LMFDB - Embedded newform 30.7.f.b.13.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,7,Mod(7,30)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("30.7"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	30.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.90162250860$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1602x^{6} + 816401x^{4} + 140305200x^{2} + 7638760000 $ x^8 + 1602x^6 + 816401x^4 + 140305200*x^2 + 7638760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$25.3784i$ of defining polynomial
Character	$\chi$	$=$	30.13
Dual form			30.7.f.b.7.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 4.00000i) q^{2} +(11.0227 + 11.0227i) q^{3} -32.0000i q^{4} +(75.4773 - 99.6402i) q^{5} -88.1816 q^{6} +(145.451 - 145.451i) q^{7} +(128.000 + 128.000i) q^{8} +243.000i q^{9} +(96.6517 + 700.470i) q^{10} +1037.11 q^{11} +(352.727 - 352.727i) q^{12} +(2027.16 + 2027.16i) q^{13} +1163.61i q^{14} +(1930.27 - 266.341i) q^{15} -1024.00 q^{16} +(4670.49 - 4670.49i) q^{17} +(-972.000 - 972.000i) q^{18} +9189.32i q^{19} +(-3188.49 - 2415.27i) q^{20} +3206.54 q^{21} +(-4148.42 + 4148.42i) q^{22} +(-13577.9 - 13577.9i) q^{23} +2821.81i q^{24} +(-4231.35 - 15041.2i) q^{25} -16217.3 q^{26} +(-2678.52 + 2678.52i) q^{27} +(-4654.44 - 4654.44i) q^{28} -8478.24i q^{29} +(-6655.71 + 8786.44i) q^{30} +17088.4 q^{31} +(4096.00 - 4096.00i) q^{32} +(11431.7 + 11431.7i) q^{33} +37364.0i q^{34} +(-3514.53 - 25471.1i) q^{35} +7776.00 q^{36} +(-14956.3 + 14956.3i) q^{37} +(-36757.3 - 36757.3i) q^{38} +44689.5i q^{39} +(22415.0 - 3092.86i) q^{40} +50688.1 q^{41} +(-12826.1 + 12826.1i) q^{42} +(-12486.6 - 12486.6i) q^{43} -33187.4i q^{44} +(24212.6 + 18341.0i) q^{45} +108624. q^{46} +(-25787.6 + 25787.6i) q^{47} +(-11287.2 - 11287.2i) q^{48} +75336.8i q^{49} +(77090.0 + 43239.2i) q^{50} +102963. q^{51} +(64869.0 - 64869.0i) q^{52} +(-166649. - 166649. i) q^{53} -21428.1i q^{54} +(78277.9 - 103337. i) q^{55} +37235.6 q^{56} +(-101291. + 101291. i) q^{57} +(33912.9 + 33912.9i) q^{58} +247188. i q^{59} +(-8522.91 - 61768.6i) q^{60} -281194. q^{61} +(-68353.5 + 68353.5i) q^{62} +(35344.7 + 35344.7i) q^{63} +32768.0i q^{64} +(354991. - 48982.0i) q^{65} -91453.6 q^{66} +(-304343. + 304343. i) q^{67} +(-149456. - 149456. i) q^{68} -299331. i q^{69} +(115942. + 87826.2i) q^{70} -288398. q^{71} +(-31104.0 + 31104.0i) q^{72} +(-487894. - 487894. i) q^{73} -119650. i q^{74} +(119153. - 212435. i) q^{75} +294058. q^{76} +(150848. - 150848. i) q^{77} +(-178758. - 178758. i) q^{78} +222009. i q^{79} +(-77288.8 + 102032. i) q^{80} -59049.0 q^{81} +(-202752. + 202752. i) q^{82} +(749160. + 749160. i) q^{83} -102609. i q^{84} +(-112853. - 817885. i) q^{85} +99892.6 q^{86} +(93453.1 - 93453.1i) q^{87} +(132749. + 132749. i) q^{88} +689800. i q^{89} +(-170214. + 23486.4i) q^{90} +589705. q^{91} +(-434494. + 434494. i) q^{92} +(188360. + 188360. i) q^{93} -206301. i q^{94} +(915626. + 693585. i) q^{95} +90298.0 q^{96} +(820944. - 820944. i) q^{97} +(-301347. - 301347. i) q^{98} +252017. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} + 60 q^{5} + 388 q^{7} + 1024 q^{8} - 976 q^{10} - 4192 q^{11} + 7884 q^{13} + 1296 q^{15} - 8192 q^{16} - 1372 q^{17} - 7776 q^{18} + 5888 q^{20} + 4536 q^{21} + 16768 q^{22} + 14888 q^{23}+ \cdots - 301888 q^{98}+O(q^{100}) $ 8 * q - 32 * q^2 + 60 * q^5 + 388 * q^7 + 1024 * q^8 - 976 * q^10 - 4192 * q^11 + 7884 * q^13 + 1296 * q^15 - 8192 * q^16 - 1372 * q^17 - 7776 * q^18 + 5888 * q^20 + 4536 * q^21 + 16768 * q^22 + 14888 * q^23 + 17932 * q^25 - 63072 * q^26 - 12416 * q^28 + 9072 * q^30 + 2240 * q^31 + 32768 * q^32 + 3564 * q^33 - 78232 * q^35 + 62208 * q^36 - 69996 * q^37 - 71008 * q^38 - 15872 * q^40 + 169064 * q^41 - 18144 * q^42 + 164136 * q^43 - 44712 * q^45 - 119104 * q^46 - 109248 * q^47 + 280832 * q^50 + 380376 * q^51 + 252288 * q^52 - 480740 * q^53 - 409068 * q^55 + 99328 * q^56 - 442584 * q^57 - 2272 * q^58 - 114048 * q^60 + 266088 * q^61 - 8960 * q^62 + 94284 * q^63 + 903396 * q^65 - 28512 * q^66 + 92488 * q^67 + 43904 * q^68 - 228352 * q^70 - 2526032 * q^71 - 248832 * q^72 + 324464 * q^73 - 38232 * q^75 + 568064 * q^76 + 2822104 * q^77 + 857952 * q^78 - 61440 * q^80 - 472392 * q^81 - 676256 * q^82 + 213264 * q^83 - 1537292 * q^85 - 1313088 * q^86 - 1707156 * q^87 - 536576 * q^88 + 120528 * q^90 + 3340176 * q^91 + 476416 * q^92 + 1264248 * q^93 + 3084784 * q^95 - 854736 * q^97 - 301888 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$2$	−4.00000	+	4.00000i	−0.500000	+	0.500000i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$4$		−	32.0000i		−	0.500000i
$5$	75.4773	−	99.6402i	0.603818	−	0.797122i
$5$	75.4773	−	99.6402i	0.603818	−	0.797122i
$6$	−88.1816			−0.408248
$7$	145.451	−	145.451i	0.424057	−	0.424057i	−0.462541	−	0.886598i	$-0.653062\pi$
$7$	145.451	−	145.451i	0.424057	−	0.424057i	0.886598	+	0.462541i	$0.153062\pi$
$8$	128.000	+	128.000i	0.250000	+	0.250000i
$9$			243.000i			0.333333i
$10$	96.6517	+	700.470i	0.0966517	+	0.700470i
$11$	1037.11			0.779193			0.389596	−	0.920986i	$-0.372615\pi$
$11$	1037.11			0.779193			0.389596	+	0.920986i	$0.372615\pi$
$12$	352.727	−	352.727i	0.204124	−	0.204124i
$13$	2027.16	+	2027.16i	0.922693	+	0.922693i	0.997219	−	0.0745260i	$-0.0237444\pi$
$13$	2027.16	+	2027.16i	0.922693	+	0.922693i	−0.0745260	+	0.997219i	$0.523744\pi$
$14$			1163.61i			0.424057i
$15$	1930.27	−	266.341i	0.571931	−	0.0789158i
$16$	−1024.00			−0.250000
$17$	4670.49	−	4670.49i	0.950640	−	0.950640i	−0.0481978	−	0.998838i	$-0.515348\pi$
$17$	4670.49	−	4670.49i	0.950640	−	0.950640i	0.998838	+	0.0481978i	$0.0153478\pi$
$18$	−972.000	−	972.000i	−0.166667	−	0.166667i
$19$			9189.32i			1.33975i	0.742476	+	0.669873i	$0.233651\pi$
$19$			9189.32i			1.33975i	−0.742476	+	0.669873i	$0.766349\pi$
$20$	−3188.49	−	2415.27i	−0.398561	−	0.301909i
$21$	3206.54			0.346241
$22$	−4148.42	+	4148.42i	−0.389596	+	0.389596i
$23$	−13577.9	−	13577.9i	−1.11597	−	1.11597i	−0.992327	−	0.123638i	$-0.960544\pi$
$23$	−13577.9	−	13577.9i	−1.11597	−	1.11597i	−0.123638	−	0.992327i	$-0.539456\pi$
$24$			2821.81i			0.204124i
$25$	−4231.35	−	15041.2i	−0.270807	−	0.962634i
$26$	−16217.3			−0.922693
$27$	−2678.52	+	2678.52i	−0.136083	+	0.136083i
$28$	−4654.44	−	4654.44i	−0.212028	−	0.212028i
$29$		−	8478.24i		−	0.347625i	−0.984779	−	0.173813i	$-0.944391\pi$
$29$		−	8478.24i		−	0.347625i	0.984779	−	0.173813i	$-0.0556087\pi$
$30$	−6655.71	+	8786.44i	−0.246508	+	0.325424i
$31$	17088.4			0.573609			0.286805	−	0.957989i	$-0.407407\pi$
$31$	17088.4			0.573609			0.286805	+	0.957989i	$0.407407\pi$
$32$	4096.00	−	4096.00i	0.125000	−	0.125000i
$33$	11431.7	+	11431.7i	0.318104	+	0.318104i
$34$			37364.0i			0.950640i
$35$	−3514.53	−	25471.1i	−0.0819716	−	0.594078i
$36$	7776.00			0.166667
$37$	−14956.3	+	14956.3i	−0.295269	+	0.295269i	−0.839158	−	0.543888i	$-0.816952\pi$
$37$	−14956.3	+	14956.3i	−0.295269	+	0.295269i	0.543888	+	0.839158i	$0.316952\pi$
$38$	−36757.3	−	36757.3i	−0.669873	−	0.669873i
$39$			44689.5i			0.753376i
$40$	22415.0	−	3092.86i	0.350235	−	0.0483259i
$41$	50688.1			0.735452			0.367726	−	0.929934i	$-0.380136\pi$
$41$	50688.1			0.735452			0.367726	+	0.929934i	$0.380136\pi$
$42$	−12826.1	+	12826.1i	−0.173120	+	0.173120i
$43$	−12486.6	−	12486.6i	−0.157050	−	0.157050i	0.624208	−	0.781258i	$-0.285422\pi$
$43$	−12486.6	−	12486.6i	−0.157050	−	0.157050i	−0.781258	+	0.624208i	$0.785422\pi$
$44$		−	33187.4i		−	0.389596i
$45$	24212.6	+	18341.0i	0.265707	+	0.201273i
$46$	108624.			1.11597
$47$	−25787.6	+	25787.6i	−0.248380	+	0.248380i	−0.820306	−	0.571925i	$-0.806197\pi$
$47$	−25787.6	+	25787.6i	−0.248380	+	0.248380i	0.571925	+	0.820306i	$0.306197\pi$
$48$	−11287.2	−	11287.2i	−0.102062	−	0.102062i
$49$			75336.8i			0.640352i
$50$	77090.0	+	43239.2i	0.616720	+	0.345914i
$51$	102963.			0.776194
$52$	64869.0	−	64869.0i	0.461347	−	0.461347i
$53$	−166649.	−	166649.i	−1.11937	−	1.11937i	−0.991833	−	0.127542i	$-0.959291\pi$
$53$	−166649.	−	166649.i	−1.11937	−	1.11937i	−0.127542	−	0.991833i	$-0.540709\pi$
$54$		−	21428.1i		−	0.136083i
$55$	78277.9	−	103337.i	0.470491	−	0.621111i
$56$	37235.6			0.212028
$57$	−101291.	+	101291.i	−0.546949	+	0.546949i
$58$	33912.9	+	33912.9i	0.173813	+	0.173813i
$59$			247188.i			1.20357i	0.798658	+	0.601785i	$0.205544\pi$
$59$			247188.i			1.20357i	−0.798658	+	0.601785i	$0.794456\pi$
$60$	−8522.91	−	61768.6i	−0.0394579	−	0.285966i
$61$	−281194.			−1.23884			−0.619422	−	0.785058i	$-0.712633\pi$
$61$	−281194.			−1.23884			−0.619422	+	0.785058i	$0.712633\pi$
$62$	−68353.5	+	68353.5i	−0.286805	+	0.286805i
$63$	35344.7	+	35344.7i	0.141352	+	0.141352i
$64$			32768.0i			0.125000i
$65$	354991.	−	48982.0i	1.29264	−	0.178360i
$66$	−91453.6			−0.318104
$67$	−304343.	+	304343.i	−1.01190	+	1.01190i	−0.0119749	+	0.999928i	$0.503812\pi$
$67$	−304343.	+	304343.i	−1.01190	+	1.01190i	−0.999928	+	0.0119749i	$0.996188\pi$
$68$	−149456.	−	149456.i	−0.475320	−	0.475320i
$69$		−	299331.i		−	0.911182i
$70$	115942.	+	87826.2i	0.338025	+	0.256053i
$71$	−288398.			−0.805780			−0.402890	−	0.915248i	$-0.631994\pi$
$71$	−288398.			−0.805780			−0.402890	+	0.915248i	$0.631994\pi$
$72$	−31104.0	+	31104.0i	−0.0833333	+	0.0833333i
$73$	−487894.	−	487894.i	−1.25417	−	1.25417i	−0.953833	−	0.300338i	$-0.902900\pi$
$73$	−487894.	−	487894.i	−1.25417	−	1.25417i	−0.300338	−	0.953833i	$-0.597100\pi$
$74$		−	119650.i		−	0.295269i
$75$	119153.	−	212435.i	0.282437	−	0.503550i
$76$	294058.			0.669873
$77$	150848.	−	150848.i	0.330422	−	0.330422i
$78$	−178758.	−	178758.i	−0.376688	−	0.376688i
$79$			222009.i			0.450286i	0.974326	+	0.225143i	$0.0722850\pi$
$79$			222009.i			0.450286i	−0.974326	+	0.225143i	$0.927715\pi$
$80$	−77288.8	+	102032.i	−0.150955	+	0.199280i
$81$	−59049.0			−0.111111
$82$	−202752.	+	202752.i	−0.367726	+	0.367726i
$83$	749160.	+	749160.i	1.31021	+	1.31021i	0.921260	+	0.388948i	$0.127161\pi$
$83$	749160.	+	749160.i	1.31021	+	1.31021i	0.388948	+	0.921260i	$0.372839\pi$
$84$		−	102609.i		−	0.173120i
$85$	−112853.	−	817885.i	−0.183762	−	1.33179i
$86$	99892.6			0.157050
$87$	93453.1	−	93453.1i	0.141917	−	0.141917i
$88$	132749.	+	132749.i	0.194798	+	0.194798i
$89$			689800.i			0.978482i	0.872149	+	0.489241i	$0.162726\pi$
$89$			689800.i			0.978482i	−0.872149	+	0.489241i	$0.837274\pi$
$90$	−170214.	+	23486.4i	−0.233490	+	0.0322172i
$91$	589705.			0.782548
$92$	−434494.	+	434494.i	−0.557983	+	0.557983i
$93$	188360.	+	188360.i	0.234175	+	0.234175i
$94$		−	206301.i		−	0.248380i
$95$	915626.	+	693585.i	1.06794	+	0.808963i
$96$	90298.0			0.102062
$97$	820944.	−	820944.i	0.899494	−	0.899494i	−0.0958974	−	0.995391i	$-0.530572\pi$
$97$	820944.	−	820944.i	0.899494	−	0.899494i	0.995391	+	0.0958974i	$0.0305721\pi$
$98$	−301347.	−	301347.i	−0.320176	−	0.320176i
$99$			252017.i			0.259731i
$100$	−481317.	+	135403.i	−0.481317	+	0.135403i
$101$	−290048.			−0.281518			−0.140759	−	0.990044i	$-0.544954\pi$
$101$	−290048.			−0.281518			−0.140759	+	0.990044i	$0.544954\pi$
$102$	−411852.	+	411852.i	−0.388097	+	0.388097i
$103$	291498.	+	291498.i	0.266762	+	0.266762i	0.827794	−	0.561032i	$-0.189596\pi$
$103$	291498.	+	291498.i	0.266762	+	0.266762i	−0.561032	+	0.827794i	$0.689596\pi$
$104$			518952.i			0.461347i
$105$	242021.	−	319500.i	0.209067	−	0.275996i
$106$	1.33319e6			1.11937
$107$	792277.	−	792277.i	0.646734	−	0.646734i	−0.305468	−	0.952202i	$-0.598813\pi$
$107$	792277.	−	792277.i	0.646734	−	0.646734i	0.952202	+	0.305468i	$0.0988129\pi$
$108$	85712.5	+	85712.5i	0.0680414	+	0.0680414i
$109$			165909.i			0.128112i	0.997946	+	0.0640559i	$0.0204036\pi$
$109$			165909.i			0.128112i	−0.997946	+	0.0640559i	$0.979596\pi$
$110$	100238.	+	726461.i	0.0753103	+	0.545801i
$111$	−329717.			−0.241086
$112$	−148942.	+	148942.i	−0.106014	+	0.106014i
$113$	−750389.	−	750389.i	−0.520057	−	0.520057i	0.397532	−	0.917589i	$-0.369867\pi$
$113$	−750389.	−	750389.i	−0.520057	−	0.520057i	−0.917589	+	0.397532i	$0.869867\pi$
$114$		−	810329.i		−	0.546949i
$115$	−2.37774e6	+	328083.i	−1.56340	+	0.215720i
$116$	−271304.			−0.173813
$117$	−492599.	+	492599.i	−0.307564	+	0.307564i
$118$	−988752.	−	988752.i	−0.601785	−	0.601785i
$119$		−	1.35866e6i		−	0.806250i
$120$	281166.	+	212983.i	0.162712	+	0.123254i
$121$	−695974.			−0.392859
$122$	1.12478e6	−	1.12478e6i	0.619422	−	0.619422i
$123$	558720.	+	558720.i	0.300247	+	0.300247i
$124$		−	546828.i		−	0.286805i
$125$	−1.81808e6	−	713653.i	−0.930854	−	0.365390i
$126$	−282757.			−0.141352
$127$	583066.	−	583066.i	0.284647	−	0.284647i	−0.550312	−	0.834959i	$-0.685491\pi$
$127$	583066.	−	583066.i	0.284647	−	0.284647i	0.834959	+	0.550312i	$0.185491\pi$
$128$	−131072.	−	131072.i	−0.0625000	−	0.0625000i
$129$		−	275272.i		−	0.128231i
$130$	−1.22403e6	+	1.61589e6i	−0.557139	+	0.735499i
$131$	−4.18868e6			−1.86321			−0.931607	−	0.363466i	$-0.881593\pi$
$131$	−4.18868e6			−1.86321			−0.931607	+	0.363466i	$0.881593\pi$
$132$	365815.	−	365815.i	0.159052	−	0.159052i
$133$	1.33660e6	+	1.33660e6i	0.568128	+	0.568128i
$134$		−	2.43474e6i		−	1.01190i
$135$	64720.8	+	469055.i	0.0263053	+	0.190644i
$136$	1.19565e6			0.475320
$137$	250638.	−	250638.i	0.0974731	−	0.0974731i	−0.656689	−	0.754162i	$-0.728043\pi$
$137$	250638.	−	250638.i	0.0974731	−	0.0974731i	0.754162	+	0.656689i	$0.228043\pi$
$138$	1.19733e6	+	1.19733e6i	0.455591	+	0.455591i
$139$			4.91265e6i			1.82924i	0.404309	+	0.914622i	$0.367512\pi$
$139$			4.91265e6i			1.82924i	−0.404309	+	0.914622i	$0.632488\pi$
$140$	−815075.	+	112465.i	−0.297039	+	0.0409858i
$141$	−568497.			−0.202801
$142$	1.15359e6	−	1.15359e6i	0.402890	−	0.402890i
$143$	2.10237e6	+	2.10237e6i	0.718956	+	0.718956i
$144$		−	248832.i		−	0.0833333i
$145$	−844774.	−	639914.i	−0.277100	−	0.209903i
$146$	3.90315e6			1.25417
$147$	−830415.	+	830415.i	−0.261423	+	0.261423i
$148$	478601.	+	478601.i	0.147635	+	0.147635i
$149$		−	3.77991e6i		−	1.14268i	−0.820715	−	0.571338i	$-0.806425\pi$
$149$		−	3.77991e6i		−	1.14268i	0.820715	−	0.571338i	$-0.193575\pi$
$150$	373128.	+	1.32635e6i	0.110556	+	0.392994i
$151$	1.19813e6			0.347996			0.173998	−	0.984746i	$-0.444331\pi$
$151$	1.19813e6			0.347996			0.173998	+	0.984746i	$0.444331\pi$
$152$	−1.17623e6	+	1.17623e6i	−0.334937	+	0.334937i
$153$	1.13493e6	+	1.13493e6i	0.316880	+	0.316880i
$154$			1.20679e6i			0.330422i
$155$	1.28979e6	−	1.70269e6i	0.346356	−	0.457236i
$156$	1.43006e6			0.376688
$157$	2.93950e6	−	2.93950e6i	0.759582	−	0.759582i	−0.216664	−	0.976246i	$-0.569518\pi$
$157$	2.93950e6	−	2.93950e6i	0.759582	−	0.759582i	0.976246	+	0.216664i	$0.0695176\pi$
$158$	−888035.	−	888035.i	−0.225143	−	0.225143i
$159$		−	3.67385e6i		−	0.913966i
$160$	−98971.4	−	717281.i	−0.0241629	−	0.175118i
$161$	−3.94986e6			−0.946465
$162$	236196.	−	236196.i	0.0555556	−	0.0555556i
$163$	3.63502e6	+	3.63502e6i	0.839351	+	0.839351i	0.988774	−	0.149422i	$-0.0477413\pi$
$163$	3.63502e6	+	3.63502e6i	0.839351	+	0.839351i	−0.149422	+	0.988774i	$0.547741\pi$
$164$		−	1.62202e6i		−	0.367726i
$165$	2.00189e6	−	276223.i	0.445645	−	0.0614906i
$166$	−5.99328e6			−1.31021
$167$	−738364.	+	738364.i	−0.158533	+	0.158533i	−0.781917	−	0.623383i	$-0.785758\pi$
$167$	−738364.	+	738364.i	−0.158533	+	0.158533i	0.623383	+	0.781917i	$0.285758\pi$
$168$	410436.	+	410436.i	0.0865602	+	0.0865602i
$169$			3.39192e6i			0.702725i
$170$	3.72295e6	+	2.82013e6i	0.757776	+	0.574014i
$171$	−2.23300e6			−0.446582
$172$	−399570.	+	399570.i	−0.0785250	+	0.0785250i
$173$	5.01441e6	+	5.01441e6i	0.968459	+	0.968459i	0.999518	−	0.0310584i	$-0.00988779\pi$
$173$	5.01441e6	+	5.01441e6i	0.968459	+	0.968459i	−0.0310584	+	0.999518i	$0.509888\pi$
$174$			747625.i			0.141917i
$175$	−2.80321e6	−	1.57230e6i	−0.523048	−	0.293374i
$176$	−1.06200e6			−0.194798
$177$	−2.72468e6	+	2.72468e6i	−0.491355	+	0.491355i
$178$	−2.75920e6	−	2.75920e6i	−0.489241	−	0.489241i
$179$		−	7.77058e6i		−	1.35486i	−0.735587	−	0.677430i	$-0.763094\pi$
$179$		−	7.77058e6i		−	1.35486i	0.735587	−	0.677430i	$-0.236906\pi$
$180$	586912.	−	774802.i	0.100636	−	0.132854i
$181$	6.98198e6			1.17745			0.588726	−	0.808333i	$-0.299630\pi$
$181$	6.98198e6			1.17745			0.588726	+	0.808333i	$0.299630\pi$
$182$	−2.35882e6	+	2.35882e6i	−0.391274	+	0.391274i
$183$	−3.09952e6	−	3.09952e6i	−0.505756	−	0.505756i
$184$		−	3.47596e6i		−	0.557983i
$185$	361387.	+	2.61911e6i	0.0570766	+	0.413655i
$186$	−1.50688e6			−0.234175
$187$	4.84379e6	−	4.84379e6i	0.740732	−	0.740732i
$188$	825202.	+	825202.i	0.124190	+	0.124190i
$189$			779188.i			0.115414i
$190$	−6.43684e6	+	888163.i	−0.938452	+	0.129489i
$191$	1.75621e6			0.252044			0.126022	−	0.992027i	$-0.459779\pi$
$191$	1.75621e6			0.252044			0.126022	+	0.992027i	$0.459779\pi$
$192$	−361192.	+	361192.i	−0.0510310	+	0.0510310i
$193$	−8.48929e6	−	8.48929e6i	−1.18086	−	1.18086i	−0.979521	−	0.201343i	$-0.935470\pi$
$193$	−8.48929e6	−	8.48929e6i	−1.18086	−	1.18086i	−0.201343	−	0.979521i	$-0.564530\pi$
$194$			6.56755e6i			0.899494i
$195$	4.45287e6	+	3.37304e6i	0.600532	+	0.454902i
$196$	2.41078e6			0.320176
$197$	−7.08383e6	+	7.08383e6i	−0.926552	+	0.926552i	−0.997481	−	0.0709298i	$-0.977403\pi$
$197$	−7.08383e6	+	7.08383e6i	−0.926552	+	0.926552i	0.0709298	+	0.997481i	$0.477403\pi$
$198$	−1.00807e6	−	1.00807e6i	−0.129865	−	0.129865i
$199$			2.34311e6i			0.297326i	0.988888	+	0.148663i	$0.0474970\pi$
$199$			2.34311e6i			0.297326i	−0.988888	+	0.148663i	$0.952503\pi$
$200$	1.38365e6	−	2.46688e6i	0.172957	−	0.308360i
$201$	−6.70937e6			−0.826216
$202$	1.16019e6	−	1.16019e6i	0.140759	−	0.140759i
$203$	−1.23317e6	−	1.23317e6i	−0.147413	−	0.147413i
$204$		−	3.29481e6i		−	0.388097i
$205$	3.82580e6	−	5.05058e6i	0.444080	−	0.586245i
$206$	−2.33199e6			−0.266762
$207$	3.29944e6	−	3.29944e6i	0.371988	−	0.371988i
$208$	−2.07581e6	−	2.07581e6i	−0.230673	−	0.230673i
$209$			9.53029e6i			1.04392i
$210$	309917.	+	2.24608e6i	0.0334648	+	0.242531i
$211$	−4.10418e6			−0.436897			−0.218448	−	0.975848i	$-0.570100\pi$
$211$	−4.10418e6			−0.436897			−0.218448	+	0.975848i	$0.570100\pi$
$212$	−5.33277e6	+	5.33277e6i	−0.559687	+	0.559687i
$213$	−3.17892e6	−	3.17892e6i	−0.328958	−	0.328958i
$214$			6.33822e6i			0.646734i
$215$	−2.18662e6	+	301712.i	−0.220018	+	0.0303583i
$216$	−685700.			−0.0680414
$217$	2.48553e6	−	2.48553e6i	0.243243	−	0.243243i
$218$	−663634.	−	663634.i	−0.0640559	−	0.0640559i
$219$		−	1.07558e7i		−	1.02403i
$220$	−3.30680e6	−	2.50489e6i	−0.310556	−	0.235245i
$221$	1.89356e7			1.75430
$222$	1.31887e6	−	1.31887e6i	0.120543	−	0.120543i
$223$	−9.84643e6	−	9.84643e6i	−0.887901	−	0.887901i	0.106421	−	0.994321i	$-0.466061\pi$
$223$	−9.84643e6	−	9.84643e6i	−0.887901	−	0.887901i	−0.994321	+	0.106421i	$0.966061\pi$
$224$		−	1.19154e6i		−	0.106014i
$225$	3.65500e6	−	1.02822e6i	0.320878	−	0.0902689i
$226$	6.00311e6			0.520057
$227$	447932.	−	447932.i	0.0382943	−	0.0382943i	−0.687700	−	0.725995i	$-0.741380\pi$
$227$	447932.	−	447932.i	0.0382943	−	0.0382943i	0.725995	+	0.687700i	$0.241380\pi$
$228$	3.24132e6	+	3.24132e6i	0.273475	+	0.273475i
$229$			2.13385e7i			1.77688i	0.458991	+	0.888441i	$0.348211\pi$
$229$			2.13385e7i			1.77688i	−0.458991	+	0.888441i	$0.651789\pi$
$230$	8.19862e6	−	1.08233e7i	0.673840	−	0.889560i
$231$	3.32551e6			0.269788
$232$	1.08521e6	−	1.08521e6i	0.0869064	−	0.0869064i
$233$	1.19508e6	+	1.19508e6i	0.0944775	+	0.0944775i	0.752766	−	0.658288i	$-0.228719\pi$
$233$	1.19508e6	+	1.19508e6i	0.0944775	+	0.0944775i	−0.658288	+	0.752766i	$0.728719\pi$
$234$		−	3.94079e6i		−	0.307564i
$235$	623103.	+	4.51586e6i	0.0480127	+	0.347966i
$236$	7.91001e6			0.601785
$237$	−2.44714e6	+	2.44714e6i	−0.183829	+	0.183829i
$238$	5.43464e6	+	5.43464e6i	0.403125	+	0.403125i
$239$		−	2.07007e6i		−	0.151632i	−0.997122	−	0.0758160i	$-0.975844\pi$
$239$		−	2.07007e6i		−	0.151632i	0.997122	−	0.0758160i	$-0.0241562\pi$
$240$	−1.97660e6	+	272733.i	−0.142983	+	0.0197289i
$241$	2.35841e7			1.68487			0.842437	−	0.538795i	$-0.181120\pi$
$241$	2.35841e7			1.68487			0.842437	+	0.538795i	$0.181120\pi$
$242$	2.78389e6	−	2.78389e6i	0.196429	−	0.196429i
$243$	−650880.	−	650880.i	−0.0453609	−	0.0453609i
$244$			8.99822e6i			0.619422i
$245$	7.50658e6	+	5.68622e6i	0.510439	+	0.386656i
$246$	−4.46976e6			−0.300247
$247$	−1.86282e7	+	1.86282e7i	−1.23617	+	1.23617i
$248$	2.18731e6	+	2.18731e6i	0.143402	+	0.143402i
$249$			1.65155e7i			1.06978i
$250$	1.01269e7	−	4.41769e6i	0.648122	−	0.282732i
$251$	−8.83541e6			−0.558734			−0.279367	−	0.960184i	$-0.590125\pi$
$251$	−8.83541e6			−0.558734			−0.279367	+	0.960184i	$0.590125\pi$
$252$	1.13103e6	−	1.13103e6i	0.0706761	−	0.0706761i
$253$	−1.40818e7	−	1.40818e7i	−0.869552	−	0.869552i
$254$			4.66453e6i			0.284647i
$255$	7.77137e6	−	1.02593e7i	0.468680	−	0.618721i
$256$	1.04858e6			0.0625000
$257$	−6.09969e6	+	6.09969e6i	−0.359342	+	0.359342i	−0.863570	−	0.504228i	$-0.831777\pi$
$257$	−6.09969e6	+	6.09969e6i	−0.359342	+	0.359342i	0.504228	+	0.863570i	$0.331777\pi$
$258$	1.10109e6	+	1.10109e6i	0.0641154	+	0.0641154i
$259$			4.35082e6i			0.250422i
$260$	−1.56743e6	−	1.13597e7i	−0.0891799	−	0.646319i
$261$	2.06021e6			0.115875
$262$	1.67547e7	−	1.67547e7i	0.931607	−	0.931607i
$263$	−4.35686e6	−	4.35686e6i	−0.239500	−	0.239500i	0.577143	−	0.816643i	$-0.304168\pi$
$263$	−4.35686e6	−	4.35686e6i	−0.239500	−	0.239500i	−0.816643	+	0.577143i	$0.804168\pi$
$264$			2.92652e6i			0.159052i
$265$	−2.91832e7	+	4.02673e6i	−1.56818	+	0.216379i
$266$	−1.06928e7			−0.568128
$267$	−7.60346e6	+	7.60346e6i	−0.399464	+	0.399464i
$268$	9.73898e6	+	9.73898e6i	0.505952	+	0.505952i
$269$		−	1.36102e7i		−	0.699208i	−0.936898	−	0.349604i	$-0.886316\pi$
$269$		−	1.36102e7i		−	0.699208i	0.936898	−	0.349604i	$-0.113684\pi$
$270$	−2.13510e6	−	1.61734e6i	−0.108475	−	0.0821693i
$271$	−8.20889e6			−0.412455			−0.206228	−	0.978504i	$-0.566119\pi$
$271$	−8.20889e6			−0.412455			−0.206228	+	0.978504i	$0.566119\pi$
$272$	−4.78259e6	+	4.78259e6i	−0.237660	+	0.237660i
$273$	6.50015e6	+	6.50015e6i	0.319474	+	0.319474i
$274$			2.00510e6i			0.0974731i
$275$	−4.38836e6	−	1.55993e7i	−0.211010	−	0.750077i
$276$	−9.57861e6			−0.455591
$277$	2.56480e7	−	2.56480e7i	1.20674	−	1.20674i	0.234665	−	0.972076i	$-0.424601\pi$
$277$	2.56480e7	−	2.56480e7i	1.20674	−	1.20674i	0.972076	−	0.234665i	$-0.0753995\pi$
$278$	−1.96506e7	−	1.96506e7i	−0.914622	−	0.914622i
$279$			4.15248e6i			0.191203i
$280$	2.81044e6	−	3.71016e6i	0.128027	−	0.169012i
$281$	−2.47592e7			−1.11588			−0.557940	−	0.829881i	$-0.688408\pi$
$281$	−2.47592e7			−1.11588			−0.557940	+	0.829881i	$0.688408\pi$
$282$	2.27399e6	−	2.27399e6i	0.101401	−	0.101401i
$283$	−1.00351e7	−	1.00351e7i	−0.442753	−	0.442753i	0.450183	−	0.892936i	$-0.351359\pi$
$283$	−1.00351e7	−	1.00351e7i	−0.442753	−	0.442753i	−0.892936	+	0.450183i	$0.851359\pi$
$284$			9.22873e6i			0.402890i
$285$	2.44749e6	+	1.77379e7i	0.105727	+	0.766243i
$286$	−1.68190e7			−0.718956
$287$	7.37266e6	−	7.37266e6i	0.311873	−	0.311873i
$288$	995328.	+	995328.i	0.0416667	+	0.0416667i
$289$		−	1.94895e7i		−	0.807433i
$290$	5.93875e6	−	819436.i	0.243501	−	0.0335986i
$291$	1.80980e7			0.734434
$292$	−1.56126e7	+	1.56126e7i	−0.627085	+	0.627085i
$293$	1.88230e6	+	1.88230e6i	0.0748319	+	0.0748319i	0.743532	−	0.668700i	$-0.233149\pi$
$293$	1.88230e6	+	1.88230e6i	0.0748319	+	0.0748319i	−0.668700	+	0.743532i	$0.733149\pi$
$294$		−	6.64332e6i		−	0.261423i
$295$	2.46299e7	+	1.86571e7i	0.959392	+	0.726737i
$296$	−3.82881e6			−0.147635
$297$	−2.77790e6	+	2.77790e6i	−0.106035	+	0.106035i
$298$	1.51196e7	+	1.51196e7i	0.571338	+	0.571338i
$299$		−	5.50493e7i		−	2.05939i
$300$	−6.79792e6	−	3.81290e6i	−0.251775	−	0.141219i
$301$	−3.63238e6			−0.133196
$302$	−4.79253e6	+	4.79253e6i	−0.173998	+	0.173998i
$303$	−3.19712e6	−	3.19712e6i	−0.114929	−	0.114929i
$304$		−	9.40986e6i		−	0.334937i
$305$	−2.12238e7	+	2.80183e7i	−0.748037	+	0.987510i
$306$	−9.07944e6			−0.316880
$307$	−3.23684e7	+	3.23684e7i	−1.11868	+	1.11868i	−0.126747	+	0.991935i	$0.540453\pi$
$307$	−3.23684e7	+	3.23684e7i	−1.11868	+	1.11868i	−0.991935	+	0.126747i	$0.959547\pi$
$308$	−4.82715e6	−	4.82715e6i	−0.165211	−	0.165211i
$309$			6.42620e6i			0.217810i
$310$	1.65162e6	+	1.19699e7i	0.0554403	+	0.401796i
$311$	1.96913e7			0.654625			0.327313	−	0.944916i	$-0.393857\pi$
$311$	1.96913e7			0.654625			0.327313	+	0.944916i	$0.393857\pi$
$312$	−5.72026e6	+	5.72026e6i	−0.188344	+	0.188344i
$313$	1.21275e7	+	1.21275e7i	0.395493	+	0.395493i	0.876640	−	0.481147i	$-0.159780\pi$
$313$	1.21275e7	+	1.21275e7i	0.395493	+	0.395493i	−0.481147	+	0.876640i	$0.659780\pi$
$314$			2.35160e7i			0.759582i
$315$	6.18947e6	−	854031.i	0.198026	−	0.0273239i
$316$	7.10428e6			0.225143
$317$	2.36698e7	−	2.36698e7i	0.743048	−	0.743048i	−0.230116	−	0.973163i	$-0.573910\pi$
$317$	2.36698e7	−	2.36698e7i	0.743048	−	0.743048i	0.973163	+	0.230116i	$0.0739104\pi$
$318$	1.46954e7	+	1.46954e7i	0.456983	+	0.456983i
$319$		−	8.79282e6i		−	0.270867i
$320$	3.26501e6	+	2.47324e6i	0.0996402	+	0.0754773i
$321$	1.74661e7			0.528056
$322$	1.57995e7	−	1.57995e7i	0.473232	−	0.473232i
$323$	4.29187e7	+	4.29187e7i	1.27362	+	1.27362i
$324$			1.88957e6i			0.0555556i
$325$	2.19132e7	−	3.90684e7i	0.638344	−	1.13809i
$326$	−2.90802e7			−0.839351
$327$	−1.82876e6	+	1.82876e6i	−0.0523014	+	0.0523014i
$328$	6.48808e6	+	6.48808e6i	0.183863	+	0.183863i
$329$			7.50167e6i			0.210654i
$330$	−6.90267e6	+	9.11246e6i	−0.192077	+	0.253568i
$331$	3.78781e7			1.04449			0.522245	−	0.852796i	$-0.325095\pi$
$331$	3.78781e7			1.04449			0.522245	+	0.852796i	$0.325095\pi$
$332$	2.39731e7	−	2.39731e7i	0.655104	−	0.655104i
$333$	−3.63438e6	−	3.63438e6i	−0.0984231	−	0.0984231i
$334$		−	5.90691e6i		−	0.158533i
$335$	7.35382e6	+	5.32958e7i	0.195604	+	1.41762i
$336$	−3.28349e6			−0.0865602
$337$	−2.24435e7	+	2.24435e7i	−0.586411	+	0.586411i	−0.936657	−	0.350247i	$-0.886098\pi$
$337$	−2.24435e7	+	2.24435e7i	−0.586411	+	0.586411i	0.350247	+	0.936657i	$0.386098\pi$
$338$	−1.35677e7	−	1.35677e7i	−0.351362	−	0.351362i
$339$		−	1.65426e7i		−	0.424625i
$340$	−2.61723e7	+	3.61129e6i	−0.665895	+	0.0918810i
$341$	1.77225e7			0.446952
$342$	8.93202e6	−	8.93202e6i	0.223291	−	0.223291i
$343$	2.80701e7	+	2.80701e7i	0.695602	+	0.695602i
$344$		−	3.19656e6i		−	0.0785250i
$345$	−2.98255e7	−	2.25927e7i	−0.726323	−	0.550188i
$346$	−4.01153e7			−0.968459
$347$	3.01955e7	−	3.01955e7i	0.722692	−	0.722692i	−0.246461	−	0.969153i	$-0.579268\pi$
$347$	3.01955e7	−	3.01955e7i	0.722692	−	0.722692i	0.969153	+	0.246461i	$0.0792677\pi$
$348$	−2.99050e6	−	2.99050e6i	−0.0709587	−	0.0709587i
$349$		−	7.82272e7i		−	1.84027i	−0.391600	−	0.920135i	$-0.628078\pi$
$349$		−	7.82272e7i		−	1.84027i	0.391600	−	0.920135i	$-0.371922\pi$
$350$	1.75021e7	−	4.92365e6i	0.408211	−	0.114837i
$351$	−1.08595e7			−0.251125
$352$	4.24798e6	−	4.24798e6i	0.0973991	−	0.0973991i
$353$	−9.45650e6	−	9.45650e6i	−0.214984	−	0.214984i	0.591397	−	0.806381i	$-0.298577\pi$
$353$	−9.45650e6	−	9.45650e6i	−0.214984	−	0.214984i	−0.806381	+	0.591397i	$0.798577\pi$
$354$		−	2.17974e7i		−	0.491355i
$355$	−2.17675e7	+	2.87360e7i	−0.486545	+	0.642305i
$356$	2.20736e7			0.489241
$357$	1.49761e7	−	1.49761e7i	0.329150	−	0.329150i
$358$	3.10823e7	+	3.10823e7i	0.677430	+	0.677430i
$359$			2.13996e7i			0.462511i	0.972893	+	0.231256i	$0.0742834\pi$
$359$			2.13996e7i			0.462511i	−0.972893	+	0.231256i	$0.925717\pi$
$360$	751564.	+	5.44686e6i	0.0161086	+	0.116745i
$361$	−3.73977e7			−0.794919
$362$	−2.79279e7	+	2.79279e7i	−0.588726	+	0.588726i
$363$	−7.67151e6	−	7.67151e6i	−0.160384	−	0.160384i
$364$		−	1.88706e7i		−	0.391274i
$365$	−8.54388e7	+	1.17889e7i	−1.75702	+	0.242436i
$366$	2.47962e7			0.505756
$367$	−1.29658e7	+	1.29658e7i	−0.262302	+	0.262302i	−0.825989	−	0.563687i	$-0.809383\pi$
$367$	−1.29658e7	+	1.29658e7i	−0.262302	+	0.262302i	0.563687	+	0.825989i	$0.309383\pi$
$368$	1.39038e7	+	1.39038e7i	0.278991	+	0.278991i
$369$			1.23172e7i			0.245151i
$370$	−1.19220e7	−	9.03088e6i	−0.235366	−	0.178289i
$371$	−4.84787e7			−0.949356
$372$	6.02753e6	−	6.02753e6i	0.117087	−	0.117087i
$373$	3.92352e6	+	3.92352e6i	0.0756048	+	0.0756048i	0.743898	−	0.668293i	$-0.232975\pi$
$373$	3.92352e6	+	3.92352e6i	0.0756048	+	0.0756048i	−0.668293	+	0.743898i	$0.732975\pi$
$374$			3.87504e7i			0.740732i
$375$	−1.21737e7	−	2.79065e7i	−0.230850	−	0.529190i
$376$	−6.60162e6			−0.124190
$377$	1.71867e7	−	1.71867e7i	0.320752	−	0.320752i
$378$	−3.11675e6	−	3.11675e6i	−0.0577068	−	0.0577068i
$379$			3.61170e7i			0.663429i	0.943380	+	0.331714i	$0.107627\pi$
$379$			3.61170e7i			0.663429i	−0.943380	+	0.331714i	$0.892373\pi$
$380$	2.21947e7	−	2.93000e7i	0.404482	−	0.533970i
$381$	1.28539e7			0.232413
$382$	−7.02485e6	+	7.02485e6i	−0.126022	+	0.126022i
$383$	−774461.	−	774461.i	−0.0137849	−	0.0137849i	0.700181	−	0.713966i	$-0.253103\pi$
$383$	−774461.	−	774461.i	−0.0137849	−	0.0137849i	−0.713966	+	0.700181i	$0.753103\pi$
$384$		−	2.88954e6i		−	0.0510310i
$385$	−3.64494e6	−	2.64162e7i	−0.0638716	−	0.462901i
$386$	6.79144e7			1.18086
$387$	3.03424e6	−	3.03424e6i	0.0523500	−	0.0523500i
$388$	−2.62702e7	−	2.62702e7i	−0.449747	−	0.449747i
$389$			4.56599e7i			0.775686i	0.921726	+	0.387843i	$0.126780\pi$
$389$			4.56599e7i			0.775686i	−0.921726	+	0.387843i	$0.873220\pi$
$390$	−3.13037e7	+	4.31932e6i	−0.527717	+	0.0728151i
$391$	−1.26831e8			−2.12176
$392$	−9.64311e6	+	9.64311e6i	−0.160088	+	0.160088i
$393$	−4.61705e7	−	4.61705e7i	−0.760654	−	0.760654i
$394$		−	5.66707e7i		−	0.926552i
$395$	2.21210e7	+	1.67566e7i	0.358933	+	0.271891i
$396$	8.06453e6			0.129865
$397$	5.08606e7	−	5.08606e7i	0.812849	−	0.812849i	−0.172211	−	0.985060i	$-0.555091\pi$
$397$	5.08606e7	−	5.08606e7i	0.812849	−	0.812849i	0.985060	+	0.172211i	$0.0550912\pi$
$398$	−9.37244e6	−	9.37244e6i	−0.148663	−	0.148663i
$399$			2.94659e7i			0.463875i
$400$	4.33291e6	+	1.54021e7i	0.0677016	+	0.240658i
$401$	−3.46994e7			−0.538133			−0.269066	−	0.963122i	$-0.586715\pi$
$401$	−3.46994e7			−0.538133			−0.269066	+	0.963122i	$0.586715\pi$
$402$	2.68375e7	−	2.68375e7i	0.413108	−	0.413108i
$403$	3.46408e7	+	3.46408e7i	0.529265	+	0.529265i
$404$			9.28155e6i			0.140759i
$405$	−4.45686e6	+	5.88366e6i	−0.0670909	+	0.0885691i
$406$	9.86537e6			0.147413
$407$	−1.55112e7	+	1.55112e7i	−0.230072	+	0.230072i
$408$	1.31793e7	+	1.31793e7i	0.194049	+	0.194049i
$409$			6.63216e6i			0.0969360i	0.998825	+	0.0484680i	$0.0154339\pi$
$409$			6.63216e6i			0.0969360i	−0.998825	+	0.0484680i	$0.984566\pi$
$410$	4.89909e6	+	3.55055e7i	0.0710827	+	0.515162i
$411$	5.52541e6			0.0795865
$412$	9.32795e6	−	9.32795e6i	0.133381	−	0.133381i
$413$	3.59538e7	+	3.59538e7i	0.510382	+	0.510382i
$414$			2.63955e7i			0.371988i
$415$	1.31191e8	−	1.81019e7i	1.83552	−	0.253268i
$416$	1.66065e7			0.230673
$417$	−5.41507e7	+	5.41507e7i	−0.746786	+	0.746786i
$418$	−3.81212e7	−	3.81212e7i	−0.521960	−	0.521960i
$419$			1.87567e7i			0.254985i	0.991840	+	0.127493i	$0.0406929\pi$
$419$			1.87567e7i			0.254985i	−0.991840	+	0.127493i	$0.959307\pi$
$420$	−1.02240e7	−	7.74466e6i	−0.137998	−	0.104533i
$421$	1.01392e8			1.35881			0.679406	−	0.733762i	$-0.262237\pi$
$421$	1.01392e8			1.35881			0.679406	+	0.733762i	$0.262237\pi$
$422$	1.64167e7	−	1.64167e7i	0.218448	−	0.218448i
$423$	−6.26638e6	−	6.26638e6i	−0.0827934	−	0.0827934i
$424$		−	4.26622e7i		−	0.559687i
$425$	−9.00121e7	−	5.04871e7i	−1.17256	−	0.657679i
$426$	2.54314e7			0.328958
$427$	−4.09001e7	+	4.09001e7i	−0.525340	+	0.525340i
$428$	−2.53529e7	−	2.53529e7i	−0.323367	−	0.323367i
$429$			4.63477e7i			0.587025i
$430$	7.53963e6	−	9.95332e6i	0.0948297	−	0.125188i
$431$	−2.54338e7			−0.317672			−0.158836	−	0.987305i	$-0.550774\pi$
$431$	−2.54338e7			−0.317672			−0.158836	+	0.987305i	$0.550774\pi$
$432$	2.74280e6	−	2.74280e6i	0.0340207	−	0.0340207i
$433$	−4.84883e7	−	4.84883e7i	−0.597273	−	0.597273i	0.342313	−	0.939586i	$-0.388790\pi$
$433$	−4.84883e7	−	4.84883e7i	−0.597273	−	0.597273i	−0.939586	+	0.342313i	$0.888790\pi$
$434$			1.98842e7i			0.243243i
$435$	−2.25810e6	−	1.63653e7i	−0.0274331	−	0.198818i
$436$	5.30907e6			0.0640559
$437$	1.24772e8	−	1.24772e8i	1.49511	−	1.49511i
$438$	4.30233e7	+	4.30233e7i	0.512013	+	0.512013i
$439$		−	3.77933e7i		−	0.446706i	−0.974738	−	0.223353i	$-0.928300\pi$
$439$		−	3.77933e7i		−	0.446706i	0.974738	−	0.223353i	$-0.0717002\pi$
$440$	2.32468e7	−	3.20762e6i	0.272901	−	0.0376551i
$441$	−1.83068e7			−0.213451
$442$	−7.57426e7	+	7.57426e7i	−0.877149	+	0.877149i
$443$	−2.16224e7	−	2.16224e7i	−0.248710	−	0.248710i	0.571731	−	0.820441i	$-0.306272\pi$
$443$	−2.16224e7	−	2.16224e7i	−0.248710	−	0.248710i	−0.820441	+	0.571731i	$0.806272\pi$
$444$			1.05510e7i			0.120543i
$445$	6.87318e7	+	5.20642e7i	0.779970	+	0.590826i
$446$	7.87715e7			0.887901
$447$	4.16648e7	−	4.16648e7i	0.466495	−	0.466495i
$448$	4.76615e6	+	4.76615e6i	0.0530071	+	0.0530071i
$449$			9.43557e7i			1.04239i	0.853439	+	0.521193i	$0.174513\pi$
$449$			9.43557e7i			1.04239i	−0.853439	+	0.521193i	$0.825487\pi$
$450$	−1.05071e7	+	1.87329e7i	−0.115305	+	0.205573i
$451$	5.25689e7			0.573059
$452$	−2.40124e7	+	2.40124e7i	−0.260028	+	0.260028i
$453$	1.32067e7	+	1.32067e7i	0.142069	+	0.142069i
$454$			3.58345e6i			0.0382943i
$455$	4.45094e7	−	5.87584e7i	0.472517	−	0.623786i
$456$	−2.59305e7			−0.273475
$457$	−3.23415e7	+	3.23415e7i	−0.338853	+	0.338853i	−0.855936	−	0.517083i	$-0.827018\pi$
$457$	−3.23415e7	+	3.23415e7i	−0.338853	+	0.338853i	0.517083	+	0.855936i	$0.327018\pi$
$458$	−8.53542e7	−	8.53542e7i	−0.888441	−	0.888441i
$459$			2.50200e7i			0.258731i
$460$	1.04987e7	+	7.60876e7i	0.107860	+	0.781700i
$461$	8.77131e7			0.895286			0.447643	−	0.894212i	$-0.352264\pi$
$461$	8.77131e7			0.895286			0.447643	+	0.894212i	$0.352264\pi$
$462$	−1.33021e7	+	1.33021e7i	−0.134894	+	0.134894i
$463$	4.91700e7	+	4.91700e7i	0.495402	+	0.495402i	0.910003	−	0.414601i	$-0.136079\pi$
$463$	4.91700e7	+	4.91700e7i	0.495402	+	0.495402i	−0.414601	+	0.910003i	$0.636079\pi$
$464$			8.68171e6i			0.0869064i
$465$	3.29852e7	−	4.55133e6i	0.328065	−	0.0452668i
$466$	−9.56063e6			−0.0944775
$467$	−9.52295e7	+	9.52295e7i	−0.935020	+	0.935020i	−0.998014	−	0.0629938i	$-0.979935\pi$
$467$	−9.52295e7	+	9.52295e7i	−0.935020	+	0.935020i	0.0629938	+	0.998014i	$0.479935\pi$
$468$	1.57632e7	+	1.57632e7i	0.153782	+	0.153782i
$469$			8.85342e7i			0.858208i
$470$	−2.05558e7	−	1.55710e7i	−0.197989	−	0.149976i
$471$	6.48025e7			0.620196
$472$	−3.16401e7	+	3.16401e7i	−0.300892	+	0.300892i
$473$	−1.29499e7	−	1.29499e7i	−0.122372	−	0.122372i
$474$		−	1.95771e7i		−	0.183829i
$475$	1.38218e8	−	3.88832e7i	1.28968	−	0.362812i
$476$	−4.34771e7			−0.403125
$477$	4.04958e7	−	4.04958e7i	0.373125	−	0.373125i
$478$	8.28027e6	+	8.28027e6i	0.0758160	+	0.0758160i
$479$		−	2.04024e8i		−	1.85642i	−0.372062	−	0.928208i	$-0.621349\pi$
$479$		−	2.04024e8i		−	1.85642i	0.372062	−	0.928208i	$-0.378651\pi$
$480$	6.81545e6	−	8.99731e6i	0.0616270	−	0.0813559i
$481$	−6.06374e7			−0.544886
$482$	−9.43362e7	+	9.43362e7i	−0.842437	+	0.842437i
$483$	−4.35382e7	−	4.35382e7i	−0.386393	−	0.386393i
$484$			2.22712e7i			0.196429i
$485$	−1.98364e7	−	1.43762e8i	−0.173875	−	1.26014i
$486$	5.20704e6			0.0453609
$487$	−1.00420e8	+	1.00420e8i	−0.869424	+	0.869424i	−0.992409	−	0.122984i	$-0.960753\pi$
$487$	−1.00420e8	+	1.00420e8i	−0.869424	+	0.869424i	0.122984	+	0.992409i	$0.460753\pi$
$488$	−3.59929e7	−	3.59929e7i	−0.309711	−	0.309711i
$489$			8.01355e7i			0.685328i
$490$	−5.27712e7	+	7.28143e6i	−0.448548	+	0.0618911i
$491$	−7.28010e7			−0.615025			−0.307512	−	0.951544i	$-0.599497\pi$
$491$	−7.28010e7			−0.615025			−0.307512	+	0.951544i	$0.599497\pi$
$492$	1.78790e7	−	1.78790e7i	0.150124	−	0.150124i
$493$	−3.95976e7	−	3.95976e7i	−0.330467	−	0.330467i
$494$		−	1.49025e8i		−	1.23617i
$495$	2.51110e7	+	1.90215e7i	0.207037	+	0.156830i
$496$	−1.74985e7			−0.143402
$497$	−4.19478e7	+	4.19478e7i	−0.341696	+	0.341696i
$498$	−6.60621e7	−	6.60621e7i	−0.534890	−	0.534890i
$499$		−	1.79824e8i		−	1.44726i	−0.690188	−	0.723630i	$-0.742472\pi$
$499$		−	1.79824e8i		−	1.44726i	0.690188	−	0.723630i	$-0.257528\pi$
$500$	−2.28369e7	+	5.81784e7i	−0.182695	+	0.465427i
$501$	−1.62775e7			−0.129442
$502$	3.53416e7	−	3.53416e7i	0.279367	−	0.279367i
$503$	−5.58642e7	−	5.58642e7i	−0.438965	−	0.438965i	0.452699	−	0.891664i	$-0.350461\pi$
$503$	−5.58642e7	−	5.58642e7i	−0.438965	−	0.438965i	−0.891664	+	0.452699i	$0.850461\pi$
$504$			9.04824e6i			0.0706761i
$505$	−2.18921e7	+	2.89005e7i	−0.169986	+	0.224404i
$506$	1.12654e8			0.869552
$507$	−3.73881e7	+	3.73881e7i	−0.286886	+	0.286886i
$508$	−1.86581e7	−	1.86581e7i	−0.142324	−	0.142324i
$509$			2.14366e6i			0.0162556i	0.999967	+	0.00812779i	$0.00258718\pi$
$509$			2.14366e6i			0.0162556i	−0.999967	+	0.00812779i	$0.997413\pi$
$510$	9.95155e6	+	7.21225e7i	0.0750205	+	0.543701i
$511$	−1.41930e8			−1.06368
$512$	−4.19430e6	+	4.19430e6i	−0.0312500	+	0.0312500i
$513$	−2.46137e7	−	2.46137e7i	−0.182316	−	0.182316i
$514$		−	4.87975e7i		−	0.359342i
$515$	5.10465e7	−	7.04345e6i	0.373718	−	0.0515661i
$516$	−8.80869e6			−0.0641154
$517$	−2.67444e7	+	2.67444e7i	−0.193536	+	0.193536i
$518$	−1.74033e7	−	1.74033e7i	−0.125211	−	0.125211i
$519$			1.10545e8i			0.790744i
$520$	5.17085e7	+	3.91691e7i	0.367749	+	0.278570i
$521$	−5.06571e7			−0.358201			−0.179101	−	0.983831i	$-0.557319\pi$
$521$	−5.06571e7			−0.358201			−0.179101	+	0.983831i	$0.557319\pi$
$522$	−8.24085e6	+	8.24085e6i	−0.0579376	+	0.0579376i
$523$	−1.58594e7	−	1.58594e7i	−0.110862	−	0.110862i	0.649500	−	0.760362i	$-0.274978\pi$
$523$	−1.58594e7	−	1.58594e7i	−0.110862	−	0.110862i	−0.760362	+	0.649500i	$0.774978\pi$
$524$			1.34038e8i			0.931607i
$525$	−1.35680e7	−	4.82300e7i	−0.0937643	−	0.333303i
$526$	3.48549e7			0.239500
$527$	7.98112e7	−	7.98112e7i	0.545296	−	0.545296i
$528$	−1.17061e7	−	1.17061e7i	−0.0795260	−	0.0795260i
$529$			2.20686e8i			1.49076i
$530$	1.00626e8	−	1.32840e8i	0.675899	−	0.892278i
$531$	−6.00667e7			−0.401190
$532$	4.27712e7	−	4.27712e7i	0.284064	−	0.284064i
$533$	1.02753e8	+	1.02753e8i	0.678597	+	0.678597i
$534$		−	6.08277e7i		−	0.399464i
$535$	−1.91437e7	−	1.38742e8i	−0.125016	−	0.906036i
$536$	−7.79118e7			−0.505952
$537$	8.56528e7	−	8.56528e7i	0.553119	−	0.553119i
$538$	5.44406e7	+	5.44406e7i	0.349604	+	0.349604i
$539$			7.81322e7i			0.498958i
$540$	1.50098e7	−	2.07107e6i	0.0953219	−	0.0131526i
$541$	4.43541e7			0.280119			0.140059	−	0.990143i	$-0.455271\pi$
$541$	4.43541e7			0.280119			0.140059	+	0.990143i	$0.455271\pi$
$542$	3.28356e7	−	3.28356e7i	0.206228	−	0.206228i
$543$	7.69603e7	+	7.69603e7i	0.480692	+	0.480692i
$544$		−	3.82607e7i		−	0.237660i
$545$	1.65312e7	+	1.25223e7i	0.102121	+	0.0773563i
$546$	−5.20012e7			−0.319474
$547$	1.89599e7	−	1.89599e7i	0.115844	−	0.115844i	−0.646808	−	0.762653i	$-0.723897\pi$
$547$	1.89599e7	−	1.89599e7i	0.115844	−	0.115844i	0.762653	+	0.646808i	$0.223897\pi$
$548$	−8.02041e6	−	8.02041e6i	−0.0487366	−	0.0487366i
$549$		−	6.83302e7i		−	0.412948i
$550$	7.99505e7	+	4.48436e7i	0.480544	+	0.269533i
$551$	7.79092e7			0.465730
$552$	3.83144e7	−	3.83144e7i	0.227795	−	0.227795i
$553$	3.22915e7	+	3.22915e7i	0.190947	+	0.190947i
$554$			2.05184e8i			1.20674i
$555$	−2.48862e7	+	3.28531e7i	−0.145572	+	0.192175i
$556$	1.57205e8			0.914622
$557$	−1.03290e8	+	1.03290e8i	−0.597712	+	0.597712i	−0.939703	−	0.341991i	$-0.888899\pi$
$557$	−1.03290e8	+	1.03290e8i	−0.597712	+	0.597712i	0.341991	+	0.939703i	$0.388899\pi$
$558$	−1.66099e7	−	1.66099e7i	−0.0956015	−	0.0956015i
$559$		−	5.06245e7i		−	0.289818i
$560$	3.59888e6	+	2.60824e7i	0.0204929	+	0.148519i
$561$	1.06783e8			0.604805
$562$	9.90369e7	−	9.90369e7i	0.557940	−	0.557940i
$563$	1.84599e8	+	1.84599e8i	1.03444	+	1.03444i	0.999385	+	0.0350521i	$0.0111597\pi$
$563$	1.84599e8	+	1.84599e8i	1.03444	+	1.03444i	0.0350521	+	0.999385i	$0.488840\pi$
$564$			1.81919e7i			0.101401i
$565$	−1.31406e8	+	1.81316e7i	−0.728569	+	0.100529i
$566$	8.02806e7			0.442753
$567$	−8.58876e6	+	8.58876e6i	−0.0471174	+	0.0471174i
$568$	−3.69149e7	−	3.69149e7i	−0.201445	−	0.201445i
$569$			9.69662e7i			0.526361i	0.964747	+	0.263180i	$0.0847715\pi$
$569$			9.69662e7i			0.526361i	−0.964747	+	0.263180i	$0.915229\pi$
$570$	−8.07414e7	−	6.11615e7i	−0.435985	−	0.330258i
$571$	−8.24057e7			−0.442638			−0.221319	−	0.975201i	$-0.571036\pi$
$571$	−8.24057e7			−0.442638			−0.221319	+	0.975201i	$0.571036\pi$
$572$	6.72760e7	−	6.72760e7i	0.359478	−	0.359478i
$573$	1.93582e7	+	1.93582e7i	0.102897	+	0.102897i
$574$			5.89812e7i			0.311873i
$575$	−1.46775e8	+	2.61681e8i	−0.772055	+	1.37648i
$576$	−7.96262e6			−0.0416667
$577$	1.75260e8	−	1.75260e8i	0.912336	−	0.912336i	−0.0841201	−	0.996456i	$-0.526808\pi$
$577$	1.75260e8	−	1.75260e8i	0.912336	−	0.912336i	0.996456	+	0.0841201i	$0.0268079\pi$
$578$	7.79579e7	+	7.79579e7i	0.403716	+	0.403716i
$579$		−	1.87150e8i		−	0.964171i
$580$	−2.04773e7	+	2.70328e7i	−0.104951	+	0.138550i
$581$	2.17933e8			1.11120
$582$	−7.23922e7	+	7.23922e7i	−0.367217	+	0.367217i
$583$	−1.72833e8	−	1.72833e8i	−0.872209	−	0.872209i
$584$		−	1.24901e8i		−	0.627085i
$585$	1.19026e7	+	8.62627e7i	0.0594532	+	0.430879i
$586$	−1.50584e7			−0.0748319
$587$	−5.98432e7	+	5.98432e7i	−0.295870	+	0.295870i	−0.839394	−	0.543524i	$-0.817090\pi$
$587$	−5.98432e7	+	5.98432e7i	−0.295870	+	0.295870i	0.543524	+	0.839394i	$0.317090\pi$
$588$	2.65733e7	+	2.65733e7i	0.130711	+	0.130711i
$589$			1.57031e8i			0.768490i
$590$	−1.73148e8	+	2.38911e7i	−0.843065	+	0.116327i
$591$	−1.56166e8			−0.756526
$592$	1.53152e7	−	1.53152e7i	0.0738173	−	0.0738173i
$593$	7.10812e7	+	7.10812e7i	0.340872	+	0.340872i	0.856695	−	0.515823i	$-0.172514\pi$
$593$	7.10812e7	+	7.10812e7i	0.340872	+	0.340872i	−0.515823	+	0.856695i	$0.672514\pi$
$594$		−	2.22232e7i		−	0.106035i
$595$	−1.35377e8	−	1.02548e8i	−0.642680	−	0.486829i
$596$	−1.20957e8			−0.571338
$597$	−2.58274e7	+	2.58274e7i	−0.121383	+	0.121383i
$598$	2.20197e8	+	2.20197e8i	1.02969	+	1.02969i
$599$		−	1.93410e8i		−	0.899911i	−0.893051	−	0.449955i	$-0.851440\pi$
$599$		−	1.93410e8i		−	0.899911i	0.893051	−	0.449955i	$-0.148560\pi$
$600$	4.24433e7	−	1.19401e7i	0.196497	−	0.0552782i
$601$	−2.04018e8			−0.939822			−0.469911	−	0.882714i	$-0.655714\pi$
$601$	−2.04018e8			−0.939822			−0.469911	+	0.882714i	$0.655714\pi$
$602$	1.45295e7	−	1.45295e7i	0.0665981	−	0.0665981i
$603$	−7.39554e7	−	7.39554e7i	−0.337301	−	0.337301i
$604$		−	3.83403e7i		−	0.173998i
$605$	−5.25302e7	+	6.93470e7i	−0.237215	+	0.313156i
$606$	2.55769e7			0.114929
$607$	2.70178e8	−	2.70178e8i	1.20805	−	1.20805i	0.236388	−	0.971659i	$-0.424036\pi$
$607$	2.70178e8	−	2.70178e8i	1.20805	−	1.20805i	0.971659	−	0.236388i	$-0.0759636\pi$
$608$	3.76394e7	+	3.76394e7i	0.167468	+	0.167468i
$609$		−	2.71858e7i		−	0.120362i
$610$	−2.71779e7	−	1.96968e8i	−0.119736	−	0.867774i
$611$	−1.04551e8			−0.458357
$612$	3.63178e7	−	3.63178e7i	0.158440	−	0.158440i
$613$	−1.48040e8	−	1.48040e8i	−0.642685	−	0.642685i	0.308529	−	0.951215i	$-0.400163\pi$
$613$	−1.48040e8	−	1.48040e8i	−0.642685	−	0.642685i	−0.951215	+	0.308529i	$0.900163\pi$
$614$		−	2.58947e8i		−	1.11868i
$615$	9.78417e7	−	1.35003e7i	0.420628	−	0.0580388i
$616$	3.86172e7			0.165211
$617$	−3.46749e7	+	3.46749e7i	−0.147625	+	0.147625i	−0.777056	−	0.629431i	$-0.783288\pi$
$617$	−3.46749e7	+	3.46749e7i	−0.147625	+	0.147625i	0.629431	+	0.777056i	$0.283288\pi$
$618$	−2.57048e7	−	2.57048e7i	−0.108905	−	0.108905i
$619$		−	3.42044e8i		−	1.44215i	−0.692858	−	0.721074i	$-0.743649\pi$
$619$		−	3.42044e8i		−	1.44215i	0.692858	−	0.721074i	$-0.256351\pi$
$620$	−5.44861e7	−	4.12731e7i	−0.228618	−	0.173178i
$621$	7.27375e7			0.303727
$622$	−7.87651e7	+	7.87651e7i	−0.327313	+	0.327313i
$623$	1.00332e8	+	1.00332e8i	0.414932	+	0.414932i
$624$		−	4.57620e7i		−	0.188344i
$625$	−2.08332e8	+	1.27289e8i	−0.853328	+	0.521375i
$626$	−9.70201e7			−0.395493
$627$	−1.05050e8	+	1.05050e8i	−0.426179	+	0.426179i
$628$	−9.40641e7	−	9.40641e7i	−0.379791	−	0.379791i
$629$			1.39706e8i			0.561390i
$630$	−2.13418e7	+	2.81740e7i	−0.0853510	+	0.112675i
$631$	8.36979e7			0.333140			0.166570	−	0.986030i	$-0.446731\pi$
$631$	8.36979e7			0.333140			0.166570	+	0.986030i	$0.446731\pi$
$632$	−2.84171e7	+	2.84171e7i	−0.112572	+	0.112572i
$633$	−4.52391e7	−	4.52391e7i	−0.178362	−	0.178362i
$634$			1.89358e8i			0.743048i
$635$	−1.40886e7	−	1.02105e8i	−0.0550233	−	0.398774i
$636$	−1.17563e8			−0.456983
$637$	−1.52719e8	+	1.52719e8i	−0.590848	+	0.590848i
$638$	3.51713e7	+	3.51713e7i	0.135434	+	0.135434i
$639$		−	7.00806e7i		−	0.268593i
$640$	−2.29530e7	+	3.16708e6i	−0.0875588	+	0.0120815i
$641$	1.80537e8			0.685475			0.342737	−	0.939431i	$-0.388646\pi$
$641$	1.80537e8			0.685475			0.342737	+	0.939431i	$0.388646\pi$
$642$	−6.98643e7	+	6.98643e7i	−0.264028	+	0.264028i
$643$	2.11026e8	+	2.11026e8i	0.793784	+	0.793784i	0.982107	−	0.188324i	$-0.0603054\pi$
$643$	2.11026e8	+	2.11026e8i	0.793784	+	0.793784i	−0.188324	+	0.982107i	$0.560305\pi$
$644$			1.26396e8i			0.473232i
$645$	−2.74281e7	−	2.07768e7i	−0.102216	−	0.0774281i
$646$	−3.43349e8			−1.27362
$647$	1.30845e8	−	1.30845e8i	0.483109	−	0.483109i	−0.423014	−	0.906123i	$-0.639028\pi$
$647$	1.30845e8	−	1.30845e8i	0.483109	−	0.483109i	0.906123	+	0.423014i	$0.139028\pi$
$648$	−7.55827e6	−	7.55827e6i	−0.0277778	−	0.0277778i
$649$			2.56360e8i			0.937812i
$650$	6.86209e7	+	2.43926e8i	0.249871	+	0.888215i
$651$	5.47945e7			0.198607
$652$	1.16321e8	−	1.16321e8i	0.419676	−	0.419676i
$653$	−3.15489e8	−	3.15489e8i	−1.13304	−	1.13304i	−0.989669	−	0.143371i	$-0.954206\pi$
$653$	−3.15489e8	−	3.15489e8i	−1.13304	−	1.13304i	−0.143371	−	0.989669i	$-0.545794\pi$
$654$		−	1.46301e7i		−	0.0523014i
$655$	−3.16150e8	+	4.17361e8i	−1.12504	+	1.48521i
$656$	−5.19046e7			−0.183863
$657$	1.18558e8	−	1.18558e8i	0.418057	−	0.418057i
$658$	−3.00067e7	−	3.00067e7i	−0.105327	−	0.105327i
$659$		−	1.90964e8i		−	0.667260i	−0.942704	−	0.333630i	$-0.891726\pi$
$659$		−	1.90964e8i		−	0.667260i	0.942704	−	0.333630i	$-0.108274\pi$
$660$	−8.83915e6	−	6.40605e7i	−0.0307453	−	0.222822i
$661$	4.57014e8			1.58243			0.791216	−	0.611536i	$-0.209448\pi$
$661$	4.57014e8			1.58243			0.791216	+	0.611536i	$0.209448\pi$
$662$	−1.51512e8	+	1.51512e8i	−0.522245	+	0.522245i
$663$	2.08722e8	+	2.08722e8i	0.716189	+	0.716189i
$664$			1.91785e8i			0.655104i
$665$	2.34062e8	−	3.22961e7i	0.795913	−	0.109821i
$666$	2.90750e7			0.0984231
$667$	−1.15117e8	+	1.15117e8i	−0.387938	+	0.387938i
$668$	2.36276e7	+	2.36276e7i	0.0792667	+	0.0792667i
$669$		−	2.17069e8i		−	0.724968i
$670$	−2.42599e8	−	1.83768e8i	−0.806610	−	0.611006i
$671$	−2.91628e8			−0.965299
$672$	1.31340e7	−	1.31340e7i	0.0432801	−	0.0432801i
$673$	2.86067e8	+	2.86067e8i	0.938474	+	0.938474i	0.998214	−	0.0597400i	$-0.0190272\pi$
$673$	2.86067e8	+	2.86067e8i	0.938474	+	0.938474i	−0.0597400	+	0.998214i	$0.519027\pi$
$674$		−	1.79548e8i		−	0.586411i
$675$	5.16217e7	+	2.89542e7i	0.167850	+	0.0941458i
$676$	1.08541e8			0.351362
$677$	2.60104e8	−	2.60104e8i	0.838266	−	0.838266i	−0.150365	−	0.988631i	$-0.548045\pi$
$677$	2.60104e8	−	2.60104e8i	0.838266	−	0.838266i	0.988631	+	0.150365i	$0.0480448\pi$
$678$	6.61705e7	+	6.61705e7i	0.212312	+	0.212312i
$679$		−	2.38815e8i		−	0.762872i
$680$	9.02442e7	−	1.19135e8i	0.287007	−	0.378888i
$681$	9.87483e6			0.0312672
$682$	−7.08898e7	+	7.08898e7i	−0.223476	+	0.223476i
$683$	−9.24222e7	−	9.24222e7i	−0.290078	−	0.290078i	0.547033	−	0.837111i	$-0.315757\pi$
$683$	−9.24222e7	−	9.24222e7i	−0.290078	−	0.290078i	−0.837111	+	0.547033i	$0.815757\pi$
$684$			7.14561e7i			0.223291i
$685$	−6.05614e6	−	4.38911e7i	−0.0188419	−	0.136554i
$686$	−2.24560e8			−0.695602
$687$	−2.35208e8	+	2.35208e8i	−0.725409	+	0.725409i
$688$	1.27863e7	+	1.27863e7i	0.0392625	+	0.0392625i
$689$		−	6.75648e8i		−	2.06568i
$690$	2.09673e8	−	2.89309e7i	0.638256	−	0.0880673i
$691$	4.54828e8			1.37852			0.689261	−	0.724513i	$-0.257935\pi$
$691$	4.54828e8			1.37852			0.689261	+	0.724513i	$0.257935\pi$
$692$	1.60461e8	−	1.60461e8i	0.484230	−	0.484230i
$693$	3.66562e7	+	3.66562e7i	0.110141	+	0.110141i
$694$			2.41564e8i			0.722692i
$695$	4.89498e8	+	3.70794e8i	1.45813	+	1.10453i
$696$	2.39240e7			0.0709587
$697$	2.36739e8	−	2.36739e8i	0.699150	−	0.699150i
$698$	3.12909e8	+	3.12909e8i	0.920135	+	0.920135i
$699$			2.63460e7i			0.0771406i
$700$	−5.03136e7	+	8.97028e7i	−0.146687	+	0.261524i
$701$	−3.98272e8			−1.15618			−0.578090	−	0.815973i	$-0.696202\pi$
$701$	−3.98272e8			−1.15618			−0.578090	+	0.815973i	$0.696202\pi$
$702$	4.34382e7	−	4.34382e7i	0.125563	−	0.125563i
$703$	−1.37438e8	−	1.37438e8i	−0.395586	−	0.395586i
$704$			3.39839e7i			0.0973991i
$705$	−4.29087e7	+	5.66452e7i	−0.122455	+	0.161658i
$706$	7.56520e7			0.214984
$707$	−4.21879e7	+	4.21879e7i	−0.119380	+	0.119380i
$708$	8.71897e7	+	8.71897e7i	0.245678	+	0.245678i
$709$			1.94492e8i			0.545711i	0.962055	+	0.272855i	$0.0879680\pi$
$709$			1.94492e8i			0.545711i	−0.962055	+	0.272855i	$0.912032\pi$
$710$	−2.78741e7	−	2.02014e8i	−0.0778801	−	0.564425i
$711$	−5.39481e7			−0.150095
$712$	−8.82943e7	+	8.82943e7i	−0.244621	+	0.244621i
$713$	−2.32025e8	−	2.32025e8i	−0.640128	−	0.640128i
$714$			1.19809e8i			0.329150i
$715$	3.68163e8	−	5.07995e7i	1.00721	−	0.138977i
$716$	−2.48659e8			−0.677430
$717$	2.28177e7	−	2.28177e7i	0.0619035	−	0.0619035i
$718$	−8.55984e7	−	8.55984e7i	−0.231256	−	0.231256i
$719$			5.36699e8i			1.44392i	0.691934	+	0.721961i	$0.256759\pi$
$719$			5.36699e8i			1.44392i	−0.691934	+	0.721961i	$0.743241\pi$
$720$	−2.47937e7	−	1.87812e7i	−0.0664268	−	0.0503182i
$721$	8.47977e7			0.226245
$722$	1.49591e8	−	1.49591e8i	0.397460	−	0.397460i
$723$	2.59960e8	+	2.59960e8i	0.687847	+	0.687847i
$724$		−	2.23423e8i		−	0.588726i
$725$	−1.27522e8	+	3.58744e7i	−0.334636	+	0.0941393i
$726$	6.13721e7			0.160384
$727$	6.70897e7	−	6.70897e7i	0.174603	−	0.174603i	−0.614395	−	0.788998i	$-0.710600\pi$
$727$	6.70897e7	−	6.70897e7i	0.174603	−	0.174603i	0.788998	+	0.614395i	$0.210600\pi$
$728$	7.54823e7	+	7.54823e7i	0.195637	+	0.195637i
$729$		−	1.43489e7i		−	0.0370370i
$730$	2.94599e8	−	3.88911e8i	0.757292	−	0.999727i
$731$	−1.16637e8			−0.298596
$732$	−9.91847e7	+	9.91847e7i	−0.252878	+	0.252878i
$733$	−2.35707e7	−	2.35707e7i	−0.0598495	−	0.0598495i	0.676549	−	0.736398i	$-0.263475\pi$
$733$	−2.35707e7	−	2.35707e7i	−0.0598495	−	0.0598495i	−0.736398	+	0.676549i	$0.763475\pi$
$734$		−	1.03727e8i		−	0.262302i
$735$	2.00653e7	+	1.45420e8i	0.0505339	+	0.366238i
$736$	−1.11231e8			−0.278991
$737$	−3.15636e8	+	3.15636e8i	−0.788467	+	0.788467i
$738$	−4.92688e7	−	4.92688e7i	−0.122575	−	0.122575i
$739$			5.18563e8i			1.28490i	0.766329	+	0.642448i	$0.222081\pi$
$739$			5.18563e8i			1.28490i	−0.766329	+	0.642448i	$0.777919\pi$
$740$	8.38114e7	−	1.15644e7i	0.206827	−	0.0285383i
$741$	−4.10666e8			−1.00933
$742$	1.93915e8	−	1.93915e8i	0.474678	−	0.474678i
$743$	−2.89312e8	−	2.89312e8i	−0.705343	−	0.705343i	0.260209	−	0.965552i	$-0.416208\pi$
$743$	−2.89312e8	−	2.89312e8i	−0.705343	−	0.705343i	−0.965552	+	0.260209i	$0.916208\pi$
$744$			4.82202e7i			0.117087i
$745$	−3.76631e8	−	2.85298e8i	−0.910851	−	0.689968i
$746$	−3.13882e7			−0.0756048
$747$	−1.82046e8	+	1.82046e8i	−0.436736	+	0.436736i
$748$	−1.55001e8	−	1.55001e8i	−0.370366	−	0.370366i
$749$		−	2.30476e8i		−	0.548504i
$750$	1.60321e8	+	6.29311e7i	0.380020	+	0.149170i
$751$	3.00670e8			0.709857			0.354928	−	0.934893i	$-0.384505\pi$
$751$	3.00670e8			0.709857			0.354928	+	0.934893i	$0.384505\pi$
$752$	2.64065e7	−	2.64065e7i	0.0620950	−	0.0620950i
$753$	−9.73901e7	−	9.73901e7i	−0.228102	−	0.228102i
$754$			1.37494e8i			0.320752i
$755$	9.04319e7	−	1.19382e8i	0.210126	−	0.277395i
$756$	2.49340e7			0.0577068
$757$	−4.36582e8	+	4.36582e8i	−1.00642	+	1.00642i	−0.00643784	+	0.999979i	$0.502049\pi$
$757$	−4.36582e8	+	4.36582e8i	−1.00642	+	1.00642i	−0.999979	+	0.00643784i	$0.997951\pi$
$758$	−1.44468e8	−	1.44468e8i	−0.331714	−	0.331714i
$759$		−	3.10438e8i		−	0.709986i
$760$	2.84212e7	+	2.05979e8i	0.0647444	+	0.469226i
$761$	5.85378e8			1.32826			0.664128	−	0.747619i	$-0.268803\pi$
$761$	5.85378e8			1.32826			0.664128	+	0.747619i	$0.268803\pi$
$762$	−5.14157e7	+	5.14157e7i	−0.116207	+	0.116207i
$763$	2.41316e7	+	2.41316e7i	0.0543267	+	0.0543267i
$764$		−	5.61988e7i		−	0.126022i
$765$	1.98746e8	−	2.74232e7i	0.443930	−	0.0612540i
$766$	6.19568e6			0.0137849
$767$	−5.01089e8	+	5.01089e8i	−1.11053	+	1.11053i
$768$	1.15581e7	+	1.15581e7i	0.0255155	+	0.0255155i
$769$			10186.9i			2.24008e-5i	1.00000		1.12004e-5i	$3.56520e-6\pi$
$769$			10186.9i			2.24008e-5i	−1.00000		1.12004e-5i	$0.999996\pi$
$770$	1.20245e8	+	9.10850e7i	0.263386	+	0.199515i
$771$	−1.34470e8			−0.293402
$772$	−2.71657e8	+	2.71657e8i	−0.590432	+	0.590432i
$773$	−1.49946e8	−	1.49946e8i	−0.324636	−	0.324636i	0.525906	−	0.850542i	$-0.323726\pi$
$773$	−1.49946e8	−	1.49946e8i	−0.324636	−	0.324636i	−0.850542	+	0.525906i	$0.823726\pi$
$774$			2.42739e7i			0.0523500i
$775$	−7.23070e7	−	2.57029e8i	−0.155337	−	0.552175i
$776$	2.10162e8			0.449747
$777$	−4.79578e7	+	4.79578e7i	−0.102234	+	0.102234i
$778$	−1.82639e8	−	1.82639e8i	−0.387843	−	0.387843i
$779$			4.65789e8i			0.985319i
$780$	1.07937e8	−	1.42492e8i	0.227451	−	0.300266i
$781$	−2.99099e8			−0.627858
$782$	5.07326e8	−	5.07326e8i	1.06088	−	1.06088i
$783$	2.27091e7	+	2.27091e7i	0.0473058	+	0.0473058i
$784$		−	7.71449e7i		−	0.160088i
$785$	−7.10270e7	−	5.14758e8i	−0.146830	−	1.06413i
$786$	3.69364e8			0.760654
$787$	3.29898e8	−	3.29898e8i	0.676793	−	0.676793i	−0.282481	−	0.959273i	$-0.591157\pi$
$787$	3.29898e8	−	3.29898e8i	0.676793	−	0.676793i	0.959273	+	0.282481i	$0.0911573\pi$
$788$	2.26683e8	+	2.26683e8i	0.463276	+	0.463276i
$789$		−	9.60487e7i		−	0.195551i
$790$	−1.55511e8	+	2.14575e7i	−0.315412	+	0.0435210i
$791$	−2.18290e8			−0.441067
$792$	−3.22581e7	+	3.22581e7i	−0.0649327	+	0.0649327i
$793$	−5.70025e8	−	5.70025e8i	−1.14307	−	1.14307i
$794$			4.06885e8i			0.812849i
$795$	−3.66063e8	−	2.77292e8i	−0.728542	−	0.551869i
$796$	7.49795e7			0.148663
$797$	−2.30664e8	+	2.30664e8i	−0.455622	+	0.455622i	−0.897215	−	0.441593i	$-0.854413\pi$
$797$	−2.30664e8	+	2.30664e8i	−0.455622	+	0.455622i	0.441593	+	0.897215i	$0.354413\pi$
$798$	−1.17863e8	−	1.17863e8i	−0.231937	−	0.231937i
$799$			2.40881e8i			0.472240i
$800$	−7.89402e7	−	4.42769e7i	−0.154180	−	0.0864784i
$801$	−1.67621e8			−0.326161
$802$	1.38798e8	−	1.38798e8i	0.269066	−	0.269066i
$803$	−5.05997e8	−	5.05997e8i	−0.977241	−	0.977241i
$804$			2.14700e8i			0.413108i
$805$	−2.98125e8	+	3.93565e8i	−0.571493	+	0.754448i
$806$	−2.77127e8			−0.529265
$807$	1.50021e8	−	1.50021e8i	0.285450	−	0.285450i
$808$	−3.71262e7	−	3.71262e7i	−0.0703795	−	0.0703795i
$809$			1.15009e8i			0.217213i	0.994085	+	0.108607i	$0.0346389\pi$
$809$			1.15009e8i			0.217213i	−0.994085	+	0.108607i	$0.965361\pi$
$810$	−5.70719e6	−	4.13621e7i	−0.0107391	−	0.0778300i
$811$	7.36769e8			1.38124			0.690619	−	0.723218i	$-0.257338\pi$
$811$	7.36769e8			1.38124			0.690619	+	0.723218i	$0.257338\pi$
$812$	−3.94615e7	+	3.94615e7i	−0.0737064	+	0.0737064i
$813$	−9.04842e7	−	9.04842e7i	−0.168384	−	0.168384i
$814$		−	1.24090e8i		−	0.230072i
$815$	6.36556e8	−	8.78327e7i	1.17588	−	0.162250i
$816$	−1.05434e8			−0.194049
$817$	1.14743e8	−	1.14743e8i	0.210407	−	0.210407i
$818$	−2.65287e7	−	2.65287e7i	−0.0484680	−	0.0484680i
$819$			1.43298e8i			0.260849i
$820$	−1.61618e8	−	1.22426e8i	−0.293123	−	0.222040i
$821$	5.00735e8			0.904854			0.452427	−	0.891802i	$-0.350558\pi$
$821$	5.00735e8			0.904854			0.452427	+	0.891802i	$0.350558\pi$
$822$	−2.21017e7	+	2.21017e7i	−0.0397932	+	0.0397932i
$823$	6.80752e6	+	6.80752e6i	0.0122121	+	0.0122121i	0.713186	−	0.700974i	$-0.247251\pi$
$823$	6.80752e6	+	6.80752e6i	0.0122121	+	0.0122121i	−0.700974	+	0.713186i	$0.747251\pi$
$824$			7.46236e7i			0.133381i
$825$	1.23574e8	−	2.20318e8i	0.220073	−	0.392362i
$826$	−2.87631e8			−0.510382
$827$	−2.59523e7	+	2.59523e7i	−0.0458838	+	0.0458838i	−0.729676	−	0.683793i	$-0.760329\pi$
$827$	−2.59523e7	+	2.59523e7i	−0.0458838	+	0.0458838i	0.683793	+	0.729676i	$0.260329\pi$
$828$	−1.05582e8	−	1.05582e8i	−0.185994	−	0.185994i
$829$			3.24193e8i			0.569037i	0.958671	+	0.284518i	$0.0918337\pi$
$829$			3.24193e8i			0.569037i	−0.958671	+	0.284518i	$0.908166\pi$
$830$	−4.52356e8	+	5.97172e8i	−0.791127	+	1.04440i
$831$	5.65421e8			0.985300
$832$	−6.64259e7	+	6.64259e7i	−0.115337	+	0.115337i
$833$	3.51860e8	+	3.51860e8i	0.608744	+	0.608744i
$834$		−	4.33206e8i		−	0.746786i
$835$	1.78410e7	+	1.29300e8i	0.0306451	+	0.222096i
$836$	3.04969e8			0.521960
$837$	−4.57715e7	+	4.57715e7i	−0.0780583	+	0.0780583i
$838$	−7.50269e7	−	7.50269e7i	−0.127493	−	0.127493i
$839$			5.69147e8i			0.963692i	0.876256	+	0.481846i	$0.160034\pi$
$839$			5.69147e8i			0.963692i	−0.876256	+	0.481846i	$0.839966\pi$
$840$	7.18746e7	−	9.91735e6i	0.121266	−	0.0167324i
$841$	5.22943e8			0.879157
$842$	−4.05570e8	+	4.05570e8i	−0.679406	+	0.679406i
$843$	−2.72913e8	−	2.72913e8i	−0.455557	−	0.455557i
$844$			1.31334e8i			0.218448i
$845$	3.37972e8	+	2.56013e8i	0.560157	+	0.424318i
$846$	5.01310e7			0.0827934
$847$	−1.01230e8	+	1.01230e8i	−0.166594	+	0.166594i
$848$	1.70649e8	+	1.70649e8i	0.279844	+	0.279844i
$849$		−	2.21227e8i		−	0.361506i
$850$	5.61997e8	−	1.58100e8i	0.915118	−	0.257440i
$851$	4.06151e8			0.659021
$852$	−1.01726e8	+	1.01726e8i	−0.164479	+	0.164479i
$853$	2.70461e7	+	2.70461e7i	0.0435770	+	0.0435770i	0.728560	−	0.684982i	$-0.240190\pi$
$853$	2.70461e7	+	2.70461e7i	0.0435770	+	0.0435770i	−0.684982	+	0.728560i	$0.740190\pi$
$854$		−	3.27201e8i		−	0.525340i
$855$	−1.68541e8	+	2.22497e8i	−0.269654	+	0.355980i
$856$	2.02823e8			0.323367
$857$	1.75013e8	−	1.75013e8i	0.278052	−	0.278052i	−0.554279	−	0.832331i	$-0.687006\pi$
$857$	1.75013e8	−	1.75013e8i	0.278052	−	0.278052i	0.832331	+	0.554279i	$0.187006\pi$
$858$	−1.85391e8	−	1.85391e8i	−0.293512	−	0.293512i
$859$		−	3.42840e8i		−	0.540894i	−0.962735	−	0.270447i	$-0.912828\pi$
$859$		−	3.42840e8i		−	0.540894i	0.962735	−	0.270447i	$-0.0871716\pi$
$860$	9.65479e6	+	6.99718e7i	0.0151792	+	0.110009i
$861$	1.62533e8			0.254644
$862$	1.01735e8	−	1.01735e8i	0.158836	−	0.158836i
$863$	7.99150e8	+	7.99150e8i	1.24336	+	1.24336i	0.958600	+	0.284757i	$0.0919130\pi$
$863$	7.99150e8	+	7.99150e8i	1.24336	+	1.24336i	0.284757	+	0.958600i	$0.408087\pi$
$864$			2.19424e7i			0.0340207i
$865$	8.78111e8	−	1.21163e8i	1.35675	−	0.187206i
$866$	3.87906e8			0.597273
$867$	2.14827e8	−	2.14827e8i	0.329633	−	0.329633i
$868$	−7.95369e7	−	7.95369e7i	−0.121621	−	0.121621i
$869$			2.30247e8i			0.350860i
$870$	7.44935e7	+	5.64287e7i	0.113126	+	0.0856924i
$871$	−1.23390e9			−1.86735
$872$	−2.12363e7	+	2.12363e7i	−0.0320280	+	0.0320280i
$873$	1.99489e8	+	1.99489e8i	0.299831	+	0.299831i
$874$			9.98177e8i			1.49511i
$875$	−3.68243e8	+	1.60640e8i	−0.549681	+	0.239789i
$876$	−3.44186e8			−0.512013
$877$	5.77037e8	−	5.77037e8i	0.855470	−	0.855470i	−0.135331	−	0.990800i	$-0.543210\pi$
$877$	5.77037e8	−	5.77037e8i	0.855470	−	0.855470i	0.990800	+	0.135331i	$0.0432097\pi$
$878$	1.51173e8	+	1.51173e8i	0.223353	+	0.223353i
$879$			4.14961e7i			0.0611000i
$880$	−8.01566e7	+	1.05818e8i	−0.117623	+	0.155278i
$881$	−2.68153e8			−0.392153			−0.196077	−	0.980589i	$-0.562820\pi$
$881$	−2.68153e8			−0.392153			−0.196077	+	0.980589i	$0.562820\pi$
$882$	7.32274e7	−	7.32274e7i	0.106725	−	0.106725i
$883$	4.48535e8	+	4.48535e8i	0.651499	+	0.651499i	0.953354	−	0.301855i	$-0.0976057\pi$
$883$	4.48535e8	+	4.48535e8i	0.651499	+	0.651499i	−0.301855	+	0.953354i	$0.597606\pi$
$884$		−	6.05941e8i		−	0.877149i
$885$	6.58362e7	+	4.77139e8i	0.0949807	+	0.688359i
$886$	1.72979e8			0.248710
$887$	4.07398e8	−	4.07398e8i	0.583779	−	0.583779i	−0.352161	−	0.935940i	$-0.614553\pi$
$887$	4.07398e8	−	4.07398e8i	0.583779	−	0.583779i	0.935940	+	0.352161i	$0.114553\pi$
$888$	−4.22038e7	−	4.22038e7i	−0.0602716	−	0.0602716i
$889$		−	1.69616e8i		−	0.241413i
$890$	−4.83184e8	+	6.66703e7i	−0.685398	+	0.0945720i
$891$	−6.12400e7			−0.0865770
$892$	−3.15086e8	+	3.15086e8i	−0.443950	+	0.443950i
$893$	−2.36970e8	−	2.36970e8i	−0.332766	−	0.332766i
$894$			3.33319e8i			0.466495i
$895$	−7.74263e8	−	5.86503e8i	−1.07999	−	0.818089i
$896$	−3.81292e7			−0.0530071
$897$	6.06792e8	−	6.06792e8i	0.840741	−	0.840741i
$898$	−3.77423e8	−	3.77423e8i	−0.521193	−	0.521193i
$899$		−	1.44879e8i		−	0.199401i
$900$	−3.29030e7	−	1.16960e8i	−0.0451344	−	0.160439i
$901$	−1.55667e9			−2.12825
$902$	−2.10276e8	+	2.10276e8i	−0.286529	+	0.286529i
$903$	−4.00386e7	−	4.00386e7i	−0.0543771	−	0.0543771i
$904$		−	1.92100e8i		−	0.260028i
$905$	5.26981e8	−	6.95686e8i	0.710967	−	0.938572i
$906$	−1.05653e8			−0.142069
$907$	−1.38639e8	+	1.38639e8i	−0.185808	+	0.185808i	−0.793881	−	0.608073i	$-0.791943\pi$
$907$	−1.38639e8	+	1.38639e8i	−0.185808	+	0.185808i	0.608073	+	0.793881i	$0.291943\pi$
$908$	−1.43338e7	−	1.43338e7i	−0.0191471	−	0.0191471i
$909$		−	7.04818e7i		−	0.0938394i
$910$	5.69960e7	+	4.13071e8i	0.0756346	+	0.548152i
$911$	7.12128e8			0.941896			0.470948	−	0.882161i	$-0.343912\pi$
$911$	7.12128e8			0.941896			0.470948	+	0.882161i	$0.343912\pi$
$912$	1.03722e8	−	1.03722e8i	0.136737	−	0.136737i
$913$	7.76957e8	+	7.76957e8i	1.02090	+	1.02090i
$914$		−	2.58732e8i		−	0.338853i
$915$	−5.42781e8	+	7.48935e7i	−0.708534	+	0.0977644i
$916$	6.82834e8			0.888441
$917$	−6.09249e8	+	6.09249e8i	−0.790108	+	0.790108i
$918$	−1.00080e8	−	1.00080e8i	−0.129366	−	0.129366i
$919$		−	4.34345e8i		−	0.559613i	−0.960056	−	0.279807i	$-0.909730\pi$
$919$		−	4.34345e8i		−	0.559613i	0.960056	−	0.279807i	$-0.0902704\pi$
$920$	−3.46345e8	−	2.62356e8i	−0.444780	−	0.336920i
$921$	−7.13575e8			−0.913400
$922$	−3.50852e8	+	3.50852e8i	−0.447643	+	0.447643i
$923$	−5.84627e8	−	5.84627e8i	−0.743488	−	0.743488i
$924$		−	1.06416e8i		−	0.134894i
$925$	2.88245e8	+	1.61674e8i	0.364197	+	0.204275i
$926$	−3.93360e8			−0.495402
$927$	−7.08341e7	+	7.08341e7i	−0.0889208	+	0.0889208i
$928$	−3.47269e7	−	3.47269e7i	−0.0434532	−	0.0434532i
$929$			3.67090e8i			0.457852i	0.973444	+	0.228926i	$0.0735213\pi$
$929$			3.67090e8i			0.457852i	−0.973444	+	0.228926i	$0.926479\pi$
$930$	−1.13735e8	+	1.50146e8i	−0.141399	+	0.186666i
$931$	−6.92294e8			−0.857909
$932$	3.82425e7	−	3.82425e7i	0.0472388	−	0.0472388i
$933$	2.17051e8	+	2.17051e8i	0.267250	+	0.267250i
$934$		−	7.61836e8i		−	0.935020i
$935$	−1.17040e8	−	8.48233e8i	−0.143186	−	1.03772i
$936$	−1.26105e8			−0.153782
$937$	1.11262e8	−	1.11262e8i	0.135248	−	0.135248i	−0.636242	−	0.771490i	$-0.719512\pi$
$937$	1.11262e8	−	1.11262e8i	0.135248	−	0.135248i	0.771490	+	0.636242i	$0.219512\pi$
$938$	−3.54137e8	−	3.54137e8i	−0.429104	−	0.429104i
$939$			2.67356e8i			0.322919i
$940$	1.44507e8	−	1.99393e7i	0.173983	−	0.0240064i
$941$	−7.63794e8			−0.916659			−0.458329	−	0.888782i	$-0.651552\pi$
$941$	−7.63794e8			−0.916659			−0.458329	+	0.888782i	$0.651552\pi$
$942$	−2.59210e8	+	2.59210e8i	−0.310098	+	0.310098i
$943$	−6.88241e8	−	6.88241e8i	−0.820739	−	0.820739i
$944$		−	2.53120e8i		−	0.300892i
$945$	7.76385e7	+	5.88110e7i	0.0919987	+	0.0696888i
$946$	1.03599e8			0.122372
$947$	1.13872e8	−	1.13872e8i	0.134081	−	0.134081i	−0.636881	−	0.770962i	$-0.719776\pi$
$947$	1.13872e8	−	1.13872e8i	0.134081	−	0.134081i	0.770962	+	0.636881i	$0.219776\pi$
$948$	7.83084e7	+	7.83084e7i	0.0919143	+	0.0919143i
$949$		−	1.97807e9i		−	2.31443i
$950$	−3.97339e8	+	7.08405e8i	−0.463436	+	0.826248i
$951$	5.21810e8			0.606696
$952$	1.73908e8	−	1.73908e8i	0.201563	−	0.201563i
$953$	9.79865e8	+	9.79865e8i	1.13211	+	1.13211i	0.989826	+	0.142280i	$0.0454434\pi$
$953$	9.79865e8	+	9.79865e8i	1.13211	+	1.13211i	0.142280	+	0.989826i	$0.454557\pi$
$954$			3.23966e8i			0.373125i
$955$	1.32554e8	−	1.74989e8i	0.152189	−	0.200910i
$956$	−6.62422e7			−0.0758160
$957$	9.69207e7	−	9.69207e7i	0.110581	−	0.110581i
$958$	8.16097e8	+	8.16097e8i	0.928208	+	0.928208i
$959$		−	7.29112e7i		−	0.0826682i
$960$	8.72746e6	+	6.32510e7i	0.00986447	+	0.0714914i
$961$	−5.95491e8			−0.670973
$962$	2.42550e8	−	2.42550e8i	0.272443	−	0.272443i
$963$	1.92523e8	+	1.92523e8i	0.215578	+	0.215578i
$964$		−	7.54690e8i		−	0.842437i
$965$	−1.48662e9	+	2.05126e8i	−1.65432	+	0.228265i
$966$	3.48305e8			0.386393
$967$	−2.18628e8	+	2.18628e8i	−0.241783	+	0.241783i	−0.817588	−	0.575804i	$-0.804689\pi$
$967$	−2.18628e8	+	2.18628e8i	−0.241783	+	0.241783i	0.575804	+	0.817588i	$0.304689\pi$
$968$	−8.90846e7	−	8.90846e7i	−0.0982147	−	0.0982147i
$969$			9.46159e8i			1.03990i
$970$	6.54392e8	+	4.95701e8i	0.717006	+	0.543131i
$971$	−9.21253e8			−1.00628			−0.503142	−	0.864203i	$-0.667823\pi$
$971$	−9.21253e8			−1.00628			−0.503142	+	0.864203i	$0.667823\pi$
$972$	−2.08281e7	+	2.08281e7i	−0.0226805	+	0.0226805i
$973$	7.14552e8	+	7.14552e8i	0.775703	+	0.775703i
$974$		−	8.03357e8i		−	0.869424i
$975$	6.72181e8	−	1.89097e8i	0.725225	−	0.204019i
$976$	2.87943e8			0.309711
$977$	−1.10660e8	+	1.10660e8i	−0.118661	+	0.118661i	−0.763944	−	0.645283i	$-0.776740\pi$
$977$	−1.10660e8	+	1.10660e8i	−0.118661	+	0.118661i	0.645283	+	0.763944i	$0.276740\pi$
$978$	−3.20542e8	−	3.20542e8i	−0.342664	−	0.342664i
$979$			7.15395e8i			0.762426i
$980$	1.81959e8	−	2.40210e8i	0.193328	−	0.255219i
$981$	−4.03158e7			−0.0427039
$982$	2.91204e8	−	2.91204e8i	0.307512	−	0.307512i
$983$	−5.81692e8	−	5.81692e8i	−0.612397	−	0.612397i	0.331173	−	0.943570i	$-0.392555\pi$
$983$	−5.81692e8	−	5.81692e8i	−0.612397	−	0.612397i	−0.943570	+	0.331173i	$0.892555\pi$
$984$			1.43032e8i			0.150124i
$985$	1.71166e8	+	1.24050e9i	0.179106	+	1.29804i
$986$	3.16780e8			0.330467
$987$	−8.26887e7	+	8.26887e7i	−0.0859993	+	0.0859993i
$988$	5.96102e8	+	5.96102e8i	0.618087	+	0.618087i
$989$			3.39084e8i			0.350525i
$990$	−1.76530e8	+	2.43578e7i	−0.181934	+	0.0251034i
$991$	−2.16687e8			−0.222644			−0.111322	−	0.993784i	$-0.535509\pi$
$991$	−2.16687e8			−0.222644			−0.111322	+	0.993784i	$0.535509\pi$
$992$	6.99940e7	−	6.99940e7i	0.0717011	−	0.0717011i
$993$	4.17519e8	+	4.17519e8i	0.426411	+	0.426411i
$994$		−	3.35583e8i		−	0.341696i
$995$	2.33468e8	+	1.76852e8i	0.237005	+	0.179531i
$996$	5.28497e8			0.534890
$997$	−3.07388e8	+	3.07388e8i	−0.310172	+	0.310172i	−0.844976	−	0.534804i	$-0.820385\pi$
$997$	−3.07388e8	+	3.07388e8i	−0.310172	+	0.310172i	0.534804	+	0.844976i	$0.320385\pi$
$998$	7.19297e8	+	7.19297e8i	0.723630	+	0.723630i
$999$		−	8.01213e7i		−	0.0803621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.7.f.b.13.4	yes	8
3.2	odd	2		90.7.g.f.73.2		8
4.3	odd	2		240.7.bg.b.193.2		8
5.2	odd	4	inner	30.7.f.b.7.4	✓	8
5.3	odd	4		150.7.f.h.7.1		8
5.4	even	2		150.7.f.h.43.1		8
15.2	even	4		90.7.g.f.37.2		8
15.8	even	4		450.7.g.r.307.2		8
15.14	odd	2		450.7.g.r.343.2		8
20.7	even	4		240.7.bg.b.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.7.f.b.7.4	✓	8	5.2	odd	4	inner
30.7.f.b.13.4	yes	8	1.1	even	1	trivial
90.7.g.f.37.2		8	15.2	even	4
90.7.g.f.73.2		8	3.2	odd	2
150.7.f.h.7.1		8	5.3	odd	4
150.7.f.h.43.1		8	5.4	even	2
240.7.bg.b.97.2		8	20.7	even	4
240.7.bg.b.193.2		8	4.3	odd	2
450.7.g.r.307.2		8	15.8	even	4
450.7.g.r.343.2		8	15.14	odd	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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	30.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 4.00000i) q^{2} +(11.0227 + 11.0227i) q^{3} -32.0000i q^{4} +(75.4773 - 99.6402i) q^{5} -88.1816 q^{6} +(145.451 - 145.451i) q^{7} +(128.000 + 128.000i) q^{8} +243.000i q^{9} +(96.6517 + 700.470i) q^{10} +1037.11 q^{11} +(352.727 - 352.727i) q^{12} +(2027.16 + 2027.16i) q^{13} +1163.61i q^{14} +(1930.27 - 266.341i) q^{15} -1024.00 q^{16} +(4670.49 - 4670.49i) q^{17} +(-972.000 - 972.000i) q^{18} +9189.32i q^{19} +(-3188.49 - 2415.27i) q^{20} +3206.54 q^{21} +(-4148.42 + 4148.42i) q^{22} +(-13577.9 - 13577.9i) q^{23} +2821.81i q^{24} +(-4231.35 - 15041.2i) q^{25} -16217.3 q^{26} +(-2678.52 + 2678.52i) q^{27} +(-4654.44 - 4654.44i) q^{28} -8478.24i q^{29} +(-6655.71 + 8786.44i) q^{30} +17088.4 q^{31} +(4096.00 - 4096.00i) q^{32} +(11431.7 + 11431.7i) q^{33} +37364.0i q^{34} +(-3514.53 - 25471.1i) q^{35} +7776.00 q^{36} +(-14956.3 + 14956.3i) q^{37} +(-36757.3 - 36757.3i) q^{38} +44689.5i q^{39} +(22415.0 - 3092.86i) q^{40} +50688.1 q^{41} +(-12826.1 + 12826.1i) q^{42} +(-12486.6 - 12486.6i) q^{43} -33187.4i q^{44} +(24212.6 + 18341.0i) q^{45} +108624. q^{46} +(-25787.6 + 25787.6i) q^{47} +(-11287.2 - 11287.2i) q^{48} +75336.8i q^{49} +(77090.0 + 43239.2i) q^{50} +102963. q^{51} +(64869.0 - 64869.0i) q^{52} +(-166649. - 166649. i) q^{53} -21428.1i q^{54} +(78277.9 - 103337. i) q^{55} +37235.6 q^{56} +(-101291. + 101291. i) q^{57} +(33912.9 + 33912.9i) q^{58} +247188. i q^{59} +(-8522.91 - 61768.6i) q^{60} -281194. q^{61} +(-68353.5 + 68353.5i) q^{62} +(35344.7 + 35344.7i) q^{63} +32768.0i q^{64} +(354991. - 48982.0i) q^{65} -91453.6 q^{66} +(-304343. + 304343. i) q^{67} +(-149456. - 149456. i) q^{68} -299331. i q^{69} +(115942. + 87826.2i) q^{70} -288398. q^{71} +(-31104.0 + 31104.0i) q^{72} +(-487894. - 487894. i) q^{73} -119650. i q^{74} +(119153. - 212435. i) q^{75} +294058. q^{76} +(150848. - 150848. i) q^{77} +(-178758. - 178758. i) q^{78} +222009. i q^{79} +(-77288.8 + 102032. i) q^{80} -59049.0 q^{81} +(-202752. + 202752. i) q^{82} +(749160. + 749160. i) q^{83} -102609. i q^{84} +(-112853. - 817885. i) q^{85} +99892.6 q^{86} +(93453.1 - 93453.1i) q^{87} +(132749. + 132749. i) q^{88} +689800. i q^{89} +(-170214. + 23486.4i) q^{90} +589705. q^{91} +(-434494. + 434494. i) q^{92} +(188360. + 188360. i) q^{93} -206301. i q^{94} +(915626. + 693585. i) q^{95} +90298.0 q^{96} +(820944. - 820944. i) q^{97} +(-301347. - 301347. i) q^{98} +252017. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} + 60 q^{5} + 388 q^{7} + 1024 q^{8} - 976 q^{10} - 4192 q^{11} + 7884 q^{13} + 1296 q^{15} - 8192 q^{16} - 1372 q^{17} - 7776 q^{18} + 5888 q^{20} + 4536 q^{21} + 16768 q^{22} + 14888 q^{23}+ \cdots - 301888 q^{98}+O(q^{100}) \) 8 * q - 32 * q^2 + 60 * q^5 + 388 * q^7 + 1024 * q^8 - 976 * q^10 - 4192 * q^11 + 7884 * q^13 + 1296 * q^15 - 8192 * q^16 - 1372 * q^17 - 7776 * q^18 + 5888 * q^20 + 4536 * q^21 + 16768 * q^22 + 14888 * q^23 + 17932 * q^25 - 63072 * q^26 - 12416 * q^28 + 9072 * q^30 + 2240 * q^31 + 32768 * q^32 + 3564 * q^33 - 78232 * q^35 + 62208 * q^36 - 69996 * q^37 - 71008 * q^38 - 15872 * q^40 + 169064 * q^41 - 18144 * q^42 + 164136 * q^43 - 44712 * q^45 - 119104 * q^46 - 109248 * q^47 + 280832 * q^50 + 380376 * q^51 + 252288 * q^52 - 480740 * q^53 - 409068 * q^55 + 99328 * q^56 - 442584 * q^57 - 2272 * q^58 - 114048 * q^60 + 266088 * q^61 - 8960 * q^62 + 94284 * q^63 + 903396 * q^65 - 28512 * q^66 + 92488 * q^67 + 43904 * q^68 - 228352 * q^70 - 2526032 * q^71 - 248832 * q^72 + 324464 * q^73 - 38232 * q^75 + 568064 * q^76 + 2822104 * q^77 + 857952 * q^78 - 61440 * q^80 - 472392 * q^81 - 676256 * q^82 + 213264 * q^83 - 1537292 * q^85 - 1313088 * q^86 - 1707156 * q^87 - 536576 * q^88 + 120528 * q^90 + 3340176 * q^91 + 476416 * q^92 + 1264248 * q^93 + 3084784 * q^95 - 854736 * q^97 - 301888 * q^98

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