LMFDB - Embedded newform 1205.2.b.c.724.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.31
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.930197i q^{2} +1.32621i q^{3} +1.13473 q^{4} +(-2.23573 + 0.0386721i) q^{5} -1.23364 q^{6} +4.33497i q^{7} +2.91592i q^{8} +1.24116 q^{9} +O(q^{10})$	\(q+0.930197i q^{2} +1.32621i q^{3} +1.13473 q^{4} +(-2.23573 + 0.0386721i) q^{5} -1.23364 q^{6} +4.33497i q^{7} +2.91592i q^{8} +1.24116 q^{9} +(-0.0359727 - 2.07967i) q^{10} +0.882357 q^{11} +1.50490i q^{12} +2.68232i q^{13} -4.03238 q^{14} +(-0.0512874 - 2.96506i) q^{15} -0.442916 q^{16} -0.304406i q^{17} +1.15452i q^{18} +4.13564 q^{19} +(-2.53696 + 0.0438825i) q^{20} -5.74909 q^{21} +0.820766i q^{22} -2.19664i q^{23} -3.86713 q^{24} +(4.99701 - 0.172921i) q^{25} -2.49509 q^{26} +5.62468i q^{27} +4.91903i q^{28} -8.97537 q^{29} +(2.75809 - 0.0477074i) q^{30} +5.91415 q^{31} +5.41984i q^{32} +1.17019i q^{33} +0.283158 q^{34} +(-0.167642 - 9.69184i) q^{35} +1.40839 q^{36} -10.9828i q^{37} +3.84696i q^{38} -3.55733 q^{39} +(-0.112765 - 6.51922i) q^{40} -6.07092 q^{41} -5.34779i q^{42} -2.71940i q^{43} +1.00124 q^{44} +(-2.77490 + 0.0479983i) q^{45} +2.04331 q^{46} -9.50435i q^{47} -0.587400i q^{48} -11.7920 q^{49} +(0.160851 + 4.64820i) q^{50} +0.403707 q^{51} +3.04372i q^{52} +11.0767i q^{53} -5.23206 q^{54} +(-1.97272 + 0.0341226i) q^{55} -12.6404 q^{56} +5.48474i q^{57} -8.34887i q^{58} +7.93694 q^{59} +(-0.0581975 - 3.36455i) q^{60} -1.60387 q^{61} +5.50133i q^{62} +5.38040i q^{63} -5.92735 q^{64} +(-0.103731 - 5.99696i) q^{65} -1.08851 q^{66} +15.5753i q^{67} -0.345420i q^{68} +2.91321 q^{69} +(9.01532 - 0.155940i) q^{70} -9.40214 q^{71} +3.61913i q^{72} -4.11094i q^{73} +10.2162 q^{74} +(0.229330 + 6.62710i) q^{75} +4.69285 q^{76} +3.82499i q^{77} -3.30902i q^{78} -9.90696 q^{79} +(0.990242 - 0.0171285i) q^{80} -3.73604 q^{81} -5.64716i q^{82} -10.7285i q^{83} -6.52368 q^{84} +(0.0117720 + 0.680571i) q^{85} +2.52958 q^{86} -11.9033i q^{87} +2.57288i q^{88} +9.48120 q^{89} +(-0.0446479 - 2.58121i) q^{90} -11.6278 q^{91} -2.49260i q^{92} +7.84342i q^{93} +8.84092 q^{94} +(-9.24619 + 0.159934i) q^{95} -7.18786 q^{96} +1.41584i q^{97} -10.9689i q^{98} +1.09515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.930197i			0.657749i	0.944374	+	0.328874i	$0.106669\pi$
$2$			0.930197i			0.657749i	−0.944374	+	0.328874i	$0.893331\pi$
$3$			1.32621i			0.765689i	0.923813	+	0.382845i	$0.125056\pi$
$3$			1.32621i			0.765689i	−0.923813	+	0.382845i	$0.874944\pi$
$4$	1.13473			0.567366
$5$	−2.23573	+	0.0386721i	−0.999850	+	0.0172947i
$5$	−2.23573	+	0.0386721i	−0.999850	+	0.0172947i
$6$	−1.23364			−0.503631
$7$			4.33497i			1.63847i	0.573461	+	0.819233i	$0.305600\pi$
$7$			4.33497i			1.63847i	−0.573461	+	0.819233i	$0.694400\pi$
$8$			2.91592i			1.03093i
$9$	1.24116			0.413720
$10$	−0.0359727	−	2.07967i	−0.0113756	−	0.657651i
$11$	0.882357			0.266041			0.133020	−	0.991113i	$-0.457532\pi$
$11$	0.882357			0.266041			0.133020	+	0.991113i	$0.457532\pi$
$12$			1.50490i			0.434426i
$13$			2.68232i			0.743943i	0.928244	+	0.371971i	$0.121318\pi$
$13$			2.68232i			0.743943i	−0.928244	+	0.371971i	$0.878682\pi$
$14$	−4.03238			−1.07770
$15$	−0.0512874	−	2.96506i	−0.0132423	−	0.765575i
$16$	−0.442916			−0.110729
$17$		−	0.304406i		−	0.0738294i	−0.999318	−	0.0369147i	$-0.988247\pi$
$17$		−	0.304406i		−	0.0738294i	0.999318	−	0.0369147i	$-0.0117530\pi$
$18$			1.15452i			0.272124i
$19$	4.13564			0.948781			0.474390	−	0.880315i	$-0.342669\pi$
$19$	4.13564			0.948781			0.474390	+	0.880315i	$0.342669\pi$
$20$	−2.53696	+	0.0438825i	−0.567282	+	0.00981242i
$21$	−5.74909			−1.25455
$22$			0.820766i			0.174988i
$23$		−	2.19664i		−	0.458031i	−0.973423	−	0.229015i	$-0.926449\pi$
$23$		−	2.19664i		−	0.458031i	0.973423	−	0.229015i	$-0.0735506\pi$
$24$	−3.86713			−0.789375
$25$	4.99701	−	0.172921i	0.999402	−	0.0345842i
$26$	−2.49509			−0.489328
$27$			5.62468i			1.08247i
$28$			4.91903i			0.929610i
$29$	−8.97537			−1.66669			−0.833343	−	0.552757i	$-0.813576\pi$
$29$	−8.97537			−1.66669			−0.833343	+	0.552757i	$0.813576\pi$
$30$	2.75809	−	0.0477074i	0.503556	−	0.00871014i
$31$	5.91415			1.06221			0.531107	−	0.847305i	$-0.321776\pi$
$31$	5.91415			1.06221			0.531107	+	0.847305i	$0.321776\pi$
$32$			5.41984i			0.958102i
$33$			1.17019i			0.203704i
$34$	0.283158			0.0485612
$35$	−0.167642	−	9.69184i	−0.0283367	−	1.63822i
$36$	1.40839			0.234731
$37$		−	10.9828i		−	1.80556i	−0.430105	−	0.902779i	$-0.641523\pi$
$37$		−	10.9828i		−	1.80556i	0.430105	−	0.902779i	$-0.358477\pi$
$38$			3.84696i			0.624059i
$39$	−3.55733			−0.569629
$40$	−0.112765	−	6.51922i	−0.0178297	−	1.03078i
$41$	−6.07092			−0.948119			−0.474059	−	0.880493i	$-0.657212\pi$
$41$	−6.07092			−0.948119			−0.474059	+	0.880493i	$0.657212\pi$
$42$		−	5.34779i		−	0.825182i
$43$		−	2.71940i		−	0.414705i	−0.978266	−	0.207352i	$-0.933515\pi$
$43$		−	2.71940i		−	0.414705i	0.978266	−	0.207352i	$-0.0664847\pi$
$44$	1.00124			0.150943
$45$	−2.77490	+	0.0479983i	−0.413658	+	0.00715516i
$46$	2.04331			0.301269
$47$		−	9.50435i		−	1.38635i	−0.720769	−	0.693176i	$-0.756211\pi$
$47$		−	9.50435i		−	1.38635i	0.720769	−	0.693176i	$-0.243789\pi$
$48$		−	0.587400i		−	0.0847839i
$49$	−11.7920			−1.68457
$50$	0.160851	+	4.64820i	0.0227477	+	0.657355i
$51$	0.403707			0.0565303
$52$			3.04372i			0.422088i
$53$			11.0767i			1.52150i	0.649048	+	0.760748i	$0.275168\pi$
$53$			11.0767i			1.52150i	−0.649048	+	0.760748i	$0.724832\pi$
$54$	−5.23206			−0.711994
$55$	−1.97272	+	0.0341226i	−0.266001	+	0.00460109i
$56$	−12.6404			−1.68915
$57$			5.48474i			0.726471i
$58$		−	8.34887i		−	1.09626i
$59$	7.93694			1.03330			0.516651	−	0.856196i	$-0.327179\pi$
$59$	7.93694			1.03330			0.516651	+	0.856196i	$0.327179\pi$
$60$	−0.0581975	−	3.36455i	−0.00751326	−	0.434361i
$61$	−1.60387			−0.205355			−0.102678	−	0.994715i	$-0.532741\pi$
$61$	−1.60387			−0.205355			−0.102678	+	0.994715i	$0.532741\pi$
$62$			5.50133i			0.698670i
$63$			5.38040i			0.677866i
$64$	−5.92735			−0.740919
$65$	−0.103731	−	5.99696i	−0.0128663	−	0.743832i
$66$	−1.08851			−0.133986
$67$			15.5753i			1.90282i	0.307926	+	0.951410i	$0.400365\pi$
$67$			15.5753i			1.90282i	−0.307926	+	0.951410i	$0.599635\pi$
$68$		−	0.345420i		−	0.0418883i
$69$	2.91321			0.350709
$70$	9.01532	−	0.155940i	1.07754	−	0.0186385i
$71$	−9.40214			−1.11583			−0.557915	−	0.829898i	$-0.688398\pi$
$71$	−9.40214			−1.11583			−0.557915	+	0.829898i	$0.688398\pi$
$72$			3.61913i			0.426518i
$73$		−	4.11094i		−	0.481150i	−0.970631	−	0.240575i	$-0.922664\pi$
$73$		−	4.11094i		−	0.481150i	0.970631	−	0.240575i	$-0.0773359\pi$
$74$	10.2162			1.18760
$75$	0.229330	+	6.62710i	0.0264807	+	0.765231i
$76$	4.69285			0.538306
$77$			3.82499i			0.435898i
$78$		−	3.30902i		−	0.374673i
$79$	−9.90696			−1.11462			−0.557310	−	0.830304i	$-0.688167\pi$
$79$	−9.90696			−1.11462			−0.557310	+	0.830304i	$0.688167\pi$
$80$	0.990242	−	0.0171285i	0.110712	−	0.00191502i
$81$	−3.73604			−0.415115
$82$		−	5.64716i		−	0.623624i
$83$		−	10.7285i		−	1.17761i	−0.808277	−	0.588803i	$-0.799599\pi$
$83$		−	10.7285i		−	1.17761i	0.808277	−	0.588803i	$-0.200401\pi$
$84$	−6.52368			−0.711792
$85$	0.0117720	+	0.680571i	0.00127686	+	0.0738183i
$86$	2.52958			0.272772
$87$		−	11.9033i		−	1.27616i
$88$			2.57288i			0.274270i
$89$	9.48120			1.00501			0.502503	−	0.864576i	$-0.332413\pi$
$89$	9.48120			1.00501			0.502503	+	0.864576i	$0.332413\pi$
$90$	−0.0446479	−	2.58121i	−0.00470630	−	0.272083i
$91$	−11.6278			−1.21892
$92$		−	2.49260i		−	0.259871i
$93$			7.84342i			0.813325i
$94$	8.84092			0.911871
$95$	−9.24619	+	0.159934i	−0.948639	+	0.0164089i
$96$	−7.18786			−0.733608
$97$			1.41584i			0.143757i	0.997413	+	0.0718784i	$0.0228994\pi$
$97$			1.41584i			0.143757i	−0.997413	+	0.0718784i	$0.977101\pi$
$98$		−	10.9689i		−	1.10802i
$99$	1.09515			0.110066
$100$	5.67027	−	0.196219i	0.567027	−	0.0196219i
$101$	16.9462			1.68621			0.843104	−	0.537750i	$-0.180726\pi$
$101$	16.9462			1.68621			0.843104	+	0.537750i	$0.180726\pi$
$102$			0.375528i			0.0371828i
$103$		−	1.90525i		−	0.187729i	−0.995585	−	0.0938647i	$-0.970078\pi$
$103$		−	1.90525i		−	0.187729i	0.995585	−	0.0938647i	$-0.0299221\pi$
$104$	−7.82144			−0.766956
$105$	12.8534	−	0.222329i	1.25437	−	0.0216971i
$106$	−10.3035			−1.00076
$107$		−	8.61469i		−	0.832814i	−0.909178	−	0.416407i	$-0.863289\pi$
$107$		−	8.61469i		−	0.832814i	0.909178	−	0.416407i	$-0.136711\pi$
$108$			6.38251i			0.614157i
$109$	8.16711			0.782267			0.391134	−	0.920334i	$-0.372083\pi$
$109$	8.16711			0.782267			0.391134	+	0.920334i	$0.372083\pi$
$110$	−0.0317407	−	1.83501i	−0.00302636	−	0.174962i
$111$	14.5655			1.38250
$112$		−	1.92003i		−	0.181426i
$113$			4.19717i			0.394837i	0.980319	+	0.197418i	$0.0632558\pi$
$113$			4.19717i			0.394837i	−0.980319	+	0.197418i	$0.936744\pi$
$114$	−5.10189			−0.477835
$115$	0.0849485	+	4.91110i	0.00792149	+	0.457962i
$116$	−10.1847			−0.945621
$117$			3.32920i			0.307784i
$118$			7.38292i			0.679653i
$119$	1.31959			0.120967
$120$	8.64587	−	0.149550i	0.789256	−	0.0136520i
$121$	−10.2214			−0.929222
$122$		−	1.49192i		−	0.135072i
$123$		−	8.05133i		−	0.725964i
$124$	6.71098			0.602664
$125$	−11.1653	+	0.579850i	−0.998654	+	0.0518633i
$126$	−5.00483			−0.445866
$127$			4.94642i			0.438924i	0.975621	+	0.219462i	$0.0704302\pi$
$127$			4.94642i			0.438924i	−0.975621	+	0.219462i	$0.929570\pi$
$128$			5.32607i			0.470763i
$129$	3.60650			0.317535
$130$	5.57836	−	0.0964904i	0.489254	−	0.00846276i
$131$	13.6851			1.19567			0.597836	−	0.801618i	$-0.296027\pi$
$131$	13.6851			1.19567			0.597836	+	0.801618i	$0.296027\pi$
$132$			1.32786i			0.115575i
$133$			17.9279i			1.55454i
$134$	−14.4881			−1.25158
$135$	−0.217518	−	12.5753i	−0.0187210	−	1.08231i
$136$	0.887624			0.0761132
$137$		−	19.0577i		−	1.62821i	−0.580717	−	0.814105i	$-0.697228\pi$
$137$		−	19.0577i		−	1.62821i	0.580717	−	0.814105i	$-0.302772\pi$
$138$			2.70986i			0.230678i
$139$	21.7352			1.84356			0.921778	−	0.387717i	$-0.126736\pi$
$139$	21.7352			1.84356			0.921778	+	0.387717i	$0.126736\pi$
$140$	−0.190229	−	10.9976i	−0.0160773	−	0.929471i
$141$	12.6048			1.06151
$142$		−	8.74585i		−	0.733935i
$143$			2.36677i			0.197919i
$144$	−0.549730			−0.0458108
$145$	20.0665	−	0.347096i	1.66644	−	0.0288248i
$146$	3.82399			0.316476
$147$		−	15.6387i		−	1.28986i
$148$		−	12.4625i		−	1.02441i
$149$	6.03822			0.494671			0.247335	−	0.968930i	$-0.420445\pi$
$149$	6.03822			0.494671			0.247335	+	0.968930i	$0.420445\pi$
$150$	−6.16451	+	0.213322i	−0.503330	+	0.0174177i
$151$	−15.0115			−1.22162			−0.610808	−	0.791779i	$-0.709155\pi$
$151$	−15.0115			−1.22162			−0.610808	+	0.791779i	$0.709155\pi$
$152$			12.0592i			0.978130i
$153$		−	0.377817i		−	0.0305447i
$154$	−3.55800			−0.286712
$155$	−13.2225	+	0.228713i	−1.06205	+	0.0183706i
$156$	−4.03662			−0.323188
$157$		−	4.38682i		−	0.350107i	−0.984559	−	0.175053i	$-0.943990\pi$
$157$		−	4.38682i		−	0.350107i	0.984559	−	0.175053i	$-0.0560098\pi$
$158$		−	9.21543i		−	0.733140i
$159$	−14.6900			−1.16499
$160$	−0.209597	−	12.1173i	−0.0165701	−	0.957958i
$161$	9.52236			0.750467
$162$		−	3.47525i		−	0.273042i
$163$		−	5.32658i		−	0.417210i	−0.978000	−	0.208605i	$-0.933108\pi$
$163$		−	5.32658i		−	0.417210i	0.978000	−	0.208605i	$-0.0668923\pi$
$164$	−6.88888			−0.537931
$165$	−0.0452538	−	2.61624i	−0.00352300	−	0.203674i
$166$	9.97963			0.774569
$167$			8.59533i			0.665127i	0.943081	+	0.332563i	$0.107914\pi$
$167$			8.59533i			0.665127i	−0.943081	+	0.332563i	$0.892086\pi$
$168$		−	16.7639i		−	1.29336i
$169$	5.80514			0.446549
$170$	−0.633066	+	0.0109503i	−0.0485539	+	0.000839850i
$171$	5.13299			0.392530
$172$		−	3.08579i		−	0.235290i
$173$			3.91350i			0.297538i	0.988872	+	0.148769i	$0.0475311\pi$
$173$			3.91350i			0.297538i	−0.988872	+	0.148769i	$0.952469\pi$
$174$	11.0724			0.839395
$175$	0.749607	+	21.6619i	0.0566650	+	1.63748i
$176$	−0.390810			−0.0294584
$177$			10.5261i			0.791187i
$178$			8.81939i			0.661041i
$179$	2.52352			0.188617			0.0943084	−	0.995543i	$-0.469936\pi$
$179$	2.52352			0.188617			0.0943084	+	0.995543i	$0.469936\pi$
$180$	−3.14878	+	0.0544652i	−0.234696	+	0.00405960i
$181$	−16.5056			−1.22685			−0.613426	−	0.789752i	$-0.710209\pi$
$181$	−16.5056			−1.22685			−0.613426	+	0.789752i	$0.710209\pi$
$182$		−	10.8161i		−	0.801746i
$183$		−	2.12708i		−	0.157238i
$184$	6.40522			0.472199
$185$	0.424727	+	24.5546i	0.0312265	+	1.80529i
$186$	−7.29593			−0.534964
$187$		−	0.268595i		−	0.0196416i
$188$		−	10.7849i		−	0.786569i
$189$	−24.3828			−1.77359
$190$	−0.148770	−	8.60078i	−0.0107929	−	0.623966i
$191$	−22.6006			−1.63532			−0.817660	−	0.575701i	$-0.804729\pi$
$191$	−22.6006			−1.63532			−0.817660	+	0.575701i	$0.804729\pi$
$192$		−	7.86093i		−	0.567314i
$193$			6.58611i			0.474079i	0.971500	+	0.237039i	$0.0761770\pi$
$193$			6.58611i			0.474079i	−0.971500	+	0.237039i	$0.923823\pi$
$194$	−1.31701			−0.0945559
$195$	7.95325	−	0.137569i	0.569544	−	0.00985155i
$196$	−13.3807			−0.955767
$197$			3.59184i			0.255908i	0.991780	+	0.127954i	$0.0408410\pi$
$197$			3.59184i			0.255908i	−0.991780	+	0.127954i	$0.959159\pi$
$198$			1.01870i			0.0723961i
$199$	21.0736			1.49387			0.746934	−	0.664899i	$-0.231525\pi$
$199$	21.0736			1.49387			0.746934	+	0.664899i	$0.231525\pi$
$200$	0.504224	+	14.5709i	0.0356540	+	1.03032i
$201$	−20.6561			−1.45697
$202$			15.7633i			1.10910i
$203$		−	38.9080i		−	2.73081i
$204$	0.458100			0.0320734
$205$	13.5730	−	0.234775i	0.947977	−	0.0163974i
$206$	1.77225			0.123479
$207$		−	2.72638i		−	0.189496i
$208$		−	1.18804i		−	0.0823760i
$209$	3.64911			0.252414
$210$	0.206810	+	11.9562i	0.0142713	+	0.825059i
$211$	28.9947			1.99607			0.998037	−	0.0626191i	$-0.0199453\pi$
$211$	28.9947			1.99607			0.998037	+	0.0626191i	$0.0199453\pi$
$212$			12.5690i			0.863245i
$213$		−	12.4692i		−	0.854378i
$214$	8.01336			0.547782
$215$	0.105165	+	6.07986i	0.00717219	+	0.414643i
$216$	−16.4011			−1.11595
$217$			25.6377i			1.74040i
$218$			7.59702i			0.514535i
$219$	5.45199			0.368411
$220$	−2.23850	+	0.0387200i	−0.150920	+	0.00261050i
$221$	0.816516			0.0549248
$222$			13.5488i			0.909335i
$223$		−	7.57709i		−	0.507399i	−0.967283	−	0.253700i	$-0.918353\pi$
$223$		−	7.57709i		−	0.507399i	0.967283	−	0.253700i	$-0.0816475\pi$
$224$	−23.4949			−1.56982
$225$	6.20209	−	0.214623i	0.413473	−	0.0143082i
$226$	−3.90420			−0.259704
$227$			9.73925i			0.646416i	0.946328	+	0.323208i	$0.104761\pi$
$227$			9.73925i			0.646416i	−0.946328	+	0.323208i	$0.895239\pi$
$228$			6.22371i			0.412175i
$229$	24.7729			1.63704			0.818520	−	0.574478i	$-0.194795\pi$
$229$	24.7729			1.63704			0.818520	+	0.574478i	$0.194795\pi$
$230$	−4.56829	+	0.0790189i	−0.301224	+	0.00521035i
$231$	−5.07275			−0.333763
$232$		−	26.1715i		−	1.71824i
$233$			20.9912i			1.37518i	0.726100	+	0.687589i	$0.241331\pi$
$233$			20.9912i			1.37518i	−0.726100	+	0.687589i	$0.758669\pi$
$234$	−3.09681			−0.202445
$235$	0.367553	+	21.2492i	0.0239765	+	1.38614i
$236$	9.00630			0.586260
$237$		−	13.1387i		−	0.853453i
$238$			1.22748i			0.0795658i
$239$	0.936020			0.0605461			0.0302730	−	0.999542i	$-0.490362\pi$
$239$	0.936020			0.0605461			0.0302730	+	0.999542i	$0.490362\pi$
$240$	0.0227160	+	1.31327i	0.00146631	+	0.0847713i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	9.50796i		−	0.611195i
$243$			11.9193i			0.764621i
$244$	−1.81997			−0.116512
$245$	26.3637	−	0.456020i	1.68432	−	0.0291341i
$246$	7.48933			0.477502
$247$			11.0931i			0.705839i
$248$			17.2452i			1.09507i
$249$	14.2283			0.901680
$250$	−0.539375	−	10.3859i	−0.0341131	−	0.656864i
$251$	11.8204			0.746099			0.373050	−	0.927811i	$-0.378312\pi$
$251$	11.8204			0.746099			0.373050	+	0.927811i	$0.378312\pi$
$252$			6.10531i			0.384598i
$253$		−	1.93822i		−	0.121855i
$254$	−4.60115			−0.288702
$255$	−0.902582	+	0.0156122i	−0.0565219	+	0.000977674i
$256$	−16.8090			−1.05056
$257$			14.9566i			0.932964i	0.884531	+	0.466482i	$0.154479\pi$
$257$			14.9566i			0.932964i	−0.884531	+	0.466482i	$0.845521\pi$
$258$			3.35476i			0.208858i
$259$	47.6100			2.95834
$260$	−0.117707	−	6.80495i	−0.00729988	−	0.422025i
$261$	−11.1399			−0.689541
$262$			12.7298i			0.786453i
$263$		−	12.3331i		−	0.760494i	−0.924885	−	0.380247i	$-0.875839\pi$
$263$		−	12.3331i		−	0.760494i	0.924885	−	0.380247i	$-0.124161\pi$
$264$	−3.41219			−0.210006
$265$	−0.428357	−	24.7644i	−0.0263138	−	1.52127i
$266$	−16.6765			−1.02250
$267$			12.5741i			0.769522i
$268$			17.6738i			1.07960i
$269$	2.61251			0.159287			0.0796437	−	0.996823i	$-0.474622\pi$
$269$	2.61251			0.159287			0.0796437	+	0.996823i	$0.474622\pi$
$270$	11.6975	−	0.202335i	0.711887	−	0.0123137i
$271$	−9.75632			−0.592654			−0.296327	−	0.955086i	$-0.595762\pi$
$271$	−9.75632			−0.592654			−0.296327	+	0.955086i	$0.595762\pi$
$272$			0.134826i			0.00817505i
$273$		−	15.4209i		−	0.933317i
$274$	17.7274			1.07095
$275$	4.40915	−	0.152578i	0.265882	−	0.00920080i
$276$	3.30571			0.198980
$277$		−	0.508682i		−	0.0305637i	−0.999883	−	0.0152819i	$-0.995135\pi$
$277$		−	0.508682i		−	0.0305637i	0.999883	−	0.0152819i	$-0.00486456\pi$
$278$			20.2180i			1.21260i
$279$	7.34042			0.439459
$280$	28.2606	−	0.488832i	1.68890	−	0.0292133i
$281$	−25.0618			−1.49506			−0.747530	−	0.664228i	$-0.768760\pi$
$281$	−25.0618			−1.49506			−0.747530	+	0.664228i	$0.768760\pi$
$282$			11.7249i			0.698210i
$283$			1.51258i			0.0899134i	0.998989	+	0.0449567i	$0.0143150\pi$
$283$			1.51258i			0.0899134i	−0.998989	+	0.0449567i	$0.985685\pi$
$284$	−10.6689			−0.633084
$285$	−0.212106	−	12.2624i	−0.0125641	−	0.726362i
$286$	−2.20156			−0.130181
$287$		−	26.3173i		−	1.55346i
$288$			6.72689i			0.396386i
$289$	16.9073			0.994549
$290$	0.322868	+	18.6658i	0.0189595	+	1.09610i
$291$	−1.87771			−0.110073
$292$		−	4.66482i		−	0.272988i
$293$			27.7625i			1.62190i	0.585115	+	0.810950i	$0.301049\pi$
$293$			27.7625i			1.62190i	−0.585115	+	0.810950i	$0.698951\pi$
$294$	14.5470			0.848401
$295$	−17.7449	+	0.306938i	−1.03315	+	0.0178706i
$296$	32.0249			1.86141
$297$			4.96298i			0.287981i
$298$			5.61674i			0.325369i
$299$	5.89209			0.340749
$300$	0.260228	+	7.51998i	0.0150243	+	0.434166i
$301$	11.7885			0.679479
$302$		−	13.9636i		−	0.803516i
$303$			22.4742i			1.29111i
$304$	−1.83174			−0.105057
$305$	3.58584	−	0.0620252i	0.205324	−	0.00355155i
$306$	0.351444			0.0200907
$307$			19.1572i			1.09336i	0.837342	+	0.546679i	$0.184108\pi$
$307$			19.1572i			1.09336i	−0.837342	+	0.546679i	$0.815892\pi$
$308$			4.34034i			0.247314i
$309$	2.52676			0.143742
$310$	−0.212748	−	12.2995i	−0.0120833	−	0.698565i
$311$	−4.09651			−0.232292			−0.116146	−	0.993232i	$-0.537054\pi$
$311$	−4.09651			−0.232292			−0.116146	+	0.993232i	$0.537054\pi$
$312$		−	10.3729i		−	0.587250i
$313$			27.8074i			1.57177i	0.618375	+	0.785883i	$0.287791\pi$
$313$			27.8074i			1.57177i	−0.618375	+	0.785883i	$0.712209\pi$
$314$	4.08061			0.230282
$315$	−0.208071	−	12.0291i	−0.0117235	−	0.677765i
$316$	−11.2418			−0.632398
$317$		−	14.6718i		−	0.824048i	−0.911173	−	0.412024i	$-0.864822\pi$
$317$		−	14.6718i		−	0.824048i	0.911173	−	0.412024i	$-0.135178\pi$
$318$		−	13.6646i		−	0.766273i
$319$	−7.91949			−0.443406
$320$	13.2520	−	0.229223i	0.740808	−	0.0128140i
$321$	11.4249			0.637676
$322$			8.85767i			0.493619i
$323$		−	1.25891i		−	0.0700479i
$324$	−4.23941			−0.235523
$325$	0.463830	+	13.4036i	0.0257287	+	0.743498i
$326$	4.95477			0.274420
$327$			10.8313i			0.598974i
$328$		−	17.7023i		−	0.977448i
$329$	41.2011			2.27149
$330$	2.43362	−	0.0420950i	0.133966	−	0.00231725i
$331$	−14.8331			−0.815303			−0.407651	−	0.913138i	$-0.633652\pi$
$331$	−14.8331			−0.815303			−0.407651	+	0.913138i	$0.633652\pi$
$332$		−	12.1740i		−	0.668134i
$333$		−	13.6314i		−	0.746996i
$334$	−7.99536			−0.437486
$335$	−0.602328	−	34.8221i	−0.0329087	−	1.90254i
$336$	2.54636			0.138916
$337$			3.92047i			0.213562i	0.994283	+	0.106781i	$0.0340543\pi$
$337$			3.92047i			0.213562i	−0.994283	+	0.106781i	$0.965946\pi$
$338$			5.39992i			0.293717i
$339$	−5.56634			−0.302322
$340$	0.0133581	+	0.772267i	0.000724445	+	0.0418820i
$341$	5.21840			0.282592
$342$			4.77470i			0.258186i
$343$		−	20.7731i		−	1.12164i
$344$	7.92956			0.427533
$345$	−6.51316	+	0.112660i	−0.350657	+	0.00606540i
$346$	−3.64033			−0.195705
$347$			1.88740i			0.101321i	0.998716	+	0.0506606i	$0.0161327\pi$
$347$			1.88740i			0.101321i	−0.998716	+	0.0506606i	$0.983867\pi$
$348$		−	13.5070i		−	0.724052i
$349$	5.79692			0.310302			0.155151	−	0.987891i	$-0.450414\pi$
$349$	5.79692			0.310302			0.155151	+	0.987891i	$0.450414\pi$
$350$	−20.1498	+	0.697283i	−1.07705	+	0.0372713i
$351$	−15.0872			−0.805296
$352$			4.78224i			0.254894i
$353$		−	20.8216i		−	1.10822i	−0.832443	−	0.554111i	$-0.813058\pi$
$353$		−	20.8216i		−	1.10822i	0.832443	−	0.554111i	$-0.186942\pi$
$354$	−9.79132			−0.520403
$355$	21.0207	−	0.363600i	1.11566	−	0.0192979i
$356$	10.7586			0.570206
$357$			1.75006i			0.0926230i
$358$			2.34737i			0.124062i
$359$	15.4514			0.815492			0.407746	−	0.913095i	$-0.366315\pi$
$359$	15.4514			0.815492			0.407746	+	0.913095i	$0.366315\pi$
$360$	−0.139959	−	8.09140i	−0.00737649	−	0.426454i
$361$	−1.89649			−0.0998153
$362$		−	15.3535i		−	0.806961i
$363$		−	13.5558i		−	0.711495i
$364$	−13.1944			−0.691577
$365$	0.158979	+	9.19098i	0.00832133	+	0.481078i
$366$	1.97860			0.103423
$367$		−	38.0380i		−	1.98557i	−0.119912	−	0.992785i	$-0.538261\pi$
$367$		−	38.0380i		−	1.98557i	0.119912	−	0.992785i	$-0.461739\pi$
$368$			0.972925i			0.0507172i
$369$	−7.53499			−0.392256
$370$	−22.8406	+	0.395080i	−1.18743	+	0.0205392i
$371$	−48.0170			−2.49292
$372$			8.90019i			0.461453i
$373$			15.6921i			0.812505i	0.913761	+	0.406253i	$0.133165\pi$
$373$			15.6921i			0.812505i	−0.913761	+	0.406253i	$0.866835\pi$
$374$	0.249846			0.0129192
$375$	−0.769004	−	14.8076i	−0.0397112	−	0.764659i
$376$	27.7139			1.42924
$377$		−	24.0749i		−	1.23992i
$378$		−	22.6808i		−	1.16658i
$379$	4.85553			0.249412			0.124706	−	0.992194i	$-0.460201\pi$
$379$	4.85553			0.249412			0.124706	+	0.992194i	$0.460201\pi$
$380$	−10.4920	+	0.181482i	−0.538226	+	0.00930983i
$381$	−6.56001			−0.336079
$382$		−	21.0230i		−	1.07563i
$383$		−	18.3938i		−	0.939878i	−0.882699	−	0.469939i	$-0.844276\pi$
$383$		−	18.3938i		−	0.939878i	0.882699	−	0.469939i	$-0.155724\pi$
$384$	−7.06351			−0.360458
$385$	−0.147920	−	8.55166i	−0.00753872	−	0.435833i
$386$	−6.12638			−0.311825
$387$		−	3.37521i		−	0.171572i
$388$			1.60660i			0.0815628i
$389$	30.6318			1.55310			0.776548	−	0.630058i	$-0.216969\pi$
$389$	30.6318			1.55310			0.776548	+	0.630058i	$0.216969\pi$
$390$	0.127967	+	7.39809i	0.00647985	+	0.374617i
$391$	−0.668670			−0.0338161
$392$		−	34.3845i		−	1.73668i
$393$			18.1494i			0.915514i
$394$	−3.34112			−0.168323
$395$	22.1493	−	0.383123i	1.11445	−	0.0192770i
$396$	1.24270			0.0624480
$397$			4.67514i			0.234639i	0.993094	+	0.117319i	$0.0374301\pi$
$397$			4.67514i			0.234639i	−0.993094	+	0.117319i	$0.962570\pi$
$398$			19.6026i			0.982590i
$399$	−23.7762			−1.19030
$400$	−2.21325	+	0.0765894i	−0.110663	+	0.00382947i
$401$	−7.50388			−0.374726			−0.187363	−	0.982291i	$-0.559994\pi$
$401$	−7.50388			−0.374726			−0.187363	+	0.982291i	$0.559994\pi$
$402$		−	19.2143i		−	0.958320i
$403$			15.8637i			0.790226i
$404$	19.2294			0.956698
$405$	8.35279	−	0.144480i	0.415053	−	0.00717929i
$406$	36.1921			1.79618
$407$		−	9.69073i		−	0.480352i
$408$			1.17718i			0.0582790i
$409$	7.22831			0.357417			0.178709	−	0.983902i	$-0.442808\pi$
$409$	7.22831			0.357417			0.178709	+	0.983902i	$0.442808\pi$
$410$	0.218387	+	12.6255i	0.0107854	+	0.623531i
$411$	25.2746			1.24670
$412$		−	2.16195i		−	0.106511i
$413$			34.4064i			1.69303i
$414$	2.53607			0.124641
$415$	0.414893	+	23.9861i	0.0203663	+	1.17743i
$416$	−14.5378			−0.712773
$417$			28.8255i			1.41159i
$418$			3.39439i			0.166025i
$419$	−12.9158			−0.630979			−0.315490	−	0.948929i	$-0.602169\pi$
$419$	−12.9158			−0.630979			−0.315490	+	0.948929i	$0.602169\pi$
$420$	14.5852	−	0.252284i	0.711686	−	0.0123102i
$421$	25.6611			1.25064			0.625322	−	0.780367i	$-0.284967\pi$
$421$	25.6611			1.25064			0.625322	+	0.780367i	$0.284967\pi$
$422$			26.9708i			1.31292i
$423$		−	11.7964i		−	0.573562i
$424$	−32.2986			−1.56856
$425$	−0.0526382	−	1.52112i	−0.00255333	−	0.0737852i
$426$	11.5989			0.561966
$427$		−	6.95275i		−	0.336467i
$428$		−	9.77537i		−	0.472510i
$429$	−3.13884			−0.151544
$430$	−5.65547	+	0.0978241i	−0.272731	+	0.00471750i
$431$	−4.38626			−0.211279			−0.105639	−	0.994404i	$-0.533689\pi$
$431$	−4.38626			−0.211279			−0.105639	+	0.994404i	$0.533689\pi$
$432$		−	2.49126i		−	0.119861i
$433$		−	10.6818i		−	0.513335i	−0.966500	−	0.256667i	$-0.917376\pi$
$433$		−	10.6818i		−	0.513335i	0.966500	−	0.256667i	$-0.0826245\pi$
$434$	−23.8481			−1.14475
$435$	0.460324	+	26.6125i	0.0220708	+	1.27597i
$436$	9.26749			0.443832
$437$		−	9.08450i		−	0.434571i
$438$			5.07142i			0.242322i
$439$	−6.07260			−0.289829			−0.144915	−	0.989444i	$-0.546291\pi$
$439$	−6.07260			−0.289829			−0.144915	+	0.989444i	$0.546291\pi$
$440$	−0.0994987	−	5.75228i	−0.00474342	−	0.274229i
$441$	−14.6357			−0.696940
$442$			0.759521i			0.0361267i
$443$		−	23.3422i		−	1.10902i	−0.832176	−	0.554512i	$-0.812905\pi$
$443$		−	23.3422i		−	1.10902i	0.832176	−	0.554512i	$-0.187095\pi$
$444$	16.5280			0.784382
$445$	−21.1974	+	0.366658i	−1.00485	+	0.0173812i
$446$	7.04819			0.333741
$447$			8.00797i			0.378764i
$448$		−	25.6949i		−	1.21397i
$449$	−14.5863			−0.688371			−0.344185	−	0.938902i	$-0.611845\pi$
$449$	−14.5863			−0.688371			−0.344185	+	0.938902i	$0.611845\pi$
$450$	0.199641	+	5.76917i	0.00941119	+	0.271961i
$451$	−5.35672			−0.252238
$452$			4.76267i			0.224017i
$453$		−	19.9084i		−	0.935378i
$454$	−9.05942			−0.425180
$455$	25.9967	−	0.449671i	1.21874	−	0.0210809i
$456$	−15.9931			−0.748943
$457$			21.6065i			1.01071i	0.862912	+	0.505355i	$0.168638\pi$
$457$			21.6065i			1.01071i	−0.862912	+	0.505355i	$0.831362\pi$
$458$			23.0437i			1.07676i
$459$	1.71219			0.0799181
$460$	0.0963939	+	5.57278i	0.00449439	+	0.259832i
$461$	−8.71776			−0.406026			−0.203013	−	0.979176i	$-0.565073\pi$
$461$	−8.71776			−0.406026			−0.203013	+	0.979176i	$0.565073\pi$
$462$		−	4.71866i		−	0.219532i
$463$			16.2752i			0.756375i	0.925729	+	0.378187i	$0.123452\pi$
$463$			16.2752i			0.756375i	−0.925729	+	0.378187i	$0.876548\pi$
$464$	3.97534			0.184550
$465$	−0.303322	−	17.5358i	−0.0140662	−	0.813204i
$466$	−19.5260			−0.904522
$467$			6.86128i			0.317502i	0.987319	+	0.158751i	$0.0507467\pi$
$467$			6.86128i			0.317502i	−0.987319	+	0.158751i	$0.949253\pi$
$468$			3.77775i			0.174626i
$469$	−67.5183			−3.11771
$470$	−19.7659	+	0.341897i	−0.911735	+	0.0157705i
$471$	5.81786			0.268073
$472$			23.1435i			1.06526i
$473$		−	2.39948i		−	0.110328i
$474$	12.2216			0.561358
$475$	20.6658	−	0.715138i	0.948213	−	0.0328128i
$476$	1.49738			0.0686325
$477$			13.7479i			0.629473i
$478$			0.870683i			0.0398241i
$479$	−17.6985			−0.808664			−0.404332	−	0.914612i	$-0.632496\pi$
$479$	−17.6985			−0.808664			−0.404332	+	0.914612i	$0.632496\pi$
$480$	16.0701	−	0.277970i	0.733498	−	0.0126875i
$481$	29.4594			1.34323
$482$			0.930197i			0.0423693i
$483$			12.6287i			0.574624i
$484$	−11.5986			−0.527210
$485$	−0.0547535	−	3.16544i	−0.00248623	−	0.143735i
$486$	−11.0873			−0.502928
$487$			9.06661i			0.410847i	0.978673	+	0.205424i	$0.0658572\pi$
$487$			9.06661i			0.410847i	−0.978673	+	0.205424i	$0.934143\pi$
$488$		−	4.67677i		−	0.211707i
$489$	7.06418			0.319453
$490$	0.424189	+	24.5235i	0.0191629	+	1.10786i
$491$	−16.2481			−0.733269			−0.366634	−	0.930365i	$-0.619490\pi$
$491$	−16.2481			−0.733269			−0.366634	+	0.930365i	$0.619490\pi$
$492$		−	9.13611i		−	0.411888i
$493$			2.73216i			0.123050i
$494$	−10.3188			−0.464265
$495$	−2.44846	+	0.0423516i	−0.110050	+	0.00190356i
$496$	−2.61947			−0.117618
$497$		−	40.7580i		−	1.82825i
$498$			13.2351i			0.593079i
$499$	−31.2373			−1.39837			−0.699186	−	0.714940i	$-0.746454\pi$
$499$	−31.2373			−1.39837			−0.699186	+	0.714940i	$0.746454\pi$
$500$	−12.6696	+	0.657975i	−0.566603	+	0.0294255i
$501$	−11.3992			−0.509280
$502$			10.9953i			0.490746i
$503$			36.0521i			1.60749i	0.594977	+	0.803743i	$0.297161\pi$
$503$			36.0521i			1.60749i	−0.594977	+	0.803743i	$0.702839\pi$
$504$	−15.6888			−0.698835
$505$	−37.8872	+	0.655344i	−1.68596	+	0.0291624i
$506$	1.80293			0.0801498
$507$			7.69884i			0.341918i
$508$			5.61287i			0.249031i
$509$	−6.06492			−0.268823			−0.134412	−	0.990926i	$-0.542914\pi$
$509$	−6.06492			−0.268823			−0.134412	+	0.990926i	$0.542914\pi$
$510$	−0.0145224	−	0.839580i	−0.000643064	−	0.0371772i
$511$	17.8208			0.788347
$512$		−	4.98355i		−	0.220244i
$513$			23.2616i			1.02703i
$514$	−13.9125			−0.613656
$515$	0.0736798	+	4.25962i	0.00324672	+	0.187701i
$516$	4.09242			0.180159
$517$		−	8.38623i		−	0.368826i
$518$			44.2867i			1.94585i
$519$	−5.19013			−0.227822
$520$	17.4867	−	0.302471i	0.766841	−	0.0132643i
$521$	−33.8087			−1.48119			−0.740593	−	0.671954i	$-0.765455\pi$
$521$	−33.8087			−1.48119			−0.740593	+	0.671954i	$0.765455\pi$
$522$		−	10.3623i		−	0.453545i
$523$		−	23.5838i		−	1.03125i	−0.856815	−	0.515625i	$-0.827560\pi$
$523$		−	23.5838i		−	1.03125i	0.856815	−	0.515625i	$-0.172440\pi$
$524$	15.5289			0.678385
$525$	−28.7283	+	0.994138i	−1.25380	+	0.0433878i
$526$	11.4723			0.500214
$527$		−	1.80031i		−	0.0784225i
$528$		−	0.518297i		−	0.0225560i
$529$	18.1748			0.790208
$530$	23.0358	−	0.398457i	1.00061	−	0.0173079i
$531$	9.85101			0.427498
$532$			20.3433i			0.881996i
$533$		−	16.2842i		−	0.705346i
$534$	−11.6964			−0.506152
$535$	0.333148	+	19.2602i	0.0144032	+	0.832689i
$536$	−45.4162			−1.96168
$537$			3.34672i			0.144422i
$538$			2.43015i			0.104771i
$539$	−10.4047			−0.448164
$540$	−0.246825	−	14.2696i	−0.0106217	−	0.614065i
$541$	−12.4241			−0.534152			−0.267076	−	0.963675i	$-0.586058\pi$
$541$	−12.4241			−0.534152			−0.267076	+	0.963675i	$0.586058\pi$
$542$		−	9.07531i		−	0.389818i
$543$		−	21.8899i		−	0.939388i
$544$	1.64983			0.0707360
$545$	−18.2595	+	0.315839i	−0.782150	+	0.0135291i
$546$	14.3445			0.613888
$547$			12.3673i			0.528786i	0.964415	+	0.264393i	$0.0851715\pi$
$547$			12.3673i			0.528786i	−0.964415	+	0.264393i	$0.914828\pi$
$548$		−	21.6254i		−	0.923792i
$549$	−1.99067			−0.0849596
$550$	0.141928	+	4.10138i	0.00605182	+	0.174883i
$551$	−37.1189			−1.58132
$552$			8.49468i			0.361558i
$553$		−	42.9464i		−	1.82627i
$554$	0.473174			0.0201033
$555$	−32.5646	+	0.563278i	−1.38229	+	0.0239098i
$556$	24.6637			1.04597
$557$		−	14.4719i		−	0.613195i	−0.951839	−	0.306598i	$-0.900809\pi$
$557$		−	14.4719i		−	0.613195i	0.951839	−	0.306598i	$-0.0991906\pi$
$558$			6.82804i			0.289054i
$559$	7.29432			0.308517
$560$	0.0742514	+	4.29267i	0.00313770	+	0.181398i
$561$	0.356214			0.0150394
$562$		−	23.3124i		−	0.983374i
$563$			2.71732i			0.114521i	0.998359	+	0.0572607i	$0.0182366\pi$
$563$			2.71732i			0.114521i	−0.998359	+	0.0572607i	$0.981763\pi$
$564$	14.3031			0.602268
$565$	−0.162313	−	9.38376i	−0.00682858	−	0.394778i
$566$	−1.40700			−0.0591404
$567$		−	16.1956i		−	0.680152i
$568$		−	27.4159i		−	1.15035i
$569$	35.2838			1.47917			0.739586	−	0.673062i	$-0.235021\pi$
$569$	35.2838			1.47917			0.739586	+	0.673062i	$0.235021\pi$
$570$	11.4065	−	0.197301i	0.477764	−	0.00826401i
$571$	−34.4873			−1.44325			−0.721625	−	0.692285i	$-0.756604\pi$
$571$	−34.4873			−1.44325			−0.721625	+	0.692285i	$0.756604\pi$
$572$			2.68565i			0.112293i
$573$		−	29.9732i		−	1.25215i
$574$	24.4803			1.02179
$575$	−0.379845	−	10.9766i	−0.0158406	−	0.457757i
$576$	−7.35680			−0.306533
$577$			6.57108i			0.273558i	0.990602	+	0.136779i	$0.0436750\pi$
$577$			6.57108i			0.273558i	−0.990602	+	0.136779i	$0.956325\pi$
$578$			15.7272i			0.654164i
$579$	−8.73458			−0.362997
$580$	22.7702	−	0.393862i	0.945480	−	0.0163542i
$581$	46.5078			1.92947
$582$		−	1.74664i		−	0.0724004i
$583$			9.77357i			0.404780i
$584$	11.9872			0.496033
$585$	−0.128747	−	7.44319i	−0.00532303	−	0.307738i
$586$	−25.8246			−1.06680
$587$		−	3.17806i		−	0.131173i	−0.997847	−	0.0655863i	$-0.979108\pi$
$587$		−	3.17806i		−	0.131173i	0.997847	−	0.0655863i	$-0.0208918\pi$
$588$		−	17.7457i		−	0.731821i
$589$	24.4588			1.00781
$590$	−0.285513	−	16.5062i	−0.0117544	−	0.679551i
$591$	−4.76354			−0.195946
$592$			4.86445i			0.199928i
$593$		−	35.0450i		−	1.43913i	−0.694428	−	0.719563i	$-0.744342\pi$
$593$		−	35.0450i		−	1.43913i	0.694428	−	0.719563i	$-0.255658\pi$
$594$	−4.61655			−0.189419
$595$	−2.95026	+	0.0510314i	−0.120949	+	0.00209208i
$596$	6.85177			0.280660
$597$			27.9481i			1.14384i
$598$			5.48081i			0.224127i
$599$	18.6149			0.760583			0.380292	−	0.924867i	$-0.375824\pi$
$599$	18.6149			0.760583			0.380292	+	0.924867i	$0.375824\pi$
$600$	−19.3241	+	0.668708i	−0.788902	+	0.0272999i
$601$	8.79674			0.358827			0.179413	−	0.983774i	$-0.442580\pi$
$601$	8.79674			0.358827			0.179413	+	0.983774i	$0.442580\pi$
$602$			10.9657i			0.446927i
$603$			19.3314i			0.787235i
$604$	−17.0340			−0.693104
$605$	22.8524	−	0.395285i	0.929083	−	0.0160706i
$606$	−20.9055			−0.849227
$607$		−	44.5048i		−	1.80639i	−0.429226	−	0.903197i	$-0.641213\pi$
$607$		−	44.5048i		−	1.80639i	0.429226	−	0.903197i	$-0.358787\pi$
$608$			22.4145i			0.909028i
$609$	51.6003			2.09095
$610$	0.0576956	+	3.33554i	0.00233603	+	0.135052i
$611$	25.4937			1.03137
$612$		−	0.428721i		−	0.0173300i
$613$		−	47.1882i		−	1.90591i	−0.303109	−	0.952956i	$-0.598025\pi$
$613$		−	47.1882i		−	1.90591i	0.303109	−	0.952956i	$-0.401975\pi$
$614$	−17.8200			−0.719155
$615$	0.311362	+	18.0006i	0.0125553	+	0.725856i
$616$	−11.1534			−0.449382
$617$		−	3.11780i		−	0.125518i	−0.998029	−	0.0627590i	$-0.980010\pi$
$617$		−	3.11780i		−	0.125518i	0.998029	−	0.0627590i	$-0.0199899\pi$
$618$			2.35039i			0.0945464i
$619$	−23.7548			−0.954787			−0.477393	−	0.878690i	$-0.658418\pi$
$619$	−23.7548			−0.954787			−0.477393	+	0.878690i	$0.658418\pi$
$620$	−15.0040	+	0.259528i	−0.602574	+	0.0104229i
$621$	12.3554			0.495804
$622$		−	3.81056i		−	0.152789i
$623$			41.1007i			1.64667i
$624$	1.57560			0.0630744
$625$	24.9402	−	1.72817i	0.997608	−	0.0691270i
$626$	−25.8664			−1.03383
$627$			4.83950i			0.193271i
$628$		−	4.97787i		−	0.198639i
$629$	−3.34323			−0.133303
$630$	11.1895	−	0.193547i	0.445799	−	0.00771110i
$631$	−47.0576			−1.87334			−0.936668	−	0.350220i	$-0.886107\pi$
$631$	−47.0576			−1.87334			−0.936668	+	0.350220i	$0.886107\pi$
$632$		−	28.8879i		−	1.14910i
$633$			38.4531i			1.52837i
$634$	13.6476			0.542016
$635$	−0.191288	−	11.0589i	−0.00759105	−	0.438858i
$636$	−16.6692			−0.660978
$637$		−	31.6299i		−	1.25322i
$638$		−	7.36668i		−	0.291650i
$639$	−11.6696			−0.461641
$640$	−0.205970	−	11.9077i	−0.00814169	−	0.470692i
$641$	25.2677			0.998015			0.499007	−	0.866598i	$-0.333698\pi$
$641$	25.2677			0.998015			0.499007	+	0.866598i	$0.333698\pi$
$642$			10.6274i			0.419431i
$643$		−	1.36761i		−	0.0539332i	−0.999636	−	0.0269666i	$-0.991415\pi$
$643$		−	1.36761i		−	0.0539332i	0.999636	−	0.0269666i	$-0.00858478\pi$
$644$	10.8053			0.425790
$645$	−8.06318	+	0.139471i	−0.317488	+	0.00549167i
$646$	1.17104			0.0460739
$647$			47.9634i			1.88563i	0.333310	+	0.942817i	$0.391834\pi$
$647$			47.9634i			1.88563i	−0.333310	+	0.942817i	$0.608166\pi$
$648$		−	10.8940i		−	0.427956i
$649$	7.00321			0.274900
$650$	−12.4680	+	0.431453i	−0.489035	+	0.0169230i
$651$	−34.0010			−1.33261
$652$		−	6.04425i		−	0.236711i
$653$		−	18.9603i		−	0.741975i	−0.928638	−	0.370987i	$-0.879019\pi$
$653$		−	18.9603i		−	0.741975i	0.928638	−	0.370987i	$-0.120981\pi$
$654$	−10.0753			−0.393974
$655$	−30.5962	+	0.529231i	−1.19549	+	0.0206788i
$656$	2.68891			0.104984
$657$		−	5.10234i		−	0.199061i
$658$			38.3251i			1.49407i
$659$	8.62976			0.336168			0.168084	−	0.985773i	$-0.446242\pi$
$659$	8.62976			0.336168			0.168084	+	0.985773i	$0.446242\pi$
$660$	−0.0513510	−	2.96873i	−0.00199883	−	0.115558i
$661$	−16.6323			−0.646920			−0.323460	−	0.946242i	$-0.604846\pi$
$661$	−16.6323			−0.646920			−0.323460	+	0.946242i	$0.604846\pi$
$662$		−	13.7977i		−	0.536265i
$663$			1.08287i			0.0420553i
$664$	31.2835			1.21403
$665$	−0.693308	−	40.0820i	−0.0268853	−	1.55431i
$666$	12.6799			0.491336
$667$			19.7156i			0.763393i
$668$			9.75341i			0.377371i
$669$	10.0488			0.388510
$670$	32.3915	−	0.560284i	1.25139	−	0.0216456i
$671$	−1.41519			−0.0546328
$672$		−	31.1592i		−	1.20199i
$673$		−	10.4577i		−	0.403113i	−0.979477	−	0.201557i	$-0.935400\pi$
$673$		−	10.4577i		−	0.403113i	0.979477	−	0.201557i	$-0.0646000\pi$
$674$	−3.64681			−0.140470
$675$	0.972625	+	28.1066i	0.0374363	+	1.08182i
$676$	6.58728			0.253357
$677$		−	41.7207i		−	1.60346i	−0.597689	−	0.801728i	$-0.703914\pi$
$677$		−	41.7207i		−	1.60346i	0.597689	−	0.801728i	$-0.296086\pi$
$678$		−	5.17780i		−	0.198852i
$679$	−6.13763			−0.235541
$680$	−1.98449	+	0.0343263i	−0.0761018	+	0.00131635i
$681$	−12.9163			−0.494954
$682$			4.85414i			0.185875i
$683$		−	32.9092i		−	1.25924i	−0.776905	−	0.629618i	$-0.783211\pi$
$683$		−	32.9092i		−	1.25924i	0.776905	−	0.629618i	$-0.216789\pi$
$684$	5.82457			0.222708
$685$	0.737002	+	42.6080i	0.0281594	+	1.62797i
$686$	19.3231			0.737758
$687$			32.8541i			1.25346i
$688$			1.20447i			0.0459198i
$689$	−29.7112			−1.13191
$690$	−0.104796	−	6.05852i	−0.00398951	−	0.230644i
$691$	23.1023			0.878855			0.439427	−	0.898278i	$-0.355181\pi$
$691$	23.1023			0.878855			0.439427	+	0.898278i	$0.355181\pi$
$692$			4.44078i			0.168813i
$693$			4.74743i			0.180340i
$694$	−1.75566			−0.0666438
$695$	−48.5941	+	0.840546i	−1.84328	+	0.0318837i
$696$	34.7089			1.31564
$697$			1.84803i			0.0699990i
$698$			5.39228i			0.204101i
$699$	−27.8388			−1.05296
$700$	0.850604	+	24.5805i	0.0321498	+	0.929054i
$701$	16.5438			0.624852			0.312426	−	0.949942i	$-0.398858\pi$
$701$	16.5438			0.624852			0.312426	+	0.949942i	$0.398858\pi$
$702$		−	14.0341i		−	0.529683i
$703$		−	45.4208i		−	1.71308i
$704$	−5.23004			−0.197115
$705$	−28.1809	+	0.487453i	−1.06136	+	0.0183585i
$706$	19.3682			0.728932
$707$			73.4612i			2.76279i
$708$			11.9443i			0.448893i
$709$	−31.5902			−1.18639			−0.593197	−	0.805058i	$-0.702134\pi$
$709$	−31.5902			−1.18639			−0.593197	+	0.805058i	$0.702134\pi$
$710$	0.338220	+	19.5534i	0.0126932	+	0.733826i
$711$	−12.2961			−0.461141
$712$			27.6464i			1.03609i
$713$		−	12.9913i		−	0.486526i
$714$	−1.62790			−0.0609227
$715$	−0.0915278	−	5.29146i	−0.00342295	−	0.197889i
$716$	2.86352			0.107015
$717$			1.24136i			0.0463595i
$718$			14.3728i			0.536389i
$719$	17.6028			0.656474			0.328237	−	0.944595i	$-0.393546\pi$
$719$	17.6028			0.656474			0.328237	+	0.944595i	$0.393546\pi$
$720$	1.22905	−	0.0212592i	0.0458040	−	0.000792283i
$721$	8.25919			0.307588
$722$		−	1.76411i		−	0.0656534i
$723$			1.32621i			0.0493224i
$724$	−18.7295			−0.696075
$725$	−44.8500	+	1.55203i	−1.66569	+	0.0576409i
$726$	12.6096			0.467985
$727$		−	34.7819i		−	1.28999i	−0.764187	−	0.644995i	$-0.776859\pi$
$727$		−	34.7819i		−	1.28999i	0.764187	−	0.644995i	$-0.223141\pi$
$728$		−	33.9057i		−	1.25663i
$729$	−27.0156			−1.00058
$730$	−8.54942	+	0.147882i	−0.316428	+	0.00547334i
$731$	−0.827803			−0.0306174
$732$		−	2.41367i		−	0.0892117i
$733$		−	35.3016i		−	1.30389i	−0.758265	−	0.651947i	$-0.773952\pi$
$733$		−	35.3016i		−	1.30389i	0.758265	−	0.651947i	$-0.226048\pi$
$734$	35.3829			1.30601
$735$	0.604780	+	34.9639i	0.0223076	+	1.28966i
$736$	11.9054			0.438840
$737$			13.7429i			0.506228i
$738$		−	7.00903i		−	0.258006i
$739$	14.8693			0.546975			0.273487	−	0.961876i	$-0.411823\pi$
$739$	14.8693			0.546975			0.273487	+	0.961876i	$0.411823\pi$
$740$	0.481952	+	27.8629i	0.0177169	+	1.02426i
$741$	−14.7118			−0.540453
$742$		−	44.6653i		−	1.63971i
$743$			28.8502i			1.05841i	0.848494	+	0.529206i	$0.177510\pi$
$743$			28.8502i			1.05841i	−0.848494	+	0.529206i	$0.822490\pi$
$744$	−22.8708			−0.838484
$745$	−13.4999	+	0.233511i	−0.494597	+	0.00855517i
$746$	−14.5967			−0.534424
$747$		−	13.3158i		−	0.487199i
$748$		−	0.304784i		−	0.0111440i
$749$	37.3444			1.36454
$750$	13.7739	−	0.715326i	0.502953	−	0.0261200i
$751$	26.4978			0.966918			0.483459	−	0.875367i	$-0.339380\pi$
$751$	26.4978			0.966918			0.483459	+	0.875367i	$0.339380\pi$
$752$			4.20963i			0.153509i
$753$			15.6764i			0.571280i
$754$	22.3944			0.815555
$755$	33.5616	−	0.580524i	1.22143	−	0.0211274i
$756$	−27.6680			−1.00628
$757$			34.8758i			1.26758i	0.773505	+	0.633790i	$0.218502\pi$
$757$			34.8758i			1.26758i	−0.773505	+	0.633790i	$0.781498\pi$
$758$			4.51660i			0.164050i
$759$	2.57049			0.0933029
$760$	−0.466354	−	26.9611i	−0.0169164	−	0.977983i
$761$	43.4881			1.57644			0.788221	−	0.615392i	$-0.211002\pi$
$761$	43.4881			1.57644			0.788221	+	0.615392i	$0.211002\pi$
$762$		−	6.10210i		−	0.221056i
$763$			35.4042i			1.28172i
$764$	−25.6456			−0.927826
$765$	0.0146110	+	0.844698i	0.000528261	+	0.0305401i
$766$	17.1098			0.618203
$767$			21.2894i			0.768717i
$768$		−	22.2923i		−	0.804405i
$769$	−49.0482			−1.76872			−0.884362	−	0.466801i	$-0.845406\pi$
$769$	−49.0482			−1.76872			−0.884362	+	0.466801i	$0.845406\pi$
$770$	7.95474	−	0.137595i	0.286669	−	0.00495859i
$771$	−19.8356			−0.714361
$772$			7.47348i			0.268976i
$773$		−	28.0305i		−	1.00819i	−0.863649	−	0.504093i	$-0.831827\pi$
$773$		−	28.0305i		−	1.00819i	0.863649	−	0.504093i	$-0.168173\pi$
$774$	3.13962			0.112851
$775$	29.5531	−	1.02268i	1.06158	−	0.0367358i
$776$	−4.12848			−0.148204
$777$			63.1410i			2.26517i
$778$			28.4937i			1.02155i
$779$	−25.1071			−0.899557
$780$	9.02481	−	0.156105i	0.323140	−	0.00558944i
$781$	−8.29605			−0.296856
$782$		−	0.621995i		−	0.0222425i
$783$		−	50.4836i		−	1.80414i
$784$	5.22285			0.186530
$785$	0.169648	+	9.80777i	0.00605498	+	0.350054i
$786$	−16.8825			−0.602178
$787$		−	14.4420i		−	0.514801i	−0.966305	−	0.257400i	$-0.917134\pi$
$787$		−	14.4420i		−	0.514801i	0.966305	−	0.257400i	$-0.0828660\pi$
$788$			4.07578i			0.145194i
$789$	16.3564			0.582302
$790$	0.356380	+	20.6032i	0.0126794	+	0.733031i
$791$	−18.1946			−0.646926
$792$			3.19336i			0.113471i
$793$		−	4.30211i		−	0.152772i
$794$	−4.34880			−0.154333
$795$	32.8429	−	0.568093i	1.16482	−	0.0201482i
$796$	23.9129			0.847570
$797$			10.9710i			0.388612i	0.980941	+	0.194306i	$0.0622455\pi$
$797$			10.9710i			0.388612i	−0.980941	+	0.194306i	$0.937755\pi$
$798$		−	22.1165i		−	0.782917i
$799$	−2.89318			−0.102353
$800$	0.937204	+	27.0830i	0.0331352	+	0.957529i
$801$	11.7677			0.415791
$802$		−	6.98009i		−	0.246475i
$803$		−	3.62732i		−	0.128005i
$804$	−23.4392			−0.826635
$805$	−21.2895	+	0.368249i	−0.750355	+	0.0129791i
$806$	−14.7564			−0.519770
$807$			3.46474i			0.121965i
$808$			49.4137i			1.73837i
$809$	39.0394			1.37255			0.686276	−	0.727342i	$-0.259244\pi$
$809$	39.0394			1.37255			0.686276	+	0.727342i	$0.259244\pi$
$810$	0.134395	+	7.76974i	0.00472217	+	0.273001i
$811$	−22.6660			−0.795912			−0.397956	−	0.917405i	$-0.630280\pi$
$811$	−22.6660			−0.795912			−0.397956	+	0.917405i	$0.630280\pi$
$812$		−	44.1502i		−	1.54937i
$813$		−	12.9390i		−	0.453789i
$814$	9.01430			0.315951
$815$	0.205990	+	11.9088i	0.00721552	+	0.417148i
$816$	−0.178808			−0.00625954
$817$		−	11.2465i		−	0.393464i
$818$			6.72376i			0.235091i
$819$	−14.4320			−0.504294
$820$	15.4017	−	0.266407i	0.537850	−	0.00930334i
$821$	24.9834			0.871926			0.435963	−	0.899965i	$-0.356408\pi$
$821$	24.9834			0.871926			0.435963	+	0.899965i	$0.356408\pi$
$822$			23.5104i			0.820018i
$823$		−	35.0663i		−	1.22233i	−0.791502	−	0.611167i	$-0.790700\pi$
$823$		−	35.0663i		−	1.22233i	0.791502	−	0.611167i	$-0.209300\pi$
$824$	5.55555			0.193537
$825$	0.202351	+	5.84746i	0.00704495	+	0.203583i
$826$	−32.0047			−1.11359
$827$		−	5.28536i		−	0.183790i	−0.995769	−	0.0918949i	$-0.970708\pi$
$827$		−	5.28536i		−	0.183790i	0.995769	−	0.0918949i	$-0.0292924\pi$
$828$		−	3.09371i		−	0.107514i
$829$	−0.699646			−0.0242997			−0.0121499	−	0.999926i	$-0.503868\pi$
$829$	−0.699646			−0.0242997			−0.0121499	+	0.999926i	$0.503868\pi$
$830$	−22.3118	+	0.385933i	−0.774453	+	0.0133959i
$831$	0.674620			0.0234023
$832$		−	15.8991i		−	0.551202i
$833$			3.58955i			0.124371i
$834$	−26.8134			−0.928473
$835$	−0.332399	−	19.2169i	−0.0115032	−	0.665027i
$836$	4.14077			0.143211
$837$			33.2652i			1.14981i
$838$		−	12.0143i		−	0.415026i
$839$	−44.8426			−1.54814			−0.774069	−	0.633101i	$-0.781782\pi$
$839$	−44.8426			−1.54814			−0.774069	+	0.633101i	$0.781782\pi$
$840$	0.648295	+	37.4796i	0.0223683	+	1.29317i
$841$	51.5573			1.77784
$842$			23.8699i			0.822610i
$843$		−	33.2372i		−	1.14475i
$844$	32.9012			1.13251
$845$	−12.9787	+	0.224497i	−0.446482	+	0.00772292i
$846$	10.9730			0.377260
$847$		−	44.3097i		−	1.52250i
$848$		−	4.90603i		−	0.168474i
$849$	−2.00600			−0.0688457
$850$	1.41494	−	0.0489639i	0.0485321	−	0.00167945i
$851$	−24.1252			−0.827001
$852$		−	14.1493i		−	0.484746i
$853$			10.7624i			0.368497i	0.982880	+	0.184249i	$0.0589851\pi$
$853$			10.7624i			0.368497i	−0.982880	+	0.184249i	$0.941015\pi$
$854$	6.46743			0.221311
$855$	−11.4760	+	0.198503i	−0.392471	+	0.00678868i
$856$	25.1197			0.858575
$857$			21.5155i			0.734956i	0.930032	+	0.367478i	$0.119779\pi$
$857$			21.5155i			0.734956i	−0.930032	+	0.367478i	$0.880221\pi$
$858$		−	2.91974i		−	0.0996782i
$859$	−2.12944			−0.0726556			−0.0363278	−	0.999340i	$-0.511566\pi$
$859$	−2.12944			−0.0726556			−0.0363278	+	0.999340i	$0.511566\pi$
$860$	0.119334	+	6.89901i	0.00406926	+	0.235254i
$861$	34.9023			1.18947
$862$		−	4.08009i		−	0.138968i
$863$		−	10.2693i		−	0.349571i	−0.984607	−	0.174785i	$-0.944077\pi$
$863$		−	10.2693i		−	0.349571i	0.984607	−	0.174785i	$-0.0559231\pi$
$864$	−30.4849			−1.03712
$865$	−0.151343	−	8.74954i	−0.00514582	−	0.297493i
$866$	9.93618			0.337645
$867$			22.4227i			0.761515i
$868$			29.0919i			0.987444i
$869$	−8.74148			−0.296534
$870$	−24.7549	+	0.428192i	−0.839269	+	0.0145171i
$871$	−41.7779			−1.41559
$872$			23.8146i			0.806466i
$873$			1.75729i			0.0594751i
$874$	8.45038			0.285838
$875$	−2.51363	−	48.4012i	−0.0849763	−	1.63626i
$876$	6.18655			0.209024
$877$			5.83603i			0.197069i	0.995134	+	0.0985343i	$0.0314154\pi$
$877$			5.83603i			0.197069i	−0.995134	+	0.0985343i	$0.968585\pi$
$878$		−	5.64871i		−	0.190635i
$879$	−36.8189			−1.24187
$880$	0.873747	−	0.0151134i	0.0294540	−	0.000509474i
$881$	23.6510			0.796823			0.398412	−	0.917207i	$-0.369562\pi$
$881$	23.6510			0.796823			0.398412	+	0.917207i	$0.369562\pi$
$882$		−	13.6141i		−	0.458411i
$883$			21.4740i			0.722658i	0.932438	+	0.361329i	$0.117677\pi$
$883$			21.4740i			0.722658i	−0.932438	+	0.361329i	$0.882323\pi$
$884$	0.926528			0.0311625
$885$	−0.407065	−	23.5335i	−0.0136833	−	0.791069i
$886$	21.7129			0.729459
$887$		−	19.7851i		−	0.664320i	−0.943223	−	0.332160i	$-0.892223\pi$
$887$		−	19.7851i		−	0.664320i	0.943223	−	0.332160i	$-0.107777\pi$
$888$			42.4718i			1.42526i
$889$	−21.4426			−0.719162
$890$	−0.341064	−	19.7178i	−0.0114325	−	0.660942i
$891$	−3.29652			−0.110438
$892$		−	8.59797i		−	0.287881i
$893$		−	39.3066i		−	1.31534i
$894$	−7.44899			−0.249132
$895$	−5.64192	+	0.0975898i	−0.188589	+	0.00326207i
$896$	−23.0884			−0.771329
$897$			7.81417i			0.260907i
$898$		−	13.5681i		−	0.452775i
$899$	−53.0817			−1.77038
$900$	7.03772	−	0.243539i	0.234591	−	0.00811798i
$901$	3.37180			0.112331
$902$		−	4.98281i		−	0.165909i
$903$			15.6341i			0.520270i
$904$	−12.2386			−0.407051
$905$	36.9022	−	0.638306i	1.22667	−	0.0212180i
$906$	18.5187			0.615244
$907$			0.445947i			0.0148074i	0.999973	+	0.00740371i	$0.00235669\pi$
$907$			0.445947i			0.0148074i	−0.999973	+	0.00740371i	$0.997643\pi$
$908$			11.0514i			0.366755i
$909$	21.0329			0.697619
$910$	0.418283	+	24.1820i	0.0138659	+	0.801626i
$911$	3.07240			0.101793			0.0508965	−	0.998704i	$-0.483792\pi$
$911$	3.07240			0.101793			0.0508965	+	0.998704i	$0.483792\pi$
$912$		−	2.42928i		−	0.0804414i
$913$		−	9.46637i		−	0.313291i
$914$	−20.0983			−0.664793
$915$	0.0822585	+	4.75558i	0.00271938	+	0.157215i
$916$	28.1106			0.928802
$917$			59.3245i			1.95907i
$918$			1.59267i			0.0525660i
$919$	−9.98217			−0.329281			−0.164641	−	0.986354i	$-0.552646\pi$
$919$	−9.98217			−0.329281			−0.164641	+	0.986354i	$0.552646\pi$
$920$	−14.3204	+	0.247703i	−0.472128	+	0.00816653i
$921$	−25.4065			−0.837172
$922$		−	8.10924i		−	0.267063i
$923$		−	25.2196i		−	0.830113i
$924$	−5.75622			−0.189366
$925$	−1.89915	−	54.8811i	−0.0624438	−	1.80448i
$926$	−15.1392			−0.497505
$927$		−	2.36472i		−	0.0776675i
$928$		−	48.6451i		−	1.59685i
$929$	−2.23534			−0.0733392			−0.0366696	−	0.999327i	$-0.511675\pi$
$929$	−2.23534			−0.0733392			−0.0366696	+	0.999327i	$0.511675\pi$
$930$	16.3118	−	0.282149i	0.534884	−	0.00925203i
$931$	−48.7674			−1.59829
$932$			23.8194i			0.780230i
$933$		−	5.43284i		−	0.177863i
$934$	−6.38235			−0.208837
$935$	0.0103871	+	0.600507i	0.000339695	+	0.0196387i
$936$	−9.70767			−0.317305
$937$		−	46.5278i		−	1.52000i	−0.649924	−	0.759999i	$-0.725199\pi$
$937$		−	46.5278i		−	1.52000i	0.649924	−	0.759999i	$-0.274801\pi$
$938$		−	62.8053i		−	2.05067i
$939$	−36.8785			−1.20348
$940$	0.417074	+	24.1122i	0.0136035	+	0.786452i
$941$	37.9006			1.23552			0.617761	−	0.786366i	$-0.288040\pi$
$941$	37.9006			1.23552			0.617761	+	0.786366i	$0.288040\pi$
$942$			5.41176i			0.176325i
$943$			13.3356i			0.434267i
$944$	−3.51539			−0.114416
$945$	54.5135	−	0.942935i	1.77332	−	0.0306737i
$946$	2.23199			0.0725684
$947$		−	22.0207i		−	0.715576i	−0.933803	−	0.357788i	$-0.883531\pi$
$947$		−	22.0207i		−	0.715576i	0.933803	−	0.357788i	$-0.116469\pi$
$948$		−	14.9090i		−	0.484220i
$949$	11.0269			0.357948
$950$	0.665220	+	19.2233i	0.0215826	+	0.623686i
$951$	19.4579			0.630964
$952$			3.84783i			0.124709i
$953$			49.8117i			1.61356i	0.590853	+	0.806779i	$0.298791\pi$
$953$			49.8117i			1.61356i	−0.590853	+	0.806779i	$0.701209\pi$
$954$	−12.7883			−0.414035
$955$	50.5289	−	0.874011i	1.63508	−	0.0282823i
$956$	1.06213			0.0343518
$957$		−	10.5029i		−	0.339511i
$958$		−	16.4631i		−	0.531898i
$959$	82.6147			2.66777
$960$	0.303999	+	17.5749i	0.00981151	+	0.567229i
$961$	3.97722			0.128297
$962$			27.4030i			0.883509i
$963$		−	10.6922i		−	0.344552i
$964$	1.13473			0.0365473
$965$	−0.254699	−	14.7248i	−0.00819904	−	0.474008i
$966$	−11.7472			−0.377959
$967$			12.7604i			0.410348i	0.978726	+	0.205174i	$0.0657760\pi$
$967$			12.7604i			0.410348i	−0.978726	+	0.205174i	$0.934224\pi$
$968$		−	29.8049i		−	0.957966i
$969$	1.66959			0.0536349
$970$	2.94449	−	0.0509316i	0.0945417	−	0.00163531i
$971$	6.51886			0.209200			0.104600	−	0.994514i	$-0.466644\pi$
$971$	6.51886			0.209200			0.104600	+	0.994514i	$0.466644\pi$
$972$			13.5252i			0.433820i
$973$			94.2215i			3.02060i
$974$	−8.43374			−0.270234
$975$	−17.7760	+	0.615137i	−0.569288	+	0.0197002i
$976$	0.710381			0.0227388
$977$		−	21.9764i		−	0.703089i	−0.936171	−	0.351544i	$-0.885657\pi$
$977$		−	21.9764i		−	0.703089i	0.936171	−	0.351544i	$-0.114343\pi$
$978$			6.57108i			0.210120i
$979$	8.36580			0.267372
$980$	29.9158	−	0.517461i	0.955624	−	0.0165297i
$981$	10.1367			0.323640
$982$		−	15.1140i		−	0.482307i
$983$		−	9.07592i		−	0.289477i	−0.989470	−	0.144738i	$-0.953766\pi$
$983$		−	9.07592i		−	0.289477i	0.989470	−	0.144738i	$-0.0462341\pi$
$984$	23.4770			0.748421
$985$	−0.138904	−	8.03039i	−0.00442584	−	0.255870i
$986$	−2.54145			−0.0809362
$987$			54.6414i			1.73925i
$988$			12.5877i			0.400469i
$989$	−5.97354			−0.189947
$990$	−0.0393954	−	2.27755i	−0.00125207	−	0.0723852i
$991$	19.4358			0.617400			0.308700	−	0.951159i	$-0.400106\pi$
$991$	19.4358			0.617400			0.308700	+	0.951159i	$0.400106\pi$
$992$			32.0538i			1.01771i
$993$		−	19.6719i		−	0.624269i
$994$	37.9130			1.20253
$995$	−47.1149	+	0.814960i	−1.49364	+	0.0258360i
$996$	16.1453			0.511583
$997$			35.1276i			1.11250i	0.831015	+	0.556250i	$0.187760\pi$
$997$			35.1276i			1.11250i	−0.831015	+	0.556250i	$0.812240\pi$
$998$		−	29.0568i		−	0.919777i
$999$	61.7746			1.95446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.31	yes	46
5.2	odd	4		6025.2.a.p.1.16		46
5.3	odd	4		6025.2.a.p.1.31		46
5.4	even	2	inner	1205.2.b.c.724.16	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.16	✓	46	5.4	even	2	inner
1205.2.b.c.724.31	yes	46	1.1	even	1	trivial
6025.2.a.p.1.16		46	5.2	odd	4
6025.2.a.p.1.31		46	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.930197i q^{2} +1.32621i q^{3} +1.13473 q^{4} +(-2.23573 + 0.0386721i) q^{5} -1.23364 q^{6} +4.33497i q^{7} +2.91592i q^{8} +1.24116 q^{9} +O(q^{10})\)	\(q+0.930197i q^{2} +1.32621i q^{3} +1.13473 q^{4} +(-2.23573 + 0.0386721i) q^{5} -1.23364 q^{6} +4.33497i q^{7} +2.91592i q^{8} +1.24116 q^{9} +(-0.0359727 - 2.07967i) q^{10} +0.882357 q^{11} +1.50490i q^{12} +2.68232i q^{13} -4.03238 q^{14} +(-0.0512874 - 2.96506i) q^{15} -0.442916 q^{16} -0.304406i q^{17} +1.15452i q^{18} +4.13564 q^{19} +(-2.53696 + 0.0438825i) q^{20} -5.74909 q^{21} +0.820766i q^{22} -2.19664i q^{23} -3.86713 q^{24} +(4.99701 - 0.172921i) q^{25} -2.49509 q^{26} +5.62468i q^{27} +4.91903i q^{28} -8.97537 q^{29} +(2.75809 - 0.0477074i) q^{30} +5.91415 q^{31} +5.41984i q^{32} +1.17019i q^{33} +0.283158 q^{34} +(-0.167642 - 9.69184i) q^{35} +1.40839 q^{36} -10.9828i q^{37} +3.84696i q^{38} -3.55733 q^{39} +(-0.112765 - 6.51922i) q^{40} -6.07092 q^{41} -5.34779i q^{42} -2.71940i q^{43} +1.00124 q^{44} +(-2.77490 + 0.0479983i) q^{45} +2.04331 q^{46} -9.50435i q^{47} -0.587400i q^{48} -11.7920 q^{49} +(0.160851 + 4.64820i) q^{50} +0.403707 q^{51} +3.04372i q^{52} +11.0767i q^{53} -5.23206 q^{54} +(-1.97272 + 0.0341226i) q^{55} -12.6404 q^{56} +5.48474i q^{57} -8.34887i q^{58} +7.93694 q^{59} +(-0.0581975 - 3.36455i) q^{60} -1.60387 q^{61} +5.50133i q^{62} +5.38040i q^{63} -5.92735 q^{64} +(-0.103731 - 5.99696i) q^{65} -1.08851 q^{66} +15.5753i q^{67} -0.345420i q^{68} +2.91321 q^{69} +(9.01532 - 0.155940i) q^{70} -9.40214 q^{71} +3.61913i q^{72} -4.11094i q^{73} +10.2162 q^{74} +(0.229330 + 6.62710i) q^{75} +4.69285 q^{76} +3.82499i q^{77} -3.30902i q^{78} -9.90696 q^{79} +(0.990242 - 0.0171285i) q^{80} -3.73604 q^{81} -5.64716i q^{82} -10.7285i q^{83} -6.52368 q^{84} +(0.0117720 + 0.680571i) q^{85} +2.52958 q^{86} -11.9033i q^{87} +2.57288i q^{88} +9.48120 q^{89} +(-0.0446479 - 2.58121i) q^{90} -11.6278 q^{91} -2.49260i q^{92} +7.84342i q^{93} +8.84092 q^{94} +(-9.24619 + 0.159934i) q^{95} -7.18786 q^{96} +1.41584i q^{97} -10.9689i q^{98} +1.09515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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