LMFDB - Embedded newform 80.6.q.a.69.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.13
Character	$\chi$	$=$	80.69
Dual form			80.6.q.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.30125 + 3.67413i) q^{2} +(-2.38770 - 2.38770i) q^{3} +(5.00149 - 31.6067i) q^{4} +(4.21193 - 55.7428i) q^{5} +(19.0429 + 1.49737i) q^{6} -204.311 q^{7} +(94.6147 + 154.325i) q^{8} -231.598i q^{9} +O(q^{10})$	\(q+(-4.30125 + 3.67413i) q^{2} +(-2.38770 - 2.38770i) q^{3} +(5.00149 - 31.6067i) q^{4} +(4.21193 - 55.7428i) q^{5} +(19.0429 + 1.49737i) q^{6} -204.311 q^{7} +(94.6147 + 154.325i) q^{8} -231.598i q^{9} +(186.690 + 255.239i) q^{10} +(7.30519 + 7.30519i) q^{11} +(-87.4096 + 63.5254i) q^{12} +(822.372 + 822.372i) q^{13} +(878.792 - 750.665i) q^{14} +(-143.154 + 123.040i) q^{15} +(-973.970 - 316.161i) q^{16} +790.697i q^{17} +(850.921 + 996.160i) q^{18} +(-939.325 + 939.325i) q^{19} +(-1740.78 - 411.922i) q^{20} +(487.834 + 487.834i) q^{21} +(-58.2617 - 4.58120i) q^{22} -2289.29 q^{23} +(142.569 - 594.393i) q^{24} +(-3089.52 - 469.570i) q^{25} +(-6558.73 - 515.722i) q^{26} +(-1133.20 + 1133.20i) q^{27} +(-1021.86 + 6457.60i) q^{28} +(-886.548 + 886.548i) q^{29} +(163.675 - 1055.20i) q^{30} +5111.23 q^{31} +(5350.91 - 2218.61i) q^{32} -34.8853i q^{33} +(-2905.13 - 3400.99i) q^{34} +(-860.544 + 11388.9i) q^{35} +(-7320.05 - 1158.33i) q^{36} +(-629.784 + 629.784i) q^{37} +(589.065 - 7491.48i) q^{38} -3927.16i q^{39} +(9000.99 - 4624.08i) q^{40} +12446.4i q^{41} +(-3890.66 - 305.928i) q^{42} +(-9649.01 + 9649.01i) q^{43} +(267.430 - 194.356i) q^{44} +(-12909.9 - 975.474i) q^{45} +(9846.81 - 8411.16i) q^{46} +3430.22i q^{47} +(1570.65 + 3080.45i) q^{48} +24935.9 q^{49} +(15014.1 - 9331.57i) q^{50} +(1887.95 - 1887.95i) q^{51} +(30105.6 - 21879.4i) q^{52} +(1764.00 - 1764.00i) q^{53} +(710.647 - 9037.70i) q^{54} +(437.981 - 376.443i) q^{55} +(-19330.8 - 31530.2i) q^{56} +4485.66 q^{57} +(555.968 - 7070.56i) q^{58} +(20136.5 + 20136.5i) q^{59} +(3172.92 + 5140.02i) q^{60} +(18141.2 - 18141.2i) q^{61} +(-21984.7 + 18779.3i) q^{62} +47317.9i q^{63} +(-14864.1 + 29202.7i) q^{64} +(49305.1 - 42377.5i) q^{65} +(128.173 + 150.050i) q^{66} +(-47365.4 - 47365.4i) q^{67} +(24991.4 + 3954.66i) q^{68} +(5466.15 + 5466.15i) q^{69} +(-38142.8 - 52148.1i) q^{70} +22178.2i q^{71} +(35741.2 - 21912.6i) q^{72} -9665.73 q^{73} +(394.947 - 5022.77i) q^{74} +(6255.66 + 8498.05i) q^{75} +(24991.0 + 34387.0i) q^{76} +(-1492.53 - 1492.53i) q^{77} +(14428.9 + 16891.7i) q^{78} -72606.8 q^{79} +(-21726.0 + 52960.2i) q^{80} -50866.8 q^{81} +(-45729.6 - 53534.9i) q^{82} +(39192.2 + 39192.2i) q^{83} +(17858.7 - 12978.9i) q^{84} +(44075.7 + 3330.37i) q^{85} +(6051.04 - 76954.5i) q^{86} +4233.63 q^{87} +(-436.192 + 1818.55i) q^{88} +109739. i q^{89} +(59112.7 - 43237.0i) q^{90} +(-168019. - 168019. i) q^{91} +(-11449.9 + 72357.0i) q^{92} +(-12204.1 - 12204.1i) q^{93} +(-12603.1 - 14754.2i) q^{94} +(48404.2 + 56317.0i) q^{95} +(-18073.8 - 7479.00i) q^{96} +49067.5i q^{97} +(-107256. + 91618.0i) q^{98} +(1691.87 - 1691.87i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−4.30125	+	3.67413i	−0.760361	+	0.649501i
$2$	−4.30125	+	3.67413i	−0.760361	+	0.649501i
$3$	−2.38770	−	2.38770i	−0.153171	−	0.153171i	0.626361	−	0.779533i	$-0.284543\pi$
$3$	−2.38770	−	2.38770i	−0.153171	−	0.153171i	−0.779533	+	0.626361i	$0.784543\pi$
$4$	5.00149	−	31.6067i	0.156296	−	0.987710i
$5$	4.21193	−	55.7428i	0.0753454	−	0.997157i
$5$	4.21193	−	55.7428i	0.0753454	−	0.997157i
$6$	19.0429	+	1.49737i	0.215950	+	0.0169805i
$7$	−204.311			−1.57596			−0.787982	−	0.615698i	$-0.788874\pi$
$7$	−204.311			−1.57596			−0.787982	+	0.615698i	$0.788874\pi$
$8$	94.6147	+	154.325i	0.522677	+	0.852531i
$9$		−	231.598i		−	0.953077i
$10$	186.690	+	255.239i	0.590365	+	0.807136i
$11$	7.30519	+	7.30519i	0.0182033	+	0.0182033i	0.716150	−	0.697947i	$-0.245903\pi$
$11$	7.30519	+	7.30519i	0.0182033	+	0.0182033i	−0.697947	+	0.716150i	$0.745903\pi$
$12$	−87.4096	+	63.5254i	−0.175229	+	0.127349i
$13$	822.372	+	822.372i	1.34961	+	1.34961i	0.886077	+	0.463537i	$0.153420\pi$
$13$	822.372	+	822.372i	1.34961	+	1.34961i	0.463537	+	0.886077i	$0.346580\pi$
$14$	878.792	−	750.665i	1.19830	−	1.02359i
$15$	−143.154	+	123.040i	−0.164277	+	0.141195i
$16$	−973.970	−	316.161i	−0.951143	−	0.308751i
$17$			790.697i			0.663572i	0.943355	+	0.331786i	$0.107651\pi$
$17$			790.697i			0.663572i	−0.943355	+	0.331786i	$0.892349\pi$
$18$	850.921	+	996.160i	0.619025	+	0.724682i
$19$	−939.325	+	939.325i	−0.596942	+	0.596942i	−0.939498	−	0.342556i	$-0.888707\pi$
$19$	−939.325	+	939.325i	−0.596942	+	0.596942i	0.342556	+	0.939498i	$0.388707\pi$
$20$	−1740.78	−	411.922i	−0.973126	−	0.230272i
$21$	487.834	+	487.834i	0.241393	+	0.241393i
$22$	−58.2617	−	4.58120i	−0.0256641	−	0.00201801i
$23$	−2289.29			−0.902364			−0.451182	−	0.892432i	$-0.648997\pi$
$23$	−2289.29			−0.902364			−0.451182	+	0.892432i	$0.648997\pi$
$24$	142.569	−	594.393i	0.0505241	−	0.210642i
$25$	−3089.52	−	469.570i	−0.988646	−	0.150262i
$26$	−6558.73	−	515.722i	−1.90277	−	0.149617i
$27$	−1133.20	+	1133.20i	−0.299155	+	0.299155i
$28$	−1021.86	+	6457.60i	−0.246318	+	1.55660i
$29$	−886.548	+	886.548i	−0.195752	+	0.195752i	−0.798176	−	0.602424i	$-0.794202\pi$
$29$	−886.548	+	886.548i	−0.195752	+	0.195752i	0.602424	+	0.798176i	$0.294202\pi$
$30$	163.675	−	1055.20i	0.0332031	−	0.214057i
$31$	5111.23			0.955258			0.477629	−	0.878562i	$-0.341496\pi$
$31$	5111.23			0.955258			0.477629	+	0.878562i	$0.341496\pi$
$32$	5350.91	−	2218.61i	0.923746	−	0.383006i
$33$		−	34.8853i		−	0.00557644i
$34$	−2905.13	−	3400.99i	−0.430991	−	0.504554i
$35$	−860.544	+	11388.9i	−0.118742	+	1.57148i
$36$	−7320.05	−	1158.33i	−0.941364	−	0.148963i
$37$	−629.784	+	629.784i	−0.0756288	+	0.0756288i	−0.743909	−	0.668281i	$-0.767031\pi$
$37$	−629.784	+	629.784i	−0.0756288	+	0.0756288i	0.668281	+	0.743909i	$0.267031\pi$
$38$	589.065	−	7491.48i	0.0661766	−	0.841605i
$39$		−	3927.16i		−	0.413444i
$40$	9000.99	−	4624.08i	0.889489	−	0.456957i
$41$			12446.4i			1.15633i	0.815919	+	0.578166i	$0.196232\pi$
$41$			12446.4i			1.15633i	−0.815919	+	0.578166i	$0.803768\pi$
$42$	−3890.66	−	305.928i	−0.340330	−	0.0267606i
$43$	−9649.01	+	9649.01i	−0.795814	+	0.795814i	−0.982432	−	0.186618i	$-0.940247\pi$
$43$	−9649.01	+	9649.01i	−0.795814	+	0.795814i	0.186618	+	0.982432i	$0.440247\pi$
$44$	267.430	−	194.356i	0.0208247	−	0.0151345i
$45$	−12909.9	−	975.474i	−0.950368	−	0.0718099i
$46$	9846.81	−	8411.16i	0.686122	−	0.586086i
$47$			3430.22i			0.226505i	0.993566	+	0.113252i	$0.0361268\pi$
$47$			3430.22i			0.226505i	−0.993566	+	0.113252i	$0.963873\pi$
$48$	1570.65	+	3080.45i	0.0983960	+	0.192980i
$49$	24935.9			1.48366
$50$	15014.1	−	9331.57i	0.849323	−	0.527873i
$51$	1887.95	−	1887.95i	0.101640	−	0.101640i
$52$	30105.6	−	21879.4i	1.54397	−	1.12209i
$53$	1764.00	−	1764.00i	0.0862598	−	0.0862598i	−0.662660	−	0.748920i	$-0.730573\pi$
$53$	1764.00	−	1764.00i	0.0862598	−	0.0862598i	0.748920	+	0.662660i	$0.230573\pi$
$54$	710.647	−	9037.70i	0.0331642	−	0.421768i
$55$	437.981	−	376.443i	0.0195231	−	0.0167800i
$56$	−19330.8	−	31530.2i	−0.823721	−	1.34356i
$57$	4485.66			0.182869
$58$	555.968	−	7070.56i	0.0217010	−	0.275984i
$59$	20136.5	+	20136.5i	0.753102	+	0.753102i	0.975057	−	0.221955i	$-0.0712439\pi$
$59$	20136.5	+	20136.5i	0.753102	+	0.753102i	−0.221955	+	0.975057i	$0.571244\pi$
$60$	3172.92	+	5140.02i	0.113784	+	0.184326i
$61$	18141.2	−	18141.2i	0.624226	−	0.624226i	−0.322384	−	0.946609i	$-0.604484\pi$
$61$	18141.2	−	18141.2i	0.624226	−	0.624226i	0.946609	+	0.322384i	$0.104484\pi$
$62$	−21984.7	+	18779.3i	−0.726341	+	0.620441i
$63$			47317.9i			1.50202i
$64$	−14864.1	+	29202.7i	−0.453617	+	0.891197i
$65$	49305.1	−	42377.5i	1.44747	−	1.24409i
$66$	128.173	+	150.050i	0.00362191	+	0.00424011i
$67$	−47365.4	−	47365.4i	−1.28906	−	1.28906i	−0.935356	−	0.353707i	$-0.884921\pi$
$67$	−47365.4	−	47365.4i	−1.28906	−	1.28906i	−0.353707	−	0.935356i	$-0.615079\pi$
$68$	24991.4	+	3954.66i	0.655417	+	0.103714i
$69$	5466.15	+	5466.15i	0.138216	+	0.138216i
$70$	−38142.8	−	52148.1i	−0.930395	−	1.27202i
$71$			22178.2i			0.522133i	0.965321	+	0.261066i	$0.0840742\pi$
$71$			22178.2i			0.522133i	−0.965321	+	0.261066i	$0.915926\pi$
$72$	35741.2	−	21912.6i	0.812527	−	0.498152i
$73$	−9665.73			−0.212289			−0.106145	−	0.994351i	$-0.533851\pi$
$73$	−9665.73			−0.212289			−0.106145	+	0.994351i	$0.533851\pi$
$74$	394.947	−	5022.77i	0.00838416	−	0.106626i
$75$	6255.66	+	8498.05i	0.128416	+	0.174448i
$76$	24991.0	+	34387.0i	0.496306	+	0.682905i
$77$	−1492.53	−	1492.53i	−0.0286877	−	0.0286877i
$78$	14428.9	+	16891.7i	0.268533	+	0.314367i
$79$	−72606.8			−1.30891			−0.654455	−	0.756101i	$-0.727102\pi$
$79$	−72606.8			−1.30891			−0.654455	+	0.756101i	$0.727102\pi$
$80$	−21726.0	+	52960.2i	−0.379538	+	0.925176i
$81$	−50866.8			−0.861433
$82$	−45729.6	−	53534.9i	−0.751040	−	0.879230i
$83$	39192.2	+	39192.2i	0.624460	+	0.624460i	0.946669	−	0.322208i	$-0.104425\pi$
$83$	39192.2	+	39192.2i	0.624460	+	0.624460i	−0.322208	+	0.946669i	$0.604425\pi$
$84$	17858.7	−	12978.9i	0.276155	−	0.200697i
$85$	44075.7	+	3330.37i	0.661686	+	0.0499971i
$86$	6051.04	−	76954.5i	0.0882235	−	1.12199i
$87$	4233.63			0.0599673
$88$	−436.192	+	1818.55i	−0.00600441	+	0.0250333i
$89$			109739.i			1.46854i	0.678857	+	0.734271i	$0.262476\pi$
$89$			109739.i			1.46854i	−0.678857	+	0.734271i	$0.737524\pi$
$90$	59112.7	−	43237.0i	0.769263	−	0.562664i
$91$	−168019.	−	168019.i	−2.12694	−	2.12694i
$92$	−11449.9	+	72357.0i	−0.141036	+	0.891274i
$93$	−12204.1	−	12204.1i	−0.146318	−	0.146318i
$94$	−12603.1	−	14754.2i	−0.147115	−	0.172225i
$95$	48404.2	+	56317.0i	0.550268	+	0.640222i
$96$	−18073.8	−	7479.00i	−0.200157	−	0.0828258i
$97$			49067.5i			0.529498i	0.964317	+	0.264749i	$0.0852892\pi$
$97$			49067.5i			0.529498i	−0.964317	+	0.264749i	$0.914711\pi$
$98$	−107256.	+	91618.0i	−1.12812	+	0.963641i
$99$	1691.87	−	1691.87i	0.0173491	−	0.0173491i
$100$	−30293.8	+	95301.0i	−0.302938	+	0.953010i
$101$	−23503.5	−	23503.5i	−0.229261	−	0.229261i	0.583123	−	0.812384i	$-0.301831\pi$
$101$	−23503.5	−	23503.5i	−0.229261	−	0.229261i	−0.812384	+	0.583123i	$0.801831\pi$
$102$	−1183.96	+	15057.1i	−0.0112678	+	0.143299i
$103$	28898.9			0.268403			0.134202	−	0.990954i	$-0.457153\pi$
$103$	28898.9			0.268403			0.134202	+	0.990954i	$0.457153\pi$
$104$	−49103.7	+	204721.i	−0.445175	+	1.85600i
$105$	29248.0	−	25138.5i	0.258894	−	0.222519i
$106$	−1106.23	+	14068.6i	−0.00956271	+	0.121614i
$107$	−72130.2	+	72130.2i	−0.609056	+	0.609056i	−0.942699	−	0.333643i	$-0.891722\pi$
$107$	−72130.2	+	72130.2i	−0.609056	+	0.609056i	0.333643	+	0.942699i	$0.391722\pi$
$108$	30149.0	+	41484.4i	0.248722	+	0.342236i
$109$	141202.	−	141202.i	1.13835	−	1.13835i	0.149598	−	0.988747i	$-0.452202\pi$
$109$	141202.	−	141202.i	1.13835	−	1.13835i	0.988747	−	0.149598i	$-0.0477981\pi$
$110$	−500.763	+	3228.37i	−0.00394594	+	0.0254391i
$111$	3007.47			0.0231683
$112$	198993.	+	64595.2i	1.49897	+	0.486581i
$113$		−	123644.i		−	0.910915i	−0.890257	−	0.455458i	$-0.849476\pi$
$113$		−	123644.i		−	0.910915i	0.890257	−	0.455458i	$-0.150524\pi$
$114$	−19293.9	+	16480.9i	−0.139046	+	0.118773i
$115$	−9642.35	+	127612.i	−0.0679889	+	0.899799i
$116$	23586.8	+	32454.9i	0.162751	+	0.223942i
$117$	190459.	−	190459.i	1.28629	−	1.28629i
$118$	−160596.	−	12627.9i	−1.06177	−	0.0834884i
$119$		−	161548.i		−	1.04577i
$120$	−32532.6	−	10450.8i	−0.206237	−	0.0662514i
$121$		−	160944.i		−	0.999337i
$122$	−11376.6	+	144683.i	−0.0692013	+	0.880072i
$123$	29718.2	−	29718.2i	0.177117	−	0.177117i
$124$	25563.7	−	161549.i	0.149303	−	0.943518i
$125$	−39188.0	+	170241.i	−0.224325	+	0.974514i
$126$	−173852.	−	203526.i	−0.975561	−	1.14207i
$127$			174877.i			0.962108i	0.876691	+	0.481054i	$0.159746\pi$
$127$			174877.i			0.962108i	−0.876691	+	0.481054i	$0.840254\pi$
$128$	−43360.5	−	180221.i	−0.233921	−	0.972256i
$129$	46078.0			0.243792
$130$	−56372.7	+	363430.i	−0.292557	+	1.88609i
$131$	−206485.	+	206485.i	−1.05126	+	1.05126i	−0.0526496	+	0.998613i	$0.516767\pi$
$131$	−206485.	+	206485.i	−1.05126	+	1.05126i	−0.998613	+	0.0526496i	$0.983233\pi$
$132$	−1102.61	−	174.478i	−0.00550791	−	0.000871578i
$133$	191914.	−	191914.i	0.940759	−	0.940759i
$134$	377757.	+	29703.6i	1.81740	+	0.142905i
$135$	58394.7	+	67940.6i	0.275765	+	0.320845i
$136$	−122024.	+	74811.6i	−0.565715	+	0.346834i
$137$	−376095.			−1.71197			−0.855985	−	0.517001i	$-0.827048\pi$
$137$	−376095.			−1.71197			−0.855985	+	0.517001i	$0.827048\pi$
$138$	−43594.7	−	3427.91i	−0.194866	−	0.0153226i
$139$	30525.2	+	30525.2i	0.134005	+	0.134005i	0.770928	−	0.636923i	$-0.219793\pi$
$139$	30525.2	+	30525.2i	0.134005	+	0.134005i	−0.636923	+	0.770928i	$0.719793\pi$
$140$	355661.	+	84160.2i	1.53361	+	0.362900i
$141$	8190.34	−	8190.34i	0.0346940	−	0.0346940i
$142$	−81485.8	−	95394.1i	−0.339126	−	0.397009i
$143$			12015.2i			0.0491348i
$144$	−73222.2	+	225569.i	−0.294264	+	0.906512i
$145$	45684.6	+	53152.7i	0.180447	+	0.209945i
$146$	41574.7	−	35513.2i	0.161416	−	0.137882i
$147$	−59539.6	−	59539.6i	−0.227255	−	0.227255i
$148$	16755.5	+	23055.3i	0.0628788	+	0.0865198i
$149$	−215061.	−	215061.i	−0.793591	−	0.793591i	0.188485	−	0.982076i	$-0.439642\pi$
$149$	−215061.	−	215061.i	−0.793591	−	0.793591i	−0.982076	+	0.188485i	$0.939642\pi$
$150$	−58130.1	−	13568.1i	−0.210947	−	0.0492369i
$151$		−	398090.i		−	1.42082i	−0.703789	−	0.710409i	$-0.748510\pi$
$151$		−	398090.i		−	1.42082i	0.703789	−	0.710409i	$-0.251490\pi$
$152$	−233835.	−	56086.9i	−0.820919	−	0.196903i
$153$	183124.			0.632435
$154$	11903.5	+	935.988i	0.0404457	+	0.00318030i
$155$	21528.1	−	284914.i	0.0719743	−	0.952543i
$156$	−124125.	−	19641.6i	−0.408363	−	0.0646199i
$157$	−288617.	−	288617.i	−0.934487	−	0.934487i	0.0634954	−	0.997982i	$-0.479775\pi$
$157$	−288617.	−	288617.i	−0.934487	−	0.934487i	−0.997982	+	0.0634954i	$0.979775\pi$
$158$	312300.	−	266767.i	0.995243	−	0.850138i
$159$	−8423.82			−0.0264251
$160$	−101134.	−	307619.i	−0.312318	−	0.949978i
$161$	467727.			1.42209
$162$	218791.	−	186891.i	0.655000	−	0.559502i
$163$	−354041.	−	354041.i	−1.04372	−	1.04372i	−0.999000	−	0.0447207i	$-0.985760\pi$
$163$	−354041.	−	354041.i	−1.04372	−	1.04372i	−0.0447207	−	0.999000i	$-0.514240\pi$
$164$	393389.	+	62250.3i	1.14212	+	0.180731i
$165$	−1944.60	−	146.934i	−0.00556059	−	0.000420159i
$166$	−312573.	−	24578.1i	−0.880403	−	0.0692273i
$167$	103799.			0.288006			0.144003	−	0.989577i	$-0.454003\pi$
$167$	103799.			0.288006			0.144003	+	0.989577i	$0.454003\pi$
$168$	−29128.5	+	121441.i	−0.0796241	+	0.331965i
$169$			981298.i			2.64292i
$170$	−201817.	+	147615.i	−0.535593	+	0.391750i
$171$	217546.	+	217546.i	0.568932	+	0.568932i
$172$	256714.	+	353233.i	0.661651	+	0.910416i
$173$	274503.	+	274503.i	0.697320	+	0.697320i	0.963832	−	0.266511i	$-0.0858710\pi$
$173$	274503.	+	274503.i	0.697320	+	0.697320i	−0.266511	+	0.963832i	$0.585871\pi$
$174$	−18209.9	+	15554.9i	−0.0455968	+	0.0389488i
$175$	631222.	+	95938.3i	1.55807	+	0.236808i
$176$	−4805.42	−	9424.65i	−0.0116936	−	0.0229342i
$177$		−	96159.9i		−	0.230707i
$178$	−403196.	−	472015.i	−0.953820	−	1.11662i
$179$	−153872.	+	153872.i	−0.358945	+	0.358945i	−0.863424	−	0.504479i	$-0.831685\pi$
$179$	−153872.	+	153872.i	−0.358945	+	0.358945i	0.504479	+	0.863424i	$0.331685\pi$
$180$	−95400.3	+	403161.i	−0.219467	+	0.927465i
$181$	−475573.	−	475573.i	−1.07900	−	1.07900i	−0.996599	−	0.0823986i	$-0.973742\pi$
$181$	−475573.	−	475573.i	−1.07900	−	1.07900i	−0.0823986	−	0.996599i	$-0.526258\pi$
$182$	1.34002e6	+	105368.i	2.99870	+	0.235792i
$183$	−86631.7			−0.191227
$184$	−216601.	−	353294.i	−0.471645	−	0.769293i
$185$	32453.3	+	37758.5i	0.0697155	+	0.0811121i
$186$	97332.3	+	7653.38i	0.206288	+	0.0162207i
$187$	−5776.19	+	5776.19i	−0.0120792	+	0.0120792i
$188$	108418.	+	17156.2i	0.223721	+	0.0354019i
$189$	231525.	−	231525.i	0.471458	−	0.471458i
$190$	−415115.	−	64389.8i	−0.834227	−	0.129400i
$191$	467996.			0.928237			0.464119	−	0.885773i	$-0.346371\pi$
$191$	467996.			0.928237			0.464119	+	0.885773i	$0.346371\pi$
$192$	105219.	−	34236.4i	0.205987	−	0.0670247i
$193$			692800.i			1.33880i	0.742904	+	0.669398i	$0.233448\pi$
$193$			692800.i			1.33880i	−0.742904	+	0.669398i	$0.766552\pi$
$194$	−180281.	−	211052.i	−0.343910	−	0.402610i
$195$	−218911.	−	16540.9i	−0.412269	−	0.0311511i
$196$	124717.	−	788143.i	0.231891	−	1.46543i
$197$	−429285.	+	429285.i	−0.788099	+	0.788099i	−0.981182	−	0.193084i	$-0.938151\pi$
$197$	−429285.	+	429285.i	−0.788099	+	0.788099i	0.193084	+	0.981182i	$0.438151\pi$
$198$	−1060.99	+	13493.3i	−0.00192331	+	0.0244599i
$199$		−	39964.9i		−	0.0715396i	−0.999360	−	0.0357698i	$-0.988612\pi$
$199$		−	39964.9i		−	0.0715396i	0.999360	−	0.0357698i	$-0.0113883\pi$
$200$	−219848.	−	521217.i	−0.388640	−	0.921390i
$201$			226189.i			0.394895i
$202$	187450.	+	14739.4i	0.323226	+	0.0254157i
$203$	181131.	−	181131.i	0.308499	−	0.308499i
$204$	−50229.4	−	69114.5i	−0.0845050	−	0.116277i
$205$	693795.	+	52423.3i	1.15305	+	0.0871243i
$206$	−124301.	+	106178.i	−0.204083	+	0.174328i
$207$			530195.i			0.860022i
$208$	−540964.	−	1.06097e6i	−0.866981	−	1.70037i
$209$	−13723.9			−0.0217326
$210$	−33440.5	+	215588.i	−0.0523269	+	0.337346i
$211$	−287809.	+	287809.i	−0.445039	+	0.445039i	−0.893701	−	0.448662i	$-0.851901\pi$
$211$	−287809.	+	287809.i	−0.445039	+	0.445039i	0.448662	+	0.893701i	$0.351901\pi$
$212$	−46931.6	−	64576.9i	−0.0717176	−	0.0986818i
$213$	52955.1	−	52955.1i	0.0799758	−	0.0799758i
$214$	45233.9	−	575266.i	0.0675196	−	0.858685i
$215$	497222.	+	578504.i	0.733591	+	0.853513i
$216$	−282098.	−	67663.1i	−0.411401	−	0.0986774i
$217$	−1.04428e6			−1.50545
$218$	−88549.8	+	1.12614e6i	−0.126196	+	1.60491i
$219$	23078.9	+	23078.9i	0.0325166	+	0.0325166i
$220$	−9707.57	−	15725.9i	−0.0135224	−	0.0219058i
$221$	−650247.	+	650247.i	−0.895566	+	0.895566i
$222$	−12935.9	+	11049.9i	−0.0176163	+	0.0150479i
$223$			181627.i			0.244579i	0.992494	+	0.122289i	$0.0390236\pi$
$223$			181627.i			0.244579i	−0.992494	+	0.122289i	$0.960976\pi$
$224$	−1.09325e6	+	453286.i	−1.45579	+	0.603604i
$225$	−108751.	+	715526.i	−0.143212	+	0.942256i
$226$	454286.	+	531825.i	0.591640	+	0.692624i
$227$	−846316.	−	846316.i	−1.09010	−	1.09010i	−0.995517	−	0.0945880i	$-0.969847\pi$
$227$	−846316.	−	846316.i	−1.09010	−	1.09010i	−0.0945880	−	0.995517i	$-0.530153\pi$
$228$	22435.0	−	141777.i	0.0285817	−	0.180621i
$229$	105988.	+	105988.i	0.133557	+	0.133557i	0.770725	−	0.637168i	$-0.219894\pi$
$229$	105988.	+	105988.i	0.133557	+	0.133557i	−0.637168	+	0.770725i	$0.719894\pi$
$230$	−427388.	−	584316.i	−0.532724	−	0.728330i
$231$			7127.44i			0.00878827i
$232$	−220697.	−	52935.6i	−0.269200	−	0.0645696i
$233$	−954607.			−1.15195			−0.575977	−	0.817466i	$-0.695378\pi$
$233$	−954607.			−1.15195			−0.575977	+	0.817466i	$0.695378\pi$
$234$	−119440.	+	1.51899e6i	−0.142597	+	1.81349i
$235$	191210.	+	14447.8i	0.225861	+	0.0170661i
$236$	737161.	−	535736.i	0.861553	−	0.626139i
$237$	173364.	+	173364.i	0.200487	+	0.200487i
$238$	593549.	+	694858.i	0.679226	+	0.795159i
$239$	388730.			0.440204			0.220102	−	0.975477i	$-0.429361\pi$
$239$	388730.			0.440204			0.220102	+	0.975477i	$0.429361\pi$
$240$	178329.	−	74578.0i	0.199845	−	0.0835762i
$241$	−930233.			−1.03169			−0.515845	−	0.856682i	$-0.672522\pi$
$241$	−930233.			−1.03169			−0.515845	+	0.856682i	$0.672522\pi$
$242$	591331.	+	692261.i	0.649071	+	0.759857i
$243$	396822.	+	396822.i	0.431102	+	0.431102i
$244$	−482651.	−	664117.i	−0.518990	−	0.714118i
$245$	105029.	−	1.39000e6i	0.111787	−	1.47945i
$246$	−18636.8	+	237014.i	−0.0196351	+	0.249710i
$247$	−1.54495e6			−1.61128
$248$	483597.	+	788787.i	0.499292	+	0.814387i
$249$		−	187159.i		−	0.191299i
$250$	−456930.	−	876229.i	−0.462380	−	0.886682i
$251$	208646.	+	208646.i	0.209039	+	0.209039i	0.803859	−	0.594820i	$-0.202777\pi$
$251$	208646.	+	208646.i	0.209039	+	0.209039i	−0.594820	+	0.803859i	$0.702777\pi$
$252$	1.49557e6	+	236660.i	1.48356	+	0.234760i
$253$	−16723.7	−	16723.7i	−0.0164260	−	0.0164260i
$254$	−642522.	−	752190.i	−0.624890	−	0.731549i
$255$	−97287.8	−	113192.i	−0.0936931	−	0.109009i
$256$	848660.	+	615863.i	0.809345	+	0.587333i
$257$			408389.i			0.385693i	0.981229	+	0.192846i	$0.0617719\pi$
$257$			408389.i			0.385693i	−0.981229	+	0.192846i	$0.938228\pi$
$258$	−198193.	+	169297.i	−0.185370	+	0.158343i
$259$	128672.	−	128672.i	0.119188	−	0.119188i
$260$	−1.09282e6	−	1.77032e6i	−1.00257	−	1.62412i
$261$	205322.	+	205322.i	0.186567	+	0.186567i
$262$	129490.	−	1.64680e6i	0.116542	−	1.48213i
$263$	2.10843e6			1.87962			0.939808	−	0.341703i	$-0.111004\pi$
$263$	2.10843e6			1.87962			0.939808	+	0.341703i	$0.111004\pi$
$264$	5383.65	−	3300.66i	0.00475409	−	0.00291468i
$265$	−90900.4	−	105760.i	−0.0795154	−	0.0925139i
$266$	−120352.	+	1.53059e6i	−0.104292	+	1.32634i
$267$	262024.	−	262024.i	0.224938	−	0.224938i
$268$	−1.73396e6	+	1.26017e6i	−1.47470	+	1.07174i
$269$	−691074.	+	691074.i	−0.582296	+	0.582296i	−0.935534	−	0.353237i	$-0.885081\pi$
$269$	−691074.	+	691074.i	−0.582296	+	0.582296i	0.353237	+	0.935534i	$0.385081\pi$
$270$	−500793.	−	77679.6i	−0.418070	−	0.0648482i
$271$	2.15686e6			1.78402			0.892009	−	0.452018i	$-0.149296\pi$
$271$	2.15686e6			1.78402			0.892009	+	0.452018i	$0.149296\pi$
$272$	249988.	−	770116.i	0.204879	−	0.631152i
$273$			802362.i			0.651574i
$274$	1.61768e6	−	1.38182e6i	1.30171	−	1.11193i
$275$	−19139.2	−	25999.8i	−0.0152613	−	0.0207319i
$276$	200106.	−	145428.i	0.158120	−	0.114915i
$277$	−278905.	+	278905.i	−0.218402	+	0.218402i	−0.807825	−	0.589423i	$-0.799355\pi$
$277$	−278905.	+	278905.i	−0.218402	+	0.218402i	0.589423	+	0.807825i	$0.299355\pi$
$278$	−243450.	−	19142.8i	−0.188929	−	0.0148557i
$279$		−	1.18375e6i		−	0.910435i
$280$	−1.83900e6	+	944751.i	−1.40180	+	0.720149i
$281$			432726.i			0.326925i	0.986550	+	0.163462i	$0.0522662\pi$
$281$			432726.i			0.326925i	−0.986550	+	0.163462i	$0.947734\pi$
$282$	−5136.29	+	65321.1i	−0.00384616	+	0.0489137i
$283$	−101578.	+	101578.i	−0.0753937	+	0.0753937i	−0.743798	−	0.668404i	$-0.766978\pi$
$283$	−101578.	+	101578.i	−0.0753937	+	0.0753937i	0.668404	+	0.743798i	$0.266978\pi$
$284$	700981.	+	110924.i	0.515716	+	0.0816075i
$285$	18893.3	−	250043.i	0.0137783	−	0.182349i
$286$	−44145.3	−	51680.2i	−0.0319131	−	0.0373602i
$287$		−	2.54293e6i		−	1.82234i
$288$	−513825.	−	1.23926e6i	−0.365034	−	0.880401i
$289$	794655.			0.559672
$290$	−391791.	−	60771.9i	−0.273564	−	0.0424334i
$291$	117159.	−	117159.i	0.0811040	−	0.0811040i
$292$	−48343.0	+	305502.i	−0.0331800	+	0.209680i
$293$	94240.7	−	94240.7i	0.0641312	−	0.0641312i	−0.674314	−	0.738445i	$-0.735560\pi$
$293$	94240.7	−	94240.7i	0.0641312	−	0.0641312i	0.738445	+	0.674314i	$0.235560\pi$
$294$	474851.	+	37338.2i	0.320398	+	0.0251933i
$295$	1.20728e6	−	1.03765e6i	0.807704	−	0.694218i
$296$	−156778.	−	37604.3i	−0.104005	−	0.0249464i
$297$	−16556.5			−0.0108912
$298$	1.71520e6	+	134868.i	1.11885	+	0.0879770i
$299$	−1.88265e6	−	1.88265e6i	−1.21784	−	1.21784i
$300$	299883.	−	155218.i	0.192375	−	0.0995725i
$301$	1.97140e6	−	1.97140e6i	1.25417	−	1.25417i
$302$	1.46263e6	+	1.71228e6i	0.922823	+	1.08033i
$303$			112239.i			0.0702323i
$304$	1.21185e6	−	617897.i	0.752083	−	0.383470i
$305$	−934832.	−	1.08765e6i	−0.575419	−	0.669484i
$306$	−787661.	+	672821.i	−0.480879	+	0.410767i
$307$	−947721.	−	947721.i	−0.573898	−	0.573898i	0.359318	−	0.933215i	$-0.383009\pi$
$307$	−947721.	−	947721.i	−0.573898	−	0.573898i	−0.933215	+	0.359318i	$0.883009\pi$
$308$	−54638.8	+	39709.1i	−0.0328189	+	0.0238514i
$309$	−69002.0	−	69002.0i	−0.0411117	−	0.0411117i
$310$	954214.	+	1.30458e6i	0.563951	+	0.771023i
$311$			2.74636e6i			1.61011i	0.593197	+	0.805057i	$0.297865\pi$
$311$			2.74636e6i			1.61011i	−0.593197	+	0.805057i	$0.702135\pi$
$312$	606057.	−	371567.i	0.352474	−	0.216098i
$313$	2.54786e6			1.46999			0.734996	−	0.678071i	$-0.237184\pi$
$313$	2.54786e6			1.46999			0.734996	+	0.678071i	$0.237184\pi$
$314$	2.30183e6	+	180996.i	1.31750	+	0.103597i
$315$	2.63763e6	+	199300.i	1.49775	+	0.113170i
$316$	−363142.	+	2.29486e6i	−0.204578	+	1.29282i
$317$	504610.	+	504610.i	0.282038	+	0.282038i	0.833921	−	0.551883i	$-0.186091\pi$
$317$	504610.	+	504610.i	0.282038	+	0.282038i	−0.551883	+	0.833921i	$0.686091\pi$
$318$	36232.9	−	30950.2i	0.0200926	−	0.0171631i
$319$	−12952.8			−0.00712667
$320$	1.56524e6	+	951568.i	0.854486	+	0.519475i
$321$	344451.			0.186580
$322$	−2.01181e6	+	1.71849e6i	−1.08130	+	0.923651i
$323$	−742722.	−	742722.i	−0.396114	−	0.396114i
$324$	−254409.	+	1.60773e6i	−0.134639	+	0.850846i
$325$	−2.15457e6	−	2.92689e6i	−1.13150	−	1.53709i
$326$	2.82361e6	+	222024.i	1.47150	+	0.115706i
$327$	−674296.			−0.348724
$328$	−1.92078e6	+	1.17761e6i	−0.985809	+	0.604389i
$329$		−	700831.i		−	0.356963i
$330$	8904.07	−	6512.73i	0.00450095	−	0.00329214i
$331$	475252.	+	475252.i	0.238426	+	0.238426i	0.816198	−	0.577772i	$-0.196078\pi$
$331$	475252.	+	475252.i	0.238426	+	0.238426i	−0.577772	+	0.816198i	$0.696078\pi$
$332$	1.43476e6	−	1.04272e6i	0.714387	−	0.519185i
$333$	145857.	+	145857.i	0.0720801	+	0.0720801i
$334$	−446464.	+	381371.i	−0.218988	+	0.187060i
$335$	−2.83978e6	+	2.44078e6i	−1.38252	+	1.18827i
$336$	−320902.	−	629370.i	−0.155069	−	0.304129i
$337$		−	938105.i		−	0.449963i	−0.974363	−	0.224981i	$-0.927768\pi$
$337$		−	938105.i		−	0.449963i	0.974363	−	0.224981i	$-0.0722322\pi$
$338$	−3.60542e6	−	4.22081e6i	−1.71658	−	2.00957i
$339$	−295226.	+	295226.i	−0.139526	+	0.139526i
$340$	325706.	−	1.37643e6i	0.152802	−	0.645739i
$341$	37338.5	+	37338.5i	0.0173888	+	0.0173888i
$342$	−1.73501e6	−	136426.i	−0.802115	−	0.0630714i
$343$	−1.66083e6			−0.762237
$344$	−2.40202e6	−	576141.i	−1.09441	−	0.262502i
$345$	327722.	−	281676.i	0.148237	−	0.127409i
$346$	−2.18927e6	−	172145.i	−0.983125	−	0.0773045i
$347$	248248.	−	248248.i	0.110678	−	0.110678i	−0.649599	−	0.760277i	$-0.725063\pi$
$347$	248248.	−	248248.i	0.110678	−	0.110678i	0.760277	+	0.649599i	$0.225063\pi$
$348$	21174.4	−	133811.i	0.00937268	−	0.0592303i
$349$	−1.93382e6	+	1.93382e6i	−0.849868	+	0.849868i	−0.990116	−	0.140248i	$-0.955210\pi$
$349$	−1.93382e6	+	1.93382e6i	−0.849868	+	0.849868i	0.140248	+	0.990116i	$0.455210\pi$
$350$	−3.06753e6	+	1.90654e6i	−1.33850	+	0.831909i
$351$	−1.86382e6			−0.807489
$352$	55296.7	+	22882.0i	0.0237872	+	0.00984324i
$353$		−	2.19854e6i		−	0.939068i	−0.882914	−	0.469534i	$-0.844422\pi$
$353$		−	2.19854e6i		−	0.939068i	0.882914	−	0.469534i	$-0.155578\pi$
$354$	353304.	+	413608.i	0.149845	+	0.175421i
$355$	1.23628e6	+	93413.2i	0.520649	+	0.0393403i
$356$	3.46849e6	+	548858.i	1.45049	+	0.229528i
$357$	−385729.	+	385729.i	−0.160181	+	0.160181i
$358$	96495.7	−	1.22719e6i	0.0397924	−	0.506063i
$359$		−	2.15212e6i		−	0.881314i	−0.897675	−	0.440657i	$-0.854745\pi$
$359$		−	2.15212e6i		−	0.881314i	0.897675	−	0.440657i	$-0.145255\pi$
$360$	−1.07093e6	−	2.08461e6i	−0.435516	−	0.847751i
$361$			711435.i			0.287321i
$362$	3.79288e6	+	298239.i	1.52124	+	0.119617i
$363$	−384287.	+	384287.i	−0.153070	+	0.153070i
$364$	−6.15089e6	+	4.47020e6i	−2.43324	+	1.76837i
$365$	−40711.4	+	538795.i	−0.0159950	+	0.211686i
$366$	372624.	−	318296.i	0.145401	−	0.124202i
$367$			3.20823e6i			1.24337i	0.783268	+	0.621684i	$0.213551\pi$
$367$			3.20823e6i			1.24337i	−0.783268	+	0.621684i	$0.786449\pi$
$368$	2.22970e6	+	723785.i	0.858277	+	0.278606i
$369$	2.88255e6			1.10207
$370$	−278320.	−	43171.0i	−0.105691	−	0.0163941i
$371$	−360404.	+	360404.i	−0.135942	+	0.135942i
$372$	−446770.	+	324693.i	−0.167389	+	0.121651i
$373$	−84251.7	+	84251.7i	−0.0313550	+	0.0313550i	−0.722610	−	0.691255i	$-0.757058\pi$
$373$	−84251.7	+	84251.7i	−0.0313550	+	0.0313550i	0.691255	+	0.722610i	$0.257058\pi$
$374$	3622.34	−	46067.4i	0.00133909	−	0.0170300i
$375$	500054.	−	312915.i	0.183628	−	0.114907i
$376$	−529367.	+	324549.i	−0.193102	+	0.118389i
$377$	−1.45814e6			−0.528381
$378$	−145193.	+	1.84650e6i	−0.0522656	+	0.664691i
$379$	−3.23099e6	−	3.23099e6i	−1.15541	−	1.15541i	−0.985450	−	0.169965i	$-0.945635\pi$
$379$	−3.23099e6	−	3.23099e6i	−1.15541	−	1.15541i	−0.169965	−	0.985450i	$-0.554365\pi$
$380$	2.02209e6	−	1.24823e6i	0.718359	−	0.443441i
$381$	417555.	−	417555.i	0.147367	−	0.147367i
$382$	−2.01297e6	+	1.71948e6i	−0.705795	+	0.602891i
$383$		−	1.61188e6i		−	0.561483i	−0.959783	−	0.280742i	$-0.909420\pi$
$383$		−	1.61188e6i		−	0.561483i	0.959783	−	0.280742i	$-0.0905804\pi$
$384$	−326782.	+	533846.i	−0.113092	+	0.184752i
$385$	−89484.2	+	76911.3i	−0.0307677	+	0.0264447i
$386$	−2.54544e6	−	2.97990e6i	−0.869550	−	1.01797i
$387$	2.23469e6	+	2.23469e6i	0.758472	+	0.758472i
$388$	1.55086e6	+	245410.i	0.522991	+	0.0827587i
$389$	3.73857e6	+	3.73857e6i	1.25266	+	1.25266i	0.954525	+	0.298132i	$0.0963634\pi$
$389$	3.73857e6	+	3.73857e6i	1.25266	+	1.25266i	0.298132	+	0.954525i	$0.403637\pi$
$390$	1.00236e6	−	733161.i	0.333706	−	0.244083i
$391$		−	1.81014e6i		−	0.598783i
$392$	2.35931e6	+	3.84823e6i	0.775477	+	1.26487i
$393$	986052.			0.322047
$394$	269212.	−	3.42372e6i	0.0873681	−	1.11111i
$395$	−305815.	+	4.04731e6i	−0.0986203	+	1.30519i
$396$	−45012.5	−	61936.2i	−0.0144243	−	0.0198475i
$397$	−1.74583e6	−	1.74583e6i	−0.555938	−	0.555938i	0.372210	−	0.928148i	$-0.378600\pi$
$397$	−1.74583e6	−	1.74583e6i	−0.555938	−	0.555938i	−0.928148	+	0.372210i	$0.878600\pi$
$398$	146836.	+	171899.i	0.0464650	+	0.0543959i
$399$	−916469.			−0.288195
$400$	2.86064e6	+	1.43413e6i	0.893950	+	0.448167i
$401$	−1.35372e6			−0.420404			−0.210202	−	0.977658i	$-0.567412\pi$
$401$	−1.35372e6			−0.420404			−0.210202	+	0.977658i	$0.567412\pi$
$402$	−831049.	−	972896.i	−0.256485	−	0.300263i
$403$	4.20333e6	+	4.20333e6i	1.28923	+	1.28923i
$404$	−860422.	+	625317.i	−0.262276	+	0.190611i
$405$	−214247.	+	2.83546e6i	−0.0649050	+	0.858984i
$406$	−113590.	+	1.44459e6i	−0.0342000	+	0.434941i
$407$	−9201.38			−0.00275338
$408$	469985.	+	112729.i	0.139776	+	0.0335263i
$409$			1.90810e6i			0.564017i	0.959412	+	0.282009i	$0.0910007\pi$
$409$			1.90810e6i			0.564017i	−0.959412	+	0.282009i	$0.908999\pi$
$410$	−3.17680e6	+	2.32361e6i	−0.933318	+	0.682659i
$411$	898003.	+	898003.i	0.262225	+	0.262225i
$412$	144537.	−	913399.i	0.0419505	−	0.265105i
$413$	−4.11410e6	−	4.11410e6i	−1.18686	−	1.18686i
$414$	−1.94801e6	−	2.28050e6i	−0.558585	−	0.653927i
$415$	2.34976e6	−	2.01961e6i	0.669735	−	0.575635i
$416$	6.22496e6	+	2.57591e6i	1.76361	+	0.729790i
$417$		−	145770.i		−	0.0410515i
$418$	59029.9	−	50423.4i	0.0165246	−	0.0141154i
$419$	−65344.2	+	65344.2i	−0.0181833	+	0.0181833i	−0.716140	−	0.697957i	$-0.754093\pi$
$419$	−65344.2	+	65344.2i	−0.0181833	+	0.0181833i	0.697957	+	0.716140i	$0.254093\pi$
$420$	−648263.	−	1.05016e6i	−0.179320	−	0.290491i
$421$	1.57640e6	+	1.57640e6i	0.433472	+	0.433472i	0.889808	−	0.456336i	$-0.150838\pi$
$421$	1.57640e6	+	1.57640e6i	0.433472	+	0.433472i	−0.456336	+	0.889808i	$0.650838\pi$
$422$	180489.	−	2.29539e6i	0.0493368	−	0.627443i
$423$	794431.			0.215876
$424$	439129.	+	105328.i	0.118625	+	0.0284531i
$425$	371288.	−	2.44287e6i	0.0997099	−	0.656038i
$426$	−33208.9	+	422337.i	−0.00886606	+	0.112755i
$427$	−3.70645e6	+	3.70645e6i	−0.983757	+	0.983757i
$428$	1.91904e6	+	2.64056e6i	0.506378	+	0.696765i
$429$	28688.7	−	28688.7i	0.00752605	−	0.00752605i
$430$	−4.26417e6	−	661429.i	−1.11215	−	0.172509i
$431$	−4.12684e6			−1.07010			−0.535050	−	0.844820i	$-0.679707\pi$
$431$	−4.12684e6			−1.07010			−0.535050	+	0.844820i	$0.679707\pi$
$432$	1.46198e6	−	745429.i	0.376904	−	0.192175i
$433$			285635.i			0.0732137i	0.999330	+	0.0366068i	$0.0116549\pi$
$433$			285635.i			0.0732137i	−0.999330	+	0.0366068i	$0.988345\pi$
$434$	4.49170e6	−	3.83682e6i	1.14469	−	0.977793i
$435$	17831.8	−	235994.i	0.00451826	−	0.0597968i
$436$	−3.75671e6	−	5.16915e6i	−0.946436	−	1.30227i
$437$	2.15039e6	−	2.15039e6i	0.538659	−	0.538659i
$438$	−184063.	−	14473.1i	−0.0458439	−	0.00360477i
$439$			873584.i			0.216343i	0.994132	+	0.108172i	$0.0344996\pi$
$439$			873584.i			0.216343i	−0.994132	+	0.108172i	$0.965500\pi$
$440$	99533.8	+	31974.1i	0.0245097	+	0.00787349i
$441$		−	5.77511e6i		−	1.41405i
$442$	407780.	−	5.18597e6i	0.0992819	−	1.26262i
$443$	−2.76738e6	+	2.76738e6i	−0.669978	+	0.669978i	−0.957711	−	0.287733i	$-0.907098\pi$
$443$	−2.76738e6	+	2.76738e6i	−0.669978	+	0.669978i	0.287733	+	0.957711i	$0.407098\pi$
$444$	15041.8	−	95056.4i	0.00362113	−	0.0228836i
$445$	6.11716e6	+	462214.i	1.46437	+	0.110648i
$446$	−667323.	−	781224.i	−0.158854	−	0.185968i
$447$			1.02701e6i			0.243111i
$448$	3.03690e6	−	5.96644e6i	0.714884	−	1.40449i
$449$	635868.			0.148851			0.0744253	−	0.997227i	$-0.476288\pi$
$449$	635868.			0.148851			0.0744253	+	0.997227i	$0.476288\pi$
$450$	−2.16117e6	−	3.47722e6i	−0.503104	−	0.809470i
$451$	−90923.0	+	90923.0i	−0.0210491	+	0.0210491i
$452$	−3.90799e6	−	618405.i	−0.899720	−	0.142373i
$453$	−950520.	+	950520.i	−0.217629	+	0.217629i
$454$	6.74970e6	+	530738.i	1.53690	+	0.120848i
$455$	−1.00736e7	+	8.65819e6i	−2.28115	+	1.96064i
$456$	424410.	+	692248.i	0.0955813	+	0.155901i
$457$	3.88189e6			0.869465			0.434733	−	0.900560i	$-0.356843\pi$
$457$	3.88189e6			0.869465			0.434733	+	0.900560i	$0.356843\pi$
$458$	−845292.	−	66466.5i	−0.188297	−	0.0148060i
$459$	−896017.	−	896017.i	−0.198511	−	0.198511i
$460$	3.98516e6	+	943010.i	0.878114	+	0.207789i
$461$	−3.23884e6	+	3.23884e6i	−0.709801	+	0.709801i	−0.966493	−	0.256692i	$-0.917367\pi$
$461$	−3.23884e6	+	3.23884e6i	−0.709801	+	0.709801i	0.256692	+	0.966493i	$0.417367\pi$
$462$	−26187.2	−	30656.9i	−0.00570799	−	0.00668226i
$463$		−	6.50893e6i		−	1.41110i	−0.708661	−	0.705549i	$-0.750700\pi$
$463$		−	6.50893e6i		−	1.41110i	0.708661	−	0.705549i	$-0.249300\pi$
$464$	1.14376e6	−	583179.i	0.246627	−	0.125750i
$465$	−731693.	+	628888.i	−0.156927	+	0.134878i
$466$	4.10600e6	−	3.50736e6i	0.875900	−	0.748195i
$467$	920279.	+	920279.i	0.195266	+	0.195266i	0.797967	−	0.602701i	$-0.205909\pi$
$467$	920279.	+	920279.i	0.195266	+	0.195266i	−0.602701	+	0.797967i	$0.705909\pi$
$468$	−5.06722e6	−	6.97238e6i	−1.06944	−	1.47152i
$469$	9.67727e6	+	9.67727e6i	2.03152	+	2.03152i
$470$	−875525.	+	640387.i	−0.182820	+	0.133720i
$471$			1.37827e6i			0.286273i
$472$	−1.20235e6	+	5.01276e6i	−0.248413	+	1.03567i
$473$	−140976.			−0.0289729
$474$	−1.38264e6	−	108719.i	−0.282660	−	0.0222259i
$475$	3.34314e6	−	2.46098e6i	0.679862	−	0.500466i
$476$	−5.10601e6	−	807980.i	−1.03291	−	0.163449i
$477$	−408538.	−	408538.i	−0.0822123	−	0.0822123i
$478$	−1.67203e6	+	1.42825e6i	−0.334713	+	0.285913i
$479$	−5.87203e6			−1.16936			−0.584682	−	0.811263i	$-0.698781\pi$
$479$	−5.87203e6			−1.16936			−0.584682	+	0.811263i	$0.698781\pi$
$480$	−493026.	+	975981.i	−0.0976712	+	0.193347i
$481$	−1.03583e6			−0.204139
$482$	4.00116e6	−	3.41780e6i	0.784456	−	0.670084i
$483$	−1.11679e6	−	1.11679e6i	−0.217824	−	0.217824i
$484$	−5.08692e6	−	804960.i	−0.987056	−	0.156193i
$485$	2.73516e6	+	206669.i	0.527993	+	0.0398953i
$486$	−3.16481e6	−	248853.i	−0.607794	−	0.0477917i
$487$	1.70380e6			0.325533			0.162767	−	0.986665i	$-0.447958\pi$
$487$	1.70380e6			0.325533			0.162767	+	0.986665i	$0.447958\pi$
$488$	4.51606e6	+	1.08321e6i	0.858440	+	0.205903i
$489$			1.69069e6i			0.319736i
$490$	4.65529e6	+	6.36462e6i	0.875904	+	1.19752i
$491$	2.80246e6	+	2.80246e6i	0.524609	+	0.524609i	0.918960	−	0.394351i	$-0.129030\pi$
$491$	2.80246e6	+	2.80246e6i	0.524609	+	0.524609i	−0.394351	+	0.918960i	$0.629030\pi$
$492$	−790661.	−	1.08793e6i	−0.147258	−	0.202623i
$493$	−700991.	−	700991.i	−0.129896	−	0.129896i
$494$	6.64521e6	−	5.67635e6i	1.22516	−	1.04653i
$495$	−87183.3	−	101435.i	−0.0159926	−	0.0186070i
$496$	−4.97818e6	−	1.61597e6i	−0.908587	−	0.294937i
$497$		−	4.53125e6i		−	0.822863i
$498$	687647.	+	805017.i	0.124249	+	0.145456i
$499$	7.03735e6	−	7.03735e6i	1.26520	−	1.26520i	0.316656	−	0.948541i	$-0.397440\pi$
$499$	7.03735e6	−	7.03735e6i	1.26520	−	1.26520i	0.948541	−	0.316656i	$-0.102560\pi$
$500$	5.18475e6	+	2.09006e6i	0.927477	+	0.373881i
$501$	−247841.	−	247841.i	−0.0441142	−	0.0441142i
$502$	−1.66404e6	−	130845.i	−0.294716	−	0.0231739i
$503$	−2.95566e6			−0.520876			−0.260438	−	0.965491i	$-0.583867\pi$
$503$	−2.95566e6			−0.520876			−0.260438	+	0.965491i	$0.583867\pi$
$504$	−7.30232e6	+	4.47697e6i	−1.28051	+	0.785069i
$505$	−1.40915e6	+	1.21116e6i	−0.245883	+	0.211335i
$506$	133378.	+	10487.7i	0.0231584	+	0.00182097i
$507$	2.34305e6	−	2.34305e6i	0.404819	−	0.404819i
$508$	5.52730e6	+	874646.i	0.950284	+	0.150374i
$509$	3.42130e6	−	3.42130e6i	0.585324	−	0.585324i	−0.351038	−	0.936361i	$-0.614171\pi$
$509$	3.42130e6	−	3.42130e6i	0.585324	−	0.585324i	0.936361	+	0.351038i	$0.114171\pi$
$510$	834340.	+	129417.i	0.142042	+	0.0220326i
$511$	1.97481e6			0.334560
$512$	−5.91306e6	+	469110.i	−0.996868	+	0.0790861i
$513$		−	2.12888e6i		−	0.357157i
$514$	−1.50048e6	−	1.75658e6i	−0.250508	−	0.293266i
$515$	121720.	−	1.61090e6i	0.0202230	−	0.267640i
$516$	230458.	−	1.45637e6i	0.0381038	−	0.240796i
$517$	−25058.4	+	25058.4i	−0.00412313	+	0.00412313i
$518$	−80692.0	+	1.02621e6i	−0.0132131	+	0.168039i
$519$		−	1.31087e6i		−	0.213619i
$520$	1.12049e7	+	3.59945e6i	1.81718	+	0.583751i
$521$		−	9.04223e6i		−	1.45942i	−0.683755	−	0.729712i	$-0.739654\pi$
$521$		−	9.04223e6i		−	1.45942i	0.683755	−	0.729712i	$-0.260346\pi$
$522$	−1.63753e6	−	128761.i	−0.263034	−	0.0206827i
$523$	−1.83296e6	+	1.83296e6i	−0.293021	+	0.293021i	−0.838272	−	0.545252i	$-0.816434\pi$
$523$	−1.83296e6	+	1.83296e6i	−0.293021	+	0.293021i	0.545252	+	0.838272i	$0.316434\pi$
$524$	5.49360e6	+	7.55906e6i	0.874034	+	1.20265i
$525$	−1.27810e6	−	1.73624e6i	−0.202380	−	0.274924i
$526$	−9.06887e6	+	7.74664e6i	−1.42919	+	1.22081i
$527$			4.04143e6i			0.633883i
$528$	−11029.4	+	33977.2i	−0.00172173	+	0.00530399i
$529$	−1.19549e6			−0.185740
$530$	779562.	+	120920.i	0.120548	+	0.0186986i
$531$	4.66356e6	−	4.66356e6i	0.717764	−	0.717764i
$532$	−5.10593e6	−	7.02564e6i	−0.782160	−	1.07623i
$533$	−1.02355e7	+	1.02355e7i	−1.56060	+	1.56060i
$534$	−164320.	+	2.08975e6i	−0.0249365	+	0.317132i
$535$	3.71693e6	+	4.32455e6i	0.561436	+	0.653215i
$536$	2.82818e6	−	1.17911e7i	0.425202	−	1.77273i
$537$	734803.			0.109960
$538$	433383.	−	5.51158e6i	0.0645530	−	0.820957i
$539$	182162.	+	182162.i	0.0270075	+	0.0270075i
$540$	2.43944e6	−	1.50586e6i	0.360003	−	0.222229i
$541$	−2.88062e6	+	2.88062e6i	−0.423149	+	0.423149i	−0.886286	−	0.463138i	$-0.846724\pi$
$541$	−2.88062e6	+	2.88062e6i	−0.423149	+	0.423149i	0.463138	+	0.886286i	$0.346724\pi$
$542$	−9.27720e6	+	7.92460e6i	−1.35650	+	1.15872i
$543$			2.27105e6i			0.330543i
$544$	1.75425e6	+	4.23095e6i	0.254152	+	0.612972i
$545$	−7.27625e6	−	8.46572e6i	−1.04934	−	1.22088i
$546$	−2.94798e6	−	3.45116e6i	−0.423198	−	0.495431i
$547$	1.38654e6	+	1.38654e6i	0.198136	+	0.198136i	0.799200	−	0.601065i	$-0.205257\pi$
$547$	1.38654e6	+	1.38654e6i	0.198136	+	0.198136i	−0.601065	+	0.799200i	$0.705257\pi$
$548$	−1.88103e6	+	1.18871e7i	−0.267575	+	1.69093i
$549$	−4.20146e6	−	4.20146e6i	−0.594935	−	0.594935i
$550$	177849.	+	41511.6i	0.0250695	+	0.00585144i
$551$		−	1.66551e6i		−	0.233706i
$552$	−326383.	+	1.36074e6i	−0.0455911	+	0.190076i
$553$	1.48344e7			2.06280
$554$	174906.	−	2.22438e6i	0.0242120	−	0.307917i
$555$	12667.3	−	167645.i	0.00174563	−	0.0231025i
$556$	1.11747e6	−	812130.i	0.153303	−	0.111414i
$557$	1.46274e6	+	1.46274e6i	0.199770	+	0.199770i	0.799901	−	0.600132i	$-0.204885\pi$
$557$	1.46274e6	+	1.46274e6i	0.199770	+	0.199770i	−0.600132	+	0.799901i	$0.704885\pi$
$558$	4.34925e6	+	5.09160e6i	0.591328	+	0.692259i
$559$	−1.58701e7			−2.14808
$560$	4.43886e6	−	1.08203e7i	0.598138	−	1.45804i
$561$	27583.7			0.00370037
$562$	−1.58989e6	−	1.86126e6i	−0.212338	−	0.248581i
$563$	7.57456e6	+	7.57456e6i	1.00713	+	1.00713i	0.999974	+	0.00715802i	$0.00227849\pi$
$563$	7.57456e6	+	7.57456e6i	1.00713	+	1.00713i	0.00715802	+	0.999974i	$0.497722\pi$
$564$	−217906.	−	299834.i	−0.0288451	−	0.0396902i
$565$	−6.89228e6	−	520782.i	−0.908326	−	0.0686332i
$566$	63701.3	−	810126.i	0.00835810	−	0.106295i
$567$	1.03926e7			1.35759
$568$	−3.42264e6	+	2.09839e6i	−0.445134	+	0.272907i
$569$			1.31326e7i			1.70047i	0.526404	+	0.850234i	$0.323540\pi$
$569$			1.31326e7i			1.70047i	−0.526404	+	0.850234i	$0.676460\pi$
$570$	837428.	+	1.14492e6i	0.107959	+	0.147600i
$571$	−3.88971e6	−	3.88971e6i	−0.499261	−	0.499261i	0.411947	−	0.911208i	$-0.364849\pi$
$571$	−3.88971e6	−	3.88971e6i	−0.499261	−	0.499261i	−0.911208	+	0.411947i	$0.864849\pi$
$572$	379760.	+	60093.7i	0.0485310	+	0.00767960i
$573$	−1.11744e6	−	1.11744e6i	−0.142179	−	0.142179i
$574$	9.34306e6	+	1.09378e7i	1.18361	+	1.38563i
$575$	7.07281e6	+	1.07498e6i	0.892118	+	0.135591i
$576$	6.76329e6	+	3.44250e6i	0.849379	+	0.432332i
$577$			6.78954e6i			0.848987i	0.905431	+	0.424493i	$0.139548\pi$
$577$			6.78954e6i			0.848987i	−0.905431	+	0.424493i	$0.860452\pi$
$578$	−3.41801e6	+	2.91967e6i	−0.425553	+	0.363508i
$579$	1.65420e6	−	1.65420e6i	0.205065	−	0.205065i
$580$	1.90847e6	−	1.17810e6i	0.235568	−	0.145416i
$581$	−8.00740e6	−	8.00740e6i	−0.984127	−	0.984127i
$582$	−73472.0	+	934385.i	−0.00899114	+	0.114345i
$583$	25772.7			0.00314043
$584$	−914520.	−	1.49166e6i	−0.110959	−	0.180983i
$585$	−9.81454e6	−	1.14189e7i	−1.18571	−	1.37955i
$586$	−59099.8	+	751606.i	−0.00710955	+	0.0904162i
$587$	1.03528e7	−	1.03528e7i	1.24011	−	1.24011i	0.280162	−	0.959953i	$-0.409612\pi$
$587$	1.03528e7	−	1.03528e7i	1.24011	−	1.24011i	0.959953	−	0.280162i	$-0.0903883\pi$
$588$	−2.17964e6	+	1.58407e6i	−0.259981	+	0.188943i
$589$	−4.80110e6	+	4.80110e6i	−0.570234	+	0.570234i
$590$	−1.38033e6	+	8.89889e6i	−0.163250	+	1.05246i
$591$	2.05001e6			0.241428
$592$	812504.	−	414278.i	0.0952843	−	0.0485833i
$593$			8.02352e6i			0.936975i	0.883470	+	0.468487i	$0.155201\pi$
$593$			8.02352e6i			0.936975i	−0.883470	+	0.468487i	$0.844799\pi$
$594$	71213.5	−	60830.7i	0.00828125	−	0.00707386i
$595$	−9.00514e6	−	680430.i	−1.04279	−	0.0787936i
$596$	−7.87301e6	+	5.72176e6i	−0.907873	+	0.659802i
$597$	−95424.4	+	95424.4i	−0.0109578	+	0.0109578i
$598$	1.50148e7	+	1.18064e6i	1.71699	+	0.135009i
$599$		−	9.69909e6i		−	1.10450i	−0.833680	−	0.552248i	$-0.813770\pi$
$599$		−	9.69909e6i		−	1.10450i	0.833680	−	0.552248i	$-0.186230\pi$
$600$	−719580.	+	1.76944e6i	−0.0816020	+	0.200659i
$601$		−	3.68052e6i		−	0.415645i	−0.978167	−	0.207822i	$-0.933362\pi$
$601$		−	3.68052e6i		−	0.415645i	0.978167	−	0.207822i	$-0.0666376\pi$
$602$	−1.23629e6	+	1.57226e7i	−0.139037	+	1.76821i
$603$	−1.09697e7	+	1.09697e7i	−1.22858	+	1.22858i
$604$	−1.25823e7	−	1.99104e6i	−1.40336	−	0.222069i
$605$	−8.97148e6	−	677887.i	−0.996497	−	0.0752954i
$606$	−412381.	−	482768.i	−0.0456160	−	0.0534019i
$607$		−	1.45674e7i		−	1.60476i	−0.596816	−	0.802378i	$-0.703568\pi$
$607$		−	1.45674e7i		−	1.60476i	0.596816	−	0.802378i	$-0.296432\pi$
$608$	−2.94225e6	+	7.11024e6i	−0.322790	+	0.780055i
$609$	−864976.			−0.0945063
$610$	8.01712e6	+	1.24356e6i	0.872356	+	0.135314i
$611$	−2.82091e6	+	2.82091e6i	−0.305694	+	0.305694i
$612$	915891.	−	5.78794e6i	0.0988474	−	0.624663i
$613$	3.01883e6	−	3.01883e6i	0.324480	−	0.324480i	−0.526003	−	0.850483i	$-0.676310\pi$
$613$	3.01883e6	−	3.01883e6i	0.324480	−	0.324480i	0.850483	+	0.526003i	$0.176310\pi$
$614$	7.55843e6	+	594330.i	0.809116	+	0.0636219i
$615$	−1.53141e6	−	1.78175e6i	−0.163269	−	0.189958i
$616$	89118.7	−	371549.i	0.00946274	−	0.0394516i
$617$	9.24495e6			0.977668			0.488834	−	0.872377i	$-0.337422\pi$
$617$	9.24495e6			0.977668			0.488834	+	0.872377i	$0.337422\pi$
$618$	550317.	+	43272.2i	0.0579618	+	0.00455762i
$619$	2.21835e6	+	2.21835e6i	0.232704	+	0.232704i	0.813821	−	0.581116i	$-0.197384\pi$
$619$	2.21835e6	+	2.21835e6i	0.232704	+	0.232704i	−0.581116	+	0.813821i	$0.697384\pi$
$620$	−8.89753e6	−	2.10543e6i	−0.929587	−	0.219969i
$621$	2.59422e6	−	2.59422e6i	0.269947	−	0.269947i
$622$	−1.00905e7	−	1.18128e7i	−1.04577	−	1.22427i
$623$		−	2.24209e7i		−	2.31437i
$624$	−1.24162e6	+	3.82494e6i	−0.127651	+	0.393245i
$625$	9.32463e6	+	2.90149e6i	0.954842	+	0.297113i
$626$	−1.09590e7	+	9.36119e6i	−1.11772	+	0.954762i
$627$	32768.6	+	32768.6i	0.00332881	+	0.00332881i
$628$	−1.05658e7	+	7.67873e6i	−1.06906	+	0.776945i
$629$	−497968.	−	497968.i	−0.0501851	−	0.0501851i
$630$	−1.20774e7	+	8.83378e6i	−1.21233	+	0.886738i
$631$			2.84036e6i			0.283988i	0.989867	+	0.141994i	$0.0453514\pi$
$631$			2.84036e6i			0.283988i	−0.989867	+	0.141994i	$0.954649\pi$
$632$	−6.86967e6	−	1.12050e7i	−0.684137	−	1.11589i
$633$	1.37440e6			0.136334
$634$	−4.02446e6	−	316449.i	−0.397635	−	0.0312666i
$635$	9.74815e6	+	736571.i	0.959373	+	0.0724904i
$636$	−42131.6	+	266249.i	−0.00413014	+	0.0261003i
$637$	2.05066e7	+	2.05066e7i	2.00237	+	2.00237i
$638$	55713.2	−	47590.3i	0.00541884	−	0.00462878i
$639$	5.13643e6			0.497633
$640$	−1.02287e7	+	1.65796e6i	−0.987117	+	0.160001i
$641$	−9.78237e6			−0.940371			−0.470185	−	0.882568i	$-0.655813\pi$
$641$	−9.78237e6			−0.940371			−0.470185	+	0.882568i	$0.655813\pi$
$642$	−1.48157e6	+	1.26556e6i	−0.141868	+	0.121184i
$643$	−9.11126e6	−	9.11126e6i	−0.869063	−	0.869063i	0.123306	−	0.992369i	$-0.460650\pi$
$643$	−9.11126e6	−	9.11126e6i	−0.869063	−	0.869063i	−0.992369	+	0.123306i	$0.960650\pi$
$644$	2.33933e6	−	1.47833e7i	0.222268	−	1.40462i
$645$	194077.	−	2.56851e6i	0.0183686	−	0.243099i
$646$	5.92349e6	+	465772.i	0.558466	+	0.0439129i
$647$	−9.19590e6			−0.863642			−0.431821	−	0.901959i	$-0.642129\pi$
$647$	−9.19590e6			−0.863642			−0.431821	+	0.901959i	$0.642129\pi$
$648$	−4.81274e6	−	7.84999e6i	−0.450252	−	0.734398i
$649$			294202.i			0.0274178i
$650$	2.00212e7	+	4.67312e6i	1.85868	+	0.433834i
$651$	2.49343e6	+	2.49343e6i	0.230592	+	0.230592i
$652$	−1.29608e7	+	9.41934e6i	−1.19402	+	0.867763i
$653$	−9.20865e6	−	9.20865e6i	−0.845110	−	0.845110i	0.144409	−	0.989518i	$-0.453872\pi$
$653$	−9.20865e6	−	9.20865e6i	−0.845110	−	0.845110i	−0.989518	+	0.144409i	$0.953872\pi$
$654$	2.90032e6	−	2.47745e6i	0.265156	−	0.226496i
$655$	1.06404e7	+	1.23798e7i	0.969067	+	1.12748i
$656$	3.93506e6	−	1.21224e7i	0.357019	−	1.09984i
$657$			2.23856e6i			0.202328i
$658$	2.57495e6	+	3.01445e6i	0.231848	+	0.271421i
$659$	−4.97483e6	+	4.97483e6i	−0.446236	+	0.446236i	−0.894101	−	0.447865i	$-0.852184\pi$
$659$	−4.97483e6	+	4.97483e6i	−0.446236	+	0.446236i	0.447865	+	0.894101i	$0.352184\pi$
$660$	−14370.0	+	60727.6i	−0.00128410	+	0.00542658i
$661$	1.14820e6	+	1.14820e6i	0.102215	+	0.102215i	0.756365	−	0.654150i	$-0.226974\pi$
$661$	1.14820e6	+	1.14820e6i	0.102215	+	0.102215i	−0.654150	+	0.756365i	$0.726974\pi$
$662$	−3.79032e6	−	298038.i	−0.336148	−	0.0264318i
$663$	3.10520e6			0.274350
$664$	−2.34016e6	+	9.75649e6i	−0.205980	+	0.858763i
$665$	−9.88951e6	−	1.15062e7i	−0.867203	−	1.00897i
$666$	−1.16326e6	−	91468.9i	−0.101623	−	0.00799075i
$667$	2.02957e6	−	2.02957e6i	0.176640	−	0.176640i
$668$	519148.	−	3.28074e6i	0.0450143	−	0.284466i
$669$	433672.	−	433672.i	0.0374624	−	0.0374624i
$670$	3.24685e6	−	2.09321e7i	0.279431	−	1.80147i
$671$	265050.			0.0227259
$672$	3.69267e6	+	1.52804e6i	0.315440	+	0.130530i
$673$			4.30351e6i			0.366256i	0.983089	+	0.183128i	$0.0586223\pi$
$673$			4.30351e6i			0.366256i	−0.983089	+	0.183128i	$0.941378\pi$
$674$	3.44672e6	+	4.03502e6i	0.292251	+	0.342134i
$675$	4.03316e6	−	2.96892e6i	0.340711	−	0.250807i
$676$	3.10156e7	+	4.90795e6i	2.61044	+	0.413079i
$677$	520806.	−	520806.i	0.0436721	−	0.0436721i	−0.684933	−	0.728606i	$-0.740169\pi$
$677$	520806.	−	520806.i	0.0436721	−	0.0436721i	0.728606	+	0.684933i	$0.240169\pi$
$678$	185141.	−	2.35454e6i	0.0154678	−	0.196712i
$679$		−	1.00250e7i		−	0.834471i
$680$	3.65625e6	+	7.11706e6i	0.303224	+	0.590240i
$681$			4.04151e6i			0.333945i
$682$	−297789.	−	23415.5i	−0.0245159	−	0.00192772i
$683$	1.18287e7	−	1.18287e7i	0.970253	−	0.970253i	−0.0293176	−	0.999570i	$-0.509333\pi$
$683$	1.18287e7	−	1.18287e7i	0.970253	−	0.970253i	0.999570	+	0.0293176i	$0.00933342\pi$
$684$	7.96396e6	−	5.78785e6i	0.650861	−	0.473018i
$685$	−1.58409e6	+	2.09646e7i	−0.128989	+	1.70710i
$686$	7.14364e6	−	6.10211e6i	0.579575	−	0.495074i
$687$		−	506134.i		−	0.0409142i
$688$	1.24485e7	−	6.34721e6i	1.00264	−	0.511224i
$689$	2.90133e6			0.232835
$690$	−374699.	+	2.41565e6i	−0.0299612	+	0.193157i
$691$	−2.29334e6	+	2.29334e6i	−0.182714	+	0.182714i	−0.792538	−	0.609823i	$-0.791240\pi$
$691$	−2.29334e6	+	2.29334e6i	−0.182714	+	0.182714i	0.609823	+	0.792538i	$0.291240\pi$
$692$	1.00491e7	−	7.30323e6i	0.797739	−	0.579762i
$693$	−345666.	+	345666.i	−0.0273416	+	0.0273416i
$694$	−155680.	+	1.97987e6i	−0.0122697	+	0.156041i
$695$	1.83013e6	−	1.57299e6i	0.143721	−	0.123528i
$696$	400563.	+	653353.i	0.0313436	+	0.0511240i
$697$	−9.84131e6			−0.767310
$698$	1.21273e6	−	1.54229e7i	0.0942159	−	1.19820i
$699$	2.27932e6	+	2.27932e6i	0.176446	+	0.176446i
$700$	6.18934e6	−	1.94710e7i	0.477419	−	1.50191i
$701$	8.18706e6	−	8.18706e6i	0.629264	−	0.629264i	−0.318619	−	0.947883i	$-0.603219\pi$
$701$	8.18706e6	−	8.18706e6i	0.629264	−	0.629264i	0.947883	+	0.318619i	$0.103219\pi$
$702$	8.01676e6	−	6.84793e6i	0.613983	−	0.524465i
$703$		−	1.18314e6i		−	0.0902920i
$704$	−321917.	+	104746.i	−0.0244800	+	0.00796539i
$705$	−422055.	−	491050.i	−0.0319813	−	0.0372094i
$706$	8.07772e6	+	9.45645e6i	0.609926	+	0.714030i
$707$	4.80203e6	+	4.80203e6i	0.361307	+	0.361307i
$708$	−3.03930e6	−	480943.i	−0.227872	−	0.0360587i
$709$	3.39423e6	+	3.39423e6i	0.253586	+	0.253586i	0.822439	−	0.568853i	$-0.192613\pi$
$709$	3.39423e6	+	3.39423e6i	0.253586	+	0.253586i	−0.568853	+	0.822439i	$0.692613\pi$
$710$	−5.66075e6	+	4.14045e6i	−0.421432	+	0.308249i
$711$			1.68156e7i			1.24749i
$712$	−1.69354e7	+	1.03829e7i	−1.25198	+	0.767573i
$713$	−1.17011e7			−0.861990
$714$	241897.	−	3.07634e6i	0.0177576	−	0.225833i
$715$	669759.	+	50607.1i	0.0489952	+	0.00370208i
$716$	4.09381e6	+	5.63299e6i	0.298432	+	0.410636i
$717$	−928173.	−	928173.i	−0.0674266	−	0.0674266i
$718$	7.90718e6	+	9.25681e6i	0.572415	+	0.670117i
$719$	1.30309e7			0.940054			0.470027	−	0.882652i	$-0.344244\pi$
$719$	1.30309e7			0.940054			0.470027	+	0.882652i	$0.344244\pi$
$720$	1.22655e7	+	5.03169e6i	0.881764	+	0.361729i
$721$	−5.90436e6			−0.422994
$722$	−2.61391e6	−	3.06006e6i	−0.186615	−	0.218468i
$723$	2.22112e6	+	2.22112e6i	0.158025	+	0.158025i
$724$	−1.74099e7	+	1.26527e7i	−1.23438	+	0.897094i
$725$	3.15530e6	−	2.32271e6i	0.222944	−	0.164116i
$726$	240992.	−	3.06484e6i	0.0169692	−	0.215807i
$727$	−2.38060e6			−0.167051			−0.0835257	−	0.996506i	$-0.526618\pi$
$727$	−2.38060e6			−0.167051			−0.0835257	+	0.996506i	$0.526618\pi$
$728$	1.00324e7	−	4.18266e7i	0.701580	−	2.92499i
$729$			1.04656e7i			0.729368i
$730$	−1.80449e6	−	2.46707e6i	−0.125328	−	0.171346i
$731$	−7.62945e6	−	7.62945e6i	−0.528080	−	0.528080i
$732$	−433287.	+	2.73814e6i	−0.0298881	+	0.188877i
$733$	−1.10593e7	−	1.10593e7i	−0.760272	−	0.760272i	0.216100	−	0.976371i	$-0.430666\pi$
$733$	−1.10593e7	−	1.10593e7i	−0.760272	−	0.760272i	−0.976371	+	0.216100i	$0.930666\pi$
$734$	−1.17875e7	−	1.37994e7i	−0.807570	−	0.945409i
$735$	−3.56968e6	+	3.06813e6i	−0.243731	+	0.209486i
$736$	−1.22498e7	+	5.07904e6i	−0.833555	+	0.345611i
$737$		−	692026.i		−	0.0469304i
$738$	−1.23986e7	+	1.05909e7i	−0.837974	+	0.715799i
$739$	1.66816e7	−	1.66816e7i	1.12364	−	1.12364i	0.132450	−	0.991190i	$-0.457716\pi$
$739$	1.66816e7	−	1.66816e7i	1.12364	−	1.12364i	0.991190	−	0.132450i	$-0.0422843\pi$
$740$	1.35574e6	−	836894.i	0.0910115	−	0.0561812i
$741$	3.68888e6	+	3.68888e6i	0.246802	+	0.246802i
$742$	226015.	−	2.87436e6i	0.0150705	−	0.191660i
$743$	1.76437e7			1.17251			0.586255	−	0.810126i	$-0.300602\pi$
$743$	1.76437e7			1.17251			0.586255	+	0.810126i	$0.300602\pi$
$744$	728704.	−	3.03808e6i	0.0482635	−	0.201218i
$745$	−1.28939e7	+	1.10823e7i	−0.851128	+	0.731542i
$746$	52835.5	−	671939.i	0.00347599	−	0.0442062i
$747$	9.07683e6	−	9.07683e6i	0.595159	−	0.595159i
$748$	153677.	+	211456.i	0.0100428	+	0.0138187i
$749$	1.47370e7	−	1.47370e7i	0.959851	−	0.959851i
$750$	−1.00116e6	+	3.18319e6i	−0.0649908	+	0.206638i
$751$	1.84260e7			1.19215			0.596076	−	0.802928i	$-0.296726\pi$
$751$	1.84260e7			1.19215			0.596076	+	0.802928i	$0.296726\pi$
$752$	1.08450e6	−	3.34093e6i	0.0699335	−	0.215438i
$753$		−	996372.i		−	0.0640375i
$754$	6.27184e6	−	5.35741e6i	0.401760	−	0.343184i
$755$	−2.21906e7	−	1.67673e6i	−1.41678	−	0.107052i
$756$	−6.15978e6	−	8.47571e6i	−0.391977	−	0.539351i
$757$	4.32086e6	−	4.32086e6i	0.274051	−	0.274051i	−0.556678	−	0.830728i	$-0.687924\pi$
$757$	4.32086e6	−	4.32086e6i	0.274051	−	0.274051i	0.830728	+	0.556678i	$0.187924\pi$
$758$	2.57684e7	+	2.02621e6i	1.62898	+	0.128089i
$759$			79862.5i			0.00503198i
$760$	−4.11134e6	+	1.27984e7i	−0.258196	+	0.803750i
$761$			2.18090e7i			1.36513i	0.730825	+	0.682565i	$0.239135\pi$
$761$			2.18090e7i			1.36513i	−0.730825	+	0.682565i	$0.760865\pi$
$762$	−261855.	+	3.33016e6i	−0.0163371	+	0.207768i
$763$	−2.88491e7	+	2.88491e7i	−1.79399	+	1.79399i
$764$	2.34068e6	−	1.47918e7i	0.145080	−	0.916829i
$765$	771305.	−	1.02078e7i	0.0476511	−	0.630637i
$766$	5.92228e6	+	6.93311e6i	0.364684	+	0.426930i
$767$			3.31194e7i			2.03279i
$768$	−555851.	−	3.49685e6i	−0.0340060	−	0.213931i
$769$	5.77566e6			0.352197			0.176099	−	0.984373i	$-0.443652\pi$
$769$	5.77566e6			0.352197			0.176099	+	0.984373i	$0.443652\pi$
$770$	102311.	−	659592.i	0.00621866	−	0.0400911i
$771$	975113.	−	975113.i	0.0590771	−	0.0590771i
$772$	2.18971e7	+	3.46503e6i	1.32234	+	0.209249i
$773$	−1.07629e7	+	1.07629e7i	−0.647859	+	0.647859i	−0.952475	−	0.304616i	$-0.901472\pi$
$773$	−1.07629e7	+	1.07629e7i	−0.647859	+	0.647859i	0.304616	+	0.952475i	$0.401472\pi$
$774$	−1.78225e7	−	1.40141e6i	−1.06934	−	0.0840838i
$775$	−1.57912e7	−	2.40008e6i	−0.944412	−	0.143539i
$776$	−7.57232e6	+	4.64251e6i	−0.451414	+	0.276757i
$777$	−614460.			−0.0365124
$778$	−2.98166e7	−	2.34452e6i	−1.76607	−	0.138869i
$779$	−1.16912e7	−	1.16912e7i	−0.690263	−	0.690263i
$780$	−1.61768e6	+	6.83633e6i	−0.0952045	+	0.402334i
$781$	−162016.	+	162016.i	−0.00950453	+	0.00950453i
$782$	6.65069e6	+	7.78585e6i	0.388910	+	0.455291i
$783$		−	2.00927e6i		−	0.117121i
$784$	−2.42869e7	−	7.88377e6i	−1.41118	−	0.458083i
$785$	−1.73040e7	+	1.48727e7i	−1.00224	+	0.861421i
$786$	−4.24126e6	+	3.62289e6i	−0.244871	+	0.209170i
$787$	−1.11231e7	−	1.11231e7i	−0.640160	−	0.640160i	0.310435	−	0.950595i	$-0.399525\pi$
$787$	−1.11231e7	−	1.11231e7i	−0.640160	−	0.640160i	−0.950595	+	0.310435i	$0.899525\pi$
$788$	1.14212e7	+	1.57154e7i	0.655236	+	0.901590i
$789$	−5.03430e6	−	5.03430e6i	−0.287903	−	0.287903i
$790$	−1.35550e7	−	1.85321e7i	−0.772735	−	1.05647i
$791$			2.52619e7i			1.43557i
$792$	421172.	+	101021.i	0.0238587	+	0.00572267i
$793$	2.98376e7			1.68493
$794$	1.39237e7	+	1.09484e6i	0.783796	+	0.0616310i
$795$	−35480.6	+	469567.i	−0.00199101	+	0.0263500i
$796$	−1.26316e6	−	199884.i	−0.0706604	−	0.0111814i
$797$	−843943.	−	843943.i	−0.0470616	−	0.0470616i	0.683184	−	0.730246i	$-0.260595\pi$
$797$	−843943.	−	843943.i	−0.0470616	−	0.0470616i	−0.730246	+	0.683184i	$0.760595\pi$
$798$	3.94196e6	−	3.36723e6i	0.219132	−	0.187183i
$799$	−2.71226e6			−0.150302
$800$	−1.75735e7	+	4.34181e6i	−0.970809	+	0.239853i
$801$	2.54153e7			1.39963
$802$	5.82268e6	−	4.97374e6i	0.319659	−	0.273053i
$803$	−70610.0	−	70610.0i	−0.00386436	−	0.00386436i
$804$	7.14910e6	+	1.13128e6i	0.390042	+	0.0617207i
$805$	1.97004e6	−	2.60724e7i	0.107148	−	1.41805i
$806$	−3.35231e7	−	2.63597e6i	−1.81764	−	0.142923i
$807$	3.30016e6			0.178382
$808$	1.40339e6	−	5.85095e6i	0.0756224	−	0.315281i
$809$			54211.8i			0.00291221i	0.999999	+	0.00145611i	$0.000463493\pi$
$809$			54211.8i			0.00291221i	−0.999999	+	0.00145611i	$0.999537\pi$
$810$	−9.49631e6	−	1.29832e7i	−0.508560	−	0.695294i
$811$	2.26429e7	+	2.26429e7i	1.20887	+	1.20887i	0.971393	+	0.237479i	$0.0763210\pi$
$811$	2.26429e7	+	2.26429e7i	1.20887	+	1.20887i	0.237479	+	0.971393i	$0.423679\pi$
$812$	−4.81904e6	−	6.63089e6i	−0.256490	−	0.352925i
$813$	−5.14995e6	−	5.14995e6i	−0.273260	−	0.273260i
$814$	39577.4	−	33807.1i	0.00209357	−	0.00178833i
$815$	−2.12264e7	+	1.82440e7i	−1.11939	+	0.962114i
$816$	−2.43571e6	+	1.24191e6i	−0.128056	+	0.0652928i
$817$		−	1.81271e7i		−	0.950109i
$818$	−7.01061e6	−	8.20721e6i	−0.366330	−	0.428857i
$819$	−3.89129e7	+	3.89129e7i	−2.02714	+	2.02714i
$820$	5.12693e6	−	2.16664e7i	0.266271	−	1.12526i
$821$	−2.79565e6	−	2.79565e6i	−0.144752	−	0.144752i	0.631017	−	0.775769i	$-0.282638\pi$
$821$	−2.79565e6	−	2.79565e6i	−0.144752	−	0.144752i	−0.775769	+	0.631017i	$0.782638\pi$
$822$	−7.16192e6	−	563152.i	−0.369700	−	0.0290701i
$823$	−9.14826e6			−0.470802			−0.235401	−	0.971898i	$-0.575640\pi$
$823$	−9.14826e6			−0.470802			−0.235401	+	0.971898i	$0.575640\pi$
$824$	2.73426e6	+	4.45981e6i	0.140288	+	0.228822i
$825$	−16381.1	+	107779.i	−0.000837929	+	0.00551313i
$826$	3.28115e7	+	2.58002e6i	1.67331	+	0.131575i
$827$	−8.20997e6	+	8.20997e6i	−0.417424	+	0.417424i	−0.884315	−	0.466891i	$-0.845374\pi$
$827$	−8.20997e6	+	8.20997e6i	−0.417424	+	0.417424i	0.466891	+	0.884315i	$0.345374\pi$
$828$	1.67577e7	+	2.65176e6i	0.849453	+	0.134418i
$829$	−2.06416e7	+	2.06416e7i	−1.04317	+	1.04317i	−0.0441490	+	0.999025i	$0.514058\pi$
$829$	−2.06416e7	+	2.06416e7i	−1.04317	+	1.04317i	−0.999025	+	0.0441490i	$0.985942\pi$
$830$	−2.68659e6	+	1.73202e7i	−0.135365	+	0.872684i
$831$	1.33189e6			0.0669060
$832$	−3.62393e7	+	1.17917e7i	−1.81498	+	0.590564i
$833$			1.97168e7i			0.984517i
$834$	535579.	+	626994.i	0.0266630	+	0.0312139i
$835$	437194.	−	5.78604e6i	0.0216999	−	0.287187i
$836$	−68639.9	+	433767.i	−0.00339673	+	0.0214655i
$837$	−5.79204e6	+	5.79204e6i	−0.285771	+	0.285771i
$838$	40978.4	−	521145.i	0.00201579	−	0.0256359i
$839$			9.11045e6i			0.446822i	0.974724	+	0.223411i	$0.0717192\pi$
$839$			9.11045e6i			0.446822i	−0.974724	+	0.223411i	$0.928281\pi$
$840$	6.64677e6	+	2.13520e6i	0.325022	+	0.104410i
$841$			1.89392e7i			0.923362i
$842$	−1.25724e7	−	988583.i	−0.611135	−	0.0480544i
$843$	1.03322e6	−	1.03322e6i	0.0500755	−	0.0500755i
$844$	7.65722e6	+	1.05362e7i	0.370012	+	0.509128i
$845$	5.47003e7	+	4.13316e6i	2.63541	+	0.199132i
$846$	−3.41704e6	+	2.91884e6i	−0.164144	+	0.140212i
$847$			3.28827e7i			1.57492i
$848$	−2.27579e6	+	1.16037e6i	−0.108678	+	0.0554126i
$849$	485078.			0.0230963
$850$	7.37845e6	+	1.18716e7i	0.350282	+	0.563587i
$851$	1.44176e6	−	1.44176e6i	0.0682447	−	0.0682447i
$852$	−1.40888e6	−	1.93859e6i	−0.0664929	−	0.0914928i
$853$	1.96053e7	−	1.96053e7i	0.922571	−	0.922571i	−0.0746395	−	0.997211i	$-0.523781\pi$
$853$	1.96053e7	−	1.96053e7i	0.922571	−	0.922571i	0.997211	+	0.0746395i	$0.0237806\pi$
$854$	2.32437e6	−	2.95603e7i	0.109059	−	1.38696i
$855$	1.30429e7	−	1.12103e7i	0.610181	−	0.524448i
$856$	−1.79560e7	−	4.30688e6i	−0.837579	−	0.200899i
$857$	−3.64873e7			−1.69703			−0.848515	−	0.529172i	$-0.822503\pi$
$857$	−3.64873e7			−1.69703			−0.848515	+	0.529172i	$0.822503\pi$
$858$	−17991.1	+	228803.i	−0.000834333	+	0.0106107i
$859$	−1.63107e7	−	1.63107e7i	−0.754203	−	0.754203i	0.221057	−	0.975261i	$-0.429049\pi$
$859$	−1.63107e7	−	1.63107e7i	−0.754203	−	0.754203i	−0.975261	+	0.221057i	$0.929049\pi$
$860$	2.07715e7	−	1.28222e7i	0.957681	−	0.591174i
$861$	−6.07176e6	+	6.07176e6i	−0.279130	+	0.279130i
$862$	1.77506e7	−	1.51626e7i	0.813662	−	0.695031i
$863$		−	1.19773e7i		−	0.547436i	−0.961810	−	0.273718i	$-0.911746\pi$
$863$		−	1.19773e7i		−	0.547436i	0.961810	−	0.273718i	$-0.0882536\pi$
$864$	−3.54952e6	+	8.57777e6i	−0.161765	+	0.390922i
$865$	1.64578e7	−	1.41454e7i	0.747878	−	0.642798i
$866$	−1.04946e6	−	1.22859e6i	−0.0475524	−	0.0556688i
$867$	−1.89740e6	−	1.89740e6i	−0.0857257	−	0.0857257i
$868$	−5.22295e6	+	3.30062e7i	−0.235297	+	1.48695i
$869$	−530407.	−	530407.i	−0.0238265	−	0.0238265i
$870$	790376.	+	1.08059e6i	0.0354026	+	0.0484018i
$871$		−	7.79039e7i		−	3.47948i
$872$	3.51507e7	+	8.43114e6i	1.56546	+	0.375487i
$873$	1.13639e7			0.504653
$874$	−1.34854e6	+	1.71502e7i	−0.0597154	+	0.759434i
$875$	8.00653e6	−	3.47820e7i	0.353528	−	1.53580i
$876$	844877.	−	614020.i	0.0371992	−	0.0270347i
$877$	−1.45799e7	−	1.45799e7i	−0.640109	−	0.640109i	0.310473	−	0.950582i	$-0.399513\pi$
$877$	−1.45799e7	−	1.45799e7i	−0.640109	−	0.640109i	−0.950582	+	0.310473i	$0.899513\pi$
$878$	−3.20966e6	−	3.75750e6i	−0.140515	−	0.164499i
$879$	−450038.			−0.0196461
$880$	−545597.	+	228172.i	−0.0237501	+	0.00993241i
$881$	2.68282e7			1.16453			0.582267	−	0.812998i	$-0.302166\pi$
$881$	2.68282e7			1.16453			0.582267	+	0.812998i	$0.302166\pi$
$882$	2.12185e7	+	2.48402e7i	0.918424	+	1.07518i
$883$	2.56769e6	+	2.56769e6i	0.110826	+	0.110826i	0.760345	−	0.649519i	$-0.225030\pi$
$883$	2.56769e6	+	2.56769e6i	0.110826	+	0.110826i	−0.649519	+	0.760345i	$0.725030\pi$
$884$	1.73000e7	+	2.38044e7i	0.744586	+	1.02453i
$885$	−5.36022e6	−	405019.i	−0.230051	−	0.0173827i
$886$	1.73547e6	−	2.20710e7i	0.0742733	−	0.944576i
$887$	2.19383e7			0.936253			0.468126	−	0.883662i	$-0.344929\pi$
$887$	2.19383e7			0.936253			0.468126	+	0.883662i	$0.344929\pi$
$888$	284551.	+	464127.i	0.0121096	+	0.0197517i
$889$		−	3.57293e7i		−	1.51625i
$890$	−2.80097e7	+	2.04872e7i	−1.18531	+	0.866976i
$891$	−371591.	−	371591.i	−0.0156809	−	0.0156809i
$892$	5.74064e6	+	908406.i	0.241573	+	0.0382268i
$893$	−3.22209e6	−	3.22209e6i	−0.135210	−	0.135210i
$894$	−3.77336e6	−	4.41741e6i	−0.157901	−	0.184852i
$895$	7.92918e6	+	9.22538e6i	0.330880	+	0.384970i
$896$	8.85902e6	+	3.68211e7i	0.368651	+	1.53224i
$897$			8.99042e6i			0.373077i
$898$	−2.73502e6	+	2.33626e6i	−0.113180	+	0.0966787i
$899$	−4.53135e6	+	4.53135e6i	−0.186994	+	0.186994i
$900$	2.20715e7	+	7.01597e6i	0.908292	+	0.288723i
$901$	1.39479e6	+	1.39479e6i	0.0572396	+	0.0572396i
$902$	57019.2	−	725146.i	0.00233349	−	0.0296763i
$903$	−9.41423e6			−0.384207
$904$	1.90813e7	−	1.16986e7i	0.776583	−	0.476115i
$905$	−2.85128e7	+	2.45067e7i	−1.15723	+	0.994633i
$906$	596086.	−	7.58076e6i	0.0241262	−	0.306826i
$907$	3.23641e6	−	3.23641e6i	0.130631	−	0.130631i	−0.638768	−	0.769399i	$-0.720556\pi$
$907$	3.23641e6	−	3.23641e6i	0.130631	−	0.130631i	0.769399	+	0.638768i	$0.220556\pi$
$908$	−3.09821e7	+	2.25165e7i	−1.24709	+	0.906328i
$909$	−5.44337e6	+	5.44337e6i	−0.218503	+	0.218503i
$910$	1.15176e7	−	7.42526e7i	0.461060	−	2.97241i
$911$	−7.31177e6			−0.291895			−0.145947	−	0.989292i	$-0.546623\pi$
$911$	−7.31177e6			−0.291895			−0.145947	+	0.989292i	$0.546623\pi$
$912$	−4.36890e6	−	1.41819e6i	−0.173934	−	0.0564609i
$913$			572613.i			0.0227345i
$914$	−1.66970e7	+	1.42626e7i	−0.661107	+	0.564719i
$915$	−364887.	+	4.82909e6i	−0.0144081	+	0.190683i
$916$	3.88002e6	−	2.81983e6i	0.152790	−	0.111041i
$917$	4.21872e7	−	4.21872e7i	1.65675	−	1.65675i
$918$	7.14608e6	+	561906.i	0.279873	+	0.0220068i
$919$		−	428349.i		−	0.0167305i	−0.999965	−	0.00836526i	$-0.997337\pi$
$919$		−	428349.i		−	0.0167305i	0.999965	−	0.00836526i	$-0.00266278\pi$
$920$	−2.06059e7	+	1.05859e7i	−0.802642	+	0.412342i
$921$			4.52575e6i			0.175809i
$922$	2.03112e6	−	2.58310e7i	0.0786881	−	1.00072i
$923$	−1.82387e7	+	1.82387e7i	−0.704678	+	0.704678i
$924$	225275.	+	35647.8i	0.00868027	+	0.00137358i
$925$	2.24146e6	−	1.65000e6i	0.0861343	−	0.0634060i
$926$	2.39147e7	+	2.79965e7i	0.916510	+	1.07294i
$927$		−	6.69292e6i		−	0.255809i
$928$	−2.77693e6	+	6.71074e6i	−0.105851	+	0.255800i
$929$	2.19323e7			0.833766			0.416883	−	0.908960i	$-0.363122\pi$
$929$	2.19323e7			0.833766			0.416883	+	0.908960i	$0.363122\pi$
$930$	836578.	−	5.39334e6i	0.0317175	−	0.204480i
$931$	−2.34230e7	+	2.34230e7i	−0.885661	+	0.885661i
$932$	−4.77446e6	+	3.01720e7i	−0.180046	+	1.13780i
$933$	6.55750e6	−	6.55750e6i	0.246623	−	0.246623i
$934$	−7.33958e6	−	577121.i	−0.275298	−	0.0216471i
$935$	297652.	+	346310.i	0.0111347	+	0.0129550i
$936$	4.74128e7	+	1.13723e7i	1.76891	+	0.424286i
$937$	−1.89926e7			−0.706699			−0.353350	−	0.935491i	$-0.614957\pi$
$937$	−1.89926e7			−0.706699			−0.353350	+	0.935491i	$0.614957\pi$
$938$	−7.71799e7	−	6.06876e6i	−2.86416	−	0.225213i
$939$	−6.08354e6	−	6.08354e6i	−0.225161	−	0.225161i
$940$	1.41298e6	−	5.97126e6i	0.0521576	−	0.220418i
$941$	1.53358e6	−	1.53358e6i	0.0564589	−	0.0564589i	−0.678314	−	0.734772i	$-0.737289\pi$
$941$	1.53358e6	−	1.53358e6i	0.0564589	−	0.0564589i	0.734772	+	0.678314i	$0.237289\pi$
$942$	−5.06393e6	−	5.92826e6i	−0.185935	−	0.217671i
$943$		−	2.84934e7i		−	1.04343i
$944$	−1.32460e7	−	2.59787e7i	−0.483786	−	0.948828i
$945$	−1.19307e7	−	1.38810e7i	−0.434596	−	0.505640i
$946$	606371.	−	517963.i	0.0220298	−	0.0188179i
$947$	4.39781e6	+	4.39781e6i	0.159354	+	0.159354i	0.782280	−	0.622927i	$-0.214056\pi$
$947$	4.39781e6	+	4.39781e6i	0.159354	+	0.159354i	−0.622927	+	0.782280i	$0.714056\pi$
$948$	6.34653e6	−	4.61238e6i	0.229359	−	0.166688i
$949$	−7.94882e6	−	7.94882e6i	−0.286508	−	0.286508i
$950$	−5.33770e6	+	2.28685e7i	−0.191887	+	0.822106i
$951$		−	2.40972e6i		−	0.0864003i
$952$	2.49308e7	−	1.52848e7i	0.891547	−	0.546598i
$953$	3.52814e7			1.25838			0.629192	−	0.777250i	$-0.283386\pi$
$953$	3.52814e7			1.25838			0.629192	+	0.777250i	$0.283386\pi$
$954$	3.25825e6	+	256201.i	0.115908	+	0.00911400i
$955$	1.97117e6	−	2.60874e7i	0.0699384	−	0.925599i
$956$	1.94423e6	−	1.22865e7i	0.0688023	−	0.434794i
$957$	30927.5	+	30927.5i	0.00109160	+	0.00109160i
$958$	2.52571e7	−	2.15746e7i	0.889138	−	0.759503i
$959$	7.68403e7			2.69800
$960$	−1.46526e6	−	6.00938e6i	−0.0513140	−	0.210451i
$961$	−2.50453e6			−0.0874817
$962$	4.45537e6	−	3.80579e6i	0.155220	−	0.132589i
$963$	1.67052e7	+	1.67052e7i	0.580478	+	0.580478i
$964$	−4.65255e6	+	2.94016e7i	−0.161249	+	1.01901i
$965$	3.86186e7	+	2.91803e6i	1.33499	+	0.100872i
$966$	8.90686e6	+	700359.i	0.307101	+	0.0241478i
$967$	−4.54849e7			−1.56423			−0.782116	−	0.623133i	$-0.785860\pi$
$967$	−4.54849e7			−1.56423			−0.782116	+	0.623133i	$0.785860\pi$
$968$	2.48376e7	−	1.52277e7i	0.851966	−	0.522331i
$969$			3.54680e6i			0.121347i
$970$	−1.25239e7	+	9.16041e6i	−0.427377	+	0.312598i
$971$	−1.07357e7	−	1.07357e7i	−0.365410	−	0.365410i	0.500390	−	0.865800i	$-0.333190\pi$
$971$	−1.07357e7	−	1.07357e7i	−0.365410	−	0.365410i	−0.865800	+	0.500390i	$0.833190\pi$
$972$	1.45269e7	−	1.05575e7i	0.493184	−	0.358424i
$973$	−6.23663e6	−	6.23663e6i	−0.211187	−	0.211187i
$974$	−7.32845e6	+	6.25997e6i	−0.247522	+	0.211434i
$975$	−1.84408e6	+	1.21330e7i	−0.0621252	+	0.408750i
$976$	−2.34045e7	+	1.19335e7i	−0.786458	+	0.400997i
$977$		−	4.69159e7i		−	1.57247i	−0.617926	−	0.786237i	$-0.712027\pi$
$977$		−	4.69159e7i		−	1.57247i	0.617926	−	0.786237i	$-0.287973\pi$
$978$	−6.21182e6	−	7.27207e6i	−0.207669	−	0.243115i
$979$	−801665.	+	801665.i	−0.0267323	+	0.0267323i
$980$	−4.34080e7	−	1.02717e7i	−1.44379	−	0.341645i
$981$	−3.27020e7	−	3.27020e7i	−1.08493	−	1.08493i
$982$	−2.23507e7	−	1.75747e6i	−0.739627	−	0.0581579i
$983$	5.08035e7			1.67691			0.838455	−	0.544971i	$-0.183459\pi$
$983$	5.08035e7			1.67691			0.838455	+	0.544971i	$0.183459\pi$
$984$	7.39803e6	+	1.77447e6i	0.243573	+	0.0584226i
$985$	2.21214e7	+	2.57377e7i	0.726479	+	0.845238i
$986$	5.59067e6	+	439602.i	0.183135	+	0.0144002i
$987$	−1.67338e6	+	1.67338e6i	−0.0546765	+	0.0546765i
$988$	−7.72704e6	+	4.88308e7i	−0.251838	+	1.59148i
$989$	2.20894e7	−	2.20894e7i	0.718114	−	0.718114i
$990$	747684.	+	115976.i	0.0242454	+	0.00376079i
$991$	−4.16886e7			−1.34845			−0.674223	−	0.738528i	$-0.735521\pi$
$991$	−4.16886e7			−1.34845			−0.674223	+	0.738528i	$0.735521\pi$
$992$	2.73497e7	−	1.13398e7i	0.882416	−	0.365870i
$993$		−	2.26952e6i		−	0.0730401i
$994$	1.66484e7	+	1.94900e7i	0.534450	+	0.625672i
$995$	−2.22776e6	−	168330.i	−0.0713362	−	0.00539018i
$996$	−5.91548e6	−	936073.i	−0.188948	−	0.0298993i
$997$	187496.	−	187496.i	0.00597384	−	0.00597384i	−0.704114	−	0.710087i	$-0.748655\pi$
$997$	187496.	−	187496.i	0.00597384	−	0.00597384i	0.710087	+	0.704114i	$0.248655\pi$
$998$	−4.41323e6	+	5.61256e7i	−0.140259	+	1.78375i
$999$		−	1.42734e6i		−	0.0452495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.69.13	yes	116
5.4	even	2	inner	80.6.q.a.69.46	yes	116
16.13	even	4	inner	80.6.q.a.29.46	yes	116
80.29	even	4	inner	80.6.q.a.29.13	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.13	✓	116	80.29	even	4	inner
80.6.q.a.29.46	yes	116	16.13	even	4	inner
80.6.q.a.69.13	yes	116	1.1	even	1	trivial
80.6.q.a.69.46	yes	116	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.30125 + 3.67413i) q^{2} +(-2.38770 - 2.38770i) q^{3} +(5.00149 - 31.6067i) q^{4} +(4.21193 - 55.7428i) q^{5} +(19.0429 + 1.49737i) q^{6} -204.311 q^{7} +(94.6147 + 154.325i) q^{8} -231.598i q^{9} +O(q^{10})\)	\(q+(-4.30125 + 3.67413i) q^{2} +(-2.38770 - 2.38770i) q^{3} +(5.00149 - 31.6067i) q^{4} +(4.21193 - 55.7428i) q^{5} +(19.0429 + 1.49737i) q^{6} -204.311 q^{7} +(94.6147 + 154.325i) q^{8} -231.598i q^{9} +(186.690 + 255.239i) q^{10} +(7.30519 + 7.30519i) q^{11} +(-87.4096 + 63.5254i) q^{12} +(822.372 + 822.372i) q^{13} +(878.792 - 750.665i) q^{14} +(-143.154 + 123.040i) q^{15} +(-973.970 - 316.161i) q^{16} +790.697i q^{17} +(850.921 + 996.160i) q^{18} +(-939.325 + 939.325i) q^{19} +(-1740.78 - 411.922i) q^{20} +(487.834 + 487.834i) q^{21} +(-58.2617 - 4.58120i) q^{22} -2289.29 q^{23} +(142.569 - 594.393i) q^{24} +(-3089.52 - 469.570i) q^{25} +(-6558.73 - 515.722i) q^{26} +(-1133.20 + 1133.20i) q^{27} +(-1021.86 + 6457.60i) q^{28} +(-886.548 + 886.548i) q^{29} +(163.675 - 1055.20i) q^{30} +5111.23 q^{31} +(5350.91 - 2218.61i) q^{32} -34.8853i q^{33} +(-2905.13 - 3400.99i) q^{34} +(-860.544 + 11388.9i) q^{35} +(-7320.05 - 1158.33i) q^{36} +(-629.784 + 629.784i) q^{37} +(589.065 - 7491.48i) q^{38} -3927.16i q^{39} +(9000.99 - 4624.08i) q^{40} +12446.4i q^{41} +(-3890.66 - 305.928i) q^{42} +(-9649.01 + 9649.01i) q^{43} +(267.430 - 194.356i) q^{44} +(-12909.9 - 975.474i) q^{45} +(9846.81 - 8411.16i) q^{46} +3430.22i q^{47} +(1570.65 + 3080.45i) q^{48} +24935.9 q^{49} +(15014.1 - 9331.57i) q^{50} +(1887.95 - 1887.95i) q^{51} +(30105.6 - 21879.4i) q^{52} +(1764.00 - 1764.00i) q^{53} +(710.647 - 9037.70i) q^{54} +(437.981 - 376.443i) q^{55} +(-19330.8 - 31530.2i) q^{56} +4485.66 q^{57} +(555.968 - 7070.56i) q^{58} +(20136.5 + 20136.5i) q^{59} +(3172.92 + 5140.02i) q^{60} +(18141.2 - 18141.2i) q^{61} +(-21984.7 + 18779.3i) q^{62} +47317.9i q^{63} +(-14864.1 + 29202.7i) q^{64} +(49305.1 - 42377.5i) q^{65} +(128.173 + 150.050i) q^{66} +(-47365.4 - 47365.4i) q^{67} +(24991.4 + 3954.66i) q^{68} +(5466.15 + 5466.15i) q^{69} +(-38142.8 - 52148.1i) q^{70} +22178.2i q^{71} +(35741.2 - 21912.6i) q^{72} -9665.73 q^{73} +(394.947 - 5022.77i) q^{74} +(6255.66 + 8498.05i) q^{75} +(24991.0 + 34387.0i) q^{76} +(-1492.53 - 1492.53i) q^{77} +(14428.9 + 16891.7i) q^{78} -72606.8 q^{79} +(-21726.0 + 52960.2i) q^{80} -50866.8 q^{81} +(-45729.6 - 53534.9i) q^{82} +(39192.2 + 39192.2i) q^{83} +(17858.7 - 12978.9i) q^{84} +(44075.7 + 3330.37i) q^{85} +(6051.04 - 76954.5i) q^{86} +4233.63 q^{87} +(-436.192 + 1818.55i) q^{88} +109739. i q^{89} +(59112.7 - 43237.0i) q^{90} +(-168019. - 168019. i) q^{91} +(-11449.9 + 72357.0i) q^{92} +(-12204.1 - 12204.1i) q^{93} +(-12603.1 - 14754.2i) q^{94} +(48404.2 + 56317.0i) q^{95} +(-18073.8 - 7479.00i) q^{96} +49067.5i q^{97} +(-107256. + 91618.0i) q^{98} +(1691.87 - 1691.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

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