LMFDB - Embedded newform 350.4.j.c.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(149,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.c.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(-3.46410 + 2.00000i) q^{3} +(2.00000 + 3.46410i) q^{4} -8.00000 q^{6} +(6.06218 + 17.5000i) q^{7} +8.00000i q^{8} +(-5.50000 + 9.52628i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(-3.46410 + 2.00000i) q^{3} +(2.00000 + 3.46410i) q^{4} -8.00000 q^{6} +(6.06218 + 17.5000i) q^{7} +8.00000i q^{8} +(-5.50000 + 9.52628i) q^{9} +(-15.0000 - 25.9808i) q^{11} +(-13.8564 - 8.00000i) q^{12} +4.00000i q^{13} +(-7.00000 + 36.3731i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(7.79423 - 4.50000i) q^{17} +(-19.0526 + 11.0000i) q^{18} +(-44.0000 + 76.2102i) q^{19} +(-56.0000 - 48.4974i) q^{21} -60.0000i q^{22} +(28.5788 + 16.5000i) q^{23} +(-16.0000 - 27.7128i) q^{24} +(-4.00000 + 6.92820i) q^{26} -152.000i q^{27} +(-48.4974 + 56.0000i) q^{28} -126.000 q^{29} +(-77.5000 - 134.234i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(103.923 + 60.0000i) q^{33} +18.0000 q^{34} -44.0000 q^{36} +(-100.459 - 58.0000i) q^{37} +(-152.420 + 88.0000i) q^{38} +(-8.00000 - 13.8564i) q^{39} -423.000 q^{41} +(-48.4974 - 140.000i) q^{42} +340.000i q^{43} +(60.0000 - 103.923i) q^{44} +(33.0000 + 57.1577i) q^{46} +(-293.583 - 169.500i) q^{47} -64.0000i q^{48} +(-269.500 + 212.176i) q^{49} +(-18.0000 + 31.1769i) q^{51} +(-13.8564 + 8.00000i) q^{52} +(270.200 - 156.000i) q^{53} +(152.000 - 263.272i) q^{54} +(-140.000 + 48.4974i) q^{56} -352.000i q^{57} +(-218.238 - 126.000i) q^{58} +(-231.000 - 400.104i) q^{59} +(-163.000 + 282.324i) q^{61} -310.000i q^{62} +(-200.052 - 38.5000i) q^{63} -64.0000 q^{64} +(120.000 + 207.846i) q^{66} +(609.682 - 352.000i) q^{67} +(31.1769 + 18.0000i) q^{68} -132.000 q^{69} +621.000 q^{71} +(-76.2102 - 44.0000i) q^{72} +(216.506 - 125.000i) q^{73} +(-116.000 - 200.918i) q^{74} -352.000 q^{76} +(363.731 - 420.000i) q^{77} -32.0000i q^{78} +(-552.500 + 956.958i) q^{79} +(155.500 + 269.334i) q^{81} +(-732.657 - 423.000i) q^{82} +198.000i q^{83} +(56.0000 - 290.985i) q^{84} +(-340.000 + 588.897i) q^{86} +(436.477 - 252.000i) q^{87} +(207.846 - 120.000i) q^{88} +(-436.500 + 756.040i) q^{89} +(-70.0000 + 24.2487i) q^{91} +132.000i q^{92} +(536.936 + 310.000i) q^{93} +(-339.000 - 587.165i) q^{94} +(64.0000 - 110.851i) q^{96} +905.000i q^{97} +(-678.964 + 98.0000i) q^{98} +330.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 32 q^{6} - 22 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 32 * q^6 - 22 * q^9	$ 4 q + 8 q^{4} - 32 q^{6} - 22 q^{9} - 60 q^{11} - 28 q^{14} - 32 q^{16} - 176 q^{19} - 224 q^{21} - 64 q^{24} - 16 q^{26} - 504 q^{29} - 310 q^{31} + 72 q^{34} - 176 q^{36} - 32 q^{39} - 1692 q^{41} + 240 q^{44} + 132 q^{46} - 1078 q^{49} - 72 q^{51} + 608 q^{54} - 560 q^{56} - 924 q^{59} - 652 q^{61} - 256 q^{64} + 480 q^{66} - 528 q^{69} + 2484 q^{71} - 464 q^{74} - 1408 q^{76} - 2210 q^{79} + 622 q^{81} + 224 q^{84} - 1360 q^{86} - 1746 q^{89} - 280 q^{91} - 1356 q^{94} + 256 q^{96} + 1320 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 - 32 * q^6 - 22 * q^9 - 60 * q^11 - 28 * q^14 - 32 * q^16 - 176 * q^19 - 224 * q^21 - 64 * q^24 - 16 * q^26 - 504 * q^29 - 310 * q^31 + 72 * q^34 - 176 * q^36 - 32 * q^39 - 1692 * q^41 + 240 * q^44 + 132 * q^46 - 1078 * q^49 - 72 * q^51 + 608 * q^54 - 560 * q^56 - 924 * q^59 - 652 * q^61 - 256 * q^64 + 480 * q^66 - 528 * q^69 + 2484 * q^71 - 464 * q^74 - 1408 * q^76 - 2210 * q^79 + 622 * q^81 + 224 * q^84 - 1360 * q^86 - 1746 * q^89 - 280 * q^91 - 1356 * q^94 + 256 * q^96 + 1320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	−3.46410	+	2.00000i	−0.666667	+	0.384900i	−0.794812	−	0.606855i	$-0.792431\pi$
$3$	−3.46410	+	2.00000i	−0.666667	+	0.384900i	0.128146	+	0.991755i	$0.459097\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−8.00000			−0.544331
$7$	6.06218	+	17.5000i	0.327327	+	0.944911i
$7$	6.06218	+	17.5000i	0.327327	+	0.944911i
$8$			8.00000i			0.353553i
$9$	−5.50000	+	9.52628i	−0.203704	+	0.352825i
$10$		0			0
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	0.583864	−	0.811851i	$-0.301540\pi$
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	−0.995016	+	0.0997155i	$0.968207\pi$
$12$	−13.8564	−	8.00000i	−0.333333	−	0.192450i
$13$			4.00000i			0.0853385i	0.999089	+	0.0426692i	$0.0135862\pi$
$13$			4.00000i			0.0853385i	−0.999089	+	0.0426692i	$0.986414\pi$
$14$	−7.00000	+	36.3731i	−0.133631	+	0.694365i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	7.79423	−	4.50000i	0.111199	−	0.0642006i	−0.443369	−	0.896339i	$-0.646217\pi$
$17$	7.79423	−	4.50000i	0.111199	−	0.0642006i	0.554568	+	0.832139i	$0.312884\pi$
$18$	−19.0526	+	11.0000i	−0.249485	+	0.144040i
$19$	−44.0000	+	76.2102i	−0.531279	+	0.920201i	0.468055	+	0.883699i	$0.344955\pi$
$19$	−44.0000	+	76.2102i	−0.531279	+	0.920201i	−0.999334	+	0.0365021i	$0.988378\pi$
$20$		0			0
$21$	−56.0000	−	48.4974i	−0.581914	−	0.503953i
$22$		−	60.0000i		−	0.581456i
$23$	28.5788	+	16.5000i	0.259091	+	0.149586i	0.623920	−	0.781488i	$-0.285539\pi$
$23$	28.5788	+	16.5000i	0.259091	+	0.149586i	−0.364829	+	0.931075i	$0.618872\pi$
$24$	−16.0000	−	27.7128i	−0.136083	−	0.235702i
$25$		0			0
$26$	−4.00000	+	6.92820i	−0.0301717	+	0.0522589i
$27$		−	152.000i		−	1.08342i
$28$	−48.4974	+	56.0000i	−0.327327	+	0.377964i
$29$	−126.000			−0.806814			−0.403407	−	0.915021i	$-0.632174\pi$
$29$	−126.000			−0.806814			−0.403407	+	0.915021i	$0.632174\pi$
$30$		0			0
$31$	−77.5000	−	134.234i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−77.5000	−	134.234i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	103.923	+	60.0000i	0.548202	+	0.316505i
$34$	18.0000			0.0907934
$35$		0			0
$36$	−44.0000			−0.203704
$37$	−100.459	−	58.0000i	−0.446361	−	0.257707i	0.259931	−	0.965627i	$-0.416300\pi$
$37$	−100.459	−	58.0000i	−0.446361	−	0.257707i	−0.706292	+	0.707921i	$0.749633\pi$
$38$	−152.420	+	88.0000i	−0.650681	+	0.375671i
$39$	−8.00000	−	13.8564i	−0.0328468	−	0.0568923i
$40$		0			0
$41$	−423.000			−1.61126			−0.805628	−	0.592422i	$-0.798172\pi$
$41$	−423.000			−1.61126			−0.805628	+	0.592422i	$0.798172\pi$
$42$	−48.4974	−	140.000i	−0.178174	−	0.514344i
$43$			340.000i			1.20580i	0.797816	+	0.602901i	$0.205989\pi$
$43$			340.000i			1.20580i	−0.797816	+	0.602901i	$0.794011\pi$
$44$	60.0000	−	103.923i	0.205576	−	0.356068i
$45$		0			0
$46$	33.0000	+	57.1577i	0.105774	+	0.183205i
$47$	−293.583	−	169.500i	−0.911137	−	0.526045i	−0.0303400	−	0.999540i	$-0.509659\pi$
$47$	−293.583	−	169.500i	−0.911137	−	0.526045i	−0.880797	+	0.473495i	$0.842992\pi$
$48$		−	64.0000i		−	0.192450i
$49$	−269.500	+	212.176i	−0.785714	+	0.618590i
$50$		0			0
$51$	−18.0000	+	31.1769i	−0.0494217	+	0.0856008i
$52$	−13.8564	+	8.00000i	−0.0369527	+	0.0213346i
$53$	270.200	−	156.000i	0.700280	−	0.404307i	−0.107172	−	0.994240i	$-0.534180\pi$
$53$	270.200	−	156.000i	0.700280	−	0.404307i	0.807452	+	0.589934i	$0.200846\pi$
$54$	152.000	−	263.272i	0.383048	−	0.663458i
$55$		0			0
$56$	−140.000	+	48.4974i	−0.334077	+	0.115728i
$57$		−	352.000i		−	0.817957i
$58$	−218.238	−	126.000i	−0.494071	−	0.285252i
$59$	−231.000	−	400.104i	−0.509723	−	0.882866i	−0.999937	−	0.0112634i	$-0.996415\pi$
$59$	−231.000	−	400.104i	−0.509723	−	0.882866i	0.490214	−	0.871602i	$-0.336919\pi$
$60$		0			0
$61$	−163.000	+	282.324i	−0.342131	+	0.592589i	−0.984828	−	0.173532i	$-0.944482\pi$
$61$	−163.000	+	282.324i	−0.342131	+	0.592589i	0.642697	+	0.766120i	$0.277815\pi$
$62$		−	310.000i		−	0.635001i
$63$	−200.052	−	38.5000i	−0.400066	−	0.0769928i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	120.000	+	207.846i	0.223803	+	0.387638i
$67$	609.682	−	352.000i	1.11171	−	0.641845i	0.172437	−	0.985020i	$-0.444836\pi$
$67$	609.682	−	352.000i	1.11171	−	0.641845i	0.939271	+	0.343175i	$0.111502\pi$
$68$	31.1769	+	18.0000i	0.0555994	+	0.0321003i
$69$	−132.000			−0.230303
$70$		0			0
$71$	621.000			1.03802			0.519008	−	0.854769i	$-0.326301\pi$
$71$	621.000			1.03802			0.519008	+	0.854769i	$0.326301\pi$
$72$	−76.2102	−	44.0000i	−0.124743	−	0.0720201i
$73$	216.506	−	125.000i	0.347125	−	0.200413i	−0.316293	−	0.948662i	$-0.602438\pi$
$73$	216.506	−	125.000i	0.347125	−	0.200413i	0.663418	+	0.748249i	$0.269105\pi$
$74$	−116.000	−	200.918i	−0.182226	−	0.315625i
$75$		0			0
$76$	−352.000			−0.531279
$77$	363.731	−	420.000i	0.538324	−	0.621603i
$78$		−	32.0000i		−	0.0464524i
$79$	−552.500	+	956.958i	−0.786849	+	1.36286i	0.141039	+	0.990004i	$0.454956\pi$
$79$	−552.500	+	956.958i	−0.786849	+	1.36286i	−0.927888	+	0.372859i	$0.878377\pi$
$80$		0			0
$81$	155.500	+	269.334i	0.213306	+	0.369457i
$82$	−732.657	−	423.000i	−0.986689	−	0.569665i
$83$			198.000i			0.261847i	0.991392	+	0.130924i	$0.0417943\pi$
$83$			198.000i			0.261847i	−0.991392	+	0.130924i	$0.958206\pi$
$84$	56.0000	−	290.985i	0.0727393	−	0.377964i
$85$		0			0
$86$	−340.000	+	588.897i	−0.426316	+	0.738400i
$87$	436.477	−	252.000i	0.537876	−	0.310543i
$88$	207.846	−	120.000i	0.251778	−	0.145364i
$89$	−436.500	+	756.040i	−0.519875	+	0.900451i	0.479858	+	0.877346i	$0.340688\pi$
$89$	−436.500	+	756.040i	−0.519875	+	0.900451i	−0.999733	+	0.0231042i	$0.992645\pi$
$90$		0			0
$91$	−70.0000	+	24.2487i	−0.0806373	+	0.0279336i
$92$			132.000i			0.149586i
$93$	536.936	+	310.000i	0.598684	+	0.345651i
$94$	−339.000	−	587.165i	−0.371970	−	0.644271i
$95$		0			0
$96$	64.0000	−	110.851i	0.0680414	−	0.117851i
$97$			905.000i			0.947308i	0.880711	+	0.473654i	$0.157065\pi$
$97$			905.000i			0.947308i	−0.880711	+	0.473654i	$0.842935\pi$
$98$	−678.964	+	98.0000i	−0.699854	+	0.101015i
$99$	330.000			0.335013
$100$		0			0
$101$	−300.000	−	519.615i	−0.295556	−	0.511917i	0.679558	−	0.733621i	$-0.262171\pi$
$101$	−300.000	−	519.615i	−0.295556	−	0.511917i	−0.975114	+	0.221704i	$0.928838\pi$
$102$	−62.3538	+	36.0000i	−0.0605289	+	0.0349464i
$103$	253.745	+	146.500i	0.242741	+	0.140146i	0.616436	−	0.787405i	$-0.288576\pi$
$103$	253.745	+	146.500i	0.242741	+	0.140146i	−0.373695	+	0.927552i	$0.621909\pi$
$104$	−32.0000			−0.0301717
$105$		0			0
$106$	624.000			0.571776
$107$	1460.12	+	843.000i	1.31921	+	0.761644i	0.983601	−	0.180359i	$-0.0577260\pi$
$107$	1460.12	+	843.000i	1.31921	+	0.761644i	0.335605	+	0.942003i	$0.391059\pi$
$108$	526.543	−	304.000i	0.469136	−	0.270856i
$109$	820.000	+	1420.28i	0.720567	+	1.24806i	0.960773	+	0.277336i	$0.0894515\pi$
$109$	820.000	+	1420.28i	0.720567	+	1.24806i	−0.240206	+	0.970722i	$0.577215\pi$
$110$		0			0
$111$	464.000			0.396765
$112$	−290.985	−	56.0000i	−0.245495	−	0.0472456i
$113$			1185.00i			0.986508i	0.869885	+	0.493254i	$0.164193\pi$
$113$			1185.00i			0.986508i	−0.869885	+	0.493254i	$0.835807\pi$
$114$	352.000	−	609.682i	0.289191	−	0.500894i
$115$		0			0
$116$	−252.000	−	436.477i	−0.201704	−	0.349361i
$117$	−38.1051	−	22.0000i	−0.0301096	−	0.0173838i
$118$		−	924.000i		−	0.720857i
$119$	126.000	+	109.119i	0.0970622	+	0.0840583i
$120$		0			0
$121$	215.500	−	373.257i	0.161908	−	0.280433i
$122$	−564.649	+	326.000i	−0.419024	+	0.241923i
$123$	1465.31	−	846.000i	1.07417	−	0.620173i
$124$	310.000	−	536.936i	0.224507	−	0.388857i
$125$		0			0
$126$	−308.000	−	266.736i	−0.217768	−	0.188593i
$127$			1976.00i			1.38064i	0.723503	+	0.690321i	$0.242531\pi$
$127$			1976.00i			1.38064i	−0.723503	+	0.690321i	$0.757469\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	−680.000	−	1177.79i	−0.464114	−	0.803868i
$130$		0			0
$131$	765.000	−	1325.02i	0.510216	−	0.883721i	−0.489713	−	0.871883i	$-0.662899\pi$
$131$	765.000	−	1325.02i	0.510216	−	0.883721i	0.999930	−	0.0118374i	$-0.00376806\pi$
$132$			480.000i			0.316505i
$133$	−1600.41	−	308.000i	−1.04341	−	0.200804i
$134$	1408.00			0.907707
$135$		0			0
$136$	36.0000	+	62.3538i	0.0226983	+	0.0393147i
$137$	−1374.38	+	793.500i	−0.857091	+	0.494841i	−0.863037	−	0.505141i	$-0.831441\pi$
$137$	−1374.38	+	793.500i	−0.857091	+	0.494841i	0.00594636	+	0.999982i	$0.498107\pi$
$138$	−228.631	−	132.000i	−0.141031	−	0.0814245i
$139$	2242.00			1.36809			0.684043	−	0.729442i	$-0.260220\pi$
$139$	2242.00			1.36809			0.684043	+	0.729442i	$0.260220\pi$
$140$		0			0
$141$	1356.00			0.809899
$142$	1075.60	+	621.000i	0.635652	+	0.366994i
$143$	103.923	−	60.0000i	0.0607726	−	0.0350871i
$144$	−88.0000	−	152.420i	−0.0509259	−	0.0882063i
$145$		0			0
$146$	500.000			0.283427
$147$	509.223	−	1274.00i	0.285714	−	0.714815i
$148$		−	464.000i		−	0.257707i
$149$	−735.000	+	1273.06i	−0.404118	+	0.699952i	−0.994218	−	0.107377i	$-0.965755\pi$
$149$	−735.000	+	1273.06i	−0.404118	+	0.699952i	0.590101	+	0.807330i	$0.299088\pi$
$150$		0			0
$151$	332.000	+	575.041i	0.178926	+	0.309908i	0.941513	−	0.336977i	$-0.109405\pi$
$151$	332.000	+	575.041i	0.178926	+	0.309908i	−0.762587	+	0.646885i	$0.776071\pi$
$152$	−609.682	−	352.000i	−0.325340	−	0.187835i
$153$			99.0000i			0.0523116i
$154$	1050.00	−	363.731i	0.549425	−	0.190326i
$155$		0			0
$156$	32.0000	−	55.4256i	0.0164234	−	0.0284462i
$157$	−1702.61	+	983.000i	−0.865495	+	0.499694i	−0.865849	−	0.500306i	$-0.833221\pi$
$157$	−1702.61	+	983.000i	−0.865495	+	0.499694i	0.000353429		1.00000i	$0.499887\pi$
$158$	−1913.92	+	1105.00i	−0.963690	+	0.556387i
$159$	−624.000	+	1080.80i	−0.311235	+	0.539075i
$160$		0			0
$161$	−115.500	+	600.156i	−0.0565384	+	0.293782i
$162$			622.000i			0.301660i
$163$	−2611.93	−	1508.00i	−1.25511	−	0.724636i	−0.282987	−	0.959124i	$-0.591325\pi$
$163$	−2611.93	−	1508.00i	−1.25511	−	0.724636i	−0.972119	+	0.234488i	$0.924659\pi$
$164$	−846.000	−	1465.31i	−0.402814	−	0.697694i
$165$		0			0
$166$	−198.000	+	342.946i	−0.0925770	+	0.160348i
$167$			1608.00i			0.745094i	0.928013	+	0.372547i	$0.121516\pi$
$167$			1608.00i			0.745094i	−0.928013	+	0.372547i	$0.878484\pi$
$168$	387.979	−	448.000i	0.178174	−	0.205738i
$169$	2181.00			0.992717
$170$		0			0
$171$	−484.000	−	838.313i	−0.216447	−	0.374897i
$172$	−1177.79	+	680.000i	−0.522128	+	0.301451i
$173$	2177.19	+	1257.00i	0.956812	+	0.552416i	0.895190	−	0.445684i	$-0.147039\pi$
$173$	2177.19	+	1257.00i	0.956812	+	0.552416i	0.0616218	+	0.998100i	$0.480373\pi$
$174$	1008.00			0.439174
$175$		0			0
$176$	480.000			0.205576
$177$	1600.41	+	924.000i	0.679630	+	0.392385i
$178$	−1512.08	+	873.000i	−0.636715	+	0.367607i
$179$	−807.000	−	1397.77i	−0.336972	−	0.583653i	0.646890	−	0.762584i	$-0.276069\pi$
$179$	−807.000	−	1397.77i	−0.336972	−	0.583653i	−0.983862	+	0.178931i	$0.942736\pi$
$180$		0			0
$181$	−2770.00			−1.13753			−0.568764	−	0.822501i	$-0.692578\pi$
$181$	−2770.00			−1.13753			−0.568764	+	0.822501i	$0.692578\pi$
$182$	−145.492	−	28.0000i	−0.0592561	−	0.0114038i
$183$		−	1304.00i		−	0.526746i
$184$	−132.000	+	228.631i	−0.0528868	+	0.0916026i
$185$		0			0
$186$	620.000	+	1073.87i	0.244412	+	0.423334i
$187$	−233.827	−	135.000i	−0.0914391	−	0.0527924i
$188$		−	1356.00i		−	0.526045i
$189$	2660.00	−	921.451i	1.02374	−	0.354633i
$190$		0			0
$191$	2317.50	−	4014.03i	0.877950	−	1.52065i	0.0243629	−	0.999703i	$-0.492244\pi$
$191$	2317.50	−	4014.03i	0.877950	−	1.52065i	0.853587	−	0.520951i	$-0.174422\pi$
$192$	221.703	−	128.000i	0.0833333	−	0.0481125i
$193$	411.362	−	237.500i	0.153422	−	0.0885784i	−0.421323	−	0.906910i	$-0.638434\pi$
$193$	411.362	−	237.500i	0.153422	−	0.0885784i	0.574746	+	0.818332i	$0.305101\pi$
$194$	−905.000	+	1567.51i	−0.334924	+	0.580105i
$195$		0			0
$196$	−1274.00	−	509.223i	−0.464286	−	0.185577i
$197$			4896.00i			1.77069i	0.464936	+	0.885344i	$0.346077\pi$
$197$			4896.00i			1.77069i	−0.464936	+	0.885344i	$0.653923\pi$
$198$	571.577	+	330.000i	0.205152	+	0.118445i
$199$	−1398.50	−	2422.27i	−0.498176	−	0.862866i	0.501822	−	0.864971i	$-0.332663\pi$
$199$	−1398.50	−	2422.27i	−0.498176	−	0.862866i	−0.999998	+	0.00210482i	$0.999330\pi$
$200$		0			0
$201$	−1408.00	+	2438.73i	−0.494093	+	0.855794i
$202$		−	1200.00i		−	0.417979i
$203$	−763.834	−	2205.00i	−0.264092	−	0.762368i
$204$	−144.000			−0.0494217
$205$		0			0
$206$	293.000	+	507.491i	0.0990984	+	0.171644i
$207$	−314.367	+	181.500i	−0.105556	+	0.0609426i
$208$	−55.4256	−	32.0000i	−0.0184763	−	0.0106673i
$209$	2640.00			0.873745
$210$		0			0
$211$	2612.00			0.852216			0.426108	−	0.904672i	$-0.359884\pi$
$211$	2612.00			0.852216			0.426108	+	0.904672i	$0.359884\pi$
$212$	1080.80	+	624.000i	0.350140	+	0.202153i
$213$	−2151.21	+	1242.00i	−0.692011	+	0.399533i
$214$	1686.00	+	2920.24i	0.538563	+	0.932819i
$215$		0			0
$216$	1216.00			0.383048
$217$	1879.28	−	2170.00i	0.587896	−	0.678844i
$218$			3280.00i			1.01904i
$219$	−500.000	+	866.025i	−0.154278	+	0.267217i
$220$		0			0
$221$	18.0000	+	31.1769i	0.00547878	+	0.00948953i
$222$	803.672	+	464.000i	0.242968	+	0.140278i
$223$		−	3629.00i		−	1.08976i	−0.838515	−	0.544879i	$-0.816576\pi$
$223$		−	3629.00i		−	1.08976i	0.838515	−	0.544879i	$-0.183424\pi$
$224$	−448.000	−	387.979i	−0.133631	−	0.115728i
$225$		0			0
$226$	−1185.00	+	2052.48i	−0.348783	+	0.604110i
$227$	−358.535	+	207.000i	−0.104832	+	0.0605245i	−0.551499	−	0.834175i	$-0.685944\pi$
$227$	−358.535	+	207.000i	−0.104832	+	0.0605245i	0.446668	+	0.894700i	$0.352611\pi$
$228$	1219.36	−	704.000i	0.354186	−	0.204489i
$229$	−785.000	+	1359.66i	−0.226525	+	0.392353i	−0.956776	−	0.290826i	$-0.906070\pi$
$229$	−785.000	+	1359.66i	−0.226525	+	0.392353i	0.730251	+	0.683179i	$0.239403\pi$
$230$		0			0
$231$	−420.000	+	2182.38i	−0.119628	+	0.621603i
$232$		−	1008.00i		−	0.285252i
$233$	4557.03	+	2631.00i	1.28129	+	0.739753i	0.977084	−	0.212853i	$-0.0682755\pi$
$233$	4557.03	+	2631.00i	1.28129	+	0.739753i	0.304206	+	0.952606i	$0.401609\pi$
$234$	−44.0000	−	76.2102i	−0.0122922	−	0.0212907i
$235$		0			0
$236$	924.000	−	1600.41i	0.254861	−	0.441433i
$237$		−	4420.00i		−	1.21143i
$238$	109.119	+	315.000i	0.0297191	+	0.0857917i
$239$	−4305.00			−1.16514			−0.582568	−	0.812782i	$-0.697952\pi$
$239$	−4305.00			−1.16514			−0.582568	+	0.812782i	$0.697952\pi$
$240$		0			0
$241$	491.000	+	850.437i	0.131237	+	0.227309i	0.924154	−	0.382021i	$-0.124772\pi$
$241$	491.000	+	850.437i	0.131237	+	0.227309i	−0.792917	+	0.609330i	$0.791438\pi$
$242$	746.514	−	431.000i	0.198296	−	0.114486i
$243$	2476.83	+	1430.00i	0.653864	+	0.377508i
$244$	−1304.00			−0.342131
$245$		0			0
$246$	3384.00			0.877057
$247$	−304.841	−	176.000i	−0.0785286	−	0.0453385i
$248$	1073.87	−	620.000i	0.274963	−	0.158750i
$249$	−396.000	−	685.892i	−0.100785	−	0.174565i
$250$		0			0
$251$	4080.00			1.02601			0.513003	−	0.858387i	$-0.328533\pi$
$251$	4080.00			1.02601			0.513003	+	0.858387i	$0.328533\pi$
$252$	−266.736	−	770.000i	−0.0666777	−	0.192482i
$253$		−	990.000i		−	0.246011i
$254$	−1976.00	+	3422.53i	−0.488131	+	0.845468i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−732.657	−	423.000i	−0.177828	−	0.102669i	0.408444	−	0.912784i	$-0.366072\pi$
$257$	−732.657	−	423.000i	−0.177828	−	0.102669i	−0.586272	+	0.810114i	$0.699405\pi$
$258$		−	2720.00i		−	0.656356i
$259$	406.000	−	2109.64i	0.0974039	−	0.506126i
$260$		0			0
$261$	693.000	−	1200.31i	0.164351	−	0.284664i
$262$	2650.04	−	1530.00i	0.624885	−	0.360778i
$263$	2834.50	−	1636.50i	0.664573	−	0.383692i	−0.129444	−	0.991587i	$-0.541319\pi$
$263$	2834.50	−	1636.50i	0.664573	−	0.383692i	0.794017	+	0.607895i	$0.207986\pi$
$264$	−480.000	+	831.384i	−0.111901	+	0.193819i
$265$		0			0
$266$	−2464.00	−	2133.89i	−0.567961	−	0.491868i
$267$		−	3492.00i		−	0.800400i
$268$	2438.73	+	1408.00i	0.555854	+	0.320923i
$269$	−3570.00	−	6183.42i	−0.809170	−	1.40152i	−0.913440	−	0.406975i	$-0.866584\pi$
$269$	−3570.00	−	6183.42i	−0.809170	−	1.40152i	0.104269	−	0.994549i	$-0.466750\pi$
$270$		0			0
$271$	−2840.50	+	4919.89i	−0.636709	+	1.10281i	0.349442	+	0.936958i	$0.386371\pi$
$271$	−2840.50	+	4919.89i	−0.636709	+	1.10281i	−0.986150	+	0.165854i	$0.946962\pi$
$272$			144.000i			0.0321003i
$273$	193.990	−	224.000i	0.0430066	−	0.0496597i
$274$	−3174.00			−0.699812
$275$		0			0
$276$	−264.000	−	457.261i	−0.0575758	−	0.0997243i
$277$	1820.39	−	1051.00i	0.394860	−	0.227973i	−0.289403	−	0.957207i	$-0.593457\pi$
$277$	1820.39	−	1051.00i	0.394860	−	0.227973i	0.684264	+	0.729234i	$0.260124\pi$
$278$	3883.26	+	2242.00i	0.837778	+	0.483691i
$279$	1705.00			0.365863
$280$		0			0
$281$	−6297.00			−1.33682			−0.668412	−	0.743791i	$-0.733026\pi$
$281$	−6297.00			−1.33682			−0.668412	+	0.743791i	$0.733026\pi$
$282$	2348.66	+	1356.00i	0.495960	+	0.286343i
$283$	−7712.82	+	4453.00i	−1.62007	+	0.935348i	−0.633170	+	0.774013i	$0.718247\pi$
$283$	−7712.82	+	4453.00i	−1.62007	+	0.935348i	−0.986900	+	0.161335i	$0.948420\pi$
$284$	1242.00	+	2151.21i	0.259504	+	0.449474i
$285$		0			0
$286$	240.000			0.0496206
$287$	−2564.30	−	7402.50i	−0.527407	−	1.52249i
$288$		−	352.000i		−	0.0720201i
$289$	−2416.00	+	4184.63i	−0.491757	+	0.851747i
$290$		0			0
$291$	−1810.00	−	3135.01i	−0.364619	−	0.631538i
$292$	866.025	+	500.000i	0.173563	+	0.100206i
$293$			4782.00i			0.953472i	0.879046	+	0.476736i	$0.158180\pi$
$293$			4782.00i			0.953472i	−0.879046	+	0.476736i	$0.841820\pi$
$294$	2156.00	−	1697.41i	0.427689	−	0.336718i
$295$		0			0
$296$	464.000	−	803.672i	0.0911130	−	0.157812i
$297$	−3949.08	+	2280.00i	−0.771544	+	0.445451i
$298$	−2546.11	+	1470.00i	−0.494941	+	0.285754i
$299$	−66.0000	+	114.315i	−0.0127655	+	0.0221105i
$300$		0			0
$301$	−5950.00	+	2061.14i	−1.13938	+	0.394692i
$302$			1328.00i			0.253039i
$303$	2078.46	+	1200.00i	0.394074	+	0.227519i
$304$	−704.000	−	1219.36i	−0.132820	−	0.230050i
$305$		0			0
$306$	−99.0000	+	171.473i	−0.0184949	+	0.0320342i
$307$		−	9412.00i		−	1.74974i	−0.484355	−	0.874872i	$-0.660946\pi$
$307$		−	9412.00i		−	1.74974i	0.484355	−	0.874872i	$-0.339054\pi$
$308$	2182.38	+	420.000i	0.403743	+	0.0777004i
$309$	−1172.00			−0.215769
$310$		0			0
$311$	3784.50	+	6554.95i	0.690030	+	1.19517i	0.971828	+	0.235693i	$0.0757360\pi$
$311$	3784.50	+	6554.95i	0.690030	+	1.19517i	−0.281798	+	0.959474i	$0.590931\pi$
$312$	110.851	−	64.0000i	0.0201145	−	0.0116131i
$313$	−7550.88	−	4359.50i	−1.36358	−	0.787264i	−0.373482	−	0.927637i	$-0.621836\pi$
$313$	−7550.88	−	4359.50i	−1.36358	−	0.787264i	−0.990099	+	0.140374i	$0.955170\pi$
$314$	−3932.00			−0.706674
$315$		0			0
$316$	−4420.00			−0.786849
$317$	−2785.14	−	1608.00i	−0.493467	−	0.284903i	0.232545	−	0.972586i	$-0.425295\pi$
$317$	−2785.14	−	1608.00i	−0.493467	−	0.284903i	−0.726011	+	0.687683i	$0.758628\pi$
$318$	−2161.60	+	1248.00i	−0.381184	+	0.220077i
$319$	1890.00	+	3273.58i	0.331723	+	0.574561i
$320$		0			0
$321$	−6744.00			−1.17263
$322$	−800.207	+	924.000i	−0.138490	+	0.159915i
$323$			792.000i			0.136434i
$324$	−622.000	+	1077.34i	−0.106653	+	0.184728i
$325$		0			0
$326$	−3016.00	−	5223.87i	−0.512395	−	0.887494i
$327$	−5681.13	−	3280.00i	−0.960755	−	0.554692i
$328$		−	3384.00i		−	0.569665i
$329$	1186.50	−	6165.23i	0.198826	−	1.03313i
$330$		0			0
$331$	2153.00	−	3729.11i	0.357521	−	0.619245i	−0.630025	−	0.776575i	$-0.716955\pi$
$331$	2153.00	−	3729.11i	0.357521	−	0.619245i	0.987546	+	0.157330i	$0.0502886\pi$
$332$	−685.892	+	396.000i	−0.113383	+	0.0654618i
$333$	1105.05	−	638.000i	0.181851	−	0.104992i
$334$	−1608.00	+	2785.14i	−0.263431	+	0.456275i
$335$		0			0
$336$	1120.00	−	387.979i	0.181848	−	0.0629941i
$337$			3179.00i			0.513861i	0.966430	+	0.256931i	$0.0827112\pi$
$337$			3179.00i			0.513861i	−0.966430	+	0.256931i	$0.917289\pi$
$338$	3777.60	+	2181.00i	0.607913	+	0.350979i
$339$	−2370.00	−	4104.96i	−0.379707	−	0.657672i
$340$		0			0
$341$	−2325.00	+	4027.02i	−0.369225	+	0.639517i
$342$		−	1936.00i		−	0.306102i
$343$	−5346.84	−	3430.00i	−0.841698	−	0.539949i
$344$	−2720.00			−0.426316
$345$		0			0
$346$	2514.00	+	4354.38i	0.390617	+	0.676568i
$347$	4172.51	−	2409.00i	0.645510	−	0.372686i	−0.141224	−	0.989978i	$-0.545104\pi$
$347$	4172.51	−	2409.00i	0.645510	−	0.372686i	0.786734	+	0.617292i	$0.211770\pi$
$348$	1745.91	+	1008.00i	0.268938	+	0.155271i
$349$	9376.00			1.43807			0.719034	−	0.694975i	$-0.244585\pi$
$349$	9376.00			1.43807			0.719034	+	0.694975i	$0.244585\pi$
$350$		0			0
$351$	608.000			0.0924577
$352$	831.384	+	480.000i	0.125889	+	0.0726821i
$353$	−8732.13	+	5041.50i	−1.31661	+	0.760147i	−0.983182	−	0.182627i	$-0.941540\pi$
$353$	−8732.13	+	5041.50i	−1.31661	+	0.760147i	−0.333431	+	0.942774i	$0.608207\pi$
$354$	1848.00	+	3200.83i	0.277458	+	0.480571i
$355$		0			0
$356$	−3492.00			−0.519875
$357$	−654.715	−	126.000i	−0.0970622	−	0.0186796i
$358$		−	3228.00i		−	0.476551i
$359$	−138.000	+	239.023i	−0.0202879	+	0.0351397i	−0.875991	−	0.482327i	$-0.839792\pi$
$359$	−138.000	+	239.023i	−0.0202879	+	0.0351397i	0.855703	+	0.517467i	$0.173125\pi$
$360$		0			0
$361$	−442.500	−	766.432i	−0.0645138	−	0.111741i
$362$	−4797.78	−	2770.00i	−0.696590	−	0.402177i
$363$			1724.00i			0.249274i
$364$	−224.000	−	193.990i	−0.0322549	−	0.0279336i
$365$		0			0
$366$	1304.00	−	2258.59i	0.186233	−	0.322565i
$367$	−5407.46	+	3122.00i	−0.769121	+	0.444052i	−0.832561	−	0.553934i	$-0.813126\pi$
$367$	−5407.46	+	3122.00i	−0.769121	+	0.444052i	0.0634402	+	0.997986i	$0.479793\pi$
$368$	−457.261	+	264.000i	−0.0647728	+	0.0373966i
$369$	2326.50	−	4029.62i	0.328219	−	0.568492i
$370$		0			0
$371$	4368.00	+	3782.80i	0.611254	+	0.529362i
$372$			2480.00i			0.345651i
$373$	360.267	+	208.000i	0.0500104	+	0.0288735i	0.524797	−	0.851228i	$-0.324141\pi$
$373$	360.267	+	208.000i	0.0500104	+	0.0288735i	−0.474786	+	0.880101i	$0.657475\pi$
$374$	−270.000	−	467.654i	−0.0373299	−	0.0646572i
$375$		0			0
$376$	1356.00	−	2348.66i	0.185985	−	0.322135i
$377$		−	504.000i		−	0.0688523i
$378$	5528.71	+	1064.00i	0.752291	+	0.144778i
$379$	−12302.0			−1.66731			−0.833656	−	0.552284i	$-0.813756\pi$
$379$	−12302.0			−1.66731			−0.833656	+	0.552284i	$0.813756\pi$
$380$		0			0
$381$	−3952.00	−	6845.06i	−0.531410	−	0.920429i
$382$	8028.06	−	4635.00i	1.07526	−	0.620804i
$383$	−5536.50	−	3196.50i	−0.738647	−	0.426458i	0.0829299	−	0.996555i	$-0.473572\pi$
$383$	−5536.50	−	3196.50i	−0.738647	−	0.426458i	−0.821577	+	0.570097i	$0.806906\pi$
$384$	512.000			0.0680414
$385$		0			0
$386$	950.000			0.125269
$387$	−3238.94	−	1870.00i	−0.425438	−	0.245626i
$388$	−3135.01	+	1810.00i	−0.410196	+	0.236827i
$389$	2034.00	+	3522.99i	0.265110	+	0.459184i	0.967593	−	0.252517i	$-0.0812583\pi$
$389$	2034.00	+	3522.99i	0.265110	+	0.459184i	−0.702482	+	0.711701i	$0.747925\pi$
$390$		0			0
$391$	297.000			0.0384142
$392$	−1697.41	−	2156.00i	−0.218704	−	0.277792i
$393$			6120.00i			0.785530i
$394$	−4896.00	+	8480.12i	−0.626033	+	1.08432i
$395$		0			0
$396$	660.000	+	1143.15i	0.0837532	+	0.145065i
$397$	12718.4	+	7343.00i	1.60786	+	0.928299i	0.989848	+	0.142131i	$0.0453953\pi$
$397$	12718.4	+	7343.00i	1.60786	+	0.928299i	0.618013	+	0.786168i	$0.287938\pi$
$398$		−	5594.00i		−	0.704527i
$399$	6160.00	−	2133.89i	0.772897	−	0.267739i
$400$		0			0
$401$	1851.00	−	3206.03i	0.230510	−	0.399255i	−0.727448	−	0.686163i	$-0.759294\pi$
$401$	1851.00	−	3206.03i	0.230510	−	0.399255i	0.957958	+	0.286907i	$0.0926272\pi$
$402$	−4877.46	+	2816.00i	−0.605138	+	0.349376i
$403$	536.936	−	310.000i	0.0663689	−	0.0383181i
$404$	1200.00	−	2078.46i	0.147778	−	0.255959i
$405$		0			0
$406$	882.000	−	4583.01i	0.107815	−	0.560224i
$407$			3480.00i			0.423826i
$408$	−249.415	−	144.000i	−0.0302645	−	0.0174732i
$409$	−4221.50	−	7311.85i	−0.510366	−	0.883980i	−0.999928	−	0.0120114i	$-0.996177\pi$
$409$	−4221.50	−	7311.85i	−0.510366	−	0.883980i	0.489562	−	0.871969i	$-0.337157\pi$
$410$		0			0
$411$	3174.00	−	5497.53i	0.380929	−	0.659789i
$412$			1172.00i			0.140146i
$413$	5601.45	−	6468.00i	0.667384	−	0.770628i
$414$	−726.000			−0.0861859
$415$		0			0
$416$	−64.0000	−	110.851i	−0.00754293	−	0.0130647i
$417$	−7766.52	+	4484.00i	−0.912057	+	0.526577i
$418$	4572.61	+	2640.00i	0.535057	+	0.308915i
$419$	13140.0			1.53205			0.766027	−	0.642808i	$-0.222231\pi$
$419$	13140.0			1.53205			0.766027	+	0.642808i	$0.222231\pi$
$420$		0			0
$421$	−9604.00			−1.11181			−0.555903	−	0.831247i	$-0.687627\pi$
$421$	−9604.00			−1.11181			−0.555903	+	0.831247i	$0.687627\pi$
$422$	4524.12	+	2612.00i	0.521873	+	0.301304i
$423$	3229.41	−	1864.50i	0.371204	−	0.214315i
$424$	1248.00	+	2161.60i	0.142944	+	0.247586i
$425$		0			0
$426$	−4968.00			−0.565024
$427$	−5928.81	−	1141.00i	−0.671933	−	0.129313i
$428$			6744.00i			0.761644i
$429$	−240.000	+	415.692i	−0.0270100	+	0.0467828i
$430$		0			0
$431$	−163.500	−	283.190i	−0.0182727	−	0.0316492i	0.856744	−	0.515741i	$-0.172483\pi$
$431$	−163.500	−	283.190i	−0.0182727	−	0.0316492i	−0.875017	+	0.484092i	$0.839150\pi$
$432$	2106.17	+	1216.00i	0.234568	+	0.135428i
$433$			5983.00i			0.664029i	0.943274	+	0.332015i	$0.107728\pi$
$433$			5983.00i			0.664029i	−0.943274	+	0.332015i	$0.892272\pi$
$434$	5425.00	−	1879.28i	0.600019	−	0.207853i
$435$		0			0
$436$	−3280.00	+	5681.13i	−0.360283	+	0.624029i
$437$	−2514.94	+	1452.00i	−0.275299	+	0.158944i
$438$	−1732.05	+	1000.00i	−0.188951	+	0.109091i
$439$	−7281.50	+	12611.9i	−0.791633	+	1.37115i	0.133322	+	0.991073i	$0.457436\pi$
$439$	−7281.50	+	12611.9i	−0.791633	+	1.37115i	−0.924955	+	0.380076i	$0.875898\pi$
$440$		0			0
$441$	−539.000	−	3734.30i	−0.0582011	−	0.403229i
$442$			72.0000i			0.00774817i
$443$	13478.8	+	7782.00i	1.44559	+	0.834614i	0.998215	−	0.0597304i	$-0.0190241\pi$
$443$	13478.8	+	7782.00i	1.44559	+	0.834614i	0.447379	+	0.894344i	$0.352357\pi$
$444$	928.000	+	1607.34i	0.0991913	+	0.171804i
$445$		0			0
$446$	3629.00	−	6285.61i	0.385287	−	0.667337i
$447$		−	5880.00i		−	0.622180i
$448$	−387.979	−	1120.00i	−0.0409159	−	0.118114i
$449$	−4017.00			−0.422214			−0.211107	−	0.977463i	$-0.567707\pi$
$449$	−4017.00			−0.422214			−0.211107	+	0.977463i	$0.567707\pi$
$450$		0			0
$451$	6345.00	+	10989.9i	0.662471	+	1.14743i
$452$	−4104.96	+	2370.00i	−0.427171	+	0.246627i
$453$	−2300.16	−	1328.00i	−0.238568	−	0.137737i
$454$	−828.000			−0.0855946
$455$		0			0
$456$	2816.00			0.289191
$457$	12967.9	+	7487.00i	1.32738	+	0.766361i	0.984893	−	0.173163i	$-0.0553986\pi$
$457$	12967.9	+	7487.00i	1.32738	+	0.766361i	0.342483	+	0.939524i	$0.388732\pi$
$458$	−2719.32	+	1570.00i	−0.277436	+	0.160177i
$459$	−684.000	−	1184.72i	−0.0695564	−	0.120475i
$460$		0			0
$461$	8076.00			0.815915			0.407958	−	0.913001i	$-0.366241\pi$
$461$	8076.00			0.815915			0.407958	+	0.913001i	$0.366241\pi$
$462$	−2909.85	+	3360.00i	−0.293027	+	0.338358i
$463$		−	14045.0i		−	1.40978i	−0.709318	−	0.704888i	$-0.750997\pi$
$463$		−	14045.0i		−	1.40978i	0.709318	−	0.704888i	$-0.249003\pi$
$464$	1008.00	−	1745.91i	0.100852	−	0.174680i
$465$		0			0
$466$	5262.00	+	9114.05i	0.523085	+	0.906009i
$467$	6635.49	+	3831.00i	0.657503	+	0.379609i	0.791325	−	0.611396i	$-0.209392\pi$
$467$	6635.49	+	3831.00i	0.657503	+	0.379609i	−0.133822	+	0.991005i	$0.542725\pi$
$468$		−	176.000i		−	0.0173838i
$469$	9856.00	+	8535.55i	0.970379	+	0.840373i
$470$		0			0
$471$	3932.00	−	6810.42i	0.384665	−	0.666259i
$472$	3200.83	−	1848.00i	0.312140	−	0.180214i
$473$	8833.46	−	5100.00i	0.858695	−	0.495768i
$474$	4420.00	−	7655.66i	0.428307	−	0.741849i
$475$		0			0
$476$	−126.000	+	654.715i	−0.0121328	+	0.0630437i
$477$			3432.00i			0.329435i
$478$	−7456.48	−	4305.00i	−0.713497	−	0.411937i
$479$	−3016.50	−	5224.73i	−0.287740	−	0.498380i	0.685530	−	0.728044i	$-0.259571\pi$
$479$	−3016.50	−	5224.73i	−0.287740	−	0.498380i	−0.973270	+	0.229664i	$0.926237\pi$
$480$		0			0
$481$	232.000	−	401.836i	0.0219923	−	0.0380918i
$482$			1964.00i			0.185597i
$483$	−800.207	−	2310.00i	−0.0753845	−	0.217616i
$484$	1724.00			0.161908
$485$		0			0
$486$	2860.00	+	4953.67i	0.266939	+	0.462351i
$487$	6354.03	−	3668.50i	0.591229	−	0.341346i	−0.174354	−	0.984683i	$-0.555784\pi$
$487$	6354.03	−	3668.50i	0.591229	−	0.341346i	0.765583	+	0.643337i	$0.222450\pi$
$488$	−2258.59	−	1304.00i	−0.209512	−	0.120962i
$489$	12064.0			1.11565
$490$		0			0
$491$	13032.0			1.19781			0.598906	−	0.800819i	$-0.295602\pi$
$491$	13032.0			1.19781			0.598906	+	0.800819i	$0.295602\pi$
$492$	5861.26	+	3384.00i	0.537085	+	0.310086i
$493$	−982.073	+	567.000i	−0.0897167	+	0.0517980i
$494$	−352.000	−	609.682i	−0.0320592	−	0.0555281i
$495$		0			0
$496$	2480.00			0.224507
$497$	3764.61	+	10867.5i	0.339771	+	0.980833i
$498$		−	1584.00i		−	0.142532i
$499$	−3893.00	+	6742.87i	−0.349248	+	0.604915i	−0.986116	−	0.166058i	$-0.946896\pi$
$499$	−3893.00	+	6742.87i	−0.349248	+	0.604915i	0.636868	+	0.770973i	$0.280229\pi$
$500$		0			0
$501$	−3216.00	−	5570.28i	−0.286787	−	0.496730i
$502$	7066.77	+	4080.00i	0.628297	+	0.362748i
$503$		−	12720.0i		−	1.12755i	−0.825929	−	0.563774i	$-0.809349\pi$
$503$		−	12720.0i		−	1.12755i	0.825929	−	0.563774i	$-0.190651\pi$
$504$	308.000	−	1600.41i	0.0272211	−	0.141445i
$505$		0			0
$506$	990.000	−	1714.73i	0.0869780	−	0.150650i
$507$	−7555.21	+	4362.00i	−0.661812	+	0.382097i
$508$	−6845.06	+	3952.00i	−0.597836	+	0.345161i
$509$	2595.00	−	4494.67i	0.225975	−	0.391400i	−0.730636	−	0.682767i	$-0.760777\pi$
$509$	2595.00	−	4494.67i	0.225975	−	0.391400i	0.956612	+	0.291366i	$0.0941098\pi$
$510$		0			0
$511$	3500.00	+	3031.09i	0.302996	+	0.262402i
$512$		−	512.000i		−	0.0441942i
$513$	11584.0	+	6688.00i	0.996967	+	0.575599i
$514$	−846.000	−	1465.31i	−0.0725982	−	0.125744i
$515$		0			0
$516$	2720.00	−	4711.18i	0.232057	−	0.401934i
$517$			10170.0i			0.865138i
$518$	2812.85	−	3248.00i	0.238590	−	0.275500i
$519$	−10056.0			−0.850500
$520$		0			0
$521$	9151.50	+	15850.9i	0.769548	+	1.33290i	0.937808	+	0.347154i	$0.112852\pi$
$521$	9151.50	+	15850.9i	0.769548	+	1.33290i	−0.168260	+	0.985743i	$0.553815\pi$
$522$	2400.62	−	1386.00i	0.201288	−	0.116214i
$523$	−7761.32	−	4481.00i	−0.648908	−	0.374647i	0.139130	−	0.990274i	$-0.455569\pi$
$523$	−7761.32	−	4481.00i	−0.648908	−	0.374647i	−0.788038	+	0.615627i	$0.788903\pi$
$524$	6120.00			0.510216
$525$		0			0
$526$	6546.00			0.542622
$527$	−1208.11	−	697.500i	−0.0998594	−	0.0576538i
$528$	−1662.77	+	960.000i	−0.137051	+	0.0791262i
$529$	−5539.00	−	9593.83i	−0.455248	−	0.788512i
$530$		0			0
$531$	5082.00			0.415330
$532$	−2133.89	−	6160.00i	−0.173902	−	0.502011i
$533$		−	1692.00i		−	0.137502i
$534$	3492.00	−	6048.32i	0.282984	−	0.490143i
$535$		0			0
$536$	2816.00	+	4877.46i	0.226927	+	0.393048i
$537$	5591.06	+	3228.00i	0.449296	+	0.259401i
$538$		−	14280.0i		−	1.14434i
$539$	9555.00	+	3819.17i	0.763568	+	0.305201i
$540$		0			0
$541$	−5170.00	+	8954.70i	−0.410861	+	0.711632i	−0.994984	−	0.100033i	$-0.968105\pi$
$541$	−5170.00	+	8954.70i	−0.410861	+	0.711632i	0.584123	+	0.811665i	$0.301438\pi$
$542$	−9839.78	+	5681.00i	−0.779806	+	0.450221i
$543$	9595.56	−	5540.00i	0.758352	−	0.437835i
$544$	−144.000	+	249.415i	−0.0113492	+	0.0196573i
$545$		0			0
$546$	560.000	−	193.990i	0.0438934	−	0.0152051i
$547$			4196.00i			0.327985i	0.986462	+	0.163993i	$0.0524373\pi$
$547$			4196.00i			0.327985i	−0.986462	+	0.163993i	$0.947563\pi$
$548$	−5497.53	−	3174.00i	−0.428545	−	0.247421i
$549$	−1793.00	−	3105.57i	−0.139387	−	0.241425i
$550$		0			0
$551$	5544.00	−	9602.49i	0.428643	−	0.742432i
$552$		−	1056.00i		−	0.0814245i
$553$	−20096.1	−	3867.50i	−1.54534	−	0.297401i
$554$	4204.00			0.322402
$555$		0			0
$556$	4484.00	+	7766.52i	0.342022	+	0.592399i
$557$	9680.43	−	5589.00i	0.736397	−	0.425159i	−0.0843609	−	0.996435i	$-0.526885\pi$
$557$	9680.43	−	5589.00i	0.736397	−	0.425159i	0.820758	+	0.571276i	$0.193552\pi$
$558$	2953.15	+	1705.00i	0.224044	+	0.129352i
$559$	−1360.00			−0.102901
$560$		0			0
$561$	1080.00			0.0812792
$562$	−10906.7	−	6297.00i	−0.818634	−	0.472639i
$563$	13032.0	−	7524.00i	0.975544	−	0.563231i	0.0746221	−	0.997212i	$-0.476225\pi$
$563$	13032.0	−	7524.00i	0.975544	−	0.563231i	0.900922	+	0.433981i	$0.142892\pi$
$564$	2712.00	+	4697.32i	0.202475	+	0.350697i
$565$		0			0
$566$	−17812.0			−1.32278
$567$	−3770.67	+	4354.00i	−0.279283	+	0.322488i
$568$			4968.00i			0.366994i
$569$	−3553.50	+	6154.84i	−0.261811	+	0.453470i	−0.966723	−	0.255825i	$-0.917653\pi$
$569$	−3553.50	+	6154.84i	−0.261811	+	0.453470i	0.704912	+	0.709295i	$0.250986\pi$
$570$		0			0
$571$	2030.00	+	3516.06i	0.148779	+	0.257693i	0.930776	−	0.365589i	$-0.119132\pi$
$571$	2030.00	+	3516.06i	0.148779	+	0.257693i	−0.781997	+	0.623282i	$0.785799\pi$
$572$	415.692	+	240.000i	0.0303863	+	0.0175435i
$573$			18540.0i			1.35169i
$574$	2961.00	−	15385.8i	0.215313	−	1.11880i
$575$		0			0
$576$	352.000	−	609.682i	0.0254630	−	0.0441031i
$577$	−14339.6	+	8279.00i	−1.03461	+	0.597330i	−0.918301	−	0.395884i	$-0.870438\pi$
$577$	−14339.6	+	8279.00i	−1.03461	+	0.597330i	−0.116305	+	0.993214i	$0.537105\pi$
$578$	−8369.27	+	4832.00i	−0.602276	+	0.347724i
$579$	−950.000	+	1645.45i	−0.0681877	+	0.118104i
$580$		0			0
$581$	−3465.00	+	1200.31i	−0.247422	+	0.0857096i
$582$		−	7240.00i		−	0.515649i
$583$	−8106.00	−	4680.00i	−0.575842	−	0.332463i
$584$	1000.00	+	1732.05i	0.0708567	+	0.122727i
$585$		0			0
$586$	−4782.00	+	8282.67i	−0.337103	+	0.583880i
$587$		−	9546.00i		−	0.671219i	−0.942001	−	0.335610i	$-0.891058\pi$
$587$		−	9546.00i		−	0.671219i	0.942001	−	0.335610i	$-0.108942\pi$
$588$	5431.71	−	784.000i	0.380952	−	0.0549857i
$589$	13640.0			0.954204
$590$		0			0
$591$	−9792.00	−	16960.2i	−0.681538	−	1.18046i
$592$	1607.34	−	928.000i	0.111590	−	0.0644266i
$593$	9750.58	+	5629.50i	0.675225	+	0.389841i	0.798053	−	0.602587i	$-0.205863\pi$
$593$	9750.58	+	5629.50i	0.675225	+	0.389841i	−0.122829	+	0.992428i	$0.539197\pi$
$594$	−9120.00			−0.629963
$595$		0			0
$596$	−5880.00			−0.404118
$597$	9689.09	+	5594.00i	0.664235	+	0.383496i
$598$	−228.631	+	132.000i	−0.0156345	+	0.00902656i
$599$	−7090.50	−	12281.1i	−0.483656	−	0.837717i	0.516168	−	0.856488i	$-0.327358\pi$
$599$	−7090.50	−	12281.1i	−0.483656	−	0.837717i	−0.999824	+	0.0187706i	$0.994025\pi$
$600$		0			0
$601$	−3562.00			−0.241759			−0.120879	−	0.992667i	$-0.538571\pi$
$601$	−3562.00			−0.241759			−0.120879	+	0.992667i	$0.538571\pi$
$602$	−12366.8	−	2380.00i	−0.837267	−	0.161132i
$603$			7744.00i			0.522985i
$604$	−1328.00	+	2300.16i	−0.0894628	+	0.154954i
$605$		0			0
$606$	2400.00	+	4156.92i	0.160880	+	0.278652i
$607$	16415.5	+	9477.50i	1.09767	+	0.633739i	0.935608	−	0.353041i	$-0.114852\pi$
$607$	16415.5	+	9477.50i	1.09767	+	0.633739i	0.162061	+	0.986781i	$0.448186\pi$
$608$		−	2816.00i		−	0.187835i
$609$	7056.00	+	6110.68i	0.469497	+	0.406596i
$610$		0			0
$611$	678.000	−	1174.33i	0.0448919	−	0.0777550i
$612$	−342.946	+	198.000i	−0.0226516	+	0.0130779i
$613$	2991.25	−	1727.00i	0.197089	−	0.113789i	−0.398208	−	0.917295i	$-0.630368\pi$
$613$	2991.25	−	1727.00i	0.197089	−	0.113789i	0.595297	+	0.803506i	$0.297034\pi$
$614$	9412.00	−	16302.1i	0.618628	−	1.07149i
$615$		0			0
$616$	3360.00	+	2909.85i	0.219770	+	0.190326i
$617$		−	20745.0i		−	1.35359i	−0.736174	−	0.676793i	$-0.763369\pi$
$617$		−	20745.0i		−	1.35359i	0.736174	−	0.676793i	$-0.236631\pi$
$618$	−2029.96	−	1172.00i	−0.132131	−	0.0762860i
$619$	8965.00	+	15527.8i	0.582122	+	1.00827i	0.995227	+	0.0975822i	$0.0311109\pi$
$619$	8965.00	+	15527.8i	0.582122	+	1.00827i	−0.413105	+	0.910683i	$0.635556\pi$
$620$		0			0
$621$	2508.00	−	4343.98i	0.162065	−	0.280705i
$622$			15138.0i			0.975850i
$623$	−15876.8	−	3055.50i	−1.02101	−	0.196494i
$624$	256.000			0.0164234
$625$		0			0
$626$	−8719.00	−	15101.8i	−0.556679	−	0.964197i
$627$	−9145.23	+	5280.00i	−0.582496	+	0.336304i
$628$	−6810.42	−	3932.00i	−0.432748	−	0.249847i
$629$	−1044.00			−0.0661797
$630$		0			0
$631$	−5689.00			−0.358915			−0.179458	−	0.983766i	$-0.557434\pi$
$631$	−5689.00			−0.358915			−0.179458	+	0.983766i	$0.557434\pi$
$632$	−7655.66	−	4420.00i	−0.481845	−	0.278193i
$633$	−9048.23	+	5224.00i	−0.568144	+	0.328018i
$634$	−3216.00	−	5570.28i	−0.201457	−	0.348934i
$635$		0			0
$636$	−4992.00			−0.311235
$637$	−848.705	−	1078.00i	−0.0527895	−	0.0670517i
$638$			7560.00i			0.469127i
$639$	−3415.50	+	5915.82i	−0.211448	+	0.366238i
$640$		0			0
$641$	−11602.5	−	20096.1i	−0.714932	−	1.23830i	−0.962986	−	0.269552i	$-0.913124\pi$
$641$	−11602.5	−	20096.1i	−0.714932	−	1.23830i	0.248054	−	0.968746i	$-0.420209\pi$
$642$	−11681.0	−	6744.00i	−0.718085	−	0.414586i
$643$			18190.0i			1.11562i	0.829969	+	0.557810i	$0.188358\pi$
$643$			18190.0i			1.11562i	−0.829969	+	0.557810i	$0.811642\pi$
$644$	−2310.00	+	800.207i	−0.141346	+	0.0489637i
$645$		0			0
$646$	−792.000	+	1371.78i	−0.0482366	+	0.0835482i
$647$	9862.30	−	5694.00i	0.599269	−	0.345988i	−0.169485	−	0.985533i	$-0.554210\pi$
$647$	9862.30	−	5694.00i	0.599269	−	0.345988i	0.768754	+	0.639545i	$0.220877\pi$
$648$	−2154.67	+	1244.00i	−0.130623	+	0.0754150i
$649$	−6930.00	+	12003.1i	−0.419147	+	0.725984i
$650$		0			0
$651$	−2170.00	+	11275.7i	−0.130644	+	0.678844i
$652$		−	12064.0i		−	0.724636i
$653$	20233.8	+	11682.0i	1.21257	+	0.700080i	0.963319	−	0.268358i	$-0.0864812\pi$
$653$	20233.8	+	11682.0i	1.21257	+	0.700080i	0.249254	+	0.968438i	$0.419814\pi$
$654$	−6560.00	−	11362.3i	−0.392227	−	0.679357i
$655$		0			0
$656$	3384.00	−	5861.26i	0.201407	−	0.348847i
$657$			2750.00i			0.163299i
$658$	8220.31	−	9492.00i	0.487023	−	0.562366i
$659$	−7890.00			−0.466390			−0.233195	−	0.972430i	$-0.574918\pi$
$659$	−7890.00			−0.466390			−0.233195	+	0.972430i	$0.574918\pi$
$660$		0			0
$661$	−1387.00	−	2402.35i	−0.0816158	−	0.141363i	0.822328	−	0.569013i	$-0.192675\pi$
$661$	−1387.00	−	2402.35i	−0.0816158	−	0.141363i	−0.903944	+	0.427651i	$0.859341\pi$
$662$	7458.21	−	4306.00i	0.437872	−	0.252806i
$663$	−124.708	−	72.0000i	−0.00730504	−	0.00421757i
$664$	−1584.00			−0.0925770
$665$		0			0
$666$	2552.00			0.148480
$667$	−3600.93	−	2079.00i	−0.209039	−	0.120688i
$668$	−5570.28	+	3216.00i	−0.322635	+	0.186274i
$669$	7258.00	+	12571.2i	0.419448	+	0.726505i
$670$		0			0
$671$	9780.00			0.562672
$672$	2327.88	+	448.000i	0.133631	+	0.0257172i
$673$			10075.0i			0.577062i	0.957471	+	0.288531i	$0.0931668\pi$
$673$			10075.0i			0.577062i	−0.957471	+	0.288531i	$0.906833\pi$
$674$	−3179.00	+	5506.19i	−0.181677	+	0.314674i
$675$		0			0
$676$	4362.00	+	7555.21i	0.248179	+	0.429859i
$677$	−5554.69	−	3207.00i	−0.315338	−	0.182061i	0.333975	−	0.942582i	$-0.391610\pi$
$677$	−5554.69	−	3207.00i	−0.315338	−	0.182061i	−0.649313	+	0.760521i	$0.724943\pi$
$678$		−	9480.00i		−	0.536987i
$679$	−15837.5	+	5486.27i	−0.895121	+	0.310079i
$680$		0			0
$681$	828.000	−	1434.14i	0.0465918	−	0.0806994i
$682$	−8054.04	+	4650.00i	−0.452207	+	0.261082i
$683$	12029.1	−	6945.00i	0.673910	−	0.389082i	−0.123647	−	0.992326i	$-0.539459\pi$
$683$	12029.1	−	6945.00i	0.673910	−	0.389082i	0.797556	+	0.603244i	$0.206126\pi$
$684$	1936.00	−	3353.25i	0.108223	−	0.187448i
$685$		0			0
$686$	−5831.00	−	11287.8i	−0.324532	−	0.628235i
$687$		−	6280.00i		−	0.348758i
$688$	−4711.18	−	2720.00i	−0.261064	−	0.150725i
$689$	624.000	+	1080.80i	0.0345029	+	0.0597608i
$690$		0			0
$691$	7865.00	−	13622.6i	0.432994	−	0.749967i	−0.564136	−	0.825682i	$-0.690791\pi$
$691$	7865.00	−	13622.6i	0.432994	−	0.749967i	0.997130	+	0.0757148i	$0.0241239\pi$
$692$			10056.0i			0.552416i
$693$	2000.52	+	5775.00i	0.109659	+	0.316557i
$694$	9636.00			0.527057
$695$		0			0
$696$	2016.00	+	3491.81i	0.109794	+	0.190168i
$697$	−3296.96	+	1903.50i	−0.179170	+	0.103444i
$698$	16239.7	+	9376.00i	0.880633	+	0.508434i
$699$	−21048.0			−1.13892
$700$		0			0
$701$	−12336.0			−0.664657			−0.332328	−	0.943164i	$-0.607834\pi$
$701$	−12336.0			−0.664657			−0.332328	+	0.943164i	$0.607834\pi$
$702$	1053.09	+	608.000i	0.0566185	+	0.0326887i
$703$	8840.39	−	5104.00i	0.474284	−	0.273828i
$704$	960.000	+	1662.77i	0.0513940	+	0.0890170i
$705$		0			0
$706$	−20166.0			−1.07501
$707$	7274.61	−	8400.00i	0.386973	−	0.446838i
$708$			7392.00i			0.392385i
$709$	−11243.0	+	19473.4i	−0.595543	+	1.03151i	0.397927	+	0.917417i	$0.369730\pi$
$709$	−11243.0	+	19473.4i	−0.595543	+	1.03151i	−0.993470	+	0.114093i	$0.963604\pi$
$710$		0			0
$711$	−6077.50	−	10526.5i	−0.320568	−	0.555241i
$712$	−6048.32	−	3492.00i	−0.318357	−	0.183804i
$713$		−	5115.00i		−	0.268665i
$714$	−1008.00	−	872.954i	−0.0528340	−	0.0457556i
$715$		0			0
$716$	3228.00	−	5591.06i	0.168486	−	0.291826i
$717$	14913.0	−	8610.00i	0.776757	−	0.448461i
$718$	−478.046	+	276.000i	−0.0248475	+	0.0143457i
$719$	3907.50	−	6767.99i	0.202678	−	0.351048i	−0.746713	−	0.665147i	$-0.768369\pi$
$719$	3907.50	−	6767.99i	0.202678	−	0.351048i	0.949390	+	0.314099i	$0.101702\pi$
$720$		0			0
$721$	−1025.50	+	5328.65i	−0.0529703	+	0.275242i
$722$		−	1770.00i		−	0.0912363i
$723$	−3401.75	−	1964.00i	−0.174983	−	0.101026i
$724$	−5540.00	−	9595.56i	−0.284382	−	0.492564i
$725$		0			0
$726$	−1724.00	+	2986.06i	−0.0881317	+	0.152649i
$727$		−	20737.0i		−	1.05790i	−0.848653	−	0.528950i	$-0.822586\pi$
$727$		−	20737.0i		−	1.05790i	0.848653	−	0.528950i	$-0.177414\pi$
$728$	−193.990	−	560.000i	−0.00987601	−	0.0285096i
$729$	−19837.0			−1.00782
$730$		0			0
$731$	1530.00	+	2650.04i	0.0774133	+	0.134084i
$732$	4517.19	−	2608.00i	0.228088	−	0.131686i
$733$	−8748.59	−	5051.00i	−0.440841	−	0.254520i	0.263113	−	0.964765i	$-0.415251\pi$
$733$	−8748.59	−	5051.00i	−0.440841	−	0.254520i	−0.703954	+	0.710245i	$0.748584\pi$
$734$	−12488.0			−0.627984
$735$		0			0
$736$	−1056.00			−0.0528868
$737$	−18290.5	−	10560.0i	−0.914162	−	0.527792i
$738$	8059.23	−	4653.00i	0.401984	−	0.232086i
$739$	7306.00	+	12654.4i	0.363675	+	0.629903i	0.988563	−	0.150812i	$-0.0481887\pi$
$739$	7306.00	+	12654.4i	0.363675	+	0.629903i	−0.624888	+	0.780714i	$0.714855\pi$
$740$		0			0
$741$	1408.00			0.0698032
$742$	3782.80	+	10920.0i	0.187158	+	0.540277i
$743$			21981.0i			1.08534i	0.839947	+	0.542668i	$0.182586\pi$
$743$			21981.0i			1.08534i	−0.839947	+	0.542668i	$0.817414\pi$
$744$	−2480.00	+	4295.49i	−0.122206	+	0.211667i
$745$		0			0
$746$	416.000	+	720.533i	0.0204167	+	0.0353627i
$747$	−1886.20	−	1089.00i	−0.0923863	−	0.0533393i
$748$		−	1080.00i		−	0.0527924i
$749$	−5901.00	+	30662.5i	−0.287874	+	1.49584i
$750$		0			0
$751$	−11092.0	+	19211.9i	−0.538952	+	0.933492i	0.460009	+	0.887914i	$0.347846\pi$
$751$	−11092.0	+	19211.9i	−0.538952	+	0.933492i	−0.998961	+	0.0455777i	$0.985487\pi$
$752$	4697.32	−	2712.00i	0.227784	−	0.131511i
$753$	−14133.5	+	8160.00i	−0.684003	+	0.394910i
$754$	504.000	−	872.954i	0.0243430	−	0.0421633i
$755$		0			0
$756$	8512.00	+	7371.61i	0.409495	+	0.354633i
$757$		−	12148.0i		−	0.583258i	−0.956531	−	0.291629i	$-0.905803\pi$
$757$		−	12148.0i		−	0.583258i	0.956531	−	0.291629i	$-0.0941973\pi$
$758$	−21307.7	−	12302.0i	−1.02102	−	0.589484i
$759$	1980.00	+	3429.46i	0.0946897	+	0.164007i
$760$		0			0
$761$	−14602.5	+	25292.3i	−0.695585	+	1.20479i	0.274398	+	0.961616i	$0.411521\pi$
$761$	−14602.5	+	25292.3i	−0.695585	+	1.20479i	−0.969983	+	0.243172i	$0.921812\pi$
$762$		−	15808.0i		−	0.751527i
$763$	−19883.9	+	22960.0i	−0.943443	+	1.08939i
$764$	18540.0			0.877950
$765$		0			0
$766$	−6393.00	−	11073.0i	−0.301552	−	0.522303i
$767$	1600.41	−	924.000i	0.0753424	−	0.0434990i
$768$	886.810	+	512.000i	0.0416667	+	0.0240563i
$769$	−5906.00			−0.276952			−0.138476	−	0.990366i	$-0.544220\pi$
$769$	−5906.00			−0.276952			−0.138476	+	0.990366i	$0.544220\pi$
$770$		0			0
$771$	3384.00			0.158070
$772$	1645.45	+	950.000i	0.0767111	+	0.0442892i
$773$	22634.4	−	13068.0i	1.05317	−	0.608051i	0.129638	−	0.991561i	$-0.458618\pi$
$773$	22634.4	−	13068.0i	1.05317	−	0.608051i	0.923537	+	0.383511i	$0.125285\pi$
$774$	−3740.00	−	6477.87i	−0.173684	−	0.300830i
$775$		0			0
$776$	−7240.00			−0.334924
$777$	2812.85	+	8120.00i	0.129872	+	0.374908i
$778$			8136.00i			0.374923i
$779$	18612.0	−	32236.9i	0.856026	−	1.48268i
$780$		0			0
$781$	−9315.00	−	16134.1i	−0.426782	−	0.739208i
$782$	514.419	+	297.000i	0.0235238	+	0.0135815i
$783$			19152.0i			0.874121i
$784$	−784.000	−	5431.71i	−0.0357143	−	0.247436i
$785$		0			0
$786$	−6120.00	+	10600.2i	−0.277727	+	0.481037i
$787$	−1915.65	+	1106.00i	−0.0867668	+	0.0500948i	−0.542756	−	0.839891i	$-0.682619\pi$
$787$	−1915.65	+	1106.00i	−0.0867668	+	0.0500948i	0.455989	+	0.889986i	$0.349286\pi$
$788$	−16960.2	+	9792.00i	−0.766730	+	0.442672i
$789$	−6546.00	+	11338.0i	−0.295366	+	0.511589i
$790$		0			0
$791$	−20737.5	+	7183.68i	−0.932163	+	0.322911i
$792$			2640.00i			0.118445i
$793$	−1129.30	−	652.000i	−0.0505706	−	0.0291970i
$794$	14686.0	+	25436.9i	0.656406	+	1.13693i
$795$		0			0
$796$	5594.00	−	9689.09i	0.249088	−	0.431433i
$797$		−	24654.0i		−	1.09572i	−0.836570	−	0.547860i	$-0.815442\pi$
$797$		−	24654.0i		−	1.09572i	0.836570	−	0.547860i	$-0.184558\pi$
$798$	12803.3	+	2464.00i	0.567961	+	0.109304i
$799$	−3051.00			−0.135090
$800$		0			0
$801$	−4801.50	−	8316.44i	−0.211801	−	0.366850i
$802$	6412.05	−	3702.00i	0.282316	−	0.162995i
$803$	−6495.19	−	3750.00i	−0.285442	−	0.164800i
$804$	−11264.0			−0.494093
$805$		0			0
$806$	1240.00			0.0541900
$807$	24733.7	+	14280.0i	1.07889	+	0.622899i
$808$	4156.92	−	2400.00i	0.180990	−	0.104495i
$809$	−18435.0	−	31930.4i	−0.801162	−	1.38765i	−0.918852	−	0.394603i	$-0.870882\pi$
$809$	−18435.0	−	31930.4i	−0.801162	−	1.38765i	0.117690	−	0.993050i	$-0.462451\pi$
$810$		0			0
$811$	5096.00			0.220647			0.110324	−	0.993896i	$-0.464811\pi$
$811$	5096.00			0.220647			0.110324	+	0.993896i	$0.464811\pi$
$812$	6110.68	−	7056.00i	0.264092	−	0.304947i
$813$		−	22724.0i		−	0.980277i
$814$	−3480.00	+	6027.54i	−0.149845	+	0.259539i
$815$		0			0
$816$	−288.000	−	498.831i	−0.0123554	−	0.0214002i
$817$	−25911.5	−	14960.0i	−1.10958	−	0.640617i
$818$		−	16886.0i		−	0.721767i
$819$	154.000	−	800.207i	0.00657045	−	0.0341410i
$820$		0			0
$821$	−6384.00	+	11057.4i	−0.271380	+	0.470044i	−0.969215	−	0.246214i	$-0.920813\pi$
$821$	−6384.00	+	11057.4i	−0.271380	+	0.470044i	0.697835	+	0.716258i	$0.254147\pi$
$822$	10995.1	−	6348.00i	0.466541	−	0.269358i
$823$	3723.91	−	2150.00i	0.157725	−	0.0910623i	−0.419060	−	0.907958i	$-0.637640\pi$
$823$	3723.91	−	2150.00i	0.157725	−	0.0910623i	0.576785	+	0.816896i	$0.304307\pi$
$824$	−1172.00	+	2029.96i	−0.0495492	+	0.0858218i
$825$		0			0
$826$	16170.0	−	5601.45i	0.681146	−	0.235956i
$827$			1374.00i			0.0577735i	0.999583	+	0.0288867i	$0.00919621\pi$
$827$			1374.00i			0.0577735i	−0.999583	+	0.0288867i	$0.990804\pi$
$828$	−1257.47	−	726.000i	−0.0527779	−	0.0304713i
$829$	−16067.0	−	27828.9i	−0.673136	−	1.16591i	−0.977010	−	0.213194i	$-0.931613\pi$
$829$	−16067.0	−	27828.9i	−0.673136	−	1.16591i	0.303874	−	0.952712i	$-0.401720\pi$
$830$		0			0
$831$	−4204.00	+	7281.54i	−0.175494	+	0.303964i
$832$		−	256.000i		−	0.0106673i
$833$	−1145.75	+	2866.50i	−0.0476566	+	0.119230i
$834$	−17936.0			−0.744692
$835$		0			0
$836$	5280.00	+	9145.23i	0.218436	+	0.378343i
$837$	−20403.6	+	11780.0i	−0.842593	+	0.486471i
$838$	22759.1	+	13140.0i	0.938188	+	0.541663i
$839$	10227.0			0.420829			0.210414	−	0.977612i	$-0.432519\pi$
$839$	10227.0			0.420829			0.210414	+	0.977612i	$0.432519\pi$
$840$		0			0
$841$	−8513.00			−0.349051
$842$	−16634.6	−	9604.00i	−0.680839	−	0.393083i
$843$	21813.4	−	12594.0i	0.891216	−	0.514544i
$844$	5224.00	+	9048.23i	0.213054	+	0.369020i
$845$		0			0
$846$	7458.00			0.303087
$847$	7838.40	+	1508.50i	0.317982	+	0.0611956i
$848$			4992.00i			0.202153i
$849$	17812.0	−	30851.3i	0.720031	−	1.24713i
$850$		0			0
$851$	−1914.00	−	3315.15i	−0.0770988	−	0.133539i
$852$	−8604.83	−	4968.00i	−0.346005	−	0.199766i
$853$		−	9560.00i		−	0.383738i	−0.981421	−	0.191869i	$-0.938545\pi$
$853$		−	9560.00i		−	0.383738i	0.981421	−	0.191869i	$-0.0614548\pi$
$854$	−9128.00	−	7905.08i	−0.365754	−	0.316752i
$855$		0			0
$856$	−6744.00	+	11681.0i	−0.269282	+	0.466410i
$857$	3081.32	−	1779.00i	0.122819	−	0.0709095i	−0.437332	−	0.899300i	$-0.644076\pi$
$857$	3081.32	−	1779.00i	0.122819	−	0.0709095i	0.560151	+	0.828391i	$0.310743\pi$
$858$	−831.384	+	480.000i	−0.0330804	+	0.0190990i
$859$	775.000	−	1342.34i	0.0307831	−	0.0533178i	−0.850223	−	0.526422i	$-0.823533\pi$
$859$	775.000	−	1342.34i	0.0307831	−	0.0533178i	0.881007	+	0.473104i	$0.156867\pi$
$860$		0			0
$861$	23688.0	+	20514.4i	0.937613	+	0.811997i
$862$		−	654.000i		−	0.0258414i
$863$	−13663.3	−	7888.50i	−0.538938	−	0.311156i	0.205710	−	0.978613i	$-0.434050\pi$
$863$	−13663.3	−	7888.50i	−0.538938	−	0.311156i	−0.744648	+	0.667457i	$0.767383\pi$
$864$	2432.00	+	4212.35i	0.0957619	+	0.165865i
$865$		0			0
$866$	−5983.00	+	10362.9i	−0.234770	+	0.406633i
$867$		−	19328.0i		−	0.757109i
$868$	11275.7	+	2170.00i	0.440922	+	0.0848555i
$869$	33150.0			1.29406
$870$		0			0
$871$	1408.00	+	2438.73i	0.0547741	+	0.0948716i
$872$	−11362.3	+	6560.00i	−0.441255	+	0.254759i
$873$	−8621.28	−	4977.50i	−0.334234	−	0.192970i
$874$	−5808.00			−0.224781
$875$		0			0
$876$	−4000.00			−0.154278
$877$	−17543.9	−	10129.0i	−0.675504	−	0.390002i	0.122655	−	0.992449i	$-0.460859\pi$
$877$	−17543.9	−	10129.0i	−0.675504	−	0.390002i	−0.798159	+	0.602447i	$0.794192\pi$
$878$	−25223.9	+	14563.0i	−0.969549	+	0.559769i
$879$	−9564.00	−	16565.3i	−0.366992	−	0.635648i
$880$		0			0
$881$	43347.0			1.65766			0.828829	−	0.559501i	$-0.189007\pi$
$881$	43347.0			1.65766			0.828829	+	0.559501i	$0.189007\pi$
$882$	2800.73	−	7007.00i	0.106922	−	0.267503i
$883$		−	1658.00i		−	0.0631893i	−0.999501	−	0.0315946i	$-0.989941\pi$
$883$		−	1658.00i		−	0.0631893i	0.999501	−	0.0315946i	$-0.0100586\pi$
$884$	−72.0000	+	124.708i	−0.00273939	+	0.00474477i
$885$		0			0
$886$	15564.0	+	26957.6i	0.590161	+	1.02219i
$887$	12928.0	+	7464.00i	0.489381	+	0.282544i	0.724318	−	0.689467i	$-0.242155\pi$
$887$	12928.0	+	7464.00i	0.489381	+	0.282544i	−0.234937	+	0.972011i	$0.575488\pi$
$888$			3712.00i			0.140278i
$889$	−34580.0	+	11978.9i	−1.30458	+	0.451921i
$890$		0			0
$891$	4665.00	−	8080.02i	0.175402	−	0.303806i
$892$	12571.2	−	7258.00i	0.471879	−	0.272439i
$893$	25835.3	−	14916.0i	0.968135	−	0.558953i
$894$	5880.00	−	10184.5i	0.219974	−	0.381006i
$895$		0			0
$896$	448.000	−	2327.88i	0.0167038	−	0.0867956i
$897$		−	528.000i		−	0.0196537i
$898$	−6957.65	−	4017.00i	−0.258552	−	0.149275i
$899$	9765.00	+	16913.5i	0.362270	+	0.627471i
$900$		0			0
$901$	1404.00	−	2431.80i	0.0519135	−	0.0899167i
$902$			25380.0i			0.936875i
$903$	16489.1	−	19040.0i	0.607667	−	0.701674i
$904$	−9480.00			−0.348783
$905$		0			0
$906$	−2656.00	−	4600.33i	−0.0973948	−	0.168693i
$907$	−5516.58	+	3185.00i	−0.201957	+	0.116600i	−0.597568	−	0.801818i	$-0.703866\pi$
$907$	−5516.58	+	3185.00i	−0.201957	+	0.116600i	0.395611	+	0.918418i	$0.370533\pi$
$908$	−1434.14	−	828.000i	−0.0524158	−	0.0302623i
$909$	6600.00			0.240823
$910$		0			0
$911$	30273.0			1.10098			0.550488	−	0.834843i	$-0.314442\pi$
$911$	30273.0			1.10098			0.550488	+	0.834843i	$0.314442\pi$
$912$	4877.46	+	2816.00i	0.177093	+	0.102245i
$913$	5144.19	−	2970.00i	0.186471	−	0.107659i
$914$	14974.0	+	25935.7i	0.541899	+	0.938597i
$915$		0			0
$916$	−6280.00			−0.226525
$917$	27825.4	+	5355.00i	1.00205	+	0.192844i
$918$		−	2736.00i		−	0.0983676i
$919$	22694.5	−	39308.0i	0.814606	−	1.41094i	−0.0950053	−	0.995477i	$-0.530287\pi$
$919$	22694.5	−	39308.0i	0.814606	−	1.41094i	0.909611	−	0.415461i	$-0.136380\pi$
$920$		0			0
$921$	18824.0	+	32604.1i	0.673477	+	1.16650i
$922$	13988.0	+	8076.00i	0.499644	+	0.288470i
$923$			2484.00i			0.0885827i
$924$	−8400.00	+	2909.85i	−0.299069	+	0.103601i
$925$		0			0
$926$	14045.0	−	24326.7i	0.498431	−	0.863308i
$927$	−2791.20	+	1611.50i	−0.0988943	+	0.0570967i
$928$	3491.81	−	2016.00i	0.123518	−	0.0713130i
$929$	17649.0	−	30569.0i	0.623299	−	1.07959i	−0.365568	−	0.930785i	$-0.619125\pi$
$929$	17649.0	−	30569.0i	0.623299	−	1.07959i	0.988867	−	0.148801i	$-0.0475414\pi$
$930$		0			0
$931$	−4312.00	−	29874.4i	−0.151794	−	1.05166i
$932$			21048.0i			0.739753i
$933$	−26219.8	−	15138.0i	−0.920040	−	0.531185i
$934$	7662.00	+	13271.0i	0.268424	+	0.464925i
$935$		0			0
$936$	176.000	−	304.841i	0.00614609	−	0.0106453i
$937$			52382.0i			1.82630i	0.407621	+	0.913151i	$0.366358\pi$
$937$			52382.0i			1.82630i	−0.407621	+	0.913151i	$0.633642\pi$
$938$	8535.55	+	24640.0i	0.297117	+	0.857702i
$939$	34876.0			1.21207
$940$		0			0
$941$	−14472.0	−	25066.2i	−0.501354	−	0.868370i	−0.999999	−	0.00156368i	$-0.999502\pi$
$941$	−14472.0	−	25066.2i	−0.501354	−	0.868370i	0.498645	−	0.866806i	$-0.333831\pi$
$942$	13620.8	−	7864.00i	0.471116	−	0.271999i
$943$	−12088.8	−	6979.50i	−0.417462	−	0.241022i
$944$	7392.00			0.254861
$945$		0			0
$946$	20400.0			0.701122
$947$	−22322.7	−	12888.0i	−0.765987	−	0.442243i	0.0654544	−	0.997856i	$-0.479150\pi$
$947$	−22322.7	−	12888.0i	−0.765987	−	0.442243i	−0.831441	+	0.555613i	$0.812484\pi$
$948$	15311.3	−	8840.00i	0.524566	−	0.302858i
$949$	500.000	+	866.025i	0.0171029	+	0.0296232i
$950$		0			0
$951$	12864.0			0.438637
$952$	−872.954	+	1008.00i	−0.0297191	+	0.0343167i
$953$		−	31062.0i		−	1.05582i	−0.849300	−	0.527910i	$-0.822976\pi$
$953$		−	31062.0i		−	1.05582i	0.849300	−	0.527910i	$-0.177024\pi$
$954$	−3432.00	+	5944.40i	−0.116473	+	0.201737i
$955$		0			0
$956$	−8610.00	−	14913.0i	−0.291284	−	0.504518i
$957$	−13094.3	−	7560.00i	−0.442298	−	0.255361i
$958$		−	12066.0i		−	0.406926i
$959$	−22218.0	−	19241.4i	−0.748130	−	0.647900i
$960$		0			0
$961$	2883.00	−	4993.50i	0.0967742	−	0.167618i
$962$	803.672	−	464.000i	0.0269349	−	0.0155509i
$963$	−16061.3	+	9273.00i	−0.537454	+	0.310299i
$964$	−1964.00	+	3401.75i	−0.0656184	+	0.113654i
$965$		0			0
$966$	924.000	−	4801.24i	0.0307756	−	0.159915i
$967$			44951.0i			1.49486i	0.664342	+	0.747428i	$0.268712\pi$
$967$			44951.0i			1.49486i	−0.664342	+	0.747428i	$0.731288\pi$
$968$	2986.06	+	1724.00i	0.0991482	+	0.0572432i
$969$	−1584.00	−	2743.57i	−0.0525133	−	0.0909557i
$970$		0			0
$971$	−23475.0	+	40659.9i	−0.775848	+	1.34381i	0.158468	+	0.987364i	$0.449344\pi$
$971$	−23475.0	+	40659.9i	−0.775848	+	1.34381i	−0.934317	+	0.356444i	$0.883989\pi$
$972$			11440.0i			0.377508i
$973$	13591.4	+	39235.0i	0.447811	+	1.29272i
$974$	14674.0			0.482736
$975$		0			0
$976$	−2608.00	−	4517.19i	−0.0855328	−	0.148147i
$977$	−21535.5	+	12433.5i	−0.705200	+	0.407147i	−0.809281	−	0.587421i	$-0.800143\pi$
$977$	−21535.5	+	12433.5i	−0.705200	+	0.407147i	0.104081	+	0.994569i	$0.466810\pi$
$978$	20895.5	+	12064.0i	0.683193	+	0.394442i
$979$	26190.0			0.854991
$980$		0			0
$981$	−18040.0			−0.587128
$982$	22572.1	+	13032.0i	0.733507	+	0.423491i
$983$	−3221.61	+	1860.00i	−0.104531	+	0.0603507i	−0.551354	−	0.834271i	$-0.685889\pi$
$983$	−3221.61	+	1860.00i	−0.104531	+	0.0603507i	0.446823	+	0.894622i	$0.352555\pi$
$984$	6768.00	+	11722.5i	0.219264	+	0.379777i
$985$		0			0
$986$	−2268.00			−0.0732534
$987$	8220.31	+	23730.0i	0.265102	+	0.765283i
$988$		−	1408.00i		−	0.0453385i
$989$	−5610.00	+	9716.81i	−0.180372	+	0.312413i
$990$		0			0
$991$	−22469.5	−	38918.3i	−0.720249	−	1.24751i	−0.960900	−	0.276897i	$-0.910694\pi$
$991$	−22469.5	−	38918.3i	−0.720249	−	1.24751i	0.240650	−	0.970612i	$-0.422639\pi$
$992$	4295.49	+	2480.00i	0.137482	+	0.0793751i
$993$			17224.0i			0.550440i
$994$	−4347.00	+	22587.7i	−0.138711	+	0.720762i
$995$		0			0
$996$	1584.00	−	2743.57i	0.0503925	−	0.0872824i
$997$	17434.8	−	10066.0i	0.553828	−	0.319753i	−0.196837	−	0.980436i	$-0.563067\pi$
$997$	17434.8	−	10066.0i	0.553828	−	0.319753i	0.750664	+	0.660684i	$0.229734\pi$
$998$	−13485.7	+	7786.00i	−0.427739	+	0.246955i
$999$	−8816.00	+	15269.8i	−0.279205	+	0.483597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.c.149.2		4
5.2	odd	4		350.4.e.c.51.1	✓	2
5.3	odd	4		350.4.e.f.51.1	yes	2
5.4	even	2	inner	350.4.j.c.149.1		4
7.4	even	3	inner	350.4.j.c.249.1		4
35.2	odd	12		2450.4.a.z.1.1		1
35.4	even	6	inner	350.4.j.c.249.2		4
35.12	even	12		2450.4.a.bl.1.1		1
35.18	odd	12		350.4.e.f.151.1	yes	2
35.23	odd	12		2450.4.a.p.1.1		1
35.32	odd	12		350.4.e.c.151.1	yes	2
35.33	even	12		2450.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.c.51.1	✓	2	5.2	odd	4
350.4.e.c.151.1	yes	2	35.32	odd	12
350.4.e.f.51.1	yes	2	5.3	odd	4
350.4.e.f.151.1	yes	2	35.18	odd	12
350.4.j.c.149.1		4	5.4	even	2	inner
350.4.j.c.149.2		4	1.1	even	1	trivial
350.4.j.c.249.1		4	7.4	even	3	inner
350.4.j.c.249.2		4	35.4	even	6	inner
2450.4.a.f.1.1		1	35.33	even	12
2450.4.a.p.1.1		1	35.23	odd	12
2450.4.a.z.1.1		1	35.2	odd	12
2450.4.a.bl.1.1		1	35.12	even	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(-3.46410 + 2.00000i) q^{3} +(2.00000 + 3.46410i) q^{4} -8.00000 q^{6} +(6.06218 + 17.5000i) q^{7} +8.00000i q^{8} +(-5.50000 + 9.52628i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(-3.46410 + 2.00000i) q^{3} +(2.00000 + 3.46410i) q^{4} -8.00000 q^{6} +(6.06218 + 17.5000i) q^{7} +8.00000i q^{8} +(-5.50000 + 9.52628i) q^{9} +(-15.0000 - 25.9808i) q^{11} +(-13.8564 - 8.00000i) q^{12} +4.00000i q^{13} +(-7.00000 + 36.3731i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(7.79423 - 4.50000i) q^{17} +(-19.0526 + 11.0000i) q^{18} +(-44.0000 + 76.2102i) q^{19} +(-56.0000 - 48.4974i) q^{21} -60.0000i q^{22} +(28.5788 + 16.5000i) q^{23} +(-16.0000 - 27.7128i) q^{24} +(-4.00000 + 6.92820i) q^{26} -152.000i q^{27} +(-48.4974 + 56.0000i) q^{28} -126.000 q^{29} +(-77.5000 - 134.234i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(103.923 + 60.0000i) q^{33} +18.0000 q^{34} -44.0000 q^{36} +(-100.459 - 58.0000i) q^{37} +(-152.420 + 88.0000i) q^{38} +(-8.00000 - 13.8564i) q^{39} -423.000 q^{41} +(-48.4974 - 140.000i) q^{42} +340.000i q^{43} +(60.0000 - 103.923i) q^{44} +(33.0000 + 57.1577i) q^{46} +(-293.583 - 169.500i) q^{47} -64.0000i q^{48} +(-269.500 + 212.176i) q^{49} +(-18.0000 + 31.1769i) q^{51} +(-13.8564 + 8.00000i) q^{52} +(270.200 - 156.000i) q^{53} +(152.000 - 263.272i) q^{54} +(-140.000 + 48.4974i) q^{56} -352.000i q^{57} +(-218.238 - 126.000i) q^{58} +(-231.000 - 400.104i) q^{59} +(-163.000 + 282.324i) q^{61} -310.000i q^{62} +(-200.052 - 38.5000i) q^{63} -64.0000 q^{64} +(120.000 + 207.846i) q^{66} +(609.682 - 352.000i) q^{67} +(31.1769 + 18.0000i) q^{68} -132.000 q^{69} +621.000 q^{71} +(-76.2102 - 44.0000i) q^{72} +(216.506 - 125.000i) q^{73} +(-116.000 - 200.918i) q^{74} -352.000 q^{76} +(363.731 - 420.000i) q^{77} -32.0000i q^{78} +(-552.500 + 956.958i) q^{79} +(155.500 + 269.334i) q^{81} +(-732.657 - 423.000i) q^{82} +198.000i q^{83} +(56.0000 - 290.985i) q^{84} +(-340.000 + 588.897i) q^{86} +(436.477 - 252.000i) q^{87} +(207.846 - 120.000i) q^{88} +(-436.500 + 756.040i) q^{89} +(-70.0000 + 24.2487i) q^{91} +132.000i q^{92} +(536.936 + 310.000i) q^{93} +(-339.000 - 587.165i) q^{94} +(64.0000 - 110.851i) q^{96} +905.000i q^{97} +(-678.964 + 98.0000i) q^{98} +330.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 32 q^{6} - 22 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 32 * q^6 - 22 * q^9	\( 4 q + 8 q^{4} - 32 q^{6} - 22 q^{9} - 60 q^{11} - 28 q^{14} - 32 q^{16} - 176 q^{19} - 224 q^{21} - 64 q^{24} - 16 q^{26} - 504 q^{29} - 310 q^{31} + 72 q^{34} - 176 q^{36} - 32 q^{39} - 1692 q^{41} + 240 q^{44} + 132 q^{46} - 1078 q^{49} - 72 q^{51} + 608 q^{54} - 560 q^{56} - 924 q^{59} - 652 q^{61} - 256 q^{64} + 480 q^{66} - 528 q^{69} + 2484 q^{71} - 464 q^{74} - 1408 q^{76} - 2210 q^{79} + 622 q^{81} + 224 q^{84} - 1360 q^{86} - 1746 q^{89} - 280 q^{91} - 1356 q^{94} + 256 q^{96} + 1320 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 - 32 * q^6 - 22 * q^9 - 60 * q^11 - 28 * q^14 - 32 * q^16 - 176 * q^19 - 224 * q^21 - 64 * q^24 - 16 * q^26 - 504 * q^29 - 310 * q^31 + 72 * q^34 - 176 * q^36 - 32 * q^39 - 1692 * q^41 + 240 * q^44 + 132 * q^46 - 1078 * q^49 - 72 * q^51 + 608 * q^54 - 560 * q^56 - 924 * q^59 - 652 * q^61 - 256 * q^64 + 480 * q^66 - 528 * q^69 + 2484 * q^71 - 464 * q^74 - 1408 * q^76 - 2210 * q^79 + 622 * q^81 + 224 * q^84 - 1360 * q^86 - 1746 * q^89 - 280 * q^91 - 1356 * q^94 + 256 * q^96 + 1320 * q^99

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