LMFDB - Embedded newform 70.5.f.a.57.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,5,Mod(43,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.43"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	70.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.23589741587$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 334x^{10} + 34233x^{8} + 1144512x^{6} + 13607616x^{4} + 38549504x^{2} + 31360000 $ x^12 + 334x^10 + 34233x^8 + 1144512x^6 + 13607616x^4 + 38549504*x^2 + 31360000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.2
Root			$-4.60707i$ of defining polynomial
Character	$\chi$	$=$	70.57
Dual form			70.5.f.a.43.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 2.00000i) q^{2} +(-7.02600 + 7.02600i) q^{3} +8.00000i q^{4} +(-24.9839 - 0.897502i) q^{5} +28.1040 q^{6} +(-13.0958 - 13.0958i) q^{7} +(16.0000 - 16.0000i) q^{8} -17.7293i q^{9} +(48.1728 + 51.7628i) q^{10} +142.126 q^{11} +(-56.2080 - 56.2080i) q^{12} +(167.395 - 167.395i) q^{13} +52.3832i q^{14} +(181.843 - 169.231i) q^{15} -64.0000 q^{16} +(-195.069 - 195.069i) q^{17} +(-35.4587 + 35.4587i) q^{18} -130.598i q^{19} +(7.18001 - 199.871i) q^{20} +184.022 q^{21} +(-284.251 - 284.251i) q^{22} +(77.4569 - 77.4569i) q^{23} +224.832i q^{24} +(623.389 + 44.8462i) q^{25} -669.581 q^{26} +(-444.540 - 444.540i) q^{27} +(104.766 - 104.766i) q^{28} +355.719i q^{29} +(-702.147 - 25.2234i) q^{30} +1190.62 q^{31} +(128.000 + 128.000i) q^{32} +(-998.574 + 998.574i) q^{33} +780.274i q^{34} +(315.430 + 338.937i) q^{35} +141.835 q^{36} +(472.084 + 472.084i) q^{37} +(-261.196 + 261.196i) q^{38} +2352.24i q^{39} +(-414.102 + 385.382i) q^{40} -73.0858 q^{41} +(-368.044 - 368.044i) q^{42} +(1495.82 - 1495.82i) q^{43} +1137.00i q^{44} +(-15.9121 + 442.948i) q^{45} -309.828 q^{46} +(-2439.36 - 2439.36i) q^{47} +(449.664 - 449.664i) q^{48} +343.000i q^{49} +(-1157.09 - 1336.47i) q^{50} +2741.10 q^{51} +(1339.16 + 1339.16i) q^{52} +(-2683.33 + 2683.33i) q^{53} +1778.16i q^{54} +(-3550.85 - 127.558i) q^{55} -419.066 q^{56} +(917.581 + 917.581i) q^{57} +(711.439 - 711.439i) q^{58} -5527.82i q^{59} +(1353.85 + 1454.74i) q^{60} +413.680 q^{61} +(-2381.24 - 2381.24i) q^{62} +(-232.180 + 232.180i) q^{63} -512.000i q^{64} +(-4332.42 + 4031.95i) q^{65} +3994.30 q^{66} +(-3561.92 - 3561.92i) q^{67} +(1560.55 - 1560.55i) q^{68} +1088.42i q^{69} +(47.0140 - 1308.74i) q^{70} +8454.30 q^{71} +(-283.669 - 283.669i) q^{72} +(7044.21 - 7044.21i) q^{73} -1888.34i q^{74} +(-4695.02 + 4064.84i) q^{75} +1044.78 q^{76} +(-1861.25 - 1861.25i) q^{77} +(4704.48 - 4704.48i) q^{78} -6515.21i q^{79} +(1598.97 + 57.4401i) q^{80} +7682.75 q^{81} +(146.172 + 146.172i) q^{82} +(-127.740 + 127.740i) q^{83} +1472.18i q^{84} +(4698.50 + 5048.65i) q^{85} -5983.30 q^{86} +(-2499.28 - 2499.28i) q^{87} +(2274.01 - 2274.01i) q^{88} +2322.67i q^{89} +(917.720 - 854.071i) q^{90} -4384.35 q^{91} +(619.655 + 619.655i) q^{92} +(-8365.30 + 8365.30i) q^{93} +9757.45i q^{94} +(-117.212 + 3262.84i) q^{95} -1798.66 q^{96} +(10168.4 + 10168.4i) q^{97} +(686.000 - 686.000i) q^{98} -2519.79i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 20 q^{3} + 8 q^{5} + 80 q^{6} + 192 q^{8} - 144 q^{10} + 4 q^{11} - 160 q^{12} - 180 q^{13} - 736 q^{15} - 768 q^{16} - 236 q^{17} - 464 q^{18} + 512 q^{20} - 196 q^{21} - 8 q^{22} - 1232 q^{23}+ \cdots + 8232 q^{98}+O(q^{100}) $ 12 * q - 24 * q^2 - 20 * q^3 + 8 * q^5 + 80 * q^6 + 192 * q^8 - 144 * q^10 + 4 * q^11 - 160 * q^12 - 180 * q^13 - 736 * q^15 - 768 * q^16 - 236 * q^17 - 464 * q^18 + 512 * q^20 - 196 * q^21 - 8 * q^22 - 1232 * q^23 + 944 * q^25 + 720 * q^26 - 908 * q^27 - 632 * q^30 - 992 * q^31 + 1536 * q^32 + 6268 * q^33 - 784 * q^35 + 1856 * q^36 + 2200 * q^37 - 2880 * q^38 - 896 * q^40 + 176 * q^41 + 392 * q^42 + 1436 * q^43 + 3436 * q^45 + 4928 * q^46 + 5708 * q^47 + 1280 * q^48 - 1352 * q^50 + 6028 * q^51 - 1440 * q^52 - 9868 * q^53 - 7036 * q^55 - 5676 * q^57 - 4376 * q^58 + 8416 * q^60 - 1512 * q^61 + 1984 * q^62 - 3920 * q^63 + 7888 * q^65 - 25072 * q^66 - 11340 * q^67 + 1888 * q^68 + 4312 * q^70 - 14544 * q^71 - 3712 * q^72 + 24744 * q^73 - 6468 * q^75 + 11520 * q^76 - 9016 * q^77 + 10152 * q^78 - 512 * q^80 + 15740 * q^81 - 352 * q^82 - 30368 * q^83 - 27972 * q^85 - 5744 * q^86 + 2084 * q^87 + 64 * q^88 - 5168 * q^90 + 11172 * q^91 - 9856 * q^92 + 34508 * q^93 + 30436 * q^95 - 5120 * q^96 + 56180 * q^97 + 8232 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−7.02600	+	7.02600i	−0.780667	+	0.780667i	−0.979943	−	0.199277i	$-0.936141\pi$
$3$	−7.02600	+	7.02600i	−0.780667	+	0.780667i	0.199277	+	0.979943i	$0.436141\pi$
$4$			8.00000i			0.500000i
$5$	−24.9839	−	0.897502i	−0.999355	−	0.0359001i
$5$	−24.9839	−	0.897502i	−0.999355	−	0.0359001i
$6$	28.1040			0.780667
$7$	−13.0958	−	13.0958i	−0.267261	−	0.267261i
$7$	−13.0958	−	13.0958i	−0.267261	−	0.267261i
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	17.7293i		−	0.218881i
$10$	48.1728	+	51.7628i	0.481728	+	0.517628i
$11$	142.126			1.17459			0.587296	−	0.809372i	$-0.300193\pi$
$11$	142.126			1.17459			0.587296	+	0.809372i	$0.300193\pi$
$12$	−56.2080	−	56.2080i	−0.390333	−	0.390333i
$13$	167.395	−	167.395i	0.990504	−	0.990504i	−0.00945101	−	0.999955i	$-0.503008\pi$
$13$	167.395	−	167.395i	0.990504	−	0.990504i	0.999955	+	0.00945101i	$0.00300840\pi$
$14$			52.3832i			0.267261i
$15$	181.843	−	169.231i	0.808189	−	0.752137i
$16$	−64.0000			−0.250000
$17$	−195.069	−	195.069i	−0.674978	−	0.674978i	0.283882	−	0.958859i	$-0.408378\pi$
$17$	−195.069	−	195.069i	−0.674978	−	0.674978i	−0.958859	+	0.283882i	$0.908378\pi$
$18$	−35.4587	+	35.4587i	−0.109440	+	0.109440i
$19$		−	130.598i		−	0.361767i	−0.983505	−	0.180884i	$-0.942104\pi$
$19$		−	130.598i		−	0.361767i	0.983505	−	0.180884i	$-0.0578957\pi$
$20$	7.18001	−	199.871i	0.0179500	−	0.499678i
$21$	184.022			0.417284
$22$	−284.251	−	284.251i	−0.587296	−	0.587296i
$23$	77.4569	−	77.4569i	0.146421	−	0.146421i	−0.630096	−	0.776517i	$-0.716984\pi$
$23$	77.4569	−	77.4569i	0.146421	−	0.146421i	0.776517	+	0.630096i	$0.216984\pi$
$24$			224.832i			0.390333i
$25$	623.389	+	44.8462i	0.997422	+	0.0717538i
$26$	−669.581			−0.990504
$27$	−444.540	−	444.540i	−0.609794	−	0.609794i
$28$	104.766	−	104.766i	0.133631	−	0.133631i
$29$			355.719i			0.422972i	0.977381	+	0.211486i	$0.0678303\pi$
$29$			355.719i			0.422972i	−0.977381	+	0.211486i	$0.932170\pi$
$30$	−702.147	−	25.2234i	−0.780163	−	0.0280260i
$31$	1190.62			1.23894			0.619470	−	0.785021i	$-0.287348\pi$
$31$	1190.62			1.23894			0.619470	+	0.785021i	$0.287348\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	−998.574	+	998.574i	−0.916964	+	0.916964i
$34$			780.274i			0.674978i
$35$	315.430	+	338.937i	0.257494	+	0.276684i
$36$	141.835			0.109440
$37$	472.084	+	472.084i	0.344839	+	0.344839i	0.858183	−	0.513344i	$-0.171594\pi$
$37$	472.084	+	472.084i	0.344839	+	0.344839i	−0.513344	+	0.858183i	$0.671594\pi$
$38$	−261.196	+	261.196i	−0.180884	+	0.180884i
$39$			2352.24i			1.54651i
$40$	−414.102	+	385.382i	−0.258814	+	0.240864i
$41$	−73.0858			−0.0434776			−0.0217388	−	0.999764i	$-0.506920\pi$
$41$	−73.0858			−0.0434776			−0.0217388	+	0.999764i	$0.506920\pi$
$42$	−368.044	−	368.044i	−0.208642	−	0.208642i
$43$	1495.82	−	1495.82i	0.808991	−	0.808991i	−0.175490	−	0.984481i	$-0.556151\pi$
$43$	1495.82	−	1495.82i	0.808991	−	0.808991i	0.984481	+	0.175490i	$0.0561510\pi$
$44$			1137.00i			0.587296i
$45$	−15.9121	+	442.948i	−0.00785783	+	0.218740i
$46$	−309.828			−0.146421
$47$	−2439.36	−	2439.36i	−1.10428	−	1.10428i	−0.993888	−	0.110395i	$-0.964788\pi$
$47$	−2439.36	−	2439.36i	−1.10428	−	1.10428i	−0.110395	−	0.993888i	$-0.535212\pi$
$48$	449.664	−	449.664i	0.195167	−	0.195167i
$49$			343.000i			0.142857i
$50$	−1157.09	−	1336.47i	−0.462834	−	0.534588i
$51$	2741.10			1.05387
$52$	1339.16	+	1339.16i	0.495252	+	0.495252i
$53$	−2683.33	+	2683.33i	−0.955260	+	0.955260i	−0.999041	−	0.0437809i	$-0.986060\pi$
$53$	−2683.33	+	2683.33i	−0.955260	+	0.955260i	0.0437809	+	0.999041i	$0.486060\pi$
$54$			1778.16i			0.609794i
$55$	−3550.85	−	127.558i	−1.17383	−	0.0421679i
$56$	−419.066			−0.133631
$57$	917.581	+	917.581i	0.282419	+	0.282419i
$58$	711.439	−	711.439i	0.211486	−	0.211486i
$59$		−	5527.82i		−	1.58800i	−0.607919	−	0.793999i	$-0.707995\pi$
$59$		−	5527.82i		−	1.58800i	0.607919	−	0.793999i	$-0.292005\pi$
$60$	1353.85	+	1454.74i	0.376069	+	0.404095i
$61$	413.680			0.111174			0.0555872	−	0.998454i	$-0.482297\pi$
$61$	413.680			0.111174			0.0555872	+	0.998454i	$0.482297\pi$
$62$	−2381.24	−	2381.24i	−0.619470	−	0.619470i
$63$	−232.180	+	232.180i	−0.0584983	+	0.0584983i
$64$		−	512.000i		−	0.125000i
$65$	−4332.42	+	4031.95i	−1.02543	+	0.954307i
$66$	3994.30			0.916964
$67$	−3561.92	−	3561.92i	−0.793478	−	0.793478i	0.188580	−	0.982058i	$-0.439611\pi$
$67$	−3561.92	−	3561.92i	−0.793478	−	0.793478i	−0.982058	+	0.188580i	$0.939611\pi$
$68$	1560.55	−	1560.55i	0.337489	−	0.337489i
$69$			1088.42i			0.228612i
$70$	47.0140	−	1308.74i	0.00959470	−	0.267089i
$71$	8454.30			1.67711			0.838554	−	0.544818i	$-0.183401\pi$
$71$	8454.30			1.67711			0.838554	+	0.544818i	$0.183401\pi$
$72$	−283.669	−	283.669i	−0.0547202	−	0.0547202i
$73$	7044.21	−	7044.21i	1.32186	−	1.32186i	0.409596	−	0.912267i	$-0.365670\pi$
$73$	7044.21	−	7044.21i	1.32186	−	1.32186i	0.912267	−	0.409596i	$-0.134330\pi$
$74$		−	1888.34i		−	0.344839i
$75$	−4695.02	+	4064.84i	−0.834670	+	0.722639i
$76$	1044.78			0.180884
$77$	−1861.25	−	1861.25i	−0.313923	−	0.313923i
$78$	4704.48	−	4704.48i	0.773254	−	0.773254i
$79$		−	6515.21i		−	1.04394i	−0.852965	−	0.521968i	$-0.825198\pi$
$79$		−	6515.21i		−	1.04394i	0.852965	−	0.521968i	$-0.174802\pi$
$80$	1598.97	+	57.4401i	0.249839	+	0.00897502i
$81$	7682.75			1.17097
$82$	146.172	+	146.172i	0.0217388	+	0.0217388i
$83$	−127.740	+	127.740i	−0.0185425	+	0.0185425i	−0.716317	−	0.697775i	$-0.754174\pi$
$83$	−127.740	+	127.740i	−0.0185425	+	0.0185425i	0.697775	+	0.716317i	$0.254174\pi$
$84$			1472.18i			0.208642i
$85$	4698.50	+	5048.65i	0.650311	+	0.698775i
$86$	−5983.30			−0.808991
$87$	−2499.28	−	2499.28i	−0.330200	−	0.330200i
$88$	2274.01	−	2274.01i	0.293648	−	0.293648i
$89$			2322.67i			0.293229i	0.989194	+	0.146615i	$0.0468377\pi$
$89$			2322.67i			0.293229i	−0.989194	+	0.146615i	$0.953162\pi$
$90$	917.720	−	854.071i	0.113299	−	0.105441i
$91$	−4384.35			−0.529447
$92$	619.655	+	619.655i	0.0732107	+	0.0732107i
$93$	−8365.30	+	8365.30i	−0.967199	+	0.967199i
$94$			9757.45i			1.10428i
$95$	−117.212	+	3262.84i	−0.0129875	+	0.361534i
$96$	−1798.66			−0.195167
$97$	10168.4	+	10168.4i	1.08071	+	1.08071i	0.996443	+	0.0842676i	$0.0268551\pi$
$97$	10168.4	+	10168.4i	1.08071	+	1.08071i	0.0842676	+	0.996443i	$0.473145\pi$
$98$	686.000	−	686.000i	0.0714286	−	0.0714286i
$99$		−	2519.79i		−	0.257095i
$100$	−358.769	+	4987.11i	−0.0358769	+	0.498711i
$101$	−15319.9			−1.50180			−0.750901	−	0.660414i	$-0.770381\pi$
$101$	−15319.9			−1.50180			−0.750901	+	0.660414i	$0.770381\pi$
$102$	−5482.21	−	5482.21i	−0.526933	−	0.526933i
$103$	−4219.97	+	4219.97i	−0.397773	+	0.397773i	−0.877447	−	0.479674i	$-0.840755\pi$
$103$	−4219.97	+	4219.97i	−0.397773	+	0.397773i	0.479674	+	0.877447i	$0.340755\pi$
$104$		−	5356.65i		−	0.495252i
$105$	−4597.59	−	165.160i	−0.417015	−	0.0149805i
$106$	10733.3			0.955260
$107$	−9579.84	−	9579.84i	−0.836740	−	0.836740i	0.151688	−	0.988428i	$-0.451529\pi$
$107$	−9579.84	−	9579.84i	−0.836740	−	0.836740i	−0.988428	+	0.151688i	$0.951529\pi$
$108$	3556.32	−	3556.32i	0.304897	−	0.304897i
$109$		−	6217.25i		−	0.523294i	−0.965164	−	0.261647i	$-0.915734\pi$
$109$		−	6217.25i		−	0.523294i	0.965164	−	0.261647i	$-0.0842655\pi$
$110$	6846.58	+	7356.81i	0.565833	+	0.608001i
$111$	−6633.73			−0.538408
$112$	838.131	+	838.131i	0.0668153	+	0.0668153i
$113$	12825.7	−	12825.7i	1.00444	−	1.00444i	0.00445163	−	0.999990i	$-0.498583\pi$
$113$	12825.7	−	12825.7i	1.00444	−	1.00444i	0.999990	−	0.00445163i	$-0.00141700\pi$
$114$		−	3670.32i		−	0.282419i
$115$	−2004.69	+	1865.66i	−0.151583	+	0.141070i
$116$	−2845.76			−0.211486
$117$	−2967.81	−	2967.81i	−0.216802	−	0.216802i
$118$	−11055.6	+	11055.6i	−0.793999	+	0.793999i
$119$			5109.16i			0.360791i
$120$	201.787	−	5617.18i	0.0140130	−	0.390082i
$121$	5558.68			0.379665
$122$	−827.360	−	827.360i	−0.0555872	−	0.0555872i
$123$	513.501	−	513.501i	0.0339415	−	0.0339415i
$124$			9524.97i			0.619470i
$125$	−15534.4	−	1679.92i	−0.994203	−	0.107515i
$126$	928.720			0.0584983
$127$	11500.2	+	11500.2i	0.713016	+	0.713016i	0.967165	−	0.254149i	$-0.0817953\pi$
$127$	11500.2	+	11500.2i	0.713016	+	0.713016i	−0.254149	+	0.967165i	$0.581795\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$			21019.3i			1.26310i
$130$	16728.7	+	600.950i	0.989866	+	0.0355592i
$131$	−13924.8			−0.811423			−0.405711	−	0.914001i	$-0.632976\pi$
$131$	−13924.8			−0.811423			−0.405711	+	0.914001i	$0.632976\pi$
$132$	−7988.59	−	7988.59i	−0.458482	−	0.458482i
$133$	−1710.28	+	1710.28i	−0.0966863	+	0.0966863i
$134$			14247.7i			0.793478i
$135$	10707.4	+	11505.3i	0.587509	+	0.631292i
$136$	−6242.20			−0.337489
$137$	−1819.33	−	1819.33i	−0.0969327	−	0.0969327i	0.656977	−	0.753910i	$-0.271835\pi$
$137$	−1819.33	−	1819.33i	−0.0969327	−	0.0969327i	−0.753910	+	0.656977i	$0.771835\pi$
$138$	2176.85	−	2176.85i	0.114306	−	0.114306i
$139$			12797.9i			0.662384i	0.943563	+	0.331192i	$0.107451\pi$
$139$			12797.9i			0.662384i	−0.943563	+	0.331192i	$0.892549\pi$
$140$	−2711.50	+	2523.44i	−0.138342	+	0.128747i
$141$	34277.9			1.72415
$142$	−16908.6	−	16908.6i	−0.838554	−	0.838554i
$143$	23791.1	−	23791.1i	1.16344	−	1.16344i
$144$			1134.68i			0.0547202i
$145$	319.259	−	8887.25i	0.0151847	−	0.422699i
$146$	−28176.8			−1.32186
$147$	−2409.92	−	2409.92i	−0.111524	−	0.111524i
$148$	−3776.68	+	3776.68i	−0.172419	+	0.172419i
$149$			5487.24i			0.247162i	0.992334	+	0.123581i	$0.0394379\pi$
$149$			5487.24i			0.247162i	−0.992334	+	0.123581i	$0.960562\pi$
$150$	17519.7	+	1260.36i	0.778654	+	0.0560158i
$151$	13562.1			0.594802			0.297401	−	0.954753i	$-0.403880\pi$
$151$	13562.1			0.594802			0.297401	+	0.954753i	$0.403880\pi$
$152$	−2089.57	−	2089.57i	−0.0904418	−	0.0904418i
$153$	−3458.44	+	3458.44i	−0.147740	+	0.147740i
$154$			7444.99i			0.313923i
$155$	−29746.3	−	1068.58i	−1.23814	−	0.0444780i
$156$	−18817.9			−0.773254
$157$	23975.6	+	23975.6i	0.972680	+	0.972680i	0.999637	−	0.0269566i	$-0.00858158\pi$
$157$	23975.6	+	23975.6i	0.972680	+	0.972680i	−0.0269566	+	0.999637i	$0.508582\pi$
$158$	−13030.4	+	13030.4i	−0.521968	+	0.521968i
$159$		−	37706.1i		−	1.49148i
$160$	−3083.06	−	3312.82i	−0.120432	−	0.129407i
$161$	−2028.72			−0.0782655
$162$	−15365.5	−	15365.5i	−0.585486	−	0.585486i
$163$	20247.0	−	20247.0i	0.762055	−	0.762055i	−0.214639	−	0.976693i	$-0.568857\pi$
$163$	20247.0	−	20247.0i	0.762055	−	0.762055i	0.976693	+	0.214639i	$0.0688575\pi$
$164$		−	584.687i		−	0.0217388i
$165$	25844.5	−	24052.0i	0.949292	−	0.883454i
$166$	510.958			0.0185425
$167$	19088.5	+	19088.5i	0.684447	+	0.684447i	0.960999	−	0.276552i	$-0.0891919\pi$
$167$	19088.5	+	19088.5i	0.684447	+	0.684447i	−0.276552	+	0.960999i	$0.589192\pi$
$168$	2944.35	−	2944.35i	0.104321	−	0.104321i
$169$		−	27481.3i		−	0.962198i
$170$	700.298	−	19494.3i	0.0242317	−	0.674543i
$171$	−2315.41			−0.0791838
$172$	11966.6	+	11966.6i	0.404496	+	0.404496i
$173$	−33924.5	+	33924.5i	−1.13350	+	1.13350i	−0.143909	+	0.989591i	$0.545967\pi$
$173$	−33924.5	+	33924.5i	−1.13350	+	1.13350i	−0.989591	+	0.143909i	$0.954033\pi$
$174$			9997.14i			0.330200i
$175$	−7576.48	−	8751.07i	−0.247395	−	0.285749i
$176$	−9096.04			−0.293648
$177$	38838.5	+	38838.5i	1.23970	+	1.23970i
$178$	4645.34	−	4645.34i	0.146615	−	0.146615i
$179$		−	63544.8i		−	1.98323i	−0.129213	−	0.991617i	$-0.541245\pi$
$179$		−	63544.8i		−	1.98323i	0.129213	−	0.991617i	$-0.458755\pi$
$180$	−3543.58	−	127.297i	−0.109370	−	0.00392892i
$181$	−9171.79			−0.279961			−0.139980	−	0.990154i	$-0.544704\pi$
$181$	−9171.79			−0.279961			−0.139980	+	0.990154i	$0.544704\pi$
$182$	8768.70	+	8768.70i	0.264723	+	0.264723i
$183$	−2906.51	+	2906.51i	−0.0867901	+	0.0867901i
$184$		−	2478.62i		−	0.0732107i
$185$	−11370.8	−	12218.2i	−0.332237	−	0.356996i
$186$	33461.2			0.967199
$187$	−27724.2	−	27724.2i	−0.792823	−	0.792823i
$188$	19514.9	−	19514.9i	0.552142	−	0.552142i
$189$			11643.2i			0.325948i
$190$	6760.11	−	6291.26i	0.187261	−	0.174273i
$191$	41456.1			1.13637			0.568187	−	0.822899i	$-0.307645\pi$
$191$	41456.1			1.13637			0.568187	+	0.822899i	$0.307645\pi$
$192$	3597.31	+	3597.31i	0.0975833	+	0.0975833i
$193$	−43070.5	+	43070.5i	−1.15628	+	1.15628i	−0.171017	+	0.985268i	$0.554705\pi$
$193$	−43070.5	+	43070.5i	−1.15628	+	1.15628i	−0.985268	+	0.171017i	$0.945295\pi$
$194$		−	40673.6i		−	1.08071i
$195$	2111.14	−	58768.0i	0.0555197	−	1.54551i
$196$	−2744.00			−0.0714286
$197$	13416.2	+	13416.2i	0.345699	+	0.345699i	0.858505	−	0.512806i	$-0.171394\pi$
$197$	13416.2	+	13416.2i	0.345699	+	0.345699i	−0.512806	+	0.858505i	$0.671394\pi$
$198$	−5039.59	+	5039.59i	−0.128548	+	0.128548i
$199$		−	40433.5i		−	1.02102i	−0.859871	−	0.510512i	$-0.829456\pi$
$199$		−	40433.5i		−	1.02102i	0.859871	−	0.510512i	$-0.170544\pi$
$200$	10691.8	−	9256.69i	0.267294	−	0.231417i
$201$	50052.1			1.23888
$202$	30639.8	+	30639.8i	0.750901	+	0.750901i
$203$	4658.43	−	4658.43i	0.113044	−	0.113044i
$204$			21928.8i			0.526933i
$205$	1825.97	+	65.5946i	0.0434496	+	0.00156085i
$206$	16879.9			0.397773
$207$	−1373.26	−	1373.26i	−0.0320488	−	0.0320488i
$208$	−10713.3	+	10713.3i	−0.247626	+	0.247626i
$209$		−	18561.3i		−	0.424929i
$210$	8864.86	+	9525.50i	0.201017	+	0.215998i
$211$	−55794.3			−1.25321			−0.626607	−	0.779335i	$-0.715557\pi$
$211$	−55794.3			−1.25321			−0.626607	+	0.779335i	$0.715557\pi$
$212$	−21466.6	−	21466.6i	−0.477630	−	0.477630i
$213$	−59399.9	+	59399.9i	−1.30926	+	1.30926i
$214$			38319.4i			0.836740i
$215$	−38714.0	+	36029.0i	−0.837512	+	0.779427i
$216$	−14225.3			−0.304897
$217$	−15592.1	−	15592.1i	−0.331121	−	0.331121i
$218$	−12434.5	+	12434.5i	−0.261647	+	0.261647i
$219$			98985.2i			2.06387i
$220$	1020.46	−	28406.8i	0.0210840	−	0.586917i
$221$	−65307.1			−1.33714
$222$	13267.5	+	13267.5i	0.269204	+	0.269204i
$223$	−27951.6	+	27951.6i	−0.562078	+	0.562078i	−0.929897	−	0.367819i	$-0.880105\pi$
$223$	−27951.6	+	27951.6i	−0.562078	+	0.562078i	0.367819	+	0.929897i	$0.380105\pi$
$224$		−	3352.53i		−	0.0668153i
$225$	795.093	−	11052.3i	0.0157055	−	0.218317i
$226$	−51302.9			−1.00444
$227$	20677.1	+	20677.1i	0.401271	+	0.401271i	0.878681	−	0.477410i	$-0.158424\pi$
$227$	20677.1	+	20677.1i	0.401271	+	0.401271i	−0.477410	+	0.878681i	$0.658424\pi$
$228$	−7340.65	+	7340.65i	−0.141210	+	0.141210i
$229$		−	55096.7i		−	1.05064i	−0.850904	−	0.525321i	$-0.823945\pi$
$229$		−	55096.7i		−	1.05064i	0.850904	−	0.525321i	$-0.176055\pi$
$230$	7740.69	+	278.071i	0.146327	+	0.00525654i
$231$	26154.3			0.490138
$232$	5691.51	+	5691.51i	0.105743	+	0.105743i
$233$	−9128.75	+	9128.75i	−0.168151	+	0.168151i	−0.786166	−	0.618015i	$-0.787937\pi$
$233$	−9128.75	+	9128.75i	−0.168151	+	0.168151i	0.618015	+	0.786166i	$0.287937\pi$
$234$			11871.2i			0.216802i
$235$	58755.4	+	63134.1i	1.06393	+	1.14322i
$236$	44222.6			0.793999
$237$	45775.9	+	45775.9i	0.814967	+	0.814967i
$238$	10218.3	−	10218.3i	0.180395	−	0.180395i
$239$			39677.3i			0.694618i	0.937751	+	0.347309i	$0.112905\pi$
$239$			39677.3i			0.694618i	−0.937751	+	0.347309i	$0.887095\pi$
$240$	−11637.9	+	10830.8i	−0.202047	+	0.188034i
$241$	−96914.9			−1.66862			−0.834308	−	0.551298i	$-0.814133\pi$
$241$	−96914.9			−1.66862			−0.834308	+	0.551298i	$0.814133\pi$
$242$	−11117.4	−	11117.4i	−0.189833	−	0.189833i
$243$	−17971.3	+	17971.3i	−0.304345	+	0.304345i
$244$			3309.44i			0.0555872i
$245$	307.843	−	8569.47i	0.00512858	−	0.142765i
$246$	−2054.00			−0.0339415
$247$	−21861.5	−	21861.5i	−0.358332	−	0.358332i
$248$	19049.9	−	19049.9i	0.309735	−	0.309735i
$249$		−	1795.00i		−	0.0289511i
$250$	27709.0	+	34428.7i	0.443344	+	0.550859i
$251$	29808.3			0.473141			0.236570	−	0.971614i	$-0.423977\pi$
$251$	29808.3			0.473141			0.236570	+	0.971614i	$0.423977\pi$
$252$	−1857.44	−	1857.44i	−0.0292492	−	0.0292492i
$253$	11008.6	−	11008.6i	0.171985	−	0.171985i
$254$		−	46001.0i		−	0.713016i
$255$	−68483.4	−	2460.15i	−1.05319	−	0.0378338i
$256$	4096.00			0.0625000
$257$	69337.4	+	69337.4i	1.04979	+	1.04979i	0.998694	+	0.0510941i	$0.0162708\pi$
$257$	69337.4	+	69337.4i	1.04979	+	1.04979i	0.0510941	+	0.998694i	$0.483729\pi$
$258$	42038.6	−	42038.6i	0.631552	−	0.631552i
$259$		−	12364.6i		−	0.184324i
$260$	−32255.6	−	34659.4i	−0.477153	−	0.512713i
$261$	6306.67			0.0925804
$262$	27849.6	+	27849.6i	0.405711	+	0.405711i
$263$	−39200.2	+	39200.2i	−0.566731	+	0.566731i	−0.931211	−	0.364480i	$-0.881247\pi$
$263$	−39200.2	+	39200.2i	−0.566731	+	0.566731i	0.364480	+	0.931211i	$0.381247\pi$
$264$			31954.4i			0.458482i
$265$	69448.2	−	64631.6i	0.988938	−	0.920351i
$266$	6841.14			0.0966863
$267$	−16319.1	−	16319.1i	−0.228914	−	0.228914i
$268$	28495.4	−	28495.4i	0.396739	−	0.396739i
$269$		−	35479.8i		−	0.490316i	−0.969483	−	0.245158i	$-0.921160\pi$
$269$		−	35479.8i		−	0.490316i	0.969483	−	0.245158i	$-0.0788398\pi$
$270$	1595.90	−	44425.3i	0.0218916	−	0.609401i
$271$	71173.4			0.969124			0.484562	−	0.874757i	$-0.338979\pi$
$271$	71173.4			0.969124			0.484562	+	0.874757i	$0.338979\pi$
$272$	12484.4	+	12484.4i	0.168744	+	0.168744i
$273$	30804.4	−	30804.4i	0.413321	−	0.413321i
$274$			7277.32i			0.0969327i
$275$	88599.5	+	6373.79i	1.17156	+	0.0842815i
$276$	−8707.39			−0.114306
$277$	−87266.6	−	87266.6i	−1.13734	−	1.13734i	−0.988926	−	0.148409i	$-0.952585\pi$
$277$	−87266.6	−	87266.6i	−1.13734	−	1.13734i	−0.148409	−	0.988926i	$-0.547415\pi$
$278$	25595.9	−	25595.9i	0.331192	−	0.331192i
$279$		−	21108.9i		−	0.271180i
$280$	10469.9	+	376.112i	0.133544	+	0.00479735i
$281$	−50104.2			−0.634544			−0.317272	−	0.948335i	$-0.602767\pi$
$281$	−50104.2			−0.634544			−0.317272	+	0.948335i	$0.602767\pi$
$282$	−68555.8	−	68555.8i	−0.862077	−	0.862077i
$283$	31754.2	−	31754.2i	0.396487	−	0.396487i	−0.480505	−	0.876992i	$-0.659547\pi$
$283$	31754.2	−	31754.2i	0.396487	−	0.396487i	0.876992	+	0.480505i	$0.159547\pi$
$284$			67634.4i			0.838554i
$285$	−22101.2	−	23748.3i	−0.272099	−	0.292376i
$286$	−95164.6			−1.16344
$287$	957.117	+	957.117i	0.0116199	+	0.0116199i
$288$	2269.36	−	2269.36i	0.0273601	−	0.0273601i
$289$		−	7417.48i		−	0.0888098i
$290$	−18413.0	+	17136.0i	−0.218942	+	0.203757i
$291$	−142886.			−1.68735
$292$	56353.7	+	56353.7i	0.660931	+	0.660931i
$293$	27048.1	−	27048.1i	0.315066	−	0.315066i	−0.531802	−	0.846868i	$-0.678485\pi$
$293$	27048.1	−	27048.1i	0.315066	−	0.315066i	0.846868	+	0.531802i	$0.178485\pi$
$294$			9639.67i			0.111524i
$295$	−4961.23	+	138106.i	−0.0570092	+	1.58697i
$296$	15106.7			0.172419
$297$	−63180.5	−	63180.5i	−0.716259	−	0.716259i
$298$	10974.5	−	10974.5i	0.123581	−	0.123581i
$299$		−	25931.8i		−	0.290062i
$300$	−32518.7	−	37560.2i	−0.361319	−	0.417335i
$301$	−39178.0			−0.432424
$302$	−27124.2	−	27124.2i	−0.297401	−	0.297401i
$303$	107638.	−	107638.i	1.17241	−	1.17241i
$304$			8358.27i			0.0904418i
$305$	−10335.3	−	371.278i	−0.111103	−	0.00399117i
$306$	13833.7			0.147740
$307$	23505.0	+	23505.0i	0.249392	+	0.249392i	0.820721	−	0.571329i	$-0.193572\pi$
$307$	23505.0	+	23505.0i	0.249392	+	0.249392i	−0.571329	+	0.820721i	$0.693572\pi$
$308$	14890.0	−	14890.0i	0.156961	−	0.156961i
$309$		−	59299.0i		−	0.621055i
$310$	57355.5	+	61629.8i	0.596831	+	0.641309i
$311$	−363.610			−0.00375937			−0.00187969	−	0.999998i	$-0.500598\pi$
$311$	−363.610			−0.00375937			−0.00187969	+	0.999998i	$0.500598\pi$
$312$	37635.8	+	37635.8i	0.386627	+	0.386627i
$313$	73662.4	−	73662.4i	0.751895	−	0.751895i	−0.222938	−	0.974833i	$-0.571565\pi$
$313$	73662.4	−	73662.4i	0.751895	−	0.751895i	0.974833	+	0.222938i	$0.0715647\pi$
$314$		−	95902.4i		−	0.972680i
$315$	6009.14	−	5592.37i	0.0605607	−	0.0563605i
$316$	52121.7			0.521968
$317$	−76995.4	−	76995.4i	−0.766208	−	0.766208i	0.211229	−	0.977437i	$-0.432253\pi$
$317$	−76995.4	−	76995.4i	−0.766208	−	0.766208i	−0.977437	+	0.211229i	$0.932253\pi$
$318$	−75412.2	+	75412.2i	−0.745740	+	0.745740i
$319$			50556.8i			0.496819i
$320$	−459.521	+	12791.7i	−0.00448751	+	0.124919i
$321$	134616.			1.30643
$322$	4057.44	+	4057.44i	0.0391327	+	0.0391327i
$323$	−25475.5	+	25475.5i	−0.244185	+	0.244185i
$324$			61462.0i			0.585486i
$325$	111859.	−	96845.3i	1.05902	−	0.916879i
$326$	−80988.1			−0.762055
$327$	43682.4	+	43682.4i	0.408518	+	0.408518i
$328$	−1169.37	+	1169.37i	−0.0108694	+	0.0108694i
$329$			63890.8i			0.590264i
$330$	−99793.1	−	3584.89i	−0.916373	−	0.0329191i
$331$	48023.0			0.438322			0.219161	−	0.975689i	$-0.429668\pi$
$331$	48023.0			0.438322			0.219161	+	0.975689i	$0.429668\pi$
$332$	−1021.92	−	1021.92i	−0.00927127	−	0.00927127i
$333$	8369.74	−	8369.74i	0.0754786	−	0.0754786i
$334$		−	76354.1i		−	0.684447i
$335$	85793.8	+	92187.4i	0.764480	+	0.821452i
$336$	−11777.4			−0.104321
$337$	−49062.7	−	49062.7i	−0.432008	−	0.432008i	0.457303	−	0.889311i	$-0.348815\pi$
$337$	−49062.7	−	49062.7i	−0.432008	−	0.432008i	−0.889311	+	0.457303i	$0.848815\pi$
$338$	−54962.7	+	54962.7i	−0.481099	+	0.481099i
$339$			180227.i			1.56827i
$340$	−40389.2	+	37588.0i	−0.349387	+	0.325156i
$341$	169218.			1.45525
$342$	4630.83	+	4630.83i	0.0395919	+	0.0395919i
$343$	4491.86	−	4491.86i	0.0381802	−	0.0381802i
$344$		−	47866.4i		−	0.404496i
$345$	976.862	−	27193.1i	0.00820720	−	0.228465i
$346$	135698.			1.13350
$347$	122068.	+	122068.i	1.01378	+	1.01378i	0.999904	+	0.0138775i	$0.00441748\pi$
$347$	122068.	+	122068.i	1.01378	+	1.01378i	0.0138775	+	0.999904i	$0.495583\pi$
$348$	19994.3	−	19994.3i	0.165100	−	0.165100i
$349$		−	17749.3i		−	0.145724i	−0.997342	−	0.0728620i	$-0.976787\pi$
$349$		−	17749.3i		−	0.145724i	0.997342	−	0.0728620i	$-0.0232133\pi$
$350$	−2349.19	+	32655.1i	−0.0191770	+	0.266572i
$351$	−148828.			−1.20801
$352$	18192.1	+	18192.1i	0.146824	+	0.146824i
$353$	110706.	−	110706.i	0.888427	−	0.888427i	−0.105945	−	0.994372i	$-0.533787\pi$
$353$	110706.	−	110706.i	0.888427	−	0.888427i	0.994372	+	0.105945i	$0.0337869\pi$
$354$		−	155354.i		−	1.23970i
$355$	−211221.	−	7587.75i	−1.67603	−	0.0602083i
$356$	−18581.4			−0.146615
$357$	−35896.9	−	35896.9i	−0.281657	−	0.281657i
$358$	−127090.	+	127090.i	−0.991617	+	0.991617i
$359$			69586.2i			0.539926i	0.962871	+	0.269963i	$0.0870115\pi$
$359$			69586.2i			0.539926i	−0.962871	+	0.269963i	$0.912988\pi$
$360$	6832.57	+	7341.76i	0.0527205	+	0.0566494i
$361$	113265.			0.869125
$362$	18343.6	+	18343.6i	0.139980	+	0.139980i
$363$	−39055.3	+	39055.3i	−0.296392	+	0.296392i
$364$		−	35074.8i		−	0.264723i
$365$	−182314.	+	169669.i	−1.36847	+	1.27356i
$366$	11626.1			0.0867901
$367$	−121457.	−	121457.i	−0.901762	−	0.901762i	0.0938265	−	0.995589i	$-0.470090\pi$
$367$	−121457.	−	121457.i	−0.901762	−	0.901762i	−0.995589	+	0.0938265i	$0.970090\pi$
$368$	−4957.24	+	4957.24i	−0.0366053	+	0.0366053i
$369$			1295.76i			0.00951640i
$370$	−1694.79	+	47178.0i	−0.0123797	+	0.344617i
$371$	70280.6			0.510608
$372$	−66922.4	−	66922.4i	−0.483599	−	0.483599i
$373$	−85881.0	+	85881.0i	−0.617276	+	0.617276i	−0.944832	−	0.327556i	$-0.893775\pi$
$373$	−85881.0	+	85881.0i	−0.617276	+	0.617276i	0.327556	+	0.944832i	$0.393775\pi$
$374$			110897.i			0.792823i
$375$	120948.	−	97341.7i	0.860075	−	0.692208i
$376$	−78059.6			−0.552142
$377$	59545.7	+	59545.7i	0.418956	+	0.418956i
$378$	23286.4	−	23286.4i	0.162974	−	0.162974i
$379$			1064.28i			0.00740929i	0.999993	+	0.00370464i	$0.00117923\pi$
$379$			1064.28i			0.00740929i	−0.999993	+	0.00370464i	$0.998821\pi$
$380$	−26102.7	−	937.695i	−0.180767	−	0.00649373i
$381$	−161601.			−1.11326
$382$	−82912.1	−	82912.1i	−0.568187	−	0.568187i
$383$	−27545.5	+	27545.5i	−0.187781	+	0.187781i	−0.794736	−	0.606955i	$-0.792391\pi$
$383$	−27545.5	+	27545.5i	−0.187781	+	0.187781i	0.606955	+	0.794736i	$0.292391\pi$
$384$		−	14389.2i		−	0.0975833i
$385$	44830.7	+	48171.7i	0.302451	+	0.324990i
$386$	172282.			1.15628
$387$	−26520.0	−	26520.0i	−0.177073	−	0.177073i
$388$	−81347.3	+	81347.3i	−0.540355	+	0.540355i
$389$			217133.i			1.43492i	0.696600	+	0.717459i	$0.254695\pi$
$389$			217133.i			1.43492i	−0.696600	+	0.717459i	$0.745305\pi$
$390$	−121758.	+	113314.i	−0.800515	+	0.744995i
$391$	−30218.8			−0.197662
$392$	5488.00	+	5488.00i	0.0357143	+	0.0357143i
$393$	97835.8	−	97835.8i	0.633451	−	0.633451i
$394$		−	53665.0i		−	0.345699i
$395$	−5847.41	+	162775.i	−0.0374774	+	1.04326i
$396$	20158.3			0.128548
$397$	−180198.	−	180198.i	−1.14332	−	1.14332i	−0.987839	−	0.155481i	$-0.950307\pi$
$397$	−180198.	−	180198.i	−1.14332	−	1.14332i	−0.155481	−	0.987839i	$-0.549693\pi$
$398$	−80867.1	+	80867.1i	−0.510512	+	0.510512i
$399$		−	24032.9i		−	0.150960i
$400$	−39896.9	−	2870.15i	−0.249356	−	0.0179385i
$401$	142883.			0.888568			0.444284	−	0.895886i	$-0.353458\pi$
$401$	142883.			0.888568			0.444284	+	0.895886i	$0.353458\pi$
$402$	−100104.	−	100104.i	−0.619441	−	0.619441i
$403$	199304.	−	199304.i	1.22717	−	1.22717i
$404$		−	122559.i		−	0.750901i
$405$	−191945.	−	6895.28i	−1.17022	−	0.0420380i
$406$	−18633.7			−0.113044
$407$	67095.3	+	67095.3i	0.405045	+	0.405045i
$408$	43857.7	−	43857.7i	0.263466	−	0.263466i
$409$			98659.2i			0.589781i	0.955531	+	0.294891i	$0.0952832\pi$
$409$			98659.2i			0.589781i	−0.955531	+	0.294891i	$0.904717\pi$
$410$	−3520.75	−	3783.12i	−0.0209444	−	0.0225052i
$411$	25565.2			0.151344
$412$	−33759.7	−	33759.7i	−0.198886	−	0.198886i
$413$	−72391.2	+	72391.2i	−0.424410	+	0.424410i
$414$			5493.04i			0.0320488i
$415$	3306.08	−	3076.78i	0.0191963	−	0.0178649i
$416$	42853.2			0.247626
$417$	−89918.3	−	89918.3i	−0.517101	−	0.517101i
$418$	−37122.6	+	37122.6i	−0.212464	+	0.212464i
$419$		−	165207.i		−	0.941021i	−0.882394	−	0.470511i	$-0.844070\pi$
$419$		−	165207.i		−	0.941021i	0.882394	−	0.470511i	$-0.155930\pi$
$420$	1321.28	−	36780.7i	0.00749026	−	0.208507i
$421$	288697.			1.62884			0.814419	−	0.580277i	$-0.197056\pi$
$421$	288697.			1.62884			0.814419	+	0.580277i	$0.197056\pi$
$422$	111589.	+	111589.i	0.626607	+	0.626607i
$423$	−43248.3	+	43248.3i	−0.241706	+	0.241706i
$424$			85866.4i			0.477630i
$425$	−112856.	−	130352.i	−0.624806	−	0.721670i
$426$	237600.			1.30926
$427$	−5417.47	−	5417.47i	−0.0297126	−	0.0297126i
$428$	76638.7	−	76638.7i	0.418370	−	0.418370i
$429$			334313.i			1.81651i
$430$	149486.	+	5370.02i	0.808470	+	0.0290428i
$431$	−103792.			−0.558739			−0.279369	−	0.960184i	$-0.590125\pi$
$431$	−103792.			−0.558739			−0.279369	+	0.960184i	$0.590125\pi$
$432$	28450.5	+	28450.5i	0.152448	+	0.152448i
$433$	−225675.	+	225675.i	−1.20367	+	1.20367i	−0.230626	+	0.973043i	$0.574077\pi$
$433$	−225675.	+	225675.i	−1.20367	+	1.20367i	−0.973043	+	0.230626i	$0.925923\pi$
$434$			62368.5i			0.331121i
$435$	60198.7	+	64684.9i	0.318133	+	0.341841i
$436$	49738.0			0.261647
$437$	−10115.7	−	10115.7i	−0.0529704	−	0.0529704i
$438$	197970.	−	197970.i	1.03193	−	1.03193i
$439$		−	171526.i		−	0.890023i	−0.895525	−	0.445012i	$-0.853200\pi$
$439$		−	171526.i		−	0.890023i	0.895525	−	0.445012i	$-0.146800\pi$
$440$	−58854.5	+	54772.7i	−0.304001	+	0.282917i
$441$	6081.16			0.0312687
$442$	130614.	+	130614.i	0.668568	+	0.668568i
$443$	224865.	−	224865.i	1.14581	−	1.14581i	0.158446	−	0.987368i	$-0.449352\pi$
$443$	224865.	−	224865.i	1.14581	−	1.14581i	0.987368	−	0.158446i	$-0.0506485\pi$
$444$		−	53069.8i		−	0.269204i
$445$	2084.60	−	58029.3i	0.0105269	−	0.293040i
$446$	111806.			0.562078
$447$	−38553.3	−	38553.3i	−0.192951	−	0.192951i
$448$	−6705.05	+	6705.05i	−0.0334077	+	0.0334077i
$449$		−	308137.i		−	1.52845i	−0.644951	−	0.764224i	$-0.723122\pi$
$449$		−	308137.i		−	1.52845i	0.644951	−	0.764224i	$-0.276878\pi$
$450$	−23694.7	+	20514.4i	−0.117011	+	0.101305i
$451$	−10387.4			−0.0510684
$452$	102606.	+	102606.i	0.502221	+	0.502221i
$453$	−95287.1	+	95287.1i	−0.464342	+	0.464342i
$454$		−	82708.4i		−	0.401271i
$455$	109538.	+	3934.96i	0.529106	+	0.0190072i
$456$	29362.6			0.141210
$457$	−120633.	−	120633.i	−0.577608	−	0.577608i	0.356635	−	0.934244i	$-0.383924\pi$
$457$	−120633.	−	120633.i	−0.577608	−	0.577608i	−0.934244	+	0.356635i	$0.883924\pi$
$458$	−110193.	+	110193.i	−0.525321	+	0.525321i
$459$			173431.i			0.823195i
$460$	−14925.2	−	16037.5i	−0.0705352	−	0.0757917i
$461$	−191542.			−0.901287			−0.450644	−	0.892704i	$-0.648805\pi$
$461$	−191542.			−0.901287			−0.450644	+	0.892704i	$0.648805\pi$
$462$	−52308.5	−	52308.5i	−0.245069	−	0.245069i
$463$	−128651.	+	128651.i	−0.600140	+	0.600140i	−0.940350	−	0.340210i	$-0.889502\pi$
$463$	−128651.	+	128651.i	−0.600140	+	0.600140i	0.340210	+	0.940350i	$0.389502\pi$
$464$		−	22766.0i		−	0.105743i
$465$	216506.	−	201490.i	1.00130	−	0.931853i
$466$	36515.0			0.168151
$467$	130887.	+	130887.i	0.600153	+	0.600153i	0.940353	−	0.340200i	$-0.110495\pi$
$467$	130887.	+	130887.i	0.600153	+	0.600153i	−0.340200	+	0.940353i	$0.610495\pi$
$468$	23742.5	−	23742.5i	0.108401	−	0.108401i
$469$			93292.4i			0.424132i
$470$	8757.32	−	243779.i	0.0396438	−	1.10357i
$471$	−336905.			−1.51868
$472$	−88445.1	−	88445.1i	−0.397000	−	0.397000i
$473$	212595.	−	212595.i	0.950234	−	0.950234i
$474$		−	183103.i		−	0.814967i
$475$	5856.81	−	81413.3i	0.0259582	−	0.360835i
$476$	−40873.3			−0.180395
$477$	47573.6	+	47573.6i	0.209088	+	0.209088i
$478$	79354.6	−	79354.6i	0.347309	−	0.347309i
$479$			94396.7i			0.411420i	0.978613	+	0.205710i	$0.0659504\pi$
$479$			94396.7i			0.411420i	−0.978613	+	0.205710i	$0.934050\pi$
$480$	44937.4	+	1614.30i	0.195041	+	0.00700650i
$481$	158049.			0.683129
$482$	193830.	+	193830.i	0.834308	+	0.834308i
$483$	14253.8	−	14253.8i	0.0610993	−	0.0610993i
$484$			44469.5i			0.189833i
$485$	−244920.	−	263172.i	−1.04122	−	1.11881i
$486$	71885.1			0.304345
$487$	−177602.	−	177602.i	−0.748843	−	0.748843i	0.225419	−	0.974262i	$-0.427625\pi$
$487$	−177602.	−	177602.i	−0.748843	−	0.748843i	−0.974262	+	0.225419i	$0.927625\pi$
$488$	6618.88	−	6618.88i	0.0277936	−	0.0277936i
$489$			284511.i			1.18982i
$490$	−17754.6	+	16523.3i	−0.0739468	+	0.0688182i
$491$	−66239.8			−0.274762			−0.137381	−	0.990518i	$-0.543868\pi$
$491$	−66239.8			−0.274762			−0.137381	+	0.990518i	$0.543868\pi$
$492$	4108.01	+	4108.01i	0.0169707	+	0.0169707i
$493$	69389.7	−	69389.7i	0.285497	−	0.285497i
$494$			87445.9i			0.358332i
$495$	−2261.52	+	62954.2i	−0.00922974	+	0.256930i
$496$	−76199.7			−0.309735
$497$	−110716.	−	110716.i	−0.448226	−	0.448226i
$498$	−3589.99	+	3589.99i	−0.0144755	+	0.0144755i
$499$			161462.i			0.648440i	0.945982	+	0.324220i	$0.105102\pi$
$499$			161462.i			0.648440i	−0.945982	+	0.324220i	$0.894898\pi$
$500$	13439.4	−	124275.i	0.0537576	−	0.497102i
$501$	−268232.			−1.06865
$502$	−59616.7	−	59616.7i	−0.236570	−	0.236570i
$503$	132042.	−	132042.i	0.521885	−	0.521885i	−0.396255	−	0.918140i	$-0.629690\pi$
$503$	132042.	−	132042.i	0.521885	−	0.521885i	0.918140	+	0.396255i	$0.129690\pi$
$504$			7429.76i			0.0292492i
$505$	382750.	+	13749.6i	1.50083	+	0.0539148i
$506$	−44034.4			−0.171985
$507$	193084.	+	193084.i	0.751156	+	0.751156i
$508$	−92001.9	+	92001.9i	−0.356508	+	0.356508i
$509$			379583.i			1.46511i	0.680706	+	0.732557i	$0.261673\pi$
$509$			379583.i			1.46511i	−0.680706	+	0.732557i	$0.738327\pi$
$510$	132047.	+	141887.i	0.507676	+	0.545510i
$511$	−184499.			−0.706565
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−58055.9	+	58055.9i	−0.220603	+	0.220603i
$514$		−	277350.i		−	1.04979i
$515$	109219.	−	101644.i	0.411796	−	0.383236i
$516$	−168155.			−0.631552
$517$	−346696.	−	346696.i	−1.29708	−	1.29708i
$518$	−24729.3	+	24729.3i	−0.0921621	+	0.0921621i
$519$		−	476707.i		−	1.76977i
$520$	−4807.60	+	133830.i	−0.0177796	+	0.494933i
$521$	246212.			0.907055			0.453528	−	0.891242i	$-0.350165\pi$
$521$	246212.			0.907055			0.453528	+	0.891242i	$0.350165\pi$
$522$	−12613.3	−	12613.3i	−0.0462902	−	0.0462902i
$523$	−85270.1	+	85270.1i	−0.311741	+	0.311741i	−0.845584	−	0.533843i	$-0.820747\pi$
$523$	−85270.1	+	85270.1i	−0.311741	+	0.311741i	0.533843	+	0.845584i	$0.320747\pi$
$524$		−	111399.i		−	0.405711i
$525$	114717.	+	8252.69i	0.416208	+	0.0299417i
$526$	156801.			0.566731
$527$	−232253.	−	232253.i	−0.836257	−	0.836257i
$528$	63908.8	−	63908.8i	0.229241	−	0.229241i
$529$			267842.i			0.957122i
$530$	−268160.	−	9633.16i	−0.954644	−	0.0342939i
$531$	−98004.6			−0.347582
$532$	−13682.3	−	13682.3i	−0.0483432	−	0.0483432i
$533$	−12234.2	+	12234.2i	−0.0430647	+	0.0430647i
$534$			65276.3i			0.228914i
$535$	230744.	+	247939.i	0.806162	+	0.866240i
$536$	−113981.			−0.396739
$537$	446466.	+	446466.i	1.54824	+	1.54824i
$538$	−70959.5	+	70959.5i	−0.245158	+	0.245158i
$539$			48749.1i			0.167799i
$540$	−92042.4	+	85658.8i	−0.315646	+	0.293755i
$541$	−263049.			−0.898757			−0.449378	−	0.893342i	$-0.648354\pi$
$541$	−263049.			−0.898757			−0.449378	+	0.893342i	$0.648354\pi$
$542$	−142347.	−	142347.i	−0.484562	−	0.484562i
$543$	64441.0	−	64441.0i	0.218556	−	0.218556i
$544$		−	49937.6i		−	0.168744i
$545$	−5579.99	+	155331.i	−0.0187863	+	0.522956i
$546$	−123218.			−0.413321
$547$	247352.	+	247352.i	0.826685	+	0.826685i	0.987057	−	0.160371i	$-0.0512692\pi$
$547$	247352.	+	247352.i	0.826685	+	0.826685i	−0.160371	+	0.987057i	$0.551269\pi$
$548$	14554.6	−	14554.6i	0.0484664	−	0.0484664i
$549$		−	7334.27i		−	0.0243339i
$550$	−164451.	−	189947.i	−0.543641	−	0.627923i
$551$	46456.2			0.153017
$552$	17414.8	+	17414.8i	0.0571531	+	0.0571531i
$553$	−85321.9	+	85321.9i	−0.279004	+	0.279004i
$554$			349066.i			1.13734i
$555$	165736.	+	5953.78i	0.538061	+	0.0193289i
$556$	−102383.			−0.331192
$557$	142879.	+	142879.i	0.460531	+	0.460531i	0.898830	−	0.438298i	$-0.144419\pi$
$557$	142879.	+	142879.i	0.460531	+	0.460531i	−0.438298	+	0.898830i	$0.644419\pi$
$558$	−42217.8	+	42217.8i	−0.135590	+	0.135590i
$559$		−	500788.i		−	1.60262i
$560$	−20187.6	−	21692.0i	−0.0643736	−	0.0691709i
$561$	389581.			1.23786
$562$	100208.	+	100208.i	0.317272	+	0.317272i
$563$	117054.	−	117054.i	0.369293	−	0.369293i	−0.497927	−	0.867219i	$-0.665905\pi$
$563$	117054.	−	117054.i	0.369293	−	0.369293i	0.867219	+	0.497927i	$0.165905\pi$
$564$			274223.i			0.862077i
$565$	−331947.	+	308925.i	−1.03985	+	0.967735i
$566$	−127017.			−0.396487
$567$	−100612.	−	100612.i	−0.312955	−	0.312955i
$568$	135269.	−	135269.i	0.419277	−	0.419277i
$569$		−	326279.i		−	1.00778i	−0.863769	−	0.503888i	$-0.831902\pi$
$569$		−	326279.i		−	1.00778i	0.863769	−	0.503888i	$-0.168098\pi$
$570$	−3294.12	+	91698.9i	−0.0101389	+	0.282237i
$571$	−271493.			−0.832697			−0.416348	−	0.909205i	$-0.636690\pi$
$571$	−271493.			−0.832697			−0.416348	+	0.909205i	$0.636690\pi$
$572$	190329.	+	190329.i	0.581719	+	0.581719i
$573$	−291270.	+	291270.i	−0.887130	+	0.887130i
$574$		−	3828.47i		−	0.0116199i
$575$	51759.4	−	44812.1i	0.156550	−	0.135538i
$576$	−9077.42			−0.0273601
$577$	213637.	+	213637.i	0.641690	+	0.641690i	0.950971	−	0.309281i	$-0.100088\pi$
$577$	213637.	+	213637.i	0.641690	+	0.641690i	−0.309281	+	0.950971i	$0.600088\pi$
$578$	−14835.0	+	14835.0i	−0.0444049	+	0.0444049i
$579$		−	605226.i		−	1.80535i
$580$	71098.0	+	2554.07i	0.211350	+	0.00759236i
$581$	3345.70			0.00991141
$582$	285773.	+	285773.i	0.843675	+	0.843675i
$583$	−381369.	+	381369.i	−1.12204	+	1.12204i
$584$		−	225415.i		−	0.660931i
$585$	71483.7	+	76811.0i	0.208879	+	0.224446i
$586$	−108192.			−0.315066
$587$	−18219.6	−	18219.6i	−0.0528766	−	0.0528766i	0.680174	−	0.733051i	$-0.261904\pi$
$587$	−18219.6	−	18219.6i	−0.0528766	−	0.0528766i	−0.733051	+	0.680174i	$0.761904\pi$
$588$	19279.3	−	19279.3i	0.0557619	−	0.0557619i
$589$		−	155493.i		−	0.448207i
$590$	286135.	−	266290.i	0.821992	−	0.764983i
$591$	−188525.			−0.539752
$592$	−30213.4	−	30213.4i	−0.0862097	−	0.0862097i
$593$	−394452.	+	394452.i	−1.12172	+	1.12172i	−0.130237	+	0.991483i	$0.541574\pi$
$593$	−394452.	+	394452.i	−1.12172	+	1.12172i	−0.991483	+	0.130237i	$0.958426\pi$
$594$			252722.i			0.716259i
$595$	4585.48	−	127647.i	0.0129524	−	0.360558i
$596$	−43897.9			−0.123581
$597$	284086.	+	284086.i	0.797079	+	0.797079i
$598$	−51863.6	+	51863.6i	−0.145031	+	0.145031i
$599$			277665.i			0.773868i	0.922107	+	0.386934i	$0.126466\pi$
$599$			277665.i			0.773868i	−0.922107	+	0.386934i	$0.873534\pi$
$600$	−10082.9	+	140158.i	−0.0280079	+	0.389327i
$601$	544885.			1.50854			0.754269	−	0.656566i	$-0.227992\pi$
$601$	544885.			1.50854			0.754269	+	0.656566i	$0.227992\pi$
$602$	78356.1	+	78356.1i	0.216212	+	0.216212i
$603$	−63150.5	+	63150.5i	−0.173677	+	0.173677i
$604$			108497.i			0.297401i
$605$	−138877.	−	4988.93i	−0.379421	−	0.0136300i
$606$	−430550.			−1.17241
$607$	306025.	+	306025.i	0.830577	+	0.830577i	0.987596	−	0.157019i	$-0.0501884\pi$
$607$	306025.	+	306025.i	0.830577	+	0.830577i	−0.157019	+	0.987596i	$0.550188\pi$
$608$	16716.5	−	16716.5i	0.0452209	−	0.0452209i
$609$			65460.3i			0.176499i
$610$	19928.1	+	21413.2i	0.0535558	+	0.0575469i
$611$	−816675.			−2.18759
$612$	−27667.5	−	27667.5i	−0.0738698	−	0.0738698i
$613$	17628.3	−	17628.3i	0.0469125	−	0.0469125i	−0.683261	−	0.730174i	$-0.739439\pi$
$613$	17628.3	−	17628.3i	0.0469125	−	0.0469125i	0.730174	+	0.683261i	$0.239439\pi$
$614$		−	94019.9i		−	0.249392i
$615$	−13290.1	+	12368.4i	−0.0351381	+	0.0327011i
$616$	−59559.9			−0.156961
$617$	−327135.	−	327135.i	−0.859324	−	0.859324i	0.131934	−	0.991258i	$-0.457881\pi$
$617$	−327135.	−	327135.i	−0.859324	−	0.859324i	−0.991258	+	0.131934i	$0.957881\pi$
$618$	−118598.	+	118598.i	−0.310528	+	0.310528i
$619$		−	107360.i		−	0.280195i	−0.990138	−	0.140098i	$-0.955258\pi$
$619$		−	107360.i		−	0.280195i	0.990138	−	0.140098i	$-0.0447416\pi$
$620$	8548.67	−	237971.i	0.0222390	−	0.619070i
$621$	−68865.3			−0.178574
$622$	727.220	+	727.220i	0.00187969	+	0.00187969i
$623$	30417.2	−	30417.2i	0.0783688	−	0.0783688i
$624$		−	150543.i		−	0.386627i
$625$	386603.	+	55913.2i	0.989703	+	0.143138i
$626$	−294650.			−0.751895
$627$	130412.	+	130412.i	0.331727	+	0.331727i
$628$	−191805.	+	191805.i	−0.486340	+	0.486340i
$629$		−	184178.i		−	0.465517i
$630$	−23203.0	−	833.527i	−0.0584606	−	0.00210009i
$631$	219042.			0.550135			0.275067	−	0.961425i	$-0.411300\pi$
$631$	219042.			0.550135			0.275067	+	0.961425i	$0.411300\pi$
$632$	−104243.	−	104243.i	−0.260984	−	0.260984i
$633$	392011.	−	392011.i	0.978342	−	0.978342i
$634$			307982.i			0.766208i
$635$	−276999.	−	297642.i	−0.686959	−	0.738154i
$636$	301649.			0.745740
$637$	57416.6	+	57416.6i	0.141501	+	0.141501i
$638$	101114.	−	101114.i	0.248410	−	0.248410i
$639$		−	149889.i		−	0.367087i
$640$	26502.5	−	24664.5i	0.0647035	−	0.0602160i
$641$	458498.			1.11589			0.557946	−	0.829878i	$-0.311590\pi$
$641$	458498.			1.11589			0.557946	+	0.829878i	$0.311590\pi$
$642$	−269232.	−	269232.i	−0.653215	−	0.653215i
$643$	−160509.	+	160509.i	−0.388220	+	0.388220i	−0.874052	−	0.485832i	$-0.838517\pi$
$643$	−160509.	+	160509.i	−0.388220	+	0.388220i	0.485832	+	0.874052i	$0.338517\pi$
$644$		−	16229.8i		−	0.0391327i
$645$	18864.9	−	525144.i	0.0453455	−	1.26229i
$646$	101902.			0.244185
$647$	174907.	+	174907.i	0.417830	+	0.417830i	0.884455	−	0.466625i	$-0.154530\pi$
$647$	174907.	+	174907.i	0.417830	+	0.417830i	−0.466625	+	0.884455i	$0.654530\pi$
$648$	122924.	−	122924.i	0.292743	−	0.292743i
$649$		−	785645.i		−	1.86525i
$650$	−417409.	−	30028.1i	−0.987951	−	0.0710725i
$651$	219101.			0.516989
$652$	161976.	+	161976.i	0.381027	+	0.381027i
$653$	85900.9	−	85900.9i	0.201452	−	0.201452i	−0.599170	−	0.800622i	$-0.704503\pi$
$653$	85900.9	−	85900.9i	0.201452	−	0.201452i	0.800622	+	0.599170i	$0.204503\pi$
$654$		−	174730.i		−	0.408518i
$655$	347896.	+	12497.6i	0.810900	+	0.0291301i
$656$	4677.49			0.0108694
$657$	−124889.	−	124889.i	−0.289330	−	0.289330i
$658$	127782.	−	127782.i	0.295132	−	0.295132i
$659$		−	503714.i		−	1.15988i	−0.814659	−	0.579940i	$-0.803076\pi$
$659$		−	503714.i		−	1.15988i	0.814659	−	0.579940i	$-0.196924\pi$
$660$	192416.	+	206756.i	0.441727	+	0.474646i
$661$	318462.			0.728878			0.364439	−	0.931227i	$-0.381261\pi$
$661$	318462.			0.728878			0.364439	+	0.931227i	$0.381261\pi$
$662$	−96046.1	−	96046.1i	−0.219161	−	0.219161i
$663$	458848.	−	458848.i	1.04386	−	1.04386i
$664$			4087.67i			0.00927127i
$665$	44264.5	−	41194.6i	0.100095	−	0.0931529i
$666$	−33479.0			−0.0754786
$667$	27552.9	+	27552.9i	0.0619321	+	0.0619321i
$668$	−152708.	+	152708.i	−0.342223	+	0.342223i
$669$		−	392776.i		−	0.877592i
$670$	12787.3	−	355962.i	0.0284859	−	0.792966i
$671$	58794.5			0.130585
$672$	23554.8	+	23554.8i	0.0521605	+	0.0521605i
$673$	−34431.0	+	34431.0i	−0.0760186	+	0.0760186i	−0.744094	−	0.668075i	$-0.767118\pi$
$673$	−34431.0	+	34431.0i	−0.0760186	+	0.0760186i	0.668075	+	0.744094i	$0.267118\pi$
$674$			196251.i			0.432008i
$675$	−257185.	−	297057.i	−0.564467	−	0.651977i
$676$	219851.			0.481099
$677$	451840.	+	451840.i	0.985842	+	0.985842i	0.999901	−	0.0140595i	$-0.00447544\pi$
$677$	451840.	+	451840.i	0.985842	+	0.985842i	−0.0140595	+	0.999901i	$0.504475\pi$
$678$	360454.	−	360454.i	0.784134	−	0.784134i
$679$		−	266327.i		−	0.577664i
$680$	155954.	+	5602.38i	0.337271	+	0.0121159i
$681$	−290555.			−0.626518
$682$	−338435.	−	338435.i	−0.727624	−	0.727624i
$683$	−146604.	+	146604.i	−0.314272	+	0.314272i	−0.846562	−	0.532290i	$-0.821331\pi$
$683$	−146604.	+	146604.i	−0.314272	+	0.314272i	0.532290	+	0.846562i	$0.321331\pi$
$684$		−	18523.3i		−	0.0395919i
$685$	43821.1	+	47086.8i	0.0933904	+	0.100350i
$686$	−17967.4			−0.0381802
$687$	387109.	+	387109.i	0.820201	+	0.820201i
$688$	−95732.8	+	95732.8i	−0.202248	+	0.202248i
$689$			898352.i			1.89238i
$690$	−56339.8	+	52432.4i	−0.118336	+	0.110129i
$691$	72668.7			0.152192			0.0760959	−	0.997101i	$-0.475754\pi$
$691$	72668.7			0.152192			0.0760959	+	0.997101i	$0.475754\pi$
$692$	−271396.	−	271396.i	−0.566750	−	0.566750i
$693$	−32998.7	+	32998.7i	−0.0687117	+	0.0687117i
$694$		−	488274.i		−	1.01378i
$695$	11486.2	−	319742.i	0.0237796	−	0.661957i
$696$	−79977.1			−0.165100
$697$	14256.7	+	14256.7i	0.0293464	+	0.0293464i
$698$	−35498.6	+	35498.6i	−0.0728620	+	0.0728620i
$699$		−	128277.i		−	0.262540i
$700$	70008.6	−	60611.9i	0.142875	−	0.123698i
$701$	−56710.7			−0.115406			−0.0577031	−	0.998334i	$-0.518378\pi$
$701$	−56710.7			−0.115406			−0.0577031	+	0.998334i	$0.518378\pi$
$702$	297655.	+	297655.i	0.604003	+	0.604003i
$703$	61653.2	−	61653.2i	0.124751	−	0.124751i
$704$		−	72768.3i		−	0.146824i
$705$	−856395.	−	30764.5i	−1.72304	−	0.0618972i
$706$	−442824.			−0.888427
$707$	200626.	+	200626.i	0.401374	+	0.401374i
$708$	−310708.	+	310708.i	−0.619849	+	0.619849i
$709$			791805.i			1.57516i	0.616209	+	0.787582i	$0.288668\pi$
$709$			791805.i			1.57516i	−0.616209	+	0.787582i	$0.711332\pi$
$710$	407267.	+	437618.i	0.807909	+	0.868118i
$711$	−115510.			−0.228498
$712$	37162.7	+	37162.7i	0.0733073	+	0.0733073i
$713$	92221.8	−	92221.8i	0.181407	−	0.181407i
$714$			143588.i			0.281657i
$715$	−615748.	+	573043.i	−1.20446	+	1.12092i
$716$	508358.			0.991617
$717$	−278773.	−	278773.i	−0.542265	−	0.542265i
$718$	139172.	−	139172.i	0.269963	−	0.269963i
$719$			20588.7i			0.0398265i	0.999802	+	0.0199132i	$0.00633900\pi$
$719$			20588.7i			0.0398265i	−0.999802	+	0.0199132i	$0.993661\pi$
$720$	1018.38	−	28348.7i	0.00196446	−	0.0546849i
$721$	110528.			0.212618
$722$	−226530.	−	226530.i	−0.434562	−	0.434562i
$723$	680924.	−	680924.i	1.30263	−	1.30263i
$724$		−	73374.3i		−	0.139980i
$725$	−15952.6	+	221752.i	−0.0303499	+	0.421882i
$726$	156221.			0.296392
$727$	69062.9	+	69062.9i	0.130670	+	0.130670i	0.769417	−	0.638747i	$-0.220547\pi$
$727$	69062.9	+	69062.9i	0.130670	+	0.130670i	−0.638747	+	0.769417i	$0.720547\pi$
$728$	−70149.6	+	70149.6i	−0.132362	+	0.132362i
$729$			369770.i			0.695788i
$730$	703967.	+	25288.8i	1.32101	+	0.0474550i
$731$	−583577.			−1.09210
$732$	−23252.1	−	23252.1i	−0.0433951	−	0.0433951i
$733$	−738060.	+	738060.i	−1.37367	+	1.37367i	−0.518746	+	0.854929i	$0.673601\pi$
$733$	−738060.	+	738060.i	−1.37367	+	1.37367i	−0.854929	+	0.518746i	$0.826399\pi$
$734$			485830.i			0.901762i
$735$	58046.2	+	62372.0i	0.107448	+	0.115456i
$736$	19829.0			0.0366053
$737$	−506240.	−	506240.i	−0.932012	−	0.932012i
$738$	2591.53	−	2591.53i	0.00475820	−	0.00475820i
$739$			201783.i			0.369484i	0.982787	+	0.184742i	$0.0591449\pi$
$739$			201783.i			0.369484i	−0.982787	+	0.184742i	$0.940855\pi$
$740$	97745.6	−	90966.4i	0.178498	−	0.166118i
$741$	307197.			0.559475
$742$	−140561.	−	140561.i	−0.255304	−	0.255304i
$743$	−729388.	+	729388.i	−1.32124	+	1.32124i	−0.408462	+	0.912775i	$0.633935\pi$
$743$	−729388.	+	729388.i	−1.32124	+	1.32124i	−0.912775	+	0.408462i	$0.866065\pi$
$744$			267690.i			0.483599i
$745$	4924.81	−	137093.i	0.00887313	−	0.247003i
$746$	343524.			0.617276
$747$	2264.74	+	2264.74i	0.00405861	+	0.00405861i
$748$	221794.	−	221794.i	0.396412	−	0.396412i
$749$			250911.i			0.447256i
$750$	−436580.	−	47212.6i	−0.776141	−	0.0839335i
$751$	276877.			0.490916			0.245458	−	0.969407i	$-0.421062\pi$
$751$	276877.			0.490916			0.245458	+	0.969407i	$0.421062\pi$
$752$	156119.	+	156119.i	0.276071	+	0.276071i
$753$	−209433.	+	209433.i	−0.369365	+	0.369365i
$754$		−	238183.i		−	0.418956i
$755$	−338833.	−	12172.0i	−0.594418	−	0.0213534i
$756$	−93145.6			−0.162974
$757$	−260172.	−	260172.i	−0.454014	−	0.454014i	0.442670	−	0.896684i	$-0.354031\pi$
$757$	−260172.	−	260172.i	−0.454014	−	0.454014i	−0.896684	+	0.442670i	$0.854031\pi$
$758$	2128.56	−	2128.56i	0.00370464	−	0.00370464i
$759$			154693.i			0.268526i
$760$	50330.1	+	54080.9i	0.0871366	+	0.0936303i
$761$	−124482.			−0.214949			−0.107475	−	0.994208i	$-0.534276\pi$
$761$	−124482.			−0.214949			−0.107475	+	0.994208i	$0.534276\pi$
$762$	323203.	+	323203.i	0.556628	+	0.556628i
$763$	−81419.9	+	81419.9i	−0.139856	+	0.139856i
$764$			331649.i			0.568187i
$765$	89509.2	−	83301.2i	0.152948	−	0.142341i
$766$	110182.			0.187781
$767$	−925331.	−	925331.i	−1.57292	−	1.57292i
$768$	−28778.5	+	28778.5i	−0.0487917	+	0.0487917i
$769$			1.05263e6i			1.78001i	0.455951	+	0.890005i	$0.349299\pi$
$769$			1.05263e6i			1.78001i	−0.455951	+	0.890005i	$0.650701\pi$
$770$	6681.89	−	186005.i	0.0112698	−	0.313720i
$771$	−974330.			−1.63907
$772$	−344564.	−	344564.i	−0.578142	−	0.578142i
$773$	91728.2	−	91728.2i	0.153513	−	0.153513i	−0.626172	−	0.779685i	$-0.715379\pi$
$773$	91728.2	−	91728.2i	0.153513	−	0.153513i	0.779685	+	0.626172i	$0.215379\pi$
$774$			106080.i			0.177073i
$775$	742220.	+	53394.8i	1.23575	+	0.0888987i
$776$	325389.			0.540355
$777$	86874.0	+	86874.0i	0.143896	+	0.143896i
$778$	434267.	−	434267.i	0.717459	−	0.717459i
$779$			9544.85i			0.0157288i
$780$	470144.	+	16889.1i	0.772755	+	0.0277599i
$781$	1.20157e6			1.96992
$782$	60437.6	+	60437.6i	0.0988312	+	0.0988312i
$783$	158131.	−	158131.i	0.257926	−	0.257926i
$784$		−	21952.0i		−	0.0357143i
$785$	−577485.	−	620522.i	−0.937134	−	1.00697i
$786$	−391343.			−0.633451
$787$	9032.35	+	9032.35i	0.0145832	+	0.0145832i	0.714361	−	0.699778i	$-0.246718\pi$
$787$	9032.35	+	9032.35i	0.0145832	+	0.0145832i	−0.699778	+	0.714361i	$0.746718\pi$
$788$	−107330.	+	107330.i	−0.172850	+	0.172850i
$789$		−	550841.i		−	0.884855i
$790$	337245.	−	313856.i	0.540371	−	0.502893i
$791$	−335926.			−0.536897
$792$	−40316.7	−	40316.7i	−0.0642739	−	0.0642739i
$793$	69248.0	−	69248.0i	0.110119	−	0.110119i
$794$			720790.i			1.14332i
$795$	−33841.3	+	942045.i	−0.0535442	+	1.49052i
$796$	323468.			0.510512
$797$	−214356.	−	214356.i	−0.337457	−	0.337457i	0.517952	−	0.855409i	$-0.326694\pi$
$797$	−214356.	−	214356.i	−0.337457	−	0.337457i	−0.855409	+	0.517952i	$0.826694\pi$
$798$	−48065.8	+	48065.8i	−0.0754798	+	0.0754798i
$799$			951686.i			1.49073i
$800$	74053.5	+	85534.1i	0.115709	+	0.133647i
$801$	41179.4			0.0641822
$802$	−285765.	−	285765.i	−0.444284	−	0.444284i
$803$	1.00116e6	−	1.00116e6i	1.55265	−	1.55265i
$804$			400417.i			0.619441i
$805$	50685.3	+	1820.78i	0.0782150	+	0.00280974i
$806$	−797217.			−1.22717
$807$	249281.	+	249281.i	0.382773	+	0.382773i
$808$	−245118.	+	245118.i	−0.375451	+	0.375451i
$809$		−	436107.i		−	0.666340i	−0.942867	−	0.333170i	$-0.891882\pi$
$809$		−	436107.i		−	0.666340i	0.942867	−	0.333170i	$-0.108118\pi$
$810$	370099.	+	397680.i	0.564090	+	0.606128i
$811$	719061.			1.09326			0.546630	−	0.837374i	$-0.315910\pi$
$811$	719061.			1.09326			0.546630	+	0.837374i	$0.315910\pi$
$812$	37267.4	+	37267.4i	0.0565220	+	0.0565220i
$813$	−500065.	+	500065.i	−0.756563	+	0.756563i
$814$		−	268381.i		−	0.405045i
$815$	−524021.	+	487678.i	−0.788921	+	0.734206i
$816$	−175431.			−0.263466
$817$	−195352.	−	195352.i	−0.292666	−	0.292666i
$818$	197318.	−	197318.i	0.294891	−	0.294891i
$819$			77731.6i			0.115886i
$820$	−524.757	+	14607.7i	−0.000780424	+	0.0217248i
$821$	−463149.			−0.687123			−0.343561	−	0.939130i	$-0.611633\pi$
$821$	−463149.			−0.687123			−0.343561	+	0.939130i	$0.611633\pi$
$822$	−51130.5	−	51130.5i	−0.0756722	−	0.0756722i
$823$	−635523.	+	635523.i	−0.938279	+	0.938279i	−0.998203	−	0.0599241i	$-0.980914\pi$
$823$	−635523.	+	635523.i	−0.938279	+	0.938279i	0.0599241	+	0.998203i	$0.480914\pi$
$824$			135039.i			0.198886i
$825$	−667282.	+	577718.i	−0.980397	+	0.848805i
$826$	289565.			0.424410
$827$	233699.	+	233699.i	0.341701	+	0.341701i	0.857006	−	0.515306i	$-0.172322\pi$
$827$	233699.	+	233699.i	0.341701	+	0.341701i	−0.515306	+	0.857006i	$0.672322\pi$
$828$	10986.1	−	10986.1i	0.0160244	−	0.0160244i
$829$			1791.15i			0.00260629i	0.999999	+	0.00130315i	$0.000414804\pi$
$829$			1791.15i			0.00260629i	−0.999999	+	0.00130315i	$0.999585\pi$
$830$	−12765.7	−	458.586i	−0.0185306	−	0.000665679i
$831$	1.22627e6			1.77576
$832$	−85706.4	−	85706.4i	−0.123813	−	0.123813i
$833$	66908.5	−	66908.5i	0.0964254	−	0.0964254i
$834$			359673.i			0.517101i
$835$	−459774.	−	494038.i	−0.659434	−	0.708577i
$836$	148490.			0.212464
$837$	−529278.	−	529278.i	−0.755498	−	0.755498i
$838$	−330413.	+	330413.i	−0.470511	+	0.470511i
$839$		−	1.19961e6i		−	1.70418i	−0.523395	−	0.852090i	$-0.675335\pi$
$839$		−	1.19961e6i		−	1.70418i	0.523395	−	0.852090i	$-0.324665\pi$
$840$	−76204.0	+	70918.9i	−0.107999	+	0.100509i
$841$	580745.			0.821095
$842$	−577394.	−	577394.i	−0.814419	−	0.814419i
$843$	352032.	−	352032.i	0.495367	−	0.495367i
$844$		−	446355.i		−	0.626607i
$845$	−24664.5	+	686590.i	−0.0345430	+	0.961577i
$846$	172993.			0.241706
$847$	−72795.4	−	72795.4i	−0.101470	−	0.101470i
$848$	171733.	−	171733.i	0.238815	−	0.238815i
$849$			446210.i			0.619048i
$850$	−34992.3	+	486414.i	−0.0484323	+	0.673238i
$851$	73132.4			0.100984
$852$	−475199.	−	475199.i	−0.654631	−	0.654631i
$853$	353036.	−	353036.i	0.485200	−	0.485200i	−0.421588	−	0.906788i	$-0.638527\pi$
$853$	353036.	−	353036.i	0.485200	−	0.485200i	0.906788	+	0.421588i	$0.138527\pi$
$854$			21669.9i			0.0297126i
$855$	57848.0	+	2078.09i	0.0791328	+	0.00284270i
$856$	−306555.			−0.418370
$857$	−254785.	−	254785.i	−0.346906	−	0.346906i	0.512050	−	0.858956i	$-0.328886\pi$
$857$	−254785.	−	254785.i	−0.346906	−	0.346906i	−0.858956	+	0.512050i	$0.828886\pi$
$858$	668626.	−	668626.i	0.908257	−	0.908257i
$859$		−	608927.i		−	0.825238i	−0.910904	−	0.412619i	$-0.864614\pi$
$859$		−	608927.i		−	0.825238i	0.910904	−	0.412619i	$-0.135386\pi$
$860$	−288232.	−	309712.i	−0.389713	−	0.418756i
$861$	−13449.4			−0.0181425
$862$	207584.	+	207584.i	0.279369	+	0.279369i
$863$	543741.	−	543741.i	0.730080	−	0.730080i	−0.240555	−	0.970635i	$-0.577329\pi$
$863$	543741.	−	543741.i	0.730080	−	0.730080i	0.970635	+	0.240555i	$0.0773295\pi$
$864$		−	113802.i		−	0.152448i
$865$	878013.	−	817119.i	1.17346	−	1.09208i
$866$	902698.			1.20367
$867$	52115.2	+	52115.2i	0.0693308	+	0.0693308i
$868$	124737.	−	124737.i	0.165560	−	0.165560i
$869$		−	925978.i		−	1.22620i
$870$	8972.45	−	249767.i	0.0118542	−	0.329987i
$871$	−1.19250e6			−1.57189
$872$	−99476.0	−	99476.0i	−0.130823	−	0.130823i
$873$	180279.	−	180279.i	0.236547	−	0.236547i
$874$			40462.8i			0.0529704i
$875$	181436.	+	225436.i	0.236977	+	0.294447i
$876$	−791882.			−1.03193
$877$	869679.	+	869679.i	1.13073	+	1.13073i	0.990056	+	0.140676i	$0.0449277\pi$
$877$	869679.	+	869679.i	1.13073	+	1.13073i	0.140676	+	0.990056i	$0.455072\pi$
$878$	−343052.	+	343052.i	−0.445012	+	0.445012i
$879$			380080.i			0.491923i
$880$	227254.	+	8163.71i	0.293459	+	0.0105420i
$881$	−793137.			−1.02187			−0.510936	−	0.859619i	$-0.670701\pi$
$881$	−793137.			−1.02187			−0.510936	+	0.859619i	$0.670701\pi$
$882$	−12162.3	−	12162.3i	−0.0156343	−	0.0156343i
$883$	−589040.	+	589040.i	−0.755480	+	0.755480i	−0.975496	−	0.220016i	$-0.929389\pi$
$883$	−589040.	+	589040.i	−0.755480	+	0.755480i	0.220016	+	0.975496i	$0.429389\pi$
$884$		−	522457.i		−	0.668568i
$885$	−935478.	−	1.00519e6i	−1.19439	−	1.28340i
$886$	−899459.			−1.14581
$887$	691175.	+	691175.i	0.878497	+	0.878497i	0.993379	−	0.114882i	$-0.0366489\pi$
$887$	691175.	+	691175.i	0.878497	+	0.878497i	−0.114882	+	0.993379i	$0.536649\pi$
$888$	−106140.	+	106140.i	−0.134602	+	0.134602i
$889$		−	301210.i		−	0.381123i
$890$	−120228.	+	111889.i	−0.151784	+	0.141257i
$891$	1.09191e6			1.37541
$892$	−223613.	−	223613.i	−0.281039	−	0.281039i
$893$	−318575.	+	318575.i	−0.399493	+	0.399493i
$894$			154213.i			0.192951i
$895$	−57031.6	+	1.58760e6i	−0.0711982	+	1.98196i
$896$	26820.2			0.0334077
$897$	182197.	+	182197.i	0.226442	+	0.226442i
$898$	−616273.	+	616273.i	−0.764224	+	0.764224i
$899$			423527.i			0.524037i
$900$	88418.2	+	6360.74i	0.109158	+	0.00785277i
$901$	1.04687e6			1.28956
$902$	20774.7	+	20774.7i	0.0255342	+	0.0255342i
$903$	275265.	−	275265.i	0.337579	−	0.337579i
$904$		−	410423.i		−	0.502221i
$905$	229147.	+	8231.69i	0.279780	+	0.0100506i
$906$	381149.			0.464342
$907$	−869238.	−	869238.i	−1.05663	−	1.05663i	−0.998297	−	0.0583365i	$-0.981420\pi$
$907$	−869238.	−	869238.i	−1.05663	−	1.05663i	−0.0583365	−	0.998297i	$-0.518580\pi$
$908$	−165417.	+	165417.i	−0.200636	+	0.200636i
$909$			271611.i			0.328716i
$910$	−211206.	−	226946.i	−0.255049	−	0.274056i
$911$	881891.			1.06262			0.531310	−	0.847177i	$-0.321700\pi$
$911$	881891.			1.06262			0.531310	+	0.847177i	$0.321700\pi$
$912$	−58725.2	−	58725.2i	−0.0706049	−	0.0706049i
$913$	−18155.1	+	18155.1i	−0.0217799	+	0.0217799i
$914$			482532.i			0.577608i
$915$	75224.6	−	70007.4i	0.0898500	−	0.0836184i
$916$	440773.			0.525321
$917$	182357.	+	182357.i	0.216862	+	0.216862i
$918$	346863.	−	346863.i	0.411597	−	0.411597i
$919$		−	1.54970e6i		−	1.83492i	−0.397831	−	0.917459i	$-0.630237\pi$
$919$		−	1.54970e6i		−	1.83492i	0.397831	−	0.917459i	$-0.369763\pi$
$920$	−2224.57	+	61925.6i	−0.00262827	+	0.0731635i
$921$	−330292.			−0.389384
$922$	383085.	+	383085.i	0.450644	+	0.450644i
$923$	1.41521e6	−	1.41521e6i	1.66118	−	1.66118i
$924$			209234.i			0.245069i
$925$	273121.	+	315463.i	0.319206	+	0.368693i
$926$	514606.			0.600140
$927$	74817.3	+	74817.3i	0.0870647	+	0.0870647i
$928$	−45532.1	+	45532.1i	−0.0528715	+	0.0528715i
$929$			991662.i			1.14903i	0.818493	+	0.574516i	$0.194810\pi$
$929$			991662.i			1.14903i	−0.818493	+	0.574516i	$0.805190\pi$
$930$	−835991.	−	30031.5i	−0.966575	−	0.0347225i
$931$	44795.1			0.0516810
$932$	−73030.0	−	73030.0i	−0.0840755	−	0.0840755i
$933$	2554.72	−	2554.72i	0.00293482	−	0.00293482i
$934$		−	523547.i		−	0.600153i
$935$	667777.	+	717542.i	0.763850	+	0.820775i
$936$	−94969.8			−0.108401
$937$	447928.	+	447928.i	0.510187	+	0.510187i	0.914584	−	0.404397i	$-0.132519\pi$
$937$	447928.	+	447928.i	0.510187	+	0.510187i	−0.404397	+	0.914584i	$0.632519\pi$
$938$	186585.	−	186585.i	0.212066	−	0.212066i
$939$			1.03510e6i			1.17396i
$940$	−505072.	+	470043.i	−0.571608	+	0.531964i
$941$	117854.			0.133096			0.0665481	−	0.997783i	$-0.478801\pi$
$941$	117854.			0.133096			0.0665481	+	0.997783i	$0.478801\pi$
$942$	673810.	+	673810.i	0.759339	+	0.759339i
$943$	−5661.00	+	5661.00i	−0.00636604	+	0.00636604i
$944$			353781.i			0.397000i
$945$	10449.8	−	290892.i	0.0117016	−	0.325738i
$946$	−850380.			−0.950234
$947$	117399.	+	117399.i	0.130908	+	0.130908i	0.769525	−	0.638617i	$-0.220493\pi$
$947$	117399.	+	117399.i	0.130908	+	0.130908i	−0.638617	+	0.769525i	$0.720493\pi$
$948$	−366207.	+	366207.i	−0.407483	+	0.407483i
$949$		−	2.35833e6i		−	2.61862i
$950$	−174540.	+	151113.i	−0.193396	+	0.167438i
$951$	1.08194e6			1.19631
$952$	81746.5	+	81746.5i	0.0901977	+	0.0901977i
$953$	1.21362e6	−	1.21362e6i	1.33628	−	1.33628i	0.436653	−	0.899630i	$-0.356164\pi$
$953$	1.21362e6	−	1.21362e6i	1.33628	−	1.33628i	0.899630	−	0.436653i	$-0.143836\pi$
$954$		−	190294.i		−	0.209088i
$955$	−1.03573e6	−	37206.9i	−1.13564	−	0.0407959i
$956$	−317418.			−0.347309
$957$	−355212.	−	355212.i	−0.387850	−	0.387850i
$958$	188793.	−	188793.i	0.205710	−	0.205710i
$959$			47651.2i			0.0518127i
$960$	−86646.2	−	93103.4i	−0.0940172	−	0.101024i
$961$	494057.			0.534971
$962$	−316099.	−	316099.i	−0.341564	−	0.341564i
$963$	−169844.	+	169844.i	−0.183146	+	0.183146i
$964$		−	775319.i		−	0.834308i
$965$	1.11472e6	−	1.03741e6i	1.19705	−	1.11403i
$966$	−57015.1			−0.0610993
$967$	−972541.	−	972541.i	−1.04005	−	1.04005i	−0.999164	−	0.0408884i	$-0.986981\pi$
$967$	−972541.	−	972541.i	−1.04005	−	1.04005i	−0.0408884	−	0.999164i	$-0.513019\pi$
$968$	88938.9	−	88938.9i	0.0949164	−	0.0949164i
$969$		−	357982.i		−	0.381254i
$970$	−36504.6	+	1.01619e6i	−0.0387976	+	1.08001i
$971$	−1.26305e6			−1.33962			−0.669810	−	0.742533i	$-0.733624\pi$
$971$	−1.26305e6			−1.33962			−0.669810	+	0.742533i	$0.733624\pi$
$972$	−143770.	−	143770.i	−0.152172	−	0.152172i
$973$	167599.	−	167599.i	0.177030	−	0.177030i
$974$			710409.i			0.748843i
$975$	−105489.	+	1.46636e6i	−0.110968	+	1.54252i
$976$	−26475.5			−0.0277936
$977$	610115.	+	610115.i	0.639179	+	0.639179i	0.950353	−	0.311174i	$-0.100722\pi$
$977$	610115.	+	610115.i	0.639179	+	0.639179i	−0.311174	+	0.950353i	$0.600722\pi$
$978$	569022.	−	569022.i	0.594911	−	0.594911i
$979$			330111.i			0.344425i
$980$	68555.8	+	2462.74i	0.0713825	+	0.00256429i
$981$	−110228.			−0.114539
$982$	132480.	+	132480.i	0.137381	+	0.137381i
$983$	120397.	−	120397.i	0.124597	−	0.124597i	−0.642058	−	0.766656i	$-0.721919\pi$
$983$	120397.	−	120397.i	0.124597	−	0.124597i	0.766656	+	0.642058i	$0.221919\pi$
$984$		−	16432.0i		−	0.0169707i
$985$	−323149.	−	347231.i	−0.333066	−	0.357887i
$986$	−277559.			−0.285497
$987$	−448897.	−	448897.i	−0.460799	−	0.460799i
$988$	174892.	−	174892.i	0.179166	−	0.179166i
$989$		−	231724.i		−	0.236907i
$990$	130431.	−	121385.i	0.133080	−	0.123850i
$991$	−280958.			−0.286084			−0.143042	−	0.989717i	$-0.545688\pi$
$991$	−280958.			−0.286084			−0.143042	+	0.989717i	$0.545688\pi$
$992$	152399.	+	152399.i	0.154867	+	0.154867i
$993$	−337410.	+	337410.i	−0.342184	+	0.342184i
$994$			442863.i			0.448226i
$995$	−36289.2	+	1.01019e6i	−0.0366548	+	1.02036i
$996$	14360.0			0.0144755
$997$	154924.	+	154924.i	0.155857	+	0.155857i	0.780728	−	0.624871i	$-0.214848\pi$
$997$	154924.	+	154924.i	0.155857	+	0.155857i	−0.624871	+	0.780728i	$0.714848\pi$
$998$	322924.	−	322924.i	0.324220	−	0.324220i
$999$		−	419720.i		−	0.420561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.5.f.a.57.2	yes	12
5.2	odd	4		350.5.f.d.43.5		12
5.3	odd	4	inner	70.5.f.a.43.2	✓	12
5.4	even	2		350.5.f.d.57.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.5.f.a.43.2	✓	12	5.3	odd	4	inner
70.5.f.a.57.2	yes	12	1.1	even	1	trivial
350.5.f.d.43.5		12	5.2	odd	4
350.5.f.d.57.5		12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	70.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-7.02600 + 7.02600i) q^{3} +8.00000i q^{4} +(-24.9839 - 0.897502i) q^{5} +28.1040 q^{6} +(-13.0958 - 13.0958i) q^{7} +(16.0000 - 16.0000i) q^{8} -17.7293i q^{9} +(48.1728 + 51.7628i) q^{10} +142.126 q^{11} +(-56.2080 - 56.2080i) q^{12} +(167.395 - 167.395i) q^{13} +52.3832i q^{14} +(181.843 - 169.231i) q^{15} -64.0000 q^{16} +(-195.069 - 195.069i) q^{17} +(-35.4587 + 35.4587i) q^{18} -130.598i q^{19} +(7.18001 - 199.871i) q^{20} +184.022 q^{21} +(-284.251 - 284.251i) q^{22} +(77.4569 - 77.4569i) q^{23} +224.832i q^{24} +(623.389 + 44.8462i) q^{25} -669.581 q^{26} +(-444.540 - 444.540i) q^{27} +(104.766 - 104.766i) q^{28} +355.719i q^{29} +(-702.147 - 25.2234i) q^{30} +1190.62 q^{31} +(128.000 + 128.000i) q^{32} +(-998.574 + 998.574i) q^{33} +780.274i q^{34} +(315.430 + 338.937i) q^{35} +141.835 q^{36} +(472.084 + 472.084i) q^{37} +(-261.196 + 261.196i) q^{38} +2352.24i q^{39} +(-414.102 + 385.382i) q^{40} -73.0858 q^{41} +(-368.044 - 368.044i) q^{42} +(1495.82 - 1495.82i) q^{43} +1137.00i q^{44} +(-15.9121 + 442.948i) q^{45} -309.828 q^{46} +(-2439.36 - 2439.36i) q^{47} +(449.664 - 449.664i) q^{48} +343.000i q^{49} +(-1157.09 - 1336.47i) q^{50} +2741.10 q^{51} +(1339.16 + 1339.16i) q^{52} +(-2683.33 + 2683.33i) q^{53} +1778.16i q^{54} +(-3550.85 - 127.558i) q^{55} -419.066 q^{56} +(917.581 + 917.581i) q^{57} +(711.439 - 711.439i) q^{58} -5527.82i q^{59} +(1353.85 + 1454.74i) q^{60} +413.680 q^{61} +(-2381.24 - 2381.24i) q^{62} +(-232.180 + 232.180i) q^{63} -512.000i q^{64} +(-4332.42 + 4031.95i) q^{65} +3994.30 q^{66} +(-3561.92 - 3561.92i) q^{67} +(1560.55 - 1560.55i) q^{68} +1088.42i q^{69} +(47.0140 - 1308.74i) q^{70} +8454.30 q^{71} +(-283.669 - 283.669i) q^{72} +(7044.21 - 7044.21i) q^{73} -1888.34i q^{74} +(-4695.02 + 4064.84i) q^{75} +1044.78 q^{76} +(-1861.25 - 1861.25i) q^{77} +(4704.48 - 4704.48i) q^{78} -6515.21i q^{79} +(1598.97 + 57.4401i) q^{80} +7682.75 q^{81} +(146.172 + 146.172i) q^{82} +(-127.740 + 127.740i) q^{83} +1472.18i q^{84} +(4698.50 + 5048.65i) q^{85} -5983.30 q^{86} +(-2499.28 - 2499.28i) q^{87} +(2274.01 - 2274.01i) q^{88} +2322.67i q^{89} +(917.720 - 854.071i) q^{90} -4384.35 q^{91} +(619.655 + 619.655i) q^{92} +(-8365.30 + 8365.30i) q^{93} +9757.45i q^{94} +(-117.212 + 3262.84i) q^{95} -1798.66 q^{96} +(10168.4 + 10168.4i) q^{97} +(686.000 - 686.000i) q^{98} -2519.79i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 20 q^{3} + 8 q^{5} + 80 q^{6} + 192 q^{8} - 144 q^{10} + 4 q^{11} - 160 q^{12} - 180 q^{13} - 736 q^{15} - 768 q^{16} - 236 q^{17} - 464 q^{18} + 512 q^{20} - 196 q^{21} - 8 q^{22} - 1232 q^{23}+ \cdots + 8232 q^{98}+O(q^{100}) \) 12 * q - 24 * q^2 - 20 * q^3 + 8 * q^5 + 80 * q^6 + 192 * q^8 - 144 * q^10 + 4 * q^11 - 160 * q^12 - 180 * q^13 - 736 * q^15 - 768 * q^16 - 236 * q^17 - 464 * q^18 + 512 * q^20 - 196 * q^21 - 8 * q^22 - 1232 * q^23 + 944 * q^25 + 720 * q^26 - 908 * q^27 - 632 * q^30 - 992 * q^31 + 1536 * q^32 + 6268 * q^33 - 784 * q^35 + 1856 * q^36 + 2200 * q^37 - 2880 * q^38 - 896 * q^40 + 176 * q^41 + 392 * q^42 + 1436 * q^43 + 3436 * q^45 + 4928 * q^46 + 5708 * q^47 + 1280 * q^48 - 1352 * q^50 + 6028 * q^51 - 1440 * q^52 - 9868 * q^53 - 7036 * q^55 - 5676 * q^57 - 4376 * q^58 + 8416 * q^60 - 1512 * q^61 + 1984 * q^62 - 3920 * q^63 + 7888 * q^65 - 25072 * q^66 - 11340 * q^67 + 1888 * q^68 + 4312 * q^70 - 14544 * q^71 - 3712 * q^72 + 24744 * q^73 - 6468 * q^75 + 11520 * q^76 - 9016 * q^77 + 10152 * q^78 - 512 * q^80 + 15740 * q^81 - 352 * q^82 - 30368 * q^83 - 27972 * q^85 - 5744 * q^86 + 2084 * q^87 + 64 * q^88 - 5168 * q^90 + 11172 * q^91 - 9856 * q^92 + 34508 * q^93 + 30436 * q^95 - 5120 * q^96 + 56180 * q^97 + 8232 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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