LMFDB - Embedded newform 1205.2.b.c.724.13

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			724.13
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45267i q^{2} -2.41257i q^{3} -0.110263 q^{4} +(-1.02000 - 1.98987i) q^{5} -3.50468 q^{6} -1.25057i q^{7} -2.74517i q^{8} -2.82049 q^{9} +O(q^{10})$	\(q-1.45267i q^{2} -2.41257i q^{3} -0.110263 q^{4} +(-1.02000 - 1.98987i) q^{5} -3.50468 q^{6} -1.25057i q^{7} -2.74517i q^{8} -2.82049 q^{9} +(-2.89064 + 1.48173i) q^{10} +2.46616 q^{11} +0.266016i q^{12} -2.06969i q^{13} -1.81667 q^{14} +(-4.80071 + 2.46082i) q^{15} -4.20837 q^{16} -1.42467i q^{17} +4.09725i q^{18} +0.479813 q^{19} +(0.112468 + 0.219409i) q^{20} -3.01709 q^{21} -3.58253i q^{22} +2.87475i q^{23} -6.62292 q^{24} +(-2.91920 + 4.05934i) q^{25} -3.00659 q^{26} -0.433079i q^{27} +0.137891i q^{28} +9.26441 q^{29} +(3.57477 + 6.97387i) q^{30} +0.180654 q^{31} +0.623041i q^{32} -5.94979i q^{33} -2.06958 q^{34} +(-2.48848 + 1.27558i) q^{35} +0.310994 q^{36} +0.824807i q^{37} -0.697012i q^{38} -4.99327 q^{39} +(-5.46255 + 2.80008i) q^{40} +1.12498 q^{41} +4.38285i q^{42} +3.43795i q^{43} -0.271925 q^{44} +(2.87690 + 5.61242i) q^{45} +4.17607 q^{46} -3.00871i q^{47} +10.1530i q^{48} +5.43607 q^{49} +(5.89691 + 4.24064i) q^{50} -3.43711 q^{51} +0.228209i q^{52} +12.3733i q^{53} -0.629123 q^{54} +(-2.51549 - 4.90735i) q^{55} -3.43303 q^{56} -1.15758i q^{57} -13.4582i q^{58} -0.433111 q^{59} +(0.529338 - 0.271336i) q^{60} -3.88745 q^{61} -0.262432i q^{62} +3.52722i q^{63} -7.51166 q^{64} +(-4.11843 + 2.11109i) q^{65} -8.64311 q^{66} +5.24447i q^{67} +0.157087i q^{68} +6.93552 q^{69} +(1.85301 + 3.61495i) q^{70} +14.3247 q^{71} +7.74273i q^{72} +4.35588i q^{73} +1.19818 q^{74} +(9.79345 + 7.04277i) q^{75} -0.0529054 q^{76} -3.08411i q^{77} +7.25360i q^{78} +7.28837 q^{79} +(4.29254 + 8.37412i) q^{80} -9.50630 q^{81} -1.63423i q^{82} +1.09208i q^{83} +0.332672 q^{84} +(-2.83491 + 1.45316i) q^{85} +4.99422 q^{86} -22.3510i q^{87} -6.77004i q^{88} +12.2161 q^{89} +(8.15302 - 4.17920i) q^{90} -2.58830 q^{91} -0.316977i q^{92} -0.435841i q^{93} -4.37068 q^{94} +(-0.489410 - 0.954768i) q^{95} +1.50313 q^{96} -9.80240i q^{97} -7.89684i q^{98} -6.95579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	1.45267i		−	1.02720i	−0.858031	−	0.513598i	$-0.828312\pi$
$2$		−	1.45267i		−	1.02720i	0.858031	−	0.513598i	$-0.171688\pi$
$3$		−	2.41257i		−	1.39290i	−0.717607	−	0.696449i	$-0.754762\pi$
$3$		−	2.41257i		−	1.39290i	0.717607	−	0.696449i	$-0.245238\pi$
$4$	−0.110263			−0.0551313
$5$	−1.02000	−	1.98987i	−0.456158	−	0.889899i
$5$	−1.02000	−	1.98987i	−0.456158	−	0.889899i
$6$	−3.50468			−1.43078
$7$		−	1.25057i		−	0.472671i	−0.971671	−	0.236336i	$-0.924054\pi$
$7$		−	1.25057i		−	0.472671i	0.971671	−	0.236336i	$-0.0759465\pi$
$8$		−	2.74517i		−	0.970565i
$9$	−2.82049			−0.940164
$10$	−2.89064	+	1.48173i	−0.914100	+	0.468564i
$11$	2.46616			0.743576			0.371788	−	0.928318i	$-0.378745\pi$
$11$	2.46616			0.743576			0.371788	+	0.928318i	$0.378745\pi$
$12$			0.266016i			0.0767922i
$13$		−	2.06969i		−	0.574029i	−0.957926	−	0.287015i	$-0.907337\pi$
$13$		−	2.06969i		−	0.574029i	0.957926	−	0.287015i	$-0.0926628\pi$
$14$	−1.81667			−0.485526
$15$	−4.80071	+	2.46082i	−1.23954	+	0.635381i
$16$	−4.20837			−1.05209
$17$		−	1.42467i		−	0.345532i	−0.984963	−	0.172766i	$-0.944729\pi$
$17$		−	1.42467i		−	0.345532i	0.984963	−	0.172766i	$-0.0552705\pi$
$18$			4.09725i			0.965732i
$19$	0.479813			0.110077			0.0550384	−	0.998484i	$-0.482472\pi$
$19$	0.479813			0.110077			0.0550384	+	0.998484i	$0.482472\pi$
$20$	0.112468	+	0.219409i	0.0251486	+	0.0490612i
$21$	−3.01709			−0.658383
$22$		−	3.58253i		−	0.763798i
$23$			2.87475i			0.599426i	0.954029	+	0.299713i	$0.0968909\pi$
$23$			2.87475i			0.599426i	−0.954029	+	0.299713i	$0.903109\pi$
$24$	−6.62292			−1.35190
$25$	−2.91920	+	4.05934i	−0.583840	+	0.811869i
$26$	−3.00659			−0.589640
$27$		−	0.433079i		−	0.0833461i
$28$			0.137891i			0.0260590i
$29$	9.26441			1.72036			0.860179	−	0.509992i	$-0.170352\pi$
$29$	9.26441			1.72036			0.860179	+	0.509992i	$0.170352\pi$
$30$	3.57477	+	6.97387i	0.652661	+	1.27325i
$31$	0.180654			0.0324465			0.0162232	−	0.999868i	$-0.494836\pi$
$31$	0.180654			0.0324465			0.0162232	+	0.999868i	$0.494836\pi$
$32$			0.623041i			0.110139i
$33$		−	5.94979i		−	1.03573i
$34$	−2.06958			−0.354929
$35$	−2.48848	+	1.27558i	−0.420630	+	0.215613i
$36$	0.310994			0.0518324
$37$			0.824807i			0.135597i	0.997699	+	0.0677987i	$0.0215976\pi$
$37$			0.824807i			0.135597i	−0.997699	+	0.0677987i	$0.978402\pi$
$38$		−	0.697012i		−	0.113070i
$39$	−4.99327			−0.799564
$40$	−5.46255	+	2.80008i	−0.863705	+	0.442731i
$41$	1.12498			0.175693			0.0878464	−	0.996134i	$-0.472002\pi$
$41$	1.12498			0.175693			0.0878464	+	0.996134i	$0.472002\pi$
$42$			4.38285i			0.676288i
$43$			3.43795i			0.524282i	0.965030	+	0.262141i	$0.0844286\pi$
$43$			3.43795i			0.524282i	−0.965030	+	0.262141i	$0.915571\pi$
$44$	−0.271925			−0.0409943
$45$	2.87690	+	5.61242i	0.428863	+	0.836650i
$46$	4.17607			0.615728
$47$		−	3.00871i		−	0.438866i	−0.975628	−	0.219433i	$-0.929579\pi$
$47$		−	3.00871i		−	0.438866i	0.975628	−	0.219433i	$-0.0704208\pi$
$48$			10.1530i			1.46546i
$49$	5.43607			0.776582
$50$	5.89691	+	4.24064i	0.833948	+	0.599718i
$51$	−3.43711			−0.481291
$52$			0.228209i			0.0316470i
$53$			12.3733i			1.69961i	0.527099	+	0.849804i	$0.323280\pi$
$53$			12.3733i			1.69961i	−0.527099	+	0.849804i	$0.676720\pi$
$54$	−0.629123			−0.0856128
$55$	−2.51549	−	4.90735i	−0.339188	−	0.661707i
$56$	−3.43303			−0.458758
$57$		−	1.15758i		−	0.153326i
$58$		−	13.4582i		−	1.76714i
$59$	−0.433111			−0.0563863			−0.0281931	−	0.999602i	$-0.508975\pi$
$59$	−0.433111			−0.0563863			−0.0281931	+	0.999602i	$0.508975\pi$
$60$	0.529338	−	0.271336i	0.0683373	−	0.0350294i
$61$	−3.88745			−0.497737			−0.248868	−	0.968537i	$-0.580059\pi$
$61$	−3.88745			−0.497737			−0.248868	+	0.968537i	$0.580059\pi$
$62$		−	0.262432i		−	0.0333289i
$63$			3.52722i			0.444388i
$64$	−7.51166			−0.938957
$65$	−4.11843	+	2.11109i	−0.510828	+	0.261848i
$66$	−8.64311			−1.06389
$67$			5.24447i			0.640714i	0.947297	+	0.320357i	$0.103803\pi$
$67$			5.24447i			0.640714i	−0.947297	+	0.320357i	$0.896197\pi$
$68$			0.157087i			0.0190496i
$69$	6.93552			0.834939
$70$	1.85301	+	3.61495i	0.221477	+	0.432069i
$71$	14.3247			1.70003			0.850013	−	0.526762i	$-0.176594\pi$
$71$	14.3247			1.70003			0.850013	+	0.526762i	$0.176594\pi$
$72$			7.74273i			0.912490i
$73$			4.35588i			0.509818i	0.966965	+	0.254909i	$0.0820455\pi$
$73$			4.35588i			0.509818i	−0.966965	+	0.254909i	$0.917955\pi$
$74$	1.19818			0.139285
$75$	9.79345	+	7.04277i	1.13085	+	0.813229i
$76$	−0.0529054			−0.00606867
$77$		−	3.08411i		−	0.351467i
$78$			7.25360i			0.821309i
$79$	7.28837			0.820005			0.410003	−	0.912084i	$-0.365528\pi$
$79$	7.28837			0.820005			0.410003	+	0.912084i	$0.365528\pi$
$80$	4.29254	+	8.37412i	0.479920	+	0.936255i
$81$	−9.50630			−1.05626
$82$		−	1.63423i		−	0.180471i
$83$			1.09208i			0.119871i	0.998202	+	0.0599357i	$0.0190896\pi$
$83$			1.09208i			0.119871i	−0.998202	+	0.0599357i	$0.980910\pi$
$84$	0.332672			0.0362975
$85$	−2.83491	+	1.45316i	−0.307489	+	0.157617i
$86$	4.99422			0.538541
$87$		−	22.3510i		−	2.39628i
$88$		−	6.77004i		−	0.721689i
$89$	12.2161			1.29490			0.647452	−	0.762106i	$-0.275834\pi$
$89$	12.2161			1.29490			0.647452	+	0.762106i	$0.275834\pi$
$90$	8.15302	−	4.17920i	0.859404	−	0.440526i
$91$	−2.58830			−0.271327
$92$		−	0.316977i		−	0.0330471i
$93$		−	0.435841i		−	0.0451946i
$94$	−4.37068			−0.450801
$95$	−0.489410	−	0.954768i	−0.0502124	−	0.0979571i
$96$	1.50313			0.153412
$97$		−	9.80240i		−	0.995283i	−0.867383	−	0.497642i	$-0.834199\pi$
$97$		−	9.80240i		−	0.995283i	0.867383	−	0.497642i	$-0.165801\pi$
$98$		−	7.89684i		−	0.797702i
$99$	−6.95579			−0.699083
$100$	0.321878	−	0.447594i	0.0321878	−	0.0447594i
$101$	−10.5462			−1.04939			−0.524695	−	0.851291i	$-0.675820\pi$
$101$	−10.5462			−1.04939			−0.524695	+	0.851291i	$0.675820\pi$
$102$			4.99300i			0.494380i
$103$		−	7.56058i		−	0.744966i	−0.928039	−	0.372483i	$-0.878506\pi$
$103$		−	7.56058i		−	0.744966i	0.928039	−	0.372483i	$-0.121494\pi$
$104$	−5.68166			−0.557133
$105$	3.07743	+	6.00363i	0.300326	+	0.585894i
$106$	17.9744			1.74583
$107$			4.30799i			0.416469i	0.978079	+	0.208234i	$0.0667717\pi$
$107$			4.30799i			0.416469i	−0.978079	+	0.208234i	$0.933228\pi$
$108$			0.0477524i			0.00459498i
$109$	3.03421			0.290625			0.145313	−	0.989386i	$-0.453581\pi$
$109$	3.03421			0.290625			0.145313	+	0.989386i	$0.453581\pi$
$110$	−7.12879	+	3.65418i	−0.679703	+	0.348413i
$111$	1.98990			0.188873
$112$			5.26286i			0.497294i
$113$		−	5.48438i		−	0.515927i	−0.966155	−	0.257964i	$-0.916949\pi$
$113$		−	5.48438i		−	0.515927i	0.966155	−	0.257964i	$-0.0830515\pi$
$114$	−1.68159			−0.157495
$115$	5.72038	−	2.93224i	0.533428	−	0.273433i
$116$	−1.02152			−0.0948455
$117$			5.83755i			0.539681i
$118$			0.629169i			0.0579197i
$119$	−1.78165			−0.163323
$120$	6.75538	+	13.1788i	0.616679	+	1.20305i
$121$	−4.91804			−0.447095
$122$			5.64720i			0.511273i
$123$		−	2.71410i		−	0.244722i
$124$	−0.0199194			−0.00178882
$125$	11.0552	+	1.66830i	0.988804	+	0.149218i
$126$	5.12390			0.456474
$127$			1.82445i			0.161894i	0.996718	+	0.0809471i	$0.0257945\pi$
$127$			1.82445i			0.161894i	−0.996718	+	0.0809471i	$0.974206\pi$
$128$			12.1581i			1.07463i
$129$	8.29429			0.730271
$130$	3.06672	+	5.98273i	0.268969	+	0.524720i
$131$	10.7564			0.939789			0.469895	−	0.882722i	$-0.344292\pi$
$131$	10.7564			0.939789			0.469895	+	0.882722i	$0.344292\pi$
$132$			0.656039i			0.0571009i
$133$		−	0.600040i		−	0.0520301i
$134$	7.61851			0.658139
$135$	−0.861773	+	0.441741i	−0.0741696	+	0.0380190i
$136$	−3.91096			−0.335362
$137$			18.0907i			1.54560i	0.634653	+	0.772798i	$0.281143\pi$
$137$			18.0907i			1.54560i	−0.634653	+	0.772798i	$0.718857\pi$
$138$		−	10.0751i		−	0.857646i
$139$	−9.24847			−0.784445			−0.392222	−	0.919870i	$-0.628294\pi$
$139$	−9.24847			−0.784445			−0.392222	+	0.919870i	$0.628294\pi$
$140$	0.274386	−	0.140649i	0.0231898	−	0.0118870i
$141$	−7.25873			−0.611296
$142$		−	20.8091i		−	1.74626i
$143$		−	5.10420i		−	0.426834i
$144$	11.8697			0.989138
$145$	−9.44970	−	18.4350i	−0.784755	−	1.53094i
$146$	6.32768			0.523683
$147$		−	13.1149i		−	1.08170i
$148$		−	0.0909453i		−	0.00747566i
$149$	−17.0170			−1.39408			−0.697042	−	0.717030i	$-0.745501\pi$
$149$	−17.0170			−1.39408			−0.697042	+	0.717030i	$0.745501\pi$
$150$	10.2308	−	14.2267i	0.835345	−	1.16160i
$151$	−9.18436			−0.747413			−0.373706	−	0.927547i	$-0.621913\pi$
$151$	−9.18436			−0.747413			−0.373706	+	0.927547i	$0.621913\pi$
$152$		−	1.31717i		−	0.106837i
$153$			4.01826i			0.324857i
$154$	−4.48021			−0.361025
$155$	−0.184268	−	0.359479i	−0.0148007	−	0.0288741i
$156$	0.550571			0.0440810
$157$			0.176439i			0.0140814i	0.999975	+	0.00704069i	$0.00224114\pi$
$157$			0.176439i			0.0140814i	−0.999975	+	0.00704069i	$0.997759\pi$
$158$		−	10.5876i		−	0.842306i
$159$	29.8515			2.36738
$160$	1.23977	−	0.635502i	0.0980127	−	0.0502408i
$161$	3.59507			0.283331
$162$			13.8096i			1.08498i
$163$		−	9.16744i		−	0.718050i	−0.933328	−	0.359025i	$-0.883109\pi$
$163$		−	9.16744i		−	0.718050i	0.933328	−	0.359025i	$-0.116891\pi$
$164$	−0.124043			−0.00968616
$165$	−11.8393	+	6.06879i	−0.921691	+	0.472454i
$166$	1.58644			0.123131
$167$			22.5003i			1.74112i	0.492058	+	0.870562i	$0.336245\pi$
$167$			22.5003i			1.74112i	−0.492058	+	0.870562i	$0.663755\pi$
$168$			8.28243i			0.639003i
$169$	8.71638			0.670491
$170$	2.11097	+	4.11820i	0.161904	+	0.315851i
$171$	−1.35331			−0.103490
$172$		−	0.379077i		−	0.0289043i
$173$			5.08571i			0.386659i	0.981134	+	0.193330i	$0.0619287\pi$
$173$			5.08571i			0.386659i	−0.981134	+	0.193330i	$0.938071\pi$
$174$	−32.4688			−2.46145
$175$	5.07650	+	3.65066i	0.383747	+	0.275964i
$176$	−10.3785			−0.782310
$177$			1.04491i			0.0785403i
$178$		−	17.7460i		−	1.33012i
$179$	15.3122			1.14449			0.572244	−	0.820084i	$-0.306073\pi$
$179$	15.3122			1.14449			0.572244	+	0.820084i	$0.306073\pi$
$180$	−0.317214	−	0.618840i	−0.0236438	−	0.0461256i
$181$	−18.4259			−1.36958			−0.684792	−	0.728738i	$-0.740107\pi$
$181$	−18.4259			−1.36958			−0.684792	+	0.728738i	$0.740107\pi$
$182$			3.75995i			0.278706i
$183$			9.37874i			0.693297i
$184$	7.89167			0.581782
$185$	1.64126	−	0.841303i	0.120668	−	0.0618538i
$186$	−0.633135			−0.0464237
$187$		−	3.51346i		−	0.256930i
$188$			0.331749i			0.0241952i
$189$	−0.541596			−0.0393953
$190$	−1.38697	+	0.710953i	−0.100621	+	0.0515779i
$191$	−13.7148			−0.992368			−0.496184	−	0.868217i	$-0.665266\pi$
$191$	−13.7148			−0.992368			−0.496184	+	0.868217i	$0.665266\pi$
$192$			18.1224i			1.30787i
$193$		−	12.4066i		−	0.893047i	−0.894772	−	0.446524i	$-0.852662\pi$
$193$		−	12.4066i		−	0.893047i	0.894772	−	0.446524i	$-0.147338\pi$
$194$	−14.2397			−1.02235
$195$	5.09314	+	9.93599i	0.364727	+	0.711531i
$196$	−0.599395			−0.0428139
$197$		−	7.72970i		−	0.550718i	−0.961341	−	0.275359i	$-0.911203\pi$
$197$		−	7.72970i		−	0.550718i	0.961341	−	0.275359i	$-0.0887968\pi$
$198$			10.1045i			0.718095i
$199$	5.15173			0.365196			0.182598	−	0.983188i	$-0.441549\pi$
$199$	5.15173			0.365196			0.182598	+	0.983188i	$0.441549\pi$
$200$	11.1436	+	8.01370i	0.787972	+	0.566654i
$201$	12.6526			0.892449
$202$			15.3202i			1.07793i
$203$		−	11.5858i		−	0.813164i
$204$	0.378984			0.0265342
$205$	−1.14748	−	2.23857i	−0.0801436	−	0.156349i
$206$	−10.9831			−0.765226
$207$		−	8.10819i		−	0.563558i
$208$			8.71002i			0.603931i
$209$	1.18330			0.0818504
$210$	8.72131	−	4.47050i	0.601828	−	0.308494i
$211$	−20.6216			−1.41965			−0.709823	−	0.704380i	$-0.751225\pi$
$211$	−20.6216			−1.41965			−0.709823	+	0.704380i	$0.751225\pi$
$212$		−	1.36431i		−	0.0937015i
$213$		−	34.5593i		−	2.36796i
$214$	6.25810			0.427795
$215$	6.84109	−	3.50671i	0.466558	−	0.239156i
$216$	−1.18888			−0.0808928
$217$		−	0.225921i		−	0.0153365i
$218$		−	4.40772i		−	0.298529i
$219$	10.5089			0.710124
$220$	0.277364	+	0.541097i	0.0186999	+	0.0364808i
$221$	−2.94862			−0.198346
$222$		−	2.89068i		−	0.194010i
$223$		−	0.789803i		−	0.0528891i	−0.999650	−	0.0264446i	$-0.991581\pi$
$223$		−	0.789803i		−	0.0528891i	0.999650	−	0.0264446i	$-0.00841855\pi$
$224$	0.779156			0.0520596
$225$	8.23357	−	11.4493i	0.548905	−	0.763290i
$226$	−7.96702			−0.529958
$227$			1.06248i			0.0705190i	0.999378	+	0.0352595i	$0.0112258\pi$
$227$			1.06248i			0.0705190i	−0.999378	+	0.0352595i	$0.988774\pi$
$228$			0.127638i			0.00845303i
$229$	−18.7377			−1.23822			−0.619110	−	0.785304i	$-0.712507\pi$
$229$	−18.7377			−1.23822			−0.619110	+	0.785304i	$0.712507\pi$
$230$	−4.25959	−	8.30985i	−0.280869	−	0.547935i
$231$	−7.44063			−0.489558
$232$		−	25.4324i		−	1.66972i
$233$		−	20.6141i		−	1.35047i	−0.737601	−	0.675237i	$-0.764041\pi$
$233$		−	20.6141i		−	1.35047i	0.737601	−	0.675237i	$-0.235959\pi$
$234$	8.48005			0.554358
$235$	−5.98696	+	3.06889i	−0.390546	+	0.200192i
$236$	0.0477559			0.00310865
$237$		−	17.5837i		−	1.14218i
$238$			2.58815i			0.167765i
$239$	17.2630			1.11665			0.558324	−	0.829623i	$-0.311445\pi$
$239$	17.2630			1.11665			0.558324	+	0.829623i	$0.311445\pi$
$240$	20.2031	−	10.3560i	1.30411	−	0.668480i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$			7.14431i			0.459254i
$243$			21.6354i			1.38791i
$244$	0.428640			0.0274409
$245$	−5.54480	−	10.8171i	−0.354244	−	0.691079i
$246$	−3.94270			−0.251377
$247$		−	0.993065i		−	0.0631872i
$248$		−	0.495927i		−	0.0314914i
$249$	2.63472			0.166969
$250$	2.42350	−	16.0596i	0.153276	−	1.01570i
$251$	−21.5943			−1.36302			−0.681510	−	0.731809i	$-0.738677\pi$
$251$	−21.5943			−1.36302			−0.681510	+	0.731809i	$0.738677\pi$
$252$		−	0.388920i		−	0.0244997i
$253$			7.08959i			0.445719i
$254$	2.65034			0.166297
$255$	3.50585	+	6.83941i	0.219545	+	0.428301i
$256$	2.63841			0.164900
$257$		−	22.2276i		−	1.38652i	−0.720687	−	0.693261i	$-0.756173\pi$
$257$		−	22.2276i		−	1.38652i	0.720687	−	0.693261i	$-0.243827\pi$
$258$		−	12.0489i		−	0.750132i
$259$	1.03148			0.0640930
$260$	0.454108	−	0.232774i	0.0281626	−	0.0144360i
$261$	−26.1302			−1.61742
$262$		−	15.6255i		−	0.965348i
$263$			3.89765i			0.240339i	0.992753	+	0.120170i	$0.0383438\pi$
$263$			3.89765i			0.240339i	−0.992753	+	0.120170i	$0.961656\pi$
$264$	−16.3332			−1.00524
$265$	24.6214	−	12.6208i	1.51248	−	0.775290i
$266$	−0.871663			−0.0534451
$267$		−	29.4722i		−	1.80367i
$268$		−	0.578268i		−	0.0353234i
$269$	−6.60591			−0.402769			−0.201385	−	0.979512i	$-0.564544\pi$
$269$	−6.60591			−0.402769			−0.201385	+	0.979512i	$0.564544\pi$
$270$	0.641706	+	1.25188i	0.0390530	+	0.0761867i
$271$	−16.8832			−1.02558			−0.512791	−	0.858513i	$-0.671388\pi$
$271$	−16.8832			−1.02558			−0.512791	+	0.858513i	$0.671388\pi$
$272$			5.99552i			0.363532i
$273$			6.24444i			0.377931i
$274$	26.2799			1.58763
$275$	−7.19922	+	10.0110i	−0.434129	+	0.603686i
$276$	−0.764728			−0.0460312
$277$		−	27.0001i		−	1.62228i	−0.584852	−	0.811140i	$-0.698847\pi$
$277$		−	27.0001i		−	1.62228i	0.584852	−	0.811140i	$-0.301153\pi$
$278$			13.4350i			0.805778i
$279$	−0.509534			−0.0305050
$280$	3.50169	+	6.83130i	0.209266	+	0.408248i
$281$	−9.48720			−0.565959			−0.282979	−	0.959126i	$-0.591323\pi$
$281$	−9.48720			−0.565959			−0.282979	+	0.959126i	$0.591323\pi$
$282$			10.5446i			0.627920i
$283$		−	13.7557i		−	0.817690i	−0.912604	−	0.408845i	$-0.865932\pi$
$283$		−	13.7557i		−	0.817690i	0.912604	−	0.408845i	$-0.134068\pi$
$284$	−1.57947			−0.0937246
$285$	−2.30344	+	1.18073i	−0.136444	+	0.0699407i
$286$	−7.41474			−0.438442
$287$		−	1.40687i		−	0.0830449i
$288$		−	1.75728i		−	0.103549i
$289$	14.9703			0.880607
$290$	−26.7801	+	13.7273i	−1.57258	+	0.806097i
$291$	−23.6490			−1.38633
$292$		−	0.480291i		−	0.0281069i
$293$			11.4782i			0.670561i	0.942118	+	0.335280i	$0.108831\pi$
$293$			11.4782i			0.670561i	−0.942118	+	0.335280i	$0.891169\pi$
$294$	−19.0517			−1.11112
$295$	0.441774	+	0.861837i	0.0257211	+	0.0501781i
$296$	2.26424			0.131606
$297$		−	1.06804i		−	0.0619742i
$298$			24.7201i			1.43200i
$299$	5.94984			0.344088
$300$	−1.07985	−	0.776554i	−0.0623452	−	0.0448343i
$301$	4.29940			0.247813
$302$			13.3419i			0.767739i
$303$			25.4435i			1.46169i
$304$	−2.01923			−0.115811
$305$	3.96520	+	7.73554i	0.227047	+	0.442936i
$306$	5.83722			0.333692
$307$			11.8355i			0.675485i	0.941238	+	0.337743i	$0.109663\pi$
$307$			11.8355i			0.675485i	−0.941238	+	0.337743i	$0.890337\pi$
$308$			0.340062i			0.0193768i
$309$	−18.2404			−1.03766
$310$	−0.522207	+	0.267681i	−0.0296593	+	0.0152032i
$311$	−5.53844			−0.314056			−0.157028	−	0.987594i	$-0.550191\pi$
$311$	−5.53844			−0.314056			−0.157028	+	0.987594i	$0.550191\pi$
$312$			13.7074i			0.776029i
$313$		−	24.8522i		−	1.40473i	−0.711817	−	0.702365i	$-0.752127\pi$
$313$		−	24.8522i		−	1.40473i	0.711817	−	0.702365i	$-0.247873\pi$
$314$	0.256309			0.0144643
$315$	7.01873	−	3.59777i	0.395461	−	0.202711i
$316$	−0.803634			−0.0452079
$317$		−	15.8127i		−	0.888130i	−0.895994	−	0.444065i	$-0.853536\pi$
$317$		−	15.8127i		−	0.888130i	0.895994	−	0.444065i	$-0.146464\pi$
$318$		−	43.3645i		−	2.43176i
$319$	22.8475			1.27922
$320$	7.66190	+	14.9473i	0.428313	+	0.835577i
$321$	10.3933			0.580098
$322$		−	5.22247i		−	0.291037i
$323$		−	0.683574i		−	0.0380351i
$324$	1.04819			0.0582327
$325$	8.40159	+	6.04184i	0.466036	+	0.335141i
$326$	−13.3173			−0.737578
$327$		−	7.32025i		−	0.404811i
$328$		−	3.08827i		−	0.170521i
$329$	−3.76261			−0.207439
$330$	8.81597	+	17.1987i	0.485303	+	0.946757i
$331$	23.4865			1.29093			0.645467	−	0.763789i	$-0.276663\pi$
$331$	23.4865			1.29093			0.645467	+	0.763789i	$0.276663\pi$
$332$		−	0.120416i		−	0.00660866i
$333$		−	2.32636i		−	0.127484i
$334$	32.6856			1.78848
$335$	10.4358	−	5.34936i	0.570171	−	0.292267i
$336$	12.6970			0.692679
$337$			11.1318i			0.606385i	0.952929	+	0.303193i	$0.0980525\pi$
$337$			11.1318i			0.606385i	−0.952929	+	0.303193i	$0.901947\pi$
$338$		−	12.6621i		−	0.688725i
$339$	−13.2315			−0.718634
$340$	0.312584	−	0.160229i	0.0169523	−	0.00868965i
$341$	0.445523			0.0241264
$342$			1.96592i			0.106305i
$343$		−	15.5522i		−	0.839739i
$344$	9.43776			0.508850
$345$	−7.07424	−	13.8008i	−0.380864	−	0.743011i
$346$	7.38788			0.397175
$347$			4.44891i			0.238830i	0.992844	+	0.119415i	$0.0381019\pi$
$347$			4.44891i			0.238830i	−0.992844	+	0.119415i	$0.961898\pi$
$348$			2.46448i			0.132110i
$349$	−0.902138			−0.0482903			−0.0241452	−	0.999708i	$-0.507686\pi$
$349$	−0.902138			−0.0482903			−0.0241452	+	0.999708i	$0.507686\pi$
$350$	5.30322	−	7.37450i	0.283469	−	0.394183i
$351$	−0.896340			−0.0478431
$352$			1.53652i			0.0818968i
$353$			0.455388i			0.0242379i	0.999927	+	0.0121189i	$0.00385767\pi$
$353$			0.455388i			0.0242379i	−0.999927	+	0.0121189i	$0.996142\pi$
$354$	1.51791			0.0806763
$355$	−14.6112	−	28.5043i	−0.775481	−	1.51285i
$356$	−1.34698			−0.0713897
$357$			4.29834i			0.227493i
$358$		−	22.2436i		−	1.17561i
$359$	8.65154			0.456611			0.228305	−	0.973590i	$-0.426682\pi$
$359$	8.65154			0.456611			0.228305	+	0.973590i	$0.426682\pi$
$360$	15.4071	−	7.89759i	0.812024	−	0.416240i
$361$	−18.7698			−0.987883
$362$			26.7668i			1.40683i
$363$			11.8651i			0.622757i
$364$	0.285392			0.0149586
$365$	8.66766	−	4.44300i	0.453686	−	0.232557i
$366$	13.6243			0.712151
$367$			23.7645i			1.24050i	0.784405	+	0.620249i	$0.212969\pi$
$367$			23.7645i			1.24050i	−0.784405	+	0.620249i	$0.787031\pi$
$368$		−	12.0980i		−	0.630651i
$369$	−3.17300			−0.165180
$370$	−1.22214	−	2.38422i	−0.0635360	−	0.123950i
$371$	15.4737			0.803355
$372$			0.0480570i			0.00249164i
$373$			7.72073i			0.399764i	0.979820	+	0.199882i	$0.0640560\pi$
$373$			7.72073i			0.399764i	−0.979820	+	0.199882i	$0.935944\pi$
$374$	−5.10391			−0.263917
$375$	4.02490	−	26.6714i	0.207845	−	1.37730i
$376$	−8.25944			−0.425948
$377$		−	19.1745i		−	0.987536i
$378$			0.786762i			0.0404667i
$379$	−27.7660			−1.42624			−0.713122	−	0.701040i	$-0.752719\pi$
$379$	−27.7660			−1.42624			−0.713122	+	0.701040i	$0.752719\pi$
$380$	0.0539636	+	0.105275i	0.00276827	+	0.00540050i
$381$	4.40162			0.225502
$382$			19.9231i			1.01936i
$383$			2.17131i			0.110949i	0.998460	+	0.0554744i	$0.0176671\pi$
$383$			2.17131i			0.110949i	−0.998460	+	0.0554744i	$0.982333\pi$
$384$	29.3322			1.49685
$385$	−6.13699	+	3.14579i	−0.312770	+	0.160325i
$386$	−18.0228			−0.917334
$387$		−	9.69670i		−	0.492911i
$388$			1.08084i			0.0548712i
$389$	16.3022			0.826556			0.413278	−	0.910605i	$-0.364384\pi$
$389$	16.3022			0.826556			0.413278	+	0.910605i	$0.364384\pi$
$390$	14.4338	−	7.39868i	0.730882	−	0.374647i
$391$	4.09555			0.207121
$392$		−	14.9230i		−	0.753723i
$393$		−	25.9505i		−	1.30903i
$394$	−11.2287			−0.565696
$395$	−7.43414	−	14.5029i	−0.374052	−	0.729722i
$396$	0.766963			0.0385413
$397$			4.91814i			0.246835i	0.992355	+	0.123417i	$0.0393854\pi$
$397$			4.91814i			0.246835i	−0.992355	+	0.123417i	$0.960615\pi$
$398$		−	7.48378i		−	0.375128i
$399$	−1.44764			−0.0724726
$400$	12.2851	−	17.0832i	0.614253	−	0.854161i
$401$	2.97380			0.148504			0.0742522	−	0.997239i	$-0.476343\pi$
$401$	2.97380			0.148504			0.0742522	+	0.997239i	$0.476343\pi$
$402$		−	18.3802i		−	0.916720i
$403$		−	0.373899i		−	0.0186252i
$404$	1.16285			0.0578542
$405$	9.69643	+	18.9164i	0.481820	+	0.939961i
$406$	−16.8304			−0.835278
$407$			2.03411i			0.100827i
$408$			9.43545i			0.467125i
$409$	24.3914			1.20608			0.603039	−	0.797712i	$-0.293956\pi$
$409$	24.3914			1.20608			0.603039	+	0.797712i	$0.293956\pi$
$410$	−3.25192	+	1.66692i	−0.160601	+	0.0823232i
$411$	43.6451			2.15286
$412$			0.833649i			0.0410709i
$413$			0.541636i			0.0266522i
$414$	−11.7786			−0.578885
$415$	2.17310	−	1.11392i	0.106673	−	0.0546803i
$416$	1.28950			0.0632231
$417$			22.3126i			1.09265i
$418$		−	1.71895i		−	0.0840764i
$419$	29.8864			1.46005			0.730023	−	0.683422i	$-0.239509\pi$
$419$	29.8864			1.46005			0.730023	+	0.683422i	$0.239509\pi$
$420$	−0.339325	−	0.661975i	−0.0165574	−	0.0323011i
$421$	−5.05042			−0.246142			−0.123071	−	0.992398i	$-0.539274\pi$
$421$	−5.05042			−0.246142			−0.123071	+	0.992398i	$0.539274\pi$
$422$			29.9564i			1.45825i
$423$			8.48605i			0.412606i
$424$	33.9669			1.64958
$425$	5.78321	+	4.15889i	0.280527	+	0.201736i
$426$	−50.2034			−2.43236
$427$			4.86153i			0.235266i
$428$		−	0.475010i		−	0.0229605i
$429$	−12.3142			−0.594537
$430$	−5.09411	−	9.93787i	−0.245660	−	0.479247i
$431$	10.0234			0.482808			0.241404	−	0.970425i	$-0.422392\pi$
$431$	10.0234			0.482808			0.241404	+	0.970425i	$0.422392\pi$
$432$			1.82256i			0.0876878i
$433$			26.9755i			1.29636i	0.761488	+	0.648179i	$0.224469\pi$
$433$			26.9755i			1.29636i	−0.761488	+	0.648179i	$0.775531\pi$
$434$	−0.328190			−0.0157536
$435$	−44.4757	+	22.7981i	−2.13245	+	1.09308i
$436$	−0.334560			−0.0160225
$437$			1.37934i			0.0659828i
$438$		−	15.2660i		−	0.729436i
$439$	−24.6330			−1.17567			−0.587835	−	0.808981i	$-0.700020\pi$
$439$	−24.6330			−1.17567			−0.587835	+	0.808981i	$0.700020\pi$
$440$	−13.4715	+	6.90545i	−0.642230	+	0.329204i
$441$	−15.3324			−0.730114
$442$			4.28339i			0.203740i
$443$			10.5621i			0.501819i	0.968010	+	0.250910i	$0.0807297\pi$
$443$			10.5621i			0.501819i	−0.968010	+	0.250910i	$0.919270\pi$
$444$	−0.219412			−0.0104128
$445$	−12.4604	−	24.3085i	−0.590681	−	1.15233i
$446$	−1.14733			−0.0543275
$447$			41.0546i			1.94182i
$448$			9.39386i			0.443818i
$449$	5.95137			0.280863			0.140431	−	0.990090i	$-0.455151\pi$
$449$	5.95137			0.280863			0.140431	+	0.990090i	$0.455151\pi$
$450$	−16.6322	−	11.9607i	−0.784048	−	0.563833i
$451$	2.77439			0.130641
$452$			0.604722i			0.0284437i
$453$			22.1579i			1.04107i
$454$	1.54343			0.0724369
$455$	2.64006	+	5.15038i	0.123768	+	0.241454i
$456$	−3.17776			−0.148812
$457$			8.98781i			0.420432i	0.977655	+	0.210216i	$0.0674168\pi$
$457$			8.98781i			0.420432i	−0.977655	+	0.210216i	$0.932583\pi$
$458$			27.2197i			1.27190i
$459$	−0.616993			−0.0287988
$460$	−0.630744	+	0.323316i	−0.0294086	+	0.0150747i
$461$	17.2131			0.801693			0.400846	−	0.916145i	$-0.368716\pi$
$461$	17.2131			0.801693			0.400846	+	0.916145i	$0.368716\pi$
$462$			10.8088i			0.502871i
$463$			17.5090i			0.813711i	0.913492	+	0.406856i	$0.133375\pi$
$463$			17.5090i			0.813711i	−0.913492	+	0.406856i	$0.866625\pi$
$464$	−38.9880			−1.80997
$465$	−0.867269	+	0.444558i	−0.0402186	+	0.0206159i
$466$	−29.9456			−1.38720
$467$		−	4.34976i		−	0.201283i	−0.994923	−	0.100641i	$-0.967911\pi$
$467$		−	4.34976i		−	0.201283i	0.994923	−	0.100641i	$-0.0320895\pi$
$468$		−	0.643663i		−	0.0297533i
$469$	6.55858			0.302847
$470$	4.45810	+	8.69711i	0.205637	+	0.401168i
$471$	0.425672			0.0196139
$472$			1.18897i			0.0547266i
$473$			8.47854i			0.389844i
$474$	−25.5434			−1.17325
$475$	−1.40067	+	1.94773i	−0.0642671	+	0.0893679i
$476$	0.196449			0.00900422
$477$		−	34.8989i		−	1.59791i
$478$		−	25.0775i		−	1.14702i
$479$	28.5754			1.30565			0.652823	−	0.757511i	$-0.273585\pi$
$479$	28.5754			1.30565			0.652823	+	0.757511i	$0.273585\pi$
$480$	−1.53319	−	2.99104i	−0.0699803	−	0.136522i
$481$	1.70710			0.0778369
$482$		−	1.45267i		−	0.0661675i
$483$		−	8.67336i		−	0.394652i
$484$	0.542276			0.0246489
$485$	−19.5055	+	9.99845i	−0.885701	+	0.454006i
$486$	31.4292			1.42566
$487$			15.6356i			0.708516i	0.935148	+	0.354258i	$0.115266\pi$
$487$			15.6356i			0.708516i	−0.935148	+	0.354258i	$0.884734\pi$
$488$			10.6717i			0.483086i
$489$	−22.1171			−1.00017
$490$	−15.7137	+	8.05478i	−0.709874	+	0.363878i
$491$	−15.4298			−0.696338			−0.348169	−	0.937432i	$-0.613196\pi$
$491$	−15.4298			−0.696338			−0.348169	+	0.937432i	$0.613196\pi$
$492$			0.299263i			0.0134918i
$493$		−	13.1987i		−	0.594439i
$494$	−1.44260			−0.0649057
$495$	7.09491	+	13.8411i	0.318892	+	0.622113i
$496$	−0.760260			−0.0341367
$497$		−	17.9140i		−	0.803553i
$498$		−	3.82739i		−	0.171509i
$499$	−1.64702			−0.0737308			−0.0368654	−	0.999320i	$-0.511737\pi$
$499$	−1.64702			−0.0737308			−0.0368654	+	0.999320i	$0.511737\pi$
$500$	−1.21897	−	0.183951i	−0.0545140	−	0.00822656i
$501$	54.2835			2.42521
$502$			31.3695i			1.40009i
$503$			39.2147i			1.74850i	0.485477	+	0.874249i	$0.338646\pi$
$503$			39.2147i			1.74850i	−0.485477	+	0.874249i	$0.661354\pi$
$504$	9.68283			0.431308
$505$	10.7572	+	20.9857i	0.478687	+	0.933850i
$506$	10.2989			0.457840
$507$		−	21.0289i		−	0.933925i
$508$		−	0.201169i		−	0.00892543i
$509$	1.68682			0.0747669			0.0373835	−	0.999301i	$-0.488098\pi$
$509$	1.68682			0.0747669			0.0373835	+	0.999301i	$0.488098\pi$
$510$	9.93544	−	5.09286i	0.439949	−	0.225516i
$511$	5.44734			0.240976
$512$			20.4834i			0.905247i
$513$		−	0.207797i		−	0.00917447i
$514$	−32.2895			−1.42423
$515$	−15.0446	+	7.71180i	−0.662945	+	0.339822i
$516$	−0.914549			−0.0402608
$517$		−	7.41998i		−	0.326330i
$518$		−	1.49840i		−	0.0658360i
$519$	12.2696			0.538577
$520$	5.79530	+	11.3058i	0.254141	+	0.495792i
$521$	16.3399			0.715862			0.357931	−	0.933748i	$-0.383482\pi$
$521$	16.3399			0.715862			0.357931	+	0.933748i	$0.383482\pi$
$522$			37.9586i			1.66140i
$523$		−	15.6795i		−	0.685617i	−0.939405	−	0.342808i	$-0.888622\pi$
$523$		−	15.6795i		−	0.685617i	0.939405	−	0.342808i	$-0.111378\pi$
$524$	−1.18603			−0.0518118
$525$	8.80748	−	12.2474i	0.384390	−	0.534520i
$526$	5.66201			0.246875
$527$		−	0.257372i		−	0.0112113i
$528$			25.0389i			1.08968i
$529$	14.7358			0.640689
$530$	−18.3339	−	35.7668i	−0.796374	−	1.55361i
$531$	1.22159			0.0530123
$532$			0.0661620i			0.00286848i
$533$		−	2.32837i		−	0.100853i
$534$	−42.8135			−1.85272
$535$	8.57235	−	4.39415i	0.370615	−	0.189976i
$536$	14.3970			0.621855
$537$		−	36.9417i		−	1.59415i
$538$			9.59623i			0.413723i
$539$	13.4062			0.577448
$540$	0.0950213	−	0.0487075i	0.00408906	−	0.00209604i
$541$	−3.92084			−0.168570			−0.0842851	−	0.996442i	$-0.526861\pi$
$541$	−3.92084			−0.168570			−0.0842851	+	0.996442i	$0.526861\pi$
$542$			24.5258i			1.05347i
$543$			44.4537i			1.90769i
$544$	0.887626			0.0380566
$545$	−3.09490	−	6.03770i	−0.132571	−	0.258627i
$546$	9.07114			0.388209
$547$			36.8903i			1.57732i	0.614832	+	0.788658i	$0.289224\pi$
$547$			36.8903i			1.57732i	−0.614832	+	0.788658i	$0.710776\pi$
$548$		−	1.99473i		−	0.0852106i
$549$	10.9645			0.467954
$550$	14.5427	+	10.4581i	0.620104	+	0.445936i
$551$	4.44519			0.189371
$552$		−	19.0392i		−	0.810363i
$553$		−	9.11462i		−	0.387593i
$554$	−39.2224			−1.66640
$555$	−2.02970	−	3.95966i	−0.0861561	−	0.168078i
$556$	1.01976			0.0432474
$557$			0.602249i			0.0255181i	0.999919	+	0.0127591i	$0.00406144\pi$
$557$			0.602249i			0.0255181i	−0.999919	+	0.0127591i	$0.995939\pi$
$558$			0.740187i			0.0313346i
$559$	7.11549			0.300953
$560$	10.4724	−	5.36812i	0.442541	−	0.226844i
$561$	−8.47647			−0.357877
$562$			13.7818i			0.581350i
$563$			7.05189i			0.297202i	0.988897	+	0.148601i	$0.0474770\pi$
$563$			7.05189i			0.297202i	−0.988897	+	0.148601i	$0.952523\pi$
$564$	0.800366			0.0337015
$565$	−10.9132	+	5.59407i	−0.459123	+	0.235344i
$566$	−19.9825			−0.839928
$567$			11.8883i			0.499262i
$568$		−	39.3237i		−	1.64999i
$569$	−32.0383			−1.34311			−0.671557	−	0.740953i	$-0.734374\pi$
$569$	−32.0383			−1.34311			−0.671557	+	0.740953i	$0.734374\pi$
$570$	1.71522	+	3.34615i	0.0718428	+	0.140155i
$571$	27.2459			1.14020			0.570102	−	0.821574i	$-0.306904\pi$
$571$	27.2459			1.14020			0.570102	+	0.821574i	$0.306904\pi$
$572$			0.562802i			0.0235319i
$573$			33.0879i			1.38227i
$574$	−2.04372			−0.0853034
$575$	−11.6696	−	8.39195i	−0.486655	−	0.349969i
$576$	21.1866			0.882773
$577$			2.31753i			0.0964802i	0.998836	+	0.0482401i	$0.0153613\pi$
$577$			2.31753i			0.0964802i	−0.998836	+	0.0482401i	$0.984639\pi$
$578$		−	21.7470i		−	0.904556i
$579$	−29.9318			−1.24392
$580$	1.04195	+	2.03269i	0.0432645	+	0.0844029i
$581$	1.36572			0.0566598
$582$			34.3543i			1.42403i
$583$			30.5146i			1.26379i
$584$	11.9577			0.494811
$585$	11.6160	−	5.95430i	0.480262	−	0.246180i
$586$	16.6740			0.688797
$587$			3.75229i			0.154874i	0.996997	+	0.0774369i	$0.0246736\pi$
$587$			3.75229i			0.154874i	−0.996997	+	0.0774369i	$0.975326\pi$
$588$			1.44608i			0.0596354i
$589$	0.0866804			0.00357160
$590$	1.25197	−	0.641753i	0.0515427	−	0.0264206i
$591$	−18.6484			−0.767094
$592$		−	3.47109i		−	0.142661i
$593$		−	34.1569i		−	1.40266i	−0.712839	−	0.701328i	$-0.752591\pi$
$593$		−	34.1569i		−	1.40266i	0.712839	−	0.701328i	$-0.247409\pi$
$594$	−1.55152			−0.0636596
$595$	1.81728	+	3.54525i	0.0745012	+	0.145341i
$596$	1.87633			0.0768577
$597$		−	12.4289i		−	0.508681i
$598$		−	8.64317i		−	0.353446i
$599$	19.0779			0.779503			0.389752	−	0.920920i	$-0.372561\pi$
$599$	19.0779			0.779503			0.389752	+	0.920920i	$0.372561\pi$
$600$	19.3336	−	26.8847i	0.789292	−	1.09756i
$601$	22.3859			0.913140			0.456570	−	0.889687i	$-0.349078\pi$
$601$	22.3859			0.913140			0.456570	+	0.889687i	$0.349078\pi$
$602$		−	6.24562i		−	0.254553i
$603$		−	14.7920i		−	0.602376i
$604$	1.01269			0.0412058
$605$	5.01640	+	9.78628i	0.203946	+	0.397869i
$606$	36.9611			1.50144
$607$		−	39.6985i		−	1.61131i	−0.592384	−	0.805656i	$-0.701813\pi$
$607$		−	39.6985i		−	1.61131i	0.592384	−	0.805656i	$-0.298187\pi$
$608$			0.298943i			0.0121237i
$609$	−27.9515			−1.13265
$610$	11.2372	−	5.76014i	0.454981	−	0.233221i
$611$	−6.22711			−0.251922
$612$		−	0.443063i		−	0.0179098i
$613$			22.1222i			0.893505i	0.894658	+	0.446753i	$0.147420\pi$
$613$			22.1222i			0.893505i	−0.894658	+	0.446753i	$0.852580\pi$
$614$	17.1931			0.693856
$615$	−5.40071	+	2.76838i	−0.217778	+	0.111632i
$616$	−8.46642			−0.341122
$617$			4.59367i			0.184934i	0.995716	+	0.0924670i	$0.0294753\pi$
$617$			4.59367i			0.184934i	−0.995716	+	0.0924670i	$0.970525\pi$
$618$			26.4974i			1.06588i
$619$	11.6527			0.468364			0.234182	−	0.972193i	$-0.424759\pi$
$619$	11.6527			0.468364			0.234182	+	0.972193i	$0.424759\pi$
$620$	0.0203178	+	0.0396371i	0.000815983	+	0.00159186i
$621$	1.24499			0.0499598
$622$			8.04555i			0.322597i
$623$		−	15.2771i		−	0.612064i
$624$	21.0135			0.841215
$625$	−7.95656	−	23.7001i	−0.318262	−	0.948003i
$626$	−36.1022			−1.44293
$627$		−	2.85479i		−	0.114009i
$628$		−	0.0194546i		−	0.000776324i
$629$	1.17507			0.0468533
$630$	−5.22638	−	10.1959i	−0.208224	−	0.406215i
$631$	−3.75293			−0.149402			−0.0747010	−	0.997206i	$-0.523800\pi$
$631$	−3.75293			−0.149402			−0.0747010	+	0.997206i	$0.523800\pi$
$632$		−	20.0078i		−	0.795869i
$633$			49.7509i			1.97742i
$634$	−22.9707			−0.912284
$635$	3.63043	−	1.86094i	0.144069	−	0.0738493i
$636$	−3.29150			−0.130517
$637$		−	11.2510i		−	0.445781i
$638$		−	33.1900i		−	1.31401i
$639$	−40.4026			−1.59830
$640$	24.1930	−	12.4012i	0.956314	−	0.490202i
$641$	30.9147			1.22106			0.610529	−	0.791994i	$-0.290957\pi$
$641$	30.9147			1.22106			0.610529	+	0.791994i	$0.290957\pi$
$642$		−	15.0981i		−	0.595875i
$643$			22.1044i			0.871712i	0.900017	+	0.435856i	$0.143554\pi$
$643$			22.1044i			0.871712i	−0.900017	+	0.435856i	$0.856446\pi$
$644$	−0.396402			−0.0156204
$645$	−8.46018	−	16.5046i	−0.333119	−	0.649868i
$646$	−0.993010			−0.0390695
$647$			32.9443i			1.29517i	0.761992	+	0.647586i	$0.224222\pi$
$647$			32.9443i			1.29517i	−0.761992	+	0.647586i	$0.775778\pi$
$648$			26.0965i			1.02517i
$649$	−1.06812			−0.0419275
$650$	8.77683	−	12.2048i	0.344255	−	0.478711i
$651$	−0.545050			−0.0213622
$652$			1.01083i			0.0395870i
$653$		−	40.1758i		−	1.57220i	−0.618100	−	0.786100i	$-0.712097\pi$
$653$		−	40.1758i		−	1.57220i	0.618100	−	0.786100i	$-0.287903\pi$
$654$	−10.6339			−0.415820
$655$	−10.9715	−	21.4038i	−0.428692	−	0.836317i
$656$	−4.73434			−0.184845
$657$		−	12.2857i		−	0.479312i
$658$			5.46585i			0.213081i
$659$	24.7128			0.962672			0.481336	−	0.876536i	$-0.340152\pi$
$659$	24.7128			0.962672			0.481336	+	0.876536i	$0.340152\pi$
$660$	1.30543	−	0.669160i	0.0508140	−	0.0260470i
$661$	12.9928			0.505361			0.252681	−	0.967550i	$-0.418688\pi$
$661$	12.9928			0.505361			0.252681	+	0.967550i	$0.418688\pi$
$662$		−	34.1182i		−	1.32604i
$663$			7.11375i			0.276275i
$664$	2.99795			0.116343
$665$	−1.19400	+	0.612041i	−0.0463015	+	0.0237339i
$666$	−3.37944			−0.130951
$667$			26.6328i			1.03123i
$668$		−	2.48094i		−	0.0959904i
$669$	−1.90545			−0.0736691
$670$	−7.77088	−	15.1599i	−0.300215	−	0.585677i
$671$	−9.58708			−0.370105
$672$		−	1.87977i		−	0.0725137i
$673$			6.53422i			0.251876i	0.992038	+	0.125938i	$0.0401940\pi$
$673$			6.53422i			0.251876i	−0.992038	+	0.125938i	$0.959806\pi$
$674$	16.1708			0.622876
$675$	1.75802	+	1.26424i	0.0676661	+	0.0486608i
$676$	−0.961090			−0.0369650
$677$		−	3.97121i		−	0.152626i	−0.997084	−	0.0763130i	$-0.975685\pi$
$677$		−	3.97121i		−	0.152626i	0.997084	−	0.0763130i	$-0.0243148\pi$
$678$			19.2210i			0.738178i
$679$	−12.2586			−0.470442
$680$	3.98918	+	7.78231i	0.152978	+	0.298438i
$681$	2.56330			0.0982258
$682$		−	0.647200i		−	0.0247826i
$683$			28.9357i			1.10719i	0.832785	+	0.553596i	$0.186745\pi$
$683$			28.9357i			1.10719i	−0.832785	+	0.553596i	$0.813255\pi$
$684$	0.149219			0.00570554
$685$	35.9983	−	18.4526i	1.37542	−	0.705036i
$686$	−22.5923			−0.862577
$687$			45.2060i			1.72471i
$688$		−	14.4682i		−	0.551593i
$689$	25.6090			0.975624
$690$	−20.0481	+	10.2766i	−0.763218	+	0.391222i
$691$	43.7038			1.66257			0.831285	−	0.555847i	$-0.187606\pi$
$691$	43.7038			1.66257			0.831285	+	0.555847i	$0.187606\pi$
$692$		−	0.560763i		−	0.0213170i
$693$			8.69870i			0.330436i
$694$	6.46282			0.245325
$695$	9.43344	+	18.4033i	0.357831	+	0.698076i
$696$	−61.3574			−2.32575
$697$		−	1.60272i		−	0.0607075i
$698$			1.31051i			0.0496036i
$699$	−49.7329			−1.88107
$700$	−0.559747	−	0.402531i	−0.0211565	−	0.0152143i
$701$	−25.3881			−0.958894			−0.479447	−	0.877571i	$-0.659163\pi$
$701$	−25.3881			−0.958894			−0.479447	+	0.877571i	$0.659163\pi$
$702$			1.30209i			0.0491442i
$703$			0.395753i			0.0149261i
$704$	−18.5250			−0.698186
$705$	7.40391	+	14.4440i	0.278847	+	0.543991i
$706$	0.661531			0.0248970
$707$			13.1888i			0.496016i
$708$		−	0.115215i		−	0.00433003i
$709$	−47.6484			−1.78947			−0.894737	−	0.446594i	$-0.852637\pi$
$709$	−47.6484			−1.78947			−0.894737	+	0.446594i	$0.852637\pi$
$710$	−41.4075	+	21.2253i	−1.55399	+	0.796570i
$711$	−20.5568			−0.770939
$712$		−	33.5353i		−	1.25679i
$713$			0.519335i			0.0194493i
$714$	6.24409			0.233679
$715$	−10.1567	+	5.20628i	−0.379839	+	0.194704i
$716$	−1.68836			−0.0630970
$717$		−	41.6481i		−	1.55538i
$718$		−	12.5679i		−	0.469028i
$719$	22.1579			0.826351			0.413175	−	0.910651i	$-0.364420\pi$
$719$	22.1579			0.826351			0.413175	+	0.910651i	$0.364420\pi$
$720$	−12.1071	−	23.6191i	−0.451203	−	0.880233i
$721$	−9.45504			−0.352124
$722$			27.2664i			1.01475i
$723$		−	2.41257i		−	0.0897244i
$724$	2.03168			0.0755069
$725$	−27.0447	+	37.6074i	−1.00441	+	1.39671i
$726$	17.2361			0.639693
$727$		−	11.4060i		−	0.423026i	−0.977375	−	0.211513i	$-0.932161\pi$
$727$		−	11.4060i		−	0.423026i	0.977375	−	0.211513i	$-0.0678391\pi$
$728$			7.10532i			0.263341i
$729$	23.6779			0.876961
$730$	−6.45424	−	12.5913i	−0.238882	−	0.466024i
$731$	4.89793			0.181157
$732$		−	1.03412i		−	0.0382223i
$733$		−	32.1861i		−	1.18882i	−0.804162	−	0.594411i	$-0.797385\pi$
$733$		−	32.1861i		−	1.18882i	0.804162	−	0.594411i	$-0.202615\pi$
$734$	34.5221			1.27423
$735$	−26.0970	+	13.3772i	−0.962603	+	0.493426i
$736$	−1.79108			−0.0660202
$737$			12.9337i			0.476420i
$738$			4.60934i			0.169672i
$739$	−6.90721			−0.254086			−0.127043	−	0.991897i	$-0.540549\pi$
$739$	−6.90721			−0.254086			−0.127043	+	0.991897i	$0.540549\pi$
$740$	−0.180970	+	0.0927642i	−0.00665258	+	0.00341008i
$741$	−2.39584			−0.0880133
$742$		−	22.4783i		−	0.825203i
$743$			31.6170i			1.15991i	0.814647	+	0.579957i	$0.196931\pi$
$743$			31.6170i			1.15991i	−0.814647	+	0.579957i	$0.803069\pi$
$744$	−1.19646			−0.0438643
$745$	17.3573	+	33.8616i	0.635923	+	1.24059i
$746$	11.2157			0.410636
$747$		−	3.08020i		−	0.112699i
$748$			0.387403i			0.0141649i
$749$	5.38744			0.196853
$750$	−38.7448	−	5.84687i	−1.41476	−	0.213497i
$751$	−14.3963			−0.525327			−0.262664	−	0.964887i	$-0.584601\pi$
$751$	−14.3963			−0.525327			−0.262664	+	0.964887i	$0.584601\pi$
$752$			12.6618i			0.461727i
$753$			52.0978i			1.89855i
$754$	−27.8543			−1.01439
$755$	9.36805	+	18.2757i	0.340938	+	0.665122i
$756$	0.0597177			0.00217191
$757$			31.1923i			1.13370i	0.823820	+	0.566852i	$0.191839\pi$
$757$			31.1923i			1.13370i	−0.823820	+	0.566852i	$0.808161\pi$
$758$			40.3350i			1.46503i
$759$	17.1041			0.620841
$760$	−2.62100	+	1.34351i	−0.0950738	+	0.0487344i
$761$	4.10282			0.148727			0.0743636	−	0.997231i	$-0.476307\pi$
$761$	4.10282			0.148727			0.0743636	+	0.997231i	$0.476307\pi$
$762$		−	6.39412i		−	0.231635i
$763$		−	3.79450i		−	0.137370i
$764$	1.51223			0.0547105
$765$	7.99583	−	4.09863i	0.289090	−	0.148186i
$766$	3.15421			0.113966
$767$			0.896407i			0.0323674i
$768$		−	6.36534i		−	0.229689i
$769$	13.7105			0.494413			0.247206	−	0.968963i	$-0.420487\pi$
$769$	13.7105			0.494413			0.247206	+	0.968963i	$0.420487\pi$
$770$	4.56981	+	8.91505i	0.164685	+	0.321276i
$771$	−53.6257			−1.93128
$772$			1.36798i			0.0492348i
$773$			34.2990i			1.23365i	0.787100	+	0.616825i	$0.211582\pi$
$773$			34.2990i			1.23365i	−0.787100	+	0.616825i	$0.788418\pi$
$774$	−14.0861			−0.506316
$775$	−0.527366	+	0.733338i	−0.0189435	+	0.0263423i
$776$	−26.9093			−0.965987
$777$		−	2.48851i		−	0.0892750i
$778$		−	23.6818i		−	0.849035i
$779$	0.539781			0.0193397
$780$	−0.561583	−	1.09557i	−0.0201079	−	0.0392276i
$781$	35.3270			1.26410
$782$		−	5.94951i		−	0.212754i
$783$		−	4.01222i		−	0.143385i
$784$	−22.8770			−0.817035
$785$	0.351092	−	0.179968i	0.0125310	−	0.00642333i
$786$	−37.6976			−1.34463
$787$			1.05124i			0.0374728i	0.999824	+	0.0187364i	$0.00596433\pi$
$787$			1.05124i			0.0374728i	−0.999824	+	0.0187364i	$0.994036\pi$
$788$			0.852296i			0.0303618i
$789$	9.40335			0.334768
$790$	−21.0680	+	10.7994i	−0.749567	+	0.384225i
$791$	−6.85861			−0.243864
$792$			19.0948i			0.678506i
$793$			8.04582i			0.285716i
$794$	7.14446			0.253547
$795$	−30.4486	−	59.4008i	−1.07990	−	2.10673i
$796$	−0.568042			−0.0201337
$797$		−	46.9746i		−	1.66393i	−0.554832	−	0.831963i	$-0.687217\pi$
$797$		−	46.9746i		−	1.66393i	0.554832	−	0.831963i	$-0.312783\pi$
$798$			2.10295i			0.0744435i
$799$	−4.28642			−0.151642
$800$	−2.52914	−	1.81878i	−0.0894185	−	0.0643036i
$801$	−34.4554			−1.21742
$802$		−	4.31996i		−	0.152543i
$803$			10.7423i			0.379088i
$804$	−1.39511			−0.0492018
$805$	−3.66697	−	7.15374i	−0.129244	−	0.252136i
$806$	−0.543153			−0.0191318
$807$			15.9372i			0.561016i
$808$			28.9512i			1.01850i
$809$	40.7051			1.43111			0.715557	−	0.698554i	$-0.246173\pi$
$809$	40.7051			1.43111			0.715557	+	0.698554i	$0.246173\pi$
$810$	27.4793	−	14.0858i	0.965524	−	0.494923i
$811$	−9.80946			−0.344457			−0.172228	−	0.985057i	$-0.555097\pi$
$811$	−9.80946			−0.344457			−0.172228	+	0.985057i	$0.555097\pi$
$812$			1.27748i			0.0448307i
$813$			40.7319i			1.42853i
$814$	2.95490			0.103569
$815$	−18.2421	+	9.35080i	−0.638992	+	0.327544i
$816$	14.4646			0.506363
$817$			1.64957i			0.0577113i
$818$		−	35.4328i		−	1.23888i
$819$	7.30026			0.255092
$820$	0.126524	+	0.246831i	0.00441842	+	0.00861970i
$821$	−7.27965			−0.254061			−0.127031	−	0.991899i	$-0.540545\pi$
$821$	−7.27965			−0.254061			−0.127031	+	0.991899i	$0.540545\pi$
$822$		−	63.4022i		−	2.21140i
$823$			10.9222i			0.380725i	0.981714	+	0.190362i	$0.0609663\pi$
$823$			10.9222i			0.380725i	−0.981714	+	0.190362i	$0.939034\pi$
$824$	−20.7551			−0.723039
$825$	24.1522	+	17.3686i	0.840873	+	0.604698i
$826$	0.786821			0.0273770
$827$		−	19.4083i		−	0.674894i	−0.941344	−	0.337447i	$-0.890437\pi$
$827$		−	19.4083i		−	0.674894i	0.941344	−	0.337447i	$-0.109563\pi$
$828$			0.894030i			0.0310697i
$829$	−28.4668			−0.988692			−0.494346	−	0.869265i	$-0.664592\pi$
$829$	−28.4668			−0.988692			−0.494346	+	0.869265i	$0.664592\pi$
$830$	−1.61817	−	3.15681i	−0.0561674	−	0.109575i
$831$	−65.1397			−2.25967
$832$			15.5468i			0.538989i
$833$		−	7.74459i		−	0.268334i
$834$	32.4129			1.12237
$835$	44.7727	−	22.9503i	1.54942	−	0.794228i
$836$	−0.130473			−0.00451252
$837$		−	0.0782376i		−	0.00270429i
$838$		−	43.4152i		−	1.49975i
$839$	19.8074			0.683826			0.341913	−	0.939732i	$-0.388925\pi$
$839$	19.8074			0.683826			0.341913	+	0.939732i	$0.388925\pi$
$840$	16.4810	−	8.44808i	0.568648	−	0.291486i
$841$	56.8293			1.95963
$842$			7.33662i			0.252836i
$843$			22.8885i			0.788322i
$844$	2.27378			0.0782669
$845$	−8.89071	−	17.3445i	−0.305850	−	0.596669i
$846$	12.3275			0.423827
$847$			6.15036i			0.211329i
$848$		−	52.0715i		−	1.78814i
$849$	−33.1865			−1.13896
$850$	6.04151	−	8.40113i	0.207222	−	0.288156i
$851$	−2.37111			−0.0812806
$852$			3.81059i			0.130549i
$853$			8.54067i			0.292427i	0.989253	+	0.146214i	$0.0467086\pi$
$853$			8.54067i			0.292427i	−0.989253	+	0.146214i	$0.953291\pi$
$854$	7.06222			0.241664
$855$	1.38038	+	2.69291i	0.0472078	+	0.0920957i
$856$	11.8262			0.404210
$857$		−	9.52177i		−	0.325257i	−0.986687	−	0.162629i	$-0.948003\pi$
$857$		−	9.52177i		−	0.325257i	0.986687	−	0.162629i	$-0.0519973\pi$
$858$			17.8886i			0.610705i
$859$	32.9092			1.12285			0.561423	−	0.827529i	$-0.310254\pi$
$859$	32.9092			1.12285			0.561423	+	0.827529i	$0.310254\pi$
$860$	−0.754315	+	0.386659i	−0.0257219	+	0.0131850i
$861$	−3.39417			−0.115673
$862$		−	14.5607i		−	0.495939i
$863$		−	2.93045i		−	0.0997538i	−0.998755	−	0.0498769i	$-0.984117\pi$
$863$		−	2.93045i		−	0.0997538i	0.998755	−	0.0498769i	$-0.0158829\pi$
$864$	0.269826			0.00917967
$865$	10.1199	−	5.18743i	0.344088	−	0.176378i
$866$	39.1866			1.33161
$867$		−	36.1169i		−	1.22660i
$868$			0.0249106i			0.000845522i
$869$	17.9743			0.609736
$870$	33.1182	+	64.6088i	1.12281	+	2.19044i
$871$	10.8544			0.367788
$872$		−	8.32944i		−	0.282071i
$873$			27.6476i			0.935729i
$874$	2.00373			0.0677773
$875$	2.08633	−	13.8253i	0.0705309	−	0.467379i
$876$	−1.15873			−0.0391500
$877$			47.5268i			1.60487i	0.596741	+	0.802434i	$0.296462\pi$
$877$			47.5268i			1.60487i	−0.596741	+	0.802434i	$0.703538\pi$
$878$			35.7838i			1.20764i
$879$	27.6918			0.934022
$880$	10.5861	+	20.6519i	0.356857	+	0.696177i
$881$	−14.8772			−0.501227			−0.250614	−	0.968087i	$-0.580632\pi$
$881$	−14.8772			−0.501227			−0.250614	+	0.968087i	$0.580632\pi$
$882$			22.2730i			0.749970i
$883$			18.1229i			0.609884i	0.952371	+	0.304942i	$0.0986371\pi$
$883$			18.1229i			0.609884i	−0.952371	+	0.304942i	$0.901363\pi$
$884$	0.325122			0.0109351
$885$	2.07924	−	1.06581i	0.0698929	−	0.0358268i
$886$	15.3433			0.515467
$887$			29.7170i			0.997799i	0.866660	+	0.498899i	$0.166262\pi$
$887$			29.7170i			0.997799i	−0.866660	+	0.498899i	$0.833738\pi$
$888$		−	5.46263i		−	0.183314i
$889$	2.28161			0.0765227
$890$	−35.3124	+	18.1010i	−1.18367	+	0.606745i
$891$	−23.4441			−0.785407
$892$			0.0870857i			0.00291584i
$893$		−	1.44362i		−	0.0483089i
$894$	59.6390			1.99463
$895$	−15.6184	−	30.4693i	−0.522067	−	1.01848i
$896$	15.2045			0.507948
$897$		−	14.3544i		−	0.479279i
$898$		−	8.64540i		−	0.288501i
$899$	1.67366			0.0558196
$900$	−0.907854	+	1.26243i	−0.0302618	+	0.0420811i
$901$	17.6279			0.587269
$902$		−	4.03028i		−	0.134194i
$903$		−	10.3726i		−	0.345178i
$904$	−15.0556			−0.500741
$905$	18.7944	+	36.6652i	0.624747	+	1.21879i
$906$	32.1882			1.06938
$907$			42.0265i			1.39547i	0.716358	+	0.697733i	$0.245808\pi$
$907$			42.0265i			1.39547i	−0.716358	+	0.697733i	$0.754192\pi$
$908$		−	0.117151i		−	0.00388780i
$909$	29.7455			0.986597
$910$	7.48183	−	3.83515i	0.248020	−	0.127134i
$911$	−48.7145			−1.61398			−0.806992	−	0.590562i	$-0.798906\pi$
$911$	−48.7145			−1.61398			−0.806992	+	0.590562i	$0.798906\pi$
$912$			4.87153i			0.161313i
$913$			2.69325i			0.0891335i
$914$	13.0564			0.431866
$915$	18.6625	−	9.56632i	0.616964	−	0.316253i
$916$	2.06606			0.0682647
$917$		−	13.4516i		−	0.444211i
$918$			0.896290i			0.0295820i
$919$	−14.6475			−0.483177			−0.241589	−	0.970379i	$-0.577668\pi$
$919$	−14.6475			−0.483177			−0.241589	+	0.970379i	$0.577668\pi$
$920$	−8.04951	−	15.7034i	−0.265384	−	0.517727i
$921$	28.5539			0.940882
$922$		−	25.0050i		−	0.823495i
$923$		−	29.6477i		−	0.975865i
$924$	0.820423			0.0269899
$925$	−3.34817	−	2.40777i	−0.110087	−	0.0791671i
$926$	25.4349			0.835841
$927$			21.3246i			0.700390i
$928$			5.77211i			0.189479i
$929$	−45.7110			−1.49973			−0.749864	−	0.661592i	$-0.769881\pi$
$929$	−45.7110			−1.49973			−0.749864	+	0.661592i	$0.769881\pi$
$930$	0.645798	+	1.25986i	0.0211766	+	0.0413124i
$931$	2.60830			0.0854836
$932$			2.27296i			0.0744533i
$933$			13.3619i			0.437448i
$934$	−6.31878			−0.206757
$935$	−6.99134	+	3.58373i	−0.228641	+	0.117201i
$936$	16.0251			0.523796
$937$		−	39.7753i		−	1.29940i	−0.760190	−	0.649701i	$-0.774894\pi$
$937$		−	39.7753i		−	1.29940i	0.760190	−	0.649701i	$-0.225106\pi$
$938$		−	9.52748i		−	0.311083i
$939$	−59.9577			−1.95665
$940$	0.660138	−	0.338384i	0.0215313	−	0.0110369i
$941$	18.0359			0.587953			0.293977	−	0.955813i	$-0.405021\pi$
$941$	18.0359			0.587953			0.293977	+	0.955813i	$0.405021\pi$
$942$		−	0.618362i		−	0.0201473i
$943$			3.23404i			0.105315i
$944$	1.82269			0.0593235
$945$	0.552428	+	1.07771i	0.0179705	+	0.0350578i
$946$	12.3166			0.400446
$947$			34.4377i			1.11908i	0.828805	+	0.559538i	$0.189021\pi$
$947$			34.4377i			1.11908i	−0.828805	+	0.559538i	$0.810979\pi$
$948$			1.93882i			0.0629700i
$949$	9.01534			0.292650
$950$	2.82941	+	2.03472i	0.0917983	+	0.0660149i
$951$	−38.1493			−1.23707
$952$			4.89093i			0.158516i
$953$		−	30.0386i		−	0.973045i	−0.873668	−	0.486522i	$-0.838265\pi$
$953$		−	30.0386i		−	0.973045i	0.873668	−	0.486522i	$-0.161735\pi$
$954$	−50.6967			−1.64137
$955$	13.9891	+	27.2907i	0.452677	+	0.883107i
$956$	−1.90346			−0.0615622
$957$		−	55.1213i		−	1.78182i
$958$		−	41.5108i		−	1.34115i
$959$	22.6237			0.730558
$960$	36.0613	−	18.4849i	1.16387	−	0.596596i
$961$	−30.9674			−0.998947
$962$		−	2.47985i		−	0.0799537i
$963$		−	12.1506i		−	0.391549i
$964$	−0.110263			−0.00355132
$965$	−24.6876	+	12.6547i	−0.794722	+	0.407371i
$966$	−12.5996			−0.405384
$967$		−	47.3839i		−	1.52376i	−0.647716	−	0.761882i	$-0.724276\pi$
$967$		−	47.3839i		−	1.52376i	0.647716	−	0.761882i	$-0.275724\pi$
$968$			13.5009i			0.433934i
$969$	−1.64917			−0.0529790
$970$	14.5245	+	28.3352i	0.466354	+	0.909789i
$971$	6.81587			0.218732			0.109366	−	0.994002i	$-0.465118\pi$
$971$	6.81587			0.218732			0.109366	+	0.994002i	$0.465118\pi$
$972$		−	2.38557i		−	0.0765173i
$973$			11.5659i			0.370784i
$974$	22.7134			0.727784
$975$	14.5764	−	20.2694i	0.466817	−	0.649141i
$976$	16.3598			0.523665
$977$		−	51.4729i		−	1.64676i	−0.567488	−	0.823382i	$-0.692085\pi$
$977$		−	51.4729i		−	1.64676i	0.567488	−	0.823382i	$-0.307915\pi$
$978$			32.1289i			1.02737i
$979$	30.1269			0.962860
$980$	0.611383	+	1.19272i	0.0195299	+	0.0381001i
$981$	−8.55797			−0.273235
$982$			22.4145i			0.715275i
$983$			17.8746i			0.570112i	0.958511	+	0.285056i	$0.0920123\pi$
$983$			17.8746i			0.570112i	−0.958511	+	0.285056i	$0.907988\pi$
$984$	−7.45067			−0.237519
$985$	−15.3811	+	7.88430i	−0.490084	+	0.251215i
$986$	−19.1734			−0.610606
$987$			9.07756i			0.288942i
$988$			0.109498i			0.00348359i
$989$	−9.88323			−0.314268
$990$	20.1067	−	10.3066i	0.639032	−	0.327565i
$991$	28.7353			0.912805			0.456403	−	0.889773i	$-0.349138\pi$
$991$	28.7353			0.912805			0.456403	+	0.889773i	$0.349138\pi$
$992$			0.112555i			0.00357363i
$993$		−	56.6627i		−	1.79814i
$994$	−26.0232			−0.825407
$995$	−5.25476	−	10.2513i	−0.166587	−	0.324988i
$996$	−0.290511			−0.00920519
$997$		−	44.7201i		−	1.41630i	−0.706062	−	0.708150i	$-0.749530\pi$
$997$		−	44.7201i		−	1.41630i	0.706062	−	0.708150i	$-0.250470\pi$
$998$			2.39258i			0.0757359i
$999$	0.357207			0.0113015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.13	✓	46
5.2	odd	4		6025.2.a.p.1.34		46
5.3	odd	4		6025.2.a.p.1.13		46
5.4	even	2	inner	1205.2.b.c.724.34	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.13	✓	46	1.1	even	1	trivial
1205.2.b.c.724.34	yes	46	5.4	even	2	inner
6025.2.a.p.1.13		46	5.3	odd	4
6025.2.a.p.1.34		46	5.2	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)

\(f(q)\)	\(=\)	\(q-1.45267i q^{2} -2.41257i q^{3} -0.110263 q^{4} +(-1.02000 - 1.98987i) q^{5} -3.50468 q^{6} -1.25057i q^{7} -2.74517i q^{8} -2.82049 q^{9} +O(q^{10})\)	\(q-1.45267i q^{2} -2.41257i q^{3} -0.110263 q^{4} +(-1.02000 - 1.98987i) q^{5} -3.50468 q^{6} -1.25057i q^{7} -2.74517i q^{8} -2.82049 q^{9} +(-2.89064 + 1.48173i) q^{10} +2.46616 q^{11} +0.266016i q^{12} -2.06969i q^{13} -1.81667 q^{14} +(-4.80071 + 2.46082i) q^{15} -4.20837 q^{16} -1.42467i q^{17} +4.09725i q^{18} +0.479813 q^{19} +(0.112468 + 0.219409i) q^{20} -3.01709 q^{21} -3.58253i q^{22} +2.87475i q^{23} -6.62292 q^{24} +(-2.91920 + 4.05934i) q^{25} -3.00659 q^{26} -0.433079i q^{27} +0.137891i q^{28} +9.26441 q^{29} +(3.57477 + 6.97387i) q^{30} +0.180654 q^{31} +0.623041i q^{32} -5.94979i q^{33} -2.06958 q^{34} +(-2.48848 + 1.27558i) q^{35} +0.310994 q^{36} +0.824807i q^{37} -0.697012i q^{38} -4.99327 q^{39} +(-5.46255 + 2.80008i) q^{40} +1.12498 q^{41} +4.38285i q^{42} +3.43795i q^{43} -0.271925 q^{44} +(2.87690 + 5.61242i) q^{45} +4.17607 q^{46} -3.00871i q^{47} +10.1530i q^{48} +5.43607 q^{49} +(5.89691 + 4.24064i) q^{50} -3.43711 q^{51} +0.228209i q^{52} +12.3733i q^{53} -0.629123 q^{54} +(-2.51549 - 4.90735i) q^{55} -3.43303 q^{56} -1.15758i q^{57} -13.4582i q^{58} -0.433111 q^{59} +(0.529338 - 0.271336i) q^{60} -3.88745 q^{61} -0.262432i q^{62} +3.52722i q^{63} -7.51166 q^{64} +(-4.11843 + 2.11109i) q^{65} -8.64311 q^{66} +5.24447i q^{67} +0.157087i q^{68} +6.93552 q^{69} +(1.85301 + 3.61495i) q^{70} +14.3247 q^{71} +7.74273i q^{72} +4.35588i q^{73} +1.19818 q^{74} +(9.79345 + 7.04277i) q^{75} -0.0529054 q^{76} -3.08411i q^{77} +7.25360i q^{78} +7.28837 q^{79} +(4.29254 + 8.37412i) q^{80} -9.50630 q^{81} -1.63423i q^{82} +1.09208i q^{83} +0.332672 q^{84} +(-2.83491 + 1.45316i) q^{85} +4.99422 q^{86} -22.3510i q^{87} -6.77004i q^{88} +12.2161 q^{89} +(8.15302 - 4.17920i) q^{90} -2.58830 q^{91} -0.316977i q^{92} -0.435841i q^{93} -4.37068 q^{94} +(-0.489410 - 0.954768i) q^{95} +1.50313 q^{96} -9.80240i q^{97} -7.89684i q^{98} -6.95579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 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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