LMFDB - Embedded newform 35.5.g.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,5,Mod(8,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			8.1
Character	$\chi$	$=$	35.8
Dual form			35.5.g.a.22.1

$q$-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} +(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} - 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}+ \cdots - 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

Character values

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

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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	−0.490387	+	0.871505i	$0.663145\pi$
$2$	−5.44757	+	5.44757i	−1.36189	+	1.36189i	−0.871505	+	0.490387i	$0.836855\pi$
$3$	1.36639	+	1.36639i	0.151821	+	0.151821i	0.778931	−	0.627110i	$-0.215762\pi$
$3$	1.36639	+	1.36639i	0.151821	+	0.151821i	−0.627110	+	0.778931i	$0.715762\pi$
$4$		−	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	0.481568	−	0.876408i	$-0.340067\pi$
$13$	−66.7280	−	66.7280i	−0.394840	−	0.394840i	−0.876408	+	0.481568i	$0.840067\pi$
$14$		−	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	0.229438	−	0.973323i	$-0.426311\pi$
$17$	347.598	−	347.598i	1.20276	−	1.20276i	0.973323	−	0.229438i	$-0.0736889\pi$
$18$	420.912	+	420.912i	1.29911	+	1.29911i
$19$		−	69.2205i		−	0.191746i	−0.995394	−	0.0958732i	$-0.969436\pi$
$19$		−	69.2205i		−	0.191746i	0.995394	−	0.0958732i	$-0.0305643\pi$
$20$	−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	0.744138	−	0.668026i	$-0.232861\pi$
$23$	40.2630	+	40.2630i	0.0761115	+	0.0761115i	−0.668026	+	0.744138i	$0.732861\pi$
$24$			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	$-0.886646\pi$
$29$		−	586.403i		−	0.697268i	0.937259	−	0.348634i	$-0.113354\pi$
$30$	−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	−0.981877	−	0.189521i	$-0.939307\pi$
$37$	−1084.74	+	1084.74i	−0.792356	+	0.792356i	0.189521	+	0.981877i	$0.439307\pi$
$38$	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	0.252030	−	0.967719i	$-0.418902\pi$
$43$	−1323.31	−	1323.31i	−0.715689	−	0.715689i	−0.967719	+	0.252030i	$0.918902\pi$
$44$		−	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	−0.237294	+	0.971438i	$0.576260\pi$
$47$	−2670.09	+	2670.09i	−1.20873	+	1.20873i	−0.971438	+	0.237294i	$0.923740\pi$
$48$	−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	0.956217	−	0.292658i	$-0.0945396\pi$
$53$	1863.94	+	1863.94i	0.663560	+	0.663560i	−0.292658	+	0.956217i	$0.594540\pi$
$54$			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	$-0.947665\pi$
$59$		−	1139.50i		−	0.327350i	0.986514	−	0.163675i	$-0.0523348\pi$
$60$	−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	−0.471781	−	0.881716i	$-0.656389\pi$
$67$	1840.20	−	1840.20i	0.409935	−	0.409935i	0.881716	+	0.471781i	$0.156389\pi$
$68$	−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	0.625650	−	0.780104i	$-0.284834\pi$
$73$	−823.082	−	823.082i	−0.154453	−	0.154453i	−0.780104	+	0.625650i	$0.784834\pi$
$74$		−	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	$-0.997806\pi$
$79$		−	86.0479i		−	0.0137875i	0.999976	−	0.00689376i	$-0.00219437\pi$
$80$	−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	0.999514	+	0.0311822i	$0.00992720\pi$
$83$	7100.46	+	7100.46i	1.03070	+	1.03070i	0.0311822	+	0.999514i	$0.490073\pi$
$84$			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	$0.278901\pi$
$89$			12171.5i			1.53662i	−0.640080	+	0.768309i	$0.721099\pi$
$90$	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	−0.989751	−	0.142804i	$-0.954388\pi$
$97$	−7968.92	+	7968.92i	−0.846947	+	0.846947i	0.142804	+	0.989751i	$0.454388\pi$
$98$	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	0.947072	−	0.321022i	$-0.104026\pi$
$103$	6641.76	+	6641.76i	0.626049	+	0.626049i	−0.321022	+	0.947072i	$0.604026\pi$
$104$		−	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	−0.743794	−	0.668409i	$-0.766976\pi$
$107$	−863.078	+	863.078i	−0.0753845	+	0.0753845i	0.668409	+	0.743794i	$0.266976\pi$
$108$	−9375.00	−	9375.00i	−0.803755	−	0.803755i
$109$			930.380i			0.0783083i	0.999233	+	0.0391541i	$0.0124663\pi$
$109$			930.380i			0.0783083i	−0.999233	+	0.0391541i	$0.987534\pi$
$110$	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	0.136451	−	0.990647i	$-0.456430\pi$
$113$	−10907.2	−	10907.2i	−0.854196	−	0.854196i	−0.990647	+	0.136451i	$0.956430\pi$
$114$			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	−0.345856	−	0.938287i	$-0.612412\pi$
$127$	9555.32	−	9555.32i	0.592431	−	0.592431i	0.938287	+	0.345856i	$0.112412\pi$
$128$	−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	−0.409347	−	0.912379i	$-0.634243\pi$
$137$	9441.41	−	9441.41i	0.503032	−	0.503032i	0.912379	+	0.409347i	$0.134243\pi$
$138$	−599.396	−	599.396i	−0.0314742	−	0.0314742i
$139$			26127.4i			1.35228i	0.736772	+	0.676141i	$0.236349\pi$
$139$			26127.4i			1.35228i	−0.736772	+	0.676141i	$0.763651\pi$
$140$	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	$-0.973417\pi$
$149$		−	3703.79i		−	0.166830i	0.996515	−	0.0834149i	$-0.0265827\pi$
$150$	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	−0.594853	−	0.803834i	$-0.702790\pi$
$157$	5151.18	−	5151.18i	0.208981	−	0.208981i	0.803834	+	0.594853i	$0.202790\pi$
$158$	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	0.209893	−	0.977724i	$-0.432688\pi$
$163$	−20400.5	−	20400.5i	−0.767831	−	0.767831i	−0.977724	+	0.209893i	$0.932688\pi$
$164$		−	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	0.124204	−	0.992257i	$-0.460362\pi$
$167$	31137.0	−	31137.0i	1.11646	−	1.11646i	0.992257	−	0.124204i	$-0.0396376\pi$
$168$	−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	0.934343	−	0.356374i	$-0.115987\pi$
$173$	17298.0	+	17298.0i	0.577969	+	0.577969i	−0.356374	+	0.934343i	$0.615987\pi$
$174$			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	$0.00661969\pi$
$179$			1332.58i			0.0415897i	−0.999784	+	0.0207949i	$0.993380\pi$
$180$	−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	0.551330	−	0.834287i	$-0.314121\pi$
$193$	−10539.9	−	10539.9i	−0.282957	−	0.282957i	−0.834287	+	0.551330i	$0.814121\pi$
$194$		−	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	−0.789400	−	0.613879i	$-0.789608\pi$
$197$	−6811.78	+	6811.78i	−0.175521	+	0.175521i	0.613879	+	0.789400i	$0.289608\pi$
$198$	34348.1	+	34348.1i	0.876139	+	0.876139i
$199$			18221.4i			0.460125i	0.973176	+	0.230063i	$0.0738931\pi$
$199$			18221.4i			0.460125i	−0.973176	+	0.230063i	$0.926107\pi$
$200$	−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	0.457174	−	0.889378i	$-0.348862\pi$
$223$	−21493.1	−	21493.1i	−0.432204	−	0.432204i	−0.889378	+	0.457174i	$0.848862\pi$
$224$			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	−0.707117	−	0.707096i	$-0.750005\pi$
$227$	−1.06812	+	1.06812i	−2.07285e−5	+	2.07285e-5i	0.707096	+	0.707117i	$0.250005\pi$
$228$	−4100.33	−	4100.33i	−0.0788767	−	0.0788767i
$229$			61585.7i			1.17438i	0.809449	+	0.587191i	$0.199766\pi$
$229$			61585.7i			1.17438i	−0.809449	+	0.587191i	$0.800234\pi$
$230$	−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	0.510361	−	0.859960i	$-0.329512\pi$
$233$	−18979.4	−	18979.4i	−0.349599	−	0.349599i	−0.859960	+	0.510361i	$0.829512\pi$
$234$		−	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	$0.372036\pi$
$239$			105134.i			1.84055i	−0.391269	+	0.920276i	$0.627964\pi$
$240$	−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	−0.181636	−	0.983366i	$-0.558139\pi$
$257$	52953.5	−	52953.5i	0.801730	−	0.801730i	0.983366	+	0.181636i	$0.0581391\pi$
$258$	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	0.862180	−	0.506602i	$-0.169099\pi$
$263$	24595.0	+	24595.0i	0.355578	+	0.355578i	−0.506602	+	0.862180i	$0.669099\pi$
$264$			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	$0.111752\pi$
$269$			49771.6i			0.687823i	−0.939002	+	0.343912i	$0.888248\pi$
$270$	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	−0.872456	−	0.488692i	$-0.837474\pi$
$277$	−29445.9	+	29445.9i	−0.383765	+	0.383765i	0.488692	+	0.872456i	$0.337474\pi$
$278$	−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	0.998865	−	0.0476314i	$-0.0151673\pi$
$283$	76183.3	+	76183.3i	0.951234	+	0.951234i	−0.0476314	+	0.998865i	$0.515167\pi$
$284$		−	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	0.468256	−	0.883593i	$-0.344883\pi$
$293$	−35656.3	−	35656.3i	−0.415337	−	0.415337i	−0.883593	+	0.468256i	$0.844883\pi$
$294$			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	−0.303626	−	0.952791i	$-0.598197\pi$
$307$	61183.2	−	61183.2i	0.649165	−	0.649165i	0.952791	+	0.303626i	$0.0981974\pi$
$308$	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	0.506786	−	0.862072i	$-0.330833\pi$
$313$	−34807.0	−	34807.0i	−0.355285	−	0.355285i	−0.862072	+	0.506786i	$0.830833\pi$
$314$			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	−0.797508	−	0.603308i	$-0.793849\pi$
$317$	−19515.0	+	19515.0i	−0.194200	+	0.194200i	0.603308	+	0.797508i	$0.293849\pi$
$318$	−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	−0.739179	−	0.673509i	$-0.764786\pi$
$337$	−7458.03	+	7458.03i	−0.0656696	+	0.0656696i	0.673509	+	0.739179i	$0.264786\pi$
$338$	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	−0.984110	−	0.177561i	$-0.943179\pi$
$347$	−97115.7	+	97115.7i	−0.806548	+	0.806548i	0.177561	+	0.984110i	$0.443179\pi$
$348$	−34736.0	−	34736.0i	−0.286828	−	0.286828i
$349$			92436.0i			0.758910i	0.925210	+	0.379455i	$0.123889\pi$
$349$			92436.0i			0.758910i	−0.925210	+	0.379455i	$0.876111\pi$
$350$	−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	0.678459	−	0.734638i	$-0.262648\pi$
$353$	−7000.38	−	7000.38i	−0.0561787	−	0.0561787i	−0.734638	+	0.678459i	$0.762648\pi$
$354$			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	$-0.713262\pi$
$359$		−	202042.i		−	1.56766i	0.620973	−	0.783832i	$-0.286738\pi$
$360$	−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	−0.998336	−	0.0576654i	$-0.981634\pi$
$367$	−126698.	+	126698.i	−0.940671	+	0.940671i	0.0576654	+	0.998336i	$0.481634\pi$
$368$	−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	0.982604	−	0.185714i	$-0.0594599\pi$
$373$	110870.	+	110870.i	0.796889	+	0.796889i	−0.185714	+	0.982604i	$0.559460\pi$
$374$			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	$0.165972\pi$
$379$			143098.i			0.996219i	−0.867114	+	0.498110i	$0.834028\pi$
$380$	−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	0.520512	−	0.853854i	$-0.325741\pi$
$383$	−48897.7	−	48897.7i	−0.333343	−	0.333343i	−0.853854	+	0.520512i	$0.825741\pi$
$384$		−	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	$-0.873866\pi$
$389$		−	116811.i		−	0.771943i	0.922511	−	0.385971i	$-0.126134\pi$
$390$	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	−0.718457	−	0.695571i	$-0.755151\pi$
$397$	−3607.04	+	3607.04i	−0.0228860	+	0.0228860i	0.695571	+	0.718457i	$0.255151\pi$
$398$	−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	$-0.670614\pi$
$409$		−	287642.i		−	1.71952i	0.510701	−	0.859758i	$-0.329386\pi$
$410$	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	$-0.990249\pi$
$419$		−	10754.6i		−	0.0612585i	0.999531	−	0.0306293i	$-0.00975113\pi$
$420$	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	0.489677	−	0.871904i	$-0.337115\pi$
$433$	−71663.4	−	71663.4i	−0.382227	−	0.382227i	−0.871904	+	0.489677i	$0.837115\pi$
$434$		−	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	$0.283408\pi$
$439$			299601.i			1.55459i	−0.629139	+	0.777293i	$0.716592\pi$
$440$	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	0.954795	−	0.297267i	$-0.0960750\pi$
$443$	129039.	+	129039.i	0.657528	+	0.657528i	−0.297267	+	0.954795i	$0.596075\pi$
$444$			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	$-0.795252\pi$
$449$		−	241835.i		−	1.19957i	0.800161	−	0.599786i	$-0.204748\pi$
$450$	−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	−0.965219	−	0.261441i	$-0.915802\pi$
$457$	−146983.	+	146983.i	−0.703778	+	0.703778i	0.261441	+	0.965219i	$0.415802\pi$
$458$	−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	0.242561	−	0.970136i	$-0.422013\pi$
$463$	−155970.	−	155970.i	−0.727575	−	0.727575i	−0.970136	+	0.242561i	$0.922013\pi$
$464$			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	−0.0356846	−	0.999363i	$-0.511361\pi$
$467$	210168.	−	210168.i	0.963678	−	0.963678i	0.999363	+	0.0356846i	$0.0113612\pi$
$468$	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	$-0.850140\pi$
$479$		−	208148.i		−	0.907196i	0.891206	−	0.453598i	$-0.149860\pi$
$480$	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	−0.618831	−	0.785524i	$-0.712393\pi$
$487$	39534.4	−	39534.4i	0.166693	−	0.166693i	0.785524	+	0.618831i	$0.212393\pi$
$488$	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	$0.401663\pi$
$499$			474425.i			1.90532i	−0.304045	+	0.952658i	$0.598337\pi$
$500$	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	0.966032	+	0.258422i	$0.0832024\pi$
$503$	309798.	+	309798.i	1.22445	+	1.22445i	0.258422	+	0.966032i	$0.416798\pi$
$504$			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	$0.318630\pi$
$509$			436300.i			1.68403i	−0.539455	+	0.842015i	$0.681370\pi$
$510$	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	0.801684	−	0.597748i	$-0.203938\pi$
$523$	55782.4	+	55782.4i	0.203936	+	0.203936i	−0.597748	+	0.801684i	$0.703938\pi$
$524$		−	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	−0.696022	−	0.718020i	$-0.745049\pi$
$547$	6581.91	−	6581.91i	0.0219977	−	0.0219977i	0.718020	+	0.696022i	$0.245049\pi$
$548$	−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	−0.0115379	+	0.999933i	$0.503673\pi$
$557$	−313808.	+	313808.i	−1.01147	+	1.01147i	−0.999933	+	0.0115379i	$0.996327\pi$
$558$	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	0.731518	−	0.681822i	$-0.238812\pi$
$563$	15752.0	+	15752.0i	0.0496957	+	0.0496957i	−0.681822	+	0.731518i	$0.738812\pi$
$564$			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	$-0.954747\pi$
$569$		−	91745.8i		−	0.283375i	0.989911	−	0.141688i	$-0.0452528\pi$
$570$	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	−0.304197	−	0.952609i	$-0.598388\pi$
$577$	215875.	−	215875.i	0.648412	−	0.648412i	0.952609	+	0.304197i	$0.0983883\pi$
$578$	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	0.233601	−	0.972333i	$-0.424949\pi$
$587$	415527.	−	415527.i	1.20593	−	1.20593i	0.972333	−	0.233601i	$-0.0750509\pi$
$588$	−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	0.390336	−	0.920673i	$-0.372359\pi$
$593$	−186492.	−	186492.i	−0.530337	−	0.530337i	−0.920673	+	0.390336i	$0.872359\pi$
$594$			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	$0.0604498\pi$
$599$			135461.i			0.377538i	−0.982022	+	0.188769i	$0.939550\pi$
$600$	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	−0.443364	−	0.896342i	$-0.646215\pi$
$607$	166899.	−	166899.i	0.452978	−	0.452978i	0.896342	+	0.443364i	$0.146215\pi$
$608$	−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	−0.993562	−	0.113290i	$-0.963861\pi$
$613$	−415920.	−	415920.i	−1.10685	−	1.10685i	−0.113290	−	0.993562i	$-0.536139\pi$
$614$			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	0.298783	−	0.954321i	$-0.403419\pi$
$617$	477043.	−	477043.i	1.25310	−	1.25310i	0.954321	−	0.298783i	$-0.0965808\pi$
$618$	−98875.9	−	98875.9i	−0.258889	−	0.258889i
$619$		−	96183.1i		−	0.251025i	−0.992092	−	0.125513i	$-0.959942\pi$
$619$		−	96183.1i		−	0.251025i	0.992092	−	0.125513i	$-0.0400575\pi$
$620$	−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	0.605716	−	0.795681i	$-0.292887\pi$
$643$	−78540.8	−	78540.8i	−0.189965	−	0.189965i	−0.795681	+	0.605716i	$0.792887\pi$
$644$			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	−0.244260	−	0.969710i	$-0.578545\pi$
$647$	303680.	−	303680.i	0.725449	−	0.725449i	0.969710	+	0.244260i	$0.0785452\pi$
$648$	−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	0.960097	−	0.279668i	$-0.0902245\pi$
$653$	290141.	+	290141.i	0.680429	+	0.680429i	−0.279668	+	0.960097i	$0.590224\pi$
$654$		−	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	$0.193353\pi$
$659$			495743.i			1.14153i	−0.821115	+	0.570763i	$0.806647\pi$
$660$	−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	−0.968382	−	0.249470i	$-0.919743\pi$
$673$	−551601.	−	551601.i	−1.21785	−	1.21785i	−0.249470	−	0.968382i	$-0.580257\pi$
$674$		−	81256.2i		−	0.178870i
$675$	−187315.	+	38060.0i	−0.411117	+	0.0835336i
$676$	−852116.			−1.86469
$677$	−112272.	+	112272.i	−0.244959	+	0.244959i	−0.818898	−	0.573939i	$-0.805415\pi$
$677$	−112272.	+	112272.i	−0.244959	+	0.244959i	0.573939	+	0.818898i	$0.305415\pi$
$678$	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	0.997764	−	0.0668362i	$-0.0212905\pi$
$683$	434268.	+	434268.i	0.930928	+	0.930928i	−0.0668362	+	0.997764i	$0.521291\pi$
$684$			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	$-0.934806\pi$
$709$		−	204474.i		−	0.406768i	0.979099	−	0.203384i	$-0.0651939\pi$
$710$	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	$0.198294\pi$
$719$			603232.i			1.16688i	−0.812156	+	0.583441i	$0.801706\pi$
$720$	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	−0.919087	−	0.394054i	$-0.871072\pi$
$727$	−277495.	+	277495.i	−0.525033	+	0.525033i	0.394054	+	0.919087i	$0.371072\pi$
$728$	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	−0.991634	−	0.129085i	$-0.958796\pi$
$733$	−602150.	−	602150.i	−1.12072	−	1.12072i	−0.129085	−	0.991634i	$-0.541204\pi$
$734$		−	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	$0.154886\pi$
$739$			510748.i			0.935228i	−0.883933	+	0.467614i	$0.845114\pi$
$740$	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	0.993090	−	0.117355i	$-0.0374416\pi$
$743$	483448.	+	483448.i	0.875735	+	0.875735i	−0.117355	+	0.993090i	$0.537442\pi$
$744$			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	−0.816701	−	0.577061i	$-0.804199\pi$
$757$	−137325.	+	137325.i	−0.239640	+	0.239640i	0.577061	+	0.816701i	$0.304199\pi$
$758$	−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	$0.0833153\pi$
$769$			306046.i			0.517529i	−0.965941	+	0.258764i	$0.916685\pi$
$770$	−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	0.955694	+	0.294363i	$0.0951074\pi$
$773$	746945.	+	746945.i	1.25006	+	1.25006i	0.294363	+	0.955694i	$0.404893\pi$
$774$		−	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	−0.457265	+	0.889330i	$0.651171\pi$
$787$	−834040.	+	834040.i	−1.34660	+	1.34660i	−0.889330	+	0.457265i	$0.848829\pi$
$788$	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	−0.925359	−	0.379092i	$-0.876236\pi$
$797$	−346993.	+	346993.i	−0.546267	+	0.546267i	0.379092	+	0.925359i	$0.376236\pi$
$798$	−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	$-0.839248\pi$
$809$		−	633306.i		−	0.967646i	0.875166	−	0.483823i	$-0.160752\pi$
$810$	−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	0.716252	−	0.697842i	$-0.245856\pi$
$823$	12469.2	+	12469.2i	0.0184094	+	0.0184094i	−0.697842	+	0.716252i	$0.745856\pi$
$824$			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	−0.953854	−	0.300270i	$-0.902923\pi$
$827$	−447005.	+	447005.i	−0.653585	+	0.653585i	0.300270	+	0.953854i	$0.402923\pi$
$828$	−134866.	−	134866.i	−0.196717	−	0.196717i
$829$		−	93265.9i		−	0.135711i	−0.997695	−	0.0678553i	$-0.978384\pi$
$829$		−	93265.9i		−	0.135711i	0.997695	−	0.0678553i	$-0.0216156\pi$
$830$	−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	$-0.695766\pi$
$839$		−	1.14987e6i		−	1.63353i	0.576972	−	0.816764i	$-0.304234\pi$
$840$	−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	0.134088	−	0.990969i	$-0.457189\pi$
$853$	−623474.	−	623474.i	−0.856881	−	0.856881i	−0.990969	+	0.134088i	$0.957189\pi$
$854$		−	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	−0.536268	−	0.844048i	$-0.680166\pi$
$857$	226049.	−	226049.i	0.307780	−	0.307780i	0.844048	+	0.536268i	$0.180166\pi$
$858$	81064.0	+	81064.0i	0.110117	+	0.110117i
$859$		−	557243.i		−	0.755193i	−0.925970	−	0.377597i	$-0.876751\pi$
$859$		−	557243.i		−	0.755193i	0.925970	−	0.377597i	$-0.123249\pi$
$860$	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	0.873364	−	0.487069i	$-0.161934\pi$
$863$	287700.	+	287700.i	0.386295	+	0.386295i	−0.487069	+	0.873364i	$0.661934\pi$
$864$		−	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	−0.729444	−	0.684041i	$-0.760221\pi$
$877$	−34920.8	+	34920.8i	−0.0454031	+	0.0454031i	0.684041	+	0.729444i	$0.260221\pi$
$878$	−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	0.477129	−	0.878833i	$-0.341677\pi$
$883$	−313204.	−	313204.i	−0.401704	−	0.401704i	−0.878833	+	0.477129i	$0.841677\pi$
$884$			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	−0.0568158	−	0.998385i	$-0.518095\pi$
$887$	740797.	−	740797.i	0.941569	−	0.941569i	0.998385	+	0.0568158i	$0.0180948\pi$
$888$	−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	−0.984104	−	0.177596i	$-0.943168\pi$
$907$	−663473.	+	663473.i	−0.806508	+	0.806508i	0.177596	+	0.984104i	$0.443168\pi$
$908$	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	$-0.770020\pi$
$919$		−	1.11696e6i		−	1.32253i	0.750153	−	0.661265i	$-0.229980\pi$
$920$	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	$-0.951316\pi$
$929$		−	262969.i		−	0.304701i	0.988327	−	0.152350i	$-0.0486842\pi$
$930$	−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	−0.756331	−	0.654189i	$-0.773010\pi$
$937$	−89677.3	+	89677.3i	−0.102142	+	0.102142i	0.654189	+	0.756331i	$0.273010\pi$
$938$	−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	0.0909682	−	0.995854i	$-0.471004\pi$
$947$	974672.	−	974672.i	1.08682	−	1.08682i	0.995854	−	0.0909682i	$-0.0289962\pi$
$948$	−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	0.849746	−	0.527193i	$-0.176755\pi$
$953$	292946.	+	292946.i	0.322553	+	0.322553i	−0.527193	+	0.849746i	$0.676755\pi$
$954$			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	−0.166378	+	0.986062i	$0.553207\pi$
$967$	−1.07763e6	+	1.07763e6i	−1.15244	+	1.15244i	−0.986062	+	0.166378i	$0.946793\pi$
$968$	−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	−0.991815	−	0.127684i	$-0.959246\pi$
$977$	−824838.	+	824838.i	−0.864131	+	0.864131i	0.127684	+	0.991815i	$0.459246\pi$
$978$	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	0.593848	−	0.804577i	$-0.297608\pi$
$983$	−203625.	−	203625.i	−0.210729	−	0.210729i	−0.804577	+	0.593848i	$0.797608\pi$
$984$			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	0.000903760	−	1.00000i	$-0.499712\pi$
$997$	994907.	−	994907.i	1.00090	−	1.00090i	1.00000		0.000903760i	$-0.000287676\pi$
$998$	−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.8.1	✓	24
5.2	odd	4	inner	35.5.g.a.22.1	yes	24
5.3	odd	4		175.5.g.c.57.12		24
5.4	even	2		175.5.g.c.43.12		24

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

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 $\F_{q}$
Belyi maps

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25}+ \cdots - 33840 q^{97}+O(q^{100}) \) 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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