LMFDB - Embedded newform 74.7.d.b.31.9

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			31.9
Root			$-44.9177i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.7.d.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 4.00000i) q^{2} +47.9177i q^{3} +32.0000i q^{4} +(99.4727 - 99.4727i) q^{5} +(191.671 - 191.671i) q^{6} +584.317 q^{7} +(128.000 - 128.000i) q^{8} -1567.10 q^{9} +O(q^{10})$	\(q+(-4.00000 - 4.00000i) q^{2} +47.9177i q^{3} +32.0000i q^{4} +(99.4727 - 99.4727i) q^{5} +(191.671 - 191.671i) q^{6} +584.317 q^{7} +(128.000 - 128.000i) q^{8} -1567.10 q^{9} -795.781 q^{10} -2321.43i q^{11} -1533.37 q^{12} +(510.323 - 510.323i) q^{13} +(-2337.27 - 2337.27i) q^{14} +(4766.50 + 4766.50i) q^{15} -1024.00 q^{16} +(2288.22 - 2288.22i) q^{17} +(6268.42 + 6268.42i) q^{18} +(4480.83 - 4480.83i) q^{19} +(3183.12 + 3183.12i) q^{20} +27999.1i q^{21} +(-9285.73 + 9285.73i) q^{22} +(6697.16 - 6697.16i) q^{23} +(6133.46 + 6133.46i) q^{24} -4164.62i q^{25} -4082.59 q^{26} -40160.0i q^{27} +18698.2i q^{28} +(-9387.24 - 9387.24i) q^{29} -38132.0i q^{30} +(37480.5 + 37480.5i) q^{31} +(4096.00 + 4096.00i) q^{32} +111238. q^{33} -18305.8 q^{34} +(58123.6 - 58123.6i) q^{35} -50147.3i q^{36} +(-50508.9 - 3817.73i) q^{37} -35846.6 q^{38} +(24453.5 + 24453.5i) q^{39} -25465.0i q^{40} +20314.8i q^{41} +(111997. - 111997. i) q^{42} +(-32203.7 + 32203.7i) q^{43} +74285.9 q^{44} +(-155884. + 155884. i) q^{45} -53577.3 q^{46} -180149. q^{47} -49067.7i q^{48} +223778. q^{49} +(-16658.5 + 16658.5i) q^{50} +(109646. + 109646. i) q^{51} +(16330.3 + 16330.3i) q^{52} +84857.9 q^{53} +(-160640. + 160640. i) q^{54} +(-230919. - 230919. i) q^{55} +(74792.6 - 74792.6i) q^{56} +(214711. + 214711. i) q^{57} +75098.0i q^{58} +(-157289. + 157289. i) q^{59} +(-152528. + 152528. i) q^{60} +(227937. + 227937. i) q^{61} -299844. i q^{62} -915686. q^{63} -32768.0i q^{64} -101526. i q^{65} +(-444951. - 444951. i) q^{66} -125717. i q^{67} +(73223.1 + 73223.1i) q^{68} +(320912. + 320912. i) q^{69} -464989. q^{70} +376847. q^{71} +(-200589. + 200589. i) q^{72} +163197. i q^{73} +(186765. + 217307. i) q^{74} +199559. q^{75} +(143386. + 143386. i) q^{76} -1.35645e6i q^{77} -195628. i q^{78} +(-109373. + 109373. i) q^{79} +(-101860. + 101860. i) q^{80} +781955. q^{81} +(81259.0 - 81259.0i) q^{82} -431565. q^{83} -895972. q^{84} -455231. i q^{85} +257630. q^{86} +(449815. - 449815. i) q^{87} +(-297143. - 297143. i) q^{88} +(-579015. - 579015. i) q^{89} +1.24707e6 q^{90} +(298191. - 298191. i) q^{91} +(214309. + 214309. i) q^{92} +(-1.79598e6 + 1.79598e6i) q^{93} +(720596. + 720596. i) q^{94} -891440. i q^{95} +(-196271. + 196271. i) q^{96} +(865584. - 865584. i) q^{97} +(-895112. - 895112. i) q^{98} +3.63793e6i 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
$3$			47.9177i			1.77473i	0.461069	+	0.887364i	$0.347466\pi$
$3$			47.9177i			1.77473i	−0.461069	+	0.887364i	$0.652534\pi$
$4$			32.0000i			0.500000i
$5$	99.4727	−	99.4727i	0.795781	−	0.795781i	−0.186646	−	0.982427i	$-0.559762\pi$
$5$	99.4727	−	99.4727i	0.795781	−	0.795781i	0.982427	+	0.186646i	$0.0597617\pi$
$6$	191.671	−	191.671i	0.887364	−	0.887364i
$7$	584.317			1.70355			0.851775	−	0.523908i	$-0.175527\pi$
$7$	584.317			1.70355			0.851775	+	0.523908i	$0.175527\pi$
$8$	128.000	−	128.000i	0.250000	−	0.250000i
$9$	−1567.10			−2.14966
$10$	−795.781			−0.795781
$11$		−	2321.43i		−	1.74413i	−0.489393	−	0.872064i	$-0.662781\pi$
$11$		−	2321.43i		−	1.74413i	0.489393	−	0.872064i	$-0.337219\pi$
$12$	−1533.37			−0.887364
$13$	510.323	−	510.323i	0.232282	−	0.232282i	−0.581363	−	0.813645i	$-0.697480\pi$
$13$	510.323	−	510.323i	0.232282	−	0.232282i	0.813645	+	0.581363i	$0.197480\pi$
$14$	−2337.27	−	2337.27i	−0.851775	−	0.851775i
$15$	4766.50	+	4766.50i	1.41230	+	1.41230i
$16$	−1024.00			−0.250000
$17$	2288.22	−	2288.22i	0.465749	−	0.465749i	−0.434785	−	0.900534i	$-0.643176\pi$
$17$	2288.22	−	2288.22i	0.465749	−	0.465749i	0.900534	+	0.434785i	$0.143176\pi$
$18$	6268.42	+	6268.42i	1.07483	+	1.07483i
$19$	4480.83	−	4480.83i	0.653277	−	0.653277i	−0.300504	−	0.953781i	$-0.597155\pi$
$19$	4480.83	−	4480.83i	0.653277	−	0.653277i	0.953781	+	0.300504i	$0.0971547\pi$
$20$	3183.12	+	3183.12i	0.397891	+	0.397891i
$21$			27999.1i			3.02334i
$22$	−9285.73	+	9285.73i	−0.872064	+	0.872064i
$23$	6697.16	−	6697.16i	0.550437	−	0.550437i	−0.376130	−	0.926567i	$-0.622745\pi$
$23$	6697.16	−	6697.16i	0.550437	−	0.550437i	0.926567	+	0.376130i	$0.122745\pi$
$24$	6133.46	+	6133.46i	0.443682	+	0.443682i
$25$		−	4164.62i		−	0.266535i
$26$	−4082.59			−0.232282
$27$		−	40160.0i		−	2.04034i
$28$			18698.2i			0.851775i
$29$	−9387.24	−	9387.24i	−0.384897	−	0.384897i	0.487966	−	0.872863i	$-0.337739\pi$
$29$	−9387.24	−	9387.24i	−0.384897	−	0.384897i	−0.872863	+	0.487966i	$0.837739\pi$
$30$		−	38132.0i		−	1.41230i
$31$	37480.5	+	37480.5i	1.25811	+	1.25811i	0.951993	+	0.306121i	$0.0990312\pi$
$31$	37480.5	+	37480.5i	1.25811	+	1.25811i	0.306121	+	0.951993i	$0.400969\pi$
$32$	4096.00	+	4096.00i	0.125000	+	0.125000i
$33$	111238.			3.09535
$34$	−18305.8			−0.465749
$35$	58123.6	−	58123.6i	1.35565	−	1.35565i
$36$		−	50147.3i		−	1.07483i
$37$	−50508.9	−	3817.73i	−0.997156	−	0.0753703i
$37$	−50508.9	−	3817.73i	−0.997156	−	0.0753703i
$38$	−35846.6			−0.653277
$39$	24453.5	+	24453.5i	0.412237	+	0.412237i
$40$		−	25465.0i		−	0.397891i
$41$			20314.8i			0.294754i	0.989080	+	0.147377i	$0.0470831\pi$
$41$			20314.8i			0.294754i	−0.989080	+	0.147377i	$0.952917\pi$
$42$	111997.	−	111997.i	1.51167	−	1.51167i
$43$	−32203.7	+	32203.7i	−0.405042	+	0.405042i	−0.880006	−	0.474963i	$-0.842461\pi$
$43$	−32203.7	+	32203.7i	−0.405042	+	0.405042i	0.474963	+	0.880006i	$0.342461\pi$
$44$	74285.9			0.872064
$45$	−155884.	+	155884.i	−1.71066	+	1.71066i
$46$	−53577.3			−0.550437
$47$	−180149.			−1.73515			−0.867577	−	0.497303i	$-0.834324\pi$
$47$	−180149.			−1.73515			−0.867577	+	0.497303i	$0.834324\pi$
$48$		−	49067.7i		−	0.443682i
$49$	223778.			1.90208
$50$	−16658.5	+	16658.5i	−0.133268	+	0.133268i
$51$	109646.	+	109646.i	0.826577	+	0.826577i
$52$	16330.3	+	16330.3i	0.116141	+	0.116141i
$53$	84857.9			0.569987			0.284993	−	0.958530i	$-0.408009\pi$
$53$	84857.9			0.569987			0.284993	+	0.958530i	$0.408009\pi$
$54$	−160640.	+	160640.i	−1.02017	+	1.02017i
$55$	−230919.	−	230919.i	−1.38794	−	1.38794i
$56$	74792.6	−	74792.6i	0.425887	−	0.425887i
$57$	214711.	+	214711.i	1.15939	+	1.15939i
$58$			75098.0i			0.384897i
$59$	−157289.	+	157289.i	−0.765846	+	0.765846i	−0.977372	−	0.211526i	$-0.932157\pi$
$59$	−157289.	+	157289.i	−0.765846	+	0.765846i	0.211526	+	0.977372i	$0.432157\pi$
$60$	−152528.	+	152528.i	−0.706148	+	0.706148i
$61$	227937.	+	227937.i	1.00421	+	1.00421i	0.999991	+	0.00422274i	$0.00134414\pi$
$61$	227937.	+	227937.i	1.00421	+	1.00421i	0.00422274	+	0.999991i	$0.498656\pi$
$62$		−	299844.i		−	1.25811i
$63$	−915686.			−3.66206
$64$		−	32768.0i		−	0.125000i
$65$		−	101526.i		−	0.369691i
$66$	−444951.	−	444951.i	−1.54768	−	1.54768i
$67$		−	125717.i		−	0.417995i	−0.977916	−	0.208997i	$-0.932980\pi$
$67$		−	125717.i		−	0.417995i	0.977916	−	0.208997i	$-0.0670200\pi$
$68$	73223.1	+	73223.1i	0.232874	+	0.232874i
$69$	320912.	+	320912.i	0.976876	+	0.976876i
$70$	−464989.			−1.35565
$71$	376847.			1.05291			0.526454	−	0.850204i	$-0.323521\pi$
$71$	376847.			1.05291			0.526454	+	0.850204i	$0.323521\pi$
$72$	−200589.	+	200589.i	−0.537416	+	0.537416i
$73$			163197.i			0.419511i	0.977754	+	0.209755i	$0.0672667\pi$
$73$			163197.i			0.419511i	−0.977754	+	0.209755i	$0.932733\pi$
$74$	186765.	+	217307.i	0.460893	+	0.536263i
$75$	199559.			0.473028
$76$	143386.	+	143386.i	0.326639	+	0.326639i
$77$		−	1.35645e6i		−	2.97121i
$78$		−	195628.i		−	0.412237i
$79$	−109373.	+	109373.i	−0.221834	+	0.221834i	−0.809270	−	0.587436i	$-0.800137\pi$
$79$	−109373.	+	109373.i	−0.221834	+	0.221834i	0.587436	+	0.809270i	$0.300137\pi$
$80$	−101860.	+	101860.i	−0.198945	+	0.198945i
$81$	781955.			1.47139
$82$	81259.0	−	81259.0i	0.147377	−	0.147377i
$83$	−431565.			−0.754766			−0.377383	−	0.926057i	$-0.623176\pi$
$83$	−431565.			−0.754766			−0.377383	+	0.926057i	$0.623176\pi$
$84$	−895972.			−1.51167
$85$		−	455231.i		−	0.741268i
$86$	257630.			0.405042
$87$	449815.	−	449815.i	0.683087	−	0.683087i
$88$	−297143.	−	297143.i	−0.436032	−	0.436032i
$89$	−579015.	−	579015.i	−0.821333	−	0.821333i	0.164966	−	0.986299i	$-0.447249\pi$
$89$	−579015.	−	579015.i	−0.821333	−	0.821333i	−0.986299	+	0.164966i	$0.947249\pi$
$90$	1.24707e6			1.71066
$91$	298191.	−	298191.i	0.395704	−	0.395704i
$92$	214309.	+	214309.i	0.275218	+	0.275218i
$93$	−1.79598e6	+	1.79598e6i	−2.23281	+	2.23281i
$94$	720596.	+	720596.i	0.867577	+	0.867577i
$95$		−	891440.i		−	1.03973i
$96$	−196271.	+	196271.i	−0.221841	+	0.221841i
$97$	865584.	−	865584.i	0.948405	−	0.948405i	−0.0503277	−	0.998733i	$-0.516027\pi$
$97$	865584.	−	865584.i	0.948405	−	0.948405i	0.998733	+	0.0503277i	$0.0160266\pi$
$98$	−895112.	−	895112.i	−0.951040	−	0.951040i
$99$			3.63793e6i			3.74928i
$100$	133268.			0.133268
$101$		−	514075.i		−	0.498956i	−0.968380	−	0.249478i	$-0.919741\pi$
$101$		−	514075.i		−	0.498956i	0.968380	−	0.249478i	$-0.0802590\pi$
$102$		−	877171.i		−	0.826577i
$103$	−170638.	−	170638.i	−0.156158	−	0.156158i	0.624704	−	0.780862i	$-0.285220\pi$
$103$	−170638.	−	170638.i	−0.156158	−	0.156158i	−0.780862	+	0.624704i	$0.785220\pi$
$104$		−	130643.i		−	0.116141i
$105$	2.78515e6	+	2.78515e6i	2.40592	+	2.40592i
$106$	−339432.	−	339432.i	−0.284993	−	0.284993i
$107$	75819.8			0.0618916			0.0309458	−	0.999521i	$-0.490148\pi$
$107$	75819.8			0.0618916			0.0309458	+	0.999521i	$0.490148\pi$
$108$	1.28512e6			1.02017
$109$	−1.12474e6	+	1.12474e6i	−0.868509	+	0.868509i	−0.992307	−	0.123798i	$-0.960492\pi$
$109$	−1.12474e6	+	1.12474e6i	−0.868509	+	0.868509i	0.123798	+	0.992307i	$0.460492\pi$
$110$			1.84735e6i			1.38794i
$111$	182937.	−	2.42027e6i	0.133762	−	1.76968i
$112$	−598341.			−0.425887
$113$	1.23966e6	+	1.23966e6i	0.859149	+	0.859149i	0.991238	−	0.132089i	$-0.0421685\pi$
$113$	1.23966e6	+	1.23966e6i	0.859149	+	0.859149i	−0.132089	+	0.991238i	$0.542169\pi$
$114$		−	1.71769e6i		−	1.15939i
$115$		−	1.33237e6i		−	0.876054i
$116$	300392.	−	300392.i	0.192448	−	0.192448i
$117$	−799730.	+	799730.i	−0.499328	+	0.499328i
$118$	1.25831e6			0.765846
$119$	1.33705e6	−	1.33705e6i	0.793426	−	0.793426i
$120$	1.22022e6			0.706148
$121$	−3.61749e6			−2.04198
$122$		−	1.82350e6i		−	1.00421i
$123$	−973436.			−0.523109
$124$	−1.19937e6	+	1.19937e6i	−0.629057	+	0.629057i
$125$	1.13999e6	+	1.13999e6i	0.583677	+	0.583677i
$126$	3.66275e6	+	3.66275e6i	1.83103	+	1.83103i
$127$	27525.2			0.0134375			0.00671876	−	0.999977i	$-0.497861\pi$
$127$	27525.2			0.0134375			0.00671876	+	0.999977i	$0.497861\pi$
$128$	−131072.	+	131072.i	−0.0625000	+	0.0625000i
$129$	−1.54313e6	−	1.54313e6i	−0.718840	−	0.718840i
$130$	−406106.	+	406106.i	−0.184846	+	0.184846i
$131$	620017.	+	620017.i	0.275797	+	0.275797i	0.831429	−	0.555631i	$-0.187523\pi$
$131$	620017.	+	620017.i	0.275797	+	0.275797i	−0.555631	+	0.831429i	$0.687523\pi$
$132$			3.55961e6i			1.54768i
$133$	2.61823e6	−	2.61823e6i	1.11289	−	1.11289i
$134$	−502869.	+	502869.i	−0.208997	+	0.208997i
$135$	−3.99482e6	−	3.99482e6i	−1.62366	−	1.62366i
$136$		−	585785.i		−	0.232874i
$137$	3.33029e6			1.29515			0.647575	−	0.762001i	$-0.275783\pi$
$137$	3.33029e6			1.29515			0.647575	+	0.762001i	$0.275783\pi$
$138$		−	2.56730e6i		−	0.976876i
$139$		−	3.44670e6i		−	1.28339i	−0.766959	−	0.641696i	$-0.778231\pi$
$139$		−	3.44670e6i		−	1.28339i	0.766959	−	0.641696i	$-0.221769\pi$
$140$	1.85996e6	+	1.85996e6i	0.677826	+	0.677826i
$141$		−	8.63232e6i		−	3.07943i
$142$	−1.50739e6	−	1.50739e6i	−0.526454	−	0.526454i
$143$	−1.18468e6	−	1.18468e6i	−0.405129	−	0.405129i
$144$	1.60471e6			0.537416
$145$	−1.86755e6			−0.612587
$146$	652787.	−	652787.i	0.209755	−	0.209755i
$147$			1.07229e7i			3.37568i
$148$	122167.	−	1.61629e6i	0.0376852	−	0.498578i
$149$	−865567.			−0.261663			−0.130831	−	0.991405i	$-0.541765\pi$
$149$	−865567.			−0.261663			−0.130831	+	0.991405i	$0.541765\pi$
$150$	−798235.	−	798235.i	−0.236514	−	0.236514i
$151$			3.89833e6i			1.13226i	0.824315	+	0.566132i	$0.191561\pi$
$151$			3.89833e6i			1.13226i	−0.824315	+	0.566132i	$0.808439\pi$
$152$		−	1.14709e6i		−	0.326639i
$153$	−3.58588e6	+	3.58588e6i	−1.00120	+	1.00120i
$154$	−5.42582e6	+	5.42582e6i	−1.48560	+	1.48560i
$155$	7.45656e6			2.00237
$156$	−782512.	+	782512.i	−0.206119	+	0.206119i
$157$	−6.01870e6			−1.55526			−0.777631	−	0.628721i	$-0.783579\pi$
$157$	−6.01870e6			−1.55526			−0.777631	+	0.628721i	$0.783579\pi$
$158$	874984.			0.221834
$159$			4.06619e6i			1.01157i
$160$	814880.			0.198945
$161$	3.91327e6	−	3.91327e6i	0.937696	−	0.937696i
$162$	−3.12782e6	−	3.12782e6i	−0.735693	−	0.735693i
$163$	−1.57647e6	−	1.57647e6i	−0.364017	−	0.364017i	0.501272	−	0.865290i	$-0.332865\pi$
$163$	−1.57647e6	−	1.57647e6i	−0.364017	−	0.364017i	−0.865290	+	0.501272i	$0.832865\pi$
$164$	−650072.			−0.147377
$165$	1.10651e7	−	1.10651e7i	2.46322	−	2.46322i
$166$	1.72626e6	+	1.72626e6i	0.377383	+	0.377383i
$167$	−1.97250e6	+	1.97250e6i	−0.423514	+	0.423514i	−0.886412	−	0.462897i	$-0.846810\pi$
$167$	−1.97250e6	+	1.97250e6i	−0.423514	+	0.423514i	0.462897	+	0.886412i	$0.346810\pi$
$168$	3.58389e6	+	3.58389e6i	0.755835	+	0.755835i
$169$			4.30595e6i			0.892090i
$170$	−1.82092e6	+	1.82092e6i	−0.370634	+	0.370634i
$171$	−7.02192e6	+	7.02192e6i	−1.40433	+	1.40433i
$172$	−1.03052e6	−	1.03052e6i	−0.202521	−	0.202521i
$173$			2.54782e6i			0.492074i	0.969260	+	0.246037i	$0.0791285\pi$
$173$			2.54782e6i			0.492074i	−0.969260	+	0.246037i	$0.920871\pi$
$174$	−3.59852e6			−0.683087
$175$		−	2.43346e6i		−	0.454056i
$176$			2.37715e6i			0.436032i
$177$	−7.53691e6	−	7.53691e6i	−1.35917	−	1.35917i
$178$			4.63212e6i			0.821333i
$179$	3.78571e6	+	3.78571e6i	0.660067	+	0.660067i	0.955396	−	0.295328i	$-0.0954291\pi$
$179$	3.78571e6	+	3.78571e6i	0.660067	+	0.660067i	−0.295328	+	0.955396i	$0.595429\pi$
$180$	−4.98829e6	−	4.98829e6i	−0.855331	−	0.855331i
$181$	−365638.			−0.0616616			−0.0308308	−	0.999525i	$-0.509815\pi$
$181$	−365638.			−0.0616616			−0.0308308	+	0.999525i	$0.509815\pi$
$182$	−2.38553e6			−0.395704
$183$	−1.09222e7	+	1.09222e7i	−1.78221	+	1.78221i
$184$		−	1.71447e6i		−	0.275218i
$185$	−5.40402e6	+	4.64450e6i	−0.853496	+	0.733539i
$186$	1.43678e7			2.23281
$187$	−5.31196e6	−	5.31196e6i	−0.812325	−	0.812325i
$188$		−	5.76476e6i		−	0.867577i
$189$		−	2.34662e7i		−	3.47582i
$190$	−3.56576e6	+	3.56576e6i	−0.519866	+	0.519866i
$191$	2.17096e6	−	2.17096e6i	0.311567	−	0.311567i	−0.533949	−	0.845517i	$-0.679293\pi$
$191$	2.17096e6	−	2.17096e6i	0.311567	−	0.311567i	0.845517	+	0.533949i	$0.179293\pi$
$192$	1.57017e6			0.221841
$193$	−5.00770e6	+	5.00770e6i	−0.696573	+	0.696573i	−0.963670	−	0.267097i	$-0.913936\pi$
$193$	−5.00770e6	+	5.00770e6i	−0.696573	+	0.696573i	0.267097	+	0.963670i	$0.413936\pi$
$194$	−6.92467e6			−0.948405
$195$	4.86491e6			0.656102
$196$			7.16089e6i			0.951040i
$197$	1.16858e7			1.52847			0.764237	−	0.644936i	$-0.223116\pi$
$197$	1.16858e7			1.52847			0.764237	+	0.644936i	$0.223116\pi$
$198$	1.45517e7	−	1.45517e7i	1.87464	−	1.87464i
$199$	−5.16119e6	−	5.16119e6i	−0.654924	−	0.654924i	0.299251	−	0.954174i	$-0.403263\pi$
$199$	−5.16119e6	−	5.16119e6i	−0.654924	−	0.654924i	−0.954174	+	0.299251i	$0.903263\pi$
$200$	−533071.	−	533071.i	−0.0666339	−	0.0666339i
$201$	6.02408e6			0.741827
$202$	−2.05630e6	+	2.05630e6i	−0.249478	+	0.249478i
$203$	−5.48513e6	−	5.48513e6i	−0.655690	−	0.655690i
$204$	−3.50868e6	+	3.50868e6i	−0.413289	+	0.413289i
$205$	2.02076e6	+	2.02076e6i	0.234560	+	0.234560i
$206$			1.36511e6i			0.156158i
$207$	−1.04951e7	+	1.04951e7i	−1.18325	+	1.18325i
$208$	−522571.	+	522571.i	−0.0580705	+	0.0580705i
$209$	−1.04019e7	−	1.04019e7i	−1.13940	−	1.13940i
$210$		−	2.22812e7i		−	2.40592i
$211$	1.32797e7			1.41365			0.706825	−	0.707388i	$-0.250127\pi$
$211$	1.32797e7			1.41365			0.706825	+	0.707388i	$0.250127\pi$
$212$			2.71545e6i			0.284993i
$213$			1.80576e7i			1.86863i
$214$	−303279.	−	303279.i	−0.0309458	−	0.0309458i
$215$			6.40678e6i			0.644650i
$216$	−5.14048e6	−	5.14048e6i	−0.510085	−	0.510085i
$217$	2.19005e7	+	2.19005e7i	2.14326	+	2.14326i
$218$	8.99796e6			0.868509
$219$	−7.82001e6			−0.744517
$220$	7.38941e6	−	7.38941e6i	0.693972	−	0.693972i
$221$		−	2.33547e6i		−	0.216370i
$222$	−1.04128e7	+	8.94933e6i	−0.951721	+	0.817960i
$223$	1.23019e7			1.10932			0.554659	−	0.832078i	$-0.312849\pi$
$223$	1.23019e7			1.10932			0.554659	+	0.832078i	$0.312849\pi$
$224$	2.39336e6	+	2.39336e6i	0.212944	+	0.212944i
$225$			6.52639e6i			0.572961i
$226$		−	9.91731e6i		−	0.859149i
$227$	−1.21261e7	+	1.21261e7i	−1.03668	+	1.03668i	−0.0373797	+	0.999301i	$0.511901\pi$
$227$	−1.21261e7	+	1.21261e7i	−1.03668	+	1.03668i	−0.999301	+	0.0373797i	$0.988099\pi$
$228$	−6.87075e6	+	6.87075e6i	−0.579695	+	0.579695i
$229$	1.06403e7			0.886026			0.443013	−	0.896515i	$-0.353910\pi$
$229$	1.06403e7			0.886026			0.443013	+	0.896515i	$0.353910\pi$
$230$	−5.32947e6	+	5.32947e6i	−0.438027	+	0.438027i
$231$	6.49981e7			5.27309
$232$	−2.40313e6			−0.192448
$233$		−	2.08290e6i		−	0.164665i	−0.996605	−	0.0823326i	$-0.973763\pi$
$233$		−	2.08290e6i		−	0.164665i	0.996605	−	0.0823326i	$-0.0262370\pi$
$234$	6.39784e6			0.499328
$235$	−1.79199e7	+	1.79199e7i	−1.38080	+	1.38080i
$236$	−5.03324e6	−	5.03324e6i	−0.382923	−	0.382923i
$237$	−5.24090e6	−	5.24090e6i	−0.393696	−	0.393696i
$238$	−1.06964e7			−0.793426
$239$	1.20833e6	−	1.20833e6i	0.0885103	−	0.0885103i	−0.661465	−	0.749976i	$-0.730065\pi$
$239$	1.20833e6	−	1.20833e6i	0.0885103	−	0.0885103i	0.749976	+	0.661465i	$0.230065\pi$
$240$	−4.88089e6	−	4.88089e6i	−0.353074	−	0.353074i
$241$	−8.60535e6	+	8.60535e6i	−0.614777	+	0.614777i	−0.944187	−	0.329410i	$-0.893150\pi$
$241$	−8.60535e6	+	8.60535e6i	−0.614777	+	0.614777i	0.329410	+	0.944187i	$0.393150\pi$
$242$	1.44700e7	+	1.44700e7i	1.02099	+	1.02099i
$243$			8.19284e6i			0.570973i
$244$	−7.29400e6	+	7.29400e6i	−0.502107	+	0.502107i
$245$	2.22598e7	−	2.22598e7i	1.51364	−	1.51364i
$246$	3.89374e6	+	3.89374e6i	0.261554	+	0.261554i
$247$		−	4.57334e6i		−	0.303489i
$248$	9.59500e6			0.629057
$249$		−	2.06796e7i		−	1.33950i
$250$		−	9.11996e6i		−	0.583677i
$251$	−8.57273e6	−	8.57273e6i	−0.542123	−	0.542123i	0.382028	−	0.924151i	$-0.375226\pi$
$251$	−8.57273e6	−	8.57273e6i	−0.542123	−	0.542123i	−0.924151	+	0.382028i	$0.875226\pi$
$252$		−	2.93020e7i		−	1.83103i
$253$	−1.55470e7	−	1.55470e7i	−0.960031	−	0.960031i
$254$	−110101.	−	110101.i	−0.00671876	−	0.00671876i
$255$	2.18136e7			1.31555
$256$	1.04858e6			0.0625000
$257$	7.88320e6	−	7.88320e6i	0.464412	−	0.464412i	−0.435687	−	0.900098i	$-0.643494\pi$
$257$	7.88320e6	−	7.88320e6i	0.464412	−	0.464412i	0.900098	+	0.435687i	$0.143494\pi$
$258$			1.23450e7i			0.718840i
$259$	−2.95132e7	−	2.23077e6i	−1.69870	−	0.128397i
$260$	3.24885e6			0.184846
$261$	1.47108e7	+	1.47108e7i	0.827398	+	0.827398i
$262$		−	4.96014e6i		−	0.275797i
$263$			2.38221e7i			1.30952i	0.755836	+	0.654761i	$0.227231\pi$
$263$			2.38221e7i			1.30952i	−0.755836	+	0.654761i	$0.772769\pi$
$264$	1.42384e7	−	1.42384e7i	0.773838	−	0.773838i
$265$	8.44104e6	−	8.44104e6i	0.453585	−	0.453585i
$266$	−2.09458e7			−1.11289
$267$	2.77450e7	−	2.77450e7i	1.45764	−	1.45764i
$268$	4.02296e6			0.208997
$269$	2.57738e7			1.32410			0.662050	−	0.749460i	$-0.269687\pi$
$269$	2.57738e7			1.32410			0.662050	+	0.749460i	$0.269687\pi$
$270$			3.19586e7i			1.62366i
$271$	−3.04399e7			−1.52945			−0.764724	−	0.644358i	$-0.777125\pi$
$271$	−3.04399e7			−1.52945			−0.764724	+	0.644358i	$0.777125\pi$
$272$	−2.34314e6	+	2.34314e6i	−0.116437	+	0.116437i
$273$	1.42886e7	+	1.42886e7i	0.702267	+	0.702267i
$274$	−1.33212e7	−	1.33212e7i	−0.647575	−	0.647575i
$275$	−9.66788e6			−0.464872
$276$	−1.02692e7	+	1.02692e7i	−0.488438	+	0.488438i
$277$	−1.44072e7	−	1.44072e7i	−0.677859	−	0.677859i	0.281656	−	0.959515i	$-0.409116\pi$
$277$	−1.44072e7	−	1.44072e7i	−0.677859	−	0.677859i	−0.959515	+	0.281656i	$0.909116\pi$
$278$	−1.37868e7	+	1.37868e7i	−0.641696	+	0.641696i
$279$	−5.87358e7	−	5.87358e7i	−2.70452	−	2.70452i
$280$		−	1.48796e7i		−	0.677826i
$281$	7.31677e6	−	7.31677e6i	0.329762	−	0.329762i	−0.522734	−	0.852496i	$-0.675088\pi$
$281$	7.31677e6	−	7.31677e6i	0.329762	−	0.329762i	0.852496	+	0.522734i	$0.175088\pi$
$282$	−3.45293e7	+	3.45293e7i	−1.53971	+	1.53971i
$283$	−9.61950e6	−	9.61950e6i	−0.424417	−	0.424417i	0.462304	−	0.886721i	$-0.347023\pi$
$283$	−9.61950e6	−	9.61950e6i	−0.424417	−	0.424417i	−0.886721	+	0.462304i	$0.847023\pi$
$284$			1.20591e7i			0.526454i
$285$	4.27157e7			1.84524
$286$			9.47745e6i			0.405129i
$287$			1.18703e7i			0.502128i
$288$	−6.41886e6	−	6.41886e6i	−0.268708	−	0.268708i
$289$			1.36656e7i			0.566157i
$290$	7.47019e6	+	7.47019e6i	0.306294	+	0.306294i
$291$	4.14768e7	+	4.14768e7i	1.68316	+	1.68316i
$292$	−5.22230e6			−0.209755
$293$	−4.24413e7			−1.68727			−0.843637	−	0.536913i	$-0.819590\pi$
$293$	−4.24413e7			−1.68727			−0.843637	+	0.536913i	$0.819590\pi$
$294$	4.28917e7	−	4.28917e7i	1.68784	−	1.68784i
$295$			3.12919e7i			1.21889i
$296$	−6.95381e6	+	5.97647e6i	−0.268131	+	0.230446i
$297$	−9.32288e7			−3.55861
$298$	3.46227e6	+	3.46227e6i	0.130831	+	0.130831i
$299$		−	6.83544e6i		−	0.255713i
$300$			6.38588e6i			0.236514i
$301$	−1.88172e7	+	1.88172e7i	−0.690010	+	0.690010i
$302$	1.55933e7	−	1.55933e7i	0.566132	−	0.566132i
$303$	2.46333e7			0.885512
$304$	−4.58837e6	+	4.58837e6i	−0.163319	+	0.163319i
$305$	4.53471e7			1.59827
$306$	2.86871e7			1.00120
$307$		−	3.80818e7i		−	1.31614i	−0.752956	−	0.658070i	$-0.771373\pi$
$307$		−	3.80818e7i		−	1.31614i	0.752956	−	0.658070i	$-0.228627\pi$
$308$	4.34065e7			1.48560
$309$	8.17658e6	−	8.17658e6i	0.277138	−	0.277138i
$310$	−2.98262e7	−	2.98262e7i	−1.00118	−	1.00118i
$311$	−1.60757e6	−	1.60757e6i	−0.0534427	−	0.0534427i	0.679880	−	0.733323i	$-0.262032\pi$
$311$	−1.60757e6	−	1.60757e6i	−0.0534427	−	0.0534427i	−0.733323	+	0.679880i	$0.762032\pi$
$312$	6.26010e6			0.206119
$313$	−3.70086e7	+	3.70086e7i	−1.20690	+	1.20690i	−0.234868	+	0.972027i	$0.575466\pi$
$313$	−3.70086e7	+	3.70086e7i	−1.20690	+	1.20690i	−0.972027	+	0.234868i	$0.924534\pi$
$314$	2.40748e7	+	2.40748e7i	0.777631	+	0.777631i
$315$	−9.10857e7	+	9.10857e7i	−2.91420	+	2.91420i
$316$	−3.49993e6	−	3.49993e6i	−0.110917	−	0.110917i
$317$			2.84100e7i			0.891853i	0.895070	+	0.445926i	$0.147126\pi$
$317$			2.84100e7i			0.891853i	−0.895070	+	0.445926i	$0.852874\pi$
$318$	1.62648e7	−	1.62648e7i	0.505786	−	0.505786i
$319$	−2.17919e7	+	2.17919e7i	−0.671309	+	0.671309i
$320$	−3.25952e6	−	3.25952e6i	−0.0994727	−	0.0994727i
$321$			3.63311e6i			0.109841i
$322$	−3.13061e7			−0.937696
$323$		−	2.05063e7i		−	0.608526i
$324$			2.50226e7i			0.735693i
$325$	−2.12530e6	−	2.12530e6i	−0.0619114	−	0.0619114i
$326$			1.26117e7i			0.364017i
$327$	−5.38952e7	−	5.38952e7i	−1.54137	−	1.54137i
$328$	2.60029e6	+	2.60029e6i	0.0736885	+	0.0736885i
$329$	−1.05264e8			−2.95592
$330$	−8.85209e7			−2.46322
$331$	2.49851e7	−	2.49851e7i	0.688964	−	0.688964i	−0.273039	−	0.962003i	$-0.588029\pi$
$331$	2.49851e7	−	2.49851e7i	0.688964	−	0.688964i	0.962003	+	0.273039i	$0.0880288\pi$
$332$		−	1.38101e7i		−	0.377383i
$333$	7.91527e7	+	5.98278e6i	2.14355	+	0.162021i
$334$	1.57800e7			0.423514
$335$	−1.25054e7	−	1.25054e7i	−0.332632	−	0.332632i
$336$		−	2.86711e7i		−	0.755835i
$337$		−	2.50890e7i		−	0.655530i	−0.944759	−	0.327765i	$-0.893704\pi$
$337$		−	2.50890e7i		−	0.655530i	0.944759	−	0.327765i	$-0.106296\pi$
$338$	1.72238e7	−	1.72238e7i	0.446045	−	0.446045i
$339$	−5.94018e7	+	5.94018e7i	−1.52476	+	1.52476i
$340$	1.45674e7			0.370634
$341$	8.70084e7	−	8.70084e7i	2.19431	−	2.19431i
$342$	5.61754e7			1.40433
$343$	6.20130e7			1.53674
$344$			8.24415e6i			0.202521i
$345$	6.38440e7			1.55476
$346$	1.01913e7	−	1.01913e7i	0.246037	−	0.246037i
$347$	−2.63783e7	−	2.63783e7i	−0.631333	−	0.631333i	0.317069	−	0.948402i	$-0.397301\pi$
$347$	−2.63783e7	−	2.63783e7i	−0.631333	−	0.631333i	−0.948402	+	0.317069i	$0.897301\pi$
$348$	1.43941e7	+	1.43941e7i	0.341544	+	0.341544i
$349$	8.57236e6			0.201662			0.100831	−	0.994904i	$-0.467850\pi$
$349$	8.57236e6			0.201662			0.100831	+	0.994904i	$0.467850\pi$
$350$	−9.73383e6	+	9.73383e6i	−0.227028	+	0.227028i
$351$	−2.04946e7	−	2.04946e7i	−0.473934	−	0.473934i
$352$	9.50859e6	−	9.50859e6i	0.218016	−	0.218016i
$353$	3.50606e7	+	3.50606e7i	0.797069	+	0.797069i	0.982632	−	0.185564i	$-0.0594111\pi$
$353$	3.50606e7	+	3.50606e7i	0.797069	+	0.797069i	−0.185564	+	0.982632i	$0.559411\pi$
$354$			6.02953e7i			1.35917i
$355$	3.74860e7	−	3.74860e7i	0.837884	−	0.837884i
$356$	1.85285e7	−	1.85285e7i	0.410667	−	0.410667i
$357$	6.40683e7	+	6.40683e7i	1.40812	+	1.40812i
$358$		−	3.02857e7i		−	0.660067i
$359$	−6.23917e7			−1.34848			−0.674239	−	0.738513i	$-0.735528\pi$
$359$	−6.23917e7			−1.34848			−0.674239	+	0.738513i	$0.735528\pi$
$360$			3.99063e7i			0.855331i
$361$			6.89025e6i			0.146458i
$362$	1.46255e6	+	1.46255e6i	0.0308308	+	0.0308308i
$363$		−	1.73342e8i		−	3.62396i
$364$	9.54211e6	+	9.54211e6i	0.197852	+	0.197852i
$365$	1.62336e7	+	1.62336e7i	0.333839	+	0.333839i
$366$	8.73779e7			1.78221
$367$	−3.49273e6			−0.0706588			−0.0353294	−	0.999376i	$-0.511248\pi$
$367$	−3.49273e6			−0.0706588			−0.0353294	+	0.999376i	$0.511248\pi$
$368$	−6.85789e6	+	6.85789e6i	−0.137609	+	0.137609i
$369$		−	3.18353e7i		−	0.633622i
$370$	4.01941e7	+	3.03808e6i	0.793518	+	0.0599783i
$371$	4.95840e7			0.971000
$372$	−5.74713e7	−	5.74713e7i	−1.11641	−	1.11641i
$373$		−	6.33314e7i		−	1.22037i	−0.792258	−	0.610186i	$-0.791095\pi$
$373$		−	6.33314e7i		−	1.22037i	0.792258	−	0.610186i	$-0.208905\pi$
$374$			4.24957e7i			0.812325i
$375$	−5.46259e7	+	5.46259e7i	−1.03587	+	1.03587i
$376$	−2.30591e7	+	2.30591e7i	−0.433788	+	0.433788i
$377$	−9.58106e6			−0.178809
$378$	−9.38648e7	+	9.38648e7i	−1.73791	+	1.73791i
$379$	2.22223e7			0.408199			0.204100	−	0.978950i	$-0.434573\pi$
$379$	2.22223e7			0.408199			0.204100	+	0.978950i	$0.434573\pi$
$380$	2.85261e7			0.519866
$381$			1.31894e6i			0.0238480i
$382$	−1.73677e7			−0.311567
$383$	−4.35674e7	+	4.35674e7i	−0.775471	+	0.775471i	−0.979057	−	0.203586i	$-0.934740\pi$
$383$	−4.35674e7	+	4.35674e7i	−0.775471	+	0.775471i	0.203586	+	0.979057i	$0.434740\pi$
$384$	−6.28067e6	−	6.28067e6i	−0.110921	−	0.110921i
$385$	−1.34930e8	−	1.34930e8i	−2.36443	−	2.36443i
$386$	4.00616e7			0.696573
$387$	5.04666e7	−	5.04666e7i	0.870704	−	0.870704i
$388$	2.76987e7	+	2.76987e7i	0.474203	+	0.474203i
$389$	3.82239e7	−	3.82239e7i	0.649361	−	0.649361i	−0.303477	−	0.952839i	$-0.598148\pi$
$389$	3.82239e7	−	3.82239e7i	0.649361	−	0.649361i	0.952839	+	0.303477i	$0.0981477\pi$
$390$	−1.94596e7	−	1.94596e7i	−0.328051	−	0.328051i
$391$		−	3.06492e7i		−	0.512730i
$392$	2.86436e7	−	2.86436e7i	0.475520	−	0.475520i
$393$	−2.97098e7	+	2.97098e7i	−0.489465	+	0.489465i
$394$	−4.67430e7	−	4.67430e7i	−0.764237	−	0.764237i
$395$			2.17592e7i			0.353063i
$396$	−1.16414e8			−1.87464
$397$			7.53055e7i			1.20352i	0.798675	+	0.601762i	$0.205535\pi$
$397$			7.53055e7i			1.20352i	−0.798675	+	0.601762i	$0.794465\pi$
$398$			4.12895e7i			0.654924i
$399$	1.25459e8	+	1.25459e8i	1.97508	+	1.97508i
$400$			4.26457e6i			0.0666339i
$401$	1.97491e6	+	1.97491e6i	0.0306277	+	0.0306277i	0.722255	−	0.691627i	$-0.243106\pi$
$401$	1.97491e6	+	1.97491e6i	0.0306277	+	0.0306277i	−0.691627	+	0.722255i	$0.743106\pi$
$402$	−2.40963e7	−	2.40963e7i	−0.370914	−	0.370914i
$403$	3.82543e7			0.584474
$404$	1.64504e7			0.249478
$405$	7.77832e7	−	7.77832e7i	1.17090	−	1.17090i
$406$			4.38810e7i			0.655690i
$407$	−8.86261e6	+	1.17253e8i	−0.131455	+	1.73917i
$408$	2.80695e7			0.413289
$409$	5.22993e7	+	5.22993e7i	0.764409	+	0.764409i	0.977116	−	0.212707i	$-0.0682281\pi$
$409$	5.22993e7	+	5.22993e7i	0.764409	+	0.764409i	−0.212707	+	0.977116i	$0.568228\pi$
$410$		−	1.61661e7i		−	0.234560i
$411$			1.59580e8i			2.29854i
$412$	5.46042e6	−	5.46042e6i	0.0780790	−	0.0780790i
$413$	−9.19065e7	+	9.19065e7i	−1.30466	+	1.30466i
$414$	8.39612e7			1.18325
$415$	−4.29289e7	+	4.29289e7i	−0.600628	+	0.600628i
$416$	4.18057e6			0.0580705
$417$	1.65158e8			2.27767
$418$			8.32155e7i			1.13940i
$419$	−1.07204e8			−1.45737			−0.728685	−	0.684849i	$-0.759868\pi$
$419$	−1.07204e8			−1.45737			−0.728685	+	0.684849i	$0.759868\pi$
$420$	−8.91247e7	+	8.91247e7i	−1.20296	+	1.20296i
$421$	−1.70302e7	−	1.70302e7i	−0.228230	−	0.228230i	0.583723	−	0.811953i	$-0.301595\pi$
$421$	−1.70302e7	−	1.70302e7i	−0.228230	−	0.228230i	−0.811953	+	0.583723i	$0.801595\pi$
$422$	−5.31189e7	−	5.31189e7i	−0.706825	−	0.706825i
$423$	2.82312e8			3.73000
$424$	1.08618e7	−	1.08618e7i	0.142497	−	0.142497i
$425$	−9.52957e6	−	9.52957e6i	−0.124139	−	0.124139i
$426$	7.22306e7	−	7.22306e7i	0.934313	−	0.934313i
$427$	1.33188e8	+	1.33188e8i	1.71073	+	1.71073i
$428$			2.42624e6i			0.0309458i
$429$	5.67672e7	−	5.67672e7i	0.718995	−	0.718995i
$430$	2.56271e7	−	2.56271e7i	0.322325	−	0.322325i
$431$	−6.41397e7	−	6.41397e7i	−0.801116	−	0.801116i	0.182154	−	0.983270i	$-0.441693\pi$
$431$	−6.41397e7	−	6.41397e7i	−0.801116	−	0.801116i	−0.983270	+	0.182154i	$0.941693\pi$
$432$			4.11238e7i			0.510085i
$433$	3.07303e7			0.378533			0.189266	−	0.981926i	$-0.439389\pi$
$433$	3.07303e7			0.378533			0.189266	+	0.981926i	$0.439389\pi$
$434$		−	1.75204e8i		−	2.14326i
$435$		−	8.94886e7i		−	1.08718i
$436$	−3.59918e7	−	3.59918e7i	−0.434255	−	0.434255i
$437$		−	6.00176e7i		−	0.719175i
$438$	3.12800e7	+	3.12800e7i	0.372259	+	0.372259i
$439$	−4.71802e7	−	4.71802e7i	−0.557655	−	0.557655i	0.370984	−	0.928639i	$-0.379021\pi$
$439$	−4.71802e7	−	4.71802e7i	−0.557655	−	0.557655i	−0.928639	+	0.370984i	$0.879021\pi$
$440$	−5.91153e7			−0.693972
$441$	−3.50683e8			−4.08883
$442$	−9.34187e6	+	9.34187e6i	−0.108185	+	0.108185i
$443$		−	1.68600e7i		−	0.193931i	−0.995288	−	0.0969654i	$-0.969086\pi$
$443$		−	1.68600e7i		−	0.193931i	0.995288	−	0.0969654i	$-0.0309136\pi$
$444$	7.74487e7	+	5.85398e6i	0.884840	+	0.0668809i
$445$	−1.15192e8			−1.30720
$446$	−4.92074e7	−	4.92074e7i	−0.554659	−	0.554659i
$447$		−	4.14760e7i		−	0.464381i
$448$		−	1.91469e7i		−	0.212944i
$449$	−1.20944e7	+	1.20944e7i	−0.133612	+	0.133612i	−0.770750	−	0.637138i	$-0.780118\pi$
$449$	−1.20944e7	+	1.20944e7i	−0.133612	+	0.133612i	0.637138	+	0.770750i	$0.280118\pi$
$450$	2.61056e7	−	2.61056e7i	0.286481	−	0.286481i
$451$	4.71593e7			0.514089
$452$	−3.96692e7	+	3.96692e7i	−0.429574	+	0.429574i
$453$	−1.86799e8			−2.00946
$454$	9.70091e7			1.03668
$455$		−	5.93237e7i		−	0.629787i
$456$	5.49660e7			0.579695
$457$	−5.90150e7	+	5.90150e7i	−0.618321	+	0.618321i	−0.945101	−	0.326780i	$-0.894036\pi$
$457$	−5.90150e7	+	5.90150e7i	−0.618321	+	0.618321i	0.326780	+	0.945101i	$0.394036\pi$
$458$	−4.25611e7	−	4.25611e7i	−0.443013	−	0.443013i
$459$	−9.18950e7	−	9.18950e7i	−0.950285	−	0.950285i
$460$	4.26358e7			0.438027
$461$	1.01611e7	−	1.01611e7i	0.103714	−	0.103714i	−0.653346	−	0.757060i	$-0.726635\pi$
$461$	1.01611e7	−	1.01611e7i	0.103714	−	0.103714i	0.757060	+	0.653346i	$0.226635\pi$
$462$	−2.59993e8	−	2.59993e8i	−2.63654	−	2.63654i
$463$	−1.62689e7	+	1.62689e7i	−0.163914	+	0.163914i	−0.784298	−	0.620384i	$-0.786977\pi$
$463$	−1.62689e7	+	1.62689e7i	−0.163914	+	0.163914i	0.620384	+	0.784298i	$0.286977\pi$
$464$	9.61254e6	+	9.61254e6i	0.0962242	+	0.0962242i
$465$			3.57301e8i			3.55366i
$466$	−8.33162e6	+	8.33162e6i	−0.0823326	+	0.0823326i
$467$	6.98986e7	−	6.98986e7i	0.686306	−	0.686306i	−0.275108	−	0.961413i	$-0.588713\pi$
$467$	6.98986e7	−	6.98986e7i	0.686306	−	0.686306i	0.961413	+	0.275108i	$0.0887135\pi$
$468$	−2.55914e7	−	2.55914e7i	−0.249664	−	0.249664i
$469$		−	7.34588e7i		−	0.712075i
$470$	1.43359e8			1.38080
$471$		−	2.88402e8i		−	2.76017i
$472$			4.02659e7i			0.382923i
$473$	7.47587e7	+	7.47587e7i	0.706445	+	0.706445i
$474$			4.19272e7i			0.393696i
$475$	−1.86609e7	−	1.86609e7i	−0.174122	−	0.174122i
$476$	4.27856e7	+	4.27856e7i	0.396713	+	0.396713i
$477$	−1.32981e8			−1.22528
$478$	−9.66668e6			−0.0885103
$479$	6.31168e6	−	6.31168e6i	0.0574300	−	0.0574300i	−0.677809	−	0.735238i	$-0.737070\pi$
$479$	6.31168e6	−	6.31168e6i	0.0574300	−	0.0574300i	0.735238	+	0.677809i	$0.237070\pi$
$480$			3.90472e7i			0.353074i
$481$	−2.77242e7	+	2.38276e7i	−0.249128	+	0.214114i
$482$	6.88428e7			0.614777
$483$	1.87515e8	+	1.87515e8i	1.66416	+	1.66416i
$484$		−	1.15760e8i		−	1.02099i
$485$		−	1.72204e8i		−	1.50945i
$486$	3.27714e7	−	3.27714e7i	0.285487	−	0.285487i
$487$	5.25302e7	−	5.25302e7i	0.454802	−	0.454802i	−0.442143	−	0.896945i	$-0.645782\pi$
$487$	5.25302e7	−	5.25302e7i	0.454802	−	0.454802i	0.896945	+	0.442143i	$0.145782\pi$
$488$	5.83520e7			0.502107
$489$	7.55406e7	−	7.55406e7i	0.646032	−	0.646032i
$490$	−1.78078e8			−1.51364
$491$	−1.12092e8			−0.946959			−0.473480	−	0.880805i	$-0.657002\pi$
$491$	−1.12092e8			−0.946959			−0.473480	+	0.880805i	$0.657002\pi$
$492$		−	3.11499e7i		−	0.261554i
$493$	−4.29602e7			−0.358530
$494$	−1.82934e7	+	1.82934e7i	−0.151744	+	0.151744i
$495$	3.61874e8	+	3.61874e8i	2.98361	+	2.98361i
$496$	−3.83800e7	−	3.83800e7i	−0.314528	−	0.314528i
$497$	2.20198e8			1.79368
$498$	−8.27184e7	+	8.27184e7i	−0.669752	+	0.669752i
$499$	1.17680e8	+	1.17680e8i	0.947111	+	0.947111i	0.998670	−	0.0515592i	$-0.0164191\pi$
$499$	1.17680e8	+	1.17680e8i	0.947111	+	0.947111i	−0.0515592	+	0.998670i	$0.516419\pi$
$500$	−3.64798e7	+	3.64798e7i	−0.291839	+	0.291839i
$501$	−9.45177e7	−	9.45177e7i	−0.751623	−	0.751623i
$502$			6.85819e7i			0.542123i
$503$	−1.08461e8	+	1.08461e8i	−0.852259	+	0.852259i	−0.990411	−	0.138152i	$-0.955884\pi$
$503$	−1.08461e8	+	1.08461e8i	−0.852259	+	0.852259i	0.138152	+	0.990411i	$0.455884\pi$
$504$	−1.17208e8	+	1.17208e8i	−0.915514	+	0.915514i
$505$	−5.11364e7	−	5.11364e7i	−0.397060	−	0.397060i
$506$			1.24376e8i			0.960031i
$507$	−2.06331e8			−1.58322
$508$			880806.i			0.00671876i
$509$		−	1.02069e7i		−	0.0773997i	−0.999251	−	0.0386998i	$-0.987678\pi$
$509$		−	1.02069e7i		−	0.0773997i	0.999251	−	0.0386998i	$-0.0123216\pi$
$510$	−8.72545e7	−	8.72545e7i	−0.657775	−	0.657775i
$511$			9.53587e7i			0.714657i
$512$	−4.19430e6	−	4.19430e6i	−0.0312500	−	0.0312500i
$513$	−1.79950e8	−	1.79950e8i	−1.33291	−	1.33291i
$514$	−6.30656e7			−0.464412
$515$	−3.39477e7			−0.248535
$516$	4.93801e7	−	4.93801e7i	0.359420	−	0.359420i
$517$			4.18204e8i			3.02633i
$518$	1.09130e8	+	1.26976e8i	0.785153	+	0.913550i
$519$	−1.22086e8			−0.873299
$520$	−1.29954e7	−	1.29954e7i	−0.0924228	−	0.0924228i
$521$			6.32068e7i			0.446941i	0.974711	+	0.223471i	$0.0717387\pi$
$521$			6.32068e7i			0.446941i	−0.974711	+	0.223471i	$0.928261\pi$
$522$		−	1.17686e8i		−	0.827398i
$523$	−6.91679e7	+	6.91679e7i	−0.483504	+	0.483504i	−0.906249	−	0.422745i	$-0.861067\pi$
$523$	−6.91679e7	+	6.91679e7i	−0.483504	+	0.483504i	0.422745	+	0.906249i	$0.361067\pi$
$524$	−1.98405e7	+	1.98405e7i	−0.137899	+	0.137899i
$525$	1.16606e8			0.805827
$526$	9.52884e7	−	9.52884e7i	0.654761	−	0.654761i
$527$	1.71527e8			1.17193
$528$	−1.13907e8			−0.773838
$529$			5.83320e7i			0.394039i
$530$	−6.75283e7			−0.453585
$531$	2.46488e8	−	2.46488e8i	1.64631	−	1.64631i
$532$	8.37832e7	+	8.37832e7i	0.556445	+	0.556445i
$533$	1.03671e7	+	1.03671e7i	0.0684661	+	0.0684661i
$534$	−2.21960e8			−1.45764
$535$	7.54200e6	−	7.54200e6i	0.0492522	−	0.0492522i
$536$	−1.60918e7	−	1.60918e7i	−0.104499	−	0.104499i
$537$	−1.81402e8	+	1.81402e8i	−1.17144	+	1.17144i
$538$	−1.03095e8	−	1.03095e8i	−0.662050	−	0.662050i
$539$		−	5.19485e8i		−	3.31747i
$540$	1.27834e8	−	1.27834e8i	0.811832	−	0.811832i
$541$	2.50822e7	−	2.50822e7i	0.158407	−	0.158407i	−0.623454	−	0.781860i	$-0.714271\pi$
$541$	2.50822e7	−	2.50822e7i	0.158407	−	0.158407i	0.781860	+	0.623454i	$0.214271\pi$
$542$	1.21759e8	+	1.21759e8i	0.764724	+	0.764724i
$543$		−	1.75205e7i		−	0.109433i
$544$	1.87451e7			0.116437
$545$			2.23763e8i			1.38229i
$546$		−	1.14309e8i		−	0.702267i
$547$	4.60044e7	+	4.60044e7i	0.281085	+	0.281085i	0.833541	−	0.552457i	$-0.186310\pi$
$547$	4.60044e7	+	4.60044e7i	0.281085	+	0.281085i	−0.552457	+	0.833541i	$0.686310\pi$
$548$			1.06569e8i			0.647575i
$549$	−3.57202e8	−	3.57202e8i	−2.15872	−	2.15872i
$550$	3.86715e7	+	3.86715e7i	0.232436	+	0.232436i
$551$	−8.41252e7			−0.502888
$552$	8.21536e7			0.488438
$553$	−6.39085e7	+	6.39085e7i	−0.377906	+	0.377906i
$554$			1.15257e8i			0.677859i
$555$	−2.22554e8	−	2.58948e8i	−1.30183	−	1.51472i
$556$	1.10294e8			0.641696
$557$	2.92932e7	+	2.92932e7i	0.169512	+	0.169512i	0.786765	−	0.617253i	$-0.211754\pi$
$557$	2.92932e7	+	2.92932e7i	0.169512	+	0.169512i	−0.617253	+	0.786765i	$0.711754\pi$
$558$			4.69886e8i			2.70452i
$559$			3.28686e7i			0.188168i
$560$	−5.95186e7	+	5.95186e7i	−0.338913	+	0.338913i
$561$	2.54537e8	−	2.54537e8i	1.44166	−	1.44166i
$562$	−5.85341e7			−0.329762
$563$	−5.62286e7	+	5.62286e7i	−0.315088	+	0.315088i	−0.846877	−	0.531789i	$-0.821520\pi$
$563$	−5.62286e7	+	5.62286e7i	−0.315088	+	0.315088i	0.531789	+	0.846877i	$0.321520\pi$
$564$	2.76234e8			1.53971
$565$	2.46625e8			1.36739
$566$			7.69560e7i			0.424417i
$567$	4.56910e8			2.50658
$568$	4.82364e7	−	4.82364e7i	0.263227	−	0.263227i
$569$	1.11760e8	+	1.11760e8i	0.606664	+	0.606664i	0.942073	−	0.335409i	$-0.108874\pi$
$569$	1.11760e8	+	1.11760e8i	0.606664	+	0.606664i	−0.335409	+	0.942073i	$0.608874\pi$
$570$	−1.70863e8	−	1.70863e8i	−0.922621	−	0.922621i
$571$	8.49006e7			0.456039			0.228020	−	0.973657i	$-0.426775\pi$
$571$	8.49006e7			0.456039			0.228020	+	0.973657i	$0.426775\pi$
$572$	3.79098e7	−	3.79098e7i	0.202565	−	0.202565i
$573$	1.04027e8	+	1.04027e8i	0.552948	+	0.552948i
$574$	4.74811e7	−	4.74811e7i	0.251064	−	0.251064i
$575$	−2.78911e7	−	2.78911e7i	−0.146711	−	0.146711i
$576$			5.13509e7i			0.268708i
$577$	3.59998e7	−	3.59998e7i	0.187401	−	0.187401i	−0.607170	−	0.794572i	$-0.707695\pi$
$577$	3.59998e7	−	3.59998e7i	0.187401	−	0.187401i	0.794572	+	0.607170i	$0.207695\pi$
$578$	5.46626e7	−	5.46626e7i	0.283078	−	0.283078i
$579$	−2.39958e8	−	2.39958e8i	−1.23623	−	1.23623i
$580$		−	5.97615e7i		−	0.306294i
$581$	−2.52171e8			−1.28578
$582$		−	3.31814e8i		−	1.68316i
$583$		−	1.96992e8i		−	0.994129i
$584$	2.08892e7	+	2.08892e7i	0.104878	+	0.104878i
$585$			1.59103e8i			0.794711i
$586$	1.69765e8	+	1.69765e8i	0.843637	+	0.843637i
$587$	−1.53658e8	−	1.53658e8i	−0.759700	−	0.759700i	0.216568	−	0.976268i	$-0.430514\pi$
$587$	−1.53658e8	−	1.53658e8i	−0.759700	−	0.759700i	−0.976268	+	0.216568i	$0.930514\pi$
$588$	−3.43133e8			−1.68784
$589$	3.35887e8			1.64379
$590$	1.25167e8	−	1.25167e8i	0.609446	−	0.609446i
$591$			5.59954e8i			2.71263i
$592$	5.17211e7	+	3.90936e6i	0.249289	+	0.0188426i
$593$	1.68437e8			0.807742			0.403871	−	0.914816i	$-0.367664\pi$
$593$	1.68437e8			0.807742			0.403871	+	0.914816i	$0.367664\pi$
$594$	3.72915e8	+	3.72915e8i	1.77931	+	1.77931i
$595$		−	2.66000e8i		−	1.26279i
$596$		−	2.76981e7i		−	0.130831i
$597$	2.47312e8	−	2.47312e8i	1.16231	−	1.16231i
$598$	−2.73417e7	+	2.73417e7i	−0.127856	+	0.127856i
$599$	1.27445e8			0.592985			0.296493	−	0.955035i	$-0.404183\pi$
$599$	1.27445e8			0.592985			0.296493	+	0.955035i	$0.404183\pi$
$600$	2.55435e7	−	2.55435e7i	0.118257	−	0.118257i
$601$	5.04366e7			0.232339			0.116170	−	0.993229i	$-0.462938\pi$
$601$	5.04366e7			0.232339			0.116170	+	0.993229i	$0.462938\pi$
$602$	1.50537e8			0.690010
$603$			1.97012e8i			0.898548i
$604$	−1.24746e8			−0.566132
$605$	−3.59841e8	+	3.59841e8i	−1.62497	+	1.62497i
$606$	−9.85331e7	−	9.85331e7i	−0.442756	−	0.442756i
$607$	2.27693e8	+	2.27693e8i	1.01809	+	1.01809i	0.999833	+	0.0182524i	$0.00581025\pi$
$607$	2.27693e8	+	2.27693e8i	1.01809	+	1.01809i	0.0182524	+	0.999833i	$0.494190\pi$
$608$	3.67069e7			0.163319
$609$	2.62835e8	−	2.62835e8i	1.16367	−	1.16367i
$610$	−1.81388e8	−	1.81388e8i	−0.799134	−	0.799134i
$611$	−9.19342e7	+	9.19342e7i	−0.403045	+	0.403045i
$612$	−1.14748e8	−	1.14748e8i	−0.500601	−	0.500601i
$613$			3.32577e8i			1.44381i	0.691991	+	0.721906i	$0.256734\pi$
$613$			3.32577e8i			1.44381i	−0.691991	+	0.721906i	$0.743266\pi$
$614$	−1.52327e8	+	1.52327e8i	−0.658070	+	0.658070i
$615$	−9.68302e7	+	9.68302e7i	−0.416280	+	0.416280i
$616$	−1.73626e8	−	1.73626e8i	−0.742802	−	0.742802i
$617$		−	3.44563e8i		−	1.46694i	−0.679720	−	0.733472i	$-0.737899\pi$
$617$		−	3.44563e8i		−	1.46694i	0.679720	−	0.733472i	$-0.262101\pi$
$618$	−6.54127e7			−0.277138
$619$		−	2.47789e7i		−	0.104474i	−0.998635	−	0.0522372i	$-0.983365\pi$
$619$		−	2.47789e7i		−	0.104474i	0.998635	−	0.0522372i	$-0.0166352\pi$
$620$			2.38610e8i			1.00118i
$621$	−2.68958e8	−	2.68958e8i	−1.12308	−	1.12308i
$622$			1.28605e7i			0.0534427i
$623$	−3.38328e8	−	3.38328e8i	−1.39918	−	1.39918i
$624$	−2.50404e7	−	2.50404e7i	−0.103059	−	0.103059i
$625$	2.91869e8			1.19549
$626$	2.96069e8			1.20690
$627$	4.98437e8	−	4.98437e8i	2.02212	−	2.02212i
$628$		−	1.92598e8i		−	0.777631i
$629$	−1.24311e8	+	1.06840e8i	−0.499527	+	0.429320i
$630$	7.28686e8			2.91420
$631$	−1.32122e8	−	1.32122e8i	−0.525881	−	0.525881i	0.393461	−	0.919341i	$-0.371278\pi$
$631$	−1.32122e8	−	1.32122e8i	−0.525881	−	0.525881i	−0.919341	+	0.393461i	$0.871278\pi$
$632$			2.79995e7i			0.110917i
$633$			6.36334e8i			2.50885i
$634$	1.13640e8	−	1.13640e8i	0.445926	−	0.445926i
$635$	2.73800e6	−	2.73800e6i	0.0106933	−	0.0106933i
$636$	−1.30118e8			−0.505786
$637$	1.14199e8	−	1.14199e8i	0.441819	−	0.441819i
$638$	1.74335e8			0.671309
$639$	−5.90559e8			−2.26340
$640$			2.60762e7i			0.0994727i
$641$	−4.98476e8			−1.89265			−0.946325	−	0.323217i	$-0.895236\pi$
$641$	−4.98476e8			−1.89265			−0.946325	+	0.323217i	$0.895236\pi$
$642$	1.45324e7	−	1.45324e7i	0.0549204	−	0.0549204i
$643$	−1.16095e8	−	1.16095e8i	−0.436696	−	0.436696i	0.454203	−	0.890898i	$-0.349924\pi$
$643$	−1.16095e8	−	1.16095e8i	−0.436696	−	0.436696i	−0.890898	+	0.454203i	$0.849924\pi$
$644$	1.25225e8	+	1.25225e8i	0.468848	+	0.468848i
$645$	−3.06998e8			−1.14408
$646$	−8.20251e7	+	8.20251e7i	−0.304263	+	0.304263i
$647$	−1.18646e8	−	1.18646e8i	−0.438066	−	0.438066i	0.453295	−	0.891361i	$-0.350249\pi$
$647$	−1.18646e8	−	1.18646e8i	−0.438066	−	0.438066i	−0.891361	+	0.453295i	$0.850249\pi$
$648$	1.00090e8	−	1.00090e8i	0.367847	−	0.367847i
$649$	3.65135e8	+	3.65135e8i	1.33573	+	1.33573i
$650$			1.70024e7i			0.0619114i
$651$	−1.04942e9	+	1.04942e9i	−3.80370	+	3.80370i
$652$	5.04469e7	−	5.04469e7i	0.182009	−	0.182009i
$653$	−4.58717e7	−	4.58717e7i	−0.164742	−	0.164742i	0.619922	−	0.784664i	$-0.287164\pi$
$653$	−4.58717e7	−	4.58717e7i	−0.164742	−	0.164742i	−0.784664	+	0.619922i	$0.787164\pi$
$654$			4.31161e8i			1.54137i
$655$	1.23350e8			0.438948
$656$		−	2.08023e7i		−	0.0736885i
$657$		−	2.55746e8i		−	0.901806i
$658$	4.21057e8	+	4.21057e8i	1.47796	+	1.47796i
$659$			5.04763e7i			0.176373i	0.996104	+	0.0881863i	$0.0281071\pi$
$659$			5.04763e7i			0.176373i	−0.996104	+	0.0881863i	$0.971893\pi$
$660$	3.54083e8	+	3.54083e8i	1.23161	+	1.23161i
$661$	−5.55721e7	−	5.55721e7i	−0.192421	−	0.192421i	0.604320	−	0.796741i	$-0.293445\pi$
$661$	−5.55721e7	−	5.55721e7i	−0.192421	−	0.192421i	−0.796741	+	0.604320i	$0.793445\pi$
$662$	−1.99880e8			−0.688964
$663$	1.11910e8			0.383998
$664$	−5.52403e7	+	5.52403e7i	−0.188691	+	0.188691i
$665$		−	5.20884e8i		−	1.77123i
$666$	−2.92680e8	−	3.40542e8i	−0.990764	−	1.15278i
$667$	−1.25736e8			−0.423722
$668$	−6.31201e7	−	6.31201e7i	−0.211757	−	0.211757i
$669$			5.89476e8i			1.96874i
$670$			1.00044e8i			0.332632i
$671$	5.29142e8	−	5.29142e8i	1.75148	−	1.75148i
$672$	−1.14684e8	+	1.14684e8i	−0.377917	+	0.377917i
$673$	4.22585e8			1.38634			0.693168	−	0.720776i	$-0.256214\pi$
$673$	4.22585e8			1.38634			0.693168	+	0.720776i	$0.256214\pi$
$674$	−1.00356e8	+	1.00356e8i	−0.327765	+	0.327765i
$675$	−1.67251e8			−0.543823
$676$	−1.37790e8			−0.446045
$677$			1.97832e8i			0.637573i	0.947827	+	0.318786i	$0.103275\pi$
$677$			1.97832e8i			0.637573i	−0.947827	+	0.318786i	$0.896725\pi$
$678$	4.75214e8			1.52476
$679$	5.05776e8	−	5.05776e8i	1.61566	−	1.61566i
$680$	−5.82696e7	−	5.82696e7i	−0.185317	−	0.185317i
$681$	−5.81057e8	−	5.81057e8i	−1.83983	−	1.83983i
$682$	−6.96067e8			−2.19431
$683$	2.99117e8	−	2.99117e8i	0.938813	−	0.938813i	−0.0594199	−	0.998233i	$-0.518925\pi$
$683$	2.99117e8	−	2.99117e8i	0.938813	−	0.938813i	0.998233	+	0.0594199i	$0.0189251\pi$
$684$	−2.24702e8	−	2.24702e8i	−0.702163	−	0.702163i
$685$	3.31273e8	−	3.31273e8i	1.03066	−	1.03066i
$686$	−2.48052e8	−	2.48052e8i	−0.768370	−	0.768370i
$687$			5.09858e8i			1.57246i
$688$	3.29766e7	−	3.29766e7i	0.101261	−	0.101261i
$689$	4.33050e7	−	4.33050e7i	0.132398	−	0.132398i
$690$	−2.55376e8	−	2.55376e8i	−0.777379	−	0.777379i
$691$		−	4.48252e8i		−	1.35859i	−0.733866	−	0.679295i	$-0.762286\pi$
$691$		−	4.48252e8i		−	1.35859i	0.733866	−	0.679295i	$-0.237714\pi$
$692$	−8.15303e7			−0.246037
$693$			2.12570e9i			6.38709i
$694$			2.11026e8i			0.631333i
$695$	−3.42852e8	−	3.42852e8i	−1.02130	−	1.02130i
$696$		−	1.15153e8i		−	0.341544i
$697$	4.64847e7	+	4.64847e7i	0.137281	+	0.137281i
$698$	−3.42894e7	−	3.42894e7i	−0.100831	−	0.100831i
$699$	9.98080e7			0.292236
$700$	7.78707e7			0.227028
$701$	−3.85035e8	+	3.85035e8i	−1.11775	+	1.11775i	−0.125682	+	0.992071i	$0.540112\pi$
$701$	−3.85035e8	+	3.85035e8i	−1.11775	+	1.11775i	−0.992071	+	0.125682i	$0.959888\pi$
$702$			1.63957e8i			0.473934i
$703$	−2.43428e8	+	2.09215e8i	−0.700657	+	0.602181i
$704$	−7.60687e7			−0.218016
$705$	−8.58679e8	−	8.58679e8i	−2.45055	−	2.45055i
$706$		−	2.80485e8i		−	0.797069i
$707$		−	3.00383e8i		−	0.849996i
$708$	2.41181e8	−	2.41181e8i	0.679585	−	0.679585i
$709$	−1.62158e8	+	1.62158e8i	−0.454987	+	0.454987i	−0.897006	−	0.442019i	$-0.854262\pi$
$709$	−1.62158e8	+	1.62158e8i	−0.454987	+	0.454987i	0.442019	+	0.897006i	$0.354262\pi$
$710$	−2.99888e8			−0.837884
$711$	1.71399e8	−	1.71399e8i	0.476869	−	0.476869i
$712$	−1.48228e8			−0.410667
$713$	5.02025e8			1.38502
$714$		−	5.12546e8i		−	1.40812i
$715$	−2.35687e8			−0.644788
$716$	−1.21143e8	+	1.21143e8i	−0.330034	+	0.330034i
$717$	5.79006e7	+	5.79006e7i	0.157082	+	0.157082i
$718$	2.49567e8	+	2.49567e8i	0.674239	+	0.674239i
$719$	−2.28189e8			−0.613915			−0.306958	−	0.951723i	$-0.599311\pi$
$719$	−2.28189e8			−0.613915			−0.306958	+	0.951723i	$0.599311\pi$
$720$	1.59625e8	−	1.59625e8i	0.427665	−	0.427665i
$721$	−9.97068e7	−	9.97068e7i	−0.266023	−	0.266023i
$722$	2.75610e7	−	2.75610e7i	0.0732291	−	0.0732291i
$723$	−4.12348e8	−	4.12348e8i	−1.09106	−	1.09106i
$724$		−	1.17004e7i		−	0.0308308i
$725$	−3.90943e7	+	3.90943e7i	−0.102589	+	0.102589i
$726$	−6.93367e8	+	6.93367e8i	−1.81198	+	1.81198i
$727$	2.39344e8	+	2.39344e8i	0.622902	+	0.622902i	0.946273	−	0.323370i	$-0.104816\pi$
$727$	2.39344e8	+	2.39344e8i	0.622902	+	0.622902i	−0.323370	+	0.946273i	$0.604816\pi$
$728$		−	7.63369e7i		−	0.197852i
$729$	1.77463e8			0.458064
$730$		−	1.29869e8i		−	0.333839i
$731$			1.47378e8i			0.377296i
$732$	−3.49511e8	−	3.49511e8i	−0.891104	−	0.891104i
$733$		−	4.92138e8i		−	1.24961i	−0.780780	−	0.624805i	$-0.785178\pi$
$733$		−	4.92138e8i		−	1.24961i	0.780780	−	0.624805i	$-0.214822\pi$
$734$	1.39709e7	+	1.39709e7i	0.0353294	+	0.0353294i
$735$	1.06664e9	+	1.06664e9i	2.68630	+	2.68630i
$736$	5.48631e7			0.137609
$737$	−2.91844e8			−0.729036
$738$	−1.27341e8	+	1.27341e8i	−0.316811	+	0.316811i
$739$		−	1.39352e8i		−	0.345286i	−0.984984	−	0.172643i	$-0.944769\pi$
$739$		−	1.39352e8i		−	0.345286i	0.984984	−	0.172643i	$-0.0552306\pi$
$740$	−1.48624e8	−	1.72929e8i	−0.366770	−	0.426748i
$741$	2.19144e8			0.538611
$742$	−1.98336e8	−	1.98336e8i	−0.485500	−	0.485500i
$743$		−	3.18952e8i		−	0.777604i	−0.921321	−	0.388802i	$-0.872889\pi$
$743$		−	3.18952e8i		−	0.777604i	0.921321	−	0.388802i	$-0.127111\pi$
$744$			4.59770e8i			1.11641i
$745$	−8.61003e7	+	8.61003e7i	−0.208226	+	0.208226i
$746$	−2.53325e8	+	2.53325e8i	−0.610186	+	0.610186i
$747$	6.76307e8			1.62249
$748$	1.69983e8	−	1.69983e8i	0.406162	−	0.406162i
$749$	4.43029e7			0.105435
$750$	4.37007e8			1.03587
$751$		−	3.93490e8i		−	0.928996i	−0.885574	−	0.464498i	$-0.846235\pi$
$751$		−	3.93490e8i		−	0.928996i	0.885574	−	0.464498i	$-0.153765\pi$
$752$	1.84472e8			0.433788
$753$	4.10786e8	−	4.10786e8i	0.962122	−	0.962122i
$754$	3.83242e7	+	3.83242e7i	0.0894045	+	0.0894045i
$755$	3.87777e8	+	3.87777e8i	0.901034	+	0.901034i
$756$	7.50918e8			1.73791
$757$	9.19159e7	−	9.19159e7i	0.211886	−	0.211886i	−0.593182	−	0.805068i	$-0.702129\pi$
$757$	9.19159e7	−	9.19159e7i	0.211886	−	0.211886i	0.805068	+	0.593182i	$0.202129\pi$
$758$	−8.88894e7	−	8.88894e7i	−0.204100	−	0.204100i
$759$	7.44977e8	−	7.44977e8i	1.70380	−	1.70380i
$760$	−1.14104e8	−	1.14104e8i	−0.259933	−	0.259933i
$761$		−	3.19052e8i		−	0.723949i	−0.932188	−	0.361974i	$-0.882103\pi$
$761$		−	3.19052e8i		−	0.723949i	0.932188	−	0.361974i	$-0.117897\pi$
$762$	5.27578e6	−	5.27578e6i	0.0119240	−	0.0119240i
$763$	−6.57208e8	+	6.57208e8i	−1.47955	+	1.47955i
$764$	6.94708e7	+	6.94708e7i	0.155784	+	0.155784i
$765$			7.13395e8i			1.59348i
$766$	3.48539e8			0.775471
$767$			1.60536e8i			0.355784i
$768$			5.02453e7i			0.110921i
$769$	4.83459e8	+	4.83459e8i	1.06312	+	1.06312i	0.997869	+	0.0652467i	$0.0207834\pi$
$769$	4.83459e8	+	4.83459e8i	1.06312	+	1.06312i	0.0652467	+	0.997869i	$0.479217\pi$
$770$			1.07944e9i			2.36443i
$771$	3.77745e8	+	3.77745e8i	0.824205	+	0.824205i
$772$	−1.60247e8	−	1.60247e8i	−0.348287	−	0.348287i
$773$	−7.51538e8			−1.62709			−0.813547	−	0.581499i	$-0.802466\pi$
$773$	−7.51538e8			−1.62709			−0.813547	+	0.581499i	$0.802466\pi$
$774$	−4.03732e8			−0.870704
$775$	1.56092e8	−	1.56092e8i	0.335332	−	0.335332i
$776$		−	2.21589e8i		−	0.474203i
$777$	1.06893e8	−	1.41421e9i	0.227870	−	3.01474i
$778$	−3.05791e8			−0.649361
$779$	9.10269e7	+	9.10269e7i	0.192556	+	0.192556i
$780$			1.55677e8i			0.328051i
$781$		−	8.74826e8i		−	1.83640i
$782$	−1.22597e8	+	1.22597e8i	−0.256365	+	0.256365i
$783$	−3.76992e8	+	3.76992e8i	−0.785320	+	0.785320i
$784$	−2.29149e8			−0.475520
$785$	−5.98696e8	+	5.98696e8i	−1.23765	+	1.23765i
$786$	2.37678e8			0.489465
$787$	−6.40968e8			−1.31496			−0.657480	−	0.753472i	$-0.728377\pi$
$787$	−6.40968e8			−1.31496			−0.657480	+	0.753472i	$0.728377\pi$
$788$			3.73944e8i			0.764237i
$789$	−1.14150e9			−2.32405
$790$	8.70369e7	−	8.70369e7i	0.176532	−	0.176532i
$791$	7.24357e8	+	7.24357e8i	1.46360	+	1.46360i
$792$	4.65655e8	+	4.65655e8i	0.937321	+	0.937321i
$793$	2.32644e8			0.466521
$794$	3.01222e8	−	3.01222e8i	0.601762	−	0.601762i
$795$	4.04475e8	+	4.04475e8i	0.804990	+	0.804990i
$796$	1.65158e8	−	1.65158e8i	0.327462	−	0.327462i
$797$	3.11851e8	+	3.11851e8i	0.615988	+	0.615988i	0.944500	−	0.328511i	$-0.106547\pi$
$797$	3.11851e8	+	3.11851e8i	0.615988	+	0.615988i	−0.328511	+	0.944500i	$0.606547\pi$
$798$		−	1.00367e9i		−	1.97508i
$799$	−4.12221e8	+	4.12221e8i	−0.808145	+	0.808145i
$800$	1.70583e7	−	1.70583e7i	0.0333169	−	0.0333169i
$801$	9.07376e8	+	9.07376e8i	1.76559	+	1.76559i
$802$		−	1.57993e7i		−	0.0306277i
$803$	3.78850e8			0.731680
$804$			1.92771e8i			0.370914i
$805$		−	7.78526e8i		−	1.49240i
$806$	−1.53017e8	−	1.53017e8i	−0.292237	−	0.292237i
$807$			1.23502e9i			2.34992i
$808$	−6.58016e7	−	6.58016e7i	−0.124739	−	0.124739i
$809$	−2.08625e8	−	2.08625e8i	−0.394022	−	0.394022i	0.482096	−	0.876118i	$-0.339876\pi$
$809$	−2.08625e8	−	2.08625e8i	−0.394022	−	0.394022i	−0.876118	+	0.482096i	$0.839876\pi$
$810$	−6.22265e8			−1.17090
$811$	4.09701e8			0.768077			0.384039	−	0.923317i	$-0.374533\pi$
$811$	4.09701e8			0.768077			0.384039	+	0.923317i	$0.374533\pi$
$812$	1.75524e8	−	1.75524e8i	0.327845	−	0.327845i
$813$		−	1.45861e9i		−	2.71436i
$814$	5.04463e8	−	4.33562e8i	0.935311	−	0.803855i
$815$	−3.13631e8			−0.579356
$816$	−1.12278e8	−	1.12278e8i	−0.206644	−	0.206644i
$817$			2.88598e8i			0.529210i
$818$		−	4.18394e8i		−	0.764409i
$819$	−4.67296e8	+	4.67296e8i	−0.850630	+	0.850630i
$820$	−6.46644e7	+	6.46644e7i	−0.117280	+	0.117280i
$821$	1.57717e8			0.285003			0.142501	−	0.989795i	$-0.454486\pi$
$821$	1.57717e8			0.285003			0.142501	+	0.989795i	$0.454486\pi$
$822$	6.38319e8	−	6.38319e8i	1.14927	−	1.14927i
$823$	9.79212e7			0.175662			0.0878309	−	0.996135i	$-0.472006\pi$
$823$	9.79212e7			0.175662			0.0878309	+	0.996135i	$0.472006\pi$
$824$	−4.36834e7			−0.0780790
$825$		−	4.63262e8i		−	0.825021i
$826$	7.35252e8			1.30466
$827$	−9.55503e7	+	9.55503e7i	−0.168933	+	0.168933i	−0.786510	−	0.617577i	$-0.788114\pi$
$827$	−9.55503e7	+	9.55503e7i	−0.168933	+	0.168933i	0.617577	+	0.786510i	$0.288114\pi$
$828$	−3.35845e8	−	3.35845e8i	−0.591626	−	0.591626i
$829$	6.51713e8	+	6.51713e8i	1.14391	+	1.14391i	0.987728	+	0.156185i	$0.0499195\pi$
$829$	6.51713e8	+	6.51713e8i	1.14391	+	1.14391i	0.156185	+	0.987728i	$0.450080\pi$
$830$	3.43431e8			0.600628
$831$	6.90358e8	−	6.90358e8i	1.20302	−	1.20302i
$832$	−1.67223e7	−	1.67223e7i	−0.0290352	−	0.0290352i
$833$	5.12054e8	−	5.12054e8i	0.885891	−	0.885891i
$834$	−6.60632e8	−	6.60632e8i	−1.13884	−	1.13884i
$835$			3.92420e8i			0.674050i
$836$	3.32862e8	−	3.32862e8i	0.569699	−	0.569699i
$837$	1.50522e9	−	1.50522e9i	2.56698	−	2.56698i
$838$	4.28817e8	+	4.28817e8i	0.728685	+	0.728685i
$839$			8.63943e8i			1.46285i	0.681923	+	0.731424i	$0.261144\pi$
$839$			8.63943e8i			1.46285i	−0.681923	+	0.731424i	$0.738856\pi$
$840$	7.12998e8			1.20296
$841$		−	4.18583e8i		−	0.703709i
$842$			1.36241e8i			0.228230i
$843$	3.50602e8	+	3.50602e8i	0.585238	+	0.585238i
$844$			4.24952e8i			0.706825i
$845$	4.28324e8	+	4.28324e8i	0.709909	+	0.709909i
$846$	−1.12925e9	−	1.12925e9i	−1.86500	−	1.86500i
$847$	−2.11376e9			−3.47861
$848$	−8.68945e7			−0.142497
$849$	4.60944e8	−	4.60944e8i	0.753226	−	0.753226i
$850$			7.62366e7i			0.124139i
$851$	−3.63834e8	+	3.12698e8i	−0.590357	+	0.507384i
$852$	−5.77845e8			−0.934313
$853$	−4.81440e7	−	4.81440e7i	−0.0775703	−	0.0775703i	0.667257	−	0.744827i	$-0.267468\pi$
$853$	−4.81440e7	−	4.81440e7i	−0.0775703	−	0.0775703i	−0.744827	+	0.667257i	$0.767468\pi$
$854$		−	1.06550e9i		−	1.71073i
$855$			1.39698e9i			2.23507i
$856$	9.70494e6	−	9.70494e6i	0.0154729	−	0.0154729i
$857$	1.12023e8	−	1.12023e8i	0.177978	−	0.177978i	−0.612496	−	0.790474i	$-0.709834\pi$
$857$	1.12023e8	−	1.12023e8i	0.177978	−	0.177978i	0.790474	+	0.612496i	$0.209834\pi$
$858$	−4.54138e8			−0.718995
$859$	−4.46687e7	+	4.46687e7i	−0.0704731	+	0.0704731i	−0.741465	−	0.670992i	$-0.765869\pi$
$859$	−4.46687e7	+	4.46687e7i	−0.0704731	+	0.0704731i	0.670992	+	0.741465i	$0.265869\pi$
$860$	−2.05017e8			−0.322325
$861$	−5.68796e8			−0.891142
$862$			5.13118e8i			0.801116i
$863$	−1.54894e8			−0.240992			−0.120496	−	0.992714i	$-0.538449\pi$
$863$	−1.54894e8			−0.240992			−0.120496	+	0.992714i	$0.538449\pi$
$864$	1.64495e8	−	1.64495e8i	0.255042	−	0.255042i
$865$	2.53439e8	+	2.53439e8i	0.391584	+	0.391584i
$866$	−1.22921e8	−	1.22921e8i	−0.189266	−	0.189266i
$867$	−6.54826e8			−1.00477
$868$	−7.00816e8	+	7.00816e8i	−1.07163	+	1.07163i
$869$	2.53902e8	+	2.53902e8i	0.386907	+	0.386907i
$870$	−3.57954e8	+	3.57954e8i	−0.543588	+	0.543588i
$871$	−6.41565e7	−	6.41565e7i	−0.0970926	−	0.0970926i
$872$			2.87935e8i			0.434255i
$873$	−1.35646e9	+	1.35646e9i	−2.03875	+	2.03875i
$874$	−2.40071e8	+	2.40071e8i	−0.359588	+	0.359588i
$875$	6.66119e8	+	6.66119e8i	0.994323	+	0.994323i
$876$		−	2.50240e8i		−	0.372259i
$877$	−1.64303e8			−0.243583			−0.121792	−	0.992556i	$-0.538864\pi$
$877$	−1.64303e8			−0.243583			−0.121792	+	0.992556i	$0.538864\pi$
$878$			3.77441e8i			0.557655i
$879$		−	2.03369e9i		−	2.99446i
$880$	2.36461e8	+	2.36461e8i	0.346986	+	0.346986i
$881$		−	1.02031e9i		−	1.49212i	−0.665880	−	0.746059i	$-0.731944\pi$
$881$		−	1.02031e9i		−	1.49212i	0.665880	−	0.746059i	$-0.268056\pi$
$882$	1.40273e9	+	1.40273e9i	2.04442	+	2.04442i
$883$	−3.83520e8	−	3.83520e8i	−0.557065	−	0.557065i	0.371406	−	0.928471i	$-0.378876\pi$
$883$	−3.83520e8	−	3.83520e8i	−0.557065	−	0.557065i	−0.928471	+	0.371406i	$0.878876\pi$
$884$	7.47350e7			0.108185
$885$	−1.49943e9			−2.16320
$886$	−6.74401e7	+	6.74401e7i	−0.0969654	+	0.0969654i
$887$		−	6.20856e8i		−	0.889651i	−0.895617	−	0.444826i	$-0.853266\pi$
$887$		−	6.20856e8i		−	0.889651i	0.895617	−	0.444826i	$-0.146734\pi$
$888$	−2.86379e8	−	3.33211e8i	−0.408980	−	0.475861i
$889$	1.60835e7			0.0228915
$890$	4.60769e8	+	4.60769e8i	0.653602	+	0.653602i
$891$		−	1.81526e9i		−	2.56629i
$892$			3.93659e8i			0.554659i
$893$	−8.07216e8	+	8.07216e8i	−1.13354	+	1.13354i
$894$	−1.65904e8	+	1.65904e8i	−0.232190	+	0.232190i
$895$	7.53149e8			1.05054
$896$	−7.65877e7	+	7.65877e7i	−0.106472	+	0.106472i
$897$	3.27538e8			0.453821
$898$	9.67551e7			0.133612
$899$		−	7.03677e8i		−	0.968487i
$900$	−2.08844e8			−0.286481
$901$	1.94174e8	−	1.94174e8i	0.265470	−	0.265470i
$902$	−1.88637e8	−	1.88637e8i	−0.257044	−	0.257044i
$903$	−9.01676e8	−	9.01676e8i	−1.22458	−	1.22458i
$904$	3.17354e8			0.429574
$905$	−3.63709e7	+	3.63709e7i	−0.0490692	+	0.0490692i
$906$	7.47195e8	+	7.47195e8i	1.00473	+	1.00473i
$907$	2.57761e8	−	2.57761e8i	0.345458	−	0.345458i	−0.512957	−	0.858414i	$-0.671450\pi$
$907$	2.57761e8	−	2.57761e8i	0.345458	−	0.345458i	0.858414	+	0.512957i	$0.171450\pi$
$908$	−3.88037e8	−	3.88037e8i	−0.518340	−	0.518340i
$909$			8.05609e8i			1.07259i
$910$	−2.37295e8	+	2.37295e8i	−0.314894	+	0.314894i
$911$	−1.43651e8	+	1.43651e8i	−0.189999	+	0.189999i	−0.795696	−	0.605696i	$-0.792895\pi$
$911$	−1.43651e8	+	1.43651e8i	−0.189999	+	0.189999i	0.605696	+	0.795696i	$0.292895\pi$
$912$	−2.19864e8	−	2.19864e8i	−0.289847	−	0.289847i
$913$			1.00185e9i			1.31641i
$914$	4.72120e8			0.618321
$915$			2.17293e9i			2.83649i
$916$			3.40489e8i			0.443013i
$917$	3.62287e8	+	3.62287e8i	0.469834	+	0.469834i
$918$			7.35160e8i			0.950285i
$919$	9.40712e8	+	9.40712e8i	1.21202	+	1.21202i	0.970361	+	0.241660i	$0.0776918\pi$
$919$	9.40712e8	+	9.40712e8i	1.21202	+	1.21202i	0.241660	+	0.970361i	$0.422308\pi$
$920$	−1.70543e8	−	1.70543e8i	−0.219014	−	0.219014i
$921$	1.82479e9			2.33579
$922$	−8.12889e7			−0.103714
$923$	1.92314e8	−	1.92314e8i	0.244571	−	0.244571i
$924$			2.07994e9i			2.63654i
$925$	−1.58994e7	+	2.10350e8i	−0.0200889	+	0.265777i
$926$	1.30151e8			0.163914
$927$	2.67408e8	+	2.67408e8i	0.335687	+	0.335687i
$928$		−	7.69003e7i		−	0.0962242i
$929$		−	6.68787e8i		−	0.834143i	−0.908874	−	0.417072i	$-0.863056\pi$
$929$		−	6.68787e8i		−	0.834143i	0.908874	−	0.417072i	$-0.136944\pi$
$930$	1.42920e9	−	1.42920e9i	1.77683	−	1.77683i
$931$	1.00271e9	−	1.00271e9i	1.24259	−	1.24259i
$932$	6.66529e7			0.0823326
$933$	7.70309e7	−	7.70309e7i	0.0948463	−	0.0948463i
$934$	−5.59189e8			−0.686306
$935$	−1.05679e9			−1.29287
$936$			2.04731e8i			0.249664i
$937$	−1.11237e9			−1.35216			−0.676081	−	0.736827i	$-0.736323\pi$
$937$	−1.11237e9			−1.35216			−0.676081	+	0.736827i	$0.736323\pi$
$938$	−2.93835e8	+	2.93835e8i	−0.356037	+	0.356037i
$939$	−1.77337e9	−	1.77337e9i	−2.14191	−	2.14191i
$940$	−5.73436e8	−	5.73436e8i	−0.690401	−	0.690401i
$941$	1.48618e9			1.78362			0.891812	−	0.452406i	$-0.149434\pi$
$941$	1.48618e9			1.78362			0.891812	+	0.452406i	$0.149434\pi$
$942$	−1.15361e9	+	1.15361e9i	−1.38008	+	1.38008i
$943$	1.36051e8	+	1.36051e8i	0.162243	+	0.162243i
$944$	1.61064e8	−	1.61064e8i	0.191462	−	0.191462i
$945$	−2.33424e9	−	2.33424e9i	−2.76599	−	2.76599i
$946$		−	5.98070e8i		−	0.706445i
$947$	−6.35766e8	+	6.35766e8i	−0.748596	+	0.748596i	−0.974215	−	0.225620i	$-0.927559\pi$
$947$	−6.35766e8	+	6.35766e8i	−0.748596	+	0.748596i	0.225620	+	0.974215i	$0.427559\pi$
$948$	1.67709e8	−	1.67709e8i	0.196848	−	0.196848i
$949$	8.32831e7	+	8.32831e7i	0.0974447	+	0.0974447i
$950$			1.49287e8i			0.174122i
$951$	−1.36134e9			−1.58280
$952$		−	3.42284e8i		−	0.396713i
$953$			7.63640e8i			0.882288i	0.897436	+	0.441144i	$0.145427\pi$
$953$			7.63640e8i			0.882288i	−0.897436	+	0.441144i	$0.854573\pi$
$954$	5.31925e8	+	5.31925e8i	0.612639	+	0.612639i
$955$		−	4.31903e8i		−	0.495879i
$956$	3.86667e7	+	3.86667e7i	0.0442551	+	0.0442551i
$957$	−1.04422e9	−	1.04422e9i	−1.19139	−	1.19139i
$958$	−5.04935e7			−0.0574300
$959$	1.94595e9			2.20635
$960$	1.56189e8	−	1.56189e8i	0.176537	−	0.176537i
$961$			1.92207e9i			2.16570i
$962$	2.06207e8	+	1.55862e7i	0.231621	+	0.0175072i
$963$	−1.18818e8			−0.133046
$964$	−2.75371e8	−	2.75371e8i	−0.307388	−	0.307388i
$965$			9.96259e8i			1.10864i
$966$		−	1.50012e9i		−	1.66416i
$967$	−7.33020e8	+	7.33020e8i	−0.810656	+	0.810656i	−0.984732	−	0.174077i	$-0.944306\pi$
$967$	−7.33020e8	+	7.33020e8i	−0.810656	+	0.810656i	0.174077	+	0.984732i	$0.444306\pi$
$968$	−4.63039e8	+	4.63039e8i	−0.510495	+	0.510495i
$969$	9.82613e8			1.07997
$970$	−6.88815e8	+	6.88815e8i	−0.754723	+	0.754723i
$971$	−7.95210e8			−0.868609			−0.434304	−	0.900766i	$-0.643006\pi$
$971$	−7.95210e8			−0.868609			−0.434304	+	0.900766i	$0.643006\pi$
$972$	−2.62171e8			−0.285487
$973$		−	2.01397e9i		−	2.18632i
$974$	−4.20241e8			−0.454802
$975$	1.01840e8	−	1.01840e8i	0.109876	−	0.109876i
$976$	−2.33408e8	−	2.33408e8i	−0.251053	−	0.251053i
$977$	1.07884e8	+	1.07884e8i	0.115684	+	0.115684i	0.762579	−	0.646895i	$-0.223933\pi$
$977$	1.07884e8	+	1.07884e8i	0.115684	+	0.115684i	−0.646895	+	0.762579i	$0.723933\pi$
$978$	−6.04325e8			−0.646032
$979$	−1.34414e9	+	1.34414e9i	−1.43251	+	1.43251i
$980$	7.12313e8	+	7.12313e8i	0.756820	+	0.756820i
$981$	1.76259e9	−	1.76259e9i	1.86700	−	1.86700i
$982$	4.48369e8	+	4.48369e8i	0.473480	+	0.473480i
$983$		−	1.13574e8i		−	0.119569i	−0.998211	−	0.0597843i	$-0.980959\pi$
$983$		−	1.13574e8i		−	0.119569i	0.998211	−	0.0597843i	$-0.0190413\pi$
$984$	−1.24600e8	+	1.24600e8i	−0.130777	+	0.130777i
$985$	1.16241e9	−	1.16241e9i	1.21633	−	1.21633i
$986$	1.71841e8	+	1.71841e8i	0.179265	+	0.179265i
$987$		−	5.04401e9i		−	5.24596i
$988$	1.46347e8			0.151744
$989$			4.31347e8i			0.445900i
$990$		−	2.89499e9i		−	2.98361i
$991$	−6.93258e8	−	6.93258e8i	−0.712318	−	0.712318i	0.254702	−	0.967020i	$-0.418023\pi$
$991$	−6.93258e8	−	6.93258e8i	−0.712318	−	0.712318i	−0.967020	+	0.254702i	$0.918023\pi$
$992$			3.07040e8i			0.314528i
$993$	1.19723e9	+	1.19723e9i	1.22272	+	1.22272i
$994$	−8.80794e8	−	8.80794e8i	−0.896840	−	0.896840i
$995$	−1.02679e9			−1.04235
$996$	6.61747e8			0.669752
$997$	−1.03574e9	+	1.03574e9i	−1.04511	+	1.04511i	−0.0461798	+	0.998933i	$0.514705\pi$
$997$	−1.03574e9	+	1.03574e9i	−1.04511	+	1.04511i	−0.998933	+	0.0461798i	$0.985295\pi$
$998$		−	9.41439e8i		−	0.947111i
$999$	−1.53320e8	+	2.02844e9i	−0.153781	+	2.03454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.7.d.b.31.9	✓	20
37.6	odd	4	inner	74.7.d.b.43.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.7.d.b.31.9	✓	20	1.1	even	1	trivial
74.7.d.b.43.2	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)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 4.00000i) q^{2} +47.9177i q^{3} +32.0000i q^{4} +(99.4727 - 99.4727i) q^{5} +(191.671 - 191.671i) q^{6} +584.317 q^{7} +(128.000 - 128.000i) q^{8} -1567.10 q^{9} +O(q^{10})\)	\(q+(-4.00000 - 4.00000i) q^{2} +47.9177i q^{3} +32.0000i q^{4} +(99.4727 - 99.4727i) q^{5} +(191.671 - 191.671i) q^{6} +584.317 q^{7} +(128.000 - 128.000i) q^{8} -1567.10 q^{9} -795.781 q^{10} -2321.43i q^{11} -1533.37 q^{12} +(510.323 - 510.323i) q^{13} +(-2337.27 - 2337.27i) q^{14} +(4766.50 + 4766.50i) q^{15} -1024.00 q^{16} +(2288.22 - 2288.22i) q^{17} +(6268.42 + 6268.42i) q^{18} +(4480.83 - 4480.83i) q^{19} +(3183.12 + 3183.12i) q^{20} +27999.1i q^{21} +(-9285.73 + 9285.73i) q^{22} +(6697.16 - 6697.16i) q^{23} +(6133.46 + 6133.46i) q^{24} -4164.62i q^{25} -4082.59 q^{26} -40160.0i q^{27} +18698.2i q^{28} +(-9387.24 - 9387.24i) q^{29} -38132.0i q^{30} +(37480.5 + 37480.5i) q^{31} +(4096.00 + 4096.00i) q^{32} +111238. q^{33} -18305.8 q^{34} +(58123.6 - 58123.6i) q^{35} -50147.3i q^{36} +(-50508.9 - 3817.73i) q^{37} -35846.6 q^{38} +(24453.5 + 24453.5i) q^{39} -25465.0i q^{40} +20314.8i q^{41} +(111997. - 111997. i) q^{42} +(-32203.7 + 32203.7i) q^{43} +74285.9 q^{44} +(-155884. + 155884. i) q^{45} -53577.3 q^{46} -180149. q^{47} -49067.7i q^{48} +223778. q^{49} +(-16658.5 + 16658.5i) q^{50} +(109646. + 109646. i) q^{51} +(16330.3 + 16330.3i) q^{52} +84857.9 q^{53} +(-160640. + 160640. i) q^{54} +(-230919. - 230919. i) q^{55} +(74792.6 - 74792.6i) q^{56} +(214711. + 214711. i) q^{57} +75098.0i q^{58} +(-157289. + 157289. i) q^{59} +(-152528. + 152528. i) q^{60} +(227937. + 227937. i) q^{61} -299844. i q^{62} -915686. q^{63} -32768.0i q^{64} -101526. i q^{65} +(-444951. - 444951. i) q^{66} -125717. i q^{67} +(73223.1 + 73223.1i) q^{68} +(320912. + 320912. i) q^{69} -464989. q^{70} +376847. q^{71} +(-200589. + 200589. i) q^{72} +163197. i q^{73} +(186765. + 217307. i) q^{74} +199559. q^{75} +(143386. + 143386. i) q^{76} -1.35645e6i q^{77} -195628. i q^{78} +(-109373. + 109373. i) q^{79} +(-101860. + 101860. i) q^{80} +781955. q^{81} +(81259.0 - 81259.0i) q^{82} -431565. q^{83} -895972. q^{84} -455231. i q^{85} +257630. q^{86} +(449815. - 449815. i) q^{87} +(-297143. - 297143. i) q^{88} +(-579015. - 579015. i) q^{89} +1.24707e6 q^{90} +(298191. - 298191. i) q^{91} +(214309. + 214309. i) q^{92} +(-1.79598e6 + 1.79598e6i) q^{93} +(720596. + 720596. i) q^{94} -891440. i q^{95} +(-196271. + 196271. i) q^{96} +(865584. - 865584. i) q^{97} +(-895112. - 895112. i) q^{98} +3.63793e6i 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more