LMFDB - Embedded newform 35.5.g.a.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.g (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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.1
Character	$\chi$	$=$	35.22
Dual form			35.5.g.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.44757 - 5.44757i) q^{2} +(1.36639 - 1.36639i) q^{3} +43.3520i q^{4} +(7.20796 + 23.9384i) q^{5} -14.8870 q^{6} +(-13.0958 - 13.0958i) q^{7} +(149.002 - 149.002i) q^{8} +77.2660i q^{9} +O(q^{10})$	\(q+(-5.44757 - 5.44757i) q^{2} +(1.36639 - 1.36639i) q^{3} +43.3520i q^{4} +(7.20796 + 23.9384i) q^{5} -14.8870 q^{6} +(-13.0958 - 13.0958i) q^{7} +(149.002 - 149.002i) q^{8} +77.2660i q^{9} +(91.1401 - 169.672i) q^{10} +81.6042 q^{11} +(59.2358 + 59.2358i) q^{12} +(-66.7280 + 66.7280i) q^{13} +142.681i q^{14} +(42.5580 + 22.8603i) q^{15} -929.763 q^{16} +(347.598 + 347.598i) q^{17} +(420.912 - 420.912i) q^{18} +69.2205i q^{19} +(-1037.78 + 312.479i) q^{20} -35.7880 q^{21} +(-444.544 - 444.544i) q^{22} +(40.2630 - 40.2630i) q^{23} -407.189i q^{24} +(-521.091 + 345.093i) q^{25} +727.010 q^{26} +(216.253 + 216.253i) q^{27} +(567.729 - 567.729i) q^{28} +586.403i q^{29} +(-107.305 - 356.371i) q^{30} +538.834 q^{31} +(2680.92 + 2680.92i) q^{32} +(111.503 - 111.503i) q^{33} -3787.13i q^{34} +(219.098 - 407.886i) q^{35} -3349.63 q^{36} +(-1084.74 - 1084.74i) q^{37} +(377.083 - 377.083i) q^{38} +182.353i q^{39} +(4640.86 + 2492.86i) q^{40} +80.0417 q^{41} +(194.957 + 194.957i) q^{42} +(-1323.31 + 1323.31i) q^{43} +3537.70i q^{44} +(-1849.62 + 556.930i) q^{45} -438.671 q^{46} +(-2670.09 - 2670.09i) q^{47} +(-1270.42 + 1270.42i) q^{48} +343.000i q^{49} +(4718.60 + 958.758i) q^{50} +949.909 q^{51} +(-2892.79 - 2892.79i) q^{52} +(1863.94 - 1863.94i) q^{53} -2356.11i q^{54} +(588.199 + 1953.47i) q^{55} -3902.60 q^{56} +(94.5822 + 94.5822i) q^{57} +(3194.47 - 3194.47i) q^{58} +1139.50i q^{59} +(-991.039 + 1844.98i) q^{60} +3393.50 q^{61} +(-2935.33 - 2935.33i) q^{62} +(1011.86 - 1011.86i) q^{63} -14332.8i q^{64} +(-2078.33 - 1116.39i) q^{65} -1214.84 q^{66} +(1840.20 + 1840.20i) q^{67} +(-15069.1 + 15069.1i) q^{68} -110.030i q^{69} +(-3415.54 + 1028.43i) q^{70} +6930.24 q^{71} +(11512.8 + 11512.8i) q^{72} +(-823.082 + 823.082i) q^{73} +11818.3i q^{74} +(-240.481 + 1183.55i) q^{75} -3000.85 q^{76} +(-1068.67 - 1068.67i) q^{77} +(993.380 - 993.380i) q^{78} +86.0479i q^{79} +(-6701.69 - 22257.0i) q^{80} -5667.57 q^{81} +(-436.033 - 436.033i) q^{82} +(7100.46 - 7100.46i) q^{83} -1551.48i q^{84} +(-5815.46 + 10826.4i) q^{85} +14417.6 q^{86} +(801.255 + 801.255i) q^{87} +(12159.2 - 12159.2i) q^{88} -12171.5i q^{89} +(13109.8 + 7042.02i) q^{90} +1747.71 q^{91} +(1745.48 + 1745.48i) q^{92} +(736.258 - 736.258i) q^{93} +29091.0i q^{94} +(-1657.02 + 498.938i) q^{95} +7326.37 q^{96} +(-7968.92 - 7968.92i) q^{97} +(1868.52 - 1868.52i) q^{98} +6305.23i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−5.44757	−	5.44757i	−1.36189	−	1.36189i	−0.871505	−	0.490387i	$-0.836855\pi$
$2$	−5.44757	−	5.44757i	−1.36189	−	1.36189i	−0.490387	−	0.871505i	$-0.663145\pi$
$3$	1.36639	−	1.36639i	0.151821	−	0.151821i	−0.627110	−	0.778931i	$-0.715762\pi$
$3$	1.36639	−	1.36639i	0.151821	−	0.151821i	0.778931	+	0.627110i	$0.215762\pi$
$4$			43.3520i			2.70950i
$5$	7.20796	+	23.9384i	0.288318	+	0.957535i
$5$	7.20796	+	23.9384i	0.288318	+	0.957535i
$6$	−14.8870			−0.413528
$7$	−13.0958	−	13.0958i	−0.267261	−	0.267261i
$7$	−13.0958	−	13.0958i	−0.267261	−	0.267261i
$8$	149.002	−	149.002i	2.32815	−	2.32815i
$9$			77.2660i			0.953901i
$10$	91.1401	−	169.672i	0.911401	−	1.69672i
$11$	81.6042			0.674415			0.337207	−	0.941430i	$-0.390518\pi$
$11$	81.6042			0.674415			0.337207	+	0.941430i	$0.390518\pi$
$12$	59.2358	+	59.2358i	0.411359	+	0.411359i
$13$	−66.7280	+	66.7280i	−0.394840	+	0.394840i	−0.876408	−	0.481568i	$-0.840067\pi$
$13$	−66.7280	+	66.7280i	−0.394840	+	0.394840i	0.481568	+	0.876408i	$0.340067\pi$
$14$			142.681i			0.727962i
$15$	42.5580	+	22.8603i	0.189147	+	0.101601i
$16$	−929.763			−3.63189
$17$	347.598	+	347.598i	1.20276	+	1.20276i	0.973323	+	0.229438i	$0.0736889\pi$
$17$	347.598	+	347.598i	1.20276	+	1.20276i	0.229438	+	0.973323i	$0.426311\pi$
$18$	420.912	−	420.912i	1.29911	−	1.29911i
$19$			69.2205i			0.191746i	0.995394	+	0.0958732i	$0.0305643\pi$
$19$			69.2205i			0.191746i	−0.995394	+	0.0958732i	$0.969436\pi$
$20$	−1037.78	+	312.479i	−2.59444	+	0.781198i
$21$	−35.7880			−0.0811518
$22$	−444.544	−	444.544i	−0.918480	−	0.918480i
$23$	40.2630	−	40.2630i	0.0761115	−	0.0761115i	−0.668026	−	0.744138i	$-0.732861\pi$
$23$	40.2630	−	40.2630i	0.0761115	−	0.0761115i	0.744138	+	0.668026i	$0.232861\pi$
$24$		−	407.189i		−	0.706926i
$25$	−521.091	+	345.093i	−0.833745	+	0.552149i
$26$	727.010			1.07546
$27$	216.253	+	216.253i	0.296644	+	0.296644i
$28$	567.729	−	567.729i	0.724144	−	0.724144i
$29$			586.403i			0.697268i	0.937259	+	0.348634i	$0.113354\pi$
$29$			586.403i			0.697268i	−0.937259	+	0.348634i	$0.886646\pi$
$30$	−107.305	−	356.371i	−0.119228	−	0.395967i
$31$	538.834			0.560701			0.280351	−	0.959898i	$-0.409549\pi$
$31$	538.834			0.560701			0.280351	+	0.959898i	$0.409549\pi$
$32$	2680.92	+	2680.92i	2.61809	+	2.61809i
$33$	111.503	−	111.503i	0.102390	−	0.102390i
$34$		−	3787.13i		−	3.27606i
$35$	219.098	−	407.886i	0.178856	−	0.332968i
$36$	−3349.63			−2.58459
$37$	−1084.74	−	1084.74i	−0.792356	−	0.792356i	0.189521	−	0.981877i	$-0.439307\pi$
$37$	−1084.74	−	1084.74i	−0.792356	−	0.792356i	−0.981877	+	0.189521i	$0.939307\pi$
$38$	377.083	−	377.083i	0.261138	−	0.261138i
$39$			182.353i			0.119890i
$40$	4640.86	+	2492.86i	2.90054	+	1.55804i
$41$	80.0417			0.0476155			0.0238078	−	0.999717i	$-0.492421\pi$
$41$	80.0417			0.0476155			0.0238078	+	0.999717i	$0.492421\pi$
$42$	194.957	+	194.957i	0.110520	+	0.110520i
$43$	−1323.31	+	1323.31i	−0.715689	+	0.715689i	−0.967719	−	0.252030i	$-0.918902\pi$
$43$	−1323.31	+	1323.31i	−0.715689	+	0.715689i	0.252030	+	0.967719i	$0.418902\pi$
$44$			3537.70i			1.82733i
$45$	−1849.62	+	556.930i	−0.913393	+	0.275027i
$46$	−438.671			−0.207311
$47$	−2670.09	−	2670.09i	−1.20873	−	1.20873i	−0.971438	−	0.237294i	$-0.923740\pi$
$47$	−2670.09	−	2670.09i	−1.20873	−	1.20873i	−0.237294	−	0.971438i	$-0.576260\pi$
$48$	−1270.42	+	1270.42i	−0.551398	+	0.551398i
$49$			343.000i			0.142857i
$50$	4718.60	+	958.758i	1.88744	+	0.383503i
$51$	949.909			0.365209
$52$	−2892.79	−	2892.79i	−1.06982	−	1.06982i
$53$	1863.94	−	1863.94i	0.663560	−	0.663560i	−0.292658	−	0.956217i	$-0.594540\pi$
$53$	1863.94	−	1863.94i	0.663560	−	0.663560i	0.956217	+	0.292658i	$0.0945396\pi$
$54$		−	2356.11i		−	0.807993i
$55$	588.199	+	1953.47i	0.194446	+	0.645776i
$56$	−3902.60			−1.24445
$57$	94.5822	+	94.5822i	0.0291112	+	0.0291112i
$58$	3194.47	−	3194.47i	0.949604	−	0.949604i
$59$			1139.50i			0.327350i	0.986514	+	0.163675i	$0.0523348\pi$
$59$			1139.50i			0.327350i	−0.986514	+	0.163675i	$0.947665\pi$
$60$	−991.039	+	1844.98i	−0.275288	+	0.512493i
$61$	3393.50			0.911985			0.455993	−	0.889984i	$-0.349284\pi$
$61$	3393.50			0.911985			0.455993	+	0.889984i	$0.349284\pi$
$62$	−2935.33	−	2935.33i	−0.763615	−	0.763615i
$63$	1011.86	−	1011.86i	0.254941	−	0.254941i
$64$		−	14332.8i		−	3.49921i
$65$	−2078.33	−	1116.39i	−0.491912	−	0.264233i
$66$	−1214.84			−0.278889
$67$	1840.20	+	1840.20i	0.409935	+	0.409935i	0.881716	−	0.471781i	$-0.156389\pi$
$67$	1840.20	+	1840.20i	0.409935	+	0.409935i	−0.471781	+	0.881716i	$0.656389\pi$
$68$	−15069.1	+	15069.1i	−3.25888	+	3.25888i
$69$		−	110.030i		−	0.0231107i
$70$	−3415.54	+	1028.43i	−0.697049	+	0.209885i
$71$	6930.24			1.37477			0.687387	−	0.726291i	$-0.258757\pi$
$71$	6930.24			1.37477			0.687387	+	0.726291i	$0.258757\pi$
$72$	11512.8	+	11512.8i	2.22083	+	2.22083i
$73$	−823.082	+	823.082i	−0.154453	+	0.154453i	−0.780104	−	0.625650i	$-0.784834\pi$
$73$	−823.082	+	823.082i	−0.154453	+	0.154453i	0.625650	+	0.780104i	$0.284834\pi$
$74$			11818.3i			2.15821i
$75$	−240.481	+	1183.55i	−0.0427522	+	0.210408i
$76$	−3000.85			−0.519537
$77$	−1068.67	−	1068.67i	−0.180245	−	0.180245i
$78$	993.380	−	993.380i	0.163277	−	0.163277i
$79$			86.0479i			0.0137875i	0.999976	+	0.00689376i	$0.00219437\pi$
$79$			86.0479i			0.0137875i	−0.999976	+	0.00689376i	$0.997806\pi$
$80$	−6701.69	−	22257.0i	−1.04714	−	3.47766i
$81$	−5667.57			−0.863827
$82$	−436.033	−	436.033i	−0.0648472	−	0.0648472i
$83$	7100.46	−	7100.46i	1.03070	−	1.03070i	0.0311822	−	0.999514i	$-0.490073\pi$
$83$	7100.46	−	7100.46i	1.03070	−	1.03070i	0.999514	−	0.0311822i	$-0.00992720\pi$
$84$		−	1551.48i		−	0.219881i
$85$	−5815.46	+	10826.4i	−0.804908	+	1.49846i
$86$	14417.6			1.94938
$87$	801.255	+	801.255i	0.105860	+	0.105860i
$88$	12159.2	−	12159.2i	1.57014	−	1.57014i
$89$		−	12171.5i		−	1.53662i	−0.640080	−	0.768309i	$-0.721099\pi$
$89$		−	12171.5i		−	1.53662i	0.640080	−	0.768309i	$-0.278901\pi$
$90$	13109.8	+	7042.02i	1.61850	+	0.869386i
$91$	1747.71			0.211051
$92$	1745.48	+	1745.48i	0.206224	+	0.206224i
$93$	736.258	−	736.258i	0.0851263	−	0.0851263i
$94$			29091.0i			3.29232i
$95$	−1657.02	+	498.938i	−0.183604	+	0.0552840i
$96$	7326.37			0.794962
$97$	−7968.92	−	7968.92i	−0.846947	−	0.846947i	0.142804	−	0.989751i	$-0.454388\pi$
$97$	−7968.92	−	7968.92i	−0.846947	−	0.846947i	−0.989751	+	0.142804i	$0.954388\pi$
$98$	1868.52	−	1868.52i	0.194556	−	0.194556i
$99$			6305.23i			0.643325i
$100$	−14960.5	−	22590.3i	−1.49605	−	2.25903i
$101$	7550.77			0.740199			0.370100	−	0.928992i	$-0.379324\pi$
$101$	7550.77			0.740199			0.370100	+	0.928992i	$0.379324\pi$
$102$	−5174.70	−	5174.70i	−0.497376	−	0.497376i
$103$	6641.76	−	6641.76i	0.626049	−	0.626049i	−0.321022	−	0.947072i	$-0.604026\pi$
$103$	6641.76	−	6641.76i	0.626049	−	0.626049i	0.947072	+	0.321022i	$0.104026\pi$
$104$			19885.2i			1.83850i
$105$	−257.958	−	856.705i	−0.0233976	−	0.0777057i
$106$	−20307.9			−1.80739
$107$	−863.078	−	863.078i	−0.0753845	−	0.0753845i	0.668409	−	0.743794i	$-0.266976\pi$
$107$	−863.078	−	863.078i	−0.0753845	−	0.0753845i	−0.743794	+	0.668409i	$0.766976\pi$
$108$	−9375.00	+	9375.00i	−0.803755	+	0.803755i
$109$		−	930.380i		−	0.0783083i	−0.999233	−	0.0391541i	$-0.987534\pi$
$109$		−	930.380i		−	0.0783083i	0.999233	−	0.0391541i	$-0.0124663\pi$
$110$	7437.41	−	13845.9i	0.614662	−	1.14429i
$111$	−2964.34			−0.240593
$112$	12176.0	+	12176.0i	0.970663	+	0.970663i
$113$	−10907.2	+	10907.2i	−0.854196	+	0.854196i	−0.990647	−	0.136451i	$-0.956430\pi$
$113$	−10907.2	+	10907.2i	−0.854196	+	0.854196i	0.136451	+	0.990647i	$0.456430\pi$
$114$		−	1030.49i		−	0.0792925i
$115$	1254.04	+	673.616i	0.0948237	+	0.0509351i
$116$	−25421.7			−1.88925
$117$	−5155.80	−	5155.80i	−0.376638	−	0.376638i
$118$	6207.53	−	6207.53i	0.445815	−	0.445815i
$119$		−	9104.15i		−	0.642903i
$120$	9747.45	−	2935.00i	0.676906	−	0.203820i
$121$	−7981.76			−0.545165
$122$	−18486.3	−	18486.3i	−1.24203	−	1.24203i
$123$	109.368	−	109.368i	0.00722905	−	0.00722905i
$124$			23359.5i			1.51922i
$125$	−12017.0	−	9986.64i	−0.769086	−	0.639145i
$126$	−11024.3			−0.694403
$127$	9555.32	+	9555.32i	0.592431	+	0.592431i	0.938287	−	0.345856i	$-0.112412\pi$
$127$	9555.32	+	9555.32i	0.592431	+	0.592431i	−0.345856	+	0.938287i	$0.612412\pi$
$128$	−35184.0	+	35184.0i	−2.14746	+	2.14746i
$129$			3616.31i			0.217314i
$130$	5240.26	+	17403.4i	0.310074	+	1.02979i
$131$	17236.3			1.00439			0.502194	−	0.864755i	$-0.332526\pi$
$131$	17236.3			1.00439			0.502194	+	0.864755i	$0.332526\pi$
$132$	4833.89	+	4833.89i	0.277427	+	0.277427i
$133$	906.497	−	906.497i	0.0512464	−	0.0512464i
$134$		−	20049.2i		−	1.11657i
$135$	−3618.00	+	6735.49i	−0.198519	+	0.369574i
$136$	103585.			5.60043
$137$	9441.41	+	9441.41i	0.503032	+	0.503032i	0.912379	−	0.409347i	$-0.134243\pi$
$137$	9441.41	+	9441.41i	0.503032	+	0.503032i	−0.409347	+	0.912379i	$0.634243\pi$
$138$	−599.396	+	599.396i	−0.0314742	+	0.0314742i
$139$		−	26127.4i		−	1.35228i	−0.736772	−	0.676141i	$-0.763651\pi$
$139$		−	26127.4i		−	1.35228i	0.736772	−	0.676141i	$-0.236349\pi$
$140$	17682.7	+	9498.34i	0.902177	+	0.484609i
$141$	−7296.77			−0.367022
$142$	−37753.0	−	37753.0i	−1.87229	−	1.87229i
$143$	−5445.28	+	5445.28i	−0.266286	+	0.266286i
$144$		−	71839.0i		−	3.46446i
$145$	−14037.5	+	4226.76i	−0.667658	+	0.201035i
$146$	8967.59			0.420697
$147$	468.672	+	468.672i	0.0216887	+	0.0216887i
$148$	47025.4	−	47025.4i	2.14689	−	2.14689i
$149$			3703.79i			0.166830i	0.996515	+	0.0834149i	$0.0265827\pi$
$149$			3703.79i			0.166830i	−0.996515	+	0.0834149i	$0.973417\pi$
$150$	7757.48	−	5137.41i	0.344777	−	0.228329i
$151$	22789.3			0.999488			0.499744	−	0.866173i	$-0.333427\pi$
$151$	22789.3			0.999488			0.499744	+	0.866173i	$0.333427\pi$
$152$	10314.0	+	10314.0i	0.446415	+	0.446415i
$153$	−26857.5	+	26857.5i	−1.14731	+	1.14731i
$154$			11643.3i			0.490948i
$155$	3883.89	+	12898.8i	0.161660	+	0.536891i
$156$	−7905.36			−0.324842
$157$	5151.18	+	5151.18i	0.208981	+	0.208981i	0.803834	−	0.594853i	$-0.202790\pi$
$157$	5151.18	+	5151.18i	0.208981	+	0.208981i	−0.594853	+	0.803834i	$0.702790\pi$
$158$	468.752	−	468.752i	0.0187771	−	0.0187771i
$159$		−	5093.74i		−	0.201485i
$160$	−44852.9	+	83500.8i	−1.75207	+	3.26175i
$161$	−1054.55			−0.0406833
$162$	30874.5	+	30874.5i	1.17644	+	1.17644i
$163$	−20400.5	+	20400.5i	−0.767831	+	0.767831i	−0.977724	−	0.209893i	$-0.932688\pi$
$163$	−20400.5	+	20400.5i	−0.767831	+	0.767831i	0.209893	+	0.977724i	$0.432688\pi$
$164$			3469.97i			0.129014i
$165$	3472.91	+	1865.49i	0.127563	+	0.0685214i
$166$	−77360.5			−2.80739
$167$	31137.0	+	31137.0i	1.11646	+	1.11646i	0.992257	+	0.124204i	$0.0396376\pi$
$167$	31137.0	+	31137.0i	1.11646	+	1.11646i	0.124204	+	0.992257i	$0.460362\pi$
$168$	−5332.47	+	5332.47i	−0.188934	+	0.188934i
$169$			19655.8i			0.688203i
$170$	90657.7	−	27297.4i	3.13694	−	0.944548i
$171$	−5348.39			−0.182907
$172$	−57368.1	−	57368.1i	−1.93916	−	1.93916i
$173$	17298.0	−	17298.0i	0.577969	−	0.577969i	−0.356374	−	0.934343i	$-0.615987\pi$
$173$	17298.0	−	17298.0i	0.577969	−	0.577969i	0.934343	+	0.356374i	$0.115987\pi$
$174$		−	8729.78i		−	0.288340i
$175$	11343.4	+	2304.83i	0.370396	+	0.0752597i
$176$	−75872.6			−2.44940
$177$	1557.01	+	1557.01i	0.0496986	+	0.0496986i
$178$	−66305.3	+	66305.3i	−2.09271	+	2.09271i
$179$		−	1332.58i		−	0.0415897i	−0.999784	−	0.0207949i	$-0.993380\pi$
$179$		−	1332.58i		−	0.0415897i	0.999784	−	0.0207949i	$-0.00661969\pi$
$180$	−24144.0	−	80184.7i	−0.745185	−	2.47484i
$181$	12567.7			0.383618			0.191809	−	0.981432i	$-0.438565\pi$
$181$	12567.7			0.383618			0.191809	+	0.981432i	$0.438565\pi$
$182$	−9520.78	−	9520.78i	−0.287428	−	0.287428i
$183$	4636.84	−	4636.84i	0.138459	−	0.138459i
$184$		−	11998.5i		−	0.354399i
$185$	18148.1	−	33785.5i	0.530258	−	0.987159i
$186$	−8021.63			−0.231866
$187$	28365.5	+	28365.5i	0.811160	+	0.811160i
$188$	115754.	−	115754.i	3.27506	−	3.27506i
$189$		−	5664.02i		−	0.158563i
$190$	11744.8	+	6308.76i	0.325339	+	0.174758i
$191$	−12088.8			−0.331373			−0.165686	−	0.986179i	$-0.552984\pi$
$191$	−12088.8			−0.331373			−0.165686	+	0.986179i	$0.552984\pi$
$192$	−19584.2	−	19584.2i	−0.531254	−	0.531254i
$193$	−10539.9	+	10539.9i	−0.282957	+	0.282957i	−0.834287	−	0.551330i	$-0.814121\pi$
$193$	−10539.9	+	10539.9i	−0.282957	+	0.282957i	0.551330	+	0.834287i	$0.314121\pi$
$194$			86822.5i			2.30690i
$195$	−4365.23	+	1314.39i	−0.114799	+	0.0345665i
$196$	−14869.7			−0.387071
$197$	−6811.78	−	6811.78i	−0.175521	−	0.175521i	0.613879	−	0.789400i	$-0.289608\pi$
$197$	−6811.78	−	6811.78i	−0.175521	−	0.175521i	−0.789400	+	0.613879i	$0.789608\pi$
$198$	34348.1	−	34348.1i	0.876139	−	0.876139i
$199$		−	18221.4i		−	0.460125i	−0.973176	−	0.230063i	$-0.926107\pi$
$199$		−	18221.4i		−	0.460125i	0.973176	−	0.230063i	$-0.0738931\pi$
$200$	−26223.9	+	129063.i	−0.655598	+	3.22658i
$201$	5028.86			0.124474
$202$	−41133.3	−	41133.3i	−1.00807	−	1.00807i
$203$	7679.41	−	7679.41i	0.186353	−	0.186353i
$204$			41180.5i			0.989535i
$205$	576.937	+	1916.07i	0.0137284	+	0.0455935i
$206$	−72362.9			−1.70522
$207$	3110.96	+	3110.96i	0.0726028	+	0.0726028i
$208$	62041.2	−	62041.2i	1.43401	−	1.43401i
$209$			5648.68i			0.129317i
$210$	−3261.72	+	6072.20i	−0.0739618	+	0.137692i
$211$	−31576.9			−0.709259			−0.354630	−	0.935007i	$-0.615393\pi$
$211$	−31576.9			−0.709259			−0.354630	+	0.935007i	$0.615393\pi$
$212$	80805.5	+	80805.5i	1.79791	+	1.79791i
$213$	9469.41	−	9469.41i	0.208720	−	0.208720i
$214$			9403.35i			0.205331i
$215$	−41216.2	−	22139.5i	−0.891643	−	0.478951i
$216$	64444.2			1.38126
$217$	−7056.46	−	7056.46i	−0.149854	−	0.149854i
$218$	−5068.31	+	5068.31i	−0.106647	+	0.106647i
$219$			2249.30i			0.0468986i
$220$	−84686.9	+	25499.6i	−1.74973	+	0.526852i
$221$	−46389.0			−0.949797
$222$	16148.5	+	16148.5i	0.327661	+	0.327661i
$223$	−21493.1	+	21493.1i	−0.432204	+	0.432204i	−0.889378	−	0.457174i	$-0.848862\pi$
$223$	−21493.1	+	21493.1i	−0.432204	+	0.432204i	0.457174	+	0.889378i	$0.348862\pi$
$224$		−	70217.6i		−	1.39943i
$225$	−26664.0	−	40262.6i	−0.526696	−	0.795310i
$226$	118836.			2.32665
$227$	−1.06812	−	1.06812i	−2.07285e−5	−	2.07285e-5i	0.707096	−	0.707117i	$-0.250005\pi$
$227$	−1.06812	−	1.06812i	−2.07285e−5	−	2.07285e-5i	−0.707117	+	0.707096i	$0.750005\pi$
$228$	−4100.33	+	4100.33i	−0.0788767	+	0.0788767i
$229$		−	61585.7i		−	1.17438i	−0.809449	−	0.587191i	$-0.800234\pi$
$229$		−	61585.7i		−	1.17438i	0.809449	−	0.587191i	$-0.199766\pi$
$230$	−3161.92	−	10501.1i	−0.0597716	−	0.198508i
$231$	−2920.45			−0.0547300
$232$	87375.1	+	87375.1i	1.62335	+	1.62335i
$233$	−18979.4	+	18979.4i	−0.349599	+	0.349599i	−0.859960	−	0.510361i	$-0.829512\pi$
$233$	−18979.4	+	18979.4i	−0.349599	+	0.349599i	0.510361	+	0.859960i	$0.329512\pi$
$234$			56173.1i			1.02588i
$235$	44671.7	−	83163.4i	0.808903	−	1.50590i
$236$	−49399.8			−0.886954
$237$	117.575	+	117.575i	0.00209324	+	0.00209324i
$238$	−49595.5	+	49595.5i	−0.875565	+	0.875565i
$239$		−	105134.i		−	1.84055i	−0.391269	−	0.920276i	$-0.627964\pi$
$239$		−	105134.i		−	1.84055i	0.391269	−	0.920276i	$-0.372036\pi$
$240$	−39568.9	−	21254.6i	−0.686960	−	0.369004i
$241$	63055.2			1.08564			0.542821	−	0.839848i	$-0.317356\pi$
$241$	63055.2			1.08564			0.542821	+	0.839848i	$0.317356\pi$
$242$	43481.2	+	43481.2i	0.742455	+	0.742455i
$243$	−25260.6	+	25260.6i	−0.427791	+	0.427791i
$244$			147115.i			2.47102i
$245$	−8210.86	+	2472.33i	−0.136791	+	0.0411883i
$246$	−1191.58			−0.0196904
$247$	−4618.94	−	4618.94i	−0.0757092	−	0.0757092i
$248$	80287.2	−	80287.2i	1.30540	−	1.30540i
$249$		−	19404.0i		−	0.312963i
$250$	11060.3	+	119866.i	0.176965	+	1.91786i
$251$	−82573.8			−1.31067			−0.655337	−	0.755337i	$-0.727473\pi$
$251$	−82573.8			−1.31067			−0.655337	+	0.755337i	$0.727473\pi$
$252$	43866.1	+	43866.1i	0.690762	+	0.690762i
$253$	3285.63	−	3285.63i	0.0513307	−	0.0513307i
$254$		−	104107.i		−	1.61365i
$255$	6846.90	+	22739.3i	0.105297	+	0.349701i
$256$	154010.			2.35001
$257$	52953.5	+	52953.5i	0.801730	+	0.801730i	0.983366	−	0.181636i	$-0.0581391\pi$
$257$	52953.5	+	52953.5i	0.801730	+	0.801730i	−0.181636	+	0.983366i	$0.558139\pi$
$258$	19700.1	−	19700.1i	0.295958	−	0.295958i
$259$			28411.0i			0.423532i
$260$	48397.6	−	90099.8i	0.715940	−	1.33284i
$261$	−45309.0			−0.665125
$262$	−93895.9	−	93895.9i	−1.36787	−	1.36787i
$263$	24595.0	−	24595.0i	0.355578	−	0.355578i	−0.506602	−	0.862180i	$-0.669099\pi$
$263$	24595.0	−	24595.0i	0.355578	−	0.355578i	0.862180	+	0.506602i	$0.169099\pi$
$264$		−	33228.4i		−	0.476761i
$265$	58054.9	+	31184.5i	0.826698	+	0.444065i
$266$	−9876.41			−0.139584
$267$	−16631.1	−	16631.1i	−0.233291	−	0.233291i
$268$	−79776.2	+	79776.2i	−1.11072	+	1.11072i
$269$		−	49771.6i		−	0.687823i	−0.939002	−	0.343912i	$-0.888248\pi$
$269$		−	49771.6i		−	0.687823i	0.939002	−	0.343912i	$-0.111752\pi$
$270$	56401.4	−	16982.7i	0.773681	−	0.232959i
$271$	39084.7			0.532192			0.266096	−	0.963947i	$-0.414266\pi$
$271$	39084.7			0.532192			0.266096	+	0.963947i	$0.414266\pi$
$272$	−323184.	−	323184.i	−4.36829	−	4.36829i
$273$	2388.06	−	2388.06i	0.0320420	−	0.0320420i
$274$		−	102865.i		−	1.37015i
$275$	−42523.2	+	28161.1i	−0.562290	+	0.372378i
$276$	4770.02			0.0626184
$277$	−29445.9	−	29445.9i	−0.383765	−	0.383765i	0.488692	−	0.872456i	$-0.337474\pi$
$277$	−29445.9	−	29445.9i	−0.383765	−	0.383765i	−0.872456	+	0.488692i	$0.837474\pi$
$278$	−142331.	+	142331.i	−1.84166	+	1.84166i
$279$			41633.5i			0.534853i
$280$	−28129.7	−	93421.8i	−0.358798	−	1.19160i
$281$	151923.			1.92402			0.962010	−	0.273013i	$-0.0880203\pi$
$281$	151923.			1.92402			0.962010	+	0.273013i	$0.0880203\pi$
$282$	39749.6	+	39749.6i	0.499844	+	0.499844i
$283$	76183.3	−	76183.3i	0.951234	−	0.951234i	−0.0476314	−	0.998865i	$-0.515167\pi$
$283$	76183.3	−	76183.3i	0.951234	−	0.951234i	0.998865	+	0.0476314i	$0.0151673\pi$
$284$			300440.i			3.72495i
$285$	−1582.40	+	2945.89i	−0.0194817	+	0.0362682i
$286$	59327.1			0.725305
$287$	−1048.21	−	1048.21i	−0.0127258	−	0.0127258i
$288$	−207144.	+	207144.i	−2.49739	+	2.49739i
$289$			158128.i			1.89327i
$290$	99495.9	+	53444.8i	1.18307	+	0.635491i
$291$	−21777.3			−0.257169
$292$	−35682.2	−	35682.2i	−0.418491	−	0.418491i
$293$	−35656.3	+	35656.3i	−0.415337	+	0.415337i	−0.883593	−	0.468256i	$-0.844883\pi$
$293$	−35656.3	+	35656.3i	−0.415337	+	0.415337i	0.468256	+	0.883593i	$0.344883\pi$
$294$		−	5106.24i		−	0.0590754i
$295$	−27277.9	+	8213.50i	−0.313449	+	0.0943809i
$296$	−323255.			−3.68945
$297$	17647.2	+	17647.2i	0.200061	+	0.200061i
$298$	20176.6	−	20176.6i	0.227204	−	0.227204i
$299$			5373.33i			0.0601037i
$300$	−51309.1	−	10425.3i	−0.570101	−	0.115837i
$301$	34659.6			0.382552
$302$	−124146.	−	124146.i	−1.36120	−	1.36120i
$303$	10317.3	−	10317.3i	0.112378	−	0.112378i
$304$		−	64358.6i		−	0.696402i
$305$	24460.2	+	81234.8i	0.262942	+	0.873258i
$306$	292616.			3.12504
$307$	61183.2	+	61183.2i	0.649165	+	0.649165i	0.952791	−	0.303626i	$-0.0981974\pi$
$307$	61183.2	+	61183.2i	0.649165	+	0.649165i	−0.303626	+	0.952791i	$0.598197\pi$
$308$	46329.1	−	46329.1i	0.488374	−	0.488374i
$309$		−	18150.5i		−	0.190095i
$310$	49109.4	−	91424.9i	0.511023	−	0.951351i
$311$	−143150.			−1.48003			−0.740015	−	0.672591i	$-0.765181\pi$
$311$	−143150.			−1.48003			−0.740015	+	0.672591i	$0.765181\pi$
$312$	27170.9	+	27170.9i	0.279123	+	0.279123i
$313$	−34807.0	+	34807.0i	−0.355285	+	0.355285i	−0.862072	−	0.506786i	$-0.830833\pi$
$313$	−34807.0	+	34807.0i	−0.355285	+	0.355285i	0.506786	+	0.862072i	$0.330833\pi$
$314$		−	56122.8i		−	0.569220i
$315$	31515.7	+	16928.8i	0.317619	+	0.170610i
$316$	−3730.35			−0.0373573
$317$	−19515.0	−	19515.0i	−0.194200	−	0.194200i	0.603308	−	0.797508i	$-0.293849\pi$
$317$	−19515.0	−	19515.0i	−0.194200	−	0.194200i	−0.797508	+	0.603308i	$0.793849\pi$
$318$	−27748.5	+	27748.5i	−0.274401	+	0.274401i
$319$			47852.9i			0.470248i
$320$	343103.	−	103310.i	3.35062	−	1.00889i
$321$	−2358.60			−0.0228899
$322$	5744.74	+	5744.74i	0.0554063	+	0.0554063i
$323$	−24060.9	+	24060.9i	−0.230625	+	0.230625i
$324$		−	245700.i		−	2.34054i
$325$	11743.9	−	57798.7i	0.111185	−	0.547207i
$326$	222266.			2.09141
$327$	−1271.26	−	1271.26i	−0.0118889	−	0.0118889i
$328$	11926.4	−	11926.4i	0.110856	−	0.110856i
$329$			69933.9i			0.646094i
$330$	−8756.53	−	29081.3i	−0.0804089	−	0.267046i
$331$	−42277.0			−0.385876			−0.192938	−	0.981211i	$-0.561802\pi$
$331$	−42277.0			−0.385876			−0.192938	+	0.981211i	$0.561802\pi$
$332$	307819.	+	307819.i	2.79267	+	2.79267i
$333$	83813.1	−	83813.1i	0.755829	−	0.755829i
$334$		−	339241.i		−	3.04100i
$335$	−30787.3	+	57315.4i	−0.274335	+	0.510718i
$336$	33274.3			0.294734
$337$	−7458.03	−	7458.03i	−0.0656696	−	0.0656696i	0.673509	−	0.739179i	$-0.264786\pi$
$337$	−7458.03	−	7458.03i	−0.0656696	−	0.0656696i	−0.739179	+	0.673509i	$0.764786\pi$
$338$	107076.	−	107076.i	0.937258	−	0.937258i
$339$			29807.1i			0.259370i
$340$	−469346.	−	252112.i	−4.06009	−	2.18090i
$341$	43971.1			0.378145
$342$	29135.7	+	29135.7i	0.249100	+	0.249100i
$343$	4491.86	−	4491.86i	0.0381802	−	0.0381802i
$344$			394351.i			3.33247i
$345$	2633.94	−	793.091i	0.0221293	−	0.00666323i
$346$	−188464.			−1.57426
$347$	−97115.7	−	97115.7i	−0.806548	−	0.806548i	0.177561	−	0.984110i	$-0.443179\pi$
$347$	−97115.7	−	97115.7i	−0.806548	−	0.806548i	−0.984110	+	0.177561i	$0.943179\pi$
$348$	−34736.0	+	34736.0i	−0.286828	+	0.286828i
$349$		−	92436.0i		−	0.758910i	−0.925210	−	0.379455i	$-0.876111\pi$
$349$		−	92436.0i		−	0.758910i	0.925210	−	0.379455i	$-0.123889\pi$
$350$	−49238.1	−	74349.5i	−0.401944	−	0.606935i
$351$	−28860.3			−0.234253
$352$	218774.	+	218774.i	1.76568	+	1.76568i
$353$	−7000.38	+	7000.38i	−0.0561787	+	0.0561787i	−0.734638	−	0.678459i	$-0.762648\pi$
$353$	−7000.38	+	7000.38i	−0.0561787	+	0.0561787i	0.678459	+	0.734638i	$0.262648\pi$
$354$		−	16963.8i		−	0.135368i
$355$	49952.9	+	165899.i	0.396373	+	1.31639i
$356$	527661.			4.16346
$357$	−12439.8	−	12439.8i	−0.0976063	−	0.0976063i
$358$	−7259.30	+	7259.30i	−0.0566407	+	0.0566407i
$359$			202042.i			1.56766i	0.620973	+	0.783832i	$0.286738\pi$
$359$			202042.i			1.56766i	−0.620973	+	0.783832i	$0.713262\pi$
$360$	−192613.	+	358580.i	−1.48621	+	2.76682i
$361$	125530.			0.963233
$362$	−68463.5	−	68463.5i	−0.522446	−	0.522446i
$363$	−10906.2	+	10906.2i	−0.0827675	+	0.0827675i
$364$			75766.8i			0.571842i
$365$	−25636.0	−	13770.5i	−0.192426	−	0.103363i
$366$	−50519.0			−0.377132
$367$	−126698.	−	126698.i	−0.940671	−	0.940671i	0.0576654	−	0.998336i	$-0.481634\pi$
$367$	−126698.	−	126698.i	−0.940671	−	0.940671i	−0.998336	+	0.0576654i	$0.981634\pi$
$368$	−37435.0	+	37435.0i	−0.276428	+	0.276428i
$369$			6184.50i			0.0454205i
$370$	−282912.	+	85186.1i	−2.06656	+	0.622250i
$371$	−48819.6			−0.354688
$372$	31918.2	+	31918.2i	0.230650	+	0.230650i
$373$	110870.	−	110870.i	0.796889	−	0.796889i	−0.185714	−	0.982604i	$-0.559460\pi$
$373$	110870.	−	110870.i	0.796889	−	0.796889i	0.982604	+	0.185714i	$0.0594599\pi$
$374$		−	309046.i		−	2.20943i
$375$	−30065.5	+	2774.22i	−0.213799	+	0.0197278i
$376$	−795696.			−5.62823
$377$	−39129.4	−	39129.4i	−0.275309	−	0.275309i
$378$	−30855.1	+	30855.1i	−0.215945	+	0.215945i
$379$		−	143098.i		−	0.996219i	−0.867114	−	0.498110i	$-0.834028\pi$
$379$		−	143098.i		−	0.996219i	0.867114	−	0.498110i	$-0.165972\pi$
$380$	−21630.0	−	71835.3i	−0.149792	−	0.497475i
$381$	26112.6			0.179887
$382$	65854.6	+	65854.6i	0.451294	+	0.451294i
$383$	−48897.7	+	48897.7i	−0.333343	+	0.333343i	−0.853854	−	0.520512i	$-0.825741\pi$
$383$	−48897.7	+	48897.7i	−0.333343	+	0.333343i	0.520512	+	0.853854i	$0.325741\pi$
$384$			96150.2i			0.652060i
$385$	17879.3	−	33285.2i	0.120623	−	0.224559i
$386$	114833.			0.770715
$387$	−102247.	−	102247.i	−0.682696	−	0.682696i
$388$	345469.	−	345469.i	2.29480	−	2.29480i
$389$			116811.i			0.771943i	0.922511	+	0.385971i	$0.126134\pi$
$389$			116811.i			0.771943i	−0.922511	+	0.385971i	$0.873866\pi$
$390$	30940.1	+	16619.7i	0.203420	+	0.109268i
$391$	27990.7			0.183088
$392$	51107.6	+	51107.6i	0.332593	+	0.332593i
$393$	23551.5	−	23551.5i	0.152487	−	0.152487i
$394$			74215.3i			0.478080i
$395$	−2059.85	+	620.229i	−0.0132020	+	0.00397519i
$396$	−273344.			−1.74309
$397$	−3607.04	−	3607.04i	−0.0228860	−	0.0228860i	0.695571	−	0.718457i	$-0.255151\pi$
$397$	−3607.04	−	3607.04i	−0.0228860	−	0.0228860i	−0.718457	+	0.695571i	$0.755151\pi$
$398$	−99262.4	+	99262.4i	−0.626641	+	0.626641i
$399$		−	2477.26i		−	0.0155606i
$400$	484491.	−	320855.i	3.02807	−	2.00534i
$401$	−19377.6			−0.120506			−0.0602532	−	0.998183i	$-0.519191\pi$
$401$	−19377.6			−0.120506			−0.0602532	+	0.998183i	$0.519191\pi$
$402$	−27395.0	−	27395.0i	−0.169520	−	0.169520i
$403$	−35955.3	+	35955.3i	−0.221387	+	0.221387i
$404$			327341.i			2.00557i
$405$	−40851.6	−	135672.i	−0.249057	−	0.827144i
$406$	−83668.2			−0.507585
$407$	−88519.0	−	88519.0i	−0.534377	−	0.534377i
$408$	141538.	−	141538.i	0.850263	−	0.850263i
$409$			287642.i			1.71952i	0.510701	+	0.859758i	$0.329386\pi$
$409$			287642.i			1.71952i	−0.510701	+	0.859758i	$0.670614\pi$
$410$	7295.01	−	13580.8i	0.0433968	−	0.0807901i
$411$	25801.3			0.152742
$412$	287933.	+	287933.i	1.69628	+	1.69628i
$413$	14922.7	−	14922.7i	0.0874879	−	0.0874879i
$414$		−	33894.3i		−	0.197754i
$415$	221153.	+	118794.i	1.28410	+	0.689759i
$416$	−357785.			−2.06745
$417$	−35700.3	−	35700.3i	−0.205305	−	0.205305i
$418$	30771.6	−	30771.6i	0.176115	−	0.176115i
$419$			10754.6i			0.0612585i	0.999531	+	0.0306293i	$0.00975113\pi$
$419$			10754.6i			0.0612585i	−0.999531	+	0.0306293i	$0.990249\pi$
$420$	37139.9	−	11183.0i	0.210544	−	0.0633957i
$421$	131257.			0.740556			0.370278	−	0.928921i	$-0.379262\pi$
$421$	131257.			0.740556			0.370278	+	0.928921i	$0.379262\pi$
$422$	172017.	+	172017.i	0.965934	+	0.965934i
$423$	206307.	−	206307.i	1.15301	−	1.15301i
$424$		−	555461.i		−	3.08974i
$425$	−301084.	−	61176.4i	−1.66690	−	0.338693i
$426$	−103171.			−0.568508
$427$	−44440.6	−	44440.6i	−0.243738	−	0.243738i
$428$	37416.1	−	37416.1i	0.204254	−	0.204254i
$429$			14880.8i			0.0808557i
$430$	103922.	+	345135.i	0.562042	+	1.86660i
$431$	−233112.			−1.25490			−0.627452	−	0.778655i	$-0.715902\pi$
$431$	−233112.			−1.25490			−0.627452	+	0.778655i	$0.715902\pi$
$432$	−201064.	−	201064.i	−1.07738	−	1.07738i
$433$	−71663.4	+	71663.4i	−0.382227	+	0.382227i	−0.871904	−	0.489677i	$-0.837115\pi$
$433$	−71663.4	+	71663.4i	−0.382227	+	0.382227i	0.489677	+	0.871904i	$0.337115\pi$
$434$			76881.1i			0.408169i
$435$	−13405.3	+	24956.1i	−0.0708433	+	0.131886i
$436$	40333.8			0.212176
$437$	2787.02	+	2787.02i	0.0145941	+	0.0145941i
$438$	12253.2	−	12253.2i	0.0638708	−	0.0638708i
$439$		−	299601.i		−	1.55459i	−0.629139	−	0.777293i	$-0.716592\pi$
$439$		−	299601.i		−	1.55459i	0.629139	−	0.777293i	$-0.283408\pi$
$440$	378714.	+	203428.i	1.95616	+	1.05076i
$441$	−26502.2			−0.136272
$442$	252707.	+	252707.i	1.29352	+	1.29352i
$443$	129039.	−	129039.i	0.657528	−	0.657528i	−0.297267	−	0.954795i	$-0.596075\pi$
$443$	129039.	−	129039.i	0.657528	−	0.657528i	0.954795	+	0.297267i	$0.0960750\pi$
$444$		−	128510.i		−	0.651886i
$445$	291367.	−	87732.0i	1.47136	−	0.443035i
$446$	234170.			1.17723
$447$	5060.82	+	5060.82i	0.0253283	+	0.0253283i
$448$	−187699.	+	187699.i	−0.935203	+	0.935203i
$449$			241835.i			1.19957i	0.800161	+	0.599786i	$0.204748\pi$
$449$			241835.i			1.19957i	−0.800161	+	0.599786i	$0.795252\pi$
$450$	−74079.3	+	364587.i	−0.365824	+	1.80043i
$451$	6531.74			0.0321126
$452$	−472850.	−	472850.i	−2.31444	−	2.31444i
$453$	31139.1	−	31139.1i	0.151744	−	0.151744i
$454$			11.6373i			5.64600e-5i
$455$	12597.4	+	41837.4i	0.0608498	+	0.202088i
$456$	28185.8			0.135551
$457$	−146983.	−	146983.i	−0.703778	−	0.703778i	0.261441	−	0.965219i	$-0.415802\pi$
$457$	−146983.	−	146983.i	−0.703778	−	0.703778i	−0.965219	+	0.261441i	$0.915802\pi$
$458$	−335492.	+	335492.i	−1.59938	+	1.59938i
$459$			150338.i			0.713583i
$460$	−29202.6	+	54365.3i	−0.138009	+	0.256925i
$461$	248662.			1.17006			0.585030	−	0.811012i	$-0.301083\pi$
$461$	248662.			1.17006			0.585030	+	0.811012i	$0.301083\pi$
$462$	15909.3	+	15909.3i	0.0745363	+	0.0745363i
$463$	−155970.	+	155970.i	−0.727575	+	0.727575i	−0.970136	−	0.242561i	$-0.922013\pi$
$463$	−155970.	+	155970.i	−0.727575	+	0.727575i	0.242561	+	0.970136i	$0.422013\pi$
$464$		−	545216.i		−	2.53240i
$465$	22931.7	+	12317.9i	0.106055	+	0.0569679i
$466$	206783.			0.952233
$467$	210168.	+	210168.i	0.963678	+	0.963678i	0.999363	−	0.0356846i	$-0.0113612\pi$
$467$	210168.	+	210168.i	0.963678	+	0.963678i	−0.0356846	+	0.999363i	$0.511361\pi$
$468$	223514.	−	223514.i	1.02050	−	1.02050i
$469$		−	48197.7i		−	0.219119i
$470$	−696390.	+	209686.i	−3.15251	+	0.949237i
$471$	14077.0			0.0634555
$472$	169788.	+	169788.i	0.762120	+	0.762120i
$473$	−107988.	+	107988.i	−0.482671	+	0.482671i
$474$		−	1281.00i		−	0.00570153i
$475$	−23887.5	−	36070.1i	−0.105873	−	0.159868i
$476$	394683.			1.74195
$477$	144019.	+	144019.i	0.632970	+	0.632970i
$478$	−572726.	+	572726.i	−2.50663	+	2.50663i
$479$			208148.i			0.907196i	0.891206	+	0.453598i	$0.149860\pi$
$479$			208148.i			0.907196i	−0.891206	+	0.453598i	$0.850140\pi$
$480$	52808.1	+	175381.i	0.229202	+	0.761203i
$481$	144764.			0.625708
$482$	−343497.	−	343497.i	−1.47853	−	1.47853i
$483$	−1440.93	+	1440.93i	−0.00617659	+	0.00617659i
$484$		−	346025.i		−	1.47712i
$485$	133323.	−	248203.i	0.566791	−	1.05517i
$486$	275218.			1.16521
$487$	39534.4	+	39534.4i	0.166693	+	0.166693i	0.785524	−	0.618831i	$-0.212393\pi$
$487$	39534.4	+	39534.4i	0.166693	+	0.166693i	−0.618831	+	0.785524i	$0.712393\pi$
$488$	505637.	−	505637.i	2.12324	−	2.12324i
$489$			55750.1i			0.233146i
$490$	58197.4	+	31261.0i	0.242388	+	0.130200i
$491$	−46929.8			−0.194664			−0.0973319	−	0.995252i	$-0.531031\pi$
$491$	−46929.8			−0.194664			−0.0973319	+	0.995252i	$0.531031\pi$
$492$	4741.33	+	4741.33i	0.0195871	+	0.0195871i
$493$	−203832.	+	203832.i	−0.838647	+	0.838647i
$494$			50324.0i			0.206215i
$495$	−150937.	+	45447.8i	−0.616006	+	0.185482i
$496$	−500988.			−2.03640
$497$	−90757.0	−	90757.0i	−0.367424	−	0.367424i
$498$	−105705.	+	105705.i	−0.426222	+	0.426222i
$499$		−	474425.i		−	1.90532i	−0.304045	−	0.952658i	$-0.598337\pi$
$499$		−	474425.i		−	1.90532i	0.304045	−	0.952658i	$-0.401663\pi$
$500$	432941.	−	520960.i	1.73176	−	2.08384i
$501$	85090.5			0.339005
$502$	449826.	+	449826.i	1.78500	+	1.78500i
$503$	309798.	−	309798.i	1.22445	−	1.22445i	0.258422	−	0.966032i	$-0.416798\pi$
$503$	309798.	−	309798.i	1.22445	−	1.22445i	0.966032	−	0.258422i	$-0.0832024\pi$
$504$		−	301538.i		−	1.18708i
$505$	54425.6	+	180753.i	0.213413	+	0.708766i
$506$	−35797.4			−0.139814
$507$	26857.4	+	26857.4i	0.104484	+	0.104484i
$508$	−414242.	+	414242.i	−1.60519	+	1.60519i
$509$		−	436300.i		−	1.68403i	−0.539455	−	0.842015i	$-0.681370\pi$
$509$		−	436300.i		−	1.68403i	0.539455	−	0.842015i	$-0.318630\pi$
$510$	86574.8	−	161173.i	0.332852	−	0.619657i
$511$	21557.8			0.0825588
$512$	−276038.	−	276038.i	−1.05300	−	1.05300i
$513$	−14969.1	+	14969.1i	−0.0568803	+	0.0568803i
$514$		−	576935.i		−	2.18374i
$515$	206866.	+	111119.i	0.779965	+	0.418963i
$516$	−156774.			−0.588811
$517$	−217890.	−	217890.i	−0.815186	−	0.815186i
$518$	154771.	−	154771.i	0.576805	−	0.576805i
$519$		−	47271.7i		−	0.175496i
$520$	−476019.	+	143331.i	−1.76042	+	0.530072i
$521$	−468198.			−1.72486			−0.862431	−	0.506174i	$-0.831059\pi$
$521$	−468198.			−1.72486			−0.862431	+	0.506174i	$0.831059\pi$
$522$	246824.	+	246824.i	0.905828	+	0.905828i
$523$	55782.4	−	55782.4i	0.203936	−	0.203936i	−0.597748	−	0.801684i	$-0.703938\pi$
$523$	55782.4	−	55782.4i	0.203936	−	0.203936i	0.801684	+	0.597748i	$0.203938\pi$
$524$			747228.i			2.72139i
$525$	18648.8	−	12350.2i	0.0676600	−	0.0448079i
$526$	−267966.			−0.968518
$527$	187298.	+	187298.i	0.674390	+	0.674390i
$528$	−103672.	+	103672.i	−0.371871	+	0.371871i
$529$			276599.i			0.988414i
$530$	−146378.	−	486137.i	−0.521104	−	1.73064i
$531$	−88044.9			−0.312259
$532$	39298.5	+	39298.5i	0.138852	+	0.138852i
$533$	−5341.02	+	5341.02i	−0.0188005	+	0.0188005i
$534$			181198.i			0.635434i
$535$	14439.6	−	26881.7i	0.0504486	−	0.0939180i
$536$	548385.			1.90878
$537$	−1820.82	−	1820.82i	−0.00631420	−	0.00631420i
$538$	−271134.	+	271134.i	−0.936741	+	0.936741i
$539$			27990.2i			0.0963450i
$540$	−291997.	−	156848.i	−1.00136	−	0.537886i
$541$	−272065.			−0.929561			−0.464780	−	0.885426i	$-0.653867\pi$
$541$	−272065.			−0.929561			−0.464780	+	0.885426i	$0.653867\pi$
$542$	−212917.	−	212917.i	−0.724788	−	0.724788i
$543$	17172.4	−	17172.4i	0.0582413	−	0.0582413i
$544$			1.86376e6i			6.29786i
$545$	22271.8	−	6706.14i	0.0749829	−	0.0225777i
$546$	−26018.2			−0.0872755
$547$	6581.91	+	6581.91i	0.0219977	+	0.0219977i	0.718020	−	0.696022i	$-0.245049\pi$
$547$	6581.91	+	6581.91i	0.0219977	+	0.0219977i	−0.696022	+	0.718020i	$0.745049\pi$
$548$	−409304.	+	409304.i	−1.36297	+	1.36297i
$549$			262202.i			0.869943i
$550$	385057.	+	78238.7i	1.27292	+	0.258640i
$551$	−40591.1			−0.133699
$552$	−16394.7	−	16394.7i	−0.0538052	−	0.0538052i
$553$	1126.87	−	1126.87i	0.00368487	−	0.00368487i
$554$			320817.i			1.04529i
$555$	−21366.9	−	70961.6i	−0.0693673	−	0.230376i
$556$	1.13268e6			3.66401
$557$	−313808.	−	313808.i	−1.01147	−	1.01147i	−0.999933	−	0.0115379i	$-0.996327\pi$
$557$	−313808.	−	313808.i	−1.01147	−	1.01147i	−0.0115379	−	0.999933i	$-0.503673\pi$
$558$	226801.	−	226801.i	0.728412	−	0.728412i
$559$		−	176603.i		−	0.565165i
$560$	−203709.	+	379237.i	−0.649584	+	1.20930i
$561$	77516.6			0.246303
$562$	−827609.	−	827609.i	−2.62031	−	2.62031i
$563$	15752.0	−	15752.0i	0.0496957	−	0.0496957i	−0.681822	−	0.731518i	$-0.738812\pi$
$563$	15752.0	−	15752.0i	0.0496957	−	0.0496957i	0.731518	+	0.681822i	$0.238812\pi$
$564$		−	316329.i		−	0.994446i
$565$	−339720.	−	182482.i	−1.06420	−	0.571642i
$566$	−830028.			−2.59095
$567$	74221.4	+	74221.4i	0.230868	+	0.230868i
$568$	1.03262e6	−	1.03262e6i	3.20069	−	3.20069i
$569$			91745.8i			0.283375i	0.989911	+	0.141688i	$0.0452528\pi$
$569$			91745.8i			0.283375i	−0.989911	+	0.141688i	$0.954747\pi$
$570$	24668.1	−	7427.70i	0.0759254	−	0.0228615i
$571$	−441760.			−1.35492			−0.677461	−	0.735558i	$-0.736920\pi$
$571$	−441760.			−1.35492			−0.677461	+	0.735558i	$0.736920\pi$
$572$	−236064.	−	236064.i	−0.721502	−	0.721502i
$573$	−16518.0	+	16518.0i	−0.0503094	+	0.0503094i
$574$			11420.4i			0.0346623i
$575$	−7086.18	+	34875.2i	−0.0214327	+	0.105483i
$576$	1.10743e6			3.33790
$577$	215875.	+	215875.i	0.648412	+	0.648412i	0.952609	−	0.304197i	$-0.0983883\pi$
$577$	215875.	+	215875.i	0.648412	+	0.648412i	−0.304197	+	0.952609i	$0.598388\pi$
$578$	861412.	−	861412.i	2.57843	−	2.57843i
$579$			28803.2i			0.0859178i
$580$	−183239.	−	608554.i	−0.544705	−	1.80902i
$581$	−185973.			−0.550930
$582$	118633.	+	118633.i	0.350236	+	0.350236i
$583$	152105.	−	152105.i	0.447515	−	0.447515i
$584$			245281.i			0.719182i
$585$	86258.6	−	160584.i	0.252052	−	0.469236i
$586$	388480.			1.13129
$587$	415527.	+	415527.i	1.20593	+	1.20593i	0.972333	+	0.233601i	$0.0750509\pi$
$587$	415527.	+	415527.i	1.20593	+	1.20593i	0.233601	+	0.972333i	$0.424949\pi$
$588$	−20317.9	+	20317.9i	−0.0587656	+	0.0587656i
$589$			37298.3i			0.107512i
$590$	193342.	+	103854.i	0.555420	+	0.298347i
$591$	−18615.1			−0.0532955
$592$	1.00855e6	+	1.00855e6i	2.87775	+	2.87775i
$593$	−186492.	+	186492.i	−0.530337	+	0.530337i	−0.920673	−	0.390336i	$-0.872359\pi$
$593$	−186492.	+	186492.i	−0.530337	+	0.530337i	0.390336	+	0.920673i	$0.372359\pi$
$594$		−	192268.i		−	0.544922i
$595$	217938.	−	65622.3i	0.615602	−	0.185361i
$596$	−160567.			−0.452025
$597$	−24897.6	−	24897.6i	−0.0698568	−	0.0698568i
$598$	29271.6	−	29271.6i	0.0818548	−	0.0818548i
$599$		−	135461.i		−	0.377538i	−0.982022	−	0.188769i	$-0.939550\pi$
$599$		−	135461.i		−	0.377538i	0.982022	−	0.188769i	$-0.0604498\pi$
$600$	140518.	+	212183.i	0.390329	+	0.589396i
$601$	−68623.2			−0.189986			−0.0949931	−	0.995478i	$-0.530283\pi$
$601$	−68623.2			−0.189986			−0.0949931	+	0.995478i	$0.530283\pi$
$602$	−188810.	−	188810.i	−0.520994	−	0.520994i
$603$	−142185.	+	142185.i	−0.391037	+	0.391037i
$604$			987963.i			2.70811i
$605$	−57532.1	−	191070.i	−0.157181	−	0.522014i
$606$	−112408.			−0.306093
$607$	166899.	+	166899.i	0.452978	+	0.452978i	0.896342	−	0.443364i	$-0.146215\pi$
$607$	166899.	+	166899.i	0.452978	+	0.452978i	−0.443364	+	0.896342i	$0.646215\pi$
$608$	−185574.	+	185574.i	−0.502009	+	0.502009i
$609$		−	20986.2i		−	0.0565846i
$610$	309284.	−	575780.i	0.831184	−	1.54738i
$611$	356339.			0.954511
$612$	−1.16433e6	−	1.16433e6i	−3.10865	−	3.10865i
$613$	−415920.	+	415920.i	−1.10685	+	1.10685i	−0.113290	+	0.993562i	$0.536139\pi$
$613$	−415920.	+	415920.i	−1.10685	+	1.10685i	−0.993562	+	0.113290i	$0.963861\pi$
$614$		−	666599.i		−	1.76819i
$615$	3406.42	+	1829.78i	0.00900633	+	0.00483780i
$616$	−318468.			−0.839276
$617$	477043.	+	477043.i	1.25310	+	1.25310i	0.954321	+	0.298783i	$0.0965808\pi$
$617$	477043.	+	477043.i	1.25310	+	1.25310i	0.298783	+	0.954321i	$0.403419\pi$
$618$	−98875.9	+	98875.9i	−0.258889	+	0.258889i
$619$			96183.1i			0.251025i	0.992092	+	0.125513i	$0.0400575\pi$
$619$			96183.1i			0.251025i	−0.992092	+	0.125513i	$0.959942\pi$
$620$	−559189.	+	168374.i	−1.45471	+	0.438019i
$621$	17414.0			0.0451560
$622$	779819.	+	779819.i	2.01564	+	2.01564i
$623$	−159396.	+	159396.i	−0.410678	+	0.410678i
$624$		−	169545.i		−	0.435428i
$625$	152446.	−	359650.i	0.390262	−	0.920704i
$626$	379226.			0.967721
$627$	7718.30	+	7718.30i	0.0196330	+	0.0196330i
$628$	−223314.	+	223314.i	−0.566234	+	0.566234i
$629$		−	754104.i		−	1.90603i
$630$	−79463.0	−	263905.i	−0.200209	−	0.664915i
$631$	−204909.			−0.514637			−0.257319	−	0.966327i	$-0.582839\pi$
$631$	−204909.			−0.514637			−0.257319	+	0.966327i	$0.582839\pi$
$632$	12821.3	+	12821.3i	0.0320995	+	0.0320995i
$633$	−43146.4	+	43146.4i	−0.107681	+	0.107681i
$634$			212618.i			0.528959i
$635$	−159864.	+	297613.i	−0.396465	+	0.738082i
$636$	220824.			0.545923
$637$	−22887.7	−	22887.7i	−0.0564057	−	0.0564057i
$638$	260682.	−	260682.i	0.640427	−	0.640427i
$639$			535472.i			1.31140i
$640$	−1.09585e6	−	588643.i	−2.67542	−	1.43712i
$641$	−32846.1			−0.0799408			−0.0399704	−	0.999201i	$-0.512726\pi$
$641$	−32846.1			−0.0799408			−0.0399704	+	0.999201i	$0.512726\pi$
$642$	12848.6	+	12848.6i	0.0311736	+	0.0311736i
$643$	−78540.8	+	78540.8i	−0.189965	+	0.189965i	−0.795681	−	0.605716i	$-0.792887\pi$
$643$	−78540.8	+	78540.8i	−0.189965	+	0.189965i	0.605716	+	0.795681i	$0.292887\pi$
$644$		−	45716.9i		−	0.110231i
$645$	−86568.7	+	26066.2i	−0.208085	+	0.0626554i
$646$	262147.			0.628173
$647$	303680.	+	303680.i	0.725449	+	0.725449i	0.969710	−	0.244260i	$-0.0785452\pi$
$647$	303680.	+	303680.i	0.725449	+	0.725449i	−0.244260	+	0.969710i	$0.578545\pi$
$648$	−844478.	+	844478.i	−2.01112	+	2.01112i
$649$			92988.3i			0.220769i
$650$	−378838.	+	250886.i	−0.896659	+	0.593814i
$651$	−19283.8			−0.0455019
$652$	−884402.	−	884402.i	−2.08044	−	2.08044i
$653$	290141.	−	290141.i	0.680429	−	0.680429i	−0.279668	−	0.960097i	$-0.590224\pi$
$653$	290141.	−	290141.i	0.680429	−	0.680429i	0.960097	+	0.279668i	$0.0902245\pi$
$654$			13850.6i			0.0323827i
$655$	124238.	+	412609.i	0.289583	+	0.961736i
$656$	−74419.9			−0.172934
$657$	−63596.2	−	63596.2i	−0.147333	−	0.147333i
$658$	380970.	−	380970.i	0.879910	−	0.879910i
$659$		−	495743.i		−	1.14153i	−0.821115	−	0.570763i	$-0.806647\pi$
$659$		−	495743.i		−	1.14153i	0.821115	−	0.570763i	$-0.193353\pi$
$660$	−80872.9	+	150558.i	−0.185659	+	0.345633i
$661$	182581.			0.417882			0.208941	−	0.977928i	$-0.432998\pi$
$661$	182581.			0.417882			0.208941	+	0.977928i	$0.432998\pi$
$662$	230307.	+	230307.i	0.525522	+	0.525522i
$663$	−63385.5	+	63385.5i	−0.144199	+	0.144199i
$664$		−	2.11596e6i		−	4.79924i
$665$	28234.1	+	15166.1i	0.0638455	+	0.0342949i
$666$	−913155.			−2.05871
$667$	23610.3	+	23610.3i	0.0530701	+	0.0530701i
$668$	−1.34985e6	+	1.34985e6i	−3.02505	+	3.02505i
$669$			58735.9i			0.131235i
$670$	479945.	−	144514.i	1.06916	−	0.321928i
$671$	276924.			0.615056
$672$	−95944.6	−	95944.6i	−0.212462	−	0.212462i
$673$	−551601.	+	551601.i	−1.21785	+	1.21785i	−0.249470	+	0.968382i	$0.580257\pi$
$673$	−551601.	+	551601.i	−1.21785	+	1.21785i	−0.968382	+	0.249470i	$0.919743\pi$
$674$			81256.2i			0.178870i
$675$	−187315.	−	38060.0i	−0.411117	−	0.0835336i
$676$	−852116.			−1.86469
$677$	−112272.	−	112272.i	−0.244959	−	0.244959i	0.573939	−	0.818898i	$-0.305415\pi$
$677$	−112272.	−	112272.i	−0.244959	−	0.244959i	−0.818898	+	0.573939i	$0.805415\pi$
$678$	162376.	−	162376.i	0.353234	−	0.353234i
$679$			208719.i			0.452712i
$680$	746640.	+	2.47967e6i	1.61471	+	5.36260i
$681$	−2.91894			−6.29406e−6
$682$	−239536.	−	239536.i	−0.514993	−	0.514993i
$683$	434268.	−	434268.i	0.930928	−	0.930928i	−0.0668362	−	0.997764i	$-0.521291\pi$
$683$	434268.	−	434268.i	0.930928	−	0.930928i	0.997764	+	0.0668362i	$0.0212905\pi$
$684$		−	231863.i		−	0.495587i
$685$	−157959.	+	294065.i	−0.336637	+	0.626704i
$686$	−48939.4			−0.103995
$687$	−84150.1	−	84150.1i	−0.178296	−	0.178296i
$688$	1.23036e6	−	1.23036e6i	2.59930	−	2.59930i
$689$			248754.i			0.524000i
$690$	−18669.0	−	10028.1i	−0.0392123	−	0.0210631i
$691$	684956.			1.43452			0.717260	−	0.696806i	$-0.245396\pi$
$691$	684956.			1.43452			0.717260	+	0.696806i	$0.245396\pi$
$692$	749904.	+	749904.i	1.56601	+	1.56601i
$693$	82572.0	−	82572.0i	0.171936	−	0.171936i
$694$			1.05809e6i			2.19686i
$695$	625448.	−	188325.i	1.29486	−	0.389887i
$696$	238777.			0.492917
$697$	27822.3	+	27822.3i	0.0572701	+	0.0572701i
$698$	−503552.	+	503552.i	−1.03355	+	1.03355i
$699$			51866.6i			0.106153i
$700$	−99918.9	+	491758.i	−0.203916	+	1.00359i
$701$	809809.			1.64796			0.823980	−	0.566619i	$-0.191749\pi$
$701$	809809.			1.64796			0.823980	+	0.566619i	$0.191749\pi$
$702$	157218.	+	157218.i	0.319028	+	0.319028i
$703$	75085.9	−	75085.9i	0.151931	−	0.151931i
$704$		−	1.16961e6i		−	2.35992i
$705$	−52594.8	−	174673.i	−0.105819	−	0.351436i
$706$	76270.0			0.153019
$707$	−98883.4	−	98883.4i	−0.197827	−	0.197827i
$708$	−67499.4	+	67499.4i	−0.134658	+	0.134658i
$709$			204474.i			0.406768i	0.979099	+	0.203384i	$0.0651939\pi$
$709$			204474.i			0.406768i	−0.979099	+	0.203384i	$0.934806\pi$
$710$	631622.	−	1.17587e6i	1.25297	−	2.33260i
$711$	−6648.57			−0.0131519
$712$	−1.81358e6	−	1.81358e6i	−3.57748	−	3.57748i
$713$	21695.1	−	21695.1i	0.0426758	−	0.0426758i
$714$			135534.i			0.265858i
$715$	−169600.	−	91101.8i	−0.331753	−	0.178203i
$716$	57769.9			0.112687
$717$	−143654.	−	143654.i	−0.279435	−	0.279435i
$718$	1.10064e6	−	1.10064e6i	2.13499	−	2.13499i
$719$		−	603232.i		−	1.16688i	−0.812156	−	0.583441i	$-0.801706\pi$
$719$		−	603232.i		−	1.16688i	0.812156	−	0.583441i	$-0.198294\pi$
$720$	1.71971e6	−	517813.i	3.31734	−	0.998867i
$721$	−173958.			−0.334637
$722$	−683831.	−	683831.i	−1.31182	−	1.31182i
$723$	86158.0	−	86158.0i	0.164823	−	0.164823i
$724$			544835.i			1.03941i
$725$	−202364.	−	305569.i	−0.384996	−	0.581344i
$726$	118824.			0.225441
$727$	−277495.	−	277495.i	−0.525033	−	0.525033i	0.394054	−	0.919087i	$-0.371072\pi$
$727$	−277495.	−	277495.i	−0.525033	−	0.525033i	−0.919087	+	0.394054i	$0.871072\pi$
$728$	260412.	−	260412.i	0.491359	−	0.491359i
$729$		−	390041.i		−	0.733932i
$730$	64638.0	+	214669.i	0.121295	+	0.402832i
$731$	−919959.			−1.72161
$732$	201016.	+	201016.i	0.375154	+	0.375154i
$733$	−602150.	+	602150.i	−1.12072	+	1.12072i	−0.129085	+	0.991634i	$0.541204\pi$
$733$	−602150.	+	602150.i	−1.12072	+	1.12072i	−0.991634	+	0.129085i	$0.958796\pi$
$734$			1.38039e6i			2.56218i
$735$	−7841.08	+	14597.4i	−0.0145145	+	0.0270210i
$736$	215884.			0.398533
$737$	150168.	+	150168.i	0.276466	+	0.276466i
$738$	33690.5	−	33690.5i	0.0618578	−	0.0618578i
$739$		−	510748.i		−	0.935228i	−0.883933	−	0.467614i	$-0.845114\pi$
$739$		−	510748.i		−	0.935228i	0.883933	−	0.467614i	$-0.154886\pi$
$740$	1.46467e6	+	786755.i	2.67471	+	1.43673i
$741$	−12622.6			−0.0229885
$742$	265948.	+	265948.i	0.483046	+	0.483046i
$743$	483448.	−	483448.i	0.875735	−	0.875735i	−0.117355	−	0.993090i	$-0.537442\pi$
$743$	483448.	−	483448.i	0.875735	−	0.875735i	0.993090	+	0.117355i	$0.0374416\pi$
$744$		−	219407.i		−	0.396374i
$745$	−88662.6	+	26696.7i	−0.159745	+	0.0481000i
$746$	−1.20795e6			−2.17055
$747$	548624.	+	548624.i	0.983181	+	0.983181i
$748$	−1.22970e6	+	1.22970e6i	−2.19784	+	2.19784i
$749$			22605.4i			0.0402947i
$750$	178897.	+	148671.i	0.318039	+	0.264305i
$751$	−803929.			−1.42540			−0.712702	−	0.701467i	$-0.752529\pi$
$751$	−803929.			−1.42540			−0.712702	+	0.701467i	$0.752529\pi$
$752$	2.48255e6	+	2.48255e6i	4.38998	+	4.38998i
$753$	−112828.	+	112828.i	−0.198988	+	0.198988i
$754$			426321.i			0.749883i
$755$	164265.	+	545539.i	0.288171	+	0.957045i
$756$	245546.			0.429625
$757$	−137325.	−	137325.i	−0.239640	−	0.239640i	0.577061	−	0.816701i	$-0.304199\pi$
$757$	−137325.	−	137325.i	−0.239640	−	0.239640i	−0.816701	+	0.577061i	$0.804199\pi$
$758$	−779536.	+	779536.i	−1.35674	+	1.35674i
$759$		−	8978.90i		−	0.0155862i
$760$	−172557.	+	321242.i	−0.298748	+	0.556168i
$761$	−410285.			−0.708462			−0.354231	−	0.935158i	$-0.615257\pi$
$761$	−410285.			−0.708462			−0.354231	+	0.935158i	$0.615257\pi$
$762$	−142250.	−	142250.i	−0.244987	−	0.244987i
$763$	−12184.1	+	12184.1i	−0.0209288	+	0.0209288i
$764$		−	524074.i		−	0.897854i
$765$	−836512.	−	449337.i	−1.42939	−	0.767802i
$766$	532747.			0.907954
$767$	−76036.8	−	76036.8i	−0.129251	−	0.129251i
$768$	210438.	−	210438.i	0.356781	−	0.356781i
$769$		−	306046.i		−	0.517529i	−0.965941	−	0.258764i	$-0.916685\pi$
$769$		−	306046.i		−	0.517529i	0.965941	−	0.258764i	$-0.0833153\pi$
$770$	−278722.	+	83924.6i	−0.470100	+	0.141549i
$771$	144710.			0.243439
$772$	−456925.	−	456925.i	−0.766673	−	0.766673i
$773$	746945.	−	746945.i	1.25006	−	1.25006i	0.294363	−	0.955694i	$-0.404893\pi$
$773$	746945.	−	746945.i	1.25006	−	1.25006i	0.955694	−	0.294363i	$-0.0951074\pi$
$774$			1.11399e6i			1.85952i
$775$	−280781.	+	185948.i	−0.467482	+	0.309591i
$776$	−2.37477e6			−3.94364
$777$	38820.5	+	38820.5i	0.0643011	+	0.0643011i
$778$	636336.	−	636336.i	1.05130	−	1.05130i
$779$			5540.53i			0.00913011i
$780$	−56981.5	−	189241.i	−0.0936579	−	0.311048i
$781$	565537.			0.927168
$782$	−152481.	−	152481.i	−0.249346	−	0.249346i
$783$	−126811.	+	126811.i	−0.206840	+	0.206840i
$784$		−	318909.i		−	0.518841i
$785$	−86181.3	+	160440.i	−0.139854	+	0.260360i
$786$	−256597.			−0.415343
$787$	−834040.	−	834040.i	−1.34660	−	1.34660i	−0.889330	−	0.457265i	$-0.848829\pi$
$787$	−834040.	−	834040.i	−1.34660	−	1.34660i	−0.457265	−	0.889330i	$-0.651171\pi$
$788$	295304.	−	295304.i	0.475573	−	0.475573i
$789$		−	67212.7i		−	0.107969i
$790$	14599.9	+	7842.41i	0.0233935	+	0.0125660i
$791$	285678.			0.456587
$792$	939490.	+	939490.i	1.49776	+	1.49776i
$793$	−226441.	+	226441.i	−0.360088	+	0.360088i
$794$			39299.2i			0.0623365i
$795$	121936.	−	36715.4i	0.192929	−	0.0580917i
$796$	789935.			1.24671
$797$	−346993.	−	346993.i	−0.546267	−	0.546267i	0.379092	−	0.925359i	$-0.376236\pi$
$797$	−346993.	−	346993.i	−0.546267	−	0.546267i	−0.925359	+	0.379092i	$0.876236\pi$
$798$	−13495.0	+	13495.0i	−0.0211918	+	0.0211918i
$799$		−	1.85623e6i		−	2.90763i
$800$	−2.32217e6	−	471835.i	−3.62839	−	0.737242i
$801$	940446.			1.46578
$802$	105561.	+	105561.i	0.164117	+	0.164117i
$803$	−67166.9	+	67166.9i	−0.104166	+	0.104166i
$804$			218011.i			0.337261i
$805$	−7601.16	−	25244.3i	−0.0117297	−	0.0389557i
$806$	391738.			0.603011
$807$	−68007.4	−	68007.4i	−0.104426	−	0.104426i
$808$	1.12508e6	−	1.12508e6i	1.72330	−	1.72330i
$809$			633306.i			0.967646i	0.875166	+	0.483823i	$0.160752\pi$
$809$			633306.i			0.967646i	−0.875166	+	0.483823i	$0.839248\pi$
$810$	−516543.	+	961626.i	−0.787292	+	1.46567i
$811$	730234.			1.11025			0.555124	−	0.831767i	$-0.312671\pi$
$811$	730234.			1.11025			0.555124	+	0.831767i	$0.312671\pi$
$812$	332918.	+	332918.i	0.504923	+	0.504923i
$813$	53405.0	−	53405.0i	0.0807980	−	0.0807980i
$814$			964426.i			1.45553i
$815$	−635401.	−	341309.i	−0.956604	−	0.513845i
$816$	−883191.			−1.32640
$817$	−91600.1	−	91600.1i	−0.137231	−	0.137231i
$818$	1.56695e6	−	1.56695e6i	2.34180	−	2.34180i
$819$			135039.i			0.201322i
$820$	−83065.4	+	25011.4i	−0.123536	+	0.0371972i
$821$	804907.			1.19415			0.597075	−	0.802185i	$-0.296329\pi$
$821$	804907.			1.19415			0.597075	+	0.802185i	$0.296329\pi$
$822$	−140554.	−	140554.i	−0.208018	−	0.208018i
$823$	12469.2	−	12469.2i	0.0184094	−	0.0184094i	−0.697842	−	0.716252i	$-0.745856\pi$
$823$	12469.2	−	12469.2i	0.0184094	−	0.0184094i	0.716252	+	0.697842i	$0.245856\pi$
$824$		−	1.97927e6i		−	2.91508i
$825$	−19624.3	+	96582.3i	−0.0288327	+	0.141902i
$826$	−162585.			−0.238298
$827$	−447005.	−	447005.i	−0.653585	−	0.653585i	0.300270	−	0.953854i	$-0.402923\pi$
$827$	−447005.	−	447005.i	−0.653585	−	0.653585i	−0.953854	+	0.300270i	$0.902923\pi$
$828$	−134866.	+	134866.i	−0.196717	+	0.196717i
$829$			93265.9i			0.135711i	0.997695	+	0.0678553i	$0.0216156\pi$
$829$			93265.9i			0.135711i	−0.997695	+	0.0678553i	$0.978384\pi$
$830$	−557611.	−	1.85188e6i	−0.809422	−	2.68818i
$831$	−80469.1			−0.116527
$832$	956396.	+	956396.i	1.38163	+	1.38163i
$833$	−119226.	+	119226.i	−0.171823	+	0.171823i
$834$			388959.i			0.559207i
$835$	−520934.	+	969802.i	−0.747154	+	1.39095i
$836$	−244882.			−0.350383
$837$	116525.	+	116525.i	0.166328	+	0.166328i
$838$	58586.5	−	58586.5i	0.0834275	−	0.0834275i
$839$			1.14987e6i			1.63353i	0.576972	+	0.816764i	$0.304234\pi$
$839$			1.14987e6i			1.63353i	−0.576972	+	0.816764i	$0.695766\pi$
$840$	−166087.	−	89214.4i	−0.235384	−	0.126438i
$841$	363413.			0.513817
$842$	−715031.	−	715031.i	−1.00856	−	1.00856i
$843$	207586.	−	207586.i	0.292107	−	0.292107i
$844$		−	1.36892e6i		−	1.92174i
$845$	−470527.	+	141678.i	−0.658978	+	0.198421i
$846$	−2.24774e6			−3.14055
$847$	104527.	+	104527.i	0.145701	+	0.145701i
$848$	−1.73302e6	+	1.73302e6i	−2.40997	+	2.40997i
$849$		−	208192.i		−	0.288835i
$850$	1.30691e6	+	1.97344e6i	1.80888	+	2.73140i
$851$	−87349.4			−0.120615
$852$	410518.	+	410518.i	0.565527	+	0.565527i
$853$	−623474.	+	623474.i	−0.856881	+	0.856881i	−0.990969	−	0.134088i	$-0.957189\pi$
$853$	−623474.	+	623474.i	−0.856881	+	0.856881i	0.134088	+	0.990969i	$0.457189\pi$
$854$			484186.i			0.663891i
$855$	−38550.9	−	128032.i	−0.0527354	−	0.175140i
$856$	−257200.			−0.351014
$857$	226049.	+	226049.i	0.307780	+	0.307780i	0.844048	−	0.536268i	$-0.180166\pi$
$857$	226049.	+	226049.i	0.307780	+	0.307780i	−0.536268	+	0.844048i	$0.680166\pi$
$858$	81064.0	−	81064.0i	0.110117	−	0.110117i
$859$			557243.i			0.755193i	0.925970	+	0.377597i	$0.123249\pi$
$859$			557243.i			0.755193i	−0.925970	+	0.377597i	$0.876751\pi$
$860$	959792.	−	1.78680e6i	1.29772	−	2.41591i
$861$	−2864.53			−0.00386409
$862$	1.26989e6	+	1.26989e6i	1.70904	+	1.70904i
$863$	287700.	−	287700.i	0.386295	−	0.386295i	−0.487069	−	0.873364i	$-0.661934\pi$
$863$	287700.	−	287700.i	0.386295	−	0.386295i	0.873364	+	0.487069i	$0.161934\pi$
$864$			1.15951e6i			1.55328i
$865$	538770.	+	289403.i	0.720064	+	0.386786i
$866$	780782.			1.04110
$867$	216064.	+	216064.i	0.287439	+	0.287439i
$868$	305912.	−	305912.i	0.406029	−	0.406029i
$869$			7021.87i			0.00929851i
$870$	208977.	−	62923.9i	0.276096	−	0.0831337i
$871$	−245585.			−0.323717
$872$	−138628.	−	138628.i	−0.182314	−	0.182314i
$873$	615726.	−	615726.i	0.807903	−	0.807903i
$874$		−	30365.0i		−	0.0397512i
$875$	26588.7	+	288155.i	0.0347281	+	0.376366i
$876$	−97511.7			−0.127072
$877$	−34920.8	−	34920.8i	−0.0454031	−	0.0454031i	0.684041	−	0.729444i	$-0.260221\pi$
$877$	−34920.8	−	34920.8i	−0.0454031	−	0.0454031i	−0.729444	+	0.684041i	$0.760221\pi$
$878$	−1.63210e6	+	1.63210e6i	−2.11718	+	2.11718i
$879$			97440.8i			0.126114i
$880$	−546886.	−	1.81627e6i	−0.706206	−	2.34538i
$881$	575336.			0.741258			0.370629	−	0.928781i	$-0.379142\pi$
$881$	575336.			0.741258			0.370629	+	0.928781i	$0.379142\pi$
$882$	144373.	+	144373.i	0.185587	+	0.185587i
$883$	−313204.	+	313204.i	−0.401704	+	0.401704i	−0.878833	−	0.477129i	$-0.841677\pi$
$883$	−313204.	+	313204.i	−0.401704	+	0.401704i	0.477129	+	0.878833i	$0.341677\pi$
$884$		−	2.01106e6i		−	2.57347i
$885$	−26049.4	+	48495.1i	−0.0332591	+	0.0619172i
$886$	−1.40590e6			−1.79096
$887$	740797.	+	740797.i	0.941569	+	0.941569i	0.998385	−	0.0568158i	$-0.0180948\pi$
$887$	740797.	+	740797.i	0.941569	+	0.941569i	−0.0568158	+	0.998385i	$0.518095\pi$
$888$	−441693.	+	441693.i	−0.560137	+	0.560137i
$889$		−	250269.i		−	0.316668i
$890$	−2.06517e6	−	1.10932e6i	−2.60720	−	1.40047i
$891$	−462497.			−0.582578
$892$	−931768.	−	931768.i	−1.17106	−	1.17106i
$893$	184825.	−	184825.i	0.231770	−	0.231770i
$894$		−	55138.3i		−	0.0689888i
$895$	31899.7	−	9605.16i	0.0398236	−	0.0119911i
$896$	921526.			1.14787
$897$	7342.07	+	7342.07i	0.00912502	+	0.00912502i
$898$	1.31741e6	−	1.31741e6i	1.63369	−	1.63369i
$899$			315974.i			0.390959i
$900$	1.74546e6	−	1.15594e6i	2.15489	−	1.42708i
$901$	1.29580e6			1.59621
$902$	−35582.1	−	35582.1i	−0.0437339	−	0.0437339i
$903$	47358.5	−	47358.5i	0.0580795	−	0.0580795i
$904$			3.25039e6i			3.97740i
$905$	90587.5	+	300850.i	0.110604	+	0.367328i
$906$	−339265.			−0.413317
$907$	−663473.	−	663473.i	−0.806508	−	0.806508i	0.177596	−	0.984104i	$-0.443168\pi$
$907$	−663473.	−	663473.i	−0.806508	−	0.806508i	−0.984104	+	0.177596i	$0.943168\pi$
$908$	46.3051	−	46.3051i	5.61639e−5	−	5.61639e-5i
$909$			583418.i			0.706076i
$910$	159287.	−	296537.i	0.192352	−	0.358094i
$911$	−1.32279e6			−1.59388			−0.796938	−	0.604061i	$-0.793548\pi$
$911$	−1.32279e6			−1.59388			−0.796938	+	0.604061i	$0.793548\pi$
$912$	−87939.1	−	87939.1i	−0.105729	−	0.105729i
$913$	579428.	−	579428.i	0.695117	−	0.695117i
$914$			1.60140e6i			1.91694i
$915$	144421.	+	77576.3i	0.172499	+	0.0926588i
$916$	2.66986e6			3.18198
$917$	−225723.	−	225723.i	−0.268434	−	0.268434i
$918$	818978.	−	818978.i	0.971823	−	0.971823i
$919$			1.11696e6i			1.32253i	0.750153	+	0.661265i	$0.229980\pi$
$919$			1.11696e6i			1.32253i	−0.750153	+	0.661265i	$0.770020\pi$
$920$	287225.	−	86484.8i	0.339349	−	0.102180i
$921$	167200.			0.197114
$922$	−1.35460e6	−	1.35460e6i	−1.59349	−	1.59349i
$923$	−462441.	+	462441.i	−0.542816	+	0.542816i
$924$		−	126607.i		−	0.148291i
$925$	939581.	+	190911.i	1.09812	+	0.223124i
$926$	1.69931e6			1.98176
$927$	513182.	+	513182.i	0.597189	+	0.597189i
$928$	−1.57210e6	+	1.57210e6i	−1.82551	+	1.82551i
$929$			262969.i			0.304701i	0.988327	+	0.152350i	$0.0486842\pi$
$929$			262969.i			0.304701i	−0.988327	+	0.152350i	$0.951316\pi$
$930$	−57819.5	−	192025.i	−0.0668511	−	0.222019i
$931$	−23742.6			−0.0273923
$932$	−822795.	−	822795.i	−0.947240	−	0.947240i
$933$	−195599.	+	195599.i	−0.224700	+	0.224700i
$934$		−	2.28981e6i		−	2.62485i
$935$	−474566.	+	883480.i	−0.542842	+	1.01059i
$936$	−1.53645e6			−1.75374
$937$	−89677.3	−	89677.3i	−0.102142	−	0.102142i	0.654189	−	0.756331i	$-0.273010\pi$
$937$	−89677.3	−	89677.3i	−0.102142	−	0.102142i	−0.756331	+	0.654189i	$0.773010\pi$
$938$	−262560.	+	262560.i	−0.298417	+	0.298417i
$939$			95119.8i			0.107880i
$940$	3.60530e6	+	1.93661e6i	4.08024	+	2.19172i
$941$	−13096.5			−0.0147902			−0.00739512	−	0.999973i	$-0.502354\pi$
$941$	−13096.5			−0.0147902			−0.00739512	+	0.999973i	$0.502354\pi$
$942$	−76685.6	−	76685.6i	−0.0864196	−	0.0864196i
$943$	3222.72	−	3222.72i	0.00362409	−	0.00362409i
$944$		−	1.05947e6i		−	1.18890i
$945$	135587.	−	40826.0i	0.151829	−	0.0457165i
$946$	1.17654e6			1.31469
$947$	974672.	+	974672.i	1.08682	+	1.08682i	0.995854	+	0.0909682i	$0.0289962\pi$
$947$	974672.	+	974672.i	1.08682	+	1.08682i	0.0909682	+	0.995854i	$0.471004\pi$
$948$	−5097.11	+	5097.11i	−0.00567163	+	0.00567163i
$949$		−	109845.i		−	0.121969i
$950$	−66365.7	+	326623.i	−0.0735354	+	0.361910i
$951$	−53330.1			−0.0589673
$952$	−1.35654e6	−	1.35654e6i	−1.49678	−	1.49678i
$953$	292946.	−	292946.i	0.322553	−	0.322553i	−0.527193	−	0.849746i	$-0.676755\pi$
$953$	292946.	−	292946.i	0.322553	−	0.322553i	0.849746	+	0.527193i	$0.176755\pi$
$954$		−	1.56911e6i		−	1.72407i
$955$	−87135.6	−	289386.i	−0.0955407	−	0.317301i
$956$	4.55778e6			4.98698
$957$	65385.8	+	65385.8i	0.0713936	+	0.0713936i
$958$	1.13390e6	−	1.13390e6i	1.23550	−	1.23550i
$959$		−	247286.i		−	0.268882i
$960$	327651.	−	609975.i	0.355524	−	0.661865i
$961$	−633179.			−0.685614
$962$	−788614.	−	788614.i	−0.852146	−	0.852146i
$963$	66686.5	−	66686.5i	0.0719094	−	0.0719094i
$964$			2.73357e6i			2.94155i
$965$	−328278.	−	176337.i	−0.352523	−	0.189360i
$966$	15699.1			0.0168237
$967$	−1.07763e6	−	1.07763e6i	−1.15244	−	1.15244i	−0.986062	−	0.166378i	$-0.946793\pi$
$967$	−1.07763e6	−	1.07763e6i	−1.15244	−	1.15244i	−0.166378	−	0.986062i	$-0.553207\pi$
$968$	−1.18930e6	+	1.18930e6i	−1.26923	+	1.26923i
$969$			65753.2i			0.0700276i
$970$	−2.07839e6	+	625812.i	−2.20894	+	0.665121i
$971$	−1.61563e6			−1.71357			−0.856787	−	0.515670i	$-0.827543\pi$
$971$	−1.61563e6			−1.71357			−0.856787	+	0.515670i	$0.827543\pi$
$972$	−1.09510e6	−	1.09510e6i	−1.15910	−	1.15910i
$973$	−342160.	+	342160.i	−0.361413	+	0.361413i
$974$		−	430733.i		−	0.454036i
$975$	−62928.8	−	95022.4i	−0.0661973	−	0.0999578i
$976$	−3.15515e6			−3.31223
$977$	−824838.	−	824838.i	−0.864131	−	0.864131i	0.127684	−	0.991815i	$-0.459246\pi$
$977$	−824838.	−	824838.i	−0.864131	−	0.864131i	−0.991815	+	0.127684i	$0.959246\pi$
$978$	303702.	−	303702.i	0.317520	−	0.317520i
$979$		−	993249.i		−	1.03632i
$980$	−107180.	−	355957.i	−0.111600	−	0.370634i
$981$	71886.7			0.0746983
$982$	255653.	+	255653.i	0.265111	+	0.265111i
$983$	−203625.	+	203625.i	−0.210729	+	0.210729i	−0.804577	−	0.593848i	$-0.797608\pi$
$983$	−203625.	+	203625.i	−0.210729	+	0.210729i	0.593848	+	0.804577i	$0.297608\pi$
$984$		−	32592.1i		−	0.0336607i
$985$	113964.	−	212162.i	0.117461	−	0.218673i
$986$	2.22078e6			2.28429
$987$	95557.0	+	95557.0i	0.0980908	+	0.0980908i
$988$	200240.	−	200240.i	0.205134	−	0.205134i
$989$			106561.i			0.108944i
$990$	1.06982e6	+	574659.i	1.09154	+	0.586326i
$991$	1.10847e6			1.12870			0.564348	−	0.825537i	$-0.309128\pi$
$991$	1.10847e6			1.12870			0.564348	+	0.825537i	$0.309128\pi$
$992$	1.44457e6	+	1.44457e6i	1.46796	+	1.46796i
$993$	−57766.9	+	57766.9i	−0.0585842	+	0.0585842i
$994$			988810.i			1.00078i
$995$	436191.	−	131339.i	0.440586	−	0.132662i
$996$	841203.			0.847973
$997$	994907.	+	994907.i	1.00090	+	1.00090i	1.00000		0.000903760i	$0.000287676\pi$
$997$	994907.	+	994907.i	1.00090	+	1.00090i	0.000903760		1.00000i	$0.499712\pi$
$998$	−2.58446e6	+	2.58446e6i	−2.59483	+	2.59483i
$999$		−	469155.i		−	0.470095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.22.1	yes	24
5.2	odd	4		175.5.g.c.43.12		24
5.3	odd	4	inner	35.5.g.a.8.1	✓	24
5.4	even	2		175.5.g.c.57.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.1	✓	24	5.3	odd	4	inner
35.5.g.a.22.1	yes	24	1.1	even	1	trivial
175.5.g.c.43.12		24	5.2	odd	4
175.5.g.c.57.12		24	5.4	even	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.44757 - 5.44757i) q^{2} +(1.36639 - 1.36639i) q^{3} +43.3520i q^{4} +(7.20796 + 23.9384i) q^{5} -14.8870 q^{6} +(-13.0958 - 13.0958i) q^{7} +(149.002 - 149.002i) q^{8} +77.2660i q^{9} +O(q^{10})\)	\(q+(-5.44757 - 5.44757i) q^{2} +(1.36639 - 1.36639i) q^{3} +43.3520i q^{4} +(7.20796 + 23.9384i) q^{5} -14.8870 q^{6} +(-13.0958 - 13.0958i) q^{7} +(149.002 - 149.002i) q^{8} +77.2660i q^{9} +(91.1401 - 169.672i) q^{10} +81.6042 q^{11} +(59.2358 + 59.2358i) q^{12} +(-66.7280 + 66.7280i) q^{13} +142.681i q^{14} +(42.5580 + 22.8603i) q^{15} -929.763 q^{16} +(347.598 + 347.598i) q^{17} +(420.912 - 420.912i) q^{18} +69.2205i q^{19} +(-1037.78 + 312.479i) q^{20} -35.7880 q^{21} +(-444.544 - 444.544i) q^{22} +(40.2630 - 40.2630i) q^{23} -407.189i q^{24} +(-521.091 + 345.093i) q^{25} +727.010 q^{26} +(216.253 + 216.253i) q^{27} +(567.729 - 567.729i) q^{28} +586.403i q^{29} +(-107.305 - 356.371i) q^{30} +538.834 q^{31} +(2680.92 + 2680.92i) q^{32} +(111.503 - 111.503i) q^{33} -3787.13i q^{34} +(219.098 - 407.886i) q^{35} -3349.63 q^{36} +(-1084.74 - 1084.74i) q^{37} +(377.083 - 377.083i) q^{38} +182.353i q^{39} +(4640.86 + 2492.86i) q^{40} +80.0417 q^{41} +(194.957 + 194.957i) q^{42} +(-1323.31 + 1323.31i) q^{43} +3537.70i q^{44} +(-1849.62 + 556.930i) q^{45} -438.671 q^{46} +(-2670.09 - 2670.09i) q^{47} +(-1270.42 + 1270.42i) q^{48} +343.000i q^{49} +(4718.60 + 958.758i) q^{50} +949.909 q^{51} +(-2892.79 - 2892.79i) q^{52} +(1863.94 - 1863.94i) q^{53} -2356.11i q^{54} +(588.199 + 1953.47i) q^{55} -3902.60 q^{56} +(94.5822 + 94.5822i) q^{57} +(3194.47 - 3194.47i) q^{58} +1139.50i q^{59} +(-991.039 + 1844.98i) q^{60} +3393.50 q^{61} +(-2935.33 - 2935.33i) q^{62} +(1011.86 - 1011.86i) q^{63} -14332.8i q^{64} +(-2078.33 - 1116.39i) q^{65} -1214.84 q^{66} +(1840.20 + 1840.20i) q^{67} +(-15069.1 + 15069.1i) q^{68} -110.030i q^{69} +(-3415.54 + 1028.43i) q^{70} +6930.24 q^{71} +(11512.8 + 11512.8i) q^{72} +(-823.082 + 823.082i) q^{73} +11818.3i q^{74} +(-240.481 + 1183.55i) q^{75} -3000.85 q^{76} +(-1068.67 - 1068.67i) q^{77} +(993.380 - 993.380i) q^{78} +86.0479i q^{79} +(-6701.69 - 22257.0i) q^{80} -5667.57 q^{81} +(-436.033 - 436.033i) q^{82} +(7100.46 - 7100.46i) q^{83} -1551.48i q^{84} +(-5815.46 + 10826.4i) q^{85} +14417.6 q^{86} +(801.255 + 801.255i) q^{87} +(12159.2 - 12159.2i) q^{88} -12171.5i q^{89} +(13109.8 + 7042.02i) q^{90} +1747.71 q^{91} +(1745.48 + 1745.48i) q^{92} +(736.258 - 736.258i) q^{93} +29091.0i q^{94} +(-1657.02 + 498.938i) q^{95} +7326.37 q^{96} +(-7968.92 - 7968.92i) q^{97} +(1868.52 - 1868.52i) q^{98} +6305.23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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