LMFDB - Embedded newform 105.4.d.b.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(64,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.d (of order $2$, degree $1$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 $ x^10 + 37x^8 + 398x^6 + 1149x^4 + 1040x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.8
Root			$4.40248i$ of defining polynomial
Character	$\chi$	$=$	105.64
Dual form			105.4.d.b.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.33774i q^{2} +3.00000i q^{3} -3.14050 q^{4} +(10.1427 + 4.70380i) q^{5} -10.0132 q^{6} +7.00000i q^{7} +16.2197i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.33774i q^{2} +3.00000i q^{3} -3.14050 q^{4} +(10.1427 + 4.70380i) q^{5} -10.0132 q^{6} +7.00000i q^{7} +16.2197i q^{8} -9.00000 q^{9} +(-15.7000 + 33.8537i) q^{10} +18.3258 q^{11} -9.42151i q^{12} -10.1457i q^{13} -23.3642 q^{14} +(-14.1114 + 30.4281i) q^{15} -79.2613 q^{16} -24.6984i q^{17} -30.0397i q^{18} -77.4282 q^{19} +(-31.8532 - 14.7723i) q^{20} -21.0000 q^{21} +61.1666i q^{22} -149.411i q^{23} -48.6592 q^{24} +(80.7486 + 95.4184i) q^{25} +33.8636 q^{26} -27.0000i q^{27} -21.9835i q^{28} +10.2984 q^{29} +(-101.561 - 47.1001i) q^{30} +124.423 q^{31} -134.796i q^{32} +54.9773i q^{33} +82.4367 q^{34} +(-32.9266 + 70.9989i) q^{35} +28.2645 q^{36} +215.905i q^{37} -258.435i q^{38} +30.4370 q^{39} +(-76.2943 + 164.512i) q^{40} +495.056 q^{41} -70.0925i q^{42} +220.606i q^{43} -57.5521 q^{44} +(-91.2843 - 42.3342i) q^{45} +498.696 q^{46} +212.957i q^{47} -237.784i q^{48} -49.0000 q^{49} +(-318.482 + 269.518i) q^{50} +74.0951 q^{51} +31.8625i q^{52} -532.455i q^{53} +90.1190 q^{54} +(185.873 + 86.2007i) q^{55} -113.538 q^{56} -232.284i q^{57} +34.3732i q^{58} +324.143 q^{59} +(44.3169 - 95.5595i) q^{60} +653.967 q^{61} +415.292i q^{62} -63.0000i q^{63} -184.178 q^{64} +(47.7232 - 102.905i) q^{65} -183.500 q^{66} -819.077i q^{67} +77.5653i q^{68} +448.234 q^{69} +(-236.976 - 109.900i) q^{70} -466.940 q^{71} -145.978i q^{72} -173.066i q^{73} -720.634 q^{74} +(-286.255 + 242.246i) q^{75} +243.163 q^{76} +128.280i q^{77} +101.591i q^{78} -810.186 q^{79} +(-803.923 - 372.829i) q^{80} +81.0000 q^{81} +1652.37i q^{82} -12.3208i q^{83} +65.9506 q^{84} +(116.176 - 250.508i) q^{85} -736.326 q^{86} +30.8951i q^{87} +297.239i q^{88} +33.8297 q^{89} +(141.300 - 304.683i) q^{90} +71.0198 q^{91} +469.227i q^{92} +373.269i q^{93} -710.795 q^{94} +(-785.330 - 364.206i) q^{95} +404.387 q^{96} -810.761i q^{97} -163.549i q^{98} -164.932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9}+O(q^{10}) $ 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9	$ 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9} + 92 q^{10} + 132 q^{11} - 14 q^{14} + 310 q^{16} - 348 q^{19} + 366 q^{20} - 210 q^{21} + 198 q^{24} - 374 q^{25} + 892 q^{26} - 740 q^{29} - 378 q^{30} + 684 q^{31} - 224 q^{34} + 486 q^{36} - 12 q^{39} - 2156 q^{40} + 1604 q^{41} - 580 q^{44} + 126 q^{45} + 1280 q^{46} - 490 q^{49} - 2504 q^{50} - 648 q^{51} + 54 q^{54} - 452 q^{55} + 462 q^{56} - 1408 q^{59} - 852 q^{60} + 1300 q^{61} - 150 q^{64} - 3296 q^{65} + 3036 q^{66} - 696 q^{69} - 882 q^{70} + 2940 q^{71} + 2624 q^{74} - 408 q^{75} + 8740 q^{76} + 1640 q^{79} - 4126 q^{80} + 810 q^{81} + 1134 q^{84} - 1704 q^{85} + 1664 q^{86} - 572 q^{89} - 828 q^{90} - 28 q^{91} - 5080 q^{94} + 1268 q^{95} + 330 q^{96} - 1188 q^{99}+O(q^{100}) $ 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9 + 92 * q^10 + 132 * q^11 - 14 * q^14 + 310 * q^16 - 348 * q^19 + 366 * q^20 - 210 * q^21 + 198 * q^24 - 374 * q^25 + 892 * q^26 - 740 * q^29 - 378 * q^30 + 684 * q^31 - 224 * q^34 + 486 * q^36 - 12 * q^39 - 2156 * q^40 + 1604 * q^41 - 580 * q^44 + 126 * q^45 + 1280 * q^46 - 490 * q^49 - 2504 * q^50 - 648 * q^51 + 54 * q^54 - 452 * q^55 + 462 * q^56 - 1408 * q^59 - 852 * q^60 + 1300 * q^61 - 150 * q^64 - 3296 * q^65 + 3036 * q^66 - 696 * q^69 - 882 * q^70 + 2940 * q^71 + 2624 * q^74 - 408 * q^75 + 8740 * q^76 + 1640 * q^79 - 4126 * q^80 + 810 * q^81 + 1134 * q^84 - 1704 * q^85 + 1664 * q^86 - 572 * q^89 - 828 * q^90 - 28 * q^91 - 5080 * q^94 + 1268 * q^95 + 330 * q^96 - 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			3.33774i			1.18007i	0.807378	+	0.590035i	$0.200886\pi$
$2$			3.33774i			1.18007i	−0.807378	+	0.590035i	$0.799114\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−3.14050			−0.392563
$5$	10.1427	+	4.70380i	0.907190	+	0.420720i
$5$	10.1427	+	4.70380i	0.907190	+	0.420720i
$6$	−10.0132			−0.681313
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$			16.2197i			0.716818i
$9$	−9.00000			−0.333333
$10$	−15.7000	+	33.8537i	−0.496479	+	1.07055i
$11$	18.3258			0.502311			0.251156	−	0.967947i	$-0.419189\pi$
$11$	18.3258			0.502311			0.251156	+	0.967947i	$0.419189\pi$
$12$		−	9.42151i		−	0.226646i
$13$		−	10.1457i		−	0.216454i	−0.994126	−	0.108227i	$-0.965483\pi$
$13$		−	10.1457i		−	0.216454i	0.994126	−	0.108227i	$-0.0345174\pi$
$14$	−23.3642			−0.446024
$15$	−14.1114	+	30.4281i	−0.242903	+	0.523767i
$16$	−79.2613			−1.23846
$17$		−	24.6984i		−	0.352367i	−0.984357	−	0.176183i	$-0.943625\pi$
$17$		−	24.6984i		−	0.352367i	0.984357	−	0.176183i	$-0.0563752\pi$
$18$		−	30.0397i		−	0.393356i
$19$	−77.4282			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$19$	−77.4282			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$20$	−31.8532	−	14.7723i	−0.356129	−	0.165159i
$21$	−21.0000			−0.218218
$22$			61.1666i			0.592762i
$23$		−	149.411i		−	1.35454i	−0.735735	−	0.677270i	$-0.763163\pi$
$23$		−	149.411i		−	1.35454i	0.735735	−	0.677270i	$-0.236837\pi$
$24$	−48.6592			−0.413855
$25$	80.7486	+	95.4184i	0.645989	+	0.763347i
$26$	33.8636			0.255431
$27$		−	27.0000i		−	0.192450i
$28$		−	21.9835i		−	0.148375i
$29$	10.2984			0.0659434			0.0329717	−	0.999456i	$-0.489503\pi$
$29$	10.2984			0.0659434			0.0329717	+	0.999456i	$0.489503\pi$
$30$	−101.561	−	47.1001i	−0.618081	−	0.286642i
$31$	124.423			0.720872			0.360436	−	0.932784i	$-0.382628\pi$
$31$	124.423			0.720872			0.360436	+	0.932784i	$0.382628\pi$
$32$		−	134.796i		−	0.744647i
$33$			54.9773i			0.290010i
$34$	82.4367			0.415817
$35$	−32.9266	+	70.9989i	−0.159017	+	0.342886i
$36$	28.2645			0.130854
$37$			215.905i			0.959312i	0.877457	+	0.479656i	$0.159239\pi$
$37$			215.905i			0.959312i	−0.877457	+	0.479656i	$0.840761\pi$
$38$		−	258.435i		−	1.10326i
$39$	30.4370			0.124970
$40$	−76.2943	+	164.512i	−0.301580	+	0.650290i
$41$	495.056			1.88573			0.942863	−	0.333181i	$-0.108122\pi$
$41$	495.056			1.88573			0.942863	+	0.333181i	$0.108122\pi$
$42$		−	70.0925i		−	0.257512i
$43$			220.606i			0.782375i	0.920311	+	0.391188i	$0.127936\pi$
$43$			220.606i			0.782375i	−0.920311	+	0.391188i	$0.872064\pi$
$44$	−57.5521			−0.197189
$45$	−91.2843	−	42.3342i	−0.302397	−	0.140240i
$46$	498.696			1.59845
$47$			212.957i			0.660915i	0.943821	+	0.330457i	$0.107203\pi$
$47$			212.957i			0.660915i	−0.943821	+	0.330457i	$0.892797\pi$
$48$		−	237.784i		−	0.715024i
$49$	−49.0000			−0.142857
$50$	−318.482	+	269.518i	−0.900802	+	0.762311i
$51$	74.0951			0.203439
$52$			31.8625i			0.0849719i
$53$		−	532.455i		−	1.37997i	−0.723825	−	0.689984i	$-0.757618\pi$
$53$		−	532.455i		−	1.37997i	0.723825	−	0.689984i	$-0.242382\pi$
$54$	90.1190			0.227104
$55$	185.873	+	86.2007i	0.455692	+	0.211333i
$56$	−113.538			−0.270932
$57$		−	232.284i		−	0.539769i
$58$			34.3732i			0.0778177i
$59$	324.143			0.715252			0.357626	−	0.933865i	$-0.383586\pi$
$59$	324.143			0.715252			0.357626	+	0.933865i	$0.383586\pi$
$60$	44.3169	−	95.5595i	0.0953547	−	0.205611i
$61$	653.967			1.37265			0.686327	−	0.727293i	$-0.259222\pi$
$61$	653.967			1.37265			0.686327	+	0.727293i	$0.259222\pi$
$62$			415.292i			0.850679i
$63$		−	63.0000i		−	0.125988i
$64$	−184.178			−0.359722
$65$	47.7232	−	102.905i	0.0910667	−	0.196365i
$66$	−183.500			−0.342231
$67$		−	819.077i		−	1.49353i	−0.665091	−	0.746763i	$-0.731607\pi$
$67$		−	819.077i		−	1.49353i	0.665091	−	0.746763i	$-0.268393\pi$
$68$			77.5653i			0.138326i
$69$	448.234			0.782044
$70$	−236.976	−	109.900i	−0.404629	−	0.187651i
$71$	−466.940			−0.780501			−0.390250	−	0.920709i	$-0.627612\pi$
$71$	−466.940			−0.780501			−0.390250	+	0.920709i	$0.627612\pi$
$72$		−	145.978i		−	0.238939i
$73$		−	173.066i		−	0.277478i	−0.990329	−	0.138739i	$-0.955695\pi$
$73$		−	173.066i		−	0.277478i	0.990329	−	0.138739i	$-0.0443048\pi$
$74$	−720.634			−1.13205
$75$	−286.255	+	242.246i	−0.440719	+	0.372962i
$76$	243.163			0.367010
$77$			128.280i			0.189856i
$78$			101.591i			0.147473i
$79$	−810.186			−1.15384			−0.576918	−	0.816802i	$-0.695745\pi$
$79$	−810.186			−1.15384			−0.576918	+	0.816802i	$0.695745\pi$
$80$	−803.923	−	372.829i	−1.12352	−	0.521044i
$81$	81.0000			0.111111
$82$			1652.37i			2.22529i
$83$		−	12.3208i		−	0.0162937i	−0.999967	−	0.00814687i	$-0.997407\pi$
$83$		−	12.3208i		−	0.0162937i	0.999967	−	0.00814687i	$-0.00259326\pi$
$84$	65.9506			0.0856642
$85$	116.176	−	250.508i	0.148248	−	0.319664i
$86$	−736.326			−0.923257
$87$			30.8951i			0.0380724i
$88$			297.239i			0.360066i
$89$	33.8297			0.0402914			0.0201457	−	0.999797i	$-0.493587\pi$
$89$	33.8297			0.0402914			0.0201457	+	0.999797i	$0.493587\pi$
$90$	141.300	−	304.683i	0.165493	−	0.356849i
$91$	71.0198			0.0818120
$92$			469.227i			0.531742i
$93$			373.269i			0.416196i
$94$	−710.795			−0.779925
$95$	−785.330	−	364.206i	−0.848139	−	0.393335i
$96$	404.387			0.429922
$97$		−	810.761i		−	0.848663i	−0.905507	−	0.424331i	$-0.860509\pi$
$97$		−	810.761i		−	0.848663i	0.905507	−	0.424331i	$-0.139491\pi$
$98$		−	163.549i		−	0.168581i
$99$	−164.932			−0.167437
$100$	−253.591	−	299.662i	−0.253591	−	0.299662i
$101$	1646.84			1.62245			0.811223	−	0.584737i	$-0.198802\pi$
$101$	1646.84			1.62245			0.811223	+	0.584737i	$0.198802\pi$
$102$			247.310i			0.240072i
$103$			921.360i			0.881401i	0.897654	+	0.440700i	$0.145270\pi$
$103$			921.360i			0.881401i	−0.897654	+	0.440700i	$0.854730\pi$
$104$	164.560			0.155158
$105$	−212.997	−	98.7797i	−0.197965	−	0.0918087i
$106$	1777.19			1.62846
$107$		−	1060.84i		−	0.958464i	−0.877688	−	0.479232i	$-0.840915\pi$
$107$		−	1060.84i		−	0.958464i	0.877688	−	0.479232i	$-0.159085\pi$
$108$			84.7936i			0.0755488i
$109$	−1533.03			−1.34713			−0.673566	−	0.739127i	$-0.735238\pi$
$109$	−1533.03			−1.34713			−0.673566	+	0.739127i	$0.735238\pi$
$110$	−287.715	+	620.394i	−0.249387	+	0.537748i
$111$	−647.715			−0.553859
$112$		−	554.829i		−	0.468093i
$113$			2072.67i			1.72549i	0.505637	+	0.862746i	$0.331257\pi$
$113$			2072.67i			1.72549i	−0.505637	+	0.862746i	$0.668743\pi$
$114$	775.305			0.636965
$115$	702.801	−	1515.43i	0.569883	−	1.22883i
$116$	−32.3420			−0.0258869
$117$			91.3111i			0.0721514i
$118$			1081.91i			0.844046i
$119$	172.889			0.133182
$120$	−493.535	−	228.883i	−0.375445	−	0.174117i
$121$	−995.166			−0.747683
$122$			2182.77i			1.61983i
$123$			1485.17i			1.08872i
$124$	−390.751			−0.282988
$125$	370.180	+	1347.62i	0.264879	+	0.964282i
$126$	210.278			0.148675
$127$		−	365.145i		−	0.255129i	−0.991830	−	0.127565i	$-0.959284\pi$
$127$		−	365.145i		−	0.255129i	0.991830	−	0.127565i	$-0.0407160\pi$
$128$		−	1693.10i		−	1.16914i
$129$	−661.819			−0.451705
$130$	343.469	+	159.288i	0.231725	+	0.107465i
$131$	1300.83			0.867586			0.433793	−	0.901013i	$-0.357175\pi$
$131$	1300.83			0.867586			0.433793	+	0.901013i	$0.357175\pi$
$132$		−	172.656i		−	0.113847i
$133$		−	541.997i		−	0.353362i
$134$	2733.87			1.76246
$135$	127.003	−	273.853i	0.0809677	−	0.174589i
$136$	400.601			0.252583
$137$		−	2578.40i		−	1.60794i	−0.594670	−	0.803970i	$-0.702717\pi$
$137$		−	2578.40i		−	1.60794i	0.594670	−	0.803970i	$-0.297283\pi$
$138$			1496.09i			0.922866i
$139$	−3065.49			−1.87059			−0.935294	−	0.353872i	$-0.884865\pi$
$139$	−3065.49			−1.87059			−0.935294	+	0.353872i	$0.884865\pi$
$140$	103.406	−	222.972i	0.0624243	−	0.134604i
$141$	−638.871			−0.381579
$142$		−	1558.52i		−	0.921044i
$143$		−	185.927i		−	0.108727i
$144$	713.351			0.412819
$145$	104.453	+	48.4414i	0.0598232	+	0.0277437i
$146$	577.650			0.327443
$147$		−	147.000i		−	0.0824786i
$148$		−	678.050i		−	0.376590i
$149$	2704.34			1.48690			0.743449	−	0.668793i	$-0.233189\pi$
$149$	2704.34			1.48690			0.743449	+	0.668793i	$0.233189\pi$
$150$	−808.553	−	955.445i	−0.440121	−	0.520078i
$151$	388.869			0.209574			0.104787	−	0.994495i	$-0.466584\pi$
$151$	388.869			0.209574			0.104787	+	0.994495i	$0.466584\pi$
$152$		−	1255.86i		−	0.670158i
$153$			222.285i			0.117456i
$154$	−428.166			−0.224043
$155$	1261.98	+	585.261i	0.653968	+	0.303286i
$156$	−95.5876			−0.0490586
$157$		−	2885.78i		−	1.46694i	−0.679720	−	0.733472i	$-0.737899\pi$
$157$		−	2885.78i		−	1.46694i	0.679720	−	0.733472i	$-0.262101\pi$
$158$		−	2704.19i		−	1.36161i
$159$	1597.36			0.796725
$160$	634.051	−	1367.19i	0.313288	−	0.675537i
$161$	1045.88			0.511968
$162$			270.357i			0.131119i
$163$		−	571.954i		−	0.274840i	−0.990513	−	0.137420i	$-0.956119\pi$
$163$		−	571.954i		−	0.274840i	0.990513	−	0.137420i	$-0.0438809\pi$
$164$	−1554.73			−0.740266
$165$	−258.602	+	557.618i	−0.122013	+	0.263094i
$166$	41.1235			0.0192277
$167$			2423.96i			1.12319i	0.827414	+	0.561593i	$0.189811\pi$
$167$			2423.96i			1.12319i	−0.827414	+	0.561593i	$0.810189\pi$
$168$		−	340.614i		−	0.156422i
$169$	2094.07			0.953148
$170$	836.131	+	387.766i	0.377225	+	0.174943i
$171$	696.853			0.311636
$172$		−	692.815i		−	0.307131i
$173$		−	626.440i		−	0.275303i	−0.990481	−	0.137651i	$-0.956045\pi$
$173$		−	626.440i		−	0.275303i	0.990481	−	0.137651i	$-0.0439554\pi$
$174$	−103.120			−0.0449281
$175$	−667.929	+	565.240i	−0.288518	+	0.244161i
$176$	−1452.52			−0.622091
$177$			972.430i			0.412951i
$178$			112.915i			0.0475467i
$179$	−2322.11			−0.969623			−0.484812	−	0.874619i	$-0.661112\pi$
$179$	−2322.11			−0.969623			−0.484812	+	0.874619i	$0.661112\pi$
$180$	286.679	+	132.951i	0.118710	+	0.0550531i
$181$	−4664.94			−1.91570			−0.957852	−	0.287263i	$-0.907255\pi$
$181$	−4664.94			−1.91570			−0.957852	+	0.287263i	$0.907255\pi$
$182$			237.045i			0.0965438i
$183$			1961.90i			0.792502i
$184$	2423.41			0.970958
$185$	−1015.57	+	2189.86i	−0.403602	+	0.870279i
$186$	−1245.87			−0.491140
$187$		−	452.617i		−	0.176998i
$188$		−	668.792i		−	0.259451i
$189$	189.000			0.0727393
$190$	1215.63	−	2621.23i	0.464162	−	1.00086i
$191$	−3730.26			−1.41315			−0.706575	−	0.707638i	$-0.749761\pi$
$191$	−3730.26			−1.41315			−0.706575	+	0.707638i	$0.749761\pi$
$192$		−	552.533i		−	0.207686i
$193$			2585.26i			0.964202i	0.876116	+	0.482101i	$0.160126\pi$
$193$			2585.26i			0.964202i	−0.876116	+	0.482101i	$0.839874\pi$
$194$	2706.11			1.00148
$195$	308.714	+	143.170i	0.113372	+	0.0525774i
$196$	153.885			0.0560804
$197$			2405.91i			0.870122i	0.900401	+	0.435061i	$0.143273\pi$
$197$			2405.91i			0.870122i	−0.900401	+	0.435061i	$0.856727\pi$
$198$		−	550.500i		−	0.197587i
$199$	−1192.35			−0.424740			−0.212370	−	0.977189i	$-0.568118\pi$
$199$	−1192.35			−0.424740			−0.212370	+	0.977189i	$0.568118\pi$
$200$	−1547.66	+	1309.72i	−0.547181	+	0.463056i
$201$	2457.23			0.862287
$202$			5496.74i			1.91460i
$203$			72.0885i			0.0249243i
$204$	−232.696			−0.0798626
$205$	5021.20	+	2328.64i	1.71071	+	0.793364i
$206$	−3075.26			−1.04011
$207$			1344.70i			0.451513i
$208$			804.160i			0.268069i
$209$	−1418.93			−0.469615
$210$	329.701	−	710.927i	0.108341	−	0.233613i
$211$	−764.904			−0.249565			−0.124782	−	0.992184i	$-0.539823\pi$
$211$	−764.904			−0.249565			−0.124782	+	0.992184i	$0.539823\pi$
$212$			1672.18i			0.541724i
$213$		−	1400.82i		−	0.450622i
$214$	3540.82			1.13105
$215$	−1037.69	+	2237.54i	−0.329161	+	0.709763i
$216$	437.933			0.137952
$217$			870.961i			0.272464i
$218$		−	5116.84i		−	1.58971i
$219$	519.199			0.160202
$220$	−583.734	−	270.713i	−0.178888	−	0.0829614i
$221$	−250.582			−0.0762713
$222$		−	2161.90i		−	0.653592i
$223$		−	1585.18i		−	0.476016i	−0.971263	−	0.238008i	$-0.923506\pi$
$223$		−	1585.18i		−	0.476016i	0.971263	−	0.238008i	$-0.0764945\pi$
$224$	943.569			0.281450
$225$	−726.737	−	858.765i	−0.215330	−	0.254449i
$226$	−6918.04			−2.03620
$227$			2363.07i			0.690936i	0.938431	+	0.345468i	$0.112280\pi$
$227$			2363.07i			0.690936i	−0.938431	+	0.345468i	$0.887720\pi$
$228$			729.490i			0.211893i
$229$	−1626.44			−0.469337			−0.234669	−	0.972075i	$-0.575401\pi$
$229$	−1626.44			−0.469337			−0.234669	+	0.972075i	$0.575401\pi$
$230$	5058.12	+	2345.77i	1.45010	+	0.672501i
$231$	−384.841			−0.109613
$232$			167.037i			0.0472694i
$233$		−	1720.34i		−	0.483705i	−0.970313	−	0.241853i	$-0.922245\pi$
$233$		−	1720.34i		−	0.483705i	0.970313	−	0.241853i	$-0.0777551\pi$
$234$	−304.773			−0.0851437
$235$	−1001.71	+	2159.96i	−0.278060	+	0.599575i
$236$	−1017.97			−0.280781
$237$		−	2430.56i		−	0.666168i
$238$			577.057i			0.157164i
$239$	−7217.75			−1.95346			−0.976732	−	0.214466i	$-0.931199\pi$
$239$	−7217.75			−1.95346			−0.976732	+	0.214466i	$0.931199\pi$
$240$	1118.49	−	2411.77i	0.300825	−	0.648663i
$241$	5094.78			1.36176			0.680879	−	0.732396i	$-0.261598\pi$
$241$	5094.78			1.36176			0.680879	+	0.732396i	$0.261598\pi$
$242$		−	3321.61i		−	0.882318i
$243$			243.000i			0.0641500i
$244$	−2053.79			−0.538853
$245$	−496.992	−	230.486i	−0.129599	−	0.0601029i
$246$	−4957.10			−1.28477
$247$			785.561i			0.202365i
$248$			2018.11i			0.516734i
$249$	36.9623			0.00940720
$250$	−4498.02	+	1235.56i	−1.13792	+	0.312575i
$251$	−4346.51			−1.09303			−0.546513	−	0.837451i	$-0.684045\pi$
$251$	−4346.51			−1.09303			−0.546513	+	0.837451i	$0.684045\pi$
$252$			197.852i			0.0494583i
$253$		−	2738.08i		−	0.680401i
$254$	1218.76			0.301070
$255$	751.524	+	348.528i	0.184558	+	0.0855910i
$256$	4177.71			1.01995
$257$		−	1428.13i		−	0.346632i	−0.984866	−	0.173316i	$-0.944552\pi$
$257$		−	1428.13i		−	0.346632i	0.984866	−	0.173316i	$-0.0554482\pi$
$258$		−	2208.98i		−	0.533043i
$259$	−1511.33			−0.362586
$260$	−149.875	+	323.172i	−0.0357494	+	0.0770857i
$261$	−92.6853			−0.0219811
$262$			4341.82i			1.02381i
$263$		−	3447.78i		−	0.808362i	−0.914679	−	0.404181i	$-0.867557\pi$
$263$		−	3447.78i		−	0.808362i	0.914679	−	0.404181i	$-0.132443\pi$
$264$	−891.717			−0.207884
$265$	2504.56	−	5400.53i	0.580581	−	1.25189i
$266$	1809.05			0.416991
$267$			101.489i			0.0232623i
$268$			2572.31i			0.586303i
$269$	22.3975			0.00507657			0.00253829	−	0.999997i	$-0.499192\pi$
$269$	22.3975			0.00507657			0.00253829	+	0.999997i	$0.499192\pi$
$270$	914.049	+	423.901i	0.206027	+	0.0955475i
$271$	−1557.33			−0.349080			−0.174540	−	0.984650i	$-0.555844\pi$
$271$	−1557.33			−0.349080			−0.174540	+	0.984650i	$0.555844\pi$
$272$			1957.62i			0.436391i
$273$			213.059i			0.0472342i
$274$	8606.03			1.89748
$275$	1479.78	+	1748.61i	0.324487	+	0.383438i
$276$	−1407.68			−0.307001
$277$		−	3734.92i		−	0.810142i	−0.914285	−	0.405071i	$-0.867247\pi$
$277$		−	3734.92i		−	0.810142i	0.914285	−	0.405071i	$-0.132753\pi$
$278$		−	10231.8i		−	2.20742i
$279$	−1119.81			−0.240291
$280$	−1151.58	−	534.060i	−0.245787	−	0.113986i
$281$	−2422.37			−0.514258			−0.257129	−	0.966377i	$-0.582777\pi$
$281$	−2422.37			−0.514258			−0.257129	+	0.966377i	$0.582777\pi$
$282$		−	2132.39i		−	0.450290i
$283$		−	283.232i		−	0.0594926i	−0.999557	−	0.0297463i	$-0.990530\pi$
$283$		−	283.232i		−	0.0594926i	0.999557	−	0.0297463i	$-0.00946994\pi$
$284$	1466.43			0.306396
$285$	1092.62	−	2355.99i	0.227092	−	0.489673i
$286$	620.577			0.128306
$287$			3465.39i			0.712737i
$288$			1213.16i			0.248216i
$289$	4302.99			0.875838
$290$	−161.685	+	348.637i	−0.0327395	+	0.0705955i
$291$	2432.28			0.489976
$292$			543.515i			0.108927i
$293$		−	8481.49i		−	1.69111i	−0.533892	−	0.845553i	$-0.679271\pi$
$293$		−	8481.49i		−	1.69111i	0.533892	−	0.845553i	$-0.320729\pi$
$294$	490.648			0.0973305
$295$	3287.69	+	1524.70i	0.648870	+	0.300921i
$296$	−3501.92			−0.687652
$297$		−	494.796i		−	0.0966699i
$298$			9026.37i			1.75464i
$299$	−1515.88			−0.293196
$300$	898.985	−	760.773i	0.173010	−	0.146411i
$301$	−1544.24			−0.295710
$302$			1297.94i			0.247312i
$303$			4940.53i			0.936720i
$304$	6137.05			1.15784
$305$	6632.99	+	3076.13i	1.24526	+	0.577504i
$306$	−741.931			−0.138606
$307$		−	2005.50i		−	0.372834i	−0.982471	−	0.186417i	$-0.940312\pi$
$307$		−	2005.50i		−	0.372834i	0.982471	−	0.186417i	$-0.0596875\pi$
$308$		−	402.865i		−	0.0745304i
$309$	−2764.08			−0.508877
$310$	−1953.45	+	4212.18i	−0.357898	+	0.771727i
$311$	10021.4			1.82720			0.913602	−	0.406609i	$-0.133289\pi$
$311$	10021.4			1.82720			0.913602	+	0.406609i	$0.133289\pi$
$312$			493.681i			0.0895807i
$313$			631.178i			0.113982i	0.998375	+	0.0569908i	$0.0181506\pi$
$313$			631.178i			0.113982i	−0.998375	+	0.0569908i	$0.981849\pi$
$314$	9631.97			1.73109
$315$	296.339	−	638.990i	0.0530058	−	0.114295i
$316$	2544.39			0.452953
$317$		−	1202.71i		−	0.213095i	−0.994308	−	0.106547i	$-0.966020\pi$
$317$		−	1202.71i		−	0.213095i	0.994308	−	0.106547i	$-0.0339796\pi$
$318$			5331.58i			0.940190i
$319$	188.725			0.0331241
$320$	−1868.06	−	866.335i	−0.326336	−	0.151342i
$321$	3182.53			0.553369
$322$			3490.87i			0.604158i
$323$			1912.35i			0.329430i
$324$	−254.381			−0.0436181
$325$	968.084	−	819.249i	0.165230	−	0.139827i
$326$	1909.03			0.324330
$327$		−	4599.08i		−	0.777767i
$328$			8029.68i			1.35172i
$329$	−1490.70			−0.249802
$330$	−1861.18	−	863.146i	−0.310469	−	0.143984i
$331$	−9297.55			−1.54393			−0.771963	−	0.635667i	$-0.780725\pi$
$331$	−9297.55			−1.54393			−0.771963	+	0.635667i	$0.780725\pi$
$332$			38.6934i			0.00639632i
$333$		−	1943.14i		−	0.319771i
$334$	−8090.56			−1.32544
$335$	3852.77	−	8307.65i	0.628357	−	1.35491i
$336$	1664.49			0.270254
$337$			507.727i			0.0820702i	0.999158	+	0.0410351i	$0.0130656\pi$
$337$			507.727i			0.0820702i	−0.999158	+	0.0410351i	$0.986934\pi$
$338$			6989.44i			1.12478i
$339$	−6218.02			−0.996213
$340$	−364.852	+	786.722i	−0.0581966	+	0.125488i
$341$	2280.15			0.362102
$342$			2325.92i			0.367752i
$343$		−	343.000i		−	0.0539949i
$344$	−3578.17			−0.560820
$345$	4546.30	+	2108.40i	0.709463	+	0.329022i
$346$	2090.89			0.324876
$347$			6860.59i			1.06137i	0.847569	+	0.530685i	$0.178065\pi$
$347$			6860.59i			1.06137i	−0.847569	+	0.530685i	$0.821935\pi$
$348$		−	97.0261i		−	0.0149458i
$349$	9236.45			1.41666			0.708332	−	0.705879i	$-0.249448\pi$
$349$	9236.45			1.41666			0.708332	+	0.705879i	$0.249448\pi$
$350$	−1886.62	−	2229.37i	−0.288127	−	0.340471i
$351$	−273.933			−0.0416566
$352$		−	2470.23i		−	0.374045i
$353$		−	9419.54i		−	1.42026i	−0.704071	−	0.710129i	$-0.748636\pi$
$353$		−	9419.54i		−	1.42026i	0.704071	−	0.710129i	$-0.251364\pi$
$354$	−3245.72			−0.487310
$355$	−4736.03	−	2196.39i	−0.708063	−	0.328373i
$356$	−106.242			−0.0158169
$357$			518.666i			0.0768927i
$358$		−	7750.59i		−	1.14422i
$359$	2890.82			0.424990			0.212495	−	0.977162i	$-0.431841\pi$
$359$	2890.82			0.424990			0.212495	+	0.977162i	$0.431841\pi$
$360$	686.649	−	1480.61i	0.100527	−	0.216763i
$361$	−863.879			−0.125948
$362$		−	15570.4i		−	2.26066i
$363$		−	2985.50i		−	0.431675i
$364$	−223.038			−0.0321164
$365$	814.068	−	1755.36i	0.116740	−	0.251725i
$366$	−6548.31			−0.935207
$367$		−	1570.51i		−	0.223379i	−0.993743	−	0.111690i	$-0.964374\pi$
$367$		−	1570.51i		−	0.223379i	0.993743	−	0.111690i	$-0.0356262\pi$
$368$			11842.5i			1.67754i
$369$	−4455.50			−0.628575
$370$	−7309.17	−	3389.72i	−1.02699	−	0.476278i
$371$	3727.18			0.521579
$372$		−	1172.25i		−	0.163383i
$373$			8713.38i			1.20955i	0.796397	+	0.604774i	$0.206737\pi$
$373$			8713.38i			1.20955i	−0.796397	+	0.604774i	$0.793263\pi$
$374$	1510.72			0.208870
$375$	−4042.87	+	1110.54i	−0.556728	+	0.152928i
$376$	−3454.11			−0.473755
$377$		−	104.484i		−	0.0142737i
$378$			630.833i			0.0858374i
$379$	5779.65			0.783326			0.391663	−	0.920109i	$-0.371900\pi$
$379$	5779.65			0.783326			0.391663	+	0.920109i	$0.371900\pi$
$380$	2466.33	+	1143.79i	0.332948	+	0.154409i
$381$	1095.44			0.147299
$382$		−	12450.6i		−	1.66762i
$383$			12340.2i			1.64636i	0.567780	+	0.823181i	$0.307803\pi$
$383$			12340.2i			1.64636i	−0.567780	+	0.823181i	$0.692197\pi$
$384$	5079.30			0.675006
$385$	−603.405	+	1301.11i	−0.0798762	+	0.172235i
$386$	−8628.92			−1.13783
$387$		−	1985.46i		−	0.260792i
$388$			2546.20i			0.333153i
$389$	−7948.44			−1.03600			−0.517998	−	0.855382i	$-0.673322\pi$
$389$	−7948.44			−1.03600			−0.517998	+	0.855382i	$0.673322\pi$
$390$	−477.863	+	1030.41i	−0.0620450	+	0.133786i
$391$	−3690.22			−0.477295
$392$		−	794.767i		−	0.102403i
$393$			3902.48i			0.500901i
$394$	−8030.30			−1.02680
$395$	−8217.47	−	3810.95i	−1.04675	−	0.485442i
$396$	517.969			0.0657296
$397$		−	5363.64i		−	0.678069i	−0.940774	−	0.339034i	$-0.889900\pi$
$397$		−	5363.64i		−	0.678069i	0.940774	−	0.339034i	$-0.110100\pi$
$398$		−	3979.75i		−	0.501223i
$399$	1625.99			0.204014
$400$	−6400.23	−	7562.98i	−0.800029	−	0.945373i
$401$	6057.13			0.754310			0.377155	−	0.926150i	$-0.376902\pi$
$401$	6057.13			0.754310			0.377155	+	0.926150i	$0.376902\pi$
$402$			8201.60i			1.01756i
$403$		−	1262.36i		−	0.156036i
$404$	−5171.92			−0.636912
$405$	821.558	+	381.008i	0.100799	+	0.0467467i
$406$	−240.613			−0.0294123
$407$			3956.62i			0.481873i
$408$			1201.80i			0.145829i
$409$	−1248.52			−0.150942			−0.0754709	−	0.997148i	$-0.524046\pi$
$409$	−1248.52			−0.150942			−0.0754709	+	0.997148i	$0.524046\pi$
$410$	−7772.41	+	16759.5i	−0.936224	+	2.01876i
$411$	7735.20			0.928344
$412$		−	2893.53i		−	0.346005i
$413$			2269.00i			0.270340i
$414$	−4488.27			−0.532817
$415$	57.9544	−	124.966i	0.00685511	−	0.0147815i
$416$	−1367.59			−0.161182
$417$		−	9196.48i		−	1.07998i
$418$		−	4736.02i		−	0.554178i
$419$	−8324.28			−0.970567			−0.485284	−	0.874357i	$-0.661284\pi$
$419$	−8324.28			−0.970567			−0.485284	+	0.874357i	$0.661284\pi$
$420$	668.917	+	310.218i	0.0777138	+	0.0360407i
$421$	1693.40			0.196036			0.0980179	−	0.995185i	$-0.468750\pi$
$421$	1693.40			0.196036			0.0980179	+	0.995185i	$0.468750\pi$
$422$		−	2553.05i		−	0.294504i
$423$		−	1916.61i		−	0.220305i
$424$	8636.27			0.989185
$425$	2356.68	−	1994.36i	0.268978	−	0.227625i
$426$	4675.57			0.531765
$427$			4577.77i			0.518814i
$428$			3331.58i			0.376257i
$429$	557.782			0.0627738
$430$	−7468.33	−	3463.53i	−0.837570	−	0.388433i
$431$	11754.6			1.31369			0.656844	−	0.754026i	$-0.271891\pi$
$431$	11754.6			1.31369			0.656844	+	0.754026i	$0.271891\pi$
$432$			2140.05i			0.238341i
$433$			14614.3i			1.62199i	0.585056	+	0.810993i	$0.301073\pi$
$433$			14614.3i			1.62199i	−0.585056	+	0.810993i	$0.698927\pi$
$434$	−2907.04			−0.321526
$435$	−145.324	+	313.359i	−0.0160178	+	0.0345389i
$436$	4814.48			0.528834
$437$			11568.6i			1.26637i
$438$			1732.95i			0.189049i
$439$	−1957.52			−0.212819			−0.106409	−	0.994322i	$-0.533935\pi$
$439$	−1957.52			−0.212819			−0.106409	+	0.994322i	$0.533935\pi$
$440$	−1398.15	+	3014.80i	−0.151487	+	0.326648i
$441$	441.000			0.0476190
$442$		−	836.377i		−	0.0900054i
$443$			356.774i			0.0382637i	0.999817	+	0.0191319i	$0.00609023\pi$
$443$			356.774i			0.0382637i	−0.999817	+	0.0191319i	$0.993910\pi$
$444$	2034.15			0.217425
$445$	343.124	+	159.128i	0.0365520	+	0.0169514i
$446$	5290.92			0.561732
$447$			8113.01i			0.858461i
$448$		−	1289.24i		−	0.135962i
$449$	−7395.30			−0.777296			−0.388648	−	0.921386i	$-0.627058\pi$
$449$	−7395.30			−0.777296			−0.388648	+	0.921386i	$0.627058\pi$
$450$	2866.34	−	2425.66i	0.300267	−	0.254104i
$451$	9072.28			0.947222
$452$		−	6509.23i		−	0.677364i
$453$			1166.61i			0.120998i
$454$	−7887.31			−0.815352
$455$	720.332	+	334.063i	0.0742191	+	0.0344200i
$456$	3767.59			0.386916
$457$			12722.2i			1.30223i	0.758979	+	0.651115i	$0.225698\pi$
$457$			12722.2i			1.30223i	−0.758979	+	0.651115i	$0.774302\pi$
$458$		−	5428.64i		−	0.553850i
$459$	−666.856			−0.0678130
$460$	−2207.15	+	4759.23i	−0.223715	+	0.482391i
$461$	−2206.45			−0.222916			−0.111458	−	0.993769i	$-0.535552\pi$
$461$	−2206.45			−0.222916			−0.111458	+	0.993769i	$0.535552\pi$
$462$		−	1284.50i		−	0.129351i
$463$		−	15912.0i		−	1.59718i	−0.601875	−	0.798591i	$-0.705579\pi$
$463$		−	15912.0i		−	1.59718i	0.601875	−	0.798591i	$-0.294421\pi$
$464$	−816.261			−0.0816681
$465$	−1755.78	+	3785.95i	−0.175102	+	0.377569i
$466$	5742.05			0.570806
$467$			7602.65i			0.753337i	0.926348	+	0.376669i	$0.122930\pi$
$467$			7602.65i			0.753337i	−0.926348	+	0.376669i	$0.877070\pi$
$468$		−	286.763i		−	0.0283240i
$469$	5733.54			0.564499
$470$	−7209.38	−	3343.44i	−0.707540	−	0.328130i
$471$	8657.33			0.846940
$472$			5257.52i			0.512705i
$473$			4042.78i			0.392996i
$474$	8112.57			0.786124
$475$	−6252.21	−	7388.07i	−0.603940	−	0.713659i
$476$	−542.957			−0.0522824
$477$			4792.09i			0.459989i
$478$		−	24091.0i		−	2.30522i
$479$	−1681.93			−0.160437			−0.0802184	−	0.996777i	$-0.525562\pi$
$479$	−1681.93			−0.160437			−0.0802184	+	0.996777i	$0.525562\pi$
$480$	4101.57	+	1902.15i	0.390021	+	0.180877i
$481$	2190.50			0.207647
$482$			17005.0i			1.60697i
$483$			3137.64i			0.295585i
$484$	3125.32			0.293513
$485$	3813.65	−	8223.30i	0.357050	−	0.769898i
$486$	−811.071			−0.0757015
$487$		−	14107.0i		−	1.31263i	−0.754487	−	0.656314i	$-0.772114\pi$
$487$		−	14107.0i		−	1.31263i	0.754487	−	0.656314i	$-0.227886\pi$
$488$			10607.2i			0.983943i
$489$	1715.86			0.158679
$490$	769.302	−	1658.83i	0.0709256	−	0.152935i
$491$	9010.20			0.828156			0.414078	−	0.910241i	$-0.364104\pi$
$491$	9010.20			0.828156			0.414078	+	0.910241i	$0.364104\pi$
$492$		−	4664.18i		−	0.427393i
$493$		−	254.353i		−	0.0232363i
$494$	−2622.00			−0.238804
$495$	−1672.85	−	775.806i	−0.151897	−	0.0704442i
$496$	−9861.92			−0.892769
$497$		−	3268.58i		−	0.295001i
$498$			123.371i			0.0111011i
$499$	−2655.07			−0.238191			−0.119096	−	0.992883i	$-0.538000\pi$
$499$	−2655.07			−0.238191			−0.119096	+	0.992883i	$0.538000\pi$
$500$	−1162.55	−	4232.22i	−0.103982	−	0.378541i
$501$	−7271.89			−0.648471
$502$		−	14507.5i		−	1.28985i
$503$		−	16559.4i		−	1.46789i	−0.679208	−	0.733946i	$-0.737677\pi$
$503$		−	16559.4i		−	1.46789i	0.679208	−	0.733946i	$-0.262323\pi$
$504$	1021.84			0.0903105
$505$	16703.4	+	7746.42i	1.47187	+	0.682596i
$506$	9138.99			0.802920
$507$			6282.20i			0.550300i
$508$			1146.74i			0.100154i
$509$	12308.6			1.07184			0.535922	−	0.844268i	$-0.319964\pi$
$509$	12308.6			1.07184			0.535922	+	0.844268i	$0.319964\pi$
$510$	−1163.30	+	2508.39i	−0.101003	+	0.217791i
$511$	1211.46			0.104877
$512$			399.294i			0.0344658i
$513$			2090.56i			0.179923i
$514$	4766.74			0.409050
$515$	−4333.89	+	9345.07i	−0.370823	+	0.799598i
$516$	2078.44			0.177322
$517$			3902.60i			0.331985i
$518$		−	5044.44i		−	0.427876i
$519$	1879.32			0.158946
$520$	1669.08	+	774.058i	0.140758	+	0.0652783i
$521$	−15045.9			−1.26521			−0.632605	−	0.774475i	$-0.718014\pi$
$521$	−15045.9			−1.26521			−0.632605	+	0.774475i	$0.718014\pi$
$522$		−	309.359i		−	0.0259392i
$523$		−	6372.16i		−	0.532763i	−0.963868	−	0.266381i	$-0.914172\pi$
$523$		−	6372.16i		−	0.532763i	0.963868	−	0.266381i	$-0.0858281\pi$
$524$	−4085.25			−0.340582
$525$	−1695.72	−	2003.79i	−0.140966	−	0.166576i
$526$	11507.8			0.953923
$527$		−	3073.05i		−	0.254011i
$528$		−	4357.57i		−	0.359164i
$529$	−10156.8			−0.834779
$530$	18025.5	+	8359.57i	1.47732	+	0.685125i
$531$	−2917.29			−0.238417
$532$			1702.14i			0.138717i
$533$		−	5022.68i		−	0.408173i
$534$	−338.744			−0.0274511
$535$	4989.99	−	10759.8i	0.403245	−	0.869509i
$536$	13285.2			1.07059
$537$		−	6966.33i		−	0.559812i
$538$			74.7569i			0.00599071i
$539$	−897.962			−0.0717588
$540$	−398.852	+	860.036i	−0.0317849	+	0.0685371i
$541$	4128.72			0.328110			0.164055	−	0.986451i	$-0.447543\pi$
$541$	4128.72			0.328110			0.164055	+	0.986451i	$0.447543\pi$
$542$		−	5197.95i		−	0.411939i
$543$		−	13994.8i		−	1.10603i
$544$	−3329.23			−0.262389
$545$	−15549.0	−	7211.05i	−1.22210	−	0.566766i
$546$	−711.136			−0.0557396
$547$			17987.6i			1.40602i	0.711179	+	0.703011i	$0.248162\pi$
$547$			17987.6i			1.40602i	−0.711179	+	0.703011i	$0.751838\pi$
$548$			8097.48i			0.631217i
$549$	−5885.70			−0.457551
$550$	−5836.42	+	4939.12i	−0.452483	+	0.382918i
$551$	−797.383			−0.0616509
$552$			7270.24i			0.560583i
$553$		−	5671.30i		−	0.436109i
$554$	12466.2			0.956024
$555$	−6569.57	−	3046.72i	−0.502456	−	0.233020i
$556$	9627.19			0.734323
$557$		−	13278.6i		−	1.01011i	−0.863086	−	0.505057i	$-0.831471\pi$
$557$		−	13278.6i		−	1.01011i	0.863086	−	0.505057i	$-0.168529\pi$
$558$		−	3737.62i		−	0.283560i
$559$	2238.20			0.169348
$560$	2609.80	−	5627.46i	0.196936	−	0.424649i
$561$	1357.85			0.102190
$562$		−	8085.24i		−	0.606860i
$563$		−	517.822i		−	0.0387630i	−0.999812	−	0.0193815i	$-0.993830\pi$
$563$		−	517.822i		−	0.0387630i	0.999812	−	0.0193815i	$-0.00616971\pi$
$564$	2006.38			0.149794
$565$	−9749.43	+	21022.5i	−0.725950	+	1.56535i
$566$	945.355			0.0702054
$567$			567.000i			0.0419961i
$568$		−	7573.64i		−	0.559477i
$569$	−1071.91			−0.0789750			−0.0394875	−	0.999220i	$-0.512573\pi$
$569$	−1071.91			−0.0789750			−0.0394875	+	0.999220i	$0.512573\pi$
$570$	7863.68	+	3646.88i	0.577848	+	0.267984i
$571$	−24489.8			−1.79486			−0.897430	−	0.441157i	$-0.854568\pi$
$571$	−24489.8			−1.79486			−0.897430	+	0.441157i	$0.854568\pi$
$572$			583.905i			0.0426824i
$573$		−	11190.8i		−	0.815883i
$574$	−11566.6			−0.841079
$575$	14256.6	−	12064.8i	1.03398	−	0.875018i
$576$	1657.60			0.119907
$577$			22765.1i			1.64250i	0.570568	+	0.821251i	$0.306723\pi$
$577$			22765.1i			1.64250i	−0.570568	+	0.821251i	$0.693277\pi$
$578$			14362.3i			1.03355i
$579$	−7755.78			−0.556682
$580$	−328.035	−	152.130i	−0.0234844	−	0.0108912i
$581$	86.2454			0.00615846
$582$			8118.32i			0.578205i
$583$		−	9757.64i		−	0.693173i
$584$	2807.09			0.198901
$585$	−429.509	+	926.141i	−0.0303556	+	0.0654551i
$586$	28309.0			1.99562
$587$		−	10106.8i		−	0.710651i	−0.934743	−	0.355325i	$-0.884370\pi$
$587$		−	10106.8i		−	0.710651i	0.934743	−	0.355325i	$-0.115630\pi$
$588$			461.654i			0.0323780i
$589$	−9633.85			−0.673949
$590$	−5089.07	+	10973.4i	−0.355108	+	0.765711i
$591$	−7217.73			−0.502365
$592$		−	17112.9i		−	1.18807i
$593$			4241.04i			0.293691i	0.989159	+	0.146845i	$0.0469120\pi$
$593$			4241.04i			0.293691i	−0.989159	+	0.146845i	$0.953088\pi$
$594$	1651.50			0.114077
$595$	1753.56	+	813.233i	0.120822	+	0.0560324i
$596$	−8492.97			−0.583701
$597$		−	3577.05i		−	0.245224i
$598$		−	5059.61i		−	0.345992i
$599$	16536.6			1.12799			0.563995	−	0.825778i	$-0.309264\pi$
$599$	16536.6			1.12799			0.563995	+	0.825778i	$0.309264\pi$
$600$	−3929.16	−	4642.98i	−0.267346	−	0.315915i
$601$	−6030.83			−0.409322			−0.204661	−	0.978833i	$-0.565609\pi$
$601$	−6030.83			−0.409322			−0.204661	+	0.978833i	$0.565609\pi$
$602$		−	5154.28i		−	0.348958i
$603$			7371.69i			0.497842i
$604$	−1221.24			−0.0822710
$605$	−10093.7	−	4681.06i	−0.678291	−	0.314566i
$606$	−16490.2			−1.10539
$607$			12639.0i			0.845143i	0.906330	+	0.422572i	$0.138872\pi$
$607$			12639.0i			0.845143i	−0.906330	+	0.422572i	$0.861128\pi$
$608$			10437.0i			0.696176i
$609$	−216.266			−0.0143900
$610$	−10267.3	+	22139.2i	−0.681494	+	1.46949i
$611$	2160.59			0.143058
$612$		−	698.088i		−	0.0461087i
$613$			226.217i			0.0149051i	0.999972	+	0.00745254i	$0.00237224\pi$
$613$			226.217i			0.0149051i	−0.999972	+	0.00745254i	$0.997628\pi$
$614$	6693.84			0.439970
$615$	−6985.93	+	15063.6i	−0.458049	+	0.987680i
$616$	−2080.67			−0.136092
$617$		−	6491.49i		−	0.423561i	−0.977317	−	0.211781i	$-0.932074\pi$
$617$		−	6491.49i		−	0.423561i	0.977317	−	0.211781i	$-0.0679263\pi$
$618$		−	9225.77i		−	0.600510i
$619$	−19224.9			−1.24833			−0.624163	−	0.781294i	$-0.714560\pi$
$619$	−19224.9			−1.24833			−0.624163	+	0.781294i	$0.714560\pi$
$620$	−3963.27	−	1838.01i	−0.256724	−	0.119059i
$621$	−4034.11			−0.260681
$622$			33448.8i			2.15623i
$623$			236.808i			0.0152287i
$624$	−2412.48			−0.154770
$625$	−2584.33	+	15409.8i	−0.165397	+	0.986227i
$626$	−2106.71			−0.134506
$627$		−	4256.79i		−	0.271132i
$628$			9062.79i			0.575868i
$629$	5332.50			0.338030
$630$	2132.78	+	989.103i	0.134876	+	0.0625505i
$631$	21123.5			1.33267			0.666334	−	0.745653i	$-0.267862\pi$
$631$	21123.5			1.33267			0.666334	+	0.745653i	$0.267862\pi$
$632$		−	13141.0i		−	0.827090i
$633$		−	2294.71i		−	0.144086i
$634$	4014.34			0.251467
$635$	1717.57	−	3703.56i	0.107338	−	0.231451i
$636$	−5016.53			−0.312765
$637$			497.138i			0.0309220i
$638$			629.916i			0.0390887i
$639$	4202.46			0.260167
$640$	7964.01	−	17172.6i	0.491883	−	1.06064i
$641$	−8079.31			−0.497837			−0.248918	−	0.968524i	$-0.580075\pi$
$641$	−8079.31			−0.497837			−0.248918	+	0.968524i	$0.580075\pi$
$642$			10622.5i			0.653014i
$643$			28025.8i			1.71887i	0.511249	+	0.859433i	$0.329183\pi$
$643$			28025.8i			1.71887i	−0.511249	+	0.859433i	$0.670817\pi$
$644$	−3284.59			−0.200980
$645$	−6712.63	−	3113.06i	−0.409782	−	0.190041i
$646$	−6382.93			−0.388751
$647$			9585.95i			0.582477i	0.956650	+	0.291239i	$0.0940674\pi$
$647$			9585.95i			0.582477i	−0.956650	+	0.291239i	$0.905933\pi$
$648$			1313.80i			0.0796464i
$649$	5940.17			0.359279
$650$	2734.44	+	3231.21i	0.165006	+	0.194982i
$651$	−2612.88			−0.157307
$652$			1796.22i			0.107892i
$653$			6356.08i			0.380908i	0.981696	+	0.190454i	$0.0609959\pi$
$653$			6356.08i			0.380908i	−0.981696	+	0.190454i	$0.939004\pi$
$654$	15350.5			0.917819
$655$	13193.9	+	6118.82i	0.787065	+	0.365011i
$656$	−39238.8			−2.33539
$657$			1557.60i			0.0924925i
$658$		−	4975.57i		−	0.294784i
$659$	−2394.70			−0.141554			−0.0707772	−	0.997492i	$-0.522548\pi$
$659$	−2394.70			−0.141554			−0.0707772	+	0.997492i	$0.522548\pi$
$660$	812.140	−	1751.20i	0.0478978	−	0.103281i
$661$	−23502.0			−1.38294			−0.691470	−	0.722406i	$-0.743036\pi$
$661$	−23502.0			−1.38294			−0.691470	+	0.722406i	$0.743036\pi$
$662$		−	31032.8i		−	1.82194i
$663$		−	751.745i		−	0.0440353i
$664$	199.840			0.0116796
$665$	2549.44	−	5497.31i	0.148667	−	0.320566i
$666$	6485.71			0.377351
$667$		−	1538.69i		−	0.0893229i
$668$		−	7612.46i		−	0.440921i
$669$	4755.54			0.274828
$670$	27728.8	+	12859.5i	1.59889	+	0.741504i
$671$	11984.4			0.689500
$672$			2830.71i			0.162495i
$673$			31304.2i			1.79300i	0.443047	+	0.896498i	$0.353897\pi$
$673$			31304.2i			1.79300i	−0.443047	+	0.896498i	$0.646103\pi$
$674$	−1694.66			−0.0968486
$675$	2576.30	−	2180.21i	0.146906	−	0.124321i
$676$	−6576.42			−0.374170
$677$			16821.3i			0.954940i	0.878648	+	0.477470i	$0.158446\pi$
$677$			16821.3i			0.954940i	−0.878648	+	0.477470i	$0.841554\pi$
$678$		−	20754.1i		−	1.17560i
$679$	5675.32			0.320764
$680$	4063.17	+	1884.35i	0.229141	+	0.106267i
$681$	−7089.21			−0.398912
$682$			7610.53i			0.427306i
$683$			106.287i			0.00595453i	0.999996	+	0.00297726i	$0.000947694\pi$
$683$			106.287i			0.00595453i	−0.999996	+	0.00297726i	$0.999052\pi$
$684$	−2188.47			−0.122337
$685$	12128.3	−	26151.9i	0.676493	−	1.45871i
$686$	1144.84			0.0637177
$687$		−	4879.32i		−	0.270972i
$688$		−	17485.5i		−	0.968938i
$689$	−5402.12			−0.298700
$690$	−7037.30	+	15174.4i	−0.388269	+	0.837215i
$691$	−19383.5			−1.06712			−0.533562	−	0.845761i	$-0.679147\pi$
$691$	−19383.5			−1.06712			−0.533562	+	0.845761i	$0.679147\pi$
$692$			1967.34i			0.108074i
$693$		−	1154.52i		−	0.0632853i
$694$	−22898.9			−1.25249
$695$	−31092.4	−	14419.5i	−1.69698	−	0.786995i
$696$	−501.110			−0.0272910
$697$		−	12227.1i		−	0.664467i
$698$			30828.9i			1.67176i
$699$	5161.03			0.279267
$700$	2097.63	−	1775.14i	0.113261	−	0.0958484i
$701$	−13338.2			−0.718652			−0.359326	−	0.933212i	$-0.616993\pi$
$701$	−13338.2			−0.718652			−0.359326	+	0.933212i	$0.616993\pi$
$702$		−	914.318i		−	0.0491577i
$703$		−	16717.1i		−	0.896868i
$704$	−3375.20			−0.180692
$705$	−6479.88	−	3005.12i	−0.346165	−	0.160538i
$706$	31440.0			1.67600
$707$			11527.9i			0.613227i
$708$		−	3053.92i		−	0.162109i
$709$	−15225.3			−0.806487			−0.403243	−	0.915093i	$-0.632117\pi$
$709$	−15225.3			−0.806487			−0.403243	+	0.915093i	$0.632117\pi$
$710$	7330.98	−	15807.6i	0.387502	−	0.835563i
$711$	7291.68			0.384612
$712$			548.708i			0.0288816i
$713$		−	18590.2i		−	0.976450i
$714$	−1731.17			−0.0907387
$715$	874.565	−	1885.80i	0.0457439	−	0.0986365i
$716$	7292.59			0.380638
$717$		−	21653.3i		−	1.12783i
$718$			9648.79i			0.501518i
$719$	23884.3			1.23885			0.619427	−	0.785054i	$-0.287365\pi$
$719$	23884.3			1.23885			0.619427	+	0.785054i	$0.287365\pi$
$720$	7235.31	+	3355.46i	0.374505	+	0.173681i
$721$	−6449.52			−0.333138
$722$		−	2883.40i		−	0.148628i
$723$			15284.3i			0.786211i
$724$	14650.3			0.752034
$725$	831.578	+	982.653i	0.0425987	+	0.0503377i
$726$	9964.82			0.509406
$727$		−	27929.5i		−	1.42482i	−0.701761	−	0.712412i	$-0.747603\pi$
$727$		−	27929.5i		−	1.42482i	0.701761	−	0.712412i	$-0.252397\pi$
$728$			1151.92i			0.0586443i
$729$	−729.000			−0.0370370
$730$	5858.93	+	2717.15i	0.297053	+	0.137762i
$731$	5448.62			0.275683
$732$		−	6161.36i		−	0.311107i
$733$			17970.8i			0.905548i	0.891625	+	0.452774i	$0.149566\pi$
$733$			17970.8i			0.905548i	−0.891625	+	0.452774i	$0.850434\pi$
$734$	5241.97			0.263603
$735$	691.458	−	1490.98i	0.0347004	−	0.0748238i
$736$	−20140.0			−1.00865
$737$		−	15010.2i		−	0.750215i
$738$		−	14871.3i		−	0.741762i
$739$	1280.61			0.0637455			0.0318728	−	0.999492i	$-0.489853\pi$
$739$	1280.61			0.0637455			0.0318728	+	0.999492i	$0.489853\pi$
$740$	3189.41	−	6877.25i	0.158439	−	0.341639i
$741$	−2356.68			−0.116835
$742$			12440.4i			0.615499i
$743$			28570.1i			1.41068i	0.708869	+	0.705340i	$0.249206\pi$
$743$			28570.1i			1.41068i	−0.708869	+	0.705340i	$0.750794\pi$
$744$	−6054.32			−0.298336
$745$	27429.3	+	12720.6i	1.34890	+	0.625568i
$746$	−29083.0			−1.42735
$747$			110.887i			0.00543125i
$748$			1421.44i			0.0694828i
$749$	7425.91			0.362265
$750$	−3706.69	−	13494.1i	−0.180466	−	0.656978i
$751$	32836.7			1.59551			0.797754	−	0.602982i	$-0.206021\pi$
$751$	32836.7			1.59551			0.797754	+	0.602982i	$0.206021\pi$
$752$		−	16879.2i		−	0.818514i
$753$		−	13039.5i		−	0.631059i
$754$	348.740			0.0168440
$755$	3944.18	+	1829.16i	0.190123	+	0.0881721i
$756$	−593.555			−0.0285547
$757$		−	1086.72i		−	0.0521763i	−0.999660	−	0.0260882i	$-0.991695\pi$
$757$		−	1086.72i		−	0.0521763i	0.999660	−	0.0260882i	$-0.00830507\pi$
$758$			19291.0i			0.924379i
$759$	8214.23			0.392830
$760$	5907.33	−	12737.8i	0.281949	−	0.607961i
$761$	−17097.7			−0.814443			−0.407221	−	0.913329i	$-0.633502\pi$
$761$	−17097.7			−0.814443			−0.407221	+	0.913329i	$0.633502\pi$
$762$			3656.28i			0.173823i
$763$		−	10731.2i		−	0.509168i
$764$	11714.9			0.554751
$765$	−1045.59	+	2254.57i	−0.0494160	+	0.106555i
$766$	−41188.5			−1.94282
$767$		−	3288.65i		−	0.154819i
$768$			12533.1i			0.588868i
$769$	24796.1			1.16277			0.581386	−	0.813628i	$-0.302511\pi$
$769$	24796.1			1.16277			0.581386	+	0.813628i	$0.302511\pi$
$770$	−4342.76	−	2014.01i	−0.203250	−	0.0942595i
$771$	4284.40			0.200128
$772$		−	8119.01i		−	0.378510i
$773$			33325.8i			1.55064i	0.631567	+	0.775321i	$0.282412\pi$
$773$			33325.8i			1.55064i	−0.631567	+	0.775321i	$0.717588\pi$
$774$	6626.93			0.307752
$775$	10047.0	+	11872.2i	0.465675	+	0.550275i
$776$	13150.3			0.608336
$777$		−	4534.00i		−	0.209339i
$778$		−	26529.8i		−	1.22255i
$779$	−38331.3			−1.76298
$780$	−969.516	−	449.625i	−0.0445054	−	0.0206399i
$781$	−8557.02			−0.392054
$782$		−	12317.0i		−	0.563241i
$783$		−	278.056i		−	0.0126908i
$784$	3883.80			0.176922
$785$	13574.1	−	29269.6i	0.617173	−	1.33080i
$786$	−13025.5			−0.591098
$787$		−	30195.2i		−	1.36765i	−0.729645	−	0.683826i	$-0.760315\pi$
$787$		−	30195.2i		−	1.36765i	0.729645	−	0.683826i	$-0.239685\pi$
$788$		−	7555.77i		−	0.341578i
$789$	10343.3			0.466708
$790$	12720.0	−	27427.8i	0.572856	−	1.23524i
$791$	−14508.7			−0.652175
$792$		−	2675.15i		−	0.120022i
$793$		−	6634.94i		−	0.297117i
$794$	17902.4			0.800168
$795$	16201.6	+	7513.68i	0.722781	+	0.335198i
$796$	3744.57			0.166737
$797$			24226.2i			1.07671i	0.842720	+	0.538353i	$0.180953\pi$
$797$			24226.2i			1.07671i	−0.842720	+	0.538353i	$0.819047\pi$
$798$			5427.14i			0.240750i
$799$	5259.69			0.232884
$800$	12862.0	−	10884.6i	0.568424	−	0.481034i
$801$	−304.467			−0.0134305
$802$			20217.1i			0.890138i
$803$		−	3171.57i		−	0.139380i
$804$	−7716.94			−0.338502
$805$	10608.0	+	4919.61i	0.464452	+	0.215395i
$806$	4213.42			0.184133
$807$			67.1924i			0.00293096i
$808$			26711.4i			1.16300i
$809$	16039.7			0.697065			0.348533	−	0.937297i	$-0.386680\pi$
$809$	16039.7			0.697065			0.348533	+	0.937297i	$0.386680\pi$
$810$	−1271.70	+	2742.15i	−0.0551644	+	0.118950i
$811$	33767.0			1.46205			0.731024	−	0.682352i	$-0.239043\pi$
$811$	33767.0			1.46205			0.731024	+	0.682352i	$0.239043\pi$
$812$		−	226.394i		−	0.00978434i
$813$		−	4671.98i		−	0.201542i
$814$	−13206.2			−0.568644
$815$	2690.35	−	5801.15i	0.115631	−	0.249332i
$816$	−5872.87			−0.251951
$817$		−	17081.1i		−	0.731448i
$818$		−	4167.22i		−	0.178122i
$819$	−639.178			−0.0272707
$820$	−15769.1	−	7313.11i	−0.671562	−	0.311445i
$821$	631.743			0.0268550			0.0134275	−	0.999910i	$-0.495726\pi$
$821$	631.743			0.0268550			0.0134275	+	0.999910i	$0.495726\pi$
$822$			25818.1i			1.09551i
$823$			30565.3i			1.29458i	0.762244	+	0.647290i	$0.224098\pi$
$823$			30565.3i			1.29458i	−0.762244	+	0.647290i	$0.775902\pi$
$824$	−14944.2			−0.631804
$825$	−5245.84	+	4439.34i	−0.221378	+	0.187343i
$826$	−7573.34			−0.319020
$827$			24472.5i			1.02901i	0.857487	+	0.514505i	$0.172024\pi$
$827$			24472.5i			1.02901i	−0.857487	+	0.514505i	$0.827976\pi$
$828$		−	4223.04i		−	0.177247i
$829$	9613.32			0.402756			0.201378	−	0.979514i	$-0.435458\pi$
$829$	9613.32			0.402756			0.201378	+	0.979514i	$0.435458\pi$
$830$	417.104	+	193.437i	0.0174432	+	0.00808951i
$831$	11204.7			0.467736
$832$			1868.61i			0.0778634i
$833$			1210.22i			0.0503381i
$834$	30695.5			1.27446
$835$	−11401.8	+	24585.5i	−0.472547	+	1.01894i
$836$	4456.15			0.184353
$837$		−	3359.42i		−	0.138732i
$838$		−	27784.3i		−	1.14534i
$839$	23320.5			0.959609			0.479805	−	0.877375i	$-0.340707\pi$
$839$	23320.5			0.959609			0.479805	+	0.877375i	$0.340707\pi$
$840$	1602.18	−	3454.75i	0.0658101	−	0.141905i
$841$	−24282.9			−0.995651
$842$			5652.11i			0.231336i
$843$		−	7267.11i		−	0.296907i
$844$	2402.18			0.0979699
$845$	21239.5	+	9850.06i	0.864686	+	0.401009i
$846$	6397.16			0.259975
$847$		−	6966.17i		−	0.282598i
$848$			42203.0i			1.70903i
$849$	849.697			0.0343481
$850$	6656.65	+	7865.98i	0.268613	+	0.317413i
$851$	32258.6			1.29943
$852$			4399.28i			0.176898i
$853$		−	2992.19i		−	0.120106i	−0.998195	−	0.0600531i	$-0.980873\pi$
$853$		−	2992.19i		−	0.120106i	0.998195	−	0.0600531i	$-0.0191270\pi$
$854$	−15279.4			−0.612237
$855$	7067.97	+	3277.86i	0.282713	+	0.131112i
$856$	17206.6			0.687044
$857$			20796.2i			0.828919i	0.910068	+	0.414459i	$0.136029\pi$
$857$			20796.2i			0.828919i	−0.910068	+	0.414459i	$0.863971\pi$
$858$			1861.73i			0.0740774i
$859$	5302.17			0.210603			0.105301	−	0.994440i	$-0.466419\pi$
$859$	5302.17			0.210603			0.105301	+	0.994440i	$0.466419\pi$
$860$	3258.86	−	7027.01i	0.129216	−	0.278627i
$861$	−10396.2			−0.411499
$862$			39233.8i			1.55024i
$863$			27066.7i			1.06762i	0.845603	+	0.533812i	$0.179241\pi$
$863$			27066.7i			1.06762i	−0.845603	+	0.533812i	$0.820759\pi$
$864$	−3639.48			−0.143307
$865$	2946.65	−	6353.79i	0.115825	−	0.249752i
$866$	−48778.8			−1.91406
$867$			12909.0i			0.505665i
$868$		−	2735.26i		−	0.106959i
$869$	−14847.3			−0.579585
$870$	−1045.91	−	485.054i	−0.0407583	−	0.0189022i
$871$	−8310.09			−0.323280
$872$		−	24865.3i		−	0.965648i
$873$			7296.85i			0.282888i
$874$	−38613.1			−1.49440
$875$	−9433.37	+	2591.26i	−0.364464	+	0.100115i
$876$	−1630.54			−0.0628893
$877$			26825.0i			1.03286i	0.856330	+	0.516429i	$0.172739\pi$
$877$			26825.0i			1.03286i	−0.856330	+	0.516429i	$0.827261\pi$
$878$		−	6533.69i		−	0.251141i
$879$	25444.5			0.976360
$880$	−14732.5	−	6832.37i	−0.564355	−	0.261726i
$881$	−47701.8			−1.82420			−0.912098	−	0.409973i	$-0.865538\pi$
$881$	−47701.8			−1.82420			−0.912098	+	0.409973i	$0.865538\pi$
$882$			1471.94i			0.0561938i
$883$		−	28447.5i		−	1.08418i	−0.840319	−	0.542092i	$-0.817632\pi$
$883$		−	28447.5i		−	1.08418i	0.840319	−	0.542092i	$-0.182368\pi$
$884$	786.953			0.0299413
$885$	−4574.11	+	9863.06i	−0.173737	+	0.374625i
$886$	−1190.82			−0.0451538
$887$		−	35046.9i		−	1.32667i	−0.748321	−	0.663337i	$-0.769140\pi$
$887$		−	35046.9i		−	1.32667i	0.748321	−	0.663337i	$-0.230860\pi$
$888$		−	10505.8i		−	0.397016i
$889$	2556.02			0.0964297
$890$	−531.128	+	1145.26i	−0.0200039	+	0.0431339i
$891$	1484.39			0.0558124
$892$			4978.27i			0.186866i
$893$		−	16488.9i		−	0.617894i
$894$	−27079.1			−1.01304
$895$	−23552.4	−	10922.7i	−0.879633	−	0.407940i
$896$	11851.7			0.441895
$897$		−	4547.64i		−	0.169277i
$898$		−	24683.6i		−	0.917262i
$899$	1281.35			0.0475367
$900$	2282.32	+	2696.96i	0.0845304	+	0.0998872i
$901$	−13150.8			−0.486255
$902$			30280.9i			1.11779i
$903$		−	4632.73i		−	0.170728i
$904$	−33618.2			−1.23686
$905$	−47315.1	−	21942.9i	−1.73791	−	0.805976i
$906$	−3893.83			−0.142786
$907$		−	19761.2i		−	0.723439i	−0.932287	−	0.361720i	$-0.882190\pi$
$907$		−	19761.2i		−	0.723439i	0.932287	−	0.361720i	$-0.117810\pi$
$908$		−	7421.23i		−	0.271236i
$909$	−14821.6			−0.540815
$910$	−1115.01	+	2404.28i	−0.0406180	+	0.0875836i
$911$	23563.4			0.856960			0.428480	−	0.903551i	$-0.359049\pi$
$911$	23563.4			0.856960			0.428480	+	0.903551i	$0.359049\pi$
$912$			18411.2i			0.668481i
$913$		−	225.788i		−	0.00818453i
$914$	−42463.4			−1.53672
$915$	−9228.38	+	19899.0i	−0.333422	+	0.718950i
$916$	5107.84			0.184244
$917$			9105.78i			0.327917i
$918$		−	2225.79i		−	0.0800240i
$919$	37601.1			1.34967			0.674834	−	0.737970i	$-0.264215\pi$
$919$	37601.1			1.34967			0.674834	+	0.737970i	$0.264215\pi$
$920$	24579.9	+	11399.2i	0.880844	+	0.408502i
$921$	6016.50			0.215256
$922$		−	7364.54i		−	0.263057i
$923$			4737.42i			0.168943i
$924$	1208.59			0.0430301
$925$	−20601.3	+	17434.0i	−0.732288	+	0.619705i
$926$	53110.2			1.88478
$927$		−	8292.24i		−	0.293800i
$928$		−	1388.17i		−	0.0491046i
$929$	17616.6			0.622154			0.311077	−	0.950385i	$-0.399310\pi$
$929$	17616.6			0.622154			0.311077	+	0.950385i	$0.399310\pi$
$930$	−12636.5	−	5860.34i	−0.445557	−	0.206632i
$931$	3793.98			0.133558
$932$			5402.74i			0.189885i
$933$			30064.2i			1.05494i
$934$	−25375.6			−0.888990
$935$	2129.02	−	4590.75i	0.0744666	−	0.160571i
$936$	−1481.04			−0.0517194
$937$		−	36717.2i		−	1.28015i	−0.768313	−	0.640074i	$-0.778904\pi$
$937$		−	36717.2i		−	1.28015i	0.768313	−	0.640074i	$-0.221096\pi$
$938$			19137.1i			0.666148i
$939$	−1893.53			−0.0658074
$940$	3145.86	−	6783.36i	0.109156	−	0.235371i
$941$	21861.7			0.757354			0.378677	−	0.925529i	$-0.376379\pi$
$941$	21861.7			0.757354			0.378677	+	0.925529i	$0.376379\pi$
$942$			28895.9i			0.999448i
$943$		−	73967.0i		−	2.55429i
$944$	−25692.0			−0.885809
$945$	1916.97	+	889.018i	0.0659884	+	0.0306029i
$946$	−13493.7			−0.463762
$947$		−	17752.1i		−	0.609149i	−0.952488	−	0.304575i	$-0.901486\pi$
$947$		−	17752.1i		−	0.609149i	0.952488	−	0.304575i	$-0.0985143\pi$
$948$			7633.18i			0.261513i
$949$	−1755.87			−0.0600612
$950$	24659.5	−	20868.3i	0.842167	−	0.712690i
$951$	3608.14			0.123030
$952$			2804.21i			0.0954673i
$953$		−	26764.9i		−	0.909758i	−0.890553	−	0.454879i	$-0.849683\pi$
$953$		−	26764.9i		−	0.909758i	0.890553	−	0.454879i	$-0.150317\pi$
$954$	−15994.8			−0.542819
$955$	−37834.9	−	17546.4i	−1.28200	−	0.594542i
$956$	22667.4			0.766857
$957$			566.176i			0.0191242i
$958$		−	5613.83i		−	0.189326i
$959$	18048.8			0.607744
$960$	2599.00	−	5604.17i	0.0873776	−	0.188410i
$961$	−14309.9			−0.480344
$962$			7311.32i			0.245038i
$963$			9547.59i			0.319488i
$964$	−16000.2			−0.534575
$965$	−12160.5	+	26221.5i	−0.405660	+	0.874715i
$966$	−10472.6			−0.348811
$967$		−	31173.9i		−	1.03669i	−0.855170	−	0.518347i	$-0.826547\pi$
$967$		−	31173.9i		−	1.03669i	0.855170	−	0.518347i	$-0.173453\pi$
$968$		−	16141.3i		−	0.535953i
$969$	−5737.05			−0.190197
$970$	27447.2	+	12729.0i	0.908533	+	0.421343i
$971$	−35414.7			−1.17046			−0.585228	−	0.810869i	$-0.698995\pi$
$971$	−35414.7			−1.17046			−0.585228	+	0.810869i	$0.698995\pi$
$972$		−	763.142i		−	0.0251829i
$973$		−	21458.5i		−	0.707016i
$974$	47085.6			1.54899
$975$	2457.75	+	2904.25i	0.0807292	+	0.0953954i
$976$	−51834.3			−1.69997
$977$			20952.6i			0.686112i	0.939315	+	0.343056i	$0.111462\pi$
$977$			20952.6i			0.686112i	−0.939315	+	0.343056i	$0.888538\pi$
$978$			5727.10i			0.187252i
$979$	619.955			0.0202388
$980$	1560.81	+	723.842i	0.0508756	+	0.0235942i
$981$	13797.2			0.449044
$982$			30073.7i			0.977281i
$983$		−	20858.6i		−	0.676793i	−0.941004	−	0.338396i	$-0.890116\pi$
$983$		−	20858.6i		−	0.676793i	0.941004	−	0.338396i	$-0.109884\pi$
$984$	−24089.0			−0.780417
$985$	−11316.9	+	24402.4i	−0.366078	+	0.789366i
$986$	848.963			0.0274204
$987$		−	4472.10i		−	0.144223i
$988$		−	2467.06i		−	0.0794409i
$989$	32961.1			1.05976
$990$	2589.44	−	5583.55i	0.0831290	−	0.179249i
$991$	−13565.0			−0.434820			−0.217410	−	0.976080i	$-0.569761\pi$
$991$	−13565.0			−0.434820			−0.217410	+	0.976080i	$0.569761\pi$
$992$		−	16771.7i		−	0.536795i
$993$		−	27892.7i		−	0.891386i
$994$	10909.7			0.348122
$995$	−12093.6	−	5608.57i	−0.385320	−	0.178697i
$996$	−116.080			−0.00369292
$997$			12520.7i			0.397727i	0.980027	+	0.198864i	$0.0637251\pi$
$997$			12520.7i			0.397727i	−0.980027	+	0.198864i	$0.936275\pi$
$998$		−	8861.94i		−	0.281082i
$999$	5829.43			0.184620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.d.b.64.8	yes	10
3.2	odd	2		315.4.d.b.64.3		10
5.2	odd	4		525.4.a.w.1.2		5
5.3	odd	4		525.4.a.x.1.4		5
5.4	even	2	inner	105.4.d.b.64.3	✓	10
15.2	even	4		1575.4.a.bp.1.4		5
15.8	even	4		1575.4.a.bo.1.2		5
15.14	odd	2		315.4.d.b.64.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.3	✓	10	5.4	even	2	inner
105.4.d.b.64.8	yes	10	1.1	even	1	trivial
315.4.d.b.64.3		10	3.2	odd	2
315.4.d.b.64.8		10	15.14	odd	2
525.4.a.w.1.2		5	5.2	odd	4
525.4.a.x.1.4		5	5.3	odd	4
1575.4.a.bo.1.2		5	15.8	even	4
1575.4.a.bp.1.4		5	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.33774i q^{2} +3.00000i q^{3} -3.14050 q^{4} +(10.1427 + 4.70380i) q^{5} -10.0132 q^{6} +7.00000i q^{7} +16.2197i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.33774i q^{2} +3.00000i q^{3} -3.14050 q^{4} +(10.1427 + 4.70380i) q^{5} -10.0132 q^{6} +7.00000i q^{7} +16.2197i q^{8} -9.00000 q^{9} +(-15.7000 + 33.8537i) q^{10} +18.3258 q^{11} -9.42151i q^{12} -10.1457i q^{13} -23.3642 q^{14} +(-14.1114 + 30.4281i) q^{15} -79.2613 q^{16} -24.6984i q^{17} -30.0397i q^{18} -77.4282 q^{19} +(-31.8532 - 14.7723i) q^{20} -21.0000 q^{21} +61.1666i q^{22} -149.411i q^{23} -48.6592 q^{24} +(80.7486 + 95.4184i) q^{25} +33.8636 q^{26} -27.0000i q^{27} -21.9835i q^{28} +10.2984 q^{29} +(-101.561 - 47.1001i) q^{30} +124.423 q^{31} -134.796i q^{32} +54.9773i q^{33} +82.4367 q^{34} +(-32.9266 + 70.9989i) q^{35} +28.2645 q^{36} +215.905i q^{37} -258.435i q^{38} +30.4370 q^{39} +(-76.2943 + 164.512i) q^{40} +495.056 q^{41} -70.0925i q^{42} +220.606i q^{43} -57.5521 q^{44} +(-91.2843 - 42.3342i) q^{45} +498.696 q^{46} +212.957i q^{47} -237.784i q^{48} -49.0000 q^{49} +(-318.482 + 269.518i) q^{50} +74.0951 q^{51} +31.8625i q^{52} -532.455i q^{53} +90.1190 q^{54} +(185.873 + 86.2007i) q^{55} -113.538 q^{56} -232.284i q^{57} +34.3732i q^{58} +324.143 q^{59} +(44.3169 - 95.5595i) q^{60} +653.967 q^{61} +415.292i q^{62} -63.0000i q^{63} -184.178 q^{64} +(47.7232 - 102.905i) q^{65} -183.500 q^{66} -819.077i q^{67} +77.5653i q^{68} +448.234 q^{69} +(-236.976 - 109.900i) q^{70} -466.940 q^{71} -145.978i q^{72} -173.066i q^{73} -720.634 q^{74} +(-286.255 + 242.246i) q^{75} +243.163 q^{76} +128.280i q^{77} +101.591i q^{78} -810.186 q^{79} +(-803.923 - 372.829i) q^{80} +81.0000 q^{81} +1652.37i q^{82} -12.3208i q^{83} +65.9506 q^{84} +(116.176 - 250.508i) q^{85} -736.326 q^{86} +30.8951i q^{87} +297.239i q^{88} +33.8297 q^{89} +(141.300 - 304.683i) q^{90} +71.0198 q^{91} +469.227i q^{92} +373.269i q^{93} -710.795 q^{94} +(-785.330 - 364.206i) q^{95} +404.387 q^{96} -810.761i q^{97} -163.549i q^{98} -164.932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9}+O(q^{10}) \) 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9	\( 10 q - 54 q^{4} - 14 q^{5} - 6 q^{6} - 90 q^{9} + 92 q^{10} + 132 q^{11} - 14 q^{14} + 310 q^{16} - 348 q^{19} + 366 q^{20} - 210 q^{21} + 198 q^{24} - 374 q^{25} + 892 q^{26} - 740 q^{29} - 378 q^{30} + 684 q^{31} - 224 q^{34} + 486 q^{36} - 12 q^{39} - 2156 q^{40} + 1604 q^{41} - 580 q^{44} + 126 q^{45} + 1280 q^{46} - 490 q^{49} - 2504 q^{50} - 648 q^{51} + 54 q^{54} - 452 q^{55} + 462 q^{56} - 1408 q^{59} - 852 q^{60} + 1300 q^{61} - 150 q^{64} - 3296 q^{65} + 3036 q^{66} - 696 q^{69} - 882 q^{70} + 2940 q^{71} + 2624 q^{74} - 408 q^{75} + 8740 q^{76} + 1640 q^{79} - 4126 q^{80} + 810 q^{81} + 1134 q^{84} - 1704 q^{85} + 1664 q^{86} - 572 q^{89} - 828 q^{90} - 28 q^{91} - 5080 q^{94} + 1268 q^{95} + 330 q^{96} - 1188 q^{99}+O(q^{100}) \) 10 * q - 54 * q^4 - 14 * q^5 - 6 * q^6 - 90 * q^9 + 92 * q^10 + 132 * q^11 - 14 * q^14 + 310 * q^16 - 348 * q^19 + 366 * q^20 - 210 * q^21 + 198 * q^24 - 374 * q^25 + 892 * q^26 - 740 * q^29 - 378 * q^30 + 684 * q^31 - 224 * q^34 + 486 * q^36 - 12 * q^39 - 2156 * q^40 + 1604 * q^41 - 580 * q^44 + 126 * q^45 + 1280 * q^46 - 490 * q^49 - 2504 * q^50 - 648 * q^51 + 54 * q^54 - 452 * q^55 + 462 * q^56 - 1408 * q^59 - 852 * q^60 + 1300 * q^61 - 150 * q^64 - 3296 * q^65 + 3036 * q^66 - 696 * q^69 - 882 * q^70 + 2940 * q^71 + 2624 * q^74 - 408 * q^75 + 8740 * q^76 + 1640 * q^79 - 4126 * q^80 + 810 * q^81 + 1134 * q^84 - 1704 * q^85 + 1664 * q^86 - 572 * q^89 - 828 * q^90 - 28 * q^91 - 5080 * q^94 + 1268 * q^95 + 330 * q^96 - 1188 * q^99

Introduction

L-functions

Modular forms

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Database

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