LMFDB - Embedded newform 22.5.d.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,5,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, 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:	$2.27413918784$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.1
Root			$0.809017 + 5.77971i$ of defining polynomial
Character	$\chi$	$=$	22.13
Dual form			22.5.d.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68999 - 0.874032i) q^{2} +(-3.20187 + 2.32629i) q^{3} +(6.47214 + 4.70228i) q^{4} +(13.3838 + 41.1910i) q^{5} +(10.6463 - 3.45918i) q^{6} +(-7.80030 + 10.7362i) q^{7} +(-13.3001 - 18.3060i) q^{8} +(-20.1901 + 62.1386i) q^{9} +O(q^{10})$	\(q+(-2.68999 - 0.874032i) q^{2} +(-3.20187 + 2.32629i) q^{3} +(6.47214 + 4.70228i) q^{4} +(13.3838 + 41.1910i) q^{5} +(10.6463 - 3.45918i) q^{6} +(-7.80030 + 10.7362i) q^{7} +(-13.3001 - 18.3060i) q^{8} +(-20.1901 + 62.1386i) q^{9} -122.501i q^{10} +(90.5882 - 80.2170i) q^{11} -31.6618 q^{12} +(-170.407 - 55.3685i) q^{13} +(30.3665 - 22.0626i) q^{14} +(-138.675 - 100.754i) q^{15} +(19.7771 + 60.8676i) q^{16} +(167.901 - 54.5543i) q^{17} +(108.622 - 149.506i) q^{18} +(213.240 + 293.500i) q^{19} +(-107.070 + 329.528i) q^{20} -52.5217i q^{21} +(-313.794 + 136.606i) q^{22} +564.946 q^{23} +(85.1701 + 27.6734i) q^{24} +(-1011.94 + 735.215i) q^{25} +(409.999 + 297.882i) q^{26} +(-178.970 - 550.813i) q^{27} +(-100.969 + 32.8069i) q^{28} +(505.658 - 695.978i) q^{29} +(284.974 + 392.233i) q^{30} +(276.141 - 849.875i) q^{31} -181.019i q^{32} +(-103.443 + 467.579i) q^{33} -499.334 q^{34} +(-546.632 - 177.611i) q^{35} +(-422.866 + 307.230i) q^{36} +(-164.418 - 119.457i) q^{37} +(-317.087 - 975.892i) q^{38} +(674.423 - 219.133i) q^{39} +(576.036 - 792.845i) q^{40} +(1540.12 + 2119.80i) q^{41} +(-45.9056 + 141.283i) q^{42} -2603.62i q^{43} +(963.502 - 93.2040i) q^{44} -2829.77 q^{45} +(-1519.70 - 493.780i) q^{46} +(-1250.87 + 908.812i) q^{47} +(-204.920 - 148.883i) q^{48} +(687.529 + 2116.00i) q^{49} +(3364.70 - 1093.26i) q^{50} +(-410.687 + 565.262i) q^{51} +(-842.537 - 1159.65i) q^{52} +(-454.551 + 1398.97i) q^{53} +1638.11i q^{54} +(4516.63 + 2657.81i) q^{55} +300.281 q^{56} +(-1365.53 - 443.689i) q^{57} +(-1968.52 + 1430.22i) q^{58} +(3977.33 + 2889.70i) q^{59} +(-423.754 - 1304.18i) q^{60} +(-1508.75 + 490.221i) q^{61} +(-1485.64 + 2044.80i) q^{62} +(-509.644 - 701.464i) q^{63} +(-158.217 + 486.941i) q^{64} -7760.26i q^{65} +(686.941 - 1167.37i) q^{66} -3004.99 q^{67} +(1343.21 + 436.434i) q^{68} +(-1808.88 + 1314.23i) q^{69} +(1315.20 + 955.547i) q^{70} +(-2625.89 - 8081.67i) q^{71} +(1406.04 - 456.849i) q^{72} +(2674.58 - 3681.24i) q^{73} +(337.875 + 465.045i) q^{74} +(1529.76 - 4708.12i) q^{75} +2902.29i q^{76} +(154.610 + 1598.29i) q^{77} -2005.72 q^{78} +(2009.88 + 653.050i) q^{79} +(-2242.51 + 1629.28i) q^{80} +(-2427.13 - 1763.41i) q^{81} +(-2290.15 - 7048.37i) q^{82} +(-8994.67 + 2922.55i) q^{83} +(246.972 - 339.927i) q^{84} +(4494.29 + 6185.86i) q^{85} +(-2275.65 + 7003.72i) q^{86} +3404.74i q^{87} +(-2673.28 - 591.414i) q^{88} +14557.2 q^{89} +(7612.06 + 2473.31i) q^{90} +(1923.67 - 1397.63i) q^{91} +(3656.40 + 2656.53i) q^{92} +(1092.89 + 3363.57i) q^{93} +(4159.17 - 1351.40i) q^{94} +(-9235.60 + 12711.7i) q^{95} +(421.104 + 579.600i) q^{96} +(2097.12 - 6454.28i) q^{97} -6292.94i q^{98} +(3155.59 + 7248.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−2.68999	−	0.874032i	−0.672499	−	0.218508i
$2$	−2.68999	−	0.874032i	−0.672499	−	0.218508i
$3$	−3.20187	+	2.32629i	−0.355763	+	0.258477i	−0.751283	−	0.659980i	$-0.770565\pi$
$3$	−3.20187	+	2.32629i	−0.355763	+	0.258477i	0.395520	+	0.918458i	$0.370565\pi$
$4$	6.47214	+	4.70228i	0.404508	+	0.293893i
$5$	13.3838	+	41.1910i	0.535350	+	1.64764i	0.742891	+	0.669413i	$0.233454\pi$
$5$	13.3838	+	41.1910i	0.535350	+	1.64764i	−0.207540	+	0.978226i	$0.566546\pi$
$6$	10.6463	−	3.45918i	0.295729	−	0.0960883i
$7$	−7.80030	+	10.7362i	−0.159190	+	0.219106i	−0.881160	−	0.472818i	$-0.843237\pi$
$7$	−7.80030	+	10.7362i	−0.159190	+	0.219106i	0.721970	+	0.691924i	$0.243237\pi$
$8$	−13.3001	−	18.3060i	−0.207813	−	0.286031i
$9$	−20.1901	+	62.1386i	−0.249260	+	0.767143i
$10$		−	122.501i		−	1.22501i
$11$	90.5882	−	80.2170i	0.748663	−	0.662951i
$11$	90.5882	−	80.2170i	0.748663	−	0.662951i
$12$	−31.6618			−0.219874
$13$	−170.407	−	55.3685i	−1.00832	−	0.327624i	−0.242137	−	0.970242i	$-0.577848\pi$
$13$	−170.407	−	55.3685i	−1.00832	−	0.327624i	−0.766187	+	0.642618i	$0.777848\pi$
$14$	30.3665	−	22.0626i	0.154931	−	0.112564i
$15$	−138.675	−	100.754i	−0.616335	−	0.447794i
$16$	19.7771	+	60.8676i	0.0772542	+	0.237764i
$17$	167.901	−	54.5543i	0.580972	−	0.188769i	−0.00376408	−	0.999993i	$-0.501198\pi$
$17$	167.901	−	54.5543i	0.580972	−	0.188769i	0.584736	+	0.811224i	$0.301198\pi$
$18$	108.622	−	149.506i	0.335254	−	0.461437i
$19$	213.240	+	293.500i	0.590693	+	0.813019i	0.994817	−	0.101685i	$-0.0324234\pi$
$19$	213.240	+	293.500i	0.590693	+	0.813019i	−0.404123	+	0.914704i	$0.632423\pi$
$20$	−107.070	+	329.528i	−0.267675	+	0.823820i
$21$		−	52.5217i		−	0.119097i
$22$	−313.794	+	136.606i	−0.648335	+	0.282244i
$23$	564.946			1.06795			0.533975	−	0.845500i	$-0.320698\pi$
$23$	564.946			1.06795			0.533975	+	0.845500i	$0.320698\pi$
$24$	85.1701	+	27.6734i	0.147865	+	0.0480442i
$25$	−1011.94	+	735.215i	−1.61910	+	1.17634i
$26$	409.999	+	297.882i	0.606508	+	0.440654i
$27$	−178.970	−	550.813i	−0.245501	−	0.755574i
$28$	−100.969	+	32.8069i	−0.128787	+	0.0418455i
$29$	505.658	−	695.978i	0.601258	−	0.827560i	−0.394565	−	0.918868i	$-0.629105\pi$
$29$	505.658	−	695.978i	0.601258	−	0.827560i	0.995823	+	0.0913079i	$0.0291048\pi$
$30$	284.974	+	392.233i	0.316638	+	0.435815i
$31$	276.141	−	849.875i	0.287348	−	0.884365i	−0.698338	−	0.715769i	$-0.746077\pi$
$31$	276.141	−	849.875i	0.287348	−	0.884365i	0.985685	−	0.168596i	$-0.0539234\pi$
$32$		−	181.019i		−	0.176777i
$33$	−103.443	+	467.579i	−0.0949893	+	0.429366i
$34$	−499.334			−0.431950
$35$	−546.632	−	177.611i	−0.446230	−	0.144989i
$36$	−422.866	+	307.230i	−0.326286	+	0.237060i
$37$	−164.418	−	119.457i	−0.120101	−	0.0872585i	0.526113	−	0.850415i	$-0.323649\pi$
$37$	−164.418	−	119.457i	−0.120101	−	0.0872585i	−0.646214	+	0.763156i	$0.723649\pi$
$38$	−317.087	−	975.892i	−0.219589	−	0.675826i
$39$	674.423	−	219.133i	0.443408	−	0.144072i
$40$	576.036	−	792.845i	0.360022	−	0.495528i
$41$	1540.12	+	2119.80i	0.916196	+	1.26103i	0.965006	+	0.262227i	$0.0844569\pi$
$41$	1540.12	+	2119.80i	0.916196	+	1.26103i	−0.0488107	+	0.998808i	$0.515543\pi$
$42$	−45.9056	+	141.283i	−0.0260236	+	0.0800924i
$43$		−	2603.62i		−	1.40812i	−0.710140	−	0.704061i	$-0.751368\pi$
$43$		−	2603.62i		−	1.40812i	0.710140	−	0.704061i	$-0.248632\pi$
$44$	963.502	−	93.2040i	0.497677	−	0.0481425i
$45$	−2829.77			−1.39742
$46$	−1519.70	−	493.780i	−0.718195	−	0.233356i
$47$	−1250.87	+	908.812i	−0.566262	+	0.411413i	−0.833745	−	0.552149i	$-0.813808\pi$
$47$	−1250.87	+	908.812i	−0.566262	+	0.411413i	0.267484	+	0.963562i	$0.413808\pi$
$48$	−204.920	−	148.883i	−0.0889408	−	0.0646193i
$49$	687.529	+	2116.00i	0.286351	+	0.881298i
$50$	3364.70	−	1093.26i	1.34588	−	0.437303i
$51$	−410.687	+	565.262i	−0.157896	+	0.217325i
$52$	−842.537	−	1159.65i	−0.311589	−	0.428866i
$53$	−454.551	+	1398.97i	−0.161820	+	0.498030i	−0.998788	−	0.0492218i	$-0.984326\pi$
$53$	−454.551	+	1398.97i	−0.161820	+	0.498030i	0.836968	+	0.547251i	$0.184326\pi$
$54$			1638.11i			0.561766i
$55$	4516.63	+	2657.81i	1.49310	+	0.878616i
$56$	300.281			0.0957528
$57$	−1365.53	−	443.689i	−0.420294	−	0.136562i
$58$	−1968.52	+	1430.22i	−0.585173	+	0.425153i
$59$	3977.33	+	2889.70i	1.14258	+	0.830135i	0.987477	−	0.157762i	$-0.0504280\pi$
$59$	3977.33	+	2889.70i	1.14258	+	0.830135i	0.155106	+	0.987898i	$0.450428\pi$
$60$	−423.754	−	1304.18i	−0.117709	−	0.362273i
$61$	−1508.75	+	490.221i	−0.405468	+	0.131745i	−0.504648	−	0.863325i	$-0.668378\pi$
$61$	−1508.75	+	490.221i	−0.405468	+	0.131745i	0.0991805	+	0.995069i	$0.468378\pi$
$62$	−1485.64	+	2044.80i	−0.386482	+	0.531946i
$63$	−509.644	−	701.464i	−0.128406	−	0.176736i
$64$	−158.217	+	486.941i	−0.0386271	+	0.118882i
$65$		−	7760.26i		−	1.83675i
$66$	686.941	−	1167.37i	0.157700	−	0.267992i
$67$	−3004.99			−0.669413			−0.334706	−	0.942323i	$-0.608637\pi$
$67$	−3004.99			−0.669413			−0.334706	+	0.942323i	$0.608637\pi$
$68$	1343.21	+	436.434i	0.290486	+	0.0943846i
$69$	−1808.88	+	1314.23i	−0.379937	+	0.276041i
$70$	1315.20	+	955.547i	0.268408	+	0.195010i
$71$	−2625.89	−	8081.67i	−0.520907	−	1.60319i	−0.772270	−	0.635295i	$-0.780879\pi$
$71$	−2625.89	−	8081.67i	−0.520907	−	1.60319i	0.251362	−	0.967893i	$-0.419121\pi$
$72$	1406.04	−	456.849i	0.271226	−	0.0881267i
$73$	2674.58	−	3681.24i	0.501891	−	0.690793i	−0.480635	−	0.876921i	$-0.659594\pi$
$73$	2674.58	−	3681.24i	0.501891	−	0.690793i	0.982526	+	0.186127i	$0.0595937\pi$
$74$	337.875	+	465.045i	0.0617011	+	0.0849243i
$75$	1529.76	−	4708.12i	0.271958	−	0.836999i
$76$			2902.29i			0.502474i
$77$	154.610	+	1598.29i	0.0260769	+	0.269572i
$78$	−2005.72			−0.329672
$79$	2009.88	+	653.050i	0.322045	+	0.104639i	0.465578	−	0.885007i	$-0.345846\pi$
$79$	2009.88	+	653.050i	0.322045	+	0.104639i	−0.143533	+	0.989645i	$0.545846\pi$
$80$	−2242.51	+	1629.28i	−0.350391	+	0.254574i
$81$	−2427.13	−	1763.41i	−0.369932	−	0.268772i
$82$	−2290.15	−	7048.37i	−0.340594	−	1.04824i
$83$	−8994.67	+	2922.55i	−1.30566	+	0.424234i	−0.877546	−	0.479493i	$-0.840821\pi$
$83$	−8994.67	+	2922.55i	−1.30566	+	0.424234i	−0.428111	+	0.903726i	$0.640821\pi$
$84$	246.972	−	339.927i	0.0350016	−	0.0481756i
$85$	4494.29	+	6185.86i	0.622047	+	0.856174i
$86$	−2275.65	+	7003.72i	−0.307686	+	0.946960i
$87$			3404.74i			0.449827i
$88$	−2673.28	−	591.414i	−0.345207	−	0.0763706i
$89$	14557.2			1.83779			0.918896	−	0.394499i	$-0.129082\pi$
$89$	14557.2			1.83779			0.918896	+	0.394499i	$0.129082\pi$
$90$	7612.06	+	2473.31i	0.939761	+	0.305347i
$91$	1923.67	−	1397.63i	0.232299	−	0.168775i
$92$	3656.40	+	2656.53i	0.431995	+	0.313863i
$93$	1092.89	+	3363.57i	0.126360	+	0.388897i
$94$	4159.17	−	1351.40i	0.470707	−	0.152942i
$95$	−9235.60	+	12711.7i	−1.02333	+	1.40850i
$96$	421.104	+	579.600i	0.0456927	+	0.0628906i
$97$	2097.12	−	6454.28i	0.222885	−	0.685969i	−0.775614	−	0.631207i	$-0.782560\pi$
$97$	2097.12	−	6454.28i	0.222885	−	0.685969i	0.998499	−	0.0547624i	$-0.0174401\pi$
$98$		−	6292.94i		−	0.655241i
$99$	3155.59	+	7248.61i	0.321966	+	0.739579i
$100$	−10006.6			−1.00066
$101$	−12997.2	−	4223.06i	−1.27411	−	0.413985i	−0.407611	−	0.913156i	$-0.633638\pi$
$101$	−12997.2	−	4223.06i	−1.27411	−	0.413985i	−0.866504	+	0.499171i	$0.833638\pi$
$102$	1598.80	−	1161.60i	0.153672	−	0.111649i
$103$	−995.164	−	723.029i	−0.0938038	−	0.0681524i	0.539895	−	0.841733i	$-0.318464\pi$
$103$	−995.164	−	723.029i	−0.0938038	−	0.0681524i	−0.633699	+	0.773580i	$0.718464\pi$
$104$	1252.85	+	3855.86i	0.115833	+	0.356496i
$105$	2163.42	−	702.937i	0.196228	−	0.0637585i
$106$	2445.48	−	3365.92i	0.217647	−	0.299565i
$107$	−4974.60	−	6846.95i	−0.434501	−	0.598040i	0.534478	−	0.845182i	$-0.320508\pi$
$107$	−4974.60	−	6846.95i	−0.434501	−	0.598040i	−0.968979	+	0.247143i	$0.920508\pi$
$108$	1431.76	−	4406.51i	0.122750	−	0.377787i
$109$			7648.65i			0.643771i	0.946779	+	0.321886i	$0.104317\pi$
$109$			7648.65i			0.643771i	−0.946779	+	0.321886i	$0.895683\pi$
$110$	−9826.69	−	11097.2i	−0.812123	−	0.917122i
$111$	804.338			0.0652819
$112$	−807.754	−	262.455i	−0.0643936	−	0.0209228i
$113$	7345.60	−	5336.89i	0.575269	−	0.417957i	−0.261747	−	0.965137i	$-0.584298\pi$
$113$	7345.60	−	5336.89i	0.575269	−	0.417957i	0.837015	+	0.547180i	$0.184298\pi$
$114$	3285.48	+	2387.04i	0.252807	+	0.183675i
$115$	7561.10	+	23270.7i	0.571728	+	1.75960i
$116$	6545.37	−	2126.72i	0.486428	−	0.158050i
$117$	6881.04	−	9470.94i	0.502670	−	0.691865i
$118$	−8173.31	−	11249.6i	−0.586994	−	0.807928i
$119$	−723.972	+	2228.16i	−0.0511243	+	0.157345i
$120$			3878.61i			0.269348i
$121$	1771.46	−	14533.4i	0.120993	−	0.992653i
$122$	4486.99			0.301464
$123$	−9862.55	−	3204.54i	−0.651897	−	0.211814i
$124$	5783.57	−	4202.01i	0.376143	−	0.273284i
$125$	−21928.3	−	15931.8i	−1.40341	−	1.01964i
$126$	757.836	+	2332.38i	0.0477347	+	0.146912i
$127$	−6550.78	+	2128.48i	−0.406149	+	0.131966i	−0.504965	−	0.863140i	$-0.668495\pi$
$127$	−6550.78	+	2128.48i	−0.406149	+	0.131966i	0.0988156	+	0.995106i	$0.468495\pi$
$128$	851.204	−	1171.58i	0.0519534	−	0.0715077i
$129$	6056.78	+	8336.44i	0.363967	+	0.500958i
$130$	−6782.72	+	20875.1i	−0.401344	+	1.23521i
$131$		−	1471.01i		−	0.0857182i	−0.999081	−	0.0428591i	$-0.986353\pi$
$131$		−	1471.01i		−	0.0857182i	0.999081	−	0.0428591i	$-0.0136467\pi$
$132$	−2868.19	+	2539.82i	−0.164611	+	0.145765i
$133$	−4814.41			−0.272170
$134$	8083.41	+	2626.46i	0.450179	+	0.146272i
$135$	20293.3	−	14743.9i	1.11348	−	0.808994i
$136$	−3231.76	−	2348.01i	−0.174728	−	0.126947i
$137$	5600.55	+	17236.7i	0.298394	+	0.918361i	0.982060	+	0.188567i	$0.0603841\pi$
$137$	5600.55	+	17236.7i	0.298394	+	0.918361i	−0.683667	+	0.729794i	$0.739616\pi$
$138$	6014.56	−	1954.25i	0.315824	−	0.102618i
$139$	5984.50	−	8236.96i	0.309741	−	0.426322i	−0.625559	−	0.780176i	$-0.715129\pi$
$139$	5984.50	−	8236.96i	0.309741	−	0.426322i	0.935300	+	0.353855i	$0.115129\pi$
$140$	−2702.70	−	3719.94i	−0.137893	−	0.189793i
$141$	1890.97	−	5819.79i	0.0951142	−	0.292731i
$142$			24034.8i			1.19196i
$143$	−19878.3	+	8653.78i	−0.972094	+	0.423189i
$144$	−4181.53			−0.201656
$145$	35435.6	+	11513.7i	1.68540	+	0.547621i
$146$	−10412.1	+	7564.84i	−0.488465	+	0.354890i
$147$	−7123.80	−	5175.75i	−0.329668	−	0.239518i
$148$	−502.418	−	1546.28i	−0.0229373	−	0.0705936i
$149$	−25251.0	+	8204.56i	−1.13738	+	0.369558i	−0.816377	−	0.577519i	$-0.804021\pi$
$149$	−25251.0	+	8204.56i	−1.13738	+	0.369558i	−0.321006	+	0.947077i	$0.604021\pi$
$150$	−8230.10	+	11327.8i	−0.365782	+	0.503456i
$151$	−11161.2	−	15362.0i	−0.489503	−	0.673744i	0.490793	−	0.871276i	$-0.336707\pi$
$151$	−11161.2	−	15362.0i	−0.489503	−	0.673744i	−0.980296	+	0.197533i	$0.936707\pi$
$152$	2536.69	−	7807.14i	0.109795	−	0.337913i
$153$			11534.6i			0.492741i
$154$	981.057	−	4434.52i	0.0413669	−	0.186984i
$155$	38703.0			1.61095
$156$	5395.39	+	1753.07i	0.221704	+	0.0720360i
$157$	2755.25	−	2001.81i	0.111779	−	0.0812124i	−0.530491	−	0.847690i	$-0.677993\pi$
$157$	2755.25	−	2001.81i	0.111779	−	0.0812124i	0.642271	+	0.766478i	$0.277993\pi$
$158$	−4835.78	−	3513.40i	−0.193710	−	0.140739i
$159$	−1798.99	−	5536.72i	−0.0711598	−	0.219007i
$160$	7456.36	−	2422.72i	0.291264	−	0.0946375i
$161$	−4406.74	+	6065.36i	−0.170007	+	0.233994i
$162$	4987.68	+	6864.95i	0.190050	+	0.261582i
$163$	2632.77	−	8102.84i	0.0990918	−	0.304973i	−0.889207	−	0.457506i	$-0.848743\pi$
$163$	2632.77	−	8102.84i	0.0990918	−	0.304973i	0.988298	+	0.152533i	$0.0487429\pi$
$164$			20961.7i			0.779362i
$165$	−20644.5	+	1997.04i	−0.758292	+	0.0733530i
$166$	26750.0			0.970751
$167$	12611.3	+	4097.65i	0.452196	+	0.146927i	0.526255	−	0.850327i	$-0.323596\pi$
$167$	12611.3	+	4097.65i	0.452196	+	0.146927i	−0.0740598	+	0.997254i	$0.523596\pi$
$168$	−961.460	+	698.541i	−0.0340653	+	0.0247499i
$169$	2866.45	+	2082.59i	0.100362	+	0.0729174i
$170$	−6682.97	−	20568.1i	−0.231245	−	0.711698i
$171$	−22543.0	+	7324.67i	−0.770939	+	0.250493i
$172$	12242.9	−	16851.0i	0.413837	−	0.569597i
$173$	−12984.4	−	17871.4i	−0.433839	−	0.597128i	0.534990	−	0.844858i	$-0.320315\pi$
$173$	−12984.4	−	17871.4i	−0.433839	−	0.597128i	−0.968829	+	0.247730i	$0.920315\pi$
$174$	2975.85	−	9158.72i	0.0982907	−	0.302508i
$175$		−	16599.2i		−	0.542016i
$176$	6674.19	+	3927.43i	0.215463	+	0.126790i
$177$	−19457.2			−0.621060
$178$	−39158.7	−	12723.4i	−1.23591	−	0.401572i
$179$	6760.86	−	4912.05i	0.211006	−	0.153305i	−0.477263	−	0.878761i	$-0.658371\pi$
$179$	6760.86	−	4912.05i	0.211006	−	0.153305i	0.688269	+	0.725456i	$0.258371\pi$
$180$	−18314.7	−	13306.4i	−0.565267	−	0.410691i
$181$	3111.80	+	9577.13i	0.0949848	+	0.292333i	0.987250	−	0.159179i	$-0.0508847\pi$
$181$	3111.80	+	9577.13i	0.0949848	+	0.292333i	−0.892265	+	0.451512i	$0.850885\pi$
$182$	−6396.23	+	2078.26i	−0.193100	+	0.0627419i
$183$	3690.41	−	5079.41i	0.110198	−	0.151674i
$184$	−7513.81	−	10341.9i	−0.221934	−	0.305466i
$185$	2720.01	−	8371.34i	0.0794744	−	0.244597i
$186$		−	10003.2i		−	0.289144i
$187$	10833.7	−	18410.5i	0.309808	−	0.526480i
$188$	−12369.3			−0.349969
$189$	7309.66	+	2375.05i	0.204632	+	0.0664890i
$190$	35954.1	−	26122.2i	0.995960	−	0.723607i
$191$	28569.5	+	20757.0i	0.783134	+	0.568980i	0.905918	−	0.423453i	$-0.139182\pi$
$191$	28569.5	+	20757.0i	0.783134	+	0.568980i	−0.122784	+	0.992433i	$0.539182\pi$
$192$	−626.178	−	1927.18i	−0.0169862	−	0.0522781i
$193$	−7441.19	+	2417.79i	−0.199769	+	0.0649088i	−0.407192	−	0.913342i	$-0.633492\pi$
$193$	−7441.19	+	2417.79i	−0.199769	+	0.0649088i	0.207424	+	0.978251i	$0.433492\pi$
$194$	−11282.5	+	15529.0i	−0.299780	+	0.412611i
$195$	18052.6	+	24847.3i	0.474757	+	0.653447i
$196$	−5500.23	+	16928.0i	−0.143175	+	0.440649i
$197$		−	1473.23i		−	0.0379610i	−0.999820	−	0.0189805i	$-0.993958\pi$
$197$		−	1473.23i		−	0.0379610i	0.999820	−	0.0189805i	$-0.00604205\pi$
$198$	−2153.00	−	22256.8i	−0.0549179	−	0.567718i
$199$	−26096.6			−0.658987			−0.329494	−	0.944158i	$-0.606878\pi$
$199$	−26096.6			−0.658987			−0.329494	+	0.944158i	$0.606878\pi$
$200$	26917.6	+	8746.07i	0.672941	+	0.218652i
$201$	9621.59	−	6990.49i	0.238152	−	0.173028i
$202$	31271.4	+	22720.0i	0.766381	+	0.556809i
$203$	3527.87	+	10857.7i	0.0856093	+	0.263478i
$204$	−5316.05	+	1727.29i	−0.127740	+	0.0415054i
$205$	−66704.0	+	91810.1i	−1.58725	+	2.18466i
$206$	2045.04	+	2814.75i	0.0481910	+	0.0663293i
$207$	−11406.3	+	35104.9i	−0.266197	+	0.819271i
$208$		−	11467.3i		−	0.265054i
$209$	42860.8	+	9482.15i	0.981222	+	0.217077i
$210$	−6433.97			−0.145895
$211$	−68859.0	−	22373.6i	−1.54666	−	0.502541i	−0.593458	−	0.804865i	$-0.702238\pi$
$211$	−68859.0	−	22373.6i	−1.54666	−	0.502541i	−0.953205	+	0.302323i	$0.902238\pi$
$212$	−9520.25	+	6916.86i	−0.211825	+	0.153900i
$213$	27208.1	+	19767.8i	0.599707	+	0.435713i
$214$	7397.20	+	22766.2i	0.161525	+	0.497123i
$215$	107246.	−	34846.2i	2.32008	−	0.753839i
$216$	−7702.86	+	10602.1i	−0.165099	+	0.227239i
$217$	6970.43	+	9593.98i	0.148027	+	0.203741i
$218$	6685.16	−	20574.8i	0.140669	−	0.432935i
$219$			18008.7i			0.375486i
$220$	16734.5	+	38440.2i	0.345753	+	0.794219i
$221$	−31632.0			−0.647653
$222$	−2163.66	−	703.017i	−0.0439020	−	0.0142646i
$223$	−22887.6	+	16628.8i	−0.460246	+	0.334388i	−0.793628	−	0.608404i	$-0.791810\pi$
$223$	−22887.6	+	16628.8i	−0.460246	+	0.334388i	0.333382	+	0.942792i	$0.391810\pi$
$224$	1943.46	+	1412.01i	0.0387328	+	0.0281410i
$225$	−25254.2	−	77724.3i	−0.498848	−	1.53530i
$226$	−24424.2	+	7935.92i	−0.478194	+	0.155375i
$227$	42352.4	−	58293.1i	0.821913	−	1.13127i	−0.167461	−	0.985879i	$-0.553557\pi$
$227$	42352.4	−	58293.1i	0.821913	−	1.13127i	0.989375	−	0.145388i	$-0.0464431\pi$
$228$	−6751.57	−	9292.74i	−0.129878	−	0.178762i
$229$	2762.09	−	8500.84i	0.0526704	−	0.162103i	−0.921261	−	0.388944i	$-0.872840\pi$
$229$	2762.09	−	8500.84i	0.0526704	−	0.162103i	0.973932	+	0.226841i	$0.0728399\pi$
$230$		−	69206.6i		−	1.30825i
$231$	−4213.13	−	4757.84i	−0.0789552	−	0.0891633i
$232$	−19465.8			−0.361657
$233$	46046.9	+	14961.6i	0.848182	+	0.275591i	0.700684	−	0.713472i	$-0.252878\pi$
$233$	46046.9	+	14961.6i	0.848182	+	0.275591i	0.147497	+	0.989062i	$0.452878\pi$
$234$	−26787.9	+	19462.5i	−0.489223	+	0.355441i
$235$	−54176.2	−	39361.3i	−0.981009	−	0.712745i
$236$	12153.6	+	37405.1i	0.218214	+	0.671594i
$237$	−7954.57	+	2584.59i	−0.141618	+	0.0460146i
$238$	3894.96	−	5360.95i	0.0687621	−	0.0946429i
$239$	−31831.6	−	43812.5i	−0.557266	−	0.767011i	0.433709	−	0.901053i	$-0.357204\pi$
$239$	−31831.6	−	43812.5i	−0.557266	−	0.767011i	−0.990976	+	0.134041i	$0.957204\pi$
$240$	3390.03	−	10433.4i	0.0588547	−	0.181136i
$241$		−	54166.9i		−	0.932610i	−0.884624	−	0.466305i	$-0.845585\pi$
$241$		−	54166.9i		−	0.932610i	0.884624	−	0.466305i	$-0.154415\pi$
$242$	−17467.9	+	37546.5i	−0.298270	+	0.641120i
$243$	58785.5			0.995537
$244$	−12070.0	−	3921.77i	−0.202734	−	0.0658723i
$245$	−77958.2	+	56640.0i	−1.29876	+	0.943606i
$246$	23729.3	+	17240.4i	0.392117	+	0.284890i
$247$	−20086.9	−	61821.2i	−0.329245	−	1.01331i
$248$	−19230.5	+	6248.36i	−0.312670	+	0.101593i
$249$	22001.0	−	30281.8i	0.354850	−	0.488409i
$250$	45062.0	+	62022.5i	0.720992	+	0.992360i
$251$	4416.42	−	13592.3i	0.0701008	−	0.215748i	−0.909868	−	0.414897i	$-0.863818\pi$
$251$	4416.42	−	13592.3i	0.0701008	−	0.215748i	0.979969	+	0.199149i	$0.0638177\pi$
$252$		−	6936.46i		−	0.109229i
$253$	51177.4	−	45318.2i	0.799535	−	0.707998i
$254$	19481.9			0.301970
$255$	−28780.2	−	9351.27i	−0.442603	−	0.143810i
$256$	−3313.73	+	2407.57i	−0.0505636	+	0.0367366i
$257$	31133.7	+	22619.9i	0.471372	+	0.342472i	0.797976	−	0.602689i	$-0.205904\pi$
$257$	31133.7	+	22619.9i	0.471372	+	0.342472i	−0.326604	+	0.945161i	$0.605904\pi$
$258$	−9006.38	−	27718.8i	−0.135304	−	0.416423i
$259$	2565.02	−	833.427i	0.0382377	−	0.0124242i
$260$	36490.9	−	50225.5i	0.539807	−	0.742980i
$261$	33037.8	+	45472.7i	0.484988	+	0.667528i
$262$	−1285.71	+	3957.01i	−0.0187301	+	0.0576454i
$263$			130054.i			1.88024i	0.340841	+	0.940121i	$0.389288\pi$
$263$			130054.i			1.88024i	−0.340841	+	0.940121i	$0.610712\pi$
$264$	9935.29	−	4325.20i	0.142552	−	0.0620581i
$265$	−63708.4			−0.907203
$266$	12950.7	+	4207.95i	0.183034	+	0.0594713i
$267$	−46610.1	+	33864.2i	−0.653819	+	0.475027i
$268$	−19448.7	−	14130.3i	−0.270783	−	0.196735i
$269$	−21831.7	−	67190.9i	−0.301705	−	0.928552i	−0.980886	−	0.194582i	$-0.937665\pi$
$269$	−21831.7	−	67190.9i	−0.301705	−	0.928552i	0.679182	−	0.733970i	$-0.262335\pi$
$270$	−67475.4	+	21924.1i	−0.925588	+	0.300742i
$271$	46867.1	−	64507.0i	0.638160	−	0.878352i	−0.360356	−	0.932815i	$-0.617345\pi$
$271$	46867.1	−	64507.0i	0.638160	−	0.878352i	0.998516	+	0.0544632i	$0.0173448\pi$
$272$	6641.18	+	9140.80i	0.0897651	+	0.123551i
$273$	−2908.05	+	8950.04i	−0.0390190	+	0.120088i
$274$		−	51261.7i		−	0.682798i
$275$	−32692.8	+	147776.i	−0.432301	+	1.95407i
$276$	−17887.2			−0.234814
$277$	42143.0	+	13693.1i	0.549245	+	0.178461i	0.570476	−	0.821314i	$-0.306759\pi$
$277$	42143.0	+	13693.1i	0.549245	+	0.178461i	−0.0212312	+	0.999775i	$0.506759\pi$
$278$	−23297.7	+	16926.7i	−0.301455	+	0.219020i
$279$	47234.7	+	34318.0i	0.606810	+	0.440874i
$280$	4018.89	+	12368.9i	0.0512613	+	0.157766i
$281$	74439.7	−	24186.9i	0.942740	−	0.306315i	0.202978	−	0.979183i	$-0.434938\pi$
$281$	74439.7	−	24186.9i	0.942740	−	0.306315i	0.739762	+	0.672868i	$0.234938\pi$
$282$	−10173.4	+	14002.4i	−0.127928	+	0.176078i
$283$	52782.1	+	72648.4i	0.659043	+	0.907095i	0.999449	−	0.0331832i	$-0.0105645\pi$
$283$	52782.1	+	72648.4i	0.659043	+	0.907095i	−0.340406	+	0.940279i	$0.610564\pi$
$284$	21007.2	−	64653.4i	0.260454	−	0.801594i
$285$		−	62185.9i		−	0.765601i
$286$	61036.3	−	5904.32i	0.746202	−	0.0721835i
$287$	−34772.0			−0.422149
$288$	11248.3	+	3654.79i	0.135613	+	0.0440634i
$289$	−42355.4	+	30773.0i	−0.507123	+	0.368446i
$290$	−85258.2	−	61943.7i	−1.01377	−	0.736549i
$291$	8299.84	+	25544.3i	0.0980131	+	0.301653i
$292$	34620.4	−	11248.9i	0.406038	−	0.131930i
$293$	12058.9	−	16597.6i	0.140466	−	0.193335i	−0.732988	−	0.680242i	$-0.761875\pi$
$293$	12058.9	−	16597.6i	0.140466	−	0.193335i	0.873454	+	0.486907i	$0.161875\pi$
$294$	14639.2	+	20149.2i	0.169365	+	0.233111i
$295$	−65798.0	+	202505.i	−0.756081	+	2.32698i
$296$			4598.62i			0.0524861i
$297$	−60397.2	−	35540.8i	−0.684706	−	0.402915i
$298$	75096.2			0.845640
$299$	−96270.5	−	31280.2i	−1.07684	−	0.349886i
$300$	32039.7	−	23278.2i	0.355997	−	0.258647i
$301$	27952.9	+	20309.0i	0.308528	+	0.224159i
$302$	16596.6	+	51079.0i	0.181972	+	0.560052i
$303$	51439.5	−	16713.7i	0.560289	−	0.182049i
$304$	−13647.4	+	18784.0i	−0.147673	+	0.203255i
$305$	−40385.4	−	55585.7i	−0.434135	−	0.597535i
$306$	10081.6	−	31028.0i	0.107668	−	0.331368i
$307$		−	133825.i		−	1.41991i	−0.704248	−	0.709954i	$-0.748716\pi$
$307$		−	133825.i		−	1.41991i	0.704248	−	0.709954i	$-0.251284\pi$
$308$	−6514.95	+	11071.4i	−0.0686768	+	0.116708i
$309$	4868.36			0.0509878
$310$	−104111.	−	33827.6i	−1.08336	−	0.352005i
$311$	−34207.5	+	24853.2i	−0.353672	+	0.256958i	−0.750408	−	0.660975i	$-0.770143\pi$
$311$	−34207.5	+	24853.2i	−0.353672	+	0.256958i	0.396736	+	0.917933i	$0.370143\pi$
$312$	−12981.3	−	9431.48i	−0.133355	−	0.0968882i
$313$	53394.1	+	164330.i	0.545011	+	1.67737i	0.720965	+	0.692972i	$0.243699\pi$
$313$	53394.1	+	164330.i	0.545011	+	1.67737i	−0.175954	+	0.984398i	$0.556301\pi$
$314$	−9161.25	+	2976.67i	−0.0929170	+	0.0301906i
$315$	22073.0	−	30380.9i	0.222455	−	0.306182i
$316$	9937.41	+	13677.7i	0.0995174	+	0.136974i
$317$	26059.8	−	80203.7i	0.259329	−	0.798134i	−0.733616	−	0.679564i	$-0.762169\pi$
$317$	26059.8	−	80203.7i	0.259329	−	0.798134i	0.992946	−	0.118570i	$-0.0378310\pi$
$318$			16466.1i			0.162831i
$319$	−10022.6	−	103610.i	−0.0984920	−	1.01817i
$320$	−22175.1			−0.216554
$321$	31856.1	+	10350.7i	0.309159	+	0.100452i
$322$	17155.4	−	12464.2i	0.165459	−	0.120213i
$323$	51814.9	+	37645.7i	0.496649	+	0.360837i
$324$	−7416.64	−	22826.1i	−0.0706508	−	0.217441i
$325$	213149.	−	69256.1i	2.01797	−	0.655679i
$326$	−14164.3	+	19495.5i	−0.133278	+	0.183442i
$327$	−17793.0	−	24490.0i	−0.166400	−	0.229030i
$328$	18321.2	−	56386.9i	0.170297	−	0.524120i
$329$		−	20518.6i		−	0.189564i
$330$	57279.1	+	12671.9i	0.525979	+	0.116363i
$331$	−130067.			−1.18717			−0.593583	−	0.804773i	$-0.702287\pi$
$331$	−130067.			−1.18717			−0.593583	+	0.804773i	$0.702287\pi$
$332$	−71957.4	−	23380.4i	−0.652828	−	0.212117i
$333$	10742.5	−	7804.89i	0.0968762	−	0.0703847i
$334$	−30342.8	−	22045.3i	−0.271996	−	0.197617i
$335$	−40218.1	−	123779.i	−0.358370	−	1.10295i
$336$	3196.87	−	1038.73i	0.0283169	−	0.00920073i
$337$	−48084.9	+	66183.1i	−0.423398	+	0.582757i	−0.966422	−	0.256960i	$-0.917279\pi$
$337$	−48084.9	+	66183.1i	−0.423398	+	0.582757i	0.543024	+	0.839717i	$0.317279\pi$
$338$	−5890.47	−	8107.53i	−0.0515604	−	0.0709668i
$339$	−11104.5	+	34176.1i	−0.0966270	+	0.297387i
$340$			61169.1i			0.529145i
$341$	−43159.3	−	99139.9i	−0.371164	−	0.852589i
$342$	67042.6			0.573190
$343$	−58384.0	−	18970.1i	−0.496256	−	0.161243i
$344$	−47661.7	+	34628.3i	−0.402766	+	0.292627i
$345$	−78344.0	−	56920.3i	−0.658215	−	0.478221i
$346$	19307.6	+	59422.8i	0.161279	+	0.496365i
$347$	−219762.	+	71404.9i	−1.82513	+	0.593019i	−0.825537	+	0.564348i	$0.809128\pi$
$347$	−219762.	+	71404.9i	−1.82513	+	0.593019i	−0.999589	+	0.0286715i	$0.990872\pi$
$348$	−16010.0	+	22035.9i	−0.132201	+	0.181959i
$349$	−7604.61	−	10466.9i	−0.0624347	−	0.0859340i	0.776658	−	0.629923i	$-0.216913\pi$
$349$	−7604.61	−	10466.9i	−0.0624347	−	0.0859340i	−0.839093	+	0.543989i	$0.816913\pi$
$350$	−14508.3	+	44651.9i	−0.118435	+	0.364505i
$351$			103772.i			0.842295i
$352$	−14520.8	−	16398.2i	−0.117194	−	0.132346i
$353$	59097.3			0.474262			0.237131	−	0.971478i	$-0.423793\pi$
$353$	59097.3			0.474262			0.237131	+	0.971478i	$0.423793\pi$
$354$	52339.7	+	17006.2i	0.417662	+	0.135707i
$355$	297748.	−	216326.i	2.36261	−	1.71654i
$356$	94215.9	+	68451.8i	0.743403	+	0.540114i
$357$	−2865.28	−	8818.43i	−0.0224818	−	0.0691918i
$358$	−22480.0	+	7304.18i	−0.175400	+	0.0569909i
$359$	−32828.5	+	45184.6i	−0.254720	+	0.350591i	−0.917157	−	0.398526i	$-0.869522\pi$
$359$	−32828.5	+	45184.6i	−0.254720	+	0.350591i	0.662438	+	0.749117i	$0.269522\pi$
$360$	37636.1	+	51801.7i	0.290402	+	0.399704i
$361$	−399.455	+	1229.40i	−0.00306517	+	0.00943361i
$362$		−	28482.2i		−	0.217349i
$363$	28137.1	+	50655.1i	0.213533	+	0.384423i
$364$	19022.3			0.143569
$365$	187430.	+	60899.6i	1.40687	+	0.457118i
$366$	−14366.7	+	10438.0i	−0.107250	+	0.0779215i
$367$	128062.	+	93042.3i	0.950796	+	0.690793i	0.950995	−	0.309207i	$-0.100063\pi$
$367$	128062.	+	93042.3i	0.950796	+	0.690793i	−0.000199318		1.00000i	$0.500063\pi$
$368$	11173.0	+	34386.9i	0.0825037	+	0.253920i
$369$	−162817.	+	52902.3i	−1.19577	+	0.388528i
$370$	−14633.6	+	20141.5i	−0.106893	+	0.147125i
$371$	−11473.9	−	15792.5i	−0.0833612	−	0.114737i
$372$	−8743.13	+	26908.6i	−0.0631802	+	0.194449i
$373$			133744.i			0.961297i	0.876913	+	0.480649i	$0.159599\pi$
$373$			133744.i			0.961297i	−0.876913	+	0.480649i	$0.840401\pi$
$374$	−45233.8	+	40055.1i	−0.323385	+	0.286362i
$375$	107274.			0.762834
$376$	33273.4	+	10811.2i	0.235354	+	0.0764710i
$377$	−124703.	+	90601.8i	−0.877391	+	0.637462i
$378$	−17587.1	−	12777.8i	−0.123086	−	0.0894274i
$379$	−16655.2	−	51259.4i	−0.115950	−	0.356858i	0.876194	−	0.481959i	$-0.160075\pi$
$379$	−16655.2	−	51259.4i	−0.115950	−	0.356858i	−0.992144	+	0.125101i	$0.960075\pi$
$380$	−119548.	+	38843.5i	−0.827895	+	0.269000i
$381$	16023.3	−	22054.1i	0.110383	−	0.151929i
$382$	−58709.6	−	80806.8i	−0.402330	−	0.553759i
$383$	15091.9	−	46448.1i	0.102884	−	0.316643i	−0.886344	−	0.463027i	$-0.846763\pi$
$383$	15091.9	−	46448.1i	0.102884	−	0.316643i	0.989228	+	0.146383i	$0.0467633\pi$
$384$			5731.40i			0.0388685i
$385$	−63765.9	+	27759.7i	−0.430196	+	0.187281i
$386$	22130.0			0.148527
$387$	161785.	+	52567.2i	1.08023	+	0.350988i
$388$	43922.7	−	31911.7i	0.291760	−	0.211976i
$389$	−221746.	−	161108.i	−1.46540	−	1.06468i	−0.981914	−	0.189329i	$-0.939369\pi$
$389$	−221746.	−	161108.i	−1.46540	−	1.06468i	−0.483491	−	0.875349i	$-0.660631\pi$
$390$	−26844.1	−	82617.7i	−0.176490	−	0.543180i
$391$	94854.8	−	30820.2i	0.620449	−	0.201596i
$392$	29591.2	−	40728.7i	0.192571	−	0.265051i
$393$	3422.00	+	4709.98i	0.0221562	+	0.0304954i
$394$	−1287.65	+	3962.98i	−0.00829479	+	0.0255287i
$395$			91529.3i			0.586632i
$396$	−13661.6	+	61752.5i	−0.0871187	+	0.393790i
$397$	49313.3			0.312884			0.156442	−	0.987687i	$-0.449998\pi$
$397$	49313.3			0.312884			0.156442	+	0.987687i	$0.449998\pi$
$398$	70199.6	+	22809.2i	0.443168	+	0.143994i
$399$	15415.1	−	11199.7i	0.0968280	−	0.0703496i
$400$	−64763.9	−	47053.7i	−0.404775	−	0.294086i
$401$	2341.63	+	7206.79i	0.0145623	+	0.0448181i	0.958074	−	0.286522i	$-0.0924992\pi$
$401$	2341.63	+	7206.79i	0.0145623	+	0.0448181i	−0.943511	+	0.331340i	$0.892499\pi$
$402$	−31991.9	+	10394.8i	−0.197965	+	0.0643227i
$403$	−94112.6	+	129535.i	−0.579479	+	0.797584i
$404$	−64261.9	−	88448.9i	−0.393723	−	0.541913i
$405$	40152.5	−	123577.i	0.244795	−	0.753402i
$406$		−	32290.6i		−	0.195895i
$407$	−24476.8	+	2367.76i	−0.147763	+	0.0142938i
$408$	15809.8			0.0949745
$409$	−13724.0	−	4459.20i	−0.0820417	−	0.0266570i	0.267709	−	0.963500i	$-0.413734\pi$
$409$	−13724.0	−	4459.20i	−0.0820417	−	0.0266570i	−0.349750	+	0.936843i	$0.613734\pi$
$410$	259678.	−	188667.i	1.54478	−	1.12235i
$411$	−58029.9	−	42161.2i	−0.343533	−	0.249591i
$412$	−3040.95	−	9359.09i	−0.0179149	−	0.0551365i
$413$	−62048.8	+	20160.9i	−0.363775	+	0.118198i
$414$	61365.7	−	84462.6i	0.358034	−	0.492792i
$415$	−240765.	−	331385.i	−1.39797	−	1.92414i
$416$	−10022.8	+	30846.9i	−0.0579163	+	0.178248i
$417$			40295.4i			0.231731i
$418$	−107007.	−	62968.6i	−0.612437	−	0.360389i
$419$	229500.			1.30724			0.653619	−	0.756824i	$-0.273250\pi$
$419$	229500.			1.30724			0.653619	+	0.756824i	$0.273250\pi$
$420$	17307.3	+	5623.50i	0.0981142	+	0.0318792i
$421$	−9854.14	+	7159.45i	−0.0555974	+	0.0403939i	−0.615237	−	0.788342i	$-0.710940\pi$
$421$	−9854.14	+	7159.45i	−0.0555974	+	0.0403939i	0.559639	+	0.828736i	$0.310940\pi$
$422$	165675.	+	120370.i	0.930320	+	0.675917i
$423$	−31217.1	−	96076.4i	−0.174467	−	0.536953i
$424$	31655.0	−	10285.3i	0.176080	−	0.0572119i
$425$	−129796.	+	178649.i	−0.718593	+	0.989058i
$426$	−55911.9	−	76956.1i	−0.308095	−	0.424057i
$427$	6505.56	−	20022.1i	0.0356803	−	0.109813i
$428$		−	67706.4i		−	0.369609i
$429$	43516.6	−	73951.1i	0.236451	−	0.401819i
$430$	−318947.			−1.72497
$431$	−40180.7	−	13055.5i	−0.216303	−	0.0702813i	0.198861	−	0.980028i	$-0.436276\pi$
$431$	−40180.7	−	13055.5i	−0.216303	−	0.0702813i	−0.415164	+	0.909747i	$0.636276\pi$
$432$	29987.2	−	21787.0i	0.160682	−	0.116743i
$433$	−53631.9	−	38965.8i	−0.286053	−	0.207830i	0.435500	−	0.900189i	$-0.356572\pi$
$433$	−53631.9	−	38965.8i	−0.286053	−	0.207830i	−0.721553	+	0.692359i	$0.756572\pi$
$434$	−10365.0	−	31900.1i	−0.0550287	−	0.169361i
$435$	−140244.	+	45568.2i	−0.741152	+	0.240815i
$436$	−35966.1	+	49503.1i	−0.189200	+	0.260411i
$437$	120469.	+	165812.i	0.630831	+	0.868264i
$438$	15740.2	−	48443.3i	0.0820467	−	0.252514i
$439$			212489.i			1.10257i	0.834316	+	0.551287i	$0.185863\pi$
$439$			212489.i			1.10257i	−0.834316	+	0.551287i	$0.814137\pi$
$440$	−11417.6	−	118030.i	−0.0589753	−	0.609661i
$441$	−145366.			−0.747457
$442$	85090.0	+	27647.4i	0.435546	+	0.141517i
$443$	289268.	−	210166.i	1.47399	−	1.07091i	0.494553	−	0.869148i	$-0.335332\pi$
$443$	289268.	−	210166.i	1.47399	−	1.07091i	0.979434	−	0.201766i	$-0.0646681\pi$
$444$	5205.78	+	3782.22i	0.0264071	+	0.0191859i
$445$	194829.	+	599624.i	0.983863	+	3.02802i
$446$	76101.5	−	24726.9i	0.382581	−	0.124308i
$447$	61764.3	−	85011.3i	0.309117	−	0.425463i
$448$	−3993.75	−	5496.93i	−0.0198987	−	0.0273882i
$449$	11170.1	−	34378.0i	0.0554069	−	0.170525i	−0.919523	−	0.393035i	$-0.871425\pi$
$449$	11170.1	−	34378.0i	0.0554069	−	0.170525i	0.974930	+	0.222510i	$0.0714251\pi$
$450$			231151.i			1.14149i
$451$	309561.	+	68484.7i	1.52193	+	0.336698i
$452$	72637.3			0.355536
$453$	71473.2	+	23223.0i	0.348295	+	0.113168i
$454$	−164878.	+	119791.i	−0.799926	+	0.581181i
$455$	83315.6	+	60532.3i	0.402442	+	0.292391i
$456$	10039.5	+	30898.5i	0.0482819	+	0.148596i
$457$	23357.6	−	7589.34i	0.111840	−	0.0363389i	−0.252563	−	0.967581i	$-0.581273\pi$
$457$	23357.6	−	7589.34i	0.111840	−	0.0363389i	0.364402	+	0.931242i	$0.381273\pi$
$458$	−14860.0	+	20453.1i	−0.0708416	+	0.0975051i
$459$	−60098.5	−	82718.4i	−0.285258	−	0.392624i
$460$	−60488.8	+	186165.i	−0.285864	+	0.879798i
$461$		−	41038.8i		−	0.193105i	−0.995328	−	0.0965523i	$-0.969218\pi$
$461$		−	41038.8i		−	0.193105i	0.995328	−	0.0965523i	$-0.0307815\pi$
$462$	7174.79	+	16481.0i	0.0336144	+	0.0772146i
$463$	−263948.			−1.23128			−0.615640	−	0.788027i	$-0.711103\pi$
$463$	−263948.			−1.23128			−0.615640	+	0.788027i	$0.711103\pi$
$464$	52363.0	+	17013.8i	0.243214	+	0.0790250i
$465$	−123922.	+	90034.5i	−0.573115	+	0.416393i
$466$	−110789.	−	80493.0i	−0.510182	−	0.370669i
$467$	−7002.66	−	21552.0i	−0.0321092	−	0.0988219i	0.933718	−	0.358011i	$-0.116545\pi$
$467$	−7002.66	−	21552.0i	−0.0321092	−	0.0988219i	−0.965827	+	0.259189i	$0.916545\pi$
$468$	89070.1	−	28940.6i	0.406668	−	0.132135i
$469$	23439.8	−	32262.2i	0.106564	−	0.146672i
$470$	111331.	+	153234.i	0.503987	+	0.693678i
$471$	−4165.16	+	12819.0i	−0.0187754	+	0.0577848i
$472$		−	111242.i		−	0.499327i
$473$	−208854.	−	235857.i	−0.933515	−	1.05421i
$474$	23656.8			0.105293
$475$	−431571.	−	140226.i	−1.91278	−	0.621500i
$476$	−15163.1	+	11016.6i	−0.0669226	+	0.0486221i
$477$	−77752.3	−	56490.4i	−0.341725	−	0.248278i
$478$	47333.4	+	145677.i	0.207163	+	0.637581i
$479$	63206.4	−	20537.0i	0.275480	−	0.0895089i	−0.168019	−	0.985784i	$-0.553737\pi$
$479$	63206.4	−	20537.0i	0.275480	−	0.0895089i	0.443499	+	0.896275i	$0.353737\pi$
$480$	−18238.3	+	25102.9i	−0.0791595	+	0.108954i
$481$	21403.8	+	29459.9i	0.0925127	+	0.127333i
$482$	−47343.6	+	145709.i	−0.203783	+	0.627179i
$483$		−	29671.9i		−	0.127189i
$484$	79805.5	−	85732.5i	0.340676	−	0.365978i
$485$	293926.			1.24955
$486$	−158133.	−	51380.4i	−0.669497	−	0.217533i
$487$	329613.	−	239478.i	1.38978	−	1.00973i	0.393890	−	0.919158i	$-0.371129\pi$
$487$	329613.	−	239478.i	1.38978	−	1.00973i	0.995890	−	0.0905764i	$-0.0288709\pi$
$488$	29040.4	+	21099.1i	0.121945	+	0.0885980i
$489$	10419.8	+	32068.8i	0.0435754	+	0.134111i
$490$	259212.	−	84223.2i	1.07960	−	0.350784i
$491$	20767.7	−	28584.3i	0.0861442	−	0.118567i	−0.763770	−	0.645489i	$-0.776654\pi$
$491$	20767.7	−	28584.3i	0.0861442	−	0.118567i	0.849914	+	0.526921i	$0.176654\pi$
$492$	−48763.1	−	67116.7i	−0.201447	−	0.277268i
$493$	46931.8	−	144441.i	0.193096	−	0.594288i
$494$			183855.i			0.753394i
$495$	−256344.	+	226996.i	−1.04619	+	0.926418i
$496$	57191.1			0.232469
$497$	107249.	+	34847.4i	0.434191	+	0.141077i
$498$	−85650.0	+	62228.4i	−0.345357	+	0.250917i
$499$	−24801.7	−	18019.5i	−0.0996046	−	0.0723670i	0.536868	−	0.843666i	$-0.319607\pi$
$499$	−24801.7	−	18019.5i	−0.0996046	−	0.0723670i	−0.636473	+	0.771299i	$0.719607\pi$
$500$	−67006.8	−	206226.i	−0.268027	−	0.824903i
$501$	−49912.0	+	16217.4i	−0.198852	+	0.0646109i
$502$	−23760.3	+	32703.2i	−0.0942854	+	0.129773i
$503$	164396.	+	226272.i	0.649764	+	0.894323i	0.999089	−	0.0426785i	$-0.0135891\pi$
$503$	164396.	+	226272.i	0.649764	+	0.894323i	−0.349325	+	0.937002i	$0.613589\pi$
$504$	−6062.69	+	18659.0i	−0.0238673	+	0.0734561i
$505$		−	591890.i		−	2.32091i
$506$	−177277.	+	77175.1i	−0.692389	+	0.301423i
$507$	−14022.7			−0.0545527
$508$	−52406.3	−	17027.8i	−0.203075	−	0.0659830i
$509$	−122810.	+	89227.0i	−0.474024	+	0.344398i	−0.799007	−	0.601321i	$-0.794641\pi$
$509$	−122810.	+	89227.0i	−0.474024	+	0.344398i	0.324984	+	0.945720i	$0.394641\pi$
$510$	69245.4	+	50309.7i	0.266226	+	0.193425i
$511$	18660.0	+	57429.5i	0.0714611	+	0.219935i
$512$	11018.2	−	3580.04i	0.0420312	−	0.0136568i
$513$	123500.	−	169983.i	0.469281	−	0.645909i
$514$	−63978.8	−	88059.3i	−0.242164	−	0.333311i
$515$	16463.2	−	50668.6i	0.0620727	−	0.191040i
$516$			82435.2i			0.309609i
$517$	−40412.1	+	182669.i	−0.151193	+	0.683414i
$518$	−7628.34			−0.0284296
$519$	83148.4	+	27016.6i	0.308688	+	0.100299i
$520$	−142059.	+	103212.i	−0.525366	+	0.381701i
$521$	1689.60	+	1227.57i	0.00622455	+	0.00452240i	0.590893	−	0.806750i	$-0.298775\pi$
$521$	1689.60	+	1227.57i	0.00622455	+	0.00452240i	−0.584669	+	0.811272i	$0.698775\pi$
$522$	−49127.0	−	151197.i	−0.180293	−	0.554885i
$523$	−290679.	+	94447.4i	−1.06270	+	0.345292i	−0.787641	−	0.616135i	$-0.788698\pi$
$523$	−290679.	+	94447.4i	−1.06270	+	0.345292i	−0.275060	+	0.961427i	$0.588698\pi$
$524$	6917.11	−	9520.58i	0.0251920	−	0.0346737i
$525$	38614.7	+	53148.6i	0.140099	+	0.192829i
$526$	113672.	−	349846.i	0.410848	−	1.26446i
$527$		−	157759.i		−	0.568033i
$528$	−30506.2	+	2951.01i	−0.109426	+	0.0105853i
$529$	39322.4			0.140517
$530$	171375.	+	55683.2i	0.610093	+	0.198231i
$531$	−259865.	+	188803.i	−0.921633	+	0.669606i
$532$	−31159.5	−	22638.7i	−0.110095	−	0.0799887i
$533$	−145077.	−	446503.i	−0.510676	−	1.57170i
$534$	154979.	−	50355.8i	0.543489	−	0.176590i
$535$	215454.	−	296547.i	0.752743	−	1.03606i
$536$	39966.6	+	55009.3i	0.139113	+	0.191473i
$537$	−10220.5	+	31455.5i	−0.0354424	+	0.109081i
$538$			199825.i			0.690375i
$539$	232021.	+	136533.i	0.798637	+	0.469959i
$540$	200671.			0.688171
$541$	−120348.	−	39103.4i	−0.411192	−	0.133604i	0.0961142	−	0.995370i	$-0.469359\pi$
$541$	−120348.	−	39103.4i	−0.411192	−	0.133604i	−0.507306	+	0.861766i	$0.669359\pi$
$542$	−182453.	+	132560.i	−0.621088	+	0.451247i
$543$	−32242.8	−	23425.8i	−0.109354	−	0.0794500i
$544$	−9875.38	−	30393.3i	−0.0333700	−	0.102702i
$545$	−315055.	+	102368.i	−1.06070	+	0.344643i
$546$	15645.2	−	21533.8i	0.0524804	−	0.0722331i
$547$	208238.	+	286615.i	0.695961	+	0.957908i	0.999986	+	0.00524442i	$0.00166936\pi$
$547$	208238.	+	286615.i	0.695961	+	0.957908i	−0.304025	+	0.952664i	$0.598331\pi$
$548$	−44804.4	+	137894.i	−0.149197	+	0.459180i
$549$		−	103649.i		−	0.343891i
$550$	217105.	−	368943.i	0.717701	−	1.21965i
$551$	312096.			1.02798
$552$	48116.5	+	15634.0i	0.157912	+	0.0513088i
$553$	−22689.0	+	16484.5i	−0.0741932	+	0.0539045i
$554$	−101396.	−	73668.7i	−0.330372	−	0.240029i
$555$	10765.1	+	33131.5i	0.0349487	+	0.107561i
$556$	77465.1	−	25169.9i	0.250586	−	0.0814202i
$557$	18181.9	−	25025.2i	0.0586042	−	0.0806618i	−0.778709	−	0.627385i	$-0.784125\pi$
$557$	18181.9	−	25025.2i	0.0586042	−	0.0806618i	0.837313	+	0.546724i	$0.184125\pi$
$558$	−97066.1	−	133600.i	−0.311745	−	0.429080i
$559$	−144158.	+	443674.i	−0.461335	+	1.41984i
$560$		−	36784.8i		−	0.117298i
$561$	8140.23	+	84150.2i	0.0258649	+	0.267380i
$562$	−221383.			−0.700924
$563$	−338262.	−	109908.i	−1.06718	−	0.346747i	−0.277789	−	0.960642i	$-0.589602\pi$
$563$	−338262.	−	109908.i	−1.06718	−	0.346747i	−0.789387	+	0.613896i	$0.789602\pi$
$564$	39604.9	−	28774.6i	0.124506	−	0.0904590i
$565$	318144.	+	231145.i	0.996613	+	0.724082i
$566$	−78486.6	−	241557.i	−0.244998	−	0.754027i
$567$	37864.6	−	12303.0i	0.117779	−	0.0382687i
$568$	−113018.	+	155556.i	−0.350309	+	0.482160i
$569$	257141.	+	353925.i	0.794232	+	1.09317i	0.993568	+	0.113235i	$0.0361213\pi$
$569$	257141.	+	353925.i	0.794232	+	1.09317i	−0.199337	+	0.979931i	$0.563879\pi$
$570$	−54352.5	+	167280.i	−0.167290	+	0.514865i
$571$		−	1830.95i		−	0.00561570i	−0.999996	−	0.00280785i	$-0.999106\pi$
$571$		−	1830.95i		−	0.00561570i	0.999996	−	0.00280785i	$-0.000893767\pi$
$572$	−169348.	−	37465.1i	−0.517592	−	0.114508i
$573$	−139763.			−0.425679
$574$	93536.5	+	30391.9i	0.283895	+	0.0922430i
$575$	−571689.	+	415356.i	−1.72912	+	1.25628i
$576$	−27063.4	−	19662.7i	−0.0815714	−	0.0592651i
$577$	71653.2	+	220526.i	0.215221	+	0.662381i	0.999138	+	0.0415155i	$0.0132186\pi$
$577$	71653.2	+	220526.i	0.215221	+	0.662381i	−0.783917	+	0.620865i	$0.786781\pi$
$578$	140832.	−	45759.2i	0.421548	−	0.136969i
$579$	18201.2	−	25051.8i	0.0542930	−	0.0747278i
$580$	175203.	+	241147.i	0.520818	+	0.716845i
$581$	38784.1	−	119365.i	0.114895	−	0.353611i
$582$		−	75968.3i		−	0.224278i
$583$	71043.8	+	163193.i	0.209021	+	0.480135i
$584$	−102961.			−0.301888
$585$	482212.	+	156680.i	1.40905	+	0.457828i
$586$	−46945.2	+	34107.7i	−0.136709	+	0.0993247i
$587$	−41941.6	−	30472.3i	−0.121722	−	0.0884361i	0.525259	−	0.850943i	$-0.323969\pi$
$587$	−41941.6	−	30472.3i	−0.121722	−	0.0884361i	−0.646981	+	0.762506i	$0.723969\pi$
$588$	−21768.4	−	66996.3i	−0.0629610	−	0.193774i
$589$	308323.	−	100180.i	0.888740	−	0.288769i
$590$	353992.	−	487229.i	1.01693	−	1.39968i
$591$	3427.16	+	4717.09i	0.00981205	+	0.0135051i
$592$	4019.34	−	12370.3i	0.0114686	−	0.0352968i
$593$			94653.9i			0.269171i	0.990902	+	0.134586i	$0.0429704\pi$
$593$			94653.9i			0.269171i	−0.990902	+	0.134586i	$0.957030\pi$
$594$	131404.	+	148394.i	0.372423	+	0.420574i
$595$	−101469.			−0.286616
$596$	−202008.	−	65636.5i	−0.568692	−	0.184779i
$597$	83557.7	−	60708.2i	0.234443	−	0.170333i
$598$	231627.	+	168287.i	0.647720	+	0.470596i
$599$	35391.5	+	108924.i	0.0986382	+	0.303577i	0.988185	−	0.153267i	$-0.0489796\pi$
$599$	35391.5	+	108924.i	0.0986382	+	0.303577i	−0.889547	+	0.456844i	$0.848980\pi$
$600$	−106533.	+	34614.6i	−0.295924	+	0.0961515i
$601$	−190529.	+	262240.i	−0.527486	+	0.726023i	−0.986745	−	0.162280i	$-0.948115\pi$
$601$	−190529.	+	262240.i	−0.527486	+	0.726023i	0.459258	+	0.888303i	$0.348115\pi$
$602$	−57442.5	−	79062.8i	−0.158504	−	0.218162i
$603$	60671.0	−	186726.i	0.166858	−	0.513535i
$604$		−	151908.i		−	0.416397i
$605$	622355.	−	121544.i	1.70031	−	0.332064i
$606$	−152980.			−0.416572
$607$	−666226.	−	216470.i	−1.80819	−	0.587517i	−0.808191	−	0.588920i	$-0.799553\pi$
$607$	−666226.	−	216470.i	−1.80819	−	0.587517i	−0.999999	+	0.00140328i	$0.999553\pi$
$608$	53129.2	−	38600.6i	0.143723	−	0.104421i
$609$	−36553.9	−	26558.0i	−0.0985597	−	0.0716078i
$610$	60052.8	+	184823.i	0.161389	+	0.496704i
$611$	263477.	−	85608.7i	0.705764	−	0.229317i
$612$	−54238.8	+	74653.4i	−0.144813	+	0.199318i
$613$	−351341.	−	483580.i	−0.934992	−	1.28691i	−0.957880	−	0.287168i	$-0.907286\pi$
$613$	−351341.	−	483580.i	−0.934992	−	1.28691i	0.0228878	−	0.999738i	$-0.492714\pi$
$614$	−116967.	+	359988.i	−0.310261	+	0.954886i
$615$		−	449137.i		−	1.18749i
$616$	27201.9	−	24087.6i	0.0716866	−	0.0634794i
$617$	−704195.			−1.84979			−0.924896	−	0.380221i	$-0.875848\pi$
$617$	−704195.			−1.84979			−0.924896	+	0.380221i	$0.875848\pi$
$618$	−13095.9	−	4255.11i	−0.0342892	−	0.0111412i
$619$	−31537.5	+	22913.3i	−0.0823087	+	0.0598008i	−0.628179	−	0.778069i	$-0.716199\pi$
$619$	−31537.5	+	22913.3i	−0.0823087	+	0.0598008i	0.545870	+	0.837870i	$0.316199\pi$
$620$	250491.	+	181992.i	0.651641	+	0.473445i
$621$	−101108.	−	311180.i	−0.262183	−	0.806915i
$622$	113740.	−	36956.5i	0.293991	−	0.0955235i
$623$	−113550.	+	156288.i	−0.292558	+	0.402671i
$624$	26676.3	+	36716.7i	0.0685103	+	0.0942963i
$625$	121186.	−	372973.i	0.310237	−	0.954811i
$626$		−	488716.i		−	1.24712i
$627$	−159293.	+	69346.1i	−0.405192	+	0.176395i
$628$	27245.4			0.0690834
$629$	−34122.9	−	11087.2i	−0.0862471	−	0.0280234i
$630$	−85930.3	+	62432.0i	−0.216504	+	0.157299i
$631$	15476.7	+	11244.5i	0.0388706	+	0.0282411i	0.607051	−	0.794663i	$-0.292352\pi$
$631$	15476.7	+	11244.5i	0.0388706	+	0.0282411i	−0.568180	+	0.822904i	$0.692352\pi$
$632$	−14776.8	−	45478.4i	−0.0369954	−	0.113860i
$633$	272525.	−	88548.8i	0.680141	−	0.220991i
$634$	−140201.	+	192970.i	−0.348797	+	0.480078i
$635$	−175348.	−	241346.i	−0.434864	−	0.598540i
$636$	14391.9	−	44293.8i	0.0355799	−	0.109504i
$637$		−	398647.i		−	0.982449i
$638$	−63597.4	+	287470.i	−0.156242	+	0.706238i
$639$	555201.			1.35972
$640$	59650.9	+	19381.8i	0.145632	+	0.0473187i
$641$	277946.	−	201939.i	0.676462	−	0.491479i	−0.195720	−	0.980660i	$-0.562704\pi$
$641$	277946.	−	201939.i	0.676462	−	0.491479i	0.872182	+	0.489181i	$0.162704\pi$
$642$	−76645.8	−	55686.4i	−0.185959	−	0.135107i
$643$	−22016.3	−	67759.1i	−0.0532503	−	0.163887i	0.920895	−	0.389812i	$-0.127460\pi$
$643$	−22016.3	−	67759.1i	−0.0532503	−	0.163887i	−0.974145	+	0.225924i	$0.927460\pi$
$644$	−57042.1	+	18534.1i	−0.137538	+	0.0446889i
$645$	−262324.	+	361058.i	−0.630548	+	0.867875i
$646$	−106478.	−	146555.i	−0.255150	−	0.351184i
$647$	42270.7	−	130096.i	0.100979	−	0.310781i	−0.887787	−	0.460255i	$-0.847758\pi$
$647$	42270.7	−	130096.i	0.100979	−	0.310781i	0.988766	+	0.149474i	$0.0477579\pi$
$648$			67884.4i			0.161666i
$649$	592103.	−	57276.8i	1.40575	−	0.135984i
$650$	−633900.			−1.50036
$651$	−44636.8	−	14503.4i	−0.105325	−	0.0342222i
$652$	55141.5	−	40062.6i	0.129713	−	0.0942419i
$653$	−439262.	−	319143.i	−1.03014	−	0.748443i	−0.0618056	−	0.998088i	$-0.519686\pi$
$653$	−439262.	−	319143.i	−1.03014	−	0.748443i	−0.968337	+	0.249646i	$0.919686\pi$
$654$	26458.0	+	81429.5i	0.0618589	+	0.190382i
$655$	60592.4	−	19687.7i	0.141233	−	0.0458893i
$656$	−98568.0	+	135667.i	−0.229049	+	0.315259i
$657$	174747.	+	240519.i	0.404836	+	0.557209i
$658$	−17933.9	+	55194.9i	−0.0414213	+	0.127482i
$659$			702060.i			1.61660i	0.588768	+	0.808302i	$0.299613\pi$
$659$			702060.i			1.61660i	−0.588768	+	0.808302i	$0.700387\pi$
$660$	−143005.	−	84151.2i	−0.328294	−	0.193185i
$661$	−226372.			−0.518108			−0.259054	−	0.965863i	$-0.583411\pi$
$661$	−226372.			−0.518108			−0.259054	+	0.965863i	$0.583411\pi$
$662$	349879.	+	113683.i	0.798367	+	0.259405i
$663$	101282.	−	73585.4i	0.230411	−	0.167403i
$664$	173130.	+	125786.i	0.392677	+	0.285296i
$665$	−64434.9	−	198310.i	−0.145706	−	0.448438i
$666$	−35719.0	+	11605.8i	−0.0805287	+	0.0261654i
$667$	285669.	−	393190.i	0.642113	−	0.883793i
$668$	62353.6	+	85822.4i	0.139736	+	0.192330i
$669$	34599.5	−	106486.i	0.0773069	−	0.237926i
$670$			368116.i			0.820039i
$671$	−97350.6	+	165435.i	−0.216219	+	0.367437i
$672$	−9507.44			−0.0210535
$673$	−41554.0	−	13501.7i	−0.0917450	−	0.0298097i	0.262785	−	0.964854i	$-0.415359\pi$
$673$	−41554.0	−	13501.7i	−0.0917450	−	0.0298097i	−0.354530	+	0.935045i	$0.615359\pi$
$674$	187194.	−	136005.i	0.412072	−	0.299388i
$675$	586073.	+	425807.i	1.28630	+	0.934555i
$676$	8759.08	+	26957.7i	0.0191675	+	0.0589914i
$677$	−488471.	+	158714.i	−1.06577	+	0.346288i	−0.788837	−	0.614602i	$-0.789317\pi$
$677$	−488471.	+	158714.i	−1.06577	+	0.346288i	−0.276929	+	0.960891i	$0.589317\pi$
$678$	59741.9	−	82227.7i	0.129963	−	0.178879i
$679$	52936.2	+	72860.5i	0.114819	+	0.158035i
$680$	53463.8	−	164545.i	0.115622	−	0.355849i
$681$			285171.i			0.614909i
$682$	29446.8	+	304408.i	0.0633096	+	0.654467i
$683$	−289751.			−0.621131			−0.310566	−	0.950552i	$-0.600518\pi$
$683$	−289751.			−0.621131			−0.310566	+	0.950552i	$0.600518\pi$
$684$	−180344.	−	58597.4i	−0.385469	−	0.125247i
$685$	−635041.	+	461384.i	−1.35338	+	0.983290i
$686$	140472.	+	102059.i	0.298499	+	0.216872i
$687$	10931.6	+	33644.0i	0.0231617	+	0.0712844i
$688$	158476.	−	51492.0i	0.334801	−	0.108783i
$689$	154917.	−	213225.i	0.326333	−	0.449159i
$690$	160995.	+	221590.i	0.338153	+	0.465428i
$691$	−148192.	+	456087.i	−0.310361	+	0.955194i	0.667261	+	0.744824i	$0.267467\pi$
$691$	−148192.	+	456087.i	−0.310361	+	0.955194i	−0.977622	+	0.210370i	$0.932533\pi$
$692$		−	176723.i		−	0.369045i
$693$	−102437.	−	22662.3i	−0.213300	−	0.0471887i
$694$	653568.			1.35697
$695$	419384.	+	136266.i	0.868245	+	0.282110i
$696$	62327.0	−	45283.2i	0.128664	−	0.0934800i
$697$	374232.	+	271896.i	0.770328	+	0.559676i
$698$	11308.0	+	34802.4i	0.0232100	+	0.0714330i
$699$	−182241.	+	59213.7i	−0.372986	+	0.121190i
$700$	78054.3	−	107433.i	0.159294	−	0.219250i
$701$	397842.	+	547582.i	0.809607	+	1.11433i	0.991384	+	0.130989i	$0.0418152\pi$
$701$	397842.	+	547582.i	0.809607	+	1.11433i	−0.181777	+	0.983340i	$0.558185\pi$
$702$	90699.7	−	279145.i	0.184048	−	0.566442i
$703$		−	73729.8i		−	0.149188i
$704$	24728.4	+	56802.8i	0.0498942	+	0.114610i
$705$	265031.			0.533235
$706$	−158971.	−	51653.0i	−0.318941	−	0.103630i
$707$	146722.	−	106600.i	0.293533	−	0.213264i
$708$	−125930.	−	91493.2i	−0.251224	−	0.182525i
$709$	−69762.5	−	214707.i	−0.138781	−	0.427124i	0.857378	−	0.514687i	$-0.172092\pi$
$709$	−69762.5	−	214707.i	−0.138781	−	0.427124i	−0.996159	+	0.0875635i	$0.972092\pi$
$710$	−990016.	+	321676.i	−1.96393	+	0.638119i
$711$	−81159.3	+	111706.i	−0.160546	+	0.220972i
$712$	−193611.	−	266483.i	−0.381918	−	0.525665i
$713$	156005.	−	480133.i	0.306873	−	0.944457i
$714$			26225.9i			0.0514439i
$715$	−622505.	−	702988.i	−1.21767	−	1.37511i
$716$	66855.0			0.130409
$717$	203841.	+	66232.0i	0.396510	+	0.128834i
$718$	127801.	−	92853.1i	0.247906	−	0.180114i
$719$	−752504.	−	546726.i	−1.45563	−	1.05758i	−0.984475	−	0.175527i	$-0.943837\pi$
$719$	−752504.	−	546726.i	−1.45563	−	1.05758i	−0.471155	−	0.882050i	$-0.656163\pi$
$720$	−55964.6	−	172241.i	−0.107956	−	0.332256i
$721$	15525.2	−	5044.43i	0.0298652	−	0.00970379i
$722$	2149.07	−	2957.93i	0.00412264	−	0.00567432i
$723$	126008.	+	173435.i	0.241058	+	0.331788i
$724$	−24894.4	+	76617.0i	−0.0474924	+	0.146167i
$725$			1.07605e6i			2.04719i
$726$	−31414.3	−	160855.i	−0.0596012	−	0.305183i
$727$	141940.			0.268556			0.134278	−	0.990944i	$-0.457128\pi$
$727$	141940.			0.268556			0.134278	+	0.990944i	$0.457128\pi$
$728$	−51169.9	−	16626.1i	−0.0965498	−	0.0313709i
$729$	8373.95	−	6084.03i	0.0157571	−	0.0114482i
$730$	−450957.	−	327639.i	−0.846231	−	0.614823i
$731$	−142039.	−	437150.i	−0.265810	−	0.818079i
$732$	47769.6	−	15521.3i	0.0891517	−	0.0289672i
$733$	−599214.	+	824747.i	−1.11525	+	1.53502i	−0.301813	+	0.953367i	$0.597592\pi$
$733$	−599214.	+	824747.i	−1.11525	+	1.53502i	−0.813441	+	0.581648i	$0.802408\pi$
$734$	−263163.	−	362213.i	−0.488465	−	0.672314i
$735$	117851.	−	362707.i	0.218151	−	0.671401i
$736$		−	102266.i		−	0.188789i
$737$	−272217.	+	241052.i	−0.501165	+	0.443787i
$738$	484214.			0.889047
$739$	902735.	+	293316.i	1.65299	+	0.537091i	0.979386	−	0.201997i	$-0.0647432\pi$
$739$	902735.	+	293316.i	1.65299	+	0.537091i	0.673609	+	0.739088i	$0.264743\pi$
$740$	56968.7	−	41390.2i	0.104033	−	0.0755847i
$741$	208130.	+	151215.i	0.379051	+	0.275397i
$742$	17061.6	+	52510.3i	0.0309894	+	0.0953755i
$743$	432128.	−	140407.i	0.782771	−	0.254338i	0.109748	−	0.993959i	$-0.464996\pi$
$743$	432128.	−	140407.i	0.782771	−	0.254338i	0.673023	+	0.739622i	$0.264996\pi$
$744$	47037.9	−	64742.1i	0.0849771	−	0.116961i
$745$	−675908.	−	930308.i	−1.21780	−	1.67615i
$746$	116897.	−	359771.i	0.210051	−	0.646471i
$747$		−	617923.i		−	1.10737i
$748$	156688.	−	68212.2i	0.280048	−	0.121916i
$749$	112314.			0.200202
$750$	−288565.	−	93760.5i	−0.513005	−	0.166685i
$751$	337489.	−	245200.i	0.598383	−	0.434751i	−0.246921	−	0.969036i	$-0.579419\pi$
$751$	337489.	−	245200.i	0.598383	−	0.434751i	0.845305	+	0.534285i	$0.179419\pi$
$752$	−80055.8	−	58164.0i	−0.141565	−	0.102853i
$753$	17479.0	+	53794.8i	0.0308266	+	0.0948747i
$754$	414638.	−	134724.i	0.729335	−	0.236975i
$755$	483399.	−	665341.i	0.848031	−	1.16721i
$756$	36140.9	+	49743.7i	0.0632348	+	0.0870352i
$757$	−344073.	+	1.05895e6i	−0.600425	+	1.84792i	−0.0748048	+	0.997198i	$0.523833\pi$
$757$	−344073.	+	1.05895e6i	−0.600425	+	1.84792i	−0.525620	+	0.850719i	$0.676167\pi$
$758$			152445.i			0.265322i
$759$	−58439.8	+	264157.i	−0.101444	+	0.458541i
$760$	355534.			0.615537
$761$	230550.	+	74910.2i	0.398103	+	0.129352i	0.501225	−	0.865317i	$-0.332883\pi$
$761$	230550.	+	74910.2i	0.398103	+	0.129352i	−0.103121	+	0.994669i	$0.532883\pi$
$762$	−62378.6	+	45320.7i	−0.107430	+	0.0780524i
$763$	−82117.3	−	59661.7i	−0.141054	−	0.102482i
$764$	87300.7	+	268684.i	0.149565	+	0.460315i
$765$	−475121.	+	154376.i	−0.811860	+	0.263789i
$766$	−81194.3	+	111754.i	−0.138378	+	0.190461i
$767$	−517766.	−	712643.i	−0.880121	−	1.21138i
$768$	5009.43	−	15417.4i	0.00849309	−	0.0261390i
$769$		−	502205.i		−	0.849235i	−0.905373	−	0.424618i	$-0.860409\pi$
$769$		−	502205.i		−	0.849235i	0.905373	−	0.424618i	$-0.139591\pi$
$770$	195793.	−	18939.9i	0.330229	−	0.0319445i
$771$	−152306.			−0.256218
$772$	−59529.5	−	19342.3i	−0.0998844	−	0.0324544i
$773$	514266.	−	373636.i	0.860654	−	0.625302i	−0.0674085	−	0.997725i	$-0.521473\pi$
$773$	514266.	−	373636.i	0.860654	−	0.625302i	0.928063	+	0.372423i	$0.121473\pi$
$774$	−389256.	−	282811.i	−0.649760	−	0.472078i
$775$	345403.	+	1.06304e6i	0.575073	+	1.76989i
$776$	−146044.	+	47452.5i	−0.242527	+	0.0788017i
$777$	−6274.08	+	8635.52i	−0.0103922	+	0.0143036i
$778$	455683.	+	627194.i	0.752841	+	1.03620i
$779$	−293745.	+	904053.i	−0.484055	+	1.48977i
$780$			245704.i			0.403853i
$781$	−886163.	−	521463.i	−1.45282	−	0.854912i
$782$	−282097.			−0.461301
$783$	−473852.	−	153964.i	−0.772892	−	0.251128i
$784$	−115198.	+	83696.5i	−0.187419	+	0.136168i
$785$	119332.	+	86699.7i	0.193650	+	0.140695i
$786$	−5088.49	−	15660.8i	−0.00823652	−	0.0253494i
$787$	573732.	−	186417.i	0.926317	−	0.300979i	0.193262	−	0.981147i	$-0.438093\pi$
$787$	573732.	−	186417.i	0.926317	−	0.300979i	0.733056	+	0.680168i	$0.238093\pi$
$788$	6927.54	−	9534.94i	0.0111565	−	0.0153556i
$789$	−302545.	−	416417.i	−0.485999	−	0.668921i
$790$	79999.5	−	246213.i	0.128184	−	0.394509i
$791$			120493.i			0.192579i
$792$	90723.3	−	154173.i	0.144633	−	0.245787i
$793$	284243.			0.452006
$794$	−132652.	−	43101.4i	−0.210414	−	0.0683676i
$795$	203986.	−	148204.i	0.322750	−	0.234491i
$796$	−168900.	−	122713.i	−0.266566	−	0.193671i
$797$	268673.	+	826889.i	0.422967	+	1.30176i	0.904927	+	0.425566i	$0.139925\pi$
$797$	268673.	+	826889.i	0.422967	+	1.30176i	−0.481960	+	0.876193i	$0.660075\pi$
$798$	−51255.5	+	16653.9i	−0.0804886	+	0.0261523i
$799$	−160443.	+	220831.i	−0.251320	+	0.345912i
$800$	133088.	+	183180.i	0.207950	+	0.286219i
$801$	−293910.	+	904561.i	−0.458088	+	1.40985i
$802$		−	21432.9i		−	0.0333221i
$803$	−53012.8	−	548023.i	−0.0822147	−	0.849900i
$804$	95143.5			0.147186
$805$	−308817.	−	100341.i	−0.476551	−	0.154841i
$806$	366380.	−	266191.i	0.563977	−	0.409753i
$807$	226208.	+	164350.i	0.347345	+	0.252361i
$808$	95557.0	+	294094.i	0.146366	+	0.450468i
$809$	344281.	−	111864.i	0.526036	−	0.170920i	−0.0339467	−	0.999424i	$-0.510808\pi$
$809$	344281.	−	111864.i	0.526036	−	0.170920i	0.559983	+	0.828504i	$0.310808\pi$
$810$	−216020.	+	297326.i	−0.329249	+	0.453172i
$811$	332769.	+	458018.i	0.505943	+	0.696371i	0.983229	−	0.182377i	$-0.0583792\pi$
$811$	332769.	+	458018.i	0.505943	+	0.696371i	−0.477285	+	0.878748i	$0.658379\pi$
$812$	−28223.0	+	86861.4i	−0.0428046	+	0.131739i
$813$			315570.i			0.477435i
$814$	67912.1	+	15024.3i	0.102494	+	0.0226749i
$815$	369000.			0.555535
$816$	−42528.4	−	13818.3i	−0.0638702	−	0.0207527i
$817$	764162.	−	555196.i	1.14483	−	0.831768i
$818$	33020.0	+	23990.4i	0.0493481	+	0.0358535i
$819$	48007.7	+	147752.i	0.0715719	+	0.220276i
$820$	−863434.	+	280547.i	−1.28411	+	0.417232i
$821$	426408.	−	586901.i	0.632615	−	0.870720i	−0.365580	−	0.930780i	$-0.619129\pi$
$821$	426408.	−	586901.i	0.632615	−	0.870720i	0.998195	+	0.0600604i	$0.0191293\pi$
$822$	119250.	+	164133.i	0.176488	+	0.242914i
$823$	291256.	−	896394.i	0.430007	−	1.32343i	−0.468110	−	0.883670i	$-0.655065\pi$
$823$	291256.	−	896394.i	0.430007	−	1.32343i	0.898118	−	0.439756i	$-0.144935\pi$
$824$			27833.8i			0.0409938i
$825$	−239093.	−	549213.i	−0.351285	−	0.806925i
$826$	184532.			0.270465
$827$	303169.	+	98505.6i	0.443276	+	0.144029i	0.522146	−	0.852856i	$-0.325131\pi$
$827$	303169.	+	98505.6i	0.443276	+	0.144029i	−0.0788708	+	0.996885i	$0.525131\pi$
$828$	−238896.	+	173568.i	−0.348457	+	0.253169i
$829$	−793128.	−	576241.i	−1.15408	−	0.838485i	−0.165058	−	0.986284i	$-0.552781\pi$
$829$	−793128.	−	576241.i	−1.15408	−	0.838485i	−0.989017	+	0.147799i	$0.952781\pi$
$830$	358016.	+	1.10186e6i	0.519692	+	1.59945i
$831$	−166791.	+	54193.6i	−0.241529	+	0.0784776i
$832$	53922.4	−	74217.8i	0.0778973	−	0.107216i
$833$	230873.	+	317770.i	0.332724	+	0.457955i
$834$	35219.5	−	108394.i	0.0506350	−	0.155838i
$835$			574313.i			0.823713i
$836$	232813.	+	262913.i	0.333115	+	0.376184i
$837$	−517543.			−0.738747
$838$	−617354.	−	200590.i	−0.879116	−	0.285642i
$839$	−423441.	+	307648.i	−0.601546	+	0.437048i	−0.846427	−	0.532505i	$-0.821251\pi$
$839$	−423441.	+	307648.i	−0.601546	+	0.437048i	0.244882	+	0.969553i	$0.421251\pi$
$840$	−41641.5	−	30254.4i	−0.0590158	−	0.0428775i
$841$	−10133.9	−	31188.9i	−0.0143280	−	0.0440969i
$842$	32765.2	−	10646.1i	0.0462156	−	0.0150163i
$843$	−182080.	+	250612.i	−0.256217	+	0.352652i
$844$	−340458.	−	468600.i	−0.477945	−	0.657835i
$845$	−47420.3	+	145945.i	−0.0664127	+	0.204397i
$846$			285730.i			0.399222i
$847$	142216.	+	132384.i	0.198235	+	0.184531i
$848$	−94141.4			−0.130915
$849$	−338003.	−	109824.i	−0.468927	−	0.152364i
$850$	505295.	−	367118.i	0.699370	−	0.508122i
$851$	−92887.4	−	67486.7i	−0.128262	−	0.0931877i
$852$	83140.6	+	255880.i	0.114534	+	0.352499i
$853$	328116.	−	106611.i	0.450951	−	0.146523i	−0.0747314	−	0.997204i	$-0.523810\pi$
$853$	328116.	−	106611.i	0.450951	−	0.146523i	0.525683	+	0.850681i	$0.323810\pi$
$854$	−34999.8	+	48173.2i	−0.0479900	+	0.0660525i
$855$	−603421.	−	830537.i	−0.825445	−	1.13613i
$856$	−59177.6	+	182130.i	−0.0807625	+	0.248561i
$857$			652071.i			0.887837i	0.896067	+	0.443919i	$0.146412\pi$
$857$			652071.i			0.887837i	−0.896067	+	0.443919i	$0.853588\pi$
$858$	−181695.	+	160893.i	−0.246813	+	0.218556i
$859$	−559418.			−0.758142			−0.379071	−	0.925368i	$-0.623756\pi$
$859$	−559418.			−0.758142			−0.379071	+	0.925368i	$0.623756\pi$
$860$	857964.	+	278770.i	1.16004	+	0.376919i
$861$	111335.	−	80889.9i	0.150185	−	0.109116i
$862$	96675.0	+	70238.5i	0.130107	+	0.0945281i
$863$	−116919.	−	359840.i	−0.156987	−	0.483157i	0.841370	−	0.540460i	$-0.181750\pi$
$863$	−116919.	−	359840.i	−0.156987	−	0.483157i	−0.998357	+	0.0573033i	$0.981750\pi$
$864$	−99707.9	+	32397.1i	−0.133568	+	0.0433988i
$865$	562363.	−	774026.i	0.751596	−	1.03448i
$866$	110212.	+	151694.i	0.146958	+	0.202270i
$867$	64029.4	−	197062.i	0.0851806	−	0.262159i
$868$			94870.5i			0.125919i
$869$	234457.	−	102068.i	0.310474	−	0.135161i
$870$	417085.			0.551044
$871$	512071.	+	166382.i	0.674985	+	0.219316i
$872$	140016.	−	101727.i	0.184138	−	0.133784i
$873$	358719.	+	260625.i	0.470680	+	0.341969i
$874$	−179137.	−	551326.i	−0.234510	−	0.721748i
$875$	342094.	−	111153.i	0.446817	−	0.145180i
$876$	−84681.9	+	116555.i	−0.110353	+	0.151887i
$877$	133607.	+	183894.i	0.173712	+	0.239094i	0.886992	−	0.461785i	$-0.152791\pi$
$877$	133607.	+	183894.i	0.173712	+	0.239094i	−0.713280	+	0.700880i	$0.752791\pi$
$878$	185722.	−	571594.i	0.240921	−	0.741479i
$879$			81196.0i			0.105089i
$880$	−72449.0	+	327480.i	−0.0935550	+	0.422883i
$881$	721351.			0.929383			0.464692	−	0.885473i	$-0.346165\pi$
$881$	721351.			0.929383			0.464692	+	0.885473i	$0.346165\pi$
$882$	391034.	+	127055.i	0.502664	+	0.163325i
$883$	−173179.	+	125822.i	−0.222113	+	0.161374i	−0.693277	−	0.720671i	$-0.743834\pi$
$883$	−173179.	+	125822.i	−0.222113	+	0.161374i	0.471165	+	0.882045i	$0.343834\pi$
$884$	−204727.	−	148743.i	−0.261981	−	0.190340i
$885$	−260410.	−	801461.i	−0.332485	−	1.02328i
$886$	−961822.	+	312515.i	−1.22526	+	0.398110i
$887$	−720290.	+	991394.i	−0.915504	+	1.26008i	0.0497477	+	0.998762i	$0.484158\pi$
$887$	−720290.	+	991394.i	−0.915504	+	1.26008i	−0.965252	+	0.261322i	$0.915842\pi$
$888$	−10697.7	−	14724.2i	−0.0135664	−	0.0186726i
$889$	28246.3	−	86933.2i	0.0357403	−	0.109997i
$890$		−	1.78327e6i		−	2.25132i
$891$	−361325.	+	34952.6i	−0.455137	+	0.0440275i
$892$	−226325.			−0.284448
$893$	−533473.	−	173336.i	−0.668974	−	0.217363i
$894$	−240448.	+	174696.i	−0.300848	+	0.218579i
$895$	292818.	+	212745.i	0.365554	+	0.265591i
$896$	5938.68	+	18277.4i	0.00739731	+	0.0227666i
$897$	381012.	−	123798.i	0.473537	−	0.153862i
$898$	−60094.9	+	82713.6i	−0.0745221	+	0.102571i
$899$	−451861.	−	621934.i	−0.559095	−	0.769528i
$900$	202033.	−	621795.i	0.249424	−	0.767648i
$901$			259685.i			0.319888i
$902$	−772860.	−	454790.i	−0.949922	−	0.558982i
$903$	−136746.			−0.167703
$904$	−195394.	−	63487.4i	−0.239097	−	0.0776874i
$905$	−352844.	+	256356.i	−0.430810	+	0.313001i
$906$	−171965.	−	124940.i	−0.209500	−	0.152210i
$907$	−313569.	−	965067.i	−0.381170	−	1.17312i	−0.939221	−	0.343314i	$-0.888450\pi$
$907$	−313569.	−	965067.i	−0.381170	−	1.17312i	0.558050	−	0.829807i	$-0.311550\pi$
$908$	548221.	−	178128.i	0.664942	−	0.216053i
$909$	524830.	−	722367.i	0.635172	−	0.874239i
$910$	−171211.	−	235652.i	−0.206752	−	0.284570i
$911$	369150.	−	1.13613e6i	0.444802	−	1.36896i	−0.437899	−	0.899024i	$-0.644277\pi$
$911$	369150.	−	1.13613e6i	0.444802	−	1.36896i	0.882701	−	0.469935i	$-0.155723\pi$
$912$		−	91891.7i		−	0.110481i
$913$	−580373.	+	986274.i	−0.696251	+	1.18319i
$914$	−69465.1			−0.0831523
$915$	258617.	+	84029.9i	0.308898	+	0.100367i
$916$	57850.0	−	42030.5i	0.0689465	−	0.0500926i
$917$	15793.0	+	11474.3i	0.0187814	+	0.0136455i
$918$	89366.0	+	275040.i	0.106044	+	0.326370i
$919$	−1.42102e6	+	461717.i	−1.68255	+	0.546695i	−0.985404	−	0.170230i	$-0.945549\pi$
$919$	−1.42102e6	+	461717.i	−1.68255	+	0.546695i	−0.697150	+	0.716925i	$0.745549\pi$
$920$	325429.	−	447914.i	0.384486	−	0.529199i
$921$	311316.	+	428490.i	0.367014	+	0.505151i
$922$	−35869.2	+	110394.i	−0.0421949	+	0.129863i
$923$			1.52256e6i			1.78719i
$924$	−4895.23	−	50604.7i	−0.00573362	−	0.0592717i
$925$	254207.			0.297101
$926$	710020.	+	230699.i	0.828034	+	0.269045i
$927$	65020.5	−	47240.1i	0.0756642	−	0.0549733i
$928$	−125985.	−	91533.8i	−0.146293	−	0.106288i
$929$	−147042.	−	452547.i	−0.170376	−	0.524364i	0.829016	−	0.559225i	$-0.188901\pi$
$929$	−147042.	−	452547.i	−0.170376	−	0.524364i	−0.999392	+	0.0348610i	$0.988901\pi$
$930$	412042.	−	133881.i	0.476404	−	0.154793i
$931$	−474436.	+	653005.i	−0.547367	+	0.753385i
$932$	227669.	+	313359.i	0.262103	+	0.360753i
$933$	51712.0	−	159153.i	0.0594057	−	0.182832i
$934$			64095.2i			0.0734737i
$935$	903341.	+	199848.i	1.03330	+	0.228600i
$936$	−264893.			−0.302356
$937$	869952.	+	282665.i	0.990869	+	0.321953i	0.759211	−	0.650845i	$-0.225585\pi$
$937$	869952.	+	282665.i	0.990869	+	0.321953i	0.231658	+	0.972797i	$0.425585\pi$
$938$	−91251.2	+	66297.9i	−0.103713	+	0.0753519i
$939$	−553241.	−	401953.i	−0.627456	−	0.455874i
$940$	−165548.	−	509504.i	−0.187356	−	0.576623i
$941$	790180.	−	256745.i	0.892374	−	0.289950i	0.173288	−	0.984871i	$-0.444561\pi$
$941$	790180.	−	256745.i	0.892374	−	0.289950i	0.719086	+	0.694921i	$0.244561\pi$
$942$	22408.5	−	30842.6i	0.0252529	−	0.0347576i
$943$	870087.	+	1.19757e6i	0.978451	+	1.34672i
$944$	−97229.2	+	299241.i	−0.109107	+	0.335797i
$945$			332879.i			0.372755i
$946$	355670.	+	817000.i	0.397434	+	0.912935i
$947$	−322279.			−0.359362			−0.179681	−	0.983725i	$-0.557506\pi$
$947$	−322279.			−0.359362			−0.179681	+	0.983725i	$0.557506\pi$
$948$	−63636.5	−	20676.8i	−0.0708092	−	0.0230073i
$949$	−659590.	+	479220.i	−0.732389	+	0.532112i
$950$	1.03836e6	+	754414.i	1.15054	+	0.835916i
$951$	103137.	+	317424.i	0.114039	+	0.350977i
$952$	50417.4	−	16381.6i	0.0556297	−	0.0180752i
$953$	−182953.	+	251813.i	−0.201444	+	0.277263i	−0.897772	−	0.440459i	$-0.854816\pi$
$953$	−182953.	+	251813.i	−0.201444	+	0.277263i	0.696329	+	0.717723i	$0.254816\pi$
$954$	159779.	+	219917.i	0.175559	+	0.241636i
$955$	−472632.	+	1.45461e6i	−0.518223	+	1.59493i
$956$		−	433241.i		−	0.474039i
$957$	273118.	+	308429.i	0.298213	+	0.336769i
$958$	−187975.			−0.204818
$959$	−228743.	−	74323.0i	−0.248720	−	0.0808139i
$960$	71001.8	−	51585.8i	0.0770419	−	0.0559742i
$961$	101111.	+	73461.5i	0.109484	+	0.0795450i
$962$	−31827.3	−	97954.5i	−0.0343914	−	0.105846i
$963$	525898.	−	170875.i	0.567086	−	0.184257i
$964$	254708.	−	350576.i	0.274087	−	0.377248i
$965$	−199182.	−	274151.i	−0.213893	−	0.294398i
$966$	−25934.2	+	79817.2i	−0.0277919	+	0.0855346i
$967$		−	852868.i		−	0.912072i	−0.889961	−	0.456036i	$-0.849269\pi$
$967$		−	852868.i		−	0.912072i	0.889961	−	0.456036i	$-0.150731\pi$
$968$	−289609.	+	160867.i	−0.309073	+	0.171679i
$969$	−253480.			−0.269957
$970$	−790659.	−	256901.i	−0.840322	−	0.273037i
$971$	−372880.	+	270914.i	−0.395486	+	0.287337i	−0.767700	−	0.640810i	$-0.778599\pi$
$971$	−372880.	+	270914.i	−0.395486	+	0.287337i	0.372214	+	0.928147i	$0.378599\pi$
$972$	380468.	+	276426.i	0.402703	+	0.292581i
$973$	41752.7	+	128502.i	0.0441021	+	0.135732i
$974$	−1.09597e6	+	356101.i	−1.15526	+	0.375367i
$975$	−521363.	+	717595.i	−0.548443	+	0.754867i
$976$	−59677.2	−	82138.6i	−0.0626482	−	0.0862279i
$977$	−252268.	+	776402.i	−0.264285	+	0.813387i	0.727572	+	0.686032i	$0.240649\pi$
$977$	−252268.	+	776402.i	−0.264285	+	0.813387i	−0.991857	+	0.127355i	$0.959351\pi$
$978$		−	95372.1i		−	0.0997112i
$979$	1.31871e6	−	1.16773e6i	1.37589	−	1.21837i
$980$	−770893.			−0.802679
$981$	−475276.	−	154427.i	−0.493865	−	0.160466i
$982$	−80848.7	+	58740.0i	−0.0838397	+	0.0609131i
$983$	1.31752e6	+	957232.i	1.36348	+	0.990627i	0.998215	+	0.0597245i	$0.0190222\pi$
$983$	1.31752e6	+	957232.i	1.36348	+	0.990627i	0.365267	+	0.930903i	$0.380978\pi$
$984$	72510.4	+	223164.i	0.0748876	+	0.230480i
$985$	60683.8	−	19717.4i	0.0625461	−	0.0203225i
$986$	−252492.	+	347526.i	−0.259713	+	0.357465i
$987$	47732.3	+	65697.9i	0.0489980	+	0.0674399i
$988$	160695.	−	494569.i	0.164623	−	0.506656i
$989$		−	1.47090e6i		−	1.50380i
$990$	887965.	−	386564.i	0.905994	−	0.394413i
$991$	−552727.			−0.562812			−0.281406	−	0.959589i	$-0.590801\pi$
$991$	−552727.			−0.562812			−0.281406	+	0.959589i	$0.590801\pi$
$992$	−153844.	−	49986.9i	−0.156335	−	0.0507964i
$993$	416457.	−	302574.i	0.422350	−	0.306855i
$994$	−258042.	−	187478.i	−0.261166	−	0.189749i
$995$	−349270.	−	1.07494e6i	−0.352789	−	1.08577i
$996$	284788.	−	92533.1i	0.287080	−	0.0932778i
$997$	701494.	−	965524.i	0.705722	−	0.971344i	−0.294156	−	0.955757i	$-0.595039\pi$
$997$	701494.	−	965524.i	0.705722	−	0.971344i	0.999879	−	0.0155861i	$-0.00496143\pi$
$998$	50966.7	+	70149.7i	0.0511712	+	0.0704311i
$999$	−36372.5	+	111943.i	−0.0364454	+	0.112167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.5.d.a.13.1	✓	16
3.2	odd	2		198.5.j.a.145.3		16
4.3	odd	2		176.5.n.c.145.3		16
11.4	even	5		242.5.b.e.241.5		16
11.6	odd	10	inner	22.5.d.a.17.1	yes	16
11.7	odd	10		242.5.b.e.241.13		16
33.17	even	10		198.5.j.a.127.3		16
44.39	even	10		176.5.n.c.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.1	✓	16	1.1	even	1	trivial
22.5.d.a.17.1	yes	16	11.6	odd	10	inner
176.5.n.c.17.3		16	44.39	even	10
176.5.n.c.145.3		16	4.3	odd	2
198.5.j.a.127.3		16	33.17	even	10
198.5.j.a.145.3		16	3.2	odd	2
242.5.b.e.241.5		16	11.4	even	5
242.5.b.e.241.13		16	11.7	odd	10

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68999 - 0.874032i) q^{2} +(-3.20187 + 2.32629i) q^{3} +(6.47214 + 4.70228i) q^{4} +(13.3838 + 41.1910i) q^{5} +(10.6463 - 3.45918i) q^{6} +(-7.80030 + 10.7362i) q^{7} +(-13.3001 - 18.3060i) q^{8} +(-20.1901 + 62.1386i) q^{9} +O(q^{10})\)	\(q+(-2.68999 - 0.874032i) q^{2} +(-3.20187 + 2.32629i) q^{3} +(6.47214 + 4.70228i) q^{4} +(13.3838 + 41.1910i) q^{5} +(10.6463 - 3.45918i) q^{6} +(-7.80030 + 10.7362i) q^{7} +(-13.3001 - 18.3060i) q^{8} +(-20.1901 + 62.1386i) q^{9} -122.501i q^{10} +(90.5882 - 80.2170i) q^{11} -31.6618 q^{12} +(-170.407 - 55.3685i) q^{13} +(30.3665 - 22.0626i) q^{14} +(-138.675 - 100.754i) q^{15} +(19.7771 + 60.8676i) q^{16} +(167.901 - 54.5543i) q^{17} +(108.622 - 149.506i) q^{18} +(213.240 + 293.500i) q^{19} +(-107.070 + 329.528i) q^{20} -52.5217i q^{21} +(-313.794 + 136.606i) q^{22} +564.946 q^{23} +(85.1701 + 27.6734i) q^{24} +(-1011.94 + 735.215i) q^{25} +(409.999 + 297.882i) q^{26} +(-178.970 - 550.813i) q^{27} +(-100.969 + 32.8069i) q^{28} +(505.658 - 695.978i) q^{29} +(284.974 + 392.233i) q^{30} +(276.141 - 849.875i) q^{31} -181.019i q^{32} +(-103.443 + 467.579i) q^{33} -499.334 q^{34} +(-546.632 - 177.611i) q^{35} +(-422.866 + 307.230i) q^{36} +(-164.418 - 119.457i) q^{37} +(-317.087 - 975.892i) q^{38} +(674.423 - 219.133i) q^{39} +(576.036 - 792.845i) q^{40} +(1540.12 + 2119.80i) q^{41} +(-45.9056 + 141.283i) q^{42} -2603.62i q^{43} +(963.502 - 93.2040i) q^{44} -2829.77 q^{45} +(-1519.70 - 493.780i) q^{46} +(-1250.87 + 908.812i) q^{47} +(-204.920 - 148.883i) q^{48} +(687.529 + 2116.00i) q^{49} +(3364.70 - 1093.26i) q^{50} +(-410.687 + 565.262i) q^{51} +(-842.537 - 1159.65i) q^{52} +(-454.551 + 1398.97i) q^{53} +1638.11i q^{54} +(4516.63 + 2657.81i) q^{55} +300.281 q^{56} +(-1365.53 - 443.689i) q^{57} +(-1968.52 + 1430.22i) q^{58} +(3977.33 + 2889.70i) q^{59} +(-423.754 - 1304.18i) q^{60} +(-1508.75 + 490.221i) q^{61} +(-1485.64 + 2044.80i) q^{62} +(-509.644 - 701.464i) q^{63} +(-158.217 + 486.941i) q^{64} -7760.26i q^{65} +(686.941 - 1167.37i) q^{66} -3004.99 q^{67} +(1343.21 + 436.434i) q^{68} +(-1808.88 + 1314.23i) q^{69} +(1315.20 + 955.547i) q^{70} +(-2625.89 - 8081.67i) q^{71} +(1406.04 - 456.849i) q^{72} +(2674.58 - 3681.24i) q^{73} +(337.875 + 465.045i) q^{74} +(1529.76 - 4708.12i) q^{75} +2902.29i q^{76} +(154.610 + 1598.29i) q^{77} -2005.72 q^{78} +(2009.88 + 653.050i) q^{79} +(-2242.51 + 1629.28i) q^{80} +(-2427.13 - 1763.41i) q^{81} +(-2290.15 - 7048.37i) q^{82} +(-8994.67 + 2922.55i) q^{83} +(246.972 - 339.927i) q^{84} +(4494.29 + 6185.86i) q^{85} +(-2275.65 + 7003.72i) q^{86} +3404.74i q^{87} +(-2673.28 - 591.414i) q^{88} +14557.2 q^{89} +(7612.06 + 2473.31i) q^{90} +(1923.67 - 1397.63i) q^{91} +(3656.40 + 2656.53i) q^{92} +(1092.89 + 3363.57i) q^{93} +(4159.17 - 1351.40i) q^{94} +(-9235.60 + 12711.7i) q^{95} +(421.104 + 579.600i) q^{96} +(2097.12 - 6454.28i) q^{97} -6292.94i q^{98} +(3155.59 + 7248.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9	\( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + 32 * q^4 + 30 * q^5 - 80 * q^6 + 150 * q^7 + 110 * q^9 - 30 * q^11 - 384 * q^12 - 510 * q^13 - 96 * q^14 - 1398 * q^15 - 256 * q^16 + 1770 * q^17 + 1120 * q^18 + 1020 * q^19 - 240 * q^20 + 240 * q^22 - 2424 * q^23 - 640 * q^24 - 858 * q^25 + 480 * q^26 + 2224 * q^27 + 1600 * q^28 + 4890 * q^29 + 3360 * q^30 + 602 * q^31 - 2648 * q^33 - 3904 * q^34 - 8670 * q^35 + 720 * q^36 - 4518 * q^37 - 4800 * q^38 - 1130 * q^39 - 1280 * q^40 + 1290 * q^41 - 3808 * q^42 + 720 * q^44 + 12152 * q^45 + 4480 * q^46 + 642 * q^47 - 128 * q^48 + 9534 * q^49 + 6720 * q^50 - 1500 * q^51 + 4000 * q^52 + 2598 * q^53 + 2582 * q^55 - 3072 * q^56 + 9140 * q^57 - 6496 * q^58 + 6660 * q^59 - 5776 * q^60 - 27410 * q^61 - 19680 * q^62 - 27260 * q^63 + 2048 * q^64 + 2528 * q^66 + 21524 * q^67 + 14160 * q^68 + 11416 * q^69 + 34400 * q^70 - 5562 * q^71 + 10240 * q^72 - 7790 * q^73 + 5760 * q^74 + 3576 * q^75 - 1110 * q^77 - 39424 * q^78 - 2770 * q^79 - 3840 * q^80 - 25464 * q^81 - 17472 * q^82 - 36900 * q^83 - 24480 * q^84 - 24750 * q^85 + 624 * q^86 - 5760 * q^88 + 46596 * q^89 + 55360 * q^90 + 32370 * q^91 + 14112 * q^92 + 20722 * q^93 + 58880 * q^94 + 74250 * q^95 - 3732 * q^97 + 45802 * q^99

Introduction

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