LMFDB - Embedded newform 230.5.f.a.47.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.20
Character	$\chi$	$=$	230.47
Dual form			230.5.f.a.93.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +(11.2589 - 11.2589i) q^{3} +8.00000i q^{4} +(19.3240 - 15.8613i) q^{5} -45.0357 q^{6} +(67.6527 + 67.6527i) q^{7} +(16.0000 - 16.0000i) q^{8} -172.526i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +(11.2589 - 11.2589i) q^{3} +8.00000i q^{4} +(19.3240 - 15.8613i) q^{5} -45.0357 q^{6} +(67.6527 + 67.6527i) q^{7} +(16.0000 - 16.0000i) q^{8} -172.526i q^{9} +(-70.3707 - 6.92536i) q^{10} -121.570 q^{11} +(90.0713 + 90.0713i) q^{12} +(43.0448 - 43.0448i) q^{13} -270.611i q^{14} +(38.9860 - 396.149i) q^{15} -64.0000 q^{16} +(215.855 + 215.855i) q^{17} +(-345.052 + 345.052i) q^{18} -344.624i q^{19} +(126.891 + 154.592i) q^{20} +1523.39 q^{21} +(243.140 + 243.140i) q^{22} +(77.9968 - 77.9968i) q^{23} -360.285i q^{24} +(121.836 - 613.010i) q^{25} -172.179 q^{26} +(-1030.49 - 1030.49i) q^{27} +(-541.221 + 541.221i) q^{28} -1123.83i q^{29} +(-870.270 + 714.326i) q^{30} +643.933 q^{31} +(128.000 + 128.000i) q^{32} +(-1368.75 + 1368.75i) q^{33} -863.419i q^{34} +(2380.38 + 234.259i) q^{35} +1380.21 q^{36} +(1875.76 + 1875.76i) q^{37} +(-689.248 + 689.248i) q^{38} -969.275i q^{39} +(55.4029 - 562.966i) q^{40} -2801.14 q^{41} +(-3046.78 - 3046.78i) q^{42} +(-372.277 + 372.277i) q^{43} -972.560i q^{44} +(-2736.50 - 3333.90i) q^{45} -311.987 q^{46} +(-887.284 - 887.284i) q^{47} +(-720.570 + 720.570i) q^{48} +6752.76i q^{49} +(-1469.69 + 982.348i) q^{50} +4860.58 q^{51} +(344.358 + 344.358i) q^{52} +(1572.77 - 1572.77i) q^{53} +4121.94i q^{54} +(-2349.22 + 1928.26i) q^{55} +2164.88 q^{56} +(-3880.09 - 3880.09i) q^{57} +(-2247.66 + 2247.66i) q^{58} -2430.11i q^{59} +(3169.19 + 311.888i) q^{60} -5546.14 q^{61} +(-1287.87 - 1287.87i) q^{62} +(11671.9 - 11671.9i) q^{63} -512.000i q^{64} +(149.050 - 1514.55i) q^{65} +5474.98 q^{66} +(-174.925 - 174.925i) q^{67} +(-1726.84 + 1726.84i) q^{68} -1756.32i q^{69} +(-4292.25 - 5229.29i) q^{70} -519.196 q^{71} +(-2760.42 - 2760.42i) q^{72} +(-1471.19 + 1471.19i) q^{73} -7503.05i q^{74} +(-5530.09 - 8273.56i) q^{75} +2756.99 q^{76} +(-8224.53 - 8224.53i) q^{77} +(-1938.55 + 1938.55i) q^{78} -1171.86i q^{79} +(-1236.74 + 1015.13i) q^{80} -9229.68 q^{81} +(5602.27 + 5602.27i) q^{82} +(-4952.74 + 4952.74i) q^{83} +12187.1i q^{84} +(7594.93 + 747.436i) q^{85} +1489.11 q^{86} +(-12653.1 - 12653.1i) q^{87} +(-1945.12 + 1945.12i) q^{88} +8331.35i q^{89} +(-1194.81 + 12140.8i) q^{90} +5824.19 q^{91} +(623.974 + 623.974i) q^{92} +(7249.99 - 7249.99i) q^{93} +3549.13i q^{94} +(-5466.20 - 6659.52i) q^{95} +2882.28 q^{96} +(8549.51 + 8549.51i) q^{97} +(13505.5 - 13505.5i) q^{98} +20974.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	11.2589	−	11.2589i	1.25099	−	1.25099i	0.295714	−	0.955277i	$-0.404443\pi$
$3$	11.2589	−	11.2589i	1.25099	−	1.25099i	0.955277	−	0.295714i	$-0.0955574\pi$
$4$			8.00000i			0.500000i
$5$	19.3240	−	15.8613i	0.772961	−	0.634454i
$5$	19.3240	−	15.8613i	0.772961	−	0.634454i
$6$	−45.0357			−1.25099
$7$	67.6527	+	67.6527i	1.38067	+	1.38067i	0.843435	+	0.537232i	$0.180530\pi$
$7$	67.6527	+	67.6527i	1.38067	+	1.38067i	0.537232	+	0.843435i	$0.319470\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	172.526i		−	2.12995i
$10$	−70.3707	−	6.92536i	−0.703707	−	0.0692536i
$11$	−121.570			−1.00471			−0.502355	−	0.864661i	$-0.667533\pi$
$11$	−121.570			−1.00471			−0.502355	+	0.864661i	$0.667533\pi$
$12$	90.0713	+	90.0713i	0.625495	+	0.625495i
$13$	43.0448	−	43.0448i	0.254703	−	0.254703i	−0.568193	−	0.822896i	$-0.692357\pi$
$13$	43.0448	−	43.0448i	0.254703	−	0.254703i	0.822896	+	0.568193i	$0.192357\pi$
$14$		−	270.611i		−	1.38067i
$15$	38.9860	−	396.149i	0.173271	−	1.76066i
$16$	−64.0000			−0.250000
$17$	215.855	+	215.855i	0.746902	+	0.746902i	0.973896	−	0.226994i	$-0.0728898\pi$
$17$	215.855	+	215.855i	0.746902	+	0.746902i	−0.226994	+	0.973896i	$0.572890\pi$
$18$	−345.052	+	345.052i	−1.06498	+	1.06498i
$19$		−	344.624i		−	0.954637i	−0.878730	−	0.477319i	$-0.841609\pi$
$19$		−	344.624i		−	0.954637i	0.878730	−	0.477319i	$-0.158391\pi$
$20$	126.891	+	154.592i	0.317227	+	0.386480i
$21$	1523.39			3.45440
$22$	243.140	+	243.140i	0.502355	+	0.502355i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	360.285i		−	0.625495i
$25$	121.836	−	613.010i	0.194937	−	0.980816i
$26$	−172.179			−0.254703
$27$	−1030.49	−	1030.49i	−1.41356	−	1.41356i
$28$	−541.221	+	541.221i	−0.690333	+	0.690333i
$29$		−	1123.83i		−	1.33630i	−0.744025	−	0.668152i	$-0.767086\pi$
$29$		−	1123.83i		−	1.33630i	0.744025	−	0.668152i	$-0.232914\pi$
$30$	−870.270	+	714.326i	−0.966967	+	0.793695i
$31$	643.933			0.670066			0.335033	−	0.942206i	$-0.391253\pi$
$31$	643.933			0.670066			0.335033	+	0.942206i	$0.391253\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−1368.75	+	1368.75i	−1.25688	+	1.25688i
$34$		−	863.419i		−	0.746902i
$35$	2380.38	+	234.259i	1.94317	+	0.191232i
$36$	1380.21			1.06498
$37$	1875.76	+	1875.76i	1.37017	+	1.37017i	0.860182	+	0.509987i	$0.170350\pi$
$37$	1875.76	+	1875.76i	1.37017	+	1.37017i	0.509987	+	0.860182i	$0.329650\pi$
$38$	−689.248	+	689.248i	−0.477319	+	0.477319i
$39$		−	969.275i		−	0.637262i
$40$	55.4029	−	562.966i	0.0346268	−	0.351854i
$41$	−2801.14			−1.66635			−0.833175	−	0.553009i	$-0.813480\pi$
$41$	−2801.14			−1.66635			−0.833175	+	0.553009i	$0.813480\pi$
$42$	−3046.78	−	3046.78i	−1.72720	−	1.72720i
$43$	−372.277	+	372.277i	−0.201339	+	0.201339i	−0.800574	−	0.599234i	$-0.795472\pi$
$43$	−372.277	+	372.277i	−0.201339	+	0.201339i	0.599234	+	0.800574i	$0.295472\pi$
$44$		−	972.560i		−	0.502355i
$45$	−2736.50	−	3333.90i	−1.35136	−	1.64637i
$46$	−311.987			−0.147442
$47$	−887.284	−	887.284i	−0.401667	−	0.401667i	0.477153	−	0.878820i	$-0.341669\pi$
$47$	−887.284	−	887.284i	−0.401667	−	0.401667i	−0.878820	+	0.477153i	$0.841669\pi$
$48$	−720.570	+	720.570i	−0.312748	+	0.312748i
$49$			6752.76i			2.81248i
$50$	−1469.69	+	982.348i	−0.587876	+	0.392939i
$51$	4860.58			1.86873
$52$	344.358	+	344.358i	0.127351	+	0.127351i
$53$	1572.77	−	1572.77i	0.559902	−	0.559902i	−0.369377	−	0.929279i	$-0.620429\pi$
$53$	1572.77	−	1572.77i	0.559902	−	0.559902i	0.929279	+	0.369377i	$0.120429\pi$
$54$			4121.94i			1.41356i
$55$	−2349.22	+	1928.26i	−0.776602	+	0.637443i
$56$	2164.88			0.690333
$57$	−3880.09	−	3880.09i	−1.19424	−	1.19424i
$58$	−2247.66	+	2247.66i	−0.668152	+	0.668152i
$59$		−	2430.11i		−	0.698107i	−0.937103	−	0.349054i	$-0.886503\pi$
$59$		−	2430.11i		−	0.698107i	0.937103	−	0.349054i	$-0.113497\pi$
$60$	3169.19	+	311.888i	0.880331	+	0.0866356i
$61$	−5546.14			−1.49050			−0.745248	−	0.666787i	$-0.767669\pi$
$61$	−5546.14			−1.49050			−0.745248	+	0.666787i	$0.767669\pi$
$62$	−1287.87	−	1287.87i	−0.335033	−	0.335033i
$63$	11671.9	−	11671.9i	2.94076	−	2.94076i
$64$		−	512.000i		−	0.125000i
$65$	149.050	−	1514.55i	0.0352782	−	0.358473i
$66$	5474.98			1.25688
$67$	−174.925	−	174.925i	−0.0389675	−	0.0389675i	0.687355	−	0.726322i	$-0.258772\pi$
$67$	−174.925	−	174.925i	−0.0389675	−	0.0389675i	−0.726322	+	0.687355i	$0.758772\pi$
$68$	−1726.84	+	1726.84i	−0.373451	+	0.373451i
$69$		−	1756.32i		−	0.368897i
$70$	−4292.25	−	5229.29i	−0.875969	−	1.06720i
$71$	−519.196			−0.102995			−0.0514974	−	0.998673i	$-0.516399\pi$
$71$	−519.196			−0.102995			−0.0514974	+	0.998673i	$0.516399\pi$
$72$	−2760.42	−	2760.42i	−0.532488	−	0.532488i
$73$	−1471.19	+	1471.19i	−0.276072	+	0.276072i	−0.831539	−	0.555467i	$-0.812540\pi$
$73$	−1471.19	+	1471.19i	−0.276072	+	0.276072i	0.555467	+	0.831539i	$0.312540\pi$
$74$		−	7503.05i		−	1.37017i
$75$	−5530.09	−	8273.56i	−0.983127	−	1.47086i
$76$	2756.99			0.477319
$77$	−8224.53	−	8224.53i	−1.38717	−	1.38717i
$78$	−1938.55	+	1938.55i	−0.318631	+	0.318631i
$79$		−	1171.86i		−	0.187767i	−0.995583	−	0.0938837i	$-0.970072\pi$
$79$		−	1171.86i		−	0.187767i	0.995583	−	0.0938837i	$-0.0299282\pi$
$80$	−1236.74	+	1015.13i	−0.193240	+	0.158613i
$81$	−9229.68			−1.40675
$82$	5602.27	+	5602.27i	0.833175	+	0.833175i
$83$	−4952.74	+	4952.74i	−0.718935	+	0.718935i	−0.968387	−	0.249452i	$-0.919750\pi$
$83$	−4952.74	+	4952.74i	−0.718935	+	0.718935i	0.249452	+	0.968387i	$0.419750\pi$
$84$			12187.1i			1.72720i
$85$	7594.93	+	747.436i	1.05120	+	0.103451i
$86$	1489.11			0.201339
$87$	−12653.1	−	12653.1i	−1.67170	−	1.67170i
$88$	−1945.12	+	1945.12i	−0.251178	+	0.251178i
$89$			8331.35i			1.05180i	0.850545	+	0.525902i	$0.176272\pi$
$89$			8331.35i			1.05180i	−0.850545	+	0.525902i	$0.823728\pi$
$90$	−1194.81	+	12140.8i	−0.147507	+	1.49886i
$91$	5824.19			0.703320
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	7249.99	−	7249.99i	0.838246	−	0.838246i
$94$			3549.13i			0.401667i
$95$	−5466.20	−	6659.52i	−0.605673	−	0.737897i
$96$	2882.28			0.312748
$97$	8549.51	+	8549.51i	0.908652	+	0.908652i	0.996163	−	0.0875116i	$-0.0278915\pi$
$97$	8549.51	+	8549.51i	0.908652	+	0.908652i	−0.0875116	+	0.996163i	$0.527891\pi$
$98$	13505.5	−	13505.5i	1.40624	−	1.40624i
$99$			20974.0i			2.13999i
$100$	4904.08	+	974.685i	0.490408	+	0.0974685i
$101$	285.348			0.0279726			0.0139863	−	0.999902i	$-0.495548\pi$
$101$	285.348			0.0279726			0.0139863	+	0.999902i	$0.495548\pi$
$102$	−9721.16	−	9721.16i	−0.934367	−	0.934367i
$103$	−7020.84	+	7020.84i	−0.661782	+	0.661782i	−0.955800	−	0.294018i	$-0.905007\pi$
$103$	−7020.84	+	7020.84i	−0.661782	+	0.661782i	0.294018	+	0.955800i	$0.405007\pi$
$104$		−	1377.43i		−	0.127351i
$105$	29438.0	−	24163.0i	2.67012	−	2.19166i
$106$	−6291.06			−0.559902
$107$	9645.22	+	9645.22i	0.842451	+	0.842451i	0.989177	−	0.146726i	$-0.0468737\pi$
$107$	9645.22	+	9645.22i	0.842451	+	0.842451i	−0.146726	+	0.989177i	$0.546874\pi$
$108$	8243.89	−	8243.89i	0.706780	−	0.706780i
$109$			4301.32i			0.362033i	0.983480	+	0.181017i	$0.0579388\pi$
$109$			4301.32i			0.362033i	−0.983480	+	0.181017i	$0.942061\pi$
$110$	8554.97	+	841.916i	0.707022	+	0.0695798i
$111$	42238.1			3.42814
$112$	−4329.77	−	4329.77i	−0.345167	−	0.345167i
$113$	4270.92	−	4270.92i	0.334476	−	0.334476i	−0.519808	−	0.854283i	$-0.673996\pi$
$113$	4270.92	−	4270.92i	0.334476	−	0.334476i	0.854283	+	0.519808i	$0.173996\pi$
$114$			15520.4i			1.19424i
$115$	270.078	−	2744.35i	0.0204218	−	0.207512i
$116$	8990.65			0.668152
$117$	−7426.36	−	7426.36i	−0.542505	−	0.542505i
$118$	−4860.22	+	4860.22i	−0.349054	+	0.349054i
$119$			29206.3i			2.06245i
$120$	−5714.61	−	6962.16i	−0.396848	−	0.483483i
$121$	138.269			0.00944399
$122$	11092.3	+	11092.3i	0.745248	+	0.745248i
$123$	−31537.7	+	31537.7i	−2.08459	+	2.08459i
$124$			5151.46i			0.335033i
$125$	−7368.80	−	13778.3i	−0.471603	−	0.881811i
$126$	−46687.4			−2.94076
$127$	17617.5	+	17617.5i	1.09229	+	1.09229i	0.995284	+	0.0970026i	$0.0309255\pi$
$127$	17617.5	+	17617.5i	1.09229	+	1.09229i	0.0970026	+	0.995284i	$0.469074\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$			8382.86i			0.503748i
$130$	−3327.19	+	2730.99i	−0.196875	+	0.161597i
$131$	−29305.0			−1.70765			−0.853825	−	0.520560i	$-0.825723\pi$
$131$	−29305.0			−1.70765			−0.853825	+	0.520560i	$0.825723\pi$
$132$	−10950.0	−	10950.0i	−0.628442	−	0.628442i
$133$	23314.7	−	23314.7i	1.31804	−	1.31804i
$134$			699.700i			0.0389675i
$135$	−36258.0	−	3568.24i	−1.98947	−	0.195788i
$136$	6907.35			0.373451
$137$	4326.89	+	4326.89i	0.230534	+	0.230534i	0.812916	−	0.582382i	$-0.197879\pi$
$137$	4326.89	+	4326.89i	0.230534	+	0.230534i	−0.582382	+	0.812916i	$0.697879\pi$
$138$	−3512.64	+	3512.64i	−0.184448	+	0.184448i
$139$			2887.39i			0.149443i	0.997204	+	0.0747216i	$0.0238068\pi$
$139$			2887.39i			0.149443i	−0.997204	+	0.0747216i	$0.976193\pi$
$140$	−1874.08	+	19043.1i	−0.0956161	+	0.971585i
$141$	−19979.7			−1.00496
$142$	1038.39	+	1038.39i	0.0514974	+	0.0514974i
$143$	−5232.96	+	5232.96i	−0.255903	+	0.255903i
$144$			11041.7i			0.532488i
$145$	−17825.5	−	21716.9i	−0.847823	−	1.03291i
$146$	5884.75			0.276072
$147$	76028.8	+	76028.8i	3.51838	+	3.51838i
$148$	−15006.1	+	15006.1i	−0.685085	+	0.685085i
$149$			15127.1i			0.681370i	0.940178	+	0.340685i	$0.110659\pi$
$149$			15127.1i			0.681370i	−0.940178	+	0.340685i	$0.889341\pi$
$150$	−5486.95	+	27607.3i	−0.243864	+	1.22699i
$151$	−17915.8			−0.785745			−0.392872	−	0.919593i	$-0.628519\pi$
$151$	−17915.8			−0.785745			−0.392872	+	0.919593i	$0.628519\pi$
$152$	−5513.99	−	5513.99i	−0.238659	−	0.238659i
$153$	37240.6	−	37240.6i	1.59087	−	1.59087i
$154$			32898.1i			1.38717i
$155$	12443.4	−	10213.6i	0.517935	−	0.425126i
$156$	7754.20			0.318631
$157$	5877.88	+	5877.88i	0.238463	+	0.238463i	0.816214	−	0.577750i	$-0.196069\pi$
$157$	5877.88	+	5877.88i	0.238463	+	0.238463i	−0.577750	+	0.816214i	$0.696069\pi$
$158$	−2343.71	+	2343.71i	−0.0938837	+	0.0938837i
$159$		−	35415.2i		−	1.40086i
$160$	4503.73	+	443.223i	0.175927	+	0.0173134i
$161$	10553.4			0.407136
$162$	18459.4	+	18459.4i	0.703374	+	0.703374i
$163$	681.208	−	681.208i	0.0256392	−	0.0256392i	−0.694171	−	0.719810i	$-0.744229\pi$
$163$	681.208	−	681.208i	0.0256392	−	0.0256392i	0.719810	+	0.694171i	$0.244229\pi$
$164$		−	22409.1i		−	0.833175i
$165$	−4739.53	+	48159.8i	−0.174087	+	1.76896i
$166$	19811.0			0.718935
$167$	1737.10	+	1737.10i	0.0622861	+	0.0622861i	0.737564	−	0.675278i	$-0.235976\pi$
$167$	1737.10	+	1737.10i	0.0622861	+	0.0622861i	−0.675278	+	0.737564i	$0.735976\pi$
$168$	24374.2	−	24374.2i	0.863600	−	0.863600i
$169$			24855.3i			0.870253i
$170$	−13695.0	−	16684.7i	−0.473875	−	0.577326i
$171$	−59456.7			−2.03333
$172$	−2978.21	−	2978.21i	−0.100670	−	0.100670i
$173$	−8057.25	+	8057.25i	−0.269212	+	0.269212i	−0.828783	−	0.559571i	$-0.810966\pi$
$173$	−8057.25	+	8057.25i	−0.269212	+	0.269212i	0.559571	+	0.828783i	$0.310966\pi$
$174$			50612.5i			1.67170i
$175$	49714.2	−	33229.2i	1.62332	−	1.08504i
$176$	7780.48			0.251178
$177$	−27360.4	−	27360.4i	−0.873325	−	0.873325i
$178$	16662.7	−	16662.7i	0.525902	−	0.525902i
$179$		−	60449.1i		−	1.88662i	−0.331915	−	0.943309i	$-0.607695\pi$
$179$		−	60449.1i		−	1.88662i	0.331915	−	0.943309i	$-0.392305\pi$
$180$	26671.2	−	21892.0i	0.823185	−	0.675678i
$181$	33545.9			1.02396			0.511980	−	0.858997i	$-0.328912\pi$
$181$	33545.9			1.02396			0.511980	+	0.858997i	$0.328912\pi$
$182$	−11648.4	−	11648.4i	−0.351660	−	0.351660i
$183$	−62443.5	+	62443.5i	−1.86460	+	1.86460i
$184$		−	2495.90i		−	0.0737210i
$185$	65999.4	+	6495.16i	1.92840	+	0.189778i
$186$	−28999.9			−0.838246
$187$	−26241.5	−	26241.5i	−0.750421	−	0.750421i
$188$	7098.27	−	7098.27i	0.200834	−	0.200834i
$189$		−	139430.i		−	3.90331i
$190$	−2386.65	+	24251.5i	−0.0661121	+	0.671785i
$191$	36301.8			0.995087			0.497543	−	0.867439i	$-0.334236\pi$
$191$	36301.8			0.995087			0.497543	+	0.867439i	$0.334236\pi$
$192$	−5764.56	−	5764.56i	−0.156374	−	0.156374i
$193$	6164.39	−	6164.39i	0.165491	−	0.165491i	−0.619503	−	0.784994i	$-0.712666\pi$
$193$	6164.39	−	6164.39i	0.165491	−	0.165491i	0.784994	+	0.619503i	$0.212666\pi$
$194$		−	34198.0i		−	0.908652i
$195$	−15374.0	−	18730.3i	−0.404313	−	0.492579i
$196$	−54022.1			−1.40624
$197$	21116.4	+	21116.4i	0.544112	+	0.544112i	0.924732	−	0.380620i	$-0.124289\pi$
$197$	21116.4	+	21116.4i	0.544112	+	0.544112i	−0.380620	+	0.924732i	$0.624289\pi$
$198$	41948.0	−	41948.0i	1.06999	−	1.06999i
$199$		−	4725.19i		−	0.119320i	−0.998219	−	0.0596600i	$-0.980998\pi$
$199$		−	4725.19i		−	0.119320i	0.998219	−	0.0596600i	$-0.0190016\pi$
$200$	−7858.79	−	11757.5i	−0.196470	−	0.293938i
$201$	−3938.93			−0.0974959
$202$	−570.696	−	570.696i	−0.0139863	−	0.0139863i
$203$	76030.2	−	76030.2i	1.84499	−	1.84499i
$204$			38884.6i			0.934367i
$205$	−54129.2	+	44429.8i	−1.28802	+	1.05722i
$206$	28083.4			0.661782
$207$	−13456.5	−	13456.5i	−0.314045	−	0.314045i
$208$	−2754.87	+	2754.87i	−0.0636757	+	0.0636757i
$209$			41896.0i			0.959135i
$210$	−107202.	−	10550.0i	−2.43089	−	0.239230i
$211$	24984.6			0.561187			0.280593	−	0.959827i	$-0.409469\pi$
$211$	24984.6			0.561187			0.280593	+	0.959827i	$0.409469\pi$
$212$	12582.1	+	12582.1i	0.279951	+	0.279951i
$213$	−5845.59	+	5845.59i	−0.128845	+	0.128845i
$214$		−	38580.9i		−	0.842451i
$215$	−1289.08	+	13098.7i	−0.0278870	+	0.283368i
$216$	−32975.5			−0.706780
$217$	43563.8	+	43563.8i	0.925137	+	0.925137i
$218$	8602.64	−	8602.64i	0.181017	−	0.181017i
$219$			33127.9i			0.690727i
$220$	−15426.1	−	18793.8i	−0.318721	−	0.388301i
$221$	18582.8			0.380476
$222$	−84476.1	−	84476.1i	−1.71407	−	1.71407i
$223$	−2361.72	+	2361.72i	−0.0474918	+	0.0474918i	−0.730454	−	0.682962i	$-0.760691\pi$
$223$	−2361.72	+	2361.72i	−0.0474918	+	0.0474918i	0.682962	+	0.730454i	$0.260691\pi$
$224$			17319.1i			0.345167i
$225$	−105760.	−	21019.8i	−2.08909	−	0.415207i
$226$	−17083.7			−0.334476
$227$	24253.0	+	24253.0i	0.470667	+	0.470667i	0.902130	−	0.431463i	$-0.142003\pi$
$227$	24253.0	+	24253.0i	0.470667	+	0.470667i	−0.431463	+	0.902130i	$0.642003\pi$
$228$	31040.7	−	31040.7i	0.597121	−	0.597121i
$229$		−	84721.7i		−	1.61556i	−0.589482	−	0.807781i	$-0.700668\pi$
$229$		−	84721.7i		−	1.61556i	0.589482	−	0.807781i	$-0.299332\pi$
$230$	−6028.85	+	4948.54i	−0.113967	+	0.0935451i
$231$	−185199.			−3.47067
$232$	−17981.3	−	17981.3i	−0.334076	−	0.334076i
$233$	−17784.0	+	17784.0i	−0.327580	+	0.327580i	−0.851665	−	0.524086i	$-0.824407\pi$
$233$	−17784.0	+	17784.0i	−0.327580	+	0.327580i	0.524086	+	0.851665i	$0.324407\pi$
$234$			29705.4i			0.542505i
$235$	−31219.4	−	3072.38i	−0.565313	−	0.0556338i
$236$	19440.9			0.349054
$237$	−13193.8	−	13193.8i	−0.234895	−	0.234895i
$238$	58412.6	−	58412.6i	1.03122	−	1.03122i
$239$		−	42956.3i		−	0.752022i	−0.926615	−	0.376011i	$-0.877295\pi$
$239$		−	42956.3i		−	0.752022i	0.926615	−	0.376011i	$-0.122705\pi$
$240$	−2495.10	+	25353.5i	−0.0433178	+	0.440165i
$241$	−33175.7			−0.571197			−0.285598	−	0.958349i	$-0.592192\pi$
$241$	−33175.7			−0.571197			−0.285598	+	0.958349i	$0.592192\pi$
$242$	−276.539	−	276.539i	−0.00472200	−	0.00472200i
$243$	−20446.8	+	20446.8i	−0.346268	+	0.346268i
$244$		−	44369.1i		−	0.745248i
$245$	107108.	+	130491.i	1.78439	+	2.17394i
$246$	126151.			2.08459
$247$	−14834.3	−	14834.3i	−0.243149	−	0.243149i
$248$	10302.9	−	10302.9i	0.167516	−	0.167516i
$249$			111525.i			1.79876i
$250$	−12819.0	+	42294.2i	−0.205104	+	0.676707i
$251$	7988.91			0.126806			0.0634030	−	0.997988i	$-0.479805\pi$
$251$	7988.91			0.126806			0.0634030	+	0.997988i	$0.479805\pi$
$252$	93374.9	+	93374.9i	1.47038	+	1.47038i
$253$	−9482.07	+	9482.07i	−0.148137	+	0.148137i
$254$		−	70470.0i		−	1.09229i
$255$	93925.9	−	77095.3i	1.44446	−	1.18563i
$256$	4096.00			0.0625000
$257$	5711.28	+	5711.28i	0.0864704	+	0.0864704i	0.749019	−	0.662549i	$-0.230525\pi$
$257$	5711.28	+	5711.28i	0.0864704	+	0.0864704i	−0.662549	+	0.749019i	$0.730525\pi$
$258$	16765.7	−	16765.7i	0.251874	−	0.251874i
$259$			253800.i			3.78349i
$260$	12116.4	+	1192.40i	0.179236	+	0.0176391i
$261$	−193890.			−2.84626
$262$	58610.0	+	58610.0i	0.853825	+	0.853825i
$263$	55522.3	−	55522.3i	0.802704	−	0.802704i	−0.180813	−	0.983517i	$-0.557873\pi$
$263$	55522.3	−	55522.3i	0.802704	−	0.802704i	0.983517	+	0.180813i	$0.0578729\pi$
$264$			43799.9i			0.628442i
$265$	5445.98	−	55338.3i	0.0775505	−	0.788014i
$266$	−93258.9			−1.31804
$267$	93801.9	+	93801.9i	1.31580	+	1.31580i
$268$	1399.40	−	1399.40i	0.0194837	−	0.0194837i
$269$			56619.2i			0.782455i	0.920294	+	0.391228i	$0.127949\pi$
$269$			56619.2i			0.782455i	−0.920294	+	0.391228i	$0.872051\pi$
$270$	65379.6	+	79652.5i	0.896839	+	1.09263i
$271$	−85174.7			−1.15977			−0.579885	−	0.814698i	$-0.696903\pi$
$271$	−85174.7			−1.15977			−0.579885	+	0.814698i	$0.696903\pi$
$272$	−13814.7	−	13814.7i	−0.186726	−	0.186726i
$273$	65574.0	−	65574.0i	0.879846	−	0.879846i
$274$		−	17307.6i		−	0.230534i
$275$	−14811.6	+	74523.6i	−0.195855	+	0.985436i
$276$	14050.5			0.184448
$277$	−105605.	−	105605.i	−1.37634	−	1.37634i	−0.850726	−	0.525610i	$-0.823837\pi$
$277$	−105605.	−	105605.i	−1.37634	−	1.37634i	−0.525610	−	0.850726i	$-0.676163\pi$
$278$	5774.78	−	5774.78i	0.0747216	−	0.0747216i
$279$		−	111095.i		−	1.42721i
$280$	41834.3	−	34338.0i	0.533601	−	0.437984i
$281$	−40788.2			−0.516562			−0.258281	−	0.966070i	$-0.583156\pi$
$281$	−40788.2			−0.516562			−0.258281	+	0.966070i	$0.583156\pi$
$282$	39959.4	+	39959.4i	0.502482	+	0.502482i
$283$	−91342.8	+	91342.8i	−1.14052	+	1.14052i	−0.152161	+	0.988356i	$0.548623\pi$
$283$	−91342.8	+	91342.8i	−1.14052	+	1.14052i	−0.988356	+	0.152161i	$0.951377\pi$
$284$		−	4153.57i		−	0.0514974i
$285$	−136522.	−	13435.5i	−1.68079	−	0.165411i
$286$	20931.8			0.255903
$287$	−189504.	−	189504.i	−2.30067	−	2.30067i
$288$	22083.4	−	22083.4i	0.266244	−	0.266244i
$289$			9665.54i			0.115726i
$290$	−7782.94	+	79084.8i	−0.0925438	+	0.940367i
$291$	192516.			2.27343
$292$	−11769.5	−	11769.5i	−0.138036	−	0.138036i
$293$	87709.7	−	87709.7i	1.02167	−	1.02167i	0.0219139	−	0.999760i	$-0.493024\pi$
$293$	87709.7	−	87709.7i	1.02167	−	1.02167i	0.999760	−	0.0219139i	$-0.00697598\pi$
$294$		−	304115.i		−	3.51838i
$295$	−38544.8	−	46959.5i	−0.442917	−	0.539610i
$296$	60024.4			0.685085
$297$	125276.	+	125276.i	1.42022	+	1.42022i
$298$	30254.2	−	30254.2i	0.340685	−	0.340685i
$299$		−	6714.71i		−	0.0751078i
$300$	66188.5	−	44240.7i	0.735428	−	0.491563i
$301$	−50371.0			−0.555965
$302$	35831.5	+	35831.5i	0.392872	+	0.392872i
$303$	3212.71	−	3212.71i	0.0349934	−	0.0349934i
$304$			22055.9i			0.238659i
$305$	−107174.	+	87969.2i	−1.15210	+	0.945651i
$306$	−148962.			−1.59087
$307$	−65758.7	−	65758.7i	−0.697713	−	0.697713i	0.266204	−	0.963917i	$-0.414230\pi$
$307$	−65758.7	−	65758.7i	−0.697713	−	0.697713i	−0.963917	+	0.266204i	$0.914230\pi$
$308$	65796.3	−	65796.3i	0.693585	−	0.693585i
$309$			158094.i			1.65577i
$310$	−45314.0	−	4459.47i	−0.471530	−	0.0464045i
$311$	−15336.5			−0.158564			−0.0792822	−	0.996852i	$-0.525263\pi$
$311$	−15336.5			−0.158564			−0.0792822	+	0.996852i	$0.525263\pi$
$312$	−15508.4	−	15508.4i	−0.159315	−	0.159315i
$313$	−28781.0	+	28781.0i	−0.293776	+	0.293776i	−0.838570	−	0.544794i	$-0.816608\pi$
$313$	−28781.0	+	28781.0i	−0.293776	+	0.293776i	0.544794	+	0.838570i	$0.316608\pi$
$314$		−	23511.5i		−	0.238463i
$315$	40415.9	−	410679.i	0.407316	−	4.13886i
$316$	9374.85			0.0938837
$317$	85519.9	+	85519.9i	0.851037	+	0.851037i	0.990261	−	0.139224i	$-0.0444607\pi$
$317$	85519.9	+	85519.9i	0.851037	+	0.851037i	−0.139224	+	0.990261i	$0.544461\pi$
$318$	−70830.5	+	70830.5i	−0.700432	+	0.700432i
$319$			136624.i			1.34260i
$320$	−8121.01	−	9893.90i	−0.0793067	−	0.0966201i
$321$	217189.			2.10780
$322$	−21106.8	−	21106.8i	−0.203568	−	0.203568i
$323$	74388.8	−	74388.8i	0.713021	−	0.713021i
$324$		−	73837.4i		−	0.703374i
$325$	−21142.5	−	31631.3i	−0.200166	−	0.299468i
$326$	−2724.83			−0.0256392
$327$	48428.2	+	48428.2i	0.452900	+	0.452900i
$328$	−44818.2	+	44818.2i	−0.416588	+	0.416588i
$329$		−	120054.i		−	1.10914i
$330$	105799.	−	86840.6i	0.971522	−	0.797434i
$331$	36860.2			0.336435			0.168218	−	0.985750i	$-0.446199\pi$
$331$	36860.2			0.336435			0.168218	+	0.985750i	$0.446199\pi$
$332$	−39622.0	−	39622.0i	−0.359468	−	0.359468i
$333$	323618.	−	323618.i	2.91840	−	2.91840i
$334$		−	6948.39i		−	0.0622861i
$335$	−6154.80	−	605.710i	−0.0548434	−	0.00539728i
$336$	−97497.0			−0.863600
$337$	10579.4	+	10579.4i	0.0931541	+	0.0931541i	0.752148	−	0.658994i	$-0.229018\pi$
$337$	10579.4	+	10579.4i	0.0931541	+	0.0931541i	−0.658994	+	0.752148i	$0.729018\pi$
$338$	49710.6	−	49710.6i	0.435126	−	0.435126i
$339$		−	96171.8i		−	0.836851i
$340$	−5979.49	+	60759.4i	−0.0517257	+	0.525601i
$341$	−78283.0			−0.673222
$342$	118913.	+	118913.i	1.01667	+	1.01667i
$343$	−294408.	+	294408.i	−2.50243	+	2.50243i
$344$			11912.9i			0.100670i
$345$	−27857.6	−	33939.1i	−0.234048	−	0.285143i
$346$	32229.0			0.269212
$347$	45870.0	+	45870.0i	0.380951	+	0.380951i	0.871445	−	0.490494i	$-0.163183\pi$
$347$	45870.0	+	45870.0i	0.380951	+	0.380951i	−0.490494	+	0.871445i	$0.663183\pi$
$348$	101225.	−	101225.i	0.835851	−	0.835851i
$349$			223724.i			1.83680i	0.395652	+	0.918400i	$0.370519\pi$
$349$			223724.i			1.83680i	−0.395652	+	0.918400i	$0.629481\pi$
$350$	−165887.	−	32970.0i	−1.35418	−	0.269143i
$351$	−88714.1			−0.720076
$352$	−15561.0	−	15561.0i	−0.125589	−	0.125589i
$353$	61661.3	−	61661.3i	0.494839	−	0.494839i	−0.414988	−	0.909827i	$-0.636214\pi$
$353$	61661.3	−	61661.3i	0.494839	−	0.494839i	0.909827	+	0.414988i	$0.136214\pi$
$354$			109442.i			0.873325i
$355$	−10033.0	+	8235.15i	−0.0796109	+	0.0653454i
$356$	−66650.8			−0.525902
$357$	328831.	+	328831.i	2.58010	+	2.58010i
$358$	−120898.	+	120898.i	−0.943309	+	0.943309i
$359$		−	34694.1i		−	0.269195i	−0.990900	−	0.134598i	$-0.957026\pi$
$359$		−	34694.1i		−	0.269195i	0.990900	−	0.134598i	$-0.0429742\pi$
$360$	−97126.4	−	9558.45i	−0.749432	−	0.0737535i
$361$	11555.2			0.0886673
$362$	−67091.9	−	67091.9i	−0.511980	−	0.511980i
$363$	1556.76	−	1556.76i	0.0118143	−	0.0118143i
$364$			46593.5i			0.351660i
$365$	−5094.25	+	51764.3i	−0.0382380	+	0.388548i
$366$	249774.			1.86460
$367$	−14654.7	−	14654.7i	−0.108804	−	0.108804i	0.650609	−	0.759413i	$-0.274514\pi$
$367$	−14654.7	−	14654.7i	−0.108804	−	0.108804i	−0.759413	+	0.650609i	$0.774514\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$			483269.i			3.54925i
$370$	−119008.	−	144989.i	−0.869309	−	1.05909i
$371$	212803.			1.54608
$372$	57999.9	+	57999.9i	0.419123	+	0.419123i
$373$	191718.	−	191718.i	1.37798	−	1.37798i	0.529963	−	0.848021i	$-0.322206\pi$
$373$	191718.	−	191718.i	1.37798	−	1.37798i	0.848021	−	0.529963i	$-0.177794\pi$
$374$			104966.i			0.750421i
$375$	−238093.	−	72163.9i	−1.69311	−	0.513165i
$376$	−28393.1			−0.200834
$377$	−48375.1	−	48375.1i	−0.340360	−	0.340360i
$378$	−278860.	+	278860.i	−1.95166	+	1.95166i
$379$			172222.i			1.19897i	0.800384	+	0.599487i	$0.204629\pi$
$379$			172222.i			1.19897i	−0.800384	+	0.599487i	$0.795371\pi$
$380$	53276.2	−	43729.6i	0.368949	−	0.302837i
$381$	396708.			2.73288
$382$	−72603.5	−	72603.5i	−0.497543	−	0.497543i
$383$	−99536.2	+	99536.2i	−0.678553	+	0.678553i	−0.959673	−	0.281120i	$-0.909294\pi$
$383$	−99536.2	+	99536.2i	−0.678553	+	0.678553i	0.281120	+	0.959673i	$0.409294\pi$
$384$			23058.3i			0.156374i
$385$	−289383.	−	28478.9i	−1.95232	−	0.192133i
$386$	−24657.5			−0.165491
$387$	64227.5	+	64227.5i	0.428844	+	0.428844i
$388$	−68396.0	+	68396.0i	−0.454326	+	0.454326i
$389$			105907.i			0.699881i	0.936772	+	0.349940i	$0.113798\pi$
$389$			105907.i			0.699881i	−0.936772	+	0.349940i	$0.886202\pi$
$390$	−6712.58	+	68208.6i	−0.0441327	+	0.448446i
$391$	33672.0			0.220249
$392$	108044.	+	108044.i	0.703120	+	0.703120i
$393$	−329942.	+	329942.i	−2.13625	+	2.13625i
$394$		−	84465.8i		−	0.544112i
$395$	−18587.2	−	22645.0i	−0.119130	−	0.145137i
$396$	−167792.			−1.06999
$397$	116792.	+	116792.i	0.741025	+	0.741025i	0.972775	−	0.231751i	$-0.0744453\pi$
$397$	116792.	+	116792.i	0.741025	+	0.741025i	−0.231751	+	0.972775i	$0.574445\pi$
$398$	−9450.38	+	9450.38i	−0.0596600	+	0.0596600i
$399$		−	524997.i		−	3.29770i
$400$	−7797.48	+	39232.6i	−0.0487343	+	0.245204i
$401$	−31863.0			−0.198152			−0.0990759	−	0.995080i	$-0.531589\pi$
$401$	−31863.0			−0.198152			−0.0990759	+	0.995080i	$0.531589\pi$
$402$	7877.87	+	7877.87i	0.0487480	+	0.0487480i
$403$	27718.0	−	27718.0i	0.170668	−	0.170668i
$404$			2282.79i			0.0139863i
$405$	−178354.	+	146395.i	−1.08736	+	0.892517i
$406$	−304121.			−1.84499
$407$	−228036.	−	228036.i	−1.37662	−	1.37662i
$408$	77769.3	−	77769.3i	0.467184	−	0.467184i
$409$		−	54381.2i		−	0.325089i	−0.986701	−	0.162544i	$-0.948030\pi$
$409$		−	54381.2i		−	0.325089i	0.986701	−	0.162544i	$-0.0519701\pi$
$410$	197118.	+	19398.9i	1.17262	+	0.115401i
$411$	97432.2			0.576792
$412$	−56166.7	−	56166.7i	−0.330891	−	0.330891i
$413$	164403.	−	164403.i	0.963853	−	0.963853i
$414$			53826.0i			0.314045i
$415$	−17149.8	+	174264.i	−0.0995777	+	1.01184i
$416$	11019.5			0.0636757
$417$	32508.9	+	32508.9i	0.186952	+	0.186952i
$418$	83791.9	−	83791.9i	0.479567	−	0.479567i
$419$		−	120434.i		−	0.685994i	−0.939337	−	0.342997i	$-0.888558\pi$
$419$		−	120434.i		−	0.685994i	0.939337	−	0.342997i	$-0.111442\pi$
$420$	193304.	+	235504.i	1.09583	+	1.33506i
$421$	213768.			1.20609			0.603044	−	0.797708i	$-0.293954\pi$
$421$	213768.			1.20609			0.603044	+	0.797708i	$0.293954\pi$
$422$	−49969.2	−	49969.2i	−0.280593	−	0.280593i
$423$	−153080.	+	153080.i	−0.855533	+	0.855533i
$424$		−	50328.5i		−	0.279951i
$425$	158620.	−	106022.i	0.878172	−	0.586975i
$426$	23382.3			0.128845
$427$	−375211.	−	375211.i	−2.05788	−	2.05788i
$428$	−77161.7	+	77161.7i	−0.421225	+	0.421225i
$429$			117835.i			0.640264i
$430$	28775.5	−	23619.2i	0.155628	−	0.127741i
$431$	−356761.			−1.92054			−0.960270	−	0.279072i	$-0.909973\pi$
$431$	−356761.			−1.92054			−0.960270	+	0.279072i	$0.909973\pi$
$432$	65951.1	+	65951.1i	0.353390	+	0.353390i
$433$	−227509.	+	227509.i	−1.21345	+	1.21345i	−0.243569	+	0.969883i	$0.578318\pi$
$433$	−227509.	+	227509.i	−1.21345	+	1.21345i	−0.969883	+	0.243569i	$0.921682\pi$
$434$		−	174255.i		−	0.925137i
$435$	−445205.	−	43813.7i	−2.35278	−	0.231543i
$436$	−34410.5			−0.181017
$437$	−26879.6	−	26879.6i	−0.140754	−	0.140754i
$438$	66255.9	−	66255.9i	0.345363	−	0.345363i
$439$		−	181502.i		−	0.941785i	−0.882191	−	0.470892i	$-0.843932\pi$
$439$		−	181502.i		−	0.941785i	0.882191	−	0.470892i	$-0.156068\pi$
$440$	−6735.33	+	68439.8i	−0.0347899	+	0.353511i
$441$	1.16503e6			5.99045
$442$	−37165.7	−	37165.7i	−0.190238	−	0.190238i
$443$	42877.8	−	42877.8i	0.218487	−	0.218487i	−0.589374	−	0.807861i	$-0.700625\pi$
$443$	42877.8	−	42877.8i	0.218487	−	0.218487i	0.807861	+	0.589374i	$0.200625\pi$
$444$			337905.i			1.71407i
$445$	132146.	+	160995.i	0.667321	+	0.813004i
$446$	9446.89			0.0474918
$447$	170315.	+	170315.i	0.852387	+	0.852387i
$448$	34638.2	−	34638.2i	0.172583	−	0.172583i
$449$		−	3368.44i		−	0.0167085i	−0.999965	−	0.00835423i	$-0.997341\pi$
$449$		−	3368.44i		−	0.0167085i	0.999965	−	0.00835423i	$-0.00265927\pi$
$450$	169481.	+	253560.i	0.836943	+	1.25215i
$451$	340534.			1.67420
$452$	34167.3	+	34167.3i	0.167238	+	0.167238i
$453$	−201712.	+	201712.i	−0.982959	+	0.982959i
$454$		−	97012.0i		−	0.470667i
$455$	112547.	−	92379.5i	0.543639	−	0.446224i
$456$	−124163.			−0.597121
$457$	−174014.	−	174014.i	−0.833203	−	0.833203i	0.154751	−	0.987954i	$-0.450542\pi$
$457$	−174014.	−	174014.i	−0.833203	−	0.833203i	−0.987954	+	0.154751i	$0.950542\pi$
$458$	−169443.	+	169443.i	−0.807781	+	0.807781i
$459$		−	444871.i		−	2.11158i
$460$	21954.8	+	2160.62i	0.103756	+	0.0102109i
$461$	−43748.7			−0.205856			−0.102928	−	0.994689i	$-0.532821\pi$
$461$	−43748.7			−0.205856			−0.102928	+	0.994689i	$0.532821\pi$
$462$	370397.	+	370397.i	1.73534	+	1.73534i
$463$	−155409.	+	155409.i	−0.724959	+	0.724959i	−0.969611	−	0.244652i	$-0.921326\pi$
$463$	−155409.	+	155409.i	−0.724959	+	0.724959i	0.244652	+	0.969611i	$0.421326\pi$
$464$			71925.2i			0.334076i
$465$	25104.4	−	255093.i	0.116103	−	1.17976i
$466$	71135.9			0.327580
$467$	−204630.	−	204630.i	−0.938285	−	0.938285i	0.0599180	−	0.998203i	$-0.480916\pi$
$467$	−204630.	−	204630.i	−0.938285	−	0.938285i	−0.998203	+	0.0599180i	$0.980916\pi$
$468$	59410.9	−	59410.9i	0.271253	−	0.271253i
$469$		−	23668.3i		−	0.107602i
$470$	56294.0	+	68583.5i	0.254839	+	0.310473i
$471$	132357.			0.596630
$472$	−38881.8	−	38881.8i	−0.174527	−	0.174527i
$473$	45257.7	−	45257.7i	0.202288	−	0.202288i
$474$			52775.3i			0.234895i
$475$	−211258.	−	41987.5i	−0.936323	−	0.186094i
$476$	−233650.			−1.03122
$477$	−271343.	−	271343.i	−1.19257	−	1.19257i
$478$	−85912.5	+	85912.5i	−0.376011	+	0.376011i
$479$			358520.i			1.56258i	0.624167	+	0.781291i	$0.285438\pi$
$479$			358520.i			1.56258i	−0.624167	+	0.781291i	$0.714562\pi$
$480$	55697.3	−	45716.9i	0.241742	−	0.198424i
$481$	161484.			0.697972
$482$	66351.4	+	66351.4i	0.285598	+	0.285598i
$483$	118820.	−	118820.i	0.509324	−	0.509324i
$484$			1106.16i			0.00472200i
$485$	300817.	+	29604.2i	1.27885	+	0.125855i
$486$	81787.1			0.346268
$487$	26877.3	+	26877.3i	0.113326	+	0.113326i	0.761496	−	0.648170i	$-0.224465\pi$
$487$	26877.3	+	26877.3i	0.113326	+	0.113326i	−0.648170	+	0.761496i	$0.724465\pi$
$488$	−88738.2	+	88738.2i	−0.372624	+	0.372624i
$489$		−	15339.3i		−	0.0641488i
$490$	46765.3	−	475197.i	0.194774	−	1.97916i
$491$	201659.			0.836479			0.418239	−	0.908337i	$-0.362647\pi$
$491$	201659.			0.836479			0.418239	+	0.908337i	$0.362647\pi$
$492$	−252302.	−	252302.i	−1.04229	−	1.04229i
$493$	242584.	−	242584.i	0.998088	−	0.998088i
$494$			59337.1i			0.243149i
$495$	332676.	+	405302.i	1.35772	+	1.65413i
$496$	−41211.7			−0.167516
$497$	−35125.0	−	35125.0i	−0.142201	−	0.142201i
$498$	223050.	−	223050.i	0.899381	−	0.899381i
$499$			43791.7i			0.175870i	0.996126	+	0.0879349i	$0.0280267\pi$
$499$			43791.7i			0.175870i	−0.996126	+	0.0879349i	$0.971973\pi$
$500$	110226.	−	58950.4i	0.440905	−	0.235802i
$501$	39115.6			0.155839
$502$	−15977.8	−	15977.8i	−0.0634030	−	0.0634030i
$503$	−249412.	+	249412.i	−0.985783	+	0.985783i	−0.999900	−	0.0141177i	$-0.995506\pi$
$503$	−249412.	+	249412.i	−0.985783	+	0.985783i	0.0141177	+	0.999900i	$0.495506\pi$
$504$		−	373499.i		−	1.47038i
$505$	5514.08	−	4526.01i	0.0216217	−	0.0177473i
$506$	37928.3			0.148137
$507$	279844.	+	279844.i	1.08868	+	1.08868i
$508$	−140940.	+	140940.i	−0.546143	+	0.546143i
$509$			404456.i			1.56112i	0.625081	+	0.780560i	$0.285066\pi$
$509$			404456.i			1.56112i	−0.625081	+	0.780560i	$0.714934\pi$
$510$	−342043.	−	33661.3i	−1.31504	−	0.129417i
$511$	−199059.			−0.762327
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−355130.	+	355130.i	−1.34944	+	1.34944i
$514$		−	22845.1i		−	0.0864704i
$515$	−24310.9	+	247031.i	−0.0916615	+	0.931401i
$516$	−67062.9			−0.251874
$517$	107867.	+	107867.i	0.403560	+	0.403560i
$518$	507601.	−	507601.i	1.89175	−	1.89175i
$519$			181432.i			0.673564i
$520$	−21847.9	−	26617.6i	−0.0807986	−	0.0984377i
$521$	−292121.			−1.07618			−0.538092	−	0.842886i	$-0.680855\pi$
$521$	−292121.			−1.07618			−0.538092	+	0.842886i	$0.680855\pi$
$522$	387781.	+	387781.i	1.42313	+	1.42313i
$523$	249241.	−	249241.i	0.911203	−	0.911203i	−0.0851637	−	0.996367i	$-0.527141\pi$
$523$	249241.	−	249241.i	0.911203	−	0.911203i	0.996367	+	0.0851637i	$0.0271413\pi$
$524$		−	234440.i		−	0.853825i
$525$	185603.	−	933853.i	0.673391	−	3.38813i
$526$	−222089.			−0.802704
$527$	138996.	+	138996.i	0.500474	+	0.500474i
$528$	87599.8	−	87599.8i	0.314221	−	0.314221i
$529$		−	12167.0i		−	0.0434783i
$530$	−121569.	+	99784.7i	−0.432782	+	0.355232i
$531$	−419258.			−1.48694
$532$	186518.	+	186518.i	0.659018	+	0.659018i
$533$	−120574.	+	120574.i	−0.424424	+	0.424424i
$534$		−	375208.i		−	1.31580i
$535$	339370.	+	33398.3i	1.18568	+	0.116685i
$536$	−5597.60			−0.0194837
$537$	−680592.	−	680592.i	−2.36014	−	2.36014i
$538$	113238.	−	113238.i	0.391228	−	0.391228i
$539$		−	820933.i		−	2.82573i
$540$	28545.9	−	290064.i	0.0978942	−	0.994733i
$541$	−175003.			−0.597931			−0.298965	−	0.954264i	$-0.596642\pi$
$541$	−175003.			−0.597931			−0.298965	+	0.954264i	$0.596642\pi$
$542$	170349.	+	170349.i	0.579885	+	0.579885i
$543$	377691.	−	377691.i	1.28096	−	1.28096i
$544$			55258.8i			0.186726i
$545$	68224.7	+	83118.8i	0.229693	+	0.279838i
$546$	−262296.			−0.879846
$547$	−366374.	−	366374.i	−1.22447	−	1.22447i	−0.966025	−	0.258449i	$-0.916789\pi$
$547$	−366374.	−	366374.i	−1.22447	−	1.22447i	−0.258449	−	0.966025i	$-0.583211\pi$
$548$	−34615.1	+	34615.1i	−0.115267	+	0.115267i
$549$			956854.i			3.17469i
$550$	178670.	−	119424.i	0.590646	−	0.394790i
$551$	−387299.			−1.27569
$552$	−28101.1	−	28101.1i	−0.0922242	−	0.0922242i
$553$	79279.2	−	79279.2i	0.259244	−	0.259244i
$554$			422419.i			1.37634i
$555$	816209.	−	669953.i	2.64982	−	2.17499i
$556$	−23099.1			−0.0747216
$557$	102755.	+	102755.i	0.331200	+	0.331200i	0.853042	−	0.521842i	$-0.174755\pi$
$557$	102755.	+	102755.i	0.331200	+	0.331200i	−0.521842	+	0.853042i	$0.674755\pi$
$558$	−222191.	+	222191.i	−0.713604	+	0.713604i
$559$			32049.2i			0.102564i
$560$	−152345.	−	14992.6i	−0.485792	−	0.0478081i
$561$	−590901.			−1.87754
$562$	81576.5	+	81576.5i	0.258281	+	0.258281i
$563$	−227110.	+	227110.i	−0.716506	+	0.716506i	−0.967888	−	0.251382i	$-0.919115\pi$
$563$	−227110.	+	227110.i	−0.716506	+	0.716506i	0.251382	+	0.967888i	$0.419115\pi$
$564$		−	159838.i		−	0.502482i
$565$	14788.8	−	150274.i	0.0463273	−	0.470746i
$566$	365371.			1.14052
$567$	−624412.	−	624412.i	−1.94225	−	1.94225i
$568$	−8307.14	+	8307.14i	−0.0257487	+	0.0257487i
$569$		−	168784.i		−	0.521323i	−0.965430	−	0.260662i	$-0.916059\pi$
$569$		−	168784.i		−	0.521323i	0.965430	−	0.260662i	$-0.0839407\pi$
$570$	246174.	+	299916.i	0.757691	+	0.923103i
$571$	−407442.			−1.24966			−0.624832	−	0.780759i	$-0.714833\pi$
$571$	−407442.			−1.24966			−0.624832	+	0.780759i	$0.714833\pi$
$572$	−41863.7	−	41863.7i	−0.127951	−	0.127951i
$573$	408718.	−	408718.i	1.24484	−	1.24484i
$574$			758017.i			2.30067i
$575$	−38310.0	−	57315.6i	−0.115871	−	0.173355i
$576$	−88333.4			−0.266244
$577$	134858.	+	134858.i	0.405065	+	0.405065i	0.880014	−	0.474948i	$-0.157533\pi$
$577$	134858.	+	134858.i	0.405065	+	0.405065i	−0.474948	+	0.880014i	$0.657533\pi$
$578$	19331.1	−	19331.1i	0.0578629	−	0.0578629i
$579$		−	138809.i		−	0.414056i
$580$	173736.	−	142604.i	0.516455	−	0.423911i
$581$	−670133.			−1.98522
$582$	−385033.	−	385033.i	−1.13671	−	1.13671i
$583$	−191201.	+	191201.i	−0.562540	+	0.562540i
$584$			47078.0i			0.138036i
$585$	−261299.	−	25715.1i	−0.763530	−	0.0751409i
$586$	−350839.			−1.02167
$587$	−126599.	−	126599.i	−0.367413	−	0.367413i	0.499120	−	0.866533i	$-0.333657\pi$
$587$	−126599.	−	126599.i	−0.367413	−	0.367413i	−0.866533	+	0.499120i	$0.833657\pi$
$588$	−608230.	+	608230.i	−1.75919	+	1.75919i
$589$		−	221915.i		−	0.639670i
$590$	−16829.4	+	171009.i	−0.0483464	+	0.491263i
$591$	475496.			1.36136
$592$	−120049.	−	120049.i	−0.342542	−	0.342542i
$593$	247783.	−	247783.i	0.704630	−	0.704630i	−0.260770	−	0.965401i	$-0.583977\pi$
$593$	247783.	−	247783.i	0.704630	−	0.704630i	0.965401	+	0.260770i	$0.0839766\pi$
$594$		−	501105.i		−	1.42022i
$595$	463251.	+	564383.i	1.30853	+	1.59419i
$596$	−121017.			−0.340685
$597$	−53200.5	−	53200.5i	−0.149268	−	0.149268i
$598$	−13429.4	+	13429.4i	−0.0375539	+	0.0375539i
$599$		−	212757.i		−	0.592966i	−0.955038	−	0.296483i	$-0.904186\pi$
$599$		−	212757.i		−	0.592966i	0.955038	−	0.296483i	$-0.0958138\pi$
$600$	−220858.	−	43895.6i	−0.613496	−	0.121932i
$601$	421400.			1.16666			0.583331	−	0.812234i	$-0.301749\pi$
$601$	421400.			1.16666			0.583331	+	0.812234i	$0.301749\pi$
$602$	100742.	+	100742.i	0.277983	+	0.277983i
$603$	−30179.2	+	30179.2i	−0.0829990	+	0.0829990i
$604$		−	143326.i		−	0.392872i
$605$	2671.92	−	2193.14i	0.00729984	−	0.00599177i
$606$	−12850.8			−0.0349934
$607$	−132361.	−	132361.i	−0.359238	−	0.359238i	0.504294	−	0.863532i	$-0.331753\pi$
$607$	−132361.	−	132361.i	−0.359238	−	0.359238i	−0.863532	+	0.504294i	$0.831753\pi$
$608$	44111.9	−	44111.9i	0.119330	−	0.119330i
$609$		−	1.71203e6i		−	4.61613i
$610$	390286.	+	38409.0i	1.04887	+	0.103222i
$611$	−76385.9			−0.204612
$612$	297925.	+	297925.i	0.795434	+	0.795434i
$613$	−129130.	+	129130.i	−0.343642	+	0.343642i	−0.857735	−	0.514092i	$-0.828129\pi$
$613$	−129130.	+	129130.i	−0.343642	+	0.343642i	0.514092	+	0.857735i	$0.328129\pi$
$614$			263035.i			0.697713i
$615$	−109205.	+	1.10967e6i	−0.288731	+	2.93388i
$616$	−263185.			−0.693585
$617$	89881.6	+	89881.6i	0.236102	+	0.236102i	0.815234	−	0.579132i	$-0.196608\pi$
$617$	89881.6	+	89881.6i	0.236102	+	0.236102i	−0.579132	+	0.815234i	$0.696608\pi$
$618$	316188.	−	316188.i	0.827883	−	0.827883i
$619$			142708.i			0.372450i	0.982507	+	0.186225i	$0.0596254\pi$
$619$			142708.i			0.372450i	−0.982507	+	0.186225i	$0.940375\pi$
$620$	81709.1	+	99547.0i	0.212563	+	0.258967i
$621$	−160749.			−0.416836
$622$	30673.0	+	30673.0i	0.0792822	+	0.0792822i
$623$	−563638.	+	563638.i	−1.45219	+	1.45219i
$624$			62033.6i			0.159315i
$625$	−360937.	−	149373.i	−0.923999	−	0.382395i
$626$	115124.			0.293776
$627$	471703.	+	471703.i	1.19987	+	1.19987i
$628$	−47023.0	+	47023.0i	−0.119232	+	0.119232i
$629$			809784.i			2.04676i
$630$	−902189.	+	740525.i	−2.27309	+	1.86577i
$631$	217728.			0.546833			0.273417	−	0.961896i	$-0.411846\pi$
$631$	217728.			0.546833			0.273417	+	0.961896i	$0.411846\pi$
$632$	−18749.7	−	18749.7i	−0.0469419	−	0.0469419i
$633$	281299.	−	281299.i	0.702039	−	0.702039i
$634$		−	342080.i		−	0.851037i
$635$	619878.	+	61003.7i	1.53730	+	0.151290i
$636$	283322.			0.700432
$637$	290671.	+	290671.i	0.716347	+	0.716347i
$638$	273248.	−	273248.i	0.671299	−	0.671299i
$639$			89575.0i			0.219374i
$640$	−3545.78	+	36029.8i	−0.00865670	+	0.0879634i
$641$	−58944.2			−0.143458			−0.0717290	−	0.997424i	$-0.522852\pi$
$641$	−58944.2			−0.143458			−0.0717290	+	0.997424i	$0.522852\pi$
$642$	−434379.	−	434379.i	−1.05390	−	1.05390i
$643$	−246191.	+	246191.i	−0.595457	+	0.595457i	−0.939100	−	0.343644i	$-0.888339\pi$
$643$	−246191.	+	246191.i	−0.595457	+	0.595457i	0.343644	+	0.939100i	$0.388339\pi$
$644$			84427.0i			0.203568i
$645$	132963.	+	161991.i	0.319604	+	0.389377i
$646$	−297555.			−0.713021
$647$	79560.6	+	79560.6i	0.190060	+	0.190060i	0.795722	−	0.605662i	$-0.207092\pi$
$647$	79560.6	+	79560.6i	0.190060	+	0.190060i	−0.605662	+	0.795722i	$0.707092\pi$
$648$	−147675.	+	147675.i	−0.351687	+	0.351687i
$649$			295429.i			0.701396i
$650$	−20977.6	+	105548.i	−0.0496510	+	0.249817i
$651$	980962.			2.31468
$652$	5449.66	+	5449.66i	0.0128196	+	0.0128196i
$653$	399867.	−	399867.i	0.937755	−	0.937755i	−0.0604179	−	0.998173i	$-0.519243\pi$
$653$	399867.	−	399867.i	0.937755	−	0.937755i	0.998173	+	0.0604179i	$0.0192433\pi$
$654$		−	193713.i		−	0.452900i
$655$	−566290.	+	464816.i	−1.31995	+	1.08342i
$656$	179273.			0.416588
$657$	253818.	+	253818.i	0.588021	+	0.588021i
$658$	−240108.	+	240108.i	−0.554569	+	0.554569i
$659$		−	715991.i		−	1.64868i	−0.566094	−	0.824340i	$-0.691546\pi$
$659$		−	715991.i		−	1.64868i	0.566094	−	0.824340i	$-0.308454\pi$
$660$	−385279.	−	37916.2i	−0.884478	−	0.0870437i
$661$	400623.			0.916923			0.458461	−	0.888714i	$-0.348401\pi$
$661$	400623.			0.916923			0.458461	+	0.888714i	$0.348401\pi$
$662$	−73720.4	−	73720.4i	−0.168218	−	0.168218i
$663$	209223.	−	209223.i	0.475972	−	0.475972i
$664$			158488.i			0.359468i
$665$	80731.5	−	820337.i	0.182557	−	1.85502i
$666$	−1.29447e6			−2.91840
$667$	−87655.2	−	87655.2i	−0.197027	−	0.197027i
$668$	−13896.8	+	13896.8i	−0.0311430	+	0.0311430i
$669$			53180.8i			0.118824i
$670$	11098.2	+	13521.0i	0.0247231	+	0.0301203i
$671$	674244.			1.49752
$672$	194994.	+	194994.i	0.431800	+	0.431800i
$673$	302334.	−	302334.i	0.667508	−	0.667508i	−0.289631	−	0.957138i	$-0.593533\pi$
$673$	302334.	−	302334.i	0.667508	−	0.667508i	0.957138	+	0.289631i	$0.0935325\pi$
$674$		−	42317.7i		−	0.0931541i
$675$	−757248.	+	506148.i	−1.66200	+	1.11089i
$676$	−198842.			−0.435126
$677$	11031.4	+	11031.4i	0.0240688	+	0.0240688i	0.719039	−	0.694970i	$-0.244582\pi$
$677$	11031.4	+	11031.4i	0.0240688	+	0.0240688i	−0.694970	+	0.719039i	$0.744582\pi$
$678$	−192344.	+	192344.i	−0.418426	+	0.418426i
$679$			1.15679e6i			2.50909i
$680$	133478.	−	109560.i	0.288663	−	0.236937i
$681$	546125.			1.17760
$682$	156566.	+	156566.i	0.336611	+	0.336611i
$683$	462293.	−	462293.i	0.991006	−	0.991006i	−0.00895387	−	0.999960i	$-0.502850\pi$
$683$	462293.	−	462293.i	0.991006	−	0.991006i	0.999960	+	0.00895387i	$0.00285014\pi$
$684$		−	475654.i		−	1.01667i
$685$	152243.	+	14982.6i	0.324457	+	0.0319306i
$686$	1.17763e6			2.50243
$687$	−953875.	−	953875.i	−2.02105	−	2.02105i
$688$	23825.7	−	23825.7i	0.0503349	−	0.0503349i
$689$		−	135399.i		−	0.285217i
$690$	−12163.1	+	123593.i	−0.0255474	+	0.259595i
$691$	233444.			0.488908			0.244454	−	0.969661i	$-0.421391\pi$
$691$	233444.			0.488908			0.244454	+	0.969661i	$0.421391\pi$
$692$	−64458.0	−	64458.0i	−0.134606	−	0.134606i
$693$	−1.41895e6	+	1.41895e6i	−2.95461	+	2.95461i
$694$		−	183480.i		−	0.380951i
$695$	45797.9	+	55796.0i	0.0948148	+	0.115514i
$696$	−404900.			−0.835851
$697$	−604638.	−	604638.i	−1.24460	−	1.24460i
$698$	447448.	−	447448.i	0.918400	−	0.918400i
$699$			400456.i			0.819598i
$700$	265834.	+	397714.i	0.542518	+	0.811661i
$701$	−311049.			−0.632984			−0.316492	−	0.948595i	$-0.602505\pi$
$701$	−311049.			−0.632984			−0.316492	+	0.948595i	$0.602505\pi$
$702$	177428.	+	177428.i	0.360038	+	0.360038i
$703$	646433.	−	646433.i	1.30801	−	1.30801i
$704$			62243.8i			0.125589i
$705$	−386088.	+	316905.i	−0.776798	+	0.637603i
$706$	−246645.			−0.494839
$707$	19304.6	+	19304.6i	0.0386208	+	0.0386208i
$708$	218883.	−	218883.i	0.436663	−	0.436663i
$709$		−	353130.i		−	0.702493i	−0.936283	−	0.351246i	$-0.885758\pi$
$709$		−	353130.i		−	0.702493i	0.936283	−	0.351246i	$-0.114242\pi$
$710$	36536.2	+	3595.62i	0.0724781	+	0.00713276i
$711$	−202176.			−0.399936
$712$	133302.	+	133302.i	0.262951	+	0.262951i
$713$	50224.7	−	50224.7i	0.0987958	−	0.0987958i
$714$		−	1.31532e6i		−	2.58010i
$715$	−18120.1	+	184124.i	−0.0354444	+	0.360161i
$716$	483593.			0.943309
$717$	−483641.	−	483641.i	−0.940773	−	0.940773i
$718$	−69388.3	+	69388.3i	−0.134598	+	0.134598i
$719$		−	392642.i		−	0.759520i	−0.925085	−	0.379760i	$-0.876007\pi$
$719$		−	392642.i		−	0.759520i	0.925085	−	0.379760i	$-0.123993\pi$
$720$	175136.	+	213370.i	0.337839	+	0.411593i
$721$	−949957.			−1.82740
$722$	−23110.4	−	23110.4i	−0.0443336	−	0.0443336i
$723$	−373522.	+	373522.i	−0.714562	+	0.714562i
$724$			268368.i			0.511980i
$725$	−688920.	−	136923.i	−1.31067	−	0.260495i
$726$	−6227.06			−0.0118143
$727$	265932.	+	265932.i	0.503156	+	0.503156i	0.912417	−	0.409262i	$-0.134214\pi$
$727$	265932.	+	265932.i	0.503156	+	0.503156i	−0.409262	+	0.912417i	$0.634214\pi$
$728$	93187.0	−	93187.0i	0.175830	−	0.175830i
$729$		−	287187.i		−	0.540393i
$730$	113717.	−	93340.0i	0.213393	−	0.175155i
$731$	−160715.			−0.300762
$732$	−499548.	−	499548.i	−0.932298	−	0.932298i
$733$	226808.	−	226808.i	0.422134	−	0.422134i	−0.463804	−	0.885938i	$-0.653516\pi$
$733$	226808.	−	226808.i	0.422134	−	0.422134i	0.885938	+	0.463804i	$0.153516\pi$
$734$			58618.9i			0.108804i
$735$	2.67510e6	+	263263.i	4.95183	+	0.487322i
$736$	19967.2			0.0368605
$737$	21265.6	+	21265.6i	0.0391511	+	0.0391511i
$738$	966539.	−	966539.i	1.77462	−	1.77462i
$739$			776289.i			1.42146i	0.703465	+	0.710730i	$0.251635\pi$
$739$			776289.i			1.42146i	−0.703465	+	0.710730i	$0.748365\pi$
$740$	−51961.3	+	527995.i	−0.0948892	+	0.964198i
$741$	−334036.			−0.608354
$742$	−425607.	−	425607.i	−0.773038	−	0.773038i
$743$	−759616.	+	759616.i	−1.37599	+	1.37599i	−0.524716	+	0.851277i	$0.675829\pi$
$743$	−759616.	+	759616.i	−1.37599	+	1.37599i	−0.851277	+	0.524716i	$0.824171\pi$
$744$		−	232000.i		−	0.419123i
$745$	239936.	+	292316.i	0.432298	+	0.526672i
$746$	−766870.			−1.37798
$747$	854478.	+	854478.i	1.53130	+	1.53130i
$748$	209932.	−	209932.i	0.375210	−	0.375210i
$749$			1.30505e6i			2.32629i
$750$	331859.	+	620514.i	0.589971	+	1.10314i
$751$	−381270.			−0.676009			−0.338005	−	0.941144i	$-0.609752\pi$
$751$	−381270.			−0.676009			−0.338005	+	0.941144i	$0.609752\pi$
$752$	56786.1	+	56786.1i	0.100417	+	0.100417i
$753$	89946.4	−	89946.4i	0.158633	−	0.158633i
$754$			193500.i			0.340360i
$755$	−346205.	+	284168.i	−0.607350	+	0.498519i
$756$	1.11544e6			1.95166
$757$	−458160.	−	458160.i	−0.799512	−	0.799512i	0.183506	−	0.983019i	$-0.441255\pi$
$757$	−458160.	−	458160.i	−0.799512	−	0.799512i	−0.983019	+	0.183506i	$0.941255\pi$
$758$	344444.	−	344444.i	0.599487	−	0.599487i
$759$			213516.i			0.370635i
$760$	−194012.	−	19093.2i	−0.335893	−	0.0330560i
$761$	484576.			0.836744			0.418372	−	0.908276i	$-0.362601\pi$
$761$	484576.			0.836744			0.418372	+	0.908276i	$0.362601\pi$
$762$	−793415.	−	793415.i	−1.36644	−	1.36644i
$763$	−290996.	+	290996.i	−0.499847	+	0.499847i
$764$			290414.i			0.497543i
$765$	128952.	−	1.31032e6i	0.220347	−	2.23901i
$766$	398145.			0.678553
$767$	−104604.	−	104604.i	−0.177810	−	0.177810i
$768$	46116.5	−	46116.5i	0.0781869	−	0.0781869i
$769$		−	1.00900e6i		−	1.70623i	−0.521720	−	0.853117i	$-0.674709\pi$
$769$		−	1.00900e6i		−	1.70623i	0.521720	−	0.853117i	$-0.325291\pi$
$770$	521809.	+	635724.i	0.880095	+	1.07223i
$771$	128606.			0.216347
$772$	49315.1	+	49315.1i	0.0827457	+	0.0827457i
$773$	22261.1	−	22261.1i	0.0372552	−	0.0372552i	−0.688234	−	0.725489i	$-0.741614\pi$
$773$	22261.1	−	22261.1i	0.0372552	−	0.0372552i	0.725489	+	0.688234i	$0.241614\pi$
$774$		−	256910.i		−	0.428844i
$775$	78454.0	−	394737.i	0.130621	−	0.657211i
$776$	273584.			0.454326
$777$	2.85752e6	+	2.85752e6i	4.73311	+	4.73311i
$778$	211813.	−	211813.i	0.349940	−	0.349940i
$779$			965339.i			1.59076i
$780$	149842.	−	122992.i	0.246289	−	0.202157i
$781$	63118.7			0.103480
$782$	−67343.9	−	67343.9i	−0.110125	−	0.110125i
$783$	−1.15809e6	+	1.15809e6i	−1.88895	+	1.88895i
$784$		−	432177.i		−	0.703120i
$785$	206815.	+	20353.2i	0.335617	+	0.0330289i
$786$	1.31977e6			2.13625
$787$	−300206.	−	300206.i	−0.484697	−	0.484697i	0.421931	−	0.906628i	$-0.361352\pi$
$787$	−300206.	−	300206.i	−0.484697	−	0.484697i	−0.906628	+	0.421931i	$0.861352\pi$
$788$	−168932.	+	168932.i	−0.272056	+	0.272056i
$789$		−	1.25024e6i		−	2.00835i
$790$	−8115.53	+	82464.4i	−0.0130036	+	0.132133i
$791$	577878.			0.923598
$792$	335584.	+	335584.i	0.534997	+	0.534997i
$793$	−238732.	+	238732.i	−0.379634	+	0.379634i
$794$		−	467169.i		−	0.741025i
$795$	−561733.	−	684365.i	−0.888783	−	1.08281i
$796$	37801.5			0.0596600
$797$	1991.80	+	1991.80i	0.00313566	+	0.00313566i	0.708673	−	0.705537i	$-0.249294\pi$
$797$	1991.80	+	1991.80i	0.00313566	+	0.00313566i	−0.705537	+	0.708673i	$0.749294\pi$
$798$	−1.04999e6	+	1.04999e6i	−1.64885	+	1.64885i
$799$		−	383049.i		−	0.600013i
$800$	94060.2	−	62870.3i	0.146969	−	0.0982348i
$801$	1.43738e6			2.24030
$802$	63726.0	+	63726.0i	0.0990759	+	0.0990759i
$803$	178852.	−	178852.i	0.277373	−	0.277373i
$804$		−	31511.5i		−	0.0487480i
$805$	203934.	−	167391.i	0.314700	−	0.258309i
$806$	−110872.			−0.170668
$807$	637471.	+	637471.i	0.978844	+	0.978844i
$808$	4565.57	−	4565.57i	0.00699314	−	0.00699314i
$809$		−	429010.i		−	0.655496i	−0.944765	−	0.327748i	$-0.893710\pi$
$809$		−	429010.i		−	0.655496i	0.944765	−	0.327748i	$-0.106290\pi$
$810$	649499.	+	63918.8i	0.989939	+	0.0974224i
$811$	116286.			0.176802			0.0884009	−	0.996085i	$-0.471824\pi$
$811$	116286.			0.176802			0.0884009	+	0.996085i	$0.471824\pi$
$812$	608241.	+	608241.i	0.922495	+	0.922495i
$813$	−958974.	+	958974.i	−1.45086	+	1.45086i
$814$			912146.i			1.37662i
$815$	2358.81	−	23968.5i	0.00355121	−	0.0360850i
$816$	−311077.			−0.467184
$817$	128296.	+	128296.i	0.192206	+	0.192206i
$818$	−108762.	+	108762.i	−0.162544	+	0.162544i
$819$		−	1.00483e6i		−	1.49804i
$820$	−355438.	−	433034.i	−0.528611	−	0.644012i
$821$	572957.			0.850033			0.425017	−	0.905186i	$-0.360268\pi$
$821$	572957.			0.850033			0.425017	+	0.905186i	$0.360268\pi$
$822$	−194864.	−	194864.i	−0.288396	−	0.288396i
$823$	−36299.1	+	36299.1i	−0.0535915	+	0.0535915i	−0.733395	−	0.679803i	$-0.762065\pi$
$823$	−36299.1	+	36299.1i	−0.0535915	+	0.0535915i	0.679803	+	0.733395i	$0.262065\pi$
$824$			224667.i			0.330891i
$825$	672293.	+	1.00582e6i	0.987758	+	1.47778i
$826$	−657614.			−0.963853
$827$	−459519.	−	459519.i	−0.671881	−	0.671881i	0.286269	−	0.958149i	$-0.407585\pi$
$827$	−459519.	−	459519.i	−0.671881	−	0.671881i	−0.958149	+	0.286269i	$0.907585\pi$
$828$	107652.	−	107652.i	0.157022	−	0.157022i
$829$		−	341288.i		−	0.496606i	−0.968682	−	0.248303i	$-0.920127\pi$
$829$		−	341288.i		−	0.496606i	0.968682	−	0.248303i	$-0.0798728\pi$
$830$	382828.	−	314229.i	0.555709	−	0.456131i
$831$	−2.37799e6			−3.44357
$832$	−22038.9	−	22038.9i	−0.0318379	−	0.0318379i
$833$	−1.45762e6	+	1.45762e6i	−2.10065	+	2.10065i
$834$		−	130036.i		−	0.186952i
$835$	61120.4	+	6015.01i	0.0876623	+	0.00862707i
$836$	−335168.			−0.479567
$837$	−663564.	−	663564.i	−0.947179	−	0.947179i
$838$	−240868.	+	240868.i	−0.342997	+	0.342997i
$839$		−	26264.9i		−	0.0373123i	−0.999826	−	0.0186561i	$-0.994061\pi$
$839$		−	26264.9i		−	0.0373123i	0.999826	−	0.0186561i	$-0.00593878\pi$
$840$	84400.2	−	857617.i	0.119615	−	1.21544i
$841$	−555716.			−0.785707
$842$	−427537.	−	427537.i	−0.603044	−	0.603044i
$843$	−459231.	+	459231.i	−0.646214	+	0.646214i
$844$			199877.i			0.280593i
$845$	394238.	+	480304.i	0.552135	+	0.672671i
$846$	612319.			0.855533
$847$	9354.30	+	9354.30i	0.0130390	+	0.0130390i
$848$	−100657.	+	100657.i	−0.139976	+	0.139976i
$849$			2.05684e6i			2.85355i
$850$	−529284.	−	105195.i	−0.732573	−	0.145599i
$851$	292607.			0.404041
$852$	−46764.7	−	46764.7i	−0.0644227	−	0.0644227i
$853$	362018.	−	362018.i	0.497545	−	0.497545i	−0.413128	−	0.910673i	$-0.635564\pi$
$853$	362018.	−	362018.i	0.497545	−	0.497545i	0.910673	+	0.413128i	$0.135564\pi$
$854$			1.50084e6i			2.05788i
$855$	−1.14894e6	+	943063.i	−1.57169	+	1.29006i
$856$	308647.			0.421225
$857$	540913.	+	540913.i	0.736488	+	0.736488i	0.971896	−	0.235409i	$-0.0756429\pi$
$857$	540913.	+	540913.i	0.736488	+	0.736488i	−0.235409	+	0.971896i	$0.575643\pi$
$858$	235670.	−	235670.i	0.320132	−	0.320132i
$859$			651158.i			0.882470i	0.897392	+	0.441235i	$0.145460\pi$
$859$			651158.i			0.882470i	−0.897392	+	0.441235i	$0.854540\pi$
$860$	−104790.	−	10312.6i	−0.141684	−	0.0139435i
$861$	−4.26722e6			−5.75624
$862$	713523.	+	713523.i	0.960270	+	0.960270i
$863$	−487076.	+	487076.i	−0.653996	+	0.653996i	−0.953953	−	0.299956i	$-0.903028\pi$
$863$	−487076.	+	487076.i	−0.653996	+	0.653996i	0.299956	+	0.953953i	$0.403028\pi$
$864$		−	263804.i		−	0.353390i
$865$	−27899.7	+	283497.i	−0.0372878	+	0.378893i
$866$	910036.			1.21345
$867$	108823.	+	108823.i	0.144772	+	0.144772i
$868$	−348510.	+	348510.i	−0.462569	+	0.462569i
$869$			142463.i			0.188652i
$870$	802782.	+	978037.i	1.06062	+	1.29216i
$871$	−15059.2			−0.0198503
$872$	68821.1	+	68821.1i	0.0905083	+	0.0905083i
$873$	1.47501e6	−	1.47501e6i	1.93539	−	1.93539i
$874$			107518.i			0.140754i
$875$	433619.	−	1.43066e6i	0.566359	−	1.86861i
$876$	−265024.			−0.345363
$877$	843570.	+	843570.i	1.09679	+	1.09679i	0.994784	+	0.102002i	$0.0325250\pi$
$877$	843570.	+	843570.i	1.09679	+	1.09679i	0.102002	+	0.994784i	$0.467475\pi$
$878$	−363003.	+	363003.i	−0.470892	+	0.470892i
$879$		−	1.97503e6i		−	2.55621i
$880$	150350.	−	123409.i	0.194151	−	0.159361i
$881$	341658.			0.440190			0.220095	−	0.975478i	$-0.429363\pi$
$881$	341658.			0.440190			0.220095	+	0.975478i	$0.429363\pi$
$882$	−2.33006e6	−	2.33006e6i	−2.99522	−	2.99522i
$883$	386897.	−	386897.i	0.496220	−	0.496220i	−0.414039	−	0.910259i	$-0.635882\pi$
$883$	386897.	−	386897.i	0.496220	−	0.496220i	0.910259	+	0.414039i	$0.135882\pi$
$884$			148663.i			0.190238i
$885$	−962686.	−	94740.3i	−1.22913	−	0.120962i
$886$	−171511.			−0.218487
$887$	−546030.	−	546030.i	−0.694016	−	0.694016i	0.269097	−	0.963113i	$-0.413275\pi$
$887$	−546030.	−	546030.i	−0.694016	−	0.694016i	−0.963113	+	0.269097i	$0.913275\pi$
$888$	675809.	−	675809.i	0.857034	−	0.857034i
$889$			2.38374e6i			3.01617i
$890$	57697.6	−	586283.i	0.0728413	−	0.740163i
$891$	1.12205e6			1.41338
$892$	−18893.8	−	18893.8i	−0.0237459	−	0.0237459i
$893$	−305779.	+	305779.i	−0.383447	+	0.383447i
$894$		−	681258.i		−	0.852387i
$895$	−958804.	−	1.16812e6i	−1.19697	−	1.45828i
$896$	−138553.			−0.172583
$897$	−75600.4	−	75600.4i	−0.0939591	−	0.0939591i
$898$	−6736.89	+	6736.89i	−0.00835423	+	0.00835423i
$899$		−	723672.i		−	0.895411i
$900$	168159.	−	846082.i	0.207603	−	1.04455i
$901$	678978.			0.836384
$902$	−681068.	−	681068.i	−0.837100	−	0.837100i
$903$	−567123.	+	567123.i	−0.695507	+	0.695507i
$904$		−	136669.i		−	0.167238i
$905$	648243.	−	532084.i	0.791481	−	0.649655i
$906$	806848.			0.982959
$907$	−820809.	−	820809.i	−0.997763	−	0.997763i	0.00223456	−	0.999998i	$-0.499289\pi$
$907$	−820809.	−	820809.i	−0.997763	−	0.997763i	−0.999998	+	0.00223456i	$0.999289\pi$
$908$	−194024.	+	194024.i	−0.235333	+	0.235333i
$909$		−	49230.1i		−	0.0595803i
$910$	−409852.	−	40334.6i	−0.494931	−	0.0487074i
$911$	948800.			1.14324			0.571621	−	0.820518i	$-0.306315\pi$
$911$	948800.			1.14324			0.571621	+	0.820518i	$0.306315\pi$
$912$	248326.	+	248326.i	0.298561	+	0.298561i
$913$	602105.	−	602105.i	0.722322	−	0.722322i
$914$			696054.i			0.833203i
$915$	−216222.	+	2.19710e6i	−0.258260	+	2.62426i
$916$	677774.			0.807781
$917$	−1.98256e6	−	1.98256e6i	−2.35769	−	2.35769i
$918$	−889741.	+	889741.i	−1.05579	+	1.05579i
$919$		−	422493.i		−	0.500251i	−0.968213	−	0.250126i	$-0.919528\pi$
$919$		−	422493.i		−	0.500251i	0.968213	−	0.250126i	$-0.0804719\pi$
$920$	−39588.3	−	48230.8i	−0.0467725	−	0.0569834i
$921$	−1.48074e6			−1.74566
$922$	87497.3	+	87497.3i	0.102928	+	0.102928i
$923$	−22348.7	+	22348.7i	−0.0262331	+	0.0262331i
$924$		−	1.48159e6i		−	1.73534i
$925$	1.37840e6	−	921326.i	1.61098	−	1.07679i
$926$	621635.			0.724959
$927$	1.21128e6	+	1.21128e6i	1.40956	+	1.40956i
$928$	143850.	−	143850.i	0.167038	−	0.167038i
$929$		−	866139.i		−	1.00359i	−0.864987	−	0.501795i	$-0.832673\pi$
$929$		−	866139.i		−	1.00359i	0.864987	−	0.501795i	$-0.167327\pi$
$930$	−560396.	+	459978.i	−0.647931	+	0.531828i
$931$	2.32716e6			2.68490
$932$	−142272.	−	142272.i	−0.163790	−	0.163790i
$933$	−172672.	+	172672.i	−0.198362	+	0.198362i
$934$			818519.i			0.938285i
$935$	−923315.	−	90865.8i	−1.05615	−	0.103939i
$936$	−237643.			−0.271253
$937$	924172.	+	924172.i	1.05262	+	1.05262i	0.998536	+	0.0540883i	$0.0172252\pi$
$937$	924172.	+	924172.i	1.05262	+	1.05262i	0.0540883	+	0.998536i	$0.482775\pi$
$938$	−47336.6	+	47336.6i	−0.0538011	+	0.0538011i
$939$			648085.i			0.735023i
$940$	24579.0	−	249755.i	0.0278169	−	0.282656i
$941$	−285158.			−0.322037			−0.161019	−	0.986951i	$-0.551478\pi$
$941$	−285158.			−0.322037			−0.161019	+	0.986951i	$0.551478\pi$
$942$	−264714.	−	264714.i	−0.298315	−	0.298315i
$943$	−218480.	+	218480.i	−0.245690	+	0.245690i
$944$			155527.i			0.174527i
$945$	−2.21155e6	−	2.69435e6i	−2.47647	−	3.01711i
$946$	−181031.			−0.202288
$947$	−173576.	−	173576.i	−0.193549	−	0.193549i	0.603679	−	0.797228i	$-0.293701\pi$
$947$	−173576.	−	173576.i	−0.193549	−	0.193549i	−0.797228	+	0.603679i	$0.793701\pi$
$948$	105551.	−	105551.i	0.117448	−	0.117448i
$949$			126654.i			0.140633i
$950$	338541.	+	506491.i	0.375115	+	0.561209i
$951$	1.92572e6			2.12928
$952$	467301.	+	467301.i	0.515611	+	0.515611i
$953$	−118957.	+	118957.i	−0.130980	+	0.130980i	−0.769558	−	0.638577i	$-0.779523\pi$
$953$	−118957.	+	118957.i	−0.130980	+	0.130980i	0.638577	+	0.769558i	$0.279523\pi$
$954$			1.08537e6i			1.19257i
$955$	701496.	−	575795.i	0.769163	−	0.631336i
$956$	343650.			0.376011
$957$	1.53824e6	+	1.53824e6i	1.67958	+	1.67958i
$958$	717041.	−	717041.i	0.781291	−	0.781291i
$959$			585452.i			0.636581i
$960$	−202828.	−	19960.8i	−0.220083	−	0.0216589i
$961$	−508871.			−0.551012
$962$	−322967.	−	322967.i	−0.348986	−	0.348986i
$963$	1.66405e6	−	1.66405e6i	1.79438	−	1.79438i
$964$		−	265405.i		−	0.285598i
$965$	21345.3	−	216896.i	0.0229217	−	0.232915i
$966$	−475278.			−0.509324
$967$	81318.5	+	81318.5i	0.0869633	+	0.0869633i	0.749250	−	0.662287i	$-0.230414\pi$
$967$	81318.5	+	81318.5i	0.0869633	+	0.0869633i	−0.662287	+	0.749250i	$0.730414\pi$
$968$	2212.31	−	2212.31i	0.00236100	−	0.00236100i
$969$		−	1.67507e6i		−	1.78396i
$970$	−542427.	−	660843.i	−0.576498	−	0.702352i
$971$	1.35495e6			1.43709			0.718547	−	0.695479i	$-0.244808\pi$
$971$	1.35495e6			1.43709			0.718547	+	0.695479i	$0.244808\pi$
$972$	−163574.	−	163574.i	−0.173134	−	0.173134i
$973$	−195340.	+	195340.i	−0.206331	+	0.206331i
$974$		−	107509.i		−	0.113326i
$975$	−594175.	−	118092.i	−0.625036	−	0.124226i
$976$	354953.			0.372624
$977$	−1.06127e6	−	1.06127e6i	−1.11183	−	1.11183i	−0.992903	−	0.118923i	$-0.962056\pi$
$977$	−1.06127e6	−	1.06127e6i	−1.11183	−	1.11183i	−0.118923	−	0.992903i	$-0.537944\pi$
$978$	−30678.6	+	30678.6i	−0.0320744	+	0.0320744i
$979$		−	1.01284e6i		−	1.05676i
$980$	−1.04392e6	+	856863.i	−1.08697	+	0.892194i
$981$	742090.			0.771114
$982$	−403318.	−	403318.i	−0.418239	−	0.418239i
$983$	−73443.1	+	73443.1i	−0.0760053	+	0.0760053i	−0.744088	−	0.668082i	$-0.767115\pi$
$983$	−73443.1	+	73443.1i	−0.0760053	+	0.0760053i	0.668082	+	0.744088i	$0.267115\pi$
$984$			1.00921e6i			1.04229i
$985$	742990.	+	73119.5i	0.765791	+	0.0753634i
$986$	−970337.			−0.998088
$987$	−1.35168e6	−	1.35168e6i	−1.38752	−	1.38752i
$988$	118674.	−	118674.i	0.121574	−	0.121574i
$989$			58072.8i			0.0593718i
$990$	145253.	−	1.47596e6i	0.148202	−	1.50592i
$991$	−643800.			−0.655547			−0.327773	−	0.944756i	$-0.606298\pi$
$991$	−643800.			−0.655547			−0.327773	+	0.944756i	$0.606298\pi$
$992$	82423.4	+	82423.4i	0.0837582	+	0.0837582i
$993$	415006.	−	415006.i	0.420877	−	0.420877i
$994$			140500.i			0.142201i
$995$	−74947.8	−	91309.6i	−0.0757030	−	0.0922296i
$996$	−892200.			−0.899381
$997$	709345.	+	709345.i	0.713621	+	0.713621i	0.967291	−	0.253670i	$-0.0816378\pi$
$997$	709345.	+	709345.i	0.713621	+	0.713621i	−0.253670	+	0.967291i	$0.581638\pi$
$998$	87583.5	−	87583.5i	0.0879349	−	0.0879349i
$999$		−	3.86589e6i		−	3.87364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.a.47.20	✓	44
5.3	odd	4	inner	230.5.f.a.93.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.a.47.20	✓	44	1.1	even	1	trivial
230.5.f.a.93.20	yes	44	5.3	odd	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(11.2589 - 11.2589i) q^{3} +8.00000i q^{4} +(19.3240 - 15.8613i) q^{5} -45.0357 q^{6} +(67.6527 + 67.6527i) q^{7} +(16.0000 - 16.0000i) q^{8} -172.526i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +(11.2589 - 11.2589i) q^{3} +8.00000i q^{4} +(19.3240 - 15.8613i) q^{5} -45.0357 q^{6} +(67.6527 + 67.6527i) q^{7} +(16.0000 - 16.0000i) q^{8} -172.526i q^{9} +(-70.3707 - 6.92536i) q^{10} -121.570 q^{11} +(90.0713 + 90.0713i) q^{12} +(43.0448 - 43.0448i) q^{13} -270.611i q^{14} +(38.9860 - 396.149i) q^{15} -64.0000 q^{16} +(215.855 + 215.855i) q^{17} +(-345.052 + 345.052i) q^{18} -344.624i q^{19} +(126.891 + 154.592i) q^{20} +1523.39 q^{21} +(243.140 + 243.140i) q^{22} +(77.9968 - 77.9968i) q^{23} -360.285i q^{24} +(121.836 - 613.010i) q^{25} -172.179 q^{26} +(-1030.49 - 1030.49i) q^{27} +(-541.221 + 541.221i) q^{28} -1123.83i q^{29} +(-870.270 + 714.326i) q^{30} +643.933 q^{31} +(128.000 + 128.000i) q^{32} +(-1368.75 + 1368.75i) q^{33} -863.419i q^{34} +(2380.38 + 234.259i) q^{35} +1380.21 q^{36} +(1875.76 + 1875.76i) q^{37} +(-689.248 + 689.248i) q^{38} -969.275i q^{39} +(55.4029 - 562.966i) q^{40} -2801.14 q^{41} +(-3046.78 - 3046.78i) q^{42} +(-372.277 + 372.277i) q^{43} -972.560i q^{44} +(-2736.50 - 3333.90i) q^{45} -311.987 q^{46} +(-887.284 - 887.284i) q^{47} +(-720.570 + 720.570i) q^{48} +6752.76i q^{49} +(-1469.69 + 982.348i) q^{50} +4860.58 q^{51} +(344.358 + 344.358i) q^{52} +(1572.77 - 1572.77i) q^{53} +4121.94i q^{54} +(-2349.22 + 1928.26i) q^{55} +2164.88 q^{56} +(-3880.09 - 3880.09i) q^{57} +(-2247.66 + 2247.66i) q^{58} -2430.11i q^{59} +(3169.19 + 311.888i) q^{60} -5546.14 q^{61} +(-1287.87 - 1287.87i) q^{62} +(11671.9 - 11671.9i) q^{63} -512.000i q^{64} +(149.050 - 1514.55i) q^{65} +5474.98 q^{66} +(-174.925 - 174.925i) q^{67} +(-1726.84 + 1726.84i) q^{68} -1756.32i q^{69} +(-4292.25 - 5229.29i) q^{70} -519.196 q^{71} +(-2760.42 - 2760.42i) q^{72} +(-1471.19 + 1471.19i) q^{73} -7503.05i q^{74} +(-5530.09 - 8273.56i) q^{75} +2756.99 q^{76} +(-8224.53 - 8224.53i) q^{77} +(-1938.55 + 1938.55i) q^{78} -1171.86i q^{79} +(-1236.74 + 1015.13i) q^{80} -9229.68 q^{81} +(5602.27 + 5602.27i) q^{82} +(-4952.74 + 4952.74i) q^{83} +12187.1i q^{84} +(7594.93 + 747.436i) q^{85} +1489.11 q^{86} +(-12653.1 - 12653.1i) q^{87} +(-1945.12 + 1945.12i) q^{88} +8331.35i q^{89} +(-1194.81 + 12140.8i) q^{90} +5824.19 q^{91} +(623.974 + 623.974i) q^{92} +(7249.99 - 7249.99i) q^{93} +3549.13i q^{94} +(-5466.20 - 6659.52i) q^{95} +2882.28 q^{96} +(8549.51 + 8549.51i) q^{97} +(13505.5 - 13505.5i) q^{98} +20974.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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