LMFDB - Embedded newform 48.6.j.a.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.j (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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	48.37
Dual form			48.6.j.a.13.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.19025 + 4.67143i) q^{2} +(-6.36396 + 6.36396i) q^{3} +(-11.6446 + 29.8061i) q^{4} +(-59.0275 - 59.0275i) q^{5} +(-50.0315 - 9.42617i) q^{6} -85.1278i q^{7} +(-176.386 + 40.6922i) q^{8} -81.0000i q^{9} +O(q^{10})$	\(q+(3.19025 + 4.67143i) q^{2} +(-6.36396 + 6.36396i) q^{3} +(-11.6446 + 29.8061i) q^{4} +(-59.0275 - 59.0275i) q^{5} +(-50.0315 - 9.42617i) q^{6} -85.1278i q^{7} +(-176.386 + 40.6922i) q^{8} -81.0000i q^{9} +(87.4303 - 464.056i) q^{10} +(71.9046 + 71.9046i) q^{11} +(-115.579 - 263.790i) q^{12} +(-63.4590 + 63.4590i) q^{13} +(397.669 - 271.579i) q^{14} +751.297 q^{15} +(-752.808 - 694.159i) q^{16} -1563.69 q^{17} +(378.386 - 258.410i) q^{18} +(-1314.60 + 1314.60i) q^{19} +(2446.73 - 1072.03i) q^{20} +(541.750 + 541.750i) q^{21} +(-106.504 + 565.291i) q^{22} -4176.22i q^{23} +(863.552 - 1381.48i) q^{24} +3843.49i q^{25} +(-498.895 - 93.9942i) q^{26} +(515.481 + 515.481i) q^{27} +(2537.33 + 991.277i) q^{28} +(-3852.02 + 3852.02i) q^{29} +(2396.83 + 3509.64i) q^{30} -4492.09 q^{31} +(841.068 - 5731.23i) q^{32} -915.196 q^{33} +(-4988.57 - 7304.68i) q^{34} +(-5024.88 + 5024.88i) q^{35} +(2414.29 + 943.210i) q^{36} +(9974.55 + 9974.55i) q^{37} +(-10335.0 - 1947.17i) q^{38} -807.702i q^{39} +(12813.6 + 8009.69i) q^{40} +6758.75i q^{41} +(-802.430 + 4259.07i) q^{42} +(1233.26 + 1233.26i) q^{43} +(-2980.49 + 1305.90i) q^{44} +(-4781.23 + 4781.23i) q^{45} +(19508.9 - 13323.2i) q^{46} +15931.3 q^{47} +(9208.44 - 373.242i) q^{48} +9560.25 q^{49} +(-17954.6 + 12261.7i) q^{50} +(9951.27 - 9951.27i) q^{51} +(-1152.51 - 2630.42i) q^{52} +(-17551.0 - 17551.0i) q^{53} +(-763.520 + 4052.55i) q^{54} -8488.70i q^{55} +(3464.04 + 15015.4i) q^{56} -16732.2i q^{57} +(-30283.4 - 5705.54i) q^{58} +(-27648.3 - 27648.3i) q^{59} +(-8748.54 + 22393.3i) q^{60} +(-15253.4 + 15253.4i) q^{61} +(-14330.9 - 20984.5i) q^{62} -6895.36 q^{63} +(29456.3 - 14355.1i) q^{64} +7491.66 q^{65} +(-2919.71 - 4275.28i) q^{66} +(19395.6 - 19395.6i) q^{67} +(18208.5 - 46607.6i) q^{68} +(26577.3 + 26577.3i) q^{69} +(-39504.1 - 7442.76i) q^{70} -75229.9i q^{71} +(3296.07 + 14287.3i) q^{72} +30785.6i q^{73} +(-14774.1 + 78416.8i) q^{74} +(-24459.8 - 24459.8i) q^{75} +(-23875.2 - 54491.2i) q^{76} +(6121.08 - 6121.08i) q^{77} +(3773.12 - 2576.77i) q^{78} +47502.1 q^{79} +(3461.92 + 85410.8i) q^{80} -6561.00 q^{81} +(-31573.1 + 21562.1i) q^{82} +(-38527.1 + 38527.1i) q^{83} +(-22455.9 + 9839.02i) q^{84} +(92300.8 + 92300.8i) q^{85} +(-1826.68 + 9695.51i) q^{86} -49028.3i q^{87} +(-15608.9 - 9757.03i) q^{88} -73974.3i q^{89} +(-37588.5 - 7081.86i) q^{90} +(5402.13 + 5402.13i) q^{91} +(124477. + 48630.3i) q^{92} +(28587.5 - 28587.5i) q^{93} +(50824.9 + 74422.0i) q^{94} +155196. q^{95} +(31120.8 + 41825.9i) q^{96} -175496. q^{97} +(30499.6 + 44660.1i) q^{98} +(5824.27 - 5824.27i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) $ 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	3.19025	+	4.67143i	0.563962	+	0.825800i
$2$	3.19025	+	4.67143i	0.563962	+	0.825800i
$3$	−6.36396	+	6.36396i	−0.408248	+	0.408248i
$3$	−6.36396	+	6.36396i	−0.408248	+	0.408248i
$4$	−11.6446	+	29.8061i	−0.363893	+	0.931441i
$5$	−59.0275	−	59.0275i	−1.05592	−	1.05592i	−0.998341	−	0.0575749i	$-0.981663\pi$
$5$	−59.0275	−	59.0275i	−1.05592	−	1.05592i	−0.0575749	−	0.998341i	$-0.518337\pi$
$6$	−50.0315	−	9.42617i	−0.567368	−	0.106895i
$7$		−	85.1278i		−	0.656639i	−0.944567	−	0.328319i	$-0.893518\pi$
$7$		−	85.1278i		−	0.656639i	0.944567	−	0.328319i	$-0.106482\pi$
$8$	−176.386	+	40.6922i	−0.974406	+	0.224795i
$9$		−	81.0000i		−	0.333333i
$10$	87.4303	−	464.056i	0.276479	−	1.46747i
$11$	71.9046	+	71.9046i	0.179174	+	0.179174i	0.790996	−	0.611822i	$-0.209563\pi$
$11$	71.9046	+	71.9046i	0.179174	+	0.179174i	−0.611822	+	0.790996i	$0.709563\pi$
$12$	−115.579	−	263.790i	−0.231700	−	0.528818i
$13$	−63.4590	+	63.4590i	−0.104144	+	0.104144i	−0.757259	−	0.653115i	$-0.773462\pi$
$13$	−63.4590	+	63.4590i	−0.104144	+	0.104144i	0.653115	+	0.757259i	$0.273462\pi$
$14$	397.669	−	271.579i	0.542253	−	0.370320i
$15$	751.297			0.862152
$16$	−752.808	−	694.159i	−0.735164	−	0.677889i
$17$	−1563.69			−1.31229			−0.656143	−	0.754636i	$-0.727813\pi$
$17$	−1563.69			−1.31229			−0.656143	+	0.754636i	$0.727813\pi$
$18$	378.386	−	258.410i	0.275267	−	0.187987i
$19$	−1314.60	+	1314.60i	−0.835432	+	0.835432i	−0.988254	−	0.152822i	$-0.951164\pi$
$19$	−1314.60	+	1314.60i	−0.835432	+	0.835432i	0.152822	+	0.988254i	$0.451164\pi$
$20$	2446.73	−	1072.03i	1.36776	−	0.599283i
$21$	541.750	+	541.750i	0.268072	+	0.268072i
$22$	−106.504	+	565.291i	−0.0469146	+	0.249009i
$23$		−	4176.22i		−	1.64613i	−0.567948	−	0.823064i	$-0.692263\pi$
$23$		−	4176.22i		−	1.64613i	0.567948	−	0.823064i	$-0.307737\pi$
$24$	863.552	−	1381.48i	0.306028	−	0.489572i
$25$			3843.49i			1.22992i
$26$	−498.895	−	93.9942i	−0.144736	−	0.0272689i
$27$	515.481	+	515.481i	0.136083	+	0.136083i
$28$	2537.33	+	991.277i	0.611620	+	0.238946i
$29$	−3852.02	+	3852.02i	−0.850538	+	0.850538i	−0.990199	−	0.139661i	$-0.955399\pi$
$29$	−3852.02	+	3852.02i	−0.850538	+	0.850538i	0.139661	+	0.990199i	$0.455399\pi$
$30$	2396.83	+	3509.64i	0.486221	+	0.711965i
$31$	−4492.09			−0.839545			−0.419773	−	0.907629i	$-0.637890\pi$
$31$	−4492.09			−0.839545			−0.419773	+	0.907629i	$0.637890\pi$
$32$	841.068	−	5731.23i	0.145196	−	0.989403i
$33$	−915.196			−0.146295
$34$	−4988.57	−	7304.68i	−0.740080	−	1.08369i
$35$	−5024.88	+	5024.88i	−0.693355	+	0.693355i
$36$	2414.29	+	943.210i	0.310480	+	0.121298i
$37$	9974.55	+	9974.55i	1.19781	+	1.19781i	0.974820	+	0.222993i	$0.0715828\pi$
$37$	9974.55	+	9974.55i	1.19781	+	1.19781i	0.222993	+	0.974820i	$0.428417\pi$
$38$	−10335.0	−	1947.17i	−1.16105	−	0.218748i
$39$		−	807.702i		−	0.0850334i
$40$	12813.6	+	8009.69i	1.26626	+	0.791527i
$41$			6758.75i			0.627924i	0.949436	+	0.313962i	$0.101656\pi$
$41$			6758.75i			0.627924i	−0.949436	+	0.313962i	$0.898344\pi$
$42$	−802.430	+	4259.07i	−0.0701914	+	0.372556i
$43$	1233.26	+	1233.26i	0.101715	+	0.101715i	0.756133	−	0.654418i	$-0.227086\pi$
$43$	1233.26	+	1233.26i	0.101715	+	0.101715i	−0.654418	+	0.756133i	$0.727086\pi$
$44$	−2980.49	+	1305.90i	−0.232090	+	0.101690i
$45$	−4781.23	+	4781.23i	−0.351972	+	0.351972i
$46$	19508.9	−	13323.2i	1.35937	−	0.928355i
$47$	15931.3			1.05198			0.525989	−	0.850492i	$-0.323695\pi$
$47$	15931.3			1.05198			0.525989	+	0.850492i	$0.323695\pi$
$48$	9208.44	−	373.242i	0.576877	−	0.0233823i
$49$	9560.25			0.568825
$50$	−17954.6	+	12261.7i	−1.01567	+	0.693627i
$51$	9951.27	−	9951.27i	0.535739	−	0.535739i
$52$	−1152.51	−	2630.42i	−0.0591068	−	0.134901i
$53$	−17551.0	−	17551.0i	−0.858247	−	0.858247i	0.132884	−	0.991132i	$-0.457576\pi$
$53$	−17551.0	−	17551.0i	−0.858247	−	0.858247i	−0.991132	+	0.132884i	$0.957576\pi$
$54$	−763.520	+	4052.55i	−0.0356316	+	0.189123i
$55$		−	8488.70i		−	0.378385i
$56$	3464.04	+	15015.4i	0.147609	+	0.639833i
$57$		−	16732.2i		−	0.682127i
$58$	−30283.4	−	5705.54i	−1.18205	−	0.222703i
$59$	−27648.3	−	27648.3i	−1.03404	−	1.03404i	−0.999400	−	0.0346418i	$-0.988971\pi$
$59$	−27648.3	−	27648.3i	−1.03404	−	1.03404i	−0.0346418	−	0.999400i	$-0.511029\pi$
$60$	−8748.54	+	22393.3i	−0.313731	+	0.803043i
$61$	−15253.4	+	15253.4i	−0.524858	+	0.524858i	−0.919035	−	0.394177i	$-0.871030\pi$
$61$	−15253.4	+	15253.4i	−0.524858	+	0.524858i	0.394177	+	0.919035i	$0.371030\pi$
$62$	−14330.9	−	20984.5i	−0.473472	−	0.693297i
$63$	−6895.36			−0.218880
$64$	29456.3	−	14355.1i	0.898935	−	0.438083i
$65$	7491.66			0.219935
$66$	−2919.71	−	4275.28i	−0.0825048	−	0.120810i
$67$	19395.6	−	19395.6i	0.527857	−	0.527857i	−0.392076	−	0.919933i	$-0.628243\pi$
$67$	19395.6	−	19395.6i	0.527857	−	0.527857i	0.919933	+	0.392076i	$0.128243\pi$
$68$	18208.5	−	46607.6i	0.477532	−	1.22232i
$69$	26577.3	+	26577.3i	0.672029	+	0.672029i
$70$	−39504.1	−	7442.76i	−0.963600	−	0.181547i
$71$		−	75229.9i		−	1.77111i	−0.464539	−	0.885553i	$-0.653780\pi$
$71$		−	75229.9i		−	1.77111i	0.464539	−	0.885553i	$-0.346220\pi$
$72$	3296.07	+	14287.3i	0.0749316	+	0.324802i
$73$			30785.6i			0.676146i	0.941120	+	0.338073i	$0.109775\pi$
$73$			30785.6i			0.676146i	−0.941120	+	0.338073i	$0.890225\pi$
$74$	−14774.1	+	78416.8i	−0.313633	+	1.66468i
$75$	−24459.8	−	24459.8i	−0.502112	−	0.502112i
$76$	−23875.2	−	54491.2i	−0.474148	−	1.08216i
$77$	6121.08	−	6121.08i	0.117653	−	0.117653i
$78$	3773.12	−	2576.77i	0.0702206	−	0.0479556i
$79$	47502.1			0.856338			0.428169	−	0.903699i	$-0.359159\pi$
$79$	47502.1			0.856338			0.428169	+	0.903699i	$0.359159\pi$
$80$	3461.92	+	85410.8i	0.0604773	+	1.49207i
$81$	−6561.00			−0.111111
$82$	−31573.1	+	21562.1i	−0.518540	+	0.354125i
$83$	−38527.1	+	38527.1i	−0.613862	+	0.613862i	−0.943950	−	0.330088i	$-0.892922\pi$
$83$	−38527.1	+	38527.1i	−0.613862	+	0.613862i	0.330088	+	0.943950i	$0.392922\pi$
$84$	−22455.9	+	9839.02i	−0.347242	+	0.152144i
$85$	92300.8	+	92300.8i	1.38566	+	1.38566i
$86$	−1826.68	+	9695.51i	−0.0266328	+	0.141359i
$87$		−	49028.3i		−	0.694462i
$88$	−15608.9	−	9757.03i	−0.214866	−	0.134311i
$89$		−	73974.3i		−	0.989933i	−0.868912	−	0.494967i	$-0.835180\pi$
$89$		−	73974.3i		−	0.989933i	0.868912	−	0.494967i	$-0.164820\pi$
$90$	−37588.5	−	7081.86i	−0.489158	−	0.0921597i
$91$	5402.13	+	5402.13i	0.0683851	+	0.0683851i
$92$	124477.	+	48630.3i	1.53327	+	0.599014i
$93$	28587.5	−	28587.5i	0.342743	−	0.342743i
$94$	50824.9	+	74422.0i	0.593276	+	0.868723i
$95$	155196.			1.76429
$96$	31120.8	+	41825.9i	0.344646	+	0.463198i
$97$	−175496.			−1.89381			−0.946907	−	0.321506i	$-0.895811\pi$
$97$	−175496.			−1.89381			−0.946907	+	0.321506i	$0.895811\pi$
$98$	30499.6	+	44660.1i	0.320796	+	0.469736i
$99$	5824.27	−	5824.27i	0.0597246	−	0.0597246i
$100$	−114560.	−	44755.8i	−1.14560	−	0.447558i
$101$	67006.1	+	67006.1i	0.653598	+	0.653598i	0.953858	−	0.300260i	$-0.0970733\pi$
$101$	67006.1	+	67006.1i	0.653598	+	0.653598i	−0.300260	+	0.953858i	$0.597073\pi$
$102$	78233.8	+	14739.6i	0.744550	+	0.140277i
$103$			33243.1i			0.308751i	0.988012	+	0.154376i	$0.0493366\pi$
$103$			33243.1i			0.308751i	−0.988012	+	0.154376i	$0.950663\pi$
$104$	8611.02	−	13775.6i	0.0780677	−	0.124890i
$105$		−	63956.3i		−	0.566122i
$106$	25996.2	−	137981.i	0.224722	−	1.19276i
$107$	98555.4	+	98555.4i	0.832187	+	0.832187i	0.987816	−	0.155628i	$-0.0497403\pi$
$107$	98555.4	+	98555.4i	0.832187	+	0.832187i	−0.155628	+	0.987816i	$0.549740\pi$
$108$	−21367.0	+	9361.92i	−0.176273	+	0.0772335i
$109$	−48538.5	+	48538.5i	−0.391309	+	0.391309i	−0.875154	−	0.483845i	$-0.839240\pi$
$109$	−48538.5	+	48538.5i	−0.391309	+	0.391309i	0.483845	+	0.875154i	$0.339240\pi$
$110$	39654.4	−	27081.1i	0.312471	−	0.213395i
$111$	−126955.			−0.978010
$112$	−59092.2	+	64084.9i	−0.445128	+	0.482737i
$113$	−144263.			−1.06282			−0.531408	−	0.847116i	$-0.678337\pi$
$113$	−144263.			−1.06282			−0.531408	+	0.847116i	$0.678337\pi$
$114$	78163.3	−	53379.9i	0.563301	−	0.384694i
$115$	−246512.	+	246512.i	−1.73817	+	1.73817i
$116$	−69958.7	−	159669.i	−0.482721	−	1.10173i
$117$	5140.18	+	5140.18i	0.0347147	+	0.0347147i
$118$	40952.1	−	217362.i	0.270751	−	1.43707i
$119$			133114.i			0.861698i
$120$	−132519.	+	30571.9i	−0.840086	+	0.193807i
$121$		−	150710.i		−	0.935793i
$122$	−119917.	−	22593.0i	−0.729428	−	0.137428i
$123$	−43012.4	−	43012.4i	−0.256349	−	0.256349i
$124$	52308.5	−	133892.i	0.305505	−	0.781987i
$125$	42410.8	−	42410.8i	0.242774	−	0.242774i
$126$	−21997.9	−	32211.2i	−0.123440	−	0.180751i
$127$	100085.			0.550632			0.275316	−	0.961354i	$-0.411217\pi$
$127$	100085.			0.550632			0.275316	+	0.961354i	$0.411217\pi$
$128$	161032.	+	91806.7i	0.868734	+	0.495279i
$129$	−15696.9			−0.0830497
$130$	23900.3	+	34996.8i	0.124035	+	0.181622i
$131$	−98672.8	+	98672.8i	−0.502365	+	0.502365i	−0.912172	−	0.409807i	$-0.865596\pi$
$131$	−98672.8	+	98672.8i	−0.502365	+	0.502365i	0.409807	+	0.912172i	$0.365596\pi$
$132$	10657.1	−	27278.4i	0.0532357	−	0.136265i
$133$	111909.	+	111909.i	0.548577	+	0.548577i
$134$	152482.	+	28728.4i	0.733596	+	0.138213i
$135$		−	60855.1i		−	0.287384i
$136$	275814.	−	63630.0i	1.27870	−	0.294995i
$137$		−	334345.i		−	1.52192i	−0.648796	−	0.760962i	$-0.724727\pi$
$137$		−	334345.i		−	1.52192i	0.648796	−	0.760962i	$-0.275273\pi$
$138$	−39365.8	+	208942.i	−0.175963	+	0.933961i
$139$	−206765.	−	206765.i	−0.907695	−	0.907695i	0.0883908	−	0.996086i	$-0.471828\pi$
$139$	−206765.	−	206765.i	−0.907695	−	0.907695i	−0.996086	+	0.0883908i	$0.971828\pi$
$140$	−91259.6	−	208285.i	−0.393512	−	0.898127i
$141$	−101386.	+	101386.i	−0.429468	+	0.429468i
$142$	351431.	−	240002.i	1.46258	−	0.998837i
$143$	−9125.99			−0.0373198
$144$	−56226.8	+	60977.4i	−0.225963	+	0.245055i
$145$	454751.			1.79619
$146$	−143813.	+	98213.9i	−0.558362	+	0.381321i
$147$	−60841.1	+	60841.1i	−0.232222	+	0.232222i
$148$	−413452.	+	181153.i	−1.55157	+	0.679816i
$149$	−243212.	−	243212.i	−0.897469	−	0.897469i	0.0977426	−	0.995212i	$-0.468838\pi$
$149$	−243212.	−	243212.i	−0.897469	−	0.897469i	−0.995212	+	0.0977426i	$0.968838\pi$
$150$	36229.4	−	192296.i	0.131472	−	0.697816i
$151$		−	27710.4i		−	0.0989010i	−0.998777	−	0.0494505i	$-0.984253\pi$
$151$		−	27710.4i		−	0.0989010i	0.998777	−	0.0494505i	$-0.0157470\pi$
$152$	178384.	−	285372.i	0.626249	−	1.00185i
$153$			126659.i			0.437429i
$154$	48122.0	+	9066.42i	0.163509	+	0.0308059i
$155$	265157.	+	265157.i	0.886490	+	0.886490i
$156$	24074.4	+	9405.34i	0.0792036	+	0.0309430i
$157$	229099.	−	229099.i	0.741779	−	0.741779i	−0.231141	−	0.972920i	$-0.574246\pi$
$157$	229099.	−	229099.i	0.741779	−	0.741779i	0.972920	+	0.231141i	$0.0742459\pi$
$158$	151544.	+	221903.i	0.482943	+	0.707165i
$159$	223388.			0.700756
$160$	−387947.	+	288654.i	−1.19804	+	0.891411i
$161$	−355513.			−1.08091
$162$	−20931.3	−	30649.3i	−0.0626625	−	0.0917556i
$163$	−154114.	+	154114.i	−0.454333	+	0.454333i	−0.896790	−	0.442457i	$-0.854107\pi$
$163$	−154114.	+	154114.i	−0.454333	+	0.454333i	0.442457	+	0.896790i	$0.354107\pi$
$164$	−201452.	−	78702.8i	−0.584874	−	0.228497i
$165$	54021.7	+	54021.7i	0.154475	+	0.154475i
$166$	−302888.	−	57065.6i	−0.853123	−	0.160733i
$167$			366613.i			1.01722i	0.860996	+	0.508612i	$0.169841\pi$
$167$			366613.i			1.01722i	−0.860996	+	0.508612i	$0.830159\pi$
$168$	−117602.	−	73512.4i	−0.321472	−	0.200950i
$169$			363239.i			0.978308i
$170$	−136714.	+	725640.i	−0.362820	+	1.92575i
$171$	106483.	+	106483.i	0.278477	+	0.278477i
$172$	−51119.5	+	22397.9i	−0.131755	+	0.0577280i
$173$	−294221.	+	294221.i	−0.747410	+	0.747410i	−0.973992	−	0.226582i	$-0.927245\pi$
$173$	−294221.	+	294221.i	−0.747410	+	0.747410i	0.226582	+	0.973992i	$0.427245\pi$
$174$	229032.	−	156413.i	0.573487	−	0.391650i
$175$	327188.			0.807612
$176$	−4217.15	−	104044.i	−0.0102621	−	0.253182i
$177$	351905.			0.844291
$178$	345566.	−	235997.i	0.817487	−	0.558285i
$179$	150021.	−	150021.i	0.349961	−	0.349961i	−0.510134	−	0.860095i	$-0.670404\pi$
$179$	150021.	−	150021.i	0.349961	−	0.349961i	0.860095	+	0.510134i	$0.170404\pi$
$180$	−86834.4	−	198185.i	−0.199761	−	0.455921i
$181$	−354478.	−	354478.i	−0.804252	−	0.804252i	0.179505	−	0.983757i	$-0.442550\pi$
$181$	−354478.	−	354478.i	−0.804252	−	0.804252i	−0.983757	+	0.179505i	$0.942550\pi$
$182$	−8001.53	+	42469.8i	−0.0179058	+	0.0950391i
$183$		−	194144.i		−	0.428545i
$184$	169940.	+	736628.i	0.370041	+	1.60400i
$185$		−	1.17755e6i		−	2.52958i
$186$	224746.	+	42343.2i	0.476331	+	0.0897432i
$187$	−112437.	−	112437.i	−0.235128	−	0.235128i
$188$	−185513.	+	474850.i	−0.382807	+	0.979855i
$189$	43881.8	−	43881.8i	0.0893572	−	0.0893572i
$190$	495113.	+	724986.i	0.994994	+	1.45695i
$191$	19130.5			0.0379439			0.0189720	−	0.999820i	$-0.493961\pi$
$191$	19130.5			0.0379439			0.0189720	+	0.999820i	$0.493961\pi$
$192$	−96103.4	+	278814.i	−0.188142	+	0.545835i
$193$	−276813.			−0.534925			−0.267463	−	0.963568i	$-0.586185\pi$
$193$	−276813.			−0.534925			−0.267463	+	0.963568i	$0.586185\pi$
$194$	−559876.	−	819817.i	−1.06804	−	1.56391i
$195$	−47676.6	+	47676.6i	−0.0897881	+	0.0897881i
$196$	−111325.	+	284954.i	−0.206992	+	0.529827i
$197$	447710.	+	447710.i	0.821924	+	0.821924i	0.986384	−	0.164460i	$-0.0525881\pi$
$197$	447710.	+	447710.i	0.821924	+	0.821924i	−0.164460	+	0.986384i	$0.552588\pi$
$198$	45788.6	+	8626.79i	0.0830031	+	0.0156382i
$199$		−	828321.i		−	1.48274i	−0.671095	−	0.741371i	$-0.734176\pi$
$199$		−	828321.i		−	1.48274i	0.671095	−	0.741371i	$-0.265824\pi$
$200$	−156400.	−	677940.i	−0.276479	−	1.19844i
$201$			246866.i			0.430993i
$202$	−99248.0	+	526781.i	−0.171137	+	0.908346i
$203$	327914.	+	327914.i	0.558497	+	0.558497i
$204$	180730.	+	412487.i	0.304058	+	0.693961i
$205$	398952.	−	398952.i	0.663035	−	0.663035i
$206$	−155293.	+	106054.i	−0.254967	+	0.174124i
$207$	−338274.			−0.548709
$208$	91823.1	−	3721.83i	0.147161	−	0.00596483i
$209$	−189052.			−0.299375
$210$	298768.	−	204037.i	0.467504	−	0.319272i
$211$	154290.	−	154290.i	0.238579	−	0.238579i	−0.577683	−	0.816261i	$-0.696043\pi$
$211$	154290.	−	154290.i	0.238579	−	0.238579i	0.816261	+	0.577683i	$0.196043\pi$
$212$	727501.	−	318753.i	1.11172	−	0.487097i
$213$	478760.	+	478760.i	0.723051	+	0.723051i
$214$	−145978.	+	774812.i	−0.217898	+	1.15654i
$215$		−	145593.i		−	0.214804i
$216$	−111900.	−	69947.7i	−0.163191	−	0.102009i
$217$			382402.i			0.551278i
$218$	−381594.	−	71894.2i	−0.543827	−	0.102460i
$219$	−195918.	−	195918.i	−0.276035	−	0.276035i
$220$	253015.	+	98847.2i	0.352444	+	0.137692i
$221$	99230.3	−	99230.3i	0.136667	−	0.136667i
$222$	−405020.	−	593063.i	−0.551561	−	0.807641i
$223$	128822.			0.173472			0.0867360	−	0.996231i	$-0.472356\pi$
$223$	128822.			0.173472			0.0867360	+	0.996231i	$0.472356\pi$
$224$	−487888.	−	71598.3i	−0.649680	−	0.0953416i
$225$	311323.			0.409973
$226$	−460235.	−	673914.i	−0.599389	−	0.877675i
$227$	485758.	−	485758.i	0.625685	−	0.625685i	−0.321295	−	0.946979i	$-0.604118\pi$
$227$	485758.	−	485758.i	0.625685	−	0.625685i	0.946979	+	0.321295i	$0.104118\pi$
$228$	498721.	+	194839.i	0.635361	+	0.248221i
$229$	−83292.0	−	83292.0i	−0.104958	−	0.104958i	0.652678	−	0.757636i	$-0.273646\pi$
$229$	−83292.0	−	83292.0i	−0.104958	−	0.104958i	−0.757636	+	0.652678i	$0.773646\pi$
$230$	−1.93800e6	−	365128.i	−2.41565	−	0.455120i
$231$			77908.7i			0.0960629i
$232$	522697.	−	836192.i	0.637573	−	1.01997i
$233$			1.27468e6i			1.53820i	0.639129	+	0.769099i	$0.279295\pi$
$233$			1.27468e6i			1.53820i	−0.639129	+	0.769099i	$0.720705\pi$
$234$	−7613.53	+	40410.5i	−0.00908964	+	0.0482452i
$235$	−940384.	−	940384.i	−1.11080	−	1.11080i
$236$	1.14604e6	−	502135.i	1.33943	−	0.586868i
$237$	−302302.	+	302302.i	−0.349599	+	0.349599i
$238$	−621832.	+	424666.i	−0.711591	+	0.485966i
$239$	−753045.			−0.852758			−0.426379	−	0.904545i	$-0.640211\pi$
$239$	−753045.			−0.852758			−0.426379	+	0.904545i	$0.640211\pi$
$240$	−565583.	−	521520.i	−0.633823	−	0.584444i
$241$	−501184.			−0.555847			−0.277923	−	0.960603i	$-0.589646\pi$
$241$	−501184.			−0.555847			−0.277923	+	0.960603i	$0.589646\pi$
$242$	704034.	−	480805.i	0.772779	−	0.527752i
$243$	41753.9	−	41753.9i	0.0453609	−	0.0453609i
$244$	−277025.	−	632263.i	−0.297882	−	0.679866i
$245$	−564318.	−	564318.i	−0.600632	−	0.600632i
$246$	63709.2	−	338150.i	0.0671219	−	0.356264i
$247$		−	166847.i		−	0.174011i
$248$	792343.	−	182793.i	0.818058	−	0.188725i
$249$		−	490370.i		−	0.501217i
$250$	333421.	+	62818.1i	0.337398	+	0.0635674i
$251$	163065.	+	163065.i	0.163371	+	0.163371i	0.784058	−	0.620687i	$-0.213146\pi$
$251$	163065.	+	163065.i	0.163371	+	0.163371i	−0.620687	+	0.784058i	$0.713146\pi$
$252$	80293.5	−	205524.i	0.0796487	−	0.203873i
$253$	300289.	−	300289.i	0.294943	−	0.294943i
$254$	319298.	+	467543.i	0.310536	+	0.454713i
$255$	−1.17480e6			−1.13139
$256$	84863.6	+	1.04514e6i	0.0809322	+	0.996720i
$257$	447295.			0.422437			0.211218	−	0.977439i	$-0.432257\pi$
$257$	447295.			0.422437			0.211218	+	0.977439i	$0.432257\pi$
$258$	−50076.9	−	73326.8i	−0.0468369	−	0.0685825i
$259$	849112.	−	849112.i	0.786531	−	0.786531i
$260$	−87237.1	+	223297.i	−0.0800328	+	0.204856i
$261$	312014.	+	312014.i	0.283513	+	0.283513i
$262$	−775735.	−	146152.i	−0.698168	−	0.131538i
$263$			1.03546e6i			0.923089i	0.887117	+	0.461545i	$0.152705\pi$
$263$			1.03546e6i			0.923089i	−0.887117	+	0.461545i	$0.847295\pi$
$264$	161428.	−	37241.3i	0.142551	−	0.0328863i
$265$			2.07198e6i			1.81247i
$266$	−165758.	+	879797.i	−0.143638	+	0.762392i
$267$	470770.	+	470770.i	0.404138	+	0.404138i
$268$	352254.	+	803961.i	0.299584	+	0.683751i
$269$	−851283.	+	851283.i	−0.717288	+	0.717288i	−0.968049	−	0.250761i	$-0.919319\pi$
$269$	−851283.	+	851283.i	−0.717288	+	0.717288i	0.250761	+	0.968049i	$0.419319\pi$
$270$	284280.	−	194143.i	0.237322	−	0.162074i
$271$	−198559.			−0.164235			−0.0821176	−	0.996623i	$-0.526168\pi$
$271$	−198559.			−0.164235			−0.0821176	+	0.996623i	$0.526168\pi$
$272$	1.17716e6	+	1.08545e6i	0.964746	+	0.889585i
$273$	−68757.9			−0.0558362
$274$	1.56187e6	−	1.06664e6i	1.25681	−	0.858308i
$275$	−276365.	+	276365.i	−0.220369	+	0.220369i
$276$	−1.10165e6	+	482685.i	−0.870502	+	0.381409i
$277$	−969747.	−	969747.i	−0.759380	−	0.759380i	0.216830	−	0.976209i	$-0.430428\pi$
$277$	−969747.	−	969747.i	−0.759380	−	0.759380i	−0.976209	+	0.216830i	$0.930428\pi$
$278$	306256.	−	1.62552e6i	0.237669	−	1.26148i
$279$			363859.i			0.279848i
$280$	681847.	−	1.09079e6i	0.519747	−	0.831472i
$281$			1.53526e6i			1.15989i	0.814656	+	0.579944i	$0.196925\pi$
$281$			1.53526e6i			1.15989i	−0.814656	+	0.579944i	$0.803075\pi$
$282$	−797066.	−	150171.i	−0.596859	−	0.112451i
$283$	−329374.	−	329374.i	−0.244468	−	0.244468i	0.574227	−	0.818696i	$-0.305303\pi$
$283$	−329374.	−	329374.i	−0.244468	−	0.244468i	−0.818696	+	0.574227i	$0.805303\pi$
$284$	2.24231e6	+	876020.i	1.64968	+	0.644493i
$285$	−987659.	+	987659.i	−0.720269	+	0.720269i
$286$	−29114.2	−	42631.4i	−0.0210470	−	0.0308187i
$287$	575358.			0.412319
$288$	−464230.	−	68126.5i	−0.329801	−	0.0483988i
$289$	1.02527e6			0.722097
$290$	1.45077e6	+	2.12434e6i	1.01299	+	1.48330i
$291$	1.11685e6	−	1.11685e6i	0.773147	−	0.773147i
$292$	−917599.	−	358485.i	−0.629790	−	0.246045i
$293$	−670330.	−	670330.i	−0.456162	−	0.456162i	0.441231	−	0.897393i	$-0.354542\pi$
$293$	−670330.	−	670330.i	−0.456162	−	0.456162i	−0.897393	+	0.441231i	$0.854542\pi$
$294$	−478313.	−	90116.6i	−0.322734	−	0.0608046i
$295$			3.26402e6i			2.18372i
$296$	−2.16526e6	−	1.35349e6i	−1.43642	−	0.897894i
$297$			74130.9i			0.0487650i
$298$	360241.	−	1.91206e6i	0.234992	−	1.24727i
$299$	265019.	+	265019.i	0.171435	+	0.171435i
$300$	1.01388e6	−	444228.i	0.650402	−	0.284973i
$301$	104985.	−	104985.i	0.0667898	−	0.0667898i
$302$	129447.	−	88403.3i	0.0816725	−	0.0557765i
$303$	−852848.			−0.533661
$304$	1.90219e6	−	77100.6i	1.18051	−	0.0478491i
$305$	1.80074e6			1.10841
$306$	−591679.	+	404074.i	−0.361229	+	0.246693i
$307$	605559.	−	605559.i	0.366700	−	0.366700i	−0.499572	−	0.866272i	$-0.666509\pi$
$307$	605559.	−	605559.i	0.366700	−	0.366700i	0.866272	+	0.499572i	$0.166509\pi$
$308$	111168.	+	253723.i	0.0667735	+	0.152399i
$309$	−211558.	−	211558.i	−0.126047	−	0.126047i
$310$	−392745.	+	2.08458e6i	−0.232117	+	1.23201i
$311$		−	673415.i		−	0.394804i	−0.980323	−	0.197402i	$-0.936750\pi$
$311$		−	673415.i		−	0.394804i	0.980323	−	0.197402i	$-0.0632504\pi$
$312$	32867.1	+	142468.i	0.0191151	+	0.0828570i
$313$			1.71175e6i			0.987599i	0.869576	+	0.493799i	$0.164392\pi$
$313$			1.71175e6i			0.987599i	−0.869576	+	0.493799i	$0.835608\pi$
$314$	1.80111e6	+	339337.i	1.03090	+	0.194226i
$315$	407016.	+	407016.i	0.231118	+	0.231118i
$316$	−553142.	+	1.41585e6i	−0.311615	+	0.797628i
$317$	194964.	−	194964.i	0.108970	−	0.108970i	−0.650520	−	0.759489i	$-0.725449\pi$
$317$	194964.	−	194964.i	0.108970	−	0.108970i	0.759489	+	0.650520i	$0.225449\pi$
$318$	712664.	+	1.04354e6i	0.395200	+	0.578685i
$319$	−553956.			−0.304789
$320$	−2.58608e6	−	891386.i	−1.41178	−	0.486621i
$321$	−1.25441e6			−0.679478
$322$	−1.13418e6	−	1.66075e6i	−0.609594	−	0.892617i
$323$	2.05564e6	−	2.05564e6i	1.09633	−	1.09633i
$324$	76400.0	−	195558.i	0.0404325	−	0.103493i
$325$	−243904.	−	243904.i	−0.128089	−	0.128089i
$326$	−1.21160e6	−	228271.i	−0.631415	−	0.118962i
$327$		−	617794.i		−	0.319502i
$328$	−275028.	−	1.19215e6i	−0.141154	−	0.611853i
$329$		−	1.35620e6i		−	0.690769i
$330$	−80015.9	+	424702.i	−0.0404475	+	0.214684i
$331$	−1.87731e6	−	1.87731e6i	−0.941815	−	0.941815i	0.0565830	−	0.998398i	$-0.481979\pi$
$331$	−1.87731e6	−	1.87731e6i	−0.941815	−	0.941815i	−0.998398	+	0.0565830i	$0.981979\pi$
$332$	−699711.	−	1.59697e6i	−0.348396	−	0.795157i
$333$	807939.	−	807939.i	0.399271	−	0.399271i
$334$	−1.71261e6	+	1.16959e6i	−0.840025	+	0.573677i
$335$	−2.28975e6			−1.11475
$336$	−31773.3	−	783895.i	−0.0153537	−	0.378800i
$337$	−130344.			−0.0625196			−0.0312598	−	0.999511i	$-0.509952\pi$
$337$	−130344.			−0.0625196			−0.0312598	+	0.999511i	$0.509952\pi$
$338$	−1.69685e6	+	1.15882e6i	−0.807887	+	0.551729i
$339$	918083.	−	918083.i	0.433893	−	0.433893i
$340$	−3.82593e6	+	1.67632e6i	−1.79490	+	0.786431i
$341$	−323002.	−	323002.i	−0.150425	−	0.150425i
$342$	−157720.	+	837135.i	−0.0729160	+	0.387017i
$343$		−	2.24459e6i		−	1.03015i
$344$	−267715.	−	167346.i	−0.121976	−	0.0762465i
$345$		−	3.13758e6i		−	1.41921i
$346$	−2.31307e6	−	435795.i	−1.03872	−	0.195700i
$347$	1.77668e6	+	1.77668e6i	0.792112	+	0.792112i	0.981837	−	0.189725i	$-0.0607597\pi$
$347$	1.77668e6	+	1.77668e6i	0.792112	+	0.792112i	−0.189725	+	0.981837i	$0.560760\pi$
$348$	1.46134e6	+	570913.i	0.646850	+	0.252710i
$349$	1.57913e6	−	1.57913e6i	0.693990	−	0.693990i	−0.269117	−	0.963107i	$-0.586732\pi$
$349$	1.57913e6	−	1.57913e6i	0.693990	−	0.693990i	0.963107	+	0.269117i	$0.0867319\pi$
$350$	1.04381e6	+	1.52844e6i	0.455463	+	0.666926i
$351$	−65423.8			−0.0283445
$352$	472579.	−	351625.i	0.203291	−	0.151260i
$353$	1.87813e6			0.802210			0.401105	−	0.916032i	$-0.368626\pi$
$353$	1.87813e6			0.802210			0.401105	+	0.916032i	$0.368626\pi$
$354$	1.12267e6	+	1.64390e6i	0.476149	+	0.697216i
$355$	−4.44063e6	+	4.44063e6i	−1.87014	+	1.87014i
$356$	2.20489e6	+	861399.i	0.922064	+	0.360230i
$357$	−847130.	−	847130.i	−0.351787	−	0.351787i
$358$	1.17942e6	+	222208.i	0.486363	+	0.0916332i
$359$		−	3.53247e6i		−	1.44658i	−0.690545	−	0.723290i	$-0.742629\pi$
$359$		−	3.53247e6i		−	1.44658i	0.690545	−	0.723290i	$-0.257371\pi$
$360$	648785.	−	1.03790e6i	0.263842	−	0.422085i
$361$		−	980270.i		−	0.395893i
$362$	525045.	−	2.78679e6i	0.210584	−	1.11772i
$363$	959116.	+	959116.i	0.382036	+	0.382036i
$364$	−223922.	+	98111.0i	−0.0885815	+	0.0388118i
$365$	1.81720e6	−	1.81720e6i	0.713953	−	0.713953i
$366$	906930.	−	619368.i	0.353892	−	0.241683i
$367$	4.98793e6			1.93310			0.966552	−	0.256470i	$-0.0825593\pi$
$367$	4.98793e6			1.93310			0.966552	+	0.256470i	$0.0825593\pi$
$368$	−2.89896e6	+	3.14389e6i	−1.11589	+	1.21017i
$369$	547459.			0.209308
$370$	5.50083e6	−	3.75667e6i	2.08893	−	1.42659i
$371$	−1.49408e6	+	1.49408e6i	−0.563559	+	0.563559i
$372$	519193.	+	1.18497e6i	0.194523	+	0.443967i
$373$	−678878.	−	678878.i	−0.252650	−	0.252650i	0.569406	−	0.822056i	$-0.307173\pi$
$373$	−678878.	−	678878.i	−0.252650	−	0.252650i	−0.822056	+	0.569406i	$0.807173\pi$
$374$	166539.	−	883941.i	0.0615654	−	0.326772i
$375$			539802.i			0.198224i
$376$	−2.81006e6	+	648279.i	−1.02505	+	0.236479i
$377$		−	488891.i		−	0.177157i
$378$	344985.	+	64996.8i	0.124185	+	0.0233971i
$379$	3.36414e6	+	3.36414e6i	1.20303	+	1.20303i	0.973241	+	0.229788i	$0.0738032\pi$
$379$	3.36414e6	+	3.36414e6i	1.20303	+	1.20303i	0.229788	+	0.973241i	$0.426197\pi$
$380$	−1.80719e6	+	4.62578e6i	−0.642013	+	1.64333i
$381$	−636940.	+	636940.i	−0.224795	+	0.224795i
$382$	61031.1	+	89366.8i	0.0213990	+	0.0313341i
$383$	−1.68577e6			−0.587220			−0.293610	−	0.955925i	$-0.594857\pi$
$383$	−1.68577e6			−0.587220			−0.293610	+	0.955925i	$0.594857\pi$
$384$	−1.60905e6	+	440546.i	−0.556856	+	0.152463i
$385$	−722624.			−0.248462
$386$	−883103.	−	1.29311e6i	−0.301678	−	0.441741i
$387$	99894.1	−	99894.1i	0.0339049	−	0.0339049i
$388$	2.04357e6	−	5.23085e6i	0.689146	−	1.76398i
$389$	−478215.	−	478215.i	−0.160232	−	0.160232i	0.622437	−	0.782670i	$-0.286142\pi$
$389$	−478215.	−	478215.i	−0.160232	−	0.160232i	−0.782670	+	0.622437i	$0.786142\pi$
$390$	−374819.	−	70617.6i	−0.124784	−	0.0235099i
$391$			6.53032e6i			2.16019i
$392$	−1.68630e6	+	389028.i	−0.554267	+	0.127869i
$393$		−	1.25590e6i		−	0.410179i
$394$	−663140.	+	3.51976e6i	−0.215211	+	1.14228i
$395$	−2.80393e6	−	2.80393e6i	−0.904221	−	0.904221i
$396$	105778.	+	241420.i	0.0338966	+	0.0773633i
$397$	3.19063e6	−	3.19063e6i	1.01602	−	1.01602i	0.0161454	−	0.999870i	$-0.494861\pi$
$397$	3.19063e6	−	3.19063e6i	1.01602	−	1.01602i	0.999870	−	0.0161454i	$-0.00513947\pi$
$398$	3.86944e6	−	2.64255e6i	1.22445	−	0.836211i
$399$	−1.42437e6			−0.447911
$400$	2.66799e6	−	2.89341e6i	0.833748	−	0.904191i
$401$	−3.68017e6			−1.14290			−0.571449	−	0.820638i	$-0.693618\pi$
$401$	−3.68017e6			−1.14290			−0.571449	+	0.820638i	$0.693618\pi$
$402$	−1.15322e6	+	787564.i	−0.355915	+	0.243064i
$403$	285064.	−	285064.i	0.0874338	−	0.0874338i
$404$	−2.77745e6	+	1.21693e6i	−0.846627	+	0.370948i
$405$	387279.	+	387279.i	0.117324	+	0.117324i
$406$	−485700.	+	2.57796e6i	−0.146236	+	0.776178i
$407$			1.43443e6i			0.429234i
$408$	−1.35033e6	+	2.16021e6i	−0.401596	+	0.642459i
$409$			2.69240e6i			0.795849i	0.917418	+	0.397925i	$0.130269\pi$
$409$			2.69240e6i			0.795849i	−0.917418	+	0.397925i	$0.869731\pi$
$410$	3.13644e6	+	590920.i	0.921461	+	0.173608i
$411$	2.12776e6	+	2.12776e6i	0.621323	+	0.621323i
$412$	−990848.	−	387102.i	−0.287583	−	0.112352i
$413$	−2.35364e6	+	2.35364e6i	−0.678992	+	0.678992i
$414$	−1.07918e6	−	1.58022e6i	−0.309452	−	0.453125i
$415$	4.54832e6			1.29637
$416$	310325.	+	417072.i	0.0879192	+	0.118162i
$417$	2.63169e6			0.741130
$418$	−603124.	−	883144.i	−0.168836	−	0.247224i
$419$	−752440.	+	752440.i	−0.209381	+	0.209381i	−0.804004	−	0.594623i	$-0.797301\pi$
$419$	−752440.	+	752440.i	−0.209381	+	0.209381i	0.594623	+	0.804004i	$0.297301\pi$
$420$	1.90629e6	+	744744.i	0.527309	+	0.206008i
$421$	−2.18257e6	−	2.18257e6i	−0.600155	−	0.600155i	0.340199	−	0.940354i	$-0.389506\pi$
$421$	−2.18257e6	−	2.18257e6i	−0.600155	−	0.600155i	−0.940354	+	0.340199i	$0.889506\pi$
$422$	1.21298e6	+	228531.i	0.331568	+	0.0624690i
$423$		−	1.29043e6i		−	0.350659i
$424$	3.80995e6	+	2.38157e6i	1.02921	+	0.643352i
$425$		−	6.01004e6i		−	1.61400i
$426$	−709130.	+	3.76386e6i	−0.189322	+	1.00487i
$427$	1.29849e6	+	1.29849e6i	0.344642	+	0.344642i
$428$	−4.08519e6	+	1.78992e6i	−1.07796	+	0.472306i
$429$	58077.4	−	58077.4i	0.0152358	−	0.0152358i
$430$	680126.	−	464477.i	0.177386	−	0.121142i
$431$	−4.00288e6			−1.03796			−0.518978	−	0.854788i	$-0.673687\pi$
$431$	−4.00288e6			−1.03796			−0.518978	+	0.854788i	$0.673687\pi$
$432$	−30232.6	−	745884.i	−0.00779410	−	0.192292i
$433$	−2.23386e6			−0.572580			−0.286290	−	0.958143i	$-0.592422\pi$
$433$	−2.23386e6			−0.572580			−0.286290	+	0.958143i	$0.592422\pi$
$434$	−1.78636e6	+	1.21996e6i	−0.455246	+	0.310900i
$435$	−2.89402e6	+	2.89402e6i	−0.733293	+	0.733293i
$436$	−881533.	−	2.01195e6i	−0.222087	−	0.506876i
$437$	5.49008e6	+	5.49008e6i	1.37523	+	1.37523i
$438$	290190.	−	1.54025e6i	0.0722766	−	0.383624i
$439$			324381.i			0.0803330i	0.999193	+	0.0401665i	$0.0127888\pi$
$439$			324381.i			0.0803330i	−0.999193	+	0.0401665i	$0.987211\pi$
$440$	345424.	+	1.49729e6i	0.0850590	+	0.368701i
$441$		−	774380.i		−	0.189608i
$442$	780118.	+	146978.i	0.189935	+	0.0357846i
$443$	−4.26571e6	−	4.26571e6i	−1.03272	−	1.03272i	−0.999446	−	0.0332711i	$-0.989408\pi$
$443$	−4.26571e6	−	4.26571e6i	−1.03272	−	1.03272i	−0.0332711	−	0.999446i	$-0.510592\pi$
$444$	1.47834e6	−	3.78404e6i	0.355891	−	0.910959i
$445$	−4.36652e6	+	4.36652e6i	−1.04529	+	1.04529i
$446$	410976.	+	601785.i	0.0978317	+	0.143253i
$447$	3.09558e6			0.732781
$448$	−1.22202e6	−	2.50755e6i	−0.287662	−	0.590275i
$449$	4.36130e6			1.02094			0.510470	−	0.859896i	$-0.329471\pi$
$449$	4.36130e6			1.02094			0.510470	+	0.859896i	$0.329471\pi$
$450$	993199.	+	1.45432e6i	0.231209	+	0.338556i
$451$	−485985.	+	485985.i	−0.112508	+	0.112508i
$452$	1.67988e6	−	4.29991e6i	0.386751	−	0.989951i
$453$	176348.	+	176348.i	0.0403762	+	0.0403762i
$454$	3.81888e6	+	719495.i	0.869553	+	0.163828i
$455$		−	637749.i		−	0.144418i
$456$	680869.	+	2.95133e6i	0.153339	+	0.664669i
$457$			7.30873e6i			1.63701i	0.574500	+	0.818505i	$0.305197\pi$
$457$			7.30873e6i			1.63701i	−0.574500	+	0.818505i	$0.694803\pi$
$458$	123370.	−	654816.i	0.0274819	−	0.145866i
$459$	−806053.	−	806053.i	−0.178580	−	0.178580i
$460$	−4.47703e6	−	1.02181e7i	−0.986497	−	2.25151i
$461$	−3.53667e6	+	3.53667e6i	−0.775073	+	0.775073i	−0.978988	−	0.203916i	$-0.934633\pi$
$461$	−3.53667e6	+	3.53667e6i	−0.775073	+	0.775073i	0.203916	+	0.978988i	$0.434633\pi$
$462$	−363945.	+	248548.i	−0.0793288	+	0.0541759i
$463$	3.76678e6			0.816616			0.408308	−	0.912844i	$-0.366119\pi$
$463$	3.76678e6			0.816616			0.408308	+	0.912844i	$0.366119\pi$
$464$	5.57375e6	−	225919.i	1.20186	−	0.0487143i
$465$	−3.37490e6			−0.723816
$466$	−5.95460e6	+	4.06656e6i	−1.27025	+	0.867486i
$467$	2.90167e6	−	2.90167e6i	0.615681	−	0.615681i	−0.328740	−	0.944421i	$-0.606624\pi$
$467$	2.90167e6	−	2.90167e6i	0.615681	−	0.615681i	0.944421	+	0.328740i	$0.106624\pi$
$468$	−213064.	+	93353.6i	−0.0449672	+	0.0197023i
$469$	−1.65111e6	−	1.65111e6i	−0.346611	−	0.346611i
$470$	1.39288e6	−	7.39301e6i	0.290850	−	1.54375i
$471$			2.91596e6i			0.605660i
$472$	6.00185e6	+	3.75171e6i	1.24002	+	0.775129i
$473$			177354.i			0.0364493i
$474$	−2.37660e6	−	447763.i	−0.485859	−	0.0915382i
$475$	−5.05267e6	−	5.05267e6i	−1.02751	−	1.02751i
$476$	−3.96760e6	−	1.55005e6i	−0.802621	−	0.313566i
$477$	−1.42163e6	+	1.42163e6i	−0.286082	+	0.286082i
$478$	−2.40240e6	−	3.51780e6i	−0.480924	−	0.704208i
$479$	−5.74532e6			−1.14413			−0.572065	−	0.820208i	$-0.693858\pi$
$479$	−5.74532e6			−1.14413			−0.572065	+	0.820208i	$0.693858\pi$
$480$	631892.	−	4.30586e6i	0.125181	−	0.853016i
$481$	−1.26595e6			−0.249491
$482$	−1.59891e6	−	2.34125e6i	−0.313477	−	0.459018i
$483$	2.26247e6	−	2.26247e6i	0.441280	−	0.441280i
$484$	4.49209e6	+	1.75496e6i	0.871636	+	0.340529i
$485$	1.03591e7	+	1.03591e7i	1.99971	+	1.99971i
$486$	328256.	+	61845.1i	0.0630409	+	0.0118772i
$487$		−	2.54081e6i		−	0.485455i	−0.970094	−	0.242728i	$-0.921958\pi$
$487$		−	2.54081e6i		−	0.485455i	0.970094	−	0.242728i	$-0.0780421\pi$
$488$	2.06980e6	−	3.31118e6i	0.393439	−	0.629410i
$489$		−	1.96155e6i		−	0.370961i
$490$	835856.	−	4.43649e6i	0.157268	−	0.834736i
$491$	4.32974e6	+	4.32974e6i	0.810510	+	0.810510i	0.984710	−	0.174201i	$-0.0557341\pi$
$491$	4.32974e6	+	4.32974e6i	0.810510	+	0.810510i	−0.174201	+	0.984710i	$0.555734\pi$
$492$	1.78289e6	−	781172.i	0.332057	−	0.145490i
$493$	6.02338e6	−	6.02338e6i	1.11615	−	1.11615i
$494$	779415.	−	532284.i	0.143698	−	0.0981355i
$495$	−687584.			−0.126128
$496$	3.38168e6	+	3.11822e6i	0.617204	+	0.569119i
$497$	−6.40416e6			−1.16298
$498$	2.29073e6	−	1.56440e6i	0.413905	−	0.282667i
$499$	−3.11165e6	+	3.11165e6i	−0.559422	+	0.559422i	−0.929143	−	0.369721i	$-0.879453\pi$
$499$	−3.11165e6	+	3.11165e6i	−0.559422	+	0.559422i	0.369721	+	0.929143i	$0.379453\pi$
$500$	770246.	+	1.75796e6i	0.137786	+	0.314473i
$501$	−2.33311e6	−	2.33311e6i	−0.415280	−	0.415280i
$502$	−241528.	+	1.28196e6i	−0.0427768	+	0.227047i
$503$			351505.i			0.0619458i	0.999520	+	0.0309729i	$0.00986055\pi$
$503$			351505.i			0.0619458i	−0.999520	+	0.0309729i	$0.990139\pi$
$504$	1.21625e6	−	280587.i	0.213278	−	0.0492030i
$505$		−	7.91040e6i		−	1.38029i
$506$	2.36078e6	+	444782.i	0.409901	+	0.0772274i
$507$	−2.31164e6	−	2.31164e6i	−0.399393	−	0.399393i
$508$	−1.16545e6	+	2.98316e6i	−0.200371	+	0.512882i
$509$	−892165.	+	892165.i	−0.152634	+	0.152634i	−0.779293	−	0.626659i	$-0.784422\pi$
$509$	−892165.	+	892165.i	−0.152634	+	0.152634i	0.626659	+	0.779293i	$0.284422\pi$
$510$	−3.74790e6	−	5.48799e6i	−0.638062	−	0.934303i
$511$	2.62071e6			0.443984
$512$	−4.61155e6	+	3.73068e6i	−0.777449	+	0.628946i
$513$	−1.35531e6			−0.227376
$514$	1.42699e6	+	2.08951e6i	0.238238	+	0.348848i
$515$	1.96226e6	−	1.96226e6i	0.326015	−	0.326015i
$516$	182783.	−	467862.i	0.0302212	−	0.0773559i
$517$	1.14553e6	+	1.14553e6i	0.188487	+	0.188487i
$518$	6.67545e6	+	1.25769e6i	1.09309	+	0.205944i
$519$		−	3.74482e6i		−	0.610257i
$520$	−1.32143e6	+	304852.i	−0.214306	+	0.0494402i
$521$			649311.i			0.104799i	0.998626	+	0.0523997i	$0.0166870\pi$
$521$			649311.i			0.104799i	−0.998626	+	0.0523997i	$0.983313\pi$
$522$	−462149.	+	2.45296e6i	−0.0742344	+	0.394016i
$523$	−5.49613e6	−	5.49613e6i	−0.878623	−	0.878623i	0.114769	−	0.993392i	$-0.463387\pi$
$523$	−5.49613e6	−	5.49613e6i	−0.878623	−	0.878623i	−0.993392	+	0.114769i	$0.963387\pi$
$524$	−1.79205e6	−	4.09005e6i	−0.285116	−	0.650730i
$525$	−2.08221e6	+	2.08221e6i	−0.329706	+	0.329706i
$526$	−4.83708e6	+	3.30338e6i	−0.762288	+	0.520588i
$527$	7.02424e6			1.10172
$528$	688967.	+	635291.i	0.107551	+	0.0991718i
$529$	−1.10045e7			−1.70974
$530$	−9.67914e6	+	6.61016e6i	−1.49674	+	1.02217i
$531$	−2.23951e6	+	2.23951e6i	−0.344681	+	0.344681i
$532$	−4.63872e6	+	2.03245e6i	−0.710590	+	0.311344i
$533$	−428904.	−	428904.i	−0.0653946	−	0.0653946i
$534$	−697294.	+	3.70104e6i	−0.105819	+	0.561657i
$535$		−	1.16350e7i		−	1.75744i
$536$	−2.63187e6	+	4.21037e6i	−0.395688	+	0.633006i
$537$			1.90946e6i			0.285742i
$538$	−6.69252e6	−	1.26090e6i	−0.996860	−	0.187813i
$539$	687426.	+	687426.i	0.101919	+	0.101919i
$540$	1.81385e6	+	708631.i	0.267681	+	0.104577i
$541$	−4.32208e6	+	4.32208e6i	−0.634892	+	0.634892i	−0.949291	−	0.314399i	$-0.898197\pi$
$541$	−4.32208e6	+	4.32208e6i	−0.634892	+	0.634892i	0.314399	+	0.949291i	$0.398197\pi$
$542$	−633453.	−	927554.i	−0.0926224	−	0.135625i
$543$	4.51176e6			0.656669
$544$	−1.31517e6	+	8.96188e6i	−0.190539	+	1.29838i
$545$	5.73021e6			0.826379
$546$	−219355.	−	321198.i	−0.0314895	−	0.0461096i
$547$	−5.43133e6	+	5.43133e6i	−0.776136	+	0.776136i	−0.979171	−	0.203035i	$-0.934919\pi$
$547$	−5.43133e6	+	5.43133e6i	−0.776136	+	0.776136i	0.203035	+	0.979171i	$0.434919\pi$
$548$	9.96551e6	+	3.89330e6i	1.41758	+	0.553817i
$549$	1.23552e6	+	1.23552e6i	0.174953	+	0.174953i
$550$	−2.17269e6	−	409346.i	−0.306261	−	0.0577010i
$551$		−	1.01278e7i		−	1.42113i
$552$	−5.76936e6	−	3.60638e6i	−0.805898	−	0.503761i
$553$		−	4.04375e6i		−	0.562305i
$554$	1.43637e6	−	7.62385e6i	0.198835	−	1.05536i
$555$	7.49386e6	+	7.49386e6i	1.03270	+	1.03270i
$556$	8.57055e6	−	3.75517e6i	1.17577	−	0.515161i
$557$	5.86602e6	−	5.86602e6i	0.801135	−	0.801135i	−0.182138	−	0.983273i	$-0.558302\pi$
$557$	5.86602e6	−	5.86602e6i	0.801135	−	0.801135i	0.983273	+	0.182138i	$0.0583018\pi$
$558$	−1.69974e6	+	1.16080e6i	−0.231099	+	0.157824i
$559$	−156523.			−0.0211860
$560$	7.27084e6	−	294706.i	0.979748	−	0.0397117i
$561$	1.43108e6			0.191981
$562$	−7.17186e6	+	4.89787e6i	−0.957836	+	0.654133i
$563$	−6.54155e6	+	6.54155e6i	−0.869781	+	0.869781i	−0.992448	−	0.122667i	$-0.960855\pi$
$563$	−6.54155e6	+	6.54155e6i	−0.869781	+	0.869781i	0.122667	+	0.992448i	$0.460855\pi$
$564$	−1.84133e6	−	4.20252e6i	−0.243744	−	0.556304i
$565$	8.51548e6	+	8.51548e6i	1.12225	+	1.12225i
$566$	487862.	−	2.58943e6i	0.0640111	−	0.339753i
$567$			558524.i			0.0729599i
$568$	3.06127e6	+	1.32695e7i	0.398135	+	1.72578i
$569$			3.40582e6i			0.441002i	0.975387	+	0.220501i	$0.0707693\pi$
$569$			3.40582e6i			0.441002i	−0.975387	+	0.220501i	$0.929231\pi$
$570$	−7.76466e6	−	1.46290e6i	−1.00100	−	0.188594i
$571$	1.94634e6	+	1.94634e6i	0.249820	+	0.249820i	0.820897	−	0.571077i	$-0.193474\pi$
$571$	1.94634e6	+	1.94634e6i	0.249820	+	0.249820i	−0.571077	+	0.820897i	$0.693474\pi$
$572$	106268.	−	272010.i	0.0135804	−	0.0347612i
$573$	−121746.	+	121746.i	−0.0154906	+	0.0154906i
$574$	1.83554e6	+	2.68775e6i	0.232532	+	0.340493i
$575$	1.60513e7			2.02460
$576$	−1.16276e6	−	2.38596e6i	−0.146028	−	0.299645i
$577$	1.27102e7			1.58932			0.794662	−	0.607052i	$-0.207648\pi$
$577$	1.27102e7			1.58932			0.794662	+	0.607052i	$0.207648\pi$
$578$	3.27088e6	+	4.78950e6i	0.407236	+	0.596308i
$579$	1.76163e6	−	1.76163e6i	0.218382	−	0.218382i
$580$	−5.29538e6	+	1.35543e7i	−0.653622	+	1.67305i
$581$	3.27973e6	+	3.27973e6i	0.403086	+	0.403086i
$582$	8.78031e6	+	1.65425e6i	1.07449	+	0.202439i
$583$		−	2.52400e6i		−	0.307551i
$584$	−1.25273e6	−	5.43016e6i	−0.151994	−	0.658841i
$585$		−	606824.i		−	0.0733117i
$586$	992879.	−	5.26992e6i	0.119441	−	0.633957i
$587$	−1.04395e6	−	1.04395e6i	−0.125050	−	0.125050i	0.641812	−	0.766862i	$-0.278183\pi$
$587$	−1.04395e6	−	1.04395e6i	−0.125050	−	0.125050i	−0.766862	+	0.641812i	$0.778183\pi$
$588$	−1.10497e6	−	2.52190e6i	−0.131797	−	0.300805i
$589$	5.90532e6	−	5.90532e6i	0.701383	−	0.701383i
$590$	−1.52476e7	+	1.04130e7i	−1.80332	+	1.23154i
$591$	−5.69842e6			−0.671098
$592$	−585001.	−	1.44328e7i	−0.0686044	−	1.69257i
$593$	−2.34930e6			−0.274348			−0.137174	−	0.990547i	$-0.543802\pi$
$593$	−2.34930e6			−0.274348			−0.137174	+	0.990547i	$0.543802\pi$
$594$	−346297.	+	236496.i	−0.0402701	+	0.0275016i
$595$	7.85737e6	−	7.85737e6i	0.909881	−	0.909881i
$596$	1.00813e7	−	4.41711e6i	1.16252	−	0.509357i
$597$	5.27140e6	+	5.27140e6i	0.605327	+	0.605327i
$598$	−392541.	+	2.08349e6i	−0.0448881	+	0.238254i
$599$		−	4.55122e6i		−	0.518276i	−0.965840	−	0.259138i	$-0.916562\pi$
$599$		−	4.55122e6i		−	0.518276i	0.965840	−	0.259138i	$-0.0834385\pi$
$600$	5.30971e6	+	3.31906e6i	0.602133	+	0.376389i
$601$		−	3.58244e6i		−	0.404569i	−0.979327	−	0.202285i	$-0.935163\pi$
$601$		−	3.58244e6i		−	0.404569i	0.979327	−	0.202285i	$-0.0648366\pi$
$602$	825358.	+	155501.i	0.0928220	+	0.0174881i
$603$	−1.57104e6	−	1.57104e6i	−0.175952	−	0.175952i
$604$	825940.	+	322676.i	0.0921205	+	0.0359894i
$605$	−8.89606e6	+	8.89606e6i	−0.988119	+	0.988119i
$606$	−2.72080e6	−	3.98402e6i	−0.300964	−	0.440697i
$607$	−9.38781e6			−1.03417			−0.517086	−	0.855934i	$-0.672983\pi$
$607$	−9.38781e6			−1.03417			−0.517086	+	0.855934i	$0.672983\pi$
$608$	6.42863e6	+	8.63997e6i	0.705277	+	0.947880i
$609$	−4.17367e6			−0.456010
$610$	5.74481e6	+	8.41203e6i	0.625102	+	0.915327i
$611$	−1.01098e6	+	1.01098e6i	−0.109557	+	0.109557i
$612$	−3.77521e6	−	1.47489e6i	−0.407439	−	0.159177i
$613$	−3.66310e6	−	3.66310e6i	−0.393729	−	0.393729i	0.482285	−	0.876014i	$-0.339807\pi$
$613$	−3.66310e6	−	3.66310e6i	−0.393729	−	0.393729i	−0.876014	+	0.482285i	$0.839807\pi$
$614$	4.76072e6	+	896942.i	0.509626	+	0.0960160i
$615$			5.07783e6i			0.541366i
$616$	−830595.	+	1.32876e6i	−0.0881937	+	0.141089i
$617$			1.14718e7i			1.21316i	0.795023	+	0.606579i	$0.207459\pi$
$617$			1.14718e7i			1.21316i	−0.795023	+	0.606579i	$0.792541\pi$
$618$	313355.	−	1.66320e6i	0.0330039	−	0.175176i
$619$	−7.34112e6	−	7.34112e6i	−0.770080	−	0.770080i	0.208040	−	0.978120i	$-0.433291\pi$
$619$	−7.34112e6	−	7.34112e6i	−0.770080	−	0.770080i	−0.978120	+	0.208040i	$0.933291\pi$
$620$	−1.09909e7	+	4.81566e6i	−1.14830	+	0.503125i
$621$	2.15276e6	−	2.15276e6i	0.224010	−	0.224010i
$622$	3.14581e6	−	2.14836e6i	0.326029	−	0.222655i
$623$	−6.29727e6			−0.650028
$624$	−560673.	+	608044.i	−0.0576432	+	0.0625135i
$625$	7.00410e6			0.717220
$626$	−7.99634e6	+	5.46093e6i	−0.815559	+	0.556968i
$627$	1.20312e6	−	1.20312e6i	0.122219	−	0.122219i
$628$	4.16080e6	+	9.49632e6i	0.420995	+	0.960852i
$629$	−1.55971e7	−	1.55971e7i	−1.57187	−	1.57187i
$630$	−602863.	+	3.19983e6i	−0.0605156	+	0.321200i
$631$		−	3.19898e6i		−	0.319844i	−0.987130	−	0.159922i	$-0.948876\pi$
$631$		−	3.19898e6i		−	0.319844i	0.987130	−	0.159922i	$-0.0511242\pi$
$632$	−8.37873e6	+	1.93297e6i	−0.834421	+	0.192500i
$633$			1.96379e6i			0.194799i
$634$	1.53274e6	+	288777.i	0.151442	+	0.0285324i
$635$	−5.90780e6	−	5.90780e6i	−0.581422	−	0.581422i
$636$	−2.60126e6	+	6.65832e6i	−0.255000	+	0.652713i
$637$	−606684.	+	606684.i	−0.0592399	+	0.0592399i
$638$	−1.76726e6	−	2.58777e6i	−0.171889	−	0.251695i
$639$	−6.09362e6			−0.590369
$640$	−4.08619e6	−	1.49244e7i	−0.394338	−	1.44028i
$641$	1.82892e6			0.175813			0.0879064	−	0.996129i	$-0.471982\pi$
$641$	1.82892e6			0.175813			0.0879064	+	0.996129i	$0.471982\pi$
$642$	−4.00187e6	−	5.85987e6i	−0.383200	−	0.561113i
$643$	4.97400e6	−	4.97400e6i	0.474437	−	0.474437i	−0.428910	−	0.903347i	$-0.641102\pi$
$643$	4.97400e6	−	4.97400e6i	0.474437	−	0.474437i	0.903347	+	0.428910i	$0.141102\pi$
$644$	4.13979e6	−	1.05964e7i	0.393336	−	1.00681i
$645$	926546.	+	926546.i	0.0876935	+	0.0876935i
$646$	1.61608e7	+	3.04477e6i	1.52363	+	0.287060i
$647$			9.56604e6i			0.898404i	0.893430	+	0.449202i	$0.148292\pi$
$647$			9.56604e6i			0.898404i	−0.893430	+	0.449202i	$0.851708\pi$
$648$	1.15727e6	−	266981.i	0.108267	−	0.0249772i
$649$		−	3.97608e6i		−	0.370547i
$650$	361266.	−	1.91750e6i	0.0335385	−	0.178013i
$651$	−2.43359e6	−	2.43359e6i	−0.225058	−	0.225058i
$652$	−2.79895e6	−	6.38814e6i	−0.257856	−	0.588512i
$653$	1.65827e6	−	1.65827e6i	0.152185	−	0.152185i	−0.626908	−	0.779093i	$-0.715680\pi$
$653$	1.65827e6	−	1.65827e6i	0.152185	−	0.152185i	0.779093	+	0.626908i	$0.215680\pi$
$654$	2.88598e6	−	1.97092e6i	0.263845	−	0.180187i
$655$	1.16488e7			1.06091
$656$	4.69165e6	−	5.08804e6i	0.425663	−	0.461627i
$657$	2.49363e6			0.225382
$658$	6.33538e6	−	4.32661e6i	0.570437	−	0.389568i
$659$	−7.62911e6	+	7.62911e6i	−0.684322	+	0.684322i	−0.960971	−	0.276649i	$-0.910776\pi$
$659$	−7.62911e6	+	7.62911e6i	−0.684322	+	0.684322i	0.276649	+	0.960971i	$0.410776\pi$
$660$	−2.23924e6	+	981118.i	−0.200097	+	0.0876721i
$661$	−9.54439e6	−	9.54439e6i	−0.849659	−	0.849659i	0.140431	−	0.990090i	$-0.455151\pi$
$661$	−9.54439e6	−	9.54439e6i	−0.849659	−	0.849659i	−0.990090	+	0.140431i	$0.955151\pi$
$662$	2.78063e6	−	1.47588e7i	0.246603	−	1.30890i
$663$			1.26300e6i			0.111588i
$664$	5.22790e6	−	8.36341e6i	0.460158	−	0.736144i
$665$		−	1.32115e7i		−	1.15850i
$666$	6.35176e6	+	1.19670e6i	0.554892	+	0.104544i
$667$	1.60869e7	+	1.60869e7i	1.40010	+	1.40010i
$668$	−1.09273e7	−	4.26905e6i	−0.947485	−	0.370161i
$669$	−819821.	+	819821.i	−0.0708196	+	0.0708196i
$670$	−7.30487e6	−	1.06964e7i	−0.628674	−	0.920557i
$671$	−2.19358e6			−0.188082
$672$	3.56055e6	−	2.64925e6i	0.304154	−	0.226308i
$673$	−1.50060e7			−1.27711			−0.638555	−	0.769576i	$-0.720467\pi$
$673$	−1.50060e7			−1.27711			−0.638555	+	0.769576i	$0.720467\pi$
$674$	−415830.	−	608893.i	−0.0352587	−	0.0516287i
$675$	−1.98125e6	+	1.98125e6i	−0.167371	+	0.167371i
$676$	−1.08267e7	−	4.22976e6i	−0.911236	−	0.355999i
$677$	−1.23861e7	−	1.23861e7i	−1.03864	−	1.03864i	−0.999223	−	0.0394120i	$-0.987452\pi$
$677$	−1.23861e7	−	1.23861e7i	−1.03864	−	1.03864i	−0.0394120	−	0.999223i	$-0.512548\pi$
$678$	7.21768e6	+	1.35985e6i	0.603009	+	0.113610i
$679$			1.49396e7i			1.24355i
$680$	−2.00365e7	−	1.25247e7i	−1.66169	−	1.03871i
$681$			6.18269e6i			0.510869i
$682$	478424.	−	2.53934e6i	0.0393869	−	0.209055i
$683$	1.64128e7	+	1.64128e7i	1.34626	+	1.34626i	0.889682	+	0.456581i	$0.150926\pi$
$683$	1.64128e7	+	1.64128e7i	1.34626	+	1.34626i	0.456581	+	0.889682i	$0.349074\pi$
$684$	−4.41379e6	+	1.93389e6i	−0.360721	+	0.158049i
$685$	−1.97355e7	+	1.97355e7i	−1.60702	+	1.60702i
$686$	1.04854e7	−	7.16080e6i	0.850700	−	0.580967i
$687$	1.06013e6			0.0856977
$688$	−72329.9	−	1.78449e6i	−0.00582568	−	0.143728i
$689$	2.22754e6			0.178763
$690$	1.46570e7	−	1.00097e7i	1.17199	−	0.800383i
$691$	1.19115e7	−	1.19115e7i	0.949012	−	0.949012i	−0.0497495	−	0.998762i	$-0.515842\pi$
$691$	1.19115e7	−	1.19115e7i	0.949012	−	0.949012i	0.998762	+	0.0497495i	$0.0158423\pi$
$692$	−5.34351e6	−	1.21957e7i	−0.424191	−	0.968145i
$693$	−495808.	−	495808.i	−0.0392175	−	0.0392175i
$694$	−2.63159e6	+	1.39677e7i	−0.207405	+	1.10085i
$695$			2.44096e7i			1.91690i
$696$	1.99507e6	+	8.64792e6i	0.156111	+	0.676688i
$697$		−	1.05686e7i		−	0.824016i
$698$	1.24146e7	+	2.33897e6i	0.964482	+	0.181713i
$699$	−8.11203e6	−	8.11203e6i	−0.627967	−	0.627967i
$700$	−3.80997e6	+	9.75221e6i	−0.293884	+	0.752242i
$701$	1.20474e7	−	1.20474e7i	0.925973	−	0.925973i	−0.0714696	−	0.997443i	$-0.522769\pi$
$701$	1.20474e7	−	1.20474e7i	0.925973	−	0.925973i	0.997443	+	0.0714696i	$0.0227689\pi$
$702$	−208719.	−	305623.i	−0.0159852	−	0.0234069i
$703$	−2.62252e7			−2.00138
$704$	3.15024e6	+	1.08585e6i	0.239559	+	0.0825727i
$705$	1.19691e7			0.906964
$706$	5.99170e6	+	8.77354e6i	0.452416	+	0.662465i
$707$	5.70408e6	−	5.70408e6i	0.429178	−	0.429178i
$708$	−4.09778e6	+	1.04889e7i	−0.307232	+	0.786408i
$709$	1.28951e7	+	1.28951e7i	0.963402	+	0.963402i	0.999354	−	0.0359511i	$-0.0114460\pi$
$709$	1.28951e7	+	1.28951e7i	0.963402	+	0.963402i	−0.0359511	+	0.999354i	$0.511446\pi$
$710$	−3.49109e7	−	6.57737e6i	−2.59905	−	0.489674i
$711$		−	3.84767e6i		−	0.285446i
$712$	3.01018e6	+	1.30481e7i	0.222532	+	0.964597i
$713$			1.87600e7i			1.38200i
$714$	1.25475e6	−	6.65987e6i	0.0921112	−	0.488900i
$715$	538684.	+	538684.i	0.0394066	+	0.0394066i
$716$	2.72462e6	+	6.21848e6i	0.198620	+	0.453317i
$717$	4.79235e6	−	4.79235e6i	0.348137	−	0.348137i
$718$	1.65017e7	−	1.12695e7i	1.19459	−	0.815816i
$719$	−2.94174e6			−0.212218			−0.106109	−	0.994355i	$-0.533839\pi$
$719$	−2.94174e6			−0.212218			−0.106109	+	0.994355i	$0.533839\pi$
$720$	6.91828e6	−	280416.i	0.497355	−	0.0201591i
$721$	2.82991e6			0.202738
$722$	4.57926e6	−	3.12731e6i	0.326928	−	0.223269i
$723$	3.18952e6	−	3.18952e6i	0.226923	−	0.226923i
$724$	1.46933e7	−	6.43786e6i	1.04178	−	0.456452i
$725$	−1.48052e7	−	1.48052e7i	−1.04609	−	1.04609i
$726$	−1.42062e6	+	7.54026e6i	−0.100032	+	0.530940i
$727$			2.45226e7i			1.72080i	0.509617	+	0.860402i	$0.329787\pi$
$727$			2.45226e7i			1.72080i	−0.509617	+	0.860402i	$0.670213\pi$
$728$	−1.17269e6	−	733038.i	−0.0820075	−	0.0512623i
$729$			531441.i			0.0370370i
$730$	1.42862e7	+	2.69160e6i	0.992226	+	0.186940i
$731$	−1.92844e6	−	1.92844e6i	−0.133479	−	0.133479i
$732$	5.78667e6	+	2.26072e6i	0.399164	+	0.155944i
$733$	8.23673e6	−	8.23673e6i	0.566233	−	0.566233i	−0.364838	−	0.931071i	$-0.618876\pi$
$733$	8.23673e6	−	8.23673e6i	0.566233	−	0.566233i	0.931071	+	0.364838i	$0.118876\pi$
$734$	1.59128e7	+	2.33008e7i	1.09020	+	1.59636i
$735$	7.18259e6			0.490414
$736$	−2.39349e7	−	3.51248e6i	−1.62868	−	0.239012i
$737$	2.78926e6			0.189156
$738$	1.74653e6	+	2.55742e6i	0.118042	+	0.172847i
$739$	−1.53167e7	+	1.53167e7i	−1.03170	+	1.03170i	−0.0322223	+	0.999481i	$0.510258\pi$
$739$	−1.53167e7	+	1.53167e7i	−1.03170	+	1.03170i	−0.999481	+	0.0322223i	$0.989742\pi$
$740$	3.50981e7	+	1.37120e7i	2.35615	+	0.920496i
$741$	1.06181e6	+	1.06181e6i	0.0710396	+	0.0710396i
$742$	−1.17460e7	−	2.21300e6i	−0.783213	−	0.147561i
$743$		−	2.95362e6i		−	0.196283i	−0.995172	−	0.0981415i	$-0.968710\pi$
$743$		−	2.95362e6i		−	0.196283i	0.995172	−	0.0981415i	$-0.0312898\pi$
$744$	−3.87915e6	+	6.20573e6i	−0.256924	+	0.411018i
$745$			2.87124e7i			1.89530i
$746$	1.00554e6	−	5.33713e6i	0.0661535	−	0.351124i
$747$	3.12070e6	+	3.12070e6i	0.204621	+	0.204621i
$748$	4.66057e6	−	2.04202e6i	0.304569	−	0.133446i
$749$	8.38981e6	−	8.38981e6i	0.546446	−	0.546446i
$750$	−2.52165e6	+	1.72210e6i	−0.163693	+	0.111791i
$751$	−1.14762e7			−0.742502			−0.371251	−	0.928533i	$-0.621071\pi$
$751$	−1.14762e7			−0.742502			−0.371251	+	0.928533i	$0.621071\pi$
$752$	−1.19932e7	−	1.10588e7i	−0.773376	−	0.713124i
$753$	−2.07548e6			−0.133392
$754$	2.28382e6	−	1.55969e6i	0.146297	−	0.0999100i
$755$	−1.63568e6	+	1.63568e6i	−0.104431	+	0.104431i
$756$	796960.	+	1.81893e6i	0.0507145	+	0.115747i
$757$	−4.35769e6	−	4.35769e6i	−0.276386	−	0.276386i	0.555278	−	0.831665i	$-0.312612\pi$
$757$	−4.35769e6	−	4.35769e6i	−0.276386	−	0.276386i	−0.831665	+	0.555278i	$0.812612\pi$
$758$	−4.98289e6	+	2.64478e7i	−0.314999	+	1.67192i
$759$			3.82206e6i			0.240820i
$760$	−2.73744e7	+	6.31525e6i	−1.71914	+	0.396603i
$761$		−	2.39649e7i		−	1.50008i	−0.661393	−	0.750039i	$-0.730034\pi$
$761$		−	2.39649e7i		−	1.50008i	0.661393	−	0.750039i	$-0.269966\pi$
$762$	−5.00742e6	−	943423.i	−0.312411	−	0.0588598i
$763$	4.13197e6	+	4.13197e6i	0.256949	+	0.256949i
$764$	−222766.	+	570205.i	−0.0138075	+	0.0353425i
$765$	7.47637e6	−	7.47637e6i	0.461888	−	0.461888i
$766$	−5.37802e6	−	7.87495e6i	−0.331170	−	0.484926i
$767$	3.50907e6			0.215379
$768$	−7.19127e6	−	6.11114e6i	−0.439950	−	0.373869i
$769$	2.53831e7			1.54785			0.773924	−	0.633278i	$-0.218291\pi$
$769$	2.53831e7			1.54785			0.773924	+	0.633278i	$0.218291\pi$
$770$	−2.30535e6	−	3.37569e6i	−0.140123	−	0.205180i
$771$	−2.84657e6	+	2.84657e6i	−0.172459	+	0.172459i
$772$	3.22337e6	−	8.25071e6i	0.194655	−	0.498251i
$773$	4.07084e6	+	4.07084e6i	0.245039	+	0.245039i	0.818931	−	0.573892i	$-0.194567\pi$
$773$	4.07084e6	+	4.07084e6i	0.245039	+	0.245039i	−0.573892	+	0.818931i	$0.694567\pi$
$774$	785336.	+	147961.i	0.0471198	+	0.00887760i
$775$		−	1.72653e7i		−	1.03257i
$776$	3.09551e7	−	7.14131e6i	1.84534	−	0.425720i
$777$			1.08074e7i			0.642200i
$778$	708323.	−	3.75958e6i	0.0419549	−	0.222685i
$779$	−8.88508e6	−	8.88508e6i	−0.524587	−	0.524587i
$780$	−865880.	−	1.97623e6i	−0.0509591	−	0.116306i
$781$	5.40937e6	−	5.40937e6i	0.317336	−	0.317336i
$782$	−3.05059e7	+	2.08334e7i	−1.78389	+	1.21827i
$783$	−3.97129e6			−0.231487
$784$	−7.19703e6	−	6.63633e6i	−0.418180	−	0.385601i
$785$	−2.70463e7			−1.56651
$786$	5.86685e6	−	4.00664e6i	0.338726	−	0.231326i
$787$	7.66788e6	−	7.66788e6i	0.441305	−	0.441305i	−0.451146	−	0.892450i	$-0.648985\pi$
$787$	7.66788e6	−	7.66788e6i	0.441305	−	0.441305i	0.892450	+	0.451146i	$0.148985\pi$
$788$	−1.85579e7	+	8.13111e6i	−1.06467	+	0.466481i
$789$	−6.58962e6	−	6.58962e6i	−0.376850	−	0.376850i
$790$	4.15313e6	−	2.20436e7i	0.236760	−	1.25665i
$791$			1.22808e7i			0.697887i
$792$	−790320.	+	1.26432e6i	−0.0447703	+	0.0716218i
$793$		−	1.93593e6i		−	0.109322i
$794$	2.50837e7	+	4.72590e6i	1.41202	+	0.266031i
$795$	−1.31860e7	−	1.31860e7i	−0.739940	−	0.739940i
$796$	2.46890e7	+	9.64544e6i	1.38109	+	0.539559i
$797$	−5.95109e6	+	5.95109e6i	−0.331857	+	0.331857i	−0.853291	−	0.521435i	$-0.825397\pi$
$797$	−5.95109e6	+	5.95109e6i	−0.331857	+	0.331857i	0.521435	+	0.853291i	$0.325397\pi$
$798$	−4.54411e6	−	6.65387e6i	−0.252605	−	0.369885i
$799$	−2.49116e7			−1.38050
$800$	2.20280e7	+	3.23264e6i	1.21688	+	0.178580i
$801$	−5.99192e6			−0.329978
$802$	−1.17407e7	−	1.71917e7i	−0.644551	−	0.943805i
$803$	−2.21363e6	+	2.21363e6i	−0.121148	+	0.121148i
$804$	−7.35810e6	−	2.87464e6i	−0.401445	−	0.156835i
$805$	2.09850e7	+	2.09850e7i	1.14135	+	1.14135i
$806$	2.24108e6	+	422231.i	0.121512	+	0.0228935i
$807$		−	1.08351e7i		−	0.585663i
$808$	−1.45456e7	−	9.09233e6i	−0.783795	−	0.489945i
$809$		−	1.81374e6i		−	0.0974326i	−0.998813	−	0.0487163i	$-0.984487\pi$
$809$		−	1.81374e6i		−	0.0974326i	0.998813	−	0.0487163i	$-0.0155130\pi$
$810$	−573631.	+	3.04467e6i	−0.0307199	+	0.163053i
$811$	2.42022e7	+	2.42022e7i	1.29212	+	1.29212i	0.933475	+	0.358643i	$0.116761\pi$
$811$	2.42022e7	+	2.42022e7i	1.29212	+	1.29212i	0.358643	+	0.933475i	$0.383239\pi$
$812$	−1.35923e7	+	5.95543e6i	−0.723439	+	0.316974i
$813$	1.26362e6	−	1.26362e6i	0.0670487	−	0.0670487i
$814$	−6.70085e6	+	4.57620e6i	−0.354461	+	0.242072i
$815$	1.81940e7			0.959474
$816$	−1.43992e7	+	583635.i	−0.757028	+	0.0306843i
$817$	−3.24250e6			−0.169951
$818$	−1.25773e7	+	8.58943e6i	−0.657213	+	0.448829i
$819$	437573.	−	437573.i	0.0227950	−	0.0227950i
$820$	7.24559e6	+	1.65368e7i	0.376304	+	0.858851i
$821$	−9.36590e6	−	9.36590e6i	−0.484944	−	0.484944i	0.421763	−	0.906706i	$-0.361412\pi$
$821$	−9.36590e6	−	9.36590e6i	−0.484944	−	0.484944i	−0.906706	+	0.421763i	$0.861412\pi$
$822$	−3.15159e6	+	1.67278e7i	−0.162686	+	0.863491i
$823$		−	1.08603e7i		−	0.558908i	−0.960159	−	0.279454i	$-0.909847\pi$
$823$		−	1.08603e7i		−	0.558908i	0.960159	−	0.279454i	$-0.0901535\pi$
$824$	−1.35274e6	−	5.86363e6i	−0.0694056	−	0.300849i
$825$		−	3.51755e6i		−	0.179931i
$826$	−1.85036e7	−	3.48616e6i	−0.943638	−	0.177786i
$827$	1.31355e7	+	1.31355e7i	0.667857	+	0.667857i	0.957219	−	0.289363i	$-0.0934434\pi$
$827$	1.31355e7	+	1.31355e7i	0.667857	+	0.667857i	−0.289363	+	0.957219i	$0.593443\pi$
$828$	3.93905e6	−	1.00826e7i	0.199671	−	0.511090i
$829$	−8.44468e6	+	8.44468e6i	−0.426773	+	0.426773i	−0.887528	−	0.460754i	$-0.847579\pi$
$829$	−8.44468e6	+	8.44468e6i	−0.426773	+	0.426773i	0.460754	+	0.887528i	$0.347579\pi$
$830$	1.45103e7	+	2.12472e7i	0.731106	+	1.07055i
$831$	1.23429e7			0.620031
$832$	−958307.	+	2.78023e6i	−0.0479951	+	0.139243i
$833$	−1.49493e7			−0.746462
$834$	8.39575e6	+	1.22938e7i	0.417969	+	0.612025i
$835$	2.16403e7	−	2.16403e7i	1.07410	−	1.07410i
$836$	2.20143e6	−	5.63491e6i	0.108941	−	0.278850i
$837$	−2.31559e6	−	2.31559e6i	−0.114248	−	0.114248i
$838$	−5.91545e6	−	1.11450e6i	−0.290990	−	0.0548239i
$839$			221983.i			0.0108872i	0.999985	+	0.00544359i	$0.00173276\pi$
$839$			221983.i			0.0108872i	−0.999985	+	0.00544359i	$0.998267\pi$
$840$	2.60252e6	+	1.12810e7i	0.127261	+	0.551633i
$841$		−	9.16502e6i		−	0.446831i
$842$	3.23278e6	−	1.71587e7i	0.157143	−	0.834073i
$843$	−9.77033e6	−	9.77033e6i	−0.473522	−	0.473522i
$844$	2.80214e6	+	6.39542e6i	0.135405	+	0.309039i
$845$	2.14411e7	−	2.14411e7i	1.03301	−	1.03301i
$846$	6.02818e6	−	4.11681e6i	0.289574	−	0.197759i
$847$	−1.28297e7			−0.614478
$848$	1.02935e6	+	2.53957e7i	0.0491559	+	1.21275i
$849$	4.19224e6			0.199608
$850$	2.80755e7	−	1.91735e7i	1.33285	−	0.910238i
$851$	4.16559e7	−	4.16559e7i	1.97175	−	1.97175i
$852$	−1.98449e7	+	8.69502e6i	−0.936592	+	0.410366i
$853$	−2.40198e7	−	2.40198e7i	−1.13031	−	1.13031i	−0.990125	−	0.140185i	$-0.955230\pi$
$853$	−2.40198e7	−	2.40198e7i	−1.13031	−	1.13031i	−0.140185	−	0.990125i	$-0.544770\pi$
$854$	−1.92329e6	+	1.02083e7i	−0.0902404	+	0.478971i
$855$		−	1.25708e7i		−	0.588097i
$856$	−2.13943e7	−	1.33734e7i	−0.997960	−	0.623817i
$857$		−	4.86232e6i		−	0.226147i	−0.993587	−	0.113074i	$-0.963930\pi$
$857$		−	4.86232e6i		−	0.226147i	0.993587	−	0.113074i	$-0.0360696\pi$
$858$	456587.	+	86023.1i	0.0211741	+	0.00398930i
$859$	−8.54195e6	−	8.54195e6i	−0.394979	−	0.394979i	0.481479	−	0.876458i	$-0.340100\pi$
$859$	−8.54195e6	−	8.54195e6i	−0.394979	−	0.394979i	−0.876458	+	0.481479i	$0.840100\pi$
$860$	4.33955e6	+	1.69536e6i	0.200078	+	0.0781658i
$861$	−3.66156e6	+	3.66156e6i	−0.168329	+	0.168329i
$862$	−1.27702e7	−	1.86992e7i	−0.585368	−	0.857145i
$863$	8.18921e6			0.374296			0.187148	−	0.982332i	$-0.440076\pi$
$863$	8.18921e6			0.374296			0.187148	+	0.982332i	$0.440076\pi$
$864$	3.38790e6	−	2.52079e6i	0.154399	−	0.114882i
$865$	3.47343e7			1.57840
$866$	−7.12658e6	−	1.04353e7i	−0.322914	−	0.472837i
$867$	−6.52481e6	+	6.52481e6i	−0.294795	+	0.294795i
$868$	−1.13979e7	−	4.45291e6i	−0.513483	−	0.200606i
$869$	3.41562e6	+	3.41562e6i	0.153434	+	0.153434i
$870$	−2.27518e7	−	4.28656e6i	−1.01910	−	0.192004i
$871$			2.46165e6i			0.109946i
$872$	6.58638e6	−	1.05367e7i	0.293330	−	0.469258i
$873$			1.42152e7i			0.631272i
$874$	−8.13179e6	+	4.31613e7i	−0.360087	+	1.91124i
$875$	−3.61034e6	−	3.61034e6i	−0.159415	−	0.159415i
$876$	8.12095e6	−	3.55818e6i	0.357558	−	0.156663i
$877$	−546535.	+	546535.i	−0.0239949	+	0.0239949i	−0.719002	−	0.695008i	$-0.755401\pi$
$877$	−546535.	+	546535.i	−0.0239949	+	0.0239949i	0.695008	+	0.719002i	$0.255401\pi$
$878$	−1.51532e6	+	1.03486e6i	−0.0663390	+	0.0453048i
$879$	8.53190e6			0.372455
$880$	−5.89250e6	+	6.39036e6i	−0.256503	+	0.278175i
$881$	2.14496e7			0.931065			0.465532	−	0.885031i	$-0.345863\pi$
$881$	2.14496e7			0.931065			0.465532	+	0.885031i	$0.345863\pi$
$882$	3.61747e6	−	2.47047e6i	0.156579	−	0.106932i
$883$	−1.69044e6	+	1.69044e6i	−0.0729624	+	0.0729624i	−0.742646	−	0.669684i	$-0.766430\pi$
$883$	−1.69044e6	+	1.69044e6i	−0.0729624	+	0.0729624i	0.669684	+	0.742646i	$0.266430\pi$
$884$	1.80218e6	+	4.11316e6i	0.0775651	+	0.177029i
$885$	−2.07721e7	−	2.07721e7i	−0.891501	−	0.891501i
$886$	6.31828e6	−	3.35356e7i	0.270405	−	1.43523i
$887$		−	6.94488e6i		−	0.296385i	−0.988959	−	0.148192i	$-0.952655\pi$
$887$		−	6.94488e6i		−	0.296385i	0.988959	−	0.148192i	$-0.0473455\pi$
$888$	2.23932e7	−	5.16609e6i	0.952979	−	0.219852i
$889$		−	8.52006e6i		−	0.361567i
$890$	−3.43282e7	−	6.46760e6i	−1.45270	−	0.273696i
$891$	−471766.	−	471766.i	−0.0199082	−	0.0199082i
$892$	−1.50008e6	+	3.83970e6i	−0.0631252	+	0.161579i
$893$	−2.09433e7	+	2.09433e7i	−0.878855	+	0.878855i
$894$	9.87570e6	+	1.44608e7i	0.413261	+	0.605130i
$895$	−1.77108e7			−0.739060
$896$	7.81531e6	−	1.37083e7i	0.325219	−	0.570445i
$897$	−3.37314e6			−0.139976
$898$	1.39137e7	+	2.03735e7i	0.575772	+	0.843093i
$899$	1.73036e7	−	1.73036e7i	0.714066	−	0.714066i
$900$	−3.62522e6	+	9.27932e6i	−0.149186	+	0.381865i
$901$	2.74444e7	+	2.74444e7i	1.12627	+	1.12627i
$902$	−3.82066e6	−	719832.i	−0.156359	−	0.0294588i
$903$			1.33624e6i			0.0545337i
$904$	2.54460e7	−	5.87037e6i	1.03562	−	0.238916i
$905$			4.18479e7i			1.69845i
$906$	−261203.	+	1.38639e6i	−0.0105720	+	0.0561133i
$907$	−1.95149e7	−	1.95149e7i	−0.787677	−	0.787677i	0.193436	−	0.981113i	$-0.438037\pi$
$907$	−1.95149e7	−	1.95149e7i	−0.787677	−	0.787677i	−0.981113	+	0.193436i	$0.938037\pi$
$908$	8.82212e6	+	2.01350e7i	0.355106	+	0.810471i
$909$	5.42749e6	−	5.42749e6i	0.217866	−	0.217866i
$910$	2.97920e6	−	2.03458e6i	0.119260	−	0.0814463i
$911$	−6.72944e6			−0.268648			−0.134324	−	0.990937i	$-0.542886\pi$
$911$	−6.72944e6			−0.268648			−0.134324	+	0.990937i	$0.542886\pi$
$912$	−1.16148e7	+	1.25961e7i	−0.462407	+	0.501475i
$913$	−5.54055e6			−0.219976
$914$	−3.41422e7	+	2.33167e7i	−1.35184	+	0.923212i
$915$	−1.14598e7	+	1.14598e7i	−0.452507	+	0.452507i
$916$	3.45251e6	−	1.51271e6i	0.135955	−	0.0595686i
$917$	8.39980e6	+	8.39980e6i	0.329872	+	0.329872i
$918$	1.19391e6	−	6.33694e6i	0.0467589	−	0.248183i
$919$		−	2.69710e7i		−	1.05344i	−0.850040	−	0.526719i	$-0.823422\pi$
$919$		−	2.69710e7i		−	1.05344i	0.850040	−	0.526719i	$-0.176578\pi$
$920$	3.34502e7	−	5.35124e7i	1.30295	−	2.08442i
$921$			7.70751e6i			0.299409i
$922$	−2.78042e7	−	5.23845e6i	−1.07717	−	0.202944i
$923$	4.77401e6	+	4.77401e6i	0.184450	+	0.184450i
$924$	−2.32215e6	−	907213.i	−0.0894769	−	0.0349566i
$925$	−3.83371e7	+	3.83371e7i	−1.47321	+	1.47321i
$926$	1.20170e7	+	1.75963e7i	0.460541	+	0.674362i
$927$	2.69269e6			0.102917
$928$	1.88370e7	+	2.53167e7i	0.718030	+	0.965020i
$929$	7.45937e6			0.283572			0.141786	−	0.989897i	$-0.454716\pi$
$929$	7.45937e6			0.283572			0.141786	+	0.989897i	$0.454716\pi$
$930$	−1.07668e7	−	1.57656e7i	−0.408205	−	0.597727i
$931$	−1.25679e7	+	1.25679e7i	−0.475215	+	0.475215i
$932$	−3.79933e7	−	1.48431e7i	−1.43274	−	0.559740i
$933$	4.28559e6	+	4.28559e6i	0.161178	+	0.161178i
$934$	2.28120e7	+	4.29789e6i	0.855651	+	0.161209i
$935$			1.32737e7i			0.496550i
$936$	−1.11582e6	−	697493.i	−0.0416299	−	0.0260226i
$937$			3.29753e7i			1.22699i	0.789700	+	0.613493i	$0.210236\pi$
$937$			3.29753e7i			1.22699i	−0.789700	+	0.613493i	$0.789764\pi$
$938$	2.44558e6	−	1.29805e7i	0.0907560	−	0.481708i
$939$	−1.08935e7	−	1.08935e7i	−0.403185	−	0.403185i
$940$	3.89796e7	−	1.70788e7i	1.43886	−	0.630432i
$941$	−1.52203e7	+	1.52203e7i	−0.560336	+	0.560336i	−0.929403	−	0.369067i	$-0.879677\pi$
$941$	−1.52203e7	+	1.52203e7i	−0.560336	+	0.560336i	0.369067	+	0.929403i	$0.379677\pi$
$942$	−1.36217e7	+	9.30265e6i	−0.500155	+	0.341570i
$943$	2.82260e7			1.03364
$944$	1.62155e6	+	4.00061e7i	0.0592244	+	1.46116i
$945$	−5.18046e6			−0.188707
$946$	−828498.	+	565805.i	−0.0300998	+	0.0205560i
$947$	−3.11761e7	+	3.11761e7i	−1.12966	+	1.12966i	−0.139426	+	0.990232i	$0.544526\pi$
$947$	−3.11761e7	+	3.11761e7i	−1.12966	+	1.12966i	−0.990232	+	0.139426i	$0.955474\pi$
$948$	−5.49026e6	−	1.25306e7i	−0.198414	−	0.452847i
$949$	−1.95362e6	−	1.95362e6i	−0.0704167	−	0.0704167i
$950$	7.48392e6	−	3.97225e7i	0.269042	−	1.42800i
$951$			2.48149e6i			0.0889734i
$952$	−5.41669e6	−	2.34794e7i	−0.193705	−	0.839644i
$953$		−	1.46499e6i		−	0.0522519i	−0.999659	−	0.0261259i	$-0.991683\pi$
$953$		−	1.46499e6i		−	0.0522519i	0.999659	−	0.0261259i	$-0.00831709\pi$
$954$	−1.11764e7	−	2.10569e6i	−0.397587	−	0.0749073i
$955$	−1.12922e6	−	1.12922e6i	−0.0400656	−	0.0400656i
$956$	8.76888e6	−	2.24453e7i	0.310313	−	0.794294i
$957$	3.52536e6	−	3.52536e6i	0.124429	−	0.124429i
$958$	−1.83290e7	−	2.68389e7i	−0.645247	−	0.944824i
$959$	−2.84620e7			−0.999354
$960$	2.21304e7	−	1.07849e7i	0.775018	−	0.377694i
$961$	−8.45028e6			−0.295163
$962$	−4.03870e6	−	5.91380e6i	−0.140703	−	0.206029i
$963$	7.98299e6	−	7.98299e6i	0.277396	−	0.277396i
$964$	5.83608e6	−	1.49384e7i	0.202269	−	0.517738i
$965$	1.63396e7	+	1.63396e7i	0.564836	+	0.564836i
$966$	1.77868e7	+	3.35112e6i	0.613275	+	0.115544i
$967$			1.56845e7i			0.539393i	0.962945	+	0.269697i	$0.0869234\pi$
$967$			1.56845e7i			0.539393i	−0.962945	+	0.269697i	$0.913077\pi$
$968$	6.13274e6	+	2.65833e7i	0.210361	+	0.911843i
$969$			2.61640e7i			0.895147i
$970$	−1.53437e7	+	8.14399e7i	−0.523600	+	2.77912i
$971$	−2.21402e7	−	2.21402e7i	−0.753586	−	0.753586i	0.221561	−	0.975147i	$-0.428885\pi$
$971$	−2.21402e7	−	2.21402e7i	−0.753586	−	0.753586i	−0.975147	+	0.221561i	$0.928885\pi$
$972$	758316.	+	1.73073e6i	0.0257445	+	0.0587575i
$973$	−1.76015e7	+	1.76015e7i	−0.596028	+	0.596028i
$974$	1.18692e7	−	8.10582e6i	0.400889	−	0.273778i
$975$	3.10439e6			0.104584
$976$	2.20711e7	−	894600.i	0.741652	−	0.0300611i
$977$	2.27949e7			0.764012			0.382006	−	0.924160i	$-0.375233\pi$
$977$	2.27949e7			0.764012			0.382006	+	0.924160i	$0.375233\pi$
$978$	9.16327e6	−	6.25786e6i	0.306340	−	0.209208i
$979$	5.31909e6	−	5.31909e6i	0.177370	−	0.177370i
$980$	2.33914e7	−	1.02489e7i	0.778019	−	0.340887i
$981$	3.93161e6	+	3.93161e6i	0.130436	+	0.130436i
$982$	−6.41312e6	+	3.40391e7i	−0.212222	+	1.12642i
$983$		−	1.28768e7i		−	0.425034i	−0.977157	−	0.212517i	$-0.931834\pi$
$983$		−	1.28768e7i		−	0.425034i	0.977157	−	0.212517i	$-0.0681660\pi$
$984$	9.33708e6	+	5.83654e6i	0.307414	+	0.192162i
$985$		−	5.28545e7i		−	1.73577i
$986$	4.73539e7	+	8.92170e6i	1.55118	+	0.292251i
$987$	8.63078e6	+	8.63078e6i	0.282005	+	0.282005i
$988$	4.97306e6	+	1.94286e6i	0.162081	+	0.0633213i
$989$	5.15037e6	−	5.15037e6i	0.167436	−	0.167436i
$990$	−2.19357e6	−	3.21200e6i	−0.0711317	−	0.104157i
$991$	2.50480e7			0.810195			0.405098	−	0.914273i	$-0.367238\pi$
$991$	2.50480e7			0.810195			0.405098	+	0.914273i	$0.367238\pi$
$992$	−3.77815e6	+	2.57452e7i	−0.121899	+	0.830649i
$993$	2.38942e7			0.768989
$994$	−2.04309e7	−	2.99166e7i	−0.655875	−	0.960387i
$995$	−4.88937e7	+	4.88937e7i	−1.56565	+	1.56565i
$996$	1.46160e7	+	5.71015e6i	0.466854	+	0.182389i
$997$	4.86071e6	+	4.86071e6i	0.154868	+	0.154868i	0.780288	−	0.625420i	$-0.215072\pi$
$997$	4.86071e6	+	4.86071e6i	0.154868	+	0.154868i	−0.625420	+	0.780288i	$0.715072\pi$
$998$	−2.44628e7	−	4.60891e6i	−0.777464	−	0.146478i
$999$			1.02834e7i			0.326003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.37.15	yes	40
3.2	odd	2		144.6.k.c.37.6		40
4.3	odd	2		192.6.j.a.49.14		40
8.3	odd	2		384.6.j.b.97.7		40
8.5	even	2		384.6.j.a.97.14		40
12.11	even	2		576.6.k.c.433.18		40
16.3	odd	4		192.6.j.a.145.14		40
16.5	even	4		384.6.j.a.289.14		40
16.11	odd	4		384.6.j.b.289.7		40
16.13	even	4	inner	48.6.j.a.13.15	✓	40
48.29	odd	4		144.6.k.c.109.6		40
48.35	even	4		576.6.k.c.145.18		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.15	✓	40	16.13	even	4	inner
48.6.j.a.37.15	yes	40	1.1	even	1	trivial
144.6.k.c.37.6		40	3.2	odd	2
144.6.k.c.109.6		40	48.29	odd	4
192.6.j.a.49.14		40	4.3	odd	2
192.6.j.a.145.14		40	16.3	odd	4
384.6.j.a.97.14		40	8.5	even	2
384.6.j.a.289.14		40	16.5	even	4
384.6.j.b.97.7		40	8.3	odd	2
384.6.j.b.289.7		40	16.11	odd	4
576.6.k.c.145.18		40	48.35	even	4
576.6.k.c.433.18		40	12.11	even	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.19025 + 4.67143i) q^{2} +(-6.36396 + 6.36396i) q^{3} +(-11.6446 + 29.8061i) q^{4} +(-59.0275 - 59.0275i) q^{5} +(-50.0315 - 9.42617i) q^{6} -85.1278i q^{7} +(-176.386 + 40.6922i) q^{8} -81.0000i q^{9} +O(q^{10})\)	\(q+(3.19025 + 4.67143i) q^{2} +(-6.36396 + 6.36396i) q^{3} +(-11.6446 + 29.8061i) q^{4} +(-59.0275 - 59.0275i) q^{5} +(-50.0315 - 9.42617i) q^{6} -85.1278i q^{7} +(-176.386 + 40.6922i) q^{8} -81.0000i q^{9} +(87.4303 - 464.056i) q^{10} +(71.9046 + 71.9046i) q^{11} +(-115.579 - 263.790i) q^{12} +(-63.4590 + 63.4590i) q^{13} +(397.669 - 271.579i) q^{14} +751.297 q^{15} +(-752.808 - 694.159i) q^{16} -1563.69 q^{17} +(378.386 - 258.410i) q^{18} +(-1314.60 + 1314.60i) q^{19} +(2446.73 - 1072.03i) q^{20} +(541.750 + 541.750i) q^{21} +(-106.504 + 565.291i) q^{22} -4176.22i q^{23} +(863.552 - 1381.48i) q^{24} +3843.49i q^{25} +(-498.895 - 93.9942i) q^{26} +(515.481 + 515.481i) q^{27} +(2537.33 + 991.277i) q^{28} +(-3852.02 + 3852.02i) q^{29} +(2396.83 + 3509.64i) q^{30} -4492.09 q^{31} +(841.068 - 5731.23i) q^{32} -915.196 q^{33} +(-4988.57 - 7304.68i) q^{34} +(-5024.88 + 5024.88i) q^{35} +(2414.29 + 943.210i) q^{36} +(9974.55 + 9974.55i) q^{37} +(-10335.0 - 1947.17i) q^{38} -807.702i q^{39} +(12813.6 + 8009.69i) q^{40} +6758.75i q^{41} +(-802.430 + 4259.07i) q^{42} +(1233.26 + 1233.26i) q^{43} +(-2980.49 + 1305.90i) q^{44} +(-4781.23 + 4781.23i) q^{45} +(19508.9 - 13323.2i) q^{46} +15931.3 q^{47} +(9208.44 - 373.242i) q^{48} +9560.25 q^{49} +(-17954.6 + 12261.7i) q^{50} +(9951.27 - 9951.27i) q^{51} +(-1152.51 - 2630.42i) q^{52} +(-17551.0 - 17551.0i) q^{53} +(-763.520 + 4052.55i) q^{54} -8488.70i q^{55} +(3464.04 + 15015.4i) q^{56} -16732.2i q^{57} +(-30283.4 - 5705.54i) q^{58} +(-27648.3 - 27648.3i) q^{59} +(-8748.54 + 22393.3i) q^{60} +(-15253.4 + 15253.4i) q^{61} +(-14330.9 - 20984.5i) q^{62} -6895.36 q^{63} +(29456.3 - 14355.1i) q^{64} +7491.66 q^{65} +(-2919.71 - 4275.28i) q^{66} +(19395.6 - 19395.6i) q^{67} +(18208.5 - 46607.6i) q^{68} +(26577.3 + 26577.3i) q^{69} +(-39504.1 - 7442.76i) q^{70} -75229.9i q^{71} +(3296.07 + 14287.3i) q^{72} +30785.6i q^{73} +(-14774.1 + 78416.8i) q^{74} +(-24459.8 - 24459.8i) q^{75} +(-23875.2 - 54491.2i) q^{76} +(6121.08 - 6121.08i) q^{77} +(3773.12 - 2576.77i) q^{78} +47502.1 q^{79} +(3461.92 + 85410.8i) q^{80} -6561.00 q^{81} +(-31573.1 + 21562.1i) q^{82} +(-38527.1 + 38527.1i) q^{83} +(-22455.9 + 9839.02i) q^{84} +(92300.8 + 92300.8i) q^{85} +(-1826.68 + 9695.51i) q^{86} -49028.3i q^{87} +(-15608.9 - 9757.03i) q^{88} -73974.3i q^{89} +(-37588.5 - 7081.86i) q^{90} +(5402.13 + 5402.13i) q^{91} +(124477. + 48630.3i) q^{92} +(28587.5 - 28587.5i) q^{93} +(50824.9 + 74422.0i) q^{94} +155196. q^{95} +(31120.8 + 41825.9i) q^{96} -175496. q^{97} +(30499.6 + 44660.1i) q^{98} +(5824.27 - 5824.27i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) \) 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

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