LMFDB - Embedded newform 80.6.q.a.29.17

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			29.17
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.62558 + 4.34225i) q^{2} +(-3.49000 + 3.49000i) q^{3} +(-5.71035 - 31.4864i) q^{4} +(-25.3489 - 49.8240i) q^{5} +(-2.50120 - 27.8078i) q^{6} -221.972 q^{7} +(157.425 + 89.3605i) q^{8} +218.640i q^{9} +O(q^{10})$	\(q+(-3.62558 + 4.34225i) q^{2} +(-3.49000 + 3.49000i) q^{3} +(-5.71035 - 31.4864i) q^{4} +(-25.3489 - 49.8240i) q^{5} +(-2.50120 - 27.8078i) q^{6} -221.972 q^{7} +(157.425 + 89.3605i) q^{8} +218.640i q^{9} +(308.253 + 70.5698i) q^{10} +(337.646 - 337.646i) q^{11} +(129.817 + 89.9584i) q^{12} +(458.387 - 458.387i) q^{13} +(804.777 - 963.859i) q^{14} +(262.354 + 85.4185i) q^{15} +(-958.784 + 359.597i) q^{16} +2274.45i q^{17} +(-949.390 - 792.696i) q^{18} +(298.101 + 298.101i) q^{19} +(-1424.03 + 1082.66i) q^{20} +(774.683 - 774.683i) q^{21} +(241.983 + 2690.31i) q^{22} +3318.66 q^{23} +(-861.283 + 237.546i) q^{24} +(-1839.87 + 2525.96i) q^{25} +(328.515 + 3652.35i) q^{26} +(-1611.12 - 1611.12i) q^{27} +(1267.54 + 6989.09i) q^{28} +(-423.320 - 423.320i) q^{29} +(-1322.09 + 829.515i) q^{30} +770.338 q^{31} +(1914.69 - 5467.03i) q^{32} +2356.77i q^{33} +(-9876.26 - 8246.21i) q^{34} +(5626.74 + 11059.5i) q^{35} +(6884.17 - 1248.51i) q^{36} +(4085.27 + 4085.27i) q^{37} +(-2375.22 + 213.642i) q^{38} +3199.54i q^{39} +(461.755 - 10108.7i) q^{40} +3542.62i q^{41} +(555.197 + 6172.55i) q^{42} +(4215.82 + 4215.82i) q^{43} +(-12559.3 - 8703.17i) q^{44} +(10893.5 - 5542.27i) q^{45} +(-12032.1 + 14410.5i) q^{46} -16811.0i q^{47} +(2091.16 - 4601.15i) q^{48} +32464.6 q^{49} +(-4297.78 - 17147.3i) q^{50} +(-7937.85 - 7937.85i) q^{51} +(-17050.5 - 11815.4i) q^{52} +(785.216 + 785.216i) q^{53} +(12837.2 - 1154.65i) q^{54} +(-25381.8 - 8263.95i) q^{55} +(-34944.0 - 19835.5i) q^{56} -2080.75 q^{57} +(3372.94 - 303.383i) q^{58} +(298.109 - 298.109i) q^{59} +(1191.39 - 8748.34i) q^{60} +(31800.2 + 31800.2i) q^{61} +(-2792.92 + 3345.01i) q^{62} -48531.9i q^{63} +(16797.4 + 28135.2i) q^{64} +(-34458.3 - 11219.1i) q^{65} +(-10233.7 - 8544.66i) q^{66} +(41685.0 - 41685.0i) q^{67} +(71614.3 - 12987.9i) q^{68} +(-11582.1 + 11582.1i) q^{69} +(-68423.5 - 15664.5i) q^{70} +30062.8i q^{71} +(-19537.8 + 34419.4i) q^{72} +60262.6 q^{73} +(-32550.7 + 2927.81i) q^{74} +(-2394.47 - 15236.8i) q^{75} +(7683.87 - 11088.4i) q^{76} +(-74948.0 + 74948.0i) q^{77} +(-13893.2 - 11600.2i) q^{78} +2752.89 q^{79} +(42220.6 + 38655.1i) q^{80} -41883.8 q^{81} +(-15383.0 - 12844.1i) q^{82} +(-15332.2 + 15332.2i) q^{83} +(-28815.7 - 19968.3i) q^{84} +(113322. - 57654.8i) q^{85} +(-33591.0 + 3021.38i) q^{86} +2954.78 q^{87} +(83326.2 - 22981.8i) q^{88} -76595.2i q^{89} +(-15429.4 + 67396.4i) q^{90} +(-101749. + 101749. i) q^{91} +(-18950.7 - 104492. i) q^{92} +(-2688.48 + 2688.48i) q^{93} +(72997.6 + 60949.6i) q^{94} +(7296.09 - 22409.1i) q^{95} +(12397.7 + 25762.2i) q^{96} +138906. i q^{97} +(-117703. + 140969. i) q^{98} +(73822.8 + 73822.8i) 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 $

$2$	−3.62558	+	4.34225i	−0.640918	+	0.767609i
$2$	−3.62558	+	4.34225i	−0.640918	+	0.767609i
$3$	−3.49000	+	3.49000i	−0.223884	+	0.223884i	−0.810132	−	0.586248i	$-0.800604\pi$
$3$	−3.49000	+	3.49000i	−0.223884	+	0.223884i	0.586248	+	0.810132i	$0.300604\pi$
$4$	−5.71035	−	31.4864i	−0.178449	−	0.983949i
$5$	−25.3489	−	49.8240i	−0.453454	−	0.891280i
$5$	−25.3489	−	49.8240i	−0.453454	−	0.891280i
$6$	−2.50120	−	27.8078i	−0.0283642	−	0.315346i
$7$	−221.972			−1.71219			−0.856097	−	0.516815i	$-0.827118\pi$
$7$	−221.972			−1.71219			−0.856097	+	0.516815i	$0.827118\pi$
$8$	157.425	+	89.3605i	0.869660	+	0.493652i
$9$			218.640i			0.899752i
$10$	308.253	+	70.5698i	0.974781	+	0.223161i
$11$	337.646	−	337.646i	0.841356	−	0.841356i	−0.147679	−	0.989035i	$-0.547180\pi$
$11$	337.646	−	337.646i	0.841356	−	0.841356i	0.989035	+	0.147679i	$0.0471803\pi$
$12$	129.817	+	89.9584i	0.260242	+	0.180339i
$13$	458.387	−	458.387i	0.752270	−	0.752270i	−0.222633	−	0.974902i	$-0.571465\pi$
$13$	458.387	−	458.387i	0.752270	−	0.752270i	0.974902	+	0.222633i	$0.0714650\pi$
$14$	804.777	−	963.859i	1.09738	−	1.31430i
$15$	262.354	+	85.4185i	0.301064	+	0.0980221i
$16$	−958.784	+	359.597i	−0.936312	+	0.351169i
$17$			2274.45i			1.90878i	0.298571	+	0.954388i	$0.403490\pi$
$17$			2274.45i			1.90878i	−0.298571	+	0.954388i	$0.596510\pi$
$18$	−949.390	−	792.696i	−0.690658	−	0.576667i
$19$	298.101	+	298.101i	0.189444	+	0.189444i	0.795456	−	0.606012i	$-0.207232\pi$
$19$	298.101	+	298.101i	0.189444	+	0.189444i	−0.606012	+	0.795456i	$0.707232\pi$
$20$	−1424.03	+	1082.66i	−0.796056	+	0.605223i
$21$	774.683	−	774.683i	0.383333	−	0.383333i
$22$	241.983	+	2690.31i	0.106593	+	1.18507i
$23$	3318.66			1.30811			0.654053	−	0.756449i	$-0.273067\pi$
$23$	3318.66			1.30811			0.654053	+	0.756449i	$0.273067\pi$
$24$	−861.283	+	237.546i	−0.305223	+	0.0841820i
$25$	−1839.87	+	2525.96i	−0.588759	+	0.808309i
$26$	328.515	+	3652.35i	0.0953063	+	1.05959i
$27$	−1611.12	−	1611.12i	−0.425324	−	0.425324i
$28$	1267.54	+	6989.09i	0.305539	+	1.68471i
$29$	−423.320	−	423.320i	−0.0934703	−	0.0934703i	0.658825	−	0.752296i	$-0.271054\pi$
$29$	−423.320	−	423.320i	−0.0934703	−	0.0934703i	−0.752296	+	0.658825i	$0.771054\pi$
$30$	−1322.09	+	829.515i	−0.268200	+	0.168276i
$31$	770.338			0.143972			0.0719859	−	0.997406i	$-0.477066\pi$
$31$	770.338			0.143972			0.0719859	+	0.997406i	$0.477066\pi$
$32$	1914.69	−	5467.03i	0.330539	−	0.943792i
$33$			2356.77i			0.376732i
$34$	−9876.26	−	8246.21i	−1.46519	−	1.22337i
$35$	5626.74	+	11059.5i	0.776402	+	1.52604i
$36$	6884.17	−	1248.51i	0.885310	−	0.160559i
$37$	4085.27	+	4085.27i	0.490587	+	0.490587i	0.908491	−	0.417904i	$-0.137235\pi$
$37$	4085.27	+	4085.27i	0.490587	+	0.490587i	−0.417904	+	0.908491i	$0.637235\pi$
$38$	−2375.22	+	213.642i	−0.266837	+	0.0240009i
$39$			3199.54i			0.336842i
$40$	461.755	−	10108.7i	0.0456312	−	0.998958i
$41$			3542.62i			0.329128i	0.986366	+	0.164564i	$0.0526217\pi$
$41$			3542.62i			0.329128i	−0.986366	+	0.164564i	$0.947378\pi$
$42$	555.197	+	6172.55i	0.0485650	+	0.539935i
$43$	4215.82	+	4215.82i	0.347705	+	0.347705i	0.859254	−	0.511549i	$-0.170928\pi$
$43$	4215.82	+	4215.82i	0.347705	+	0.347705i	−0.511549	+	0.859254i	$0.670928\pi$
$44$	−12559.3	−	8703.17i	−0.977990	−	0.677713i
$45$	10893.5	−	5542.27i	0.801931	−	0.407996i
$46$	−12032.1	+	14410.5i	−0.838388	+	1.00411i
$47$		−	16811.0i		−	1.11007i	−0.831828	−	0.555033i	$-0.812706\pi$
$47$		−	16811.0i		−	1.11007i	0.831828	−	0.555033i	$-0.187294\pi$
$48$	2091.16	−	4601.15i	0.131004	−	0.288246i
$49$	32464.6			1.93161
$50$	−4297.78	−	17147.3i	−0.243119	−	0.969996i
$51$	−7937.85	−	7937.85i	−0.427344	−	0.427344i
$52$	−17050.5	−	11815.4i	−0.874437	−	0.605954i
$53$	785.216	+	785.216i	0.0383972	+	0.0383972i	0.726045	−	0.687647i	$-0.241357\pi$
$53$	785.216	+	785.216i	0.0383972	+	0.0383972i	−0.687647	+	0.726045i	$0.741357\pi$
$54$	12837.2	−	1154.65i	0.599080	−	0.0538849i
$55$	−25381.8	−	8263.95i	−1.13140	−	0.368367i
$56$	−34944.0	−	19835.5i	−1.48903	−	0.845228i
$57$	−2080.75			−0.0848267
$58$	3372.94	−	303.383i	0.131656	−	0.0118419i
$59$	298.109	−	298.109i	0.0111492	−	0.0111492i	−0.701510	−	0.712659i	$-0.747491\pi$
$59$	298.109	−	298.109i	0.0111492	−	0.0111492i	0.712659	+	0.701510i	$0.247491\pi$
$60$	1191.39	−	8748.34i	0.0427243	−	0.313724i
$61$	31800.2	+	31800.2i	1.09422	+	1.09422i	0.995072	+	0.0991502i	$0.0316124\pi$
$61$	31800.2	+	31800.2i	1.09422	+	1.09422i	0.0991502	+	0.995072i	$0.468388\pi$
$62$	−2792.92	+	3345.01i	−0.0922741	+	0.110514i
$63$		−	48531.9i		−	1.54055i
$64$	16797.4	+	28135.2i	0.512616	+	0.858618i
$65$	−34458.3	−	11219.1i	−1.01160	−	0.329363i
$66$	−10233.7	−	8544.66i	−0.289183	−	0.241454i
$67$	41685.0	−	41685.0i	1.13447	−	1.13447i	0.145043	−	0.989425i	$-0.453668\pi$
$67$	41685.0	−	41685.0i	1.13447	−	1.13447i	0.989425	−	0.145043i	$-0.0463320\pi$
$68$	71614.3	−	12987.9i	1.87814	−	0.340618i
$69$	−11582.1	+	11582.1i	−0.292864	+	0.292864i
$70$	−68423.5	−	15664.5i	−1.66902	−	0.382096i
$71$			30062.8i			0.707757i	0.935291	+	0.353879i	$0.115137\pi$
$71$			30062.8i			0.707757i	−0.935291	+	0.353879i	$0.884863\pi$
$72$	−19537.8	+	34419.4i	−0.444164	+	0.782478i
$73$	60262.6			1.32355			0.661776	−	0.749702i	$-0.269803\pi$
$73$	60262.6			1.32355			0.661776	+	0.749702i	$0.269803\pi$
$74$	−32550.7	+	2927.81i	−0.691006	+	0.0621533i
$75$	−2394.47	−	15236.8i	−0.0491537	−	0.312781i
$76$	7683.87	−	11088.4i	0.152597	−	0.220209i
$77$	−74948.0	+	74948.0i	−1.44057	+	1.44057i
$78$	−13893.2	−	11600.2i	−0.258563	−	0.215888i
$79$	2752.89			0.0496274			0.0248137	−	0.999692i	$-0.492101\pi$
$79$	2752.89			0.0496274			0.0248137	+	0.999692i	$0.492101\pi$
$80$	42220.6	+	38655.1i	0.737564	+	0.675277i
$81$	−41883.8			−0.709306
$82$	−15383.0	−	12844.1i	−0.252642	−	0.210944i
$83$	−15332.2	+	15332.2i	−0.244292	+	0.244292i	−0.818623	−	0.574331i	$-0.805262\pi$
$83$	−15332.2	+	15332.2i	−0.244292	+	0.244292i	0.574331	+	0.818623i	$0.305262\pi$
$84$	−28815.7	−	19968.3i	−0.445585	−	0.308775i
$85$	113322.	−	57654.8i	1.70125	−	0.865542i
$86$	−33591.0	+	3021.38i	−0.489752	+	0.0440513i
$87$	2954.78			0.0418530
$88$	83326.2	−	22981.8i	1.14703	−	0.316356i
$89$		−	76595.2i		−	1.02501i	−0.858685	−	0.512503i	$-0.828718\pi$
$89$		−	76595.2i		−	1.02501i	0.858685	−	0.512503i	$-0.171282\pi$
$90$	−15429.4	+	67396.4i	−0.200790	+	0.877062i
$91$	−101749.	+	101749.i	−1.28803	+	1.28803i
$92$	−18950.7	−	104492.i	−0.233429	−	1.28711i
$93$	−2688.48	+	2688.48i	−0.0322329	+	0.0322329i
$94$	72997.6	+	60949.6i	0.852097	+	0.711461i
$95$	7296.09	−	22409.1i	0.0829433	−	0.254751i
$96$	12397.7	+	25762.2i	0.137298	+	0.285302i
$97$			138906.i			1.49897i	0.662021	+	0.749485i	$0.269699\pi$
$97$			138906.i			1.49897i	−0.662021	+	0.749485i	$0.730301\pi$
$98$	−117703.	+	140969.i	−1.23800	+	1.48272i
$99$	73822.8	+	73822.8i	0.757012	+	0.757012i
$100$	90039.8	+	43506.7i	0.900398	+	0.435067i
$101$	−44314.1	+	44314.1i	−0.432254	+	0.432254i	−0.889394	−	0.457141i	$-0.848874\pi$
$101$	−44314.1	+	44314.1i	−0.432254	+	0.432254i	0.457141	+	0.889394i	$0.348874\pi$
$102$	63247.5	−	5688.86i	0.601926	−	0.0541409i
$103$	−14146.6			−0.131389			−0.0656944	−	0.997840i	$-0.520926\pi$
$103$	−14146.6			−0.131389			−0.0656944	+	0.997840i	$0.520926\pi$
$104$	113123.	−	31199.9i	1.02558	−	0.282859i
$105$	−58235.2	−	18960.5i	−0.515480	−	0.167833i
$106$	−6256.47	+	562.746i	−0.0540835	+	0.00486460i
$107$	−100646.	−	100646.i	−0.849836	−	0.849836i	0.140276	−	0.990112i	$-0.455201\pi$
$107$	−100646.	−	100646.i	−0.849836	−	0.849836i	−0.990112	+	0.140276i	$0.955201\pi$
$108$	−41528.4	+	59928.6i	−0.342599	+	0.494395i
$109$	−610.474	−	610.474i	−0.00492154	−	0.00492154i	0.704642	−	0.709563i	$-0.251108\pi$
$109$	−610.474	−	610.474i	−0.00492154	−	0.00492154i	−0.709563	+	0.704642i	$0.751108\pi$
$110$	127908.	−	80252.8i	1.00790	−	0.632380i
$111$	−28515.2			−0.219669
$112$	212823.	−	79820.4i	1.60315	−	0.601269i
$113$			179973.i			1.32590i	0.748664	+	0.662950i	$0.230696\pi$
$113$			179973.i			1.32590i	−0.748664	+	0.662950i	$0.769304\pi$
$114$	7543.92	−	9035.15i	0.0543670	−	0.0651138i
$115$	−84124.1	−	165349.i	−0.593166	−	1.16589i
$116$	−10911.5	+	15746.1i	−0.0752904	+	0.108650i
$117$	100222.	+	100222.i	0.676856	+	0.676856i
$118$	213.647	+	2375.28i	0.00141251	+	0.0157040i
$119$		−	504865.i		−	3.26819i
$120$	33668.0	+	36891.1i	0.213435	+	0.233867i
$121$		−	66958.6i		−	0.415760i
$122$	−253379.	+	22790.5i	−1.54124	+	0.138629i
$123$	−12363.8	−	12363.8i	−0.0736865	−	0.0736865i
$124$	−4398.90	−	24255.2i	−0.0256915	−	0.141661i
$125$	172492.	+	27639.5i	0.987404	+	0.158218i
$126$	210738.	+	175956.i	1.18254	+	0.987367i
$127$			171523.i			0.943653i	0.881691	+	0.471826i	$0.156405\pi$
$127$			171523.i			0.943653i	−0.881691	+	0.471826i	$0.843595\pi$
$128$	−183070.	−	29067.9i	−0.987628	−	0.156815i
$129$	−29426.5			−0.155691
$130$	173647.	−	108951.i	0.901176	−	0.565421i
$131$	−78184.0	−	78184.0i	−0.398052	−	0.398052i	0.479494	−	0.877545i	$-0.340820\pi$
$131$	−78184.0	−	78184.0i	−0.398052	−	0.398052i	−0.877545	+	0.479494i	$0.840820\pi$
$132$	74206.2	−	13458.0i	0.370685	−	0.0672273i
$133$	−66170.2	−	66170.2i	−0.324364	−	0.324364i
$134$	29874.6	+	332139.i	0.143728	+	1.59793i
$135$	−39432.6	+	121113.i	−0.186218	+	0.571947i
$136$	−203246.	+	358056.i	−0.942270	+	1.65998i
$137$	171360.			0.780024			0.390012	−	0.920810i	$-0.372471\pi$
$137$	171360.			0.780024			0.390012	+	0.920810i	$0.372471\pi$
$138$	−8300.63	−	92284.4i	−0.0371033	−	0.412506i
$139$	−254036.	+	254036.i	−1.11522	+	1.11522i	−0.122782	+	0.992434i	$0.539182\pi$
$139$	−254036.	+	254036.i	−1.11522	+	1.11522i	−0.992434	+	0.122782i	$0.960818\pi$
$140$	316094.	−	240319.i	1.36300	−	1.03626i
$141$	58670.4	+	58670.4i	0.248526	+	0.248526i
$142$	−130541.	−	108995.i	−0.543281	−	0.453614i
$143$		−	309545.i		−	1.26585i
$144$	−78622.1	−	209628.i	−0.315965	−	0.842449i
$145$	−10360.8	+	31822.2i	−0.0409237	+	0.125693i
$146$	−218487.	+	261676.i	−0.848288	+	1.01597i
$147$	−113302.	+	113302.i	−0.432456	+	0.432456i
$148$	105302.	−	151959.i	0.395169	−	0.570258i
$149$	−63078.2	+	63078.2i	−0.232763	+	0.232763i	−0.813845	−	0.581082i	$-0.802629\pi$
$149$	−63078.2	+	63078.2i	−0.232763	+	0.232763i	0.581082	+	0.813845i	$0.302629\pi$
$150$	74843.3	+	44844.8i	0.271597	+	0.162736i
$151$			72466.2i			0.258639i	0.991603	+	0.129319i	$0.0412792\pi$
$151$			72466.2i			0.258639i	−0.991603	+	0.129319i	$0.958721\pi$
$152$	20290.2	+	73567.2i	0.0712323	+	0.258271i
$153$	−497286.			−1.71742
$154$	−53713.4	−	597173.i	−0.182508	−	2.02908i
$155$	−19527.2	−	38381.4i	−0.0652846	−	0.128319i
$156$	100742.	−	18270.5i	0.331436	−	0.0601090i
$157$	185789.	−	185789.i	0.601550	−	0.601550i	−0.339174	−	0.940724i	$-0.610148\pi$
$157$	185789.	−	185789.i	0.601550	−	0.601550i	0.940724	+	0.339174i	$0.110148\pi$
$158$	−9980.84	+	11953.8i	−0.0318071	+	0.0380945i
$159$	−5480.82			−0.0171930
$160$	−320925.	+	43185.5i	−0.991067	+	0.133364i
$161$	−736649.			−2.23973
$162$	151853.	−	181870.i	0.454607	−	0.544470i
$163$	218642.	−	218642.i	0.644562	−	0.644562i	−0.307112	−	0.951673i	$-0.599363\pi$
$163$	218642.	−	218642.i	0.644562	−	0.644562i	0.951673	+	0.307112i	$0.0993625\pi$
$164$	111544.	−	20229.6i	0.323845	−	0.0587324i
$165$	117424.	−	59741.4i	0.335774	−	0.170831i
$166$	−10988.2	−	122164.i	−0.0309497	−	0.344091i
$167$	−192821.			−0.535012			−0.267506	−	0.963556i	$-0.586200\pi$
$167$	−192821.			−0.535012			−0.267506	+	0.963556i	$0.586200\pi$
$168$	191181.	−	52728.6i	0.522602	−	0.144136i
$169$		−	48943.9i		−	0.131820i
$170$	−160508.	+	701107.i	−0.425965	+	1.86064i
$171$	−65176.8	+	65176.8i	−0.170452	+	0.170452i
$172$	108667.	−	156815.i	0.280077	−	0.404172i
$173$	−13776.2	+	13776.2i	−0.0349958	+	0.0349958i	−0.724388	−	0.689392i	$-0.757878\pi$
$173$	−13776.2	+	13776.2i	−0.0349958	+	0.0349958i	0.689392	+	0.724388i	$0.257878\pi$
$174$	−10712.8	+	12830.4i	−0.0268243	+	0.0321268i
$175$	408400.	−	560694.i	1.00807	−	1.38398i
$176$	−202313.	+	445146.i	−0.492314	+	1.08323i
$177$			2080.80i			0.00499226i
$178$	332596.	+	277702.i	0.786805	+	0.656945i
$179$	444475.	+	444475.i	1.03685	+	1.03685i	0.999295	+	0.0375514i	$0.0119558\pi$
$179$	444475.	+	444475.i	1.03685	+	1.03685i	0.0375514	+	0.999295i	$0.488044\pi$
$180$	−236712.	−	311349.i	−0.544551	−	0.716253i
$181$	452613.	−	452613.i	1.02690	−	1.02690i	0.0272768	−	0.999628i	$-0.491316\pi$
$181$	452613.	−	452613.i	1.02690	−	1.02690i	0.999628	−	0.0272768i	$-0.00868355\pi$
$182$	−72921.1	−	810719.i	−0.163183	−	1.81423i
$183$	−221966.			−0.489957
$184$	522440.	+	296557.i	1.13761	+	0.645749i
$185$	99987.8	−	307102.i	0.214792	−	0.659709i
$186$	−1926.77	−	21421.4i	−0.00408364	−	0.0454010i
$187$	767960.	+	767960.i	1.60596	+	1.60596i
$188$	−529317.	+	95996.7i	−1.09225	+	0.198090i
$189$	357625.	+	357625.i	0.728237	+	0.728237i
$190$	70853.7	+	112928.i	0.142390	+	0.226943i
$191$	81220.6			0.161095			0.0805476	−	0.996751i	$-0.474333\pi$
$191$	81220.6			0.161095			0.0805476	+	0.996751i	$0.474333\pi$
$192$	−156815.	−	39569.0i	−0.306997	−	0.0774644i
$193$		−	374008.i		−	0.722749i	−0.932421	−	0.361375i	$-0.882308\pi$
$193$		−	374008.i		−	0.722749i	0.932421	−	0.361375i	$-0.117692\pi$
$194$	−603167.	−	503616.i	−1.15062	−	0.960717i
$195$	159414.	−	81104.7i	0.300221	−	0.152742i
$196$	−185384.	−	1.02219e6i	−0.344693	−	1.90061i
$197$	−16211.5	−	16211.5i	−0.0297616	−	0.0297616i	0.692069	−	0.721831i	$-0.256699\pi$
$197$	−16211.5	−	16211.5i	−0.0297616	−	0.0297616i	−0.721831	+	0.692069i	$0.756699\pi$
$198$	−588208.	+	52907.0i	−1.06627	+	0.0959070i
$199$		−	571634.i		−	1.02326i	−0.859207	−	0.511629i	$-0.829042\pi$
$199$		−	571634.i		−	1.02326i	0.859207	−	0.511629i	$-0.170958\pi$
$200$	−515364.	+	233239.i	−0.911043	+	0.412312i
$201$			290961.i			0.507978i
$202$	−31758.9	−	353088.i	−0.0547629	−	0.608841i
$203$	93965.2	+	93965.2i	0.160039	+	0.160039i
$204$	−204606.	+	295262.i	−0.344226	+	0.496744i
$205$	176508.	−	89801.4i	0.293345	−	0.149245i
$206$	51289.5	−	61428.1i	0.0842094	−	0.100855i
$207$			725590.i			1.17697i
$208$	−274659.	+	604328.i	−0.440186	+	0.968533i
$209$	201305.			0.318779
$210$	293468.	−	184129.i	0.459211	−	0.288121i
$211$	506339.	+	506339.i	0.782953	+	0.782953i	0.980328	−	0.197375i	$-0.0632417\pi$
$211$	506339.	+	506339.i	0.782953	+	0.782953i	−0.197375	+	0.980328i	$0.563242\pi$
$212$	20239.8	−	29207.5i	0.0309290	−	0.0446328i
$213$	−104919.	−	104919.i	−0.158455	−	0.158455i
$214$	801927.	−	72130.2i	1.19702	−	0.107667i
$215$	103183.	−	316916.i	0.152234	−	0.467571i
$216$	−109661.	−	397603.i	−0.159925	−	0.579849i
$217$	−170994.			−0.246508
$218$	4864.16	−	437.512i	0.00693212	−	0.000623518i
$219$	−210317.	+	210317.i	−0.296322	+	0.296322i
$220$	−115263.	+	846372.i	−0.160558	+	1.17897i
$221$	1.04258e6	+	1.04258e6i	1.43591	+	1.43591i
$222$	103384.	−	123820.i	0.140790	−	0.168620i
$223$			961659.i			1.29497i	0.762079	+	0.647484i	$0.224179\pi$
$223$			961659.i			1.29497i	−0.762079	+	0.647484i	$0.775821\pi$
$224$	−425007.	+	1.21353e6i	−0.565947	+	1.61596i
$225$	−552276.	−	402269.i	−0.727277	−	0.529737i
$226$	−781488.	−	652506.i	−1.01777	−	0.849793i
$227$	−855226.	+	855226.i	−1.10158	+	1.10158i	−0.107360	+	0.994220i	$0.534240\pi$
$227$	−855226.	+	855226.i	−1.10158	+	1.10158i	−0.994220	+	0.107360i	$0.965760\pi$
$228$	11881.8	+	65515.3i	0.0151372	+	0.0834652i
$229$	−771529.	+	771529.i	−0.972218	+	0.972218i	−0.999624	−	0.0274064i	$-0.991275\pi$
$229$	−771529.	+	771529.i	−0.972218	+	0.972218i	0.0274064	+	0.999624i	$0.491275\pi$
$230$	1.02299e6	+	234197.i	1.27512	+	0.291919i
$231$		−	523137.i		−	0.645039i
$232$	−28813.1	−	104469.i	−0.0351456	−	0.127429i
$233$	295620.			0.356734			0.178367	−	0.983964i	$-0.442919\pi$
$233$	295620.			0.356734			0.178367	+	0.983964i	$0.442919\pi$
$234$	−798549.	+	71826.4i	−0.953371	+	0.0857520i
$235$	−837592.	+	426140.i	−0.989379	+	0.503364i
$236$	−11088.7	−	7684.05i	−0.0129598	−	0.00898070i
$237$	−9607.61	+	9607.61i	−0.0111108	+	0.0111108i
$238$	2.19225e6	+	1.83043e6i	2.50870	+	2.09464i
$239$	1.43370e6			1.62355			0.811774	−	0.583972i	$-0.198502\pi$
$239$	1.43370e6			1.62355			0.811774	+	0.583972i	$0.198502\pi$
$240$	−282257.	+	12443.6i	−0.316312	+	0.0139450i
$241$	70460.4			0.0781452			0.0390726	−	0.999236i	$-0.487560\pi$
$241$	70460.4			0.0781452			0.0390726	+	0.999236i	$0.487560\pi$
$242$	290751.	+	242764.i	0.319141	+	0.266468i
$243$	537678.	−	537678.i	0.584126	−	0.584126i
$244$	819684.	−	1.18286e6i	0.881397	−	1.27192i
$245$	−822940.	−	1.61752e6i	−0.875897	−	1.72161i
$246$	98512.4	−	8860.81i	0.103789	−	0.00933546i
$247$	273291.			0.285025
$248$	121271.	+	68837.9i	0.125206	+	0.0710719i
$249$		−	107019.i		−	0.109386i
$250$	−745403.	+	648797.i	−0.754295	+	0.656536i
$251$	−550203.	+	550203.i	−0.551237	+	0.551237i	−0.926798	−	0.375561i	$-0.877450\pi$
$251$	−550203.	+	550203.i	−0.551237	+	0.551237i	0.375561	+	0.926798i	$0.377450\pi$
$252$	−1.52809e6	+	277134.i	−1.51582	+	0.274909i
$253$	1.12053e6	−	1.12053e6i	1.10058	−	1.10058i
$254$	−744795.	−	621869.i	−0.724357	−	0.604804i
$255$	−194280.	+	596711.i	−0.187102	+	0.574664i
$256$	789956.	−	689551.i	0.753361	−	0.657607i
$257$			1.21495e6i			1.14743i	0.819056	+	0.573713i	$0.194497\pi$
$257$			1.21495e6i			1.14743i	−0.819056	+	0.573713i	$0.805503\pi$
$258$	106688.	−	127777.i	0.0997853	−	0.119510i
$259$	−906816.	−	906816.i	−0.839981	−	0.839981i
$260$	−156480.	+	1.14903e6i	−0.143557	+	1.05414i
$261$	92554.6	−	92554.6i	0.0841001	−	0.0841001i
$262$	622957.	−	56032.6i	0.560667	−	0.0504298i
$263$	451461.			0.402467			0.201234	−	0.979543i	$-0.435505\pi$
$263$	451461.			0.402467			0.201234	+	0.979543i	$0.435505\pi$
$264$	−210602.	+	371015.i	−0.185974	+	0.327629i
$265$	19218.3	−	59027.0i	0.0168113	−	0.0516340i
$266$	527233.	−	47422.6i	0.456876	−	0.0410942i
$267$	267318.	+	267318.i	0.229482	+	0.229482i
$268$	−1.55054e6	−	1.07447e6i	−1.31870	−	0.913815i
$269$	43219.3	+	43219.3i	0.0364164	+	0.0364164i	0.725081	−	0.688664i	$-0.241803\pi$
$269$	43219.3	+	43219.3i	0.0364164	+	0.0364164i	−0.688664	+	0.725081i	$0.741803\pi$
$270$	−382937.	−	610331.i	−0.319682	−	0.509514i
$271$	654121.			0.541047			0.270524	−	0.962713i	$-0.412803\pi$
$271$	654121.			0.541047			0.270524	+	0.962713i	$0.412803\pi$
$272$	−817886.	−	2.18071e6i	−0.670302	−	1.78721i
$273$		−	710209.i		−	0.576739i
$274$	−621279.	+	744089.i	−0.499931	+	0.598754i
$275$	231657.	+	1.47411e6i	0.184720	+	1.17543i
$276$	430817.	+	298541.i	0.340424	+	0.235902i
$277$	355976.	+	355976.i	0.278754	+	0.278754i	0.832611	−	0.553857i	$-0.186845\pi$
$277$	355976.	+	355976.i	0.278754	+	0.278754i	−0.553857	+	0.832611i	$0.686845\pi$
$278$	−182062.	−	2.02412e6i	−0.141288	−	1.57081i
$279$			168427.i			0.129539i
$280$	−102497.	+	2.24386e6i	−0.0781295	+	1.71041i
$281$		−	2.50734e6i		−	1.89430i	−0.320794	−	0.947149i	$-0.603950\pi$
$281$		−	2.50734e6i		−	1.89430i	0.320794	−	0.947149i	$-0.396050\pi$
$282$	−467476.	+	42047.7i	−0.350055	+	0.0314861i
$283$	347736.	+	347736.i	0.258097	+	0.258097i	0.824280	−	0.566183i	$-0.191580\pi$
$283$	347736.	+	347736.i	0.258097	+	0.258097i	−0.566183	+	0.824280i	$0.691580\pi$
$284$	946570.	−	171669.i	0.696397	−	0.126298i
$285$	52744.6	+	103671.i	0.0384650	+	0.0756043i
$286$	1.34412e6	+	1.12228e6i	0.971681	+	0.811308i
$287$		−	786363.i		−	0.563532i
$288$	1.19531e6	+	418626.i	0.849179	+	0.297403i
$289$	−3.75328e6			−2.64342
$290$	−100616.	−	160363.i	−0.0702542	−	0.111972i
$291$	−484784.	−	484784.i	−0.335595	−	0.335595i
$292$	−344121.	−	1.89745e6i	−0.236186	−	1.30231i
$293$	−957669.	−	957669.i	−0.651698	−	0.651698i	0.301704	−	0.953402i	$-0.402445\pi$
$293$	−957669.	−	957669.i	−0.651698	−	0.651698i	−0.953402	+	0.301704i	$0.902445\pi$
$294$	−81200.4	−	902768.i	−0.0547886	−	0.609127i
$295$	−22409.7	−	7296.27i	−0.0149927	−	0.00488141i
$296$	278063.	+	1.00819e6i	0.184465	+	0.668823i
$297$	−1.08798e6			−0.715697
$298$	−45206.6	−	502596.i	−0.0294891	−	0.327853i
$299$	1.52123e6	−	1.52123e6i	0.984048	−	0.984048i
$300$	−466078.	+	162401.i	−0.298989	+	0.104180i
$301$	−935795.	−	935795.i	−0.595339	−	0.595339i
$302$	−314667.	−	262732.i	−0.198533	−	0.165766i
$303$		−	309313.i		−	0.193549i
$304$	−393011.	−	178619.i	−0.243905	−	0.110852i
$305$	778317.	−	2.39052e6i	0.479079	−	1.47144i
$306$	1.80295e6	−	2.15934e6i	1.10073	−	1.31831i
$307$	651375.	−	651375.i	0.394444	−	0.394444i	−0.481824	−	0.876268i	$-0.660026\pi$
$307$	651375.	−	651375.i	0.394444	−	0.394444i	0.876268	+	0.481824i	$0.160026\pi$
$308$	2.78782e6	+	1.93186e6i	1.67451	+	1.16038i
$309$	49371.6	−	49371.6i	0.0294158	−	0.0294158i
$310$	237459.	+	54362.7i	0.140341	+	0.0321289i
$311$		−	1.64203e6i		−	0.962674i	−0.876536	−	0.481337i	$-0.840151\pi$
$311$		−	1.64203e6i		−	0.962674i	0.876536	−	0.481337i	$-0.159849\pi$
$312$	−285913.	+	503689.i	−0.166283	+	0.292938i
$313$	715763.			0.412960			0.206480	−	0.978451i	$-0.433799\pi$
$313$	715763.			0.412960			0.206480	+	0.978451i	$0.433799\pi$
$314$	133151.	+	1.48034e6i	0.0762113	+	0.847299i
$315$	−2.41806e6	+	1.23023e6i	−1.37306	+	0.698569i
$316$	−15720.0	−	86678.7i	−0.00885594	−	0.0488309i
$317$	−1.47526e6	+	1.47526e6i	−0.824555	+	0.824555i	−0.986758	−	0.162202i	$-0.948140\pi$
$317$	−1.47526e6	+	1.47526e6i	−0.824555	+	0.824555i	0.162202	+	0.986758i	$0.448140\pi$
$318$	19871.1	−	23799.1i	0.0110193	−	0.0131975i
$319$	−285865.			−0.157284
$320$	976015.	−	1.55011e6i	0.532821	−	0.846228i
$321$	702507.			0.380529
$322$	2.67078e6	−	3.19872e6i	1.43548	−	1.71924i
$323$	−678018.	+	678018.i	−0.361605	+	0.361605i
$324$	239171.	+	1.31877e6i	0.126575	+	0.697921i
$325$	314496.	+	2.00124e6i	0.165161	+	1.05097i
$326$	156695.	+	1.74210e6i	0.0816605	+	0.907883i
$327$	4261.11			0.00220371
$328$	−316571.	+	557698.i	−0.162475	+	0.286230i
$329$			3.73157e6i			1.90065i
$330$	−166317.	+	726482.i	−0.0840721	+	0.367231i
$331$	1.35229e6	−	1.35229e6i	0.678420	−	0.678420i	−0.281223	−	0.959643i	$-0.590740\pi$
$331$	1.35229e6	−	1.35229e6i	0.678420	−	0.678420i	0.959643	+	0.281223i	$0.0907400\pi$
$332$	570307.	+	395202.i	0.283964	+	0.196777i
$333$	−893202.	+	893202.i	−0.441407	+	0.441407i
$334$	699089.	−	837279.i	0.342899	−	0.410681i
$335$	−3.13358e6	−	1.02025e6i	−1.52556	−	0.496699i
$336$	−464180.	+	1.02133e6i	−0.224305	+	0.493534i
$337$			1.10877e6i			0.531821i	0.963998	+	0.265910i	$0.0856726\pi$
$337$			1.10877e6i			0.531821i	−0.963998	+	0.265910i	$0.914327\pi$
$338$	212527.	+	177450.i	0.101186	+	0.0844859i
$339$	−628106.	−	628106.i	−0.296848	−	0.296848i
$340$	−2.46245e6	−	3.23889e6i	−1.15524	−	1.51949i
$341$	260102.	−	260102.i	0.121132	−	0.121132i
$342$	−46710.6	−	519318.i	−0.0215949	−	0.240087i
$343$	−3.47555e6			−1.59510
$344$	286949.	+	1.04041e6i	0.130740	+	0.474031i
$345$	870662.	+	283475.i	0.393824	+	0.128223i
$346$	−9873.10	−	109767.i	−0.00443367	−	0.0492925i
$347$	1.80080e6	+	1.80080e6i	0.802864	+	0.802864i	0.983542	−	0.180678i	$-0.0578293\pi$
$347$	1.80080e6	+	1.80080e6i	0.802864	+	0.802864i	−0.180678	+	0.983542i	$0.557829\pi$
$348$	−16872.8	−	93035.2i	−0.00746861	−	0.0411812i
$349$	722743.	+	722743.i	0.317629	+	0.317629i	0.847856	−	0.530227i	$-0.177893\pi$
$349$	722743.	+	722743.i	0.317629	+	0.317629i	−0.530227	+	0.847856i	$0.677893\pi$
$350$	953988.	+	3.80622e6i	0.416268	+	1.66082i
$351$	−1.47704e6			−0.639917
$352$	−1.19943e6	−	2.49241e6i	−0.515965	−	1.07217i
$353$			1.65970e6i			0.708915i	0.935072	+	0.354457i	$0.115334\pi$
$353$			1.65970e6i			0.708915i	−0.935072	+	0.354457i	$0.884666\pi$
$354$	−9035.36	−	7544.10i	−0.00383211	−	0.00319963i
$355$	1.49785e6	−	762059.i	0.630809	−	0.320935i
$356$	−2.41171e6	+	437386.i	−1.00855	+	0.182911i
$357$	1.76198e6	+	1.76198e6i	0.731696	+	0.731696i
$358$	−3.54150e6	+	318544.i	−1.46043	+	0.131360i
$359$		−	1.03853e6i		−	0.425288i	−0.977130	−	0.212644i	$-0.931793\pi$
$359$		−	1.03853e6i		−	0.425288i	0.977130	−	0.212644i	$-0.0682074\pi$
$360$	2.21017e6	+	100958.i	0.898815	+	0.0410568i
$361$		−	2.29837e6i		−	0.928222i
$362$	324376.	+	3.60634e6i	0.130100	+	1.44642i
$363$	233686.	+	233686.i	0.0930820	+	0.0930820i
$364$	3.78473e6	+	2.62269e6i	1.49721	+	1.03751i
$365$	−1.52759e6	−	3.00253e6i	−0.600170	−	1.17965i
$366$	804755.	−	963832.i	0.314023	−	0.376096i
$367$			1.45397e6i			0.563497i	0.959488	+	0.281748i	$0.0909144\pi$
$367$			1.45397e6i			0.563497i	−0.959488	+	0.281748i	$0.909086\pi$
$368$	−3.18187e6	+	1.19338e6i	−1.22479	+	0.459365i
$369$	−774558.			−0.296134
$370$	971000.	+	1.54759e6i	0.368735	+	0.587696i
$371$	−174296.	−	174296.i	−0.0657435	−	0.0657435i
$372$	100003.	+	69298.4i	0.0374675	+	0.0259637i
$373$	−408561.	−	408561.i	−0.152049	−	0.152049i	0.626983	−	0.779033i	$-0.284289\pi$
$373$	−408561.	−	408561.i	−0.152049	−	0.152049i	−0.779033	+	0.626983i	$0.784289\pi$
$374$	−6.11898e6	+	550378.i	−2.26204	+	0.203462i
$375$	−698461.	+	505537.i	−0.256486	+	0.185641i
$376$	1.50224e6	−	2.64647e6i	0.547986	−	0.965380i
$377$	−388089.			−0.140630
$378$	−2.84949e6	+	256301.i	−1.02574	+	0.0922615i
$379$	1.46754e6	−	1.46754e6i	0.524797	−	0.524797i	−0.394219	−	0.919016i	$-0.628985\pi$
$379$	1.46754e6	−	1.46754e6i	0.524797	−	0.524797i	0.919016	+	0.394219i	$0.128985\pi$
$380$	−747246.	−	101763.i	−0.265463	−	0.0361520i
$381$	−598615.	−	598615.i	−0.211269	−	0.211269i
$382$	−294472.	+	352680.i	−0.103249	+	0.123658i
$383$		−	3.39962e6i		−	1.18422i	−0.805856	−	0.592111i	$-0.798295\pi$
$383$		−	3.39962e6i		−	1.18422i	0.805856	−	0.592111i	$-0.201705\pi$
$384$	740363.	−	537470.i	0.256222	−	0.186006i
$385$	5.63406e6	+	1.83437e6i	1.93718	+	0.630716i
$386$	1.62404e6	+	1.35600e6i	0.554789	+	0.463223i
$387$	−921747.	+	921747.i	−0.312849	+	0.312849i
$388$	4.37366e6	−	793205.i	1.47491	−	0.267489i
$389$	2.54394e6	−	2.54394e6i	0.852380	−	0.852380i	−0.138046	−	0.990426i	$-0.544082\pi$
$389$	2.54394e6	−	2.54394e6i	0.852380	−	0.852380i	0.990426	+	0.138046i	$0.0440821\pi$
$390$	−225791.	+	986269.i	−0.0751702	+	0.328347i
$391$			7.54813e6i			2.49688i
$392$	5.11074e6	+	2.90105e6i	1.67984	+	0.953543i
$393$	545725.			0.178235
$394$	129170.	−	11618.4i	0.0419200	−	0.00377055i
$395$	−69782.7	−	137160.i	−0.0225038	−	0.0442319i
$396$	1.90286e6	−	2.74597e6i	0.609774	−	0.879949i
$397$	833324.	−	833324.i	0.265361	−	0.265361i	−0.561867	−	0.827228i	$-0.689917\pi$
$397$	833324.	−	833324.i	0.265361	−	0.265361i	0.827228	+	0.561867i	$0.189917\pi$
$398$	2.48218e6	+	2.07250e6i	0.785462	+	0.655824i
$399$	461868.			0.145240
$400$	855710.	−	3.08347e6i	0.267409	−	0.963583i
$401$	2.61069e6			0.810763			0.405381	−	0.914148i	$-0.367139\pi$
$401$	2.61069e6			0.810763			0.405381	+	0.914148i	$0.367139\pi$
$402$	−1.26343e6	−	1.05490e6i	−0.389929	−	0.325572i
$403$	353113.	−	353113.i	0.108306	−	0.108306i
$404$	1.64834e6	+	1.14224e6i	0.502451	+	0.348181i
$405$	1.06171e6	+	2.08682e6i	0.321638	+	0.632190i
$406$	−748699.	+	67342.6i	−0.225420	+	0.0202756i
$407$	2.75875e6			0.825517
$408$	−540287.	−	1.95895e6i	−0.160685	−	0.582603i
$409$			2.72635e6i			0.805886i	0.915225	+	0.402943i	$0.132013\pi$
$409$			2.72635e6i			0.805886i	−0.915225	+	0.402943i	$0.867987\pi$
$410$	−250002.	+	1.09202e6i	−0.0734487	+	0.320828i
$411$	−598047.	+	598047.i	−0.174635	+	0.174635i
$412$	80782.0	+	445425.i	0.0234461	+	0.129280i
$413$	−66171.8	+	66171.8i	−0.0190896	+	0.0190896i
$414$	−3.15070e6	−	2.63068e6i	−0.903454	−	0.754341i
$415$	1.15256e6	+	375258.i	0.328507	+	0.106957i
$416$	−1.62835e6	−	3.38368e6i	−0.461332	−	0.958641i
$417$		−	1.77318e6i		−	0.499358i
$418$	−729849.	+	874120.i	−0.204311	+	0.244698i
$419$	−1.28951e6	−	1.28951e6i	−0.358831	−	0.358831i	0.504551	−	0.863382i	$-0.331658\pi$
$419$	−1.28951e6	−	1.28951e6i	−0.358831	−	0.358831i	−0.863382	+	0.504551i	$0.831658\pi$
$420$	−264455.	+	1.94189e6i	−0.0731523	+	0.537156i
$421$	228457.	−	228457.i	0.0628203	−	0.0628203i	−0.674999	−	0.737819i	$-0.735856\pi$
$421$	228457.	−	228457.i	0.0628203	−	0.0628203i	0.737819	+	0.674999i	$0.235856\pi$
$422$	−4.03443e6	+	362881.i	−1.10281	+	0.0991935i
$423$	3.67555e6			0.998784
$424$	53445.5	+	193780.i	0.0144376	+	0.0523474i
$425$	−5.74519e6	−	4.18470e6i	−1.54288	−	1.12381i
$426$	835981.	−	75193.2i	0.223189	−	0.0200750i
$427$	−7.05876e6	−	7.05876e6i	−1.87352	−	1.87352i
$428$	−2.59424e6	+	3.74368e6i	−0.684543	+	0.987847i
$429$	1.08031e6	+	1.08031e6i	0.283404	+	0.283404i
$430$	1.00203e6	+	1.59705e6i	0.261342	+	0.416531i
$431$	338329.			0.0877297			0.0438648	−	0.999037i	$-0.486033\pi$
$431$	338329.			0.0877297			0.0438648	+	0.999037i	$0.486033\pi$
$432$	2.12407e6	+	965365.i	0.547596	+	0.248875i
$433$			5.26031e6i			1.34832i	0.738587	+	0.674158i	$0.235493\pi$
$433$			5.26031e6i			1.34832i	−0.738587	+	0.674158i	$0.764507\pi$
$434$	619951.	−	742498.i	0.157991	−	0.189222i
$435$	−74900.2	−	147219.i	−0.0189784	−	0.0373027i
$436$	−15735.6	+	22707.6i	−0.00396430	+	0.00572079i
$437$	989296.	+	989296.i	0.247812	+	0.247812i
$438$	−150729.	−	1.67577e6i	−0.0375415	−	0.417377i
$439$			65687.9i			0.0162676i	0.999967	+	0.00813381i	$0.00258910\pi$
$439$			65687.9i			0.0162676i	−0.999967	+	0.00813381i	$0.997411\pi$
$440$	−3.25727e6	−	3.56909e6i	−0.802088	−	0.878872i
$441$			7.09805e6i			1.73797i
$442$	−8.30710e6	+	747191.i	−2.02252	+	0.181918i
$443$	−4.95646e6	−	4.95646e6i	−1.19995	−	1.19995i	−0.974182	−	0.225766i	$-0.927512\pi$
$443$	−4.95646e6	−	4.95646e6i	−1.19995	−	1.19995i	−0.225766	−	0.974182i	$-0.572488\pi$
$444$	162832.	+	897841.i	0.0391996	+	0.216143i
$445$	−3.81628e6	+	1.94160e6i	−0.913568	+	0.464793i
$446$	−4.17577e6	−	3.48657e6i	−0.994029	−	0.829968i
$447$		−	440286.i		−	0.104224i
$448$	−3.72855e6	−	6.24523e6i	−0.877698	−	1.47012i
$449$	3.58664e6			0.839599			0.419799	−	0.907617i	$-0.362100\pi$
$449$	3.58664e6			0.839599			0.419799	+	0.907617i	$0.362100\pi$
$450$	3.74908e6	−	939666.i	0.872756	−	0.218747i
$451$	1.19615e6	+	1.19615e6i	0.276914	+	0.276914i
$452$	5.66669e6	−	1.02771e6i	1.30462	−	0.236605i
$453$	−252907.	−	252907.i	−0.0579050	−	0.0579050i
$454$	−612920.	−	6.81430e6i	−0.139561	−	1.55161i
$455$	7.64877e6	+	2.49033e6i	1.73206	+	0.563934i
$456$	−327562.	−	185937.i	−0.0737704	−	0.0418749i
$457$	6.58077e6			1.47396			0.736981	−	0.675914i	$-0.236251\pi$
$457$	6.58077e6			1.47396			0.736981	+	0.675914i	$0.236251\pi$
$458$	−552936.	−	6.14742e6i	−0.123172	−	1.36940i
$459$	3.66443e6	−	3.66443e6i	0.811847	−	0.811847i
$460$	−4.72586e6	+	3.59296e6i	−1.04132	+	0.791696i
$461$	259892.	+	259892.i	0.0569562	+	0.0569562i	0.735011	−	0.678055i	$-0.237177\pi$
$461$	259892.	+	259892.i	0.0569562	+	0.0569562i	−0.678055	+	0.735011i	$0.737177\pi$
$462$	2.27160e6	+	1.89668e6i	0.495138	+	0.413417i
$463$			2.74420e6i			0.594926i	0.954733	+	0.297463i	$0.0961404\pi$
$463$			2.74420e6i			0.594926i	−0.954733	+	0.297463i	$0.903860\pi$
$464$	558097.	+	253648.i	0.120341	+	0.0546936i
$465$	202101.	+	65801.2i	0.0433447	+	0.0141124i
$466$	−1.07180e6	+	1.28366e6i	−0.228637	+	0.273832i
$467$	2.71101e6	−	2.71101e6i	0.575226	−	0.575226i	−0.358358	−	0.933584i	$-0.616663\pi$
$467$	2.71101e6	−	2.71101e6i	0.575226	−	0.575226i	0.933584	+	0.358358i	$0.116663\pi$
$468$	2.58331e6	−	3.72791e6i	0.545208	−	0.786776i
$469$	−9.25289e6	+	9.25289e6i	−1.94243	+	1.94243i
$470$	1.18635e6	−	5.18204e6i	0.247724	−	1.08207i
$471$			1.29681e6i			0.269354i
$472$	73569.0	−	20290.7i	0.0151999	−	0.00419219i
$473$	2.84691e6			0.585088
$474$	−6885.54	−	76551.9i	−0.00140764	−	0.0156498i
$475$	−1.30146e6	+	204525.i	−0.264666	+	0.0415923i
$476$	−1.58964e7	+	2.88296e6i	−3.21574	+	0.583205i
$477$	−171680.	+	171680.i	−0.0345480	+	0.0345480i
$478$	−5.19801e6	+	6.22551e6i	−1.04056	+	1.24625i
$479$	3.15475e6			0.628240			0.314120	−	0.949383i	$-0.398291\pi$
$479$	3.15475e6			0.628240			0.314120	+	0.949383i	$0.398291\pi$
$480$	969310.	−	1.27075e6i	0.192026	−	0.251742i
$481$	3.74527e6			0.738108
$482$	−255460.	+	305957.i	−0.0500847	+	0.0599850i
$483$	2.57091e6	−	2.57091e6i	0.501440	−	0.501440i
$484$	−2.10828e6	+	382357.i	−0.409087	+	0.0741918i
$485$	6.92088e6	−	3.52112e6i	1.33600	−	0.679714i
$486$	385341.	+	4.28413e6i	0.0740038	+	0.822757i
$487$	−3.58080e6			−0.684160			−0.342080	−	0.939671i	$-0.611131\pi$
$487$	−3.58080e6			−0.684160			−0.342080	+	0.939671i	$0.611131\pi$
$488$	2.16447e6	+	7.84784e6i	0.411436	+	1.49177i
$489$			1.52612e6i			0.288614i
$490$	1.00073e7	+	2.29102e6i	1.88290	+	0.431061i
$491$	−543805.	+	543805.i	−0.101798	+	0.101798i	−0.756172	−	0.654373i	$-0.772932\pi$
$491$	−543805.	+	543805.i	−0.101798	+	0.101798i	0.654373	+	0.756172i	$0.272932\pi$
$492$	−318689.	+	459891.i	−0.0593545	+	0.0856530i
$493$	962822.	−	962822.i	0.178414	−	0.178414i
$494$	−990840.	+	1.18670e6i	−0.182678	+	0.218788i
$495$	1.80683e6	−	5.54948e6i	0.331439	−	1.01798i
$496$	−738588.	+	277011.i	−0.134803	+	0.0505584i
$497$		−	6.67311e6i		−	1.21182i
$498$	464702.	+	388005.i	0.0839656	+	0.0701073i
$499$	−1.60637e6	−	1.60637e6i	−0.288797	−	0.288797i	0.547807	−	0.836605i	$-0.315463\pi$
$499$	−1.60637e6	−	1.60637e6i	−0.288797	−	0.288797i	−0.836605	+	0.547807i	$0.815463\pi$
$500$	−114724.	−	5.58899e6i	−0.0205225	−	0.999789i
$501$	672947.	−	672947.i	0.119781	−	0.119781i
$502$	−394317.	−	4.38392e6i	−0.0698371	−	0.776432i
$503$	−8.92503e6			−1.57286			−0.786429	−	0.617680i	$-0.788073\pi$
$503$	−8.92503e6			−1.57286			−0.786429	+	0.617680i	$0.788073\pi$
$504$	4.33684e6	−	7.64015e6i	0.760496	−	1.33975i
$505$	3.33122e6	+	1.08460e6i	0.581266	+	0.189252i
$506$	803057.	+	8.92820e6i	0.139435	+	1.55020i
$507$	170814.	+	170814.i	0.0295124	+	0.0295124i
$508$	5.40063e6	−	979455.i	0.928507	−	0.168393i
$509$	−7.40379e6	−	7.40379e6i	−1.26666	−	1.26666i	−0.947803	−	0.318856i	$-0.896701\pi$
$509$	−7.40379e6	−	7.40379e6i	−1.26666	−	1.26666i	−0.318856	−	0.947803i	$-0.603299\pi$
$510$	−1.88669e6	−	3.00704e6i	−0.321200	−	0.511934i
$511$	−1.33766e7			−2.26618
$512$	130156.	+	5.93021e6i	0.0219426	+	0.999759i
$513$		−	960557.i		−	0.161150i
$514$	−5.27561e6	−	4.40489e6i	−0.880775	−	0.735406i
$515$	358600.	+	704840.i	0.0595788	+	0.117104i
$516$	168036.	+	926533.i	0.0277829	+	0.153192i
$517$	−5.67617e6	−	5.67617e6i	−0.933961	−	0.933961i
$518$	7.22536e6	−	649893.i	1.18314	−	0.106419i
$519$		−	96158.3i		−	0.0156700i
$520$	−4.42205e6	−	4.84538e6i	−0.717159	−	0.785813i
$521$		−	2.32522e6i		−	0.375293i	−0.982237	−	0.187646i	$-0.939914\pi$
$521$		−	2.32522e6i		−	0.375293i	0.982237	−	0.187646i	$-0.0600859\pi$
$522$	66331.6	+	737460.i	0.0106548	+	0.118457i
$523$	6.80815e6	+	6.80815e6i	1.08837	+	1.08837i	0.995697	+	0.0926688i	$0.0295398\pi$
$523$	6.80815e6	+	6.80815e6i	1.08837	+	1.08837i	0.0926688	+	0.995697i	$0.470460\pi$
$524$	−2.01527e6	+	2.90819e6i	−0.320631	+	0.462694i
$525$	531505.	+	3.38214e6i	0.0841607	+	0.535542i
$526$	−1.63681e6	+	1.96036e6i	−0.257948	+	0.308938i
$527$			1.75210e6i			0.274810i
$528$	−847487.	−	2.25963e6i	−0.132296	−	0.352739i
$529$	4.57714e6			0.711139
$530$	186633.	+	297458.i	0.0288601	+	0.0459977i
$531$	65178.4	+	65178.4i	0.0100315	+	0.0100315i
$532$	−1.70560e6	+	2.46131e6i	−0.261276	+	0.377040i
$533$	1.62389e6	+	1.62389e6i	0.247593	+	0.247593i
$534$	−2.12994e6	+	191580.i	−0.323232	+	0.0290735i
$535$	−2.46332e6	+	7.56582e6i	−0.372080	+	1.14280i
$536$	1.02873e7	−	2.83727e6i	1.54663	−	0.426569i
$537$	−3.10244e6			−0.464266
$538$	−344364.	+	30974.2i	−0.0512935	+	0.00461365i
$539$	1.09615e7	−	1.09615e7i	1.62517	−	1.62517i
$540$	4.03858e6	+	549992.i	0.595997	+	0.0811656i
$541$	−3.19138e6	−	3.19138e6i	−0.468798	−	0.468798i	0.432727	−	0.901525i	$-0.357551\pi$
$541$	−3.19138e6	−	3.19138e6i	−0.468798	−	0.468798i	−0.901525	+	0.432727i	$0.857551\pi$
$542$	−2.37157e6	+	2.84036e6i	−0.346767	+	0.415313i
$543$			3.15924e6i			0.459815i
$544$	1.24345e7	+	4.35486e6i	1.80149	+	0.630924i
$545$	−14941.5	+	45891.1i	−0.00215478	+	0.00661816i
$546$	3.08391e6	+	2.57492e6i	0.442711	+	0.369643i
$547$	−4.74228e6	+	4.74228e6i	−0.677671	+	0.677671i	−0.959473	−	0.281802i	$-0.909068\pi$
$547$	−4.74228e6	+	4.74228e6i	−0.677671	+	0.677671i	0.281802	+	0.959473i	$0.409068\pi$
$548$	−978526.	−	5.39551e6i	−0.139194	−	0.767504i
$549$	−6.95279e6	+	6.95279e6i	−0.984529	+	0.984529i
$550$	−7.24084e6	−	4.33858e6i	−1.02066	−	0.611562i
$551$		−	252385.i		−	0.0354147i
$552$	−2.85830e6	+	788333.i	−0.399264	+	0.110119i
$553$	−611066.			−0.0849718
$554$	−2.83636e6	+	255119.i	−0.392633	+	0.0353158i
$555$	722828.	+	1.42074e6i	0.0996099	+	0.195787i
$556$	9.44932e6	+	6.54805e6i	1.29632	+	0.898307i
$557$	−7.15597e6	+	7.15597e6i	−0.977305	+	0.977305i	−0.999748	−	0.0224429i	$-0.992856\pi$
$557$	−7.15597e6	+	7.15597e6i	−0.977305	+	0.977305i	0.0224429	+	0.999748i	$0.492856\pi$
$558$	−731351.	−	610644.i	−0.0994353	−	0.0830238i
$559$	3.86496e6			0.523136
$560$	−9.37180e6	−	8.58036e6i	−1.26285	−	1.15621i
$561$	−5.36037e6			−0.719097
$562$	1.08875e7	+	9.09058e6i	1.45408	+	1.21409i
$563$	5.00546e6	−	5.00546e6i	0.665538	−	0.665538i	−0.291142	−	0.956680i	$-0.594035\pi$
$563$	5.00546e6	−	5.00546e6i	0.665538	−	0.665538i	0.956680	+	0.291142i	$0.0940351\pi$
$564$	1.51229e6	−	2.18235e6i	0.200188	−	0.288886i
$565$	8.96697e6	−	4.56210e6i	1.18175	−	0.601235i
$566$	−2.77070e6	+	249214.i	−0.363537	+	0.0326987i
$567$	9.29703e6			1.21447
$568$	−2.68643e6	+	4.73265e6i	−0.349386	+	0.615508i
$569$			6.93687e6i			0.898221i	0.893476	+	0.449110i	$0.148259\pi$
$569$			6.93687e6i			0.898221i	−0.893476	+	0.449110i	$0.851741\pi$
$570$	−641397.	−	146838.i	−0.0826875	−	0.0189301i
$571$	543586.	−	543586.i	0.0697714	−	0.0697714i	−0.671360	−	0.741131i	$-0.734290\pi$
$571$	543586.	−	543586.i	0.0697714	−	0.0697714i	0.741131	+	0.671360i	$0.234290\pi$
$572$	−9.74645e6	+	1.76761e6i	−1.24554	+	0.225890i
$573$	−283460.	+	283460.i	−0.0360666	+	0.0360666i
$574$	3.41459e6	+	2.85102e6i	0.432572	+	0.361177i
$575$	−6.10590e6	+	8.38281e6i	−0.770159	+	1.05735i
$576$	−6.15147e6	+	3.67258e6i	−0.772544	+	0.461227i
$577$		−	1.24743e7i		−	1.55983i	−0.625883	−	0.779917i	$-0.715261\pi$
$577$		−	1.24743e7i		−	1.55983i	0.625883	−	0.779917i	$-0.284739\pi$
$578$	1.36078e7	−	1.62977e7i	1.69422	−	2.02912i
$579$	1.30529e6	+	1.30529e6i	0.161812	+	0.161812i
$580$	1.06113e6	+	144509.i	0.130978	+	0.0178372i
$581$	3.40331e6	−	3.40331e6i	0.418275	−	0.418275i
$582$	3.86268e6	−	347433.i	0.472695	−	0.0425171i
$583$	530250.			0.0646115
$584$	9.48685e6	+	5.38510e6i	1.15104	+	0.653374i
$585$	2.45294e6	−	7.53395e6i	0.296345	−	0.910192i
$586$	7.63054e6	−	686338.i	0.917934	−	0.0825646i
$587$	−576877.	−	576877.i	−0.0691016	−	0.0691016i	0.671711	−	0.740813i	$-0.265560\pi$
$587$	−576877.	−	576877.i	−0.0691016	−	0.0691016i	−0.740813	+	0.671711i	$0.765560\pi$
$588$	4.21445e6	+	2.92046e6i	0.502686	+	0.348344i
$589$	229639.	+	229639.i	0.0272745	+	0.0272745i
$590$	112930.	−	70855.4i	0.0133561	−	0.00837998i
$591$	113156.			0.0133263
$592$	−5.38594e6	−	2.44784e6i	−0.631622	−	0.287064i
$593$			5.63837e6i			0.658441i	0.944253	+	0.329220i	$0.106786\pi$
$593$			5.63837e6i			0.658441i	−0.944253	+	0.329220i	$0.893214\pi$
$594$	3.94455e6	−	4.72428e6i	0.458703	−	0.549376i
$595$	−2.51544e7	+	1.27978e7i	−2.91288	+	1.48198i
$596$	2.34630e6	+	1.62590e6i	0.270563	+	0.187491i
$597$	1.99500e6	+	1.99500e6i	0.229091	+	0.229091i
$598$	1.09023e6	+	1.21209e7i	0.124671	+	1.38606i
$599$		−	9.22167e6i		−	1.05013i	−0.851062	−	0.525064i	$-0.824041\pi$
$599$		−	9.22167e6i		−	1.05013i	0.851062	−	0.525064i	$-0.175959\pi$
$600$	984617.	−	2.61262e6i	0.111658	−	0.296278i
$601$			564095.i			0.0637039i	0.999493	+	0.0318519i	$0.0101405\pi$
$601$			564095.i			0.0637039i	−0.999493	+	0.0318519i	$0.989859\pi$
$602$	7.45626e6	−	670661.i	0.838551	−	0.0754244i
$603$	9.11399e6	+	9.11399e6i	1.02074	+	1.02074i
$604$	2.28170e6	−	413808.i	0.254487	−	0.0461537i
$605$	−3.33615e6	+	1.69732e6i	−0.370559	+	0.188528i
$606$	1.34312e6	+	1.12144e6i	0.148570	+	0.124049i
$607$		−	1.64721e7i		−	1.81459i	−0.420495	−	0.907295i	$-0.638144\pi$
$607$		−	1.64721e7i		−	1.81459i	0.420495	−	0.907295i	$-0.361856\pi$
$608$	2.20050e6	−	1.05896e6i	0.241414	−	0.116177i
$609$	−655878.			−0.0716605
$610$	7.55838e6	+	1.20467e7i	0.822440	+	1.31082i
$611$	−7.70594e6	−	7.70594e6i	−0.835069	−	0.835069i
$612$	2.83968e6	+	1.56577e7i	0.306472	+	1.68986i
$613$	−4.44832e6	−	4.44832e6i	−0.478129	−	0.478129i	0.426404	−	0.904533i	$-0.359780\pi$
$613$	−4.44832e6	−	4.44832e6i	−0.478129	−	0.478129i	−0.904533	+	0.426404i	$0.859780\pi$
$614$	466824.	+	5.19005e6i	0.0499727	+	0.555585i
$615$	−302605.	+	929420.i	−0.0322618	+	0.0990887i
$616$	−1.84961e7	+	5.10131e6i	−1.96394	+	0.541664i
$617$	−6.62182e6			−0.700269			−0.350134	−	0.936700i	$-0.613864\pi$
$617$	−6.62182e6			−0.700269			−0.350134	+	0.936700i	$0.613864\pi$
$618$	35383.4	+	393385.i	0.00372674	+	0.0414330i
$619$	−5.73384e6	+	5.73384e6i	−0.601477	+	0.601477i	−0.940704	−	0.339228i	$-0.889834\pi$
$619$	−5.73384e6	+	5.73384e6i	−0.601477	+	0.601477i	0.339228	+	0.940704i	$0.389834\pi$
$620$	−1.09698e6	+	834012.i	−0.114610	+	0.0871351i
$621$	−5.34677e6	−	5.34677e6i	−0.556368	−	0.556368i
$622$	7.13010e6	+	5.95330e6i	0.738958	+	0.616995i
$623$			1.70020e7i			1.75501i
$624$	−1.15054e6	−	3.06767e6i	−0.118288	−	0.315389i
$625$	−2.99537e6	−	9.29490e6i	−0.306726	−	0.951798i
$626$	−2.59505e6	+	3.10802e6i	−0.264674	+	0.316992i
$627$	−702557.	+	702557.i	−0.0713695	+	0.0713695i
$628$	−6.91075e6	−	4.78891e6i	−0.699240	−	0.484549i
$629$	−9.29176e6	+	9.29176e6i	−0.936421	+	0.936421i
$630$	3.42489e6	−	1.49601e7i	0.343792	−	1.50170i
$631$			1.61041e7i			1.61014i	0.593181	+	0.805069i	$0.297872\pi$
$631$			1.61041e7i			1.61014i	−0.593181	+	0.805069i	$0.702128\pi$
$632$	433375.	+	246000.i	0.0431590	+	0.0244987i
$633$	−3.53425e6			−0.350581
$634$	−1.05728e6	−	1.17546e7i	−0.104464	−	1.16141i
$635$	8.54595e6	−	4.34790e6i	0.841059	−	0.427903i
$636$	31297.4	+	172571.i	0.00306807	+	0.0169171i
$637$	1.48813e7	−	1.48813e7i	1.45309	−	1.45309i
$638$	1.03642e6	−	1.24130e6i	0.100806	−	0.120732i
$639$	−6.57293e6			−0.636806
$640$	3.19235e6	+	9.85815e6i	0.308078	+	0.951361i
$641$	−3.13561e6			−0.301423			−0.150712	−	0.988578i	$-0.548157\pi$
$641$	−3.13561e6			−0.301423			−0.150712	+	0.988578i	$0.548157\pi$
$642$	−2.54699e6	+	3.05046e6i	−0.243888	+	0.292098i
$643$	2.03054e6	−	2.03054e6i	0.193680	−	0.193680i	−0.603604	−	0.797284i	$-0.706269\pi$
$643$	2.03054e6	−	2.03054e6i	0.193680	−	0.193680i	0.797284	+	0.603604i	$0.206269\pi$
$644$	4.20653e6	+	2.31944e7i	0.399677	+	2.20378i
$645$	745927.	+	1.46615e6i	0.0705988	+	0.138764i
$646$	−485919.	−	5.40233e6i	−0.0458123	−	0.509331i
$647$	1.06692e6			0.100201			0.0501004	−	0.998744i	$-0.484046\pi$
$647$	1.06692e6			0.100201			0.0501004	+	0.998744i	$0.484046\pi$
$648$	−6.59357e6	−	3.74276e6i	−0.616855	−	0.350150i
$649$		−	201310.i		−	0.0187609i
$650$	−9.83013e6	−	5.89004e6i	−0.912591	−	0.546808i
$651$	596768.	−	596768.i	0.0551891	−	0.0551891i
$652$	−8.13277e6	−	5.63572e6i	−0.749237	−	0.519195i
$653$	1.00908e7	−	1.00908e7i	0.926063	−	0.926063i	−0.0713854	−	0.997449i	$-0.522742\pi$
$653$	1.00908e7	−	1.00908e7i	0.926063	−	0.926063i	0.997449	+	0.0713854i	$0.0227420\pi$
$654$	−15449.0	+	18502.8i	−0.00141239	+	0.00169159i
$655$	−1.91357e6	+	5.87732e6i	−0.174277	+	0.535274i
$656$	−1.27391e6	−	3.39661e6i	−0.115579	−	0.308167i
$657$			1.31758e7i			1.19087i
$658$	−1.62034e7	−	1.35291e7i	−1.45896	−	1.21816i
$659$	8.49791e6	+	8.49791e6i	0.762252	+	0.762252i	0.976729	−	0.214477i	$-0.0688047\pi$
$659$	8.49791e6	+	8.49791e6i	0.762252	+	0.762252i	−0.214477	+	0.976729i	$0.568805\pi$
$660$	−2.55157e6	−	3.35611e6i	−0.228007	−	0.299900i
$661$	−4.93765e6	+	4.93765e6i	−0.439558	+	0.439558i	−0.891863	−	0.452305i	$-0.850602\pi$
$661$	−4.93765e6	+	4.93765e6i	−0.439558	+	0.439558i	0.452305	+	0.891863i	$0.350602\pi$
$662$	969150.	+	1.07748e7i	0.0859501	+	0.955573i
$663$	−7.27721e6			−0.642956
$664$	−3.78376e6	+	1.04358e6i	−0.333045	+	0.0918555i
$665$	−1.61953e6	+	4.97420e6i	−0.142015	+	0.436184i
$666$	−640136.	−	7.11689e6i	−0.0559226	−	0.621734i
$667$	−1.40485e6	−	1.40485e6i	−0.122269	−	0.122269i
$668$	1.10108e6	+	6.07124e6i	0.0954722	+	0.526425i
$669$	−3.35619e6	−	3.35619e6i	−0.289922	−	0.289922i
$670$	1.57912e7	−	9.90781e6i	1.35903	−	0.852689i
$671$	2.14744e7			1.84126
$672$	−2.75194e6	−	5.71849e6i	−0.235080	−	0.488493i
$673$			8.24915e6i			0.702056i	0.936365	+	0.351028i	$0.114168\pi$
$673$			8.24915e6i			0.702056i	−0.936365	+	0.351028i	$0.885832\pi$
$674$	−4.81455e6	−	4.01992e6i	−0.408231	−	0.340854i
$675$	7.03390e6	−	1.10538e6i	0.594206	−	0.0933798i
$676$	−1.54107e6	+	279487.i	−0.129704	+	0.0235231i
$677$	−7.16246e6	−	7.16246e6i	−0.600607	−	0.600607i	0.339866	−	0.940474i	$-0.389618\pi$
$677$	−7.16246e6	−	7.16246e6i	−0.600607	−	0.600607i	−0.940474	+	0.339866i	$0.889618\pi$
$678$	5.00464e6	−	450148.i	0.418118	−	0.0376081i
$679$		−	3.08333e7i		−	2.56653i
$680$	2.29919e7	+	1.05024e6i	1.90679	+	0.0870997i
$681$		−	5.96948e6i		−	0.493252i
$682$	186409.	+	2.07245e6i	0.0153463	+	0.170617i
$683$	−907654.	−	907654.i	−0.0744506	−	0.0744506i	0.668901	−	0.743352i	$-0.266765\pi$
$683$	−907654.	−	907654.i	−0.0744506	−	0.0744506i	−0.743352	+	0.668901i	$0.766765\pi$
$684$	2.42436e6	+	1.68000e6i	0.198133	+	0.137299i
$685$	−4.34378e6	−	8.53785e6i	−0.353705	−	0.695220i
$686$	1.26009e7	−	1.50917e7i	1.02233	−	1.22441i
$687$		−	5.38528e6i		−	0.435328i
$688$	−5.55806e6	−	2.52607e6i	−0.447664	−	0.203458i
$689$	719866.			0.0577701
$690$	−4.38757e6	+	2.75287e6i	−0.350834	+	0.220122i
$691$	7.86695e6	+	7.86695e6i	0.626774	+	0.626774i	0.947255	−	0.320481i	$-0.103844\pi$
$691$	7.86695e6	+	7.86695e6i	0.626774	+	0.626774i	−0.320481	+	0.947255i	$0.603844\pi$
$692$	512431.	+	355097.i	0.0406790	+	0.0281891i
$693$	−1.63866e7	−	1.63866e7i	−1.29615	−	1.29615i
$694$	−1.43485e7	+	1.29059e6i	−1.13086	+	0.101716i
$695$	1.90967e7	+	6.21759e6i	1.49967	+	0.488270i
$696$	465156.	+	264040.i	0.0363979	+	0.0206608i
$697$	−8.05753e6			−0.628232
$698$	−5.75869e6	+	517972.i	−0.447389	+	0.0402409i
$699$	−1.03172e6	+	1.03172e6i	−0.0798670	+	0.0798670i
$700$	−1.99863e7	−	9.65728e6i	−1.54166	−	0.744920i
$701$	6.60257e6	+	6.60257e6i	0.507479	+	0.507479i	0.913752	−	0.406273i	$-0.133172\pi$
$701$	6.60257e6	+	6.60257e6i	0.507479	+	0.507479i	−0.406273	+	0.913752i	$0.633172\pi$
$702$	5.35511e6	−	6.41367e6i	0.410134	−	0.491206i
$703$			2.43565e6i			0.185877i
$704$	1.51713e7	+	3.82817e6i	1.15370	+	0.291111i
$705$	1.43597e6	−	4.41043e6i	0.108811	−	0.334201i
$706$	−7.20686e6	−	6.01739e6i	−0.544169	−	0.454356i
$707$	9.83650e6	−	9.83650e6i	0.740103	−	0.740103i
$708$	65516.9	−	11882.1i	0.00491213	−	0.000890861i
$709$	1.42731e7	−	1.42731e7i	1.06636	−	1.06636i	0.0687214	−	0.997636i	$-0.478108\pi$
$709$	1.42731e7	−	1.42731e7i	1.06636	−	1.06636i	0.997636	−	0.0687214i	$-0.0218919\pi$
$710$	−2.12153e6	+	9.26696e6i	−0.157944	+	0.689908i
$711$			601892.i			0.0446524i
$712$	6.84459e6	−	1.20580e7i	0.505996	−	0.891407i
$713$	2.55649e6			0.188330
$714$	−1.40392e7	+	1.26277e6i	−1.03061	+	0.0926997i
$715$	−1.54228e7	+	7.84661e6i	−1.12823	+	0.574007i
$716$	1.14568e7	−	1.65330e7i	0.835180	−	1.20523i
$717$	−5.00363e6	+	5.00363e6i	−0.363486	+	0.363486i
$718$	4.50956e6	+	3.76527e6i	0.326455	+	0.272575i
$719$	−9.86603e6			−0.711738			−0.355869	−	0.934536i	$-0.615815\pi$
$719$	−9.86603e6			−0.711738			−0.355869	+	0.934536i	$0.615815\pi$
$720$	−8.45155e6	+	9.23111e6i	−0.607582	+	0.663625i
$721$	3.14015e6			0.224963
$722$	9.98011e6	+	8.33292e6i	0.712512	+	0.594914i
$723$	−245907.	+	245907.i	−0.0174955	+	0.0174955i
$724$	−1.68357e7	−	1.16666e7i	−1.19367	−	0.827172i
$725$	1.84815e6	−	290437.i	0.130584	−	0.0205214i
$726$	−1.86197e6	+	167477.i	−0.131109	+	0.0117927i
$727$	864734.			0.0606801			0.0303400	−	0.999540i	$-0.490341\pi$
$727$	864734.			0.0606801			0.0303400	+	0.999540i	$0.490341\pi$
$728$	−2.51102e7	+	6.92551e6i	−1.75599	+	0.484310i
$729$		−	6.42477e6i		−	0.447753i
$730$	1.85761e7	+	4.25272e6i	1.29017	+	0.295366i
$731$	−9.58869e6	+	9.58869e6i	−0.663691	+	0.663691i
$732$	1.26750e6	+	6.98890e6i	0.0874322	+	0.482093i
$733$	−4.55613e6	+	4.55613e6i	−0.313210	+	0.313210i	−0.846152	−	0.532942i	$-0.821087\pi$
$733$	−4.55613e6	+	4.55613e6i	−0.313210	+	0.313210i	0.532942	+	0.846152i	$0.321087\pi$
$734$	−6.31353e6	−	5.27150e6i	−0.432545	−	0.361155i
$735$	8.51720e6	+	2.77308e6i	0.581539	+	0.189340i
$736$	6.35418e6	−	1.81432e7i	0.432380	−	1.23458i
$737$		−	2.81495e7i		−	1.90898i
$738$	2.80822e6	−	3.36333e6i	0.189797	−	0.227315i
$739$	7.76849e6	+	7.76849e6i	0.523270	+	0.523270i	0.918557	−	0.395288i	$-0.129355\pi$
$739$	7.76849e6	+	7.76849e6i	0.523270	+	0.523270i	−0.395288	+	0.918557i	$0.629355\pi$
$740$	−1.02405e7	−	1.39459e6i	−0.687450	−	0.0936200i
$741$	−953788.	+	953788.i	−0.0638126	+	0.0638126i
$742$	1.38876e6	−	124914.i	0.0926015	−	0.00832915i
$743$	−1.61518e7			−1.07337			−0.536685	−	0.843783i	$-0.680324\pi$
$743$	−1.61518e7			−1.07337			−0.536685	+	0.843783i	$0.680324\pi$
$744$	−663479.	+	182991.i	−0.0439435	+	0.0121198i
$745$	4.74177e6	+	1.54385e6i	0.313004	+	0.101909i
$746$	3.25534e6	−	292806.i	0.214166	−	0.0192634i
$747$	−3.35222e6	−	3.35222e6i	−0.219802	−	0.219802i
$748$	1.97950e7	−	2.85656e7i	1.29360	−	1.86676i
$749$	2.23405e7	+	2.23405e7i	1.45508	+	1.45508i
$750$	337155.	−	4.86576e6i	0.0218865	−	0.315862i
$751$	7.80825e6			0.505189			0.252595	−	0.967572i	$-0.418716\pi$
$751$	7.80825e6			0.505189			0.252595	+	0.967572i	$0.418716\pi$
$752$	6.04518e6	+	1.61181e7i	0.389820	+	1.03937i
$753$		−	3.84042e6i		−	0.246826i
$754$	1.40705e6	−	1.68518e6i	0.0901322	−	0.107949i
$755$	3.61056e6	−	1.83694e6i	0.230519	−	0.117281i
$756$	9.21814e6	−	1.33025e7i	0.586595	−	0.846501i
$757$	1.70280e7	+	1.70280e7i	1.08000	+	1.08000i	0.996509	+	0.0834890i	$0.0266064\pi$
$757$	1.70280e7	+	1.70280e7i	1.08000	+	1.08000i	0.0834890	+	0.996509i	$0.473394\pi$
$758$	1.05175e6	+	1.16931e7i	0.0664873	+	0.739191i
$759$			7.82131e6i			0.492805i
$760$	3.15108e6	−	2.87578e6i	0.197891	−	0.180602i
$761$		−	2.76106e6i		−	0.172828i	−0.996259	−	0.0864141i	$-0.972459\pi$
$761$		−	2.76106e6i		−	0.172828i	0.996259	−	0.0864141i	$-0.0275408\pi$
$762$	4.76966e6	−	429013.i	0.297578	−	0.0267660i
$763$	135508.	+	135508.i	0.00842663	+	0.00842663i
$764$	−463798.	−	2.55734e6i	−0.0287472	−	0.158510i
$765$	1.26056e7	+	2.47768e7i	0.778773	+	1.53071i
$766$	1.47620e7	+	1.23256e7i	0.909020	+	0.758989i
$767$		−	273298.i		−	0.0167744i
$768$	−350416.	+	5.16349e6i	−0.0214378	+	0.315893i
$769$	−3.18656e7			−1.94315			−0.971574	−	0.236737i	$-0.923922\pi$
$769$	−3.18656e7			−1.94315			−0.971574	+	0.236737i	$0.923922\pi$
$770$	−2.83920e7	+	1.78139e7i	−1.72572	+	1.08276i
$771$	−4.24017e6	−	4.24017e6i	−0.256890	−	0.256890i
$772$	−1.17762e7	+	2.13572e6i	−0.711148	+	0.128974i
$773$	−7.90830e6	−	7.90830e6i	−0.476030	−	0.476030i	0.427830	−	0.903859i	$-0.359278\pi$
$773$	−7.90830e6	−	7.90830e6i	−0.476030	−	0.476030i	−0.903859	+	0.427830i	$0.859278\pi$
$774$	−660593.	−	7.34432e6i	−0.0396353	−	0.440656i
$775$	−1.41732e6	+	1.94585e6i	−0.0847646	+	0.116374i
$776$	−1.24128e7	+	2.18674e7i	−0.739969	+	1.30359i
$777$	6.32958e6			0.376116
$778$	1.82318e6	+	2.02697e7i	0.107989	+	1.20060i
$779$	−1.05606e6	+	1.05606e6i	−0.0623512	+	0.0623512i
$780$	−3.46401e6	−	4.55624e6i	−0.203865	−	0.268145i
$781$	1.01506e7	+	1.01506e7i	0.595476	+	0.595476i
$782$	−3.27759e7	−	2.73663e7i	−1.91663	−	1.60029i
$783$			1.36404e6i			0.0795103i
$784$	−3.11265e7	+	1.16742e7i	−1.80859	+	0.678321i
$785$	−1.39663e7	−	4.54723e6i	−0.808924	−	0.263374i
$786$	−1.97857e6	+	2.36968e6i	−0.114234	+	0.136815i
$787$	−2.11766e7	+	2.11766e7i	−1.21876	+	1.21876i	−0.250696	+	0.968066i	$0.580659\pi$
$787$	−2.11766e7	+	2.11766e7i	−1.21876	+	1.21876i	−0.968066	+	0.250696i	$0.919341\pi$
$788$	−417867.	+	603013.i	−0.0239730	+	0.0345948i
$789$	−1.57560e6	+	1.57560e6i	−0.0901059	+	0.0901059i
$790$	848588.	+	194271.i	0.0483759	+	0.0110749i
$791$		−	3.99489e7i		−	2.27020i
$792$	5.02473e6	+	1.82184e7i	0.284642	+	1.03204i
$793$	2.91536e7			1.64630
$794$	597223.	+	6.63978e6i	0.0336190	+	0.373768i
$795$	138932.	+	273076.i	0.00779625	+	0.0153238i
$796$	−1.79987e7	+	3.26423e6i	−1.00683	+	0.182599i
$797$	7.29908e6	−	7.29908e6i	0.407026	−	0.407026i	−0.473674	−	0.880700i	$-0.657073\pi$
$797$	7.29908e6	−	7.29908e6i	0.407026	−	0.407026i	0.880700	+	0.473674i	$0.157073\pi$
$798$	−1.67454e6	+	2.00555e6i	−0.0930868	+	0.111487i
$799$	3.82358e7			2.11887
$800$	1.02867e7	+	1.48951e7i	0.568268	+	0.822844i
$801$	1.67468e7			0.922252
$802$	−9.46525e6	+	1.13363e7i	−0.519632	+	0.622349i
$803$	2.03474e7	−	2.03474e7i	1.11358	−	1.11358i
$804$	9.16131e6	−	1.66149e6i	0.499825	−	0.0906479i
$805$	1.86732e7	+	3.67028e7i	1.01562	+	1.99623i
$806$	253067.	+	2.81355e6i	0.0137214	+	0.152551i
$807$	−301671.			−0.0163061
$808$	−1.09361e7	+	3.01623e6i	−0.589297	+	0.162531i
$809$			2.30201e7i			1.23662i	0.785935	+	0.618309i	$0.212182\pi$
$809$			2.30201e7i			1.23662i	−0.785935	+	0.618309i	$0.787818\pi$
$810$	−1.29108e7	−	2.95573e6i	−0.691418	−	0.158290i
$811$	367830.	−	367830.i	0.0196379	−	0.0196379i	−0.697220	−	0.716858i	$-0.745580\pi$
$811$	367830.	−	367830.i	0.0196379	−	0.0196379i	0.716858	+	0.697220i	$0.245580\pi$
$812$	2.42205e6	−	3.49520e6i	0.128912	−	0.186029i
$813$	−2.28289e6	+	2.28289e6i	−0.121132	+	0.121132i
$814$	−1.00021e7	+	1.19792e7i	−0.529089	+	0.633675i
$815$	−1.64360e7	−	5.35131e6i	−0.866764	−	0.282206i
$816$	1.04651e7	+	4.75626e6i	0.550197	+	0.250058i
$817$			2.51349e6i			0.131741i
$818$	−1.18385e7	−	9.88460e6i	−0.618605	−	0.516507i
$819$	−2.22464e7	−	2.22464e7i	−1.15891	−	1.15891i
$820$	−3.83544e6	−	5.04479e6i	−0.199196	−	0.262004i
$821$	1.92296e7	−	1.92296e7i	0.995663	−	0.995663i	−0.00432789	−	0.999991i	$-0.501378\pi$
$821$	1.92296e7	−	1.92296e7i	0.995663	−	0.995663i	0.999991	+	0.00432789i	$0.00137762\pi$
$822$	−428606.	−	4.76514e6i	−0.0221248	−	0.245978i
$823$	−2.24215e7			−1.15389			−0.576947	−	0.816782i	$-0.695756\pi$
$823$	−2.24215e7			−1.15389			−0.576947	+	0.816782i	$0.695756\pi$
$824$	−2.22703e6	−	1.26415e6i	−0.114264	−	0.0648603i
$825$	−5.95312e6	−	4.33616e6i	−0.304516	−	0.221804i
$826$	−47423.7	−	527246.i	−0.00241850	−	0.0268883i
$827$	1.76422e7	+	1.76422e7i	0.896993	+	0.896993i	0.995169	−	0.0981762i	$-0.0313009\pi$
$827$	1.76422e7	+	1.76422e7i	0.896993	+	0.896993i	−0.0981762	+	0.995169i	$0.531301\pi$
$828$	2.28462e7	−	4.14338e6i	1.15808	−	0.210029i
$829$	8.75846e6	+	8.75846e6i	0.442630	+	0.442630i	0.892895	−	0.450265i	$-0.148670\pi$
$829$	8.75846e6	+	8.75846e6i	0.442630	+	0.442630i	−0.450265	+	0.892895i	$0.648670\pi$
$830$	−5.80818e6	+	3.64420e6i	−0.292647	+	0.183614i
$831$	−2.48471e6			−0.124817
$832$	2.05965e7	+	5.19710e6i	1.03154	+	0.260287i
$833$			7.38392e7i			3.68701i
$834$	7.69958e6	+	6.42879e6i	0.383312	+	0.320047i
$835$	4.88780e6	+	9.60714e6i	0.242604	+	0.476846i
$836$	−1.14953e6	−	6.33838e6i	−0.0568857	−	0.313662i
$837$	−1.24111e6	−	1.24111e6i	−0.0612346	−	0.0612346i
$838$	1.02746e7	−	924160.i	0.505423	−	0.0454608i
$839$			3.24026e7i			1.58919i	0.607141	+	0.794594i	$0.292316\pi$
$839$			3.24026e7i			1.58919i	−0.607141	+	0.794594i	$0.707684\pi$
$840$	−7.47336e6	−	8.18879e6i	−0.365441	−	0.400425i
$841$		−	2.01527e7i		−	0.982527i
$842$	163730.	+	1.82031e6i	0.00795880	+	0.0884841i
$843$	8.75064e6	+	8.75064e6i	0.424103	+	0.424103i
$844$	1.30514e7	−	1.88342e7i	0.630669	−	0.910103i
$845$	−2.43858e6	+	1.24067e6i	−0.117489	+	0.0597744i
$846$	−1.33260e7	+	1.59602e7i	−0.640139	+	0.766676i
$847$			1.48629e7i			0.711862i
$848$	−1.03521e6	−	470492.i	−0.0494357	−	0.0224679i
$849$	−2.42720e6			−0.115568
$850$	3.90007e7	−	9.77511e6i	1.85150	−	0.464060i
$851$	1.35576e7	+	1.35576e7i	0.641740	+	0.641740i
$852$	−2.70441e6	+	3.90266e6i	−0.127636	+	0.184188i
$853$	−1.38251e7	−	1.38251e7i	−0.650573	−	0.650573i	0.302558	−	0.953131i	$-0.402159\pi$
$853$	−1.38251e7	−	1.38251e7i	−0.650573	−	0.650573i	−0.953131	+	0.302558i	$0.902159\pi$
$854$	5.62430e7	−	5.05884e6i	2.63891	−	0.237359i
$855$	4.89953e6	+	1.59522e6i	0.229213	+	0.0746284i
$856$	−6.85041e6	−	2.48379e7i	−0.319545	−	1.15859i
$857$	−1.34067e7			−0.623546			−0.311773	−	0.950157i	$-0.600923\pi$
$857$	−1.34067e7			−0.623546			−0.311773	+	0.950157i	$0.600923\pi$
$858$	−8.60775e6	+	774234.i	−0.399183	+	0.0359049i
$859$	−9.16200e6	+	9.16200e6i	−0.423650	+	0.423650i	−0.886458	−	0.462808i	$-0.846842\pi$
$859$	−9.16200e6	+	9.16200e6i	−0.423650	+	0.423650i	0.462808	+	0.886458i	$0.346842\pi$
$860$	−1.05677e7	−	1.43916e6i	−0.487232	−	0.0663534i
$861$	2.74441e6	+	2.74441e6i	0.126166	+	0.126166i
$862$	−1.22664e6	+	1.46911e6i	−0.0562275	+	0.0673421i
$863$		−	4.05570e7i		−	1.85370i	−0.375434	−	0.926849i	$-0.622506\pi$
$863$		−	4.05570e7i		−	1.85370i	0.375434	−	0.926849i	$-0.377494\pi$
$864$	−1.18929e7	+	5.72327e6i	−0.542003	+	0.260831i
$865$	1.03560e6	+	337176.i	0.0470600	+	0.0153220i
$866$	−2.28416e7	−	1.90717e7i	−1.03498	−	0.864160i
$867$	1.30990e7	−	1.30990e7i	0.591820	−	0.591820i
$868$	976434.	+	5.38397e6i	0.0439889	+	0.242551i
$869$	929504.	−	929504.i	0.0417544	−	0.0417544i
$870$	910819.	+	208518.i	0.0407975	+	0.00933997i
$871$		−	3.82157e7i		−	1.70685i
$872$	−41551.7	−	150656.i	−0.00185054	−	0.00670959i
$873$	−3.03705e7			−1.34870
$874$	−7.88255e6	+	709004.i	−0.349050	+	0.0313957i
$875$	−3.82885e7	−	6.13520e6i	−1.69063	−	0.270900i
$876$	7.82309e6	+	5.42113e6i	0.344444	+	0.238687i
$877$	−4.28148e6	+	4.28148e6i	−0.187973	+	0.187973i	−0.794819	−	0.606846i	$-0.792434\pi$
$877$	−4.28148e6	+	4.28148e6i	−0.187973	+	0.187973i	0.606846	+	0.794819i	$0.292434\pi$
$878$	−285234.	−	238157.i	−0.0124872	−	0.0104262i
$879$	6.68453e6			0.291809
$880$	2.73074e7	−	1.20388e6i	1.18870	−	0.0524054i
$881$	−1.08150e6			−0.0469449			−0.0234725	−	0.999724i	$-0.507472\pi$
$881$	−1.08150e6			−0.0469449			−0.0234725	+	0.999724i	$0.507472\pi$
$882$	−3.08215e7	−	2.57345e7i	−1.33408	−	1.11390i
$883$	1.36983e7	−	1.36983e7i	0.591242	−	0.591242i	−0.346725	−	0.937967i	$-0.612706\pi$
$883$	1.36983e7	−	1.36983e7i	0.591242	−	0.591242i	0.937967	+	0.346725i	$0.112706\pi$
$884$	2.68736e7	−	3.87805e7i	1.15663	−	1.66910i
$885$	103674.	−	52745.9i	0.00444950	−	0.00226376i
$886$	3.94922e7	−	3.55217e6i	1.69016	−	0.152023i
$887$	−1.64146e7			−0.700521			−0.350261	−	0.936652i	$-0.613907\pi$
$887$	−1.64146e7			−0.700521			−0.350261	+	0.936652i	$0.613907\pi$
$888$	−4.48901e6	−	2.54813e6i	−0.191037	−	0.108440i
$889$		−	3.80732e7i		−	1.61572i
$890$	5.40531e6	−	2.36107e7i	0.228742	−	0.999158i
$891$	−1.41419e7	+	1.41419e7i	−0.596779	+	0.596779i
$892$	3.02792e7	−	5.49141e6i	1.27418	−	0.231085i
$893$	5.01138e6	−	5.01138e6i	0.210295	−	0.210295i
$894$	1.91183e6	+	1.59629e6i	0.0800030	+	0.0667988i
$895$	1.08786e7	−	3.34124e7i	0.453958	−	1.39428i
$896$	4.06365e7	+	6.45225e6i	1.69101	+	0.268498i
$897$			1.06182e7i			0.440625i
$898$	−1.30036e7	+	1.55741e7i	−0.538114	+	0.644484i
$899$	−326100.	−	326100.i	−0.0134571	−	0.0134571i
$900$	−9.51230e6	+	1.96863e7i	−0.391453	+	0.810135i
$901$	−1.78594e6	+	1.78594e6i	−0.0732916	+	0.0732916i
$902$	−9.53074e6	+	857253.i	−0.390041	+	0.0350827i
$903$	6.53185e6			0.266574
$904$	−1.60825e7	+	2.83323e7i	−0.654533	+	1.15308i
$905$	−3.40242e7	−	1.10778e7i	−1.38091	−	0.449605i
$906$	2.01512e6	−	181253.i	0.0815607	−	0.00733607i
$907$	−2.68794e7	−	2.68794e7i	−1.08493	−	1.08493i	−0.996042	−	0.0888882i	$-0.971669\pi$
$907$	−2.68794e7	−	2.68794e7i	−1.08493	−	1.08493i	−0.0888882	−	0.996042i	$-0.528331\pi$
$908$	3.18116e7	+	2.20443e7i	1.28047	+	0.887324i
$909$	−9.68883e6	−	9.68883e6i	−0.388921	−	0.388921i
$910$	−3.85449e7	+	2.41840e7i	−1.54299	+	0.968111i
$911$	−1.66805e7			−0.665905			−0.332952	−	0.942944i	$-0.608045\pi$
$911$	−1.66805e7			−0.665905			−0.332952	+	0.942944i	$0.608045\pi$
$912$	1.99499e6	−	748231.i	0.0794243	−	0.0297885i
$913$			1.03537e7i			0.411072i
$914$	−2.38591e7	+	2.85754e7i	−0.944688	+	1.13143i
$915$	5.62658e6	+	1.10592e7i	0.222173	+	0.436689i
$916$	2.86984e7	+	1.98870e7i	1.13010	+	0.783122i
$917$	1.73547e7	+	1.73547e7i	0.681542	+	0.681542i
$918$	2.62621e6	+	2.91975e7i	0.102854	+	1.14351i
$919$			2.61235e7i			1.02034i	0.860075	+	0.510168i	$0.170417\pi$
$919$			2.61235e7i			1.02034i	−0.860075	+	0.510168i	$0.829583\pi$
$920$	1.53241e6	−	3.35475e7i	0.0596904	−	1.30674i
$921$			4.54660e6i			0.176619i
$922$	−2.07078e6	+	186258.i	−0.0802244	+	0.00721587i
$923$	1.37804e7	+	1.37804e7i	0.532424	+	0.532424i
$924$	−1.64717e7	+	2.98730e6i	−0.634685	+	0.115106i
$925$	−1.78356e7	+	2.80288e6i	−0.685384	+	0.107708i
$926$	−1.19160e7	−	9.94930e6i	−0.456671	−	0.381299i
$927$		−	3.09300e6i		−	0.118217i
$928$	−3.12483e6	+	1.50378e6i	−0.119112	+	0.0573210i
$929$	−2.38162e7			−0.905386			−0.452693	−	0.891666i	$-0.649537\pi$
$929$	−2.38162e7			−0.905386			−0.452693	+	0.891666i	$0.649537\pi$
$930$	−1.01846e6	+	639007.i	−0.0386132	+	0.0242269i
$931$	9.67774e6	+	9.67774e6i	0.365931	+	0.365931i
$932$	−1.68810e6	−	9.30802e6i	−0.0636587	−	0.351008i
$933$	5.73068e6	+	5.73068e6i	0.215527	+	0.215527i
$934$	1.94291e6	+	2.16009e7i	0.0728763	+	0.810222i
$935$	1.87960e7	−	5.77298e7i	0.703130	−	2.15959i
$936$	6.82155e6	+	2.47333e7i	0.254503	+	0.922766i
$937$	3.24217e7			1.20639			0.603194	−	0.797595i	$-0.293895\pi$
$937$	3.24217e7			1.20639			0.603194	+	0.797595i	$0.293895\pi$
$938$	−6.63132e6	−	7.37255e7i	−0.246090	−	2.73597i
$939$	−2.49801e6	+	2.49801e6i	−0.0924551	+	0.0924551i
$940$	1.82005e7	+	2.39393e7i	0.671838	+	0.883675i
$941$	−2.51652e7	−	2.51652e7i	−0.926458	−	0.926458i	0.0710169	−	0.997475i	$-0.477376\pi$
$941$	−2.51652e7	−	2.51652e7i	−0.926458	−	0.926458i	−0.997475	+	0.0710169i	$0.977376\pi$
$942$	−5.63108e6	−	4.70169e6i	−0.206759	−	0.172634i
$943$			1.17567e7i			0.430534i
$944$	−178623.	+	393021.i	−0.00652389	+	0.0143544i
$945$	8.75293e6	−	2.68837e7i	0.318841	−	0.979285i
$946$	−1.03217e7	+	1.23620e7i	−0.374993	+	0.449119i
$947$	−3.13328e7	+	3.13328e7i	−1.13534	+	1.13534i	−0.146061	+	0.989276i	$0.546660\pi$
$947$	−3.13328e7	+	3.13328e7i	−1.13534	+	1.13534i	−0.989276	+	0.146061i	$0.953340\pi$
$948$	357372.	+	247646.i	0.0129151	+	0.00894974i
$949$	2.76236e7	−	2.76236e7i	0.995668	−	0.995668i
$950$	3.83045e6	−	6.39280e6i	0.137702	−	0.229817i
$951$		−	1.02973e7i		−	0.369209i
$952$	4.51150e7	−	7.94785e7i	1.61335	−	2.84222i
$953$	1.91722e7			0.683816			0.341908	−	0.939733i	$-0.388927\pi$
$953$	1.91722e7			0.683816			0.341908	+	0.939733i	$0.388927\pi$
$954$	−123039.	−	1.36791e6i	−0.00437694	−	0.0486618i
$955$	−2.05885e6	−	4.04674e6i	−0.0730493	−	0.143581i
$956$	−8.18696e6	−	4.51422e7i	−0.289720	−	1.59749i
$957$	997668.	−	997668.i	0.0352133	−	0.0352133i
$958$	−1.14378e7	+	1.36987e7i	−0.402651	+	0.482243i
$959$	−3.80371e7			−1.33555
$960$	2.00359e6	+	8.81618e6i	0.0701666	+	0.308747i
$961$	−2.80357e7			−0.979272
$962$	−1.35788e7	+	1.62629e7i	−0.473067	+	0.566579i
$963$	2.20051e7	−	2.20051e7i	0.764642	−	0.764642i
$964$	−402354.	−	2.21854e6i	−0.0139449	−	0.0768909i
$965$	−1.86346e7	+	9.48067e6i	−0.644171	+	0.327733i
$966$	1.84251e6	+	2.04846e7i	0.0635282	+	0.706291i
$967$	3.64829e7			1.25465			0.627326	−	0.778757i	$-0.284149\pi$
$967$	3.64829e7			1.25465			0.627326	+	0.778757i	$0.284149\pi$
$968$	5.98346e6	−	1.05410e7i	0.205241	−	0.361570i
$969$		−	4.73257e6i		−	0.161915i
$970$	−9.80260e6	+	4.28183e7i	−0.334512	+	1.46117i
$971$	−1.74107e7	+	1.74107e7i	−0.592608	+	0.592608i	−0.938335	−	0.345727i	$-0.887632\pi$
$971$	−1.74107e7	+	1.74107e7i	−0.592608	+	0.592608i	0.345727	+	0.938335i	$0.387632\pi$
$972$	−1.99999e7	−	1.38592e7i	−0.678987	−	0.470514i
$973$	5.63890e7	−	5.63890e7i	1.90947	−	1.90947i
$974$	1.29825e7	−	1.55488e7i	0.438491	−	0.525168i
$975$	−8.08193e6	−	5.88675e6i	−0.272272	−	0.198319i
$976$	−4.19248e7	−	1.90543e7i	−1.40879	−	0.640277i
$977$			3.27363e7i			1.09722i	0.836079	+	0.548609i	$0.184842\pi$
$977$			3.27363e7i			1.09722i	−0.836079	+	0.548609i	$0.815158\pi$
$978$	−6.62681e6	−	5.53308e6i	−0.221543	−	0.184978i
$979$	−2.58621e7	−	2.58621e7i	−0.862396	−	0.862396i
$980$	−4.62305e7	+	3.51480e7i	−1.53767	+	1.16906i
$981$	133474.	−	133474.i	0.00442817	−	0.00442817i
$982$	−389732.	−	4.33295e6i	−0.0128970	−	0.143385i
$983$	−4.69454e7			−1.54956			−0.774782	−	0.632229i	$-0.782140\pi$
$983$	−4.69454e7			−1.54956			−0.774782	+	0.632229i	$0.782140\pi$
$984$	−841535.	−	3.05120e6i	−0.0277067	−	0.100458i
$985$	−396779.	+	1.21866e6i	−0.0130304	+	0.0400214i
$986$	690031.	+	7.67160e6i	0.0226035	+	0.251301i
$987$	−1.30232e7	−	1.30232e7i	−0.425525	−	0.425525i
$988$	−1.56059e6	−	8.60496e6i	−0.0508624	−	0.280451i
$989$	1.39909e7	+	1.39909e7i	0.454835	+	0.454835i
$990$	1.75464e7	+	2.79658e7i	0.568985	+	0.906857i
$991$	−3.48347e7			−1.12675			−0.563375	−	0.826201i	$-0.690497\pi$
$991$	−3.48347e7			−1.12675			−0.563375	+	0.826201i	$0.690497\pi$
$992$	1.47496e6	−	4.21146e6i	0.0475883	−	0.135879i
$993$			9.43896e6i			0.303774i
$994$	2.89763e7	+	2.41939e7i	0.930203	+	0.776676i
$995$	−2.84811e7	+	1.44903e7i	−0.912009	+	0.464000i
$996$	−3.36963e6	+	611114.i	−0.107630	+	0.0195197i
$997$	1.71344e7	+	1.71344e7i	0.545923	+	0.545923i	0.925259	−	0.379336i	$-0.123847\pi$
$997$	1.71344e7	+	1.71344e7i	0.545923	+	0.545923i	−0.379336	+	0.925259i	$0.623847\pi$
$998$	1.27993e7	−	1.15124e6i	0.406779	−	0.0365882i
$999$		−	1.31638e7i		−	0.417317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.17	✓	116
5.4	even	2	inner	80.6.q.a.29.42	yes	116
16.5	even	4	inner	80.6.q.a.69.42	yes	116
80.69	even	4	inner	80.6.q.a.69.17	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.17	✓	116	1.1	even	1	trivial
80.6.q.a.29.42	yes	116	5.4	even	2	inner
80.6.q.a.69.17	yes	116	80.69	even	4	inner
80.6.q.a.69.42	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)

\(f(q)\)	\(=\)	\(q+(-3.62558 + 4.34225i) q^{2} +(-3.49000 + 3.49000i) q^{3} +(-5.71035 - 31.4864i) q^{4} +(-25.3489 - 49.8240i) q^{5} +(-2.50120 - 27.8078i) q^{6} -221.972 q^{7} +(157.425 + 89.3605i) q^{8} +218.640i q^{9} +O(q^{10})\)	\(q+(-3.62558 + 4.34225i) q^{2} +(-3.49000 + 3.49000i) q^{3} +(-5.71035 - 31.4864i) q^{4} +(-25.3489 - 49.8240i) q^{5} +(-2.50120 - 27.8078i) q^{6} -221.972 q^{7} +(157.425 + 89.3605i) q^{8} +218.640i q^{9} +(308.253 + 70.5698i) q^{10} +(337.646 - 337.646i) q^{11} +(129.817 + 89.9584i) q^{12} +(458.387 - 458.387i) q^{13} +(804.777 - 963.859i) q^{14} +(262.354 + 85.4185i) q^{15} +(-958.784 + 359.597i) q^{16} +2274.45i q^{17} +(-949.390 - 792.696i) q^{18} +(298.101 + 298.101i) q^{19} +(-1424.03 + 1082.66i) q^{20} +(774.683 - 774.683i) q^{21} +(241.983 + 2690.31i) q^{22} +3318.66 q^{23} +(-861.283 + 237.546i) q^{24} +(-1839.87 + 2525.96i) q^{25} +(328.515 + 3652.35i) q^{26} +(-1611.12 - 1611.12i) q^{27} +(1267.54 + 6989.09i) q^{28} +(-423.320 - 423.320i) q^{29} +(-1322.09 + 829.515i) q^{30} +770.338 q^{31} +(1914.69 - 5467.03i) q^{32} +2356.77i q^{33} +(-9876.26 - 8246.21i) q^{34} +(5626.74 + 11059.5i) q^{35} +(6884.17 - 1248.51i) q^{36} +(4085.27 + 4085.27i) q^{37} +(-2375.22 + 213.642i) q^{38} +3199.54i q^{39} +(461.755 - 10108.7i) q^{40} +3542.62i q^{41} +(555.197 + 6172.55i) q^{42} +(4215.82 + 4215.82i) q^{43} +(-12559.3 - 8703.17i) q^{44} +(10893.5 - 5542.27i) q^{45} +(-12032.1 + 14410.5i) q^{46} -16811.0i q^{47} +(2091.16 - 4601.15i) q^{48} +32464.6 q^{49} +(-4297.78 - 17147.3i) q^{50} +(-7937.85 - 7937.85i) q^{51} +(-17050.5 - 11815.4i) q^{52} +(785.216 + 785.216i) q^{53} +(12837.2 - 1154.65i) q^{54} +(-25381.8 - 8263.95i) q^{55} +(-34944.0 - 19835.5i) q^{56} -2080.75 q^{57} +(3372.94 - 303.383i) q^{58} +(298.109 - 298.109i) q^{59} +(1191.39 - 8748.34i) q^{60} +(31800.2 + 31800.2i) q^{61} +(-2792.92 + 3345.01i) q^{62} -48531.9i q^{63} +(16797.4 + 28135.2i) q^{64} +(-34458.3 - 11219.1i) q^{65} +(-10233.7 - 8544.66i) q^{66} +(41685.0 - 41685.0i) q^{67} +(71614.3 - 12987.9i) q^{68} +(-11582.1 + 11582.1i) q^{69} +(-68423.5 - 15664.5i) q^{70} +30062.8i q^{71} +(-19537.8 + 34419.4i) q^{72} +60262.6 q^{73} +(-32550.7 + 2927.81i) q^{74} +(-2394.47 - 15236.8i) q^{75} +(7683.87 - 11088.4i) q^{76} +(-74948.0 + 74948.0i) q^{77} +(-13893.2 - 11600.2i) q^{78} +2752.89 q^{79} +(42220.6 + 38655.1i) q^{80} -41883.8 q^{81} +(-15383.0 - 12844.1i) q^{82} +(-15332.2 + 15332.2i) q^{83} +(-28815.7 - 19968.3i) q^{84} +(113322. - 57654.8i) q^{85} +(-33591.0 + 3021.38i) q^{86} +2954.78 q^{87} +(83326.2 - 22981.8i) q^{88} -76595.2i q^{89} +(-15429.4 + 67396.4i) q^{90} +(-101749. + 101749. i) q^{91} +(-18950.7 - 104492. i) q^{92} +(-2688.48 + 2688.48i) q^{93} +(72997.6 + 60949.6i) q^{94} +(7296.09 - 22409.1i) q^{95} +(12397.7 + 25762.2i) q^{96} +138906. i q^{97} +(-117703. + 140969. i) q^{98} +(73822.8 + 73822.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

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