LMFDB - Embedded newform 300.3.c.d.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.c (of order $2$, degree $1$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.1
Root			$1.04064 + 0.957636i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.d.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 + 2.61185i) q^{4} +(-1.20651 + 3.24721i) q^{6} +5.46770i q^{7} +(-3.86039 - 7.00695i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 + 2.61185i) q^{4} +(-1.20651 + 3.24721i) q^{6} +5.46770i q^{7} +(-3.86039 - 7.00695i) q^{8} -3.00000 q^{9} -11.0403i q^{11} +(4.52386 - 5.24735i) q^{12} -10.1242 q^{13} +(3.80867 - 10.2507i) q^{14} +(2.35649 + 15.8255i) q^{16} +24.4146 q^{17} +(5.62432 + 2.08973i) q^{18} -23.7757i q^{19} +9.47033 q^{21} +(-7.69043 + 20.6981i) q^{22} -37.2526i q^{23} +(-12.1364 + 6.68640i) q^{24} +(18.9806 + 7.05227i) q^{26} +5.19615i q^{27} +(-14.2808 + 16.5647i) q^{28} -25.7726 q^{29} +4.83647i q^{31} +(6.60580 - 31.3108i) q^{32} -19.1224 q^{33} +(-45.7719 - 17.0066i) q^{34} +(-9.08868 - 7.83555i) q^{36} -35.6493 q^{37} +(-16.5616 + 44.5741i) q^{38} +17.5356i q^{39} -9.30410 q^{41} +(-17.7547 - 6.59682i) q^{42} -70.0287i q^{43} +(28.8356 - 33.4473i) q^{44} +(-25.9493 + 69.8401i) q^{46} -38.0223i q^{47} +(27.4106 - 4.08156i) q^{48} +19.1043 q^{49} -42.2873i q^{51} +(-30.6718 - 26.4428i) q^{52} -55.7762 q^{53} +(3.61952 - 9.74162i) q^{54} +(38.3119 - 21.1075i) q^{56} -41.1808 q^{57} +(48.3179 + 17.9526i) q^{58} -55.5411i q^{59} -82.2412 q^{61} +(3.36897 - 9.06729i) q^{62} -16.4031i q^{63} +(-34.1947 + 54.0992i) q^{64} +(35.8502 + 13.3202i) q^{66} +104.493i q^{67} +(73.9656 + 63.7673i) q^{68} -64.5233 q^{69} -76.7471i q^{71} +(11.5812 + 21.0209i) q^{72} +93.5215 q^{73} +(66.8344 + 24.8325i) q^{74} +(62.0986 - 72.0300i) q^{76} +60.3651 q^{77} +(12.2149 - 32.8753i) q^{78} +49.3762i q^{79} +9.00000 q^{81} +(17.4431 + 6.48102i) q^{82} +72.3768i q^{83} +(28.6910 + 24.7351i) q^{84} +(-48.7804 + 131.288i) q^{86} +44.6395i q^{87} +(-77.3589 + 42.6199i) q^{88} +115.691 q^{89} -55.3560i q^{91} +(97.2980 - 112.859i) q^{92} +8.37701 q^{93} +(-26.4854 + 71.2832i) q^{94} +(-54.2318 - 11.4416i) q^{96} +72.9589 q^{97} +(-35.8162 - 13.3076i) q^{98} +33.1209i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.87477	−	0.696577i	−0.937387	−	0.348288i
$2$	−1.87477	−	0.696577i	−0.937387	−	0.348288i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.02956	+	2.61185i	0.757390	+	0.652962i
$5$		0			0
$5$		0			0
$6$	−1.20651	+	3.24721i	−0.201084	+	0.541201i
$7$			5.46770i			0.781100i	0.920582	+	0.390550i	$0.127715\pi$
$7$			5.46770i			0.781100i	−0.920582	+	0.390550i	$0.872285\pi$
$8$	−3.86039	−	7.00695i	−0.482549	−	0.875869i
$9$	−3.00000			−0.333333
$10$		0			0
$11$		−	11.0403i		−	1.00366i	−0.864965	−	0.501832i	$-0.832659\pi$
$11$		−	11.0403i		−	1.00366i	0.864965	−	0.501832i	$-0.167341\pi$
$12$	4.52386	−	5.24735i	0.376988	−	0.437280i
$13$	−10.1242			−0.778784			−0.389392	−	0.921072i	$-0.627315\pi$
$13$	−10.1242			−0.778784			−0.389392	+	0.921072i	$0.627315\pi$
$14$	3.80867	−	10.2507i	0.272048	−	0.732193i
$15$		0			0
$16$	2.35649	+	15.8255i	0.147280	+	0.989095i
$17$	24.4146			1.43615			0.718077	−	0.695964i	$-0.245023\pi$
$17$	24.4146			1.43615			0.718077	+	0.695964i	$0.245023\pi$
$18$	5.62432	+	2.08973i	0.312462	+	0.116096i
$19$		−	23.7757i		−	1.25135i	−0.780082	−	0.625677i	$-0.784823\pi$
$19$		−	23.7757i		−	1.25135i	0.780082	−	0.625677i	$-0.215177\pi$
$20$		0			0
$21$	9.47033			0.450968
$22$	−7.69043	+	20.6981i	−0.349565	+	0.940823i
$23$		−	37.2526i		−	1.61968i	−0.586653	−	0.809838i	$-0.699555\pi$
$23$		−	37.2526i		−	1.61968i	0.586653	−	0.809838i	$-0.300445\pi$
$24$	−12.1364	+	6.68640i	−0.505683	+	0.278600i
$25$		0			0
$26$	18.9806	+	7.05227i	0.730022	+	0.271241i
$27$			5.19615i			0.192450i
$28$	−14.2808	+	16.5647i	−0.510029	+	0.591598i
$29$	−25.7726			−0.888712			−0.444356	−	0.895850i	$-0.646567\pi$
$29$	−25.7726			−0.888712			−0.444356	+	0.895850i	$0.646567\pi$
$30$		0			0
$31$			4.83647i			0.156015i	0.996953	+	0.0780076i	$0.0248558\pi$
$31$			4.83647i			0.156015i	−0.996953	+	0.0780076i	$0.975144\pi$
$32$	6.60580	−	31.3108i	0.206431	−	0.978461i
$33$	−19.1224			−0.579466
$34$	−45.7719	−	17.0066i	−1.34623	−	0.500196i
$35$		0			0
$36$	−9.08868	−	7.83555i	−0.252463	−	0.217654i
$37$	−35.6493			−0.963495			−0.481747	−	0.876310i	$-0.659998\pi$
$37$	−35.6493			−0.963495			−0.481747	+	0.876310i	$0.659998\pi$
$38$	−16.5616	+	44.5741i	−0.435832	+	1.17300i
$39$			17.5356i			0.449631i
$40$		0			0
$41$	−9.30410			−0.226929			−0.113465	−	0.993542i	$-0.536195\pi$
$41$	−9.30410			−0.226929			−0.113465	+	0.993542i	$0.536195\pi$
$42$	−17.7547	−	6.59682i	−0.422732	−	0.157067i
$43$		−	70.0287i		−	1.62857i	−0.580462	−	0.814287i	$-0.697128\pi$
$43$		−	70.0287i		−	1.62857i	0.580462	−	0.814287i	$-0.302872\pi$
$44$	28.8356	−	33.4473i	0.655355	−	0.760166i
$45$		0			0
$46$	−25.9493	+	69.8401i	−0.564114	+	1.51826i
$47$		−	38.0223i		−	0.808984i	−0.914542	−	0.404492i	$-0.867448\pi$
$47$		−	38.0223i		−	0.808984i	0.914542	−	0.404492i	$-0.132552\pi$
$48$	27.4106	−	4.08156i	0.571054	−	0.0850324i
$49$	19.1043			0.389883
$50$		0			0
$51$		−	42.2873i		−	0.829164i
$52$	−30.6718	−	26.4428i	−0.589843	−	0.508516i
$53$	−55.7762			−1.05238			−0.526191	−	0.850366i	$-0.676380\pi$
$53$	−55.7762			−1.05238			−0.526191	+	0.850366i	$0.676380\pi$
$54$	3.61952	−	9.74162i	0.0670281	−	0.180400i
$55$		0			0
$56$	38.3119	−	21.1075i	0.684141	−	0.376919i
$57$	−41.1808			−0.722470
$58$	48.3179	+	17.9526i	0.833067	+	0.309528i
$59$		−	55.5411i		−	0.941374i	−0.882300	−	0.470687i	$-0.844006\pi$
$59$		−	55.5411i		−	0.941374i	0.882300	−	0.470687i	$-0.155994\pi$
$60$		0			0
$61$	−82.2412			−1.34822			−0.674108	−	0.738633i	$-0.735472\pi$
$61$	−82.2412			−1.34822			−0.674108	+	0.738633i	$0.735472\pi$
$62$	3.36897	−	9.06729i	0.0543383	−	0.146247i
$63$		−	16.4031i		−	0.260367i
$64$	−34.1947	+	54.0992i	−0.534293	+	0.845299i
$65$		0			0
$66$	35.8502	+	13.3202i	0.543184	+	0.201821i
$67$			104.493i			1.55960i	0.626026	+	0.779802i	$0.284680\pi$
$67$			104.493i			1.55960i	−0.626026	+	0.779802i	$0.715320\pi$
$68$	73.9656	+	63.7673i	1.08773	+	0.937754i
$69$	−64.5233			−0.935120
$70$		0			0
$71$		−	76.7471i		−	1.08094i	−0.841362	−	0.540472i	$-0.818246\pi$
$71$		−	76.7471i		−	1.08094i	0.841362	−	0.540472i	$-0.181754\pi$
$72$	11.5812	+	21.0209i	0.160850	+	0.291956i
$73$	93.5215			1.28112			0.640558	−	0.767910i	$-0.278703\pi$
$73$	93.5215			1.28112			0.640558	+	0.767910i	$0.278703\pi$
$74$	66.8344	+	24.8325i	0.903168	+	0.335574i
$75$		0			0
$76$	62.0986	−	72.0300i	0.817087	−	0.947764i
$77$	60.3651			0.783963
$78$	12.2149	−	32.8753i	0.156601	−	0.421478i
$79$			49.3762i			0.625016i	0.949915	+	0.312508i	$0.101169\pi$
$79$			49.3762i			0.625016i	−0.949915	+	0.312508i	$0.898831\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	17.4431	+	6.48102i	0.212721	+	0.0790368i
$83$			72.3768i			0.872010i	0.899944	+	0.436005i	$0.143607\pi$
$83$			72.3768i			0.872010i	−0.899944	+	0.436005i	$0.856393\pi$
$84$	28.6910	+	24.7351i	0.341559	+	0.294465i
$85$		0			0
$86$	−48.7804	+	131.288i	−0.567214	+	1.52661i
$87$			44.6395i			0.513098i
$88$	−77.3589	+	42.6199i	−0.879079	+	0.484318i
$89$	115.691			1.29990			0.649950	−	0.759977i	$-0.274790\pi$
$89$	115.691			1.29990			0.649950	+	0.759977i	$0.274790\pi$
$90$		0			0
$91$		−	55.3560i		−	0.608308i
$92$	97.2980	−	112.859i	1.05759	−	1.22673i
$93$	8.37701			0.0900754
$94$	−26.4854	+	71.2832i	−0.281760	+	0.758332i
$95$		0			0
$96$	−54.2318	−	11.4416i	−0.564915	−	0.119183i
$97$	72.9589			0.752154			0.376077	−	0.926588i	$-0.377273\pi$
$97$	72.9589			0.752154			0.376077	+	0.926588i	$0.377273\pi$
$98$	−35.8162	−	13.3076i	−0.365471	−	0.135792i
$99$			33.1209i			0.334555i
$100$		0			0
$101$	29.4092			0.291180			0.145590	−	0.989345i	$-0.453492\pi$
$101$	29.4092			0.291180			0.145590	+	0.989345i	$0.453492\pi$
$102$	−29.4564	+	79.2792i	−0.288788	+	0.777247i
$103$		−	28.1884i		−	0.273673i	−0.990594	−	0.136837i	$-0.956306\pi$
$103$		−	28.1884i		−	0.273673i	0.990594	−	0.136837i	$-0.0436935\pi$
$104$	39.0833	+	70.9397i	0.375801	+	0.682112i
$105$		0			0
$106$	104.568	+	38.8524i	0.986490	+	0.366532i
$107$		−	4.50700i		−	0.0421215i	−0.999778	−	0.0210607i	$-0.993296\pi$
$107$		−	4.50700i		−	0.0421215i	0.999778	−	0.0210607i	$-0.00670434\pi$
$108$	−13.5716	+	15.7421i	−0.125663	+	0.145760i
$109$	193.315			1.77353			0.886767	−	0.462217i	$-0.152946\pi$
$109$	193.315			1.77353			0.886767	+	0.462217i	$0.152946\pi$
$110$		0			0
$111$			61.7464i			0.556274i
$112$	−86.5292	+	12.8846i	−0.772582	+	0.115041i
$113$	−75.5727			−0.668785			−0.334392	−	0.942434i	$-0.608531\pi$
$113$	−75.5727			−0.668785			−0.334392	+	0.942434i	$0.608531\pi$
$114$	77.2047	+	28.6856i	0.677234	+	0.251628i
$115$		0			0
$116$	−78.0798	−	67.3142i	−0.673102	−	0.580295i
$117$	30.3726			0.259595
$118$	−38.6886	+	104.127i	−0.327870	+	0.882432i
$119$			133.492i			1.12178i
$120$		0			0
$121$	−0.888544			−0.00734334
$122$	154.184	+	57.2873i	1.26380	+	0.469568i
$123$			16.1152i			0.131018i
$124$	−12.6321	+	14.6524i	−0.101872	+	0.118164i
$125$		0			0
$126$	−11.4260	+	30.7521i	−0.0906827	+	0.244064i
$127$		−	131.306i		−	1.03390i	−0.856015	−	0.516951i	$-0.827067\pi$
$127$		−	131.306i		−	1.03390i	0.856015	−	0.516951i	$-0.172933\pi$
$128$	101.792	−	77.6045i	0.795247	−	0.606285i
$129$	−121.293			−0.940258
$130$		0			0
$131$			75.7533i			0.578270i	0.957288	+	0.289135i	$0.0933676\pi$
$131$			75.7533i			0.578270i	−0.957288	+	0.289135i	$0.906632\pi$
$132$	−57.9324	−	49.9448i	−0.438882	−	0.378370i
$133$	129.999			0.977433
$134$	72.7877	−	195.902i	0.543192	−	1.46195i
$135$		0			0
$136$	−94.2500	−	171.072i	−0.693014	−	1.25788i
$137$	−66.7927			−0.487538			−0.243769	−	0.969833i	$-0.578384\pi$
$137$	−66.7927			−0.487538			−0.243769	+	0.969833i	$0.578384\pi$
$138$	120.967	+	44.9454i	0.876570	+	0.325692i
$139$		−	38.1214i		−	0.274255i	−0.990553	−	0.137127i	$-0.956213\pi$
$139$		−	38.1214i		−	0.274255i	0.990553	−	0.137127i	$-0.0437869\pi$
$140$		0			0
$141$	−65.8565			−0.467067
$142$	−53.4602	+	143.884i	−0.376481	+	1.01326i
$143$			111.774i			0.781638i
$144$	−7.06946	−	47.4765i	−0.0490935	−	0.329698i
$145$		0			0
$146$	−175.332	−	65.1449i	−1.20090	−	0.446198i
$147$		−	33.0895i		−	0.225099i
$148$	−108.002	−	93.1106i	−0.729742	−	0.629126i
$149$	−126.717			−0.850449			−0.425225	−	0.905088i	$-0.639805\pi$
$149$	−126.717			−0.850449			−0.425225	+	0.905088i	$0.639805\pi$
$150$		0			0
$151$			68.4403i			0.453247i	0.973982	+	0.226623i	$0.0727687\pi$
$151$			68.4403i			0.453247i	−0.973982	+	0.226623i	$0.927231\pi$
$152$	−166.595	+	91.7836i	−1.09602	+	0.603840i
$153$	−73.2438			−0.478718
$154$	−113.171	−	42.0489i	−0.734877	−	0.273045i
$155$		0			0
$156$	−45.8004	+	53.1252i	−0.293592	+	0.340546i
$157$	−25.5777			−0.162915			−0.0814577	−	0.996677i	$-0.525958\pi$
$157$	−25.5777			−0.162915			−0.0814577	+	0.996677i	$0.525958\pi$
$158$	34.3943	−	92.5693i	0.217686	−	0.585882i
$159$			96.6073i			0.607593i
$160$		0			0
$161$	203.686			1.26513
$162$	−16.8730	−	6.26919i	−0.104154	−	0.0386987i
$163$			63.4771i			0.389430i	0.980860	+	0.194715i	$0.0623782\pi$
$163$			63.4771i			0.389430i	−0.980860	+	0.194715i	$0.937622\pi$
$164$	−28.1873	−	24.3009i	−0.171874	−	0.148176i
$165$		0			0
$166$	50.4160	−	135.690i	0.303711	−	0.817411i
$167$			12.3771i			0.0741144i	0.999313	+	0.0370572i	$0.0117984\pi$
$167$			12.3771i			0.0741144i	−0.999313	+	0.0370572i	$0.988202\pi$
$168$	−36.5592	−	66.3582i	−0.217614	−	0.394989i
$169$	−66.5008			−0.393496
$170$		0			0
$171$			71.3272i			0.417118i
$172$	182.904	−	212.156i	1.06340	−	1.23347i
$173$	−59.3729			−0.343196			−0.171598	−	0.985167i	$-0.554893\pi$
$173$	−59.3729			−0.343196			−0.171598	+	0.985167i	$0.554893\pi$
$174$	31.0948	−	83.6890i	0.178706	−	0.480971i
$175$		0			0
$176$	174.719	−	26.0164i	0.992720	−	0.147820i
$177$	−96.2000			−0.543503
$178$	−216.895	−	80.5877i	−1.21851	−	0.452740i
$179$		−	252.782i		−	1.41219i	−0.708118	−	0.706094i	$-0.750455\pi$
$179$		−	252.782i		−	1.41219i	0.708118	−	0.706094i	$-0.249545\pi$
$180$		0			0
$181$	125.373			0.692670			0.346335	−	0.938111i	$-0.387426\pi$
$181$	125.373			0.692670			0.346335	+	0.938111i	$0.387426\pi$
$182$	−38.5597	+	103.780i	−0.211867	+	0.570220i
$183$			142.446i			0.778393i
$184$	−261.027	+	143.809i	−1.41862	+	0.781573i
$185$		0			0
$186$	−15.7050	−	5.83523i	−0.0844355	−	0.0313722i
$187$		−	269.545i		−	1.44142i
$188$	99.3084	−	115.191i	0.528236	−	0.612717i
$189$	−28.4110			−0.150323
$190$		0			0
$191$			97.4640i			0.510283i	0.966904	+	0.255141i	$0.0821220\pi$
$191$			97.4640i			0.510283i	−0.966904	+	0.255141i	$0.917878\pi$
$192$	93.7025	+	59.2270i	0.488034	+	0.308474i
$193$	342.376			1.77397			0.886985	−	0.461798i	$-0.152796\pi$
$193$	342.376			1.77397			0.886985	+	0.461798i	$0.152796\pi$
$194$	−136.782	−	50.8215i	−0.705060	−	0.261966i
$195$		0			0
$196$	57.8775	+	49.8974i	0.295293	+	0.254579i
$197$	−74.4829			−0.378086			−0.189043	−	0.981969i	$-0.560539\pi$
$197$	−74.4829			−0.378086			−0.189043	+	0.981969i	$0.560539\pi$
$198$	23.0713	−	62.0943i	0.116522	−	0.313608i
$199$		−	178.027i		−	0.894606i	−0.894382	−	0.447303i	$-0.852385\pi$
$199$		−	178.027i		−	0.894606i	0.894382	−	0.447303i	$-0.147615\pi$
$200$		0			0
$201$	180.988			0.900438
$202$	−55.1356	−	20.4858i	−0.272949	−	0.101415i
$203$		−	140.917i		−	0.694173i
$204$	110.448	−	128.112i	0.541413	−	0.628000i
$205$		0			0
$206$	−19.6354	+	52.8468i	−0.0953172	+	0.256538i
$207$			111.758i			0.539892i
$208$	−23.8575	−	160.220i	−0.114700	−	0.770291i
$209$	−262.491			−1.25594
$210$		0			0
$211$			185.893i			0.881008i	0.897751	+	0.440504i	$0.145200\pi$
$211$			185.893i			0.881008i	−0.897751	+	0.440504i	$0.854800\pi$
$212$	−168.978	−	145.679i	−0.797064	−	0.687166i
$213$	−132.930			−0.624084
$214$	−3.13947	+	8.44961i	−0.0146704	+	0.0394842i
$215$		0			0
$216$	36.4092	−	20.0592i	0.168561	−	0.0928666i
$217$	−26.4444			−0.121863
$218$	−362.422	−	134.659i	−1.66249	−	0.617701i
$219$		−	161.984i		−	0.739653i
$220$		0			0
$221$	−247.178			−1.11845
$222$	43.0111	−	115.761i	0.193744	−	0.521444i
$223$			202.724i			0.909074i	0.890728	+	0.454537i	$0.150195\pi$
$223$			202.724i			0.909074i	−0.890728	+	0.454537i	$0.849805\pi$
$224$	171.198	+	36.1186i	0.764276	+	0.161244i
$225$		0			0
$226$	141.682	+	52.6422i	0.626910	+	0.232930i
$227$			51.2708i			0.225863i	0.993603	+	0.112931i	$0.0360240\pi$
$227$			51.2708i			0.225863i	−0.993603	+	0.112931i	$0.963976\pi$
$228$	−124.760	−	107.558i	−0.547192	−	0.471745i
$229$	337.056			1.47186			0.735930	−	0.677058i	$-0.236745\pi$
$229$	337.056			1.47186			0.735930	+	0.677058i	$0.236745\pi$
$230$		0			0
$231$		−	104.555i		−	0.452621i
$232$	99.4925	+	180.588i	0.428847	+	0.778395i
$233$	80.2851			0.344571			0.172286	−	0.985047i	$-0.444885\pi$
$233$	80.2851			0.344571			0.172286	+	0.985047i	$0.444885\pi$
$234$	−56.9417	−	21.1568i	−0.243341	−	0.0904138i
$235$		0			0
$236$	145.065	−	168.265i	0.614682	−	0.712988i
$237$	85.5221			0.360853
$238$	92.9873	−	250.267i	0.390703	−	1.05154i
$239$			330.808i			1.38413i	0.721834	+	0.692066i	$0.243299\pi$
$239$			330.808i			1.38413i	−0.721834	+	0.692066i	$0.756701\pi$
$240$		0			0
$241$	−359.914			−1.49342			−0.746710	−	0.665150i	$-0.768368\pi$
$241$	−359.914			−1.49342			−0.746710	+	0.665150i	$0.768368\pi$
$242$	1.66582	+	0.618939i	0.00688355	+	0.00255760i
$243$		−	15.5885i		−	0.0641500i
$244$	−249.155	−	214.802i	−1.02113	−	0.880334i
$245$		0			0
$246$	11.2255	−	30.2123i	0.0456319	−	0.122814i
$247$			240.710i			0.974534i
$248$	33.8889	−	18.6707i	0.136649	−	0.0752850i
$249$	125.360			0.503455
$250$		0			0
$251$			312.213i			1.24388i	0.783067	+	0.621938i	$0.213654\pi$
$251$			312.213i			1.24388i	−0.783067	+	0.621938i	$0.786346\pi$
$252$	42.8424	−	49.6942i	0.170010	−	0.197199i
$253$	−411.280			−1.62561
$254$	−91.4645	+	246.169i	−0.360096	+	0.969167i
$255$		0			0
$256$	−244.894	+	74.5853i	−0.956617	+	0.291349i
$257$	−80.2592			−0.312293			−0.156146	−	0.987734i	$-0.549907\pi$
$257$	−80.2592			−0.312293			−0.156146	+	0.987734i	$0.549907\pi$
$258$	227.398	+	84.4901i	0.881386	+	0.327481i
$259$		−	194.920i		−	0.752586i
$260$		0			0
$261$	77.3179			0.296237
$262$	52.7680	−	142.020i	0.201405	−	0.542063i
$263$			487.967i			1.85539i	0.373342	+	0.927694i	$0.378212\pi$
$263$			487.967i			1.85539i	−0.373342	+	0.927694i	$0.621788\pi$
$264$	73.8199	+	133.990i	0.279621	+	0.507536i
$265$		0			0
$266$	−243.718	−	90.5540i	−0.916233	−	0.340428i
$267$		−	200.383i		−	0.750498i
$268$	−272.921	+	316.569i	−1.01836	+	1.18123i
$269$	−309.553			−1.15076			−0.575378	−	0.817888i	$-0.695145\pi$
$269$	−309.553			−1.15076			−0.575378	+	0.817888i	$0.695145\pi$
$270$		0			0
$271$			48.9693i			0.180698i	0.995910	+	0.0903492i	$0.0287983\pi$
$271$			48.9693i			0.180698i	−0.995910	+	0.0903492i	$0.971202\pi$
$272$	57.5327	+	386.374i	0.211517	+	1.42049i
$273$	−95.8794			−0.351207
$274$	125.221	+	46.5262i	0.457012	+	0.169804i
$275$		0			0
$276$	−195.477	−	168.525i	−0.708251	−	0.610598i
$277$	199.644			0.720736			0.360368	−	0.932810i	$-0.382651\pi$
$277$	199.644			0.720736			0.360368	+	0.932810i	$0.382651\pi$
$278$	−26.5545	+	71.4690i	−0.0955197	+	0.257083i
$279$		−	14.5094i		−	0.0520051i
$280$		0			0
$281$	61.1598			0.217650			0.108825	−	0.994061i	$-0.465291\pi$
$281$	61.1598			0.217650			0.108825	+	0.994061i	$0.465291\pi$
$282$	123.466	+	45.8741i	0.437823	+	0.162674i
$283$		−	432.506i		−	1.52829i	−0.645044	−	0.764145i	$-0.723161\pi$
$283$		−	432.506i		−	1.52829i	0.645044	−	0.764145i	$-0.276839\pi$
$284$	200.452	−	232.510i	0.705816	−	0.818697i
$285$		0			0
$286$	77.8593	−	209.551i	0.272235	−	0.732697i
$287$		−	50.8720i		−	0.177254i
$288$	−19.8174	+	93.9323i	−0.0688105	+	0.326154i
$289$	307.073			1.06254
$290$		0			0
$291$		−	126.369i		−	0.434256i
$292$	283.329	+	244.264i	0.970305	+	0.836521i
$293$	283.234			0.966668			0.483334	−	0.875436i	$-0.339426\pi$
$293$	283.234			0.966668			0.483334	+	0.875436i	$0.339426\pi$
$294$	−23.0494	+	62.0354i	−0.0783993	+	0.211005i
$295$		0			0
$296$	137.620	+	249.793i	0.464933	+	0.843895i
$297$	57.3672			0.193155
$298$	237.566	+	88.2681i	0.797200	+	0.296202i
$299$			377.152i			1.26138i
$300$		0			0
$301$	382.896			1.27208
$302$	47.6739	−	128.310i	0.157861	−	0.424868i
$303$		−	50.9382i		−	0.168113i
$304$	376.263	−	56.0272i	1.23771	−	0.184300i
$305$		0			0
$306$	137.316	+	51.0199i	0.448744	+	0.166732i
$307$			100.077i			0.325983i	0.986627	+	0.162992i	$0.0521144\pi$
$307$			100.077i			0.325983i	−0.986627	+	0.162992i	$0.947886\pi$
$308$	182.880	+	157.665i	0.593766	+	0.511898i
$309$	−48.8237			−0.158005
$310$		0			0
$311$		−	404.185i		−	1.29963i	−0.760092	−	0.649815i	$-0.774846\pi$
$311$		−	404.185i		−	1.29963i	0.760092	−	0.649815i	$-0.225154\pi$
$312$	122.871	−	67.6943i	0.393818	−	0.216969i
$313$	128.579			0.410795			0.205398	−	0.978679i	$-0.434151\pi$
$313$	128.579			0.410795			0.205398	+	0.978679i	$0.434151\pi$
$314$	47.9525	+	17.8168i	0.152715	+	0.0567415i
$315$		0			0
$316$	−128.963	+	149.588i	−0.408112	+	0.473381i
$317$	−85.9315			−0.271077			−0.135539	−	0.990772i	$-0.543276\pi$
$317$	−85.9315			−0.271077			−0.135539	+	0.990772i	$0.543276\pi$
$318$	67.2944	−	181.117i	0.211618	−	0.569550i
$319$			284.538i			0.891969i
$320$		0			0
$321$	−7.80635			−0.0243189
$322$	−381.865	−	141.883i	−1.18592	−	0.440630i
$323$		−	580.475i		−	1.79714i
$324$	27.2661	+	23.5066i	0.0841545	+	0.0725514i
$325$		0			0
$326$	44.2167	−	119.005i	0.135634	−	0.365047i
$327$		−	334.832i		−	1.02395i
$328$	35.9175	+	65.1934i	0.109505	+	0.198760i
$329$	207.894			0.631898
$330$		0			0
$331$			183.391i			0.554052i	0.960862	+	0.277026i	$0.0893488\pi$
$331$			183.391i			0.554052i	−0.960862	+	0.277026i	$0.910651\pi$
$332$	−189.037	+	219.270i	−0.569390	+	0.660452i
$333$	106.948			0.321165
$334$	8.62160	−	23.2043i	0.0258132	−	0.0694739i
$335$		0			0
$336$	22.3167	+	149.873i	0.0664188	+	0.446050i
$337$	−168.130			−0.498901			−0.249451	−	0.968388i	$-0.580250\pi$
$337$	−168.130			−0.498901			−0.249451	+	0.968388i	$0.580250\pi$
$338$	124.674	+	46.3229i	0.368858	+	0.137050i
$339$			130.896i			0.386123i
$340$		0			0
$341$	53.3962			0.156587
$342$	49.6849	−	133.722i	0.145277	−	0.391001i
$343$			372.374i			1.08564i
$344$	−490.688	+	270.338i	−1.42642	+	0.785867i
$345$		0			0
$346$	111.311	+	41.3578i	0.321708	+	0.119531i
$347$			137.414i			0.396006i	0.980201	+	0.198003i	$0.0634455\pi$
$347$			137.414i			0.396006i	−0.980201	+	0.198003i	$0.936554\pi$
$348$	−116.592	+	135.238i	−0.335034	+	0.388615i
$349$	−13.4893			−0.0386513			−0.0193256	−	0.999813i	$-0.506152\pi$
$349$	−13.4893			−0.0386513			−0.0193256	+	0.999813i	$0.506152\pi$
$350$		0			0
$351$		−	52.6068i		−	0.149877i
$352$	−345.681	−	72.9301i	−0.982047	−	0.207188i
$353$	−243.547			−0.689935			−0.344968	−	0.938615i	$-0.612110\pi$
$353$	−243.547			−0.689935			−0.344968	+	0.938615i	$0.612110\pi$
$354$	180.353	+	67.0107i	0.509473	+	0.189296i
$355$		0			0
$356$	350.493	+	302.168i	0.984532	+	0.848786i
$357$	231.215			0.647660
$358$	−176.082	+	473.909i	−0.491849	+	1.32377i
$359$			17.9166i			0.0499068i	0.999689	+	0.0249534i	$0.00794374\pi$
$359$			17.9166i			0.0499068i	−0.999689	+	0.0249534i	$0.992056\pi$
$360$		0			0
$361$	−204.285			−0.565887
$362$	−235.047	−	87.3321i	−0.649300	−	0.241249i
$363$			1.53900i			0.00423968i
$364$	144.582	−	167.704i	0.397202	−	0.460727i
$365$		0			0
$366$	99.2245	−	267.054i	0.271105	−	0.729656i
$367$			238.417i			0.649637i	0.945776	+	0.324818i	$0.105303\pi$
$367$			238.417i			0.649637i	−0.945776	+	0.324818i	$0.894697\pi$
$368$	589.541	−	87.7852i	1.60201	−	0.238547i
$369$	27.9123			0.0756431
$370$		0			0
$371$		−	304.968i		−	0.822016i
$372$	25.3787	+	21.8795i	0.0682222	+	0.0588158i
$373$	181.271			0.485981			0.242990	−	0.970029i	$-0.421872\pi$
$373$	181.271			0.485981			0.242990	+	0.970029i	$0.421872\pi$
$374$	−187.759	+	505.336i	−0.502029	+	1.35117i
$375$		0			0
$376$	−266.420	+	146.781i	−0.708564	+	0.390375i
$377$	260.927			0.692114
$378$	53.2642	+	19.7904i	0.140911	+	0.0523557i
$379$		−	306.206i		−	0.807931i	−0.914774	−	0.403965i	$-0.867632\pi$
$379$		−	306.206i		−	0.807931i	0.914774	−	0.403965i	$-0.132368\pi$
$380$		0			0
$381$	−227.428			−0.596924
$382$	67.8912	−	182.723i	0.177726	−	0.478333i
$383$		−	144.027i		−	0.376050i	−0.982164	−	0.188025i	$-0.939791\pi$
$383$		−	144.027i		−	0.376050i	0.982164	−	0.188025i	$-0.0602086\pi$
$384$	−134.415	−	176.308i	−0.350039	−	0.459136i
$385$		0			0
$386$	−641.878	−	238.491i	−1.66290	−	0.617853i
$387$			210.086i			0.542858i
$388$	221.034	+	190.558i	0.569674	+	0.491128i
$389$	14.0099			0.0360152			0.0180076	−	0.999838i	$-0.494268\pi$
$389$	14.0099			0.0360152			0.0180076	+	0.999838i	$0.494268\pi$
$390$		0			0
$391$		−	909.506i		−	2.32610i
$392$	−73.7499	−	133.863i	−0.188138	−	0.341486i
$393$	131.209			0.333864
$394$	139.639	+	51.8831i	0.354413	+	0.131683i
$395$		0			0
$396$	−86.5069	+	100.342i	−0.218452	+	0.253389i
$397$	−39.1084			−0.0985098			−0.0492549	−	0.998786i	$-0.515685\pi$
$397$	−39.1084			−0.0985098			−0.0492549	+	0.998786i	$0.515685\pi$
$398$	−124.009	+	333.760i	−0.311581	+	0.838592i
$399$		−	225.164i		−	0.564321i
$400$		0			0
$401$	−121.067			−0.301913			−0.150957	−	0.988540i	$-0.548235\pi$
$401$	−121.067			−0.301913			−0.150957	+	0.988540i	$0.548235\pi$
$402$	−339.312	−	126.072i	−0.844059	−	0.313612i
$403$		−	48.9653i		−	0.121502i
$404$	89.0970	+	76.8124i	0.220537	+	0.190130i
$405$		0			0
$406$	−98.1595	+	264.188i	−0.241772	+	0.650709i
$407$			393.579i			0.967026i
$408$	−296.305	+	163.246i	−0.726239	+	0.400112i
$409$	−541.795			−1.32468			−0.662342	−	0.749202i	$-0.730437\pi$
$409$	−541.795			−1.32468			−0.662342	+	0.749202i	$0.730437\pi$
$410$		0			0
$411$			115.688i			0.281480i
$412$	73.6237	−	85.3983i	0.178698	−	0.207278i
$413$	303.682			0.735307
$414$	77.8478	−	209.520i	0.188038	−	0.506088i
$415$		0			0
$416$	−66.8784	+	316.996i	−0.160765	+	0.762009i
$417$	−66.0282			−0.158341
$418$	492.112	+	182.845i	1.17730	+	0.437429i
$419$		−	687.825i		−	1.64159i	−0.571224	−	0.820794i	$-0.693531\pi$
$419$		−	687.825i		−	1.64159i	0.571224	−	0.820794i	$-0.306469\pi$
$420$		0			0
$421$	−454.396			−1.07932			−0.539662	−	0.841882i	$-0.681448\pi$
$421$	−454.396			−1.07932			−0.539662	+	0.841882i	$0.681448\pi$
$422$	129.489	−	348.507i	0.306845	−	0.825846i
$423$			114.067i			0.269661i
$424$	215.318	+	390.821i	0.507826	+	0.921749i
$425$		0			0
$426$	249.214	+	92.5959i	0.585008	+	0.217361i
$427$		−	449.670i		−	1.05309i
$428$	11.7716	−	13.6542i	0.0275037	−	0.0319024i
$429$	193.599			0.451279
$430$		0			0
$431$		−	466.145i		−	1.08154i	−0.841169	−	0.540772i	$-0.818132\pi$
$431$		−	466.145i		−	1.08154i	0.841169	−	0.540772i	$-0.181868\pi$
$432$	−82.2318	+	12.2447i	−0.190351	+	0.0283441i
$433$	−457.094			−1.05565			−0.527823	−	0.849355i	$-0.676991\pi$
$433$	−457.094			−1.05565			−0.527823	+	0.849355i	$0.676991\pi$
$434$	49.5772	+	18.4205i	0.114233	+	0.0424436i
$435$		0			0
$436$	585.660	+	504.910i	1.34326	+	1.15805i
$437$	−885.706			−2.02679
$438$	−112.834	+	303.684i	−0.257613	+	0.693341i
$439$			777.467i			1.77100i	0.464644	+	0.885498i	$0.346182\pi$
$439$			777.467i			1.77100i	−0.464644	+	0.885498i	$0.653818\pi$
$440$		0			0
$441$	−57.3128			−0.129961
$442$	463.403	+	172.178i	1.04842	+	0.389544i
$443$		−	247.484i		−	0.558654i	−0.960196	−	0.279327i	$-0.909889\pi$
$443$		−	247.484i		−	0.558654i	0.960196	−	0.279327i	$-0.0901114\pi$
$444$	−161.272	+	187.065i	−0.363226	+	0.421316i
$445$		0			0
$446$	141.213	−	380.061i	0.316620	−	0.852155i
$447$			219.480i			0.491007i
$448$	−295.798	−	186.967i	−0.660263	−	0.417336i
$449$	412.508			0.918726			0.459363	−	0.888249i	$-0.348078\pi$
$449$	412.508			0.918726			0.459363	+	0.888249i	$0.348078\pi$
$450$		0			0
$451$			102.720i			0.227761i
$452$	−228.952	−	197.384i	−0.506531	−	0.436691i
$453$	118.542			0.261682
$454$	35.7141	−	96.1213i	0.0786654	−	0.211721i
$455$		0			0
$456$	158.974	+	288.552i	0.348627	+	0.632789i
$457$	745.400			1.63107			0.815537	−	0.578706i	$-0.196442\pi$
$457$	745.400			1.63107			0.815537	+	0.578706i	$0.196442\pi$
$458$	−631.904	−	234.785i	−1.37970	−	0.512631i
$459$			126.862i			0.276388i
$460$		0			0
$461$	81.6151			0.177039			0.0885196	−	0.996074i	$-0.471786\pi$
$461$	81.6151			0.177039			0.0885196	+	0.996074i	$0.471786\pi$
$462$	−72.8309	+	196.018i	−0.157643	+	0.424281i
$463$		−	292.248i		−	0.631205i	−0.948891	−	0.315603i	$-0.897793\pi$
$463$		−	292.248i		−	0.631205i	0.948891	−	0.315603i	$-0.102207\pi$
$464$	−60.7329	−	407.865i	−0.130890	−	0.879020i
$465$		0			0
$466$	−150.517	−	55.9248i	−0.322997	−	0.120010i
$467$			51.4163i			0.110099i	0.998484	+	0.0550495i	$0.0175317\pi$
$467$			51.4163i			0.110099i	−0.998484	+	0.0550495i	$0.982468\pi$
$468$	92.0155	+	79.3285i	0.196614	+	0.169505i
$469$	−571.339			−1.21821
$470$		0			0
$471$			44.3019i			0.0940592i
$472$	−389.174	+	214.410i	−0.824520	+	0.454259i
$473$	−773.139			−1.63454
$474$	−160.335	−	59.5727i	−0.338259	−	0.125681i
$475$		0			0
$476$	−348.660	+	404.422i	−0.732480	+	0.849625i
$477$	167.329			0.350794
$478$	230.433	−	620.190i	0.482077	−	1.29747i
$479$			122.593i			0.255935i	0.991778	+	0.127967i	$0.0408453\pi$
$479$			122.593i			0.255935i	−0.991778	+	0.127967i	$0.959155\pi$
$480$		0			0
$481$	360.920			0.750354
$482$	674.758	+	250.708i	1.39991	+	0.520141i
$483$		−	352.794i		−	0.730423i
$484$	−2.69190	−	2.32074i	−0.00556177	−	0.00479492i
$485$		0			0
$486$	−10.8586	+	29.2248i	−0.0223427	+	0.0601334i
$487$		−	65.9859i		−	0.135495i	−0.997703	−	0.0677474i	$-0.978419\pi$
$487$		−	65.9859i		−	0.135495i	0.997703	−	0.0677474i	$-0.0215812\pi$
$488$	317.483	+	576.260i	0.650580	+	1.18086i
$489$	109.946			0.224837
$490$		0			0
$491$			361.163i			0.735567i	0.929911	+	0.367783i	$0.119883\pi$
$491$			361.163i			0.735567i	−0.929911	+	0.367783i	$0.880117\pi$
$492$	−42.0904	+	48.8219i	−0.0855496	+	0.0992315i
$493$	−629.229			−1.27633
$494$	167.673	−	451.277i	0.339419	−	0.913516i
$495$		0			0
$496$	−76.5396	+	11.3971i	−0.154314	+	0.0229780i
$497$	419.630			0.844326
$498$	−235.022	−	87.3231i	−0.471933	−	0.175348i
$499$		−	711.138i		−	1.42513i	−0.701608	−	0.712564i	$-0.747534\pi$
$499$		−	711.138i		−	1.42513i	0.701608	−	0.712564i	$-0.252466\pi$
$500$		0			0
$501$	21.4378			0.0427900
$502$	217.480	−	585.328i	0.433227	−	1.16599i
$503$		−	353.756i		−	0.703292i	−0.936133	−	0.351646i	$-0.885622\pi$
$503$		−	353.756i		−	0.703292i	0.936133	−	0.351646i	$-0.114378\pi$
$504$	−114.936	+	63.3224i	−0.228047	+	0.125640i
$505$		0			0
$506$	771.057	+	286.488i	1.52383	+	0.566182i
$507$			115.183i			0.227185i
$508$	342.951	−	397.799i	0.675100	−	0.783068i
$509$	478.049			0.939192			0.469596	−	0.882881i	$-0.344400\pi$
$509$	478.049			0.939192			0.469596	+	0.882881i	$0.344400\pi$
$510$		0			0
$511$			511.348i			1.00068i
$512$	511.075	+	30.7568i	0.998194	+	0.0600720i
$513$	123.542			0.240823
$514$	150.468	+	55.9067i	0.292739	+	0.108768i
$515$		0			0
$516$	−367.466	−	316.800i	−0.712142	−	0.613953i
$517$	−419.778			−0.811949
$518$	−135.777	+	365.431i	−0.262117	+	0.705464i
$519$			102.837i			0.198144i
$520$		0			0
$521$	−35.7365			−0.0685921			−0.0342960	−	0.999412i	$-0.510919\pi$
$521$	−35.7365			−0.0685921			−0.0342960	+	0.999412i	$0.510919\pi$
$522$	−144.954	−	53.8579i	−0.277689	−	0.103176i
$523$		−	733.562i		−	1.40260i	−0.712864	−	0.701302i	$-0.752602\pi$
$523$		−	733.562i		−	1.40260i	0.712864	−	0.701302i	$-0.247398\pi$
$524$	−197.856	+	229.499i	−0.377588	+	0.437976i
$525$		0			0
$526$	339.906	−	914.828i	0.646210	−	1.73922i
$527$			118.081i			0.224062i
$528$	−45.0617	−	302.622i	−0.0853441	−	0.573147i
$529$	−858.753			−1.62335
$530$		0			0
$531$			166.623i			0.313791i
$532$	393.839	+	339.537i	0.740298	+	0.638227i
$533$	94.1965			0.176729
$534$	−139.582	+	375.673i	−0.261390	+	0.703507i
$535$		0			0
$536$	732.181	−	403.386i	1.36601	−	0.752585i
$537$	−437.831			−0.815327
$538$	580.342	+	215.628i	1.07870	+	0.400795i
$539$		−	210.917i		−	0.391312i
$540$		0			0
$541$	608.939			1.12558			0.562790	−	0.826600i	$-0.309728\pi$
$541$	608.939			1.12558			0.562790	+	0.826600i	$0.309728\pi$
$542$	34.1109	−	91.8064i	0.0629352	−	0.169384i
$543$		−	217.153i		−	0.399913i
$544$	161.278	−	764.440i	0.296467	−	1.40522i
$545$		0			0
$546$	179.752	+	66.7874i	0.329217	+	0.122321i
$547$			78.5868i			0.143669i	0.997417	+	0.0718344i	$0.0228853\pi$
$547$			78.5868i			0.143669i	−0.997417	+	0.0718344i	$0.977115\pi$
$548$	−202.353	−	174.452i	−0.369257	−	0.318344i
$549$	246.724			0.449405
$550$		0			0
$551$			612.763i			1.11209i
$552$	249.085	+	452.112i	0.451242	+	0.819043i
$553$	−269.974			−0.488200
$554$	−374.287	−	139.067i	−0.675609	−	0.251024i
$555$		0			0
$556$	99.5673	−	115.491i	0.179078	−	0.207718i
$557$	928.488			1.66694			0.833472	−	0.552561i	$-0.186349\pi$
$557$	928.488			1.66694			0.833472	+	0.552561i	$0.186349\pi$
$558$	−10.1069	+	27.2019i	−0.0181128	+	0.0487489i
$559$			708.984i			1.26831i
$560$		0			0
$561$	−466.866			−0.832202
$562$	−114.661	−	42.6025i	−0.204023	−	0.0758051i
$563$			447.978i			0.795697i	0.917451	+	0.397849i	$0.130243\pi$
$563$			447.978i			0.795697i	−0.917451	+	0.397849i	$0.869757\pi$
$564$	−199.516	−	172.007i	−0.353752	−	0.304977i
$565$		0			0
$566$	−301.274	+	810.852i	−0.532286	+	1.43260i
$567$			49.2093i			0.0867889i
$568$	−537.763	+	296.274i	−0.946766	+	0.521609i
$569$	571.441			1.00429			0.502145	−	0.864783i	$-0.332544\pi$
$569$	571.441			1.00429			0.502145	+	0.864783i	$0.332544\pi$
$570$		0			0
$571$		−	990.801i		−	1.73520i	−0.497260	−	0.867602i	$-0.665660\pi$
$571$		−	990.801i		−	1.73520i	0.497260	−	0.867602i	$-0.334340\pi$
$572$	−291.937	+	338.627i	−0.510380	+	0.592005i
$573$	168.813			0.294612
$574$	−35.4363	+	95.3736i	−0.0617357	+	0.166156i
$575$		0			0
$576$	102.584	−	162.298i	0.178098	−	0.281766i
$577$	−826.638			−1.43265			−0.716324	−	0.697768i	$-0.754177\pi$
$577$	−826.638			−1.43265			−0.716324	+	0.697768i	$0.754177\pi$
$578$	−575.693	−	213.900i	−0.996008	−	0.370069i
$579$		−	593.013i		−	1.02420i
$580$		0			0
$581$	−395.735			−0.681127
$582$	−88.0254	+	236.913i	−0.151246	+	0.407066i
$583$			615.787i			1.05624i
$584$	−361.030	−	655.301i	−0.618202	−	1.12209i
$585$		0			0
$586$	−530.999	−	197.294i	−0.906142	−	0.336679i
$587$		−	900.009i		−	1.53323i	−0.642104	−	0.766617i	$-0.721938\pi$
$587$		−	900.009i		−	1.53323i	0.642104	−	0.766617i	$-0.278062\pi$
$588$	86.4249	−	100.247i	0.146981	−	0.170488i
$589$	114.991			0.195230
$590$		0			0
$591$			129.008i			0.218288i
$592$	−84.0071	−	564.169i	−0.141904	−	0.952987i
$593$	704.088			1.18733			0.593666	−	0.804711i	$-0.297680\pi$
$593$	704.088			1.18733			0.593666	+	0.804711i	$0.297680\pi$
$594$	−107.551	−	39.9606i	−0.181061	−	0.0672738i
$595$		0			0
$596$	−383.897	−	330.965i	−0.644122	−	0.555311i
$597$	−308.351			−0.516501
$598$	262.715	−	707.075i	0.439323	−	1.18240i
$599$		−	376.098i		−	0.627876i	−0.949444	−	0.313938i	$-0.898352\pi$
$599$		−	376.098i		−	0.627876i	0.949444	−	0.313938i	$-0.101648\pi$
$600$		0			0
$601$	430.191			0.715791			0.357896	−	0.933762i	$-0.383494\pi$
$601$	430.191			0.715791			0.357896	+	0.933762i	$0.383494\pi$
$602$	−717.844	−	266.716i	−1.19243	−	0.443051i
$603$		−	313.480i		−	0.519868i
$604$	−178.756	+	207.344i	−0.295953	+	0.343285i
$605$		0			0
$606$	−35.4824	+	95.4977i	−0.0585518	+	0.157587i
$607$			93.4019i			0.153875i	0.997036	+	0.0769373i	$0.0245141\pi$
$607$			93.4019i			0.153875i	−0.997036	+	0.0769373i	$0.975486\pi$
$608$	−744.436	−	157.058i	−1.22440	−	0.258319i
$609$	−244.075			−0.400781
$610$		0			0
$611$			384.944i			0.630024i
$612$	−221.897	−	191.302i	−0.362576	−	0.312585i
$613$	156.506			0.255312			0.127656	−	0.991818i	$-0.459255\pi$
$613$	156.506			0.255312			0.127656	+	0.991818i	$0.459255\pi$
$614$	69.7113	−	187.622i	0.113536	−	0.305573i
$615$		0			0
$616$	−233.033	−	422.976i	−0.378301	−	0.686649i
$617$	553.493			0.897072			0.448536	−	0.893765i	$-0.351946\pi$
$617$	553.493			0.897072			0.448536	+	0.893765i	$0.351946\pi$
$618$	91.5334	+	34.0094i	0.148112	+	0.0550314i
$619$		−	14.4398i		−	0.0233276i	−0.999932	−	0.0116638i	$-0.996287\pi$
$619$		−	14.4398i		−	0.0233276i	0.999932	−	0.0116638i	$-0.00371278\pi$
$620$		0			0
$621$	193.570			0.311707
$622$	−281.546	+	757.756i	−0.452646	+	1.21826i
$623$			632.564i			1.01535i
$624$	−277.510	+	41.3224i	−0.444728	+	0.0662219i
$625$		0			0
$626$	−241.056	−	89.5651i	−0.385074	−	0.143075i
$627$			454.649i			0.725117i
$628$	−77.4893	−	66.8051i	−0.123391	−	0.106378i
$629$	−870.364			−1.38373
$630$		0			0
$631$		−	352.389i		−	0.558460i	−0.960224	−	0.279230i	$-0.909921\pi$
$631$		−	352.389i		−	0.558460i	0.960224	−	0.279230i	$-0.0900793\pi$
$632$	345.977	−	190.612i	0.547432	−	0.301601i
$633$	321.976			0.508650
$634$	161.102	+	59.8579i	0.254104	+	0.0944130i
$635$		0			0
$636$	−252.324	+	292.678i	−0.396735	+	0.460185i
$637$	−193.415			−0.303634
$638$	198.203	−	533.445i	0.310662	−	0.836120i
$639$			230.241i			0.360315i
$640$		0			0
$641$	−545.742			−0.851391			−0.425696	−	0.904866i	$-0.639971\pi$
$641$	−545.742			−0.851391			−0.425696	+	0.904866i	$0.639971\pi$
$642$	14.6352	+	5.43772i	0.0227962	+	0.00846997i
$643$			757.447i			1.17799i	0.808137	+	0.588995i	$0.200476\pi$
$643$			757.447i			1.17799i	−0.808137	+	0.588995i	$0.799524\pi$
$644$	617.079	+	531.997i	0.958197	+	0.826082i
$645$		0			0
$646$	−404.345	+	1088.26i	−0.625922	+	1.68461i
$647$		−	1161.36i		−	1.79500i	−0.441016	−	0.897499i	$-0.645382\pi$
$647$		−	1161.36i		−	1.79500i	0.441016	−	0.897499i	$-0.354618\pi$
$648$	−34.7435	−	63.0626i	−0.0536166	−	0.0973188i
$649$	−613.191			−0.944824
$650$		0			0
$651$			45.8030i			0.0703579i
$652$	−165.793	+	192.308i	−0.254283	+	0.294950i
$653$	621.231			0.951348			0.475674	−	0.879622i	$-0.342204\pi$
$653$	621.231			0.951348			0.475674	+	0.879622i	$0.342204\pi$
$654$	−233.236	+	627.734i	−0.356630	+	0.959838i
$655$		0			0
$656$	−21.9250	−	147.242i	−0.0334223	−	0.224455i
$657$	−280.565			−0.427039
$658$	−389.755	−	144.814i	−0.592333	−	0.220083i
$659$		−	736.047i		−	1.11692i	−0.829533	−	0.558458i	$-0.811393\pi$
$659$		−	736.047i		−	1.11692i	0.829533	−	0.558458i	$-0.188607\pi$
$660$		0			0
$661$	383.845			0.580704			0.290352	−	0.956920i	$-0.406228\pi$
$661$	383.845			0.580704			0.290352	+	0.956920i	$0.406228\pi$
$662$	127.746	−	343.817i	0.192970	−	0.519362i
$663$			428.125i			0.645739i
$664$	507.141	−	279.403i	0.763766	−	0.420788i
$665$		0			0
$666$	−200.503	−	74.4974i	−0.301056	−	0.111858i
$667$			960.096i			1.43942i
$668$	−32.3271	+	37.4972i	−0.0483939	+	0.0561335i
$669$	351.128			0.524854
$670$		0			0
$671$			907.968i			1.35316i
$672$	62.5592	−	296.523i	0.0930940	−	0.441255i
$673$	−984.464			−1.46280			−0.731400	−	0.681949i	$-0.761133\pi$
$673$	−984.464			−1.46280			−0.731400	+	0.681949i	$0.761133\pi$
$674$	315.205	+	117.115i	0.467664	+	0.173761i
$675$		0			0
$676$	−201.468	−	173.690i	−0.298030	−	0.256938i
$677$	−673.154			−0.994319			−0.497160	−	0.867659i	$-0.665624\pi$
$677$	−673.154			−0.994319			−0.497160	+	0.867659i	$0.665624\pi$
$678$	91.1789	−	245.400i	0.134482	−	0.361947i
$679$			398.918i			0.587507i
$680$		0			0
$681$	88.8037			0.130402
$682$	−100.106	−	37.1945i	−0.146783	−	0.0545374i
$683$			291.192i			0.426343i	0.977015	+	0.213171i	$0.0683793\pi$
$683$			291.192i			0.426343i	−0.977015	+	0.213171i	$0.931621\pi$
$684$	−186.296	+	216.090i	−0.272362	+	0.315921i
$685$		0			0
$686$	259.387	−	698.117i	0.378115	−	1.01766i
$687$		−	583.798i		−	0.849778i
$688$	1108.24	−	165.022i	1.61081	−	0.239857i
$689$	564.689			0.819578
$690$		0			0
$691$			943.693i			1.36569i	0.730563	+	0.682846i	$0.239258\pi$
$691$			943.693i			1.36569i	−0.730563	+	0.682846i	$0.760742\pi$
$692$	−179.874	−	155.073i	−0.259933	−	0.224094i
$693$	−181.095			−0.261321
$694$	95.7193	−	257.620i	0.137924	−	0.371211i
$695$		0			0
$696$	312.787	−	172.326i	0.449406	−	0.247595i
$697$	−227.156			−0.325905
$698$	25.2894	+	9.39633i	0.0362312	+	0.0134618i
$699$		−	139.058i		−	0.198938i
$700$		0			0
$701$	885.681			1.26345			0.631727	−	0.775191i	$-0.282346\pi$
$701$	885.681			1.26345			0.631727	+	0.775191i	$0.282346\pi$
$702$	−36.6447	+	98.6259i	−0.0522004	+	0.140493i
$703$			847.588i			1.20567i
$704$	597.272	+	377.521i	0.848397	+	0.536251i
$705$		0			0
$706$	456.596	+	169.649i	0.646737	+	0.240296i
$707$			160.801i			0.227441i
$708$	−291.444	−	251.260i	−0.411644	−	0.354887i
$709$	−286.183			−0.403644			−0.201822	−	0.979422i	$-0.564686\pi$
$709$	−286.183			−0.403644			−0.201822	+	0.979422i	$0.564686\pi$
$710$		0			0
$711$		−	148.129i		−	0.208339i
$712$	−446.613	−	810.642i	−0.627266	−	1.13854i
$713$	180.171			0.252694
$714$	−433.475	−	161.059i	−0.607108	−	0.225572i
$715$		0			0
$716$	660.228	−	765.818i	0.922106	−	1.06958i
$717$	572.976			0.799129
$718$	12.4803	−	33.5895i	0.0173820	−	0.0467820i
$719$			666.163i			0.926513i	0.886224	+	0.463257i	$0.153319\pi$
$719$			666.163i			0.926513i	−0.886224	+	0.463257i	$0.846681\pi$
$720$		0			0
$721$	154.125			0.213766
$722$	382.989	+	142.300i	0.530455	+	0.197092i
$723$			623.389i			0.862226i
$724$	379.826	+	327.456i	0.524622	+	0.452287i
$725$		0			0
$726$	1.07203	−	2.88528i	0.00147663	−	0.00397422i
$727$		−	856.270i		−	1.17781i	−0.808201	−	0.588907i	$-0.799559\pi$
$727$		−	856.270i		−	1.17781i	0.808201	−	0.588907i	$-0.200441\pi$
$728$	−387.877	+	213.696i	−0.532798	+	0.293538i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	1709.72i		−	2.33888i
$732$	−372.047	+	431.549i	−0.508261	+	0.589547i
$733$	769.487			1.04978			0.524889	−	0.851171i	$-0.324107\pi$
$733$	769.487			1.04978			0.524889	+	0.851171i	$0.324107\pi$
$734$	166.076	−	446.978i	0.226261	−	0.608961i
$735$		0			0
$736$	−1166.41	−	246.083i	−1.58479	−	0.334352i
$737$	1153.64			1.56532
$738$	−52.3293	−	19.4431i	−0.0709069	−	0.0263456i
$739$			1156.70i			1.56522i	0.622511	+	0.782611i	$0.286113\pi$
$739$			1156.70i			1.56522i	−0.622511	+	0.782611i	$0.713887\pi$
$740$		0			0
$741$	416.922			0.562647
$742$	−212.433	+	571.746i	−0.286298	+	0.770547i
$743$			426.794i			0.574421i	0.957868	+	0.287210i	$0.0927278\pi$
$743$			426.794i			0.574421i	−0.957868	+	0.287210i	$0.907272\pi$
$744$	−32.3386	−	58.6973i	−0.0434658	−	0.0788942i
$745$		0			0
$746$	−339.842	−	126.269i	−0.455552	−	0.169261i
$747$		−	217.130i		−	0.290670i
$748$	704.011	−	816.603i	0.941191	−	1.09172i
$749$	24.6429			0.0329011
$750$		0			0
$751$			1222.03i			1.62721i	0.581420	+	0.813604i	$0.302497\pi$
$751$			1222.03i			1.62721i	−0.581420	+	0.813604i	$0.697503\pi$
$752$	601.722	−	89.5990i	0.800162	−	0.119148i
$753$	540.768			0.718152
$754$	−489.179	−	181.756i	−0.648779	−	0.241055i
$755$		0			0
$756$	−86.0729	−	74.2053i	−0.113853	−	0.0981551i
$757$	1312.95			1.73442			0.867209	−	0.497945i	$-0.165912\pi$
$757$	1312.95			1.73442			0.867209	+	0.497945i	$0.165912\pi$
$758$	−213.296	+	574.067i	−0.281393	+	0.757344i
$759$			712.358i			0.938548i
$760$		0			0
$761$	−189.584			−0.249124			−0.124562	−	0.992212i	$-0.539753\pi$
$761$	−189.584			−0.249124			−0.124562	+	0.992212i	$0.539753\pi$
$762$	426.376	+	158.421i	0.559549	+	0.207902i
$763$			1056.99i			1.38531i
$764$	−254.561	+	295.273i	−0.333195	+	0.386483i
$765$		0			0
$766$	−100.326	+	270.019i	−0.130974	+	0.352505i
$767$			562.308i			0.733127i
$768$	129.185	+	424.169i	0.168210	+	0.552303i
$769$	254.995			0.331594			0.165797	−	0.986160i	$-0.446980\pi$
$769$	254.995			0.331594			0.165797	+	0.986160i	$0.446980\pi$
$770$		0			0
$771$			139.013i			0.180302i
$772$	1037.25	+	894.235i	1.34359	+	1.15834i
$773$	−23.2536			−0.0300823			−0.0150411	−	0.999887i	$-0.504788\pi$
$773$	−23.2536			−0.0300823			−0.0150411	+	0.999887i	$0.504788\pi$
$774$	146.341	−	393.864i	0.189071	−	0.508869i
$775$		0			0
$776$	−281.650	−	511.220i	−0.362951	−	0.658788i
$777$	−337.611			−0.434506
$778$	−26.2654	−	9.75897i	−0.0337602	−	0.0125437i
$779$			221.212i			0.283969i
$780$		0			0
$781$	−847.312			−1.08491
$782$	−633.541	+	1705.12i	−0.810155	+	2.18046i
$783$		−	133.919i		−	0.171033i
$784$	45.0189	+	302.335i	0.0574221	+	0.385631i
$785$		0			0
$786$	−245.987	−	91.3969i	−0.312960	−	0.116281i
$787$			220.593i			0.280296i	0.990131	+	0.140148i	$0.0447579\pi$
$787$			220.593i			0.280296i	−0.990131	+	0.140148i	$0.955242\pi$
$788$	−225.651	−	194.538i	−0.286359	−	0.246876i
$789$	845.183			1.07121
$790$		0			0
$791$		−	413.209i		−	0.522388i
$792$	232.077	−	127.860i	0.293026	−	0.161439i
$793$	832.625			1.04997
$794$	73.3194	+	27.2420i	0.0923418	+	0.0343098i
$795$		0			0
$796$	464.979	−	539.343i	0.584144	−	0.677566i
$797$	−1010.38			−1.26773			−0.633867	−	0.773442i	$-0.718533\pi$
$797$	−1010.38			−1.26773			−0.633867	+	0.773442i	$0.718533\pi$
$798$	−156.844	+	422.132i	−0.196546	+	0.528987i
$799$		−	928.298i		−	1.16183i
$800$		0			0
$801$	−347.073			−0.433300
$802$	226.974	+	84.3327i	0.283010	+	0.105153i
$803$		−	1032.51i		−	1.28581i
$804$	548.314	+	472.713i	0.681983	+	0.587952i
$805$		0			0
$806$	−34.1081	+	91.7990i	−0.0423178	+	0.113894i
$807$			536.162i			0.664389i
$808$	−113.531	−	206.069i	−0.140509	−	0.255036i
$809$	1410.37			1.74335			0.871674	−	0.490086i	$-0.163035\pi$
$809$	1410.37			1.74335			0.871674	+	0.490086i	$0.163035\pi$
$810$		0			0
$811$			950.157i			1.17159i	0.810460	+	0.585793i	$0.199217\pi$
$811$			950.157i			1.17159i	−0.810460	+	0.585793i	$0.800783\pi$
$812$	368.054	−	426.917i	0.453269	−	0.525760i
$813$	84.8173			0.104326
$814$	274.158	−	737.873i	0.336804	−	0.906478i
$815$		0			0
$816$	669.219	−	99.6496i	0.820121	−	0.122120i
$817$	−1664.98			−2.03792
$818$	1015.74	+	377.402i	1.24174	+	0.461372i
$819$			166.068i			0.202769i
$820$		0			0
$821$	77.3347			0.0941957			0.0470979	−	0.998890i	$-0.485003\pi$
$821$	77.3347			0.0941957			0.0470979	+	0.998890i	$0.485003\pi$
$822$	80.5858	−	216.890i	0.0980363	−	0.263856i
$823$		−	1260.16i		−	1.53118i	−0.643328	−	0.765591i	$-0.722447\pi$
$823$		−	1260.16i		−	1.53118i	0.643328	−	0.765591i	$-0.277553\pi$
$824$	−197.514	+	108.818i	−0.239702	+	0.132061i
$825$		0			0
$826$	−569.335	−	211.538i	−0.689268	−	0.256099i
$827$		−	438.047i		−	0.529681i	−0.964292	−	0.264841i	$-0.914681\pi$
$827$		−	438.047i		−	0.529681i	0.964292	−	0.264841i	$-0.0853194\pi$
$828$	−291.894	+	338.577i	−0.352529	+	0.408909i
$829$	361.388			0.435933			0.217966	−	0.975956i	$-0.430058\pi$
$829$	361.388			0.435933			0.217966	+	0.975956i	$0.430058\pi$
$830$		0			0
$831$		−	345.793i		−	0.416117i
$832$	346.194	−	547.710i	0.416098	−	0.658305i
$833$	466.423			0.559931
$834$	123.788	+	45.9937i	0.148427	+	0.0551483i
$835$		0			0
$836$	−795.234	−	685.588i	−0.951237	−	0.820082i
$837$	−25.1310			−0.0300251
$838$	−479.123	+	1289.52i	−0.571746	+	1.53880i
$839$			785.017i			0.935658i	0.883819	+	0.467829i	$0.154964\pi$
$839$			785.017i			0.935658i	−0.883819	+	0.467829i	$0.845036\pi$
$840$		0			0
$841$	−176.771			−0.210192
$842$	851.890	+	316.521i	1.01175	+	0.375916i
$843$		−	105.932i		−	0.125661i
$844$	−485.524	+	563.173i	−0.575265	+	0.667267i
$845$		0			0
$846$	79.4563	−	213.849i	0.0939199	−	0.252777i
$847$		−	4.85829i		−	0.00573588i
$848$	−131.436	−	882.688i	−0.154995	−	1.04091i
$849$	−749.123			−0.882359
$850$		0			0
$851$			1328.03i			1.56055i
$852$	−402.719	−	347.193i	−0.472675	−	0.407503i
$853$	−1113.79			−1.30573			−0.652865	−	0.757474i	$-0.726433\pi$
$853$	−1113.79			−1.30573			−0.652865	+	0.757474i	$0.726433\pi$
$854$	−313.230	+	843.030i	−0.366780	+	0.987155i
$855$		0			0
$856$	−31.5803	+	17.3988i	−0.0368929	+	0.0203257i
$857$	306.591			0.357749			0.178875	−	0.983872i	$-0.442754\pi$
$857$	306.591			0.357749			0.178875	+	0.983872i	$0.442754\pi$
$858$	−362.954	−	134.856i	−0.423023	−	0.157175i
$859$			204.542i			0.238116i	0.992887	+	0.119058i	$0.0379875\pi$
$859$			204.542i			0.238116i	−0.992887	+	0.119058i	$0.962013\pi$
$860$		0			0
$861$	−88.1130			−0.102338
$862$	−324.706	+	873.918i	−0.376689	+	1.01383i
$863$			654.384i			0.758266i	0.925342	+	0.379133i	$0.123778\pi$
$863$			654.384i			0.758266i	−0.925342	+	0.379133i	$0.876222\pi$
$864$	162.695	+	34.3248i	0.188305	+	0.0397277i
$865$		0			0
$866$	856.949	+	318.401i	0.989549	+	0.367669i
$867$		−	531.866i		−	0.613456i
$868$	−80.1149	−	69.0687i	−0.0922982	−	0.0795722i
$869$	545.129			0.627306
$870$		0			0
$871$		−	1057.91i		−	1.21459i
$872$	−746.272	−	1354.55i	−0.855817	−	1.55338i
$873$	−218.877			−0.250718
$874$	1660.50	+	616.963i	1.89989	+	0.705907i
$875$		0			0
$876$	423.078	−	490.741i	0.482966	−	0.560206i
$877$	604.453			0.689228			0.344614	−	0.938744i	$-0.388010\pi$
$877$	604.453			0.689228			0.344614	+	0.938744i	$0.388010\pi$
$878$	541.565	−	1457.58i	0.616817	−	1.66011i
$879$		−	490.575i		−	0.558106i
$880$		0			0
$881$	1436.81			1.63089			0.815445	−	0.578834i	$-0.196492\pi$
$881$	1436.81			1.63089			0.815445	+	0.578834i	$0.196492\pi$
$882$	107.449	+	39.9227i	0.121824	+	0.0452639i
$883$		−	120.993i		−	0.137025i	−0.997650	−	0.0685123i	$-0.978175\pi$
$883$		−	120.993i		−	0.137025i	0.997650	−	0.0685123i	$-0.0218252\pi$
$884$	−748.841	−	645.592i	−0.847105	−	0.730307i
$885$		0			0
$886$	−172.392	+	463.977i	−0.194573	+	0.523676i
$887$			286.448i			0.322941i	0.986878	+	0.161470i	$0.0516236\pi$
$887$			286.448i			0.322941i	−0.986878	+	0.161470i	$0.948376\pi$
$888$	432.654	−	238.365i	0.487223	−	0.268429i
$889$	717.940			0.807582
$890$		0			0
$891$		−	99.3628i		−	0.111518i
$892$	−529.483	+	614.164i	−0.593591	+	0.688524i
$893$	−904.007			−1.01233
$894$	152.885	−	411.476i	0.171012	−	0.460264i
$895$		0			0
$896$	424.318	+	556.566i	0.473569	+	0.621168i
$897$	653.246			0.728256
$898$	−773.360	−	287.344i	−0.861203	−	0.319982i
$899$		−	124.649i		−	0.138652i
$900$		0			0
$901$	−1361.75			−1.51138
$902$	71.5525	−	192.577i	0.0793265	−	0.213500i
$903$		−	663.195i		−	0.734436i
$904$	291.740	+	529.534i	0.322721	+	0.585768i
$905$		0			0
$906$	−222.240	−	82.5736i	−0.245298	−	0.0911409i
$907$		−	234.706i		−	0.258772i	−0.991594	−	0.129386i	$-0.958699\pi$
$907$		−	234.706i		−	0.258772i	0.991594	−	0.129386i	$-0.0413006\pi$
$908$	−133.912	+	155.328i	−0.147480	+	0.171066i
$909$	−88.2276			−0.0970601
$910$		0			0
$911$			491.244i			0.539236i	0.962967	+	0.269618i	$0.0868974\pi$
$911$			491.244i			0.539236i	−0.962967	+	0.269618i	$0.913103\pi$
$912$	−97.0420	−	651.707i	−0.106406	−	0.714591i
$913$	799.063			0.875206
$914$	−1397.46	−	519.229i	−1.52895	−	0.568084i
$915$		0			0
$916$	1021.13	+	880.339i	1.11477	+	0.961069i
$917$	−414.197			−0.451687
$918$	88.3691	−	237.838i	0.0962627	−	0.259082i
$919$		−	356.091i		−	0.387477i	−0.981053	−	0.193738i	$-0.937939\pi$
$919$		−	356.091i		−	0.387477i	0.981053	−	0.193738i	$-0.0620613\pi$
$920$		0			0
$921$	173.338			0.188207
$922$	−153.010	−	56.8511i	−0.165954	−	0.0616607i
$923$			777.002i			0.841822i
$924$	273.083	−	316.757i	0.295545	−	0.342811i
$925$		0			0
$926$	−203.573	+	547.899i	−0.219841	+	0.591684i
$927$			84.5651i			0.0912244i
$928$	−170.249	+	806.961i	−0.183458	+	0.869570i
$929$	−916.019			−0.986027			−0.493014	−	0.870022i	$-0.664105\pi$
$929$	−916.019			−0.986027			−0.493014	+	0.870022i	$0.664105\pi$
$930$		0			0
$931$		−	454.217i		−	0.487881i
$932$	243.229	+	209.693i	0.260975	+	0.224992i
$933$	−700.069			−0.750342
$934$	35.8154	−	96.3939i	0.0383462	−	0.103205i
$935$		0			0
$936$	−117.250	−	212.819i	−0.125267	−	0.227371i
$937$	−143.818			−0.153488			−0.0767440	−	0.997051i	$-0.524452\pi$
$937$	−143.818			−0.153488			−0.0767440	+	0.997051i	$0.524452\pi$
$938$	1071.13	+	397.981i	1.14193	+	0.424287i
$939$		−	222.705i		−	0.237173i
$940$		0			0
$941$	−1488.04			−1.58133			−0.790667	−	0.612246i	$-0.790266\pi$
$941$	−1488.04			−1.58133			−0.790667	+	0.612246i	$0.790266\pi$
$942$	30.8597	−	83.0561i	0.0327597	−	0.0881699i
$943$			346.602i			0.367552i
$944$	878.966	−	130.882i	0.931108	−	0.138646i
$945$		0			0
$946$	1449.46	+	538.551i	1.53220	+	0.569292i
$947$			1095.51i			1.15682i	0.815745	+	0.578411i	$0.196327\pi$
$947$			1095.51i			1.15682i	−0.815745	+	0.578411i	$0.803673\pi$
$948$	259.095	+	223.371i	0.273307	+	0.235623i
$949$	−946.829			−0.997713
$950$		0			0
$951$			148.838i			0.156506i
$952$	935.370	−	515.331i	0.982532	−	0.541314i
$953$	−1277.86			−1.34089			−0.670443	−	0.741961i	$-0.733896\pi$
$953$	−1277.86			−1.34089			−0.670443	+	0.741961i	$0.733896\pi$
$954$	−313.704	−	116.557i	−0.328830	−	0.122177i
$955$		0			0
$956$	−864.020	+	1002.20i	−0.903786	+	1.04833i
$957$	492.834			0.514978
$958$	85.3953	−	229.834i	0.0891392	−	0.239910i
$959$		−	365.202i		−	0.380816i
$960$		0			0
$961$	937.609			0.975659
$962$	−676.644	−	251.409i	−0.703372	−	0.261339i
$963$			13.5210i			0.0140405i
$964$	−1090.38	−	940.041i	−1.13110	−	0.975146i
$965$		0			0
$966$	−245.748	+	661.410i	−0.254398	+	0.684689i
$967$			237.958i			0.246079i	0.992402	+	0.123039i	$0.0392641\pi$
$967$			237.958i			0.246079i	−0.992402	+	0.123039i	$0.960736\pi$
$968$	3.43013	+	6.22598i	0.00354352	+	0.00643180i
$969$	−1005.41			−1.03758
$970$		0			0
$971$		−	1602.10i		−	1.64995i	−0.565169	−	0.824975i	$-0.691189\pi$
$971$		−	1602.10i		−	1.64995i	0.565169	−	0.824975i	$-0.308811\pi$
$972$	40.7147	−	47.2262i	0.0418876	−	0.0485866i
$973$	208.436			0.214220
$974$	−45.9643	+	123.709i	−0.0471912	+	0.127011i
$975$		0			0
$976$	−193.800	−	1301.51i	−0.198566	−	1.33351i
$977$	−918.977			−0.940611			−0.470305	−	0.882504i	$-0.655856\pi$
$977$	−918.977			−0.940611			−0.470305	+	0.882504i	$0.655856\pi$
$978$	−206.123	−	76.5855i	−0.210760	−	0.0783083i
$979$		−	1277.27i		−	1.30466i
$980$		0			0
$981$	−579.945			−0.591178
$982$	251.578	−	677.100i	0.256189	−	0.689511i
$983$		−	1162.30i		−	1.18240i	−0.806525	−	0.591200i	$-0.798654\pi$
$983$		−	1162.30i		−	1.18240i	0.806525	−	0.591200i	$-0.201346\pi$
$984$	112.918	−	62.2109i	0.114754	−	0.0632225i
$985$		0			0
$986$	1179.66	+	438.306i	1.19641	+	0.444530i
$987$		−	360.083i		−	0.364826i
$988$	−628.698	+	729.245i	−0.636334	+	0.738103i
$989$	−2608.75			−2.63776
$990$		0			0
$991$		−	491.614i		−	0.496079i	−0.968750	−	0.248040i	$-0.920214\pi$
$991$		−	491.614i		−	0.496079i	0.968750	−	0.248040i	$-0.0797863\pi$
$992$	151.434	+	31.9488i	0.152655	+	0.0322064i
$993$	317.643			0.319882
$994$	−786.712	−	292.305i	−0.791461	−	0.294069i
$995$		0			0
$996$	379.787	+	327.422i	0.381312	+	0.328737i
$997$	1262.51			1.26630			0.633152	−	0.774027i	$-0.281761\pi$
$997$	1262.51			1.26630			0.633152	+	0.774027i	$0.281761\pi$
$998$	−495.363	+	1333.22i	−0.496355	+	1.33590i
$999$		−	185.239i		−	0.185425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.d.151.1		8
3.2	odd	2		900.3.c.u.451.8		8
4.3	odd	2	inner	300.3.c.d.151.2		8
5.2	odd	4		300.3.f.b.199.11		16
5.3	odd	4		300.3.f.b.199.6		16
5.4	even	2		60.3.c.a.31.8	yes	8
12.11	even	2		900.3.c.u.451.7		8
15.2	even	4		900.3.f.f.199.6		16
15.8	even	4		900.3.f.f.199.11		16
15.14	odd	2		180.3.c.b.91.1		8
20.3	even	4		300.3.f.b.199.12		16
20.7	even	4		300.3.f.b.199.5		16
20.19	odd	2		60.3.c.a.31.7	✓	8
40.19	odd	2		960.3.e.c.511.8		8
40.29	even	2		960.3.e.c.511.3		8
60.23	odd	4		900.3.f.f.199.5		16
60.47	odd	4		900.3.f.f.199.12		16
60.59	even	2		180.3.c.b.91.2		8
120.29	odd	2		2880.3.e.j.2431.2		8
120.59	even	2		2880.3.e.j.2431.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.7	✓	8	20.19	odd	2
60.3.c.a.31.8	yes	8	5.4	even	2
180.3.c.b.91.1		8	15.14	odd	2
180.3.c.b.91.2		8	60.59	even	2
300.3.c.d.151.1		8	1.1	even	1	trivial
300.3.c.d.151.2		8	4.3	odd	2	inner
300.3.f.b.199.5		16	20.7	even	4
300.3.f.b.199.6		16	5.3	odd	4
300.3.f.b.199.11		16	5.2	odd	4
300.3.f.b.199.12		16	20.3	even	4
900.3.c.u.451.7		8	12.11	even	2
900.3.c.u.451.8		8	3.2	odd	2
900.3.f.f.199.5		16	60.23	odd	4
900.3.f.f.199.6		16	15.2	even	4
900.3.f.f.199.11		16	15.8	even	4
900.3.f.f.199.12		16	60.47	odd	4
960.3.e.c.511.3		8	40.29	even	2
960.3.e.c.511.8		8	40.19	odd	2
2880.3.e.j.2431.2		8	120.29	odd	2
2880.3.e.j.2431.3		8	120.59	even	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 + 2.61185i) q^{4} +(-1.20651 + 3.24721i) q^{6} +5.46770i q^{7} +(-3.86039 - 7.00695i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.87477 - 0.696577i) q^{2} -1.73205i q^{3} +(3.02956 + 2.61185i) q^{4} +(-1.20651 + 3.24721i) q^{6} +5.46770i q^{7} +(-3.86039 - 7.00695i) q^{8} -3.00000 q^{9} -11.0403i q^{11} +(4.52386 - 5.24735i) q^{12} -10.1242 q^{13} +(3.80867 - 10.2507i) q^{14} +(2.35649 + 15.8255i) q^{16} +24.4146 q^{17} +(5.62432 + 2.08973i) q^{18} -23.7757i q^{19} +9.47033 q^{21} +(-7.69043 + 20.6981i) q^{22} -37.2526i q^{23} +(-12.1364 + 6.68640i) q^{24} +(18.9806 + 7.05227i) q^{26} +5.19615i q^{27} +(-14.2808 + 16.5647i) q^{28} -25.7726 q^{29} +4.83647i q^{31} +(6.60580 - 31.3108i) q^{32} -19.1224 q^{33} +(-45.7719 - 17.0066i) q^{34} +(-9.08868 - 7.83555i) q^{36} -35.6493 q^{37} +(-16.5616 + 44.5741i) q^{38} +17.5356i q^{39} -9.30410 q^{41} +(-17.7547 - 6.59682i) q^{42} -70.0287i q^{43} +(28.8356 - 33.4473i) q^{44} +(-25.9493 + 69.8401i) q^{46} -38.0223i q^{47} +(27.4106 - 4.08156i) q^{48} +19.1043 q^{49} -42.2873i q^{51} +(-30.6718 - 26.4428i) q^{52} -55.7762 q^{53} +(3.61952 - 9.74162i) q^{54} +(38.3119 - 21.1075i) q^{56} -41.1808 q^{57} +(48.3179 + 17.9526i) q^{58} -55.5411i q^{59} -82.2412 q^{61} +(3.36897 - 9.06729i) q^{62} -16.4031i q^{63} +(-34.1947 + 54.0992i) q^{64} +(35.8502 + 13.3202i) q^{66} +104.493i q^{67} +(73.9656 + 63.7673i) q^{68} -64.5233 q^{69} -76.7471i q^{71} +(11.5812 + 21.0209i) q^{72} +93.5215 q^{73} +(66.8344 + 24.8325i) q^{74} +(62.0986 - 72.0300i) q^{76} +60.3651 q^{77} +(12.2149 - 32.8753i) q^{78} +49.3762i q^{79} +9.00000 q^{81} +(17.4431 + 6.48102i) q^{82} +72.3768i q^{83} +(28.6910 + 24.7351i) q^{84} +(-48.7804 + 131.288i) q^{86} +44.6395i q^{87} +(-77.3589 + 42.6199i) q^{88} +115.691 q^{89} -55.3560i q^{91} +(97.2980 - 112.859i) q^{92} +8.37701 q^{93} +(-26.4854 + 71.2832i) q^{94} +(-54.2318 - 11.4416i) q^{96} +72.9589 q^{97} +(-35.8162 - 13.3076i) q^{98} +33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

Introduction

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