LMFDB - Embedded newform 80.6.l.a.21.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

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, 1, 0]))

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.l (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:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.19
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.350398 + 5.64599i) q^{2} +(-18.9032 + 18.9032i) q^{3} +(-31.7544 - 3.95669i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-100.104 - 113.351i) q^{6} -174.451i q^{7} +(33.4661 - 177.899i) q^{8} -471.664i q^{9} +O(q^{10})$	\(q+(-0.350398 + 5.64599i) q^{2} +(-18.9032 + 18.9032i) q^{3} +(-31.7544 - 3.95669i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-100.104 - 113.351i) q^{6} -174.451i q^{7} +(33.4661 - 177.899i) q^{8} -471.664i q^{9} +(-106.002 + 93.6138i) q^{10} +(189.274 + 189.274i) q^{11} +(675.056 - 525.467i) q^{12} +(-782.038 + 782.038i) q^{13} +(984.949 + 61.1273i) q^{14} -668.330 q^{15} +(992.689 + 251.285i) q^{16} -923.717 q^{17} +(2663.01 + 165.270i) q^{18} +(898.863 - 898.863i) q^{19} +(-491.399 - 631.290i) q^{20} +(3297.69 + 3297.69i) q^{21} +(-1134.96 + 1002.32i) q^{22} -3820.93i q^{23} +(2730.25 + 3995.48i) q^{24} +625.000i q^{25} +(-4141.36 - 4689.41i) q^{26} +(4322.49 + 4322.49i) q^{27} +(-690.248 + 5539.59i) q^{28} +(978.529 - 978.529i) q^{29} +(234.182 - 3773.39i) q^{30} +4974.58 q^{31} +(-1766.59 + 5516.67i) q^{32} -7155.78 q^{33} +(323.669 - 5215.30i) q^{34} +(3083.89 - 3083.89i) q^{35} +(-1866.23 + 14977.4i) q^{36} +(-5788.44 - 5788.44i) q^{37} +(4760.01 + 5389.93i) q^{38} -29566.1i q^{39} +(3736.44 - 2553.23i) q^{40} -639.645i q^{41} +(-19774.2 + 17463.2i) q^{42} +(8062.21 + 8062.21i) q^{43} +(-5261.39 - 6759.19i) q^{44} +(8337.92 - 8337.92i) q^{45} +(21573.0 + 1338.85i) q^{46} +22043.6 q^{47} +(-23515.1 + 14014.9i) q^{48} -13626.1 q^{49} +(-3528.74 - 218.999i) q^{50} +(17461.2 - 17461.2i) q^{51} +(27927.5 - 21738.9i) q^{52} +(-14377.5 - 14377.5i) q^{53} +(-25919.3 + 22890.2i) q^{54} +6691.84i q^{55} +(-31034.6 - 5838.20i) q^{56} +33982.8i q^{57} +(5181.89 + 5867.64i) q^{58} +(-28515.2 - 28515.2i) q^{59} +(21222.4 + 2644.37i) q^{60} +(19210.1 - 19210.1i) q^{61} +(-1743.08 + 28086.4i) q^{62} -82282.3 q^{63} +(-30528.0 - 11907.2i) q^{64} -27649.2 q^{65} +(2507.37 - 40401.5i) q^{66} +(-25147.9 + 25147.9i) q^{67} +(29332.1 + 3654.86i) q^{68} +(72228.0 + 72228.0i) q^{69} +(16331.0 + 18492.2i) q^{70} -52863.6i q^{71} +(-83908.5 - 15784.8i) q^{72} -20764.0i q^{73} +(34709.7 - 30653.2i) q^{74} +(-11814.5 - 11814.5i) q^{75} +(-32099.4 + 24986.4i) q^{76} +(33019.0 - 33019.0i) q^{77} +(166930. + 10359.9i) q^{78} -51350.5 q^{79} +(13106.3 + 21990.6i) q^{80} -48803.7 q^{81} +(3611.43 + 224.130i) q^{82} +(18480.4 - 18480.4i) q^{83} +(-91668.3 - 117764. i) q^{84} +(-16329.2 - 16329.2i) q^{85} +(-48344.1 + 42694.2i) q^{86} +36994.7i q^{87} +(40005.9 - 27337.4i) q^{88} +53694.4i q^{89} +(44154.2 + 49997.4i) q^{90} +(136427. + 136427. i) q^{91} +(-15118.2 + 121332. i) q^{92} +(-94035.5 + 94035.5i) q^{93} +(-7724.04 + 124458. i) q^{94} +31779.6 q^{95} +(-70888.6 - 137677. i) q^{96} +52155.5 q^{97} +(4774.58 - 76933.1i) q^{98} +(89273.7 - 89273.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.350398	+	5.64599i	−0.0619422	+	0.998080i
$2$	−0.350398	+	5.64599i	−0.0619422	+	0.998080i
$3$	−18.9032	+	18.9032i	−1.21264	+	1.21264i	−0.242488	+	0.970154i	$0.577964\pi$
$3$	−18.9032	+	18.9032i	−1.21264	+	1.21264i	−0.970154	+	0.242488i	$0.922036\pi$
$4$	−31.7544	−	3.95669i	−0.992326	−	0.123647i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$	−100.104	−	113.351i	−1.13520	−	1.28543i
$7$		−	174.451i		−	1.34564i	−0.739807	−	0.672819i	$-0.765083\pi$
$7$		−	174.451i		−	1.34564i	0.739807	−	0.672819i	$-0.234917\pi$
$8$	33.4661	−	177.899i	0.184876	−	0.982762i
$9$		−	471.664i		−	1.94100i
$10$	−106.002	+	93.6138i	−0.335208	+	0.296033i
$11$	189.274	+	189.274i	0.471638	+	0.471638i	0.902444	−	0.430806i	$-0.141771\pi$
$11$	189.274	+	189.274i	0.471638	+	0.471638i	−0.430806	+	0.902444i	$0.641771\pi$
$12$	675.056	−	525.467i	1.35328	−	1.05340i
$13$	−782.038	+	782.038i	−1.28342	+	1.28342i	−0.344715	+	0.938707i	$0.612024\pi$
$13$	−782.038	+	782.038i	−1.28342	+	1.28342i	−0.938707	+	0.344715i	$0.887976\pi$
$14$	984.949	+	61.1273i	1.34305	+	0.0833518i
$15$	−668.330			−0.766943
$16$	992.689	+	251.285i	0.969423	+	0.245395i
$17$	−923.717			−0.775205			−0.387603	−	0.921827i	$-0.626697\pi$
$17$	−923.717			−0.775205			−0.387603	+	0.921827i	$0.626697\pi$
$18$	2663.01	+	165.270i	1.93728	+	0.120230i
$19$	898.863	−	898.863i	0.571228	−	0.571228i	−0.361244	−	0.932471i	$-0.617648\pi$
$19$	898.863	−	898.863i	0.571228	−	0.571228i	0.932471	+	0.361244i	$0.117648\pi$
$20$	−491.399	−	631.290i	−0.274701	−	0.352902i
$21$	3297.69	+	3297.69i	1.63178	+	1.63178i
$22$	−1134.96	+	1002.32i	−0.499947	+	0.441518i
$23$		−	3820.93i		−	1.50609i	−0.657971	−	0.753043i	$-0.728585\pi$
$23$		−	3820.93i		−	1.50609i	0.657971	−	0.753043i	$-0.271415\pi$
$24$	2730.25	+	3995.48i	0.967550	+	1.41593i
$25$			625.000i			0.200000i
$26$	−4141.36	−	4689.41i	−1.20146	−	1.36046i
$27$	4322.49	+	4322.49i	1.14110	+	1.14110i
$28$	−690.248	+	5539.59i	−0.166384	+	1.33531i
$29$	978.529	−	978.529i	0.216062	−	0.216062i	−0.590775	−	0.806837i	$-0.701178\pi$
$29$	978.529	−	978.529i	0.216062	−	0.216062i	0.806837	+	0.590775i	$0.201178\pi$
$30$	234.182	−	3773.39i	0.0475061	−	0.765470i
$31$	4974.58			0.929719			0.464860	−	0.885384i	$-0.346105\pi$
$31$	4974.58			0.929719			0.464860	+	0.885384i	$0.346105\pi$
$32$	−1766.59	+	5516.67i	−0.304972	+	0.952361i
$33$	−7155.78			−1.14386
$34$	323.669	−	5215.30i	0.0480179	−	0.773717i
$35$	3083.89	−	3083.89i	0.425528	−	0.425528i
$36$	−1866.23	+	14977.4i	−0.239998	+	1.92611i
$37$	−5788.44	−	5788.44i	−0.695116	−	0.695116i	0.268237	−	0.963353i	$-0.413559\pi$
$37$	−5788.44	−	5788.44i	−0.695116	−	0.695116i	−0.963353	+	0.268237i	$0.913559\pi$
$38$	4760.01	+	5389.93i	0.534748	+	0.605514i
$39$		−	29566.1i		−	3.11267i
$40$	3736.44	−	2553.23i	0.369240	−	0.252314i
$41$		−	639.645i		−	0.0594264i	−0.999558	−	0.0297132i	$-0.990541\pi$
$41$		−	639.645i		−	0.0594264i	0.999558	−	0.0297132i	$-0.00945940\pi$
$42$	−19774.2	+	17463.2i	−1.72972	+	1.52757i
$43$	8062.21	+	8062.21i	0.664941	+	0.664941i	0.956540	−	0.291600i	$-0.0941875\pi$
$43$	8062.21	+	8062.21i	0.664941	+	0.664941i	−0.291600	+	0.956540i	$0.594188\pi$
$44$	−5261.39	−	6759.19i	−0.409703	−	0.526336i
$45$	8337.92	−	8337.92i	0.613800	−	0.613800i
$46$	21573.0	+	1338.85i	1.50319	+	0.0932903i
$47$	22043.6			1.45559			0.727794	−	0.685796i	$-0.240546\pi$
$47$	22043.6			1.45559			0.727794	+	0.685796i	$0.240546\pi$
$48$	−23515.1	+	14014.9i	−1.47314	+	0.877987i
$49$	−13626.1			−0.810743
$50$	−3528.74	−	218.999i	−0.199616	−	0.0123884i
$51$	17461.2	−	17461.2i	0.940047	−	0.940047i
$52$	27927.5	−	21738.9i	1.43226	−	1.11488i
$53$	−14377.5	−	14377.5i	−0.703063	−	0.703063i	0.262003	−	0.965067i	$-0.415617\pi$
$53$	−14377.5	−	14377.5i	−0.703063	−	0.703063i	−0.965067	+	0.262003i	$0.915617\pi$
$54$	−25919.3	+	22890.2i	−1.20959	+	1.06823i
$55$			6691.84i			0.298290i
$56$	−31034.6	−	5838.20i	−1.32244	−	0.248776i
$57$			33982.8i			1.38539i
$58$	5181.89	+	5867.64i	0.202264	+	0.229031i
$59$	−28515.2	−	28515.2i	−1.06646	−	1.06646i	−0.997628	−	0.0688356i	$-0.978072\pi$
$59$	−28515.2	−	28515.2i	−1.06646	−	1.06646i	−0.0688356	−	0.997628i	$-0.521928\pi$
$60$	21222.4	+	2644.37i	0.761057	+	0.0948298i
$61$	19210.1	−	19210.1i	0.661007	−	0.661007i	−0.294611	−	0.955617i	$-0.595190\pi$
$61$	19210.1	−	19210.1i	0.661007	−	0.661007i	0.955617	+	0.294611i	$0.0951899\pi$
$62$	−1743.08	+	28086.4i	−0.0575889	+	0.927934i
$63$	−82282.3			−2.61189
$64$	−30528.0	−	11907.2i	−0.931642	−	0.363378i
$65$	−27649.2			−0.811708
$66$	2507.37	−	40401.5i	0.0708531	−	1.14166i
$67$	−25147.9	+	25147.9i	−0.684407	+	0.684407i	−0.960990	−	0.276583i	$-0.910798\pi$
$67$	−25147.9	+	25147.9i	−0.684407	+	0.684407i	0.276583	+	0.960990i	$0.410798\pi$
$68$	29332.1	+	3654.86i	0.769257	+	0.0958514i
$69$	72228.0	+	72228.0i	1.82634	+	1.82634i
$70$	16331.0	+	18492.2i	0.398353	+	0.451069i
$71$		−	52863.6i		−	1.24454i	−0.782801	−	0.622272i	$-0.786210\pi$
$71$		−	52863.6i		−	1.24454i	0.782801	−	0.622272i	$-0.213790\pi$
$72$	−83908.5	−	15784.8i	−1.90755	−	0.358845i
$73$		−	20764.0i		−	0.456040i	−0.973656	−	0.228020i	$-0.926775\pi$
$73$		−	20764.0i		−	0.456040i	0.973656	−	0.228020i	$-0.0732252\pi$
$74$	34709.7	−	30653.2i	0.736838	−	0.650724i
$75$	−11814.5	−	11814.5i	−0.242529	−	0.242529i
$76$	−32099.4	+	24986.4i	−0.637475	+	0.496214i
$77$	33019.0	−	33019.0i	0.634655	−	0.634655i
$78$	166930.	+	10359.9i	3.10669	+	0.192805i
$79$	−51350.5			−0.925714			−0.462857	−	0.886433i	$-0.653176\pi$
$79$	−51350.5			−0.925714			−0.462857	+	0.886433i	$0.653176\pi$
$80$	13106.3	+	21990.6i	0.228958	+	0.384159i
$81$	−48803.7			−0.826494
$82$	3611.43	+	224.130i	0.0593123	+	0.00368100i
$83$	18480.4	−	18480.4i	0.294454	−	0.294454i	−0.544383	−	0.838837i	$-0.683236\pi$
$83$	18480.4	−	18480.4i	0.294454	−	0.294454i	0.838837	+	0.544383i	$0.183236\pi$
$84$	−91668.3	−	117764.i	−1.41749	−	1.82102i
$85$	−16329.2	−	16329.2i	−0.245141	−	0.245141i
$86$	−48344.1	+	42694.2i	−0.704852	+	0.622476i
$87$			36994.7i			0.524012i
$88$	40005.9	−	27337.4i	0.550703	−	0.376314i
$89$			53694.4i			0.718545i	0.933233	+	0.359273i	$0.116975\pi$
$89$			53694.4i			0.718545i	−0.933233	+	0.359273i	$0.883025\pi$
$90$	44154.2	+	49997.4i	0.574601	+	0.650641i
$91$	136427.	+	136427.i	1.72702	+	1.72702i
$92$	−15118.2	+	121332.i	−0.186222	+	1.49453i
$93$	−94035.5	+	94035.5i	−1.12742	+	1.12742i
$94$	−7724.04	+	124458.i	−0.0901623	+	1.45279i
$95$	31779.6			0.361276
$96$	−70888.6	−	137677.i	−0.785051	−	1.52470i
$97$	52155.5			0.562821			0.281411	−	0.959587i	$-0.409198\pi$
$97$	52155.5			0.562821			0.281411	+	0.959587i	$0.409198\pi$
$98$	4774.58	−	76933.1i	0.0502192	−	0.809186i
$99$	89273.7	−	89273.7i	0.915452	−	0.915452i
$100$	2472.93	−	19846.5i	0.0247293	−	0.198465i
$101$	5024.10	+	5024.10i	0.0490066	+	0.0490066i	0.731185	−	0.682179i	$-0.238967\pi$
$101$	5024.10	+	5024.10i	0.0490066	+	0.0490066i	−0.682179	+	0.731185i	$0.738967\pi$
$102$	92467.6	+	104704.i	0.880013	+	0.996470i
$103$		−	129174.i		−	1.19973i	−0.800102	−	0.599864i	$-0.795222\pi$
$103$		−	129174.i		−	1.19973i	0.800102	−	0.599864i	$-0.204778\pi$
$104$	112952.	+	165296.i	1.02402	+	1.49857i
$105$			116591.i			1.03203i
$106$	86213.3	−	76137.5i	0.745263	−	0.658164i
$107$	−137173.	−	137173.i	−1.15827	−	1.15827i	−0.984847	−	0.173425i	$-0.944516\pi$
$107$	−137173.	−	137173.i	−1.15827	−	1.15827i	−0.173425	−	0.984847i	$-0.555484\pi$
$108$	−120156.	−	154361.i	−0.991253	−	1.27344i
$109$	120643.	−	120643.i	0.972605	−	0.972605i	−0.0270299	−	0.999635i	$-0.508605\pi$
$109$	120643.	−	120643.i	0.972605	−	0.972605i	0.999635	+	0.0270299i	$0.00860494\pi$
$110$	−37782.1	−	2344.81i	−0.297717	−	0.0184768i
$111$	218840.			1.68585
$112$	43836.9	−	173176.i	0.330213	−	1.30449i
$113$	−97424.5			−0.717748			−0.358874	−	0.933386i	$-0.616839\pi$
$113$	−97424.5			−0.717748			−0.358874	+	0.933386i	$0.616839\pi$
$114$	−191867.	−	11907.5i	−1.38273	−	0.0858141i
$115$	67545.2	−	67545.2i	0.476266	−	0.476266i
$116$	−34944.4	+	27200.9i	−0.241120	+	0.187689i
$117$	368859.	+	368859.i	2.49113	+	2.49113i
$118$	170988.	−	151005.i	1.13047	−	0.998357i
$119$			161143.i			1.04315i
$120$	−22366.4	+	118895.i	−0.141789	+	0.753722i
$121$		−	89401.8i		−	0.555115i
$122$	101729.	+	115191.i	0.618793	+	0.700682i
$123$	12091.4	+	12091.4i	0.0720630	+	0.0720630i
$124$	−157965.	−	19682.9i	−0.922585	−	0.114957i
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$	28831.6	−	464565.i	0.161786	−	2.60687i
$127$	−64797.8			−0.356493			−0.178247	−	0.983986i	$-0.557042\pi$
$127$	−64797.8			−0.356493			−0.178247	+	0.983986i	$0.557042\pi$
$128$	77924.8	−	168189.i	0.420388	−	0.907344i
$129$	−304804.			−1.61267
$130$	9688.24	−	156107.i	0.0502790	−	0.810149i
$131$	−50841.6	+	50841.6i	−0.258846	+	0.258846i	−0.824585	−	0.565739i	$-0.808591\pi$
$131$	−50841.6	+	50841.6i	−0.258846	+	0.258846i	0.565739	+	0.824585i	$0.308591\pi$
$132$	227228.	+	28313.2i	1.13508	+	0.141434i
$133$	−156807.	−	156807.i	−0.768666	−	0.768666i
$134$	−133173.	−	150797.i	−0.640700	−	0.725487i
$135$			152823.i			0.721696i
$136$	−30913.2	+	164328.i	−0.143317	+	0.761842i
$137$			130279.i			0.593025i	0.955029	+	0.296512i	$0.0958236\pi$
$137$			130279.i			0.593025i	−0.955029	+	0.296512i	$0.904176\pi$
$138$	−433107.	+	382490.i	−1.93597	+	1.70971i
$139$	−291251.	−	291251.i	−1.27859	−	1.27859i	−0.941458	−	0.337131i	$-0.890544\pi$
$139$	−291251.	−	291251.i	−1.27859	−	1.27859i	−0.337131	−	0.941458i	$-0.609456\pi$
$140$	−110129.	+	85725.1i	−0.474878	+	0.369648i
$141$	−416696.	+	416696.i	−1.76511	+	1.76511i
$142$	298467.	+	18523.3i	1.24215	+	0.0770898i
$143$	−296039.			−1.21062
$144$	118522.	−	468216.i	0.476314	−	1.88165i
$145$	34596.2			0.136650
$146$	117233.	+	7275.65i	0.455164	+	0.0282481i
$147$	257578.	−	257578.i	0.983141	−	0.983141i
$148$	160906.	+	206712.i	0.603833	+	0.775730i
$149$	44747.5	+	44747.5i	0.165121	+	0.165121i	0.784831	−	0.619710i	$-0.212750\pi$
$149$	44747.5	+	44747.5i	0.165121	+	0.165121i	−0.619710	+	0.784831i	$0.712750\pi$
$150$	70844.5	−	62564.9i	0.257086	−	0.227040i
$151$			235506.i			0.840544i	0.907398	+	0.420272i	$0.138065\pi$
$151$			235506.i			0.840544i	−0.907398	+	0.420272i	$0.861935\pi$
$152$	−129825.	−	189988.i	−0.455775	−	0.666987i
$153$			435684.i			1.50468i
$154$	174855.	+	197995.i	0.594124	+	0.672748i
$155$	87938.9	+	87938.9i	0.294003	+	0.294003i
$156$	−116984.	+	938855.i	−0.384870	+	3.08878i
$157$	−310538.	+	310538.i	−1.00546	+	1.00546i	−0.00547617	+	0.999985i	$0.501743\pi$
$157$	−310538.	+	310538.i	−1.00546	+	1.00546i	−0.999985	+	0.00547617i	$0.998257\pi$
$158$	17993.1	−	289924.i	0.0573408	−	0.923936i
$159$	543563.			1.70513
$160$	−128751.	+	66292.6i	−0.397604	+	0.204722i
$161$	−666566.			−2.02665
$162$	17100.7	−	275545.i	0.0511949	−	0.824907i
$163$	191250.	−	191250.i	0.563810	−	0.563810i	−0.366578	−	0.930387i	$-0.619471\pi$
$163$	191250.	−	191250.i	0.563810	−	0.563810i	0.930387	+	0.366578i	$0.119471\pi$
$164$	−2530.88	+	20311.6i	−0.00734787	+	0.0589704i
$165$	−126497.	−	126497.i	−0.361719	−	0.361719i
$166$	97864.9	+	110816.i	0.275649	+	0.312128i
$167$			494594.i			1.37233i	0.727447	+	0.686164i	$0.240707\pi$
$167$			494594.i			1.37233i	−0.727447	+	0.686164i	$0.759293\pi$
$168$	697016.	−	476294.i	1.90533	−	1.30197i
$169$		−	851875.i		−	2.29435i
$170$	97916.0	−	86472.6i	0.259855	−	0.229486i
$171$	−423961.	−	423961.i	−1.10876	−	1.10876i
$172$	−224111.	−	287911.i	−0.577620	−	0.742056i
$173$	−1961.84	+	1961.84i	−0.00498366	+	0.00498366i	−0.709594	−	0.704611i	$-0.751122\pi$
$173$	−1961.84	+	1961.84i	−0.00498366	+	0.00498366i	0.704611	+	0.709594i	$0.251122\pi$
$174$	−208872.	−	12962.9i	−0.523006	−	0.0324585i
$175$	109032.			0.269128
$176$	140328.	+	235452.i	0.341479	+	0.572955i
$177$	1.07806e6			2.58648
$178$	−303158.	−	18814.4i	−0.717166	−	0.0445083i
$179$	21400.2	−	21400.2i	0.0499211	−	0.0499211i	−0.681706	−	0.731627i	$-0.738761\pi$
$179$	21400.2	−	21400.2i	0.0499211	−	0.0499211i	0.731627	+	0.681706i	$0.238761\pi$
$180$	−297757.	+	231776.i	−0.684984	+	0.533195i
$181$	50340.2	+	50340.2i	0.114214	+	0.114214i	0.761904	−	0.647690i	$-0.224265\pi$
$181$	50340.2	+	50340.2i	0.114214	+	0.114214i	−0.647690	+	0.761904i	$0.724265\pi$
$182$	−818072.	+	722464.i	−1.83068	+	1.61673i
$183$			726267.i			1.60313i
$184$	−679740.	−	127872.i	−1.48012	−	0.278439i
$185$		−	204652.i		−	0.439630i
$186$	−497974.	−	563874.i	−1.05542	−	1.19509i
$187$	−174836.	−	174836.i	−0.365616	−	0.365616i
$188$	−699983.	−	87219.8i	−1.44442	−	0.179978i
$189$	754063.	−	754063.i	1.53551	−	1.53551i
$190$	−11135.5	+	179427.i	−0.0223782	+	0.360582i
$191$	−170075.			−0.337332			−0.168666	−	0.985673i	$-0.553946\pi$
$191$	−170075.			−0.337332			−0.168666	+	0.985673i	$0.553946\pi$
$192$	802163.	−	351994.i	1.57040	−	0.689101i
$193$	157998.			0.305323			0.152661	−	0.988279i	$-0.451216\pi$
$193$	157998.			0.305323			0.152661	+	0.988279i	$0.451216\pi$
$194$	−18275.2	+	294469.i	−0.0348624	+	0.561740i
$195$	522660.	−	522660.i	0.984311	−	0.984311i
$196$	432691.	+	53914.4i	0.804521	+	0.100246i
$197$	−527247.	−	527247.i	−0.967939	−	0.967939i	0.0315624	−	0.999502i	$-0.489952\pi$
$197$	−527247.	−	527247.i	−0.967939	−	0.967939i	−0.999502	+	0.0315624i	$0.989952\pi$
$198$	472757.	+	535320.i	0.856989	+	0.970399i
$199$		−	665722.i		−	1.19168i	−0.803103	−	0.595841i	$-0.796819\pi$
$199$		−	665722.i		−	1.19168i	0.803103	−	0.595841i	$-0.203181\pi$
$200$	111187.	+	20916.3i	0.196552	+	0.0369752i
$201$		−	950753.i		−	1.65988i
$202$	−30126.5	+	26605.6i	−0.0519481	+	0.0458770i
$203$	−170705.	−	170705.i	−0.290742	−	0.290742i
$204$	−623560.	+	485383.i	−1.04907	+	0.816600i
$205$	11307.4	−	11307.4i	0.0187923	−	0.0187923i
$206$	729316.	+	45262.4i	1.19742	+	0.0743137i
$207$	−1.80220e6			−2.92332
$208$	−972835.	+	579807.i	−1.55913	+	0.929233i
$209$	340262.			0.538826
$210$	−658271.	−	40853.2i	−1.03005	−	0.0639261i
$211$	−53299.1	+	53299.1i	−0.0824164	+	0.0824164i	−0.747113	−	0.664697i	$-0.768561\pi$
$211$	−53299.1	+	53299.1i	−0.0824164	+	0.0824164i	0.664697	+	0.747113i	$0.268561\pi$
$212$	399663.	+	513438.i	0.610737	+	0.784600i
$213$	999292.	+	999292.i	1.50919	+	1.50919i
$214$	822546.	−	726415.i	1.22779	−	1.08430i
$215$			285042.i			0.420545i
$216$	913623.	−	624309.i	1.33239	−	0.910469i
$217$		−	867820.i		−	1.25107i
$218$	638877.	+	723423.i	0.910492	+	1.03098i
$219$	392506.	+	392506.i	0.553014	+	0.553014i
$220$	26477.5	−	212496.i	0.0368826	−	0.296001i
$221$	722382.	−	722382.i	0.994916	−	0.994916i
$222$	−76681.2	+	1.23557e6i	−0.104426	+	1.68262i
$223$	614968.			0.828114			0.414057	−	0.910251i	$-0.364111\pi$
$223$	614968.			0.828114			0.414057	+	0.910251i	$0.364111\pi$
$224$	962388.	+	308183.i	1.28153	+	0.410383i
$225$	294790.			0.388201
$226$	34137.4	−	550058.i	0.0444589	−	0.716370i
$227$	56125.4	−	56125.4i	0.0722928	−	0.0722928i	−0.670036	−	0.742329i	$-0.733721\pi$
$227$	56125.4	−	56125.4i	0.0722928	−	0.0722928i	0.742329	+	0.670036i	$0.233721\pi$
$228$	134459.	−	1.07911e6i	0.171299	−	1.37476i
$229$	1.08807e6	+	1.08807e6i	1.37110	+	1.37110i	0.858818	+	0.512281i	$0.171199\pi$
$229$	1.08807e6	+	1.08807e6i	1.37110	+	1.37110i	0.512281	+	0.858818i	$0.328801\pi$
$230$	357692.	+	405027.i	0.445851	+	0.504853i
$231$			1.24833e6i			1.53922i
$232$	−141332.	−	206827.i	−0.172393	−	0.252282i
$233$		−	227380.i		−	0.274387i	−0.990544	−	0.137193i	$-0.956192\pi$
$233$		−	227380.i		−	0.274387i	0.990544	−	0.137193i	$-0.0438081\pi$
$234$	−2.21182e6	+	1.95333e6i	−2.64065	+	2.33204i
$235$	389680.	+	389680.i	0.460297	+	0.460297i
$236$	792658.	+	1.01831e6i	0.926415	+	1.19014i
$237$	970690.	−	970690.i	1.12256	−	1.12256i
$238$	−909814.	−	56464.3i	−1.04114	−	0.0646148i
$239$	−723958.			−0.819820			−0.409910	−	0.912126i	$-0.634440\pi$
$239$	−723958.			−0.819820			−0.409910	+	0.912126i	$0.634440\pi$
$240$	−663444.	−	167941.i	−0.743492	−	0.188204i
$241$	−1.53614e6			−1.70368			−0.851840	−	0.523803i	$-0.824513\pi$
$241$	−1.53614e6			−1.70368			−0.851840	+	0.523803i	$0.824513\pi$
$242$	504762.	+	31326.2i	0.554049	+	0.0343850i
$243$	−127818.	+	127818.i	−0.138860	+	0.138860i
$244$	−686016.	+	533999.i	−0.737666	+	0.574203i
$245$	−240879.	−	240879.i	−0.256379	−	0.256379i
$246$	−72504.5	+	64030.9i	−0.0763883	+	0.0674609i
$247$			1.40589e6i			1.46625i
$248$	166480.	−	884972.i	0.171883	−	0.913693i
$249$			698680.i			0.714135i
$250$	−58508.6	−	66251.4i	−0.0592065	−	0.0670417i
$251$	485905.	+	485905.i	0.486819	+	0.486819i	0.907301	−	0.420482i	$-0.138139\pi$
$251$	485905.	+	485905.i	0.486819	+	0.486819i	−0.420482	+	0.907301i	$0.638139\pi$
$252$	2.61283e6	+	325565.i	2.59185	+	0.322951i
$253$	723203.	−	723203.i	0.710328	−	0.710328i
$254$	22705.0	−	365848.i	0.0220820	−	0.355809i
$255$	617348.			0.594538
$256$	922288.	+	498896.i	0.879562	+	0.475784i
$257$	−1.02007e6			−0.963375			−0.481688	−	0.876343i	$-0.659976\pi$
$257$	−1.02007e6			−0.963375			−0.481688	+	0.876343i	$0.659976\pi$
$258$	106803.	−	1.72092e6i	0.0998924	−	1.60957i
$259$	−1.00980e6	+	1.00980e6i	−0.935374	+	0.935374i
$260$	877986.	+	109399.i	0.805479	+	0.100365i
$261$	−461537.	−	461537.i	−0.419378	−	0.419378i
$262$	−269236.	−	304866.i	−0.242315	−	0.274382i
$263$		−	133056.i		−	0.118617i	−0.998240	−	0.0593085i	$-0.981110\pi$
$263$		−	133056.i		−	0.118617i	0.998240	−	0.0593085i	$-0.0188896\pi$
$264$	−239476.	+	1.27300e6i	−0.211472	+	1.12414i
$265$		−	508322.i		−	0.444656i
$266$	940279.	−	830389.i	0.814803	−	0.719577i
$267$	−1.01500e6	−	1.01500e6i	−0.871339	−	0.871339i
$268$	898060.	−	699055.i	0.763780	−	0.594531i
$269$	482170.	−	482170.i	0.406274	−	0.406274i	−0.474163	−	0.880437i	$-0.657249\pi$
$269$	482170.	−	482170.i	0.406274	−	0.406274i	0.880437	+	0.474163i	$0.157249\pi$
$270$	−862838.	−	53548.9i	−0.720311	−	0.0447035i
$271$	848589.			0.701898			0.350949	−	0.936395i	$-0.385859\pi$
$271$	848589.			0.701898			0.350949	+	0.936395i	$0.385859\pi$
$272$	−916964.	−	232116.i	−0.751502	−	0.190232i
$273$	−5.15783e6			−4.18852
$274$	−735554.	−	45649.5i	−0.591886	−	0.0367333i
$275$	−118296.	+	118296.i	−0.0943277	+	0.0943277i
$276$	−2.00778e6	−	2.57934e6i	−1.58651	−	2.03815i
$277$	−603958.	−	603958.i	−0.472941	−	0.472941i	0.429924	−	0.902865i	$-0.358540\pi$
$277$	−603958.	−	603958.i	−0.472941	−	0.472941i	−0.902865	+	0.429924i	$0.858540\pi$
$278$	1.74646e6	−	1.54235e6i	1.35533	−	1.19693i
$279$		−	2.34633e6i		−	1.80459i
$280$	−445414.	−	651826.i	−0.339523	−	0.496863i
$281$			1.56617e6i			1.18324i	0.806218	+	0.591619i	$0.201511\pi$
$281$			1.56617e6i			1.18324i	−0.806218	+	0.591619i	$0.798489\pi$
$282$	−2.20665e6	−	2.49867e6i	−1.65238	−	1.87105i
$283$	220893.	+	220893.i	0.163951	+	0.163951i	0.784315	−	0.620363i	$-0.213015\pi$
$283$	220893.	+	220893.i	0.163951	+	0.163951i	−0.620363	+	0.784315i	$0.713015\pi$
$284$	−209165.	+	1.67865e6i	−0.153884	+	1.23499i
$285$	−600737.	+	600737.i	−0.438099	+	0.438099i
$286$	103731.	−	1.67143e6i	0.0749886	−	1.20830i
$287$	−111587.			−0.0799664
$288$	2.60201e6	+	833237.i	1.84854	+	0.591953i
$289$	−566604.			−0.399057
$290$	−12122.5	+	195330.i	−0.00846439	+	0.136387i
$291$	−985907.	+	985907.i	−0.682501	+	0.682501i
$292$	−82156.6	+	659348.i	−0.0563878	+	0.452541i
$293$	−287839.	−	287839.i	−0.195875	−	0.195875i	0.602354	−	0.798229i	$-0.294230\pi$
$293$	−287839.	−	287839.i	−0.195875	−	0.195875i	−0.798229	+	0.602354i	$0.794230\pi$
$294$	1.36403e6	+	1.54454e6i	0.920355	+	1.04215i
$295$		−	1.00816e6i		−	0.674491i
$296$	−1.22347e6	+	836040.i	−0.811643	+	0.554623i
$297$			1.63627e6i			1.07638i
$298$	−268323.	+	236964.i	−0.175032	+	0.154576i
$299$	2.98812e6	+	2.98812e6i	1.93294	+	1.93294i
$300$	328417.	+	421910.i	0.210680	+	0.270655i
$301$	1.40646e6	−	1.40646e6i	0.894770	−	0.894770i
$302$	−1.32967e6	−	82521.0i	−0.838929	−	0.0520651i
$303$	−189943.			−0.118855
$304$	1.11816e6	−	666421.i	0.693938	−	0.413585i
$305$	679181.			0.418057
$306$	−2.45987e6	−	152663.i	−1.50179	−	0.0932030i
$307$	1.86981e6	−	1.86981e6i	1.13228	−	1.13228i	0.142478	−	0.989798i	$-0.454493\pi$
$307$	1.86981e6	−	1.86981e6i	1.13228	−	1.13228i	0.989798	−	0.142478i	$-0.0455071\pi$
$308$	−1.17915e6	+	917855.i	−0.708257	+	0.551312i
$309$	2.44181e6	+	2.44181e6i	1.45484	+	1.45484i
$310$	−527316.	+	465689.i	−0.311650	+	0.275227i
$311$		−	1.39161e6i		−	0.815864i	−0.913012	−	0.407932i	$-0.866250\pi$
$311$		−	1.39161e6i		−	0.815864i	0.913012	−	0.407932i	$-0.133750\pi$
$312$	−5.25978e6	−	989463.i	−3.05901	−	0.575457i
$313$			464454.i			0.267967i	0.990984	+	0.133984i	$0.0427769\pi$
$313$			464454.i			0.267967i	−0.990984	+	0.133984i	$0.957223\pi$
$314$	−1.64448e6	−	1.86211e6i	−0.941250	−	1.06581i
$315$	−1.45456e6	−	1.45456e6i	−0.825952	−	0.825952i
$316$	1.63061e6	+	203178.i	0.918610	+	0.114461i
$317$	−1.02338e6	+	1.02338e6i	−0.571993	+	0.571993i	−0.932685	−	0.360692i	$-0.882540\pi$
$317$	−1.02338e6	+	1.02338e6i	−0.571993	+	0.571993i	0.360692	+	0.932685i	$0.382540\pi$
$318$	−190464.	+	3.06895e6i	−0.105619	+	1.70186i
$319$	370420.			0.203806
$320$	−329173.	−	750156.i	−0.179701	−	0.409521i
$321$	5.18604e6			2.80914
$322$	233563.	−	3.76342e6i	0.125535	−	2.02276i
$323$	−830295.	+	830295.i	−0.442819	+	0.442819i
$324$	1.54973e6	+	193101.i	0.820152	+	0.102193i
$325$	−488774.	−	488774.i	−0.256684	−	0.256684i
$326$	1.01278e6	+	1.14681e6i	0.527804	+	0.597651i
$327$			4.56109e6i			2.35884i
$328$	−113792.	−	21406.4i	−0.0584020	−	0.0109865i
$329$		−	3.84553e6i		−	1.95869i
$330$	758528.	−	669879.i	0.383431	−	0.338619i
$331$	−89356.4	−	89356.4i	−0.0448286	−	0.0448286i	0.684337	−	0.729166i	$-0.260092\pi$
$331$	−89356.4	−	89356.4i	−0.0448286	−	0.0448286i	−0.729166	+	0.684337i	$0.760092\pi$
$332$	−659958.	+	513715.i	−0.328603	+	0.255786i
$333$	−2.73020e6	+	2.73020e6i	−1.34922	+	1.34922i
$334$	−2.79248e6	−	173305.i	−1.36969	−	0.0850051i
$335$	−889113.			−0.432857
$336$	2.44492e6	+	4.10224e6i	1.18145	+	1.98231i
$337$	1.64073e6			0.786977			0.393489	−	0.919330i	$-0.371268\pi$
$337$	1.64073e6			0.786977			0.393489	+	0.919330i	$0.371268\pi$
$338$	4.80968e6	+	298495.i	2.28994	+	0.142117i
$339$	1.84164e6	−	1.84164e6i	0.870372	−	0.870372i
$340$	453914.	+	583133.i	0.212949	+	0.273571i
$341$	941557.	+	941557.i	0.438491	+	0.438491i
$342$	2.54224e6	−	2.24513e6i	1.17531	−	1.03795i
$343$		−	554903.i		−	0.254672i
$344$	1.70407e6	−	1.16445e6i	0.776410	−	0.530547i
$345$			2.55364e6i			1.15508i
$346$	−10389.1	−	11764.0i	−0.00466539	−	0.00528279i
$347$	63290.7	+	63290.7i	0.0282173	+	0.0282173i	0.721075	−	0.692857i	$-0.243648\pi$
$347$	63290.7	+	63290.7i	0.0282173	+	0.0282173i	−0.692857	+	0.721075i	$0.743648\pi$
$348$	146377.	−	1.17475e6i	0.0647923	−	0.519991i
$349$	−1.63122e6	+	1.63122e6i	−0.716885	+	0.716885i	−0.967966	−	0.251081i	$-0.919214\pi$
$349$	−1.63122e6	+	1.63122e6i	−0.716885	+	0.716885i	0.251081	+	0.967966i	$0.419214\pi$
$350$	−38204.6	+	615593.i	−0.0166704	+	0.268611i
$351$	−6.76071e6			−2.92903
$352$	−1.37853e6	+	709792.i	−0.593007	+	0.305333i
$353$	−3.02063e6			−1.29021			−0.645106	−	0.764093i	$-0.723187\pi$
$353$	−3.02063e6			−1.29021			−0.645106	+	0.764093i	$0.723187\pi$
$354$	−377749.	+	6.08671e6i	−0.160212	+	2.58151i
$355$	934504.	−	934504.i	0.393560	−	0.393560i
$356$	212452.	−	1.70504e6i	0.0888457	−	0.713032i
$357$	−3.04613e6	−	3.04613e6i	−1.26496	−	1.26496i
$358$	113327.	+	128324.i	0.0467330	+	0.0529175i
$359$		−	958938.i		−	0.392694i	−0.980534	−	0.196347i	$-0.937092\pi$
$359$		−	958938.i		−	0.392694i	0.980534	−	0.196347i	$-0.0629079\pi$
$360$	−1.20427e6	−	1.76235e6i	−0.489742	−	0.716696i
$361$			860191.i			0.347398i
$362$	−301859.	+	266581.i	−0.121069	+	0.106920i
$363$	1.68998e6	+	1.68998e6i	0.673156	+	0.673156i
$364$	−3.79237e6	−	4.87197e6i	−1.50023	−	1.92731i
$365$	367059.	−	367059.i	0.144213	−	0.144213i
$366$	−4.10050e6	−	254483.i	−1.60005	−	0.0993014i
$367$	441626.			0.171155			0.0855776	−	0.996332i	$-0.472726\pi$
$367$	441626.			0.171155			0.0855776	+	0.996332i	$0.472726\pi$
$368$	960143.	−	3.79300e6i	0.369587	−	1.46003i
$369$	−301698.			−0.115347
$370$	1.15546e6	+	71709.7i	0.438786	+	0.0272316i
$371$	−2.50817e6	+	2.50817e6i	−0.946069	+	0.946069i
$372$	3.35812e6	−	2.61398e6i	1.25817	−	0.979365i
$373$	1.98731e6	+	1.98731e6i	0.739594	+	0.739594i	0.972499	−	0.232905i	$-0.0748232\pi$
$373$	1.98731e6	+	1.98731e6i	0.739594	+	0.739594i	−0.232905	+	0.972499i	$0.574823\pi$
$374$	1.04838e6	−	925858.i	0.387561	−	0.342267i
$375$		−	417706.i		−	0.153389i
$376$	737715.	−	3.92154e6i	0.269103	−	1.43050i
$377$			1.53049e6i			0.554598i
$378$	3.99321e6	+	4.52165e6i	1.43745	+	1.62768i
$379$	−8992.62	−	8992.62i	−0.00321579	−	0.00321579i	0.705497	−	0.708713i	$-0.250724\pi$
$379$	−8992.62	−	8992.62i	−0.00321579	−	0.00321579i	−0.708713	+	0.705497i	$0.750724\pi$
$380$	−1.00914e6	−	125742.i	−0.358504	−	0.0446705i
$381$	1.22489e6	−	1.22489e6i	0.432299	−	0.432299i
$382$	59594.1	−	960244.i	0.0208951	−	0.336685i
$383$	5.27561e6			1.83770			0.918852	−	0.394603i	$-0.129118\pi$
$383$	5.27561e6			1.83770			0.918852	+	0.394603i	$0.129118\pi$
$384$	1.70628e6	+	4.65234e6i	0.590504	+	1.61007i
$385$	1.16740e6			0.401391
$386$	−55362.3	+	892057.i	−0.0189124	+	0.304736i
$387$	3.80265e6	−	3.80265e6i	1.29065	−	1.29065i
$388$	−1.65617e6	−	206363.i	−0.558502	−	0.0695909i
$389$	−2.46145e6	−	2.46145e6i	−0.824741	−	0.824741i	0.162043	−	0.986784i	$-0.448192\pi$
$389$	−2.46145e6	−	2.46145e6i	−0.824741	−	0.824741i	−0.986784	+	0.162043i	$0.948192\pi$
$390$	2.76779e6	+	3.13407e6i	0.921451	+	1.04339i
$391$			3.52946e6i			1.16753i
$392$	−456014.	+	2.42408e6i	−0.149887	+	0.796767i
$393$		−	1.92214e6i		−	0.627775i
$394$	3.16158e6	−	2.79208e6i	1.02604	−	0.906124i
$395$	−907757.	−	907757.i	−0.292736	−	0.292736i
$396$	−3.18807e6	+	2.48161e6i	−1.02162	+	0.795235i
$397$	−1.45382e6	+	1.45382e6i	−0.462951	+	0.462951i	−0.899622	−	0.436670i	$-0.856158\pi$
$397$	−1.45382e6	+	1.45382e6i	−0.462951	+	0.462951i	0.436670	+	0.899622i	$0.356158\pi$
$398$	3.75866e6	+	233268.i	1.18939	+	0.0738154i
$399$	5.92834e6			1.86423
$400$	−157053.	+	620431.i	−0.0490791	+	0.193885i
$401$	2.98503e6			0.927016			0.463508	−	0.886093i	$-0.346590\pi$
$401$	2.98503e6			0.927016			0.463508	+	0.886093i	$0.346590\pi$
$402$	5.36794e6	+	333142.i	1.65670	+	0.102817i
$403$	−3.89031e6	+	3.89031e6i	−1.19322	+	1.19322i
$404$	−139659.	−	179416.i	−0.0425711	−	0.0546901i
$405$	−862735.	−	862735.i	−0.261360	−	0.261360i
$406$	1.02362e6	−	903986.i	0.308192	−	0.272174i
$407$		−	2.19120e6i		−	0.655686i
$408$	−2.52197e6	−	3.69069e6i	−0.750050	−	1.09763i
$409$		−	532252.i		−	0.157329i	−0.996901	−	0.0786645i	$-0.974934\pi$
$409$		−	532252.i		−	0.157329i	0.996901	−	0.0786645i	$-0.0250656\pi$
$410$	59879.6	+	67803.8i	0.0175922	+	0.0199202i
$411$	−2.46269e6	−	2.46269e6i	−0.719127	−	0.719127i
$412$	−511102.	+	4.10185e6i	−0.148342	+	1.19052i
$413$	−4.97450e6	+	4.97450e6i	−1.43507	+	1.43507i
$414$	631486.	−	1.01752e7i	0.181077	−	2.91771i
$415$	653382.			0.186229
$416$	−2.93270e6	−	5.69578e6i	−0.830873	−	1.61369i
$417$	1.10112e7			3.10094
$418$	−119227.	+	1.92112e6i	−0.0333761	+	0.537791i
$419$	−4.31407e6	+	4.31407e6i	−1.20047	+	1.20047i	−0.226450	+	0.974023i	$0.572712\pi$
$419$	−4.31407e6	+	4.31407e6i	−1.20047	+	1.20047i	−0.974023	+	0.226450i	$0.927288\pi$
$420$	461314.	−	3.70228e6i	0.127607	−	1.02411i
$421$	2.89172e6	+	2.89172e6i	0.795153	+	0.795153i	0.982327	−	0.187174i	$-0.0599328\pi$
$421$	2.89172e6	+	2.89172e6i	0.795153	+	0.795153i	−0.187174	+	0.982327i	$0.559933\pi$
$422$	−282250.	−	319602.i	−0.0771531	−	0.0873632i
$423$		−	1.03972e7i		−	2.82530i
$424$	−3.03891e6	+	2.07659e6i	−0.820923	+	0.560964i
$425$		−	577323.i		−	0.155041i
$426$	−5.99214e6	+	5.29184e6i	−1.59977	+	1.41281i
$427$	−3.35123e6	−	3.35123e6i	−0.889476	−	0.889476i
$428$	3.81311e6	+	4.89862e6i	1.00617	+	1.29260i
$429$	5.59609e6	−	5.59609e6i	1.46805	−	1.46805i
$430$	−1.60935e6	−	99878.2i	−0.419738	−	0.0260495i
$431$	1.51871e6			0.393806			0.196903	−	0.980423i	$-0.436912\pi$
$431$	1.51871e6			0.393806			0.196903	+	0.980423i	$0.436912\pi$
$432$	3.20471e6	+	5.37707e6i	0.826190	+	1.38623i
$433$	3.00917e6			0.771306			0.385653	−	0.922644i	$-0.373976\pi$
$433$	3.00917e6			0.771306			0.385653	+	0.922644i	$0.373976\pi$
$434$	4.89970e6	+	304082.i	1.24866	+	0.0774938i
$435$	−653980.	+	653980.i	−0.165707	+	0.165707i
$436$	−4.30830e6	+	3.35361e6i	−1.08540	+	0.844882i
$437$	−3.43449e6	−	3.43449e6i	−0.860318	−	0.860318i
$438$	−2.35362e6	+	2.07855e6i	−0.586207	+	0.517697i
$439$		−	375602.i		−	0.0930179i	−0.998918	−	0.0465089i	$-0.985190\pi$
$439$		−	375602.i		−	0.0930179i	0.998918	−	0.0465089i	$-0.0148096\pi$
$440$	1.19047e6	+	223950.i	0.293148	+	0.0551467i
$441$			6.42697e6i			1.57365i
$442$	3.82544e6	+	4.33168e6i	0.931378	+	1.05463i
$443$	−3.49838e6	−	3.49838e6i	−0.846950	−	0.846950i	0.142801	−	0.989751i	$-0.454389\pi$
$443$	−3.49838e6	−	3.49838e6i	−0.846950	−	0.846950i	−0.989751	+	0.142801i	$0.954389\pi$
$444$	−6.94915e6	−	865883.i	−1.67292	−	0.208450i
$445$	−949193.	+	949193.i	−0.227224	+	0.227224i
$446$	−215484.	+	3.47210e6i	−0.0512952	+	0.826524i
$447$	−1.69174e6			−0.400466
$448$	−2.07722e6	+	5.32565e6i	−0.488976	+	1.25365i
$449$	−6.84616e6			−1.60262			−0.801311	−	0.598249i	$-0.795864\pi$
$449$	−6.84616e6			−1.60262			−0.801311	+	0.598249i	$0.795864\pi$
$450$	−103294.	+	1.66438e6i	−0.0240460	+	0.387455i
$451$	121068.	−	121068.i	0.0280278	−	0.0280278i
$452$	3.09366e6	+	385478.i	0.712240	+	0.0887471i
$453$	−4.45183e6	−	4.45183e6i	−1.01928	−	1.01928i
$454$	297217.	+	336550.i	0.0676760	+	0.0766319i
$455$			4.82344e6i			1.09226i
$456$	6.04550e6	+	1.13727e6i	1.36151	+	0.256125i
$457$		−	8.03888e6i		−	1.80055i	−0.435321	−	0.900275i	$-0.643365\pi$
$457$		−	8.03888e6i		−	1.80055i	0.435321	−	0.900275i	$-0.356635\pi$
$458$	−6.52450e6	+	5.76198e6i	−1.45339	+	1.28354i
$459$	−3.99276e6	−	3.99276e6i	−0.884588	−	0.884588i
$460$	−2.41212e6	+	1.87760e6i	−0.531500	+	0.413723i
$461$	1.72098e6	−	1.72098e6i	0.377159	−	0.377159i	−0.492917	−	0.870076i	$-0.664070\pi$
$461$	1.72098e6	−	1.72098e6i	0.377159	−	0.377159i	0.870076	+	0.492917i	$0.164070\pi$
$462$	−7.04807e6	−	437413.i	−1.53626	−	0.0953426i
$463$	4.66774e6			1.01194			0.505969	−	0.862552i	$-0.331135\pi$
$463$	4.66774e6			1.01194			0.505969	+	0.862552i	$0.331135\pi$
$464$	1.21726e6	−	725486.i	0.262476	−	0.156435i
$465$	−3.32466e6			−0.713041
$466$	1.28379e6	+	79673.6i	0.273860	+	0.0169961i
$467$	927821.	−	927821.i	0.196867	−	0.196867i	−0.601789	−	0.798655i	$-0.705545\pi$
$467$	927821.	−	927821.i	0.196867	−	0.196867i	0.798655	+	0.601789i	$0.205545\pi$
$468$	−1.02535e7	−	1.31724e7i	−2.16399	−	2.78003i
$469$	4.38708e6	+	4.38708e6i	0.920965	+	0.920965i
$470$	−2.33667e6	+	2.06359e6i	−0.487925	+	0.430902i
$471$		−	1.17403e7i		−	2.43853i
$472$	−6.02711e6	+	4.11853e6i	−1.24524	+	0.850916i
$473$			3.05193e6i			0.627223i
$474$	5.14038e6	+	5.82064e6i	1.05087	+	1.18994i
$475$	561789.	+	561789.i	0.114246	+	0.114246i
$476$	637594.	−	5.11702e6i	0.128981	−	1.03514i
$477$	−6.78136e6	+	6.78136e6i	−1.36465	+	1.36465i
$478$	253673.	−	4.08746e6i	0.0507815	−	0.818246i
$479$	1.02994e6			0.205103			0.102552	−	0.994728i	$-0.467299\pi$
$479$	1.02994e6			0.205103			0.102552	+	0.994728i	$0.467299\pi$
$480$	1.18066e6	−	3.68695e6i	0.233896	−	0.730406i
$481$	9.05356e6			1.78425
$482$	538260.	−	8.67303e6i	0.105530	−	1.70041i
$483$	1.26002e7	−	1.26002e7i	2.45760	−	2.45760i
$484$	−353735.	+	2.83890e6i	−0.0686380	+	0.550855i
$485$	921987.	+	921987.i	0.177980	+	0.177980i
$486$	−676874.	−	766449.i	−0.129992	−	0.147195i
$487$			3.74970e6i			0.716431i	0.933639	+	0.358216i	$0.116615\pi$
$487$			3.74970e6i			0.716431i	−0.933639	+	0.358216i	$0.883385\pi$
$488$	−2.77457e6	−	4.06035e6i	−0.527408	−	0.771817i
$489$			7.23049e6i			1.36740i
$490$	1.44440e6	−	1.27559e6i	0.271768	−	0.240006i
$491$	−3.17911e6	−	3.17911e6i	−0.595116	−	0.595116i	0.343893	−	0.939009i	$-0.388254\pi$
$491$	−3.17911e6	−	3.17911e6i	−0.595116	−	0.595116i	−0.939009	+	0.343893i	$0.888254\pi$
$492$	−336113.	−	431796.i	−0.0625997	−	0.0804203i
$493$	−903884.	+	903884.i	−0.167493	+	0.167493i
$494$	−7.93764e6	−	492621.i	−1.46344	−	0.0908230i
$495$	3.15630e6			0.578983
$496$	4.93821e6	+	1.25004e6i	0.901291	+	0.228149i
$497$	−9.22210e6			−1.67471
$498$	−3.94474e6	−	244816.i	−0.712763	−	0.0442351i
$499$	−935696.	+	935696.i	−0.168222	+	0.168222i	−0.786198	−	0.617975i	$-0.787953\pi$
$499$	−935696.	+	935696.i	−0.168222	+	0.168222i	0.617975	+	0.786198i	$0.287953\pi$
$500$	394556.	−	307125.i	0.0705803	−	0.0549401i
$501$	−9.34943e6	−	9.34943e6i	−1.66414	−	1.66414i
$502$	−2.91368e6	+	2.57316e6i	−0.516038	+	0.455729i
$503$		−	3.96538e6i		−	0.698819i	−0.936970	−	0.349409i	$-0.886382\pi$
$503$		−	3.96538e6i		−	0.698819i	0.936970	−	0.349409i	$-0.113618\pi$
$504$	−2.75367e6	+	1.46379e7i	−0.482876	+	2.56687i
$505$			177629.i			0.0309945i
$506$	3.82979e6	+	4.33661e6i	0.664965	+	0.752963i
$507$	1.61032e7	+	1.61032e7i	2.78222	+	2.78222i
$508$	2.05762e6	+	256385.i	0.353758	+	0.0440792i
$509$	−6.45393e6	+	6.45393e6i	−1.10415	+	1.10415i	−0.110251	+	0.993904i	$0.535165\pi$
$509$	−6.45393e6	+	6.45393e6i	−1.10415	+	1.10415i	−0.993904	+	0.110251i	$0.964835\pi$
$510$	−216318.	+	3.48554e6i	−0.0368270	+	0.593396i
$511$	−3.62229e6			−0.613665
$512$	−3.13993e6	+	5.03242e6i	−0.529352	+	0.848402i
$513$	7.77065e6			1.30366
$514$	357429.	−	5.75928e6i	0.0596736	−	0.961525i
$515$	2.28350e6	−	2.28350e6i	0.379387	−	0.379387i
$516$	9.67887e6	+	1.20601e6i	1.60030	+	0.199401i
$517$	4.17228e6	+	4.17228e6i	0.686511	+	0.686511i
$518$	−5.34748e6	−	6.05515e6i	−0.875639	−	0.991517i
$519$		−	74170.3i		−	0.0120868i
$520$	−925313.	+	4.91877e6i	−0.150065	+	0.797715i
$521$		−	9.69172e6i		−	1.56425i	−0.623121	−	0.782125i	$-0.714136\pi$
$521$		−	9.69172e6i		−	1.56425i	0.623121	−	0.782125i	$-0.285864\pi$
$522$	2.76756e6	−	2.44411e6i	0.444549	−	0.392595i
$523$	8.02434e6	+	8.02434e6i	1.28279	+	1.28279i	0.939075	+	0.343714i	$0.111685\pi$
$523$	8.02434e6	+	8.02434e6i	1.28279	+	1.28279i	0.343714	+	0.939075i	$0.388315\pi$
$524$	1.81561e6	−	1.41328e6i	0.288865	−	0.224854i
$525$	−2.06105e6	+	2.06105e6i	−0.326356	+	0.326356i
$526$	751236.	+	46622.7i	0.118389	+	0.00734740i
$527$	−4.59510e6			−0.720723
$528$	−7.10346e6	−	1.79814e6i	−1.10888	−	0.280697i
$529$	−8.16319e6			−1.26830
$530$	2.86998e6	+	178115.i	0.443803	+	0.0275430i
$531$	−1.34496e7	+	1.34496e7i	−2.07001	+	2.07001i
$532$	4.35890e6	+	5.59977e6i	0.667725	+	0.857810i
$533$	500227.	+	500227.i	0.0762692	+	0.0762692i
$534$	6.08632e6	−	5.37502e6i	0.923638	−	0.815693i
$535$		−	4.84981e6i		−	0.732556i
$536$	3.63218e6	+	5.31539e6i	0.546079	+	0.799140i
$537$			809064.i			0.121073i
$538$	2.55338e6	+	2.89128e6i	0.380329	+	0.430660i
$539$	−2.57907e6	−	2.57907e6i	−0.382377	−	0.382377i
$540$	604674.	−	4.85281e6i	0.0892353	−	0.716158i
$541$	−1.80623e6	+	1.80623e6i	−0.265327	+	0.265327i	−0.827214	−	0.561887i	$-0.810076\pi$
$541$	−1.80623e6	+	1.80623e6i	−0.265327	+	0.265327i	0.561887	+	0.827214i	$0.310076\pi$
$542$	−297344.	+	4.79113e6i	−0.0434771	+	0.700550i
$543$	−1.90318e6			−0.277001
$544$	1.63183e6	−	5.09584e6i	0.236416	−	0.738275i
$545$	4.26538e6			0.615129
$546$	1.80730e6	−	2.91211e7i	0.259446	−	4.18048i
$547$	−5.63925e6	+	5.63925e6i	−0.805848	+	0.805848i	−0.984003	−	0.178154i	$-0.942987\pi$
$547$	−5.63925e6	+	5.63925e6i	−0.805848	+	0.805848i	0.178154	+	0.984003i	$0.442987\pi$
$548$	515473.	−	4.13694e6i	0.0733255	−	0.588474i
$549$	−9.06073e6	−	9.06073e6i	−1.28302	−	1.28302i
$550$	−626449.	−	709350.i	−0.0883037	−	0.0999894i
$551$		−	1.75913e6i		−	0.246841i
$552$	1.52665e7	−	1.04321e7i	2.13251	−	1.45721i
$553$			8.95814e6i			1.24568i
$554$	3.62157e6	−	3.19832e6i	0.501328	−	0.442738i
$555$	3.86859e6	+	3.86859e6i	0.533114	+	0.533114i
$556$	8.09613e6	+	1.04009e7i	1.11068	+	1.42687i
$557$	5.02067e6	−	5.02067e6i	0.685684	−	0.685684i	−0.275591	−	0.961275i	$-0.588874\pi$
$557$	5.02067e6	−	5.02067e6i	0.685684	−	0.685684i	0.961275	+	0.275591i	$0.0888736\pi$
$558$	1.32474e7	+	822149.i	1.80112	+	0.111780i
$559$	−1.26099e7			−1.70680
$560$	3.83628e6	−	2.28641e6i	0.516940	−	0.308094i
$561$	6.60991e6			0.886724
$562$	−8.84256e6	−	548782.i	−1.18097	−	0.0732924i
$563$	7.18447e6	−	7.18447e6i	0.955264	−	0.955264i	−0.0437769	−	0.999041i	$-0.513939\pi$
$563$	7.18447e6	−	7.18447e6i	0.955264	−	0.955264i	0.999041	+	0.0437769i	$0.0139391\pi$
$564$	1.48807e7	−	1.15832e7i	1.96981	−	1.53331i
$565$	−1.72224e6	−	1.72224e6i	−0.226972	−	0.226972i
$566$	−1.32456e6	+	1.16976e6i	−0.173792	+	0.153481i
$567$			8.51385e6i			1.11216i
$568$	−9.40437e6	−	1.76914e6i	−1.22309	−	0.230086i
$569$			96843.1i			0.0125397i	0.999980	+	0.00626986i	$0.00199577\pi$
$569$			96843.1i			0.0125397i	−0.999980	+	0.00626986i	$0.998004\pi$
$570$	−3.18126e6	−	3.60225e6i	−0.410121	−	0.464394i
$571$	−3.13884e6	−	3.13884e6i	−0.402883	−	0.402883i	0.476365	−	0.879248i	$-0.341954\pi$
$571$	−3.13884e6	−	3.13884e6i	−0.402883	−	0.402883i	−0.879248	+	0.476365i	$0.841954\pi$
$572$	9.40055e6	+	1.17133e6i	1.20133	+	0.149689i
$573$	3.21497e6	−	3.21497e6i	0.409064	−	0.409064i
$574$	39099.8	−	630018.i	0.00495330	−	0.0798129i
$575$	2.38808e6			0.301217
$576$	−5.61619e6	+	1.43990e7i	−0.705319	+	1.80832i
$577$	5.70394e6			0.713240			0.356620	−	0.934250i	$-0.383929\pi$
$577$	5.70394e6			0.713240			0.356620	+	0.934250i	$0.383929\pi$
$578$	198537.	−	3.19904e6i	0.0247185	−	0.398291i
$579$	−2.98668e6	+	2.98668e6i	−0.370247	+	0.370247i
$580$	−1.09858e6	−	136887.i	−0.135601	−	0.0168963i
$581$	−3.22393e6	−	3.22393e6i	−0.396228	−	0.396228i
$582$	−5.22096e6	−	5.91188e6i	−0.638915	−	0.723466i
$583$		−	5.44258e6i		−	0.663183i
$584$	−3.69389e6	−	694890.i	−0.448179	−	0.0843109i
$585$			1.30411e7i			1.57553i
$586$	1.72599e6	−	1.52428e6i	0.207632	−	0.183366i
$587$	−8.41205e6	−	8.41205e6i	−1.00764	−	1.00764i	−0.999971	−	0.00767212i	$-0.997558\pi$
$587$	−8.41205e6	−	8.41205e6i	−1.00764	−	1.00764i	−0.00767212	−	0.999971i	$-0.502442\pi$
$588$	−9.19841e6	+	7.16010e6i	−1.09716	+	0.854035i
$589$	4.47146e6	−	4.47146e6i	0.531081	−	0.531081i
$590$	5.69208e6	+	353259.i	0.673196	+	0.0417795i
$591$	1.99333e7			2.34753
$592$	−4.29157e6	−	7.20067e6i	−0.503283	−	0.844439i
$593$	−1.27299e7			−1.48658			−0.743288	−	0.668971i	$-0.766735\pi$
$593$	−1.27299e7			−1.48658			−0.743288	+	0.668971i	$0.766735\pi$
$594$	−9.23836e6	−	573346.i	−1.07431	−	0.0666731i
$595$	−2.84864e6	+	2.84864e6i	−0.329872	+	0.329872i
$596$	−1.24388e6	−	1.59798e6i	−0.143437	−	0.184271i
$597$	1.25843e7	+	1.25843e7i	1.44508	+	1.44508i
$598$	−1.79179e7	+	1.58238e7i	−2.04896	+	1.80950i
$599$			8.52462e6i			0.970752i	0.874306	+	0.485376i	$0.161317\pi$
$599$			8.52462e6i			0.970752i	−0.874306	+	0.485376i	$0.838683\pi$
$600$	−2.49718e6	+	1.70640e6i	−0.283186	+	0.193510i
$601$		−	1.30387e6i		−	0.147247i	−0.997286	−	0.0736236i	$-0.976544\pi$
$601$		−	1.30387e6i		−	0.147247i	0.997286	−	0.0736236i	$-0.0234563\pi$
$602$	7.44804e6	+	8.43368e6i	0.837627	+	0.948475i
$603$	1.18614e7	+	1.18614e7i	1.32844	+	1.32844i
$604$	931825.	−	7.47837e6i	0.103930	−	0.834093i
$605$	1.58042e6	−	1.58042e6i	0.175543	−	0.175543i
$606$	66555.8	−	1.07242e6i	0.00736215	−	0.118627i
$607$	907557.			0.0999775			0.0499887	−	0.998750i	$-0.484081\pi$
$607$	907557.			0.0999775			0.0499887	+	0.998750i	$0.484081\pi$
$608$	3.37080e6	+	6.54664e6i	0.369806	+	0.718224i
$609$	6.45376e6			0.705131
$610$	−237984.	+	3.83465e6i	−0.0258954	+	0.417255i
$611$	−1.72390e7	+	1.72390e7i	−1.86813	+	1.86813i
$612$	1.72387e6	−	1.38349e7i	0.186048	−	1.49313i
$613$	−1.12318e6	−	1.12318e6i	−0.120725	−	0.120725i	0.644163	−	0.764888i	$-0.277206\pi$
$613$	−1.12318e6	−	1.12318e6i	−0.120725	−	0.120725i	−0.764888	+	0.644163i	$0.777206\pi$
$614$	9.90177e6	+	1.12121e7i	1.05997	+	1.20024i
$615$			427494.i			0.0455766i
$616$	−4.76903e6	−	6.97907e6i	−0.506382	−	0.741047i
$617$		−	4.14807e6i		−	0.438665i	−0.975650	−	0.219333i	$-0.929612\pi$
$617$		−	4.14807e6i		−	0.438665i	0.975650	−	0.219333i	$-0.0703880\pi$
$618$	−1.46420e7	+	1.29308e7i	−1.54216	+	1.36193i
$619$	5.66898e6	+	5.66898e6i	0.594673	+	0.594673i	0.938890	−	0.344217i	$-0.111856\pi$
$619$	5.66898e6	+	5.66898e6i	0.594673	+	0.594673i	−0.344217	+	0.938890i	$0.611856\pi$
$620$	−2.44450e6	−	3.14040e6i	−0.255394	−	0.328099i
$621$	1.65159e7	−	1.65159e7i	1.71860	−	1.71860i
$622$	7.85704e6	+	487619.i	0.814297	+	0.0505364i
$623$	9.36705e6			0.966902
$624$	7.42951e6	−	2.93499e7i	0.763834	−	3.01749i
$625$	−390625.			−0.0400000
$626$	−2.62230e6	−	162744.i	−0.267452	−	0.0165985i
$627$	−6.43206e6	+	6.43206e6i	−0.653403	+	0.653403i
$628$	1.10897e7	−	8.63225e6i	1.12207	−	0.873424i
$629$	5.34688e6	+	5.34688e6i	0.538857	+	0.538857i
$630$	8.72210e6	−	7.70275e6i	0.875527	−	0.773205i
$631$		−	1.29134e6i		−	0.129113i	−0.997914	−	0.0645563i	$-0.979437\pi$
$631$		−	1.29134e6i		−	0.129113i	0.997914	−	0.0645563i	$-0.0205632\pi$
$632$	−1.71850e6	+	9.13519e6i	−0.171142	+	0.909756i
$633$		−	2.01505e6i		−	0.199883i
$634$	−5.41943e6	−	6.13661e6i	−0.535464	−	0.606325i
$635$	−1.14547e6	−	1.14547e6i	−0.112733	−	0.112733i
$636$	−1.72606e7	−	2.15071e6i	−1.69204	−	0.210833i
$637$	1.06562e7	−	1.06562e7i	1.04053	−	1.04053i
$638$	−129794.	+	2.09139e6i	−0.0126242	+	0.203415i
$639$	−2.49338e7			−2.41567
$640$	4.35071e6	−	1.59566e6i	0.419866	−	0.153989i
$641$	−5.37811e6			−0.516993			−0.258496	−	0.966012i	$-0.583227\pi$
$641$	−5.37811e6			−0.516993			−0.258496	+	0.966012i	$0.583227\pi$
$642$	−1.81718e6	+	2.92804e7i	−0.174004	+	2.80375i
$643$	−1.13475e7	+	1.13475e7i	−1.08236	+	1.08236i	−0.0860758	+	0.996289i	$0.527433\pi$
$643$	−1.13475e7	+	1.13475e7i	−1.08236	+	1.08236i	−0.996289	+	0.0860758i	$0.972567\pi$
$644$	2.11664e7	+	2.63739e6i	2.01110	+	0.250588i
$645$	−5.38822e6	−	5.38822e6i	−0.509971	−	0.509971i
$646$	−4.39690e6	−	4.97877e6i	−0.414539	−	0.469398i
$647$		−	1.70776e7i		−	1.60386i	−0.597418	−	0.801930i	$-0.703807\pi$
$647$		−	1.70776e7i		−	1.60386i	0.597418	−	0.801930i	$-0.296193\pi$
$648$	−1.63327e6	+	8.68212e6i	−0.152799	+	0.812247i
$649$		−	1.07944e7i		−	1.00597i
$650$	2.93088e6	−	2.58835e6i	0.272091	−	0.240292i
$651$	1.64046e7	+	1.64046e7i	1.51710	+	1.51710i
$652$	−6.82976e6	+	5.31632e6i	−0.629197	+	0.489770i
$653$	8.80276e6	−	8.80276e6i	0.807860	−	0.807860i	−0.176450	−	0.984310i	$-0.556461\pi$
$653$	8.80276e6	−	8.80276e6i	0.807860	−	0.807860i	0.984310	+	0.176450i	$0.0564614\pi$
$654$	−2.57519e7	−	1.59820e6i	−2.35431	−	0.146112i
$655$	−1.79752e6			−0.163708
$656$	160733.	−	634969.i	0.0145830	−	0.0576093i
$657$	−9.79362e6			−0.885176
$658$	2.17118e7	+	1.34747e6i	1.95493	+	0.121326i
$659$	3.66172e6	−	3.66172e6i	0.328452	−	0.328452i	−0.523546	−	0.851997i	$-0.675391\pi$
$659$	3.66172e6	−	3.66172e6i	0.328452	−	0.328452i	0.851997	+	0.523546i	$0.175391\pi$
$660$	3.51634e6	+	4.51737e6i	0.314218	+	0.403669i
$661$	9.07999e6	+	9.07999e6i	0.808317	+	0.808317i	0.984379	−	0.176062i	$-0.0563359\pi$
$661$	9.07999e6	+	9.07999e6i	0.808317	+	0.808317i	−0.176062	+	0.984379i	$0.556336\pi$
$662$	535816.	−	473195.i	0.0475193	−	0.0419658i
$663$			2.73107e7i			2.41295i
$664$	−2.66918e6	−	3.90612e6i	−0.234941	−	0.343815i
$665$		−	5.54398e6i		−	0.486147i
$666$	−1.44580e7	−	1.63713e7i	−1.26306	−	1.43021i
$667$	−3.73889e6	−	3.73889e6i	−0.325408	−	0.325408i
$668$	1.95696e6	−	1.57056e7i	0.169684	−	1.36180i
$669$	−1.16249e7	+	1.16249e7i	−1.00421	+	1.00421i
$670$	311543.	−	5.01992e6i	0.0268121	−	0.432026i
$671$	7.27196e6			0.623512
$672$	−2.40179e7	+	1.23666e7i	−2.05169	+	1.05640i
$673$	7.73983e6			0.658709			0.329355	−	0.944206i	$-0.393169\pi$
$673$	7.73983e6			0.658709			0.329355	+	0.944206i	$0.393169\pi$
$674$	−574908.	+	9.26354e6i	−0.0487471	+	0.785466i
$675$	−2.70156e6	+	2.70156e6i	−0.228220	+	0.228220i
$676$	−3.37060e6	+	2.70508e7i	−0.283688	+	2.27674i
$677$	9.05485e6	+	9.05485e6i	0.759293	+	0.759293i	0.976194	−	0.216901i	$-0.0695947\pi$
$677$	9.05485e6	+	9.05485e6i	0.759293	+	0.759293i	−0.216901	+	0.976194i	$0.569595\pi$
$678$	9.75256e6	+	1.10432e7i	0.814788	+	0.922613i
$679$		−	9.09857e6i		−	0.757354i
$680$	−3.45141e6	+	2.35847e6i	−0.286236	+	0.195595i
$681$			2.12190e6i			0.175331i
$682$	−5.64595e6	+	4.98611e6i	−0.464810	+	0.410488i
$683$	−9.68823e6	−	9.68823e6i	−0.794681	−	0.794681i	0.187571	−	0.982251i	$-0.439939\pi$
$683$	−9.68823e6	−	9.68823e6i	−0.794681	−	0.794681i	−0.982251	+	0.187571i	$0.939939\pi$
$684$	1.17852e7	+	1.51401e7i	0.963154	+	1.23734i
$685$	−2.30303e6	+	2.30303e6i	−0.187531	+	0.187531i
$686$	3.13297e6	+	194437.i	0.254183	+	0.0157750i
$687$	−4.11361e7			−3.32531
$688$	5.97736e6	+	1.00292e7i	0.481435	+	0.807782i
$689$	2.24876e7			1.80465
$690$	−1.44179e7	−	894792.i	−1.15286	−	0.0715483i
$691$	1.51556e7	−	1.51556e7i	1.20748	−	1.20748i	0.235633	−	0.971842i	$-0.424284\pi$
$691$	1.51556e7	−	1.51556e7i	1.20748	−	1.20748i	0.971842	−	0.235633i	$-0.0757165\pi$
$692$	70059.6	−	54534.8i	0.00556163	−	0.00432921i
$693$	−1.55739e7	−	1.55739e7i	−1.23187	−	1.23187i
$694$	−379515.	+	335162.i	−0.0299110	+	0.0264153i
$695$		−	1.02973e7i		−	0.808650i
$696$	6.58132e6	+	1.23807e6i	0.514979	+	0.0968773i
$697$			590851.i			0.0460677i
$698$	−8.63829e6	−	9.78145e6i	−0.671103	−	0.759914i
$699$	4.29822e6	+	4.29822e6i	0.332733	+	0.332733i
$700$	−3.46225e6	−	431405.i	−0.267062	−	0.0332767i
$701$	−8.54126e6	+	8.54126e6i	−0.656488	+	0.656488i	−0.954547	−	0.298059i	$-0.903661\pi$
$701$	−8.54126e6	+	8.54126e6i	−0.656488	+	0.656488i	0.298059	+	0.954547i	$0.403661\pi$
$702$	2.36894e6	−	3.81709e7i	0.181431	−	2.92341i
$703$	−1.04060e7			−0.794139
$704$	−3.52444e6	−	8.03188e6i	−0.268015	−	0.610781i
$705$	−1.47324e7			−1.11635
$706$	1.05842e6	−	1.70545e7i	0.0799186	−	1.28773i
$707$	876460.	−	876460.i	0.0659452	−	0.0659452i
$708$	−3.42331e7	−	4.26554e6i	−2.56663	−	0.319809i
$709$	1.75193e6	+	1.75193e6i	0.130889	+	0.130889i	0.769516	−	0.638627i	$-0.220497\pi$
$709$	1.75193e6	+	1.75193e6i	0.130889	+	0.130889i	−0.638627	+	0.769516i	$0.720497\pi$
$710$	4.94876e6	+	5.60365e6i	0.368426	+	0.417182i
$711$			2.42202e7i			1.79682i
$712$	9.55218e6	+	1.79694e6i	0.706159	+	0.132842i
$713$		−	1.90075e7i		−	1.40024i
$714$	1.82658e7	−	1.61311e7i	1.34089	−	1.18418i
$715$	−5.23328e6	−	5.23328e6i	−0.382832	−	0.382832i
$716$	−764224.	+	594876.i	−0.0557106	+	0.0433655i
$717$	1.36851e7	−	1.36851e7i	0.994149	−	0.994149i
$718$	5.41416e6	+	336010.i	0.391940	+	0.0243243i
$719$	5.01363e6			0.361684			0.180842	−	0.983512i	$-0.442118\pi$
$719$	5.01363e6			0.361684			0.180842	+	0.983512i	$0.442118\pi$
$720$	1.03722e7	−	6.18177e6i	0.745655	−	0.444408i
$721$	−2.25346e7			−1.61440
$722$	−4.85663e6	−	301409.i	−0.346731	−	0.0215186i
$723$	2.90380e7	−	2.90380e7i	2.06595	−	2.06595i
$724$	−1.39934e6	−	1.79770e6i	−0.0992151	−	0.127459i
$725$	611581.	+	611581.i	0.0432124	+	0.0432124i
$726$	−1.01338e7	+	8.94946e6i	−0.713560	+	0.630166i
$727$		−	1.46450e7i		−	1.02767i	−0.857889	−	0.513835i	$-0.828225\pi$
$727$		−	1.46450e7i		−	1.02767i	0.857889	−	0.513835i	$-0.171775\pi$
$728$	2.88360e7	−	1.97046e7i	2.01654	−	1.37797i
$729$		−	1.66916e7i		−	1.16327i
$730$	1.94379e6	+	2.20103e6i	0.135003	+	0.152868i
$731$	−7.44720e6	−	7.44720e6i	−0.515465	−	0.515465i
$732$	2.87361e6	−	2.30622e7i	0.198222	−	1.59083i
$733$	−7.22552e6	+	7.22552e6i	−0.496718	+	0.496718i	−0.910415	−	0.413697i	$-0.864237\pi$
$733$	−7.22552e6	+	7.22552e6i	−0.496718	+	0.496718i	0.413697	+	0.910415i	$0.364237\pi$
$734$	−154745.	+	2.49342e6i	−0.0106017	+	0.170826i
$735$	9.10677e6			0.621793
$736$	2.10788e7	+	6.75002e6i	1.43434	+	0.459315i
$737$	−9.51968e6			−0.645586
$738$	105714.	−	1.70338e6i	0.00714484	−	0.115125i
$739$	−1.22662e7	+	1.22662e7i	−0.826226	+	0.826226i	−0.986993	−	0.160766i	$-0.948604\pi$
$739$	−1.22662e7	+	1.22662e7i	−0.826226	+	0.826226i	0.160766	+	0.986993i	$0.448604\pi$
$740$	−809745.	+	6.49862e6i	−0.0543587	+	0.436256i
$741$	−2.65759e7	−	2.65759e7i	−1.77804	−	1.77804i
$742$	−1.32823e7	−	1.50400e7i	−0.885651	−	1.00285i
$743$			8.77727e6i			0.583294i	0.956526	+	0.291647i	$0.0942032\pi$
$743$			8.77727e6i			0.583294i	−0.956526	+	0.291647i	$0.905797\pi$
$744$	1.35818e7	+	1.98758e7i	0.899550	+	1.31642i
$745$			1.58206e6i			0.104432i
$746$	−1.19167e7	+	1.05240e7i	−0.783986	+	0.692362i
$747$	−8.71656e6	−	8.71656e6i	−0.571536	−	0.571536i
$748$	4.86004e6	+	6.24358e6i	0.317604	+	0.408018i
$749$	−2.39300e7	+	2.39300e7i	−1.55862	+	1.55862i
$750$	2.35837e6	+	146363.i	0.153094	+	0.00950122i
$751$	1.91758e7			1.24066			0.620331	−	0.784340i	$-0.286998\pi$
$751$	1.91758e7			1.24066			0.620331	+	0.784340i	$0.286998\pi$
$752$	2.18825e7	+	5.53923e6i	1.41108	+	0.357195i
$753$	−1.83704e7			−1.18067
$754$	−8.64116e6	−	536282.i	−0.553533	−	0.0343530i
$755$	−4.16320e6	+	4.16320e6i	−0.265803	+	0.265803i
$756$	−2.69284e7	+	2.09612e7i	−1.71359	+	1.33387i
$757$	2.09939e7	+	2.09939e7i	1.33154	+	1.33154i	0.903993	+	0.427547i	$0.140622\pi$
$757$	2.09939e7	+	2.09939e7i	1.33154	+	1.33154i	0.427547	+	0.903993i	$0.359378\pi$
$758$	53923.3	−	47621.3i	0.00340881	−	0.00301043i
$759$			2.73417e7i			1.72275i
$760$	1.06354e6	−	5.65355e6i	0.0667913	−	0.355048i
$761$			1.15891e7i			0.725419i	0.931902	+	0.362709i	$0.118148\pi$
$761$			1.15891e7i			0.725419i	−0.931902	+	0.362709i	$0.881852\pi$
$762$	6.48651e6	+	7.34491e6i	0.404691	+	0.458246i
$763$	−2.10463e7	−	2.10463e7i	−1.30877	−	1.30877i
$764$	5.40065e6	+	672935.i	0.334744	+	0.0417100i
$765$	−7.70188e6	+	7.70188e6i	−0.475821	+	0.475821i
$766$	−1.84856e6	+	2.97860e7i	−0.113831	+	1.83417i
$767$	4.45999e7			2.73745
$768$	−2.68650e7	+	8.00348e6i	−1.64355	+	0.489639i
$769$	2.27526e7			1.38744			0.693721	−	0.720244i	$-0.255970\pi$
$769$	2.27526e7			1.38744			0.693721	+	0.720244i	$0.255970\pi$
$770$	−409054.	+	6.59112e6i	−0.0248630	+	0.400620i
$771$	1.92825e7	−	1.92825e7i	1.16823	−	1.16823i
$772$	−5.01715e6	−	625150.i	−0.302980	−	0.0377521i
$773$	1.08132e7	+	1.08132e7i	0.650887	+	0.650887i	0.953207	−	0.302319i	$-0.0977609\pi$
$773$	1.08132e7	+	1.08132e7i	0.650887	+	0.650887i	−0.302319	+	0.953207i	$0.597761\pi$
$774$	2.01373e7	+	2.28022e7i	1.20823	+	1.36812i
$775$			3.10911e6i			0.185944i
$776$	1.74544e6	−	9.27840e6i	0.104052	−	0.553119i
$777$		−	3.81769e7i		−	2.26855i
$778$	1.47598e7	−	1.30349e7i	0.874243	−	0.772071i
$779$	−574953.	−	574953.i	−0.0339460	−	0.0339460i
$780$	−1.86648e7	+	1.45288e7i	−1.09846	+	0.855051i
$781$	1.00057e7	−	1.00057e7i	0.586975	−	0.586975i
$782$	−1.99273e7	−	1.23672e6i	−1.16528	−	0.0723191i
$783$	8.45936e6			0.493098
$784$	−1.35265e7	−	3.42405e6i	−0.785953	−	0.198953i
$785$	−1.09792e7			−0.635909
$786$	1.08524e7	+	673514.i	0.626569	+	0.0388858i
$787$	5.08019e6	−	5.08019e6i	0.292377	−	0.292377i	−0.545642	−	0.838019i	$-0.683714\pi$
$787$	5.08019e6	−	5.08019e6i	0.292377	−	0.292377i	0.838019	+	0.545642i	$0.183714\pi$
$788$	1.46563e7	+	1.88286e7i	0.840829	+	1.08019i
$789$	2.51520e6	+	2.51520e6i	0.143840	+	0.143840i
$790$	5.44326e6	−	4.80711e6i	0.310307	−	0.274042i
$791$			1.69958e7i			0.965829i
$792$	−1.28940e7	−	1.88693e7i	−0.730426	−	1.06892i
$793$			3.00461e7i			1.69670i
$794$	−7.69886e6	−	8.71769e6i	−0.433386	−	0.490739i
$795$	9.60893e6	+	9.60893e6i	0.539209	+	0.539209i
$796$	−2.63405e6	+	2.11396e7i	−0.147347	+	1.18254i
$797$	−1.03785e6	+	1.03785e6i	−0.0578749	+	0.0578749i	−0.735452	−	0.677577i	$-0.763030\pi$
$797$	−1.03785e6	+	1.03785e6i	−0.0578749	+	0.0578749i	0.677577	+	0.735452i	$0.263030\pi$
$798$	−2.07728e6	+	3.34713e7i	−0.115475	+	1.86065i
$799$	−2.03621e7			−1.12838
$800$	−3.44792e6	−	1.10412e6i	−0.190472	−	0.0609945i
$801$	2.53257e7			1.39470
$802$	−1.04595e6	+	1.68534e7i	−0.0574215	+	0.925236i
$803$	3.93008e6	−	3.93008e6i	0.215086	−	0.215086i
$804$	−3.76183e6	+	3.01906e7i	−0.205239	+	1.64715i
$805$	−1.17833e7	−	1.17833e7i	−0.640882	−	0.640882i
$806$	−2.06015e7	−	2.33278e7i	−1.11702	−	1.26484i
$807$			1.82291e7i			0.985331i
$808$	1.06192e6	−	725645.i	0.0572220	−	0.0391017i
$809$			2.79921e7i			1.50371i	0.659327	+	0.751856i	$0.270841\pi$
$809$			2.79921e7i			1.50371i	−0.659327	+	0.751856i	$0.729159\pi$
$810$	5.17330e6	−	4.56869e6i	0.277048	−	0.244669i
$811$	−1.35385e7	−	1.35385e7i	−0.722799	−	0.722799i	0.246375	−	0.969174i	$-0.420760\pi$
$811$	−1.35385e7	−	1.35385e7i	−0.722799	−	0.722799i	−0.969174	+	0.246375i	$0.920760\pi$
$812$	4.74523e6	+	6.09608e6i	0.252561	+	0.324460i
$813$	−1.60411e7	+	1.60411e7i	−0.851152	+	0.851152i
$814$	1.23715e7	+	767793.i	0.654427	+	0.0406147i
$815$	6.76171e6			0.356585
$816$	2.17213e7	−	1.29458e7i	1.14199	−	0.680620i
$817$	1.44936e7			0.759665
$818$	3.00509e6	+	186500.i	0.157027	+	0.00974531i
$819$	6.43479e7	−	6.43479e7i	3.35216	−	3.35216i
$820$	−403801.	+	314321.i	−0.0209717	+	0.0163245i
$821$	−1.19363e7	−	1.19363e7i	−0.618033	−	0.618033i	0.326993	−	0.945027i	$-0.393964\pi$
$821$	−1.19363e7	−	1.19363e7i	−0.618033	−	0.618033i	−0.945027	+	0.326993i	$0.893964\pi$
$822$	1.47673e7	−	1.30414e7i	0.762291	−	0.673202i
$823$		−	2.57975e7i		−	1.32763i	−0.747897	−	0.663815i	$-0.768936\pi$
$823$		−	2.57975e7i		−	1.32763i	0.747897	−	0.663815i	$-0.231064\pi$
$824$	−2.29799e7	−	4.32296e6i	−1.17905	−	0.221801i
$825$		−	4.47236e6i		−	0.228771i
$826$	−2.63429e7	−	2.98290e7i	−1.34343	−	1.52121i
$827$	1.25623e7	+	1.25623e7i	0.638715	+	0.638715i	0.950238	−	0.311524i	$-0.100839\pi$
$827$	1.25623e7	+	1.25623e7i	0.638715	+	0.638715i	−0.311524	+	0.950238i	$0.600839\pi$
$828$	5.72278e7	+	7.13073e6i	2.90089	+	0.361458i
$829$	1.41127e7	−	1.41127e7i	0.713218	−	0.713218i	−0.253989	−	0.967207i	$-0.581743\pi$
$829$	1.41127e7	−	1.41127e7i	0.713218	−	0.713218i	0.967207	+	0.253989i	$0.0817427\pi$
$830$	−228944.	+	3.68899e6i	−0.0115354	+	0.185871i
$831$	2.28335e7			1.14702
$832$	3.31860e7	−	1.45622e7i	1.66206	−	0.729322i
$833$	1.25867e7			0.628492
$834$	−3.85830e6	+	6.21690e7i	−0.192079	+	3.09499i
$835$	−8.74328e6	+	8.74328e6i	−0.433968	+	0.433968i
$836$	−1.08048e7	−	1.34631e6i	−0.534691	−	0.0666239i
$837$	2.15026e7	+	2.15026e7i	1.06090	+	1.06090i
$838$	−2.28456e7	−	2.58689e7i	−1.12381	−	1.27253i
$839$			3.23608e7i			1.58714i	0.608481	+	0.793568i	$0.291779\pi$
$839$			3.23608e7i			1.58714i	−0.608481	+	0.793568i	$0.708221\pi$
$840$	2.07414e7	+	3.90184e6i	1.01424	+	0.190797i
$841$			1.85961e7i			0.906634i
$842$	−1.73399e7	+	1.53134e7i	−0.842880	+	0.744373i
$843$	−2.96056e7	−	2.96056e7i	−1.43484	−	1.43484i
$844$	1.90337e6	−	1.48159e6i	0.0919745	−	0.0715934i
$845$	1.50592e7	−	1.50592e7i	0.725536	−	0.725536i
$846$	5.87024e7	+	3.64315e6i	2.81988	+	0.175005i
$847$	−1.55962e7			−0.746984
$848$	−1.06596e7	−	1.78853e7i	−0.509037	−	0.854094i
$849$	−8.35117e6			−0.397629
$850$	3.25956e6	+	202293.i	0.154743	+	0.00960359i
$851$	−2.21172e7	+	2.21172e7i	−1.04690	+	1.04690i
$852$	−2.77781e7	−	3.56858e7i	−1.31100	−	1.68421i
$853$	1.51141e7	+	1.51141e7i	0.711231	+	0.711231i	0.966793	−	0.255561i	$-0.0822603\pi$
$853$	1.51141e7	+	1.51141e7i	0.711231	+	0.711231i	−0.255561	+	0.966793i	$0.582260\pi$
$854$	2.00953e7	−	1.77467e7i	0.942864	−	0.832672i
$855$		−	1.49893e7i		−	0.701239i
$856$	−2.89937e7	+	1.98123e7i	−1.35244	+	0.924169i
$857$		−	2.54307e7i		−	1.18279i	−0.806383	−	0.591393i	$-0.798578\pi$
$857$		−	2.54307e7i		−	1.18279i	0.806383	−	0.591393i	$-0.201422\pi$
$858$	2.96346e7	+	3.35563e7i	1.37430	+	1.55617i
$859$	−1.86611e7	−	1.86611e7i	−0.862888	−	0.862888i	0.128785	−	0.991673i	$-0.458892\pi$
$859$	−1.86611e7	−	1.86611e7i	−0.862888	−	0.862888i	−0.991673	+	0.128785i	$0.958892\pi$
$860$	1.12782e6	−	9.05135e6i	0.0519990	−	0.417318i
$861$	2.10935e6	−	2.10935e6i	0.0969707	−	0.0969707i
$862$	−532154.	+	8.57464e6i	−0.0243932	+	0.393050i
$863$	−1.51436e7			−0.692151			−0.346076	−	0.938207i	$-0.612486\pi$
$863$	−1.51436e7			−0.692151			−0.346076	+	0.938207i	$0.612486\pi$
$864$	−3.14818e7	+	1.62097e7i	−1.43475	+	0.738737i
$865$	−69361.6			−0.00315194
$866$	−1.05441e6	+	1.69897e7i	−0.0477764	+	0.769825i
$867$	1.07106e7	−	1.07106e7i	0.483913	−	0.483913i
$868$	−3.43369e6	+	2.75571e7i	−0.154690	+	1.24147i
$869$	−9.71931e6	−	9.71931e6i	−0.436602	−	0.436602i
$870$	−3.46321e6	−	3.92152e6i	−0.155125	−	0.175653i
$871$		−	3.93332e7i		−	1.75677i
$872$	−1.74248e7	−	2.54997e7i	−0.776028	−	1.13565i
$873$		−	2.45999e7i		−	1.09244i
$874$	2.05946e7	−	1.81877e7i	0.911956	−	0.805376i
$875$	1.92743e6	+	1.92743e6i	0.0851056	+	0.0851056i
$876$	−1.09108e7	−	1.40168e7i	−0.480392	−	0.617148i
$877$	−2.37412e7	+	2.37412e7i	−1.04233	+	1.04233i	−0.0432628	+	0.999064i	$0.513775\pi$
$877$	−2.37412e7	+	2.37412e7i	−1.04233	+	1.04233i	−0.999064	+	0.0432628i	$0.986225\pi$
$878$	2.12064e6	+	131610.i	0.0928393	+	0.00576173i
$879$	1.08822e7			0.475054
$880$	−1.68156e6	+	6.64292e6i	−0.0731991	+	0.289169i
$881$	2.76050e7			1.19825			0.599125	−	0.800655i	$-0.295515\pi$
$881$	2.76050e7			1.19825			0.599125	+	0.800655i	$0.295515\pi$
$882$	−3.62866e7	−	2.25200e6i	−1.57063	−	0.0974757i
$883$	1.16330e7	−	1.16330e7i	0.502099	−	0.502099i	−0.409991	−	0.912090i	$-0.634468\pi$
$883$	1.16330e7	−	1.16330e7i	0.502099	−	0.502099i	0.912090	+	0.409991i	$0.134468\pi$
$884$	−2.57971e7	+	2.00806e7i	−1.11030	+	0.864263i
$885$	1.90575e7	+	1.90575e7i	0.817916	+	0.817916i
$886$	2.09777e7	−	1.85260e7i	0.897786	−	0.792862i
$887$		−	1.76720e7i		−	0.754184i	−0.926176	−	0.377092i	$-0.876924\pi$
$887$		−	1.76720e7i		−	0.754184i	0.926176	−	0.377092i	$-0.123076\pi$
$888$	7.32374e6	−	3.89315e7i	0.311674	−	1.65679i
$889$			1.13040e7i			0.479711i
$890$	−5.02654e6	−	5.69173e6i	−0.212713	−	0.240862i
$891$	−9.23726e6	−	9.23726e6i	−0.389806	−	0.389806i
$892$	−1.95280e7	−	2.43324e6i	−0.821760	−	0.102393i
$893$	1.98142e7	−	1.98142e7i	0.831472	−	0.831472i
$894$	592783.	−	9.55156e6i	0.0248057	−	0.399697i
$895$	756610.			0.0315729
$896$	−2.93407e7	−	1.35941e7i	−1.22096	−	0.565691i
$897$	−1.12970e8			−4.68794
$898$	2.39888e6	−	3.86533e7i	0.0992699	−	1.59954i
$899$	4.86777e6	−	4.86777e6i	0.200877	−	0.200877i
$900$	−9.36089e6	−	1.16639e6i	−0.385222	−	0.0479997i
$901$	1.32808e7	+	1.32808e7i	0.545018	+	0.545018i
$902$	641128.	+	725972.i	0.0262378	+	0.0297100i
$903$			5.31733e7i			2.17007i
$904$	−3.26042e6	+	1.73317e7i	−0.132694	+	0.705375i
$905$			1.77979e6i			0.0722351i
$906$	2.66949e7	−	2.35751e7i	1.08046	−	0.954185i
$907$	−9.33679e6	−	9.33679e6i	−0.376859	−	0.376859i	0.493108	−	0.869968i	$-0.335861\pi$
$907$	−9.33679e6	−	9.33679e6i	−0.376859	−	0.376859i	−0.869968	+	0.493108i	$0.835861\pi$
$908$	−2.00430e6	+	1.56016e6i	−0.0806768	+	0.0627993i
$909$	2.36969e6	−	2.36969e6i	0.0951221	−	0.0951221i
$910$	−2.72331e7	−	1.69012e6i	−1.09017	−	0.0676573i
$911$	−2.27888e7			−0.909759			−0.454879	−	0.890553i	$-0.650318\pi$
$911$	−2.27888e7			−0.909759			−0.454879	+	0.890553i	$0.650318\pi$
$912$	−8.53937e6	+	3.37344e7i	−0.339968	+	1.34303i
$913$	6.99573e6			0.277751
$914$	4.53875e7	+	2.81681e6i	1.79709	+	0.111530i
$915$	−1.28387e7	+	1.28387e7i	−0.506954	+	0.506954i
$916$	−3.02459e7	−	3.88563e7i	−1.19105	−	1.53011i
$917$	8.86937e6	+	8.86937e6i	0.348313	+	0.348313i
$918$	2.39421e7	−	2.11440e7i	0.937683	−	0.828096i
$919$			4.21933e7i			1.64799i	0.566596	+	0.823995i	$0.308260\pi$
$919$			4.21933e7i			1.64799i	−0.566596	+	0.823995i	$0.691740\pi$
$920$	−9.75574e6	−	1.42767e7i	−0.380006	−	0.556107i
$921$			7.06910e7i			2.74609i
$922$	9.11362e6	+	1.03197e7i	0.353072	+	0.399796i
$923$	4.13413e7	+	4.13413e7i	1.59728	+	1.59728i
$924$	4.93926e6	−	3.96401e7i	0.190319	−	1.52741i
$925$	3.61777e6	−	3.61777e6i	0.139023	−	0.139023i
$926$	−1.63557e6	+	2.63540e7i	−0.0626817	+	1.00999i
$927$	−6.09268e7			−2.32868
$928$	3.66956e6	+	7.12688e6i	0.139876	+	0.271662i
$929$	−3.17743e7			−1.20791			−0.603957	−	0.797017i	$-0.706410\pi$
$929$	−3.17743e7			−1.20791			−0.603957	+	0.797017i	$0.706410\pi$
$930$	1.16495e6	−	1.87710e7i	0.0441674	−	0.711672i
$931$	−1.22480e7	+	1.22480e7i	−0.463119	+	0.463119i
$932$	−899673.	+	7.22033e6i	−0.0339269	+	0.272281i
$933$	2.63060e7	+	2.63060e7i	0.989351	+	0.989351i
$934$	4.91336e6	+	5.56358e6i	0.184294	+	0.208683i
$935$		−	6.18137e6i		−	0.231236i
$936$	7.79640e7	−	5.32754e7i	2.90874	−	1.98764i
$937$		−	4.05781e7i		−	1.50988i	−0.655793	−	0.754941i	$-0.727666\pi$
$937$		−	4.05781e7i		−	1.50988i	0.655793	−	0.754941i	$-0.272334\pi$
$938$	−2.63066e7	+	2.32322e7i	−0.976243	+	0.862150i
$939$	−8.77967e6	−	8.77967e6i	−0.324948	−	0.324948i
$940$	−1.08322e7	−	1.39159e7i	−0.399851	−	0.513679i
$941$	−1.12070e7	+	1.12070e7i	−0.412587	+	0.412587i	−0.882639	−	0.470052i	$-0.844235\pi$
$941$	−1.12070e7	+	1.12070e7i	−0.412587	+	0.412587i	0.470052	+	0.882639i	$0.344235\pi$
$942$	6.62858e7	+	4.11379e6i	2.43385	+	0.151048i
$943$	−2.44404e6			−0.0895013
$944$	−2.11413e7	−	3.54721e7i	−0.772149	−	1.29556i
$945$	2.66601e7			0.971142
$946$	−1.72312e7	−	1.06939e6i	−0.626018	−	0.0388516i
$947$	7.79436e6	−	7.79436e6i	0.282427	−	0.282427i	−0.551649	−	0.834076i	$-0.686001\pi$
$947$	7.79436e6	−	7.79436e6i	0.282427	−	0.282427i	0.834076	+	0.551649i	$0.186001\pi$
$948$	−3.46644e7	+	2.69830e7i	−1.25275	+	0.975145i
$949$	1.62382e7	+	1.62382e7i	0.585292	+	0.585292i
$950$	−3.36871e6	+	2.97501e6i	−0.121103	+	0.106950i
$951$		−	3.86905e7i		−	1.38725i
$952$	2.86672e7	+	5.39284e6i	1.02516	+	0.192853i
$953$			1.50521e7i			0.536864i	0.963299	+	0.268432i	$0.0865055\pi$
$953$			1.50521e7i			0.536864i	−0.963299	+	0.268432i	$0.913495\pi$
$954$	−3.59113e7	−	4.06637e7i	−1.27750	−	1.44656i
$955$	−3.00654e6	−	3.00654e6i	−0.106674	−	0.106674i
$956$	2.29889e7	+	2.86448e6i	0.813529	+	0.101368i
$957$	−7.00213e6	+	7.00213e6i	−0.247144	+	0.247144i
$958$	−360889.	+	5.81503e6i	−0.0127046	+	0.204710i
$959$	2.27273e7			0.797997
$960$	2.04028e7	+	7.95792e6i	0.714516	+	0.278690i
$961$	−3.88275e6			−0.135622
$962$	−3.17235e6	+	5.11163e7i	−0.110521	+	1.78083i
$963$	−6.46998e7	+	6.46998e7i	−2.24821	+	2.24821i
$964$	4.87792e7	+	6.07802e6i	1.69061	+	0.210654i
$965$	2.79304e6	+	2.79304e6i	0.0965515	+	0.0965515i
$966$	6.67258e7	+	7.55560e7i	2.30065	+	2.60511i
$967$			2.76392e7i			0.950516i	0.879846	+	0.475258i	$0.157645\pi$
$967$			2.76392e7i			0.950516i	−0.879846	+	0.475258i	$0.842355\pi$
$968$	−1.59045e7	−	2.99193e6i	−0.545546	−	0.102627i
$969$		−	3.13905e7i		−	1.07396i
$970$	−5.52859e6	+	4.88247e6i	−0.188662	+	0.166613i
$971$	8.33388e6	+	8.33388e6i	0.283661	+	0.283661i	0.834567	−	0.550906i	$-0.185718\pi$
$971$	8.33388e6	+	8.33388e6i	0.283661	+	0.283661i	−0.550906	+	0.834567i	$0.685718\pi$
$972$	4.56454e6	−	3.55306e6i	0.154964	−	0.120625i
$973$	−5.08091e7	+	5.08091e7i	−1.72052	+	1.72052i
$974$	−2.11708e7	−	1.31389e6i	−0.715055	−	0.0443773i
$975$	1.84788e7			0.622533
$976$	2.38969e7	−	1.42425e7i	0.803003	−	0.478587i
$977$	−3.12703e7			−1.04808			−0.524041	−	0.851693i	$-0.675576\pi$
$977$	−3.12703e7			−1.04808			−0.524041	+	0.851693i	$0.675576\pi$
$978$	−4.08233e7	−	2.53355e6i	−1.36477	−	0.0846998i
$979$	−1.01630e7	+	1.01630e7i	−0.338894	+	0.338894i
$980$	6.69588e6	+	8.60205e6i	0.222712	+	0.286112i
$981$	−5.69030e7	−	5.69030e7i	−1.88783	−	1.88783i
$982$	1.90632e7	−	1.68353e7i	0.630836	−	0.557110i
$983$		−	3.33999e7i		−	1.10246i	−0.834355	−	0.551228i	$-0.814159\pi$
$983$		−	3.33999e7i		−	1.10246i	0.834355	−	0.551228i	$-0.185841\pi$
$984$	2.55569e6	−	1.74639e6i	0.0841435	−	0.0574980i
$985$		−	1.86410e7i		−	0.612179i
$986$	−4.78660e6	−	5.42004e6i	−0.156796	−	0.177546i
$987$	7.26930e7	+	7.26930e7i	2.37520	+	2.37520i
$988$	5.56267e6	−	4.46432e7i	0.181297	−	1.45500i
$989$	3.08052e7	−	3.08052e7i	1.00146	−	1.00146i
$990$	−1.10596e6	+	1.78205e7i	−0.0358635	+	0.577871i
$991$	−4.48473e7			−1.45061			−0.725307	−	0.688425i	$-0.758302\pi$
$991$	−4.48473e7			−1.45061			−0.725307	+	0.688425i	$0.758302\pi$
$992$	−8.78803e6	+	2.74431e7i	−0.283539	+	0.885429i
$993$	3.37825e6			0.108722
$994$	3.23141e6	−	5.20679e7i	0.103735	−	1.67149i
$995$	1.17684e7	−	1.17684e7i	0.376843	−	0.376843i
$996$	2.76446e6	−	2.21862e7i	0.0883003	−	0.708655i
$997$	8.52485e6	+	8.52485e6i	0.271612	+	0.271612i	0.829749	−	0.558137i	$-0.188484\pi$
$997$	8.52485e6	+	8.52485e6i	0.271612	+	0.271612i	−0.558137	+	0.829749i	$0.688484\pi$
$998$	−4.95507e6	−	5.61080e6i	−0.157479	−	0.178319i
$999$		−	5.00409e7i		−	1.58640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.19	✓	80
4.3	odd	2		320.6.l.a.241.38		80
16.3	odd	4		320.6.l.a.81.38		80
16.13	even	4	inner	80.6.l.a.61.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.19	✓	80	1.1	even	1	trivial
80.6.l.a.61.19	yes	80	16.13	even	4	inner
320.6.l.a.81.38		80	16.3	odd	4
320.6.l.a.241.38		80	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.350398 + 5.64599i) q^{2} +(-18.9032 + 18.9032i) q^{3} +(-31.7544 - 3.95669i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-100.104 - 113.351i) q^{6} -174.451i q^{7} +(33.4661 - 177.899i) q^{8} -471.664i q^{9} +O(q^{10})\)	\(q+(-0.350398 + 5.64599i) q^{2} +(-18.9032 + 18.9032i) q^{3} +(-31.7544 - 3.95669i) q^{4} +(17.6777 + 17.6777i) q^{5} +(-100.104 - 113.351i) q^{6} -174.451i q^{7} +(33.4661 - 177.899i) q^{8} -471.664i q^{9} +(-106.002 + 93.6138i) q^{10} +(189.274 + 189.274i) q^{11} +(675.056 - 525.467i) q^{12} +(-782.038 + 782.038i) q^{13} +(984.949 + 61.1273i) q^{14} -668.330 q^{15} +(992.689 + 251.285i) q^{16} -923.717 q^{17} +(2663.01 + 165.270i) q^{18} +(898.863 - 898.863i) q^{19} +(-491.399 - 631.290i) q^{20} +(3297.69 + 3297.69i) q^{21} +(-1134.96 + 1002.32i) q^{22} -3820.93i q^{23} +(2730.25 + 3995.48i) q^{24} +625.000i q^{25} +(-4141.36 - 4689.41i) q^{26} +(4322.49 + 4322.49i) q^{27} +(-690.248 + 5539.59i) q^{28} +(978.529 - 978.529i) q^{29} +(234.182 - 3773.39i) q^{30} +4974.58 q^{31} +(-1766.59 + 5516.67i) q^{32} -7155.78 q^{33} +(323.669 - 5215.30i) q^{34} +(3083.89 - 3083.89i) q^{35} +(-1866.23 + 14977.4i) q^{36} +(-5788.44 - 5788.44i) q^{37} +(4760.01 + 5389.93i) q^{38} -29566.1i q^{39} +(3736.44 - 2553.23i) q^{40} -639.645i q^{41} +(-19774.2 + 17463.2i) q^{42} +(8062.21 + 8062.21i) q^{43} +(-5261.39 - 6759.19i) q^{44} +(8337.92 - 8337.92i) q^{45} +(21573.0 + 1338.85i) q^{46} +22043.6 q^{47} +(-23515.1 + 14014.9i) q^{48} -13626.1 q^{49} +(-3528.74 - 218.999i) q^{50} +(17461.2 - 17461.2i) q^{51} +(27927.5 - 21738.9i) q^{52} +(-14377.5 - 14377.5i) q^{53} +(-25919.3 + 22890.2i) q^{54} +6691.84i q^{55} +(-31034.6 - 5838.20i) q^{56} +33982.8i q^{57} +(5181.89 + 5867.64i) q^{58} +(-28515.2 - 28515.2i) q^{59} +(21222.4 + 2644.37i) q^{60} +(19210.1 - 19210.1i) q^{61} +(-1743.08 + 28086.4i) q^{62} -82282.3 q^{63} +(-30528.0 - 11907.2i) q^{64} -27649.2 q^{65} +(2507.37 - 40401.5i) q^{66} +(-25147.9 + 25147.9i) q^{67} +(29332.1 + 3654.86i) q^{68} +(72228.0 + 72228.0i) q^{69} +(16331.0 + 18492.2i) q^{70} -52863.6i q^{71} +(-83908.5 - 15784.8i) q^{72} -20764.0i q^{73} +(34709.7 - 30653.2i) q^{74} +(-11814.5 - 11814.5i) q^{75} +(-32099.4 + 24986.4i) q^{76} +(33019.0 - 33019.0i) q^{77} +(166930. + 10359.9i) q^{78} -51350.5 q^{79} +(13106.3 + 21990.6i) q^{80} -48803.7 q^{81} +(3611.43 + 224.130i) q^{82} +(18480.4 - 18480.4i) q^{83} +(-91668.3 - 117764. i) q^{84} +(-16329.2 - 16329.2i) q^{85} +(-48344.1 + 42694.2i) q^{86} +36994.7i q^{87} +(40005.9 - 27337.4i) q^{88} +53694.4i q^{89} +(44154.2 + 49997.4i) q^{90} +(136427. + 136427. i) q^{91} +(-15118.2 + 121332. i) q^{92} +(-94035.5 + 94035.5i) q^{93} +(-7724.04 + 124458. i) q^{94} +31779.6 q^{95} +(-70888.6 - 137677. i) q^{96} +52155.5 q^{97} +(4774.58 - 76933.1i) q^{98} +(89273.7 - 89273.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

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