LMFDB - Embedded newform 105.3.c.a.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(71,105)]

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([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.c (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 46x^{14} + 823x^{12} + 7252x^{10} + 32831x^{8} + 71486x^{6} + 60809x^{4} + 15680x^{2} + 576 $ x^16 + 46x^14 + 823x^12 + 7252x^10 + 32831x^8 + 71486x^6 + 60809x^4 + 15680*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.6
Root			$-1.02879i$ of defining polynomial
Character	$\chi$	$=$	105.71
Dual form			105.3.c.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.02879i q^{2} +(-2.94860 + 0.552947i) q^{3} +2.94159 q^{4} -2.23607i q^{5} +(0.568867 + 3.03349i) q^{6} +2.64575 q^{7} -7.14144i q^{8} +(8.38850 - 3.26084i) q^{9} +O(q^{10})$	\(q-1.02879i q^{2} +(-2.94860 + 0.552947i) q^{3} +2.94159 q^{4} -2.23607i q^{5} +(0.568867 + 3.03349i) q^{6} +2.64575 q^{7} -7.14144i q^{8} +(8.38850 - 3.26084i) q^{9} -2.30045 q^{10} -20.5440i q^{11} +(-8.67358 + 1.62654i) q^{12} -5.97956 q^{13} -2.72192i q^{14} +(1.23643 + 6.59327i) q^{15} +4.41931 q^{16} +4.50220i q^{17} +(-3.35472 - 8.63001i) q^{18} +20.5994 q^{19} -6.57759i q^{20} +(-7.80127 + 1.46296i) q^{21} -21.1354 q^{22} +4.04941i q^{23} +(3.94884 + 21.0573i) q^{24} -5.00000 q^{25} +6.15171i q^{26} +(-22.9313 + 14.2533i) q^{27} +7.78271 q^{28} +52.3317i q^{29} +(6.78310 - 1.27202i) q^{30} -4.73636 q^{31} -33.1123i q^{32} +(11.3597 + 60.5759i) q^{33} +4.63182 q^{34} -5.91608i q^{35} +(24.6755 - 9.59205i) q^{36} -23.9217 q^{37} -21.1924i q^{38} +(17.6313 - 3.30638i) q^{39} -15.9688 q^{40} +35.5530i q^{41} +(1.50508 + 8.02587i) q^{42} +57.9713 q^{43} -60.4319i q^{44} +(-7.29146 - 18.7573i) q^{45} +4.16600 q^{46} +26.2680i q^{47} +(-13.0308 + 2.44364i) q^{48} +7.00000 q^{49} +5.14395i q^{50} +(-2.48948 - 13.2752i) q^{51} -17.5894 q^{52} -0.292140i q^{53} +(14.6637 + 23.5915i) q^{54} -45.9377 q^{55} -18.8945i q^{56} +(-60.7393 + 11.3904i) q^{57} +53.8384 q^{58} -77.1700i q^{59} +(3.63706 + 19.3947i) q^{60} -105.850 q^{61} +4.87273i q^{62} +(22.1939 - 8.62737i) q^{63} -16.3884 q^{64} +13.3707i q^{65} +(62.3200 - 11.6868i) q^{66} -23.8346 q^{67} +13.2436i q^{68} +(-2.23911 - 11.9401i) q^{69} -6.08641 q^{70} +71.2671i q^{71} +(-23.2871 - 59.9060i) q^{72} +49.8528 q^{73} +24.6104i q^{74} +(14.7430 - 2.76473i) q^{75} +60.5949 q^{76} -54.3542i q^{77} +(-3.40157 - 18.1390i) q^{78} +50.9463 q^{79} -9.88188i q^{80} +(59.7339 - 54.7071i) q^{81} +36.5766 q^{82} -89.5847i q^{83} +(-22.9481 + 4.30343i) q^{84} +10.0672 q^{85} -59.6403i q^{86} +(-28.9367 - 154.305i) q^{87} -146.714 q^{88} +125.277i q^{89} +(-19.2973 + 7.50138i) q^{90} -15.8204 q^{91} +11.9117i q^{92} +(13.9656 - 2.61896i) q^{93} +27.0243 q^{94} -46.0616i q^{95} +(18.3093 + 97.6350i) q^{96} +162.046 q^{97} -7.20153i q^{98} +(-66.9906 - 172.333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * 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 $

$2$		−	1.02879i		−	0.514395i	−0.966359	−	0.257198i	$-0.917201\pi$
$2$		−	1.02879i		−	0.514395i	0.966359	−	0.257198i	$-0.0827991\pi$
$3$	−2.94860	+	0.552947i	−0.982867	+	0.184316i
$3$	−2.94860	+	0.552947i	−0.982867	+	0.184316i
$4$	2.94159			0.735397
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	0.568867	+	3.03349i	0.0948111	+	0.505582i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$		−	7.14144i		−	0.892680i
$9$	8.38850	−	3.26084i	0.932056	−	0.362315i
$10$	−2.30045			−0.230045
$11$		−	20.5440i		−	1.86763i	−0.357753	−	0.933816i	$-0.616457\pi$
$11$		−	20.5440i		−	1.86763i	0.357753	−	0.933816i	$-0.383543\pi$
$12$	−8.67358	+	1.62654i	−0.722798	+	0.135545i
$13$	−5.97956			−0.459966			−0.229983	−	0.973195i	$-0.573867\pi$
$13$	−5.97956			−0.459966			−0.229983	+	0.973195i	$0.573867\pi$
$14$		−	2.72192i		−	0.194423i
$15$	1.23643	+	6.59327i	0.0824284	+	0.439552i
$16$	4.41931			0.276207
$17$			4.50220i			0.264835i	0.991194	+	0.132418i	$0.0422740\pi$
$17$			4.50220i			0.264835i	−0.991194	+	0.132418i	$0.957726\pi$
$18$	−3.35472	−	8.63001i	−0.186373	−	0.479445i
$19$	20.5994			1.08418			0.542088	−	0.840321i	$-0.317634\pi$
$19$	20.5994			1.08418			0.542088	+	0.840321i	$0.317634\pi$
$20$		−	6.57759i		−	0.328880i
$21$	−7.80127	+	1.46296i	−0.371489	+	0.0696647i
$22$	−21.1354			−0.960702
$23$			4.04941i			0.176062i	0.996118	+	0.0880308i	$0.0280574\pi$
$23$			4.04941i			0.176062i	−0.996118	+	0.0880308i	$0.971943\pi$
$24$	3.94884	+	21.0573i	0.164535	+	0.877386i
$25$	−5.00000			−0.200000
$26$			6.15171i			0.236604i
$27$	−22.9313	+	14.2533i	−0.849306	+	0.527900i
$28$	7.78271			0.277954
$29$			52.3317i			1.80454i	0.431169	+	0.902271i	$0.358101\pi$
$29$			52.3317i			1.80454i	−0.431169	+	0.902271i	$0.641899\pi$
$30$	6.78310	−	1.27202i	0.226103	−	0.0424008i
$31$	−4.73636			−0.152786			−0.0763930	−	0.997078i	$-0.524340\pi$
$31$	−4.73636			−0.152786			−0.0763930	+	0.997078i	$0.524340\pi$
$32$		−	33.1123i		−	1.03476i
$33$	11.3597	+	60.5759i	0.344234	+	1.83563i
$34$	4.63182			0.136230
$35$		−	5.91608i		−	0.169031i
$36$	24.6755	−	9.59205i	0.685431	−	0.266446i
$37$	−23.9217			−0.646531			−0.323266	−	0.946308i	$-0.604781\pi$
$37$	−23.9217			−0.646531			−0.323266	+	0.946308i	$0.604781\pi$
$38$		−	21.1924i		−	0.557696i
$39$	17.6313	−	3.30638i	0.452085	−	0.0847789i
$40$	−15.9688			−0.399219
$41$			35.5530i			0.867147i	0.901118	+	0.433574i	$0.142748\pi$
$41$			35.5530i			0.867147i	−0.901118	+	0.433574i	$0.857252\pi$
$42$	1.50508	+	8.02587i	0.0358352	+	0.191092i
$43$	57.9713			1.34817			0.674085	−	0.738654i	$-0.264538\pi$
$43$	57.9713			1.34817			0.674085	+	0.738654i	$0.264538\pi$
$44$		−	60.4319i		−	1.37345i
$45$	−7.29146	−	18.7573i	−0.162032	−	0.416828i
$46$	4.16600			0.0905652
$47$			26.2680i			0.558894i	0.960161	+	0.279447i	$0.0901512\pi$
$47$			26.2680i			0.558894i	−0.960161	+	0.279447i	$0.909849\pi$
$48$	−13.0308	+	2.44364i	−0.271475	+	0.0509092i
$49$	7.00000			0.142857
$50$			5.14395i			0.102879i
$51$	−2.48948	−	13.2752i	−0.0488133	−	0.260298i
$52$	−17.5894			−0.338258
$53$		−	0.292140i		−	0.00551207i	−0.999996	−	0.00275604i	$-0.999123\pi$
$53$		−	0.292140i		−	0.00551207i	0.999996	−	0.00275604i	$-0.000877274\pi$
$54$	14.6637	+	23.5915i	0.271549	+	0.436879i
$55$	−45.9377			−0.835231
$56$		−	18.8945i		−	0.337401i
$57$	−60.7393	+	11.3904i	−1.06560	+	0.199831i
$58$	53.8384			0.928248
$59$		−	77.1700i		−	1.30797i	−0.756509	−	0.653983i	$-0.773097\pi$
$59$		−	77.1700i		−	1.30797i	0.756509	−	0.653983i	$-0.226903\pi$
$60$	3.63706	+	19.3947i	0.0606177	+	0.323245i
$61$	−105.850			−1.73524			−0.867619	−	0.497229i	$-0.834351\pi$
$61$	−105.850			−1.73524			−0.867619	+	0.497229i	$0.834351\pi$
$62$			4.87273i			0.0785924i
$63$	22.1939	−	8.62737i	0.352284	−	0.136942i
$64$	−16.3884			−0.256069
$65$			13.3707i			0.205703i
$66$	62.3200	−	11.6868i	0.944242	−	0.177072i
$67$	−23.8346			−0.355740			−0.177870	−	0.984054i	$-0.556921\pi$
$67$	−23.8346			−0.355740			−0.177870	+	0.984054i	$0.556921\pi$
$68$			13.2436i			0.194759i
$69$	−2.23911	−	11.9401i	−0.0324509	−	0.173045i
$70$	−6.08641			−0.0869487
$71$			71.2671i			1.00376i	0.864937	+	0.501881i	$0.167358\pi$
$71$			71.2671i			1.00376i	−0.864937	+	0.501881i	$0.832642\pi$
$72$	−23.2871	−	59.9060i	−0.323432	−	0.832028i
$73$	49.8528			0.682915			0.341458	−	0.939897i	$-0.389079\pi$
$73$	49.8528			0.682915			0.341458	+	0.939897i	$0.389079\pi$
$74$			24.6104i			0.332573i
$75$	14.7430	−	2.76473i	0.196573	−	0.0368631i
$76$	60.5949			0.797301
$77$		−	54.3542i		−	0.705899i
$78$	−3.40157	−	18.1390i	−0.0436099	−	0.232551i
$79$	50.9463			0.644890			0.322445	−	0.946588i	$-0.395495\pi$
$79$	50.9463			0.644890			0.322445	+	0.946588i	$0.395495\pi$
$80$		−	9.88188i		−	0.123523i
$81$	59.7339	−	54.7071i	0.737455	−	0.675396i
$82$	36.5766			0.446056
$83$		−	89.5847i		−	1.07933i	−0.841878	−	0.539667i	$-0.818550\pi$
$83$		−	89.5847i		−	1.07933i	0.841878	−	0.539667i	$-0.181450\pi$
$84$	−22.9481	+	4.30343i	−0.273192	+	0.0512313i
$85$	10.0672			0.118438
$86$		−	59.6403i		−	0.693492i
$87$	−28.9367	−	154.305i	−0.332605	−	1.77363i
$88$	−146.714			−1.66720
$89$			125.277i			1.40760i	0.710397	+	0.703801i	$0.248515\pi$
$89$			125.277i			1.40760i	−0.710397	+	0.703801i	$0.751485\pi$
$90$	−19.2973	+	7.50138i	−0.214414	+	0.0833487i
$91$	−15.8204			−0.173851
$92$			11.9117i			0.129475i
$93$	13.9656	−	2.61896i	0.150168	−	0.0281608i
$94$	27.0243			0.287493
$95$		−	46.0616i		−	0.484859i
$96$	18.3093	+	97.6350i	0.190722	+	1.01703i
$97$	162.046			1.67058			0.835288	−	0.549812i	$-0.185301\pi$
$97$	162.046			1.67058			0.835288	+	0.549812i	$0.185301\pi$
$98$		−	7.20153i		−	0.0734850i
$99$	−66.9906	−	172.333i	−0.676672	−	1.74074i
$100$	−14.7079			−0.147079
$101$			67.0315i			0.663678i	0.943336	+	0.331839i	$0.107669\pi$
$101$			67.0315i			0.663678i	−0.943336	+	0.331839i	$0.892331\pi$
$102$	−13.6574	+	2.56115i	−0.133896	+	0.0251093i
$103$	−31.8666			−0.309385			−0.154692	−	0.987963i	$-0.549439\pi$
$103$	−31.8666			−0.309385			−0.154692	+	0.987963i	$0.549439\pi$
$104$			42.7027i			0.410603i
$105$	3.27128	+	17.4442i	0.0311550	+	0.166135i
$106$	−0.300551			−0.00283538
$107$			133.539i			1.24803i	0.781414	+	0.624013i	$0.214499\pi$
$107$			133.539i			1.24803i	−0.781414	+	0.624013i	$0.785501\pi$
$108$	−67.4544	+	41.9274i	−0.624578	+	0.388217i
$109$	177.121			1.62496			0.812482	−	0.582987i	$-0.198116\pi$
$109$	177.121			1.62496			0.812482	+	0.582987i	$0.198116\pi$
$110$			47.2603i			0.429639i
$111$	70.5354	−	13.2274i	0.635454	−	0.119166i
$112$	11.6924			0.104396
$113$			197.438i			1.74724i	0.486611	+	0.873619i	$0.338233\pi$
$113$			197.438i			1.74724i	−0.486611	+	0.873619i	$0.661767\pi$
$114$	11.7183	+	62.4880i	0.102792	+	0.548141i
$115$	9.05477			0.0787371
$116$			153.938i			1.32706i
$117$	−50.1595	+	19.4984i	−0.428714	+	0.166653i
$118$	−79.3918			−0.672812
$119$			11.9117i			0.100098i
$120$	47.0855	−	8.82987i	0.392379	−	0.0735823i
$121$	−301.054			−2.48805
$122$			108.897i			0.892599i
$123$	−19.6589	−	104.832i	−0.159829	−	0.852290i
$124$	−13.9324			−0.112358
$125$			11.1803i			0.0894427i
$126$	−8.87576	−	22.8329i	−0.0704425	−	0.181213i
$127$	26.3611			0.207568			0.103784	−	0.994600i	$-0.466905\pi$
$127$	26.3611			0.207568			0.103784	+	0.994600i	$0.466905\pi$
$128$		−	115.589i		−	0.903039i
$129$	−170.934	+	32.0550i	−1.32507	+	0.248489i
$130$	13.7556			0.105813
$131$		−	99.1579i		−	0.756930i	−0.925616	−	0.378465i	$-0.876452\pi$
$131$		−	99.1579i		−	0.756930i	0.925616	−	0.378465i	$-0.123548\pi$
$132$	33.4156	+	178.190i	0.253149	+	1.34992i
$133$	54.5008			0.409780
$134$			24.5208i			0.182991i
$135$	31.8714	+	51.2759i	0.236084	+	0.379821i
$136$	32.1522			0.236413
$137$		−	68.0932i		−	0.497031i	−0.968628	−	0.248515i	$-0.920057\pi$
$137$		−	68.0932i		−	0.497031i	0.968628	−	0.248515i	$-0.0799427\pi$
$138$	−12.2839	+	2.30358i	−0.0890136	+	0.0166926i
$139$	−46.4929			−0.334481			−0.167241	−	0.985916i	$-0.553486\pi$
$139$	−46.4929			−0.334481			−0.167241	+	0.985916i	$0.553486\pi$
$140$		−	17.4027i		−	0.124305i
$141$	−14.5248	−	77.4540i	−0.103013	−	0.549319i
$142$	73.3189			0.516330
$143$			122.844i			0.859048i
$144$	37.0714	−	14.4107i	0.257440	−	0.100074i
$145$	117.017			0.807016
$146$		−	51.2881i		−	0.351288i
$147$	−20.6402	+	3.87063i	−0.140410	+	0.0263308i
$148$	−70.3677			−0.475458
$149$		−	128.382i		−	0.861625i	−0.902441	−	0.430812i	$-0.858227\pi$
$149$		−	128.382i		−	0.861625i	0.902441	−	0.430812i	$-0.141773\pi$
$150$	−2.84433	−	15.1675i	−0.0189622	−	0.101116i
$151$	−100.696			−0.666863			−0.333431	−	0.942774i	$-0.608207\pi$
$151$	−100.696			−0.666863			−0.333431	+	0.942774i	$0.608207\pi$
$152$		−	147.109i		−	0.967823i
$153$	14.6809	+	37.7667i	0.0959539	+	0.246841i
$154$	−55.9191			−0.363111
$155$			10.5908i			0.0683279i
$156$	51.8641	−	9.72601i	0.332462	−	0.0623462i
$157$	151.763			0.966643			0.483321	−	0.875443i	$-0.339430\pi$
$157$	151.763			0.966643			0.483321	+	0.875443i	$0.339430\pi$
$158$		−	52.4131i		−	0.331728i
$159$	0.161538	+	0.861404i	0.00101596	+	0.00541763i
$160$	−74.0414			−0.462759
$161$			10.7137i			0.0665450i
$162$	−56.2822	−	61.4536i	−0.347421	−	0.379343i
$163$	64.7948			0.397514			0.198757	−	0.980049i	$-0.436310\pi$
$163$	64.7948			0.397514			0.198757	+	0.980049i	$0.436310\pi$
$164$			104.582i			0.637698i
$165$	135.452	−	25.4011i	0.820921	−	0.153946i
$166$	−92.1639			−0.555204
$167$		−	97.9869i		−	0.586748i	−0.955998	−	0.293374i	$-0.905222\pi$
$167$		−	97.9869i		−	0.586748i	0.955998	−	0.293374i	$-0.0947781\pi$
$168$	10.4476	+	55.7123i	0.0621884	+	0.331621i
$169$	−133.245			−0.788431
$170$		−	10.3571i		−	0.0609239i
$171$	172.798	−	67.1712i	1.01051	−	0.392814i
$172$	170.528			0.991441
$173$		−	240.801i		−	1.39191i	−0.718083	−	0.695957i	$-0.754980\pi$
$173$		−	240.801i		−	1.39191i	0.718083	−	0.695957i	$-0.245020\pi$
$174$	−158.748	+	29.7698i	−0.912345	+	0.171091i
$175$	−13.2288			−0.0755929
$176$		−	90.7901i		−	0.515853i
$177$	42.6709	+	227.544i	0.241079	+	1.28556i
$178$	128.883			0.724064
$179$			53.9971i			0.301660i	0.988560	+	0.150830i	$0.0481946\pi$
$179$			53.9971i			0.301660i	−0.988560	+	0.150830i	$0.951805\pi$
$180$	−21.4485	−	55.1762i	−0.119158	−	0.306534i
$181$	29.0590			0.160547			0.0802735	−	0.996773i	$-0.474421\pi$
$181$	29.0590			0.160547			0.0802735	+	0.996773i	$0.474421\pi$
$182$			16.2759i			0.0894280i
$183$	312.108	−	58.5292i	1.70551	−	0.319832i
$184$	28.9187			0.157167
$185$			53.4905i			0.289138i
$186$	−2.69436	−	14.3677i	−0.0144858	−	0.0772459i
$187$	92.4930			0.494615
$188$			77.2698i			0.411009i
$189$	−60.6704	+	37.7107i	−0.321008	+	0.199528i
$190$	−47.3877			−0.249409
$191$		−	121.364i		−	0.635414i	−0.948189	−	0.317707i	$-0.897087\pi$
$191$		−	121.364i		−	0.635414i	0.948189	−	0.317707i	$-0.102913\pi$
$192$	48.3229	−	9.06192i	0.251682	−	0.0471975i
$193$	−326.351			−1.69094			−0.845469	−	0.534024i	$-0.820679\pi$
$193$	−326.351			−1.69094			−0.845469	+	0.534024i	$0.820679\pi$
$194$		−	166.711i		−	0.859337i
$195$	−7.39328	−	39.4249i	−0.0379143	−	0.202179i
$196$	20.5911			0.105057
$197$			193.857i			0.984047i	0.870582	+	0.492023i	$0.163743\pi$
$197$			193.857i			0.984047i	−0.870582	+	0.492023i	$0.836257\pi$
$198$	−177.295	+	68.9193i	−0.895427	+	0.348077i
$199$	−369.485			−1.85671			−0.928353	−	0.371699i	$-0.878775\pi$
$199$	−369.485			−1.85671			−0.928353	+	0.371699i	$0.878775\pi$
$200$			35.7072i			0.178536i
$201$	70.2788	−	13.1793i	0.349646	−	0.0655685i
$202$	68.9614			0.341393
$203$			138.457i			0.682053i
$204$	−7.32302	−	39.0502i	−0.0358971	−	0.191422i
$205$	79.4990			0.387800
$206$			32.7841i			0.159146i
$207$	13.2045	+	33.9685i	0.0637898	+	0.164099i
$208$	−26.4255			−0.127046
$209$		−	423.192i		−	2.02484i
$210$	17.9464	−	3.36546i	0.0854590	−	0.0160260i
$211$	0.588768			0.00279037			0.00139518	−	0.999999i	$-0.499556\pi$
$211$	0.588768			0.00279037			0.00139518	+	0.999999i	$0.499556\pi$
$212$		−	0.859355i		−	0.00405356i
$213$	−39.4069	−	210.138i	−0.185009	−	0.986564i
$214$	137.384			0.641979
$215$		−	129.628i		−	0.602920i
$216$	101.789	+	163.762i	0.471246	+	0.758159i
$217$	−12.5312			−0.0577477
$218$		−	182.220i		−	0.835874i
$219$	−146.996	+	27.5660i	−0.671215	+	0.125872i
$220$	−135.130			−0.614227
$221$		−	26.9212i		−	0.121815i
$222$	−13.6082	−	72.5662i	−0.0612983	−	0.326875i
$223$	206.666			0.926752			0.463376	−	0.886162i	$-0.346638\pi$
$223$	206.666			0.926752			0.463376	+	0.886162i	$0.346638\pi$
$224$		−	87.6070i		−	0.391102i
$225$	−41.9425	+	16.3042i	−0.186411	+	0.0724631i
$226$	203.122			0.898771
$227$		−	174.060i		−	0.766784i	−0.923586	−	0.383392i	$-0.874756\pi$
$227$		−	174.060i		−	0.766784i	0.923586	−	0.383392i	$-0.125244\pi$
$228$	−178.670	+	33.5057i	−0.783641	+	0.146955i
$229$	135.285			0.590764			0.295382	−	0.955379i	$-0.404553\pi$
$229$	135.285			0.590764			0.295382	+	0.955379i	$0.404553\pi$
$230$		−	9.31546i		−	0.0405020i
$231$	30.0550	+	160.269i	0.130108	+	0.693805i
$232$	373.724			1.61088
$233$			117.237i			0.503161i	0.967836	+	0.251581i	$0.0809504\pi$
$233$			117.237i			0.503161i	−0.967836	+	0.251581i	$0.919050\pi$
$234$	20.0597	+	51.6036i	0.0857254	+	0.220528i
$235$	58.7371			0.249945
$236$		−	227.003i		−	0.961876i
$237$	−150.220	+	28.1706i	−0.633841	+	0.118863i
$238$	12.2546			0.0514901
$239$			152.243i			0.637001i	0.947923	+	0.318500i	$0.103179\pi$
$239$			152.243i			0.637001i	−0.947923	+	0.318500i	$0.896821\pi$
$240$	5.46415	+	29.1377i	0.0227673	+	0.121407i
$241$	−200.630			−0.832491			−0.416245	−	0.909252i	$-0.636654\pi$
$241$	−200.630			−0.832491			−0.416245	+	0.909252i	$0.636654\pi$
$242$			309.722i			1.27984i
$243$	−145.881	+	194.339i	−0.600334	+	0.799749i
$244$	−311.366			−1.27609
$245$		−	15.6525i		−	0.0638877i
$246$	−107.850	+	20.2249i	−0.438414	+	0.0822152i
$247$	−123.175			−0.498684
$248$			33.8245i			0.136389i
$249$	49.5356	+	264.150i	0.198938	+	1.06084i
$250$	11.5022			0.0460089
$251$		−	17.1347i		−	0.0682659i	−0.999417	−	0.0341330i	$-0.989133\pi$
$251$		−	17.1347i		−	0.0682659i	0.999417	−	0.0341330i	$-0.0108670\pi$
$252$	65.2853	−	25.3782i	0.259069	−	0.100707i
$253$	83.1910			0.328818
$254$		−	27.1201i		−	0.106772i
$255$	−29.6842	+	5.56664i	−0.116409	+	0.0218300i
$256$	−184.471			−0.720588
$257$		−	233.287i		−	0.907732i	−0.891070	−	0.453866i	$-0.850044\pi$
$257$		−	233.287i		−	0.907732i	0.891070	−	0.453866i	$-0.149956\pi$
$258$	32.9779	+	175.856i	0.127821	+	0.681611i
$259$	−63.2908			−0.244366
$260$			39.3311i			0.151273i
$261$	170.645	+	438.985i	0.653814	+	1.68193i
$262$	−102.013			−0.389361
$263$			276.662i			1.05195i	0.850501	+	0.525973i	$0.176299\pi$
$263$			276.662i			1.05195i	−0.850501	+	0.525973i	$0.823701\pi$
$264$	432.600	−	81.1248i	1.63864	−	0.307291i
$265$	−0.653244			−0.00246507
$266$		−	56.0699i		−	0.210789i
$267$	−69.2713	−	369.391i	−0.259443	−	1.38349i
$268$	−70.1116			−0.261611
$269$			362.110i			1.34613i	0.739582	+	0.673066i	$0.235023\pi$
$269$			362.110i			1.34613i	−0.739582	+	0.673066i	$0.764977\pi$
$270$	52.7521	−	32.7890i	0.195378	−	0.121441i
$271$	−6.53530			−0.0241155			−0.0120577	−	0.999927i	$-0.503838\pi$
$271$	−6.53530			−0.0241155			−0.0120577	+	0.999927i	$0.503838\pi$
$272$			19.8966i			0.0731493i
$273$	46.6481	−	8.74785i	0.170872	−	0.0320434i
$274$	−70.0537			−0.255670
$275$			102.720i			0.373527i
$276$	−6.58655	−	35.1229i	−0.0238643	−	0.127257i
$277$	−334.559			−1.20779			−0.603897	−	0.797062i	$-0.706386\pi$
$277$	−334.559			−1.20779			−0.603897	+	0.797062i	$0.706386\pi$
$278$			47.8315i			0.172056i
$279$	−39.7310	+	15.4445i	−0.142405	+	0.0553567i
$280$	−42.2493			−0.150891
$281$		−	10.2999i		−	0.0366544i	−0.999832	−	0.0183272i	$-0.994166\pi$
$281$		−	10.2999i		−	0.0366544i	0.999832	−	0.0183272i	$-0.00583405\pi$
$282$	−79.6839	+	14.9430i	−0.282567	+	0.0529894i
$283$	435.453			1.53870			0.769351	−	0.638826i	$-0.220580\pi$
$283$	435.453			1.53870			0.769351	+	0.638826i	$0.220580\pi$
$284$			209.638i			0.738164i
$285$	25.4696	+	135.817i	0.0893670	+	0.476552i
$286$	126.381			0.441890
$287$			94.0645i			0.327751i
$288$	−107.974	−	277.763i	−0.374910	−	0.964454i
$289$	268.730			0.929862
$290$		−	120.386i		−	0.415125i
$291$	−477.809	+	89.6028i	−1.64195	+	0.307913i
$292$	146.647			0.502214
$293$		−	327.016i		−	1.11609i	−0.829809	−	0.558047i	$-0.811551\pi$
$293$		−	327.016i		−	1.11609i	0.829809	−	0.558047i	$-0.188449\pi$
$294$	3.98207	+	21.2345i	0.0135444	+	0.0722260i
$295$	−172.557			−0.584941
$296$			170.835i			0.577146i
$297$	292.819	+	471.099i	0.985924	+	1.58619i
$298$	−132.078			−0.443216
$299$		−	24.2137i		−	0.0809823i
$300$	43.3679	−	8.13271i	0.144560	−	0.0271090i
$301$	153.378			0.509560
$302$			103.595i			0.343031i
$303$	−37.0649	−	197.649i	−0.122326	−	0.652308i
$304$	91.0349			0.299457
$305$			236.687i			0.776022i
$306$	38.8540	−	15.1036i	0.126974	−	0.0493582i
$307$	−354.704			−1.15539			−0.577694	−	0.816253i	$-0.696047\pi$
$307$	−354.704			−1.15539			−0.577694	+	0.816253i	$0.696047\pi$
$308$		−	159.888i		−	0.519116i
$309$	93.9620	−	17.6206i	0.304084	−	0.0570245i
$310$	10.8957			0.0351476
$311$			96.7606i			0.311127i	0.987826	+	0.155564i	$0.0497194\pi$
$311$			96.7606i			0.311127i	−0.987826	+	0.155564i	$0.950281\pi$
$312$	−23.6123	−	125.913i	−0.0756805	−	0.403568i
$313$	−235.892			−0.753650			−0.376825	−	0.926284i	$-0.622984\pi$
$313$	−235.892			−0.753650			−0.376825	+	0.926284i	$0.622984\pi$
$314$		−	156.132i		−	0.497236i
$315$	−19.2914	−	49.6270i	−0.0612425	−	0.157546i
$316$	149.863			0.474251
$317$		−	57.4076i		−	0.181096i	−0.995892	−	0.0905482i	$-0.971138\pi$
$317$		−	57.4076i		−	0.181096i	0.995892	−	0.0905482i	$-0.0288619\pi$
$318$	0.886204	−	0.166189i	0.00278681	−	0.000522605i
$319$	1075.10			3.37022
$320$			36.6456i			0.114517i
$321$	−73.8399	−	393.753i	−0.230031	−	1.22664i
$322$	11.0222			0.0342304
$323$			92.7424i			0.287128i
$324$	175.712	−	160.926i	0.542322	−	0.496685i
$325$	29.8978			0.0919932
$326$		−	66.6603i		−	0.204479i
$327$	−522.259	+	97.9385i	−1.59712	+	0.299506i
$328$	253.900			0.774085
$329$			69.4987i			0.211242i
$330$	−26.1324	−	139.352i	−0.0791891	−	0.422278i
$331$	−8.17934			−0.0247110			−0.0123555	−	0.999924i	$-0.503933\pi$
$331$	−8.17934			−0.0247110			−0.0123555	+	0.999924i	$0.503933\pi$
$332$		−	263.522i		−	0.793740i
$333$	−200.667	+	78.0047i	−0.602603	+	0.234248i
$334$	−100.808			−0.301820
$335$			53.2958i			0.159092i
$336$	−34.4762	+	6.46527i	−0.102608	+	0.0192419i
$337$	9.35744			0.0277669			0.0138834	−	0.999904i	$-0.495581\pi$
$337$	9.35744			0.0277669			0.0138834	+	0.999904i	$0.495581\pi$
$338$			137.081i			0.405565i
$339$	−109.173	−	582.165i	−0.322043	−	1.71730i
$340$	29.6136			0.0870989
$341$			97.3037i			0.285348i
$342$	−69.1051	−	177.773i	−0.202062	−	0.519803i
$343$	18.5203			0.0539949
$344$		−	413.999i		−	1.20348i
$345$	−26.6989	+	5.00680i	−0.0773881	+	0.0145125i
$346$	−247.734			−0.715994
$347$		−	515.037i		−	1.48426i	−0.670258	−	0.742128i	$-0.733817\pi$
$347$		−	515.037i		−	1.48426i	0.670258	−	0.742128i	$-0.266183\pi$
$348$	−85.1198	−	453.903i	−0.244597	−	1.30432i
$349$	−337.450			−0.966905			−0.483452	−	0.875371i	$-0.660617\pi$
$349$	−337.450			−0.966905			−0.483452	+	0.875371i	$0.660617\pi$
$350$			13.6096i			0.0388846i
$351$	137.119	−	85.2285i	0.390652	−	0.242816i
$352$	−680.258			−1.93255
$353$			364.081i			1.03139i	0.856772	+	0.515696i	$0.172467\pi$
$353$			364.081i			1.03139i	−0.856772	+	0.515696i	$0.827533\pi$
$354$	234.095	−	43.8995i	0.661285	−	0.124010i
$355$	159.358			0.448896
$356$			368.512i			1.03515i
$357$	−6.58653	−	35.1228i	−0.0184497	−	0.0983833i
$358$	55.5517			0.155172
$359$			547.289i			1.52448i	0.647293	+	0.762241i	$0.275901\pi$
$359$			547.289i			1.52448i	−0.647293	+	0.762241i	$0.724099\pi$
$360$	−133.954	+	52.0715i	−0.372094	+	0.144643i
$361$	63.3336			0.175439
$362$		−	29.8957i		−	0.0825847i
$363$	887.689	−	166.467i	2.44542	−	0.458587i
$364$	−46.5372			−0.127849
$365$		−	111.474i		−	0.305409i
$366$	−60.2143	−	321.094i	−0.164520	−	0.877306i
$367$	−357.882			−0.975155			−0.487578	−	0.873080i	$-0.662119\pi$
$367$	−357.882			−0.975155			−0.487578	+	0.873080i	$0.662119\pi$
$368$			17.8956i			0.0486294i
$369$	115.933	+	298.237i	0.314181	+	0.808229i
$370$	55.0305			0.148731
$371$		−	0.772929i		−	0.00208337i
$372$	41.0812	−	7.70390i	0.110433	−	0.0207094i
$373$	−400.685			−1.07422			−0.537111	−	0.843512i	$-0.680484\pi$
$373$	−400.685			−1.07422			−0.537111	+	0.843512i	$0.680484\pi$
$374$		−	95.1559i		−	0.254428i
$375$	−6.18213	−	32.9664i	−0.0164857	−	0.0879103i
$376$	187.592			0.498914
$377$		−	312.921i		−	0.830028i
$378$	38.7964	+	62.4172i	0.102636	+	0.165125i
$379$	61.3266			0.161812			0.0809058	−	0.996722i	$-0.474219\pi$
$379$	61.3266			0.161812			0.0809058	+	0.996722i	$0.474219\pi$
$380$		−	135.494i		−	0.356564i
$381$	−77.7284	+	14.5763i	−0.204012	+	0.0382580i
$382$	−124.858			−0.326854
$383$		−	75.4942i		−	0.197113i	−0.995131	−	0.0985564i	$-0.968578\pi$
$383$		−	75.4942i		−	0.197113i	0.995131	−	0.0985564i	$-0.0314225\pi$
$384$	63.9146	+	340.826i	0.166444	+	0.887568i
$385$	−121.540			−0.315688
$386$			335.747i			0.869811i
$387$	486.292	−	189.035i	1.25657	−	0.488463i
$388$	476.673			1.22854
$389$		−	259.083i		−	0.666022i	−0.942923	−	0.333011i	$-0.891935\pi$
$389$		−	259.083i		−	0.666022i	0.942923	−	0.333011i	$-0.108065\pi$
$390$	−40.5599	+	7.60614i	−0.104000	+	0.0195029i
$391$	−18.2313			−0.0466273
$392$		−	49.9901i		−	0.127526i
$393$	54.8290	+	292.377i	0.139514	+	0.743962i
$394$	199.438			0.506189
$395$		−	113.919i		−	0.288404i
$396$	−197.059	−	506.933i	−0.497623	−	1.28013i
$397$	150.640			0.379445			0.189722	−	0.981838i	$-0.439241\pi$
$397$	150.640			0.379445			0.189722	+	0.981838i	$0.439241\pi$
$398$			380.122i			0.955081i
$399$	−160.701	+	30.1360i	−0.402760	+	0.0755289i
$400$	−22.0965			−0.0552414
$401$		−	249.906i		−	0.623206i	−0.950212	−	0.311603i	$-0.899134\pi$
$401$		−	249.906i		−	0.623206i	0.950212	−	0.311603i	$-0.100866\pi$
$402$	−13.5587	−	72.3021i	−0.0337281	−	0.179856i
$403$	28.3214			0.0702763
$404$			197.179i			0.488067i
$405$	−122.329	−	133.569i	−0.302046	−	0.329800i
$406$	142.443			0.350845
$407$			491.446i			1.20748i
$408$	−94.8040	+	17.7785i	−0.232363	+	0.0435746i
$409$	−171.282			−0.418784			−0.209392	−	0.977832i	$-0.567148\pi$
$409$	−171.282			−0.418784			−0.209392	+	0.977832i	$0.567148\pi$
$410$		−	81.7878i		−	0.199483i
$411$	37.6519	+	200.780i	0.0916105	+	0.488515i
$412$	−93.7386			−0.227521
$413$		−	204.173i		−	0.494365i
$414$	34.9465	−	13.5847i	0.0844118	−	0.0328132i
$415$	−200.318			−0.482693
$416$			197.997i			0.475954i
$417$	137.089	−	25.7081i	0.328751	−	0.0616502i
$418$	−435.376			−1.04157
$419$			470.254i			1.12232i	0.827706	+	0.561162i	$0.189645\pi$
$419$			470.254i			1.12232i	−0.827706	+	0.561162i	$0.810355\pi$
$420$	9.62276	+	51.3136i	0.0229113	+	0.122175i
$421$	−91.5469			−0.217451			−0.108726	−	0.994072i	$-0.534677\pi$
$421$	−91.5469			−0.217451			−0.108726	+	0.994072i	$0.534677\pi$
$422$		−	0.605719i		−	0.00143535i
$423$	85.6558	+	220.349i	0.202496	+	0.520921i
$424$	−2.08630			−0.00492052
$425$		−	22.5110i		−	0.0529670i
$426$	−216.188	+	40.5414i	−0.507484	+	0.0951677i
$427$	−280.052			−0.655859
$428$			392.816i			0.917795i
$429$	−67.9261	−	362.217i	−0.158336	−	0.844330i
$430$	−133.360			−0.310139
$431$		−	194.007i		−	0.450132i	−0.974343	−	0.225066i	$-0.927740\pi$
$431$		−	194.007i		−	0.450132i	0.974343	−	0.225066i	$-0.0722598\pi$
$432$	−101.340	+	62.9898i	−0.234584	+	0.145810i
$433$	448.944			1.03682			0.518411	−	0.855132i	$-0.326524\pi$
$433$	448.944			1.03682			0.518411	+	0.855132i	$0.326524\pi$
$434$			12.8920i			0.0297051i
$435$	−345.037	+	64.7043i	−0.793189	+	0.148746i
$436$	521.017			1.19499
$437$			83.4153i			0.190882i
$438$	28.3596	+	151.228i	0.0647479	+	0.345270i
$439$	65.8596			0.150022			0.0750109	−	0.997183i	$-0.476101\pi$
$439$	65.8596			0.150022			0.0750109	+	0.997183i	$0.476101\pi$
$440$			328.061i			0.745594i
$441$	58.7195	−	22.8259i	0.133151	−	0.0517594i
$442$	−27.6962			−0.0626612
$443$		−	544.274i		−	1.22861i	−0.789069	−	0.614305i	$-0.789436\pi$
$443$		−	544.274i		−	1.22861i	0.789069	−	0.614305i	$-0.210564\pi$
$444$	207.486	−	38.9096i	0.467312	−	0.0876342i
$445$	280.127			0.629499
$446$		−	212.616i		−	0.476717i
$447$	70.9885	+	378.548i	0.158811	+	0.846863i
$448$	−43.3596			−0.0967849
$449$			95.5434i			0.212792i	0.994324	+	0.106396i	$0.0339311\pi$
$449$			95.5434i			0.212792i	−0.994324	+	0.106396i	$0.966069\pi$
$450$	16.7736	+	43.1501i	0.0372747	+	0.0958890i
$451$	730.400			1.61951
$452$			580.781i			1.28491i
$453$	296.913	−	55.6797i	0.655437	−	0.122913i
$454$	−179.071			−0.394430
$455$			35.3755i			0.0777484i
$456$	81.3435	+	433.766i	0.178385	+	0.951242i
$457$	466.890			1.02164			0.510821	−	0.859687i	$-0.329342\pi$
$457$	466.890			1.02164			0.510821	+	0.859687i	$0.329342\pi$
$458$		−	139.180i		−	0.303886i
$459$	−64.1712	−	103.241i	−0.139807	−	0.224926i
$460$	26.6354			0.0579031
$461$			16.4314i			0.0356429i	0.999841	+	0.0178215i	$0.00567305\pi$
$461$			16.4314i			0.0356429i	−0.999841	+	0.0178215i	$0.994327\pi$
$462$	164.883	−	30.9203i	0.356890	−	0.0669270i
$463$	−564.803			−1.21988			−0.609938	−	0.792449i	$-0.708806\pi$
$463$	−564.803			−1.21988			−0.609938	+	0.792449i	$0.708806\pi$
$464$			231.270i			0.498427i
$465$	−5.85617	−	31.2281i	−0.0125939	−	0.0671573i
$466$	120.612			0.258824
$467$			726.422i			1.55551i	0.628569	+	0.777754i	$0.283641\pi$
$467$			726.422i			1.55551i	−0.628569	+	0.777754i	$0.716359\pi$
$468$	−147.549	+	57.3562i	−0.315275	+	0.122556i
$469$	−63.0604			−0.134457
$470$		−	60.4282i		−	0.128571i
$471$	−447.488	+	83.9168i	−0.950081	+	0.178167i
$472$	−551.105			−1.16760
$473$		−	1190.96i		−	2.51789i
$474$	28.9817	+	154.545i	0.0611427	+	0.326045i
$475$	−102.997			−0.216835
$476$			35.0393i			0.0736120i
$477$	−0.952621	−	2.45061i	−0.00199711	−	0.00513756i
$478$	156.626			0.327670
$479$		−	619.122i		−	1.29253i	−0.763113	−	0.646265i	$-0.776330\pi$
$479$		−	619.122i		−	1.29253i	0.763113	−	0.646265i	$-0.223670\pi$
$480$	218.319	−	40.9409i	0.454830	−	0.0852936i
$481$	143.041			0.297382
$482$			206.407i			0.428229i
$483$	−5.92413	−	31.5906i	−0.0122653	−	0.0654049i
$484$	−885.578			−1.82971
$485$		−	362.346i		−	0.747105i
$486$	199.934	+	150.081i	0.411387	+	0.308809i
$487$	−613.218			−1.25917			−0.629587	−	0.776930i	$-0.716776\pi$
$487$	−613.218			−1.25917			−0.629587	+	0.776930i	$0.716776\pi$
$488$			755.919i			1.54901i
$489$	−191.054	+	35.8281i	−0.390703	+	0.0732680i
$490$	−16.1031			−0.0328635
$491$		−	336.386i		−	0.685105i	−0.939499	−	0.342552i	$-0.888709\pi$
$491$		−	336.386i		−	0.685105i	0.939499	−	0.342552i	$-0.111291\pi$
$492$	−57.8285	−	308.372i	−0.117538	−	0.626772i
$493$	−235.608			−0.477906
$494$			126.721i			0.256521i
$495$	−385.348	+	149.795i	−0.778481	+	0.302617i
$496$	−20.9315			−0.0422005
$497$			188.555i			0.379386i
$498$	271.755	−	50.9618i	0.545692	−	0.102333i
$499$	402.697			0.807009			0.403504	−	0.914978i	$-0.367792\pi$
$499$	402.697			0.807009			0.403504	+	0.914978i	$0.367792\pi$
$500$			32.8880i			0.0657759i
$501$	54.1815	+	288.924i	0.108147	+	0.576695i
$502$	−17.6281			−0.0351157
$503$			825.608i			1.64137i	0.571382	+	0.820684i	$0.306407\pi$
$503$			825.608i			1.64137i	−0.571382	+	0.820684i	$0.693593\pi$
$504$	−61.6119	−	158.496i	−0.122246	−	0.314477i
$505$	149.887			0.296806
$506$		−	85.5861i		−	0.169143i
$507$	392.886	−	73.6773i	0.774923	−	0.145320i
$508$	77.5436			0.152645
$509$		−	226.779i		−	0.445539i	−0.974871	−	0.222769i	$-0.928490\pi$
$509$		−	226.779i		−	0.445539i	0.974871	−	0.222769i	$-0.0715097\pi$
$510$	5.72691	+	30.5389i	0.0112292	+	0.0598801i
$511$	131.898			0.258118
$512$		−	272.575i		−	0.532372i
$513$	−472.369	+	293.609i	−0.920798	+	0.572337i
$514$	−240.004			−0.466933
$515$			71.2560i			0.138361i
$516$	−502.818	+	94.2928i	−0.974454	+	0.182738i
$517$	539.649			1.04381
$518$			65.1130i			0.125701i
$519$	133.150	+	710.027i	0.256552	+	1.36807i
$520$	95.4861			0.183627
$521$		−	617.289i		−	1.18482i	−0.805638	−	0.592408i	$-0.798178\pi$
$521$		−	617.289i		−	1.18482i	0.805638	−	0.592408i	$-0.201822\pi$
$522$	451.623	−	175.558i	0.865179	−	0.336319i
$523$	−666.518			−1.27441			−0.637206	−	0.770693i	$-0.719910\pi$
$523$	−666.518			−1.27441			−0.637206	+	0.770693i	$0.719910\pi$
$524$		−	291.682i		−	0.556645i
$525$	39.0063	−	7.31480i	0.0742978	−	0.0139329i
$526$	284.627			0.541117
$527$		−	21.3240i		−	0.0404631i
$528$	50.2021	+	267.704i	0.0950797	+	0.507015i
$529$	512.602			0.969002
$530$			0.672052i			0.00126802i
$531$	−251.639	−	647.341i	−0.473897	−	1.21910i
$532$	160.319			0.301351
$533$		−	212.591i		−	0.398858i
$534$	−380.026	+	71.2657i	−0.711659	+	0.133456i
$535$	298.602			0.558134
$536$			170.213i			0.317562i
$537$	−29.8575	−	159.216i	−0.0556006	−	0.296492i
$538$	372.535			0.692444
$539$		−	143.808i		−	0.266805i
$540$	93.7525	+	150.833i	0.173616	+	0.279320i
$541$	−314.054			−0.580507			−0.290253	−	0.956950i	$-0.593740\pi$
$541$	−314.054			−0.580507			−0.290253	+	0.956950i	$0.593740\pi$
$542$			6.72345i			0.0124049i
$543$	−85.6835	+	16.0681i	−0.157796	+	0.0295913i
$544$	149.078			0.274041
$545$		−	396.055i		−	0.726706i
$546$	−8.99971	−	47.9912i	−0.0164830	−	0.0878959i
$547$	−204.829			−0.374459			−0.187230	−	0.982316i	$-0.559951\pi$
$547$	−204.829			−0.374459			−0.187230	+	0.982316i	$0.559951\pi$
$548$		−	200.302i		−	0.365515i
$549$	−887.919	+	345.158i	−1.61734	+	0.628704i
$550$	105.677			0.192140
$551$			1078.00i			1.95644i
$552$	−85.2696	+	15.9905i	−0.154474	+	0.0289683i
$553$	134.791			0.243746
$554$			344.191i			0.621284i
$555$	−29.5774	−	157.722i	−0.0532926	−	0.284184i
$556$	−136.763			−0.245977
$557$		−	799.521i		−	1.43541i	−0.696350	−	0.717703i	$-0.745194\pi$
$557$		−	799.521i		−	1.43541i	0.696350	−	0.717703i	$-0.254806\pi$
$558$	15.8892	+	40.8749i	0.0284752	+	0.0732525i
$559$	−346.643			−0.620112
$560$		−	26.1450i		−	0.0466875i
$561$	−272.725	+	51.1437i	−0.486141	+	0.0911652i
$562$	−10.5964			−0.0188548
$563$		−	837.076i		−	1.48681i	−0.668840	−	0.743407i	$-0.733209\pi$
$563$		−	837.076i		−	1.48681i	0.668840	−	0.743407i	$-0.266791\pi$
$564$	−42.7261	−	227.838i	−0.0757555	−	0.403968i
$565$	441.484			0.781388
$566$		−	447.990i		−	0.791501i
$567$	158.041	−	144.741i	0.278732	−	0.255276i
$568$	508.950			0.896038
$569$		−	336.023i		−	0.590551i	−0.955412	−	0.295275i	$-0.904589\pi$
$569$		−	336.023i		−	0.590551i	0.955412	−	0.295275i	$-0.0954114\pi$
$570$	139.727	−	26.2029i	0.245136	−	0.0459700i
$571$	−220.579			−0.386303			−0.193152	−	0.981169i	$-0.561871\pi$
$571$	−220.579			−0.386303			−0.193152	+	0.981169i	$0.561871\pi$
$572$			361.356i			0.631741i
$573$	67.1079	+	357.854i	0.117117	+	0.624528i
$574$	96.7727			0.168593
$575$		−	20.2471i		−	0.0352123i
$576$	−137.474	+	53.4400i	−0.238670	+	0.0927777i
$577$	509.489			0.882997			0.441498	−	0.897262i	$-0.354447\pi$
$577$	509.489			0.882997			0.441498	+	0.897262i	$0.354447\pi$
$578$		−	276.467i		−	0.478317i
$579$	962.279	−	180.455i	1.66197	−	0.311666i
$580$	344.217			0.593477
$581$		−	237.019i		−	0.407950i
$582$	92.1825	+	491.565i	0.158389	+	0.844614i
$583$	−6.00171			−0.0102945
$584$		−	356.021i		−	0.609625i
$585$	43.5997	+	112.160i	0.0745294	+	0.191727i
$586$	−336.431			−0.574114
$587$		−	412.170i		−	0.702164i	−0.936345	−	0.351082i	$-0.885814\pi$
$587$		−	412.170i		−	0.702164i	0.936345	−	0.351082i	$-0.114186\pi$
$588$	−60.7150	+	11.3858i	−0.103257	+	0.0193636i
$589$	−97.5661			−0.165647
$590$			177.526i			0.300891i
$591$	−107.193	−	571.608i	−0.181375	−	0.967187i
$592$	−105.717			−0.178576
$593$		−	269.322i		−	0.454169i	−0.973875	−	0.227085i	$-0.927081\pi$
$593$		−	269.322i		−	0.454169i	0.973875	−	0.227085i	$-0.0729194\pi$
$594$	484.662	−	301.250i	0.815930	−	0.507155i
$595$	26.6354			0.0447653
$596$		−	377.647i		−	0.633637i
$597$	1089.46	−	204.305i	1.82490	−	0.342220i
$598$	−24.9108			−0.0416569
$599$		−	90.4738i		−	0.151041i	−0.997144	−	0.0755207i	$-0.975938\pi$
$599$		−	90.4738i		−	0.151041i	0.997144	−	0.0755207i	$-0.0240619\pi$
$600$	−19.7442	−	105.286i	−0.0329070	−	0.175477i
$601$	−296.897			−0.494006			−0.247003	−	0.969015i	$-0.579446\pi$
$601$	−296.897			−0.494006			−0.247003	+	0.969015i	$0.579446\pi$
$602$		−	157.793i		−	0.262115i
$603$	−199.937	+	77.7208i	−0.331570	+	0.128890i
$604$	−296.207			−0.490409
$605$			673.178i			1.11269i
$606$	−203.340	+	38.1320i	−0.335544	+	0.0629241i
$607$	510.228			0.840573			0.420286	−	0.907392i	$-0.361930\pi$
$607$	510.228			0.840573			0.420286	+	0.907392i	$0.361930\pi$
$608$		−	682.092i		−	1.12186i
$609$	−76.5592	−	408.254i	−0.125713	−	0.670367i
$610$	243.501			0.399182
$611$		−	157.071i		−	0.257072i
$612$	43.1853	+	111.094i	0.0705642	+	0.181526i
$613$	−664.205			−1.08353			−0.541766	−	0.840529i	$-0.682244\pi$
$613$	−664.205			−1.08353			−0.541766	+	0.840529i	$0.682244\pi$
$614$			364.916i			0.594326i
$615$	−234.411	+	43.9587i	−0.381156	+	0.0714776i
$616$	−388.167			−0.630142
$617$		−	961.407i		−	1.55820i	−0.626902	−	0.779098i	$-0.715677\pi$
$617$		−	961.407i		−	1.55820i	0.626902	−	0.779098i	$-0.284323\pi$
$618$	−18.1279	−	96.6673i	−0.0293331	−	0.156420i
$619$	312.937			0.505552			0.252776	−	0.967525i	$-0.418656\pi$
$619$	312.937			0.505552			0.252776	+	0.967525i	$0.418656\pi$
$620$			31.1539i			0.0502482i
$621$	−57.7176	−	92.8582i	−0.0929429	−	0.149530i
$622$	99.5464			0.160042
$623$			331.451i			0.532024i
$624$	77.9183	−	14.6119i	0.124869	−	0.0234165i
$625$	25.0000			0.0400000
$626$			242.684i			0.387674i
$627$	234.003	+	1247.83i	0.373210	+	1.99015i
$628$	446.424			0.710866
$629$		−	107.700i		−	0.171224i
$630$	−51.0558	+	19.8468i	−0.0810410	+	0.0315029i
$631$	1033.58			1.63801			0.819005	−	0.573787i	$-0.194526\pi$
$631$	1033.58			1.63801			0.819005	+	0.573787i	$0.194526\pi$
$632$		−	363.830i		−	0.575681i
$633$	−1.73604	+	0.325557i	−0.00274256	+	0.000514308i
$634$	−59.0604			−0.0931552
$635$		−	58.9453i		−	0.0928272i
$636$	0.475178	+	2.53390i	0.000747135	+	0.00398411i
$637$	−41.8569			−0.0657094
$638$		−	1106.05i		−	1.73363i
$639$	232.390	+	597.824i	0.363678	+	0.935561i
$640$	−258.465			−0.403851
$641$		−	52.2653i		−	0.0815371i	−0.999169	−	0.0407685i	$-0.987019\pi$
$641$		−	52.2653i		−	0.0815371i	0.999169	−	0.0407685i	$-0.0129806\pi$
$642$	−405.089	+	75.9658i	−0.630980	+	0.118327i
$643$	−1131.51			−1.75974			−0.879871	−	0.475213i	$-0.842371\pi$
$643$	−1131.51			−1.75974			−0.879871	+	0.475213i	$0.842371\pi$
$644$			31.5154i			0.0489370i
$645$	71.6773	+	382.221i	0.111128	+	0.592590i
$646$	95.4125			0.147697
$647$			473.603i			0.731998i	0.930615	+	0.365999i	$0.119273\pi$
$647$			473.603i			0.731998i	−0.930615	+	0.365999i	$0.880727\pi$
$648$	−390.688	−	426.586i	−0.602913	−	0.658312i
$649$	−1585.38			−2.44280
$650$		−	30.7586i		−	0.0473209i
$651$	36.9496	−	6.92911i	0.0567583	−	0.0106438i
$652$	190.600			0.292331
$653$			913.225i			1.39851i	0.714874	+	0.699253i	$0.246484\pi$
$653$			913.225i			1.39851i	−0.714874	+	0.699253i	$0.753516\pi$
$654$	100.758	+	537.296i	0.154065	+	0.821553i
$655$	−221.724			−0.338510
$656$			157.120i			0.239512i
$657$	418.190	−	162.562i	0.636515	−	0.247431i
$658$	71.4996			0.108662
$659$		−	33.9225i		−	0.0514757i	−0.999669	−	0.0257379i	$-0.991806\pi$
$659$		−	33.9225i		−	0.0514757i	0.999669	−	0.0257379i	$-0.00819352\pi$
$660$	398.444	−	74.7196i	0.603703	−	0.113212i
$661$	827.517			1.25192			0.625958	−	0.779856i	$-0.284708\pi$
$661$	827.517			1.25192			0.625958	+	0.779856i	$0.284708\pi$
$662$			8.41483i			0.0127112i
$663$	14.8860	+	79.3798i	0.0224524	+	0.119728i
$664$	−639.764			−0.963500
$665$		−	121.867i		−	0.183259i
$666$	80.2505	+	206.444i	0.120496	+	0.309976i
$667$	−211.913			−0.317710
$668$		−	288.237i		−	0.431493i
$669$	−609.375	+	114.275i	−0.910874	+	0.170815i
$670$	54.8302			0.0818362
$671$			2174.57i			3.24079i
$672$	48.4420	+	258.318i	0.0720863	+	0.384402i
$673$	−235.138			−0.349389			−0.174694	−	0.984623i	$-0.555894\pi$
$673$	−235.138			−0.349389			−0.174694	+	0.984623i	$0.555894\pi$
$674$		−	9.62685i		−	0.0142832i
$675$	114.656	−	71.2665i	0.169861	−	0.105580i
$676$	−391.952			−0.579810
$677$			771.550i			1.13966i	0.821763	+	0.569830i	$0.192991\pi$
$677$			771.550i			1.13966i	−0.821763	+	0.569830i	$0.807009\pi$
$678$	−598.926	+	112.316i	−0.883372	+	0.165657i
$679$	428.733			0.631419
$680$		−	71.8945i		−	0.105727i
$681$	96.2459	+	513.233i	0.141330	+	0.753647i
$682$	100.105			0.146782
$683$			1007.13i			1.47457i	0.675581	+	0.737285i	$0.263893\pi$
$683$			1007.13i			1.47457i	−0.675581	+	0.737285i	$0.736107\pi$
$684$	508.300	−	197.590i	0.743129	−	0.288874i
$685$	−152.261			−0.222279
$686$		−	19.0535i		−	0.0277747i
$687$	−398.902	+	74.8054i	−0.580643	+	0.108887i
$688$	256.193			0.372374
$689$			1.74687i			0.00253537i
$690$	5.15095	+	27.4676i	0.00746515	+	0.0398081i
$691$	102.867			0.148867			0.0744336	−	0.997226i	$-0.476285\pi$
$691$	102.867			0.148867			0.0744336	+	0.997226i	$0.476285\pi$
$692$		−	708.338i		−	1.02361i
$693$	−177.240	−	455.950i	−0.255758	−	0.657937i
$694$	−529.865			−0.763495
$695$			103.961i			0.149585i
$696$	−1101.96	+	206.650i	−1.58328	+	0.296910i
$697$	−160.067			−0.229651
$698$			347.165i			0.497371i
$699$	−64.8256	−	345.684i	−0.0927405	−	0.494541i
$700$	−38.9136			−0.0555908
$701$		−	175.191i		−	0.249917i	−0.992162	−	0.124958i	$-0.960120\pi$
$701$		−	175.191i		−	0.249917i	0.992162	−	0.124958i	$-0.0398797\pi$
$702$	−87.6823	−	141.067i	−0.124904	−	0.200950i
$703$	−492.771			−0.700954
$704$			336.683i			0.478243i
$705$	−173.192	+	32.4785i	−0.245663	+	0.0460688i
$706$	374.564			0.530543
$707$			177.349i			0.250847i
$708$	125.520	+	669.340i	0.177289	+	0.945396i
$709$	−482.429			−0.680435			−0.340218	−	0.940347i	$-0.610501\pi$
$709$	−482.429			−0.680435			−0.340218	+	0.940347i	$0.610501\pi$
$710$		−	163.946i		−	0.230910i
$711$	427.363	−	166.128i	0.601073	−	0.233654i
$712$	894.656			1.25654
$713$		−	19.1795i		−	0.0268997i
$714$	−36.1341	+	6.77617i	−0.0506079	+	0.00949043i
$715$	274.687			0.384178
$716$			158.837i			0.221840i
$717$	−84.1824	−	448.905i	−0.117409	−	0.626087i
$718$	563.046			0.784187
$719$		−	439.787i		−	0.611664i	−0.952085	−	0.305832i	$-0.901065\pi$
$719$		−	439.787i		−	0.611664i	0.952085	−	0.305832i	$-0.0989346\pi$
$720$	−32.2232	−	82.8941i	−0.0447545	−	0.115131i
$721$	−84.3112			−0.116936
$722$		−	65.1570i		−	0.0902452i
$723$	591.579	−	110.938i	0.818228	−	0.153441i
$724$	85.4797			0.118066
$725$		−	261.659i		−	0.360908i
$726$	−171.260	−	913.246i	−0.235895	−	1.25792i
$727$	115.242			0.158517			0.0792587	−	0.996854i	$-0.474745\pi$
$727$	115.242			0.158517			0.0792587	+	0.996854i	$0.474745\pi$
$728$			112.981i			0.155193i
$729$	322.686	−	653.693i	0.442642	−	0.896698i
$730$	−114.684			−0.157101
$731$			260.998i			0.357043i
$732$	918.094	−	172.169i	1.25423	−	0.235203i
$733$	−177.630			−0.242333			−0.121167	−	0.992632i	$-0.538664\pi$
$733$	−177.630			−0.242333			−0.121167	+	0.992632i	$0.538664\pi$
$734$			368.186i			0.501615i
$735$	8.65499	+	46.1529i	0.0117755	+	0.0627931i
$736$	134.085			0.182181
$737$			489.657i			0.664392i
$738$	306.823	−	119.271i	0.415749	−	0.161613i
$739$	−330.830			−0.447673			−0.223836	−	0.974627i	$-0.571858\pi$
$739$	−330.830			−0.447673			−0.223836	+	0.974627i	$0.571858\pi$
$740$			157.347i			0.212631i
$741$	363.194	−	68.1093i	0.490141	−	0.0919153i
$742$	−0.795182			−0.00107167
$743$			976.271i			1.31396i	0.753909	+	0.656979i	$0.228166\pi$
$743$			976.271i			1.31396i	−0.753909	+	0.656979i	$0.771834\pi$
$744$	−18.7031	−	99.7349i	−0.0251386	−	0.134052i
$745$	−287.071			−0.385330
$746$			412.220i			0.552574i
$747$	−292.121	−	751.482i	−0.391060	−	1.00600i
$748$	272.076			0.363739
$749$			353.311i			0.471710i
$750$	−33.9155	+	6.36012i	−0.0452207	+	0.00848016i
$751$	−434.266			−0.578250			−0.289125	−	0.957291i	$-0.593364\pi$
$751$	−434.266			−0.578250			−0.289125	+	0.957291i	$0.593364\pi$
$752$			116.087i			0.154370i
$753$	9.47460	+	50.5235i	0.0125825	+	0.0670963i
$754$	−321.930			−0.426963
$755$			225.164i			0.298230i
$756$	−178.468	+	110.929i	−0.236068	+	0.146732i
$757$	773.007			1.02115			0.510573	−	0.859835i	$-0.329433\pi$
$757$	773.007			1.02115			0.510573	+	0.859835i	$0.329433\pi$
$758$		−	63.0922i		−	0.0832351i
$759$	−245.297	+	46.0002i	−0.323185	+	0.0606063i
$760$	−328.946			−0.432824
$761$		−	1064.65i		−	1.39902i	−0.714624	−	0.699509i	$-0.753402\pi$
$761$		−	1064.65i		−	1.39902i	0.714624	−	0.699509i	$-0.246598\pi$
$762$	14.9960	+	79.9663i	0.0196797	+	0.104943i
$763$	468.618			0.614179
$764$		−	357.003i		−	0.467282i
$765$	84.4489	−	32.8276i	0.110391	−	0.0429119i
$766$	−77.6677			−0.101394
$767$			461.443i			0.601620i
$768$	543.930	−	102.002i	0.708242	−	0.132816i
$769$	899.095			1.16917			0.584587	−	0.811331i	$-0.301256\pi$
$769$	899.095			1.16917			0.584587	+	0.811331i	$0.301256\pi$
$770$			125.039i			0.162388i
$771$	128.995	+	687.871i	0.167309	+	0.892180i
$772$	−959.991			−1.24351
$773$			256.623i			0.331983i	0.986127	+	0.165991i	$0.0530824\pi$
$773$			256.623i			0.331983i	−0.986127	+	0.165991i	$0.946918\pi$
$774$	−194.478	−	500.293i	−0.251263	−	0.646373i
$775$	23.6818			0.0305572
$776$		−	1157.24i		−	1.49129i
$777$	186.619	−	34.9964i	0.240179	−	0.0450404i
$778$	−266.542			−0.342599
$779$			732.370i			0.940141i
$780$	−21.7480	−	115.972i	−0.0278821	−	0.148682i
$781$	1464.11			1.87466
$782$			18.7562i			0.0239849i
$783$	−745.900	−	1200.03i	−0.952619	−	1.53261i
$784$	30.9352			0.0394581
$785$		−	339.352i		−	0.432296i
$786$	300.795	−	56.4076i	0.382691	−	0.0717654i
$787$	−1014.37			−1.28891			−0.644456	−	0.764641i	$-0.722916\pi$
$787$	−1014.37			−1.28891			−0.644456	+	0.764641i	$0.722916\pi$
$788$			570.248i			0.723665i
$789$	−152.979	−	815.766i	−0.193890	−	1.03392i
$790$	−117.199			−0.148353
$791$			522.371i			0.660394i
$792$	−1230.71	+	478.409i	−1.55392	+	0.604052i
$793$	632.934			0.798151
$794$		−	154.977i		−	0.195185i
$795$	1.92616	−	0.361209i	0.00242284	−	0.000454351i
$796$	−1086.87			−1.36542
$797$			1302.24i			1.63392i	0.576692	+	0.816962i	$0.304343\pi$
$797$			1302.24i			1.63392i	−0.576692	+	0.816962i	$0.695657\pi$
$798$	31.0037	+	165.328i	0.0388517	+	0.207178i
$799$	−118.264			−0.148015
$800$			165.562i			0.206952i
$801$	408.507	+	1050.88i	0.509996	+	1.31196i
$802$	−257.101			−0.320574
$803$		−	1024.17i		−	1.27544i
$804$	206.731	−	38.7680i	0.257128	−	0.0482189i
$805$	23.9567			0.0297598
$806$		−	29.1368i		−	0.0361498i
$807$	−200.227	−	1067.72i	−0.248113	−	1.32307i
$808$	478.702			0.592453
$809$		−	723.273i		−	0.894033i	−0.894526	−	0.447017i	$-0.852486\pi$
$809$		−	723.273i		−	0.894033i	0.894526	−	0.447017i	$-0.147514\pi$
$810$	−137.414	+	125.851i	−0.169648	+	0.155371i
$811$	434.496			0.535753			0.267877	−	0.963453i	$-0.413678\pi$
$811$	434.496			0.535753			0.267877	+	0.963453i	$0.413678\pi$
$812$			407.283i			0.501580i
$813$	19.2700	−	3.61367i	0.0237023	−	0.00444486i
$814$	505.595			0.621124
$815$		−	144.886i		−	0.177774i
$816$	−11.0018	−	58.6672i	−0.0134826	−	0.0718960i
$817$	1194.17			1.46165
$818$			176.214i			0.215420i
$819$	−132.710	+	51.5879i	−0.162039	+	0.0629888i
$820$	233.853			0.285187
$821$		−	45.8761i		−	0.0558784i	−0.999610	−	0.0279392i	$-0.991106\pi$
$821$		−	45.8761i		−	0.0558784i	0.999610	−	0.0279392i	$-0.00889448\pi$
$822$	206.560	−	38.7360i	0.251290	−	0.0471240i
$823$	23.9140			0.0290571			0.0145286	−	0.999894i	$-0.495375\pi$
$823$	23.9140			0.0290571			0.0145286	+	0.999894i	$0.495375\pi$
$824$			227.574i			0.276182i
$825$	−56.7986	−	302.880i	−0.0688468	−	0.367127i
$826$	−210.051			−0.254299
$827$		−	621.672i		−	0.751720i	−0.926677	−	0.375860i	$-0.877347\pi$
$827$		−	621.672i		−	0.751720i	0.926677	−	0.375860i	$-0.122653\pi$
$828$	38.8422	+	99.9214i	0.0469109	+	0.120678i
$829$	584.119			0.704606			0.352303	−	0.935886i	$-0.385399\pi$
$829$	584.119			0.704606			0.352303	+	0.935886i	$0.385399\pi$
$830$			206.085i			0.248295i
$831$	986.482	−	184.993i	1.18710	−	0.222615i
$832$	97.9954			0.117783
$833$			31.5154i			0.0378336i
$834$	−26.4483	−	141.036i	−0.0317126	−	0.169108i
$835$	−219.105			−0.262402
$836$		−	1244.86i		−	1.48907i
$837$	108.611	−	67.5089i	0.129762	−	0.0806557i
$838$	483.793			0.577318
$839$			1262.57i			1.50485i	0.658676	+	0.752427i	$0.271117\pi$
$839$			1262.57i			1.50485i	−0.658676	+	0.752427i	$0.728883\pi$
$840$	124.576	−	23.3616i	0.148305	−	0.0278115i
$841$	−1897.61			−2.25637
$842$			94.1826i			0.111856i
$843$	5.69529	+	30.3703i	0.00675598	+	0.0360264i
$844$	1.73191			0.00205203
$845$			297.945i			0.352597i
$846$	226.693	−	88.1219i	0.267959	−	0.104163i
$847$	−796.515			−0.940395
$848$		−	1.29106i		−	0.00152247i
$849$	−1283.98	+	240.782i	−1.51234	+	0.283607i
$850$	−23.1591			−0.0272460
$851$		−	96.8687i		−	0.113829i
$852$	−115.919	−	618.140i	−0.136055	−	0.725517i
$853$	−583.104			−0.683592			−0.341796	−	0.939774i	$-0.611035\pi$
$853$	−583.104			−0.683592			−0.341796	+	0.939774i	$0.611035\pi$
$854$			288.115i			0.337371i
$855$	−150.199	−	386.387i	−0.175672	−	0.451915i
$856$	953.660			1.11409
$857$			1221.67i			1.42551i	0.701411	+	0.712757i	$0.252554\pi$
$857$			1221.67i			1.42551i	−0.701411	+	0.712757i	$0.747446\pi$
$858$	−372.646	+	69.8817i	−0.434319	+	0.0814472i
$859$	55.6241			0.0647544			0.0323772	−	0.999476i	$-0.489692\pi$
$859$	55.6241			0.0647544			0.0323772	+	0.999476i	$0.489692\pi$
$860$		−	381.312i		−	0.443386i
$861$	−52.0127	−	277.359i	−0.0604096	−	0.322135i
$862$	−199.593			−0.231546
$863$		−	91.0854i		−	0.105545i	−0.998607	−	0.0527725i	$-0.983194\pi$
$863$		−	91.0854i		−	0.105545i	0.998607	−	0.0527725i	$-0.0168058\pi$
$864$	471.960	+	759.307i	0.546250	+	0.878828i
$865$	−538.448			−0.622483
$866$		−	461.869i		−	0.533336i
$867$	−792.378	+	148.594i	−0.913931	+	0.171388i
$868$	−36.8618			−0.0424675
$869$		−	1046.64i		−	1.20442i
$870$	66.5672	+	354.971i	0.0765141	+	0.408013i
$871$	142.520			0.163628
$872$		−	1264.90i		−	1.45057i
$873$	1359.32	−	528.406i	1.55707	−	0.605276i
$874$	85.8169			0.0981887
$875$			29.5804i			0.0338062i
$876$	−432.402	+	81.0877i	−0.493610	+	0.0925659i
$877$	−417.258			−0.475779			−0.237890	−	0.971292i	$-0.576456\pi$
$877$	−417.258			−0.475779			−0.237890	+	0.971292i	$0.576456\pi$
$878$		−	67.7557i		−	0.0771705i
$879$	180.822	+	964.239i	0.205714	+	1.09697i
$880$	−203.013			−0.230696
$881$			429.379i			0.487377i	0.969854	+	0.243688i	$0.0783574\pi$
$881$			429.379i			0.487377i	−0.969854	+	0.243688i	$0.921643\pi$
$882$	−23.4830	−	60.4101i	−0.0266248	−	0.0684921i
$883$	1170.43			1.32551			0.662757	−	0.748834i	$-0.269386\pi$
$883$	1170.43			1.32551			0.662757	+	0.748834i	$0.269386\pi$
$884$		−	79.1910i		−	0.0895826i
$885$	508.803	−	95.4151i	0.574919	−	0.107814i
$886$	−559.944			−0.631991
$887$		−	1607.16i		−	1.81190i	−0.423380	−	0.905952i	$-0.639157\pi$
$887$		−	1607.16i		−	1.81190i	0.423380	−	0.905952i	$-0.360843\pi$
$888$	−94.4628	−	503.725i	−0.106377	−	0.567258i
$889$	69.7450			0.0784533
$890$		−	288.192i		−	0.323811i
$891$	−1123.90	−	1227.17i	−1.26139	−	1.37730i
$892$	607.926			0.681531
$893$			541.105i			0.605940i
$894$	389.446	−	73.0323i	0.435622	−	0.0816916i
$895$	120.741			0.134906
$896$		−	305.820i		−	0.341317i
$897$	13.3889	+	71.3966i	0.0149263	+	0.0795948i
$898$	98.2942			0.109459
$899$		−	247.862i		−	0.275709i
$900$	−123.378	+	47.9603i	−0.137086	+	0.0532892i
$901$	1.31527			0.00145979
$902$		−	751.429i		−	0.833070i
$903$	−452.249	+	84.8097i	−0.500830	+	0.0939199i
$904$	1409.99			1.55972
$905$		−	64.9780i		−	0.0717988i
$906$	−57.2827	−	305.461i	−0.0632260	−	0.337154i
$907$	−1571.84			−1.73301			−0.866505	−	0.499169i	$-0.833639\pi$
$907$	−1571.84			−1.73301			−0.866505	+	0.499169i	$0.833639\pi$
$908$		−	512.013i		−	0.563891i
$909$	218.579	+	562.294i	0.240461	+	0.618585i
$910$	36.3940			0.0399934
$911$		−	667.566i		−	0.732783i	−0.930461	−	0.366392i	$-0.880593\pi$
$911$		−	667.566i		−	0.732783i	0.930461	−	0.366392i	$-0.119407\pi$
$912$	−268.426	+	50.3375i	−0.294326	+	0.0551946i
$913$	−1840.43			−2.01580
$914$		−	480.332i		−	0.525528i
$915$	−130.875	−	697.895i	−0.143033	−	0.762727i
$916$	397.953			0.434447
$917$		−	262.347i		−	0.286093i
$918$	−106.214	+	66.0188i	−0.115701	+	0.0719159i
$919$	1103.17			1.20040			0.600202	−	0.799849i	$-0.295087\pi$
$919$	1103.17			1.20040			0.600202	+	0.799849i	$0.295087\pi$
$920$		−	64.6641i		−	0.0702871i
$921$	1045.88	−	196.133i	1.13559	−	0.212956i
$922$	16.9045			0.0183346
$923$		−	426.146i		−	0.461696i
$924$	88.4094	+	471.445i	0.0956812	+	0.510222i
$925$	119.608			0.129306
$926$			581.064i			0.627499i
$927$	−267.313	+	103.912i	−0.288364	+	0.112095i
$928$	1732.82			1.86727
$929$			717.793i			0.772652i	0.922362	+	0.386326i	$0.126256\pi$
$929$			717.793i			0.772652i	−0.922362	+	0.386326i	$0.873744\pi$
$930$	−32.1272	+	6.02477i	−0.0345454	+	0.00647825i
$931$	144.196			0.154882
$932$			344.862i			0.370024i
$933$	−53.5034	−	285.308i	−0.0573456	−	0.305797i
$934$	747.336			0.800146
$935$		−	206.821i		−	0.221198i
$936$	139.247	+	358.211i	0.148768	+	0.382704i
$937$	1071.19			1.14322			0.571608	−	0.820527i	$-0.306320\pi$
$937$	1071.19			1.14322			0.571608	+	0.820527i	$0.306320\pi$
$938$			64.8760i			0.0691642i
$939$	695.553	−	130.436i	0.740738	−	0.138909i
$940$	172.780			0.183809
$941$			1352.41i			1.43720i	0.695421	+	0.718602i	$0.255218\pi$
$941$			1352.41i			1.43720i	−0.695421	+	0.718602i	$0.744782\pi$
$942$	86.3328	+	460.372i	0.0916484	+	0.488717i
$943$	−143.969			−0.152671
$944$		−	341.038i		−	0.361269i
$945$	84.3237	+	135.663i	0.0892314	+	0.143559i
$946$	−1225.25			−1.29519
$947$			374.426i			0.395381i	0.980265	+	0.197690i	$0.0633441\pi$
$947$			374.426i			0.395381i	−0.980265	+	0.197690i	$0.936656\pi$
$948$	−441.887	+	82.8664i	−0.466125	+	0.0874118i
$949$	−298.098			−0.314118
$950$			105.962i			0.111539i
$951$	31.7433	+	169.272i	0.0333789	+	0.177994i
$952$	85.0667			0.0893558
$953$		−	611.283i		−	0.641430i	−0.947176	−	0.320715i	$-0.896077\pi$
$953$		−	611.283i		−	0.641430i	0.947176	−	0.320715i	$-0.103923\pi$
$954$	−2.52117	+	0.980047i	−0.00264273	+	0.00102730i
$955$	−271.378			−0.284166
$956$			447.837i			0.468449i
$957$	−3170.04	+	594.474i	−3.31248	+	0.621185i
$958$	−636.947			−0.664872
$959$		−	180.158i		−	0.187860i
$960$	−20.2631	−	108.053i	−0.0211074	−	0.112555i
$961$	−938.567			−0.976656
$962$		−	147.159i		−	0.152972i
$963$	435.449	+	1120.19i	0.452179	+	1.16323i
$964$	−590.172			−0.612212
$965$			729.743i			0.756211i
$966$	−32.5001	+	6.09469i	−0.0336440	+	0.00630920i
$967$	−154.558			−0.159832			−0.0799161	−	0.996802i	$-0.525465\pi$
$967$	−154.558			−0.159832			−0.0799161	+	0.996802i	$0.525465\pi$
$968$			2149.96i			2.22104i
$969$	−51.2816	−	273.460i	−0.0529222	−	0.282209i
$970$	−372.778			−0.384307
$971$		−	1412.17i		−	1.45434i	−0.686455	−	0.727172i	$-0.740834\pi$
$971$		−	1412.17i		−	1.45434i	0.686455	−	0.727172i	$-0.259166\pi$
$972$	−429.123	+	571.666i	−0.441484	+	0.588134i
$973$	−123.009			−0.126422
$974$			630.873i			0.647713i
$975$	−88.1567	+	16.5319i	−0.0904171	+	0.0169558i
$976$	−467.782			−0.479285
$977$			1391.10i			1.42385i	0.702257	+	0.711924i	$0.252176\pi$
$977$			1391.10i			1.42385i	−0.702257	+	0.711924i	$0.747824\pi$
$978$	36.8596	+	196.555i	0.0376887	+	0.200976i
$979$	2573.68			2.62888
$980$		−	46.0432i		−	0.0469828i
$981$	1485.78	−	577.563i	1.51456	−	0.588749i
$982$	−346.071			−0.352415
$983$			382.093i			0.388701i	0.980932	+	0.194351i	$0.0622599\pi$
$983$			382.093i			0.388701i	−0.980932	+	0.194351i	$0.937740\pi$
$984$	−748.650	+	140.393i	−0.760823	+	0.142676i
$985$	433.478			0.440079
$986$			242.391i			0.245833i
$987$	−38.4291	−	204.924i	−0.0389352	−	0.207623i
$988$	−362.331			−0.366731
$989$			234.750i			0.237361i
$990$	154.108	+	396.443i	0.155665	+	0.400447i
$991$	256.531			0.258861			0.129431	−	0.991588i	$-0.458685\pi$
$991$	256.531			0.258861			0.129431	+	0.991588i	$0.458685\pi$
$992$			156.832i			0.158097i
$993$	24.1176	−	4.52274i	0.0242876	−	0.00455462i
$994$	193.984			0.195154
$995$			826.193i			0.830345i
$996$	145.713	+	777.020i	0.146299	+	0.780141i
$997$	−922.236			−0.925011			−0.462506	−	0.886616i	$-0.653050\pi$
$997$	−922.236			−0.925011			−0.462506	+	0.886616i	$0.653050\pi$
$998$		−	414.291i		−	0.415122i
$999$	548.554	−	340.963i	0.549103	−	0.341304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.c.a.71.6	✓	16
3.2	odd	2	inner	105.3.c.a.71.11	yes	16
4.3	odd	2		1680.3.l.a.1121.13		16
5.2	odd	4		525.3.f.b.449.22		32
5.3	odd	4		525.3.f.b.449.12		32
5.4	even	2		525.3.c.b.176.11		16
12.11	even	2		1680.3.l.a.1121.14		16
15.2	even	4		525.3.f.b.449.11		32
15.8	even	4		525.3.f.b.449.21		32
15.14	odd	2		525.3.c.b.176.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.6	✓	16	1.1	even	1	trivial
105.3.c.a.71.11	yes	16	3.2	odd	2	inner
525.3.c.b.176.6		16	15.14	odd	2
525.3.c.b.176.11		16	5.4	even	2
525.3.f.b.449.11		32	15.2	even	4
525.3.f.b.449.12		32	5.3	odd	4
525.3.f.b.449.21		32	15.8	even	4
525.3.f.b.449.22		32	5.2	odd	4
1680.3.l.a.1121.13		16	4.3	odd	2
1680.3.l.a.1121.14		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.02879i q^{2} +(-2.94860 + 0.552947i) q^{3} +2.94159 q^{4} -2.23607i q^{5} +(0.568867 + 3.03349i) q^{6} +2.64575 q^{7} -7.14144i q^{8} +(8.38850 - 3.26084i) q^{9} +O(q^{10})\)	\(q-1.02879i q^{2} +(-2.94860 + 0.552947i) q^{3} +2.94159 q^{4} -2.23607i q^{5} +(0.568867 + 3.03349i) q^{6} +2.64575 q^{7} -7.14144i q^{8} +(8.38850 - 3.26084i) q^{9} -2.30045 q^{10} -20.5440i q^{11} +(-8.67358 + 1.62654i) q^{12} -5.97956 q^{13} -2.72192i q^{14} +(1.23643 + 6.59327i) q^{15} +4.41931 q^{16} +4.50220i q^{17} +(-3.35472 - 8.63001i) q^{18} +20.5994 q^{19} -6.57759i q^{20} +(-7.80127 + 1.46296i) q^{21} -21.1354 q^{22} +4.04941i q^{23} +(3.94884 + 21.0573i) q^{24} -5.00000 q^{25} +6.15171i q^{26} +(-22.9313 + 14.2533i) q^{27} +7.78271 q^{28} +52.3317i q^{29} +(6.78310 - 1.27202i) q^{30} -4.73636 q^{31} -33.1123i q^{32} +(11.3597 + 60.5759i) q^{33} +4.63182 q^{34} -5.91608i q^{35} +(24.6755 - 9.59205i) q^{36} -23.9217 q^{37} -21.1924i q^{38} +(17.6313 - 3.30638i) q^{39} -15.9688 q^{40} +35.5530i q^{41} +(1.50508 + 8.02587i) q^{42} +57.9713 q^{43} -60.4319i q^{44} +(-7.29146 - 18.7573i) q^{45} +4.16600 q^{46} +26.2680i q^{47} +(-13.0308 + 2.44364i) q^{48} +7.00000 q^{49} +5.14395i q^{50} +(-2.48948 - 13.2752i) q^{51} -17.5894 q^{52} -0.292140i q^{53} +(14.6637 + 23.5915i) q^{54} -45.9377 q^{55} -18.8945i q^{56} +(-60.7393 + 11.3904i) q^{57} +53.8384 q^{58} -77.1700i q^{59} +(3.63706 + 19.3947i) q^{60} -105.850 q^{61} +4.87273i q^{62} +(22.1939 - 8.62737i) q^{63} -16.3884 q^{64} +13.3707i q^{65} +(62.3200 - 11.6868i) q^{66} -23.8346 q^{67} +13.2436i q^{68} +(-2.23911 - 11.9401i) q^{69} -6.08641 q^{70} +71.2671i q^{71} +(-23.2871 - 59.9060i) q^{72} +49.8528 q^{73} +24.6104i q^{74} +(14.7430 - 2.76473i) q^{75} +60.5949 q^{76} -54.3542i q^{77} +(-3.40157 - 18.1390i) q^{78} +50.9463 q^{79} -9.88188i q^{80} +(59.7339 - 54.7071i) q^{81} +36.5766 q^{82} -89.5847i q^{83} +(-22.9481 + 4.30343i) q^{84} +10.0672 q^{85} -59.6403i q^{86} +(-28.9367 - 154.305i) q^{87} -146.714 q^{88} +125.277i q^{89} +(-19.2973 + 7.50138i) q^{90} -15.8204 q^{91} +11.9117i q^{92} +(13.9656 - 2.61896i) q^{93} +27.0243 q^{94} -46.0616i q^{95} +(18.3093 + 97.6350i) q^{96} +162.046 q^{97} -7.20153i q^{98} +(-66.9906 - 172.333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

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