LMFDB - Embedded newform 900.3.c.u.451.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, 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("900.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.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:	$24.5232237924$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.8
Root			$1.04064 + 0.957636i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.u.451.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87477 + 0.696577i) q^{2} +(3.02956 + 2.61185i) q^{4} +5.46770i q^{7} +(3.86039 + 7.00695i) q^{8} +O(q^{10})$	\(q+(1.87477 + 0.696577i) q^{2} +(3.02956 + 2.61185i) q^{4} +5.46770i q^{7} +(3.86039 + 7.00695i) q^{8} +11.0403i q^{11} -10.1242 q^{13} +(-3.80867 + 10.2507i) q^{14} +(2.35649 + 15.8255i) q^{16} -24.4146 q^{17} -23.7757i q^{19} +(-7.69043 + 20.6981i) q^{22} +37.2526i q^{23} +(-18.9806 - 7.05227i) q^{26} +(-14.2808 + 16.5647i) q^{28} +25.7726 q^{29} +4.83647i q^{31} +(-6.60580 + 31.3108i) q^{32} +(-45.7719 - 17.0066i) q^{34} -35.6493 q^{37} +(16.5616 - 44.5741i) q^{38} +9.30410 q^{41} -70.0287i q^{43} +(-28.8356 + 33.4473i) q^{44} +(-25.9493 + 69.8401i) q^{46} +38.0223i q^{47} +19.1043 q^{49} +(-30.6718 - 26.4428i) q^{52} +55.7762 q^{53} +(-38.3119 + 21.1075i) q^{56} +(48.3179 + 17.9526i) q^{58} +55.5411i q^{59} -82.2412 q^{61} +(-3.36897 + 9.06729i) q^{62} +(-34.1947 + 54.0992i) q^{64} +104.493i q^{67} +(-73.9656 - 63.7673i) q^{68} +76.7471i q^{71} +93.5215 q^{73} +(-66.8344 - 24.8325i) q^{74} +(62.0986 - 72.0300i) q^{76} -60.3651 q^{77} +49.3762i q^{79} +(17.4431 + 6.48102i) q^{82} -72.3768i q^{83} +(48.7804 - 131.288i) q^{86} +(-77.3589 + 42.6199i) q^{88} -115.691 q^{89} -55.3560i q^{91} +(-97.2980 + 112.859i) q^{92} +(-26.4854 + 71.2832i) q^{94} +72.9589 q^{97} +(35.8162 + 13.3076i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8	$ 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8} - 16 q^{13} + 20 q^{14} + 34 q^{16} - 68 q^{22} + 36 q^{26} - 28 q^{28} - 64 q^{29} - 76 q^{32} - 92 q^{34} + 112 q^{37} - 40 q^{38} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} + 128 q^{52} + 352 q^{53} - 116 q^{56} + 204 q^{58} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 184 q^{68} + 240 q^{73} - 132 q^{74} - 24 q^{76} - 288 q^{77} - 40 q^{82} + 200 q^{86} - 140 q^{88} - 80 q^{89} + 144 q^{92} - 96 q^{94} - 432 q^{97} + 660 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8 - 16 * q^13 + 20 * q^14 + 34 * q^16 - 68 * q^22 + 36 * q^26 - 28 * q^28 - 64 * q^29 - 76 * q^32 - 92 * q^34 + 112 * q^37 - 40 * q^38 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 + 128 * q^52 + 352 * q^53 - 116 * q^56 + 204 * q^58 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 184 * q^68 + 240 * q^73 - 132 * q^74 - 24 * q^76 - 288 * q^77 - 40 * q^82 + 200 * q^86 - 140 * q^88 - 80 * q^89 + 144 * q^92 - 96 * q^94 - 432 * q^97 + 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$	3.02956	+	2.61185i	0.757390	+	0.652962i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			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
$9$		0			0
$10$		0			0
$11$			11.0403i			1.00366i	0.864965	+	0.501832i	$0.167341\pi$
$11$			11.0403i			1.00366i	−0.864965	+	0.501832i	$0.832659\pi$
$12$		0			0
$13$	−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	$-0.754977\pi$
$17$	−24.4146			−1.43615			−0.718077	+	0.695964i	$0.754977\pi$
$18$		0			0
$19$		−	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
$21$		0			0
$22$	−7.69043	+	20.6981i	−0.349565	+	0.940823i
$23$			37.2526i			1.61968i	0.586653	+	0.809838i	$0.300445\pi$
$23$			37.2526i			1.61968i	−0.586653	+	0.809838i	$0.699555\pi$
$24$		0			0
$25$		0			0
$26$	−18.9806	−	7.05227i	−0.730022	−	0.271241i
$27$		0			0
$28$	−14.2808	+	16.5647i	−0.510029	+	0.591598i
$29$	25.7726			0.888712			0.444356	−	0.895850i	$-0.353433\pi$
$29$	25.7726			0.888712			0.444356	+	0.895850i	$0.353433\pi$
$30$		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
$33$		0			0
$34$	−45.7719	−	17.0066i	−1.34623	−	0.500196i
$35$		0			0
$36$		0			0
$37$	−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
$39$		0			0
$40$		0			0
$41$	9.30410			0.226929			0.113465	−	0.993542i	$-0.463805\pi$
$41$	9.30410			0.226929			0.113465	+	0.993542i	$0.463805\pi$
$42$		0			0
$43$		−	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	$0.132552\pi$
$47$			38.0223i			0.808984i	−0.914542	+	0.404492i	$0.867448\pi$
$48$		0			0
$49$	19.1043			0.389883
$50$		0			0
$51$		0			0
$52$	−30.6718	−	26.4428i	−0.589843	−	0.508516i
$53$	55.7762			1.05238			0.526191	−	0.850366i	$-0.323620\pi$
$53$	55.7762			1.05238			0.526191	+	0.850366i	$0.323620\pi$
$54$		0			0
$55$		0			0
$56$	−38.3119	+	21.1075i	−0.684141	+	0.376919i
$57$		0			0
$58$	48.3179	+	17.9526i	0.833067	+	0.309528i
$59$			55.5411i			0.941374i	0.882300	+	0.470687i	$0.155994\pi$
$59$			55.5411i			0.941374i	−0.882300	+	0.470687i	$0.844006\pi$
$60$		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
$63$		0			0
$64$	−34.1947	+	54.0992i	−0.534293	+	0.845299i
$65$		0			0
$66$		0			0
$67$			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
$69$		0			0
$70$		0			0
$71$			76.7471i			1.08094i	0.841362	+	0.540472i	$0.181754\pi$
$71$			76.7471i			1.08094i	−0.841362	+	0.540472i	$0.818246\pi$
$72$		0			0
$73$	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
$78$		0			0
$79$			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
$81$		0			0
$82$	17.4431	+	6.48102i	0.212721	+	0.0790368i
$83$		−	72.3768i		−	0.872010i	−0.899944	−	0.436005i	$-0.856393\pi$
$83$		−	72.3768i		−	0.872010i	0.899944	−	0.436005i	$-0.143607\pi$
$84$		0			0
$85$		0			0
$86$	48.7804	−	131.288i	0.567214	−	1.52661i
$87$		0			0
$88$	−77.3589	+	42.6199i	−0.879079	+	0.484318i
$89$	−115.691			−1.29990			−0.649950	−	0.759977i	$-0.725210\pi$
$89$	−115.691			−1.29990			−0.649950	+	0.759977i	$0.725210\pi$
$90$		0			0
$91$		−	55.3560i		−	0.608308i
$92$	−97.2980	+	112.859i	−1.05759	+	1.22673i
$93$		0			0
$94$	−26.4854	+	71.2832i	−0.281760	+	0.758332i
$95$		0			0
$96$		0			0
$97$	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
$99$		0			0
$100$		0			0
$101$	−29.4092			−0.291180			−0.145590	−	0.989345i	$-0.546508\pi$
$101$	−29.4092			−0.291180			−0.145590	+	0.989345i	$0.546508\pi$
$102$		0			0
$103$		−	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	$0.00670434\pi$
$107$			4.50700i			0.0421215i	−0.999778	+	0.0210607i	$0.993296\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−86.5292	+	12.8846i	−0.772582	+	0.115041i
$113$	75.5727			0.668785			0.334392	−	0.942434i	$-0.391469\pi$
$113$	75.5727			0.668785			0.334392	+	0.942434i	$0.391469\pi$
$114$		0			0
$115$		0			0
$116$	78.0798	+	67.3142i	0.673102	+	0.580295i
$117$		0			0
$118$	−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
$123$		0			0
$124$	−12.6321	+	14.6524i	−0.101872	+	0.118164i
$125$		0			0
$126$		0			0
$127$		−	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
$129$		0			0
$130$		0			0
$131$		−	75.7533i		−	0.578270i	−0.957288	−	0.289135i	$-0.906632\pi$
$131$		−	75.7533i		−	0.578270i	0.957288	−	0.289135i	$-0.0933676\pi$
$132$		0			0
$133$	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	$-0.421616\pi$
$137$	66.7927			0.487538			0.243769	+	0.969833i	$0.421616\pi$
$138$		0			0
$139$		−	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
$141$		0			0
$142$	−53.4602	+	143.884i	−0.376481	+	1.01326i
$143$		−	111.774i		−	0.781638i
$144$		0			0
$145$		0			0
$146$	175.332	+	65.1449i	1.20090	+	0.446198i
$147$		0			0
$148$	−108.002	−	93.1106i	−0.729742	−	0.629126i
$149$	126.717			0.850449			0.425225	−	0.905088i	$-0.360195\pi$
$149$	126.717			0.850449			0.425225	+	0.905088i	$0.360195\pi$
$150$		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
$153$		0			0
$154$	−113.171	−	42.0489i	−0.734877	−	0.273045i
$155$		0			0
$156$		0			0
$157$	−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
$159$		0			0
$160$		0			0
$161$	−203.686			−1.26513
$162$		0			0
$163$			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	$-0.988202\pi$
$167$		−	12.3771i		−	0.0741144i	0.999313	−	0.0370572i	$-0.0117984\pi$
$168$		0			0
$169$	−66.5008			−0.393496
$170$		0			0
$171$		0			0
$172$	182.904	−	212.156i	1.06340	−	1.23347i
$173$	59.3729			0.343196			0.171598	−	0.985167i	$-0.445107\pi$
$173$	59.3729			0.343196			0.171598	+	0.985167i	$0.445107\pi$
$174$		0			0
$175$		0			0
$176$	−174.719	+	26.0164i	−0.992720	+	0.147820i
$177$		0			0
$178$	−216.895	−	80.5877i	−1.21851	−	0.452740i
$179$			252.782i			1.41219i	0.708118	+	0.706094i	$0.249545\pi$
$179$			252.782i			1.41219i	−0.708118	+	0.706094i	$0.750455\pi$
$180$		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
$183$		0			0
$184$	−261.027	+	143.809i	−1.41862	+	0.781573i
$185$		0			0
$186$		0			0
$187$		−	269.545i		−	1.44142i
$188$	−99.3084	+	115.191i	−0.528236	+	0.612717i
$189$		0			0
$190$		0			0
$191$		−	97.4640i		−	0.510283i	−0.966904	−	0.255141i	$-0.917878\pi$
$191$		−	97.4640i		−	0.510283i	0.966904	−	0.255141i	$-0.0821220\pi$
$192$		0			0
$193$	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	$-0.439461\pi$
$197$	74.4829			0.378086			0.189043	+	0.981969i	$0.439461\pi$
$198$		0			0
$199$		−	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
$201$		0			0
$202$	−55.1356	−	20.4858i	−0.272949	−	0.101415i
$203$			140.917i			0.694173i
$204$		0			0
$205$		0			0
$206$	19.6354	−	52.8468i	0.0953172	−	0.256538i
$207$		0			0
$208$	−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
$213$		0			0
$214$	−3.13947	+	8.44961i	−0.0146704	+	0.0394842i
$215$		0			0
$216$		0			0
$217$	−26.4444			−0.121863
$218$	362.422	+	134.659i	1.66249	+	0.617701i
$219$		0			0
$220$		0			0
$221$	247.178			1.11845
$222$		0			0
$223$			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	$-0.963976\pi$
$227$		−	51.2708i		−	0.225863i	0.993603	−	0.112931i	$-0.0360240\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	99.4925	+	180.588i	0.428847	+	0.778395i
$233$	−80.2851			−0.344571			−0.172286	−	0.985047i	$-0.555115\pi$
$233$	−80.2851			−0.344571			−0.172286	+	0.985047i	$0.555115\pi$
$234$		0			0
$235$		0			0
$236$	−145.065	+	168.265i	−0.614682	+	0.712988i
$237$		0			0
$238$	92.9873	−	250.267i	0.390703	−	1.05154i
$239$		−	330.808i		−	1.38413i	−0.721834	−	0.692066i	$-0.756701\pi$
$239$		−	330.808i		−	1.38413i	0.721834	−	0.692066i	$-0.243299\pi$
$240$		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
$243$		0			0
$244$	−249.155	−	214.802i	−1.02113	−	0.880334i
$245$		0			0
$246$		0			0
$247$			240.710i			0.974534i
$248$	−33.8889	+	18.6707i	−0.136649	+	0.0752850i
$249$		0			0
$250$		0			0
$251$		−	312.213i		−	1.24388i	−0.783067	−	0.621938i	$-0.786346\pi$
$251$		−	312.213i		−	1.24388i	0.783067	−	0.621938i	$-0.213654\pi$
$252$		0			0
$253$	−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	$-0.450093\pi$
$257$	80.2592			0.312293			0.156146	+	0.987734i	$0.450093\pi$
$258$		0			0
$259$		−	194.920i		−	0.752586i
$260$		0			0
$261$		0			0
$262$	52.7680	−	142.020i	0.201405	−	0.542063i
$263$		−	487.967i		−	1.85539i	−0.373342	−	0.927694i	$-0.621788\pi$
$263$		−	487.967i		−	1.85539i	0.373342	−	0.927694i	$-0.378212\pi$
$264$		0			0
$265$		0			0
$266$	243.718	+	90.5540i	0.916233	+	0.340428i
$267$		0			0
$268$	−272.921	+	316.569i	−1.01836	+	1.18123i
$269$	309.553			1.15076			0.575378	−	0.817888i	$-0.304855\pi$
$269$	309.553			1.15076			0.575378	+	0.817888i	$0.304855\pi$
$270$		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
$273$		0			0
$274$	125.221	+	46.5262i	0.457012	+	0.169804i
$275$		0			0
$276$		0			0
$277$	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
$279$		0			0
$280$		0			0
$281$	−61.1598			−0.217650			−0.108825	−	0.994061i	$-0.534709\pi$
$281$	−61.1598			−0.217650			−0.108825	+	0.994061i	$0.534709\pi$
$282$		0			0
$283$		−	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
$288$		0			0
$289$	307.073			1.06254
$290$		0			0
$291$		0			0
$292$	283.329	+	244.264i	0.970305	+	0.836521i
$293$	−283.234			−0.966668			−0.483334	−	0.875436i	$-0.660574\pi$
$293$	−283.234			−0.966668			−0.483334	+	0.875436i	$0.660574\pi$
$294$		0			0
$295$		0			0
$296$	−137.620	−	249.793i	−0.464933	−	0.843895i
$297$		0			0
$298$	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
$303$		0			0
$304$	376.263	−	56.0272i	1.23771	−	0.184300i
$305$		0			0
$306$		0			0
$307$			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
$309$		0			0
$310$		0			0
$311$			404.185i			1.29963i	0.760092	+	0.649815i	$0.225154\pi$
$311$			404.185i			1.29963i	−0.760092	+	0.649815i	$0.774846\pi$
$312$		0			0
$313$	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	$-0.456724\pi$
$317$	85.9315			0.271077			0.135539	+	0.990772i	$0.456724\pi$
$318$		0			0
$319$			284.538i			0.891969i
$320$		0			0
$321$		0			0
$322$	−381.865	−	141.883i	−1.18592	−	0.440630i
$323$			580.475i			1.79714i
$324$		0			0
$325$		0			0
$326$	−44.2167	+	119.005i	−0.135634	+	0.365047i
$327$		0			0
$328$	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
$333$		0			0
$334$	8.62160	−	23.2043i	0.0258132	−	0.0694739i
$335$		0			0
$336$		0			0
$337$	−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
$339$		0			0
$340$		0			0
$341$	−53.3962			−0.156587
$342$		0			0
$343$			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	$-0.936554\pi$
$347$		−	137.414i		−	0.396006i	0.980201	−	0.198003i	$-0.0634455\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	−345.681	−	72.9301i	−0.982047	−	0.207188i
$353$	243.547			0.689935			0.344968	−	0.938615i	$-0.387890\pi$
$353$	243.547			0.689935			0.344968	+	0.938615i	$0.387890\pi$
$354$		0			0
$355$		0			0
$356$	−350.493	−	302.168i	−0.984532	−	0.848786i
$357$		0			0
$358$	−176.082	+	473.909i	−0.491849	+	1.32377i
$359$		−	17.9166i		−	0.0499068i	−0.999689	−	0.0249534i	$-0.992056\pi$
$359$		−	17.9166i		−	0.0499068i	0.999689	−	0.0249534i	$-0.00794374\pi$
$360$		0			0
$361$	−204.285			−0.565887
$362$	235.047	+	87.3321i	0.649300	+	0.241249i
$363$		0			0
$364$	144.582	−	167.704i	0.397202	−	0.460727i
$365$		0			0
$366$		0			0
$367$			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
$369$		0			0
$370$		0			0
$371$			304.968i			0.822016i
$372$		0			0
$373$	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
$378$		0			0
$379$		−	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
$381$		0			0
$382$	67.8912	−	182.723i	0.177726	−	0.478333i
$383$			144.027i			0.376050i	0.982164	+	0.188025i	$0.0602086\pi$
$383$			144.027i			0.376050i	−0.982164	+	0.188025i	$0.939791\pi$
$384$		0			0
$385$		0			0
$386$	641.878	+	238.491i	1.66290	+	0.617853i
$387$		0			0
$388$	221.034	+	190.558i	0.569674	+	0.491128i
$389$	−14.0099			−0.0360152			−0.0180076	−	0.999838i	$-0.505732\pi$
$389$	−14.0099			−0.0360152			−0.0180076	+	0.999838i	$0.505732\pi$
$390$		0			0
$391$		−	909.506i		−	2.32610i
$392$	73.7499	+	133.863i	0.188138	+	0.341486i
$393$		0			0
$394$	139.639	+	51.8831i	0.354413	+	0.131683i
$395$		0			0
$396$		0			0
$397$	−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
$399$		0			0
$400$		0			0
$401$	121.067			0.301913			0.150957	−	0.988540i	$-0.451765\pi$
$401$	121.067			0.301913			0.150957	+	0.988540i	$0.451765\pi$
$402$		0			0
$403$		−	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
$408$		0			0
$409$	−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
$411$		0			0
$412$	73.6237	−	85.3983i	0.178698	−	0.207278i
$413$	−303.682			−0.735307
$414$		0			0
$415$		0			0
$416$	66.8784	−	316.996i	0.160765	−	0.762009i
$417$		0			0
$418$	492.112	+	182.845i	1.17730	+	0.437429i
$419$			687.825i			1.64159i	0.571224	+	0.820794i	$0.306469\pi$
$419$			687.825i			1.64159i	−0.571224	+	0.820794i	$0.693531\pi$
$420$		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
$423$		0			0
$424$	215.318	+	390.821i	0.507826	+	0.921749i
$425$		0			0
$426$		0			0
$427$		−	449.670i		−	1.05309i
$428$	−11.7716	+	13.6542i	−0.0275037	+	0.0319024i
$429$		0			0
$430$		0			0
$431$			466.145i			1.08154i	0.841169	+	0.540772i	$0.181868\pi$
$431$			466.145i			1.08154i	−0.841169	+	0.540772i	$0.818132\pi$
$432$		0			0
$433$	−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
$438$		0			0
$439$			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
$441$		0			0
$442$	463.403	+	172.178i	1.04842	+	0.389544i
$443$			247.484i			0.558654i	0.960196	+	0.279327i	$0.0901114\pi$
$443$			247.484i			0.558654i	−0.960196	+	0.279327i	$0.909889\pi$
$444$		0			0
$445$		0			0
$446$	−141.213	+	380.061i	−0.316620	+	0.852155i
$447$		0			0
$448$	−295.798	−	186.967i	−0.660263	−	0.417336i
$449$	−412.508			−0.918726			−0.459363	−	0.888249i	$-0.651922\pi$
$449$	−412.508			−0.918726			−0.459363	+	0.888249i	$0.651922\pi$
$450$		0			0
$451$			102.720i			0.227761i
$452$	228.952	+	197.384i	0.506531	+	0.436691i
$453$		0			0
$454$	35.7141	−	96.1213i	0.0786654	−	0.211721i
$455$		0			0
$456$		0			0
$457$	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
$459$		0			0
$460$		0			0
$461$	−81.6151			−0.177039			−0.0885196	−	0.996074i	$-0.528214\pi$
$461$	−81.6151			−0.177039			−0.0885196	+	0.996074i	$0.528214\pi$
$462$		0			0
$463$		−	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	$-0.982468\pi$
$467$		−	51.4163i		−	0.110099i	0.998484	−	0.0550495i	$-0.0175317\pi$
$468$		0			0
$469$	−571.339			−1.21821
$470$		0			0
$471$		0			0
$472$	−389.174	+	214.410i	−0.824520	+	0.454259i
$473$	773.139			1.63454
$474$		0			0
$475$		0			0
$476$	348.660	−	404.422i	0.732480	−	0.849625i
$477$		0			0
$478$	230.433	−	620.190i	0.482077	−	1.29747i
$479$		−	122.593i		−	0.255935i	−0.991778	−	0.127967i	$-0.959155\pi$
$479$		−	122.593i		−	0.255935i	0.991778	−	0.127967i	$-0.0408453\pi$
$480$		0			0
$481$	360.920			0.750354
$482$	−674.758	−	250.708i	−1.39991	−	0.520141i
$483$		0			0
$484$	−2.69190	−	2.32074i	−0.00556177	−	0.00479492i
$485$		0			0
$486$		0			0
$487$		−	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
$489$		0			0
$490$		0			0
$491$		−	361.163i		−	0.735567i	−0.929911	−	0.367783i	$-0.880117\pi$
$491$		−	361.163i		−	0.735567i	0.929911	−	0.367783i	$-0.119883\pi$
$492$		0			0
$493$	−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
$498$		0			0
$499$		−	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
$501$		0			0
$502$	217.480	−	585.328i	0.433227	−	1.16599i
$503$			353.756i			0.703292i	0.936133	+	0.351646i	$0.114378\pi$
$503$			353.756i			0.703292i	−0.936133	+	0.351646i	$0.885622\pi$
$504$		0			0
$505$		0			0
$506$	−771.057	−	286.488i	−1.52383	−	0.566182i
$507$		0			0
$508$	342.951	−	397.799i	0.675100	−	0.783068i
$509$	−478.049			−0.939192			−0.469596	−	0.882881i	$-0.655600\pi$
$509$	−478.049			−0.939192			−0.469596	+	0.882881i	$0.655600\pi$
$510$		0			0
$511$			511.348i			1.00068i
$512$	−511.075	−	30.7568i	−0.998194	−	0.0600720i
$513$		0			0
$514$	150.468	+	55.9067i	0.292739	+	0.108768i
$515$		0			0
$516$		0			0
$517$	−419.778			−0.811949
$518$	135.777	−	365.431i	0.262117	−	0.705464i
$519$		0			0
$520$		0			0
$521$	35.7365			0.0685921			0.0342960	−	0.999412i	$-0.489081\pi$
$521$	35.7365			0.0685921			0.0342960	+	0.999412i	$0.489081\pi$
$522$		0			0
$523$		−	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
$528$		0			0
$529$	−858.753			−1.62335
$530$		0			0
$531$		0			0
$532$	393.839	+	339.537i	0.740298	+	0.638227i
$533$	−94.1965			−0.176729
$534$		0			0
$535$		0			0
$536$	−732.181	+	403.386i	−1.36601	+	0.752585i
$537$		0			0
$538$	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
$543$		0			0
$544$	161.278	−	764.440i	0.296467	−	1.40522i
$545$		0			0
$546$		0			0
$547$			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
$549$		0			0
$550$		0			0
$551$		−	612.763i		−	1.11209i
$552$		0			0
$553$	−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	$-0.813651\pi$
$557$	−928.488			−1.66694			−0.833472	+	0.552561i	$0.813651\pi$
$558$		0			0
$559$			708.984i			1.26831i
$560$		0			0
$561$		0			0
$562$	−114.661	−	42.6025i	−0.204023	−	0.0758051i
$563$		−	447.978i		−	0.795697i	−0.917451	−	0.397849i	$-0.869757\pi$
$563$		−	447.978i		−	0.795697i	0.917451	−	0.397849i	$-0.130243\pi$
$564$		0			0
$565$		0			0
$566$	301.274	−	810.852i	0.532286	−	1.43260i
$567$		0			0
$568$	−537.763	+	296.274i	−0.946766	+	0.521609i
$569$	−571.441			−1.00429			−0.502145	−	0.864783i	$-0.667456\pi$
$569$	−571.441			−1.00429			−0.502145	+	0.864783i	$0.667456\pi$
$570$		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
$573$		0			0
$574$	−35.4363	+	95.3736i	−0.0617357	+	0.166156i
$575$		0			0
$576$		0			0
$577$	−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
$579$		0			0
$580$		0			0
$581$	395.735			0.681127
$582$		0			0
$583$			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	$0.278062\pi$
$587$			900.009i			1.53323i	−0.642104	+	0.766617i	$0.721938\pi$
$588$		0			0
$589$	114.991			0.195230
$590$		0			0
$591$		0			0
$592$	−84.0071	−	564.169i	−0.141904	−	0.952987i
$593$	−704.088			−1.18733			−0.593666	−	0.804711i	$-0.702320\pi$
$593$	−704.088			−1.18733			−0.593666	+	0.804711i	$0.702320\pi$
$594$		0			0
$595$		0			0
$596$	383.897	+	330.965i	0.644122	+	0.555311i
$597$		0			0
$598$	262.715	−	707.075i	0.439323	−	1.18240i
$599$			376.098i			0.627876i	0.949444	+	0.313938i	$0.101648\pi$
$599$			376.098i			0.627876i	−0.949444	+	0.313938i	$0.898352\pi$
$600$		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
$603$		0			0
$604$	−178.756	+	207.344i	−0.295953	+	0.343285i
$605$		0			0
$606$		0			0
$607$			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
$609$		0			0
$610$		0			0
$611$		−	384.944i		−	0.630024i
$612$		0			0
$613$	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	$-0.648054\pi$
$617$	−553.493			−0.897072			−0.448536	+	0.893765i	$0.648054\pi$
$618$		0			0
$619$		−	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
$621$		0			0
$622$	−281.546	+	757.756i	−0.452646	+	1.21826i
$623$		−	632.564i		−	1.01535i
$624$		0			0
$625$		0			0
$626$	241.056	+	89.5651i	0.385074	+	0.143075i
$627$		0			0
$628$	−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
$633$		0			0
$634$	161.102	+	59.8579i	0.254104	+	0.0944130i
$635$		0			0
$636$		0			0
$637$	−193.415			−0.303634
$638$	−198.203	+	533.445i	−0.310662	+	0.836120i
$639$		0			0
$640$		0			0
$641$	545.742			0.851391			0.425696	−	0.904866i	$-0.360029\pi$
$641$	545.742			0.851391			0.425696	+	0.904866i	$0.360029\pi$
$642$		0			0
$643$			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	$0.354618\pi$
$647$			1161.36i			1.79500i	−0.441016	+	0.897499i	$0.645382\pi$
$648$		0			0
$649$	−613.191			−0.944824
$650$		0			0
$651$		0			0
$652$	−165.793	+	192.308i	−0.254283	+	0.294950i
$653$	−621.231			−0.951348			−0.475674	−	0.879622i	$-0.657796\pi$
$653$	−621.231			−0.951348			−0.475674	+	0.879622i	$0.657796\pi$
$654$		0			0
$655$		0			0
$656$	21.9250	+	147.242i	0.0334223	+	0.224455i
$657$		0			0
$658$	−389.755	−	144.814i	−0.592333	−	0.220083i
$659$			736.047i			1.11692i	0.829533	+	0.558458i	$0.188607\pi$
$659$			736.047i			1.11692i	−0.829533	+	0.558458i	$0.811393\pi$
$660$		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
$663$		0			0
$664$	507.141	−	279.403i	0.763766	−	0.420788i
$665$		0			0
$666$		0			0
$667$			960.096i			1.43942i
$668$	32.3271	−	37.4972i	0.0483939	−	0.0561335i
$669$		0			0
$670$		0			0
$671$		−	907.968i		−	1.35316i
$672$		0			0
$673$	−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	$-0.334376\pi$
$677$	673.154			0.994319			0.497160	+	0.867659i	$0.334376\pi$
$678$		0			0
$679$			398.918i			0.587507i
$680$		0			0
$681$		0			0
$682$	−100.106	−	37.1945i	−0.146783	−	0.0545374i
$683$		−	291.192i		−	0.426343i	−0.977015	−	0.213171i	$-0.931621\pi$
$683$		−	291.192i		−	0.426343i	0.977015	−	0.213171i	$-0.0683793\pi$
$684$		0			0
$685$		0			0
$686$	−259.387	+	698.117i	−0.378115	+	1.01766i
$687$		0			0
$688$	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
$693$		0			0
$694$	95.7193	−	257.620i	0.137924	−	0.371211i
$695$		0			0
$696$		0			0
$697$	−227.156			−0.325905
$698$	−25.2894	−	9.39633i	−0.0362312	−	0.0134618i
$699$		0			0
$700$		0			0
$701$	−885.681			−1.26345			−0.631727	−	0.775191i	$-0.717654\pi$
$701$	−885.681			−1.26345			−0.631727	+	0.775191i	$0.717654\pi$
$702$		0			0
$703$			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
$708$		0			0
$709$	−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
$711$		0			0
$712$	−446.613	−	810.642i	−0.627266	−	1.13854i
$713$	−180.171			−0.252694
$714$		0			0
$715$		0			0
$716$	−660.228	+	765.818i	−0.922106	+	1.06958i
$717$		0			0
$718$	12.4803	−	33.5895i	0.0173820	−	0.0467820i
$719$		−	666.163i		−	0.926513i	−0.886224	−	0.463257i	$-0.846681\pi$
$719$		−	666.163i		−	0.926513i	0.886224	−	0.463257i	$-0.153319\pi$
$720$		0			0
$721$	154.125			0.213766
$722$	−382.989	−	142.300i	−0.530455	−	0.197092i
$723$		0			0
$724$	379.826	+	327.456i	0.524622	+	0.452287i
$725$		0			0
$726$		0			0
$727$		−	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
$729$		0			0
$730$		0			0
$731$			1709.72i			2.33888i
$732$		0			0
$733$	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
$738$		0			0
$739$			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
$741$		0			0
$742$	−212.433	+	571.746i	−0.286298	+	0.770547i
$743$		−	426.794i		−	0.574421i	−0.957868	−	0.287210i	$-0.907272\pi$
$743$		−	426.794i		−	0.574421i	0.957868	−	0.287210i	$-0.0927278\pi$
$744$		0			0
$745$		0			0
$746$	339.842	+	126.269i	0.455552	+	0.169261i
$747$		0			0
$748$	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
$753$		0			0
$754$	−489.179	−	181.756i	−0.648779	−	0.241055i
$755$		0			0
$756$		0			0
$757$	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
$759$		0			0
$760$		0			0
$761$	189.584			0.249124			0.124562	−	0.992212i	$-0.460247\pi$
$761$	189.584			0.249124			0.124562	+	0.992212i	$0.460247\pi$
$762$		0			0
$763$			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
$768$		0			0
$769$	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
$771$		0			0
$772$	1037.25	+	894.235i	1.34359	+	1.15834i
$773$	23.2536			0.0300823			0.0150411	−	0.999887i	$-0.495212\pi$
$773$	23.2536			0.0300823			0.0150411	+	0.999887i	$0.495212\pi$
$774$		0			0
$775$		0			0
$776$	281.650	+	511.220i	0.362951	+	0.658788i
$777$		0			0
$778$	−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
$783$		0			0
$784$	45.0189	+	302.335i	0.0574221	+	0.385631i
$785$		0			0
$786$		0			0
$787$			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
$789$		0			0
$790$		0			0
$791$			413.209i			0.522388i
$792$		0			0
$793$	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	$-0.281467\pi$
$797$	1010.38			1.26773			0.633867	+	0.773442i	$0.281467\pi$
$798$		0			0
$799$		−	928.298i		−	1.16183i
$800$		0			0
$801$		0			0
$802$	226.974	+	84.3327i	0.283010	+	0.105153i
$803$			1032.51i			1.28581i
$804$		0			0
$805$		0			0
$806$	34.1081	−	91.7990i	0.0423178	−	0.113894i
$807$		0			0
$808$	−113.531	−	206.069i	−0.140509	−	0.255036i
$809$	−1410.37			−1.74335			−0.871674	−	0.490086i	$-0.836965\pi$
$809$	−1410.37			−1.74335			−0.871674	+	0.490086i	$0.836965\pi$
$810$		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
$813$		0			0
$814$	274.158	−	737.873i	0.336804	−	0.906478i
$815$		0			0
$816$		0			0
$817$	−1664.98			−2.03792
$818$	−1015.74	−	377.402i	−1.24174	−	0.461372i
$819$		0			0
$820$		0			0
$821$	−77.3347			−0.0941957			−0.0470979	−	0.998890i	$-0.514997\pi$
$821$	−77.3347			−0.0941957			−0.0470979	+	0.998890i	$0.514997\pi$
$822$		0			0
$823$		−	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	$0.0853194\pi$
$827$			438.047i			0.529681i	−0.964292	+	0.264841i	$0.914681\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	346.194	−	547.710i	0.416098	−	0.658305i
$833$	−466.423			−0.559931
$834$		0			0
$835$		0			0
$836$	795.234	+	685.588i	0.951237	+	0.820082i
$837$		0			0
$838$	−479.123	+	1289.52i	−0.571746	+	1.53880i
$839$		−	785.017i		−	0.935658i	−0.883819	−	0.467829i	$-0.845036\pi$
$839$		−	785.017i		−	0.935658i	0.883819	−	0.467829i	$-0.154964\pi$
$840$		0			0
$841$	−176.771			−0.210192
$842$	−851.890	−	316.521i	−1.01175	−	0.375916i
$843$		0			0
$844$	−485.524	+	563.173i	−0.575265	+	0.667267i
$845$		0			0
$846$		0			0
$847$		−	4.85829i		−	0.00573588i
$848$	131.436	+	882.688i	0.154995	+	1.04091i
$849$		0			0
$850$		0			0
$851$		−	1328.03i		−	1.56055i
$852$		0			0
$853$	−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	$-0.557246\pi$
$857$	−306.591			−0.357749			−0.178875	+	0.983872i	$0.557246\pi$
$858$		0			0
$859$			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
$861$		0			0
$862$	−324.706	+	873.918i	−0.376689	+	1.01383i
$863$		−	654.384i		−	0.758266i	−0.925342	−	0.379133i	$-0.876222\pi$
$863$		−	654.384i		−	0.758266i	0.925342	−	0.379133i	$-0.123778\pi$
$864$		0			0
$865$		0			0
$866$	−856.949	−	318.401i	−0.989549	−	0.367669i
$867$		0			0
$868$	−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
$873$		0			0
$874$	1660.50	+	616.963i	1.89989	+	0.705907i
$875$		0			0
$876$		0			0
$877$	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
$879$		0			0
$880$		0			0
$881$	−1436.81			−1.63089			−0.815445	−	0.578834i	$-0.803508\pi$
$881$	−1436.81			−1.63089			−0.815445	+	0.578834i	$0.803508\pi$
$882$		0			0
$883$		−	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	$-0.948376\pi$
$887$		−	286.448i		−	0.322941i	0.986878	−	0.161470i	$-0.0516236\pi$
$888$		0			0
$889$	717.940			0.807582
$890$		0			0
$891$		0			0
$892$	−529.483	+	614.164i	−0.593591	+	0.688524i
$893$	904.007			1.01233
$894$		0			0
$895$		0			0
$896$	−424.318	−	556.566i	−0.473569	−	0.621168i
$897$		0			0
$898$	−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
$903$		0			0
$904$	291.740	+	529.534i	0.322721	+	0.585768i
$905$		0			0
$906$		0			0
$907$		−	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
$909$		0			0
$910$		0			0
$911$		−	491.244i		−	0.539236i	−0.962967	−	0.269618i	$-0.913103\pi$
$911$		−	491.244i		−	0.539236i	0.962967	−	0.269618i	$-0.0868974\pi$
$912$		0			0
$913$	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
$918$		0			0
$919$		−	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
$921$		0			0
$922$	−153.010	−	56.8511i	−0.165954	−	0.0616607i
$923$		−	777.002i		−	0.841822i
$924$		0			0
$925$		0			0
$926$	203.573	−	547.899i	0.219841	−	0.591684i
$927$		0			0
$928$	−170.249	+	806.961i	−0.183458	+	0.869570i
$929$	916.019			0.986027			0.493014	−	0.870022i	$-0.335895\pi$
$929$	916.019			0.986027			0.493014	+	0.870022i	$0.335895\pi$
$930$		0			0
$931$		−	454.217i		−	0.487881i
$932$	−243.229	−	209.693i	−0.260975	−	0.224992i
$933$		0			0
$934$	35.8154	−	96.3939i	0.0383462	−	0.103205i
$935$		0			0
$936$		0			0
$937$	−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
$939$		0			0
$940$		0			0
$941$	1488.04			1.58133			0.790667	−	0.612246i	$-0.209734\pi$
$941$	1488.04			1.58133			0.790667	+	0.612246i	$0.209734\pi$
$942$		0			0
$943$			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	$-0.803673\pi$
$947$		−	1095.51i		−	1.15682i	0.815745	−	0.578411i	$-0.196327\pi$
$948$		0			0
$949$	−946.829			−0.997713
$950$		0			0
$951$		0			0
$952$	935.370	−	515.331i	0.982532	−	0.541314i
$953$	1277.86			1.34089			0.670443	−	0.741961i	$-0.266104\pi$
$953$	1277.86			1.34089			0.670443	+	0.741961i	$0.266104\pi$
$954$		0			0
$955$		0			0
$956$	864.020	−	1002.20i	0.903786	−	1.04833i
$957$		0			0
$958$	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
$963$		0			0
$964$	−1090.38	−	940.041i	−1.13110	−	0.975146i
$965$		0			0
$966$		0			0
$967$			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
$969$		0			0
$970$		0			0
$971$			1602.10i			1.64995i	0.565169	+	0.824975i	$0.308811\pi$
$971$			1602.10i			1.64995i	−0.565169	+	0.824975i	$0.691189\pi$
$972$		0			0
$973$	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	$-0.344144\pi$
$977$	918.977			0.940611			0.470305	+	0.882504i	$0.344144\pi$
$978$		0			0
$979$		−	1277.27i		−	1.30466i
$980$		0			0
$981$		0			0
$982$	251.578	−	677.100i	0.256189	−	0.689511i
$983$			1162.30i			1.18240i	0.806525	+	0.591200i	$0.201346\pi$
$983$			1162.30i			1.18240i	−0.806525	+	0.591200i	$0.798654\pi$
$984$		0			0
$985$		0			0
$986$	−1179.66	−	438.306i	−1.19641	−	0.444530i
$987$		0			0
$988$	−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
$993$		0			0
$994$	−786.712	−	292.305i	−0.791461	−	0.294069i
$995$		0			0
$996$		0			0
$997$	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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.7	✓	8	60.59	even	2
60.3.c.a.31.8	yes	8	15.14	odd	2
180.3.c.b.91.1		8	5.4	even	2
180.3.c.b.91.2		8	20.19	odd	2
300.3.c.d.151.1		8	3.2	odd	2
300.3.c.d.151.2		8	12.11	even	2
300.3.f.b.199.5		16	60.47	odd	4
300.3.f.b.199.6		16	15.8	even	4
300.3.f.b.199.11		16	15.2	even	4
300.3.f.b.199.12		16	60.23	odd	4
900.3.c.u.451.7		8	4.3	odd	2	inner
900.3.c.u.451.8		8	1.1	even	1	trivial
900.3.f.f.199.5		16	20.3	even	4
900.3.f.f.199.6		16	5.2	odd	4
900.3.f.f.199.11		16	5.3	odd	4
900.3.f.f.199.12		16	20.7	even	4
960.3.e.c.511.3		8	120.29	odd	2
960.3.e.c.511.8		8	120.59	even	2
2880.3.e.j.2431.2		8	40.29	even	2
2880.3.e.j.2431.3		8	40.19	odd	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.87477 + 0.696577i) q^{2} +(3.02956 + 2.61185i) q^{4} +5.46770i q^{7} +(3.86039 + 7.00695i) q^{8} +O(q^{10})\)	\(q+(1.87477 + 0.696577i) q^{2} +(3.02956 + 2.61185i) q^{4} +5.46770i q^{7} +(3.86039 + 7.00695i) q^{8} +11.0403i q^{11} -10.1242 q^{13} +(-3.80867 + 10.2507i) q^{14} +(2.35649 + 15.8255i) q^{16} -24.4146 q^{17} -23.7757i q^{19} +(-7.69043 + 20.6981i) q^{22} +37.2526i q^{23} +(-18.9806 - 7.05227i) q^{26} +(-14.2808 + 16.5647i) q^{28} +25.7726 q^{29} +4.83647i q^{31} +(-6.60580 + 31.3108i) q^{32} +(-45.7719 - 17.0066i) q^{34} -35.6493 q^{37} +(16.5616 - 44.5741i) q^{38} +9.30410 q^{41} -70.0287i q^{43} +(-28.8356 + 33.4473i) q^{44} +(-25.9493 + 69.8401i) q^{46} +38.0223i q^{47} +19.1043 q^{49} +(-30.6718 - 26.4428i) q^{52} +55.7762 q^{53} +(-38.3119 + 21.1075i) q^{56} +(48.3179 + 17.9526i) q^{58} +55.5411i q^{59} -82.2412 q^{61} +(-3.36897 + 9.06729i) q^{62} +(-34.1947 + 54.0992i) q^{64} +104.493i q^{67} +(-73.9656 - 63.7673i) q^{68} +76.7471i q^{71} +93.5215 q^{73} +(-66.8344 - 24.8325i) q^{74} +(62.0986 - 72.0300i) q^{76} -60.3651 q^{77} +49.3762i q^{79} +(17.4431 + 6.48102i) q^{82} -72.3768i q^{83} +(48.7804 - 131.288i) q^{86} +(-77.3589 + 42.6199i) q^{88} -115.691 q^{89} -55.3560i q^{91} +(-97.2980 + 112.859i) q^{92} +(-26.4854 + 71.2832i) q^{94} +72.9589 q^{97} +(35.8162 + 13.3076i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8	\( 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8} - 16 q^{13} + 20 q^{14} + 34 q^{16} - 68 q^{22} + 36 q^{26} - 28 q^{28} - 64 q^{29} - 76 q^{32} - 92 q^{34} + 112 q^{37} - 40 q^{38} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} + 128 q^{52} + 352 q^{53} - 116 q^{56} + 204 q^{58} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 184 q^{68} + 240 q^{73} - 132 q^{74} - 24 q^{76} - 288 q^{77} - 40 q^{82} + 200 q^{86} - 140 q^{88} - 80 q^{89} + 144 q^{92} - 96 q^{94} - 432 q^{97} + 660 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8 - 16 * q^13 + 20 * q^14 + 34 * q^16 - 68 * q^22 + 36 * q^26 - 28 * q^28 - 64 * q^29 - 76 * q^32 - 92 * q^34 + 112 * q^37 - 40 * q^38 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 + 128 * q^52 + 352 * q^53 - 116 * q^56 + 204 * q^58 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 184 * q^68 + 240 * q^73 - 132 * q^74 - 24 * q^76 - 288 * q^77 - 40 * q^82 + 200 * q^86 - 140 * q^88 - 80 * q^89 + 144 * q^92 - 96 * q^94 - 432 * q^97 + 660 * q^98

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