LMFDB - Embedded newform 74.7.d.b.43.5

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			43.5
Root			$6.30032i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.7.d.b.31.6

$q$-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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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	$-0.944903\pi$
$3$		−	9.30032i		−	0.344456i	0.985057	−	0.172228i	$-0.0550966\pi$
$4$		−	32.0000i		−	0.500000i
$5$	9.75519	+	9.75519i	0.0780415	+	0.0780415i	0.745050	−	0.667009i	$-0.232426\pi$
$5$	9.75519	+	9.75519i	0.0780415	+	0.0780415i	−0.667009	+	0.745050i	$0.732426\pi$
$6$	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	$0.117936\pi$
$11$			963.875i			0.724173i	−0.932144	+	0.362087i	$0.882064\pi$
$12$	−297.610			−0.172228
$13$	−2541.87	−	2541.87i	−1.15697	−	1.15697i	−0.985123	−	0.171851i	$-0.945025\pi$
$13$	−2541.87	−	2541.87i	−1.15697	−	1.15697i	−0.171851	−	0.985123i	$-0.554975\pi$
$14$	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	0.971783	−	0.235877i	$-0.0757962\pi$
$17$	3615.51	+	3615.51i	0.735906	+	0.735906i	−0.235877	+	0.971783i	$0.575796\pi$
$18$	−2570.02	+	2570.02i	−0.440675	+	0.440675i
$19$	−4174.71	−	4174.71i	−0.608648	−	0.608648i	0.333945	−	0.942593i	$-0.391620\pi$
$19$	−4174.71	−	4174.71i	−0.608648	−	0.608648i	−0.942593	+	0.333945i	$0.891620\pi$
$20$	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	0.0281206	−	0.999605i	$-0.491048\pi$
$23$	−11820.0	−	11820.0i	−0.971484	−	0.971484i	−0.999605	+	0.0281206i	$0.991048\pi$
$24$	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	−0.528090	−	0.849188i	$-0.677092\pi$
$29$	7831.26	−	7831.26i	0.321098	−	0.321098i	0.849188	+	0.528090i	$0.177092\pi$
$30$			725.811i			0.0268819i
$31$	22236.8	−	22236.8i	0.746427	−	0.746427i	−0.227380	−	0.973806i	$-0.573016\pi$
$31$	22236.8	−	22236.8i	0.746427	−	0.746427i	0.973806	+	0.227380i	$0.0730158\pi$
$32$	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	$-0.664630\pi$
$41$		−	119813.i		−	1.73841i	0.494450	−	0.869206i	$-0.335370\pi$
$42$	−3979.35	−	3979.35i	−0.0537111	−	0.0537111i
$43$	41343.2	+	41343.2i	0.519995	+	0.519995i	0.917570	−	0.397575i	$-0.130148\pi$
$43$	41343.2	+	41343.2i	0.519995	+	0.519995i	−0.397575	+	0.917570i	$0.630148\pi$
$44$	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	0.953080	+	0.302720i	$0.0978945\pi$
$59$	257915.	+	257915.i	1.25580	+	1.25580i	0.302720	+	0.953080i	$0.402105\pi$
$60$	−2903.24	−	2903.24i	−0.0134409	−	0.0134409i
$61$	−96073.9	+	96073.9i	−0.423269	+	0.423269i	−0.886327	−	0.463059i	$-0.846752\pi$
$61$	−96073.9	+	96073.9i	−0.423269	+	0.423269i	0.463059	+	0.886327i	$0.346752\pi$
$62$			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	$-0.852961\pi$
$67$		−	268089.i		−	0.891364i	0.895191	−	0.445682i	$-0.147039\pi$
$68$	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	$0.287583\pi$
$73$			611128.i			1.57096i	−0.618890	+	0.785478i	$0.712417\pi$
$74$	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	0.269805	−	0.962915i	$-0.413041\pi$
$79$	−341731.	−	341731.i	−0.693111	−	0.693111i	−0.962915	+	0.269805i	$0.913041\pi$
$80$	−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	−0.113466	−	0.993542i	$-0.536195\pi$
$89$	620426.	−	620426.i	0.880076	−	0.880076i	0.993542	+	0.113466i	$0.0361954\pi$
$90$	−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	−0.971445	−	0.237267i	$-0.923748\pi$
$97$	−1.10316e6	−	1.10316e6i	−1.20871	−	1.20871i	−0.237267	−	0.971445i	$-0.576252\pi$
$98$	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	$-0.797754\pi$
$101$		−	1.22292e6i		−	1.18696i	0.804850	−	0.593479i	$-0.202246\pi$
$102$			269003.i			0.253487i
$103$	−1.10488e6	+	1.10488e6i	−1.01112	+	1.01112i	−0.0111801	+	0.999938i	$0.503559\pi$
$103$	−1.10488e6	+	1.10488e6i	−1.01112	+	1.01112i	−0.999938	+	0.0111801i	$0.996441\pi$
$104$		−	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	0.935041	+	0.354541i	$0.115363\pi$
$109$	1.67005e6	+	1.67005e6i	1.28958	+	1.28958i	0.354541	+	0.935041i	$0.384637\pi$
$110$		−	75222.2i		−	0.0565156i
$111$	−469913.	+	33266.6i	−0.343596	+	0.0243242i
$112$	109535.			0.0779651
$113$	283675.	−	283675.i	0.196601	−	0.196601i	−0.601940	−	0.798541i	$-0.705605\pi$
$113$	283675.	−	283675.i	0.196601	−	0.196601i	0.798541	+	0.601940i	$0.205605\pi$
$114$		−	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	−0.956650	−	0.291239i	$-0.905933\pi$
$131$	−1.49591e6	+	1.49591e6i	−0.665412	+	0.665412i	0.291239	+	0.956650i	$0.405933\pi$
$132$		−	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	$-0.975993\pi$
$139$		−	404709.i		−	0.150695i	0.997157	−	0.0753475i	$-0.0240066\pi$
$140$	−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	$0.0699563\pi$
$151$			1.50119e6i			0.436019i	−0.975947	+	0.218009i	$0.930044\pi$
$152$		−	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	−0.876127	−	0.482081i	$-0.839881\pi$
$163$	−1.70651e6	+	1.70651e6i	−0.394045	+	0.394045i	0.482081	+	0.876127i	$0.339881\pi$
$164$	−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	0.841993	−	0.539488i	$-0.181382\pi$
$167$	1.40891e6	+	1.40891e6i	0.302506	+	0.302506i	−0.539488	+	0.841993i	$0.681382\pi$
$168$	−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	$-0.699848\pi$
$173$		−	8.38063e6i		−	1.61859i	0.587399	−	0.809297i	$-0.300152\pi$
$174$	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	−0.523361	+	0.852111i	$0.675322\pi$
$179$	−7.88880e6	+	7.88880e6i	−1.37547	+	1.37547i	−0.852111	+	0.523361i	$0.824678\pi$
$180$	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	0.883267	−	0.468870i	$-0.155339\pi$
$191$	2.88746e6	+	2.88746e6i	0.414397	+	0.414397i	−0.468870	+	0.883267i	$0.655339\pi$
$192$	304753.			0.0430570
$193$	−6.39706e6	−	6.39706e6i	−0.889833	−	0.889833i	0.104674	−	0.994507i	$-0.466620\pi$
$193$	−6.39706e6	−	6.39706e6i	−0.889833	−	0.889833i	−0.994507	+	0.104674i	$0.966620\pi$
$194$	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	−0.997434	−	0.0715899i	$-0.977193\pi$
$199$	−7.29621e6	+	7.29621e6i	−0.925844	+	0.925844i	0.0715899	+	0.997434i	$0.477193\pi$
$200$	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	−0.990367	−	0.138470i	$-0.955782\pi$
$227$	−1.32041e7	−	1.32041e7i	−1.12884	−	1.12884i	−0.138470	−	0.990367i	$-0.544218\pi$
$228$	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	$-0.998311\pi$
$233$		−	134218.i		−	0.0106107i	0.999986	−	0.00530534i	$-0.00168875\pi$
$234$	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	−0.999050	−	0.0435876i	$-0.986121\pi$
$239$	−1.42340e7	−	1.42340e7i	−1.04264	−	1.04264i	−0.0435876	−	0.999050i	$-0.513879\pi$
$240$	−92903.8	+	92903.8i	−0.00672047	+	0.00672047i
$241$	−1.24547e7	−	1.24547e7i	−0.889781	−	0.889781i	0.104721	−	0.994502i	$-0.466605\pi$
$241$	−1.24547e7	−	1.24547e7i	−0.889781	−	0.889781i	−0.994502	+	0.104721i	$0.966605\pi$
$242$	−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	−0.375258	−	0.926920i	$-0.622446\pi$
$251$	8.72357e6	−	8.72357e6i	0.551662	−	0.551662i	0.926920	+	0.375258i	$0.122446\pi$
$252$			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	0.949888	−	0.312590i	$-0.101197\pi$
$257$	1.08179e7	+	1.08179e7i	0.637298	+	0.637298i	−0.312590	+	0.949888i	$0.601197\pi$
$258$			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	$0.117754\pi$
$263$			1.31544e7i			0.723108i	−0.932351	+	0.361554i	$0.882246\pi$
$264$	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	−0.700641	−	0.713514i	$-0.747102\pi$
$277$	273619.	−	273619.i	0.0128738	−	0.0128738i	0.713514	+	0.700641i	$0.247102\pi$
$278$	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	0.669954	−	0.742402i	$-0.266314\pi$
$281$	−1.60747e6	−	1.60747e6i	−0.0724477	−	0.0724477i	−0.742402	+	0.669954i	$0.766314\pi$
$282$	−6.63880e6	−	6.63880e6i	−0.296035	−	0.296035i
$283$	−2.91515e7	+	2.91515e7i	−1.28618	+	1.28618i	−0.349088	+	0.937090i	$0.613508\pi$
$283$	−2.91515e7	+	2.91515e7i	−1.28618	+	1.28618i	−0.937090	+	0.349088i	$0.886492\pi$
$284$			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	$0.0849876\pi$
$307$			1.52679e7i			0.527671i	−0.964568	+	0.263836i	$0.915012\pi$
$308$	−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	−0.906940	−	0.421260i	$-0.861588\pi$
$311$	−1.46093e7	+	1.46093e7i	−0.485679	+	0.485679i	0.421260	+	0.906940i	$0.361588\pi$
$312$	−6.05190e6			−0.199263
$313$	2.99603e7	+	2.99603e7i	0.977041	+	0.977041i	0.999742	−	0.0227018i	$-0.00722682\pi$
$313$	2.99603e7	+	2.99603e7i	0.977041	+	0.977041i	−0.0227018	+	0.999742i	$0.507227\pi$
$314$	−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	$-0.939527\pi$
$317$		−	1.20311e7i		−	0.377684i	0.982007	−	0.188842i	$-0.0604734\pi$
$318$	−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	0.968644	−	0.248451i	$-0.0799215\pi$
$331$	2.61176e7	+	2.61176e7i	0.720194	+	0.720194i	−0.248451	+	0.968644i	$0.579921\pi$
$332$		−	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	$-0.975124\pi$
$337$		−	5.97595e6i		−	0.156141i	0.996948	−	0.0780705i	$-0.0248759\pi$
$338$	−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	−0.392794	−	0.919627i	$-0.628491\pi$
$347$	2.20121e7	−	2.20121e7i	0.526833	−	0.526833i	0.919627	+	0.392794i	$0.128491\pi$
$348$	−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	−0.756938	−	0.653487i	$-0.773305\pi$
$353$	−4.55047e6	+	4.55047e6i	−0.103450	+	0.103450i	0.653487	+	0.756938i	$0.273305\pi$
$354$			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	$-0.901664\pi$
$373$		−	3.15566e7i		−	0.608083i	0.952659	−	0.304042i	$-0.0983362\pi$
$374$		−	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	0.619976	−	0.784621i	$-0.287142\pi$
$383$	−9.25009e6	−	9.25009e6i	−0.164645	−	0.164645i	−0.784621	+	0.619976i	$0.787142\pi$
$384$	−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	0.777627	−	0.628726i	$-0.216423\pi$
$389$	8.76492e6	+	8.76492e6i	0.148901	+	0.148901i	−0.628726	+	0.777627i	$0.716423\pi$
$390$	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	$0.0183654\pi$
$397$			7.21623e6i			0.115329i	−0.998336	+	0.0576646i	$0.981635\pi$
$398$		−	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	−0.945536	−	0.325518i	$-0.894461\pi$
$401$	−3.99795e7	+	3.99795e7i	−0.620018	+	0.620018i	0.325518	+	0.945536i	$0.394461\pi$
$402$	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	−0.918448	−	0.395542i	$-0.870557\pi$
$409$	−3.57762e7	+	3.57762e7i	−0.522906	+	0.522906i	0.395542	+	0.918448i	$0.370557\pi$
$410$			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	−0.556362	−	0.830940i	$-0.687803\pi$
$421$	2.04887e7	−	2.04887e7i	0.274579	−	0.274579i	0.830940	+	0.556362i	$0.187803\pi$
$422$	−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	−0.00432610	−	0.999991i	$-0.501377\pi$
$431$	7.97159e7	−	7.97159e7i	0.995665	−	0.995665i	0.999991	+	0.00432610i	$0.00137704\pi$
$432$			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	−0.734350	−	0.678772i	$-0.762513\pi$
$439$	−4.70215e6	+	4.70215e6i	−0.0555780	+	0.0555780i	0.678772	+	0.734350i	$0.262513\pi$
$440$	−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	$0.109003\pi$
$443$			5.83857e7i			0.671576i	−0.941938	+	0.335788i	$0.890997\pi$
$444$	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	0.933353	+	0.358961i	$0.116869\pi$
$449$	1.16979e8	+	1.16979e8i	1.29231	+	1.29231i	0.358961	+	0.933353i	$0.383131\pi$
$450$	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	0.241410	−	0.970423i	$-0.422390\pi$
$457$	−6.95800e7	−	6.95800e7i	−0.729013	−	0.729013i	−0.970423	+	0.241410i	$0.922390\pi$
$458$	−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	0.742279	−	0.670091i	$-0.233745\pi$
$461$	7.07242e6	+	7.07242e6i	0.0721881	+	0.0721881i	−0.670091	+	0.742279i	$0.733745\pi$
$462$	3.83560e6	−	3.83560e6i	0.0388962	−	0.0388962i
$463$	−1.12799e8	−	1.12799e8i	−1.13648	−	1.13648i	−0.989077	−	0.147401i	$-0.952909\pi$
$463$	−1.12799e8	−	1.12799e8i	−1.13648	−	1.13648i	−0.147401	−	0.989077i	$-0.547091\pi$
$464$	−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	0.370165	−	0.928966i	$-0.379301\pi$
$467$	−5.69125e7	−	5.69125e7i	−0.558801	−	0.558801i	−0.928966	+	0.370165i	$0.879301\pi$
$468$	−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	0.908574	−	0.417724i	$-0.137172\pi$
$479$	5.39455e7	+	5.39455e7i	0.490850	+	0.490850i	−0.417724	+	0.908574i	$0.637172\pi$
$480$		−	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	0.716618	−	0.697466i	$-0.245689\pi$
$487$	2.21201e6	+	2.21201e6i	0.0191514	+	0.0191514i	−0.697466	+	0.716618i	$0.745689\pi$
$488$	−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	−0.191155	+	0.981560i	$0.561223\pi$
$499$	−1.45712e8	+	1.45712e8i	−1.17272	+	1.17272i	−0.981560	+	0.191155i	$0.938777\pi$
$500$	−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	0.442183	−	0.896925i	$-0.354204\pi$
$503$	−5.78721e7	−	5.78721e7i	−0.454742	−	0.454742i	−0.896925	+	0.442183i	$0.854204\pi$
$504$	−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	$-0.935987\pi$
$509$		−	5.26832e7i		−	0.399502i	0.979847	−	0.199751i	$-0.0640133\pi$
$510$	−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	$0.00421733\pi$
$521$			3.74730e6i			0.0264975i	−0.999912	+	0.0132487i	$0.995783\pi$
$522$			4.02529e7i			0.283000i
$523$	−9.64173e7	−	9.64173e7i	−0.673984	−	0.673984i	0.284648	−	0.958632i	$-0.408123\pi$
$523$	−9.64173e7	−	9.64173e7i	−0.673984	−	0.673984i	−0.958632	+	0.284648i	$0.908123\pi$
$524$	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	0.419371	−	0.907815i	$-0.362251\pi$
$541$	−7.73404e7	−	7.73404e7i	−0.488444	−	0.488444i	−0.907815	+	0.419371i	$0.862251\pi$
$542$	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	0.580275	−	0.814421i	$-0.302945\pi$
$547$	2.28266e8	−	2.28266e8i	1.39470	−	1.39470i	0.814421	−	0.580275i	$-0.197055\pi$
$548$		−	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	−0.694876	−	0.719129i	$-0.744541\pi$
$557$	4.19107e6	−	4.19107e6i	0.0242526	−	0.0242526i	0.719129	+	0.694876i	$0.244541\pi$
$558$			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	0.440248	−	0.897876i	$-0.354891\pi$
$563$	−8.16655e7	−	8.16655e7i	−0.457629	−	0.457629i	−0.897876	+	0.440248i	$0.854891\pi$
$564$	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	0.162409	−	0.986724i	$-0.448074\pi$
$569$	2.11693e8	−	2.11693e8i	1.14913	−	1.14913i	0.986724	−	0.162409i	$-0.0519263\pi$
$570$	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	−0.916675	−	0.399634i	$-0.869137\pi$
$577$	−2.52863e8	−	2.52863e8i	−1.31631	−	1.31631i	−0.399634	−	0.916675i	$-0.630863\pi$
$578$	−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	−0.799404	−	0.600794i	$-0.794851\pi$
$587$	−4.01713e7	+	4.01713e7i	−0.198610	+	0.198610i	0.600794	+	0.799404i	$0.294851\pi$
$588$	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	−0.532371	−	0.846511i	$-0.678699\pi$
$607$	7.02570e7	−	7.02570e7i	0.314140	−	0.314140i	0.846511	+	0.532371i	$0.178699\pi$
$608$	−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	$0.0698775\pi$
$613$			1.00324e8i			0.435535i	−0.976001	+	0.217768i	$0.930123\pi$
$614$	−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	$-0.932875\pi$
$617$		−	9.83326e7i		−	0.418641i	0.977847	−	0.209321i	$-0.0671253\pi$
$618$	−8.22055e7			−0.348286
$619$		−	5.68169e7i		−	0.239555i	−0.992801	−	0.119778i	$-0.961782\pi$
$619$		−	5.68169e7i		−	0.239555i	0.992801	−	0.119778i	$-0.0382182\pi$
$620$		−	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	0.121859	−	0.992547i	$-0.461115\pi$
$631$	2.79983e8	−	2.79983e8i	1.11441	−	1.11441i	0.992547	−	0.121859i	$-0.0388855\pi$
$632$		−	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	−0.181227	−	0.983441i	$-0.558007\pi$
$643$	2.13267e8	−	2.13267e8i	0.802214	−	0.802214i	0.983441	+	0.181227i	$0.0580070\pi$
$644$	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	−0.926761	−	0.375651i	$-0.877419\pi$
$647$	−1.49263e8	+	1.49263e8i	−0.551110	+	0.551110i	0.375651	+	0.926761i	$0.377419\pi$
$648$	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	−0.874992	−	0.484137i	$-0.839134\pi$
$653$	−1.08832e8	+	1.08832e8i	−0.390855	+	0.390855i	0.484137	+	0.874992i	$0.339134\pi$
$654$			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	$0.00757292\pi$
$659$			1.36163e7i			0.0475776i	−0.999717	+	0.0237888i	$0.992427\pi$
$660$	2.79836e6	−	2.79836e6i	0.00973357	−	0.00973357i
$661$	1.84283e8	−	1.84283e8i	0.638090	−	0.638090i	−0.311994	−	0.950084i	$-0.600997\pi$
$661$	1.84283e8	−	1.84283e8i	0.638090	−	0.638090i	0.950084	+	0.311994i	$0.100997\pi$
$662$	−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	$0.136405\pi$
$677$			2.57871e8i			0.831069i	−0.909577	+	0.415534i	$0.863595\pi$
$678$	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	0.997315	−	0.0732297i	$-0.0233306\pi$
$683$	2.94425e8	+	2.94425e8i	0.924085	+	0.924085i	−0.0732297	+	0.997315i	$0.523331\pi$
$684$	−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	$0.134320\pi$
$691$			2.70264e8i			0.819133i	−0.912280	+	0.409566i	$0.865680\pi$
$692$	−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	0.968889	+	0.247495i	$0.0796075\pi$
$701$	4.19011e8	+	4.19011e8i	1.21638	+	1.21638i	0.247495	+	0.968889i	$0.420392\pi$
$702$		−	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	−0.987057	−	0.160371i	$-0.948731\pi$
$709$	−4.08944e8	−	4.08944e8i	−1.14743	−	1.14743i	−0.160371	−	0.987057i	$-0.551269\pi$
$710$	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	−0.977763	−	0.209715i	$-0.932746\pi$
$727$	−2.95115e8	+	2.95115e8i	−0.768047	+	0.768047i	0.209715	+	0.977763i	$0.432746\pi$
$728$			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	$-0.858410\pi$
$733$		−	3.38927e8i		−	0.860587i	0.902689	−	0.430293i	$-0.141590\pi$
$734$	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	$-0.924425\pi$
$739$		−	1.89847e8i		−	0.470403i	0.971947	−	0.235202i	$-0.0755751\pi$
$740$	−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	$0.192363\pi$
$743$			4.66125e8i			1.13641i	−0.822886	+	0.568207i	$0.807637\pi$
$744$		−	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	$-0.987813\pi$
$751$		−	3.24248e7i		−	0.0765523i	0.999267	−	0.0382761i	$-0.0121866\pi$
$752$	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	0.673160	−	0.739497i	$-0.264937\pi$
$757$	−2.87768e7	−	2.87768e7i	−0.0663368	−	0.0663368i	−0.739497	+	0.673160i	$0.764937\pi$
$758$	−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	$-0.840237\pi$
$761$		−	4.24053e8i		−	0.962202i	0.876665	−	0.481101i	$-0.159763\pi$
$762$	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	−0.162660	−	0.986682i	$-0.552007\pi$
$769$	3.74730e8	−	3.74730e8i	0.824022	−	0.824022i	0.986682	+	0.162660i	$0.0520073\pi$
$770$			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	−0.594837	−	0.803846i	$-0.702783\pi$
$797$	1.05813e8	−	1.05813e8i	0.209009	−	0.209009i	0.803846	+	0.594837i	$0.202783\pi$
$798$			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	−0.976483	−	0.215596i	$-0.930831\pi$
$809$	−4.02871e8	+	4.02871e8i	−0.760887	+	0.760887i	0.215596	+	0.976483i	$0.430831\pi$
$810$	−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	0.581590	−	0.813482i	$-0.302431\pi$
$827$	−1.31160e8	−	1.31160e8i	−0.231892	−	0.231892i	−0.813482	+	0.581590i	$0.802431\pi$
$828$	−2.43022e8	+	2.43022e8i	−0.428109	+	0.428109i
$829$	−7.19907e8	+	7.19907e8i	−1.26361	+	1.26361i	−0.314279	+	0.949331i	$0.601763\pi$
$829$	−7.19907e8	+	7.19907e8i	−1.26361	+	1.26361i	−0.949331	+	0.314279i	$0.898237\pi$
$830$	−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	$-0.657088\pi$
$839$		−	1.04024e9i		−	1.76136i	0.473716	−	0.880678i	$-0.342912\pi$
$840$	−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	−0.637889	−	0.770129i	$-0.720192\pi$
$853$	8.20748e7	−	8.20748e7i	0.132240	−	0.132240i	0.770129	+	0.637889i	$0.220192\pi$
$854$			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	0.891357	−	0.453301i	$-0.149754\pi$
$857$	2.75723e8	+	2.75723e8i	0.438056	+	0.438056i	−0.453301	+	0.891357i	$0.649754\pi$
$858$	1.82290e8			0.288603
$859$	5.56993e8	+	5.56993e8i	0.878759	+	0.878759i	0.993406	−	0.114647i	$-0.0365737\pi$
$859$	5.56993e8	+	5.56993e8i	0.878759	+	0.878759i	−0.114647	+	0.993406i	$0.536574\pi$
$860$	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	$-0.856676\pi$
$881$		−	5.95185e8i		−	0.870411i	0.900331	−	0.435205i	$-0.143324\pi$
$882$	2.72953e8	−	2.72953e8i	0.397816	−	0.397816i
$883$	7.68108e7	−	7.68108e7i	0.111568	−	0.111568i	−0.649119	−	0.760687i	$-0.724862\pi$
$883$	7.68108e7	−	7.68108e7i	0.111568	−	0.111568i	0.760687	+	0.649119i	$0.224862\pi$
$884$	−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	$-0.974107\pi$
$887$		−	1.13410e8i		−	0.162510i	0.996693	−	0.0812548i	$-0.0258927\pi$
$888$	−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	0.962589	+	0.270966i	$0.0873431\pi$
$907$	9.20408e8	+	9.20408e8i	1.23355	+	1.23355i	0.270966	+	0.962589i	$0.412657\pi$
$908$	−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	0.603080	−	0.797681i	$-0.293940\pi$
$911$	−1.47130e8	−	1.47130e8i	−0.194601	−	0.194601i	−0.797681	+	0.603080i	$0.793940\pi$
$912$	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	−0.975494	−	0.220025i	$-0.929386\pi$
$919$	−5.86358e8	+	5.86358e8i	−0.755469	+	0.755469i	0.220025	+	0.975494i	$0.429386\pi$
$920$	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	$0.229666\pi$
$929$			1.05917e9i			1.32105i	−0.750804	+	0.660525i	$0.770334\pi$
$930$	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	0.756459	−	0.654041i	$-0.226928\pi$
$947$	8.69813e7	+	8.69813e7i	0.102418	+	0.102418i	−0.654041	+	0.756459i	$0.726928\pi$
$948$	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	$0.198788\pi$
$953$			1.01214e9i			1.16940i	−0.811250	+	0.584700i	$0.801212\pi$
$954$	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	0.547660	−	0.836701i	$-0.315519\pi$
$967$	−2.61360e8	−	2.61360e8i	−0.289042	−	0.289042i	−0.836701	+	0.547660i	$0.815519\pi$
$968$	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	0.406731	−	0.913548i	$-0.366668\pi$
$977$	1.23126e9	−	1.23126e9i	1.32028	−	1.32028i	0.913548	−	0.406731i	$-0.133332\pi$
$978$	−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	$-0.773602\pi$
$983$		−	1.24011e9i		−	1.30556i	0.757546	−	0.652782i	$-0.226398\pi$
$984$	−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	−0.591919	−	0.805997i	$-0.701630\pi$
$991$	2.08350e8	−	2.08350e8i	0.214078	−	0.214078i	0.805997	+	0.591919i	$0.201630\pi$
$992$		−	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	0.999652	−	0.0263982i	$-0.00840379\pi$
$997$	9.64520e8	+	9.64520e8i	0.973253	+	0.973253i	−0.0263982	+	0.999652i	$0.508404\pi$
$998$		−	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.43.5	yes	20
37.31	odd	4	inner	74.7.d.b.31.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.6	✓	20	37.31	odd	4	inner
74.7.d.b.43.5	yes	20	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
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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