LMFDB - Embedded newform 42.6.f.a.17.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,6,Mod(5,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("42.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, 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:	$6.73612043215$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	42.17
Dual form			42.6.f.a.5.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.46410 - 2.00000i) q^{2} +(9.95138 + 11.9988i) q^{3} +(8.00000 - 13.8564i) q^{4} +(41.5931 + 72.0414i) q^{5} +(58.4701 + 21.6621i) q^{6} +(-128.746 - 15.2171i) q^{7} -64.0000i q^{8} +(-44.9401 + 238.808i) q^{9} +(288.166 + 166.372i) q^{10} +(455.598 + 263.039i) q^{11} +(245.871 - 41.9003i) q^{12} -776.119i q^{13} +(-476.422 + 204.778i) q^{14} +(-450.498 + 1215.98i) q^{15} +(-128.000 - 221.703i) q^{16} +(236.487 - 409.607i) q^{17} +(321.939 + 917.136i) q^{18} +(1715.14 - 990.236i) q^{19} +1330.98 q^{20} +(-1098.61 - 1696.22i) q^{21} +2104.32 q^{22} +(-1495.70 + 863.545i) q^{23} +(767.920 - 636.888i) q^{24} +(-1897.48 + 3286.52i) q^{25} +(-1552.24 - 2688.56i) q^{26} +(-3312.62 + 1837.25i) q^{27} +(-1240.82 + 1662.22i) q^{28} -6041.29i q^{29} +(871.383 + 5113.26i) q^{30} +(-7504.86 - 4332.93i) q^{31} +(-886.810 - 512.000i) q^{32} +(1377.68 + 8084.21i) q^{33} -1891.89i q^{34} +(-4258.67 - 9907.94i) q^{35} +(2949.50 + 2533.17i) q^{36} +(1507.67 + 2611.36i) q^{37} +(3960.94 - 6860.55i) q^{38} +(9312.46 - 7723.46i) q^{39} +(4610.65 - 2661.96i) q^{40} -1633.44 q^{41} +(-7198.14 - 3678.65i) q^{42} -1198.75 q^{43} +(7289.56 - 4208.63i) q^{44} +(-19073.3 + 6695.23i) q^{45} +(-3454.18 + 5982.81i) q^{46} +(1937.57 + 3355.97i) q^{47} +(1386.38 - 3742.09i) q^{48} +(16343.9 + 3918.26i) q^{49} +15179.8i q^{50} +(7268.14 - 1238.61i) q^{51} +(-10754.2 - 6208.95i) q^{52} +(3242.15 + 1871.86i) q^{53} +(-7800.75 + 12989.6i) q^{54} +43762.5i q^{55} +(-973.892 + 8239.72i) q^{56} +(28949.6 + 10725.3i) q^{57} +(-12082.6 - 20927.6i) q^{58} +(3242.61 - 5616.36i) q^{59} +(13245.1 + 15970.1i) q^{60} +(38557.1 - 22260.9i) q^{61} -34663.5 q^{62} +(9419.81 - 30061.7i) q^{63} -4096.00 q^{64} +(55912.7 - 32281.2i) q^{65} +(20940.8 + 25249.2i) q^{66} +(-12183.6 + 21102.5i) q^{67} +(-3783.79 - 6553.71i) q^{68} +(-25245.8 - 9353.12i) q^{69} +(-34568.4 - 25804.8i) q^{70} +83508.1i q^{71} +(15283.7 + 2876.17i) q^{72} +(11102.7 + 6410.14i) q^{73} +(10445.5 + 6030.69i) q^{74} +(-58316.7 + 9938.11i) q^{75} -31687.5i q^{76} +(-54653.5 - 40798.0i) q^{77} +(16812.4 - 45379.8i) q^{78} +(-20166.2 - 34928.9i) q^{79} +(10647.8 - 18442.6i) q^{80} +(-55009.8 - 21464.1i) q^{81} +(-5658.42 + 3266.89i) q^{82} -72802.8 q^{83} +(-32292.4 + 1653.06i) q^{84} +39344.9 q^{85} +(-4152.59 + 2397.50i) q^{86} +(72487.9 - 60119.1i) q^{87} +(16834.5 - 29158.2i) q^{88} +(-29278.3 - 50711.6i) q^{89} +(-52681.3 + 61339.5i) q^{90} +(-11810.3 + 99922.0i) q^{91} +27633.4i q^{92} +(-22693.9 - 133168. i) q^{93} +(13423.9 + 7750.29i) q^{94} +(142676. + 82374.0i) q^{95} +(-2681.62 - 15735.7i) q^{96} -1016.75i q^{97} +(64453.4 - 19114.5i) q^{98} +(-83290.6 + 96979.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 224 q^{4} - 154 q^{7} - 30 q^{9} + 744 q^{10} - 516 q^{15} - 3584 q^{16} + 1632 q^{18} + 2652 q^{19} + 7236 q^{21} + 3312 q^{22} - 1920 q^{24} - 13208 q^{25} - 5024 q^{28} + 2448 q^{30} + 22458 q^{31}+ \cdots + 153216 q^{99}+O(q^{100}) $ 28 * q + 224 * q^4 - 154 * q^7 - 30 * q^9 + 744 * q^10 - 516 * q^15 - 3584 * q^16 + 1632 * q^18 + 2652 * q^19 + 7236 * q^21 + 3312 * q^22 - 1920 * q^24 - 13208 * q^25 - 5024 * q^28 + 2448 * q^30 + 22458 * q^31 - 43542 * q^33 - 960 * q^36 + 5488 * q^37 + 21888 * q^39 + 11904 * q^40 + 33288 * q^42 - 40352 * q^43 + 5796 * q^45 - 11568 * q^46 - 2126 * q^49 - 34572 * q^51 - 41472 * q^52 - 60408 * q^54 + 57168 * q^57 + 42552 * q^58 - 4128 * q^60 + 298200 * q^61 + 46560 * q^63 - 114688 * q^64 + 165312 * q^66 + 55148 * q^67 - 36120 * q^70 - 26112 * q^72 - 427596 * q^73 - 458640 * q^75 + 87840 * q^78 + 471794 * q^79 - 245538 * q^81 + 118176 * q^82 + 4608 * q^84 - 562056 * q^85 + 833454 * q^87 + 26496 * q^88 - 132876 * q^91 - 560448 * q^93 - 444576 * q^94 - 30720 * q^96 + 153216 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	3.46410	−	2.00000i	0.612372	−	0.353553i
$2$	3.46410	−	2.00000i	0.612372	−	0.353553i
$3$	9.95138	+	11.9988i	0.638381	+	0.769720i
$3$	9.95138	+	11.9988i	0.638381	+	0.769720i
$4$	8.00000	−	13.8564i	0.250000	−	0.433013i
$5$	41.5931	+	72.0414i	0.744040	+	1.28872i	0.950642	+	0.310291i	$0.100426\pi$
$5$	41.5931	+	72.0414i	0.744040	+	1.28872i	−0.206601	+	0.978425i	$0.566240\pi$
$6$	58.4701	+	21.6621i	0.663064	+	0.245654i
$7$	−128.746	−	15.2171i	−0.993087	−	0.117378i
$7$	−128.746	−	15.2171i	−0.993087	−	0.117378i
$8$		−	64.0000i		−	0.353553i
$9$	−44.9401	+	238.808i	−0.184939	+	0.982750i
$10$	288.166	+	166.372i	0.911260	+	0.526116i
$11$	455.598	+	263.039i	1.13527	+	0.655449i	0.945255	−	0.326332i	$-0.105813\pi$
$11$	455.598	+	263.039i	1.13527	+	0.655449i	0.190016	+	0.981781i	$0.439146\pi$
$12$	245.871	−	41.9003i	0.492894	−	0.0839971i
$13$		−	776.119i		−	1.27371i	−0.770984	−	0.636854i	$-0.780235\pi$
$13$		−	776.119i		−	1.27371i	0.770984	−	0.636854i	$-0.219765\pi$
$14$	−476.422	+	204.778i	−0.649639	+	0.279230i
$15$	−450.498	+	1215.98i	−0.516969	+	1.39540i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	236.487	−	409.607i	0.198465	−	0.343752i	−0.749566	−	0.661930i	$-0.769738\pi$
$17$	236.487	−	409.607i	0.198465	−	0.343752i	0.948031	+	0.318178i	$0.103071\pi$
$18$	321.939	+	917.136i	0.234203	+	0.667195i
$19$	1715.14	−	990.236i	1.08997	−	0.629295i	0.156403	−	0.987693i	$-0.450010\pi$
$19$	1715.14	−	990.236i	1.08997	−	0.629295i	0.933569	+	0.358398i	$0.116677\pi$
$20$	1330.98			0.744040
$21$	−1098.61	−	1696.22i	−0.543620	−	0.839331i
$22$	2104.32			0.926945
$23$	−1495.70	+	863.545i	−0.589557	+	0.340381i	−0.764922	−	0.644122i	$-0.777223\pi$
$23$	−1495.70	+	863.545i	−0.589557	+	0.340381i	0.175365	+	0.984503i	$0.443889\pi$
$24$	767.920	−	636.888i	0.272137	−	0.225702i
$25$	−1897.48	+	3286.52i	−0.607192	+	1.05169i
$26$	−1552.24	−	2688.56i	−0.450324	−	0.779984i
$27$	−3312.62	+	1837.25i	−0.874504	+	0.485018i
$28$	−1240.82	+	1662.22i	−0.299098	+	0.400675i
$29$		−	6041.29i		−	1.33393i	−0.745087	−	0.666967i	$-0.767592\pi$
$29$		−	6041.29i		−	1.33393i	0.745087	−	0.666967i	$-0.232408\pi$
$30$	871.383	+	5113.26i	0.176769	+	1.03728i
$31$	−7504.86	−	4332.93i	−1.40262	−	0.809800i	−0.407955	−	0.913002i	$-0.633758\pi$
$31$	−7504.86	−	4332.93i	−1.40262	−	0.809800i	−0.994660	+	0.103202i	$0.967091\pi$
$32$	−886.810	−	512.000i	−0.153093	−	0.0883883i
$33$	1377.68	+	8084.21i	0.220223	+	1.29227i
$34$		−	1891.89i		−	0.280672i
$35$	−4258.67	−	9907.94i	−0.587631	−	1.36714i
$36$	2949.50	+	2533.17i	0.379309	+	0.325768i
$37$	1507.67	+	2611.36i	0.181052	+	0.313591i	0.942239	−	0.334941i	$-0.108717\pi$
$37$	1507.67	+	2611.36i	0.181052	+	0.313591i	−0.761187	+	0.648532i	$0.775383\pi$
$38$	3960.94	−	6860.55i	0.444979	−	0.770726i
$39$	9312.46	−	7723.46i	0.980399	−	0.813112i
$40$	4610.65	−	2661.96i	0.455630	−	0.263058i
$41$	−1633.44			−0.151756			−0.0758778	−	0.997117i	$-0.524176\pi$
$41$	−1633.44			−0.151756			−0.0758778	+	0.997117i	$0.524176\pi$
$42$	−7198.14	−	3678.65i	−0.629646	−	0.321785i
$43$	−1198.75			−0.0988682			−0.0494341	−	0.998777i	$-0.515742\pi$
$43$	−1198.75			−0.0988682			−0.0494341	+	0.998777i	$0.515742\pi$
$44$	7289.56	−	4208.63i	0.567636	−	0.327725i
$45$	−19073.3	+	6695.23i	−1.40409	+	0.492872i
$46$	−3454.18	+	5982.81i	−0.240686	+	0.416880i
$47$	1937.57	+	3355.97i	0.127942	+	0.221602i	0.922879	−	0.385090i	$-0.125830\pi$
$47$	1937.57	+	3355.97i	0.127942	+	0.221602i	−0.794937	+	0.606692i	$0.792496\pi$
$48$	1386.38	−	3742.09i	0.0868517	−	0.234429i
$49$	16343.9	+	3918.26i	0.972445	+	0.233133i
$50$			15179.8i			0.858700i
$51$	7268.14	−	1238.61i	0.391289	−	0.0666820i
$52$	−10754.2	−	6208.95i	−0.551532	−	0.318427i
$53$	3242.15	+	1871.86i	0.158542	+	0.0915342i	0.577172	−	0.816623i	$-0.304156\pi$
$53$	3242.15	+	1871.86i	0.158542	+	0.0915342i	−0.418630	+	0.908157i	$0.637490\pi$
$54$	−7800.75	+	12989.6i	−0.364042	+	0.606196i
$55$			43762.5i			1.95072i
$56$	−973.892	+	8239.72i	−0.0414993	+	0.351109i
$57$	28949.6	+	10725.3i	1.18020	+	0.437243i
$58$	−12082.6	−	20927.6i	−0.471617	−	0.816865i
$59$	3242.61	−	5616.36i	0.121273	−	0.210051i	−0.798997	−	0.601335i	$-0.794636\pi$
$59$	3242.61	−	5616.36i	0.121273	−	0.210051i	0.920270	+	0.391284i	$0.127969\pi$
$60$	13245.1	+	15970.1i	0.474981	+	0.572703i
$61$	38557.1	−	22260.9i	1.32672	−	0.765983i	0.341930	−	0.939725i	$-0.388919\pi$
$61$	38557.1	−	22260.9i	1.32672	−	0.765983i	0.984791	+	0.173742i	$0.0555860\pi$
$62$	−34663.5			−1.14523
$63$	9419.81	−	30061.7i	0.299013	−	0.954249i
$64$	−4096.00			−0.125000
$65$	55912.7	−	32281.2i	1.64145	−	0.947691i
$66$	20940.8	+	25249.2i	0.591744	+	0.713489i
$67$	−12183.6	+	21102.5i	−0.331579	+	0.574312i	−0.982822	−	0.184558i	$-0.940915\pi$
$67$	−12183.6	+	21102.5i	−0.331579	+	0.574312i	0.651243	+	0.758870i	$0.274248\pi$
$68$	−3783.79	−	6553.71i	−0.0992326	−	0.171876i
$69$	−25245.8	−	9353.12i	−0.638360	−	0.236501i
$70$	−34568.4	−	25804.8i	−0.843206	−	0.629441i
$71$			83508.1i			1.96600i	0.183614	+	0.982999i	$0.441221\pi$
$71$			83508.1i			1.96600i	−0.183614	+	0.982999i	$0.558779\pi$
$72$	15283.7	+	2876.17i	0.347455	+	0.0653857i
$73$	11102.7	+	6410.14i	0.243849	+	0.140786i	0.616944	−	0.787007i	$-0.288370\pi$
$73$	11102.7	+	6410.14i	0.243849	+	0.140786i	−0.373096	+	0.927793i	$0.621704\pi$
$74$	10445.5	+	6030.69i	0.221742	+	0.128023i
$75$	−58316.7	+	9938.11i	−1.19713	+	0.204010i
$76$		−	31687.5i		−	0.629295i
$77$	−54653.5	−	40798.0i	−1.05049	−	0.784174i
$78$	16812.4	−	45379.8i	0.312891	−	0.844551i
$79$	−20166.2	−	34928.9i	−0.363544	−	0.629677i	0.624997	−	0.780627i	$-0.285100\pi$
$79$	−20166.2	−	34928.9i	−0.363544	−	0.629677i	−0.988541	+	0.150950i	$0.951767\pi$
$80$	10647.8	−	18442.6i	0.186010	−	0.322179i
$81$	−55009.8	−	21464.1i	−0.931595	−	0.363497i
$82$	−5658.42	+	3266.89i	−0.0929310	+	0.0536537i
$83$	−72802.8			−1.15999			−0.579993	−	0.814621i	$-0.696945\pi$
$83$	−72802.8			−1.15999			−0.579993	+	0.814621i	$0.696945\pi$
$84$	−32292.4	+	1653.06i	−0.499346	+	0.0255617i
$85$	39344.9			0.590664
$86$	−4152.59	+	2397.50i	−0.0605442	+	0.0349552i
$87$	72487.9	−	60119.1i	1.02676	−	0.851559i
$88$	16834.5	−	29158.2i	0.231736	−	0.401379i
$89$	−29278.3	−	50711.6i	−0.391806	−	0.678629i	0.600882	−	0.799338i	$-0.294816\pi$
$89$	−29278.3	−	50711.6i	−0.391806	−	0.678629i	−0.992688	+	0.120710i	$0.961483\pi$
$90$	−52681.3	+	61339.5i	−0.685568	+	0.798241i
$91$	−11810.3	+	99922.0i	−0.149505	+	1.26490i
$92$			27633.4i			0.340381i
$93$	−22693.9	−	133168.i	−0.272083	−	1.59658i
$94$	13423.9	+	7750.29i	0.156696	+	0.0904687i
$95$	142676.	+	82374.0i	1.62197	+	0.936442i
$96$	−2681.62	−	15735.7i	−0.0296975	−	0.174264i
$97$		−	1016.75i		−	0.0109720i	−0.999985	−	0.00548598i	$-0.998254\pi$
$97$		−	1016.75i		−	0.0109720i	0.999985	−	0.00548598i	$-0.00174625\pi$
$98$	64453.4	−	19114.5i	0.677923	−	0.201047i
$99$	−83290.6	+	96979.4i	−0.854099	+	0.994470i
$100$	30359.6	+	52584.4i	0.303596	+	0.525844i
$101$	−38949.4	+	67462.3i	−0.379924	+	0.658048i	−0.991051	−	0.133485i	$-0.957383\pi$
$101$	−38949.4	+	67462.3i	−0.379924	+	0.658048i	0.611127	+	0.791533i	$0.290717\pi$
$102$	22700.4	−	18826.9i	0.216039	−	0.179176i
$103$	−27539.1	+	15899.7i	−0.255774	+	0.147671i	−0.622405	−	0.782695i	$-0.713844\pi$
$103$	−27539.1	+	15899.7i	−0.255774	+	0.147671i	0.366631	+	0.930366i	$0.380511\pi$
$104$	−49671.6			−0.450324
$105$	76503.3	−	149696.i	0.677184	−	1.32507i
$106$	14974.9			0.129449
$107$	−16416.1	+	9477.84i	−0.138615	+	0.0800295i	−0.567704	−	0.823233i	$-0.692168\pi$
$107$	−16416.1	+	9477.84i	−0.138615	+	0.0800295i	0.429089	+	0.903262i	$0.358835\pi$
$108$	−1043.31	+	60598.9i	−0.00860706	+	0.499926i
$109$	73590.8	−	127463.i	0.593277	−	1.02759i	−0.400511	−	0.916292i	$-0.631167\pi$
$109$	73590.8	−	127463.i	0.593277	−	1.02759i	0.993788	−	0.111293i	$-0.0354993\pi$
$110$	87525.0	+	151598.i	0.689685	+	1.19457i
$111$	−16329.7	+	44076.9i	−0.125797	+	0.339550i
$112$	13105.8	+	30491.0i	0.0987229	+	0.229682i
$113$			156121.i			1.15018i	0.818090	+	0.575091i	$0.195033\pi$
$113$			156121.i			1.15018i	−0.818090	+	0.575091i	$0.804967\pi$
$114$	121735.	−	20745.6i	0.877310	−	0.149508i
$115$	−124422.	−	71835.1i	−0.877309	−	0.506514i
$116$	−83710.5	−	48330.3i	−0.577610	−	0.333484i
$117$	185344.	+	34878.9i	1.25174	+	0.235558i
$118$		−	25940.9i		−	0.171506i
$119$	−36679.6	+	49136.5i	−0.237442	+	0.318080i
$120$	77822.5	+	28831.9i	0.493347	+	0.182776i
$121$	57853.9	+	100206.i	0.359227	+	0.622200i
$122$	89043.8	−	154228.i	0.541632	−	0.938134i
$123$	−16255.0	−	19599.3i	−0.0968779	−	0.116809i
$124$	−120078.	+	69327.0i	−0.701308	+	0.404900i
$125$	−55730.8			−0.319022
$126$	−27492.2	−	122976.i	−0.154270	−	0.690073i
$127$	−93493.1			−0.514364			−0.257182	−	0.966363i	$-0.582794\pi$
$127$	−93493.1			−0.514364			−0.257182	+	0.966363i	$0.582794\pi$
$128$	−14189.0	+	8192.00i	−0.0765466	+	0.0441942i
$129$	−11929.2	−	14383.5i	−0.0631156	−	0.0761009i
$130$	129125.	−	223651.i	0.670118	−	1.16068i
$131$	41351.8	+	71623.4i	0.210531	+	0.364651i	0.951881	−	0.306468i	$-0.0991474\pi$
$131$	41351.8	+	71623.4i	0.210531	+	0.364651i	−0.741350	+	0.671119i	$0.765814\pi$
$132$	123039.	+	45584.0i	0.614624	+	0.227707i
$133$	−235885.	+	101389.i	−1.15630	+	0.497007i
$134$			97468.4i			0.468924i
$135$	−270140.	−	162229.i	−1.27572	−	0.766114i
$136$	−26214.8	−	15135.1i	−0.121535	−	0.0701680i
$137$	67342.4	+	38880.2i	0.306540	+	0.176981i	0.645377	−	0.763864i	$-0.276700\pi$
$137$	67342.4	+	38880.2i	0.306540	+	0.176981i	−0.338837	+	0.940845i	$0.610034\pi$
$138$	−106160.	+	18091.4i	−0.474530	+	0.0808676i
$139$			37846.0i			0.166143i	0.996544	+	0.0830717i	$0.0264731\pi$
$139$			37846.0i			0.166143i	−0.996544	+	0.0830717i	$0.973527\pi$
$140$	−171358.	−	20253.6i	−0.738897	−	0.0873338i
$141$	−20986.0	+	56645.0i	−0.0888959	+	0.239946i
$142$	167016.	+	289281.i	0.695085	+	1.20392i
$143$	204150.	−	353598.i	0.834851	−	1.44600i
$144$	58696.7	−	20604.1i	0.235889	−	0.0828033i
$145$	435223.	−	251276.i	1.71906	−	0.992501i
$146$	51281.1			0.199102
$147$	115630.	+	235098.i	0.441344	+	0.897338i
$148$	48245.5			0.181052
$149$	−27044.6	+	15614.2i	−0.0997963	+	0.0576174i	−0.549068	−	0.835778i	$-0.685017\pi$
$149$	−27044.6	+	15614.2i	−0.0997963	+	0.0576174i	0.449271	+	0.893395i	$0.351684\pi$
$150$	−182139.	+	151060.i	−0.660958	+	0.548178i
$151$	−178073.	+	308431.i	−0.635559	+	1.10082i	0.350838	+	0.936436i	$0.385897\pi$
$151$	−178073.	+	308431.i	−0.635559	+	1.10082i	−0.986397	+	0.164383i	$0.947437\pi$
$152$	−63375.1	−	109769.i	−0.222490	−	0.385363i
$153$	87189.8	+	74882.7i	0.301118	+	0.258615i
$154$	−270921.	−	32021.5i	−0.920538	−	0.108803i
$155$		−	720881.i		−	2.41010i
$156$	−32519.7	−	190825.i	−0.106988	−	0.627803i
$157$	274500.	+	158483.i	0.888778	+	0.513136i	0.873543	−	0.486748i	$-0.161817\pi$
$157$	274500.	+	158483.i	0.888778	+	0.513136i	0.0152354	+	0.999884i	$0.495150\pi$
$158$	−139716.	−	80664.9i	−0.445249	−	0.257064i
$159$	9803.94	+	57529.4i	0.0307544	+	0.180467i
$160$		−	85182.7i		−	0.263058i
$161$	205706.	−	88417.4i	0.625435	−	0.268827i
$162$	−233488.	+	35665.6i	−0.698999	+	0.106773i
$163$	−82192.0	−	142361.i	−0.242304	−	0.419683i	0.719066	−	0.694942i	$-0.244570\pi$
$163$	−82192.0	−	142361.i	−0.242304	−	0.419683i	−0.961370	+	0.275259i	$0.911236\pi$
$164$	−13067.6	+	22633.7i	−0.0379389	+	0.0657121i
$165$	−525096.	+	435497.i	−1.50151	+	1.24530i
$166$	−252196.	+	145606.i	−0.710344	+	0.410117i
$167$	−628234.			−1.74313			−0.871565	−	0.490279i	$-0.836895\pi$
$167$	−628234.			−1.74313			−0.871565	+	0.490279i	$0.836895\pi$
$168$	−108558.	+	70311.1i	−0.296748	+	0.192199i
$169$	−231068.			−0.622334
$170$	136295.	−	78689.7i	0.361707	−	0.208831i
$171$	159398.	+	454091.i	0.416862	+	1.18755i
$172$	−9589.98	+	16610.3i	−0.0247171	+	0.0428112i
$173$	−305092.	−	528435.i	−0.775024	−	1.34238i	−0.934781	−	0.355225i	$-0.884404\pi$
$173$	−305092.	−	528435.i	−0.775024	−	1.34238i	0.159756	−	0.987156i	$-0.448929\pi$
$174$	130867.	−	353235.i	0.327686	−	0.884484i
$175$	294303.	−	394252.i	0.726440	−	0.973147i
$176$		−	134676.i		−	0.327725i
$177$	99657.8	−	16983.3i	0.239099	−	0.0407464i
$178$	−202846.	−	117113.i	−0.479863	−	0.277049i
$179$	663103.	+	382843.i	1.54685	+	0.893075i	0.998380	+	0.0569050i	$0.0181232\pi$
$179$	663103.	+	382843.i	1.54685	+	0.893075i	0.548471	+	0.836170i	$0.315210\pi$
$180$	−59814.4	+	317849.i	−0.137602	+	0.731206i
$181$		−	490433.i		−	1.11271i	−0.830944	−	0.556356i	$-0.812199\pi$
$181$		−	490433.i		−	1.11271i	0.830944	−	0.556356i	$-0.187801\pi$
$182$	158932.	+	369760.i	0.355658	+	0.827450i
$183$	650800.	+	241110.i	1.43655	+	0.532215i
$184$	55266.9	+	95725.0i	0.120343	+	0.208440i
$185$	−125418.	+	217230.i	−0.269420	+	0.466648i
$186$	−344949.	−	415918.i	−0.731094	−	0.881507i
$187$	215485.	−	124411.i	0.450624	−	0.260168i
$188$	62002.3			0.127942
$189$	454443.	−	186129.i	0.925389	−	0.379018i
$190$	658992.			1.32433
$191$	−295276.	+	170477.i	−0.585658	+	0.338130i	−0.763379	−	0.645951i	$-0.776461\pi$
$191$	−295276.	+	170477.i	−0.585658	+	0.338130i	0.177721	+	0.984081i	$0.443128\pi$
$192$	−40760.8	−	49146.9i	−0.0797977	−	0.0962150i
$193$	−108547.	+	188009.i	−0.209761	+	0.363316i	−0.951639	−	0.307218i	$-0.900602\pi$
$193$	−108547.	+	188009.i	−0.209761	+	0.363316i	0.741878	+	0.670534i	$0.233935\pi$
$194$	−2033.50	−	3522.12i	−0.00387918	−	0.00671893i
$195$	943743.	+	349640.i	1.77733	+	0.658468i
$196$	185044.	−	195121.i	0.344061	−	0.362798i
$197$		−	7576.18i		−	0.0139086i	−0.999976	−	0.00695432i	$-0.997786\pi$
$197$		−	7576.18i		−	0.0139086i	0.999976	−	0.00695432i	$-0.00221365\pi$
$198$	−94568.2	+	502528.i	−0.171428	+	0.910955i
$199$	−634693.	−	366440.i	−1.13614	−	0.655950i	−0.190667	−	0.981655i	$-0.561065\pi$
$199$	−634693.	−	366440.i	−1.13614	−	0.655950i	−0.945472	+	0.325705i	$0.894398\pi$
$200$	210338.	+	121438.i	0.371828	+	0.214675i
$201$	−374447.	+	63811.9i	−0.653733	+	0.111407i
$202$			311595.i			0.537294i
$203$	−91930.7	+	777789.i	−0.156574	+	1.32471i
$204$	40982.4	−	110619.i	0.0689481	−	0.186104i
$205$	−67940.1	−	117676.i	−0.112912	−	0.195570i
$206$	−63598.9	+	110156.i	−0.104419	+	0.180860i
$207$	−139005.	−	395994.i	−0.225477	−	0.642337i
$208$	−172068.	+	99343.3i	−0.275766	+	0.159214i
$209$	1.04188e6			1.64988
$210$	−34377.9	−	671570.i	−0.0537936	−	1.05086i
$211$	−438196.			−0.677583			−0.338791	−	0.940862i	$-0.610018\pi$
$211$	−438196.			−0.677583			−0.338791	+	0.940862i	$0.610018\pi$
$212$	51874.5	−	29949.7i	0.0792709	−	0.0457671i
$213$	−1.00199e6	+	831021.i	−1.51327	+	1.25506i
$214$	−37911.4	+	65664.4i	−0.0565894	+	0.0980157i
$215$	−49859.7	−	86359.5i	−0.0735620	−	0.127413i
$216$	117584.	+	212008.i	0.171480	+	0.309184i
$217$	900284.	+	672048.i	1.29787	+	0.968838i
$218$		−	588726.i		−	0.839020i
$219$	33573.4	+	197008.i	0.0473026	+	0.277571i
$220$	606391.	+	350100.i	0.844688	+	0.487681i
$221$	−317904.	−	183542.i	−0.437840	−	0.252787i
$222$	31586.0	+	185346.i	0.0430142	+	0.252407i
$223$			650877.i			0.876470i	0.898860	+	0.438235i	$0.144396\pi$
$223$			650877.i			0.876470i	−0.898860	+	0.438235i	$0.855604\pi$
$224$	106382.	+	79412.4i	0.141660	+	0.105747i
$225$	−699576.	−	600830.i	−0.921253	−	0.791216i
$226$	312243.	+	540820.i	0.406651	+	0.704339i
$227$	233294.	−	404077.i	0.300496	−	0.520475i	−0.675752	−	0.737129i	$-0.736181\pi$
$227$	233294.	−	404077.i	0.300496	−	0.520475i	0.976248	+	0.216654i	$0.0695143\pi$
$228$	380211.	−	315335.i	0.484381	−	0.401730i
$229$	268050.	−	154759.i	0.337775	−	0.195015i	−0.321513	−	0.946905i	$-0.604191\pi$
$229$	268050.	−	154759.i	0.337775	−	0.195015i	0.659288	+	0.751891i	$0.270858\pi$
$230$	−574680.			−0.716320
$231$	−54352.3	−	1.06177e6i	−0.0670175	−	1.30918i
$232$	−386642.			−0.471617
$233$	−1.09359e6	+	631387.i	−1.31967	+	0.761914i	−0.983676	−	0.179949i	$-0.942407\pi$
$233$	−1.09359e6	+	631387.i	−1.31967	+	0.761914i	−0.335998	+	0.941863i	$0.609073\pi$
$234$	711807.	−	249863.i	0.849812	−	0.298307i
$235$	−161179.	+	279171.i	−0.190388	+	0.329762i
$236$	−51881.7	−	89861.8i	−0.0606365	−	0.105026i
$237$	218422.	−	589561.i	0.252595	−	0.681801i
$238$	−28789.1	+	243573.i	−0.0329447	+	0.278732i
$239$		−	110206.i		−	0.124799i	−0.998051	−	0.0623997i	$-0.980125\pi$
$239$		−	110206.i		−	0.124799i	0.998051	−	0.0623997i	$-0.0198753\pi$
$240$	327249.	−	55768.5i	0.366733	−	0.0624972i
$241$	−918936.	−	530548.i	−1.01916	−	0.588412i	−0.105300	−	0.994441i	$-0.533580\pi$
$241$	−918936.	−	530548.i	−1.01916	−	0.588412i	−0.913861	+	0.406028i	$0.866914\pi$
$242$	400824.	+	231416.i	0.439962	+	0.254012i
$243$	−289880.	−	873646.i	−0.314922	−	0.949118i
$244$		−	712350.i		−	0.765983i
$245$	397516.	+	1.34041e6i	0.423096	+	1.42667i
$246$	−95507.7	−	35383.9i	−0.100624	−	0.0372793i
$247$	−768541.	−	1.33115e6i	−0.801539	−	1.38831i
$248$	−277308.	+	480311.i	−0.286308	+	0.495899i
$249$	−724488.	−	873543.i	−0.740514	−	0.892865i
$250$	−193057.	+	111462.i	−0.195360	+	0.112791i
$251$	982577.			0.984424			0.492212	−	0.870475i	$-0.336188\pi$
$251$	982577.			0.984424			0.492212	+	0.870475i	$0.336188\pi$
$252$	−341188.	−	371018.i	−0.338449	−	0.368039i
$253$	−908585.			−0.892410
$254$	−323870.	+	186986.i	−0.314982	+	0.181855i
$255$	391536.	+	472089.i	0.377069	+	0.454646i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−107232.	−	185731.i	−0.101272	−	0.175409i	0.810937	−	0.585134i	$-0.198958\pi$
$257$	−107232.	−	185731.i	−0.101272	−	0.175409i	−0.912209	+	0.409725i	$0.865625\pi$
$258$	−70090.9	−	25967.4i	−0.0655560	−	0.0242873i
$259$	−154369.	−	359144.i	−0.142992	−	0.332674i
$260$		−	1.03300e6i		−	0.947691i
$261$	1.44271e6	+	271496.i	1.31092	+	0.246696i
$262$	286494.	+	165407.i	0.257847	+	0.148868i
$263$	−815650.	−	470916.i	−0.727134	−	0.419811i	0.0902388	−	0.995920i	$-0.471237\pi$
$263$	−815650.	−	470916.i	−0.727134	−	0.419811i	−0.817373	+	0.576109i	$0.804570\pi$
$264$	517389.	−	88171.5i	0.456886	−	0.0778607i
$265$			311426.i			0.272421i
$266$	−614352.	+	822992.i	−0.532369	+	0.713168i
$267$	317116.	−	855954.i	0.272232	−	0.734805i
$268$	194937.	+	337641.i	0.165790	+	0.287156i
$269$	928208.	−	1.60770e6i	0.782104	−	1.35464i	−0.148610	−	0.988896i	$-0.547480\pi$
$269$	928208.	−	1.60770e6i	0.782104	−	1.35464i	0.930714	−	0.365748i	$-0.119187\pi$
$270$	−1.26025e6	−	21697.3i	−1.05208	−	0.0181133i
$271$	295454.	−	170581.i	0.244381	−	0.141093i	−0.372808	−	0.927909i	$-0.621605\pi$
$271$	295454.	−	170581.i	0.244381	−	0.141093i	0.617189	+	0.786815i	$0.288272\pi$
$272$	−121081.			−0.0992326
$273$	−1.31647e6	+	852653.i	−1.06906	+	0.692414i
$274$	311041.			0.250289
$275$	−1.72897e6	+	998222.i	−1.37866	+	0.795967i
$276$	−331567.	+	274991.i	−0.261998	+	0.217293i
$277$	−297325.	+	514983.i	−0.232827	+	0.403268i	−0.958639	−	0.284625i	$-0.908131\pi$
$277$	−297325.	+	514983.i	−0.232827	+	0.403268i	0.725812	+	0.687893i	$0.241464\pi$
$278$	75692.1	+	131102.i	0.0587406	+	0.101742i
$279$	1.37201e6	−	1.59750e6i	1.05523	−	1.22866i
$280$	−634108.	+	272555.i	−0.483357	+	0.207759i
$281$			1.03881e6i			0.784819i	0.919791	+	0.392409i	$0.128358\pi$
$281$			1.03881e6i			0.784819i	−0.919791	+	0.392409i	$0.871642\pi$
$282$	40592.5	+	238196.i	0.0303964	+	0.178366i
$283$	2.18141e6	+	1.25944e6i	1.61909	+	0.934782i	0.987156	+	0.159761i	$0.0510722\pi$
$283$	2.18141e6	+	1.25944e6i	1.61909	+	0.934782i	0.631935	+	0.775022i	$0.282261\pi$
$284$	1.15712e6	+	668065.i	0.851302	+	0.491499i
$285$	431437.	+	2.53167e6i	0.314634	+	1.84627i
$286$		−	1.63320e6i		−	1.18066i
$287$	210299.	+	24856.2i	0.150707	+	0.0178127i
$288$	162123.	−	188768.i	0.115177	−	0.134106i
$289$	598077.	+	1.03590e6i	0.421223	+	0.729580i
$290$	1.00510e6	−	1.74089e6i	0.701804	−	1.21556i
$291$	12199.7	−	10118.1i	0.00844535	−	0.00700430i
$292$	177643.	−	102562.i	0.121924	−	0.0703931i
$293$	−2.51299e6			−1.71010			−0.855049	−	0.518547i	$-0.826473\pi$
$293$	−2.51299e6			−1.71010			−0.855049	+	0.518547i	$0.826473\pi$
$294$	870750.	+	583145.i	0.587524	+	0.393467i
$295$	539481.			0.360928
$296$	167127.	−	96491.0i	0.110871	−	0.0640114i
$297$	−1.99249e6	−	34304.0i	−1.31070	−	0.0225660i
$298$	−62456.8	+	108178.i	−0.0407417	+	0.0705666i
$299$	670214.	+	1.16084e6i	0.433546	+	0.750924i
$300$	−328827.	+	887565.i	−0.210943	+	0.569373i
$301$	154334.	+	18241.4i	0.0981848	+	0.0116049i
$302$			1.42458e6i			0.898815i
$303$	−1.19706e6	+	203999.i	−0.749049	+	0.127650i
$304$	−439075.	−	253500.i	−0.272493	−	0.157324i
$305$	3.20742e6	+	1.85180e6i	1.97427	+	1.13984i
$306$	451800.	+	85021.9i	0.275831	+	0.0519072i
$307$			791101.i			0.479055i	0.970890	+	0.239528i	$0.0769926\pi$
$307$			791101.i			0.479055i	−0.970890	+	0.239528i	$0.923007\pi$
$308$	−1.00254e6	+	430917.i	−0.602179	+	0.258831i
$309$	−464829.	−	172211.i	−0.276947	−	0.102604i
$310$	−1.44176e6	−	2.49721e6i	−0.852098	−	1.47588i
$311$	83650.7	−	144887.i	0.0490420	−	0.0849433i	−0.840462	−	0.541870i	$-0.817717\pi$
$311$	83650.7	−	144887.i	0.0490420	−	0.0849433i	0.889504	+	0.456927i	$0.151050\pi$
$312$	−494301.	−	595998.i	−0.287478	−	0.346624i
$313$	1.09825e6	−	634075.i	0.633637	−	0.365830i	−0.148523	−	0.988909i	$-0.547452\pi$
$313$	1.09825e6	−	634075.i	0.633637	−	0.365830i	0.782159	+	0.623079i	$0.214118\pi$
$314$	1.26786e6			0.725684
$315$	2.55748e6	−	571743.i	1.45223	−	0.324657i
$316$	−645319.			−0.363544
$317$	2.59960e6	−	1.50088e6i	1.45297	−	0.838875i	0.454326	−	0.890836i	$-0.349880\pi$
$317$	2.59960e6	−	1.50088e6i	1.45297	−	0.838875i	0.998649	+	0.0519603i	$0.0165469\pi$
$318$	149021.	+	179680.i	0.0826378	+	0.0996395i
$319$	1.58910e6	−	2.75240e6i	0.874326	−	1.51438i
$320$	−170365.	−	295082.i	−0.0930051	−	0.161089i
$321$	−277085.	−	102655.i	−0.150090	−	0.0556056i
$322$	535751.	−	717699.i	0.287954	−	0.385747i
$323$		−	936710.i		−	0.499573i
$324$	−737494.	+	590525.i	−0.390298	+	0.312518i
$325$	2.55073e6	+	1.47267e6i	1.33954	+	0.773386i
$326$	−569443.	−	328768.i	−0.296761	−	0.171335i
$327$	2.26173e6	−	385435.i	1.16969	−	0.199334i
$328$			104540.i			0.0536537i
$329$	−198386.	−	461551.i	−0.101046	−	0.235088i
$330$	−947990.	+	2.55880e6i	−0.479202	+	1.29345i
$331$	300997.	+	521341.i	0.151005	+	0.261549i	0.931597	−	0.363492i	$-0.118416\pi$
$331$	300997.	+	521341.i	0.151005	+	0.261549i	−0.780592	+	0.625041i	$0.785082\pi$
$332$	−582422.	+	1.00879e6i	−0.289997	+	0.502289i
$333$	−691370.	+	242689.i	−0.341665	+	0.119933i
$334$	−2.17627e6	+	1.25647e6i	−1.06745	+	0.616290i
$335$	−2.02701e6			−0.986833
$336$	−235434.	+	460681.i	−0.113768	+	0.222614i
$337$	−515158.			−0.247096			−0.123548	−	0.992339i	$-0.539427\pi$
$337$	−515158.			−0.247096			−0.123548	+	0.992339i	$0.539427\pi$
$338$	−800443.	+	462136.i	−0.381100	+	0.220028i
$339$	−1.87326e6	+	1.55362e6i	−0.885318	+	0.734254i
$340$	314759.	−	545178.i	0.147666	−	0.255765i
$341$	−2.27946e6	−	3.94815e6i	−1.06157	−	1.83869i
$342$	1.46035e6	+	1.25422e6i	0.675137	+	0.579840i
$343$	−2.04458e6	−	753165.i	−0.938358	−	0.345665i
$344$			76719.9i			0.0349552i
$345$	−376239.	−	2.20777e6i	−0.170183	−	0.998632i
$346$	−2.11374e6	−	1.22037e6i	−0.949207	−	0.548025i
$347$	−1.93407e6	−	1.11664e6i	−0.862281	−	0.497838i	0.00249446	−	0.999997i	$-0.499206\pi$
$347$	−1.93407e6	−	1.11664e6i	−0.862281	−	0.497838i	−0.864775	+	0.502159i	$0.832539\pi$
$348$	−253132.	−	1.48537e6i	−0.112047	−	0.657488i
$349$			2.51946e6i			1.10725i	0.832767	+	0.553623i	$0.186755\pi$
$349$			2.51946e6i			1.10725i	−0.832767	+	0.553623i	$0.813245\pi$
$350$	230992.	−	1.95433e6i	0.100792	−	0.852764i
$351$	1.42592e6	+	2.57099e6i	0.617772	+	1.11386i
$352$	−269352.	−	466532.i	−0.115868	−	0.200690i
$353$	888524.	−	1.53897e6i	0.379518	−	0.657345i	−0.611474	−	0.791264i	$-0.709423\pi$
$353$	888524.	−	1.53897e6i	0.379518	−	0.657345i	0.990992	+	0.133920i	$0.0427565\pi$
$354$	311258.	−	258147.i	0.132012	−	0.109486i
$355$	−6.01604e6	+	3.47336e6i	−2.53361	+	1.46278i
$356$	−936907.			−0.391806
$357$	−954589.	+	48865.7i	−0.396411	+	0.0202924i
$358$	3.06274e6			1.26300
$359$	3.92647e6	−	2.26695e6i	1.60793	−	0.928337i	0.618093	−	0.786105i	$-0.287905\pi$
$359$	3.92647e6	−	2.26695e6i	1.60793	−	0.928337i	0.989833	−	0.142232i	$-0.0454280\pi$
$360$	428495.	+	1.22069e6i	0.174257	+	0.496420i
$361$	723084.	−	1.25242e6i	0.292025	−	0.505803i
$362$	−980865.	−	1.69891e6i	−0.393403	−	0.681394i
$363$	−626620.	+	1.69136e6i	−0.249596	+	0.673706i
$364$	1.29008e6	+	963024.i	0.510343	+	0.380964i
$365$			1.06647e6i			0.419003i
$366$	2.73666e6	−	466371.i	1.06787	−	0.181982i
$367$	−1.18287e6	−	682930.i	−0.458428	−	0.264674i	0.252955	−	0.967478i	$-0.418598\pi$
$367$	−1.18287e6	−	682930.i	−0.458428	−	0.264674i	−0.711383	+	0.702804i	$0.751931\pi$
$368$	382900.	+	221067.i	0.147389	+	0.0850953i
$369$	73407.2	−	390080.i	0.0280655	−	0.149138i
$370$			1.00334e6i			0.381017i
$371$	−388929.	−	290330.i	−0.146702	−	0.109511i
$372$	−2.02678e6	−	750885.i	−0.759361	−	0.281330i
$373$	1.44131e6	+	2.49642e6i	0.536395	+	0.929063i	0.999094	+	0.0425480i	$0.0135475\pi$
$373$	1.44131e6	+	2.49642e6i	0.536395	+	0.929063i	−0.462700	+	0.886515i	$0.653119\pi$
$374$	497642.	−	861942.i	0.183966	−	0.318639i
$375$	−554598.	−	668700.i	−0.203657	−	0.245557i
$376$	214782.	−	124005.i	0.0783482	−	0.0452343i
$377$	−4.68876e6			−1.69904
$378$	1.20198e6	−	1.55366e6i	0.432680	−	0.559275i
$379$	1.79197e6			0.640815			0.320408	−	0.947280i	$-0.396180\pi$
$379$	1.79197e6			0.640815			0.320408	+	0.947280i	$0.396180\pi$
$380$	2.28281e6	−	1.31798e6i	0.810983	−	0.468221i
$381$	−930386.	−	1.12180e6i	−0.328360	−	0.395916i
$382$	−681910.	+	1.18110e6i	−0.239094	+	0.414123i
$383$	814355.	+	1.41050e6i	0.283672	+	0.491335i	0.972286	−	0.233793i	$-0.0751139\pi$
$383$	814355.	+	1.41050e6i	0.283672	+	0.491335i	−0.688614	+	0.725128i	$0.741781\pi$
$384$	−239493.	−	88728.1i	−0.0828830	−	0.0307067i
$385$	665937.	−	5.63423e6i	0.228971	−	1.93724i
$386$			868375.i			0.296646i
$387$	53871.9	−	286271.i	0.0182846	−	0.0971628i
$388$	−14088.5	−	8133.99i	−0.00475100	−	0.00274299i
$389$	4.13271e6	+	2.38602e6i	1.38472	+	0.799466i	0.992714	−	0.120498i	$-0.0384490\pi$
$389$	4.13271e6	+	2.38602e6i	1.38472	+	0.799466i	0.392003	+	0.919964i	$0.371782\pi$
$390$	3.96850e6	−	676297.i	1.32119	−	0.225152i
$391$			816867.i			0.270215i
$392$	250769.	−	1.04601e6i	0.0824249	−	0.343811i
$393$	−447884.	+	1.20892e6i	−0.146280	+	0.394836i
$394$	−15152.4	−	26244.7i	−0.00491745	−	0.00851727i
$395$	1.67755e6	−	2.90561e6i	0.540983	−	0.937010i
$396$	677462.	+	1.92994e6i	0.217094	+	0.618453i
$397$	87165.5	−	50325.0i	0.0277567	−	0.0160254i	−0.486057	−	0.873927i	$-0.661565\pi$
$397$	87165.5	−	50325.0i	0.0277567	−	0.0160254i	0.513814	+	0.857902i	$0.328232\pi$
$398$	−2.93152e6			−0.927653
$399$	−3.56393e6	−	1.82136e6i	−1.12072	−	0.572750i
$400$	971508.			0.303596
$401$	−4.80374e6	+	2.77344e6i	−1.49183	+	0.861307i	−0.999956	−	0.00936110i	$-0.997020\pi$
$401$	−4.80374e6	+	2.77344e6i	−1.49183	+	0.861307i	−0.491871	+	0.870668i	$0.663687\pi$
$402$	−1.16950e6	+	969945.i	−0.360940	+	0.299352i
$403$	−3.36287e6	+	5.82467e6i	−1.03145	+	1.78652i
$404$	623190.	+	1.07940e6i	0.189962	+	0.329024i
$405$	−741721.	−	4.85574e6i	−0.224700	−	1.47102i
$406$	1.23712e6	+	2.87820e6i	0.372475	+	0.866575i
$407$			1.58631e6i			0.474681i
$408$	−79270.9	−	465161.i	−0.0235756	−	0.138342i
$409$	629717.	+	363567.i	0.186139	+	0.107467i	0.590174	−	0.807276i	$-0.299059\pi$
$409$	629717.	+	363567.i	0.186139	+	0.107467i	−0.404035	+	0.914744i	$0.632393\pi$
$410$	−470703.	−	271760.i	−0.138289	−	0.0798411i
$411$	203637.	+	1.19494e6i	0.0594636	+	0.348932i
$412$			508791.i			0.147671i
$413$	−502936.	+	673739.i	−0.145090	+	0.194364i
$414$	−1.27351e6	−	1.09376e6i	−0.365177	−	0.313631i
$415$	−3.02810e6	−	5.24482e6i	−0.863077	−	1.49489i
$416$	−397373.	+	688270.i	−0.112581	+	0.194996i
$417$	−454105.	+	376620.i	−0.127884	+	0.106063i
$418$	3.60919e6	−	2.08377e6i	1.01034	−	0.583322i
$419$	1.32060e6			0.367482			0.183741	−	0.982975i	$-0.441179\pi$
$419$	1.32060e6			0.367482			0.183741	+	0.982975i	$0.441179\pi$
$420$	−1.46223e6	−	2.25763e6i	−0.404475	−	0.624496i
$421$	5.02517e6			1.38180			0.690901	−	0.722950i	$-0.257214\pi$
$421$	5.02517e6			1.38180			0.690901	+	0.722950i	$0.257214\pi$
$422$	−1.51796e6	+	876392.i	−0.414933	+	0.239562i
$423$	−888509.	+	311890.i	−0.241441	+	0.0847522i
$424$	119799.	−	207498.i	0.0323622	−	0.0560530i
$425$	897455.	+	1.55444e6i	0.241013	+	0.417447i
$426$	−1.80896e6	+	4.88273e6i	−0.482954	+	1.30358i
$427$	−5.30280e6	+	2.27927e6i	−1.40746	+	0.604960i
$428$			303291.i			0.0800295i
$429$	6.27431e6	−	1.06924e6i	1.64597	−	0.280500i
$430$	−345438.	−	199439.i	−0.0900946	−	0.0520162i
$431$	1.60910e6	+	929013.i	0.417243	+	0.240895i	0.693897	−	0.720074i	$-0.255892\pi$
$431$	1.60910e6	+	929013.i	0.417243	+	0.240895i	−0.276654	+	0.960970i	$0.589226\pi$
$432$	831337.	+	499248.i	0.214323	+	0.128708i
$433$		−	5.52697e6i		−	1.41667i	−0.705878	−	0.708333i	$-0.749447\pi$
$433$		−	5.52697e6i		−	1.41667i	0.705878	−	0.708333i	$-0.250553\pi$
$434$	4.46277e6	+	527476.i	1.13731	+	0.134425i
$435$	7.34606e6	+	2.72159e6i	1.86137	+	0.689603i
$436$	−1.17745e6	−	2.03941e6i	−0.296638	−	0.513793i
$437$	−1.71023e6	+	2.96220e6i	−0.428400	+	0.742011i
$438$	510318.	+	615309.i	0.127103	+	0.153253i
$439$	4.94162e6	−	2.85305e6i	1.22379	−	0.706558i	0.258069	−	0.966126i	$-0.416914\pi$
$439$	4.94162e6	−	2.85305e6i	1.22379	−	0.706558i	0.965725	+	0.259569i	$0.0835805\pi$
$440$	2.80080e6			0.689685
$441$	−1.67021e6	+	3.72697e6i	−0.408954	+	0.912555i
$442$	−1.46833e6			−0.357494
$443$	4.44494e6	−	2.56629e6i	1.07611	−	0.621293i	0.146266	−	0.989245i	$-0.453274\pi$
$443$	4.44494e6	−	2.56629e6i	1.07611	−	0.621293i	0.929845	+	0.367952i	$0.119941\pi$
$444$	480109.	+	578886.i	0.115580	+	0.139359i
$445$	2.43556e6	−	4.21851e6i	0.583040	−	1.00985i
$446$	1.30175e6	+	2.25471e6i	0.309879	+	0.536726i
$447$	−456482.	−	169118.i	−0.108057	−	0.0400334i
$448$	527342.	+	62329.1i	0.124136	+	0.0146722i
$449$		−	1.56362e6i		−	0.366030i	−0.983110	−	0.183015i	$-0.941414\pi$
$449$		−	1.56362e6i		−	0.366030i	0.983110	−	0.183015i	$-0.0585856\pi$
$450$	−3.62506e6	−	682182.i	−0.843887	−	0.158807i
$451$	−744193.	−	429660.i	−0.172284	−	0.0994681i
$452$	2.16328e6	+	1.24897e6i	0.498043	+	0.287545i
$453$	−5.47286e6	+	932664.i	−1.25305	+	0.213540i
$454$		−	1.86635e6i		−	0.424966i
$455$	−7.68974e6	+	3.30524e6i	−1.74134	+	0.748470i
$456$	686420.	−	1.85277e6i	0.154589	−	0.417263i
$457$	3.15021e6	+	5.45633e6i	0.705585	+	1.22211i	0.966480	+	0.256742i	$0.0826492\pi$
$457$	3.15021e6	+	5.45633e6i	0.705585	+	1.22211i	−0.260895	+	0.965367i	$0.584018\pi$
$458$	619036.	−	1.07220e6i	0.137896	−	0.238843i
$459$	−30841.2	+	1.79135e6i	−0.00683281	+	0.396871i
$460$	−1.99075e6	+	1.14936e6i	−0.438654	+	0.253257i
$461$	−162855.			−0.0356901			−0.0178450	−	0.999841i	$-0.505681\pi$
$461$	−162855.			−0.0356901			−0.0178450	+	0.999841i	$0.505681\pi$
$462$	−2.31182e6	−	3.56938e6i	−0.503906	−	0.778014i
$463$	−8.40996e6			−1.82323			−0.911615	−	0.411044i	$-0.865164\pi$
$463$	−8.40996e6			−1.82323			−0.911615	+	0.411044i	$0.865164\pi$
$464$	−1.33937e6	+	773285.i	−0.288805	+	0.166742i
$465$	8.64967e6	−	7.17376e6i	1.85510	−	1.53856i
$466$	−2.52555e6	+	4.37438e6i	−0.538754	+	0.933150i
$467$	3.23078e6	+	5.59588e6i	0.685513	+	1.18734i	0.973275	+	0.229641i	$0.0737553\pi$
$467$	3.23078e6	+	5.59588e6i	0.685513	+	1.18734i	−0.287762	+	0.957702i	$0.592911\pi$
$468$	1.96605e6	−	2.28917e6i	0.414934	−	0.483129i
$469$	1.88970e6	−	2.53146e6i	0.396698	−	0.531422i
$470$			1.28943e6i			0.269249i
$471$	830060.	+	4.87078e6i	0.172408	+	1.01169i
$472$	−359447.	−	207527.i	−0.0742643	−	0.0428765i
$473$	−546147.	−	315318.i	−0.112242	−	0.0648031i
$474$	−422486.	−	2.47914e6i	−0.0863707	−	0.506822i
$475$			7.51579e6i			1.52841i
$476$	387418.	+	901340.i	0.0783722	+	0.182335i
$477$	−592718.	+	690132.i	−0.119276	+	0.138879i
$478$	−220413.	−	381766.i	−0.0441232	−	0.0764237i
$479$	−2.65810e6	+	4.60397e6i	−0.529338	+	0.916841i	0.470076	+	0.882626i	$0.344226\pi$
$479$	−2.65810e6	+	4.60397e6i	−0.529338	+	0.916841i	−0.999414	+	0.0342149i	$0.989107\pi$
$480$	1.02209e6	−	847685.i	0.202481	−	0.167931i
$481$	2.02673e6	−	1.17013e6i	0.399423	−	0.230607i
$482$	−4.24438e6			−0.832141
$483$	3.10796e6	+	1.58834e6i	0.606188	+	0.309796i
$484$	1.85133e6			0.359227
$485$	73248.0	−	42289.8i	0.0141397	−	0.00816359i
$486$	−2.75147e6	−	2.44664e6i	−0.528413	−	0.469872i
$487$	3.81386e6	−	6.60581e6i	0.728690	−	1.26213i	−0.228747	−	0.973486i	$-0.573463\pi$
$487$	3.81386e6	−	6.60581e6i	0.728690	−	1.26213i	0.957437	−	0.288642i	$-0.0932038\pi$
$488$	−1.42470e6	−	2.46765e6i	−0.270816	−	0.469067i
$489$	890228.	−	2.40289e6i	0.168356	−	0.454424i
$490$	4.05785e6	+	3.84828e6i	0.763495	+	0.724063i
$491$		−	2.32379e6i		−	0.435003i	−0.976060	−	0.217502i	$-0.930209\pi$
$491$		−	2.32379e6i		−	0.435003i	0.976060	−	0.217502i	$-0.0697908\pi$
$492$	−401616.	+	68441.9i	−0.0747994	+	0.0127470i
$493$	−2.47455e6	−	1.42868e6i	−0.458542	−	0.264739i
$494$	−5.32461e6	−	3.07416e6i	−0.981681	−	0.566774i
$495$	−1.04509e7	−	1.96669e6i	−1.91707	−	0.360764i
$496$			2.21846e6i			0.404900i
$497$	1.27075e6	−	1.07513e7i	0.230764	−	1.95241i
$498$	−4.25679e6	−	1.57706e6i	−0.769146	−	0.284955i
$499$	2.49887e6	+	4.32818e6i	0.449255	+	0.778133i	0.998338	−	0.0576355i	$-0.0183561\pi$
$499$	2.49887e6	+	4.32818e6i	0.449255	+	0.778133i	−0.549083	+	0.835768i	$0.685023\pi$
$500$	−445846.	+	772228.i	−0.0797554	+	0.138140i
$501$	−6.25179e6	−	7.53802e6i	−1.11278	−	1.34172i
$502$	3.40375e6	−	1.96515e6i	0.602834	−	0.348046i
$503$	3.01055e6			0.530549			0.265275	−	0.964173i	$-0.414537\pi$
$503$	3.01055e6			0.530549			0.265275	+	0.964173i	$0.414537\pi$
$504$	−1.92395e6	−	602868.i	−0.337378	−	0.105717i
$505$	−6.48010e6			−1.13072
$506$	−3.14743e6	+	1.81717e6i	−0.546487	+	0.315515i
$507$	−2.29945e6	−	2.77253e6i	−0.397286	−	0.479023i
$508$	−747945.	+	1.29548e6i	−0.128591	+	0.222726i
$509$	449651.	+	778819.i	0.0769274	+	0.133242i	0.901923	−	0.431897i	$-0.142156\pi$
$509$	449651.	+	778819.i	0.0769274	+	0.133242i	−0.824995	+	0.565139i	$0.808822\pi$
$510$	2.30050e6	+	852294.i	0.391648	+	0.145099i
$511$	−1.33188e6	−	994228.i	−0.225638	−	0.168435i
$512$			262144.i			0.0441942i
$513$	−3.86229e6	+	6.43140e6i	−0.647965	+	1.07898i
$514$	−742923.	−	428927.i	−0.124033	−	0.0716103i
$515$	−2.29088e6	−	1.32264e6i	−0.380613	−	0.219747i
$516$	−294737.	+	50227.9i	−0.0487316	+	0.00830465i
$517$			2.03863e6i			0.335438i
$518$	−1.25304e6	−	935374.i	−0.205182	−	0.153165i
$519$	3.30447e6	−	8.91937e6i	0.538497	−	1.45350i
$520$	−2.06600e6	−	3.57841e6i	−0.335059	−	0.580340i
$521$	359362.	−	622433.i	0.0580013	−	0.100461i	−0.835567	−	0.549389i	$-0.814861\pi$
$521$	359362.	−	622433.i	0.0580013	−	0.100461i	0.893568	+	0.448928i	$0.148194\pi$
$522$	5.54068e6	−	1.94493e6i	0.889994	−	0.312412i
$523$	5.01382e6	−	2.89473e6i	0.801520	−	0.462758i	−0.0424821	−	0.999097i	$-0.513527\pi$
$523$	5.01382e6	−	2.89473e6i	0.801520	−	0.462758i	0.844003	+	0.536339i	$0.180193\pi$
$524$	1.32326e6			0.210531
$525$	7.65925e6	−	392079.i	1.21280	−	0.0620834i
$526$	−3.76733e6			−0.593702
$527$	−3.54960e6	+	2.04936e6i	−0.556740	+	0.321434i
$528$	1.61595e6	−	1.34021e6i	0.252256	−	0.209213i
$529$	−1.72675e6	+	2.99082e6i	−0.268282	+	0.464677i
$530$	622852.	+	1.07881e6i	0.0963152	+	0.166823i
$531$	1.19551e6	+	1.02676e6i	0.184000	+	0.158028i
$532$	−482191.	+	4.07963e6i	−0.0738653	+	0.624945i
$533$			1.26775e6i			0.193292i
$534$	−613386.	−	3.59934e6i	−0.0930852	−	0.546223i
$535$	−1.36559e6	−	788426.i	−0.206270	−	0.119090i
$536$	1.35056e6	+	779748.i	0.203050	+	0.117231i
$537$	2.00515e6	+	1.17662e7i	0.300063	+	1.76076i
$538$		−	7.42566e6i		−	1.10606i
$539$	6.41558e6	+	6.08424e6i	0.951182	+	0.902057i
$540$	−4.40903e6	+	2.44534e6i	−0.650666	+	0.360873i
$541$	−3.26861e6	−	5.66140e6i	−0.480143	−	0.831632i	0.519598	−	0.854411i	$-0.326082\pi$
$541$	−3.26861e6	−	5.66140e6i	−0.480143	−	0.831632i	−0.999741	+	0.0227794i	$0.992748\pi$
$542$	682323.	−	1.18182e6i	0.0997681	−	0.172803i
$543$	5.88458e6	−	4.88048e6i	0.856477	−	0.710335i
$544$	−419437.	+	242162.i	−0.0607673	+	0.0350840i
$545$	1.22435e7			1.76569
$546$	−2.85507e6	+	5.58661e6i	−0.409860	+	0.801986i
$547$	3.31420e6			0.473598			0.236799	−	0.971559i	$-0.423902\pi$
$547$	3.31420e6			0.473598			0.236799	+	0.971559i	$0.423902\pi$
$548$	1.07748e6	−	622083.i	0.153270	−	0.0884905i
$549$	3.58334e6	+	1.02082e7i	0.507408	+	1.44550i
$550$	−3.99289e6	+	6.91588e6i	−0.562834	+	0.974857i
$551$	−5.98230e6	−	1.03616e7i	−0.839439	−	1.45395i
$552$	−598599.	+	1.61573e6i	−0.0836158	+	0.225694i
$553$	2.06480e6	+	4.80382e6i	0.287121	+	0.667996i
$554$			2.37860e6i			0.329267i
$555$	−3.85456e6	+	656880.i	−0.531181	+	0.0905218i
$556$	524410.	+	302768.i	0.0719422	+	0.0415359i
$557$	−6.74821e6	−	3.89608e6i	−0.921618	−	0.532096i	−0.0374668	−	0.999298i	$-0.511929\pi$
$557$	−6.74821e6	−	3.89608e6i	−0.921618	−	0.532096i	−0.884151	+	0.467202i	$0.845262\pi$
$558$	1.55778e6	−	8.27792e6i	0.211798	−	1.12548i
$559$			930371.i			0.125929i
$560$	−1.65151e6	+	2.21238e6i	−0.222541	+	0.298118i
$561$	3.63715e6	+	1.34750e6i	0.487926	+	0.180768i
$562$	2.07762e6	+	3.59854e6i	0.277475	+	0.480601i
$563$	−3.38663e6	+	5.86582e6i	−0.450295	+	0.779933i	−0.998404	−	0.0564733i	$-0.982014\pi$
$563$	−3.38663e6	+	5.86582e6i	−0.450295	+	0.779933i	0.548109	+	0.836407i	$0.315348\pi$
$564$	617009.	+	743950.i	0.0816758	+	0.0984796i
$565$	−1.12472e7	+	6.49358e6i	−1.48226	+	0.855781i
$566$	1.00755e7			1.32198
$567$	6.75565e6	+	3.60050e6i	0.882489	+	0.470333i
$568$	5.34452e6			0.695085
$569$	−230925.	+	133325.i	−0.0299013	+	0.0172635i	−0.514876	−	0.857265i	$-0.672162\pi$
$569$	−230925.	+	133325.i	−0.0299013	+	0.0172635i	0.484975	+	0.874528i	$0.338829\pi$
$570$	6.55788e6	+	7.90708e6i	0.845427	+	1.01936i
$571$	6.04858e6	−	1.04764e7i	0.776359	−	1.34469i	−0.157668	−	0.987492i	$-0.550398\pi$
$571$	6.04858e6	−	1.04764e7i	0.776359	−	1.34469i	0.934027	−	0.357202i	$-0.116269\pi$
$572$	−3.26640e6	−	5.65757e6i	−0.417426	−	0.723002i
$573$	−4.98392e6	−	1.84645e6i	−0.634138	−	0.234937i
$574$	778209.	−	334493.i	0.0985863	−	0.0423748i
$575$		−	6.55422e6i		−	0.826707i
$576$	184075.	−	978159.i	0.0231173	−	0.122844i
$577$	1.21462e7	+	7.01259e6i	1.51880	+	0.876877i	0.999755	+	0.0221276i	$0.00704399\pi$
$577$	1.21462e7	+	7.01259e6i	1.51880	+	0.876877i	0.519041	+	0.854750i	$0.326289\pi$
$578$	4.14360e6	+	2.39231e6i	0.515891	+	0.297850i
$579$	−3.33606e6	+	568519.i	−0.413559	+	0.0704771i
$580$		−	8.04083e6i		−	0.992501i
$581$	9.37304e6	+	1.10785e6i	1.15197	+	0.136157i
$582$	22025.0	−	59449.4i	0.00269530	−	0.00727512i
$583$	984745.	+	1.70563e6i	0.119992	+	0.207832i
$584$	410249.	−	710572.i	0.0497755	−	0.0862136i
$585$	5.19630e6	+	1.48031e7i	0.627776	+	1.78840i
$586$	−8.70524e6	+	5.02597e6i	−1.04722	+	0.604611i
$587$	−689161.			−0.0825516			−0.0412758	−	0.999148i	$-0.513142\pi$
$587$	−689161.			−0.0825516			−0.0412758	+	0.999148i	$0.513142\pi$
$588$	4.18266e6	+	278571.i	0.498895	+	0.0332272i
$589$	−1.71625e7			−2.03841
$590$	1.86882e6	−	1.07896e6i	0.221023	−	0.127607i
$591$	90904.7	−	75393.4i	0.0107058	−	0.00887902i
$592$	385964.	−	668509.i	0.0452629	−	0.0783977i
$593$	5.54269e6	+	9.60022e6i	0.647267	+	1.12110i	0.983773	+	0.179418i	$0.0574216\pi$
$593$	5.54269e6	+	9.60022e6i	0.647267	+	1.12110i	−0.336505	+	0.941682i	$0.609245\pi$
$594$	−6.97079e6	+	3.86614e6i	−0.810617	+	0.449585i
$595$	−5.06548e6	−	598713.i	−0.586581	−	0.0693309i
$596$			499654.i			0.0576174i
$597$	−1.91925e6	−	1.12621e7i	−0.220392	−	1.29326i
$598$	4.64338e6	+	2.68086e6i	0.530983	+	0.306563i
$599$	−1.11153e7	−	6.41740e6i	−1.26576	−	0.730789i	−0.291580	−	0.956546i	$-0.594181\pi$
$599$	−1.11153e7	−	6.41740e6i	−1.26576	−	0.730789i	−0.974184	+	0.225757i	$0.927514\pi$
$600$	636039.	+	3.73227e6i	0.0721283	+	0.423248i
$601$		−	1.35097e7i		−	1.52566i	−0.646597	−	0.762832i	$-0.723808\pi$
$601$		−	1.35097e7i		−	1.52566i	0.646597	−	0.762832i	$-0.276192\pi$
$602$	571110.	−	245477.i	0.0642286	−	0.0276070i
$603$	−4.49193e6	−	3.85788e6i	−0.503083	−	0.432072i
$604$	2.84917e6	+	4.93490e6i	0.317779	+	0.550410i
$605$	−4.81265e6	+	8.33576e6i	−0.534559	+	0.925884i
$606$	−3.73875e6	+	3.10080e6i	−0.413566	+	0.342998i
$607$	8.39395e6	−	4.84625e6i	0.924686	−	0.533868i	0.0395592	−	0.999217i	$-0.487405\pi$
$607$	8.39395e6	−	4.84625e6i	0.924686	−	0.533868i	0.885127	+	0.465349i	$0.154071\pi$
$608$	−2.02800e6			−0.222490
$609$	−1.02473e7	+	6.63702e6i	−1.11961	+	0.725154i
$610$	1.48144e7			1.61198
$611$	2.60464e6	−	1.50379e6i	0.282257	−	0.162961i
$612$	1.73512e6	−	609075.i	0.187263	−	0.0657343i
$613$	−3.85451e6	+	6.67621e6i	−0.414303	+	0.717594i	−0.995355	−	0.0962726i	$-0.969308\pi$
$613$	−3.85451e6	+	6.67621e6i	−0.414303	+	0.717594i	0.581052	+	0.813866i	$0.302641\pi$
$614$	1.58220e6	+	2.74045e6i	0.169372	+	0.293360i
$615$	735864.	−	1.98623e6i	0.0784530	−	0.211759i
$616$	−2.61107e6	+	3.49783e6i	−0.277247	+	0.371404i
$617$		−	9.52706e6i		−	1.00750i	−0.863849	−	0.503751i	$-0.831953\pi$
$617$		−	9.52706e6i		−	1.00750i	0.863849	−	0.503751i	$-0.168047\pi$
$618$	−1.95464e6	+	333102.i	−0.205871	+	0.0350837i
$619$	−7.10455e6	−	4.10181e6i	−0.745263	−	0.430278i	0.0787166	−	0.996897i	$-0.474918\pi$
$619$	−7.10455e6	−	4.10181e6i	−0.745263	−	0.430278i	−0.823980	+	0.566619i	$0.808251\pi$
$620$	−9.98882e6	−	5.76705e6i	−1.04360	−	0.602524i
$621$	3.36815e6	−	5.60857e6i	0.350479	−	0.583610i
$622$		−	669205.i		−	0.0693559i
$623$	2.99778e6	+	6.97443e6i	0.309442	+	0.719927i
$624$	−2.90430e6	−	1.07599e6i	−0.298594	−	0.110624i
$625$	3.61160e6	+	6.25547e6i	0.369827	+	0.640560i
$626$	2.53630e6	−	4.39300e6i	0.258681	−	0.448049i
$627$	1.03682e7	+	1.25013e7i	1.05326	+	1.26995i
$628$	4.39200e6	−	2.53572e6i	0.444389	−	0.256568i
$629$	1.42618e6			0.143730
$630$	7.71590e6	−	7.09554e6i	0.774524	−	0.712253i
$631$	8.59744e6			0.859599			0.429799	−	0.902924i	$-0.358584\pi$
$631$	8.59744e6			0.859599			0.429799	+	0.902924i	$0.358584\pi$
$632$	−2.23545e6	+	1.29064e6i	−0.222624	+	0.128532i
$633$	−4.36065e6	−	5.25780e6i	−0.432556	−	0.521549i
$634$	6.00351e6	−	1.03984e7i	0.593174	−	1.02741i
$635$	−3.88867e6	−	6.73538e6i	−0.382708	−	0.662869i
$636$	875582.	+	324388.i	0.0858329	+	0.0317996i
$637$	3.04104e6	−	1.26848e7i	0.296943	−	1.23861i
$638$		−	1.27128e7i		−	1.23648i
$639$	−1.99424e7	−	3.75287e6i	−1.93208	−	0.363589i
$640$	−1.18033e6	−	681462.i	−0.113907	−	0.0657645i
$641$	−1.42405e7	−	8.22176e6i	−1.36893	−	0.790350i	−0.378136	−	0.925750i	$-0.623435\pi$
$641$	−1.42405e7	−	8.22176e6i	−1.36893	−	0.790350i	−0.990791	+	0.135400i	$0.956768\pi$
$642$	−1.16516e6	+	198562.i	−0.111570	+	0.0190134i
$643$			5.31877e6i			0.507322i	0.967293	+	0.253661i	$0.0816348\pi$
$643$			5.31877e6i			0.507322i	−0.967293	+	0.253661i	$0.918365\pi$
$644$	420500.	−	3.55768e6i	0.0399532	−	0.338028i
$645$	540034.	−	1.45765e6i	0.0511118	−	0.137960i
$646$	−1.87342e6	−	3.24486e6i	−0.176626	−	0.305925i
$647$	1.32944e6	−	2.30266e6i	0.124856	−	0.216257i	−0.796821	−	0.604216i	$-0.793486\pi$
$647$	1.32944e6	−	2.30266e6i	0.124856	−	0.216257i	0.921677	+	0.387959i	$0.126820\pi$
$648$	−1.37371e6	+	3.52063e6i	−0.128516	+	0.329369i
$649$	2.95465e6	−	1.70587e6i	0.275356	−	0.158977i
$650$	1.17813e7			1.09373
$651$	895322.	+	1.74901e7i	0.0827994	+	1.61748i
$652$	−2.63014e6			−0.242304
$653$	1.02822e6	−	593641.i	0.0943630	−	0.0544805i	−0.452076	−	0.891979i	$-0.649316\pi$
$653$	1.02822e6	−	593641.i	0.0943630	−	0.0544805i	0.546439	+	0.837499i	$0.315983\pi$
$654$	7.06398e6	−	5.85864e6i	0.645811	−	0.535615i
$655$	−3.43990e6	+	5.95808e6i	−0.313287	+	0.542629i
$656$	209081.	+	362139.i	0.0189695	+	0.0328561i
$657$	−2.02975e6	+	2.36334e6i	−0.183455	+	0.213606i
$658$	−1.61033e6	−	1.20209e6i	−0.144994	−	0.108236i
$659$			373152.i			0.0334713i	0.999860	+	0.0167356i	$0.00532737\pi$
$659$			373152.i			0.0334713i	−0.999860	+	0.0167356i	$0.994673\pi$
$660$	1.83366e6	+	1.07599e7i	0.163855	+	0.961500i
$661$	−5.30523e6	−	3.06297e6i	−0.472281	−	0.272671i	0.244913	−	0.969545i	$-0.421241\pi$
$661$	−5.30523e6	−	3.06297e6i	−0.472281	−	0.272671i	−0.717194	+	0.696874i	$0.754574\pi$
$662$	2.08537e6	+	1.20399e6i	0.184943	+	0.106777i
$663$	−961308.	−	5.64094e6i	−0.0849334	−	0.498388i
$664$			4.65938e6i			0.410117i
$665$	−1.71154e7	−	1.27764e7i	−1.50084	−	1.12035i
$666$	−1.90960e6	+	2.22344e6i	−0.166823	+	0.194241i
$667$	5.21692e6	+	9.03597e6i	0.454046	+	0.786431i
$668$	−5.02587e6	+	8.70506e6i	−0.435783	+	0.754798i
$669$	−7.80972e6	+	6.47713e6i	−0.674637	+	0.559522i
$670$	−7.02176e6	+	4.05402e6i	−0.604309	+	0.348898i
$671$	2.34220e7			2.00825
$672$	105796.	+	2.06671e6i	0.00903741	+	0.176546i
$673$	−2.06386e7			−1.75647			−0.878237	−	0.478226i	$-0.841280\pi$
$673$	−2.06386e7			−1.75647			−0.878237	+	0.478226i	$0.841280\pi$
$674$	−1.78456e6	+	1.03032e6i	−0.151315	+	0.0873616i
$675$	247457.	−	1.43731e7i	0.0209046	−	1.21420i
$676$	−1.84854e6	+	3.20177e6i	−0.155583	+	0.269478i
$677$	−3.56149e6	−	6.16868e6i	−0.298648	−	0.517274i	0.677179	−	0.735819i	$-0.263202\pi$
$677$	−3.56149e6	−	6.16868e6i	−0.298648	−	0.517274i	−0.975827	+	0.218545i	$0.929869\pi$
$678$	−3.38192e6	+	9.12843e6i	−0.282546	+	0.762644i
$679$	−15471.9	+	130902.i	−0.00128786	+	0.0108961i
$680$		−	2.51807e6i		−	0.208831i
$681$	7.17002e6	−	1.22189e6i	0.592452	−	0.100963i
$682$	−1.57926e7	−	9.11786e6i	−1.30015	−	0.750640i
$683$	639959.	+	369480.i	0.0524929	+	0.0303068i	0.526017	−	0.850474i	$-0.323685\pi$
$683$	639959.	+	369480.i	0.0524929	+	0.0303068i	−0.473524	+	0.880781i	$0.657018\pi$
$684$	7.56725e6	+	1.42404e6i	0.618440	+	0.116381i
$685$			6.46859e6i			0.526724i
$686$	−8.58896e6	+	1.48012e6i	−0.696836	+	0.120084i
$687$	4.52438e6	+	1.67620e6i	0.365736	+	0.135499i
$688$	153440.	+	265765.i	0.0123585	+	0.0214056i
$689$	1.45279e6	−	2.51630e6i	0.116588	−	0.201936i
$690$	−5.71886e6	−	6.89545e6i	−0.457285	−	0.551366i
$691$	7.52113e6	−	4.34233e6i	0.599223	−	0.345961i	−0.169513	−	0.985528i	$-0.554219\pi$
$691$	7.52113e6	−	4.34233e6i	0.599223	−	0.345961i	0.768736	+	0.639567i	$0.220886\pi$
$692$	−9.76294e6			−0.775024
$693$	1.21990e7	−	1.12182e7i	0.964923	−	0.887343i
$694$	−8.93309e6			−0.704050
$695$	−2.72648e6	+	1.57413e6i	−0.214112	+	0.123617i
$696$	−3.84762e6	−	4.63923e6i	−0.301071	−	0.363013i
$697$	−386288.	+	669070.i	−0.0301182	+	0.0521663i
$698$	5.03892e6	+	8.72767e6i	0.391471	+	0.678047i
$699$	−1.84586e7	−	6.83860e6i	−1.42892	−	0.529388i
$700$	−3.10849e6	−	7.23200e6i	−0.239775	−	0.557844i
$701$			2.53605e7i			1.94923i	0.223887	+	0.974615i	$0.428125\pi$
$701$			2.53605e7i			1.94923i	−0.223887	+	0.974615i	$0.571875\pi$
$702$	1.00815e7	+	6.05431e6i	0.772117	+	0.463684i
$703$	5.17173e6	+	2.98590e6i	0.394682	+	0.227870i
$704$	−1.86613e6	−	1.07741e6i	−0.141909	−	0.0819312i
$705$	−4.95366e6	+	844184.i	−0.375365	+	0.0639682i
$706$		−	7.10819e6i		−	0.536720i
$707$	6.04114e6	−	8.09278e6i	0.454538	−	0.608904i
$708$	561935.	−	1.51676e6i	0.0421311	−	0.113720i
$709$	9.54640e6	+	1.65348e7i	0.713221	+	1.23533i	0.963642	+	0.267197i	$0.0860975\pi$
$709$	9.54640e6	+	1.65348e7i	0.713221	+	1.23533i	−0.250421	+	0.968137i	$0.580569\pi$
$710$	−1.38935e7	+	2.40642e7i	−1.03434	+	1.79153i
$711$	9.24759e6	−	3.24615e6i	0.686048	−	0.240821i
$712$	−3.24554e6	+	1.87381e6i	−0.239931	+	0.138524i
$713$	1.49667e7			1.10256
$714$	−3.20906e6	+	2.07845e6i	−0.235577	+	0.152579i
$715$	3.39649e7			2.48465
$716$	1.06096e7	−	6.12548e6i	0.773425	−	0.446537i
$717$	1.32234e6	−	1.09671e6i	0.0960606	−	0.0796695i
$718$	9.06780e6	−	1.57059e7i	0.656433	−	1.13698i
$719$	7.75609e6	+	1.34339e7i	0.559526	+	0.969128i	0.997536	+	0.0701578i	$0.0223503\pi$
$719$	7.75609e6	+	1.34339e7i	0.559526	+	0.969128i	−0.438009	+	0.898970i	$0.644316\pi$
$720$	3.92573e6	+	3.37160e6i	0.282221	+	0.242385i
$721$	3.78749e6	−	1.62795e6i	0.271340	−	0.116628i
$722$		−	5.78467e6i		−	0.412986i
$723$	−2.77877e6	−	1.63058e7i	−0.197700	−	1.16010i
$724$	−6.79563e6	−	3.92346e6i	−0.481819	−	0.278178i
$725$	1.98548e7	+	1.14632e7i	1.40288	+	0.809955i
$726$	1.21205e6	+	7.11229e6i	0.0853451	+	0.500804i
$727$			2.14536e7i			1.50544i	0.658338	+	0.752722i	$0.271260\pi$
$727$			2.14536e7i			1.50544i	−0.658338	+	0.752722i	$0.728740\pi$
$728$	6.39501e6	+	755856.i	0.447211	+	0.0528580i
$729$	7.59796e6	−	1.21722e7i	0.529515	−	0.848301i
$730$	2.13294e6	+	3.69436e6i	0.148140	+	0.256586i
$731$	−283488.	+	491015.i	−0.0196219	+	0.0339861i
$732$	8.54732e6	−	7.08887e6i	0.589593	−	0.488989i
$733$	179972.	−	103907.i	0.0123721	−	0.00714306i	−0.493801	−	0.869575i	$-0.664393\pi$
$733$	179972.	−	103907.i	0.0123721	−	0.00714306i	0.506173	+	0.862432i	$0.331060\pi$
$734$	−5.46344e6			−0.374305
$735$	−1.21274e7	+	1.81086e7i	−0.828036	+	1.23642i
$736$	1.76854e6			0.120343
$737$	−1.11016e7	+	6.40951e6i	−0.752864	+	0.434666i
$738$	−525870.	−	1.49809e6i	−0.0355416	−	0.101251i
$739$	5.29314e6	−	9.16799e6i	0.356535	−	0.617537i	−0.630844	−	0.775909i	$-0.717291\pi$
$739$	5.29314e6	−	9.16799e6i	0.356535	−	0.617537i	0.987379	+	0.158372i	$0.0506247\pi$
$740$	2.00668e6	+	3.47567e6i	0.134710	+	0.233324i
$741$	8.32412e6	−	2.24683e7i	0.556920	−	1.50323i
$742$	−1.92795e6	−	227874.i	−0.128554	−	0.0151944i
$743$			8.74779e6i			0.581335i	0.956824	+	0.290667i	$0.0938773\pi$
$743$			8.74779e6i			0.581335i	−0.956824	+	0.290667i	$0.906123\pi$
$744$	−8.52273e6	+	1.45241e6i	−0.564477	+	0.0961960i
$745$	−2.24974e6	−	1.29889e6i	−0.148505	−	0.0857394i
$746$	9.98567e6	+	5.76523e6i	0.656947	+	0.379288i
$747$	3.27177e6	−	1.73859e7i	0.214526	−	1.13998i
$748$		−	3.98114e6i		−	0.260168i
$749$	2.25773e6	−	970426.i	0.147051	−	0.0632059i
$750$	−3.25858e6	−	1.20725e6i	−0.211532	−	0.0783688i
$751$	−7.94497e6	−	1.37611e7i	−0.514035	−	0.890334i	−0.999867	−	0.0162823i	$-0.994817\pi$
$751$	−7.94497e6	−	1.37611e7i	−0.514035	−	0.890334i	0.485833	−	0.874052i	$-0.338516\pi$
$752$	496019.	−	859129.i	0.0319855	−	0.0554005i
$753$	9.77800e6	+	1.17897e7i	0.628438	+	0.757731i
$754$	−1.62423e7	+	9.37752e6i	−1.04045	+	0.600703i
$755$	−2.96264e7			−1.89152
$756$	1.05646e6	−	7.78597e6i	0.0672277	−	0.495460i
$757$	−1.26269e7			−0.800860			−0.400430	−	0.916327i	$-0.631139\pi$
$757$	−1.26269e7			−0.800860			−0.400430	+	0.916327i	$0.631139\pi$
$758$	6.20757e6	−	3.58394e6i	0.392418	−	0.226562i
$759$	−9.04168e6	−	1.09019e7i	−0.569698	−	0.686906i
$760$	5.27194e6	−	9.13126e6i	0.331082	−	0.573452i
$761$	7.44430e6	+	1.28939e7i	0.465974	+	0.807091i	0.999245	−	0.0388535i	$-0.0123706\pi$
$761$	7.44430e6	+	1.28939e7i	0.465974	+	0.807091i	−0.533271	+	0.845945i	$0.679037\pi$
$762$	−5.46655e6	−	2.02526e6i	−0.341056	−	0.126355i
$763$	−1.14141e7	+	1.52905e7i	−0.709791	+	0.950845i
$764$			5.45528e6i			0.338130i
$765$	−1.76816e6	+	9.39588e6i	−0.109237	+	0.580475i
$766$	5.64202e6	+	3.25742e6i	0.347426	+	0.200587i
$767$	−4.35897e6	−	2.51665e6i	−0.267544	−	0.154467i
$768$	−1.00709e6	+	171624.i	−0.0616117	+	0.0104996i
$769$			6.82644e6i			0.416273i	0.978100	+	0.208137i	$0.0667399\pi$
$769$			6.82644e6i			0.416273i	−0.978100	+	0.208137i	$0.933260\pi$
$770$	−8.96159e6	−	2.08494e7i	−0.544701	−	1.26726i
$771$	1.16143e6	−	3.13493e6i	0.0703653	−	0.189929i
$772$	1.73675e6	+	3.00814e6i	0.104880	+	0.181658i
$773$	−3.58514e6	+	6.20964e6i	−0.215803	+	0.373781i	−0.953521	−	0.301328i	$-0.902570\pi$
$773$	−3.58514e6	+	6.20964e6i	−0.215803	+	0.373781i	0.737718	+	0.675109i	$0.235903\pi$
$774$	−385924.	−	1.09942e6i	−0.0231553	−	0.0659644i
$775$	2.84806e7	−	1.64433e7i	1.70331	−	0.983409i
$776$	−65071.9			−0.00387918
$777$	2.77310e6	−	5.42621e6i	0.164783	−	0.322437i
$778$	1.90882e7			1.13062
$779$	−2.80158e6	+	1.61750e6i	−0.165409	+	0.0954991i
$780$	1.23947e7	−	1.02798e7i	0.729457	−	0.604988i
$781$	−2.19659e7	+	3.80461e7i	−1.28861	+	2.23194i
$782$	1.63373e6	+	2.82971e6i	0.0955355	+	0.165472i
$783$	1.10993e7	+	2.00125e7i	0.646982	+	1.16653i
$784$	−1.22333e6	−	4.12502e6i	−0.0710809	−	0.239682i
$785$			2.63672e7i			1.52718i
$786$	866327.	+	5.08360e6i	0.0500179	+	0.293504i
$787$	1.03687e7	+	5.98637e6i	0.596743	+	0.344530i	0.767759	−	0.640738i	$-0.221372\pi$
$787$	1.03687e7	+	5.98637e6i	0.596743	+	0.344530i	−0.171016	+	0.985268i	$0.554705\pi$
$788$	−104979.	−	60609.5i	−0.00602262	−	0.00347716i
$789$	−2.46644e6	−	1.44730e7i	−0.141052	−	0.827689i
$790$		−	1.34204e7i		−	0.765065i
$791$	2.37571e6	−	2.01000e7i	0.135006	−	1.14223i
$792$	6.20668e6	+	5.33060e6i	0.351598	+	0.301969i
$793$	−1.72772e7	−	2.99249e7i	−0.975639	−	1.68986i
$794$	201300.	−	348662.i	0.0113316	−	0.0196270i
$795$	−3.73672e6	+	3.09912e6i	−0.209688	+	0.173908i
$796$	−1.01551e7	+	5.86305e6i	−0.568069	+	0.327975i
$797$	−2.26127e7			−1.26097			−0.630487	−	0.776200i	$-0.717145\pi$
$797$	−2.26127e7			−1.26097			−0.630487	+	0.776200i	$0.717145\pi$
$798$	−1.59885e7	+	818457.i	−0.888794	+	0.0454976i
$799$	1.83284e6			0.101568
$800$	3.36540e6	−	1.94302e6i	0.185914	−	0.107337i
$801$	1.34261e7	−	4.71293e6i	0.739382	−	0.259543i
$802$	−1.10938e7	+	1.92150e7i	−0.609036	+	1.05488i
$803$	3.37224e6	+	5.84089e6i	0.184557	+	0.319661i
$804$	−2.11138e6	+	5.69899e6i	−0.115193	+	0.310926i
$805$	1.49257e7	+	1.11418e7i	0.811791	+	0.605990i
$806$			2.69030e7i			1.45869i
$807$	2.85274e7	−	4.86153e6i	1.54198	−	0.262778i
$808$	4.31758e6	+	2.49276e6i	0.232655	+	0.134323i
$809$	−2.77615e6	−	1.60281e6i	−0.149132	−	0.0861015i	0.423577	−	0.905860i	$-0.360774\pi$
$809$	−2.77615e6	−	1.60281e6i	−0.149132	−	0.0861015i	−0.572709	+	0.819759i	$0.694108\pi$
$810$	−1.22809e7	−	1.53373e7i	−0.657684	−	0.821368i
$811$		−	1.69321e7i		−	0.903979i	−0.892023	−	0.451989i	$-0.850715\pi$
$811$		−	1.69321e7i		−	0.903979i	0.892023	−	0.451989i	$-0.149285\pi$
$812$	1.00419e7	+	7.49614e6i	0.534474	+	0.398977i
$813$	4.98693e6	+	1.84757e6i	0.264611	+	0.0980335i
$814$	3.17262e6	+	5.49513e6i	0.167825	+	0.290681i
$815$	6.83725e6	−	1.18425e7i	0.360568	−	0.624522i
$816$	−1.20492e6	−	1.45282e6i	−0.0633482	−	0.0763813i
$817$	−2.05602e6	+	1.18704e6i	−0.107764	+	0.0622173i
$818$	2.90854e6			0.151982
$819$	−2.33314e7	−	7.31089e6i	−1.21544	−	0.380856i
$820$	−2.17408e6			−0.112912
$821$	1.95734e7	−	1.13007e7i	1.01346	−	0.585123i	0.101259	−	0.994860i	$-0.467713\pi$
$821$	1.95734e7	−	1.13007e7i	1.01346	−	0.585123i	0.912204	+	0.409737i	$0.134380\pi$
$822$	3.09529e6	+	3.73211e6i	0.159780	+	0.192653i
$823$	−8.63253e6	+	1.49520e7i	−0.444261	+	0.769483i	−0.998000	−	0.0632072i	$-0.979867\pi$
$823$	−8.63253e6	+	1.49520e7i	−0.444261	+	0.769483i	0.553739	+	0.832690i	$0.313200\pi$
$824$	1.01758e6	+	1.76250e6i	0.0522097	+	0.0904299i
$825$	−2.91831e7	−	1.08118e7i	−1.49278	−	0.553049i
$826$	−394744.	+	3.33977e6i	−0.0201310	+	0.170320i
$827$		−	1.66638e7i		−	0.847246i	−0.905839	−	0.423623i	$-0.860758\pi$
$827$		−	1.66638e7i		−	0.847246i	0.905839	−	0.423623i	$-0.139242\pi$
$828$	−6.59909e6	−	1.24185e6i	−0.334509	−	0.0629497i
$829$	7.96656e6	+	4.59949e6i	0.402610	+	0.232447i	0.687609	−	0.726081i	$-0.258660\pi$
$829$	7.96656e6	+	4.59949e6i	0.402610	+	0.232447i	−0.285000	+	0.958528i	$0.591993\pi$
$830$	−2.09793e7	−	1.21124e7i	−1.05705	−	0.610287i
$831$	−9.13795e6	+	1.55725e6i	−0.459035	+	0.0782270i
$832$			3.17898e6i			0.159214i
$833$	5.47006e6	−	5.76795e6i	0.273136	−	0.288011i
$834$	−819826.	+	2.21286e6i	−0.0408138	+	0.110164i
$835$	−2.61302e7	−	4.52588e7i	−1.29696	−	2.24640i
$836$	8.33507e6	−	1.44368e7i	0.412471	−	0.714421i
$837$	3.28214e7	+	565075.i	1.61936	+	0.0278800i
$838$	4.57470e6	−	2.64120e6i	0.225036	−	0.129925i
$839$	−1.21622e7			−0.596495			−0.298248	−	0.954489i	$-0.596402\pi$
$839$	−1.21622e7			−0.596495			−0.298248	+	0.954489i	$0.596402\pi$
$840$	−9.58057e6	−	4.89621e6i	−0.468482	−	0.239421i
$841$	−1.59860e7			−0.779381
$842$	1.74077e7	−	1.00503e7i	0.846177	−	0.488541i
$843$	−1.24644e7	+	1.03376e7i	−0.604091	+	0.501014i
$844$	−3.50557e6	+	6.07182e6i	−0.169396	+	0.293402i
$845$	−9.61084e6	−	1.66465e7i	−0.463041	−	0.802011i
$846$	−2.45410e6	+	2.85744e6i	−0.117887	+	0.137262i
$847$	−5.92360e6	−	1.37814e7i	−0.283712	−	0.660064i
$848$		−	958392.i		−	0.0457671i
$849$	6.59635e6	+	3.87073e7i	0.314076	+	1.84299i
$850$	6.21775e6	+	3.58982e6i	0.295179	+	0.170422i
$851$	−4.51006e6	−	2.60389e6i	−0.213481	−	0.123253i
$852$	3.49902e6	+	2.05322e7i	0.165138	+	0.969028i
$853$			2.68757e6i			0.126470i	0.997999	+	0.0632349i	$0.0201417\pi$
$853$			2.68757e6i			0.126470i	−0.997999	+	0.0632349i	$0.979858\pi$
$854$	−1.38109e7	+	1.85012e7i	−0.648004	+	0.868073i
$855$	−2.60835e7	+	3.03703e7i	−1.22025	+	1.42080i
$856$	606582.	+	1.05063e6i	0.0282947	+	0.0490078i
$857$	16391.7	−	28391.2i	0.000762380	−	0.00132048i	−0.865644	−	0.500660i	$-0.833091\pi$
$857$	16391.7	−	28391.2i	0.000762380	−	0.00132048i	0.866406	+	0.499340i	$0.166424\pi$
$858$	1.95964e7	−	1.62526e7i	0.908777	−	0.753710i
$859$	−2.24671e7	+	1.29714e7i	−1.03888	+	0.599796i	−0.919515	−	0.393055i	$-0.871418\pi$
$859$	−2.24671e7	+	1.29714e7i	−1.03888	+	0.599796i	−0.119362	+	0.992851i	$0.538085\pi$
$860$	−1.59551e6			−0.0735620
$861$	1.79452e6	+	2.77068e6i	0.0824974	+	0.127373i
$862$	7.43210e6			0.340678
$863$	1.00839e7	−	5.82196e6i	0.460896	−	0.266098i	−0.251525	−	0.967851i	$-0.580932\pi$
$863$	1.00839e7	−	5.82196e6i	0.460896	−	0.266098i	0.712421	+	0.701752i	$0.247599\pi$
$864$	3.87833e6	+	66772.0i	0.176751	+	0.00304306i
$865$	2.53794e7	−	4.39585e7i	1.15330	−	1.99757i
$866$	−1.10539e7	−	1.91460e7i	−0.500867	−	0.867528i
$867$	−6.47781e6	+	1.74848e7i	−0.292672	+	0.789974i
$868$	1.65144e7	−	7.09831e6i	0.743986	−	0.319783i
$869$		−	2.12181e7i		−	0.953139i
$870$	3.08907e7	−	5.26427e6i	1.38366	−	0.235798i
$871$	1.63781e7	+	9.45589e6i	0.731506	+	0.422335i
$872$	−8.15763e6	−	4.70981e6i	−0.363306	−	0.209755i
$873$	242808.	+	45692.8i	0.0107827	+	0.00202914i
$874$			1.36818e7i			0.605850i
$875$	7.17509e6	+	848059.i	0.316816	+	0.0374460i
$876$	2.99841e6	+	1.11086e6i	0.132017	+	0.0489101i
$877$	−1.21388e7	−	2.10250e7i	−0.532936	−	0.923073i	−0.999260	−	0.0384589i	$-0.987755\pi$
$877$	−1.21388e7	−	2.10250e7i	−0.532936	−	0.923073i	0.466324	−	0.884614i	$-0.345578\pi$
$878$	1.14122e7	−	1.97665e7i	0.499612	−	0.865353i
$879$	−2.50077e7	−	3.01527e7i	−1.09169	−	1.31630i
$880$	9.70226e6	−	5.60160e6i	0.422344	−	0.243840i
$881$	−3.00774e7			−1.30557			−0.652787	−	0.757542i	$-0.726400\pi$
$881$	−3.00774e7			−1.30557			−0.652787	+	0.757542i	$0.726400\pi$
$882$	1.66816e6	+	1.62510e7i	0.0722048	+	0.703411i
$883$	1.55262e6			0.0670139			0.0335069	−	0.999438i	$-0.489332\pi$
$883$	1.55262e6			0.0670139			0.0335069	+	0.999438i	$0.489332\pi$
$884$	−5.08646e6	+	2.93667e6i	−0.218920	+	0.126393i
$885$	5.36858e6	+	6.47310e6i	0.230410	+	0.277814i
$886$	1.02652e7	−	1.77798e7i	0.439320	−	0.760925i
$887$	658464.	+	1.14049e6i	0.0281011	+	0.0486725i	0.879734	−	0.475466i	$-0.157721\pi$
$887$	658464.	+	1.14049e6i	0.0281011	+	0.0486725i	−0.851633	+	0.524139i	$0.824387\pi$
$888$	2.82092e6	+	1.04510e6i	0.120049	+	0.0444760i
$889$	1.20368e7	+	1.42269e6i	0.510808	+	0.0603749i
$890$		−	1.94844e7i		−	0.824542i
$891$	−1.94164e7	−	2.42487e7i	−0.819360	−	1.02328i
$892$	9.01882e6	+	5.20702e6i	0.379523	+	0.219118i
$893$	6.64641e6	+	3.83731e6i	0.278906	+	0.161027i
$894$	−1.91954e6	+	327120.i	−0.0803253	+	0.0136887i
$895$			6.36945e7i			2.65793i
$896$	1.95143e6	−	838770.i	0.0812048	−	0.0349038i
$897$	−7.25913e6	+	1.95937e7i	−0.301234	+	0.813085i
$898$	−3.12725e6	−	5.41655e6i	−0.129411	−	0.224146i
$899$	−2.61765e7	+	4.53390e7i	−1.08022	+	1.87100i
$900$	−1.39220e7	+	4.88698e6i	−0.572920	+	0.201110i
$901$	1.53345e6	−	885339.i	0.0629301	−	0.0363327i
$902$	−3.43728e6			−0.140669
$903$	1.31696e6	+	2.03334e6i	0.0537468	+	0.0829832i
$904$	9.99177e6			0.406651
$905$	3.53314e7	−	2.03986e7i	1.43397	−	0.827903i
$906$	−1.70932e7	+	1.41766e7i	−0.691837	+	0.573787i
$907$	8.12564e6	−	1.40740e7i	0.327974	−	0.568068i	−0.654136	−	0.756377i	$-0.726967\pi$
$907$	8.12564e6	−	1.40740e7i	0.327974	−	0.568068i	0.982110	+	0.188310i	$0.0603008\pi$
$908$	−3.73271e6	−	6.46524e6i	−0.150248	−	0.260238i
$909$	−1.43602e7	−	1.23332e7i	−0.576434	−	0.495069i
$910$	−2.00276e7	+	2.68292e7i	−0.801724	+	1.07400i
$911$			2.24793e7i			0.897402i	0.893682	+	0.448701i	$0.148113\pi$
$911$			2.24793e7i			0.897402i	−0.893682	+	0.448701i	$0.851887\pi$
$912$	−1.32772e6	−	7.79104e6i	−0.0528590	−	0.310176i
$913$	−3.31688e7	−	1.91500e7i	−1.31690	−	0.760312i
$914$	2.18253e7	+	1.26009e7i	0.864162	+	0.498924i
$915$	9.69890e6	+	5.69131e7i	0.382975	+	2.24729i
$916$		−	4.95229e6i		−	0.195015i
$917$	−4.23397e6	−	9.85046e6i	−0.166274	−	0.386841i
$918$	3.47587e6	+	6.26712e6i	0.136131	+	0.245449i
$919$	5.60967e6	+	9.71623e6i	0.219103	+	0.379498i	0.954534	−	0.298102i	$-0.0963536\pi$
$919$	5.60967e6	+	9.71623e6i	0.219103	+	0.379498i	−0.735431	+	0.677600i	$0.763020\pi$
$920$	−4.59744e6	+	7.96301e6i	−0.179080	+	0.310175i
$921$	−9.49222e6	+	7.87254e6i	−0.368739	+	0.305820i
$922$	−564145.	+	325709.i	−0.0218556	+	0.0126184i
$923$	6.48123e7			2.50411
$924$	−1.51471e7	−	7.74104e6i	−0.583648	−	0.298277i
$925$	−1.14431e7			−0.439733
$926$	−2.91330e7	+	1.68199e7i	−1.11650	+	0.644609i
$927$	−2.55937e6	−	7.29110e6i	−0.0978215	−	0.278672i
$928$	−3.09314e6	+	5.35747e6i	−0.117904	+	0.204216i
$929$	585570.	+	1.01424e6i	0.0222607	+	0.0385567i	0.876941	−	0.480598i	$-0.159580\pi$
$929$	585570.	+	1.01424e6i	0.0222607	+	0.0385567i	−0.854680	+	0.519154i	$0.826247\pi$
$930$	1.56158e7	−	4.21500e7i	0.592049	−	1.59805i
$931$	3.19120e7	−	9.46393e6i	1.20665	−	0.357847i
$932$			2.02044e7i			0.761914i
$933$	2.57091e6	−	438124.i	0.0966901	−	0.0164776i
$934$	2.23835e7	+	1.29231e7i	0.839578	+	0.484731i
$935$	1.79254e7	+	1.03492e7i	0.670564	+	0.387151i
$936$	2.23225e6	−	1.18620e7i	0.0832824	−	0.442556i
$937$		−	2.95716e7i		−	1.10034i	−0.835053	−	0.550169i	$-0.814563\pi$
$937$		−	2.95716e7i		−	1.10034i	0.835053	−	0.550169i	$-0.185437\pi$
$938$	1.48318e6	−	1.25486e7i	0.0550412	−	0.465682i
$939$	1.85372e7	+	6.86771e6i	0.686089	+	0.254184i
$940$	2.57887e6	+	4.46673e6i	0.0951940	+	0.164881i
$941$	2.26652e7	−	3.92573e7i	0.834421	−	1.44526i	−0.0600797	−	0.998194i	$-0.519135\pi$
$941$	2.26652e7	−	3.92573e7i	0.834421	−	1.44526i	0.894501	−	0.447066i	$-0.147531\pi$
$942$	1.26170e7	+	1.52128e7i	0.463263	+	0.558574i
$943$	2.44315e6	−	1.41055e6i	0.0894686	−	0.0516547i
$944$	−1.66022e6			−0.0606365
$945$	3.23107e7	+	2.49970e7i	1.17697	+	0.910559i
$946$	−2.52254e6			−0.0916454
$947$	−3.82062e7	+	2.20584e7i	−1.38439	+	0.799279i	−0.992676	−	0.120806i	$-0.961452\pi$
$947$	−3.82062e7	+	2.20584e7i	−1.38439	+	0.799279i	−0.391717	+	0.920086i	$0.628119\pi$
$948$	−6.42182e6	−	7.74303e6i	−0.232080	−	0.279827i
$949$	4.97503e6	−	8.61701e6i	0.179321	−	0.310593i
$950$	1.50316e7	+	2.60355e7i	0.540376	+	0.935958i
$951$	4.38783e7	+	1.62561e7i	1.57325	+	0.582862i
$952$	3.14473e6	+	2.34750e6i	0.112458	+	0.0839484i
$953$			5.71596e6i			0.203872i	0.994791	+	0.101936i	$0.0325036\pi$
$953$			5.71596e6i			0.203872i	−0.994791	+	0.101936i	$0.967496\pi$
$954$	−672972.	+	3.57612e6i	−0.0239401	+	0.127216i
$955$	−2.45629e7	−	1.41814e7i	−0.871506	−	0.503164i
$956$	−1.52707e6	−	881652.i	−0.0540397	−	0.0311998i
$957$	4.88390e7	−	8.32296e6i	1.72380	−	0.293763i
$958$			2.12648e7i			0.748597i
$959$	−8.07840e6	−	6.03041e6i	−0.283648	−	0.211739i
$960$	1.84524e6	−	4.98064e6i	0.0646212	−	0.174424i
$961$	2.32341e7	+	4.02426e7i	0.811553	+	1.40565i
$962$	4.68053e6	−	8.10692e6i	0.163064	−	0.282435i
$963$	−1.52564e6	−	4.34624e6i	−0.0530137	−	0.151025i
$964$	−1.47030e7	+	8.48876e6i	−0.509580	+	0.294206i
$965$	−1.80592e7			−0.624282
$966$	1.39430e7	−	713744.i	0.480742	−	0.0246093i
$967$	−1.87898e7			−0.646182			−0.323091	−	0.946368i	$-0.604722\pi$
$967$	−1.87898e7			−0.646182			−0.323091	+	0.946368i	$0.604722\pi$
$968$	6.41318e6	−	3.70265e6i	0.219981	−	0.127006i
$969$	1.12394e7	−	9.32155e6i	0.384531	−	0.318918i
$970$	169159.	−	292992.i	0.00577253	−	0.00999831i
$971$	−3.13939e6	−	5.43759e6i	−0.106856	−	0.185080i	0.807639	−	0.589677i	$-0.200745\pi$
$971$	−3.13939e6	−	5.43759e6i	−0.106856	−	0.185080i	−0.914495	+	0.404598i	$0.867412\pi$
$972$	−1.44246e7	−	2.97248e6i	−0.489710	−	0.100914i
$973$	575906.	−	4.87251e6i	0.0195016	−	0.164995i
$974$		−	3.05109e7i		−	1.03052i
$975$	7.71316e6	+	4.52607e7i	0.259849	+	1.52479i
$976$	−9.87062e6	−	5.69880e6i	−0.331680	−	0.191496i
$977$	−2.64868e7	−	1.52922e7i	−0.887754	−	0.512545i	−0.0145471	−	0.999894i	$-0.504631\pi$
$977$	−2.64868e7	−	1.52922e7i	−0.887754	−	0.512545i	−0.873207	+	0.487349i	$0.837964\pi$
$978$	−1.72194e6	−	1.01043e7i	−0.0575665	−	0.337800i
$979$		−	3.08054e7i		−	1.02724i
$980$	2.17534e7	+	5.21513e6i	0.723538	+	0.173460i
$981$	2.71320e7	+	2.33023e7i	0.900140	+	0.773083i
$982$	−4.64758e6	−	8.04984e6i	−0.153797	−	0.266384i
$983$	−93556.9	+	162045.i	−0.00308811	+	0.00534876i	−0.867565	−	0.497323i	$-0.834316\pi$
$983$	−93556.9	+	162045.i	−0.00308811	+	0.00534876i	0.864477	+	0.502672i	$0.167650\pi$
$984$	−1.25436e6	+	1.04032e6i	−0.0412984	+	0.0342515i
$985$	545799.	−	315117.i	0.0179243	−	0.0103486i
$986$	−1.14295e7			−0.374398
$987$	3.56382e6	−	6.97345e6i	0.116446	−	0.227853i
$988$	−2.45933e7			−0.801539
$989$	1.79297e6	−	1.03517e6i	0.0582885	−	0.0336529i
$990$	−4.01362e7	+	1.40889e7i	−1.30151	+	0.456866i
$991$	−2.73564e7	+	4.73826e7i	−0.884860	+	1.53262i	−0.0389850	+	0.999240i	$0.512412\pi$
$991$	−2.73564e7	+	4.73826e7i	−0.884860	+	1.53262i	−0.845875	+	0.533382i	$0.820921\pi$
$992$	4.43692e6	+	7.68498e6i	0.143154	+	0.247950i
$993$	−3.26012e6	+	8.79965e6i	−0.104920	+	0.283199i
$994$	−1.71006e7	−	3.97851e7i	−0.548966	−	1.27719i
$995$		−	6.09656e7i		−	1.95221i
$996$	−1.79001e7	+	3.05046e6i	−0.571750	+	0.0974355i
$997$	1.17404e7	+	6.77833e6i	0.374063	+	0.215966i	0.675232	−	0.737605i	$-0.264043\pi$
$997$	1.17404e7	+	6.77833e6i	0.374063	+	0.215966i	−0.301169	+	0.953571i	$0.597377\pi$
$998$	1.73127e7	+	9.99550e6i	0.550223	+	0.317671i
$999$	−9.79206e6	−	5.88049e6i	−0.310428	−	0.186423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.6.f.a.17.12	yes	28
3.2	odd	2	inner	42.6.f.a.17.7	yes	28
7.3	odd	6		294.6.d.a.293.6		28
7.4	even	3		294.6.d.a.293.24		28
7.5	odd	6	inner	42.6.f.a.5.7	✓	28
21.5	even	6	inner	42.6.f.a.5.12	yes	28
21.11	odd	6		294.6.d.a.293.5		28
21.17	even	6		294.6.d.a.293.23		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.f.a.5.7	✓	28	7.5	odd	6	inner
42.6.f.a.5.12	yes	28	21.5	even	6	inner
42.6.f.a.17.7	yes	28	3.2	odd	2	inner
42.6.f.a.17.12	yes	28	1.1	even	1	trivial
294.6.d.a.293.5		28	21.11	odd	6
294.6.d.a.293.6		28	7.3	odd	6
294.6.d.a.293.23		28	21.17	even	6
294.6.d.a.293.24		28	7.4	even	3

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.46410 - 2.00000i) q^{2} +(9.95138 + 11.9988i) q^{3} +(8.00000 - 13.8564i) q^{4} +(41.5931 + 72.0414i) q^{5} +(58.4701 + 21.6621i) q^{6} +(-128.746 - 15.2171i) q^{7} -64.0000i q^{8} +(-44.9401 + 238.808i) q^{9} +(288.166 + 166.372i) q^{10} +(455.598 + 263.039i) q^{11} +(245.871 - 41.9003i) q^{12} -776.119i q^{13} +(-476.422 + 204.778i) q^{14} +(-450.498 + 1215.98i) q^{15} +(-128.000 - 221.703i) q^{16} +(236.487 - 409.607i) q^{17} +(321.939 + 917.136i) q^{18} +(1715.14 - 990.236i) q^{19} +1330.98 q^{20} +(-1098.61 - 1696.22i) q^{21} +2104.32 q^{22} +(-1495.70 + 863.545i) q^{23} +(767.920 - 636.888i) q^{24} +(-1897.48 + 3286.52i) q^{25} +(-1552.24 - 2688.56i) q^{26} +(-3312.62 + 1837.25i) q^{27} +(-1240.82 + 1662.22i) q^{28} -6041.29i q^{29} +(871.383 + 5113.26i) q^{30} +(-7504.86 - 4332.93i) q^{31} +(-886.810 - 512.000i) q^{32} +(1377.68 + 8084.21i) q^{33} -1891.89i q^{34} +(-4258.67 - 9907.94i) q^{35} +(2949.50 + 2533.17i) q^{36} +(1507.67 + 2611.36i) q^{37} +(3960.94 - 6860.55i) q^{38} +(9312.46 - 7723.46i) q^{39} +(4610.65 - 2661.96i) q^{40} -1633.44 q^{41} +(-7198.14 - 3678.65i) q^{42} -1198.75 q^{43} +(7289.56 - 4208.63i) q^{44} +(-19073.3 + 6695.23i) q^{45} +(-3454.18 + 5982.81i) q^{46} +(1937.57 + 3355.97i) q^{47} +(1386.38 - 3742.09i) q^{48} +(16343.9 + 3918.26i) q^{49} +15179.8i q^{50} +(7268.14 - 1238.61i) q^{51} +(-10754.2 - 6208.95i) q^{52} +(3242.15 + 1871.86i) q^{53} +(-7800.75 + 12989.6i) q^{54} +43762.5i q^{55} +(-973.892 + 8239.72i) q^{56} +(28949.6 + 10725.3i) q^{57} +(-12082.6 - 20927.6i) q^{58} +(3242.61 - 5616.36i) q^{59} +(13245.1 + 15970.1i) q^{60} +(38557.1 - 22260.9i) q^{61} -34663.5 q^{62} +(9419.81 - 30061.7i) q^{63} -4096.00 q^{64} +(55912.7 - 32281.2i) q^{65} +(20940.8 + 25249.2i) q^{66} +(-12183.6 + 21102.5i) q^{67} +(-3783.79 - 6553.71i) q^{68} +(-25245.8 - 9353.12i) q^{69} +(-34568.4 - 25804.8i) q^{70} +83508.1i q^{71} +(15283.7 + 2876.17i) q^{72} +(11102.7 + 6410.14i) q^{73} +(10445.5 + 6030.69i) q^{74} +(-58316.7 + 9938.11i) q^{75} -31687.5i q^{76} +(-54653.5 - 40798.0i) q^{77} +(16812.4 - 45379.8i) q^{78} +(-20166.2 - 34928.9i) q^{79} +(10647.8 - 18442.6i) q^{80} +(-55009.8 - 21464.1i) q^{81} +(-5658.42 + 3266.89i) q^{82} -72802.8 q^{83} +(-32292.4 + 1653.06i) q^{84} +39344.9 q^{85} +(-4152.59 + 2397.50i) q^{86} +(72487.9 - 60119.1i) q^{87} +(16834.5 - 29158.2i) q^{88} +(-29278.3 - 50711.6i) q^{89} +(-52681.3 + 61339.5i) q^{90} +(-11810.3 + 99922.0i) q^{91} +27633.4i q^{92} +(-22693.9 - 133168. i) q^{93} +(13423.9 + 7750.29i) q^{94} +(142676. + 82374.0i) q^{95} +(-2681.62 - 15735.7i) q^{96} -1016.75i q^{97} +(64453.4 - 19114.5i) q^{98} +(-83290.6 + 96979.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 224 q^{4} - 154 q^{7} - 30 q^{9} + 744 q^{10} - 516 q^{15} - 3584 q^{16} + 1632 q^{18} + 2652 q^{19} + 7236 q^{21} + 3312 q^{22} - 1920 q^{24} - 13208 q^{25} - 5024 q^{28} + 2448 q^{30} + 22458 q^{31}+ \cdots + 153216 q^{99}+O(q^{100}) \) 28 * q + 224 * q^4 - 154 * q^7 - 30 * q^9 + 744 * q^10 - 516 * q^15 - 3584 * q^16 + 1632 * q^18 + 2652 * q^19 + 7236 * q^21 + 3312 * q^22 - 1920 * q^24 - 13208 * q^25 - 5024 * q^28 + 2448 * q^30 + 22458 * q^31 - 43542 * q^33 - 960 * q^36 + 5488 * q^37 + 21888 * q^39 + 11904 * q^40 + 33288 * q^42 - 40352 * q^43 + 5796 * q^45 - 11568 * q^46 - 2126 * q^49 - 34572 * q^51 - 41472 * q^52 - 60408 * q^54 + 57168 * q^57 + 42552 * q^58 - 4128 * q^60 + 298200 * q^61 + 46560 * q^63 - 114688 * q^64 + 165312 * q^66 + 55148 * q^67 - 36120 * q^70 - 26112 * q^72 - 427596 * q^73 - 458640 * q^75 + 87840 * q^78 + 471794 * q^79 - 245538 * q^81 + 118176 * q^82 + 4608 * q^84 - 562056 * q^85 + 833454 * q^87 + 26496 * q^88 - 132876 * q^91 - 560448 * q^93 - 444576 * q^94 - 30720 * q^96 + 153216 * q^99

Introduction

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