LMFDB - Embedded newform 126.4.g.g.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1345})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 337x^{2} + 336x + 112896 $ x^4 - x^3 + 337x^2 + 336x + 112896
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$-8.91856 + 15.4474i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.4.g.g.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.91856 + 13.7153i) q^{5} +(18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.91856 + 13.7153i) q^{5} +(18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +(15.8371 + 27.4307i) q^{10} +(25.9186 + 44.8923i) q^{11} +38.8371 q^{13} +(22.8371 - 29.1627i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(13.6742 + 23.6845i) q^{17} +(-38.2557 + 66.2608i) q^{19} +63.3485 q^{20} +103.674 q^{22} +(73.6742 - 127.608i) q^{23} +(-62.9072 - 108.958i) q^{25} +(38.8371 - 67.2679i) q^{26} +(-27.6742 - 68.7178i) q^{28} -240.208 q^{29} +(148.337 + 256.927i) q^{31} +(16.0000 + 27.7128i) q^{32} +54.6970 q^{34} +(-180.837 + 230.927i) q^{35} +(80.7670 - 139.893i) q^{37} +(76.5114 + 132.522i) q^{38} +(63.3485 - 109.723i) q^{40} +102.977 q^{41} -328.557 q^{43} +(103.674 - 179.569i) q^{44} +(-147.348 - 255.215i) q^{46} +(33.9773 - 58.8504i) q^{47} +(329.500 + 95.2825i) q^{49} -251.629 q^{50} +(-77.6742 - 134.536i) q^{52} +(-33.2443 - 57.5808i) q^{53} -820.951 q^{55} +(-146.697 - 20.7846i) q^{56} +(-240.208 + 416.053i) q^{58} +(-230.964 - 400.041i) q^{59} +(-92.6742 + 160.516i) q^{61} +593.348 q^{62} +64.0000 q^{64} +(-307.534 + 532.665i) q^{65} +(-272.604 - 472.164i) q^{67} +(54.6970 - 94.7379i) q^{68} +(219.140 + 544.146i) q^{70} +130.742 q^{71} +(-90.6496 - 157.010i) q^{73} +(-161.534 - 279.785i) q^{74} +306.045 q^{76} +(358.638 + 890.533i) q^{77} +(204.848 - 354.808i) q^{79} +(-126.697 - 219.446i) q^{80} +(102.977 - 178.362i) q^{82} -347.928 q^{83} -433.121 q^{85} +(-328.557 + 569.077i) q^{86} +(-207.348 - 359.138i) q^{88} +(578.580 - 1002.13i) q^{89} +(712.161 + 100.902i) q^{91} -589.394 q^{92} +(-67.9546 - 117.701i) q^{94} +(-605.860 - 1049.38i) q^{95} +1618.30 q^{97} +(494.534 - 475.428i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8} - 10 q^{10} + 67 q^{11} + 82 q^{13} + 18 q^{14} - 32 q^{16} - 92 q^{17} - 43 q^{19} - 40 q^{20} + 268 q^{22} + 148 q^{23} - 435 q^{25} + 82 q^{26} + 36 q^{28} - 154 q^{29} + 520 q^{31} + 64 q^{32} - 368 q^{34} - 650 q^{35} - 7 q^{37} + 86 q^{38} - 40 q^{40} + 852 q^{41} - 214 q^{43} + 268 q^{44} - 296 q^{46} + 576 q^{47} + 1318 q^{49} - 1740 q^{50} - 164 q^{52} - 243 q^{53} - 1010 q^{55} - 154 q^{58} - 7 q^{59} - 224 q^{61} + 2080 q^{62} + 256 q^{64} - 570 q^{65} - 687 q^{67} - 368 q^{68} + 1390 q^{70} - 944 q^{71} + 921 q^{73} + 14 q^{74} + 344 q^{76} + 371 q^{77} + 526 q^{79} + 80 q^{80} + 852 q^{82} + 442 q^{83} - 5840 q^{85} - 214 q^{86} - 536 q^{88} + 774 q^{89} + 1345 q^{91} - 1184 q^{92} - 1152 q^{94} - 1910 q^{95} + 3906 q^{97} + 1318 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8 - 10 * q^10 + 67 * q^11 + 82 * q^13 + 18 * q^14 - 32 * q^16 - 92 * q^17 - 43 * q^19 - 40 * q^20 + 268 * q^22 + 148 * q^23 - 435 * q^25 + 82 * q^26 + 36 * q^28 - 154 * q^29 + 520 * q^31 + 64 * q^32 - 368 * q^34 - 650 * q^35 - 7 * q^37 + 86 * q^38 - 40 * q^40 + 852 * q^41 - 214 * q^43 + 268 * q^44 - 296 * q^46 + 576 * q^47 + 1318 * q^49 - 1740 * q^50 - 164 * q^52 - 243 * q^53 - 1010 * q^55 - 154 * q^58 - 7 * q^59 - 224 * q^61 + 2080 * q^62 + 256 * q^64 - 570 * q^65 - 687 * q^67 - 368 * q^68 + 1390 * q^70 - 944 * q^71 + 921 * q^73 + 14 * q^74 + 344 * q^76 + 371 * q^77 + 526 * q^79 + 80 * q^80 + 852 * q^82 + 442 * q^83 - 5840 * q^85 - 214 * q^86 - 536 * q^88 + 774 * q^89 + 1345 * q^91 - 1184 * q^92 - 1152 * q^94 - 1910 * q^95 + 3906 * q^97 + 1318 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−7.91856	+	13.7153i	−0.708258	+	1.22674i	0.257245	+	0.966346i	$0.417185\pi$
$5$	−7.91856	+	13.7153i	−0.708258	+	1.22674i	−0.965503	+	0.260392i	$0.916148\pi$
$6$		0			0
$7$	18.3371	+	2.59808i	0.990111	+	0.140283i
$7$	18.3371	+	2.59808i	0.990111	+	0.140283i
$8$	−8.00000			−0.353553
$9$		0			0
$10$	15.8371	+	27.4307i	0.500814	+	0.867435i
$11$	25.9186	+	44.8923i	0.710431	+	1.23050i	0.964696	+	0.263368i	$0.0848333\pi$
$11$	25.9186	+	44.8923i	0.710431	+	1.23050i	−0.254265	+	0.967135i	$0.581833\pi$
$12$		0			0
$13$	38.8371			0.828575			0.414288	−	0.910146i	$-0.364031\pi$
$13$	38.8371			0.828575			0.414288	+	0.910146i	$0.364031\pi$
$14$	22.8371	−	29.1627i	0.435963	−	0.556719i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	13.6742	+	23.6845i	0.195088	+	0.337902i	0.946929	−	0.321442i	$-0.104168\pi$
$17$	13.6742	+	23.6845i	0.195088	+	0.337902i	−0.751842	+	0.659344i	$0.770834\pi$
$18$		0			0
$19$	−38.2557	+	66.2608i	−0.461919	+	0.800067i	−0.999057	−	0.0434278i	$-0.986172\pi$
$19$	−38.2557	+	66.2608i	−0.461919	+	0.800067i	0.537138	+	0.843494i	$0.319505\pi$
$20$	63.3485			0.708258
$21$		0			0
$22$	103.674			1.00470
$23$	73.6742	−	127.608i	0.667919	−	1.15687i	−0.310566	−	0.950552i	$-0.600519\pi$
$23$	73.6742	−	127.608i	0.667919	−	1.15687i	0.978485	−	0.206318i	$-0.0661482\pi$
$24$		0			0
$25$	−62.9072	−	108.958i	−0.503258	−	0.871668i
$26$	38.8371	−	67.2679i	0.292946	−	0.507397i
$27$		0			0
$28$	−27.6742	−	68.7178i	−0.186784	−	0.463802i
$29$	−240.208			−1.53812			−0.769061	−	0.639175i	$-0.779276\pi$
$29$	−240.208			−1.53812			−0.769061	+	0.639175i	$0.779276\pi$
$30$		0			0
$31$	148.337	+	256.927i	0.859424	+	1.48857i	0.872480	+	0.488651i	$0.162511\pi$
$31$	148.337	+	256.927i	0.859424	+	1.48857i	−0.0130559	+	0.999915i	$0.504156\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	54.6970			0.275896
$35$	−180.837	+	230.927i	−0.873344	+	1.11525i
$36$		0			0
$37$	80.7670	−	139.893i	0.358865	−	0.621573i	−0.628906	−	0.777481i	$-0.716497\pi$
$37$	80.7670	−	139.893i	0.358865	−	0.621573i	0.987772	+	0.155908i	$0.0498304\pi$
$38$	76.5114	+	132.522i	0.326626	+	0.565733i
$39$		0			0
$40$	63.3485	−	109.723i	0.250407	−	0.433717i
$41$	102.977			0.392252			0.196126	−	0.980579i	$-0.437164\pi$
$41$	102.977			0.392252			0.196126	+	0.980579i	$0.437164\pi$
$42$		0			0
$43$	−328.557			−1.16522			−0.582610	−	0.812752i	$-0.697968\pi$
$43$	−328.557			−1.16522			−0.582610	+	0.812752i	$0.697968\pi$
$44$	103.674	−	179.569i	0.355215	−	0.615251i
$45$		0			0
$46$	−147.348	−	255.215i	−0.472290	−	0.818031i
$47$	33.9773	−	58.8504i	0.105449	−	0.182643i	−0.808473	−	0.588534i	$-0.799705\pi$
$47$	33.9773	−	58.8504i	0.105449	−	0.182643i	0.913921	+	0.405891i	$0.133039\pi$
$48$		0			0
$49$	329.500	+	95.2825i	0.960641	+	0.277791i
$50$	−251.629			−0.711714
$51$		0			0
$52$	−77.6742	−	134.536i	−0.207144	−	0.358784i
$53$	−33.2443	−	57.5808i	−0.0861596	−	0.149233i	0.819725	−	0.572757i	$-0.194126\pi$
$53$	−33.2443	−	57.5808i	−0.0861596	−	0.149233i	−0.905885	+	0.423524i	$0.860793\pi$
$54$		0			0
$55$	−820.951			−2.01267
$56$	−146.697	−	20.7846i	−0.350057	−	0.0495975i
$57$		0			0
$58$	−240.208	+	416.053i	−0.543809	+	0.941904i
$59$	−230.964	−	400.041i	−0.509643	−	0.882728i	−0.999938	−	0.0111711i	$-0.996444\pi$
$59$	−230.964	−	400.041i	−0.509643	−	0.882728i	0.490294	−	0.871557i	$-0.336889\pi$
$60$		0			0
$61$	−92.6742	+	160.516i	−0.194520	+	0.336919i	−0.946743	−	0.321990i	$-0.895648\pi$
$61$	−92.6742	+	160.516i	−0.194520	+	0.336919i	0.752223	+	0.658909i	$0.228982\pi$
$62$	593.348			1.21541
$63$		0			0
$64$	64.0000			0.125000
$65$	−307.534	+	532.665i	−0.586845	+	1.01644i
$66$		0			0
$67$	−272.604	−	472.164i	−0.497073	−	0.860956i	0.502921	−	0.864332i	$-0.332259\pi$
$67$	−272.604	−	472.164i	−0.497073	−	0.860956i	−0.999994	+	0.00337637i	$0.998925\pi$
$68$	54.6970	−	94.7379i	0.0975438	−	0.168951i
$69$		0			0
$70$	219.140	+	544.146i	0.374175	+	0.929113i
$71$	130.742			0.218539			0.109270	−	0.994012i	$-0.465149\pi$
$71$	130.742			0.218539			0.109270	+	0.994012i	$0.465149\pi$
$72$		0			0
$73$	−90.6496	−	157.010i	−0.145339	−	0.251734i	0.784160	−	0.620558i	$-0.213094\pi$
$73$	−90.6496	−	157.010i	−0.145339	−	0.251734i	−0.929499	+	0.368824i	$0.879761\pi$
$74$	−161.534	−	279.785i	−0.253756	−	0.439519i
$75$		0			0
$76$	306.045			0.461919
$77$	358.638	+	890.533i	0.530787	+	1.31800i
$78$		0			0
$79$	204.848	−	354.808i	0.291737	−	0.505304i	−0.682483	−	0.730901i	$-0.739100\pi$
$79$	204.848	−	354.808i	0.291737	−	0.505304i	0.974221	+	0.225597i	$0.0724333\pi$
$80$	−126.697	−	219.446i	−0.177064	−	0.306685i
$81$		0			0
$82$	102.977	−	178.362i	0.138682	−	0.240205i
$83$	−347.928			−0.460121			−0.230061	−	0.973176i	$-0.573892\pi$
$83$	−347.928			−0.460121			−0.230061	+	0.973176i	$0.573892\pi$
$84$		0			0
$85$	−433.121			−0.552689
$86$	−328.557	+	569.077i	−0.411967	+	0.713548i
$87$		0			0
$88$	−207.348	−	359.138i	−0.251175	−	0.435048i
$89$	578.580	−	1002.13i	0.689093	−	1.19354i	−0.283038	−	0.959109i	$-0.591342\pi$
$89$	578.580	−	1002.13i	0.689093	−	1.19354i	0.972132	−	0.234436i	$-0.0753243\pi$
$90$		0			0
$91$	712.161	+	100.902i	0.820382	+	0.116235i
$92$	−589.394			−0.667919
$93$		0			0
$94$	−67.9546	−	117.701i	−0.0745636	−	0.129148i
$95$	−605.860	−	1049.38i	−0.654315	−	1.13331i
$96$		0			0
$97$	1618.30			1.69395			0.846976	−	0.531631i	$-0.178421\pi$
$97$	1618.30			1.69395			0.846976	+	0.531631i	$0.178421\pi$
$98$	494.534	−	475.428i	0.509750	−	0.490056i
$99$		0			0
$100$	−251.629	+	435.834i	−0.251629	+	0.435834i
$101$	359.371	+	622.449i	0.354047	+	0.613228i	0.986954	−	0.161000i	$-0.0514719\pi$
$101$	359.371	+	622.449i	0.354047	+	0.613228i	−0.632907	+	0.774228i	$0.718139\pi$
$102$		0			0
$103$	805.790	−	1395.67i	0.770843	−	1.33514i	−0.166259	−	0.986082i	$-0.553169\pi$
$103$	805.790	−	1395.67i	0.770843	−	1.33514i	0.937102	−	0.349057i	$-0.113498\pi$
$104$	−310.697			−0.292946
$105$		0			0
$106$	−132.977			−0.121848
$107$	467.335	−	809.448i	0.422234	−	0.731330i	−0.573924	−	0.818909i	$-0.694580\pi$
$107$	467.335	−	809.448i	0.422234	−	0.731330i	0.996158	+	0.0875784i	$0.0279128\pi$
$108$		0			0
$109$	598.509	+	1036.65i	0.525934	+	0.910944i	0.999544	+	0.0302095i	$0.00961746\pi$
$109$	598.509	+	1036.65i	0.525934	+	0.910944i	−0.473610	+	0.880735i	$0.657049\pi$
$110$	−820.951	+	1421.93i	−0.711587	+	1.23251i
$111$		0			0
$112$	−182.697	+	233.302i	−0.154136	+	0.196830i
$113$	2384.64			1.98521			0.992604	−	0.121400i	$-0.0387384\pi$
$113$	2384.64			1.98521			0.992604	+	0.121400i	$0.0387384\pi$
$114$		0			0
$115$	1166.79	+	2020.94i	0.946118	+	1.63872i
$116$	480.417	+	832.106i	0.384531	+	0.666027i
$117$		0			0
$118$	−923.856			−0.720744
$119$	189.212	+	469.832i	0.145757	+	0.361928i
$120$		0			0
$121$	−678.044	+	1174.41i	−0.509424	+	0.882349i
$122$	185.348	+	321.033i	0.137546	+	0.238237i
$123$		0			0
$124$	593.348	−	1027.71i	0.429712	−	0.744283i
$125$	12.8977			0.00922883
$126$		0			0
$127$	−2673.92			−1.86829			−0.934143	−	0.356898i	$-0.883834\pi$
$127$	−2673.92			−1.86829			−0.934143	+	0.356898i	$0.883834\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	615.068	+	1065.33i	0.414962	+	0.718735i
$131$	−19.4299	+	33.6536i	−0.0129588	+	0.0224453i	−0.872432	−	0.488735i	$-0.837458\pi$
$131$	−19.4299	+	33.6536i	−0.0129588	+	0.0224453i	0.859473	+	0.511181i	$0.170792\pi$
$132$		0			0
$133$	−873.650	+	1115.64i	−0.569587	+	0.727356i
$134$	−1090.42			−0.702968
$135$		0			0
$136$	−109.394	−	189.476i	−0.0689739	−	0.119466i
$137$	−384.072	−	665.232i	−0.239514	−	0.414851i	0.721061	−	0.692872i	$-0.243655\pi$
$137$	−384.072	−	665.232i	−0.239514	−	0.414851i	−0.960575	+	0.278021i	$0.910322\pi$
$138$		0			0
$139$	1052.55			0.642274			0.321137	−	0.947033i	$-0.395935\pi$
$139$	1052.55			0.642274			0.321137	+	0.947033i	$0.395935\pi$
$140$	1161.63	+	164.584i	0.701254	+	0.0993564i
$141$		0			0
$142$	130.742	−	226.453i	0.0772652	−	0.133827i
$143$	1006.60	+	1743.49i	0.588646	+	1.01956i
$144$		0			0
$145$	1902.10	−	3294.54i	1.08939	−	1.88687i
$146$	−362.598			−0.205540
$147$		0			0
$148$	−646.136			−0.358865
$149$	180.489	−	312.615i	0.0992363	−	0.171882i	−0.812132	−	0.583473i	$-0.801693\pi$
$149$	180.489	−	312.615i	0.0992363	−	0.171882i	0.911369	+	0.411591i	$0.135027\pi$
$150$		0			0
$151$	−774.195	−	1340.95i	−0.417239	−	0.722679i	0.578422	−	0.815738i	$-0.303669\pi$
$151$	−774.195	−	1340.95i	−0.417239	−	0.722679i	−0.995661	+	0.0930587i	$0.970336\pi$
$152$	306.045	−	530.086i	0.163313	−	0.282866i
$153$		0			0
$154$	1901.09	+	269.354i	0.994766	+	0.140942i
$155$	−4698.47			−2.43477
$156$		0			0
$157$	483.534	+	837.506i	0.245798	+	0.425734i	0.962356	−	0.271794i	$-0.0876168\pi$
$157$	483.534	+	837.506i	0.245798	+	0.425734i	−0.716558	+	0.697528i	$0.754283\pi$
$158$	−409.697	−	709.616i	−0.206289	−	0.357304i
$159$		0			0
$160$	−506.788			−0.250407
$161$	1682.51	−	2148.54i	0.823604	−	1.05173i
$162$		0			0
$163$	663.250	−	1148.78i	0.318710	−	0.552022i	−0.661509	−	0.749937i	$-0.730084\pi$
$163$	663.250	−	1148.78i	0.318710	−	0.552022i	0.980219	+	0.197915i	$0.0634170\pi$
$164$	−205.955	−	356.724i	−0.0980631	−	0.169850i
$165$		0			0
$166$	−347.928	+	602.629i	−0.162677	+	0.281766i
$167$	−1416.70			−0.656451			−0.328225	−	0.944599i	$-0.606451\pi$
$167$	−1416.70			−0.656451			−0.328225	+	0.944599i	$0.606451\pi$
$168$		0			0
$169$	−688.678			−0.313463
$170$	−433.121	+	750.188i	−0.195405	+	0.338452i
$171$		0			0
$172$	657.114	+	1138.15i	0.291305	+	0.504555i
$173$	−518.299	+	897.721i	−0.227778	+	0.394523i	−0.957149	−	0.289595i	$-0.906479\pi$
$173$	−518.299	+	897.721i	−0.227778	+	0.394523i	0.729371	+	0.684118i	$0.239813\pi$
$174$		0			0
$175$	−870.454	−	2161.42i	−0.376001	−	0.933647i
$176$	−829.394			−0.355215
$177$		0			0
$178$	−1157.16	−	2004.26i	−0.487263	−	0.843964i
$179$	−383.716	−	664.615i	−0.160225	−	0.277518i	0.774724	−	0.632299i	$-0.217889\pi$
$179$	−383.716	−	664.615i	−0.160225	−	0.277518i	−0.934949	+	0.354781i	$0.884555\pi$
$180$		0			0
$181$	−3957.71			−1.62527			−0.812636	−	0.582772i	$-0.801968\pi$
$181$	−3957.71			−1.62527			−0.812636	+	0.582772i	$0.801968\pi$
$182$	886.928	−	1132.60i	0.361228	−	0.461284i
$183$		0			0
$184$	−589.394	+	1020.86i	−0.236145	+	0.409015i
$185$	1279.12	+	2215.50i	0.508338	+	0.880468i
$186$		0			0
$187$	−708.833	+	1227.74i	−0.277193	+	0.480112i
$188$	−271.818			−0.105449
$189$		0			0
$190$	−2423.44			−0.925341
$191$	−902.648	+	1563.43i	−0.341954	+	0.592282i	−0.984796	−	0.173717i	$-0.944422\pi$
$191$	−902.648	+	1563.43i	−0.341954	+	0.592282i	0.642841	+	0.765999i	$0.277756\pi$
$192$		0			0
$193$	−1685.42	−	2919.23i	−0.628597	−	1.08876i	−0.987833	−	0.155515i	$-0.950296\pi$
$193$	−1685.42	−	2919.23i	−0.628597	−	1.08876i	0.359237	−	0.933247i	$-0.383037\pi$
$194$	1618.30	−	2802.98i	0.598903	−	1.03733i
$195$		0			0
$196$	−328.932	−	1331.99i	−0.119873	−	0.485418i
$197$	4612.31			1.66809			0.834044	−	0.551697i	$-0.186020\pi$
$197$	4612.31			1.66809			0.834044	+	0.551697i	$0.186020\pi$
$198$		0			0
$199$	1114.93	+	1931.12i	0.397163	+	0.687906i	0.993375	−	0.114921i	$-0.0366615\pi$
$199$	1114.93	+	1931.12i	0.397163	+	0.687906i	−0.596212	+	0.802827i	$0.703328\pi$
$200$	503.258	+	871.668i	0.177928	+	0.308181i
$201$		0			0
$202$	1437.48			0.500698
$203$	−4404.73	−	624.080i	−1.52291	−	0.215772i
$204$		0			0
$205$	−815.432	+	1412.37i	−0.277816	+	0.481191i
$206$	−1611.58	−	2791.34i	−0.545068	−	0.944086i
$207$		0			0
$208$	−310.697	+	538.143i	−0.103572	+	0.179392i
$209$	−3966.13			−1.31265
$210$		0			0
$211$	912.614			0.297758			0.148879	−	0.988855i	$-0.452434\pi$
$211$	912.614			0.297758			0.148879	+	0.988855i	$0.452434\pi$
$212$	−132.977	+	230.323i	−0.0430798	+	0.0746164i
$213$		0			0
$214$	−934.670	−	1618.90i	−0.298564	−	0.517129i
$215$	2601.70	−	4506.27i	0.825276	−	1.42942i
$216$		0			0
$217$	2052.56	+	5096.70i	0.642105	+	1.59441i
$218$	2394.04			0.743783
$219$		0			0
$220$	1641.90	+	2843.86i	0.503168	+	0.871513i
$221$	531.068	+	919.837i	0.161645	+	0.279977i
$222$		0			0
$223$	−4319.47			−1.29710			−0.648549	−	0.761173i	$-0.724624\pi$
$223$	−4319.47			−1.29710			−0.648549	+	0.761173i	$0.724624\pi$
$224$	221.394	+	549.742i	0.0660380	+	0.163979i
$225$		0			0
$226$	2384.64	−	4130.32i	0.701877	−	1.21569i
$227$	1030.64	+	1785.12i	0.301349	+	0.521951i	0.976442	−	0.215782i	$-0.0692299\pi$
$227$	1030.64	+	1785.12i	0.301349	+	0.521951i	−0.675093	+	0.737733i	$0.735897\pi$
$228$		0			0
$229$	1737.32	−	3009.12i	0.501332	−	0.868333i	−0.498667	−	0.866794i	$-0.666177\pi$
$229$	1737.32	−	3009.12i	0.501332	−	0.868333i	0.999999	−	0.00153905i	$-0.000489896\pi$
$230$	4667.15			1.33801
$231$		0			0
$232$	1921.67			0.543809
$233$	388.049	−	672.121i	0.109107	−	0.188979i	−0.806302	−	0.591505i	$-0.798534\pi$
$233$	388.049	−	672.121i	0.109107	−	0.188979i	0.915409	+	0.402525i	$0.131868\pi$
$234$		0			0
$235$	538.102	+	932.020i	0.149370	+	0.258716i
$236$	−923.856	+	1600.17i	−0.254822	+	0.441364i
$237$		0			0
$238$	1002.98	+	142.107i	0.273167	+	0.0387035i
$239$	−2006.80			−0.543133			−0.271567	−	0.962420i	$-0.587542\pi$
$239$	−2006.80			−0.543133			−0.271567	+	0.962420i	$0.587542\pi$
$240$		0			0
$241$	−402.824	−	697.711i	−0.107669	−	0.186488i	0.807157	−	0.590337i	$-0.201005\pi$
$241$	−402.824	−	697.711i	−0.107669	−	0.186488i	−0.914825	+	0.403850i	$0.867672\pi$
$242$	1356.09	+	2348.81i	0.360217	+	0.623915i
$243$		0			0
$244$	741.394			0.194520
$245$	−3916.00	+	3764.71i	−1.02116	+	0.981707i
$246$		0			0
$247$	−1485.74	+	2573.38i	−0.382734	+	0.662915i
$248$	−1186.70	−	2055.42i	−0.303852	−	0.526287i
$249$		0			0
$250$	12.8977	−	22.3394i	0.00326289	−	0.00565148i
$251$	−1421.78			−0.357539			−0.178769	−	0.983891i	$-0.557212\pi$
$251$	−1421.78			−0.357539			−0.178769	+	0.983891i	$0.557212\pi$
$252$		0			0
$253$	7638.12			1.89804
$254$	−2673.92	+	4631.37i	−0.660539	+	1.14409i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−732.909	+	1269.44i	−0.177890	+	0.308114i	−0.941157	−	0.337968i	$-0.890260\pi$
$257$	−732.909	+	1269.44i	−0.177890	+	0.308114i	0.763268	+	0.646082i	$0.223594\pi$
$258$		0			0
$259$	1844.49	−	2355.39i	0.442513	−	0.565084i
$260$	2460.27			0.586845
$261$		0			0
$262$	38.8598	+	67.3072i	0.00916324	+	0.0158712i
$263$	3495.69	+	6054.72i	0.819596	+	1.41958i	0.905980	+	0.423320i	$0.139135\pi$
$263$	3495.69	+	6054.72i	0.819596	+	1.41958i	−0.0863847	+	0.996262i	$0.527531\pi$
$264$		0			0
$265$	1052.99			0.244093
$266$	1058.70	+	2628.85i	0.244033	+	0.605958i
$267$		0			0
$268$	−1090.42	+	1888.66i	−0.248537	+	0.430478i
$269$	404.479	+	700.578i	0.0916786	+	0.158792i	0.908218	−	0.418498i	$-0.137443\pi$
$269$	404.479	+	700.578i	0.0916786	+	0.158792i	−0.816539	+	0.577290i	$0.804110\pi$
$270$		0			0
$271$	−3330.88	+	5769.26i	−0.746630	+	1.29320i	0.202799	+	0.979220i	$0.434996\pi$
$271$	−3330.88	+	5769.26i	−0.746630	+	1.29320i	−0.949429	+	0.313981i	$0.898337\pi$
$272$	−437.576			−0.0975438
$273$		0			0
$274$	−1536.29			−0.338725
$275$	3260.93	−	5648.09i	0.715059	−	1.23852i
$276$		0			0
$277$	3765.73	+	6522.44i	0.816827	+	1.41479i	0.908009	+	0.418951i	$0.137602\pi$
$277$	3765.73	+	6522.44i	0.816827	+	1.41479i	−0.0911823	+	0.995834i	$0.529065\pi$
$278$	1052.55	−	1823.07i	0.227078	−	0.393311i
$279$		0			0
$280$	1446.70	−	1847.42i	0.308774	−	0.394301i
$281$	−1690.19			−0.358819			−0.179410	−	0.983774i	$-0.557419\pi$
$281$	−1690.19			−0.358819			−0.179410	+	0.983774i	$0.557419\pi$
$282$		0			0
$283$	−1589.12	−	2752.43i	−0.333792	−	0.578145i	0.649460	−	0.760396i	$-0.274995\pi$
$283$	−1589.12	−	2752.43i	−0.333792	−	0.578145i	−0.983252	+	0.182251i	$0.941662\pi$
$284$	−261.485	−	452.905i	−0.0546348	−	0.0946302i
$285$		0			0
$286$	4026.41			0.832470
$287$	1888.31	+	267.543i	0.388374	+	0.0550263i
$288$		0			0
$289$	2082.53	−	3607.05i	0.423882	−	0.734184i
$290$	−3804.21	−	6589.08i	−0.770313	−	1.33422i
$291$		0			0
$292$	−362.598	+	628.039i	−0.0726694	+	0.125867i
$293$	2176.53			0.433974			0.216987	−	0.976174i	$-0.430377\pi$
$293$	2176.53			0.433974			0.216987	+	0.976174i	$0.430377\pi$
$294$		0			0
$295$	7315.61			1.44383
$296$	−646.136	+	1119.14i	−0.126878	+	0.219759i
$297$		0			0
$298$	−360.977	−	625.231i	−0.0701706	−	0.121539i
$299$	2861.30	−	4955.91i	0.553421	−	0.958554i
$300$		0			0
$301$	−6024.79	−	853.616i	−1.15370	−	0.163460i
$302$	−3096.78			−0.590065
$303$		0			0
$304$	−612.091	−	1060.17i	−0.115480	−	0.200017i
$305$	−1467.69	−	2542.12i	−0.275541	−	0.477250i
$306$		0			0
$307$	623.504			0.115913			0.0579564	−	0.998319i	$-0.481542\pi$
$307$	623.504			0.115913			0.0579564	+	0.998319i	$0.481542\pi$
$308$	2367.62	−	3023.43i	0.438012	−	0.559337i
$309$		0			0
$310$	−4698.47	+	8137.98i	−0.860822	+	1.49099i
$311$	233.996	+	405.293i	0.0426647	+	0.0738973i	0.886569	−	0.462596i	$-0.153082\pi$
$311$	233.996	+	405.293i	0.0426647	+	0.0738973i	−0.843905	+	0.536493i	$0.819749\pi$
$312$		0			0
$313$	−1806.41	+	3128.79i	−0.326211	+	0.565014i	−0.981757	−	0.190141i	$-0.939105\pi$
$313$	−1806.41	+	3128.79i	−0.326211	+	0.565014i	0.655546	+	0.755156i	$0.272439\pi$
$314$	1934.14			0.347610
$315$		0			0
$316$	−1638.79			−0.291737
$317$	2265.87	−	3924.60i	0.401463	−	0.695355i	−0.592439	−	0.805615i	$-0.701835\pi$
$317$	2265.87	−	3924.60i	0.401463	−	0.695355i	0.993903	+	0.110260i	$0.0351684\pi$
$318$		0			0
$319$	−6225.85	−	10783.5i	−1.09273	−	1.89266i
$320$	−506.788	+	877.782i	−0.0885322	+	0.153342i
$321$		0			0
$322$	−2038.88	−	5062.73i	−0.352864	−	0.876196i
$323$	−2092.47			−0.360459
$324$		0			0
$325$	−2443.13	−	4231.63i	−0.416987	−	0.722242i
$326$	−1326.50	−	2297.57i	−0.225362	−	0.390339i
$327$		0			0
$328$	−823.818			−0.138682
$329$	775.943	−	990.871i	0.130028	−	0.166044i
$330$		0			0
$331$	618.528	−	1071.32i	0.102711	−	0.177901i	−0.810090	−	0.586306i	$-0.800582\pi$
$331$	618.528	−	1071.32i	0.102711	−	0.177901i	0.912801	+	0.408405i	$0.133915\pi$
$332$	695.856	+	1205.26i	0.115030	+	0.199238i
$333$		0			0
$334$	−1416.70	+	2453.79i	−0.232090	+	0.401992i
$335$	8634.53			1.40822
$336$		0			0
$337$	−1867.83			−0.301921			−0.150960	−	0.988540i	$-0.548237\pi$
$337$	−1867.83			−0.301921			−0.150960	+	0.988540i	$0.548237\pi$
$338$	−688.678	+	1192.83i	−0.110826	+	0.191956i
$339$		0			0
$340$	866.242	+	1500.38i	0.138172	+	0.239322i
$341$	−7689.37	+	13318.4i	−1.22112	+	2.11505i
$342$		0			0
$343$	5794.53	+	2603.27i	0.912173	+	0.409806i
$344$	2628.45			0.411967
$345$		0			0
$346$	1036.60	+	1795.44i	0.161063	+	0.278970i
$347$	−31.6819	−	54.8746i	−0.00490136	−	0.00848940i	0.863564	−	0.504239i	$-0.168227\pi$
$347$	−31.6819	−	54.8746i	−0.00490136	−	0.00848940i	−0.868466	+	0.495749i	$0.834893\pi$
$348$		0			0
$349$	1223.79			0.187702			0.0938508	−	0.995586i	$-0.470082\pi$
$349$	1223.79			0.187702			0.0938508	+	0.995586i	$0.470082\pi$
$350$	−4614.15	−	653.751i	−0.704676	−	0.0998413i
$351$		0			0
$352$	−829.394	+	1436.55i	−0.125588	+	0.217524i
$353$	−2257.81	−	3910.64i	−0.340428	−	0.589638i	0.644085	−	0.764954i	$-0.277238\pi$
$353$	−2257.81	−	3910.64i	−0.340428	−	0.589638i	−0.984512	+	0.175316i	$0.943905\pi$
$354$		0			0
$355$	−1035.29	+	1793.18i	−0.154782	+	0.268090i
$356$	−4628.64			−0.689093
$357$		0			0
$358$	−1534.86			−0.226592
$359$	1114.25	−	1929.93i	0.163810	−	0.283727i	−0.772422	−	0.635109i	$-0.780955\pi$
$359$	1114.25	−	1929.93i	0.163810	−	0.283727i	0.936232	+	0.351383i	$0.114288\pi$
$360$		0			0
$361$	502.506	+	870.365i	0.0732622	+	0.126894i
$362$	−3957.71	+	6854.95i	−0.574620	+	0.995271i
$363$		0			0
$364$	−1074.79	−	2668.80i	−0.154764	−	0.384295i
$365$	2871.26			0.411749
$366$		0			0
$367$	718.670	+	1244.77i	0.102219	+	0.177048i	0.912598	−	0.408857i	$-0.134072\pi$
$367$	718.670	+	1244.77i	0.102219	+	0.177048i	−0.810380	+	0.585905i	$0.800739\pi$
$368$	1178.79	+	2041.72i	0.166980	+	0.289217i
$369$		0			0
$370$	5116.47			0.718899
$371$	−460.006	−	1142.24i	−0.0643728	−	0.159844i
$372$		0			0
$373$	6118.71	−	10597.9i	0.849370	−	1.47115i	−0.0324014	−	0.999475i	$-0.510315\pi$
$373$	6118.71	−	10597.9i	0.849370	−	1.47115i	0.881771	−	0.471677i	$-0.156351\pi$
$374$	1417.67	+	2455.47i	0.196005	+	0.339490i
$375$		0			0
$376$	−271.818	+	470.803i	−0.0372818	+	0.0645740i
$377$	−9329.00			−1.27445
$378$		0			0
$379$	−10647.0			−1.44301			−0.721503	−	0.692411i	$-0.756549\pi$
$379$	−10647.0			−1.44301			−0.721503	+	0.692411i	$0.756549\pi$
$380$	−2423.44	+	4197.52i	−0.327157	+	0.566653i
$381$		0			0
$382$	1805.30	+	3126.86i	0.241798	+	0.418807i
$383$	−3357.41	+	5815.20i	−0.447925	+	0.775829i	−0.998251	−	0.0591208i	$-0.981170\pi$
$383$	−3357.41	+	5815.20i	−0.447925	+	0.775829i	0.550326	+	0.834950i	$0.314504\pi$
$384$		0			0
$385$	−15053.9	−	2132.89i	−1.99277	−	0.282344i
$386$	−6741.68			−0.888970
$387$		0			0
$388$	−3236.60	−	5605.95i	−0.423488	−	0.733503i
$389$	−5326.54	−	9225.83i	−0.694258	−	1.20249i	−0.970430	−	0.241381i	$-0.922400\pi$
$389$	−5326.54	−	9225.83i	−0.694258	−	1.20249i	0.276173	−	0.961108i	$-0.410934\pi$
$390$		0			0
$391$	4029.76			0.521211
$392$	−2636.00	−	762.260i	−0.339638	−	0.0982141i
$393$		0			0
$394$	4612.31	−	7988.76i	0.589758	−	1.02149i
$395$	3244.21	+	5619.14i	0.413250	+	0.715771i
$396$		0			0
$397$	−1610.52	+	2789.50i	−0.203601	+	0.352648i	−0.949686	−	0.313203i	$-0.898598\pi$
$397$	−1610.52	+	2789.50i	−0.203601	+	0.352648i	0.746085	+	0.665851i	$0.231931\pi$
$398$	4459.73			0.561673
$399$		0			0
$400$	2013.03			0.251629
$401$	6242.50	−	10812.3i	0.777395	−	1.34649i	−0.156043	−	0.987750i	$-0.549874\pi$
$401$	6242.50	−	10812.3i	0.777395	−	1.34649i	0.933438	−	0.358738i	$-0.116793\pi$
$402$		0			0
$403$	5760.99	+	9978.32i	0.712097	+	1.23339i
$404$	1437.48	−	2489.80i	0.177024	−	0.306614i
$405$		0			0
$406$	−5485.67	+	7005.14i	−0.670564	+	0.856303i
$407$	8373.46			1.01980
$408$		0			0
$409$	−3518.69	−	6094.56i	−0.425399	−	0.736813i	0.571059	−	0.820909i	$-0.306533\pi$
$409$	−3518.69	−	6094.56i	−0.425399	−	0.736813i	−0.996458	+	0.0840967i	$0.973200\pi$
$410$	1630.86	+	2824.74i	0.196445	+	0.340253i
$411$		0			0
$412$	−6446.32			−0.770843
$413$	−3195.88	−	7935.67i	−0.380772	−	0.945493i
$414$		0			0
$415$	2755.09	−	4771.95i	0.325884	−	0.564448i
$416$	621.394	+	1076.29i	0.0732364	+	0.126849i
$417$		0			0
$418$	−3966.13	+	6869.54i	−0.464090	+	0.803828i
$419$	1549.66			0.180682			0.0903410	−	0.995911i	$-0.471204\pi$
$419$	1549.66			0.180682			0.0903410	+	0.995911i	$0.471204\pi$
$420$		0			0
$421$	5531.63			0.640369			0.320184	−	0.947355i	$-0.396255\pi$
$421$	5531.63			0.640369			0.320184	+	0.947355i	$0.396255\pi$
$422$	912.614	−	1580.69i	0.105273	−	0.182339i
$423$		0			0
$424$	265.955	+	460.647i	0.0304620	+	0.0527618i
$425$	1720.42	−	2979.85i	0.196359	−	0.340103i
$426$		0			0
$427$	−2116.41	+	2702.64i	−0.239860	+	0.306299i
$428$	−3738.68			−0.422234
$429$		0			0
$430$	−5203.39	−	9012.54i	−0.583558	−	1.01075i
$431$	−1014.97	−	1757.97i	−0.113432	−	0.196470i	0.803720	−	0.595008i	$-0.202851\pi$
$431$	−1014.97	−	1757.97i	−0.113432	−	0.196470i	−0.917152	+	0.398538i	$0.869518\pi$
$432$		0			0
$433$	−327.739			−0.0363744			−0.0181872	−	0.999835i	$-0.505789\pi$
$433$	−327.739			−0.0363744			−0.0181872	+	0.999835i	$0.505789\pi$
$434$	10880.3	+	1541.56i	1.20339	+	0.170501i
$435$		0			0
$436$	2394.04	−	4146.60i	0.262967	−	0.455472i
$437$	5636.92	+	9763.43i	0.617049	+	1.06876i
$438$		0			0
$439$	−3954.34	+	6849.12i	−0.429910	+	0.744625i	−0.996865	−	0.0791234i	$-0.974788\pi$
$439$	−3954.34	+	6849.12i	−0.429910	+	0.744625i	0.566955	+	0.823749i	$0.308121\pi$
$440$	6567.61			0.711587
$441$		0			0
$442$	2124.27			0.228600
$443$	−1460.41	+	2529.51i	−0.156628	+	0.271288i	−0.933651	−	0.358185i	$-0.883396\pi$
$443$	−1460.41	+	2529.51i	−0.156628	+	0.271288i	0.777023	+	0.629473i	$0.216729\pi$
$444$		0			0
$445$	9163.03	+	15870.8i	0.976111	+	1.69067i
$446$	−4319.47	+	7481.53i	−0.458593	+	0.794307i
$447$		0			0
$448$	1173.58	+	166.277i	0.123764	+	0.0175354i
$449$	10240.2			1.07631			0.538156	−	0.842845i	$-0.319121\pi$
$449$	10240.2			1.07631			0.538156	+	0.842845i	$0.319121\pi$
$450$		0			0
$451$	2669.02	+	4622.88i	0.278668	+	0.482668i
$452$	−4769.29	−	8260.65i	−0.496302	−	0.859620i
$453$		0			0
$454$	4122.57			0.426171
$455$	−7023.19	+	8968.54i	−0.723632	+	0.924069i
$456$		0			0
$457$	−2946.31	+	5103.17i	−0.301582	+	0.522355i	−0.976494	−	0.215543i	$-0.930848\pi$
$457$	−2946.31	+	5103.17i	−0.301582	+	0.522355i	0.674913	+	0.737897i	$0.264181\pi$
$458$	−3474.63	−	6018.24i	−0.354495	−	0.614004i
$459$		0			0
$460$	4667.15	−	8083.74i	0.473059	−	0.819362i
$461$	12643.4			1.27735			0.638677	−	0.769475i	$-0.279482\pi$
$461$	12643.4			1.27735			0.638677	+	0.769475i	$0.279482\pi$
$462$		0			0
$463$	15093.2			1.51499			0.757494	−	0.652842i	$-0.226423\pi$
$463$	15093.2			1.51499			0.757494	+	0.652842i	$0.226423\pi$
$464$	1921.67	−	3328.42i	0.192265	−	0.333013i
$465$		0			0
$466$	−776.099	−	1344.24i	−0.0771504	−	0.133628i
$467$	−1410.12	+	2442.39i	−0.139727	+	0.242014i	−0.927393	−	0.374088i	$-0.877956\pi$
$467$	−1410.12	+	2442.39i	−0.139727	+	0.242014i	0.787666	+	0.616102i	$0.211289\pi$
$468$		0			0
$469$	−3772.06	−	9366.38i	−0.371380	−	0.922173i
$470$	2152.41			0.211241
$471$		0			0
$472$	1847.71	+	3200.33i	0.180186	+	0.312091i
$473$	−8515.72	−	14749.7i	−0.827808	−	1.43381i
$474$		0			0
$475$	9626.23			0.929856
$476$	1249.12	−	1595.11i	0.120280	−	0.153596i
$477$		0			0
$478$	−2006.80	+	3475.87i	−0.192027	+	0.332600i
$479$	−8224.25	−	14244.8i	−0.784500	−	1.35879i	−0.929297	−	0.369332i	$-0.879586\pi$
$479$	−8224.25	−	14244.8i	−0.784500	−	1.35879i	0.144798	−	0.989461i	$-0.453747\pi$
$480$		0			0
$481$	3136.76	−	5433.03i	0.297347	−	0.515020i
$482$	−1611.30			−0.152267
$483$		0			0
$484$	5424.35			0.509424
$485$	−12814.6	+	22195.5i	−1.19975	+	2.07804i
$486$		0			0
$487$	−3165.53	−	5482.87i	−0.294546	−	0.510169i	0.680333	−	0.732903i	$-0.261835\pi$
$487$	−3165.53	−	5482.87i	−0.294546	−	0.510169i	−0.974879	+	0.222734i	$0.928502\pi$
$488$	741.394	−	1284.13i	0.0687732	−	0.119119i
$489$		0			0
$490$	2604.67	+	10547.4i	0.240136	+	0.972416i
$491$	9286.90			0.853588			0.426794	−	0.904349i	$-0.359643\pi$
$491$	9286.90			0.853588			0.426794	+	0.904349i	$0.359643\pi$
$492$		0			0
$493$	−3284.67	−	5689.21i	−0.300069	−	0.519735i
$494$	2971.48	+	5146.76i	0.270634	+	0.468752i
$495$		0			0
$496$	−4746.79			−0.429712
$497$	2397.44	+	339.679i	0.216378	+	0.0306573i
$498$		0			0
$499$	121.725	−	210.835i	0.0109202	−	0.0189143i	−0.860514	−	0.509427i	$-0.829857\pi$
$499$	121.725	−	210.835i	0.0109202	−	0.0189143i	0.871434	+	0.490513i	$0.163191\pi$
$500$	−25.7954	−	44.6789i	−0.00230721	−	0.00399620i
$501$		0			0
$502$	−1421.78	+	2462.60i	−0.126409	+	0.218947i
$503$	−8499.30			−0.753409			−0.376705	−	0.926333i	$-0.622943\pi$
$503$	−8499.30			−0.753409			−0.376705	+	0.926333i	$0.622943\pi$
$504$		0			0
$505$	−11382.8			−1.00303
$506$	7638.12	−	13229.6i	0.671059	−	1.16231i
$507$		0			0
$508$	5347.85	+	9262.75i	0.467072	+	0.808992i
$509$	−3841.55	+	6653.76i	−0.334526	+	0.579416i	−0.983394	−	0.181485i	$-0.941910\pi$
$509$	−3841.55	+	6653.76i	−0.334526	+	0.579416i	0.648868	+	0.760901i	$0.275243\pi$
$510$		0			0
$511$	−1254.33	−	3114.62i	−0.108588	−	0.269634i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	1465.82	+	2538.87i	0.125787	+	0.217869i
$515$	12761.4	+	22103.4i	1.09191	+	1.89124i
$516$		0			0
$517$	3522.57			0.299656
$518$	−2235.17	−	5550.13i	−0.189590	−	0.470770i
$519$		0			0
$520$	2460.27	−	4261.32i	0.207481	−	0.359368i
$521$	−10765.3	−	18646.1i	−0.905253	−	1.56794i	−0.820578	−	0.571535i	$-0.806348\pi$
$521$	−10765.3	−	18646.1i	−0.905253	−	1.56794i	−0.0846750	−	0.996409i	$-0.526985\pi$
$522$		0			0
$523$	8423.53	−	14590.0i	0.704274	−	1.21984i	−0.262679	−	0.964883i	$-0.584606\pi$
$523$	8423.53	−	14590.0i	0.704274	−	1.21984i	0.966953	−	0.254955i	$-0.0820606\pi$
$524$	155.439			0.0129588
$525$		0			0
$526$	13982.8			1.15908
$527$	−4056.80	+	7026.58i	−0.335326	+	0.580802i
$528$		0			0
$529$	−4772.29	−	8265.84i	−0.392232	−	0.679366i
$530$	1052.99	−	1823.83i	0.0862998	−	0.149476i
$531$		0			0
$532$	5611.99	+	795.129i	0.457351	+	0.0647993i
$533$	3999.34			0.325011
$534$		0			0
$535$	7401.24	+	12819.3i	0.598100	+	1.03594i
$536$	2180.83	+	3777.31i	0.175742	+	0.304394i
$537$		0			0
$538$	1617.92			0.129653
$539$	4262.72	+	17261.6i	0.340646	+	1.37942i
$540$		0			0
$541$	−8720.02	+	15103.5i	−0.692981	+	1.20028i	0.277875	+	0.960617i	$0.410370\pi$
$541$	−8720.02	+	15103.5i	−0.692981	+	1.20028i	−0.970856	+	0.239662i	$0.922963\pi$
$542$	6661.77	+	11538.5i	0.527947	+	0.914432i
$543$		0			0
$544$	−437.576	+	757.903i	−0.0344870	+	0.0597332i
$545$	−18957.3			−1.48999
$546$		0			0
$547$	11520.7			0.900530			0.450265	−	0.892895i	$-0.351329\pi$
$547$	11520.7			0.900530			0.450265	+	0.892895i	$0.351329\pi$
$548$	−1536.29	+	2660.93i	−0.119757	+	0.207426i
$549$		0			0
$550$	−6521.86	−	11296.2i	−0.505623	−	0.875765i
$551$	9189.33	−	15916.4i	0.710488	−	1.23060i
$552$		0			0
$553$	4678.15	−	5973.94i	0.359738	−	0.459382i
$554$	15062.9			1.15517
$555$		0			0
$556$	−2105.10	−	3646.14i	−0.160568	−	0.278113i
$557$	5746.51	+	9953.25i	0.437141	+	0.757151i	0.997468	−	0.0711212i	$-0.0226577\pi$
$557$	5746.51	+	9953.25i	0.437141	+	0.757151i	−0.560327	+	0.828272i	$0.689324\pi$
$558$		0			0
$559$	−12760.2			−0.965472
$560$	−1753.12	−	4353.17i	−0.132291	−	0.328491i
$561$		0			0
$562$	−1690.19	+	2927.49i	−0.126862	+	0.219731i
$563$	9055.65	+	15684.8i	0.677886	+	1.17413i	0.975616	+	0.219483i	$0.0704372\pi$
$563$	9055.65	+	15684.8i	0.677886	+	1.17413i	−0.297730	+	0.954650i	$0.596230\pi$
$564$		0			0
$565$	−18882.9	+	32706.2i	−1.40604	+	2.43533i
$566$	−6356.46			−0.472053
$567$		0			0
$568$	−1045.94			−0.0772652
$569$	2208.81	−	3825.77i	0.162738	−	0.281871i	−0.773112	−	0.634270i	$-0.781301\pi$
$569$	2208.81	−	3825.77i	0.162738	−	0.281871i	0.935850	+	0.352399i	$0.114634\pi$
$570$		0			0
$571$	−6609.87	−	11448.6i	−0.484439	−	0.839073i	0.515401	−	0.856949i	$-0.327643\pi$
$571$	−6609.87	−	11448.6i	−0.484439	−	0.839073i	−0.999840	+	0.0178762i	$0.994310\pi$
$572$	4026.41	−	6973.95i	0.294323	−	0.509782i
$573$		0			0
$574$	2351.70	−	3003.10i	0.171007	−	0.218375i
$575$	−18538.6			−1.34454
$576$		0			0
$577$	8748.20	+	15152.3i	0.631182	+	1.09324i	0.987310	+	0.158803i	$0.0507634\pi$
$577$	8748.20	+	15152.3i	0.631182	+	1.09324i	−0.356128	+	0.934437i	$0.615903\pi$
$578$	−4165.06	−	7214.10i	−0.299730	−	0.519147i
$579$		0			0
$580$	−15216.8			−1.08939
$581$	−6380.00	−	903.944i	−0.455571	−	0.0645472i
$582$		0			0
$583$	1723.29	−	2984.83i	0.122421	−	0.212039i
$584$	725.197	+	1256.08i	0.0513850	+	0.0890015i
$585$		0			0
$586$	2176.53	−	3769.87i	0.153433	−	0.265754i
$587$	4280.53			0.300982			0.150491	−	0.988611i	$-0.451915\pi$
$587$	4280.53			0.300982			0.150491	+	0.988611i	$0.451915\pi$
$588$		0			0
$589$	−22699.0			−1.58794
$590$	7315.61	−	12671.0i	0.510473	−	0.884165i
$591$		0			0
$592$	1292.27	+	2238.28i	0.0897164	+	0.155393i
$593$	−795.466	+	1377.79i	−0.0550858	+	0.0954114i	−0.892253	−	0.451535i	$-0.850877\pi$
$593$	−795.466	+	1377.79i	−0.0550858	+	0.0954114i	0.837168	+	0.546946i	$0.184210\pi$
$594$		0			0
$595$	−7942.20	−	1125.28i	−0.547224	−	0.0775329i
$596$	−1443.91			−0.0992363
$597$		0			0
$598$	−5722.59	−	9911.82i	−0.391328	−	0.677800i
$599$	−6961.42	−	12057.5i	−0.474851	−	0.822467i	0.524734	−	0.851266i	$-0.324165\pi$
$599$	−6961.42	−	12057.5i	−0.474851	−	0.822467i	−0.999585	+	0.0287997i	$0.990831\pi$
$600$		0			0
$601$	12559.7			0.852446			0.426223	−	0.904618i	$-0.359844\pi$
$601$	12559.7			0.852446			0.426223	+	0.904618i	$0.359844\pi$
$602$	−7503.29	+	9581.62i	−0.507992	+	0.648700i
$603$		0			0
$604$	−3096.78	+	5363.78i	−0.208620	+	0.361340i
$605$	−10738.3	−	18599.2i	−0.721607	−	1.24986i
$606$		0			0
$607$	−3839.19	+	6649.66i	−0.256718	+	0.444648i	−0.965361	−	0.260919i	$-0.915974\pi$
$607$	−3839.19	+	6649.66i	−0.256718	+	0.444648i	0.708643	+	0.705567i	$0.249308\pi$
$608$	−2448.36			−0.163313
$609$		0			0
$610$	−5870.77			−0.389673
$611$	1319.58	−	2285.58i	0.0873723	−	0.151333i
$612$		0			0
$613$	−3079.19	−	5333.31i	−0.202883	−	0.351403i	0.746573	−	0.665303i	$-0.231698\pi$
$613$	−3079.19	−	5333.31i	−0.202883	−	0.351403i	−0.949456	+	0.313900i	$0.898364\pi$
$614$	623.504	−	1079.94i	0.0409814	−	0.0709818i
$615$		0			0
$616$	−2869.11	−	7124.27i	−0.187662	−	0.465982i
$617$	−8813.12			−0.575045			−0.287523	−	0.957774i	$-0.592832\pi$
$617$	−8813.12			−0.575045			−0.287523	+	0.957774i	$0.592832\pi$
$618$		0			0
$619$	−11595.0	−	20083.1i	−0.752894	−	1.30405i	−0.946415	−	0.322954i	$-0.895324\pi$
$619$	−11595.0	−	20083.1i	−0.752894	−	1.30405i	0.193521	−	0.981096i	$-0.438009\pi$
$620$	9396.93	+	16276.0i	0.608693	+	1.05429i
$621$		0			0
$622$	935.985			0.0603369
$623$	13213.1	−	16873.0i	0.849713	−	1.08507i
$624$		0			0
$625$	7761.27	−	13442.9i	0.496721	−	0.860346i
$626$	3612.81	+	6257.57i	0.230666	+	0.399525i
$627$		0			0
$628$	1934.14	−	3350.02i	0.122899	−	0.212867i
$629$	4417.71			0.280041
$630$		0			0
$631$	7936.94			0.500736			0.250368	−	0.968151i	$-0.419448\pi$
$631$	7936.94			0.500736			0.250368	+	0.968151i	$0.419448\pi$
$632$	−1638.79	+	2838.46i	−0.103145	+	0.178652i
$633$		0			0
$634$	−4531.74	−	7849.20i	−0.283877	−	0.491690i
$635$	21173.6	−	36673.8i	1.32323	−	2.29190i
$636$		0			0
$637$	12796.8	+	3700.50i	0.795964	+	0.230171i
$638$	−24903.4			−1.54535
$639$		0			0
$640$	1013.58	+	1755.56i	0.0626017	+	0.108429i
$641$	16057.3	+	27812.1i	0.989432	+	1.71375i	0.620286	+	0.784376i	$0.287016\pi$
$641$	16057.3	+	27812.1i	0.989432	+	1.71375i	0.369146	+	0.929371i	$0.379650\pi$
$642$		0			0
$643$	−24786.7			−1.52021			−0.760104	−	0.649802i	$-0.774852\pi$
$643$	−24786.7			−1.52021			−0.760104	+	0.649802i	$0.774852\pi$
$644$	−10807.8	−	1531.29i	−0.661314	−	0.0936977i
$645$		0			0
$646$	−2092.47	+	3624.26i	−0.127441	+	0.220735i
$647$	3772.80	+	6534.67i	0.229249	+	0.397070i	0.957586	−	0.288149i	$-0.0930398\pi$
$647$	3772.80	+	6534.67i	0.229249	+	0.397070i	−0.728337	+	0.685219i	$0.759706\pi$
$648$		0			0
$649$	11972.5	−	20737.0i	0.724133	−	1.25423i
$650$	−9772.54			−0.589708
$651$		0			0
$652$	−5306.00			−0.318710
$653$	−2444.49	+	4233.99i	−0.146494	+	0.253735i	−0.929929	−	0.367738i	$-0.880132\pi$
$653$	−2444.49	+	4233.99i	−0.146494	+	0.253735i	0.783435	+	0.621473i	$0.213466\pi$
$654$		0			0
$655$	−307.714	−	532.976i	−0.0183563	−	0.0317941i
$656$	−823.818	+	1426.89i	−0.0490316	+	0.0849251i
$657$		0			0
$658$	−940.295	−	2334.84i	−0.0557090	−	0.138331i
$659$	−25895.9			−1.53075			−0.765374	−	0.643586i	$-0.777446\pi$
$659$	−25895.9			−1.53075			−0.765374	+	0.643586i	$0.777446\pi$
$660$		0			0
$661$	−4091.68	−	7087.00i	−0.240769	−	0.417023i	0.720165	−	0.693803i	$-0.244066\pi$
$661$	−4091.68	−	7087.00i	−0.240769	−	0.417023i	−0.960933	+	0.276780i	$0.910733\pi$
$662$	−1237.06	−	2142.65i	−0.0726278	−	0.125795i
$663$		0			0
$664$	2783.42			0.162677
$665$	−8383.36	−	20816.7i	−0.488861	−	1.21389i
$666$		0			0
$667$	−17697.2	+	30652.4i	−1.02734	+	1.77941i
$668$	2833.39	+	4907.58i	0.164113	+	0.284252i
$669$		0			0
$670$	8634.53	−	14955.4i	0.497882	−	0.862357i
$671$	−9607.93			−0.552772
$672$		0			0
$673$	−4635.02			−0.265478			−0.132739	−	0.991151i	$-0.542377\pi$
$673$	−4635.02			−0.265478			−0.132739	+	0.991151i	$0.542377\pi$
$674$	−1867.83	+	3235.18i	−0.106745	+	0.184888i
$675$		0			0
$676$	1377.36	+	2385.65i	0.0783657	+	0.135733i
$677$	−12192.9	+	21118.7i	−0.692187	+	1.19890i	0.278932	+	0.960311i	$0.410020\pi$
$677$	−12192.9	+	21118.7i	−0.692187	+	1.19890i	−0.971120	+	0.238593i	$0.923314\pi$
$678$		0			0
$679$	29674.9	+	4204.46i	1.67720	+	0.237633i
$680$	3464.97			0.195405
$681$		0			0
$682$	15378.7	+	26636.8i	0.863464	+	1.49556i
$683$	−9196.71	−	15929.2i	−0.515230	−	0.892405i	−0.999844	−	0.0176767i	$-0.994373\pi$
$683$	−9196.71	−	15929.2i	−0.515230	−	0.892405i	0.484613	−	0.874728i	$-0.338960\pi$
$684$		0			0
$685$	12165.2			0.678552
$686$	10303.5	−	7433.15i	0.573456	−	0.413701i
$687$		0			0
$688$	2628.45	−	4552.62i	0.145652	−	0.252277i
$689$	−1291.11	−	2236.27i	−0.0713897	−	0.123651i
$690$		0			0
$691$	7449.44	−	12902.8i	0.410116	−	0.710341i	−0.584786	−	0.811187i	$-0.698822\pi$
$691$	7449.44	−	12902.8i	0.410116	−	0.710341i	0.994902	+	0.100846i	$0.0321550\pi$
$692$	4146.39			0.227778
$693$		0			0
$694$	−126.727			−0.00693157
$695$	−8334.67	+	14436.1i	−0.454895	+	0.787902i
$696$		0			0
$697$	1408.14	+	2438.96i	0.0765236	+	0.132543i
$698$	1223.79	−	2119.66i	0.0663625	−	0.114943i
$699$		0			0
$700$	−5746.48	+	7338.19i	−0.310281	+	0.396225i
$701$	5725.70			0.308497			0.154249	−	0.988032i	$-0.450704\pi$
$701$	5725.70			0.308497			0.154249	+	0.988032i	$0.450704\pi$
$702$		0			0
$703$	6179.60	+	10703.4i	0.331533	+	0.574232i
$704$	1658.79	+	2873.10i	0.0888039	+	0.153813i
$705$		0			0
$706$	−9031.23			−0.481437
$707$	4972.66	+	12347.6i	0.264521	+	0.656831i
$708$		0			0
$709$	11728.4	−	20314.2i	0.621255	−	1.07604i	−0.367998	−	0.929827i	$-0.619957\pi$
$709$	11728.4	−	20314.2i	0.621255	−	1.07604i	0.989252	−	0.146218i	$-0.0467101\pi$
$710$	2070.58	+	3586.36i	0.109447	+	0.189568i
$711$		0			0
$712$	−4628.64	+	8017.03i	−0.243631	+	0.421982i
$713$	43714.5			2.29610
$714$		0			0
$715$	−31883.4			−1.66765
$716$	−1534.86	+	2658.46i	−0.0801125	+	0.138759i
$717$		0			0
$718$	−2228.49	−	3859.86i	−0.115831	−	0.200625i
$719$	−4229.50	+	7325.71i	−0.219379	+	0.379976i	−0.954618	−	0.297832i	$-0.903737\pi$
$719$	−4229.50	+	7325.71i	−0.219379	+	0.379976i	0.735239	+	0.677808i	$0.237070\pi$
$720$		0			0
$721$	18401.9	−	23499.0i	0.950518	−	1.21380i
$722$	2010.02			0.103608
$723$		0			0
$724$	7915.42	+	13709.9i	0.406318	+	0.703763i
$725$	15110.8	+	26172.7i	0.774072	+	1.34073i
$726$		0			0
$727$	−11822.2			−0.603111			−0.301555	−	0.953449i	$-0.597506\pi$
$727$	−11822.2			−0.603111			−0.301555	+	0.953449i	$0.597506\pi$
$728$	−5697.29	−	807.214i	−0.290049	−	0.0410953i
$729$		0			0
$730$	2871.26	−	4973.16i	0.145575	−	0.252144i
$731$	−4492.77	−	7781.70i	−0.227320	−	0.393730i
$732$		0			0
$733$	−2514.48	+	4355.20i	−0.126704	+	0.219458i	−0.922398	−	0.386241i	$-0.873773\pi$
$733$	−2514.48	+	4355.20i	−0.126704	+	0.219458i	0.795694	+	0.605699i	$0.207107\pi$
$734$	2874.68			0.144559
$735$		0			0
$736$	4715.15			0.236145
$737$	14131.0	−	24475.6i	0.706272	−	1.22330i
$738$		0			0
$739$	8871.95	+	15366.7i	0.441624	+	0.764914i	0.997810	−	0.0661431i	$-0.0210694\pi$
$739$	8871.95	+	15366.7i	0.441624	+	0.764914i	−0.556187	+	0.831057i	$0.687736\pi$
$740$	5116.47	−	8861.99i	0.254169	−	0.440234i
$741$		0			0
$742$	−2438.42	−	345.485i	−0.120643	−	0.0170932i
$743$	13202.3			0.651877			0.325938	−	0.945391i	$-0.394320\pi$
$743$	13202.3			0.651877			0.325938	+	0.945391i	$0.394320\pi$
$744$		0			0
$745$	2858.42	+	4950.93i	0.140570	+	0.243474i
$746$	−12237.4	−	21195.8i	−0.600595	−	1.04026i
$747$		0			0
$748$	5670.67			0.277193
$749$	10672.6	−	13628.8i	0.520652	−	0.664866i
$750$		0			0
$751$	−7800.49	+	13510.8i	−0.379020	+	0.656482i	−0.990920	−	0.134453i	$-0.957072\pi$
$751$	−7800.49	+	13510.8i	−0.379020	+	0.656482i	0.611900	+	0.790935i	$0.290406\pi$
$752$	543.636	+	941.606i	0.0263622	+	0.0456607i
$753$		0			0
$754$	−9329.00	+	16158.3i	−0.450586	+	0.780439i
$755$	24522.0			1.18205
$756$		0			0
$757$	2948.08			0.141545			0.0707725	−	0.997492i	$-0.477454\pi$
$757$	2948.08			0.141545			0.0707725	+	0.997492i	$0.477454\pi$
$758$	−10647.0	+	18441.1i	−0.510180	+	0.883657i
$759$		0			0
$760$	4846.88	+	8395.04i	0.231335	+	0.400684i
$761$	848.515	−	1469.67i	0.0404187	−	0.0700073i	−0.845108	−	0.534595i	$-0.820464\pi$
$761$	848.515	−	1469.67i	0.0404187	−	0.0700073i	0.885527	+	0.464588i	$0.153797\pi$
$762$		0			0
$763$	8281.65	+	20564.1i	0.392943	+	0.975716i
$764$	7221.18			0.341954
$765$		0			0
$766$	6714.81	+	11630.4i	0.316731	+	0.548594i
$767$	−8969.98	−	15536.5i	−0.422278	−	0.731407i
$768$		0			0
$769$	−96.7799			−0.00453833			−0.00226916	−	0.999997i	$-0.500722\pi$
$769$	−96.7799			−0.00453833			−0.00226916	+	0.999997i	$0.500722\pi$
$770$	−18748.2	+	23941.2i	−0.877450	+	1.12049i
$771$		0			0
$772$	−6741.68	+	11676.9i	−0.314298	+	0.544381i
$773$	18163.4	+	31459.9i	0.845138	+	1.46382i	0.885501	+	0.464637i	$0.153815\pi$
$773$	18163.4	+	31459.9i	0.845138	+	1.46382i	−0.0403629	+	0.999185i	$0.512851\pi$
$774$		0			0
$775$	18662.9	−	32325.2i	0.865023	−	1.49826i
$776$	−12946.4			−0.598903
$777$		0			0
$778$	−21306.2			−0.981828
$779$	−3939.47	+	6823.35i	−0.181189	+	0.313828i
$780$		0			0
$781$	3388.66	+	5869.32i	0.155257	+	0.268913i
$782$	4029.76	−	6979.74i	0.184276	−	0.319175i
$783$		0			0
$784$	−3956.27	+	3803.43i	−0.180224	+	0.173261i
$785$	−15315.6			−0.696352
$786$		0			0
$787$	−3548.23	−	6145.72i	−0.160713	−	0.278362i	0.774412	−	0.632682i	$-0.218046\pi$
$787$	−3548.23	−	6145.72i	−0.160713	−	0.278362i	−0.935124	+	0.354319i	$0.884713\pi$
$788$	−9224.62	−	15977.5i	−0.417022	−	0.722304i
$789$		0			0
$790$	12976.8			0.584424
$791$	43727.5	+	6195.49i	1.96558	+	0.278491i
$792$		0			0
$793$	−3599.20	+	6234.00i	−0.161174	+	0.279162i
$794$	3221.04	+	5579.01i	0.143968	+	0.249360i
$795$		0			0
$796$	4459.73	−	7724.47i	0.198581	−	0.343953i
$797$	−40289.6			−1.79063			−0.895314	−	0.445436i	$-0.853049\pi$
$797$	−40289.6			−1.79063			−0.895314	+	0.445436i	$0.853049\pi$
$798$		0			0
$799$	1858.45			0.0822871
$800$	2013.03	−	3486.67i	0.0889642	−	0.154091i
$801$		0			0
$802$	−12485.0	−	21624.7i	−0.549702	−	0.952111i
$803$	4699.02	−	8138.93i	0.206506	−	0.357680i
$804$		0			0
$805$	16145.0	+	40089.5i	0.706877	+	1.75524i
$806$	23043.9			1.00706
$807$		0			0
$808$	−2874.97	−	4979.59i	−0.125175	−	0.216809i
$809$	−5782.98	−	10016.4i	−0.251321	−	0.435301i	0.712569	−	0.701602i	$-0.247532\pi$
$809$	−5782.98	−	10016.4i	−0.251321	−	0.435301i	−0.963890	+	0.266301i	$0.914198\pi$
$810$		0			0
$811$	18014.2			0.779981			0.389991	−	0.920819i	$-0.372478\pi$
$811$	18014.2			0.779981			0.389991	+	0.920819i	$0.372478\pi$
$812$	6647.58	+	16506.6i	0.287296	+	0.713384i
$813$		0			0
$814$	8373.46	−	14503.3i	0.360552	−	0.624495i
$815$	10504.0	+	18193.4i	0.451458	+	0.781948i
$816$		0			0
$817$	12569.2	−	21770.4i	0.538237	−	0.932253i
$818$	−14074.8			−0.601605
$819$		0			0
$820$	6523.45			0.277816
$821$	−8396.22	+	14542.7i	−0.356918	+	0.618201i	−0.987444	−	0.157967i	$-0.949506\pi$
$821$	−8396.22	+	14542.7i	−0.356918	+	0.618201i	0.630526	+	0.776168i	$0.282839\pi$
$822$		0			0
$823$	4409.52	+	7637.50i	0.186763	+	0.323483i	0.944169	−	0.329461i	$-0.106867\pi$
$823$	4409.52	+	7637.50i	0.186763	+	0.323483i	−0.757406	+	0.652944i	$0.773534\pi$
$824$	−6446.32	+	11165.4i	−0.272534	+	0.472043i
$825$		0			0
$826$	−16940.9	−	2400.25i	−0.713617	−	0.101108i
$827$	−8250.13			−0.346898			−0.173449	−	0.984843i	$-0.555491\pi$
$827$	−8250.13			−0.346898			−0.173449	+	0.984843i	$0.555491\pi$
$828$		0			0
$829$	10775.2	+	18663.3i	0.451435	+	0.781909i	0.998475	−	0.0551975i	$-0.0175789\pi$
$829$	10775.2	+	18663.3i	0.451435	+	0.781909i	−0.547040	+	0.837106i	$0.684246\pi$
$830$	−5510.18	−	9543.91i	−0.230435	−	0.399125i
$831$		0			0
$832$	2485.58			0.103572
$833$	2248.95	+	9106.95i	0.0935431	+	0.378796i
$834$		0			0
$835$	11218.2	−	19430.5i	0.464936	−	0.805293i
$836$	7932.26	+	13739.1i	0.328161	+	0.568392i
$837$		0			0
$838$	1549.66	−	2684.09i	0.0638808	−	0.110645i
$839$	−30130.4			−1.23983			−0.619916	−	0.784669i	$-0.712833\pi$
$839$	−30130.4			−1.23983			−0.619916	+	0.784669i	$0.712833\pi$
$840$		0			0
$841$	33311.0			1.36582
$842$	5531.63	−	9581.07i	0.226405	−	0.392144i
$843$		0			0
$844$	−1825.23	−	3161.39i	−0.0744395	−	0.128933i
$845$	5453.34	−	9445.46i	0.222012	−	0.384537i
$846$		0			0
$847$	−15484.6	+	19773.6i	−0.628165	+	0.802160i
$848$	1063.82			0.0430798
$849$		0			0
$850$	−3440.83	−	5959.70i	−0.138847	−	0.240489i
$851$	−11900.9	−	20613.0i	−0.479386	−	0.830321i
$852$		0			0
$853$	−40738.6			−1.63525			−0.817623	−	0.575754i	$-0.804709\pi$
$853$	−40738.6			−1.63525			−0.817623	+	0.575754i	$0.804709\pi$
$854$	2564.69	+	6368.37i	0.102766	+	0.255177i
$855$		0			0
$856$	−3738.68	+	6475.59i	−0.149282	+	0.258564i
$857$	−18254.1	−	31617.0i	−0.727594	−	1.26023i	−0.957897	−	0.287111i	$-0.907305\pi$
$857$	−18254.1	−	31617.0i	−0.727594	−	1.26023i	0.230303	−	0.973119i	$-0.426028\pi$
$858$		0			0
$859$	10990.4	−	19036.0i	0.436541	−	0.756110i	−0.560879	−	0.827897i	$-0.689537\pi$
$859$	10990.4	−	19036.0i	0.436541	−	0.756110i	0.997420	+	0.0717871i	$0.0228702\pi$
$860$	−20813.6			−0.825276
$861$		0			0
$862$	−4059.86			−0.160417
$863$	−11713.0	+	20287.6i	−0.462012	+	0.800228i	−0.999061	−	0.0433226i	$-0.986206\pi$
$863$	−11713.0	+	20287.6i	−0.462012	+	0.800228i	0.537049	+	0.843551i	$0.319539\pi$
$864$		0			0
$865$	−8208.37	−	14217.3i	−0.322651	−	0.558847i
$866$	−327.739	+	567.660i	−0.0128603	+	0.0222747i
$867$		0			0
$868$	13550.4	−	17303.7i	0.529873	−	0.676642i
$869$	21237.5			0.829037
$870$		0			0
$871$	−10587.2	−	18337.5i	−0.411863	−	0.713367i
$872$	−4788.08	−	8293.19i	−0.185946	−	0.322068i
$873$		0			0
$874$	22547.7			0.872639
$875$	236.506	+	33.5092i	0.00913757	+	0.00129465i
$876$		0			0
$877$	−153.701	+	266.217i	−0.00591802	+	0.0102503i	−0.868969	−	0.494866i	$-0.835217\pi$
$877$	−153.701	+	266.217i	−0.00591802	+	0.0102503i	0.863051	+	0.505116i	$0.168550\pi$
$878$	7908.68	+	13698.2i	0.303992	+	0.526530i
$879$		0			0
$880$	6567.61	−	11375.4i	0.251584	−	0.435756i
$881$	19941.7			0.762605			0.381302	−	0.924450i	$-0.375476\pi$
$881$	19941.7			0.762605			0.381302	+	0.924450i	$0.375476\pi$
$882$		0			0
$883$	−37524.1			−1.43011			−0.715056	−	0.699068i	$-0.753599\pi$
$883$	−37524.1			−1.43011			−0.715056	+	0.699068i	$0.753599\pi$
$884$	2124.27	−	3679.35i	0.0808224	−	0.139989i
$885$		0			0
$886$	2920.82	+	5059.01i	0.110753	+	0.191829i
$887$	−1440.10	+	2494.33i	−0.0545140	+	0.0944210i	−0.891995	−	0.452046i	$-0.850694\pi$
$887$	−1440.10	+	2494.33i	−0.0545140	+	0.0944210i	0.837481	+	0.546467i	$0.184028\pi$
$888$		0			0
$889$	−49032.1	−	6947.06i	−1.84981	−	0.262089i
$890$	36652.1			1.38043
$891$		0			0
$892$	8638.93	+	14963.1i	0.324274	+	0.561660i
$893$	2599.65	+	4502.72i	0.0974176	+	0.168732i
$894$		0			0
$895$	12153.9			0.453922
$896$	1461.58	−	1866.42i	0.0544953	−	0.0695899i
$897$		0			0
$898$	10240.2	−	17736.5i	0.380534	−	0.659104i
$899$	−35631.8	−	61716.1i	−1.32190	−	2.28960i
$900$		0			0
$901$	909.182	−	1574.75i	0.0336174	−	0.0582270i
$902$	10676.1			0.394096
$903$		0			0
$904$	−19077.2			−0.701877
$905$	31339.4	−	54281.4i	1.15111	−	1.99378i
$906$		0			0
$907$	−9159.62	−	15864.9i	−0.335326	−	0.580801i	0.648222	−	0.761452i	$-0.275513\pi$
$907$	−9159.62	−	15864.9i	−0.335326	−	0.580801i	−0.983547	+	0.180651i	$0.942180\pi$
$908$	4122.57	−	7140.50i	0.150674	−	0.260975i
$909$		0			0
$910$	8510.77	+	21133.1i	0.310032	+	0.769840i
$911$	−46150.7			−1.67842			−0.839210	−	0.543807i	$-0.816982\pi$
$911$	−46150.7			−1.67842			−0.839210	+	0.543807i	$0.816982\pi$
$912$		0			0
$913$	−9017.79	−	15619.3i	−0.326884	−	0.566180i
$914$	5892.63	+	10206.3i	0.213250	+	0.369360i
$915$		0			0
$916$	−13898.5			−0.501332
$917$	−443.723	+	566.630i	−0.0159793	+	0.0204054i
$918$		0			0
$919$	−23632.1	+	40932.1i	−0.848261	+	1.46923i	0.0344969	+	0.999405i	$0.489017\pi$
$919$	−23632.1	+	40932.1i	−0.848261	+	1.46923i	−0.882758	+	0.469827i	$0.844316\pi$
$920$	−9334.30	−	16167.5i	−0.334503	−	0.579376i
$921$		0			0
$922$	12643.4	−	21899.0i	0.451613	−	0.782217i
$923$	5077.66			0.181076
$924$		0			0
$925$	−20323.3			−0.722407
$926$	15093.2	−	26142.2i	0.535629	−	0.927737i
$927$		0			0
$928$	−3843.33	−	6656.85i	−0.135952	−	0.235476i
$929$	−26635.7	+	46134.4i	−0.940678	+	1.62930i	−0.176496	+	0.984301i	$0.556476\pi$
$929$	−26635.7	+	46134.4i	−0.940678	+	1.62930i	−0.764182	+	0.645001i	$0.776857\pi$
$930$		0			0
$931$	−18918.7	+	18187.8i	−0.665990	+	0.640260i
$932$	−3104.39			−0.109107
$933$		0			0
$934$	2820.23	+	4884.79i	0.0988018	+	0.171130i
$935$	−11225.9	−	19443.8i	−0.392648	−	0.680086i
$936$		0			0
$937$	17197.8			0.599602			0.299801	−	0.954002i	$-0.403080\pi$
$937$	17197.8			0.599602			0.299801	+	0.954002i	$0.403080\pi$
$938$	−19995.1	−	2832.99i	−0.696016	−	0.0986143i
$939$		0			0
$940$	2152.41	−	3728.08i	0.0746849	−	0.129358i
$941$	14417.4	+	24971.7i	0.499463	+	0.865096i	1.00000		0.000619696i	$-0.000197256\pi$
$941$	14417.4	+	24971.7i	0.499463	+	0.865096i	−0.500537	+	0.865715i	$0.666864\pi$
$942$		0			0
$943$	7586.77	−	13140.7i	0.261993	−	0.453785i
$944$	7390.85			0.254822
$945$		0			0
$946$	−34062.9			−1.17070
$947$	−25920.6	+	44895.8i	−0.889448	+	1.54057i	−0.0489180	+	0.998803i	$0.515577\pi$
$947$	−25920.6	+	44895.8i	−0.889448	+	1.54057i	−0.840530	+	0.541766i	$0.817756\pi$
$948$		0			0
$949$	−3520.57	−	6097.81i	−0.120424	−	0.208581i
$950$	9626.23	−	16673.1i	0.328754	−	0.569418i
$951$		0			0
$952$	−1513.70	−	3758.66i	−0.0515328	−	0.127961i
$953$	5887.31			0.200114			0.100057	−	0.994982i	$-0.468097\pi$
$953$	5887.31			0.200114			0.100057	+	0.994982i	$0.468097\pi$
$954$		0			0
$955$	−14295.3	−	24760.3i	−0.484384	−	0.838977i
$956$	4013.59	+	6951.74i	0.135783	+	0.235184i
$957$		0			0
$958$	−32897.0			−1.10945
$959$	−5314.45	−	13196.3i	−0.178949	−	0.444349i
$960$		0			0
$961$	−29112.3	+	50424.0i	−0.977218	+	1.69259i
$962$	−6273.52	−	10866.1i	−0.210256	−	0.364174i
$963$		0			0
$964$	−1611.30	+	2790.85i	−0.0538344	+	0.0932439i
$965$	53384.4			1.78083
$966$		0			0
$967$	−36620.0			−1.21781			−0.608904	−	0.793244i	$-0.708391\pi$
$967$	−36620.0			−1.21781			−0.608904	+	0.793244i	$0.708391\pi$
$968$	5424.35	−	9395.25i	0.180109	−	0.311957i
$969$		0			0
$970$	25629.2	+	44391.1i	0.848355	+	1.46939i
$971$	−21182.4	+	36689.1i	−0.700079	+	1.21257i	0.268359	+	0.963319i	$0.413519\pi$
$971$	−21182.4	+	36689.1i	−0.700079	+	1.21257i	−0.968438	+	0.249254i	$0.919815\pi$
$972$		0			0
$973$	19300.7	+	2734.60i	0.635923	+	0.0901001i
$974$	−12662.1			−0.416551
$975$		0			0
$976$	−1482.79	−	2568.26i	−0.0486300	−	0.0842296i
$977$	2511.16	+	4349.46i	0.0822304	+	0.142427i	0.904208	−	0.427093i	$-0.140462\pi$
$977$	2511.16	+	4349.46i	0.0822304	+	0.142427i	−0.821977	+	0.569520i	$0.807129\pi$
$978$		0			0
$979$	59983.8			1.95821
$980$	20873.3	+	6036.00i	0.680382	+	0.196748i
$981$		0			0
$982$	9286.90	−	16085.4i	0.301789	−	0.522714i
$983$	14146.4	+	24502.3i	0.459003	+	0.795016i	0.998909	−	0.0467095i	$-0.0148735\pi$
$983$	14146.4	+	24502.3i	0.459003	+	0.795016i	−0.539906	+	0.841725i	$0.681540\pi$
$984$		0			0
$985$	−36522.9	+	63259.4i	−1.18144	+	2.04631i
$986$	−13138.7			−0.424361
$987$		0			0
$988$	11885.9			0.382734
$989$	−24206.2	+	41926.3i	−0.778273	+	1.34801i
$990$		0			0
$991$	−18200.5	−	31524.2i	−0.583410	−	1.01050i	−0.995072	−	0.0991586i	$-0.968385\pi$
$991$	−18200.5	−	31524.2i	−0.583410	−	1.01050i	0.411662	−	0.911337i	$-0.364948\pi$
$992$	−4746.79	+	8221.68i	−0.151926	+	0.263144i
$993$		0			0
$994$	2985.78	−	3812.81i	0.0952749	−	0.121665i
$995$	−35314.6			−1.12517
$996$		0			0
$997$	1178.60	+	2041.39i	0.0374389	+	0.0648460i	0.884138	−	0.467226i	$-0.154747\pi$
$997$	1178.60	+	2041.39i	0.0374389	+	0.0648460i	−0.846699	+	0.532072i	$0.821413\pi$
$998$	−243.451	−	421.669i	−0.00772174	−	0.0133745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.g.g.37.1		4
3.2	odd	2		42.4.e.c.37.2	yes	4
7.2	even	3		882.4.a.v.1.2		2
7.3	odd	6		882.4.g.bf.361.2		4
7.4	even	3	inner	126.4.g.g.109.1		4
7.5	odd	6		882.4.a.z.1.1		2
7.6	odd	2		882.4.g.bf.667.2		4
12.11	even	2		336.4.q.j.289.2		4
21.2	odd	6		294.4.a.n.1.1		2
21.5	even	6		294.4.a.m.1.2		2
21.11	odd	6		42.4.e.c.25.2	✓	4
21.17	even	6		294.4.e.l.67.1		4
21.20	even	2		294.4.e.l.79.1		4
84.11	even	6		336.4.q.j.193.2		4
84.23	even	6		2352.4.a.bq.1.1		2
84.47	odd	6		2352.4.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.2	✓	4	21.11	odd	6
42.4.e.c.37.2	yes	4	3.2	odd	2
126.4.g.g.37.1		4	1.1	even	1	trivial
126.4.g.g.109.1		4	7.4	even	3	inner
294.4.a.m.1.2		2	21.5	even	6
294.4.a.n.1.1		2	21.2	odd	6
294.4.e.l.67.1		4	21.17	even	6
294.4.e.l.79.1		4	21.20	even	2
336.4.q.j.193.2		4	84.11	even	6
336.4.q.j.289.2		4	12.11	even	2
882.4.a.v.1.2		2	7.2	even	3
882.4.a.z.1.1		2	7.5	odd	6
882.4.g.bf.361.2		4	7.3	odd	6
882.4.g.bf.667.2		4	7.6	odd	2
2352.4.a.bq.1.1		2	84.23	even	6
2352.4.a.ca.1.2		2	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.91856 + 13.7153i) q^{5} +(18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-7.91856 + 13.7153i) q^{5} +(18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +(15.8371 + 27.4307i) q^{10} +(25.9186 + 44.8923i) q^{11} +38.8371 q^{13} +(22.8371 - 29.1627i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(13.6742 + 23.6845i) q^{17} +(-38.2557 + 66.2608i) q^{19} +63.3485 q^{20} +103.674 q^{22} +(73.6742 - 127.608i) q^{23} +(-62.9072 - 108.958i) q^{25} +(38.8371 - 67.2679i) q^{26} +(-27.6742 - 68.7178i) q^{28} -240.208 q^{29} +(148.337 + 256.927i) q^{31} +(16.0000 + 27.7128i) q^{32} +54.6970 q^{34} +(-180.837 + 230.927i) q^{35} +(80.7670 - 139.893i) q^{37} +(76.5114 + 132.522i) q^{38} +(63.3485 - 109.723i) q^{40} +102.977 q^{41} -328.557 q^{43} +(103.674 - 179.569i) q^{44} +(-147.348 - 255.215i) q^{46} +(33.9773 - 58.8504i) q^{47} +(329.500 + 95.2825i) q^{49} -251.629 q^{50} +(-77.6742 - 134.536i) q^{52} +(-33.2443 - 57.5808i) q^{53} -820.951 q^{55} +(-146.697 - 20.7846i) q^{56} +(-240.208 + 416.053i) q^{58} +(-230.964 - 400.041i) q^{59} +(-92.6742 + 160.516i) q^{61} +593.348 q^{62} +64.0000 q^{64} +(-307.534 + 532.665i) q^{65} +(-272.604 - 472.164i) q^{67} +(54.6970 - 94.7379i) q^{68} +(219.140 + 544.146i) q^{70} +130.742 q^{71} +(-90.6496 - 157.010i) q^{73} +(-161.534 - 279.785i) q^{74} +306.045 q^{76} +(358.638 + 890.533i) q^{77} +(204.848 - 354.808i) q^{79} +(-126.697 - 219.446i) q^{80} +(102.977 - 178.362i) q^{82} -347.928 q^{83} -433.121 q^{85} +(-328.557 + 569.077i) q^{86} +(-207.348 - 359.138i) q^{88} +(578.580 - 1002.13i) q^{89} +(712.161 + 100.902i) q^{91} -589.394 q^{92} +(-67.9546 - 117.701i) q^{94} +(-605.860 - 1049.38i) q^{95} +1618.30 q^{97} +(494.534 - 475.428i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 5 q^{5} - 32 q^{8} - 10 q^{10} + 67 q^{11} + 82 q^{13} + 18 q^{14} - 32 q^{16} - 92 q^{17} - 43 q^{19} - 40 q^{20} + 268 q^{22} + 148 q^{23} - 435 q^{25} + 82 q^{26} + 36 q^{28} - 154 q^{29} + 520 q^{31} + 64 q^{32} - 368 q^{34} - 650 q^{35} - 7 q^{37} + 86 q^{38} - 40 q^{40} + 852 q^{41} - 214 q^{43} + 268 q^{44} - 296 q^{46} + 576 q^{47} + 1318 q^{49} - 1740 q^{50} - 164 q^{52} - 243 q^{53} - 1010 q^{55} - 154 q^{58} - 7 q^{59} - 224 q^{61} + 2080 q^{62} + 256 q^{64} - 570 q^{65} - 687 q^{67} - 368 q^{68} + 1390 q^{70} - 944 q^{71} + 921 q^{73} + 14 q^{74} + 344 q^{76} + 371 q^{77} + 526 q^{79} + 80 q^{80} + 852 q^{82} + 442 q^{83} - 5840 q^{85} - 214 q^{86} - 536 q^{88} + 774 q^{89} + 1345 q^{91} - 1184 q^{92} - 1152 q^{94} - 1910 q^{95} + 3906 q^{97} + 1318 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 5 * q^5 - 32 * q^8 - 10 * q^10 + 67 * q^11 + 82 * q^13 + 18 * q^14 - 32 * q^16 - 92 * q^17 - 43 * q^19 - 40 * q^20 + 268 * q^22 + 148 * q^23 - 435 * q^25 + 82 * q^26 + 36 * q^28 - 154 * q^29 + 520 * q^31 + 64 * q^32 - 368 * q^34 - 650 * q^35 - 7 * q^37 + 86 * q^38 - 40 * q^40 + 852 * q^41 - 214 * q^43 + 268 * q^44 - 296 * q^46 + 576 * q^47 + 1318 * q^49 - 1740 * q^50 - 164 * q^52 - 243 * q^53 - 1010 * q^55 - 154 * q^58 - 7 * q^59 - 224 * q^61 + 2080 * q^62 + 256 * q^64 - 570 * q^65 - 687 * q^67 - 368 * q^68 + 1390 * q^70 - 944 * q^71 + 921 * q^73 + 14 * q^74 + 344 * q^76 + 371 * q^77 + 526 * q^79 + 80 * q^80 + 852 * q^82 + 442 * q^83 - 5840 * q^85 - 214 * q^86 - 536 * q^88 + 774 * q^89 + 1345 * q^91 - 1184 * q^92 - 1152 * q^94 - 1910 * q^95 + 3906 * q^97 + 1318 * q^98

Introduction

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