LMFDB - Embedded newform 21.9.f.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,9,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.55495081128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + \cdots + 556282980265104 $ x^12 - 3x^11 + 1331x^10 + 1482x^9 + 1359381x^8 + 1222227x^7 + 474169529x^6 + 1911324162x^5 + 121870629463x^4 + 259296590901x^3 + 9508380016437x^2 - 12075311354004*x + 556282980265104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Root			$-7.37103 - 12.7670i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.9.f.b.10.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.87103 - 13.6330i) q^{2} +(40.5000 - 23.3827i) q^{3} +(4.09363 + 7.09038i) q^{4} +(-872.651 - 503.826i) q^{5} -736.184i q^{6} +(-1325.41 - 2002.02i) q^{7} +4158.85 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})$	\(q+(7.87103 - 13.6330i) q^{2} +(40.5000 - 23.3827i) q^{3} +(4.09363 + 7.09038i) q^{4} +(-872.651 - 503.826i) q^{5} -736.184i q^{6} +(-1325.41 - 2002.02i) q^{7} +4158.85 q^{8} +(1093.50 - 1894.00i) q^{9} +(-13737.3 + 7931.26i) q^{10} +(-9280.43 - 16074.2i) q^{11} +(331.584 + 191.440i) q^{12} +17472.4i q^{13} +(-37726.0 + 2311.44i) q^{14} -47123.2 q^{15} +(31686.5 - 54882.7i) q^{16} +(-25777.7 + 14882.8i) q^{17} +(-17214.0 - 29815.4i) q^{18} +(119032. + 68723.1i) q^{19} -8249.90i q^{20} +(-100492. - 50090.1i) q^{21} -292186. q^{22} +(186158. - 322435. i) q^{23} +(168434. - 97245.2i) q^{24} +(312368. + 541037. i) q^{25} +(238202. + 137526. i) q^{26} -102276. i q^{27} +(8769.32 - 17593.2i) q^{28} +1.12419e6 q^{29} +(-370908. + 642432. i) q^{30} +(-408850. + 236050. i) q^{31} +(33522.0 + 58061.8i) q^{32} +(-751715. - 434003. i) q^{33} +468571. i q^{34} +(147955. + 2.41484e6i) q^{35} +17905.5 q^{36} +(1.30971e6 - 2.26848e6i) q^{37} +(1.87381e6 - 1.08184e6i) q^{38} +(408552. + 707633. i) q^{39} +(-3.62923e6 - 2.09534e6i) q^{40} -3.18083e6i q^{41} +(-1.47385e6 + 975748. i) q^{42} -4.06574e6 q^{43} +(75981.3 - 131603. i) q^{44} +(-1.90849e6 + 1.10187e6i) q^{45} +(-2.93051e6 - 5.07579e6i) q^{46} +(-390448. - 225425. i) q^{47} -2.96366e6i q^{48} +(-2.25136e6 + 5.30701e6i) q^{49} +9.83463e6 q^{50} +(-695998. + 1.20550e6i) q^{51} +(-123886. + 71525.6i) q^{52} +(5.50434e6 + 9.53379e6i) q^{53} +(-1.39433e6 - 805017. i) q^{54} +1.87029e7i q^{55} +(-5.51220e6 - 8.32611e6i) q^{56} +6.42772e6 q^{57} +(8.84855e6 - 1.53261e7i) q^{58} +(-5.81314e6 + 3.35622e6i) q^{59} +(-192905. - 334121. i) q^{60} +(4.12986e6 + 2.38438e6i) q^{61} +7.43182e6i q^{62} +(-5.24116e6 + 321121. i) q^{63} +1.72789e7 q^{64} +(8.80305e6 - 1.52473e7i) q^{65} +(-1.18335e7 + 6.83210e6i) q^{66} +(-4.32181e6 - 7.48559e6i) q^{67} +(-211049. - 121849. i) q^{68} -1.74115e7i q^{69} +(3.40862e7 + 1.69902e7i) q^{70} -4.14167e6 q^{71} +(4.54771e6 - 7.87686e6i) q^{72} +(-2.08313e7 + 1.20269e7i) q^{73} +(-2.06175e7 - 3.57106e7i) q^{74} +(2.53018e7 + 1.46080e7i) q^{75} +1.12531e6i q^{76} +(-1.98804e7 + 3.98845e7i) q^{77} +1.28629e7 q^{78} +(-1.15384e7 + 1.99851e7i) q^{79} +(-5.53026e7 + 3.19290e7i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(-4.33644e7 - 2.50364e7i) q^{82} -6.29479e7i q^{83} +(-56219.0 - 917575. i) q^{84} +2.99933e7 q^{85} +(-3.20016e7 + 5.54284e7i) q^{86} +(4.55298e7 - 2.62866e7i) q^{87} +(-3.85959e7 - 6.68501e7i) q^{88} +(2.43930e7 + 1.40833e7i) q^{89} +3.46913e7i q^{90} +(3.49801e7 - 2.31582e7i) q^{91} +3.04825e6 q^{92} +(-1.10389e7 + 1.91200e7i) q^{93} +(-6.14646e6 + 3.54866e6i) q^{94} +(-6.92489e7 - 1.19943e8i) q^{95} +(2.71528e6 + 1.56767e6i) q^{96} -7.60071e7i q^{97} +(5.46300e7 + 7.24645e7i) q^{98} -4.05926e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	7.87103	−	13.6330i	0.491940	−	0.852064i	−0.508017	−	0.861347i	$-0.669621\pi$
$2$	7.87103	−	13.6330i	0.491940	−	0.852064i	0.999957	+	0.00928241i	$0.00295472\pi$
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$4$	4.09363	+	7.09038i	0.0159907	+	0.0276968i
$5$	−872.651	−	503.826i	−1.39624	−	0.806121i	−0.402246	−	0.915532i	$-0.631770\pi$
$5$	−872.651	−	503.826i	−1.39624	−	0.806121i	−0.993997	+	0.109411i	$0.965104\pi$
$6$		−	736.184i		−	0.568043i
$7$	−1325.41	−	2002.02i	−0.552025	−	0.833827i
$7$	−1325.41	−	2002.02i	−0.552025	−	0.833827i
$8$	4158.85			1.01535
$9$	1093.50	−	1894.00i	0.166667	−	0.288675i
$10$	−13737.3	+	7931.26i	−1.37373	+	0.793126i
$11$	−9280.43	−	16074.2i	−0.633866	−	1.09789i	−0.986754	−	0.162222i	$-0.948134\pi$
$11$	−9280.43	−	16074.2i	−0.633866	−	1.09789i	0.352889	−	0.935665i	$-0.385199\pi$
$12$	331.584	+	191.440i	0.0159907	+	0.00923226i
$13$			17472.4i			0.611758i	0.952070	+	0.305879i	$0.0989503\pi$
$13$			17472.4i			0.611758i	−0.952070	+	0.305879i	$0.901050\pi$
$14$	−37726.0	+	2311.44i	−0.982038	+	0.0601686i
$15$	−47123.2			−0.930828
$16$	31686.5	−	54882.7i	0.483498	−	0.837443i
$17$	−25777.7	+	14882.8i	−0.308637	+	0.178192i	−0.646317	−	0.763069i	$-0.723691\pi$
$17$	−25777.7	+	14882.8i	−0.308637	+	0.178192i	0.337679	+	0.941261i	$0.390358\pi$
$18$	−17214.0	−	29815.4i	−0.163980	−	0.284021i
$19$	119032.	+	68723.1i	0.913374	+	0.527337i	0.881515	−	0.472156i	$-0.156524\pi$
$19$	119032.	+	68723.1i	0.913374	+	0.527337i	0.0318589	+	0.999492i	$0.489857\pi$
$20$		−	8249.90i		−	0.0515619i
$21$	−100492.	−	50090.1i	−0.516718	−	0.257558i
$22$	−292186.			−1.24729
$23$	186158.	−	322435.i	0.665227	−	1.15221i	−0.313996	−	0.949424i	$-0.601668\pi$
$23$	186158.	−	322435.i	0.665227	−	1.15221i	0.979224	−	0.202783i	$-0.0649987\pi$
$24$	168434.	−	97245.2i	0.507673	−	0.293105i
$25$	312368.	+	541037.i	0.799662	+	1.38505i
$26$	238202.	+	137526.i	0.521257	+	0.300948i
$27$		−	102276.i		−	0.192450i
$28$	8769.32	−	17593.2i	0.0142670	−	0.0286228i
$29$	1.12419e6			1.58946			0.794728	−	0.606966i	$-0.207614\pi$
$29$	1.12419e6			1.58946			0.794728	+	0.606966i	$0.207614\pi$
$30$	−370908.	+	642432.i	−0.457911	+	0.793126i
$31$	−408850.	+	236050.i	−0.442708	+	0.255597i	−0.704745	−	0.709460i	$-0.748939\pi$
$31$	−408850.	+	236050.i	−0.442708	+	0.255597i	0.262038	+	0.965058i	$0.415605\pi$
$32$	33522.0	+	58061.8i	0.0319691	+	0.0553721i
$33$	−751715.	−	434003.i	−0.633866	−	0.365962i
$34$			468571.i			0.350639i
$35$	147955.	+	2.41484e6i	0.0985957	+	1.60922i
$36$	17905.5			0.0106605
$37$	1.30971e6	−	2.26848e6i	0.698824	−	1.21040i	−0.270050	−	0.962846i	$-0.587040\pi$
$37$	1.30971e6	−	2.26848e6i	0.698824	−	1.21040i	0.968874	−	0.247553i	$-0.0796263\pi$
$38$	1.87381e6	−	1.08184e6i	0.898650	−	0.518836i
$39$	408552.	+	707633.i	0.176599	+	0.305879i
$40$	−3.62923e6	−	2.09534e6i	−1.41767	−	0.818491i
$41$		−	3.18083e6i		−	1.12566i	−0.826574	−	0.562828i	$-0.809713\pi$
$41$		−	3.18083e6i		−	1.12566i	0.826574	−	0.562828i	$-0.190287\pi$
$42$	−1.47385e6	+	975748.i	−0.473650	+	0.313574i
$43$	−4.06574e6			−1.18923			−0.594615	−	0.804010i	$-0.702696\pi$
$43$	−4.06574e6			−1.18923			−0.594615	+	0.804010i	$0.702696\pi$
$44$	75981.3	−	131603.i	0.0202720	−	0.0351121i
$45$	−1.90849e6	+	1.10187e6i	−0.465414	+	0.268707i
$46$	−2.93051e6	−	5.07579e6i	−0.654503	−	1.13363i
$47$	−390448.	−	225425.i	−0.0800151	−	0.0461967i	0.459459	−	0.888199i	$-0.348043\pi$
$47$	−390448.	−	225425.i	−0.0800151	−	0.0461967i	−0.539474	+	0.842002i	$0.681377\pi$
$48$		−	2.96366e6i		−	0.558295i
$49$	−2.25136e6	+	5.30701e6i	−0.390536	+	0.920588i
$50$	9.83463e6			1.57354
$51$	−695998.	+	1.20550e6i	−0.102879	+	0.178192i
$52$	−123886.	+	71525.6i	−0.0169437	+	0.00978247i
$53$	5.50434e6	+	9.53379e6i	0.697592	+	1.20826i	0.969299	+	0.245885i	$0.0790784\pi$
$53$	5.50434e6	+	9.53379e6i	0.697592	+	1.20826i	−0.271707	+	0.962380i	$0.587588\pi$
$54$	−1.39433e6	−	805017.i	−0.163980	−	0.0946738i
$55$			1.87029e7i			2.04389i
$56$	−5.51220e6	−	8.32611e6i	−0.560496	−	0.846623i
$57$	6.42772e6			0.608916
$58$	8.84855e6	−	1.53261e7i	0.781916	−	1.35432i
$59$	−5.81314e6	+	3.35622e6i	−0.479737	+	0.276976i	−0.720307	−	0.693656i	$-0.755999\pi$
$59$	−5.81314e6	+	3.35622e6i	−0.479737	+	0.276976i	0.240570	+	0.970632i	$0.422666\pi$
$60$	−192905.	−	334121.i	−0.0148846	−	0.0257809i
$61$	4.12986e6	+	2.38438e6i	0.298274	+	0.172209i	0.641667	−	0.766983i	$-0.278243\pi$
$61$	4.12986e6	+	2.38438e6i	0.298274	+	0.172209i	−0.343393	+	0.939192i	$0.611576\pi$
$62$			7.43182e6i			0.502954i
$63$	−5.24116e6	+	321121.i	−0.332709	+	0.0203848i
$64$	1.72789e7			1.02990
$65$	8.80305e6	−	1.52473e7i	0.493151	−	0.854162i
$66$	−1.18335e7	+	6.83210e6i	−0.623647	+	0.360063i
$67$	−4.32181e6	−	7.48559e6i	−0.214470	−	0.371473i	0.738639	−	0.674102i	$-0.235469\pi$
$67$	−4.32181e6	−	7.48559e6i	−0.214470	−	0.371473i	−0.953108	+	0.302629i	$0.902136\pi$
$68$	−211049.	−	121849.i	−0.00987068	−	0.00569884i
$69$		−	1.74115e7i		−	0.768138i
$70$	3.40862e7	+	1.69902e7i	1.41967	+	0.707631i
$71$	−4.14167e6			−0.162983			−0.0814914	−	0.996674i	$-0.525968\pi$
$71$	−4.14167e6			−0.162983			−0.0814914	+	0.996674i	$0.525968\pi$
$72$	4.54771e6	−	7.87686e6i	0.169224	−	0.293105i
$73$	−2.08313e7	+	1.20269e7i	−0.733541	+	0.423510i	−0.819716	−	0.572770i	$-0.805869\pi$
$73$	−2.08313e7	+	1.20269e7i	−0.733541	+	0.423510i	0.0861754	+	0.996280i	$0.472535\pi$
$74$	−2.06175e7	−	3.57106e7i	−0.687559	−	1.19089i
$75$	2.53018e7	+	1.46080e7i	0.799662	+	0.461685i
$76$			1.12531e6i			0.0337300i
$77$	−1.98804e7	+	3.98845e7i	−0.565539	+	1.13460i
$78$	1.28629e7			0.347505
$79$	−1.15384e7	+	1.99851e7i	−0.296236	+	0.513096i	−0.975272	−	0.221009i	$-0.929065\pi$
$79$	−1.15384e7	+	1.99851e7i	−0.296236	+	0.513096i	0.679035	+	0.734106i	$0.262398\pi$
$80$	−5.53026e7	+	3.19290e7i	−1.35016	+	0.779515i
$81$	−2.39148e6	−	4.14217e6i	−0.0555556	−	0.0962250i
$82$	−4.33644e7	−	2.50364e7i	−0.959131	−	0.553755i
$83$		−	6.29479e7i		−	1.32638i	−0.748450	−	0.663191i	$-0.769202\pi$
$83$		−	6.29479e7i		−	1.32638i	0.748450	−	0.663191i	$-0.230798\pi$
$84$	−56219.0	−	917575.i	−0.00112919	−	0.0184300i
$85$	2.99933e7			0.574577
$86$	−3.20016e7	+	5.54284e7i	−0.585030	+	1.01330i
$87$	4.55298e7	−	2.62866e7i	0.794728	−	0.458836i
$88$	−3.85959e7	−	6.68501e7i	−0.643592	−	1.11473i
$89$	2.43930e7	+	1.40833e7i	0.388781	+	0.224463i	0.681632	−	0.731695i	$-0.261271\pi$
$89$	2.43930e7	+	1.40833e7i	0.388781	+	0.224463i	−0.292851	+	0.956158i	$0.594604\pi$
$90$			3.46913e7i			0.528750i
$91$	3.49801e7	−	2.31582e7i	0.510101	−	0.337706i
$92$	3.04825e6			0.0425499
$93$	−1.10389e7	+	1.91200e7i	−0.147569	+	0.255597i
$94$	−6.14646e6	+	3.54866e6i	−0.0787252	+	0.0454520i
$95$	−6.92489e7	−	1.19943e8i	−0.850194	−	1.47258i
$96$	2.71528e6	+	1.56767e6i	0.0319691	+	0.0184574i
$97$		−	7.60071e7i		−	0.858553i	−0.903173	−	0.429276i	$-0.858769\pi$
$97$		−	7.60071e7i		−	0.858553i	0.903173	−	0.429276i	$-0.141231\pi$
$98$	5.46300e7	+	7.24645e7i	0.592280	+	0.785635i
$99$	−4.05926e7			−0.422577
$100$	−2.55744e6	+	4.42961e6i	−0.0255744	+	0.0442961i
$101$	−7.74100e7	+	4.46927e7i	−0.743895	+	0.429488i	−0.823484	−	0.567340i	$-0.807973\pi$
$101$	−7.74100e7	+	4.46927e7i	−0.743895	+	0.429488i	0.0795890	+	0.996828i	$0.474639\pi$
$102$	1.09564e7	+	1.89771e7i	0.101221	+	0.175319i
$103$	1.45997e8	+	8.42913e7i	1.29716	+	0.748917i	0.979913	−	0.199425i	$-0.0639073\pi$
$103$	1.45997e8	+	8.42913e7i	1.29716	+	0.748917i	0.317250	+	0.948342i	$0.397241\pi$
$104$			7.26652e7i			0.621146i
$105$	6.24577e7	+	9.43415e7i	0.513841	+	0.776150i
$106$	1.73299e8			1.37269
$107$	7.39387e7	−	1.28066e8i	0.564075	−	0.977007i	−0.433060	−	0.901365i	$-0.642566\pi$
$107$	7.39387e7	−	1.28066e8i	0.564075	−	0.977007i	0.997135	−	0.0756416i	$-0.0241005\pi$
$108$	725174.	−	418680.i	0.00533025	−	0.00307742i
$109$	−1.61014e7	−	2.78885e7i	−0.114067	−	0.197569i	0.803340	−	0.595521i	$-0.203054\pi$
$109$	−1.61014e7	−	2.78885e7i	−0.114067	−	0.197569i	−0.917406	+	0.397952i	$0.869721\pi$
$110$	2.54977e8	+	1.47211e8i	1.74153	+	1.00547i
$111$		−	1.22498e8i		−	0.806933i
$112$	−1.51874e8	+	9.30518e6i	−0.965186	+	0.0591361i
$113$	−6.05070e7			−0.371101			−0.185550	−	0.982635i	$-0.559407\pi$
$113$	−6.05070e7			−0.371101			−0.185550	+	0.982635i	$0.559407\pi$
$114$	5.05928e7	−	8.76293e7i	0.299550	−	0.518836i
$115$	−3.24902e8	+	1.87582e8i	−1.85764	+	1.07251i
$116$	4.60203e6	+	7.97094e6i	0.0254166	+	0.0440228i
$117$	3.30927e7	+	1.91061e7i	0.176599	+	0.101960i
$118$			1.05668e8i			0.545022i
$119$	6.39617e7	+	3.18816e7i	0.318957	+	0.158984i
$120$	−1.95978e8			−0.945112
$121$	−6.50732e7	+	1.12710e8i	−0.303571	+	0.525801i
$122$	6.50125e7	−	3.75350e7i	0.293466	−	0.169433i
$123$	−7.43764e7	−	1.28824e8i	−0.324949	−	0.562828i
$124$	−3.34736e6	−	1.93260e6i	−0.0141585	−	0.00817438i
$125$		−	2.35902e8i		−	0.966254i
$126$	−3.68755e7	+	7.39804e7i	−0.146304	+	0.293518i
$127$	4.84450e8			1.86223			0.931116	−	0.364723i	$-0.118836\pi$
$127$	4.84450e8			1.86223			0.931116	+	0.364723i	$0.118836\pi$
$128$	1.27421e8	−	2.20700e8i	0.474681	−	0.822172i
$129$	−1.64663e8	+	9.50680e7i	−0.594615	+	0.343301i
$130$	−1.38578e8	−	2.40025e8i	−0.485201	−	0.840393i
$131$	−2.92489e8	−	1.68869e8i	−0.993172	−	0.573408i	−0.0869510	−	0.996213i	$-0.527712\pi$
$131$	−2.92489e8	−	1.68869e8i	−0.993172	−	0.573408i	−0.906221	+	0.422805i	$0.861046\pi$
$132$		−	7.10658e6i		−	0.0234080i
$133$	−2.01815e7	−	3.29390e8i	−0.0644980	−	1.05270i
$134$	−1.36068e8			−0.422025
$135$	−5.15292e7	+	8.92512e7i	−0.155138	+	0.268707i
$136$	−1.07206e8	+	6.18952e7i	−0.313374	+	0.180926i
$137$	1.67337e8	+	2.89835e8i	0.475016	+	0.822753i	0.999591	−	0.0286121i	$-0.00910877\pi$
$137$	1.67337e8	+	2.89835e8i	0.475016	+	0.822753i	−0.524574	+	0.851365i	$0.675775\pi$
$138$	−2.37371e8	−	1.37046e8i	−0.654503	−	0.377878i
$139$			2.89151e8i			0.774578i	0.921958	+	0.387289i	$0.126589\pi$
$139$			2.89151e8i			0.774578i	−0.921958	+	0.387289i	$0.873411\pi$
$140$	−1.65165e7	+	1.09345e7i	−0.0429937	+	0.0284635i
$141$	−2.10842e7			−0.0533434
$142$	−3.25992e7	+	5.64635e7i	−0.0801777	+	0.138872i
$143$	2.80855e8	−	1.62152e8i	0.671641	−	0.387772i
$144$	−6.92984e7	−	1.20028e8i	−0.161166	−	0.279148i
$145$	−9.81028e8	−	5.66397e8i	−2.21927	−	1.28129i
$146$			3.78658e8i			0.833365i
$147$	3.29119e7	+	2.67577e8i	0.0704829	+	0.573032i
$148$	2.14459e7			0.0446989
$149$	6.58119e7	−	1.13989e8i	0.133524	−	0.231270i	−0.791509	−	0.611158i	$-0.790704\pi$
$149$	6.58119e7	−	1.13989e8i	0.133524	−	0.231270i	0.925033	+	0.379888i	$0.124037\pi$
$150$	3.98303e8	−	2.29960e8i	0.786771	−	0.454242i
$151$	1.92934e8	+	3.34171e8i	0.371108	+	0.642779i	0.989736	−	0.142905i	$-0.0456445\pi$
$151$	1.92934e8	+	3.34171e8i	0.371108	+	0.642779i	−0.618628	+	0.785684i	$0.712311\pi$
$152$	4.95036e8	+	2.85809e8i	0.927390	+	0.535429i
$153$			6.50972e7i			0.118795i
$154$	3.87267e8	+	5.84962e8i	0.688538	+	1.04003i
$155$	4.75711e8			0.824170
$156$	−3.34492e6	+	5.79358e6i	−0.00564791	+	0.00978247i
$157$	5.62628e8	−	3.24834e8i	0.926026	−	0.534641i	0.0404733	−	0.999181i	$-0.487113\pi$
$157$	5.62628e8	−	3.24834e8i	0.926026	−	0.534641i	0.885552	+	0.464539i	$0.153780\pi$
$158$	1.81639e8	+	3.14608e8i	0.291461	+	0.504825i
$159$	4.45851e8	+	2.57412e8i	0.697592	+	0.402755i
$160$		−	6.75570e7i		−	0.103084i
$161$	−8.92257e8	+	5.46678e7i	−1.32796	+	0.0813632i
$162$	−7.52938e7			−0.109320
$163$	−1.92407e8	+	3.33259e8i	−0.272565	+	0.472097i	−0.969518	−	0.245020i	$-0.921205\pi$
$163$	−1.92407e8	+	3.33259e8i	−0.272565	+	0.472097i	0.696953	+	0.717117i	$0.254539\pi$
$164$	2.25533e7	−	1.30212e7i	0.0311770	−	0.0180001i
$165$	4.37323e8	+	7.57466e8i	0.590020	+	1.02194i
$166$	−8.58171e8	−	4.95465e8i	−1.13016	−	0.652500i
$167$		−	1.93972e8i		−	0.249387i	−0.992195	−	0.124693i	$-0.960205\pi$
$167$		−	1.93972e8i		−	0.249387i	0.992195	−	0.124693i	$-0.0397947\pi$
$168$	−4.17931e8	−	2.08317e8i	−0.524647	−	0.261510i
$169$	5.10445e8			0.625752
$170$	2.36078e8	−	4.08899e8i	0.282657	−	0.489576i
$171$	2.60323e8	−	1.50297e8i	0.304458	−	0.175779i
$172$	−1.66436e7	−	2.88276e7i	−0.0190167	−	0.0329379i
$173$	5.81713e8	+	3.35852e8i	0.649418	+	0.374942i	0.788233	−	0.615377i	$-0.210996\pi$
$173$	5.81713e8	+	3.35852e8i	0.649418	+	0.374942i	−0.138815	+	0.990318i	$0.544329\pi$
$174$		−	8.27612e8i		−	0.902879i
$175$	6.69150e8	−	1.34246e9i	0.713463	−	1.43137i
$176$	−1.17626e9			−1.22589
$177$	−1.56955e8	+	2.71854e8i	−0.159912	+	0.276976i
$178$	3.83996e8	−	2.21700e8i	0.382514	−	0.220844i
$179$	−2.53632e8	−	4.39303e8i	−0.247054	−	0.427910i	0.715653	−	0.698456i	$-0.246129\pi$
$179$	−2.53632e8	−	4.39303e8i	−0.247054	−	0.427910i	−0.962707	+	0.270546i	$0.912796\pi$
$180$	−1.56253e7	−	9.02127e6i	−0.0148846	−	0.00859365i
$181$			1.68497e9i			1.56992i	0.619547	+	0.784959i	$0.287316\pi$
$181$			1.68497e9i			1.56992i	−0.619547	+	0.784959i	$0.712684\pi$
$182$	−4.03864e7	−	6.59164e8i	−0.0368086	−	0.600770i
$183$	2.23012e8			0.198850
$184$	7.74203e8	−	1.34096e9i	0.675435	−	1.16989i
$185$	−2.28584e9	+	1.31973e9i	−1.95146	+	1.12667i
$186$	1.73776e8	+	3.00989e8i	0.145190	+	0.251477i
$187$	4.78456e8	+	2.76237e8i	0.391269	+	0.225899i
$188$		−	3.69123e6i		−	0.00295488i
$189$	−2.04758e8	+	1.35558e8i	−0.160470	+	0.106237i
$190$	−2.18024e9			−1.67298
$191$	−1.57788e8	+	2.73297e8i	−0.118561	+	0.205353i	−0.919198	−	0.393797i	$-0.871161\pi$
$191$	−1.57788e8	+	2.73297e8i	−0.118561	+	0.205353i	0.800637	+	0.599150i	$0.204495\pi$
$192$	6.99796e8	−	4.04027e8i	0.514952	−	0.297307i
$193$	6.78514e8	+	1.17522e9i	0.489023	+	0.847013i	0.999920	−	0.0126286i	$-0.00401992\pi$
$193$	6.78514e8	+	1.17522e9i	0.489023	+	0.847013i	−0.510897	+	0.859642i	$0.670687\pi$
$194$	−1.03621e9	−	5.98254e8i	−0.731542	−	0.422356i
$195$		−	8.23356e8i		−	0.569442i
$196$	−4.68449e7	+	5.76192e6i	−0.0317423	+	0.00390430i
$197$	−2.46394e9			−1.63593			−0.817965	−	0.575268i	$-0.804898\pi$
$197$	−2.46394e9			−1.63593			−0.817965	+	0.575268i	$0.804898\pi$
$198$	−3.19506e8	+	5.53400e8i	−0.207882	+	0.360063i
$199$	2.13666e9	−	1.23360e9i	1.36246	−	0.786617i	0.372510	−	0.928028i	$-0.378497\pi$
$199$	2.13666e9	−	1.23360e9i	1.36246	−	0.786617i	0.989951	+	0.141411i	$0.0451640\pi$
$200$	1.29909e9	+	2.25009e9i	0.811933	+	1.40631i
$201$	−3.50067e8	−	2.02111e8i	−0.214470	−	0.123824i
$202$			1.40711e9i			0.845128i
$203$	−1.49002e9	−	2.25065e9i	−0.877420	−	1.32533i
$204$	−1.13966e7			−0.00658046
$205$	−1.60259e9	+	2.77576e9i	−0.907414	+	1.57169i
$206$	2.29829e9	−	1.32692e9i	1.27625	−	0.736844i
$207$	−4.07127e8	−	7.05165e8i	−0.221742	−	0.384069i
$208$	9.58933e8	+	5.53640e8i	0.512312	+	0.295784i
$209$		−	2.55112e9i		−	1.33704i
$210$	1.77777e9	−	1.08922e8i	0.914108	−	0.0560066i
$211$	−9.35569e8			−0.472004			−0.236002	−	0.971753i	$-0.575837\pi$
$211$	−9.35569e8			−0.472004			−0.236002	+	0.971753i	$0.575837\pi$
$212$	−4.50654e7	+	7.80556e7i	−0.0223100	+	0.0386421i
$213$	−1.67737e8	+	9.68433e7i	−0.0814914	+	0.0470491i
$214$	−1.16395e9	−	2.01602e9i	−0.554982	−	0.961257i
$215$	3.54798e9	+	2.04842e9i	1.66045	+	0.958663i
$216$		−	4.25350e8i		−	0.195403i
$217$	1.01447e9	+	5.05662e8i	0.457510	+	0.228045i
$218$	−5.06940e8			−0.224455
$219$	−5.62444e8	+	9.74182e8i	−0.244514	+	0.423510i
$220$	−1.32610e8	+	7.65626e7i	−0.0566091	+	0.0326833i
$221$	−2.60038e8	−	4.50399e8i	−0.109010	−	0.188811i
$222$	−1.67002e9	−	9.64186e8i	−0.687559	−	0.396962i
$223$		−	3.87315e9i		−	1.56619i	−0.621901	−	0.783096i	$-0.713639\pi$
$223$		−	3.87315e9i		−	1.56619i	0.621901	−	0.783096i	$-0.286361\pi$
$224$	7.18104e7	−	1.44068e8i	0.0285230	−	0.0572235i
$225$	1.36630e9			0.533108
$226$	−4.76253e8	+	8.24894e8i	−0.182559	+	0.316202i
$227$	1.04401e9	−	6.02759e8i	0.393189	−	0.227008i	−0.290352	−	0.956920i	$-0.593772\pi$
$227$	1.04401e9	−	6.02759e8i	0.393189	−	0.227008i	0.683541	+	0.729912i	$0.260439\pi$
$228$	2.63127e7	+	4.55749e7i	0.00973702	+	0.0168650i
$229$	−8.48896e8	−	4.90111e8i	−0.308683	−	0.178218i	0.337654	−	0.941270i	$-0.390367\pi$
$229$	−8.48896e8	−	4.90111e8i	−0.308683	−	0.178218i	−0.646337	+	0.763052i	$0.723700\pi$
$230$			5.90586e9i			2.11044i
$231$	1.27451e8	+	2.08018e9i	0.0447605	+	0.730555i
$232$	4.67535e9			1.61385
$233$	−4.13285e8	+	7.15831e8i	−0.140225	+	0.242877i	−0.927581	−	0.373621i	$-0.878116\pi$
$233$	−4.13285e8	+	7.15831e8i	−0.140225	+	0.242877i	0.787356	+	0.616498i	$0.211449\pi$
$234$	5.20948e8	−	3.00769e8i	0.173752	−	0.100316i
$235$	2.27150e8	+	3.93435e8i	0.0744803	+	0.129004i
$236$	−4.75937e7	−	2.74782e7i	−0.0153427	−	0.00885811i
$237$			1.07920e9i			0.342064i
$238$	9.38088e8	−	6.21050e8i	0.292372	−	0.193561i
$239$	2.33371e9			0.715245			0.357623	−	0.933866i	$-0.383587\pi$
$239$	2.33371e9			0.715245			0.357623	+	0.933866i	$0.383587\pi$
$240$	−1.49317e9	+	2.58624e9i	−0.450053	+	0.779515i
$241$	−4.77508e8	+	2.75689e8i	−0.141551	+	0.0817244i	−0.569103	−	0.822266i	$-0.692709\pi$
$241$	−4.77508e8	+	2.75689e8i	−0.141551	+	0.0817244i	0.427552	+	0.903991i	$0.359376\pi$
$242$	1.02439e9	+	1.77429e9i	0.298677	+	0.517324i
$243$	−1.93710e8	−	1.11839e8i	−0.0555556	−	0.0320750i
$244$			3.90430e7i			0.0110150i
$245$	4.63846e9	−	3.49687e9i	1.28739	−	0.970544i
$246$	−2.34168e9			−0.639421
$247$	−1.20076e9	+	2.07977e9i	−0.322603	+	0.558764i
$248$	−1.70035e9	+	9.81696e8i	−0.449501	+	0.259520i
$249$	−1.47189e9	−	2.54939e9i	−0.382894	−	0.663191i
$250$	−3.21606e9	−	1.85679e9i	−0.823311	−	0.475339i
$251$			2.81546e9i			0.709340i	0.934992	+	0.354670i	$0.115407\pi$
$251$			2.81546e9i			0.709340i	−0.934992	+	0.354670i	$0.884593\pi$
$252$	−2.37322e7	−	3.58472e7i	−0.00588487	−	0.00888901i
$253$	−6.91050e9			−1.68666
$254$	3.81312e9	−	6.60452e9i	0.916106	−	1.58674i
$255$	1.21473e9	−	7.01323e8i	0.287288	−	0.165866i
$256$	2.05826e8	+	3.56501e8i	0.0479226	+	0.0830044i
$257$	3.28132e9	+	1.89447e9i	0.752171	+	0.434266i	0.826478	−	0.562969i	$-0.190341\pi$
$257$	3.28132e9	+	1.89447e9i	0.752171	+	0.434266i	−0.0743069	+	0.997235i	$0.523674\pi$
$258$			2.99313e9i			0.675534i
$259$	−6.27745e9	+	3.84614e8i	−1.39503	+	0.0854724i
$260$	1.44146e8			0.0315434
$261$	1.22930e9	−	2.12922e9i	0.264909	−	0.458836i
$262$	−4.60438e9	+	2.65834e9i	−0.977161	+	0.564164i
$263$	−2.55786e9	−	4.43035e9i	−0.534631	−	0.926009i	−0.999181	−	0.0404618i	$-0.987117\pi$
$263$	−2.55786e9	−	4.43035e9i	−0.534631	−	0.926009i	0.464550	−	0.885547i	$-0.346216\pi$
$264$	−3.12627e9	−	1.80495e9i	−0.643592	−	0.371578i
$265$		−	1.10929e10i		−	2.24937i
$266$	−4.64944e9	−	2.31751e9i	−0.928697	−	0.462908i
$267$	1.31722e9			0.259187
$268$	3.53838e7	−	6.12865e7i	0.00685907	−	0.0118803i
$269$	−5.56209e9	+	3.21128e9i	−1.06226	+	0.613294i	−0.926055	−	0.377387i	$-0.876823\pi$
$269$	−5.56209e9	+	3.21128e9i	−1.06226	+	0.613294i	−0.136201	+	0.990681i	$0.543489\pi$
$270$	8.11176e8	+	1.40500e9i	0.152637	+	0.264375i
$271$	1.03976e9	+	6.00309e8i	0.192778	+	0.111301i	0.593283	−	0.804994i	$-0.297832\pi$
$271$	1.03976e9	+	6.00309e8i	0.192778	+	0.111301i	−0.400504	+	0.916295i	$0.631165\pi$
$272$			1.88633e9i			0.344622i
$273$	8.75195e8	−	1.75584e9i	0.157563	−	0.316106i
$274$	5.26845e9			0.934718
$275$	5.79781e9	−	1.00421e10i	1.01376	−	1.75588i
$276$	1.23454e8	−	7.12762e7i	0.0212750	−	0.0122831i
$277$	3.65035e9	+	6.32259e9i	0.620034	+	1.07393i	0.989479	+	0.144678i	$0.0462146\pi$
$277$	3.65035e9	+	6.32259e9i	0.620034	+	1.07393i	−0.369445	+	0.929253i	$0.620452\pi$
$278$	3.94200e9	+	2.27592e9i	0.659991	+	0.381046i
$279$			1.03248e9i			0.170398i
$280$	6.15324e8	+	1.00430e10i	0.100109	+	1.63392i
$281$	1.61654e9			0.259276			0.129638	−	0.991561i	$-0.458619\pi$
$281$	1.61654e9			0.259276			0.129638	+	0.991561i	$0.458619\pi$
$282$	−1.65954e8	+	2.87441e8i	−0.0262417	+	0.0454520i
$283$	8.70947e9	−	5.02842e9i	1.35783	−	0.783945i	0.368501	−	0.929627i	$-0.379871\pi$
$283$	8.70947e9	−	5.02842e9i	1.35783	−	0.783945i	0.989331	+	0.145683i	$0.0465379\pi$
$284$	−1.69545e7	−	2.93660e7i	−0.00260622	−	0.00451410i
$285$	−5.60916e9	−	3.23845e9i	−0.850194	−	0.490860i
$286$		−	5.10520e9i		−	0.763042i
$287$	−6.36809e9	+	4.21592e9i	−0.938602	+	0.621391i
$288$	1.46625e8			0.0213127
$289$	−3.04489e9	+	5.27390e9i	−0.436495	+	0.756032i
$290$	−1.54434e10	+	8.91625e9i	−2.18349	+	1.26064i
$291$	−1.77725e9	−	3.07829e9i	−0.247843	−	0.429276i
$292$	−1.70551e8	−	9.84677e7i	−0.0234597	−	0.0135445i
$293$			7.04818e9i			0.956327i	0.878271	+	0.478164i	$0.158697\pi$
$293$			7.04818e9i			0.956327i	−0.878271	+	0.478164i	$0.841303\pi$
$294$	3.90693e9	+	1.65742e9i	0.522933	+	0.221841i
$295$	6.76379e9			0.893105
$296$	5.44689e9	−	9.43429e9i	0.709548	−	1.22897i
$297$	−1.64400e9	+	9.49164e8i	−0.211289	+	0.121987i
$298$	−1.03601e9	−	1.79443e9i	−0.131371	−	0.227542i
$299$	5.63372e9	+	3.25263e9i	0.704872	+	0.406958i
$300$			2.39199e8i			0.0295307i
$301$	5.38879e9	+	8.13969e9i	0.656485	+	0.991613i
$302$	6.07436e9			0.730252
$303$	−2.09007e9	+	3.62011e9i	−0.247965	+	0.429488i
$304$	7.54341e9	−	4.35519e9i	0.883229	−	0.509932i
$305$	−2.40262e9	−	4.16146e9i	−0.277642	−	0.480890i
$306$	8.87472e8	+	5.12382e8i	0.101221	+	0.0584398i
$307$			1.31396e10i			1.47920i	0.673046	+	0.739601i	$0.264986\pi$
$307$			1.31396e10i			1.47920i	−0.673046	+	0.739601i	$0.735014\pi$
$308$	−3.64179e8	+	2.23129e7i	−0.0404680	+	0.00247944i
$309$	7.88383e9			0.864775
$310$	3.74434e9	−	6.48539e9i	0.405442	−	0.702246i
$311$	8.73214e7	−	5.04150e7i	0.00933424	−	0.00538913i	−0.495326	−	0.868707i	$-0.664951\pi$
$311$	8.73214e7	−	5.04150e7i	0.00933424	−	0.00538913i	0.504660	+	0.863318i	$0.331618\pi$
$312$	1.69911e9	+	2.94294e9i	0.179309	+	0.310573i
$313$	4.88033e9	+	2.81766e9i	0.508478	+	0.293570i	0.732208	−	0.681081i	$-0.238490\pi$
$313$	4.88033e9	+	2.81766e9i	0.508478	+	0.293570i	−0.223730	+	0.974651i	$0.571823\pi$
$314$		−	1.02271e10i		−	1.05204i
$315$	4.73549e9	+	2.36040e9i	0.480976	+	0.239742i
$316$	−1.88936e8			−0.0189482
$317$	−5.83122e9	+	1.01000e10i	−0.577461	+	1.00019i	0.418309	+	0.908305i	$0.362623\pi$
$317$	−5.83122e9	+	1.01000e10i	−0.577461	+	1.00019i	−0.995769	+	0.0918867i	$0.970710\pi$
$318$	7.01862e9	−	4.05220e9i	0.686346	−	0.396262i
$319$	−1.04330e10	−	1.80704e10i	−1.00750	−	1.74504i
$320$	−1.50785e10	−	8.70555e9i	−1.43799	−	0.830226i
$321$		−	6.91554e9i		−	0.651338i
$322$	−6.27770e9	+	1.25945e10i	−0.583952	+	1.17154i
$323$	−4.09116e9			−0.375869
$324$	1.95797e7	−	3.39130e7i	0.00177675	−	0.00307742i
$325$	−9.45323e9	+	5.45782e9i	−0.847318	+	0.489199i
$326$	3.02888e9	+	5.24618e9i	0.268171	+	0.464486i
$327$	−1.30422e9	−	7.52989e8i	−0.114067	−	0.0658564i
$328$		−	1.32286e10i		−	1.14293i
$329$	6.61992e7	+	1.08047e9i	0.00565027	+	0.0922205i
$330$	1.37687e10			1.16102
$331$	3.03853e9	−	5.26288e9i	0.253134	−	0.438442i	−0.711253	−	0.702936i	$-0.751872\pi$
$331$	3.03853e9	−	5.26288e9i	0.253134	−	0.438442i	0.964387	+	0.264495i	$0.0852052\pi$
$332$	4.46324e8	−	2.57685e8i	0.0367365	−	0.0212098i
$333$	−2.86433e9	−	4.96117e9i	−0.232941	−	0.403466i
$334$	−2.64443e9	−	1.52676e9i	−0.212494	−	0.122683i
$335$			8.70975e9i			0.691555i
$336$	−5.93331e9	+	3.92808e9i	−0.465522	+	0.308193i
$337$	−1.57174e10			−1.21860			−0.609301	−	0.792939i	$-0.708550\pi$
$337$	−1.57174e10			−1.21860			−0.609301	+	0.792939i	$0.708550\pi$
$338$	4.01773e9	−	6.95892e9i	0.307832	−	0.533181i
$339$	−2.45053e9	+	1.41482e9i	−0.185550	+	0.107128i
$340$	1.22781e8	+	2.12664e8i	0.00918791	+	0.0159139i
$341$	7.58860e9	+	4.38128e9i	0.561234	+	0.324029i
$342$		−	4.73198e9i		−	0.345891i
$343$	1.36087e10	−	2.52671e9i	0.983197	−	0.182549i
$344$	−1.69088e10			−1.20748
$345$	−8.77235e9	+	1.51942e10i	−0.619212	+	1.07251i
$346$	9.15736e9	−	5.28701e9i	0.638949	−	0.368897i
$347$	3.30785e9	+	5.72937e9i	0.228154	+	0.395175i	0.957261	−	0.289225i	$-0.0933976\pi$
$347$	3.30785e9	+	5.72937e9i	0.228154	+	0.395175i	−0.729107	+	0.684400i	$0.760064\pi$
$348$	3.72764e8	+	2.15215e8i	0.0254166	+	0.0146743i
$349$		−	2.03751e10i		−	1.37340i	−0.726939	−	0.686702i	$-0.759058\pi$
$349$		−	2.03751e10i		−	1.37340i	0.726939	−	0.686702i	$-0.240942\pi$
$350$	−1.30349e10	−	1.96891e10i	−0.868635	−	1.31206i
$351$	1.78701e9			0.117733
$352$	6.22197e8	−	1.07768e9i	0.0405282	−	0.0701969i
$353$	−2.48043e10	+	1.43208e10i	−1.59745	+	0.922290i	−0.605477	+	0.795863i	$0.707017\pi$
$353$	−2.48043e10	+	1.43208e10i	−1.59745	+	0.922290i	−0.991976	+	0.126427i	$0.959649\pi$
$354$	2.47079e9	+	4.27954e9i	0.157334	+	0.272511i
$355$	3.61423e9	+	2.08668e9i	0.227563	+	0.131384i
$356$			2.30607e8i			0.0143573i
$357$	3.33593e9	−	2.04389e8i	0.205373	−	0.0125830i
$358$	−7.98538e9			−0.486142
$359$	−3.83481e9	+	6.64209e9i	−0.230869	+	0.399877i	−0.958064	−	0.286554i	$-0.907490\pi$
$359$	−3.83481e9	+	6.64209e9i	−0.230869	+	0.399877i	0.727195	+	0.686431i	$0.240824\pi$
$360$	−7.93713e9	+	4.58250e9i	−0.472556	+	0.272830i
$361$	9.53936e8	+	1.65227e9i	0.0561682	+	0.0972862i
$362$	2.29712e10	+	1.32624e10i	1.33767	+	0.772305i
$363$			6.08634e9i			0.350534i
$364$	3.07396e8	+	1.53221e8i	0.0175103	+	0.00872797i
$365$	2.42379e10			1.36560
$366$	1.75534e9	−	3.04034e9i	0.0978220	−	0.169433i
$367$	−1.97907e10	+	1.14262e10i	−1.09093	+	0.629850i	−0.933824	−	0.357732i	$-0.883550\pi$
$367$	−1.97907e10	+	1.14262e10i	−1.09093	+	0.629850i	−0.157108	+	0.987581i	$0.550217\pi$
$368$	−1.17974e10	−	2.04337e10i	−0.643272	−	1.11418i
$369$	−6.02449e9	−	3.47824e9i	−0.324949	−	0.187609i
$370$			4.15505e10i			2.21702i
$371$	1.17913e10	−	2.36560e10i	0.622395	−	1.24866i
$372$	−1.80757e8			−0.00943897
$373$	7.98697e9	−	1.38338e10i	0.412617	−	0.714673i	−0.582558	−	0.812789i	$-0.697948\pi$
$373$	7.98697e9	−	1.38338e10i	0.412617	−	0.714673i	0.995175	+	0.0981158i	$0.0312816\pi$
$374$	7.53189e9	−	4.34854e9i	0.384962	−	0.222258i
$375$	−5.51602e9	−	9.55402e9i	−0.278933	−	0.483127i
$376$	−1.62382e9	−	9.37511e8i	−0.0812429	−	0.0469056i
$377$			1.96424e10i			0.972362i
$378$	2.36404e8	+	3.85846e9i	0.0115795	+	0.188993i
$379$	−1.44920e10			−0.702379			−0.351189	−	0.936304i	$-0.614223\pi$
$379$	−1.44920e10			−0.702379			−0.351189	+	0.936304i	$0.614223\pi$
$380$	5.66958e8	−	9.82001e8i	0.0271905	−	0.0470953i
$381$	1.96202e10	−	1.13277e10i	0.931116	−	0.537580i
$382$	2.48391e9	+	4.30226e9i	0.116650	+	0.202043i
$383$	2.73451e10	+	1.57877e10i	1.27082	+	0.733708i	0.975142	−	0.221579i	$-0.0711211\pi$
$383$	2.73451e10	+	1.57877e10i	1.27082	+	0.733708i	0.295678	+	0.955288i	$0.404454\pi$
$384$		−	1.19178e10i		−	0.548115i
$385$	3.74435e10	−	2.47890e10i	1.70425	−	1.12828i
$386$	2.13624e10			0.962280
$387$	−4.44589e9	+	7.70051e9i	−0.198205	+	0.343301i
$388$	5.38919e8	−	3.11145e8i	0.0237791	−	0.0137289i
$389$	−5.54492e8	−	9.60409e8i	−0.0242157	−	0.0419428i	0.853664	−	0.520825i	$-0.174376\pi$
$389$	−5.54492e8	−	9.60409e8i	−0.0242157	−	0.0419428i	−0.877879	+	0.478882i	$0.841042\pi$
$390$	−1.12248e10	−	6.48066e9i	−0.485201	−	0.280131i
$391$			1.10822e10i			0.474152i
$392$	−9.36308e9	+	2.20711e10i	−0.396529	+	0.934714i
$393$	−1.57944e10			−0.662115
$394$	−1.93937e10	+	3.35909e10i	−0.804779	+	1.39392i
$395$	2.01381e10	−	1.16267e10i	0.827235	−	0.477605i
$396$	−1.66171e8	−	2.87817e8i	−0.00675732	−	0.0117040i
$397$	−7.59392e8	−	4.38435e8i	−0.0305706	−	0.0176499i	0.484637	−	0.874715i	$-0.338952\pi$
$397$	−7.59392e8	−	4.38435e8i	−0.0305706	−	0.0176499i	−0.515207	+	0.857066i	$0.672285\pi$
$398$		−	3.88389e10i		−	1.54787i
$399$	−8.51938e9	−	1.28684e10i	−0.336137	−	0.507731i
$400$	3.95914e10			1.54654
$401$	1.69326e10	−	2.93281e10i	0.654856	−	1.13424i	−0.327074	−	0.944999i	$-0.606062\pi$
$401$	1.69326e10	−	2.93281e10i	0.654856	−	1.13424i	0.981930	−	0.189245i	$-0.0606042\pi$
$402$	−5.51077e9	+	3.18165e9i	−0.211012	+	0.121828i
$403$	−4.12436e9	−	7.14360e9i	−0.156364	−	0.270830i
$404$	−6.33776e8	−	3.65911e8i	−0.0237909	−	0.0137357i
$405$			4.81956e9i			0.179138i
$406$	−4.24112e10	+	2.59850e9i	−1.56091	+	0.0956353i
$407$	−4.86186e10			−1.77184
$408$	−2.89455e9	+	5.01352e9i	−0.104458	+	0.180926i
$409$	2.78407e10	−	1.60738e10i	0.994916	−	0.574415i	0.0881759	−	0.996105i	$-0.471896\pi$
$409$	2.78407e10	−	1.60738e10i	0.994916	−	0.574415i	0.906740	+	0.421690i	$0.138563\pi$
$410$	2.52280e10	+	4.36962e10i	0.892786	+	1.54635i
$411$	1.35543e10	+	7.82556e9i	0.475016	+	0.274251i
$412$			1.38023e9i			0.0479030i
$413$	1.44240e10	+	7.18964e9i	0.495777	+	0.247120i
$414$	−1.28180e10			−0.436336
$415$	−3.17148e10	+	5.49316e10i	−1.06922	+	1.85195i
$416$	−1.01448e9	+	5.85711e8i	−0.0338743	+	0.0195573i
$417$	6.76113e9	+	1.17106e10i	0.223602	+	0.387289i
$418$	−3.47795e10	−	2.00799e10i	−1.13925	−	0.657744i
$419$		−	1.49018e10i		−	0.483484i	−0.970341	−	0.241742i	$-0.922281\pi$
$419$		−	1.49018e10i		−	0.483484i	0.970341	−	0.241742i	$-0.0777188\pi$
$420$	−4.13238e8	+	8.29048e8i	−0.0132802	+	0.0266430i
$421$	−7.62768e9			−0.242808			−0.121404	−	0.992603i	$-0.538740\pi$
$421$	−7.62768e9			−0.242808			−0.121404	+	0.992603i	$0.538740\pi$
$422$	−7.36390e9	+	1.27546e10i	−0.232198	+	0.402178i
$423$	−8.53910e8	+	4.93005e8i	−0.0266717	+	0.0153989i
$424$	2.28917e10	+	3.96496e10i	0.708297	+	1.22681i
$425$	−1.61043e10	−	9.29779e9i	−0.493611	−	0.284986i
$426$			3.04903e9i			0.0925812i
$427$	−7.00204e8	−	1.14283e10i	−0.0210627	−	0.343773i
$428$	1.21071e9			0.0360799
$429$	7.58308e9	−	1.31343e10i	0.223880	−	0.387772i
$430$	5.58525e10	−	3.22464e10i	1.63369	−	0.943209i
$431$	−3.30726e9	−	5.72834e9i	−0.0958428	−	0.166005i	0.814117	−	0.580701i	$-0.197221\pi$
$431$	−3.30726e9	−	5.72834e9i	−0.0958428	−	0.166005i	−0.909960	+	0.414696i	$0.863888\pi$
$432$	−5.61317e9	−	3.24077e9i	−0.161166	−	0.0930492i
$433$		−	4.41900e10i		−	1.25711i	−0.777766	−	0.628553i	$-0.783647\pi$
$433$		−	4.41900e10i		−	1.25711i	0.777766	−	0.628553i	$-0.216353\pi$
$434$	1.48786e10	−	9.85023e9i	0.419377	−	0.277643i
$435$	−5.29755e10			−1.47951
$436$	1.31827e8	−	2.28330e8i	0.00364802	−	0.00631855i
$437$	4.43174e10	−	2.55867e10i	1.21520	−	0.701598i
$438$	8.85403e9	+	1.53356e10i	0.240572	+	0.416683i
$439$	−3.52730e10	−	2.03648e10i	−0.949694	−	0.548306i	−0.0567082	−	0.998391i	$-0.518060\pi$
$439$	−3.52730e10	−	2.03648e10i	−0.949694	−	0.548306i	−0.892986	+	0.450085i	$0.851394\pi$
$440$			7.77825e10i			2.07525i
$441$	7.58959e9	+	1.00673e10i	0.200661	+	0.266169i
$442$	−8.18707e9			−0.214506
$443$	−8.89217e9	+	1.54017e10i	−0.230883	+	0.399902i	−0.958068	−	0.286540i	$-0.907495\pi$
$443$	−8.89217e9	+	1.54017e10i	−0.230883	+	0.399902i	0.727185	+	0.686442i	$0.240828\pi$
$444$	8.68557e8	−	5.01462e8i	0.0223494	−	0.0129035i
$445$	−1.41911e10	−	2.45796e10i	−0.361888	−	0.626809i
$446$	−5.28028e10	−	3.04857e10i	−1.33450	−	0.770472i
$447$		−	6.15543e9i		−	0.154180i
$448$	−2.29017e10	−	3.45927e10i	−0.568533	−	0.858761i
$449$	−5.71972e10			−1.40731			−0.703655	−	0.710542i	$-0.748450\pi$
$449$	−5.71972e10			−1.40731			−0.703655	+	0.710542i	$0.748450\pi$
$450$	1.07542e10	−	1.86268e10i	0.262257	−	0.454242i
$451$	−5.11293e10	+	2.95195e10i	−1.23584	+	0.713514i
$452$	−2.47693e8	−	4.29017e8i	−0.00593418	−	0.0102783i
$453$	1.56277e10	+	9.02263e9i	0.371108	+	0.214260i
$454$		−	1.89773e10i		−	0.446696i
$455$	−4.21931e10	+	2.58514e9i	−0.984456	+	0.0603167i
$456$	2.67319e10			0.618260
$457$	1.65622e10	−	2.86866e10i	0.379711	−	0.657678i	−0.611309	−	0.791392i	$-0.709357\pi$
$457$	1.65622e10	−	2.86866e10i	0.379711	−	0.657678i	0.991020	+	0.133713i	$0.0426902\pi$
$458$	−1.33634e10	+	7.71535e9i	−0.303707	+	0.175345i
$459$	1.52215e9	+	2.63644e9i	0.0342930	+	0.0593973i
$460$	−2.66006e9	−	1.53578e9i	−0.0594100	−	0.0343004i
$461$		−	3.42499e10i		−	0.758324i	−0.925330	−	0.379162i	$-0.876212\pi$
$461$		−	3.42499e10i		−	0.758324i	0.925330	−	0.379162i	$-0.123788\pi$
$462$	2.93623e10	+	1.46356e10i	0.644499	+	0.321250i
$463$	7.30532e10			1.58970			0.794850	−	0.606806i	$-0.207550\pi$
$463$	7.30532e10			1.58970			0.794850	+	0.606806i	$0.207550\pi$
$464$	3.56217e10	−	6.16986e10i	0.768498	−	1.33108i
$465$	1.92663e10	−	1.11234e10i	0.412085	−	0.237917i
$466$	6.50596e9	+	1.12687e10i	0.137965	+	0.238962i
$467$	1.63254e10	+	9.42550e9i	0.343240	+	0.198169i	0.661704	−	0.749765i	$-0.269834\pi$
$467$	1.63254e10	+	9.42550e9i	0.343240	+	0.198169i	−0.318464	+	0.947935i	$0.603167\pi$
$468$			3.12853e8i			0.00652164i
$469$	−9.25812e9	+	1.85738e10i	−0.191351	+	0.383893i
$470$	7.15162e9			0.146559
$471$	1.51910e10	−	2.63115e10i	0.308675	−	0.534641i
$472$	−2.41760e10	+	1.39580e10i	−0.487098	+	0.281226i
$473$	3.77318e10	+	6.53534e10i	0.753812	+	1.30564i
$474$	1.47127e10	+	8.49440e9i	0.291461	+	0.168275i
$475$			8.58675e10i			1.68676i
$476$	3.57826e7	+	5.84024e8i	0.000697019	+	0.0113764i
$477$	2.40760e10			0.465061
$478$	1.83687e10	−	3.18155e10i	0.351857	−	0.609435i
$479$	3.90691e10	−	2.25565e10i	0.742149	−	0.428480i	−0.0807011	−	0.996738i	$-0.525716\pi$
$479$	3.90691e10	−	2.25565e10i	0.742149	−	0.428480i	0.822850	+	0.568258i	$0.192383\pi$
$480$	−1.57966e9	−	2.73606e9i	−0.0297577	−	0.0515419i
$481$	3.96359e10	+	2.28838e10i	0.740471	+	0.427511i
$482$			8.67984e9i			0.160814i
$483$	−3.48581e10	+	2.30774e10i	−0.640495	+	0.424032i
$484$	−1.06554e9			−0.0194173
$485$	−3.82943e10	+	6.63277e10i	−0.692097	+	1.19875i
$486$	−3.04940e9	+	1.76057e9i	−0.0546600	+	0.0315579i
$487$	4.37687e10	+	7.58096e10i	0.778122	+	1.34775i	0.933023	+	0.359817i	$0.117161\pi$
$487$	4.37687e10	+	7.58096e10i	0.778122	+	1.34775i	−0.154901	+	0.987930i	$0.549506\pi$
$488$	1.71755e10	+	9.91627e9i	0.302851	+	0.174851i
$489$			1.79960e10i			0.314731i
$490$	−1.11635e10	−	9.07602e10i	−0.193650	−	1.57439i
$491$	−9.88294e10			−1.70044			−0.850218	−	0.526431i	$-0.823530\pi$
$491$	−9.88294e10			−1.70044			−0.850218	+	0.526431i	$0.823530\pi$
$492$	6.08939e8	−	1.05471e9i	0.0103923	−	0.0180001i
$493$	−2.89791e10	+	1.67311e10i	−0.490565	+	0.283228i
$494$	1.89024e10	+	3.27399e10i	0.317402	+	0.549756i
$495$	3.54232e10	+	2.04516e10i	0.590020	+	0.340648i
$496$			2.99184e10i			0.494323i
$497$	5.48942e9	+	8.29170e9i	0.0899706	+	0.135899i
$498$	−4.63412e10			−0.753442
$499$	2.41387e10	−	4.18095e10i	0.389325	−	0.674330i	−0.603034	−	0.797715i	$-0.706042\pi$
$499$	2.41387e10	−	4.18095e10i	0.389325	−	0.674330i	0.992359	+	0.123385i	$0.0393751\pi$
$500$	1.67263e9	−	9.65695e8i	0.0267621	−	0.0154511i
$501$	−4.53559e9	−	7.85587e9i	−0.0719918	−	0.124693i
$502$	3.83832e10	+	2.21606e10i	0.604403	+	0.348952i
$503$		−	8.59769e10i		−	1.34310i	−0.740957	−	0.671552i	$-0.765628\pi$
$503$		−	8.59769e10i		−	1.34310i	0.740957	−	0.671552i	$-0.234372\pi$
$504$	−2.17972e10	+	1.33550e9i	−0.337815	+	0.0206976i
$505$	9.00692e10			1.38488
$506$	−5.43928e10	+	9.42110e10i	−0.829734	+	1.43714i
$507$	2.06730e10	−	1.19356e10i	0.312876	−	0.180639i
$508$	1.98316e9	+	3.43493e9i	0.0297785	+	0.0515778i
$509$	−5.58850e10	−	3.22652e10i	−0.832576	−	0.480688i	0.0221580	−	0.999754i	$-0.492946\pi$
$509$	−5.58850e10	−	3.22652e10i	−0.832576	−	0.480688i	−0.854734	+	0.519067i	$0.826280\pi$
$510$		−	2.20806e10i		−	0.326384i
$511$	5.16882e10	+	2.57639e10i	0.758067	+	0.377858i
$512$	7.17199e10			1.04366
$513$	7.02871e9	−	1.21741e10i	0.101486	−	0.175779i
$514$	5.16548e10	−	2.98229e10i	0.740045	−	0.427265i
$515$	−8.49362e10	−	1.47114e11i	−1.20744	−	2.09134i
$516$	−1.34814e9	−	7.78346e8i	−0.0190167	−	0.0109793i
$517$			8.36817e9i			0.117130i
$518$	−4.41666e10	+	8.86080e10i	−0.613444	+	1.23070i
$519$	3.14125e10			0.432945
$520$	3.66106e10	−	6.34114e10i	0.500718	−	0.867270i
$521$	2.57618e10	−	1.48736e10i	0.349643	−	0.201867i	−0.314885	−	0.949130i	$-0.601966\pi$
$521$	2.57618e10	−	1.48736e10i	0.349643	−	0.201867i	0.664528	+	0.747263i	$0.268633\pi$
$522$	−1.93518e10	−	3.35183e10i	−0.260639	−	0.451440i
$523$	−3.79626e10	−	2.19177e10i	−0.507399	−	0.292947i	0.224365	−	0.974505i	$-0.427969\pi$
$523$	−3.79626e10	−	2.19177e10i	−0.507399	−	0.292947i	−0.731764	+	0.681558i	$0.761303\pi$
$524$		−	2.76514e9i		−	0.0366769i
$525$	−4.28984e9	−	7.00163e10i	−0.0564682	−	0.921641i
$526$	−8.05322e10			−1.05203
$527$	7.02614e9	−	1.21696e10i	0.0910908	−	0.157774i
$528$	−4.76384e10	+	2.75041e10i	−0.612945	+	0.353884i
$529$	−3.01540e10	−	5.22283e10i	−0.385055	−	0.666934i
$530$	−1.51230e11	−	8.73126e10i	−1.91661	−	1.10656i
$531$			1.46801e10i			0.184651i
$532$	2.25289e9	−	1.49150e9i	0.0281250	−	0.0186198i
$533$	5.55769e10			0.688629
$534$	1.03679e10	−	1.79577e10i	0.127505	−	0.220844i
$535$	−1.29045e11	+	7.45044e10i	−1.57517	+	0.909425i
$536$	−1.79738e10	−	3.11315e10i	−0.217761	−	0.377173i
$537$	−2.05442e10	−	1.18612e10i	−0.247054	−	0.142637i
$538$			1.01104e11i			1.20681i
$539$	1.06199e11	−	1.30625e10i	1.25825	−	0.154765i
$540$	−8.43766e8			−0.00992309
$541$	−7.28527e10	+	1.26185e11i	−0.850465	+	1.47305i	0.0303234	+	0.999540i	$0.490346\pi$
$541$	−7.28527e10	+	1.26185e11i	−0.850465	+	1.47305i	−0.880789	+	0.473509i	$0.842987\pi$
$542$	1.63681e10	−	9.45010e9i	0.189671	−	0.109506i
$543$	3.93991e10	+	6.82412e10i	0.453197	+	0.784959i
$544$	−1.72824e9	−	9.97801e8i	−0.0197337	−	0.0113933i
$545$			3.24492e10i			0.367806i
$546$	−1.70487e10	−	2.57518e10i	−0.191832	−	0.289759i
$547$	−9.83889e10			−1.09900			−0.549499	−	0.835495i	$-0.685181\pi$
$547$	−9.83889e10			−1.09900			−0.549499	+	0.835495i	$0.685181\pi$
$548$	−1.37003e9	+	2.37296e9i	−0.0151917	+	0.0263129i
$549$	9.03200e9	−	5.21463e9i	0.0994248	−	0.0574029i
$550$	−9.12696e10	−	1.58084e11i	−0.997414	−	1.72757i
$551$	1.33815e11	+	7.72579e10i	1.45177	+	0.838178i
$552$		−	7.24118e10i		−	0.779926i
$553$	5.53038e10	−	3.38842e9i	0.591364	−	0.0362323i
$554$	1.14928e11			1.22008
$555$	−6.17176e10	+	1.06898e11i	−0.650485	+	1.12667i
$556$	−2.05019e9	+	1.18368e9i	−0.0214533	+	0.0123861i
$557$	−5.08002e10	−	8.79886e10i	−0.527770	−	0.914125i	−0.999476	−	0.0323688i	$-0.989695\pi$
$557$	−5.08002e10	−	8.79886e10i	−0.527770	−	0.914125i	0.471706	−	0.881756i	$-0.343638\pi$
$558$	1.40758e10	+	8.12669e9i	0.145190	+	0.0838257i
$559$		−	7.10384e10i		−	0.727521i
$560$	1.37221e11	+	6.83977e10i	1.39530	+	0.695488i
$561$	2.58366e10			0.260846
$562$	1.27239e10	−	2.20384e10i	0.127548	−	0.220920i
$563$	−7.65819e10	+	4.42146e10i	−0.762241	+	0.440080i	−0.830100	−	0.557615i	$-0.811717\pi$
$563$	−7.65819e10	+	4.42146e10i	−0.762241	+	0.440080i	0.0678587	+	0.997695i	$0.478383\pi$
$564$	−8.63109e7	−	1.49495e8i	−0.000853000	−	0.00147744i
$565$	5.28015e10	+	3.04850e10i	0.518147	+	0.299152i
$566$		−	1.58315e11i		−	1.54261i
$567$	−5.12300e9	+	1.02779e10i	−0.0495670	+	0.0994424i
$568$	−1.72246e10			−0.165484
$569$	−9.12017e10	+	1.57966e11i	−0.870069	+	1.50700i	−0.00814484	+	0.999967i	$0.502593\pi$
$569$	−9.12017e10	+	1.57966e11i	−0.870069	+	1.50700i	−0.861924	+	0.507037i	$0.830741\pi$
$570$	−8.82998e10	+	5.09799e10i	−0.836489	+	0.482947i
$571$	1.78143e10	+	3.08552e10i	0.167580	+	0.290258i	0.937569	−	0.347800i	$-0.113071\pi$
$571$	1.78143e10	+	3.08552e10i	0.167580	+	0.290258i	−0.769988	+	0.638058i	$0.779738\pi$
$572$	2.29943e9	+	1.32758e9i	0.0214801	+	0.0124015i
$573$			1.47581e10i			0.136902i
$574$	7.35230e9	+	1.20000e11i	0.0677291	+	1.10544i
$575$	2.32599e11			2.12783
$576$	1.88945e10	−	3.27262e10i	0.171651	−	0.297307i
$577$	1.23110e9	−	7.10774e8i	0.0111068	−	0.00641251i	−0.494436	−	0.869214i	$-0.664625\pi$
$577$	1.23110e9	−	7.10774e8i	0.0111068	−	0.00641251i	0.505543	+	0.862801i	$0.331292\pi$
$578$	4.79328e10	+	8.30220e10i	0.429459	+	0.743844i
$579$	5.49596e10	+	3.17310e10i	0.489023	+	0.282338i
$580$		−	9.27447e9i		−	0.0819553i
$581$	−1.26023e11	+	8.34320e10i	−1.10597	+	0.732197i
$582$	−5.59552e10			−0.487695
$583$	1.02165e11	−	1.76955e11i	0.884359	−	1.53175i
$584$	−8.66342e10	+	5.00183e10i	−0.744797	+	0.430009i
$585$	−1.92523e10	−	3.33459e10i	−0.164384	−	0.284721i
$586$	9.60881e10	+	5.54765e10i	0.814853	+	0.470455i
$587$		−	4.96798e10i		−	0.418434i	−0.977869	−	0.209217i	$-0.932908\pi$
$587$		−	4.96798e10i		−	0.418434i	0.977869	−	0.209217i	$-0.0670915\pi$
$588$	−1.76249e9	+	1.32872e9i	−0.0147441	+	0.0111154i
$589$	−6.48882e10			−0.539144
$590$	5.32381e10	−	9.22110e10i	0.439354	−	0.760983i
$591$	−9.97894e10	+	5.76134e10i	−0.817965	+	0.472252i
$592$	−8.30002e10	−	1.43761e11i	−0.675760	−	1.17045i
$593$	2.85382e10	+	1.64766e10i	0.230785	+	0.133244i	0.610934	−	0.791681i	$-0.290794\pi$
$593$	2.85382e10	+	1.64766e10i	0.230785	+	0.133244i	−0.380149	+	0.924925i	$0.624127\pi$
$594$			2.98836e10i			0.240042i
$595$	−3.97535e10	−	6.00471e10i	−0.317181	−	0.479098i
$596$	1.07764e9			0.00854059
$597$	5.76899e10	−	9.99219e10i	0.454154	−	0.786617i
$598$	8.86864e10	−	5.12031e10i	0.693509	−	0.400398i
$599$	1.29323e10	+	2.23993e10i	0.100454	+	0.173991i	0.911872	−	0.410475i	$-0.134637\pi$
$599$	1.29323e10	+	2.23993e10i	0.100454	+	0.173991i	−0.811418	+	0.584467i	$0.801304\pi$
$600$	1.05226e11	+	6.07525e10i	0.811933	+	0.468770i
$601$		−	1.51646e10i		−	0.116234i	−0.998310	−	0.0581171i	$-0.981490\pi$
$601$		−	1.51646e10i		−	0.116234i	0.998310	−	0.0581171i	$-0.0185097\pi$
$602$	1.53384e11	−	9.39771e9i	1.16787	−	0.0715543i
$603$	−1.89036e10			−0.142980
$604$	−1.57960e9	+	2.73595e9i	−0.0118686	+	0.0205570i
$605$	1.13572e11	−	6.55711e10i	0.847718	−	0.489430i
$606$	3.29020e10	+	5.69880e10i	0.243968	+	0.422564i
$607$	6.90692e10	+	3.98771e10i	0.508780	+	0.293744i	0.732332	−	0.680948i	$-0.238432\pi$
$607$	6.90692e10	+	3.98771e10i	0.508780	+	0.293744i	−0.223552	+	0.974692i	$0.571765\pi$
$608$			9.21494e9i			0.0674339i
$609$	−1.12972e11	−	5.63108e10i	−0.821300	−	0.409376i
$610$	−7.56444e10			−0.546333
$611$	3.93872e9	−	6.82207e9i	0.0282612	−	0.0489499i
$612$	−4.61564e8	+	2.66484e8i	−0.00329023	+	0.00189961i
$613$	−1.80887e10	−	3.13306e10i	−0.128105	−	0.221885i	0.794837	−	0.606823i	$-0.207556\pi$
$613$	−1.80887e10	−	3.13306e10i	−0.128105	−	0.221885i	−0.922942	+	0.384938i	$0.874223\pi$
$614$	1.79132e11	+	1.03422e11i	1.26037	+	0.727678i
$615$			1.49891e11i			1.04779i
$616$	−8.26797e10	+	1.65874e11i	−0.574217	+	1.15201i
$617$	1.94419e10			0.134152			0.0670762	−	0.997748i	$-0.478633\pi$
$617$	1.94419e10			0.134152			0.0670762	+	0.997748i	$0.478633\pi$
$618$	6.20539e10	−	1.07480e11i	0.425417	−	0.736844i
$619$	−1.11944e11	+	6.46308e10i	−0.762496	+	0.440227i	−0.830191	−	0.557479i	$-0.811769\pi$
$619$	−1.11944e11	+	6.46308e10i	−0.762496	+	0.440227i	0.0676951	+	0.997706i	$0.478435\pi$
$620$	1.94739e9	+	3.37297e9i	0.0131791	+	0.0228268i
$621$	−3.29773e10	−	1.90395e10i	−0.221742	−	0.128023i
$622$		−	1.58727e9i		−	0.0106045i
$623$	−4.13575e9	−	6.75014e10i	−0.0274538	−	0.448085i
$624$	5.17824e10			0.341542
$625$	3.16531e9	−	5.48248e9i	0.0207442	−	0.0359300i
$626$	7.68265e10	−	4.43558e10i	0.500281	−	0.288837i
$627$	−5.96520e10	−	1.03320e11i	−0.385971	−	0.668521i
$628$	4.60639e9	+	2.65950e9i	0.0296157	+	0.0170986i
$629$			7.79684e10i			0.498099i
$630$	6.94527e10	−	4.59803e10i	0.440887	−	0.291884i
$631$	9.16394e10			0.578049			0.289024	−	0.957322i	$-0.406669\pi$
$631$	9.16394e10			0.578049			0.289024	+	0.957322i	$0.406669\pi$
$632$	−4.79866e10	+	8.31153e10i	−0.300782	+	0.520970i
$633$	−3.78906e10	+	2.18761e10i	−0.236002	+	0.136256i
$634$	9.17955e10	+	1.58994e11i	0.568152	+	0.984068i
$635$	−4.22756e11	−	2.44078e11i	−2.60013	−	1.50118i
$636$			4.21500e9i			0.0257614i
$637$	−9.27262e10	−	3.93367e10i	−0.563177	−	0.238913i
$638$	−3.28473e11			−1.98252
$639$	−4.52891e9	+	7.84431e9i	−0.0271638	+	0.0470491i
$640$	−2.22389e11	+	1.28396e11i	−1.32554	+	0.765301i
$641$	−1.13147e11	−	1.95977e11i	−0.670213	−	1.16084i	−0.977844	−	0.209337i	$-0.932869\pi$
$641$	−1.13147e11	−	1.95977e11i	−0.670213	−	1.16084i	0.307631	−	0.951506i	$-0.400464\pi$
$642$	−9.42798e10	−	5.44325e10i	−0.554982	−	0.320419i
$643$		−	1.20991e11i		−	0.707799i	−0.935283	−	0.353899i	$-0.884856\pi$
$643$		−	1.20991e11i		−	0.707799i	0.935283	−	0.353899i	$-0.115144\pi$
$644$	−4.04018e9	−	6.10265e9i	−0.0234886	−	0.0354793i
$645$	1.91591e11			1.10697
$646$	−3.22016e10	+	5.57749e10i	−0.184905	+	0.320264i
$647$	1.57050e11	−	9.06729e10i	0.896233	−	0.517440i	0.0202567	−	0.999795i	$-0.493552\pi$
$647$	1.57050e11	−	9.06729e10i	0.896233	−	0.517440i	0.875976	+	0.482355i	$0.160218\pi$
$648$	−9.94584e9	−	1.72267e10i	−0.0564081	−	0.0977016i
$649$	1.07897e11	+	6.22943e10i	0.608177	+	0.351131i
$650$			1.71835e11i			0.962626i
$651$	5.29098e10	−	3.24174e9i	0.294586	−	0.0180490i
$652$	−3.15057e9			−0.0174341
$653$	−4.21763e10	+	7.30516e10i	−0.231962	+	0.401769i	−0.958385	−	0.285478i	$-0.907848\pi$
$653$	−4.21763e10	+	7.30516e10i	−0.231962	+	0.401769i	0.726424	+	0.687247i	$0.241181\pi$
$654$	−2.05311e10	+	1.18536e10i	−0.112228	+	0.0647947i
$655$	1.70161e11	+	2.94727e11i	0.924472	+	1.60123i
$656$	−1.74573e11	−	1.00790e11i	−0.942672	−	0.544252i
$657$			5.26058e10i			0.282340i
$658$	1.52511e10	+	7.60189e9i	0.0813574	+	0.0405525i
$659$	6.53766e10			0.346641			0.173321	−	0.984865i	$-0.444550\pi$
$659$	6.53766e10			0.346641			0.173321	+	0.984865i	$0.444550\pi$
$660$	−3.58048e9	+	6.20157e9i	−0.0188697	+	0.0326833i
$661$	4.52833e10	−	2.61443e10i	0.237209	−	0.136953i	−0.376684	−	0.926342i	$-0.622936\pi$
$661$	4.52833e10	−	2.61443e10i	0.237209	−	0.136953i	0.613893	+	0.789389i	$0.289602\pi$
$662$	−4.78327e10	−	8.28487e10i	−0.249054	−	0.431374i
$663$	−2.10631e10	−	1.21608e10i	−0.109010	−	0.0629371i
$664$		−	2.61791e11i		−	1.34674i
$665$	−1.48344e11	+	2.97611e11i	−0.758548	+	1.52182i
$666$	−9.01811e10			−0.458372
$667$	2.09277e11	−	3.62479e11i	1.05735	−	1.83138i
$668$	1.37534e9	−	7.94050e8i	0.00690721	−	0.00398788i
$669$	−9.05647e10	−	1.56863e11i	−0.452121	−	0.783096i
$670$	1.18740e11	+	6.85547e10i	0.589249	+	0.340203i
$671$		−	8.85121e10i		−	0.436629i
$672$	−4.60368e8	−	7.51386e9i	−0.00225750	−	0.0368456i
$673$	1.53502e11			0.748263			0.374132	−	0.927376i	$-0.377941\pi$
$673$	1.53502e11			0.748263			0.374132	+	0.927376i	$0.377941\pi$
$674$	−1.23712e11	+	2.14276e11i	−0.599478	+	1.03833i
$675$	5.53350e10	−	3.19477e10i	0.266554	−	0.153895i
$676$	2.08957e9	+	3.61925e9i	0.0100062	+	0.0173313i
$677$	−1.87901e11	−	1.08485e11i	−0.894490	−	0.516434i	−0.0190813	−	0.999818i	$-0.506074\pi$
$677$	−1.87901e11	−	1.08485e11i	−0.894490	−	0.516434i	−0.875408	+	0.483384i	$0.839407\pi$
$678$			4.45443e10i			0.210801i
$679$	−1.52168e11	+	1.00741e11i	−0.715885	+	0.473943i
$680$	1.24738e11			0.583394
$681$	2.81883e10	−	4.88235e10i	0.131063	−	0.227008i
$682$	1.19460e11	−	6.89704e10i	0.552187	−	0.318805i
$683$	1.49718e11	+	2.59320e11i	0.688006	+	1.19166i	0.972482	+	0.232978i	$0.0748470\pi$
$683$	1.49718e11	+	2.59320e11i	0.688006	+	1.19166i	−0.284476	+	0.958683i	$0.591820\pi$
$684$	2.13133e9	+	1.23052e9i	0.00973702	+	0.00562167i
$685$		−	3.37234e11i		−	1.53168i
$686$	7.26680e10	−	2.05416e11i	0.328130	−	0.927550i
$687$	−4.58404e10			−0.205789
$688$	−1.28829e11	+	2.23139e11i	−0.574990	+	0.995913i
$689$	−1.66578e11	+	9.61741e10i	−0.739166	+	0.426757i
$690$	1.38095e11	+	2.39187e11i	0.609230	+	1.05522i
$691$	−1.48567e11	−	8.57754e10i	−0.651645	−	0.376227i	0.137441	−	0.990510i	$-0.456112\pi$
$691$	−1.48567e11	−	8.57754e10i	−0.651645	−	0.376227i	−0.789086	+	0.614283i	$0.789445\pi$
$692$			5.49942e9i			0.0239824i
$693$	5.38019e10	+	8.12671e10i	0.233273	+	0.352356i
$694$	1.04145e11			0.448952
$695$	1.45682e11	−	2.52328e11i	0.624404	−	1.08150i
$696$	1.89352e11	−	1.09322e11i	0.806923	−	0.465877i
$697$	4.73396e10	+	8.19946e10i	0.200583	+	0.347419i
$698$	−2.77775e11	−	1.60373e11i	−1.17023	−	0.675632i
$699$			3.86549e10i			0.161918i
$700$	1.22578e10	−	7.51026e8i	0.0510530	−	0.00312797i
$701$	1.41932e10			0.0587771			0.0293886	−	0.999568i	$-0.490644\pi$
$701$	1.41932e10			0.0587771			0.0293886	+	0.999568i	$0.490644\pi$
$702$	1.40656e10	−	2.43623e10i	0.0579175	−	0.100316i
$703$	3.11794e11	−	1.80014e11i	1.27658	−	0.737031i
$704$	−1.60356e11	−	2.77744e11i	−0.652820	−	1.13072i
$705$	1.83991e10	+	1.06228e10i	0.0744803	+	0.0430012i
$706$			4.50877e11i			1.81484i
$707$	1.92076e11	+	9.57400e10i	0.768767	+	0.383191i
$708$	−2.57006e9			−0.0102285
$709$	−1.50553e11	+	2.60765e11i	−0.595804	+	1.03196i	0.397629	+	0.917546i	$0.369833\pi$
$709$	−1.50553e11	+	2.60765e11i	−0.595804	+	1.03196i	−0.993433	+	0.114416i	$0.963500\pi$
$710$	5.68955e10	−	3.28486e10i	0.223895	−	0.129266i
$711$	2.52345e10	+	4.37075e10i	0.0987454	+	0.171032i
$712$	1.01447e11	+	5.85704e10i	0.394747	+	0.227907i
$713$			1.75770e11i			0.680121i
$714$	2.34708e10	−	4.70876e10i	0.0903096	−	0.181181i
$715$	−3.26784e11			−1.25037
$716$	2.07655e9	−	3.59669e9i	0.00790115	−	0.0136852i
$717$	9.45152e10	−	5.45684e10i	0.357623	−	0.206473i
$718$	6.03678e10	+	1.04560e11i	0.227147	+	0.393431i
$719$	1.61667e11	+	9.33386e10i	0.604932	+	0.349258i	0.770979	−	0.636860i	$-0.219767\pi$
$719$	1.61667e11	+	9.33386e10i	0.604932	+	0.349258i	−0.166048	+	0.986118i	$0.553101\pi$
$720$			1.39657e11i			0.519677i
$721$	−2.47533e10	−	4.04009e11i	−0.0915992	−	1.49503i
$722$	3.00339e10			0.110525
$723$	−1.28927e10	+	2.23308e10i	−0.0471836	+	0.0817244i
$724$	−1.19471e10	+	6.89763e9i	−0.0434817	+	0.0251042i
$725$	3.51161e11	+	6.08229e11i	1.27103	+	2.20148i
$726$	8.29753e10	+	4.79058e10i	0.298677	+	0.172441i
$727$			1.05714e11i			0.378437i	0.981935	+	0.189218i	$0.0605954\pi$
$727$			1.05714e11i			0.378437i	−0.981935	+	0.189218i	$0.939405\pi$
$728$	1.45477e11	−	9.63115e10i	0.517928	−	0.342888i
$729$	−1.04604e10			−0.0370370
$730$	1.90777e11	−	3.30436e11i	0.671793	−	1.16358i
$731$	1.04806e11	−	6.05095e10i	0.367041	−	0.211911i
$732$	9.12930e8	+	1.58124e9i	0.00317975	+	0.00550749i
$733$	−1.74850e11	−	1.00950e11i	−0.605691	−	0.349696i	0.165586	−	0.986195i	$-0.447048\pi$
$733$	−1.74850e11	−	1.00950e11i	−0.605691	−	0.349696i	−0.771277	+	0.636500i	$0.780382\pi$
$734$			3.59744e11i			1.23939i
$735$	1.06091e11	−	2.50083e11i	0.363522	−	0.856909i
$736$	2.49615e10			0.0850668
$737$	−8.02165e10	+	1.38939e11i	−0.271890	+	0.470928i
$738$	−9.48379e10	+	5.47547e10i	−0.319710	+	0.184585i
$739$	1.37019e11	+	2.37325e11i	0.459414	+	0.795729i	0.998930	−	0.0462465i	$-0.0147260\pi$
$739$	1.37019e11	+	2.37325e11i	0.459414	+	0.795729i	−0.539516	+	0.841976i	$0.681393\pi$
$740$	−1.87148e10	−	1.08050e10i	−0.0624104	−	0.0360327i
$741$			1.12308e11i			0.372509i
$742$	−2.29693e11	−	3.46948e11i	−0.757761	−	1.14459i
$743$	4.81477e10			0.157987			0.0789933	−	0.996875i	$-0.474829\pi$
$743$	4.81477e10			0.157987			0.0789933	+	0.996875i	$0.474829\pi$
$744$	−4.59094e10	+	7.95174e10i	−0.149834	+	0.259520i
$745$	−1.14862e11	+	6.63154e10i	−0.372864	+	0.215273i
$746$	−1.25731e11	−	2.17773e11i	−0.405965	−	0.703152i
$747$	−1.19223e11	−	6.88335e10i	−0.382894	−	0.221064i
$748$			4.52325e9i			0.0144492i
$749$	−3.54389e11	+	2.17131e10i	−1.12604	+	0.0689914i
$750$	−1.73667e11			−0.548874
$751$	−1.13711e11	+	1.96953e11i	−0.357472	+	0.619160i	−0.987538	−	0.157382i	$-0.949695\pi$
$751$	−1.13711e11	+	1.96953e11i	−0.357472	+	0.619160i	0.630065	+	0.776542i	$0.283028\pi$
$752$	−2.47439e10	+	1.42859e10i	−0.0773742	+	0.0446720i
$753$	6.58330e10	+	1.14026e11i	0.204769	+	0.354670i
$754$	2.67785e11	+	1.54606e11i	0.828515	+	0.478344i
$755$		−	3.88820e11i		−	1.19663i
$756$	−1.79936e9	−	8.96890e8i	−0.00550847	−	0.00274569i
$757$	−6.14527e11			−1.87136			−0.935680	−	0.352850i	$-0.885213\pi$
$757$	−6.14527e11			−1.87136			−0.935680	+	0.352850i	$0.885213\pi$
$758$	−1.14067e11	+	1.97570e11i	−0.345528	+	0.598472i
$759$	−2.79875e11	+	1.61586e11i	−0.843329	+	0.486896i
$760$	−2.87996e11	−	4.98824e11i	−0.863241	−	1.49518i
$761$	5.26986e11	+	3.04256e11i	1.57131	+	0.907194i	0.996009	+	0.0892482i	$0.0284464\pi$
$761$	5.26986e11	+	3.04256e11i	1.57131	+	0.907194i	0.575296	+	0.817945i	$0.304887\pi$
$762$		−	3.56644e11i		−	1.05783i
$763$	−3.44923e10	+	6.91991e10i	−0.101771	+	0.204175i
$764$	−2.58371e9			−0.00758350
$765$	3.27976e10	−	5.68072e10i	0.0957628	−	0.165866i
$766$	4.30468e11	−	2.48531e11i	1.25033	−	0.721881i
$767$	−5.86413e10	−	1.01570e11i	−0.169442	−	0.293483i
$768$	1.66719e10	+	9.62554e9i	0.0479226	+	0.0276681i
$769$			8.40725e10i			0.240408i	0.992749	+	0.120204i	$0.0383548\pi$
$769$			8.40725e10i			0.240408i	−0.992749	+	0.120204i	$0.961645\pi$
$770$	−4.32305e10	−	7.05584e11i	−0.122978	−	2.00718i
$771$	1.77191e11			0.501447
$772$	−5.55517e9	+	9.62184e9i	−0.0156397	+	0.0270887i
$773$	1.31236e11	−	7.57690e10i	0.367565	−	0.212214i	−0.304829	−	0.952407i	$-0.598599\pi$
$773$	1.31236e11	−	7.57690e10i	0.367565	−	0.212214i	0.672394	+	0.740193i	$0.265266\pi$
$774$	6.99875e10	+	1.21222e11i	0.195010	+	0.337767i
$775$	−2.55423e11	−	1.47469e11i	−0.708033	−	0.408783i
$776$		−	3.16102e11i		−	0.871727i
$777$	−2.45243e11	+	1.62361e11i	−0.672842	+	0.445447i
$778$	−1.74577e10			−0.0476507
$779$	2.18597e11	−	3.78620e11i	0.593600	−	1.02814i
$780$	5.83790e9	−	3.37051e9i	0.0157717	−	0.00910579i
$781$	3.84364e10	+	6.65739e10i	0.103309	+	0.178937i
$782$	1.51084e11	+	8.72282e10i	0.404008	+	0.233254i
$783$		−	1.14978e11i		−	0.305891i
$784$	2.19925e11	+	2.91721e11i	0.582116	+	0.772154i
$785$	−6.54638e11			−1.72394
$786$	−1.24318e11	+	2.15326e11i	−0.325720	+	0.564164i
$787$	−1.47424e10	+	8.51151e9i	−0.0384298	+	0.0221875i	−0.519092	−	0.854718i	$-0.673730\pi$
$787$	−1.47424e10	+	8.51151e9i	−0.0384298	+	0.0221875i	0.480662	+	0.876906i	$0.340396\pi$
$788$	−1.00864e10	−	1.74702e10i	−0.0261597	−	0.0453100i
$789$	−2.07187e11	−	1.19619e11i	−0.534631	−	0.308670i
$790$		−	3.66057e11i		−	0.939810i
$791$	8.01968e10	+	1.21136e11i	0.204857	+	0.309434i
$792$	−1.68819e11			−0.429062
$793$	−4.16608e10	+	7.21586e10i	−0.105350	+	0.182472i
$794$	−1.19544e10	+	6.90187e9i	−0.0300778	+	0.0173654i
$795$	−2.59382e11	−	4.49262e11i	−0.649338	−	1.12469i
$796$	1.74934e10	+	1.00998e10i	0.0435735	+	0.0251572i
$797$			1.98970e11i			0.493121i	0.969127	+	0.246561i	$0.0793004\pi$
$797$			1.98970e11i			0.493121i	−0.969127	+	0.246561i	$0.920700\pi$
$798$	−2.42492e11	+	1.48573e10i	−0.597979	+	0.0366376i
$799$	1.34198e10			0.0329275
$800$	−2.09424e10	+	3.62733e10i	−0.0511289	+	0.0885579i
$801$	5.33475e10	−	3.08002e10i	0.129594	−	0.0748209i
$802$	−2.66554e11	−	4.61685e11i	−0.644300	−	1.11596i
$803$	3.86646e11	+	2.23230e11i	0.929932	+	0.536897i
$804$		−	3.30947e9i		−	0.00792017i
$805$	8.06172e11	+	4.01836e11i	1.91975	+	0.956897i
$806$	−1.29852e11			−0.307686
$807$	−1.50177e11	+	2.60113e11i	−0.354085	+	0.613294i
$808$	−3.21937e11	+	1.85870e11i	−0.755310	+	0.436078i
$809$	2.13488e11	+	3.69772e11i	0.498402	+	0.863257i	0.999998	−	0.00184455i	$-0.000587138\pi$
$809$	2.13488e11	+	3.69772e11i	0.498402	+	0.863257i	−0.501597	+	0.865102i	$0.667254\pi$
$810$	6.57053e10	+	3.79350e10i	0.152637	+	0.0881251i
$811$			7.34733e11i			1.69842i	0.528052	+	0.849212i	$0.322923\pi$
$811$			7.34733e11i			1.69842i	−0.528052	+	0.849212i	$0.677077\pi$
$812$	9.85839e9	−	1.97781e10i	0.0226768	−	0.0454947i
$813$	5.61473e10			0.128519
$814$	−3.82679e11	+	6.62819e11i	−0.871639	+	1.50972i
$815$	3.35808e11	−	1.93879e11i	0.761134	−	0.439441i
$816$	4.41075e10	+	7.63964e10i	0.0994837	+	0.172311i
$817$	−4.83953e11	−	2.79410e11i	−1.08621	−	0.627125i
$818$		−	5.06070e11i		−	1.13031i
$819$	−5.61076e9	−	9.15757e10i	−0.0124706	−	0.203538i
$820$	−2.62416e10			−0.0580409
$821$	5.35205e10	−	9.27002e10i	0.117801	−	0.204037i	−0.801095	−	0.598537i	$-0.795749\pi$
$821$	5.35205e10	−	9.27002e10i	0.117801	−	0.204037i	0.918896	+	0.394500i	$0.129082\pi$
$822$	2.13372e11	−	1.23190e11i	0.467359	−	0.269830i
$823$	2.68869e11	+	4.65695e11i	0.586060	+	1.01509i	0.994742	+	0.102409i	$0.0326550\pi$
$823$	2.68869e11	+	4.65695e11i	0.586060	+	1.01509i	−0.408683	+	0.912677i	$0.634012\pi$
$824$	6.07179e11	+	3.50555e11i	1.31707	+	0.760410i
$825$		−	5.42274e11i		−	1.17058i
$826$	2.11549e11	−	1.40053e11i	0.454454	−	0.300866i
$827$	−1.46908e11			−0.314068			−0.157034	−	0.987593i	$-0.550193\pi$
$827$	−1.46908e11			−0.314068			−0.157034	+	0.987593i	$0.550193\pi$
$828$	3.33326e9	−	5.77337e9i	0.00709165	−	0.0122831i
$829$	2.45136e11	−	1.41529e11i	0.519026	−	0.299660i	−0.217510	−	0.976058i	$-0.569794\pi$
$829$	2.45136e11	−	1.41529e11i	0.519026	−	0.299660i	0.736536	+	0.676398i	$0.236460\pi$
$830$	4.99256e11	+	8.64737e11i	1.05199	+	1.82210i
$831$	2.95678e11	+	1.70710e11i	0.620034	+	0.357977i
$832$			3.01904e11i			0.630052i
$833$	−2.09480e10	−	1.70309e11i	−0.0435073	−	0.353718i
$834$	2.12868e11			0.439994
$835$	−9.77281e10	+	1.69270e11i	−0.201036	+	0.348204i
$836$	1.80884e10	−	1.04433e10i	0.0370318	−	0.0213803i
$837$	2.41422e10	+	4.18155e10i	0.0491897	+	0.0851991i
$838$	−2.03156e11	−	1.17292e11i	−0.411960	−	0.237845i
$839$			2.26175e11i			0.456453i	0.973608	+	0.228227i	$0.0732927\pi$
$839$			2.26175e11i			0.456453i	−0.973608	+	0.228227i	$0.926707\pi$
$840$	2.59752e11	+	3.92353e11i	0.521726	+	0.788060i
$841$	7.63561e11			1.52637
$842$	−6.00377e10	+	1.03988e11i	−0.119447	+	0.206888i
$843$	6.54700e10	−	3.77991e10i	0.129638	−	0.0748464i
$844$	−3.82987e9	−	6.63354e9i	−0.00754770	−	0.0130730i
$845$	−4.45441e11	−	2.57175e11i	−0.873702	−	0.504432i
$846$			1.55218e10i			0.0303013i
$847$	3.11897e11	−	1.91096e10i	0.606006	−	0.0371295i
$848$	6.97653e11			1.34914
$849$	2.35156e11	−	4.07302e11i	0.452611	−	0.783945i
$850$	−2.53514e11	+	1.46367e11i	−0.485654	+	0.280392i
$851$	−4.87625e11	−	8.44592e11i	−0.929754	−	1.61038i
$852$	−1.37331e9	−	7.92881e8i	−0.00260622	−	0.00150470i
$853$			1.11072e11i			0.209801i	0.994483	+	0.104901i	$0.0334525\pi$
$853$			1.11072e11i			0.209801i	−0.994483	+	0.104901i	$0.966548\pi$
$854$	−1.61314e11	−	8.04070e10i	−0.303278	−	0.151169i
$855$	−3.02895e11			−0.566796
$856$	3.07500e11	−	5.32606e11i	0.572731	−	0.991999i
$857$	−3.50029e11	+	2.02089e11i	−0.648904	+	0.374645i	−0.788036	−	0.615629i	$-0.788902\pi$
$857$	−3.50029e11	+	2.02089e11i	−0.648904	+	0.374645i	0.139132	+	0.990274i	$0.455569\pi$
$858$	−1.19373e11	−	2.06761e11i	−0.220271	−	0.381521i
$859$	−6.28349e11	−	3.62778e11i	−1.15406	−	0.666297i	−0.204187	−	0.978932i	$-0.565455\pi$
$859$	−6.28349e11	−	3.62778e11i	−1.15406	−	0.666297i	−0.949873	+	0.312635i	$0.898788\pi$
$860$			3.35420e10i			0.0613190i
$861$	−1.59328e11	+	3.19648e11i	−0.289921	+	0.581646i
$862$	−1.04126e11			−0.188595
$863$	−1.90617e10	+	3.30158e10i	−0.0343651	+	0.0595221i	−0.882696	−	0.469944i	$-0.844274\pi$
$863$	−1.90617e10	+	3.30158e10i	−0.0343651	+	0.0595221i	0.848331	+	0.529466i	$0.177608\pi$
$864$	5.93832e9	−	3.42849e9i	0.0106564	−	0.00615245i
$865$	−3.38422e11	−	5.86164e11i	−0.604496	−	1.04702i
$866$	−6.02443e11	−	3.47821e11i	−1.07114	−	0.618421i
$867$			2.84790e11i			0.504021i
$868$	5.67534e8	+	9.26297e9i	0.000999800	+	0.0163182i
$869$	4.28326e11			0.751096
$870$	−4.16972e11	+	7.22216e11i	−0.727830	+	1.26064i
$871$	1.30791e11	−	7.55125e10i	0.227251	−	0.131204i
$872$	−6.69635e10	−	1.15984e11i	−0.115817	−	0.200601i
$873$	−1.43957e11	−	8.31137e10i	−0.247843	−	0.143092i
$874$		−	8.05574e11i		−	1.38057i
$875$	−4.72280e11	+	3.12667e11i	−0.805689	+	0.533397i
$876$	−9.20975e9			−0.0156398
$877$	4.71089e11	−	8.15950e11i	0.796351	−	1.37932i	−0.125627	−	0.992078i	$-0.540094\pi$
$877$	4.71089e11	−	8.15950e11i	0.796351	−	1.37932i	0.921978	−	0.387243i	$-0.126572\pi$
$878$	−5.55269e11	+	3.20585e11i	−0.934384	+	0.539467i
$879$	1.64805e11	+	2.85451e11i	0.276068	+	0.478164i
$880$	1.02646e12	+	5.92629e11i	1.71164	+	0.988216i
$881$		−	1.02165e11i		−	0.169589i	−0.996398	−	0.0847943i	$-0.972977\pi$
$881$		−	1.02165e11i		−	0.169589i	0.996398	−	0.0847943i	$-0.0270233\pi$
$882$	1.96986e11	−	2.42292e10i	0.325507	−	0.0400373i
$883$	4.89722e11			0.805576			0.402788	−	0.915293i	$-0.368041\pi$
$883$	4.89722e11			0.805576			0.402788	+	0.915293i	$0.368041\pi$
$884$	2.12900e9	−	3.68753e9i	0.00348631	−	0.00603847i
$885$	2.73934e11	−	1.58156e11i	0.446552	−	0.257817i
$886$	1.39981e11	+	2.42454e11i	0.227161	+	0.393455i
$887$	1.03716e12	+	5.98804e11i	1.67553	+	0.967365i	0.964456	+	0.264244i	$0.0851225\pi$
$887$	1.03716e12	+	5.98804e11i	1.67553	+	0.967365i	0.711070	+	0.703121i	$0.248211\pi$
$888$		−	5.09451e11i		−	0.819315i
$889$	−6.42096e11	−	9.69878e11i	−1.02800	−	1.55278i
$890$	−4.46793e11			−0.712109
$891$	−4.43880e10	+	7.68823e10i	−0.0704295	+	0.121987i
$892$	2.74621e10	−	1.58552e10i	0.0433785	−	0.0250446i
$893$	−3.09838e10	−	5.36656e10i	−0.0487225	−	0.0843898i
$894$	−8.39172e10	−	4.84496e10i	−0.131371	−	0.0758473i
$895$			5.11145e11i			0.796621i
$896$	−6.10732e11	+	3.74190e10i	−0.947585	+	0.0580577i
$897$	3.04221e11			0.469915
$898$	−4.50201e11	+	7.79771e11i	−0.692311	+	1.19912i
$899$	−4.59626e11	+	2.65365e11i	−0.703664	+	0.406261i
$900$	5.59311e9	+	9.68756e9i	0.00852479	+	0.0147654i
$901$	−2.83778e11	−	1.63839e11i	−0.430606	−	0.248610i
$902$			9.29396e11i			1.40402i
$903$	4.08574e11	+	2.03653e11i	0.614497	+	0.306295i
$904$	−2.51640e11			−0.376795
$905$	8.48930e11	−	1.47039e12i	1.26554	−	2.19199i
$906$	2.46012e11	−	1.42035e11i	0.365126	−	0.210806i
$907$	−3.57747e11	−	6.19635e11i	−0.528623	−	0.915602i	−0.999443	−	0.0333730i	$-0.989375\pi$
$907$	−3.57747e11	−	6.19635e11i	−0.528623	−	0.915602i	0.470820	−	0.882229i	$-0.343958\pi$
$908$	8.54758e9	+	4.93495e9i	0.0125748	+	0.00726004i
$909$			1.95486e11i			0.286325i
$910$	−2.96860e11	+	5.95568e11i	−0.432899	+	0.868492i
$911$	−1.10556e12			−1.60512			−0.802562	−	0.596569i	$-0.796530\pi$
$911$	−1.10556e12			−1.60512			−0.802562	+	0.596569i	$0.796530\pi$
$912$	2.03672e11	−	3.52770e11i	0.294410	−	0.509932i
$913$	−1.01184e12	+	5.84183e11i	−1.45622	+	0.840748i
$914$	−2.60723e11	−	4.51586e11i	−0.373590	−	0.647076i
$915$	−1.94612e11	−	1.12359e11i	−0.277642	−	0.160297i
$916$		−	8.02533e9i		−	0.0113994i
$917$	4.95906e10	+	8.09389e11i	0.0701329	+	1.14467i
$918$	4.79235e10			0.0674804
$919$	2.23733e11	−	3.87516e11i	0.313666	−	0.543285i	−0.665487	−	0.746409i	$-0.731776\pi$
$919$	2.23733e11	−	3.87516e11i	0.313666	−	0.543285i	0.979153	+	0.203124i	$0.0651095\pi$
$920$	−1.35122e12	+	7.80127e11i	−1.88614	+	1.08896i
$921$	3.07238e11	+	5.32152e11i	0.427009	+	0.739601i
$922$	−4.66929e11	−	2.69582e11i	−0.646141	−	0.373050i
$923$		−	7.23649e10i		−	0.0997060i
$924$	−1.42275e10	+	9.41916e9i	−0.0195183	+	0.0129218i
$925$	1.63644e12			2.23529
$926$	5.75004e11	−	9.95936e11i	0.782036	−	1.35453i
$927$	3.19295e11	−	1.84345e11i	0.432388	−	0.249639i
$928$	3.76852e10	+	6.52726e10i	0.0508134	+	0.0880115i
$929$	−2.06190e11	−	1.19044e11i	−0.276824	−	0.159824i	0.355161	−	0.934805i	$-0.384426\pi$
$929$	−2.06190e11	−	1.19044e11i	−0.276824	−	0.159824i	−0.631985	+	0.774981i	$0.717759\pi$
$930$		−	3.50211e11i		−	0.468164i
$931$	−6.32697e11	+	4.76982e11i	−0.842165	+	0.634897i
$932$	−6.76735e9			−0.00896922
$933$	2.35768e9	−	4.08362e9i	0.00311141	−	0.00538913i
$934$	2.56996e11	−	1.48377e11i	0.337706	−	0.194975i
$935$	−2.78350e11	−	4.82117e11i	−0.364204	−	0.630821i
$936$	1.37628e11	+	7.94595e10i	0.179309	+	0.103524i
$937$			9.33941e11i			1.21161i	0.795615	+	0.605803i	$0.207148\pi$
$937$			9.33941e11i			1.21161i	−0.795615	+	0.605803i	$0.792852\pi$
$938$	1.80347e11	+	2.72412e11i	0.232969	+	0.351896i
$939$	2.63538e11			0.338985
$940$	−1.85974e9	+	3.22116e9i	−0.00238199	+	0.00412573i
$941$	−1.07728e12	+	6.21966e11i	−1.37394	+	0.793246i	−0.991422	−	0.130700i	$-0.958277\pi$
$941$	−1.07728e12	+	6.21966e11i	−1.37394	+	0.793246i	−0.382521	+	0.923947i	$0.624944\pi$
$942$	−2.39137e11	−	4.14198e11i	−0.303699	−	0.526022i
$943$	−1.02561e12	−	5.92137e11i	−1.29699	−	0.748817i
$944$			4.25387e11i			0.535669i
$945$	2.46980e11	−	1.51323e10i	0.309695	−	0.0189748i
$946$	1.18795e12			1.48332
$947$	5.44392e11	−	9.42914e11i	0.676880	−	1.17239i	−0.299036	−	0.954242i	$-0.596665\pi$
$947$	5.44392e11	−	9.42914e11i	0.676880	−	1.17239i	0.975916	−	0.218149i	$-0.0700018\pi$
$948$	−7.65192e9	+	4.41784e9i	−0.00947408	+	0.00546986i
$949$	−2.10140e11	−	3.63973e11i	−0.259086	−	0.448749i
$950$	1.17063e12	+	6.75866e11i	1.43723	+	0.829786i
$951$			5.45399e11i			0.666794i
$952$	2.66007e11	+	1.32591e11i	0.323851	+	0.161423i
$953$	1.97791e11			0.239792			0.119896	−	0.992786i	$-0.461744\pi$
$953$	1.97791e11			0.239792			0.119896	+	0.992786i	$0.461744\pi$
$954$	1.89503e11	−	3.28228e11i	0.228782	−	0.396262i
$955$	2.75388e11	−	1.58996e11i	0.331079	−	0.191149i
$956$	9.55334e9	+	1.65469e10i	0.0114373	+	0.0198100i
$957$	−8.45071e11	−	4.87902e11i	−1.00750	−	0.581681i
$958$		−	7.10173e11i		−	0.843145i
$959$	3.58466e11	−	7.19163e11i	0.423812	−	0.850262i
$960$	−8.14237e11			−0.958663
$961$	−3.15007e11	+	5.45608e11i	−0.369340	+	0.639716i
$962$	6.23951e11	−	3.60238e11i	0.728534	−	0.420619i
$963$	−1.61704e11	−	2.80080e11i	−0.188025	−	0.325669i
$964$	−3.90948e9	−	2.25714e9i	−0.00452700	−	0.00261367i
$965$		−	1.36741e12i		−	1.57685i
$966$	4.02455e10	+	6.56865e11i	0.0462178	+	0.754341i
$967$	1.06753e12			1.22089			0.610444	−	0.792059i	$-0.290991\pi$
$967$	1.06753e12			1.22089			0.610444	+	0.792059i	$0.290991\pi$
$968$	−2.70630e11	+	4.68745e11i	−0.308230	+	0.533869i
$969$	−1.65692e11	+	9.56622e10i	−0.187934	+	0.108504i
$970$	6.02831e11	+	1.04413e12i	0.680940	+	1.17942i
$971$	−8.78566e11	−	5.07240e11i	−0.988320	−	0.570607i	−0.0835482	−	0.996504i	$-0.526625\pi$
$971$	−8.78566e11	−	5.07240e11i	−0.988320	−	0.570607i	−0.904772	+	0.425897i	$0.859959\pi$
$972$		−	1.83130e9i		−	0.00205161i
$973$	5.78886e11	−	3.83244e11i	0.645865	−	0.427587i
$974$	1.37802e12			1.53116
$975$	−2.55237e11	+	4.42084e11i	−0.282439	+	0.489199i
$976$	2.61722e11	−	1.51105e11i	0.288430	−	0.166525i
$977$	6.49763e11	+	1.12542e12i	0.713143	+	1.23520i	0.963671	+	0.267091i	$0.0860624\pi$
$977$	6.49763e11	+	1.12542e12i	0.713143	+	1.23520i	−0.250528	+	0.968109i	$0.580604\pi$
$978$	2.45340e11	+	1.41647e11i	0.268171	+	0.154829i
$979$		−	5.22796e11i		−	0.569117i
$980$	4.37823e10	+	1.85735e10i	0.0474672	+	0.0201368i
$981$	−7.04276e10			−0.0760444
$982$	−7.77890e11	+	1.34734e12i	−0.836512	+	1.44888i
$983$	8.87072e11	−	5.12151e11i	0.950046	−	0.548509i	0.0569508	−	0.998377i	$-0.481862\pi$
$983$	8.87072e11	−	5.12151e11i	0.950046	−	0.548509i	0.893095	+	0.449868i	$0.148529\pi$
$984$	−3.09321e11	−	5.35759e11i	−0.329935	−	0.571464i
$985$	2.15016e12	+	1.24139e12i	2.28415	+	1.31876i
$986$			5.26764e11i			0.557325i
$987$	2.79453e10	+	4.22110e10i	0.0294469	+	0.0444792i
$988$	−1.96618e10			−0.0206346
$989$	−7.56870e11	+	1.31094e12i	−0.791108	+	1.37024i
$990$	5.57634e11	−	3.21950e11i	0.580508	−	0.335157i
$991$	1.47452e10	+	2.55394e10i	0.0152881	+	0.0264798i	0.873568	−	0.486702i	$-0.161800\pi$
$991$	1.47452e10	+	2.55394e10i	0.0152881	+	0.0264798i	−0.858280	+	0.513181i	$0.828467\pi$
$992$	−2.74109e10	−	1.58257e10i	−0.0283059	−	0.0163424i
$993$		−	2.84196e11i		−	0.292294i
$994$	1.56248e11	−	9.57320e9i	0.160055	−	0.00980645i
$995$	−2.48608e12			−2.53643
$996$	1.20508e10	−	2.08725e10i	0.0122455	−	0.0212098i
$997$	−1.22588e11	+	7.07760e10i	−0.124070	+	0.0716317i	−0.560750	−	0.827985i	$-0.689487\pi$
$997$	−1.22588e11	+	7.07760e10i	−0.124070	+	0.0716317i	0.436681	+	0.899617i	$0.356154\pi$
$998$	−3.79993e11	−	6.58167e11i	−0.383048	−	0.663459i
$999$	−2.32011e11	−	1.33952e11i	−0.232941	−	0.134489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.9.f.b.19.5	yes	12
3.2	odd	2		63.9.m.d.19.2		12
7.2	even	3		147.9.d.b.97.4		12
7.3	odd	6	inner	21.9.f.b.10.5	✓	12
7.5	odd	6		147.9.d.b.97.3		12
21.17	even	6		63.9.m.d.10.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.9.f.b.10.5	✓	12	7.3	odd	6	inner
21.9.f.b.19.5	yes	12	1.1	even	1	trivial
63.9.m.d.10.2		12	21.17	even	6
63.9.m.d.19.2		12	3.2	odd	2
147.9.d.b.97.3		12	7.5	odd	6
147.9.d.b.97.4		12	7.2	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.87103 - 13.6330i) q^{2} +(40.5000 - 23.3827i) q^{3} +(4.09363 + 7.09038i) q^{4} +(-872.651 - 503.826i) q^{5} -736.184i q^{6} +(-1325.41 - 2002.02i) q^{7} +4158.85 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\)	\(q+(7.87103 - 13.6330i) q^{2} +(40.5000 - 23.3827i) q^{3} +(4.09363 + 7.09038i) q^{4} +(-872.651 - 503.826i) q^{5} -736.184i q^{6} +(-1325.41 - 2002.02i) q^{7} +4158.85 q^{8} +(1093.50 - 1894.00i) q^{9} +(-13737.3 + 7931.26i) q^{10} +(-9280.43 - 16074.2i) q^{11} +(331.584 + 191.440i) q^{12} +17472.4i q^{13} +(-37726.0 + 2311.44i) q^{14} -47123.2 q^{15} +(31686.5 - 54882.7i) q^{16} +(-25777.7 + 14882.8i) q^{17} +(-17214.0 - 29815.4i) q^{18} +(119032. + 68723.1i) q^{19} -8249.90i q^{20} +(-100492. - 50090.1i) q^{21} -292186. q^{22} +(186158. - 322435. i) q^{23} +(168434. - 97245.2i) q^{24} +(312368. + 541037. i) q^{25} +(238202. + 137526. i) q^{26} -102276. i q^{27} +(8769.32 - 17593.2i) q^{28} +1.12419e6 q^{29} +(-370908. + 642432. i) q^{30} +(-408850. + 236050. i) q^{31} +(33522.0 + 58061.8i) q^{32} +(-751715. - 434003. i) q^{33} +468571. i q^{34} +(147955. + 2.41484e6i) q^{35} +17905.5 q^{36} +(1.30971e6 - 2.26848e6i) q^{37} +(1.87381e6 - 1.08184e6i) q^{38} +(408552. + 707633. i) q^{39} +(-3.62923e6 - 2.09534e6i) q^{40} -3.18083e6i q^{41} +(-1.47385e6 + 975748. i) q^{42} -4.06574e6 q^{43} +(75981.3 - 131603. i) q^{44} +(-1.90849e6 + 1.10187e6i) q^{45} +(-2.93051e6 - 5.07579e6i) q^{46} +(-390448. - 225425. i) q^{47} -2.96366e6i q^{48} +(-2.25136e6 + 5.30701e6i) q^{49} +9.83463e6 q^{50} +(-695998. + 1.20550e6i) q^{51} +(-123886. + 71525.6i) q^{52} +(5.50434e6 + 9.53379e6i) q^{53} +(-1.39433e6 - 805017. i) q^{54} +1.87029e7i q^{55} +(-5.51220e6 - 8.32611e6i) q^{56} +6.42772e6 q^{57} +(8.84855e6 - 1.53261e7i) q^{58} +(-5.81314e6 + 3.35622e6i) q^{59} +(-192905. - 334121. i) q^{60} +(4.12986e6 + 2.38438e6i) q^{61} +7.43182e6i q^{62} +(-5.24116e6 + 321121. i) q^{63} +1.72789e7 q^{64} +(8.80305e6 - 1.52473e7i) q^{65} +(-1.18335e7 + 6.83210e6i) q^{66} +(-4.32181e6 - 7.48559e6i) q^{67} +(-211049. - 121849. i) q^{68} -1.74115e7i q^{69} +(3.40862e7 + 1.69902e7i) q^{70} -4.14167e6 q^{71} +(4.54771e6 - 7.87686e6i) q^{72} +(-2.08313e7 + 1.20269e7i) q^{73} +(-2.06175e7 - 3.57106e7i) q^{74} +(2.53018e7 + 1.46080e7i) q^{75} +1.12531e6i q^{76} +(-1.98804e7 + 3.98845e7i) q^{77} +1.28629e7 q^{78} +(-1.15384e7 + 1.99851e7i) q^{79} +(-5.53026e7 + 3.19290e7i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(-4.33644e7 - 2.50364e7i) q^{82} -6.29479e7i q^{83} +(-56219.0 - 917575. i) q^{84} +2.99933e7 q^{85} +(-3.20016e7 + 5.54284e7i) q^{86} +(4.55298e7 - 2.62866e7i) q^{87} +(-3.85959e7 - 6.68501e7i) q^{88} +(2.43930e7 + 1.40833e7i) q^{89} +3.46913e7i q^{90} +(3.49801e7 - 2.31582e7i) q^{91} +3.04825e6 q^{92} +(-1.10389e7 + 1.91200e7i) q^{93} +(-6.14646e6 + 3.54866e6i) q^{94} +(-6.92489e7 - 1.19943e8i) q^{95} +(2.71528e6 + 1.56767e6i) q^{96} -7.60071e7i q^{97} +(5.46300e7 + 7.24645e7i) q^{98} -4.05926e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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