LMFDB - Embedded newform 9.5.d.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,5,Mod(2,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, 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:	$0.930329667755$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.39400128.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 $ x^6 - x^5 + 11x^4 + 14x^3 + 98x^2 + 20x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$1.89154 + 3.27625i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.5.d.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.67463 + 3.27625i) q^{2} +(-1.11837 + 8.93024i) q^{3} +(13.4676 - 23.3266i) q^{4} +(10.2044 + 5.89150i) q^{5} +(-22.9114 - 54.3399i) q^{6} +(26.6364 + 46.1356i) q^{7} +71.6534i q^{8} +(-78.4985 - 19.9746i) q^{9} +O(q^{10})$	\(q+(-5.67463 + 3.27625i) q^{2} +(-1.11837 + 8.93024i) q^{3} +(13.4676 - 23.3266i) q^{4} +(10.2044 + 5.89150i) q^{5} +(-22.9114 - 54.3399i) q^{6} +(26.6364 + 46.1356i) q^{7} +71.6534i q^{8} +(-78.4985 - 19.9746i) q^{9} -77.2081 q^{10} +(108.228 - 62.4856i) q^{11} +(193.251 + 146.357i) q^{12} +(37.3052 - 64.6145i) q^{13} +(-302.304 - 174.535i) q^{14} +(-64.0248 + 84.5387i) q^{15} +(-19.2722 - 33.3805i) q^{16} -7.70989i q^{17} +(510.892 - 143.832i) q^{18} -54.1307 q^{19} +(274.858 - 158.689i) q^{20} +(-441.792 + 186.273i) q^{21} +(-409.437 + 709.166i) q^{22} +(346.370 + 199.977i) q^{23} +(-639.882 - 80.1350i) q^{24} +(-243.080 - 421.028i) q^{25} +488.885i q^{26} +(266.169 - 678.672i) q^{27} +1434.92 q^{28} +(-468.219 + 270.326i) q^{29} +(86.3473 - 689.487i) q^{30} +(766.083 - 1326.89i) q^{31} +(-774.133 - 446.946i) q^{32} +(436.973 + 1036.39i) q^{33} +(25.2595 + 43.7508i) q^{34} +627.714i q^{35} +(-1523.13 + 1562.09i) q^{36} -1719.10 q^{37} +(307.172 - 177.346i) q^{38} +(535.302 + 405.408i) q^{39} +(-422.146 + 731.178i) q^{40} +(1090.87 + 629.816i) q^{41} +(1896.73 - 2504.45i) q^{42} +(1303.89 + 2258.41i) q^{43} -3366.13i q^{44} +(-683.348 - 666.303i) q^{45} -2620.70 q^{46} +(-692.850 + 400.017i) q^{47} +(319.649 - 134.774i) q^{48} +(-218.498 + 378.449i) q^{49} +(2758.78 + 1592.79i) q^{50} +(68.8512 + 8.62251i) q^{51} +(-1004.83 - 1740.41i) q^{52} -4229.81i q^{53} +(713.088 + 4723.25i) q^{54} +1472.54 q^{55} +(-3305.77 + 1908.59i) q^{56} +(60.5381 - 483.400i) q^{57} +(1771.31 - 3068.01i) q^{58} +(-2886.63 - 1666.60i) q^{59} +(1109.74 + 2632.02i) q^{60} +(7.50843 + 13.0050i) q^{61} +10039.5i q^{62} +(-1169.38 - 4153.63i) q^{63} +6473.94 q^{64} +(761.353 - 439.567i) q^{65} +(-5875.12 - 4449.48i) q^{66} +(-2591.20 + 4488.08i) q^{67} +(-179.846 - 103.834i) q^{68} +(-2173.21 + 2869.52i) q^{69} +(-2056.55 - 3562.05i) q^{70} -1924.16i q^{71} +(1431.25 - 5624.68i) q^{72} +949.554 q^{73} +(9755.28 - 5632.21i) q^{74} +(4031.73 - 1699.90i) q^{75} +(-729.012 + 1262.69i) q^{76} +(5765.63 + 3328.79i) q^{77} +(-4365.86 - 546.754i) q^{78} +(118.990 + 206.097i) q^{79} -454.169i q^{80} +(5763.03 + 3135.96i) q^{81} -8253.75 q^{82} +(-11402.0 + 6582.95i) q^{83} +(-1604.77 + 12814.2i) q^{84} +(45.4228 - 78.6746i) q^{85} +(-14798.2 - 8543.77i) q^{86} +(-1890.44 - 4483.64i) q^{87} +(4477.31 + 7754.92i) q^{88} -575.925i q^{89} +(6060.72 + 1542.20i) q^{90} +3974.71 q^{91} +(9329.58 - 5386.44i) q^{92} +(10992.7 + 8325.27i) q^{93} +(2621.11 - 4539.90i) q^{94} +(-552.370 - 318.911i) q^{95} +(4857.10 - 6413.34i) q^{96} +(-7561.70 - 13097.3i) q^{97} -2863.41i q^{98} +(-9743.88 + 2743.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20} + 480 q^{21} - 369 q^{22} - 282 q^{23} - 1449 q^{24} - 273 q^{25} + 54 q^{27} + 1308 q^{28} - 1056 q^{29} - 1278 q^{30} + 1290 q^{31} - 1161 q^{32} + 279 q^{33} + 513 q^{34} - 2385 q^{36} + 12 q^{37} - 789 q^{38} + 1974 q^{39} - 1314 q^{40} + 7629 q^{41} + 9612 q^{42} - 285 q^{43} - 4212 q^{45} - 5760 q^{46} - 9642 q^{47} - 6771 q^{48} - 1863 q^{49} + 3027 q^{50} + 2457 q^{51} - 240 q^{52} - 405 q^{54} + 2016 q^{55} - 462 q^{56} + 5367 q^{57} + 6462 q^{58} + 6225 q^{59} + 7470 q^{60} + 3630 q^{61} - 7578 q^{63} + 15450 q^{64} - 7158 q^{65} - 13734 q^{66} - 5055 q^{67} - 10503 q^{68} - 13878 q^{69} - 9684 q^{70} + 8451 q^{72} - 14622 q^{73} + 26454 q^{74} + 21021 q^{75} - 4047 q^{76} + 2580 q^{77} - 12060 q^{78} + 4764 q^{79} + 18387 q^{81} - 9702 q^{82} - 1866 q^{83} - 6486 q^{84} + 12366 q^{85} - 37731 q^{86} - 21564 q^{87} + 14787 q^{88} + 20790 q^{90} + 34836 q^{91} + 33636 q^{92} + 19254 q^{93} - 12708 q^{94} - 13362 q^{95} - 3672 q^{96} - 28959 q^{97} - 9126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−5.67463	+	3.27625i	−1.41866	+	0.819063i	−0.996181	−	0.0873110i	$-0.972173\pi$
$2$	−5.67463	+	3.27625i	−1.41866	+	0.819063i	−0.422477	+	0.906374i	$0.638839\pi$
$3$	−1.11837	+	8.93024i	−0.124263	+	0.992249i
$3$	−1.11837	+	8.93024i	−0.124263	+	0.992249i
$4$	13.4676	−	23.3266i	0.841727	−	1.45791i
$5$	10.2044	+	5.89150i	0.408175	+	0.235660i	0.690005	−	0.723804i	$-0.257608\pi$
$5$	10.2044	+	5.89150i	0.408175	+	0.235660i	−0.281830	+	0.959464i	$0.590942\pi$
$6$	−22.9114	−	54.3399i	−0.636427	−	1.50944i
$7$	26.6364	+	46.1356i	0.543600	+	0.941544i	0.998694	+	0.0510997i	$0.0162726\pi$
$7$	26.6364	+	46.1356i	0.543600	+	0.941544i	−0.455093	+	0.890444i	$0.650394\pi$
$8$			71.6534i			1.11958i
$9$	−78.4985	−	19.9746i	−0.969117	−	0.246601i
$10$	−77.2081			−0.772081
$11$	108.228	−	62.4856i	0.894449	−	0.516410i	0.0190536	−	0.999818i	$-0.493935\pi$
$11$	108.228	−	62.4856i	0.894449	−	0.516410i	0.875395	+	0.483408i	$0.160601\pi$
$12$	193.251	+	146.357i	1.34202	+	1.01637i
$13$	37.3052	−	64.6145i	0.220741	−	0.382334i	−0.734292	−	0.678833i	$-0.762486\pi$
$13$	37.3052	−	64.6145i	0.220741	−	0.382334i	0.955033	+	0.296499i	$0.0958192\pi$
$14$	−302.304	−	174.535i	−1.54237	−	0.890486i
$15$	−64.0248	+	84.5387i	−0.284555	+	0.375727i
$16$	−19.2722	−	33.3805i	−0.0752822	−	0.130393i
$17$		−	7.70989i		−	0.0266778i	−0.999911	−	0.0133389i	$-0.995754\pi$
$17$		−	7.70989i		−	0.0266778i	0.999911	−	0.0133389i	$-0.00424603\pi$
$18$	510.892	−	143.832i	1.57683	−	0.443926i
$19$	−54.1307			−0.149946			−0.0749732	−	0.997186i	$-0.523887\pi$
$19$	−54.1307			−0.149946			−0.0749732	+	0.997186i	$0.523887\pi$
$20$	274.858	−	158.689i	0.687144	−	0.396723i
$21$	−441.792	+	186.273i	−1.00180	+	0.422388i
$22$	−409.437	+	709.166i	−0.845944	+	1.46522i
$23$	346.370	+	199.977i	0.654765	+	0.378029i	0.790279	−	0.612747i	$-0.209935\pi$
$23$	346.370	+	199.977i	0.654765	+	0.378029i	−0.135515	+	0.990775i	$0.543269\pi$
$24$	−639.882	−	80.1350i	−1.11091	−	0.139123i
$25$	−243.080	−	421.028i	−0.388929	−	0.673644i
$26$			488.885i			0.723202i
$27$	266.169	−	678.672i	0.365115	−	0.930962i
$28$	1434.92			1.83025
$29$	−468.219	+	270.326i	−0.556741	+	0.321435i	−0.751836	−	0.659350i	$-0.770832\pi$
$29$	−468.219	+	270.326i	−0.556741	+	0.321435i	0.195095	+	0.980784i	$0.437498\pi$
$30$	86.3473	−	689.487i	0.0959414	−	0.766097i
$31$	766.083	−	1326.89i	0.797173	−	1.38074i	−0.124278	−	0.992247i	$-0.539661\pi$
$31$	766.083	−	1326.89i	0.797173	−	1.38074i	0.921450	−	0.388496i	$-0.127005\pi$
$32$	−774.133	−	446.946i	−0.755989	−	0.436470i
$33$	436.973	+	1036.39i	0.401260	+	0.951687i
$34$	25.2595	+	43.7508i	0.0218508	+	0.0378467i
$35$			627.714i			0.512419i
$36$	−1523.13	+	1562.09i	−1.17525	+	1.20532i
$37$	−1719.10			−1.25574			−0.627868	−	0.778320i	$-0.716072\pi$
$37$	−1719.10			−1.25574			−0.627868	+	0.778320i	$0.716072\pi$
$38$	307.172	−	177.346i	0.212723	−	0.122816i
$39$	535.302	+	405.408i	0.351941	+	0.266540i
$40$	−422.146	+	731.178i	−0.263841	+	0.456986i
$41$	1090.87	+	629.816i	0.648944	+	0.374668i	0.788051	−	0.615610i	$-0.211090\pi$
$41$	1090.87	+	629.816i	0.648944	+	0.374668i	−0.139108	+	0.990277i	$0.544423\pi$
$42$	1896.73	−	2504.45i	1.07524	−	1.41976i
$43$	1303.89	+	2258.41i	0.705189	+	1.22142i	0.966623	+	0.256202i	$0.0824711\pi$
$43$	1303.89	+	2258.41i	0.705189	+	1.22142i	−0.261434	+	0.965221i	$0.584196\pi$
$44$		−	3366.13i		−	1.73871i
$45$	−683.348	−	666.303i	−0.337456	−	0.329038i
$46$	−2620.70			−1.23852
$47$	−692.850	+	400.017i	−0.313649	+	0.181085i	−0.648558	−	0.761165i	$-0.724628\pi$
$47$	−692.850	+	400.017i	−0.313649	+	0.181085i	0.334909	+	0.942250i	$0.391294\pi$
$48$	319.649	−	134.774i	0.138737	−	0.0584957i
$49$	−218.498	+	378.449i	−0.0910029	+	0.157622i
$50$	2758.78	+	1592.79i	1.10351	+	0.637114i
$51$	68.8512	+	8.62251i	0.0264710	+	0.00331508i
$52$	−1004.83	−	1740.41i	−0.371607	−	0.643643i
$53$		−	4229.81i		−	1.50581i	−0.658131	−	0.752904i	$-0.728653\pi$
$53$		−	4229.81i		−	1.50581i	0.658131	−	0.752904i	$-0.271347\pi$
$54$	713.088	+	4723.25i	0.244543	+	1.61977i
$55$	1472.54			0.486789
$56$	−3305.77	+	1908.59i	−1.05414	+	0.608606i
$57$	60.5381	−	483.400i	0.0186329	−	0.148784i
$58$	1771.31	−	3068.01i	0.526550	−	0.912011i
$59$	−2886.63	−	1666.60i	−0.829253	−	0.478769i	0.0243441	−	0.999704i	$-0.492250\pi$
$59$	−2886.63	−	1666.60i	−0.829253	−	0.478769i	−0.853597	+	0.520934i	$0.825584\pi$
$60$	1109.74	+	2632.02i	0.308261	+	0.731116i
$61$	7.50843	+	13.0050i	0.00201785	+	0.00349502i	0.867033	−	0.498251i	$-0.166024\pi$
$61$	7.50843	+	13.0050i	0.00201785	+	0.00349502i	−0.865015	+	0.501746i	$0.832691\pi$
$62$			10039.5i			2.61174i
$63$	−1169.38	−	4153.63i	−0.294627	−	1.04652i
$64$	6473.94			1.58055
$65$	761.353	−	439.567i	0.180202	−	0.104040i
$66$	−5875.12	−	4449.48i	−1.34874	−	1.02146i
$67$	−2591.20	+	4488.08i	−0.577233	+	0.999796i	0.418563	+	0.908188i	$0.362534\pi$
$67$	−2591.20	+	4488.08i	−0.577233	+	0.999796i	−0.995795	+	0.0916081i	$0.970799\pi$
$68$	−179.846	−	103.834i	−0.0388940	−	0.0224554i
$69$	−2173.21	+	2869.52i	−0.456462	+	0.602715i
$70$	−2056.55	−	3562.05i	−0.419704	−	0.726948i
$71$		−	1924.16i		−	0.381701i	−0.981619	−	0.190851i	$-0.938875\pi$
$71$		−	1924.16i		−	0.381701i	0.981619	−	0.190851i	$-0.0611246\pi$
$72$	1431.25	−	5624.68i	0.276090	−	1.08501i
$73$	949.554			0.178186			0.0890931	−	0.996023i	$-0.471603\pi$
$73$	949.554			0.178186			0.0890931	+	0.996023i	$0.471603\pi$
$74$	9755.28	−	5632.21i	1.78146	−	1.02853i
$75$	4031.73	−	1699.90i	0.716753	−	0.302205i
$76$	−729.012	+	1262.69i	−0.126214	+	0.218609i
$77$	5765.63	+	3328.79i	0.972445	+	0.561442i
$78$	−4365.86	−	546.754i	−0.717597	−	0.0898676i
$79$	118.990	+	206.097i	0.0190659	+	0.0330231i	0.875401	−	0.483398i	$-0.160597\pi$
$79$	118.990	+	206.097i	0.0190659	+	0.0330231i	−0.856335	+	0.516421i	$0.827264\pi$
$80$		−	454.169i		−	0.0709640i
$81$	5763.03	+	3135.96i	0.878376	+	0.477970i
$82$	−8253.75			−1.22751
$83$	−11402.0	+	6582.95i	−1.65510	+	0.955574i	−0.680177	+	0.733048i	$0.738097\pi$
$83$	−11402.0	+	6582.95i	−1.65510	+	0.955574i	−0.974927	+	0.222526i	$0.928570\pi$
$84$	−1604.77	+	12814.2i	−0.227433	+	1.81607i
$85$	45.4228	−	78.6746i	0.00628689	−	0.0108892i
$86$	−14798.2	−	8543.77i	−2.00084	−	1.15519i
$87$	−1890.44	−	4483.64i	−0.249761	−	0.592368i
$88$	4477.31	+	7754.92i	0.578164	+	1.00141i
$89$		−	575.925i		−	0.0727086i	−0.999339	−	0.0363543i	$-0.988426\pi$
$89$		−	575.925i		−	0.0727086i	0.999339	−	0.0363543i	$-0.0115745\pi$
$90$	6060.72	+	1542.20i	0.748237	+	0.190396i
$91$	3974.71			0.479979
$92$	9329.58	−	5386.44i	1.10227	−	0.636394i
$93$	10992.7	+	8325.27i	1.27098	+	0.962570i
$94$	2621.11	−	4539.90i	0.296640	−	0.513796i
$95$	−552.370	−	318.911i	−0.0612044	−	0.0353364i
$96$	4857.10	−	6413.34i	0.527029	−	0.695892i
$97$	−7561.70	−	13097.3i	−0.803667	−	1.39199i	−0.917187	−	0.398456i	$-0.869546\pi$
$97$	−7561.70	−	13097.3i	−0.803667	−	1.39199i	0.113520	−	0.993536i	$-0.463787\pi$
$98$		−	2863.41i		−	0.298148i
$99$	−9743.88	+	2743.21i	−0.994172	+	0.279890i
$100$	−13094.9			−1.30949
$101$	9578.90	−	5530.38i	0.939016	−	0.542141i	0.0493643	−	0.998781i	$-0.484280\pi$
$101$	9578.90	−	5530.38i	0.939016	−	0.542141i	0.889652	+	0.456640i	$0.150947\pi$
$102$	−418.955	+	176.644i	−0.0402686	+	0.0169785i
$103$	1781.46	−	3085.58i	0.167920	−	0.290846i	−0.769769	−	0.638323i	$-0.779628\pi$
$103$	1781.46	−	3085.58i	0.167920	−	0.290846i	0.937688	+	0.347478i	$0.112962\pi$
$104$	4629.85	+	2673.04i	0.428055	+	0.247138i
$105$	−5605.64	−	702.017i	−0.508448	−	0.0636750i
$106$	13857.9	+	24002.6i	1.23335	+	2.13623i
$107$			11432.7i			0.998576i	0.866436	+	0.499288i	$0.166405\pi$
$107$			11432.7i			0.998576i	−0.866436	+	0.499288i	$0.833595\pi$
$108$	−12246.5	−	15348.9i	−1.04994	−	1.31592i
$109$	−4780.43			−0.402359			−0.201180	−	0.979554i	$-0.564478\pi$
$109$	−4780.43			−0.402359			−0.201180	+	0.979554i	$0.564478\pi$
$110$	−8356.10	+	4824.40i	−0.690587	+	0.398710i
$111$	1922.59	−	15352.0i	0.156042	−	1.24600i
$112$	1026.69	−	1778.27i	0.0818468	−	0.141763i
$113$	3889.66	+	2245.69i	0.304617	+	0.175871i	0.644515	−	0.764592i	$-0.277059\pi$
$113$	3889.66	+	2245.69i	0.304617	+	0.175871i	−0.339898	+	0.940462i	$0.610393\pi$
$114$	1240.21	+	2941.46i	0.0954300	+	0.226335i
$115$	2356.33	+	4081.28i	0.178172	+	0.308604i
$116$			14562.6i			1.08224i
$117$	−4219.05	+	4326.98i	−0.308208	+	0.316092i
$118$	21840.7			1.56857
$119$	355.701	−	205.364i	0.0251183	−	0.0145021i
$120$	−6057.48	−	4587.59i	−0.420658	−	0.318583i
$121$	488.406	−	845.944i	0.0333588	−	0.0577791i
$122$	−85.2151	−	49.1990i	−0.00572528	−	0.00330549i
$123$	−6844.42	+	9037.40i	−0.452404	+	0.597356i
$124$	−20634.7	−	35740.3i	−1.34200	−	2.32442i
$125$		−	13092.8i		−	0.837940i
$126$	20244.1	+	19739.2i	1.27514	+	1.24333i
$127$	13521.3			0.838322			0.419161	−	0.907912i	$-0.362324\pi$
$127$	13521.3			0.838322			0.419161	+	0.907912i	$0.362324\pi$
$128$	−24351.1	+	14059.1i	−1.48627	+	0.858100i
$129$	−21626.4	+	9118.35i	−1.29959	+	0.547945i
$130$	−2880.26	+	4988.76i	−0.170430	+	0.295193i
$131$	2941.86	+	1698.48i	0.171427	+	0.0989735i	0.583259	−	0.812287i	$-0.301777\pi$
$131$	2941.86	+	1698.48i	0.171427	+	0.0989735i	−0.411831	+	0.911260i	$0.635111\pi$
$132$	30060.4	+	3764.59i	1.72523	+	0.216057i
$133$	−1441.85	−	2497.35i	−0.0815110	−	0.141181i
$134$		−	33957.6i		−	1.89116i
$135$	6714.48	−	5357.29i	0.368421	−	0.293953i
$136$	552.439			0.0298680
$137$	3310.98	−	1911.60i	0.176407	−	0.101849i	−0.409197	−	0.912446i	$-0.634191\pi$
$137$	3310.98	−	1911.60i	0.176407	−	0.101849i	0.585603	+	0.810598i	$0.300858\pi$
$138$	2930.91	−	23403.5i	0.153902	−	1.22892i
$139$	−1738.31	+	3010.85i	−0.0899702	+	0.155833i	−0.907498	−	0.420056i	$-0.862010\pi$
$139$	−1738.31	+	3010.85i	−0.0899702	+	0.155833i	0.817528	+	0.575889i	$0.195344\pi$
$140$	14642.4	+	8453.82i	0.747064	+	0.431317i
$141$	−2797.39	−	6634.68i	−0.140707	−	0.333720i
$142$	6304.02	+	10918.9i	0.312637	+	0.541504i
$143$		−	9324.16i		−	0.455971i
$144$	846.078	+	3005.27i	0.0408024	+	0.144930i
$145$	−6370.51			−0.302997
$146$	−5388.37	+	3110.98i	−0.252785	+	0.145946i
$147$	−3135.28	−	2374.49i	−0.145092	−	0.109884i
$148$	−23152.3	+	40100.9i	−1.05699	+	1.83076i
$149$	7717.10	+	4455.47i	0.347602	+	0.200688i	0.663628	−	0.748062i	$-0.269016\pi$
$149$	7717.10	+	4455.47i	0.347602	+	0.200688i	−0.316027	+	0.948750i	$0.602349\pi$
$150$	−17309.3	+	22855.3i	−0.769302	+	1.01579i
$151$	4957.66	+	8586.92i	0.217432	+	0.376603i	0.954022	−	0.299736i	$-0.0968987\pi$
$151$	4957.66	+	8586.92i	0.217432	+	0.376603i	−0.736590	+	0.676339i	$0.763565\pi$
$152$		−	3878.65i		−	0.167878i
$153$	−154.002	+	605.215i	−0.00657876	+	0.0258539i
$154$	−43623.8			−1.83942
$155$	15634.8	−	9026.75i	0.650772	−	0.375723i
$156$	16666.0	−	7026.92i	0.684831	−	0.288746i
$157$	−2823.47	+	4890.39i	−0.114547	+	0.198401i	−0.917599	−	0.397508i	$-0.869875\pi$
$157$	−2823.47	+	4890.39i	−0.114547	+	0.198401i	0.803052	+	0.595909i	$0.203208\pi$
$158$	−1350.45	−	779.684i	−0.0540960	−	0.0312323i
$159$	37773.3	+	4730.50i	1.49414	+	0.187117i
$160$	−5266.36	−	9121.60i	−0.205717	−	0.356313i
$161$			21306.7i			0.821986i
$162$	−42977.2	+	1085.71i	−1.63760	+	0.0413698i
$163$	−2153.55			−0.0810552			−0.0405276	−	0.999178i	$-0.512904\pi$
$163$	−2153.55			−0.0810552			−0.0405276	+	0.999178i	$0.512904\pi$
$164$	29383.0	−	16964.3i	1.09247	−	0.630736i
$165$	−1646.84	+	13150.1i	−0.0604900	+	0.483016i
$166$	43134.8	−	74711.7i	1.56535	−	2.71127i
$167$	−32060.4	−	18510.1i	−1.14957	−	0.663706i	−0.200789	−	0.979635i	$-0.564351\pi$
$167$	−32060.4	−	18510.1i	−1.14957	−	0.663706i	−0.948783	+	0.315929i	$0.897684\pi$
$168$	−13347.1	−	31655.9i	−0.472899	−	1.12159i
$169$	11497.1	+	19913.6i	0.402547	+	0.697232i
$170$			595.266i			0.0205974i
$171$	4249.18	+	1081.24i	0.145316	+	0.0369769i
$172$	70241.5			2.37431
$173$	−42076.2	+	24292.7i	−1.40587	+	0.811678i	−0.994986	−	0.100010i	$-0.968112\pi$
$173$	−42076.2	+	24292.7i	−1.40587	+	0.811678i	−0.410882	+	0.911689i	$0.634779\pi$
$174$	25417.1	+	19249.4i	0.839512	+	0.635799i
$175$	12949.6	−	22429.3i	0.422844	−	0.732387i
$176$	−4171.60	−	2408.48i	−0.134672	−	0.0777530i
$177$	18111.4	−	23914.4i	0.578104	−	0.763332i
$178$	1886.87	+	3268.16i	0.0595529	+	0.103149i
$179$			47717.9i			1.48928i	0.667468	+	0.744639i	$0.267378\pi$
$179$			47717.9i			1.48928i	−0.667468	+	0.744639i	$0.732622\pi$
$180$	−24745.7	+	6966.68i	−0.763755	+	0.215021i
$181$	−45767.2			−1.39700			−0.698502	−	0.715608i	$-0.746150\pi$
$181$	−45767.2			−1.39700			−0.698502	+	0.715608i	$0.746150\pi$
$182$	−22555.0	+	13022.1i	−0.680927	+	0.393133i
$183$	−124.535	+	52.5077i	−0.00371868	+	0.00156791i
$184$	−14329.0	+	24818.6i	−0.423235	+	0.733064i
$185$	−17542.4	−	10128.1i	−0.512560	−	0.295927i
$186$	−89655.3	−	11227.9i	−2.59149	−	0.324543i
$187$	−481.757	−	834.428i	−0.0137767	−	0.0238619i
$188$			21549.1i			0.609697i
$189$	38400.7	−	5797.52i	1.07502	−	0.162300i
$190$	4179.33			0.115771
$191$	40460.3	−	23359.7i	1.10908	−	0.640326i	0.170487	−	0.985360i	$-0.445466\pi$
$191$	40460.3	−	23359.7i	1.10908	−	0.640326i	0.938590	+	0.345034i	$0.112133\pi$
$192$	−7240.26	+	57813.8i	−0.196405	+	1.56830i
$193$	13603.9	−	23562.6i	0.365215	−	0.632571i	−0.623596	−	0.781747i	$-0.714329\pi$
$193$	13603.9	−	23562.6i	0.365215	−	0.632571i	0.988811	+	0.149176i	$0.0476621\pi$
$194$	85819.8	+	49548.1i	2.28026	+	1.31651i
$195$	3073.97	+	7290.66i	0.0808407	+	0.191733i
$196$	5885.30	+	10193.6i	0.153199	+	0.265349i
$197$		−	64665.2i		−	1.66624i	−0.553090	−	0.833122i	$-0.686551\pi$
$197$		−	64665.2i		−	1.66624i	0.553090	−	0.833122i	$-0.313449\pi$
$198$	46305.5	−	47490.1i	1.18114	−	1.21136i
$199$	−25841.3			−0.652542			−0.326271	−	0.945276i	$-0.605792\pi$
$199$	−25841.3			−0.652542			−0.326271	+	0.945276i	$0.605792\pi$
$200$	30168.1	−	17417.5i	0.754201	−	0.435438i
$201$	−37181.8	−	28159.4i	−0.920318	−	0.696997i
$202$	−36237.8	+	62765.8i	−0.888095	+	1.53823i
$203$	−24943.4	−	14401.1i	−0.605289	−	0.349464i
$204$	1128.40	−	1489.94i	0.0271145	−	0.0358021i
$205$	7421.13	+	12853.8i	0.176588	+	0.305860i
$206$			23346.0i			0.550147i
$207$	−23195.1	−	22616.5i	−0.541322	−	0.527819i
$208$	−2875.82			−0.0664714
$209$	−5858.47	+	3382.39i	−0.134119	+	0.0774339i
$210$	34109.9	−	14381.8i	0.773467	−	0.326118i
$211$	−23029.3	+	39888.0i	−0.517269	+	0.895936i	0.482530	+	0.875879i	$0.339718\pi$
$211$	−23029.3	+	39888.0i	−0.517269	+	0.895936i	−0.999799	+	0.0200565i	$0.993615\pi$
$212$	−98667.3	−	56965.6i	−2.19534	−	1.26748i
$213$	17183.2	+	2151.92i	0.378743	+	0.0474315i
$214$	−37456.4	−	64876.4i	−0.817896	−	1.41664i
$215$			30727.6i			0.664739i
$216$	48629.1	+	19071.9i	1.04229	+	0.408777i
$217$	81622.8			1.73337
$218$	27127.2	−	15661.9i	0.570810	−	0.329558i
$219$	−1061.95	+	8479.75i	−0.0221420	+	0.176805i
$220$	19831.6	−	34349.3i	0.409743	−	0.709696i
$221$	−498.171	−	287.619i	−0.0101998	−	0.00588888i
$222$	39387.0	+	93415.9i	0.799185	+	1.89546i
$223$	−10955.5	−	18975.6i	−0.220305	−	0.381579i	0.734596	−	0.678505i	$-0.237372\pi$
$223$	−10955.5	−	18975.6i	−0.220305	−	0.381579i	−0.954901	+	0.296926i	$0.904039\pi$
$224$		−	47620.1i		−	0.949062i
$225$	10671.6	+	37905.5i	0.210797	+	0.748750i
$226$	−29429.8			−0.576197
$227$	43115.6	−	24892.8i	0.836726	−	0.483084i	−0.0194241	−	0.999811i	$-0.506183\pi$
$227$	43115.6	−	24892.8i	0.836726	−	0.483084i	0.856150	+	0.516727i	$0.172850\pi$
$228$	−10460.8	−	7922.41i	−0.201231	−	0.152401i
$229$	−14260.5	+	24699.9i	−0.271934	+	0.471003i	−0.969357	−	0.245656i	$-0.920996\pi$
$229$	−14260.5	+	24699.9i	−0.271934	+	0.471003i	0.697423	+	0.716660i	$0.254330\pi$
$230$	−26742.6	−	15439.9i	−0.505531	−	0.291869i
$231$	−36175.0	+	47765.6i	−0.677929	+	0.895141i
$232$	−19369.8	−	33549.5i	−0.359873	−	0.623318i
$233$			44050.2i			0.811403i	0.914006	+	0.405701i	$0.132973\pi$
$233$			44050.2i			0.811403i	−0.914006	+	0.405701i	$0.867027\pi$
$234$	9765.30	−	38376.7i	0.178342	−	0.700868i
$235$	−9426.80			−0.170698
$236$	−77752.1	+	44890.2i	−1.39601	+	0.805986i
$237$	−1973.57	+	832.119i	−0.0351363	+	0.0148146i
$238$	−1345.65	+	2330.73i	−0.0237562	+	0.0411470i
$239$	17818.6	+	10287.6i	0.311945	+	0.180102i	0.647797	−	0.761813i	$-0.275691\pi$
$239$	17818.6	+	10287.6i	0.311945	+	0.180102i	−0.335851	+	0.941915i	$0.609024\pi$
$240$	4055.84	+	507.930i	0.0704140	+	0.00881823i
$241$	28958.8	+	50158.0i	0.498593	+	0.863588i	0.999999	−	0.00162435i	$-0.000517045\pi$
$241$	28958.8	+	50158.0i	0.498593	+	0.863588i	−0.501406	+	0.865212i	$0.667184\pi$
$242$			6400.56i			0.109292i
$243$	−34450.1	+	47958.1i	−0.583415	+	0.812174i
$244$	404.483			0.00679392
$245$	−4459.27	+	2574.56i	−0.0742902	+	0.0428915i
$246$	9230.75	−	73708.0i	0.152534	−	1.21799i
$247$	−2019.36	+	3497.63i	−0.0330993	+	0.0573297i
$248$	95076.5	+	54892.4i	1.54586	+	0.892502i
$249$	−46035.7	−	109185.i	−0.742499	−	1.76102i
$250$	42895.3	+	74296.9i	0.686325	+	1.18875i
$251$		−	54140.4i		−	0.859357i	−0.902982	−	0.429679i	$-0.858627\pi$
$251$		−	54140.4i		−	0.859357i	0.902982	−	0.429679i	$-0.141373\pi$
$252$	−112639.	−	28662.0i	−1.77373	−	0.451341i
$253$	49982.8			0.780871
$254$	−76728.4	+	44299.2i	−1.18929	+	0.686639i
$255$	651.784	+	493.624i	0.0100236	+	0.00759130i
$256$	40330.8	−	69855.0i	0.615399	−	1.06590i
$257$	98522.7	+	56882.1i	1.49166	+	0.861211i	0.999954	−	0.00955057i	$-0.00304009\pi$
$257$	98522.7	+	56882.1i	1.49166	+	0.861211i	0.491706	+	0.870761i	$0.336373\pi$
$258$	92847.8	−	122597.i	1.39487	−	1.84179i
$259$	−45790.8	−	79311.9i	−0.682619	−	1.18233i
$260$		−	23679.7i		−	0.350292i
$261$	42154.2	−	11867.7i	0.618813	−	0.174215i
$262$	−22258.6			−0.324262
$263$	38420.1	−	22181.8i	0.555452	−	0.320691i	−0.195866	−	0.980631i	$-0.562752\pi$
$263$	38420.1	−	22181.8i	0.555452	−	0.320691i	0.751318	+	0.659940i	$0.229418\pi$
$264$	−74260.6	+	31310.6i	−1.06549	+	0.449245i
$265$	24919.9	−	43162.6i	0.354859	−	0.614633i
$266$	16363.9	+	9447.71i	0.231272	+	0.133525i
$267$	5143.15	+	644.097i	0.0721451	+	0.00903502i
$268$	69794.6	+	120888.i	0.971745	+	1.68311i
$269$		−	4429.77i		−	0.0612176i	−0.999531	−	0.0306088i	$-0.990255\pi$
$269$		−	4429.77i		−	0.0612176i	0.999531	−	0.0306088i	$-0.00974461\pi$
$270$	−20550.4	+	52399.0i	−0.281898	+	0.718779i
$271$	−86111.9			−1.17253			−0.586266	−	0.810119i	$-0.699403\pi$
$271$	−86111.9			−1.17253			−0.586266	+	0.810119i	$0.699403\pi$
$272$	−257.360	+	148.587i	−0.00347859	+	0.00200836i
$273$	−4445.20	+	35495.1i	−0.0596439	+	0.476259i
$274$	−12525.7	+	21695.2i	−0.166841	+	0.288977i
$275$	−52616.4	−	30378.1i	−0.695754	−	0.401693i
$276$	37668.3	+	89339.5i	0.494490	+	1.17280i
$277$	−35306.7	−	61153.0i	−0.460148	−	0.797000i	0.538820	−	0.842421i	$-0.318870\pi$
$277$	−35306.7	−	61153.0i	−0.460148	−	0.797000i	−0.998968	+	0.0454210i	$0.985537\pi$
$278$		−	22780.6i		−	0.294765i
$279$	−86640.6	+	88857.0i	−1.11305	+	1.14152i
$280$	−44977.8			−0.573697
$281$	−129258.	+	74627.2i	−1.63699	+	0.945114i	−0.655123	+	0.755522i	$0.727383\pi$
$281$	−129258.	+	74627.2i	−1.63699	+	0.945114i	−0.981863	+	0.189592i	$0.939283\pi$
$282$	37611.0	+	28484.5i	0.472952	+	0.358187i
$283$	41963.4	−	72682.7i	0.523959	−	0.907524i	−0.475652	−	0.879634i	$-0.657788\pi$
$283$	41963.4	−	72682.7i	0.523959	−	0.907524i	0.999611	−	0.0278902i	$-0.00887887\pi$
$284$	−44884.1	−	25913.8i	−0.556488	−	0.321288i
$285$	3465.71	−	4576.14i	0.0426680	−	0.0563390i
$286$	30548.3	+	52911.2i	0.373469	+	0.646867i
$287$			67104.2i			0.814678i
$288$	51840.7	+	50547.6i	0.625008	+	0.609418i
$289$	83461.6			0.999288
$290$	36150.3	−	20871.4i	0.429849	−	0.248174i
$291$	125418.	−	52880.3i	1.48107	−	0.624464i
$292$	12788.2	−	22149.9i	0.149984	−	0.259780i
$293$	−31092.9	−	17951.5i	−0.362182	−	0.209106i	0.307856	−	0.951433i	$-0.400389\pi$
$293$	−31092.9	−	17951.5i	−0.362182	−	0.209106i	−0.670037	+	0.742327i	$0.733722\pi$
$294$	25571.0	+	3202.36i	0.295837	+	0.0370489i
$295$	−19637.5	−	34013.1i	−0.225653	−	0.390843i
$296$		−	123180.i		−	1.40590i
$297$	−13600.2	−	90083.2i	−0.154182	−	1.02125i
$298$	−58389.0			−0.657504
$299$	25842.8	−	14920.4i	0.289067	−	0.166893i
$300$	14644.9	−	116940.i	0.162721	−	1.29934i
$301$	−69462.2	+	120312.i	−0.766682	+	1.32793i
$302$	−56265.8	−	32485.1i	−0.616923	−	0.356181i
$303$	38674.9	+	91727.0i	0.421254	+	0.999106i
$304$	1043.22	+	1806.91i	0.0112883	+	0.0195519i
$305$			176.944i			0.00190211i
$306$	−1108.93	−	3938.92i	−0.0118430	−	0.0420663i
$307$	7054.30			0.0748475			0.0374238	−	0.999299i	$-0.488085\pi$
$307$	7054.30			0.0748475			0.0374238	+	0.999299i	$0.488085\pi$
$308$	155299.	−	89661.8i	1.63707	−	0.945161i
$309$	25562.6	+	19359.7i	0.267725	+	0.202760i
$310$	−59147.8	+	102447.i	−0.615482	+	1.06605i
$311$	74184.9	+	42830.7i	0.766999	+	0.442827i	0.831803	−	0.555071i	$-0.187309\pi$
$311$	74184.9	+	42830.7i	0.766999	+	0.442827i	−0.0648038	+	0.997898i	$0.520642\pi$
$312$	−29048.8	+	38356.2i	−0.298414	+	0.394028i
$313$	−36721.2	−	63603.1i	−0.374825	−	0.649216i	0.615476	−	0.788156i	$-0.288964\pi$
$313$	−36721.2	−	63603.1i	−0.374825	−	0.649216i	−0.990301	+	0.138940i	$0.955631\pi$
$314$		−	37001.5i		−	0.375284i
$315$	12538.4	−	49274.6i	0.126363	−	0.496595i
$316$	6410.07			0.0641931
$317$	42642.8	−	24619.8i	0.424353	−	0.245000i	−0.272585	−	0.962132i	$-0.587879\pi$
$317$	42642.8	−	24619.8i	0.424353	−	0.245000i	0.696938	+	0.717132i	$0.254545\pi$
$318$	−229848.	+	96910.8i	−2.27293	+	0.958336i
$319$	−33783.0	+	58513.9i	−0.331984	+	0.575013i
$320$	66062.5	+	38141.2i	0.645141	+	0.372473i
$321$	−102097.	−	12786.0i	−0.990836	−	0.124086i
$322$	−69806.1	−	120908.i	−0.673258	−	1.16612i
$323$			417.341i			0.00400024i
$324$	150766.	−	92198.1i	1.43619	−	0.878277i
$325$	−36272.7			−0.343410
$326$	12220.6	−	7055.58i	0.114990	−	0.0663893i
$327$	5346.29	−	42690.4i	0.0499985	−	0.399241i
$328$	−45128.5	+	78164.8i	−0.419472	+	0.726547i
$329$	−36910.1	−	21310.0i	−0.340999	−	0.196876i
$330$	−33737.8	−	80017.5i	−0.309806	−	0.734779i
$331$	41005.6	+	71023.7i	0.374271	+	0.648257i	0.990218	−	0.139531i	$-0.0445595\pi$
$331$	41005.6	+	71023.7i	0.374271	+	0.648257i	−0.615946	+	0.787788i	$0.711226\pi$
$332$			354627.i			3.21733i
$333$	134947.	+	34338.5i	1.21696	+	0.309665i
$334$	242575.			2.17447
$335$	−52883.1	+	30532.1i	−0.471224	+	0.272061i
$336$	14732.2	+	11157.3i	0.130494	+	0.0988284i
$337$	23491.4	−	40688.3i	0.206847	−	0.358270i	−0.743873	−	0.668322i	$-0.767013\pi$
$337$	23491.4	−	40688.3i	0.206847	−	0.358270i	0.950720	+	0.310052i	$0.100346\pi$
$338$	−130484.	−	75335.0i	−1.14215	−	0.659422i
$339$	−24404.7	+	32224.1i	−0.212360	+	0.280402i
$340$	−1223.48	−	2119.12i	−0.0105837	−	0.0183315i
$341$		−	191477.i		−	1.64667i
$342$	−27654.9	+	7785.72i	−0.236440	+	0.0665651i
$343$	104628.			0.889324
$344$	−161823.	+	93428.4i	−1.36749	+	0.789518i
$345$	−39082.1	+	16478.2i	−0.328352	+	0.138443i
$346$	159178.	−	275705.i	1.32963	−	2.30299i
$347$	38382.0	+	22159.8i	0.318763	+	0.184038i	0.650841	−	0.759214i	$-0.274416\pi$
$347$	38382.0	+	22159.8i	0.318763	+	0.184038i	−0.332078	+	0.943252i	$0.607750\pi$
$348$	−130048.	−	16286.4i	−1.07385	−	0.134483i
$349$	93231.7	+	161482.i	0.765442	+	1.32579i	0.940012	+	0.341140i	$0.110813\pi$
$349$	93231.7	+	161482.i	0.765442	+	1.32579i	−0.174570	+	0.984645i	$0.555853\pi$
$350$			169704.i			1.38534i
$351$	−33922.6	−	42516.4i	−0.275343	−	0.345097i
$352$	−111711.			−0.901591
$353$	−146959.	+	84847.1i	−1.17936	+	0.680907i	−0.955868	−	0.293798i	$-0.905081\pi$
$353$	−146959.	+	84847.1i	−1.17936	+	0.680907i	−0.223497	+	0.974705i	$0.571747\pi$
$354$	−24426.0	+	195043.i	−0.194916	+	1.55641i
$355$	11336.2	−	19634.8i	0.0899517	−	0.155801i
$356$	−13434.4	−	7756.35i	−0.106003	−	0.0612008i
$357$	1436.14	+	3406.17i	0.0112684	+	0.0267257i
$358$	−156336.	−	270782.i	−1.21981	−	2.11278i
$359$		−	69656.7i		−	0.540473i	−0.962794	−	0.270236i	$-0.912898\pi$
$359$		−	69656.7i		−	0.540473i	0.962794	−	0.270236i	$-0.0871019\pi$
$360$	47742.8	−	48964.2i	0.368386	−	0.377810i
$361$	−127391.			−0.977516
$362$	259712.	−	149945.i	1.98187	−	1.14423i
$363$	7008.27	+	5307.66i	0.0531860	+	0.0402801i
$364$	53529.9	−	92716.6i	0.404012	−	0.699769i
$365$	9689.60	+	5594.30i	0.0727311	+	0.0419913i
$366$	534.661	−	705.969i	0.00399132	−	0.00527016i
$367$	88084.2	+	152566.i	0.653982	+	1.13273i	0.982148	+	0.188110i	$0.0602361\pi$
$367$	88084.2	+	152566.i	0.653982	+	1.13273i	−0.328166	+	0.944620i	$0.606431\pi$
$368$		−	15416.0i		−	0.113835i
$369$	−73051.6	−	71229.5i	−0.536509	−	0.523127i
$370$	132729.			0.969531
$371$	195145.	−	112667.i	1.41778	−	0.818558i
$372$	342246.	−	144302.i	2.47316	−	1.04276i
$373$	−33593.6	+	58185.7i	−0.241456	+	0.418214i	−0.961129	−	0.276099i	$-0.910958\pi$
$373$	−33593.6	+	58185.7i	−0.241456	+	0.418214i	0.719673	+	0.694313i	$0.244292\pi$
$374$	5467.59	+	3156.71i	0.0390888	+	0.0225679i
$375$	116922.	+	14642.6i	0.831445	+	0.104125i
$376$	−28662.6	−	49645.0i	−0.202740	−	0.351156i
$377$			40338.3i			0.283815i
$378$	−198916.	+	158709.i	−1.39215	+	1.11076i
$379$	43976.9			0.306158			0.153079	−	0.988214i	$-0.451081\pi$
$379$	43976.9			0.306158			0.153079	+	0.988214i	$0.451081\pi$
$380$	−14878.2	+	8589.95i	−0.103035	+	0.0594872i
$381$	−15121.8	+	120749.i	−0.104173	+	0.831825i
$382$	−153065.	+	265116.i	−1.04893	+	1.81681i
$383$	−160336.	−	92569.8i	−1.09303	−	0.631062i	−0.158649	−	0.987335i	$-0.550714\pi$
$383$	−160336.	−	92569.8i	−1.09303	−	0.631062i	−0.934382	+	0.356273i	$0.884047\pi$
$384$	−98317.7	−	233184.i	−0.666759	−	1.58138i
$385$	39223.1	+	67936.4i	0.264619	+	0.458333i
$386$			178279.i			1.19654i
$387$	−57242.8	−	203327.i	−0.382207	−	1.35760i
$388$	−407353.			−2.70587
$389$	−26364.0	+	15221.3i	−0.174226	+	0.100589i	−0.584577	−	0.811338i	$-0.698740\pi$
$389$	−26364.0	+	15221.3i	−0.174226	+	0.100589i	0.410351	+	0.911928i	$0.365406\pi$
$390$	−41329.7	−	31300.8i	−0.271727	−	0.205791i
$391$	1541.80	−	2670.48i	0.0100850	−	0.0174677i
$392$	−27117.2	−	15656.1i	−0.176471	−	0.101885i
$393$	−18458.0	+	24372.0i	−0.119508	+	0.157800i
$394$	211860.	+	366951.i	1.36476	+	2.36383i
$395$			2804.12i			0.0179723i
$396$	−67237.3	+	264236.i	−0.428766	+	1.68501i
$397$	−235724.			−1.49563			−0.747813	−	0.663910i	$-0.768896\pi$
$397$	−235724.			−1.49563			−0.747813	+	0.663910i	$0.768896\pi$
$398$	146640.	−	84662.7i	0.925734	−	0.534473i
$399$	23914.5	−	10083.1i	0.150216	−	0.0633355i
$400$	−9369.41	+	16228.3i	−0.0585588	+	0.101427i
$401$	202830.	+	117104.i	1.26137	+	0.728254i	0.973340	−	0.229367i	$-0.0736656\pi$
$401$	202830.	+	117104.i	1.26137	+	0.728254i	0.288032	+	0.957621i	$0.406999\pi$
$402$	303250.	+	37977.2i	1.87650	+	0.235002i
$403$	−57157.8	−	99000.1i	−0.351937	−	0.609573i
$404$		−	297925.i		−	1.82534i
$405$	40332.6	+	65953.4i	0.245893	+	0.402093i
$406$	188726.			1.14493
$407$	−186056.	+	107419.i	−1.12319	+	0.648475i
$408$	−617.832	+	4933.42i	−0.00371150	+	0.0296365i
$409$	148893.	−	257890.i	0.890076	−	1.54166i	0.0502930	−	0.998735i	$-0.483984\pi$
$409$	148893.	−	257890.i	0.890076	−	1.54166i	0.839783	−	0.542922i	$-0.182682\pi$
$410$	−84224.3	−	48626.9i	−0.501037	−	0.289274i
$411$	13368.1	+	31705.7i	0.0791382	+	0.187696i
$412$	−47984.1	−	83110.9i	−0.282685	−	0.489625i
$413$		−	177569.i		−	1.04104i
$414$	205721.	+	52347.5i	1.20027	+	0.305419i
$415$	−155134.			−0.900763
$416$	−57758.3	+	33346.8i	−0.333755	+	0.192694i
$417$	−24943.5	−	18890.8i	−0.143445	−	0.108637i
$418$	22163.1	−	38387.6i	0.126846	−	0.219704i
$419$	−31934.0	−	18437.1i	−0.181897	−	0.105018i	0.406287	−	0.913746i	$-0.366823\pi$
$419$	−31934.0	−	18437.1i	−0.181897	−	0.105018i	−0.588184	+	0.808727i	$0.700157\pi$
$420$	−91870.4	+	121306.i	−0.520807	+	0.687676i
$421$	−120305.	−	208374.i	−0.678764	−	1.17565i	−0.975353	−	0.220649i	$-0.929183\pi$
$421$	−120305.	−	208374.i	−0.678764	−	1.17565i	0.296589	−	0.955005i	$-0.404151\pi$
$422$		−	301799.i		−	1.69470i
$423$	62377.9	−	17561.3i	0.348618	−	0.0981468i
$424$	303080.			1.68588
$425$	−3246.08	+	1874.12i	−0.0179714	+	0.0103758i
$426$	−104559.	+	44085.1i	−0.576156	+	0.242925i
$427$	−399.995	+	692.812i	−0.00219381	+	0.00379979i
$428$	266686.	+	153971.i	1.45584	+	0.840529i
$429$	83267.0	+	10427.9i	0.452437	+	0.0566605i
$430$	−100671.	−	174368.i	−0.544463	−	0.943038i
$431$			162758.i			0.876169i	0.898934	+	0.438084i	$0.144343\pi$
$431$			162758.i			0.876169i	−0.898934	+	0.438084i	$0.855657\pi$
$432$	−27784.1	+	4194.67i	−0.148877	+	0.0224766i
$433$	266637.			1.42215			0.711073	−	0.703118i	$-0.248209\pi$
$433$	266637.			1.42215			0.711073	+	0.703118i	$0.248209\pi$
$434$	−463180.	+	267417.i	−2.45906	+	1.41974i
$435$	7124.59	−	56890.2i	0.0376514	−	0.300649i
$436$	−64381.1	+	111511.i	−0.338677	+	0.586605i
$437$	−18749.3	−	10824.9i	−0.0981796	−	0.0566840i
$438$	−21755.6	−	51598.7i	−0.113402	−	0.268962i
$439$	18408.7	+	31884.8i	0.0955201	+	0.165446i	0.909826	−	0.414991i	$-0.136215\pi$
$439$	18408.7	+	31884.8i	0.0955201	+	0.165446i	−0.814305	+	0.580437i	$0.802882\pi$
$440$			105512.i			0.545001i
$441$	24711.1	−	25343.3i	0.127062	−	0.130312i
$442$	3769.25			0.0192935
$443$	−119117.	+	68772.0i	−0.606967	+	0.350432i	−0.771777	−	0.635893i	$-0.780632\pi$
$443$	−119117.	+	68772.0i	−0.606967	+	0.350432i	0.164811	+	0.986325i	$0.447299\pi$
$444$	−332218.	−	251603.i	−1.68522	−	1.27629i
$445$	3393.06	−	5876.95i	0.0171345	−	0.0296778i
$446$	124337.	+	71786.2i	0.625075	+	0.360887i
$447$	−48419.0	+	63932.7i	−0.242326	+	0.319969i
$448$	172442.	+	298679.i	0.859188	+	1.48816i
$449$			174405.i			0.865101i	0.901610	+	0.432550i	$0.142386\pi$
$449$			174405.i			0.865101i	−0.901610	+	0.432550i	$0.857614\pi$
$450$	−184745.	−	180137.i	−0.912322	−	0.889565i
$451$	157418.			0.773929
$452$	104769.	−	60488.4i	0.512809	−	0.296070i
$453$	−82227.8	+	34669.8i	−0.400703	+	0.168949i
$454$	−163110.	+	282515.i	−0.791352	+	1.37066i
$455$	40559.4	+	23417.0i	0.195916	+	0.113112i
$456$	34637.2	+	4337.76i	0.166576	+	0.0208610i
$457$	−57654.7	−	99860.9i	−0.276059	−	0.478149i	0.694342	−	0.719645i	$-0.255695\pi$
$457$	−57654.7	−	99860.9i	−0.276059	−	0.478149i	−0.970402	+	0.241496i	$0.922362\pi$
$458$		−	186884.i		−	0.890923i
$459$	−5232.48	−	2052.13i	−0.0248360	−	0.00974047i
$460$	126937.			0.599890
$461$	351141.	−	202731.i	1.65226	−	0.953936i	0.676127	−	0.736785i	$-0.263657\pi$
$461$	351141.	−	202731.i	1.65226	−	0.953936i	0.976138	−	0.217150i	$-0.0696762\pi$
$462$	48787.5	−	389571.i	0.228573	−	1.82517i
$463$	−36293.4	+	62861.9i	−0.169303	+	0.293242i	−0.938175	−	0.346161i	$-0.887485\pi$
$463$	−36293.4	+	62861.9i	−0.169303	+	0.293242i	0.768872	+	0.639403i	$0.220818\pi$
$464$	18047.3	+	10419.6i	0.0838253	+	0.0483966i
$465$	63125.6	+	149718.i	0.291944	+	0.692417i
$466$	−144320.	−	249969.i	−0.664590	−	1.15110i
$467$			358806.i			1.64523i	0.568602	+	0.822613i	$0.307485\pi$
$467$			358806.i			1.64523i	−0.568602	+	0.822613i	$0.692515\pi$
$468$	44113.3	+	156691.i	0.201408	+	0.715404i
$469$	−276081.			−1.25514
$470$	53493.6	−	30884.6i	0.242162	−	0.139812i
$471$	−40514.7	−	30683.5i	−0.182629	−	0.138313i
$472$	119417.	−	206837.i	0.536022	−	0.928418i
$473$	282236.	+	162949.i	1.26151	+	0.728333i
$474$	8473.07	−	11187.9i	0.0377124	−	0.0497956i
$475$	13158.1	+	22790.5i	0.0583185	+	0.101011i
$476$		−	11063.1i		−	0.0488271i
$477$	−84489.0	+	332034.i	−0.371333	+	1.45930i
$478$	−134819.			−0.590058
$479$	−22169.8	+	12799.8i	−0.0966255	+	0.0557867i	−0.547534	−	0.836783i	$-0.684433\pi$
$479$	−22169.8	+	12799.8i	−0.0966255	+	0.0557867i	0.450909	+	0.892570i	$0.351100\pi$
$480$	87347.9	−	36828.5i	0.379114	−	0.159846i
$481$	−64131.5	+	111079.i	−0.277192	+	0.480111i
$482$	−328661.	−	189752.i	−1.41466	−	0.816757i
$483$	−190274.	−	23828.8i	−0.815615	−	0.102143i
$484$	−13155.4	−	22785.7i	−0.0561580	−	0.0972685i
$485$		−	178199.i		−	0.757569i
$486$	38368.8	−	385012.i	0.162445	−	1.63005i
$487$	247261.			1.04255			0.521277	−	0.853388i	$-0.325456\pi$
$487$	247261.			1.04255			0.521277	+	0.853388i	$0.325456\pi$
$488$	−931.850	+	538.004i	−0.00391297	+	0.00225915i
$489$	2408.47	−	19231.8i	0.0100722	−	0.0804269i
$490$	16869.8	−	29219.4i	0.0702616	−	0.121697i
$491$	−296403.	−	171128.i	−1.22947	−	0.709837i	−0.262554	−	0.964917i	$-0.584565\pi$
$491$	−296403.	−	171128.i	−1.22947	−	0.709837i	−0.966920	+	0.255081i	$0.917898\pi$
$492$	118634.	+	281370.i	0.490094	+	1.16238i
$493$	2084.19	+	3609.92i	0.00857517	+	0.0148526i
$494$		−	26463.7i		−	0.108442i
$495$	−115592.	−	29413.4i	−0.471755	−	0.120042i
$496$	−59056.5			−0.240052
$497$	88772.2	−	51252.7i	0.359389	−	0.207493i
$498$	618953.	+	468760.i	2.49574	+	1.89013i
$499$	98919.1	−	171333.i	0.397264	−	0.688081i	−0.596124	−	0.802893i	$-0.703293\pi$
$499$	98919.1	−	171333.i	0.397264	−	0.688081i	0.993387	+	0.114812i	$0.0366265\pi$
$500$	−305411.	−	176329.i	−1.22164	−	0.705317i
$501$	201155.	−	265606.i	0.801411	−	1.05819i
$502$	177377.	+	307227.i	0.703867	+	1.21913i
$503$		−	187051.i		−	0.739305i	−0.929170	−	0.369652i	$-0.879477\pi$
$503$		−	187051.i		−	0.739305i	0.929170	−	0.369652i	$-0.120523\pi$
$504$	297622.	−	83789.7i	1.17167	−	0.329860i
$505$	130329.			0.511044
$506$	−283634.	+	163756.i	−1.10779	+	0.639582i
$507$	−190692.	+	80401.5i	−0.741850	+	0.312787i
$508$	182100.	−	315406.i	0.705639	−	1.22220i
$509$	−25011.5	−	14440.4i	−0.0965393	−	0.0557370i	0.450953	−	0.892548i	$-0.351084\pi$
$509$	−25011.5	−	14440.4i	−0.0965393	−	0.0557370i	−0.547492	+	0.836811i	$0.684417\pi$
$510$	−5315.87	−	665.728i	−0.0204378	−	0.00255951i
$511$	25292.7	+	43808.3i	0.0968620	+	0.167770i
$512$			78644.0i			0.300003i
$513$	−14407.9	+	36736.9i	−0.0547477	+	0.139595i
$514$	−745440.			−2.82154
$515$	36357.4	−	20990.9i	0.137081	−	0.0791439i
$516$	−78556.0	+	627274.i	−0.295039	+	2.35590i
$517$	−49990.6	+	86586.3i	−0.187028	+	0.323943i
$518$	519692.	+	300044.i	1.93681	+	1.11822i
$519$	−169883.	−	402919.i	−0.630689	−	1.49583i
$520$	31496.5	+	54553.5i	0.116481	+	0.201751i
$521$		−	269661.i		−	0.993443i	−0.867910	−	0.496721i	$-0.834537\pi$
$521$		−	269661.i		−	0.993443i	0.867910	−	0.496721i	$-0.165463\pi$
$522$	−200328.	+	205453.i	−0.735191	+	0.753998i
$523$	−187282.			−0.684689			−0.342344	−	0.939575i	$-0.611221\pi$
$523$	−187282.			−0.684689			−0.342344	+	0.939575i	$0.611221\pi$
$524$	79239.8	−	45749.1i	0.288590	−	0.166617i
$525$	185817.	+	140727.i	0.674166	+	0.510575i
$526$	−145347.	+	251748.i	−0.525331	+	0.909901i
$527$	−10230.2	−	5906.41i	−0.0368352	−	0.0212668i
$528$	26173.7	−	34559.9i	0.0938851	−	0.123966i
$529$	−59938.8	−	103817.i	−0.214189	−	0.370986i
$530$			326576.i			1.16261i
$531$	193306.	+	188485.i	0.685578	+	0.668478i
$532$	−77673.1			−0.274440
$533$	81390.6	−	46990.9i	0.286497	−	0.165409i
$534$	−31295.7	+	13195.2i	−0.109749	+	0.0462737i
$535$	−67355.7	+	116664.i	−0.235324	+	0.407594i
$536$	−321586.	−	185668.i	−1.11936	−	0.646260i
$537$	−426133.	−	53366.3i	−1.47773	−	0.185063i
$538$	14513.0	+	25137.3i	0.0501411	+	0.0868469i
$539$			54611.9i			0.187979i
$540$	−34539.3	−	228776.i	−0.118447	−	0.784555i
$541$	−25587.9			−0.0874259			−0.0437129	−	0.999044i	$-0.513919\pi$
$541$	−25587.9			−0.0874259			−0.0437129	+	0.999044i	$0.513919\pi$
$542$	488653.	−	282124.i	1.66342	−	0.960377i
$543$	51184.7	−	408713.i	0.173596	−	1.38618i
$544$	−3445.90	+	5968.47i	−0.0116441	+	0.0201681i
$545$	−48781.3	−	28163.9i	−0.164233	−	0.0948200i
$546$	−91066.0	−	215985.i	−0.305472	−	0.724501i
$547$	138424.	+	239758.i	0.462634	+	0.801306i	0.999091	−	0.0426215i	$-0.0135710\pi$
$547$	138424.	+	239758.i	0.462634	+	0.801306i	−0.536457	+	0.843928i	$0.680238\pi$
$548$		−	102979.i		−	0.342915i
$549$	−329.630	−	1170.85i	−0.00109366	−	0.00388469i
$550$	398105.			1.31605
$551$	25345.0	−	14633.0i	0.0834813	−	0.0481980i
$552$	−205611.	−	155718.i	−0.674790	−	0.511047i
$553$	−6338.95	+	10979.4i	−0.0207285	+	0.0359027i
$554$	400705.	+	231347.i	1.30559	+	0.753780i
$555$	110065.	−	145331.i	0.357326	−	0.471815i
$556$	46821.9	+	81098.0i	0.151461	+	0.262338i
$557$			461786.i			1.48844i	0.667936	+	0.744219i	$0.267178\pi$
$557$			461786.i			1.48844i	−0.667936	+	0.744219i	$0.732822\pi$
$558$	200536.	−	788087.i	0.644056	−	2.53108i
$559$	194568.			0.622656
$560$	20953.4	−	12097.4i	0.0668157	−	0.0385761i
$561$	7990.43	−	3369.01i	0.0253889	−	0.0107047i
$562$	488995.	−	846964.i	1.54822	−	2.68159i
$563$	−154104.	−	88972.1i	−0.486181	−	0.280697i	0.236808	−	0.971556i	$-0.423899\pi$
$563$	−154104.	−	88972.1i	−0.486181	−	0.280697i	−0.722989	+	0.690860i	$0.757232\pi$
$564$	−192439.	−	24099.9i	−0.604971	−	0.0757630i
$565$	26461.0	+	45831.8i	0.0828914	+	0.143572i
$566$			549930.i			1.71662i
$567$	8826.98	+	349412.i	0.0274566	+	1.08685i
$568$	137872.			0.427347
$569$	−5111.83	+	2951.31i	−0.0157889	+	0.00911572i	−0.507874	−	0.861432i	$-0.669568\pi$
$569$	−5111.83	+	2951.31i	−0.0157889	+	0.00911572i	0.492085	+	0.870547i	$0.336235\pi$
$570$	−4674.04	+	37322.4i	−0.0143861	+	0.114874i
$571$	−238346.	+	412828.i	−0.731031	+	1.26618i	0.225411	+	0.974264i	$0.427627\pi$
$571$	−238346.	+	412828.i	−0.731031	+	1.26618i	−0.956443	+	0.291920i	$0.905706\pi$
$572$	−217501.	−	125574.i	−0.664767	−	0.383803i
$573$	163359.	+	387445.i	0.497545	+	1.18005i
$574$	−219850.	−	380792.i	−0.667272	−	1.15575i
$575$		−	194442.i		−	0.588105i
$576$	−508194.	−	129315.i	−1.53174	−	0.389765i
$577$	209901.			0.630468			0.315234	−	0.949014i	$-0.397917\pi$
$577$	209901.			0.630468			0.315234	+	0.949014i	$0.397917\pi$
$578$	−473614.	+	273441.i	−1.41765	+	0.818480i
$579$	195206.	+	147838.i	0.582285	+	0.440990i
$580$	−85795.7	+	148603.i	−0.255041	+	0.441744i
$581$	−607417.	−	350693.i	−1.79943	−	1.03890i
$582$	−538455.	+	710978.i	−1.58966	+	2.09899i
$583$	−264302.	−	457785.i	−0.777614	−	1.34687i
$584$			68038.7i			0.199494i
$585$	−68545.2	+	19297.6i	−0.200293	+	0.0563887i
$586$	235255.			0.685083
$587$	−156552.	+	90385.1i	−0.454340	+	0.262313i	−0.709661	−	0.704543i	$-0.751152\pi$
$587$	−156552.	+	90385.1i	−0.454340	+	0.262313i	0.255321	+	0.966856i	$0.417819\pi$
$588$	−97613.6	+	41156.9i	−0.282329	+	0.119039i
$589$	−41468.6	+	71825.7i	−0.119533	+	0.207038i
$590$	222871.	+	128675.i	0.640250	+	0.369649i
$591$	577476.	+	72319.7i	1.65333	+	0.207053i
$592$	33131.0	+	57384.5i	0.0945346	+	0.163739i
$593$			468097.i			1.33115i	0.746332	+	0.665574i	$0.231813\pi$
$593$			468097.i			1.33115i	−0.746332	+	0.665574i	$0.768187\pi$
$594$	372311.	+	466631.i	1.05520	+	1.32252i
$595$	4839.60			0.0136702
$596$	207862.	−	120009.i	0.585171	−	0.337849i
$597$	28900.2	−	230769.i	0.0810871	−	0.647485i
$598$	−97765.8	+	169335.i	−0.273391	+	0.473527i
$599$	558557.	+	322483.i	1.55673	+	0.898780i	0.997566	+	0.0697251i	$0.0222122\pi$
$599$	558557.	+	322483.i	1.55673	+	0.898780i	0.559167	+	0.829055i	$0.311121\pi$
$600$	121804.	+	288887.i	0.338344	+	0.802465i
$601$	−127517.	−	220865.i	−0.353035	−	0.611474i	0.633745	−	0.773542i	$-0.281517\pi$
$601$	−127517.	−	220865.i	−0.353035	−	0.611474i	−0.986780	+	0.162068i	$0.948184\pi$
$602$		−	910302.i		−	2.51184i
$603$	293053.	−	300550.i	0.805956	−	0.826574i
$604$	267072.			0.732073
$605$	9967.76	−	5754.89i	0.0272325	−	0.0157227i
$606$	−519986.	−	393808.i	−1.41595	−	1.07236i
$607$	176351.	−	305449.i	0.478631	−	0.829013i	−0.521069	−	0.853514i	$-0.674467\pi$
$607$	176351.	−	305449.i	0.478631	−	0.829013i	0.999700	+	0.0245019i	$0.00779999\pi$
$608$	41904.3	+	24193.5i	0.113358	+	0.0654472i
$609$	156501.	−	206645.i	0.421971	−	0.557172i
$610$	−579.711	−	1004.09i	−0.00155795	−	0.00269844i
$611$			59690.9i			0.159892i
$612$	12043.6	+	11743.2i	0.0321553	+	0.0313532i
$613$	−37013.8			−0.0985015			−0.0492508	−	0.998786i	$-0.515683\pi$
$613$	−37013.8			−0.0985015			−0.0492508	+	0.998786i	$0.515683\pi$
$614$	−40030.6	+	23111.7i	−0.106183	+	0.0613048i
$615$	−123087.	+	51897.2i	−0.325433	+	0.137212i
$616$	−238519.	+	413127.i	−0.628581	+	1.08873i
$617$	−493797.	−	285094.i	−1.29711	−	0.748888i	−0.317208	−	0.948356i	$-0.602745\pi$
$617$	−493797.	−	285094.i	−1.29711	−	0.748888i	−0.979904	+	0.199467i	$0.936079\pi$
$618$	−208486.	−	26109.5i	−0.545883	−	0.0683631i
$619$	220407.	+	381756.i	0.575233	+	0.996333i	0.996016	+	0.0891715i	$0.0284219\pi$
$619$	220407.	+	381756.i	0.575233	+	0.996333i	−0.420783	+	0.907161i	$0.638245\pi$
$620$		−	486276.i		−	1.26503i
$621$	227912.	−	181844.i	0.590995	−	0.471537i
$622$	−561296.			−1.45081
$623$	26570.7	−	15340.6i	0.0684583	−	0.0395244i
$624$	3216.23	−	25681.8i	0.00825996	−	0.0659562i
$625$	−74789.0	+	129538.i	−0.191460	+	0.331618i
$626$	416759.	+	240616.i	1.06350	+	0.614011i
$627$	−23653.6	−	56100.3i	−0.0601676	−	0.142702i
$628$	76050.9	+	131724.i	0.192835	+	0.333999i
$629$			13254.1i			0.0335003i
$630$	90285.3	+	320694.i	0.227476	+	0.807997i
$631$	−80926.3			−0.203250			−0.101625	−	0.994823i	$-0.532404\pi$
$631$	−80926.3			−0.203250			−0.101625	+	0.994823i	$0.532404\pi$
$632$	−14767.6	+	8526.05i	−0.0369721	+	0.0213459i
$633$	−330454.	−	250267.i	−0.824714	−	0.624592i
$634$	−161321.	+	279417.i	−0.401341	+	0.695143i
$635$	137976.	+	79660.7i	0.342182	+	0.197559i
$636$	619063.	−	817414.i	1.53046	−	2.02082i
$637$	16302.2	+	28236.3i	0.0401761	+	0.0695870i
$638$		−	442727.i		−	1.08766i
$639$	−38434.3	+	151043.i	−0.0941278	+	0.369913i
$640$	−331317.			−0.808879
$641$	−131917.	+	76162.1i	−0.321058	+	0.185363i	−0.651864	−	0.758336i	$-0.726013\pi$
$641$	−131917.	+	76162.1i	−0.321058	+	0.185363i	0.330806	+	0.943699i	$0.392679\pi$
$642$	621252.	−	261939.i	1.50729	−	0.635521i
$643$	−58437.1	+	101216.i	−0.141340	+	0.244809i	−0.928002	−	0.372576i	$-0.878475\pi$
$643$	−58437.1	+	101216.i	−0.141340	+	0.244809i	0.786661	+	0.617385i	$0.211808\pi$
$644$	497013.	+	286951.i	1.19838	+	0.691888i
$645$	−274405.	−	34364.8i	−0.659587	−	0.0826027i
$646$	−1367.31	−	2368.26i	−0.00327645	−	0.00567498i
$647$		−	481407.i		−	1.15002i	−0.818148	−	0.575008i	$-0.804999\pi$
$647$		−	481407.i		−	1.15002i	0.818148	−	0.575008i	$-0.195001\pi$
$648$	−224702.	+	412940.i	−0.535127	+	0.983416i
$649$	−416553.			−0.988965
$650$	205834.	−	118838.i	0.487181	−	0.281274i
$651$	−91284.6	+	728912.i	−0.215395	+	1.71994i
$652$	−29003.3	+	50235.2i	−0.0682263	+	0.118171i
$653$	399091.	+	230415.i	0.935935	+	0.540363i	0.888684	−	0.458520i	$-0.151620\pi$
$653$	399091.	+	230415.i	0.935935	+	0.540363i	0.0472516	+	0.998883i	$0.484954\pi$
$654$	109526.	+	259768.i	0.256072	+	0.607338i
$655$	20013.2	+	34663.9i	0.0466482	+	0.0807970i
$656$		−	48551.9i		−	0.112823i
$657$	−74538.5	−	18967.0i	−0.172683	−	0.0439408i
$658$	279268.			0.645015
$659$	142960.	−	82538.2i	0.329189	−	0.190057i	−0.326292	−	0.945269i	$-0.605799\pi$
$659$	142960.	−	82538.2i	0.329189	−	0.190057i	0.655481	+	0.755212i	$0.272466\pi$
$660$	284569.	+	215516.i	0.653280	+	0.494757i
$661$	140878.	−	244008.i	0.322434	−	0.558472i	−0.658556	−	0.752532i	$-0.728832\pi$
$661$	140878.	−	244008.i	0.322434	−	0.558472i	0.980990	+	0.194060i	$0.0621657\pi$
$662$	−465383.	−	268689.i	−1.06193	−	0.613104i
$663$	3125.65	−	4127.12i	0.00711071	−	0.00938902i
$664$	−471691.	−	816992.i	−1.06985	−	1.85303i
$665$		−	33978.6i		−	0.0768355i
$666$	−878276.	+	247262.i	−1.98008	+	0.557454i
$667$	−216236.			−0.486046
$668$	−863556.	+	498574.i	−1.93525	+	1.11732i
$669$	181709.	−	76614.0i	0.405998	−	0.171181i
$670$	200061.	−	346517.i	0.445670	−	0.771924i
$671$	1625.25	+	938.337i	0.00360973	+	0.00208408i
$672$	425259.	+	53256.9i	0.941706	+	0.117934i
$673$	378387.	+	655386.i	0.835423	+	1.44699i	0.893686	+	0.448694i	$0.148111\pi$
$673$	378387.	+	655386.i	0.835423	+	1.44699i	−0.0582627	+	0.998301i	$0.518556\pi$
$674$			307855.i			0.677683i
$675$	−350440.	+	52907.4i	−0.769141	+	0.116120i
$676$	619357.			1.35534
$677$	−59053.2	+	34094.4i	−0.128845	+	0.0743885i	−0.563037	−	0.826432i	$-0.690367\pi$
$677$	−59053.2	+	34094.4i	−0.128845	+	0.0743885i	0.434192	+	0.900820i	$0.357034\pi$
$678$	32913.4	−	262815.i	0.0716002	−	0.571731i
$679$	402833.	−	697728.i	0.873747	−	1.51337i
$680$	5637.30	+	3254.70i	0.0121914	+	0.00703870i
$681$	174080.	+	412873.i	0.375365	+	0.890270i
$682$	627326.	+	1.08656e6i	1.34873	+	2.33606i
$683$		−	31351.1i		−	0.0672066i	−0.999435	−	0.0336033i	$-0.989302\pi$
$683$		−	31351.1i		−	0.0672066i	0.999435	−	0.0336033i	$-0.0106983\pi$
$684$	82448.1	−	84557.2i	0.176225	−	0.180733i
$685$	45048.7			0.0960065
$686$	−593726.	+	342788.i	−1.26165	+	0.728412i
$687$	−204627.	−	154973.i	−0.433561	−	0.328355i
$688$	50257.9	−	87049.3i	0.106176	−	0.183903i
$689$	−273307.	−	157794.i	−0.575722	−	0.332393i
$690$	167790.	−	221551.i	0.352426	−	0.465345i
$691$	−187442.	−	324659.i	−0.392565	−	0.679942i	0.600222	−	0.799833i	$-0.295079\pi$
$691$	−187442.	−	324659.i	−0.392565	−	0.679942i	−0.992787	+	0.119891i	$0.961745\pi$
$692$			1.30866e6i			2.73285i
$693$	−386102.	−	376471.i	−0.803962	−	0.783908i
$694$	−290405.			−0.602955
$695$	−35476.8	+	20482.5i	−0.0734471	+	0.0424047i
$696$	321268.	−	135456.i	0.663206	−	0.279628i
$697$	4855.81	−	8410.52i	0.00999531	−	0.0173124i
$698$	−1.05811e6	−	610901.i	−2.17180	−	1.25389i
$699$	−393379.	−	49264.5i	−0.805114	−	0.100828i
$700$	−348801.	−	604140.i	−0.711838	−	1.23294i
$701$		−	97448.5i		−	0.198308i	−0.995072	−	0.0991538i	$-0.968386\pi$
$701$		−	97448.5i		−	0.198308i	0.995072	−	0.0991538i	$-0.0316136\pi$
$702$	331792.	+	130126.i	0.673274	+	0.264052i
$703$	93056.2			0.188293
$704$	700663.	−	404528.i	1.41372	−	0.816212i
$705$	10542.7	−	84183.6i	0.0212115	−	0.169375i
$706$	555961.	−	962952.i	1.11541	−	1.93195i
$707$	510295.	+	294619.i	1.02090	+	0.589416i
$708$	−313925.	−	744549.i	−0.626266	−	1.48534i
$709$	146263.	+	253334.i	0.290965	+	0.503967i	0.974038	−	0.226383i	$-0.0726902\pi$
$709$	146263.	+	253334.i	0.290965	+	0.503967i	−0.683073	+	0.730350i	$0.739357\pi$
$710$			148561.i			0.294704i
$711$	−5223.84	−	18555.1i	−0.0103336	−	0.0367049i
$712$	41267.0			0.0814034
$713$	530697.	−	306398.i	1.04392	−	0.602708i
$714$	−19309.0	−	14623.6i	−0.0378760	−	0.0286851i
$715$	54933.3	−	95147.2i	0.107454	−	0.186116i
$716$	1.11310e6	+	642648.i	2.17124	+	1.25357i
$717$	−111798.	+	147619.i	−0.217469	+	0.287147i
$718$	228213.	+	395276.i	0.442681	+	0.766746i
$719$		−	655579.i		−	1.26814i	−0.773276	−	0.634070i	$-0.781383\pi$
$719$		−	655579.i		−	1.26814i	0.773276	−	0.634070i	$-0.218617\pi$
$720$	−9071.87	+	35651.6i	−0.0174998	+	0.0687724i
$721$	189807.			0.365125
$722$	722896.	−	417364.i	1.38676	−	0.800647i
$723$	−480310.	+	202513.i	−0.918851	+	0.387416i
$724$	−616376.	+	1.06760e6i	−1.17590	+	2.03671i
$725$	227630.	+	131422.i	0.433065	+	0.250030i
$726$	−57158.6	−	7158.20i	−0.108445	−	0.0135810i
$727$	−129630.	−	224526.i	−0.245266	−	0.424814i	0.716940	−	0.697135i	$-0.245542\pi$
$727$	−129630.	−	224526.i	−0.245266	−	0.424814i	−0.962206	+	0.272321i	$0.912209\pi$
$728$			284801.i			0.537377i
$729$	−389749.	−	361282.i	−0.733382	−	0.679817i
$730$	−73313.3			−0.137574
$731$	17412.1	−	10052.9i	0.0325849	−	0.0188129i
$732$	−452.362	+	3612.13i	−0.000844236	+	0.00674126i
$733$	−41254.4	+	71454.8i	−0.0767826	+	0.132991i	−0.901860	−	0.432028i	$-0.857798\pi$
$733$	−41254.4	+	71454.8i	−0.0767826	+	0.132991i	0.825077	+	0.565020i	$0.191131\pi$
$734$	−999691.	−	577172.i	−1.85555	−	1.07130i
$735$	−18004.3	−	42701.7i	−0.0333275	−	0.0790442i
$736$	−178758.	−	309618.i	−0.329996	−	0.571571i
$737$			647650.i			1.19235i
$738$	647907.	+	164866.i	1.18960	+	0.302703i
$739$	−730583.			−1.33777			−0.668884	−	0.743367i	$-0.733228\pi$
$739$	−730583.			−1.33777			−0.668884	+	0.743367i	$0.733228\pi$
$740$	−472509.	+	272803.i	−0.862872	+	0.498179i
$741$	−28976.3	−	21945.0i	−0.0527723	−	0.0399667i
$742$	−738251.	+	1.27869e6i	−1.34090	+	2.32251i
$743$	391257.	+	225892.i	0.708735	+	0.409189i	0.810593	−	0.585611i	$-0.199145\pi$
$743$	391257.	+	225892.i	0.708735	+	0.409189i	−0.101857	+	0.994799i	$0.532479\pi$
$744$	−596533.	+	787666.i	−1.07768	+	1.42297i
$745$	52498.8	+	90930.6i	0.0945882	+	0.163832i
$746$		−	440244.i		−	0.791071i
$747$	1.02653e6	−	289001.i	1.83963	−	0.517914i
$748$	−25952.5			−0.0463849
$749$	−527455.	+	304526.i	−0.940203	+	0.542826i
$750$	−711462.	+	299974.i	−1.26482	+	0.533287i
$751$	−290081.	+	502435.i	−0.514327	+	0.890840i	0.485535	+	0.874217i	$0.338625\pi$
$751$	−290081.	+	502435.i	−0.514327	+	0.890840i	−0.999862	+	0.0166228i	$0.994709\pi$
$752$	26705.5	+	15418.4i	0.0472243	+	0.0272650i
$753$	483487.	+	60549.0i	0.852696	+	0.106787i
$754$	−132158.	−	228905.i	−0.232462	−	0.402636i
$755$			116832.i			0.204960i
$756$	381931.	−	973838.i	0.668253	−	1.70390i
$757$	1.00242e6			1.74928			0.874641	−	0.484771i	$-0.161097\pi$
$757$	1.00242e6			1.74928			0.874641	+	0.484771i	$0.161097\pi$
$758$	−249553.	+	144079.i	−0.434334	+	0.250763i
$759$	−55899.3	+	446358.i	−0.0970337	+	0.774819i
$760$	22851.0	−	39579.2i	0.0395620	−	0.0685235i
$761$	−73367.2	−	42358.6i	−0.126687	−	0.0731429i	0.435317	−	0.900277i	$-0.356636\pi$
$761$	−73367.2	−	42358.6i	−0.126687	−	0.0731429i	−0.562004	+	0.827134i	$0.689970\pi$
$762$	−309792.	−	734746.i	−0.533531	−	1.26540i
$763$	−127334.	−	220548.i	−0.218723	−	0.378839i
$764$		−	1.25840e6i		−	2.15592i
$765$	−5137.12	+	5268.53i	−0.00877802	+	0.00900258i
$766$	1.21313e6			2.06752
$767$	−215373.	+	124345.i	−0.366100	+	0.211368i
$768$	578717.	+	438288.i	0.981170	+	0.743082i
$769$	341763.	−	591950.i	0.577926	−	1.00100i	−0.417791	−	0.908543i	$-0.637196\pi$
$769$	341763.	−	591950.i	0.577926	−	1.00100i	0.995717	−	0.0924535i	$-0.0294710\pi$
$770$	−445153.	−	257009.i	−0.750807	−	0.433478i
$771$	−618156.	+	816216.i	−1.03989	+	1.37308i
$772$	−366425.	−	634666.i	−0.614823	−	1.06490i
$773$			235888.i			0.394772i	0.980326	+	0.197386i	$0.0632453\pi$
$773$			235888.i			0.394772i	−0.980326	+	0.197386i	$0.936755\pi$
$774$	990981.	+	966263.i	1.65418	+	1.61292i
$775$	−744879.			−1.24017
$776$	938462.	−	541821.i	1.55845	−	0.899773i
$777$	759486.	−	320223.i	1.25799	−	0.530408i
$778$	99737.5	−	172750.i	0.164778	−	0.285404i
$779$	−59049.7	−	34092.4i	−0.0973068	−	0.0561801i
$780$	211466.	+	26482.7i	0.347577	+	0.0435284i
$781$	−120232.	−	208248.i	−0.197114	−	0.341412i
$782$			20205.3i			0.0330409i
$783$	58837.6	+	389720.i	0.0959690	+	0.635665i
$784$	16843.8			0.0274036
$785$	−57623.5	+	33268.9i	−0.0935104	+	0.0539883i
$786$	24893.4	−	198775.i	0.0402939	−	0.321749i
$787$	228728.	−	396169.i	0.369292	−	0.639633i	−0.620163	−	0.784473i	$-0.712933\pi$
$787$	228728.	−	396169.i	0.369292	−	0.639633i	0.989455	+	0.144840i	$0.0462668\pi$
$788$	−1.50842e6	−	870888.i	−2.42924	−	1.40252i
$789$	155121.	+	367908.i	0.249183	+	0.590997i
$790$	−9187.01	−	15912.4i	−0.0147204	−	0.0254965i
$791$			239269.i			0.382414i
$792$	−196560.	−	698182.i	−0.313361	−	1.11306i
$793$	1120.41			0.00178169
$794$	1.33765e6	−	772291.i	2.12178	−	1.22501i
$795$	357583.	+	270813.i	0.565773	+	0.428484i
$796$	−348022.	+	602791.i	−0.549263	+	0.951351i
$797$	−148023.	−	85461.0i	−0.233030	−	0.134540i	0.378939	−	0.925422i	$-0.376289\pi$
$797$	−148023.	−	85461.0i	−0.233030	−	0.134540i	−0.611969	+	0.790882i	$0.709622\pi$
$798$	−102671.	+	135568.i	−0.161229	+	0.212888i
$799$	3084.09	+	5341.79i	0.00483095	+	0.00836746i
$800$			434575.i			0.679023i
$801$	−11503.9	+	45209.2i	−0.0179300	+	0.0704632i
$802$	−1.53465e6			−2.38594
$803$	102769.	−	59333.5i	0.159378	−	0.0920171i
$804$	−1.15761e6	+	488085.i	−1.79082	+	0.755064i
$805$	−125528.	+	217422.i	−0.193709	+	0.335514i
$806$	648699.	+	374526.i	0.998557	+	0.576517i
$807$	39558.9	+	4954.12i	0.0607432	+	0.00760711i
$808$	396271.	+	686361.i	0.606973	+	1.05131i
$809$		−	252280.i		−	0.385465i	−0.981251	−	0.192733i	$-0.938265\pi$
$809$		−	252280.i		−	0.385465i	0.981251	−	0.192733i	$-0.0617350\pi$
$810$	−444952.	−	242121.i	−0.678178	−	0.369031i
$811$	166784.			0.253579			0.126789	−	0.991930i	$-0.459533\pi$
$811$	166784.			0.253579			0.126789	+	0.991930i	$0.459533\pi$
$812$	−671856.	+	387896.i	−1.01898	+	0.588307i
$813$	96305.0	−	769000.i	0.145703	−	1.16344i
$814$	703865.	−	1.21913e6i	1.06228	−	1.83993i
$815$	−21975.7	−	12687.7i	−0.0330847	−	0.0191015i
$816$	−1039.09	−	2464.46i	−0.00156054	−	0.00370119i
$817$	−70580.7	−	122249.i	−0.105741	−	0.183148i
$818$			1.95124e6i			2.91611i
$819$	−312009.	−	79393.4i	−0.465156	−	0.118363i
$820$	399780.			0.594557
$821$	−235829.	+	136156.i	−0.349873	+	0.201999i	−0.664629	−	0.747173i	$-0.731411\pi$
$821$	−235829.	+	136156.i	−0.349873	+	0.201999i	0.314756	+	0.949173i	$0.398077\pi$
$822$	−179735.	−	136121.i	−0.266005	−	0.201457i
$823$	−482314.	+	835392.i	−0.712082	+	1.23336i	0.251992	+	0.967729i	$0.418914\pi$
$823$	−482314.	+	835392.i	−0.712082	+	1.23336i	−0.964074	+	0.265633i	$0.914419\pi$
$824$	221092.	+	127648.i	0.325626	+	0.188000i
$825$	330128.	−	435903.i	0.485037	−	0.640445i
$826$	581759.	+	1.00764e6i	0.852674	+	1.47687i
$827$		−	430905.i		−	0.630043i	−0.949085	−	0.315021i	$-0.897988\pi$
$827$		−	430905.i		−	0.630043i	0.949085	−	0.315021i	$-0.102012\pi$
$828$	−839950.	+	236472.i	−1.22516	+	0.344921i
$829$	462870.			0.673520			0.336760	−	0.941591i	$-0.390669\pi$
$829$	462870.			0.673520			0.336760	+	0.941591i	$0.390669\pi$
$830$	880328.	−	508257.i	1.27787	−	0.737781i
$831$	585597.	−	246906.i	0.848002	−	0.357544i
$832$	241511.	−	418310.i	0.348892	−	0.604299i
$833$	2917.80	+	1684.59i	0.00420500	+	0.00242776i
$834$	203436.	+	25477.2i	0.292480	+	0.0366285i
$835$	−218104.	−	377768.i	−0.312818	−	0.541816i
$836$			182211.i			0.260713i
$837$	−696618.	−	873097.i	−0.994361	−	1.24627i
$838$	241618.			0.344066
$839$	−696889.	+	402349.i	−0.990010	+	0.571583i	−0.905277	−	0.424821i	$-0.860337\pi$
$839$	−696889.	+	402349.i	−0.990010	+	0.571583i	−0.0847327	+	0.996404i	$0.527004\pi$
$840$	50301.9	−	401663.i	0.0712895	−	0.569250i
$841$	−207488.	+	359379.i	−0.293360	+	0.508114i
$842$	1.36537e6	+	788297.i	1.92587	+	1.11190i
$843$	−521880.	−	1.23777e6i	−0.734372	−	1.74174i
$844$	620301.	+	1.07439e6i	0.870799	+	1.50827i
$845$			270942.i			0.379457i
$846$	−296436.	+	304019.i	−0.414181	+	0.424777i
$847$	52037.6			0.0725354
$848$	−141193.	+	81518.0i	−0.196346	+	0.113360i
$849$	602143.	+	456029.i	0.835381	+	0.632670i
$850$	12280.2	−	21269.9i	0.0169968	−	0.0294393i
$851$	−595447.	−	343781.i	−0.822212	−	0.474704i
$852$	281614.	−	371845.i	0.387949	−	0.512250i
$853$	−105790.	−	183234.i	−0.145394	−	0.251830i	0.784126	−	0.620602i	$-0.213112\pi$
$853$	−105790.	−	183234.i	−0.145394	−	0.251830i	−0.929520	+	0.368772i	$0.879778\pi$
$854$		−	5241.94i		−	0.00718747i
$855$	36990.1	+	36067.4i	0.0506003	+	0.0493381i
$856$	−819191.			−1.11799
$857$	−245348.	+	141652.i	−0.334057	+	0.192868i	−0.657641	−	0.753332i	$-0.728446\pi$
$857$	−245348.	+	141652.i	−0.334057	+	0.192868i	0.323584	+	0.946199i	$0.395112\pi$
$858$	−506674.	+	213629.i	−0.688262	+	0.290192i
$859$	15498.6	−	26844.3i	0.0210042	−	0.0363803i	−0.855332	−	0.518080i	$-0.826647\pi$
$859$	15498.6	−	26844.3i	0.0210042	−	0.0363803i	0.876336	+	0.481700i	$0.159980\pi$
$860$	716771.	+	413828.i	0.969133	+	0.559529i
$861$	−599257.	−	75047.4i	−0.808364	−	0.101235i
$862$	−533236.	−	923592.i	−0.717637	−	1.24298i
$863$		−	1.35611e6i		−	1.82085i	−0.413677	−	0.910424i	$-0.635756\pi$
$863$		−	1.35611e6i		−	1.82085i	0.413677	−	0.910424i	$-0.364244\pi$
$864$	−509379.	+	406419.i	−0.682360	+	0.544435i
$865$	−572482.			−0.765120
$866$	−1.51307e6	+	873569.i	−2.01754	+	1.16483i
$867$	−93340.9	+	745332.i	−0.124175	+	0.991543i
$868$	1.09927e6	−	1.90399e6i	1.45903	−	2.52711i
$869$	25756.2	+	14870.4i	0.0341069	+	0.0196916i
$870$	145957.	+	346173.i	0.192835	+	0.457356i
$871$	193330.	+	334858.i	0.254838	+	0.441392i
$872$		−	342534.i		−	0.450475i
$873$	331969.	+	1.17916e6i	0.435582	+	1.54719i
$874$	141860.			0.185711
$875$	604045.	−	348746.i	0.788957	−	0.455504i
$876$	183502.	+	138974.i	0.239129	+	0.181103i
$877$	226465.	−	392249.i	0.294443	−	0.509991i	−0.680412	−	0.732830i	$-0.738199\pi$
$877$	226465.	−	392249.i	0.294443	−	0.509991i	0.974855	+	0.222839i	$0.0715324\pi$
$878$	−208926.	−	120623.i	−0.271021	−	0.156474i
$879$	195085.	−	257591.i	0.252491	−	0.333390i
$880$	−28379.1	−	49154.0i	−0.0366465	−	0.0634736i
$881$		−	1.13788e6i		−	1.46603i	−0.680211	−	0.733016i	$-0.738112\pi$
$881$		−	1.13788e6i		−	1.46603i	0.680211	−	0.733016i	$-0.261888\pi$
$882$	−57195.7	+	224774.i	−0.0735235	+	0.288941i
$883$	970367.			1.24456			0.622279	−	0.782796i	$-0.286207\pi$
$883$	970367.			1.24456			0.622279	+	0.782796i	$0.286207\pi$
$884$	−13418.4	+	7747.09i	−0.0171710	+	0.00991367i
$885$	325708.	−	137328.i	0.415854	−	0.175337i
$886$	450629.	−	780512.i	0.574052	−	0.994287i
$887$	1.12349e6	+	648647.i	1.42798	+	0.824444i	0.996961	−	0.0779001i	$-0.0248215\pi$
$887$	1.12349e6	+	648647.i	1.42798	+	0.824444i	0.431017	+	0.902344i	$0.358155\pi$
$888$	1.10002e6	+	137760.i	1.39501	+	0.174702i
$889$	360159.	+	623814.i	0.455712	+	0.789317i
$890$			44466.1i			0.0561369i
$891$	819675.	−	20707.0i	1.03249	−	0.0260832i
$892$	−590181.			−0.741747
$893$	37504.4	−	21653.2i	0.0470305	−	0.0271531i
$894$	65300.5	−	521428.i	0.0817036	−	0.652407i
$895$	−281130.	+	486932.i	−0.350963	+	0.607886i
$896$	−1.29725e6	−	748968.i	−1.61588	−	0.932927i
$897$	104341.	+	247469.i	0.129679	+	0.307565i
$898$	−571395.	−	989685.i	−0.708572	−	1.22728i
$899$			828370.i			1.02496i
$900$	1.02793e6	+	261565.i	1.26905	+	0.322920i
$901$	−32611.4			−0.0401716
$902$	−893289.	+	515740.i	−1.09794	+	0.633896i
$903$	−996731.	−	754867.i	−1.22237	−	0.925753i
$904$	−160912.	+	278707.i	−0.196902	+	0.341044i
$905$	−467026.	−	269638.i	−0.570222	−	0.329218i
$906$	353026.	−	466137.i	0.430081	−	0.567881i
$907$	−76984.1	−	133340.i	−0.0935807	−	0.162087i	0.815435	−	0.578849i	$-0.196498\pi$
$907$	−76984.1	−	133340.i	−0.0935807	−	0.162087i	−0.909015	+	0.416763i	$0.863165\pi$
$908$		−	1.34099e6i		−	1.62650i
$909$	−862397.	+	242792.i	−1.04371	+	0.293837i
$910$	−306880.			−0.370583
$911$	−927466.	+	535473.i	−1.11753	+	0.645209i	−0.940770	−	0.339044i	$-0.889896\pi$
$911$	−927466.	+	535473.i	−1.11753	+	0.645209i	−0.176764	+	0.984253i	$0.556563\pi$
$912$	−17302.8	+	7295.41i	−0.0208031	+	0.00877122i
$913$	−822680.	+	1.42492e6i	−0.986937	+	1.70942i
$914$	654339.	+	377783.i	0.783268	+	0.452220i
$915$	−1580.15	−	197.888i	−0.00188736	−	0.000236362i
$916$	384110.	+	665298.i	0.457788	+	0.792912i
$917$			180966.i			0.215208i
$918$	36415.7	−	5497.83i	0.0432119	−	0.00652388i
$919$	747688.			0.885298			0.442649	−	0.896695i	$-0.354039\pi$
$919$	747688.			0.885298			0.442649	+	0.896695i	$0.354039\pi$
$920$	−292438.	+	168839.i	−0.345508	+	0.199479i
$921$	−7889.33	+	62996.6i	−0.00930081	+	0.0742674i
$922$	−1.32840e6	+	2.30085e6i	−1.56267	+	2.70662i
$923$	−124328.	−	71781.1i	−0.145938	−	0.0842571i
$924$	627020.	+	1.48713e6i	0.734408	+	1.74183i
$925$	417881.	+	723790.i	0.488392	+	0.845920i
$926$		−	475625.i		−	0.554680i
$927$	−201475.	+	206629.i	−0.234457	+	0.240454i
$928$	483285.			0.561187
$929$	1.28522e6	−	742020.i	1.48917	−	0.859774i	0.489249	−	0.872144i	$-0.337271\pi$
$929$	1.28522e6	−	742020.i	1.48917	−	0.859774i	0.999923	+	0.0123702i	$0.00393765\pi$
$930$	−848728.	−	642778.i	−0.981302	−	0.743182i
$931$	11827.4	−	20485.7i	0.0136456	−	0.0236348i
$932$	1.02754e6	+	593253.i	1.18296	+	0.682980i
$933$	−465455.	+	614589.i	−0.534705	+	0.706027i
$934$	−1.17554e6	−	2.03609e6i	−1.34754	−	2.33401i
$935$		−	11353.1i		−	0.0129865i
$936$	−310043.	−	302309.i	−0.353892	−	0.345064i
$937$	−650560.			−0.740983			−0.370491	−	0.928836i	$-0.620811\pi$
$937$	−650560.			−0.740983			−0.370491	+	0.928836i	$0.620811\pi$
$938$	1.56666e6	−	904510.i	1.78061	−	1.02803i
$939$	609059.	−	256798.i	0.690761	−	0.291246i
$940$	−126957.	+	219895.i	−0.143681	+	0.248863i
$941$	−352436.	−	203479.i	−0.398017	−	0.229795i	0.287611	−	0.957747i	$-0.407139\pi$
$941$	−352436.	−	203479.i	−0.398017	−	0.229795i	−0.685628	+	0.727952i	$0.740472\pi$
$942$	330433.	+	41381.4i	0.372376	+	0.0466341i
$943$	251898.	+	436300.i	0.283270	+	0.490638i
$944$			128476.i			0.144171i
$945$	426012.	+	167078.i	0.477043	+	0.187092i
$946$	−2.13545e6			−2.38620
$947$	718809.	−	415005.i	0.801519	−	0.462757i	−0.0424832	−	0.999097i	$-0.513527\pi$
$947$	718809.	−	415005.i	0.801519	−	0.462757i	0.844002	+	0.536340i	$0.180194\pi$
$948$	−7168.83	+	57243.5i	−0.00797685	+	0.0636956i
$949$	35423.3	−	61355.0i	0.0393330	−	0.0681267i
$950$	−149335.	−	86218.5i	−0.165468	−	0.0955330i
$951$	172170.	+	408344.i	0.190370	+	0.451508i
$952$	14715.0	+	25487.1i	0.0162363	+	0.0281221i
$953$			927863.i			1.02164i	0.859688	+	0.510820i	$0.170658\pi$
$953$			927863.i			1.02164i	−0.859688	+	0.510820i	$0.829342\pi$
$954$	−608382.	−	2.16098e6i	−0.668467	−	2.37440i
$955$	550496.			0.603597
$956$	479949.	−	277099.i	0.525145	−	0.303193i
$957$	−484762.	−	367131.i	−0.529303	−	0.400864i
$958$	83870.5	−	145268.i	0.0913857	−	0.158285i
$959$	176385.	+	101836.i	0.191790	+	0.110730i
$960$	−414492.	+	547298.i	−0.449753	+	0.593856i
$961$	−712006.	−	1.23323e6i	−0.770968	−	1.33536i
$962$		−	840444.i		−	0.908152i
$963$	228364.	−	897450.i	0.246249	−	0.967737i
$964$	1.56002e6			1.67872
$965$	277639.	−	160295.i	0.298143	−	0.172133i
$966$	1.15780e6	−	488166.i	1.24074	−	0.523134i
$967$	556238.	−	963433.i	0.594851	−	1.03031i	−0.398717	−	0.917074i	$-0.630544\pi$
$967$	556238.	−	963433.i	0.594851	−	1.03031i	0.993568	−	0.113238i	$-0.0361222\pi$
$968$	60614.8	+	34995.9i	0.0646886	+	0.0373480i
$969$	−3726.96	−	466.742i	−0.00396924	−	0.000497084i
$970$	583825.	+	1.01121e6i	0.620496	+	1.07473i
$971$		−	68160.6i		−	0.0722927i	−0.999347	−	0.0361464i	$-0.988492\pi$
$971$		−	68160.6i		−	0.0722927i	0.999347	−	0.0361464i	$-0.0115083\pi$
$972$	654739.	+	1.44949e6i	0.693004	+	1.53420i
$973$	−185210.			−0.195631
$974$	−1.40312e6	+	810090.i	−1.47903	+	0.853917i
$975$	40566.3	−	323924.i	0.0426733	−	0.340748i
$976$	289.408	−	501.270i	0.000303817	−	0.000526226i
$977$	−685124.	−	395556.i	−0.717761	−	0.414399i	0.0961671	−	0.995365i	$-0.469342\pi$
$977$	−685124.	−	395556.i	−0.717761	−	0.414399i	−0.813928	+	0.580966i	$0.802675\pi$
$978$	49340.9	+	117024.i	0.0515857	+	0.122348i
$979$	−35987.0	−	62331.4i	−0.0375475	−	0.0650341i
$980$			138693.i			0.144412i
$981$	375257.	+	95487.4i	0.389933	+	0.0992220i
$982$	2.24263e6			2.32560
$983$	−948495.	+	547614.i	−0.981585	+	0.566718i	−0.902748	−	0.430169i	$-0.858454\pi$
$983$	−948495.	+	547614.i	−0.981585	+	0.566718i	−0.0788368	+	0.996888i	$0.525121\pi$
$984$	−647560.	−	490425.i	−0.668790	−	0.506504i
$985$	380975.	−	659868.i	0.392667	−	0.680119i
$986$	−23654.0	−	13656.6i	−0.0243305	−	0.0140472i
$987$	231583.	−	305783.i	0.237724	−	0.313892i
$988$	54391.9	+	94209.5i	0.0557212	+	0.0965119i
$989$			1.04300e6i			1.06633i
$990$	752307.	−	211798.i	0.767582	−	0.216098i
$991$	278492.			0.283573			0.141787	−	0.989897i	$-0.454715\pi$
$991$	278492.			0.283573			0.141787	+	0.989897i	$0.454715\pi$
$992$	−1.18610e6	+	684795.i	−1.20531	+	0.695884i
$993$	−680118.	+	286759.i	−0.689741	+	0.290816i
$994$	−335833.	+	581680.i	−0.339900	+	0.588723i
$995$	−263695.	−	152244.i	−0.266351	−	0.153778i
$996$	−3.16691e6	−	396605.i	−3.19240	−	0.399797i
$997$	−665723.	−	1.15307e6i	−0.669736	−	1.16002i	−0.977978	−	0.208708i	$-0.933074\pi$
$997$	−665723.	−	1.15307e6i	−0.669736	−	1.16002i	0.308242	−	0.951308i	$-0.400259\pi$
$998$			1.29633e6i			1.30154i
$999$	−457572.	+	1.16671e6i	−0.458488	+	1.16904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.5.d.a.5.1	yes	6
3.2	odd	2		27.5.d.a.17.3		6
4.3	odd	2		144.5.q.a.113.2		6
9.2	odd	6	inner	9.5.d.a.2.1	✓	6
9.4	even	3		81.5.b.a.80.1		6
9.5	odd	6		81.5.b.a.80.6		6
9.7	even	3		27.5.d.a.8.3		6
12.11	even	2		432.5.q.a.17.2		6
36.7	odd	6		432.5.q.a.305.2		6
36.11	even	6		144.5.q.a.65.2		6
36.23	even	6		1296.5.e.c.161.4		6
36.31	odd	6		1296.5.e.c.161.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.1	✓	6	9.2	odd	6	inner
9.5.d.a.5.1	yes	6	1.1	even	1	trivial
27.5.d.a.8.3		6	9.7	even	3
27.5.d.a.17.3		6	3.2	odd	2
81.5.b.a.80.1		6	9.4	even	3
81.5.b.a.80.6		6	9.5	odd	6
144.5.q.a.65.2		6	36.11	even	6
144.5.q.a.113.2		6	4.3	odd	2
432.5.q.a.17.2		6	12.11	even	2
432.5.q.a.305.2		6	36.7	odd	6
1296.5.e.c.161.3		6	36.31	odd	6
1296.5.e.c.161.4		6	36.23	even	6

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.67463 + 3.27625i) q^{2} +(-1.11837 + 8.93024i) q^{3} +(13.4676 - 23.3266i) q^{4} +(10.2044 + 5.89150i) q^{5} +(-22.9114 - 54.3399i) q^{6} +(26.6364 + 46.1356i) q^{7} +71.6534i q^{8} +(-78.4985 - 19.9746i) q^{9} +O(q^{10})\)	\(q+(-5.67463 + 3.27625i) q^{2} +(-1.11837 + 8.93024i) q^{3} +(13.4676 - 23.3266i) q^{4} +(10.2044 + 5.89150i) q^{5} +(-22.9114 - 54.3399i) q^{6} +(26.6364 + 46.1356i) q^{7} +71.6534i q^{8} +(-78.4985 - 19.9746i) q^{9} -77.2081 q^{10} +(108.228 - 62.4856i) q^{11} +(193.251 + 146.357i) q^{12} +(37.3052 - 64.6145i) q^{13} +(-302.304 - 174.535i) q^{14} +(-64.0248 + 84.5387i) q^{15} +(-19.2722 - 33.3805i) q^{16} -7.70989i q^{17} +(510.892 - 143.832i) q^{18} -54.1307 q^{19} +(274.858 - 158.689i) q^{20} +(-441.792 + 186.273i) q^{21} +(-409.437 + 709.166i) q^{22} +(346.370 + 199.977i) q^{23} +(-639.882 - 80.1350i) q^{24} +(-243.080 - 421.028i) q^{25} +488.885i q^{26} +(266.169 - 678.672i) q^{27} +1434.92 q^{28} +(-468.219 + 270.326i) q^{29} +(86.3473 - 689.487i) q^{30} +(766.083 - 1326.89i) q^{31} +(-774.133 - 446.946i) q^{32} +(436.973 + 1036.39i) q^{33} +(25.2595 + 43.7508i) q^{34} +627.714i q^{35} +(-1523.13 + 1562.09i) q^{36} -1719.10 q^{37} +(307.172 - 177.346i) q^{38} +(535.302 + 405.408i) q^{39} +(-422.146 + 731.178i) q^{40} +(1090.87 + 629.816i) q^{41} +(1896.73 - 2504.45i) q^{42} +(1303.89 + 2258.41i) q^{43} -3366.13i q^{44} +(-683.348 - 666.303i) q^{45} -2620.70 q^{46} +(-692.850 + 400.017i) q^{47} +(319.649 - 134.774i) q^{48} +(-218.498 + 378.449i) q^{49} +(2758.78 + 1592.79i) q^{50} +(68.8512 + 8.62251i) q^{51} +(-1004.83 - 1740.41i) q^{52} -4229.81i q^{53} +(713.088 + 4723.25i) q^{54} +1472.54 q^{55} +(-3305.77 + 1908.59i) q^{56} +(60.5381 - 483.400i) q^{57} +(1771.31 - 3068.01i) q^{58} +(-2886.63 - 1666.60i) q^{59} +(1109.74 + 2632.02i) q^{60} +(7.50843 + 13.0050i) q^{61} +10039.5i q^{62} +(-1169.38 - 4153.63i) q^{63} +6473.94 q^{64} +(761.353 - 439.567i) q^{65} +(-5875.12 - 4449.48i) q^{66} +(-2591.20 + 4488.08i) q^{67} +(-179.846 - 103.834i) q^{68} +(-2173.21 + 2869.52i) q^{69} +(-2056.55 - 3562.05i) q^{70} -1924.16i q^{71} +(1431.25 - 5624.68i) q^{72} +949.554 q^{73} +(9755.28 - 5632.21i) q^{74} +(4031.73 - 1699.90i) q^{75} +(-729.012 + 1262.69i) q^{76} +(5765.63 + 3328.79i) q^{77} +(-4365.86 - 546.754i) q^{78} +(118.990 + 206.097i) q^{79} -454.169i q^{80} +(5763.03 + 3135.96i) q^{81} -8253.75 q^{82} +(-11402.0 + 6582.95i) q^{83} +(-1604.77 + 12814.2i) q^{84} +(45.4228 - 78.6746i) q^{85} +(-14798.2 - 8543.77i) q^{86} +(-1890.44 - 4483.64i) q^{87} +(4477.31 + 7754.92i) q^{88} -575.925i q^{89} +(6060.72 + 1542.20i) q^{90} +3974.71 q^{91} +(9329.58 - 5386.44i) q^{92} +(10992.7 + 8325.27i) q^{93} +(2621.11 - 4539.90i) q^{94} +(-552.370 - 318.911i) q^{95} +(4857.10 - 6413.34i) q^{96} +(-7561.70 - 13097.3i) q^{97} -2863.41i q^{98} +(-9743.88 + 2743.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20} + 480 q^{21} - 369 q^{22} - 282 q^{23} - 1449 q^{24} - 273 q^{25} + 54 q^{27} + 1308 q^{28} - 1056 q^{29} - 1278 q^{30} + 1290 q^{31} - 1161 q^{32} + 279 q^{33} + 513 q^{34} - 2385 q^{36} + 12 q^{37} - 789 q^{38} + 1974 q^{39} - 1314 q^{40} + 7629 q^{41} + 9612 q^{42} - 285 q^{43} - 4212 q^{45} - 5760 q^{46} - 9642 q^{47} - 6771 q^{48} - 1863 q^{49} + 3027 q^{50} + 2457 q^{51} - 240 q^{52} - 405 q^{54} + 2016 q^{55} - 462 q^{56} + 5367 q^{57} + 6462 q^{58} + 6225 q^{59} + 7470 q^{60} + 3630 q^{61} - 7578 q^{63} + 15450 q^{64} - 7158 q^{65} - 13734 q^{66} - 5055 q^{67} - 10503 q^{68} - 13878 q^{69} - 9684 q^{70} + 8451 q^{72} - 14622 q^{73} + 26454 q^{74} + 21021 q^{75} - 4047 q^{76} + 2580 q^{77} - 12060 q^{78} + 4764 q^{79} + 18387 q^{81} - 9702 q^{82} - 1866 q^{83} - 6486 q^{84} + 12366 q^{85} - 37731 q^{86} - 21564 q^{87} + 14787 q^{88} + 20790 q^{90} + 34836 q^{91} + 33636 q^{92} + 19254 q^{93} - 12708 q^{94} - 13362 q^{95} - 3672 q^{96} - 28959 q^{97} - 9126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 + 15 * q^4 - 12 * q^5 - 99 * q^6 + 12 * q^7 + 99 * q^9 - 36 * q^10 + 483 * q^11 + 330 * q^12 - 6 * q^13 - 1146 * q^14 - 1026 * q^15 + 15 * q^16 + 1404 * q^18 - 258 * q^19 + 1614 * q^20 + 480 * q^21 - 369 * q^22 - 282 * q^23 - 1449 * q^24 - 273 * q^25 + 54 * q^27 + 1308 * q^28 - 1056 * q^29 - 1278 * q^30 + 1290 * q^31 - 1161 * q^32 + 279 * q^33 + 513 * q^34 - 2385 * q^36 + 12 * q^37 - 789 * q^38 + 1974 * q^39 - 1314 * q^40 + 7629 * q^41 + 9612 * q^42 - 285 * q^43 - 4212 * q^45 - 5760 * q^46 - 9642 * q^47 - 6771 * q^48 - 1863 * q^49 + 3027 * q^50 + 2457 * q^51 - 240 * q^52 - 405 * q^54 + 2016 * q^55 - 462 * q^56 + 5367 * q^57 + 6462 * q^58 + 6225 * q^59 + 7470 * q^60 + 3630 * q^61 - 7578 * q^63 + 15450 * q^64 - 7158 * q^65 - 13734 * q^66 - 5055 * q^67 - 10503 * q^68 - 13878 * q^69 - 9684 * q^70 + 8451 * q^72 - 14622 * q^73 + 26454 * q^74 + 21021 * q^75 - 4047 * q^76 + 2580 * q^77 - 12060 * q^78 + 4764 * q^79 + 18387 * q^81 - 9702 * q^82 - 1866 * q^83 - 6486 * q^84 + 12366 * q^85 - 37731 * q^86 - 21564 * q^87 + 14787 * q^88 + 20790 * q^90 + 34836 * q^91 + 33636 * q^92 + 19254 * q^93 - 12708 * q^94 - 13362 * q^95 - 3672 * q^96 - 28959 * q^97 - 9126 * q^99

Introduction

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