LMFDB - Embedded newform 20.9.b.a.11.15

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			11.15
Root			$-5.64565 + 3.35245i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.5274 - 6.70489i) q^{2} -150.211i q^{3} +(166.089 - 194.809i) q^{4} +279.508 q^{5} +(-1007.15 - 2182.17i) q^{6} +2626.96i q^{7} +(1106.66 - 3943.67i) q^{8} -16002.3 q^{9} +O(q^{10})$	\(q+(14.5274 - 6.70489i) q^{2} -150.211i q^{3} +(166.089 - 194.809i) q^{4} +279.508 q^{5} +(-1007.15 - 2182.17i) q^{6} +2626.96i q^{7} +(1106.66 - 3943.67i) q^{8} -16002.3 q^{9} +(4060.52 - 1874.07i) q^{10} +2300.68i q^{11} +(-29262.4 - 24948.4i) q^{12} +47058.2 q^{13} +(17613.5 + 38162.8i) q^{14} -41985.3i q^{15} +(-10365.0 - 64711.2i) q^{16} -51967.0 q^{17} +(-232472. + 107294. i) q^{18} -59554.7i q^{19} +(46423.2 - 54450.7i) q^{20} +394598. q^{21} +(15425.8 + 33422.9i) q^{22} +77570.5i q^{23} +(-592382. - 166233. i) q^{24} +78125.0 q^{25} +(683632. - 315520. i) q^{26} +1.41819e6i q^{27} +(511754. + 436308. i) q^{28} +902211. q^{29} +(-281507. - 609935. i) q^{30} +340014. i q^{31} +(-584457. - 870587. i) q^{32} +345588. q^{33} +(-754943. + 348433. i) q^{34} +734257. i q^{35} +(-2.65781e6 + 3.11740e6i) q^{36} -584324. q^{37} +(-399308. - 865173. i) q^{38} -7.06866e6i q^{39} +(309321. - 1.10229e6i) q^{40} +293985. q^{41} +(5.73247e6 - 2.64573e6i) q^{42} -2.95292e6i q^{43} +(448194. + 382118. i) q^{44} -4.47279e6 q^{45} +(520102. + 1.12689e6i) q^{46} +5.03746e6i q^{47} +(-9.72033e6 + 1.55693e6i) q^{48} -1.13610e6 q^{49} +(1.13495e6 - 523820. i) q^{50} +7.80601e6i q^{51} +(7.81585e6 - 9.16736e6i) q^{52} -7.54985e6 q^{53} +(9.50883e6 + 2.06026e7i) q^{54} +643061. i q^{55} +(1.03598e7 + 2.90715e6i) q^{56} -8.94577e6 q^{57} +(1.31068e7 - 6.04923e6i) q^{58} +8.82594e6i q^{59} +(-8.17910e6 - 6.97328e6i) q^{60} +1.08173e7 q^{61} +(2.27976e6 + 4.93951e6i) q^{62} -4.20375e7i q^{63} +(-1.43278e7 - 8.72861e6i) q^{64} +1.31532e7 q^{65} +(5.02049e6 - 2.31713e6i) q^{66} +1.44347e7i q^{67} +(-8.63113e6 + 1.01236e7i) q^{68} +1.16519e7 q^{69} +(4.92311e6 + 1.06668e7i) q^{70} -3.71149e6i q^{71} +(-1.77092e7 + 6.31079e7i) q^{72} -3.62775e7 q^{73} +(-8.48869e6 + 3.91783e6i) q^{74} -1.17352e7i q^{75} +(-1.16018e7 - 9.89137e6i) q^{76} -6.04380e6 q^{77} +(-4.73946e7 - 1.02689e8i) q^{78} +4.88562e7i q^{79} +(-2.89710e6 - 1.80873e7i) q^{80} +1.08037e8 q^{81} +(4.27083e6 - 1.97114e6i) q^{82} +6.93862e7i q^{83} +(6.55383e7 - 7.68711e7i) q^{84} -1.45252e7 q^{85} +(-1.97990e7 - 4.28982e7i) q^{86} -1.35522e8i q^{87} +(9.07314e6 + 2.54608e6i) q^{88} -1.05906e8 q^{89} +(-6.49779e7 + 2.99896e7i) q^{90} +1.23620e8i q^{91} +(1.51114e7 + 1.28836e7i) q^{92} +5.10738e7 q^{93} +(3.37756e7 + 7.31810e7i) q^{94} -1.66460e7i q^{95} +(-1.30772e8 + 8.77919e7i) q^{96} +1.33519e8 q^{97} +(-1.65045e7 + 7.61742e6i) q^{98} -3.68163e7i 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 $

$2$	14.5274	−	6.70489i	0.907961	−	0.419056i
$2$	14.5274	−	6.70489i	0.907961	−	0.419056i
$3$		−	150.211i		−	1.85446i	−0.374496	−	0.927228i	$-0.622184\pi$
$3$		−	150.211i		−	1.85446i	0.374496	−	0.927228i	$-0.377816\pi$
$4$	166.089	−	194.809i	0.648785	−	0.760972i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$	−1007.15	−	2182.17i	−0.777121	−	1.68377i
$7$			2626.96i			1.09411i	0.837097	+	0.547055i	$0.184251\pi$
$7$			2626.96i			1.09411i	−0.837097	+	0.547055i	$0.815749\pi$
$8$	1106.66	−	3943.67i	0.270181	−	0.962810i
$9$	−16002.3			−2.43901
$10$	4060.52	−	1874.07i	0.406052	−	0.187407i
$11$			2300.68i			0.157140i	0.996909	+	0.0785699i	$0.0250354\pi$
$11$			2300.68i			0.157140i	−0.996909	+	0.0785699i	$0.974965\pi$
$12$	−29262.4	−	24948.4i	−1.41119	−	1.20314i
$13$	47058.2			1.64764			0.823820	−	0.566852i	$-0.191839\pi$
$13$	47058.2			1.64764			0.823820	+	0.566852i	$0.191839\pi$
$14$	17613.5	+	38162.8i	0.458493	+	0.993408i
$15$		−	41985.3i		−	0.829338i
$16$	−10365.0	−	64711.2i	−0.158157	−	0.987414i
$17$	−51967.0			−0.622202			−0.311101	−	0.950377i	$-0.600698\pi$
$17$	−51967.0			−0.622202			−0.311101	+	0.950377i	$0.600698\pi$
$18$	−232472.	+	107294.i	−2.21452	+	1.02208i
$19$		−	59554.7i		−	0.456985i	−0.973546	−	0.228492i	$-0.926620\pi$
$19$		−	59554.7i		−	0.456985i	0.973546	−	0.228492i	$-0.0733796\pi$
$20$	46423.2	−	54450.7i	0.290145	−	0.340317i
$21$	394598.			2.02898
$22$	15425.8	+	33422.9i	0.0658503	+	0.142677i
$23$			77570.5i			0.277195i	0.990349	+	0.138597i	$0.0442594\pi$
$23$			77570.5i			0.277195i	−0.990349	+	0.138597i	$0.955741\pi$
$24$	−592382.	−	166233.i	−1.78549	−	0.501039i
$25$	78125.0			0.200000
$26$	683632.	−	315520.i	1.49599	−	0.690453i
$27$			1.41819e6i			2.66858i
$28$	511754.	+	436308.i	0.832587	+	0.709841i
$29$	902211.			1.27561			0.637803	−	0.770200i	$-0.279844\pi$
$29$	902211.			1.27561			0.637803	+	0.770200i	$0.279844\pi$
$30$	−281507.	−	609935.i	−0.347539	−	0.753006i
$31$			340014.i			0.368171i	0.982910	+	0.184086i	$0.0589324\pi$
$31$			340014.i			0.368171i	−0.982910	+	0.184086i	$0.941068\pi$
$32$	−584457.	−	870587.i	−0.557382	−	0.830256i
$33$	345588.			0.291409
$34$	−754943.	+	348433.i	−0.564935	+	0.260737i
$35$			734257.i			0.489301i
$36$	−2.65781e6	+	3.11740e6i	−1.58239	+	1.85602i
$37$	−584324.			−0.311779			−0.155890	−	0.987774i	$-0.549824\pi$
$37$	−584324.			−0.311779			−0.155890	+	0.987774i	$0.549824\pi$
$38$	−399308.	−	865173.i	−0.191502	−	0.414924i
$39$		−	7.06866e6i		−	3.05548i
$40$	309321.	−	1.10229e6i	0.120829	−	0.430582i
$41$	293985.			0.104037			0.0520187	−	0.998646i	$-0.483434\pi$
$41$	293985.			0.104037			0.0520187	+	0.998646i	$0.483434\pi$
$42$	5.73247e6	−	2.64573e6i	1.84223	−	0.850255i
$43$		−	2.95292e6i		−	0.863731i	−0.901938	−	0.431866i	$-0.857856\pi$
$43$		−	2.95292e6i		−	0.863731i	0.901938	−	0.431866i	$-0.142144\pi$
$44$	448194.	+	382118.i	0.119579	+	0.101950i
$45$	−4.47279e6			−1.09076
$46$	520102.	+	1.12689e6i	0.116160	+	0.251682i
$47$			5.03746e6i			1.03233i	0.856488	+	0.516167i	$0.172642\pi$
$47$			5.03746e6i			1.03233i	−0.856488	+	0.516167i	$0.827358\pi$
$48$	−9.72033e6	+	1.55693e6i	−1.83112	+	0.293295i
$49$	−1.13610e6			−0.197075
$50$	1.13495e6	−	523820.i	0.181592	−	0.0838111i
$51$			7.80601e6i			1.15385i
$52$	7.81585e6	−	9.16736e6i	1.06896	−	1.25381i
$53$	−7.54985e6			−0.956830			−0.478415	−	0.878134i	$-0.658789\pi$
$53$	−7.54985e6			−0.956830			−0.478415	+	0.878134i	$0.658789\pi$
$54$	9.50883e6	+	2.06026e7i	1.11828	+	2.42297i
$55$			643061.i			0.0702751i
$56$	1.03598e7	+	2.90715e6i	1.05342	+	0.295608i
$57$	−8.94577e6			−0.847458
$58$	1.31068e7	−	6.04923e6i	1.15820	−	0.534550i
$59$			8.82594e6i			0.728372i	0.931326	+	0.364186i	$0.118653\pi$
$59$			8.82594e6i			0.728372i	−0.931326	+	0.364186i	$0.881347\pi$
$60$	−8.17910e6	−	6.97328e6i	−0.631103	−	0.538062i
$61$	1.08173e7			0.781269			0.390634	−	0.920546i	$-0.372256\pi$
$61$	1.08173e7			0.781269			0.390634	+	0.920546i	$0.372256\pi$
$62$	2.27976e6	+	4.93951e6i	0.154284	+	0.334285i
$63$		−	4.20375e7i		−	2.66854i
$64$	−1.43278e7	−	8.72861e6i	−0.854004	−	0.520266i
$65$	1.31532e7			0.736847
$66$	5.02049e6	−	2.31713e6i	0.264588	−	0.122117i
$67$			1.44347e7i			0.716324i	0.933659	+	0.358162i	$0.116596\pi$
$67$			1.44347e7i			0.716324i	−0.933659	+	0.358162i	$0.883404\pi$
$68$	−8.63113e6	+	1.01236e7i	−0.403675	+	0.473479i
$69$	1.16519e7			0.514046
$70$	4.92311e6	+	1.06668e7i	0.205044	+	0.444266i
$71$		−	3.71149e6i		−	0.146054i	−0.997330	−	0.0730272i	$-0.976734\pi$
$71$		−	3.71149e6i		−	0.146054i	0.997330	−	0.0730272i	$-0.0232660\pi$
$72$	−1.77092e7	+	6.31079e7i	−0.658975	+	2.34830i
$73$	−3.62775e7			−1.27746			−0.638728	−	0.769433i	$-0.720539\pi$
$73$	−3.62775e7			−1.27746			−0.638728	+	0.769433i	$0.720539\pi$
$74$	−8.48869e6	+	3.91783e6i	−0.283083	+	0.130653i
$75$		−	1.17352e7i		−	0.370891i
$76$	−1.16018e7	−	9.89137e6i	−0.347752	−	0.296485i
$77$	−6.04380e6			−0.171928
$78$	−4.73946e7	−	1.02689e8i	−1.28041	−	2.77425i
$79$			4.88562e7i			1.25433i	0.778887	+	0.627164i	$0.215785\pi$
$79$			4.88562e7i			1.25433i	−0.778887	+	0.627164i	$0.784215\pi$
$80$	−2.89710e6	−	1.80873e7i	−0.0707300	−	0.441585i
$81$	1.08037e8			2.50976
$82$	4.27083e6	−	1.97114e6i	0.0944619	−	0.0435975i
$83$			6.93862e7i			1.46205i	0.682353	+	0.731023i	$0.260957\pi$
$83$			6.93862e7i			1.46205i	−0.682353	+	0.731023i	$0.739043\pi$
$84$	6.55383e7	−	7.68711e7i	1.31637	−	1.54400i
$85$	−1.45252e7			−0.278257
$86$	−1.97990e7	−	4.28982e7i	−0.361951	−	0.784234i
$87$		−	1.35522e8i		−	2.36555i
$88$	9.07314e6	+	2.54608e6i	0.151296	+	0.0424562i
$89$	−1.05906e8			−1.68796			−0.843979	−	0.536377i	$-0.819793\pi$
$89$	−1.05906e8			−1.68796			−0.843979	+	0.536377i	$0.819793\pi$
$90$	−6.49779e7	+	2.99896e7i	−0.990366	+	0.457089i
$91$			1.23620e8i			1.80270i
$92$	1.51114e7	+	1.28836e7i	0.210938	+	0.179840i
$93$	5.10738e7			0.682758
$94$	3.37756e7	+	7.31810e7i	0.432605	+	0.937319i
$95$		−	1.66460e7i		−	0.204370i
$96$	−1.30772e8	+	8.77919e7i	−1.53967	+	1.03364i
$97$	1.33519e8			1.50819			0.754093	−	0.656768i	$-0.228077\pi$
$97$	1.33519e8			1.50819			0.754093	+	0.656768i	$0.228077\pi$
$98$	−1.65045e7	+	7.61742e6i	−0.178936	+	0.0825854i
$99$		−	3.68163e7i		−	0.383266i
$100$	1.29757e7	−	1.52194e7i	0.129757	−	0.152194i
$101$	−6.08853e7			−0.585096			−0.292548	−	0.956251i	$-0.594503\pi$
$101$	−6.08853e7			−0.585096			−0.292548	+	0.956251i	$0.594503\pi$
$102$	5.23384e7	+	1.13401e8i	0.483526	+	1.04765i
$103$			2.63324e7i			0.233960i	0.993134	+	0.116980i	$0.0373214\pi$
$103$			2.63324e7i			0.233960i	−0.993134	+	0.116980i	$0.962679\pi$
$104$	5.20776e7	−	1.85582e8i	0.445161	−	1.58636i
$105$	1.10293e8			0.907387
$106$	−1.09679e8	+	5.06209e7i	−0.868764	+	0.400965i
$107$		−	1.26375e8i		−	0.964108i	−0.876141	−	0.482054i	$-0.839891\pi$
$107$		−	1.26375e8i		−	0.964108i	0.876141	−	0.482054i	$-0.160109\pi$
$108$	2.76277e8	+	2.35546e8i	2.03072	+	1.73133i
$109$	7.75869e7			0.549645			0.274822	−	0.961495i	$-0.411381\pi$
$109$	7.75869e7			0.549645			0.274822	+	0.961495i	$0.411381\pi$
$110$	4.31165e6	+	9.34198e6i	0.0294492	+	0.0638070i
$111$			8.77719e7i			0.578181i
$112$	1.69993e8	−	2.72283e7i	1.08034	−	0.173041i
$113$	−9.07281e7			−0.556453			−0.278226	−	0.960516i	$-0.589747\pi$
$113$	−9.07281e7			−0.556453			−0.278226	+	0.960516i	$0.589747\pi$
$114$	−1.29958e8	+	5.99804e7i	−0.769459	+	0.355132i
$115$			2.16816e7i			0.123965i
$116$	1.49847e8	−	1.75759e8i	0.827593	−	0.970700i
$117$	−7.53042e8			−4.01861
$118$	5.91770e7	+	1.28218e8i	0.305228	+	0.661333i
$119$		−	1.36515e8i		−	0.680757i
$120$	−1.65576e8	−	4.64635e7i	−0.798495	−	0.224072i
$121$	2.09066e8			0.975307
$122$	1.57147e8	−	7.25290e7i	0.709361	−	0.327395i
$123$		−	4.41598e7i		−	0.192933i
$124$	6.62377e7	+	5.64725e7i	0.280168	+	0.238864i
$125$	2.18366e7			0.0894427
$126$	−2.81857e8	−	6.10694e8i	−1.11827	−	2.42293i
$127$			3.10844e8i			1.19489i	0.801910	+	0.597445i	$0.203817\pi$
$127$			3.10844e8i			1.19489i	−0.801910	+	0.597445i	$0.796183\pi$
$128$	−2.66670e8	−	3.07374e7i	−0.993423	−	0.114506i
$129$	−4.43562e8			−1.60175
$130$	1.91081e8	−	8.81906e7i	0.669028	−	0.308780i
$131$		−	5.44781e8i		−	1.84985i	−0.380150	−	0.924925i	$-0.624128\pi$
$131$		−	5.44781e8i		−	1.84985i	0.380150	−	0.924925i	$-0.375872\pi$
$132$	5.73983e7	−	6.73236e7i	0.189062	−	0.221754i
$133$	1.56448e8			0.499991
$134$	9.67833e7	+	2.09699e8i	0.300180	+	0.650394i
$135$			3.96397e8i			1.19343i
$136$	−5.75099e7	+	2.04940e8i	−0.168107	+	0.599062i
$137$	−1.23319e8			−0.350065			−0.175033	−	0.984563i	$-0.556003\pi$
$137$	−1.23319e8			−0.350065			−0.175033	+	0.984563i	$0.556003\pi$
$138$	1.69272e8	−	7.81250e7i	0.466733	−	0.215414i
$139$		−	6.72621e8i		−	1.80182i	−0.434008	−	0.900909i	$-0.642901\pi$
$139$		−	6.72621e8i		−	1.80182i	0.434008	−	0.900909i	$-0.357099\pi$
$140$	1.43040e8	+	1.21952e8i	0.372344	+	0.317451i
$141$	7.56682e8			1.91442
$142$	−2.48851e7	−	5.39181e7i	−0.0612049	−	0.132612i
$143$			1.08266e8i			0.258910i
$144$	1.65864e8	+	1.03553e9i	0.385746	+	2.40831i
$145$	2.52176e8			0.570468
$146$	−5.27017e8	+	2.43237e8i	−1.15988	+	0.535325i
$147$			1.70655e8i			0.365467i
$148$	−9.70497e7	+	1.13832e8i	−0.202277	+	0.237255i
$149$	2.47048e8			0.501229			0.250615	−	0.968087i	$-0.419367\pi$
$149$	2.47048e8			0.501229			0.250615	+	0.968087i	$0.419367\pi$
$150$	−7.86835e7	−	1.70482e8i	−0.155424	−	0.336755i
$151$			4.00056e8i			0.769508i	0.923019	+	0.384754i	$0.125714\pi$
$151$			4.00056e8i			0.769508i	−0.923019	+	0.384754i	$0.874286\pi$
$152$	−2.34864e8	−	6.59069e7i	−0.439989	−	0.123469i
$153$	8.31593e8			1.51756
$154$	−8.78005e7	+	4.05230e7i	−0.156104	+	0.0720475i
$155$			9.50368e7i			0.164651i
$156$	−1.37704e9	−	1.17403e9i	−2.32513	−	1.98235i
$157$	−7.00538e8			−1.15301			−0.576505	−	0.817094i	$-0.695584\pi$
$157$	−7.00538e8			−1.15301			−0.576505	+	0.817094i	$0.695584\pi$
$158$	3.27575e8	+	7.09752e8i	0.525634	+	1.13888i
$159$			1.13407e9i			1.77440i
$160$	−1.63361e8	−	2.43336e8i	−0.249269	−	0.371302i
$161$	−2.03774e8			−0.303281
$162$	1.56949e9	−	7.24376e8i	2.27876	−	1.05173i
$163$			2.24412e8i			0.317903i	0.987286	+	0.158952i	$0.0508114\pi$
$163$			2.24412e8i			0.317903i	−0.987286	+	0.158952i	$0.949189\pi$
$164$	4.88277e7	−	5.72709e7i	0.0674979	−	0.0791696i
$165$	9.65948e7			0.130322
$166$	4.65227e8	+	1.00800e9i	0.612678	+	1.32748i
$167$		−	1.11919e9i		−	1.43893i	−0.694530	−	0.719464i	$-0.744387\pi$
$167$		−	1.11919e9i		−	1.43893i	0.694530	−	0.719464i	$-0.255613\pi$
$168$	4.36686e8	−	1.55616e9i	0.548192	−	1.95352i
$169$	1.39875e9			1.71472
$170$	−2.11013e8	+	9.73899e7i	−0.252647	+	0.116605i
$171$			9.53015e8i			1.11459i
$172$	−5.75256e8	−	4.90448e8i	−0.657275	−	0.560375i
$173$	−1.58033e9			−1.76426			−0.882130	−	0.471005i	$-0.843891\pi$
$173$	−1.58033e9			−1.76426			−0.882130	+	0.471005i	$0.843891\pi$
$174$	−9.08661e8	−	1.96878e9i	−0.991299	−	2.14783i
$175$			2.05231e8i			0.218822i
$176$	1.48880e8	−	2.38465e7i	0.155162	−	0.0248528i
$177$	1.32575e9			1.35073
$178$	−1.53854e9	+	7.10090e8i	−1.53260	+	0.707348i
$179$		−	4.43340e8i		−	0.431841i	−0.976411	−	0.215921i	$-0.930725\pi$
$179$		−	4.43340e8i		−	0.431841i	0.976411	−	0.215921i	$-0.0692753\pi$
$180$	−7.42881e8	+	8.71339e8i	−0.707667	+	0.830037i
$181$	−1.87230e8			−0.174446			−0.0872232	−	0.996189i	$-0.527799\pi$
$181$	−1.87230e8			−0.174446			−0.0872232	+	0.996189i	$0.527799\pi$
$182$	8.28858e8	+	1.79587e9i	0.755431	+	1.63678i
$183$		−	1.62488e9i		−	1.44883i
$184$	3.05912e8	+	8.58443e7i	0.266886	+	0.0748928i
$185$	−1.63324e8			−0.139432
$186$	7.41968e8	−	3.42444e8i	0.619917	−	0.286114i
$187$		−	1.19560e8i		−	0.0977728i
$188$	9.81342e8	+	8.36666e8i	0.785577	+	0.669762i
$189$	−3.72553e9			−2.91972
$190$	−1.11610e8	−	2.41823e8i	−0.0856423	−	0.185560i
$191$			5.22344e8i			0.392485i	0.980555	+	0.196242i	$0.0628740\pi$
$191$			5.22344e8i			0.392485i	−0.980555	+	0.196242i	$0.937126\pi$
$192$	−1.31113e9	+	2.15220e9i	−0.964811	+	1.58371i
$193$	5.01793e7			0.0361655			0.0180828	−	0.999836i	$-0.494244\pi$
$193$	5.01793e7			0.0361655			0.0180828	+	0.999836i	$0.494244\pi$
$194$	1.93967e9	−	8.95227e8i	1.36937	−	0.632014i
$195$		−	1.97575e9i		−	1.36645i
$196$	−1.88693e8	+	2.21322e8i	−0.127859	+	0.149969i
$197$	−2.63629e8			−0.175036			−0.0875181	−	0.996163i	$-0.527894\pi$
$197$	−2.63629e8			−0.175036			−0.0875181	+	0.996163i	$0.527894\pi$
$198$	−2.46850e8	−	5.34845e8i	−0.160610	−	0.347990i
$199$		−	1.26573e9i		−	0.807105i	−0.914956	−	0.403553i	$-0.867775\pi$
$199$		−	1.26573e9i		−	0.807105i	0.914956	−	0.403553i	$-0.132225\pi$
$200$	8.64580e7	−	3.08099e8i	0.0540362	−	0.192562i
$201$	2.16826e9			1.32839
$202$	−8.84503e8	+	4.08229e8i	−0.531244	+	0.245188i
$203$			2.37007e9i			1.39565i
$204$	1.52068e9	+	1.29649e9i	0.878046	+	0.748598i
$205$	8.21713e7			0.0465270
$206$	1.76556e8	+	3.82541e8i	0.0980423	+	0.212427i
$207$		−	1.24131e9i		−	0.676081i
$208$	−4.87757e8	−	3.04519e9i	−0.260586	−	1.62690i
$209$	1.37017e8			0.0718105
$210$	1.60227e9	−	7.39505e8i	0.823871	−	0.380246i
$211$		−	9.34053e8i		−	0.471240i	−0.971845	−	0.235620i	$-0.924288\pi$
$211$		−	9.34053e8i		−	0.471240i	0.971845	−	0.235620i	$-0.0757120\pi$
$212$	−1.25395e9	+	1.47078e9i	−0.620777	+	0.728121i
$213$	−5.57506e8			−0.270852
$214$	−8.47330e8	−	1.83590e9i	−0.404015	−	0.875372i
$215$		−	8.25367e8i		−	0.386272i
$216$	5.59288e9	+	1.56946e9i	2.56934	+	0.721000i
$217$	−8.93202e8			−0.402820
$218$	1.12713e9	−	5.20212e8i	0.499056	−	0.230332i
$219$			5.44928e9i			2.36899i
$220$	1.25274e8	+	1.06805e8i	0.0534774	+	0.0455934i
$221$	−2.44547e9			−1.02517
$222$	5.88501e8	+	1.27509e9i	0.242290	+	0.524965i
$223$			5.22225e8i			0.211173i	0.994410	+	0.105586i	$0.0336720\pi$
$223$			5.22225e8i			0.211173i	−0.994410	+	0.105586i	$0.966328\pi$
$224$	2.28699e9	−	1.53534e9i	0.908391	−	0.609837i
$225$	−1.25018e9			−0.487802
$226$	−1.31804e9	+	6.08322e8i	−0.505237	+	0.233185i
$227$			3.46698e9i			1.30571i	0.757482	+	0.652856i	$0.226430\pi$
$227$			3.46698e9i			1.30571i	−0.757482	+	0.652856i	$0.773570\pi$
$228$	−1.48579e9	+	1.74271e9i	−0.549818	+	0.644892i
$229$	1.31243e9			0.477239			0.238619	−	0.971113i	$-0.423305\pi$
$229$	1.31243e9			0.477239			0.238619	+	0.971113i	$0.423305\pi$
$230$	1.45373e8	+	3.14977e8i	0.0519484	+	0.112556i
$231$			9.07845e8i			0.318833i
$232$	9.98443e8	−	3.55802e9i	0.344644	−	1.22816i
$233$	−2.43802e9			−0.827207			−0.413604	−	0.910457i	$-0.635730\pi$
$233$	−2.43802e9			−0.827207			−0.413604	+	0.910457i	$0.635730\pi$
$234$	−1.09397e10	+	5.04906e9i	−3.64874	+	1.68402i
$235$			1.40801e9i			0.461674i
$236$	1.71937e9	+	1.46589e9i	0.554271	+	0.472556i
$237$	7.33874e9			2.32610
$238$	−9.15318e8	−	1.98320e9i	−0.285275	−	0.618101i
$239$		−	2.78783e9i		−	0.854427i	−0.904151	−	0.427214i	$-0.859495\pi$
$239$		−	2.78783e9i		−	0.854427i	0.904151	−	0.427214i	$-0.140505\pi$
$240$	−2.71691e9	+	4.35176e8i	−0.818900	+	0.131166i
$241$	1.16299e9			0.344753			0.172376	−	0.985031i	$-0.444856\pi$
$241$	1.16299e9			0.344753			0.172376	+	0.985031i	$0.444856\pi$
$242$	3.03717e9	−	1.40176e9i	0.885540	−	0.408708i
$243$		−	6.92356e9i		−	1.98566i
$244$	1.79664e9	−	2.10731e9i	0.506875	−	0.594524i
$245$	−3.17549e8			−0.0881347
$246$	−2.96087e8	−	6.41526e8i	−0.0808497	−	0.175176i
$247$		−	2.80254e9i		−	0.752946i
$248$	1.34090e9	+	3.76281e8i	0.354479	+	0.0994729i
$249$	1.04226e10			2.71130
$250$	3.17228e8	−	1.46412e8i	0.0812105	−	0.0374815i
$251$		−	6.20014e9i		−	1.56209i	−0.624474	−	0.781046i	$-0.714687\pi$
$251$		−	6.20014e9i		−	1.56209i	0.624474	−	0.781046i	$-0.285313\pi$
$252$	−8.18927e9	−	6.98195e9i	−2.03069	−	1.73131i
$253$	−1.78465e8			−0.0435584
$254$	2.08418e9	+	4.51575e9i	0.500725	+	1.08491i
$255$			2.18185e9i			0.516016i
$256$	−4.08010e9	+	1.34146e9i	−0.949973	+	0.312333i
$257$	−1.12108e9			−0.256983			−0.128491	−	0.991711i	$-0.541013\pi$
$257$	−1.12108e9			−0.256983			−0.128491	+	0.991711i	$0.541013\pi$
$258$	−6.44378e9	+	2.97403e9i	−1.45433	+	0.671223i
$259$		−	1.53499e9i		−	0.341120i
$260$	2.18460e9	−	2.56235e9i	0.478055	−	0.560720i
$261$	−1.44375e10			−3.11121
$262$	−3.65269e9	−	7.91423e9i	−0.775190	−	1.67959i
$263$		−	1.51480e9i		−	0.316616i	−0.987390	−	0.158308i	$-0.949396\pi$
$263$		−	1.51480e9i		−	0.316616i	0.987390	−	0.158308i	$-0.0506038\pi$
$264$	3.82449e8	−	1.36288e9i	0.0787332	−	0.280571i
$265$	−2.11025e9			−0.427907
$266$	2.27277e9	−	1.04896e9i	0.453972	−	0.209524i
$267$			1.59083e10i			3.13024i
$268$	2.81201e9	+	2.39745e9i	0.545102	+	0.464740i
$269$	−2.73389e9			−0.522121			−0.261060	−	0.965322i	$-0.584072\pi$
$269$	−2.73389e9			−0.522121			−0.261060	+	0.965322i	$0.584072\pi$
$270$	2.65780e9	+	5.75861e9i	0.500112	+	1.08358i
$271$			9.38092e9i			1.73927i	0.493691	+	0.869637i	$0.335647\pi$
$271$			9.38092e9i			1.73927i	−0.493691	+	0.869637i	$0.664353\pi$
$272$	5.38636e8	+	3.36284e9i	0.0984056	+	0.614371i
$273$	1.85691e10			3.34302
$274$	−1.79151e9	+	8.26843e8i	−0.317845	+	0.146697i
$275$			1.79741e8i			0.0314280i
$276$	1.93526e9	−	2.26990e9i	0.333505	−	0.391174i
$277$	1.88891e9			0.320842			0.160421	−	0.987049i	$-0.448715\pi$
$277$	1.88891e9			0.320842			0.160421	+	0.987049i	$0.448715\pi$
$278$	−4.50985e9	−	9.77141e9i	−0.755062	−	1.63598i
$279$		−	5.44102e9i		−	0.897973i
$280$	2.89566e9	+	8.12574e8i	0.471103	+	0.132200i
$281$	−1.65526e9			−0.265485			−0.132743	−	0.991151i	$-0.542378\pi$
$281$	−1.65526e9			−0.265485			−0.132743	+	0.991151i	$0.542378\pi$
$282$	1.09926e10	−	5.07347e9i	1.73822	−	0.802248i
$283$			8.61833e9i			1.34362i	0.740722	+	0.671811i	$0.234483\pi$
$283$			8.61833e9i			1.34362i	−0.740722	+	0.671811i	$0.765517\pi$
$284$	−7.23031e8	−	6.16437e8i	−0.111143	−	0.0947578i
$285$	−2.50042e9			−0.378995
$286$	7.25913e8	+	1.57282e9i	0.108498	+	0.235080i
$287$			7.72286e8i			0.113828i
$288$	9.35268e9	+	1.39314e10i	1.35946	+	2.02500i
$289$	−4.27519e9			−0.612864
$290$	3.66345e9	−	1.69081e9i	0.517962	−	0.239058i
$291$		−	2.00560e10i		−	2.79686i
$292$	−6.02529e9	+	7.06718e9i	−0.828794	+	0.972108i
$293$	−5.51315e9			−0.748048			−0.374024	−	0.927419i	$-0.622022\pi$
$293$	−5.51315e9			−0.748048			−0.374024	+	0.927419i	$0.622022\pi$
$294$	1.14422e9	+	2.47916e9i	0.153151	+	0.331830i
$295$			2.46693e9i			0.325738i
$296$	−6.46649e8	+	2.30438e9i	−0.0842368	+	0.300184i
$297$	−3.26282e9			−0.419341
$298$	3.58896e9	−	1.65643e9i	0.455096	−	0.210043i
$299$			3.65033e9i			0.456717i
$300$	−2.28613e9	−	1.94909e9i	−0.282238	−	0.240629i
$301$	7.75720e9			0.945016
$302$	2.68233e9	+	5.81177e9i	0.322467	+	0.698683i
$303$			9.14564e9i			1.08504i
$304$	−3.85385e9	+	6.17283e8i	−0.451233	+	0.0722753i
$305$	3.02353e9			0.349394
$306$	1.20809e10	−	5.57574e9i	1.37788	−	0.635941i
$307$		−	1.53502e10i		−	1.72806i	−0.503437	−	0.864032i	$-0.667931\pi$
$307$		−	1.53502e10i		−	1.72806i	0.503437	−	0.864032i	$-0.332069\pi$
$308$	−1.00381e9	+	1.17739e9i	−0.111544	+	0.130833i
$309$	3.95542e9			0.433869
$310$	6.37211e8	+	1.38063e9i	0.0689980	+	0.149497i
$311$		−	5.55831e9i		−	0.594157i	−0.954853	−	0.297079i	$-0.903988\pi$
$311$		−	5.55831e9i		−	0.594157i	0.954853	−	0.297079i	$-0.0960123\pi$
$312$	−2.78765e10	−	7.82262e9i	−2.94184	−	0.825532i
$313$	−1.76829e10			−1.84237			−0.921183	−	0.389131i	$-0.872775\pi$
$313$	−1.76829e10			−1.84237			−0.921183	+	0.389131i	$0.872775\pi$
$314$	−1.01770e10	+	4.69703e9i	−1.04689	+	0.483176i
$315$		−	1.17498e10i		−	1.19341i
$316$	9.51762e9	+	8.11447e9i	0.954509	+	0.813789i
$317$	−2.84291e9			−0.281531			−0.140766	−	0.990043i	$-0.544956\pi$
$317$	−2.84291e9			−0.281531			−0.140766	+	0.990043i	$0.544956\pi$
$318$	7.60382e9	+	1.64751e10i	0.743572	+	1.61109i
$319$			2.07570e9i			0.200448i
$320$	−4.00475e9	−	2.43972e9i	−0.381922	−	0.232670i
$321$	−1.89829e10			−1.78790
$322$	−2.96030e9	+	1.36628e9i	−0.275368	+	0.127092i
$323$			3.09488e9i			0.284337i
$324$	1.79437e10	−	2.10465e10i	1.62829	−	1.90986i
$325$	3.67642e9			0.329528
$326$	1.50466e9	+	3.26011e9i	0.133219	+	0.288643i
$327$		−	1.16544e10i		−	1.01929i
$328$	3.25342e8	−	1.15938e9i	0.0281090	−	0.100168i
$329$	−1.32332e10			−1.12949
$330$	1.40327e9	−	6.47658e8i	0.118327	−	0.0546122i
$331$		−	1.16323e10i		−	0.969068i	−0.874773	−	0.484534i	$-0.838989\pi$
$331$		−	1.16323e10i		−	0.969068i	0.874773	−	0.484534i	$-0.161011\pi$
$332$	1.35171e10	+	1.15243e10i	1.11258	+	0.948553i
$333$	9.35056e9			0.760432
$334$	−7.50407e9	−	1.62589e10i	−0.602991	−	1.30649i
$335$			4.03463e9i			0.320350i
$336$	−4.09000e9	−	2.55349e10i	−0.320897	−	2.00344i
$337$	2.09960e10			1.62786			0.813930	−	0.580963i	$-0.197324\pi$
$337$	2.09960e10			1.62786			0.813930	+	0.580963i	$0.197324\pi$
$338$	2.03201e10	−	9.37844e9i	1.55689	−	0.718561i
$339$			1.36284e10i			1.03192i
$340$	−2.41248e9	+	2.82964e9i	−0.180529	+	0.211746i
$341$	−7.82265e8			−0.0578544
$342$	6.38986e9	+	1.38448e10i	0.467075	+	1.01200i
$343$			1.21594e10i			0.878488i
$344$	−1.16454e10	−	3.26789e9i	−0.831608	−	0.233364i
$345$	3.25682e9			0.229888
$346$	−2.29580e10	+	1.05959e10i	−1.60188	+	0.739324i
$347$			7.43114e9i			0.512552i	0.966604	+	0.256276i	$0.0824955\pi$
$347$			7.43114e9i			0.512552i	−0.966604	+	0.256276i	$0.917504\pi$
$348$	−2.64009e10	−	2.25087e10i	−1.80012	−	1.53474i
$349$	5.43305e9			0.366220			0.183110	−	0.983092i	$-0.441384\pi$
$349$	5.43305e9			0.366220			0.183110	+	0.983092i	$0.441384\pi$
$350$	1.37605e9	+	2.98147e9i	0.0916985	+	0.198682i
$351$			6.67377e10i			4.39686i
$352$	2.00295e9	−	1.34465e9i	0.130466	−	0.0875869i
$353$	7.17687e9			0.462207			0.231103	−	0.972929i	$-0.425766\pi$
$353$	7.17687e9			0.462207			0.231103	+	0.972929i	$0.425766\pi$
$354$	1.92597e10	−	8.88904e9i	1.22641	−	0.566033i
$355$		−	1.03739e9i		−	0.0653175i
$356$	−1.75898e10	+	2.06315e10i	−1.09512	+	1.28449i
$357$	−2.05060e10			−1.26244
$358$	−2.97254e9	−	6.44056e9i	−0.180966	−	0.392095i
$359$		−	1.10278e10i		−	0.663913i	−0.943295	−	0.331957i	$-0.892291\pi$
$359$		−	1.10278e10i		−	0.663913i	0.943295	−	0.331957i	$-0.107709\pi$
$360$	−4.94987e9	+	1.76392e10i	−0.294702	+	1.05019i
$361$	1.34368e10			0.791165
$362$	−2.71996e9	+	1.25536e9i	−0.158390	+	0.0731027i
$363$		−	3.14040e10i		−	1.80866i
$364$	2.40823e10	+	2.05319e10i	1.37180	+	1.16956i
$365$	−1.01399e10			−0.571296
$366$	−1.08947e10	−	2.36052e10i	−0.607140	−	1.31548i
$367$		−	3.39042e10i		−	1.86891i	−0.356076	−	0.934457i	$-0.615886\pi$
$367$		−	3.39042e10i		−	1.86891i	0.356076	−	0.934457i	$-0.384114\pi$
$368$	5.01968e9	−	8.04016e8i	0.273706	−	0.0438403i
$369$	−4.70445e9			−0.253748
$370$	−2.37266e9	+	1.09507e9i	−0.126599	+	0.0584297i
$371$		−	1.98331e10i		−	1.04688i
$372$	8.48279e9	−	9.94963e9i	0.442963	−	0.519560i
$373$	3.19254e10			1.64930			0.824651	−	0.565641i	$-0.191371\pi$
$373$	3.19254e10			1.64930			0.824651	+	0.565641i	$0.191371\pi$
$374$	−8.01634e8	−	1.73689e9i	−0.0409722	−	0.0887738i
$375$		−	3.28010e9i		−	0.165868i
$376$	1.98661e10	+	5.57477e9i	0.993941	+	0.278917i
$377$	4.24565e10			2.10174
$378$	−5.41222e10	+	2.49793e10i	−2.65099	+	1.22353i
$379$			2.66340e10i			1.29086i	0.763819	+	0.645430i	$0.223322\pi$
$379$			2.66340e10i			1.29086i	−0.763819	+	0.645430i	$0.776678\pi$
$380$	−3.24280e9	−	2.76472e9i	−0.155520	−	0.132592i
$381$	4.66922e10			2.21587
$382$	3.50226e9	+	7.58828e9i	0.164473	+	0.356361i
$383$		−	1.61064e10i		−	0.748518i	−0.927324	−	0.374259i	$-0.877897\pi$
$383$		−	1.61064e10i		−	0.748518i	0.927324	−	0.374259i	$-0.122103\pi$
$384$	−4.61709e9	+	4.00567e10i	−0.212346	+	1.84226i
$385$	−1.68929e9			−0.0768886
$386$	7.28973e8	−	3.36446e8i	0.0328369	−	0.0151554i
$387$			4.72537e10i			2.10665i
$388$	2.21759e10	−	2.60106e10i	0.978487	−	1.14769i
$389$	1.81674e10			0.793405			0.396702	−	0.917947i	$-0.370154\pi$
$389$	1.81674e10			0.793405			0.396702	+	0.917947i	$0.370154\pi$
$390$	−1.32472e10	−	2.87025e10i	−0.572619	−	1.24068i
$391$		−	4.03110e9i		−	0.172471i
$392$	−1.25728e9	+	4.48040e9i	−0.0532460	+	0.189746i
$393$	−8.18320e10			−3.43047
$394$	−3.82983e9	+	1.76760e9i	−0.158926	+	0.0733499i
$395$			1.36557e10i			0.560953i
$396$	−7.17215e9	−	6.11479e9i	−0.291654	−	0.248657i
$397$	−4.03325e10			−1.62365			−0.811827	−	0.583898i	$-0.801527\pi$
$397$	−4.03325e10			−1.62365			−0.811827	+	0.583898i	$0.801527\pi$
$398$	−8.48661e9	−	1.83878e10i	−0.338222	−	0.732820i
$399$		−	2.35001e10i		−	0.927212i
$400$	−8.09764e8	−	5.05556e9i	−0.0316314	−	0.197483i
$401$	1.86384e10			0.720826			0.360413	−	0.932793i	$-0.382636\pi$
$401$	1.86384e10			0.720826			0.360413	+	0.932793i	$0.382636\pi$
$402$	3.14990e10	−	1.45379e10i	1.20613	−	0.556670i
$403$			1.60005e10i			0.606614i
$404$	−1.01124e10	+	1.18610e10i	−0.379601	+	0.445242i
$405$	3.01972e10			1.12240
$406$	1.58911e10	+	3.44309e10i	0.584856	+	1.26720i
$407$		−	1.34435e9i		−	0.0489929i
$408$	3.07843e10	+	8.63861e9i	1.11094	+	0.311748i
$409$	−1.95383e10			−0.698222			−0.349111	−	0.937081i	$-0.613516\pi$
$409$	−1.95383e10			−0.698222			−0.349111	+	0.937081i	$0.613516\pi$
$410$	1.19373e9	−	5.50950e8i	0.0422447	−	0.0194974i
$411$			1.85239e10i			0.649181i
$412$	5.12979e9	+	4.37352e9i	0.178037	+	0.151790i
$413$	−2.31854e10			−0.796918
$414$	−8.32284e9	−	1.80330e10i	−0.283316	−	0.613855i
$415$			1.93940e10i			0.653847i
$416$	−2.75035e10	−	4.09683e10i	−0.918364	−	1.36796i
$417$	−1.01035e11			−3.34139
$418$	1.99049e9	−	9.18681e8i	0.0652011	−	0.0300926i
$419$		−	1.60399e10i		−	0.520410i	−0.965553	−	0.260205i	$-0.916210\pi$
$419$		−	1.60399e10i		−	0.520410i	0.965553	−	0.260205i	$-0.0837901\pi$
$420$	1.83185e10	−	2.14861e10i	0.588699	−	0.690496i
$421$	8.80074e9			0.280150			0.140075	−	0.990141i	$-0.455266\pi$
$421$	8.80074e9			0.280150			0.140075	+	0.990141i	$0.455266\pi$
$422$	−6.26273e9	−	1.35693e10i	−0.197476	−	0.427867i
$423$		−	8.06112e10i		−	2.51787i
$424$	−8.35513e9	+	2.97741e10i	−0.258517	+	0.921245i
$425$	−4.05992e9			−0.124440
$426$	−8.09910e9	+	3.73802e9i	−0.245922	+	0.113502i
$427$			2.84166e10i			0.854794i
$428$	−2.46190e10	−	2.09895e10i	−0.733659	−	0.625499i
$429$	1.62628e10			0.480137
$430$	−5.53400e9	−	1.19904e10i	−0.161870	−	0.350720i
$431$		−	2.17255e10i		−	0.629593i	−0.949159	−	0.314797i	$-0.898064\pi$
$431$		−	2.17255e10i		−	0.629593i	0.949159	−	0.314797i	$-0.101936\pi$
$432$	9.17730e10	−	1.46995e10i	2.63499	−	0.422055i
$433$	2.50658e10			0.713066			0.356533	−	0.934283i	$-0.383959\pi$
$433$	2.50658e10			0.713066			0.356533	+	0.934283i	$0.383959\pi$
$434$	−1.29759e10	+	5.98882e9i	−0.365744	+	0.168804i
$435$		−	3.78796e10i		−	1.05791i
$436$	1.28863e10	−	1.51146e10i	0.356601	−	0.418264i
$437$	4.61969e9			0.126674
$438$	3.65368e10	+	7.91637e10i	0.992738	+	2.15095i
$439$		−	2.69059e10i		−	0.724419i	−0.932097	−	0.362210i	$-0.882022\pi$
$439$		−	2.69059e10i		−	0.724419i	0.932097	−	0.362210i	$-0.117978\pi$
$440$	2.53602e9	+	7.11651e8i	0.0676615	+	0.0189870i
$441$	1.81802e10			0.480668
$442$	−3.55263e10	+	1.63966e10i	−0.930809	+	0.429601i
$443$			5.16514e10i			1.34112i	0.741856	+	0.670560i	$0.233946\pi$
$443$			5.16514e10i			1.34112i	−0.741856	+	0.670560i	$0.766054\pi$
$444$	1.70987e10	+	1.45779e10i	0.439979	+	0.375115i
$445$	−2.96017e10			−0.754878
$446$	3.50146e9	+	7.58655e9i	0.0884932	+	0.191737i
$447$		−	3.71093e10i		−	0.929508i
$448$	2.29297e10	−	3.76385e10i	0.569228	−	0.934374i
$449$	−4.61561e10			−1.13565			−0.567825	−	0.823150i	$-0.692215\pi$
$449$	−4.61561e10			−1.13565			−0.567825	+	0.823150i	$0.692215\pi$
$450$	−1.81619e10	+	8.38234e9i	−0.442905	+	0.204416i
$451$			6.76367e8i			0.0163484i
$452$	−1.50689e10	+	1.76746e10i	−0.361018	+	0.423445i
$453$	6.00929e10			1.42702
$454$	2.32457e10	+	5.03661e10i	0.547166	+	1.18554i
$455$			3.45528e10i			0.806191i
$456$	−9.89994e9	+	3.52791e10i	−0.228967	+	0.815941i
$457$	−3.11288e10			−0.713669			−0.356835	−	0.934168i	$-0.616144\pi$
$457$	−3.11288e10			−0.713669			−0.356835	+	0.934168i	$0.616144\pi$
$458$	1.90662e10	−	8.79973e9i	0.433314	−	0.199990i
$459$		−	7.36992e10i		−	1.66040i
$460$	4.22377e9	+	3.60107e9i	0.0943341	+	0.0804268i
$461$	4.68016e10			1.03623			0.518116	−	0.855310i	$-0.326634\pi$
$461$	4.68016e10			1.03623			0.518116	+	0.855310i	$0.326634\pi$
$462$	6.08700e9	+	1.31886e10i	0.133609	+	0.289488i
$463$			2.03332e10i			0.442468i	0.975221	+	0.221234i	$0.0710085\pi$
$463$			2.03332e10i			0.442468i	−0.975221	+	0.221234i	$0.928992\pi$
$464$	−9.35140e9	−	5.83831e10i	−0.201746	−	1.25955i
$465$	1.42756e10			0.305339
$466$	−3.54181e10	+	1.63467e10i	−0.751072	+	0.346646i
$467$			5.89675e10i			1.23978i	0.784688	+	0.619891i	$0.212823\pi$
$467$			5.89675e10i			1.23978i	−0.784688	+	0.619891i	$0.787177\pi$
$468$	−1.25072e11	+	1.46699e11i	−2.60721	+	3.05805i
$469$	−3.79194e10			−0.783737
$470$	9.44057e9	+	2.04547e10i	0.193467	+	0.419182i
$471$			1.05229e11i			2.13821i
$472$	3.48066e10	+	9.76734e9i	0.701283	+	0.196792i
$473$	6.79375e9			0.135727
$474$	1.06613e11	−	4.92054e10i	2.11201	−	0.974765i
$475$		−	4.65271e9i		−	0.0913969i
$476$	−2.65943e10	−	2.26736e10i	−0.518037	−	0.441665i
$477$	1.20815e11			2.33372
$478$	−1.86921e10	−	4.04999e10i	−0.358053	−	0.775786i
$479$			1.20229e10i			0.228384i	0.993459	+	0.114192i	$0.0364279\pi$
$479$			1.20229e10i			0.228384i	−0.993459	+	0.114192i	$0.963572\pi$
$480$	−3.65518e10	+	2.45386e10i	−0.688563	+	0.462258i
$481$	−2.74973e10			−0.513699
$482$	1.68952e10	−	7.79772e9i	0.313022	−	0.144471i
$483$			3.06091e10i			0.562422i
$484$	3.47235e10	−	4.07279e10i	0.632764	−	0.742181i
$485$	3.73196e10			0.674481
$486$	−4.64217e10	−	1.00581e11i	−0.832102	−	1.80290i
$487$		−	4.85939e10i		−	0.863905i	−0.901896	−	0.431953i	$-0.857825\pi$
$487$		−	4.85939e10i		−	0.863905i	0.901896	−	0.431953i	$-0.142175\pi$
$488$	1.19711e10	−	4.26599e10i	0.211084	−	0.752213i
$489$	3.37091e10			0.589538
$490$	−4.61315e9	+	2.12913e9i	−0.0800228	+	0.0369333i
$491$		−	1.71586e9i		−	0.0295226i	−0.999891	−	0.0147613i	$-0.995301\pi$
$491$		−	1.71586e9i		−	0.0295226i	0.999891	−	0.0147613i	$-0.00469884\pi$
$492$	−8.60272e9	−	7.33445e9i	−0.146817	−	0.125172i
$493$	−4.68852e10			−0.793685
$494$	−1.87907e10	−	4.07135e10i	−0.315526	−	0.683645i
$495$		−	1.02905e10i		−	0.171402i
$496$	2.20027e10	−	3.52424e9i	0.363537	−	0.0582289i
$497$	9.74991e9			0.159799
$498$	1.51413e11	−	6.98822e10i	2.46175	−	1.13619i
$499$			6.25565e10i			1.00895i	0.863426	+	0.504476i	$0.168314\pi$
$499$			6.25565e10i			1.00895i	−0.863426	+	0.504476i	$0.831686\pi$
$500$	3.62682e9	−	4.25396e9i	0.0580291	−	0.0680634i
$501$	−1.68115e11			−2.66843
$502$	−4.15712e10	−	9.00717e10i	−0.654603	−	1.41832i
$503$			8.60985e10i			1.34500i	0.740095	+	0.672502i	$0.234780\pi$
$503$			8.60985e10i			1.34500i	−0.740095	+	0.672502i	$0.765220\pi$
$504$	−1.65782e11	−	4.65213e10i	−2.56930	−	0.720990i
$505$	−1.70180e10			−0.261663
$506$	−2.59263e9	+	1.19659e9i	−0.0395493	+	0.0182534i
$507$		−	2.10107e11i		−	3.17987i
$508$	6.05552e10	+	5.16277e10i	0.909278	+	0.775226i
$509$	5.17187e10			0.770506			0.385253	−	0.922811i	$-0.374114\pi$
$509$	5.17187e10			0.770506			0.385253	+	0.922811i	$0.374114\pi$
$510$	1.46290e10	+	3.16965e10i	0.216240	+	0.468522i
$511$		−	9.52994e10i		−	1.39768i
$512$	−5.02788e10	+	4.68445e10i	−0.731653	+	0.681677i
$513$	8.44601e10			1.21950
$514$	−1.62863e10	+	7.51672e9i	−0.233330	+	0.107690i
$515$			7.36013e9i			0.104630i
$516$	−7.36707e10	+	8.64098e10i	−1.03919	+	1.21889i
$517$	−1.15896e10			−0.162221
$518$	−1.02920e10	−	2.22994e10i	−0.142948	−	0.309724i
$519$			2.37383e11i			3.27175i
$520$	1.45561e10	−	5.18717e10i	0.199082	−	0.709443i
$521$	6.36828e10			0.864313			0.432157	−	0.901799i	$-0.357753\pi$
$521$	6.36828e10			0.864313			0.432157	+	0.901799i	$0.357753\pi$
$522$	−2.09739e11	+	9.68018e10i	−2.82486	+	1.30377i
$523$		−	3.05582e10i		−	0.408434i	−0.978926	−	0.204217i	$-0.934535\pi$
$523$		−	3.05582e10i		−	0.408434i	0.978926	−	0.204217i	$-0.0654648\pi$
$524$	−1.06128e11	−	9.04820e10i	−1.40768	−	1.20015i
$525$	3.08279e10			0.405796
$526$	−1.01566e10	−	2.20061e10i	−0.132680	−	0.287474i
$527$		−	1.76695e10i		−	0.229077i
$528$	−3.58201e9	−	2.23634e10i	−0.0460884	−	0.287741i
$529$	7.22938e10			0.923163
$530$	−3.06563e10	+	1.41490e10i	−0.388523	+	0.179317i
$531$		−	1.41236e11i		−	1.77651i
$532$	2.59842e10	−	3.04774e10i	0.324387	−	0.380479i
$533$	1.38344e10			0.171416
$534$	1.06663e11	+	2.31105e11i	1.31175	+	2.84214i
$535$		−	3.53229e10i		−	0.431162i
$536$	5.69258e10	+	1.59744e10i	0.689683	+	0.193537i
$537$	−6.65945e10			−0.800831
$538$	−3.97162e10	+	1.83304e10i	−0.474065	+	0.218798i
$539$		−	2.61380e9i		−	0.0309683i
$540$	7.72217e10	+	6.58372e10i	0.908164	+	0.774276i
$541$	2.53545e10			0.295982			0.147991	−	0.988989i	$-0.452719\pi$
$541$	2.53545e10			0.295982			0.147991	+	0.988989i	$0.452719\pi$
$542$	6.28980e10	+	1.36280e11i	0.728853	+	1.57919i
$543$			2.81240e10i			0.323503i
$544$	3.03725e10	+	4.52418e10i	0.346804	+	0.516587i
$545$	2.16862e10			0.245809
$546$	2.69760e11	−	1.24504e11i	3.03533	−	1.40091i
$547$			5.79915e10i			0.647762i	0.946098	+	0.323881i	$0.104988\pi$
$547$			5.79915e10i			0.647762i	−0.946098	+	0.323881i	$0.895012\pi$
$548$	−2.04820e10	+	2.40237e10i	−0.227117	+	0.266390i
$549$	−1.73103e11			−1.90552
$550$	1.20514e9	+	2.61116e9i	0.0131701	+	0.0285354i
$551$		−	5.37309e10i		−	0.582932i
$552$	1.28948e10	−	4.59514e10i	0.138885	−	0.494928i
$553$	−1.28343e11			−1.37237
$554$	2.74408e10	−	1.26649e10i	0.291312	−	0.134451i
$555$			2.45330e10i			0.258570i
$556$	−1.31032e11	−	1.11715e11i	−1.37113	−	1.16899i
$557$	1.71554e11			1.78230			0.891149	−	0.453710i	$-0.149900\pi$
$557$	1.71554e11			1.78230			0.891149	+	0.453710i	$0.149900\pi$
$558$	−3.64814e10	−	7.90437e10i	−0.376301	−	0.815324i
$559$		−	1.38959e11i		−	1.42312i
$560$	4.75146e10	−	7.61055e9i	0.483142	−	0.0773863i
$561$	−1.79592e10			−0.181315
$562$	−2.40465e10	+	1.10983e10i	−0.241050	+	0.111253i
$563$			5.49966e8i			0.00547397i	0.999996	+	0.00273698i	$0.000871210\pi$
$563$			5.49966e8i			0.00547397i	−0.999996	+	0.00273698i	$0.999129\pi$
$564$	1.25676e11	−	1.47408e11i	1.24205	−	1.45682i
$565$	−2.53593e10			−0.248853
$566$	5.77850e10	+	1.25202e11i	0.563053	+	1.21996i
$567$			2.83808e11i			2.74595i
$568$	−1.46369e10	−	4.10736e9i	−0.140623	−	0.0394611i
$569$	−1.48683e10			−0.141845			−0.0709223	−	0.997482i	$-0.522594\pi$
$569$	−1.48683e10			−0.141845			−0.0709223	+	0.997482i	$0.522594\pi$
$570$	−3.63245e10	+	1.67650e10i	−0.344112	+	0.158820i
$571$			3.55169e10i			0.334111i	0.985947	+	0.167056i	$0.0534259\pi$
$571$			3.55169e10i			0.334111i	−0.985947	+	0.167056i	$0.946574\pi$
$572$	2.10912e10	+	1.79818e10i	0.197023	+	0.167977i
$573$	7.84618e10			0.727846
$574$	5.17809e9	+	1.12193e10i	0.0477004	+	0.103352i
$575$			6.06019e9i			0.0554390i
$576$	2.29279e11	+	1.39678e11i	2.08292	+	1.26893i
$577$	4.14670e10			0.374110			0.187055	−	0.982349i	$-0.440106\pi$
$577$	4.14670e10			0.374110			0.187055	+	0.982349i	$0.440106\pi$
$578$	−6.21073e10	+	2.86647e10i	−0.556457	+	0.256824i
$579$		−	7.53748e9i		−	0.0670674i
$580$	4.18836e10	−	4.91261e10i	0.370111	−	0.434110i
$581$	−1.82275e11			−1.59964
$582$	−1.34473e11	−	2.91360e11i	−1.17204	−	2.53944i
$583$		−	1.73698e10i		−	0.150356i
$584$	−4.01469e10	+	1.43066e11i	−0.345145	+	1.22995i
$585$	−2.10482e11			−1.79718
$586$	−8.00916e10	+	3.69651e10i	−0.679198	+	0.313474i
$587$			2.88322e10i			0.242843i	0.992601	+	0.121421i	$0.0387453\pi$
$587$			2.88322e10i			0.242843i	−0.992601	+	0.121421i	$0.961255\pi$
$588$	3.32450e10	+	2.83438e10i	0.278110	+	0.237110i
$589$	2.02494e10			0.168249
$590$	1.65405e10	+	3.58379e10i	0.136502	+	0.295757i
$591$			3.95999e10i			0.324597i
$592$	6.05651e9	+	3.78123e10i	0.0493100	+	0.307855i
$593$	−4.33851e10			−0.350850			−0.175425	−	0.984493i	$-0.556130\pi$
$593$	−4.33851e10			−0.350850			−0.175425	+	0.984493i	$0.556130\pi$
$594$	−4.74001e10	+	2.18768e10i	−0.380745	+	0.175727i
$595$		−	3.81571e10i		−	0.304444i
$596$	4.10319e10	−	4.81272e10i	0.325190	−	0.381422i
$597$	−1.90127e11			−1.49674
$598$	2.44751e10	+	5.30297e10i	0.191390	+	0.414681i
$599$		−	1.41612e11i		−	1.10000i	−0.835164	−	0.550000i	$-0.814628\pi$
$599$		−	1.41612e11i		−	1.10000i	0.835164	−	0.550000i	$-0.185372\pi$
$600$	−4.62799e10	−	1.29869e10i	−0.357098	−	0.100208i
$601$	−1.16789e11			−0.895170			−0.447585	−	0.894241i	$-0.647716\pi$
$601$	−1.16789e11			−0.895170			−0.447585	+	0.894241i	$0.647716\pi$
$602$	1.12692e11	−	5.20112e10i	0.858037	−	0.396014i
$603$		−	2.30989e11i		−	1.74712i
$604$	7.79345e10	+	6.64449e10i	0.585574	+	0.499245i
$605$	5.84356e10			0.436171
$606$	6.13205e10	+	1.32862e11i	0.454690	+	0.985169i
$607$			4.19809e10i			0.309241i	0.987974	+	0.154620i	$0.0494155\pi$
$607$			4.19809e10i			0.309241i	−0.987974	+	0.154620i	$0.950585\pi$
$608$	−5.18475e10	+	3.48072e10i	−0.379414	+	0.254715i
$609$	3.56011e11			2.58818
$610$	4.39240e10	−	2.02725e10i	0.317236	−	0.146416i
$611$			2.37054e11i			1.70091i
$612$	1.38118e11	−	1.62002e11i	0.984568	−	1.15482i
$613$	1.73299e11			1.22731			0.613655	−	0.789575i	$-0.289699\pi$
$613$	1.73299e11			1.22731			0.613655	+	0.789575i	$0.289699\pi$
$614$	−1.02921e11	−	2.22998e11i	−0.724155	−	1.56901i
$615$		−	1.23430e10i		−	0.0862823i
$616$	−6.68844e9	+	2.38347e10i	−0.0464518	+	0.165534i
$617$	2.09205e11			1.44355			0.721773	−	0.692130i	$-0.243328\pi$
$617$	2.09205e11			1.44355			0.721773	+	0.692130i	$0.243328\pi$
$618$	5.74618e10	−	2.65206e10i	0.393936	−	0.181815i
$619$		−	1.25079e11i		−	0.851965i	−0.904731	−	0.425983i	$-0.859928\pi$
$619$		−	1.25079e11i		−	0.851965i	0.904731	−	0.425983i	$-0.140072\pi$
$620$	1.85140e10	+	1.57846e10i	0.125295	+	0.106823i
$621$	−1.10010e11			−0.739717
$622$	−3.72679e10	−	8.07476e10i	−0.248985	−	0.539471i
$623$		−	2.78211e11i		−	1.84681i
$624$	−4.57421e11	+	7.32665e10i	−3.01702	+	0.483245i
$625$	6.10352e9			0.0400000
$626$	−2.56886e11	+	1.18562e11i	−1.67279	+	0.772054i
$627$		−	2.05814e10i		−	0.133169i
$628$	−1.16352e11	+	1.36471e11i	−0.748055	+	0.877409i
$629$	3.03656e10			0.193990
$630$	−7.87813e10	−	1.70694e11i	−0.500105	−	1.08357i
$631$		−	2.63720e11i		−	1.66351i	−0.555143	−	0.831755i	$-0.687337\pi$
$631$		−	2.63720e11i		−	1.66351i	0.555143	−	0.831755i	$-0.312663\pi$
$632$	1.92673e11	+	5.40673e10i	1.20768	+	0.338896i
$633$	−1.40305e11			−0.873894
$634$	−4.13001e10	+	1.90614e10i	−0.255619	+	0.117977i
$635$			8.68836e10i			0.534371i
$636$	2.20927e11	+	1.88356e11i	1.35027	+	1.15120i
$637$	−5.34628e10			−0.324709
$638$	1.39174e10	+	3.01545e10i	0.0839990	+	0.181999i
$639$			5.93925e10i			0.356228i
$640$	−7.45365e10	−	8.59135e9i	−0.444272	−	0.0512085i
$641$	1.68400e10			0.0997495			0.0498748	−	0.998755i	$-0.484118\pi$
$641$	1.68400e10			0.0997495			0.0498748	+	0.998755i	$0.484118\pi$
$642$	−2.75772e11	+	1.27278e11i	−1.62334	+	0.749228i
$643$			2.84422e11i			1.66387i	0.554871	+	0.831936i	$0.312767\pi$
$643$			2.84422e11i			1.66387i	−0.554871	+	0.831936i	$0.687233\pi$
$644$	−3.38446e10	+	3.96970e10i	−0.196764	+	0.230789i
$645$	−1.23979e11			−0.716325
$646$	2.07508e10	+	4.49604e10i	0.119153	+	0.258167i
$647$			2.11657e11i			1.20785i	0.797040	+	0.603927i	$0.206398\pi$
$647$			2.11657e11i			1.20785i	−0.797040	+	0.603927i	$0.793602\pi$
$648$	1.19560e11	−	4.26062e11i	0.678090	−	2.41642i
$649$	−2.03057e10			−0.114456
$650$	5.34088e10	−	2.46500e10i	0.299198	−	0.138091i
$651$			1.34169e11i			0.747012i
$652$	4.37174e10	+	3.72723e10i	0.241915	+	0.206251i
$653$	−2.94426e11			−1.61929			−0.809644	−	0.586922i	$-0.800340\pi$
$653$	−2.94426e11			−1.61929			−0.809644	+	0.586922i	$0.800340\pi$
$654$	−7.81415e10	−	1.69308e11i	−0.427140	−	0.925478i
$655$		−	1.52271e11i		−	0.827278i
$656$	−3.04715e9	−	1.90241e10i	−0.0164543	−	0.102728i
$657$	5.80525e11			3.11573
$658$	−1.92243e11	+	8.87271e10i	−1.02553	+	0.473318i
$659$		−	1.18352e11i		−	0.627529i	−0.949501	−	0.313765i	$-0.898410\pi$
$659$		−	1.18352e11i		−	0.627529i	0.949501	−	0.313765i	$-0.101590\pi$
$660$	1.60433e10	−	1.88175e10i	0.0845510	−	0.0991715i
$661$	2.01300e11			1.05448			0.527239	−	0.849717i	$-0.323227\pi$
$661$	2.01300e11			1.05448			0.527239	+	0.849717i	$0.323227\pi$
$662$	−7.79934e10	−	1.68987e11i	−0.406093	−	0.879875i
$663$			3.67337e11i			1.90112i
$664$	2.73636e11	+	7.67871e10i	1.40767	+	0.395017i
$665$	4.37284e10			0.223603
$666$	1.35839e11	−	6.26945e10i	0.690442	−	0.318663i
$667$			6.99850e10i			0.353591i
$668$	−2.18029e11	−	1.85886e11i	−1.09498	−	0.933555i
$669$	7.84439e10			0.391611
$670$	2.70518e10	+	5.86125e10i	0.134244	+	0.290865i
$671$			2.48873e10i			0.122768i
$672$	−2.30625e11	−	3.43532e11i	−1.13092	−	1.68457i
$673$	2.21745e11			1.08092			0.540461	−	0.841369i	$-0.318250\pi$
$673$	2.21745e11			1.08092			0.540461	+	0.841369i	$0.318250\pi$
$674$	3.05017e11	−	1.40776e11i	1.47803	−	0.682164i
$675$			1.10796e11i			0.533716i
$676$	2.32316e11	−	2.72488e11i	1.11248	−	1.30485i
$677$	−3.56145e11			−1.69540			−0.847701	−	0.530475i	$-0.822014\pi$
$677$	−3.56145e11			−1.69540			−0.847701	+	0.530475i	$0.822014\pi$
$678$	9.13767e10	+	1.97984e11i	0.432431	+	0.936940i
$679$			3.50747e11i			1.65012i
$680$	−1.60745e10	+	5.72826e10i	−0.0751799	+	0.267909i
$681$	5.20778e11			2.42139
$682$	−1.13642e10	+	5.24500e9i	−0.0525295	+	0.0242442i
$683$		−	2.15409e11i		−	0.989878i	−0.868928	−	0.494939i	$-0.835190\pi$
$683$		−	2.15409e11i		−	0.989878i	0.868928	−	0.494939i	$-0.164810\pi$
$684$	1.85656e11	+	1.58285e11i	0.848172	+	0.723129i
$685$	−3.44688e10			−0.156554
$686$	8.15274e10	+	1.76644e11i	0.368135	+	0.797632i
$687$		−	1.97142e11i		−	0.885018i
$688$	−1.91087e11	+	3.06070e10i	−0.852860	+	0.136605i
$689$	−3.55283e11			−1.57651
$690$	4.73130e10	−	2.18366e10i	0.208729	−	0.0963360i
$691$			2.64031e11i			1.15809i	0.815296	+	0.579045i	$0.196574\pi$
$691$			2.64031e11i			1.15809i	−0.815296	+	0.579045i	$0.803426\pi$
$692$	−2.62475e11	+	3.07862e11i	−1.14463	+	1.34255i
$693$	9.67149e10			0.419334
$694$	4.98250e10	+	1.07955e11i	0.214788	+	0.465377i
$695$		−	1.88003e11i		−	0.805797i
$696$	−5.34454e11	−	1.49977e11i	−2.27758	−	0.639128i
$697$	−1.52775e10			−0.0647324
$698$	7.89280e10	−	3.64280e10i	0.332514	−	0.153467i
$699$			3.66218e11i			1.53402i
$700$	3.99808e10	+	3.40866e10i	0.166517	+	0.141968i
$701$	−1.98676e11			−0.822758			−0.411379	−	0.911464i	$-0.634953\pi$
$701$	−1.98676e11			−0.822758			−0.411379	+	0.911464i	$0.634953\pi$
$702$	4.47469e11	+	9.69523e11i	1.84253	+	3.99218i
$703$			3.47992e10i			0.142478i
$704$	2.00818e10	−	3.29638e10i	0.0817545	−	0.134198i
$705$	2.11499e11			0.856154
$706$	1.04261e11	−	4.81201e10i	0.419666	−	0.193690i
$707$		−	1.59943e11i		−	0.640159i
$708$	2.20193e11	−	2.58269e11i	0.876335	−	1.02787i
$709$	−1.08511e11			−0.429427			−0.214713	−	0.976677i	$-0.568882\pi$
$709$	−1.08511e11			−0.429427			−0.214713	+	0.976677i	$0.568882\pi$
$710$	−6.95560e9	−	1.50706e10i	−0.0273717	−	0.0593057i
$711$		−	7.81814e11i		−	3.05932i
$712$	−1.17202e11	+	4.17659e11i	−0.456054	+	1.62518i
$713$	−2.63750e10			−0.102055
$714$	−2.97899e11	+	1.37491e11i	−1.14624	+	0.529031i
$715$			3.02613e10i			0.115788i
$716$	−8.63665e10	−	7.36338e10i	−0.328619	−	0.280172i
$717$	−4.18763e11			−1.58450
$718$	−7.39403e10	−	1.60205e11i	−0.278217	−	0.602807i
$719$		−	3.56644e11i		−	1.33450i	−0.744832	−	0.667252i	$-0.767471\pi$
$719$		−	3.56644e11i		−	1.33450i	0.744832	−	0.667252i	$-0.232529\pi$
$720$	4.63604e10	+	2.89440e11i	0.172511	+	1.07703i
$721$	−6.91741e10			−0.255978
$722$	1.95201e11	−	9.00923e10i	0.718347	−	0.331542i
$723$		−	1.74694e11i		−	0.639329i
$724$	−3.10969e10	+	3.64741e10i	−0.113178	+	0.132749i
$725$	7.04853e10			0.255121
$726$	−2.10560e11	−	4.56217e11i	−0.757931	−	1.64220i
$727$		−	8.05781e10i		−	0.288456i	−0.989544	−	0.144228i	$-0.953930\pi$
$727$		−	8.05781e10i		−	0.288456i	0.989544	−	0.144228i	$-0.0460699\pi$
$728$	4.87516e11	+	1.36805e11i	1.73565	+	0.487055i
$729$	−3.31165e11			−1.17256
$730$	−1.47306e11	+	6.79867e10i	−0.518714	+	0.239405i
$731$			1.53455e11i			0.537415i
$732$	−3.16541e11	−	2.69875e11i	−1.10252	−	0.939978i
$733$	3.80343e11			1.31753			0.658763	−	0.752351i	$-0.271080\pi$
$733$	3.80343e11			1.31753			0.658763	+	0.752351i	$0.271080\pi$
$734$	−2.27324e11	−	4.92539e11i	−0.783179	−	1.69690i
$735$			4.76994e10i			0.163442i
$736$	6.75318e10	−	4.53366e10i	0.230143	−	0.154503i
$737$	−3.32098e10			−0.112563
$738$	−6.83433e10	+	3.15428e10i	−0.230394	+	0.106335i
$739$			4.01614e11i			1.34658i	0.739381	+	0.673288i	$0.235118\pi$
$739$			4.01614e11i			1.34658i	−0.739381	+	0.673288i	$0.764882\pi$
$740$	−2.71262e10	+	3.18169e10i	−0.0904612	+	0.106104i
$741$	−4.20972e11			−1.39631
$742$	−1.32979e11	−	2.88123e11i	−0.438700	−	0.950523i
$743$		−	3.54474e11i		−	1.16313i	−0.813499	−	0.581566i	$-0.802440\pi$
$743$		−	3.54474e11i		−	1.16313i	0.813499	−	0.581566i	$-0.197560\pi$
$744$	5.65215e10	−	2.01418e11i	0.184468	−	0.657366i
$745$	6.90521e10			0.224157
$746$	4.63791e11	−	2.14056e11i	1.49750	−	0.691150i
$747$		−	1.11034e12i		−	3.56594i
$748$	−2.32913e10	−	1.98575e10i	−0.0744024	−	0.0634335i
$749$	3.31981e11			1.05484
$750$	−2.19927e10	−	4.76512e10i	−0.0695078	−	0.150601i
$751$			4.84888e11i			1.52434i	0.647378	+	0.762169i	$0.275866\pi$
$751$			4.84888e11i			1.52434i	−0.647378	+	0.762169i	$0.724134\pi$
$752$	3.25980e11	−	5.22132e10i	1.01934	−	0.163271i
$753$	−9.31329e11			−2.89683
$754$	6.16781e11	−	2.84666e11i	1.90829	−	0.880745i
$755$			1.11819e11i			0.344135i
$756$	−6.18770e11	+	7.25767e11i	−1.89427	+	2.22183i
$757$	1.22819e11			0.374009			0.187004	−	0.982359i	$-0.440122\pi$
$757$	1.22819e11			0.374009			0.187004	+	0.982359i	$0.440122\pi$
$758$	1.78578e11	+	3.86922e11i	0.540942	+	1.17205i
$759$			2.68074e10i			0.0807771i
$760$	−6.56465e10	−	1.84215e10i	−0.196769	−	0.0552168i
$761$	−1.93019e11			−0.575521			−0.287761	−	0.957702i	$-0.592911\pi$
$761$	−1.93019e11			−0.575521			−0.287761	+	0.957702i	$0.592911\pi$
$762$	6.78315e11	−	3.13066e11i	2.01192	−	0.928573i
$763$			2.03817e11i			0.601372i
$764$	1.01757e11	+	8.67555e10i	0.298670	+	0.254638i
$765$	2.32437e11			0.678672
$766$	−1.07991e11	−	2.33983e11i	−0.313671	−	0.679625i
$767$			4.15333e11i			1.20009i
$768$	2.01502e11	+	6.12876e11i	0.579208	+	1.76168i
$769$	1.34359e11			0.384202			0.192101	−	0.981375i	$-0.438470\pi$
$769$	1.34359e11			0.384202			0.192101	+	0.981375i	$0.438470\pi$
$770$	−2.45410e10	+	1.13265e10i	−0.0698118	+	0.0322206i
$771$			1.68399e11i			0.476564i
$772$	8.33422e9	−	9.77536e9i	0.0234636	−	0.0275210i
$773$	−1.97017e11			−0.551804			−0.275902	−	0.961186i	$-0.588976\pi$
$773$	−1.97017e11			−0.551804			−0.275902	+	0.961186i	$0.588976\pi$
$774$	3.16831e11	+	6.86472e11i	0.882803	+	1.91275i
$775$			2.65636e10i			0.0736343i
$776$	1.47760e11	−	5.26553e11i	0.407483	−	1.45210i
$777$	−2.30573e11			−0.632593
$778$	2.63925e11	−	1.21811e11i	0.720380	−	0.332481i
$779$		−	1.75082e10i		−	0.0475435i
$780$	−3.84894e11	−	3.28150e11i	−1.03983	−	0.886532i
$781$	8.53896e9			0.0229510
$782$	−2.70281e10	−	5.85613e10i	−0.0722751	−	0.156597i
$783$			1.27951e12i			3.40406i
$784$	1.17756e10	+	7.35183e10i	0.0311688	+	0.194595i
$785$	−1.95806e11			−0.515642
$786$	−1.18880e12	+	5.48675e11i	−3.11473	+	1.43756i
$787$		−	3.63175e11i		−	0.946711i	−0.880871	−	0.473356i	$-0.843043\pi$
$787$		−	3.63175e11i		−	0.946711i	0.880871	−	0.473356i	$-0.156957\pi$
$788$	−4.37858e10	+	5.13572e10i	−0.113561	+	0.133198i
$789$	−2.27540e11			−0.587150
$790$	9.15601e10	+	1.98382e11i	0.235070	+	0.509323i
$791$		−	2.38339e11i		−	0.608820i
$792$	−1.45191e11	−	4.07433e10i	−0.369012	−	0.103551i
$793$	5.09044e11			1.28725
$794$	−5.85926e11	+	2.70425e11i	−1.47421	+	0.680402i
$795$			3.16982e11i			0.793536i
$796$	−2.46576e11	−	2.10224e11i	−0.614184	−	0.523637i
$797$	−5.78264e10			−0.143316			−0.0716578	−	0.997429i	$-0.522829\pi$
$797$	−5.78264e10			−0.143316			−0.0716578	+	0.997429i	$0.522829\pi$
$798$	−1.57566e11	−	3.41395e11i	−0.388553	−	0.841872i
$799$		−	2.61782e11i		−	0.642321i
$800$	−4.56607e10	−	6.80146e10i	−0.111476	−	0.166051i
$801$	1.69475e12			4.11694
$802$	2.70766e11	−	1.24968e11i	0.654481	−	0.302066i
$803$		−	8.34631e10i		−	0.200739i
$804$	3.60123e11	−	4.22395e11i	0.861840	−	1.01087i
$805$	−5.69566e10			−0.135632
$806$	1.07281e11	+	2.32444e11i	0.254205	+	0.550781i
$807$			4.10660e11i			0.968251i
$808$	−6.73795e10	+	2.40111e11i	−0.158082	+	0.563336i
$809$	−1.75206e11			−0.409031			−0.204515	−	0.978863i	$-0.565562\pi$
$809$	−1.75206e11			−0.409031			−0.204515	+	0.978863i	$0.565562\pi$
$810$	4.38686e11	−	2.02469e11i	1.01909	−	0.470347i
$811$			1.53398e11i			0.354599i	0.984157	+	0.177299i	$0.0567361\pi$
$811$			1.53398e11i			0.354599i	−0.984157	+	0.177299i	$0.943264\pi$
$812$	4.61711e11	+	3.93642e11i	1.06205	+	0.905477i
$813$	1.40912e12			3.22541
$814$	−9.01369e9	−	1.95298e10i	−0.0205308	−	0.0444836i
$815$			6.27249e10i			0.142171i
$816$	5.05136e11	−	8.09091e10i	1.13932	−	0.182489i
$817$	−1.75860e11			−0.394712
$818$	−2.83840e11	+	1.31002e11i	−0.633958	+	0.292594i
$819$		−	1.97821e12i		−	4.39680i
$820$	1.36477e10	−	1.60077e10i	0.0301860	−	0.0354057i
$821$	−3.12544e11			−0.687922			−0.343961	−	0.938984i	$-0.611769\pi$
$821$	−3.12544e11			−0.687922			−0.343961	+	0.938984i	$0.611769\pi$
$822$	1.24201e11	+	2.69104e11i	0.272043	+	0.589431i
$823$		−	6.75905e11i		−	1.47328i	−0.676283	−	0.736641i	$-0.736411\pi$
$823$		−	6.75905e11i		−	1.47328i	0.676283	−	0.736641i	$-0.263589\pi$
$824$	1.03846e11	+	2.91411e10i	0.225259	+	0.0632116i
$825$	2.69991e10			0.0582818
$826$	−3.36822e11	+	1.55455e11i	−0.723570	+	0.333953i
$827$			7.49212e11i			1.60171i	0.598861	+	0.800853i	$0.295620\pi$
$827$			7.49212e11i			1.60171i	−0.598861	+	0.800853i	$0.704380\pi$
$828$	−2.41818e11	−	2.06168e11i	−0.514479	−	0.438631i
$829$	−6.27639e11			−1.32890			−0.664449	−	0.747333i	$-0.731334\pi$
$829$	−6.27639e11			−1.32890			−0.664449	+	0.747333i	$0.731334\pi$
$830$	1.30035e11	+	2.81744e11i	0.273998	+	0.593667i
$831$		−	2.83735e11i		−	0.594988i
$832$	−6.74242e11	−	4.10753e11i	−1.40709	−	0.857211i
$833$	5.90396e10			0.122621
$834$	−1.46777e12	+	6.77429e11i	−3.03385	+	1.40023i
$835$		−	3.12824e11i		−	0.643508i
$836$	2.27569e10	−	2.66920e10i	0.0465895	−	0.0546458i
$837$	−4.82206e11			−0.982495
$838$	−1.07546e11	−	2.33018e11i	−0.218081	−	0.472512i
$839$			8.86257e11i			1.78860i	0.447473	+	0.894298i	$0.352324\pi$
$839$			8.86257e11i			1.78860i	−0.447473	+	0.894298i	$0.647676\pi$
$840$	1.22058e11	−	4.34961e11i	0.245159	−	0.873641i
$841$	3.13739e11			0.627168
$842$	1.27852e11	−	5.90080e10i	0.254365	−	0.117398i
$843$			2.48638e11i			0.492331i
$844$	−1.81962e11	−	1.55136e11i	−0.358600	−	0.305733i
$845$	3.90961e11			0.766844
$846$	−5.40489e11	−	1.17107e12i	−1.05513	−	2.28613i
$847$			5.49207e11i			1.06709i
$848$	7.82540e10	+	4.88560e11i	0.151329	+	0.944787i
$849$	1.29457e12			2.49169
$850$	−5.89799e10	+	2.72213e10i	−0.112987	+	0.0521475i
$851$		−	4.53263e10i		−	0.0864235i
$852$	−9.25956e10	+	1.08607e11i	−0.175724	+	0.206110i
$853$	−4.42385e10			−0.0835611			−0.0417805	−	0.999127i	$-0.513303\pi$
$853$	−4.42385e10			−0.0835611			−0.0417805	+	0.999127i	$0.513303\pi$
$854$	1.90530e11	+	4.12819e11i	0.358206	+	0.776119i
$855$			2.66376e11i			0.498460i
$856$	−4.98381e11	−	1.39854e11i	−0.928253	−	0.260484i
$857$	−1.03847e12			−1.92517			−0.962586	−	0.270976i	$-0.912654\pi$
$857$	−1.03847e12			−1.92517			−0.962586	+	0.270976i	$0.912654\pi$
$858$	2.36255e11	−	1.09040e11i	0.435945	−	0.201204i
$859$		−	5.28066e11i		−	0.969874i	−0.874549	−	0.484937i	$-0.838842\pi$
$859$		−	5.28066e11i		−	0.969874i	0.874549	−	0.484937i	$-0.161158\pi$
$860$	−1.60789e11	−	1.37084e11i	−0.293942	−	0.250608i
$861$	1.16006e11			0.211090
$862$	−1.45667e11	−	3.15614e11i	−0.263835	−	0.571646i
$863$		−	1.90850e11i		−	0.344072i	−0.985091	−	0.172036i	$-0.944965\pi$
$863$		−	1.90850e11i		−	0.344072i	0.985091	−	0.172036i	$-0.0550346\pi$
$864$	1.23466e12	−	8.28873e11i	2.21561	−	1.48742i
$865$	−4.41715e11			−0.789001
$866$	3.64140e11	−	1.68063e11i	0.647436	−	0.298814i
$867$			6.42181e11i			1.13653i
$868$	−1.48351e11	+	1.74004e11i	−0.261343	+	0.306534i
$869$	−1.12403e11			−0.197105
$870$	−2.53978e11	−	5.50290e11i	−0.443322	−	0.960539i
$871$			6.79273e11i			1.18024i
$872$	8.58624e10	−	3.05977e11i	0.148504	−	0.529203i
$873$	−2.13661e12			−3.67848
$874$	6.71119e10	−	3.09745e10i	0.115015	−	0.0530834i
$875$			5.73638e10i			0.0978601i
$876$	1.06157e12	+	9.05065e11i	1.80273	+	1.53696i
$877$	2.36707e11			0.400140			0.200070	−	0.979782i	$-0.435883\pi$
$877$	2.36707e11			0.400140			0.200070	+	0.979782i	$0.435883\pi$
$878$	−1.80401e11	−	3.90872e11i	−0.303572	−	0.657744i
$879$			8.28136e11i			1.38722i
$880$	4.16132e10	−	6.66531e9i	0.0693906	−	0.0111145i
$881$	3.49205e11			0.579665			0.289832	−	0.957077i	$-0.406400\pi$
$881$	3.49205e11			0.579665			0.289832	+	0.957077i	$0.406400\pi$
$882$	2.64111e11	−	1.21897e11i	0.436428	−	0.201427i
$883$		−	5.98818e11i		−	0.985035i	−0.870302	−	0.492518i	$-0.836077\pi$
$883$		−	5.98818e11i		−	0.985035i	0.870302	−	0.492518i	$-0.163923\pi$
$884$	−4.06166e11	+	4.76400e11i	−0.665111	+	0.780122i
$885$	3.70559e11			0.604067
$886$	3.46317e11	+	7.50359e11i	0.562004	+	1.21768i
$887$		−	5.75931e11i		−	0.930413i	−0.885202	−	0.465207i	$-0.845980\pi$
$887$		−	5.75931e11i		−	0.930413i	0.885202	−	0.465207i	$-0.154020\pi$
$888$	3.46143e11	+	9.71338e10i	0.556678	+	0.156214i
$889$	−8.16574e11			−1.30734
$890$	−4.30035e11	+	1.98476e11i	−0.685399	+	0.316336i
$891$			2.48559e11i			0.394383i
$892$	1.01734e11	+	8.67357e10i	0.160697	+	0.137006i
$893$	3.00004e11			0.471761
$894$	−2.48814e11	−	5.39101e11i	−0.389516	−	0.843957i
$895$		−	1.23917e11i		−	0.193125i
$896$	8.07457e10	−	7.00530e11i	0.125282	−	1.08691i
$897$	5.48320e11			0.846962
$898$	−6.70527e11	+	3.09472e11i	−1.03112	+	0.475900i
$899$			3.06764e11i			0.469641i
$900$	−2.07641e11	+	2.43547e11i	−0.316478	+	0.371204i
$901$	3.92343e11			0.595342
$902$	4.53497e9	+	9.82583e9i	0.00685091	+	0.0148437i
$903$		−	1.16522e12i		−	1.75249i
$904$	−1.00405e11	+	3.57802e11i	−0.150343	+	0.535758i
$905$	−5.23325e10			−0.0780148
$906$	8.72991e11	−	4.02916e11i	1.29568	−	0.598001i
$907$		−	4.04494e11i		−	0.597699i	−0.954300	−	0.298849i	$-0.903397\pi$
$907$		−	4.04494e11i		−	0.597699i	0.954300	−	0.298849i	$-0.0966029\pi$
$908$	6.75398e11	+	5.75827e11i	0.993611	+	0.847126i
$909$	9.74308e11			1.42705
$910$	2.31673e11	+	5.01961e11i	0.337839	+	0.731989i
$911$		−	6.18016e11i		−	0.897276i	−0.893714	−	0.448638i	$-0.851909\pi$
$911$		−	6.18016e11i		−	0.897276i	0.893714	−	0.448638i	$-0.148091\pi$
$912$	9.27227e10	+	5.78891e11i	0.134031	+	0.836792i
$913$	−1.59636e11			−0.229746
$914$	−4.52219e11	+	2.08715e11i	−0.647984	+	0.299067i
$915$		−	4.54168e11i		−	0.647936i
$916$	2.17981e11	−	2.55674e11i	0.309625	−	0.363165i
$917$	1.43111e12			2.02394
$918$	−4.94145e11	−	1.07066e12i	−0.695799	−	1.50758i
$919$		−	5.11050e11i		−	0.716476i	−0.933630	−	0.358238i	$-0.883378\pi$
$919$		−	5.11050e11i		−	0.716476i	0.933630	−	0.358238i	$-0.116622\pi$
$920$	8.55051e10	+	2.39942e10i	0.119355	+	0.0334931i
$921$	−2.30577e12			−3.20462
$922$	6.79904e11	−	3.13800e11i	0.940858	−	0.434239i
$923$		−	1.74656e11i		−	0.240645i
$924$	1.76856e11	+	1.50783e11i	0.242623	+	0.206854i
$925$	−4.56503e10			−0.0623558
$926$	1.36332e11	+	2.95388e11i	0.185419	+	0.401744i
$927$		−	4.21380e11i		−	0.570631i
$928$	−5.27304e11	−	7.85453e11i	−0.710999	−	1.05908i
$929$	3.49578e11			0.469333			0.234666	−	0.972076i	$-0.424600\pi$
$929$	3.49578e11			0.469333			0.234666	+	0.972076i	$0.424600\pi$
$930$	2.07386e11	−	9.57161e10i	0.277235	−	0.127954i
$931$			6.76600e10i			0.0900603i
$932$	−4.04929e11	+	4.74949e11i	−0.536680	+	0.629482i
$933$	−8.34919e11			−1.10184
$934$	3.95371e11	+	8.56642e11i	0.519537	+	1.12567i
$935$		−	3.34179e10i		−	0.0437253i
$936$	−8.33363e11	+	2.96975e12i	−1.08575	+	3.86915i
$937$	−1.37124e11			−0.177891			−0.0889457	−	0.996036i	$-0.528350\pi$
$937$	−1.37124e11			−0.177891			−0.0889457	+	0.996036i	$0.528350\pi$
$938$	−5.50869e11	+	2.54245e11i	−0.711602	+	0.328429i
$939$			2.65616e12i			3.41659i
$940$	2.74293e11	+	2.33855e11i	0.351321	+	0.299527i
$941$	−4.32170e10			−0.0551183			−0.0275592	−	0.999620i	$-0.508773\pi$
$941$	−4.32170e10			−0.0551183			−0.0275592	+	0.999620i	$0.508773\pi$
$942$	7.05546e11	+	1.52869e12i	0.896028	+	1.94141i
$943$			2.28046e10i			0.0288387i
$944$	5.71137e11	−	9.14807e10i	0.719204	−	0.115197i
$945$	−1.04132e12			−1.30574
$946$	9.86953e10	−	4.55513e10i	0.123234	−	0.0568770i
$947$		−	1.24527e12i		−	1.54832i	−0.632987	−	0.774162i	$-0.718171\pi$
$947$		−	1.24527e12i		−	1.54832i	0.632987	−	0.774162i	$-0.281829\pi$
$948$	1.21888e12	−	1.42965e12i	1.50914	−	1.77010i
$949$	−1.70716e12			−2.10479
$950$	−3.11959e10	−	6.75916e10i	−0.0383004	−	0.0829848i
$951$			4.27037e11i			0.522088i
$952$	−5.38370e11	−	1.51076e11i	−0.655440	−	0.183928i
$953$	9.35275e11			1.13388			0.566941	−	0.823759i	$-0.308127\pi$
$953$	9.35275e11			1.13388			0.566941	+	0.823759i	$0.308127\pi$
$954$	1.75513e12	−	8.10053e11i	2.11892	−	0.977958i
$955$			1.46000e11i			0.175525i
$956$	−5.43095e11	−	4.63028e11i	−0.650195	−	0.554339i
$957$	3.11793e11			0.371723
$958$	8.06120e10	+	1.74661e11i	0.0957057	+	0.207364i
$959$		−	3.23955e11i		−	0.383010i
$960$	−3.66473e11	+	6.01557e11i	−0.431476	+	0.708258i
$961$	7.37282e11			0.864450
$962$	−3.99463e11	+	1.84366e11i	−0.466419	+	0.215269i
$963$			2.02229e12i			2.35147i
$964$	1.93160e11	−	2.26561e11i	0.223670	−	0.262347i
$965$	1.40255e10			0.0161737
$966$	2.05231e11	+	4.44670e11i	0.235686	+	0.510657i
$967$		−	1.52906e12i		−	1.74871i	−0.485286	−	0.874355i	$-0.661285\pi$
$967$		−	1.52906e12i		−	1.74871i	0.485286	−	0.874355i	$-0.338715\pi$
$968$	2.31365e11	−	8.24486e11i	0.263510	−	0.939035i
$969$	4.64884e11			0.527290
$970$	5.42155e11	−	2.50224e11i	0.612402	−	0.282645i
$971$			5.95468e11i			0.669856i	0.942244	+	0.334928i	$0.108712\pi$
$971$			5.95468e11i			0.669856i	−0.942244	+	0.334928i	$0.891288\pi$
$972$	−1.34877e12	−	1.14993e12i	−1.51103	−	1.28826i
$973$	1.76694e12			1.97139
$974$	−3.25817e11	−	7.05942e11i	−0.362024	−	0.784392i
$975$		−	5.52239e11i		−	0.611095i
$976$	−1.12121e11	−	7.00002e11i	−0.123563	−	0.771436i
$977$	1.10548e12			1.21332			0.606659	−	0.794962i	$-0.292509\pi$
$977$	1.10548e12			1.21332			0.606659	+	0.794962i	$0.292509\pi$
$978$	4.89704e11	−	2.26016e11i	0.535277	−	0.247049i
$979$		−	2.43657e11i		−	0.265245i
$980$	−5.27414e10	+	6.18614e10i	−0.0571804	+	0.0670680i
$981$	−1.24157e12			−1.34059
$982$	−1.15046e10	−	2.49269e10i	−0.0123716	−	0.0268054i
$983$			1.26644e10i			0.0135634i	0.999977	+	0.00678172i	$0.00215871\pi$
$983$			1.26644e10i			0.0135634i	−0.999977	+	0.00678172i	$0.997841\pi$
$984$	−1.74152e11	−	4.88700e10i	−0.185758	−	0.0521269i
$985$	−7.36865e10			−0.0782786
$986$	−6.81118e11	+	3.14360e11i	−0.720634	+	0.332598i
$987$			1.98777e12i			2.09458i
$988$	−5.45959e11	−	4.65470e11i	−0.572971	−	0.488500i
$989$	2.29060e11			0.239422
$990$	−6.89966e10	−	1.49494e11i	−0.0718268	−	0.155626i
$991$			7.11883e11i			0.738098i	0.929410	+	0.369049i	$0.120317\pi$
$991$			7.11883e11i			0.738098i	−0.929410	+	0.369049i	$0.879683\pi$
$992$	2.96012e11	−	1.98724e11i	0.305677	−	0.205212i
$993$	−1.74730e12			−1.79709
$994$	1.41641e11	−	6.53721e10i	0.145092	−	0.0669649i
$995$		−	3.53783e11i		−	0.360948i
$996$	1.73107e12	−	2.03041e12i	1.75905	−	2.06322i
$997$	2.60515e11			0.263665			0.131832	−	0.991272i	$-0.457914\pi$
$997$	2.60515e11			0.263665			0.131832	+	0.991272i	$0.457914\pi$
$998$	4.19435e11	+	9.08782e11i	0.422807	+	0.916089i
$999$		−	8.28685e11i		−	0.832008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.15	✓	16
3.2	odd	2		180.9.c.a.91.2		16
4.3	odd	2	inner	20.9.b.a.11.16	yes	16
5.2	odd	4		100.9.d.c.99.22		32
5.3	odd	4		100.9.d.c.99.11		32
5.4	even	2		100.9.b.d.51.2		16
8.3	odd	2		320.9.b.d.191.1		16
8.5	even	2		320.9.b.d.191.16		16
12.11	even	2		180.9.c.a.91.1		16
20.3	even	4		100.9.d.c.99.21		32
20.7	even	4		100.9.d.c.99.12		32
20.19	odd	2		100.9.b.d.51.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.15	✓	16	1.1	even	1	trivial
20.9.b.a.11.16	yes	16	4.3	odd	2	inner
100.9.b.d.51.1		16	20.19	odd	2
100.9.b.d.51.2		16	5.4	even	2
100.9.d.c.99.11		32	5.3	odd	4
100.9.d.c.99.12		32	20.7	even	4
100.9.d.c.99.21		32	20.3	even	4
100.9.d.c.99.22		32	5.2	odd	4
180.9.c.a.91.1		16	12.11	even	2
180.9.c.a.91.2		16	3.2	odd	2
320.9.b.d.191.1		16	8.3	odd	2
320.9.b.d.191.16		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(14.5274 - 6.70489i) q^{2} -150.211i q^{3} +(166.089 - 194.809i) q^{4} +279.508 q^{5} +(-1007.15 - 2182.17i) q^{6} +2626.96i q^{7} +(1106.66 - 3943.67i) q^{8} -16002.3 q^{9} +O(q^{10})\)	\(q+(14.5274 - 6.70489i) q^{2} -150.211i q^{3} +(166.089 - 194.809i) q^{4} +279.508 q^{5} +(-1007.15 - 2182.17i) q^{6} +2626.96i q^{7} +(1106.66 - 3943.67i) q^{8} -16002.3 q^{9} +(4060.52 - 1874.07i) q^{10} +2300.68i q^{11} +(-29262.4 - 24948.4i) q^{12} +47058.2 q^{13} +(17613.5 + 38162.8i) q^{14} -41985.3i q^{15} +(-10365.0 - 64711.2i) q^{16} -51967.0 q^{17} +(-232472. + 107294. i) q^{18} -59554.7i q^{19} +(46423.2 - 54450.7i) q^{20} +394598. q^{21} +(15425.8 + 33422.9i) q^{22} +77570.5i q^{23} +(-592382. - 166233. i) q^{24} +78125.0 q^{25} +(683632. - 315520. i) q^{26} +1.41819e6i q^{27} +(511754. + 436308. i) q^{28} +902211. q^{29} +(-281507. - 609935. i) q^{30} +340014. i q^{31} +(-584457. - 870587. i) q^{32} +345588. q^{33} +(-754943. + 348433. i) q^{34} +734257. i q^{35} +(-2.65781e6 + 3.11740e6i) q^{36} -584324. q^{37} +(-399308. - 865173. i) q^{38} -7.06866e6i q^{39} +(309321. - 1.10229e6i) q^{40} +293985. q^{41} +(5.73247e6 - 2.64573e6i) q^{42} -2.95292e6i q^{43} +(448194. + 382118. i) q^{44} -4.47279e6 q^{45} +(520102. + 1.12689e6i) q^{46} +5.03746e6i q^{47} +(-9.72033e6 + 1.55693e6i) q^{48} -1.13610e6 q^{49} +(1.13495e6 - 523820. i) q^{50} +7.80601e6i q^{51} +(7.81585e6 - 9.16736e6i) q^{52} -7.54985e6 q^{53} +(9.50883e6 + 2.06026e7i) q^{54} +643061. i q^{55} +(1.03598e7 + 2.90715e6i) q^{56} -8.94577e6 q^{57} +(1.31068e7 - 6.04923e6i) q^{58} +8.82594e6i q^{59} +(-8.17910e6 - 6.97328e6i) q^{60} +1.08173e7 q^{61} +(2.27976e6 + 4.93951e6i) q^{62} -4.20375e7i q^{63} +(-1.43278e7 - 8.72861e6i) q^{64} +1.31532e7 q^{65} +(5.02049e6 - 2.31713e6i) q^{66} +1.44347e7i q^{67} +(-8.63113e6 + 1.01236e7i) q^{68} +1.16519e7 q^{69} +(4.92311e6 + 1.06668e7i) q^{70} -3.71149e6i q^{71} +(-1.77092e7 + 6.31079e7i) q^{72} -3.62775e7 q^{73} +(-8.48869e6 + 3.91783e6i) q^{74} -1.17352e7i q^{75} +(-1.16018e7 - 9.89137e6i) q^{76} -6.04380e6 q^{77} +(-4.73946e7 - 1.02689e8i) q^{78} +4.88562e7i q^{79} +(-2.89710e6 - 1.80873e7i) q^{80} +1.08037e8 q^{81} +(4.27083e6 - 1.97114e6i) q^{82} +6.93862e7i q^{83} +(6.55383e7 - 7.68711e7i) q^{84} -1.45252e7 q^{85} +(-1.97990e7 - 4.28982e7i) q^{86} -1.35522e8i q^{87} +(9.07314e6 + 2.54608e6i) q^{88} -1.05906e8 q^{89} +(-6.49779e7 + 2.99896e7i) q^{90} +1.23620e8i q^{91} +(1.51114e7 + 1.28836e7i) q^{92} +5.10738e7 q^{93} +(3.37756e7 + 7.31810e7i) q^{94} -1.66460e7i q^{95} +(-1.30772e8 + 8.77919e7i) q^{96} +1.33519e8 q^{97} +(-1.65045e7 + 7.61742e6i) q^{98} -3.68163e7i 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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