LMFDB - Embedded newform 76.7.b.a.39.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.4
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.93032 + 1.05361i) q^{2} +19.7809i q^{3} +(61.7798 - 16.7110i) q^{4} +65.3551 q^{5} +(-20.8415 - 156.869i) q^{6} +574.962i q^{7} +(-472.326 + 197.615i) q^{8} +337.714 q^{9} +O(q^{10})$	\(q+(-7.93032 + 1.05361i) q^{2} +19.7809i q^{3} +(61.7798 - 16.7110i) q^{4} +65.3551 q^{5} +(-20.8415 - 156.869i) q^{6} +574.962i q^{7} +(-472.326 + 197.615i) q^{8} +337.714 q^{9} +(-518.287 + 68.8591i) q^{10} -1341.52i q^{11} +(330.559 + 1222.06i) q^{12} +4064.37 q^{13} +(-605.788 - 4559.63i) q^{14} +1292.79i q^{15} +(3537.49 - 2064.80i) q^{16} +358.254 q^{17} +(-2678.18 + 355.820i) q^{18} +1573.56i q^{19} +(4037.63 - 1092.15i) q^{20} -11373.3 q^{21} +(1413.44 + 10638.7i) q^{22} -798.982i q^{23} +(-3909.02 - 9343.06i) q^{24} -11353.7 q^{25} +(-32231.7 + 4282.28i) q^{26} +21100.6i q^{27} +(9608.18 + 35521.0i) q^{28} +23352.1 q^{29} +(-1362.10 - 10252.2i) q^{30} +44382.4i q^{31} +(-25877.9 + 20101.7i) q^{32} +26536.5 q^{33} +(-2841.07 + 377.461i) q^{34} +37576.7i q^{35} +(20863.9 - 5643.53i) q^{36} +13034.5 q^{37} +(-1657.93 - 12478.8i) q^{38} +80397.1i q^{39} +(-30869.0 + 12915.2i) q^{40} -131111. q^{41} +(90193.8 - 11983.1i) q^{42} -39531.9i q^{43} +(-22418.1 - 82878.7i) q^{44} +22071.4 q^{45} +(841.819 + 6336.18i) q^{46} +127049. i q^{47} +(40843.7 + 69974.8i) q^{48} -212932. q^{49} +(90038.5 - 11962.4i) q^{50} +7086.60i q^{51} +(251096. - 67919.6i) q^{52} +174431. q^{53} +(-22231.9 - 167335. i) q^{54} -87675.1i q^{55} +(-113621. - 271570. i) q^{56} -31126.6 q^{57} +(-185190. + 24604.1i) q^{58} +109720. i q^{59} +(21603.7 + 79868.1i) q^{60} -96366.5 q^{61} +(-46761.9 - 351967. i) q^{62} +194173. i q^{63} +(184040. - 186678. i) q^{64} +265627. q^{65} +(-210443. + 27959.2i) q^{66} +100617. i q^{67} +(22132.9 - 5986.77i) q^{68} +15804.6 q^{69} +(-39591.3 - 297995. i) q^{70} -595464. i q^{71} +(-159511. + 66737.5i) q^{72} -111742. q^{73} +(-103368. + 13733.3i) q^{74} -224587. i q^{75} +(26295.8 + 97214.4i) q^{76} +771322. q^{77} +(-84707.5 - 637574. i) q^{78} +631096. i q^{79} +(231193. - 134945. i) q^{80} -171197. q^{81} +(1.03975e6 - 138140. i) q^{82} -405628. i q^{83} +(-702640. + 190059. i) q^{84} +23413.7 q^{85} +(41651.3 + 313500. i) q^{86} +461927. i q^{87} +(265105. + 633635. i) q^{88} +621145. q^{89} +(-175033. + 23254.7i) q^{90} +2.33686e6i q^{91} +(-13351.8 - 49361.0i) q^{92} -877927. q^{93} +(-133860. - 1.00754e6i) q^{94} +102840. i q^{95} +(-397630. - 511889. i) q^{96} -902638. q^{97} +(1.68862e6 - 224348. i) q^{98} -453050. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−7.93032	+	1.05361i	−0.991289	+	0.131702i
$2$	−7.93032	+	1.05361i	−0.991289	+	0.131702i
$3$			19.7809i			0.732628i	0.930491	+	0.366314i	$0.119380\pi$
$3$			19.7809i			0.732628i	−0.930491	+	0.366314i	$0.880620\pi$
$4$	61.7798	−	16.7110i	0.965309	−	0.261109i
$5$	65.3551			0.522841			0.261421	−	0.965225i	$-0.415809\pi$
$5$	65.3551			0.522841			0.261421	+	0.965225i	$0.415809\pi$
$6$	−20.8415	−	156.869i	−0.0964883	−	0.726246i
$7$			574.962i			1.67627i	0.545460	+	0.838137i	$0.316355\pi$
$7$			574.962i			1.67627i	−0.545460	+	0.838137i	$0.683645\pi$
$8$	−472.326	+	197.615i	−0.922512	+	0.385967i
$9$	337.714			0.463257
$10$	−518.287	+	68.8591i	−0.518287	+	0.0688591i
$11$		−	1341.52i		−	1.00790i	−0.863732	−	0.503951i	$-0.831879\pi$
$11$		−	1341.52i		−	1.00790i	0.863732	−	0.503951i	$-0.168121\pi$
$12$	330.559	+	1222.06i	0.191296	+	0.707212i
$13$	4064.37			1.84996			0.924982	−	0.380012i	$-0.124080\pi$
$13$	4064.37			1.84996			0.924982	+	0.380012i	$0.124080\pi$
$14$	−605.788	−	4559.63i	−0.220768	−	1.66167i
$15$			1292.79i			0.383048i
$16$	3537.49	−	2064.80i	0.863644	−	0.504102i
$17$	358.254			0.0729196			0.0364598	−	0.999335i	$-0.488392\pi$
$17$	358.254			0.0729196			0.0364598	+	0.999335i	$0.488392\pi$
$18$	−2678.18	+	355.820i	−0.459222	+	0.0610117i
$19$			1573.56i			0.229416i
$19$			1573.56i			0.229416i
$20$	4037.63	−	1092.15i	0.504703	−	0.136519i
$21$	−11373.3			−1.22808
$22$	1413.44	+	10638.7i	0.132743	+	0.999123i
$23$		−	798.982i		−	0.0656680i	−0.999461	−	0.0328340i	$-0.989547\pi$
$23$		−	798.982i		−	0.0656680i	0.999461	−	0.0328340i	$-0.0104533\pi$
$24$	−3909.02	−	9343.06i	−0.282770	−	0.675858i
$25$	−11353.7			−0.726637
$26$	−32231.7	+	4282.28i	−1.83385	+	0.243643i
$27$			21100.6i			1.07202i
$28$	9608.18	+	35521.0i	0.437690	+	1.61812i
$29$	23352.1			0.957485			0.478742	−	0.877955i	$-0.341093\pi$
$29$	23352.1			0.957485			0.478742	+	0.877955i	$0.341093\pi$
$30$	−1362.10	−	10252.2i	−0.0504481	−	0.379711i
$31$			44382.4i			1.48979i	0.667180	+	0.744897i	$0.267501\pi$
$31$			44382.4i			1.48979i	−0.667180	+	0.744897i	$0.732499\pi$
$32$	−25877.9	+	20101.7i	−0.789730	+	0.613454i
$33$	26536.5			0.738417
$34$	−2841.07	+	377.461i	−0.0722844	+	0.00960364i
$35$			37576.7i			0.876425i
$36$	20863.9	−	5643.53i	0.447186	−	0.120961i
$37$	13034.5			0.257329			0.128665	−	0.991688i	$-0.458931\pi$
$37$	13034.5			0.257329			0.128665	+	0.991688i	$0.458931\pi$
$38$	−1657.93	−	12478.8i	−0.0302144	−	0.227417i
$39$			80397.1i			1.35533i
$40$	−30869.0	+	12915.2i	−0.482327	+	0.201800i
$41$	−131111.			−1.90234			−0.951169	−	0.308669i	$-0.900116\pi$
$41$	−131111.			−1.90234			−0.951169	+	0.308669i	$0.900116\pi$
$42$	90193.8	−	11983.1i	1.21739	−	0.161741i
$43$		−	39531.9i		−	0.497212i	−0.968605	−	0.248606i	$-0.920028\pi$
$43$		−	39531.9i		−	0.497212i	0.968605	−	0.248606i	$-0.0799725\pi$
$44$	−22418.1	−	82878.7i	−0.263173	−	0.972938i
$45$	22071.4			0.242210
$46$	841.819	+	6336.18i	0.00864858	+	0.0650960i
$47$			127049.i			1.22371i	0.790971	+	0.611853i	$0.209576\pi$
$47$			127049.i			1.22371i	−0.790971	+	0.611853i	$0.790424\pi$
$48$	40843.7	+	69974.8i	0.369319	+	0.632730i
$49$	−212932.			−1.80989
$50$	90038.5	−	11962.4i	0.720308	−	0.0956994i
$51$			7086.60i			0.0534229i
$52$	251096.	−	67919.6i	1.78579	−	0.483042i
$53$	174431.			1.17164			0.585821	−	0.810441i	$-0.300772\pi$
$53$	174431.			1.17164			0.585821	+	0.810441i	$0.300772\pi$
$54$	−22231.9	−	167335.i	−0.141187	−	1.06268i
$55$		−	87675.1i		−	0.526973i
$56$	−113621.	−	271570.i	−0.646987	−	1.54638i
$57$	−31126.6			−0.168076
$58$	−185190.	+	24604.1i	−0.949145	+	0.126102i
$59$			109720.i			0.534233i	0.963664	+	0.267116i	$0.0860708\pi$
$59$			109720.i			0.534233i	−0.963664	+	0.267116i	$0.913929\pi$
$60$	21603.7	+	79868.1i	0.100017	+	0.369760i
$61$	−96366.5			−0.424557			−0.212279	−	0.977209i	$-0.568088\pi$
$61$	−96366.5			−0.424557			−0.212279	+	0.977209i	$0.568088\pi$
$62$	−46761.9	−	351967.i	−0.196208	−	1.47682i
$63$			194173.i			0.776545i
$64$	184040.	−	186678.i	0.702058	−	0.712120i
$65$	265627.			0.967237
$66$	−210443.	+	27959.2i	−0.731985	+	0.0972508i
$67$			100617.i			0.334539i	0.985911	+	0.167269i	$0.0534949\pi$
$67$			100617.i			0.334539i	−0.985911	+	0.167269i	$0.946505\pi$
$68$	22132.9	−	5986.77i	0.0703900	−	0.0190400i
$69$	15804.6			0.0481102
$70$	−39591.3	−	297995.i	−0.115427	−	0.868791i
$71$		−	595464.i		−	1.66372i	−0.554984	−	0.831861i	$-0.687276\pi$
$71$		−	595464.i		−	1.66372i	0.554984	−	0.831861i	$-0.312724\pi$
$72$	−159511.	+	66737.5i	−0.427360	+	0.178802i
$73$	−111742.			−0.287241			−0.143621	−	0.989633i	$-0.545874\pi$
$73$	−111742.			−0.287241			−0.143621	+	0.989633i	$0.545874\pi$
$74$	−103368.	+	13733.3i	−0.255088	+	0.0338907i
$75$		−	224587.i		−	0.532354i
$76$	26295.8	+	97214.4i	0.0599025	+	0.221457i
$77$	771322.			1.68952
$78$	−84707.5	−	637574.i	−0.178500	−	1.34353i
$79$			631096.i			1.28001i	0.768370	+	0.640006i	$0.221068\pi$
$79$			631096.i			1.28001i	−0.768370	+	0.640006i	$0.778932\pi$
$80$	231193.	−	134945.i	0.451549	−	0.263565i
$81$	−171197.			−0.322136
$82$	1.03975e6	−	138140.i	1.88577	−	0.250541i
$83$		−	405628.i		−	0.709405i	−0.934979	−	0.354702i	$-0.884582\pi$
$83$		−	405628.i		−	0.709405i	0.934979	−	0.354702i	$-0.115418\pi$
$84$	−702640.	+	190059.i	−1.18548	+	0.320664i
$85$	23413.7			0.0381254
$86$	41651.3	+	313500.i	0.0654837	+	0.492881i
$87$			461927.i			0.701480i
$88$	265105.	+	633635.i	0.389018	+	0.929803i
$89$	621145.			0.881095			0.440547	−	0.897729i	$-0.354784\pi$
$89$	621145.			0.881095			0.440547	+	0.897729i	$0.354784\pi$
$90$	−175033.	+	23254.7i	−0.240100	+	0.0318994i
$91$			2.33686e6i			3.10105i
$92$	−13351.8	−	49361.0i	−0.0171465	−	0.0633899i
$93$	−877927.			−1.09146
$94$	−133860.	−	1.00754e6i	−0.161164	−	1.21305i
$95$			102840.i			0.119948i
$96$	−397630.	−	511889.i	−0.449434	−	0.578578i
$97$	−902638.			−0.989005			−0.494502	−	0.869176i	$-0.664650\pi$
$97$	−902638.			−0.989005			−0.494502	+	0.869176i	$0.664650\pi$
$98$	1.68862e6	−	224348.i	1.79413	−	0.238366i
$99$		−	453050.i		−	0.466918i
$100$	−701430.	+	189732.i	−0.701430	+	0.189732i
$101$	−1.23115e6			−1.19495			−0.597473	−	0.801889i	$-0.703828\pi$
$101$	−1.23115e6			−1.19495			−0.597473	+	0.801889i	$0.703828\pi$
$102$	−7466.54	−	56199.0i	−0.00703589	−	0.0529576i
$103$		−	2.01931e6i		−	1.84795i	−0.382452	−	0.923976i	$-0.624920\pi$
$103$		−	2.01931e6i		−	1.84795i	0.382452	−	0.923976i	$-0.375080\pi$
$104$	−1.91971e6	+	803182.i	−1.70661	+	0.714026i
$105$	−743303.			−0.642093
$106$	−1.38329e6	+	183782.i	−1.16144	+	0.154307i
$107$			77111.8i			0.0629462i	0.999505	+	0.0314731i	$0.0100198\pi$
$107$			77111.8i			0.0629462i	−0.999505	+	0.0314731i	$0.989980\pi$
$108$	352612.	+	1.30359e6i	0.279915	+	1.03483i
$109$	294799.			0.227639			0.113819	−	0.993501i	$-0.463692\pi$
$109$	294799.			0.227639			0.113819	+	0.993501i	$0.463692\pi$
$110$	92375.7	+	695292.i	0.0694033	+	0.522383i
$111$			257835.i			0.188526i
$112$	1.18718e6	+	2.03392e6i	0.845013	+	1.44770i
$113$	2.42875e6			1.68325			0.841623	−	0.540065i	$-0.181600\pi$
$113$	2.42875e6			1.68325			0.841623	+	0.540065i	$0.181600\pi$
$114$	246843.	−	32795.4i	0.166612	−	0.0221359i
$115$		−	52217.6i		−	0.0343339i
$116$	1.44269e6	−	390236.i	0.924269	−	0.250008i
$117$	1.37260e6			0.857008
$118$	−115603.	−	870116.i	−0.0703594	−	0.529579i
$119$			205982.i			0.122233i
$120$	−255474.	−	610617.i	−0.147844	−	0.353366i
$121$	−28111.2			−0.0158681
$122$	764216.	−	101533.i	0.420859	−	0.0559149i
$123$		−	2.59350e6i		−	1.39371i
$124$	741674.	+	2.74194e6i	0.388998	+	1.43811i
$125$	−1.76320e6			−0.902757
$126$	−204583.	−	1.53985e6i	−0.102272	−	0.769781i
$127$			2.91226e6i			1.42173i	0.703326	+	0.710867i	$0.251697\pi$
$127$			2.91226e6i			1.42173i	−0.703326	+	0.710867i	$0.748303\pi$
$128$	−1.26281e6	+	1.67432e6i	−0.602155	+	0.798379i
$129$	781978.			0.364271
$130$	−2.10651e6	+	279869.i	−0.958812	+	0.127387i
$131$		−	3.30951e6i		−	1.47214i	−0.676905	−	0.736071i	$-0.736679\pi$
$131$		−	3.30951e6i		−	1.47214i	0.676905	−	0.736071i	$-0.263321\pi$
$132$	1.63942e6	−	443451.i	0.712801	−	0.192807i
$133$	−904738.			−0.384564
$134$	−106011.	−	797923.i	−0.0440593	−	0.331625i
$135$			1.37903e6i			0.560497i
$136$	−169213.	+	70796.5i	−0.0672692	+	0.0281446i
$137$	287210.			0.111696			0.0558481	−	0.998439i	$-0.482214\pi$
$137$	287210.			0.111696			0.0558481	+	0.998439i	$0.482214\pi$
$138$	−125336.	+	16652.0i	−0.0476911	+	0.00633619i
$139$		−	426164.i		−	0.158684i	−0.996847	−	0.0793419i	$-0.974718\pi$
$139$		−	426164.i		−	0.158684i	0.996847	−	0.0793419i	$-0.0252819\pi$
$140$	627944.	+	2.32148e6i	0.228842	+	0.846021i
$141$	−2.51315e6			−0.896521
$142$	627390.	+	4.72222e6i	0.219115	+	1.64923i
$143$		−	5.45243e6i		−	1.86458i
$144$	1.19466e6	−	697313.i	0.400089	−	0.233529i
$145$	1.52618e6			0.500613
$146$	886147.	−	117733.i	0.284739	−	0.0378302i
$147$		−	4.21200e6i		−	1.32598i
$148$	805268.	−	217819.i	0.248402	−	0.0671910i
$149$	135209.			0.0408741			0.0204370	−	0.999791i	$-0.493494\pi$
$149$	135209.			0.0408741			0.0204370	+	0.999791i	$0.493494\pi$
$150$	236628.	+	1.78105e6i	0.0701120	+	0.527717i
$151$			3.39474e6i			0.985998i	0.870030	+	0.492999i	$0.164099\pi$
$151$			3.39474e6i			0.985998i	−0.870030	+	0.492999i	$0.835901\pi$
$152$	−310960.	−	743235.i	−0.0885470	−	0.211639i
$153$	120987.			0.0337805
$154$	−6.11683e6	+	812676.i	−1.67480	+	0.222513i
$155$			2.90062e6i			0.778925i
$156$	1.34351e6	+	4.96692e6i	0.353890	+	1.30832i
$157$	−2.01273e6			−0.520099			−0.260050	−	0.965595i	$-0.583739\pi$
$157$	−2.01273e6			−0.520099			−0.260050	+	0.965595i	$0.583739\pi$
$158$	−664932.	−	5.00479e6i	−0.168580	−	1.26886i
$159$			3.45040e6i			0.858377i
$160$	−1.69125e6	+	1.31375e6i	−0.412903	+	0.320739i
$161$	459384.			0.110077
$162$	1.35764e6	−	180375.i	0.319330	−	0.0424259i
$163$		−	2.00548e6i		−	0.463078i	−0.972826	−	0.231539i	$-0.925624\pi$
$163$		−	2.00548e6i		−	0.463078i	0.972826	−	0.231539i	$-0.0743761\pi$
$164$	−8.10002e6	+	2.19099e6i	−1.83635	+	0.496718i
$165$	1.73430e6			0.386075
$166$	427376.	+	3.21676e6i	0.0934298	+	0.703225i
$167$		−	3.44634e6i		−	0.739960i	−0.929040	−	0.369980i	$-0.879364\pi$
$167$		−	3.44634e6i		−	0.739960i	0.929040	−	0.369980i	$-0.120636\pi$
$168$	5.37190e6	−	2.24754e6i	1.13292	−	0.474001i
$169$	1.16923e7			2.42236
$170$	−185678.	+	24669.0i	−0.0377933	+	0.00502118i
$171$			531414.i			0.106278i
$172$	−660616.	−	2.44227e6i	−0.129827	−	0.479964i
$173$	−2.30460e6			−0.445099			−0.222549	−	0.974921i	$-0.571438\pi$
$173$	−2.30460e6			−0.445099			−0.222549	+	0.974921i	$0.571438\pi$
$174$	−486692.	−	3.66322e6i	−0.0923861	−	0.695370i
$175$		−	6.52795e6i		−	1.21804i
$176$	−2.76997e6	−	4.74560e6i	−0.508086	−	0.870469i
$177$	−2.17037e6			−0.391394
$178$	−4.92587e6	+	654446.i	−0.873420	+	0.116042i
$179$		−	1.32103e6i		−	0.230331i	−0.993346	−	0.115166i	$-0.963260\pi$
$179$		−	1.32103e6i		−	0.230331i	0.993346	−	0.115166i	$-0.0367399\pi$
$180$	1.36356e6	−	368834.i	0.233807	−	0.0632431i
$181$	5.80780e6			0.979436			0.489718	−	0.871881i	$-0.337100\pi$
$181$	5.80780e6			0.979436			0.489718	+	0.871881i	$0.337100\pi$
$182$	−2.46215e6	−	1.85320e7i	−0.408413	−	3.07403i
$183$		−	1.90622e6i		−	0.311042i
$184$	157891.	+	377380.i	0.0253457	+	0.0605795i
$185$	851871.			0.134542
$186$	6.96223e6	−	924995.i	1.08196	−	0.143748i
$187$		−	480604.i		−	0.0734959i
$188$	2.12311e6	+	7.84905e6i	0.319521	+	1.18126i
$189$	−1.21320e7			−1.79700
$190$	−108354.	−	815557.i	−0.0157974	−	0.118903i
$191$		−	7.08518e6i		−	1.01684i	−0.861110	−	0.508418i	$-0.830231\pi$
$191$		−	7.08518e6i		−	1.01684i	0.861110	−	0.508418i	$-0.169769\pi$
$192$	3.69267e6	+	3.64049e6i	0.521718	+	0.514347i
$193$	5.57563e6			0.775571			0.387786	−	0.921750i	$-0.373240\pi$
$193$	5.57563e6			0.775571			0.387786	+	0.921750i	$0.373240\pi$
$194$	7.15820e6	−	951031.i	0.980390	−	0.130254i
$195$			5.25436e6i			0.708625i
$196$	−1.31549e7	+	3.55830e6i	−1.74711	+	0.472580i
$197$	−939477.			−0.122882			−0.0614409	−	0.998111i	$-0.519570\pi$
$197$	−939477.			−0.122882			−0.0614409	+	0.998111i	$0.519570\pi$
$198$	477340.	+	3.59283e6i	0.0614939	+	0.462851i
$199$		−	1.48279e7i		−	1.88157i	−0.339010	−	0.940783i	$-0.610092\pi$
$199$		−	1.48279e7i		−	1.88157i	0.339010	−	0.940783i	$-0.389908\pi$
$200$	5.36265e6	−	2.24367e6i	0.670332	−	0.280458i
$201$	−1.99030e6			−0.245092
$202$	9.76344e6	−	1.29716e6i	1.18454	−	0.157376i
$203$			1.34266e7i			1.60501i
$204$	118424.	+	437809.i	0.0139492	+	0.0515696i
$205$	−8.56879e6			−0.994621
$206$	2.12757e6	+	1.60137e7i	0.243378	+	1.83185i
$207$		−	269828.i		−	0.0304211i
$208$	1.43777e7	−	8.39212e6i	1.59771	−	0.932570i
$209$	2.11096e6			0.231229
$210$	5.89463e6	−	783154.i	0.636500	−	0.0845648i
$211$			1.47993e7i			1.57541i	0.616052	+	0.787705i	$0.288731\pi$
$211$			1.47993e7i			1.57541i	−0.616052	+	0.787705i	$0.711269\pi$
$212$	1.07763e7	−	2.91490e6i	1.13100	−	0.305926i
$213$	1.17789e7			1.21889
$214$	−81246.0	−	611521.i	−0.00829012	−	0.0623979i
$215$		−	2.58361e6i		−	0.259963i
$216$	−4.16981e6	−	9.96638e6i	−0.413766	−	0.988954i
$217$	−2.55182e7			−2.49730
$218$	−2.33785e6	+	310604.i	−0.225656	+	0.0299804i
$219$		−	2.21036e6i		−	0.210441i
$220$	−1.46514e6	−	5.41655e6i	−0.137597	−	0.508692i
$221$	1.45608e6			0.134899
$222$	−271658.	−	2.04471e6i	−0.0248293	−	0.186884i
$223$			1.65788e7i			1.49499i	0.664267	+	0.747495i	$0.268744\pi$
$223$			1.65788e7i			1.49499i	−0.664267	+	0.747495i	$0.731256\pi$
$224$	−1.15577e7	−	1.48788e7i	−1.02832	−	1.32380i
$225$	−3.83431e6			−0.336620
$226$	−1.92608e7	+	2.55897e6i	−1.66858	+	0.221686i
$227$			7.10761e6i			0.607639i	0.952730	+	0.303820i	$0.0982620\pi$
$227$			7.10761e6i			0.607639i	−0.952730	+	0.303820i	$0.901738\pi$
$228$	−1.92299e6	+	520155.i	−0.162246	+	0.0438862i
$229$	5.30587e6			0.441825			0.220913	−	0.975294i	$-0.429096\pi$
$229$	5.30587e6			0.441825			0.220913	+	0.975294i	$0.429096\pi$
$230$	55017.2	+	414102.i	0.00452184	+	0.0340349i
$231$			1.52575e7i			1.23779i
$232$	−1.10298e7	+	4.61473e6i	−0.883292	+	0.369558i
$233$	1.63903e7			1.29575			0.647873	−	0.761748i	$-0.275659\pi$
$233$	1.63903e7			1.29575			0.647873	+	0.761748i	$0.275659\pi$
$234$	−1.08851e7	+	1.44619e6i	−0.849543	+	0.112869i
$235$			8.30330e6i			0.639804i
$236$	1.83353e6	+	6.77849e6i	0.139493	+	0.515700i
$237$	−1.24837e7			−0.937773
$238$	−217026.	−	1.63351e6i	−0.0160983	−	0.121168i
$239$			803620.i			0.0588650i	0.999567	+	0.0294325i	$0.00937001\pi$
$239$			803620.i			0.0588650i	−0.999567	+	0.0294325i	$0.990630\pi$
$240$	2.66935e6	+	4.57322e6i	0.193095	+	0.330817i
$241$	4.31054e6			0.307950			0.153975	−	0.988075i	$-0.450792\pi$
$241$	4.31054e6			0.307950			0.153975	+	0.988075i	$0.450792\pi$
$242$	222931.	−	29618.4i	0.0157298	−	0.00208985i
$243$			1.19959e7i			0.836016i
$244$	−5.95350e6	+	1.61038e6i	−0.409829	+	0.110856i
$245$	−1.39162e7			−0.946287
$246$	2.73255e6	+	2.05673e7i	0.183553	+	1.38157i
$247$			6.39554e6i			0.424411i
$248$	−8.77065e6	−	2.09630e7i	−0.575012	−	1.37435i
$249$	8.02371e6			0.519730
$250$	1.39827e7	−	1.85773e6i	0.894893	−	0.118895i
$251$			176629.i			0.0111697i	0.999984	+	0.00558484i	$0.00177772\pi$
$251$			176629.i			0.0111697i	−0.999984	+	0.00558484i	$0.998222\pi$
$252$	3.24482e6	+	1.19960e7i	0.202763	+	0.749606i
$253$	−1.07185e6			−0.0661869
$254$	−3.06839e6	−	2.30951e7i	−0.187245	−	1.40935i
$255$			463146.i			0.0279317i
$256$	8.25041e6	−	1.46084e7i	0.491762	−	0.870729i
$257$	548086.			0.0322886			0.0161443	−	0.999870i	$-0.494861\pi$
$257$	548086.			0.0322886			0.0161443	+	0.999870i	$0.494861\pi$
$258$	−6.20133e6	+	823902.i	−0.361098	+	0.0479752i
$259$			7.49434e6i			0.431354i
$260$	1.64104e7	−	4.43889e6i	0.933683	−	0.252554i
$261$	7.88633e6			0.443561
$262$	3.48694e6	+	2.62454e7i	0.193884	+	1.45932i
$263$			5.41907e6i			0.297891i	0.988845	+	0.148945i	$0.0475879\pi$
$263$			5.41907e6i			0.297891i	−0.988845	+	0.148945i	$0.952412\pi$
$264$	−1.25339e7	+	5.24402e6i	−0.681199	+	0.285005i
$265$	1.13999e7			0.612583
$266$	7.17486e6	−	953245.i	0.381214	−	0.0506477i
$267$			1.22868e7i			0.645515i
$268$	1.68141e6	+	6.21609e6i	0.0873510	+	0.322933i
$269$	2.27028e7			1.16633			0.583166	−	0.812353i	$-0.301814\pi$
$269$	2.27028e7			1.16633			0.583166	+	0.812353i	$0.301814\pi$
$270$	−1.45297e6	−	1.09362e7i	−0.0738185	−	0.555615i
$271$			9.58262e6i			0.481478i	0.970590	+	0.240739i	$0.0773898\pi$
$271$			9.58262e6i			0.481478i	−0.970590	+	0.240739i	$0.922610\pi$
$272$	1.26732e6	−	739723.i	0.0629766	−	0.0367589i
$273$	−4.62253e7			−2.27191
$274$	−2.27767e6	+	302609.i	−0.110723	+	0.0147106i
$275$			1.52312e7i			0.732380i
$276$	976406.	−	264111.i	0.0464412	−	0.0125620i
$277$	−1.66808e6			−0.0784834			−0.0392417	−	0.999230i	$-0.512494\pi$
$277$	−1.66808e6			−0.0784834			−0.0392417	+	0.999230i	$0.512494\pi$
$278$	449013.	+	3.37962e6i	0.0208989	+	0.157302i
$279$			1.49886e7i			0.690157i
$280$	−7.42574e6	−	1.77485e7i	−0.338272	−	0.808513i
$281$	−4.77636e6			−0.215267			−0.107634	−	0.994191i	$-0.534327\pi$
$281$	−4.77636e6			−0.215267			−0.107634	+	0.994191i	$0.534327\pi$
$282$	1.99300e7	−	2.64789e6i	0.888712	−	0.118073i
$283$		−	1.13456e7i		−	0.500575i	−0.968171	−	0.250288i	$-0.919475\pi$
$283$		−	1.13456e7i		−	0.500575i	0.968171	−	0.250288i	$-0.0805252\pi$
$284$	−9.95079e6	−	3.67877e7i	−0.434413	−	1.60601i
$285$	−2.03428e6			−0.0878772
$286$	5.74475e6	+	4.32395e7i	0.245569	+	1.84834i
$287$		−	7.53839e7i		−	3.18884i
$288$	−8.73933e6	+	6.78862e6i	−0.365848	+	0.284187i
$289$	−2.40092e7			−0.994683
$290$	−1.21031e7	+	1.60800e6i	−0.496252	+	0.0659315i
$291$		−	1.78550e7i		−	0.724572i
$292$	−6.90338e6	+	1.86731e6i	−0.277277	+	0.0750013i
$293$	2.84362e7			1.13050			0.565248	−	0.824921i	$-0.308780\pi$
$293$	2.84362e7			1.13050			0.565248	+	0.824921i	$0.308780\pi$
$294$	4.43782e6	+	3.34025e7i	0.174634	+	1.31443i
$295$			7.17078e6i			0.279319i
$296$	−6.15654e6	+	2.57582e6i	−0.237389	+	0.0993207i
$297$	2.83069e7			1.08049
$298$	−1.07225e6	+	142458.i	−0.0405180	+	0.00538318i
$299$		−	3.24736e6i		−	0.121483i
$300$	−3.75307e6	−	1.38749e7i	−0.139003	−	0.513887i
$301$	2.27293e7			0.833464
$302$	−3.57675e6	−	2.69214e7i	−0.129858	−	0.977409i
$303$		−	2.43534e7i		−	0.875450i
$304$	3.24909e6	+	5.56646e6i	0.115649	+	0.198134i
$305$	−6.29804e6			−0.221976
$306$	−959469.	+	127474.i	−0.0334862	+	0.00444895i
$307$		−	4.50183e7i		−	1.55587i	−0.628343	−	0.777936i	$-0.716267\pi$
$307$		−	4.50183e7i		−	1.55587i	0.628343	−	0.777936i	$-0.283733\pi$
$308$	4.76521e7	−	1.28895e7i	1.63091	−	0.441149i
$309$	3.99438e7			1.35386
$310$	−3.05613e6	−	2.30028e7i	−0.102586	−	0.772140i
$311$		−	6.35854e6i		−	0.211386i	−0.994399	−	0.105693i	$-0.966294\pi$
$311$		−	6.35854e6i		−	0.211386i	0.994399	−	0.105693i	$-0.0337061\pi$
$312$	−1.58877e7	−	3.79737e7i	−0.523115	−	1.25031i
$313$	2.14683e7			0.700109			0.350054	−	0.936729i	$-0.386163\pi$
$313$	2.14683e7			0.700109			0.350054	+	0.936729i	$0.386163\pi$
$314$	1.59616e7	−	2.12064e6i	0.515569	−	0.0684980i
$315$			1.26902e7i			0.406010i
$316$	1.05462e7	+	3.89890e7i	0.334223	+	1.23561i
$317$	−2.08297e7			−0.653891			−0.326945	−	0.945043i	$-0.606019\pi$
$317$	−2.08297e7			−0.653891			−0.326945	+	0.945043i	$0.606019\pi$
$318$	−3.63539e6	−	2.73628e7i	−0.113050	−	0.850900i
$319$		−	3.13273e7i		−	0.965052i
$320$	1.20280e7	−	1.22004e7i	0.367065	−	0.372325i
$321$	−1.52534e6			−0.0461161
$322$	−3.64306e6	+	484014.i	−0.109119	+	0.0144974i
$323$			563735.i			0.0167289i
$324$	−1.05765e7	+	2.86086e6i	−0.310961	+	0.0841127i
$325$	−4.61457e7			−1.34425
$326$	2.11300e6	+	1.59040e7i	0.0609882	+	0.459045i
$327$			5.83139e6i			0.166774i
$328$	6.19272e7	−	2.59096e7i	1.75493	−	0.734241i
$329$	−7.30483e7			−2.05127
$330$	−1.37535e7	+	1.82728e6i	−0.382712	+	0.0508467i
$331$		−	6.11321e7i		−	1.68572i	−0.538134	−	0.842859i	$-0.680871\pi$
$331$		−	6.11321e7i		−	1.68572i	0.538134	−	0.842859i	$-0.319129\pi$
$332$	−6.77845e6	−	2.50596e7i	−0.185232	−	0.684795i
$333$	4.40193e6			0.119209
$334$	3.63111e6	+	2.73305e7i	0.0974540	+	0.733515i
$335$			6.57583e6i			0.174911i
$336$	−4.02329e7	+	2.34836e7i	−1.06063	+	0.619080i
$337$	3.25617e7			0.850779			0.425390	−	0.905010i	$-0.360137\pi$
$337$	3.25617e7			0.850779			0.425390	+	0.905010i	$0.360137\pi$
$338$	−9.27236e7	+	1.23192e7i	−2.40126	+	0.319030i
$339$			4.80430e7i			1.23319i
$340$	1.44650e6	−	391267.i	0.0368028	−	0.00995488i
$341$	5.95399e7			1.50157
$342$	−559905.	−	4.21428e6i	−0.0139970	−	0.105353i
$343$		−	5.47842e7i		−	1.35760i
$344$	7.81210e6	+	1.86719e7i	0.191908	+	0.458684i
$345$	1.03291e6			0.0251540
$346$	1.82762e7	−	2.42815e6i	0.441222	−	0.0586203i
$347$			1.77431e6i			0.0424659i	0.999775	+	0.0212329i	$0.00675916\pi$
$347$			1.77431e6i			0.0424659i	−0.999775	+	0.0212329i	$0.993241\pi$
$348$	7.71925e6	+	2.85377e7i	0.183163	+	0.677145i
$349$	−5.00971e7			−1.17852			−0.589260	−	0.807944i	$-0.700580\pi$
$349$	−5.00971e7			−1.17852			−0.589260	+	0.807944i	$0.700580\pi$
$350$	6.87793e6	+	5.17687e7i	0.160418	+	1.20743i
$351$			8.57607e7i			1.98320i
$352$	2.69668e7	+	3.47157e7i	0.618302	+	0.795971i
$353$	−4.10099e7			−0.932318			−0.466159	−	0.884701i	$-0.654363\pi$
$353$	−4.10099e7			−0.932318			−0.466159	+	0.884701i	$0.654363\pi$
$354$	1.72117e7	−	2.28673e6i	0.387984	−	0.0515472i
$355$		−	3.89167e7i		−	0.869862i
$356$	3.83742e7	−	1.03799e7i	0.850529	−	0.230062i
$357$	−4.07453e6			−0.0895514
$358$	1.39185e6	+	1.04762e7i	0.0303350	+	0.228325i
$359$		−	7.62977e6i		−	0.164903i	−0.996595	−	0.0824514i	$-0.973725\pi$
$359$		−	7.62977e6i		−	0.164903i	0.996595	−	0.0824514i	$-0.0262749\pi$
$360$	−1.04249e7	+	4.36164e6i	−0.223441	+	0.0934851i
$361$	−2.47610e6			−0.0526316
$362$	−4.60577e7	+	6.11918e6i	−0.970905	+	0.128993i
$363$		−	556067.i		−	0.0116254i
$364$	3.90512e7	+	1.44371e8i	0.809711	+	2.99347i
$365$	−7.30290e6			−0.150182
$366$	2.00842e6	+	1.51169e7i	0.0409648	+	0.308333i
$367$		−	5.72134e7i		−	1.15744i	−0.815525	−	0.578722i	$-0.803552\pi$
$367$		−	5.72134e7i		−	1.15744i	0.815525	−	0.578722i	$-0.196448\pi$
$368$	−1.64974e6	−	2.82639e6i	−0.0331034	−	0.0567138i
$369$	−4.42781e7			−0.881271
$370$	−6.75561e6	+	897543.i	−0.133370	+	0.0177195i
$371$			1.00291e8i			1.96399i
$372$	−5.42381e7	+	1.46710e7i	−1.05360	+	0.284991i
$373$	2.86014e7			0.551138			0.275569	−	0.961281i	$-0.411134\pi$
$373$	2.86014e7			0.551138			0.275569	+	0.961281i	$0.411134\pi$
$374$	506371.	+	3.81134e6i	0.00967953	+	0.0728557i
$375$		−	3.48777e7i		−	0.661385i
$376$	−2.51068e7	−	6.00085e7i	−0.472311	−	1.12888i
$377$	9.49116e7			1.77131
$378$	9.62110e7	−	1.27825e7i	1.78135	−	0.236668i
$379$		−	2.02438e7i		−	0.371855i	−0.982563	−	0.185928i	$-0.940471\pi$
$379$		−	2.02438e7i		−	0.371855i	0.982563	−	0.185928i	$-0.0595290\pi$
$380$	1.71856e6	+	6.35346e6i	0.0313195	+	0.115787i
$381$	−5.76072e7			−1.04160
$382$	7.46504e6	+	5.61877e7i	0.133919	+	1.00798i
$383$		−	7.47108e7i		−	1.32980i	−0.746932	−	0.664901i	$-0.768474\pi$
$383$		−	7.47108e7i		−	1.32980i	0.746932	−	0.664901i	$-0.231526\pi$
$384$	−3.31197e7	−	2.49796e7i	−0.584914	−	0.441156i
$385$	5.04099e7			0.883351
$386$	−4.42165e7	+	5.87456e6i	−0.768815	+	0.102144i
$387$		−	1.33505e7i		−	0.230337i
$388$	−5.57648e7	+	1.50840e7i	−0.954695	+	0.258238i
$389$	3.89722e7			0.662073			0.331036	−	0.943618i	$-0.392602\pi$
$389$	3.89722e7			0.662073			0.331036	+	0.943618i	$0.392602\pi$
$390$	−5.53607e6	−	4.16688e7i	−0.0933271	−	0.702452i
$391$		−	286239.i		−	0.00478848i
$392$	1.00573e8	−	4.20787e7i	1.66965	−	0.698560i
$393$	6.54652e7			1.07853
$394$	7.45035e6	−	989846.i	0.121811	−	0.0161837i
$395$			4.12454e7i			0.669243i
$396$	−7.57091e6	−	2.79893e7i	−0.121916	−	0.450720i
$397$	−3.46261e6			−0.0553391			−0.0276695	−	0.999617i	$-0.508809\pi$
$397$	−3.46261e6			−0.0553391			−0.0276695	+	0.999617i	$0.508809\pi$
$398$	1.56228e7	+	1.17590e8i	0.247805	+	1.86518i
$399$		−	1.78966e7i		−	0.281742i
$400$	−4.01636e7	+	2.34431e7i	−0.627556	+	0.366299i
$401$	−1.72402e6			−0.0267368			−0.0133684	−	0.999911i	$-0.504255\pi$
$401$	−1.72402e6			−0.0267368			−0.0133684	+	0.999911i	$0.504255\pi$
$402$	1.57837e7	−	2.09700e6i	0.242957	−	0.0322791i
$403$			1.80387e8i			2.75606i
$404$	−7.60604e7	+	2.05738e7i	−1.15349	+	0.312011i
$405$	−1.11886e7			−0.168426
$406$	−1.41464e7	−	1.06477e8i	−0.211382	−	1.59103i
$407$		−	1.74860e7i		−	0.259363i
$408$	−1.40042e6	−	3.34719e6i	−0.0206195	−	0.0492833i
$409$	−2.77941e7			−0.406241			−0.203120	−	0.979154i	$-0.565108\pi$
$409$	−2.77941e7			−0.406241			−0.203120	+	0.979154i	$0.565108\pi$
$410$	6.79532e7	−	9.02819e6i	0.985957	−	0.130993i
$411$			5.68129e6i			0.0818317i
$412$	−3.37446e7	−	1.24752e8i	−0.482517	−	1.78384i
$413$	−6.30849e7			−0.895520
$414$	284294.	+	2.13982e6i	0.00400652	+	0.0301561i
$415$		−	2.65099e7i		−	0.370906i
$416$	−1.05177e8	+	8.17006e7i	−1.46097	+	1.13487i
$417$	8.42993e6			0.116256
$418$	−1.67406e7	+	2.22414e6i	−0.229215	+	0.0304532i
$419$		−	2.54309e7i		−	0.345716i	−0.984947	−	0.172858i	$-0.944700\pi$
$419$		−	2.54309e7i		−	0.345716i	0.984947	−	0.172858i	$-0.0553002\pi$
$420$	−4.59211e7	+	1.24213e7i	−0.619818	+	0.167656i
$421$	6.39263e7			0.856708			0.428354	−	0.903611i	$-0.359094\pi$
$421$	6.39263e7			0.856708			0.428354	+	0.903611i	$0.359094\pi$
$422$	−1.55927e7	−	1.17363e8i	−0.207484	−	1.56169i
$423$			4.29062e7i			0.566890i
$424$	−8.23881e7	+	3.44701e7i	−1.08085	+	0.452216i
$425$	−4.06751e6			−0.0529861
$426$	−9.34100e7	+	1.24104e7i	−1.20827	+	0.160530i
$427$		−	5.54070e7i		−	0.711674i
$428$	1.28861e6	+	4.76395e6i	0.0164358	+	0.0607625i
$429$	1.07854e8			1.36605
$430$	2.72213e6	+	2.04888e7i	0.0342376	+	0.257699i
$431$		−	6.28571e7i		−	0.785096i	−0.919732	−	0.392548i	$-0.871594\pi$
$431$		−	6.28571e7i		−	0.785096i	0.919732	−	0.392548i	$-0.128406\pi$
$432$	4.35686e7	+	7.46431e7i	0.540409	+	0.925846i
$433$	−9.03626e7			−1.11308			−0.556538	−	0.830822i	$-0.687871\pi$
$433$	−9.03626e7			−1.11308			−0.556538	+	0.830822i	$0.687871\pi$
$434$	2.02367e8	−	2.68863e7i	2.47555	−	0.328899i
$435$			3.01893e7i			0.366763i
$436$	1.82126e7	−	4.92637e6i	0.219742	−	0.0594385i
$437$	1.25725e6			0.0150653
$438$	2.32886e6	+	1.75288e7i	0.0277154	+	0.208608i
$439$		−	5.09136e7i		−	0.601783i	−0.953658	−	0.300892i	$-0.902716\pi$
$439$		−	5.09136e7i		−	0.601783i	0.953658	−	0.300892i	$-0.0972843\pi$
$440$	1.73260e7	+	4.14113e7i	0.203394	+	0.486139i
$441$	−7.19102e7			−0.838445
$442$	−1.15471e7	+	1.53414e6i	−0.133724	+	0.0177664i
$443$			6.77423e7i			0.779199i	0.920984	+	0.389600i	$0.127387\pi$
$443$			6.77423e7i			0.779199i	−0.920984	+	0.389600i	$0.872613\pi$
$444$	4.30867e6	+	1.59290e7i	0.0492260	+	0.181986i
$445$	4.05950e7			0.460673
$446$	−1.74677e7	−	1.31475e8i	−0.196893	−	1.48197i
$447$			2.67457e6i			0.0299455i
$448$	1.07333e8	+	1.05816e8i	1.19371	+	1.17684i
$449$	2.41036e7			0.266283			0.133141	−	0.991097i	$-0.457494\pi$
$449$	2.41036e7			0.266283			0.133141	+	0.991097i	$0.457494\pi$
$450$	3.04073e7	−	4.03988e6i	0.333687	−	0.0443334i
$451$			1.75888e8i			1.91737i
$452$	1.50048e8	−	4.05868e7i	1.62485	−	0.439511i
$453$	−6.71512e7			−0.722369
$454$	−7.48867e6	−	5.63655e7i	−0.0800271	−	0.602346i
$455$			1.52726e8i			1.62135i
$456$	1.47019e7	−	6.15109e6i	0.155052	−	0.0648720i
$457$	9.94808e6			0.104230			0.0521148	−	0.998641i	$-0.483404\pi$
$457$	9.94808e6			0.104230			0.0521148	+	0.998641i	$0.483404\pi$
$458$	−4.20773e7	+	5.59034e6i	−0.437977	+	0.0581891i
$459$			7.55938e6i			0.0781714i
$460$	−872607.	−	3.22599e6i	−0.00896490	−	0.0331429i
$461$	−1.89293e8			−1.93211			−0.966056	−	0.258335i	$-0.916826\pi$
$461$	−1.89293e8			−1.93211			−0.966056	+	0.258335i	$0.916826\pi$
$462$	−1.60755e7	−	1.20997e8i	−0.163019	−	1.22701i
$463$			1.32990e7i			0.133991i	0.997753	+	0.0669956i	$0.0213414\pi$
$463$			1.32990e7i			0.133991i	−0.997753	+	0.0669956i	$0.978659\pi$
$464$	8.26077e7	−	4.82175e7i	0.826926	−	0.482670i
$465$	−5.73770e7			−0.570662
$466$	−1.29981e8	+	1.72691e7i	−1.28446	+	0.170652i
$467$		−	1.98017e7i		−	0.194425i	−0.995264	−	0.0972124i	$-0.969007\pi$
$467$		−	1.98017e7i		−	0.194425i	0.995264	−	0.0972124i	$-0.0309926\pi$
$468$	8.47987e7	−	2.29374e7i	0.827278	−	0.223773i
$469$	−5.78508e7			−0.560778
$470$	−8.74847e6	−	6.58478e7i	−0.0842633	−	0.634231i
$471$		−	3.98137e7i		−	0.381039i
$472$	−2.16824e7	−	5.18237e7i	−0.206196	−	0.492836i
$473$	−5.30327e7			−0.501142
$474$	9.89995e7	−	1.31530e7i	0.929604	−	0.123506i
$475$		−	1.78658e7i		−	0.166702i
$476$	3.44217e6	+	1.27256e7i	0.0319162	+	0.117993i
$477$	5.89077e7			0.542771
$478$	−846705.	−	6.37296e6i	−0.00775262	−	0.0583522i
$479$			3.19125e7i			0.290372i	0.989404	+	0.145186i	$0.0463780\pi$
$479$			3.19125e7i			0.290372i	−0.989404	+	0.145186i	$0.953622\pi$
$480$	−2.59872e7	−	3.34546e7i	−0.234982	−	0.302504i
$481$	5.29770e7			0.476050
$482$	−3.41839e7	+	4.54164e6i	−0.305268	+	0.0405576i
$483$			9.08706e6i			0.0806458i
$484$	−1.73671e6	+	469766.i	−0.0153176	+	0.00414329i
$485$	−5.89920e7			−0.517092
$486$	−1.26391e7	−	9.51314e7i	−0.110105	−	0.828734i
$487$		−	6.33141e7i		−	0.548168i	−0.961706	−	0.274084i	$-0.911625\pi$
$487$		−	6.33141e7i		−	0.548168i	0.961706	−	0.274084i	$-0.0883746\pi$
$488$	4.55164e7	−	1.90435e7i	0.391659	−	0.163865i
$489$	3.96702e7			0.339264
$490$	1.10360e8	−	1.46623e7i	0.938044	−	0.124628i
$491$			7.11423e7i			0.601012i	0.953780	+	0.300506i	$0.0971556\pi$
$491$			7.11423e7i			0.601012i	−0.953780	+	0.300506i	$0.902844\pi$
$492$	−4.33399e7	−	1.60226e8i	−0.363909	−	1.34536i
$493$	8.36598e6			0.0698194
$494$	−6.73843e6	−	5.07186e7i	−0.0558956	−	0.420714i
$495$		−	2.96091e7i		−	0.244124i
$496$	9.16409e7	+	1.57002e8i	0.751008	+	1.28665i
$497$	3.42369e8			2.78885
$498$	−6.36306e7	+	8.45389e6i	−0.515202	+	0.0684493i
$499$		−	6.45626e6i		−	0.0519613i	−0.999662	−	0.0259806i	$-0.991729\pi$
$499$		−	6.45626e6i		−	0.0519613i	0.999662	−	0.0259806i	$-0.00827082\pi$
$500$	−1.08930e8	+	2.94647e7i	−0.871440	+	0.235718i
$501$	6.81718e7			0.542115
$502$	−186099.	−	1.40072e6i	−0.00147107	−	0.0110724i
$503$		−	9.40074e7i		−	0.738683i	−0.929294	−	0.369342i	$-0.879583\pi$
$503$		−	9.40074e7i		−	0.738683i	0.929294	−	0.369342i	$-0.120417\pi$
$504$	−3.83715e7	−	9.17129e7i	−0.299721	−	0.716372i
$505$	−8.04622e7			−0.624767
$506$	8.50010e6	−	1.12932e6i	0.0656104	−	0.00871693i
$507$			2.31285e8i			1.77469i
$508$	4.86667e7	+	1.79919e8i	0.371228	+	1.37241i
$509$	−2.90145e6			−0.0220019			−0.0110010	−	0.999939i	$-0.503502\pi$
$509$	−2.90145e6			−0.0220019			−0.0110010	+	0.999939i	$0.503502\pi$
$510$	−487977.	−	3.67289e6i	−0.00367865	−	0.0276884i
$511$		−	6.42472e7i		−	0.481495i
$512$	−5.00367e7	+	1.24542e8i	−0.372802	+	0.927911i
$513$	−3.32031e7			−0.245939
$514$	−4.34650e6	+	577471.i	−0.0320074	+	0.00425247i
$515$		−	1.31972e8i		−	0.966185i
$516$	4.83104e7	−	1.30676e7i	0.351635	−	0.0951146i
$517$	1.70438e8			1.23338
$518$	−7.89614e6	−	5.94325e7i	−0.0568101	−	0.427597i
$519$		−	4.55871e7i		−	0.326092i
$520$	−1.25463e8	+	5.24921e7i	−0.892288	+	0.373322i
$521$	−1.85245e8			−1.30988			−0.654941	−	0.755680i	$-0.727307\pi$
$521$	−1.85245e8			−1.30988			−0.654941	+	0.755680i	$0.727307\pi$
$522$	−6.25411e7	+	8.30915e6i	−0.439698	+	0.0584178i
$523$		−	1.72734e8i		−	1.20746i	−0.797189	−	0.603730i	$-0.793680\pi$
$523$		−	1.72734e8i		−	1.20746i	0.797189	−	0.603730i	$-0.206320\pi$
$524$	−5.53051e7	−	2.04461e8i	−0.384389	−	1.42107i
$525$	1.29129e8			0.892372
$526$	−5.70960e6	−	4.29749e7i	−0.0392327	−	0.295296i
$527$			1.59002e7i			0.108635i
$528$	9.38725e7	−	5.47926e7i	0.637730	−	0.372238i
$529$	1.47398e8			0.995688
$530$	−9.04050e7	+	1.20111e7i	−0.607247	+	0.0806782i
$531$			3.70541e7i			0.247487i
$532$	−5.58946e7	+	1.51191e7i	−0.371223	+	0.100413i
$533$	−5.32884e8			−3.51926
$534$	−1.29456e7	−	9.74384e7i	−0.0850154	−	0.639892i
$535$			5.03965e6i			0.0329108i
$536$	−1.98834e7	−	4.75240e7i	−0.129121	−	0.308616i
$537$	2.61312e7			0.168747
$538$	−1.80040e8	+	2.39200e7i	−1.15617	+	0.153608i
$539$			2.85652e8i			1.82420i
$540$	2.30450e7	+	8.51964e7i	0.146351	+	0.541053i
$541$	1.78881e8			1.12973			0.564863	−	0.825185i	$-0.308929\pi$
$541$	1.78881e8			1.12973			0.564863	+	0.825185i	$0.308929\pi$
$542$	−1.00964e7	−	7.59932e7i	−0.0634115	−	0.477284i
$543$			1.14884e8i			0.717562i
$544$	−9.27085e6	+	7.20150e6i	−0.0575868	+	0.0447328i
$545$	1.92666e7			0.119019
$546$	3.66581e8	−	4.87036e7i	2.25212	−	0.299215i
$547$		−	1.51587e8i		−	0.926192i	−0.886308	−	0.463096i	$-0.846739\pi$
$547$		−	1.51587e8i		−	0.926192i	0.886308	−	0.463096i	$-0.153261\pi$
$548$	1.77438e7	−	4.79956e6i	0.107821	−	0.0291649i
$549$	−3.25443e7			−0.196679
$550$	−1.60478e7	−	1.20788e8i	−0.0964556	−	0.726000i
$551$			3.67460e7i			0.219662i
$552$	−7.46494e6	+	3.12324e6i	−0.0443822	+	0.0185690i
$553$	−3.62856e8			−2.14565
$554$	1.32284e7	−	1.75751e6i	0.0777998	−	0.0103364i
$555$			1.68508e7i			0.0985694i
$556$	−7.12162e6	−	2.63283e7i	−0.0414338	−	0.153179i
$557$	2.18273e8			1.26309			0.631547	−	0.775338i	$-0.282420\pi$
$557$	2.18273e8			1.26309			0.631547	+	0.775338i	$0.282420\pi$
$558$	−1.57922e7	−	1.18864e8i	−0.0908948	−	0.684145i
$559$		−	1.60672e8i		−	0.919825i
$560$	7.75885e7	+	1.32927e8i	0.441808	+	0.756919i
$561$	9.50681e6			0.0538451
$562$	3.78780e7	−	5.03244e6i	0.213392	−	0.0283511i
$563$			1.53468e8i			0.859987i	0.902832	+	0.429993i	$0.141484\pi$
$563$			1.53468e8i			0.859987i	−0.902832	+	0.429993i	$0.858516\pi$
$564$	−1.55262e8	+	4.19971e7i	−0.865420	+	0.234090i
$565$	1.58731e8			0.880071
$566$	1.19539e7	+	8.99745e7i	0.0659266	+	0.496215i
$567$		−	9.84315e7i		−	0.539989i
$568$	1.17673e8	+	2.81254e8i	0.642143	+	1.53480i
$569$	−1.61022e8			−0.874076			−0.437038	−	0.899443i	$-0.643972\pi$
$569$	−1.61022e8			−0.874076			−0.437038	+	0.899443i	$0.643972\pi$
$570$	1.61325e7	−	2.14335e6i	0.0871118	−	0.0115736i
$571$			8.98903e7i			0.482841i	0.970421	+	0.241421i	$0.0776134\pi$
$571$			8.98903e7i			0.482841i	−0.970421	+	0.241421i	$0.922387\pi$
$572$	−9.11154e7	−	3.36850e8i	−0.486860	−	1.79990i
$573$	1.40152e8			0.744962
$574$	7.94255e7	+	5.97818e8i	0.419976	+	3.16106i
$575$			9.07141e6i			0.0477168i
$576$	6.21530e7	−	6.30438e7i	0.325233	−	0.329894i
$577$	−2.27591e8			−1.18475			−0.592375	−	0.805662i	$-0.701810\pi$
$577$	−2.27591e8			−1.18475			−0.592375	+	0.805662i	$0.701810\pi$
$578$	1.90401e8	−	2.52964e7i	0.986018	−	0.131001i
$579$			1.10291e8i			0.568205i
$580$	9.42871e7	−	2.55040e7i	0.483246	−	0.130714i
$581$	2.33221e8			1.18916
$582$	1.88123e7	+	1.41596e8i	0.0954274	+	0.718261i
$583$		−	2.34002e8i		−	1.18090i
$584$	5.27786e7	−	2.20819e7i	0.264984	−	0.110866i
$585$	8.97062e7			0.448079
$586$	−2.25508e8	+	2.99608e7i	−1.12065	+	0.148888i
$587$		−	3.04271e8i		−	1.50434i	−0.658967	−	0.752172i	$-0.729006\pi$
$587$		−	3.04271e8i		−	1.50434i	0.658967	−	0.752172i	$-0.270994\pi$
$588$	−7.03866e7	−	2.60216e8i	−0.346225	−	1.27998i
$589$	−6.98385e7			−0.341782
$590$	−7.55523e6	−	5.68665e7i	−0.0367868	−	0.276886i
$591$		−	1.85837e7i		−	0.0900266i
$592$	4.61094e7	−	2.69136e7i	0.222241	−	0.129720i
$593$	1.90333e8			0.912748			0.456374	−	0.889788i	$-0.349148\pi$
$593$	1.90333e8			0.912748			0.456374	+	0.889788i	$0.349148\pi$
$594$	−2.24482e8	+	2.98245e7i	−1.07108	+	0.142303i
$595$			1.34620e7i			0.0639086i
$596$	8.35320e6	−	2.25948e6i	0.0394561	−	0.0106726i
$597$	2.93309e8			1.37849
$598$	3.42146e6	+	2.57526e7i	0.0159996	+	0.120425i
$599$		−	9.98812e7i		−	0.464733i	−0.972628	−	0.232366i	$-0.925353\pi$
$599$		−	9.98812e7i		−	0.464733i	0.972628	−	0.232366i	$-0.0746469\pi$
$600$	4.43818e7	+	1.06078e8i	0.205472	+	0.491104i
$601$	9.60765e7			0.442582			0.221291	−	0.975208i	$-0.428973\pi$
$601$	9.60765e7			0.442582			0.221291	+	0.975208i	$0.428973\pi$
$602$	−1.80251e8	+	2.39479e7i	−0.826204	+	0.109769i
$603$			3.39797e7i			0.154977i
$604$	5.67295e7	+	2.09727e8i	0.257453	+	0.951793i
$605$	−1.83721e6			−0.00829648
$606$	2.56591e7	+	1.93130e8i	0.115298	+	0.867825i
$607$		−	1.45744e8i		−	0.651663i	−0.945428	−	0.325832i	$-0.894356\pi$
$607$		−	1.45744e8i		−	0.651663i	0.945428	−	0.325832i	$-0.105644\pi$
$608$	−3.16312e7	−	4.07205e7i	−0.140736	−	0.181177i
$609$	−2.65590e8			−1.17587
$610$	4.99455e7	−	6.63571e6i	0.220043	−	0.0292346i
$611$			5.16374e8i			2.26381i
$612$	7.47458e6	−	2.02182e6i	0.0326086	−	0.00882039i
$613$	−3.13320e8			−1.36021			−0.680105	−	0.733114i	$-0.738066\pi$
$613$	−3.13320e8			−1.36021			−0.680105	+	0.733114i	$0.738066\pi$
$614$	4.74319e7	+	3.57009e8i	0.204911	+	1.54232i
$615$		−	1.69499e8i		−	0.728687i
$616$	−3.64316e8	+	1.52425e8i	−1.55860	+	0.652100i
$617$	3.68202e8			1.56758			0.783792	−	0.621023i	$-0.213283\pi$
$617$	3.68202e8			1.56758			0.783792	+	0.621023i	$0.213283\pi$
$618$	−3.16767e8	+	4.20853e7i	−1.34207	+	0.178306i
$619$			3.23264e8i			1.36297i	0.731834	+	0.681483i	$0.238665\pi$
$619$			3.23264e8i			1.36297i	−0.731834	+	0.681483i	$0.761335\pi$
$620$	4.84722e7	+	1.79200e8i	0.203384	+	0.751904i
$621$	1.68590e7			0.0703975
$622$	6.69944e6	+	5.04252e7i	0.0278399	+	0.209545i
$623$			3.57134e8i			1.47696i
$624$	1.66004e8	+	2.84404e8i	0.683227	+	1.17053i
$625$	6.21676e7			0.254639
$626$	−1.70251e8	+	2.26193e7i	−0.694011	+	0.0922056i
$627$			4.17569e7i			0.169405i
$628$	−1.24346e8	+	3.36347e7i	−0.502057	+	0.135803i
$629$	4.66966e6			0.0187643
$630$	−1.33706e7	−	1.00637e8i	−0.0534722	−	0.402473i
$631$		−	3.97907e8i		−	1.58377i	−0.610667	−	0.791887i	$-0.709099\pi$
$631$		−	3.97907e8i		−	1.58377i	0.610667	−	0.791887i	$-0.290901\pi$
$632$	−1.24714e8	−	2.98083e8i	−0.494043	−	1.18083i
$633$	−2.92744e8			−1.15419
$634$	1.65186e8	−	2.19465e7i	0.648195	−	0.0861186i
$635$			1.90331e8i			0.743341i
$636$	5.76596e7	+	2.13165e8i	0.224130	+	0.828599i
$637$	−8.65435e8			−3.34824
$638$	3.30068e7	+	2.48435e8i	0.127099	+	0.956646i
$639$		−	2.01097e8i		−	0.770731i
$640$	−8.25312e7	+	1.09426e8i	−0.314832	+	0.417425i
$641$	1.70862e8			0.648743			0.324371	−	0.945930i	$-0.394847\pi$
$641$	1.70862e8			0.648743			0.324371	+	0.945930i	$0.394847\pi$
$642$	1.20965e7	−	1.60712e6i	0.0457144	−	0.00607357i
$643$		−	1.36900e8i		−	0.514955i	−0.966284	−	0.257477i	$-0.917109\pi$
$643$		−	1.36900e8i		−	0.514955i	0.966284	−	0.257477i	$-0.0828913\pi$
$644$	2.83807e7	−	7.67676e6i	0.106259	−	0.0287422i
$645$	5.11063e7			0.190456
$646$	−593959.	−	4.47060e6i	−0.00220323	−	0.0165832i
$647$		−	2.63717e8i		−	0.973701i	−0.873485	−	0.486850i	$-0.838146\pi$
$647$		−	2.63717e8i		−	0.973701i	0.873485	−	0.486850i	$-0.161854\pi$
$648$	8.08606e7	−	3.38311e7i	0.297175	−	0.124334i
$649$	1.47192e8			0.538455
$650$	3.65950e8	−	4.86197e7i	1.33254	−	0.177040i
$651$		−	5.04774e8i		−	1.82959i
$652$	−3.35134e7	−	1.23898e8i	−0.120914	−	0.447014i
$653$	8.15129e7			0.292743			0.146372	−	0.989230i	$-0.453240\pi$
$653$	8.15129e7			0.292743			0.146372	+	0.989230i	$0.453240\pi$
$654$	−6.14404e6	−	4.62448e7i	−0.0219645	−	0.165322i
$655$		−	2.16293e8i		−	0.769696i
$656$	−4.63804e8	+	2.70718e8i	−1.64294	+	0.958973i
$657$	−3.77368e7			−0.133066
$658$	5.79296e8	−	7.69646e7i	2.03340	−	0.270155i
$659$			3.74709e8i			1.30930i	0.755934	+	0.654648i	$0.227183\pi$
$659$			3.74709e8i			1.30930i	−0.755934	+	0.654648i	$0.772817\pi$
$660$	1.07145e8	−	2.89818e7i	0.372682	−	0.100808i
$661$	2.71872e7			0.0941369			0.0470684	−	0.998892i	$-0.485012\pi$
$661$	2.71872e7			0.0941369			0.0470684	+	0.998892i	$0.485012\pi$
$662$	6.44096e7	+	4.84797e8i	0.222012	+	1.67104i
$663$			2.88026e7i			0.0988304i
$664$	8.01584e7	+	1.91589e8i	0.273807	+	0.654435i
$665$	−5.91293e7			−0.201066
$666$	−3.49087e7	+	4.63794e6i	−0.118171	+	0.0157001i
$667$		−	1.86579e7i		−	0.0628761i
$668$	−5.75917e7	−	2.12914e8i	−0.193210	−	0.714290i
$669$	−3.27944e8			−1.09527
$670$	−6.92838e6	−	5.21484e7i	−0.0230360	−	0.173387i
$671$			1.29277e8i			0.427913i
$672$	2.94317e8	−	2.28622e8i	0.969855	−	0.753374i
$673$	3.45806e8			1.13445			0.567227	−	0.823562i	$-0.308016\pi$
$673$	3.45806e8			1.13445			0.567227	+	0.823562i	$0.308016\pi$
$674$	−2.58224e8	+	3.43074e7i	−0.843369	+	0.112049i
$675$		−	2.39570e8i		−	0.778971i
$676$	7.22347e8	−	1.95390e8i	2.33833	−	0.632501i
$677$	−5.41605e8			−1.74549			−0.872744	−	0.488178i	$-0.837662\pi$
$677$	−5.41605e8			−1.74549			−0.872744	+	0.488178i	$0.837662\pi$
$678$	−5.06188e7	−	3.80996e8i	−0.162414	−	1.22245i
$679$		−	5.18982e8i		−	1.65784i
$680$	−1.10589e7	+	4.62692e6i	−0.0351711	+	0.0147152i
$681$	−1.40595e8			−0.445173
$682$	−4.72170e8	+	6.27320e7i	−1.48849	+	0.197759i
$683$			8.50132e7i			0.266823i	0.991061	+	0.133412i	$0.0425933\pi$
$683$			8.50132e7i			0.266823i	−0.991061	+	0.133412i	$0.957407\pi$
$684$	8.88045e6	+	3.28307e7i	0.0277502	+	0.102592i
$685$	1.87707e7			0.0583994
$686$	5.77214e7	+	4.34456e8i	0.178799	+	1.34578i
$687$			1.04955e8i			0.323693i
$688$	−8.16254e7	−	1.39843e8i	−0.250646	−	0.429414i
$689$	7.08950e8			2.16749
$690$	−8.19133e6	+	1.08829e6i	−0.0249349	+	0.00331282i
$691$		−	4.51097e8i		−	1.36721i	−0.729852	−	0.683605i	$-0.760411\pi$
$691$		−	4.51097e8i		−	1.36721i	0.729852	−	0.683605i	$-0.239589\pi$
$692$	−1.42377e8	+	3.85120e7i	−0.429658	+	0.116219i
$693$	2.60486e8			0.782682
$694$	−1.86943e6	−	1.40708e7i	−0.00559283	−	0.0420959i
$695$		−	2.78520e7i		−	0.0829665i
$696$	−9.12838e7	−	2.18180e8i	−0.270748	−	0.647124i
$697$	−4.69711e7			−0.138718
$698$	3.97286e8	−	5.27830e7i	1.16825	−	0.155213i
$699$			3.24216e8i			0.949300i
$700$	−1.09088e8	−	4.03295e8i	−0.318042	−	1.17579i
$701$	−3.48768e8			−1.01247			−0.506236	−	0.862395i	$-0.668964\pi$
$701$	−3.48768e8			−1.01247			−0.506236	+	0.862395i	$0.668964\pi$
$702$	−9.03586e7	−	6.80109e8i	−0.261191	−	1.96593i
$703$			2.05106e7i			0.0590354i
$704$	−2.50432e8	−	2.46894e8i	−0.717747	−	0.707606i
$705$	−1.64247e8			−0.468738
$706$	3.25221e8	−	4.32085e7i	0.924197	−	0.122788i
$707$		−	7.07866e8i		−	2.00306i
$708$	−1.34085e8	+	3.62690e7i	−0.377816	+	0.102196i
$709$	4.38006e8			1.22897			0.614485	−	0.788929i	$-0.289364\pi$
$709$	4.38006e8			1.22897			0.614485	+	0.788929i	$0.289364\pi$
$710$	4.10031e7	+	3.08621e8i	0.114562	+	0.862285i
$711$			2.13130e8i			0.592975i
$712$	−2.93383e8	+	1.22748e8i	−0.812821	+	0.340074i
$713$	3.54608e7			0.0978317
$714$	3.23123e7	−	4.29298e6i	0.0887714	−	0.0117941i
$715$		−	3.56344e8i		−	0.974881i
$716$	−2.20757e7	−	8.16128e7i	−0.0601415	−	0.222341i
$717$	−1.58964e7			−0.0431261
$718$	8.03883e6	+	6.05065e7i	0.0217180	+	0.163466i
$719$			2.03392e8i			0.547202i	0.961843	+	0.273601i	$0.0882147\pi$
$719$			2.03392e8i			0.547202i	−0.961843	+	0.273601i	$0.911785\pi$
$720$	7.80771e7	−	4.55730e7i	0.209183	−	0.122098i
$721$	1.16102e9			3.09767
$722$	1.96362e7	−	2.60885e6i	0.0521731	−	0.00693167i
$723$			8.52665e7i			0.225613i
$724$	3.58805e8	−	9.70541e7i	0.945459	−	0.255740i
$725$	−2.65133e8			−0.695744
$726$	585880.	+	4.40979e6i	0.00153108	+	0.0115241i
$727$			4.82036e8i			1.25452i	0.778811	+	0.627258i	$0.215823\pi$
$727$			4.82036e8i			1.25452i	−0.778811	+	0.627258i	$0.784177\pi$
$728$	−4.61799e8	−	1.10376e9i	−1.19690	−	2.86075i
$729$	−3.62093e8			−0.934625
$730$	5.79143e7	−	7.69443e6i	0.148873	−	0.0197792i
$731$		−	1.41624e7i		−	0.0362565i
$732$	−3.18548e7	−	1.17766e8i	−0.0812160	−	0.300252i
$733$	6.67907e8			1.69592			0.847958	−	0.530064i	$-0.177832\pi$
$733$	6.67907e8			1.69592			0.847958	+	0.530064i	$0.177832\pi$
$734$	6.02808e7	+	4.53720e8i	0.152437	+	1.14736i
$735$		−	2.75276e8i		−	0.693276i
$736$	1.60609e7	+	2.06760e7i	0.0402843	+	0.0518600i
$737$	1.34979e8			0.337182
$738$	3.51139e8	−	4.66520e7i	0.873595	−	0.116065i
$739$			3.25734e8i			0.807106i	0.914956	+	0.403553i	$0.132225\pi$
$739$			3.25734e8i			0.807106i	−0.914956	+	0.403553i	$0.867775\pi$
$740$	5.26284e7	−	1.42356e7i	0.129875	−	0.0351302i
$741$	−1.26510e8			−0.310935
$742$	−1.05668e8	−	7.95338e8i	−0.258661	−	1.94688i
$743$			6.03137e8i			1.47045i	0.677825	+	0.735223i	$0.262923\pi$
$743$			6.03137e8i			1.47045i	−0.677825	+	0.735223i	$0.737077\pi$
$744$	4.14668e8	−	1.73492e8i	1.00689	−	0.421270i
$745$	8.83662e6			0.0213706
$746$	−2.26818e8	+	3.01348e7i	−0.546337	+	0.0725858i
$747$		−	1.36986e8i		−	0.328637i
$748$	−8.03137e6	−	2.96916e7i	−0.0191904	−	0.0709462i
$749$	−4.43363e7			−0.105515
$750$	3.67476e7	+	2.76591e8i	0.0871055	+	0.655624i
$751$		−	5.93003e8i		−	1.40003i	−0.714128	−	0.700015i	$-0.753177\pi$
$751$		−	5.93003e8i		−	1.40003i	0.714128	−	0.700015i	$-0.246823\pi$
$752$	2.62331e8	+	4.49434e8i	0.616873	+	1.05685i
$753$	−3.49389e6			−0.00818321
$754$	−7.52679e8	+	1.00000e8i	−1.75588	+	0.233285i
$755$			2.21864e8i			0.515520i
$756$	−7.49516e8	+	2.02738e8i	−1.73466	+	0.469214i
$757$	5.60747e8			1.29265			0.646323	−	0.763064i	$-0.276306\pi$
$757$	5.60747e8			1.29265			0.646323	+	0.763064i	$0.276306\pi$
$758$	2.13291e7	+	1.60540e8i	0.0489740	+	0.368616i
$759$		−	2.12022e7i		−	0.0484904i
$760$	−2.03228e7	−	4.85742e7i	−0.0462960	−	0.110654i
$761$	−2.28214e8			−0.517830			−0.258915	−	0.965900i	$-0.583365\pi$
$761$	−2.28214e8			−0.517830			−0.258915	+	0.965900i	$0.583365\pi$
$762$	4.56843e8	−	6.06957e7i	1.03253	−	0.137181i
$763$			1.69498e8i			0.381585i
$764$	−1.18400e8	−	4.37721e8i	−0.265505	−	0.981561i
$765$	7.90715e6			0.0176618
$766$	7.87163e7	+	5.92480e8i	0.175137	+	1.31822i
$767$			4.45943e8i			0.988311i
$768$	2.88968e8	+	1.63201e8i	0.637920	+	0.360279i
$769$	−1.83495e8			−0.403501			−0.201751	−	0.979437i	$-0.564663\pi$
$769$	−1.83495e8			−0.403501			−0.201751	+	0.979437i	$0.564663\pi$
$770$	−3.99766e8	+	5.31125e7i	−0.875657	+	0.116339i
$771$			1.08417e7i			0.0236555i
$772$	3.44461e8	−	9.31741e7i	0.748666	−	0.202509i
$773$	−3.86353e7			−0.0836461			−0.0418231	−	0.999125i	$-0.513317\pi$
$773$	−3.86353e7			−0.0836461			−0.0418231	+	0.999125i	$0.513317\pi$
$774$	1.40662e7	+	1.05873e8i	0.0303358	+	0.228331i
$775$		−	5.03905e8i		−	1.08254i
$776$	4.26340e8	−	1.78375e8i	0.912369	−	0.381724i
$777$	−1.48245e8			−0.316022
$778$	−3.09062e8	+	4.10616e7i	−0.656306	+	0.0871961i
$779$		−	2.06312e8i		−	0.436426i
$780$	8.78055e7	+	3.24613e8i	0.185028	+	0.684042i
$781$	−7.98827e8			−1.67687
$782$	301585.	+	2.26996e6i	0.000630651	+	0.00474677i
$783$			4.92744e8i			1.02645i
$784$	−7.53245e8	+	4.39663e8i	−1.56310	+	0.912371i
$785$	−1.31542e8			−0.271929
$786$	−5.19160e8	+	6.89750e7i	−1.06914	+	0.142044i
$787$		−	1.95992e8i		−	0.402082i	−0.979583	−	0.201041i	$-0.935567\pi$
$787$		−	1.95992e8i		−	0.402082i	0.979583	−	0.201041i	$-0.0644325\pi$
$788$	−5.80407e7	+	1.56996e7i	−0.118619	+	0.0320855i
$789$	−1.07194e8			−0.218243
$790$	−4.34567e7	−	3.27089e8i	−0.0881405	−	0.663414i
$791$			1.39644e9i			2.82158i
$792$	8.95296e7	+	2.13987e8i	0.180215	+	0.430737i
$793$	−3.91669e8			−0.785416
$794$	2.74596e7	−	3.64825e6i	0.0548570	−	0.00728825i
$795$			2.25501e8i			0.448795i
$796$	−2.47788e8	−	9.16062e8i	−0.491294	−	1.81629i
$797$	−7.84989e8			−1.55056			−0.775280	−	0.631617i	$-0.782391\pi$
$797$	−7.84989e8			−1.55056			−0.775280	+	0.631617i	$0.782391\pi$
$798$	1.88561e7	+	1.41926e8i	0.0371059	+	0.279288i
$799$			4.55158e7i			0.0892322i
$800$	2.93810e8	−	2.28228e8i	0.573847	−	0.445759i
$801$	2.09769e8			0.408173
$802$	1.36720e7	−	1.81645e6i	0.0265039	−	0.00352128i
$803$			1.49904e8i			0.289511i
$804$	−1.22960e8	+	3.32598e7i	−0.236590	+	0.0639958i
$805$	3.00231e7			0.0575530
$806$	−1.90058e8	−	1.43052e9i	−0.362978	−	2.73206i
$807$			4.49083e8i			0.854488i
$808$	5.81506e8	−	2.43295e8i	1.10235	−	0.461210i
$809$	5.35629e8			1.01162			0.505812	−	0.862644i	$-0.331193\pi$
$809$	5.35629e8			1.01162			0.505812	+	0.862644i	$0.331193\pi$
$810$	8.87289e7	−	1.17884e7i	0.166959	−	0.0221820i
$811$			4.03077e8i			0.755659i	0.925875	+	0.377829i	$0.123329\pi$
$811$			4.03077e8i			0.755659i	−0.925875	+	0.377829i	$0.876671\pi$
$812$	2.24371e8	+	8.29491e8i	0.419082	+	1.54933i
$813$	−1.89553e8			−0.352744
$814$	1.84235e7	+	1.38670e8i	0.0341585	+	0.257104i
$815$		−	1.31068e8i		−	0.242116i
$816$	1.46324e7	+	2.50688e7i	0.0269306	+	0.0461384i
$817$	6.22058e7			0.114068
$818$	2.20416e8	−	2.92843e7i	0.402702	−	0.0535026i
$819$			7.89190e8i			1.43658i
$820$	−5.29378e8	+	1.43193e8i	−0.960117	+	0.259705i
$821$	−8.58679e8			−1.55168			−0.775838	−	0.630932i	$-0.782673\pi$
$821$	−8.58679e8			−1.55168			−0.775838	+	0.630932i	$0.782673\pi$
$822$	−5.98589e6	−	4.50544e7i	−0.0107774	−	0.0811189i
$823$			1.83526e8i			0.329229i	0.986358	+	0.164614i	$0.0526379\pi$
$823$			1.83526e8i			0.329229i	−0.986358	+	0.164614i	$0.947362\pi$
$824$	3.99046e8	+	9.53771e8i	0.713249	+	1.70476i
$825$	−3.01288e8			−0.536562
$826$	5.00283e8	−	6.64671e7i	0.887720	−	0.117942i
$827$			7.91755e8i			1.39983i	0.714228	+	0.699913i	$0.246778\pi$
$827$			7.91755e8i			1.39983i	−0.714228	+	0.699913i	$0.753222\pi$
$828$	−4.50908e6	−	1.66699e7i	−0.00794323	−	0.0293658i
$829$	2.72636e8			0.478541			0.239271	−	0.970953i	$-0.423092\pi$
$829$	2.72636e8			0.478541			0.239271	+	0.970953i	$0.423092\pi$
$830$	2.79312e7	+	2.10232e8i	0.0488490	+	0.367675i
$831$		−	3.29962e7i		−	0.0574991i
$832$	7.48008e8	−	7.58728e8i	1.29878	−	1.31740i
$833$	−7.62838e7			−0.131977
$834$	−6.68520e7	+	8.88189e6i	−0.115244	+	0.0153111i
$835$		−	2.25236e8i		−	0.386882i
$836$	1.30415e8	−	3.52763e7i	0.223207	−	0.0603759i
$837$	−9.36497e8			−1.59709
$838$	2.67944e7	+	2.01675e8i	0.0455314	+	0.342705i
$839$		−	9.36031e8i		−	1.58491i	−0.609931	−	0.792454i	$-0.708803\pi$
$839$		−	9.36031e8i		−	1.58491i	0.609931	−	0.792454i	$-0.291197\pi$
$840$	3.51082e8	−	1.46888e8i	0.592339	−	0.247827i
$841$	−4.95028e7			−0.0832227
$842$	−5.06955e8	+	6.73536e7i	−0.849246	+	0.112830i
$843$		−	9.44809e7i		−	0.157711i
$844$	2.47311e8	+	9.14297e8i	0.411354	+	1.52076i
$845$	7.64151e8			1.26651
$846$	−4.52066e7	−	3.40260e8i	−0.0746604	−	0.561952i
$847$		−	1.61629e7i		−	0.0265992i
$848$	6.17046e8	−	3.60164e8i	1.01188	−	0.590627i
$849$	2.24427e8			0.366735
$850$	3.22566e7	−	4.28558e6i	0.0525245	−	0.00697836i
$851$		−	1.04143e7i		−	0.0168983i
$852$	7.27695e8	−	1.96836e8i	1.17660	−	0.318263i
$853$	1.12044e9			1.80527			0.902637	−	0.430403i	$-0.141628\pi$
$853$	1.12044e9			1.80527			0.902637	+	0.430403i	$0.141628\pi$
$854$	5.83776e7	+	4.39395e8i	0.0937287	+	0.705475i
$855$			3.47307e7i			0.0555667i
$856$	−1.52385e7	−	3.64219e7i	−0.0242952	−	0.0580686i
$857$	−8.71813e8			−1.38510			−0.692550	−	0.721370i	$-0.743513\pi$
$857$	−8.71813e8			−1.38510			−0.692550	+	0.721370i	$0.743513\pi$
$858$	−8.55318e8	+	1.13637e8i	−1.35415	+	0.179911i
$859$			2.98214e8i			0.470489i	0.971936	+	0.235244i	$0.0755890\pi$
$859$			2.98214e8i			0.470489i	−0.971936	+	0.235244i	$0.924411\pi$
$860$	−4.31747e7	−	1.59615e8i	−0.0678787	−	0.250945i
$861$	1.49116e9			2.33623
$862$	6.62271e7	+	4.98477e8i	0.103398	+	0.778257i
$863$			5.30892e8i			0.825988i	0.910734	+	0.412994i	$0.135517\pi$
$863$			5.30892e8i			0.825988i	−0.910734	+	0.412994i	$0.864483\pi$
$864$	−4.24158e8	−	5.46039e8i	−0.657637	−	0.846608i
$865$	−1.50617e8			−0.232716
$866$	7.16604e8	−	9.52072e7i	1.10338	−	0.146594i
$867$		−	4.74925e8i		−	0.728732i
$868$	−1.57651e9	+	4.26434e8i	−2.41067	+	0.652068i
$869$	8.46627e8			1.29013
$870$	−3.18078e7	−	2.39411e8i	−0.0483033	−	0.363568i
$871$			4.08944e8i			0.618884i
$872$	−1.39241e8	+	5.82567e7i	−0.209999	+	0.0878611i
$873$	−3.04834e8			−0.458163
$874$	−9.97038e6	+	1.32465e6i	−0.0149340	+	0.00198412i
$875$		−	1.01377e9i		−	1.51327i
$876$	−3.69372e7	−	1.36555e8i	−0.0549480	−	0.203141i
$877$	8.53423e8			1.26522			0.632609	−	0.774471i	$-0.281984\pi$
$877$	8.53423e8			1.26522			0.632609	+	0.774471i	$0.281984\pi$
$878$	5.36433e7	+	4.03761e8i	0.0792559	+	0.596541i
$879$			5.62496e8i			0.828233i
$880$	−1.81032e8	−	3.10150e8i	−0.265648	−	0.455117i
$881$	−8.97084e8			−1.31191			−0.655957	−	0.754798i	$-0.727735\pi$
$881$	−8.97084e8			−1.31191			−0.655957	+	0.754798i	$0.727735\pi$
$882$	5.70271e8	−	7.57656e7i	0.831142	−	0.110425i
$883$			4.69583e8i			0.682072i	0.940050	+	0.341036i	$0.110778\pi$
$883$			4.69583e8i			0.682072i	−0.940050	+	0.341036i	$0.889222\pi$
$884$	8.99561e7	−	2.43325e7i	0.130219	−	0.0352232i
$885$	−1.41845e8			−0.204637
$886$	−7.13742e7	−	5.37218e8i	−0.102622	−	0.772412i
$887$		−	1.32039e9i		−	1.89204i	−0.324103	−	0.946022i	$-0.605062\pi$
$887$		−	1.32039e9i		−	1.89204i	0.324103	−	0.946022i	$-0.394938\pi$
$888$	−5.09521e7	−	1.21782e8i	−0.0727651	−	0.173918i
$889$	−1.67444e9			−2.38322
$890$	−3.21931e8	+	4.27714e7i	−0.456660	+	0.0606714i
$891$			2.29663e8i			0.324682i
$892$	2.77048e8	+	1.02423e9i	0.390356	+	1.44313i
$893$	−1.99919e8			−0.280738
$894$	−2.81796e6	−	2.12102e7i	−0.00394387	−	0.0296846i
$895$		−	8.63359e7i		−	0.120427i
$896$	−9.62671e8	−	7.26069e8i	−1.33830	−	1.00938i
$897$	6.42358e7			0.0890021
$898$	−1.91149e8	+	2.53959e7i	−0.263963	+	0.0350699i
$899$			1.03642e9i			1.42645i
$900$	−2.36883e8	+	6.40750e7i	−0.324942	+	0.0878944i
$901$	6.24904e7			0.0854356
$902$	−1.85318e8	−	1.39485e9i	−0.252521	−	1.90067i
$903$			4.49607e8i			0.610619i
$904$	−1.14716e9	+	4.79959e8i	−1.55282	+	0.649678i
$905$	3.79570e8			0.512090
$906$	5.32530e8	−	7.07514e7i	0.716077	−	0.0951373i
$907$			5.47193e8i			0.733362i	0.930347	+	0.366681i	$0.119506\pi$
$907$			5.47193e8i			0.733362i	−0.930347	+	0.366681i	$0.880494\pi$
$908$	1.18775e8	+	4.39106e8i	0.158660	+	0.586560i
$909$	−4.15778e8			−0.553567
$910$	−1.60914e8	−	1.21116e9i	−0.213535	−	1.60723i
$911$			2.74602e8i			0.363202i	0.983372	+	0.181601i	$0.0581279\pi$
$911$			2.74602e8i			0.363202i	−0.983372	+	0.181601i	$0.941872\pi$
$912$	−1.10110e8	+	6.42702e7i	−0.145158	+	0.0847276i
$913$	−5.44158e8			−0.715011
$914$	−7.88914e7	+	1.04814e7i	−0.103322	+	0.0137272i
$915$		−	1.24581e8i		−	0.162626i
$916$	3.27796e8	−	8.86663e7i	0.426498	−	0.115365i
$917$	1.90284e9			2.46771
$918$	−7.96467e6	−	5.99483e7i	−0.0102953	−	0.0774905i
$919$		−	1.08459e9i		−	1.39739i	−0.715418	−	0.698696i	$-0.753764\pi$
$919$		−	1.08459e9i		−	1.39739i	0.715418	−	0.698696i	$-0.246236\pi$
$920$	1.03190e7	+	2.46637e7i	0.0132518	+	0.0316735i
$921$	8.90505e8			1.13988
$922$	1.50115e9	−	1.99442e8i	1.91528	−	0.254462i
$923$		−	2.42019e9i		−	3.07783i
$924$	2.54967e8	+	9.42604e8i	0.323198	+	1.19485i
$925$	−1.47990e8			−0.186985
$926$	−1.40120e7	−	1.05465e8i	−0.0176469	−	0.132824i
$927$		−	6.81948e8i		−	0.856076i
$928$	−6.04303e8	+	4.69416e8i	−0.756155	+	0.587373i
$929$	−2.57011e8			−0.320557			−0.160278	−	0.987072i	$-0.551239\pi$
$929$	−2.57011e8			−0.320557			−0.160278	+	0.987072i	$0.551239\pi$
$930$	4.55018e8	−	6.04532e7i	0.565691	−	0.0751572i
$931$		−	3.35062e8i		−	0.415218i
$932$	1.01259e9	−	2.73899e8i	1.25080	−	0.338331i
$933$	1.25778e8			0.154867
$934$	2.08633e7	+	1.57034e8i	0.0256061	+	0.192731i
$935$		−	3.14100e7i		−	0.0384267i
$936$	−6.48313e8	+	2.71246e8i	−0.790601	+	0.330777i
$937$	7.61989e8			0.926253			0.463127	−	0.886292i	$-0.346728\pi$
$937$	7.61989e8			0.926253			0.463127	+	0.886292i	$0.346728\pi$
$938$	4.58775e8	−	6.09524e7i	0.555894	−	0.0738555i
$939$			4.24664e8i			0.512919i
$940$	1.38756e8	+	5.12976e8i	0.167059	+	0.617609i
$941$	−3.60941e8			−0.433179			−0.216589	−	0.976263i	$-0.569493\pi$
$941$	−3.60941e8			−0.433179			−0.216589	+	0.976263i	$0.569493\pi$
$942$	4.19482e7	+	3.15735e8i	0.0501835	+	0.377720i
$943$			1.04755e8i			0.124923i
$944$	2.26550e8	+	3.88134e8i	0.269308	+	0.461387i
$945$	−7.92892e8			−0.939547
$946$	4.20566e8	−	5.58760e7i	0.496776	−	0.0660012i
$947$		−	1.16685e9i		−	1.37393i	−0.726689	−	0.686967i	$-0.758942\pi$
$947$		−	1.16685e9i		−	1.37393i	0.726689	−	0.686967i	$-0.241058\pi$
$948$	−7.71239e8	+	2.08615e8i	−0.905241	+	0.244861i
$949$	−4.54160e8			−0.531386
$950$	1.88236e7	+	1.41681e8i	0.0219549	+	0.165250i
$951$		−	4.12031e8i		−	0.479059i
$952$	−4.07053e7	−	9.72909e7i	−0.0471780	−	0.112762i
$953$	4.43633e8			0.512560			0.256280	−	0.966603i	$-0.417503\pi$
$953$	4.43633e8			0.512560			0.256280	+	0.966603i	$0.417503\pi$
$954$	−4.67156e8	+	6.20659e7i	−0.538043	+	0.0714839i
$955$		−	4.63053e8i		−	0.531644i
$956$	1.34293e7	+	4.96475e7i	0.0153702	+	0.0568229i
$957$	6.19683e8			0.707024
$958$	−3.36235e7	−	2.53076e8i	−0.0382425	−	0.287842i
$959$			1.65135e8i			0.187233i
$960$	2.41335e8	+	2.37925e8i	0.272776	+	0.268922i
$961$	−1.08230e9			−1.21948
$962$	−4.20124e8	+	5.58173e7i	−0.471903	+	0.0626965i
$963$			2.60417e7i			0.0291602i
$964$	2.66304e8	−	7.20333e7i	0.297267	−	0.0804086i
$965$	3.64396e8			0.405501
$966$	−9.57425e6	−	7.20632e7i	−0.0106212	−	0.0799433i
$967$			1.79140e9i			1.98114i	0.137025	+	0.990568i	$0.456246\pi$
$967$			1.79140e9i			1.98114i	−0.137025	+	0.990568i	$0.543754\pi$
$968$	1.32777e7	−	5.55521e6i	0.0146385	−	0.00612456i
$969$	−1.11512e7			−0.0122561
$970$	4.67825e8	−	6.21548e7i	0.512588	−	0.0681019i
$971$		−	1.74393e9i		−	1.90489i	−0.304708	−	0.952446i	$-0.598559\pi$
$971$		−	1.74393e9i		−	1.90489i	0.304708	−	0.952446i	$-0.401441\pi$
$972$	2.00464e8	+	7.41105e8i	0.218291	+	0.807014i
$973$	2.45028e8			0.265998
$974$	6.67086e7	+	5.02100e8i	0.0721946	+	0.543393i
$975$		−	9.12805e8i		−	0.984836i
$976$	−3.40895e8	+	1.98978e8i	−0.366667	+	0.214020i
$977$	−1.42583e9			−1.52891			−0.764457	−	0.644675i	$-0.776993\pi$
$977$	−1.42583e9			−1.52891			−0.764457	+	0.644675i	$0.776993\pi$
$978$	−3.14597e8	+	4.17971e7i	−0.336309	+	0.0446816i
$979$		−	8.33277e8i		−	0.888058i
$980$	−8.59741e8	+	2.32554e8i	−0.913460	+	0.247084i
$981$	9.95577e7			0.105455
$982$	−7.49565e7	−	5.64181e8i	−0.0791543	−	0.595777i
$983$		−	5.90551e7i		−	0.0621723i	−0.999517	−	0.0310862i	$-0.990103\pi$
$983$		−	5.90551e7i		−	0.0621723i	0.999517	−	0.0310862i	$-0.00989663\pi$
$984$	5.12516e8	+	1.22498e9i	0.537925	+	1.28571i
$985$	−6.13997e7			−0.0642476
$986$	−6.63449e7	+	8.81451e6i	−0.0692112	+	0.00919534i
$987$		−	1.44496e9i		−	1.50281i
$988$	1.06876e8	+	3.95115e8i	0.110817	+	0.409688i
$989$	−3.15853e7			−0.0326509
$990$	3.11966e7	+	2.34810e8i	0.0321515	+	0.241997i
$991$			3.18603e8i			0.327363i	0.986513	+	0.163681i	$0.0523369\pi$
$991$			3.18603e8i			0.327363i	−0.986513	+	0.163681i	$0.947663\pi$
$992$	−8.92161e8	−	1.14852e9i	−0.913920	−	1.17653i
$993$	1.20925e9			1.23500
$994$	−2.71510e9	+	3.60725e8i	−2.76456	+	0.367297i
$995$		−	9.69077e8i		−	0.983760i
$996$	4.95703e8	−	1.34084e8i	0.501700	−	0.135706i
$997$	−6.51411e8			−0.657309			−0.328654	−	0.944450i	$-0.606595\pi$
$997$	−6.51411e8			−0.657309			−0.328654	+	0.944450i	$0.606595\pi$
$998$	6.80241e6	+	5.12002e7i	0.00684339	+	0.0515086i
$999$			2.75036e8i			0.275863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.4	yes	54
4.3	odd	2	inner	76.7.b.a.39.3	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.3	✓	54	4.3	odd	2	inner
76.7.b.a.39.4	yes	54	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.93032 + 1.05361i) q^{2} +19.7809i q^{3} +(61.7798 - 16.7110i) q^{4} +65.3551 q^{5} +(-20.8415 - 156.869i) q^{6} +574.962i q^{7} +(-472.326 + 197.615i) q^{8} +337.714 q^{9} +O(q^{10})\)	\(q+(-7.93032 + 1.05361i) q^{2} +19.7809i q^{3} +(61.7798 - 16.7110i) q^{4} +65.3551 q^{5} +(-20.8415 - 156.869i) q^{6} +574.962i q^{7} +(-472.326 + 197.615i) q^{8} +337.714 q^{9} +(-518.287 + 68.8591i) q^{10} -1341.52i q^{11} +(330.559 + 1222.06i) q^{12} +4064.37 q^{13} +(-605.788 - 4559.63i) q^{14} +1292.79i q^{15} +(3537.49 - 2064.80i) q^{16} +358.254 q^{17} +(-2678.18 + 355.820i) q^{18} +1573.56i q^{19} +(4037.63 - 1092.15i) q^{20} -11373.3 q^{21} +(1413.44 + 10638.7i) q^{22} -798.982i q^{23} +(-3909.02 - 9343.06i) q^{24} -11353.7 q^{25} +(-32231.7 + 4282.28i) q^{26} +21100.6i q^{27} +(9608.18 + 35521.0i) q^{28} +23352.1 q^{29} +(-1362.10 - 10252.2i) q^{30} +44382.4i q^{31} +(-25877.9 + 20101.7i) q^{32} +26536.5 q^{33} +(-2841.07 + 377.461i) q^{34} +37576.7i q^{35} +(20863.9 - 5643.53i) q^{36} +13034.5 q^{37} +(-1657.93 - 12478.8i) q^{38} +80397.1i q^{39} +(-30869.0 + 12915.2i) q^{40} -131111. q^{41} +(90193.8 - 11983.1i) q^{42} -39531.9i q^{43} +(-22418.1 - 82878.7i) q^{44} +22071.4 q^{45} +(841.819 + 6336.18i) q^{46} +127049. i q^{47} +(40843.7 + 69974.8i) q^{48} -212932. q^{49} +(90038.5 - 11962.4i) q^{50} +7086.60i q^{51} +(251096. - 67919.6i) q^{52} +174431. q^{53} +(-22231.9 - 167335. i) q^{54} -87675.1i q^{55} +(-113621. - 271570. i) q^{56} -31126.6 q^{57} +(-185190. + 24604.1i) q^{58} +109720. i q^{59} +(21603.7 + 79868.1i) q^{60} -96366.5 q^{61} +(-46761.9 - 351967. i) q^{62} +194173. i q^{63} +(184040. - 186678. i) q^{64} +265627. q^{65} +(-210443. + 27959.2i) q^{66} +100617. i q^{67} +(22132.9 - 5986.77i) q^{68} +15804.6 q^{69} +(-39591.3 - 297995. i) q^{70} -595464. i q^{71} +(-159511. + 66737.5i) q^{72} -111742. q^{73} +(-103368. + 13733.3i) q^{74} -224587. i q^{75} +(26295.8 + 97214.4i) q^{76} +771322. q^{77} +(-84707.5 - 637574. i) q^{78} +631096. i q^{79} +(231193. - 134945. i) q^{80} -171197. q^{81} +(1.03975e6 - 138140. i) q^{82} -405628. i q^{83} +(-702640. + 190059. i) q^{84} +23413.7 q^{85} +(41651.3 + 313500. i) q^{86} +461927. i q^{87} +(265105. + 633635. i) q^{88} +621145. q^{89} +(-175033. + 23254.7i) q^{90} +2.33686e6i q^{91} +(-13351.8 - 49361.0i) q^{92} -877927. q^{93} +(-133860. - 1.00754e6i) q^{94} +102840. i q^{95} +(-397630. - 511889. i) q^{96} -902638. q^{97} +(1.68862e6 - 224348. i) q^{98} -453050. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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