LMFDB - Embedded newform 74.7.d.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,7,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.0240021879$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 $ x^20 + 10424x^18 + 44844916x^16 + 103219343022x^14 + 138101513095620x^12 + 109787124347520192x^10 + 51172837440825906441x^8 + 13199761586736849750156x^6 + 1629475196758519705300656x^4 + 65381450766316829487245376*x^2 + 736627437450607950694158336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.6
Root			$-6.30032i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.b.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 4.00000i) q^{2} +9.30032i q^{3} +32.0000i q^{4} +(9.75519 - 9.75519i) q^{5} +(37.2013 - 37.2013i) q^{6} -106.968 q^{7} +(128.000 - 128.000i) q^{8} +642.504 q^{9} +O(q^{10})$	\(q+(-4.00000 - 4.00000i) q^{2} +9.30032i q^{3} +32.0000i q^{4} +(9.75519 - 9.75519i) q^{5} +(37.2013 - 37.2013i) q^{6} -106.968 q^{7} +(128.000 - 128.000i) q^{8} +642.504 q^{9} -78.0415 q^{10} -963.875i q^{11} -297.610 q^{12} +(-2541.87 + 2541.87i) q^{13} +(427.873 + 427.873i) q^{14} +(90.7264 + 90.7264i) q^{15} -1024.00 q^{16} +(3615.51 - 3615.51i) q^{17} +(-2570.02 - 2570.02i) q^{18} +(-4174.71 + 4174.71i) q^{19} +(312.166 + 312.166i) q^{20} -994.838i q^{21} +(-3855.50 + 3855.50i) q^{22} +(-11820.0 + 11820.0i) q^{23} +(1190.44 + 1190.44i) q^{24} +15434.7i q^{25} +20335.0 q^{26} +12755.4i q^{27} -3422.98i q^{28} +(7831.26 + 7831.26i) q^{29} -725.811i q^{30} +(22236.8 + 22236.8i) q^{31} +(4096.00 + 4096.00i) q^{32} +8964.34 q^{33} -28924.0 q^{34} +(-1043.49 + 1043.49i) q^{35} +20560.1i q^{36} +(-3576.93 + 50526.5i) q^{37} +33397.7 q^{38} +(-23640.2 - 23640.2i) q^{39} -2497.33i q^{40} +119813. i q^{41} +(-3979.35 + 3979.35i) q^{42} +(41343.2 - 41343.2i) q^{43} +30844.0 q^{44} +(6267.75 - 6267.75i) q^{45} +94560.4 q^{46} -178456. q^{47} -9523.53i q^{48} -106207. q^{49} +(61738.7 - 61738.7i) q^{50} +(33625.4 + 33625.4i) q^{51} +(-81339.9 - 81339.9i) q^{52} -87252.5 q^{53} +(51021.7 - 51021.7i) q^{54} +(-9402.78 - 9402.78i) q^{55} +(-13691.9 + 13691.9i) q^{56} +(-38826.2 - 38826.2i) q^{57} -62650.1i q^{58} +(257915. - 257915. i) q^{59} +(-2903.24 + 2903.24i) q^{60} +(-96073.9 - 96073.9i) q^{61} -177894. i q^{62} -68727.5 q^{63} -32768.0i q^{64} +49592.9i q^{65} +(-35857.4 - 35857.4i) q^{66} +268089. i q^{67} +(115696. + 115696. i) q^{68} +(-109930. - 109930. i) q^{69} +8347.96 q^{70} -166369. q^{71} +(82240.5 - 82240.5i) q^{72} -611128. i q^{73} +(216414. - 187798. i) q^{74} -143547. q^{75} +(-133591. - 133591. i) q^{76} +103104. i q^{77} +189122. i q^{78} +(-341731. + 341731. i) q^{79} +(-9989.31 + 9989.31i) q^{80} +349756. q^{81} +(479253. - 479253. i) q^{82} +554671. q^{83} +31834.8 q^{84} -70539.9i q^{85} -330746. q^{86} +(-72833.2 + 72833.2i) q^{87} +(-123376. - 123376. i) q^{88} +(620426. + 620426. i) q^{89} -50142.0 q^{90} +(271899. - 271899. i) q^{91} +(-378241. - 378241. i) q^{92} +(-206809. + 206809. i) q^{93} +(713825. + 713825. i) q^{94} +81450.3i q^{95} +(-38094.1 + 38094.1i) q^{96} +(-1.10316e6 + 1.10316e6i) q^{97} +(424827. + 424827. i) q^{98} -619293. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) $ 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−4.00000	−	4.00000i	−0.500000	−	0.500000i
$2$	−4.00000	−	4.00000i	−0.500000	−	0.500000i
$3$			9.30032i			0.344456i	0.985057	+	0.172228i	$0.0550966\pi$
$3$			9.30032i			0.344456i	−0.985057	+	0.172228i	$0.944903\pi$
$4$			32.0000i			0.500000i
$5$	9.75519	−	9.75519i	0.0780415	−	0.0780415i	−0.667009	−	0.745050i	$-0.732426\pi$
$5$	9.75519	−	9.75519i	0.0780415	−	0.0780415i	0.745050	+	0.667009i	$0.232426\pi$
$6$	37.2013	−	37.2013i	0.172228	−	0.172228i
$7$	−106.968			−0.311860			−0.155930	−	0.987768i	$-0.549838\pi$
$7$	−106.968			−0.311860			−0.155930	+	0.987768i	$0.549838\pi$
$8$	128.000	−	128.000i	0.250000	−	0.250000i
$9$	642.504			0.881350
$10$	−78.0415			−0.0780415
$11$		−	963.875i		−	0.724173i	−0.932144	−	0.362087i	$-0.882064\pi$
$11$		−	963.875i		−	0.724173i	0.932144	−	0.362087i	$-0.117936\pi$
$12$	−297.610			−0.172228
$13$	−2541.87	+	2541.87i	−1.15697	+	1.15697i	−0.171851	+	0.985123i	$0.554975\pi$
$13$	−2541.87	+	2541.87i	−1.15697	+	1.15697i	−0.985123	+	0.171851i	$0.945025\pi$
$14$	427.873	+	427.873i	0.155930	+	0.155930i
$15$	90.7264	+	90.7264i	0.0268819	+	0.0268819i
$16$	−1024.00			−0.250000
$17$	3615.51	−	3615.51i	0.735906	−	0.735906i	−0.235877	−	0.971783i	$-0.575796\pi$
$17$	3615.51	−	3615.51i	0.735906	−	0.735906i	0.971783	+	0.235877i	$0.0757962\pi$
$18$	−2570.02	−	2570.02i	−0.440675	−	0.440675i
$19$	−4174.71	+	4174.71i	−0.608648	+	0.608648i	−0.942593	−	0.333945i	$-0.891620\pi$
$19$	−4174.71	+	4174.71i	−0.608648	+	0.608648i	0.333945	+	0.942593i	$0.391620\pi$
$20$	312.166	+	312.166i	0.0390208	+	0.0390208i
$21$		−	994.838i		−	0.107422i
$22$	−3855.50	+	3855.50i	−0.362087	+	0.362087i
$23$	−11820.0	+	11820.0i	−0.971484	+	0.971484i	−0.999605	−	0.0281206i	$-0.991048\pi$
$23$	−11820.0	+	11820.0i	−0.971484	+	0.971484i	0.0281206	+	0.999605i	$0.491048\pi$
$24$	1190.44	+	1190.44i	0.0861141	+	0.0861141i
$25$			15434.7i			0.987819i
$26$	20335.0			1.15697
$27$			12755.4i			0.648043i
$28$		−	3422.98i		−	0.155930i
$29$	7831.26	+	7831.26i	0.321098	+	0.321098i	0.849188	−	0.528090i	$-0.177092\pi$
$29$	7831.26	+	7831.26i	0.321098	+	0.321098i	−0.528090	+	0.849188i	$0.677092\pi$
$30$		−	725.811i		−	0.0268819i
$31$	22236.8	+	22236.8i	0.746427	+	0.746427i	0.973806	−	0.227380i	$-0.0730158\pi$
$31$	22236.8	+	22236.8i	0.746427	+	0.746427i	−0.227380	+	0.973806i	$0.573016\pi$
$32$	4096.00	+	4096.00i	0.125000	+	0.125000i
$33$	8964.34			0.249446
$34$	−28924.0			−0.735906
$35$	−1043.49	+	1043.49i	−0.0243381	+	0.0243381i
$36$			20560.1i			0.440675i
$37$	−3576.93	+	50526.5i	−0.0706163	+	0.997504i
$37$	−3576.93	+	50526.5i	−0.0706163	+	0.997504i
$38$	33397.7			0.608648
$39$	−23640.2	−	23640.2i	−0.398527	−	0.398527i
$40$		−	2497.33i		−	0.0390208i
$41$			119813.i			1.73841i	0.494450	+	0.869206i	$0.335370\pi$
$41$			119813.i			1.73841i	−0.494450	+	0.869206i	$0.664630\pi$
$42$	−3979.35	+	3979.35i	−0.0537111	+	0.0537111i
$43$	41343.2	−	41343.2i	0.519995	−	0.519995i	−0.397575	−	0.917570i	$-0.630148\pi$
$43$	41343.2	−	41343.2i	0.519995	−	0.519995i	0.917570	+	0.397575i	$0.130148\pi$
$44$	30844.0			0.362087
$45$	6267.75	−	6267.75i	0.0687819	−	0.0687819i
$46$	94560.4			0.971484
$47$	−178456.			−1.71885			−0.859426	−	0.511261i	$-0.829179\pi$
$47$	−178456.			−1.71885			−0.859426	+	0.511261i	$0.829179\pi$
$48$		−	9523.53i		−	0.0861141i
$49$	−106207.			−0.902743
$50$	61738.7	−	61738.7i	0.493910	−	0.493910i
$51$	33625.4	+	33625.4i	0.253487	+	0.253487i
$52$	−81339.9	−	81339.9i	−0.578487	−	0.578487i
$53$	−87252.5			−0.586071			−0.293035	−	0.956102i	$-0.594665\pi$
$53$	−87252.5			−0.586071			−0.293035	+	0.956102i	$0.594665\pi$
$54$	51021.7	−	51021.7i	0.324021	−	0.324021i
$55$	−9402.78	−	9402.78i	−0.0565156	−	0.0565156i
$56$	−13691.9	+	13691.9i	−0.0779651	+	0.0779651i
$57$	−38826.2	−	38826.2i	−0.209653	−	0.209653i
$58$		−	62650.1i		−	0.321098i
$59$	257915.	−	257915.i	1.25580	−	1.25580i	0.302720	−	0.953080i	$-0.402105\pi$
$59$	257915.	−	257915.i	1.25580	−	1.25580i	0.953080	−	0.302720i	$-0.0978945\pi$
$60$	−2903.24	+	2903.24i	−0.0134409	+	0.0134409i
$61$	−96073.9	−	96073.9i	−0.423269	−	0.423269i	0.463059	−	0.886327i	$-0.346752\pi$
$61$	−96073.9	−	96073.9i	−0.423269	−	0.423269i	−0.886327	+	0.463059i	$0.846752\pi$
$62$		−	177894.i		−	0.746427i
$63$	−68727.5			−0.274858
$64$		−	32768.0i		−	0.125000i
$65$			49592.9i			0.180584i
$66$	−35857.4	−	35857.4i	−0.124723	−	0.124723i
$67$			268089.i			0.891364i	0.895191	+	0.445682i	$0.147039\pi$
$67$			268089.i			0.891364i	−0.895191	+	0.445682i	$0.852961\pi$
$68$	115696.	+	115696.i	0.367953	+	0.367953i
$69$	−109930.	−	109930.i	−0.334634	−	0.334634i
$70$	8347.96			0.0243381
$71$	−166369.			−0.464835			−0.232417	−	0.972616i	$-0.574664\pi$
$71$	−166369.			−0.464835			−0.232417	+	0.972616i	$0.574664\pi$
$72$	82240.5	−	82240.5i	0.220337	−	0.220337i
$73$		−	611128.i		−	1.57096i	−0.618890	−	0.785478i	$-0.712417\pi$
$73$		−	611128.i		−	1.57096i	0.618890	−	0.785478i	$-0.287583\pi$
$74$	216414.	−	187798.i	0.534060	−	0.463444i
$75$	−143547.			−0.340260
$76$	−133591.	−	133591.i	−0.304324	−	0.304324i
$77$			103104.i			0.225841i
$78$			189122.i			0.398527i
$79$	−341731.	+	341731.i	−0.693111	+	0.693111i	−0.962915	−	0.269805i	$-0.913041\pi$
$79$	−341731.	+	341731.i	−0.693111	+	0.693111i	0.269805	+	0.962915i	$0.413041\pi$
$80$	−9989.31	+	9989.31i	−0.0195104	+	0.0195104i
$81$	349756.			0.658128
$82$	479253.	−	479253.i	0.869206	−	0.869206i
$83$	554671.			0.970066			0.485033	−	0.874496i	$-0.338808\pi$
$83$	554671.			0.970066			0.485033	+	0.874496i	$0.338808\pi$
$84$	31834.8			0.0537111
$85$		−	70539.9i		−	0.114862i
$86$	−330746.			−0.519995
$87$	−72833.2	+	72833.2i	−0.110604	+	0.110604i
$88$	−123376.	−	123376.i	−0.181043	−	0.181043i
$89$	620426.	+	620426.i	0.880076	+	0.880076i	0.993542	−	0.113466i	$-0.0361954\pi$
$89$	620426.	+	620426.i	0.880076	+	0.880076i	−0.113466	+	0.993542i	$0.536195\pi$
$90$	−50142.0			−0.0687819
$91$	271899.	−	271899.i	0.360815	−	0.360815i
$92$	−378241.	−	378241.i	−0.485742	−	0.485742i
$93$	−206809.	+	206809.i	−0.257111	+	0.257111i
$94$	713825.	+	713825.i	0.859426	+	0.859426i
$95$			81450.3i			0.0949996i
$96$	−38094.1	+	38094.1i	−0.0430570	+	0.0430570i
$97$	−1.10316e6	+	1.10316e6i	−1.20871	+	1.20871i	−0.237267	+	0.971445i	$0.576252\pi$
$97$	−1.10316e6	+	1.10316e6i	−1.20871	+	1.20871i	−0.971445	+	0.237267i	$0.923748\pi$
$98$	424827.	+	424827.i	0.451372	+	0.451372i
$99$		−	619293.i		−	0.638250i
$100$	−493910.			−0.493910
$101$			1.22292e6i			1.18696i	0.804850	+	0.593479i	$0.202246\pi$
$101$			1.22292e6i			1.18696i	−0.804850	+	0.593479i	$0.797754\pi$
$102$		−	269003.i		−	0.253487i
$103$	−1.10488e6	−	1.10488e6i	−1.01112	−	1.01112i	−0.999938	−	0.0111801i	$-0.996441\pi$
$103$	−1.10488e6	−	1.10488e6i	−1.01112	−	1.01112i	−0.0111801	−	0.999938i	$-0.503559\pi$
$104$			650719.i			0.578487i
$105$	−9704.83	−	9704.83i	−0.00838340	−	0.00838340i
$106$	349010.	+	349010.i	0.293035	+	0.293035i
$107$	754684.			0.616047			0.308023	−	0.951379i	$-0.400333\pi$
$107$	754684.			0.616047			0.308023	+	0.951379i	$0.400333\pi$
$108$	−408174.			−0.324021
$109$	1.67005e6	−	1.67005e6i	1.28958	−	1.28958i	0.354541	−	0.935041i	$-0.384637\pi$
$109$	1.67005e6	−	1.67005e6i	1.28958	−	1.28958i	0.935041	−	0.354541i	$-0.115363\pi$
$110$			75222.2i			0.0565156i
$111$	−469913.	−	33266.6i	−0.343596	−	0.0243242i
$112$	109535.			0.0779651
$113$	283675.	+	283675.i	0.196601	+	0.196601i	0.798541	−	0.601940i	$-0.205605\pi$
$113$	283675.	+	283675.i	0.196601	+	0.196601i	−0.601940	+	0.798541i	$0.705605\pi$
$114$			310609.i			0.209653i
$115$			230614.i			0.151632i
$116$	−250600.	+	250600.i	−0.160549	+	0.160549i
$117$	−1.63316e6	+	1.63316e6i	−1.01970	+	1.01970i
$118$	−2.06332e6			−1.25580
$119$	−386744.	+	386744.i	−0.229500	+	0.229500i
$120$	23225.9			0.0134409
$121$	842507.			0.475573
$122$			768591.i			0.423269i
$123$	−1.11430e6			−0.598807
$124$	−711577.	+	711577.i	−0.373213	+	0.373213i
$125$	302993.	+	302993.i	0.155132	+	0.155132i
$126$	274910.	+	274910.i	0.137429	+	0.137429i
$127$	2.19694e6			1.07252			0.536262	−	0.844052i	$-0.319836\pi$
$127$	2.19694e6			1.07252			0.536262	+	0.844052i	$0.319836\pi$
$128$	−131072.	+	131072.i	−0.0625000	+	0.0625000i
$129$	384505.	+	384505.i	0.179115	+	0.179115i
$130$	198372.	−	198372.i	0.0902920	−	0.0902920i
$131$	−1.49591e6	−	1.49591e6i	−0.665412	−	0.665412i	0.291239	−	0.956650i	$-0.405933\pi$
$131$	−1.49591e6	−	1.49591e6i	−0.665412	−	0.665412i	−0.956650	+	0.291239i	$0.905933\pi$
$132$			286859.i			0.124723i
$133$	446562.	−	446562.i	0.189813	−	0.189813i
$134$	1.07236e6	−	1.07236e6i	0.445682	−	0.445682i
$135$	124432.	+	124432.i	0.0505742	+	0.0505742i
$136$		−	925570.i		−	0.367953i
$137$	1.31224e6			0.510330			0.255165	−	0.966898i	$-0.417870\pi$
$137$	1.31224e6			0.510330			0.255165	+	0.966898i	$0.417870\pi$
$138$			879441.i			0.334634i
$139$			404709.i			0.150695i	0.997157	+	0.0753475i	$0.0240066\pi$
$139$			404709.i			0.150695i	−0.997157	+	0.0753475i	$0.975993\pi$
$140$	−33391.8	−	33391.8i	−0.0121690	−	0.0121690i
$141$		−	1.65970e6i		−	0.592069i
$142$	665478.	+	665478.i	0.232417	+	0.232417i
$143$	2.45005e6	+	2.45005e6i	0.837850	+	0.837850i
$144$	−657924.			−0.220337
$145$	152791.			0.0501179
$146$	−2.44451e6	+	2.44451e6i	−0.785478	+	0.785478i
$147$		−	987757.i		−	0.310955i
$148$	−1.61685e6	−	114462.i	−0.498752	−	0.0353082i
$149$	−240148.			−0.0725973			−0.0362987	−	0.999341i	$-0.511557\pi$
$149$	−240148.			−0.0725973			−0.0362987	+	0.999341i	$0.511557\pi$
$150$	574189.	+	574189.i	0.170130	+	0.170130i
$151$		−	1.50119e6i		−	0.436019i	−0.975947	−	0.218009i	$-0.930044\pi$
$151$		−	1.50119e6i		−	0.436019i	0.975947	−	0.218009i	$-0.0699563\pi$
$152$			1.06873e6i			0.304324i
$153$	2.32298e6	−	2.32298e6i	0.648591	−	0.648591i
$154$	412416.	−	412416.i	0.112921	−	0.112921i
$155$	433848.			0.116505
$156$	756487.	−	756487.i	0.199263	−	0.199263i
$157$	1.06443e6			0.275055			0.137528	−	0.990498i	$-0.456084\pi$
$157$	1.06443e6			0.275055			0.137528	+	0.990498i	$0.456084\pi$
$158$	2.73384e6			0.693111
$159$		−	811476.i		−	0.201876i
$160$	79914.5			0.0195104
$161$	1.26437e6	−	1.26437e6i	0.302967	−	0.302967i
$162$	−1.39902e6	−	1.39902e6i	−0.329064	−	0.329064i
$163$	−1.70651e6	−	1.70651e6i	−0.394045	−	0.394045i	0.482081	−	0.876127i	$-0.339881\pi$
$163$	−1.70651e6	−	1.70651e6i	−0.394045	−	0.394045i	−0.876127	+	0.482081i	$0.839881\pi$
$164$	−3.83402e6			−0.869206
$165$	87448.8	−	87448.8i	0.0194671	−	0.0194671i
$166$	−2.21868e6	−	2.21868e6i	−0.485033	−	0.485033i
$167$	1.40891e6	−	1.40891e6i	0.302506	−	0.302506i	−0.539488	−	0.841993i	$-0.681382\pi$
$167$	1.40891e6	−	1.40891e6i	0.302506	−	0.302506i	0.841993	+	0.539488i	$0.181382\pi$
$168$	−127339.	−	127339.i	−0.0268556	−	0.0268556i
$169$		−	8.09542e6i		−	1.67718i
$170$	−282160.	+	282160.i	−0.0574312	+	0.0574312i
$171$	−2.68227e6	+	2.68227e6i	−0.536432	+	0.536432i
$172$	1.32298e6	+	1.32298e6i	0.259997	+	0.259997i
$173$			8.38063e6i			1.61859i	0.587399	+	0.809297i	$0.300152\pi$
$173$			8.38063e6i			1.61859i	−0.587399	+	0.809297i	$0.699848\pi$
$174$	582665.			0.110604
$175$		−	1.65102e6i		−	0.308062i
$176$			987008.i			0.181043i
$177$	2.39869e6	+	2.39869e6i	0.432568	+	0.432568i
$178$		−	4.96341e6i		−	0.880076i
$179$	−7.88880e6	−	7.88880e6i	−1.37547	−	1.37547i	−0.852111	−	0.523361i	$-0.824678\pi$
$179$	−7.88880e6	−	7.88880e6i	−1.37547	−	1.37547i	−0.523361	−	0.852111i	$-0.675322\pi$
$180$	200568.	+	200568.i	0.0343909	+	0.0343909i
$181$	3.13101e6			0.528018			0.264009	−	0.964520i	$-0.414955\pi$
$181$	3.13101e6			0.528018			0.264009	+	0.964520i	$0.414955\pi$
$182$	−2.17520e6			−0.360815
$183$	893518.	−	893518.i	0.145797	−	0.145797i
$184$			3.02593e6i			0.485742i
$185$	458002.	+	527790.i	0.0723357	+	0.0833577i
$186$	1.65447e6			0.257111
$187$	−3.48489e6	−	3.48489e6i	−0.532923	−	0.532923i
$188$		−	5.71060e6i		−	0.859426i
$189$		−	1.36442e6i		−	0.202099i
$190$	325801.	−	325801.i	0.0474998	−	0.0474998i
$191$	2.88746e6	−	2.88746e6i	0.414397	−	0.414397i	−0.468870	−	0.883267i	$-0.655339\pi$
$191$	2.88746e6	−	2.88746e6i	0.414397	−	0.414397i	0.883267	+	0.468870i	$0.155339\pi$
$192$	304753.			0.0430570
$193$	−6.39706e6	+	6.39706e6i	−0.889833	+	0.889833i	−0.994507	−	0.104674i	$-0.966620\pi$
$193$	−6.39706e6	+	6.39706e6i	−0.889833	+	0.889833i	0.104674	+	0.994507i	$0.466620\pi$
$194$	8.82527e6			1.20871
$195$	−461230.			−0.0622033
$196$		−	3.39862e6i		−	0.451372i
$197$	6.73497e6			0.880921			0.440461	−	0.897772i	$-0.354815\pi$
$197$	6.73497e6			0.880921			0.440461	+	0.897772i	$0.354815\pi$
$198$	−2.47717e6	+	2.47717e6i	−0.319125	+	0.319125i
$199$	−7.29621e6	−	7.29621e6i	−0.925844	−	0.925844i	0.0715899	−	0.997434i	$-0.477193\pi$
$199$	−7.29621e6	−	7.29621e6i	−0.925844	−	0.925844i	−0.997434	+	0.0715899i	$0.977193\pi$
$200$	1.97564e6	+	1.97564e6i	0.246955	+	0.246955i
$201$	−2.49332e6			−0.307036
$202$	4.89170e6	−	4.89170e6i	0.593479	−	0.593479i
$203$	−837695.	−	837695.i	−0.100138	−	0.100138i
$204$	−1.07601e6	+	1.07601e6i	−0.126744	+	0.126744i
$205$	1.16880e6	+	1.16880e6i	0.135668	+	0.135668i
$206$			8.83900e6i			1.01112i
$207$	−7.59443e6	+	7.59443e6i	−0.856217	+	0.856217i
$208$	2.60288e6	−	2.60288e6i	0.289244	−	0.289244i
$209$	4.02390e6	+	4.02390e6i	0.440766	+	0.440766i
$210$			77638.6i			0.00838340i
$211$	8.52914e6			0.907942			0.453971	−	0.891016i	$-0.350007\pi$
$211$	8.52914e6			0.907942			0.453971	+	0.891016i	$0.350007\pi$
$212$		−	2.79208e6i		−	0.293035i
$213$		−	1.54729e6i		−	0.160115i
$214$	−3.01873e6	−	3.01873e6i	−0.308023	−	0.308023i
$215$		−	806622.i		−	0.0811624i
$216$	1.63269e6	+	1.63269e6i	0.162011	+	0.162011i
$217$	−2.37863e6	−	2.37863e6i	−0.232781	−	0.232781i
$218$	−1.33604e7			−1.28958
$219$	5.68369e6			0.541125
$220$	300889.	−	300889.i	0.0282578	−	0.0282578i
$221$			1.83803e7i			1.70285i
$222$	1.74659e6	+	2.01272e6i	0.159636	+	0.183960i
$223$	−5.81722e6			−0.524567			−0.262284	−	0.964991i	$-0.584476\pi$
$223$	−5.81722e6			−0.524567			−0.262284	+	0.964991i	$0.584476\pi$
$224$	−438142.	−	438142.i	−0.0389826	−	0.0389826i
$225$			9.91684e6i			0.870614i
$226$		−	2.26940e6i		−	0.196601i
$227$	−1.32041e7	+	1.32041e7i	−1.12884	+	1.12884i	−0.138470	+	0.990367i	$0.544218\pi$
$227$	−1.32041e7	+	1.32041e7i	−1.12884	+	1.12884i	−0.990367	+	0.138470i	$0.955782\pi$
$228$	1.24244e6	−	1.24244e6i	0.104826	−	0.104826i
$229$	1.01986e7			0.849244			0.424622	−	0.905371i	$-0.360407\pi$
$229$	1.01986e7			0.849244			0.424622	+	0.905371i	$0.360407\pi$
$230$	922454.	−	922454.i	0.0758161	−	0.0758161i
$231$	−958899.			−0.0777923
$232$	2.00480e6			0.160549
$233$			134218.i			0.0106107i	0.999986	+	0.00530534i	$0.00168875\pi$
$233$			134218.i			0.0106107i	−0.999986	+	0.00530534i	$0.998311\pi$
$234$	1.30653e7			1.01970
$235$	−1.74088e6	+	1.74088e6i	−0.134142	+	0.134142i
$236$	8.25327e6	+	8.25327e6i	0.627900	+	0.627900i
$237$	−3.17820e6	−	3.17820e6i	−0.238746	−	0.238746i
$238$	3.09395e6			0.229500
$239$	−1.42340e7	+	1.42340e7i	−1.04264	+	1.04264i	−0.0435876	+	0.999050i	$0.513879\pi$
$239$	−1.42340e7	+	1.42340e7i	−1.04264	+	1.04264i	−0.999050	+	0.0435876i	$0.986121\pi$
$240$	−92903.8	−	92903.8i	−0.00672047	−	0.00672047i
$241$	−1.24547e7	+	1.24547e7i	−0.889781	+	0.889781i	−0.994502	−	0.104721i	$-0.966605\pi$
$241$	−1.24547e7	+	1.24547e7i	−0.889781	+	0.889781i	0.104721	+	0.994502i	$0.466605\pi$
$242$	−3.37003e6	−	3.37003e6i	−0.237787	−	0.237787i
$243$			1.25515e7i			0.874739i
$244$	3.07437e6	−	3.07437e6i	0.211634	−	0.211634i
$245$	−1.03607e6	+	1.03607e6i	−0.0704514	+	0.0704514i
$246$	4.45720e6	+	4.45720e6i	0.299404	+	0.299404i
$247$		−	2.12232e7i		−	1.40838i
$248$	5.69262e6			0.373213
$249$			5.15862e6i			0.334145i
$250$		−	2.42394e6i		−	0.155132i
$251$	8.72357e6	+	8.72357e6i	0.551662	+	0.551662i	0.926920	−	0.375258i	$-0.122446\pi$
$251$	8.72357e6	+	8.72357e6i	0.551662	+	0.551662i	−0.375258	+	0.926920i	$0.622446\pi$
$252$		−	2.19928e6i		−	0.137429i
$253$	1.13930e7	+	1.13930e7i	0.703523	+	0.703523i
$254$	−8.78775e6	−	8.78775e6i	−0.536262	−	0.536262i
$255$	656043.			0.0395651
$256$	1.04858e6			0.0625000
$257$	1.08179e7	−	1.08179e7i	0.637298	−	0.637298i	−0.312590	−	0.949888i	$-0.601197\pi$
$257$	1.08179e7	−	1.08179e7i	0.637298	−	0.637298i	0.949888	+	0.312590i	$0.101197\pi$
$258$		−	3.07604e6i		−	0.179115i
$259$	382618.	−	5.40473e6i	0.0220224	−	0.311082i
$260$	−1.58697e6			−0.0902920
$261$	5.03161e6	+	5.03161e6i	0.283000	+	0.283000i
$262$			1.19672e7i			0.665412i
$263$		−	1.31544e7i		−	0.723108i	−0.932351	−	0.361554i	$-0.882246\pi$
$263$		−	1.31544e7i		−	0.723108i	0.932351	−	0.361554i	$-0.117754\pi$
$264$	1.14744e6	−	1.14744e6i	0.0623615	−	0.0623615i
$265$	−851164.	+	851164.i	−0.0457379	+	0.0457379i
$266$	−3.57249e6			−0.189813
$267$	−5.77016e6	+	5.77016e6i	−0.303148	+	0.303148i
$268$	−8.57886e6			−0.445682
$269$	1.16102e7			0.596462			0.298231	−	0.954494i	$-0.403603\pi$
$269$	1.16102e7			0.596462			0.298231	+	0.954494i	$0.403603\pi$
$270$		−	995453.i		−	0.0505742i
$271$	−6.85044e6			−0.344200			−0.172100	−	0.985079i	$-0.555055\pi$
$271$	−6.85044e6			−0.344200			−0.172100	+	0.985079i	$0.555055\pi$
$272$	−3.70228e6	+	3.70228e6i	−0.183976	+	0.183976i
$273$	2.52875e6	+	2.52875e6i	0.124285	+	0.124285i
$274$	−5.24895e6	−	5.24895e6i	−0.255165	−	0.255165i
$275$	1.48771e7			0.715352
$276$	3.51777e6	−	3.51777e6i	0.167317	−	0.167317i
$277$	273619.	+	273619.i	0.0128738	+	0.0128738i	0.713514	−	0.700641i	$-0.247102\pi$
$277$	273619.	+	273619.i	0.0128738	+	0.0128738i	−0.700641	+	0.713514i	$0.747102\pi$
$278$	1.61884e6	−	1.61884e6i	0.0753475	−	0.0753475i
$279$	1.42872e7	+	1.42872e7i	0.657863	+	0.657863i
$280$			267135.i			0.0121690i
$281$	−1.60747e6	+	1.60747e6i	−0.0724477	+	0.0724477i	−0.742402	−	0.669954i	$-0.766314\pi$
$281$	−1.60747e6	+	1.60747e6i	−0.0724477	+	0.0724477i	0.669954	+	0.742402i	$0.266314\pi$
$282$	−6.63880e6	+	6.63880e6i	−0.296035	+	0.296035i
$283$	−2.91515e7	−	2.91515e7i	−1.28618	−	1.28618i	−0.937090	−	0.349088i	$-0.886492\pi$
$283$	−2.91515e7	−	2.91515e7i	−1.28618	−	1.28618i	−0.349088	−	0.937090i	$-0.613508\pi$
$284$		−	5.32382e6i		−	0.232417i
$285$	−757513.			−0.0327232
$286$		−	1.96004e7i		−	0.837850i
$287$		−	1.28162e7i		−	0.542142i
$288$	2.63170e6	+	2.63170e6i	0.110169	+	0.110169i
$289$		−	2.00620e6i		−	0.0831151i
$290$	−611163.	−	611163.i	−0.0250590	−	0.0250590i
$291$	−1.02597e7	−	1.02597e7i	−0.416348	−	0.416348i
$292$	1.95561e7			0.785478
$293$	−2.60299e7			−1.03483			−0.517415	−	0.855734i	$-0.673106\pi$
$293$	−2.60299e7			−1.03483			−0.517415	+	0.855734i	$0.673106\pi$
$294$	−3.95103e6	+	3.95103e6i	−0.155478	+	0.155478i
$295$		−	5.03201e6i		−	0.196009i
$296$	6.00955e6	+	6.92525e6i	0.231722	+	0.267030i
$297$	1.22946e7			0.469295
$298$	960593.	+	960593.i	0.0362987	+	0.0362987i
$299$		−	6.00901e7i		−	2.24796i
$300$		−	4.59352e6i		−	0.170130i
$301$	−4.42241e6	+	4.42241e6i	−0.162166	+	0.162166i
$302$	−6.00476e6	+	6.00476e6i	−0.218009	+	0.218009i
$303$	−1.13736e7			−0.408855
$304$	4.27491e6	−	4.27491e6i	0.152162	−	0.152162i
$305$	−1.87444e6			−0.0660650
$306$	−1.85838e7			−0.648591
$307$		−	1.52679e7i		−	0.527671i	−0.964568	−	0.263836i	$-0.915012\pi$
$307$		−	1.52679e7i		−	0.527671i	0.964568	−	0.263836i	$-0.0849876\pi$
$308$	−3.29932e6			−0.112921
$309$	1.02757e7	−	1.02757e7i	0.348286	−	0.348286i
$310$	−1.73539e6	−	1.73539e6i	−0.0582523	−	0.0582523i
$311$	−1.46093e7	−	1.46093e7i	−0.485679	−	0.485679i	0.421260	−	0.906940i	$-0.361588\pi$
$311$	−1.46093e7	−	1.46093e7i	−0.485679	−	0.485679i	−0.906940	+	0.421260i	$0.861588\pi$
$312$	−6.05190e6			−0.199263
$313$	2.99603e7	−	2.99603e7i	0.977041	−	0.977041i	−0.0227018	−	0.999742i	$-0.507227\pi$
$313$	2.99603e7	−	2.99603e7i	0.977041	−	0.977041i	0.999742	+	0.0227018i	$0.00722682\pi$
$314$	−4.25773e6	−	4.25773e6i	−0.137528	−	0.137528i
$315$	−670449.	+	670449.i	−0.0214503	+	0.0214503i
$316$	−1.09354e7	−	1.09354e7i	−0.346555	−	0.346555i
$317$			1.20311e7i			0.377684i	0.982007	+	0.188842i	$0.0604734\pi$
$317$			1.20311e7i			0.377684i	−0.982007	+	0.188842i	$0.939527\pi$
$318$	−3.24590e6	+	3.24590e6i	−0.100938	+	0.100938i
$319$	7.54835e6	−	7.54835e6i	0.232531	−	0.232531i
$320$	−319658.	−	319658.i	−0.00975519	−	0.00975519i
$321$			7.01880e6i			0.212201i
$322$	−1.01149e7			−0.302967
$323$			3.01874e7i			0.895815i
$324$			1.11922e7i			0.329064i
$325$	−3.92330e7	−	3.92330e7i	−1.14288	−	1.14288i
$326$			1.36521e7i			0.394045i
$327$	1.55320e7	+	1.55320e7i	0.444204	+	0.444204i
$328$	1.53361e7	+	1.53361e7i	0.434603	+	0.434603i
$329$	1.90891e7			0.536042
$330$	−699591.			−0.0194671
$331$	2.61176e7	−	2.61176e7i	0.720194	−	0.720194i	−0.248451	−	0.968644i	$-0.579921\pi$
$331$	2.61176e7	−	2.61176e7i	0.720194	−	0.720194i	0.968644	+	0.248451i	$0.0799215\pi$
$332$			1.77495e7i			0.485033i
$333$	−2.29819e6	+	3.24635e7i	−0.0622377	+	0.879150i
$334$	−1.12713e7			−0.302506
$335$	2.61526e6	+	2.61526e6i	0.0695634	+	0.0695634i
$336$			1.01871e6i			0.0268556i
$337$			5.97595e6i			0.156141i	0.996948	+	0.0780705i	$0.0248759\pi$
$337$			5.97595e6i			0.156141i	−0.996948	+	0.0780705i	$0.975124\pi$
$338$	−3.23817e7	+	3.23817e7i	−0.838589	+	0.838589i
$339$	−2.63827e6	+	2.63827e6i	−0.0677204	+	0.0677204i
$340$	2.25728e6			0.0574312
$341$	2.14335e7	−	2.14335e7i	0.540542	−	0.540542i
$342$	2.14582e7			0.536432
$343$	2.39454e7			0.593390
$344$		−	1.05839e7i		−	0.259997i
$345$	−2.14478e6			−0.0522306
$346$	3.35225e7	−	3.35225e7i	0.809297	−	0.809297i
$347$	2.20121e7	+	2.20121e7i	0.526833	+	0.526833i	0.919627	−	0.392794i	$-0.128491\pi$
$347$	2.20121e7	+	2.20121e7i	0.526833	+	0.526833i	−0.392794	+	0.919627i	$0.628491\pi$
$348$	−2.33066e6	−	2.33066e6i	−0.0553021	−	0.0553021i
$349$	8.16126e7			1.91991			0.959956	−	0.280152i	$-0.0903849\pi$
$349$	8.16126e7			1.91991			0.959956	+	0.280152i	$0.0903849\pi$
$350$	−6.60407e6	+	6.60407e6i	−0.154031	+	0.154031i
$351$	−3.24227e7	−	3.24227e7i	−0.749769	−	0.749769i
$352$	3.94803e6	−	3.94803e6i	0.0905217	−	0.0905217i
$353$	−4.55047e6	−	4.55047e6i	−0.103450	−	0.103450i	0.653487	−	0.756938i	$-0.273305\pi$
$353$	−4.55047e6	−	4.55047e6i	−0.103450	−	0.103450i	−0.756938	+	0.653487i	$0.773305\pi$
$354$		−	1.91895e7i		−	0.432568i
$355$	−1.62297e6	+	1.62297e6i	−0.0362764	+	0.0362764i
$356$	−1.98536e7	+	1.98536e7i	−0.440038	+	0.440038i
$357$	−3.59684e6	−	3.59684e6i	−0.0790527	−	0.0790527i
$358$			6.31104e7i			1.37547i
$359$	−1.83455e7			−0.396503			−0.198252	−	0.980151i	$-0.563526\pi$
$359$	−1.83455e7			−0.396503			−0.198252	+	0.980151i	$0.563526\pi$
$360$		−	1.60454e6i		−	0.0343909i
$361$			1.21894e7i			0.259096i
$362$	−1.25240e7	−	1.25240e7i	−0.264009	−	0.264009i
$363$			7.83558e6i			0.163814i
$364$	8.70078e6	+	8.70078e6i	0.180407	+	0.180407i
$365$	−5.96167e6	−	5.96167e6i	−0.122600	−	0.122600i
$366$	−7.14814e6			−0.145797
$367$	−1.10723e7			−0.223995			−0.111998	−	0.993708i	$-0.535725\pi$
$367$	−1.10723e7			−0.223995			−0.111998	+	0.993708i	$0.535725\pi$
$368$	1.21037e7	−	1.21037e7i	0.242871	−	0.242871i
$369$			7.69804e7i			1.53215i
$370$	279149.	−	3.94317e6i	0.00551101	−	0.0778467i
$371$	9.33323e6			0.182772
$372$	−6.61790e6	−	6.61790e6i	−0.128556	−	0.128556i
$373$			3.15566e7i			0.608083i	0.952659	+	0.304042i	$0.0983362\pi$
$373$			3.15566e7i			0.608083i	−0.952659	+	0.304042i	$0.901664\pi$
$374$			2.78792e7i			0.532923i
$375$	−2.81793e6	+	2.81793e6i	−0.0534363	+	0.0534363i
$376$	−2.28424e7	+	2.28424e7i	−0.429713	+	0.429713i
$377$	−3.98121e7			−0.743004
$378$	−5.45770e6	+	5.45770e6i	−0.101049	+	0.101049i
$379$	4.83104e7			0.887407			0.443703	−	0.896174i	$-0.353664\pi$
$379$	4.83104e7			0.887407			0.443703	+	0.896174i	$0.353664\pi$
$380$	−2.60641e6			−0.0474998
$381$			2.04322e7i			0.369437i
$382$	−2.30997e7			−0.414397
$383$	−9.25009e6	+	9.25009e6i	−0.164645	+	0.164645i	−0.784621	−	0.619976i	$-0.787142\pi$
$383$	−9.25009e6	+	9.25009e6i	−0.164645	+	0.164645i	0.619976	+	0.784621i	$0.287142\pi$
$384$	−1.21901e6	−	1.21901e6i	−0.0215285	−	0.0215285i
$385$	1.00580e6	+	1.00580e6i	0.0176250	+	0.0176250i
$386$	5.11765e7			0.889833
$387$	2.65632e7	−	2.65632e7i	0.458297	−	0.458297i
$388$	−3.53011e7	−	3.53011e7i	−0.604356	−	0.604356i
$389$	8.76492e6	−	8.76492e6i	0.148901	−	0.148901i	−0.628726	−	0.777627i	$-0.716423\pi$
$389$	8.76492e6	−	8.76492e6i	0.148901	−	0.148901i	0.777627	+	0.628726i	$0.216423\pi$
$390$	1.84492e6	+	1.84492e6i	0.0311016	+	0.0311016i
$391$			8.54709e7i			1.42984i
$392$	−1.35945e7	+	1.35945e7i	−0.225686	+	0.225686i
$393$	1.39124e7	−	1.39124e7i	0.229205	−	0.229205i
$394$	−2.69399e7	−	2.69399e7i	−0.440461	−	0.440461i
$395$			6.66729e6i			0.108183i
$396$	1.98174e7			0.319125
$397$		−	7.21623e6i		−	0.115329i	−0.998336	−	0.0576646i	$-0.981635\pi$
$397$		−	7.21623e6i		−	0.115329i	0.998336	−	0.0576646i	$-0.0183654\pi$
$398$			5.83697e7i			0.925844i
$399$	4.15316e6	+	4.15316e6i	0.0653823	+	0.0653823i
$400$		−	1.58051e7i		−	0.246955i
$401$	−3.99795e7	−	3.99795e7i	−0.620018	−	0.620018i	0.325518	−	0.945536i	$-0.394461\pi$
$401$	−3.99795e7	−	3.99795e7i	−0.620018	−	0.620018i	−0.945536	+	0.325518i	$0.894461\pi$
$402$	9.97326e6	+	9.97326e6i	0.153518	+	0.153518i
$403$	−1.13046e8			−1.72719
$404$	−3.91336e7			−0.593479
$405$	3.41194e6	−	3.41194e6i	0.0513613	−	0.0513613i
$406$			6.70156e6i			0.100138i
$407$	4.87013e7	+	3.44771e6i	0.722365	+	0.0511385i
$408$	8.60809e6			0.126744
$409$	−3.57762e7	−	3.57762e7i	−0.522906	−	0.522906i	0.395542	−	0.918448i	$-0.370557\pi$
$409$	−3.57762e7	−	3.57762e7i	−0.522906	−	0.522906i	−0.918448	+	0.395542i	$0.870557\pi$
$410$		−	9.35040e6i		−	0.135668i
$411$			1.22042e7i			0.175786i
$412$	3.53560e7	−	3.53560e7i	0.505559	−	0.505559i
$413$	−2.75887e7	+	2.75887e7i	−0.391634	+	0.391634i
$414$	6.07554e7			0.856217
$415$	5.41092e6	−	5.41092e6i	0.0757054	−	0.0757054i
$416$	−2.08230e7			−0.289244
$417$	−3.76392e6			−0.0519078
$418$		−	3.21912e7i		−	0.440766i
$419$	−5.50911e6			−0.0748926			−0.0374463	−	0.999299i	$-0.511922\pi$
$419$	−5.50911e6			−0.0748926			−0.0374463	+	0.999299i	$0.511922\pi$
$420$	310555.	−	310555.i	0.00419170	−	0.00419170i
$421$	2.04887e7	+	2.04887e7i	0.274579	+	0.274579i	0.830940	−	0.556362i	$-0.187803\pi$
$421$	2.04887e7	+	2.04887e7i	0.274579	+	0.274579i	−0.556362	+	0.830940i	$0.687803\pi$
$422$	−3.41166e7	−	3.41166e7i	−0.453971	−	0.453971i
$423$	−1.14659e8			−1.51491
$424$	−1.11683e7	+	1.11683e7i	−0.146518	+	0.146518i
$425$	5.58041e7	+	5.58041e7i	0.726942	+	0.726942i
$426$	−6.18916e6	+	6.18916e6i	−0.0800576	+	0.0800576i
$427$	1.02768e7	+	1.02768e7i	0.132001	+	0.132001i
$428$			2.41499e7i			0.308023i
$429$	−2.27862e7	+	2.27862e7i	−0.288603	+	0.288603i
$430$	−3.22649e6	+	3.22649e6i	−0.0405812	+	0.0405812i
$431$	7.97159e7	+	7.97159e7i	0.995665	+	0.995665i	0.999991	−	0.00432610i	$-0.00137704\pi$
$431$	7.97159e7	+	7.97159e7i	0.995665	+	0.995665i	−0.00432610	+	0.999991i	$0.501377\pi$
$432$		−	1.30616e7i		−	0.162011i
$433$	−4.67243e7			−0.575545			−0.287772	−	0.957699i	$-0.592915\pi$
$433$	−4.67243e7			−0.575545			−0.287772	+	0.957699i	$0.592915\pi$
$434$			1.90290e7i			0.232781i
$435$			1.42100e6i			0.0172634i
$436$	5.34414e7	+	5.34414e7i	0.644791	+	0.644791i
$437$		−	9.86906e7i		−	1.18258i
$438$	−2.27348e7	−	2.27348e7i	−0.270563	−	0.270563i
$439$	−4.70215e6	−	4.70215e6i	−0.0555780	−	0.0555780i	0.678772	−	0.734350i	$-0.262513\pi$
$439$	−4.70215e6	−	4.70215e6i	−0.0555780	−	0.0555780i	−0.734350	+	0.678772i	$0.762513\pi$
$440$	−2.40711e6			−0.0282578
$441$	−6.82383e7			−0.795632
$442$	7.35212e7	−	7.35212e7i	0.851424	−	0.851424i
$443$		−	5.83857e7i		−	0.671576i	−0.941938	−	0.335788i	$-0.890997\pi$
$443$		−	5.83857e7i		−	0.671576i	0.941938	−	0.335788i	$-0.109003\pi$
$444$	1.06453e6	−	1.50372e7i	0.0121621	−	0.171798i
$445$	1.21047e7			0.137365
$446$	2.32689e7	+	2.32689e7i	0.262284	+	0.262284i
$447$		−	2.23346e6i		−	0.0250066i
$448$			3.50513e6i			0.0389826i
$449$	1.16979e8	−	1.16979e8i	1.29231	−	1.29231i	0.358961	−	0.933353i	$-0.383131\pi$
$449$	1.16979e8	−	1.16979e8i	1.29231	−	1.29231i	0.933353	−	0.358961i	$-0.116869\pi$
$450$	3.96674e7	−	3.96674e7i	0.435307	−	0.435307i
$451$	1.15485e8			1.25891
$452$	−9.07760e6	+	9.07760e6i	−0.0983005	+	0.0983005i
$453$	1.39616e7			0.150189
$454$	1.05633e8			1.12884
$455$		−	5.30486e6i		−	0.0563170i
$456$	−9.93950e6			−0.104826
$457$	−6.95800e7	+	6.95800e7i	−0.729013	+	0.729013i	−0.970423	−	0.241410i	$-0.922390\pi$
$457$	−6.95800e7	+	6.95800e7i	−0.729013	+	0.729013i	0.241410	+	0.970423i	$0.422390\pi$
$458$	−4.07943e7	−	4.07943e7i	−0.424622	−	0.424622i
$459$	4.61173e7	+	4.61173e7i	0.476898	+	0.476898i
$460$	−7.37963e6			−0.0758161
$461$	7.07242e6	−	7.07242e6i	0.0721881	−	0.0721881i	−0.670091	−	0.742279i	$-0.733745\pi$
$461$	7.07242e6	−	7.07242e6i	0.0721881	−	0.0721881i	0.742279	+	0.670091i	$0.233745\pi$
$462$	3.83560e6	+	3.83560e6i	0.0388962	+	0.0388962i
$463$	−1.12799e8	+	1.12799e8i	−1.13648	+	1.13648i	−0.147401	+	0.989077i	$0.547091\pi$
$463$	−1.12799e8	+	1.12799e8i	−1.13648	+	1.13648i	−0.989077	+	0.147401i	$0.952909\pi$
$464$	−8.01921e6	−	8.01921e6i	−0.0802745	−	0.0802745i
$465$			4.03493e6i			0.0401307i
$466$	536872.	−	536872.i	0.00530534	−	0.00530534i
$467$	−5.69125e7	+	5.69125e7i	−0.558801	+	0.558801i	−0.928966	−	0.370165i	$-0.879301\pi$
$467$	−5.69125e7	+	5.69125e7i	−0.558801	+	0.558801i	0.370165	+	0.928966i	$0.379301\pi$
$468$	−5.22612e7	−	5.22612e7i	−0.509850	−	0.509850i
$469$		−	2.86770e7i		−	0.277981i
$470$	1.39270e7			0.134142
$471$			9.89957e6i			0.0947444i
$472$		−	6.60262e7i		−	0.627900i
$473$	−3.98497e7	−	3.98497e7i	−0.376566	−	0.376566i
$474$			2.54256e7i			0.238746i
$475$	−6.44354e7	−	6.44354e7i	−0.601234	−	0.601234i
$476$	−1.23758e7	−	1.23758e7i	−0.114750	−	0.114750i
$477$	−5.60601e7			−0.516533
$478$	1.13872e8			1.04264
$479$	5.39455e7	−	5.39455e7i	0.490850	−	0.490850i	−0.417724	−	0.908574i	$-0.637172\pi$
$479$	5.39455e7	−	5.39455e7i	0.490850	−	0.490850i	0.908574	+	0.417724i	$0.137172\pi$
$480$			743230.i			0.00672047i
$481$	−1.19340e8	−	1.37524e8i	−1.07238	−	1.23579i
$482$	9.96378e7			0.889781
$483$	1.17590e7	+	1.17590e7i	0.104359	+	0.104359i
$484$			2.69602e7i			0.237787i
$485$			2.15230e7i			0.188659i
$486$	5.02062e7	−	5.02062e7i	0.437369	−	0.437369i
$487$	2.21201e6	−	2.21201e6i	0.0191514	−	0.0191514i	−0.697466	−	0.716618i	$-0.745689\pi$
$487$	2.21201e6	−	2.21201e6i	0.0191514	−	0.0191514i	0.716618	+	0.697466i	$0.245689\pi$
$488$	−2.45949e7			−0.211634
$489$	1.58711e7	−	1.58711e7i	0.135731	−	0.135731i
$490$	8.28854e6			0.0704514
$491$	2.16548e8			1.82940			0.914701	−	0.404130i	$-0.132426\pi$
$491$	2.16548e8			1.82940			0.914701	+	0.404130i	$0.132426\pi$
$492$		−	3.56576e7i		−	0.299404i
$493$	5.66279e7			0.472596
$494$	−8.48927e7	+	8.48927e7i	−0.704190	+	0.704190i
$495$	−6.04132e6	−	6.04132e6i	−0.0498100	−	0.0498100i
$496$	−2.27705e7	−	2.27705e7i	−0.186607	−	0.186607i
$497$	1.77962e7			0.144964
$498$	2.06345e7	−	2.06345e7i	0.167073	−	0.167073i
$499$	−1.45712e8	−	1.45712e8i	−1.17272	−	1.17272i	−0.981560	−	0.191155i	$-0.938777\pi$
$499$	−1.45712e8	−	1.45712e8i	−1.17272	−	1.17272i	−0.191155	−	0.981560i	$-0.561223\pi$
$500$	−9.69578e6	+	9.69578e6i	−0.0775662	+	0.0775662i
$501$	1.31033e7	+	1.31033e7i	0.104200	+	0.104200i
$502$		−	6.97886e7i		−	0.551662i
$503$	−5.78721e7	+	5.78721e7i	−0.454742	+	0.454742i	−0.896925	−	0.442183i	$-0.854204\pi$
$503$	−5.78721e7	+	5.78721e7i	−0.454742	+	0.454742i	0.442183	+	0.896925i	$0.354204\pi$
$504$	−8.79712e6	+	8.79712e6i	−0.0687146	+	0.0687146i
$505$	1.19299e7	+	1.19299e7i	0.0926320	+	0.0926320i
$506$		−	9.11443e7i		−	0.703523i
$507$	7.52900e7			0.577715
$508$			7.03020e7i			0.536262i
$509$			5.26832e7i			0.399502i	0.979847	+	0.199751i	$0.0640133\pi$
$509$			5.26832e7i			0.399502i	−0.979847	+	0.199751i	$0.935987\pi$
$510$	−2.62417e6	−	2.62417e6i	−0.0197825	−	0.0197825i
$511$			6.53713e7i			0.489919i
$512$	−4.19430e6	−	4.19430e6i	−0.0312500	−	0.0312500i
$513$	−5.32503e7	−	5.32503e7i	−0.394430	−	0.394430i
$514$	−8.65430e7			−0.637298
$515$	−2.15565e7			−0.157818
$516$	−1.23042e7	+	1.23042e7i	−0.0895577	+	0.0895577i
$517$			1.72010e8i			1.24475i
$518$	−2.31494e7	+	2.00885e7i	−0.166552	+	0.144530i
$519$	−7.79425e7			−0.557535
$520$	6.34789e6	+	6.34789e6i	0.0451460	+	0.0451460i
$521$		−	3.74730e6i		−	0.0264975i	−0.999912	−	0.0132487i	$-0.995783\pi$
$521$		−	3.74730e6i		−	0.0264975i	0.999912	−	0.0132487i	$-0.00421733\pi$
$522$		−	4.02529e7i		−	0.283000i
$523$	−9.64173e7	+	9.64173e7i	−0.673984	+	0.673984i	−0.958632	−	0.284648i	$-0.908123\pi$
$523$	−9.64173e7	+	9.64173e7i	−0.673984	+	0.673984i	0.284648	+	0.958632i	$0.408123\pi$
$524$	4.78690e7	−	4.78690e7i	0.332706	−	0.332706i
$525$	1.53550e7			0.106114
$526$	−5.26175e7	+	5.26175e7i	−0.361554	+	0.361554i
$527$	1.60795e8			1.09860
$528$	−9.17948e6			−0.0623615
$529$		−	1.31391e8i		−	0.887562i
$530$	6.80931e6			0.0457379
$531$	1.65711e8	−	1.65711e8i	1.10680	−	1.10680i
$532$	1.42900e7	+	1.42900e7i	0.0949066	+	0.0949066i
$533$	−3.04550e8	−	3.04550e8i	−2.01130	−	2.01130i
$534$	4.61613e7			0.303148
$535$	7.36208e6	−	7.36208e6i	0.0480772	−	0.0480772i
$536$	3.43154e7	+	3.43154e7i	0.222841	+	0.222841i
$537$	7.33683e7	−	7.33683e7i	0.473790	−	0.473790i
$538$	−4.64408e7	−	4.64408e7i	−0.298231	−	0.298231i
$539$			1.02370e8i			0.653742i
$540$	−3.98181e6	+	3.98181e6i	−0.0252871	+	0.0252871i
$541$	−7.73404e7	+	7.73404e7i	−0.488444	+	0.488444i	−0.907815	−	0.419371i	$-0.862251\pi$
$541$	−7.73404e7	+	7.73404e7i	−0.488444	+	0.488444i	0.419371	+	0.907815i	$0.362251\pi$
$542$	2.74018e7	+	2.74018e7i	0.172100	+	0.172100i
$543$			2.91194e7i			0.181879i
$544$	2.96182e7			0.183976
$545$		−	3.25832e7i		−	0.201282i
$546$		−	2.02300e7i		−	0.124285i
$547$	2.28266e8	+	2.28266e8i	1.39470	+	1.39470i	0.814421	+	0.580275i	$0.197055\pi$
$547$	2.28266e8	+	2.28266e8i	1.39470	+	1.39470i	0.580275	+	0.814421i	$0.302945\pi$
$548$			4.19916e7i			0.255165i
$549$	−6.17279e7	−	6.17279e7i	−0.373048	−	0.373048i
$550$	−5.95084e7	−	5.95084e7i	−0.357676	−	0.357676i
$551$	−6.53865e7			−0.390871
$552$	−2.81421e7			−0.167317
$553$	3.65543e7	−	3.65543e7i	0.216154	−	0.216154i
$554$		−	2.18895e6i		−	0.0128738i
$555$	−4.90861e6	+	4.25957e6i	−0.0287131	+	0.0249165i
$556$	−1.29507e7			−0.0753475
$557$	4.19107e6	+	4.19107e6i	0.0242526	+	0.0242526i	0.719129	−	0.694876i	$-0.244541\pi$
$557$	4.19107e6	+	4.19107e6i	0.0242526	+	0.0242526i	−0.694876	+	0.719129i	$0.744541\pi$
$558$		−	1.14298e8i		−	0.657863i
$559$			2.10178e8i			1.20324i
$560$	1.06854e6	−	1.06854e6i	0.00608452	−	0.00608452i
$561$	3.24106e7	−	3.24106e7i	0.183569	−	0.183569i
$562$	1.28598e7			0.0724477
$563$	−8.16655e7	+	8.16655e7i	−0.457629	+	0.457629i	−0.897876	−	0.440248i	$-0.854891\pi$
$563$	−8.16655e7	+	8.16655e7i	−0.457629	+	0.457629i	0.440248	+	0.897876i	$0.354891\pi$
$564$	5.31104e7			0.296035
$565$	5.53461e6			0.0306861
$566$			2.33212e8i			1.28618i
$567$	−3.74127e7			−0.205244
$568$	−2.12953e7	+	2.12953e7i	−0.116209	+	0.116209i
$569$	2.11693e8	+	2.11693e8i	1.14913	+	1.14913i	0.986724	+	0.162409i	$0.0519263\pi$
$569$	2.11693e8	+	2.11693e8i	1.14913	+	1.14913i	0.162409	+	0.986724i	$0.448074\pi$
$570$	3.03005e6	+	3.03005e6i	0.0163616	+	0.0163616i
$571$	1.70353e8			0.915041			0.457521	−	0.889199i	$-0.348738\pi$
$571$	1.70353e8			0.915041			0.457521	+	0.889199i	$0.348738\pi$
$572$	−7.84015e7	+	7.84015e7i	−0.418925	+	0.418925i
$573$	2.68543e7	+	2.68543e7i	0.142742	+	0.142742i
$574$	−5.12648e7	+	5.12648e7i	−0.271071	+	0.271071i
$575$	−1.82439e8	−	1.82439e8i	−0.959650	−	0.959650i
$576$		−	2.10536e7i		−	0.110169i
$577$	−2.52863e8	+	2.52863e8i	−1.31631	+	1.31631i	−0.399634	+	0.916675i	$0.630863\pi$
$577$	−2.52863e8	+	2.52863e8i	−1.31631	+	1.31631i	−0.916675	+	0.399634i	$0.869137\pi$
$578$	−8.02479e6	+	8.02479e6i	−0.0415576	+	0.0415576i
$579$	−5.94947e7	−	5.94947e7i	−0.306508	−	0.306508i
$580$			4.88930e6i			0.0250590i
$581$	−5.93321e7			−0.302525
$582$			8.20778e7i			0.416348i
$583$			8.41004e7i			0.424417i
$584$	−7.82244e7	−	7.82244e7i	−0.392739	−	0.392739i
$585$			3.18636e7i			0.159158i
$586$	1.04120e8	+	1.04120e8i	0.517415	+	0.517415i
$587$	−4.01713e7	−	4.01713e7i	−0.198610	−	0.198610i	0.600794	−	0.799404i	$-0.294851\pi$
$587$	−4.01713e7	−	4.01713e7i	−0.198610	−	0.198610i	−0.799404	+	0.600794i	$0.794851\pi$
$588$	3.16082e7			0.155478
$589$	−1.85665e8			−0.908622
$590$	−2.01281e7	+	2.01281e7i	−0.0980045	+	0.0980045i
$591$			6.26374e7i			0.303439i
$592$	3.66278e6	−	5.17392e7i	0.0176541	−	0.249376i
$593$	3.23718e8			1.55239			0.776197	−	0.630490i	$-0.217146\pi$
$593$	3.23718e8			1.55239			0.776197	+	0.630490i	$0.217146\pi$
$594$	−4.91785e7	−	4.91785e7i	−0.234648	−	0.234648i
$595$			7.54552e6i			0.0358211i
$596$		−	7.68474e6i		−	0.0362987i
$597$	6.78570e7	−	6.78570e7i	0.318913	−	0.318913i
$598$	−2.40360e8	+	2.40360e8i	−1.12398	+	1.12398i
$599$	3.67464e8			1.70976			0.854880	−	0.518827i	$-0.173631\pi$
$599$	3.67464e8			1.70976			0.854880	+	0.518827i	$0.173631\pi$
$600$	−1.83741e7	+	1.83741e7i	−0.0850651	+	0.0850651i
$601$	7.54154e7			0.347405			0.173703	−	0.984798i	$-0.444427\pi$
$601$	7.54154e7			0.347405			0.173703	+	0.984798i	$0.444427\pi$
$602$	3.53793e7			0.162166
$603$			1.72248e8i			0.785603i
$604$	4.80381e7			0.218009
$605$	8.21881e6	−	8.21881e6i	0.0371144	−	0.0371144i
$606$	4.54943e7	+	4.54943e7i	0.204428	+	0.204428i
$607$	7.02570e7	+	7.02570e7i	0.314140	+	0.314140i	0.846511	−	0.532371i	$-0.178699\pi$
$607$	7.02570e7	+	7.02570e7i	0.314140	+	0.314140i	−0.532371	+	0.846511i	$0.678699\pi$
$608$	−3.41993e7			−0.152162
$609$	7.79083e6	−	7.79083e6i	0.0344931	−	0.0344931i
$610$	7.49775e6	+	7.49775e6i	0.0330325	+	0.0330325i
$611$	4.53613e8	−	4.53613e8i	1.98867	−	1.98867i
$612$	7.43353e7	+	7.43353e7i	0.324295	+	0.324295i
$613$		−	1.00324e8i		−	0.435535i	−0.976001	−	0.217768i	$-0.930123\pi$
$613$		−	1.00324e8i		−	0.435535i	0.976001	−	0.217768i	$-0.0698775\pi$
$614$	−6.10715e7	+	6.10715e7i	−0.263836	+	0.263836i
$615$	−1.08702e7	+	1.08702e7i	−0.0467318	+	0.0467318i
$616$	1.31973e7	+	1.31973e7i	0.0564603	+	0.0564603i
$617$			9.83326e7i			0.418641i	0.977847	+	0.209321i	$0.0671253\pi$
$617$			9.83326e7i			0.418641i	−0.977847	+	0.209321i	$0.932875\pi$
$618$	−8.22055e7			−0.348286
$619$			5.68169e7i			0.239555i	0.992801	+	0.119778i	$0.0382182\pi$
$619$			5.68169e7i			0.239555i	−0.992801	+	0.119778i	$0.961782\pi$
$620$			1.38831e7i			0.0582523i
$621$	−1.50770e8	−	1.50770e8i	−0.629563	−	0.629563i
$622$			1.16875e8i			0.485679i
$623$	−6.63658e7	−	6.63658e7i	−0.274461	−	0.274461i
$624$	2.42076e7	+	2.42076e7i	0.0996317	+	0.0996317i
$625$	−2.35255e8			−0.963606
$626$	−2.39682e8			−0.977041
$627$	−3.74236e7	+	3.74236e7i	−0.151825	+	0.151825i
$628$			3.40619e7i			0.137528i
$629$	1.69747e8	+	1.95611e8i	0.682102	+	0.786036i
$630$	5.36360e6			0.0214503
$631$	2.79983e8	+	2.79983e8i	1.11441	+	1.11441i	0.992547	+	0.121859i	$0.0388855\pi$
$631$	2.79983e8	+	2.79983e8i	1.11441	+	1.11441i	0.121859	+	0.992547i	$0.461115\pi$
$632$			8.74830e7i			0.346555i
$633$			7.93238e7i			0.312746i
$634$	4.81245e7	−	4.81245e7i	0.188842	−	0.188842i
$635$	2.14316e7	−	2.14316e7i	0.0837013	−	0.0837013i
$636$	2.59672e7			0.100938
$637$	2.69964e8	−	2.69964e8i	1.04445	−	1.04445i
$638$	−6.03868e7			−0.232531
$639$	−1.06893e8			−0.409682
$640$			2.55726e6i			0.00975519i
$641$	−4.00606e8			−1.52105			−0.760526	−	0.649308i	$-0.775059\pi$
$641$	−4.00606e8			−1.52105			−0.760526	+	0.649308i	$0.775059\pi$
$642$	2.80752e7	−	2.80752e7i	0.106101	−	0.106101i
$643$	2.13267e8	+	2.13267e8i	0.802214	+	0.802214i	0.983441	−	0.181227i	$-0.0580070\pi$
$643$	2.13267e8	+	2.13267e8i	0.802214	+	0.802214i	−0.181227	+	0.983441i	$0.558007\pi$
$644$	4.04598e7	+	4.04598e7i	0.151484	+	0.151484i
$645$	7.50184e6			0.0279569
$646$	1.20750e8	−	1.20750e8i	0.447907	−	0.447907i
$647$	−1.49263e8	−	1.49263e8i	−0.551110	−	0.551110i	0.375651	−	0.926761i	$-0.377419\pi$
$647$	−1.49263e8	−	1.49263e8i	−0.551110	−	0.551110i	−0.926761	+	0.375651i	$0.877419\pi$
$648$	4.47688e7	−	4.47688e7i	0.164532	−	0.164532i
$649$	−2.48598e8	−	2.48598e8i	−0.909416	−	0.909416i
$650$			3.13864e8i			1.14288i
$651$	2.21220e7	−	2.21220e7i	0.0801829	−	0.0801829i
$652$	5.46083e7	−	5.46083e7i	0.197023	−	0.197023i
$653$	−1.08832e8	−	1.08832e8i	−0.390855	−	0.390855i	0.484137	−	0.874992i	$-0.339134\pi$
$653$	−1.08832e8	−	1.08832e8i	−0.390855	−	0.390855i	−0.874992	+	0.484137i	$0.839134\pi$
$654$		−	1.24256e8i		−	0.444204i
$655$	−2.91857e7			−0.103859
$656$		−	1.22689e8i		−	0.434603i
$657$		−	3.92652e8i		−	1.38456i
$658$	−7.63566e7	−	7.63566e7i	−0.268021	−	0.268021i
$659$		−	1.36163e7i		−	0.0475776i	−0.999717	−	0.0237888i	$-0.992427\pi$
$659$		−	1.36163e7i		−	0.0475776i	0.999717	−	0.0237888i	$-0.00757292\pi$
$660$	2.79836e6	+	2.79836e6i	0.00973357	+	0.00973357i
$661$	1.84283e8	+	1.84283e8i	0.638090	+	0.638090i	0.950084	−	0.311994i	$-0.100997\pi$
$661$	1.84283e8	+	1.84283e8i	0.638090	+	0.638090i	−0.311994	+	0.950084i	$0.600997\pi$
$662$	−2.08941e8			−0.720194
$663$	−1.70943e8			−0.586557
$664$	7.09979e7	−	7.09979e7i	0.242517	−	0.242517i
$665$		−	8.71258e6i		−	0.0296266i
$666$	1.39047e8	−	1.20661e8i	0.470694	−	0.408456i
$667$	−1.85132e8			−0.623883
$668$	4.50851e7	+	4.50851e7i	0.151253	+	0.151253i
$669$		−	5.41020e7i		−	0.180690i
$670$		−	2.09221e7i		−	0.0695634i
$671$	−9.26032e7	+	9.26032e7i	−0.306520	+	0.306520i
$672$	4.07486e6	−	4.07486e6i	0.0134278	−	0.0134278i
$673$	−4.52488e7			−0.148444			−0.0742218	−	0.997242i	$-0.523647\pi$
$673$	−4.52488e7			−0.148444			−0.0742218	+	0.997242i	$0.523647\pi$
$674$	2.39038e7	−	2.39038e7i	0.0780705	−	0.0780705i
$675$	−1.96876e8			−0.640149
$676$	2.59053e8			0.838589
$677$		−	2.57871e8i		−	0.831069i	−0.909577	−	0.415534i	$-0.863595\pi$
$677$		−	2.57871e8i		−	0.831069i	0.909577	−	0.415534i	$-0.136405\pi$
$678$	2.11061e7			0.0677204
$679$	1.18003e8	−	1.18003e8i	0.376949	−	0.376949i
$680$	−9.02911e6	−	9.02911e6i	−0.0287156	−	0.0287156i
$681$	−1.22802e8	−	1.22802e8i	−0.388835	−	0.388835i
$682$	−1.71468e8			−0.540542
$683$	2.94425e8	−	2.94425e8i	0.924085	−	0.924085i	−0.0732297	−	0.997315i	$-0.523331\pi$
$683$	2.94425e8	−	2.94425e8i	0.924085	−	0.924085i	0.997315	+	0.0732297i	$0.0233306\pi$
$684$	−8.58327e7	−	8.58327e7i	−0.268216	−	0.268216i
$685$	1.28011e7	−	1.28011e7i	0.0398269	−	0.0398269i
$686$	−9.57818e7	−	9.57818e7i	−0.296695	−	0.296695i
$687$			9.48499e7i			0.292527i
$688$	−4.23355e7	+	4.23355e7i	−0.129999	+	0.129999i
$689$	2.21785e8	−	2.21785e8i	0.678069	−	0.678069i
$690$	8.57912e6	+	8.57912e6i	0.0261153	+	0.0261153i
$691$		−	2.70264e8i		−	0.819133i	−0.912280	−	0.409566i	$-0.865680\pi$
$691$		−	2.70264e8i		−	0.819133i	0.912280	−	0.409566i	$-0.134320\pi$
$692$	−2.68180e8			−0.809297
$693$			6.62447e7i			0.199045i
$694$		−	1.76097e8i		−	0.526833i
$695$	3.94801e6	+	3.94801e6i	0.0117605	+	0.0117605i
$696$			1.86453e7i			0.0553021i
$697$	4.33185e8	+	4.33185e8i	1.27931	+	1.27931i
$698$	−3.26451e8	−	3.26451e8i	−0.959956	−	0.959956i
$699$	−1.24827e6			−0.00365492
$700$	5.28326e7			0.154031
$701$	4.19011e8	−	4.19011e8i	1.21638	−	1.21638i	0.247495	−	0.968889i	$-0.420392\pi$
$701$	4.19011e8	−	4.19011e8i	1.21638	−	1.21638i	0.968889	−	0.247495i	$-0.0796075\pi$
$702$			2.59381e8i			0.749769i
$703$	−1.96001e8	−	2.25867e8i	−0.564148	−	0.650109i
$704$	−3.15842e7			−0.0905217
$705$	−1.61907e7	−	1.61907e7i	−0.0462060	−	0.0462060i
$706$			3.64037e7i			0.103450i
$707$		−	1.30814e8i		−	0.370165i
$708$	−7.67581e7	+	7.67581e7i	−0.216284	+	0.216284i
$709$	−4.08944e8	+	4.08944e8i	−1.14743	+	1.14743i	−0.160371	+	0.987057i	$0.551269\pi$
$709$	−4.08944e8	+	4.08944e8i	−1.14743	+	1.14743i	−0.987057	+	0.160371i	$0.948731\pi$
$710$	1.29837e7			0.0362764
$711$	−2.19563e8	+	2.19563e8i	−0.610873	+	0.610873i
$712$	1.58829e8			0.440038
$713$	−5.25680e8			−1.45028
$714$			2.87747e7i			0.0790527i
$715$	4.78013e7			0.130774
$716$	2.52442e8	−	2.52442e8i	0.687736	−	0.687736i
$717$	−1.32381e8	−	1.32381e8i	−0.359143	−	0.359143i
$718$	7.33821e7	+	7.33821e7i	0.198252	+	0.198252i
$719$	3.86556e8			1.03998			0.519991	−	0.854172i	$-0.325935\pi$
$719$	3.86556e8			1.03998			0.519991	+	0.854172i	$0.325935\pi$
$720$	−6.41817e6	+	6.41817e6i	−0.0171955	+	0.0171955i
$721$	1.18186e8	+	1.18186e8i	0.315328	+	0.315328i
$722$	4.87576e7	−	4.87576e7i	0.129548	−	0.129548i
$723$	−1.15833e8	−	1.15833e8i	−0.306491	−	0.306491i
$724$			1.00192e8i			0.264009i
$725$	−1.20873e8	+	1.20873e8i	−0.317187	+	0.317187i
$726$	3.13423e7	−	3.13423e7i	0.0819071	−	0.0819071i
$727$	−2.95115e8	−	2.95115e8i	−0.768047	−	0.768047i	0.209715	−	0.977763i	$-0.432746\pi$
$727$	−2.95115e8	−	2.95115e8i	−0.768047	−	0.768047i	−0.977763	+	0.209715i	$0.932746\pi$
$728$		−	6.96062e7i		−	0.180407i
$729$	1.38239e8			0.356818
$730$			4.76934e7i			0.122600i
$731$		−	2.98953e8i		−	0.765335i
$732$	2.85926e7	+	2.85926e7i	0.0728987	+	0.0728987i
$733$			3.38927e8i			0.860587i	0.902689	+	0.430293i	$0.141590\pi$
$733$			3.38927e8i			0.860587i	−0.902689	+	0.430293i	$0.858410\pi$
$734$	4.42891e7	+	4.42891e7i	0.111998	+	0.111998i
$735$	−9.63576e6	−	9.63576e6i	−0.0242674	−	0.0242674i
$736$	−9.68298e7			−0.242871
$737$	2.58404e8			0.645502
$738$	3.07922e8	−	3.07922e8i	0.766075	−	0.766075i
$739$			1.89847e8i			0.470403i	0.971947	+	0.235202i	$0.0755751\pi$
$739$			1.89847e8i			0.470403i	−0.971947	+	0.235202i	$0.924425\pi$
$740$	−1.68893e7	+	1.46561e7i	−0.0416788	+	0.0361678i
$741$	1.97382e8			0.485125
$742$	−3.73329e7	−	3.73329e7i	−0.0913862	−	0.0913862i
$743$		−	4.66125e8i		−	1.13641i	−0.822886	−	0.568207i	$-0.807637\pi$
$743$		−	4.66125e8i		−	1.13641i	0.822886	−	0.568207i	$-0.192363\pi$
$744$			5.29432e7i			0.128556i
$745$	−2.34269e6	+	2.34269e6i	−0.00566560	+	0.00566560i
$746$	1.26226e8	−	1.26226e8i	0.304042	−	0.304042i
$747$	3.56379e8			0.854968
$748$	1.11517e8	−	1.11517e8i	0.266462	−	0.266462i
$749$	−8.07271e7			−0.192121
$750$	2.25434e7			0.0534363
$751$			3.24248e7i			0.0765523i	0.999267	+	0.0382761i	$0.0121866\pi$
$751$			3.24248e7i			0.0765523i	−0.999267	+	0.0382761i	$0.987813\pi$
$752$	1.82739e8			0.429713
$753$	−8.11320e7	+	8.11320e7i	−0.190023	+	0.190023i
$754$	1.59248e8	+	1.59248e8i	0.371502	+	0.371502i
$755$	−1.46444e7	−	1.46444e7i	−0.0340276	−	0.0340276i
$756$	4.36616e7			0.101049
$757$	−2.87768e7	+	2.87768e7i	−0.0663368	+	0.0663368i	−0.739497	−	0.673160i	$-0.764937\pi$
$757$	−2.87768e7	+	2.87768e7i	−0.0663368	+	0.0663368i	0.673160	+	0.739497i	$0.264937\pi$
$758$	−1.93241e8	−	1.93241e8i	−0.443703	−	0.443703i
$759$	−1.05959e8	+	1.05959e8i	−0.242333	+	0.242333i
$760$	1.04256e7	+	1.04256e7i	0.0237499	+	0.0237499i
$761$			4.24053e8i			0.962202i	0.876665	+	0.481101i	$0.159763\pi$
$761$			4.24053e8i			0.962202i	−0.876665	+	0.481101i	$0.840237\pi$
$762$	8.17289e7	−	8.17289e7i	0.184719	−	0.184719i
$763$	−1.78642e8	+	1.78642e8i	−0.402169	+	0.402169i
$764$	9.23988e7	+	9.23988e7i	0.207198	+	0.207198i
$765$		−	4.53222e7i		−	0.101234i
$766$	7.40007e7			0.164645
$767$			1.31117e9i			2.90585i
$768$			9.75209e6i			0.0215285i
$769$	3.74730e8	+	3.74730e8i	0.824022	+	0.824022i	0.986682	−	0.162660i	$-0.0520073\pi$
$769$	3.74730e8	+	3.74730e8i	0.824022	+	0.824022i	−0.162660	+	0.986682i	$0.552007\pi$
$770$		−	8.04638e6i		−	0.0176250i
$771$	1.00610e8	+	1.00610e8i	0.219521	+	0.219521i
$772$	−2.04706e8	−	2.04706e8i	−0.444916	−	0.444916i
$773$	−8.61740e8			−1.86568			−0.932842	−	0.360286i	$-0.882679\pi$
$773$	−8.61740e8			−1.86568			−0.932842	+	0.360286i	$0.882679\pi$
$774$	−2.12506e8			−0.458297
$775$	−3.43218e8	+	3.43218e8i	−0.737334	+	0.737334i
$776$			2.82409e8i			0.604356i
$777$	5.02657e7	+	3.55846e6i	0.107154	+	0.00758577i
$778$	−7.01193e7			−0.148901
$779$	−5.00186e8	−	5.00186e8i	−1.05808	−	1.05808i
$780$		−	1.47593e7i		−	0.0311016i
$781$			1.60359e8i			0.336621i
$782$	3.41884e8	−	3.41884e8i	0.714921	−	0.714921i
$783$	−9.98910e7	+	9.98910e7i	−0.208085	+	0.208085i
$784$	1.08756e8			0.225686
$785$	1.03837e7	−	1.03837e7i	0.0214657	−	0.0214657i
$786$	−1.11299e8			−0.229205
$787$	6.68618e8			1.37168			0.685842	−	0.727751i	$-0.259434\pi$
$787$	6.68618e8			1.37168			0.685842	+	0.727751i	$0.259434\pi$
$788$			2.15519e8i			0.440461i
$789$	1.22340e8			0.249079
$790$	2.66692e7	−	2.66692e7i	0.0540914	−	0.0540914i
$791$	−3.03442e7	−	3.03442e7i	−0.0613121	−	0.0613121i
$792$	−7.92696e7	−	7.92696e7i	−0.159563	−	0.159563i
$793$	4.88415e8			0.979422
$794$	−2.88649e7	+	2.88649e7i	−0.0576646	+	0.0576646i
$795$	−7.91610e6	−	7.91610e6i	−0.0157547	−	0.0157547i
$796$	2.33479e8	−	2.33479e8i	0.462922	−	0.462922i
$797$	1.05813e8	+	1.05813e8i	0.209009	+	0.209009i	0.803846	−	0.594837i	$-0.202783\pi$
$797$	1.05813e8	+	1.05813e8i	0.209009	+	0.209009i	−0.594837	+	0.803846i	$0.702783\pi$
$798$		−	3.32253e7i		−	0.0653823i
$799$	−6.45210e8	+	6.45210e8i	−1.26491	+	1.26491i
$800$	−6.32204e7	+	6.32204e7i	−0.123477	+	0.123477i
$801$	3.98626e8	+	3.98626e8i	0.775655	+	0.775655i
$802$			3.19836e8i			0.620018i
$803$	−5.89051e8			−1.13764
$804$		−	7.97861e7i		−	0.153518i
$805$		−	2.46683e7i		−	0.0472881i
$806$	4.52185e8	+	4.52185e8i	0.863596	+	0.863596i
$807$			1.07979e8i			0.205455i
$808$	1.56534e8	+	1.56534e8i	0.296739	+	0.296739i
$809$	−4.02871e8	−	4.02871e8i	−0.760887	−	0.760887i	0.215596	−	0.976483i	$-0.430831\pi$
$809$	−4.02871e8	−	4.02871e8i	−0.760887	−	0.760887i	−0.976483	+	0.215596i	$0.930831\pi$
$810$	−2.72955e7			−0.0513613
$811$	2.16291e8			0.405485			0.202743	−	0.979232i	$-0.435015\pi$
$811$	2.16291e8			0.405485			0.202743	+	0.979232i	$0.435015\pi$
$812$	2.68062e7	−	2.68062e7i	0.0500689	−	0.0500689i
$813$		−	6.37113e7i		−	0.118562i
$814$	−1.81014e8	−	2.08596e8i	−0.335613	−	0.386752i
$815$	−3.32947e7			−0.0615038
$816$	−3.44324e7	−	3.44324e7i	−0.0633718	−	0.0633718i
$817$			3.45192e8i			0.632987i
$818$			2.86209e8i			0.522906i
$819$	1.74696e8	−	1.74696e8i	0.318004	−	0.318004i
$820$	−3.74016e7	+	3.74016e7i	−0.0678342	+	0.0678342i
$821$	9.62549e8			1.73938			0.869688	−	0.493602i	$-0.164320\pi$
$821$	9.62549e8			1.73938			0.869688	+	0.493602i	$0.164320\pi$
$822$	4.88170e7	−	4.88170e7i	0.0878932	−	0.0878932i
$823$	−1.73054e7			−0.0310443			−0.0155221	−	0.999880i	$-0.504941\pi$
$823$	−1.73054e7			−0.0310443			−0.0155221	+	0.999880i	$0.504941\pi$
$824$	−2.82848e8			−0.505559
$825$			1.38362e8i			0.246408i
$826$	2.20709e8			0.391634
$827$	−1.31160e8	+	1.31160e8i	−0.231892	+	0.231892i	−0.813482	−	0.581590i	$-0.802431\pi$
$827$	−1.31160e8	+	1.31160e8i	−0.231892	+	0.231892i	0.581590	+	0.813482i	$0.302431\pi$
$828$	−2.43022e8	−	2.43022e8i	−0.428109	−	0.428109i
$829$	−7.19907e8	−	7.19907e8i	−1.26361	−	1.26361i	−0.949331	−	0.314279i	$-0.898237\pi$
$829$	−7.19907e8	−	7.19907e8i	−1.26361	−	1.26361i	−0.314279	−	0.949331i	$-0.601763\pi$
$830$	−4.32874e7			−0.0757054
$831$	−2.54474e6	+	2.54474e6i	−0.00443446	+	0.00443446i
$832$	8.32921e7	+	8.32921e7i	0.144622	+	0.144622i
$833$	−3.83991e8	+	3.83991e8i	−0.664334	+	0.664334i
$834$	1.50557e7	+	1.50557e7i	0.0259539	+	0.0259539i
$835$		−	2.74883e7i		−	0.0472160i
$836$	−1.28765e8	+	1.28765e8i	−0.220383	+	0.220383i
$837$	−2.83640e8	+	2.83640e8i	−0.483716	+	0.483716i
$838$	2.20364e7	+	2.20364e7i	0.0374463	+	0.0374463i
$839$			1.04024e9i			1.76136i	0.473716	+	0.880678i	$0.342912\pi$
$839$			1.04024e9i			1.76136i	−0.473716	+	0.880678i	$0.657088\pi$
$840$	−2.48444e6			−0.00419170
$841$		−	4.72166e8i		−	0.793792i
$842$		−	1.63909e8i		−	0.274579i
$843$	−1.49500e7	−	1.49500e7i	−0.0249551	−	0.0249551i
$844$			2.72933e8i			0.453971i
$845$	−7.89724e7	−	7.89724e7i	−0.130890	−	0.130890i
$846$	4.58636e8	+	4.58636e8i	0.757455	+	0.757455i
$847$	−9.01214e7			−0.148312
$848$	8.93465e7			0.146518
$849$	2.71118e8	−	2.71118e8i	0.443032	−	0.443032i
$850$		−	4.46433e8i		−	0.726942i
$851$	−5.54947e8	−	6.39506e8i	−0.900456	−	1.03766i
$852$	4.95133e7			0.0800576
$853$	8.20748e7	+	8.20748e7i	0.132240	+	0.132240i	0.770129	−	0.637889i	$-0.220192\pi$
$853$	8.20748e7	+	8.20748e7i	0.132240	+	0.132240i	−0.637889	+	0.770129i	$0.720192\pi$
$854$		−	8.22148e7i		−	0.132001i
$855$			5.23321e7i			0.0837279i
$856$	9.65995e7	−	9.65995e7i	0.154012	−	0.154012i
$857$	2.75723e8	−	2.75723e8i	0.438056	−	0.438056i	−0.453301	−	0.891357i	$-0.649754\pi$
$857$	2.75723e8	−	2.75723e8i	0.438056	−	0.438056i	0.891357	+	0.453301i	$0.149754\pi$
$858$	1.82290e8			0.288603
$859$	5.56993e8	−	5.56993e8i	0.878759	−	0.878759i	−0.114647	−	0.993406i	$-0.536574\pi$
$859$	5.56993e8	−	5.56993e8i	0.878759	−	0.878759i	0.993406	+	0.114647i	$0.0365737\pi$
$860$	2.58119e7			0.0405812
$861$	1.19195e8			0.186744
$862$		−	6.37727e8i		−	0.995665i
$863$	2.93000e8			0.455865			0.227932	−	0.973677i	$-0.426803\pi$
$863$	2.93000e8			0.455865			0.227932	+	0.973677i	$0.426803\pi$
$864$	−5.22462e7	+	5.22462e7i	−0.0810053	+	0.0810053i
$865$	8.17546e7	+	8.17546e7i	0.126318	+	0.126318i
$866$	1.86897e8	+	1.86897e8i	0.287772	+	0.287772i
$867$	1.86583e7			0.0286295
$868$	7.61161e7	−	7.61161e7i	0.116390	−	0.116390i
$869$	3.29385e8	+	3.29385e8i	0.501932	+	0.501932i
$870$	5.68401e6	−	5.68401e6i	0.00863172	−	0.00863172i
$871$	−6.81449e8	−	6.81449e8i	−1.03128	−	1.03128i
$872$		−	4.27532e8i		−	0.644791i
$873$	−7.08784e8	+	7.08784e8i	−1.06530	+	1.06530i
$874$	−3.94763e8	+	3.94763e8i	−0.591291	+	0.591291i
$875$	−3.24106e7	−	3.24106e7i	−0.0483797	−	0.0483797i
$876$			1.81878e8i			0.270563i
$877$	1.45595e8			0.215848			0.107924	−	0.994159i	$-0.465580\pi$
$877$	1.45595e8			0.215848			0.107924	+	0.994159i	$0.465580\pi$
$878$			3.76172e7i			0.0555780i
$879$		−	2.42086e8i		−	0.356454i
$880$	9.62845e6	+	9.62845e6i	0.0141289	+	0.0141289i
$881$			5.95185e8i			0.870411i	0.900331	+	0.435205i	$0.143324\pi$
$881$			5.95185e8i			0.870411i	−0.900331	+	0.435205i	$0.856676\pi$
$882$	2.72953e8	+	2.72953e8i	0.397816	+	0.397816i
$883$	7.68108e7	+	7.68108e7i	0.111568	+	0.111568i	0.760687	−	0.649119i	$-0.224862\pi$
$883$	7.68108e7	+	7.68108e7i	0.111568	+	0.111568i	−0.649119	+	0.760687i	$0.724862\pi$
$884$	−5.88170e8			−0.851424
$885$	4.67993e7			0.0675165
$886$	−2.33543e8	+	2.33543e8i	−0.335788	+	0.335788i
$887$			1.13410e8i			0.162510i	0.996693	+	0.0812548i	$0.0258927\pi$
$887$			1.13410e8i			0.162510i	−0.996693	+	0.0812548i	$0.974107\pi$
$888$	−6.44070e7	+	5.58907e7i	−0.0919801	+	0.0798180i
$889$	−2.35002e8			−0.334478
$890$	−4.84190e7	−	4.84190e7i	−0.0686824	−	0.0686824i
$891$		−	3.37121e8i		−	0.476598i
$892$		−	1.86151e8i		−	0.262284i
$893$	7.45004e8	−	7.45004e8i	1.04618	−	1.04618i
$894$	−8.93382e6	+	8.93382e6i	−0.0125033	+	0.0125033i
$895$	−1.53913e8			−0.214688
$896$	1.40205e7	−	1.40205e7i	0.0194913	−	0.0194913i
$897$	5.58857e8			0.774325
$898$	−9.35830e8			−1.29231
$899$			3.48284e8i			0.479352i
$900$	−3.17339e8			−0.435307
$901$	−3.15462e8	+	3.15462e8i	−0.431293	+	0.431293i
$902$	−4.61939e8	−	4.61939e8i	−0.629456	−	0.629456i
$903$	−4.11298e7	−	4.11298e7i	−0.0558590	−	0.0558590i
$904$	7.26208e7			0.0983005
$905$	3.05436e7	−	3.05436e7i	0.0412073	−	0.0412073i
$906$	−5.58462e7	−	5.58462e7i	−0.0750947	−	0.0750947i
$907$	9.20408e8	−	9.20408e8i	1.23355	−	1.23355i	0.270966	−	0.962589i	$-0.412657\pi$
$907$	9.20408e8	−	9.20408e8i	1.23355	−	1.23355i	0.962589	−	0.270966i	$-0.0873431\pi$
$908$	−4.22531e8	−	4.22531e8i	−0.564418	−	0.564418i
$909$			7.85734e8i			1.04613i
$910$	−2.12194e7	+	2.12194e7i	−0.0281585	+	0.0281585i
$911$	−1.47130e8	+	1.47130e8i	−0.194601	+	0.194601i	−0.797681	−	0.603080i	$-0.793940\pi$
$911$	−1.47130e8	+	1.47130e8i	−0.194601	+	0.194601i	0.603080	+	0.797681i	$0.293940\pi$
$912$	3.97580e7	+	3.97580e7i	0.0524131	+	0.0524131i
$913$		−	5.34633e8i		−	0.702496i
$914$	5.56640e8			0.729013
$915$		−	1.74329e7i		−	0.0227565i
$916$			3.26354e8i			0.424622i
$917$	1.60014e8	+	1.60014e8i	0.207516	+	0.207516i
$918$		−	3.68938e8i		−	0.476898i
$919$	−5.86358e8	−	5.86358e8i	−0.755469	−	0.755469i	0.220025	−	0.975494i	$-0.429386\pi$
$919$	−5.86358e8	−	5.86358e8i	−0.755469	−	0.755469i	−0.975494	+	0.220025i	$0.929386\pi$
$920$	2.95185e7	+	2.95185e7i	0.0379080	+	0.0379080i
$921$	1.41996e8			0.181760
$922$	−5.65794e7			−0.0721881
$923$	4.22890e8	−	4.22890e8i	0.537802	−	0.537802i
$924$		−	3.06848e7i		−	0.0388962i
$925$	−7.79861e8	−	5.52087e7i	−0.985353	−	0.0697562i
$926$	9.02389e8			1.13648
$927$	−7.09887e8	−	7.09887e8i	−0.891148	−	0.891148i
$928$			6.41537e7i			0.0802745i
$929$		−	1.05917e9i		−	1.32105i	−0.750804	−	0.660525i	$-0.770334\pi$
$929$		−	1.05917e9i		−	1.32105i	0.750804	−	0.660525i	$-0.229666\pi$
$930$	1.61397e7	−	1.61397e7i	0.0200654	−	0.0200654i
$931$	4.43383e8	−	4.43383e8i	0.549453	−	0.549453i
$932$	−4.29498e6			−0.00530534
$933$	1.35872e8	−	1.35872e8i	0.167295	−	0.167295i
$934$	4.55300e8			0.558801
$935$	−6.79916e7			−0.0831803
$936$			4.18090e8i			0.509850i
$937$	1.67864e8			0.204051			0.102025	−	0.994782i	$-0.467468\pi$
$937$	1.67864e8			0.204051			0.102025	+	0.994782i	$0.467468\pi$
$938$	−1.14708e8	+	1.14708e8i	−0.138991	+	0.138991i
$939$	2.78640e8	+	2.78640e8i	0.336548	+	0.336548i
$940$	−5.57080e7	−	5.57080e7i	−0.0670709	−	0.0670709i
$941$	5.01244e8			0.601562			0.300781	−	0.953693i	$-0.402753\pi$
$941$	5.01244e8			0.601562			0.300781	+	0.953693i	$0.402753\pi$
$942$	3.95983e7	−	3.95983e7i	0.0473722	−	0.0473722i
$943$	−1.41620e9	−	1.41620e9i	−1.68884	−	1.68884i
$944$	−2.64105e8	+	2.64105e8i	−0.313950	+	0.313950i
$945$	−1.33102e7	−	1.33102e7i	−0.0157721	−	0.0157721i
$946$			3.18797e8i			0.376566i
$947$	8.69813e7	−	8.69813e7i	0.102418	−	0.102418i	−0.654041	−	0.756459i	$-0.726928\pi$
$947$	8.69813e7	−	8.69813e7i	0.102418	−	0.102418i	0.756459	+	0.654041i	$0.226928\pi$
$948$	1.01702e8	−	1.01702e8i	0.119373	−	0.119373i
$949$	1.55341e9	+	1.55341e9i	1.81756	+	1.81756i
$950$			5.15483e8i			0.601234i
$951$	−1.11893e8			−0.130096
$952$			9.90065e7i			0.114750i
$953$		−	1.01214e9i		−	1.16940i	−0.811250	−	0.584700i	$-0.801212\pi$
$953$		−	1.01214e9i		−	1.16940i	0.811250	−	0.584700i	$-0.198788\pi$
$954$	2.24240e8	+	2.24240e8i	0.258267	+	0.258267i
$955$		−	5.63355e7i		−	0.0646803i
$956$	−4.55488e8	−	4.55488e8i	−0.521319	−	0.521319i
$957$	7.02020e7	+	7.02020e7i	0.0800966	+	0.0800966i
$958$	−4.31564e8			−0.490850
$959$	−1.40368e8			−0.159152
$960$	2.97292e6	−	2.97292e6i	0.00336024	−	0.00336024i
$961$			1.01446e8i			0.114305i
$962$	−7.27368e7	+	1.02746e9i	−0.0817013	+	1.15409i
$963$	4.84887e8			0.542953
$964$	−3.98551e8	−	3.98551e8i	−0.444890	−	0.444890i
$965$			1.24809e8i			0.138888i
$966$		−	9.40722e7i		−	0.104359i
$967$	−2.61360e8	+	2.61360e8i	−0.289042	+	0.289042i	−0.836701	−	0.547660i	$-0.815519\pi$
$967$	−2.61360e8	+	2.61360e8i	−0.289042	+	0.289042i	0.547660	+	0.836701i	$0.315519\pi$
$968$	1.07841e8	−	1.07841e8i	0.118893	−	0.118893i
$969$	−2.80753e8			−0.308569
$970$	8.60921e7	−	8.60921e7i	0.0943297	−	0.0943297i
$971$	−2.11283e8			−0.230785			−0.115392	−	0.993320i	$-0.536813\pi$
$971$	−2.11283e8			−0.230785			−0.115392	+	0.993320i	$0.536813\pi$
$972$	−4.01649e8			−0.437369
$973$		−	4.32910e7i		−	0.0469958i
$974$	−1.76960e7			−0.0191514
$975$	3.64879e8	−	3.64879e8i	0.393673	−	0.393673i
$976$	9.83797e7	+	9.83797e7i	0.105817	+	0.105817i
$977$	1.23126e9	+	1.23126e9i	1.32028	+	1.32028i	0.913548	+	0.406731i	$0.133332\pi$
$977$	1.23126e9	+	1.23126e9i	1.32028	+	1.32028i	0.406731	+	0.913548i	$0.366668\pi$
$978$	−1.26969e8			−0.135731
$979$	5.98013e8	−	5.98013e8i	0.637327	−	0.637327i
$980$	−3.31542e7	−	3.31542e7i	−0.0352257	−	0.0352257i
$981$	1.07301e9	−	1.07301e9i	1.13657	−	1.13657i
$982$	−8.66191e8	−	8.66191e8i	−0.914701	−	0.914701i
$983$			1.24011e9i			1.30556i	0.757546	+	0.652782i	$0.226398\pi$
$983$			1.24011e9i			1.30556i	−0.757546	+	0.652782i	$0.773602\pi$
$984$	−1.42630e8	+	1.42630e8i	−0.149702	+	0.149702i
$985$	6.57009e7	−	6.57009e7i	0.0687484	−	0.0687484i
$986$	−2.26512e8	−	2.26512e8i	−0.236298	−	0.236298i
$987$			1.77535e8i			0.184643i
$988$	6.79142e8			0.704190
$989$			9.77358e8i			1.01033i
$990$			4.83306e7i			0.0498100i
$991$	2.08350e8	+	2.08350e8i	0.214078	+	0.214078i	0.805997	−	0.591919i	$-0.201630\pi$
$991$	2.08350e8	+	2.08350e8i	0.214078	+	0.214078i	−0.591919	+	0.805997i	$0.701630\pi$
$992$			1.82164e8i			0.186607i
$993$	2.42902e8	+	2.42902e8i	0.248075	+	0.248075i
$994$	−7.11849e7	−	7.11849e7i	−0.0724818	−	0.0724818i
$995$	−1.42352e8			−0.144509
$996$	−1.65076e8			−0.167073
$997$	9.64520e8	−	9.64520e8i	0.973253	−	0.973253i	−0.0263982	−	0.999652i	$-0.508404\pi$
$997$	9.64520e8	−	9.64520e8i	0.973253	−	0.973253i	0.999652	+	0.0263982i	$0.00840379\pi$
$998$			1.16569e9i			1.17272i
$999$	−6.44488e8	−	4.56253e7i	−0.646425	−	0.0457624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.31.6	✓	20
37.6	odd	4	inner	74.7.d.b.43.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.6	✓	20	1.1	even	1	trivial
74.7.d.b.43.5	yes	20	37.6	odd	4	inner

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 4.00000i) q^{2} +9.30032i q^{3} +32.0000i q^{4} +(9.75519 - 9.75519i) q^{5} +(37.2013 - 37.2013i) q^{6} -106.968 q^{7} +(128.000 - 128.000i) q^{8} +642.504 q^{9} +O(q^{10})\)	\(q+(-4.00000 - 4.00000i) q^{2} +9.30032i q^{3} +32.0000i q^{4} +(9.75519 - 9.75519i) q^{5} +(37.2013 - 37.2013i) q^{6} -106.968 q^{7} +(128.000 - 128.000i) q^{8} +642.504 q^{9} -78.0415 q^{10} -963.875i q^{11} -297.610 q^{12} +(-2541.87 + 2541.87i) q^{13} +(427.873 + 427.873i) q^{14} +(90.7264 + 90.7264i) q^{15} -1024.00 q^{16} +(3615.51 - 3615.51i) q^{17} +(-2570.02 - 2570.02i) q^{18} +(-4174.71 + 4174.71i) q^{19} +(312.166 + 312.166i) q^{20} -994.838i q^{21} +(-3855.50 + 3855.50i) q^{22} +(-11820.0 + 11820.0i) q^{23} +(1190.44 + 1190.44i) q^{24} +15434.7i q^{25} +20335.0 q^{26} +12755.4i q^{27} -3422.98i q^{28} +(7831.26 + 7831.26i) q^{29} -725.811i q^{30} +(22236.8 + 22236.8i) q^{31} +(4096.00 + 4096.00i) q^{32} +8964.34 q^{33} -28924.0 q^{34} +(-1043.49 + 1043.49i) q^{35} +20560.1i q^{36} +(-3576.93 + 50526.5i) q^{37} +33397.7 q^{38} +(-23640.2 - 23640.2i) q^{39} -2497.33i q^{40} +119813. i q^{41} +(-3979.35 + 3979.35i) q^{42} +(41343.2 - 41343.2i) q^{43} +30844.0 q^{44} +(6267.75 - 6267.75i) q^{45} +94560.4 q^{46} -178456. q^{47} -9523.53i q^{48} -106207. q^{49} +(61738.7 - 61738.7i) q^{50} +(33625.4 + 33625.4i) q^{51} +(-81339.9 - 81339.9i) q^{52} -87252.5 q^{53} +(51021.7 - 51021.7i) q^{54} +(-9402.78 - 9402.78i) q^{55} +(-13691.9 + 13691.9i) q^{56} +(-38826.2 - 38826.2i) q^{57} -62650.1i q^{58} +(257915. - 257915. i) q^{59} +(-2903.24 + 2903.24i) q^{60} +(-96073.9 - 96073.9i) q^{61} -177894. i q^{62} -68727.5 q^{63} -32768.0i q^{64} +49592.9i q^{65} +(-35857.4 - 35857.4i) q^{66} +268089. i q^{67} +(115696. + 115696. i) q^{68} +(-109930. - 109930. i) q^{69} +8347.96 q^{70} -166369. q^{71} +(82240.5 - 82240.5i) q^{72} -611128. i q^{73} +(216414. - 187798. i) q^{74} -143547. q^{75} +(-133591. - 133591. i) q^{76} +103104. i q^{77} +189122. i q^{78} +(-341731. + 341731. i) q^{79} +(-9989.31 + 9989.31i) q^{80} +349756. q^{81} +(479253. - 479253. i) q^{82} +554671. q^{83} +31834.8 q^{84} -70539.9i q^{85} -330746. q^{86} +(-72833.2 + 72833.2i) q^{87} +(-123376. - 123376. i) q^{88} +(620426. + 620426. i) q^{89} -50142.0 q^{90} +(271899. - 271899. i) q^{91} +(-378241. - 378241. i) q^{92} +(-206809. + 206809. i) q^{93} +(713825. + 713825. i) q^{94} +81450.3i q^{95} +(-38094.1 + 38094.1i) q^{96} +(-1.10316e6 + 1.10316e6i) q^{97} +(424827. + 424827. i) q^{98} -619293. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9}+O(q^{10}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9	\( 20 q - 80 q^{2} + 60 q^{5} + 256 q^{6} + 104 q^{7} + 2560 q^{8} - 6472 q^{9} - 480 q^{10} - 2048 q^{12} + 1560 q^{13} - 416 q^{14} - 2136 q^{15} - 20480 q^{16} + 16000 q^{17} + 25888 q^{18} + 3838 q^{19} + 1920 q^{20} + 8928 q^{22} - 6478 q^{23} + 8192 q^{24} - 12480 q^{26} - 1964 q^{29} + 117662 q^{31} + 81920 q^{32} - 92624 q^{33} - 128000 q^{34} - 104456 q^{35} - 17618 q^{37} - 30704 q^{38} + 121012 q^{39} + 213472 q^{42} + 65582 q^{43} - 71424 q^{44} - 466848 q^{45} + 51824 q^{46} - 168176 q^{47} + 563124 q^{49} - 379904 q^{50} + 560888 q^{51} + 49920 q^{52} + 561604 q^{53} - 139120 q^{54} - 1395304 q^{55} + 13312 q^{56} + 631036 q^{57} - 376510 q^{59} + 68352 q^{60} + 836700 q^{61} - 275908 q^{63} + 370496 q^{66} + 512000 q^{68} - 1616748 q^{69} + 835648 q^{70} - 94584 q^{71} - 828416 q^{72} + 133200 q^{74} + 20340 q^{75} + 122816 q^{76} - 2525594 q^{79} - 61440 q^{80} + 2933572 q^{81} - 1816480 q^{82} + 715304 q^{83} - 1707776 q^{84} - 524656 q^{86} + 900256 q^{87} + 285696 q^{88} - 952068 q^{89} + 3734784 q^{90} - 1351840 q^{91} - 207296 q^{92} + 580320 q^{93} + 672704 q^{94} - 262144 q^{96} + 178132 q^{97} - 2252496 q^{98}+O(q^{100}) \) 20 * q - 80 * q^2 + 60 * q^5 + 256 * q^6 + 104 * q^7 + 2560 * q^8 - 6472 * q^9 - 480 * q^10 - 2048 * q^12 + 1560 * q^13 - 416 * q^14 - 2136 * q^15 - 20480 * q^16 + 16000 * q^17 + 25888 * q^18 + 3838 * q^19 + 1920 * q^20 + 8928 * q^22 - 6478 * q^23 + 8192 * q^24 - 12480 * q^26 - 1964 * q^29 + 117662 * q^31 + 81920 * q^32 - 92624 * q^33 - 128000 * q^34 - 104456 * q^35 - 17618 * q^37 - 30704 * q^38 + 121012 * q^39 + 213472 * q^42 + 65582 * q^43 - 71424 * q^44 - 466848 * q^45 + 51824 * q^46 - 168176 * q^47 + 563124 * q^49 - 379904 * q^50 + 560888 * q^51 + 49920 * q^52 + 561604 * q^53 - 139120 * q^54 - 1395304 * q^55 + 13312 * q^56 + 631036 * q^57 - 376510 * q^59 + 68352 * q^60 + 836700 * q^61 - 275908 * q^63 + 370496 * q^66 + 512000 * q^68 - 1616748 * q^69 + 835648 * q^70 - 94584 * q^71 - 828416 * q^72 + 133200 * q^74 + 20340 * q^75 + 122816 * q^76 - 2525594 * q^79 - 61440 * q^80 + 2933572 * q^81 - 1816480 * q^82 + 715304 * q^83 - 1707776 * q^84 - 524656 * q^86 + 900256 * q^87 + 285696 * q^88 - 952068 * q^89 + 3734784 * q^90 - 1351840 * q^91 - 207296 * q^92 + 580320 * q^93 + 672704 * q^94 - 262144 * q^96 + 178132 * q^97 - 2252496 * q^98

Introduction

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