LMFDB - Embedded newform 230.4.b.a.139.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("230.139");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.b (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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 212 x^{12} + 17560 x^{10} + 728073 x^{8} + 16036416 x^{6} + 183184060 x^{4} + 961600400 x^{2} + 1560250000 $ x^14 + 212x^12 + 17560x^10 + 728073x^8 + 16036416x^6 + 183184060x^4 + 961600400x^2 + 1560250000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.13
Root			$6.41782i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.4.b.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +7.41782i q^{3} -4.00000 q^{4} +(2.14945 + 10.9718i) q^{5} -14.8356 q^{6} -26.7462i q^{7} -8.00000i q^{8} -28.0240 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +7.41782i q^{3} -4.00000 q^{4} +(2.14945 + 10.9718i) q^{5} -14.8356 q^{6} -26.7462i q^{7} -8.00000i q^{8} -28.0240 q^{9} +(-21.9436 + 4.29890i) q^{10} -54.5721 q^{11} -29.6713i q^{12} -77.3832i q^{13} +53.4923 q^{14} +(-81.3866 + 15.9442i) q^{15} +16.0000 q^{16} +76.1065i q^{17} -56.0480i q^{18} -125.597 q^{19} +(-8.59780 - 43.8871i) q^{20} +198.398 q^{21} -109.144i q^{22} -23.0000i q^{23} +59.3425 q^{24} +(-115.760 + 47.1665i) q^{25} +154.766 q^{26} -7.59574i q^{27} +106.985i q^{28} +156.599 q^{29} +(-31.8884 - 162.773i) q^{30} -53.3110 q^{31} +32.0000i q^{32} -404.805i q^{33} -152.213 q^{34} +(293.453 - 57.4895i) q^{35} +112.096 q^{36} +130.806i q^{37} -251.194i q^{38} +574.014 q^{39} +(87.7742 - 17.1956i) q^{40} -463.560 q^{41} +396.796i q^{42} -125.366i q^{43} +218.288 q^{44} +(-60.2361 - 307.473i) q^{45} +46.0000 q^{46} +297.322i q^{47} +118.685i q^{48} -372.357 q^{49} +(-94.3331 - 231.519i) q^{50} -564.544 q^{51} +309.533i q^{52} +417.759i q^{53} +15.1915 q^{54} +(-117.300 - 598.752i) q^{55} -213.969 q^{56} -931.654i q^{57} +313.199i q^{58} +311.028 q^{59} +(325.546 - 63.7769i) q^{60} +226.749 q^{61} -106.622i q^{62} +749.534i q^{63} -64.0000 q^{64} +(849.031 - 166.331i) q^{65} +809.611 q^{66} -544.207i q^{67} -304.426i q^{68} +170.610 q^{69} +(114.979 + 586.906i) q^{70} -924.282 q^{71} +224.192i q^{72} -559.650i q^{73} -261.613 q^{74} +(-349.873 - 858.684i) q^{75} +502.387 q^{76} +1459.59i q^{77} +1148.03i q^{78} -224.441 q^{79} +(34.3912 + 175.548i) q^{80} -700.304 q^{81} -927.119i q^{82} +723.415i q^{83} -793.592 q^{84} +(-835.024 + 163.587i) q^{85} +250.732 q^{86} +1161.63i q^{87} +436.576i q^{88} -561.018 q^{89} +(614.946 - 120.472i) q^{90} -2069.70 q^{91} +92.0000i q^{92} -395.451i q^{93} -594.645 q^{94} +(-269.964 - 1378.02i) q^{95} -237.370 q^{96} +1041.19i q^{97} -744.714i q^{98} +1529.33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) $ 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9	$ 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) $ 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9 - 40 * q^10 - 146 * q^11 + 176 * q^14 - 206 * q^15 + 224 * q^16 + 154 * q^19 + 24 * q^20 - 220 * q^21 + 144 * q^24 - 286 * q^25 - 180 * q^26 + 790 * q^29 - 232 * q^30 - 320 * q^31 - 200 * q^34 - 426 * q^35 + 272 * q^36 + 1616 * q^39 + 160 * q^40 - 1904 * q^41 + 584 * q^44 + 622 * q^45 + 644 * q^46 + 610 * q^49 + 200 * q^50 - 1834 * q^51 + 192 * q^54 + 854 * q^55 - 704 * q^56 + 2814 * q^59 + 824 * q^60 - 3742 * q^61 - 896 * q^64 + 1730 * q^65 - 612 * q^66 + 414 * q^69 + 348 * q^70 - 3808 * q^71 + 268 * q^74 + 2904 * q^75 - 616 * q^76 - 1528 * q^79 - 96 * q^80 - 4618 * q^81 + 880 * q^84 + 2574 * q^85 - 2024 * q^86 + 2336 * q^89 + 2092 * q^90 - 3866 * q^91 + 456 * q^94 + 838 * q^95 - 576 * q^96 + 3342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$			7.41782i			1.42756i	0.700370	+	0.713780i	$0.253018\pi$
$3$			7.41782i			1.42756i	−0.700370	+	0.713780i	$0.746982\pi$
$4$	−4.00000			−0.500000
$5$	2.14945	+	10.9718i	0.192253	+	0.981345i
$5$	2.14945	+	10.9718i	0.192253	+	0.981345i
$6$	−14.8356			−1.00944
$7$		−	26.7462i		−	1.44416i	−0.691811	−	0.722078i	$-0.743187\pi$
$7$		−	26.7462i		−	1.44416i	0.691811	−	0.722078i	$-0.256813\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−28.0240			−1.03793
$10$	−21.9436	+	4.29890i	−0.693916	+	0.135943i
$11$	−54.5721			−1.49583			−0.747913	−	0.663796i	$-0.768944\pi$
$11$	−54.5721			−1.49583			−0.747913	+	0.663796i	$0.768944\pi$
$12$		−	29.6713i		−	0.713780i
$13$		−	77.3832i		−	1.65094i	−0.564445	−	0.825470i	$-0.690910\pi$
$13$		−	77.3832i		−	1.65094i	0.564445	−	0.825470i	$-0.309090\pi$
$14$	53.4923			1.02117
$15$	−81.3866	+	15.9442i	−1.40093	+	0.274452i
$16$	16.0000			0.250000
$17$			76.1065i			1.08580i	0.839798	+	0.542898i	$0.182673\pi$
$17$			76.1065i			1.08580i	−0.839798	+	0.542898i	$0.817327\pi$
$18$		−	56.0480i		−	0.733924i
$19$	−125.597			−1.51652			−0.758260	−	0.651952i	$-0.773950\pi$
$19$	−125.597			−1.51652			−0.758260	+	0.651952i	$0.773950\pi$
$20$	−8.59780	−	43.8871i	−0.0961263	−	0.490673i
$21$	198.398			2.06162
$22$		−	109.144i		−	1.05771i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	59.3425			0.504718
$25$	−115.760	+	47.1665i	−0.926078	+	0.377332i
$26$	154.766			1.16739
$27$		−	7.59574i		−	0.0541408i
$28$			106.985i			0.722078i
$29$	156.599			1.00275			0.501375	−	0.865230i	$-0.332828\pi$
$29$	156.599			1.00275			0.501375	+	0.865230i	$0.332828\pi$
$30$	−31.8884	−	162.773i	−0.194067	−	0.990606i
$31$	−53.3110			−0.308869			−0.154434	−	0.988003i	$-0.549356\pi$
$31$	−53.3110			−0.308869			−0.154434	+	0.988003i	$0.549356\pi$
$32$			32.0000i			0.176777i
$33$		−	404.805i		−	2.13538i
$34$	−152.213			−0.767774
$35$	293.453	−	57.4895i	1.41722	−	0.277643i
$36$	112.096			0.518963
$37$			130.806i			0.581201i	0.956844	+	0.290601i	$0.0938551\pi$
$37$			130.806i			0.581201i	−0.956844	+	0.290601i	$0.906145\pi$
$38$		−	251.194i		−	1.07234i
$39$	574.014			2.35682
$40$	87.7742	−	17.1956i	0.346958	−	0.0679715i
$41$	−463.560			−1.76575			−0.882876	−	0.469605i	$-0.844396\pi$
$41$	−463.560			−1.76575			−0.882876	+	0.469605i	$0.844396\pi$
$42$			396.796i			1.45778i
$43$		−	125.366i		−	0.444608i	−0.974977	−	0.222304i	$-0.928642\pi$
$43$		−	125.366i		−	0.444608i	0.974977	−	0.222304i	$-0.0713578\pi$
$44$	218.288			0.747913
$45$	−60.2361	−	307.473i	−0.199544	−	1.01856i
$46$	46.0000			0.147442
$47$			297.322i			0.922743i	0.887207	+	0.461372i	$0.152642\pi$
$47$			297.322i			0.922743i	−0.887207	+	0.461372i	$0.847358\pi$
$48$			118.685i			0.356890i
$49$	−372.357			−1.08559
$50$	−94.3331	−	231.519i	−0.266814	−	0.654836i
$51$	−564.544			−1.55004
$52$			309.533i			0.825470i
$53$			417.759i			1.08271i	0.840794	+	0.541355i	$0.182089\pi$
$53$			417.759i			1.08271i	−0.840794	+	0.541355i	$0.817911\pi$
$54$	15.1915			0.0382833
$55$	−117.300	−	598.752i	−0.287577	−	1.46792i
$56$	−213.969			−0.510587
$57$		−	931.654i		−	2.16492i
$58$			313.199i			0.709052i
$59$	311.028			0.686312			0.343156	−	0.939278i	$-0.388504\pi$
$59$	311.028			0.686312			0.343156	+	0.939278i	$0.388504\pi$
$60$	325.546	−	63.7769i	0.700464	−	0.137226i
$61$	226.749			0.475938			0.237969	−	0.971273i	$-0.423518\pi$
$61$	226.749			0.475938			0.237969	+	0.971273i	$0.423518\pi$
$62$		−	106.622i		−	0.218403i
$63$			749.534i			1.49893i
$64$	−64.0000			−0.125000
$65$	849.031	−	166.331i	1.62014	−	0.317398i
$66$	809.611			1.50994
$67$		−	544.207i		−	0.992321i	−0.868231	−	0.496160i	$-0.834743\pi$
$67$		−	544.207i		−	0.992321i	0.868231	−	0.496160i	$-0.165257\pi$
$68$		−	304.426i		−	0.542898i
$69$	170.610			0.297667
$70$	114.979	+	586.906i	0.196323	+	1.00212i
$71$	−924.282			−1.54496			−0.772479	−	0.635040i	$-0.780984\pi$
$71$	−924.282			−1.54496			−0.772479	+	0.635040i	$0.780984\pi$
$72$			224.192i			0.366962i
$73$		−	559.650i		−	0.897289i	−0.893710	−	0.448644i	$-0.851907\pi$
$73$		−	559.650i		−	0.897289i	0.893710	−	0.448644i	$-0.148093\pi$
$74$	−261.613			−0.410971
$75$	−349.873	−	858.684i	−0.538664	−	1.32203i
$76$	502.387			0.758260
$77$			1459.59i			2.16021i
$78$			1148.03i			1.66652i
$79$	−224.441			−0.319640			−0.159820	−	0.987146i	$-0.551091\pi$
$79$	−224.441			−0.319640			−0.159820	+	0.987146i	$0.551091\pi$
$80$	34.3912	+	175.548i	0.0480631	+	0.245336i
$81$	−700.304			−0.960636
$82$		−	927.119i		−	1.24858i
$83$			723.415i			0.956689i	0.878172	+	0.478344i	$0.158763\pi$
$83$			723.415i			0.956689i	−0.878172	+	0.478344i	$0.841237\pi$
$84$	−793.592			−1.03081
$85$	−835.024	+	163.587i	−1.06554	+	0.208747i
$86$	250.732			0.314386
$87$			1161.63i			1.43149i
$88$			436.576i			0.528855i
$89$	−561.018			−0.668177			−0.334089	−	0.942542i	$-0.608428\pi$
$89$	−561.018			−0.668177			−0.334089	+	0.942542i	$0.608428\pi$
$90$	614.946	−	120.472i	0.720233	−	0.141099i
$91$	−2069.70			−2.38422
$92$			92.0000i			0.104257i
$93$		−	395.451i		−	0.440928i
$94$	−594.645			−0.652478
$95$	−269.964	−	1378.02i	−0.291555	−	1.48823i
$96$	−237.370			−0.252359
$97$			1041.19i			1.08987i	0.838479	+	0.544935i	$0.183446\pi$
$97$			1041.19i			1.08987i	−0.838479	+	0.544935i	$0.816554\pi$
$98$		−	744.714i		−	0.767627i
$99$	1529.33			1.55256
$100$	463.039	−	188.666i	0.463039	−	0.188666i
$101$	1060.71			1.04499			0.522496	−	0.852642i	$-0.325001\pi$
$101$	1060.71			1.04499			0.522496	+	0.852642i	$0.325001\pi$
$102$		−	1129.09i		−	1.09604i
$103$			425.375i			0.406927i	0.979083	+	0.203464i	$0.0652198\pi$
$103$			425.375i			0.406927i	−0.979083	+	0.203464i	$0.934780\pi$
$104$	−619.065			−0.583696
$105$	426.447	+	2176.78i	0.396352	+	2.02316i
$106$	−835.519			−0.765592
$107$		−	420.550i		−	0.379964i	−0.981788	−	0.189982i	$-0.939157\pi$
$107$		−	420.550i		−	0.379964i	0.981788	−	0.189982i	$-0.0608429\pi$
$108$			30.3829i			0.0270704i
$109$	−132.177			−0.116149			−0.0580745	−	0.998312i	$-0.518496\pi$
$109$	−132.177			−0.116149			−0.0580745	+	0.998312i	$0.518496\pi$
$110$	1197.50	−	234.600i	1.03798	−	0.203347i
$111$	−970.298			−0.829699
$112$		−	427.939i		−	0.361039i
$113$			1770.91i			1.47427i	0.675743	+	0.737137i	$0.263823\pi$
$113$			1770.91i			1.47427i	−0.675743	+	0.737137i	$0.736177\pi$
$114$	1863.31			1.53083
$115$	252.351	−	49.4373i	0.204625	−	0.0400874i
$116$	−626.397			−0.501375
$117$			2168.59i			1.71355i
$118$			622.056i			0.485296i
$119$	2035.56			1.56806
$120$	127.554	+	651.093i	0.0970334	+	0.495303i
$121$	1647.11			1.23750
$122$			453.498i			0.336539i
$123$		−	3438.60i		−	2.52072i
$124$	213.244			0.154434
$125$	−766.320	−	1168.71i	−0.548334	−	0.836259i
$126$	−1499.07			−1.05990
$127$		−	1545.13i		−	1.07959i	−0.841796	−	0.539795i	$-0.818502\pi$
$127$		−	1545.13i		−	1.07959i	0.841796	−	0.539795i	$-0.181498\pi$
$128$		−	128.000i		−	0.0883883i
$129$	929.943			0.634705
$130$	332.662	+	1698.06i	0.224434	+	1.14561i
$131$	−2183.96			−1.45659			−0.728296	−	0.685262i	$-0.759687\pi$
$131$	−2183.96			−1.45659			−0.728296	+	0.685262i	$0.759687\pi$
$132$			1619.22i			1.06769i
$133$			3359.23i			2.19009i
$134$	1088.41			0.701677
$135$	83.3387	−	16.3266i	0.0531308	−	0.0104087i
$136$	608.852			0.383887
$137$		−	501.339i		−	0.312645i	−0.987706	−	0.156322i	$-0.950036\pi$
$137$		−	501.339i		−	0.312645i	0.987706	−	0.156322i	$-0.0499639\pi$
$138$			341.220i			0.210482i
$139$	−216.753			−0.132264			−0.0661322	−	0.997811i	$-0.521066\pi$
$139$	−216.753			−0.132264			−0.0661322	+	0.997811i	$0.521066\pi$
$140$	−1173.81	+	229.958i	−0.708608	+	0.138821i
$141$	−2205.48			−1.31727
$142$		−	1848.56i		−	1.09245i
$143$			4222.96i			2.46952i
$144$	−448.384			−0.259481
$145$	336.602	+	1718.17i	0.192781	+	0.984045i
$146$	1119.30			0.634479
$147$		−	2762.07i		−	1.54974i
$148$		−	523.226i		−	0.290601i
$149$	1599.80			0.879601			0.439801	−	0.898095i	$-0.355049\pi$
$149$	1599.80			0.879601			0.439801	+	0.898095i	$0.355049\pi$
$150$	1717.37	−	699.745i	0.934817	−	0.380893i
$151$	1466.08			0.790119			0.395060	−	0.918655i	$-0.370724\pi$
$151$	1466.08			0.790119			0.395060	+	0.918655i	$0.370724\pi$
$152$			1004.77i			0.536171i
$153$		−	2132.81i		−	1.12698i
$154$	−2919.19			−1.52750
$155$	−114.589	−	584.916i	−0.0593808	−	0.303107i
$156$	−2296.06			−1.17841
$157$			1430.05i			0.726945i	0.931605	+	0.363473i	$0.118409\pi$
$157$			1430.05i			0.726945i	−0.931605	+	0.363473i	$0.881591\pi$
$158$		−	448.881i		−	0.226019i
$159$	−3098.86			−1.54563
$160$	−351.097	+	68.7824i	−0.173479	+	0.0339858i
$161$	−615.162			−0.301127
$162$		−	1400.61i		−	0.679272i
$163$		−	1093.56i		−	0.525486i	−0.964866	−	0.262743i	$-0.915373\pi$
$163$		−	1093.56i		−	0.525486i	0.964866	−	0.262743i	$-0.0846272\pi$
$164$	1854.24			0.882876
$165$	4441.44	−	870.109i	2.09555	−	0.410533i
$166$	−1446.83			−0.676481
$167$		−	2779.02i		−	1.28771i	−0.765148	−	0.643854i	$-0.777334\pi$
$167$		−	2779.02i		−	1.28771i	0.765148	−	0.643854i	$-0.222666\pi$
$168$		−	1587.18i		−	0.728892i
$169$	−3791.16			−1.72561
$170$	−327.174	−	1670.05i	−0.147607	−	0.753452i
$171$	3519.72			1.57404
$172$			501.465i			0.222304i
$173$		−	4246.47i		−	1.86620i	−0.359611	−	0.933102i	$-0.617090\pi$
$173$		−	4246.47i		−	1.86620i	0.359611	−	0.933102i	$-0.382910\pi$
$174$	−2323.25			−1.01221
$175$	1261.52	+	3096.13i	0.544927	+	1.33740i
$176$	−873.153			−0.373957
$177$			2307.15i			0.979751i
$178$		−	1122.04i		−	0.472473i
$179$	−1098.73			−0.458785			−0.229393	−	0.973334i	$-0.573674\pi$
$179$	−1098.73			−0.458785			−0.229393	+	0.973334i	$0.573674\pi$
$180$	240.945	+	1229.89i	0.0997719	+	0.509282i
$181$	476.628			0.195732			0.0978660	−	0.995200i	$-0.468798\pi$
$181$	476.628			0.195732			0.0978660	+	0.995200i	$0.468798\pi$
$182$		−	4139.41i		−	1.68590i
$183$			1681.98i			0.679430i
$184$	−184.000			−0.0737210
$185$	−1435.18	+	281.162i	−0.570359	+	0.111737i
$186$	790.902			0.311783
$187$		−	4153.29i		−	1.62416i
$188$		−	1189.29i		−	0.461372i
$189$	−203.157			−0.0781877
$190$	2756.04	−	539.928i	1.05234	−	0.206160i
$191$	−4164.41			−1.57762			−0.788812	−	0.614634i	$-0.789304\pi$
$191$	−4164.41			−1.57762			−0.788812	+	0.614634i	$0.789304\pi$
$192$		−	474.740i		−	0.178445i
$193$			2275.49i			0.848669i	0.905505	+	0.424335i	$0.139492\pi$
$193$			2275.49i			0.848669i	−0.905505	+	0.424335i	$0.860508\pi$
$194$	−2082.39			−0.770654
$195$	1233.81	+	6297.95i	0.453104	+	2.31285i
$196$	1489.43			0.542794
$197$		−	4470.86i		−	1.61693i	−0.588544	−	0.808465i	$-0.700299\pi$
$197$		−	4470.86i		−	1.61693i	0.588544	−	0.808465i	$-0.299701\pi$
$198$			3058.65i			1.09782i
$199$	5347.50			1.90489			0.952447	−	0.304704i	$-0.0985576\pi$
$199$	5347.50			1.90489			0.952447	+	0.304704i	$0.0985576\pi$
$200$	377.332	+	926.078i	0.133407	+	0.327418i
$201$	4036.83			1.41660
$202$			2121.41i			0.738921i
$203$		−	4188.43i		−	1.44813i
$204$	2258.18			0.775019
$205$	−996.398	−	5086.07i	−0.339470	−	1.73281i
$206$	−850.751			−0.287741
$207$			644.552i			0.216422i
$208$		−	1238.13i		−	0.412735i
$209$	6854.08			2.26845
$210$	−4353.56	+	852.893i	−1.43059	+	0.280263i
$211$	−3059.52			−0.998228			−0.499114	−	0.866536i	$-0.666341\pi$
$211$	−3059.52			−0.998228			−0.499114	+	0.866536i	$0.666341\pi$
$212$		−	1671.04i		−	0.541355i
$213$		−	6856.15i		−	2.20552i
$214$	841.100			0.268675
$215$	1375.49	−	269.468i	0.436314	−	0.0854771i
$216$	−60.7659			−0.0191416
$217$			1425.86i			0.446055i
$218$		−	264.353i		−	0.0821297i
$219$	4151.38			1.28093
$220$	469.199	+	2395.01i	0.143788	+	0.733961i
$221$	5889.36			1.79259
$222$		−	1940.60i		−	0.586686i
$223$			2449.79i			0.735650i	0.929895	+	0.367825i	$0.119897\pi$
$223$			2449.79i			0.735650i	−0.929895	+	0.367825i	$0.880103\pi$
$224$	855.877			0.255293
$225$	3244.05	−	1321.79i	0.961200	−	0.391643i
$226$	−3541.82			−1.04247
$227$			3193.53i			0.933755i	0.884322	+	0.466877i	$0.154621\pi$
$227$			3193.53i			0.933755i	−0.884322	+	0.466877i	$0.845379\pi$
$228$			3726.62i			1.08246i
$229$	3128.13			0.902675			0.451338	−	0.892353i	$-0.350947\pi$
$229$	3128.13			0.902675			0.451338	+	0.892353i	$0.350947\pi$
$230$	98.8747	+	504.702i	0.0283461	+	0.144691i
$231$	−10827.0			−3.08383
$232$		−	1252.79i		−	0.354526i
$233$			4840.99i			1.36113i	0.732686	+	0.680567i	$0.238266\pi$
$233$			4840.99i			1.36113i	−0.732686	+	0.680567i	$0.761734\pi$
$234$	−4337.17			−1.21167
$235$	−3262.15	+	639.079i	−0.905530	+	0.177400i
$236$	−1244.11			−0.343156
$237$		−	1664.86i		−	0.456305i
$238$			4071.11i			1.10879i
$239$	−903.371			−0.244495			−0.122247	−	0.992500i	$-0.539010\pi$
$239$	−903.371			−0.244495			−0.122247	+	0.992500i	$0.539010\pi$
$240$	−1302.19	+	255.107i	−0.350232	+	0.0686130i
$241$	2149.23			0.574456			0.287228	−	0.957862i	$-0.407266\pi$
$241$	2149.23			0.574456			0.287228	+	0.957862i	$0.407266\pi$
$242$			3294.22i			0.875043i
$243$		−	5399.81i		−	1.42551i
$244$	−906.996			−0.237969
$245$	−800.362	−	4085.42i	−0.208707	−	1.06534i
$246$	6877.20			1.78242
$247$			9719.08i			2.50369i
$248$			426.488i			0.109202i
$249$	−5366.16			−1.36573
$250$	2337.42	−	1532.64i	0.591325	−	0.387731i
$251$	1936.69			0.487022			0.243511	−	0.969898i	$-0.421701\pi$
$251$	1936.69			0.487022			0.243511	+	0.969898i	$0.421701\pi$
$252$		−	2998.14i		−	0.749463i
$253$			1255.16i			0.311901i
$254$	3090.26			0.763386
$255$	−1213.46	−	6194.05i	−0.297999	−	1.52112i
$256$	256.000			0.0625000
$257$			1431.11i			0.347356i	0.984803	+	0.173678i	$0.0555652\pi$
$257$			1431.11i			0.347356i	−0.984803	+	0.173678i	$0.944435\pi$
$258$			1859.89i			0.448804i
$259$	3498.57			0.839345
$260$	−3396.12	+	665.325i	−0.810072	+	0.158699i
$261$	−4388.54			−1.04078
$262$		−	4367.92i		−	1.02997i
$263$		−	776.181i		−	0.181982i	−0.995852	−	0.0909912i	$-0.970996\pi$
$263$		−	776.181i		−	0.181982i	0.995852	−	0.0909912i	$-0.0290035\pi$
$264$	−3238.44			−0.754971
$265$	−4583.56	+	897.953i	−1.06251	+	0.208154i
$266$	−6718.47			−1.54863
$267$		−	4161.53i		−	0.953862i
$268$			2176.83i			0.496160i
$269$	1691.89			0.383481			0.191741	−	0.981446i	$-0.438587\pi$
$269$	1691.89			0.383481			0.191741	+	0.981446i	$0.438587\pi$
$270$	32.6533	+	166.677i	0.00736006	+	0.0375691i
$271$	−4521.51			−1.01351			−0.506757	−	0.862089i	$-0.669156\pi$
$271$	−4521.51			−1.01351			−0.506757	+	0.862089i	$0.669156\pi$
$272$			1217.70i			0.271449i
$273$		−	15352.7i		−	3.40361i
$274$	1002.68			0.221073
$275$	6317.25	−	2573.98i	1.38525	−	0.564424i
$276$	−682.439			−0.148833
$277$		−	991.809i		−	0.215134i	−0.994198	−	0.107567i	$-0.965694\pi$
$277$		−	991.809i		−	0.215134i	0.994198	−	0.107567i	$-0.0343059\pi$
$278$		−	433.506i		−	0.0935251i
$279$	1493.99			0.320583
$280$	−459.916	−	2347.62i	−0.0981616	−	0.501062i
$281$	378.405			0.0803336			0.0401668	−	0.999193i	$-0.487211\pi$
$281$	378.405			0.0803336			0.0401668	+	0.999193i	$0.487211\pi$
$282$		−	4410.96i		−	0.931451i
$283$			2668.96i			0.560613i	0.959911	+	0.280306i	$0.0904361\pi$
$283$			2668.96i			0.560613i	−0.959911	+	0.280306i	$0.909564\pi$
$284$	3697.13			0.772479
$285$	10221.9	−	2002.54i	2.12454	−	0.416212i
$286$	−8445.92			−1.74622
$287$			12398.4i			2.55002i
$288$		−	896.768i		−	0.183481i
$289$	−879.201			−0.178954
$290$	−3436.35	+	673.205i	−0.695825	+	0.136317i
$291$	−7723.39			−1.55585
$292$			2238.60i			0.448644i
$293$			288.436i			0.0575105i	0.999586	+	0.0287553i	$0.00915435\pi$
$293$			288.436i			0.0575105i	−0.999586	+	0.0287553i	$0.990846\pi$
$294$	5524.15			1.09583
$295$	668.539	+	3412.53i	0.131945	+	0.673509i
$296$	1046.45			0.205486
$297$			414.515i			0.0809852i
$298$			3199.60i			0.621972i
$299$	−1779.81			−0.344245
$300$	1399.49	+	3434.74i	0.269332	+	0.661016i
$301$	−3353.06			−0.642084
$302$			2932.16i			0.558699i
$303$			7868.13i			1.49179i
$304$	−2009.55			−0.379130
$305$	487.385	+	2487.84i	0.0915003	+	0.467060i
$306$	4265.62			0.796892
$307$			5158.97i			0.959081i	0.877520	+	0.479540i	$0.159197\pi$
$307$			5158.97i			0.959081i	−0.877520	+	0.479540i	$0.840803\pi$
$308$		−	5838.37i		−	1.08010i
$309$	−3155.36			−0.580912
$310$	1169.83	−	229.178i	0.214329	−	0.0419886i
$311$	618.008			0.112682			0.0563409	−	0.998412i	$-0.482057\pi$
$311$	618.008			0.112682			0.0563409	+	0.998412i	$0.482057\pi$
$312$		−	4592.11i		−	0.833260i
$313$			6237.69i			1.12644i	0.826308	+	0.563219i	$0.190437\pi$
$313$			6237.69i			1.12644i	−0.826308	+	0.563219i	$0.809563\pi$
$314$	−2860.10			−0.514028
$315$	−8223.72	+	1611.08i	−1.47097	+	0.288173i
$316$	897.762			0.159820
$317$			7826.96i			1.38677i	0.720568	+	0.693385i	$0.243881\pi$
$317$			7826.96i			1.38677i	−0.720568	+	0.693385i	$0.756119\pi$
$318$		−	6197.72i		−	1.09293i
$319$	−8545.95			−1.49994
$320$	−137.565	−	702.194i	−0.0240316	−	0.122668i
$321$	3119.56			0.542421
$322$		−	1230.32i		−	0.212929i
$323$		−	9558.74i		−	1.64663i
$324$	2801.22			0.480318
$325$	3649.90	+	8957.86i	0.622953	+	1.52890i
$326$	2187.12			0.371575
$327$		−	980.462i		−	0.165809i
$328$			3708.48i			0.624288i
$329$	7952.23			1.33259
$330$	1740.22	+	8882.87i	0.290290	+	1.48178i
$331$	−6006.80			−0.997473			−0.498737	−	0.866754i	$-0.666203\pi$
$331$	−6006.80			−0.997473			−0.498737	+	0.866754i	$0.666203\pi$
$332$		−	2893.66i		−	0.478344i
$333$		−	3665.72i		−	0.603243i
$334$	5558.05			0.910547
$335$	5970.92	−	1169.75i	0.973810	−	0.190776i
$336$	3174.37			0.515405
$337$			8184.80i			1.32301i	0.749941	+	0.661505i	$0.230082\pi$
$337$			8184.80i			1.32301i	−0.749941	+	0.661505i	$0.769918\pi$
$338$		−	7582.31i		−	1.22019i
$339$	−13136.3			−2.10461
$340$	3340.09	−	654.348i	0.532771	−	0.104374i
$341$	2909.29			0.462014
$342$			7039.45i			1.11301i
$343$			785.185i			0.123604i
$344$	−1002.93			−0.157193
$345$	366.717	+	1871.89i	0.0572272	+	0.292114i
$346$	8492.95			1.31961
$347$			5345.31i			0.826948i	0.910516	+	0.413474i	$0.135685\pi$
$347$			5345.31i			0.826948i	−0.910516	+	0.413474i	$0.864315\pi$
$348$		−	4646.50i		−	0.715743i
$349$	−4776.66			−0.732632			−0.366316	−	0.930490i	$-0.619381\pi$
$349$	−4776.66			−0.732632			−0.366316	+	0.930490i	$0.619381\pi$
$350$	−6192.26	+	2523.05i	−0.945686	+	0.385322i
$351$	−587.782			−0.0893832
$352$		−	1746.31i		−	0.264427i
$353$			9684.03i			1.46014i	0.683373	+	0.730069i	$0.260512\pi$
$353$			9684.03i			1.46014i	−0.683373	+	0.730069i	$0.739488\pi$
$354$	−4614.30			−0.692789
$355$	−1986.70	−	10141.0i	−0.297022	−	1.51614i
$356$	2244.07			0.334089
$357$			15099.4i			2.23850i
$358$		−	2197.45i		−	0.324410i
$359$	−5444.64			−0.800437			−0.400219	−	0.916420i	$-0.631066\pi$
$359$	−5444.64			−0.800437			−0.400219	+	0.916420i	$0.631066\pi$
$360$	−2459.78	+	481.889i	−0.360117	+	0.0705494i
$361$	8915.57			1.29983
$362$			953.257i			0.138403i
$363$			12218.0i			1.76660i
$364$	8278.81			1.19211
$365$	6140.35	−	1202.94i	0.880550	−	0.172506i
$366$	−3363.96			−0.480430
$367$			11039.4i			1.57017i	0.619389	+	0.785084i	$0.287380\pi$
$367$			11039.4i			1.57017i	−0.619389	+	0.785084i	$0.712620\pi$
$368$		−	368.000i		−	0.0521286i
$369$	12990.8			1.83272
$370$	−562.323	−	2870.36i	−0.0790103	−	0.403305i
$371$	11173.5			1.56360
$372$			1581.80i			0.220464i
$373$			2944.75i			0.408776i	0.978890	+	0.204388i	$0.0655204\pi$
$373$			2944.75i			0.408776i	−0.978890	+	0.204388i	$0.934480\pi$
$374$	8306.58			1.14846
$375$	8669.26	−	5684.42i	1.19381	−	0.782780i
$376$	2378.58			0.326239
$377$		−	12118.2i		−	1.65548i
$378$		−	406.314i		−	0.0552871i
$379$	3779.69			0.512269			0.256134	−	0.966641i	$-0.417551\pi$
$379$	3779.69			0.512269			0.256134	+	0.966641i	$0.417551\pi$
$380$	1079.86	+	5512.08i	0.145777	+	0.744115i
$381$	11461.5			1.54118
$382$		−	8328.83i		−	1.11555i
$383$		−	8569.73i		−	1.14332i	−0.820490	−	0.571661i	$-0.806299\pi$
$383$		−	8569.73i		−	1.14332i	0.820490	−	0.571661i	$-0.193701\pi$
$384$	949.480			0.126180
$385$	−16014.3	+	3137.32i	−2.11991	+	0.415306i
$386$	−4550.98			−0.600100
$387$			3513.26i			0.461470i
$388$		−	4164.78i		−	0.544935i
$389$	−11490.2			−1.49763			−0.748813	−	0.662781i	$-0.769376\pi$
$389$	−11490.2			−1.49763			−0.748813	+	0.662781i	$0.769376\pi$
$390$	−12595.9	+	2467.63i	−1.63543	+	0.320393i
$391$	1750.45			0.226404
$392$			2978.86i			0.383814i
$393$		−	16200.2i		−	2.07937i
$394$	8941.71			1.14334
$395$	−482.424	−	2462.51i	−0.0614516	−	0.313677i
$396$	−6117.31			−0.776278
$397$		−	10783.0i		−	1.36319i	−0.731732	−	0.681593i	$-0.761288\pi$
$397$		−	10783.0i		−	1.36319i	0.731732	−	0.681593i	$-0.238712\pi$
$398$			10695.0i			1.34696i
$399$	−24918.2			−3.12649
$400$	−1852.16	+	754.665i	−0.231519	+	0.0943331i
$401$	1598.32			0.199044			0.0995219	−	0.995035i	$-0.468269\pi$
$401$	1598.32			0.199044			0.0995219	+	0.995035i	$0.468269\pi$
$402$			8073.66i			1.00169i
$403$			4125.37i			0.509924i
$404$	−4242.83			−0.522496
$405$	−1505.27	−	7683.58i	−0.184685	−	0.942716i
$406$	8376.86			1.02398
$407$		−	7138.37i		−	0.869376i
$408$			4516.35i			0.548021i
$409$	11966.2			1.44668			0.723340	−	0.690492i	$-0.242606\pi$
$409$	11966.2			1.44668			0.723340	+	0.690492i	$0.242606\pi$
$410$	10172.1	−	1992.80i	1.22528	−	0.240042i
$411$	3718.84			0.446319
$412$		−	1701.50i		−	0.203464i
$413$		−	8318.81i		−	0.991142i
$414$	−1289.10			−0.153034
$415$	−7937.15	+	1554.94i	−0.938842	+	0.183926i
$416$	2476.26			0.291848
$417$		−	1607.83i		−	0.188815i
$418$			13708.2i			1.60404i
$419$	1246.41			0.145325			0.0726625	−	0.997357i	$-0.476850\pi$
$419$	1246.41			0.145325			0.0726625	+	0.997357i	$0.476850\pi$
$420$	−1705.79	−	8707.12i	−0.198176	−	1.01158i
$421$	−9795.87			−1.13402			−0.567009	−	0.823712i	$-0.691899\pi$
$421$	−9795.87			−1.13402			−0.567009	+	0.823712i	$0.691899\pi$
$422$		−	6119.04i		−	0.705854i
$423$		−	8332.16i		−	0.957738i
$424$	3342.08			0.382796
$425$	−3589.68	−	8810.07i	−0.409706	−	1.00553i
$426$	13712.3			1.55954
$427$		−	6064.66i		−	0.687329i
$428$			1682.20i			0.189982i
$429$	−31325.1			−3.52539
$430$	538.936	+	2750.98i	0.0604414	+	0.308521i
$431$	9750.70			1.08973			0.544866	−	0.838523i	$-0.316580\pi$
$431$	9750.70			1.08973			0.544866	+	0.838523i	$0.316580\pi$
$432$		−	121.532i		−	0.0135352i
$433$		−	1069.70i		−	0.118722i	−0.998237	−	0.0593609i	$-0.981094\pi$
$433$		−	1069.70i		−	0.118722i	0.998237	−	0.0593609i	$-0.0189063\pi$
$434$	−2851.73			−0.315408
$435$	−12745.1	+	2496.85i	−1.40478	+	0.275207i
$436$	528.707			0.0580745
$437$			2888.73i			0.316216i
$438$			8302.76i			0.905756i
$439$	3615.60			0.393082			0.196541	−	0.980496i	$-0.437029\pi$
$439$	3615.60			0.393082			0.196541	+	0.980496i	$0.437029\pi$
$440$	−4790.02	+	938.399i	−0.518989	+	0.101674i
$441$	10434.9			1.12676
$442$			11778.7i			1.26755i
$443$		−	5071.52i		−	0.543917i	−0.962309	−	0.271958i	$-0.912329\pi$
$443$		−	5071.52i		−	0.543917i	0.962309	−	0.271958i	$-0.0876713\pi$
$444$	3881.19			0.414849
$445$	−1205.88	−	6155.36i	−0.128459	−	0.655713i
$446$	−4899.58			−0.520183
$447$			11867.0i			1.25568i
$448$			1711.75i			0.180520i
$449$	−14216.7			−1.49427			−0.747133	−	0.664674i	$-0.768570\pi$
$449$	−14216.7			−1.49427			−0.747133	+	0.664674i	$0.768570\pi$
$450$	2643.59	+	6488.10i	0.276933	+	0.679671i
$451$	25297.4			2.64126
$452$		−	7083.63i		−	0.737137i
$453$			10875.1i			1.12794i
$454$	−6387.07			−0.660264
$455$	−4448.72	−	22708.3i	−0.458372	−	2.33974i
$456$	−7453.23			−0.765416
$457$		−	5354.56i		−	0.548087i	−0.961717	−	0.274044i	$-0.911639\pi$
$457$		−	5354.56i		−	0.548087i	0.961717	−	0.274044i	$-0.0883613\pi$
$458$			6256.26i			0.638288i
$459$	578.085			0.0587858
$460$	−1009.40	+	197.749i	−0.102312	+	0.0200437i
$461$	−15690.7			−1.58523			−0.792613	−	0.609725i	$-0.791280\pi$
$461$	−15690.7			−1.58523			−0.792613	+	0.609725i	$0.791280\pi$
$462$		−	21654.0i		−	2.18059i
$463$		−	811.540i		−	0.0814589i	−0.999170	−	0.0407294i	$-0.987032\pi$
$463$		−	811.540i		−	0.0814589i	0.999170	−	0.0407294i	$-0.0129682\pi$
$464$	2505.59			0.250688
$465$	4338.80	−	850.001i	0.432703	−	0.0847696i
$466$	−9681.99			−0.962467
$467$		−	3834.38i		−	0.379944i	−0.981790	−	0.189972i	$-0.939160\pi$
$467$		−	3834.38i		−	0.379944i	0.981790	−	0.189972i	$-0.0608397\pi$
$468$		−	8674.34i		−	0.856777i
$469$	−14555.5			−1.43307
$470$	−1278.16	−	6524.31i	−0.125441	−	0.640306i
$471$	−10607.8			−1.03776
$472$		−	2488.22i		−	0.242648i
$473$			6841.49i			0.665057i
$474$	3329.72			0.322656
$475$	14539.1	−	5923.97i	1.40442	−	0.572232i
$476$	−8142.23			−0.784030
$477$		−	11707.3i		−	1.12377i
$478$		−	1806.74i		−	0.172884i
$479$	6238.11			0.595045			0.297522	−	0.954715i	$-0.403840\pi$
$479$	6238.11			0.595045			0.297522	+	0.954715i	$0.403840\pi$
$480$	−510.215	−	2604.37i	−0.0485167	−	0.247652i
$481$	10122.2			0.959529
$482$			4298.46i			0.406202i
$483$		−	4563.16i		−	0.429877i
$484$	−6588.44			−0.618749
$485$	−11423.8	+	2238.00i	−1.06954	+	0.209530i
$486$	10799.6			1.00798
$487$		−	15837.8i		−	1.47368i	−0.676069	−	0.736839i	$-0.736318\pi$
$487$		−	15837.8i		−	1.47368i	0.676069	−	0.736839i	$-0.263682\pi$
$488$		−	1813.99i		−	0.168270i
$489$	8111.83			0.750163
$490$	8170.83	−	1600.72i	0.753307	−	0.147578i
$491$	−20341.2			−1.86963			−0.934813	−	0.355139i	$-0.884433\pi$
$491$	−20341.2			−1.86963			−0.934813	+	0.355139i	$0.884433\pi$
$492$			13754.4i			1.26036i
$493$			11918.2i			1.08878i
$494$	−19438.2			−1.77037
$495$	3287.21	+	16779.4i	0.298483	+	1.52359i
$496$	−852.975			−0.0772172
$497$			24721.0i			2.23116i
$498$		−	10732.3i		−	0.965717i
$499$	9098.09			0.816205			0.408102	−	0.912936i	$-0.366191\pi$
$499$	9098.09			0.816205			0.408102	+	0.912936i	$0.366191\pi$
$500$	3065.28	+	4674.83i	0.274167	+	0.418130i
$501$	20614.3			1.83828
$502$			3873.37i			0.344376i
$503$		−	7021.97i		−	0.622454i	−0.950336	−	0.311227i	$-0.899260\pi$
$503$		−	7021.97i		−	0.622454i	0.950336	−	0.311227i	$-0.100740\pi$
$504$	5996.27			0.529951
$505$	2279.93	+	11637.8i	0.200903	+	1.02550i
$506$	−2510.31			−0.220548
$507$		−	28122.1i		−	2.46340i
$508$			6180.51i			0.539795i
$509$	17973.5			1.56515			0.782576	−	0.622555i	$-0.213905\pi$
$509$	17973.5			1.56515			0.782576	+	0.622555i	$0.213905\pi$
$510$	12388.1	−	2426.92i	1.07560	−	0.210717i
$511$	−14968.5			−1.29583
$512$			512.000i			0.0441942i
$513$			954.001i			0.0821056i
$514$	−2862.23			−0.245618
$515$	−4667.12	+	914.323i	−0.399336	+	0.0782328i
$516$	−3719.77			−0.317352
$517$		−	16225.5i		−	1.38026i
$518$			6997.14i			0.593507i
$519$	31499.6			2.66412
$520$	−1330.65	−	6792.25i	−0.112217	−	0.572807i
$521$	−1596.92			−0.134285			−0.0671425	−	0.997743i	$-0.521388\pi$
$521$	−1596.92			−0.134285			−0.0671425	+	0.997743i	$0.521388\pi$
$522$		−	8777.08i		−	0.735943i
$523$			1808.84i			0.151234i	0.997137	+	0.0756168i	$0.0240926\pi$
$523$			1808.84i			0.151234i	−0.997137	+	0.0756168i	$0.975907\pi$
$524$	8735.85			0.728296
$525$	−22966.5	+	9357.75i	−1.90922	+	0.777916i
$526$	1552.36			0.128681
$527$		−	4057.31i		−	0.335369i
$528$		−	6476.89i		−	0.533845i
$529$	−529.000			−0.0434783
$530$	−1795.91	−	9167.13i	−0.147187	−	0.751310i
$531$	−8716.25			−0.712341
$532$		−	13436.9i		−	1.09505i
$533$			35871.7i			2.91515i
$534$	8323.05			0.674483
$535$	4614.18	−	903.951i	0.372876	−	0.0730490i
$536$	−4353.66			−0.350838
$537$		−	8150.14i		−	0.654943i
$538$			3383.79i			0.271162i
$539$	20320.3			1.62385
$540$	−333.355	+	65.3066i	−0.0265654	+	0.00520435i
$541$	16927.8			1.34525			0.672626	−	0.739983i	$-0.265166\pi$
$541$	16927.8			1.34525			0.672626	+	0.739983i	$0.265166\pi$
$542$		−	9043.02i		−	0.716662i
$543$			3535.54i			0.279419i
$544$	−2435.41			−0.191944
$545$	−284.107	−	1450.21i	−0.0223299	−	0.113982i
$546$	30705.3			2.40672
$547$		−	9785.97i		−	0.764932i	−0.923969	−	0.382466i	$-0.875075\pi$
$547$		−	9785.97i		−	0.764932i	0.923969	−	0.382466i	$-0.124925\pi$
$548$			2005.36i			0.156322i
$549$	−6354.41			−0.493988
$550$	5147.95	+	12634.5i	0.399108	+	0.979521i
$551$	−19668.4			−1.52069
$552$		−	1364.88i		−	0.105241i
$553$			6002.92i			0.461610i
$554$	1983.62			0.152122
$555$	−2085.61	−	10645.9i	−0.159512	−	0.814221i
$556$	867.012			0.0661322
$557$		−	17960.7i		−	1.36628i	−0.730286	−	0.683141i	$-0.760613\pi$
$557$		−	17960.7i		−	1.36628i	0.730286	−	0.683141i	$-0.239387\pi$
$558$			2987.97i			0.226686i
$559$	−9701.23			−0.734022
$560$	4695.25	−	919.832i	0.354304	−	0.0694107i
$561$	30808.3			2.31859
$562$			756.809i			0.0568044i
$563$			19202.4i			1.43745i	0.695293	+	0.718726i	$0.255275\pi$
$563$			19202.4i			1.43745i	−0.695293	+	0.718726i	$0.744725\pi$
$564$	8821.93			0.658635
$565$	−19430.0	+	3806.48i	−1.44677	+	0.283433i
$566$	−5337.93			−0.396413
$567$			18730.4i			1.38731i
$568$			7394.26i			0.546225i
$569$	4384.98			0.323072			0.161536	−	0.986867i	$-0.448355\pi$
$569$	4384.98			0.323072			0.161536	+	0.986867i	$0.448355\pi$
$570$	4005.09	+	20443.8i	0.294306	+	1.50227i
$571$	1169.91			0.0857427			0.0428713	−	0.999081i	$-0.486349\pi$
$571$	1169.91			0.0857427			0.0428713	+	0.999081i	$0.486349\pi$
$572$		−	16891.8i		−	1.23476i
$573$		−	30890.8i		−	2.25215i
$574$	−24796.9			−1.80314
$575$	1084.83	+	2662.47i	0.0786792	+	0.193101i
$576$	1793.54			0.129741
$577$		−	4694.03i		−	0.338674i	−0.985558	−	0.169337i	$-0.945837\pi$
$577$		−	4694.03i		−	0.338674i	0.985558	−	0.169337i	$-0.0541627\pi$
$578$		−	1758.40i		−	0.126540i
$579$	−16879.1			−1.21153
$580$	−1346.41	−	6872.69i	−0.0963907	−	0.492022i
$581$	19348.6			1.38161
$582$		−	15446.8i		−	1.10015i
$583$		−	22798.0i		−	1.61955i
$584$	−4477.20			−0.317239
$585$	−23793.2	+	4661.26i	−1.68159	+	0.329435i
$586$	−576.871			−0.0406661
$587$		−	23057.4i		−	1.62126i	−0.585559	−	0.810630i	$-0.699125\pi$
$587$		−	23057.4i		−	1.62126i	0.585559	−	0.810630i	$-0.300875\pi$
$588$			11048.3i			0.774871i
$589$	6695.69			0.468406
$590$	−6825.06	+	1337.08i	−0.476243	+	0.0932994i
$591$	33164.0			2.30826
$592$			2092.90i			0.145300i
$593$		−	16230.0i		−	1.12392i	−0.827164	−	0.561960i	$-0.810047\pi$
$593$		−	16230.0i		−	1.12392i	0.827164	−	0.561960i	$-0.189953\pi$
$594$	−829.030			−0.0572652
$595$	4375.33	+	22333.7i	0.301464	+	1.53881i
$596$	−6399.19			−0.439801
$597$			39666.7i			2.71935i
$598$		−	3559.63i		−	0.243418i
$599$	−10291.0			−0.701971			−0.350985	−	0.936381i	$-0.614153\pi$
$599$	−10291.0			−0.701971			−0.350985	+	0.936381i	$0.614153\pi$
$600$	−6869.47	+	2798.98i	−0.467409	+	0.190447i
$601$	−7267.32			−0.493245			−0.246622	−	0.969112i	$-0.579321\pi$
$601$	−7267.32			−0.493245			−0.246622	+	0.969112i	$0.579321\pi$
$602$		−	6706.12i		−	0.454022i
$603$			15250.9i			1.02996i
$604$	−5864.33			−0.395060
$605$	3540.38	+	18071.7i	0.237912	+	1.21441i
$606$	−15736.3			−1.05485
$607$		−	2482.26i		−	0.165983i	−0.996550	−	0.0829915i	$-0.973553\pi$
$607$		−	2482.26i		−	0.165983i	0.996550	−	0.0829915i	$-0.0264475\pi$
$608$		−	4019.10i		−	0.268086i
$609$	31069.0			2.06729
$610$	−4975.68	+	974.771i	−0.330261	+	0.0647005i
$611$	23007.7			1.52339
$612$			8531.23i			0.563488i
$613$			19565.6i			1.28914i	0.764544	+	0.644572i	$0.222964\pi$
$613$			19565.6i			1.28914i	−0.764544	+	0.644572i	$0.777036\pi$
$614$	−10317.9			−0.678173
$615$	37727.6	−	7391.10i	2.47369	−	0.484614i
$616$	11676.7			0.763749
$617$			13606.1i			0.887778i	0.896082	+	0.443889i	$0.146402\pi$
$617$			13606.1i			0.887778i	−0.896082	+	0.443889i	$0.853598\pi$
$618$		−	6310.71i		−	0.410767i
$619$	−20471.3			−1.32926			−0.664630	−	0.747172i	$-0.731411\pi$
$619$	−20471.3			−1.32926			−0.664630	+	0.747172i	$0.731411\pi$
$620$	458.357	+	2339.66i	0.0296904	+	0.151553i
$621$	−174.702			−0.0112891
$622$			1236.02i			0.0796780i
$623$			15005.1i			0.964952i
$624$	9184.23			0.589204
$625$	11175.6	−	10920.0i	0.715241	−	0.698878i
$626$	−12475.4			−0.796512
$627$			50842.3i			3.23835i
$628$		−	5720.20i		−	0.363473i
$629$	−9955.22			−0.631066
$630$	−3222.17	−	16447.4i	−0.203769	−	1.04013i
$631$	−24864.2			−1.56867			−0.784334	−	0.620338i	$-0.786995\pi$
$631$	−24864.2			−1.56867			−0.784334	+	0.620338i	$0.786995\pi$
$632$			1795.52i			0.113010i
$633$		−	22695.0i		−	1.42503i
$634$	−15653.9			−0.980594
$635$	16952.8	−	3321.17i	1.05945	−	0.207554i
$636$	12395.4			0.772817
$637$			28814.2i			1.79224i
$638$		−	17091.9i		−	1.06062i
$639$	25902.1			1.60355
$640$	1404.39	−	275.129i	0.0867395	−	0.0169929i
$641$	−8353.98			−0.514762			−0.257381	−	0.966310i	$-0.582859\pi$
$641$	−8353.98			−0.514762			−0.257381	+	0.966310i	$0.582859\pi$
$642$			6239.12i			0.383549i
$643$		−	13920.0i		−	0.853737i	−0.904314	−	0.426869i	$-0.859617\pi$
$643$		−	13920.0i		−	0.853737i	0.904314	−	0.426869i	$-0.140383\pi$
$644$	2460.65			0.150564
$645$	1998.86	+	10203.1i	0.122024	+	0.622865i
$646$	19117.5			1.16435
$647$			2346.12i			0.142559i	0.997456	+	0.0712793i	$0.0227082\pi$
$647$			2346.12i			0.142559i	−0.997456	+	0.0712793i	$0.977292\pi$
$648$			5602.43i			0.339636i
$649$	−16973.4			−1.02660
$650$	−17915.7	+	7299.79i	−1.08110	+	0.440495i
$651$	−10576.8			−0.636770
$652$			4374.24i			0.262743i
$653$			13054.8i			0.782351i	0.920316	+	0.391176i	$0.127932\pi$
$653$			13054.8i			0.782351i	−0.920316	+	0.391176i	$0.872068\pi$
$654$	1960.92			0.117245
$655$	−4694.31	−	23961.9i	−0.280034	−	1.42942i
$656$	−7416.96			−0.441438
$657$			15683.6i			0.931319i
$658$			15904.5i			0.942280i
$659$	−2702.02			−0.159720			−0.0798601	−	0.996806i	$-0.525447\pi$
$659$	−2702.02			−0.159720			−0.0798601	+	0.996806i	$0.525447\pi$
$660$	−17765.7	+	3480.43i	−1.04777	+	0.205266i
$661$	−12769.0			−0.751372			−0.375686	−	0.926747i	$-0.622593\pi$
$661$	−12769.0			−0.751372			−0.375686	+	0.926747i	$0.622593\pi$
$662$		−	12013.6i		−	0.705320i
$663$			43686.2i			2.55902i
$664$	5787.32			0.338241
$665$	−36856.8	+	7220.50i	−2.14924	+	0.421051i
$666$	7331.43			0.426557
$667$		−	3601.79i		−	0.209088i
$668$			11116.1i			0.643854i
$669$	−18172.1			−1.05018
$670$	2339.49	+	11941.8i	0.134899	+	0.688587i
$671$	−12374.2			−0.711921
$672$			6348.74i			0.364446i
$673$		−	19694.2i		−	1.12802i	−0.825768	−	0.564009i	$-0.809258\pi$
$673$		−	19694.2i		−	1.12802i	0.825768	−	0.564009i	$-0.190742\pi$
$674$	−16369.6			−0.935509
$675$	358.265	+	879.281i	0.0204291	+	0.0501386i
$676$	15164.6			0.862803
$677$		−	20154.9i		−	1.14419i	−0.820189	−	0.572093i	$-0.806132\pi$
$677$		−	20154.9i		−	1.14419i	0.820189	−	0.572093i	$-0.193868\pi$
$678$		−	26272.5i		−	1.48819i
$679$	27848.0			1.57394
$680$	1308.70	+	6680.19i	0.0738033	+	0.376726i
$681$	−23689.0			−1.33299
$682$			5818.58i			0.326693i
$683$		−	3347.66i		−	0.187547i	−0.995594	−	0.0937734i	$-0.970107\pi$
$683$		−	3347.66i		−	0.187547i	0.995594	−	0.0937734i	$-0.0298929\pi$
$684$	−14078.9			−0.787018
$685$	5500.58	−	1077.60i	0.306812	−	0.0601067i
$686$	−1570.37			−0.0874009
$687$			23203.9i			1.28862i
$688$		−	2005.86i		−	0.111152i
$689$	32327.6			1.78749
$690$	−3743.78	+	733.434i	−0.206556	+	0.0404657i
$691$	4318.63			0.237754			0.118877	−	0.992909i	$-0.462071\pi$
$691$	4318.63			0.237754			0.118877	+	0.992909i	$0.462071\pi$
$692$			16985.9i			0.933102i
$693$		−	40903.6i		−	2.24214i
$694$	−10690.6			−0.584741
$695$	−465.900	−	2378.17i	−0.0254282	−	0.129797i
$696$	9293.00			0.506107
$697$		−	35279.9i		−	1.91725i
$698$		−	9553.32i		−	0.518049i
$699$	−35909.6			−1.94310
$700$	−5046.10	−	12384.5i	−0.272464	−	0.668701i
$701$	24921.7			1.34277			0.671383	−	0.741111i	$-0.265701\pi$
$701$	24921.7			1.34277			0.671383	+	0.741111i	$0.265701\pi$
$702$		−	1175.56i		−	0.0632035i
$703$		−	16428.9i		−	0.881403i
$704$	3492.61			0.186978
$705$	−4740.57	−	24198.1i	−0.253249	−	1.29270i
$706$	−19368.1			−1.03247
$707$		−	28369.8i		−	1.50913i
$708$		−	9228.59i		−	0.489875i
$709$	6255.09			0.331333			0.165666	−	0.986182i	$-0.447023\pi$
$709$	6255.09			0.331333			0.165666	+	0.986182i	$0.447023\pi$
$710$	20282.0	−	3973.39i	1.07207	−	0.210026i
$711$	6289.72			0.331762
$712$			4488.14i			0.236236i
$713$			1226.15i			0.0644036i
$714$	−30198.8			−1.58286
$715$	−46333.4	+	9077.04i	−2.42345	+	0.474772i
$716$	4394.90			0.229393
$717$		−	6701.04i		−	0.349031i
$718$		−	10889.3i		−	0.565995i
$719$	3760.70			0.195063			0.0975317	−	0.995232i	$-0.468905\pi$
$719$	3760.70			0.195063			0.0975317	+	0.995232i	$0.468905\pi$
$720$	−963.778	−	4919.57i	−0.0498860	−	0.254641i
$721$	11377.2			0.587666
$722$			17831.1i			0.919122i
$723$			15942.6i			0.820071i
$724$	−1906.51			−0.0978660
$725$	−18127.9	+	7386.25i	−0.928625	+	0.378370i
$726$	−24435.9			−1.24918
$727$			24743.8i			1.26231i	0.775658	+	0.631153i	$0.217418\pi$
$727$			24743.8i			1.26231i	−0.775658	+	0.631153i	$0.782582\pi$
$728$			16557.6i			0.842948i
$729$	21146.6			1.07436
$730$	2405.88	+	12280.7i	0.121980	+	0.622643i
$731$	9541.18			0.482754
$732$		−	6727.93i		−	0.339715i
$733$			19060.7i			0.960466i	0.877141	+	0.480233i	$0.159448\pi$
$733$			19060.7i			0.960466i	−0.877141	+	0.480233i	$0.840552\pi$
$734$	−22078.8			−1.11028
$735$	30304.9	−	5936.94i	1.52083	−	0.297942i
$736$	736.000			0.0368605
$737$			29698.5i			1.48434i
$738$			25981.6i			1.29593i
$739$	−4966.90			−0.247240			−0.123620	−	0.992330i	$-0.539450\pi$
$739$	−4966.90			−0.247240			−0.123620	+	0.992330i	$0.539450\pi$
$740$	5740.71	−	1124.65i	0.285180	−	0.0558687i
$741$	−72094.4			−3.57416
$742$			22346.9i			1.10564i
$743$			20358.1i			1.00520i	0.864518	+	0.502601i	$0.167624\pi$
$743$			20358.1i			1.00520i	−0.864518	+	0.502601i	$0.832376\pi$
$744$	−3163.61			−0.155892
$745$	3438.68	+	17552.6i	0.169106	+	0.863193i
$746$	−5889.50			−0.289048
$747$		−	20273.0i		−	0.992971i
$748$			16613.2i			0.812082i
$749$	−11248.1			−0.548727
$750$	11368.8	+	17338.5i	0.553509	+	0.844151i
$751$	5064.97			0.246103			0.123052	−	0.992400i	$-0.460732\pi$
$751$	5064.97			0.246103			0.123052	+	0.992400i	$0.460732\pi$
$752$			4757.16i			0.230686i
$753$			14366.0i			0.695253i
$754$	24236.3			1.17060
$755$	3151.27	+	16085.5i	0.151902	+	0.775380i
$756$	812.627			0.0390939
$757$		−	5956.80i		−	0.286002i	−0.989723	−	0.143001i	$-0.954325\pi$
$757$		−	5956.80i		−	0.286002i	0.989723	−	0.143001i	$-0.0456752\pi$
$758$			7559.39i			0.362229i
$759$	−9310.53			−0.445258
$760$	−11024.2	+	2159.71i	−0.526169	+	0.103080i
$761$	−3698.30			−0.176167			−0.0880836	−	0.996113i	$-0.528074\pi$
$761$	−3698.30			−0.176167			−0.0880836	+	0.996113i	$0.528074\pi$
$762$			22923.0i			1.08978i
$763$			3535.22i			0.167737i
$764$	16657.7			0.788812
$765$	23400.7	−	4584.36i	1.10595	−	0.216664i
$766$	17139.5			0.808451
$767$		−	24068.3i		−	1.13306i
$768$			1898.96i			0.0892225i
$769$	−33110.8			−1.55267			−0.776337	−	0.630319i	$-0.782924\pi$
$769$	−33110.8			−1.55267			−0.776337	+	0.630319i	$0.782924\pi$
$770$	−6274.64	−	32028.7i	−0.293665	−	1.49900i
$771$	−10615.7			−0.495871
$772$		−	9101.95i		−	0.424335i
$773$		−	31263.6i		−	1.45469i	−0.686274	−	0.727343i	$-0.740755\pi$
$773$		−	31263.6i		−	1.45469i	0.686274	−	0.727343i	$-0.259245\pi$
$774$	−7026.52			−0.326309
$775$	6171.26	−	2514.49i	0.286036	−	0.116546i
$776$	8329.56			0.385327
$777$			25951.7i			1.19822i
$778$		−	22980.4i		−	1.05898i
$779$	58221.6			2.67780
$780$	−4935.26	−	25191.8i	−0.226552	−	1.15643i
$781$	50440.0			2.31099
$782$			3500.90i			0.160092i
$783$		−	1189.49i		−	0.0542897i
$784$	−5957.71			−0.271397
$785$	−15690.2	+	3073.82i	−0.713384	+	0.139757i
$786$	32400.4			1.47034
$787$		−	17372.2i		−	0.786851i	−0.919356	−	0.393426i	$-0.871290\pi$
$787$		−	17372.2i		−	0.786851i	0.919356	−	0.393426i	$-0.128710\pi$
$788$			17883.4i			0.808465i
$789$	5757.57			0.259791
$790$	4925.02	−	964.847i	0.221803	−	0.0434528i
$791$	47365.0			2.12908
$792$		−	12234.6i		−	0.548912i
$793$		−	17546.6i		−	0.785746i
$794$	21566.1			0.963918
$795$	−6660.85	−	34000.0i	−0.297152	−	1.51680i
$796$	−21390.0			−0.952447
$797$		−	32834.9i		−	1.45931i	−0.683814	−	0.729656i	$-0.739680\pi$
$797$		−	32834.9i		−	1.45931i	0.683814	−	0.729656i	$-0.260320\pi$
$798$		−	49836.3i		−	2.21076i
$799$	−22628.2			−1.00191
$800$	−1509.33	−	3704.31i	−0.0667036	−	0.163709i
$801$	15722.0			0.693518
$802$			3196.65i			0.140745i
$803$			30541.3i			1.34219i
$804$	−16147.3			−0.708298
$805$	−1322.26	−	6749.42i	−0.0578925	−	0.295510i
$806$	−8250.74			−0.360571
$807$			12550.1i			0.547443i
$808$		−	8485.65i		−	0.369461i
$809$	25828.8			1.12249			0.561244	−	0.827650i	$-0.310323\pi$
$809$	25828.8			1.12249			0.561244	+	0.827650i	$0.310323\pi$
$810$	15367.2	−	3010.53i	0.666601	−	0.130592i
$811$	−12634.0			−0.547030			−0.273515	−	0.961868i	$-0.588186\pi$
$811$	−12634.0			−0.547030			−0.273515	+	0.961868i	$0.588186\pi$
$812$			16753.7i			0.724065i
$813$		−	33539.7i		−	1.44685i
$814$	14276.7			0.614742
$815$	11998.3	−	2350.55i	0.515684	−	0.101026i
$816$	−9032.70			−0.387510
$817$			15745.6i			0.674258i
$818$			23932.5i			1.02296i
$819$	58001.3			2.47464
$820$	3985.59	+	20344.3i	0.169735	+	0.866407i
$821$	−1352.46			−0.0574922			−0.0287461	−	0.999587i	$-0.509151\pi$
$821$	−1352.46			−0.0574922			−0.0287461	+	0.999587i	$0.509151\pi$
$822$			7437.69i			0.315595i
$823$			3242.82i			0.137348i	0.997639	+	0.0686740i	$0.0218768\pi$
$823$			3242.82i			0.137348i	−0.997639	+	0.0686740i	$0.978123\pi$
$824$	3403.00			0.143870
$825$	19093.3	+	46860.2i	0.805749	+	1.97753i
$826$	16637.6			0.700843
$827$		−	300.316i		−	0.0126276i	−0.999980	−	0.00631378i	$-0.997990\pi$
$827$		−	300.316i		−	0.0126276i	0.999980	−	0.00631378i	$-0.00200975\pi$
$828$		−	2578.21i		−	0.108211i
$829$	26921.7			1.12790			0.563949	−	0.825810i	$-0.309281\pi$
$829$	26921.7			1.12790			0.563949	+	0.825810i	$0.309281\pi$
$830$	−3109.89	−	15874.3i	−0.130055	−	0.663862i
$831$	7357.05			0.307116
$832$			4952.52i			0.206368i
$833$		−	28338.8i		−	1.17873i
$834$	3215.67			0.133513
$835$	30490.8	−	5973.37i	1.26369	−	0.247565i
$836$	−27416.3			−1.13423
$837$			404.936i			0.0167224i
$838$			2492.82i			0.102760i
$839$	−11275.5			−0.463974			−0.231987	−	0.972719i	$-0.574523\pi$
$839$	−11275.5			−0.463974			−0.231987	+	0.972719i	$0.574523\pi$
$840$	17414.2	−	3411.57i	0.715295	−	0.140131i
$841$	134.362			0.00550913
$842$		−	19591.7i		−	0.801871i
$843$			2806.94i			0.114681i
$844$	12238.1			0.499114
$845$	−8148.90	−	41595.7i	−0.331752	−	1.69342i
$846$	16664.3			0.677223
$847$		−	44053.9i		−	1.78714i
$848$			6684.15i			0.270678i
$849$	−19797.9			−0.800308
$850$	17620.1	−	7179.36i	0.711019	−	0.289706i
$851$	3008.55			0.121189
$852$			27424.6i			1.10276i
$853$			22356.1i			0.897372i	0.893690	+	0.448686i	$0.148108\pi$
$853$			22356.1i			0.897372i	−0.893690	+	0.448686i	$0.851892\pi$
$854$	12129.3			0.486015
$855$	7565.47	+	38617.6i	0.302612	+	1.54467i
$856$	−3364.40			−0.134337
$857$			9835.53i			0.392037i	0.980600	+	0.196018i	$0.0628012\pi$
$857$			9835.53i			0.392037i	−0.980600	+	0.196018i	$0.937199\pi$
$858$		−	62650.3i		−	2.49283i
$859$	30200.8			1.19958			0.599789	−	0.800159i	$-0.295251\pi$
$859$	30200.8			1.19958			0.599789	+	0.800159i	$0.295251\pi$
$860$	−5501.96	+	1077.87i	−0.218157	+	0.0427385i
$861$	−91969.3			−3.64031
$862$			19501.4i			0.770557i
$863$			32103.7i			1.26631i	0.774026	+	0.633154i	$0.218240\pi$
$863$			32103.7i			1.26631i	−0.774026	+	0.633154i	$0.781760\pi$
$864$	243.064			0.00957082
$865$	46591.4	−	9127.58i	1.83139	−	0.358783i
$866$	2139.40			0.0839489
$867$		−	6521.75i		−	0.255467i
$868$		−	5703.45i		−	0.223027i
$869$	12248.2			0.478126
$870$	−4993.71	−	25490.2i	−0.194601	−	0.993331i
$871$	−42112.5			−1.63826
$872$			1057.41i			0.0410648i
$873$		−	29178.4i		−	1.13120i
$874$	−5777.45			−0.223599
$875$	−31258.4	+	20496.1i	−1.20769	+	0.791881i
$876$	−16605.5			−0.640466
$877$		−	14145.5i		−	0.544651i	−0.962205	−	0.272326i	$-0.912207\pi$
$877$		−	14145.5i		−	0.544651i	0.962205	−	0.272326i	$-0.0877928\pi$
$878$			7231.20i			0.277951i
$879$	−2139.56			−0.0820997
$880$	−1876.80	−	9580.04i	−0.0718941	−	0.366981i
$881$	−15769.1			−0.603035			−0.301518	−	0.953461i	$-0.597493\pi$
$881$	−15769.1			−0.603035			−0.301518	+	0.953461i	$0.597493\pi$
$882$			20869.9i			0.796740i
$883$		−	17074.2i		−	0.650727i	−0.945589	−	0.325364i	$-0.894513\pi$
$883$		−	17074.2i		−	0.650727i	0.945589	−	0.325364i	$-0.105487\pi$
$884$	−23557.5			−0.896293
$885$	−25313.5	+	4959.10i	−0.961474	+	0.188360i
$886$	10143.0			0.384607
$887$			21656.2i			0.819780i	0.912135	+	0.409890i	$0.134433\pi$
$887$			21656.2i			0.819780i	−0.912135	+	0.409890i	$0.865567\pi$
$888$			7762.38i			0.293343i
$889$	−41326.2			−1.55910
$890$	12310.7	−	2411.76i	0.463659	−	0.0908341i
$891$	38217.0			1.43695
$892$		−	9799.15i		−	0.367825i
$893$		−	37342.7i		−	1.39936i
$894$	−23734.0			−0.887902
$895$	−2361.65	−	12055.0i	−0.0882027	−	0.450227i
$896$	−3423.51			−0.127647
$897$		−	13202.3i		−	0.491430i
$898$		−	28433.3i		−	1.05661i
$899$	−8348.46			−0.309718
$900$	−12976.2	+	5287.18i	−0.480600	+	0.195821i
$901$	−31794.2			−1.17560
$902$			50594.8i			1.86765i
$903$		−	24872.4i		−	0.916613i
$904$	14167.3			0.521235
$905$	1024.49	+	5229.46i	0.0376300	+	0.192081i
$906$	−21750.2			−0.797576
$907$		−	40426.1i		−	1.47996i	−0.672626	−	0.739982i	$-0.734834\pi$
$907$		−	40426.1i		−	1.47996i	0.672626	−	0.739982i	$-0.265166\pi$
$908$		−	12774.1i		−	0.466877i
$909$	−29725.2			−1.08462
$910$	45416.6	−	8897.44i	1.65445	−	0.324118i
$911$	33812.2			1.22969			0.614845	−	0.788648i	$-0.289218\pi$
$911$	33812.2			1.22969			0.614845	+	0.788648i	$0.289218\pi$
$912$		−	14906.5i		−	0.541231i
$913$		−	39478.3i		−	1.43104i
$914$	10709.1			0.387556
$915$	−18454.3	+	3615.33i	−0.666756	+	0.130622i
$916$	−12512.5			−0.451338
$917$			58412.6i			2.10355i
$918$			1156.17i			0.0415679i
$919$	−49508.6			−1.77708			−0.888540	−	0.458799i	$-0.848280\pi$
$919$	−49508.6			−1.77708			−0.888540	+	0.458799i	$0.848280\pi$
$920$	−395.499	−	2018.81i	−0.0141730	−	0.0723457i
$921$	−38268.3			−1.36914
$922$		−	31381.4i		−	1.12092i
$923$			71523.9i			2.55064i
$924$	43308.0			1.54191
$925$	−6169.69	−	15142.1i	−0.219306	−	0.538237i
$926$	1623.08			0.0576001
$927$		−	11920.7i		−	0.422360i
$928$			5011.18i			0.177263i
$929$	−23543.2			−0.831460			−0.415730	−	0.909488i	$-0.636474\pi$
$929$	−23543.2			−0.831460			−0.415730	+	0.909488i	$0.636474\pi$
$930$	1700.00	+	8677.60i	0.0599412	+	0.305967i
$931$	46766.9			1.64632
$932$		−	19364.0i		−	0.680567i
$933$			4584.27i			0.160860i
$934$	7668.75			0.268661
$935$	45569.0	−	8927.28i	1.59387	−	0.312250i
$936$	17348.7			0.605833
$937$			28656.7i			0.999116i	0.866280	+	0.499558i	$0.166504\pi$
$937$			28656.7i			0.999116i	−0.866280	+	0.499558i	$0.833496\pi$
$938$		−	29110.9i		−	1.01333i
$939$	−46270.0			−1.60806
$940$	13048.6	−	2556.32i	0.452765	−	0.0886999i
$941$	−36353.9			−1.25941			−0.629704	−	0.776835i	$-0.716824\pi$
$941$	−36353.9			−1.25941			−0.629704	+	0.776835i	$0.716824\pi$
$942$		−	21215.7i		−	0.733805i
$943$			10661.9i			0.368185i
$944$	4976.45			0.171578
$945$	−436.675	−	2228.99i	−0.0150318	−	0.0767292i
$946$	−13683.0			−0.470266
$947$			56916.4i			1.95304i	0.215416	+	0.976522i	$0.430889\pi$
$947$			56916.4i			1.95304i	−0.215416	+	0.976522i	$0.569111\pi$
$948$			6659.44i			0.228152i
$949$	−43307.5			−1.48137
$950$	11847.9	+	29078.1i	0.404629	+	0.993072i
$951$	−58058.9			−1.97970
$952$		−	16284.5i		−	0.554393i
$953$		−	10305.1i		−	0.350279i	−0.984544	−	0.175139i	$-0.943962\pi$
$953$		−	10305.1i		−	0.350279i	0.984544	−	0.175139i	$-0.0560376\pi$
$954$	23414.6			0.794628
$955$	−8951.19	−	45691.0i	−0.303302	−	1.54819i
$956$	3613.49			0.122247
$957$		−	63392.3i		−	2.14126i
$958$			12476.2i			0.420760i
$959$	−13408.9			−0.451508
$960$	5208.74	−	1020.43i	0.175116	−	0.0343065i
$961$	−26948.9			−0.904600
$962$			20244.4i			0.678489i
$963$			11785.5i			0.394374i
$964$	−8596.92			−0.287228
$965$	−24966.1	+	4891.05i	−0.832838	+	0.163159i
$966$	9126.31			0.303969
$967$			9853.83i			0.327692i	0.986486	+	0.163846i	$0.0523900\pi$
$967$			9853.83i			0.327692i	−0.986486	+	0.163846i	$0.947610\pi$
$968$		−	13176.9i		−	0.437522i
$969$	70904.9			2.35067
$970$	−4475.99	−	22847.5i	−0.148160	−	0.756278i
$971$	1210.04			0.0399919			0.0199960	−	0.999800i	$-0.493635\pi$
$971$	1210.04			0.0399919			0.0199960	+	0.999800i	$0.493635\pi$
$972$			21599.2i			0.712753i
$973$			5797.31i			0.191011i
$974$	31675.7			1.04205
$975$	−66447.7	+	27074.3i	−2.18260	+	0.889303i
$976$	3627.98			0.118985
$977$			10894.6i			0.356754i	0.983962	+	0.178377i	$0.0570847\pi$
$977$			10894.6i			0.356754i	−0.983962	+	0.178377i	$0.942915\pi$
$978$			16223.7i			0.530445i
$979$	30615.9			0.999477
$980$	3201.45	+	16341.7i	0.104354	+	0.532669i
$981$	3704.12			0.120554
$982$		−	40682.5i		−	1.32203i
$983$		−	25753.9i		−	0.835628i	−0.908532	−	0.417814i	$-0.862796\pi$
$983$		−	25753.9i		−	0.835628i	0.908532	−	0.417814i	$-0.137204\pi$
$984$	−27508.8			−0.891208
$985$	49053.2	−	9609.88i	1.58677	−	0.310859i
$986$	−23836.5			−0.769886
$987$			58988.2i			1.90234i
$988$		−	38876.3i		−	1.25184i
$989$	−2883.42			−0.0927072
$990$	−33558.9	+	6574.42i	−1.07734	+	0.211059i
$991$	−7622.66			−0.244341			−0.122170	−	0.992509i	$-0.538985\pi$
$991$	−7622.66			−0.244341			−0.122170	+	0.992509i	$0.538985\pi$
$992$		−	1705.95i		−	0.0546008i
$993$		−	44557.3i		−	1.42395i
$994$	−49442.0			−1.57767
$995$	11494.2	+	58671.5i	0.366221	+	1.86936i
$996$	21464.6			0.682865
$997$		−	5160.94i		−	0.163940i	−0.996635	−	0.0819701i	$-0.973879\pi$
$997$		−	5160.94i		−	0.163940i	0.996635	−	0.0819701i	$-0.0261212\pi$
$998$			18196.2i			0.577144i
$999$	993.571			0.0314667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.b.a.139.13	yes	14
5.2	odd	4		1150.4.a.y.1.6		7
5.3	odd	4		1150.4.a.z.1.2		7
5.4	even	2	inner	230.4.b.a.139.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.a.139.2	✓	14	5.4	even	2	inner
230.4.b.a.139.13	yes	14	1.1	even	1	trivial
1150.4.a.y.1.6		7	5.2	odd	4
1150.4.a.z.1.2		7	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +7.41782i q^{3} -4.00000 q^{4} +(2.14945 + 10.9718i) q^{5} -14.8356 q^{6} -26.7462i q^{7} -8.00000i q^{8} -28.0240 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +7.41782i q^{3} -4.00000 q^{4} +(2.14945 + 10.9718i) q^{5} -14.8356 q^{6} -26.7462i q^{7} -8.00000i q^{8} -28.0240 q^{9} +(-21.9436 + 4.29890i) q^{10} -54.5721 q^{11} -29.6713i q^{12} -77.3832i q^{13} +53.4923 q^{14} +(-81.3866 + 15.9442i) q^{15} +16.0000 q^{16} +76.1065i q^{17} -56.0480i q^{18} -125.597 q^{19} +(-8.59780 - 43.8871i) q^{20} +198.398 q^{21} -109.144i q^{22} -23.0000i q^{23} +59.3425 q^{24} +(-115.760 + 47.1665i) q^{25} +154.766 q^{26} -7.59574i q^{27} +106.985i q^{28} +156.599 q^{29} +(-31.8884 - 162.773i) q^{30} -53.3110 q^{31} +32.0000i q^{32} -404.805i q^{33} -152.213 q^{34} +(293.453 - 57.4895i) q^{35} +112.096 q^{36} +130.806i q^{37} -251.194i q^{38} +574.014 q^{39} +(87.7742 - 17.1956i) q^{40} -463.560 q^{41} +396.796i q^{42} -125.366i q^{43} +218.288 q^{44} +(-60.2361 - 307.473i) q^{45} +46.0000 q^{46} +297.322i q^{47} +118.685i q^{48} -372.357 q^{49} +(-94.3331 - 231.519i) q^{50} -564.544 q^{51} +309.533i q^{52} +417.759i q^{53} +15.1915 q^{54} +(-117.300 - 598.752i) q^{55} -213.969 q^{56} -931.654i q^{57} +313.199i q^{58} +311.028 q^{59} +(325.546 - 63.7769i) q^{60} +226.749 q^{61} -106.622i q^{62} +749.534i q^{63} -64.0000 q^{64} +(849.031 - 166.331i) q^{65} +809.611 q^{66} -544.207i q^{67} -304.426i q^{68} +170.610 q^{69} +(114.979 + 586.906i) q^{70} -924.282 q^{71} +224.192i q^{72} -559.650i q^{73} -261.613 q^{74} +(-349.873 - 858.684i) q^{75} +502.387 q^{76} +1459.59i q^{77} +1148.03i q^{78} -224.441 q^{79} +(34.3912 + 175.548i) q^{80} -700.304 q^{81} -927.119i q^{82} +723.415i q^{83} -793.592 q^{84} +(-835.024 + 163.587i) q^{85} +250.732 q^{86} +1161.63i q^{87} +436.576i q^{88} -561.018 q^{89} +(614.946 - 120.472i) q^{90} -2069.70 q^{91} +92.0000i q^{92} -395.451i q^{93} -594.645 q^{94} +(-269.964 - 1378.02i) q^{95} -237.370 q^{96} +1041.19i q^{97} -744.714i q^{98} +1529.33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) \) 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9	\( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) \) 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9 - 40 * q^10 - 146 * q^11 + 176 * q^14 - 206 * q^15 + 224 * q^16 + 154 * q^19 + 24 * q^20 - 220 * q^21 + 144 * q^24 - 286 * q^25 - 180 * q^26 + 790 * q^29 - 232 * q^30 - 320 * q^31 - 200 * q^34 - 426 * q^35 + 272 * q^36 + 1616 * q^39 + 160 * q^40 - 1904 * q^41 + 584 * q^44 + 622 * q^45 + 644 * q^46 + 610 * q^49 + 200 * q^50 - 1834 * q^51 + 192 * q^54 + 854 * q^55 - 704 * q^56 + 2814 * q^59 + 824 * q^60 - 3742 * q^61 - 896 * q^64 + 1730 * q^65 - 612 * q^66 + 414 * q^69 + 348 * q^70 - 3808 * q^71 + 268 * q^74 + 2904 * q^75 - 616 * q^76 - 1528 * q^79 - 96 * q^80 - 4618 * q^81 + 880 * q^84 + 2574 * q^85 - 2024 * q^86 + 2336 * q^89 + 2092 * q^90 - 3866 * q^91 + 456 * q^94 + 838 * q^95 - 576 * q^96 + 3342 * q^99

Introduction

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