LMFDB - Embedded newform 169.4.e.h.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.129088 + 0.0745292i) q^{2} +(3.24429 + 5.61927i) q^{3} +(-3.98889 + 6.90896i) q^{4} +10.2526i q^{5} +(-0.837600 - 0.483588i) q^{6} +(25.6987 + 14.8372i) q^{7} -2.38162i q^{8} +(-7.55083 + 13.0784i) q^{9} +O(q^{10})$	\(q+(-0.129088 + 0.0745292i) q^{2} +(3.24429 + 5.61927i) q^{3} +(-3.98889 + 6.90896i) q^{4} +10.2526i q^{5} +(-0.837600 - 0.483588i) q^{6} +(25.6987 + 14.8372i) q^{7} -2.38162i q^{8} +(-7.55083 + 13.0784i) q^{9} +(-0.764114 - 1.32348i) q^{10} +(32.9965 - 19.0505i) q^{11} -51.7645 q^{12} -4.42320 q^{14} +(-57.6119 + 33.2623i) q^{15} +(-31.7336 - 54.9643i) q^{16} +(-35.6507 + 61.7488i) q^{17} -2.25103i q^{18} +(8.74230 + 5.04737i) q^{19} +(-70.8345 - 40.8963i) q^{20} +192.544i q^{21} +(-2.83964 + 4.91840i) q^{22} +(-99.3326 - 172.049i) q^{23} +(13.3830 - 7.72667i) q^{24} +19.8851 q^{25} +77.2033 q^{27} +(-205.019 + 118.368i) q^{28} +(-15.4082 - 26.6877i) q^{29} +(4.95802 - 8.58754i) q^{30} -151.549i q^{31} +(24.6932 + 14.2566i) q^{32} +(214.100 + 123.611i) q^{33} -10.6281i q^{34} +(-152.119 + 263.477i) q^{35} +(-60.2389 - 104.337i) q^{36} +(131.099 - 75.6903i) q^{37} -1.50470 q^{38} +24.4177 q^{40} +(179.496 - 103.632i) q^{41} +(-14.3502 - 24.8552i) q^{42} +(-151.607 + 262.592i) q^{43} +303.962i q^{44} +(-134.087 - 77.4153i) q^{45} +(25.6453 + 14.8063i) q^{46} +12.2241i q^{47} +(205.906 - 356.640i) q^{48} +(268.783 + 465.545i) q^{49} +(-2.56694 + 1.48202i) q^{50} -462.645 q^{51} -250.726 q^{53} +(-9.96604 + 5.75390i) q^{54} +(195.317 + 338.298i) q^{55} +(35.3365 - 61.2046i) q^{56} +65.5005i q^{57} +(3.97803 + 2.29672i) q^{58} +(-338.185 - 195.251i) q^{59} -530.718i q^{60} +(78.2638 - 135.557i) q^{61} +(11.2948 + 19.5632i) q^{62} +(-388.093 + 224.066i) q^{63} +503.488 q^{64} -36.8505 q^{66} +(263.017 - 151.853i) q^{67} +(-284.413 - 492.619i) q^{68} +(644.527 - 1116.35i) q^{69} -45.3491i q^{70} +(791.087 + 456.734i) q^{71} +(31.1479 + 17.9832i) q^{72} -249.855i q^{73} +(-11.2823 + 19.5415i) q^{74} +(64.5132 + 111.740i) q^{75} +(-69.7442 + 40.2668i) q^{76} +1130.62 q^{77} -147.055 q^{79} +(563.524 - 325.351i) q^{80} +(454.342 + 786.944i) q^{81} +(-15.4473 + 26.7554i) q^{82} -1020.16i q^{83} +(-1330.28 - 768.038i) q^{84} +(-633.083 - 365.511i) q^{85} -45.1967i q^{86} +(99.9772 - 173.166i) q^{87} +(-45.3712 - 78.5852i) q^{88} +(-819.314 + 473.031i) q^{89} +23.0788 q^{90} +1584.91 q^{92} +(851.594 - 491.668i) q^{93} +(-0.911055 - 1.57799i) q^{94} +(-51.7484 + 89.6309i) q^{95} +185.011i q^{96} +(361.721 + 208.840i) q^{97} +(-69.3934 - 40.0643i) q^{98} +575.390i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.129088	+	0.0745292i	−0.0456396	+	0.0263500i	−0.522646	−	0.852550i	$-0.675055\pi$
$2$	−0.129088	+	0.0745292i	−0.0456396	+	0.0263500i	0.477007	+	0.878900i	$0.341722\pi$
$3$	3.24429	+	5.61927i	0.624364	+	1.08143i	0.988664	+	0.150148i	$0.0479751\pi$
$3$	3.24429	+	5.61927i	0.624364	+	1.08143i	−0.364300	+	0.931282i	$0.618692\pi$
$4$	−3.98889	+	6.90896i	−0.498611	+	0.863620i
$5$			10.2526i			0.917016i	0.888690	+	0.458508i	$0.151616\pi$
$5$			10.2526i			0.917016i	−0.888690	+	0.458508i	$0.848384\pi$
$6$	−0.837600	−	0.483588i	−0.0569914	−	0.0329040i
$7$	25.6987	+	14.8372i	1.38760	+	0.801131i	0.993044	−	0.117741i	$-0.0375652\pi$
$7$	25.6987	+	14.8372i	1.38760	+	0.801131i	0.394556	+	0.918872i	$0.370899\pi$
$8$		−	2.38162i		−	0.105254i
$9$	−7.55083	+	13.0784i	−0.279660	+	0.484386i
$10$	−0.764114	−	1.32348i	−0.0241634	−	0.0418523i
$11$	32.9965	−	19.0505i	0.904438	−	0.522178i	0.0258006	−	0.999667i	$-0.491787\pi$
$11$	32.9965	−	19.0505i	0.904438	−	0.522178i	0.878637	+	0.477490i	$0.158453\pi$
$12$	−51.7645			−1.24526
$13$		0			0
$13$		0			0
$14$	−4.42320			−0.0844394
$15$	−57.6119	+	33.2623i	−0.991689	+	0.572552i
$16$	−31.7336	−	54.9643i	−0.495838	−	0.858816i
$17$	−35.6507	+	61.7488i	−0.508621	+	0.880958i	0.491329	+	0.870974i	$0.336511\pi$
$17$	−35.6507	+	61.7488i	−0.508621	+	0.880958i	−0.999950	+	0.00998393i	$0.996822\pi$
$18$		−	2.25103i		−	0.0294763i
$19$	8.74230	+	5.04737i	0.105559	+	0.0609445i	0.551850	−	0.833943i	$-0.313922\pi$
$19$	8.74230	+	5.04737i	0.105559	+	0.0609445i	−0.446291	+	0.894888i	$0.647255\pi$
$20$	−70.8345	−	40.8963i	−0.791954	−	0.457235i
$21$			192.544i			2.00079i
$22$	−2.83964	+	4.91840i	−0.0275188	+	0.0476639i
$23$	−99.3326	−	172.049i	−0.900534	−	1.55977i	−0.826803	−	0.562492i	$-0.809843\pi$
$23$	−99.3326	−	172.049i	−0.900534	−	1.55977i	−0.0737310	−	0.997278i	$-0.523491\pi$
$24$	13.3830	−	7.72667i	0.113825	−	0.0657167i
$25$	19.8851			0.159081
$26$		0			0
$27$	77.2033			0.550288
$28$	−205.019	+	118.368i	−1.38375	+	0.798906i
$29$	−15.4082	−	26.6877i	−0.0986630	−	0.170889i	0.812468	−	0.583005i	$-0.198123\pi$
$29$	−15.4082	−	26.6877i	−0.0986630	−	0.170889i	−0.911131	+	0.412116i	$0.864790\pi$
$30$	4.95802	−	8.58754i	0.0301735	−	0.0522621i
$31$		−	151.549i		−	0.878031i	−0.898479	−	0.439016i	$-0.855327\pi$
$31$		−	151.549i		−	0.878031i	0.898479	−	0.439016i	$-0.144673\pi$
$32$	24.6932	+	14.2566i	0.136412	+	0.0787576i
$33$	214.100	+	123.611i	1.12940	+	0.652058i
$34$		−	10.6281i		−	0.0536088i
$35$	−152.119	+	263.477i	−0.734650	+	1.27245i
$36$	−60.2389	−	104.337i	−0.278884	−	0.483041i
$37$	131.099	−	75.6903i	0.582503	−	0.336308i	−0.179624	−	0.983735i	$-0.557488\pi$
$37$	131.099	−	75.6903i	0.582503	−	0.336308i	0.762128	+	0.647427i	$0.224155\pi$
$38$	−1.50470			−0.00642356
$39$		0			0
$40$	24.4177			0.0965194
$41$	179.496	−	103.632i	0.683723	−	0.394748i	−0.117533	−	0.993069i	$-0.537499\pi$
$41$	179.496	−	103.632i	0.683723	−	0.394748i	0.801256	+	0.598321i	$0.204165\pi$
$42$	−14.3502	−	24.8552i	−0.0527209	−	0.0913152i
$43$	−151.607	+	262.592i	−0.537672	+	0.931275i	0.461357	+	0.887215i	$0.347363\pi$
$43$	−151.607	+	262.592i	−0.537672	+	0.931275i	−0.999029	+	0.0440607i	$0.985971\pi$
$44$			303.962i			1.04145i
$45$	−134.087	−	77.4153i	−0.444190	−	0.256453i
$46$	25.6453	+	14.8063i	0.0822000	+	0.0474582i
$47$			12.2241i			0.0379377i	0.999820	+	0.0189689i	$0.00603834\pi$
$47$			12.2241i			0.0379377i	−0.999820	+	0.0189689i	$0.993962\pi$
$48$	205.906	−	356.640i	0.619167	−	1.07243i
$49$	268.783	+	465.545i	0.783623	+	1.35727i
$50$	−2.56694	+	1.48202i	−0.00726040	+	0.00419179i
$51$	−462.645			−1.27026
$52$		0			0
$53$	−250.726			−0.649808			−0.324904	−	0.945747i	$-0.605332\pi$
$53$	−250.726			−0.649808			−0.324904	+	0.945747i	$0.605332\pi$
$54$	−9.96604	+	5.75390i	−0.0251149	+	0.0145001i
$55$	195.317	+	338.298i	0.478845	+	0.829384i
$56$	35.3365	−	61.2046i	0.0843221	−	0.146050i
$57$			65.5005i			0.152206i
$58$	3.97803	+	2.29672i	0.00900588	+	0.00519955i
$59$	−338.185	−	195.251i	−0.746236	−	0.430840i	0.0780962	−	0.996946i	$-0.475116\pi$
$59$	−338.185	−	195.251i	−0.746236	−	0.430840i	−0.824332	+	0.566106i	$0.808449\pi$
$60$		−	530.718i		−	1.14192i
$61$	78.2638	−	135.557i	0.164273	−	0.284529i	−0.772124	−	0.635472i	$-0.780806\pi$
$61$	78.2638	−	135.557i	0.164273	−	0.284529i	0.936397	+	0.350943i	$0.114139\pi$
$62$	11.2948	+	19.5632i	0.0231362	+	0.0400730i
$63$	−388.093	+	224.066i	−0.776114	+	0.448090i
$64$	503.488			0.983375
$65$		0			0
$66$	−36.8505			−0.0687270
$67$	263.017	−	151.853i	0.479592	−	0.276893i	−0.240654	−	0.970611i	$-0.577362\pi$
$67$	263.017	−	151.853i	0.479592	−	0.276893i	0.720247	+	0.693718i	$0.244029\pi$
$68$	−284.413	−	492.619i	−0.507209	−	0.878511i
$69$	644.527	−	1116.35i	1.12452	−	1.94773i
$70$		−	45.3491i		−	0.0774323i
$71$	791.087	+	456.734i	1.32232	+	0.763442i	0.984098	−	0.177625i	$-0.0568412\pi$
$71$	791.087	+	456.734i	1.32232	+	0.763442i	0.338222	+	0.941066i	$0.390175\pi$
$72$	31.1479	+	17.9832i	0.0509835	+	0.0294353i
$73$		−	249.855i		−	0.400594i	−0.979735	−	0.200297i	$-0.935809\pi$
$73$		−	249.855i		−	0.400594i	0.979735	−	0.200297i	$-0.0641907\pi$
$74$	−11.2823	+	19.5415i	−0.0177235	+	0.0306980i
$75$	64.5132	+	111.740i	0.0993245	+	0.172035i
$76$	−69.7442	+	40.2668i	−0.105266	+	0.0607753i
$77$	1130.62			1.67333
$78$		0			0
$79$	−147.055			−0.209430			−0.104715	−	0.994502i	$-0.533393\pi$
$79$	−147.055			−0.209430			−0.104715	+	0.994502i	$0.533393\pi$
$80$	563.524	−	325.351i	0.787549	−	0.454691i
$81$	454.342	+	786.944i	0.623241	+	1.07948i
$82$	−15.4473	+	26.7554i	−0.0208032	+	0.0360322i
$83$		−	1020.16i		−	1.34913i	−0.738217	−	0.674564i	$-0.764332\pi$
$83$		−	1020.16i		−	1.34913i	0.738217	−	0.674564i	$-0.235668\pi$
$84$	−1330.28	−	768.038i	−1.72792	−	0.997616i
$85$	−633.083	−	365.511i	−0.807853	−	0.466414i
$86$		−	45.1967i		−	0.0566707i
$87$	99.9772	−	173.166i	0.123203	−	0.213394i
$88$	−45.3712	−	78.5852i	−0.0549612	−	0.0951955i
$89$	−819.314	+	473.031i	−0.975810	+	0.563384i	−0.901002	−	0.433814i	$-0.857168\pi$
$89$	−819.314	+	473.031i	−0.975810	+	0.563384i	−0.0748073	+	0.997198i	$0.523834\pi$
$90$	23.0788			0.0270302
$91$		0			0
$92$	1584.91			1.79607
$93$	851.594	−	491.668i	0.949529	−	0.548211i
$94$	−0.911055	−	1.57799i	−0.000999661	−	0.00173146i
$95$	−51.7484	+	89.6309i	−0.0558871	+	0.0967993i
$96$			185.011i			0.196694i
$97$	361.721	+	208.840i	0.378631	+	0.218603i	0.677223	−	0.735778i	$-0.263183\pi$
$97$	361.721	+	208.840i	0.378631	+	0.218603i	−0.298591	+	0.954381i	$0.596517\pi$
$98$	−69.3934	−	40.0643i	−0.0715285	−	0.0412970i
$99$			575.390i			0.584130i
$100$	−79.3197	+	137.386i	−0.0793197	+	0.137386i
$101$	425.346	+	736.720i	0.419044	+	0.725806i	0.995844	−	0.0910800i	$-0.0290319\pi$
$101$	425.346	+	736.720i	0.419044	+	0.725806i	−0.576799	+	0.816886i	$0.695699\pi$
$102$	59.7220	−	34.4805i	0.0579741	−	0.0334714i
$103$	−996.615			−0.953392			−0.476696	−	0.879068i	$-0.658166\pi$
$103$	−996.615			−0.953392			−0.476696	+	0.879068i	$0.658166\pi$
$104$		0			0
$105$	−1974.07			−1.83476
$106$	32.3657	−	18.6864i	0.0296570	−	0.0171225i
$107$	−346.962	−	600.956i	−0.313478	−	0.542959i	0.665635	−	0.746277i	$-0.268161\pi$
$107$	−346.962	−	600.956i	−0.313478	−	0.542959i	−0.979113	+	0.203318i	$0.934827\pi$
$108$	−307.955	+	533.395i	−0.274380	+	0.475240i
$109$			1130.33i			0.993267i	0.867960	+	0.496634i	$0.165431\pi$
$109$			1130.33i			0.993267i	−0.867960	+	0.496634i	$0.834569\pi$
$110$	−50.4262	−	29.1136i	−0.0437086	−	0.0252352i
$111$	850.649	+	491.123i	0.727388	+	0.419958i
$112$		−	1883.35i		−	1.58893i
$113$	131.770	−	228.232i	0.109698	−	0.190002i	−0.805950	−	0.591983i	$-0.798345\pi$
$113$	131.770	−	228.232i	0.109698	−	0.190002i	0.915648	+	0.401982i	$0.131678\pi$
$114$	−4.88170	−	8.45535i	−0.00401064	−	0.00694663i
$115$	1763.94	−	1018.41i	1.43033	−	0.825804i
$116$	245.846			0.196778
$117$		0			0
$118$	58.2076			0.0454106
$119$	−1832.35	+	1057.91i	−1.41153	+	0.814945i
$120$	79.2181	+	137.210i	0.0602632	+	0.104379i
$121$	60.3458	−	104.522i	0.0453387	−	0.0785289i
$122$			23.3317i			0.0173144i
$123$	1164.68	+	672.427i	0.853784	+	0.492932i
$124$	1047.04	+	604.512i	0.758286	+	0.437796i
$125$			1485.44i			1.06290i
$126$	33.3989	−	57.8485i	0.0236143	−	0.0409013i
$127$	−50.8811	−	88.1287i	−0.0355510	−	0.0615761i	0.847702	−	0.530472i	$-0.177985\pi$
$127$	−50.8811	−	88.1287i	−0.0355510	−	0.0615761i	−0.883253	+	0.468896i	$0.844652\pi$
$128$	−262.540	+	151.578i	−0.181293	+	0.104670i
$129$	−1967.43			−1.34281
$130$		0			0
$131$	−382.888			−0.255367			−0.127684	−	0.991815i	$-0.540754\pi$
$131$	−382.888			−0.255367			−0.127684	+	0.991815i	$0.540754\pi$
$132$	−1708.05	+	986.141i	−1.12626	+	0.650247i
$133$	149.777	+	259.422i	0.0976491	+	0.169133i
$134$	−22.6350	+	39.2049i	−0.0145923	+	0.0252746i
$135$			791.531i			0.504623i
$136$	147.062	+	84.9065i	0.0927242	+	0.0535343i
$137$	−886.335	−	511.726i	−0.552735	−	0.319122i	0.197489	−	0.980305i	$-0.436721\pi$
$137$	−886.335	−	511.726i	−0.552735	−	0.319122i	−0.750224	+	0.661183i	$0.770055\pi$
$138$			192.144i			0.118525i
$139$	−509.473	+	882.432i	−0.310884	+	0.538467i	−0.978554	−	0.205990i	$-0.933958\pi$
$139$	−509.473	+	882.432i	−0.310884	+	0.538467i	0.667670	+	0.744458i	$0.267292\pi$
$140$	−1213.57	−	2101.97i	−0.732610	−	1.26892i
$141$	−68.6908	+	39.6586i	−0.0410270	+	0.0236870i
$142$	−136.160			−0.0804669
$143$		0			0
$144$	958.461			0.554665
$145$	273.618	−	157.973i	0.156708	−	0.0904756i
$146$	18.6215	+	32.2534i	0.0105557	+	0.0182829i
$147$	−1744.02	+	3020.73i	−0.978531	+	1.69487i
$148$			1207.68i			0.670749i
$149$	−1712.40	−	988.653i	−0.941510	−	0.543581i	−0.0510768	−	0.998695i	$-0.516265\pi$
$149$	−1712.40	−	988.653i	−0.941510	−	0.543581i	−0.890433	+	0.455114i	$0.849599\pi$
$150$	−16.6558	−	9.61623i	−0.00906626	−	0.00523441i
$151$			3488.30i			1.87996i	0.341234	+	0.939979i	$0.389155\pi$
$151$			3488.30i			1.87996i	−0.341234	+	0.939979i	$0.610845\pi$
$152$	12.0209	−	20.8208i	0.00641464	−	0.0111105i
$153$	−538.385	−	932.510i	−0.284483	−	0.492738i
$154$	−145.950	+	84.2644i	−0.0763702	+	0.0440923i
$155$	1553.76			0.805169
$156$		0			0
$157$	1783.21			0.906471			0.453236	−	0.891391i	$-0.350270\pi$
$157$	1783.21			0.906471			0.453236	+	0.891391i	$0.350270\pi$
$158$	18.9830	−	10.9599i	0.00955828	−	0.00551848i
$159$	−813.427	−	1408.90i	−0.405717	−	0.702722i
$160$	−146.167	+	253.169i	−0.0722220	+	0.125092i
$161$		−	5895.25i		−	2.88578i
$162$	−117.301	−	67.7235i	−0.0568889	−	0.0328448i
$163$	1423.23	+	821.702i	0.683901	+	0.394851i	0.801323	−	0.598231i	$-0.204130\pi$
$163$	1423.23	+	821.702i	0.683901	+	0.394851i	−0.117422	+	0.993082i	$0.537463\pi$
$164$			1653.51i			0.787303i
$165$	−1267.33	+	2195.08i	−0.597947	+	1.03568i
$166$	76.0320	+	131.691i	0.0355496	+	0.0615736i
$167$	2111.19	−	1218.89i	0.978255	−	0.564796i	0.0765122	−	0.997069i	$-0.475622\pi$
$167$	2111.19	−	1218.89i	0.978255	−	0.564796i	0.901743	+	0.432273i	$0.142288\pi$
$168$	458.567			0.210591
$169$		0			0
$170$	108.965			0.0491601
$171$	−132.023	+	76.2237i	−0.0590414	+	0.0340875i
$172$	−1209.49	−	2094.90i	−0.536179	−	0.928689i
$173$	1493.32	−	2586.50i	0.656271	−	1.13669i	−0.325302	−	0.945610i	$-0.605466\pi$
$173$	1493.32	−	2586.50i	0.656271	−	1.13669i	0.981574	−	0.191085i	$-0.0612006\pi$
$174$			29.8049i			0.0129856i
$175$	511.023	+	295.039i	0.220741	+	0.127445i
$176$	−2094.20	−	1209.09i	−0.896909	−	0.517831i
$177$		−	2533.81i		−	1.07600i
$178$	70.5092	−	122.126i	0.0296904	−	0.0514252i
$179$	−1687.45	−	2922.75i	−0.704614	−	1.22043i	−0.966831	−	0.255419i	$-0.917787\pi$
$179$	−1687.45	−	2922.75i	−0.704614	−	1.22043i	0.262216	−	0.965009i	$-0.415547\pi$
$180$	1069.72	−	617.603i	0.442956	−	0.255741i
$181$	−2266.57			−0.930790			−0.465395	−	0.885103i	$-0.654088\pi$
$181$	−2266.57			−0.930790			−0.465395	+	0.885103i	$0.654088\pi$
$182$		0			0
$183$	1015.64			0.410264
$184$	−409.756	+	236.573i	−0.164172	+	0.0947846i
$185$	776.019	+	1344.10i	0.308400	+	0.534165i
$186$	−73.2872	+	126.937i	−0.0288908	+	0.0500403i
$187$			2716.66i			1.06236i
$188$	−84.4561	−	48.7608i	−0.0327638	−	0.0189162i
$189$	1984.03	+	1145.48i	0.763580	+	0.440853i
$190$		−	15.4271i		−	0.00589051i
$191$	−335.359	+	580.859i	−0.127046	+	0.220050i	−0.922531	−	0.385924i	$-0.873883\pi$
$191$	−335.359	+	580.859i	−0.127046	+	0.220050i	0.795485	+	0.605973i	$0.207216\pi$
$192$	1633.46	+	2829.24i	0.613984	+	1.06345i
$193$	−3979.97	+	2297.84i	−1.48438	+	0.857006i	−0.999842	−	0.0177660i	$-0.994345\pi$
$193$	−3979.97	+	2297.84i	−1.48438	+	0.857006i	−0.484535	+	0.874772i	$0.661011\pi$
$194$	−62.2586			−0.0230408
$195$		0			0
$196$	−4288.58			−1.56289
$197$	−453.031	+	261.557i	−0.163843	+	0.0945949i	−0.579679	−	0.814845i	$-0.696822\pi$
$197$	−453.031	+	261.557i	−0.163843	+	0.0945949i	0.415836	+	0.909439i	$0.363489\pi$
$198$	−42.8833	−	74.2761i	−0.0153918	−	0.0266594i
$199$	−786.627	+	1362.48i	−0.280213	+	0.485344i	−0.971437	−	0.237297i	$-0.923739\pi$
$199$	−786.627	+	1362.48i	−0.280213	+	0.485344i	0.691224	+	0.722641i	$0.257072\pi$
$200$		−	47.3589i		−	0.0167439i
$201$	1706.61	+	985.311i	0.598880	+	0.345764i
$202$	−109.814	−	63.4013i	−0.0382500	−	0.0220837i
$203$		−	914.454i		−	0.316168i
$204$	1845.44	−	3196.39i	0.633366	−	1.09702i
$205$	1062.50	+	1840.30i	0.361990	+	0.626985i
$206$	128.651	−	74.2769i	0.0435125	−	0.0251219i
$207$	3000.17			1.00737
$208$		0			0
$209$	384.620			0.127295
$210$	254.829	−	147.126i	0.0837376	−	0.0483459i
$211$	2391.05	+	4141.42i	0.780127	+	1.35122i	0.931868	+	0.362799i	$0.118179\pi$
$211$	2391.05	+	4141.42i	0.780127	+	1.35122i	−0.151741	+	0.988420i	$0.548488\pi$
$212$	1000.12	−	1732.25i	0.324002	−	0.561187i
$213$			5927.11i			1.90666i
$214$	89.5776	+	51.7176i	0.0286140	+	0.0165203i
$215$	−2692.23	−	1554.36i	−0.853995	−	0.493054i
$216$		−	183.869i		−	0.0579199i
$217$	2248.55	−	3894.61i	0.703418	−	1.21836i
$218$	−84.2426	−	145.913i	−0.0261726	−	0.0453323i
$219$	1404.01	−	810.603i	0.433214	−	0.250116i
$220$	−3116.39			−0.955031
$221$		0			0
$222$	−146.412			−0.0442636
$223$	1810.32	−	1045.19i	0.543622	−	0.313860i	−0.202924	−	0.979195i	$-0.565044\pi$
$223$	1810.32	−	1045.19i	0.543622	−	0.313860i	0.746546	+	0.665334i	$0.231711\pi$
$224$	423.056	+	732.755i	0.126190	+	0.218568i
$225$	−150.149	+	260.066i	−0.0444887	+	0.0770567i
$226$			39.2827i			0.0115622i
$227$	−1882.88	−	1087.08i	−0.550534	−	0.317851i	0.198804	−	0.980039i	$-0.436294\pi$
$227$	−1882.88	−	1087.08i	−0.550534	−	0.317851i	−0.749337	+	0.662189i	$0.769628\pi$
$228$	−452.541	−	261.274i	−0.131448	−	0.0758918i
$229$		−	5997.16i		−	1.73058i	−0.501270	−	0.865291i	$-0.667134\pi$
$229$		−	5997.16i		−	1.73058i	0.501270	−	0.865291i	$-0.332866\pi$
$230$	−151.803	+	262.930i	−0.0435199	+	0.0753787i
$231$	3668.07	+	6353.28i	1.04477	+	1.80959i
$232$	−63.5601	+	36.6964i	−0.0179867	+	0.0103847i
$233$	1550.00			0.435810			0.217905	−	0.975970i	$-0.430078\pi$
$233$	1550.00			0.435810			0.217905	+	0.975970i	$0.430078\pi$
$234$		0			0
$235$	−125.329			−0.0347895
$236$	2697.97	−	1557.67i	0.744164	−	0.429643i
$237$	−477.088	−	826.340i	−0.130760	−	0.226483i
$238$	157.690	−	273.128i	0.0429477	−	0.0743875i
$239$		−	3895.06i		−	1.05419i	−0.849807	−	0.527093i	$-0.823282\pi$
$239$		−	3895.06i		−	1.05419i	0.849807	−	0.527093i	$-0.176718\pi$
$240$	3656.47	+	2111.06i	0.983434	+	0.567786i
$241$	3540.48	+	2044.10i	0.946316	+	0.546356i	0.891935	−	0.452164i	$-0.149348\pi$
$241$	3540.48	+	2044.10i	0.946316	+	0.546356i	0.0543816	+	0.998520i	$0.482681\pi$
$242$			17.9901i			0.00477870i
$243$	−1905.79	+	3300.93i	−0.503114	+	0.871418i
$244$	624.371	+	1081.44i	0.163817	+	0.283739i
$245$	−4773.03	+	2755.71i	−1.24464	+	0.718595i
$246$	−200.462			−0.0519551
$247$		0			0
$248$	−360.932			−0.0924161
$249$	5732.58	−	3309.71i	1.45899	−	0.842346i
$250$	−110.709	−	191.753i	−0.0280074	−	0.0485102i
$251$	2880.71	−	4989.54i	0.724417	−	1.25473i	−0.234796	−	0.972045i	$-0.575442\pi$
$251$	2880.71	−	4989.54i	0.724417	−	1.25473i	0.959213	−	0.282683i	$-0.0912245\pi$
$252$		−	3575.10i		−	0.893690i
$253$	−6555.25	−	3784.68i	−1.62895	−	0.940477i
$254$	13.1363	+	7.58426i	0.00324506	+	0.00187354i
$255$		−	4743.29i		−	1.16485i
$256$	−1991.36	+	3449.13i	−0.486171	+	0.842073i
$257$	−2449.55	−	4242.74i	−0.594547	−	1.02979i	−0.993611	−	0.112862i	$-0.963998\pi$
$257$	−2449.55	−	4242.74i	−0.594547	−	1.02979i	0.399064	−	0.916923i	$-0.369335\pi$
$258$	253.972	−	146.631i	0.0612854	−	0.0353831i
$259$	4492.12			1.07771
$260$		0			0
$261$	465.378			0.110369
$262$	49.4264	−	28.5364i	0.0116549	−	0.00672894i
$263$	−3805.79	−	6591.81i	−0.892300	−	1.54551i	−0.837112	−	0.547032i	$-0.815758\pi$
$263$	−3805.79	−	6591.81i	−0.892300	−	1.54551i	−0.0551879	−	0.998476i	$-0.517576\pi$
$264$	294.394	−	509.906i	0.0686315	−	0.118873i
$265$		−	2570.58i		−	0.595884i
$266$	−38.6690	−	22.3255i	−0.00891333	−	0.00514612i
$267$	−5316.18	−	3069.30i	−1.21852	−	0.703513i
$268$			2422.90i			0.552248i
$269$	3298.28	−	5712.78i	0.747582	−	1.29485i	−0.201397	−	0.979510i	$-0.564548\pi$
$269$	3298.28	−	5712.78i	0.747582	−	1.29485i	0.948979	−	0.315340i	$-0.102119\pi$
$270$	−58.9921	−	102.177i	−0.0132968	−	0.0230308i
$271$	2515.56	−	1452.36i	0.563872	−	0.325552i	−0.190826	−	0.981624i	$-0.561117\pi$
$271$	2515.56	−	1452.36i	0.563872	−	0.325552i	0.754698	+	0.656072i	$0.227783\pi$
$272$	4525.30			1.00878
$273$		0			0
$274$	152.554			0.0336355
$275$	656.140	−	378.823i	0.143879	−	0.0830686i
$276$	5141.90	+	8906.03i	1.12140	+	1.94232i
$277$	580.555	−	1005.55i	0.125928	−	0.218115i	−0.796167	−	0.605077i	$-0.793142\pi$
$277$	580.555	−	1005.55i	0.125928	−	0.218115i	0.922095	+	0.386962i	$0.126476\pi$
$278$		−	151.882i		−	0.0327672i
$279$	1982.02	+	1144.32i	0.425306	+	0.245551i
$280$	627.503	+	362.289i	0.133930	+	0.0773247i
$281$			8132.21i			1.72643i	0.504836	+	0.863215i	$0.331553\pi$
$281$			8132.21i			1.72643i	−0.504836	+	0.863215i	$0.668447\pi$
$282$	5.91145	−	10.2389i	0.00124830	−	0.00216213i
$283$	565.932	+	980.222i	0.118873	+	0.205895i	0.919321	−	0.393507i	$-0.128738\pi$
$283$	565.932	+	980.222i	0.118873	+	0.205895i	−0.800448	+	0.599402i	$0.795405\pi$
$284$	−6311.12	+	3643.73i	−1.31865	+	0.761322i
$285$	−671.548			−0.139576
$286$		0			0
$287$	6150.44			1.26498
$288$	−372.909	+	215.299i	−0.0762982	+	0.0440508i
$289$	−85.4444	−	147.994i	−0.0173915	−	0.0301229i
$290$	−23.5472	+	40.7850i	−0.00476807	+	0.00825854i
$291$			2710.15i			0.545951i
$292$	1726.24	+	996.646i	0.345961	+	0.199741i
$293$	−3320.63	−	1917.17i	−0.662094	−	0.382260i	0.130981	−	0.991385i	$-0.458187\pi$
$293$	−3320.63	−	1917.17i	−0.662094	−	0.382260i	−0.793074	+	0.609125i	$0.791521\pi$
$294$		−	519.920i		−	0.103137i
$295$	2001.82	−	3467.26i	0.395087	−	0.684311i
$296$	−180.266	−	312.229i	−0.0353977	−	0.0613107i
$297$	2547.44	−	1470.76i	0.497701	−	0.287348i
$298$	294.734			0.0572935
$299$		0			0
$300$	−1029.34			−0.198097
$301$	−7792.23	+	4498.84i	−1.49215	+	0.861492i
$302$	−259.980	−	450.298i	−0.0495369	−	0.0858005i
$303$	−2759.89	+	4780.27i	−0.523272	+	0.906334i
$304$		−	640.685i		−	0.120874i
$305$	1389.80	+	802.404i	0.260918	+	0.150641i
$306$	138.998	+	80.2507i	0.0259673	+	0.0149923i
$307$		−	6574.27i		−	1.22219i	−0.791556	−	0.611097i	$-0.790729\pi$
$307$		−	6574.27i		−	1.22219i	0.791556	−	0.611097i	$-0.209271\pi$
$308$	−4509.93	+	7811.43i	−0.834342	+	1.44512i
$309$	−3233.31	−	5600.26i	−0.595264	−	1.03103i
$310$	−200.573	+	115.801i	−0.0367476	+	0.0212162i
$311$	−662.775			−0.120844			−0.0604220	−	0.998173i	$-0.519245\pi$
$311$	−662.775			−0.120844			−0.0604220	+	0.998173i	$0.519245\pi$
$312$		0			0
$313$	−8353.04			−1.50844			−0.754220	−	0.656622i	$-0.771985\pi$
$313$	−8353.04			−1.50844			−0.754220	+	0.656622i	$0.771985\pi$
$314$	−230.192	+	132.901i	−0.0413710	+	0.0238856i
$315$	−2297.25	−	3978.95i	−0.410905	−	0.711709i
$316$	586.585	−	1015.99i	0.104424	−	0.180868i
$317$			5258.80i			0.931746i	0.884852	+	0.465873i	$0.154260\pi$
$317$			5258.80i			0.931746i	−0.884852	+	0.465873i	$0.845740\pi$
$318$	210.008	+	121.248i	0.0370335	+	0.0213813i
$319$	−1016.83	−	587.068i	−0.178469	−	0.103039i
$320$			5162.04i			0.901771i
$321$	2251.29	−	3899.35i	0.391448	−	0.678008i
$322$	439.368	+	761.008i	0.0760405	+	0.131706i
$323$	−623.338	+	359.884i	−0.107379	+	0.0619954i
$324$	−7249.29			−1.24302
$325$		0			0
$326$	−244.963			−0.0416173
$327$	−6351.64	+	3667.12i	−1.07415	+	0.620160i
$328$	−246.813	−	427.493i	−0.0415487	−	0.0719644i
$329$	−181.371	+	314.145i	−0.0303931	+	0.0526424i
$330$		−	377.811i		−	0.0630237i
$331$	2430.48	+	1403.24i	0.403599	+	0.233018i	0.688036	−	0.725677i	$-0.258473\pi$
$331$	2430.48	+	1403.24i	0.403599	+	0.233018i	−0.284437	+	0.958695i	$0.591807\pi$
$332$	7048.28	+	4069.32i	1.16513	+	0.672690i
$333$			2286.10i			0.376209i
$334$	−181.686	+	314.690i	−0.0297648	+	0.0515541i
$335$	1556.88	+	2696.60i	0.253915	+	0.439794i
$336$	10583.0	−	6110.12i	1.71831	−	0.992067i
$337$	−10987.6			−1.77607			−0.888033	−	0.459780i	$-0.847928\pi$
$337$	−10987.6			−1.77607			−0.888033	+	0.459780i	$0.847928\pi$
$338$		0			0
$339$	1709.99			0.273965
$340$	5050.60	−	2915.96i	0.805609	−	0.465119i
$341$	−2887.09	−	5000.58i	−0.458488	−	0.794125i
$342$	11.3618	−	19.6792i	0.00179642	−	0.00311148i
$343$			5773.59i			0.908876i
$344$	625.394	+	361.071i	0.0980203	+	0.0565920i
$345$	11445.5	+	6608.05i	1.78610	+	1.03120i
$346$			445.183i			0.0691711i
$347$	−1988.48	+	3444.15i	−0.307629	+	0.532829i	−0.977843	−	0.209339i	$-0.932869\pi$
$347$	−1988.48	+	3444.15i	−0.307629	+	0.532829i	0.670214	+	0.742168i	$0.266202\pi$
$348$	797.596	+	1381.48i	0.122861	+	0.212802i
$349$	7822.84	−	4516.52i	1.19985	−	0.692732i	0.239326	−	0.970939i	$-0.423073\pi$
$349$	7822.84	−	4516.52i	1.19985	−	0.692732i	0.960521	+	0.278207i	$0.0897401\pi$
$350$	−87.9561			−0.0134327
$351$		0			0
$352$	1086.39			0.164502
$353$	−4547.71	+	2625.62i	−0.685694	+	0.395886i	−0.801997	−	0.597328i	$-0.796229\pi$
$353$	−4547.71	+	2625.62i	−0.685694	+	0.395886i	0.116303	+	0.993214i	$0.462896\pi$
$354$	188.842	+	327.085i	0.0283527	+	0.0491083i
$355$	−4682.69	+	8110.66i	−0.700089	+	1.21259i
$356$		−	7547.48i		−	1.12364i
$357$	−11889.4	−	6864.33i	−1.76261	−	1.01764i
$358$	435.660	+	251.528i	0.0643166	+	0.0371332i
$359$		−	3850.22i		−	0.566035i	−0.959115	−	0.283018i	$-0.908664\pi$
$359$		−	3850.22i		−	0.566035i	0.959115	−	0.283018i	$-0.0913355\pi$
$360$	−184.374	+	319.345i	−0.0269927	+	0.0467527i
$361$	−3378.55	−	5851.82i	−0.492572	−	0.853159i
$362$	292.588	−	168.926i	0.0424809	−	0.0245263i
$363$	783.117			0.113231
$364$		0			0
$365$	2561.66			0.367351
$366$	−131.107	+	75.6949i	−0.0187243	+	0.0108105i
$367$	3847.20	+	6663.54i	0.547199	+	0.947777i	0.998465	+	0.0553872i	$0.0176393\pi$
$367$	3847.20	+	6663.54i	0.547199	+	0.947777i	−0.451266	+	0.892390i	$0.649027\pi$
$368$	−6304.37	+	10919.5i	−0.893038	+	1.54679i
$369$			3130.04i			0.441581i
$370$	−200.350	−	115.672i	−0.0281505	−	0.0162527i
$371$	−6443.33	−	3720.06i	−0.901673	−	0.520581i
$372$			7844.84i			1.09338i
$373$	−4090.32	+	7084.64i	−0.567798	+	0.983455i	0.428985	+	0.903311i	$0.358871\pi$
$373$	−4090.32	+	7084.64i	−0.567798	+	0.983455i	−0.996783	+	0.0801436i	$0.974462\pi$
$374$	−202.470	−	350.689i	−0.0279933	−	0.0484858i
$375$	−8347.11	+	4819.21i	−1.14945	+	0.663634i
$376$	29.1133			0.00399309
$377$		0			0
$378$	−341.486			−0.0464660
$379$	−1301.82	+	751.608i	−0.176438	+	0.101867i	−0.585618	−	0.810587i	$-0.699148\pi$
$379$	−1301.82	+	751.608i	−0.176438	+	0.101867i	0.409180	+	0.912454i	$0.365815\pi$
$380$	−412.838	−	715.056i	−0.0557319	−	0.0965305i
$381$	330.146	−	571.830i	0.0443935	−	0.0768917i
$382$		−	99.9762i		−	0.0133906i
$383$	10743.4	+	6202.72i	1.43333	+	0.827531i	0.997373	−	0.0724390i	$-0.0230783\pi$
$383$	10743.4	+	6202.72i	1.43333	+	0.827531i	0.435952	+	0.899970i	$0.356412\pi$
$384$	−1703.51	−	983.524i	−0.226386	−	0.130704i
$385$			11591.8i			1.53447i
$386$	342.512	−	593.248i	0.0451643	−	0.0782268i
$387$	−2289.52	−	3965.57i	−0.300731	−	0.520882i
$388$	−2885.73	+	1666.08i	−0.377580	+	0.217996i
$389$	3610.27			0.470560			0.235280	−	0.971928i	$-0.424399\pi$
$389$	3610.27			0.470560			0.235280	+	0.971928i	$0.424399\pi$
$390$		0			0
$391$	14165.1			1.83212
$392$	1108.75	−	640.138i	0.142858	−	0.0824792i
$393$	−1242.20	−	2151.56i	−0.159442	−	0.276162i
$394$	38.9873	−	67.5280i	0.00498516	−	0.00863454i
$395$		−	1507.69i		−	0.192050i
$396$	−3975.34	−	2295.17i	−0.504466	−	0.291254i
$397$	2062.33	+	1190.69i	0.260719	+	0.150526i	0.624662	−	0.780895i	$-0.285237\pi$
$397$	2062.33	+	1190.69i	0.260719	+	0.150526i	−0.363944	+	0.931421i	$0.618570\pi$
$398$		−	234.506i		−	0.0295345i
$399$	−971.842	+	1683.28i	−0.121937	+	0.211201i
$400$	−631.028	−	1092.97i	−0.0788785	−	0.136622i
$401$	2677.84	−	1546.05i	0.333479	−	0.192534i	−0.323906	−	0.946089i	$-0.604996\pi$
$401$	2677.84	−	1546.05i	0.333479	−	0.192534i	0.657385	+	0.753555i	$0.271663\pi$
$402$	−293.738			−0.0364435
$403$		0			0
$404$	−6786.63			−0.835761
$405$	−8068.19	+	4658.17i	−0.989905	+	0.571522i
$406$	68.1535	+	118.045i	0.00833104	+	0.0144298i
$407$	2883.88	−	4995.03i	0.351225	−	0.608340i
$408$			1101.84i			0.133700i
$409$	−295.585	−	170.656i	−0.0357353	−	0.0206318i	0.482026	−	0.876157i	$-0.339901\pi$
$409$	−295.585	−	170.656i	−0.0357353	−	0.0206318i	−0.517761	+	0.855525i	$0.673234\pi$
$410$	−274.312	−	158.374i	−0.0330422	−	0.0190769i
$411$		−	6640.74i		−	0.796992i
$412$	3975.39	−	6885.58i	0.475372	−	0.823369i
$413$	−5793.95	−	10035.4i	−0.690318	−	1.19567i
$414$	−387.287	+	223.601i	−0.0459762	+	0.0265444i
$415$	10459.3			1.23717
$416$		0			0
$417$	−6611.51			−0.776419
$418$	−49.6500	+	28.6654i	−0.00580971	+	0.00335424i
$419$	272.835	+	472.564i	0.0318111	+	0.0550985i	0.881493	−	0.472198i	$-0.156539\pi$
$419$	272.835	+	472.564i	0.0318111	+	0.0550985i	−0.849682	+	0.527296i	$0.823206\pi$
$420$	7874.35	−	13638.8i	0.914831	−	1.58453i
$421$		−	10508.0i		−	1.21645i	−0.793764	−	0.608226i	$-0.791881\pi$
$421$		−	10508.0i		−	1.21645i	0.793764	−	0.608226i	$-0.208119\pi$
$422$	−617.313	−	356.406i	−0.0712093	−	0.0411127i
$423$	−159.872	−	92.3024i	−0.0183765	−	0.0106097i
$424$			597.134i			0.0683947i
$425$	−708.919	+	1227.88i	−0.0809121	+	0.140144i
$426$	−441.743	−	765.121i	−0.0502406	−	0.0870193i
$427$	4022.56	−	2322.42i	0.455890	−	0.263208i
$428$	5535.98			0.625214
$429$		0			0
$430$	463.381			0.0519680
$431$	4778.77	−	2759.02i	0.534072	−	0.308347i	−0.208601	−	0.978001i	$-0.566891\pi$
$431$	4778.77	−	2759.02i	0.534072	−	0.308347i	0.742673	+	0.669654i	$0.233558\pi$
$432$	−2449.94	−	4243.42i	−0.272854	−	0.472597i
$433$	3036.15	−	5258.77i	0.336971	−	0.583650i	−0.646891	−	0.762583i	$-0.723931\pi$
$433$	3036.15	−	5258.77i	0.336971	−	0.583650i	0.983861	+	0.178933i	$0.0572644\pi$
$434$			670.331i			0.0741404i
$435$	1775.39	+	1025.02i	0.195686	+	0.112979i
$436$	−7809.42	−	4508.77i	−0.857805	−	0.495254i
$437$		−	2005.47i		−	0.219530i
$438$	−120.827	+	209.279i	−0.0131812	+	0.0228304i
$439$	7236.28	+	12533.6i	0.786717	+	1.36263i	0.927968	+	0.372660i	$0.121554\pi$
$439$	7236.28	+	12533.6i	0.786717	+	1.36263i	−0.141251	+	0.989974i	$0.545112\pi$
$440$	805.698	−	465.170i	0.0872958	−	0.0504003i
$441$	−8118.13			−0.876593
$442$		0			0
$443$	−8593.87			−0.921686			−0.460843	−	0.887482i	$-0.652453\pi$
$443$	−8593.87			−0.921686			−0.460843	+	0.887482i	$0.652453\pi$
$444$	−6786.29	+	3918.07i	−0.725368	+	0.418791i
$445$	−4849.78	−	8400.06i	−0.516632	−	0.894833i
$446$	−155.794	+	269.843i	−0.0165405	+	0.0286489i
$447$		−	12829.9i		−	1.35757i
$448$	12939.0	+	7470.33i	1.36453	+	0.787812i
$449$	−6664.63	−	3847.83i	−0.700497	−	0.404432i	0.107035	−	0.994255i	$-0.465864\pi$
$449$	−6664.63	−	3847.83i	−0.700497	−	0.404432i	−0.807533	+	0.589823i	$0.799198\pi$
$450$		−	44.7620i		−	0.00468912i
$451$	3948.50	−	6839.01i	0.412257	−	0.714049i
$452$	1051.23	+	1820.78i	0.109393	+	0.189474i
$453$	−19601.7	+	11317.0i	−2.03304	+	1.17378i
$454$	324.077			0.0335015
$455$		0			0
$456$	155.997			0.0160203
$457$	11577.7	−	6684.39i	1.18508	−	0.684207i	0.227896	−	0.973685i	$-0.426815\pi$
$457$	11577.7	−	6684.39i	1.18508	−	0.684207i	0.957184	+	0.289479i	$0.0934819\pi$
$458$	446.963	+	774.163i	0.0456009	+	0.0789831i
$459$	−2752.35	+	4767.21i	−0.279888	+	0.484781i
$460$			16249.3i			1.64702i
$461$	−13425.2	−	7751.06i	−1.35635	−	0.783086i	−0.367216	−	0.930136i	$-0.619689\pi$
$461$	−13425.2	−	7751.06i	−1.35635	−	0.783086i	−0.989129	+	0.147050i	$0.953022\pi$
$462$	−947.010	−	546.756i	−0.0953655	−	0.0550593i
$463$		−	9877.67i		−	0.991478i	−0.868472	−	0.495739i	$-0.834897\pi$
$463$		−	9877.67i		−	0.991478i	0.868472	−	0.495739i	$-0.165103\pi$
$464$	−977.915	+	1693.80i	−0.0978417	+	0.169467i
$465$	5040.86	+	8731.02i	0.502718	+	0.870734i
$466$	−200.087	+	115.520i	−0.0198902	+	0.0114836i
$467$	−3509.82			−0.347784			−0.173892	−	0.984765i	$-0.555634\pi$
$467$	−3509.82			−0.347784			−0.173892	+	0.984765i	$0.555634\pi$
$468$		0			0
$469$	9012.28			0.887310
$470$	16.1785	−	9.34064i	0.00158778	−	0.000916705i
$471$	5785.26	+	10020.4i	0.565968	+	0.980285i
$472$	−465.014	+	805.429i	−0.0453475	+	0.0785442i
$473$			11552.8i			1.12304i
$474$	123.173	+	71.1139i	0.0119357	+	0.00689108i
$475$	173.842	+	100.368i	0.0167925	+	0.00969513i
$476$		−	16879.6i		−	1.62536i
$477$	1893.19	−	3279.10i	0.181726	−	0.314758i
$478$	290.296	+	502.807i	0.0277779	+	0.0481126i
$479$	17218.5	−	9941.08i	1.64245	−	0.948266i	0.662485	−	0.749075i	$-0.269502\pi$
$479$	17218.5	−	9941.08i	1.64245	−	0.948266i	0.979961	−	0.199191i	$-0.0638314\pi$
$480$	−1896.83			−0.180371
$481$		0			0
$482$	−609.379			−0.0575860
$483$	33127.0	−	19125.9i	3.12077	−	1.80178i
$484$	481.426	+	833.854i	0.0452128	+	0.0783108i
$485$	−2141.14	+	3708.57i	−0.200462	+	0.347211i
$486$		−	568.148i		−	0.0530283i
$487$	−353.103	−	203.864i	−0.0328555	−	0.0189691i	0.483482	−	0.875354i	$-0.339372\pi$
$487$	−353.103	−	203.864i	−0.0328555	−	0.0189691i	−0.516338	+	0.856385i	$0.672705\pi$
$488$	−322.845	−	186.395i	−0.0299478	−	0.0172903i
$489$			10663.4i			0.986122i
$490$	410.761	−	711.459i	0.0378700	−	0.0655928i
$491$	10065.0	+	17433.2i	0.925109	+	1.60234i	0.791385	+	0.611318i	$0.209360\pi$
$491$	10065.0	+	17433.2i	0.925109	+	1.60234i	0.133724	+	0.991019i	$0.457306\pi$
$492$	−9291.54	+	5364.47i	−0.851413	+	0.491563i
$493$	2197.25			0.200728
$494$		0			0
$495$	−5899.21			−0.535656
$496$	−8329.77	+	4809.19i	−0.754068	+	0.435361i
$497$	13553.3	+	23475.0i	1.22323	+	2.11870i
$498$	−493.340	+	854.489i	−0.0443917	+	0.0768887i
$499$		−	772.760i		−	0.0693256i	−0.999399	−	0.0346628i	$-0.988964\pi$
$499$		−	772.760i		−	0.0693256i	0.999399	−	0.0346628i	$-0.0110357\pi$
$500$	−10262.9	−	5925.27i	−0.917939	−	0.529972i
$501$	13698.6	+	7908.90i	1.22157	+	0.705276i
$502$			858.787i			0.0763537i
$503$	3722.12	−	6446.91i	0.329943	−	0.571478i	−0.652557	−	0.757739i	$-0.726304\pi$
$503$	3722.12	−	6446.91i	0.329943	−	0.571478i	0.982500	+	0.186261i	$0.0596372\pi$
$504$	533.640	+	924.291i	0.0471631	+	0.0816889i
$505$	−7553.26	+	4360.88i	−0.665576	+	0.384270i
$506$	1128.28			0.0991264
$507$		0			0
$508$	811.837			0.0709044
$509$	−3110.30	+	1795.73i	−0.270848	+	0.156374i	−0.629273	−	0.777184i	$-0.716647\pi$
$509$	−3110.30	+	1795.73i	−0.270848	+	0.156374i	0.358425	+	0.933559i	$0.383314\pi$
$510$	353.513	+	612.303i	0.0306938	+	0.0531632i
$511$	3707.14	−	6420.96i	0.320928	−	0.555864i
$512$		−	3018.90i		−	0.260582i
$513$	674.934	+	389.674i	0.0580879	+	0.0335370i
$514$	632.416	+	365.125i	0.0542698	+	0.0313327i
$515$		−	10217.9i		−	0.874276i
$516$	7847.87	−	13592.9i	0.669541	−	1.15968i
$517$	232.876	+	403.354i	0.0198102	+	0.0343123i
$518$	−579.880	+	334.794i	−0.0491862	+	0.0283977i
$519$	19379.0			1.63901
$520$		0			0
$521$	1822.89			0.153286			0.0766432	−	0.997059i	$-0.475580\pi$
$521$	1822.89			0.153286			0.0766432	+	0.997059i	$0.475580\pi$
$522$	−60.0749	+	34.6842i	−0.00503718	+	0.00290822i
$523$	−6101.58	−	10568.2i	−0.510140	−	0.883589i	−0.999931	−	0.0117487i	$-0.996260\pi$
$523$	−6101.58	−	10568.2i	−0.510140	−	0.883589i	0.489791	−	0.871840i	$-0.337073\pi$
$524$	1527.30	−	2645.36i	0.127329	−	0.220540i
$525$			3828.77i			0.318288i
$526$	982.565	+	567.284i	0.0814484	+	0.0470242i
$527$	9357.96	+	5402.82i	0.773509	+	0.446586i
$528$		−	15690.5i		−	1.29326i
$529$	−13650.4	+	23643.2i	−1.12192	+	1.94323i
$530$	191.583	+	331.832i	0.0157016	+	0.0271959i
$531$	5107.16	−	2948.62i	0.417386	−	0.240978i
$532$	−2389.78			−0.194756
$533$		0			0
$534$	915.009			0.0741504
$535$	6161.34	−	3557.25i	0.497903	−	0.287464i
$536$	−361.657	−	626.408i	−0.0291440	−	0.0504789i
$537$	10949.2	−	18964.5i	0.879871	−	1.52398i
$538$			983.271i			0.0787952i
$539$	17737.8	+	10240.9i	1.41748	+	0.818380i
$540$	−5468.66	−	3157.33i	−0.435803	−	0.251611i
$541$		−	6728.89i		−	0.534746i	−0.963593	−	0.267373i	$-0.913844\pi$
$541$		−	6728.89i		−	0.534746i	0.963593	−	0.267373i	$-0.0861556\pi$
$542$	−216.486	+	374.965i	−0.0171566	+	0.0297161i
$543$	−7353.42	−	12736.5i	−0.581152	−	1.00658i
$544$	−1760.66	+	1016.52i	−0.138764	+	0.0801156i
$545$	−11588.8			−0.910842
$546$		0			0
$547$	−14650.8			−1.14519			−0.572597	−	0.819837i	$-0.694064\pi$
$547$	−14650.8			−1.14519			−0.572597	+	0.819837i	$0.694064\pi$
$548$	7070.98	−	4082.43i	0.551200	−	0.318235i
$549$	1181.91	+	2047.13i	0.0918813	+	0.159143i
$550$	−56.4667	+	97.8031i	−0.00437772	+	0.00758244i
$551$		−	311.083i		−	0.0240519i
$552$	−2658.73	−	1535.02i	−0.205006	−	0.118360i
$553$	−3779.11	−	2181.87i	−0.290605	−	0.167781i
$554$			173.073i			0.0132729i
$555$	−5035.26	+	8721.33i	−0.385108	+	0.667026i
$556$	−4064.46	−	7039.85i	−0.310021	−	0.536972i
$557$	−3645.03	+	2104.46i	−0.277280	+	0.160087i	−0.632191	−	0.774812i	$-0.717844\pi$
$557$	−3645.03	+	2104.46i	−0.277280	+	0.160087i	0.354912	+	0.934900i	$0.384511\pi$
$558$	−341.141			−0.0258811
$559$		0			0
$560$	19309.1			1.45707
$561$	−15265.7	+	8813.63i	−1.14887	+	0.663301i
$562$	−606.087	−	1049.77i	−0.0454915	−	0.0787936i
$563$	−4612.14	+	7988.46i	−0.345255	+	0.597999i	−0.985400	−	0.170255i	$-0.945541\pi$
$563$	−4612.14	+	7988.46i	−0.345255	+	0.597999i	0.640145	+	0.768254i	$0.278874\pi$
$564$		−	632.776i		−	0.0472423i
$565$	2339.96	+	1350.97i	0.174235	+	0.100595i
$566$	−146.110	−	84.3568i	−0.0108507	−	0.00626463i
$567$			26964.6i			1.99719i
$568$	1087.77	−	1884.07i	0.0803551	−	0.139179i
$569$	7066.44	+	12239.4i	0.520634	+	0.901765i	0.999712	+	0.0239924i	$0.00763774\pi$
$569$	7066.44	+	12239.4i	0.520634	+	0.901765i	−0.479078	+	0.877772i	$0.659029\pi$
$570$	86.6889	−	50.0499i	0.00637017	−	0.00367782i
$571$	17983.4			1.31801			0.659003	−	0.752140i	$-0.270978\pi$
$571$	17983.4			1.31801			0.659003	+	0.752140i	$0.270978\pi$
$572$		0			0
$573$	−4352.01			−0.317291
$574$	−793.949	+	458.387i	−0.0577331	+	0.0333322i
$575$	−1975.24	−	3421.22i	−0.143258	−	0.248130i
$576$	−3801.75	+	6584.83i	−0.275011	+	0.476333i
$577$		−	24401.8i		−	1.76059i	−0.474427	−	0.880295i	$-0.657345\pi$
$577$		−	24401.8i		−	1.76059i	0.474427	−	0.880295i	$-0.342655\pi$
$578$	22.0597	+	12.7362i	0.00158748	+	0.000916533i
$579$	−25824.4	−	14909.7i	−1.85358	−	1.07017i
$580$			2520.55i			0.180449i
$581$	15136.3	−	26216.9i	1.08083	−	1.87205i
$582$	−201.985	−	349.848i	−0.0143858	−	0.0249170i
$583$	−8273.07	+	4776.46i	−0.587711	+	0.339315i
$584$	−595.061			−0.0421640
$585$		0			0
$586$	571.540			0.0402902
$587$	−17828.5	+	10293.3i	−1.25359	+	0.723763i	−0.971821	−	0.235719i	$-0.924256\pi$
$587$	−17828.5	+	10293.3i	−1.25359	+	0.723763i	−0.281772	+	0.959481i	$0.590922\pi$
$588$	−13913.4	−	24098.7i	−0.975814	−	1.69016i
$589$	764.923	−	1324.89i	0.0535112	−	0.0926841i
$590$			596.777i			0.0416422i
$591$	−2939.53	−	1697.14i	−0.204595	−	0.118123i
$592$	−8320.52	−	4803.86i	−0.577654	−	0.333509i
$593$			19701.5i			1.36432i	0.731201	+	0.682162i	$0.238960\pi$
$593$			19701.5i			1.36432i	−0.731201	+	0.682162i	$0.761040\pi$
$594$	−219.230	+	379.717i	−0.0151433	+	0.0262289i
$595$	−10846.3	−	18786.3i	−0.747318	−	1.29439i
$596$	13661.1	−	7887.26i	0.938895	−	0.542072i
$597$	−10208.2			−0.699821
$598$		0			0
$599$	−3645.91			−0.248694			−0.124347	−	0.992239i	$-0.539684\pi$
$599$	−3645.91			−0.248694			−0.124347	+	0.992239i	$0.539684\pi$
$600$	266.123	−	153.646i	0.0181073	−	0.0104543i
$601$	3142.87	+	5443.60i	0.213311	+	0.369466i	0.952749	−	0.303759i	$-0.0982418\pi$
$601$	3142.87	+	5443.60i	0.213311	+	0.369466i	−0.739437	+	0.673225i	$0.764908\pi$
$602$	670.590	−	1161.50i	0.0454007	−	0.0786363i
$603$			4586.47i			0.309744i
$604$	−24100.5	−	13914.4i	−1.62357	−	0.937368i
$605$	1071.62	+	618.699i	0.0720123	+	0.0415763i
$606$		−	822.769i		−	0.0551530i
$607$	915.936	−	1586.45i	0.0612466	−	0.106082i	−0.833776	−	0.552102i	$-0.813826\pi$
$607$	915.936	−	1586.45i	0.0612466	−	0.106082i	0.895023	+	0.446020i	$0.147159\pi$
$608$	143.917	+	249.272i	0.00959969	+	0.0166271i
$609$	5138.57	−	2966.75i	0.341914	−	0.197404i
$610$	−239.210			−0.0158776
$611$		0			0
$612$	8590.23			0.567385
$613$	3807.12	−	2198.04i	0.250846	−	0.144826i	−0.369306	−	0.929308i	$-0.620405\pi$
$613$	3807.12	−	2198.04i	0.250846	−	0.144826i	0.620151	+	0.784482i	$0.287071\pi$
$614$	489.975	+	848.662i	0.0322049	+	0.0557805i
$615$	−6894.09	+	11940.9i	−0.452027	+	0.782934i
$616$		−	2692.72i		−	0.176124i
$617$	13112.3	+	7570.39i	0.855562	+	0.493959i	0.862523	−	0.506017i	$-0.168883\pi$
$617$	13112.3	+	7570.39i	0.855562	+	0.493959i	−0.00696192	+	0.999976i	$0.502216\pi$
$618$	834.765	+	481.952i	0.0543352	+	0.0313704i
$619$			20913.0i			1.35794i	0.734165	+	0.678971i	$0.237574\pi$
$619$			20913.0i			1.35794i	−0.734165	+	0.678971i	$0.762426\pi$
$620$	−6197.79	+	10734.9i	−0.401466	+	0.695360i
$621$	−7668.80	−	13282.8i	−0.495553	−	0.858323i
$622$	85.5565	−	49.3960i	0.00551528	−	0.00318425i
$623$	−28073.7			−1.80538
$624$		0			0
$625$	−12743.9			−0.815612
$626$	1078.28	−	622.545i	0.0688446	−	0.0397474i
$627$	1247.82	+	2161.29i	0.0794787	+	0.137661i
$628$	−7113.05	+	12320.2i	−0.451977	+	0.782847i
$629$			10793.6i			0.684215i
$630$	593.095	+	342.424i	0.0375071	+	0.0216547i
$631$	6152.75	+	3552.29i	0.388173	+	0.224112i	0.681368	−	0.731941i	$-0.261385\pi$
$631$	6152.75	+	3552.29i	0.388173	+	0.224112i	−0.293195	+	0.956053i	$0.594719\pi$
$632$			350.228i			0.0220433i
$633$	−15514.5	+	26871.9i	−0.974166	+	1.68730i
$634$	−391.934	−	678.849i	−0.0245515	−	0.0425245i
$635$	903.544	−	521.662i	0.0564662	−	0.0326008i
$636$	12978.7			0.809180
$637$		0			0
$638$	175.015			0.0108603
$639$	−11946.7	+	6897.45i	−0.739601	+	0.427009i
$640$	−1554.06	−	2691.71i	−0.0959837	−	0.166249i
$641$	−1348.05	+	2334.90i	−0.0830653	+	0.143873i	−0.904565	−	0.426335i	$-0.859804\pi$
$641$	−1348.05	+	2334.90i	−0.0830653	+	0.143873i	0.821500	+	0.570209i	$0.193138\pi$
$642$			671.148i			0.0412587i
$643$	10387.7	+	5997.35i	0.637094	+	0.367826i	0.783494	−	0.621399i	$-0.213435\pi$
$643$	10387.7	+	5997.35i	0.637094	+	0.367826i	−0.146400	+	0.989225i	$0.546769\pi$
$644$	40730.1	+	23515.5i	2.49222	+	1.43888i
$645$		−	20171.2i		−	1.23138i
$646$	53.6438	−	92.9137i	0.00326716	−	0.00565889i
$647$	8119.89	+	14064.1i	0.493394	+	0.854583i	0.999971	−	0.00761133i	$-0.00242279\pi$
$647$	8119.89	+	14064.1i	0.493394	+	0.854583i	−0.506577	+	0.862195i	$0.669089\pi$
$648$	1874.20	−	1082.07i	0.113620	−	0.0655984i
$649$	−14878.6			−0.899899
$650$		0			0
$651$	29179.8			1.75676
$652$	−11354.2	+	6555.36i	−0.682002	+	0.393754i
$653$	−3658.49	−	6336.70i	−0.219246	−	0.379746i	0.735331	−	0.677708i	$-0.237027\pi$
$653$	−3658.49	−	6336.70i	−0.219246	−	0.379746i	−0.954578	+	0.297962i	$0.903693\pi$
$654$	546.615	−	946.765i	0.0326825	−	0.0566077i
$655$		−	3925.58i		−	0.234176i
$656$	−11392.1	−	6577.26i	−0.678031	−	0.391462i
$657$	3267.71	+	1886.62i	0.194042	+	0.112030i
$658$		−	54.0699i		−	0.00320344i
$659$	−4286.70	+	7424.77i	−0.253393	+	0.438889i	−0.964458	−	0.264237i	$-0.914880\pi$
$659$	−4286.70	+	7424.77i	−0.253393	+	0.438889i	0.711065	+	0.703126i	$0.248213\pi$
$660$	−10110.5	−	17511.8i	−0.596287	−	1.03280i
$661$	12351.7	−	7131.26i	0.726817	−	0.419628i	−0.0904399	−	0.995902i	$-0.528827\pi$
$661$	12351.7	−	7131.26i	0.726817	−	0.419628i	0.817256	+	0.576274i	$0.195494\pi$
$662$	−418.329			−0.0245601
$663$		0			0
$664$	−2429.64			−0.142001
$665$	−2659.74	+	1535.60i	−0.155098	+	0.0895458i
$666$	−170.381	−	295.109i	−0.00991311	−	0.0171700i
$667$	−3061.07	+	5301.92i	−0.177699	+	0.307783i
$668$			19448.2i			1.12645i
$669$	11746.4	+	6781.77i	0.678836	+	0.391926i
$670$	−401.951	−	232.066i	−0.0231772	−	0.0133813i
$671$		−	5963.87i		−	0.343119i
$672$	−2745.03	+	4754.54i	−0.157577	+	0.272932i
$673$	−1345.04	−	2329.68i	−0.0770394	−	0.133436i	0.824932	−	0.565232i	$-0.191213\pi$
$673$	−1345.04	−	2329.68i	−0.0770394	−	0.133436i	−0.901971	+	0.431796i	$0.857880\pi$
$674$	1418.37	−	818.898i	0.0810589	−	0.0467994i
$675$	1535.20			0.0875405
$676$		0			0
$677$	−25288.0			−1.43559			−0.717795	−	0.696254i	$-0.754849\pi$
$677$	−25288.0			−1.43559			−0.717795	+	0.696254i	$0.754849\pi$
$678$	−220.740	+	127.444i	−0.0125037	+	0.00721899i
$679$	6197.18	+	10733.8i	0.350259	+	0.606667i
$680$	−870.508	+	1507.76i	−0.0490918	+	0.0850296i
$681$		−	14107.2i		−	0.793818i
$682$	745.378	+	430.344i	0.0418504	+	0.0241624i
$683$	25098.7	+	14490.8i	1.40612	+	0.811821i	0.995011	−	0.0997673i	$-0.0318098\pi$
$683$	25098.7	+	14490.8i	1.40612	+	0.811821i	0.411104	+	0.911588i	$0.365143\pi$
$684$		−	1216.19i		−	0.0679858i
$685$	5246.49	−	9087.19i	0.292640	−	0.506867i
$686$	−430.301	−	745.303i	−0.0239489	−	0.0414807i
$687$	33699.7	−	19456.5i	1.87150	−	1.08051i
$688$	19244.2			1.06639
$689$		0			0
$690$	−1969.97			−0.108689
$691$	−27057.5	+	15621.7i	−1.48960	+	0.860023i	−0.999929	−	0.0118826i	$-0.996218\pi$
$691$	−27057.5	+	15621.7i	−1.48960	+	0.860023i	−0.489674	+	0.871906i	$0.662884\pi$
$692$	11913.4	+	20634.6i	0.654448	+	1.13354i
$693$	−8537.15	+	14786.8i	−0.467965	+	0.810538i
$694$		−	592.799i		−	0.0324241i
$695$	−9047.19	−	5223.40i	−0.493783	−	0.285086i
$696$	−412.415	−	238.108i	−0.0224605	−	0.0129676i
$697$			14778.3i			0.803108i
$698$	−673.224	+	1166.06i	−0.0365070	+	0.0632320i
$699$	5028.64	+	8709.87i	0.272104	+	0.471298i
$700$	−4076.83	+	2353.76i	−0.220128	+	0.127091i
$701$	−25077.1			−1.35114			−0.675570	−	0.737296i	$-0.736102\pi$
$701$	−25077.1			−1.35114			−0.675570	+	0.737296i	$0.736102\pi$
$702$		0			0
$703$	1528.15			0.0819846
$704$	16613.3	−	9591.71i	0.889401	−	0.513496i
$705$	−406.602	−	704.256i	−0.0217213	−	0.0376224i
$706$	391.371	−	677.874i	0.0208632	−	0.0361361i
$707$			25243.7i			1.34284i
$708$	17506.0	+	10107.1i	0.929258	+	0.536507i
$709$	−5104.69	−	2947.19i	−0.270396	−	0.156113i	0.358672	−	0.933464i	$-0.383230\pi$
$709$	−5104.69	−	2947.19i	−0.270396	−	0.156113i	−0.629067	+	0.777351i	$0.716563\pi$
$710$		−	1395.99i		−	0.0737894i
$711$	1110.38	−	1923.24i	0.0585692	−	0.101445i
$712$	1126.58	+	1951.29i	0.0592983	+	0.102708i
$713$	−26073.8	+	15053.7i	−1.36953	+	0.790697i
$714$	2046.37			0.107260
$715$		0			0
$716$	26924.2			1.40531
$717$	21887.4	−	12636.7i	1.14003	−	0.658196i
$718$	286.953	+	497.018i	0.0149151	+	0.0258336i
$719$	−2715.32	+	4703.07i	−0.140841	+	0.243943i	−0.927813	−	0.373045i	$-0.878314\pi$
$719$	−2715.32	+	4703.07i	−0.140841	+	0.243943i	0.786973	+	0.616988i	$0.211647\pi$
$720$			9826.68i			0.508637i
$721$	−25611.7	−	14786.9i	−1.32293	−	0.763793i
$722$	872.262	+	503.601i	0.0449615	+	0.0259586i
$723$			26526.6i			1.36450i
$724$	9041.11	−	15659.7i	0.464102	−	0.803849i
$725$	−306.394	−	530.690i	−0.0156954	−	0.0271853i
$726$	−101.091	+	58.3651i	−0.00516783	+	0.00298365i
$727$	−17033.7			−0.868974			−0.434487	−	0.900678i	$-0.643070\pi$
$727$	−17033.7			−0.868974			−0.434487	+	0.900678i	$0.643070\pi$
$728$		0			0
$729$	−197.281			−0.0100229
$730$	−330.680	+	190.918i	−0.0167658	+	0.00967972i
$731$	−10809.8	−	18723.1i	−0.546943	−	0.947333i
$732$	−4051.28	+	7017.03i	−0.204562	+	0.354313i
$733$			7130.74i			0.359318i	0.983729	+	0.179659i	$0.0574994\pi$
$733$			7130.74i			0.359318i	−0.983729	+	0.179659i	$0.942501\pi$
$734$	−993.256	−	573.457i	−0.0499479	−	0.0288374i
$735$	−30970.2	−	17880.6i	−1.55422	−	0.897329i
$736$		−	5664.60i		−	0.283695i
$737$	5785.77	−	10021.2i	0.289174	−	0.500865i
$738$	−233.279	−	404.052i	−0.0116357	−	0.0201536i
$739$	−23842.6	+	13765.6i	−1.18683	+	0.685215i	−0.957584	−	0.288154i	$-0.906959\pi$
$739$	−23842.6	+	13765.6i	−1.18683	+	0.685215i	−0.229244	+	0.973369i	$0.573625\pi$
$740$	−12381.8			−0.615087
$741$		0			0
$742$	1109.01			0.0548694
$743$	−10318.7	+	5957.48i	−0.509495	+	0.294157i	−0.732626	−	0.680631i	$-0.761706\pi$
$743$	−10318.7	+	5957.48i	−0.509495	+	0.294157i	0.223131	+	0.974788i	$0.428372\pi$
$744$	−1170.97	−	2028.18i	−0.0577013	−	0.0999416i
$745$	10136.2	−	17556.4i	0.498473	−	0.863380i
$746$		−	1219.39i		−	0.0598460i
$747$	13342.1	+	7703.09i	0.653499	+	0.377298i
$748$	−18769.3	−	10836.5i	−0.917478	−	0.529706i
$749$		−	20591.7i		−	1.00455i
$750$	718.343	−	1244.21i	0.0349736	−	0.0605760i
$751$	−2365.20	−	4096.65i	−0.114923	−	0.199053i	0.802826	−	0.596214i	$-0.203329\pi$
$751$	−2365.20	−	4096.65i	−0.114923	−	0.199053i	−0.917749	+	0.397161i	$0.869996\pi$
$752$	671.891	−	387.916i	0.0325816	−	0.0188110i
$753$	37383.4			1.80920
$754$		0			0
$755$	−35763.9			−1.72395
$756$	−15828.1	+	9138.37i	−0.761459	+	0.439629i
$757$	−7955.14	−	13778.7i	−0.381948	−	0.661553i	0.609393	−	0.792868i	$-0.291413\pi$
$757$	−7955.14	−	13778.7i	−0.381948	−	0.661553i	−0.991341	+	0.131316i	$0.958080\pi$
$758$	112.033	−	194.047i	0.00536838	−	0.00929831i
$759$		−	49114.4i		−	2.34880i
$760$	213.467	+	123.245i	0.0101885	+	0.00588233i
$761$	−29286.6	−	16908.6i	−1.39506	−	0.805436i	−0.401187	−	0.915996i	$-0.631402\pi$
$761$	−29286.6	−	16908.6i	−1.39506	−	0.805436i	−0.993869	+	0.110560i	$0.964735\pi$
$762$			98.4221i			0.00467908i
$763$	−16770.9	+	29048.1i	−0.795737	+	1.37826i
$764$	−2675.42	−	4633.97i	−0.126693	−	0.219439i
$765$	9560.61	−	5519.82i	0.451849	−	0.260875i
$766$	−1849.13			−0.0872219
$767$		0			0
$768$	−25842.2			−1.21419
$769$	31229.8	−	18030.5i	1.46447	−	0.845510i	0.465253	−	0.885178i	$-0.345964\pi$
$769$	31229.8	−	18030.5i	1.46447	−	0.845510i	0.999213	+	0.0396685i	$0.0126302\pi$
$770$	−863.925	−	1496.36i	−0.0404334	−	0.0700327i
$771$	15894.1	−	27529.4i	0.742427	−	1.28592i
$772$		−	36663.3i		−	1.70925i
$773$	−401.618	−	231.874i	−0.0186872	−	0.0107891i	0.490627	−	0.871370i	$-0.336768\pi$
$773$	−401.618	−	231.874i	−0.0186872	−	0.0107891i	−0.509315	+	0.860580i	$0.670101\pi$
$774$	591.101	+	341.272i	0.0274505	+	0.0158486i
$775$		−	3013.57i		−	0.139678i
$776$	497.377	−	861.483i	0.0230088	−	0.0398524i
$777$	14573.7	+	25242.4i	0.672882	+	1.16547i
$778$	−466.043	+	269.070i	−0.0214762	+	0.0123993i
$779$	2092.28			0.0962308
$780$		0			0
$781$	34804.1			1.59461
$782$	−1828.55	+	1055.71i	−0.0836174	+	0.0482765i
$783$	−1189.56	−	2060.38i	−0.0542931	−	0.0940383i
$784$	17058.9	−	29546.9i	0.777100	−	1.34598i
$785$			18282.5i			0.831249i
$786$	320.707	+	185.160i	0.0145537	+	0.00840261i
$787$	11875.6	+	6856.38i	0.537890	+	0.310551i	0.744223	−	0.667931i	$-0.232820\pi$
$787$	11875.6	+	6856.38i	0.537890	+	0.310551i	−0.206334	+	0.978482i	$0.566153\pi$
$788$		−	4173.29i		−	0.188664i
$789$	24694.1	−	42771.5i	1.11424	−	1.92992i
$790$	112.367	+	194.625i	0.00506053	+	0.00876510i
$791$	6772.62	−	3910.17i	0.304433	−	0.175764i
$792$	1370.36			0.0614819
$793$		0			0
$794$	−354.963			−0.0158655
$795$	14444.8	−	8339.70i	0.644407	−	0.372049i
$796$	−6275.53	−	10869.5i	−0.279435	−	0.483996i
$797$	2002.71	−	3468.79i	0.0890081	−	0.154167i	−0.818084	−	0.575099i	$-0.804964\pi$
$797$	2002.71	−	3468.79i	0.0890081	−	0.154167i	0.907092	+	0.420932i	$0.138297\pi$
$798$		−	289.722i		−	0.0128522i
$799$	−754.826	−	435.799i	−0.0334216	−	0.0192959i
$800$	491.029	+	283.495i	0.0217006	+	0.0125288i
$801$		−	14287.1i		−	0.630225i
$802$	−230.452	+	399.155i	−0.0101466	+	0.0175744i
$803$	−4759.88	−	8244.35i	−0.209181	−	0.362312i
$804$	−13615.0	+	7860.60i	−0.597217	+	0.344803i
$805$	60441.4			2.64631
$806$		0			0
$807$	42802.3			1.86705
$808$	1754.59	−	1013.01i	0.0763938	−	0.0441060i
$809$	11210.0	+	19416.2i	0.487171	+	0.843805i	0.999891	−	0.0147508i	$-0.00469549\pi$
$809$	11210.0	+	19416.2i	0.487171	+	0.843805i	−0.512720	+	0.858556i	$0.671362\pi$
$810$	694.339	−	1202.63i	0.0301192	−	0.0521680i
$811$			14185.7i			0.614213i	0.951675	+	0.307107i	$0.0993608\pi$
$811$			14185.7i			0.614213i	−0.951675	+	0.307107i	$0.900639\pi$
$812$	6317.93	+	3647.66i	0.273049	+	0.157645i
$813$	16322.4	+	9423.75i	0.704123	+	0.406526i
$814$			859.733i			0.0370192i
$815$	−8424.54	+	14591.7i	−0.362084	+	0.627149i
$816$	14681.4	+	25428.9i	0.629843	+	1.09092i
$817$	−2650.79	+	1530.44i	−0.113512	+	0.0655363i
$818$	50.8754			0.00217459
$819$		0			0
$820$	−16952.7			−0.721969
$821$	25993.3	−	15007.2i	1.10496	−	0.637949i	0.167440	−	0.985882i	$-0.446450\pi$
$821$	25993.3	−	15007.2i	1.10496	−	0.637949i	0.937519	+	0.347934i	$0.113117\pi$
$822$	494.929	+	857.242i	0.0210008	+	0.0363744i
$823$	5895.69	−	10211.6i	0.249709	−	0.432509i	−0.713736	−	0.700415i	$-0.752998\pi$
$823$	5895.69	−	10211.6i	0.249709	−	0.432509i	0.963445	+	0.267906i	$0.0863316\pi$
$824$			2373.56i			0.100348i
$825$	4257.42	+	2458.02i	0.179666	+	0.103730i
$826$	1495.86	+	863.636i	0.0630117	+	0.0363798i
$827$		−	26657.2i		−	1.12087i	−0.828198	−	0.560436i	$-0.810634\pi$
$827$		−	26657.2i		−	1.12087i	0.828198	−	0.560436i	$-0.189366\pi$
$828$	−11967.4	+	20728.1i	−0.502288	+	0.869989i
$829$	−11725.3	−	20308.8i	−0.491238	−	0.850849i	0.508711	−	0.860937i	$-0.330122\pi$
$829$	−11725.3	−	20308.8i	−0.491238	−	0.850849i	−0.999949	+	0.0100885i	$0.996789\pi$
$830$	−1350.17	+	779.522i	−0.0564640	+	0.0325995i
$831$	7533.96			0.314501
$832$		0			0
$833$	−38329.1			−1.59427
$834$	853.468	−	492.750i	0.0354355	−	0.0204587i
$835$	12496.8	+	21645.1i	0.517927	+	0.897076i
$836$	−1534.21	+	2657.33i	−0.0634709	+	0.109935i
$837$		−	11700.1i		−	0.483170i
$838$	−70.4397	−	40.6684i	−0.00290370	−	0.00167645i
$839$	9709.92	+	5606.03i	0.399551	+	0.230681i	0.686290	−	0.727328i	$-0.259238\pi$
$839$	9709.92	+	5606.03i	0.399551	+	0.230681i	−0.286739	+	0.958009i	$0.592571\pi$
$840$			4701.49i			0.193115i
$841$	11719.7	−	20299.1i	0.480531	−	0.832305i
$842$	783.149	+	1356.45i	0.0320536	+	0.0555184i
$843$	−45697.1	+	26383.2i	−1.86701	+	1.07792i
$844$	−38150.6			−1.55592
$845$		0			0
$846$	27.5169			0.00111826
$847$	3101.62	−	1790.72i	0.125824	−	0.0726445i
$848$	7956.43	+	13780.9i	0.322199	+	0.558066i
$849$	−3672.09	+	6360.25i	−0.148440	+	0.257106i
$850$		−	211.341i		−	0.00852815i
$851$	−26044.9	−	15037.0i	−1.04913	−	0.605714i
$852$	−40950.2	−	23642.6i	−1.64663	−	0.950683i
$853$		−	10447.0i		−	0.419342i	−0.977772	−	0.209671i	$-0.932761\pi$
$853$		−	10447.0i		−	0.419342i	0.977772	−	0.209671i	$-0.0672393\pi$
$854$	−346.177	+	599.596i	−0.0138711	+	0.0240255i
$855$	−781.487	−	1353.58i	−0.0312588	−	0.0541419i
$856$	−1431.25	+	826.333i	−0.0571485	+	0.0329947i
$857$	37041.9			1.47646			0.738230	−	0.674549i	$-0.235662\pi$
$857$	37041.9			1.47646			0.738230	+	0.674549i	$0.235662\pi$
$858$		0			0
$859$	15972.0			0.634409			0.317204	−	0.948357i	$-0.397256\pi$
$859$	15972.0			0.634409			0.317204	+	0.948357i	$0.397256\pi$
$860$	21478.1	−	12400.4i	0.851623	−	0.491685i
$861$	19953.8	+	34561.0i	0.789807	+	1.36799i
$862$	−411.255	+	712.315i	−0.0162499	+	0.0281456i
$863$			32985.8i			1.30110i	0.759464	+	0.650549i	$0.225461\pi$
$863$			32985.8i			1.30110i	−0.759464	+	0.650549i	$0.774539\pi$
$864$	1906.40	+	1100.66i	0.0750660	+	0.0433394i
$865$	26518.3	+	15310.3i	1.04237	+	0.601811i
$866$			905.128i			0.0355167i
$867$	554.413	−	960.271i	0.0217172	−	0.0376154i
$868$	17938.5	+	31070.3i	0.701465	+	1.21497i
$869$	−4852.29	+	2801.47i	−0.189416	+	0.109359i
$870$	−305.576			−0.0119080
$871$		0			0
$872$	2692.02			0.104545
$873$	−5462.59	+	3153.83i	−0.211776	+	0.122269i
$874$	149.466	+	258.883i	0.00578463	+	0.0100193i
$875$	−22039.7	+	38174.0i	−0.851519	+	1.47487i
$876$			12933.6i			0.498843i
$877$	10634.4	+	6139.75i	0.409460	+	0.236402i	0.690558	−	0.723277i	$-0.257365\pi$
$877$	10634.4	+	6139.75i	0.409460	+	0.236402i	−0.281098	+	0.959679i	$0.590698\pi$
$878$	−1868.24	−	1078.63i	−0.0718109	−	0.0414601i
$879$		−	24879.4i		−	0.954677i
$880$	12396.2	−	21470.9i	0.474859	−	0.822480i
$881$	15469.5	+	26794.0i	0.591579	+	1.02464i	0.994020	+	0.109199i	$0.0348285\pi$
$881$	15469.5	+	26794.0i	0.591579	+	1.02464i	−0.402441	+	0.915446i	$0.631838\pi$
$882$	1047.96	−	605.037i	0.0400074	−	0.0230983i
$883$	−31309.8			−1.19327			−0.596636	−	0.802512i	$-0.703497\pi$
$883$	−31309.8			−1.19327			−0.596636	+	0.802512i	$0.703497\pi$
$884$		0			0
$885$	25978.0			0.986712
$886$	1109.37	−	640.494i	0.0420654	−	0.0242865i
$887$	2016.63	+	3492.91i	0.0763380	+	0.132221i	0.901667	−	0.432430i	$-0.142344\pi$
$887$	2016.63	+	3492.91i	0.0763380	+	0.132221i	−0.825329	+	0.564652i	$0.809011\pi$
$888$	1169.67	−	2025.92i	0.0442021	−	0.0765603i
$889$		−	3019.73i		−	0.113924i
$890$	1252.10	+	722.899i	0.0471578	+	0.0272266i
$891$	29983.4	+	17310.9i	1.12736	+	0.650884i
$892$			16676.5i			0.625977i
$893$	−61.6997	+	106.867i	−0.00231210	+	0.00400467i
$894$	956.202	+	1656.19i	0.0357720	+	0.0619589i
$895$	29965.6	−	17300.7i	1.11915	−	0.646143i
$896$	−8995.93			−0.335416
$897$		0			0
$898$	1147.10			0.0426272
$899$	−4044.50	+	2335.09i	−0.150046	+	0.0866292i
$900$	−1197.86	−	2074.75i	−0.0443652	−	0.0768427i
$901$	8938.54	−	15482.0i	0.330506	−	0.572454i
$902$			1177.11i			0.0434519i
$903$	−50560.5	−	29191.1i	−1.86329	−	1.07577i
$904$	−543.561	−	313.825i	−0.0199984	−	0.0115461i
$905$		−	23238.2i		−	0.853550i
$906$	1686.90	−	2921.80i	0.0618581	−	0.107141i
$907$	4404.69	+	7629.15i	0.161252	+	0.279296i	0.935318	−	0.353809i	$-0.115114\pi$
$907$	4404.69	+	7629.15i	0.161252	+	0.279296i	−0.774066	+	0.633105i	$0.781780\pi$
$908$	15021.2	−	8672.50i	0.549005	−	0.316968i
$909$	−12846.9			−0.468760
$910$		0			0
$911$	−33046.9			−1.20186			−0.600930	−	0.799302i	$-0.705203\pi$
$911$	−33046.9			−1.20186			−0.600930	+	0.799302i	$0.705203\pi$
$912$	3600.19	−	2078.57i	0.130717	−	0.0754696i
$913$	−19434.7	−	33661.8i	−0.704484	−	1.22020i
$914$	−996.364	+	1725.75i	−0.0360577	+	0.0624538i
$915$			10412.9i			0.376219i
$916$	41434.1	+	23922.0i	1.49457	+	0.862888i
$917$	−9839.74	−	5680.98i	−0.354348	−	0.204583i
$918$		−	820.522i		−	0.0295003i
$919$	2256.42	−	3908.24i	0.0809930	−	0.140284i	−0.822684	−	0.568499i	$-0.807524\pi$
$919$	2256.42	−	3908.24i	0.0809930	−	0.140284i	0.903677	+	0.428215i	$0.140858\pi$
$920$	−2425.47	−	4201.04i	−0.0869190	−	0.150548i
$921$	36942.6	−	21328.8i	1.32172	−	0.763094i
$922$	2310.72			0.0825374
$923$		0			0
$924$	−58526.1			−2.08373
$925$	2606.93	−	1505.11i	0.0926653	−	0.0535003i
$926$	736.175	+	1275.09i	0.0261255	+	0.0452507i
$927$	7525.28	−	13034.2i	0.266626	−	0.461810i
$928$		−	878.676i		−	0.0310818i
$929$	29287.7	+	16909.3i	1.03434	+	0.597174i	0.918224	−	0.396062i	$-0.129623\pi$
$929$	29287.7	+	16909.3i	1.03434	+	0.597174i	0.116112	+	0.993236i	$0.462957\pi$
$930$	−1301.43	−	751.381i	−0.0458877	−	0.0264933i
$931$			5426.58i			0.191030i
$932$	−6182.77	+	10708.9i	−0.217300	+	0.376374i
$933$	−2150.23	−	3724.31i	−0.0754507	−	0.130684i
$934$	453.077	−	261.584i	0.0158727	−	0.00916412i
$935$	−27852.7			−0.974204
$936$		0			0
$937$	19737.5			0.688150			0.344075	−	0.938942i	$-0.388193\pi$
$937$	19737.5			0.688150			0.344075	+	0.938942i	$0.388193\pi$
$938$	−1163.38	+	671.677i	−0.0404965	+	0.0233806i
$939$	−27099.7	−	46938.0i	−0.941815	−	1.63127i
$940$	499.922	−	865.891i	0.0173465	−	0.0300449i
$941$		−	21587.6i		−	0.747860i	−0.927457	−	0.373930i	$-0.878010\pi$
$941$		−	21587.6i		−	0.747860i	0.927457	−	0.373930i	$-0.121990\pi$
$942$	−1493.62	−	862.342i	−0.0516611	−	0.0298266i
$943$	−35659.7	−	20588.1i	−1.23143	−	0.710967i
$944$			24784.1i			0.854507i
$945$	−11744.1	+	20341.3i	−0.404269	+	0.700215i
$946$	−861.021	−	1491.33i	−0.0295922	−	0.0512551i
$947$	−5049.04	+	2915.07i	−0.173254	+	0.100028i	−0.584119	−	0.811668i	$-0.698560\pi$
$947$	−5049.04	+	2915.07i	−0.173254	+	0.100028i	0.410865	+	0.911696i	$0.365227\pi$
$948$	7612.20			0.260794
$949$		0			0
$950$	−29.9213			−0.00102187
$951$	−29550.6	+	17061.1i	−1.00762	+	0.581748i
$952$	2519.54	+	4363.97i	0.0857760	+	0.148568i
$953$	4419.89	−	7655.47i	0.150235	−	0.260215i	−0.781079	−	0.624433i	$-0.785330\pi$
$953$	4419.89	−	7655.47i	0.150235	−	0.260215i	0.931314	+	0.364218i	$0.118664\pi$
$954$			564.391i			0.0191539i
$955$	−5955.29	−	3438.29i	−0.201789	−	0.116503i
$956$	26910.8	+	15537.0i	0.910417	+	0.525629i
$957$		−	7618.47i		−	0.257336i
$958$	−1481.80	+	2566.55i	−0.0499737	+	0.0865570i
$959$	−15185.1	−	26301.4i	−0.511317	−	0.885626i
$960$	−29006.9	+	16747.1i	−0.975202	+	0.563033i
$961$	6823.95			0.229061
$962$		0			0
$963$	10479.4			0.350669
$964$	−28245.2	+	16307.4i	−0.943688	+	0.544839i
$965$	−23558.7	−	40804.9i	−0.785888	−	1.36120i
$966$	−2850.88	+	4937.86i	−0.0949539	+	0.164465i
$967$			10346.1i			0.344063i	0.985091	+	0.172032i	$0.0550331\pi$
$967$			10346.1i			0.344063i	−0.985091	+	0.172032i	$0.944967\pi$
$968$	−248.932	−	143.721i	−0.00826547	−	0.00477207i
$969$	−4044.58	−	2335.14i	−0.134087	−	0.0774153i
$970$		−	638.310i		−	0.0211288i
$971$	8709.99	−	15086.1i	0.287865	−	0.498597i	−0.685435	−	0.728134i	$-0.740388\pi$
$971$	8709.99	−	15086.1i	0.287865	−	0.498597i	0.973300	+	0.229537i	$0.0737213\pi$
$972$	−15204.0	−	26334.1i	−0.501716	−	0.868998i
$973$	−26185.6	+	15118.3i	−0.862766	+	0.498118i
$974$	60.7753			0.00199935
$975$		0			0
$976$	−9934.37			−0.325811
$977$	−36143.6	+	20867.5i	−1.18356	+	0.683327i	−0.956835	−	0.290633i	$-0.906134\pi$
$977$	−36143.6	+	20867.5i	−1.18356	+	0.683327i	−0.226722	+	0.973959i	$0.572801\pi$
$978$	−794.731	−	1376.51i	−0.0259843	−	0.0450062i
$979$	−18023.0	+	31216.7i	−0.588373	+	1.01909i
$980$		−	43968.9i		−	1.43320i
$981$	−14783.0	−	8534.94i	−0.481125	−	0.277778i
$982$	−2598.56	−	1500.28i	−0.0844433	−	0.0487533i
$983$			34123.8i			1.10720i	0.832781	+	0.553602i	$0.186747\pi$
$983$			34123.8i			1.10720i	−0.832781	+	0.553602i	$0.813253\pi$
$984$	1601.47	−	2773.82i	0.0518830	−	0.0898640i
$985$	−2681.63	−	4644.72i	−0.0867450	−	0.150247i
$986$	−283.639	+	163.759i	−0.00916116	+	0.00528920i
$987$	−2353.69			−0.0759054
$988$		0			0
$989$	60238.2			1.93677
$990$	761.519	−	439.663i	0.0244471	−	0.0141146i
$991$	27148.4	+	47022.4i	0.870228	+	1.50728i	0.861760	+	0.507316i	$0.169362\pi$
$991$	27148.4	+	47022.4i	0.870228	+	1.50728i	0.00846804	+	0.999964i	$0.497305\pi$
$992$	2160.58	−	3742.23i	0.0691516	−	0.119774i
$993$			18210.1i			0.581952i
$994$	−3499.14	−	2020.23i	−0.111656	−	0.0644645i
$995$	−13968.9	−	8064.93i	−0.445068	−	0.256960i
$996$			52808.3i			1.68001i
$997$	−23439.7	+	40598.7i	−0.744575	+	1.28964i	0.205817	+	0.978590i	$0.434015\pi$
$997$	−23439.7	+	40598.7i	−0.744575	+	1.28964i	−0.950393	+	0.311052i	$0.899319\pi$
$998$	57.5932	+	99.7543i	0.00182673	+	0.00316399i
$999$	10121.3	−	5843.54i	0.320545	−	0.185066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.9		36
13.2	odd	12		169.4.a.k.1.5	✓	9
13.3	even	3		169.4.b.g.168.9		18
13.4	even	6	inner	169.4.e.h.147.9		36
13.5	odd	4		169.4.c.l.146.5		18
13.6	odd	12		169.4.c.l.22.5		18
13.7	odd	12		169.4.c.k.22.5		18
13.8	odd	4		169.4.c.k.146.5		18
13.9	even	3	inner	169.4.e.h.147.10		36
13.10	even	6		169.4.b.g.168.10		18
13.11	odd	12		169.4.a.l.1.5	yes	9
13.12	even	2	inner	169.4.e.h.23.10		36
39.2	even	12		1521.4.a.bh.1.5		9
39.11	even	12		1521.4.a.bg.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.5	✓	9	13.2	odd	12
169.4.a.l.1.5	yes	9	13.11	odd	12
169.4.b.g.168.9		18	13.3	even	3
169.4.b.g.168.10		18	13.10	even	6
169.4.c.k.22.5		18	13.7	odd	12
169.4.c.k.146.5		18	13.8	odd	4
169.4.c.l.22.5		18	13.6	odd	12
169.4.c.l.146.5		18	13.5	odd	4
169.4.e.h.23.9		36	1.1	even	1	trivial
169.4.e.h.23.10		36	13.12	even	2	inner
169.4.e.h.147.9		36	13.4	even	6	inner
169.4.e.h.147.10		36	13.9	even	3	inner
1521.4.a.bg.1.5		9	39.11	even	12
1521.4.a.bh.1.5		9	39.2	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.129088 + 0.0745292i) q^{2} +(3.24429 + 5.61927i) q^{3} +(-3.98889 + 6.90896i) q^{4} +10.2526i q^{5} +(-0.837600 - 0.483588i) q^{6} +(25.6987 + 14.8372i) q^{7} -2.38162i q^{8} +(-7.55083 + 13.0784i) q^{9} +O(q^{10})\)	\(q+(-0.129088 + 0.0745292i) q^{2} +(3.24429 + 5.61927i) q^{3} +(-3.98889 + 6.90896i) q^{4} +10.2526i q^{5} +(-0.837600 - 0.483588i) q^{6} +(25.6987 + 14.8372i) q^{7} -2.38162i q^{8} +(-7.55083 + 13.0784i) q^{9} +(-0.764114 - 1.32348i) q^{10} +(32.9965 - 19.0505i) q^{11} -51.7645 q^{12} -4.42320 q^{14} +(-57.6119 + 33.2623i) q^{15} +(-31.7336 - 54.9643i) q^{16} +(-35.6507 + 61.7488i) q^{17} -2.25103i q^{18} +(8.74230 + 5.04737i) q^{19} +(-70.8345 - 40.8963i) q^{20} +192.544i q^{21} +(-2.83964 + 4.91840i) q^{22} +(-99.3326 - 172.049i) q^{23} +(13.3830 - 7.72667i) q^{24} +19.8851 q^{25} +77.2033 q^{27} +(-205.019 + 118.368i) q^{28} +(-15.4082 - 26.6877i) q^{29} +(4.95802 - 8.58754i) q^{30} -151.549i q^{31} +(24.6932 + 14.2566i) q^{32} +(214.100 + 123.611i) q^{33} -10.6281i q^{34} +(-152.119 + 263.477i) q^{35} +(-60.2389 - 104.337i) q^{36} +(131.099 - 75.6903i) q^{37} -1.50470 q^{38} +24.4177 q^{40} +(179.496 - 103.632i) q^{41} +(-14.3502 - 24.8552i) q^{42} +(-151.607 + 262.592i) q^{43} +303.962i q^{44} +(-134.087 - 77.4153i) q^{45} +(25.6453 + 14.8063i) q^{46} +12.2241i q^{47} +(205.906 - 356.640i) q^{48} +(268.783 + 465.545i) q^{49} +(-2.56694 + 1.48202i) q^{50} -462.645 q^{51} -250.726 q^{53} +(-9.96604 + 5.75390i) q^{54} +(195.317 + 338.298i) q^{55} +(35.3365 - 61.2046i) q^{56} +65.5005i q^{57} +(3.97803 + 2.29672i) q^{58} +(-338.185 - 195.251i) q^{59} -530.718i q^{60} +(78.2638 - 135.557i) q^{61} +(11.2948 + 19.5632i) q^{62} +(-388.093 + 224.066i) q^{63} +503.488 q^{64} -36.8505 q^{66} +(263.017 - 151.853i) q^{67} +(-284.413 - 492.619i) q^{68} +(644.527 - 1116.35i) q^{69} -45.3491i q^{70} +(791.087 + 456.734i) q^{71} +(31.1479 + 17.9832i) q^{72} -249.855i q^{73} +(-11.2823 + 19.5415i) q^{74} +(64.5132 + 111.740i) q^{75} +(-69.7442 + 40.2668i) q^{76} +1130.62 q^{77} -147.055 q^{79} +(563.524 - 325.351i) q^{80} +(454.342 + 786.944i) q^{81} +(-15.4473 + 26.7554i) q^{82} -1020.16i q^{83} +(-1330.28 - 768.038i) q^{84} +(-633.083 - 365.511i) q^{85} -45.1967i q^{86} +(99.9772 - 173.166i) q^{87} +(-45.3712 - 78.5852i) q^{88} +(-819.314 + 473.031i) q^{89} +23.0788 q^{90} +1584.91 q^{92} +(851.594 - 491.668i) q^{93} +(-0.911055 - 1.57799i) q^{94} +(-51.7484 + 89.6309i) q^{95} +185.011i q^{96} +(361.721 + 208.840i) q^{97} +(-69.3934 - 40.0643i) q^{98} +575.390i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more