LMFDB - Embedded newform 80.6.l.a.61.20

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			61.20
Character	$\chi$	$=$	80.61
Dual form			80.6.l.a.21.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0219870 - 5.65681i) q^{2} +(9.88924 + 9.88924i) q^{3} +(-31.9990 + 0.248752i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(55.7241 - 56.1590i) q^{6} -122.335i q^{7} +(2.11071 + 181.007i) q^{8} -47.4058i q^{9} +O(q^{10})$	\(q+(-0.0219870 - 5.65681i) q^{2} +(9.88924 + 9.88924i) q^{3} +(-31.9990 + 0.248752i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(55.7241 - 56.1590i) q^{6} -122.335i q^{7} +(2.11071 + 181.007i) q^{8} -47.4058i q^{9} +(100.388 + 99.6106i) q^{10} +(-301.232 + 301.232i) q^{11} +(-318.906 - 313.986i) q^{12} +(-384.386 - 384.386i) q^{13} +(-692.028 + 2.68978i) q^{14} -349.637 q^{15} +(1023.88 - 15.9197i) q^{16} -1558.08 q^{17} +(-268.166 + 1.04231i) q^{18} +(-2096.85 - 2096.85i) q^{19} +(561.271 - 570.066i) q^{20} +(1209.80 - 1209.80i) q^{21} +(1710.63 + 1697.39i) q^{22} +4768.93i q^{23} +(-1769.15 + 1810.90i) q^{24} -625.000i q^{25} +(-2165.95 + 2182.85i) q^{26} +(2871.89 - 2871.89i) q^{27} +(30.4312 + 3914.61i) q^{28} +(-1907.21 - 1907.21i) q^{29} +(7.68747 + 1977.83i) q^{30} +1152.69 q^{31} +(-112.567 - 5791.52i) q^{32} -5957.91 q^{33} +(34.2576 + 8813.79i) q^{34} +(2162.60 + 2162.60i) q^{35} +(11.7923 + 1516.94i) q^{36} +(-7429.66 + 7429.66i) q^{37} +(-11815.4 + 11907.6i) q^{38} -7602.58i q^{39} +(-3237.09 - 3162.47i) q^{40} +4115.54i q^{41} +(-6870.23 - 6817.03i) q^{42} +(8400.86 - 8400.86i) q^{43} +(9564.19 - 9714.06i) q^{44} +(838.025 + 838.025i) q^{45} +(26976.9 - 104.854i) q^{46} -8941.71 q^{47} +(10282.8 + 9967.93i) q^{48} +1841.08 q^{49} +(-3535.51 + 13.7419i) q^{50} +(-15408.3 - 15408.3i) q^{51} +(12395.6 + 12204.4i) q^{52} +(24969.5 - 24969.5i) q^{53} +(-16308.9 - 16182.6i) q^{54} -10650.2i q^{55} +(22143.5 - 258.214i) q^{56} -41472.4i q^{57} +(-10746.8 + 10830.6i) q^{58} +(23257.6 - 23257.6i) q^{59} +(11188.1 - 86.9731i) q^{60} +(14305.9 + 14305.9i) q^{61} +(-25.3441 - 6520.54i) q^{62} -5799.41 q^{63} +(-32759.1 + 764.106i) q^{64} +13590.1 q^{65} +(130.996 + 33702.8i) q^{66} +(-38864.6 - 38864.6i) q^{67} +(49857.2 - 387.577i) q^{68} +(-47161.1 + 47161.1i) q^{69} +(12185.9 - 12281.0i) q^{70} +12843.7i q^{71} +(8580.79 - 100.060i) q^{72} +28584.7i q^{73} +(42191.5 + 41864.8i) q^{74} +(6180.78 - 6180.78i) q^{75} +(67618.6 + 66575.4i) q^{76} +(36851.3 + 36851.3i) q^{77} +(-43006.4 + 167.158i) q^{78} -50757.6 q^{79} +(-17818.3 + 18381.2i) q^{80} +45282.1 q^{81} +(23280.9 - 90.4884i) q^{82} +(-39493.3 - 39493.3i) q^{83} +(-38411.6 + 39013.5i) q^{84} +(27543.3 - 27543.3i) q^{85} +(-47706.8 - 47337.3i) q^{86} -37721.7i q^{87} +(-55160.9 - 53889.3i) q^{88} +97259.4i q^{89} +(4722.12 - 4758.97i) q^{90} +(-47024.0 + 47024.0i) q^{91} +(-1186.28 - 152601. i) q^{92} +(11399.2 + 11399.2i) q^{93} +(196.601 + 50581.6i) q^{94} +74134.7 q^{95} +(56160.6 - 58387.0i) q^{96} -46757.9 q^{97} +(-40.4798 - 10414.6i) q^{98} +(14280.1 + 14280.1i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0219870	−	5.65681i	−0.00388679	−	0.999992i
$2$	−0.0219870	−	5.65681i	−0.00388679	−	0.999992i
$3$	9.88924	+	9.88924i	0.634395	+	0.634395i	0.949167	−	0.314772i	$-0.101928\pi$
$3$	9.88924	+	9.88924i	0.634395	+	0.634395i	−0.314772	+	0.949167i	$0.601928\pi$
$4$	−31.9990	+	0.248752i	−0.999970	+	0.00777351i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$	55.7241	−	56.1590i	0.631925	−	0.636856i
$7$		−	122.335i		−	0.943641i	−0.881695	−	0.471820i	$-0.843597\pi$
$7$		−	122.335i		−	0.943641i	0.881695	−	0.471820i	$-0.156403\pi$
$8$	2.11071	+	181.007i	0.0116601	+	0.999932i
$9$		−	47.4058i		−	0.195086i
$10$	100.388	+	99.6106i	0.317454	+	0.314996i
$11$	−301.232	+	301.232i	−0.750618	+	0.750618i	−0.974595	−	0.223976i	$-0.928096\pi$
$11$	−301.232	+	301.232i	−0.750618	+	0.750618i	0.223976	+	0.974595i	$0.428096\pi$
$12$	−318.906	−	313.986i	−0.639307	−	0.629444i
$13$	−384.386	−	384.386i	−0.630826	−	0.630826i	0.317449	−	0.948275i	$-0.397174\pi$
$13$	−384.386	−	384.386i	−0.630826	−	0.630826i	−0.948275	+	0.317449i	$0.897174\pi$
$14$	−692.028	+	2.68978i	−0.943633	+	0.00366773i
$15$	−349.637			−0.401227
$16$	1023.88	−	15.9197i	0.999879	−	0.0155466i
$17$	−1558.08			−1.30758			−0.653791	−	0.756676i	$-0.726822\pi$
$17$	−1558.08			−1.30758			−0.653791	+	0.756676i	$0.726822\pi$
$18$	−268.166	+	1.04231i	−0.195084	+	0.000758256i
$19$	−2096.85	−	2096.85i	−1.33255	−	1.33255i	−0.903085	−	0.429462i	$-0.858703\pi$
$19$	−2096.85	−	2096.85i	−1.33255	−	1.33255i	−0.429462	−	0.903085i	$-0.641297\pi$
$20$	561.271	−	570.066i	0.313760	−	0.318676i
$21$	1209.80	−	1209.80i	0.598641	−	0.598641i
$22$	1710.63	+	1697.39i	0.753530	+	0.747695i
$23$			4768.93i			1.87975i	0.341513	+	0.939877i	$0.389061\pi$
$23$			4768.93i			1.87975i	−0.341513	+	0.939877i	$0.610939\pi$
$24$	−1769.15	+	1810.90i	−0.626955	+	0.641749i
$25$		−	625.000i		−	0.200000i
$26$	−2165.95	+	2182.85i	−0.628370	+	0.633273i
$27$	2871.89	−	2871.89i	0.758157	−	0.758157i
$28$	30.4312	+	3914.61i	0.00733540	+	0.943612i
$29$	−1907.21	−	1907.21i	−0.421117	−	0.421117i	0.464471	−	0.885588i	$-0.346244\pi$
$29$	−1907.21	−	1907.21i	−0.421117	−	0.421117i	−0.885588	+	0.464471i	$0.846244\pi$
$30$	7.68747	+	1977.83i	0.00155948	+	0.401224i
$31$	1152.69			0.215431			0.107715	−	0.994182i	$-0.465646\pi$
$31$	1152.69			0.215431			0.107715	+	0.994182i	$0.465646\pi$
$32$	−112.567	−	5791.52i	−0.0194328	−	0.999811i
$33$	−5957.91			−0.952377
$34$	34.2576	+	8813.79i	0.00508229	+	1.30757i
$35$	2162.60	+	2162.60i	0.298405	+	0.298405i
$36$	11.7923	+	1516.94i	0.00151650	+	0.195080i
$37$	−7429.66	+	7429.66i	−0.892205	+	0.892205i	−0.994730	−	0.102525i	$-0.967308\pi$
$37$	−7429.66	+	7429.66i	−0.892205	+	0.892205i	0.102525	+	0.994730i	$0.467308\pi$
$38$	−11815.4	+	11907.6i	−1.32736	+	1.33772i
$39$		−	7602.58i		−	0.800386i
$40$	−3237.09	−	3162.47i	−0.319894	−	0.312519i
$41$			4115.54i			0.382356i	0.981555	+	0.191178i	$0.0612307\pi$
$41$			4115.54i			0.382356i	−0.981555	+	0.191178i	$0.938769\pi$
$42$	−6870.23	−	6817.03i	−0.600963	−	0.596310i
$43$	8400.86	−	8400.86i	0.692871	−	0.692871i	−0.269992	−	0.962863i	$-0.587021\pi$
$43$	8400.86	−	8400.86i	0.692871	−	0.692871i	0.962863	+	0.269992i	$0.0870210\pi$
$44$	9564.19	−	9714.06i	0.744761	−	0.756430i
$45$	838.025	+	838.025i	0.0616915	+	0.0616915i
$46$	26976.9	−	104.854i	1.87974	−	0.00730620i
$47$	−8941.71			−0.590441			−0.295220	−	0.955429i	$-0.595393\pi$
$47$	−8941.71			−0.590441			−0.295220	+	0.955429i	$0.595393\pi$
$48$	10282.8	+	9967.93i	0.644181	+	0.624456i
$49$	1841.08			0.109543
$50$	−3535.51	+	13.7419i	−0.199998	+	0.000777357i
$51$	−15408.3	−	15408.3i	−0.829523	−	0.829523i
$52$	12395.6	+	12204.4i	0.635711	+	0.625903i
$53$	24969.5	−	24969.5i	1.22101	−	1.22101i	0.253738	−	0.967273i	$-0.418340\pi$
$53$	24969.5	−	24969.5i	1.22101	−	1.22101i	0.967273	−	0.253738i	$-0.0816601\pi$
$54$	−16308.9	−	16182.6i	−0.761098	−	0.755204i
$55$		−	10650.2i		−	0.474733i
$56$	22143.5	−	258.214i	0.943576	−	0.0110030i
$57$		−	41472.4i		−	1.69072i
$58$	−10746.8	+	10830.6i	−0.419477	+	0.422751i
$59$	23257.6	−	23257.6i	0.869831	−	0.869831i	−0.122622	−	0.992453i	$-0.539130\pi$
$59$	23257.6	−	23257.6i	0.869831	−	0.869831i	0.992453	+	0.122622i	$0.0391303\pi$
$60$	11188.1	−	86.9731i	0.401215	−	0.00311894i
$61$	14305.9	+	14305.9i	0.492257	+	0.492257i	0.909017	−	0.416760i	$-0.136834\pi$
$61$	14305.9	+	14305.9i	0.492257	+	0.492257i	−0.416760	+	0.909017i	$0.636834\pi$
$62$	−25.3441	−	6520.54i	−0.000837333	−	0.215429i
$63$	−5799.41			−0.184091
$64$	−32759.1	+	764.106i	−0.999728	+	0.0233187i
$65$	13590.1			0.398970
$66$	130.996	+	33702.8i	0.00370168	+	0.952370i
$67$	−38864.6	−	38864.6i	−1.05771	−	1.05771i	−0.998229	−	0.0594820i	$-0.981055\pi$
$67$	−38864.6	−	38864.6i	−1.05771	−	1.05771i	−0.0594820	−	0.998229i	$-0.518945\pi$
$68$	49857.2	−	387.577i	1.30754	−	0.0101645i
$69$	−47161.1	+	47161.1i	−1.19251	+	1.19251i
$70$	12185.9	−	12281.0i	0.297243	−	0.299563i
$71$			12843.7i			0.302373i	0.988505	+	0.151187i	$0.0483094\pi$
$71$			12843.7i			0.302373i	−0.988505	+	0.151187i	$0.951691\pi$
$72$	8580.79	−	100.060i	0.195073	−	0.00227472i
$73$			28584.7i			0.627807i	0.949455	+	0.313904i	$0.101637\pi$
$73$			28584.7i			0.627807i	−0.949455	+	0.313904i	$0.898363\pi$
$74$	42191.5	+	41864.8i	0.895666	+	0.888731i
$75$	6180.78	−	6180.78i	0.126879	−	0.126879i
$76$	67618.6	+	66575.4i	1.34287	+	1.32215i
$77$	36851.3	+	36851.3i	0.708314	+	0.708314i
$78$	−43006.4	+	167.158i	−0.800380	+	0.00311093i
$79$	−50757.6			−0.915025			−0.457513	−	0.889203i	$-0.651260\pi$
$79$	−50757.6			−0.915025			−0.457513	+	0.889203i	$0.651260\pi$
$80$	−17818.3	+	18381.2i	−0.311273	+	0.321106i
$81$	45282.1			0.766856
$82$	23280.9	−	90.4884i	0.382353	−	0.00148613i
$83$	−39493.3	−	39493.3i	−0.629257	−	0.629257i	0.318624	−	0.947881i	$-0.396779\pi$
$83$	−39493.3	−	39493.3i	−0.629257	−	0.629257i	−0.947881	+	0.318624i	$0.896779\pi$
$84$	−38411.6	+	39013.5i	−0.593969	+	0.603276i
$85$	27543.3	−	27543.3i	0.413493	−	0.413493i
$86$	−47706.8	−	47337.3i	−0.695559	−	0.690173i
$87$		−	37721.7i		−	0.534309i
$88$	−55160.9	−	53889.3i	−0.759319	−	0.741815i
$89$			97259.4i			1.30154i	0.759276	+	0.650768i	$0.225553\pi$
$89$			97259.4i			1.30154i	−0.759276	+	0.650768i	$0.774447\pi$
$90$	4722.12	−	4758.97i	0.0614513	−	0.0619309i
$91$	−47024.0	+	47024.0i	−0.595273	+	0.595273i
$92$	−1186.28	−	152601.i	−0.0146123	−	1.87970i
$93$	11399.2	+	11399.2i	0.136668	+	0.136668i
$94$	196.601	+	50581.6i	0.00229492	+	0.590436i
$95$	74134.7			0.842777
$96$	56160.6	−	58387.0i	0.621947	−	0.646603i
$97$	−46757.9			−0.504575			−0.252287	−	0.967652i	$-0.581183\pi$
$97$	−46757.9			−0.504575			−0.252287	+	0.967652i	$0.581183\pi$
$98$	−40.4798	−	10414.6i	−0.000425768	−	0.109542i
$99$	14280.1	+	14280.1i	0.146435	+	0.146435i
$100$	155.470	+	19999.4i	0.00155470	+	0.199994i
$101$	−62869.3	+	62869.3i	−0.613247	+	0.613247i	−0.943791	−	0.330544i	$-0.892768\pi$
$101$	−62869.3	+	62869.3i	−0.613247	+	0.613247i	0.330544	+	0.943791i	$0.392768\pi$
$102$	−86822.9	+	87500.5i	−0.826293	+	0.832741i
$103$		−	8850.12i		−	0.0821971i	−0.999155	−	0.0410985i	$-0.986914\pi$
$103$		−	8850.12i		−	0.0821971i	0.999155	−	0.0410985i	$-0.0130858\pi$
$104$	68765.3	−	70388.0i	0.623428	−	0.638139i
$105$			42773.0i			0.378614i
$106$	−141797.	−	140699.i	−1.22575	−	1.21626i
$107$	119180.	−	119180.i	1.00634	−	1.00634i	0.00636140	−	0.999980i	$-0.497975\pi$
$107$	119180.	−	119180.i	1.00634	−	1.00634i	0.999980	−	0.00636140i	$-0.00202491\pi$
$108$	−91183.4	+	92612.2i	−0.752240	+	0.764027i
$109$	118189.	+	118189.i	0.952819	+	0.952819i	0.998936	−	0.0461173i	$-0.0146848\pi$
$109$	118189.	+	118189.i	0.952819	+	0.952819i	−0.0461173	+	0.998936i	$0.514685\pi$
$110$	−60245.9	+	234.165i	−0.474729	+	0.00184518i
$111$	−146947.			−1.13202
$112$	−1947.54	−	125256.i	−0.0146704	−	0.943526i
$113$	72392.2			0.533329			0.266665	−	0.963789i	$-0.414078\pi$
$113$	72392.2			0.533329			0.266665	+	0.963789i	$0.414078\pi$
$114$	−234602.	+	911.853i	−1.69071	+	0.00657147i
$115$	−84303.5	−	84303.5i	−0.594430	−	0.594430i
$116$	61503.2	+	60554.4i	0.424378	+	0.417831i
$117$	−18222.2	+	18222.2i	−0.123065	+	0.123065i
$118$	−132075.	−	131053.i	−0.873206	−	0.866444i
$119$			190609.i			1.23389i
$120$	−737.982	−	63286.8i	−0.00467835	−	0.401199i
$121$		−	20430.2i		−	0.126855i
$122$	80611.4	−	81240.5i	0.490340	−	0.494166i
$123$	−40699.6	+	40699.6i	−0.242565	+	0.242565i
$124$	−36884.9	+	286.734i	−0.215424	+	0.00167465i
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$	127.511	+	32806.1i	0.000715522	+	0.184089i
$127$	122901.			0.676153			0.338076	−	0.941119i	$-0.390224\pi$
$127$	122901.			0.676153			0.338076	+	0.941119i	$0.390224\pi$
$128$	5042.68	+	185295.i	0.0272042	+	0.999630i
$129$	166156.			0.879108
$130$	−298.806	−	76876.7i	−0.00155071	−	0.398967i
$131$	−75109.1	−	75109.1i	−0.382397	−	0.382397i	0.489568	−	0.871965i	$-0.337154\pi$
$131$	−75109.1	−	75109.1i	−0.382397	−	0.382397i	−0.871965	+	0.489568i	$0.837154\pi$
$132$	190647.	−	1482.04i	0.952348	−	0.00740331i
$133$	−256518.	+	256518.i	−1.25745	+	1.25745i
$134$	−218995.	+	220704.i	−1.05359	+	1.06181i
$135$			101537.i			0.479500i
$136$	−3288.66	−	282024.i	−0.0152466	−	1.30749i
$137$			73685.1i			0.335412i	0.985837	+	0.167706i	$0.0536359\pi$
$137$			73685.1i			0.335412i	−0.985837	+	0.167706i	$0.946364\pi$
$138$	267818.	+	265744.i	1.19713	+	1.18786i
$139$	18908.2	−	18908.2i	0.0830067	−	0.0830067i	−0.664384	−	0.747391i	$-0.731306\pi$
$139$	18908.2	−	18908.2i	0.0830067	−	0.0830067i	0.747391	+	0.664384i	$0.231306\pi$
$140$	−69739.1	−	68663.2i	−0.300716	−	0.296077i
$141$	−88426.8	−	88426.8i	−0.374573	−	0.374573i
$142$	72654.2	−	282.393i	0.302371	−	0.00117526i
$143$	231579.			0.947019
$144$	−754.685	−	48537.7i	−0.00303291	−	0.195062i
$145$	67430.0			0.266338
$146$	161698.	−	628.491i	0.627803	−	0.00244015i
$147$	18206.9	+	18206.9i	0.0694932	+	0.0694932i
$148$	235894.	−	239590.i	0.885243	−	0.899114i
$149$	−147704.	+	147704.i	−0.545039	+	0.545039i	−0.925002	−	0.379963i	$-0.875937\pi$
$149$	−147704.	+	147704.i	−0.545039	+	0.545039i	0.379963	+	0.925002i	$0.375937\pi$
$150$	−35099.4	−	34827.6i	−0.127371	−	0.126385i
$151$		−	86096.9i		−	0.307288i	−0.988126	−	0.153644i	$-0.950899\pi$
$151$		−	86096.9i		−	0.307288i	0.988126	−	0.153644i	$-0.0491008\pi$
$152$	375118.	−	383970.i	1.31692	−	1.34799i
$153$			73862.3i			0.255090i
$154$	207650.	−	209271.i	0.705555	−	0.711061i
$155$	−20376.8	+	20376.8i	−0.0681251	+	0.0681251i
$156$	1891.16	+	243275.i	0.00622181	+	0.800362i
$157$	−141259.	−	141259.i	−0.457370	−	0.457370i	0.440421	−	0.897791i	$-0.354829\pi$
$157$	−141259.	−	141259.i	−0.457370	−	0.457370i	−0.897791	+	0.440421i	$0.854829\pi$
$158$	1116.01	+	287126.i	0.00355651	+	0.915018i
$159$	493858.			1.54921
$160$	104371.	+	100391.i	0.322313	+	0.310023i
$161$	583408.			1.77381
$162$	−995.616	−	256152.i	−0.00298060	−	0.766850i
$163$	−283813.	−	283813.i	−0.836687	−	0.836687i	0.151734	−	0.988421i	$-0.451514\pi$
$163$	−283813.	−	283813.i	−0.836687	−	0.836687i	−0.988421	+	0.151734i	$0.951514\pi$
$164$	−1023.75	−	131693.i	−0.00297225	−	0.382344i
$165$	105322.	−	105322.i	0.301168	−	0.301168i
$166$	−222538.	+	224274.i	−0.626806	+	0.631698i
$167$			15467.8i			0.0429178i	0.999770	+	0.0214589i	$0.00683110\pi$
$167$			15467.8i			0.0429178i	−0.999770	+	0.0214589i	$0.993169\pi$
$168$	221536.	+	216429.i	0.605580	+	0.591620i
$169$		−	75787.0i		−	0.204117i
$170$	−156413.	−	155202.i	−0.415097	−	0.411883i
$171$	−99402.7	+	99402.7i	−0.259961	+	0.259961i
$172$	−266730.	+	270909.i	−0.687464	+	0.698236i
$173$	−433381.	−	433381.i	−1.10092	−	1.10092i	−0.994300	−	0.106617i	$-0.965998\pi$
$173$	−433381.	−	433381.i	−1.10092	−	1.10092i	−0.106617	−	0.994300i	$-0.534002\pi$
$174$	−213384.	+	829.386i	−0.534305	+	0.00207675i
$175$	−76459.5			−0.188728
$176$	−303629.	+	313220.i	−0.738858	+	0.762197i
$177$	460000.			1.10363
$178$	550178.	−	2138.44i	1.30153	−	0.00505879i
$179$	197142.	+	197142.i	0.459883	+	0.459883i	0.898617	−	0.438734i	$-0.144573\pi$
$179$	197142.	+	197142.i	0.459883	+	0.459883i	−0.438734	+	0.898617i	$0.644573\pi$
$180$	−27024.4	−	26607.5i	−0.0621692	−	0.0612101i
$181$	−86411.6	+	86411.6i	−0.196054	+	0.196054i	−0.798306	−	0.602252i	$-0.794270\pi$
$181$	−86411.6	+	86411.6i	−0.196054	+	0.196054i	0.602252	+	0.798306i	$0.294270\pi$
$182$	267040.	+	264972.i	0.597582	+	0.592955i
$183$			282950.i			0.624570i
$184$	−863209.	+	10065.8i	−1.87963	+	0.0219182i
$185$		−	262678.i		−	0.564280i
$186$	64232.5	−	64733.8i	0.136136	−	0.137198i
$187$	469344.	−	469344.i	0.981494	−	0.981494i
$188$	286126.	−	2224.27i	0.590423	−	0.00458980i
$189$	−351334.	−	351334.i	−0.715427	−	0.715427i
$190$	−1630.00	−	419366.i	−0.00327569	−	0.842770i
$191$	−697785.			−1.38401			−0.692003	−	0.721895i	$-0.743271\pi$
$191$	−697785.			−1.38401			−0.692003	+	0.721895i	$0.743271\pi$
$192$	−331519.	−	316406.i	−0.649016	−	0.619429i
$193$	−573139.			−1.10756			−0.553779	−	0.832663i	$-0.686815\pi$
$193$	−573139.			−1.10756			−0.553779	+	0.832663i	$0.686815\pi$
$194$	1028.06	+	264501.i	0.00196117	+	0.504571i
$195$	134396.	+	134396.i	0.253104	+	0.253104i
$196$	−58912.8	+	457.973i	−0.109539	+	0.000851530i
$197$	−259965.	+	259965.i	−0.477254	+	0.477254i	−0.904252	−	0.426999i	$-0.859571\pi$
$197$	−259965.	+	259965.i	−0.477254	+	0.477254i	0.426999	+	0.904252i	$0.359571\pi$
$198$	80466.1	−	81094.1i	0.145865	−	0.147003i
$199$		−	80858.1i		−	0.144741i	−0.997378	−	0.0723704i	$-0.976944\pi$
$199$		−	80858.1i		−	0.144741i	0.997378	−	0.0723704i	$-0.0230564\pi$
$200$	113129.	−	1319.19i	0.199986	−	0.00233202i
$201$		−	768683.i		−	1.34201i
$202$	357022.	+	354258.i	0.615626	+	0.610859i
$203$	−233319.	+	233319.i	−0.397383	+	0.397383i
$204$	496883.	+	489217.i	0.835946	+	0.823050i
$205$	−72753.2	−	72753.2i	−0.120912	−	0.120912i
$206$	−50063.5	+	194.587i	−0.0821964	+	0.000319482i
$207$	226075.			0.366713
$208$	−399684.	−	387445.i	−0.640557	−	0.620943i
$209$	1.26327e6			2.00047
$210$	241959.	−	940.449i	0.378611	−	0.00147159i
$211$	−520212.	−	520212.i	−0.804404	−	0.804404i	0.179377	−	0.983780i	$-0.442592\pi$
$211$	−520212.	−	520212.i	−0.804404	−	0.804404i	−0.983780	+	0.179377i	$0.942592\pi$
$212$	−792788.	+	805210.i	−1.21148	+	1.23047i
$213$	−127014.	+	127014.i	−0.191824	+	0.191824i
$214$	−676801.	−	671560.i	−1.01024	−	1.00242i
$215$			297015.i			0.438210i
$216$	525895.	+	513771.i	0.766945	+	0.749265i
$217$		−	141014.i		−	0.203289i
$218$	665973.	−	671171.i	0.949108	−	0.956515i
$219$	−282681.	+	282681.i	−0.398278	+	0.398278i
$220$	2649.25	+	340795.i	0.00369034	+	0.474718i
$221$	598907.	+	598907.i	0.824856	+	0.824856i
$222$	3230.93	+	831254.i	0.00439992	+	1.13201i
$223$	−126355.			−0.170150			−0.0850749	−	0.996375i	$-0.527113\pi$
$223$	−126355.			−0.170150			−0.0850749	+	0.996375i	$0.527113\pi$
$224$	−708508.	+	13770.9i	−0.943462	+	0.0183375i
$225$	−29628.7			−0.0390172
$226$	−1591.69	−	409509.i	−0.00207294	−	0.533325i
$227$	−918677.	−	918677.i	−1.18331	−	1.18331i	−0.978882	−	0.204427i	$-0.934467\pi$
$227$	−918677.	−	918677.i	−1.18331	−	1.18331i	−0.204427	−	0.978882i	$-0.565533\pi$
$228$	10316.4	+	1.32708e6i	0.0131428	+	1.69067i
$229$	−347876.	+	347876.i	−0.438365	+	0.438365i	−0.891461	−	0.453097i	$-0.850319\pi$
$229$	−347876.	+	347876.i	−0.438365	+	0.438365i	0.453097	+	0.891461i	$0.350319\pi$
$230$	−475035.	+	478743.i	−0.592116	+	0.596736i
$231$			728862.i			0.898702i
$232$	341192.	−	349244.i	0.416178	−	0.425999i
$233$		−	728178.i		−	0.878714i	−0.898313	−	0.439357i	$-0.855206\pi$
$233$		−	728178.i		−	0.878714i	0.898313	−	0.439357i	$-0.144794\pi$
$234$	103480.	+	102679.i	0.123543	+	0.122586i
$235$	158069.	−	158069.i	0.186714	−	0.186714i
$236$	−738436.	+	750007.i	−0.863044	+	0.876567i
$237$	−501954.	−	501954.i	−0.580488	−	0.580488i
$238$	1.07824e6	−	4190.91i	1.23388	−	0.00479585i
$239$	203434.			0.230372			0.115186	−	0.993344i	$-0.463254\pi$
$239$	203434.			0.230372			0.115186	+	0.993344i	$0.463254\pi$
$240$	−357985.	+	5566.11i	−0.401178	+	0.00623769i
$241$	−131370.			−0.145698			−0.0728490	−	0.997343i	$-0.523209\pi$
$241$	−131370.			−0.145698			−0.0728490	+	0.997343i	$0.523209\pi$
$242$	−115570.	+	449.198i	−0.126854	+	0.000493059i
$243$	−250065.	−	250065.i	−0.271667	−	0.271667i
$244$	−461335.	−	454217.i	−0.496068	−	0.488415i
$245$	−32546.0	+	32546.0i	−0.0346404	+	0.0346404i
$246$	231125.	+	229335.i	0.243506	+	0.241620i
$247$			1.61200e6i			1.68121i
$248$	2432.99	+	208645.i	0.00251195	+	0.215416i
$249$		−	781117.i		−	0.798395i
$250$	62256.6	−	62742.5i	0.0629993	−	0.0634909i
$251$	487551.	−	487551.i	0.488467	−	0.488467i	−0.419355	−	0.907822i	$-0.637744\pi$
$251$	487551.	−	487551.i	0.488467	−	0.488467i	0.907822	+	0.419355i	$0.137744\pi$
$252$	185575.	−	1442.62i	0.184085	−	0.00143103i
$253$	−1.43655e6	−	1.43655e6i	−1.41098	−	1.41098i
$254$	−2702.21	−	695226.i	−0.00262806	−	0.676148i
$255$	544765.			0.524636
$256$	1.04807e6	−	32599.5i	0.999517	−	0.0310893i
$257$	−1.90822e6			−1.80217			−0.901084	−	0.433645i	$-0.857227\pi$
$257$	−1.90822e6			−1.80217			−0.901084	+	0.433645i	$0.857227\pi$
$258$	−3653.27	−	939914.i	−0.00341690	−	0.879101i
$259$	908910.	+	908910.i	0.841921	+	0.841921i
$260$	−434871.	+	3380.57i	−0.398957	+	0.00310139i
$261$	−90412.8	+	90412.8i	−0.0821540	+	0.0821540i
$262$	−423226.	+	426529.i	−0.380908	+	0.383880i
$263$			484503.i			0.431924i	0.976402	+	0.215962i	$0.0692887\pi$
$263$			484503.i			0.431924i	−0.976402	+	0.215962i	$0.930711\pi$
$264$	−12575.4	−	1.07842e6i	−0.0111048	−	0.952312i
$265$			882804.i			0.772235i
$266$	1.45672e6	+	1.44543e6i	1.26232	+	1.25255i
$267$	−961821.	+	961821.i	−0.825689	+	0.825689i
$268$	1.25330e6	+	1.23396e6i	1.06590	+	1.04946i
$269$	986492.	+	986492.i	0.831214	+	0.831214i	0.987683	−	0.156469i	$-0.0500110\pi$
$269$	986492.	+	986492.i	0.831214	+	0.831214i	−0.156469	+	0.987683i	$0.550011\pi$
$270$	574374.	−	2232.49i	0.479497	−	0.00186371i
$271$	1.22694e6			1.01484			0.507422	−	0.861698i	$-0.330599\pi$
$271$	1.22694e6			1.01484			0.507422	+	0.861698i	$0.330599\pi$
$272$	−1.59529e6	+	24804.2i	−1.30742	+	0.0203284i
$273$	−930064.			−0.755277
$274$	416823.	−	1620.11i	0.335409	−	0.00130367i
$275$	188270.	+	188270.i	0.150124	+	0.150124i
$276$	1.49738e6	−	1.52084e6i	1.18320	−	1.20174i
$277$	1.69007e6	−	1.69007e6i	1.32344	−	1.32344i	0.412473	−	0.910970i	$-0.364665\pi$
$277$	1.69007e6	−	1.69007e6i	1.32344	−	1.32344i	0.910970	−	0.412473i	$-0.135335\pi$
$278$	−107376.	−	106544.i	−0.0833287	−	0.0826834i
$279$		−	54644.1i		−	0.0420275i
$280$	−386882.	+	396011.i	−0.294906	+	0.301864i
$281$		−	1.34620e6i		−	1.01705i	−0.861046	−	0.508527i	$-0.830190\pi$
$281$		−	1.34620e6i		−	1.01705i	0.861046	−	0.508527i	$-0.169810\pi$
$282$	−498269.	+	502158.i	−0.373114	+	0.376026i
$283$	944602.	−	944602.i	0.701104	−	0.701104i	−0.263543	−	0.964648i	$-0.584891\pi$
$283$	944602.	−	944602.i	0.701104	−	0.701104i	0.964648	+	0.263543i	$0.0848912\pi$
$284$	−3194.89	−	410985.i	−0.00235050	−	0.302364i
$285$	733136.	+	733136.i	0.534653	+	0.534653i
$286$	−5091.72	−	1.31000e6i	−0.00368086	−	0.947012i
$287$	503476.			0.360806
$288$	−274552.	+	5336.31i	−0.195049	+	0.00379105i
$289$	1.00777e6			0.709768
$290$	−1482.58	−	381439.i	−0.00103520	−	0.266336i
$291$	−462400.	−	462400.i	−0.320100	−	0.320100i
$292$	−7110.51	−	914683.i	−0.00488027	−	0.627788i
$293$	−838880.	+	838880.i	−0.570862	+	0.570862i	−0.932369	−	0.361508i	$-0.882262\pi$
$293$	−838880.	+	838880.i	−0.570862	+	0.570862i	0.361508	+	0.932369i	$0.382262\pi$
$294$	102593.	−	103393.i	0.0692226	−	0.0697628i
$295$			822281.i			0.550130i
$296$	−1.36050e6	−	1.32914e6i	−0.902548	−	0.881741i
$297$			1.73021e6i			1.13817i
$298$	838783.	+	832288.i	0.547153	+	0.542916i
$299$	1.83311e6	−	1.83311e6i	1.18580	−	1.18580i
$300$	−196241.	+	199316.i	−0.125889	+	0.127861i
$301$	−1.02772e6	−	1.02772e6i	−0.653821	−	0.653821i
$302$	−487034.	+	1893.01i	−0.307285	+	0.00119436i
$303$	−1.24346e6			−0.778082
$304$	−2.18029e6	−	2.11353e6i	−1.35310	−	1.31167i
$305$	−505791.			−0.311330
$306$	417825.	−	1624.01i	0.255089	−	0.000991482i
$307$	−521897.	−	521897.i	−0.316038	−	0.316038i	0.531205	−	0.847243i	$-0.321739\pi$
$307$	−521897.	−	521897.i	−0.316038	−	0.316038i	−0.847243	+	0.531205i	$0.821739\pi$
$308$	−1.18837e6	−	1.17004e6i	−0.713798	−	0.702786i
$309$	87521.0	−	87521.0i	0.0521454	−	0.0521454i
$310$	115716.	+	114820.i	0.0683894	+	0.0678598i
$311$			1.29428e6i			0.758798i	0.925233	+	0.379399i	$0.123869\pi$
$311$			1.29428e6i			0.758798i	−0.925233	+	0.379399i	$0.876131\pi$
$312$	1.37612e6	−	16046.8i	0.800332	−	0.00933260i
$313$		−	2.45861e6i		−	1.41850i	−0.704957	−	0.709251i	$-0.749034\pi$
$313$		−	2.45861e6i		−	1.41850i	0.704957	−	0.709251i	$-0.250966\pi$
$314$	−795970.	+	802182.i	−0.455589	+	0.459144i
$315$	102520.	−	102520.i	0.0582146	−	0.0582146i
$316$	1.62419e6	−	12626.1i	0.914998	−	0.00711296i
$317$	1.88035e6	+	1.88035e6i	1.05097	+	1.05097i	0.998629	+	0.0523414i	$0.0166684\pi$
$317$	1.88035e6	+	1.88035e6i	1.05097	+	1.05097i	0.0523414	+	0.998629i	$0.483332\pi$
$318$	−10858.4	−	2.79366e6i	−0.00602143	−	1.54920i
$319$	1.14902e6			0.632197
$320$	565597.	−	592612.i	0.308768	−	0.323516i
$321$	2.35721e6			1.27684
$322$	−12827.4	−	3.30023e6i	−0.00689443	−	1.77380i
$323$	3.26706e6	+	3.26706e6i	1.74241	+	1.74241i
$324$	−1.44898e6	+	11264.0i	−0.766833	+	0.00596116i
$325$	−240242.	+	240242.i	−0.126165	+	0.126165i
$326$	−1.59924e6	+	1.61172e6i	−0.833429	+	0.839933i
$327$			2.33760e6i			1.20893i
$328$	−744943.	+	8686.71i	−0.382330	+	0.00445831i
$329$			1.09389e6i			0.557164i
$330$	−598102.	−	593471.i	−0.302336	−	0.299995i
$331$	−2.05885e6	+	2.05885e6i	−1.03289	+	1.03289i	−0.0334519	+	0.999440i	$0.510650\pi$
$331$	−2.05885e6	+	2.05885e6i	−1.03289	+	1.03289i	−0.999440	+	0.0334519i	$0.989350\pi$
$332$	1.27357e6	+	1.25392e6i	0.634129	+	0.624346i
$333$	352209.	+	352209.i	0.174057	+	0.174057i
$334$	87498.4	−	340.090i	0.0429175	−	0.000166812i
$335$	1.37407e6			0.668955
$336$	1.21943e6	−	1.25795e6i	0.589262	−	0.607875i
$337$	−256497.			−0.123029			−0.0615145	−	0.998106i	$-0.519593\pi$
$337$	−256497.			−0.123029			−0.0615145	+	0.998106i	$0.519593\pi$
$338$	−428713.	+	1666.33i	−0.204115	+	0.000793357i
$339$	715904.	+	715904.i	0.338342	+	0.338342i
$340$	−874507.	+	888210.i	−0.410267	+	0.416695i
$341$	−347226.	+	347226.i	−0.161706	+	0.161706i
$342$	564488.	+	560117.i	0.260969	+	0.258949i
$343$		−	2.28132e6i		−	1.04701i
$344$	1.53835e6	+	1.50288e6i	0.700903	+	0.684745i
$345$		−	1.66740e6i		−	0.754207i
$346$	−2.44203e6	+	2.46108e6i	−1.09663	+	1.10519i
$347$	−297841.	+	297841.i	−0.132789	+	0.132789i	−0.770377	−	0.637589i	$-0.779932\pi$
$347$	−297841.	+	297841.i	−0.132789	+	0.132789i	0.637589	+	0.770377i	$0.279932\pi$
$348$	9383.36	+	1.20706e6i	0.00415346	+	0.534293i
$349$	−1.06398e6	−	1.06398e6i	−0.467597	−	0.467597i	0.433538	−	0.901135i	$-0.357265\pi$
$349$	−1.06398e6	−	1.06398e6i	−0.467597	−	0.467597i	−0.901135	+	0.433538i	$0.857265\pi$
$350$	1681.11	+	432517.i	0.000733546	+	0.188727i
$351$	−2.20783e6			−0.956530
$352$	1.77850e6	+	1.71068e6i	0.765063	+	0.735890i
$353$	2.71943e6			1.16156			0.580780	−	0.814060i	$-0.302748\pi$
$353$	2.71943e6			1.16156			0.580780	+	0.814060i	$0.302748\pi$
$354$	−10114.0	−	2.60213e6i	−0.00428959	−	1.10363i
$355$	−227046.	−	227046.i	−0.0956187	−	0.0956187i
$356$	−24193.5	−	3.11221e6i	−0.0101175	−	1.30150i
$357$	−1.88497e6	+	1.88497e6i	−0.782771	+	0.782771i
$358$	1.11086e6	−	1.11953e6i	0.458092	−	0.461667i
$359$		−	1.93088e6i		−	0.790714i	−0.918528	−	0.395357i	$-0.870621\pi$
$359$		−	1.93088e6i		−	0.790714i	0.918528	−	0.395357i	$-0.129379\pi$
$360$	−149920.	+	153457.i	−0.0609680	+	0.0624067i
$361$			6.31742e6i			2.55136i
$362$	490714.	+	486914.i	0.196814	+	0.195290i
$363$	202039.	−	202039.i	0.0804764	−	0.0804764i
$364$	1.49303e6	−	1.51642e6i	0.590628	−	0.599883i
$365$	−505311.	−	505311.i	−0.198530	−	0.198530i
$366$	1.60059e6	−	6221.21i	0.624566	−	0.00242757i
$367$	−4.26731e6			−1.65382			−0.826911	−	0.562332i	$-0.809904\pi$
$367$	−4.26731e6			−1.65382			−0.826911	+	0.562332i	$0.809904\pi$
$368$	75919.7	+	4.88279e6i	0.0292237	+	1.87953i
$369$	195101.			0.0745922
$370$	−1.48592e6	+	5775.50i	−0.564276	+	0.00219324i
$371$	−3.05465e6	−	3.05465e6i	−1.15220	−	1.15220i
$372$	−367599.	−	361928.i	−0.137726	−	0.135602i
$373$	−1.60230e6	+	1.60230e6i	−0.596311	+	0.596311i	−0.939329	−	0.343018i	$-0.888551\pi$
$373$	−1.60230e6	+	1.60230e6i	−0.596311	+	0.596311i	0.343018	+	0.939329i	$0.388551\pi$
$374$	−2.66531e6	−	2.64467e6i	−0.985302	−	0.977672i
$375$			218523.i			0.0802453i
$376$	−18873.3	−	1.61851e6i	−0.00688461	−	0.590400i
$377$			1.46621e6i			0.531304i
$378$	−1.97970e6	+	1.99515e6i	−0.712641	+	0.718203i
$379$	−1.32305e6	+	1.32305e6i	−0.473127	+	0.473127i	−0.902925	−	0.429798i	$-0.858585\pi$
$379$	−1.32305e6	+	1.32305e6i	−0.473127	+	0.473127i	0.429798	+	0.902925i	$0.358585\pi$
$380$	−2.37224e6	+	18441.2i	−0.842751	+	0.00655133i
$381$	1.21539e6	+	1.21539e6i	0.428948	+	0.428948i
$382$	15342.2	+	3.94724e6i	0.00537933	+	1.38400i
$383$	2.69607e6			0.939149			0.469574	−	0.882893i	$-0.344407\pi$
$383$	2.69607e6			0.939149			0.469574	+	0.882893i	$0.344407\pi$
$384$	−1.78256e6	+	1.88230e6i	−0.616902	+	0.651419i
$385$	−1.30289e6			−0.447977
$386$	12601.6	+	3.24214e6i	0.00430484	+	1.10755i
$387$	−398250.	−	398250.i	−0.135169	−	0.135169i
$388$	1.49621e6	−	11631.1i	0.504560	−	0.00392232i
$389$	2.79493e6	−	2.79493e6i	0.936475	−	0.936475i	−0.0616242	−	0.998099i	$-0.519628\pi$
$389$	2.79493e6	−	2.79493e6i	0.936475	−	0.936475i	0.998099	+	0.0616242i	$0.0196280\pi$
$390$	757297.	−	763207.i	0.252119	−	0.254086i
$391$		−	7.43039e6i		−	2.45793i
$392$	3885.98	+	333249.i	0.00127728	+	0.109535i
$393$		−	1.48554e6i		−	0.485181i
$394$	1.47629e6	+	1.46486e6i	0.479105	+	0.475395i
$395$	897276.	−	897276.i	0.289356	−	0.289356i
$396$	−460503.	−	453399.i	−0.147569	−	0.145292i
$397$	2.49038e6	+	2.49038e6i	0.793030	+	0.793030i	0.981986	−	0.188956i	$-0.0605103\pi$
$397$	2.49038e6	+	2.49038e6i	0.793030	+	0.793030i	−0.188956	+	0.981986i	$0.560510\pi$
$398$	−457399.	+	1777.83i	−0.144740	+	0.000562576i
$399$	−5.07354e6			−1.59543
$400$	−9949.79	−	639923.i	−0.00310931	−	0.199976i
$401$	−4.48252e6			−1.39207			−0.696036	−	0.718007i	$-0.745054\pi$
$401$	−4.48252e6			−1.39207			−0.696036	+	0.718007i	$0.745054\pi$
$402$	−4.34829e6	+	16901.0i	−1.34200	+	0.00521612i
$403$	−443078.	−	443078.i	−0.135899	−	0.135899i
$404$	1.99612e6	−	2.02740e6i	0.608461	−	0.617995i
$405$	−800481.	+	800481.i	−0.242501	+	0.242501i
$406$	1.32497e6	+	1.31471e6i	0.398925	+	0.395836i
$407$		−	4.47610e6i		−	1.33941i
$408$	2.75648e6	−	2.82153e6i	0.819794	−	0.839139i
$409$			2.36608e6i			0.699393i	0.936863	+	0.349696i	$0.113715\pi$
$409$			2.36608e6i			0.699393i	−0.936863	+	0.349696i	$0.886285\pi$
$410$	−409952.	+	413151.i	−0.120441	+	0.121381i
$411$	−728690.	+	728690.i	−0.212784	+	0.212784i
$412$	2201.49	+	283195.i	0.000638960	+	0.0821946i
$413$	−2.84523e6	−	2.84523e6i	−0.820808	−	0.820808i
$414$	−4970.71	−	1.27886e6i	−0.00142534	−	0.366711i
$415$	1.39630e6			0.397977
$416$	−2.18291e6	+	2.26945e6i	−0.618448	+	0.642966i
$417$	373975.			0.105318
$418$	−27775.6	−	7.14610e6i	−0.00777539	−	2.00045i
$419$	−1.04928e6	−	1.04928e6i	−0.291983	−	0.291983i	0.545880	−	0.837863i	$-0.316195\pi$
$419$	−1.04928e6	−	1.04928e6i	−0.291983	−	0.291983i	−0.837863	+	0.545880i	$0.816195\pi$
$420$	−10639.9	−	1.36869e6i	−0.00294316	−	0.378602i
$421$	−83315.8	+	83315.8i	−0.0229099	+	0.0229099i	−0.718469	−	0.695559i	$-0.755157\pi$
$421$	−83315.8	+	83315.8i	−0.0229099	+	0.0229099i	0.695559	+	0.718469i	$0.255157\pi$
$422$	−2.93130e6	+	2.95418e6i	−0.801271	+	0.807524i
$423$			423890.i			0.115187i
$424$	4.57235e6	+	4.46695e6i	1.23517	+	1.20669i
$425$			973803.i			0.261516i
$426$	721287.	+	715702.i	0.192568	+	0.191077i
$427$	1.75012e6	−	1.75012e6i	0.464513	−	0.464513i
$428$	−3.78401e6	+	3.84330e6i	−0.998488	+	1.01413i
$429$	2.29014e6	+	2.29014e6i	0.600784	+	0.600784i
$430$	1.68016e6	−	6530.46i	0.438207	−	0.00170323i
$431$	1.89615e6			0.491676			0.245838	−	0.969311i	$-0.420937\pi$
$431$	1.89615e6			0.491676			0.245838	+	0.969311i	$0.420937\pi$
$432$	2.89474e6	−	2.98618e6i	0.746278	−	0.769852i
$433$	−6.49433e6			−1.66462			−0.832309	−	0.554312i	$-0.812982\pi$
$433$	−6.49433e6			−1.66462			−0.832309	+	0.554312i	$0.812982\pi$
$434$	−797692.	+	3100.48i	−0.203288	+	0.000790141i
$435$	666831.	+	666831.i	0.168963	+	0.168963i
$436$	−3.81133e6	−	3.75253e6i	−0.960197	−	0.945383i
$437$	9.99970e6	−	9.99970e6i	2.50486	−	2.50486i
$438$	1.60529e6	+	1.59286e6i	0.399823	+	0.396727i
$439$		−	2.58577e6i		−	0.640365i	−0.947356	−	0.320183i	$-0.896256\pi$
$439$		−	2.58577e6i		−	0.640365i	0.947356	−	0.320183i	$-0.103744\pi$
$440$	1.92775e6	−	22479.4i	0.474700	−	0.00553544i
$441$		−	87278.0i		−	0.0213702i
$442$	3.37473e6	−	3.40107e6i	0.821644	−	0.828056i
$443$	−562901.	+	562901.i	−0.136277	+	0.136277i	−0.771955	−	0.635678i	$-0.780721\pi$
$443$	−562901.	+	562901.i	−0.136277	+	0.136277i	0.635678	+	0.771955i	$0.280721\pi$
$444$	4.70217e6	−	36553.5i	1.13199	−	0.00879978i
$445$	−1.71932e6	−	1.71932e6i	−0.411582	−	0.411582i
$446$	2778.17	+	714768.i	0.000661335	+	0.170148i
$447$	−2.92137e6			−0.691540
$448$	93477.1	+	4.00759e6i	0.0220044	+	0.943384i
$449$	6.62708e6			1.55134			0.775669	−	0.631141i	$-0.217413\pi$
$449$	6.62708e6			1.55134			0.775669	+	0.631141i	$0.217413\pi$
$450$	651.444	+	167604.i	0.000151651	+	0.0390169i
$451$	−1.23973e6	−	1.23973e6i	−0.287003	−	0.287003i
$452$	−2.31648e6	+	18007.7i	−0.533313	+	0.00414584i
$453$	851433.	−	851433.i	0.194942	−	0.194942i
$454$	−5.17658e6	+	5.21698e6i	−1.17870	+	1.18790i
$455$		−	1.66255e6i		−	0.376484i
$456$	7.50680e6	−	87536.1i	1.69061	−	0.0197140i
$457$			2.47813e6i			0.555052i	0.960718	+	0.277526i	$0.0895145\pi$
$457$			2.47813e6i			0.555052i	−0.960718	+	0.277526i	$0.910485\pi$
$458$	1.97552e6	+	1.96022e6i	0.440065	+	0.436658i
$459$	−4.47465e6	+	4.47465e6i	−0.991351	+	0.991351i
$460$	2.71860e6	+	2.67666e6i	0.599033	+	0.589792i
$461$	2.88325e6	+	2.88325e6i	0.631872	+	0.631872i	0.948537	−	0.316665i	$-0.102563\pi$
$461$	2.88325e6	+	2.88325e6i	0.631872	+	0.631872i	−0.316665	+	0.948537i	$0.602563\pi$
$462$	4.12304e6	−	16025.5i	0.898695	−	0.00349306i
$463$	4.18992e6			0.908351			0.454175	−	0.890912i	$-0.349934\pi$
$463$	4.18992e6			0.908351			0.454175	+	0.890912i	$0.349934\pi$
$464$	−1.98311e6	−	1.92238e6i	−0.427613	−	0.414519i
$465$	−403023.			−0.0864365
$466$	−4.11916e6	+	16010.4i	−0.878707	+	0.00341537i
$467$	−1.38927e6	−	1.38927e6i	−0.294777	−	0.294777i	0.544187	−	0.838964i	$-0.316838\pi$
$467$	−1.38927e6	−	1.38927e6i	−0.294777	−	0.294777i	−0.838964	+	0.544187i	$0.816838\pi$
$468$	578559.	−	587624.i	0.122105	−	0.124018i
$469$	−4.75451e6	+	4.75451e6i	−0.998099	+	0.998099i
$470$	−897640.	−	890689.i	−0.187438	−	0.185987i
$471$		−	2.79389e6i		−	0.580306i
$472$	4.25888e6	+	4.16070e6i	0.879915	+	0.859630i
$473$			5.06121e6i			1.04016i
$474$	−2.82842e6	+	2.85049e6i	−0.578227	+	0.582739i
$475$	−1.31053e6	+	1.31053e6i	−0.266509	+	0.266509i
$476$	−47414.4	−	6.09929e6i	−0.00959163	−	1.23385i
$477$	−1.18370e6	−	1.18370e6i	−0.238202	−	0.238202i
$478$	−4472.90	−	1.15079e6i	−0.000895405	−	0.230370i
$479$	−3.01097e6			−0.599609			−0.299804	−	0.954001i	$-0.596921\pi$
$479$	−3.01097e6			−0.599609			−0.299804	+	0.954001i	$0.596921\pi$
$480$	39357.5	+	2.02493e6i	0.00779694	+	0.401151i
$481$	5.71172e6			1.12565
$482$	2888.43	+	743135.i	0.000566297	+	0.145697i
$483$	5.76946e6	+	5.76946e6i	1.12530	+	1.12530i
$484$	5082.05	+	653746.i	0.000986111	+	0.126851i
$485$	826570.	−	826570.i	0.159561	−	0.159561i
$486$	−1.40907e6	+	1.42007e6i	−0.270609	+	0.272721i
$487$		−	1.73420e6i		−	0.331341i	−0.986181	−	0.165671i	$-0.947021\pi$
$487$		−	1.73420e6i		−	0.331341i	0.986181	−	0.165671i	$-0.0529789\pi$
$488$	−2.55928e6	+	2.61967e6i	−0.486483	+	0.497963i
$489$		−	5.61339e6i		−	1.06158i
$490$	184822.	+	183391.i	0.0347748	+	0.0345055i
$491$	2.65718e6	−	2.65718e6i	0.497414	−	0.497414i	−0.413218	−	0.910632i	$-0.635595\pi$
$491$	2.65718e6	−	2.65718e6i	0.497414	−	0.497414i	0.910632	+	0.413218i	$0.135595\pi$
$492$	1.29222e6	−	1.31247e6i	0.240672	−	0.244443i
$493$	2.97159e6	+	2.97159e6i	0.550645	+	0.550645i
$494$	9.11877e6	−	35443.0i	1.68120	−	0.00653451i
$495$	−504879.			−0.0926136
$496$	1.18021e6	−	18350.4i	0.215405	−	0.00334920i
$497$	1.57123e6			0.285331
$498$	−4.41863e6	+	17174.4i	−0.798389	+	0.00310319i
$499$	7.30951e6	+	7.30951e6i	1.31413	+	1.31413i	0.918345	+	0.395781i	$0.129526\pi$
$499$	7.30951e6	+	7.30951e6i	1.31413	+	1.31413i	0.395781	+	0.918345i	$0.370474\pi$
$500$	−356291.	−	350794.i	−0.0637353	−	0.0627520i
$501$	−152965.	+	152965.i	−0.0272268	+	0.0272268i
$502$	−2.76870e6	−	2.74726e6i	−0.490362	−	0.486565i
$503$		−	5.49766e6i		−	0.968853i	−0.874832	−	0.484426i	$-0.839028\pi$
$503$		−	5.49766e6i		−	0.968853i	0.874832	−	0.484426i	$-0.160972\pi$
$504$	−12240.8	−	1.04973e6i	−0.00214652	−	0.184078i
$505$		−	2.22277e6i		−	0.387851i
$506$	−8.09472e6	+	8.15789e6i	−1.40548	+	1.41645i
$507$	749476.	−	749476.i	0.129491	−	0.129491i
$508$	−3.93270e6	+	30571.8i	−0.676132	+	0.00525608i
$509$	−2.60875e6	−	2.60875e6i	−0.446311	−	0.446311i	0.447815	−	0.894126i	$-0.352202\pi$
$509$	−2.60875e6	−	2.60875e6i	−0.446311	−	0.446311i	−0.894126	+	0.447815i	$0.852202\pi$
$510$	−11977.7	−	3.08163e6i	−0.00203915	−	0.524632i
$511$	3.49692e6			0.592424
$512$	−207453.	−	5.92801e6i	−0.0349740	−	0.999388i
$513$	−1.20438e7			−2.02056
$514$	41955.9	+	1.07944e7i	0.00700464	+	1.80215i
$515$	156450.	+	156450.i	0.0259930	+	0.0259930i
$516$	−5.31684e6	+	41331.7i	−0.879081	+	0.00683375i
$517$	2.69353e6	−	2.69353e6i	0.443195	−	0.443195i
$518$	5.12155e6	−	5.16151e6i	0.838642	−	0.845187i
$519$		−	8.57162e6i		−	1.39683i
$520$	28684.8	+	2.45991e6i	0.00465203	+	0.398942i
$521$		−	9.50774e6i		−	1.53456i	−0.641314	−	0.767279i	$-0.721610\pi$
$521$		−	9.50774e6i		−	1.53456i	0.641314	−	0.767279i	$-0.278390\pi$
$522$	513436.	+	509460.i	0.0824727	+	0.0818341i
$523$	2.12191e6	−	2.12191e6i	0.339213	−	0.339213i	−0.516858	−	0.856071i	$-0.672898\pi$
$523$	2.12191e6	−	2.12191e6i	0.339213	−	0.339213i	0.856071	+	0.516858i	$0.172898\pi$
$524$	2.42210e6	+	2.38473e6i	0.385358	+	0.379413i
$525$	−756127.	−	756127.i	−0.119728	−	0.119728i
$526$	2.74074e6	−	10652.8i	0.431920	−	0.00167879i
$527$	−1.79598e6			−0.281693
$528$	−6.10016e6	+	94847.9i	−0.952262	+	0.0148062i
$529$	−1.63063e7			−2.53348
$530$	4.99386e6	−	19410.2i	0.772229	−	0.00300151i
$531$	−1.10255e6	−	1.10255e6i	−0.169692	−	0.169692i
$532$	8.14452e6	−	8.27214e6i	1.24763	−	1.26718i
$533$	1.58196e6	−	1.58196e6i	0.241200	−	0.241200i
$534$	5.46199e6	+	5.41969e6i	0.828892	+	0.822473i
$535$			4.21366e6i			0.636466i
$536$	6.95273e6	−	7.11680e6i	1.04531	−	1.06997i
$537$			3.89918e6i			0.583495i
$538$	5.55871e6	−	5.60209e6i	0.827977	−	0.834439i
$539$	−554592.	+	554592.i	−0.0822246	+	0.0822246i
$540$	−25257.5	−	3.24908e6i	−0.00372740	−	0.479486i
$541$	7.92767e6	+	7.92767e6i	1.16454	+	1.16454i	0.983471	+	0.181064i	$0.0579541\pi$
$541$	7.92767e6	+	7.92767e6i	1.16454	+	1.16454i	0.181064	+	0.983471i	$0.442046\pi$
$542$	−26976.6	−	6.94055e6i	−0.00394448	−	1.01484i
$543$	−1.70909e6			−0.248751
$544$	175388.	+	9.02368e6i	0.0254099	+	1.30733i
$545$	−4.17861e6			−0.602615
$546$	20449.3	+	5.26120e6i	0.00293560	+	0.755271i
$547$	2.38242e6	+	2.38242e6i	0.340447	+	0.340447i	0.856535	−	0.516088i	$-0.172612\pi$
$547$	2.38242e6	+	2.38242e6i	0.340447	+	0.340447i	−0.516088	+	0.856535i	$0.672612\pi$
$548$	−18329.3	−	2.35785e6i	−0.00260733	−	0.335402i
$549$	678185.	−	678185.i	0.0960323	−	0.0960323i
$550$	1.06087e6	−	1.06915e6i	0.149539	−	0.150706i
$551$			7.99824e6i			1.12232i
$552$	−8.63603e6	−	8.43694e6i	−1.20633	−	1.17852i
$553$			6.20944e6i			0.863455i
$554$	−9.59757e6	−	9.52325e6i	−1.32858	−	1.31829i
$555$	2.59769e6	−	2.59769e6i	0.357976	−	0.357976i
$556$	−600341.	+	609747.i	−0.0823589	+	0.0836494i
$557$	−2.36995e6	−	2.36995e6i	−0.323669	−	0.323669i	0.526504	−	0.850173i	$-0.323503\pi$
$557$	−2.36995e6	−	2.36995e6i	−0.323669	−	0.323669i	−0.850173	+	0.526504i	$0.823503\pi$
$558$	−309112.	+	1201.46i	−0.0420271	+	0.000163352i
$559$	−6.45835e6			−0.874162
$560$	2.24867e6	+	2.17981e6i	0.303008	+	0.293730i
$561$	9.28292e6			1.24531
$562$	−7.61521e6	+	29598.9i	−1.01705	+	0.00395307i
$563$	6.69440e6	+	6.69440e6i	0.890104	+	0.890104i	0.994532	−	0.104429i	$-0.0333014\pi$
$563$	6.69440e6	+	6.69440e6i	0.890104	+	0.890104i	−0.104429	+	0.994532i	$0.533301\pi$
$564$	2.85157e6	+	2.80757e6i	0.377473	+	0.371650i
$565$	−1.27973e6	+	1.27973e6i	−0.168654	+	0.168654i
$566$	−5.36420e6	−	5.32266e6i	−0.703824	−	0.698374i
$567$		−	5.53959e6i		−	0.723636i
$568$	−2.32479e6	+	27109.2i	−0.302352	+	0.00352571i
$569$			6.90268e6i			0.893793i	0.894586	+	0.446897i	$0.147471\pi$
$569$			6.90268e6i			0.893793i	−0.894586	+	0.446897i	$0.852529\pi$
$570$	4.13109e6	−	4.16333e6i	0.532571	−	0.536727i
$571$	−6.09499e6	+	6.09499e6i	−0.782317	+	0.782317i	−0.980221	−	0.197904i	$-0.936586\pi$
$571$	−6.09499e6	+	6.09499e6i	−0.782317	+	0.782317i	0.197904	+	0.980221i	$0.436586\pi$
$572$	−7.41030e6	+	57605.8i	−0.946991	+	0.00736167i
$573$	−6.90056e6	−	6.90056e6i	−0.878006	−	0.878006i
$574$	−11069.9	−	2.84807e6i	−0.00140238	−	0.360804i
$575$	2.98058e6			0.375951
$576$	36223.1	+	1.55297e6i	0.00454914	+	0.195033i
$577$	−6.40682e6			−0.801130			−0.400565	−	0.916268i	$-0.631186\pi$
$577$	−6.40682e6			−0.801130			−0.400565	+	0.916268i	$0.631186\pi$
$578$	−22157.8	−	5.70076e6i	−0.00275872	−	0.709763i
$579$	−5.66791e6	−	5.66791e6i	−0.702630	−	0.702630i
$580$	−2.15769e6	+	16773.4i	−0.266330	+	0.00207038i
$581$	−4.83142e6	+	4.83142e6i	−0.593792	+	0.593792i
$582$	−2.60554e6	+	2.62588e6i	−0.318853	+	0.321341i
$583$			1.50432e7i			1.83303i
$584$	−5.17403e6	+	60333.9i	−0.627765	+	0.00732031i
$585$		−	644251.i		−	0.0778333i
$586$	4.76383e6	+	4.72694e6i	0.573076	+	0.568638i
$587$	−3.17862e6	+	3.17862e6i	−0.380754	+	0.380754i	−0.871374	−	0.490620i	$-0.836770\pi$
$587$	−3.17862e6	+	3.17862e6i	−0.380754	+	0.380754i	0.490620	+	0.871374i	$0.336770\pi$
$588$	−587132.	−	578074.i	−0.0700313	−	0.0689509i
$589$	−2.41701e6	−	2.41701e6i	−0.287071	−	0.287071i
$590$	4.65149e6	−	18079.5i	0.550126	−	0.00213824i
$591$	−5.14171e6			−0.605535
$592$	−7.48878e6	+	7.72533e6i	−0.878227	+	0.905968i
$593$	6.93794e6			0.810203			0.405102	−	0.914272i	$-0.367236\pi$
$593$	6.93794e6			0.810203			0.405102	+	0.914272i	$0.367236\pi$
$594$	9.78748e6	−	38042.1i	1.13816	−	0.00442383i
$595$	−3.36952e6	−	3.36952e6i	−0.390189	−	0.390189i
$596$	4.68965e6	−	4.76314e6i	0.540785	−	0.549259i
$597$	799625.	−	799625.i	0.0918228	−	0.0918228i
$598$	−1.04099e7	−	1.03293e7i	−1.19040	−	1.18118i
$599$			1.29586e7i			1.47568i	0.674978	+	0.737838i	$0.264153\pi$
$599$			1.29586e7i			1.47568i	−0.674978	+	0.737838i	$0.735847\pi$
$600$	1.13181e6	+	1.10572e6i	0.128350	+	0.125391i
$601$		−	3.22149e6i		−	0.363806i	−0.983316	−	0.181903i	$-0.941774\pi$
$601$		−	3.22149e6i		−	0.363806i	0.983316	−	0.181903i	$-0.0582257\pi$
$602$	−5.79103e6	+	5.83622e6i	−0.651275	+	0.656357i
$603$	−1.84241e6	+	1.84241e6i	−0.206344	+	0.206344i
$604$	21416.8	+	2.75502e6i	0.00238870	+	0.307278i
$605$	361158.	+	361158.i	0.0401152	+	0.0401152i
$606$	27339.9	+	7.03402e6i	0.00302424	+	0.778076i
$607$	−2.77321e6			−0.305500			−0.152750	−	0.988265i	$-0.548813\pi$
$607$	−2.77321e6			−0.305500			−0.152750	+	0.988265i	$0.548813\pi$
$608$	−1.19079e7	+	1.23800e7i	−1.30640	+	1.35819i
$609$	−4.61469e6			−0.504196
$610$	11120.8	+	2.86117e6i	0.00121007	+	0.311328i
$611$	3.43707e6	+	3.43707e6i	0.372465	+	0.372465i
$612$	−18373.4	−	2.36352e6i	−0.00198295	−	0.255083i
$613$	3.18104e6	−	3.18104e6i	0.341915	−	0.341915i	−0.515172	−	0.857087i	$-0.672272\pi$
$613$	3.18104e6	−	3.18104e6i	0.341915	−	0.341915i	0.857087	+	0.515172i	$0.172272\pi$
$614$	−2.94080e6	+	2.96375e6i	−0.314807	+	0.317264i
$615$		−	1.43895e6i		−	0.153411i
$616$	−6.59256e6	+	6.74812e6i	−0.700007	+	0.716525i
$617$			2.69222e6i			0.284707i	0.989816	+	0.142353i	$0.0454669\pi$
$617$			2.69222e6i			0.284707i	−0.989816	+	0.142353i	$0.954533\pi$
$618$	−497014.	−	493165.i	−0.0523477	−	0.0519423i
$619$	1.97397e6	−	1.97397e6i	0.207069	−	0.207069i	−0.595952	−	0.803020i	$-0.703225\pi$
$619$	1.97397e6	−	1.97397e6i	0.207069	−	0.207069i	0.803020	+	0.595952i	$0.203225\pi$
$620$	646970.	−	657108.i	0.0675935	−	0.0686527i
$621$	1.36958e7	+	1.36958e7i	1.42515	+	1.42515i
$622$	7.32148e6	−	28457.2i	0.758792	−	0.00294928i
$623$	1.18983e7			1.22818
$624$	−121031.	−	7.78410e6i	−0.0124432	−	0.800289i
$625$	−390625.			−0.0400000
$626$	−1.39079e7	+	54057.5i	−1.41849	+	0.00551341i
$627$	1.24928e7	+	1.24928e7i	1.26909	+	1.26909i
$628$	4.55529e6	+	4.48502e6i	0.460911	+	0.453801i
$629$	1.15760e7	−	1.15760e7i	1.16663	−	1.16663i
$630$	−582190.	−	577682.i	−0.0584405	−	0.0579879i
$631$			7.74739e6i			0.774608i	0.921952	+	0.387304i	$0.126594\pi$
$631$			7.74739e6i			0.774608i	−0.921952	+	0.387304i	$0.873406\pi$
$632$	−107134.	−	9.18748e6i	−0.0106693	−	0.914963i
$633$		−	1.02890e7i		−	1.02062i
$634$	1.05954e7	−	1.06781e7i	1.04688	−	1.05505i
$635$	−2.17260e6	+	2.17260e6i	−0.213818	+	0.213818i
$636$	−1.58030e7	+	122848.i	−1.54916	+	0.0120428i
$637$	−707687.	−	707687.i	−0.0691023	−	0.0691023i
$638$	−25263.5	−	6.49981e6i	−0.00245721	−	0.632192i
$639$	608865.			0.0589887
$640$	−3.36473e6	−	3.18644e6i	−0.324713	−	0.307508i
$641$	1.28304e7			1.23337			0.616687	−	0.787209i	$-0.288475\pi$
$641$	1.28304e7			1.23337			0.616687	+	0.787209i	$0.288475\pi$
$642$	−51827.8	−	1.33343e7i	−0.00496279	−	1.27683i
$643$	4.34386e6	+	4.34386e6i	0.414332	+	0.414332i	0.883245	−	0.468912i	$-0.155354\pi$
$643$	4.34386e6	+	4.34386e6i	0.414332	+	0.414332i	−0.468912	+	0.883245i	$0.655354\pi$
$644$	−1.86685e7	+	145124.i	−1.77376	+	0.0137887i
$645$	−2.93725e6	+	2.93725e6i	−0.277998	+	0.277998i
$646$	1.84093e7	−	1.85530e7i	1.73563	−	1.74917i
$647$		−	4.82724e6i		−	0.453355i	−0.973970	−	0.226678i	$-0.927214\pi$
$647$		−	4.82724e6i		−	0.453355i	0.973970	−	0.226678i	$-0.0727863\pi$
$648$	95577.2	+	8.19637e6i	0.00894163	+	0.766804i
$649$			1.40119e7i			1.30582i
$650$	1.36428e6	+	1.35372e6i	0.126655	+	0.125674i
$651$	1.39453e6	−	1.39453e6i	0.128966	−	0.128966i
$652$	9.15234e6	+	9.01114e6i	0.843166	+	0.830158i
$653$	4.17503e6	+	4.17503e6i	0.383157	+	0.383157i	0.872238	−	0.489081i	$-0.162668\pi$
$653$	4.17503e6	+	4.17503e6i	0.383157	+	0.383157i	−0.489081	+	0.872238i	$0.662668\pi$
$654$	1.32233e7	−	51396.7i	1.20892	−	0.00469884i
$655$	2.65551e6			0.241849
$656$	65518.1	+	4.21381e6i	0.00594431	+	0.382310i
$657$	1.35508e6			0.122476
$658$	6.18791e6	−	24051.3i	0.557159	−	0.00216558i
$659$	−1.12655e7	−	1.12655e7i	−1.01051	−	1.01051i	−0.999944	−	0.0105615i	$-0.996638\pi$
$659$	−1.12655e7	−	1.12655e7i	−1.01051	−	1.01051i	−0.0105615	−	0.999944i	$-0.503362\pi$
$660$	−3.34400e6	+	3.39640e6i	−0.298818	+	0.303500i
$661$	6.22807e6	−	6.22807e6i	0.554434	−	0.554434i	−0.373284	−	0.927717i	$-0.621768\pi$
$661$	6.22807e6	−	6.22807e6i	0.554434	−	0.554434i	0.927717	+	0.373284i	$0.121768\pi$
$662$	1.16918e7	+	1.16013e7i	1.03690	+	1.02887i
$663$			1.18455e7i			1.04657i
$664$	7.06520e6	−	7.23192e6i	0.621877	−	0.636551i
$665$		−	9.06929e6i		−	0.795278i
$666$	1.98464e6	−	2.00013e6i	0.173379	−	0.174732i
$667$	9.09533e6	−	9.09533e6i	0.791597	−	0.791597i
$668$	−3847.65	−	494955.i	−0.000333622	−	0.0429165i
$669$	−1.24956e6	−	1.24956e6i	−0.107942	−	0.107942i
$670$	−30211.7	−	7.77286e6i	−0.00260009	−	0.668950i
$671$	−8.61880e6			−0.738994
$672$	−7.14279e6	−	6.87042e6i	−0.610161	−	0.586895i
$673$	−5.79021e6			−0.492784			−0.246392	−	0.969170i	$-0.579245\pi$
$673$	−5.79021e6			−0.492784			−0.246392	+	0.969170i	$0.579245\pi$
$674$	5639.59	+	1.45095e6i	0.000478187	+	0.123028i
$675$	−1.79493e6	−	1.79493e6i	−0.151631	−	0.151631i
$676$	18852.2	+	2.42511e6i	0.00158670	+	0.204110i
$677$	−1.96617e6	+	1.96617e6i	−0.164873	+	0.164873i	−0.784721	−	0.619849i	$-0.787194\pi$
$677$	−1.96617e6	+	1.96617e6i	−0.164873	+	0.164873i	0.619849	+	0.784721i	$0.287194\pi$
$678$	4.03399e6	−	4.06547e6i	0.337024	−	0.339654i
$679$			5.72014e6i			0.476137i
$680$	5.04367e6	+	4.92739e6i	0.418287	+	0.408644i
$681$		−	1.81700e7i		−	1.50137i
$682$	1.97183e6	+	1.95656e6i	0.162333	+	0.161076i
$683$	−554999.	+	554999.i	−0.0455240	+	0.0455240i	−0.729502	−	0.683978i	$-0.760248\pi$
$683$	−554999.	+	554999.i	−0.0455240	+	0.0455240i	0.683978	+	0.729502i	$0.260248\pi$
$684$	3.15606e6	−	3.20552e6i	0.257932	−	0.261974i
$685$	−1.30258e6	−	1.30258e6i	−0.106067	−	0.106067i
$686$	−1.29050e7	+	50159.3i	−1.04700	+	0.00406950i
$687$	−6.88046e6			−0.556193
$688$	8.46770e6	−	8.73517e6i	0.682015	−	0.703559i
$689$	−1.91959e7			−1.54049
$690$	−9.43214e6	+	36661.0i	−0.754202	+	0.00293144i
$691$	−1.32042e7	−	1.32042e7i	−1.05200	−	1.05200i	−0.998572	−	0.0534279i	$-0.982985\pi$
$691$	−1.32042e7	−	1.32042e7i	−1.05200	−	1.05200i	−0.0534279	−	0.998572i	$-0.517015\pi$
$692$	1.39756e7	+	1.37600e7i	1.10944	+	1.09233i
$693$	1.74697e6	−	1.74697e6i	0.138182	−	0.138182i
$694$	1.69138e6	+	1.67828e6i	0.133304	+	0.132271i
$695$			668506.i			0.0524980i
$696$	6.82789e6	−	79619.4i	0.534273	−	0.00623011i
$697$		−	6.41236e6i		−	0.499961i
$698$	−5.99536e6	+	6.04215e6i	−0.465776	+	0.469411i
$699$	7.20112e6	−	7.20112e6i	0.557452	−	0.557452i
$700$	2.44663e6	−	19019.5i	0.188722	−	0.00146708i
$701$	−1.03528e7	−	1.03528e7i	−0.795723	−	0.795723i	0.186695	−	0.982418i	$-0.440222\pi$
$701$	−1.03528e7	−	1.03528e7i	−0.795723	−	0.795723i	−0.982418	+	0.186695i	$0.940222\pi$
$702$	48543.6	+	1.24893e7i	0.00371783	+	0.956523i
$703$	3.11577e7			2.37781
$704$	9.63791e6	−	1.00983e7i	0.732911	−	0.767917i
$705$	3.12636e6			0.236900
$706$	−59792.1	−	1.53833e7i	−0.00451473	−	1.16155i
$707$	7.69114e6	+	7.69114e6i	0.578685	+	0.578685i
$708$	−1.47196e7	+	114426.i	−1.10360	+	0.00857911i
$709$	−2.20601e6	+	2.20601e6i	−0.164813	+	0.164813i	−0.784695	−	0.619882i	$-0.787181\pi$
$709$	−2.20601e6	+	2.20601e6i	−0.164813	+	0.164813i	0.619882	+	0.784695i	$0.287181\pi$
$710$	−1.27936e6	+	1.28935e6i	−0.0952464	+	0.0959897i
$711$			2.40621e6i			0.178508i
$712$	−1.76046e7	+	205286.i	−1.30145	+	0.0151761i
$713$			5.49708e6i			0.404957i
$714$	1.07044e7	+	1.06215e7i	0.785808	+	0.779723i
$715$	−4.09377e6	+	4.09377e6i	−0.299474	+	0.299474i
$716$	−6.35741e6	−	6.25933e6i	−0.463444	−	0.456294i
$717$	2.01181e6	+	2.01181e6i	0.146147	+	0.146147i
$718$	−1.09226e7	+	42454.2i	−0.790708	+	0.00307333i
$719$	−7.60007e6			−0.548271			−0.274136	−	0.961691i	$-0.588392\pi$
$719$	−7.60007e6			−0.548271			−0.274136	+	0.961691i	$0.588392\pi$
$720$	871375.	+	844693.i	0.0626432	+	0.0607250i
$721$	−1.08268e6			−0.0775645
$722$	3.57365e7	−	138901.i	2.55134	−	0.00991660i
$723$	−1.29915e6	−	1.29915e6i	−0.0924301	−	0.0924301i
$724$	2.74359e6	−	2.78658e6i	0.194524	−	0.197572i
$725$	−1.19200e6	+	1.19200e6i	−0.0842235	+	0.0842235i
$726$	−1.14734e6	−	1.13845e6i	−0.0807886	−	0.0801630i
$727$		−	1.18770e7i		−	0.833432i	−0.909037	−	0.416716i	$-0.863181\pi$
$727$		−	1.18770e7i		−	0.833432i	0.909037	−	0.416716i	$-0.136819\pi$
$728$	−8.61093e6	−	8.41243e6i	−0.602174	−	0.588292i
$729$		−	1.59494e7i		−	1.11154i
$730$	−2.84734e6	+	2.86956e6i	−0.197757	+	0.199300i
$731$	−1.30892e7	+	1.30892e7i	−0.905985	+	0.905985i
$732$	−70384.4	−	9.05412e6i	−0.00485511	−	0.624552i
$733$	−1.72162e7	−	1.72162e7i	−1.18352	−	1.18352i	−0.978825	−	0.204698i	$-0.934379\pi$
$733$	−1.72162e7	−	1.72162e7i	−1.18352	−	1.18352i	−0.204698	−	0.978825i	$-0.565621\pi$
$734$	93825.2	+	2.41394e7i	0.00642805	+	1.65381i
$735$	−643711.			−0.0439514
$736$	2.76194e7	−	536821.i	1.87940	−	0.0365288i
$737$	2.34145e7			1.58787
$738$	−4289.68	−	1.10365e6i	−0.000289924	−	0.0745916i
$739$	7.02153e6	+	7.02153e6i	0.472956	+	0.472956i	0.902870	−	0.429914i	$-0.141456\pi$
$739$	7.02153e6	+	7.02153e6i	0.472956	+	0.472956i	−0.429914	+	0.902870i	$0.641456\pi$
$740$	65341.8	+	8.40545e6i	0.00438644	+	0.564263i
$741$	−1.59414e7	+	1.59414e7i	−1.06655	+	1.06655i
$742$	−1.72124e7	+	1.73467e7i	−1.14771	+	1.15667i
$743$			3.78191e6i			0.251327i	0.992073	+	0.125664i	$0.0401060\pi$
$743$			3.78191e6i			0.251327i	−0.992073	+	0.125664i	$0.959894\pi$
$744$	−2.03928e6	+	2.08740e6i	−0.135065	+	0.138252i
$745$		−	5.22214e6i		−	0.344713i
$746$	9.09916e6	+	9.02870e6i	0.598624	+	0.593989i
$747$	−1.87221e6	+	1.87221e6i	−0.122759	+	0.122759i
$748$	−1.49018e7	+	1.51353e7i	−0.973835	+	0.989094i
$749$	−1.45800e7	−	1.45800e7i	−0.949624	−	0.949624i
$750$	1.23615e6	−	4804.67i	0.0802447	−	0.000311896i
$751$	1.35554e7			0.877027			0.438514	−	0.898725i	$-0.355505\pi$
$751$	1.35554e7			0.877027			0.438514	+	0.898725i	$0.355505\pi$
$752$	−9.15521e6	+	142349.i	−0.590369	+	0.00917932i
$753$	9.64301e6			0.619762
$754$	8.29407e6	−	32237.5i	0.531300	−	0.00206506i
$755$	1.52199e6	+	1.52199e6i	0.0971729	+	0.0971729i
$756$	1.13297e7	+	1.11549e7i	0.720967	+	0.709844i
$757$	−1.42526e7	+	1.42526e7i	−0.903974	+	0.903974i	−0.995777	−	0.0918036i	$-0.970737\pi$
$757$	−1.42526e7	+	1.42526e7i	−0.903974	+	0.903974i	0.0918036	+	0.995777i	$0.470737\pi$
$758$	7.51332e6	+	7.45514e6i	0.474962	+	0.471284i
$759$		−	2.84128e7i		−	1.79023i
$760$	156477.	+	1.34189e7i	0.00982688	+	0.842719i
$761$			5.64585e6i			0.353401i	0.984265	+	0.176701i	$0.0565424\pi$
$761$			5.64585e6i			0.353401i	−0.984265	+	0.176701i	$0.943458\pi$
$762$	6.84853e6	−	6.90198e6i	0.427278	−	0.430612i
$763$	1.44587e7	−	1.44587e7i	0.899118	−	0.899118i
$764$	2.23284e7	−	173576.i	1.38396	−	0.0107586i
$765$	−1.30571e6	−	1.30571e6i	−0.0806667	−	0.0806667i
$766$	−59278.4	−	1.52512e7i	−0.00365027	−	0.939141i
$767$	−1.78798e7			−1.09743
$768$	1.06870e7	+	1.00422e7i	0.653811	+	0.614365i
$769$	1.87425e7			1.14291			0.571455	−	0.820633i	$-0.306379\pi$
$769$	1.87425e7			1.14291			0.571455	+	0.820633i	$0.306379\pi$
$770$	28646.6	+	7.37020e6i	0.00174119	+	0.447974i
$771$	−1.88708e7	−	1.88708e7i	−1.14329	−	1.14329i
$772$	1.83399e7	−	142570.i	1.10753	−	0.00860962i
$773$	5.14466e6	−	5.14466e6i	0.309676	−	0.309676i	−0.535108	−	0.844784i	$-0.679729\pi$
$773$	5.14466e6	−	5.14466e6i	0.309676	−	0.309676i	0.844784	+	0.535108i	$0.179729\pi$
$774$	−2.24407e6	+	2.26158e6i	−0.134643	+	0.135694i
$775$		−	720430.i		−	0.0430861i
$776$	−98692.2	−	8.46351e6i	−0.00588340	−	0.504540i
$777$			1.79769e7i			1.06822i
$778$	−1.58718e7	−	1.57489e7i	−0.940108	−	0.932828i
$779$	8.62966e6	−	8.62966e6i	0.509507	−	0.509507i
$780$	−4.33397e6	−	4.26711e6i	−0.255064	−	0.251129i
$781$	−3.86892e6	−	3.86892e6i	−0.226967	−	0.226967i
$782$	−4.20323e7	+	163372.i	−2.45791	+	0.00955345i
$783$	−1.09546e7			−0.638546
$784$	1.88504e6	−	29309.4i	0.109529	−	0.00170301i
$785$	4.99426e6			0.289266
$786$	−8.40344e6	+	32662.6i	−0.485178	+	0.00188580i
$787$	3.76779e6	+	3.76779e6i	0.216845	+	0.216845i	0.807168	−	0.590322i	$-0.200999\pi$
$787$	3.76779e6	+	3.76779e6i	0.216845	+	0.216845i	−0.590322	+	0.807168i	$0.700999\pi$
$788$	8.25396e6	−	8.38329e6i	0.473529	−	0.480949i
$789$	−4.79136e6	+	4.79136e6i	−0.274010	+	0.274010i
$790$	−5.09545e6	−	5.05599e6i	−0.290479	−	0.288230i
$791$		−	8.85612e6i		−	0.503271i
$792$	−2.55467e6	+	2.61495e6i	−0.144718	+	0.148132i
$793$		−	1.09980e7i		−	0.621057i
$794$	1.40329e7	−	1.41424e7i	0.789941	−	0.796106i
$795$	−8.73026e6	+	8.73026e6i	−0.489902	+	0.489902i
$796$	20113.6	+	2.58738e6i	0.00112514	+	0.144736i
$797$	−1.12687e7	−	1.12687e7i	−0.628388	−	0.628388i	0.319274	−	0.947662i	$-0.396561\pi$
$797$	−1.12687e7	−	1.12687e7i	−0.628388	−	0.628388i	−0.947662	+	0.319274i	$0.896561\pi$
$798$	111552.	+	2.87001e7i	0.00620111	+	1.59542i
$799$	1.39319e7			0.772049
$800$	−3.61970e6	+	70354.1i	−0.199962	+	0.00388655i
$801$	4.61066e6			0.253911
$802$	98557.1	+	2.53568e7i	0.00541068	+	1.39206i
$803$	−8.61062e6	−	8.61062e6i	−0.471244	−	0.471244i
$804$	191212.	+	2.45971e7i	0.0104322	+	1.34197i
$805$	−1.03133e7	+	1.03133e7i	−0.560929	+	0.560929i
$806$	−2.49666e6	+	2.51615e6i	−0.135370	+	0.136426i
$807$			1.95113e7i			1.05464i
$808$	−1.15125e7	−	1.12471e7i	−0.620356	−	0.606055i
$809$			3.50449e6i			0.188258i	0.995560	+	0.0941291i	$0.0300066\pi$
$809$			3.50449e6i			0.188258i	−0.995560	+	0.0941291i	$0.969993\pi$
$810$	4.54577e6	+	4.51057e6i	0.243442	+	0.241557i
$811$	−3.02322e6	+	3.02322e6i	−0.161405	+	0.161405i	−0.783189	−	0.621784i	$-0.786408\pi$
$811$	−3.02322e6	+	3.02322e6i	−0.161405	+	0.161405i	0.621784	+	0.783189i	$0.286408\pi$
$812$	7.40794e6	−	7.52401e6i	0.394282	−	0.400460i
$813$	1.21335e7	+	1.21335e7i	0.643812	+	0.643812i
$814$	−2.53205e7	+	98415.9i	−1.33940	+	0.00520600i
$815$	1.00343e7			0.529167
$816$	−1.60215e7	−	1.55309e7i	−0.842319	−	0.816526i
$817$	−3.52306e7			−1.84657
$818$	1.33845e7	−	52022.9i	0.699387	−	0.00271839i
$819$	2.22921e6	+	2.22921e6i	0.116129	+	0.116129i
$820$	2.34613e6	+	2.30994e6i	0.121848	+	0.119968i
$821$	247372.	−	247372.i	0.0128083	−	0.0128083i	−0.700674	−	0.713482i	$-0.747117\pi$
$821$	247372.	−	247372.i	0.0128083	−	0.0128083i	0.713482	+	0.700674i	$0.247117\pi$
$822$	4.13808e6	+	4.10604e6i	0.213609	+	0.211955i
$823$		−	2.01832e7i		−	1.03870i	−0.854562	−	0.519350i	$-0.826174\pi$
$823$		−	2.01832e7i		−	1.03870i	0.854562	−	0.519350i	$-0.173826\pi$
$824$	1.60193e6	−	18680.0i	0.0821915	−	0.000958428i
$825$			3.72369e6i			0.190475i
$826$	−1.60324e7	+	1.61575e7i	−0.817612	+	0.823992i
$827$	−1.59793e7	+	1.59793e7i	−0.812445	+	0.812445i	−0.985000	−	0.172555i	$-0.944798\pi$
$827$	−1.59793e7	+	1.59793e7i	−0.812445	+	0.812445i	0.172555	+	0.985000i	$0.444798\pi$
$828$	−7.23418e6	+	56236.7i	−0.366702	+	0.00285065i
$829$	1.10547e7	+	1.10547e7i	0.558675	+	0.558675i	0.928930	−	0.370255i	$-0.120730\pi$
$829$	1.10547e7	+	1.10547e7i	0.558675	+	0.558675i	−0.370255	+	0.928930i	$0.620730\pi$
$830$	−30700.4	−	7.89860e6i	−0.00154685	−	0.397974i
$831$	3.34270e7			1.67917
$832$	1.28859e7	+	1.22984e7i	0.645365	+	0.615945i
$833$	−2.86856e6			−0.143236
$834$	−8222.59	−	2.11551e6i	−0.000409349	−	0.105317i
$835$	−273435.	−	273435.i	−0.0135718	−	0.0135718i
$836$	−4.04235e7	+	314242.i	−2.00041	+	0.0155507i
$837$	3.31040e6	−	3.31040e6i	0.163330	−	0.163330i
$838$	−5.91252e6	+	5.95866e6i	−0.290846	+	0.293115i
$839$			3.34841e7i			1.64223i	0.570762	+	0.821116i	$0.306648\pi$
$839$			3.34841e7i			1.64223i	−0.570762	+	0.821116i	$0.693352\pi$
$840$	−7.74221e6	+	90281.3i	−0.378588	+	0.00441468i
$841$		−	1.32363e7i		−	0.645320i
$842$	473134.	+	469470.i	0.0229987	+	0.0228206i
$843$	1.33129e7	−	1.33129e7i	0.645215	−	0.645215i
$844$	1.67757e7	+	1.65169e7i	0.810632	+	0.798126i
$845$	1.33974e6	+	1.33974e6i	0.0645473	+	0.0645473i
$846$	2.39786e6	−	9320.05i	0.115186	−	0.000447705i
$847$	−2.49933e6			−0.119706
$848$	2.51681e7	−	2.59631e7i	1.20188	−	1.23985i
$849$	1.86828e7			0.889554
$850$	5.50862e6	−	21411.0i	0.261514	−	0.00101646i
$851$	−3.54315e7	−	3.54315e7i	−1.67713	−	1.67713i
$852$	4.03273e6	−	4.09592e6i	0.190327	−	0.193309i
$853$	−1.30905e7	+	1.30905e7i	−0.616004	+	0.616004i	−0.944504	−	0.328500i	$-0.893457\pi$
$853$	−1.30905e7	+	1.30905e7i	−0.616004	+	0.616004i	0.328500	+	0.944504i	$0.393457\pi$
$854$	−9.93858e6	−	9.86162e6i	−0.466315	−	0.462704i
$855$		−	3.51442e6i		−	0.164414i
$856$	2.18240e7	+	2.13209e7i	1.01801	+	0.994539i
$857$			3.48281e7i			1.61986i	0.586525	+	0.809931i	$0.300496\pi$
$857$			3.48281e7i			1.61986i	−0.586525	+	0.809931i	$0.699504\pi$
$858$	1.29045e7	−	1.30052e7i	0.598445	−	0.603115i
$859$	−9.28672e6	+	9.28672e6i	−0.429417	+	0.429417i	−0.888430	−	0.459013i	$-0.848203\pi$
$859$	−9.28672e6	+	9.28672e6i	−0.429417	+	0.429417i	0.459013	+	0.888430i	$0.348203\pi$
$860$	−73883.2	−	9.50420e6i	−0.00340643	−	0.438197i
$861$	4.97900e6	+	4.97900e6i	0.228894	+	0.228894i
$862$	−41690.5	−	1.07261e7i	−0.00191104	−	0.491672i
$863$	−3.92643e7			−1.79462			−0.897308	−	0.441406i	$-0.854480\pi$
$863$	−3.92643e7			−1.79462			−0.897308	+	0.441406i	$0.854480\pi$
$864$	−1.69559e7	−	1.63094e7i	−0.772746	−	0.743280i
$865$	1.53223e7			0.696281
$866$	142791.	+	3.67372e7i	0.00647001	+	1.66461i
$867$	9.96607e6	+	9.96607e6i	0.450273	+	0.450273i
$868$	35077.7	+	4.51232e6i	0.00158027	+	0.203283i
$869$	1.52898e7	−	1.52898e7i	0.686835	−	0.686835i
$870$	3.75748e6	−	3.78680e6i	0.168305	−	0.169619i
$871$			2.98781e7i			1.33446i
$872$	−2.11436e7	+	2.16425e7i	−0.941644	+	0.963864i
$873$			2.21660e6i			0.0984354i
$874$	−5.67863e7	−	5.63466e7i	−2.51458	−	2.49511i
$875$	1.35163e6	−	1.35163e6i	0.0596811	−	0.0596811i
$876$	8.97520e6	−	9.11583e6i	0.395170	−	0.401362i
$877$	−1.40868e7	−	1.40868e7i	−0.618462	−	0.618462i	0.326675	−	0.945137i	$-0.394072\pi$
$877$	−1.40868e7	−	1.40868e7i	−0.618462	−	0.618462i	−0.945137	+	0.326675i	$0.894072\pi$
$878$	−1.46272e7	+	56853.2i	−0.640361	+	0.00248896i
$879$	−1.65918e7			−0.724303
$880$	−169547.	−	1.09044e7i	−0.00738046	−	0.474675i
$881$	4.17564e7			1.81252			0.906261	−	0.422718i	$-0.138924\pi$
$881$	4.17564e7			1.81252			0.906261	+	0.422718i	$0.138924\pi$
$882$	−493715.	+	1918.98i	−0.0213700	+	8.30613e-5i
$883$	−1.75653e7	−	1.75653e7i	−0.758148	−	0.758148i	0.217837	−	0.975985i	$-0.430100\pi$
$883$	−1.75653e7	−	1.75653e7i	−0.758148	−	0.758148i	−0.975985	+	0.217837i	$0.930100\pi$
$884$	−1.93134e7	−	1.90154e7i	−0.831244	−	0.818419i
$885$	−8.13173e6	+	8.13173e6i	−0.349000	+	0.349000i
$886$	3.19660e6	+	3.17185e6i	0.136806	+	0.135746i
$887$		−	1.97380e7i		−	0.842353i	−0.906979	−	0.421177i	$-0.861617\pi$
$887$		−	1.97380e7i		−	0.842353i	0.906979	−	0.421177i	$-0.138383\pi$
$888$	−310163.	−	2.65985e7i	−0.0131995	−	1.13194i
$889$		−	1.50351e7i		−	0.638045i
$890$	−9.68806e6	+	9.76367e6i	−0.409979	+	0.413179i
$891$	−1.36404e7	+	1.36404e7i	−0.575616	+	0.575616i
$892$	4.04325e6	−	31431.2i	0.170145	−	0.00132266i
$893$	1.87494e7	+	1.87494e7i	0.786790	+	0.786790i
$894$	64232.0	+	1.65256e7i	0.00268787	+	0.691535i
$895$	−6.97004e6			−0.290856
$896$	2.26681e7	−	616897.i	0.943291	−	0.0256710i
$897$	3.62562e7			1.50453
$898$	−145709.	−	3.74881e7i	−0.00602971	−	1.55133i
$899$	−2.19842e6	−	2.19842e6i	−0.0907216	−	0.0907216i
$900$	948088.	−	7370.20i	0.0390160	−	0.000303300i
$901$	−3.89045e7	+	3.89045e7i	−1.59657	+	1.59657i
$902$	−6.98568e6	+	7.04019e6i	−0.285886	+	0.288117i
$903$		−	2.03268e7i		−	0.829562i
$904$	152799.	+	1.31035e7i	0.00621869	+	0.533293i
$905$		−	3.05511e6i		−	0.123995i
$906$	−4.83511e6	−	4.79767e6i	−0.195698	−	0.194183i
$907$	3.47142e7	−	3.47142e7i	1.40116	−	1.40116i	0.604738	−	0.796424i	$-0.293278\pi$
$907$	3.47142e7	−	3.47142e7i	1.40116	−	1.40116i	0.796424	−	0.604738i	$-0.206722\pi$
$908$	2.96253e7	+	2.91683e7i	1.19247	+	1.17407i
$909$	2.98037e6	+	2.98037e6i	0.119636	+	0.119636i
$910$	−9.40473e6	+	36554.5i	−0.376481	+	0.00146331i
$911$	3.91881e7			1.56444			0.782220	−	0.623003i	$-0.214087\pi$
$911$	3.91881e7			1.56444			0.782220	+	0.623003i	$0.214087\pi$
$912$	−660227.	−	4.24626e7i	−0.0262849	−	1.69052i
$913$	2.37933e7			0.944663
$914$	1.40183e7	−	54486.6i	0.555048	−	0.00215737i
$915$	−5.00189e6	−	5.00189e6i	−0.197507	−	0.197507i
$916$	1.10452e7	−	1.12182e7i	0.434944	−	0.441759i
$917$	−9.18849e6	+	9.18849e6i	−0.360845	+	0.360845i
$918$	2.54106e7	+	2.52139e7i	0.995197	+	0.987490i
$919$		−	1.20777e7i		−	0.471732i	−0.971786	−	0.235866i	$-0.924207\pi$
$919$		−	1.20777e7i		−	0.471732i	0.971786	−	0.235866i	$-0.0757926\pi$
$920$	1.50816e7	−	1.54375e7i	0.587459	−	0.601321i
$921$		−	1.03223e7i		−	0.400985i
$922$	1.62466e7	−	1.63734e7i	0.629412	−	0.634323i
$923$	4.93693e6	−	4.93693e6i	0.190745	−	0.190745i
$924$	−181306.	−	2.33229e7i	−0.00698607	−	0.898674i
$925$	4.64354e6	+	4.64354e6i	0.178441	+	0.178441i
$926$	−92123.7	−	2.37016e7i	−0.00353056	−	0.908344i
$927$	−419548.			−0.0160355
$928$	−1.08310e7	+	1.12603e7i	−0.412854	+	0.429221i
$929$	−2.07335e7			−0.788196			−0.394098	−	0.919068i	$-0.628943\pi$
$929$	−2.07335e7			−0.788196			−0.394098	+	0.919068i	$0.628943\pi$
$930$	8861.25	+	2.27982e6i	0.000335960	+	0.0864359i
$931$	−3.86046e6	−	3.86046e6i	−0.145971	−	0.145971i
$932$	181136.	+	2.33010e7i	0.00683069	+	0.878687i
$933$	−1.27994e7	+	1.27994e7i	−0.481377	+	0.481377i
$934$	−7.82828e6	+	7.88937e6i	−0.293629	+	0.295921i
$935$			1.65938e7i			0.620751i
$936$	−3.33680e6	−	3.25988e6i	−0.124492	−	0.121622i
$937$			2.96264e6i			0.110238i	0.998480	+	0.0551188i	$0.0175538\pi$
$937$			2.96264e6i			0.110238i	−0.998480	+	0.0551188i	$0.982446\pi$
$938$	2.69999e7	+	2.67908e7i	1.00197	+	0.994212i
$939$	2.43138e7	−	2.43138e7i	0.899890	−	0.899890i
$940$	−5.01873e6	+	5.09736e6i	−0.185257	+	0.188159i
$941$	−3.93651e6	−	3.93651e6i	−0.144923	−	0.144923i	0.630923	−	0.775846i	$-0.282676\pi$
$941$	−3.93651e6	−	3.93651e6i	−0.144923	−	0.144923i	−0.775846	+	0.630923i	$0.782676\pi$
$942$	−1.58045e7	+	61429.2i	−0.580302	+	0.00225553i
$943$	−1.96267e7			−0.718735
$944$	2.34427e7	−	2.41832e7i	0.856203	−	0.883249i
$945$	1.24215e7			0.452476
$946$	2.86303e7	−	111281.i	1.04016	−	0.00404289i
$947$	3.98729e6	+	3.98729e6i	0.144478	+	0.144478i	0.775646	−	0.631168i	$-0.217424\pi$
$947$	3.98729e6	+	3.98729e6i	0.144478	+	0.144478i	−0.631168	+	0.775646i	$0.717424\pi$
$948$	1.61869e7	+	1.59372e7i	0.584982	+	0.575958i
$949$	1.09876e7	−	1.09876e7i	0.396037	−	0.396037i
$950$	7.44223e6	+	7.38460e6i	0.267543	+	0.265471i
$951$			3.71905e7i			1.33346i
$952$	−3.45015e7	+	402319.i	−1.23380	+	0.0143873i
$953$			2.98015e7i			1.06293i	0.847079	+	0.531467i	$0.178359\pi$
$953$			2.98015e7i			1.06293i	−0.847079	+	0.531467i	$0.821641\pi$
$954$	−6.66993e6	+	6.72199e6i	−0.237274	+	0.239126i
$955$	1.23352e7	−	1.23352e7i	0.437661	−	0.437661i
$956$	−6.50970e6	+	50604.7i	−0.230365	+	0.00179080i
$957$	1.13630e7	+	1.13630e7i	0.401062	+	0.401062i
$958$	66202.2	+	1.70325e7i	0.00233055	+	0.599604i
$959$	9.01429e6			0.316508
$960$	1.14538e7	−	267160.i	0.401118	−	0.00935607i
$961$	−2.73005e7			−0.953590
$962$	−125584.	−	3.23101e7i	−0.00437517	−	1.12564i
$963$	−5.64985e6	−	5.64985e6i	−0.196323	−	0.196323i
$964$	4.20371e6	−	32678.6i	0.145694	−	0.00113258i
$965$	1.01318e7	−	1.01318e7i	0.350241	−	0.350241i
$966$	3.25099e7	−	3.27636e7i	1.12092	−	1.12966i
$967$		−	1.00777e7i		−	0.346574i	−0.984871	−	0.173287i	$-0.944561\pi$
$967$		−	1.00777e7i		−	0.346574i	0.984871	−	0.173287i	$-0.0554388\pi$
$968$	3.69800e6	−	43122.1i	0.126847	−	0.00147915i
$969$			6.46175e7i			2.21076i
$970$	−4.69393e6	−	4.65758e6i	−0.160180	−	0.158939i
$971$	1.87643e7	−	1.87643e7i	0.638683	−	0.638683i	−0.311548	−	0.950231i	$-0.600847\pi$
$971$	1.87643e7	−	1.87643e7i	0.638683	−	0.638683i	0.950231	+	0.311548i	$0.100847\pi$
$972$	8.06404e6	+	7.93963e6i	0.273771	+	0.269547i
$973$	−2.31314e6	−	2.31314e6i	−0.0783285	−	0.0783285i
$974$	−9.81002e6	+	38129.7i	−0.331339	+	0.00128785i
$975$	−4.75161e6			−0.160077
$976$	1.48753e7	+	1.44198e7i	0.499850	+	0.484544i
$977$	2.26099e6			0.0757812			0.0378906	−	0.999282i	$-0.487936\pi$
$977$	2.26099e6			0.0757812			0.0378906	+	0.999282i	$0.487936\pi$
$978$	−3.17539e7	+	123421.i	−1.06157	+	0.00412613i
$979$	−2.92976e7	−	2.92976e7i	−0.976957	−	0.976957i
$980$	1.03335e6	−	1.04954e6i	0.0343701	−	0.0349086i
$981$	5.60284e6	−	5.60284e6i	0.185881	−	0.185881i
$982$	−1.50896e7	−	1.49728e7i	−0.499343	−	0.495477i
$983$			3.91938e7i			1.29370i	0.762618	+	0.646849i	$0.223914\pi$
$983$			3.91938e7i			1.29370i	−0.762618	+	0.646849i	$0.776086\pi$
$984$	−7.45282e6	−	7.28101e6i	−0.245376	−	0.239720i
$985$		−	9.19115e6i		−	0.301842i
$986$	1.67444e7	−	1.68751e7i	0.548501	−	0.552781i
$987$	−1.08177e7	+	1.08177e7i	−0.353462	+	0.353462i
$988$	−400988.	−	5.15824e7i	−0.0130689	−	1.68116i
$989$	4.00631e7	+	4.00631e7i	1.30243	+	1.30243i
$990$	11100.8	+	2.85601e6i	0.000359969	+	0.0926129i
$991$	5.81615e7			1.88127			0.940635	−	0.339420i	$-0.110231\pi$
$991$	5.81615e7			1.88127			0.940635	+	0.339420i	$0.110231\pi$
$992$	−129754.	−	6.67582e6i	−0.00418641	−	0.215390i
$993$	−4.07210e7			−1.31052
$994$	−34546.7	−	8.88817e6i	−0.00110902	−	0.285329i
$995$	1.42938e6	+	1.42938e6i	0.0457710	+	0.0457710i
$996$	194305.	+	2.49950e7i	0.00620633	+	0.798371i
$997$	4.33030e7	−	4.33030e7i	1.37969	−	1.37969i	0.534546	−	0.845139i	$-0.320483\pi$
$997$	4.33030e7	−	4.33030e7i	1.37969	−	1.37969i	0.845139	−	0.534546i	$-0.179517\pi$
$998$	4.11878e7	−	4.15092e7i	1.30901	−	1.31922i
$999$			4.26744e7i			1.35286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.61.20	yes	80
4.3	odd	2		320.6.l.a.81.11		80
16.5	even	4	inner	80.6.l.a.21.20	✓	80
16.11	odd	4		320.6.l.a.241.11		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.20	✓	80	16.5	even	4	inner
80.6.l.a.61.20	yes	80	1.1	even	1	trivial
320.6.l.a.81.11		80	4.3	odd	2
320.6.l.a.241.11		80	16.11	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.0219870 - 5.65681i) q^{2} +(9.88924 + 9.88924i) q^{3} +(-31.9990 + 0.248752i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(55.7241 - 56.1590i) q^{6} -122.335i q^{7} +(2.11071 + 181.007i) q^{8} -47.4058i q^{9} +O(q^{10})\)	\(q+(-0.0219870 - 5.65681i) q^{2} +(9.88924 + 9.88924i) q^{3} +(-31.9990 + 0.248752i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(55.7241 - 56.1590i) q^{6} -122.335i q^{7} +(2.11071 + 181.007i) q^{8} -47.4058i q^{9} +(100.388 + 99.6106i) q^{10} +(-301.232 + 301.232i) q^{11} +(-318.906 - 313.986i) q^{12} +(-384.386 - 384.386i) q^{13} +(-692.028 + 2.68978i) q^{14} -349.637 q^{15} +(1023.88 - 15.9197i) q^{16} -1558.08 q^{17} +(-268.166 + 1.04231i) q^{18} +(-2096.85 - 2096.85i) q^{19} +(561.271 - 570.066i) q^{20} +(1209.80 - 1209.80i) q^{21} +(1710.63 + 1697.39i) q^{22} +4768.93i q^{23} +(-1769.15 + 1810.90i) q^{24} -625.000i q^{25} +(-2165.95 + 2182.85i) q^{26} +(2871.89 - 2871.89i) q^{27} +(30.4312 + 3914.61i) q^{28} +(-1907.21 - 1907.21i) q^{29} +(7.68747 + 1977.83i) q^{30} +1152.69 q^{31} +(-112.567 - 5791.52i) q^{32} -5957.91 q^{33} +(34.2576 + 8813.79i) q^{34} +(2162.60 + 2162.60i) q^{35} +(11.7923 + 1516.94i) q^{36} +(-7429.66 + 7429.66i) q^{37} +(-11815.4 + 11907.6i) q^{38} -7602.58i q^{39} +(-3237.09 - 3162.47i) q^{40} +4115.54i q^{41} +(-6870.23 - 6817.03i) q^{42} +(8400.86 - 8400.86i) q^{43} +(9564.19 - 9714.06i) q^{44} +(838.025 + 838.025i) q^{45} +(26976.9 - 104.854i) q^{46} -8941.71 q^{47} +(10282.8 + 9967.93i) q^{48} +1841.08 q^{49} +(-3535.51 + 13.7419i) q^{50} +(-15408.3 - 15408.3i) q^{51} +(12395.6 + 12204.4i) q^{52} +(24969.5 - 24969.5i) q^{53} +(-16308.9 - 16182.6i) q^{54} -10650.2i q^{55} +(22143.5 - 258.214i) q^{56} -41472.4i q^{57} +(-10746.8 + 10830.6i) q^{58} +(23257.6 - 23257.6i) q^{59} +(11188.1 - 86.9731i) q^{60} +(14305.9 + 14305.9i) q^{61} +(-25.3441 - 6520.54i) q^{62} -5799.41 q^{63} +(-32759.1 + 764.106i) q^{64} +13590.1 q^{65} +(130.996 + 33702.8i) q^{66} +(-38864.6 - 38864.6i) q^{67} +(49857.2 - 387.577i) q^{68} +(-47161.1 + 47161.1i) q^{69} +(12185.9 - 12281.0i) q^{70} +12843.7i q^{71} +(8580.79 - 100.060i) q^{72} +28584.7i q^{73} +(42191.5 + 41864.8i) q^{74} +(6180.78 - 6180.78i) q^{75} +(67618.6 + 66575.4i) q^{76} +(36851.3 + 36851.3i) q^{77} +(-43006.4 + 167.158i) q^{78} -50757.6 q^{79} +(-17818.3 + 18381.2i) q^{80} +45282.1 q^{81} +(23280.9 - 90.4884i) q^{82} +(-39493.3 - 39493.3i) q^{83} +(-38411.6 + 39013.5i) q^{84} +(27543.3 - 27543.3i) q^{85} +(-47706.8 - 47337.3i) q^{86} -37721.7i q^{87} +(-55160.9 - 53889.3i) q^{88} +97259.4i q^{89} +(4722.12 - 4758.97i) q^{90} +(-47024.0 + 47024.0i) q^{91} +(-1186.28 - 152601. i) q^{92} +(11399.2 + 11399.2i) q^{93} +(196.601 + 50581.6i) q^{94} +74134.7 q^{95} +(56160.6 - 58387.0i) q^{96} -46757.9 q^{97} +(-40.4798 - 10414.6i) q^{98} +(14280.1 + 14280.1i) 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

Introduction

L-functions

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