LMFDB - Embedded newform 76.7.b.a.39.6

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			39.6
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.73539 + 2.04054i) q^{2} -48.2920i q^{3} +(55.6724 - 31.5687i) q^{4} -82.2790 q^{5} +(98.5416 + 373.557i) q^{6} -359.057i q^{7} +(-366.231 + 357.798i) q^{8} -1603.11 q^{9} +O(q^{10})$	\(q+(-7.73539 + 2.04054i) q^{2} -48.2920i q^{3} +(55.6724 - 31.5687i) q^{4} -82.2790 q^{5} +(98.5416 + 373.557i) q^{6} -359.057i q^{7} +(-366.231 + 357.798i) q^{8} -1603.11 q^{9} +(636.459 - 167.893i) q^{10} -2504.92i q^{11} +(-1524.51 - 2688.53i) q^{12} -1511.40 q^{13} +(732.669 + 2777.45i) q^{14} +3973.41i q^{15} +(2102.83 - 3515.01i) q^{16} +5229.33 q^{17} +(12400.7 - 3271.22i) q^{18} +1573.56i q^{19} +(-4580.67 + 2597.44i) q^{20} -17339.6 q^{21} +(5111.39 + 19376.5i) q^{22} -11195.6i q^{23} +(17278.8 + 17686.0i) q^{24} -8855.17 q^{25} +(11691.2 - 3084.06i) q^{26} +42212.7i q^{27} +(-11335.0 - 19989.6i) q^{28} +33925.0 q^{29} +(-8107.90 - 30735.9i) q^{30} +19449.1i q^{31} +(-9093.73 + 31480.9i) q^{32} -120968. q^{33} +(-40450.9 + 10670.7i) q^{34} +29542.8i q^{35} +(-89249.3 + 50608.2i) q^{36} -39956.4 q^{37} +(-3210.91 - 12172.1i) q^{38} +72988.3i q^{39} +(30133.1 - 29439.2i) q^{40} +49241.4 q^{41} +(134128. - 35382.1i) q^{42} +105511. i q^{43} +(-79077.1 - 139455. i) q^{44} +131903. q^{45} +(22845.0 + 86602.0i) q^{46} +8104.39i q^{47} +(-169747. - 101550. i) q^{48} -11273.0 q^{49} +(68498.2 - 18069.3i) q^{50} -252535. i q^{51} +(-84143.0 + 47712.8i) q^{52} +244054. q^{53} +(-86136.7 - 326532. i) q^{54} +206102. i q^{55} +(128470. + 131498. i) q^{56} +75990.4 q^{57} +(-262423. + 69225.3i) q^{58} +26040.5i q^{59} +(125435. + 221209. i) q^{60} +62773.1 q^{61} +(-39686.6 - 150446. i) q^{62} +575610. i q^{63} +(6105.59 - 262073. i) q^{64} +124356. q^{65} +(935732. - 246839. i) q^{66} -473921. i q^{67} +(291130. - 165083. i) q^{68} -540656. q^{69} +(-60283.3 - 228525. i) q^{70} +140823. i q^{71} +(587110. - 573591. i) q^{72} -569273. q^{73} +(309078. - 81532.6i) q^{74} +427634. i q^{75} +(49675.3 + 87604.0i) q^{76} -899410. q^{77} +(-148935. - 564593. i) q^{78} +52609.7i q^{79} +(-173019. + 289211. i) q^{80} +869865. q^{81} +(-380901. + 100479. i) q^{82} -513228. i q^{83} +(-965336. + 547388. i) q^{84} -430264. q^{85} +(-215298. - 816165. i) q^{86} -1.63831e6i q^{87} +(896256. + 917379. i) q^{88} -700620. q^{89} +(-1.02032e6 + 269152. i) q^{90} +542677. i q^{91} +(-353429. - 623284. i) q^{92} +939234. q^{93} +(-16537.3 - 62690.6i) q^{94} -129471. i q^{95} +(1.52027e6 + 439154. i) q^{96} +337832. q^{97} +(87200.9 - 23002.9i) q^{98} +4.01568e6i 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 $

$2$	−7.73539	+	2.04054i	−0.966923	+	0.255067i
$2$	−7.73539	+	2.04054i	−0.966923	+	0.255067i
$3$		−	48.2920i		−	1.78859i	−0.447476	−	0.894296i	$-0.647677\pi$
$3$		−	48.2920i		−	1.78859i	0.447476	−	0.894296i	$-0.352323\pi$
$4$	55.6724	−	31.5687i	0.869881	−	0.493261i
$5$	−82.2790			−0.658232			−0.329116	−	0.944290i	$-0.606751\pi$
$5$	−82.2790			−0.658232			−0.329116	+	0.944290i	$0.606751\pi$
$6$	98.5416	+	373.557i	0.456211	+	1.72943i
$7$		−	359.057i		−	1.04681i	−0.852083	−	0.523407i	$-0.824661\pi$
$7$		−	359.057i		−	1.04681i	0.852083	−	0.523407i	$-0.175339\pi$
$8$	−366.231	+	357.798i	−0.715294	+	0.698824i
$9$	−1603.11			−2.19906
$10$	636.459	−	167.893i	0.636459	−	0.167893i
$11$		−	2504.92i		−	1.88199i	−0.338427	−	0.940993i	$-0.609895\pi$
$11$		−	2504.92i		−	1.88199i	0.338427	−	0.940993i	$-0.390105\pi$
$12$	−1524.51	−	2688.53i	−0.882242	−	1.55586i
$13$	−1511.40			−0.687936			−0.343968	−	0.938981i	$-0.611771\pi$
$13$	−1511.40			−0.687936			−0.343968	+	0.938981i	$0.611771\pi$
$14$	732.669	+	2777.45i	0.267008	+	1.01219i
$15$			3973.41i			1.17731i
$16$	2102.83	−	3515.01i	0.513387	−	0.858157i
$17$	5229.33			1.06439			0.532194	−	0.846623i	$-0.321368\pi$
$17$	5229.33			1.06439			0.532194	+	0.846623i	$0.321368\pi$
$18$	12400.7	−	3271.22i	2.12632	−	0.560908i
$19$			1573.56i			0.229416i
$19$			1573.56i			0.229416i
$20$	−4580.67	+	2597.44i	−0.572583	+	0.324680i
$21$	−17339.6			−1.87232
$22$	5111.39	+	19376.5i	0.480033	+	1.81974i
$23$		−	11195.6i		−	0.920158i	−0.887878	−	0.460079i	$-0.847821\pi$
$23$		−	11195.6i		−	0.920158i	0.887878	−	0.460079i	$-0.152179\pi$
$24$	17278.8	+	17686.0i	1.24991	+	1.27937i
$25$	−8855.17			−0.566731
$26$	11691.2	−	3084.06i	0.665182	−	0.175470i
$27$			42212.7i			2.14463i
$28$	−11335.0	−	19989.6i	−0.516352	−	0.910604i
$29$	33925.0			1.39100			0.695498	−	0.718528i	$-0.255184\pi$
$29$	33925.0			1.39100			0.695498	+	0.718528i	$0.255184\pi$
$30$	−8107.90	−	30735.9i	−0.300293	−	1.13837i
$31$			19449.1i			0.652850i	0.945223	+	0.326425i	$0.105844\pi$
$31$			19449.1i			0.652850i	−0.945223	+	0.326425i	$0.894156\pi$
$32$	−9093.73	+	31480.9i	−0.277519	+	0.960720i
$33$	−120968.			−3.36610
$34$	−40450.9	+	10670.7i	−1.02918	+	0.271490i
$35$			29542.8i			0.689046i
$36$	−89249.3	+	50608.2i	−1.91292	+	1.08471i
$37$	−39956.4			−0.788826			−0.394413	−	0.918933i	$-0.629052\pi$
$37$	−39956.4			−0.788826			−0.394413	+	0.918933i	$0.629052\pi$
$38$	−3210.91	−	12172.1i	−0.0585164	−	0.221827i
$39$			72988.3i			1.23044i
$40$	30133.1	−	29439.2i	0.470829	−	0.459988i
$41$	49241.4			0.714461			0.357230	−	0.934016i	$-0.383721\pi$
$41$	49241.4			0.714461			0.357230	+	0.934016i	$0.383721\pi$
$42$	134128.	−	35382.1i	1.81039	−	0.477568i
$43$			105511.i			1.32706i	0.748150	+	0.663530i	$0.230943\pi$
$43$			105511.i			1.32706i	−0.748150	+	0.663530i	$0.769057\pi$
$44$	−79077.1	−	139455.i	−0.928310	−	1.63710i
$45$	131903.			1.44749
$46$	22845.0	+	86602.0i	0.234702	+	0.889722i
$47$			8104.39i			0.0780597i	0.999238	+	0.0390298i	$0.0124267\pi$
$47$			8104.39i			0.0780597i	−0.999238	+	0.0390298i	$0.987573\pi$
$48$	−169747.	−	101550.i	−1.53489	−	0.918240i
$49$	−11273.0			−0.0958188
$50$	68498.2	−	18069.3i	0.547986	−	0.144555i
$51$		−	252535.i		−	1.90375i
$52$	−84143.0	+	47712.8i	−0.598423	+	0.339332i
$53$	244054.			1.63930			0.819648	−	0.572867i	$-0.194169\pi$
$53$	244054.			1.63930			0.819648	+	0.572867i	$0.194169\pi$
$54$	−86136.7	−	326532.i	−0.547024	−	2.07369i
$55$			206102.i			1.23878i
$56$	128470.	+	131498.i	0.731538	+	0.748779i
$57$	75990.4			0.410331
$58$	−262423.	+	69225.3i	−1.34499	+	0.354798i
$59$			26040.5i			0.126792i	0.997988	+	0.0633962i	$0.0201932\pi$
$59$			26040.5i			0.126792i	−0.997988	+	0.0633962i	$0.979807\pi$
$60$	125435.	+	221209.i	0.580720	+	1.02412i
$61$	62773.1			0.276556			0.138278	−	0.990393i	$-0.455843\pi$
$61$	62773.1			0.276556			0.138278	+	0.990393i	$0.455843\pi$
$62$	−39686.6	−	150446.i	−0.166521	−	0.631256i
$63$			575610.i			2.30201i
$64$	6105.59	−	262073.i	0.0232910	−	0.999729i
$65$	124356.			0.452821
$66$	935732.	−	246839.i	3.25476	−	0.858583i
$67$		−	473921.i		−	1.57573i	−0.615849	−	0.787865i	$-0.711187\pi$
$67$		−	473921.i		−	1.57573i	0.615849	−	0.787865i	$-0.288813\pi$
$68$	291130.	−	165083.i	0.925891	−	0.525020i
$69$	−540656.			−1.64579
$70$	−60283.3	−	228525.i	−0.175753	−	0.666254i
$71$			140823.i			0.393458i	0.980458	+	0.196729i	$0.0630320\pi$
$71$			140823.i			0.393458i	−0.980458	+	0.196729i	$0.936968\pi$
$72$	587110.	−	573591.i	1.57297	−	1.53676i
$73$	−569273.			−1.46336			−0.731681	−	0.681647i	$-0.761264\pi$
$73$	−569273.			−1.46336			−0.731681	+	0.681647i	$0.761264\pi$
$74$	309078.	−	81532.6i	0.762735	−	0.201204i
$75$			427634.i			1.01365i
$76$	49675.3	+	87604.0i	0.113162	+	0.199564i
$77$	−899410.			−1.97009
$78$	−148935.	−	564593.i	−0.313844	−	1.18974i
$79$			52609.7i			0.106705i	0.998576	+	0.0533525i	$0.0169907\pi$
$79$			52609.7i			0.106705i	−0.998576	+	0.0533525i	$0.983009\pi$
$80$	−173019.	+	289211.i	−0.337928	+	0.564866i
$81$	869865.			1.63680
$82$	−380901.	+	100479.i	−0.690829	+	0.182236i
$83$		−	513228.i		−	0.897587i	−0.893636	−	0.448793i	$-0.851854\pi$
$83$		−	513228.i		−	0.897587i	0.893636	−	0.448793i	$-0.148146\pi$
$84$	−965336.	+	547388.i	−1.62870	+	0.923543i
$85$	−430264.			−0.700613
$86$	−215298.	−	816165.i	−0.338490	−	1.28317i
$87$		−	1.63831e6i		−	2.48792i
$88$	896256.	+	917379.i	1.31518	+	1.34617i
$89$	−700620.			−0.993831			−0.496915	−	0.867799i	$-0.665534\pi$
$89$	−700620.			−0.993831			−0.496915	+	0.867799i	$0.665534\pi$
$90$	−1.02032e6	+	269152.i	−1.39961	+	0.369207i
$91$			542677.i			0.720141i
$92$	−353429.	−	623284.i	−0.453878	−	0.800428i
$93$	939234.			1.16768
$94$	−16537.3	−	62690.6i	−0.0199105	−	0.0754777i
$95$		−	129471.i		−	0.151009i
$96$	1.52027e6	+	439154.i	1.71834	+	0.496367i
$97$	337832.			0.370157			0.185078	−	0.982724i	$-0.440746\pi$
$97$	337832.			0.370157			0.185078	+	0.982724i	$0.440746\pi$
$98$	87200.9	−	23002.9i	0.0926494	−	0.0244402i
$99$			4.01568e6i			4.13860i
$100$	−492989.	+	279546.i	−0.492989	+	0.279546i
$101$	−878050.			−0.852227			−0.426113	−	0.904670i	$-0.640118\pi$
$101$	−878050.			−0.852227			−0.426113	+	0.904670i	$0.640118\pi$
$102$	515307.	+	1.95345e6i	0.485585	+	1.84078i
$103$		−	861088.i		−	0.788017i	−0.919107	−	0.394009i	$-0.871088\pi$
$103$		−	861088.i		−	0.788017i	0.919107	−	0.394009i	$-0.128912\pi$
$104$	553519.	−	540774.i	0.492077	−	0.480746i
$105$	1.42668e6			1.23242
$106$	−1.88785e6	+	498001.i	−1.58507	+	0.418131i
$107$		−	1.31051e6i		−	1.06977i	−0.844925	−	0.534885i	$-0.820355\pi$
$107$		−	1.31051e6i		−	1.06977i	0.844925	−	0.534885i	$-0.179645\pi$
$108$	1.33260e6	+	2.35008e6i	1.05786	+	1.86557i
$109$	1.98114e6			1.52980			0.764901	−	0.644148i	$-0.222788\pi$
$109$	1.98114e6			1.52980			0.764901	+	0.644148i	$0.222788\pi$
$110$	−420560.	−	1.59428e6i	−0.315973	−	1.19781i
$111$			1.92957e6i			1.41089i
$112$	−1.26209e6	−	755038.i	−0.898330	−	0.537421i
$113$	−1.82029e6			−1.26155			−0.630775	−	0.775966i	$-0.717263\pi$
$113$	−1.82029e6			−1.26155			−0.630775	+	0.775966i	$0.717263\pi$
$114$	−587815.	+	155061.i	−0.396759	+	0.104662i
$115$			921159.i			0.605677i
$116$	1.88869e6	−	1.07097e6i	1.21000	−	0.686124i
$117$	2.42294e6			1.51281
$118$	−53136.7	−	201433.i	−0.0323406	−	0.122599i
$119$		−	1.87763e6i		−	1.11421i
$120$	−1.42168e6	−	1.45519e6i	−0.822730	−	0.842121i
$121$	−4.50308e6			−2.54187
$122$	−485574.	+	128091.i	−0.267409	+	0.0705405i
$123$		−	2.37796e6i		−	1.27788i
$124$	613982.	+	1.08278e6i	0.322026	+	0.567902i
$125$	2.01420e6			1.03127
$126$	−1.17455e6	−	4.45256e6i	−0.587166	−	2.22586i
$127$		−	1.69166e6i		−	0.825851i	−0.910765	−	0.412926i	$-0.864507\pi$
$127$		−	1.69166e6i		−	0.825851i	0.910765	−	0.412926i	$-0.135493\pi$
$128$	487540.	+	2.03969e6i	0.232477	+	0.972602i
$129$	5.09531e6			2.37357
$130$	−961942.	+	253753.i	−0.437843	+	0.115500i
$131$			907898.i			0.403853i	0.979401	+	0.201926i	$0.0647202\pi$
$131$			907898.i			0.403853i	−0.979401	+	0.201926i	$0.935280\pi$
$132$	−6.73456e6	+	3.81879e6i	−2.92811	+	1.66037i
$133$	564999.			0.240156
$134$	967054.	+	3.66596e6i	0.401917	+	1.52361i
$135$		−	3.47322e6i		−	1.41166i
$136$	−1.91514e6	+	1.87104e6i	−0.761350	+	0.743819i
$137$	−2.20338e6			−0.856896			−0.428448	−	0.903566i	$-0.640940\pi$
$137$	−2.20338e6			−0.856896			−0.428448	+	0.903566i	$0.640940\pi$
$138$	4.18218e6	−	1.10323e6i	1.59135	−	0.419786i
$139$		−	670706.i		−	0.249740i	−0.992173	−	0.124870i	$-0.960149\pi$
$139$		−	670706.i		−	0.249740i	0.992173	−	0.124870i	$-0.0398514\pi$
$140$	932629.	+	1.64472e6i	0.339879	+	0.599388i
$141$	391377.			0.139617
$142$	−287355.	−	1.08932e6i	−0.100358	−	0.380444i
$143$			3.78593e6i			1.29469i
$144$	−3.37109e6	+	5.63497e6i	−1.12897	+	1.88714i
$145$	−2.79131e6			−0.915598
$146$	4.40355e6	−	1.16162e6i	1.41496	−	0.373256i
$147$			544395.i			0.171381i
$148$	−2.22447e6	+	1.26137e6i	−0.686185	+	0.389097i
$149$	3.07570e6			0.929790			0.464895	−	0.885366i	$-0.346092\pi$
$149$	3.07570e6			0.929790			0.464895	+	0.885366i	$0.346092\pi$
$150$	−872603.	−	3.30791e6i	−0.258549	−	0.980122i
$151$			770677.i			0.223842i	0.993717	+	0.111921i	$0.0357004\pi$
$151$			770677.i			0.223842i	−0.993717	+	0.111921i	$0.964300\pi$
$152$	−563017.	−	576287.i	−0.160321	−	0.164100i
$153$	−8.38322e6			−2.34065
$154$	6.95728e6	−	1.83528e6i	1.90492	−	0.502505i
$155$		−	1.60025e6i		−	0.429727i
$156$	2.30414e6	+	4.06343e6i	0.606926	+	1.07033i
$157$	−5.26942e6			−1.36165			−0.680823	−	0.732448i	$-0.738378\pi$
$157$	−5.26942e6			−1.36165			−0.680823	+	0.732448i	$0.738378\pi$
$158$	−107352.	−	406956.i	−0.0272169	−	0.103175i
$159$		−	1.17858e7i		−	2.93203i
$160$	748223.	−	2.59021e6i	0.182672	−	0.632376i
$161$	−4.01984e6			−0.963233
$162$	−6.72874e6	+	1.77499e6i	−1.58266	+	0.417495i
$163$			4.60269e6i			1.06279i	0.847123	+	0.531397i	$0.178333\pi$
$163$			4.60269e6i			1.06279i	−0.847123	+	0.531397i	$0.821667\pi$
$164$	2.74138e6	−	1.55449e6i	0.621496	−	0.352416i
$165$	9.95309e6			2.21568
$166$	1.04726e6	+	3.97002e6i	0.228945	+	0.867898i
$167$		−	5.06489e6i		−	1.08748i	−0.839254	−	0.543739i	$-0.817008\pi$
$167$		−	5.06489e6i		−	1.08748i	0.839254	−	0.543739i	$-0.182992\pi$
$168$	6.35028e6	−	6.20406e6i	1.33926	−	1.30842i
$169$	−2.54249e6			−0.526744
$170$	3.32826e6	−	877970.i	0.677439	−	0.178703i
$171$		−	2.52260e6i		−	0.504499i
$172$	3.33083e6	+	5.87403e6i	0.654587	+	1.15439i
$173$	3.89476e6			0.752215			0.376108	−	0.926576i	$-0.377262\pi$
$173$	3.89476e6			0.752215			0.376108	+	0.926576i	$0.377262\pi$
$174$	3.34303e6	+	1.26729e7i	0.634588	+	2.40563i
$175$			3.17951e6i			0.593262i
$176$	−8.80483e6	−	5.26744e6i	−1.61504	−	0.966188i
$177$	1.25755e6			0.226780
$178$	5.41957e6	−	1.42964e6i	0.960958	−	0.253494i
$179$			2.86319e6i			0.499219i	0.968347	+	0.249610i	$0.0803023\pi$
$179$			2.86319e6i			0.499219i	−0.968347	+	0.249610i	$0.919698\pi$
$180$	7.34334e6	−	4.16399e6i	1.25915	−	0.713991i
$181$	2.04811e6			0.345396			0.172698	−	0.984975i	$-0.444751\pi$
$181$	2.04811e6			0.345396			0.172698	+	0.984975i	$0.444751\pi$
$182$	−1.10735e6	−	4.19782e6i	−0.183684	−	0.696321i
$183$		−	3.03143e6i		−	0.494647i
$184$	4.00574e6	+	4.10015e6i	0.643028	+	0.658183i
$185$	3.28757e6			0.519230
$186$	−7.26534e6	+	1.91654e6i	−1.12906	+	0.297838i
$187$		−	1.30991e7i		−	2.00316i
$188$	255845.	+	451191.i	0.0385038	+	0.0679027i
$189$	1.51568e7			2.24503
$190$	264191.	+	1.00151e6i	0.0385174	+	0.146014i
$191$			8.77547e6i			1.25942i	0.776830	+	0.629710i	$0.216826\pi$
$191$			8.77547e6i			1.25942i	−0.776830	+	0.629710i	$0.783174\pi$
$192$	−1.26560e7	−	294851.i	−1.78811	−	0.0416580i
$193$	−4.12144e6			−0.573293			−0.286646	−	0.958036i	$-0.592541\pi$
$193$	−4.12144e6			−0.573293			−0.286646	+	0.958036i	$0.592541\pi$
$194$	−2.61326e6	+	689359.i	−0.357913	+	0.0944149i
$195$		−	6.00540e6i		−	0.809912i
$196$	−627594.	+	355873.i	−0.0833510	+	0.0472636i
$197$	3.10926e6			0.406685			0.203343	−	0.979108i	$-0.434819\pi$
$197$	3.10926e6			0.406685			0.203343	+	0.979108i	$0.434819\pi$
$198$	−8.19414e6	−	3.10628e7i	−1.05562	−	4.00171i
$199$			9.11949e6i			1.15721i	0.815609	+	0.578604i	$0.196402\pi$
$199$			9.11949e6i			1.15721i	−0.815609	+	0.578604i	$0.803598\pi$
$200$	3.24304e6	−	3.16836e6i	0.405379	−	0.396045i
$201$	−2.28866e7			−2.81834
$202$	6.79206e6	−	1.79169e6i	0.824038	−	0.217375i
$203$		−	1.21810e7i		−	1.45611i
$204$	−7.97220e6	−	1.40592e7i	−0.939047	−	1.65604i
$205$	−4.05153e6			−0.470281
$206$	1.75708e6	+	6.66085e6i	0.200997	+	0.761952i
$207$			1.79478e7i			2.02348i
$208$	−3.17822e6	+	5.31257e6i	−0.353178	+	0.590357i
$209$	3.94165e6			0.431757
$210$	−1.10359e7	+	2.91120e6i	−1.19166	+	0.314350i
$211$			8.39339e6i			0.893491i	0.894661	+	0.446745i	$0.147417\pi$
$211$			8.39339e6i			0.893491i	−0.894661	+	0.446745i	$0.852583\pi$
$212$	1.35871e7	−	7.70445e6i	1.42599	−	0.808601i
$213$	6.80062e6			0.703736
$214$	2.67415e6	+	1.01373e7i	0.272863	+	1.03439i
$215$		−	8.68130e6i		−	0.873513i
$216$	−1.51036e7	−	1.54596e7i	−1.49872	−	1.53404i
$217$	6.98332e6			0.683413
$218$	−1.53249e7	+	4.04258e6i	−1.47920	+	0.390202i
$219$			2.74913e7i			2.61736i
$220$	6.50638e6	+	1.14742e7i	0.611043	+	1.07759i
$221$	−7.90359e6			−0.732230
$222$	−3.93737e6	−	1.49260e7i	−0.359871	−	1.36422i
$223$		−	3.92014e6i		−	0.353498i	−0.984256	−	0.176749i	$-0.943442\pi$
$223$		−	3.92014e6i		−	0.353498i	0.984256	−	0.176749i	$-0.0565581\pi$
$224$	1.13034e7	+	3.26517e6i	1.00570	+	0.290510i
$225$	1.41959e7			1.24628
$226$	1.40806e7	−	3.71436e6i	1.21982	−	0.321780i
$227$		−	82538.0i		−	0.00705629i	−0.999994	−	0.00352814i	$-0.998877\pi$
$227$		−	82538.0i		−	0.00705629i	0.999994	−	0.00352814i	$-0.00112305\pi$
$228$	4.23057e6	−	2.39892e6i	0.356939	−	0.202400i
$229$	−1.01294e6			−0.0843487			−0.0421743	−	0.999110i	$-0.513428\pi$
$229$	−1.01294e6			−0.0843487			−0.0421743	+	0.999110i	$0.513428\pi$
$230$	−1.87966e6	−	7.12552e6i	−0.154488	−	0.585643i
$231$			4.34343e7i			3.52368i
$232$	−1.24244e7	+	1.21383e7i	−0.994972	+	0.972061i
$233$	1.68646e7			1.33324			0.666619	−	0.745399i	$-0.267741\pi$
$233$	1.68646e7			1.33324			0.666619	+	0.745399i	$0.267741\pi$
$234$	−1.87424e7	+	4.94410e6i	−1.46277	+	0.385869i
$235$		−	666821.i		−	0.0513814i
$236$	822065.	+	1.44974e6i	0.0625418	+	0.110294i
$237$	2.54063e6			0.190852
$238$	3.83137e6	+	1.45242e7i	0.284200	+	1.07736i
$239$		−	1.36074e7i		−	0.996742i	−0.866964	−	0.498371i	$-0.833932\pi$
$239$		−	1.36074e7i		−	0.996742i	0.866964	−	0.498371i	$-0.166068\pi$
$240$	1.39666e7	+	8.35543e6i	1.01031	+	0.604415i
$241$	2.21346e6			0.158133			0.0790663	−	0.996869i	$-0.474806\pi$
$241$	2.21346e6			0.158133			0.0790663	+	0.996869i	$0.474806\pi$
$242$	3.48330e7	−	9.18869e6i	2.45779	−	0.648347i
$243$		−	1.12344e7i		−	0.782947i
$244$	3.49473e6	−	1.98166e6i	0.240571	−	0.136414i
$245$	927529.			0.0630709
$246$	4.85232e6	+	1.83945e7i	0.325945	+	1.23561i
$247$		−	2.37828e6i		−	0.157823i
$248$	−6.95883e6	−	7.12284e6i	−0.456227	−	0.466980i
$249$	−2.47848e7			−1.60542
$250$	−1.55806e7	+	4.11006e6i	−0.997161	+	0.263044i
$251$			1.15827e6i			0.0732466i	0.999329	+	0.0366233i	$0.0116602\pi$
$251$			1.15827e6i			0.0732466i	−0.999329	+	0.0366233i	$0.988340\pi$
$252$	1.81712e7	+	3.20456e7i	1.13549	+	2.00247i
$253$	−2.80440e7			−1.73172
$254$	3.45189e6	+	1.30856e7i	0.210648	+	0.798535i
$255$			2.07783e7i			1.25311i
$256$	−7.93339e6	−	1.47830e7i	−0.472867	−	0.881134i
$257$	−2.11096e7			−1.24360			−0.621801	−	0.783175i	$-0.713599\pi$
$257$	−2.11096e7			−1.24360			−0.621801	+	0.783175i	$0.713599\pi$
$258$	−3.94142e7	+	1.03972e7i	−2.29506	+	0.605420i
$259$			1.43466e7i			0.825754i
$260$	6.92320e6	−	3.92576e6i	0.393901	−	0.223359i
$261$	−5.43857e7			−3.05889
$262$	−1.85260e6	−	7.02294e6i	−0.103010	−	0.390495i
$263$		−	2.63276e7i		−	1.44725i	−0.690193	−	0.723625i	$-0.742475\pi$
$263$		−	2.63276e7i		−	1.44725i	0.690193	−	0.723625i	$-0.257525\pi$
$264$	4.43020e7	−	4.32819e7i	2.40775	−	2.35231i
$265$	−2.00805e7			−1.07904
$266$	−4.37048e6	+	1.15290e6i	−0.232212	+	0.0612558i
$267$			3.38343e7i			1.77756i
$268$	−1.49611e7	−	2.63843e7i	−0.777245	−	1.37070i
$269$	2.21101e7			1.13589			0.567943	−	0.823068i	$-0.307739\pi$
$269$	2.21101e7			1.13589			0.567943	+	0.823068i	$0.307739\pi$
$270$	7.08723e6	+	2.68667e7i	0.360069	+	1.36497i
$271$			5.23582e6i			0.263073i	0.991311	+	0.131537i	$0.0419911\pi$
$271$			5.23582e6i			0.263073i	−0.991311	+	0.131537i	$0.958009\pi$
$272$	1.09964e7	−	1.83812e7i	0.546443	−	0.913411i
$273$	2.62070e7			1.28804
$274$	1.70440e7	−	4.49609e6i	0.828553	−	0.218566i
$275$			2.21815e7i			1.06658i
$276$	−3.00996e7	+	1.70678e7i	−1.43164	+	0.811802i
$277$	1.18508e7			0.557582			0.278791	−	0.960352i	$-0.410066\pi$
$277$	1.18508e7			0.557582			0.278791	+	0.960352i	$0.410066\pi$
$278$	1.36860e6	+	5.18817e6i	0.0637004	+	0.241479i
$279$		−	3.11791e7i		−	1.43566i
$280$	−1.05704e7	−	1.08195e7i	−0.481522	−	0.492870i
$281$	−2.01629e7			−0.908731			−0.454365	−	0.890815i	$-0.650134\pi$
$281$	−2.01629e7			−0.908731			−0.454365	+	0.890815i	$0.650134\pi$
$282$	−3.02745e6	+	798620.i	−0.134999	+	0.0356117i
$283$		−	2.46061e7i		−	1.08563i	−0.839851	−	0.542817i	$-0.817358\pi$
$283$		−	2.46061e7i		−	1.08563i	0.839851	−	0.542817i	$-0.182642\pi$
$284$	4.44560e6	+	7.83996e6i	0.194078	+	0.342262i
$285$	−6.25241e6			−0.270093
$286$	−7.72533e6	−	2.92856e7i	−0.330232	−	1.25186i
$287$		−	1.76805e7i		−	0.747907i
$288$	1.45783e7	−	5.04675e7i	0.610280	−	2.11268i
$289$	3.20836e6			0.132920
$290$	2.15919e7	−	5.69578e6i	0.885313	−	0.233539i
$291$		−	1.63146e7i		−	0.662059i
$292$	−3.16928e7	+	1.79712e7i	−1.27295	+	0.721819i
$293$	−3.40820e7			−1.35495			−0.677474	−	0.735547i	$-0.736925\pi$
$293$	−3.40820e7			−1.35495			−0.677474	+	0.735547i	$0.736925\pi$
$294$	−1.11086e6	−	4.21110e6i	−0.0437136	−	0.165712i
$295$		−	2.14259e6i		−	0.0834588i
$296$	1.46333e7	−	1.42963e7i	0.564243	−	0.551251i
$297$	1.05740e8			4.03616
$298$	−2.37917e7	+	6.27608e6i	−0.899036	+	0.237159i
$299$			1.69209e7i			0.633010i
$300$	1.34998e7	+	2.38074e7i	0.499994	+	0.881756i
$301$	3.78843e7			1.38918
$302$	−1.57260e6	−	5.96148e6i	−0.0570947	−	0.216438i
$303$			4.24028e7i			1.52429i
$304$	5.53109e6	+	3.30894e6i	0.196875	+	0.117779i
$305$	−5.16490e6			−0.182038
$306$	6.48475e7	−	1.71063e7i	2.26323	−	0.597023i
$307$			2.89285e7i			0.999793i	0.866085	+	0.499897i	$0.166629\pi$
$307$			2.89285e7i			0.999793i	−0.866085	+	0.499897i	$0.833371\pi$
$308$	−5.00723e7	+	2.83932e7i	−1.71374	+	0.971767i
$309$	−4.15836e7			−1.40944
$310$	3.26537e6	+	1.23785e7i	0.109609	+	0.415513i
$311$		−	5.75337e7i		−	1.91267i	−0.292265	−	0.956337i	$-0.594409\pi$
$311$		−	5.75337e7i		−	1.91267i	0.292265	−	0.956337i	$-0.405591\pi$
$312$	−2.61150e7	−	2.67305e7i	−0.859858	−	0.880124i
$313$	4.64530e7			1.51489			0.757444	−	0.652900i	$-0.226448\pi$
$313$	4.64530e7			1.51489			0.757444	+	0.652900i	$0.226448\pi$
$314$	4.07610e7	−	1.07525e7i	1.31661	−	0.347311i
$315$		−	4.73606e7i		−	1.51525i
$316$	1.66082e6	+	2.92891e6i	0.0526334	+	0.0928206i
$317$	2.19991e7			0.690599			0.345300	−	0.938492i	$-0.387777\pi$
$317$	2.19991e7			0.690599			0.345300	+	0.938492i	$0.387777\pi$
$318$	2.40494e7	+	9.11679e7i	0.747865	+	2.83505i
$319$		−	8.49795e7i		−	2.61784i
$320$	−502362.	+	2.15631e7i	−0.0153309	+	0.658053i
$321$	−6.32873e7			−1.91338
$322$	3.10950e7	−	8.20264e6i	0.931373	−	0.245689i
$323$			8.22868e6i			0.244187i
$324$	4.84275e7	−	2.74605e7i	1.42383	−	0.807372i
$325$	1.33837e7			0.389875
$326$	−9.39196e6	−	3.56036e7i	−0.271084	−	1.02764i
$327$		−	9.56730e7i		−	2.73619i
$328$	−1.80337e7	+	1.76184e7i	−0.511049	+	0.499282i
$329$	2.90994e6			0.0817139
$330$	−7.69910e7	+	2.03097e7i	−2.14239	+	0.565146i
$331$		−	978340.i		−	0.0269778i	−0.999909	−	0.0134889i	$-0.995706\pi$
$331$		−	978340.i		−	0.0269778i	0.999909	−	0.0134889i	$-0.00429377\pi$
$332$	−1.62020e7	−	2.85727e7i	−0.442744	−	0.780794i
$333$	6.40547e7			1.73468
$334$	1.03351e7	+	3.91789e7i	0.277380	+	1.05151i
$335$			3.89937e7i			1.03719i
$336$	−3.64623e7	+	6.09488e7i	−0.961227	+	1.60675i
$337$	7.26346e7			1.89781			0.948907	−	0.315556i	$-0.102191\pi$
$337$	7.26346e7			1.89781			0.948907	+	0.315556i	$0.102191\pi$
$338$	1.96672e7	−	5.18805e6i	0.509321	−	0.134355i
$339$			8.79052e7i			2.25640i
$340$	−2.39538e7	+	1.35829e7i	−0.609450	+	0.345585i
$341$	4.87184e7			1.22865
$342$	5.14746e6	+	1.95133e7i	0.128681	+	0.487812i
$343$		−	3.81951e7i		−	0.946509i
$344$	−3.77514e7	−	3.86412e7i	−0.927381	−	0.949238i
$345$	4.44846e7			1.08331
$346$	−3.01274e7	+	7.94740e6i	−0.727334	+	0.191865i
$347$		−	4.28971e6i		−	0.102669i	−0.998682	−	0.0513345i	$-0.983653\pi$
$347$		−	4.28971e6i		−	0.102669i	0.998682	−	0.0513345i	$-0.0163475\pi$
$348$	−5.17192e7	−	9.12085e7i	−1.22720	−	2.16420i
$349$	−2.78572e7			−0.655331			−0.327666	−	0.944794i	$-0.606262\pi$
$349$	−2.78572e7			−0.655331			−0.327666	+	0.944794i	$0.606262\pi$
$350$	−6.48792e6	−	2.45948e7i	−0.151322	−	0.573639i
$351$		−	6.38001e7i		−	1.47537i
$352$	7.88572e7	+	2.27791e7i	1.80806	+	0.522286i
$353$	−2.47434e7			−0.562516			−0.281258	−	0.959632i	$-0.590752\pi$
$353$	−2.47434e7			−0.562516			−0.281258	+	0.959632i	$0.590752\pi$
$354$	−9.72762e6	+	2.56607e6i	−0.219279	+	0.0578441i
$355$		−	1.15868e7i		−	0.258987i
$356$	−3.90052e7	+	2.21177e7i	−0.864515	+	0.490218i
$357$	−9.06744e7			−1.99288
$358$	−5.84245e6	−	2.21479e7i	−0.127334	−	0.482707i
$359$			3.58715e7i			0.775293i	0.921808	+	0.387647i	$0.126712\pi$
$359$			3.58715e7i			0.775293i	−0.921808	+	0.387647i	$0.873288\pi$
$360$	−4.83068e7	+	4.71944e7i	−1.03538	+	1.01154i
$361$	−2.47610e6			−0.0526316
$362$	−1.58429e7	+	4.17925e6i	−0.333972	+	0.0880993i
$363$			2.17462e8i			4.54637i
$364$	1.71316e7	+	3.02122e7i	0.355217	+	0.626437i
$365$	4.68392e7			0.963231
$366$	6.18576e6	+	2.34493e7i	0.126168	+	0.478285i
$367$			8.44140e7i			1.70772i	0.520504	+	0.853859i	$0.325744\pi$
$367$			8.44140e7i			1.70772i	−0.520504	+	0.853859i	$0.674256\pi$
$368$	−3.93525e7	−	2.35424e7i	−0.789640	−	0.472397i
$369$	−7.89395e7			−1.57114
$370$	−2.54306e7	+	6.70842e6i	−0.502056	+	0.132439i
$371$		−	8.76292e7i		−	1.71604i
$372$	5.22894e7	−	2.96504e7i	1.01575	−	0.575972i
$373$	−7.87938e7			−1.51833			−0.759164	−	0.650900i	$-0.774392\pi$
$373$	−7.87938e7			−1.51833			−0.759164	+	0.650900i	$0.774392\pi$
$374$	2.67292e7	+	1.01326e8i	0.510941	+	1.93690i
$375$		−	9.72698e7i		−	1.84452i
$376$	−2.89973e6	−	2.96808e6i	−0.0545500	−	0.0558356i
$377$	−5.12741e7			−0.956917
$378$	−1.17244e8	+	3.09280e7i	−2.17077	+	0.572633i
$379$		−	7.03334e7i		−	1.29195i	−0.763360	−	0.645973i	$-0.776452\pi$
$379$		−	7.03334e7i		−	1.29195i	0.763360	−	0.645973i	$-0.223548\pi$
$380$	−4.08723e6	−	7.20797e6i	−0.0744867	−	0.131360i
$381$	−8.16936e7			−1.47711
$382$	−1.79067e7	−	6.78817e7i	−0.321237	−	1.21776i
$383$			4.60539e7i			0.819728i	0.912147	+	0.409864i	$0.134424\pi$
$383$			4.60539e7i			0.819728i	−0.912147	+	0.409864i	$0.865576\pi$
$384$	9.85008e7	−	2.35443e7i	1.73959	−	0.415807i
$385$	7.40025e7			1.29677
$386$	3.18809e7	−	8.40994e6i	0.554330	−	0.146228i
$387$		−	1.69146e8i		−	2.91829i
$388$	1.88079e7	−	1.06649e7i	0.321993	−	0.182584i
$389$	3.81887e7			0.648763			0.324381	−	0.945926i	$-0.394844\pi$
$389$	3.81887e7			0.648763			0.324381	+	0.945926i	$0.394844\pi$
$390$	1.22542e7	+	4.64541e7i	0.206582	+	0.783123i
$391$		−	5.85453e7i		−	0.979404i
$392$	4.12851e6	−	4.03345e6i	0.0685386	−	0.0669604i
$393$	4.38442e7			0.722328
$394$	−2.40513e7	+	6.34456e6i	−0.393234	+	0.103732i
$395$		−	4.32867e6i		−	0.0702366i
$396$	1.26770e8	+	2.23562e8i	2.04141	+	3.60009i
$397$	−8.28073e7			−1.32342			−0.661709	−	0.749761i	$-0.730168\pi$
$397$	−8.28073e7			−1.32342			−0.661709	+	0.749761i	$0.730168\pi$
$398$	−1.86087e7	−	7.05428e7i	−0.295166	−	1.11893i
$399$		−	2.72849e7i		−	0.429540i
$400$	−1.86210e7	+	3.11260e7i	−0.290953	+	0.486344i
$401$	−1.18588e7			−0.183911			−0.0919555	−	0.995763i	$-0.529312\pi$
$401$	−1.18588e7			−0.183911			−0.0919555	+	0.995763i	$0.529312\pi$
$402$	1.77037e8	−	4.67009e7i	2.72511	−	0.718865i
$403$		−	2.93952e7i		−	0.449119i
$404$	−4.88832e7	+	2.77189e7i	−0.741336	+	0.420370i
$405$	−7.15716e7			−1.07740
$406$	2.48558e7	+	9.42249e7i	0.371407	+	1.40795i
$407$			1.00088e8i			1.48456i
$408$	9.03564e7	+	9.24860e7i	1.33039	+	1.36174i
$409$	1.34754e7			0.196957			0.0984787	−	0.995139i	$-0.468602\pi$
$409$	1.34754e7			0.196957			0.0984787	+	0.995139i	$0.468602\pi$
$410$	3.13401e7	−	8.26729e6i	0.454725	−	0.119953i
$411$			1.06406e8i			1.53264i
$412$	−2.71834e7	−	4.79388e7i	−0.388698	−	0.685482i
$413$	9.35003e6			0.132728
$414$	−3.66231e7	−	1.38833e8i	−0.516124	−	1.95655i
$415$			4.22279e7i			0.590820i
$416$	1.37442e7	−	4.75801e7i	0.190915	−	0.660914i
$417$	−3.23897e7			−0.446683
$418$	−3.04902e7	+	8.04309e6i	−0.417476	+	0.110127i
$419$			1.18620e8i			1.61256i	0.591534	+	0.806280i	$0.298523\pi$
$419$			1.18620e8i			1.61256i	−0.591534	+	0.806280i	$0.701477\pi$
$420$	7.94268e7	−	4.50385e7i	1.07206	−	0.607905i
$421$	−2.48333e7			−0.332803			−0.166402	−	0.986058i	$-0.553215\pi$
$421$	−2.48333e7			−0.332803			−0.166402	+	0.986058i	$0.553215\pi$
$422$	−1.71270e7	−	6.49261e7i	−0.227900	−	0.863937i
$423$		−	1.29923e7i		−	0.171658i
$424$	−8.93799e7	+	8.73218e7i	−1.17258	+	1.14558i
$425$	−4.63067e7			−0.603221
$426$	−5.26055e7	+	1.38769e7i	−0.680459	+	0.179500i
$427$		−	2.25391e7i		−	0.289503i
$428$	−4.13712e7	−	7.29595e7i	−0.527676	−	0.930573i
$429$	1.82830e8			2.31566
$430$	1.77145e7	+	6.71532e7i	0.222805	+	0.844620i
$431$			4.23106e7i			0.528466i	0.964459	+	0.264233i	$0.0851189\pi$
$431$			4.23106e7i			0.528466i	−0.964459	+	0.264233i	$0.914881\pi$
$432$	1.48378e8	+	8.87664e7i	1.84043	+	1.10103i
$433$	7.59981e7			0.936136			0.468068	−	0.883692i	$-0.344950\pi$
$433$	7.59981e7			0.936136			0.468068	+	0.883692i	$0.344950\pi$
$434$	−5.40187e7	+	1.42497e7i	−0.660808	+	0.174316i
$435$			1.34798e8i			1.63763i
$436$	1.10295e8	−	6.25419e7i	1.33075	−	0.754591i
$437$	1.76169e7			0.211099
$438$	−5.60971e7	−	2.12656e8i	−0.667602	−	2.53078i
$439$			6.66957e7i			0.788324i	0.919041	+	0.394162i	$0.128965\pi$
$439$			6.66957e7i			0.788324i	−0.919041	+	0.394162i	$0.871035\pi$
$440$	−7.37430e7	−	7.54810e7i	−0.865690	−	0.886093i
$441$	1.80719e7			0.210711
$442$	6.11373e7	−	1.61276e7i	0.708011	−	0.186768i
$443$		−	2.25074e7i		−	0.258889i	−0.991587	−	0.129445i	$-0.958681\pi$
$443$		−	2.25074e7i		−	0.258889i	0.991587	−	0.129445i	$-0.0413194\pi$
$444$	6.09141e7	+	1.07424e8i	0.695936	+	1.22731i
$445$	5.76463e7			0.654171
$446$	7.99920e6	+	3.03238e7i	0.0901658	+	0.341806i
$447$		−	1.48532e8i		−	1.66302i
$448$	−9.40991e7	−	2.19226e6i	−1.04653	−	0.0243813i
$449$	−9.29233e7			−1.02656			−0.513281	−	0.858220i	$-0.671570\pi$
$449$	−9.29233e7			−1.02656			−0.513281	+	0.858220i	$0.671570\pi$
$450$	−1.09810e8	+	2.89672e7i	−1.20505	+	0.317884i
$451$		−	1.23346e8i		−	1.34460i
$452$	−1.01340e8	+	5.74640e7i	−1.09740	+	0.622273i
$453$	3.72175e7			0.400362
$454$	168422.	+	638463.i	0.00179983	+	0.00682289i
$455$		−	4.46509e7i		−	0.474020i
$456$	−2.78300e7	+	2.71892e7i	−0.293507	+	0.286749i
$457$	−1.57094e7			−0.164593			−0.0822964	−	0.996608i	$-0.526225\pi$
$457$	−1.57094e7			−0.164593			−0.0822964	+	0.996608i	$0.526225\pi$
$458$	7.83550e6	−	2.06695e6i	0.0815587	−	0.0215146i
$459$			2.20744e8i			2.28271i
$460$	2.90798e7	+	5.12831e7i	0.298757	+	0.526867i
$461$	9.56746e7			0.976549			0.488274	−	0.872690i	$-0.337627\pi$
$461$	9.56746e7			0.976549			0.488274	+	0.872690i	$0.337627\pi$
$462$	−8.86293e7	−	3.35981e8i	−0.898776	−	3.40713i
$463$		−	1.41181e8i		−	1.42244i	−0.702968	−	0.711221i	$-0.748143\pi$
$463$		−	1.41181e8i		−	1.42244i	0.702968	−	0.711221i	$-0.251857\pi$
$464$	7.13387e7	−	1.19247e8i	0.714120	−	1.19369i
$465$	−7.72792e7			−0.768606
$466$	−1.30454e8	+	3.44128e7i	−1.28914	+	0.340065i
$467$		−	2.20137e7i		−	0.216144i	−0.994143	−	0.108072i	$-0.965532\pi$
$467$		−	2.20137e7i		−	0.216144i	0.994143	−	0.108072i	$-0.0344677\pi$
$468$	1.34891e8	−	7.64891e7i	1.31597	−	0.746211i
$469$	−1.70165e8			−1.64949
$470$	1.36067e6	+	5.15812e6i	0.0131057	+	0.0496818i
$471$			2.54471e8i			2.43543i
$472$	−9.31724e6	−	9.53683e6i	−0.0886056	−	0.0906939i
$473$	2.64296e8			2.49751
$474$	−1.96527e7	+	5.18424e6i	−0.184539	+	0.0486800i
$475$		−	1.39342e7i		−	0.130017i
$476$	−5.92743e7	−	1.04532e8i	−0.549599	−	0.969235i
$477$	−3.91246e8			−3.60491
$478$	2.77665e7	+	1.05259e8i	0.254236	+	0.963773i
$479$		−	1.11880e8i		−	1.01800i	−0.860768	−	0.508998i	$-0.830016\pi$
$479$		−	1.11880e8i		−	1.01800i	0.860768	−	0.508998i	$-0.169984\pi$
$480$	−1.25087e8	−	3.61331e7i	−1.13106	−	0.326725i
$481$	6.03900e7			0.542662
$482$	−1.71220e7	+	4.51666e6i	−0.152902	+	0.0403344i
$483$			1.94126e8i			1.72283i
$484$	−2.50697e8	+	1.42156e8i	−2.21112	+	1.25380i
$485$	−2.77965e7			−0.243649
$486$	2.29243e7	+	8.69027e7i	0.199704	+	0.757049i
$487$		−	3.79408e7i		−	0.328488i	−0.986420	−	0.164244i	$-0.947482\pi$
$487$		−	3.79408e7i		−	0.328488i	0.986420	−	0.164244i	$-0.0525184\pi$
$488$	−2.29894e7	+	2.24601e7i	−0.197819	+	0.193264i
$489$	2.22273e8			1.90090
$490$	−7.17480e6	+	1.89266e6i	−0.0609848	+	0.0160873i
$491$			5.44109e7i			0.459665i	0.973230	+	0.229833i	$0.0738178\pi$
$491$			5.44109e7i			0.459665i	−0.973230	+	0.229833i	$0.926182\pi$
$492$	−7.50692e7	−	1.32387e8i	−0.630327	−	1.11160i
$493$	1.77405e8			1.48056
$494$	4.85296e6	+	1.83969e7i	0.0402556	+	0.152603i
$495$		−	3.30406e8i		−	2.72416i
$496$	6.83637e7	+	4.08982e7i	0.560248	+	0.335165i
$497$	5.05635e7			0.411878
$498$	1.91720e8	−	5.05743e7i	1.55231	−	0.409489i
$499$		−	8.64804e7i		−	0.696011i	−0.937492	−	0.348006i	$-0.886859\pi$
$499$		−	8.64804e7i		−	0.696011i	0.937492	−	0.348006i	$-0.113141\pi$
$500$	1.12136e8	−	6.35858e7i	0.897084	−	0.508686i
$501$	−2.44594e8			−1.94505
$502$	−2.36349e6	−	8.95964e6i	−0.0186828	−	0.0708238i
$503$			1.63899e8i			1.28787i	0.765080	+	0.643935i	$0.222699\pi$
$503$			1.63899e8i			1.28787i	−0.765080	+	0.643935i	$0.777301\pi$
$504$	−2.05952e8	−	2.10806e8i	−1.60870	−	1.64661i
$505$	7.22450e7			0.560963
$506$	2.16931e8	−	5.72248e7i	1.67444	−	0.441706i
$507$			1.22782e8i			0.942130i
$508$	−5.34035e7	−	9.41788e7i	−0.407360	−	0.718393i
$509$	2.04007e8			1.54700			0.773501	−	0.633795i	$-0.218504\pi$
$509$	2.04007e8			1.54700			0.773501	+	0.633795i	$0.218504\pi$
$510$	−4.23989e7	−	1.60728e8i	−0.319627	−	1.21166i
$511$			2.04401e8i			1.53187i
$512$	9.15330e7	+	9.81637e7i	0.681974	+	0.731376i
$513$	−6.64244e7			−0.492012
$514$	1.63291e8	−	4.30750e7i	1.20247	−	0.317202i
$515$			7.08494e7i			0.518698i
$516$	2.83668e8	−	1.60852e8i	2.06472	−	1.17079i
$517$	2.03009e7			0.146907
$518$	−2.92748e7	−	1.10977e8i	−0.210623	−	0.798441i
$519$		−	1.88085e8i		−	1.34541i
$520$	−4.55430e7	+	4.44943e7i	−0.323900	+	0.316442i
$521$	−2.05591e8			−1.45376			−0.726878	−	0.686767i	$-0.759029\pi$
$521$	−2.05591e8			−1.45376			−0.726878	+	0.686767i	$0.759029\pi$
$522$	4.20694e8	−	1.10976e8i	2.95771	−	0.780221i
$523$			1.50208e8i			1.04999i	0.851104	+	0.524997i	$0.175933\pi$
$523$			1.50208e8i			1.04999i	−0.851104	+	0.524997i	$0.824067\pi$
$524$	2.86612e7	+	5.05449e7i	0.199205	+	0.351304i
$525$	1.53545e8			1.06110
$526$	5.37224e7	+	2.03654e8i	0.369146	+	1.39938i
$527$			1.01706e8i			0.694886i
$528$	−2.54375e8	+	4.25203e8i	−1.72812	+	2.88864i
$529$	2.26954e7			0.153310
$530$	1.55330e8	−	4.09750e7i	1.04335	−	0.275227i
$531$		−	4.17459e7i		−	0.278824i
$532$	3.14548e7	−	1.78363e7i	0.208907	−	0.118459i
$533$	−7.44232e7			−0.491503
$534$	−6.90402e7	−	2.61722e8i	−0.453397	−	1.71876i
$535$			1.07828e8i			0.704156i
$536$	1.69568e8	+	1.73564e8i	1.10116	+	1.12711i
$537$	1.38269e8			0.892899
$538$	−1.71030e8	+	4.51166e7i	−1.09831	+	0.289727i
$539$			2.82379e7i			0.180330i
$540$	−1.09645e8	−	1.93362e8i	−0.696318	−	1.22798i
$541$	−4.39712e7			−0.277701			−0.138850	−	0.990313i	$-0.544341\pi$
$541$	−4.39712e7			−0.277701			−0.138850	+	0.990313i	$0.544341\pi$
$542$	−1.06839e7	−	4.05011e7i	−0.0671013	−	0.254372i
$543$		−	9.89073e7i		−	0.617773i
$544$	−4.75541e7	+	1.64624e8i	−0.295387	+	1.02258i
$545$	−1.63006e8			−1.00696
$546$	−2.02721e8	+	5.34763e7i	−1.24543	+	0.328536i
$547$		−	1.66991e8i		−	1.02030i	−0.860084	−	0.510152i	$-0.829589\pi$
$547$		−	1.66991e8i		−	1.02030i	0.860084	−	0.510152i	$-0.170411\pi$
$548$	−1.22668e8	+	6.95579e7i	−0.745398	+	0.422673i
$549$	−1.00632e8			−0.608164
$550$	−4.52622e7	−	1.71583e8i	−0.272050	−	1.03130i
$551$			5.33831e7i			0.319117i
$552$	1.98005e8	−	1.93445e8i	1.17722	−	1.15011i
$553$	1.88899e7			0.111700
$554$	−9.16705e7	+	2.41820e7i	−0.539139	+	0.142221i
$555$		−	1.58763e8i		−	0.928691i
$556$	−2.11733e7	−	3.73398e7i	−0.123187	−	0.217244i
$557$	−1.23329e8			−0.713672			−0.356836	−	0.934167i	$-0.616145\pi$
$557$	−1.23329e8			−0.713672			−0.356836	+	0.934167i	$0.616145\pi$
$558$	6.36221e7	+	2.41182e8i	0.366189	+	1.38817i
$559$		−	1.59468e8i		−	0.912933i
$560$	1.03843e8	+	6.21237e7i	0.591309	+	0.353747i
$561$	−6.32580e8			−3.58284
$562$	1.55968e8	−	4.11433e7i	0.878673	−	0.231787i
$563$			1.82847e8i			1.02462i	0.858800	+	0.512311i	$0.171210\pi$
$563$			1.82847e8i			1.02462i	−0.858800	+	0.512311i	$0.828790\pi$
$564$	2.17889e7	−	1.23553e7i	0.121450	−	0.0688675i
$565$	1.49771e8			0.830392
$566$	5.02097e7	+	1.90338e8i	0.276910	+	1.04972i
$567$		−	3.12331e8i		−	1.71343i
$568$	−5.03862e7	−	5.15737e7i	−0.274958	−	0.281438i
$569$	1.60414e8			0.870774			0.435387	−	0.900243i	$-0.356611\pi$
$569$	1.60414e8			0.870774			0.435387	+	0.900243i	$0.356611\pi$
$570$	4.83648e7	−	1.27583e7i	0.261159	−	0.0688918i
$571$		−	2.93526e7i		−	0.157666i	−0.996888	−	0.0788331i	$-0.974881\pi$
$571$		−	2.93526e7i		−	0.157666i	0.996888	−	0.0788331i	$-0.0251194\pi$
$572$	1.19517e8	+	2.10772e8i	0.638618	+	1.12622i
$573$	4.23785e8			2.25259
$574$	3.60776e7	+	1.36765e8i	0.190767	+	0.723169i
$575$			9.91386e7i			0.521482i
$576$	−9.78796e6	+	4.20133e8i	−0.0512183	+	2.19846i
$577$	4.45013e7			0.231657			0.115829	−	0.993269i	$-0.463048\pi$
$577$	4.45013e7			0.231657			0.115829	+	0.993269i	$0.463048\pi$
$578$	−2.48179e7	+	6.54678e6i	−0.128523	+	0.0339035i
$579$			1.99032e8i			1.02539i
$580$	−1.55399e8	+	8.81182e7i	−0.796462	+	0.451629i
$581$	−1.84278e8			−0.939606
$582$	3.32905e7	+	1.26200e8i	0.168870	+	0.640161i
$583$		−	6.11335e8i		−	3.08513i
$584$	2.08485e8	−	2.03685e8i	1.04673	−	1.02263i
$585$	−1.99357e8			−0.995781
$586$	2.63638e8	−	6.95456e7i	1.31013	−	0.345603i
$587$		−	3.64234e8i		−	1.80080i	−0.435062	−	0.900400i	$-0.643274\pi$
$587$		−	3.64234e8i		−	1.80080i	0.435062	−	0.900400i	$-0.356726\pi$
$588$	1.71858e7	+	3.03078e7i	0.0845354	+	0.149081i
$589$	−3.06043e7			−0.149774
$590$	4.37203e6	+	1.65737e7i	0.0212876	+	0.0806983i
$591$		−	1.50152e8i		−	0.727394i
$592$	−8.40218e7	+	1.40447e8i	−0.404974	+	0.676937i
$593$	−6.07879e7			−0.291510			−0.145755	−	0.989321i	$-0.546561\pi$
$593$	−6.07879e7			−0.291510			−0.145755	+	0.989321i	$0.546561\pi$
$594$	−8.17937e8	+	2.15766e8i	−3.90266	+	1.02949i
$595$			1.54489e8i			0.733411i
$596$	1.71232e8	−	9.70958e7i	0.808807	−	0.458629i
$597$	4.40398e8			2.06977
$598$	−3.45278e7	−	1.30890e8i	−0.161460	−	0.612072i
$599$		−	5.82355e7i		−	0.270962i	−0.990780	−	0.135481i	$-0.956742\pi$
$599$		−	5.82355e7i		−	0.270962i	0.990780	−	0.135481i	$-0.0432579\pi$
$600$	−1.53006e8	−	1.56613e8i	−0.708363	−	0.725058i
$601$	−4.01876e7			−0.185127			−0.0925633	−	0.995707i	$-0.529506\pi$
$601$	−4.01876e7			−0.185127			−0.0925633	+	0.995707i	$0.529506\pi$
$602$	−2.93050e8	+	7.73044e7i	−1.34324	+	0.354335i
$603$			7.59750e8i			3.46512i
$604$	2.43293e7	+	4.29054e7i	0.110412	+	0.194716i
$605$	3.70508e8			1.67314
$606$	−8.65244e7	−	3.28002e8i	−0.388795	−	1.47387i
$607$		−	9.92257e7i		−	0.443668i	−0.975084	−	0.221834i	$-0.928796\pi$
$607$		−	9.92257e7i		−	0.443668i	0.975084	−	0.221834i	$-0.0712043\pi$
$608$	−4.95371e7	−	1.43096e7i	−0.220404	−	0.0636671i
$609$	−5.88245e8			−2.60439
$610$	3.99525e7	−	1.05392e7i	0.176017	−	0.0464320i
$611$		−	1.22489e7i		−	0.0537001i
$612$	−4.66714e8	+	2.64647e8i	−2.03609	+	1.15455i
$613$	−2.11691e8			−0.919010			−0.459505	−	0.888175i	$-0.651973\pi$
$613$	−2.11691e8			−0.919010			−0.459505	+	0.888175i	$0.651973\pi$
$614$	−5.90296e7	−	2.23773e8i	−0.255014	−	0.966723i
$615$			1.95656e8i			0.841140i
$616$	3.29391e8	−	3.21807e8i	1.40919	−	1.37674i
$617$	−2.82765e8			−1.20385			−0.601923	−	0.798554i	$-0.705599\pi$
$617$	−2.82765e8			−1.20385			−0.601923	+	0.798554i	$0.705599\pi$
$618$	3.21665e8	−	8.48530e7i	1.36282	−	0.359502i
$619$			1.81094e8i			0.763539i	0.924258	+	0.381770i	$0.124685\pi$
$619$			1.81094e8i			0.763539i	−0.924258	+	0.381770i	$0.875315\pi$
$620$	−5.05178e7	−	8.90897e7i	−0.211967	−	0.373811i
$621$	4.72595e8			1.97340
$622$	1.17400e8	+	4.45045e8i	0.487861	+	1.84941i
$623$			2.51563e8i			1.04036i
$624$	2.56555e8	+	1.53482e8i	1.05591	+	0.631691i
$625$	−2.73644e7			−0.112085
$626$	−3.59332e8	+	9.47891e7i	−1.46478	+	0.386398i
$627$		−	1.90350e8i		−	0.772237i
$628$	−2.93362e8	+	1.66349e8i	−1.18447	+	0.671647i
$629$	−2.08945e8			−0.839617
$630$	9.66410e7	+	3.66352e8i	0.386491	+	1.46513i
$631$			4.76664e7i			0.189725i	0.995490	+	0.0948624i	$0.0302411\pi$
$631$			4.76664e7i			0.189725i	−0.995490	+	0.0948624i	$0.969759\pi$
$632$	−1.88236e7	−	1.92673e7i	−0.0745679	−	0.0763254i
$633$	4.05333e8			1.59809
$634$	−1.70171e8	+	4.48899e7i	−0.667757	+	0.176149i
$635$			1.39188e8i			0.543601i
$636$	−3.72063e8	−	6.56146e8i	−1.44626	−	2.55052i
$637$	1.70379e7			0.0659172
$638$	1.73404e8	+	6.57350e8i	0.667724	+	2.53125i
$639$		−	2.25756e8i		−	0.865239i
$640$	−4.01143e7	−	1.67824e8i	−0.153024	−	0.640197i
$641$	2.34991e7			0.0892231			0.0446115	−	0.999004i	$-0.485795\pi$
$641$	2.34991e7			0.0892231			0.0446115	+	0.999004i	$0.485795\pi$
$642$	4.89552e8	−	1.29140e8i	1.85009	−	0.488041i
$643$		−	176446.i		−	0.000663710i	−1.00000		0.000331855i	$-0.999894\pi$
$643$		−	176446.i		−	0.000663710i	1.00000		0.000331855i	$-0.000105633\pi$
$644$	−2.23794e8	+	1.26901e8i	−0.837899	+	0.475125i
$645$	−4.19237e8			−1.56236
$646$	−1.67909e7	−	6.36520e7i	−0.0622841	−	0.236110i
$647$			9.23923e7i			0.341132i	0.985346	+	0.170566i	$0.0545597\pi$
$647$			9.23923e7i			0.341132i	−0.985346	+	0.170566i	$0.945440\pi$
$648$	−3.18571e8	+	3.11236e8i	−1.17080	+	1.14384i
$649$	6.52295e7			0.238622
$650$	−1.03528e8	+	2.73099e7i	−0.376979	+	0.0994443i
$651$		−	3.37239e8i		−	1.22235i
$652$	1.45301e8	+	2.56243e8i	0.524234	+	0.924504i
$653$	2.44394e7			0.0877710			0.0438855	−	0.999037i	$-0.486026\pi$
$653$	2.44394e7			0.0877710			0.0438855	+	0.999037i	$0.486026\pi$
$654$	1.95224e8	+	7.40068e8i	0.697912	+	2.64569i
$655$		−	7.47009e7i		−	0.265829i
$656$	1.03546e8	−	1.73084e8i	0.366795	−	0.613119i
$657$	9.12610e8			3.21802
$658$	−2.25095e7	+	5.93784e6i	−0.0790111	+	0.0208425i
$659$			2.63308e8i			0.920042i	0.887908	+	0.460021i	$0.152158\pi$
$659$			2.63308e8i			0.920042i	−0.887908	+	0.460021i	$0.847842\pi$
$660$	5.54113e8	−	3.14206e8i	1.92737	−	1.09291i
$661$	4.02712e8			1.39441			0.697205	−	0.716871i	$-0.254427\pi$
$661$	4.02712e8			1.39441			0.697205	+	0.716871i	$0.254427\pi$
$662$	1.99634e6	+	7.56784e6i	0.00688114	+	0.0260854i
$663$			3.81680e8i			1.30966i
$664$	1.83632e8	+	1.87960e8i	0.627255	+	0.642038i
$665$	−4.64875e7			−0.158078
$666$	−4.95488e8	+	1.30706e8i	−1.67730	+	0.442459i
$667$		−	3.79809e8i		−	1.27994i
$668$	−1.59892e8	−	2.81975e8i	−0.536410	−	0.945977i
$669$	−1.89311e8			−0.632264
$670$	−7.95682e7	−	3.01632e8i	−0.264554	−	1.00289i
$671$		−	1.57242e8i		−	0.520475i
$672$	1.57681e8	−	5.45865e8i	0.519604	−	1.79878i
$673$	−4.34441e8			−1.42523			−0.712616	−	0.701555i	$-0.752490\pi$
$673$	−4.34441e8			−1.42523			−0.712616	+	0.701555i	$0.752490\pi$
$674$	−5.61856e8	+	1.48214e8i	−1.83504	+	0.484070i
$675$		−	3.73801e8i		−	1.21543i
$676$	−1.41547e8	+	8.02632e7i	−0.458205	+	0.259822i
$677$	4.81073e8			1.55040			0.775202	−	0.631713i	$-0.217648\pi$
$677$	4.81073e8			1.55040			0.775202	+	0.631713i	$0.217648\pi$
$678$	−1.79374e8	−	6.79981e8i	−0.575533	−	2.18176i
$679$		−	1.21301e8i		−	0.387485i
$680$	1.57576e8	−	1.53948e8i	0.501144	−	0.489605i
$681$	−3.98592e6			−0.0126208
$682$	−3.76856e8	+	9.94117e7i	−1.18802	+	0.313390i
$683$		−	2.18383e8i		−	0.685418i	−0.939442	−	0.342709i	$-0.888655\pi$
$683$		−	2.18383e8i		−	0.685418i	0.939442	−	0.342709i	$-0.111345\pi$
$684$	−7.96352e7	−	1.40439e8i	−0.248850	−	0.438854i
$685$	1.81292e8			0.564036
$686$	7.79385e7	+	2.95454e8i	0.241423	+	0.915202i
$687$			4.89170e7i			0.150865i
$688$	3.70871e8	+	2.21871e8i	1.13883	+	0.681296i
$689$	−3.68862e8			−1.12773
$690$	−3.44105e8	+	9.07724e7i	−1.04748	+	0.276316i
$691$			7.88603e7i			0.239015i	0.992833	+	0.119507i	$0.0381315\pi$
$691$			7.88603e7i			0.239015i	−0.992833	+	0.119507i	$0.961869\pi$
$692$	2.16830e8	−	1.22952e8i	0.654338	−	0.371038i
$693$	1.44186e9			4.33234
$694$	8.75332e6	+	3.31826e7i	0.0261875	+	0.0992731i
$695$			5.51850e7i			0.164387i
$696$	5.86182e8	+	5.99998e8i	1.73862	+	1.77960i
$697$	2.57499e8			0.760463
$698$	2.15486e8	−	5.68436e7i	0.633655	−	0.167153i
$699$		−	8.14423e8i		−	2.38462i
$700$	1.00373e8	+	1.77011e8i	0.292633	+	0.516068i
$701$	−5.62633e8			−1.63332			−0.816659	−	0.577120i	$-0.804176\pi$
$701$	−5.62633e8			−1.63332			−0.816659	+	0.577120i	$0.804176\pi$
$702$	1.30187e8	+	4.93519e8i	0.376318	+	1.42657i
$703$		−	6.28739e7i		−	0.180969i
$704$	−6.56472e8	−	1.52940e7i	−1.88147	−	0.0438333i
$705$	−3.22021e7			−0.0919003
$706$	1.91400e8	−	5.04898e7i	0.543910	−	0.143479i
$707$			3.15270e8i			0.892123i
$708$	7.00107e7	−	3.96991e7i	0.197272	−	0.111862i
$709$	2.78449e8			0.781280			0.390640	−	0.920544i	$-0.372254\pi$
$709$	2.78449e8			0.781280			0.390640	+	0.920544i	$0.372254\pi$
$710$	2.36433e7	+	8.96282e7i	0.0660590	+	0.250420i
$711$		−	8.43394e7i		−	0.234651i
$712$	2.56588e8	−	2.50680e8i	0.710881	−	0.694513i
$713$	2.17743e8			0.600725
$714$	7.01402e8	−	1.85025e8i	1.92696	−	0.508317i
$715$		−	3.11502e8i		−	0.852203i
$716$	9.03872e7	+	1.59401e8i	0.246245	+	0.434262i
$717$	−6.57130e8			−1.78276
$718$	−7.31971e7	−	2.77480e8i	−0.197752	−	0.749649i
$719$		−	1.29123e8i		−	0.347388i	−0.984800	−	0.173694i	$-0.944430\pi$
$719$		−	1.29123e8i		−	0.347388i	0.984800	−	0.173694i	$-0.0555704\pi$
$720$	2.77369e8	−	4.63639e8i	0.743124	−	1.24217i
$721$	−3.09180e8			−0.824907
$722$	1.91536e7	−	5.05257e6i	0.0508907	−	0.0134246i
$723$		−	1.06893e8i		−	0.282835i
$724$	1.14023e8	−	6.46562e7i	0.300454	−	0.170371i
$725$	−3.00412e8			−0.788321
$726$	−4.43740e8	−	1.68216e9i	−1.15963	−	4.39599i
$727$		−	6.69981e8i		−	1.74365i	−0.489817	−	0.871826i	$-0.662936\pi$
$727$		−	6.69981e8i		−	1.74365i	0.489817	−	0.871826i	$-0.337064\pi$
$728$	−1.94169e8	−	1.98745e8i	−0.503252	−	0.515112i
$729$	9.15989e7			0.236433
$730$	−3.62319e8	+	9.55771e7i	−0.931371	+	0.245689i
$731$			5.51750e8i			1.41251i
$732$	−9.56984e7	−	1.68767e8i	−0.243990	−	0.430284i
$733$	−6.18110e8			−1.56947			−0.784737	−	0.619829i	$-0.787202\pi$
$733$	−6.18110e8			−1.56947			−0.784737	+	0.619829i	$0.787202\pi$
$734$	−1.72250e8	−	6.52975e8i	−0.435583	−	1.65123i
$735$		−	4.47922e7i		−	0.112808i
$736$	3.52446e8	+	1.01809e8i	0.884014	+	0.255361i
$737$	−1.18714e9			−2.96550
$738$	6.10628e8	−	1.61079e8i	1.51917	−	0.400747i
$739$		−	4.24026e8i		−	1.05065i	−0.850901	−	0.525327i	$-0.823943\pi$
$739$		−	4.24026e8i		−	1.05065i	0.850901	−	0.525327i	$-0.176057\pi$
$740$	1.83027e8	−	1.03784e8i	0.451669	−	0.256116i
$741$	−1.14852e8			−0.282282
$742$	1.78811e8	+	6.77845e8i	0.437705	+	1.65928i
$743$		−	6.24199e8i		−	1.52180i	−0.648871	−	0.760898i	$-0.724759\pi$
$743$		−	6.24199e8i		−	1.52180i	0.648871	−	0.760898i	$-0.275241\pi$
$744$	−3.43976e8	+	3.36056e8i	−0.835236	+	0.816004i
$745$	−2.53065e8			−0.612017
$746$	6.09500e8	−	1.60782e8i	1.46811	−	0.387276i
$747$			8.22764e8i			1.97385i
$748$	−4.13521e8	−	7.29257e8i	−0.988081	−	1.74251i
$749$	−4.70549e8			−1.11985
$750$	1.98483e8	+	7.52420e8i	0.470478	+	1.78351i
$751$			1.82866e8i			0.431732i	0.976423	+	0.215866i	$0.0692574\pi$
$751$			1.82866e8i			0.431732i	−0.976423	+	0.215866i	$0.930743\pi$
$752$	2.84870e7	+	1.70422e7i	0.0669875	+	0.0400749i
$753$	5.59350e7			0.131008
$754$	3.96625e8	−	1.04627e8i	0.925265	−	0.244078i
$755$		−	6.34105e7i		−	0.147340i
$756$	8.43814e8	−	4.78480e8i	1.95291	−	1.10738i
$757$	−6.57939e8			−1.51669			−0.758347	−	0.651851i	$-0.773993\pi$
$757$	−6.57939e8			−1.51669			−0.758347	+	0.651851i	$0.773993\pi$
$758$	1.43518e8	+	5.44056e8i	0.329533	+	1.24921i
$759$			1.35430e9i			3.09735i
$760$	4.63245e7	+	4.74163e7i	0.105528	+	0.108016i
$761$	−5.74786e8			−1.30422			−0.652112	−	0.758123i	$-0.726117\pi$
$761$	−5.74786e8			−1.30422			−0.652112	+	0.758123i	$0.726117\pi$
$762$	6.31931e8	−	1.66699e8i	1.42825	−	0.376762i
$763$		−	7.11341e8i		−	1.60142i
$764$	2.77030e8	+	4.88552e8i	0.621222	+	1.09555i
$765$	6.89763e8			1.54069
$766$	−9.39746e7	−	3.56244e8i	−0.209086	−	0.792614i
$767$		−	3.93575e7i		−	0.0872251i
$768$	−7.13899e8	+	3.83119e8i	−1.57599	+	0.845765i
$769$	3.75438e8			0.825581			0.412790	−	0.910826i	$-0.364554\pi$
$769$	3.75438e8			0.825581			0.412790	+	0.910826i	$0.364554\pi$
$770$	−5.72438e8	+	1.51005e8i	−1.25388	+	0.330765i
$771$			1.01943e9i			2.22430i
$772$	−2.29450e8	+	1.30108e8i	−0.498697	+	0.282783i
$773$	4.91185e8			1.06342			0.531712	−	0.846925i	$-0.321549\pi$
$773$	4.91185e8			1.06342			0.531712	+	0.846925i	$0.321549\pi$
$774$	3.45148e8	+	1.30841e9i	0.744359	+	2.82176i
$775$		−	1.72225e8i		−	0.369991i
$776$	−1.23724e8	+	1.20876e8i	−0.264771	+	0.258674i
$777$	6.92827e8			1.47694
$778$	−2.95404e8	+	7.79255e7i	−0.627304	+	0.165478i
$779$			7.74843e7i			0.163909i
$780$	−1.89583e8	−	3.34335e8i	−0.399498	−	0.704528i
$781$	3.52751e8			0.740483
$782$	1.19464e8	+	4.52871e8i	0.249814	+	0.947008i
$783$			1.43207e9i			2.98317i
$784$	−2.37052e7	+	3.96247e7i	−0.0491921	+	0.0822275i
$785$	4.33563e8			0.896278
$786$	−3.39152e8	+	8.94657e7i	−0.698436	+	0.184242i
$787$		−	3.93360e8i		−	0.806987i	−0.914983	−	0.403493i	$-0.867796\pi$
$787$		−	3.93360e8i		−	0.806987i	0.914983	−	0.403493i	$-0.132204\pi$
$788$	1.73100e8	−	9.81553e7i	0.353768	−	0.200602i
$789$	−1.27141e9			−2.58854
$790$	8.83281e6	+	3.34839e7i	0.0179150	+	0.0679134i
$791$			6.53586e8i			1.32061i
$792$	−1.43680e9	−	1.47066e9i	−2.89215	−	2.96031i
$793$	−9.48749e7			−0.190253
$794$	6.40546e8	−	1.68971e8i	1.27964	−	0.337560i
$795$			9.69726e8i			1.92996i
$796$	2.87891e8	+	5.07704e8i	0.570806	+	1.00663i
$797$	9.32022e8			1.84099			0.920494	−	0.390757i	$-0.127787\pi$
$797$	9.32022e8			1.84099			0.920494	+	0.390757i	$0.127787\pi$
$798$	5.56759e7	+	2.11059e8i	0.109562	+	0.415332i
$799$			4.23806e7i			0.0830857i
$800$	8.05266e7	−	2.78769e8i	0.157278	−	0.544470i
$801$	1.12317e9			2.18549
$802$	9.17324e7	−	2.41983e7i	0.177828	−	0.0469097i
$803$			1.42598e9i			2.75403i
$804$	−1.27415e9	+	7.22499e8i	−2.45162	+	1.39017i
$805$	3.30749e8			0.634031
$806$	5.99821e7	+	2.27384e8i	0.114556	+	0.434264i
$807$		−	1.06774e9i		−	2.03164i
$808$	3.21569e8	−	3.14164e8i	0.609593	−	0.595556i
$809$	−4.21370e8			−0.795826			−0.397913	−	0.917423i	$-0.630265\pi$
$809$	−4.21370e8			−0.795826			−0.397913	+	0.917423i	$0.630265\pi$
$810$	5.53634e8	−	1.46045e8i	1.04176	−	0.274809i
$811$			1.33493e8i			0.250262i	0.992140	+	0.125131i	$0.0399351\pi$
$811$			1.33493e8i			0.250262i	−0.992140	+	0.125131i	$0.960065\pi$
$812$	−3.84539e8	−	6.78147e8i	−0.718244	−	1.26665i
$813$	2.52848e8			0.470531
$814$	−2.04233e8	−	7.74217e8i	−0.378662	−	1.43546i
$815$		−	3.78704e8i		−	0.699564i
$816$	−8.87663e8	−	5.31039e8i	−1.63372	−	0.977363i
$817$	−1.66027e8			−0.304448
$818$	−1.04238e8	+	2.74971e7i	−0.190443	+	0.0502374i
$819$		−	8.69974e8i		−	1.58363i
$820$	−2.25558e8	+	1.27901e8i	−0.409088	+	0.231971i
$821$	−9.43811e8			−1.70552			−0.852758	−	0.522306i	$-0.825072\pi$
$821$	−9.43811e8			−1.70552			−0.852758	+	0.522306i	$0.825072\pi$
$822$	−2.17125e8	−	8.23089e8i	−0.390926	−	1.48194i
$823$		−	5.97602e8i		−	1.07204i	−0.844204	−	0.536022i	$-0.819926\pi$
$823$		−	5.97602e8i		−	1.07204i	0.844204	−	0.536022i	$-0.180074\pi$
$824$	3.08095e8	+	3.15357e8i	0.550685	+	0.563664i
$825$	1.07119e9			1.90768
$826$	−7.23261e7	+	1.90791e7i	−0.128338	+	0.0338546i
$827$			5.02109e8i			0.887731i	0.896093	+	0.443865i	$0.146393\pi$
$827$			5.02109e8i			0.887731i	−0.896093	+	0.443865i	$0.853607\pi$
$828$	5.66587e8	+	9.99195e8i	0.998104	+	1.76019i
$829$	−1.37713e8			−0.241720			−0.120860	−	0.992670i	$-0.538565\pi$
$829$	−1.37713e8			−0.241720			−0.120860	+	0.992670i	$0.538565\pi$
$830$	−8.61676e7	−	3.26649e8i	−0.150699	−	0.571278i
$831$		−	5.72299e8i		−	0.997286i
$832$	−9.22796e6	+	3.96096e8i	−0.0160227	+	0.687750i
$833$	−5.89502e7			−0.101988
$834$	2.50547e8	−	6.60924e7i	0.431908	−	0.113934i
$835$			4.16734e8i			0.715813i
$836$	2.19441e8	−	1.24433e8i	0.375577	−	0.212969i
$837$	−8.20998e8			−1.40012
$838$	−2.42049e8	−	9.17572e8i	−0.411311	−	1.55922i
$839$		−	6.49417e8i		−	1.09961i	−0.835294	−	0.549804i	$-0.814702\pi$
$839$		−	6.49417e8i		−	1.09961i	0.835294	−	0.549804i	$-0.185298\pi$
$840$	−5.22494e8	+	5.10464e8i	−0.881544	+	0.861245i
$841$	5.56084e8			0.934872
$842$	1.92095e8	−	5.06732e7i	0.321795	−	0.0848871i
$843$			9.73709e8i			1.62535i
$844$	2.64968e8	+	4.67280e8i	0.440724	+	0.777231i
$845$	2.09194e8			0.346719
$846$	2.65112e7	+	1.00500e8i	0.0437843	+	0.165980i
$847$			1.61686e9i			2.66086i
$848$	5.13204e8	−	8.57851e8i	0.841594	−	1.40677i
$849$	−1.18828e9			−1.94176
$850$	3.58200e8	−	9.44905e7i	0.583269	−	0.153862i
$851$			4.47334e8i			0.725845i
$852$	3.78607e8	−	2.14687e8i	0.612167	−	0.347126i
$853$	−3.15563e8			−0.508439			−0.254219	−	0.967147i	$-0.581819\pi$
$853$	−3.15563e8			−0.508439			−0.254219	+	0.967147i	$0.581819\pi$
$854$	4.59919e7	+	1.74349e8i	0.0738427	+	0.279927i
$855$			2.07557e8i			0.332077i
$856$	4.68899e8	+	4.79950e8i	0.747581	+	0.765200i
$857$	3.07046e8			0.487822			0.243911	−	0.969798i	$-0.421570\pi$
$857$	3.07046e8			0.487822			0.243911	+	0.969798i	$0.421570\pi$
$858$	−1.41426e9	+	3.73071e8i	−2.23907	+	0.590650i
$859$			2.35602e7i			0.0371705i	0.999827	+	0.0185853i	$0.00591622\pi$
$859$			2.35602e7i			0.0371705i	−0.999827	+	0.0185853i	$0.994084\pi$
$860$	−2.74057e8	−	4.83309e8i	−0.430870	−	0.759853i
$861$	−8.53824e8			−1.33770
$862$	−8.63364e7	−	3.27289e8i	−0.134794	−	0.510986i
$863$		−	5.55471e8i		−	0.864229i	−0.901819	−	0.432114i	$-0.857768\pi$
$863$		−	5.55471e8i		−	0.864229i	0.901819	−	0.432114i	$-0.142232\pi$
$864$	−1.32889e9	−	3.83871e8i	−2.06039	−	0.595174i
$865$	−3.20456e8			−0.495132
$866$	−5.87875e8	+	1.55077e8i	−0.905172	+	0.238778i
$867$		−	1.54938e8i		−	0.237739i
$868$	3.88779e8	−	2.20454e8i	0.594488	−	0.337101i
$869$	1.31783e8			0.200817
$870$	−2.75061e8	−	1.04272e9i	−0.417706	−	1.58346i
$871$			7.16282e8i			1.08400i
$872$	−7.25553e8	+	7.08846e8i	−1.09426	+	1.06906i
$873$	−5.41584e8			−0.813997
$874$	−1.36274e8	+	3.59480e7i	−0.204116	+	0.0538443i
$875$		−	7.23214e8i		−	1.07955i
$876$	8.67865e8	+	1.53051e9i	1.29104	+	2.27679i
$877$	6.78056e8			1.00523			0.502617	−	0.864509i	$-0.332371\pi$
$877$	6.78056e8			1.00523			0.502617	+	0.864509i	$0.332371\pi$
$878$	−1.36095e8	−	5.15917e8i	−0.201075	−	0.762248i
$879$			1.64589e9i			2.42345i
$880$	7.24452e8	+	4.33399e8i	1.06307	+	0.635975i
$881$	5.69424e8			0.832737			0.416369	−	0.909196i	$-0.363303\pi$
$881$	5.69424e8			0.832737			0.416369	+	0.909196i	$0.363303\pi$
$882$	−1.39793e8	+	3.68764e7i	−0.203742	+	0.0537455i
$883$			2.57956e8i			0.374682i	0.982295	+	0.187341i	$0.0599870\pi$
$883$			2.57956e8i			0.374682i	−0.982295	+	0.187341i	$0.940013\pi$
$884$	−4.40012e8	+	2.49506e8i	−0.636954	+	0.361181i
$885$	−1.03470e8			−0.149274
$886$	4.59272e7	+	1.74103e8i	0.0660341	+	0.250326i
$887$		−	4.77476e8i		−	0.684196i	−0.939664	−	0.342098i	$-0.888863\pi$
$887$		−	4.77476e8i		−	0.684196i	0.939664	−	0.342098i	$-0.111137\pi$
$888$	−6.90397e8	−	7.06669e8i	−0.985962	−	1.00920i
$889$	−6.07402e8			−0.864512
$890$	−4.45916e8	+	1.17629e8i	−0.632533	+	0.166858i
$891$		−	2.17894e9i		−	3.08044i
$892$	−1.23754e8	−	2.18244e8i	−0.174367	−	0.307502i
$893$	−1.27528e7			−0.0179081
$894$	3.03084e8	+	1.14895e9i	0.424181	+	1.60801i
$895$		−	2.35580e8i		−	0.328602i
$896$	7.32366e8	−	1.75055e8i	1.01813	−	0.243361i
$897$	8.17144e8			1.13220
$898$	7.18797e8	−	1.89613e8i	0.992607	−	0.261842i
$899$			6.59810e8i			0.908113i
$900$	7.90318e8	−	4.48145e8i	1.08411	−	0.614739i
$901$	1.27624e9			1.74485
$902$	2.51692e8	+	9.54127e8i	0.342965	+	1.30013i
$903$		−	1.82951e9i		−	2.48468i
$904$	6.66644e8	−	6.51294e8i	0.902379	−	0.881600i
$905$	−1.68516e8			−0.227351
$906$	−2.87892e8	+	7.59437e7i	−0.387119	+	0.102119i
$907$		−	9.69290e8i		−	1.29907i	−0.760333	−	0.649534i	$-0.774964\pi$
$907$		−	9.69290e8i		−	1.29907i	0.760333	−	0.649534i	$-0.225036\pi$
$908$	−2.60562e6	−	4.59509e6i	−0.00348059	−	0.00613813i
$909$	1.40761e9			1.87410
$910$	9.11119e7	+	3.45392e8i	0.120907	+	0.458341i
$911$		−	9.65924e8i		−	1.27758i	−0.769382	−	0.638789i	$-0.779436\pi$
$911$		−	9.65924e8i		−	1.27758i	0.769382	−	0.638789i	$-0.220564\pi$
$912$	1.59795e8	−	2.67107e8i	0.210659	−	0.352128i
$913$	−1.28560e9			−1.68925
$914$	1.21518e8	−	3.20556e7i	0.159149	−	0.0419822i
$915$			2.49423e8i			0.325592i
$916$	−5.63929e7	+	3.19773e7i	−0.0733733	+	0.0416059i
$917$	3.25987e8			0.422759
$918$	−4.50437e8	−	1.70754e9i	−0.582246	−	2.20721i
$919$			1.81018e8i			0.233225i	0.993178	+	0.116612i	$0.0372035\pi$
$919$			1.81018e8i			0.233225i	−0.993178	+	0.116612i	$0.962796\pi$
$920$	−3.29588e8	−	3.37356e8i	−0.423261	−	0.433237i
$921$	1.39701e9			1.78822
$922$	−7.40080e8	+	1.95228e8i	−0.944248	+	0.249086i
$923$		−	2.12839e8i		−	0.270674i
$924$	1.37116e9	+	2.41809e9i	1.73809	+	3.06519i
$925$	3.53821e8			0.447052
$926$	2.88086e8	+	1.09209e9i	0.362818	+	1.37539i
$927$			1.38042e9i			1.73290i
$928$	−3.08505e8	+	1.06799e9i	−0.386027	+	1.33636i
$929$	−1.78665e8			−0.222839			−0.111420	−	0.993773i	$-0.535540\pi$
$929$	−1.78665e8			−0.222839			−0.111420	+	0.993773i	$0.535540\pi$
$930$	5.97784e8	−	1.57691e8i	0.743183	−	0.196046i
$931$		−	1.77387e7i		−	0.0219823i
$932$	9.38891e8	−	5.32392e8i	1.15976	−	0.657634i
$933$	−2.77842e9			−3.42099
$934$	4.49199e7	+	1.70285e8i	0.0551313	+	0.208995i
$935$			1.07778e9i			1.31854i
$936$	−8.87355e8	+	8.66923e8i	−1.08211	+	1.05719i
$937$	1.27982e9			1.55571			0.777857	−	0.628442i	$-0.216307\pi$
$937$	1.27982e9			1.55571			0.777857	+	0.628442i	$0.216307\pi$
$938$	1.31629e9	−	3.47227e8i	1.59493	−	0.420732i
$939$		−	2.24331e9i		−	2.70952i
$940$	−2.10507e7	−	3.71235e7i	−0.0253444	−	0.0446957i
$941$	3.45454e8			0.414592			0.207296	−	0.978278i	$-0.433534\pi$
$941$	3.45454e8			0.414592			0.207296	+	0.978278i	$0.433534\pi$
$942$	−5.19257e8	−	1.96843e9i	−0.621198	−	2.35487i
$943$		−	5.51284e8i		−	0.657416i
$944$	9.15327e7	+	5.47589e7i	0.108808	+	0.0650937i
$945$	−1.24708e9			−1.47775
$946$	−2.04443e9	+	5.39306e8i	−2.41490	+	0.637032i
$947$		−	5.09568e8i		−	0.600001i	−0.953939	−	0.300001i	$-0.903013\pi$
$947$		−	5.09568e8i		−	0.600001i	0.953939	−	0.300001i	$-0.0969869\pi$
$948$	1.41443e8	−	8.02042e7i	0.166018	−	0.0941396i
$949$	8.60397e8			1.00670
$950$	2.84332e7	+	1.07786e8i	0.0331631	+	0.125717i
$951$		−	1.06238e9i		−	1.23520i
$952$	6.71811e8	+	6.87645e8i	0.778640	+	0.796991i
$953$	1.13954e9			1.31659			0.658295	−	0.752760i	$-0.271278\pi$
$953$	1.13954e9			1.31659			0.658295	+	0.752760i	$0.271278\pi$
$954$	3.02644e9	−	7.98352e8i	3.48567	−	0.919495i
$955$		−	7.22037e8i		−	0.828990i
$956$	−4.29569e8	−	7.57559e8i	−0.491654	−	0.867047i
$957$	−4.10383e9			−4.68224
$958$	2.28295e8	+	8.65435e8i	0.259657	+	0.984323i
$959$			7.91140e8i			0.897011i
$960$	1.04132e9	+	2.42600e7i	1.17699	+	0.0274206i
$961$	5.09238e8			0.573786
$962$	−4.67140e8	+	1.23228e8i	−0.524713	+	0.138415i
$963$			2.10090e9i			2.35249i
$964$	1.23229e8	−	6.98761e7i	0.137557	−	0.0780006i
$965$	3.39107e8			0.377360
$966$	−3.96122e8	−	1.50164e9i	−0.439438	−	1.66585i
$967$			9.15673e7i			0.101265i	0.998717	+	0.0506327i	$0.0161238\pi$
$967$			9.15673e7i			0.101265i	−0.998717	+	0.0506327i	$0.983876\pi$
$968$	1.64916e9	−	1.61119e9i	1.81818	−	1.77632i
$969$	3.97379e8			0.436751
$970$	2.15016e8	−	5.67198e7i	0.235590	−	0.0621469i
$971$		−	1.45596e9i		−	1.59034i	−0.606384	−	0.795172i	$-0.707381\pi$
$971$		−	1.45596e9i		−	1.59034i	0.606384	−	0.795172i	$-0.292619\pi$
$972$	−3.54656e8	−	6.25448e8i	−0.386197	−	0.681071i
$973$	−2.40822e8			−0.261431
$974$	7.74196e7	+	2.93486e8i	0.0837865	+	0.317622i
$975$		−	6.46324e8i		−	0.697327i
$976$	1.32001e8	−	2.20648e8i	0.141981	−	0.237329i
$977$	1.39700e9			1.49800			0.749000	−	0.662571i	$-0.230535\pi$
$977$	1.39700e9			1.49800			0.749000	+	0.662571i	$0.230535\pi$
$978$	−1.71937e9	+	4.53556e8i	−1.83803	+	0.484858i
$979$			1.75500e9i			1.87038i
$980$	5.16378e7	−	2.92809e7i	0.0548642	−	0.0311104i
$981$	−3.17599e9			−3.36412
$982$	−1.11027e8	−	4.20889e8i	−0.117245	−	0.444461i
$983$			1.52689e9i			1.60749i	0.594977	+	0.803743i	$0.297161\pi$
$983$			1.52689e9i			1.60749i	−0.594977	+	0.803743i	$0.702839\pi$
$984$	8.50829e8	+	8.70882e8i	0.893012	+	0.914059i
$985$	−2.55827e8			−0.267693
$986$	−1.37230e9	+	3.62002e8i	−1.43159	+	0.377642i
$987$		−	1.40527e8i		−	0.146153i
$988$	−7.50791e7	−	1.32404e8i	−0.0778481	−	0.137288i
$989$	1.18125e9			1.22110
$990$	6.74205e8	+	2.55582e9i	0.694843	+	2.63405i
$991$			5.72594e8i			0.588337i	0.955754	+	0.294168i	$0.0950427\pi$
$991$			5.72594e8i			0.588337i	−0.955754	+	0.294168i	$0.904957\pi$
$992$	−6.12274e8	−	1.76865e8i	−0.627207	−	0.181178i
$993$	−4.72460e7			−0.0482522
$994$	−3.91128e8	+	1.03177e8i	−0.398254	+	0.105056i
$995$		−	7.50342e8i		−	0.761711i
$996$	−1.37983e9	+	7.82424e8i	−1.39652	+	0.791889i
$997$	−1.39206e9			−1.40466			−0.702332	−	0.711850i	$-0.747858\pi$
$997$	−1.39206e9			−1.40466			−0.702332	+	0.711850i	$0.747858\pi$
$998$	1.76467e8	+	6.68960e8i	0.177530	+	0.672990i
$999$		−	1.68667e9i		−	1.69174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.6	yes	54
4.3	odd	2	inner	76.7.b.a.39.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.5	✓	54	4.3	odd	2	inner
76.7.b.a.39.6	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)

\(f(q)\)	\(=\)	\(q+(-7.73539 + 2.04054i) q^{2} -48.2920i q^{3} +(55.6724 - 31.5687i) q^{4} -82.2790 q^{5} +(98.5416 + 373.557i) q^{6} -359.057i q^{7} +(-366.231 + 357.798i) q^{8} -1603.11 q^{9} +O(q^{10})\)	\(q+(-7.73539 + 2.04054i) q^{2} -48.2920i q^{3} +(55.6724 - 31.5687i) q^{4} -82.2790 q^{5} +(98.5416 + 373.557i) q^{6} -359.057i q^{7} +(-366.231 + 357.798i) q^{8} -1603.11 q^{9} +(636.459 - 167.893i) q^{10} -2504.92i q^{11} +(-1524.51 - 2688.53i) q^{12} -1511.40 q^{13} +(732.669 + 2777.45i) q^{14} +3973.41i q^{15} +(2102.83 - 3515.01i) q^{16} +5229.33 q^{17} +(12400.7 - 3271.22i) q^{18} +1573.56i q^{19} +(-4580.67 + 2597.44i) q^{20} -17339.6 q^{21} +(5111.39 + 19376.5i) q^{22} -11195.6i q^{23} +(17278.8 + 17686.0i) q^{24} -8855.17 q^{25} +(11691.2 - 3084.06i) q^{26} +42212.7i q^{27} +(-11335.0 - 19989.6i) q^{28} +33925.0 q^{29} +(-8107.90 - 30735.9i) q^{30} +19449.1i q^{31} +(-9093.73 + 31480.9i) q^{32} -120968. q^{33} +(-40450.9 + 10670.7i) q^{34} +29542.8i q^{35} +(-89249.3 + 50608.2i) q^{36} -39956.4 q^{37} +(-3210.91 - 12172.1i) q^{38} +72988.3i q^{39} +(30133.1 - 29439.2i) q^{40} +49241.4 q^{41} +(134128. - 35382.1i) q^{42} +105511. i q^{43} +(-79077.1 - 139455. i) q^{44} +131903. q^{45} +(22845.0 + 86602.0i) q^{46} +8104.39i q^{47} +(-169747. - 101550. i) q^{48} -11273.0 q^{49} +(68498.2 - 18069.3i) q^{50} -252535. i q^{51} +(-84143.0 + 47712.8i) q^{52} +244054. q^{53} +(-86136.7 - 326532. i) q^{54} +206102. i q^{55} +(128470. + 131498. i) q^{56} +75990.4 q^{57} +(-262423. + 69225.3i) q^{58} +26040.5i q^{59} +(125435. + 221209. i) q^{60} +62773.1 q^{61} +(-39686.6 - 150446. i) q^{62} +575610. i q^{63} +(6105.59 - 262073. i) q^{64} +124356. q^{65} +(935732. - 246839. i) q^{66} -473921. i q^{67} +(291130. - 165083. i) q^{68} -540656. q^{69} +(-60283.3 - 228525. i) q^{70} +140823. i q^{71} +(587110. - 573591. i) q^{72} -569273. q^{73} +(309078. - 81532.6i) q^{74} +427634. i q^{75} +(49675.3 + 87604.0i) q^{76} -899410. q^{77} +(-148935. - 564593. i) q^{78} +52609.7i q^{79} +(-173019. + 289211. i) q^{80} +869865. q^{81} +(-380901. + 100479. i) q^{82} -513228. i q^{83} +(-965336. + 547388. i) q^{84} -430264. q^{85} +(-215298. - 816165. i) q^{86} -1.63831e6i q^{87} +(896256. + 917379. i) q^{88} -700620. q^{89} +(-1.02032e6 + 269152. i) q^{90} +542677. i q^{91} +(-353429. - 623284. i) q^{92} +939234. q^{93} +(-16537.3 - 62690.6i) q^{94} -129471. i q^{95} +(1.52027e6 + 439154. i) q^{96} +337832. q^{97} +(87200.9 - 23002.9i) q^{98} +4.01568e6i 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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