LMFDB - Embedded newform 13.7.d.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,7,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99070308706$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + \cdots + 56070144 $ x^12 - 6x^11 + 18x^10 + 488x^9 + 36205x^8 - 155430x^7 + 399962x^6 + 9502784x^5 + 275595012x^4 - 541321656x^3 + 523196552x^2 - 242221824*x + 56070144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5^{2}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.3
Root			$0.561862 - 0.561862i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.7.d.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438138 + 0.438138i) q^{2} -27.8396 q^{3} -63.6161i q^{4} +(-78.9164 - 78.9164i) q^{5} +(-12.1976 - 12.1976i) q^{6} +(-88.1833 + 88.1833i) q^{7} +(55.9134 - 55.9134i) q^{8} +46.0426 q^{9} +O(q^{10})$	\(q+(0.438138 + 0.438138i) q^{2} -27.8396 q^{3} -63.6161i q^{4} +(-78.9164 - 78.9164i) q^{5} +(-12.1976 - 12.1976i) q^{6} +(-88.1833 + 88.1833i) q^{7} +(55.9134 - 55.9134i) q^{8} +46.0426 q^{9} -69.1525i q^{10} +(345.814 - 345.814i) q^{11} +1771.05i q^{12} +(1962.64 + 987.350i) q^{13} -77.2729 q^{14} +(2197.00 + 2197.00i) q^{15} -4022.43 q^{16} -7953.63i q^{17} +(20.1730 + 20.1730i) q^{18} +(-3967.21 - 3967.21i) q^{19} +(-5020.35 + 5020.35i) q^{20} +(2454.99 - 2454.99i) q^{21} +303.028 q^{22} +19.3887i q^{23} +(-1556.61 + 1556.61i) q^{24} -3169.41i q^{25} +(427.310 + 1292.50i) q^{26} +19013.3 q^{27} +(5609.88 + 5609.88i) q^{28} -21532.8 q^{29} +1925.18i q^{30} +(31391.5 + 31391.5i) q^{31} +(-5340.84 - 5340.84i) q^{32} +(-9627.33 + 9627.33i) q^{33} +(3484.79 - 3484.79i) q^{34} +13918.2 q^{35} -2929.05i q^{36} +(20434.9 - 20434.9i) q^{37} -3476.37i q^{38} +(-54639.0 - 27487.4i) q^{39} -8824.96 q^{40} +(-83835.3 - 83835.3i) q^{41} +2151.25 q^{42} +84146.3i q^{43} +(-21999.3 - 21999.3i) q^{44} +(-3633.52 - 3633.52i) q^{45} +(-8.49490 + 8.49490i) q^{46} +(85478.5 - 85478.5i) q^{47} +111983. q^{48} +102096. i q^{49} +(1388.64 - 1388.64i) q^{50} +221426. i q^{51} +(62811.4 - 124855. i) q^{52} -150336. q^{53} +(8330.42 + 8330.42i) q^{54} -54580.8 q^{55} +9861.26i q^{56} +(110446. + 110446. i) q^{57} +(-9434.35 - 9434.35i) q^{58} +(24220.8 - 24220.8i) q^{59} +(139764. - 139764. i) q^{60} +70980.8 q^{61} +27507.6i q^{62} +(-4060.19 + 4060.19i) q^{63} +252756. i q^{64} +(-76966.2 - 232802. i) q^{65} -8436.19 q^{66} +(-179083. - 179083. i) q^{67} -505979. q^{68} -539.772i q^{69} +(6098.09 + 6098.09i) q^{70} +(-155987. - 155987. i) q^{71} +(2574.40 - 2574.40i) q^{72} +(451890. - 451890. i) q^{73} +17906.6 q^{74} +88235.2i q^{75} +(-252379. + 252379. i) q^{76} +60990.1i q^{77} +(-11896.1 - 35982.7i) q^{78} +632360. q^{79} +(317436. + 317436. i) q^{80} -562886. q^{81} -73462.8i q^{82} +(741398. + 741398. i) q^{83} +(-156177. - 156177. i) q^{84} +(-627672. + 627672. i) q^{85} +(-36867.7 + 36867.7i) q^{86} +599465. q^{87} -38671.3i q^{88} +(746592. - 746592. i) q^{89} -3183.96i q^{90} +(-260140. + 86004.1i) q^{91} +1233.43 q^{92} +(-873927. - 873927. i) q^{93} +74902.7 q^{94} +626156. i q^{95} +(148687. + 148687. i) q^{96} +(-576739. - 576739. i) q^{97} +(-44732.3 + 44732.3i) q^{98} +(15922.2 - 15922.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9 + 1686 * q^11 - 3926 * q^13 + 5484 * q^14 - 15268 * q^15 + 2132 * q^16 + 15254 * q^18 + 1766 * q^19 - 19044 * q^20 + 3428 * q^21 + 28832 * q^22 + 31608 * q^24 - 58266 * q^26 - 20464 * q^27 + 4092 * q^28 - 90108 * q^29 + 61014 * q^31 - 64932 * q^32 - 44452 * q^33 + 259896 * q^34 + 158772 * q^35 - 40212 * q^37 + 137852 * q^39 - 104196 * q^40 - 190416 * q^41 - 959204 * q^42 + 489372 * q^44 - 151444 * q^45 - 44412 * q^46 + 562446 * q^47 + 930308 * q^48 + 82422 * q^50 - 578500 * q^52 + 509136 * q^53 - 871432 * q^54 - 1264036 * q^55 + 939908 * q^57 - 1019980 * q^58 - 994458 * q^59 + 2407804 * q^60 + 1013696 * q^61 + 865778 * q^63 - 1130064 * q^65 - 418352 * q^66 - 1442386 * q^67 - 2313132 * q^68 + 2958968 * q^70 - 655866 * q^71 - 1706508 * q^72 + 2588228 * q^73 + 3373752 * q^74 + 246984 * q^76 + 77480 * q^78 - 75316 * q^79 - 2685408 * q^80 - 4016140 * q^81 + 894966 * q^83 - 3220504 * q^84 + 105396 * q^85 + 3704832 * q^86 + 2109064 * q^87 - 977376 * q^89 + 1088750 * q^91 + 3682872 * q^92 - 216268 * q^93 - 6238300 * q^94 + 896384 * q^96 + 983388 * q^97 + 1039302 * q^98 + 2894714 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.438138	+	0.438138i	0.0547672	+	0.0547672i	0.733960	−	0.679193i	$-0.237670\pi$
$2$	0.438138	+	0.438138i	0.0547672	+	0.0547672i	−0.679193	+	0.733960i	$0.737670\pi$
$3$	−27.8396			−1.03110			−0.515548	−	0.856861i	$-0.672412\pi$
$3$	−27.8396			−1.03110			−0.515548	+	0.856861i	$0.672412\pi$
$4$		−	63.6161i		−	0.994001i
$5$	−78.9164	−	78.9164i	−0.631331	−	0.631331i	0.317071	−	0.948402i	$-0.397301\pi$
$5$	−78.9164	−	78.9164i	−0.631331	−	0.631331i	−0.948402	+	0.317071i	$0.897301\pi$
$6$	−12.1976	−	12.1976i	−0.0564702	−	0.0564702i
$7$	−88.1833	+	88.1833i	−0.257094	+	0.257094i	−0.823871	−	0.566777i	$-0.808190\pi$
$7$	−88.1833	+	88.1833i	−0.257094	+	0.257094i	0.566777	+	0.823871i	$0.308190\pi$
$8$	55.9134	−	55.9134i	0.109206	−	0.109206i
$9$	46.0426			0.0631586
$10$		−	69.1525i		−	0.0691525i
$11$	345.814	−	345.814i	0.259815	−	0.259815i	−0.565164	−	0.824979i	$-0.691187\pi$
$11$	345.814	−	345.814i	0.259815	−	0.259815i	0.824979	+	0.565164i	$0.191187\pi$
$12$			1771.05i			1.02491i
$13$	1962.64	+	987.350i	0.893326	+	0.449408i
$13$	1962.64	+	987.350i	0.893326	+	0.449408i
$14$	−77.2729			−0.0281607
$15$	2197.00	+	2197.00i	0.650963	+	0.650963i
$16$	−4022.43			−0.982039
$17$		−	7953.63i		−	1.61890i	−0.587192	−	0.809448i	$-0.699767\pi$
$17$		−	7953.63i		−	1.61890i	0.587192	−	0.809448i	$-0.300233\pi$
$18$	20.1730	+	20.1730i	0.00345902	+	0.00345902i
$19$	−3967.21	−	3967.21i	−0.578395	−	0.578395i	0.356066	−	0.934461i	$-0.384118\pi$
$19$	−3967.21	−	3967.21i	−0.578395	−	0.578395i	−0.934461	+	0.356066i	$0.884118\pi$
$20$	−5020.35	+	5020.35i	−0.627544	+	0.627544i
$21$	2454.99	−	2454.99i	0.265089	−	0.265089i
$22$	303.028			0.0284587
$23$			19.3887i			0.00159354i	1.00000		0.000796772i	$0.000253620\pi$
$23$			19.3887i			0.00159354i	−1.00000		0.000796772i	$0.999746\pi$
$24$	−1556.61	+	1556.61i	−0.112602	+	0.112602i
$25$		−	3169.41i		−	0.202843i
$26$	427.310	+	1292.50i	0.0243121	+	0.0735378i
$27$	19013.3			0.965973
$28$	5609.88	+	5609.88i	0.255552	+	0.255552i
$29$	−21532.8			−0.882892			−0.441446	−	0.897288i	$-0.645534\pi$
$29$	−21532.8			−0.882892			−0.441446	+	0.897288i	$0.645534\pi$
$30$			1925.18i			0.0713028i
$31$	31391.5	+	31391.5i	1.05373	+	1.05373i	0.998472	+	0.0552528i	$0.0175965\pi$
$31$	31391.5	+	31391.5i	1.05373	+	1.05373i	0.0552528	+	0.998472i	$0.482404\pi$
$32$	−5340.84	−	5340.84i	−0.162989	−	0.162989i
$33$	−9627.33	+	9627.33i	−0.267895	+	0.267895i
$34$	3484.79	−	3484.79i	0.0886624	−	0.0886624i
$35$	13918.2			0.324623
$36$		−	2929.05i		−	0.0627797i
$37$	20434.9	−	20434.9i	0.403429	−	0.403429i	−0.476011	−	0.879439i	$-0.657918\pi$
$37$	20434.9	−	20434.9i	0.403429	−	0.403429i	0.879439	+	0.476011i	$0.157918\pi$
$38$		−	3476.37i		−	0.0633542i
$39$	−54639.0	−	27487.4i	−0.921105	−	0.463383i
$40$	−8824.96			−0.137890
$41$	−83835.3	−	83835.3i	−1.21640	−	1.21640i	−0.968885	−	0.247511i	$-0.920387\pi$
$41$	−83835.3	−	83835.3i	−1.21640	−	1.21640i	−0.247511	−	0.968885i	$-0.579613\pi$
$42$	2151.25			0.0290364
$43$			84146.3i			1.05835i	0.848512	+	0.529175i	$0.177499\pi$
$43$			84146.3i			1.05835i	−0.848512	+	0.529175i	$0.822501\pi$
$44$	−21999.3	−	21999.3i	−0.258257	−	0.258257i
$45$	−3633.52	−	3633.52i	−0.0398740	−	0.0398740i
$46$	−8.49490	+	8.49490i	−8.72740e−5	+	8.72740e-5i
$47$	85478.5	−	85478.5i	0.823310	−	0.823310i	−0.163271	−	0.986581i	$-0.552205\pi$
$47$	85478.5	−	85478.5i	0.823310	−	0.823310i	0.986581	+	0.163271i	$0.0522045\pi$
$48$	111983.			1.01258
$49$			102096.i			0.867805i
$50$	1388.64	−	1388.64i	0.0111091	−	0.0111091i
$51$			221426.i			1.66924i
$52$	62811.4	−	124855.i	0.446712	−	0.887967i
$53$	−150336.			−1.00980			−0.504899	−	0.863179i	$-0.668470\pi$
$53$	−150336.			−1.00980			−0.504899	+	0.863179i	$0.668470\pi$
$54$	8330.42	+	8330.42i	0.0529037	+	0.0529037i
$55$	−54580.8			−0.328059
$56$			9861.26i			0.0561524i
$57$	110446.	+	110446.i	0.596381	+	0.596381i
$58$	−9434.35	−	9434.35i	−0.0483535	−	0.0483535i
$59$	24220.8	−	24220.8i	0.117932	−	0.117932i	−0.645678	−	0.763610i	$-0.723425\pi$
$59$	24220.8	−	24220.8i	0.117932	−	0.117932i	0.763610	+	0.645678i	$0.223425\pi$
$60$	139764.	−	139764.i	0.647058	−	0.647058i
$61$	70980.8			0.312717			0.156358	−	0.987700i	$-0.450024\pi$
$61$	70980.8			0.312717			0.156358	+	0.987700i	$0.450024\pi$
$62$			27507.6i			0.115419i
$63$	−4060.19	+	4060.19i	−0.0162377	+	0.0162377i
$64$			252756.i			0.964186i
$65$	−76966.2	−	232802.i	−0.280259	−	0.847710i
$66$	−8436.19			−0.0293437
$67$	−179083.	−	179083.i	−0.595429	−	0.595429i	0.343664	−	0.939093i	$-0.388332\pi$
$67$	−179083.	−	179083.i	−0.595429	−	0.595429i	−0.939093	+	0.343664i	$0.888332\pi$
$68$	−505979.			−1.60918
$69$		−	539.772i		−	0.00164310i
$70$	6098.09	+	6098.09i	0.0177787	+	0.0177787i
$71$	−155987.	−	155987.i	−0.435825	−	0.435825i	0.454779	−	0.890604i	$-0.349718\pi$
$71$	−155987.	−	155987.i	−0.435825	−	0.435825i	−0.890604	+	0.454779i	$0.849718\pi$
$72$	2574.40	−	2574.40i	0.00689729	−	0.00689729i
$73$	451890.	−	451890.i	1.16162	−	1.16162i	0.177500	−	0.984121i	$-0.443199\pi$
$73$	451890.	−	451890.i	1.16162	−	1.16162i	0.984121	−	0.177500i	$-0.0568010\pi$
$74$	17906.6			0.0441893
$75$			88235.2i			0.209150i
$76$	−252379.	+	252379.i	−0.574926	+	0.574926i
$77$			60990.1i			0.133594i
$78$	−11896.1	−	35982.7i	−0.0250681	−	0.0758245i
$79$	632360.			1.28258			0.641288	−	0.767300i	$-0.278400\pi$
$79$	632360.			1.28258			0.641288	+	0.767300i	$0.278400\pi$
$80$	317436.	+	317436.i	0.619992	+	0.619992i
$81$	−562886.			−1.05917
$82$		−	73462.8i		−	0.133237i
$83$	741398.	+	741398.i	1.29663	+	1.29663i	0.930603	+	0.366029i	$0.119283\pi$
$83$	741398.	+	741398.i	1.29663	+	1.29663i	0.366029	+	0.930603i	$0.380717\pi$
$84$	−156177.	−	156177.i	−0.263499	−	0.263499i
$85$	−627672.	+	627672.i	−1.02206	+	1.02206i
$86$	−36867.7	+	36867.7i	−0.0579629	+	0.0579629i
$87$	599465.			0.910346
$88$		−	38671.3i		−	0.0567467i
$89$	746592.	−	746592.i	1.05904	−	1.05904i	0.0608984	−	0.998144i	$-0.480603\pi$
$89$	746592.	−	746592.i	1.05904	−	1.05904i	0.998144	−	0.0608984i	$-0.0193966\pi$
$90$		−	3183.96i		−	0.00436757i
$91$	−260140.	+	86004.1i	−0.345209	+	0.114129i
$92$	1233.43			0.00158398
$93$	−873927.	−	873927.i	−1.08649	−	1.08649i
$94$	74902.7			0.0901808
$95$			626156.i			0.730318i
$96$	148687.	+	148687.i	0.168058	+	0.168058i
$97$	−576739.	−	576739.i	−0.631923	−	0.631923i	0.316627	−	0.948550i	$-0.397450\pi$
$97$	−576739.	−	576739.i	−0.631923	−	0.631923i	−0.948550	+	0.316627i	$0.897450\pi$
$98$	−44732.3	+	44732.3i	−0.0475273	+	0.0475273i
$99$	15922.2	−	15922.2i	0.0164096	−	0.0164096i
$100$	−201626.			−0.201626
$101$			168363.i			0.163411i	0.996657	+	0.0817057i	$0.0260367\pi$
$101$			168363.i			0.163411i	−0.996657	+	0.0817057i	$0.973963\pi$
$102$	−97015.0	+	97015.0i	−0.0914194	+	0.0914194i
$103$		−	32261.9i		−	0.0295242i	−0.999891	−	0.0147621i	$-0.995301\pi$
$103$		−	32261.9i		−	0.0295242i	0.999891	−	0.0147621i	$-0.00469909\pi$
$104$	164944.	−	54531.7i	0.146635	−	0.0484784i
$105$	−387477.			−0.334718
$106$	−65867.7	−	65867.7i	−0.0553038	−	0.0553038i
$107$	741191.			0.605033			0.302516	−	0.953144i	$-0.402173\pi$
$107$	741191.			0.605033			0.302516	+	0.953144i	$0.402173\pi$
$108$		−	1.20955e6i		−	0.960178i
$109$	−884706.	−	884706.i	−0.683155	−	0.683155i	0.277555	−	0.960710i	$-0.410476\pi$
$109$	−884706.	−	884706.i	−0.683155	−	0.683155i	−0.960710	+	0.277555i	$0.910476\pi$
$110$	−23913.9	−	23913.9i	−0.0179669	−	0.0179669i
$111$	−568898.	+	568898.i	−0.415974	+	0.415974i
$112$	354712.	−	354712.i	0.252477	−	0.252477i
$113$	292098.			0.202439			0.101219	−	0.994864i	$-0.467726\pi$
$113$	292098.			0.202439			0.101219	+	0.994864i	$0.467726\pi$
$114$			96780.7i			0.0653242i
$115$	1530.08	−	1530.08i	0.00100605	−	0.00100605i
$116$			1.36983e6i			0.877595i
$117$	90365.0	+	45460.2i	0.0564212	+	0.0283840i
$118$	21224.1			0.0129176
$119$	701378.	+	701378.i	0.416209	+	0.416209i
$120$	245683.			0.142178
$121$			1.53239e6i			0.864992i
$122$	31099.4	+	31099.4i	0.0171266	+	0.0171266i
$123$	2.33394e6	+	2.33394e6i	1.25422	+	1.25422i
$124$	1.99701e6	−	1.99701e6i	1.04740	−	1.04740i
$125$	−1.48319e6	+	1.48319e6i	−0.759392	+	0.759392i
$126$	−3557.85			−0.00177859
$127$		−	273825.i		−	0.133679i	−0.997764	−	0.0668394i	$-0.978708\pi$
$127$		−	273825.i		−	0.133679i	0.997764	−	0.0668394i	$-0.0212915\pi$
$128$	−452555.	+	452555.i	−0.215795	+	0.215795i
$129$		−	2.34260e6i		−	1.09126i
$130$	68277.7	−	135721.i	0.0310777	−	0.0617757i
$131$	−2.11892e6			−0.942540			−0.471270	−	0.881989i	$-0.656204\pi$
$131$	−2.11892e6			−0.942540			−0.471270	+	0.881989i	$0.656204\pi$
$132$	612453.	+	612453.i	0.266288	+	0.266288i
$133$	699684.			0.297404
$134$		−	156926.i		−	0.0652200i
$135$	−1.50046e6	−	1.50046e6i	−0.609849	−	0.609849i
$136$	−444715.	−	444715.i	−0.176793	−	0.176793i
$137$	2.31501e6	−	2.31501e6i	0.900308	−	0.900308i	−0.0951549	−	0.995462i	$-0.530335\pi$
$137$	2.31501e6	−	2.31501e6i	0.900308	−	0.900308i	0.995462	+	0.0951549i	$0.0303346\pi$
$138$	236.494	−	236.494i	8.99878e−5	−	8.99878e-5i
$139$	−4.04107e6			−1.50471			−0.752353	−	0.658760i	$-0.771081\pi$
$139$	−4.04107e6			−1.50471			−0.752353	+	0.658760i	$0.771081\pi$
$140$		−	885422.i		−	0.322676i
$141$	−2.37969e6	+	2.37969e6i	−0.848912	+	0.848912i
$142$		−	136687.i		−	0.0477379i
$143$	1.02015e6	−	337268.i	0.348863	−	0.115337i
$144$	−185203.			−0.0620242
$145$	1.69929e6	+	1.69929e6i	0.557397	+	0.557397i
$146$	395980.			0.127237
$147$		−	2.84232e6i		−	0.894790i
$148$	−1.29999e6	−	1.29999e6i	−0.401008	−	0.401008i
$149$	1.23989e6	+	1.23989e6i	0.374820	+	0.374820i	0.869229	−	0.494409i	$-0.164616\pi$
$149$	1.23989e6	+	1.23989e6i	0.374820	+	0.374820i	−0.494409	+	0.869229i	$0.664616\pi$
$150$	−38659.2	+	38659.2i	−0.0114546	+	0.0114546i
$151$	−1.23226e6	+	1.23226e6i	−0.357908	+	0.357908i	−0.863041	−	0.505133i	$-0.831443\pi$
$151$	−1.23226e6	+	1.23226e6i	−0.357908	+	0.357908i	0.505133	+	0.863041i	$0.331443\pi$
$152$	−443641.			−0.126328
$153$		−	366206.i		−	0.102247i
$154$	−26722.1	+	26722.1i	−0.00731658	+	0.00731658i
$155$		−	4.95461e6i		−	1.33050i
$156$	−1.74864e6	+	3.47592e6i	−0.460603	+	0.915580i
$157$	3.82433e6			0.988227			0.494113	−	0.869398i	$-0.335493\pi$
$157$	3.82433e6			0.988227			0.494113	+	0.869398i	$0.335493\pi$
$158$	277061.	+	277061.i	0.0702431	+	0.0702431i
$159$	4.18528e6			1.04120
$160$			842959.i			0.205800i
$161$	−1709.76	−	1709.76i	−0.000409691	−	0.000409691i
$162$	−246622.	−	246622.i	−0.0580078	−	0.0580078i
$163$	−2.76028e6	+	2.76028e6i	−0.637368	+	0.637368i	−0.949905	−	0.312538i	$-0.898821\pi$
$163$	−2.76028e6	+	2.76028e6i	−0.637368	+	0.637368i	0.312538	+	0.949905i	$0.398821\pi$
$164$	−5.33327e6	+	5.33327e6i	−1.20910	+	1.20910i
$165$	1.51951e6			0.338260
$166$			649668.i			0.142026i
$167$	4.20793e6	−	4.20793e6i	0.903480	−	0.903480i	−0.0922552	−	0.995735i	$-0.529408\pi$
$167$	4.20793e6	−	4.20793e6i	0.903480	−	0.903480i	0.995735	+	0.0922552i	$0.0294075\pi$
$168$		−	274533.i		−	0.0578985i
$169$	2.87709e6	+	3.87562e6i	0.596064	+	0.802937i
$170$	−550013.			−0.111951
$171$	−182661.	−	182661.i	−0.0365306	−	0.0365306i
$172$	5.35306e6			1.05200
$173$		−	443902.i		−	0.0857331i	−0.999081	−	0.0428666i	$-0.986351\pi$
$173$		−	443902.i		−	0.0857331i	0.999081	−	0.0428666i	$-0.0136490\pi$
$174$	262648.	+	262648.i	0.0498571	+	0.0498571i
$175$	279490.	+	279490.i	0.0521497	+	0.0521497i
$176$	−1.39101e6	+	1.39101e6i	−0.255149	+	0.255149i
$177$	−674296.	+	674296.i	−0.121599	+	0.121599i
$178$	654220.			0.116002
$179$		−	3.62477e6i		−	0.632007i	−0.948758	−	0.316003i	$-0.897659\pi$
$179$		−	3.62477e6i		−	0.632007i	0.948758	−	0.316003i	$-0.102341\pi$
$180$	−231150.	+	231150.i	−0.0396348	+	0.0396348i
$181$		−	2.29994e6i		−	0.387865i	−0.981015	−	0.193933i	$-0.937876\pi$
$181$		−	2.29994e6i		−	0.387865i	0.981015	−	0.193933i	$-0.0621243\pi$
$182$	−151659.	−	76295.4i	−0.0251567	−	0.0126556i
$183$	−1.97608e6			−0.322441
$184$	1084.09	+	1084.09i	0.000174024	+	0.000174024i
$185$	−3.22529e6			−0.509394
$186$		−	765801.i		−	0.119008i
$187$	−2.75048e6	−	2.75048e6i	−0.420614	−	0.420614i
$188$	−5.43781e6	−	5.43781e6i	−0.818371	−	0.818371i
$189$	−1.67665e6	+	1.67665e6i	−0.248346	+	0.248346i
$190$	−274343.	+	274343.i	−0.0399975	+	0.0399975i
$191$	−1.18019e7			−1.69376			−0.846881	−	0.531783i	$-0.821522\pi$
$191$	−1.18019e7			−1.69376			−0.846881	+	0.531783i	$0.821522\pi$
$192$		−	7.03661e6i		−	0.994169i
$193$	1.69911e6	−	1.69911e6i	0.236346	−	0.236346i	−0.578989	−	0.815335i	$-0.696553\pi$
$193$	1.69911e6	−	1.69911e6i	0.236346	−	0.236346i	0.815335	+	0.578989i	$0.196553\pi$
$194$		−	505382.i		−	0.0692173i
$195$	2.14271e6	+	6.48112e6i	0.288974	+	0.874070i
$196$	6.49497e6			0.862599
$197$	755533.	+	755533.i	0.0988222	+	0.0988222i	0.754789	−	0.655967i	$-0.227739\pi$
$197$	755533.	+	755533.i	0.0988222	+	0.0988222i	−0.655967	+	0.754789i	$0.727739\pi$
$198$	13952.2			0.00179741
$199$		−	6.22148e6i		−	0.789468i	−0.918795	−	0.394734i	$-0.870837\pi$
$199$		−	6.22148e6i		−	0.789468i	0.918795	−	0.394734i	$-0.129163\pi$
$200$	−177213.	−	177213.i	−0.0221516	−	0.0221516i
$201$	4.98560e6	+	4.98560e6i	0.613944	+	0.613944i
$202$	−73766.1	+	73766.1i	−0.00894958	+	0.00894958i
$203$	1.89884e6	−	1.89884e6i	0.226986	−	0.226986i
$204$	1.40862e7			1.65922
$205$			1.32319e7i			1.53590i
$206$	14135.1	−	14135.1i	0.00161696	−	0.00161696i
$207$			892.704i			0.000100646i
$208$	−7.89458e6	−	3.97155e6i	−0.877282	−	0.441337i
$209$	−2.74384e6			−0.300552
$210$	−169768.	−	169768.i	−0.0183315	−	0.0183315i
$211$	−3.50732e6			−0.373360			−0.186680	−	0.982421i	$-0.559773\pi$
$211$	−3.50732e6			−0.373360			−0.186680	+	0.982421i	$0.559773\pi$
$212$			9.56376e6i			1.00374i
$213$	4.34260e6	+	4.34260e6i	0.449378	+	0.449378i
$214$	324744.	+	324744.i	0.0331359	+	0.0331359i
$215$	6.64052e6	−	6.64052e6i	0.668170	−	0.668170i
$216$	1.06310e6	−	1.06310e6i	0.105490	−	0.105490i
$217$	−5.53642e6			−0.541813
$218$		−	775246.i		−	0.0748290i
$219$	−1.25804e7	+	1.25804e7i	−1.19774	+	1.19774i
$220$			3.47222e6i			0.326091i
$221$	7.85302e6	−	1.56101e7i	0.727545	−	1.44620i
$222$	−498511.			−0.0455634
$223$	4.77854e6	+	4.77854e6i	0.430904	+	0.430904i	0.888936	−	0.458032i	$-0.151445\pi$
$223$	4.77854e6	+	4.77854e6i	0.430904	+	0.430904i	−0.458032	+	0.888936i	$0.651445\pi$
$224$	941946.			0.0838073
$225$		−	145928.i		−	0.0128113i
$226$	127979.	+	127979.i	0.0110870	+	0.0110870i
$227$	4.96621e6	+	4.96621e6i	0.424568	+	0.424568i	0.886773	−	0.462205i	$-0.152942\pi$
$227$	4.96621e6	+	4.96621e6i	0.424568	+	0.424568i	−0.462205	+	0.886773i	$0.652942\pi$
$228$	7.02612e6	−	7.02612e6i	0.592803	−	0.592803i
$229$	1.02034e7	−	1.02034e7i	0.849648	−	0.849648i	−0.140441	−	0.990089i	$-0.544852\pi$
$229$	1.02034e7	−	1.02034e7i	0.849648	−	0.849648i	0.990089	+	0.140441i	$0.0448522\pi$
$230$	1340.77			0.000110197
$231$		−	1.69794e6i		−	0.137748i
$232$	−1.20397e6	+	1.20397e6i	−0.0964169	+	0.0964169i
$233$			1.34335e7i			1.06199i	0.847374	+	0.530996i	$0.178182\pi$
$233$			1.34335e7i			1.06199i	−0.847374	+	0.530996i	$0.821818\pi$
$234$	19674.5	+	59510.1i	0.00153552	+	0.00464455i
$235$	−1.34913e7			−1.03956
$236$	−1.54083e6	−	1.54083e6i	−0.117225	−	0.117225i
$237$	−1.76046e7			−1.32246
$238$			614600.i			0.0455892i
$239$	1.09843e6	+	1.09843e6i	0.0804599	+	0.0804599i	0.746191	−	0.665731i	$-0.231880\pi$
$239$	1.09843e6	+	1.09843e6i	0.0804599	+	0.0804599i	−0.665731	+	0.746191i	$0.731880\pi$
$240$	−8.83728e6	−	8.83728e6i	−0.639271	−	0.639271i
$241$	−3.77898e6	+	3.77898e6i	−0.269975	+	0.269975i	−0.829090	−	0.559115i	$-0.811141\pi$
$241$	−3.77898e6	+	3.77898e6i	−0.269975	+	0.269975i	0.559115	+	0.829090i	$0.311141\pi$
$242$	−671396.	+	671396.i	−0.0473732	+	0.0473732i
$243$	1.80986e6			0.126132
$244$		−	4.51552e6i		−	0.310841i
$245$	8.05708e6	−	8.05708e6i	0.547872	−	0.547872i
$246$			2.04517e6i			0.137380i
$247$	−3.86918e6	−	1.17032e7i	−0.256760	−	0.776632i
$248$	3.51041e6			0.230146
$249$	−2.06402e7	−	2.06402e7i	−1.33695	−	1.33695i
$250$	−1.29968e6			−0.0831795
$251$			8.07793e6i			0.510833i	0.966831	+	0.255416i	$0.0822125\pi$
$251$			8.07793e6i			0.510833i	−0.966831	+	0.255416i	$0.917787\pi$
$252$	258293.	+	258293.i	0.0161403	+	0.0161403i
$253$	6704.87	+	6704.87i	0.000414027	+	0.000414027i
$254$	119973.	−	119973.i	0.00732122	−	0.00732122i
$255$	1.74741e7	−	1.74741e7i	1.05384	−	1.05384i
$256$	1.57798e7			0.940549
$257$			2.38435e7i			1.40466i	0.711853	+	0.702329i	$0.247856\pi$
$257$			2.38435e7i			1.40466i	−0.711853	+	0.702329i	$0.752144\pi$
$258$	1.02638e6	−	1.02638e6i	0.0597653	−	0.0597653i
$259$			3.60403e6i			0.207438i
$260$	−1.48100e7	+	4.89628e6i	−0.842625	+	0.278578i
$261$	−991428.			−0.0557622
$262$	−928377.	−	928377.i	−0.0516203	−	0.0516203i
$263$	8.47441e6			0.465846			0.232923	−	0.972495i	$-0.425171\pi$
$263$	8.47441e6			0.465846			0.232923	+	0.972495i	$0.425171\pi$
$264$			1.07659e6i			0.0585113i
$265$	1.18639e7	+	1.18639e7i	0.637516	+	0.637516i
$266$	306558.	+	306558.i	0.0162880	+	0.0162880i
$267$	−2.07848e7	+	2.07848e7i	−1.09197	+	1.09197i
$268$	−1.13926e7	+	1.13926e7i	−0.591857	+	0.591857i
$269$	1.89267e7			0.972339			0.486170	−	0.873864i	$-0.338394\pi$
$269$	1.89267e7			0.972339			0.486170	+	0.873864i	$0.338394\pi$
$270$		−	1.31481e6i		−	0.0667994i
$271$	2.14982e7	−	2.14982e7i	1.08017	−	1.08017i	0.0836811	−	0.996493i	$-0.473332\pi$
$271$	2.14982e7	−	2.14982e7i	1.08017	−	1.08017i	0.996493	−	0.0836811i	$-0.0266677\pi$
$272$			3.19930e7i			1.58982i
$273$	7.24219e6	−	2.39432e6i	0.355944	−	0.117678i
$274$	2.02858e6			0.0986147
$275$	−1.09603e6	−	1.09603e6i	−0.0527016	−	0.0527016i
$276$	−34338.2			−0.00163324
$277$			3.57411e6i			0.168162i	0.996459	+	0.0840812i	$0.0267955\pi$
$277$			3.57411e6i			0.168162i	−0.996459	+	0.0840812i	$0.973204\pi$
$278$	−1.77054e6	−	1.77054e6i	−0.0824085	−	0.0824085i
$279$	1.44535e6	+	1.44535e6i	0.0665518	+	0.0665518i
$280$	778215.	−	778215.i	0.0354508	−	0.0354508i
$281$	1.97283e7	−	1.97283e7i	0.889142	−	0.889142i	−0.105299	−	0.994441i	$-0.533580\pi$
$281$	1.97283e7	−	1.97283e7i	0.889142	−	0.889142i	0.994441	+	0.105299i	$0.0335799\pi$
$282$	−2.08526e6			−0.0929850
$283$		−	1.08781e7i		−	0.479950i	−0.970779	−	0.239975i	$-0.922861\pi$
$283$		−	1.08781e7i		−	0.479950i	0.970779	−	0.239975i	$-0.0771392\pi$
$284$	−9.92326e6	+	9.92326e6i	−0.433211	+	0.433211i
$285$		−	1.74319e7i		−	0.753028i
$286$	594735.	+	299195.i	0.0254229	+	0.0127896i
$287$	1.47857e7			0.625457
$288$	−245906.	−	245906.i	−0.0102942	−	0.0102942i
$289$	−3.91227e7			−1.62082
$290$			1.48905e6i			0.0610541i
$291$	1.60562e7	+	1.60562e7i	0.651573	+	0.651573i
$292$	−2.87475e7	−	2.87475e7i	−1.15465	−	1.15465i
$293$	−1.48246e7	+	1.48246e7i	−0.589358	+	0.589358i	−0.937458	−	0.348099i	$-0.886827\pi$
$293$	−1.48246e7	+	1.48246e7i	−0.589358	+	0.589358i	0.348099	+	0.937458i	$0.386827\pi$
$294$	1.24533e6	−	1.24533e6i	0.0490052	−	0.0490052i
$295$	−3.82283e6			−0.148908
$296$		−	2.28517e6i		−	0.0881135i
$297$	6.57505e6	−	6.57505e6i	0.250975	−	0.250975i
$298$			1.08648e6i			0.0410557i
$299$	−19143.4	+	38052.9i	−0.000716152	+	0.00142356i
$300$	5.61318e6			0.207895
$301$	−7.42030e6	−	7.42030e6i	−0.272096	−	0.272096i
$302$	−1.07980e6			−0.0392033
$303$		−	4.68715e6i		−	0.168493i
$304$	1.59579e7	+	1.59579e7i	0.568007	+	0.568007i
$305$	−5.60155e6	−	5.60155e6i	−0.197428	−	0.197428i
$306$	160449.	−	160449.i	0.00559979	−	0.00559979i
$307$	−2.24431e7	+	2.24431e7i	−0.775652	+	0.775652i	−0.979088	−	0.203436i	$-0.934789\pi$
$307$	−2.24431e7	+	2.24431e7i	−0.775652	+	0.775652i	0.203436	+	0.979088i	$0.434789\pi$
$308$	3.87995e6			0.132793
$309$			898157.i			0.0304423i
$310$	2.17080e6	−	2.17080e6i	0.0728677	−	0.0728677i
$311$		−	4.42917e7i		−	1.47245i	−0.676735	−	0.736226i	$-0.736606\pi$
$311$		−	4.42917e7i		−	1.47245i	0.676735	−	0.736226i	$-0.263394\pi$
$312$	−4.59197e6	+	1.51814e6i	−0.151194	+	0.0499859i
$313$	1.35387e7			0.441514			0.220757	−	0.975329i	$-0.429147\pi$
$313$	1.35387e7			0.441514			0.220757	+	0.975329i	$0.429147\pi$
$314$	1.67558e6	+	1.67558e6i	0.0541224	+	0.0541224i
$315$	640831.			0.0205027
$316$		−	4.02282e7i		−	1.27488i
$317$	−1.14322e7	−	1.14322e7i	−0.358882	−	0.358882i	0.504519	−	0.863401i	$-0.331670\pi$
$317$	−1.14322e7	−	1.14322e7i	−0.358882	−	0.358882i	−0.863401	+	0.504519i	$0.831670\pi$
$318$	1.83373e6	+	1.83373e6i	0.0570235	+	0.0570235i
$319$	−7.44636e6	+	7.44636e6i	−0.229389	+	0.229389i
$320$	1.99466e7	−	1.99466e7i	0.608721	−	0.608721i
$321$	−2.06344e7			−0.623846
$322$		−	1498.22i		−	4.48753e-5i
$323$	−3.15538e7	+	3.15538e7i	−0.936362	+	0.936362i
$324$			3.58086e7i			1.05282i
$325$	3.12932e6	−	6.22041e6i	0.0911592	−	0.181205i
$326$	−2.41876e6			−0.0698137
$327$	2.46298e7	+	2.46298e7i	0.704398	+	0.704398i
$328$	−9.37503e6			−0.265675
$329$			1.50756e7i			0.423337i
$330$	665753.	+	665753.i	0.0185256	+	0.0185256i
$331$	4.21089e7	+	4.21089e7i	1.16115	+	1.16115i	0.984223	+	0.176930i	$0.0566166\pi$
$331$	4.21089e7	+	4.21089e7i	1.16115	+	1.16115i	0.176930	+	0.984223i	$0.443383\pi$
$332$	4.71648e7	−	4.71648e7i	1.28885	−	1.28885i
$333$	940875.	−	940875.i	0.0254800	−	0.0254800i
$334$	3.68730e6			0.0989622
$335$			2.82652e7i			0.751825i
$336$	−9.87502e6	+	9.87502e6i	−0.260328	+	0.260328i
$337$			8.70205e6i			0.227369i	0.993517	+	0.113685i	$0.0362654\pi$
$337$			8.70205e6i			0.227369i	−0.993517	+	0.113685i	$0.963735\pi$
$338$	−437496.	+	2.95862e6i	−0.0113298	+	0.0766194i
$339$	−8.13189e6			−0.208734
$340$	3.99300e7	+	3.99300e7i	1.01593	+	1.01593i
$341$	2.17113e7			0.547548
$342$		−	160061.i		−	0.00400136i
$343$	−1.93779e7	−	1.93779e7i	−0.480202	−	0.480202i
$344$	4.70491e6	+	4.70491e6i	0.115578	+	0.115578i
$345$	−42596.8	+	42596.8i	−0.00103734	+	0.00103734i
$346$	194490.	−	194490.i	0.00469536	−	0.00469536i
$347$	−2.58466e7			−0.618607			−0.309303	−	0.950963i	$-0.600096\pi$
$347$	−2.58466e7			−0.618607			−0.309303	+	0.950963i	$0.600096\pi$
$348$		−	3.81356e7i		−	0.904885i
$349$	7.46165e6	−	7.46165e6i	0.175533	−	0.175533i	−0.613872	−	0.789405i	$-0.710389\pi$
$349$	7.46165e6	−	7.46165e6i	0.175533	−	0.175533i	0.789405	+	0.613872i	$0.210389\pi$
$350$			244910.i			0.00571218i
$351$	3.73161e7	+	1.87727e7i	0.862929	+	0.434117i
$352$	−3.69388e6			−0.0846943
$353$	−3.16106e7	−	3.16106e7i	−0.718636	−	0.718636i	0.249690	−	0.968326i	$-0.419671\pi$
$353$	−3.16106e7	−	3.16106e7i	−0.718636	−	0.718636i	−0.968326	+	0.249690i	$0.919671\pi$
$354$	−590869.			−0.0133193
$355$			2.46198e7i			0.550300i
$356$	−4.74953e7	−	4.74953e7i	−1.05269	−	1.05269i
$357$	−1.95261e7	−	1.95261e7i	−0.429151	−	0.429151i
$358$	1.58815e6	−	1.58815e6i	0.0346132	−	0.0346132i
$359$	−2.80007e7	+	2.80007e7i	−0.605182	+	0.605182i	−0.941683	−	0.336501i	$-0.890756\pi$
$359$	−2.80007e7	+	2.80007e7i	−0.605182	+	0.605182i	0.336501	+	0.941683i	$0.390756\pi$
$360$	−406324.			−0.00870894
$361$		−	1.55683e7i		−	0.330918i
$362$	1.00769e6	−	1.00769e6i	0.0212423	−	0.0212423i
$363$		−	4.26610e7i		−	0.891890i
$364$	5.47125e6	+	1.65491e7i	0.113444	+	0.343139i
$365$	−7.13231e7			−1.46673
$366$	−865793.	−	865793.i	−0.0176592	−	0.0176592i
$367$	8.19304e7			1.65748			0.828738	−	0.559637i	$-0.189060\pi$
$367$	8.19304e7			1.65748			0.828738	+	0.559637i	$0.189060\pi$
$368$		−	77989.6i		−	0.00156492i
$369$	−3.85999e6	−	3.85999e6i	−0.0768259	−	0.0768259i
$370$	−1.41312e6	−	1.41312e6i	−0.0278981	−	0.0278981i
$371$	1.32571e7	−	1.32571e7i	0.259613	−	0.259613i
$372$	−5.55958e7	+	5.55958e7i	−1.07997	+	1.07997i
$373$	−1.53228e7			−0.295266			−0.147633	−	0.989042i	$-0.547165\pi$
$373$	−1.53228e7			−0.295266			−0.147633	+	0.989042i	$0.547165\pi$
$374$		−	2.41018e6i		−	0.0460717i
$375$	4.12913e7	−	4.12913e7i	0.783006	−	0.783006i
$376$		−	9.55879e6i		−	0.179821i
$377$	−4.22612e7	−	2.12605e7i	−0.788710	−	0.396779i
$378$	−1.46921e6			−0.0272025
$379$	−2.68687e7	−	2.68687e7i	−0.493548	−	0.493548i	0.415874	−	0.909422i	$-0.363476\pi$
$379$	−2.68687e7	−	2.68687e7i	−0.493548	−	0.493548i	−0.909422	+	0.415874i	$0.863476\pi$
$380$	3.98336e7			0.725937
$381$			7.62319e6i			0.137836i
$382$	−5.17086e6	−	5.17086e6i	−0.0927626	−	0.0927626i
$383$	6.48385e7	+	6.48385e7i	1.15408	+	1.15408i	0.985726	+	0.168355i	$0.0538454\pi$
$383$	6.48385e7	+	6.48385e7i	1.15408	+	1.15408i	0.168355	+	0.985726i	$0.446155\pi$
$384$	1.25990e7	−	1.25990e7i	0.222506	−	0.222506i
$385$	4.81312e6	−	4.81312e6i	0.0843421	−	0.0843421i
$386$	1.48888e6			0.0258880
$387$			3.87432e6i			0.0668440i
$388$	−3.66899e7	+	3.66899e7i	−0.628132	+	0.628132i
$389$		−	7.35682e6i		−	0.124980i	−0.998046	−	0.0624901i	$-0.980096\pi$
$389$		−	7.35682e6i		−	0.124980i	0.998046	−	0.0624901i	$-0.0199042\pi$
$390$	−1.90082e6	+	3.77842e6i	−0.0320441	+	0.0636967i
$391$	154210.			0.00257978
$392$	5.70856e6	+	5.70856e6i	0.0947694	+	0.0947694i
$393$	5.89897e7			0.971849
$394$			662055.i			0.0108244i
$395$	−4.99035e7	−	4.99035e7i	−0.809730	−	0.809730i
$396$	−1.01291e6	−	1.01291e6i	−0.0163111	−	0.0163111i
$397$	−2.80659e6	+	2.80659e6i	−0.0448546	+	0.0448546i	−0.729178	−	0.684324i	$-0.760098\pi$
$397$	−2.80659e6	+	2.80659e6i	−0.0448546	+	0.0448546i	0.684324	+	0.729178i	$0.260098\pi$
$398$	2.72586e6	−	2.72586e6i	0.0432369	−	0.0432369i
$399$	−1.94789e7			−0.306652
$400$			1.27488e7i			0.199199i
$401$	1.67749e6	−	1.67749e6i	0.0260152	−	0.0260152i	−0.693980	−	0.719995i	$-0.744144\pi$
$401$	1.67749e6	−	1.67749e6i	0.0260152	−	0.0260152i	0.719995	+	0.693980i	$0.244144\pi$
$402$			4.36876e6i			0.0672480i
$403$	3.06158e7	+	9.26046e7i	0.467768	+	1.41487i
$404$	1.07106e7			0.162431
$405$	4.44209e7	+	4.44209e7i	0.668687	+	0.668687i
$406$	1.66390e6			0.0248628
$407$		−	1.41333e7i		−	0.209634i
$408$	1.23807e7	+	1.23807e7i	0.182290	+	0.182290i
$409$	−1.08063e7	−	1.08063e7i	−0.157945	−	0.157945i	0.623710	−	0.781656i	$-0.285624\pi$
$409$	−1.08063e7	−	1.08063e7i	−0.157945	−	0.157945i	−0.781656	+	0.623710i	$0.785624\pi$
$410$	−5.79741e6	+	5.79741e6i	−0.0841168	+	0.0841168i
$411$	−6.44489e7	+	6.44489e7i	−0.928303	+	0.928303i
$412$	−2.05237e6			−0.0293471
$413$			4.27174e6i			0.0606393i
$414$	−391.127	+	391.127i	−5.51210e−6	+	5.51210e-6i
$415$		−	1.17017e8i		−	1.63721i
$416$	−5.20885e6	−	1.57554e7i	−0.0723539	−	0.218852i
$417$	1.12502e8			1.55150
$418$	−1.20218e6	−	1.20218e6i	−0.0164604	−	0.0164604i
$419$	4.55034e7			0.618588			0.309294	−	0.950966i	$-0.399907\pi$
$419$	4.55034e7			0.618588			0.309294	+	0.950966i	$0.399907\pi$
$420$			2.46498e7i			0.332710i
$421$	6.74507e7	+	6.74507e7i	0.903941	+	0.903941i	0.995774	−	0.0918335i	$-0.0292727\pi$
$421$	6.74507e7	+	6.74507e7i	0.903941	+	0.903941i	−0.0918335	+	0.995774i	$0.529273\pi$
$422$	−1.53669e6	−	1.53669e6i	−0.0204479	−	0.0204479i
$423$	3.93566e6	−	3.93566e6i	0.0519991	−	0.0519991i
$424$	−8.40578e6	+	8.40578e6i	−0.110276	+	0.110276i
$425$	−2.52084e7			−0.328381
$426$			3.80532e6i			0.0492223i
$427$	−6.25932e6	+	6.25932e6i	−0.0803977	+	0.0803977i
$428$		−	4.71516e7i		−	0.601403i
$429$	−2.84005e7	+	9.38941e6i	−0.359711	+	0.118923i
$430$	5.81892e6			0.0731876
$431$	−1.24974e7	−	1.24974e7i	−0.156095	−	0.156095i	0.624739	−	0.780834i	$-0.285205\pi$
$431$	−1.24974e7	−	1.24974e7i	−0.156095	−	0.156095i	−0.780834	+	0.624739i	$0.785205\pi$
$432$	−7.64795e7			−0.948624
$433$		−	5.37286e7i		−	0.661823i	−0.943662	−	0.330912i	$-0.892644\pi$
$433$		−	5.37286e7i		−	0.661823i	0.943662	−	0.330912i	$-0.107356\pi$
$434$	−2.42571e6	−	2.42571e6i	−0.0296736	−	0.0296736i
$435$	−4.73076e7	−	4.73076e7i	−0.574729	−	0.574729i
$436$	−5.62815e7	+	5.62815e7i	−0.679057	+	0.679057i
$437$	76918.9	−	76918.9i	0.000921699	−	0.000921699i
$438$	−1.10239e7			−0.131194
$439$		−	1.32374e8i		−	1.56462i	−0.622891	−	0.782308i	$-0.714042\pi$
$439$		−	1.32374e8i		−	1.56462i	0.622891	−	0.782308i	$-0.285958\pi$
$440$	−3.05180e6	+	3.05180e6i	−0.0358260	+	0.0358260i
$441$			4.70079e6i			0.0548093i
$442$	1.02801e7	−	3.39867e6i	0.119050	−	0.0393588i
$443$	−5.85636e7			−0.673623			−0.336811	−	0.941572i	$-0.609348\pi$
$443$	−5.85636e7			−0.673623			−0.336811	+	0.941572i	$0.609348\pi$
$444$	3.61911e7	+	3.61911e7i	0.413478	+	0.413478i
$445$	−1.17837e8			−1.33721
$446$			4.18732e6i			0.0471988i
$447$	−3.45179e7	−	3.45179e7i	−0.386475	−	0.386475i
$448$	−2.22888e7	−	2.22888e7i	−0.247887	−	0.247887i
$449$	4.08359e7	−	4.08359e7i	0.451132	−	0.451132i	−0.444598	−	0.895730i	$-0.646654\pi$
$449$	4.08359e7	−	4.08359e7i	0.451132	−	0.451132i	0.895730	+	0.444598i	$0.146654\pi$
$450$	63936.6	−	63936.6i	0.000701636	−	0.000701636i
$451$	−5.79829e7			−0.632077
$452$		−	1.85821e7i		−	0.201224i
$453$	3.43056e7	−	3.43056e7i	0.369038	−	0.369038i
$454$			4.35176e6i			0.0465048i
$455$	2.73164e7	+	1.37422e7i	0.289994	+	0.145888i
$456$	1.23508e7			0.130257
$457$	7.64845e7	+	7.64845e7i	0.801354	+	0.801354i	0.983307	−	0.181953i	$-0.0582418\pi$
$457$	7.64845e7	+	7.64845e7i	0.801354	+	0.801354i	−0.181953	+	0.983307i	$0.558242\pi$
$458$	8.94099e6			0.0930656
$459$		−	1.51224e8i		−	1.56381i
$460$	−97337.8	−	97337.8i	−0.00100002	−	0.00100002i
$461$	8.91531e7	+	8.91531e7i	0.909984	+	0.909984i	0.996270	−	0.0862866i	$-0.0275001\pi$
$461$	8.91531e7	+	8.91531e7i	0.909984	+	0.909984i	−0.0862866	+	0.996270i	$0.527500\pi$
$462$	743931.	−	743931.i	0.00754409	−	0.00754409i
$463$	3.63044e7	−	3.63044e7i	0.365777	−	0.365777i	−0.500158	−	0.865934i	$-0.666725\pi$
$463$	3.63044e7	−	3.63044e7i	0.365777	−	0.365777i	0.865934	+	0.500158i	$0.166725\pi$
$464$	8.66144e7			0.867034
$465$			1.37934e8i			1.37187i
$466$	−5.88572e6	+	5.88572e6i	−0.0581623	+	0.0581623i
$467$			1.55723e8i			1.52898i	0.644633	+	0.764492i	$0.277010\pi$
$467$			1.55723e8i			1.52898i	−0.644633	+	0.764492i	$0.722990\pi$
$468$	2.89200e6	−	5.74867e6i	0.0282137	−	0.0560828i
$469$	3.15843e7			0.306163
$470$	−5.91105e6	−	5.91105e6i	−0.0569339	−	0.0569339i
$471$	−1.06468e8			−1.01896
$472$		−	2.70853e6i		−	0.0257577i
$473$	2.90990e7	+	2.90990e7i	0.274976	+	0.274976i
$474$	−7.71325e6	−	7.71325e6i	−0.0724273	−	0.0724273i
$475$	−1.25737e7	+	1.25737e7i	−0.117323	+	0.117323i
$476$	4.46189e7	−	4.46189e7i	0.413712	−	0.413712i
$477$	−6.92185e6			−0.0637774
$478$			962529.i			0.00881313i
$479$	−1.29914e8	+	1.29914e8i	−1.18208	+	1.18208i	−0.202881	+	0.979203i	$0.565030\pi$
$479$	−1.29914e8	+	1.29914e8i	−1.18208	+	1.18208i	−0.979203	+	0.202881i	$0.934970\pi$
$480$		−	2.34676e7i		−	0.212200i
$481$	6.02826e7	−	1.99299e7i	0.541698	−	0.179089i
$482$	−3.31143e6			−0.0295716
$483$	47598.9	+	47598.9i	0.000422431	+	0.000422431i
$484$	9.74844e7			0.859803
$485$			9.10283e7i			0.797905i
$486$	792967.	+	792967.i	0.00690790	+	0.00690790i
$487$	−1.29458e8	−	1.29458e8i	−1.12083	−	1.12083i	−0.991616	−	0.129219i	$-0.958753\pi$
$487$	−1.29458e8	−	1.29458e8i	−1.12083	−	1.12083i	−0.129219	−	0.991616i	$-0.541247\pi$
$488$	3.96878e6	−	3.96878e6i	0.0341505	−	0.0341505i
$489$	7.68450e7	−	7.68450e7i	0.657187	−	0.657187i
$490$	7.06022e6			0.0600108
$491$			6.12521e7i			0.517460i	0.965950	+	0.258730i	$0.0833039\pi$
$491$			6.12521e7i			0.517460i	−0.965950	+	0.258730i	$0.916696\pi$
$492$	1.48476e8	−	1.48476e8i	1.24670	−	1.24670i
$493$			1.71264e8i			1.42931i
$494$	3.43240e6	−	6.82286e6i	0.0284719	−	0.0565960i
$495$	−2.51304e6			−0.0207197
$496$	−1.26270e8	−	1.26270e8i	−1.03480	−	1.03480i
$497$	2.75108e7			0.224096
$498$		−	1.80865e7i		−	0.146442i
$499$	1.30676e7	+	1.30676e7i	0.105171	+	0.105171i	0.757734	−	0.652563i	$-0.226306\pi$
$499$	1.30676e7	+	1.30676e7i	0.105171	+	0.105171i	−0.652563	+	0.757734i	$0.726306\pi$
$500$	9.43545e7	+	9.43545e7i	0.754836	+	0.754836i
$501$	−1.17147e8	+	1.17147e8i	−0.931575	+	0.931575i
$502$	−3.53924e6	+	3.53924e6i	−0.0279769	+	0.0279769i
$503$	2.02329e8			1.58984			0.794922	−	0.606711i	$-0.207512\pi$
$503$	2.02329e8			1.58984			0.794922	+	0.606711i	$0.207512\pi$
$504$			454038.i			0.00354651i
$505$	1.32866e7	−	1.32866e7i	0.103167	−	0.103167i
$506$			5875.31i			4.53502e-5i
$507$	−8.00969e7	−	1.07896e8i	−0.614599	−	0.827905i
$508$	−1.74197e7			−0.132877
$509$	−7.33599e7	−	7.33599e7i	−0.556295	−	0.556295i	0.371955	−	0.928251i	$-0.378687\pi$
$509$	−7.33599e7	−	7.33599e7i	−0.556295	−	0.556295i	−0.928251	+	0.371955i	$0.878687\pi$
$510$	1.53121e7			0.115432
$511$			7.96984e7i			0.597292i
$512$	3.58773e7	+	3.58773e7i	0.267306	+	0.267306i
$513$	−7.54296e7	−	7.54296e7i	−0.558714	−	0.558714i
$514$	−1.04467e7	+	1.04467e7i	−0.0769292	+	0.0769292i
$515$	−2.54599e6	+	2.54599e6i	−0.0186395	+	0.0186395i
$516$	−1.49027e8			−1.08471
$517$		−	5.91194e7i		−	0.427817i
$518$	−1.57906e6	+	1.57906e6i	−0.0113608	+	0.0113608i
$519$			1.23580e7i			0.0883990i
$520$	−1.73202e7	−	8.71333e6i	−0.123181	−	0.0619690i
$521$	−2.56095e8			−1.81087			−0.905437	−	0.424481i	$-0.860456\pi$
$521$	−2.56095e8			−1.81087			−0.905437	+	0.424481i	$0.860456\pi$
$522$	−434382.	−	434382.i	−0.00305394	−	0.00305394i
$523$	−1.51258e8			−1.05734			−0.528668	−	0.848828i	$-0.677308\pi$
$523$	−1.51258e8			−1.05734			−0.528668	+	0.848828i	$0.677308\pi$
$524$			1.34797e8i			0.936886i
$525$	−7.78088e6	−	7.78088e6i	−0.0537713	−	0.0537713i
$526$	3.71296e6	+	3.71296e6i	0.0255131	+	0.0255131i
$527$	2.49677e8	−	2.49677e8i	1.70587	−	1.70587i
$528$	3.87253e7	−	3.87253e7i	0.263083	−	0.263083i
$529$	1.48036e8			0.999997
$530$			1.03961e7i			0.0698300i
$531$	1.11519e6	−	1.11519e6i	0.00744842	−	0.00744842i
$532$		−	4.45112e7i		−	0.295620i
$533$	−8.17635e7	−	2.47313e8i	−0.539980	−	1.63330i
$534$	−1.82132e7			−0.119609
$535$	−5.84921e7	−	5.84921e7i	−0.381976	−	0.381976i
$536$	−2.00263e7			−0.130049
$537$			1.00912e8i			0.651660i
$538$	8.29249e6	+	8.29249e6i	0.0532523	+	0.0532523i
$539$	3.53064e7	+	3.53064e7i	0.225469	+	0.225469i
$540$	−9.54532e7	+	9.54532e7i	−0.606190	+	0.606190i
$541$	1.29927e8	−	1.29927e8i	0.820552	−	0.820552i	−0.165635	−	0.986187i	$-0.552967\pi$
$541$	1.29927e8	−	1.29927e8i	0.820552	−	0.820552i	0.986187	+	0.165635i	$0.0529675\pi$
$542$	1.88383e7			0.118316
$543$			6.40294e7i			0.399926i
$544$	−4.24791e7	+	4.24791e7i	−0.263863	+	0.263863i
$545$			1.39636e8i			0.862594i
$546$	4.22212e6	+	2.12403e6i	0.0259389	+	0.0130492i
$547$	2.28364e8			1.39530			0.697648	−	0.716441i	$-0.254230\pi$
$547$	2.28364e8			1.39530			0.697648	+	0.716441i	$0.254230\pi$
$548$	−1.47272e8	−	1.47272e8i	−0.894907	−	0.894907i
$549$	3.26814e6			0.0197508
$550$		−	960423.i		−	0.00577264i
$551$	8.54254e7	+	8.54254e7i	0.510660	+	0.510660i
$552$	−30180.5	−	30180.5i	−0.000179436	−	0.000179436i
$553$	−5.57636e7	+	5.57636e7i	−0.329743	+	0.329743i
$554$	−1.56595e6	+	1.56595e6i	−0.00920978	+	0.00920978i
$555$	8.97908e7			0.525234
$556$			2.57077e8i			1.49568i
$557$	1.46612e7	−	1.46612e7i	0.0848409	−	0.0848409i	−0.663413	−	0.748254i	$-0.730893\pi$
$557$	1.46612e7	−	1.46612e7i	0.0848409	−	0.0848409i	0.748254	+	0.663413i	$0.230893\pi$
$558$			1.26652e6i			0.00728971i
$559$	−8.30819e7	+	1.65149e8i	−0.475632	+	0.945453i
$560$	−5.59851e7			−0.318793
$561$	7.65722e7	+	7.65722e7i	0.433693	+	0.433693i
$562$	1.72874e7			0.0973916
$563$			1.66734e8i			0.934327i	0.884171	+	0.467163i	$0.154724\pi$
$563$			1.66734e8i			0.934327i	−0.884171	+	0.467163i	$0.845276\pi$
$564$	1.51386e8	+	1.51386e8i	0.843819	+	0.843819i
$565$	−2.30513e7	−	2.30513e7i	−0.127806	−	0.127806i
$566$	4.76613e6	−	4.76613e6i	0.0262855	−	0.0262855i
$567$	4.96372e7	−	4.96372e7i	0.272306	−	0.272306i
$568$	−1.74435e7			−0.0951893
$569$		−	2.22715e8i		−	1.20896i	−0.796620	−	0.604481i	$-0.793381\pi$
$569$		−	2.22715e8i		−	1.20896i	0.796620	−	0.604481i	$-0.206619\pi$
$570$	7.63758e6	−	7.63758e6i	0.0412412	−	0.0412412i
$571$		−	6.64884e7i		−	0.357139i	−0.983927	−	0.178570i	$-0.942853\pi$
$571$		−	6.64884e7i		−	0.357139i	0.983927	−	0.178570i	$-0.0571470\pi$
$572$	−2.14557e7	−	6.48978e7i	−0.114645	−	0.346770i
$573$	3.28560e8			1.74643
$574$	6.47819e6	+	6.47819e6i	0.0342545	+	0.0342545i
$575$	61450.7			0.000323239
$576$			1.16375e7i			0.0608967i
$577$	−5.11978e7	−	5.11978e7i	−0.266516	−	0.266516i	0.561179	−	0.827695i	$-0.310348\pi$
$577$	−5.11978e7	−	5.11978e7i	−0.266516	−	0.266516i	−0.827695	+	0.561179i	$0.810348\pi$
$578$	−1.71411e7	−	1.71411e7i	−0.0887680	−	0.0887680i
$579$	−4.73024e7	+	4.73024e7i	−0.243696	+	0.243696i
$580$	1.08102e8	−	1.08102e8i	0.554053	−	0.554053i
$581$	−1.30758e8			−0.666714
$582$			1.40696e7i			0.0713697i
$583$	−5.19882e7	+	5.19882e7i	−0.262361	+	0.262361i
$584$		−	5.05334e7i		−	0.253712i
$585$	−3.54372e6	−	1.07188e7i	−0.0177008	−	0.0535402i
$586$	−1.29904e7			−0.0645550
$587$	2.22439e7	+	2.22439e7i	0.109975	+	0.109975i	0.759953	−	0.649978i	$-0.225222\pi$
$587$	2.22439e7	+	2.22439e7i	0.109975	+	0.109975i	−0.649978	+	0.759953i	$0.725222\pi$
$588$	−1.80817e8			−0.889422
$589$		−	2.49074e8i		−	1.21894i
$590$	−1.67493e6	−	1.67493e6i	−0.00815529	−	0.00815529i
$591$	−2.10337e7	−	2.10337e7i	−0.101895	−	0.101895i
$592$	−8.21979e7	+	8.21979e7i	−0.396183	+	0.396183i
$593$	−7.89052e7	+	7.89052e7i	−0.378391	+	0.378391i	−0.870522	−	0.492130i	$-0.836218\pi$
$593$	−7.89052e7	+	7.89052e7i	−0.378391	+	0.378391i	0.492130	+	0.870522i	$0.336218\pi$
$594$	5.76156e6			0.0274904
$595$		−	1.10700e8i		−	0.525531i
$596$	7.88767e7	−	7.88767e7i	0.372572	−	0.372572i
$597$			1.73203e8i			0.814017i
$598$	−25059.8	+	8284.97i	−0.000117186	+	3.87425e-5i
$599$	−3.53483e8			−1.64471			−0.822353	−	0.568978i	$-0.807339\pi$
$599$	−3.53483e8			−1.64471			−0.822353	+	0.568978i	$0.807339\pi$
$600$	4.93353e6	+	4.93353e6i	0.0228404	+	0.0228404i
$601$	−2.13718e8			−0.984502			−0.492251	−	0.870453i	$-0.663826\pi$
$601$	−2.13718e8			−0.984502			−0.492251	+	0.870453i	$0.663826\pi$
$602$		−	6.50223e6i		−	0.0298039i
$603$	−8.24545e6	−	8.24545e6i	−0.0376065	−	0.0376065i
$604$	7.83916e7	+	7.83916e7i	0.355761	+	0.355761i
$605$	1.20930e8	−	1.20930e8i	0.546096	−	0.546096i
$606$	2.05362e6	−	2.05362e6i	0.00922787	−	0.00922787i
$607$	2.14913e8			0.960939			0.480470	−	0.877011i	$-0.340466\pi$
$607$	2.14913e8			0.960939			0.480470	+	0.877011i	$0.340466\pi$
$608$			4.23765e7i			0.188545i
$609$	−5.28629e7	+	5.28629e7i	−0.234045	+	0.234045i
$610$		−	4.90850e6i		−	0.0216251i
$611$	2.52161e8	−	8.33662e7i	1.10549	−	0.365482i
$612$	−2.32966e7			−0.101634
$613$	2.01248e8	+	2.01248e8i	0.873675	+	0.873675i	0.992871	−	0.119195i	$-0.0380315\pi$
$613$	2.01248e8	+	2.01248e8i	0.873675	+	0.873675i	−0.119195	+	0.992871i	$0.538032\pi$
$614$	−1.96663e7			−0.0849606
$615$		−	3.68372e8i		−	1.58366i
$616$	3.41017e6	+	3.41017e6i	0.0145893	+	0.0145893i
$617$	−2.93439e8	−	2.93439e8i	−1.24929	−	1.24929i	−0.956036	−	0.293250i	$-0.905263\pi$
$617$	−2.93439e8	−	2.93439e8i	−1.24929	−	1.24929i	−0.293250	−	0.956036i	$-0.594737\pi$
$618$	−393516.	+	393516.i	−0.00166724	+	0.00166724i
$619$	−1.08664e8	+	1.08664e8i	−0.458156	+	0.458156i	−0.898050	−	0.439894i	$-0.855016\pi$
$619$	−1.08664e8	+	1.08664e8i	−0.458156	+	0.458156i	0.439894	+	0.898050i	$0.355016\pi$
$620$	−3.15193e8			−1.32252
$621$			368641.i			0.00153932i
$622$	1.94059e7	−	1.94059e7i	0.0806421	−	0.0806421i
$623$			1.31674e8i			0.544548i
$624$	2.19782e8	+	1.10566e8i	0.904561	+	0.455060i
$625$	1.84573e8			0.756012
$626$	5.93182e6	+	5.93182e6i	0.0241805	+	0.0241805i
$627$	7.63873e7			0.309898
$628$		−	2.43289e8i		−	0.982298i
$629$	−1.62531e8	−	1.62531e8i	−0.653109	−	0.653109i
$630$	280772.	+	280772.i	0.00112288	+	0.00112288i
$631$	−2.20637e8	+	2.20637e8i	−0.878194	+	0.878194i	−0.993348	−	0.115153i	$-0.963264\pi$
$631$	−2.20637e8	+	2.20637e8i	−0.878194	+	0.878194i	0.115153	+	0.993348i	$0.463264\pi$
$632$	3.53574e7	−	3.53574e7i	0.140065	−	0.140065i
$633$	9.76422e7			0.384970
$634$		−	1.00178e7i		−	0.0393100i
$635$	−2.16093e7	+	2.16093e7i	−0.0843956	+	0.0843956i
$636$		−	2.66251e8i		−	1.03495i
$637$	−1.00805e8	+	2.00378e8i	−0.389999	+	0.775233i
$638$	−6.52506e6			−0.0251260
$639$	−7.18203e6	−	7.18203e6i	−0.0275261	−	0.0275261i
$640$	7.14280e7			0.272476
$641$			2.50036e8i			0.949355i	0.880160	+	0.474677i	$0.157435\pi$
$641$			2.50036e8i			0.949355i	−0.880160	+	0.474677i	$0.842565\pi$
$642$	−9.04073e6	−	9.04073e6i	−0.0341663	−	0.0341663i
$643$	2.84330e7	+	2.84330e7i	0.106952	+	0.106952i	0.758558	−	0.651606i	$-0.225904\pi$
$643$	2.84330e7	+	2.84330e7i	0.106952	+	0.106952i	−0.651606	+	0.758558i	$0.725904\pi$
$644$	−108768.	+	108768.i	−0.000407233	+	0.000407233i
$645$	−1.84869e8	+	1.84869e8i	−0.688947	+	0.688947i
$646$	−2.76498e7			−0.102564
$647$			1.49390e7i			0.0551580i	0.999620	+	0.0275790i	$0.00877977\pi$
$647$			1.49390e7i			0.0551580i	−0.999620	+	0.0275790i	$0.991220\pi$
$648$	−3.14729e7	+	3.14729e7i	−0.115668	+	0.115668i
$649$		−	1.67518e7i		−	0.0612811i
$650$	4.09647e6	−	1.35432e6i	0.0149166	−	0.00493154i
$651$	1.54132e8			0.558662
$652$	1.75598e8	+	1.75598e8i	0.633544	+	0.633544i
$653$	4.23252e8			1.52005			0.760027	−	0.649891i	$-0.225186\pi$
$653$	4.23252e8			1.52005			0.760027	+	0.649891i	$0.225186\pi$
$654$			2.15825e7i			0.0771559i
$655$	1.67217e8	+	1.67217e8i	0.595055	+	0.595055i
$656$	3.37222e8	+	3.37222e8i	1.19455	+	1.19455i
$657$	2.08062e7	−	2.08062e7i	0.0733663	−	0.0733663i
$658$	−6.60517e6	+	6.60517e6i	−0.0231850	+	0.0231850i
$659$	2.48537e7			0.0868431			0.0434216	−	0.999057i	$-0.486174\pi$
$659$	2.48537e7			0.0868431			0.0434216	+	0.999057i	$0.486174\pi$
$660$		−	9.66651e7i		−	0.336231i
$661$	2.32320e8	−	2.32320e8i	0.804420	−	0.804420i	−0.179363	−	0.983783i	$-0.557404\pi$
$661$	2.32320e8	−	2.32320e8i	0.804420	−	0.804420i	0.983783	+	0.179363i	$0.0574036\pi$
$662$			3.68990e7i			0.127186i
$663$	−2.18625e8	+	4.34579e8i	−0.750169	+	1.49117i
$664$	8.29081e7			0.283200
$665$	−5.52166e7	−	5.52166e7i	−0.187761	−	0.187761i
$666$	824465.			0.00279093
$667$		−	417493.i		−	0.00140693i
$668$	−2.67692e8	−	2.67692e8i	−0.898060	−	0.898060i
$669$	−1.33033e8	−	1.33033e8i	−0.444303	−	0.444303i
$670$	−1.23840e7	+	1.23840e7i	−0.0411754	+	0.0411754i
$671$	2.45462e7	−	2.45462e7i	0.0812487	−	0.0812487i
$672$	−2.62234e7			−0.0864134
$673$			1.53748e8i			0.504388i	0.967677	+	0.252194i	$0.0811520\pi$
$673$			1.53748e8i			0.504388i	−0.967677	+	0.252194i	$0.918848\pi$
$674$	−3.81270e6	+	3.81270e6i	−0.0124524	+	0.0124524i
$675$		−	6.02609e7i		−	0.195940i
$676$	2.46552e8	−	1.83029e8i	0.798120	−	0.592488i
$677$	−2.80955e8			−0.905464			−0.452732	−	0.891647i	$-0.649551\pi$
$677$	−2.80955e8			−0.905464			−0.452732	+	0.891647i	$0.649551\pi$
$678$	−3.56289e6	−	3.56289e6i	−0.0114318	−	0.0114318i
$679$	1.01718e8			0.324927
$680$			7.01905e7i			0.223230i
$681$	−1.38257e8	−	1.38257e8i	−0.437770	−	0.437770i
$682$	9.51253e6	+	9.51253e6i	0.0299877	+	0.0299877i
$683$	3.38825e8	−	3.38825e8i	1.06344	−	1.06344i	0.0655951	−	0.997846i	$-0.479105\pi$
$683$	3.38825e8	−	3.38825e8i	1.06344	−	1.06344i	0.997846	−	0.0655951i	$-0.0208946\pi$
$684$	−1.16202e7	+	1.16202e7i	−0.0363115	+	0.0363115i
$685$	−3.65384e8			−1.13678
$686$		−	1.69804e7i		−	0.0525986i
$687$	−2.84059e8	+	2.84059e8i	−0.876068	+	0.876068i
$688$		−	3.38473e8i		−	1.03934i
$689$	−2.95054e8	−	1.48434e8i	−0.902079	−	0.453812i
$690$	−37326.6			−0.000113624
$691$	−1.75432e8	−	1.75432e8i	−0.531710	−	0.531710i	0.389371	−	0.921081i	$-0.372692\pi$
$691$	−1.75432e8	−	1.75432e8i	−0.531710	−	0.531710i	−0.921081	+	0.389371i	$0.872692\pi$
$692$	−2.82393e7			−0.0852188
$693$			2.80814e6i			0.00843762i
$694$	−1.13244e7	−	1.13244e7i	−0.0338793	−	0.0338793i
$695$	3.18906e8	+	3.18906e8i	0.949967	+	0.949967i
$696$	3.35181e7	−	3.35181e7i	0.0994151	−	0.0994151i
$697$	−6.66795e8	+	6.66795e8i	−1.96922	+	1.96922i
$698$	6.53846e6			0.0192269
$699$		−	3.73983e8i		−	1.09502i
$700$	1.77800e7	−	1.77800e7i	0.0518368	−	0.0518368i
$701$		−	5.62829e8i		−	1.63389i	−0.576717	−	0.816944i	$-0.695666\pi$
$701$		−	5.62829e8i		−	1.63389i	0.576717	−	0.816944i	$-0.304334\pi$
$702$	8.12456e6	+	2.45746e7i	0.0234849	+	0.0710356i
$703$	−1.62139e8			−0.466682
$704$	8.74065e7	+	8.74065e7i	0.250510	+	0.250510i
$705$	3.75592e8			1.07189
$706$		−	2.76996e7i		−	0.0787154i
$707$	−1.48468e7	−	1.48468e7i	−0.0420121	−	0.0420121i
$708$	4.28961e7	+	4.28961e7i	0.120870	+	0.120870i
$709$	3.11558e8	−	3.11558e8i	0.874178	−	0.874178i	−0.118747	−	0.992925i	$-0.537888\pi$
$709$	3.11558e8	−	3.11558e8i	0.874178	−	0.874178i	0.992925	+	0.118747i	$0.0378877\pi$
$710$	−1.07869e7	+	1.07869e7i	−0.0301384	+	0.0301384i
$711$	2.91155e7			0.0810057
$712$		−	8.34890e7i		−	0.231307i
$713$	−608639.	+	608639.i	−0.00167916	+	0.00167916i
$714$		−	1.71102e7i		−	0.0470068i
$715$	−1.07122e8	−	5.38904e7i	−0.293064	−	0.147432i
$716$	−2.30594e8			−0.628216
$717$	−3.05799e7	−	3.05799e7i	−0.0829619	−	0.0829619i
$718$	−2.45363e7			−0.0662882
$719$			6.30506e8i			1.69630i	0.529756	+	0.848150i	$0.322284\pi$
$719$			6.30506e8i			1.69630i	−0.529756	+	0.848150i	$0.677716\pi$
$720$	1.46156e7	+	1.46156e7i	0.0391578	+	0.0391578i
$721$	2.84496e6	+	2.84496e6i	0.00759050	+	0.00759050i
$722$	6.82106e6	−	6.82106e6i	0.0181234	−	0.0181234i
$723$	1.05205e8	−	1.05205e8i	0.278370	−	0.278370i
$724$	−1.46313e8			−0.385538
$725$			6.82465e7i			0.179088i
$726$	1.86914e7	−	1.86914e7i	0.0488463	−	0.0488463i
$727$		−	8.11038e6i		−	0.0211076i	−0.999944	−	0.0105538i	$-0.996641\pi$
$727$		−	8.11038e6i		−	0.0211076i	0.999944	−	0.0105538i	$-0.00335943\pi$
$728$	−9.73652e6	+	1.93541e7i	−0.0252354	+	0.0501624i
$729$	3.59958e8			0.929115
$730$	−3.12493e7	−	3.12493e7i	−0.0803289	−	0.0803289i
$731$	6.69269e8			1.71336
$732$			1.25710e8i			0.320507i
$733$	−1.68410e8	−	1.68410e8i	−0.427619	−	0.427619i	0.460197	−	0.887817i	$-0.347779\pi$
$733$	−1.68410e8	−	1.68410e8i	−0.427619	−	0.427619i	−0.887817	+	0.460197i	$0.847779\pi$
$734$	3.58968e7	+	3.58968e7i	0.0907753	+	0.0907753i
$735$	−2.24306e8	+	2.24306e8i	−0.564909	+	0.564909i
$736$	103552.	−	103552.i	0.000259731	−	0.000259731i
$737$	−1.23859e8			−0.309403
$738$		−	3.38242e6i		−	0.00841508i
$739$	1.32537e8	−	1.32537e8i	0.328400	−	0.328400i	−0.523578	−	0.851978i	$-0.675403\pi$
$739$	1.32537e8	−	1.32537e8i	0.328400	−	0.328400i	0.851978	+	0.523578i	$0.175403\pi$
$740$			2.05180e8i			0.506338i
$741$	1.07716e8	+	3.25813e8i	0.264744	+	0.800782i
$742$	1.16169e7			0.0284366
$743$	5.62970e7	+	5.62970e7i	0.137252	+	0.137252i	0.772395	−	0.635143i	$-0.219059\pi$
$743$	5.62970e7	+	5.62970e7i	0.137252	+	0.137252i	−0.635143	+	0.772395i	$0.719059\pi$
$744$	−9.77285e7			−0.237303
$745$		−	1.95695e8i		−	0.473271i
$746$	−6.71351e6	−	6.71351e6i	−0.0161709	−	0.0161709i
$747$	3.41359e7	+	3.41359e7i	0.0818935	+	0.0818935i
$748$	−1.74975e8	+	1.74975e8i	−0.418091	+	0.418091i
$749$	−6.53607e7	+	6.53607e7i	−0.155550	+	0.155550i
$750$	3.61826e7			0.0857660
$751$		−	1.81307e8i		−	0.428050i	−0.976828	−	0.214025i	$-0.931343\pi$
$751$		−	1.81307e8i		−	0.428050i	0.976828	−	0.214025i	$-0.0686574\pi$
$752$	−3.43832e8	+	3.43832e8i	−0.808523	+	0.808523i
$753$		−	2.24886e8i		−	0.526717i
$754$	−9.20120e6	−	2.78312e7i	−0.0214650	−	0.0649259i
$755$	1.94491e8			0.451917
$756$	1.06662e8	+	1.06662e8i	0.246856	+	0.246856i
$757$	1.39909e8			0.322522			0.161261	−	0.986912i	$-0.448444\pi$
$757$	1.39909e8			0.322522			0.161261	+	0.986912i	$0.448444\pi$
$758$		−	2.35444e7i		−	0.0540605i
$759$	−186661.	−	186661.i	−0.000426902	−	0.000426902i
$760$	3.50105e7	+	3.50105e7i	0.0797550	+	0.0797550i
$761$	4.96372e8	−	4.96372e8i	1.12630	−	1.12630i	0.135523	−	0.990774i	$-0.456728\pi$
$761$	4.96372e8	−	4.96372e8i	1.12630	−	1.12630i	0.990774	−	0.135523i	$-0.0432715\pi$
$762$	−3.34000e6	+	3.34000e6i	−0.00754887	+	0.00754887i
$763$	1.56033e8			0.351271
$764$			7.50791e8i			1.68360i
$765$	−2.88997e7	+	2.88997e7i	−0.0645518	+	0.0645518i
$766$			5.68163e7i			0.126412i
$767$	7.14510e7	−	2.36222e7i	0.158351	−	0.0523522i
$768$	−4.39303e8			−0.969797
$769$	3.82702e8	+	3.82702e8i	0.841553	+	0.841553i	0.989061	−	0.147508i	$-0.0471252\pi$
$769$	3.82702e8	+	3.82702e8i	0.841553	+	0.841553i	−0.147508	+	0.989061i	$0.547125\pi$
$770$	4.21762e6			0.00923836
$771$		−	6.63793e8i		−	1.44834i
$772$	−1.08090e8	−	1.08090e8i	−0.234928	−	0.234928i
$773$	1.15663e8	+	1.15663e8i	0.250412	+	0.250412i	0.821140	−	0.570727i	$-0.193339\pi$
$773$	1.15663e8	+	1.15663e8i	0.250412	+	0.250412i	−0.570727	+	0.821140i	$0.693339\pi$
$774$	−1.69748e6	+	1.69748e6i	−0.00366086	+	0.00366086i
$775$	9.94928e7	−	9.94928e7i	0.213740	−	0.213740i
$776$	−6.44949e7			−0.138019
$777$		−	1.00335e8i		−	0.213889i
$778$	3.22330e6	−	3.22330e6i	0.00684482	−	0.00684482i
$779$			6.65185e8i			1.40712i
$780$	4.12303e8	−	1.36311e8i	0.868827	−	0.287240i
$781$	−1.07885e8			−0.226468
$782$	67565.3	+	67565.3i	0.000141287	+	0.000141287i
$783$	−4.09409e8			−0.852850
$784$		−	4.10676e8i		−	0.852219i
$785$	−3.01802e8	−	3.01802e8i	−0.623898	−	0.623898i
$786$	2.58456e7	+	2.58456e7i	0.0532255	+	0.0532255i
$787$	−1.47331e8	+	1.47331e8i	−0.302252	+	0.302252i	−0.841894	−	0.539643i	$-0.818559\pi$
$787$	−1.47331e8	+	1.47331e8i	−0.302252	+	0.302252i	0.539643	+	0.841894i	$0.318559\pi$
$788$	4.80640e7	−	4.80640e7i	0.0982294	−	0.0982294i
$789$	−2.35924e8			−0.480332
$790$		−	4.37292e7i		−	0.0886933i
$791$	−2.57582e7	+	2.57582e7i	−0.0520458	+	0.0520458i
$792$		−	1.78053e6i		−	0.00358404i
$793$	1.39310e8	+	7.00829e7i	0.279358	+	0.140538i
$794$	−2.45934e6			−0.00491312
$795$	−3.30287e8	−	3.30287e8i	−0.657340	−	0.657340i
$796$	−3.95786e8			−0.784732
$797$			4.46703e6i			0.00882356i	0.999990	+	0.00441178i	$0.00140432\pi$
$797$			4.46703e6i			0.00882356i	−0.999990	+	0.00441178i	$0.998596\pi$
$798$	−8.53445e6	−	8.53445e6i	−0.0167945	−	0.0167945i
$799$	−6.79865e8	−	6.79865e8i	−1.33285	−	1.33285i
$800$	−1.69273e7	+	1.69273e7i	−0.0330612	+	0.0330612i
$801$	3.43751e7	−	3.43751e7i	0.0668876	−	0.0668876i
$802$	1.46994e6			0.00284956
$803$		−	3.12540e8i		−	0.603614i
$804$	3.17164e8	−	3.17164e8i	0.610261	−	0.610261i
$805$			269855.i			0.000517301i
$806$	−2.71597e7	+	5.39875e7i	−0.0518703	+	0.103107i
$807$	−5.26911e8			−1.00257
$808$	9.41374e6	+	9.41374e6i	0.0178455	+	0.0178455i
$809$	−3.95862e8			−0.747649			−0.373825	−	0.927499i	$-0.621954\pi$
$809$	−3.95862e8			−0.747649			−0.373825	+	0.927499i	$0.621954\pi$
$810$			3.89250e7i			0.0732442i
$811$	4.80197e8	+	4.80197e8i	0.900237	+	0.900237i	0.995456	−	0.0952197i	$-0.0303554\pi$
$811$	4.80197e8	+	4.80197e8i	0.900237	+	0.900237i	−0.0952197	+	0.995456i	$0.530355\pi$
$812$	−1.20797e8	−	1.20797e8i	−0.225625	−	0.225625i
$813$	−5.98500e8	+	5.98500e8i	−1.11376	+	1.11376i
$814$	6.19235e6	−	6.19235e6i	0.0114811	−	0.0114811i
$815$	4.35662e8			0.804780
$816$		−	8.90671e8i		−	1.63926i
$817$	3.33826e8	−	3.33826e8i	0.612145	−	0.612145i
$818$		−	9.46928e6i		−	0.0173004i
$819$	−1.19775e7	+	3.95986e6i	−0.0218029	+	0.00720821i
$820$	8.41765e8			1.52668
$821$	2.36409e8	+	2.36409e8i	0.427204	+	0.427204i	0.887675	−	0.460471i	$-0.152319\pi$
$821$	2.36409e8	+	2.36409e8i	0.427204	+	0.427204i	−0.460471	+	0.887675i	$0.652319\pi$
$822$	−5.64750e7			−0.101681
$823$			1.11250e8i			0.199573i	0.995009	+	0.0997866i	$0.0318160\pi$
$823$			1.11250e8i			0.199573i	−0.995009	+	0.0997866i	$0.968184\pi$
$824$	−1.80387e6	−	1.80387e6i	−0.00322421	−	0.00322421i
$825$	3.05130e7	+	3.05130e7i	0.0543404	+	0.0543404i
$826$	−1.87161e6	+	1.87161e6i	−0.00332105	+	0.00332105i
$827$	4.03461e8	−	4.03461e8i	0.713321	−	0.713321i	−0.253908	−	0.967228i	$-0.581716\pi$
$827$	4.03461e8	−	4.03461e8i	0.713321	−	0.713321i	0.967228	+	0.253908i	$0.0817159\pi$
$828$	56790.3			0.000100042
$829$			7.87505e8i			1.38226i	0.722730	+	0.691130i	$0.242887\pi$
$829$			7.87505e8i			1.38226i	−0.722730	+	0.691130i	$0.757113\pi$
$830$	5.12695e7	−	5.12695e7i	0.0896653	−	0.0896653i
$831$		−	9.95018e7i		−	0.173392i
$832$	−2.49558e8	+	4.96068e8i	−0.433313	+	0.861333i
$833$	8.12037e8			1.40489
$834$	4.92912e7	+	4.92912e7i	0.0849711	+	0.0849711i
$835$	−6.64148e8			−1.14079
$836$			1.74552e8i			0.298749i
$837$	5.96855e8	+	5.96855e8i	1.01787	+	1.01787i
$838$	1.99367e7	+	1.99367e7i	0.0338783	+	0.0338783i
$839$	−3.76613e8	+	3.76613e8i	−0.637690	+	0.637690i	−0.949985	−	0.312295i	$-0.898902\pi$
$839$	−3.76613e8	+	3.76613e8i	−0.637690	+	0.637690i	0.312295	+	0.949985i	$0.398902\pi$
$840$	−2.16652e7	+	2.16652e7i	−0.0365531	+	0.0365531i
$841$	−1.31160e8			−0.220503
$842$			5.91054e7i			0.0990126i
$843$	−5.49228e8	+	5.49228e8i	−0.916790	+	0.916790i
$844$			2.23122e8i			0.371120i
$845$	7.88008e7	−	5.32899e8i	0.130605	−	0.883233i
$846$	3.44872e6			0.00569569
$847$	−1.35131e8	−	1.35131e8i	−0.222384	−	0.222384i
$848$	6.04715e8			0.991661
$849$			3.02843e8i			0.494874i
$850$	−1.10447e7	−	1.10447e7i	−0.0179845	−	0.0179845i
$851$	396205.	+	396205.i	0.000642881	+	0.000642881i
$852$	2.76259e8	−	2.76259e8i	0.446682	−	0.446682i
$853$	1.76034e8	−	1.76034e8i	0.283629	−	0.283629i	−0.550926	−	0.834554i	$-0.685725\pi$
$853$	1.76034e8	−	1.76034e8i	0.283629	−	0.283629i	0.834554	+	0.550926i	$0.185725\pi$
$854$	−5.48489e6			−0.00880632
$855$			2.88299e7i			0.0461258i
$856$	4.14425e7	−	4.14425e7i	0.0660731	−	0.0660731i
$857$			3.03207e8i			0.481723i	0.970560	+	0.240861i	$0.0774299\pi$
$857$			3.03207e8i			0.481723i	−0.970560	+	0.240861i	$0.922570\pi$
$858$	−1.65572e7	−	8.32947e6i	−0.0262135	−	0.0131873i
$859$	−2.42563e7			−0.0382688			−0.0191344	−	0.999817i	$-0.506091\pi$
$859$	−2.42563e7			−0.0382688			−0.0191344	+	0.999817i	$0.506091\pi$
$860$	−4.22444e8	−	4.22444e8i	−0.664161	−	0.664161i
$861$	−4.11629e8			−0.644906
$862$		−	1.09512e7i		−	0.0170978i
$863$	−1.54169e8	−	1.54169e8i	−0.239864	−	0.239864i	0.576930	−	0.816794i	$-0.304251\pi$
$863$	−1.54169e8	−	1.54169e8i	−0.239864	−	0.239864i	−0.816794	+	0.576930i	$0.804251\pi$
$864$	−1.01547e8	−	1.01547e8i	−0.157443	−	0.157443i
$865$	−3.50311e7	+	3.50311e7i	−0.0541260	+	0.0541260i
$866$	2.35405e7	−	2.35405e7i	0.0362462	−	0.0362462i
$867$	1.08916e9			1.67122
$868$			3.52205e8i			0.538563i
$869$	2.18679e8	−	2.18679e8i	0.333233	−	0.333233i
$870$		−	4.14545e7i		−	0.0629526i
$871$	−1.74657e8	−	5.28293e8i	−0.264322	−	0.799503i
$872$	−9.89338e7			−0.149209
$873$	−2.65546e7	−	2.65546e7i	−0.0399114	−	0.0399114i
$874$	67402.2			0.000100958
$875$		−	2.61585e8i		−	0.390471i
$876$	8.00318e8	+	8.00318e8i	1.19056	+	1.19056i
$877$	4.14872e6	+	4.14872e6i	0.00615057	+	0.00615057i	0.710175	−	0.704025i	$-0.248616\pi$
$877$	4.14872e6	+	4.14872e6i	0.00615057	+	0.00615057i	−0.704025	+	0.710175i	$0.748616\pi$
$878$	5.79979e7	−	5.79979e7i	0.0856897	−	0.0856897i
$879$	4.12710e8	−	4.12710e8i	0.607685	−	0.607685i
$880$	2.19548e8			0.322167
$881$			8.05289e8i			1.17767i	0.808253	+	0.588836i	$0.200413\pi$
$881$			8.05289e8i			1.17767i	−0.808253	+	0.588836i	$0.799587\pi$
$882$	−2.05959e6	+	2.05959e6i	−0.00300175	+	0.00300175i
$883$		−	4.68302e7i		−	0.0680211i	−0.999421	−	0.0340106i	$-0.989172\pi$
$883$		−	4.68302e7i		−	0.0680211i	0.999421	−	0.0340106i	$-0.0108280\pi$
$884$	−9.93054e8	−	4.99579e8i	−1.43753	−	0.723181i
$885$	1.06426e8			0.153539
$886$	−2.56589e7	−	2.56589e7i	−0.0368924	−	0.0368924i
$887$	−5.79957e8			−0.831045			−0.415523	−	0.909583i	$-0.636401\pi$
$887$	−5.79957e8			−0.831045			−0.415523	+	0.909583i	$0.636401\pi$
$888$			6.36181e7i			0.0908535i
$889$	2.41468e7	+	2.41468e7i	0.0343681	+	0.0343681i
$890$	−5.16287e7	−	5.16287e7i	−0.0732354	−	0.0732354i
$891$	−1.94654e8	+	1.94654e8i	−0.275189	+	0.275189i
$892$	3.03992e8	−	3.03992e8i	0.428319	−	0.428319i
$893$	−6.78223e8			−0.952398
$894$		−	3.02472e7i		−	0.0423324i
$895$	−2.86054e8	+	2.86054e8i	−0.399005	+	0.399005i
$896$		−	7.98157e7i		−	0.110959i
$897$	532944.	−	1.05938e6i	0.000738422	−	0.00146782i
$898$	3.57835e7			0.0494144
$899$	−6.75949e8	−	6.75949e8i	−0.930325	−	0.930325i
$900$	−9.28338e6			−0.0127344
$901$			1.19571e9i			1.63476i
$902$	−2.54045e7	−	2.54045e7i	−0.0346171	−	0.0346171i
$903$	2.06578e8	+	2.06578e8i	0.280557	+	0.280557i
$904$	1.63322e7	−	1.63322e7i	0.0221075	−	0.0221075i
$905$	−1.81503e8	+	1.81503e8i	−0.244871	+	0.244871i
$906$	3.00612e7			0.0404223
$907$		−	1.37442e9i		−	1.84203i	−0.389529	−	0.921014i	$-0.627362\pi$
$907$		−	1.37442e9i		−	1.84203i	0.389529	−	0.921014i	$-0.372638\pi$
$908$	3.15931e8	−	3.15931e8i	0.422021	−	0.422021i
$909$			7.75187e6i			0.0103208i
$910$	5.94740e6	+	1.79893e7i	0.00789228	+	0.0238721i
$911$	−1.01210e9			−1.33866			−0.669329	−	0.742966i	$-0.733418\pi$
$911$	−1.01210e9			−1.33866			−0.669329	+	0.742966i	$0.733418\pi$
$912$	−4.44260e8	−	4.44260e8i	−0.585670	−	0.585670i
$913$	5.12772e8			0.673770
$914$			6.70214e7i			0.0877759i
$915$	1.55945e8	+	1.55945e8i	0.203567	+	0.203567i
$916$	−6.49101e8	−	6.49101e8i	−0.844551	−	0.844551i
$917$	1.86853e8	−	1.86853e8i	0.242322	−	0.242322i
$918$	6.62571e7	−	6.62571e7i	0.0856455	−	0.0856455i
$919$	9.32032e7			0.120084			0.0600419	−	0.998196i	$-0.480877\pi$
$919$	9.32032e7			0.120084			0.0600419	+	0.998196i	$0.480877\pi$
$920$		−	171104.i		−	0.000219734i
$921$	6.24805e8	−	6.24805e8i	0.799771	−	0.799771i
$922$			7.81226e7i			0.0996745i
$923$	−1.52132e8	−	4.60159e8i	−0.193471	−	0.585198i
$924$	−1.08016e8			−0.136922
$925$	−6.47666e7	−	6.47666e7i	−0.0818325	−	0.0818325i
$926$	3.18126e7			0.0400651
$927$		−	1.48542e6i		−	0.00186471i
$928$	1.15003e8	+	1.15003e8i	0.143902	+	0.143902i
$929$	5.92932e7	+	5.92932e7i	0.0739534	+	0.0739534i	0.743116	−	0.669163i	$-0.233347\pi$
$929$	5.92932e7	+	5.92932e7i	0.0739534	+	0.0739534i	−0.669163	+	0.743116i	$0.733347\pi$
$930$	−6.04342e7	+	6.04342e7i	−0.0751336	+	0.0751336i
$931$	4.05038e8	−	4.05038e8i	0.501934	−	0.501934i
$932$	8.54586e8			1.05562
$933$			1.23306e9i			1.51824i
$934$	−6.82282e7	+	6.82282e7i	−0.0837382	+	0.0837382i
$935$			4.34116e8i			0.531093i
$936$	7.59445e6	−	2.51078e6i	0.00926123	−	0.00306183i
$937$	−2.67343e8			−0.324975			−0.162487	−	0.986711i	$-0.551952\pi$
$937$	−2.67343e8			−0.324975			−0.162487	+	0.986711i	$0.551952\pi$
$938$	1.38383e7	+	1.38383e7i	0.0167677	+	0.0167677i
$939$	−3.76912e8			−0.455243
$940$			8.58264e8i			1.03333i
$941$	−6.48054e8	−	6.48054e8i	−0.777755	−	0.777755i	0.201694	−	0.979449i	$-0.435355\pi$
$941$	−6.48054e8	−	6.48054e8i	−0.777755	−	0.777755i	−0.979449	+	0.201694i	$0.935355\pi$
$942$	−4.66475e7	−	4.66475e7i	−0.0558054	−	0.0558054i
$943$	1.62545e6	−	1.62545e6i	0.00193838	−	0.00193838i
$944$	−9.74264e7	+	9.74264e7i	−0.115814	+	0.115814i
$945$	2.64631e8			0.313577
$946$			2.54987e7i			0.0301193i
$947$	−5.09741e8	+	5.09741e8i	−0.600205	+	0.600205i	−0.940367	−	0.340162i	$-0.889518\pi$
$947$	−5.09741e8	+	5.09741e8i	−0.600205	+	0.600205i	0.340162	+	0.940367i	$0.389518\pi$
$948$			1.11994e9i			1.31453i
$949$	1.33307e9	−	4.40723e8i	1.55975	−	0.515664i
$950$	−1.10181e7			−0.0128509
$951$	3.18268e8	+	3.18268e8i	0.370042	+	0.370042i
$952$	7.84329e7			0.0909049
$953$		−	8.76603e8i		−	1.01280i	−0.862298	−	0.506400i	$-0.830976\pi$
$953$		−	8.76603e8i		−	1.01280i	0.862298	−	0.506400i	$-0.169024\pi$
$954$	−3.03272e6	−	3.03272e6i	−0.00349291	−	0.00349291i
$955$	9.31364e8	+	9.31364e8i	1.06932	+	1.06932i
$956$	6.98780e7	−	6.98780e7i	0.0799773	−	0.0799773i
$957$	2.07304e8	−	2.07304e8i	0.236522	−	0.236522i
$958$	−1.13840e8			−0.129479
$959$			4.08290e8i			0.462928i
$960$	−5.55304e8	+	5.55304e8i	−0.627649	+	0.627649i
$961$			1.08335e9i			1.22067i
$962$	3.51441e7	+	1.76801e7i	0.0394755	+	0.0198590i
$963$	3.41264e7			0.0382130
$964$	2.40404e8	+	2.40404e8i	0.268356	+	0.268356i
$965$	−2.68175e8			−0.298425
$966$			41709.7i			4.62707e-5i
$967$	3.55486e8	+	3.55486e8i	0.393136	+	0.393136i	0.875804	−	0.482668i	$-0.160332\pi$
$967$	3.55486e8	+	3.55486e8i	0.393136	+	0.393136i	−0.482668	+	0.875804i	$0.660332\pi$
$968$	8.56809e7	+	8.56809e7i	0.0944622	+	0.0944622i
$969$	8.78444e8	−	8.78444e8i	0.965479	−	0.965479i
$970$	−3.98829e7	+	3.98829e7i	−0.0436990	+	0.0436990i
$971$	9.31707e7			0.101770			0.0508852	−	0.998705i	$-0.483796\pi$
$971$	9.31707e7			0.101770			0.0508852	+	0.998705i	$0.483796\pi$
$972$		−	1.15136e8i		−	0.125375i
$973$	3.56355e8	−	3.56355e8i	0.386851	−	0.386851i
$974$		−	1.13441e8i		−	0.122770i
$975$	−8.71191e7	+	1.73174e8i	−0.0939938	+	0.186839i
$976$	−2.85516e8			−0.307100
$977$	4.23541e8	+	4.23541e8i	0.454163	+	0.454163i	0.896734	−	0.442571i	$-0.145933\pi$
$977$	4.23541e8	+	4.23541e8i	0.454163	+	0.454163i	−0.442571	+	0.896734i	$0.645933\pi$
$978$	6.73374e7			0.0719846
$979$		−	5.16364e8i		−	0.550311i
$980$	−5.12560e8	−	5.12560e8i	−0.544586	−	0.544586i
$981$	−4.07342e7	−	4.07342e7i	−0.0431471	−	0.0431471i
$982$	−2.68369e7	+	2.68369e7i	−0.0283398	+	0.0283398i
$983$	1.14903e9	−	1.14903e9i	1.20968	−	1.20968i	0.238549	−	0.971130i	$-0.423328\pi$
$983$	1.14903e9	−	1.14903e9i	1.20968	−	1.20968i	0.971130	−	0.238549i	$-0.0766719\pi$
$984$	2.60997e8			0.273937
$985$		−	1.19248e8i		−	0.124779i
$986$	−7.50374e7	+	7.50374e7i	−0.0782793	+	0.0782793i
$987$		−	4.19698e8i		−	0.436501i
$988$	−7.44514e8	+	2.46142e8i	−0.771973	+	0.255220i
$989$	−1.63148e6			−0.00168653
$990$	−1.10106e6	−	1.10106e6i	−0.00113476	−	0.00113476i
$991$	−5.39397e8			−0.554227			−0.277113	−	0.960837i	$-0.589378\pi$
$991$	−5.39397e8			−0.554227			−0.277113	+	0.960837i	$0.589378\pi$
$992$		−	3.35314e8i		−	0.343492i
$993$	−1.17229e9	−	1.17229e9i	−1.19726	−	1.19726i
$994$	1.20535e7	+	1.20535e7i	0.0122731	+	0.0122731i
$995$	−4.90977e8	+	4.90977e8i	−0.498415	+	0.498415i
$996$	−1.31305e9	+	1.31305e9i	−1.32893	+	1.32893i
$997$	−1.17531e9			−1.18595			−0.592976	−	0.805220i	$-0.702047\pi$
$997$	−1.17531e9			−1.18595			−0.592976	+	0.805220i	$0.702047\pi$
$998$			1.14508e7i			0.0115198i
$999$	3.88533e8	−	3.88533e8i	0.389701	−	0.389701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.d.a.8.3	yes	12
3.2	odd	2		117.7.j.b.73.4		12
4.3	odd	2		208.7.t.c.177.5		12
13.5	odd	4	inner	13.7.d.a.5.3	✓	12
39.5	even	4		117.7.j.b.109.4		12
52.31	even	4		208.7.t.c.161.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.d.a.5.3	✓	12	13.5	odd	4	inner
13.7.d.a.8.3	yes	12	1.1	even	1	trivial
117.7.j.b.73.4		12	3.2	odd	2
117.7.j.b.109.4		12	39.5	even	4
208.7.t.c.161.5		12	52.31	even	4
208.7.t.c.177.5		12	4.3	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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.438138 + 0.438138i) q^{2} -27.8396 q^{3} -63.6161i q^{4} +(-78.9164 - 78.9164i) q^{5} +(-12.1976 - 12.1976i) q^{6} +(-88.1833 + 88.1833i) q^{7} +(55.9134 - 55.9134i) q^{8} +46.0426 q^{9} +O(q^{10})\)	\(q+(0.438138 + 0.438138i) q^{2} -27.8396 q^{3} -63.6161i q^{4} +(-78.9164 - 78.9164i) q^{5} +(-12.1976 - 12.1976i) q^{6} +(-88.1833 + 88.1833i) q^{7} +(55.9134 - 55.9134i) q^{8} +46.0426 q^{9} -69.1525i q^{10} +(345.814 - 345.814i) q^{11} +1771.05i q^{12} +(1962.64 + 987.350i) q^{13} -77.2729 q^{14} +(2197.00 + 2197.00i) q^{15} -4022.43 q^{16} -7953.63i q^{17} +(20.1730 + 20.1730i) q^{18} +(-3967.21 - 3967.21i) q^{19} +(-5020.35 + 5020.35i) q^{20} +(2454.99 - 2454.99i) q^{21} +303.028 q^{22} +19.3887i q^{23} +(-1556.61 + 1556.61i) q^{24} -3169.41i q^{25} +(427.310 + 1292.50i) q^{26} +19013.3 q^{27} +(5609.88 + 5609.88i) q^{28} -21532.8 q^{29} +1925.18i q^{30} +(31391.5 + 31391.5i) q^{31} +(-5340.84 - 5340.84i) q^{32} +(-9627.33 + 9627.33i) q^{33} +(3484.79 - 3484.79i) q^{34} +13918.2 q^{35} -2929.05i q^{36} +(20434.9 - 20434.9i) q^{37} -3476.37i q^{38} +(-54639.0 - 27487.4i) q^{39} -8824.96 q^{40} +(-83835.3 - 83835.3i) q^{41} +2151.25 q^{42} +84146.3i q^{43} +(-21999.3 - 21999.3i) q^{44} +(-3633.52 - 3633.52i) q^{45} +(-8.49490 + 8.49490i) q^{46} +(85478.5 - 85478.5i) q^{47} +111983. q^{48} +102096. i q^{49} +(1388.64 - 1388.64i) q^{50} +221426. i q^{51} +(62811.4 - 124855. i) q^{52} -150336. q^{53} +(8330.42 + 8330.42i) q^{54} -54580.8 q^{55} +9861.26i q^{56} +(110446. + 110446. i) q^{57} +(-9434.35 - 9434.35i) q^{58} +(24220.8 - 24220.8i) q^{59} +(139764. - 139764. i) q^{60} +70980.8 q^{61} +27507.6i q^{62} +(-4060.19 + 4060.19i) q^{63} +252756. i q^{64} +(-76966.2 - 232802. i) q^{65} -8436.19 q^{66} +(-179083. - 179083. i) q^{67} -505979. q^{68} -539.772i q^{69} +(6098.09 + 6098.09i) q^{70} +(-155987. - 155987. i) q^{71} +(2574.40 - 2574.40i) q^{72} +(451890. - 451890. i) q^{73} +17906.6 q^{74} +88235.2i q^{75} +(-252379. + 252379. i) q^{76} +60990.1i q^{77} +(-11896.1 - 35982.7i) q^{78} +632360. q^{79} +(317436. + 317436. i) q^{80} -562886. q^{81} -73462.8i q^{82} +(741398. + 741398. i) q^{83} +(-156177. - 156177. i) q^{84} +(-627672. + 627672. i) q^{85} +(-36867.7 + 36867.7i) q^{86} +599465. q^{87} -38671.3i q^{88} +(746592. - 746592. i) q^{89} -3183.96i q^{90} +(-260140. + 86004.1i) q^{91} +1233.43 q^{92} +(-873927. - 873927. i) q^{93} +74902.7 q^{94} +626156. i q^{95} +(148687. + 148687. i) q^{96} +(-576739. - 576739. i) q^{97} +(-44732.3 + 44732.3i) q^{98} +(15922.2 - 15922.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} + 108 q^{5} - 640 q^{6} + 398 q^{7} - 912 q^{8} + 1940 q^{9} + 1686 q^{11} - 3926 q^{13} + 5484 q^{14} - 15268 q^{15} + 2132 q^{16} + 15254 q^{18} + 1766 q^{19} - 19044 q^{20} + 3428 q^{21} + 28832 q^{22} + 31608 q^{24} - 58266 q^{26} - 20464 q^{27} + 4092 q^{28} - 90108 q^{29} + 61014 q^{31} - 64932 q^{32} - 44452 q^{33} + 259896 q^{34} + 158772 q^{35} - 40212 q^{37} + 137852 q^{39} - 104196 q^{40} - 190416 q^{41} - 959204 q^{42} + 489372 q^{44} - 151444 q^{45} - 44412 q^{46} + 562446 q^{47} + 930308 q^{48} + 82422 q^{50} - 578500 q^{52} + 509136 q^{53} - 871432 q^{54} - 1264036 q^{55} + 939908 q^{57} - 1019980 q^{58} - 994458 q^{59} + 2407804 q^{60} + 1013696 q^{61} + 865778 q^{63} - 1130064 q^{65} - 418352 q^{66} - 1442386 q^{67} - 2313132 q^{68} + 2958968 q^{70} - 655866 q^{71} - 1706508 q^{72} + 2588228 q^{73} + 3373752 q^{74} + 246984 q^{76} + 77480 q^{78} - 75316 q^{79} - 2685408 q^{80} - 4016140 q^{81} + 894966 q^{83} - 3220504 q^{84} + 105396 q^{85} + 3704832 q^{86} + 2109064 q^{87} - 977376 q^{89} + 1088750 q^{91} + 3682872 q^{92} - 216268 q^{93} - 6238300 q^{94} + 896384 q^{96} + 983388 q^{97} + 1039302 q^{98} + 2894714 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 + 108 * q^5 - 640 * q^6 + 398 * q^7 - 912 * q^8 + 1940 * q^9 + 1686 * q^11 - 3926 * q^13 + 5484 * q^14 - 15268 * q^15 + 2132 * q^16 + 15254 * q^18 + 1766 * q^19 - 19044 * q^20 + 3428 * q^21 + 28832 * q^22 + 31608 * q^24 - 58266 * q^26 - 20464 * q^27 + 4092 * q^28 - 90108 * q^29 + 61014 * q^31 - 64932 * q^32 - 44452 * q^33 + 259896 * q^34 + 158772 * q^35 - 40212 * q^37 + 137852 * q^39 - 104196 * q^40 - 190416 * q^41 - 959204 * q^42 + 489372 * q^44 - 151444 * q^45 - 44412 * q^46 + 562446 * q^47 + 930308 * q^48 + 82422 * q^50 - 578500 * q^52 + 509136 * q^53 - 871432 * q^54 - 1264036 * q^55 + 939908 * q^57 - 1019980 * q^58 - 994458 * q^59 + 2407804 * q^60 + 1013696 * q^61 + 865778 * q^63 - 1130064 * q^65 - 418352 * q^66 - 1442386 * q^67 - 2313132 * q^68 + 2958968 * q^70 - 655866 * q^71 - 1706508 * q^72 + 2588228 * q^73 + 3373752 * q^74 + 246984 * q^76 + 77480 * q^78 - 75316 * q^79 - 2685408 * q^80 - 4016140 * q^81 + 894966 * q^83 - 3220504 * q^84 + 105396 * q^85 + 3704832 * q^86 + 2109064 * q^87 - 977376 * q^89 + 1088750 * q^91 + 3682872 * q^92 - 216268 * q^93 - 6238300 * q^94 + 896384 * q^96 + 983388 * q^97 + 1039302 * q^98 + 2894714 * q^99

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