$		0			0
$536$	0.189935	−	0.328977i	0.00820394	−	0.0142096i
$537$	−13.1405	−	22.7600i	−0.567054	−	0.982166i
$538$	8.45474	−	14.6440i	0.364510	−	0.631350i
$539$	−0.679967			−0.0292883
$540$		0			0
$541$	14.4949	−	25.1059i	0.623183	−	1.07939i	−0.365706	−	0.930730i	$-0.619172\pi$
$541$	14.4949	−	25.1059i	0.623183	−	1.07939i	0.988889	−	0.148655i	$-0.0474943\pi$
$542$	−7.94483	+	13.7609i	−0.341260	+	0.591079i
$543$	68.7283			2.94941
$544$	3.65996			0.156919
$545$		0			0
$546$	19.8674	+	34.4113i	0.850245	+	1.47267i
$547$	17.8242	−	30.8724i	0.762108	−	1.32001i	−0.179654	−	0.983730i	$-0.557498\pi$
$547$	17.8242	−	30.8724i	0.762108	−	1.32001i	0.941762	−	0.336280i	$-0.109169\pi$
$548$	8.71751	+	15.0992i	0.372393	+	0.645004i
$549$	−0.498053	−	0.862653i	−0.0212564	−	0.0368171i
$550$		0			0
$551$	−27.1547	−	22.1531i	−1.15683	−	0.943753i
$552$	−15.2952			−0.651008
$553$	−10.4343	−	18.0728i	−0.443713	−	0.768534i
$554$	−5.74261	−	9.94648i	−0.243980	−	0.422586i
$555$		0			0
$556$	−4.78487	−	8.28764i	−0.202924	−	0.351474i
$557$	−6.27731	+	10.8726i	−0.265978	+	0.460688i	−0.967819	−	0.251646i	$-0.919028\pi$
$557$	−6.27731	+	10.8726i	−0.265978	+	0.460688i	0.701841	+	0.712333i	$0.252362\pi$
$558$	25.1253			1.06364
$559$	−2.69540			−0.114003
$560$		0			0
$561$	−30.1120	+	52.1555i	−1.27133	+	2.20201i
$562$	14.2897			0.602773
$563$	−2.88509			−0.121592			−0.0607960	−	0.998150i	$-0.519364\pi$
$563$	−2.88509			−0.121592			−0.0607960	+	0.998150i	$0.519364\pi$
$564$	7.54227	−	13.0636i	0.317587	−	0.550076i
$565$		0			0
$566$	−1.58215	+	2.74037i	−0.0665029	+	0.115186i
$567$	34.9723	+	60.5738i	1.46870	+	2.54386i
$568$	−4.56746	−	7.91107i	−0.191646	−	0.331941i
$569$	−10.9249			−0.457996			−0.228998	−	0.973427i	$-0.573545\pi$
$569$	−10.9249			−0.457996			−0.228998	+	0.973427i	$0.573545\pi$
$570$		0			0
$571$	6.27911			0.262772			0.131386	−	0.991331i	$-0.458057\pi$
$571$	6.27911			0.262772			0.131386	+	0.991331i	$0.458057\pi$
$572$	−11.7046	−	20.2729i	−0.489393	−	0.847653i
$573$	13.1249	+	22.7329i	0.548299	+	0.949681i
$574$	7.61763	−	13.1941i	0.317954	−	0.550712i
$575$		0			0
$576$	−3.82998	+	6.63372i	−0.159582	+	0.276405i
$577$	−25.9848			−1.08176			−0.540880	−	0.841100i	$-0.681909\pi$
$577$	−25.9848			−1.08176			−0.540880	+	0.841100i	$0.681909\pi$
$578$	3.60470			0.149936
$579$	33.0493	−	57.2430i	1.37348	−	2.37894i
$580$		0			0
$581$	−20.6203			−0.855475
$582$	−52.8593			−2.19109
$583$	11.6423	−	20.1651i	0.482176	−	0.835154i
$584$	−4.25261	−	7.36574i	−0.175974	−	0.304796i
$585$		0			0
$586$	−7.35468	−	12.7387i	−0.303819	−	0.526230i
$587$	−18.1547	−	31.4448i	−0.749324	−	1.29787i	−0.948147	−	0.317832i	$-0.897045\pi$
$587$	−18.1547	−	31.4448i	−0.749324	−	1.29787i	0.198823	−	0.980035i	$-0.436288\pi$
$588$	0.440504			0.0181661
$589$	−2.28786	+	14.1133i	−0.0942697	+	0.581530i
$590$		0			0
$591$	4.76691	+	8.25652i	0.196084	+	0.339628i
$592$	2.87752	+	4.98402i	0.118266	+	0.204842i
$593$	15.8646	−	27.4783i	0.651482	−	1.12840i	−0.331281	−	0.943532i	$-0.607481\pi$
$593$	15.8646	−	27.4783i	0.651482	−	1.12840i	0.982763	−	0.184868i	$-0.0591858\pi$
$594$	−38.3394	−	66.4058i	−1.57309	−	2.72466i
$595$		0			0
$596$	−17.1244			−0.701441
$597$	50.9493			2.08522
$598$	−10.8797	+	18.8442i	−0.444905	+	0.770598i
$599$	0.174654	−	0.302510i	0.00713619	−	0.0123602i	−0.862435	−	0.506167i	$-0.831062\pi$
$599$	0.174654	−	0.302510i	0.00713619	−	0.0123602i	0.869571	+	0.493807i	$0.164395\pi$
$600$		0			0
$601$	33.7305			1.37590			0.687949	−	0.725759i	$-0.258511\pi$
$601$	33.7305			1.37590			0.687949	+	0.725759i	$0.258511\pi$
$602$	0.760232	−	1.31676i	0.0309847	−	0.0536671i
$603$	−1.45489	−	2.51995i	−0.0592479	−	0.102620i
$604$	2.72220	−	4.71499i	0.110765	−	0.191850i
$605$		0			0
$606$	−13.8196	−	23.9362i	−0.561382	−	0.972342i
$607$	28.0561			1.13876			0.569382	−	0.822073i	$-0.307183\pi$
$607$	28.0561			1.13876			0.569382	+	0.822073i	$0.307183\pi$
$608$	−3.37752	−	2.75542i	−0.136977	−	0.111747i
$609$	−68.7777			−2.78701
$610$		0			0
$611$	−10.7299	−	18.5847i	−0.434084	−	0.751855i
$612$	14.0176	−	24.2791i	0.566627	−	0.981426i
$613$	−20.7251	−	35.8969i	−0.837078	−	1.44986i	−0.892327	−	0.451389i	$-0.850929\pi$
$613$	−20.7251	−	35.8969i	−0.837078	−	1.44986i	0.0552496	−	0.998473i	$-0.482405\pi$
$614$	13.0727	−	22.6425i	0.527570	−	0.913779i
$615$		0			0
$616$	13.2050			0.532045
$617$	2.94440	−	5.09985i	0.118537	−	0.205312i	−0.800651	−	0.599131i	$-0.795513\pi$
$617$	2.94440	−	5.09985i	0.118537	−	0.205312i	0.919188	+	0.393819i	$0.128846\pi$
$618$	−19.3446	+	33.5059i	−0.778155	+	1.34780i
$619$	13.7152			0.551261			0.275631	−	0.961264i	$-0.411113\pi$
$619$	13.7152			0.551261			0.275631	+	0.961264i	$0.411113\pi$
$620$		0			0
$621$	−35.6375	+	61.7260i	−1.43009	+	2.47698i
$622$	3.32519	+	5.75941i	0.133328	+	0.230931i
$623$	−10.8600	+	18.8101i	−0.435096	+	0.753609i
$624$	7.58259	+	13.1334i	0.303547	+	0.525758i
$625$		0			0
$626$	−17.3798			−0.694635
$627$	67.0539	−	25.4608i	2.67787	−	1.01681i
$628$	0.0246993			0.000985608
$629$	−10.5316	−	18.2413i	−0.419923	−	0.727328i
$630$		0			0
$631$	8.14468	−	14.1070i	0.324235	−	0.561591i	−0.657123	−	0.753784i	$-0.728227\pi$
$631$	8.14468	−	14.1070i	0.324235	−	0.561591i	0.981357	+	0.192193i	$0.0615600\pi$
$632$	−3.98237	−	6.89767i	−0.158410	−	0.274375i
$633$	1.86947	−	3.23801i	0.0743047	−	0.128699i
$634$	1.37529			0.0546199
$635$		0			0
$636$	−7.54227	+	13.0636i	−0.299070	+	0.518005i
$637$	0.313337	−	0.542716i	0.0124149	−	0.0215032i
$638$	40.5194			1.60418
$639$	−69.9731			−2.76809
$640$		0			0
$641$	−14.8124	−	25.6559i	−0.585056	−	1.01335i	−0.994868	−	0.101177i	$-0.967739\pi$
$641$	−14.8124	−	25.6559i	−0.585056	−	1.01335i	0.409812	−	0.912170i	$-0.365594\pi$
$642$	−27.4420	+	47.5309i	−1.08305	+	1.87590i
$643$	−6.01050	−	10.4105i	−0.237031	−	0.410549i	0.722830	−	0.691026i	$-0.242841\pi$
$643$	−6.01050	−	10.4105i	−0.237031	−	0.410549i	−0.959861	+	0.280476i	$0.909508\pi$
$644$	−6.13721	−	10.6300i	−0.241840	−	0.418879i
$645$		0			0
$646$	12.3616	+	10.0847i	0.486361	+	0.396778i
$647$	−3.16079			−0.124263			−0.0621317	−	0.998068i	$-0.519790\pi$
$647$	−3.16079			−0.124263			−0.0621317	+	0.998068i	$0.519790\pi$
$648$	13.3475	+	23.1186i	0.524341	+	0.908186i
$649$	9.51235	+	16.4759i	0.373392	+	0.646735i
$650$		0			0
$651$	14.0300	+	24.3006i	0.549877	+	0.952415i
$652$	−5.41735	+	9.38313i	−0.212160	+	0.367472i
$653$	19.6097			0.767387			0.383693	−	0.923461i	$-0.374652\pi$
$653$	19.6097			0.767387			0.383693	+	0.923461i	$0.374652\pi$
$654$	65.3141			2.55398
$655$		0			0
$656$	2.90735	−	5.03568i	0.113513	−	0.196610i
$657$	−65.1496			−2.54173
$658$	12.1053			0.471915
$659$	9.03748	−	15.6534i	0.352050	−	0.609769i	−0.634558	−	0.772875i	$-0.718818\pi$
$659$	9.03748	−	15.6534i	0.352050	−	0.609769i	0.986609	+	0.163106i	$0.0521512\pi$
$660$		0			0
$661$	7.26715	−	12.5871i	0.282660	−	0.489581i	−0.689379	−	0.724400i	$-0.742117\pi$
$661$	7.26715	−	12.5871i	0.282660	−	0.489581i	0.972039	+	0.234820i	$0.0754500\pi$
$662$	5.86996	+	10.1671i	0.228142	+	0.395154i
$663$	−27.7520	−	48.0678i	−1.07780	−	1.86680i
$664$	−7.86996			−0.305414
$665$		0			0
$666$	44.0834			1.70820
$667$	−18.8319	−	32.6179i	−0.729175	−	1.26297i
$668$	−3.14239	−	5.44278i	−0.121583	−	0.210587i
$669$	25.0251	−	43.3447i	0.967525	−	1.67580i
$670$		0			0
$671$	−0.327691	+	0.567578i	−0.0126504	+	0.0219111i
$672$	−8.55462			−0.330002
$673$	−6.13522			−0.236495			−0.118248	−	0.992984i	$-0.537728\pi$
$673$	−6.13522			−0.236495			−0.118248	+	0.992984i	$0.537728\pi$
$674$	−6.44005	+	11.1545i	−0.248061	+	0.429655i
$675$		0			0
$676$	8.57444			0.329786
$677$	13.6380			0.524150			0.262075	−	0.965047i	$-0.415593\pi$
$677$	13.6380			0.524150			0.262075	+	0.965047i	$0.415593\pi$
$678$	23.4269	−	40.5765i	0.899703	−	1.55833i
$679$	−21.2098	−	36.7364i	−0.813957	−	1.40982i
$680$		0			0
$681$	−31.4823	−	54.5290i	−1.20640	−	2.08955i
$682$	−8.26554	−	14.3163i	−0.316504	−	0.548201i
$683$	−16.7550			−0.641114			−0.320557	−	0.947229i	$-0.603870\pi$
$683$	−16.7550			−0.641114			−0.320557	+	0.947229i	$0.603870\pi$
$684$	−31.2145	+	11.8524i	−1.19352	+	0.453186i
$685$		0			0
$686$	9.34721	+	16.1898i	0.356878	+	0.618131i
$687$	23.4672	+	40.6464i	0.895329	+	1.55076i
$688$	0.290150	−	0.502555i	0.0110619	−	0.0191597i
$689$	10.7299	+	18.5847i	0.408775	+	0.708019i
$690$		0			0
$691$	21.5889			0.821280			0.410640	−	0.911798i	$-0.365305\pi$
$691$	21.5889			0.821280			0.410640	+	0.911798i	$0.365305\pi$
$692$	0.375179			0.0142622
$693$	50.5749	−	87.5983i	1.92118	−	3.32758i
$694$	2.46724	−	4.27339i	0.0936553	−	0.162216i
$695$		0			0
$696$	−26.2497			−0.994993
$697$	−10.6408	+	18.4304i	−0.403048	+	0.698100i
$698$	0.632972	+	1.09634i	0.0239583	+	0.0414970i
$699$	22.5697	−	39.0919i	0.853666	−	1.47859i
$700$		0			0
$701$	18.8628	+	32.6713i	0.712437	+	1.23398i	0.963940	+	0.266121i	$0.0857419\pi$
$701$	18.8628	+	32.6713i	0.712437	+	1.23398i	−0.251503	+	0.967857i	$0.580925\pi$
$702$	70.6691			2.66723
$703$	−4.01415	+	24.7624i	−0.151396	+	0.933933i
$704$	5.03983			0.189946
$705$		0			0
$706$	1.08030	+	1.87114i	0.0406577	+	0.0704211i
$707$	11.0902	−	19.2088i	0.417090	−	0.722422i
$708$	−6.16240	−	10.6736i	−0.231597	−	0.401138i
$709$	10.4795	−	18.1511i	0.393567	−	0.681678i	−0.599350	−	0.800487i	$-0.704574\pi$
$709$	10.4795	−	18.1511i	0.393567	−	0.681678i	0.992917	+	0.118809i	$0.0379075\pi$
$710$		0			0
$711$	−61.0096			−2.28804
$712$	−4.14483	+	7.17905i	−0.155334	+	0.269046i
$713$	−7.68305	+	13.3074i	−0.287732	+	0.498367i
$714$	31.3096			1.17173
$715$		0			0
$716$	4.02470	−	6.97098i	0.150410	−	0.260518i
$717$	−24.4376	−	42.3272i	−0.912639	−	1.58074i
$718$	−2.36981	+	4.10463i	−0.0884405	+	0.153183i
$719$	22.1401	+	38.3477i	0.825686	+	1.43013i	0.901394	+	0.433000i	$0.142545\pi$
$719$	22.1401	+	38.3477i	0.825686	+	1.43013i	−0.0757084	+	0.997130i	$0.524122\pi$
$720$		0			0
$721$	−31.0481			−1.15629
$722$	−3.81534	−	18.6130i	−0.141992	−	0.692704i
$723$	63.1096			2.34707
$724$	10.5251	+	18.2301i	0.391164	+	0.677515i
$725$		0			0
$726$	−23.5075	+	40.7162i	−0.872445	+	1.51112i
$727$	24.2169	+	41.9448i	0.898154	+	1.55565i	0.829852	+	0.557983i	$0.188425\pi$
$727$	24.2169	+	41.9448i	0.898154	+	1.55565i	0.0683017	+	0.997665i	$0.478242\pi$
$728$	−6.08503	+	10.5396i	−0.225526	+	0.390623i
$729$	55.4584			2.05402
$730$		0			0
$731$	−1.06194	+	1.83933i	−0.0392772	+	0.0680301i
$732$	0.212289	−	0.367695i	0.00784641	−	0.0135904i
$733$	−9.62940			−0.355670			−0.177835	−	0.984060i	$-0.556909\pi$
$733$	−9.62940			−0.355670			−0.177835	+	0.984060i	$0.556909\pi$
$734$	22.8944			0.845046
$735$		0			0
$736$	−2.34233	−	4.05703i	−0.0863394	−	0.149544i
$737$	−0.957240	+	1.65799i	−0.0352604	+	0.0610728i
$738$	−22.2702	−	38.5731i	−0.819777	−	1.41989i
$739$	20.3423	+	35.2338i	0.748303	+	1.29610i	0.948636	+	0.316370i	$0.102464\pi$
$739$	20.3423	+	35.2338i	0.748303	+	1.29610i	−0.200333	+	0.979728i	$0.564202\pi$
$740$		0			0
$741$	−10.5777	+	65.2517i	−0.388582	+	2.39708i
$742$	−12.1053			−0.444401
$743$	−1.43254	−	2.48123i	−0.0525548	−	0.0910276i	0.838551	−	0.544823i	$-0.183403\pi$
$743$	−1.43254	−	2.48123i	−0.0525548	−	0.0910276i	−0.891106	+	0.453795i	$0.850070\pi$
$744$	5.35468	+	9.27458i	0.196312	+	0.340022i
$745$		0			0
$746$	9.61964	+	16.6617i	0.352200	+	0.610028i
$747$	−30.1418	+	52.2071i	−1.10283	+	1.91016i
$748$	−18.4456			−0.674437
$749$	−44.0444			−1.60935
$750$		0			0
$751$	13.1148	−	22.7155i	0.478566	−	0.828900i	−0.521132	−	0.853476i	$-0.674490\pi$
$751$	13.1148	−	22.7155i	0.478566	−	0.828900i	0.999698	+	0.0245758i	$0.00782351\pi$
$752$	4.62013			0.168479
$753$	−33.7104			−1.22848
$754$	−18.6718	+	32.3405i	−0.679987	+	1.17777i
$755$		0			0
$756$	−19.9321	+	34.5234i	−0.724923	+	1.25560i
$757$	−3.29195	−	5.70182i	−0.119648	−	0.207236i	0.799980	−	0.600026i	$-0.204843\pi$
$757$	−3.29195	−	5.70182i	−0.119648	−	0.207236i	−0.919628	+	0.392790i	$0.871510\pi$
$758$	−3.22976	−	5.59412i	−0.117310	−	0.203187i
$759$	77.0853			2.79802
$760$		0			0
$761$	−27.7549			−1.00612			−0.503058	−	0.864253i	$-0.667792\pi$
$761$	−27.7549			−1.00612			−0.503058	+	0.864253i	$0.667792\pi$
$762$	−12.8722	−	22.2954i	−0.466312	−	0.807677i
$763$	26.2073	+	45.3924i	0.948768	+	1.64331i
$764$	−4.01991	+	6.96270i	−0.145435	+	0.251902i
$765$		0			0
$766$	4.56746	−	7.91107i	0.165029	−	0.285839i
$767$	−17.5336			−0.633103
$768$	−3.26496			−0.117814
$769$	−8.32285	+	14.4156i	−0.300130	+	0.519840i	−0.976165	−	0.217029i	$-0.930363\pi$
$769$	−8.32285	+	14.4156i	−0.300130	+	0.519840i	0.676035	+	0.736869i	$0.263697\pi$
$770$		0			0
$771$	93.9303			3.38282
$772$	20.2448			0.728628
$773$	12.1049	−	20.9664i	0.435385	−	0.754108i	−0.561942	−	0.827176i	$-0.689946\pi$
$773$	12.1049	−	20.9664i	0.435385	−	0.754108i	0.997327	+	0.0730682i	$0.0232791\pi$
$774$	−2.22254	−	3.84955i	−0.0798876	−	0.138369i
$775$		0			0
$776$	−8.09494	−	14.0208i	−0.290591	−	0.503319i
$777$	24.6161	+	42.6364i	0.883098	+	1.52957i
$778$	26.6848			0.956698
$779$	23.6950	−	8.99716i	0.848963	−	0.322357i
$780$		0			0
$781$	23.0192	+	39.8704i	0.823692	+	1.42668i
$782$	8.57283	+	14.8486i	0.306564	+	0.530984i
$783$	−61.1613	+	105.934i	−2.18573	+	3.78579i
$784$	0.0674593	+	0.116843i	0.00240926	+	0.00417296i
$785$		0			0
$786$	7.85082			0.280030
$787$	−1.63409			−0.0582490			−0.0291245	−	0.999576i	$-0.509272\pi$
$787$	−1.63409			−0.0582490			−0.0291245	+	0.999576i	$0.509272\pi$
$788$	−1.46002	+	2.52883i	−0.0520111	+	0.0900858i
$789$	14.9126	−	25.8293i	0.530902	−	0.919548i
$790$		0			0
$791$	37.6001			1.33691
$792$	19.3024	−	33.4328i	0.685882	−	1.18798i
$793$	−0.302008	−	0.523094i	−0.0107246	−	0.0185756i
$794$	−7.37459	+	12.7732i	−0.261715	+	0.453303i
$795$		0			0
$796$	7.80244	+	13.5142i	0.276550	+	0.478999i
$797$	−12.2802			−0.434987			−0.217494	−	0.976062i	$-0.569788\pi$
$797$	−12.2802			−0.434987			−0.217494	+	0.976062i	$0.569788\pi$
$798$	−28.8934	−	23.5715i	−1.02282	−	0.834424i
$799$	−16.9095			−0.598215
$800$		0			0
$801$	31.7492	+	54.9913i	1.12180	+	1.94302i
$802$	5.82720	−	10.0930i	0.205766	−	0.356396i
$803$	21.4324	+	37.1221i	0.756334	+	1.31001i
$804$	0.620130	−	1.07410i	0.0218703	−	0.0378805i
$805$		0			0
$806$	15.2355			0.536646
$807$	27.6044	−	47.8122i	0.971721	−	1.68307i
$808$	4.23270	−	7.33124i	0.148906	−	0.257912i
$809$	49.2846			1.73275			0.866376	−	0.499392i	$-0.166443\pi$
$809$	49.2846			1.73275			0.866376	+	0.499392i	$0.166443\pi$
$810$		0			0
$811$	−11.5927	+	20.0791i	−0.407073	+	0.705071i	−0.994560	−	0.104162i	$-0.966784\pi$
$811$	−11.5927	+	20.0791i	−0.407073	+	0.705071i	0.587487	+	0.809233i	$0.300117\pi$
$812$	−10.5327	−	18.2432i	−0.369625	−	0.640210i
$813$	−25.9396	+	44.9286i	−0.909740	+	1.57572i
$814$	−14.5022	−	25.1186i	−0.508303	−	0.880407i
$815$		0			0
$816$	11.9496			0.418320
$817$	2.36474	−	0.897907i	0.0827318	−	0.0314138i
$818$	−39.5648			−1.38335
$819$	46.6111	+	80.7327i	1.62872	+	2.82103i
$820$		0			0
$821$	−13.5793	+	23.5201i	−0.473921	+	0.820856i	−0.999554	−	0.0298556i	$-0.990495\pi$
$821$	−13.5793	+	23.5201i	−0.473921	+	0.820856i	0.525633	+	0.850712i	$0.323829\pi$
$822$	28.4623	+	49.2982i	0.992737	+	1.71947i
$823$	4.48722	−	7.77209i	0.156415	−	0.270918i	−0.777159	−	0.629305i	$-0.783340\pi$
$823$	4.48722	−	7.77209i	0.156415	−	0.270918i	0.933573	+	0.358387i	$0.116673\pi$
$824$	−11.8498			−0.412809
$825$		0			0
$826$	4.94532	−	8.56555i	0.172070	−	0.298034i
$827$	−12.0025	+	20.7890i	−0.417369	+	0.722904i	−0.995674	−	0.0929165i	$-0.970381\pi$
$827$	−12.0025	+	20.7890i	−0.417369	+	0.722904i	0.578305	+	0.815821i	$0.303714\pi$
$828$	−35.8843			−1.24707
$829$	25.7361			0.893852			0.446926	−	0.894571i	$-0.352519\pi$
$829$	25.7361			0.893852			0.446926	+	0.894571i	$0.352519\pi$
$830$		0			0
$831$	−18.7494	−	32.4749i	−0.650409	−	1.12654i
$832$	−2.32241	+	4.02254i	−0.0805152	+	0.139456i
$833$	−0.246898	−	0.427641i	−0.00855452	−	0.0148169i
$834$	−15.6224	−	27.0588i	−0.540960	−	0.936970i
$835$		0			0
$836$	17.0221	+	13.8868i	0.588723	+	0.480286i
$837$	49.9052			1.72498
$838$	8.66459	+	15.0075i	0.299313	+	0.518426i
$839$	16.3570	+	28.3311i	0.564705	+	0.978098i	0.997077	+	0.0764027i	$0.0243435\pi$
$839$	16.3570	+	28.3311i	0.564705	+	0.978098i	−0.432372	+	0.901695i	$0.642323\pi$
$840$		0			0
$841$	−17.8194	−	30.8642i	−0.614463	−	1.06428i
$842$	12.1652	−	21.0707i	0.419240	−	0.726145i
$843$	46.6552			1.60689
$844$	1.14517			0.0394184
$845$		0			0
$846$	17.6950	−	30.6486i	0.608367	−	1.05372i
$847$	−37.7296			−1.29640
$848$	−4.62013			−0.158656
$849$	−5.16567	+	8.94720i	−0.177285	+	0.307067i
$850$		0			0
$851$	−13.4802	+	23.3484i	−0.462096	+	0.800374i
$852$	−14.9126	−	25.8293i	−0.510896	−	0.884898i
$853$	−15.4952	−	26.8384i	−0.530544	−	0.918929i	−0.999365	−	0.0356360i	$-0.988654\pi$
$853$	−15.4952	−	26.8384i	−0.530544	−	0.918929i	0.468821	−	0.883293i	$-0.344679\pi$
$854$	0.340723			0.0116593
$855$		0			0
$856$	−16.8100			−0.574554
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$	−38.2150	−	66.1902i	−1.30464	−	2.25970i
$859$	−14.1575	+	24.5215i	−0.483048	+	0.836664i	−0.999811	−	0.0194647i	$-0.993804\pi$
$859$	−14.1575	+	24.5215i	−0.483048	+	0.836664i	0.516762	+	0.856129i	$0.327137\pi$
$860$		0			0
$861$	24.8713	−	43.0783i	0.847610	−	1.46810i
$862$	−28.2346			−0.961674
$863$	−10.9254			−0.371905			−0.185953	−	0.982559i	$-0.559537\pi$
$863$	−10.9254			−0.371905			−0.185953	+	0.982559i	$0.559537\pi$
$864$	−7.60729	+	13.1762i	−0.258805	+	0.448264i
$865$		0			0
$866$	−23.3798			−0.794476
$867$	11.7692			0.399703
$868$	−4.29713	+	7.44285i	−0.145854	+	0.252627i
$869$	20.0705	+	34.7631i	0.680845	+	1.17926i
$870$		0			0
$871$	−0.882216	−	1.52804i	−0.0298927	−	0.0517757i
$872$	10.0023	+	17.3245i	0.338720	+	0.586681i
$873$	−124.014			−4.19723
$874$	3.26755	−	20.1568i	0.110526	−	0.681815i
$875$		0			0
$876$	−13.8846	−	24.0488i	−0.469117	−	0.812535i
$877$	−16.9148	−	29.2972i	−0.571171	−	0.989297i	−0.996446	−	0.0842330i	$-0.973156\pi$
$877$	−16.9148	−	29.2972i	−0.571171	−	0.989297i	0.425275	−	0.905064i	$-0.360177\pi$
$878$	13.3775	−	23.1705i	0.451468	−	0.781965i
$879$	−24.0127	−	41.5913i	−0.809929	−	1.40284i
$880$		0			0
$881$	29.3696			0.989488			0.494744	−	0.869039i	$-0.335262\pi$
$881$	29.3696			0.989488			0.494744	+	0.869039i	$0.335262\pi$
$882$	1.03347			0.0347988
$883$	20.6000	−	35.6803i	0.693245	−	1.20074i	−0.277523	−	0.960719i	$-0.589514\pi$
$883$	20.6000	−	35.6803i	0.693245	−	1.20074i	0.970769	−	0.240017i	$-0.0771531\pi$
$884$	8.49994	−	14.7223i	0.285884	−	0.495166i
$885$		0			0
$886$	−17.6998			−0.594636
$887$	12.9454	−	22.4221i	0.434665	−	0.752861i	−0.562604	−	0.826727i	$-0.690200\pi$
$887$	12.9454	−	22.4221i	0.434665	−	0.752861i	0.997268	+	0.0738656i	$0.0235336\pi$
$888$	9.39500	+	16.2726i	0.315276	+	0.546073i
$889$	10.3300	−	17.8920i	0.346456	−	0.600080i
$890$		0			0
$891$	−67.2694	−	116.514i	−2.25361	−	3.90336i
$892$	15.3295			0.513269
$893$	15.6046	+	12.7304i	0.522188	+	0.426006i
$894$	−55.9104			−1.86992
$895$		0			0
$896$	−1.31007	−	2.26910i	−0.0437662	−	0.0758053i
$897$	−35.5218	+	61.5256i	−1.18604	+	2.05428i
$898$	14.1770	+	24.5553i	0.473094	+	0.819423i
$899$	−13.1857	+	22.8383i	−0.439767	+	0.761699i
$900$		0			0
$901$	16.9095			0.563337
$902$	−14.6525	+	25.3790i	−0.487876	+	0.845027i
$903$	2.48213	−	4.29917i	0.0826000	−	0.143067i
$904$	14.3505			0.477290
$905$		0			0
$906$	8.88787	−	15.3942i	0.295280	−	0.511439i
$907$	−12.7425	−	22.0706i	−0.423106	−	0.732842i	0.573135	−	0.819461i	$-0.305727\pi$
$907$	−12.7425	−	22.0706i	−0.423106	−	0.732842i	−0.996241	+	0.0866192i	$0.972394\pi$
$908$	9.64248	−	16.7013i	0.319997	−	0.554251i
$909$	−32.4223	−	56.1570i	−1.07538	−	1.86261i
$910$		0			0
$911$	10.1197			0.335280			0.167640	−	0.985848i	$-0.446385\pi$
$911$	10.1197			0.335280			0.167640	+	0.985848i	$0.446385\pi$
$912$	−11.0275	−	8.99633i	−0.365156	−	0.297898i
$913$	39.6633			1.31266
$914$	−5.79488	−	10.0370i	−0.191678	−	0.331995i
$915$		0			0
$916$	−7.18759	+	12.4493i	−0.237485	+	0.411335i
$917$	3.15014	+	5.45621i	0.104027	+	0.180180i
$918$	27.8424	−	48.2244i	0.918935	−	1.59164i
$919$	−15.0939			−0.497902			−0.248951	−	0.968516i	$-0.580086\pi$
$919$	−15.0939			−0.497902			−0.248951	+	0.968516i	$0.580086\pi$
$920$		0			0
$921$	42.6818	−	73.9270i	1.40641	−	2.43598i
$922$	17.8899	−	30.9862i	0.589172	−	1.02048i
$923$	−42.4301			−1.39660
$924$	43.1138			1.41834
$925$		0			0
$926$	−11.7520	−	20.3550i	−0.386194	−	0.668907i
$927$	−45.3846	+	78.6085i	−1.49063	+	2.58184i
$928$	−4.01991	−	6.96270i	−0.131960	−	0.228562i
$929$	5.40003	+	9.35312i	0.177169	+	0.306866i	0.940910	−	0.338657i	$-0.109973\pi$
$929$	5.40003	+	9.35312i	0.177169	+	0.306866i	−0.763741	+	0.645523i	$0.776639\pi$
$930$		0			0
$931$	−0.0941058	+	0.580519i	−0.00308419	+	0.0190257i
$932$	13.8254			0.452867
$933$	10.8566	+	18.8042i	0.355430	+	0.615623i
$934$	0.560236	+	0.970357i	0.0183315	+	0.0317510i
$935$		0			0
$936$	17.7896	+	30.8125i	0.581471	+	1.00714i
$937$	−22.6993	+	39.3163i	−0.741554	+	1.28441i	0.210234	+	0.977651i	$0.432577\pi$
$937$	−22.6993	+	39.3163i	−0.741554	+	1.28441i	−0.951788	+	0.306758i	$0.900756\pi$
$938$	0.995309			0.0324980
$939$	−56.7442			−1.85178
$940$		0			0
$941$	−0.155325	+	0.269031i	−0.00506346	+	0.00877016i	−0.868546	−	0.495609i	$-0.834945\pi$
$941$	−0.155325	+	0.269031i	−0.00506346	+	0.00877016i	0.863483	+	0.504379i	$0.168278\pi$
$942$	0.0806421			0.00262746
$943$	27.2399			0.887053
$944$	1.88743	−	3.26913i	0.0614308	−	0.106401i
$945$		0			0
$946$	−1.46231	+	2.53279i	−0.0475438	+	0.0823482i
$947$	−2.11251	−	3.65897i	−0.0686473	−	0.118901i	0.829659	−	0.558271i	$-0.188535\pi$
$947$	−2.11251	−	3.65897i	−0.0686473	−	0.118901i	−0.898306	+	0.439370i	$0.855202\pi$
$948$	−13.0023	−	22.5206i	−0.422295	−	0.731436i
$949$	−39.5053			−1.28240
$950$		0			0
$951$	4.49028			0.145607
$952$	4.79478	+	8.30481i	0.155400	+	0.269160i
$953$	16.9168	+	29.3008i	0.547989	+	0.949145i	0.998412	+	0.0563297i	$0.0179398\pi$
$953$	16.9168	+	29.3008i	0.547989	+	0.949145i	−0.450423	+	0.892815i	$0.648727\pi$
$954$	−17.6950	+	30.6486i	−0.572897	+	0.992287i
$955$		0			0
$956$	7.48481	−	12.9641i	0.242076	−	0.419288i
$957$	132.294			4.27646
$958$	−27.3094			−0.882326
$959$	−22.8410	+	39.5618i	−0.737574	+	1.27752i
$960$		0			0
$961$	−20.2410			−0.652936
$962$	26.7312			0.861849
$963$	−64.3820	+	111.513i	−2.07468	+	3.59345i
$964$	9.66469	+	16.7397i	0.311279	+	0.539150i
$965$		0			0
$966$	−20.0377	−	34.7064i	−0.644703	−	1.11666i
$967$	−19.6227	−	33.9875i	−0.631024	−	1.09296i	−0.987343	−	0.158601i	$-0.949302\pi$
$967$	−19.6227	−	33.9875i	−0.631024	−	1.09296i	0.356319	−	0.934364i	$-0.384032\pi$
$968$	−14.3999			−0.462830
$969$	40.3601	+	32.9262i	1.29655	+	1.05774i
$970$		0			0
$971$	−20.3469	−	35.2419i	−0.652963	−	1.13097i	−0.982400	−	0.186788i	$-0.940192\pi$
$971$	−20.3469	−	35.2419i	−0.652963	−	1.13097i	0.329437	−	0.944178i	$-0.393141\pi$
$972$	20.7573	+	35.9528i	0.665792	+	1.15319i
$973$	12.5370	−	21.7147i	0.401918	−	0.696142i
$974$	−3.16002	−	5.47331i	−0.101253	−	0.175376i
$975$		0			0
$976$	0.130041			0.00416250
$977$	−26.7081			−0.854467			−0.427233	−	0.904141i	$-0.640512\pi$
$977$	−26.7081			−0.854467			−0.427233	+	0.904141i	$0.640512\pi$
$978$	−17.6874	+	30.6355i	−0.565582	+	0.979617i
$979$	20.8892	−	36.1812i	0.667623	−	1.15636i
$980$		0			0
$981$	153.234			4.89239
$982$	−12.9025	+	22.3478i	−0.411736	+	0.713147i
$983$	12.4842	+	21.6233i	0.398185	+	0.689677i	0.993502	−	0.113814i	$-0.0363069\pi$
$983$	12.4842	+	21.6233i	0.398185	+	0.689677i	−0.595317	+	0.803491i	$0.702974\pi$
$984$	9.49238	−	16.4413i	0.302606	−	0.524129i
$985$		0			0
$986$	14.7127	+	25.4832i	0.468549	+	0.811550i
$987$	39.5234			1.25805
$988$	−18.9278	+	7.18700i	−0.602173	+	0.228649i
$989$	2.71851			0.0864436
$990$		0			0
$991$	7.53968	+	13.0591i	0.239506	+	0.414836i	0.960573	−	0.278029i	$-0.0896813\pi$
$991$	7.53968	+	13.0591i	0.239506	+	0.414836i	−0.721067	+	0.692866i	$0.756348\pi$
$992$	−1.64004	+	2.84064i	−0.0520715	+	0.0901904i
$993$	19.1652	+	33.1951i	0.608189	+	1.05341i
$994$	11.9673	−	20.7280i	0.379581	−	0.657453i
$995$		0			0
$996$	−25.6951			−0.814180
$997$	20.5628	−	35.6158i	0.651229	−	1.12796i	−0.331595	−	0.943422i	$-0.607587\pi$
$997$	20.5628	−	35.6158i	0.651229	−	1.12796i	0.982825	−	0.184541i	$-0.0590798\pi$
$998$	−14.4572	+	25.0406i	−0.457634	+	0.792646i
$999$	87.5606			2.77030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.m.501.4	yes	8
5.2	odd	4		950.2.j.i.349.4		16
5.3	odd	4		950.2.j.i.349.5		16
5.4	even	2		950.2.e.l.501.1	yes	8
19.11	even	3	inner	950.2.e.m.201.4	yes	8
95.49	even	6		950.2.e.l.201.1	✓	8
95.68	odd	12		950.2.j.i.49.4		16
95.87	odd	12		950.2.j.i.49.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.l.201.1	✓	8	95.49	even	6
950.2.e.l.501.1	yes	8	5.4	even	2
950.2.e.m.201.4	yes	8	19.11	even	3	inner
950.2.e.m.501.4	yes	8	1.1	even	1	trivial
950.2.j.i.49.4		16	95.68	odd	12
950.2.j.i.49.5		16	95.87	odd	12
950.2.j.i.349.4		16	5.2	odd	4
950.2.j.i.349.5		16	5.3	odd	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.63248 + 2.82754i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.63248 + 2.82754i) q^{6} -2.62013 q^{7} -1.00000 q^{8} +(-3.82998 + 6.63372i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.63248 + 2.82754i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.63248 + 2.82754i) q^{6} -2.62013 q^{7} -1.00000 q^{8} +(-3.82998 + 6.63372i) q^{9} +5.03983 q^{11} -3.26496 q^{12} +(-2.32241 + 4.02254i) q^{13} +(-1.31007 - 2.26910i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82998 + 3.16962i) q^{17} -7.65996 q^{18} +(0.697500 - 4.30273i) q^{19} +(-4.27731 - 7.40852i) q^{21} +(2.51991 + 4.36462i) q^{22} +(2.34233 - 4.05703i) q^{23} +(-1.63248 - 2.82754i) q^{24} -4.64483 q^{26} -15.2146 q^{27} +(1.31007 - 2.26910i) q^{28} +(4.01991 - 6.96270i) q^{29} -3.28009 q^{31} +(0.500000 - 0.866025i) q^{32} +(8.22742 + 14.2503i) q^{33} +(-1.82998 + 3.16962i) q^{34} +(-3.82998 - 6.63372i) q^{36} -5.75505 q^{37} +(4.07502 - 1.54731i) q^{38} -15.1652 q^{39} +(2.90735 + 5.03568i) q^{41} +(4.27731 - 7.40852i) q^{42} +(0.290150 + 0.502555i) q^{43} +(-2.51991 + 4.36462i) q^{44} +4.68466 q^{46} +(-2.31007 + 4.00115i) q^{47} +(1.63248 - 2.82754i) q^{48} -0.134919 q^{49} +(-5.97481 + 10.3487i) q^{51} +(-2.32241 - 4.02254i) q^{52} +(2.31007 - 4.00115i) q^{53} +(-7.60729 - 13.1762i) q^{54} +2.62013 q^{56} +(13.3048 - 5.05191i) q^{57} +8.03983 q^{58} +(1.88743 + 3.26913i) q^{59} +(-0.0650203 + 0.112618i) q^{61} +(-1.64004 - 2.84064i) q^{62} +(10.0350 - 17.3812i) q^{63} +1.00000 q^{64} +(-8.22742 + 14.2503i) q^{66} +(-0.189935 + 0.328977i) q^{67} -3.65996 q^{68} +15.2952 q^{69} +(4.56746 + 7.91107i) q^{71} +(3.82998 - 6.63372i) q^{72} +(4.25261 + 7.36574i) q^{73} +(-2.87752 - 4.98402i) q^{74} +(3.37752 + 2.75542i) q^{76} -13.2050 q^{77} +(-7.58259 - 13.1334i) q^{78} +(3.98237 + 6.89767i) q^{79} +(-13.3475 - 23.1186i) q^{81} +(-2.90735 + 5.03568i) q^{82} +7.86996 q^{83} +8.55462 q^{84} +(-0.290150 + 0.502555i) q^{86} +26.2497 q^{87} -5.03983 q^{88} +(4.14483 - 7.17905i) q^{89} +(6.08503 - 10.5396i) q^{91} +(2.34233 + 4.05703i) q^{92} +(-5.35468 - 9.27458i) q^{93} -4.62013 q^{94} +3.26496 q^{96} +(8.09494 + 14.0208i) q^{97} +(-0.0674593 - 0.116843i) q^{98} +(-19.3024 + 33.4328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + q^{6} - 12 q^{7} - 8 q^{8} - 11 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + q^6 - 12 * q^7 - 8 * q^8 - 11 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + q^{6} - 12 q^{7} - 8 q^{8} - 11 q^{9} + 10 q^{11} + 2 q^{12} - 9 q^{13} - 6 q^{14} - 4 q^{16} - 5 q^{17} - 22 q^{18} - q^{21} + 5 q^{22} - 6 q^{23} + q^{24} - 18 q^{26} - 16 q^{27} + 6 q^{28} + 17 q^{29} + 22 q^{31} + 4 q^{32} + 4 q^{33} + 5 q^{34} - 11 q^{36} + 8 q^{37} - 36 q^{39} + 7 q^{41} + q^{42} + 13 q^{43} - 5 q^{44} - 12 q^{46} - 14 q^{47} - q^{48} + 44 q^{49} - 9 q^{51} - 9 q^{52} + 14 q^{53} - 8 q^{54} + 12 q^{56} + 48 q^{57} + 34 q^{58} + 14 q^{59} - 9 q^{61} + 11 q^{62} + 45 q^{63} + 8 q^{64} - 4 q^{66} - 6 q^{67} + 10 q^{68} + 54 q^{69} + 14 q^{71} + 11 q^{72} + 11 q^{73} + 4 q^{74} + 10 q^{77} - 18 q^{78} - 17 q^{79} - 36 q^{81} - 7 q^{82} + 46 q^{83} + 2 q^{84} - 13 q^{86} + 2 q^{87} - 10 q^{88} + 14 q^{89} - 25 q^{91} - 6 q^{92} - 13 q^{93} - 28 q^{94} - 2 q^{96} + 17 q^{97} + 22 q^{98} - 60 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + q^6 - 12 * q^7 - 8 * q^8 - 11 * q^9 + 10 * q^11 + 2 * q^12 - 9 * q^13 - 6 * q^14 - 4 * q^16 - 5 * q^17 - 22 * q^18 - q^21 + 5 * q^22 - 6 * q^23 + q^24 - 18 * q^26 - 16 * q^27 + 6 * q^28 + 17 * q^29 + 22 * q^31 + 4 * q^32 + 4 * q^33 + 5 * q^34 - 11 * q^36 + 8 * q^37 - 36 * q^39 + 7 * q^41 + q^42 + 13 * q^43 - 5 * q^44 - 12 * q^46 - 14 * q^47 - q^48 + 44 * q^49 - 9 * q^51 - 9 * q^52 + 14 * q^53 - 8 * q^54 + 12 * q^56 + 48 * q^57 + 34 * q^58 + 14 * q^59 - 9 * q^61 + 11 * q^62 + 45 * q^63 + 8 * q^64 - 4 * q^66 - 6 * q^67 + 10 * q^68 + 54 * q^69 + 14 * q^71 + 11 * q^72 + 11 * q^73 + 4 * q^74 + 10 * q^77 - 18 * q^78 - 17 * q^79 - 36 * q^81 - 7 * q^82 + 46 * q^83 + 2 * q^84 - 13 * q^86 + 2 * q^87 - 10 * q^88 + 14 * q^89 - 25 * q^91 - 6 * q^92 - 13 * q^93 - 28 * q^94 - 2 * q^96 + 17 * q^97 + 22 * q^98 - 60 * q^99

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