LMFDB - Embedded newform 20.9.b.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.14757220122$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{58}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.13
Root			$-4.16577 + 5.52698i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.5676 - 11.0540i) q^{2} +27.2434i q^{3} +(11.6196 - 255.736i) q^{4} +279.508 q^{5} +(301.148 + 315.141i) q^{6} -3325.58i q^{7} +(-2692.49 - 3086.70i) q^{8} +5818.80 q^{9} +O(q^{10})$	\(q+(11.5676 - 11.0540i) q^{2} +27.2434i q^{3} +(11.6196 - 255.736i) q^{4} +279.508 q^{5} +(301.148 + 315.141i) q^{6} -3325.58i q^{7} +(-2692.49 - 3086.70i) q^{8} +5818.80 q^{9} +(3233.25 - 3089.68i) q^{10} -6361.21i q^{11} +(6967.12 + 316.557i) q^{12} -30777.4 q^{13} +(-36760.8 - 38469.0i) q^{14} +7614.76i q^{15} +(-65266.0 - 5943.09i) q^{16} +122375. q^{17} +(67309.6 - 64320.8i) q^{18} +7554.43i q^{19} +(3247.77 - 71480.4i) q^{20} +90600.1 q^{21} +(-70316.6 - 73584.1i) q^{22} +406311. i q^{23} +(84092.2 - 73352.6i) q^{24} +78125.0 q^{25} +(-356021. + 340213. i) q^{26} +337268. i q^{27} +(-850471. - 38641.8i) q^{28} +828838. q^{29} +(84173.4 + 88084.7i) q^{30} +1.39549e6i q^{31} +(-820666. + 652701. i) q^{32} +173301. q^{33} +(1.41559e6 - 1.35273e6i) q^{34} -929527. i q^{35} +(67611.9 - 1.48808e6i) q^{36} -386059. q^{37} +(83506.4 + 87386.8i) q^{38} -838482. i q^{39} +(-752574. - 862759. i) q^{40} -972335. q^{41} +(1.04803e6 - 1.00149e6i) q^{42} -4.61450e6i q^{43} +(-1.62679e6 - 73914.5i) q^{44} +1.62640e6 q^{45} +(4.49135e6 + 4.70005e6i) q^{46} -1.87219e6i q^{47} +(161910. - 1.77807e6i) q^{48} -5.29467e6 q^{49} +(903720. - 863591. i) q^{50} +3.33392e6i q^{51} +(-357620. + 7.87090e6i) q^{52} -8.01944e6 q^{53} +(3.72815e6 + 3.90139e6i) q^{54} -1.77801e6i q^{55} +(-1.02651e7 + 8.95408e6i) q^{56} -205808. q^{57} +(9.58768e6 - 9.16195e6i) q^{58} +6.18263e6i q^{59} +(1.94737e6 + 88480.2i) q^{60} +9.79320e6 q^{61} +(1.54257e7 + 1.61425e7i) q^{62} -1.93509e7i q^{63} +(-2.27822e6 + 1.66218e7i) q^{64} -8.60255e6 q^{65} +(2.00468e6 - 1.91566e6i) q^{66} +1.19411e6i q^{67} +(1.42195e6 - 3.12958e7i) q^{68} -1.10693e7 q^{69} +(-1.02750e7 - 1.07524e7i) q^{70} +3.62332e7i q^{71} +(-1.56670e7 - 1.79609e7i) q^{72} +3.35548e7 q^{73} +(-4.46578e6 + 4.26748e6i) q^{74} +2.12839e6i q^{75} +(1.93194e6 + 87779.2i) q^{76} -2.11547e7 q^{77} +(-9.26855e6 - 9.69923e6i) q^{78} -1.22874e6i q^{79} +(-1.82424e7 - 1.66114e6i) q^{80} +2.89888e7 q^{81} +(-1.12476e7 + 1.07482e7i) q^{82} -6.96923e7i q^{83} +(1.05273e6 - 2.31697e7i) q^{84} +3.42049e7 q^{85} +(-5.10086e7 - 5.33788e7i) q^{86} +2.25804e7i q^{87} +(-1.96352e7 + 1.71275e7i) q^{88} +5.58347e7 q^{89} +(1.88136e7 - 1.79782e7i) q^{90} +1.02353e8i q^{91} +(1.03908e8 + 4.72116e6i) q^{92} -3.80180e7 q^{93} +(-2.06951e7 - 2.16567e7i) q^{94} +2.11153e6i q^{95} +(-1.77818e7 - 2.23578e7i) q^{96} -5.97582e7 q^{97} +(-6.12467e7 + 5.85271e7i) q^{98} -3.70146e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	11.5676	−	11.0540i	0.722976	−	0.690873i
$2$	11.5676	−	11.0540i	0.722976	−	0.690873i
$3$			27.2434i			0.336338i	0.985758	+	0.168169i	$0.0537855\pi$
$3$			27.2434i			0.336338i	−0.985758	+	0.168169i	$0.946215\pi$
$4$	11.6196	−	255.736i	0.0453889	−	0.998969i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$	301.148	+	315.141i	0.232367	+	0.243165i
$7$		−	3325.58i		−	1.38508i	−0.721379	−	0.692540i	$-0.756492\pi$
$7$		−	3325.58i		−	1.38508i	0.721379	−	0.692540i	$-0.243508\pi$
$8$	−2692.49	−	3086.70i	−0.657346	−	0.753589i
$9$	5818.80			0.886877
$10$	3233.25	−	3089.68i	0.323325	−	0.308968i
$11$		−	6361.21i		−	0.434479i	−0.976118	−	0.217240i	$-0.930295\pi$
$11$		−	6361.21i		−	0.434479i	0.976118	−	0.217240i	$-0.0697053\pi$
$12$	6967.12	+	316.557i	0.335992	+	0.0152660i
$13$	−30777.4			−1.07760			−0.538801	−	0.842433i	$-0.681123\pi$
$13$	−30777.4			−1.07760			−0.538801	+	0.842433i	$0.681123\pi$
$14$	−36760.8	−	38469.0i	−0.956915	−	1.00138i
$15$			7614.76i			0.150415i
$16$	−65266.0	−	5943.09i	−0.995880	−	0.0906843i
$17$	122375.			1.46520			0.732601	−	0.680658i	$-0.238306\pi$
$17$	122375.			1.46520			0.732601	+	0.680658i	$0.238306\pi$
$18$	67309.6	−	64320.8i	0.641191	−	0.612719i
$19$			7554.43i			0.0579679i	0.999580	+	0.0289839i	$0.00922717\pi$
$19$			7554.43i			0.0579679i	−0.999580	+	0.0289839i	$0.990773\pi$
$20$	3247.77	−	71480.4i	0.0202985	−	0.446753i
$21$	90600.1			0.465856
$22$	−70316.6	−	73584.1i	−0.300170	−	0.314118i
$23$			406311.i			1.45194i	0.687729	+	0.725968i	$0.258608\pi$
$23$			406311.i			1.45194i	−0.687729	+	0.725968i	$0.741392\pi$
$24$	84092.2	−	73352.6i	0.253461	−	0.221091i
$25$	78125.0			0.200000
$26$	−356021.	+	340213.i	−0.779081	+	0.744487i
$27$			337268.i			0.634629i
$28$	−850471.	−	38641.8i	−1.38365	−	0.0628673i
$29$	828838.			1.17187			0.585933	−	0.810360i	$-0.300728\pi$
$29$	828838.			1.17187			0.585933	+	0.810360i	$0.300728\pi$
$30$	84173.4	+	88084.7i	0.103918	+	0.108747i
$31$			1.39549e6i			1.51106i	0.655116	+	0.755528i	$0.272620\pi$
$31$			1.39549e6i			1.51106i	−0.655116	+	0.755528i	$0.727380\pi$
$32$	−820666.	+	652701.i	−0.782649	+	0.622464i
$33$	173301.			0.146132
$34$	1.41559e6	−	1.35273e6i	1.05931	−	1.01227i
$35$		−	929527.i		−	0.619427i
$36$	67611.9	−	1.48808e6i	0.0402544	−	0.885962i
$37$	−386059.			−0.205990			−0.102995	−	0.994682i	$-0.532843\pi$
$37$	−386059.			−0.205990			−0.102995	+	0.994682i	$0.532843\pi$
$38$	83506.4	+	87386.8i	0.0400484	+	0.0419094i
$39$		−	838482.i		−	0.362439i
$40$	−752574.	−	862759.i	−0.293974	−	0.337015i
$41$	−972335.			−0.344097			−0.172048	−	0.985089i	$-0.555039\pi$
$41$	−972335.			−0.344097			−0.172048	+	0.985089i	$0.555039\pi$
$42$	1.04803e6	−	1.00149e6i	0.336803	−	0.321847i
$43$		−	4.61450e6i		−	1.34974i	−0.737935	−	0.674871i	$-0.764199\pi$
$43$		−	4.61450e6i		−	1.34974i	0.737935	−	0.674871i	$-0.235801\pi$
$44$	−1.62679e6	−	73914.5i	−0.434032	−	0.0197205i
$45$	1.62640e6			0.396623
$46$	4.49135e6	+	4.70005e6i	1.00310	+	1.04971i
$47$		−	1.87219e6i		−	0.383670i	−0.981427	−	0.191835i	$-0.938556\pi$
$47$		−	1.87219e6i		−	0.383670i	0.981427	−	0.191835i	$-0.0614438\pi$
$48$	161910.	−	1.77807e6i	0.0305006	−	0.334953i
$49$	−5.29467e6			−0.918447
$50$	903720.	−	863591.i	0.144595	−	0.138175i
$51$			3.33392e6i			0.492804i
$52$	−357620.	+	7.87090e6i	−0.0489112	+	1.07649i
$53$	−8.01944e6			−1.01634			−0.508172	−	0.861256i	$-0.669678\pi$
$53$	−8.01944e6			−1.01634			−0.508172	+	0.861256i	$0.669678\pi$
$54$	3.72815e6	+	3.90139e6i	0.438448	+	0.458822i
$55$		−	1.77801e6i		−	0.194305i
$56$	−1.02651e7	+	8.95408e6i	−1.04378	+	0.910477i
$57$	−205808.			−0.0194968
$58$	9.58768e6	−	9.16195e6i	0.847231	−	0.809610i
$59$			6.18263e6i			0.510229i	0.966911	+	0.255115i	$0.0821132\pi$
$59$			6.18263e6i			0.510229i	−0.966911	+	0.255115i	$0.917887\pi$
$60$	1.94737e6	+	88480.2i	0.150260	+	0.00682718i
$61$	9.79320e6			0.707303			0.353651	−	0.935377i	$-0.384940\pi$
$61$	9.79320e6			0.707303			0.353651	+	0.935377i	$0.384940\pi$
$62$	1.54257e7	+	1.61425e7i	1.04395	+	1.09246i
$63$		−	1.93509e7i		−	1.22840i
$64$	−2.27822e6	+	1.66218e7i	−0.135793	+	0.990737i
$65$	−8.60255e6			−0.481919
$66$	2.00468e6	−	1.91566e6i	0.105650	−	0.100959i
$67$			1.19411e6i			0.0592579i	0.999561	+	0.0296290i	$0.00943257\pi$
$67$			1.19411e6i			0.0592579i	−0.999561	+	0.0296290i	$0.990567\pi$
$68$	1.42195e6	−	3.12958e7i	0.0665039	−	1.46369i
$69$	−1.10693e7			−0.488342
$70$	−1.02750e7	−	1.07524e7i	−0.427945	−	0.447831i
$71$			3.62332e7i			1.42585i	0.701242	+	0.712923i	$0.252629\pi$
$71$			3.62332e7i			1.42585i	−0.701242	+	0.712923i	$0.747371\pi$
$72$	−1.56670e7	−	1.79609e7i	−0.582985	−	0.668340i
$73$	3.35548e7			1.18158			0.590790	−	0.806826i	$-0.298816\pi$
$73$	3.35548e7			1.18158			0.590790	+	0.806826i	$0.298816\pi$
$74$	−4.46578e6	+	4.26748e6i	−0.148926	+	0.142313i
$75$			2.12839e6i			0.0672677i
$76$	1.93194e6	+	87779.2i	0.0579081	+	0.00263110i
$77$	−2.11547e7			−0.601789
$78$	−9.26855e6	−	9.69923e6i	−0.250399	−	0.262035i
$79$		−	1.22874e6i		−	0.0315466i	−0.999876	−	0.0157733i	$-0.994979\pi$
$79$		−	1.22874e6i		−	0.0315466i	0.999876	−	0.0157733i	$-0.00502101\pi$
$80$	−1.82424e7	−	1.66114e6i	−0.445371	−	0.0405552i
$81$	2.89888e7			0.673426
$82$	−1.12476e7	+	1.07482e7i	−0.248774	+	0.237727i
$83$		−	6.96923e7i		−	1.46849i	−0.678882	−	0.734247i	$-0.737535\pi$
$83$		−	6.96923e7i		−	1.46849i	0.678882	−	0.734247i	$-0.262465\pi$
$84$	1.05273e6	−	2.31697e7i	0.0211447	−	0.465376i
$85$	3.42049e7			0.655258
$86$	−5.10086e7	−	5.33788e7i	−0.932501	−	0.975832i
$87$			2.25804e7i			0.394143i
$88$	−1.96352e7	+	1.71275e7i	−0.327419	+	0.285603i
$89$	5.58347e7			0.889907			0.444953	−	0.895554i	$-0.353220\pi$
$89$	5.58347e7			0.889907			0.444953	+	0.895554i	$0.353220\pi$
$90$	1.88136e7	−	1.79782e7i	0.286749	−	0.274016i
$91$			1.02353e8i			1.49257i
$92$	1.03908e8	+	4.72116e6i	1.45044	+	0.0659018i
$93$	−3.80180e7			−0.508226
$94$	−2.06951e7	−	2.16567e7i	−0.265067	−	0.277384i
$95$			2.11153e6i			0.0259240i
$96$	−1.77818e7	−	2.23578e7i	−0.209358	−	0.263235i
$97$	−5.97582e7			−0.675010			−0.337505	−	0.941324i	$-0.609583\pi$
$97$	−5.97582e7			−0.675010			−0.337505	+	0.941324i	$0.609583\pi$
$98$	−6.12467e7	+	5.85271e7i	−0.664016	+	0.634531i
$99$		−	3.70146e7i		−	0.385329i
$100$	907778.	−	1.99794e7i	0.00907778	−	0.199794i
$101$	9.62751e7			0.925185			0.462593	−	0.886571i	$-0.346919\pi$
$101$	9.62751e7			0.925185			0.462593	+	0.886571i	$0.346919\pi$
$102$	3.68530e7	+	3.85655e7i	0.340465	+	0.356285i
$103$			1.96312e8i			1.74421i	0.489320	+	0.872104i	$0.337245\pi$
$103$			1.96312e8i			1.74421i	−0.489320	+	0.872104i	$0.662755\pi$
$104$	8.28678e7	+	9.50006e7i	0.708358	+	0.812070i
$105$	2.53235e7			0.208337
$106$	−9.27658e7	+	8.86466e7i	−0.734792	+	0.702164i
$107$		−	1.64435e8i		−	1.25447i	−0.778832	−	0.627233i	$-0.784187\pi$
$107$		−	1.64435e8i		−	1.25447i	0.778832	−	0.627233i	$-0.215813\pi$
$108$	8.62516e7	+	3.91891e6i	0.633975	+	0.0288051i
$109$	−1.81680e8			−1.28707			−0.643534	−	0.765417i	$-0.722533\pi$
$109$	−1.81680e8			−1.28707			−0.643534	+	0.765417i	$0.722533\pi$
$110$	−1.96541e7	−	2.05674e7i	−0.134240	−	0.140478i
$111$		−	1.05176e7i		−	0.0692824i
$112$	−1.97642e7	+	2.17047e8i	−0.125605	+	1.37937i
$113$	−1.30629e8			−0.801172			−0.400586	−	0.916259i	$-0.631193\pi$
$113$	−1.30629e8			−0.801172			−0.400586	+	0.916259i	$0.631193\pi$
$114$	−2.38071e6	+	2.27500e6i	−0.0140957	+	0.0134698i
$115$			1.13567e8i			0.649325i
$116$	9.63074e6	−	2.11964e8i	0.0531897	−	1.17066i
$117$	−1.79087e8			−0.955700
$118$	6.83426e7	+	7.15183e7i	0.352504	+	0.368883i
$119$		−	4.06968e8i		−	2.02942i
$120$	2.35045e7	−	2.05027e7i	0.113351	−	0.0988747i
$121$	1.73894e8			0.811228
$122$	1.13284e8	−	1.08254e8i	0.511363	−	0.488656i
$123$		−	2.64897e7i		−	0.115733i
$124$	3.56878e8	+	1.62150e7i	1.50950	+	0.0685852i
$125$	2.18366e7			0.0894427
$126$	−2.13904e8	−	2.23843e8i	−0.848665	−	0.888100i
$127$		−	4.45982e8i		−	1.71436i	−0.515015	−	0.857181i	$-0.672214\pi$
$127$		−	4.45982e8i		−	1.71436i	0.515015	−	0.857181i	$-0.327786\pi$
$128$	1.57383e8	+	2.17458e8i	0.586299	+	0.810095i
$129$	1.25715e8			0.453970
$130$	−9.95110e7	+	9.50923e7i	−0.348416	+	0.332945i
$131$		−	1.31555e8i		−	0.446707i	−0.974738	−	0.223353i	$-0.928300\pi$
$131$		−	1.31555e8i		−	0.446707i	0.974738	−	0.223353i	$-0.0717004\pi$
$132$	2.01368e6	−	4.43194e7i	0.00663278	−	0.145981i
$133$	2.51228e7			0.0802902
$134$	1.31997e7	+	1.38130e7i	0.0409397	+	0.0428421i
$135$			9.42692e7i			0.283815i
$136$	−3.29494e8	−	3.77735e8i	−0.963145	−	1.10416i
$137$	−3.26396e8			−0.926536			−0.463268	−	0.886218i	$-0.653323\pi$
$137$	−3.26396e8			−0.926536			−0.463268	+	0.886218i	$0.653323\pi$
$138$	−1.28045e8	+	1.22360e8i	−0.353059	+	0.337382i
$139$			6.48927e8i			1.73835i	0.494506	+	0.869174i	$0.335349\pi$
$139$			6.48927e8i			1.73835i	−0.494506	+	0.869174i	$0.664651\pi$
$140$	−2.37714e8	−	1.08007e7i	−0.618788	−	0.0281151i
$141$	5.10048e7			0.129043
$142$	4.00520e8	+	4.19131e8i	0.985079	+	1.03085i
$143$			1.95782e8i			0.468196i
$144$	−3.79769e8	−	3.45816e7i	−0.883222	−	0.0804258i
$145$	2.31667e8			0.524074
$146$	3.88149e8	−	3.70913e8i	0.854253	−	0.816321i
$147$		−	1.44245e8i		−	0.308909i
$148$	−4.48584e6	+	9.87292e7i	−0.00934968	+	0.205778i
$149$	−7.30660e8			−1.48242			−0.741208	−	0.671276i	$-0.765747\pi$
$149$	−7.30660e8			−1.48242			−0.741208	+	0.671276i	$0.765747\pi$
$150$	2.35272e7	+	2.46204e7i	0.0464734	+	0.0486329i
$151$			7.74114e8i			1.48901i	0.667618	+	0.744504i	$0.267314\pi$
$151$			7.74114e8i			1.48901i	−0.667618	+	0.744504i	$0.732686\pi$
$152$	2.33183e7	−	2.03402e7i	0.0436840	−	0.0381049i
$153$	7.12076e8			1.29945
$154$	−2.44710e8	+	2.33843e8i	−0.435079	+	0.415760i
$155$			3.90052e8i			0.675765i
$156$	−2.14430e8	−	9.74279e6i	−0.362066	−	0.0164507i
$157$	3.17523e8			0.522609			0.261304	−	0.965256i	$-0.415847\pi$
$157$	3.17523e8			0.522609			0.261304	+	0.965256i	$0.415847\pi$
$158$	−1.35825e7	−	1.42136e7i	−0.0217947	−	0.0228075i
$159$		−	2.18477e8i		−	0.341835i
$160$	−2.29383e8	+	1.82435e8i	−0.350011	+	0.278374i
$161$	1.35122e9			2.01105
$162$	3.35331e8	−	3.20441e8i	0.486871	−	0.465252i
$163$			2.02004e7i			0.0286161i	0.999898	+	0.0143081i	$0.00455455\pi$
$163$			2.02004e7i			0.0286161i	−0.999898	+	0.0143081i	$0.995445\pi$
$164$	−1.12981e7	+	2.48661e8i	−0.0156182	+	0.343742i
$165$	4.84391e7			0.0653522
$166$	−7.70376e8	−	8.06174e8i	−1.01454	−	1.06169i
$167$			5.65743e7i			0.0727366i	0.999338	+	0.0363683i	$0.0115789\pi$
$167$			5.65743e7i			0.0727366i	−0.999338	+	0.0363683i	$0.988421\pi$
$168$	−2.43940e8	−	2.79655e8i	−0.306228	−	0.351064i
$169$	1.31518e8			0.161228
$170$	3.95669e8	−	3.78100e8i	0.473736	−	0.452700i
$171$			4.39577e7i			0.0514103i
$172$	−1.18009e9	−	5.36185e7i	−1.34835	−	0.0612634i
$173$	−1.09785e9			−1.22563			−0.612813	−	0.790228i	$-0.709962\pi$
$173$	−1.09785e9			−1.22563			−0.612813	+	0.790228i	$0.709962\pi$
$174$	2.49603e8	+	2.61201e8i	0.272303	+	0.284956i
$175$		−	2.59811e8i		−	0.277016i
$176$	−3.78052e7	+	4.15171e8i	−0.0394004	+	0.432689i
$177$	−1.68436e8			−0.171610
$178$	6.45875e8	−	6.17196e8i	0.643381	−	0.614813i
$179$		−	6.44793e8i		−	0.628070i	−0.949411	−	0.314035i	$-0.898319\pi$
$179$		−	6.44793e8i		−	0.628070i	0.949411	−	0.314035i	$-0.101681\pi$
$180$	1.88981e7	−	4.15930e8i	0.0180023	−	0.396214i
$181$	−6.79018e8			−0.632655			−0.316328	−	0.948650i	$-0.602450\pi$
$181$	−6.79018e8			−0.632655			−0.316328	+	0.948650i	$0.602450\pi$
$182$	1.13140e9	+	1.18398e9i	1.03117	+	1.07909i
$183$			2.66800e8i			0.237893i
$184$	1.25416e9	−	1.09399e9i	1.09416	−	0.954424i
$185$	−1.07907e8			−0.0921217
$186$	−4.39777e8	+	4.20250e8i	−0.367436	+	0.351120i
$187$		−	7.78454e8i		−	0.636600i
$188$	−4.78786e8	−	2.17540e7i	−0.383275	−	0.0174144i
$189$	1.12161e9			0.879012
$190$	2.33408e7	+	2.44253e7i	0.0179102	+	0.0187424i
$191$		−	1.53738e8i		−	0.115518i	−0.998331	−	0.0577588i	$-0.981605\pi$
$191$		−	1.53738e8i		−	0.115518i	0.998331	−	0.0577588i	$-0.0183954\pi$
$192$	−4.52835e8	−	6.20666e7i	−0.333223	−	0.0456723i
$193$	9.67761e7			0.0697491			0.0348746	−	0.999392i	$-0.488897\pi$
$193$	9.67761e7			0.0697491			0.0348746	+	0.999392i	$0.488897\pi$
$194$	−6.91259e8	+	6.60565e8i	−0.488016	+	0.466346i
$195$		−	2.34363e8i		−	0.162088i
$196$	−6.15217e7	+	1.35404e9i	−0.0416873	+	0.917501i
$197$	−2.84766e9			−1.89070			−0.945352	−	0.326051i	$-0.894282\pi$
$197$	−2.84766e9			−1.89070			−0.945352	+	0.326051i	$0.894282\pi$
$198$	−4.09158e8	−	4.28171e8i	−0.266214	−	0.278584i
$199$		−	8.71254e8i		−	0.555562i	−0.960644	−	0.277781i	$-0.910401\pi$
$199$		−	8.71254e8i		−	0.555562i	0.960644	−	0.277781i	$-0.0895990\pi$
$200$	−2.10351e8	−	2.41148e8i	−0.131469	−	0.150718i
$201$	−3.25317e7			−0.0199307
$202$	1.11367e9	−	1.06422e9i	0.668887	−	0.639185i
$203$		−	2.75637e9i		−	1.62313i
$204$	8.52603e8	+	3.87387e7i	0.492296	+	0.0223678i
$205$	−2.71776e8			−0.153885
$206$	2.17003e9	+	2.27087e9i	1.20503	+	1.26102i
$207$			2.36424e9i			1.28769i
$208$	2.00872e9	+	1.82913e8i	1.07316	+	0.0977216i
$209$	4.80553e7			0.0251858
$210$	2.92932e8	−	2.79925e8i	0.150623	−	0.143934i
$211$			2.22378e9i			1.12192i	0.827843	+	0.560960i	$0.189568\pi$
$211$			2.22378e9i			1.12192i	−0.827843	+	0.560960i	$0.810432\pi$
$212$	−9.31824e7	+	2.05086e9i	−0.0461307	+	1.01530i
$213$	−9.87114e8			−0.479567
$214$	−1.81766e9	−	1.90212e9i	−0.866676	−	0.906949i
$215$		−	1.28979e9i		−	0.603623i
$216$	1.04104e9	−	9.08090e8i	0.478249	−	0.417171i
$217$	4.64082e9			2.09293
$218$	−2.10161e9	+	2.00829e9i	−0.930520	+	0.889201i
$219$			9.14146e8i			0.397410i
$220$	−4.54702e8	−	2.06597e7i	−0.194105	−	0.00881930i
$221$	−3.76639e9			−1.57891
$222$	−1.16261e8	−	1.21663e8i	−0.0478654	−	0.0500895i
$223$		−	1.76089e9i		−	0.712054i	−0.934476	−	0.356027i	$-0.884131\pi$
$223$		−	1.76089e9i		−	0.712054i	0.934476	−	0.356027i	$-0.115869\pi$
$224$	2.17061e9	+	2.72919e9i	0.862162	+	1.08403i
$225$	4.54593e8			0.177375
$226$	−1.51107e9	+	1.44397e9i	−0.579228	+	0.553508i
$227$			1.85447e9i			0.698418i	0.937045	+	0.349209i	$0.113550\pi$
$227$			1.85447e9i			0.698418i	−0.937045	+	0.349209i	$0.886450\pi$
$228$	−2.39140e6	+	5.26327e7i	−0.000884940	+	0.0194767i
$229$	−1.13087e9			−0.411218			−0.205609	−	0.978634i	$-0.565917\pi$
$229$	−1.13087e9			−0.411218			−0.205609	+	0.978634i	$0.565917\pi$
$230$	1.25537e9	+	1.31370e9i	0.448601	+	0.469447i
$231$		−	5.76326e8i		−	0.202405i
$232$	−2.23164e9	−	2.55837e9i	−0.770321	−	0.883105i
$233$	2.24935e9			0.763191			0.381596	−	0.924329i	$-0.375375\pi$
$233$	2.24935e9			0.763191			0.381596	+	0.924329i	$0.375375\pi$
$234$	−2.07162e9	+	1.97963e9i	−0.690949	+	0.660268i
$235$		−	5.23292e8i		−	0.171582i
$236$	1.58112e9	+	7.18395e7i	0.509703	+	0.0231587i
$237$	3.34752e7			0.0106103
$238$	−4.49861e9	−	4.70765e9i	−1.40207	−	1.46722i
$239$			2.77234e9i			0.849679i	0.905269	+	0.424840i	$0.139669\pi$
$239$			2.77234e9i			0.849679i	−0.905269	+	0.424840i	$0.860331\pi$
$240$	4.52552e7	−	4.96985e8i	0.0136403	−	0.149795i
$241$	−1.60515e8			−0.0475826			−0.0237913	−	0.999717i	$-0.507574\pi$
$241$	−1.60515e8			−0.0475826			−0.0237913	+	0.999717i	$0.507574\pi$
$242$	2.01154e9	−	1.92222e9i	0.586498	−	0.560455i
$243$			3.00257e9i			0.861128i
$244$	1.13793e8	−	2.50448e9i	0.0321037	−	0.706574i
$245$	−1.47990e9			−0.410742
$246$	−2.92817e8	−	3.06423e8i	−0.0799568	−	0.0836721i
$247$		−	2.32506e8i		−	0.0624663i
$248$	4.30747e9	−	3.75735e9i	1.13872	−	0.993287i
$249$	1.89866e9			0.493911
$250$	2.52597e8	−	2.41381e8i	0.0646649	−	0.0617936i
$251$		−	5.77680e9i		−	1.45543i	−0.685877	−	0.727717i	$-0.740581\pi$
$251$		−	5.77680e9i		−	1.45543i	0.685877	−	0.727717i	$-0.259419\pi$
$252$	−4.94871e9	−	2.24849e8i	−1.22713	−	0.0557555i
$253$	2.58463e9			0.630836
$254$	−4.92987e9	−	5.15895e9i	−1.18441	−	1.23944i
$255$			9.31858e8i			0.220389i
$256$	4.22433e9	+	7.75762e8i	0.983553	+	0.180621i
$257$	4.57743e9			1.04928			0.524638	−	0.851326i	$-0.324201\pi$
$257$	4.57743e9			1.04928			0.524638	+	0.851326i	$0.324201\pi$
$258$	1.45422e9	−	1.38965e9i	0.328210	−	0.313636i
$259$			1.28387e9i			0.285313i
$260$	−9.99578e7	+	2.19998e9i	−0.0218738	+	0.481422i
$261$	4.82284e9			1.03930
$262$	−1.45421e9	−	1.52178e9i	−0.308618	−	0.322958i
$263$			4.85941e8i			0.101569i	0.998710	+	0.0507844i	$0.0161721\pi$
$263$			4.85941e8i			0.101569i	−0.998710	+	0.0507844i	$0.983828\pi$
$264$	−4.66611e8	−	5.34929e8i	−0.0960593	−	0.110124i
$265$	−2.24150e9			−0.454523
$266$	2.90612e8	−	2.77707e8i	0.0580479	−	0.0554703i
$267$			1.52113e9i			0.299310i
$268$	3.05378e8	+	1.38751e7i	0.0591968	+	0.00268965i
$269$	−1.48731e9			−0.284049			−0.142024	−	0.989863i	$-0.545361\pi$
$269$	−1.48731e9			−0.284049			−0.142024	+	0.989863i	$0.545361\pi$
$270$	1.04205e9	+	1.09047e9i	0.196080	+	0.205191i
$271$		−	6.79398e9i		−	1.25964i	−0.776740	−	0.629821i	$-0.783128\pi$
$271$		−	6.79398e9i		−	1.25964i	0.776740	−	0.629821i	$-0.216872\pi$
$272$	−7.98693e9	−	7.27286e8i	−1.45917	−	0.132871i
$273$	−2.78844e9			−0.502007
$274$	−3.77562e9	+	3.60797e9i	−0.669863	+	0.640118i
$275$		−	4.96970e8i		−	0.0868959i
$276$	−1.28620e8	+	2.83082e9i	−0.0221653	+	0.487838i
$277$	1.54730e9			0.262818			0.131409	−	0.991328i	$-0.458050\pi$
$277$	1.54730e9			0.262818			0.131409	+	0.991328i	$0.458050\pi$
$278$	7.17322e9	+	7.50654e9i	1.20098	+	1.25678i
$279$			8.12009e9i			1.34012i
$280$	−2.86917e9	+	2.50274e9i	−0.466793	+	0.407178i
$281$	−9.33090e9			−1.49657			−0.748287	−	0.663375i	$-0.769123\pi$
$281$	−9.33090e9			−1.49657			−0.748287	+	0.663375i	$0.769123\pi$
$282$	5.90004e8	−	5.63805e8i	0.0932950	−	0.0891523i
$283$			7.43824e9i			1.15964i	0.814743	+	0.579822i	$0.196878\pi$
$283$			7.43824e9i			1.15964i	−0.814743	+	0.579822i	$0.803122\pi$
$284$	9.26613e9	+	4.21013e8i	1.42438	+	0.0647176i
$285$	−5.75252e7			−0.00871924
$286$	2.16416e9	+	2.26473e9i	0.323464	+	0.338495i
$287$			3.23358e9i			0.476602i
$288$	−4.77529e9	+	3.79793e9i	−0.694113	+	0.552049i
$289$	7.99992e9			1.14682
$290$	2.67984e9	−	2.56084e9i	0.378893	−	0.362069i
$291$		−	1.62802e9i		−	0.227032i
$292$	3.89892e8	−	8.58117e9i	0.0536306	−	1.18036i
$293$	−1.59214e9			−0.216028			−0.108014	−	0.994149i	$-0.534449\pi$
$293$	−1.59214e9			−0.216028			−0.108014	+	0.994149i	$0.534449\pi$
$294$	−1.59448e9	−	1.66857e9i	−0.213417	−	0.223334i
$295$			1.72810e9i			0.228181i
$296$	1.03946e9	+	1.19165e9i	0.135407	+	0.155232i
$297$	2.14543e9			0.275733
$298$	−8.45199e9	+	8.07669e9i	−1.07175	+	1.02416i
$299$		−	1.25052e10i		−	1.56461i
$300$	5.44307e8	+	2.47310e7i	0.0671983	+	0.00305321i
$301$	−1.53459e10			−1.86950
$302$	8.55703e9	+	8.95465e9i	1.02872	+	1.07652i
$303$			2.62286e9i			0.311175i
$304$	4.48966e7	−	4.93047e8i	0.00525678	−	0.0577290i
$305$	2.73728e9			0.316315
$306$	8.23702e9	−	7.87127e9i	0.939474	−	0.897757i
$307$		−	3.36362e9i		−	0.378663i	−0.981913	−	0.189332i	$-0.939368\pi$
$307$		−	3.36362e9i		−	0.378663i	0.981913	−	0.189332i	$-0.0606321\pi$
$308$	−2.45808e8	+	5.41002e9i	−0.0273145	+	0.601169i
$309$	−5.34821e9			−0.586644
$310$	4.31162e9	+	4.51197e9i	0.466868	+	0.488562i
$311$		−	1.23254e10i		−	1.31752i	−0.752352	−	0.658761i	$-0.771081\pi$
$311$		−	1.23254e10i		−	1.31752i	0.752352	−	0.658761i	$-0.228919\pi$
$312$	−2.58814e9	+	2.25760e9i	−0.273130	+	0.238248i
$313$	2.77987e9			0.289633			0.144816	−	0.989459i	$-0.453741\pi$
$313$	2.77987e9			0.289633			0.144816	+	0.989459i	$0.453741\pi$
$314$	3.67299e9	−	3.50989e9i	0.377834	−	0.361056i
$315$		−	5.40873e9i		−	0.549355i
$316$	−3.14234e8	−	1.42775e7i	−0.0315141	−	0.00143187i
$317$	−5.40177e8			−0.0534933			−0.0267466	−	0.999642i	$-0.508515\pi$
$317$	−5.40177e8			−0.0534933			−0.0267466	+	0.999642i	$0.508515\pi$
$318$	−2.41504e9	−	2.52726e9i	−0.236165	−	0.247139i
$319$		−	5.27241e9i		−	0.509151i
$320$	−6.36783e8	+	4.64594e9i	−0.0607284	+	0.443071i
$321$	4.47977e9			0.421925
$322$	1.56304e10	−	1.49363e10i	1.45394	−	1.38938i
$323$			9.24475e8i			0.0849347i
$324$	3.36837e8	−	7.41348e9i	0.0305661	−	0.672732i
$325$	−2.40449e9			−0.215521
$326$	2.23295e8	+	2.33671e8i	0.0197701	+	0.0206888i
$327$		−	4.94959e9i		−	0.432891i
$328$	2.61800e9	+	3.00131e9i	0.226191	+	0.259307i
$329$	−6.22610e9			−0.531414
$330$	5.60325e8	−	5.35445e8i	0.0472481	−	0.0451501i
$331$			1.21115e10i			1.00899i	0.863414	+	0.504495i	$0.168321\pi$
$331$			1.21115e10i			1.00899i	−0.863414	+	0.504495i	$0.831679\pi$
$332$	−1.78228e10	−	8.09794e8i	−1.46698	−	0.0666534i
$333$	−2.24640e9			−0.182688
$334$	6.25370e8	+	6.54429e8i	0.0502518	+	0.0525868i
$335$			3.33765e8i			0.0265009i
$336$	−5.91310e9	−	5.38444e8i	−0.463936	−	0.0422458i
$337$	−9.48812e9			−0.735632			−0.367816	−	0.929899i	$-0.619894\pi$
$337$	−9.48812e9			−0.735632			−0.367816	+	0.929899i	$0.619894\pi$
$338$	1.52135e9	−	1.45380e9i	0.116564	−	0.111388i
$339$		−	3.55878e9i		−	0.269465i
$340$	3.97446e8	−	8.74743e9i	0.0297415	−	0.654583i
$341$	8.87702e9			0.656523
$342$	4.85907e8	+	5.08486e8i	0.0355180	+	0.0371685i
$343$		−	1.56347e9i		−	0.112957i
$344$	−1.42436e10	+	1.24245e10i	−1.01715	+	0.887248i
$345$	−3.09396e9			−0.218393
$346$	−1.26995e10	+	1.21356e10i	−0.886099	+	0.846752i
$347$			9.01032e9i			0.621473i	0.950496	+	0.310737i	$0.100576\pi$
$347$			9.01032e9i			0.621473i	−0.950496	+	0.310737i	$0.899424\pi$
$348$	5.77462e9	+	2.62374e8i	0.393737	+	0.0178897i
$349$	2.17409e10			1.46547			0.732733	−	0.680517i	$-0.238245\pi$
$349$	2.17409e10			1.46547			0.732733	+	0.680517i	$0.238245\pi$
$350$	−2.87194e9	−	3.00539e9i	−0.191383	−	0.200276i
$351$		−	1.03802e10i		−	0.683878i
$352$	4.15197e9	+	5.22043e9i	0.270448	+	0.340045i
$353$	−5.60018e9			−0.360664			−0.180332	−	0.983606i	$-0.557717\pi$
$353$	−5.60018e9			−0.360664			−0.180332	+	0.983606i	$0.557717\pi$
$354$	−1.94840e9	+	1.86189e9i	−0.124070	+	0.118560i
$355$			1.01275e10i			0.637658i
$356$	6.48775e8	−	1.42790e10i	0.0403919	−	0.888990i
$357$	1.10872e10			0.682573
$358$	−7.12752e9	−	7.45872e9i	−0.433917	−	0.454080i
$359$			1.31213e10i			0.789952i	0.918692	+	0.394976i	$0.129247\pi$
$359$			1.31213e10i			0.789952i	−0.918692	+	0.394976i	$0.870753\pi$
$360$	−4.37907e9	−	5.02022e9i	−0.260719	−	0.298891i
$361$	1.69265e10			0.996640
$362$	−7.85462e9	+	7.50585e9i	−0.457395	+	0.437085i
$363$			4.73746e9i			0.272847i
$364$	2.61753e10	+	1.18929e9i	1.49103	+	0.0677460i
$365$	9.37884e9			0.528418
$366$	2.94920e9	+	3.08624e9i	0.164354	+	0.171991i
$367$			9.89380e9i			0.545379i	0.962102	+	0.272690i	$0.0879132\pi$
$367$			9.89380e9i			0.545379i	−0.962102	+	0.272690i	$0.912087\pi$
$368$	2.41474e9	−	2.65183e10i	0.131668	−	1.44595i
$369$	−5.65782e9			−0.305171
$370$	−1.24822e9	+	1.19280e9i	−0.0666018	+	0.0636444i
$371$			2.66693e10i			1.40772i
$372$	−4.41752e8	+	9.72257e9i	−0.0230678	+	0.507703i
$373$	1.01496e10			0.524339			0.262170	−	0.965022i	$-0.415562\pi$
$373$	1.01496e10			0.524339			0.262170	+	0.965022i	$0.415562\pi$
$374$	−8.60501e9	−	9.00486e9i	−0.439810	−	0.460247i
$375$			5.94903e8i			0.0300830i
$376$	−5.77888e9	+	5.04084e9i	−0.289129	+	0.252204i
$377$	−2.55095e10			−1.26281
$378$	1.29744e10	−	1.23982e10i	0.635505	−	0.607286i
$379$			1.39748e10i			0.677312i	0.940910	+	0.338656i	$0.109972\pi$
$379$			1.39748e10i			0.677312i	−0.940910	+	0.338656i	$0.890028\pi$
$380$	5.39994e8	+	2.45350e7i	0.0258973	+	0.00117666i
$381$	1.21501e10			0.576606
$382$	−1.69942e9	−	1.77838e9i	−0.0798080	−	0.0835165i
$383$		−	2.31617e10i		−	1.07640i	−0.842816	−	0.538201i	$-0.819104\pi$
$383$		−	2.31617e10i		−	1.07640i	0.842816	−	0.538201i	$-0.180896\pi$
$384$	−5.92430e9	+	4.28766e9i	−0.272466	+	0.197195i
$385$	−5.91292e9			−0.269128
$386$	1.11947e9	−	1.06976e9i	0.0504269	−	0.0481878i
$387$		−	2.68508e10i		−	1.19706i
$388$	−6.94364e8	+	1.52823e10i	−0.0306380	+	0.674314i
$389$	−1.13177e10			−0.494267			−0.247133	−	0.968981i	$-0.579489\pi$
$389$	−1.13177e10			−0.494267			−0.247133	+	0.968981i	$0.579489\pi$
$390$	−2.59064e9	−	2.71102e9i	−0.111982	−	0.117186i
$391$			4.97224e10i			2.12738i
$392$	1.42558e10	+	1.63430e10i	0.603738	+	0.692132i
$393$	3.58401e9			0.150245
$394$	−3.29407e10	+	3.14780e10i	−1.36693	+	1.30624i
$395$		−	3.43444e8i		−	0.0141081i
$396$	−9.46597e9	−	4.30093e8i	−0.384932	−	0.0174897i
$397$	1.01291e10			0.407765			0.203882	−	0.978995i	$-0.434644\pi$
$397$	1.01291e10			0.407765			0.203882	+	0.978995i	$0.434644\pi$
$398$	−9.63082e9	−	1.00783e10i	−0.383823	−	0.401658i
$399$			6.84432e8i			0.0270047i
$400$	−5.09890e9	−	4.64304e8i	−0.199176	−	0.0181369i
$401$	1.52259e10			0.588850			0.294425	−	0.955675i	$-0.404872\pi$
$401$	1.52259e10			0.588850			0.294425	+	0.955675i	$0.404872\pi$
$402$	−3.76315e8	+	3.59605e8i	−0.0144094	+	0.0137696i
$403$		−	4.29496e10i		−	1.62832i
$404$	1.11867e9	−	2.46210e10i	0.0419931	−	0.924232i
$405$	8.10262e9			0.301165
$406$	−3.04688e10	−	3.18846e10i	−1.12137	−	1.17348i
$407$			2.45580e9i			0.0894985i
$408$	1.02908e10	−	8.97653e9i	0.371371	−	0.323942i
$409$	−5.16482e10			−1.84570			−0.922851	−	0.385156i	$-0.874148\pi$
$409$	−5.16482e10			−1.84570			−0.922851	+	0.385156i	$0.874148\pi$
$410$	−3.14380e9	+	3.00420e9i	−0.111255	+	0.106315i
$411$		−	8.89213e9i		−	0.311629i
$412$	5.02041e10	+	2.28106e9i	1.74241	+	0.0791678i
$413$	2.05608e10			0.706708
$414$	2.61343e10	+	2.73487e10i	0.889629	+	0.930968i
$415$		−	1.94796e10i		−	0.656731i
$416$	2.52580e10	−	2.00884e10i	0.843384	−	0.670769i
$417$	−1.76790e10			−0.584673
$418$	5.55886e8	−	5.31202e8i	0.0182088	−	0.0174002i
$419$		−	2.90780e10i		−	0.943427i	−0.881752	−	0.471714i	$-0.843636\pi$
$419$		−	2.90780e10i		−	0.943427i	0.881752	−	0.471714i	$-0.156364\pi$
$420$	2.94248e8	−	6.47613e9i	0.00945619	−	0.208122i
$421$	−2.02634e9			−0.0645037			−0.0322519	−	0.999480i	$-0.510268\pi$
$421$	−2.02634e9			−0.0645037			−0.0322519	+	0.999480i	$0.510268\pi$
$422$	2.45816e10	+	2.57239e10i	0.775105	+	0.811122i
$423$		−	1.08939e10i		−	0.340268i
$424$	2.15923e10	+	2.47536e10i	0.668089	+	0.765905i
$425$	9.56056e9			0.293040
$426$	−1.14186e10	+	1.09115e10i	−0.346715	+	0.331320i
$427$		−	3.25681e10i		−	0.979671i
$428$	−4.20519e10	−	1.91066e9i	−1.25317	−	0.0569388i
$429$	−5.33376e9			−0.157472
$430$	−1.42573e10	−	1.49198e10i	−0.417027	−	0.436405i
$431$			2.31188e10i			0.669972i	0.942223	+	0.334986i	$0.108732\pi$
$431$			2.31188e10i			0.669972i	−0.942223	+	0.334986i	$0.891268\pi$
$432$	2.00441e9	−	2.20121e10i	0.0575509	−	0.632014i
$433$	−5.16117e10			−1.46824			−0.734119	−	0.679021i	$-0.762405\pi$
$433$	−5.16117e10			−1.46824			−0.734119	+	0.679021i	$0.762405\pi$
$434$	5.36832e10	−	5.12995e10i	1.51314	−	1.44595i
$435$			6.31141e9i			0.176266i
$436$	−2.11105e9	+	4.64622e10i	−0.0584187	+	1.28574i
$437$	−3.06945e9			−0.0841656
$438$	1.01049e10	+	1.05745e10i	0.274560	+	0.287318i
$439$		−	4.07914e10i		−	1.09827i	−0.835733	−	0.549137i	$-0.814957\pi$
$439$		−	4.07914e10i		−	1.09827i	0.835733	−	0.549137i	$-0.185043\pi$
$440$	−5.48819e9	+	4.78728e9i	−0.146426	+	0.127726i
$441$	−3.08086e10			−0.814549
$442$	−4.35682e10	+	4.16336e10i	−1.14151	+	1.09082i
$443$			1.78192e9i			0.0462671i	0.999732	+	0.0231336i	$0.00736430\pi$
$443$			1.78192e9i			0.0462671i	−0.999732	+	0.0231336i	$0.992636\pi$
$444$	−2.68972e9	−	1.22209e8i	−0.0692110	−	0.00314466i
$445$	1.56063e10			0.397978
$446$	−1.94648e10	−	2.03693e10i	−0.491939	−	0.514798i
$447$		−	1.99057e10i		−	0.498593i
$448$	5.52771e10	+	7.57641e9i	1.37225	+	0.188084i
$449$	5.74811e10			1.41429			0.707147	−	0.707067i	$-0.249982\pi$
$449$	5.74811e10			1.41429			0.707147	+	0.707067i	$0.249982\pi$
$450$	5.25856e9	−	5.02506e9i	0.128238	−	0.122544i
$451$			6.18523e9i			0.149503i
$452$	−1.51785e9	+	3.34066e10i	−0.0363643	+	0.800347i
$453$	−2.10895e10			−0.500811
$454$	2.04992e10	+	2.14518e10i	0.482518	+	0.504940i
$455$			2.86084e10i			0.667496i
$456$	5.54137e8	+	6.35269e8i	0.0128162	+	0.0146926i
$457$	−4.50957e10			−1.03388			−0.516941	−	0.856021i	$-0.672929\pi$
$457$	−4.50957e10			−1.03388			−0.516941	+	0.856021i	$0.672929\pi$
$458$	−1.30815e10	+	1.25006e10i	−0.297301	+	0.284099i
$459$			4.12732e10i			0.929860i
$460$	2.90433e10	+	1.31960e9i	0.648656	+	0.0294722i
$461$	7.73092e10			1.71170			0.855850	−	0.517225i	$-0.173035\pi$
$461$	7.73092e10			1.71170			0.855850	+	0.517225i	$0.173035\pi$
$462$	−6.37069e9	−	6.66672e9i	−0.139836	−	0.146334i
$463$			8.52854e10i			1.85588i	0.372726	+	0.927941i	$0.378423\pi$
$463$			8.52854e10i			1.85588i	−0.372726	+	0.927941i	$0.621577\pi$
$464$	−5.40949e10	−	4.92586e9i	−1.16704	−	0.106270i
$465$	−1.06263e10			−0.227286
$466$	2.60196e10	−	2.48643e10i	0.551769	−	0.527268i
$467$			3.20726e10i			0.674320i	0.941447	+	0.337160i	$0.109466\pi$
$467$			3.20726e10i			0.674320i	−0.941447	+	0.337160i	$0.890534\pi$
$468$	−2.08092e9	+	4.57991e10i	−0.0433782	+	0.954716i
$469$	3.97112e9			0.0820770
$470$	−5.78446e9	−	6.05324e9i	−0.118542	−	0.124050i
$471$			8.65041e9i			0.175773i
$472$	1.90839e10	−	1.66467e10i	0.384503	−	0.335397i
$473$	−2.93538e10			−0.586435
$474$	3.87228e8	−	3.70033e8i	0.00767102	−	0.00733040i
$475$			5.90190e8i			0.0115936i
$476$	−1.04076e11	−	4.72879e9i	−2.02733	−	0.0921133i
$477$	−4.66635e10			−0.901371
$478$	3.06454e10	+	3.20694e10i	0.587020	+	0.614298i
$479$		−	3.58893e10i		−	0.681746i	−0.940109	−	0.340873i	$-0.889277\pi$
$479$		−	3.58893e10i		−	0.681746i	0.940109	−	0.340873i	$-0.110723\pi$
$480$	−4.97016e9	−	6.24918e9i	−0.0936280	−	0.117722i
$481$	1.18819e10			0.221976
$482$	−1.85678e9	+	1.77433e9i	−0.0344010	+	0.0328735i
$483$			3.68118e10i			0.676393i
$484$	2.02057e9	−	4.44710e10i	0.0368208	−	0.810392i
$485$	−1.67029e10			−0.301874
$486$	3.31903e10	+	3.47326e10i	0.594930	+	0.622575i
$487$		−	5.98567e10i		−	1.06414i	−0.846702	−	0.532068i	$-0.821415\pi$
$487$		−	5.98567e10i		−	1.06414i	0.846702	−	0.532068i	$-0.178585\pi$
$488$	−2.63681e10	−	3.02287e10i	−0.464943	−	0.533016i
$489$	−5.50329e8			−0.00962470
$490$	−1.71190e10	+	1.63588e10i	−0.296957	+	0.283771i
$491$		−	3.00275e10i		−	0.516645i	−0.966059	−	0.258323i	$-0.916830\pi$
$491$		−	3.00275e10i		−	0.516645i	0.966059	−	0.258323i	$-0.0831698\pi$
$492$	−6.77438e9	−	3.07799e8i	−0.115614	−	0.00525299i
$493$	1.01429e11			1.71702
$494$	−2.57011e9	−	2.68954e9i	−0.0431563	−	0.0451617i
$495$		−	1.03459e10i		−	0.172325i
$496$	8.29353e9	−	9.10782e10i	0.137029	−	1.50483i
$497$	1.20496e11			1.97491
$498$	2.19629e10	−	2.09877e10i	0.357086	−	0.341230i
$499$			2.32602e10i			0.375156i	0.982250	+	0.187578i	$0.0600637\pi$
$499$			2.32602e10i			0.375156i	−0.982250	+	0.187578i	$0.939936\pi$
$500$	2.53732e8	−	5.58441e9i	0.00405971	−	0.0893505i
$501$	−1.54128e9			−0.0244641
$502$	−6.38566e10	−	6.68238e10i	−1.00552	−	1.05224i
$503$			2.16574e10i			0.338326i	0.985588	+	0.169163i	$0.0541064\pi$
$503$			2.16574e10i			0.338326i	−0.985588	+	0.169163i	$0.945894\pi$
$504$	−5.97303e10	+	5.21020e10i	−0.925705	+	0.807481i
$505$	2.69097e10			0.413755
$506$	2.98980e10	−	2.85704e10i	0.456079	−	0.435828i
$507$			3.58300e9i			0.0542270i
$508$	−1.14054e11	−	5.18212e9i	−1.71260	−	0.0778131i
$509$	1.21565e10			0.181108			0.0905541	−	0.995892i	$-0.471136\pi$
$509$	1.21565e10			0.181108			0.0905541	+	0.995892i	$0.471136\pi$
$510$	1.03007e10	+	1.07794e10i	0.152260	+	0.159336i
$511$		−	1.11589e11i		−	1.63658i
$512$	5.74407e10	−	3.77219e10i	0.835871	−	0.548925i
$513$	−2.54787e9			−0.0367881
$514$	5.29500e10	−	5.05988e10i	0.758601	−	0.724916i
$515$			5.48709e10i			0.780034i
$516$	1.46075e9	−	3.21498e10i	0.0206052	−	0.453502i
$517$	−1.19094e10			−0.166697
$518$	1.41918e10	+	1.48513e10i	0.197115	+	0.206275i
$519$		−	2.99091e10i		−	0.412225i
$520$	2.31623e10	+	2.65535e10i	0.316787	+	0.363169i
$521$	−5.20805e10			−0.706845			−0.353422	−	0.935464i	$-0.614982\pi$
$521$	−5.20805e10			−0.706845			−0.353422	+	0.935464i	$0.614982\pi$
$522$	5.57888e10	−	5.33115e10i	0.751389	−	0.718024i
$523$		−	2.42007e10i		−	0.323461i	−0.986835	−	0.161731i	$-0.948292\pi$
$523$		−	2.42007e10i		−	0.323461i	0.986835	−	0.161731i	$-0.0517075\pi$
$524$	−3.36434e10	−	1.52861e9i	−0.446246	−	0.0202755i
$525$	7.07813e9			0.0931711
$526$	5.37158e9	+	5.62118e9i	0.0701712	+	0.0734319i
$527$			1.70774e11i			2.21400i
$528$	−1.13107e10	−	1.02994e9i	−0.145530	−	0.0132519i
$529$	−8.67778e10			−1.10812
$530$	−2.59288e10	+	2.47775e10i	−0.328609	+	0.314017i
$531$			3.59755e10i			0.452510i
$532$	2.91917e8	−	6.42482e9i	0.00364428	−	0.0802074i
$533$	2.99260e10			0.370800
$534$	1.68145e10	+	1.75958e10i	0.206785	+	0.216394i
$535$		−	4.59609e10i		−	0.561014i
$536$	3.68587e9	−	3.21514e9i	0.0446561	−	0.0389530i
$537$	1.75664e10			0.211244
$538$	−1.72047e10	+	1.64407e10i	−0.205361	+	0.196242i
$539$			3.36805e10i			0.399046i
$540$	2.41081e10	+	1.09537e9i	0.283522	+	0.0128820i
$541$	−7.39316e10			−0.863060			−0.431530	−	0.902099i	$-0.642026\pi$
$541$	−7.39316e10			−0.863060			−0.431530	+	0.902099i	$0.642026\pi$
$542$	−7.51005e10	−	7.85902e10i	−0.870253	−	0.910692i
$543$		−	1.84988e10i		−	0.212786i
$544$	−1.00429e11	+	7.98743e10i	−1.14674	+	0.912035i
$545$	−5.07812e10			−0.575595
$546$	−3.22556e10	+	3.08233e10i	−0.362939	+	0.346823i
$547$		−	9.08736e10i		−	1.01505i	−0.861636	−	0.507526i	$-0.830560\pi$
$547$		−	9.08736e10i		−	1.01505i	0.861636	−	0.507526i	$-0.169440\pi$
$548$	−3.79257e9	+	8.34712e10i	−0.0420544	+	0.925581i
$549$	5.69847e10			0.627290
$550$	−5.49349e9	−	5.74875e9i	−0.0600340	−	0.0628236i
$551$			6.26140e9i			0.0679305i
$552$	2.98040e10	+	3.41676e10i	0.321009	+	0.368009i
$553$	−4.08628e9			−0.0436946
$554$	1.78985e10	−	1.71038e10i	0.190011	−	0.181574i
$555$		−	2.93975e9i		−	0.0309840i
$556$	1.65954e11	+	7.54025e9i	1.73656	+	0.0789018i
$557$	−7.25820e9			−0.0754064			−0.0377032	−	0.999289i	$-0.512004\pi$
$557$	−7.25820e9			−0.0754064			−0.0377032	+	0.999289i	$0.512004\pi$
$558$	8.97592e10	+	9.39301e10i	0.925853	+	0.968875i
$559$			1.42022e11i			1.45449i
$560$	−5.52426e9	+	6.06665e10i	−0.0561723	+	0.616875i
$561$	2.12077e10			0.214113
$562$	−1.07936e11	+	1.03143e11i	−1.08199	+	1.03394i
$563$		−	4.02851e10i		−	0.400969i	−0.979697	−	0.200485i	$-0.935748\pi$
$563$		−	4.02851e10i		−	0.400969i	0.979697	−	0.200485i	$-0.0642517\pi$
$564$	5.92653e8	−	1.30438e10i	0.00585712	−	0.128910i
$565$	−3.65119e10			−0.358295
$566$	8.22221e10	+	8.60427e10i	0.801166	+	0.838394i
$567$		−	9.64045e10i		−	0.932750i
$568$	1.11841e11	−	9.75574e10i	1.07450	−	0.937274i
$569$	4.42204e10			0.421866			0.210933	−	0.977501i	$-0.432350\pi$
$569$	4.42204e10			0.421866			0.210933	+	0.977501i	$0.432350\pi$
$570$	−6.65430e8	+	6.35882e8i	−0.00630380	+	0.00602389i
$571$		−	1.92416e11i		−	1.81008i	−0.425327	−	0.905040i	$-0.639841\pi$
$571$		−	1.92416e11i		−	1.81008i	0.425327	−	0.905040i	$-0.360159\pi$
$572$	5.00684e10	+	2.27490e9i	0.467714	+	0.0212509i
$573$	4.18835e9			0.0388530
$574$	3.57438e10	+	3.74048e10i	0.329271	+	0.344572i
$575$			3.17431e10i			0.290387i
$576$	−1.32565e10	+	9.67190e10i	−0.120431	+	0.878662i
$577$	5.62180e10			0.507192			0.253596	−	0.967310i	$-0.418387\pi$
$577$	5.62180e10			0.507192			0.253596	+	0.967310i	$0.418387\pi$
$578$	9.25400e10	−	8.84309e10i	0.829122	−	0.792305i
$579$			2.63651e9i			0.0234593i
$580$	2.69187e9	−	5.92457e10i	0.0237872	−	0.523534i
$581$	−2.31767e11			−2.03398
$582$	−1.79960e10	−	1.88323e10i	−0.156850	−	0.164139i
$583$			5.10133e10i			0.441580i
$584$	−9.03458e10	−	1.03574e11i	−0.776706	−	0.890425i
$585$	−5.00565e10			−0.427402
$586$	−1.84172e10	+	1.75994e10i	−0.156183	+	0.149248i
$587$			2.12589e11i			1.79056i	0.445508	+	0.895278i	$0.353023\pi$
$587$			2.12589e11i			1.79056i	−0.445508	+	0.895278i	$0.646977\pi$
$588$	−3.68886e10	−	1.67606e9i	−0.308591	−	0.0140211i
$589$	−1.05422e10			−0.0875927
$590$	1.91023e10	+	1.99900e10i	0.157644	+	0.164970i
$591$		−	7.75800e10i		−	0.635916i
$592$	2.51965e10	+	2.29438e9i	0.205142	+	0.0186801i
$593$	−3.64674e10			−0.294908			−0.147454	−	0.989069i	$-0.547108\pi$
$593$	−3.64674e10			−0.294908			−0.147454	+	0.989069i	$0.547108\pi$
$594$	2.48175e10	−	2.37155e10i	0.199348	−	0.190497i
$595$		−	1.13751e11i		−	0.907585i
$596$	−8.48995e9	+	1.86856e11i	−0.0672853	+	1.48089i
$597$	2.37359e10			0.186857
$598$	−1.38232e11	−	1.44655e11i	−1.08095	−	1.13118i
$599$		−	1.54791e11i		−	1.20237i	−0.799111	−	0.601184i	$-0.794696\pi$
$599$		−	1.54791e11i		−	1.20237i	0.799111	−	0.601184i	$-0.205304\pi$
$600$	6.56971e9	−	5.73067e9i	0.0506922	−	0.0442181i
$601$	1.37850e11			1.05659			0.528297	−	0.849059i	$-0.322831\pi$
$601$	1.37850e11			1.05659			0.528297	+	0.849059i	$0.322831\pi$
$602$	−1.77515e11	+	1.69633e11i	−1.35161	+	1.29159i
$603$			6.94830e9i			0.0525545i
$604$	1.97969e11	+	8.99487e9i	1.48747	+	0.0675845i
$605$	4.86048e10			0.362792
$606$	2.89930e10	+	3.03403e10i	0.214983	+	0.224972i
$607$			4.21916e10i			0.310793i	0.987852	+	0.155396i	$0.0496655\pi$
$607$			4.21916e10i			0.310793i	−0.987852	+	0.155396i	$0.950335\pi$
$608$	−4.93078e9	−	6.19967e9i	−0.0360829	−	0.0453685i
$609$	7.50928e10			0.545920
$610$	3.16638e10	−	3.02578e10i	0.228689	−	0.218534i
$611$			5.76211e10i			0.413444i
$612$	8.27401e9	−	1.82104e11i	0.0589808	−	1.29811i
$613$	−1.76436e11			−1.24953			−0.624763	−	0.780815i	$-0.714804\pi$
$613$	−1.76436e11			−1.24953			−0.624763	+	0.780815i	$0.714804\pi$
$614$	−3.71813e10	−	3.89091e10i	−0.261608	−	0.273765i
$615$		−	7.40410e9i		−	0.0517573i
$616$	5.69588e10	+	6.52982e10i	0.395583	+	0.453501i
$617$	3.80722e10			0.262705			0.131352	−	0.991336i	$-0.458068\pi$
$617$	3.80722e10			0.262705			0.131352	+	0.991336i	$0.458068\pi$
$618$	−6.18661e10	+	5.91190e10i	−0.424130	+	0.405297i
$619$		−	4.67363e10i		−	0.318340i	−0.987251	−	0.159170i	$-0.949118\pi$
$619$		−	4.67363e10i		−	0.318340i	0.987251	−	0.159170i	$-0.0508818\pi$
$620$	9.97504e10	+	4.53223e9i	0.675069	+	0.0306722i
$621$	−1.37036e11			−0.921441
$622$	−1.36244e11	−	1.42575e11i	−0.910240	−	0.952537i
$623$		−	1.85683e11i		−	1.23259i
$624$	−4.98317e9	+	5.47243e10i	−0.0328675	+	0.360946i
$625$	6.10352e9			0.0400000
$626$	3.21565e10	−	3.07286e10i	0.209398	−	0.200099i
$627$			1.30919e9i			0.00847096i
$628$	3.68948e9	−	8.12021e10i	0.0237206	−	0.522070i
$629$	−4.72440e10			−0.301817
$630$	−5.97879e10	−	6.25661e10i	−0.379535	−	0.397171i
$631$			1.82629e11i			1.15200i	0.817450	+	0.576000i	$0.195387\pi$
$631$			1.82629e11i			1.15200i	−0.817450	+	0.576000i	$0.804613\pi$
$632$	−3.79276e9	+	3.30838e9i	−0.0237732	+	0.0207370i
$633$	−6.05834e10			−0.377345
$634$	−6.24857e9	+	5.97110e9i	−0.0386744	+	0.0369571i
$635$		−	1.24656e11i		−	0.766686i
$636$	−5.58724e10	−	2.53861e9i	−0.341483	−	0.0155155i
$637$	1.62956e11			0.989721
$638$	−5.82811e10	−	6.09893e10i	−0.351759	−	0.368104i
$639$			2.10833e11i			1.26455i
$640$	4.39900e10	+	6.07814e10i	0.262201	+	0.362285i
$641$	1.05531e11			0.625100			0.312550	−	0.949901i	$-0.398817\pi$
$641$	1.05531e11			0.625100			0.312550	+	0.949901i	$0.398817\pi$
$642$	5.18202e10	−	4.95192e10i	0.305042	−	0.291497i
$643$			1.09834e11i			0.642528i	0.946990	+	0.321264i	$0.104108\pi$
$643$			1.09834e11i			0.642528i	−0.946990	+	0.321264i	$0.895892\pi$
$644$	1.57006e10	−	3.45556e11i	0.0912793	−	2.00898i
$645$	3.51383e10			0.203022
$646$	1.02191e10	+	1.06940e10i	0.0586791	+	0.0614057i
$647$			4.48807e9i			0.0256119i	0.999918	+	0.0128060i	$0.00407638\pi$
$647$			4.48807e9i			0.0256119i	−0.999918	+	0.0128060i	$0.995924\pi$
$648$	−7.80520e10	−	8.94797e10i	−0.442674	−	0.507487i
$649$	3.93290e10			0.221684
$650$	−2.78142e10	+	2.65791e10i	−0.155816	+	0.148897i
$651$			1.26432e11i			0.703934i
$652$	5.16599e9	+	2.34720e8i	0.0285866	+	0.00129885i
$653$	2.96586e11			1.63117			0.815583	−	0.578640i	$-0.196416\pi$
$653$	2.96586e11			1.63117			0.815583	+	0.578640i	$0.196416\pi$
$654$	−5.47126e10	−	5.72550e10i	−0.299072	−	0.312970i
$655$		−	3.67708e10i		−	0.199773i
$656$	6.34604e10	+	5.77867e9i	0.342679	+	0.0312042i
$657$	1.95248e11			1.04791
$658$	−7.20212e10	+	6.88232e10i	−0.384199	+	0.367139i
$659$		−	8.22505e10i		−	0.436111i	−0.975936	−	0.218056i	$-0.930029\pi$
$659$		−	8.22505e10i		−	0.436111i	0.975936	−	0.218056i	$-0.0699714\pi$
$660$	5.62841e8	−	1.23876e10i	0.00296627	−	0.0652849i
$661$	−1.54172e11			−0.807608			−0.403804	−	0.914845i	$-0.632312\pi$
$661$	−1.54172e11			−0.807608			−0.403804	+	0.914845i	$0.632312\pi$
$662$	1.33881e11	+	1.40102e11i	0.697085	+	0.729476i
$663$		−	1.02609e11i		−	0.531047i
$664$	−2.15119e11	+	1.87646e11i	−1.10664	+	0.965309i
$665$	7.02205e9			0.0359068
$666$	−2.59855e10	+	2.48316e10i	−0.132079	+	0.126214i
$667$			3.36766e11i			1.70147i
$668$	1.44681e10	+	6.57368e8i	0.0726616	+	0.00330144i
$669$	4.79726e10			0.239491
$670$	3.68943e9	+	3.86086e9i	0.0183088	+	0.0191596i
$671$		−	6.22966e10i		−	0.307308i
$672$	−7.43524e10	+	5.91347e10i	−0.364601	+	0.289978i
$673$	2.82157e11			1.37541			0.687703	−	0.725992i	$-0.258619\pi$
$673$	2.82157e11			1.37541			0.687703	+	0.725992i	$0.258619\pi$
$674$	−1.09755e11	+	1.04881e11i	−0.531844	+	0.508228i
$675$			2.63491e10i			0.126926i
$676$	1.52818e9	−	3.36340e10i	0.00731794	−	0.161061i
$677$	−2.70699e11			−1.28864			−0.644320	−	0.764756i	$-0.722860\pi$
$677$	−2.70699e11			−1.28864			−0.644320	+	0.764756i	$0.722860\pi$
$678$	−3.93386e10	−	4.11666e10i	−0.186166	−	0.194817i
$679$			1.98730e11i			0.934943i
$680$	−9.20963e10	−	1.05580e11i	−0.430731	−	0.493795i
$681$	−5.05220e10			−0.234905
$682$	1.02686e11	−	9.81263e10i	0.474650	−	0.453574i
$683$		−	3.96155e10i		−	0.182046i	−0.995849	−	0.0910232i	$-0.970986\pi$
$683$		−	3.96155e10i		−	0.182046i	0.995849	−	0.0910232i	$-0.0290137\pi$
$684$	1.12416e10	+	5.10769e8i	0.0513574	+	0.00233346i
$685$	−9.12304e10			−0.414359
$686$	−1.72825e10	−	1.80856e10i	−0.0780389	−	0.0816651i
$687$		−	3.08088e10i		−	0.138308i
$688$	−2.74244e10	+	3.01170e11i	−0.122400	+	1.34418i
$689$	2.46818e11			1.09521
$690$	−3.57898e10	+	3.42006e10i	−0.157893	+	0.150882i
$691$			1.26869e11i			0.556472i	0.960513	+	0.278236i	$0.0897497\pi$
$691$			1.26869e11i			0.556472i	−0.960513	+	0.278236i	$0.910250\pi$
$692$	−1.27565e10	+	2.80760e11i	−0.0556299	+	1.22436i
$693$	−1.23095e11			−0.533712
$694$	9.95998e10	+	1.04228e11i	0.429359	+	0.449310i
$695$			1.81381e11i			0.777413i
$696$	6.96988e10	−	6.07974e10i	0.297022	−	0.259088i
$697$	−1.18990e11			−0.504171
$698$	2.51490e11	−	2.40323e11i	1.05950	−	1.01245i
$699$			6.12800e10i			0.256691i
$700$	−6.64430e10	−	3.01889e9i	−0.276731	−	0.0125735i
$701$	−6.26836e10			−0.259587			−0.129793	−	0.991541i	$-0.541431\pi$
$701$	−6.26836e10			−0.259587			−0.129793	+	0.991541i	$0.541431\pi$
$702$	−1.14743e11	−	1.20075e11i	−0.472473	−	0.494427i
$703$		−	2.91646e9i		−	0.0119408i
$704$	1.05735e11	+	1.44923e10i	0.430455	+	0.0589991i
$705$	1.42563e10			0.0577098
$706$	−6.47808e10	+	6.19042e10i	−0.260752	+	0.249173i
$707$		−	3.20170e11i		−	1.28146i
$708$	−1.95715e9	+	4.30752e10i	−0.00778918	+	0.171433i
$709$	−3.57762e11			−1.41582			−0.707912	−	0.706300i	$-0.750363\pi$
$709$	−3.57762e11			−1.41582			−0.707912	+	0.706300i	$0.750363\pi$
$710$	1.11949e11	+	1.17151e11i	0.440541	+	0.461011i
$711$		−	7.14981e9i		−	0.0279780i
$712$	−1.50334e11	−	1.72345e11i	−0.584977	−	0.670624i
$713$	−5.67004e11			−2.19396
$714$	1.28252e11	−	1.22558e11i	0.493484	−	0.471571i
$715$			5.47226e10i			0.209384i
$716$	−1.64897e11	−	7.49222e9i	−0.627423	−	0.0285074i
$717$	−7.55280e10			−0.285780
$718$	1.45043e11	+	1.51783e11i	0.545756	+	0.571116i
$719$		−	1.70342e11i		−	0.637392i	−0.947857	−	0.318696i	$-0.896755\pi$
$719$		−	1.70342e11i		−	0.637392i	0.947857	−	0.318696i	$-0.103245\pi$
$720$	−1.06149e11	−	9.66585e9i	−0.394989	−	0.0359675i
$721$	6.52852e11			2.41587
$722$	1.95799e11	−	1.87105e11i	0.720547	−	0.688552i
$723$		−	4.37298e9i		−	0.0160038i
$724$	−7.88990e9	+	1.73650e11i	−0.0287155	+	0.632003i
$725$	6.47530e10			0.234373
$726$	5.23678e10	+	5.48011e10i	0.188503	+	0.197262i
$727$		−	6.56094e10i		−	0.234870i	−0.993081	−	0.117435i	$-0.962533\pi$
$727$		−	6.56094e10i		−	0.234870i	0.993081	−	0.117435i	$-0.0374672\pi$
$728$	3.15932e11	−	2.75583e11i	1.12478	−	0.981132i
$729$	1.08395e11			0.383796
$730$	1.08491e11	−	1.03673e11i	0.382034	−	0.365070i
$731$		−	5.64700e11i		−	1.97765i
$732$	6.82305e10	+	3.10010e9i	0.237648	+	0.0107977i
$733$	2.60967e11			0.904003			0.452001	−	0.892017i	$-0.350710\pi$
$733$	2.60967e11			0.904003			0.452001	+	0.892017i	$0.350710\pi$
$734$	1.09366e11	+	1.14448e11i	0.376788	+	0.394296i
$735$		−	4.03176e10i		−	0.138148i
$736$	−2.65200e11	−	3.33446e11i	−0.903778	−	1.13636i
$737$	7.59601e9			0.0257463
$738$	−6.54475e10	+	6.25414e10i	−0.220632	+	0.210835i
$739$		−	4.19763e11i		−	1.40743i	−0.710483	−	0.703715i	$-0.751523\pi$
$739$		−	4.19763e11i		−	1.40743i	0.710483	−	0.703715i	$-0.248477\pi$
$740$	−1.25383e9	+	2.75957e10i	−0.00418130	+	0.0920267i
$741$	6.33425e9			0.0210098
$742$	2.94801e11	+	3.08500e11i	0.972554	+	1.01775i
$743$		−	1.42604e11i		−	0.467925i	−0.972246	−	0.233962i	$-0.924831\pi$
$743$		−	1.42604e11i		−	0.467925i	0.972246	−	0.233962i	$-0.0751693\pi$
$744$	1.02363e11	+	1.17350e11i	0.334081	+	0.382994i
$745$	−2.04226e11			−0.662957
$746$	1.17406e11	−	1.12193e11i	0.379085	−	0.362252i
$747$		−	4.05525e11i		−	1.30237i
$748$	−1.99079e11	−	9.04530e9i	−0.635944	−	0.0288946i
$749$	−5.46841e11			−1.73754
$750$	6.57604e9	+	6.88162e9i	0.0207835	+	0.0217493i
$751$		−	3.26311e10i		−	0.102582i	−0.998684	−	0.0512911i	$-0.983666\pi$
$751$		−	3.26311e10i		−	0.102582i	0.998684	−	0.0512911i	$-0.0163336\pi$
$752$	−1.11266e10	+	1.22190e11i	−0.0347928	+	0.382089i
$753$	1.57380e11			0.489518
$754$	−2.95084e11	+	2.81981e11i	−0.912978	+	0.872438i
$755$			2.16371e11i			0.665905i
$756$	1.30326e10	−	2.86836e11i	0.0398974	−	0.878106i
$757$	−4.36612e11			−1.32957			−0.664787	−	0.747033i	$-0.731478\pi$
$757$	−4.36612e11			−1.32957			−0.664787	+	0.747033i	$0.731478\pi$
$758$	1.54477e11	+	1.61655e11i	0.467937	+	0.489680i
$759$			7.04142e10i			0.212174i
$760$	6.51765e9	−	5.68526e9i	0.0195361	−	0.0170410i
$761$	−1.98059e11			−0.590548			−0.295274	−	0.955413i	$-0.595411\pi$
$761$	−1.98059e11			−0.590548			−0.295274	+	0.955413i	$0.595411\pi$
$762$	1.40547e11	−	1.34307e11i	0.416872	−	0.398361i
$763$			6.04192e11i			1.78269i
$764$	−3.93164e10	−	1.78637e9i	−0.115399	−	0.00524322i
$765$	1.99031e11			0.581133
$766$	−2.56028e11	−	2.67925e11i	−0.743657	−	0.778213i
$767$		−	1.90285e11i		−	0.549824i
$768$	−2.11344e10	+	1.15085e11i	−0.0607499	+	0.330807i
$769$	−1.42097e10			−0.0406329			−0.0203165	−	0.999794i	$-0.506467\pi$
$769$	−1.42097e10			−0.0406329			−0.0203165	+	0.999794i	$0.506467\pi$
$770$	−6.83984e10	+	6.53612e10i	−0.194573	+	0.185933i
$771$			1.24705e11i			0.352912i
$772$	1.12450e9	−	2.47491e10i	0.00316584	−	0.0696772i
$773$	6.62483e10			0.185548			0.0927741	−	0.995687i	$-0.470427\pi$
$773$	6.62483e10			0.185548			0.0927741	+	0.995687i	$0.470427\pi$
$774$	−2.96808e11	−	3.10600e11i	−0.827013	−	0.865442i
$775$			1.09023e11i			0.302211i
$776$	1.60898e11	+	1.84456e11i	0.443715	+	0.508680i
$777$	−3.49770e10			−0.0959617
$778$	−1.30919e11	+	1.25106e11i	−0.357343	+	0.341476i
$779$		−	7.34544e9i		−	0.0199466i
$780$	−5.99350e10	−	2.72319e9i	−0.161921	−	0.00735699i
$781$	2.30487e11			0.619501
$782$	5.49630e11	+	5.75170e11i	1.46975	+	1.53804i
$783$			2.79540e11i			0.743700i
$784$	3.45562e11	+	3.14667e10i	0.914663	+	0.0832887i
$785$	8.87504e10			0.233718
$786$	4.14584e10	−	3.96175e10i	0.108623	−	0.103800i
$787$		−	7.13437e10i		−	0.185976i	−0.995667	−	0.0929880i	$-0.970358\pi$
$787$		−	7.13437e10i		−	0.185976i	0.995667	−	0.0929880i	$-0.0296418\pi$
$788$	−3.30886e10	+	7.28250e11i	−0.0858170	+	1.88876i
$789$	−1.32387e10			−0.0341615
$790$	−3.79642e9	−	3.97283e9i	−0.00974689	−	0.0101998i
$791$			4.34417e11i			1.10969i
$792$	−1.14253e11	+	9.96614e10i	−0.290380	+	0.253295i
$793$	−3.01409e11			−0.762191
$794$	1.17170e11	−	1.11967e11i	0.294804	−	0.281714i
$795$		−	6.10661e10i		−	0.152873i
$796$	−2.22811e11	−	1.01236e10i	−0.554990	−	0.0252164i
$797$	1.11980e11			0.277527			0.138764	−	0.990326i	$-0.455687\pi$
$797$	1.11980e11			0.277527			0.138764	+	0.990326i	$0.455687\pi$
$798$	7.56569e9	+	7.91725e9i	0.0186568	+	0.0195237i
$799$		−	2.29109e11i		−	0.562154i
$800$	−6.41146e10	+	5.09922e10i	−0.156530	+	0.124493i
$801$	3.24891e11			0.789237
$802$	1.76127e11	−	1.68306e11i	0.425725	−	0.406821i
$803$		−	2.13449e11i		−	0.513372i
$804$	−3.78004e8	+	8.31954e9i	−0.000904634	+	0.0199102i
$805$	3.77677e11			0.899368
$806$	−4.74764e11	−	4.96825e11i	−1.12496	−	1.17724i
$807$		−	4.05195e10i		−	0.0955365i
$808$	−2.59220e11	−	2.97172e11i	−0.608167	−	0.697209i
$809$	5.57023e10			0.130041			0.0650203	−	0.997884i	$-0.479289\pi$
$809$	5.57023e10			0.130041			0.0650203	+	0.997884i	$0.479289\pi$
$810$	9.37280e10	−	8.95661e10i	0.217735	−	0.208067i
$811$			7.06448e11i			1.63304i	0.577317	+	0.816520i	$0.304100\pi$
$811$			7.06448e11i			1.63304i	−0.577317	+	0.816520i	$0.695900\pi$
$812$	−7.04902e11	−	3.20278e10i	−1.62145	−	0.0736720i
$813$	1.85091e11			0.423666
$814$	2.71464e10	+	2.84078e10i	0.0618321	+	0.0647053i
$815$			5.64620e9i			0.0127975i
$816$	1.98137e10	−	2.17591e11i	0.0446896	−	0.490773i
$817$	3.48599e10			0.0782417
$818$	−5.97446e11	+	5.70917e11i	−1.33440	+	1.27515i
$819$			5.95569e11i			1.32372i
$820$	−3.15792e9	+	6.95029e10i	−0.00698466	+	0.153726i
$821$	−8.39733e10			−0.184828			−0.0924142	−	0.995721i	$-0.529458\pi$
$821$	−8.39733e10			−0.184828			−0.0924142	+	0.995721i	$0.529458\pi$
$822$	−9.82933e10	−	1.02861e11i	−0.215296	−	0.225301i
$823$			1.90143e11i			0.414459i	0.978292	+	0.207229i	$0.0664446\pi$
$823$			1.90143e11i			0.414459i	−0.978292	+	0.207229i	$0.933555\pi$
$824$	6.05957e11	−	5.28569e11i	1.31442	−	1.14655i
$825$	1.35391e10			0.0292264
$826$	2.37840e11	−	2.27279e11i	0.510933	−	0.488246i
$827$			3.98982e11i			0.852965i	0.904496	+	0.426483i	$0.140247\pi$
$827$			3.98982e11i			0.852965i	−0.904496	+	0.426483i	$0.859753\pi$
$828$	6.04622e11	+	2.74715e10i	1.28636	+	0.0584468i
$829$	9.18641e11			1.94504			0.972518	−	0.232827i	$-0.0747977\pi$
$829$	9.18641e11			1.94504			0.972518	+	0.232827i	$0.0747977\pi$
$830$	−2.15327e11	−	2.25332e11i	−0.453718	−	0.474801i
$831$			4.21536e10i			0.0883957i
$832$	7.01178e10	−	5.11576e11i	0.146331	−	1.06762i
$833$	−6.47936e11			−1.34571
$834$	−2.04504e11	+	1.95423e11i	−0.422705	+	0.403935i
$835$			1.58130e10i			0.0325288i
$836$	5.58382e8	−	1.22895e10i	0.00114316	−	0.0251599i
$837$	−4.70655e11			−0.958960
$838$	−3.21427e11	−	3.36363e11i	−0.651789	−	0.682075i
$839$		−	4.31925e11i		−	0.871688i	−0.900022	−	0.435844i	$-0.856450\pi$
$839$		−	4.31925e11i		−	0.871688i	0.900022	−	0.435844i	$-0.143550\pi$
$840$	−6.81832e10	−	7.81660e10i	−0.136949	−	0.157000i
$841$	1.86726e11			0.373268
$842$	−2.34400e10	+	2.23991e10i	−0.0466347	+	0.0445639i
$843$		−	2.54205e11i		−	0.503355i
$844$	5.68701e11	+	2.58394e10i	1.12076	+	0.0509228i
$845$	3.67605e10			0.0721031
$846$	−1.20421e11	−	1.26016e11i	−0.235082	−	0.246006i
$847$		−	5.78298e11i		−	1.12362i
$848$	5.23396e11	+	4.76602e10i	1.01216	+	0.0921664i
$849$	−2.02643e11			−0.390033
$850$	1.10593e11	−	1.05682e11i	0.211861	−	0.202454i
$851$		−	1.56860e11i		−	0.299085i
$852$	−1.14698e10	+	2.52441e11i	−0.0217670	+	0.479073i
$853$	9.29871e11			1.75641			0.878206	−	0.478282i	$-0.158740\pi$
$853$	9.29871e11			1.75641			0.878206	+	0.478282i	$0.158740\pi$
$854$	−3.60006e11	−	3.76735e11i	−0.676828	−	0.708279i
$855$			1.22866e10i			0.0229914i
$856$	−5.07561e11	+	4.42739e11i	−0.945351	+	0.824618i
$857$	1.19713e11			0.221931			0.110965	−	0.993824i	$-0.464606\pi$
$857$	1.19713e11			0.221931			0.110965	+	0.993824i	$0.464606\pi$
$858$	−6.16989e10	+	5.89592e10i	−0.113849	+	0.108793i
$859$		−	4.22514e11i		−	0.776012i	−0.921657	−	0.388006i	$-0.873164\pi$
$859$		−	4.22514e11i		−	0.776012i	0.921657	−	0.388006i	$-0.126836\pi$
$860$	−3.29847e11	−	1.49868e10i	−0.603001	−	0.0273978i
$861$	−8.80936e10			−0.160299
$862$	2.55555e11	+	2.67430e11i	0.462865	+	0.484374i
$863$			2.84698e11i			0.513264i	0.966509	+	0.256632i	$0.0826129\pi$
$863$			2.84698e11i			0.513264i	−0.966509	+	0.256632i	$0.917387\pi$
$864$	−2.20135e11	−	2.76784e11i	−0.395034	−	0.496691i
$865$	−3.06858e11			−0.548117
$866$	−5.97024e11	+	5.70514e11i	−1.06150	+	1.01437i
$867$			2.17945e11i			0.385719i
$868$	5.39243e10	−	1.18683e12i	0.0949961	−	2.09078i
$869$	−7.81630e9			−0.0137064
$870$	6.97661e10	+	7.30079e10i	0.121778	+	0.127436i
$871$		−	3.67517e10i		−	0.0638565i
$872$	4.89172e11	+	5.60793e11i	0.846049	+	0.969921i
$873$	−3.47721e11			−0.598651
$874$	−3.55062e10	+	3.39296e10i	−0.0608497	+	0.0581478i
$875$		−	7.26193e10i		−	0.123885i
$876$	2.33780e11	+	1.06220e10i	0.397001	+	0.0180380i
$877$	1.94476e11			0.328752			0.164376	−	0.986398i	$-0.447439\pi$
$877$	1.94476e11			0.328752			0.164376	+	0.986398i	$0.447439\pi$
$878$	−4.50907e11	−	4.71859e11i	−0.758767	−	0.794025i
$879$		−	4.33753e10i		−	0.0726585i
$880$	−1.05669e10	+	1.16044e11i	−0.0176204	+	0.193504i
$881$	9.06691e11			1.50507			0.752533	−	0.658555i	$-0.228832\pi$
$881$	9.06691e11			1.50507			0.752533	+	0.658555i	$0.228832\pi$
$882$	−3.56382e11	+	3.40557e11i	−0.588900	+	0.562750i
$883$		−	2.26542e11i		−	0.372654i	−0.982488	−	0.186327i	$-0.940342\pi$
$883$		−	2.26542e11i		−	0.372654i	0.982488	−	0.186327i	$-0.0596584\pi$
$884$	−4.37638e10	+	9.63202e11i	−0.0716648	+	1.57728i
$885$	−4.70793e10			−0.0767462
$886$	1.96973e10	+	2.06125e10i	0.0319647	+	0.0334500i
$887$		−	1.70744e11i		−	0.275837i	−0.990444	−	0.137918i	$-0.955959\pi$
$887$		−	1.70744e11i		−	0.275837i	0.990444	−	0.137918i	$-0.0440412\pi$
$888$	−3.24646e10	+	2.83184e10i	−0.0522105	+	0.0455425i
$889$	−1.48315e12			−2.37453
$890$	1.80528e11	−	1.72511e11i	0.287729	−	0.274953i
$891$		−	1.84404e11i		−	0.292590i
$892$	−4.50323e11	−	2.04608e10i	−0.711320	−	0.0323193i
$893$	1.41433e10			0.0222405
$894$	−2.20037e11	−	2.30261e11i	−0.344465	−	0.360471i
$895$		−	1.80225e11i		−	0.280882i
$896$	7.23174e11	−	5.23391e11i	1.12205	−	0.812071i
$897$	3.40684e11			0.526238
$898$	6.64919e11	−	6.35394e11i	1.02250	−	0.977097i
$899$			1.15664e12i			1.77075i
$900$	5.28218e9	−	1.16256e11i	0.00805087	−	0.177192i
$901$	−9.81380e11			−1.48915
$902$	6.83713e10	+	7.15484e10i	0.103288	+	0.108087i
$903$		−	4.18074e11i		−	0.628785i
$904$	3.51717e11	+	4.03213e11i	0.526647	+	0.603755i
$905$	−1.89791e11			−0.282932
$906$	−2.43955e11	+	2.33123e11i	−0.362074	+	0.345997i
$907$		−	5.20431e11i		−	0.769013i	−0.923122	−	0.384507i	$-0.874372\pi$
$907$		−	5.20431e11i		−	0.769013i	0.923122	−	0.384507i	$-0.125628\pi$
$908$	4.74254e11	+	2.15481e10i	0.697698	+	0.0317004i
$909$	5.60205e11			0.820525
$910$	3.16237e11	+	3.30932e11i	0.461155	+	0.482584i
$911$			5.42499e11i			0.787635i	0.919189	+	0.393818i	$0.128846\pi$
$911$			5.42499e11i			0.787635i	−0.919189	+	0.393818i	$0.871154\pi$
$912$	1.34323e10	+	1.22314e9i	0.0194165	+	0.00176806i
$913$	−4.43327e11			−0.638030
$914$	−5.21650e11	+	4.98487e11i	−0.747472	+	0.714281i
$915$			7.45729e10i			0.106389i
$916$	−1.31403e10	+	2.89205e11i	−0.0186647	+	0.410794i
$917$	−4.37497e11			−0.618725
$918$	4.56233e11	+	4.77433e11i	0.642415	+	0.672266i
$919$		−	6.49225e11i		−	0.910192i	−0.890442	−	0.455096i	$-0.849605\pi$
$919$		−	6.49225e11i		−	0.910192i	0.890442	−	0.455096i	$-0.150395\pi$
$920$	3.50549e11	−	3.05779e11i	0.489325	−	0.426831i
$921$	9.16364e10			0.127359
$922$	8.94283e11	−	8.54573e11i	1.23752	−	1.18257i
$923$		−	1.11516e12i		−	1.53650i
$924$	−1.47387e11	−	6.69666e9i	−0.202196	−	0.00918693i
$925$	−3.01609e10			−0.0411981
$926$	9.42742e11	+	9.86549e11i	1.28218	+	1.34176i
$927$			1.14230e12i			1.54690i
$928$	−6.80200e11	+	5.40983e11i	−0.917159	+	0.729444i
$929$	4.98636e11			0.669455			0.334727	−	0.942315i	$-0.391356\pi$
$929$	4.98636e11			0.669455			0.334727	+	0.942315i	$0.391356\pi$
$930$	−1.22922e11	+	1.17463e11i	−0.164322	+	0.157026i
$931$		−	3.99982e10i		−	0.0532404i
$932$	2.61365e10	−	5.75240e11i	0.0346404	−	0.762405i
$933$	3.35785e11			0.443133
$934$	3.54529e11	+	3.71003e11i	0.465870	+	0.487518i
$935$		−	2.17585e11i		−	0.284696i
$936$	4.82191e11	+	5.52789e11i	0.628226	+	0.720205i
$937$	4.01408e11			0.520748			0.260374	−	0.965508i	$-0.416154\pi$
$937$	4.01408e11			0.520748			0.260374	+	0.965508i	$0.416154\pi$
$938$	4.59364e10	−	4.38966e10i	0.0593397	−	0.0567048i
$939$			7.57332e10i			0.0974146i
$940$	−1.33825e11	−	6.08043e9i	−0.171406	−	0.00778794i
$941$	−2.64682e10			−0.0337572			−0.0168786	−	0.999858i	$-0.505373\pi$
$941$	−2.64682e10			−0.0337572			−0.0168786	+	0.999858i	$0.505373\pi$
$942$	9.56214e10	+	1.00065e11i	0.121437	+	0.127080i
$943$		−	3.95071e11i		−	0.499606i
$944$	3.67439e10	−	4.03515e11i	0.0462698	−	0.508127i
$945$	3.13500e11			0.393106
$946$	−3.39554e11	+	3.24476e11i	−0.423979	+	0.405152i
$947$			5.71352e11i			0.710401i	0.934790	+	0.355201i	$0.115587\pi$
$947$			5.71352e11i			0.710401i	−0.934790	+	0.355201i	$0.884413\pi$
$948$	3.88967e8	−	8.56081e9i	0.000481592	−	0.0105994i
$949$	−1.03273e12			−1.27327
$950$	6.52394e9	+	6.82709e9i	0.00800969	+	0.00838188i
$951$		−	1.47163e10i		−	0.0179918i
$952$	−1.25619e12	+	1.09576e12i	−1.52935	+	1.33403i
$953$	−1.09917e12			−1.33258			−0.666288	−	0.745694i	$-0.732118\pi$
$953$	−1.09917e12			−1.33258			−0.666288	+	0.745694i	$0.732118\pi$
$954$	−5.39785e11	+	5.15817e11i	−0.651670	+	0.622733i
$955$		−	4.29711e10i		−	0.0516611i
$956$	7.08988e11	+	3.22134e10i	0.848803	+	0.0385660i
$957$	1.43639e11			0.171247
$958$	−3.96719e11	−	4.15153e11i	−0.471000	−	0.492886i
$959$			1.08545e12i			1.28333i
$960$	−1.26571e11	−	1.73481e10i	−0.149022	−	0.0204253i
$961$	−1.09451e12			−1.28329
$962$	1.37445e11	−	1.31342e11i	0.160483	−	0.153357i
$963$		−	9.56813e11i		−	1.11256i
$964$	−1.86512e9	+	4.10495e10i	−0.00215972	+	0.0475335i
$965$	2.70497e10			0.0311928
$966$	4.06917e11	+	4.25825e11i	0.467301	+	0.489016i
$967$			8.78566e11i			1.00477i	0.864643	+	0.502387i	$0.167545\pi$
$967$			8.78566e11i			1.00477i	−0.864643	+	0.502387i	$0.832455\pi$
$968$	−4.68207e11	−	5.36758e11i	−0.533257	−	0.611332i
$969$	−2.51858e10			−0.0285668
$970$	−1.93213e11	+	1.84633e11i	−0.218247	+	0.208556i
$971$		−	7.91945e11i		−	0.890878i	−0.895312	−	0.445439i	$-0.853048\pi$
$971$		−	7.91945e11i		−	0.890878i	0.895312	−	0.445439i	$-0.146952\pi$
$972$	7.67865e11	+	3.48885e10i	0.860241	+	0.0390857i
$973$	2.15806e12			2.40775
$974$	−6.61654e11	−	6.92399e11i	−0.735182	−	0.769344i
$975$		−	6.55064e10i		−	0.0724878i
$976$	−6.39163e11	−	5.82018e10i	−0.704389	−	0.0641413i
$977$	−5.46919e11			−0.600268			−0.300134	−	0.953897i	$-0.597031\pi$
$977$	−5.46919e11			−0.600268			−0.300134	+	0.953897i	$0.597031\pi$
$978$	−6.36600e9	+	6.08332e9i	−0.00695843	+	0.00664944i
$979$		−	3.55177e11i		−	0.386646i
$980$	−1.71958e10	+	3.78465e11i	−0.0186431	+	0.410319i
$981$	−1.05716e12			−1.14147
$982$	−3.31923e11	−	3.47346e11i	−0.356936	−	0.373522i
$983$			7.38083e11i			0.790481i	0.918578	+	0.395240i	$0.129339\pi$
$983$			7.38083e11i			0.790481i	−0.918578	+	0.395240i	$0.870661\pi$
$984$	−8.17658e10	+	7.13233e10i	−0.0872151	+	0.0760766i
$985$	−7.95946e11			−0.845549
$986$	1.17329e12	−	1.12119e12i	1.24136	−	1.18624i
$987$		−	1.69620e11i		−	0.178735i
$988$	−5.94601e10	−	2.70162e9i	−0.0624020	−	0.00283528i
$989$	1.87492e12			1.95974
$990$	−1.14363e11	−	1.19677e11i	−0.119054	−	0.124587i
$991$		−	3.73877e11i		−	0.387645i	−0.981037	−	0.193823i	$-0.937911\pi$
$991$		−	3.73877e11i		−	0.387645i	0.981037	−	0.193823i	$-0.0620886\pi$
$992$	−9.10839e11	−	1.14523e12i	−0.940578	−	1.18263i
$993$	−3.29959e11			−0.339362
$994$	1.39385e12	−	1.33196e12i	1.42781	−	1.36441i
$995$		−	2.43523e11i		−	0.248455i
$996$	2.20615e10	−	4.85555e11i	0.0224181	−	0.493402i
$997$	1.14224e12			1.15605			0.578025	−	0.816019i	$-0.303823\pi$
$997$	1.14224e12			1.15605			0.578025	+	0.816019i	$0.303823\pi$
$998$	2.57118e11	+	2.69066e11i	0.259185	+	0.271229i
$999$		−	1.30205e11i		−	0.130727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.13	✓	16
3.2	odd	2		180.9.c.a.91.4		16
4.3	odd	2	inner	20.9.b.a.11.14	yes	16
5.2	odd	4		100.9.d.c.99.24		32
5.3	odd	4		100.9.d.c.99.9		32
5.4	even	2		100.9.b.d.51.4		16
8.3	odd	2		320.9.b.d.191.10		16
8.5	even	2		320.9.b.d.191.7		16
12.11	even	2		180.9.c.a.91.3		16
20.3	even	4		100.9.d.c.99.23		32
20.7	even	4		100.9.d.c.99.10		32
20.19	odd	2		100.9.b.d.51.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.13	✓	16	1.1	even	1	trivial
20.9.b.a.11.14	yes	16	4.3	odd	2	inner
100.9.b.d.51.3		16	20.19	odd	2
100.9.b.d.51.4		16	5.4	even	2
100.9.d.c.99.9		32	5.3	odd	4
100.9.d.c.99.10		32	20.7	even	4
100.9.d.c.99.23		32	20.3	even	4
100.9.d.c.99.24		32	5.2	odd	4
180.9.c.a.91.3		16	12.11	even	2
180.9.c.a.91.4		16	3.2	odd	2
320.9.b.d.191.7		16	8.5	even	2
320.9.b.d.191.10		16	8.3	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(11.5676 - 11.0540i) q^{2} +27.2434i q^{3} +(11.6196 - 255.736i) q^{4} +279.508 q^{5} +(301.148 + 315.141i) q^{6} -3325.58i q^{7} +(-2692.49 - 3086.70i) q^{8} +5818.80 q^{9} +O(q^{10})\)	\(q+(11.5676 - 11.0540i) q^{2} +27.2434i q^{3} +(11.6196 - 255.736i) q^{4} +279.508 q^{5} +(301.148 + 315.141i) q^{6} -3325.58i q^{7} +(-2692.49 - 3086.70i) q^{8} +5818.80 q^{9} +(3233.25 - 3089.68i) q^{10} -6361.21i q^{11} +(6967.12 + 316.557i) q^{12} -30777.4 q^{13} +(-36760.8 - 38469.0i) q^{14} +7614.76i q^{15} +(-65266.0 - 5943.09i) q^{16} +122375. q^{17} +(67309.6 - 64320.8i) q^{18} +7554.43i q^{19} +(3247.77 - 71480.4i) q^{20} +90600.1 q^{21} +(-70316.6 - 73584.1i) q^{22} +406311. i q^{23} +(84092.2 - 73352.6i) q^{24} +78125.0 q^{25} +(-356021. + 340213. i) q^{26} +337268. i q^{27} +(-850471. - 38641.8i) q^{28} +828838. q^{29} +(84173.4 + 88084.7i) q^{30} +1.39549e6i q^{31} +(-820666. + 652701. i) q^{32} +173301. q^{33} +(1.41559e6 - 1.35273e6i) q^{34} -929527. i q^{35} +(67611.9 - 1.48808e6i) q^{36} -386059. q^{37} +(83506.4 + 87386.8i) q^{38} -838482. i q^{39} +(-752574. - 862759. i) q^{40} -972335. q^{41} +(1.04803e6 - 1.00149e6i) q^{42} -4.61450e6i q^{43} +(-1.62679e6 - 73914.5i) q^{44} +1.62640e6 q^{45} +(4.49135e6 + 4.70005e6i) q^{46} -1.87219e6i q^{47} +(161910. - 1.77807e6i) q^{48} -5.29467e6 q^{49} +(903720. - 863591. i) q^{50} +3.33392e6i q^{51} +(-357620. + 7.87090e6i) q^{52} -8.01944e6 q^{53} +(3.72815e6 + 3.90139e6i) q^{54} -1.77801e6i q^{55} +(-1.02651e7 + 8.95408e6i) q^{56} -205808. q^{57} +(9.58768e6 - 9.16195e6i) q^{58} +6.18263e6i q^{59} +(1.94737e6 + 88480.2i) q^{60} +9.79320e6 q^{61} +(1.54257e7 + 1.61425e7i) q^{62} -1.93509e7i q^{63} +(-2.27822e6 + 1.66218e7i) q^{64} -8.60255e6 q^{65} +(2.00468e6 - 1.91566e6i) q^{66} +1.19411e6i q^{67} +(1.42195e6 - 3.12958e7i) q^{68} -1.10693e7 q^{69} +(-1.02750e7 - 1.07524e7i) q^{70} +3.62332e7i q^{71} +(-1.56670e7 - 1.79609e7i) q^{72} +3.35548e7 q^{73} +(-4.46578e6 + 4.26748e6i) q^{74} +2.12839e6i q^{75} +(1.93194e6 + 87779.2i) q^{76} -2.11547e7 q^{77} +(-9.26855e6 - 9.69923e6i) q^{78} -1.22874e6i q^{79} +(-1.82424e7 - 1.66114e6i) q^{80} +2.89888e7 q^{81} +(-1.12476e7 + 1.07482e7i) q^{82} -6.96923e7i q^{83} +(1.05273e6 - 2.31697e7i) q^{84} +3.42049e7 q^{85} +(-5.10086e7 - 5.33788e7i) q^{86} +2.25804e7i q^{87} +(-1.96352e7 + 1.71275e7i) q^{88} +5.58347e7 q^{89} +(1.88136e7 - 1.79782e7i) q^{90} +1.02353e8i q^{91} +(1.03908e8 + 4.72116e6i) q^{92} -3.80180e7 q^{93} +(-2.06951e7 - 2.16567e7i) q^{94} +2.11153e6i q^{95} +(-1.77818e7 - 2.23578e7i) q^{96} -5.97582e7 q^{97} +(-6.12467e7 + 5.85271e7i) q^{98} -3.70146e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

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