LMFDB - Embedded newform 11.6.c.a.5.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [11,6,Mod(3,11)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("11.3"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(11, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	11.c (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.76422201794$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 86 x^{14} - 146 x^{13} + 7205 x^{12} - 23732 x^{11} + 774165 x^{10} + \cdots + 393784336 $ x^16 - 5x^15 + 86x^14 - 146x^13 + 7205x^12 - 23732x^11 + 774165x^10 - 1228996x^9 + 44649817x^8 - 92720004x^7 + 943915592x^6 - 1892495035x^5 + 8611100939x^4 - 17760110698x^3 + 18348896492x^2 - 4224271656*x + 393784336
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.3
Root			$0.136182 + 0.0989419i$ of defining polynomial
Character	$\chi$	$=$	11.5
Dual form			11.6.c.a.9.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.361034 - 1.11115i) q^{2} +(12.7716 + 9.27912i) q^{3} +(24.7842 - 18.0068i) q^{4} +(1.31139 - 4.03604i) q^{5} +(5.69949 - 17.5412i) q^{6} +(-146.551 + 106.476i) q^{7} +(-59.2025 - 43.0132i) q^{8} +(1.92087 + 5.91183i) q^{9} -4.95810 q^{10} +(-240.502 - 321.262i) q^{11} +483.622 q^{12} +(185.552 + 571.070i) q^{13} +(171.220 + 124.399i) q^{14} +(54.1995 - 39.3782i) q^{15} +(276.516 - 851.028i) q^{16} +(-58.8034 + 180.978i) q^{17} +(5.87542 - 4.26874i) q^{18} +(581.843 + 422.733i) q^{19} +(-40.1744 - 123.644i) q^{20} -2859.70 q^{21} +(-270.141 + 383.220i) q^{22} -2310.03 q^{23} +(-356.988 - 1098.69i) q^{24} +(2513.61 + 1826.24i) q^{25} +(567.553 - 412.351i) q^{26} +(1155.11 - 3555.06i) q^{27} +(-1714.87 + 5277.84i) q^{28} +(6320.18 - 4591.88i) q^{29} +(-63.3229 - 46.0068i) q^{30} +(2092.98 + 6441.53i) q^{31} -3387.16 q^{32} +(-90.5706 - 6334.69i) q^{33} +222.324 q^{34} +(237.555 + 731.118i) q^{35} +(154.061 + 111.932i) q^{36} +(2492.25 - 1810.73i) q^{37} +(259.654 - 799.134i) q^{38} +(-2929.23 + 9015.24i) q^{39} +(-251.241 + 182.537i) q^{40} +(-10121.7 - 7353.86i) q^{41} +(1032.45 + 3177.55i) q^{42} -11900.8 q^{43} +(-11745.6 - 3631.57i) q^{44} +26.3794 q^{45} +(833.998 + 2566.78i) q^{46} +(22907.4 + 16643.2i) q^{47} +(11428.3 - 8303.17i) q^{48} +(4946.54 - 15223.9i) q^{49} +(1121.73 - 3452.33i) q^{50} +(-2430.33 + 1765.74i) q^{51} +(14881.9 + 10812.3i) q^{52} +(-2986.90 - 9192.73i) q^{53} -4367.23 q^{54} +(-1612.02 + 549.378i) q^{55} +13256.1 q^{56} +(3508.47 + 10798.0i) q^{57} +(-7384.06 - 5364.83i) q^{58} +(-27184.0 + 19750.3i) q^{59} +(634.217 - 1951.92i) q^{60} +(512.623 - 1577.69i) q^{61} +(6401.85 - 4651.22i) q^{62} +(-910.973 - 661.860i) q^{63} +(-7625.63 - 23469.3i) q^{64} +2548.19 q^{65} +(-7006.08 + 2387.67i) q^{66} -18724.7 q^{67} +(1801.44 + 5544.27i) q^{68} +(-29502.8 - 21435.0i) q^{69} +(726.615 - 527.917i) q^{70} +(-9853.69 + 30326.5i) q^{71} +(140.566 - 432.618i) q^{72} +(9015.22 - 6549.94i) q^{73} +(-2911.77 - 2115.53i) q^{74} +(15156.9 + 46648.1i) q^{75} +22032.6 q^{76} +(69452.6 + 21473.8i) q^{77} +11074.8 q^{78} +(-21447.7 - 66009.1i) q^{79} +(-3072.17 - 2232.06i) q^{80} +(48962.4 - 35573.3i) q^{81} +(-4516.94 + 13901.7i) q^{82} +(16445.3 - 50613.5i) q^{83} +(-70875.4 + 51494.0i) q^{84} +(653.322 + 474.666i) q^{85} +(4296.58 + 13223.5i) q^{86} +123328. q^{87} +(419.838 + 29364.3i) q^{88} -63932.5 q^{89} +(-9.52386 - 29.3114i) q^{90} +(-87998.0 - 63934.3i) q^{91} +(-57252.3 + 41596.2i) q^{92} +(-33041.0 + 101690. i) q^{93} +(10222.7 - 31462.2i) q^{94} +(2469.19 - 1793.97i) q^{95} +(-43259.4 - 31429.8i) q^{96} +(-21792.6 - 67070.8i) q^{97} -18701.9 q^{98} +(1437.28 - 2038.91i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9} - 672 q^{10} - 692 q^{11} - 1562 q^{12} + 1162 q^{13} + 560 q^{14} + 1796 q^{15} + 6399 q^{16} - 22 q^{17}+ \cdots + 724964 q^{99}+O(q^{100}) $ 16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9 - 672 * q^10 - 692 * q^11 - 1562 * q^12 + 1162 * q^13 + 560 * q^14 + 1796 * q^15 + 6399 * q^16 - 22 * q^17 + 834 * q^18 - 3236 * q^19 - 5514 * q^20 - 7772 * q^21 - 13059 * q^22 - 10848 * q^23 + 13233 * q^24 + 15686 * q^25 + 16216 * q^26 + 22500 * q^27 + 8838 * q^28 + 13070 * q^29 - 22830 * q^30 - 14764 * q^31 - 58812 * q^32 - 48544 * q^33 - 26966 * q^34 + 43368 * q^35 + 63696 * q^36 + 4638 * q^37 + 68144 * q^38 + 20300 * q^39 + 52284 * q^40 - 14806 * q^41 - 69922 * q^42 - 24376 * q^43 - 104960 * q^44 - 97480 * q^45 + 50452 * q^46 + 40364 * q^47 + 30236 * q^48 + 32246 * q^49 + 10839 * q^50 + 75564 * q^51 - 80654 * q^52 - 11654 * q^53 + 43796 * q^54 + 7052 * q^55 + 70632 * q^56 - 40020 * q^57 + 10276 * q^58 + 70804 * q^59 + 46116 * q^60 - 31446 * q^61 - 153388 * q^62 - 7064 * q^63 + 17695 * q^64 - 41284 * q^65 + 48006 * q^66 - 64200 * q^67 - 94114 * q^68 - 62412 * q^69 - 103768 * q^70 - 184380 * q^71 - 14729 * q^72 - 1750 * q^73 + 306048 * q^74 + 246596 * q^75 + 174806 * q^76 + 384646 * q^77 + 360916 * q^78 + 24324 * q^79 - 386444 * q^80 - 259412 * q^81 - 316255 * q^82 - 46028 * q^83 - 271956 * q^84 + 63914 * q^85 + 22931 * q^86 - 47592 * q^87 + 211871 * q^88 + 148364 * q^89 - 347186 * q^90 - 258448 * q^91 - 58658 * q^92 - 387478 * q^93 - 55370 * q^94 - 4716 * q^95 + 328396 * q^96 + 484296 * q^97 + 743692 * q^98 + 724964 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.361034	−	1.11115i	−0.0638224	−	0.196425i	0.914061	−	0.405577i	$-0.132930\pi$
$2$	−0.361034	−	1.11115i	−0.0638224	−	0.196425i	−0.977883	+	0.209152i	$0.932930\pi$
$3$	12.7716	+	9.27912i	0.819299	+	0.595256i	0.916512	−	0.400008i	$-0.130993\pi$
$3$	12.7716	+	9.27912i	0.819299	+	0.595256i	−0.0972125	+	0.995264i	$0.530993\pi$
$4$	24.7842	−	18.0068i	0.774507	−	0.562713i
$5$	1.31139	−	4.03604i	0.0234589	−	0.0721989i	−0.938642	−	0.344894i	$-0.887915\pi$
$5$	1.31139	−	4.03604i	0.0234589	−	0.0721989i	0.962101	+	0.272695i	$0.0879149\pi$
$6$	5.69949	−	17.5412i	0.0646335	−	0.198922i
$7$	−146.551	+	106.476i	−1.13043	+	0.821307i	−0.985758	−	0.168172i	$-0.946213\pi$
$7$	−146.551	+	106.476i	−1.13043	+	0.821307i	−0.144674	+	0.989479i	$0.546213\pi$
$8$	−59.2025	−	43.0132i	−0.327051	−	0.237616i
$9$	1.92087	+	5.91183i	0.00790482	+	0.0243285i
$10$	−4.95810			−0.0156789
$11$	−240.502	−	321.262i	−0.599291	−	0.800531i
$11$	−240.502	−	321.262i	−0.599291	−	0.800531i
$12$	483.622			0.969511
$13$	185.552	+	571.070i	0.304514	+	0.937197i	0.979858	+	0.199695i	$0.0639950\pi$
$13$	185.552	+	571.070i	0.304514	+	0.937197i	−0.675344	+	0.737503i	$0.736005\pi$
$14$	171.220	+	124.399i	0.233472	+	0.169627i
$15$	54.1995	−	39.3782i	0.0621966	−	0.0451885i
$16$	276.516	−	851.028i	0.270035	−	0.831082i
$17$	−58.8034	+	180.978i	−0.0493492	+	0.151881i	−0.972694	−	0.232090i	$-0.925444\pi$
$17$	−58.8034	+	180.978i	−0.0493492	+	0.151881i	0.923345	+	0.383971i	$0.125444\pi$
$18$	5.87542	−	4.26874i	0.00427423	−	0.00310541i
$19$	581.843	+	422.733i	0.369761	+	0.268647i	0.757112	−	0.653285i	$-0.226610\pi$
$19$	581.843	+	422.733i	0.369761	+	0.268647i	−0.387351	+	0.921933i	$0.626610\pi$
$20$	−40.1744	−	123.644i	−0.0224582	−	0.0691192i
$21$	−2859.70			−1.41505
$22$	−270.141	+	383.220i	−0.118996	+	0.168808i
$23$	−2310.03			−0.910537			−0.455269	−	0.890354i	$-0.650457\pi$
$23$	−2310.03			−0.910537			−0.455269	+	0.890354i	$0.650457\pi$
$24$	−356.988	−	1098.69i	−0.126510	−	0.389358i
$25$	2513.61	+	1826.24i	0.804355	+	0.584398i
$26$	567.553	−	412.351i	0.164654	−	0.119628i
$27$	1155.11	−	3555.06i	0.304939	−	0.938506i
$28$	−1714.87	+	5277.84i	−0.413368	+	1.27222i
$29$	6320.18	−	4591.88i	1.39552	−	1.01390i	0.400281	−	0.916392i	$-0.368913\pi$
$29$	6320.18	−	4591.88i	1.39552	−	1.01390i	0.995235	−	0.0975090i	$-0.0310875\pi$
$30$	−63.3229	−	46.0068i	−0.0128457	−	0.00933294i
$31$	2092.98	+	6441.53i	0.391166	+	1.20388i	0.931908	+	0.362695i	$0.118143\pi$
$31$	2092.98	+	6441.53i	0.391166	+	1.20388i	−0.540742	+	0.841188i	$0.681857\pi$
$32$	−3387.16			−0.584737
$33$	−90.5706	−	6334.69i	−0.0144778	−	1.01261i
$34$	222.324			0.0329829
$35$	237.555	+	731.118i	0.0327788	+	0.100883i
$36$	154.061	+	111.932i	0.0198123	+	0.0143945i
$37$	2492.25	−	1810.73i	0.299287	−	0.217444i	−0.427999	−	0.903779i	$-0.640781\pi$
$37$	2492.25	−	1810.73i	0.299287	−	0.217444i	0.727286	+	0.686335i	$0.240781\pi$
$38$	259.654	−	799.134i	0.0291700	−	0.0897761i
$39$	−2929.23	+	9015.24i	−0.308384	+	0.949108i
$40$	−251.241	+	182.537i	−0.0248279	+	0.0180385i
$41$	−10121.7	−	7353.86i	−0.940362	−	0.683213i	0.00814615	−	0.999967i	$-0.497407\pi$
$41$	−10121.7	−	7353.86i	−0.940362	−	0.683213i	−0.948508	+	0.316754i	$0.897407\pi$
$42$	1032.45	+	3177.55i	0.0903118	+	0.277951i
$43$	−11900.8			−0.981532			−0.490766	−	0.871292i	$-0.663283\pi$
$43$	−11900.8			−0.981532			−0.490766	+	0.871292i	$0.663283\pi$
$44$	−11745.6	−	3631.57i	−0.914624	−	0.282789i
$45$	26.3794			0.00194193
$46$	833.998	+	2566.78i	0.0581126	+	0.178852i
$47$	22907.4	+	16643.2i	1.51262	+	1.09898i	0.964997	+	0.262259i	$0.0844676\pi$
$47$	22907.4	+	16643.2i	1.51262	+	1.09898i	0.547624	+	0.836724i	$0.315532\pi$
$48$	11428.3	−	8303.17i	0.715946	−	0.520165i
$49$	4946.54	−	15223.9i	0.294315	−	0.905807i
$50$	1121.73	−	3452.33i	0.0634546	−	0.195293i
$51$	−2430.33	+	1765.74i	−0.130840	+	0.0950609i
$52$	14881.9	+	10812.3i	0.763221	+	0.554512i
$53$	−2986.90	−	9192.73i	−0.146060	−	0.449526i	0.851086	−	0.525026i	$-0.175945\pi$
$53$	−2986.90	−	9192.73i	−0.146060	−	0.449526i	−0.997146	+	0.0755004i	$0.975945\pi$
$54$	−4367.23			−0.203808
$55$	−1612.02	+	549.378i	−0.0718562	+	0.0244886i
$56$	13256.1			0.564865
$57$	3508.47	+	10798.0i	0.143031	+	0.440205i
$58$	−7384.06	−	5364.83i	−0.288221	−	0.209405i
$59$	−27184.0	+	19750.3i	−1.01668	+	0.738659i	−0.965599	−	0.260035i	$-0.916266\pi$
$59$	−27184.0	+	19750.3i	−1.01668	+	0.738659i	−0.0510783	+	0.998695i	$0.516266\pi$
$60$	634.217	−	1951.92i	0.0227436	−	0.0699977i
$61$	512.623	−	1577.69i	0.0176390	−	0.0542873i	−0.941850	−	0.336035i	$-0.890914\pi$
$61$	512.623	−	1577.69i	0.0176390	−	0.0542873i	0.959489	+	0.281747i	$0.0909140\pi$
$62$	6401.85	−	4651.22i	0.211508	−	0.153669i
$63$	−910.973	−	661.860i	−0.0289171	−	0.0210095i
$64$	−7625.63	−	23469.3i	−0.232716	−	0.716225i
$65$	2548.19			0.0748082
$66$	−7006.08	+	2387.67i	−0.197977	+	0.0674707i
$67$	−18724.7			−0.509599			−0.254800	−	0.966994i	$-0.582010\pi$
$67$	−18724.7			−0.509599			−0.254800	+	0.966994i	$0.582010\pi$
$68$	1801.44	+	5544.27i	0.0472442	+	0.145403i
$69$	−29502.8	−	21435.0i	−0.746002	−	0.542002i
$70$	726.615	−	527.917i	0.0177239	−	0.0128772i
$71$	−9853.69	+	30326.5i	−0.231981	+	0.713965i	0.765526	+	0.643405i	$0.222479\pi$
$71$	−9853.69	+	30326.5i	−0.231981	+	0.713965i	−0.997508	+	0.0705605i	$0.977521\pi$
$72$	140.566	−	432.618i	0.00319558	−	0.00983498i
$73$	9015.22	−	6549.94i	0.198002	−	0.143857i	−0.484367	−	0.874865i	$-0.660950\pi$
$73$	9015.22	−	6549.94i	0.198002	−	0.143857i	0.682369	+	0.731008i	$0.260950\pi$
$74$	−2911.77	−	2115.53i	−0.0618127	−	0.0449096i
$75$	15156.9	+	46648.1i	0.311141	+	0.957593i
$76$	22032.6			0.437554
$77$	69452.6	+	21473.8i	1.33494	+	0.412744i
$78$	11074.8			0.206110
$79$	−21447.7	−	66009.1i	−0.386645	−	1.18997i	−0.935280	−	0.353908i	$-0.884852\pi$
$79$	−21447.7	−	66009.1i	−0.386645	−	1.18997i	0.548635	−	0.836062i	$-0.315148\pi$
$80$	−3072.17	−	2232.06i	−0.0536685	−	0.0389925i
$81$	48962.4	−	35573.3i	0.829183	−	0.602436i
$82$	−4516.94	+	13901.7i	−0.0741840	+	0.228315i
$83$	16445.3	−	50613.5i	0.262027	−	0.806437i	−0.730336	−	0.683088i	$-0.760636\pi$
$83$	16445.3	−	50613.5i	0.262027	−	0.806437i	0.992363	−	0.123349i	$-0.0393636\pi$
$84$	−70875.4	+	51494.0i	−1.09597	+	0.796266i
$85$	653.322	+	474.666i	0.00980799	+	0.00712592i
$86$	4296.58	+	13223.5i	0.0626437	+	0.192797i
$87$	123328.			1.74688
$88$	419.838	+	29364.3i	0.00577930	+	0.404216i
$89$	−63932.5			−0.855552			−0.427776	−	0.903885i	$-0.640703\pi$
$89$	−63932.5			−0.855552			−0.427776	+	0.903885i	$0.640703\pi$
$90$	−9.52386	−	29.3114i	−0.000123939	−	0.000381444i
$91$	−87998.0	−	63934.3i	−1.11396	−	0.809338i
$92$	−57252.3	+	41596.2i	−0.705218	+	0.512371i
$93$	−33041.0	+	101690.i	−0.396137	+	1.21918i
$94$	10222.7	−	31462.2i	0.119329	−	0.367256i
$95$	2469.19	−	1793.97i	0.0280702	−	0.0203942i
$96$	−43259.4	−	31429.8i	−0.479074	−	0.348068i
$97$	−21792.6	−	67070.8i	−0.235169	−	0.723776i	−0.997099	−	0.0761166i	$-0.975748\pi$
$97$	−21792.6	−	67070.8i	−0.235169	−	0.723776i	0.761930	−	0.647660i	$-0.224252\pi$
$98$	−18701.9			−0.196707
$99$	1437.28	−	2038.91i	0.0147385	−	0.0209079i
$100$	95182.7			0.951827
$101$	6783.58	+	20877.7i	0.0661692	+	0.203648i	0.978675	−	0.205417i	$-0.0658550\pi$
$101$	6783.58	+	20877.7i	0.0661692	+	0.203648i	−0.912505	+	0.409065i	$0.865855\pi$
$102$	2839.43	+	2062.97i	0.0270229	+	0.0196333i
$103$	−53251.4	+	38689.4i	−0.494582	+	0.359335i	−0.806944	−	0.590628i	$-0.798880\pi$
$103$	−53251.4	+	38689.4i	−0.494582	+	0.359335i	0.312362	+	0.949963i	$0.398880\pi$
$104$	13578.4	−	41790.0i	0.123102	−	0.378869i
$105$	−3750.18	+	11541.9i	−0.0331954	+	0.102165i
$106$	−9136.11	+	6637.77i	−0.0789763	+	0.0573796i
$107$	107282.	+	77945.2i	0.905877	+	0.658158i	0.939969	−	0.341261i	$-0.110854\pi$
$107$	107282.	+	77945.2i	0.905877	+	0.658158i	−0.0340919	+	0.999419i	$0.510854\pi$
$108$	−35386.7	−	108909.i	−0.291932	−	0.898473i
$109$	44774.4			0.360964			0.180482	−	0.983578i	$-0.442234\pi$
$109$	44774.4			0.360964			0.180482	+	0.983578i	$0.442234\pi$
$110$	1192.43	+	1592.85i	0.00939621	+	0.0125514i
$111$	48632.0			0.374640
$112$	50090.1	+	154161.i	0.377317	+	1.16126i
$113$	−20158.4	−	14645.9i	−0.148511	−	0.107900i	0.511048	−	0.859552i	$-0.329257\pi$
$113$	−20158.4	−	14645.9i	−0.148511	−	0.107900i	−0.659560	+	0.751652i	$0.729257\pi$
$114$	10731.5	−	7796.87i	0.0773387	−	0.0561899i
$115$	−3029.35	+	9323.37i	−0.0213602	+	0.0657398i
$116$	73955.8	−	227613.i	0.510302	−	1.57055i
$117$	−3019.65	+	2193.90i	−0.0203935	+	0.0148167i
$118$	31759.9	+	23074.9i	0.209978	+	0.152558i
$119$	−10652.1	−	32783.8i	−0.0689552	−	0.212222i
$120$	−4902.53			−0.0310790
$121$	−45368.2	+	154529.i	−0.281701	+	0.959502i
$122$	−1938.12			−0.0117891
$123$	−61033.4	−	187841.i	−0.363751	−	1.11951i
$124$	167864.	+	121960.i	0.980401	+	0.712303i
$125$	21396.1	−	15545.1i	0.122478	−	0.0889856i
$126$	−406.533	+	1251.18i	−0.00228123	+	0.00702091i
$127$	−69424.9	+	213668.i	−0.381949	+	1.17552i	0.556720	+	0.830700i	$0.312060\pi$
$127$	−69424.9	+	213668.i	−0.381949	+	1.17552i	−0.938669	+	0.344819i	$0.887940\pi$
$128$	−111013.	+	80655.9i	−0.598894	+	0.435122i
$129$	−151992.	−	110429.i	−0.804168	−	0.584262i
$130$	−919.984	−	2831.42i	−0.00477443	−	0.0146942i
$131$	−193807.			−0.986712			−0.493356	−	0.869827i	$-0.664230\pi$
$131$	−193807.			−0.986712			−0.493356	+	0.869827i	$0.664230\pi$
$132$	−116312.	−	155370.i	−0.581019	−	0.776124i
$133$	−130281.			−0.638632
$134$	6760.27	+	20806.0i	0.0325238	+	0.100098i
$135$	−12833.6	−	9324.13i	−0.0606056	−	0.0440326i
$136$	11265.8	−	8185.06i	0.0522292	−	0.0379467i
$137$	24846.4	−	76469.2i	0.113100	−	0.348085i	−0.878446	−	0.477841i	$-0.841419\pi$
$137$	24846.4	−	76469.2i	0.113100	−	0.348085i	0.991546	+	0.129756i	$0.0414194\pi$
$138$	−13166.0	+	40520.7i	−0.0588512	+	0.181125i
$139$	252199.	−	183234.i	1.10715	−	0.804393i	0.124939	−	0.992164i	$-0.460126\pi$
$139$	252199.	−	183234.i	1.10715	−	0.804393i	0.982213	+	0.187771i	$0.0601264\pi$
$140$	19052.7	+	13842.6i	0.0821555	+	0.0596895i
$141$	138130.	+	425120.i	0.585113	+	1.80079i
$142$	37254.8			0.155046
$143$	138838.	−	196955.i	0.567763	−	0.805427i
$144$	5562.29			0.0223536
$145$	−10244.8	−	31530.3i	−0.0404654	−	0.124540i
$146$	−10532.8	−	7652.49i	−0.0408940	−	0.0297112i
$147$	204440.	−	148534.i	0.780319	−	0.566935i
$148$	29163.1	−	89754.9i	0.109441	−	0.336825i
$149$	−138206.	+	425355.i	−0.509990	+	1.56959i	0.282226	+	0.959348i	$0.408927\pi$
$149$	−138206.	+	425355.i	−0.509990	+	1.56959i	−0.792216	+	0.610241i	$0.791073\pi$
$150$	46360.8	−	33683.1i	0.168238	−	0.122232i
$151$	−84139.2	−	61130.7i	−0.300300	−	0.218181i	0.427423	−	0.904052i	$-0.359422\pi$
$151$	−84139.2	−	61130.7i	−0.300300	−	0.218181i	−0.727723	+	0.685871i	$0.759422\pi$
$152$	−16263.5	−	50053.8i	−0.0570958	−	0.175723i
$153$	−1182.87			−0.00408515
$154$	−1214.22	−	84924.8i	−0.00412567	−	0.288558i
$155$	28743.0			0.0960954
$156$	89737.0	+	276182.i	0.295230	+	0.908623i
$157$	41161.5	+	29905.5i	0.133273	+	0.0968284i	0.652424	−	0.757854i	$-0.273752\pi$
$157$	41161.5	+	29905.5i	0.133273	+	0.0968284i	−0.519152	+	0.854682i	$0.673752\pi$
$158$	−65602.5	+	47663.0i	−0.209063	+	0.151893i
$159$	47152.9	−	145122.i	0.147916	−	0.455239i
$160$	−4441.88	+	13670.7i	−0.0137173	+	0.0422174i
$161$	338537.	−	245962.i	1.02930	−	0.747830i
$162$	−57204.2	−	41561.3i	−0.171254	−	0.124423i
$163$	59930.4	+	184447.i	0.176676	+	0.543753i	0.999706	−	0.0242448i	$-0.00771812\pi$
$163$	59930.4	+	184447.i	0.176676	+	0.543753i	−0.823030	+	0.567998i	$0.807718\pi$
$164$	−383279.			−1.11277
$165$	−25685.9	−	7941.70i	−0.0734487	−	0.0227093i
$166$	−62176.3			−0.175128
$167$	−136143.	−	419005.i	−0.377750	−	1.16259i	−0.941605	−	0.336720i	$-0.890682\pi$
$167$	−136143.	−	419005.i	−0.377750	−	1.16259i	0.563855	−	0.825874i	$-0.309318\pi$
$168$	169301.	+	123005.i	0.462793	+	0.336239i
$169$	8690.90	−	6314.31i	0.0234071	−	0.0170063i
$170$	291.553	−	897.308i	0.000773741	−	0.00238133i
$171$	−1381.48	+	4251.77i	−0.00361290	+	0.0111194i
$172$	−294952.	+	214295.i	−0.760204	+	0.552320i
$173$	237244.	+	172368.i	0.602671	+	0.437866i	0.846826	−	0.531870i	$-0.178510\pi$
$173$	237244.	+	172368.i	0.602671	+	0.437866i	−0.244155	+	0.969736i	$0.578510\pi$
$174$	−44525.4	−	137035.i	−0.111490	−	0.343130i
$175$	−562823.			−1.38924
$176$	−339906.	+	115840.i	−0.827137	+	0.281889i
$177$	−530449.			−1.27265
$178$	23081.8	+	71038.4i	0.0546034	+	0.168052i
$179$	315173.	+	228987.i	0.735219	+	0.534168i	0.891210	−	0.453590i	$-0.149857\pi$
$179$	315173.	+	228987.i	0.735219	+	0.534168i	−0.155991	+	0.987758i	$0.549857\pi$
$180$	653.794	−	475.009i	0.00150404	−	0.00109275i
$181$	184766.	−	568651.i	0.419204	−	1.29018i	−0.489232	−	0.872154i	$-0.662723\pi$
$181$	184766.	−	568651.i	0.419204	−	1.29018i	0.908436	−	0.418024i	$-0.137277\pi$
$182$	−39270.2	+	120861.i	−0.0878789	+	0.270463i
$183$	21186.6	−	15393.0i	0.0467664	−	0.0339778i
$184$	136759.	+	99361.6i	0.297792	+	0.216358i
$185$	−4039.86	−	12433.4i	−0.00867834	−	0.0267092i
$186$	124921.			0.264761
$187$	72283.9	−	24634.4i	0.151160	−	0.0515155i
$188$	867432.			1.78995
$189$	209245.	+	643989.i	0.426089	+	1.31137i
$190$	−2884.83	−	2095.95i	−0.00579744	−	0.00421209i
$191$	−48811.3	+	35463.5i	−0.0968137	+	0.0703393i	−0.635139	−	0.772398i	$-0.719057\pi$
$191$	−48811.3	+	35463.5i	−0.0968137	+	0.0703393i	0.538325	+	0.842737i	$0.319057\pi$
$192$	120383.	−	370499.i	0.235673	−	0.725328i
$193$	165821.	−	510345.i	0.320440	−	0.986213i	−0.653017	−	0.757343i	$-0.726497\pi$
$193$	165821.	−	510345.i	0.320440	−	0.986213i	0.973457	−	0.228870i	$-0.0735030\pi$
$194$	−66657.7	+	48429.7i	−0.127159	+	0.0923862i
$195$	32544.5	+	23645.0i	0.0612903	+	0.0445300i
$196$	−151537.	−	466384.i	−0.281760	−	0.867169i
$197$	308427.			0.566222			0.283111	−	0.959087i	$-0.408634\pi$
$197$	308427.			0.566222			0.283111	+	0.959087i	$0.408634\pi$
$198$	−2784.44	−	860.909i	−0.00504748	−	0.00156061i
$199$	66819.8			0.119611			0.0598057	−	0.998210i	$-0.480952\pi$
$199$	66819.8			0.119611			0.0598057	+	0.998210i	$0.480952\pi$
$200$	−70259.5	−	216236.i	−0.124202	−	0.382256i
$201$	−239145.	−	173749.i	−0.417514	−	0.303342i
$202$	20749.1	−	15075.1i	0.0357785	−	0.0259946i
$203$	−437307.	+	1.34589e6i	−0.744811	+	2.29229i
$204$	−28438.6	+	87525.1i	−0.0478446	+	0.147251i
$205$	−42954.0	+	31207.9i	−0.0713870	+	0.0518657i
$206$	62215.3	+	45202.0i	0.102148	+	0.0742147i
$207$	−4437.27	−	13656.5i	−0.00719763	−	0.0221520i
$208$	537305.			0.861117
$209$	−4126.17	−	288593.i	−0.00653404	−	0.457004i
$210$	14178.7			0.0221864
$211$	62961.0	+	193774.i	0.0973567	+	0.299633i	0.987861	−	0.155342i	$-0.0496481\pi$
$211$	62961.0	+	193774.i	0.0973567	+	0.299633i	−0.890504	+	0.454975i	$0.849648\pi$
$212$	−239560.	−	174050.i	−0.366078	−	0.265972i
$213$	−407251.	+	295885.i	−0.615054	+	0.446863i
$214$	47876.1	−	147347.i	0.0714635	−	0.219942i
$215$	−15606.6	+	48032.1i	−0.0230256	+	0.0708655i
$216$	−221300.	+	160784.i	−0.322735	+	0.234481i
$217$	−992595.	−	721162.i	−1.43094	−	1.03964i
$218$	−16165.1	−	49751.0i	−0.0230376	−	0.0709024i
$219$	175917.			0.247854
$220$	−30060.2	+	42643.3i	−0.0418731	+	0.0594010i
$221$	−114262.			−0.157370
$222$	−17557.8	−	54037.3i	−0.0239104	−	0.0735888i
$223$	−436218.	−	316931.i	−0.587410	−	0.426778i	0.253978	−	0.967210i	$-0.418261\pi$
$223$	−436218.	−	316931.i	−0.587410	−	0.426778i	−0.841388	+	0.540432i	$0.818261\pi$
$224$	496392.	−	360650.i	0.661005	−	0.480248i
$225$	−5968.13	+	18368.0i	−0.00785926	+	0.0241883i
$226$	−8995.93	+	27686.6i	−0.0117159	+	0.0360578i
$227$	−373130.	+	271095.i	−0.480613	+	0.349186i	−0.801563	−	0.597910i	$-0.795998\pi$
$227$	−373130.	+	271095.i	−0.480613	+	0.349186i	0.320950	+	0.947096i	$0.395998\pi$
$228$	281392.	+	204443.i	0.358488	+	0.260457i
$229$	230151.	+	708332.i	0.290018	+	0.892582i	0.984850	+	0.173410i	$0.0554787\pi$
$229$	230151.	+	708332.i	0.290018	+	0.892582i	−0.694832	+	0.719172i	$0.744521\pi$
$230$	11453.3			0.0142762
$231$	687764.	+	918713.i	0.848027	+	1.13279i
$232$	−571682.			−0.697324
$233$	−438526.	−	1.34965e6i	−0.529183	−	1.62866i	−0.755893	−	0.654696i	$-0.772797\pi$
$233$	−438526.	−	1.34965e6i	−0.529183	−	1.62866i	0.226709	−	0.973962i	$-0.427203\pi$
$234$	3527.95	+	2563.20i	0.00421194	+	0.00306015i
$235$	97213.0	−	70629.4i	0.114830	−	0.0834287i
$236$	−318094.	+	978994.i	−0.371771	+	1.14419i
$237$	338585.	−	1.04206e6i	0.391559	−	1.20509i
$238$	−32581.8	+	23672.1i	−0.0372849	+	0.0270891i
$239$	528029.	+	383635.i	0.597947	+	0.434434i	0.845150	−	0.534530i	$-0.179511\pi$
$239$	528029.	+	383635.i	0.597947	+	0.434434i	−0.247203	+	0.968964i	$0.579511\pi$
$240$	−18525.0	−	57014.0i	−0.0207601	−	0.0638930i
$241$	1.64843e6			1.82822			0.914111	−	0.405465i	$-0.132890\pi$
$241$	1.64843e6			1.82822			0.914111	+	0.405465i	$0.132890\pi$
$242$	188084.	−	5379.38i	0.206449	−	0.00590464i
$243$	47081.4			0.0511486
$244$	−15704.2	−	48332.6i	−0.0168866	−	0.0519716i
$245$	−54957.5	−	39928.9i	−0.0584940	−	0.0424984i
$246$	−186684.	+	135634.i	−0.196685	+	0.142900i
$247$	−133448.	+	410712.i	−0.139178	+	0.428346i
$248$	153161.	−	471380.i	0.158131	−	0.486679i
$249$	679681.	−	493817.i	0.694715	−	0.504740i
$250$	−24997.7	−	18161.9i	−0.0252959	−	0.0183785i
$251$	−269495.	−	829421.i	−0.270002	−	0.830981i	−0.990499	−	0.137522i	$-0.956086\pi$
$251$	−269495.	−	829421.i	−0.270002	−	0.830981i	0.720497	−	0.693458i	$-0.243914\pi$
$252$	−34495.8			−0.0342188
$253$	555567.	+	742125.i	0.545677	+	0.728913i
$254$	262481.			0.255278
$255$	3939.49	+	12124.5i	0.00379393	+	0.0116765i
$256$	−509153.	−	369921.i	−0.485566	−	0.352784i
$257$	−681496.	+	495136.i	−0.643622	+	0.467619i	−0.861093	−	0.508448i	$-0.830219\pi$
$257$	−681496.	+	495136.i	−0.643622	+	0.467619i	0.217471	+	0.976067i	$0.430219\pi$
$258$	−67828.4	+	208754.i	−0.0634398	+	0.195248i
$259$	−172444.	+	530728.i	−0.159735	+	0.491612i
$260$	63155.0	−	45884.8i	0.0579395	−	0.0420955i
$261$	39286.7	+	28543.5i	0.0356980	+	0.0259361i
$262$	69970.8	+	215348.i	0.0629743	+	0.193815i
$263$	−604334.			−0.538751			−0.269375	−	0.963035i	$-0.586817\pi$
$263$	−604334.			−0.538751			−0.269375	+	0.963035i	$0.586817\pi$
$264$	−267113.	+	378925.i	−0.235877	+	0.334614i
$265$	−41019.2			−0.0358817
$266$	47035.7	+	144761.i	0.0407590	+	0.125443i
$267$	−816521.	−	593237.i	−0.700953	−	0.509272i
$268$	−464079.	+	337173.i	−0.394689	+	0.286758i
$269$	163136.	−	502081.i	0.137458	−	0.423051i	−0.858506	−	0.512803i	$-0.828607\pi$
$269$	163136.	−	502081.i	0.137458	−	0.423051i	0.995964	+	0.0897513i	$0.0286072\pi$
$270$	−5727.14	+	17626.3i	−0.00478110	+	0.0147147i
$271$	−566450.	+	411550.i	−0.468531	+	0.340408i	−0.796869	−	0.604153i	$-0.793512\pi$
$271$	−566450.	+	411550.i	−0.468531	+	0.340408i	0.328337	+	0.944560i	$0.393512\pi$
$272$	137758.	+	100087.i	0.112900	+	0.0820265i
$273$	−530622.	−	1.63309e6i	−0.430902	−	1.32618i
$274$	−93939.0			−0.0755909
$275$	−17825.4	−	1.24674e6i	−0.0142137	−	0.994135i
$276$	−1.11718e6			−0.882776
$277$	589788.	+	1.81518e6i	0.461845	+	1.42141i	0.862907	+	0.505363i	$0.168641\pi$
$277$	589788.	+	1.81518e6i	0.461845	+	1.42141i	−0.401062	+	0.916051i	$0.631359\pi$
$278$	−294652.	−	214077.i	−0.228664	−	0.166134i
$279$	−34060.9	+	24746.7i	−0.0261966	+	0.0190330i
$280$	17383.9	−	53502.0i	0.0132511	−	0.0407826i
$281$	139788.	−	430223.i	0.105610	−	0.325033i	−0.884263	−	0.466989i	$-0.845339\pi$
$281$	139788.	−	430223.i	0.105610	−	0.325033i	0.989873	+	0.141955i	$0.0453389\pi$
$282$	422502.	−	306965.i	0.316378	−	0.229862i
$283$	555496.	+	403591.i	0.412301	+	0.299554i	0.774533	−	0.632534i	$-0.217985\pi$
$283$	555496.	+	403591.i	0.412301	+	0.299554i	−0.362232	+	0.932088i	$0.617985\pi$
$284$	301868.	+	929054.i	0.222086	+	0.683510i
$285$	48182.1			0.0351377
$286$	−268971.	−	83161.9i	−0.194442	−	0.0601187i
$287$	2.26636e6			1.62414
$288$	−6506.29	−	20024.3i	−0.00462224	−	0.0142258i
$289$	1.11939e6	+	813287.i	0.788384	+	0.572795i
$290$	−31336.1	+	22767.0i	−0.0218801	+	0.0158968i
$291$	344031.	−	1.05882e6i	0.238158	−	0.732975i
$292$	105492.	−	324671.i	0.0724039	−	0.222836i
$293$	−2.04809e6	+	1.48803e6i	−1.39374	+	1.01261i	−0.398292	+	0.917259i	$0.630397\pi$
$293$	−2.04809e6	+	1.48803e6i	−1.39374	+	1.01261i	−0.995444	+	0.0953492i	$0.969603\pi$
$294$	−238853.	−	173537.i	−0.161162	−	0.117091i
$295$	44064.3	+	135616.i	0.0294803	+	0.0907311i
$296$	−225433.			−0.149550
$297$	−1.41991e6	+	483907.i	−0.934051	+	0.318325i
$298$	522529.			0.340855
$299$	−428630.	−	1.31919e6i	−0.277271	−	0.853353i
$300$	1.21564e6	+	883211.i	0.779831	+	0.566580i
$301$	1.74407e6	−	1.26714e6i	1.10955	−	0.806139i
$302$	−37548.2	+	115561.i	−0.0236903	+	0.0729114i
$303$	−107090.	+	329588.i	−0.0670102	+	0.206236i
$304$	520647.	−	378272.i	0.323116	−	0.234758i
$305$	−5695.39	−	4137.94i	−0.00350569	−	0.00254703i
$306$	427.055	+	1314.34i	0.000260724	+	0.000802425i
$307$	313287.			0.189713			0.0948564	−	0.995491i	$-0.469761\pi$
$307$	313287.			0.189713			0.0948564	+	0.995491i	$0.469761\pi$
$308$	2.10800e6	−	718409.i	1.26618	−	0.431514i
$309$	−1.03911e6			−0.619107
$310$	−10377.2	−	31937.7i	−0.00613304	−	0.0188755i
$311$	758078.	+	550776.i	0.444440	+	0.322904i	0.787396	−	0.616447i	$-0.211428\pi$
$311$	758078.	+	550776.i	0.444440	+	0.322904i	−0.342957	+	0.939351i	$0.611428\pi$
$312$	561192.	−	407730.i	0.326381	−	0.237130i
$313$	8634.28	−	26573.6i	0.00498156	−	0.0153317i	−0.948535	−	0.316673i	$-0.897434\pi$
$313$	8634.28	−	26573.6i	0.00498156	−	0.0153317i	0.953516	+	0.301341i	$0.0974343\pi$
$314$	18368.8	−	56533.4i	0.0105137	−	0.0323579i
$315$	−3865.94	+	2808.77i	−0.00219522	+	0.00159492i
$316$	−1.72018e6	−	1.24978e6i	−0.969070	−	0.704071i
$317$	541030.	+	1.66512e6i	0.302394	+	0.930673i	0.980637	+	0.195835i	$0.0627418\pi$
$317$	541030.	+	1.66512e6i	0.302394	+	0.930673i	−0.678243	+	0.734838i	$0.737258\pi$
$318$	−178276.			−0.0988607
$319$	−2.99522e6	−	926079.i	−1.64798	−	0.509532i
$320$	−104723.			−0.0571699
$321$	646906.	+	1.99097e6i	0.350412	+	1.07846i
$322$	−395523.	−	287365.i	−0.212585	−	0.154452i
$323$	−110720.	+	80442.8i	−0.0590500	+	0.0429023i
$324$	572935.	−	1.76331e6i	0.303210	−	0.933183i
$325$	−576508.	+	1.77431e6i	−0.302759	+	0.931796i
$326$	183311.	−	133183.i	0.0955309	−	0.0694072i
$327$	571842.	+	415467.i	0.295738	+	0.214866i
$328$	282919.	+	870735.i	0.145204	+	0.446891i
$329$	−5.12920e6			−2.61252
$330$	449.058	+	31408.0i	0.000226996	+	0.0158765i
$331$	−972232.			−0.487753			−0.243876	−	0.969806i	$-0.578419\pi$
$331$	−972232.			−0.487753			−0.243876	+	0.969806i	$0.578419\pi$
$332$	−503802.	−	1.55054e6i	−0.250850	−	0.772038i
$333$	15492.0	+	11255.6i	0.00765591	+	0.00556235i
$334$	−416424.	+	302550.i	−0.204254	+	0.148399i
$335$	−24555.4	+	75573.9i	−0.0119546	+	0.0367925i
$336$	−790751.	+	2.43368e6i	−0.382113	+	1.17602i
$337$	1.72068e6	−	1.25015e6i	0.825325	−	0.599634i	−0.0929080	−	0.995675i	$-0.529616\pi$
$337$	1.72068e6	−	1.25015e6i	0.825325	−	0.599634i	0.918233	+	0.396041i	$0.129616\pi$
$338$	−10153.8	−	7377.20i	−0.00483435	−	0.00351236i
$339$	−121554.	−	374104.i	−0.0574472	−	0.176804i
$340$	24739.3			0.0116062
$341$	1.56605e6	−	2.22160e6i	0.729325	−	1.03462i
$342$	5223.11			0.00241470
$343$	−44762.2	−	137764.i	−0.0205436	−	0.0632266i
$344$	704556.	+	511890.i	0.321011	+	0.233228i
$345$	−125202.	+	90964.8i	−0.0566323	+	0.0411458i
$346$	105873.	−	325844.i	0.0475440	−	0.146325i
$347$	−363739.	+	1.11947e6i	−0.162168	+	0.499103i	−0.998816	−	0.0486378i	$-0.984512\pi$
$347$	−363739.	+	1.11947e6i	−0.162168	+	0.499103i	0.836648	+	0.547741i	$0.184512\pi$
$348$	3.05658e6	−	2.22073e6i	1.35297	−	0.982989i
$349$	168550.	+	122459.i	0.0740739	+	0.0538178i	0.624206	−	0.781260i	$-0.285423\pi$
$349$	168550.	+	122459.i	0.0740739	+	0.0538178i	−0.550132	+	0.835078i	$0.685423\pi$
$350$	203198.	+	625380.i	0.0886645	+	0.272881i
$351$	2.24452e6			0.972424
$352$	814619.	+	1.08817e6i	0.350427	+	0.468100i
$353$	1.18986e6			0.508229			0.254115	−	0.967174i	$-0.418216\pi$
$353$	1.18986e6			0.508229			0.254115	+	0.967174i	$0.418216\pi$
$354$	191510.	+	589407.i	0.0812238	+	0.249981i
$355$	109477.	+	79539.8i	0.0461055	+	0.0334976i
$356$	−1.58452e6	+	1.15122e6i	−0.662632	+	0.481430i
$357$	168160.	−	517543.i	0.0698316	−	0.214920i
$358$	140650.	−	432876.i	0.0580005	−	0.178507i
$359$	2.06614e6	−	1.50114e6i	0.846103	−	0.614730i	−0.0779659	−	0.996956i	$-0.524843\pi$
$359$	2.06614e6	−	1.50114e6i	0.846103	−	0.614730i	0.924069	+	0.382226i	$0.124843\pi$
$360$	−1561.73	−	1134.66i	−0.000635110	−	0.000461435i
$361$	−605319.	−	1.86298e6i	−0.244465	−	0.752386i
$362$	−698562.			−0.280178
$363$	−2.01332e6	+	1.55261e6i	−0.801946	+	0.618436i
$364$	−3.33221e6			−1.31819
$365$	−14613.4	−	44975.3i	−0.00574141	−	0.0176702i
$366$	−24753.0	−	17984.1i	−0.00965883	−	0.00701755i
$367$	2.18325e6	−	1.58623e6i	0.846133	−	0.614752i	−0.0779440	−	0.996958i	$-0.524836\pi$
$367$	2.18325e6	−	1.58623e6i	0.846133	−	0.614752i	0.924077	+	0.382206i	$0.124836\pi$
$368$	−638759.	+	1.96590e6i	−0.245877	+	0.756731i
$369$	24032.3	−	73963.8i	0.00918817	−	0.0282783i
$370$	−12356.8	+	8977.75i	−0.00469248	+	0.00340929i
$371$	1.41654e6	+	1.02917e6i	0.534310	+	0.388199i
$372$	1.01221e6	+	3.11526e6i	0.379239	+	1.16718i
$373$	−737149.			−0.274336			−0.137168	−	0.990548i	$-0.543800\pi$
$373$	−737149.			−0.274336			−0.137168	+	0.990548i	$0.543800\pi$
$374$	−53469.4	−	71424.3i	−0.0197663	−	0.0264038i
$375$	417507.			0.153315
$376$	−640298.	−	1.97064e6i	−0.233568	−	0.718847i
$377$	3.79501e6	+	2.75723e6i	1.37518	+	0.999126i
$378$	640023.	−	465004.i	0.230391	−	0.167389i
$379$	1.41497e6	−	4.35483e6i	0.505998	−	1.55730i	−0.293088	−	0.956086i	$-0.594683\pi$
$379$	1.41497e6	−	4.35483e6i	0.505998	−	1.55730i	0.799086	−	0.601217i	$-0.205317\pi$
$380$	28893.3	−	88924.5i	0.0102645	−	0.0315909i
$381$	−2.86932e6	+	2.08468e6i	−1.01267	+	0.735745i
$382$	57027.7	+	41433.0i	0.0199953	+	0.0145274i
$383$	−586683.	−	1.80563e6i	−0.204365	−	0.628971i	−0.999739	−	0.0228520i	$-0.992725\pi$
$383$	−586683.	−	1.80563e6i	−0.204365	−	0.628971i	0.795374	−	0.606119i	$-0.207275\pi$
$384$	−2.16623e6			−0.749682
$385$	177748.	−	252153.i	0.0611159	−	0.0866987i
$386$	−626936.			−0.214168
$387$	−22859.9	−	70355.4i	−0.00775883	−	0.0238792i
$388$	−1.74784e6	−	1.26988e6i	−0.589418	−	0.428237i
$389$	−2.87277e6	+	2.08719e6i	−0.962558	+	0.699340i	−0.953744	−	0.300622i	$-0.902806\pi$
$389$	−2.87277e6	+	2.08719e6i	−0.962558	+	0.699340i	−0.00881487	+	0.999961i	$0.502806\pi$
$390$	14523.4	−	44698.4i	0.00483512	−	0.0148810i
$391$	135838.	−	418065.i	0.0449343	−	0.138294i
$392$	−947676.	+	688527.i	−0.311490	+	0.226311i
$393$	−2.47522e6	−	1.79836e6i	−0.808413	−	0.587346i
$394$	−111353.	−	342708.i	−0.0361376	−	0.111220i
$395$	−294542.			−0.0949848
$396$	−1092.53	−	76413.7i	−0.000350102	−	0.0244869i
$397$	2.15116e6			0.685010			0.342505	−	0.939516i	$-0.388725\pi$
$397$	2.15116e6			0.685010			0.342505	+	0.939516i	$0.388725\pi$
$398$	−24124.2	−	74246.7i	−0.00763389	−	0.0234947i
$399$	−1.66389e6	−	1.20889e6i	−0.523231	−	0.380149i
$400$	2.24924e6	−	1.63417e6i	0.702886	−	0.510677i
$401$	−1.13193e6	+	3.48372e6i	−0.351527	+	1.08189i	0.606469	+	0.795107i	$0.292586\pi$
$401$	−1.13193e6	+	3.48372e6i	−0.351527	+	1.08189i	−0.957996	+	0.286782i	$0.907414\pi$
$402$	−106721.	+	328455.i	−0.0329372	+	0.101370i
$403$	−3.29021e6	+	2.39047e6i	−1.00916	+	0.733198i
$404$	544067.	+	395288.i	0.165844	+	0.120493i
$405$	−79366.4	−	244265.i	−0.0240436	−	0.0739986i
$406$	1.65337e6			0.497799
$407$	−1.18111e6	−	365183.i	−0.353431	−	0.109276i
$408$	219832.			0.0653794
$409$	1.43058e6	+	4.40288e6i	0.422868	+	1.30145i	0.905021	+	0.425366i	$0.139855\pi$
$409$	1.43058e6	+	4.40288e6i	0.422868	+	1.30145i	−0.482154	+	0.876087i	$0.660145\pi$
$410$	50184.5	+	36461.2i	0.0147438	+	0.0107120i
$411$	1.02690e6	−	746083.i	0.299862	−	0.217863i
$412$	−623123.	+	1.91778e6i	−0.180855	+	0.556615i
$413$	1.88092e6	−	5.78887e6i	0.542619	−	1.67001i
$414$	−13572.4	+	9860.92i	−0.00389184	+	0.00282759i
$415$	−182712.	−	132748.i	−0.0520771	−	0.0378362i
$416$	−628493.	−	1.93430e6i	−0.178060	−	0.548014i
$417$	4.92124e6			1.38591
$418$	−319179.	+	108776.i	−0.0893499	+	0.0304505i
$419$	5.15655e6			1.43491			0.717454	−	0.696606i	$-0.245307\pi$
$419$	5.15655e6			1.43491			0.717454	+	0.696606i	$0.245307\pi$
$420$	114887.	+	353585.i	0.0317795	+	0.0978071i
$421$	−1.07409e6	−	780373.i	−0.295349	−	0.214584i	0.430235	−	0.902717i	$-0.358431\pi$
$421$	−1.07409e6	−	780373.i	−0.295349	−	0.214584i	−0.725585	+	0.688133i	$0.758431\pi$
$422$	192581.	−	139918.i	0.0526419	−	0.0382466i
$423$	−54389.6	+	167394.i	−0.0147797	+	0.0454871i
$424$	−218576.	+	672709.i	−0.0590457	+	0.181724i
$425$	−478319.	+	347519.i	−0.128453	+	0.0933269i
$426$	475804.	+	345692.i	0.127029	+	0.0922922i
$427$	92860.4	+	285795.i	0.0246468	+	0.0758551i
$428$	4.06246e6			1.07196
$429$	3.60075e6	−	1.22714e6i	0.944603	−	0.321921i
$430$	59005.2			0.0153893
$431$	−111758.	−	343955.i	−0.0289791	−	0.0891884i	0.935521	−	0.353271i	$-0.114931\pi$
$431$	−111758.	−	343955.i	−0.0289791	−	0.0891884i	−0.964500	+	0.264083i	$0.914931\pi$
$432$	−2.70605e6	−	1.96606e6i	−0.697631	−	0.506859i
$433$	−4.60469e6	+	3.34550e6i	−1.18027	+	0.857515i	−0.992202	−	0.124641i	$-0.960222\pi$
$433$	−4.60469e6	+	3.34550e6i	−1.18027	+	0.857515i	−0.188066	+	0.982156i	$0.560222\pi$
$434$	−442958.	+	1.36328e6i	−0.112885	+	0.347426i
$435$	161730.	−	497755.i	0.0409797	−	0.126123i
$436$	1.10970e6	−	806245.i	0.279569	−	0.203119i
$437$	−1.34407e6	−	976526.i	−0.336681	−	0.244613i
$438$	−63511.8	−	195469.i	−0.0158186	−	0.0486848i
$439$	1.16384e6			0.288224			0.144112	−	0.989561i	$-0.453967\pi$
$439$	1.16384e6			0.288224			0.144112	+	0.989561i	$0.453967\pi$
$440$	119066.	+	36813.6i	0.0293195	+	0.00906518i
$441$	99502.8			0.0243635
$442$	41252.6	+	126962.i	0.0100437	+	0.0309115i
$443$	−2.77119e6	−	2.01339e6i	−0.670900	−	0.487437i	0.199427	−	0.979913i	$-0.436092\pi$
$443$	−2.77119e6	−	2.01339e6i	−0.670900	−	0.487437i	−0.870326	+	0.492476i	$0.836092\pi$
$444$	1.20531e6	−	875707.i	0.290162	−	0.210815i
$445$	−83840.4	+	258034.i	−0.0200703	+	0.0617700i
$446$	−194667.	+	599125.i	−0.0463400	+	0.142620i
$447$	−5.71204e6	+	4.15004e6i	−1.35214	+	0.982388i
$448$	3.61645e6	+	2.62751e6i	0.851310	+	0.618513i
$449$	−637292.	−	1.96138e6i	−0.149184	−	0.459141i	0.848341	−	0.529450i	$-0.177602\pi$
$449$	−637292.	−	1.96138e6i	−0.149184	−	0.459141i	−0.997525	+	0.0703086i	$0.977602\pi$
$450$	22564.3			0.00525279
$451$	71778.8	+	5.02035e6i	0.0166171	+	1.16223i
$452$	−763336.			−0.175740
$453$	−507354.	−	1.56147e6i	−0.116162	−	0.357511i
$454$	435939.	+	316728.i	0.0992627	+	0.0721186i
$455$	−373441.	+	271321.i	−0.0845656	+	0.0614405i
$456$	256744.	−	790178.i	0.0578214	−	0.177956i
$457$	1.77640e6	−	5.46720e6i	0.397879	−	1.22454i	−0.528818	−	0.848735i	$-0.677365\pi$
$457$	1.77640e6	−	5.46720e6i	0.397879	−	1.22454i	0.926697	−	0.375810i	$-0.122635\pi$
$458$	703969.	−	511464.i	0.156816	−	0.113933i
$459$	575464.	+	418099.i	0.127493	+	0.0926291i
$460$	92804.1	+	285621.i	0.0204490	+	0.0629356i
$461$	−5.34566e6			−1.17152			−0.585759	−	0.810485i	$-0.699204\pi$
$461$	−5.34566e6			−1.17152			−0.585759	+	0.810485i	$0.699204\pi$
$462$	772520.	−	1.09589e6i	0.168386	−	0.238871i
$463$	−8.36736e6			−1.81399			−0.906997	−	0.421136i	$-0.861631\pi$
$463$	−8.36736e6			−1.81399			−0.906997	+	0.421136i	$0.861631\pi$
$464$	−2.16019e6	−	6.64838e6i	−0.465797	−	1.43358i
$465$	367094.	+	266710.i	0.0787309	+	0.0572013i
$466$	−1.34133e6	+	974535.i	−0.286136	+	0.207890i
$467$	−1.15066e6	+	3.54137e6i	−0.244149	+	0.751414i	0.751626	+	0.659590i	$0.229270\pi$
$467$	−1.15066e6	+	3.54137e6i	−0.244149	+	0.751414i	−0.995775	+	0.0918244i	$0.970730\pi$
$468$	−35334.5	+	108748.i	−0.00745735	+	0.0229514i
$469$	2.74413e6	−	1.99373e6i	0.576067	−	0.418538i
$470$	−113577.	−	82518.4i	−0.0237162	−	0.0172308i
$471$	248201.	+	763884.i	0.0515527	+	0.158663i
$472$	2.45888e6			0.508023
$473$	2.86217e6	+	3.82327e6i	0.588223	+	0.785747i
$474$	−1.28012e6			−0.261701
$475$	690510.	+	2.12517e6i	0.140422	+	0.432176i
$476$	−854335.	−	620710.i	−0.172827	−	0.125566i
$477$	48608.4	−	35316.1i	0.00978173	−	0.00710684i
$478$	235639.	−	725223.i	0.0471713	−	0.145178i
$479$	−866969.	+	2.66826e6i	−0.172649	+	0.531360i	−0.999518	−	0.0310347i	$-0.990120\pi$
$479$	−866969.	+	2.66826e6i	−0.172649	+	0.531360i	0.826869	+	0.562394i	$0.190120\pi$
$480$	−183582.	+	133380.i	−0.0363687	+	0.0264234i
$481$	1.49649e6	+	1.08727e6i	0.294925	+	0.214276i
$482$	−595140.	−	1.83165e6i	−0.116681	−	0.359108i
$483$	6.60598e6			1.28846
$484$	1.65815e6	+	4.64681e6i	0.321745	+	0.901658i
$485$	−299279.			−0.0577727
$486$	−16998.0	−	52314.4i	−0.00326443	−	0.0100469i
$487$	−1.90348e6	−	1.38296e6i	−0.363685	−	0.264233i	0.390902	−	0.920432i	$-0.372163\pi$
$487$	−1.90348e6	−	1.38296e6i	−0.363685	−	0.264233i	−0.754587	+	0.656199i	$0.772163\pi$
$488$	−98210.2	+	71353.9i	−0.0186684	+	0.0135634i
$489$	−946095.	+	2.91178e6i	−0.178922	+	0.550664i
$490$	−24525.4	+	75481.6i	−0.00461452	+	0.0142020i
$491$	5.51611e6	−	4.00769e6i	1.03259	−	0.750222i	0.0637666	−	0.997965i	$-0.479689\pi$
$491$	5.51611e6	−	4.00769e6i	1.03259	−	0.750222i	0.968826	+	0.247742i	$0.0796887\pi$
$492$	−4.89509e6	−	3.55649e6i	−0.911691	−	0.662382i
$493$	459383.	+	1.41384e6i	0.0851251	+	0.261988i
$494$	504541.			0.0930206
$495$	−6344.31	−	8474.72i	−0.00116378	−	0.00155458i
$496$	6.06066e6			1.10615
$497$	−1.78497e6	−	5.49357e6i	−0.324145	−	0.997617i
$498$	−794092.	−	576942.i	−0.143482	−	0.104246i
$499$	1.81240e6	−	1.31679e6i	0.325839	−	0.236736i	−0.412824	−	0.910811i	$-0.635457\pi$
$499$	1.81240e6	−	1.31679e6i	0.325839	−	0.236736i	0.738663	+	0.674075i	$0.235457\pi$
$500$	250367.	−	770549.i	0.0447870	−	0.137840i
$501$	2.14923e6	−	6.61465e6i	0.382551	−	1.17737i
$502$	−824313.	+	598898.i	−0.145993	+	0.106070i
$503$	4.66764e6	+	3.39124e6i	0.822578	+	0.597638i	0.917450	−	0.397851i	$-0.130244\pi$
$503$	4.66764e6	+	3.39124e6i	0.822578	+	0.597638i	−0.0948717	+	0.995490i	$0.530244\pi$
$504$	25463.2	+	78367.6i	0.00446515	+	0.0137423i
$505$	93159.3			0.0162554
$506$	624032.	−	885250.i	0.108350	−	0.153706i
$507$	169588.			0.0293005
$508$	2.12683e6	+	6.54572e6i	0.365657	+	1.12538i
$509$	1.63866e6	+	1.19056e6i	0.280347	+	0.203684i	0.719069	−	0.694939i	$-0.244569\pi$
$509$	1.63866e6	+	1.19056e6i	0.280347	+	0.203684i	−0.438722	+	0.898623i	$0.644569\pi$
$510$	12049.8	−	8754.72i	0.00205142	−	0.00149045i
$511$	−623782.	+	1.91980e6i	−0.105677	+	0.325241i
$512$	−1.58412e6	+	4.87542e6i	−0.267063	+	0.821935i
$513$	2.17493e6	−	1.58018e6i	0.364882	−	0.265102i
$514$	796212.	+	578482.i	0.132929	+	0.0965789i
$515$	86318.8	+	265662.i	0.0143413	+	0.0441379i
$516$	−5.75548e6			−0.951606
$517$	−162449.	−	1.13620e7i	−0.0267295	−	1.86951i
$518$	651976.			0.106760
$519$	1.43057e6	+	4.40284e6i	0.233126	+	0.717487i
$520$	−150860.	−	109606.i	−0.0244661	−	0.0177756i
$521$	−1.85868e6	+	1.35041e6i	−0.299993	+	0.217957i	−0.727591	−	0.686012i	$-0.759360\pi$
$521$	−1.85868e6	+	1.35041e6i	−0.299993	+	0.217957i	0.427598	+	0.903969i	$0.359360\pi$
$522$	17532.2	−	53958.5i	0.00281617	−	0.00866729i
$523$	−2.43812e6	+	7.50377e6i	−0.389764	+	1.19957i	0.543201	+	0.839603i	$0.317212\pi$
$523$	−2.43812e6	+	7.50377e6i	−0.389764	+	1.19957i	−0.932965	+	0.359967i	$0.882788\pi$
$524$	−4.80335e6	+	3.48984e6i	−0.764216	+	0.555235i
$525$	−7.18816e6	−	5.22250e6i	−1.13820	−	0.826952i
$526$	218185.	+	671505.i	0.0343843	+	0.105824i
$527$	−1.28885e6			−0.202151
$528$	−5.41604e6	−	1.67456e6i	−0.845468	−	0.261407i
$529$	−1.10011e6			−0.170922
$530$	14809.3	+	45578.4i	0.00229005	+	0.00704806i
$531$	−168978.	−	122769.i	−0.0260071	−	0.0188953i
$532$	−3.22891e6	+	2.34594e6i	−0.494625	+	0.359366i
$533$	2.32147e6	−	7.14474e6i	0.353952	−	1.08935i
$534$	−364382.	+	1.12145e6i	−0.0552974	+	0.170188i
$535$	455279.	−	330780.i	0.0687691	−	0.0499637i
$536$	1.10855e6	+	805410.i	0.166665	+	0.121089i
$537$	1.90048e6	+	5.84906e6i	0.284398	+	0.875287i
$538$	−616784.			−0.0918708
$539$	−6.08052e6	+	2.07225e6i	−0.901507	+	0.307234i
$540$	−485968.			−0.0717172
$541$	−1.60958e6	−	4.95376e6i	−0.236439	−	0.727683i	−0.996927	−	0.0783319i	$-0.975041\pi$
$541$	−1.60958e6	−	4.95376e6i	−0.236439	−	0.727683i	0.760489	−	0.649351i	$-0.224959\pi$
$542$	661801.	+	480826.i	0.0967674	+	0.0703056i
$543$	7.63634e6	−	5.54812e6i	1.11144	−	0.807508i
$544$	199176.	−	613002.i	0.0288563	−	0.0888106i
$545$	58716.8	−	180712.i	0.00846780	−	0.0260612i
$546$	−1.62303e6	+	1.17920e6i	−0.232994	+	0.169280i
$547$	−5.80627e6	−	4.21851e6i	−0.829716	−	0.602824i	0.0897633	−	0.995963i	$-0.471389\pi$
$547$	−5.80627e6	−	4.21851e6i	−0.829716	−	0.602824i	−0.919479	+	0.393139i	$0.871389\pi$
$548$	−761168.	−	2.34264e6i	−0.108275	−	0.333237i
$549$	10311.7			0.00146016
$550$	−1.37888e6	+	469923.i	−0.194366	+	0.0662400i
$551$	5.61850e6			0.788390
$552$	824651.	+	2.53801e6i	0.115192	+	0.354525i
$553$	1.01715e7	+	7.39006e6i	1.41441	+	1.02763i
$554$	1.80400e6	−	1.31068e6i	0.249725	−	0.181436i
$555$	63775.5	−	196281.i	0.00878863	−	0.0270486i
$556$	2.95112e6	−	9.08261e6i	0.404855	−	1.24602i
$557$	−5.17980e6	+	3.76334e6i	−0.707416	+	0.513968i	−0.882339	−	0.470615i	$-0.844032\pi$
$557$	−5.17980e6	+	3.76334e6i	−0.707416	+	0.513968i	0.174923	+	0.984582i	$0.444032\pi$
$558$	39794.4	+	28912.3i	0.00541048	+	0.00393095i
$559$	−2.20821e6	−	6.79618e6i	−0.298890	−	0.919889i
$560$	687890.			0.0926934
$561$	1.15177e6	+	356110.i	0.154510	+	0.0477724i
$562$	−528510.			−0.0705849
$563$	1.25277e6	+	3.85563e6i	0.166571	+	0.512654i	0.999149	−	0.0412550i	$-0.0131356\pi$
$563$	1.25277e6	+	3.85563e6i	0.166571	+	0.512654i	−0.832577	+	0.553909i	$0.813136\pi$
$564$	1.10785e7	+	8.04900e6i	1.46650	+	1.06548i
$565$	−85547.1	+	62153.6i	−0.0112742	+	0.00819115i
$566$	247897.	−	762948.i	0.0325259	−	0.100105i
$567$	−3.38781e6	+	1.04266e7i	−0.442549	+	1.36203i
$568$	1.88780e6	−	1.37157e6i	0.245520	−	0.178380i
$569$	9.46671e6	+	6.87797e6i	1.22580	+	0.890594i	0.996568	−	0.0827787i	$-0.0263794\pi$
$569$	9.46671e6	+	6.87797e6i	1.22580	+	0.890594i	0.229229	+	0.973372i	$0.426379\pi$
$570$	−17395.4	−	53537.4i	−0.00224257	−	0.00690192i
$571$	−1.12121e7			−1.43912			−0.719558	−	0.694432i	$-0.755655\pi$
$571$	−1.12121e7			−1.43912			−0.719558	+	0.694432i	$0.755655\pi$
$572$	−105536.	−	7.38139e6i	−0.0134868	−	0.943297i
$573$	−952469.			−0.121189
$574$	−818232.	−	2.51826e6i	−0.103657	−	0.319022i
$575$	−5.80650e6	−	4.21867e6i	−0.732395	−	0.532116i
$576$	124099.	−	90162.8i	0.0155851	−	0.0113233i
$577$	1.38010e6	−	4.24752e6i	0.172573	−	0.531124i	−0.826942	−	0.562288i	$-0.809921\pi$
$577$	1.38010e6	−	4.24752e6i	0.172573	−	0.531124i	0.999514	+	0.0311636i	$0.00992128\pi$
$578$	499543.	−	1.53744e6i	0.0621947	−	0.191416i
$579$	6.85336e6	−	4.97926e6i	0.849585	−	0.617260i
$580$	−821669.	−	596978.i	−0.101421	−	0.0736865i
$581$	2.97902e6	+	9.16849e6i	0.366129	+	1.12683i
$582$	−1.30071e6			−0.159174
$583$	−2.23492e6	+	3.17045e6i	−0.272327	+	0.386322i
$584$	−815457.			−0.0989394
$585$	4894.75	+	15064.5i	0.000591345	+	0.00181997i
$586$	2.39285e6	+	1.73851e6i	0.287853	+	0.209137i
$587$	7.70872e6	−	5.60072e6i	0.923394	−	0.670885i	−0.0209723	−	0.999780i	$-0.506676\pi$
$587$	7.70872e6	−	5.60072e6i	0.923394	−	0.670885i	0.944367	+	0.328895i	$0.106676\pi$
$588$	2.39226e6	−	7.36261e6i	0.285341	−	0.878190i
$589$	−1.50526e6	+	4.63273e6i	−0.178782	+	0.550235i
$590$	134781.	−	97924.0i	0.0159404	−	0.0115813i
$591$	3.93911e6	+	2.86193e6i	0.463905	+	0.337047i
$592$	−851832.	−	2.62167e6i	−0.0998964	−	0.307449i
$593$	−9.50659e6			−1.11017			−0.555083	−	0.831795i	$-0.687314\pi$
$593$	−9.50659e6			−1.11017			−0.555083	+	0.831795i	$0.687314\pi$
$594$	1.05033e6	+	1.40303e6i	0.122140	+	0.163155i
$595$	−146286.			−0.0169398
$596$	4.23395e6	+	1.30308e7i	0.488236	+	1.50264i
$597$	853397.	+	620029.i	0.0979976	+	0.0711994i
$598$	−1.31106e6	+	952543.i	−0.149924	+	0.108926i
$599$	2.95570e6	−	9.09671e6i	0.336584	−	1.03590i	−0.629353	−	0.777120i	$-0.716680\pi$
$599$	2.95570e6	−	9.09671e6i	0.336584	−	1.03590i	0.965937	−	0.258779i	$-0.0833200\pi$
$600$	1.10916e6	−	3.41363e6i	0.125781	−	0.387114i
$601$	7.35060e6	−	5.34052e6i	0.830112	−	0.603112i	−0.0894791	−	0.995989i	$-0.528520\pi$
$601$	7.35060e6	−	5.34052e6i	0.830112	−	0.603112i	0.919591	+	0.392877i	$0.128520\pi$
$602$	−2.03765e6	−	1.48044e6i	−0.229160	−	0.166495i
$603$	−35967.8	−	110698.i	−0.00402829	−	0.0123978i
$604$	−3.18609e6			−0.355358
$605$	564190.	+	385755.i	0.0626667	+	0.0428473i
$606$	404884.			0.0447867
$607$	−3.66056e6	−	1.12661e7i	−0.403252	−	1.24108i	−0.922346	−	0.386364i	$-0.873731\pi$
$607$	−3.66056e6	−	1.12661e7i	−0.403252	−	1.24108i	0.519094	−	0.854717i	$-0.326269\pi$
$608$	−1.97079e6	−	1.43186e6i	−0.216213	−	0.157088i
$609$	−1.80738e7	+	1.31314e7i	−1.97472	+	1.43472i
$610$	−2541.64	+	7822.35i	−0.000276560	+	0.000851163i
$611$	−5.25391e6	+	1.61699e7i	−0.569350	+	1.75228i
$612$	−29316.5	+	21299.7i	−0.00316398	+	0.00229876i
$613$	−7.97639e6	−	5.79518e6i	−0.857344	−	0.622897i	0.0698172	−	0.997560i	$-0.477758\pi$
$613$	−7.97639e6	−	5.79518e6i	−0.857344	−	0.622897i	−0.927161	+	0.374663i	$0.877758\pi$
$614$	−113107.	−	348108.i	−0.0121079	−	0.0372643i
$615$	−838174.			−0.0893607
$616$	−3.18812e6	−	4.25868e6i	−0.338518	−	0.452192i
$617$	−1.27512e7			−1.34847			−0.674233	−	0.738519i	$-0.735525\pi$
$617$	−1.27512e7			−1.34847			−0.674233	+	0.738519i	$0.735525\pi$
$618$	375154.	+	1.15461e6i	0.0395129	+	0.121608i
$619$	−1.00983e7	−	7.33687e6i	−1.05931	−	0.769634i	−0.0853497	−	0.996351i	$-0.527201\pi$
$619$	−1.00983e7	−	7.33687e6i	−1.05931	−	0.769634i	−0.973961	+	0.226717i	$0.927201\pi$
$620$	712373.	−	517569.i	0.0744266	−	0.0540741i
$621$	−2.66833e6	+	8.21228e6i	−0.277658	+	0.854545i
$622$	338302.	−	1.04118e6i	0.0350613	−	0.107908i
$623$	9.36939e6	−	6.80726e6i	0.967144	−	0.702671i
$624$	6.86224e6	+	4.98571e6i	0.705512	+	0.512585i
$625$	2.96567e6	+	9.12740e6i	0.303685	+	0.934645i
$626$	−32644.4			−0.00332946
$627$	2.62519e6	−	3.72408e6i	0.266681	−	0.378312i
$628$	1.55866e6			0.157707
$629$	181149.	+	557520.i	0.0182562	+	0.0561868i
$630$	4516.69	+	3281.57i	0.000453387	+	0.000329405i
$631$	6.76159e6	−	4.91258e6i	0.676045	−	0.491175i	−0.195998	−	0.980604i	$-0.562795\pi$
$631$	6.76159e6	−	4.91258e6i	0.676045	−	0.491175i	0.872043	+	0.489429i	$0.162795\pi$
$632$	−1.56950e6	+	4.83044e6i	−0.156304	+	0.481054i
$633$	−993939.	+	3.05903e6i	−0.0985940	+	0.303441i
$634$	1.65486e6	−	1.20233e6i	0.163508	−	0.118796i
$635$	771329.	+	560404.i	0.0759112	+	0.0551527i
$636$	−1.44453e6	−	4.44581e6i	−0.141607	−	0.435821i
$637$	9.61175e6			0.938543
$638$	52364.5	+	3.66248e6i	0.00509314	+	0.356224i
$639$	−198213.			−0.0192035
$640$	179949.	+	553826.i	0.0173660	+	0.0534470i
$641$	2.53001e6	+	1.83816e6i	0.243207	+	0.176700i	0.702711	−	0.711475i	$-0.251973\pi$
$641$	2.53001e6	+	1.83816e6i	0.243207	+	0.176700i	−0.459504	+	0.888176i	$0.651973\pi$
$642$	1.97871e6	−	1.43762e6i	0.189472	−	0.137659i
$643$	147654.	−	454432.i	0.0140837	−	0.0433452i	−0.943768	−	0.330609i	$-0.892746\pi$
$643$	147654.	−	454432.i	0.0140837	−	0.0433452i	0.957851	+	0.287264i	$0.0927457\pi$
$644$	3.96141e6	−	1.21920e7i	0.376387	−	1.15840i
$645$	−645016.	+	468632.i	−0.0610480	+	0.0443539i
$646$	129357.	+	93983.7i	0.0121958	+	0.00886077i
$647$	2.06257e6	+	6.34794e6i	0.193708	+	0.596172i	0.999989	+	0.00463983i	$0.00147691\pi$
$647$	2.06257e6	+	6.34794e6i	0.193708	+	0.596172i	−0.806281	+	0.591533i	$0.798523\pi$
$648$	−4.42882e6			−0.414334
$649$	1.28829e7	+	3.98320e6i	1.20061	+	0.371210i
$650$	2.17966e6			0.202351
$651$	−5.98528e6	−	1.84208e7i	−0.553519	−	1.70356i
$652$	4.80662e6	+	3.49222e6i	0.442814	+	0.321723i
$653$	4.88919e6	−	3.55220e6i	0.448698	−	0.325998i	−0.340384	−	0.940287i	$-0.610557\pi$
$653$	4.88919e6	−	3.55220e6i	0.448698	−	0.325998i	0.789081	+	0.614289i	$0.210557\pi$
$654$	255191.	−	785399.i	0.0233304	−	0.0718035i
$655$	−254156.	+	782212.i	−0.0231471	+	0.0712396i
$656$	−9.05716e6	+	6.58041e6i	−0.821736	+	0.597026i
$657$	56039.2	+	40714.9i	0.00506499	+	0.00367993i
$658$	1.85181e6	+	5.69929e6i	0.166737	+	0.513164i
$659$	1.79600e7			1.61099			0.805494	−	0.592604i	$-0.201900\pi$
$659$	1.79600e7			1.61099			0.805494	+	0.592604i	$0.201900\pi$
$660$	−779609.	+	265691.i	−0.0696654	+	0.0237420i
$661$	365793.			0.0325635			0.0162818	−	0.999867i	$-0.494817\pi$
$661$	365793.			0.0325635			0.0162818	+	0.999867i	$0.494817\pi$
$662$	351009.	+	1.08029e6i	0.0311295	+	0.0958069i
$663$	−1.45932e6	−	1.06025e6i	−0.128933	−	0.0936756i
$664$	−3.15065e6	+	2.28908e6i	−0.277319	+	0.201484i
$665$	−170849.	+	525818.i	−0.0149816	+	0.0461086i
$666$	6913.50	−	21277.6i	0.000603966	−	0.00185881i
$667$	−1.45998e7	+	1.06074e7i	−1.27067	+	0.923195i
$668$	−1.09191e7	−	7.93322e6i	−0.946776	−	0.687873i
$669$	−2.63036e6	−	8.09543e6i	−0.227222	−	0.699318i
$670$	92839.1			0.00798994
$671$	−630141.	+	214752.i	−0.0540295	+	0.0184133i
$672$	9.68624e6			0.827432
$673$	3.27872e6	+	1.00909e7i	0.279040	+	0.858796i	0.988122	+	0.153671i	$0.0491095\pi$
$673$	3.27872e6	+	1.00909e7i	0.279040	+	0.858796i	−0.709082	+	0.705126i	$0.750891\pi$
$674$	−2.01032e6	−	1.46058e6i	−0.170457	−	0.123844i
$675$	9.39589e6	−	6.82651e6i	0.793740	−	0.576686i
$676$	101697.	−	312991.i	0.00855935	−	0.0263430i
$677$	2.71723e6	−	8.36278e6i	0.227853	−	0.701260i	−0.770136	−	0.637879i	$-0.779812\pi$
$677$	2.71723e6	−	8.36278e6i	0.227853	−	0.701260i	0.997989	−	0.0633803i	$-0.0201881\pi$
$678$	−371800.	+	270128.i	−0.0310624	+	0.0225682i
$679$	1.03352e7	+	7.50893e6i	0.860285	+	0.625034i
$680$	−18261.4	−	56202.9i	−0.00151448	−	0.00466108i
$681$	−7.28099e6			−0.601621
$682$	−3.03392e6	−	938046.i	−0.249772	−	0.0772259i
$683$	−1.25712e7			−1.03116			−0.515579	−	0.856842i	$-0.672423\pi$
$683$	−1.25712e7			−1.03116			−0.515579	+	0.856842i	$0.672423\pi$
$684$	42321.8	+	130253.i	0.00345879	+	0.0106451i
$685$	−276050.	−	200562.i	−0.0224782	−	0.0163314i
$686$	−136915.	+	99474.8i	−0.0111082	+	0.00807055i
$687$	−3.63330e6	+	1.11821e7i	−0.293704	+	0.903927i
$688$	−3.29075e6	+	1.01279e7i	−0.265048	+	0.815733i
$689$	4.69547e6	−	3.41146e6i	0.376817	−	0.273774i
$690$	146278.	+	106277.i	0.0116965	+	0.00849799i
$691$	−949084.	−	2.92098e6i	−0.0756153	−	0.232720i	0.906104	−	0.423055i	$-0.139042\pi$
$691$	−949084.	−	2.92098e6i	−0.0756153	−	0.232720i	−0.981719	+	0.190335i	$0.939042\pi$
$692$	8.98372e6			0.713166
$693$	6460.22	+	451840.i	0.000510992	+	0.0357398i
$694$	1.37522e6			0.108386
$695$	−408807.	−	1.25818e6i	−0.0321038	−	0.0988053i
$696$	−7.30130e6	−	5.30471e6i	−0.571317	−	0.415086i
$697$	1.92608e6	−	1.39938e6i	0.150173	−	0.109107i
$698$	75217.5	−	231496.i	0.00584360	−	0.0179847i
$699$	6.92283e6	−	2.13063e7i	0.535909	−	1.64936i
$700$	−1.39491e7	+	1.01346e7i	−1.07598	+	0.781742i
$701$	−2.01356e7	−	1.46294e7i	−1.54764	−	1.12442i	−0.945309	−	0.326177i	$-0.894239\pi$
$701$	−2.01356e7	−	1.46294e7i	−1.54764	−	1.12442i	−0.602329	−	0.798248i	$-0.705761\pi$
$702$	−810347.	−	2.49399e6i	−0.0620624	−	0.191008i
$703$	2.21555e6			0.169081
$704$	−5.70581e6	+	8.09424e6i	−0.433896	+	0.615523i
$705$	1.89694e6			0.143741
$706$	−429580.	−	1.32211e6i	−0.0324364	−	0.0998290i
$707$	−3.21711e6	−	2.33737e6i	−0.242057	−	0.175865i
$708$	−1.31468e7	+	9.55169e6i	−0.985680	+	0.716139i
$709$	−6.48613e6	+	1.99622e7i	−0.484585	+	1.49140i	0.347996	+	0.937496i	$0.386862\pi$
$709$	−6.48613e6	+	1.99622e7i	−0.484585	+	1.49140i	−0.832581	+	0.553903i	$0.813138\pi$
$710$	48855.6	−	150362.i	0.00363721	−	0.0111942i
$711$	349037.	−	253590.i	0.0258939	−	0.0188130i
$712$	3.78496e6	+	2.74994e6i	0.279809	+	0.203293i
$713$	−4.83484e6	−	1.48801e7i	−0.356171	−	1.09618i
$714$	−635779.			−0.0466724
$715$	−612847.	−	818639.i	−0.0448319	−	0.0598863i
$716$	1.19347e7			0.870016
$717$	3.18398e6	+	9.79928e6i	0.231298	+	0.711863i
$718$	−2.41393e6	−	1.75382e6i	−0.174749	−	0.126962i
$719$	−1.91017e7	+	1.38782e7i	−1.37800	+	1.00118i	−0.380937	+	0.924601i	$0.624399\pi$
$719$	−1.91017e7	+	1.38782e7i	−1.37800	+	1.00118i	−0.997064	+	0.0765755i	$0.975601\pi$
$720$	7294.32	−	22449.6i	0.000524389	−	0.00161390i
$721$	3.68458e6	−	1.13400e7i	0.263967	−	0.812407i
$722$	−1.85151e6	+	1.34520e6i	−0.132185	+	0.0960381i
$723$	2.10532e7	+	1.52960e7i	1.49786	+	1.08826i
$724$	−5.66030e6	−	1.74206e7i	−0.401322	−	1.23514i
$725$	2.42724e7			1.71501
$726$	2.45205e6	+	1.67655e6i	0.172658	+	0.118052i
$727$	2.51178e7			1.76257			0.881283	−	0.472590i	$-0.156681\pi$
$727$	2.51178e7			1.76257			0.881283	+	0.472590i	$0.156681\pi$
$728$	2.45969e6	+	7.57014e6i	0.172009	+	0.529390i
$729$	−1.12966e7	−	8.20743e6i	−0.787277	−	0.571990i
$730$	−44698.3	+	32475.2i	−0.00310445	+	0.00225551i
$731$	699807.	−	2.15378e6i	0.0484378	−	0.149076i
$732$	247916.	−	763007.i	0.0171012	−	0.0526321i
$733$	3.33459e6	−	2.42272e6i	0.229236	−	0.166549i	−0.467238	−	0.884131i	$-0.654751\pi$
$733$	3.33459e6	−	2.42272e6i	0.229236	−	0.166549i	0.696474	+	0.717582i	$0.254751\pi$
$734$	−2.55076e6	−	1.85323e6i	−0.174755	−	0.126967i
$735$	−331390.	−	1.01991e6i	−0.0226267	−	0.0696378i
$736$	7.82443e6			0.532424
$737$	4.50335e6	+	6.01556e6i	0.305398	+	0.407950i
$738$	−90861.1			−0.00614097
$739$	−2.53850e6	−	7.81270e6i	−0.170988	−	0.526248i	0.828439	−	0.560079i	$-0.189229\pi$
$739$	−2.53850e6	−	7.81270e6i	−0.170988	−	0.526248i	−0.999428	+	0.0338311i	$0.989229\pi$
$740$	−324010.	−	235407.i	−0.0217510	−	0.0158030i
$741$	−5.51540e6	+	4.00717e6i	−0.369004	+	0.268097i
$742$	632147.	−	1.94555e6i	0.0421510	−	0.129728i
$743$	2.23902e6	−	6.89098e6i	0.148794	−	0.457940i	−0.848685	−	0.528898i	$-0.822605\pi$
$743$	2.23902e6	−	6.89098e6i	0.148794	−	0.457940i	0.997479	+	0.0709575i	$0.0226055\pi$
$744$	6.33010e6	−	4.59909e6i	0.419255	−	0.304607i
$745$	1.53551e6	+	1.11561e6i	0.101359	+	0.0736415i
$746$	266136.	+	819081.i	0.0175088	+	0.0538865i
$747$	330808.			0.0216907
$748$	1.34792e6	−	1.91215e6i	0.0880864	−	0.124959i
$749$	−2.40217e7			−1.56458
$750$	−150734.	−	463912.i	−0.00978496	−	0.0301150i
$751$	2.48301e6	+	1.80401e6i	0.160649	+	0.116719i	0.665206	−	0.746660i	$-0.268344\pi$
$751$	2.48301e6	+	1.80401e6i	0.160649	+	0.116719i	−0.504556	+	0.863379i	$0.668344\pi$
$752$	2.04980e7	−	1.48927e7i	1.32181	−	0.960348i
$753$	4.25441e6	−	1.30937e7i	0.273434	−	0.841542i
$754$	1.69357e6	−	5.21227e6i	0.108486	−	0.333886i
$755$	−357065.	+	259423.i	−0.0227971	+	0.0165631i
$756$	1.67822e7	+	1.21930e7i	1.06793	+	0.775897i
$757$	6.58486e6	+	2.02661e7i	0.417645	+	1.28538i	0.909864	+	0.414907i	$0.136186\pi$
$757$	6.58486e6	+	2.02661e7i	0.417645	+	1.28538i	−0.492220	+	0.870471i	$0.663814\pi$
$758$	−5.34971e6			−0.338187
$759$	209221.	+	1.46333e7i	0.0131826	+	0.922015i
$760$	−223347.			−0.0140264
$761$	4.90461e6	+	1.50948e7i	0.307003	+	0.944859i	0.978922	+	0.204234i	$0.0654703\pi$
$761$	4.90461e6	+	1.50948e7i	0.307003	+	0.944859i	−0.671919	+	0.740625i	$0.734530\pi$
$762$	3.35231e6	+	2.43560e6i	0.209149	+	0.151956i
$763$	−6.56175e6	+	4.76739e6i	−0.408045	+	0.296462i
$764$	−571167.	+	1.75787e6i	−0.0354021	+	0.108957i
$765$	−1551.20	+	4774.11i	−9.58329e−5	+	0.000294943i
$766$	−1.79450e6	+	1.30378e6i	−0.110503	+	0.0802849i
$767$	−1.63229e7	−	1.18593e7i	−1.00186	−	0.727895i
$768$	−3.07016e6	−	9.44897e6i	−0.187827	−	0.578072i
$769$	−1.62876e7			−0.993209			−0.496605	−	0.867977i	$-0.665420\pi$
$769$	−1.62876e7			−0.993209			−0.496605	+	0.867977i	$0.665420\pi$
$770$	−344353.	−	106469.i	−0.0209304	−	0.00647137i
$771$	−1.32982e7			−0.805671
$772$	−5.07993e6	−	1.56344e7i	−0.306771	−	0.944145i
$773$	1.11623e7	+	8.10988e6i	0.671900	+	0.488164i	0.870661	−	0.491884i	$-0.163692\pi$
$773$	1.11623e7	+	8.10988e6i	0.671900	+	0.488164i	−0.198761	+	0.980048i	$0.563692\pi$
$774$	−69922.1	+	50801.4i	−0.00419529	+	0.00304806i
$775$	−6.50287e6	+	2.00138e7i	−0.388911	+	1.19695i
$776$	−1.59475e6	+	4.90813e6i	−0.0950688	+	0.292592i
$777$	−7.12708e6	+	5.17813e6i	−0.423506	+	0.307695i
$778$	3.35634e6	+	2.43853e6i	0.198801	+	0.144437i
$779$	−2.78053e6	−	8.55758e6i	−0.164166	−	0.505251i
$780$	1.23236e6			0.0725274
$781$	1.21126e7	−	4.12799e6i	0.710576	−	0.242165i
$782$	−513574.			−0.0300321
$783$	−9.02391e6	−	2.77727e7i	−0.526005	−	1.61888i
$784$	−1.15882e7	−	8.41930e6i	−0.673325	−	0.489199i
$785$	174679.	−	126912.i	0.0101173	−	0.00735067i
$786$	−1.10460e6	+	3.39961e6i	−0.0637747	+	0.196278i
$787$	−6.30921e6	+	1.94178e7i	−0.363110	+	1.11754i	0.588046	+	0.808827i	$0.299897\pi$
$787$	−6.30921e6	+	1.94178e7i	−0.363110	+	1.11754i	−0.951156	+	0.308710i	$0.900103\pi$
$788$	7.64413e6	−	5.55378e6i	0.438543	−	0.318620i
$789$	−7.71832e6	−	5.60769e6i	−0.441398	−	0.320694i
$790$	106340.	+	327279.i	0.00606215	+	0.0186574i
$791$	4.51367e6			0.256501
$792$	−172791.	+	58887.1i	−0.00978829	+	0.00333585i
$793$	996091.			0.0562492
$794$	−776642.	−	2.39026e6i	−0.0437190	−	0.134553i
$795$	−523882.	−	380622.i	−0.0293978	−	0.0213588i
$796$	1.65608e6	−	1.20321e6i	0.0926400	−	0.0673069i
$797$	1.38675e6	−	4.26799e6i	0.0773310	−	0.238000i	−0.904917	−	0.425589i	$-0.860067\pi$
$797$	1.38675e6	−	4.26799e6i	0.0773310	−	0.238000i	0.982248	+	0.187588i	$0.0600671\pi$
$798$	−742533.	+	2.28528e6i	−0.0412770	+	0.127038i
$799$	−4.35909e6	+	3.16706e6i	−0.241562	+	0.175505i
$800$	−8.51398e6	−	6.18577e6i	−0.470336	−	0.341719i
$801$	−122806.	−	377958.i	−0.00676299	−	0.0208143i
$802$	4.27960e6			0.234945
$803$	−4.27243e6	−	1.32098e6i	−0.233823	−	0.0722946i
$804$	−9.05570e6			−0.494062
$805$	−548758.	−	1.68890e6i	−0.0298463	−	0.0918576i
$806$	3.84405e6	+	2.79286e6i	0.208426	+	0.151430i
$807$	6.74238e6	−	4.89863e6i	0.364443	−	0.264783i
$808$	496412.	−	1.52780e6i	0.0267494	−	0.0823261i
$809$	3.73408e6	−	1.14923e7i	0.200591	−	0.617357i	−0.799274	−	0.600967i	$-0.794782\pi$
$809$	3.73408e6	−	1.14923e7i	0.200591	−	0.617357i	0.999866	−	0.0163905i	$-0.00521750\pi$
$810$	−242760.	+	176376.i	−0.0130007	+	0.00944553i
$811$	−619519.	−	450107.i	−0.0330752	−	0.0240306i	0.571125	−	0.820863i	$-0.306507\pi$
$811$	−619519.	−	450107.i	−0.0330752	−	0.0240306i	−0.604200	+	0.796833i	$0.706507\pi$
$812$	1.33969e7	+	4.12314e7i	0.713041	+	2.19451i
$813$	−1.10533e7			−0.586497
$814$	20649.0	+	1.44423e6i	0.00109229	+	0.0763969i
$815$	823027.			0.0434030
$816$	830670.	+	2.55654e6i	0.0436720	+	0.134409i
$817$	−6.92438e6	−	5.03086e6i	−0.362933	−	0.263686i
$818$	4.37576e6	−	3.17918e6i	0.228650	−	0.166124i
$819$	208936.	−	643039.i	0.0108844	−	0.0334987i
$820$	−502628.	+	1.54693e6i	−0.0261043	+	0.0803408i
$821$	6.59201e6	−	4.78938e6i	0.341319	−	0.247983i	−0.403899	−	0.914803i	$-0.632345\pi$
$821$	6.59201e6	−	4.78938e6i	0.341319	−	0.247983i	0.745218	+	0.666821i	$0.232345\pi$
$822$	−1.19975e6	−	871671.i	−0.0619316	−	0.0449959i
$823$	4.45500e6	+	1.37111e7i	0.229270	+	0.705622i	0.997830	+	0.0658435i	$0.0209738\pi$
$823$	4.45500e6	+	1.37111e7i	0.229270	+	0.705622i	−0.768560	+	0.639778i	$0.779026\pi$
$824$	4.81678e6			0.247137
$825$	1.13410e7	−	1.60883e7i	0.580119	−	0.822955i
$826$	−7.11137e6			−0.362663
$827$	9.24299e6	+	2.84470e7i	0.469947	+	1.44635i	0.852653	+	0.522477i	$0.174992\pi$
$827$	9.24299e6	+	2.84470e7i	0.469947	+	1.44635i	−0.382706	+	0.923870i	$0.625008\pi$
$828$	−355884.	−	258565.i	−0.0180398	−	0.0131067i
$829$	6.36896e6	−	4.62732e6i	0.321871	−	0.233853i	−0.415102	−	0.909775i	$-0.636254\pi$
$829$	6.36896e6	−	4.62732e6i	0.321871	−	0.233853i	0.736973	+	0.675922i	$0.236254\pi$
$830$	−81537.4	+	250946.i	−0.00410830	+	0.0126440i
$831$	−9.31073e6	+	2.86555e7i	−0.467715	+	1.43948i
$832$	1.19876e7	−	8.70953e6i	0.600379	−	0.436201i
$833$	2.46432e6	+	1.79044e6i	0.123051	+	0.0894018i
$834$	−1.77673e6	−	5.46823e6i	−0.0884519	−	0.272227i
$835$	−1.86966e6			−0.0927996
$836$	−5.29890e6	−	7.07825e6i	−0.262222	−	0.350276i
$837$	2.53176e7			1.24913
$838$	−1.86169e6	−	5.72969e6i	−0.0915792	−	0.281852i
$839$	−2.39346e6	−	1.73895e6i	−0.117388	−	0.0852870i	0.527543	−	0.849529i	$-0.323114\pi$
$839$	−2.39346e6	−	1.73895e6i	−0.117388	−	0.0852870i	−0.644930	+	0.764242i	$0.723114\pi$
$840$	718472.	−	522000.i	0.0351327	−	0.0255254i
$841$	1.25210e7	−	3.85358e7i	0.610451	−	1.87877i
$842$	−479327.	+	1.47522e6i	−0.0232998	+	0.0717093i
$843$	5.77741e6	−	4.19753e6i	0.280004	−	0.203435i
$844$	5.04969e6	+	3.66882e6i	0.244011	+	0.177284i
$845$	−14087.7	−	43357.4i	−0.000678730	−	0.00208892i
$846$	205636.			0.00987808
$847$	−9.80480e6	−	2.74770e7i	−0.469603	−	1.31601i
$848$	−8.64919e6			−0.413034
$849$	3.34960e6	+	1.03090e7i	0.159487	+	0.490849i
$850$	558835.	+	406017.i	0.0265299	+	0.0192751i
$851$	−5.75717e6	+	4.18283e6i	−0.272512	+	0.197991i
$852$	−4.76546e6	+	1.46666e7i	−0.224909	+	0.692197i
$853$	396203.	−	1.21939e6i	0.0186442	−	0.0573811i	−0.941302	−	0.337567i	$-0.890396\pi$
$853$	396203.	−	1.21939e6i	0.0186442	−	0.0573811i	0.959946	+	0.280186i	$0.0903961\pi$
$854$	284035.	−	206363.i	0.0133268	−	0.00968250i
$855$	15348.7	+	11151.5i	0.000718051	+	0.000521695i
$856$	−2.99872e6	−	9.22911e6i	−0.139879	−	0.430502i
$857$	1.95541e6			0.0909464			0.0454732	−	0.998966i	$-0.485520\pi$
$857$	1.95541e6			0.0909464			0.0454732	+	0.998966i	$0.485520\pi$
$858$	−2.66352e6	−	3.55792e6i	−0.123520	−	0.164998i
$859$	2.83084e7			1.30898			0.654489	−	0.756072i	$-0.272884\pi$
$859$	2.83084e7			1.30898			0.654489	+	0.756072i	$0.272884\pi$
$860$	478107.	+	1.47146e6i	0.0220434	+	0.0678427i
$861$	2.89451e7	+	2.10298e7i	1.33066	+	0.966780i
$862$	−341836.	+	248359.i	−0.0156693	+	0.0113844i
$863$	8.52559e6	−	2.62391e7i	0.389671	−	1.19928i	−0.543364	−	0.839497i	$-0.682850\pi$
$863$	8.52559e6	−	2.62391e7i	0.389671	−	1.19928i	0.933035	−	0.359786i	$-0.117150\pi$
$864$	−3.91253e6	+	1.20415e7i	−0.178309	+	0.548779i
$865$	1.00680e6	−	731486.i	0.0457515	−	0.0332404i
$866$	5.37980e6	+	3.90865e6i	0.243765	+	0.177106i
$867$	6.74987e6	+	2.07740e7i	0.304963	+	0.938581i
$868$	−3.75865e7			−1.69330
$869$	−1.60480e7	+	2.27657e7i	−0.720896	+	1.02266i
$870$	−611470.			−0.0273890
$871$	−3.47441e6	−	1.06931e7i	−0.155180	−	0.477595i
$872$	−2.65076e6	−	1.92589e6i	−0.118054	−	0.0857710i
$873$	354651.	−	257669.i	0.0157494	−	0.0114426i
$874$	−599809.	+	1.84602e6i	−0.0265604	+	0.0817445i
$875$	−1.48044e6	+	4.55632e6i	−0.0653688	+	0.201184i
$876$	4.35996e6	−	3.16769e6i	0.191965	−	0.139471i
$877$	−2.48123e7	−	1.80272e7i	−1.08935	−	0.791459i	−0.110061	−	0.993925i	$-0.535104\pi$
$877$	−2.48123e7	−	1.80272e7i	−1.08935	−	0.791459i	−0.979289	+	0.202466i	$0.935104\pi$
$878$	−420184.	−	1.29319e6i	−0.0183952	−	0.0566145i
$879$	−3.99650e7			−1.74465
$880$	21786.4	+	1.52379e6i	0.000948374	+	0.0663312i
$881$	−3.78279e7			−1.64200			−0.820999	−	0.570930i	$-0.806583\pi$
$881$	−3.78279e7			−1.64200			−0.820999	+	0.570930i	$0.806583\pi$
$882$	−35923.9	−	110562.i	−0.00155493	−	0.00478559i
$883$	2.21825e7	+	1.61166e7i	0.957435	+	0.695617i	0.952554	−	0.304371i	$-0.0984462\pi$
$883$	2.21825e7	+	1.61166e7i	0.957435	+	0.695617i	0.00488150	+	0.999988i	$0.498446\pi$
$884$	−2.83191e6	+	2.05750e6i	−0.121884	+	0.0885543i
$885$	−695625.	+	2.14091e6i	−0.0298550	+	0.0918843i
$886$	−1.23668e6	+	3.80611e6i	−0.0529265	+	0.162891i
$887$	−1.56277e7	+	1.13542e7i	−0.666940	+	0.484560i	−0.869000	−	0.494813i	$-0.835237\pi$
$887$	−1.56277e7	+	1.13542e7i	−0.666940	+	0.484560i	0.202059	+	0.979373i	$0.435237\pi$
$888$	−2.87914e6	−	2.09182e6i	−0.122526	−	0.0890207i
$889$	−1.25761e7	−	3.87054e7i	−0.533695	−	1.64254i
$890$	316983.			0.0134141
$891$	−2.32039e7	−	7.17433e6i	−0.979191	−	0.302752i
$892$	−1.65182e7			−0.695106
$893$	6.29285e6	+	1.93674e7i	0.264070	+	0.812724i
$894$	6.67354e6	+	4.84861e6i	0.279262	+	0.202896i
$895$	1.33752e6	−	971762.i	0.0558138	−	0.0405511i
$896$	7.68124e6	−	2.36404e7i	0.319640	−	0.983752i
$897$	6.76660e6	−	2.08255e7i	0.280795	−	0.864198i
$898$	−1.94930e6	+	1.41625e6i	−0.0806656	+	0.0586070i
$899$	4.28067e7	+	3.11009e7i	1.76650	+	1.28344i
$900$	182834.	+	562704.i	0.00752402	+	0.0231565i
$901$	1.83933e6			0.0754826
$902$	5.55244e6	−	1.89227e6i	0.227231	−	0.0774404i
$903$	3.40326e7			1.38892
$904$	563460.	+	1.73415e6i	0.0229320	+	0.0705774i
$905$	−2.05280e6	−	1.49145e6i	−0.0833154	−	0.0605321i
$906$	−1.55186e6	+	1.12749e6i	−0.0628104	+	0.0456344i
$907$	−4.35815e6	+	1.34130e7i	−0.175908	+	0.541388i	−0.999674	−	0.0255420i	$-0.991869\pi$
$907$	−4.35815e6	+	1.34130e7i	−0.175908	+	0.541388i	0.823766	+	0.566930i	$0.191869\pi$
$908$	−4.36619e6	+	1.34378e7i	−0.175747	+	0.540894i
$909$	−110395.	+	80206.8i	−0.00443140	+	0.00321960i
$910$	436302.	+	316992.i	0.0174656	+	0.0126895i
$911$	−8.66268e6	−	2.66610e7i	−0.345825	−	1.06434i	−0.961141	−	0.276059i	$-0.910971\pi$
$911$	−8.66268e6	−	2.66610e7i	−0.345825	−	1.06434i	0.615316	−	0.788281i	$-0.289029\pi$
$912$	1.01595e7			0.404470
$913$	−2.02153e7	+	6.88940e6i	−0.802609	+	0.273530i
$914$	−6.71621e6			−0.265925
$915$	−34342.8	−	105696.i	−0.00135607	−	0.00417356i
$916$	1.84589e7	+	1.34112e7i	0.726888	+	0.528115i
$917$	2.84026e7	−	2.06357e7i	1.11541	−	0.810394i
$918$	256808.	−	790374.i	0.0100578	−	0.0309546i
$919$	5.19228e6	−	1.59802e7i	0.202801	−	0.624156i	−0.796996	−	0.603985i	$-0.793579\pi$
$919$	5.19228e6	−	1.59802e7i	0.202801	−	0.624156i	0.999797	−	0.0201716i	$-0.00642125\pi$
$920$	580373.	−	421665.i	0.0226067	−	0.0164247i
$921$	4.00118e6	+	2.90703e6i	0.155432	+	0.112928i
$922$	1.92996e6	+	5.93982e6i	0.0747691	+	0.230116i
$923$	−1.91470e7			−0.739768
$924$	3.35888e7	+	1.03852e7i	1.29424	+	0.400160i
$925$	9.57137e6			0.367807
$926$	3.02090e6	+	9.29738e6i	0.115773	+	0.356314i
$927$	−331015.	−	240496.i	−0.0126517	−	0.00919198i
$928$	−2.14075e7	+	1.55534e7i	−0.816009	+	0.592865i
$929$	1.16145e7	−	3.57456e7i	0.441530	−	1.35889i	−0.444716	−	0.895672i	$-0.646695\pi$
$929$	1.16145e7	−	3.57456e7i	0.441530	−	1.35889i	0.886245	−	0.463216i	$-0.153305\pi$
$930$	163820.	−	504187.i	0.00621098	−	0.0191154i
$931$	9.31376e6	−	6.76685e6i	0.352169	−	0.255866i
$932$	−3.51713e7	−	2.55535e7i	−1.32632	−	0.963630i
$933$	4.57116e6	+	1.40686e7i	0.171918	+	0.529110i
$934$	4.35041e6			0.163179
$935$	−4633.07	−	324046.i	−0.000173317	−	0.0121221i
$936$	273138.			0.0101904
$937$	654333.	+	2.01383e6i	0.0243473	+	0.0749331i	0.962492	−	0.271311i	$-0.0874570\pi$
$937$	654333.	+	2.01383e6i	0.0243473	+	0.0749331i	−0.938145	+	0.346244i	$0.887457\pi$
$938$	−3.20605e6	−	2.32934e6i	−0.118977	−	0.0864420i
$939$	356853.	−	259269.i	0.0132076	−	0.00959591i
$940$	1.13754e6	−	3.50099e6i	0.0419901	−	0.129232i
$941$	−9.45148e6	+	2.90887e7i	−0.347957	+	1.07090i	0.612025	+	0.790839i	$0.290355\pi$
$941$	−9.45148e6	+	2.90887e7i	−0.347957	+	1.07090i	−0.959982	+	0.280063i	$0.909645\pi$
$942$	759179.	−	551576.i	0.0278751	−	0.0202525i
$943$	2.33815e7	+	1.69876e7i	0.856234	+	0.622090i
$944$	9.29128e6	+	2.85956e7i	0.339348	+	1.04441i
$945$	2.87357e6			0.104675
$946$	3.21488e6	−	4.56062e6i	0.116799	−	0.165690i
$947$	5.98348e6			0.216810			0.108405	−	0.994107i	$-0.465426\pi$
$947$	5.98348e6			0.216810			0.108405	+	0.994107i	$0.465426\pi$
$948$	−1.03726e7	−	3.19234e7i	−0.374856	−	1.15369i
$949$	5.41327e6	+	3.93297e6i	0.195116	+	0.141760i
$950$	2.11208e6	−	1.53452e6i	0.0759280	−	0.0551649i
$951$	−8.54102e6	+	2.62865e7i	−0.306237	+	0.942502i
$952$	−779502.	+	2.39906e6i	−0.0278756	+	0.0857924i
$953$	1.35985e7	−	9.87986e6i	0.485018	−	0.352386i	−0.318247	−	0.948008i	$-0.603094\pi$
$953$	1.35985e7	−	9.87986e6i	0.485018	−	0.352386i	0.803265	+	0.595622i	$0.203094\pi$
$954$	−56790.7	−	41260.9i	−0.00202026	−	0.00146780i
$955$	79121.5	+	243511.i	0.00280728	+	0.00863992i
$956$	1.99948e7			0.707576
$957$	−2.96606e7	−	3.96205e7i	−1.04689	−	1.39843i
$958$	3.27783e6			0.115391
$959$	4.50085e6	+	1.38522e7i	0.158033	+	0.486376i
$960$	−1.33748e6	−	971738.i	−0.0468393	−	0.0340307i
$961$	−1.39512e7	+	1.01362e7i	−0.487309	+	0.354050i
$962$	667828.	−	2.05536e6i	0.0232663	−	0.0716063i
$963$	−254724.	+	783958.i	−0.00885123	+	0.0272413i
$964$	4.08552e7	−	2.96830e7i	1.41597	−	1.02876i
$965$	−1.84232e6	−	1.33852e6i	−0.0636864	−	0.0462709i
$966$	−2.38498e6	−	7.34022e6i	−0.0822323	−	0.253085i
$967$	2.88854e6			0.0993373			0.0496686	−	0.998766i	$-0.484183\pi$
$967$	2.88854e6			0.0993373			0.0496686	+	0.998766i	$0.484183\pi$
$968$	9.33268e6	−	7.19707e6i	0.320124	−	0.246869i
$969$	−2.16051e6			−0.0739175
$970$	108050.	+	332544.i	0.00368719	+	0.0113480i
$971$	−3.76342e7	−	2.73428e7i	−1.28096	−	0.930669i	−0.281375	−	0.959598i	$-0.590790\pi$
$971$	−3.76342e7	−	2.73428e7i	−1.28096	−	0.930669i	−0.999581	+	0.0289289i	$0.990790\pi$
$972$	1.16688e6	−	847786.i	0.0396150	−	0.0287820i
$973$	−1.74502e7	+	5.37063e7i	−0.590907	+	1.81862i
$974$	−849451.	+	2.61434e6i	−0.0286907	+	0.0883008i
$975$	−2.38270e7	+	1.73113e7i	−0.802707	+	0.583201i
$976$	−1.20091e6	−	872514.i	−0.0403540	−	0.0293189i
$977$	2.48365e6	+	7.64389e6i	0.0832442	+	0.256199i	0.984012	−	0.178101i	$-0.0569955\pi$
$977$	2.48365e6	+	7.64389e6i	0.0832442	+	0.256199i	−0.900768	+	0.434301i	$0.856996\pi$
$978$	3.57699e6			0.119583
$979$	1.53759e7	+	2.05391e7i	0.512725	+	0.684896i
$980$	−2.08107e6			−0.0692184
$981$	86005.9	+	264699.i	0.00285336	+	0.00878173i
$982$	−6.44463e6	−	4.68230e6i	−0.213265	−	0.154946i
$983$	3.15666e6	−	2.29345e6i	0.104194	−	0.0757016i	−0.534468	−	0.845189i	$-0.679488\pi$
$983$	3.15666e6	−	2.29345e6i	0.104194	−	0.0757016i	0.638662	+	0.769487i	$0.279488\pi$
$984$	−4.46632e6	+	1.37459e7i	−0.147049	+	0.452570i
$985$	404468.	−	1.24482e6i	0.0132829	−	0.0408806i
$986$	1.40513e6	−	1.02088e6i	0.0460281	−	0.0334414i
$987$	−6.55081e7	−	4.75944e7i	−2.14043	−	1.55512i
$988$	4.08819e6	+	1.25822e7i	0.133241	+	0.410075i
$989$	2.74911e7			0.893721
$990$	−7126.15	+	10109.1i	−0.000231083	+	0.000327813i
$991$	−3.15036e7			−1.01900			−0.509502	−	0.860469i	$-0.670170\pi$
$991$	−3.15036e7			−1.01900			−0.509502	+	0.860469i	$0.670170\pi$
$992$	−7.08925e6	−	2.18185e7i	−0.228729	−	0.703955i
$993$	−1.24170e7	−	9.02145e6i	−0.399615	−	0.290338i
$994$	−5.45974e6	+	3.96673e6i	−0.175269	+	0.127341i
$995$	87626.9	−	269688.i	0.00280595	−	0.00863582i
$996$	7.95331e6	−	2.44778e7i	0.254039	−	0.781850i
$997$	−4.84446e7	+	3.51971e7i	−1.54350	+	1.12142i	−0.595415	+	0.803418i	$0.703012\pi$
$997$	−4.84446e7	+	3.51971e7i	−1.54350	+	1.12142i	−0.948090	+	0.318003i	$0.896988\pi$
$998$	−2.11749e6	−	1.53844e6i	−0.0672967	−	0.0488939i
$999$	−3.55842e6	−	1.09517e7i	−0.112809	−	0.347190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.6.c.a.5.3	✓	16
3.2	odd	2		99.6.f.a.82.2		16
11.3	even	5		121.6.a.g.1.5		8
11.8	odd	10		121.6.a.i.1.4		8
11.9	even	5	inner	11.6.c.a.9.3	yes	16
33.8	even	10		1089.6.a.bb.1.5		8
33.14	odd	10		1089.6.a.bg.1.4		8
33.20	odd	10		99.6.f.a.64.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.c.a.5.3	✓	16	1.1	even	1	trivial
11.6.c.a.9.3	yes	16	11.9	even	5	inner
99.6.f.a.64.2		16	33.20	odd	10
99.6.f.a.82.2		16	3.2	odd	2
121.6.a.g.1.5		8	11.3	even	5
121.6.a.i.1.4		8	11.8	odd	10
1089.6.a.bb.1.5		8	33.8	even	10
1089.6.a.bg.1.4		8	33.14	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.361034 - 1.11115i) q^{2} +(12.7716 + 9.27912i) q^{3} +(24.7842 - 18.0068i) q^{4} +(1.31139 - 4.03604i) q^{5} +(5.69949 - 17.5412i) q^{6} +(-146.551 + 106.476i) q^{7} +(-59.2025 - 43.0132i) q^{8} +(1.92087 + 5.91183i) q^{9} -4.95810 q^{10} +(-240.502 - 321.262i) q^{11} +483.622 q^{12} +(185.552 + 571.070i) q^{13} +(171.220 + 124.399i) q^{14} +(54.1995 - 39.3782i) q^{15} +(276.516 - 851.028i) q^{16} +(-58.8034 + 180.978i) q^{17} +(5.87542 - 4.26874i) q^{18} +(581.843 + 422.733i) q^{19} +(-40.1744 - 123.644i) q^{20} -2859.70 q^{21} +(-270.141 + 383.220i) q^{22} -2310.03 q^{23} +(-356.988 - 1098.69i) q^{24} +(2513.61 + 1826.24i) q^{25} +(567.553 - 412.351i) q^{26} +(1155.11 - 3555.06i) q^{27} +(-1714.87 + 5277.84i) q^{28} +(6320.18 - 4591.88i) q^{29} +(-63.3229 - 46.0068i) q^{30} +(2092.98 + 6441.53i) q^{31} -3387.16 q^{32} +(-90.5706 - 6334.69i) q^{33} +222.324 q^{34} +(237.555 + 731.118i) q^{35} +(154.061 + 111.932i) q^{36} +(2492.25 - 1810.73i) q^{37} +(259.654 - 799.134i) q^{38} +(-2929.23 + 9015.24i) q^{39} +(-251.241 + 182.537i) q^{40} +(-10121.7 - 7353.86i) q^{41} +(1032.45 + 3177.55i) q^{42} -11900.8 q^{43} +(-11745.6 - 3631.57i) q^{44} +26.3794 q^{45} +(833.998 + 2566.78i) q^{46} +(22907.4 + 16643.2i) q^{47} +(11428.3 - 8303.17i) q^{48} +(4946.54 - 15223.9i) q^{49} +(1121.73 - 3452.33i) q^{50} +(-2430.33 + 1765.74i) q^{51} +(14881.9 + 10812.3i) q^{52} +(-2986.90 - 9192.73i) q^{53} -4367.23 q^{54} +(-1612.02 + 549.378i) q^{55} +13256.1 q^{56} +(3508.47 + 10798.0i) q^{57} +(-7384.06 - 5364.83i) q^{58} +(-27184.0 + 19750.3i) q^{59} +(634.217 - 1951.92i) q^{60} +(512.623 - 1577.69i) q^{61} +(6401.85 - 4651.22i) q^{62} +(-910.973 - 661.860i) q^{63} +(-7625.63 - 23469.3i) q^{64} +2548.19 q^{65} +(-7006.08 + 2387.67i) q^{66} -18724.7 q^{67} +(1801.44 + 5544.27i) q^{68} +(-29502.8 - 21435.0i) q^{69} +(726.615 - 527.917i) q^{70} +(-9853.69 + 30326.5i) q^{71} +(140.566 - 432.618i) q^{72} +(9015.22 - 6549.94i) q^{73} +(-2911.77 - 2115.53i) q^{74} +(15156.9 + 46648.1i) q^{75} +22032.6 q^{76} +(69452.6 + 21473.8i) q^{77} +11074.8 q^{78} +(-21447.7 - 66009.1i) q^{79} +(-3072.17 - 2232.06i) q^{80} +(48962.4 - 35573.3i) q^{81} +(-4516.94 + 13901.7i) q^{82} +(16445.3 - 50613.5i) q^{83} +(-70875.4 + 51494.0i) q^{84} +(653.322 + 474.666i) q^{85} +(4296.58 + 13223.5i) q^{86} +123328. q^{87} +(419.838 + 29364.3i) q^{88} -63932.5 q^{89} +(-9.52386 - 29.3114i) q^{90} +(-87998.0 - 63934.3i) q^{91} +(-57252.3 + 41596.2i) q^{92} +(-33041.0 + 101690. i) q^{93} +(10222.7 - 31462.2i) q^{94} +(2469.19 - 1793.97i) q^{95} +(-43259.4 - 31429.8i) q^{96} +(-21792.6 - 67070.8i) q^{97} -18701.9 q^{98} +(1437.28 - 2038.91i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9} - 672 q^{10} - 692 q^{11} - 1562 q^{12} + 1162 q^{13} + 560 q^{14} + 1796 q^{15} + 6399 q^{16} - 22 q^{17}+ \cdots + 724964 q^{99}+O(q^{100}) \) 16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9 - 672 * q^10 - 692 * q^11 - 1562 * q^12 + 1162 * q^13 + 560 * q^14 + 1796 * q^15 + 6399 * q^16 - 22 * q^17 + 834 * q^18 - 3236 * q^19 - 5514 * q^20 - 7772 * q^21 - 13059 * q^22 - 10848 * q^23 + 13233 * q^24 + 15686 * q^25 + 16216 * q^26 + 22500 * q^27 + 8838 * q^28 + 13070 * q^29 - 22830 * q^30 - 14764 * q^31 - 58812 * q^32 - 48544 * q^33 - 26966 * q^34 + 43368 * q^35 + 63696 * q^36 + 4638 * q^37 + 68144 * q^38 + 20300 * q^39 + 52284 * q^40 - 14806 * q^41 - 69922 * q^42 - 24376 * q^43 - 104960 * q^44 - 97480 * q^45 + 50452 * q^46 + 40364 * q^47 + 30236 * q^48 + 32246 * q^49 + 10839 * q^50 + 75564 * q^51 - 80654 * q^52 - 11654 * q^53 + 43796 * q^54 + 7052 * q^55 + 70632 * q^56 - 40020 * q^57 + 10276 * q^58 + 70804 * q^59 + 46116 * q^60 - 31446 * q^61 - 153388 * q^62 - 7064 * q^63 + 17695 * q^64 - 41284 * q^65 + 48006 * q^66 - 64200 * q^67 - 94114 * q^68 - 62412 * q^69 - 103768 * q^70 - 184380 * q^71 - 14729 * q^72 - 1750 * q^73 + 306048 * q^74 + 246596 * q^75 + 174806 * q^76 + 384646 * q^77 + 360916 * q^78 + 24324 * q^79 - 386444 * q^80 - 259412 * q^81 - 316255 * q^82 - 46028 * q^83 - 271956 * q^84 + 63914 * q^85 + 22931 * q^86 - 47592 * q^87 + 211871 * q^88 + 148364 * q^89 - 347186 * q^90 - 258448 * q^91 - 58658 * q^92 - 387478 * q^93 - 55370 * q^94 - 4716 * q^95 + 328396 * q^96 + 484296 * q^97 + 743692 * q^98 + 724964 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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