LMFDB - Embedded newform 80.6.q.a.29.3

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			29.3
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.61624 - 0.676673i) q^{2} +(18.5525 - 18.5525i) q^{3} +(31.0842 + 7.60071i) q^{4} +(8.85788 - 55.1955i) q^{5} +(-116.749 + 91.6413i) q^{6} -206.395 q^{7} +(-169.433 - 63.7213i) q^{8} -445.391i q^{9} +O(q^{10})$	\(q+(-5.61624 - 0.676673i) q^{2} +(18.5525 - 18.5525i) q^{3} +(31.0842 + 7.60071i) q^{4} +(8.85788 - 55.1955i) q^{5} +(-116.749 + 91.6413i) q^{6} -206.395 q^{7} +(-169.433 - 63.7213i) q^{8} -445.391i q^{9} +(-87.0972 + 303.997i) q^{10} +(-431.215 + 431.215i) q^{11} +(717.703 - 435.678i) q^{12} +(325.010 - 325.010i) q^{13} +(1159.16 + 139.662i) q^{14} +(-859.678 - 1188.35i) q^{15} +(908.458 + 472.525i) q^{16} +11.3173i q^{17} +(-301.384 + 2501.42i) q^{18} +(633.012 + 633.012i) q^{19} +(694.865 - 1648.38i) q^{20} +(-3829.15 + 3829.15i) q^{21} +(2713.60 - 2130.01i) q^{22} +633.812 q^{23} +(-4325.60 + 1961.22i) q^{24} +(-2968.08 - 977.829i) q^{25} +(-2045.26 + 1605.41i) q^{26} +(-3754.87 - 3754.87i) q^{27} +(-6415.63 - 1568.75i) q^{28} +(-5806.14 - 5806.14i) q^{29} +(4024.03 + 7255.78i) q^{30} +4462.77 q^{31} +(-4782.37 - 3268.54i) q^{32} +16000.2i q^{33} +(7.65811 - 63.5606i) q^{34} +(-1828.22 + 11392.1i) q^{35} +(3385.29 - 13844.6i) q^{36} +(1633.96 + 1633.96i) q^{37} +(-3126.80 - 3983.48i) q^{38} -12059.5i q^{39} +(-5017.94 + 8787.51i) q^{40} +2095.37i q^{41} +(24096.5 - 18914.3i) q^{42} +(-3517.93 - 3517.93i) q^{43} +(-16681.5 + 10126.4i) q^{44} +(-24583.6 - 3945.22i) q^{45} +(-3559.64 - 428.883i) q^{46} -8225.47i q^{47} +(25620.7 - 8087.66i) q^{48} +25791.9 q^{49} +(16007.7 + 7500.14i) q^{50} +(209.964 + 209.964i) q^{51} +(12573.0 - 7632.38i) q^{52} +(-14407.9 - 14407.9i) q^{53} +(18547.4 + 23629.0i) q^{54} +(19981.4 + 27620.7i) q^{55} +(34970.2 + 13151.8i) q^{56} +23487.9 q^{57} +(28679.8 + 36537.5i) q^{58} +(6023.12 - 6023.12i) q^{59} +(-17690.1 - 43473.1i) q^{60} +(-27741.1 - 27741.1i) q^{61} +(-25064.0 - 3019.84i) q^{62} +91926.6i q^{63} +(24647.2 + 21593.0i) q^{64} +(-15060.2 - 20818.0i) q^{65} +(10826.9 - 89861.1i) q^{66} +(-11643.0 + 11643.0i) q^{67} +(-86.0195 + 351.789i) q^{68} +(11758.8 - 11758.8i) q^{69} +(17976.4 - 62743.4i) q^{70} -73970.7i q^{71} +(-28380.9 + 75464.1i) q^{72} -43814.9 q^{73} +(-8071.03 - 10282.3i) q^{74} +(-73206.4 + 36924.1i) q^{75} +(14865.3 + 24488.0i) q^{76} +(89000.6 - 89000.6i) q^{77} +(-8160.35 + 67729.0i) q^{78} +4592.73 q^{79} +(34128.2 - 45957.2i) q^{80} -31094.3 q^{81} +(1417.88 - 11768.1i) q^{82} +(-24957.5 + 24957.5i) q^{83} +(-148130. + 89921.8i) q^{84} +(624.663 + 100.247i) q^{85} +(17377.1 + 22138.0i) q^{86} -215437. q^{87} +(100540. - 45584.5i) q^{88} -127683. i q^{89} +(135398. + 38792.4i) q^{90} +(-67080.5 + 67080.5i) q^{91} +(19701.5 + 4817.42i) q^{92} +(82795.5 - 82795.5i) q^{93} +(-5565.96 + 46196.2i) q^{94} +(40546.5 - 29332.2i) q^{95} +(-149365. + 28085.4i) q^{96} +176164. i q^{97} +(-144854. - 17452.7i) q^{98} +(192059. + 192059. i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−5.61624	−	0.676673i	−0.992820	−	0.119620i
$2$	−5.61624	−	0.676673i	−0.992820	−	0.119620i
$3$	18.5525	−	18.5525i	1.19014	−	1.19014i	0.213118	−	0.977027i	$-0.431638\pi$
$3$	18.5525	−	18.5525i	1.19014	−	1.19014i	0.977027	−	0.213118i	$-0.0683617\pi$
$4$	31.0842	+	7.60071i	0.971382	+	0.237522i
$5$	8.85788	−	55.1955i	0.158455	−	0.987366i
$5$	8.85788	−	55.1955i	0.158455	−	0.987366i
$6$	−116.749	+	91.6413i	−1.32396	+	1.03923i
$7$	−206.395			−1.59204			−0.796020	−	0.605270i	$-0.793065\pi$
$7$	−206.395			−1.59204			−0.796020	+	0.605270i	$0.793065\pi$
$8$	−169.433	−	63.7213i	−0.935995	−	0.352014i
$9$		−	445.391i		−	1.83289i
$10$	−87.0972	+	303.997i	−0.275426	+	0.961322i
$11$	−431.215	+	431.215i	−1.07451	+	1.07451i	−0.0775232	+	0.996991i	$0.524701\pi$
$11$	−431.215	+	431.215i	−1.07451	+	1.07451i	−0.996991	+	0.0775232i	$0.975299\pi$
$12$	717.703	−	435.678i	1.43877	−	0.873399i
$13$	325.010	−	325.010i	0.533382	−	0.533382i	−0.388195	−	0.921577i	$-0.626901\pi$
$13$	325.010	−	325.010i	0.533382	−	0.533382i	0.921577	+	0.388195i	$0.126901\pi$
$14$	1159.16	+	139.662i	1.58061	+	0.190440i
$15$	−859.678	−	1188.35i	−0.986524	−	1.36369i
$16$	908.458	+	472.525i	0.887166	+	0.461450i
$17$			11.3173i			0.00949774i	0.999989	+	0.00474887i	$0.00151162\pi$
$17$			11.3173i			0.00949774i	−0.999989	+	0.00474887i	$0.998488\pi$
$18$	−301.384	+	2501.42i	−0.219250	+	1.81973i
$19$	633.012	+	633.012i	0.402279	+	0.402279i	0.879036	−	0.476756i	$-0.158188\pi$
$19$	633.012	+	633.012i	0.402279	+	0.402279i	−0.476756	+	0.879036i	$0.658188\pi$
$20$	694.865	−	1648.38i	0.388441	−	0.921473i
$21$	−3829.15	+	3829.15i	−1.89476	+	1.89476i
$22$	2713.60	−	2130.01i	1.19533	−	0.938265i
$23$	633.812			0.249828			0.124914	−	0.992168i	$-0.460135\pi$
$23$	633.812			0.249828			0.124914	+	0.992168i	$0.460135\pi$
$24$	−4325.60	+	1961.22i	−1.53292	+	0.695022i
$25$	−2968.08	−	977.829i	−0.949784	−	0.312905i
$26$	−2045.26	+	1605.41i	−0.593356	+	0.465749i
$27$	−3754.87	−	3754.87i	−0.991255	−	0.991255i
$28$	−6415.63	−	1568.75i	−1.54648	−	0.378145i
$29$	−5806.14	−	5806.14i	−1.28201	−	1.28201i	−0.939520	−	0.342494i	$-0.888728\pi$
$29$	−5806.14	−	5806.14i	−1.28201	−	1.28201i	−0.342494	−	0.939520i	$-0.611272\pi$
$30$	4024.03	+	7255.78i	0.816316	+	1.47191i
$31$	4462.77			0.834065			0.417033	−	0.908892i	$-0.363070\pi$
$31$	4462.77			0.834065			0.417033	+	0.908892i	$0.363070\pi$
$32$	−4782.37	−	3268.54i	−0.825598	−	0.564259i
$33$			16000.2i			2.55765i
$34$	7.65811	−	63.5606i	0.00113612	−	0.00942954i
$35$	−1828.22	+	11392.1i	−0.252266	+	1.57193i
$36$	3385.29	−	13844.6i	0.435351	−	1.78043i
$37$	1633.96	+	1633.96i	0.196217	+	0.196217i	0.798376	−	0.602159i	$-0.205693\pi$
$37$	1633.96	+	1633.96i	0.196217	+	0.196217i	−0.602159	+	0.798376i	$0.705693\pi$
$38$	−3126.80	−	3983.48i	−0.351270	−	0.447511i
$39$		−	12059.5i		−	1.26960i
$40$	−5017.94	+	8787.51i	−0.495879	+	0.868392i
$41$			2095.37i			0.194670i	0.995252	+	0.0973352i	$0.0310319\pi$
$41$			2095.37i			0.194670i	−0.995252	+	0.0973352i	$0.968968\pi$
$42$	24096.5	−	18914.3i	2.10780	−	1.65450i
$43$	−3517.93	−	3517.93i	−0.290146	−	0.290146i	0.546992	−	0.837138i	$-0.315773\pi$
$43$	−3517.93	−	3517.93i	−0.290146	−	0.290146i	−0.837138	+	0.546992i	$0.815773\pi$
$44$	−16681.5	+	10126.4i	−1.29898	+	0.788542i
$45$	−24583.6	−	3945.22i	−1.80973	−	0.290429i
$46$	−3559.64	−	428.883i	−0.248034	−	0.0298844i
$47$		−	8225.47i		−	0.543145i	−0.962418	−	0.271573i	$-0.912456\pi$
$47$		−	8225.47i		−	0.543145i	0.962418	−	0.271573i	$-0.0875438\pi$
$48$	25620.7	−	8087.66i	1.60505	−	0.506664i
$49$	25791.9			1.53459
$50$	16007.7	+	7500.14i	0.905535	+	0.424272i
$51$	209.964	+	209.964i	0.0113037	+	0.0113037i
$52$	12573.0	−	7632.38i	0.644808	−	0.391428i
$53$	−14407.9	−	14407.9i	−0.704549	−	0.704549i	0.260834	−	0.965384i	$-0.416002\pi$
$53$	−14407.9	−	14407.9i	−0.704549	−	0.704549i	−0.965384	+	0.260834i	$0.916002\pi$
$54$	18547.4	+	23629.0i	0.865563	+	1.10271i
$55$	19981.4	+	27620.7i	0.890677	+	1.23120i
$56$	34970.2	+	13151.8i	1.49014	+	0.560420i
$57$	23487.9			0.957541
$58$	28679.8	+	36537.5i	1.11945	+	1.42616i
$59$	6023.12	−	6023.12i	0.225264	−	0.225264i	−0.585447	−	0.810711i	$-0.699081\pi$
$59$	6023.12	−	6023.12i	0.225264	−	0.225264i	0.810711	+	0.585447i	$0.199081\pi$
$60$	−17690.1	−	43473.1i	−0.634385	−	1.55899i
$61$	−27741.1	−	27741.1i	−0.954551	−	0.954551i	0.0444600	−	0.999011i	$-0.485843\pi$
$61$	−27741.1	−	27741.1i	−0.954551	−	0.954551i	−0.999011	+	0.0444600i	$0.985843\pi$
$62$	−25064.0	−	3019.84i	−0.828076	−	0.0997709i
$63$			91926.6i			2.91803i
$64$	24647.2	+	21593.0i	0.752173	+	0.658966i
$65$	−15060.2	−	20818.0i	−0.442127	−	0.611160i
$66$	10826.9	−	89861.1i	0.305947	−	2.53929i
$67$	−11643.0	+	11643.0i	−0.316869	+	0.316869i	−0.847563	−	0.530694i	$-0.821931\pi$
$67$	−11643.0	+	11643.0i	−0.316869	+	0.316869i	0.530694	+	0.847563i	$0.321931\pi$
$68$	−86.0195	+	351.789i	−0.00225593	+	0.00922593i
$69$	11758.8	−	11758.8i	0.297331	−	0.297331i
$70$	17976.4	−	62743.4i	0.438489	−	1.53046i
$71$		−	73970.7i		−	1.74146i	−0.491761	−	0.870730i	$-0.663647\pi$
$71$		−	73970.7i		−	1.74146i	0.491761	−	0.870730i	$-0.336353\pi$
$72$	−28380.9	+	75464.1i	−0.645201	+	1.71557i
$73$	−43814.9			−0.962310			−0.481155	−	0.876635i	$-0.659783\pi$
$73$	−43814.9			−0.962310			−0.481155	+	0.876635i	$0.659783\pi$
$74$	−8071.03	−	10282.3i	−0.171336	−	0.218279i
$75$	−73206.4	+	36924.1i	−1.50278	+	0.757978i
$76$	14865.3	+	24488.0i	0.295217	+	0.486317i
$77$	89000.6	−	89000.6i	1.71067	−	1.71067i
$78$	−8160.35	+	67729.0i	−0.151870	+	1.26049i
$79$	4592.73			0.0827948			0.0413974	−	0.999143i	$-0.486819\pi$
$79$	4592.73			0.0827948			0.0413974	+	0.999143i	$0.486819\pi$
$80$	34128.2	−	45957.2i	0.596196	−	0.802839i
$81$	−31094.3			−0.526585
$82$	1417.88	−	11768.1i	0.0232865	−	0.193273i
$83$	−24957.5	+	24957.5i	−0.397654	+	0.397654i	−0.877405	−	0.479751i	$-0.840727\pi$
$83$	−24957.5	+	24957.5i	−0.397654	+	0.397654i	0.479751	+	0.877405i	$0.340727\pi$
$84$	−148130.	+	89921.8i	−2.29058	+	1.39049i
$85$	624.663	+	100.247i	0.00937775	+	0.00150496i
$86$	17377.1	+	22138.0i	0.253355	+	0.322770i
$87$	−215437.			−3.05156
$88$	100540.	−	45584.5i	1.38398	−	0.627496i
$89$		−	127683.i		−	1.70867i	−0.519719	−	0.854337i	$-0.673963\pi$
$89$		−	127683.i		−	1.70867i	0.519719	−	0.854337i	$-0.326037\pi$
$90$	135398.	+	38792.4i	1.76199	+	0.504824i
$91$	−67080.5	+	67080.5i	−0.849166	+	0.849166i
$92$	19701.5	+	4817.42i	0.242678	+	0.0593397i
$93$	82795.5	−	82795.5i	0.992658	−	0.992658i
$94$	−5565.96	+	46196.2i	−0.0649711	+	0.539246i
$95$	40546.5	−	29332.2i	0.460940	−	0.333454i
$96$	−149365.	+	28085.4i	−1.65413	+	0.311030i
$97$			176164.i			1.90102i	0.310693	+	0.950510i	$0.399439\pi$
$97$			176164.i			1.90102i	−0.310693	+	0.950510i	$0.600561\pi$
$98$	−144854.	−	17452.7i	−1.52358	−	0.183568i
$99$	192059.	+	192059.i	1.96946	+	1.96946i
$100$	−84828.1	−	52954.6i	−0.848281	−	0.529546i
$101$	39702.8	−	39702.8i	0.387273	−	0.387273i	−0.486440	−	0.873714i	$-0.661705\pi$
$101$	39702.8	−	39702.8i	0.387273	−	0.387273i	0.873714	+	0.486440i	$0.161705\pi$
$102$	−1037.13	−	1321.29i	−0.00987037	−	0.0125747i
$103$	189748.			1.76231			0.881157	−	0.472824i	$-0.156765\pi$
$103$	189748.			1.76231			0.881157	+	0.472824i	$0.156765\pi$
$104$	−75777.6	+	34357.4i	−0.687001	+	0.311485i
$105$	177433.	+	245270.i	1.57059	+	2.17105i
$106$	71168.8	+	90667.7i	0.615212	+	0.783768i
$107$	48791.8	+	48791.8i	0.411991	+	0.411991i	0.882432	−	0.470441i	$-0.155905\pi$
$107$	48791.8	+	48791.8i	0.411991	+	0.411991i	−0.470441	+	0.882432i	$0.655905\pi$
$108$	−88177.5	−	145257.i	−0.727442	−	1.19833i
$109$	33432.1	+	33432.1i	0.269524	+	0.269524i	0.828908	−	0.559384i	$-0.188962\pi$
$109$	33432.1	+	33432.1i	0.269524	+	0.269524i	−0.559384	+	0.828908i	$0.688962\pi$
$110$	−93530.3	−	168646.i	−0.737005	−	1.32890i
$111$	60628.0			0.467052
$112$	−187501.	−	97526.8i	−1.41240	−	0.734647i
$113$		−	204550.i		−	1.50697i	−0.657467	−	0.753483i	$-0.728372\pi$
$113$		−	204550.i		−	1.50697i	0.657467	−	0.753483i	$-0.271628\pi$
$114$	−131914.	−	15893.6i	−0.950665	−	0.114541i
$115$	5614.23	−	34983.5i	0.0395863	−	0.246671i
$116$	−136349.	−	224610.i	−0.940818	−	1.54983i
$117$	−144757.	−	144757.i	−0.977629	−	0.977629i
$118$	−37902.9	+	29751.6i	−0.250592	+	0.196700i
$119$		−	2335.83i		−	0.0151208i
$120$	69934.8	+	256126.i	0.443344	+	1.62368i
$121$		−	210841.i		−	1.30916i
$122$	137029.	+	174572.i	0.833514	+	1.06188i
$123$	38874.3	+	38874.3i	0.231686	+	0.231686i
$124$	138722.	+	33920.2i	0.810196	+	0.198109i
$125$	−80262.6	+	155163.i	−0.459450	+	0.888204i
$126$	62204.3	−	516281.i	0.349055	−	2.89708i
$127$		−	177859.i		−	0.978513i	−0.872140	−	0.489257i	$-0.837268\pi$
$127$		−	177859.i		−	0.978513i	0.872140	−	0.489257i	$-0.162732\pi$
$128$	−123813.	−	137949.i	−0.667946	−	0.744209i
$129$	−130533.			−0.690631
$130$	70494.6	+	127110.i	0.365845	+	0.659659i
$131$	156919.	+	156919.i	0.798909	+	0.798909i	0.982924	−	0.184014i	$-0.0589093\pi$
$131$	156919.	+	156919.i	0.798909	+	0.798909i	−0.184014	+	0.982924i	$0.558909\pi$
$132$	−121613.	+	497355.i	−0.607500	+	2.48446i
$133$	−130650.	−	130650.i	−0.640445	−	0.640445i
$134$	73268.6	−	57511.5i	0.352497	−	0.276690i
$135$	−240512.	+	173991.i	−1.13580	+	0.821663i
$136$	721.152	−	1917.52i	0.00334333	−	0.00888983i
$137$	243007.			1.10616			0.553079	−	0.833129i	$-0.313453\pi$
$137$	243007.			1.10616			0.553079	+	0.833129i	$0.313453\pi$
$138$	−73997.1	+	58083.3i	−0.330763	+	0.259629i
$139$	156573.	−	156573.i	0.687352	−	0.687352i	−0.274294	−	0.961646i	$-0.588444\pi$
$139$	156573.	−	156573.i	0.687352	−	0.687352i	0.961646	+	0.274294i	$0.0884440\pi$
$140$	−143417.	+	340218.i	−0.618415	+	1.46702i
$141$	−152603.	−	152603.i	−0.646421	−	0.646421i
$142$	−50054.0	+	415437.i	−0.208314	+	1.72896i
$143$			280298.i			1.14625i
$144$	210458.	−	404619.i	0.845785	−	1.62607i
$145$	−371903.	+	269043.i	−1.46896	+	1.06268i
$146$	246075.	+	29648.4i	0.955401	+	0.115112i
$147$	478505.	−	478505.i	1.82639	−	1.82639i
$148$	38371.0	+	63209.5i	0.143996	+	0.237207i
$149$	−44779.2	+	44779.2i	−0.165238	+	0.165238i	−0.784883	−	0.619644i	$-0.787277\pi$
$149$	−44779.2	+	44779.2i	−0.165238	+	0.165238i	0.619644	+	0.784883i	$0.287277\pi$
$150$	436130.	−	157837.i	1.58266	−	0.572772i
$151$			111293.i			0.397216i	0.980079	+	0.198608i	$0.0636421\pi$
$151$			111293.i			0.397216i	−0.980079	+	0.198608i	$0.936358\pi$
$152$	−66916.9	−	147589.i	−0.234924	−	0.518139i
$153$	5040.62			0.0174083
$154$	−560073.	+	439624.i	−1.90302	+	1.49376i
$155$	39530.6	−	246324.i	0.132161	−	0.823528i
$156$	91660.9	−	374860.i	0.301559	−	1.23327i
$157$	71652.6	−	71652.6i	0.231997	−	0.231997i	−0.581529	−	0.813526i	$-0.697545\pi$
$157$	71652.6	−	71652.6i	0.231997	−	0.231997i	0.813526	+	0.581529i	$0.197545\pi$
$158$	−25793.8	−	3107.78i	−0.0822003	−	0.00990392i
$159$	−534606.			−1.67703
$160$	−222770.	+	235013.i	−0.687950	+	0.725758i
$161$	−130816.			−0.397736
$162$	174633.	+	21040.7i	0.522804	+	0.0629902i
$163$	182118.	−	182118.i	0.536887	−	0.536887i	−0.385726	−	0.922613i	$-0.626049\pi$
$163$	182118.	−	182118.i	0.536887	−	0.536887i	0.922613	+	0.385726i	$0.126049\pi$
$164$	−15926.3	+	65132.8i	−0.0462386	+	0.189099i
$165$	883140.	+	141728.i	2.52534	+	0.405272i
$166$	157055.	−	123279.i	0.442367	−	0.347232i
$167$	−154635.			−0.429058			−0.214529	−	0.976718i	$-0.568822\pi$
$167$	−154635.			−0.429058			−0.214529	+	0.976718i	$0.568822\pi$
$168$	892783.	−	404786.i	2.44046	−	1.10650i
$169$			160030.i			0.431007i
$170$	−3440.42	−	985.705i	−0.00913039	−	0.00261592i
$171$	281938.	−	281938.i	0.737332	−	0.737332i
$172$	−82613.4	−	136091.i	−0.212926	−	0.350759i
$173$	−244108.	+	244108.i	−0.620107	+	0.620107i	−0.945559	−	0.325452i	$-0.894484\pi$
$173$	−244108.	+	244108.i	−0.620107	+	0.620107i	0.325452	+	0.945559i	$0.394484\pi$
$174$	1.20995e6	+	145781.i	3.02965	+	0.365028i
$175$	612596.	+	201819.i	1.51210	+	0.498158i
$176$	−595500.	+	187981.i	−1.44911	+	0.457438i
$177$		−	223488.i		−	0.536193i
$178$	−86399.9	+	717100.i	−0.204392	+	1.69641i
$179$	−242500.	−	242500.i	−0.565690	−	0.565690i	0.365228	−	0.930918i	$-0.380991\pi$
$179$	−242500.	−	242500.i	−0.565690	−	0.565690i	−0.930918	+	0.365228i	$0.880991\pi$
$180$	−734175.	−	309487.i	−1.68896	−	0.711969i
$181$	315882.	−	315882.i	0.716684	−	0.716684i	−0.251240	−	0.967925i	$-0.580838\pi$
$181$	315882.	−	315882.i	0.716684	−	0.716684i	0.967925	+	0.251240i	$0.0808385\pi$
$182$	422131.	−	331348.i	0.944646	−	0.741492i
$183$	−1.02933e6			−2.27211
$184$	−107389.	−	40387.3i	−0.233837	−	0.0879428i
$185$	104660.	−	75713.6i	0.224829	−	0.162646i
$186$	−521025.	+	408974.i	−1.10427	+	0.866788i
$187$	−4880.18	−	4880.18i	−0.0102055	−	0.0102055i
$188$	62519.5	−	255682.i	0.129009	−	0.527602i
$189$	774986.	+	774986.i	1.57812	+	1.57812i
$190$	−247567.	+	137300.i	−0.497518	+	0.275922i
$191$	−673272.			−1.33539			−0.667693	−	0.744436i	$-0.732718\pi$
$191$	−673272.			−1.33539			−0.667693	+	0.744436i	$0.732718\pi$
$192$	857872.	−	56663.1i	1.67946	−	0.110930i
$193$			170490.i			0.329462i	0.986338	+	0.164731i	$0.0526757\pi$
$193$			170490.i			0.329462i	−0.986338	+	0.164731i	$0.947324\pi$
$194$	119205.	−	989376.i	0.227400	−	1.88737i
$195$	−665630.	−	106822.i	−1.25356	−	0.201174i
$196$	801722.	+	196037.i	1.49068	+	0.364500i
$197$	−210873.	−	210873.i	−0.387129	−	0.387129i	0.486533	−	0.873662i	$-0.338261\pi$
$197$	−210873.	−	210873.i	−0.387129	−	0.387129i	−0.873662	+	0.486533i	$0.838261\pi$
$198$	−948689.	−	1.20861e6i	−1.71973	−	2.19091i
$199$			248390.i			0.444633i	0.974975	+	0.222317i	$0.0713619\pi$
$199$			248390.i			0.444633i	−0.974975	+	0.222317i	$0.928638\pi$
$200$	440582.	+	354806.i	0.778846	+	0.627215i
$201$			432015.i			0.754239i
$202$	−249846.	+	196114.i	−0.430818	+	0.338167i
$203$	1.19836e6	+	1.19836e6i	2.04102	+	2.04102i
$204$	4930.70	+	8122.45i	0.00829531	+	0.0136651i
$205$	115655.	+	18560.5i	0.192211	+	0.0308464i
$206$	−1.06567e6	−	128397.i	−1.74966	−	0.210808i
$207$		−	282294.i		−	0.457906i
$208$	448833.	−	141683.i	0.719328	−	0.227070i
$209$	−545928.			−0.864509
$210$	−830540.	−	1.49756e6i	−1.29961	−	2.34334i
$211$	255913.	+	255913.i	0.395718	+	0.395718i	0.876720	−	0.481001i	$-0.159727\pi$
$211$	255913.	+	255913.i	0.395718	+	0.395718i	−0.481001	+	0.876720i	$0.659727\pi$
$212$	−338348.	−	557369.i	−0.517040	−	0.851733i
$213$	−1.37234e6	−	1.37234e6i	−2.07259	−	2.07259i
$214$	−241010.	−	307043.i	−0.359750	−	0.458315i
$215$	−225335.	+	163013.i	−0.332455	+	0.240505i
$216$	396934.	+	875464.i	0.578874	+	1.27674i
$217$	−921093.			−1.32787
$218$	−165140.	−	210385.i	−0.235348	−	0.299829i
$219$	−812877.	+	812877.i	−1.14529	+	1.14529i
$220$	411170.	+	1.01044e6i	0.572750	+	1.40752i
$221$	3678.23	+	3678.23i	0.00506592	+	0.00506592i
$222$	−340501.	−	41025.3i	−0.463699	−	0.0558688i
$223$			1.06376e6i			1.43246i	0.697866	+	0.716229i	$0.254133\pi$
$223$			1.06376e6i			1.43246i	−0.697866	+	0.716229i	$0.745867\pi$
$224$	987058.	+	674611.i	1.31438	+	0.898324i
$225$	−435517.	+	1.32196e6i	−0.573520	+	1.74085i
$226$	−138414.	+	1.14880e6i	−0.180263	+	1.49615i
$227$	232844.	−	232844.i	0.299917	−	0.299917i	−0.541064	−	0.840981i	$-0.681978\pi$
$227$	232844.	−	232844.i	0.299917	−	0.299917i	0.840981	+	0.541064i	$0.181978\pi$
$228$	730103.	+	178525.i	0.930138	+	0.227437i
$229$	261751.	−	261751.i	0.329837	−	0.329837i	−0.522687	−	0.852525i	$-0.675070\pi$
$229$	261751.	−	261751.i	0.329837	−	0.329837i	0.852525	+	0.522687i	$0.175070\pi$
$230$	−55203.2	+	192677.i	−0.0688090	+	0.240165i
$231$		−	3.30237e6i		−	4.07189i
$232$	613778.	+	1.35373e6i	0.748672	+	1.65124i
$233$	719528.			0.868276			0.434138	−	0.900846i	$-0.357053\pi$
$233$	719528.			0.868276			0.434138	+	0.900846i	$0.357053\pi$
$234$	715035.	+	910941.i	0.853665	+	1.08755i
$235$	−454009.	−	72860.2i	−0.536284	−	0.0860639i
$236$	233004.	−	141444.i	0.272322	−	0.165312i
$237$	85206.6	−	85206.6i	0.0985377	−	0.0985377i
$238$	−1580.60	+	13118.6i	−0.00180875	+	0.0150122i
$239$	−1.47462e6			−1.66988			−0.834941	−	0.550339i	$-0.814498\pi$
$239$	−1.47462e6			−1.66988			−0.834941	+	0.550339i	$0.814498\pi$
$240$	−219457.	−	1.48579e6i	−0.245936	−	1.66505i
$241$	1.48713e6			1.64933			0.824664	−	0.565622i	$-0.191364\pi$
$241$	1.48713e6			1.64933			0.824664	+	0.565622i	$0.191364\pi$
$242$	−142671.	+	1.18414e6i	−0.156602	+	1.29976i
$243$	335555.	−	335555.i	0.364542	−	0.364542i
$244$	−651459.	−	1.07316e6i	−0.700507	−	1.15396i
$245$	228462.	−	1.42360e6i	0.243163	−	1.51521i
$246$	−192022.	−	244632.i	−0.202308	−	0.257737i
$247$	411470.			0.429137
$248$	−756141.	−	284373.i	−0.780681	−	0.293602i
$249$			926048.i			0.946532i
$250$	555768.	−	817119.i	0.562398	−	0.826867i
$251$	−537301.	+	537301.i	−0.538311	+	0.538311i	−0.923033	−	0.384722i	$-0.874297\pi$
$251$	−537301.	+	537301.i	−0.538311	+	0.538311i	0.384722	+	0.923033i	$0.374297\pi$
$252$	−698708.	+	2.85747e6i	−0.693097	+	2.83452i
$253$	−273309.	+	273309.i	−0.268443	+	0.268443i
$254$	−120353.	+	998899.i	−0.117050	+	0.971487i
$255$	13448.9	−	9729.23i	0.0129520	−	0.00936975i
$256$	602017.	+	858538.i	0.574128	+	0.818766i
$257$		−	128023.i		−	0.120908i	−0.998171	−	0.0604542i	$-0.980745\pi$
$257$		−	128023.i		−	0.120908i	0.998171	−	0.0604542i	$-0.0192549\pi$
$258$	733104.	+	88328.2i	0.685672	+	0.0826133i
$259$	−337240.	−	337240.i	−0.312385	−	0.312385i
$260$	−309903.	−	761579.i	−0.284310	−	0.698685i
$261$	−2.58601e6	+	2.58601e6i	−2.34979	+	2.34979i
$262$	−775111.	−	987477.i	−0.697607	−	0.888738i
$263$	1.59175e6			1.41901			0.709506	−	0.704700i	$-0.248918\pi$
$263$	1.59175e6			1.41901			0.709506	+	0.704700i	$0.248918\pi$
$264$	1.01956e6	−	2.71097e6i	0.900329	−	2.39395i
$265$	−922875.	+	667628.i	−0.807287	+	0.584009i
$266$	645356.	+	822172.i	0.559236	+	0.712457i
$267$	−2.36885e6	−	2.36885e6i	−2.03357	−	2.03357i
$268$	−450410.	+	273419.i	−0.383064	+	0.232537i
$269$	−517091.	−	517091.i	−0.435699	−	0.435699i	0.454863	−	0.890562i	$-0.349688\pi$
$269$	−517091.	−	517091.i	−0.435699	−	0.435699i	−0.890562	+	0.454863i	$0.849688\pi$
$270$	1.46851e6	−	814429.i	1.22593	−	0.679898i
$271$	23212.2			0.0191996			0.00959981	−	0.999954i	$-0.496944\pi$
$271$	23212.2			0.0191996			0.00959981	+	0.999954i	$0.496944\pi$
$272$	−5347.70	+	10281.3i	−0.00438273	+	0.00842607i
$273$			2.48902e6i			2.02126i
$274$	−1.36478e6	−	164436.i	−1.09822	−	0.132319i
$275$	1.70153e6	−	858224.i	1.35678	−	0.684335i
$276$	454888.	−	276138.i	0.359445	−	0.218199i
$277$	−372295.	−	372295.i	−0.291533	−	0.291533i	0.546153	−	0.837686i	$-0.316092\pi$
$277$	−372295.	−	372295.i	−0.291533	−	0.291533i	−0.837686	+	0.546153i	$0.816092\pi$
$278$	−985299.	+	773402.i	−0.764638	+	0.600196i
$279$		−	1.98768e6i		−	1.52875i
$280$	1.03568e6	−	1.81370e6i	0.789460	−	1.38251i
$281$		−	568423.i		−	0.429443i	−0.976675	−	0.214722i	$-0.931116\pi$
$281$		−	568423.i		−	0.429443i	0.976675	−	0.214722i	$-0.0688844\pi$
$282$	753793.	+	960318.i	0.564455	+	0.719105i
$283$	−260140.	−	260140.i	−0.193082	−	0.193082i	0.603944	−	0.797026i	$-0.293595\pi$
$283$	−260140.	−	260140.i	−0.193082	−	0.193082i	−0.797026	+	0.603944i	$0.793595\pi$
$284$	562230.	−	2.29932e6i	0.413636	−	1.69162i
$285$	208053.	−	1.29643e6i	0.151727	−	0.945443i
$286$	189670.	−	1.57422e6i	0.137115	−	1.13802i
$287$		−	432473.i		−	0.309923i
$288$	−1.45578e6	+	2.13003e6i	−1.03422	+	1.51323i
$289$	1.41973e6			0.999910
$290$	2.27075e6	−	1.25935e6i	1.58553	−	0.879329i
$291$	3.26828e6	+	3.26828e6i	2.26249	+	2.26249i
$292$	−1.36195e6	−	333025.i	−0.934771	−	0.228570i
$293$	1.56562e6	+	1.56562e6i	1.06541	+	1.06541i	0.997705	+	0.0677046i	$0.0215675\pi$
$293$	1.56562e6	+	1.56562e6i	1.06541	+	1.06541i	0.0677046	+	0.997705i	$0.478432\pi$
$294$	−3.01119e6	+	2.36361e6i	−2.03175	+	1.59480i
$295$	−279097.	−	385801.i	−0.186724	−	0.258112i
$296$	−172729.	−	380964.i	−0.114587	−	0.252729i
$297$	3.23831e6			2.13023
$298$	281791.	−	221189.i	0.183817	−	0.144286i
$299$	205995.	−	205995.i	0.133254	−	0.133254i
$300$	−2.55622e6	+	591335.i	−1.63981	+	0.379342i
$301$	726084.	+	726084.i	0.461924	+	0.461924i
$302$	75309.3	−	625050.i	0.0475150	−	0.394364i
$303$		−	1.47317e6i		−	0.921822i
$304$	275951.	+	874178.i	0.171257	+	0.542520i
$305$	−1.77691e6	+	1.28546e6i	−1.09374	+	0.791239i
$306$	−28309.3	−	3410.86i	−0.0172833	−	0.00208238i
$307$	367810.	−	367810.i	0.222729	−	0.222729i	−0.586917	−	0.809647i	$-0.699659\pi$
$307$	367810.	−	367810.i	0.222729	−	0.222729i	0.809647	+	0.586917i	$0.199659\pi$
$308$	3.44298e6	−	2.09005e6i	2.06804	−	1.25539i
$309$	3.52029e6	−	3.52029e6i	2.09741	−	2.09741i
$310$	−388695.	+	1.35667e6i	−0.229723	+	0.801805i
$311$			1.21854e6i			0.714395i	0.934029	+	0.357198i	$0.116268\pi$
$311$			1.21854e6i			0.714395i	−0.934029	+	0.357198i	$0.883732\pi$
$312$	−768447.	+	2.04328e6i	−0.446918	+	1.18834i
$313$	−1.84640e6			−1.06529			−0.532643	−	0.846340i	$-0.678801\pi$
$313$	−1.84640e6			−1.06529			−0.532643	+	0.846340i	$0.678801\pi$
$314$	−450903.	+	353932.i	−0.258083	+	0.202580i
$315$	5.07393e6	+	814274.i	2.88116	+	0.462375i
$316$	142761.	+	34908.0i	0.0804254	+	0.0196656i
$317$	195597.	−	195597.i	0.109323	−	0.109323i	−0.650329	−	0.759653i	$-0.725369\pi$
$317$	195597.	−	195597.i	0.109323	−	0.109323i	0.759653	+	0.650329i	$0.225369\pi$
$318$	3.00247e6	+	361753.i	1.66499	+	0.200606i
$319$	5.00739e6			2.75508
$320$	1.41016e6	−	1.16915e6i	0.769826	−	0.638254i
$321$	1.81042e6			0.980657
$322$	734691.	+	88519.4i	0.394880	+	0.0475772i
$323$	−7163.98	+	7163.98i	−0.00382074	+	0.00382074i
$324$	−966544.	−	236339.i	−0.511516	−	0.125076i
$325$	−1.28246e6	+	646850.i	−0.673496	+	0.339700i
$326$	−1.14605e6	+	899582.i	−0.597255	+	0.468810i
$327$	1.24050e6			0.641545
$328$	133519.	−	355024.i	0.0685267	−	0.182211i
$329$			1.69770e6i			0.864710i
$330$	−4.86402e6	−	1.39358e6i	−2.45873	−	0.704443i
$331$	−2.55769e6	+	2.55769e6i	−1.28315	+	1.28315i	−0.344284	+	0.938865i	$0.611878\pi$
$331$	−2.55769e6	+	2.55769e6i	−1.28315	+	1.28315i	−0.938865	+	0.344284i	$0.888122\pi$
$332$	−965479.	+	586090.i	−0.480726	+	0.291823i
$333$	727750.	−	727750.i	0.359643	−	0.359643i
$334$	868465.	+	104637.i	0.425977	+	0.0513239i
$335$	539510.	+	745775.i	0.262656	+	0.363075i
$336$	−5.28799e6	+	1.66925e6i	−2.55530	+	0.806630i
$337$		−	2.31360e6i		−	1.10972i	−0.831943	−	0.554861i	$-0.812772\pi$
$337$		−	2.31360e6i		−	1.10972i	0.831943	−	0.554861i	$-0.187228\pi$
$338$	108288.	−	898765.i	0.0515571	−	0.427912i
$339$	−3.79492e6	−	3.79492e6i	−1.79351	−	1.79351i
$340$	18655.2	+	7863.99i	0.00875191	+	0.00368932i
$341$	−1.92441e6	+	1.92441e6i	−0.896214	+	0.896214i
$342$	−1.77421e6	+	1.39265e6i	−0.820238	+	0.643838i
$343$	−1.85444e6			−0.851096
$344$	371887.	+	820222.i	0.169440	+	0.373710i
$345$	−544874.	−	753190.i	−0.246461	−	0.340688i
$346$	1.53615e6	−	1.20579e6i	0.689832	−	0.541477i
$347$	1.32216e6	+	1.32216e6i	0.589468	+	0.589468i	0.937487	−	0.348019i	$-0.113146\pi$
$347$	1.32216e6	+	1.32216e6i	0.589468	+	0.589468i	−0.348019	+	0.937487i	$0.613146\pi$
$348$	−6.69669e6	−	1.63748e6i	−2.96423	−	0.724814i
$349$	−51911.1	−	51911.1i	−0.0228137	−	0.0228137i	0.695608	−	0.718422i	$-0.255135\pi$
$349$	−51911.1	−	51911.1i	−0.0228137	−	0.0228137i	−0.718422	+	0.695608i	$0.755135\pi$
$350$	−3.30392e6	−	1.54799e6i	−1.44165	−	0.675458i
$351$	−2.44074e6			−1.05743
$352$	3.47167e6	−	652787.i	1.49342	−	0.280811i
$353$		−	1.20346e6i		−	0.514037i	−0.966407	−	0.257018i	$-0.917260\pi$
$353$		−	1.20346e6i		−	0.514037i	0.966407	−	0.257018i	$-0.0827401\pi$
$354$	−151228.	+	1.25516e6i	−0.0641394	+	0.532343i
$355$	−4.08284e6	−	655223.i	−1.71946	−	0.275942i
$356$	970485.	−	3.96894e6i	0.405848	−	1.65978i
$357$	−43335.6	−	43335.6i	−0.0179959	−	0.0179959i
$358$	1.19784e6	+	1.52603e6i	0.493961	+	0.629296i
$359$			4.58387e6i			1.87714i	0.345090	+	0.938570i	$0.387848\pi$
$359$			4.58387e6i			1.87714i	−0.345090	+	0.938570i	$0.612152\pi$
$360$	3.91388e6	+	2.23495e6i	1.59166	+	0.908890i
$361$		−	1.67469e6i		−	0.676343i
$362$	−1.98781e6	+	1.56032e6i	−0.797268	+	0.625809i
$363$	−3.91164e6	−	3.91164e6i	−1.55809	−	1.55809i
$364$	−2.59500e6	+	1.57529e6i	−1.02656	+	0.623169i
$365$	−388107.	+	2.41839e6i	−0.152482	+	0.950153i
$366$	5.78099e6	+	696523.i	2.25579	+	0.271790i
$367$		−	1.87893e6i		−	0.728190i	−0.931362	−	0.364095i	$-0.881378\pi$
$367$		−	1.87893e6i		−	0.728190i	0.931362	−	0.364095i	$-0.118622\pi$
$368$	575792.	+	299492.i	0.221639	+	0.115283i
$369$	933257.			0.356809
$370$	−639031.	+	354404.i	−0.242671	+	0.134584i
$371$	2.97372e6	+	2.97372e6i	1.12167	+	1.12167i
$372$	3.20294e6	−	1.94433e6i	1.20003	−	0.728471i
$373$	774892.	+	774892.i	0.288383	+	0.288383i	0.836440	−	0.548058i	$-0.184633\pi$
$373$	774892.	+	774892.i	0.288383	+	0.288383i	−0.548058	+	0.836440i	$0.684633\pi$
$374$	24106.0	+	30710.6i	0.00891140	+	0.0113529i
$375$	1.38959e6	+	4.36773e6i	0.510279	+	1.60390i
$376$	−524138.	+	1.39367e6i	−0.191195	+	0.508381i
$377$	−3.77411e6			−1.36761
$378$	−3.82809e6	−	4.87692e6i	−1.37801	−	1.75556i
$379$	−66164.9	+	66164.9i	−0.0236608	+	0.0236608i	−0.718838	−	0.695177i	$-0.755326\pi$
$379$	−66164.9	+	66164.9i	−0.0236608	+	0.0236608i	0.695177	+	0.718838i	$0.255326\pi$
$380$	1.48330e6	−	603587.i	0.526952	−	0.214428i
$381$	−3.29973e6	−	3.29973e6i	−1.16457	−	1.16457i
$382$	3.78125e6	+	455585.i	1.32580	+	0.159739i
$383$			2.35966e6i			0.821964i	0.911643	+	0.410982i	$0.134814\pi$
$383$			2.35966e6i			0.821964i	−0.911643	+	0.410982i	$0.865186\pi$
$384$	−4.85635e6	−	262266.i	−1.68067	−	0.0907639i
$385$	−4.12407e6	−	5.70079e6i	−1.41799	−	1.96012i
$386$	115366.	−	957513.i	0.0394103	−	0.327097i
$387$	−1.56686e6	+	1.56686e6i	−0.531804	+	0.531804i
$388$	−1.33897e6	+	5.47591e6i	−0.451535	+	1.84662i
$389$	1.54044e6	−	1.54044e6i	0.516144	−	0.516144i	−0.400259	−	0.916402i	$-0.631080\pi$
$389$	1.54044e6	−	1.54044e6i	0.516144	−	0.516144i	0.916402	+	0.400259i	$0.131080\pi$
$390$	3.66605e6	+	1.05035e6i	1.22050	+	0.349681i
$391$			7173.03i			0.00237280i
$392$	−4.37001e6	−	1.64349e6i	−1.43637	−	0.540198i
$393$	5.82248e6			1.90163
$394$	1.04162e6	+	1.32700e6i	0.338041	+	0.430657i
$395$	40681.8	−	253498.i	0.0131192	−	0.0817488i
$396$	4.51023e6	+	7.42980e6i	1.44531	+	2.38089i
$397$	2.77633e6	−	2.77633e6i	0.884086	−	0.884086i	−0.109861	−	0.993947i	$-0.535040\pi$
$397$	2.77633e6	−	2.77633e6i	0.884086	−	0.884086i	0.993947	+	0.109861i	$0.0350405\pi$
$398$	168079.	−	1.39502e6i	0.0531871	−	0.441441i
$399$	−4.84779e6			−1.52444
$400$	−2.23432e6	−	2.29081e6i	−0.698226	−	0.715877i
$401$	−177492.			−0.0551212			−0.0275606	−	0.999620i	$-0.508774\pi$
$401$	−177492.			−0.0551212			−0.0275606	+	0.999620i	$0.508774\pi$
$402$	292333.	−	2.42630e6i	0.0902221	−	0.748823i
$403$	1.45044e6	−	1.45044e6i	0.444875	−	0.444875i
$404$	1.53590e6	−	932361.i	0.468176	−	0.284204i
$405$	−275430.	+	1.71627e6i	−0.0834398	+	0.519933i
$406$	−5.91937e6	−	7.54117e6i	−1.78222	−	2.27051i
$407$	−1.40917e6			−0.421675
$408$	−22195.7	−	48954.1i	−0.00660114	−	0.0145592i
$409$			1.07032e6i			0.316377i	0.987409	+	0.158189i	$0.0505654\pi$
$409$			1.07032e6i			0.316377i	−0.987409	+	0.158189i	$0.949435\pi$
$410$	−636984.	−	182500.i	−0.187141	−	0.0536172i
$411$	4.50839e6	−	4.50839e6i	1.31649	−	1.31649i
$412$	5.89816e6	+	1.44222e6i	1.71188	+	0.418589i
$413$	−1.24314e6	+	1.24314e6i	−0.358629	+	0.358629i
$414$	−191021.	+	1.58543e6i	−0.0547747	+	0.454618i
$415$	1.15647e6	+	1.59861e6i	0.329620	+	0.455641i
$416$	−2.61663e6	+	492011.i	−0.741325	+	0.139393i
$417$		−	5.80964e6i		−	1.63610i
$418$	3.06606e6	+	369415.i	0.858302	+	0.103413i
$419$	−3.73689e6	−	3.73689e6i	−1.03986	−	1.03986i	−0.999172	−	0.0406886i	$-0.987045\pi$
$419$	−3.73689e6	−	3.73689e6i	−1.03986	−	1.03986i	−0.0406886	−	0.999172i	$-0.512955\pi$
$420$	3.65115e6	+	8.97264e6i	1.00997	+	2.48197i
$421$	−2.62619e6	+	2.62619e6i	−0.722138	+	0.722138i	−0.969040	−	0.246902i	$-0.920587\pi$
$421$	−2.62619e6	+	2.62619e6i	−0.722138	+	0.722138i	0.246902	+	0.969040i	$0.420587\pi$
$422$	−1.26410e6	−	1.61044e6i	−0.345541	−	0.440213i
$423$	−3.66355e6			−0.995524
$424$	1.52309e6	+	3.35927e6i	0.411443	+	0.907465i
$425$	11066.4	−	33590.6i	0.00297189	−	0.00902080i
$426$	6.77877e6	+	8.63602e6i	1.80978	+	2.30563i
$427$	5.72563e6	+	5.72563e6i	1.51968	+	1.51968i
$428$	1.14580e6	+	1.88751e6i	0.302344	+	0.498058i
$429$	5.20024e6	+	5.20024e6i	1.36421	+	1.36421i
$430$	1.37584e6	−	763038.i	0.358837	−	0.199010i
$431$	721640.			0.187123			0.0935615	−	0.995613i	$-0.470175\pi$
$431$	721640.			0.187123			0.0935615	+	0.995613i	$0.470175\pi$
$432$	−1.63687e6	−	5.18541e6i	−0.421993	−	1.33682i
$433$			2.32124e6i			0.594977i	0.954725	+	0.297489i	$0.0961491\pi$
$433$			2.32124e6i			0.594977i	−0.954725	+	0.297489i	$0.903851\pi$
$434$	5.17308e6	+	623279.i	1.31833	+	0.158839i
$435$	−1.90832e6	+	1.18911e7i	−0.483534	+	3.01301i
$436$	785103.	+	1.29332e6i	0.197793	+	0.325829i
$437$	401210.	+	401210.i	0.100501	+	0.100501i
$438$	5.11536e6	−	4.01526e6i	1.27406	−	1.00006i
$439$		−	3093.44i		−	0.000766092i	−1.00000		0.000383046i	$-0.999878\pi$
$439$		−	3093.44i		−	0.000766092i	1.00000		0.000383046i	$-0.000121927\pi$
$440$	−1.62549e6	−	5.95311e6i	−0.400270	−	1.46593i
$441$		−	1.14875e7i		−	2.81274i
$442$	−18168.9	−	23146.8i	−0.00442356	−	0.00563554i
$443$	−2.88549e6	−	2.88549e6i	−0.698571	−	0.698571i	0.265531	−	0.964102i	$-0.414453\pi$
$443$	−2.88549e6	−	2.88549e6i	−0.698571	−	0.698571i	−0.964102	+	0.265531i	$0.914453\pi$
$444$	1.88457e6	+	460816.i	0.453686	+	0.110935i
$445$	−7.04754e6	−	1.13100e6i	−1.68709	−	0.270747i
$446$	719818.	−	5.97433e6i	0.171351	−	1.42217i
$447$			1.66153e6i			0.393314i
$448$	−5.08706e6	−	4.45669e6i	−1.19749	−	1.04910i
$449$	2.56587e6			0.600646			0.300323	−	0.953838i	$-0.402906\pi$
$449$	2.56587e6			0.600646			0.300323	+	0.953838i	$0.402906\pi$
$450$	3.34050e6	−	7.12971e6i	0.777642	−	1.65974i
$451$	−903552.	−	903552.i	−0.209176	−	0.209176i
$452$	1.55473e6	−	6.35828e6i	0.357938	−	1.46384i
$453$	2.06477e6	+	2.06477e6i	0.472745	+	0.472745i
$454$	−1.46527e6	+	1.15015e6i	−0.333639	+	0.261887i
$455$	3.10835e6	+	4.29673e6i	0.703884	+	0.972992i
$456$	−3.97963e6	−	1.49668e6i	−0.896253	−	0.337067i
$457$	−3.63334e6			−0.813796			−0.406898	−	0.913474i	$-0.633390\pi$
$457$	−3.63334e6			−0.813796			−0.406898	+	0.913474i	$0.633390\pi$
$458$	−1.64718e6	+	1.29294e6i	−0.366924	+	0.288014i
$459$	42494.9	−	42494.9i	0.00941468	−	0.00941468i
$460$	440414.	−	1.04476e6i	0.0970435	−	0.230210i
$461$	−1.29705e6	−	1.29705e6i	−0.284253	−	0.284253i	0.550550	−	0.834802i	$-0.314418\pi$
$461$	−1.29705e6	−	1.29705e6i	−0.284253	−	0.284253i	−0.834802	+	0.550550i	$0.814418\pi$
$462$	−2.23463e6	+	1.85469e7i	−0.487079	+	4.04265i
$463$			522295.i			0.113230i	0.998396	+	0.0566152i	$0.0180308\pi$
$463$			522295.i			0.113230i	−0.998396	+	0.0566152i	$0.981969\pi$
$464$	−2.53109e6	−	8.01818e6i	−0.545774	−	1.72894i
$465$	−3.83654e6	−	5.30333e6i	−0.822826	−	1.13741i
$466$	−4.04104e6	−	486885.i	−0.862042	−	0.103863i
$467$	−3.63598e6	+	3.63598e6i	−0.771487	+	0.771487i	−0.978367	−	0.206879i	$-0.933669\pi$
$467$	−3.63598e6	+	3.63598e6i	−0.771487	+	0.771487i	0.206879	+	0.978367i	$0.433669\pi$
$468$	−3.39940e6	−	5.59990e6i	−0.717442	−	1.18186i
$469$	2.40307e6	−	2.40307e6i	0.504468	−	0.504468i
$470$	2.50052e6	+	716416.i	0.522138	+	0.149596i
$471$		−	2.65867e6i		−	0.552220i
$472$	−1.40432e6	+	636715.i	−0.290142	+	0.131550i
$473$	3.03397e6			0.623532
$474$	−536198.	+	420884.i	−0.109617	+	0.0860431i
$475$	−1.25985e6	−	2.49780e6i	−0.256203	−	0.507954i
$476$	17754.0	−	72607.6i	0.00359152	−	0.0146881i
$477$	−6.41716e6	+	6.41716e6i	−1.29136	+	1.29136i
$478$	8.28182e6	+	997837.i	1.65789	+	0.199751i
$479$	−3.71225e6			−0.739263			−0.369631	−	0.929178i	$-0.620516\pi$
$479$	−3.71225e6			−0.739263			−0.369631	+	0.929178i	$0.620516\pi$
$480$	227132.	+	8.49302e6i	0.0449961	+	1.68252i
$481$	1.06210e6			0.209317
$482$	−8.35209e6	−	1.00630e6i	−1.63749	−	0.197293i
$483$	−2.42696e6	+	2.42696e6i	−0.473363	+	0.473363i
$484$	1.60255e6	−	6.55384e6i	0.310955	−	1.27169i
$485$	9.72343e6	+	1.56044e6i	1.87700	+	0.301225i
$486$	−2.11162e6	+	1.65749e6i	−0.405531	+	0.318318i
$487$	−1.40634e6			−0.268701			−0.134350	−	0.990934i	$-0.542895\pi$
$487$	−1.40634e6			−0.268701			−0.134350	+	0.990934i	$0.542895\pi$
$488$	2.93256e6	+	6.46796e6i	0.557440	+	1.22947i
$489$		−	6.75748e6i		−	1.27795i
$490$	−2.24641e6	+	7.84066e6i	−0.422667	+	1.47524i
$491$	−581671.	+	581671.i	−0.108886	+	0.108886i	−0.759451	−	0.650565i	$-0.774532\pi$
$491$	−581671.	+	581671.i	−0.108886	+	0.108886i	0.650565	+	0.759451i	$0.274532\pi$
$492$	912905.	+	1.50385e6i	0.170025	+	0.280086i
$493$	65709.8	−	65709.8i	0.0121762	−	0.0121762i
$494$	−2.31091e6	−	278431.i	−0.426056	−	0.0513334i
$495$	1.23020e7	−	8.89956e6i	2.25665	−	1.63251i
$496$	4.05424e6	+	2.10877e6i	0.739954	+	0.384879i
$497$			1.52672e7i			2.77248i
$498$	626632.	−	5.20091e6i	0.113224	−	0.939736i
$499$	−532938.	−	532938.i	−0.0958132	−	0.0958132i	0.657575	−	0.753389i	$-0.271582\pi$
$499$	−532938.	−	532938.i	−0.0958132	−	0.0958132i	−0.753389	+	0.657575i	$0.771582\pi$
$500$	−3.67425e6	+	4.21306e6i	−0.657270	+	0.753656i
$501$	−2.86886e6	+	2.86886e6i	−0.510640	+	0.510640i
$502$	3.38118e6	−	2.65403e6i	0.598838	−	0.470053i
$503$	2.67259e6			0.470991			0.235495	−	0.971875i	$-0.424329\pi$
$503$	2.67259e6			0.470991			0.235495	+	0.971875i	$0.424329\pi$
$504$	5.85768e6	−	1.55754e7i	1.02719	−	2.73126i
$505$	−1.83973e6	−	2.54310e6i	−0.321015	−	0.443746i
$506$	1.71991e6	−	1.35003e6i	0.298627	−	0.234405i
$507$	2.96896e6	+	2.96896e6i	0.512960	+	0.512960i
$508$	1.35186e6	−	5.52861e6i	0.232419	−	0.950510i
$509$	−1.75682e6	−	1.75682e6i	−0.300561	−	0.300561i	0.540673	−	0.841233i	$-0.318170\pi$
$509$	−1.75682e6	−	1.75682e6i	−0.300561	−	0.300561i	−0.841233	+	0.540673i	$0.818170\pi$
$510$	−82115.7	+	45541.1i	−0.0139798	+	0.00775316i
$511$	9.04319e6			1.53204
$512$	−2.80012e6	−	5.22912e6i	−0.472065	−	0.881564i
$513$		−	4.75375e6i		−	0.797522i
$514$	−86630.0	+	719009.i	−0.0144631	+	0.120040i
$515$	1.68076e6	−	1.04732e7i	0.279247	−	1.74005i
$516$	−4.05752e6	−	992144.i	−0.670867	−	0.164040i
$517$	3.54695e6	+	3.54695e6i	0.583617	+	0.583617i
$518$	1.66582e6	+	2.12222e6i	0.272775	+	0.347510i
$519$			9.05763e6i			1.47603i
$520$	1.22515e6	+	4.48691e6i	0.198692	+	0.727678i
$521$			1.19270e7i			1.92502i	0.271246	+	0.962510i	$0.412564\pi$
$521$			1.19270e7i			1.92502i	−0.271246	+	0.962510i	$0.587436\pi$
$522$	1.62735e7	−	1.27737e7i	2.61399	−	2.05183i
$523$	−2.80132e6	−	2.80132e6i	−0.447825	−	0.447825i	0.446806	−	0.894631i	$-0.352561\pi$
$523$	−2.80132e6	−	2.80132e6i	−0.447825	−	0.447825i	−0.894631	+	0.446806i	$0.852561\pi$
$524$	3.68501e6	+	6.07040e6i	0.586287	+	0.965805i
$525$	1.51094e7	−	7.62095e6i	2.39249	−	1.20673i
$526$	−8.93965e6	−	1.07710e6i	−1.40882	−	0.169742i
$527$			50506.4i			0.00792173i
$528$	−7.56051e6	+	1.45355e7i	−1.18023	+	2.26906i
$529$	−6.03463e6			−0.937586
$530$	5.63485e6	−	3.12507e6i	0.871350	−	0.483248i
$531$	−2.68264e6	−	2.68264e6i	−0.412883	−	0.412883i
$532$	−3.06813e6	−	5.05421e6i	−0.469997	−	0.774237i
$533$	681015.	+	681015.i	0.103834	+	0.103834i
$534$	1.17011e7	+	1.49069e7i	1.77571	+	2.26222i
$535$	3.12528e6	−	2.26090e6i	0.472068	−	0.341504i
$536$	2.71463e6	−	1.23081e6i	0.408130	−	0.185045i
$537$	−8.99796e6			−1.34651
$538$	2.55420e6	+	3.25401e6i	0.380452	+	0.484689i
$539$	−1.11219e7	+	1.11219e7i	−1.64894	+	1.64894i
$540$	−8.79858e6	+	3.58033e6i	−1.29846	+	0.528370i
$541$	−2.61698e6	−	2.61698e6i	−0.384422	−	0.384422i	0.488271	−	0.872692i	$-0.337628\pi$
$541$	−2.61698e6	−	2.61698e6i	−0.384422	−	0.384422i	−0.872692	+	0.488271i	$0.837628\pi$
$542$	−130365.	−	15707.1i	−0.0190618	−	0.00229666i
$543$		−	1.17208e7i		−	1.70592i
$544$	36991.0	−	54123.5i	0.00535919	−	0.00784131i
$545$	2.14144e6	−	1.54916e6i	0.308826	−	0.223412i
$546$	1.68426e6	−	1.39789e7i	0.241783	−	2.00675i
$547$	1.91210e6	−	1.91210e6i	0.273238	−	0.273238i	−0.557164	−	0.830402i	$-0.688111\pi$
$547$	1.91210e6	−	1.91210e6i	0.273238	−	0.273238i	0.830402	+	0.557164i	$0.188111\pi$
$548$	7.55368e6	+	1.84703e6i	1.07450	+	0.262737i
$549$	−1.23556e7	+	1.23556e7i	−1.74958	+	1.74958i
$550$	−1.01369e7	+	3.66861e6i	−1.42890	+	0.517124i
$551$		−	7.35071e6i		−	1.03146i
$552$	−2.74162e6	+	1.24304e6i	−0.382965	+	0.173636i
$553$	−947916.			−0.131813
$554$	1.83897e6	+	2.34282e6i	0.254567	+	0.324313i
$555$	537035.	−	3.34639e6i	0.0740066	−	0.461152i
$556$	6.05701e6	−	3.67688e6i	0.830943	−	0.504420i
$557$	4.99710e6	−	4.99710e6i	0.682465	−	0.682465i	−0.278090	−	0.960555i	$-0.589701\pi$
$557$	4.99710e6	−	4.99710e6i	0.682465	−	0.682465i	0.960555	+	0.278090i	$0.0897014\pi$
$558$	−1.34501e6	+	1.11633e7i	−0.182869	+	1.51777i
$559$	−2.28673e6			−0.309517
$560$	−7.04390e6	+	9.48534e6i	−0.949168	+	1.27815i
$561$	−181079.			−0.0242919
$562$	−384636.	+	3.19240e6i	−0.0513700	+	0.426360i
$563$	944316.	−	944316.i	0.125559	−	0.125559i	−0.641535	−	0.767094i	$-0.721702\pi$
$563$	944316.	−	944316.i	0.125559	−	0.125559i	0.767094	+	0.641535i	$0.221702\pi$
$564$	−3.58366e6	−	5.90344e6i	−0.474383	−	0.781462i
$565$	−1.12902e7	−	1.81188e6i	−1.48793	−	0.238786i
$566$	1.28498e6	+	1.63704e6i	0.168599	+	0.214792i
$567$	6.41772e6			0.838345
$568$	−4.71351e6	+	1.25331e7i	−0.613018	+	1.63000i
$569$			5.38187e6i			0.696871i	0.937333	+	0.348436i	$0.113287\pi$
$569$			5.38187e6i			0.696871i	−0.937333	+	0.348436i	$0.886713\pi$
$570$	−2.04573e6	+	7.14025e6i	−0.263731	+	0.920505i
$571$	9.80482e6	−	9.80482e6i	1.25849	−	1.25849i	0.306675	−	0.951814i	$-0.400784\pi$
$571$	9.80482e6	−	9.80482e6i	1.25849	−	1.25849i	0.951814	−	0.306675i	$-0.0992164\pi$
$572$	−2.13047e6	+	8.71286e6i	−0.272261	+	1.11345i
$573$	−1.24909e7	+	1.24909e7i	−1.58930	+	1.58930i
$574$	−292643.	+	2.42887e6i	−0.0370731	+	0.307698i
$575$	−1.88120e6	−	619760.i	−0.237282	−	0.0781724i
$576$	9.61733e6	−	1.09776e7i	1.20781	−	1.37865i
$577$		−	1.09597e7i		−	1.37044i	−0.728338	−	0.685218i	$-0.759707\pi$
$577$		−	1.09597e7i		−	1.37044i	0.728338	−	0.685218i	$-0.240293\pi$
$578$	−7.97353e6	−	960693.i	−0.992730	−	0.119609i
$579$	3.16302e6	+	3.16302e6i	0.392108	+	0.392108i
$580$	−1.36052e7	+	5.53625e6i	−1.67933	+	0.683354i
$581$	5.15110e6	−	5.15110e6i	0.633082	−	0.633082i
$582$	−1.61439e7	−	2.05670e7i	−1.97560	−	2.51688i
$583$	1.24258e7			1.51410
$584$	7.42370e6	+	2.79194e6i	0.900717	+	0.338746i
$585$	−9.27215e6	+	6.70767e6i	−1.12019	+	0.810368i
$586$	−7.73347e6	−	9.85229e6i	−0.930316	−	1.18520i
$587$	−9.23412e6	−	9.23412e6i	−1.10612	−	1.10612i	−0.993656	−	0.112459i	$-0.964127\pi$
$587$	−9.23412e6	−	9.23412e6i	−1.10612	−	1.10612i	−0.112459	−	0.993656i	$-0.535873\pi$
$588$	1.85109e7	−	1.12370e7i	2.20793	−	1.34031i
$589$	2.82498e6	+	2.82498e6i	0.335527	+	0.335527i
$590$	1.30641e6	+	2.35560e6i	0.154508	+	0.278594i
$591$	−7.82445e6			−0.921478
$592$	712296.	+	2.25647e6i	0.0835327	+	0.264621i
$593$		−	8.84290e6i		−	1.03266i	−0.856389	−	0.516331i	$-0.827297\pi$
$593$		−	8.84290e6i		−	1.03266i	0.856389	−	0.516331i	$-0.172703\pi$
$594$	−1.81871e7	−	2.19128e6i	−2.11494	−	0.254819i
$595$	−128927.	−	20690.5i	−0.0149298	−	0.00239596i
$596$	−1.73228e6	+	1.05157e6i	−0.199757	+	0.121262i
$597$	4.60826e6	+	4.60826e6i	0.529178	+	0.529178i
$598$	−1.29631e6	+	1.01753e6i	−0.148237	+	0.116357i
$599$		−	6.31283e6i		−	0.718881i	−0.933168	−	0.359441i	$-0.882967\pi$
$599$		−	6.31283e6i		−	0.718881i	0.933168	−	0.359441i	$-0.117033\pi$
$600$	1.47564e7	−	1.59135e6i	1.67342	−	0.180463i
$601$			2.42258e6i			0.273584i	0.990600	+	0.136792i	$0.0436793\pi$
$601$			2.42258e6i			0.273584i	−0.990600	+	0.136792i	$0.956321\pi$
$602$	−3.58654e6	−	4.56918e6i	−0.403352	−	0.513863i
$603$	5.18571e6	+	5.18571e6i	0.580784	+	0.580784i
$604$	−845909.	+	3.45947e6i	−0.0943477	+	0.385849i
$605$	−1.16375e7	−	1.86761e6i	−1.29262	−	0.207442i
$606$	−996857.	+	8.27369e6i	−0.110268	+	0.915203i
$607$			2.98236e6i			0.328540i	0.986415	+	0.164270i	$0.0525269\pi$
$607$			2.98236e6i			0.328540i	−0.986415	+	0.164270i	$0.947473\pi$
$608$	−958273.	−	5.09632e6i	−0.105131	−	0.559111i
$609$	4.44651e7			4.85821
$610$	1.08494e7	−	6.01704e6i	1.18054	−	0.654724i
$611$	−2.67336e6	−	2.67336e6i	−0.289704	−	0.289704i
$612$	156684.	+	38312.3i	0.0169101	+	0.00413485i
$613$	−6.32855e6	−	6.32855e6i	−0.680225	−	0.680225i	0.279825	−	0.960051i	$-0.409723\pi$
$613$	−6.32855e6	−	6.32855e6i	−0.680225	−	0.680225i	−0.960051	+	0.279825i	$0.909723\pi$
$614$	−2.31459e6	+	1.81682e6i	−0.247773	+	0.194487i
$615$	2.49003e6	−	1.80134e6i	0.265471	−	0.192047i
$616$	−2.07509e7	+	9.40842e6i	−2.20336	+	0.998999i
$617$	1.23802e7			1.30922			0.654612	−	0.755965i	$-0.272832\pi$
$617$	1.23802e7			1.30922			0.654612	+	0.755965i	$0.272832\pi$
$618$	−2.21529e7	+	1.73887e7i	−2.33324	+	1.83146i
$619$	2.69809e6	−	2.69809e6i	0.283028	−	0.283028i	−0.551287	−	0.834316i	$-0.685863\pi$
$619$	2.69809e6	−	2.69809e6i	0.283028	−	0.283028i	0.834316	+	0.551287i	$0.185863\pi$
$620$	3.10102e6	−	7.35634e6i	0.323985	−	0.768569i
$621$	−2.37988e6	−	2.37988e6i	−0.247643	−	0.247643i
$622$	824553.	−	6.84360e6i	0.0854560	−	0.709266i
$623$			2.63532e7i			2.72028i
$624$	5.69842e6	−	1.09556e7i	0.585858	−	1.12635i
$625$	7.85333e6	+	5.80454e6i	0.804180	+	0.594385i
$626$	1.03698e7	+	1.24941e6i	1.05764	+	0.127430i
$627$	−1.01283e7	+	1.01283e7i	−1.02889	+	1.02889i
$628$	2.77188e6	−	1.68265e6i	0.280462	−	0.170253i
$629$	−18492.0	+	18492.0i	−0.00186362	+	0.00186362i
$630$	−2.79454e7	−	8.00655e6i	−2.80517	−	0.803700i
$631$			1.65763e7i			1.65735i	0.559729	+	0.828676i	$0.310905\pi$
$631$			1.65763e7i			1.65735i	−0.559729	+	0.828676i	$0.689095\pi$
$632$	−778160.	−	292654.i	−0.0774955	−	0.0291449i
$633$	9.49566e6			0.941924
$634$	−1.23087e6	+	966163.i	−0.121616	+	0.0954612i
$635$	−9.81701e6	−	1.57545e6i	−0.966151	−	0.155050i
$636$	−1.66178e7	−	4.06339e6i	−1.62904	−	0.398332i
$637$	8.38264e6	−	8.38264e6i	0.818525	−	0.818525i
$638$	−2.81227e7	−	3.38837e6i	−2.73530	−	0.329563i
$639$	−3.29459e7			−3.19190
$640$	−8.71091e6	+	5.61198e6i	−0.840646	+	0.541584i
$641$	9.75119e6			0.937373			0.468687	−	0.883365i	$-0.344727\pi$
$641$	9.75119e6			0.937373			0.468687	+	0.883365i	$0.344727\pi$
$642$	−1.01678e7	−	1.22506e6i	−0.973616	−	0.117306i
$643$	5.16371e6	−	5.16371e6i	0.492532	−	0.492532i	−0.416571	−	0.909103i	$-0.636768\pi$
$643$	5.16371e6	−	5.16371e6i	0.492532	−	0.492532i	0.909103	+	0.416571i	$0.136768\pi$
$644$	−4.06630e6	−	994292.i	−0.386354	−	0.0944712i
$645$	−1.15625e6	+	7.20483e6i	−0.109434	+	0.681906i
$646$	45082.3	−	35386.9i	0.00425035	−	0.00333627i
$647$	1.15819e7			1.08772			0.543861	−	0.839175i	$-0.316962\pi$
$647$	1.15819e7			1.08772			0.543861	+	0.839175i	$0.316962\pi$
$648$	5.26841e6	+	1.98137e6i	0.492881	+	0.185365i
$649$			5.19451e6i			0.484098i
$650$	7.64030e6	−	2.76506e6i	0.709295	−	0.256697i
$651$	−1.70886e7	+	1.70886e7i	−1.58035	+	1.58035i
$652$	7.04521e6	−	4.27676e6i	0.649045	−	0.394000i
$653$	9.92125e6	−	9.92125e6i	0.910507	−	0.910507i	−0.0858047	−	0.996312i	$-0.527346\pi$
$653$	9.92125e6	−	9.92125e6i	0.910507	−	0.910507i	0.996312	+	0.0858047i	$0.0273461\pi$
$654$	−6.96694e6	−	839413.i	−0.636939	−	0.0767417i
$655$	1.00512e7	−	7.27125e6i	0.915407	−	0.662225i
$656$	−990112.	+	1.90355e6i	−0.0898307	+	0.172705i
$657$			1.95148e7i			1.76380i
$658$	1.14879e6	−	9.53467e6i	0.103437	−	0.858501i
$659$	−2.32456e6	−	2.32456e6i	−0.208510	−	0.208510i	0.595124	−	0.803634i	$-0.297103\pi$
$659$	−2.32456e6	−	2.32456e6i	−0.208510	−	0.208510i	−0.803634	+	0.595124i	$0.797103\pi$
$660$	2.63745e7	+	1.11180e7i	2.35681	+	0.993498i
$661$	6.64432e6	−	6.64432e6i	0.591490	−	0.591490i	−0.346544	−	0.938034i	$-0.612645\pi$
$661$	6.64432e6	−	6.64432e6i	0.591490	−	0.591490i	0.938034	+	0.346544i	$0.112645\pi$
$662$	1.60953e7	−	1.26339e7i	1.42743	−	1.12045i
$663$	136481.			0.0120584
$664$	5.81895e6	−	2.63830e6i	0.512182	−	0.232223i
$665$	−8.36860e6	+	6.05403e6i	−0.733835	+	0.530872i
$666$	−4.57966e6	+	3.59477e6i	−0.400081	+	0.314040i
$667$	−3.68000e6	−	3.68000e6i	−0.320283	−	0.320283i
$668$	−4.80670e6	−	1.17533e6i	−0.416779	−	0.101911i
$669$	1.97354e7	+	1.97354e7i	1.70483	+	1.70483i
$670$	−2.52537e6	−	4.55352e6i	−0.217339	−	0.391887i
$671$	2.39248e7			2.05136
$672$	3.08281e7	−	5.79668e6i	2.63344	−	0.495172i
$673$			2.97354e6i			0.253067i	0.991962	+	0.126534i	$0.0403851\pi$
$673$			2.97354e6i			0.253067i	−0.991962	+	0.126534i	$0.959615\pi$
$674$	−1.56555e6	+	1.29937e7i	−0.132745	+	1.10175i
$675$	7.47311e6	+	1.48164e7i	0.631309	+	1.25165i
$676$	−1.21634e6	+	4.97440e6i	−0.102374	+	0.418672i
$677$	1.01471e7	+	1.01471e7i	0.850885	+	0.850885i	0.990242	−	0.139357i	$-0.0445036\pi$
$677$	1.01471e7	+	1.01471e7i	0.850885	+	0.850885i	−0.139357	+	0.990242i	$0.544504\pi$
$678$	1.87452e7	+	2.38811e7i	1.56609	+	1.99517i
$679$		−	3.63593e7i		−	3.02650i
$680$	−99450.8	−	56789.5i	−0.00824776	−	0.00470973i
$681$		−	8.63969e6i		−	0.713889i
$682$	1.21101e7	−	9.50575e6i	0.996985	−	0.782574i
$683$	9.41097e6	+	9.41097e6i	0.771939	+	0.771939i	0.978445	−	0.206507i	$-0.0662095\pi$
$683$	9.41097e6	+	9.41097e6i	0.771939	+	0.771939i	−0.206507	+	0.978445i	$0.566210\pi$
$684$	1.09068e7	−	6.62089e6i	0.891364	−	0.541098i
$685$	2.15253e6	−	1.34129e7i	0.175276	−	1.09218i
$686$	1.04150e7	+	1.25485e6i	0.844985	+	0.101808i
$687$		−	9.71228e6i		−	0.785108i
$688$	−1.53359e6	−	4.85821e6i	−0.123520	−	0.391296i
$689$	−9.36543e6			−0.751588
$690$	2.55048e6	+	4.59880e6i	0.203938	+	0.367724i
$691$	−1.05835e7	−	1.05835e7i	−0.843209	−	0.843209i	0.146066	−	0.989275i	$-0.453339\pi$
$691$	−1.05835e7	−	1.05835e7i	−0.843209	−	0.843209i	−0.989275	+	0.146066i	$0.953339\pi$
$692$	−9.44330e6	+	5.73251e6i	−0.749650	+	0.455071i
$693$	−3.96401e7	−	3.96401e7i	−3.13546	−	3.13546i
$694$	−6.53090e6	−	8.32024e6i	−0.514724	−	0.655748i
$695$	−7.25521e6	−	1.00290e7i	−0.569754	−	0.787583i
$696$	3.65022e7	+	1.37279e7i	2.85625	+	1.07419i
$697$	−23713.9			−0.00184893
$698$	256418.	+	326672.i	0.0199209	+	0.0253789i
$699$	1.33491e7	−	1.33491e7i	1.03337	−	1.03337i
$700$	1.75081e7	+	1.09296e7i	1.35050	+	0.843058i
$701$	1.15757e6	+	1.15757e6i	0.0889714	+	0.0889714i	0.750192	−	0.661220i	$-0.229961\pi$
$701$	1.15757e6	+	1.15757e6i	0.0889714	+	0.0889714i	−0.661220	+	0.750192i	$0.729961\pi$
$702$	1.37078e7	+	1.65158e6i	1.04984	+	0.126490i
$703$			2.06863e6i			0.157868i
$704$	−1.99395e7	+	1.31702e6i	−1.51629	+	0.100152i
$705$	−9.77474e6	+	7.07126e6i	−0.740683	+	0.535826i
$706$	−814348.	+	6.75890e6i	−0.0614891	+	0.510346i
$707$	−8.19446e6	+	8.19446e6i	−0.616555	+	0.616555i
$708$	1.69867e6	−	6.94695e6i	0.127358	−	0.520848i
$709$	458574.	−	458574.i	0.0342605	−	0.0342605i	−0.689769	−	0.724030i	$-0.742288\pi$
$709$	458574.	−	458574.i	0.0342605	−	0.0342605i	0.724030	+	0.689769i	$0.242288\pi$
$710$	2.24869e7	+	6.44264e6i	1.67411	+	0.479643i
$711$		−	2.04556e6i		−	0.151753i
$712$	−8.13615e6	+	2.16338e7i	−0.601477	+	1.59931i
$713$	2.82855e6			0.208373
$714$	214059.	+	272707.i	0.0157140	+	0.0200194i
$715$	1.54712e7	+	2.48285e6i	1.13177	+	0.181629i
$716$	−5.69475e6	−	9.38109e6i	−0.415137	−	0.683866i
$717$	−2.73579e7	+	2.73579e7i	−1.98740	+	1.98740i
$718$	3.10179e6	−	2.57441e7i	0.224544	−	1.86366i
$719$	9.42662e6			0.680039			0.340019	−	0.940418i	$-0.389566\pi$
$719$	9.42662e6			0.680039			0.340019	+	0.940418i	$0.389566\pi$
$720$	−2.04689e7	−	1.52004e7i	−1.47151	−	1.09276i
$721$	−3.91630e7			−2.80568
$722$	−1.13322e6	+	9.40546e6i	−0.0809042	+	0.671486i
$723$	2.75901e7	−	2.75901e7i	1.96294	−	1.96294i
$724$	1.22199e7	−	7.41801e6i	0.866403	−	0.525946i
$725$	1.15557e7	+	2.29105e7i	0.816488	+	1.61879i
$726$	1.93218e7	+	2.46156e7i	1.36052	+	1.73328i
$727$	−9.00346e6			−0.631791			−0.315895	−	0.948794i	$-0.602305\pi$
$727$	−9.00346e6			−0.631791			−0.315895	+	0.948794i	$0.602305\pi$
$728$	1.56401e7	−	7.09120e6i	1.09373	−	0.495897i
$729$		−	2.00067e7i		−	1.39430i
$730$	3.81616e6	−	1.33196e7i	0.265045	−	0.925090i
$731$	39813.5	−	39813.5i	0.00275573	−	0.00275573i
$732$	−3.19961e7	−	7.82368e6i	−2.20708	−	0.539676i
$733$	−1.95184e6	+	1.95184e6i	−0.134179	+	0.134179i	−0.771006	−	0.636827i	$-0.780246\pi$
$733$	−1.95184e6	+	1.95184e6i	−0.134179	+	0.134179i	0.636827	+	0.771006i	$0.280246\pi$
$734$	−1.27142e6	+	1.05525e7i	−0.0871062	+	0.722962i
$735$	−2.21728e7	−	3.06498e7i	−1.51391	−	2.09271i
$736$	−3.03112e6	−	2.07164e6i	−0.206257	−	0.140968i
$737$		−	1.00413e7i		−	0.680960i
$738$	−5.24139e6	−	631510.i	−0.354247	−	0.0426815i
$739$	−7.21495e6	−	7.21495e6i	−0.485984	−	0.485984i	0.421052	−	0.907036i	$-0.361661\pi$
$739$	−7.21495e6	−	7.21495e6i	−0.485984	−	0.485984i	−0.907036	+	0.421052i	$0.861661\pi$
$740$	3.82876e6	−	1.55800e6i	0.257027	−	0.104590i
$741$	7.63381e6	−	7.63381e6i	0.510735	−	0.510735i
$742$	−1.46889e7	−	1.87134e7i	−0.979443	−	1.24779i
$743$	−2.58570e7			−1.71833			−0.859163	−	0.511703i	$-0.829015\pi$
$743$	−2.58570e7			−1.71833			−0.859163	+	0.511703i	$0.829015\pi$
$744$	−1.93041e7	+	8.75247e6i	−1.27855	+	0.579693i
$745$	2.07496e6	+	2.86825e6i	0.136968	+	0.189333i
$746$	−3.82763e6	−	4.87632e6i	−0.251816	−	0.320808i
$747$	1.11159e7	+	1.11159e7i	0.728855	+	0.728855i
$748$	−114604.	−	188790.i	−0.00748937	−	0.0123374i
$749$	−1.00704e7	−	1.00704e7i	−0.655907	−	0.655907i
$750$	−4.84872e6	−	2.54705e7i	−0.314756	−	1.65343i
$751$	79211.9			0.00512496			0.00256248	−	0.999997i	$-0.499184\pi$
$751$	79211.9			0.00512496			0.00256248	+	0.999997i	$0.499184\pi$
$752$	3.88674e6	−	7.47250e6i	0.250634	−	0.481860i
$753$			1.99365e7i			1.28133i
$754$	2.11963e7	+	2.55384e6i	1.35779	+	0.163593i
$755$	6.14289e6	+	985823.i	0.392198	+	0.0629407i
$756$	1.81994e7	+	2.99803e7i	1.15812	+	1.90779i
$757$	1.53181e7	+	1.53181e7i	0.971549	+	0.971549i	0.999606	−	0.0280571i	$-0.00893201\pi$
$757$	1.53181e7	+	1.53181e7i	0.971549	+	0.971549i	−0.0280571	+	0.999606i	$0.508932\pi$
$758$	416370.	−	326826.i	0.0263212	−	0.0206606i
$759$			1.01411e7i			0.638973i
$760$	−8.73901e6	+	2.38618e6i	−0.548818	+	0.149854i
$761$			2.03506e7i			1.27384i	0.770930	+	0.636920i	$0.219792\pi$
$761$			2.03506e7i			1.27384i	−0.770930	+	0.636920i	$0.780208\pi$
$762$	1.62992e7	+	2.07649e7i	1.01690	+	1.29552i
$763$	−6.90022e6	−	6.90022e6i	−0.429093	−	0.429093i
$764$	−2.09281e7	−	5.11735e6i	−1.29717	−	0.317184i
$765$	44649.2	−	278219.i	0.00275842	−	0.0171883i
$766$	1.59672e6	−	1.32524e7i	0.0983234	−	0.816062i
$767$		−	3.91515e6i		−	0.240303i
$768$	2.70970e7	+	4.75911e6i	1.65774	+	0.291154i
$769$	−1.57137e7			−0.958211			−0.479106	−	0.877757i	$-0.659039\pi$
$769$	−1.57137e7			−0.958211			−0.479106	+	0.877757i	$0.659039\pi$
$770$	1.93042e7	+	3.48076e7i	1.17334	+	2.11567i
$771$	−2.37515e6	−	2.37515e6i	−0.143898	−	0.143898i
$772$	−1.29585e6	+	5.29955e6i	−0.0782547	+	0.320034i
$773$	−6.52151e6	−	6.52151e6i	−0.392554	−	0.392554i	0.483043	−	0.875597i	$-0.339532\pi$
$773$	−6.52151e6	−	6.52151e6i	−0.392554	−	0.392554i	−0.875597	+	0.483043i	$0.839532\pi$
$774$	9.86009e6	−	7.73959e6i	0.591600	−	0.464372i
$775$	−1.32458e7	−	4.36382e6i	−0.792182	−	0.260983i
$776$	1.12254e7	−	2.98480e7i	0.669185	−	1.77935i
$777$	−1.25133e7			−0.743567
$778$	−9.69385e6	+	7.60910e6i	−0.574179	+	0.450697i
$779$	−1.32639e6	+	1.32639e6i	−0.0783119	+	0.0783119i
$780$	−1.98787e7	−	8.37973e6i	−1.16991	−	0.493167i
$781$	3.18973e7	+	3.18973e7i	1.87122	+	1.87122i
$782$	4853.80	−	40285.4i	0.000283834	−	0.00235576i
$783$			4.36026e7i			2.54160i
$784$	2.34309e7	+	1.21873e7i	1.36144	+	0.708138i
$785$	−3.32021e6	−	4.58959e6i	−0.192305	−	0.265827i
$786$	−3.27004e7	−	3.93992e6i	−1.88798	−	0.227474i
$787$	3.18840e6	−	3.18840e6i	0.183500	−	0.183500i	−0.609379	−	0.792879i	$-0.708581\pi$
$787$	3.18840e6	−	3.18840e6i	0.183500	−	0.183500i	0.792879	+	0.609379i	$0.208581\pi$
$788$	−4.95204e6	−	8.15761e6i	−0.284098	−	0.468002i
$789$	2.95310e7	−	2.95310e7i	1.68883	−	1.68883i
$790$	−400014.	+	1.39617e6i	−0.0228038	+	0.0795925i
$791$			4.22181e7i			2.39915i
$792$	−2.03030e7	−	4.47795e7i	−1.15013	−	2.53668i
$793$	−1.80323e7			−1.01828
$794$	−1.74712e7	+	1.37139e7i	−0.983493	+	0.771984i
$795$	−4.73547e6	+	2.95078e7i	−0.265733	+	1.65584i
$796$	−1.88794e6	+	7.72102e6i	−0.105610	+	0.431909i
$797$	−1.15821e7	+	1.15821e7i	−0.645862	+	0.645862i	−0.951990	−	0.306128i	$-0.900966\pi$
$797$	−1.15821e7	+	1.15821e7i	−0.645862	+	0.645862i	0.306128	+	0.951990i	$0.400966\pi$
$798$	2.72263e7	+	3.28037e6i	1.51350	+	0.182354i
$799$	93090.1			0.00515865
$800$	1.09984e7	+	1.43776e7i	0.607580	+	0.794259i
$801$	−5.68691e7			−3.13181
$802$	996839.	+	120104.i	0.0547254	+	0.00659360i
$803$	1.88937e7	−	1.88937e7i	1.03402	−	1.03402i
$804$	−3.28362e6	+	1.34289e7i	−0.179149	+	0.732654i
$805$	−1.15875e6	+	7.22043e6i	−0.0630231	+	0.392711i
$806$	−9.12752e6	+	7.16456e6i	−0.494897	+	0.388465i
$807$	−1.91867e7			−1.03709
$808$	−9.25688e6	+	4.19706e6i	−0.498811	+	0.226160i
$809$		−	1.39930e7i		−	0.751692i	−0.926682	−	0.375846i	$-0.877352\pi$
$809$		−	1.39930e7i		−	0.751692i	0.926682	−	0.375846i	$-0.122648\pi$
$810$	2.70823e6	−	9.45258e6i	0.145035	−	0.506218i
$811$	1.94275e7	−	1.94275e7i	1.03721	−	1.03721i	0.0379244	−	0.999281i	$-0.487925\pi$
$811$	1.94275e7	−	1.94275e7i	1.03721	−	1.03721i	0.999281	−	0.0379244i	$-0.0120746\pi$
$812$	2.81417e7	+	4.63585e7i	1.49782	+	2.46740i
$813$	430644.	−	430644.i	0.0228503	−	0.0228503i
$814$	7.91424e6	+	953549.i	0.418647	+	0.0504408i
$815$	−8.43889e6	−	1.16652e7i	−0.445032	−	0.615177i
$816$	91530.4	+	289957.i	0.00481216	+	0.0152443i
$817$		−	4.45379e6i		−	0.233439i
$818$	724256.	−	6.01116e6i	0.0378450	−	0.314105i
$819$	2.98771e7	+	2.98771e7i	1.55642	+	1.55642i
$820$	3.45396e6	+	1.45600e6i	0.179384	+	0.0756181i
$821$	1.48459e7	−	1.48459e7i	0.768683	−	0.768683i	−0.209192	−	0.977875i	$-0.567083\pi$
$821$	1.48459e7	−	1.48459e7i	0.768683	−	0.768683i	0.977875	+	0.209192i	$0.0670833\pi$
$822$	−2.83709e7	+	2.22695e7i	−1.46451	+	1.14956i
$823$	−2.39073e7			−1.23035			−0.615177	−	0.788389i	$-0.710916\pi$
$823$	−2.39073e7			−1.23035			−0.615177	+	0.788389i	$0.710916\pi$
$824$	−3.21495e7	−	1.20910e7i	−1.64952	−	0.620358i
$825$	1.56455e7	−	4.74899e7i	0.800303	−	2.42922i
$826$	7.82298e6	−	6.14058e6i	0.398953	−	0.313155i
$827$	−3.15447e6	−	3.15447e6i	−0.160385	−	0.160385i	0.622353	−	0.782737i	$-0.286177\pi$
$827$	−3.15447e6	−	3.15447e6i	−0.160385	−	0.160385i	−0.782737	+	0.622353i	$0.786177\pi$
$828$	2.14564e6	−	8.77490e6i	0.108763	−	0.444802i
$829$	−1.45812e7	−	1.45812e7i	−0.736895	−	0.736895i	0.235081	−	0.971976i	$-0.424464\pi$
$829$	−1.45812e7	−	1.45812e7i	−0.736895	−	0.736895i	−0.971976	+	0.235081i	$0.924464\pi$
$830$	−5.41327e6	−	9.76073e6i	−0.272750	−	0.491798i
$831$	−1.38140e7			−0.693933
$832$	1.50285e7	−	992646.i	0.752676	−	0.0497148i
$833$			291895.i			0.0145752i
$834$	−3.93123e6	+	3.26283e7i	−0.195710	+	1.62435i
$835$	−1.36973e6	+	8.53513e6i	−0.0679861	+	0.423637i
$836$	−1.69697e7	−	4.14944e6i	−0.839769	−	0.205340i
$837$	−1.67571e7	−	1.67571e7i	−0.826771	−	0.826771i
$838$	1.84586e7	+	2.35159e7i	0.908006	+	1.15678i
$839$			6.91576e6i			0.339184i	0.985514	+	0.169592i	$0.0542450\pi$
$839$			6.91576e6i			0.339184i	−0.985514	+	0.169592i	$0.945755\pi$
$840$	−1.44342e7	−	5.28631e7i	−0.705821	−	2.58496i
$841$			4.69114e7i			2.28712i
$842$	1.65263e7	−	1.29722e7i	0.803335	−	0.630571i
$843$	−1.05457e7	−	1.05457e7i	−0.511099	−	0.511099i
$844$	6.00974e6	+	9.89998e6i	0.290402	+	0.478386i
$845$	8.83292e6	+	1.41752e6i	0.425562	+	0.0682950i
$846$	2.05754e7	+	2.47903e6i	0.988376	+	0.119085i
$847$			4.35166e7i			2.08424i
$848$	−6.28089e6	−	1.98971e7i	−0.299938	−	0.950166i
$849$	−9.65251e6			−0.459591
$850$	−84881.2	+	181164.i	−0.00402962	+	0.00860053i
$851$	1.03562e6	+	1.03562e6i	0.0490204	+	0.0490204i
$852$	−3.22274e7	−	5.30890e7i	−1.52099	−	2.50556i
$853$	−5.11953e6	−	5.11953e6i	−0.240911	−	0.240911i	0.576316	−	0.817227i	$-0.304490\pi$
$853$	−5.11953e6	−	5.11953e6i	−0.240911	−	0.240911i	−0.817227	+	0.576316i	$0.804490\pi$
$854$	−2.82821e7	−	3.60309e7i	−1.32699	−	1.69056i
$855$	−1.30643e7	−	1.80591e7i	−0.611183	−	0.844850i
$856$	−5.15788e6	−	1.13760e7i	−0.240595	−	0.530648i
$857$	66932.9			0.00311306			0.00155653	−	0.999999i	$-0.499505\pi$
$857$	66932.9			0.00311306			0.00155653	+	0.999999i	$0.499505\pi$
$858$	−2.56869e7	−	3.27246e7i	−1.19122	−	1.51760i
$859$	−9.59329e6	+	9.59329e6i	−0.443593	+	0.443593i	−0.893218	−	0.449625i	$-0.851558\pi$
$859$	−9.59329e6	+	9.59329e6i	−0.443593	+	0.443593i	0.449625	+	0.893218i	$0.351558\pi$
$860$	−8.24339e6	+	3.35441e6i	−0.380067	+	0.154657i
$861$	−8.02346e6	−	8.02346e6i	−0.368853	−	0.368853i
$862$	−4.05290e6	−	488314.i	−0.185779	−	0.0223837i
$863$			2.02130e7i			0.923854i	0.886918	+	0.461927i	$0.152842\pi$
$863$			2.02130e7i			0.923854i	−0.886918	+	0.461927i	$0.847158\pi$
$864$	5.68424e6	+	3.02301e7i	0.259053	+	1.37770i
$865$	1.13114e7	+	1.56359e7i	0.514014	+	0.710531i
$866$	1.57072e6	−	1.30366e7i	0.0711713	−	0.590705i
$867$	2.63395e7	−	2.63395e7i	1.19004	−	1.19004i
$868$	−2.86315e7	−	7.00097e6i	−1.28986	−	0.315398i
$869$	−1.98045e6	+	1.98045e6i	−0.0889641	+	0.0889641i
$870$	1.87640e7	−	6.54922e7i	0.840478	−	2.93354i
$871$			7.56821e6i			0.338024i
$872$	−3.53417e6	−	7.79485e6i	−0.157397	−	0.347149i
$873$	7.84617e7			3.48435
$874$	−1.98180e6	−	2.52478e6i	−0.0877570	−	0.111801i
$875$	1.65658e7	−	3.20248e7i	0.731463	−	1.41406i
$876$	−3.14461e7	+	1.90892e7i	−1.38454	+	0.840481i
$877$	1.45590e7	−	1.45590e7i	0.639195	−	0.639195i	−0.311162	−	0.950357i	$-0.600718\pi$
$877$	1.45590e7	−	1.45590e7i	0.639195	−	0.639195i	0.950357	+	0.311162i	$0.100718\pi$
$878$	−2093.25	+	17373.5i	−9.16399e−5	+	0.000760591i
$879$	5.80923e7			2.53598
$880$	5.10083e6	+	3.45340e7i	0.222041	+	1.50328i
$881$	3.53273e7			1.53345			0.766726	−	0.641974i	$-0.221884\pi$
$881$	3.53273e7			1.53345			0.766726	+	0.641974i	$0.221884\pi$
$882$	−7.77328e6	+	6.45165e7i	−0.336460	+	2.79254i
$883$	−2.24106e7	+	2.24106e7i	−0.967280	+	0.967280i	−0.999481	−	0.0322017i	$-0.989748\pi$
$883$	−2.24106e7	+	2.24106e7i	−0.967280	+	0.967280i	0.0322017	+	0.999481i	$0.489748\pi$
$884$	86377.9	+	142292.i	0.00371768	+	0.00612422i
$885$	−1.23355e7	−	1.97963e6i	−0.529418	−	0.0849621i
$886$	1.42531e7	+	1.81581e7i	0.609992	+	0.777118i
$887$	−544528.			−0.0232387			−0.0116193	−	0.999932i	$-0.503699\pi$
$887$	−544528.			−0.0232387			−0.0116193	+	0.999932i	$0.503699\pi$
$888$	−1.02724e7	−	3.86329e6i	−0.437159	−	0.164409i
$889$			3.67092e7i			1.55783i
$890$	3.88153e7	+	1.11209e7i	1.64259	+	0.470613i
$891$	1.34083e7	−	1.34083e7i	0.565823	−	0.565823i
$892$	−8.08534e6	+	3.30662e7i	−0.340241	+	1.39146i
$893$	5.20682e6	−	5.20682e6i	0.218496	−	0.218496i
$894$	1.12431e6	−	9.33156e6i	0.0470483	−	0.390490i
$895$	−1.55329e7	+	1.12369e7i	−0.648180	+	0.468907i
$896$	2.55544e7	+	2.84721e7i	1.06340	+	1.18481i
$897$		−	7.64346e6i		−	0.317182i
$898$	−1.44105e7	−	1.73625e6i	−0.596333	−	0.0718493i
$899$	−2.59115e7	−	2.59115e7i	−1.06928	−	1.06928i
$900$	−2.35855e7	+	3.77817e7i	−0.970597	+	1.55480i
$901$	163058.	−	163058.i	0.00669162	−	0.00669162i
$902$	4.46315e6	+	5.68597e6i	0.182652	+	0.232696i
$903$	2.69414e7			1.09951
$904$	−1.30342e7	+	3.46576e7i	−0.530473	+	1.41051i
$905$	−1.46372e7	−	2.02333e7i	−0.594068	−	0.821192i
$906$	−1.01991e7	−	1.29934e7i	−0.412800	−	0.525900i
$907$	2.13276e7	+	2.13276e7i	0.860843	+	0.860843i	0.991436	−	0.130593i	$-0.0416881\pi$
$907$	2.13276e7	+	2.13276e7i	0.860843	+	0.860843i	−0.130593	+	0.991436i	$0.541688\pi$
$908$	9.00757e6	−	5.46800e6i	0.362571	−	0.220097i
$909$	−1.76833e7	−	1.76833e7i	−0.709828	−	0.709828i
$910$	−1.45497e7	−	2.62348e7i	−0.582440	−	1.05020i
$911$	−1.41783e7			−0.566016			−0.283008	−	0.959118i	$-0.591332\pi$
$911$	−1.41783e7			−0.566016			−0.283008	+	0.959118i	$0.591332\pi$
$912$	2.13378e7	+	1.10986e7i	0.849498	+	0.441857i
$913$		−	2.15241e7i		−	0.854570i
$914$	2.04057e7	+	2.45858e6i	0.807952	+	0.0973463i
$915$	−9.11772e6	+	5.68146e7i	−0.360026	+	2.24340i
$916$	1.01258e7	−	6.14684e6i	0.398742	−	0.242054i
$917$	−3.23873e7	−	3.23873e7i	−1.27190	−	1.27190i
$918$	−267417.	+	209906.i	−0.0104733	+	0.00822089i
$919$			6.63678e6i			0.259220i	0.991565	+	0.129610i	$0.0413726\pi$
$919$			6.63678e6i			0.259220i	−0.991565	+	0.129610i	$0.958627\pi$
$920$	−3.18043e6	+	5.56962e6i	−0.123884	+	0.216948i
$921$		−	1.36476e7i		−	0.530160i
$922$	6.40687e6	+	8.16223e6i	0.248209	+	0.316214i
$923$	−2.40412e7	−	2.40412e7i	−0.928864	−	0.928864i
$924$	2.51004e7	−	1.02652e8i	0.967164	−	3.95536i
$925$	−3.25198e6	−	6.44744e6i	−0.124966	−	0.247761i
$926$	353423.	−	2.93333e6i	0.0135446	−	0.112417i
$927$		−	8.45119e7i		−	3.23012i
$928$	8.78952e6	+	4.67447e7i	0.335039	+	1.78182i
$929$	−7.69328e6			−0.292464			−0.146232	−	0.989250i	$-0.546715\pi$
$929$	−7.69328e6			−0.292464			−0.146232	+	0.989250i	$0.546715\pi$
$930$	1.79583e7	+	3.23808e7i	0.680861	+	1.22767i
$931$	1.63266e7	+	1.63266e7i	0.617335	+	0.617335i
$932$	2.23660e7	+	5.46893e6i	0.843428	+	0.206235i
$933$	2.26070e7	+	2.26070e7i	0.850233	+	0.850233i
$934$	2.28809e7	−	1.79601e7i	0.858233	−	0.673663i
$935$	−312592.	+	226136.i	−0.0116936	+	0.00845942i
$936$	1.53025e7	+	3.37507e7i	0.570917	+	1.25919i
$937$	2.74246e7			1.02045			0.510225	−	0.860041i	$-0.329562\pi$
$937$	2.74246e7			1.02045			0.510225	+	0.860041i	$0.329562\pi$
$938$	−1.51223e7	+	1.18701e7i	−0.561190	+	0.440501i
$939$	−3.42554e7	+	3.42554e7i	−1.26784	+	1.26784i
$940$	−1.35587e7	−	5.71559e6i	−0.500494	−	0.210980i
$941$	−7.10209e6	−	7.10209e6i	−0.261464	−	0.261464i	0.564184	−	0.825649i	$-0.309191\pi$
$941$	−7.10209e6	−	7.10209e6i	−0.261464	−	0.261464i	−0.825649	+	0.564184i	$0.809191\pi$
$942$	−1.79905e6	+	1.49317e7i	−0.0660566	+	0.548255i
$943$			1.32807e6i			0.0486341i
$944$	8.31782e6	−	2.62568e6i	0.303794	−	0.0958984i
$945$	4.96404e7	−	3.59110e7i	1.80824	−	1.30812i
$946$	−1.70395e7	−	2.05301e6i	−0.619055	−	0.0745869i
$947$	−1.05611e7	+	1.05611e7i	−0.382679	+	0.382679i	−0.872066	−	0.489388i	$-0.837220\pi$
$947$	−1.05611e7	+	1.05611e7i	−0.382679	+	0.382679i	0.489388	+	0.872066i	$0.337220\pi$
$948$	3.29621e6	−	2.00095e6i	0.119123	−	0.0723129i
$949$	−1.42403e7	+	1.42403e7i	−0.513279	+	0.513279i
$950$	5.38541e6	+	1.48808e7i	0.193602	+	0.534954i
$951$		−	7.25762e6i		−	0.260221i
$952$	−148842.	+	395768.i	−0.00532272	+	0.0141530i
$953$	3.65764e7			1.30457			0.652287	−	0.757972i	$-0.273810\pi$
$953$	3.65764e7			1.30457			0.652287	+	0.757972i	$0.273810\pi$
$954$	4.03826e7	−	3.16980e7i	1.43656	−	1.12761i
$955$	−5.96376e6	+	3.71615e7i	−0.211598	+	1.31852i
$956$	−4.58375e7	−	1.12082e7i	−1.62209	−	0.396634i
$957$	9.28996e7	−	9.28996e7i	3.27895	−	3.27895i
$958$	2.08489e7	+	2.51198e6i	0.733955	+	0.0884307i
$959$	−5.01554e7			−1.76105
$960$	4.47138e6	−	4.78525e7i	0.156590	−	1.67582i
$961$	−8.71286e6			−0.304335
$962$	−5.96503e6	−	718698.i	−0.207814	−	0.0250385i
$963$	2.17315e7	−	2.17315e7i	0.755133	−	0.755133i
$964$	4.62264e7	+	1.13033e7i	1.60213	+	0.391752i
$965$	9.41028e6	+	1.51018e6i	0.325300	+	0.0522048i
$966$	1.52726e7	−	1.19881e7i	0.526588	−	0.413341i
$967$	−2.82856e6			−0.0972747			−0.0486373	−	0.998817i	$-0.515488\pi$
$967$	−2.82856e6			−0.0972747			−0.0486373	+	0.998817i	$0.515488\pi$
$968$	−1.34351e7	+	3.57235e7i	−0.460842	+	1.22537i
$969$			265820.i			0.00909447i
$970$	−5.35532e7	−	1.53434e7i	−1.82749	−	0.523590i
$971$	−2.94418e7	+	2.94418e7i	−1.00211	+	1.00211i	−0.00211491	+	0.999998i	$0.500673\pi$
$971$	−2.94418e7	+	2.94418e7i	−1.00211	+	1.00211i	−0.999998	+	0.00211491i	$0.999327\pi$
$972$	1.29809e7	−	7.88000e6i	0.440696	−	0.267523i
$973$	−3.23159e7	+	3.23159e7i	−1.09429	+	1.09429i
$974$	7.89835e6	+	951634.i	0.266771	+	0.0321420i
$975$	−1.17921e7	+	3.57935e7i	−0.397266	+	1.20585i
$976$	−1.20933e7	−	3.83100e7i	−0.406368	−	1.28732i
$977$			2.25848e7i			0.756972i	0.925607	+	0.378486i	$0.123555\pi$
$977$			2.25848e7i			0.756972i	−0.925607	+	0.378486i	$0.876445\pi$
$978$	−4.57261e6	+	3.79516e7i	−0.152868	+	1.26877i
$979$	5.50590e7	+	5.50590e7i	1.83599	+	1.83599i
$980$	1.79219e7	−	4.25149e7i	0.596100	−	1.41409i
$981$	1.48904e7	−	1.48904e7i	0.494007	−	0.494007i
$982$	3.66040e6	−	2.87320e6i	0.121130	−	0.0950795i
$983$	−1.30782e7			−0.431682			−0.215841	−	0.976429i	$-0.569249\pi$
$983$	−1.30782e7			−0.431682			−0.215841	+	0.976429i	$0.569249\pi$
$984$	−4.10947e6	−	9.06371e6i	−0.135300	−	0.298413i
$985$	−1.35071e7	+	9.77134e6i	−0.443580	+	0.320895i
$986$	−413506.	+	324578.i	−0.0135453	+	0.0106323i
$987$	3.14965e7	+	3.14965e7i	1.02913	+	1.02913i
$988$	1.27902e7	+	3.12747e6i	0.416856	+	0.101930i
$989$	−2.22971e6	−	2.22971e6i	−0.0724865	−	0.0724865i
$990$	−7.51133e7	+	4.16576e7i	−2.43573	+	1.35085i
$991$	4.60506e7			1.48954			0.744768	−	0.667323i	$-0.232560\pi$
$991$	4.60506e7			1.48954			0.744768	+	0.667323i	$0.232560\pi$
$992$	−2.13426e7	−	1.45867e7i	−0.688602	−	0.470629i
$993$			9.49030e7i			3.05427i
$994$	1.03309e7	−	8.57441e7i	0.331644	−	2.75257i
$995$	1.37100e7	+	2.20021e6i	0.439016	+	0.0704542i
$996$	−7.03863e6	+	2.87855e7i	−0.224822	+	0.919444i
$997$	−3.34691e7	−	3.34691e7i	−1.06636	−	1.06636i	−0.997635	−	0.0687291i	$-0.978106\pi$
$997$	−3.34691e7	−	3.34691e7i	−1.06636	−	1.06636i	−0.0687291	−	0.997635i	$-0.521894\pi$
$998$	2.63248e6	+	3.35373e6i	0.0836640	+	0.106586i
$999$		−	1.22706e7i		−	0.389001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.3	✓	116
5.4	even	2	inner	80.6.q.a.29.56	yes	116
16.5	even	4	inner	80.6.q.a.69.56	yes	116
80.69	even	4	inner	80.6.q.a.69.3	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.3	✓	116	1.1	even	1	trivial
80.6.q.a.29.56	yes	116	5.4	even	2	inner
80.6.q.a.69.3	yes	116	80.69	even	4	inner
80.6.q.a.69.56	yes	116	16.5	even	4	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)

\(f(q)\)	\(=\)	\(q+(-5.61624 - 0.676673i) q^{2} +(18.5525 - 18.5525i) q^{3} +(31.0842 + 7.60071i) q^{4} +(8.85788 - 55.1955i) q^{5} +(-116.749 + 91.6413i) q^{6} -206.395 q^{7} +(-169.433 - 63.7213i) q^{8} -445.391i q^{9} +O(q^{10})\)	\(q+(-5.61624 - 0.676673i) q^{2} +(18.5525 - 18.5525i) q^{3} +(31.0842 + 7.60071i) q^{4} +(8.85788 - 55.1955i) q^{5} +(-116.749 + 91.6413i) q^{6} -206.395 q^{7} +(-169.433 - 63.7213i) q^{8} -445.391i q^{9} +(-87.0972 + 303.997i) q^{10} +(-431.215 + 431.215i) q^{11} +(717.703 - 435.678i) q^{12} +(325.010 - 325.010i) q^{13} +(1159.16 + 139.662i) q^{14} +(-859.678 - 1188.35i) q^{15} +(908.458 + 472.525i) q^{16} +11.3173i q^{17} +(-301.384 + 2501.42i) q^{18} +(633.012 + 633.012i) q^{19} +(694.865 - 1648.38i) q^{20} +(-3829.15 + 3829.15i) q^{21} +(2713.60 - 2130.01i) q^{22} +633.812 q^{23} +(-4325.60 + 1961.22i) q^{24} +(-2968.08 - 977.829i) q^{25} +(-2045.26 + 1605.41i) q^{26} +(-3754.87 - 3754.87i) q^{27} +(-6415.63 - 1568.75i) q^{28} +(-5806.14 - 5806.14i) q^{29} +(4024.03 + 7255.78i) q^{30} +4462.77 q^{31} +(-4782.37 - 3268.54i) q^{32} +16000.2i q^{33} +(7.65811 - 63.5606i) q^{34} +(-1828.22 + 11392.1i) q^{35} +(3385.29 - 13844.6i) q^{36} +(1633.96 + 1633.96i) q^{37} +(-3126.80 - 3983.48i) q^{38} -12059.5i q^{39} +(-5017.94 + 8787.51i) q^{40} +2095.37i q^{41} +(24096.5 - 18914.3i) q^{42} +(-3517.93 - 3517.93i) q^{43} +(-16681.5 + 10126.4i) q^{44} +(-24583.6 - 3945.22i) q^{45} +(-3559.64 - 428.883i) q^{46} -8225.47i q^{47} +(25620.7 - 8087.66i) q^{48} +25791.9 q^{49} +(16007.7 + 7500.14i) q^{50} +(209.964 + 209.964i) q^{51} +(12573.0 - 7632.38i) q^{52} +(-14407.9 - 14407.9i) q^{53} +(18547.4 + 23629.0i) q^{54} +(19981.4 + 27620.7i) q^{55} +(34970.2 + 13151.8i) q^{56} +23487.9 q^{57} +(28679.8 + 36537.5i) q^{58} +(6023.12 - 6023.12i) q^{59} +(-17690.1 - 43473.1i) q^{60} +(-27741.1 - 27741.1i) q^{61} +(-25064.0 - 3019.84i) q^{62} +91926.6i q^{63} +(24647.2 + 21593.0i) q^{64} +(-15060.2 - 20818.0i) q^{65} +(10826.9 - 89861.1i) q^{66} +(-11643.0 + 11643.0i) q^{67} +(-86.0195 + 351.789i) q^{68} +(11758.8 - 11758.8i) q^{69} +(17976.4 - 62743.4i) q^{70} -73970.7i q^{71} +(-28380.9 + 75464.1i) q^{72} -43814.9 q^{73} +(-8071.03 - 10282.3i) q^{74} +(-73206.4 + 36924.1i) q^{75} +(14865.3 + 24488.0i) q^{76} +(89000.6 - 89000.6i) q^{77} +(-8160.35 + 67729.0i) q^{78} +4592.73 q^{79} +(34128.2 - 45957.2i) q^{80} -31094.3 q^{81} +(1417.88 - 11768.1i) q^{82} +(-24957.5 + 24957.5i) q^{83} +(-148130. + 89921.8i) q^{84} +(624.663 + 100.247i) q^{85} +(17377.1 + 22138.0i) q^{86} -215437. q^{87} +(100540. - 45584.5i) q^{88} -127683. i q^{89} +(135398. + 38792.4i) q^{90} +(-67080.5 + 67080.5i) q^{91} +(19701.5 + 4817.42i) q^{92} +(82795.5 - 82795.5i) q^{93} +(-5565.96 + 46196.2i) q^{94} +(40546.5 - 29332.2i) q^{95} +(-149365. + 28085.4i) q^{96} +176164. i q^{97} +(-144854. - 17452.7i) q^{98} +(192059. + 192059. i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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