LMFDB - Embedded newform 169.4.e.h.23.10

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			23.10
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.10

$q$-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	−0.477007	−	0.878900i	$-0.658278\pi$
$2$	0.129088	−	0.0745292i	0.0456396	−	0.0263500i	0.522646	+	0.852550i	$0.324945\pi$
$3$	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	$-0.848384\pi$
$5$		−	10.2526i		−	0.917016i	0.888690	−	0.458508i	$-0.151616\pi$
$6$	0.837600	+	0.483588i	0.0569914	+	0.0329040i
$7$	−25.6987	−	14.8372i	−1.38760	−	0.801131i	−0.394556	−	0.918872i	$-0.629101\pi$
$7$	−25.6987	−	14.8372i	−1.38760	−	0.801131i	−0.993044	+	0.117741i	$0.962435\pi$
$8$			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	−0.878637	−	0.477490i	$-0.841547\pi$
$11$	−32.9965	+	19.0505i	−0.904438	+	0.522178i	−0.0258006	+	0.999667i	$0.508213\pi$
$12$	−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	0.446291	−	0.894888i	$-0.352745\pi$
$19$	−8.74230	−	5.04737i	−0.105559	−	0.0609445i	−0.551850	+	0.833943i	$0.686078\pi$
$20$	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	$0.144673\pi$
$31$			151.549i			0.878031i	−0.898479	+	0.439016i	$0.855327\pi$
$32$	−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	−0.762128	−	0.647427i	$-0.775845\pi$
$37$	−131.099	+	75.6903i	−0.582503	+	0.336308i	0.179624	+	0.983735i	$0.442512\pi$
$38$	−1.50470			−0.00642356
$39$		0			0
$40$	24.4177			0.0965194
$41$	−179.496	+	103.632i	−0.683723	+	0.394748i	−0.801256	−	0.598321i	$-0.795835\pi$
$41$	−179.496	+	103.632i	−0.683723	+	0.394748i	0.117533	+	0.993069i	$0.462501\pi$
$42$	−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	$-0.993962\pi$
$47$		−	12.2241i		−	0.0379377i	0.999820	−	0.0189689i	$-0.00603834\pi$
$48$	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	0.824332	−	0.566106i	$-0.191551\pi$
$59$	338.185	+	195.251i	0.746236	+	0.430840i	−0.0780962	+	0.996946i	$0.524884\pi$
$60$			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	−0.720247	−	0.693718i	$-0.755971\pi$
$67$	−263.017	+	151.853i	−0.479592	+	0.276893i	0.240654	+	0.970611i	$0.422638\pi$
$68$	−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	−0.338222	−	0.941066i	$-0.609825\pi$
$71$	−791.087	−	456.734i	−1.32232	−	0.763442i	−0.984098	+	0.177625i	$0.943159\pi$
$72$	−31.1479	−	17.9832i	−0.0509835	−	0.0294353i
$73$			249.855i			0.400594i	0.979735	+	0.200297i	$0.0641907\pi$
$73$			249.855i			0.400594i	−0.979735	+	0.200297i	$0.935809\pi$
$74$	−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	$0.235668\pi$
$83$			1020.16i			1.34913i	−0.738217	+	0.674564i	$0.764332\pi$
$84$	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	0.0748073	−	0.997198i	$-0.476166\pi$
$89$	819.314	−	473.031i	0.975810	−	0.563384i	0.901002	+	0.433814i	$0.142832\pi$
$90$	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	0.298591	−	0.954381i	$-0.403483\pi$
$97$	−361.721	−	208.840i	−0.378631	−	0.218603i	−0.677223	+	0.735778i	$0.736817\pi$
$98$	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	$-0.834569\pi$
$109$		−	1130.33i		−	0.993267i	0.867960	−	0.496634i	$-0.165431\pi$
$110$	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	0.750224	−	0.661183i	$-0.229945\pi$
$137$	886.335	+	511.726i	0.552735	+	0.319122i	−0.197489	+	0.980305i	$0.563279\pi$
$138$		−	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	0.890433	−	0.455114i	$-0.150401\pi$
$149$	1712.40	+	988.653i	0.941510	+	0.543581i	0.0510768	+	0.998695i	$0.483735\pi$
$150$	16.6558	+	9.61623i	0.00906626	+	0.00523441i
$151$		−	3488.30i		−	1.87996i	−0.341234	−	0.939979i	$-0.610845\pi$
$151$		−	3488.30i		−	1.87996i	0.341234	−	0.939979i	$-0.389155\pi$
$152$	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	0.117422	−	0.993082i	$-0.462537\pi$
$163$	−1423.23	−	821.702i	−0.683901	−	0.394851i	−0.801323	+	0.598231i	$0.795870\pi$
$164$		−	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	−0.901743	−	0.432273i	$-0.857712\pi$
$167$	−2111.19	+	1218.89i	−0.978255	+	0.564796i	−0.0765122	+	0.997069i	$0.524378\pi$
$168$	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	0.484535	−	0.874772i	$-0.338989\pi$
$193$	3979.97	−	2297.84i	1.48438	−	0.857006i	0.999842	+	0.0177660i	$0.00565540\pi$
$194$	−62.2586			−0.0230408
$195$		0			0
$196$	−4288.58			−1.56289
$197$	453.031	−	261.557i	0.163843	−	0.0945949i	−0.415836	−	0.909439i	$-0.636511\pi$
$197$	453.031	−	261.557i	0.163843	−	0.0945949i	0.579679	+	0.814845i	$0.303178\pi$
$198$	−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	−0.746546	−	0.665334i	$-0.768289\pi$
$223$	−1810.32	+	1045.19i	−0.543622	+	0.313860i	0.202924	+	0.979195i	$0.434956\pi$
$224$	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	0.749337	−	0.662189i	$-0.230372\pi$
$227$	1882.88	+	1087.08i	0.550534	+	0.317851i	−0.198804	+	0.980039i	$0.563706\pi$
$228$	452.541	+	261.274i	0.131448	+	0.0758918i
$229$			5997.16i			1.73058i	0.501270	+	0.865291i	$0.332866\pi$
$229$			5997.16i			1.73058i	−0.501270	+	0.865291i	$0.667134\pi$
$230$	−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	$0.176718\pi$
$239$			3895.06i			1.05419i	−0.849807	+	0.527093i	$0.823282\pi$
$240$	−3656.47	−	2111.06i	−0.983434	−	0.567786i
$241$	−3540.48	−	2044.10i	−0.946316	−	0.546356i	−0.0543816	−	0.998520i	$-0.517319\pi$
$241$	−3540.48	−	2044.10i	−0.946316	−	0.546356i	−0.891935	+	0.452164i	$0.850652\pi$
$242$		−	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	−0.754698	−	0.656072i	$-0.772217\pi$
$271$	−2515.56	+	1452.36i	−0.563872	+	0.325552i	0.190826	+	0.981624i	$0.438883\pi$
$272$	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	$-0.668447\pi$
$281$		−	8132.21i		−	1.72643i	0.504836	−	0.863215i	$-0.331553\pi$
$282$	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	0.793074	−	0.609125i	$-0.208479\pi$
$293$	3320.63	+	1917.17i	0.662094	+	0.382260i	−0.130981	+	0.991385i	$0.541813\pi$
$294$			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	$0.209271\pi$
$307$			6574.27i			1.22219i	−0.791556	+	0.611097i	$0.790729\pi$
$308$	−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	$-0.845740\pi$
$317$		−	5258.80i		−	0.931746i	0.884852	−	0.465873i	$-0.154260\pi$
$318$	−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	0.284437	−	0.958695i	$-0.408193\pi$
$331$	−2430.48	−	1403.24i	−0.403599	−	0.233018i	−0.688036	+	0.725677i	$0.741527\pi$
$332$	−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	−0.960521	−	0.278207i	$-0.910260\pi$
$349$	−7822.84	+	4516.52i	−1.19985	+	0.692732i	−0.239326	+	0.970939i	$0.576927\pi$
$350$	−87.9561			−0.0134327
$351$		0			0
$352$	1086.39			0.164502
$353$	4547.71	−	2625.62i	0.685694	−	0.395886i	−0.116303	−	0.993214i	$-0.537104\pi$
$353$	4547.71	−	2625.62i	0.685694	−	0.395886i	0.801997	+	0.597328i	$0.203771\pi$
$354$	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	$0.0913355\pi$
$359$			3850.22i			0.566035i	−0.959115	+	0.283018i	$0.908664\pi$
$360$	−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	−0.409180	−	0.912454i	$-0.634185\pi$
$379$	1301.82	−	751.608i	0.176438	−	0.101867i	0.585618	+	0.810587i	$0.300852\pi$
$380$	−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	−0.435952	−	0.899970i	$-0.643588\pi$
$383$	−10743.4	−	6202.72i	−1.43333	−	0.827531i	−0.997373	+	0.0724390i	$0.976922\pi$
$384$	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	0.363944	−	0.931421i	$-0.381430\pi$
$397$	−2062.33	−	1190.69i	−0.260719	−	0.150526i	−0.624662	+	0.780895i	$0.714763\pi$
$398$			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	−0.657385	−	0.753555i	$-0.728337\pi$
$401$	−2677.84	+	1546.05i	−0.333479	+	0.192534i	0.323906	+	0.946089i	$0.395004\pi$
$402$	−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	0.517761	−	0.855525i	$-0.326766\pi$
$409$	295.585	+	170.656i	0.0357353	+	0.0206318i	−0.482026	+	0.876157i	$0.660099\pi$
$410$	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	$0.208119\pi$
$421$			10508.0i			1.21645i	−0.793764	+	0.608226i	$0.791881\pi$
$422$	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	−0.742673	−	0.669654i	$-0.766442\pi$
$431$	−4778.77	+	2759.02i	−0.534072	+	0.308347i	0.208601	+	0.978001i	$0.433109\pi$
$432$	−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	0.807533	−	0.589823i	$-0.200802\pi$
$449$	6664.63	+	3847.83i	0.700497	+	0.404432i	−0.107035	+	0.994255i	$0.534136\pi$
$450$			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	−0.957184	−	0.289479i	$-0.906518\pi$
$457$	−11577.7	+	6684.39i	−1.18508	+	0.684207i	−0.227896	+	0.973685i	$0.573185\pi$
$458$	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	0.989129	−	0.147050i	$-0.0469777\pi$
$461$	13425.2	+	7751.06i	1.35635	+	0.783086i	0.367216	+	0.930136i	$0.380311\pi$
$462$	947.010	+	546.756i	0.0953655	+	0.0550593i
$463$			9877.67i			0.991478i	0.868472	+	0.495739i	$0.165103\pi$
$463$			9877.67i			0.991478i	−0.868472	+	0.495739i	$0.834897\pi$
$464$	−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	$0.730498\pi$
$479$	−17218.5	+	9941.08i	−1.64245	+	0.948266i	−0.979961	+	0.199191i	$0.936169\pi$
$480$	−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	0.516338	−	0.856385i	$-0.327295\pi$
$487$	353.103	+	203.864i	0.0328555	+	0.0189691i	−0.483482	+	0.875354i	$0.660628\pi$
$488$	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	$0.0110357\pi$
$499$			772.760i			0.0693256i	−0.999399	+	0.0346628i	$0.988964\pi$
$500$	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	−0.358425	−	0.933559i	$-0.616686\pi$
$509$	3110.30	−	1795.73i	0.270848	−	0.156374i	0.629273	+	0.777184i	$0.283353\pi$
$510$	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	$0.0861556\pi$
$541$			6728.89i			0.534746i	−0.963593	+	0.267373i	$0.913844\pi$
$542$	−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	−0.354912	−	0.934900i	$-0.615489\pi$
$557$	3645.03	−	2104.46i	0.277280	−	0.160087i	0.632191	+	0.774812i	$0.282156\pi$
$558$	−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	$0.342655\pi$
$577$			24401.8i			1.76059i	−0.474427	+	0.880295i	$0.657345\pi$
$578$	−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	0.281772	−	0.959481i	$-0.409078\pi$
$587$	17828.5	−	10293.3i	1.25359	−	0.723763i	0.971821	+	0.235719i	$0.0757444\pi$
$588$	−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	$-0.761040\pi$
$593$		−	19701.5i		−	1.36432i	0.731201	−	0.682162i	$-0.238960\pi$
$594$	−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	−0.620151	−	0.784482i	$-0.712929\pi$
$613$	−3807.12	+	2198.04i	−0.250846	+	0.144826i	0.369306	+	0.929308i	$0.379595\pi$
$614$	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	0.00696192	−	0.999976i	$-0.497784\pi$
$617$	−13112.3	−	7570.39i	−0.855562	−	0.493959i	−0.862523	+	0.506017i	$0.831117\pi$
$618$	−834.765	−	481.952i	−0.0543352	−	0.0313704i
$619$		−	20913.0i		−	1.35794i	−0.734165	−	0.678971i	$-0.762426\pi$
$619$		−	20913.0i		−	1.35794i	0.734165	−	0.678971i	$-0.237574\pi$
$620$	−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	0.293195	−	0.956053i	$-0.405281\pi$
$631$	−6152.75	−	3552.29i	−0.388173	−	0.224112i	−0.681368	+	0.731941i	$0.738615\pi$
$632$		−	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	0.146400	−	0.989225i	$-0.453231\pi$
$643$	−10387.7	−	5997.35i	−0.637094	−	0.367826i	−0.783494	+	0.621399i	$0.786565\pi$
$644$	−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	−0.817256	−	0.576274i	$-0.804506\pi$
$661$	−12351.7	+	7131.26i	−0.726817	+	0.419628i	0.0904399	+	0.995902i	$0.471173\pi$
$662$	−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	−0.411104	−	0.911588i	$-0.634857\pi$
$683$	−25098.7	−	14490.8i	−1.40612	−	0.811821i	−0.995011	+	0.0997673i	$0.968190\pi$
$684$			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	0.489674	−	0.871906i	$-0.337116\pi$
$691$	27057.5	−	15621.7i	1.48960	−	0.860023i	0.999929	+	0.0118826i	$0.00378245\pi$
$692$	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	0.629067	−	0.777351i	$-0.283437\pi$
$709$	5104.69	+	2947.19i	0.270396	+	0.156113i	−0.358672	+	0.933464i	$0.616770\pi$
$710$			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	$-0.942501\pi$
$733$		−	7130.74i		−	0.359318i	0.983729	−	0.179659i	$-0.0574994\pi$
$734$	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	0.229244	−	0.973369i	$-0.426375\pi$
$739$	23842.6	−	13765.6i	1.18683	−	0.685215i	0.957584	+	0.288154i	$0.0930414\pi$
$740$	−12381.8			−0.615087
$741$		0			0
$742$	1109.01			0.0548694
$743$	10318.7	−	5957.48i	0.509495	−	0.294157i	−0.223131	−	0.974788i	$-0.571628\pi$
$743$	10318.7	−	5957.48i	0.509495	−	0.294157i	0.732626	+	0.680631i	$0.238294\pi$
$744$	−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	0.993869	−	0.110560i	$-0.0352645\pi$
$761$	29286.6	+	16908.6i	1.39506	+	0.805436i	0.401187	+	0.915996i	$0.368598\pi$
$762$		−	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	−0.999213	−	0.0396685i	$-0.987370\pi$
$769$	−31229.8	+	18030.5i	−1.46447	+	0.845510i	−0.465253	+	0.885178i	$0.654036\pi$
$770$	−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	0.509315	−	0.860580i	$-0.329899\pi$
$773$	401.618	+	231.874i	0.0186872	+	0.0107891i	−0.490627	+	0.871370i	$0.663232\pi$
$774$	−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	0.206334	−	0.978482i	$-0.433847\pi$
$787$	−11875.6	−	6856.38i	−0.537890	−	0.310551i	−0.744223	+	0.667931i	$0.767180\pi$
$788$			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	$-0.900639\pi$
$811$		−	14185.7i		−	0.614213i	0.951675	−	0.307107i	$-0.0993608\pi$
$812$	−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	−0.937519	−	0.347934i	$-0.886883\pi$
$821$	−25993.3	+	15007.2i	−1.10496	+	0.637949i	−0.167440	+	0.985882i	$0.553550\pi$
$822$	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	$0.189366\pi$
$827$			26657.2i			1.12087i	−0.828198	+	0.560436i	$0.810634\pi$
$828$	−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	0.286739	−	0.958009i	$-0.407429\pi$
$839$	−9709.92	−	5606.03i	−0.399551	−	0.230681i	−0.686290	+	0.727328i	$0.740762\pi$
$840$		−	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	$0.0672393\pi$
$853$			10447.0i			0.419342i	−0.977772	+	0.209671i	$0.932761\pi$
$854$	−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	$-0.774539\pi$
$863$		−	32985.8i		−	1.30110i	0.759464	−	0.650549i	$-0.225461\pi$
$864$	−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	0.281098	−	0.959679i	$-0.409302\pi$
$877$	−10634.4	−	6139.75i	−0.409460	−	0.236402i	−0.690558	+	0.723277i	$0.742635\pi$
$878$	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	−0.116112	−	0.993236i	$-0.537043\pi$
$929$	−29287.7	−	16909.3i	−1.03434	−	0.597174i	−0.918224	+	0.396062i	$0.870377\pi$
$930$	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	$0.121990\pi$
$941$			21587.6i			0.747860i	−0.927457	+	0.373930i	$0.878010\pi$
$942$	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	−0.410865	−	0.911696i	$-0.634773\pi$
$947$	5049.04	−	2915.07i	0.173254	−	0.100028i	0.584119	+	0.811668i	$0.301440\pi$
$948$	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	$-0.944967\pi$
$967$		−	10346.1i		−	0.344063i	0.985091	−	0.172032i	$-0.0550331\pi$
$968$	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	0.226722	−	0.973959i	$-0.427199\pi$
$977$	36143.6	−	20867.5i	1.18356	−	0.683327i	0.956835	+	0.290633i	$0.0938657\pi$
$978$	−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	$-0.813253\pi$
$983$		−	34123.8i		−	1.10720i	0.832781	−	0.553602i	$-0.186747\pi$
$984$	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.23.10		36
13.2	odd	12		169.4.a.l.1.5	yes	9
13.3	even	3		169.4.b.g.168.10		18
13.4	even	6	inner	169.4.e.h.147.10		36
13.5	odd	4		169.4.c.k.146.5		18
13.6	odd	12		169.4.c.k.22.5		18
13.7	odd	12		169.4.c.l.22.5		18
13.8	odd	4		169.4.c.l.146.5		18
13.9	even	3	inner	169.4.e.h.147.9		36
13.10	even	6		169.4.b.g.168.9		18
13.11	odd	12		169.4.a.k.1.5	✓	9
13.12	even	2	inner	169.4.e.h.23.9		36
39.2	even	12		1521.4.a.bg.1.5		9
39.11	even	12		1521.4.a.bh.1.5		9

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

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Representations

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Database

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