LMFDB - Embedded newform 55.6.e.b.32.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,6,Mod(32,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("55.32");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	55.e (of order $4$, 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:	$8.82111008971$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.20
Character	$\chi$	$=$	55.32
Dual form			55.6.e.b.43.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.80775 - 4.80775i) q^{2} +(-19.8987 + 19.8987i) q^{3} -14.2290i q^{4} +(-6.50942 - 55.5214i) q^{5} +191.336i q^{6} +(113.651 - 113.651i) q^{7} +(85.4386 + 85.4386i) q^{8} -548.917i q^{9} +(-298.229 - 235.638i) q^{10} +(-251.789 - 312.495i) q^{11} +(283.139 + 283.139i) q^{12} +(-493.356 - 493.356i) q^{13} -1092.81i q^{14} +(1234.33 + 975.275i) q^{15} +1276.86 q^{16} +(584.735 - 584.735i) q^{17} +(-2639.06 - 2639.06i) q^{18} +938.862 q^{19} +(-790.015 + 92.6226i) q^{20} +4523.02i q^{21} +(-2712.94 - 291.859i) q^{22} +(624.927 - 624.927i) q^{23} -3400.23 q^{24} +(-3040.25 + 722.824i) q^{25} -4743.87 q^{26} +(6087.35 + 6087.35i) q^{27} +(-1617.14 - 1617.14i) q^{28} -3410.26 q^{29} +(10623.3 - 1245.49i) q^{30} +2196.25 q^{31} +(3404.81 - 3404.81i) q^{32} +(11228.5 + 1207.97i) q^{33} -5622.53i q^{34} +(-7049.88 - 5570.27i) q^{35} -7810.54 q^{36} +(-5215.24 - 5215.24i) q^{37} +(4513.82 - 4513.82i) q^{38} +19634.3 q^{39} +(4187.51 - 5299.83i) q^{40} +19758.4i q^{41} +(21745.6 + 21745.6i) q^{42} +(-9303.47 - 9303.47i) q^{43} +(-4446.50 + 3582.71i) q^{44} +(-30476.6 + 3573.13i) q^{45} -6008.99i q^{46} +(-2876.41 - 2876.41i) q^{47} +(-25407.9 + 25407.9i) q^{48} -9026.17i q^{49} +(-11141.6 + 18092.0i) q^{50} +23271.0i q^{51} +(-7019.97 + 7019.97i) q^{52} +(18168.1 - 18168.1i) q^{53} +58533.0 q^{54} +(-15711.2 + 16013.9i) q^{55} +19420.4 q^{56} +(-18682.1 + 18682.1i) q^{57} +(-16395.7 + 16395.7i) q^{58} -3286.52i q^{59} +(13877.2 - 17563.3i) q^{60} -26664.2i q^{61} +(10559.0 - 10559.0i) q^{62} +(-62385.0 - 62385.0i) q^{63} +8120.62i q^{64} +(-24180.4 + 30603.3i) q^{65} +(59791.6 - 48176.4i) q^{66} +(-29564.9 - 29564.9i) q^{67} +(-8320.21 - 8320.21i) q^{68} +24870.5i q^{69} +(-60674.6 + 7113.58i) q^{70} +54859.4 q^{71} +(46898.7 - 46898.7i) q^{72} +(24957.0 + 24957.0i) q^{73} -50147.2 q^{74} +(46113.9 - 74880.4i) q^{75} -13359.1i q^{76} +(-64131.6 - 6899.30i) q^{77} +(94396.9 - 94396.9i) q^{78} +37251.8 q^{79} +(-8311.64 - 70893.3i) q^{80} -108874. q^{81} +(94993.4 + 94993.4i) q^{82} +(68038.2 + 68038.2i) q^{83} +64358.1 q^{84} +(-36271.6 - 28659.1i) q^{85} -89457.6 q^{86} +(67859.8 - 67859.8i) q^{87} +(5186.63 - 48211.6i) q^{88} +136703. i q^{89} +(-129345. + 163703. i) q^{90} -112141. q^{91} +(-8892.09 - 8892.09i) q^{92} +(-43702.5 + 43702.5i) q^{93} -27658.1 q^{94} +(-6111.45 - 52127.0i) q^{95} +135503. i q^{96} +(-37533.8 - 37533.8i) q^{97} +(-43395.6 - 43395.6i) q^{98} +(-171534. + 138211. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) $ 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	4.80775	−	4.80775i	0.849899	−	0.849899i	−0.140221	−	0.990120i	$-0.544781\pi$
$2$	4.80775	−	4.80775i	0.849899	−	0.849899i	0.990120	+	0.140221i	$0.0447814\pi$
$3$	−19.8987	+	19.8987i	−1.27650	+	1.27650i	−0.333891	+	0.942612i	$0.608362\pi$
$3$	−19.8987	+	19.8987i	−1.27650	+	1.27650i	−0.942612	+	0.333891i	$0.891638\pi$
$4$		−	14.2290i		−	0.444657i
$5$	−6.50942	−	55.5214i	−0.116444	−	0.993197i
$5$	−6.50942	−	55.5214i	−0.116444	−	0.993197i
$6$			191.336i			2.16980i
$7$	113.651	−	113.651i	0.876655	−	0.876655i	−0.116532	−	0.993187i	$-0.537178\pi$
$7$	113.651	−	113.651i	0.876655	−	0.876655i	0.993187	+	0.116532i	$0.0371777\pi$
$8$	85.4386	+	85.4386i	0.471986	+	0.471986i
$9$		−	548.917i		−	2.25892i
$10$	−298.229	−	235.638i	−0.943083	−	0.745152i
$11$	−251.789	−	312.495i	−0.627416	−	0.778684i
$11$	−251.789	−	312.495i	−0.627416	−	0.778684i
$12$	283.139	+	283.139i	0.567605	+	0.567605i
$13$	−493.356	−	493.356i	−0.809659	−	0.809659i	0.174923	−	0.984582i	$-0.444032\pi$
$13$	−493.356	−	493.356i	−0.809659	−	0.809659i	−0.984582	+	0.174923i	$0.944032\pi$
$14$		−	1092.81i		−	1.49014i
$15$	1234.33	+	975.275i	1.41646	+	1.11918i
$16$	1276.86			1.24694
$17$	584.735	−	584.735i	0.490724	−	0.490724i	−0.417810	−	0.908534i	$-0.637202\pi$
$17$	584.735	−	584.735i	0.490724	−	0.490724i	0.908534	+	0.417810i	$0.137202\pi$
$18$	−2639.06	−	2639.06i	−1.91985	−	1.91985i
$19$	938.862			0.596648			0.298324	−	0.954465i	$-0.403572\pi$
$19$	938.862			0.596648			0.298324	+	0.954465i	$0.403572\pi$
$20$	−790.015	+	92.6226i	−0.441632	+	0.0517776i
$21$			4523.02i			2.23810i
$22$	−2712.94	−	291.859i	−1.19504	−	0.128563i
$23$	624.927	−	624.927i	0.246325	−	0.246325i	−0.573135	−	0.819461i	$-0.694273\pi$
$23$	624.927	−	624.927i	0.246325	−	0.246325i	0.819461	+	0.573135i	$0.194273\pi$
$24$	−3400.23			−1.20498
$25$	−3040.25	+	722.824i	−0.972882	+	0.231304i
$26$	−4743.87			−1.37626
$27$	6087.35	+	6087.35i	1.60701	+	1.60701i
$28$	−1617.14	−	1617.14i	−0.389810	−	0.389810i
$29$	−3410.26			−0.752996			−0.376498	−	0.926417i	$-0.622872\pi$
$29$	−3410.26			−0.752996			−0.376498	+	0.926417i	$0.622872\pi$
$30$	10623.3	−	1245.49i	2.15504	−	0.252660i
$31$	2196.25			0.410466			0.205233	−	0.978713i	$-0.434205\pi$
$31$	2196.25			0.410466			0.205233	+	0.978713i	$0.434205\pi$
$32$	3404.81	−	3404.81i	0.587785	−	0.587785i
$33$	11228.5	+	1207.97i	1.79489	+	0.193095i
$34$		−	5622.53i		−	0.834131i
$35$	−7049.88	−	5570.27i	−0.972773	−	0.768610i
$36$	−7810.54			−1.00444
$37$	−5215.24	−	5215.24i	−0.626282	−	0.626282i	0.320848	−	0.947131i	$-0.396032\pi$
$37$	−5215.24	−	5215.24i	−0.626282	−	0.626282i	−0.947131	+	0.320848i	$0.896032\pi$
$38$	4513.82	−	4513.82i	0.507090	−	0.507090i
$39$	19634.3			2.06706
$40$	4187.51	−	5299.83i	0.413815	−	0.523735i
$41$			19758.4i			1.83566i	0.396976	+	0.917829i	$0.370059\pi$
$41$			19758.4i			1.83566i	−0.396976	+	0.917829i	$0.629941\pi$
$42$	21745.6	+	21745.6i	1.90216	+	1.90216i
$43$	−9303.47	−	9303.47i	−0.767315	−	0.767315i	0.210318	−	0.977633i	$-0.432550\pi$
$43$	−9303.47	−	9303.47i	−0.767315	−	0.767315i	−0.977633	+	0.210318i	$0.932550\pi$
$44$	−4446.50	+	3582.71i	−0.346247	+	0.278985i
$45$	−30476.6	+	3573.13i	−2.24355	+	0.263037i
$46$		−	6008.99i		−	0.418704i
$47$	−2876.41	−	2876.41i	−0.189935	−	0.189935i	0.605733	−	0.795668i	$-0.292880\pi$
$47$	−2876.41	−	2876.41i	−0.189935	−	0.189935i	−0.795668	+	0.605733i	$0.792880\pi$
$48$	−25407.9	+	25407.9i	−1.59172	+	1.59172i
$49$		−	9026.17i		−	0.537048i
$50$	−11141.6	+	18092.0i	−0.630266	+	1.02344i
$51$			23271.0i			1.25282i
$52$	−7019.97	+	7019.97i	−0.360020	+	0.360020i
$53$	18168.1	−	18168.1i	0.888425	−	0.888425i	−0.105947	−	0.994372i	$-0.533787\pi$
$53$	18168.1	−	18168.1i	0.888425	−	0.888425i	0.994372	+	0.105947i	$0.0337873\pi$
$54$	58533.0			2.73159
$55$	−15711.2	+	16013.9i	−0.700329	+	0.713821i
$56$	19420.4			0.827538
$57$	−18682.1	+	18682.1i	−0.761622	+	0.761622i
$58$	−16395.7	+	16395.7i	−0.639970	+	0.639970i
$59$		−	3286.52i		−	0.122915i	−0.998110	−	0.0614576i	$-0.980425\pi$
$59$		−	3286.52i		−	0.122915i	0.998110	−	0.0614576i	$-0.0195749\pi$
$60$	13877.2	−	17563.3i	0.497650	−	0.629838i
$61$		−	26664.2i		−	0.917494i	−0.888567	−	0.458747i	$-0.848298\pi$
$61$		−	26664.2i		−	0.917494i	0.888567	−	0.458747i	$-0.151702\pi$
$62$	10559.0	−	10559.0i	0.348855	−	0.348855i
$63$	−62385.0	−	62385.0i	−1.98029	−	1.98029i
$64$			8120.62i			0.247822i
$65$	−24180.4	+	30603.3i	−0.709871	+	0.898431i
$66$	59791.6	−	48176.4i	1.68959	−	1.36136i
$67$	−29564.9	−	29564.9i	−0.804617	−	0.804617i	0.179197	−	0.983813i	$-0.442650\pi$
$67$	−29564.9	−	29564.9i	−0.804617	−	0.804617i	−0.983813	+	0.179197i	$0.942650\pi$
$68$	−8320.21	−	8320.21i	−0.218204	−	0.218204i
$69$			24870.5i			0.628870i
$70$	−60674.6	+	7113.58i	−1.48000	+	0.173517i
$71$	54859.4			1.29153			0.645766	−	0.763535i	$-0.276538\pi$
$71$	54859.4			1.29153			0.645766	+	0.763535i	$0.276538\pi$
$72$	46898.7	−	46898.7i	1.06618	−	1.06618i
$73$	24957.0	+	24957.0i	0.548131	+	0.548131i	0.925900	−	0.377769i	$-0.123309\pi$
$73$	24957.0	+	24957.0i	0.548131	+	0.548131i	−0.377769	+	0.925900i	$0.623309\pi$
$74$	−50147.2			−1.06455
$75$	46113.9	−	74880.4i	0.946626	−	1.53715i
$76$		−	13359.1i		−	0.265303i
$77$	−64131.6	−	6899.30i	−1.23266	−	0.132611i
$78$	94396.9	−	94396.9i	1.75679	−	1.75679i
$79$	37251.8			0.671552			0.335776	−	0.941942i	$-0.391001\pi$
$79$	37251.8			0.671552			0.335776	+	0.941942i	$0.391001\pi$
$80$	−8311.64	−	70893.3i	−0.145198	−	1.23845i
$81$	−108874.			−1.84379
$82$	94993.4	+	94993.4i	1.56012	+	1.56012i
$83$	68038.2	+	68038.2i	1.08407	+	1.08407i	0.996125	+	0.0879451i	$0.0280300\pi$
$83$	68038.2	+	68038.2i	1.08407	+	1.08407i	0.0879451	+	0.996125i	$0.471970\pi$
$84$	64358.1			0.995188
$85$	−36271.6	−	28659.1i	−0.544527	−	0.430244i
$86$	−89457.6			−1.30428
$87$	67859.8	−	67859.8i	0.961201	−	0.961201i
$88$	5186.63	−	48211.6i	0.0713967	−	0.663659i
$89$			136703.i			1.82937i	0.404163	+	0.914687i	$0.367563\pi$
$89$			136703.i			1.82937i	−0.404163	+	0.914687i	$0.632437\pi$
$90$	−129345.	+	163703.i	−1.68324	+	2.13035i
$91$	−112141.			−1.41958
$92$	−8892.09	−	8892.09i	−0.109530	−	0.109530i
$93$	−43702.5	+	43702.5i	−0.523961	+	0.523961i
$94$	−27658.1			−0.322852
$95$	−6111.45	−	52127.0i	−0.0694760	−	0.592589i
$96$			135503.i			1.50062i
$97$	−37533.8	−	37533.8i	−0.405035	−	0.405035i	0.474968	−	0.880003i	$-0.342460\pi$
$97$	−37533.8	−	37533.8i	−0.405035	−	0.405035i	−0.880003	+	0.474968i	$0.842460\pi$
$98$	−43395.6	−	43395.6i	−0.456437	−	0.456437i
$99$	−171534.	+	138211.i	−1.75898	+	1.41728i
$100$	10285.1	+	43259.8i	0.102851	+	0.432598i
$101$			75348.3i			0.734971i	0.930029	+	0.367485i	$0.119781\pi$
$101$			75348.3i			0.734971i	−0.930029	+	0.367485i	$0.880219\pi$
$102$	111881.	+	111881.i	1.06477	+	1.06477i
$103$	32141.2	−	32141.2i	0.298517	−	0.298517i	−0.541916	−	0.840433i	$-0.682301\pi$
$103$	32141.2	−	32141.2i	0.298517	−	0.298517i	0.840433	+	0.541916i	$0.182301\pi$
$104$		−	84303.3i		−	0.764295i
$105$	251125.	−	29442.2i	2.22288	−	0.260614i
$106$		−	174696.i		−	1.51014i
$107$	73943.8	−	73943.8i	0.624371	−	0.624371i	−0.322275	−	0.946646i	$-0.604448\pi$
$107$	73943.8	−	73943.8i	0.624371	−	0.624371i	0.946646	+	0.322275i	$0.104448\pi$
$108$	86617.0	−	86617.0i	0.714568	−	0.714568i
$109$	115968.			0.934917			0.467458	−	0.884015i	$-0.345170\pi$
$109$	115968.			0.934917			0.467458	+	0.884015i	$0.345170\pi$
$110$	1455.23	+	152526.i	0.0114670	+	1.20188i
$111$	207553.			1.59890
$112$	145117.	−	145117.i	1.09313	−	1.09313i
$113$	−16531.8	+	16531.8i	−0.121793	+	0.121793i	−0.765376	−	0.643583i	$-0.777447\pi$
$113$	−16531.8	+	16531.8i	−0.121793	+	0.121793i	0.643583	+	0.765376i	$0.277447\pi$
$114$			179638.i			1.29460i
$115$	−38764.7	−	30628.9i	−0.273333	−	0.215967i
$116$			48524.6i			0.334825i
$117$	−270811.	+	270811.i	−1.82895	+	1.82895i
$118$	−15800.8	−	15800.8i	−0.104466	−	0.104466i
$119$		−	132912.i		−	0.860391i
$120$	22133.5	+	188786.i	0.140313	+	1.19679i
$121$	−34255.4	+	157366.i	−0.212699	+	0.977118i
$122$	−128195.	−	128195.i	−0.779777	−	0.779777i
$123$	−393166.	−	393166.i	−2.34322	−	2.34322i
$124$		−	31250.5i		−	0.182517i
$125$	59922.5	+	164094.i	0.343016	+	0.939329i
$126$	−599864.			−3.36610
$127$	110090.	−	110090.i	0.605673	−	0.605673i	−0.336139	−	0.941812i	$-0.609121\pi$
$127$	110090.	−	110090.i	0.605673	−	0.605673i	0.941812	+	0.336139i	$0.109121\pi$
$128$	147996.	+	147996.i	0.798408	+	0.798408i
$129$	370254.			1.95896
$130$	30879.8	+	263386.i	0.160257	+	1.36689i
$131$			207869.i			1.05831i	0.848526	+	0.529154i	$0.177491\pi$
$131$			207869.i			1.05831i	−0.848526	+	0.529154i	$0.822509\pi$
$132$	17188.2	−	159771.i	0.0858610	−	0.798110i
$133$	106703.	−	106703.i	0.523054	−	0.523054i
$134$	−284281.			−1.36769
$135$	298353.	−	377603.i	1.40895	−	1.78321i
$136$	99917.9			0.463229
$137$	−124546.	−	124546.i	−0.566930	−	0.566930i	0.364337	−	0.931267i	$-0.381296\pi$
$137$	−124546.	−	124546.i	−0.566930	−	0.566930i	−0.931267	+	0.364337i	$0.881296\pi$
$138$	119571.	+	119571.i	0.534476	+	0.534476i
$139$	20361.5			0.0893865			0.0446933	−	0.999001i	$-0.485769\pi$
$139$	20361.5			0.0893865			0.0446933	+	0.999001i	$0.485769\pi$
$140$	−79259.4	+	100313.i	−0.341768	+	0.432550i
$141$	114474.			0.484906
$142$	263750.	−	263750.i	1.09767	−	1.09767i
$143$	−29949.6	+	278393.i	−0.122476	+	1.13846i
$144$		−	700892.i		−	2.81673i
$145$	22198.8	+	189343.i	0.0876819	+	0.747873i
$146$	239974.			0.931712
$147$	179609.	+	179609.i	0.685544	+	0.685544i
$148$	−74207.7	+	74207.7i	−0.278481	+	0.278481i
$149$	−323022.			−1.19197			−0.595986	−	0.802995i	$-0.703239\pi$
$149$	−323022.			−1.19197			−0.595986	+	0.802995i	$0.703239\pi$
$150$	−138302.	−	581711.i	−0.501882	−	2.11095i
$151$		−	8331.10i		−	0.0297344i	−0.999889	−	0.0148672i	$-0.995267\pi$
$151$		−	8331.10i		−	0.0297344i	0.999889	−	0.0148672i	$-0.00473256\pi$
$152$	80215.0	+	80215.0i	0.281609	+	0.281609i
$153$	−320971.	−	320971.i	−1.10850	−	1.10850i
$154$	−341499.	+	275159.i	−1.16035	+	0.934935i
$155$	−14296.3	−	121939.i	−0.0477963	−	0.407674i
$156$		−	279377.i		−	0.919133i
$157$	139106.	+	139106.i	0.450399	+	0.450399i	0.895487	−	0.445088i	$-0.146828\pi$
$157$	139106.	+	139106.i	0.450399	+	0.450399i	−0.445088	+	0.895487i	$0.646828\pi$
$158$	179098.	−	179098.i	0.570751	−	0.570751i
$159$			723045.i			2.26815i
$160$	−211203.	−	166877.i	−0.652230	−	0.515342i
$161$		−	142047.i		−	0.431885i
$162$	−523439.	+	523439.i	−1.56704	+	1.56704i
$163$	237642.	−	237642.i	0.700574	−	0.700574i	−0.263959	−	0.964534i	$-0.585028\pi$
$163$	237642.	−	237642.i	0.700574	−	0.700574i	0.964534	+	0.263959i	$0.0850285\pi$
$164$	281142.			0.816237
$165$	−6023.01	−	631287.i	−0.0172228	−	1.80516i
$166$	654222.			1.84270
$167$	−207356.	+	207356.i	−0.575341	+	0.575341i	−0.933616	−	0.358275i	$-0.883365\pi$
$167$	−207356.	+	207356.i	−0.575341	+	0.575341i	0.358275	+	0.933616i	$0.383365\pi$
$168$	−386440.	+	386440.i	−1.05635	+	1.05635i
$169$			115507.i			0.311095i
$170$	−312171.	+	36599.4i	−0.828457	+	0.0971296i
$171$		−	515357.i		−	1.34778i
$172$	−132379.	+	132379.i	−0.341192	+	0.341192i
$173$	−121414.	−	121414.i	−0.308429	−	0.308429i	0.535871	−	0.844300i	$-0.319983\pi$
$173$	−121414.	−	121414.i	−0.308429	−	0.308429i	−0.844300	+	0.535871i	$0.819983\pi$
$174$		−	652506.i		−	1.63385i
$175$	−263379.	+	427678.i	−0.650108	+	1.05566i
$176$	−321500.	−	399014.i	−0.782348	−	0.970971i
$177$	65397.4	+	65397.4i	0.156902	+	0.156902i
$178$	657234.	+	657234.i	1.55478	+	1.55478i
$179$		−	690982.i		−	1.61188i	−0.591994	−	0.805942i	$-0.701659\pi$
$179$		−	690982.i		−	1.61188i	0.591994	−	0.805942i	$-0.298341\pi$
$180$	50842.1	+	433652.i	0.116961	+	0.997609i
$181$	542596.			1.23106			0.615531	−	0.788112i	$-0.288941\pi$
$181$	542596.			1.23106			0.615531	+	0.788112i	$0.288941\pi$
$182$	−539146.	+	539146.i	−1.20650	+	1.20650i
$183$	530582.	+	530582.i	1.17118	+	1.17118i
$184$	106786.			0.232524
$185$	−255609.	+	323506.i	−0.549095	+	0.694949i
$186$			420222.i			0.890628i
$187$	−329957.	−	35496.9i	−0.690007	−	0.0742312i
$188$	−40928.4	+	40928.4i	−0.0844560	+	0.0844560i
$189$	1.38367e6			2.81759
$190$	−279996.	−	221231.i	−0.562688	−	0.444593i
$191$	−399115.			−0.791616			−0.395808	−	0.918333i	$-0.629535\pi$
$191$	−399115.			−0.791616			−0.395808	+	0.918333i	$0.629535\pi$
$192$	−161590.	−	161590.i	−0.316345	−	0.316345i
$193$	38070.0	+	38070.0i	0.0735680	+	0.0735680i	0.742933	−	0.669365i	$-0.233434\pi$
$193$	38070.0	+	38070.0i	0.0735680	+	0.0735680i	−0.669365	+	0.742933i	$0.733434\pi$
$194$	−360906.			−0.688478
$195$	−127808.	−	1.09012e6i	−0.240697	−	2.05300i
$196$	−128433.			−0.238802
$197$	226766.	−	226766.i	0.416305	−	0.416305i	−0.467623	−	0.883928i	$-0.654889\pi$
$197$	226766.	−	226766.i	0.416305	−	0.416305i	0.883928	+	0.467623i	$0.154889\pi$
$198$	−160206.	+	1.48918e6i	−0.290414	+	2.69950i
$199$			578962.i			1.03638i	0.855267	+	0.518188i	$0.173393\pi$
$199$			578962.i			1.03638i	−0.855267	+	0.518188i	$0.826607\pi$
$200$	−321512.	−	197998.i	−0.568358	−	0.350014i
$201$	1.17661e6			2.05419
$202$	362256.	+	362256.i	0.624651	+	0.624651i
$203$	−387580.	+	387580.i	−0.660118	+	0.660118i
$204$	331123.			0.557075
$205$	1.09701e6	−	128616.i	1.82317	−	0.213751i
$206$		−	309054.i		−	0.507419i
$207$	−343033.	−	343033.i	−0.556429	−	0.556429i
$208$	−629948.	−	629948.i	−1.00959	−	1.00959i
$209$	−236395.	−	293390.i	−0.374346	−	0.464600i
$210$	1.06579e6	−	1.34890e6i	1.66773	−	2.11072i
$211$			715989.i			1.10713i	0.832805	+	0.553567i	$0.186734\pi$
$211$			715989.i			1.10713i	−0.832805	+	0.553567i	$0.813266\pi$
$212$	−258515.	−	258515.i	−0.395044	−	0.395044i
$213$	−1.09163e6	+	1.09163e6i	−1.64864	+	1.64864i
$214$		−	711008.i		−	1.06130i
$215$	−455982.	+	577102.i	−0.672746	+	0.851445i
$216$			1.04019e6i			1.51697i
$217$	249606.	−	249606.i	0.359837	−	0.359837i
$218$	557547.	−	557547.i	0.794585	−	0.794585i
$219$	−993222.			−1.39938
$220$	227861.	+	223554.i	0.317405	+	0.311406i
$221$	−576966.			−0.794638
$222$	997865.	−	997865.i	1.35891	−	1.35891i
$223$	−120748.	+	120748.i	−0.162599	+	0.162599i	−0.783717	−	0.621118i	$-0.786679\pi$
$223$	−120748.	+	120748.i	−0.162599	+	0.162599i	0.621118	+	0.783717i	$0.286679\pi$
$224$		−	773922.i		−	1.03057i
$225$	396770.	+	1.66885e6i	0.522496	+	2.19766i
$226$			158961.i			0.207024i
$227$	181269.	−	181269.i	0.233485	−	0.233485i	−0.580661	−	0.814146i	$-0.697206\pi$
$227$	181269.	−	181269.i	0.233485	−	0.233485i	0.814146	+	0.580661i	$0.197206\pi$
$228$	265828.	+	265828.i	0.338660	+	0.338660i
$229$		−	1.19389e6i		−	1.50444i	−0.658909	−	0.752222i	$-0.728982\pi$
$229$		−	1.19389e6i		−	1.50444i	0.658909	−	0.752222i	$-0.271018\pi$
$230$	−333627.	+	39115.0i	−0.415855	+	0.0487555i
$231$	1.41342e6	−	1.13885e6i	1.74278	−	1.40422i
$232$	−291368.	−	291368.i	−0.355403	−	0.355403i
$233$	81851.1	+	81851.1i	0.0987721	+	0.0987721i	0.754766	−	0.655994i	$-0.227750\pi$
$233$	81851.1	+	81851.1i	0.0987721	+	0.0987721i	−0.655994	+	0.754766i	$0.727750\pi$
$234$			2.60399e6i			3.10885i
$235$	−140978.	+	178426.i	−0.166526	+	0.210760i
$236$	−46763.9			−0.0546551
$237$	−741263.	+	741263.i	−0.857238	+	0.857238i
$238$	−639007.	−	639007.i	−0.731246	−	0.731246i
$239$	420038.			0.475657			0.237829	−	0.971307i	$-0.423564\pi$
$239$	420038.			0.475657			0.237829	+	0.971307i	$0.423564\pi$
$240$	1.57608e6	+	1.24529e6i	1.76624	+	1.39554i
$241$		−	903311.i		−	1.00183i	−0.865496	−	0.500916i	$-0.832997\pi$
$241$		−	903311.i		−	1.00183i	0.865496	−	0.500916i	$-0.167003\pi$
$242$	591885.	+	921268.i	0.649679	+	1.01122i
$243$	687225.	−	687225.i	0.746591	−	0.746591i
$244$	−379405.			−0.407970
$245$	−501146.	+	58755.1i	−0.533395	+	0.0625361i
$246$	−3.78049e6			−3.98300
$247$	−463193.	−	463193.i	−0.483081	−	0.483081i
$248$	187644.	+	187644.i	0.193734	+	0.193734i
$249$	−2.70774e6			−2.76764
$250$	1.07702e6	+	500831.i	1.08986	+	0.506806i
$251$	−840809.			−0.842390			−0.421195	−	0.906970i	$-0.638389\pi$
$251$	−840809.			−0.842390			−0.421195	+	0.906970i	$0.638389\pi$
$252$	−887677.	+	887677.i	−0.880550	+	0.880550i
$253$	−352636.	−	37936.7i	−0.346358	−	0.0372614i
$254$		−	1.05857e6i		−	1.02952i
$255$	1.29204e6	−	151480.i	1.24430	−	0.145883i
$256$	1.16320e6			1.10931
$257$	70122.9	+	70122.9i	0.0662258	+	0.0662258i	0.739444	−	0.673218i	$-0.235089\pi$
$257$	70122.9	+	70122.9i	0.0662258	+	0.0662258i	−0.673218	+	0.739444i	$0.735089\pi$
$258$	1.78009e6	−	1.78009e6i	1.66492	−	1.66492i
$259$	−1.18544e6			−1.09807
$260$	435454.	+	344063.i	0.399493	+	0.315649i
$261$			1.87195e6i			1.70096i
$262$	999384.	+	999384.i	0.899454	+	0.899454i
$263$	678442.	+	678442.i	0.604816	+	0.604816i	0.941587	−	0.336771i	$-0.109335\pi$
$263$	678442.	+	678442.i	0.604816	+	0.604816i	−0.336771	+	0.941587i	$0.609335\pi$
$264$	856142.	+	1.06256e6i	0.756025	+	0.938301i
$265$	−1.12698e6	−	890457.i	−0.985833	−	0.778930i
$266$		−	1.02600e6i		−	0.889086i
$267$	−2.72021e6	−	2.72021e6i	−2.33520	−	2.33520i
$268$	−420679.	+	420679.i	−0.357778	+	0.357778i
$269$			1.06682e6i			0.898900i	0.893305	+	0.449450i	$0.148380\pi$
$269$			1.06682e6i			0.898900i	−0.893305	+	0.449450i	$0.851620\pi$
$270$	−381016.	−	3.24983e6i	−0.318078	−	2.71301i
$271$		−	1.90509e6i		−	1.57577i	−0.615825	−	0.787883i	$-0.711177\pi$
$271$		−	1.90509e6i		−	1.57577i	0.615825	−	0.787883i	$-0.288823\pi$
$272$	746627.	−	746627.i	0.611902	−	0.611902i
$273$	2.23146e6	−	2.23146e6i	1.81210	−	1.81210i
$274$	−1.19758e6			−0.963666
$275$	991382.	+	768066.i	0.790514	+	0.612444i
$276$	353882.			0.279631
$277$	−1.02263e6	+	1.02263e6i	−0.800788	+	0.800788i	−0.983219	−	0.182431i	$-0.941603\pi$
$277$	−1.02263e6	+	1.02263e6i	−0.800788	+	0.800788i	0.182431	+	0.983219i	$0.441603\pi$
$278$	97892.9	−	97892.9i	0.0759695	−	0.0759695i
$279$		−	1.20556e6i		−	0.927210i
$280$	−126415.	−	1.07825e6i	−0.0963618	−	0.821908i
$281$			590173.i			0.445875i	0.974833	+	0.222938i	$0.0715646\pi$
$281$			590173.i			0.445875i	−0.974833	+	0.222938i	$0.928435\pi$
$282$	550361.	−	550361.i	0.412121	−	0.412121i
$283$	−311913.	−	311913.i	−0.231509	−	0.231509i	0.581813	−	0.813322i	$-0.302343\pi$
$283$	−311913.	−	311913.i	−0.231509	−	0.231509i	−0.813322	+	0.581813i	$0.802343\pi$
$284$		−	780595.i		−	0.574288i
$285$	1.15887e6	+	915649.i	0.845127	+	0.667755i
$286$	1.19446e6	+	1.48244e6i	0.863485	+	1.07167i
$287$	2.24556e6	+	2.24556e6i	1.60924	+	1.60924i
$288$	−1.86896e6	−	1.86896e6i	−1.32776	−	1.32776i
$289$			736026.i			0.518380i
$290$	1.01704e6	+	803586.i	0.710138	+	0.561096i
$291$	1.49375e6			1.03406
$292$	355113.	−	355113.i	0.243730	−	0.243730i
$293$	708764.	+	708764.i	0.482317	+	0.482317i	0.905871	−	0.423554i	$-0.139218\pi$
$293$	708764.	+	708764.i	0.482317	+	0.482317i	−0.423554	+	0.905871i	$0.639218\pi$
$294$	1.72703e6			1.16529
$295$	−182472.	+	21393.3i	−0.122079	+	0.0143127i
$296$		−	891166.i		−	0.591193i
$297$	369538.	−	3.43500e6i	0.243091	−	2.25962i
$298$	−1.55301e6	+	1.55301e6i	−1.01306	+	1.01306i
$299$	−616623.			−0.398879
$300$	−1.06547e6	−	656155.i	−0.683502	−	0.420923i
$301$	−2.11470e6			−1.34534
$302$	−40053.9	−	40053.9i	−0.0252713	−	0.0252713i
$303$	−1.49933e6	−	1.49933e6i	−0.938192	−	0.938192i
$304$	1.19880e6			0.743982
$305$	−1.48043e6	+	173568.i	−0.911253	+	0.106837i
$306$	−3.08630e6			−1.88423
$307$	550551.	−	550551.i	0.333390	−	0.333390i	−0.520483	−	0.853872i	$-0.674248\pi$
$307$	550551.	−	550551.i	0.333390	−	0.333390i	0.853872	+	0.520483i	$0.174248\pi$
$308$	−98170.2	+	912529.i	−0.0589662	+	0.548113i
$309$			1.27914e6i			0.762116i
$310$	−654986.	−	517519.i	−0.387104	−	0.305860i
$311$	774805.			0.454246			0.227123	−	0.973866i	$-0.427068\pi$
$311$	774805.			0.454246			0.227123	+	0.973866i	$0.427068\pi$
$312$	1.67753e6	+	1.67753e6i	0.975624	+	0.975624i
$313$	425908.	−	425908.i	0.245728	−	0.245728i	−0.573487	−	0.819215i	$-0.694410\pi$
$313$	425908.	−	425908.i	0.245728	−	0.245728i	0.819215	+	0.573487i	$0.194410\pi$
$314$	1.33758e6			0.765586
$315$	−3.05762e6	+	3.86980e6i	−1.73623	+	2.19741i
$316$		−	530056.i		−	0.298610i
$317$	811586.	+	811586.i	0.453614	+	0.453614i	0.896552	−	0.442938i	$-0.146064\pi$
$317$	811586.	+	811586.i	0.453614	+	0.453614i	−0.442938	+	0.896552i	$0.646064\pi$
$318$	3.47622e6	+	3.47622e6i	1.92770	+	1.92770i
$319$	858667.	+	1.06569e6i	0.472441	+	0.586346i
$320$	450869.	−	52860.5i	0.246136	−	0.0288574i
$321$			2.94277e6i			1.59402i
$322$	−682928.	−	682928.i	−0.367059	−	0.367059i
$323$	548986.	−	548986.i	0.292789	−	0.292789i
$324$			1.54917e6i			0.819853i
$325$	1.85654e6	+	1.14332e6i	0.974979	+	0.600425i
$326$		−	2.28505e6i		−	1.19084i
$327$	−2.30762e6	+	2.30762e6i	−1.19342	+	1.19342i
$328$	−1.68813e6	+	1.68813e6i	−0.866404	+	0.866404i
$329$	−653814.			−0.333016
$330$	−3.06403e6	−	3.00612e6i	−1.54885	−	1.51957i
$331$	2.47139e6			1.23986			0.619928	−	0.784659i	$-0.287162\pi$
$331$	2.47139e6			1.23986			0.619928	+	0.784659i	$0.287162\pi$
$332$	968116.	−	968116.i	0.482039	−	0.482039i
$333$	−2.86274e6	+	2.86274e6i	−1.41472	+	1.41472i
$334$			1.99383e6i			0.977963i
$335$	−1.44903e6	+	1.83393e6i	−0.705450	+	0.892836i
$336$			5.77528e6i			2.79078i
$337$	2.04350e6	−	2.04350e6i	0.980168	−	0.980168i	−0.0196388	−	0.999807i	$-0.506252\pi$
$337$	2.04350e6	−	2.04350e6i	0.980168	−	0.980168i	0.999807	+	0.0196388i	$0.00625161\pi$
$338$	555331.	+	555331.i	0.264399	+	0.264399i
$339$		−	657922.i		−	0.310939i
$340$	−407790.	+	516109.i	−0.191311	+	0.242128i
$341$	−552992.	−	686317.i	−0.257533	−	0.319624i
$342$	−2.47771e6	−	2.47771e6i	−1.14547	−	1.14547i
$343$	884300.	+	884300.i	0.405849	+	0.405849i
$344$		−	1.58975e6i		−	0.724324i
$345$	1.38084e6	−	161892.i	0.624592	−	0.0732282i
$346$	−1.16746e6			−0.524266
$347$	−1.80338e6	+	1.80338e6i	−0.804015	+	0.804015i	−0.983721	−	0.179705i	$-0.942486\pi$
$347$	−1.80338e6	+	1.80338e6i	−0.804015	+	0.804015i	0.179705	+	0.983721i	$0.442486\pi$
$348$	−965577.	−	965577.i	−0.427404	−	0.427404i
$349$	−321051.			−0.141095			−0.0705474	−	0.997508i	$-0.522475\pi$
$349$	−321051.			−0.141095			−0.0705474	+	0.997508i	$0.522475\pi$
$350$	789912.	+	3.32243e6i	0.344674	+	1.44973i
$351$		−	6.00646e6i		−	2.60226i
$352$	−1.92128e6	−	206692.i	−0.826484	−	0.0889135i
$353$	−122286.	+	122286.i	−0.0522323	+	0.0522323i	−0.732740	−	0.680508i	$-0.761759\pi$
$353$	−122286.	+	122286.i	−0.0522323	+	0.0522323i	0.680508	+	0.732740i	$0.261759\pi$
$354$	628829.			0.266701
$355$	−357103.	−	3.04587e6i	−0.150391	−	1.28275i
$356$	1.94515e6			0.813443
$357$	2.64477e6	+	2.64477e6i	1.09829	+	1.09829i
$358$	−3.32207e6	−	3.32207e6i	−1.36994	−	1.36994i
$359$	4.73652e6			1.93965			0.969825	−	0.243802i	$-0.0783948\pi$
$359$	4.73652e6			1.93965			0.969825	+	0.243802i	$0.0783948\pi$
$360$	−2.90916e6	−	2.29860e6i	−1.18307	−	0.934774i
$361$	−1.59464e6			−0.644012
$362$	2.60867e6	−	2.60867e6i	1.04628	−	1.04628i
$363$	−2.44974e6	−	3.81301e6i	−0.975782	−	1.51880i
$364$			1.59565e6i			0.631227i
$365$	1.22319e6	−	1.54810e6i	0.480576	−	0.608229i
$366$	5.10182e6			1.99078
$367$	381643.	+	381643.i	0.147908	+	0.147908i	0.777183	−	0.629275i	$-0.216648\pi$
$367$	381643.	+	381643.i	0.147908	+	0.147908i	−0.629275	+	0.777183i	$0.716648\pi$
$368$	797946.	−	797946.i	0.307152	−	0.307152i
$369$	1.08457e7			4.14660
$370$	326429.	+	2.78424e6i	0.123961	+	1.05731i
$371$		−	4.12966e6i		−	1.55768i
$372$	621844.	+	621844.i	0.232983	+	0.232983i
$373$	1.67208e6	+	1.67208e6i	0.622280	+	0.622280i	0.946114	−	0.323834i	$-0.104972\pi$
$373$	1.67208e6	+	1.67208e6i	0.622280	+	0.622280i	−0.323834	+	0.946114i	$0.604972\pi$
$374$	−1.75701e6	+	1.41569e6i	−0.649525	+	0.523347i
$375$	−4.45764e6	−	2.07288e6i	−1.63692	−	0.761195i
$376$		−	491512.i		−	0.179294i
$377$	1.68247e6	+	1.68247e6i	0.609670	+	0.609670i
$378$	6.65234e6	−	6.65234e6i	2.39467	−	2.39467i
$379$		−	3.50188e6i		−	1.25229i	−0.779708	−	0.626143i	$-0.784632\pi$
$379$		−	3.50188e6i		−	1.25229i	0.779708	−	0.626143i	$-0.215368\pi$
$380$	−741715.	+	86959.8i	−0.263498	+	0.0308930i
$381$			4.38130e6i			1.54629i
$382$	−1.91885e6	+	1.91885e6i	−0.672793	+	0.672793i
$383$	1.82068e6	−	1.82068e6i	0.634217	−	0.634217i	−0.314906	−	0.949123i	$-0.601973\pi$
$383$	1.82068e6	−	1.82068e6i	0.634217	−	0.634217i	0.949123	+	0.314906i	$0.101973\pi$
$384$	−5.88986e6			−2.03834
$385$	34400.3	+	3.60559e6i	0.0118280	+	1.23972i
$386$	366062.			0.125051
$387$	−5.10683e6	+	5.10683e6i	−1.73330	+	1.73330i
$388$	−534068.	+	534068.i	−0.180102	+	0.180102i
$389$		−	5.49459e6i		−	1.84103i	−0.390707	−	0.920515i	$-0.627769\pi$
$389$		−	5.49459e6i		−	1.84103i	0.390707	−	0.920515i	$-0.372231\pi$
$390$	−5.85552e6	−	4.62658e6i	−1.94941	−	1.54028i
$391$		−	730833.i		−	0.241756i
$392$	771183.	−	771183.i	0.253479	−	0.253479i
$393$	−4.13633e6	−	4.13633e6i	−1.35093	−	1.35093i
$394$		−	2.18047e6i		−	0.707635i
$395$	−242488.	−	2.06827e6i	−0.0781982	−	0.666984i
$396$	1.96661e6	+	2.44076e6i	0.630203	+	0.782144i
$397$	−386841.	−	386841.i	−0.123184	−	0.123184i	0.642827	−	0.766011i	$-0.277761\pi$
$397$	−386841.	−	386841.i	−0.123184	−	0.123184i	−0.766011	+	0.642827i	$0.777761\pi$
$398$	2.78351e6	+	2.78351e6i	0.880815	+	0.880815i
$399$			4.24649e6i			1.33536i
$400$	−3.88199e6	+	922948.i	−1.21312	+	0.288421i
$401$	−5.83802e6			−1.81303			−0.906514	−	0.422175i	$-0.861267\pi$
$401$	−5.83802e6			−1.81303			−0.906514	+	0.422175i	$0.861267\pi$
$402$	5.65683e6	−	5.65683e6i	1.74585	−	1.74585i
$403$	−1.08353e6	−	1.08353e6i	−0.332338	−	0.332338i
$404$	1.07213e6			0.326810
$405$	708706.	+	6.04484e6i	0.214698	+	1.83125i
$406$			3.72678e6i			1.12207i
$407$	−316596.	+	2.94288e6i	−0.0947370	+	0.880616i
$408$	−1.98824e6	+	1.98824e6i	−0.591313	+	0.591313i
$409$	−3.91524e6			−1.15731			−0.578656	−	0.815572i	$-0.696423\pi$
$409$	−3.91524e6			−1.15731			−0.578656	+	0.815572i	$0.696423\pi$
$410$	4.65582e6	−	5.89252e6i	1.36784	−	1.73118i
$411$	4.95662e6			1.44737
$412$	−457338.	−	457338.i	−0.132738	−	0.132738i
$413$	−373516.	−	373516.i	−0.107754	−	0.107754i
$414$	−3.29843e6			−0.945817
$415$	3.33469e6	−	4.22047e6i	0.950462	−	1.20293i
$416$	−3.35957e6			−0.951810
$417$	−405167.	+	405167.i	−0.114102	+	0.114102i
$418$	−2.54708e6	−	274016.i	−0.713020	−	0.0767069i
$419$			4.87591e6i			1.35681i	0.734686	+	0.678407i	$0.237329\pi$
$419$			4.87591e6i			1.35681i	−0.734686	+	0.678407i	$0.762671\pi$
$420$	−418934.	−	3.57325e6i	−0.115884	−	0.988418i
$421$	−2.23285e6			−0.613981			−0.306991	−	0.951713i	$-0.599322\pi$
$421$	−2.23285e6			−0.613981			−0.306991	+	0.951713i	$0.599322\pi$
$422$	3.44230e6	+	3.44230e6i	0.940952	+	0.940952i
$423$	−1.57891e6	+	1.57891e6i	−0.429048	+	0.429048i
$424$	3.10452e6			0.838648
$425$	−1.35508e6	+	2.20041e6i	−0.363910	+	0.590922i
$426$			1.04966e7i			2.80236i
$427$	−3.03041e6	−	3.03041e6i	−0.804326	−	0.804326i
$428$	−1.05215e6	−	1.05215e6i	−0.277631	−	0.277631i
$429$	−4.94370e6	−	6.13562e6i	−1.29691	−	1.60959i
$430$	582317.	+	4.96681e6i	0.151876	+	1.29541i
$431$		−	2.27903e6i		−	0.590959i	−0.955349	−	0.295480i	$-0.904521\pi$
$431$		−	2.27903e6i		−	0.590959i	0.955349	−	0.295480i	$-0.0954794\pi$
$432$	7.77272e6	+	7.77272e6i	2.00384	+	2.00384i
$433$	5.30458e6	−	5.30458e6i	1.35966	−	1.35966i	0.485331	−	0.874330i	$-0.338699\pi$
$433$	5.30458e6	−	5.30458e6i	1.35966	−	1.35966i	0.874330	−	0.485331i	$-0.161301\pi$
$434$		−	2.40009e6i		−	0.611651i
$435$	−4.20940e6	−	3.32594e6i	−1.06659	−	0.842736i
$436$		−	1.65011e6i		−	0.415717i
$437$	586720.	−	586720.i	0.146970	−	0.146970i
$438$	−4.77517e6	+	4.77517e6i	−1.18933	+	1.18933i
$439$	632367.			0.156606			0.0783029	−	0.996930i	$-0.475050\pi$
$439$	632367.			0.156606			0.0783029	+	0.996930i	$0.475050\pi$
$440$	−2.71054e6	+	25860.8i	−0.667458	+	0.00636812i
$441$	−4.95462e6			−1.21315
$442$	−2.77391e6	+	2.77391e6i	−0.675362	+	0.675362i
$443$	1.34502e6	−	1.34502e6i	0.325627	−	0.325627i	−0.525294	−	0.850921i	$-0.676045\pi$
$443$	1.34502e6	−	1.34502e6i	0.325627	−	0.325627i	0.850921	+	0.525294i	$0.176045\pi$
$444$		−	2.95328e6i		−	0.710962i
$445$	7.58993e6	−	889856.i	1.81693	−	0.213020i
$446$			1.16105e6i			0.276386i
$447$	6.42771e6	−	6.42771e6i	1.52155	−	1.52155i
$448$	922918.	+	922918.i	0.217254	+	0.217254i
$449$			3.71518e6i			0.869689i	0.900506	+	0.434845i	$0.143197\pi$
$449$			3.71518e6i			0.869689i	−0.900506	+	0.434845i	$0.856803\pi$
$450$	9.93098e6	+	6.11583e6i	2.31186	+	1.42372i
$451$	6.17440e6	−	4.97495e6i	1.42940	−	1.15172i
$452$	235231.	+	235231.i	0.0541562	+	0.0541562i
$453$	165778.	+	165778.i	0.0379561	+	0.0379561i
$454$		−	1.74300e6i		−	0.396878i
$455$	729972.	+	6.22623e6i	0.165302	+	1.40993i
$456$	−3.19235e6			−0.718950
$457$	−5.51258e6	+	5.51258e6i	−1.23471	+	1.23471i	−0.272574	+	0.962135i	$0.587875\pi$
$457$	−5.51258e6	+	5.51258e6i	−1.23471	+	1.23471i	−0.962135	+	0.272574i	$0.912125\pi$
$458$	−5.73994e6	−	5.73994e6i	−1.27863	−	1.27863i
$459$	7.11898e6			1.57720
$460$	−435819.	+	551583.i	−0.0960310	+	0.121539i
$461$		−	1.76799e6i		−	0.387461i	−0.981055	−	0.193730i	$-0.937941\pi$
$461$		−	1.76799e6i		−	0.387461i	0.981055	−	0.193730i	$-0.0620587\pi$
$462$	1.32009e6	−	1.22707e7i	0.287738	−	2.67463i
$463$	3.74476e6	−	3.74476e6i	0.811843	−	0.811843i	−0.173067	−	0.984910i	$-0.555368\pi$
$463$	3.74476e6	−	3.74476e6i	0.811843	−	0.811843i	0.984910	+	0.173067i	$0.0553678\pi$
$464$	−4.35444e6			−0.938938
$465$	2.71090e6	+	2.14195e6i	0.581409	+	0.459385i
$466$	787040.			0.167893
$467$	1.12610e6	+	1.12610e6i	0.238938	+	0.238938i	0.816410	−	0.577472i	$-0.195961\pi$
$467$	1.12610e6	+	1.12610e6i	0.238938	+	0.238938i	−0.577472	+	0.816410i	$0.695961\pi$
$468$	3.85338e6	+	3.85338e6i	0.813256	+	0.813256i
$469$	−6.72016e6			−1.41074
$470$	180038.	+	1.53562e6i	0.0375941	+	0.320655i
$471$	−5.53606e6			−1.14987
$472$	280795.	−	280795.i	0.0580143	−	0.0580143i
$473$	−564776.	+	5.24980e6i	−0.116071	+	1.07892i
$474$			7.12762e6i			1.45713i
$475$	−2.85438e6	+	678632.i	−0.580467	+	0.138007i
$476$	−1.89120e6			−0.382579
$477$	−9.97280e6	−	9.97280e6i	−2.00688	−	2.00688i
$478$	2.01944e6	−	2.01944e6i	0.404261	−	0.404261i
$479$	7.74813e6			1.54297			0.771486	−	0.636247i	$-0.219514\pi$
$479$	7.74813e6			1.54297			0.771486	+	0.636247i	$0.219514\pi$
$480$	7.52330e6	−	882044.i	1.49041	−	0.174738i
$481$			5.14594e6i			1.01415i
$482$	−4.34290e6	−	4.34290e6i	−0.851456	−	0.851456i
$483$	2.82656e6	+	2.82656e6i	0.551302	+	0.551302i
$484$	2.23916e6	+	487420.i	0.434482	+	0.0945780i
$485$	−1.83961e6	+	2.32825e6i	−0.355116	+	0.449444i
$486$		−	6.60801e6i		−	1.26905i
$487$	−2.34690e6	−	2.34690e6i	−0.448407	−	0.448407i	0.446418	−	0.894825i	$-0.352700\pi$
$487$	−2.34690e6	−	2.34690e6i	−0.448407	−	0.448407i	−0.894825	+	0.446418i	$0.852700\pi$
$488$	2.27815e6	−	2.27815e6i	0.433044	−	0.433044i
$489$			9.45754e6i			1.78857i
$490$	−2.12691e6	+	2.69187e6i	−0.400183	+	0.506481i
$491$			9.77955e6i			1.83069i	0.402670	+	0.915345i	$0.368082\pi$
$491$			9.77955e6i			1.83069i	−0.402670	+	0.915345i	$0.631918\pi$
$492$	−5.59437e6	+	5.59437e6i	−1.04193	+	1.04193i
$493$	−1.99410e6	+	1.99410e6i	−0.369513	+	0.369513i
$494$	−4.45384e6			−0.821140
$495$	8.79027e6	+	8.62413e6i	1.61246	+	1.58198i
$496$	2.80431e6			0.511826
$497$	6.23483e6	−	6.23483e6i	1.13223	−	1.13223i
$498$	−1.30182e7	+	1.30182e7i	−2.35221	+	2.35221i
$499$			1.31910e6i			0.237151i	0.992945	+	0.118576i	$0.0378328\pi$
$499$			1.31910e6i			0.237151i	−0.992945	+	0.118576i	$0.962167\pi$
$500$	2.33490e6	−	852638.i	0.417679	−	0.152525i
$501$		−	8.25223e6i		−	1.46885i
$502$	−4.04240e6	+	4.04240e6i	−0.715946	+	0.715946i
$503$	1.89636e6	+	1.89636e6i	0.334196	+	0.334196i	0.854178	−	0.519981i	$-0.174061\pi$
$503$	1.89636e6	+	1.89636e6i	0.334196	+	0.334196i	−0.519981	+	0.854178i	$0.674061\pi$
$504$		−	1.06602e7i		−	1.86934i
$505$	4.18344e6	−	490474.i	0.729971	−	0.0855829i
$506$	−1.87778e6	+	1.51300e6i	−0.326038	+	0.262701i
$507$	−2.29845e6	−	2.29845e6i	−0.397113	−	0.397113i
$508$	−1.56647e6	−	1.56647e6i	−0.269317	−	0.269317i
$509$		−	6.88984e6i		−	1.17873i	−0.807867	−	0.589365i	$-0.799378\pi$
$509$		−	6.88984e6i		−	1.17873i	0.807867	−	0.589365i	$-0.200622\pi$
$510$	5.48351e6	−	6.94007e6i	0.933541	−	1.18151i
$511$	5.67277e6			0.961044
$512$	856493.	−	856493.i	0.144394	−	0.144394i
$513$	5.71518e6	+	5.71518e6i	0.958819	+	0.958819i
$514$	674267.			0.112570
$515$	−1.99375e6	−	1.57531e6i	−0.331247	−	0.261726i
$516$		−	5.26835e6i		−	0.871064i
$517$	−174615.	+	1.62311e6i	−0.0287313	+	0.267068i
$518$	−5.69929e6	+	5.69929e6i	−0.933246	+	0.933246i
$519$	4.83198e6			0.787420
$520$	−4.68064e6	+	548765.i	−0.759096	+	0.0889976i
$521$	−2.98298e6			−0.481456			−0.240728	−	0.970593i	$-0.577386\pi$
$521$	−2.98298e6			−0.481456			−0.240728	+	0.970593i	$0.577386\pi$
$522$	8.99988e6	+	8.99988e6i	1.44564	+	1.44564i
$523$	2.79659e6	+	2.79659e6i	0.447069	+	0.447069i	0.894379	−	0.447310i	$-0.147618\pi$
$523$	2.79659e6	+	2.79659e6i	0.447069	+	0.447069i	−0.447310	+	0.894379i	$0.647618\pi$
$524$	2.95777e6			0.470583
$525$	−3.26935e6	−	1.37511e7i	−0.517682	−	2.17741i
$526$	6.52357e6			1.02807
$527$	1.28423e6	−	1.28423e6i	0.201426	−	0.201426i
$528$	1.43373e7	+	1.54241e6i	2.23812	+	0.240777i
$529$			5.65528e6i			0.878648i
$530$	−9.69937e6	+	1.13717e6i	−1.49987	+	0.175847i
$531$	−1.80402e6			−0.277655
$532$	−1.51828e6	−	1.51828e6i	−0.232579	−	0.232579i
$533$	9.74792e6	−	9.74792e6i	1.48626	−	1.48626i
$534$	−2.61562e7			−3.96937
$535$	−4.58680e6	−	3.62414e6i	−0.692828	−	0.547419i
$536$		−	5.05196e6i		−	0.759535i
$537$	1.37496e7	+	1.37496e7i	2.05757	+	2.05757i
$538$	5.12902e6	+	5.12902e6i	0.763974	+	0.763974i
$539$	−2.82063e6	+	2.27269e6i	−0.418191	+	0.336953i
$540$	−5.37292e6	−	4.24527e6i	−0.792914	−	0.626500i
$541$			2.47213e6i			0.363143i	0.983378	+	0.181571i	$0.0581183\pi$
$541$			2.47213e6i			0.363143i	−0.983378	+	0.181571i	$0.941882\pi$
$542$	−9.15919e6	−	9.15919e6i	−1.33924	−	1.33924i
$543$	−1.07970e7	+	1.07970e7i	−1.57145	+	1.57145i
$544$		−	3.98183e6i		−	0.576880i
$545$	−754886.	−	6.43872e6i	−0.108865	−	0.928557i
$546$		−	2.14566e7i		−	3.08021i
$547$	971370.	−	971370.i	0.138809	−	0.138809i	−0.634288	−	0.773097i	$-0.718707\pi$
$547$	971370.	−	971370.i	0.138809	−	0.138809i	0.773097	+	0.634288i	$0.218707\pi$
$548$	−1.77217e6	+	1.77217e6i	−0.252089	+	0.252089i
$549$	−1.46364e7			−2.07254
$550$	8.45899e6	−	1.07365e6i	1.19237	−	0.151341i
$551$	−3.20177e6			−0.449273
$552$	−2.12490e6	+	2.12490e6i	−0.296818	+	0.296818i
$553$	4.23371e6	−	4.23371e6i	0.588720	−	0.588720i
$554$			9.83307e6i			1.36118i
$555$	−1.35105e6	−	1.15236e7i	−0.186183	−	1.58803i
$556$		−	289723.i		−	0.0397463i
$557$	−7.14860e6	+	7.14860e6i	−0.976300	+	0.976300i	−0.999726	−	0.0234260i	$-0.992543\pi$
$557$	−7.14860e6	+	7.14860e6i	−0.976300	+	0.976300i	0.0234260	+	0.999726i	$0.492543\pi$
$558$	−5.79603e6	−	5.79603e6i	−0.788034	−	0.788034i
$559$			9.17984e6i			1.24253i
$560$	−9.00173e6	−	7.11248e6i	−1.21299	−	0.958409i
$561$	7.27206e6	−	5.85938e6i	0.975552	−	0.786039i
$562$	2.83741e6	+	2.83741e6i	0.378949	+	0.378949i
$563$	980173.	+	980173.i	0.130326	+	0.130326i	0.769261	−	0.638935i	$-0.220625\pi$
$563$	980173.	+	980173.i	0.130326	+	0.130326i	−0.638935	+	0.769261i	$0.720625\pi$
$564$		−	1.62885e6i		−	0.215617i
$565$	1.02548e6	+	810255.i	0.135147	+	0.106783i
$566$	−2.99920e6			−0.393518
$567$	−1.23737e7	+	1.23737e7i	−1.61637	+	1.61637i
$568$	4.68711e6	+	4.68711e6i	0.609585	+	0.609585i
$569$	6.01913e6			0.779386			0.389693	−	0.920945i	$-0.372581\pi$
$569$	6.01913e6			0.779386			0.389693	+	0.920945i	$0.372581\pi$
$570$	9.97377e6	−	1.16934e6i	1.28580	−	0.150749i
$571$			2.55442e6i			0.327870i	0.986471	+	0.163935i	$0.0524188\pi$
$571$			2.55442e6i			0.327870i	−0.986471	+	0.163935i	$0.947581\pi$
$572$	3.96126e6	+	426154.i	0.506224	+	0.0544598i
$573$	7.94187e6	−	7.94187e6i	1.01050	−	1.01050i
$574$	2.15922e7			2.73538
$575$	−1.44822e6	+	2.35165e6i	−0.182670	+	0.296622i
$576$	4.45755e6			0.559809
$577$	−9.05944e6	−	9.05944e6i	−1.13282	−	1.13282i	−0.989706	−	0.143117i	$-0.954287\pi$
$577$	−9.05944e6	−	9.05944e6i	−1.13282	−	1.13282i	−0.143117	−	0.989706i	$-0.545713\pi$
$578$	3.53863e6	+	3.53863e6i	0.440571	+	0.440571i
$579$	−1.51509e6			−0.187820
$580$	2.69416e6	−	315867.i	0.332547	−	0.0389883i
$581$	1.54652e7			1.90071
$582$	7.18157e6	−	7.18157e6i	0.878844	−	0.878844i
$583$	−1.02520e7	−	1.10291e6i	−1.24921	−	0.134391i
$584$			4.26457e6i			0.517420i
$585$	1.67987e7	+	1.32730e7i	2.02948	+	1.60354i
$586$	6.81513e6			0.819842
$587$	−6.37807e6	−	6.37807e6i	−0.764001	−	0.764001i	0.213042	−	0.977043i	$-0.431663\pi$
$587$	−6.37807e6	−	6.37807e6i	−0.764001	−	0.764001i	−0.977043	+	0.213042i	$0.931663\pi$
$588$	2.55566e6	−	2.55566e6i	0.304831	−	0.304831i
$589$	2.06198e6			0.244904
$590$	−774427.	+	980135.i	−0.0915905	+	0.115919i
$591$			9.02469e6i			1.06283i
$592$	−6.65915e6	−	6.65915e6i	−0.780935	−	0.780935i
$593$	−8.49917e6	−	8.49917e6i	−0.992522	−	0.992522i	0.00745055	−	0.999972i	$-0.497628\pi$
$593$	−8.49917e6	−	8.49917e6i	−0.992522	−	0.992522i	−0.999972	+	0.00745055i	$0.997628\pi$
$594$	−1.47380e7	−	1.82913e7i	−1.71385	−	2.12705i
$595$	−7.37945e6	+	865178.i	−0.854538	+	0.100187i
$596$			4.59628e6i			0.530018i
$597$	−1.15206e7	−	1.15206e7i	−1.32294	−	1.32294i
$598$	−2.96457e6	+	2.96457e6i	−0.339007	+	0.339007i
$599$		−	3.36901e6i		−	0.383651i	−0.981429	−	0.191825i	$-0.938559\pi$
$599$		−	3.36901e6i		−	0.383651i	0.981429	−	0.191825i	$-0.0614407\pi$
$600$	1.03376e7	−	2.45777e6i	1.17230	−	0.278717i
$601$		−	6.41669e6i		−	0.724644i	−0.932053	−	0.362322i	$-0.881984\pi$
$601$		−	6.41669e6i		−	0.724644i	0.932053	−	0.362322i	$-0.118016\pi$
$602$	−1.01670e7	+	1.01670e7i	−1.14340	+	1.14340i
$603$	−1.62287e7	+	1.62287e7i	−1.81756	+	1.81756i
$604$	−118543.			−0.0132216
$605$	8.96015e6	+	877549.i	0.995238	+	0.0974726i
$606$	−1.44169e7			−1.59474
$607$	5.47848e6	−	5.47848e6i	0.603515	−	0.603515i	−0.337728	−	0.941244i	$-0.609659\pi$
$607$	5.47848e6	−	5.47848e6i	0.603515	−	0.603515i	0.941244	+	0.337728i	$0.109659\pi$
$608$	3.19665e6	−	3.19665e6i	0.350700	−	0.350700i
$609$		−	1.54247e7i		−	1.68528i
$610$	−6.28308e6	+	7.95203e6i	−0.683672	+	0.865273i
$611$			2.83819e6i			0.307566i
$612$	−4.56710e6	+	4.56710e6i	−0.492904	+	0.492904i
$613$	−6.14742e6	−	6.14742e6i	−0.660757	−	0.660757i	0.294802	−	0.955558i	$-0.404746\pi$
$613$	−6.14742e6	−	6.14742e6i	−0.660757	−	0.660757i	−0.955558	+	0.294802i	$0.904746\pi$
$614$		−	5.29383e6i		−	0.566695i
$615$	−1.92699e7	+	2.43884e7i	−2.05443	+	2.60014i
$616$	−4.88984e6	−	6.06877e6i	−0.519210	−	0.644391i
$617$	4.50167e6	+	4.50167e6i	0.476059	+	0.476059i	0.903869	−	0.427810i	$-0.140715\pi$
$617$	4.50167e6	+	4.50167e6i	0.476059	+	0.476059i	−0.427810	+	0.903869i	$0.640715\pi$
$618$	6.14978e6	+	6.14978e6i	0.647722	+	0.647722i
$619$			1.02925e7i			1.07968i	0.841769	+	0.539838i	$0.181514\pi$
$619$			1.02925e7i			1.07968i	−0.841769	+	0.539838i	$0.818486\pi$
$620$	−1.73507e6	+	203422.i	−0.181275	+	0.0212530i
$621$	7.60829e6			0.791696
$622$	3.72507e6	−	3.72507e6i	0.386063	−	0.386063i
$623$	1.55364e7	+	1.55364e7i	1.60373	+	1.60373i
$624$	2.50703e7			2.57750
$625$	8.72068e6	−	4.39514e6i	0.892997	−	0.450062i
$626$		−	4.09532e6i		−	0.417688i
$627$	1.05420e7	+	1.13412e6i	1.07092	+	0.115210i
$628$	1.97934e6	−	1.97934e6i	0.200273	−	0.200273i
$629$	−6.09908e6			−0.614663
$630$	3.90476e6	+	3.33053e7i	0.391962	+	3.34320i
$631$	−7.72095e6			−0.771964			−0.385982	−	0.922506i	$-0.626137\pi$
$631$	−7.72095e6			−0.771964			−0.385982	+	0.922506i	$0.626137\pi$
$632$	3.18274e6	+	3.18274e6i	0.316963	+	0.316963i
$633$	−1.42472e7	−	1.42472e7i	−1.41326	−	1.41326i
$634$	7.80381e6			0.771052
$635$	−6.82897e6	−	5.39573e6i	−0.672080	−	0.531026i
$636$	1.02882e7			1.00855
$637$	−4.45312e6	+	4.45312e6i	−0.434826	+	0.434826i
$638$	9.25183e6	+	995316.i	0.899863	+	0.0968076i
$639$		−	3.01132e7i		−	2.91746i
$640$	7.25358e6	−	9.18031e6i	0.700007	−	0.885947i
$641$	−1.68566e7			−1.62041			−0.810207	−	0.586144i	$-0.800645\pi$
$641$	−1.68566e7			−1.62041			−0.810207	+	0.586144i	$0.800645\pi$
$642$	1.41481e7	+	1.41481e7i	1.35476	+	1.35476i
$643$	557526.	−	557526.i	0.0531787	−	0.0531787i	−0.680017	−	0.733196i	$-0.738028\pi$
$643$	557526.	−	557526.i	0.0531787	−	0.0531787i	0.733196	+	0.680017i	$0.238028\pi$
$644$	−2.02119e6			−0.192040
$645$	−2.41014e6	−	2.05570e7i	−0.228109	−	1.94563i
$646$		−	5.27878e6i		−	0.497682i
$647$	−3.01057e6	−	3.01057e6i	−0.282741	−	0.282741i	0.551460	−	0.834201i	$-0.314071\pi$
$647$	−3.01057e6	−	3.01057e6i	−0.282741	−	0.282741i	−0.834201	+	0.551460i	$0.814071\pi$
$648$	−9.30203e6	−	9.30203e6i	−0.870243	−	0.870243i
$649$	−1.02702e6	+	827509.i	−0.0957122	+	0.0771190i
$650$	1.44226e7	−	3.42898e6i	1.33893	−	0.318333i
$651$			9.93369e6i			0.918667i
$652$	−3.38141e6	−	3.38141e6i	−0.311515	−	0.311515i
$653$	−4.69643e6	+	4.69643e6i	−0.431008	+	0.431008i	−0.888971	−	0.457963i	$-0.848579\pi$
$653$	−4.69643e6	+	4.69643e6i	−0.431008	+	0.431008i	0.457963	+	0.888971i	$0.348579\pi$
$654$			2.21889e7i			2.02858i
$655$	1.15412e7	−	1.35311e6i	1.05111	−	0.123234i
$656$			2.52288e7i			2.28895i
$657$	1.36993e7	−	1.36993e7i	1.23818	−	1.23818i
$658$	−3.14338e6	+	3.14338e6i	−0.283030	+	0.283030i
$659$	9.81111e6			0.880045			0.440022	−	0.897987i	$-0.354970\pi$
$659$	9.81111e6			0.880045			0.440022	+	0.897987i	$0.354970\pi$
$660$	−8.98259e6	+	85701.5i	−0.802678	+	0.00765823i
$661$	1.82322e6			0.162306			0.0811532	−	0.996702i	$-0.474140\pi$
$661$	1.82322e6			0.162306			0.0811532	+	0.996702i	$0.474140\pi$
$662$	1.18818e7	−	1.18818e7i	1.05375	−	1.05375i
$663$	1.14809e7	−	1.14809e7i	1.01436	−	1.01436i
$664$			1.16262e7i			1.02333i
$665$	−6.61886e6	−	5.22972e6i	−0.580402	−	0.458589i
$666$			2.75267e7i			2.40474i
$667$	−2.13116e6	+	2.13116e6i	−0.185482	+	0.185482i
$668$	2.95047e6	+	2.95047e6i	0.255829	+	0.255829i
$669$		−	4.80546e6i		−	0.415116i
$670$	1.85051e6	+	1.57837e7i	0.159259	+	1.35838i
$671$	−8.33242e6	+	6.71375e6i	−0.714439	+	0.575650i
$672$	1.54000e7	+	1.54000e7i	1.31552	+	1.31552i
$673$	−1.21965e7	−	1.21965e7i	−1.03800	−	1.03800i	−0.999249	−	0.0387530i	$-0.987661\pi$
$673$	−1.21965e7	−	1.21965e7i	−1.03800	−	1.03800i	−0.0387530	−	0.999249i	$-0.512339\pi$
$674$		−	1.96493e7i		−	1.66609i
$675$	−2.29072e7	−	1.41070e7i	−1.93514	−	1.19172i
$676$	1.64356e6			0.138330
$677$	−2.72593e6	+	2.72593e6i	−0.228583	+	0.228583i	−0.812100	−	0.583518i	$-0.801676\pi$
$677$	−2.72593e6	+	2.72593e6i	−0.228583	+	0.228583i	0.583518	+	0.812100i	$0.301676\pi$
$678$	−3.16313e6	−	3.16313e6i	−0.264267	−	0.264267i
$679$	−8.53151e6			−0.710153
$680$	−650407.	−	5.54758e6i	−0.0539403	−	0.460078i
$681$			7.21404e6i			0.596089i
$682$	−5.95830e6	−	640996.i	−0.490525	−	0.0527709i
$683$	−1.04556e7	+	1.04556e7i	−0.857624	+	0.857624i	−0.991058	−	0.133434i	$-0.957400\pi$
$683$	−1.04556e7	+	1.04556e7i	−0.857624	+	0.857624i	0.133434	+	0.991058i	$0.457400\pi$
$684$	−7.33303e6			−0.599298
$685$	−6.10426e6	+	7.72571e6i	−0.497058	+	0.629089i
$686$	8.50300e6			0.689861
$687$	2.37569e7	+	2.37569e7i	1.92043	+	1.92043i
$688$	−1.18793e7	−	1.18793e7i	−0.956794	−	0.956794i
$689$	−1.79267e7			−1.43864
$690$	5.86042e6	−	7.41709e6i	0.468604	−	0.593077i
$691$	−8.82023e6			−0.702724			−0.351362	−	0.936240i	$-0.614281\pi$
$691$	−8.82023e6			−0.702724			−0.351362	+	0.936240i	$0.614281\pi$
$692$	−1.72761e6	+	1.72761e6i	−0.137145	+	0.137145i
$693$	−3.78714e6	+	3.52029e7i	−0.299556	+	2.78449i
$694$			1.73405e7i			1.36666i
$695$	−132541.	−	1.13050e6i	−0.0104085	−	0.0887784i
$696$	1.15957e7			0.907347
$697$	1.15534e7	+	1.15534e7i	0.900801	+	0.900801i
$698$	−1.54354e6	+	1.54354e6i	−0.119916	+	0.119916i
$699$	−3.25746e6			−0.252166
$700$	6.08544e6	+	3.74762e6i	0.469404	+	0.289075i
$701$			2.17775e7i			1.67383i	0.547330	+	0.836917i	$0.315644\pi$
$701$			2.17775e7i			1.67383i	−0.547330	+	0.836917i	$0.684356\pi$
$702$	−2.88776e7	−	2.88776e7i	−2.21166	−	2.21166i
$703$	−4.89640e6	−	4.89640e6i	−0.373670	−	0.373670i
$704$	2.53766e6	−	2.04469e6i	0.192975	−	0.155487i
$705$	−745156.	−	6.35573e6i	−0.0564644	−	0.481607i
$706$			1.17584e6i			0.0887844i
$707$	8.56342e6	+	8.56342e6i	0.644316	+	0.644316i
$708$	930540.	−	930540.i	0.0697673	−	0.0697673i
$709$			755557.i			0.0564484i	0.999602	+	0.0282242i	$0.00898523\pi$
$709$			755557.i			0.0564484i	−0.999602	+	0.0282242i	$0.991015\pi$
$710$	−1.63607e7	−	1.29269e7i	−1.21802	−	0.962387i
$711$		−	2.04481e7i		−	1.51698i
$712$	−1.16797e7	+	1.16797e7i	−0.863438	+	0.863438i
$713$	1.37249e6	−	1.37249e6i	0.101108	−	0.101108i
$714$	2.54308e7			1.86687
$715$	1.56517e7	−	149331.i	1.14498	−	0.0109241i
$716$	−9.83198e6			−0.716735
$717$	−8.35822e6	+	8.35822e6i	−0.607178	+	0.607178i
$718$	2.27720e7	−	2.27720e7i	1.64851	−	1.64851i
$719$			7.40823e6i			0.534432i	0.963637	+	0.267216i	$0.0861037\pi$
$719$			7.40823e6i			0.534432i	−0.963637	+	0.267216i	$0.913896\pi$
$720$	−3.89145e7	+	4.56240e6i	−2.79757	+	0.327991i
$721$		−	7.30578e6i		−	0.523393i
$722$	−7.66662e6	+	7.66662e6i	−0.547345	+	0.547345i
$723$	1.79747e7	+	1.79747e7i	1.27884	+	1.27884i
$724$		−	7.72060e6i		−	0.547400i
$725$	1.03681e7	−	2.46502e6i	0.732576	−	0.174171i
$726$	−3.01098e7	−	6.55430e6i	−2.12015	−	0.461514i
$727$	6.15038e6	+	6.15038e6i	0.431585	+	0.431585i	0.889167	−	0.457582i	$-0.151285\pi$
$727$	6.15038e6	+	6.15038e6i	0.431585	+	0.431585i	−0.457582	+	0.889167i	$0.651285\pi$
$728$	−9.58116e6	−	9.58116e6i	−0.670023	−	0.670023i
$729$			893389.i			0.0622618i
$730$	−1.56209e6	−	1.33237e7i	−0.108492	−	0.925374i
$731$	−1.08801e7			−0.753080
$732$	7.54966e6	−	7.54966e6i	0.520775	−	0.520775i
$733$	−7.07583e6	−	7.07583e6i	−0.486427	−	0.486427i	0.420750	−	0.907177i	$-0.361767\pi$
$733$	−7.07583e6	−	7.07583e6i	−0.486427	−	0.486427i	−0.907177	+	0.420750i	$0.861767\pi$
$734$	3.66969e6			0.251414
$735$	8.80300e6	−	1.11413e7i	0.601053	−	0.760707i
$736$		−	4.25552e6i		−	0.289573i
$737$	−1.79476e6	+	1.66830e7i	−0.121713	+	1.13137i
$738$	5.21435e7	−	5.21435e7i	3.52419	−	3.52419i
$739$	3.11620e6			0.209901			0.104951	−	0.994477i	$-0.466532\pi$
$739$	3.11620e6			0.209901			0.104951	+	0.994477i	$0.466532\pi$
$740$	4.60317e6	+	3.63707e6i	0.309014	+	0.244159i
$741$	1.84339e7			1.23331
$742$	−1.98544e7	−	1.98544e7i	−1.32387	−	1.32387i
$743$	1.16477e7	+	1.16477e7i	0.774049	+	0.774049i	0.978812	−	0.204763i	$-0.0656423\pi$
$743$	1.16477e7	+	1.16477e7i	0.774049	+	0.774049i	−0.204763	+	0.978812i	$0.565642\pi$
$744$	−7.46776e6			−0.494605
$745$	2.10268e6	+	1.79346e7i	0.138798	+	1.18386i
$746$	1.60779e7			1.05775
$747$	3.73473e7	−	3.73473e7i	2.44883	−	2.44883i
$748$	−505086.	+	4.69496e6i	−0.0330074	+	0.306816i
$749$		−	1.68076e7i		−	1.09472i
$750$	−3.13971e7	+	1.14653e7i	−2.03815	+	0.744276i
$751$	2.04492e7			1.32305			0.661527	−	0.749921i	$-0.269909\pi$
$751$	2.04492e7			1.32305			0.661527	+	0.749921i	$0.269909\pi$
$752$	−3.67278e6	−	3.67278e6i	−0.236837	−	0.236837i
$753$	1.67310e7	−	1.67310e7i	1.07531	−	1.07531i
$754$	1.61778e7			1.03632
$755$	−462554.	+	54230.6i	−0.0295322	+	0.00346240i
$756$		−	1.96882e7i		−	1.25286i
$757$	−1.20677e7	−	1.20677e7i	−0.765390	−	0.765390i	0.211901	−	0.977291i	$-0.432035\pi$
$757$	−1.20677e7	−	1.20677e7i	−0.765390	−	0.765390i	−0.977291	+	0.211901i	$0.932035\pi$
$758$	−1.68362e7	−	1.68362e7i	−1.06432	−	1.06432i
$759$	7.77190e6	−	6.26211e6i	0.489691	−	0.394563i
$760$	3.93150e6	−	4.97581e6i	0.246902	−	0.312485i
$761$		−	1.83294e7i		−	1.14732i	−0.819092	−	0.573662i	$-0.805522\pi$
$761$		−	1.83294e7i		−	1.14732i	0.819092	−	0.573662i	$-0.194478\pi$
$762$	2.10642e7	+	2.10642e7i	1.31419	+	1.31419i
$763$	1.31799e7	−	1.31799e7i	0.819599	−	0.819599i
$764$			5.67901e6i			0.351997i
$765$	−1.57314e7	+	1.99101e7i	−0.971885	+	1.23004i
$766$		−	1.75068e7i		−	1.07804i
$767$	−1.62142e6	+	1.62142e6i	−0.0995194	+	0.0995194i
$768$	−2.31461e7	+	2.31461e7i	−1.41604	+	1.41604i
$769$	−70599.8			−0.00430514			−0.00215257	−	0.999998i	$-0.500685\pi$
$769$	−70599.8			−0.00430514			−0.00215257	+	0.999998i	$0.500685\pi$
$770$	1.75002e7	+	1.71694e7i	1.06369	+	1.04359i
$771$	−2.79071e6			−0.169075
$772$	541698.	−	541698.i	0.0327125	−	0.0327125i
$773$	−1.50550e7	+	1.50550e7i	−0.906217	+	0.906217i	−0.995965	−	0.0897473i	$-0.971394\pi$
$773$	−1.50550e7	+	1.50550e7i	−0.906217	+	0.906217i	0.0897473	+	0.995965i	$0.471394\pi$
$774$			4.91048e7i			2.94626i
$775$	−6.67716e6	+	1.58750e6i	−0.399335	+	0.0949424i
$776$		−	6.41366e6i		−	0.382342i
$777$	2.35887e7	−	2.35887e7i	1.40169	−	1.40169i
$778$	−2.64166e7	−	2.64166e7i	−1.56469	−	1.56469i
$779$			1.85504e7i			1.09524i
$780$	−1.55114e7	+	1.81858e6i	−0.912881	+	0.107028i
$781$	−1.38130e7	−	1.71433e7i	−0.810327	−	1.00570i
$782$	−3.51367e6	−	3.51367e6i	−0.205468	−	0.205468i
$783$	−2.07595e7	−	2.07595e7i	−1.21007	−	1.21007i
$784$		−	1.15252e7i		−	0.669666i
$785$	6.81787e6	−	8.62887e6i	0.394888	−	0.499781i
$786$	−3.97729e7			−2.29631
$787$	277032.	−	277032.i	0.0159439	−	0.0159439i	−0.699090	−	0.715034i	$-0.746411\pi$
$787$	277032.	−	277032.i	0.0159439	−	0.0159439i	0.715034	+	0.699090i	$0.246411\pi$
$788$	−3.22665e6	−	3.22665e6i	−0.185113	−	0.185113i
$789$	−2.70002e7			−1.54410
$790$	−1.11096e7	−	8.77793e6i	−0.633329	−	0.500408i
$791$			3.75771e6i			0.213541i
$792$	−2.64642e7	−	2.84703e6i	−1.49915	−	0.161279i
$793$	−1.31549e7	+	1.31549e7i	−0.742857	+	0.742857i
$794$	−3.71967e6			−0.209389
$795$	4.01445e7	−	4.70660e6i	2.25272	−	0.264113i
$796$	8.23805e6			0.460831
$797$	−9.09495e6	−	9.09495e6i	−0.507171	−	0.507171i	0.406486	−	0.913657i	$-0.366754\pi$
$797$	−9.09495e6	−	9.09495e6i	−0.507171	−	0.507171i	−0.913657	+	0.406486i	$0.866754\pi$
$798$	2.04161e7	+	2.04161e7i	1.13492	+	1.13492i
$799$	−3.36387e6			−0.186412
$800$	−7.89042e6	+	1.28126e7i	−0.435888	+	0.707802i
$801$	7.50385e7			4.13240
$802$	−2.80678e7	+	2.80678e7i	−1.54089	+	1.54089i
$803$	1.51503e6	−	1.40828e7i	0.0829151	−	0.770727i
$804$		−	1.67419e7i		−	0.913409i
$805$	−7.88666e6	+	924645.i	−0.428947	+	0.0502904i
$806$	−1.04187e7			−0.564907
$807$	−2.12284e7	−	2.12284e7i	−1.14745	−	1.14745i
$808$	−6.43765e6	+	6.43765e6i	−0.346896	+	0.346896i
$809$	1.50118e7			0.806420			0.403210	−	0.915107i	$-0.367894\pi$
$809$	1.50118e7			0.806420			0.403210	+	0.915107i	$0.367894\pi$
$810$	3.24694e7	+	2.56548e7i	1.73885	+	1.37390i
$811$			1.19904e7i			0.640147i	0.947393	+	0.320074i	$0.103708\pi$
$811$			1.19904e7i			0.640147i	−0.947393	+	0.320074i	$0.896292\pi$
$812$	5.51488e6	+	5.51488e6i	0.293526	+	0.293526i
$813$	3.79088e7	+	3.79088e7i	2.01147	+	2.01147i
$814$	1.26265e7	+	1.56708e7i	0.667918	+	0.828951i
$815$	−1.47411e7	−	1.16473e7i	−0.777386	−	0.614231i
$816$			2.97138e7i			1.56219i
$817$	−8.73468e6	−	8.73468e6i	−0.457817	−	0.457817i
$818$	−1.88235e7	+	1.88235e7i	−0.983598	+	0.983598i
$819$			6.15561e7i			3.20672i
$820$	−1.83007e6	−	1.56094e7i	−0.0950459	−	0.810685i
$821$			3.44685e7i			1.78470i	0.451347	+	0.892348i	$0.350944\pi$
$821$			3.44685e7i			1.78470i	−0.451347	+	0.892348i	$0.649056\pi$
$822$	2.38302e7	−	2.38302e7i	1.23012	−	1.23012i
$823$	−2.41542e6	+	2.41542e6i	−0.124306	+	0.124306i	−0.766523	−	0.642217i	$-0.778015\pi$
$823$	−2.41542e6	+	2.41542e6i	−0.124306	+	0.124306i	0.642217	+	0.766523i	$0.278015\pi$
$824$	5.49220e6			0.281792
$825$	−3.50107e7	+	4.44372e6i	−1.79088	+	0.227306i
$826$	−3.59155e6			−0.183161
$827$	8.17100e6	−	8.17100e6i	0.415443	−	0.415443i	−0.468187	−	0.883630i	$-0.655092\pi$
$827$	8.17100e6	−	8.17100e6i	0.415443	−	0.415443i	0.883630	+	0.468187i	$0.155092\pi$
$828$	−4.88102e6	+	4.88102e6i	−0.247420	+	0.247420i
$829$			1.73241e6i			0.0875515i	0.999041	+	0.0437758i	$0.0139387\pi$
$829$			1.73241e6i			0.0875515i	−0.999041	+	0.0437758i	$0.986061\pi$
$830$	−4.25860e6	−	3.63233e7i	−0.214571	−	1.83017i
$831$		−	4.06979e7i		−	2.04442i
$832$	4.00636e6	−	4.00636e6i	0.200651	−	0.200651i
$833$	−5.27792e6	−	5.27792e6i	−0.263542	−	0.263542i
$834$			3.89589e6i			0.193951i
$835$	1.28625e7	+	1.01629e7i	0.638422	+	0.504432i
$836$	−4.17465e6	+	3.36367e6i	−0.206588	+	0.166455i
$837$	1.33693e7	+	1.33693e7i	0.659624	+	0.659624i
$838$	2.34422e7	+	2.34422e7i	1.15315	+	1.15315i
$839$		−	1.97419e6i		−	0.0968240i	−0.998827	−	0.0484120i	$-0.984584\pi$
$839$		−	1.97419e6i		−	0.0968240i	0.998827	−	0.0484120i	$-0.0154161\pi$
$840$	2.39712e7	+	1.89402e7i	1.17217	+	0.926162i
$841$	−8.88127e6			−0.432997
$842$	−1.07350e7	+	1.07350e7i	−0.521822	+	0.521822i
$843$	−1.17437e7	−	1.17437e7i	−0.569161	−	0.569161i
$844$	1.01878e7			0.492294
$845$	6.41313e6	−	751886.i	0.308979	−	0.0362251i
$846$			1.51820e7i			0.729295i
$847$	1.39916e7	+	2.17780e7i	0.670132	+	1.04306i
$848$	2.31982e7	−	2.31982e7i	1.10781	−	1.10781i
$849$	1.24133e7			0.591043
$850$	4.06410e6	+	1.70939e7i	0.192938	+	0.811511i
$851$	−6.51829e6			−0.308539
$852$	1.55328e7	+	1.55328e7i	0.733080	+	0.733080i
$853$	1.80698e7	+	1.80698e7i	0.850318	+	0.850318i	0.990172	−	0.139854i	$-0.0446635\pi$
$853$	1.80698e7	+	1.80698e7i	0.850318	+	0.850318i	−0.139854	+	0.990172i	$0.544663\pi$
$854$	−2.91390e7			−1.36719
$855$	−2.86134e7	+	3.35468e6i	−1.33861	+	0.156941i
$856$	1.26353e7			0.589388
$857$	1.25388e7	−	1.25388e7i	0.583180	−	0.583180i	−0.352596	−	0.935776i	$-0.614701\pi$
$857$	1.25388e7	−	1.25388e7i	0.583180	−	0.583180i	0.935776	+	0.352596i	$0.114701\pi$
$858$	−5.32667e7	−	5.73045e6i	−2.47023	−	0.265748i
$859$		−	517790.i		−	0.0239426i	−0.999928	−	0.0119713i	$-0.996189\pi$
$859$		−	517790.i		−	0.0239426i	0.999928	−	0.0119713i	$-0.00381067\pi$
$860$	8.21159e6	+	6.48817e6i	0.378600	+	0.299141i
$861$	−8.93676e7			−4.10839
$862$	−1.09570e7	−	1.09570e7i	−0.502256	−	0.502256i
$863$	4.62496e6	−	4.62496e6i	0.211388	−	0.211388i	−0.593469	−	0.804857i	$-0.702242\pi$
$863$	4.62496e6	−	4.62496e6i	0.211388	−	0.211388i	0.804857	+	0.593469i	$0.202242\pi$
$864$	4.14526e7			1.88915
$865$	−5.95076e6	+	7.53143e6i	−0.270416	+	0.342245i
$866$		−	5.10062e7i		−	2.31115i
$867$	−1.46460e7	−	1.46460e7i	−0.661714	−	0.661714i
$868$	−3.55165e6	−	3.55165e6i	−0.160004	−	0.160004i
$869$	−9.37960e6	−	1.16410e7i	−0.421342	−	0.522927i
$870$	−3.62281e7	+	4.24744e6i	−1.62273	+	0.190252i
$871$			2.91720e7i			1.30293i
$872$	9.90816e6	+	9.90816e6i	0.441267	+	0.441267i
$873$	−2.06029e7	+	2.06029e7i	−0.914941	+	0.914941i
$874$		−	5.64161e6i		−	0.249818i
$875$	2.54597e7	+	1.18392e7i	1.12418	+	0.522761i
$876$			1.41326e7i			0.622244i
$877$	−7.93630e6	+	7.93630e6i	−0.348433	+	0.348433i	−0.859526	−	0.511093i	$-0.829241\pi$
$877$	−7.93630e6	+	7.93630e6i	−0.348433	+	0.348433i	0.511093	+	0.859526i	$0.329241\pi$
$878$	3.04026e6	−	3.04026e6i	0.133099	−	0.133099i
$879$	−2.82070e7			−1.23136
$880$	−2.00610e7	+	2.04475e7i	−0.873266	+	0.890090i
$881$	2.68957e7			1.16746			0.583731	−	0.811947i	$-0.301592\pi$
$881$	2.68957e7			1.16746			0.583731	+	0.811947i	$0.301592\pi$
$882$	−2.38206e7	+	2.38206e7i	−1.03105	+	1.03105i
$883$	1.35731e7	−	1.35731e7i	0.585836	−	0.585836i	−0.350665	−	0.936501i	$-0.614044\pi$
$883$	1.35731e7	−	1.35731e7i	0.585836	−	0.585836i	0.936501	+	0.350665i	$0.114044\pi$
$884$			8.20965e6i			0.353341i
$885$	3.20526e6	−	4.05666e6i	0.137564	−	0.174105i
$886$		−	1.29331e7i		−	0.553500i
$887$	2.61635e7	−	2.61635e7i	1.11657	−	1.11657i	0.124330	−	0.992241i	$-0.460322\pi$
$887$	2.61635e7	−	2.61635e7i	1.11657	−	1.11657i	0.992241	−	0.124330i	$-0.0396780\pi$
$888$	1.77330e7	+	1.77330e7i	0.754659	+	0.754659i
$889$		−	2.50237e7i		−	1.06193i
$890$	3.22123e7	−	4.07687e7i	1.36316	−	1.72525i
$891$	2.74133e7	+	3.40226e7i	1.15682	+	1.43573i
$892$	1.71813e6	+	1.71813e6i	0.0723008	+	0.0723008i
$893$	−2.70055e6	−	2.70055e6i	−0.113324	−	0.113324i
$894$		−	6.18057e7i		−	2.58634i
$895$	−3.83643e7	+	4.49789e6i	−1.60092	+	0.187694i
$896$	3.36398e7			1.39986
$897$	1.22700e7	−	1.22700e7i	0.509170	−	0.509170i
$898$	1.78617e7	+	1.78617e7i	0.739148	+	0.739148i
$899$	−7.48979e6			−0.309079
$900$	2.37460e7	−	5.64565e6i	0.977203	−	0.232331i
$901$		−	2.12471e7i		−	0.871943i
$902$	5.76666e6	−	5.36033e7i	0.235998	−	2.19369i
$903$	4.20798e7	−	4.20798e7i	1.71733	−	1.71733i
$904$	−2.82490e6			−0.114969
$905$	−3.53198e6	−	3.01257e7i	−0.143350	−	1.22269i
$906$	1.59404e6			0.0645177
$907$	3.32894e7	+	3.32894e7i	1.34366	+	1.34366i	0.892390	+	0.451266i	$0.149027\pi$
$907$	3.32894e7	+	3.32894e7i	1.34366	+	1.34366i	0.451266	+	0.892390i	$0.350973\pi$
$908$	−2.57928e6	−	2.57928e6i	−0.103821	−	0.103821i
$909$	4.13600e7			1.66024
$910$	3.34437e7	+	2.64246e7i	1.33878	+	1.05780i
$911$	−1.54739e7			−0.617737			−0.308868	−	0.951105i	$-0.599950\pi$
$911$	−1.54739e7			−0.617737			−0.308868	+	0.951105i	$0.599950\pi$
$912$	−2.38545e7	+	2.38545e7i	−0.949695	+	0.949695i
$913$	4.13032e6	−	3.83929e7i	0.163986	−	1.52431i
$914$			5.30063e7i			2.09876i
$915$	2.60049e7	−	3.29125e7i	1.02684	−	1.29959i
$916$	−1.69879e7			−0.668961
$917$	2.36246e7	+	2.36246e7i	0.927771	+	0.927771i
$918$	3.42263e7	−	3.42263e7i	1.34046	−	1.34046i
$919$	−1.41326e7			−0.551991			−0.275996	−	0.961159i	$-0.589008\pi$
$919$	−1.41326e7			−0.551991			−0.275996	+	0.961159i	$0.589008\pi$
$920$	−695112.	−	5.92889e6i	−0.0270761	−	0.230942i
$921$			2.19105e7i			0.851145i
$922$	−8.50006e6	−	8.50006e6i	−0.329302	−	0.329302i
$923$	−2.70652e7	−	2.70652e7i	−1.04570	−	1.04570i
$924$	−1.62047e7	−	2.01116e7i	−0.624397	−	0.774937i
$925$	1.96254e7	+	1.20860e7i	0.754160	+	0.464437i
$926$		−	3.60078e7i		−	1.37997i
$927$	−1.76429e7	−	1.76429e7i	−0.674326	−	0.674326i
$928$	−1.16113e7	+	1.16113e7i	−0.442599	+	0.442599i
$929$			2.00017e7i			0.760375i	0.924909	+	0.380188i	$0.124141\pi$
$929$			2.00017e7i			0.760375i	−0.924909	+	0.380188i	$0.875859\pi$
$930$	2.33313e7	−	2.73540e6i	0.884570	−	0.103708i
$931$		−	8.47433e6i		−	0.320429i
$932$	1.16466e6	−	1.16466e6i	0.0439197	−	0.0439197i
$933$	−1.54176e7	+	1.54176e7i	−0.579846	+	0.579846i
$934$	1.08280e7			0.406146
$935$	176990.	+	1.85507e7i	0.00662093	+	0.693957i
$936$	−4.62755e7			−1.72648
$937$	−2.69465e7	+	2.69465e7i	−1.00266	+	1.00266i	−0.00266242	+	0.999996i	$0.500847\pi$
$937$	−2.69465e7	+	2.69465e7i	−1.00266	+	1.00266i	−0.999996	+	0.00266242i	$0.999153\pi$
$938$	−3.23089e7	+	3.23089e7i	−1.19899	+	1.19899i
$939$			1.69500e7i			0.627345i
$940$	2.53882e6	+	2.00598e6i	0.0937158	+	0.0740471i
$941$			4.92100e7i			1.81167i	0.423632	+	0.905835i	$0.360755\pi$
$941$			4.92100e7i			1.81167i	−0.423632	+	0.905835i	$0.639245\pi$
$942$	−2.66160e7	+	2.66160e7i	−0.977273	+	0.977273i
$943$	1.23475e7	+	1.23475e7i	0.452169	+	0.452169i
$944$		−	4.19643e6i		−	0.153268i
$945$	−9.00688e6	−	7.68232e7i	−0.328091	−	2.79842i
$946$	2.25245e7	+	2.79551e7i	0.818326	+	1.01562i
$947$	−5.05735e6	−	5.05735e6i	−0.183252	−	0.183252i	0.609519	−	0.792771i	$-0.291362\pi$
$947$	−5.05735e6	−	5.05735e6i	−0.183252	−	0.183252i	−0.792771	+	0.609519i	$0.791362\pi$
$948$	1.05474e7	+	1.05474e7i	0.381176	+	0.381176i
$949$		−	2.46253e7i		−	0.887598i
$950$	−1.04605e7	+	1.69859e7i	−0.376047	+	0.610631i
$951$	−3.22990e7			−1.15808
$952$	1.13558e7	−	1.13558e7i	0.406092	−	0.406092i
$953$	2.54418e7	+	2.54418e7i	0.907435	+	0.907435i	0.996065	−	0.0886294i	$-0.0282487\pi$
$953$	2.54418e7	+	2.54418e7i	0.907435	+	0.907435i	−0.0886294	+	0.996065i	$0.528249\pi$
$954$	−9.58936e7			−3.41129
$955$	2.59801e6	+	2.21594e7i	0.0921789	+	0.786231i
$956$		−	5.97673e6i		−	0.211504i
$957$	−3.82922e7	−	4.11949e6i	−1.35155	−	0.145400i
$958$	3.72511e7	−	3.72511e7i	1.31137	−	1.31137i
$959$	−2.83097e7			−0.994004
$960$	−7.91984e6	+	1.00236e7i	−0.277357	+	0.351030i
$961$	−2.38056e7			−0.831517
$962$	2.47404e7	+	2.47404e7i	0.861925	+	0.861925i
$963$	−4.05890e7	−	4.05890e7i	−1.41040	−	1.41040i
$964$	−1.28532e7			−0.445471
$965$	1.86589e6	−	2.36151e6i	0.0645010	−	0.0816341i
$966$	2.71788e7			0.937103
$967$	−2.27010e7	+	2.27010e7i	−0.780689	+	0.780689i	−0.979947	−	0.199258i	$-0.936147\pi$
$967$	−2.27010e7	+	2.27010e7i	−0.780689	+	0.780689i	0.199258	+	0.979947i	$0.436147\pi$
$968$	−1.63718e7	+	1.05184e7i	−0.561577	+	0.360795i
$969$			2.18482e7i			0.747492i
$970$	2.34929e6	+	2.00380e7i	0.0801692	+	0.683795i
$971$	8.64768e6			0.294342			0.147171	−	0.989111i	$-0.452983\pi$
$971$	8.64768e6			0.294342			0.147171	+	0.989111i	$0.452983\pi$
$972$	−9.77853e6	−	9.77853e6i	−0.331977	−	0.331977i
$973$	2.31410e6	−	2.31410e6i	0.0783612	−	0.0783612i
$974$	−2.25667e7			−0.762202
$975$	−5.96933e7	+	1.41921e7i	−2.01101	+	0.478119i
$976$		−	3.40465e7i		−	1.14406i
$977$	6.03261e6	+	6.03261e6i	0.202194	+	0.202194i	0.800940	−	0.598745i	$-0.204334\pi$
$977$	6.03261e6	+	6.03261e6i	0.202194	+	0.202194i	−0.598745	+	0.800940i	$0.704334\pi$
$978$	4.54695e7	+	4.54695e7i	1.52010	+	1.52010i
$979$	4.27190e7	−	3.44203e7i	1.42450	−	1.14778i
$980$	836027.	+	7.13081e6i	0.0278071	+	0.237178i
$981$		−	6.36569e7i		−	2.11190i
$982$	4.70177e7	+	4.70177e7i	1.55590	+	1.55590i
$983$	−2.67686e7	+	2.67686e7i	−0.883572	+	0.883572i	−0.993896	−	0.110323i	$-0.964811\pi$
$983$	−2.67686e7	+	2.67686e7i	−0.883572	+	0.883572i	0.110323	+	0.993896i	$0.464811\pi$
$984$		−	6.71831e7i		−	2.21193i
$985$	−1.40665e7	−	1.11142e7i	−0.461949	−	0.364997i
$986$			1.91743e7i			0.628097i
$987$	1.30101e7	−	1.30101e7i	0.425095	−	0.425095i
$988$	−6.59078e6	+	6.59078e6i	−0.214805	+	0.214805i
$989$	−1.16280e7			−0.378019
$990$	8.37242e7	−	798799.i	2.71496	−	0.0259030i
$991$	6.30395e6			0.203905			0.101953	−	0.994789i	$-0.467491\pi$
$991$	6.30395e6			0.203905			0.101953	+	0.994789i	$0.467491\pi$
$992$	7.47782e6	−	7.47782e6i	0.241266	−	0.241266i
$993$	−4.91774e7	+	4.91774e7i	−1.58268	+	1.58268i
$994$		−	5.99511e7i		−	1.92456i
$995$	3.21448e7	−	3.76870e6i	1.02933	−	0.120680i
$996$			3.85285e7i			1.23065i
$997$	9.01007e6	−	9.01007e6i	0.287072	−	0.287072i	−0.548849	−	0.835921i	$-0.684934\pi$
$997$	9.01007e6	−	9.01007e6i	0.287072	−	0.287072i	0.835921	+	0.548849i	$0.184934\pi$
$998$	6.34189e6	+	6.34189e6i	0.201555	+	0.201555i
$999$		−	6.34940e7i		−	2.01289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.6.e.b.32.20	yes	52
5.3	odd	4	inner	55.6.e.b.43.7	yes	52
11.10	odd	2	inner	55.6.e.b.32.7	✓	52
55.43	even	4	inner	55.6.e.b.43.20	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.e.b.32.7	✓	52	11.10	odd	2	inner
55.6.e.b.32.20	yes	52	1.1	even	1	trivial
55.6.e.b.43.7	yes	52	5.3	odd	4	inner
55.6.e.b.43.20	yes	52	55.43	even	4	inner

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.80775 - 4.80775i) q^{2} +(-19.8987 + 19.8987i) q^{3} -14.2290i q^{4} +(-6.50942 - 55.5214i) q^{5} +191.336i q^{6} +(113.651 - 113.651i) q^{7} +(85.4386 + 85.4386i) q^{8} -548.917i q^{9} +(-298.229 - 235.638i) q^{10} +(-251.789 - 312.495i) q^{11} +(283.139 + 283.139i) q^{12} +(-493.356 - 493.356i) q^{13} -1092.81i q^{14} +(1234.33 + 975.275i) q^{15} +1276.86 q^{16} +(584.735 - 584.735i) q^{17} +(-2639.06 - 2639.06i) q^{18} +938.862 q^{19} +(-790.015 + 92.6226i) q^{20} +4523.02i q^{21} +(-2712.94 - 291.859i) q^{22} +(624.927 - 624.927i) q^{23} -3400.23 q^{24} +(-3040.25 + 722.824i) q^{25} -4743.87 q^{26} +(6087.35 + 6087.35i) q^{27} +(-1617.14 - 1617.14i) q^{28} -3410.26 q^{29} +(10623.3 - 1245.49i) q^{30} +2196.25 q^{31} +(3404.81 - 3404.81i) q^{32} +(11228.5 + 1207.97i) q^{33} -5622.53i q^{34} +(-7049.88 - 5570.27i) q^{35} -7810.54 q^{36} +(-5215.24 - 5215.24i) q^{37} +(4513.82 - 4513.82i) q^{38} +19634.3 q^{39} +(4187.51 - 5299.83i) q^{40} +19758.4i q^{41} +(21745.6 + 21745.6i) q^{42} +(-9303.47 - 9303.47i) q^{43} +(-4446.50 + 3582.71i) q^{44} +(-30476.6 + 3573.13i) q^{45} -6008.99i q^{46} +(-2876.41 - 2876.41i) q^{47} +(-25407.9 + 25407.9i) q^{48} -9026.17i q^{49} +(-11141.6 + 18092.0i) q^{50} +23271.0i q^{51} +(-7019.97 + 7019.97i) q^{52} +(18168.1 - 18168.1i) q^{53} +58533.0 q^{54} +(-15711.2 + 16013.9i) q^{55} +19420.4 q^{56} +(-18682.1 + 18682.1i) q^{57} +(-16395.7 + 16395.7i) q^{58} -3286.52i q^{59} +(13877.2 - 17563.3i) q^{60} -26664.2i q^{61} +(10559.0 - 10559.0i) q^{62} +(-62385.0 - 62385.0i) q^{63} +8120.62i q^{64} +(-24180.4 + 30603.3i) q^{65} +(59791.6 - 48176.4i) q^{66} +(-29564.9 - 29564.9i) q^{67} +(-8320.21 - 8320.21i) q^{68} +24870.5i q^{69} +(-60674.6 + 7113.58i) q^{70} +54859.4 q^{71} +(46898.7 - 46898.7i) q^{72} +(24957.0 + 24957.0i) q^{73} -50147.2 q^{74} +(46113.9 - 74880.4i) q^{75} -13359.1i q^{76} +(-64131.6 - 6899.30i) q^{77} +(94396.9 - 94396.9i) q^{78} +37251.8 q^{79} +(-8311.64 - 70893.3i) q^{80} -108874. q^{81} +(94993.4 + 94993.4i) q^{82} +(68038.2 + 68038.2i) q^{83} +64358.1 q^{84} +(-36271.6 - 28659.1i) q^{85} -89457.6 q^{86} +(67859.8 - 67859.8i) q^{87} +(5186.63 - 48211.6i) q^{88} +136703. i q^{89} +(-129345. + 163703. i) q^{90} -112141. q^{91} +(-8892.09 - 8892.09i) q^{92} +(-43702.5 + 43702.5i) q^{93} -27658.1 q^{94} +(-6111.45 - 52127.0i) q^{95} +135503. i q^{96} +(-37533.8 - 37533.8i) q^{97} +(-43395.6 - 43395.6i) q^{98} +(-171534. + 138211. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 56 q^{3} - 48 q^{5} - 364 q^{11} + 4792 q^{12} + 2564 q^{15} - 6416 q^{16} + 18272 q^{20} + 2680 q^{22} - 144 q^{23} - 12248 q^{25} + 2432 q^{26} + 3644 q^{27} + 9672 q^{31} + 30576 q^{33} - 148776 q^{36}+ \cdots - 633128 q^{97}+O(q^{100}) \) 52 * q + 56 * q^3 - 48 * q^5 - 364 * q^11 + 4792 * q^12 + 2564 * q^15 - 6416 * q^16 + 18272 * q^20 + 2680 * q^22 - 144 * q^23 - 12248 * q^25 + 2432 * q^26 + 3644 * q^27 + 9672 * q^31 + 30576 * q^33 - 148776 * q^36 + 24152 * q^37 + 4400 * q^38 - 43480 * q^42 - 4984 * q^45 - 44148 * q^47 + 26416 * q^48 + 75596 * q^53 + 59092 * q^55 + 304264 * q^56 - 220200 * q^58 - 240016 * q^60 + 207000 * q^66 - 17888 * q^67 - 216880 * q^70 + 285704 * q^71 + 278404 * q^75 - 341160 * q^77 + 15160 * q^78 + 616192 * q^80 - 397204 * q^81 + 349720 * q^82 - 94768 * q^86 + 539000 * q^88 - 864768 * q^91 + 242072 * q^92 + 15772 * q^93 - 633128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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