LMFDB - Embedded newform 1045.2.b.d.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.1
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.d.419.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74370i q^{2} -2.61424i q^{3} -5.52788 q^{4} +(1.89425 - 1.18821i) q^{5} -7.17269 q^{6} -3.68386i q^{7} +9.67944i q^{8} -3.83426 q^{9} +O(q^{10})$	\(q-2.74370i q^{2} -2.61424i q^{3} -5.52788 q^{4} +(1.89425 - 1.18821i) q^{5} -7.17269 q^{6} -3.68386i q^{7} +9.67944i q^{8} -3.83426 q^{9} +(-3.26008 - 5.19724i) q^{10} -1.00000 q^{11} +14.4512i q^{12} +5.13085i q^{13} -10.1074 q^{14} +(-3.10626 - 4.95202i) q^{15} +15.5017 q^{16} -1.38082i q^{17} +10.5201i q^{18} +1.00000 q^{19} +(-10.4712 + 6.56826i) q^{20} -9.63051 q^{21} +2.74370i q^{22} +2.22531i q^{23} +25.3044 q^{24} +(2.17634 - 4.50151i) q^{25} +14.0775 q^{26} +2.18097i q^{27} +20.3640i q^{28} -5.87923 q^{29} +(-13.5868 + 8.52263i) q^{30} -6.00489 q^{31} -23.1731i q^{32} +2.61424i q^{33} -3.78854 q^{34} +(-4.37719 - 6.97814i) q^{35} +21.1953 q^{36} +10.0716i q^{37} -2.74370i q^{38} +13.4133 q^{39} +(11.5012 + 18.3352i) q^{40} +1.40525 q^{41} +26.4232i q^{42} -9.33434i q^{43} +5.52788 q^{44} +(-7.26304 + 4.55589i) q^{45} +6.10558 q^{46} -4.35299i q^{47} -40.5252i q^{48} -6.57085 q^{49} +(-12.3508 - 5.97121i) q^{50} -3.60979 q^{51} -28.3627i q^{52} -7.73192i q^{53} +5.98391 q^{54} +(-1.89425 + 1.18821i) q^{55} +35.6577 q^{56} -2.61424i q^{57} +16.1308i q^{58} +0.926037 q^{59} +(17.1710 + 27.3742i) q^{60} +0.458163 q^{61} +16.4756i q^{62} +14.1249i q^{63} -32.5766 q^{64} +(6.09650 + 9.71908i) q^{65} +7.17269 q^{66} -10.9326i q^{67} +7.63298i q^{68} +5.81750 q^{69} +(-19.1459 + 12.0097i) q^{70} +7.40293 q^{71} -37.1135i q^{72} -10.2839i q^{73} +27.6334 q^{74} +(-11.7680 - 5.68947i) q^{75} -5.52788 q^{76} +3.68386i q^{77} -36.8020i q^{78} -15.1511 q^{79} +(29.3640 - 18.4192i) q^{80} -5.80122 q^{81} -3.85559i q^{82} -2.23255i q^{83} +53.2363 q^{84} +(-1.64069 - 2.61560i) q^{85} -25.6106 q^{86} +15.3697i q^{87} -9.67944i q^{88} +17.5548 q^{89} +(12.5000 + 19.9276i) q^{90} +18.9013 q^{91} -12.3013i q^{92} +15.6982i q^{93} -11.9433 q^{94} +(1.89425 - 1.18821i) q^{95} -60.5801 q^{96} -1.79515i q^{97} +18.0284i q^{98} +3.83426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	$ 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) $ 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.74370i		−	1.94009i	−0.242930	−	0.970044i	$-0.578109\pi$
$2$		−	2.74370i		−	1.94009i	0.242930	−	0.970044i	$-0.421891\pi$
$3$		−	2.61424i		−	1.50933i	−0.656108	−	0.754667i	$-0.727799\pi$
$3$		−	2.61424i		−	1.50933i	0.656108	−	0.754667i	$-0.272201\pi$
$4$	−5.52788			−2.76394
$5$	1.89425	−	1.18821i	0.847133	−	0.531382i
$5$	1.89425	−	1.18821i	0.847133	−	0.531382i
$6$	−7.17269			−2.92824
$7$		−	3.68386i		−	1.39237i	−0.717863	−	0.696185i	$-0.754879\pi$
$7$		−	3.68386i		−	1.39237i	0.717863	−	0.696185i	$-0.245121\pi$
$8$			9.67944i			3.42220i
$9$	−3.83426			−1.27809
$10$	−3.26008	−	5.19724i	−1.03093	−	1.64351i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			14.4512i			4.17171i
$13$			5.13085i			1.42304i	0.702666	+	0.711520i	$0.251993\pi$
$13$			5.13085i			1.42304i	−0.702666	+	0.711520i	$0.748007\pi$
$14$	−10.1074			−2.70132
$15$	−3.10626	−	4.95202i	−0.802032	−	1.27861i
$16$	15.5017			3.87542
$17$		−	1.38082i		−	0.334897i	−0.985881	−	0.167448i	$-0.946447\pi$
$17$		−	1.38082i		−	0.334897i	0.985881	−	0.167448i	$-0.0535528\pi$
$18$			10.5201i			2.47960i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−10.4712	+	6.56826i	−2.34142	+	1.46871i
$21$	−9.63051			−2.10155
$22$			2.74370i			0.584958i
$23$			2.22531i			0.464010i	0.972715	+	0.232005i	$0.0745285\pi$
$23$			2.22531i			0.464010i	−0.972715	+	0.232005i	$0.925471\pi$
$24$	25.3044			5.16524
$25$	2.17634	−	4.50151i	0.435267	−	0.900301i
$26$	14.0775			2.76082
$27$			2.18097i			0.419727i
$28$			20.3640i			3.84843i
$29$	−5.87923			−1.09175			−0.545873	−	0.837868i	$-0.683802\pi$
$29$	−5.87923			−1.09175			−0.545873	+	0.837868i	$0.683802\pi$
$30$	−13.5868	+	8.52263i	−2.48061	+	1.55601i
$31$	−6.00489			−1.07851			−0.539255	−	0.842142i	$-0.681294\pi$
$31$	−6.00489			−1.07851			−0.539255	+	0.842142i	$0.681294\pi$
$32$		−	23.1731i		−	4.09647i
$33$			2.61424i			0.455081i
$34$	−3.78854			−0.649729
$35$	−4.37719	−	6.97814i	−0.739879	−	1.17952i
$36$	21.1953			3.53256
$37$			10.0716i			1.65576i	0.560905	+	0.827880i	$0.310453\pi$
$37$			10.0716i			1.65576i	−0.560905	+	0.827880i	$0.689547\pi$
$38$		−	2.74370i		−	0.445087i
$39$	13.4133			2.14784
$40$	11.5012	+	18.3352i	1.81849	+	2.89906i
$41$	1.40525			0.219463			0.109732	−	0.993961i	$-0.465001\pi$
$41$	1.40525			0.219463			0.109732	+	0.993961i	$0.465001\pi$
$42$			26.4232i			4.07719i
$43$		−	9.33434i		−	1.42347i	−0.702446	−	0.711737i	$-0.747909\pi$
$43$		−	9.33434i		−	1.42347i	0.702446	−	0.711737i	$-0.252091\pi$
$44$	5.52788			0.833359
$45$	−7.26304	+	4.55589i	−1.08271	+	0.679152i
$46$	6.10558			0.900219
$47$		−	4.35299i		−	0.634948i	−0.948267	−	0.317474i	$-0.897165\pi$
$47$		−	4.35299i		−	0.634948i	0.948267	−	0.317474i	$-0.102835\pi$
$48$		−	40.5252i		−	5.84931i
$49$	−6.57085			−0.938693
$50$	−12.3508	−	5.97121i	−1.74666	−	0.844457i
$51$	−3.60979			−0.505471
$52$		−	28.3627i		−	3.93320i
$53$		−	7.73192i		−	1.06206i	−0.847353	−	0.531030i	$-0.821805\pi$
$53$		−	7.73192i		−	1.06206i	0.847353	−	0.531030i	$-0.178195\pi$
$54$	5.98391			0.814307
$55$	−1.89425	+	1.18821i	−0.255420	+	0.160218i
$56$	35.6577			4.76496
$57$		−	2.61424i		−	0.346265i
$58$			16.1308i			2.11808i
$59$	0.926037			0.120560			0.0602799	−	0.998182i	$-0.480801\pi$
$59$	0.926037			0.120560			0.0602799	+	0.998182i	$0.480801\pi$
$60$	17.1710	+	27.3742i	2.21677	+	3.53399i
$61$	0.458163			0.0586618			0.0293309	−	0.999570i	$-0.490662\pi$
$61$	0.458163			0.0586618			0.0293309	+	0.999570i	$0.490662\pi$
$62$			16.4756i			2.09240i
$63$			14.1249i			1.77957i
$64$	−32.5766			−4.07208
$65$	6.09650	+	9.71908i	0.756178	+	1.20550i
$66$	7.17269			0.882897
$67$		−	10.9326i		−	1.33563i	−0.744328	−	0.667814i	$-0.767230\pi$
$67$		−	10.9326i		−	1.33563i	0.744328	−	0.667814i	$-0.232770\pi$
$68$			7.63298i			0.925635i
$69$	5.81750			0.700345
$70$	−19.1459	+	12.0097i	−2.28838	+	1.43543i
$71$	7.40293			0.878567			0.439283	−	0.898349i	$-0.355232\pi$
$71$	7.40293			0.878567			0.439283	+	0.898349i	$0.355232\pi$
$72$		−	37.1135i		−	4.37387i
$73$		−	10.2839i		−	1.20364i	−0.798632	−	0.601819i	$-0.794443\pi$
$73$		−	10.2839i		−	1.20364i	0.798632	−	0.601819i	$-0.205557\pi$
$74$	27.6334			3.21232
$75$	−11.7680	−	5.68947i	−1.35885	−	0.656963i
$76$	−5.52788			−0.634091
$77$			3.68386i			0.419815i
$78$		−	36.8020i		−	4.16700i
$79$	−15.1511			−1.70464			−0.852318	−	0.523024i	$-0.824804\pi$
$79$	−15.1511			−1.70464			−0.852318	+	0.523024i	$0.824804\pi$
$80$	29.3640	−	18.4192i	3.28300	−	2.05933i
$81$	−5.80122			−0.644579
$82$		−	3.85559i		−	0.425778i
$83$		−	2.23255i		−	0.245055i	−0.992465	−	0.122527i	$-0.960900\pi$
$83$		−	2.23255i		−	0.245055i	0.992465	−	0.122527i	$-0.0390999\pi$
$84$	53.2363			5.80856
$85$	−1.64069	−	2.61560i	−0.177958	−	0.283702i
$86$	−25.6106			−2.76166
$87$			15.3697i			1.64781i
$88$		−	9.67944i		−	1.03183i
$89$	17.5548			1.86081			0.930403	−	0.366538i	$-0.119457\pi$
$89$	17.5548			1.86081			0.930403	+	0.366538i	$0.119457\pi$
$90$	12.5000	+	19.9276i	1.31761	+	2.10055i
$91$	18.9013			1.98140
$92$		−	12.3013i		−	1.28249i
$93$			15.6982i			1.62783i
$94$	−11.9433			−1.23186
$95$	1.89425	−	1.18821i	0.194346	−	0.121907i
$96$	−60.5801			−6.18293
$97$		−	1.79515i		−	0.182269i	−0.995839	−	0.0911347i	$-0.970951\pi$
$97$		−	1.79515i		−	0.182269i	0.995839	−	0.0911347i	$-0.0290494\pi$
$98$			18.0284i			1.82115i
$99$	3.83426			0.385358
$100$	−12.0305	+	24.8838i	−1.20305	+	2.48838i
$101$	−11.9425			−1.18832			−0.594161	−	0.804346i	$-0.702516\pi$
$101$	−11.9425			−1.18832			−0.594161	+	0.804346i	$0.702516\pi$
$102$			9.90416i			0.980658i
$103$		−	4.44232i		−	0.437715i	−0.975757	−	0.218857i	$-0.929767\pi$
$103$		−	4.44232i		−	0.437715i	0.975757	−	0.218857i	$-0.0702329\pi$
$104$	−49.6637			−4.86993
$105$	−18.2426	+	11.4430i	−1.78029	+	1.11672i
$106$	−21.2140			−2.06049
$107$		−	13.1887i		−	1.27500i	−0.770451	−	0.637499i	$-0.779969\pi$
$107$		−	13.1887i		−	1.27500i	0.770451	−	0.637499i	$-0.220031\pi$
$108$		−	12.0561i		−	1.16010i
$109$	−2.47401			−0.236968			−0.118484	−	0.992956i	$-0.537803\pi$
$109$	−2.47401			−0.236968			−0.118484	+	0.992956i	$0.537803\pi$
$110$	3.26008	+	5.19724i	0.310836	+	0.495537i
$111$	26.3296			2.49910
$112$		−	57.1061i		−	5.39602i
$113$			3.69942i			0.348012i	0.984745	+	0.174006i	$0.0556712\pi$
$113$			3.69942i			0.348012i	−0.984745	+	0.174006i	$0.944329\pi$
$114$	−7.17269			−0.671784
$115$	2.64413	+	4.21529i	0.246566	+	0.393078i
$116$	32.4997			3.01752
$117$		−	19.6730i		−	1.81877i
$118$		−	2.54077i		−	0.233896i
$119$	−5.08673			−0.466300
$120$	47.9328	−	30.0668i	4.37564	−	2.74471i
$121$	1.00000			0.0909091
$122$		−	1.25706i		−	0.113809i
$123$		−	3.67367i		−	0.331243i
$124$	33.1943			2.98094
$125$	−1.22620	−	11.1129i	−0.109674	−	0.993968i
$126$	38.7545			3.45252
$127$			11.7683i			1.04426i	0.852864	+	0.522132i	$0.174863\pi$
$127$			11.7683i			1.04426i	−0.852864	+	0.522132i	$0.825137\pi$
$128$			43.0342i			3.80372i
$129$	−24.4022			−2.14850
$130$	26.6662	−	16.7270i	2.33878	−	1.46705i
$131$	12.9737			1.13352			0.566758	−	0.823884i	$-0.308198\pi$
$131$	12.9737			1.13352			0.566758	+	0.823884i	$0.308198\pi$
$132$		−	14.4512i		−	1.25782i
$133$		−	3.68386i		−	0.319431i
$134$	−29.9957			−2.59124
$135$	2.59144	+	4.13129i	0.223035	+	0.355565i
$136$	13.3655			1.14608
$137$		−	1.63879i		−	0.140012i	−0.997547	−	0.0700058i	$-0.977698\pi$
$137$		−	1.63879i		−	0.140012i	0.997547	−	0.0700058i	$-0.0223018\pi$
$138$		−	15.9615i		−	1.35873i
$139$	6.02266			0.510835			0.255418	−	0.966831i	$-0.417787\pi$
$139$	6.02266			0.510835			0.255418	+	0.966831i	$0.417787\pi$
$140$	24.1966	+	38.5743i	2.04498	+	3.26013i
$141$	−11.3798			−0.958349
$142$		−	20.3114i		−	1.70450i
$143$		−	5.13085i		−	0.429063i
$144$	−59.4376			−4.95313
$145$	−11.1367	+	6.98573i	−0.924853	+	0.580133i
$146$	−28.2159			−2.33516
$147$			17.1778i			1.41680i
$148$		−	55.6746i		−	4.57642i
$149$	−7.67234			−0.628543			−0.314271	−	0.949333i	$-0.601760\pi$
$149$	−7.67234			−0.628543			−0.314271	+	0.949333i	$0.601760\pi$
$150$	−15.6102	+	32.2879i	−1.27457	+	2.63630i
$151$	14.7348			1.19910			0.599551	−	0.800337i	$-0.295346\pi$
$151$	14.7348			1.19910			0.599551	+	0.800337i	$0.295346\pi$
$152$			9.67944i			0.785106i
$153$			5.29441i			0.428028i
$154$	10.1074			0.814478
$155$	−11.3747	+	7.13504i	−0.913641	+	0.573100i
$156$	−74.1470			−5.93651
$157$			10.6763i			0.852062i	0.904709	+	0.426031i	$0.140088\pi$
$157$			10.6763i			0.852062i	−0.904709	+	0.426031i	$0.859912\pi$
$158$			41.5702i			3.30714i
$159$	−20.2131			−1.60300
$160$	−27.5344	−	43.8956i	−2.17679	−	3.47025i
$161$	8.19774			0.646073
$162$			15.9168i			1.25054i
$163$		−	16.3666i		−	1.28193i	−0.767570	−	0.640965i	$-0.778534\pi$
$163$		−	16.3666i		−	1.28193i	0.767570	−	0.640965i	$-0.221466\pi$
$164$	−7.76806			−0.606584
$165$	3.10626	+	4.95202i	0.241822	+	0.385514i
$166$	−6.12545			−0.475427
$167$			17.5267i			1.35626i	0.734943	+	0.678128i	$0.237209\pi$
$167$			17.5267i			1.35626i	−0.734943	+	0.678128i	$0.762791\pi$
$168$		−	93.2179i		−	7.19192i
$169$	−13.3256			−1.02504
$170$	−7.17643	+	4.50156i	−0.550407	+	0.345254i
$171$	−3.83426			−0.293213
$172$			51.5991i			3.93440i
$173$			3.44589i			0.261987i	0.991383	+	0.130993i	$0.0418166\pi$
$173$			3.44589i			0.261987i	−0.991383	+	0.130993i	$0.958183\pi$
$174$	42.1699			3.19689
$175$	−16.5829	−	8.01733i	−1.25355	−	0.606053i
$176$	−15.5017			−1.16848
$177$		−	2.42089i		−	0.181965i
$178$		−	48.1651i		−	3.61013i
$179$	−1.23037			−0.0919620			−0.0459810	−	0.998942i	$-0.514641\pi$
$179$	−1.23037			−0.0919620			−0.0459810	+	0.998942i	$0.514641\pi$
$180$	40.1492	−	25.1844i	2.99254	−	1.87714i
$181$	15.3103			1.13801			0.569004	−	0.822335i	$-0.307329\pi$
$181$	15.3103			1.13801			0.569004	+	0.822335i	$0.307329\pi$
$182$		−	51.8596i		−	3.84409i
$183$		−	1.19775i		−	0.0885402i
$184$	−21.5398			−1.58793
$185$	11.9671	+	19.0781i	0.879841	+	1.40265i
$186$	43.0712			3.15814
$187$			1.38082i			0.100975i
$188$			24.0628i			1.75496i
$189$	8.03438			0.584415
$190$	−3.26008	−	5.19724i	−0.236511	−	0.377047i
$191$	23.4727			1.69842			0.849212	−	0.528052i	$-0.177078\pi$
$191$	23.4727			1.69842			0.849212	+	0.528052i	$0.177078\pi$
$192$			85.1632i			6.14612i
$193$			5.06830i			0.364824i	0.983222	+	0.182412i	$0.0583905\pi$
$193$			5.06830i			0.364824i	−0.983222	+	0.182412i	$0.941609\pi$
$194$	−4.92534			−0.353619
$195$	25.4080	−	15.9377i	1.81951	−	1.14132i
$196$	36.3229			2.59449
$197$		−	8.56446i		−	0.610192i	−0.952322	−	0.305096i	$-0.901311\pi$
$197$		−	8.56446i		−	0.610192i	0.952322	−	0.305096i	$-0.0986886\pi$
$198$		−	10.5201i		−	0.747628i
$199$	−19.3144			−1.36916			−0.684582	−	0.728936i	$-0.740015\pi$
$199$	−19.3144			−1.36916			−0.684582	+	0.728936i	$0.740015\pi$
$200$	43.5721	+	21.0657i	3.08101	+	1.48957i
$201$	−28.5804			−2.01591
$202$			32.7666i			2.30545i
$203$			21.6583i			1.52011i
$204$	19.9545			1.39709
$205$	2.66189	−	1.66973i	0.185915	−	0.116619i
$206$	−12.1884			−0.849205
$207$		−	8.53243i		−	0.593045i
$208$			79.5368i			5.51489i
$209$	−1.00000			−0.0691714
$210$	31.3962	+	50.0521i	2.16654	+	3.45392i
$211$	18.8889			1.30037			0.650183	−	0.759777i	$-0.274692\pi$
$211$	18.8889			1.30037			0.650183	+	0.759777i	$0.274692\pi$
$212$			42.7411i			2.93547i
$213$		−	19.3531i		−	1.32605i
$214$	−36.1857			−2.47361
$215$	−11.0911	−	17.6815i	−0.756408	−	1.20587i
$216$	−21.1105			−1.43639
$217$			22.1212i			1.50168i
$218$			6.78795i			0.459738i
$219$	−26.8846			−1.81669
$220$	10.4712	−	6.56826i	0.705966	−	0.442832i
$221$	7.08475			0.476572
$222$		−	72.2405i		−	4.84846i
$223$		−	9.26749i		−	0.620597i	−0.950639	−	0.310299i	$-0.899571\pi$
$223$		−	9.26749i		−	0.620597i	0.950639	−	0.310299i	$-0.100429\pi$
$224$	−85.3666			−5.70379
$225$	−8.34465	+	17.2600i	−0.556310	+	1.15066i
$226$	10.1501			0.675174
$227$			22.6909i			1.50605i	0.657993	+	0.753024i	$0.271406\pi$
$227$			22.6909i			1.50605i	−0.657993	+	0.753024i	$0.728594\pi$
$228$			14.4512i			0.957055i
$229$	9.50739			0.628266			0.314133	−	0.949379i	$-0.398286\pi$
$229$	9.50739			0.628266			0.314133	+	0.949379i	$0.398286\pi$
$230$	11.5655	−	7.25469i	0.762605	−	0.478360i
$231$	9.63051			0.633641
$232$		−	56.9076i		−	3.73617i
$233$			20.6167i			1.35064i	0.737523	+	0.675322i	$0.235995\pi$
$233$			20.6167i			1.35064i	−0.737523	+	0.675322i	$0.764005\pi$
$234$	−53.9768			−3.52857
$235$	−5.17224	−	8.24563i	−0.337400	−	0.537885i
$236$	−5.11902			−0.333220
$237$			39.6088i			2.57286i
$238$			13.9565i			0.904663i
$239$	12.3042			0.795891			0.397945	−	0.917409i	$-0.369723\pi$
$239$	12.3042			0.795891			0.397945	+	0.917409i	$0.369723\pi$
$240$	−48.1523	−	76.7647i	−3.10821	−	4.95514i
$241$	−0.851459			−0.0548473			−0.0274236	−	0.999624i	$-0.508730\pi$
$241$	−0.851459			−0.0548473			−0.0274236	+	0.999624i	$0.508730\pi$
$242$		−	2.74370i		−	0.176372i
$243$			21.7087i			1.39261i
$244$	−2.53267			−0.162138
$245$	−12.4468	+	7.80752i	−0.795197	+	0.498804i
$246$	−10.0794			−0.642641
$247$			5.13085i			0.326468i
$248$		−	58.1240i		−	3.69088i
$249$	−5.83644			−0.369869
$250$	−30.4904	+	3.36432i	−1.92838	+	0.212778i
$251$	−16.1494			−1.01934			−0.509671	−	0.860370i	$-0.670233\pi$
$251$	−16.1494			−1.01934			−0.509671	+	0.860370i	$0.670233\pi$
$252$		−	78.0808i		−	4.91863i
$253$		−	2.22531i		−	0.139904i
$254$	32.2886			2.02597
$255$	−6.83782	+	4.28917i	−0.428201	+	0.268598i
$256$	52.9196			3.30747
$257$			12.9845i			0.809953i	0.914327	+	0.404977i	$0.132720\pi$
$257$			12.9845i			0.809953i	−0.914327	+	0.404977i	$0.867280\pi$
$258$			66.9524i			4.16827i
$259$	37.1024			2.30543
$260$	−33.7007	−	53.7259i	−2.09003	−	3.33194i
$261$	22.5425			1.39535
$262$		−	35.5959i		−	2.19912i
$263$			12.7098i			0.783723i	0.920024	+	0.391861i	$0.128169\pi$
$263$			12.7098i			0.783723i	−0.920024	+	0.391861i	$0.871831\pi$
$264$	−25.3044			−1.55738
$265$	−9.18710	−	14.6462i	−0.564359	−	0.899706i
$266$	−10.1074			−0.619725
$267$		−	45.8925i		−	2.80858i
$268$			60.4341i			3.69160i
$269$	6.36108			0.387842			0.193921	−	0.981017i	$-0.437879\pi$
$269$	6.36108			0.387842			0.193921	+	0.981017i	$0.437879\pi$
$270$	11.3350	−	7.11012i	0.689826	−	0.432708i
$271$	7.48812			0.454871			0.227435	−	0.973793i	$-0.426966\pi$
$271$	7.48812			0.454871			0.227435	+	0.973793i	$0.426966\pi$
$272$		−	21.4050i		−	1.29787i
$273$		−	49.4127i		−	2.99059i
$274$	−4.49636			−0.271635
$275$	−2.17634	+	4.50151i	−0.131238	+	0.271451i
$276$	−32.1585			−1.93571
$277$			12.2052i			0.733336i	0.930352	+	0.366668i	$0.119502\pi$
$277$			12.2052i			0.733336i	−0.930352	+	0.366668i	$0.880498\pi$
$278$		−	16.5244i		−	0.991065i
$279$	23.0243			1.37843
$280$	67.5445	−	42.3687i	4.03656	−	2.53201i
$281$	−11.8351			−0.706022			−0.353011	−	0.935619i	$-0.614842\pi$
$281$	−11.8351			−0.706022			−0.353011	+	0.935619i	$0.614842\pi$
$282$			31.2226i			1.85928i
$283$			1.83629i			0.109156i	0.998510	+	0.0545782i	$0.0173814\pi$
$283$			1.83629i			0.109156i	−0.998510	+	0.0545782i	$0.982619\pi$
$284$	−40.9225			−2.42831
$285$	−3.10626	−	4.95202i	−0.183999	−	0.293332i
$286$	−14.0775			−0.832420
$287$		−	5.17675i		−	0.305574i
$288$			88.8518i			5.23564i
$289$	15.0933			0.887844
$290$	19.1667	+	30.5558i	1.12551	+	1.79430i
$291$	−4.69295			−0.275105
$292$			56.8481i			3.32679i
$293$		−	32.7284i		−	1.91201i	−0.293347	−	0.956006i	$-0.594769\pi$
$293$		−	32.7284i		−	1.91201i	0.293347	−	0.956006i	$-0.405231\pi$
$294$	47.1307			2.74872
$295$	1.75414	−	1.10032i	0.102130	−	0.0640632i
$296$	−97.4874			−5.66634
$297$		−	2.18097i		−	0.126552i
$298$			21.0506i			1.21943i
$299$	−11.4177			−0.660304
$300$	65.0523	+	31.4507i	3.75579	+	1.81581i
$301$	−34.3864			−1.98200
$302$		−	40.4279i		−	2.32636i
$303$			31.2206i			1.79358i
$304$	15.5017			0.889083
$305$	0.867874	−	0.544392i	0.0496943	−	0.0311718i
$306$	14.5263			0.830411
$307$			1.46423i			0.0835679i	0.999127	+	0.0417840i	$0.0133041\pi$
$307$			1.46423i			0.0835679i	−0.999127	+	0.0417840i	$0.986696\pi$
$308$		−	20.3640i		−	1.16034i
$309$	−11.6133			−0.660658
$310$	19.5764	+	31.2089i	1.11187	+	1.77254i
$311$	−1.75717			−0.0996400			−0.0498200	−	0.998758i	$-0.515865\pi$
$311$	−1.75717			−0.0996400			−0.0498200	+	0.998758i	$0.515865\pi$
$312$			129.833i			7.35034i
$313$			1.78367i			0.100819i	0.998729	+	0.0504095i	$0.0160526\pi$
$313$			1.78367i			0.100819i	−0.998729	+	0.0504095i	$0.983947\pi$
$314$	29.2925			1.65307
$315$	16.7833	+	26.7560i	0.945631	+	1.50753i
$316$	83.7537			4.71151
$317$		−	8.05011i		−	0.452139i	−0.974111	−	0.226070i	$-0.927412\pi$
$317$		−	8.05011i		−	0.452139i	0.974111	−	0.226070i	$-0.0725877\pi$
$318$			55.4587i			3.10997i
$319$	5.87923			0.329174
$320$	−61.7081	+	38.7077i	−3.44959	+	2.16383i
$321$	−34.4784			−1.92440
$322$		−	22.4921i		−	1.25344i
$323$		−	1.38082i		−	0.0768306i
$324$	32.0684			1.78158
$325$	23.0965	+	11.1664i	1.28117	+	0.619403i
$326$	−44.9050			−2.48706
$327$			6.46767i			0.357663i
$328$			13.6020i			0.751047i
$329$	−16.0358			−0.884082
$330$	13.5868	−	8.52263i	0.747931	−	0.469155i
$331$	24.5510			1.34944			0.674721	−	0.738073i	$-0.264264\pi$
$331$	24.5510			1.34944			0.674721	+	0.738073i	$0.264264\pi$
$332$			12.3413i			0.677316i
$333$		−	38.6172i		−	2.11621i
$334$	48.0880			2.63126
$335$	−12.9902	−	20.7090i	−0.709729	−	1.13145i
$336$	−149.289			−8.14440
$337$		−	15.5103i		−	0.844901i	−0.906386	−	0.422450i	$-0.861170\pi$
$337$		−	15.5103i		−	0.844901i	0.906386	−	0.422450i	$-0.138830\pi$
$338$			36.5614i			1.98868i
$339$	9.67118			0.525266
$340$	9.06955	+	14.4587i	0.491865	+	0.784136i
$341$	6.00489			0.325183
$342$			10.5201i			0.568860i
$343$		−	1.58093i		−	0.0853624i
$344$	90.3512			4.87141
$345$	11.0198	−	6.91239i	0.593285	−	0.372151i
$346$	9.45449			0.508277
$347$			7.09672i			0.380972i	0.981690	+	0.190486i	$0.0610064\pi$
$347$			7.09672i			0.380972i	−0.981690	+	0.190486i	$0.938994\pi$
$348$		−	84.9620i		−	4.55444i
$349$	−18.2877			−0.978921			−0.489460	−	0.872026i	$-0.662806\pi$
$349$	−18.2877			−0.978921			−0.489460	+	0.872026i	$0.662806\pi$
$350$	−21.9971	+	45.4986i	−1.17580	+	2.43200i
$351$	−11.1902			−0.597289
$352$			23.1731i			1.23513i
$353$		−	26.6722i		−	1.41962i	−0.704394	−	0.709809i	$-0.748781\pi$
$353$		−	26.6722i		−	1.41962i	0.704394	−	0.709809i	$-0.251219\pi$
$354$	−6.64218			−0.353028
$355$	14.0230	−	8.79621i	0.744263	−	0.466854i
$356$	−97.0409			−5.14316
$357$			13.2980i			0.703803i
$358$			3.37576i			0.178414i
$359$	−8.18413			−0.431942			−0.215971	−	0.976400i	$-0.569292\pi$
$359$	−8.18413			−0.431942			−0.215971	+	0.976400i	$0.569292\pi$
$360$	−44.0985	−	70.3021i	−2.32419	−	3.70525i
$361$	1.00000			0.0526316
$362$		−	42.0069i		−	2.20783i
$363$		−	2.61424i		−	0.137212i
$364$	−104.484			−5.47647
$365$	−12.2194	−	19.4802i	−0.639592	−	1.01964i
$366$	−3.28626			−0.171776
$367$		−	24.5888i		−	1.28353i	−0.766903	−	0.641763i	$-0.778203\pi$
$367$		−	24.5888i		−	1.28353i	0.766903	−	0.641763i	$-0.221797\pi$
$368$			34.4961i			1.79823i
$369$	−5.38810			−0.280493
$370$	52.3445	−	32.8342i	2.72126	−	1.70697i
$371$	−28.4833			−1.47878
$372$		−	86.7780i		−	4.49923i
$373$		−	29.8613i		−	1.54616i	−0.634309	−	0.773079i	$-0.718715\pi$
$373$		−	29.8613i		−	1.54616i	0.634309	−	0.773079i	$-0.281285\pi$
$374$	3.78854			0.195901
$375$	−29.0518	+	3.20558i	−1.50023	+	0.165535i
$376$	42.1345			2.17292
$377$		−	30.1654i		−	1.55360i
$378$		−	22.0439i		−	1.13382i
$379$	−2.96981			−0.152549			−0.0762744	−	0.997087i	$-0.524303\pi$
$379$	−2.96981			−0.152549			−0.0762744	+	0.997087i	$0.524303\pi$
$380$	−10.4712	+	6.56826i	−0.537159	+	0.336944i
$381$	30.7651			1.57614
$382$		−	64.4020i		−	3.29509i
$383$		−	9.19360i		−	0.469771i	−0.972023	−	0.234885i	$-0.924528\pi$
$383$		−	9.19360i		−	0.469771i	0.972023	−	0.234885i	$-0.0754715\pi$
$384$	112.502			5.74108
$385$	4.37719	+	6.97814i	0.223082	+	0.355639i
$386$	13.9059			0.707791
$387$			35.7903i			1.81932i
$388$			9.92335i			0.503782i
$389$	−1.46191			−0.0741216			−0.0370608	−	0.999313i	$-0.511800\pi$
$389$	−1.46191			−0.0741216			−0.0370608	+	0.999313i	$0.511800\pi$
$390$	−43.7283	−	69.7120i	−2.21427	−	3.53000i
$391$	3.07274			0.155395
$392$		−	63.6021i		−	3.21239i
$393$		−	33.9163i		−	1.71085i
$394$	−23.4983			−1.18383
$395$	−28.7000	+	18.0027i	−1.44405	+	0.905812i
$396$	−21.1953			−1.06511
$397$		−	0.928569i		−	0.0466036i	−0.999728	−	0.0233018i	$-0.992582\pi$
$397$		−	0.928569i		−	0.0466036i	0.999728	−	0.0233018i	$-0.00741786\pi$
$398$			52.9930i			2.65630i
$399$	−9.63051			−0.482129
$400$	33.7369	−	69.7810i	1.68685	−	3.48905i
$401$	14.1167			0.704955			0.352478	−	0.935820i	$-0.385339\pi$
$401$	14.1167			0.704955			0.352478	+	0.935820i	$0.385339\pi$
$402$			78.4161i			3.91104i
$403$		−	30.8102i		−	1.53476i
$404$	66.0167			3.28445
$405$	−10.9889	+	6.89303i	−0.546044	+	0.342518i
$406$	59.4238			2.94915
$407$		−	10.0716i		−	0.499231i
$408$		−	34.9407i		−	1.72982i
$409$	0.311173			0.0153865			0.00769325	−	0.999970i	$-0.497551\pi$
$409$	0.311173			0.0153865			0.00769325	+	0.999970i	$0.497551\pi$
$410$	−4.58123	−	7.30343i	−0.226251	−	0.360691i
$411$	−4.28421			−0.211324
$412$			24.5566i			1.20982i
$413$		−	3.41139i		−	0.167864i
$414$	−23.4104			−1.15056
$415$	−2.65273	−	4.22901i	−0.130217	−	0.207594i
$416$	118.898			5.82944
$417$		−	15.7447i		−	0.771021i
$418$			2.74370i			0.134199i
$419$	27.2577			1.33163			0.665814	−	0.746118i	$-0.268085\pi$
$419$	27.2577			1.33163			0.665814	+	0.746118i	$0.268085\pi$
$420$	100.843	−	63.2557i	4.92062	−	3.08656i
$421$	−8.80584			−0.429170			−0.214585	−	0.976705i	$-0.568840\pi$
$421$	−8.80584			−0.429170			−0.214585	+	0.976705i	$0.568840\pi$
$422$		−	51.8255i		−	2.52282i
$423$			16.6905i			0.811519i
$424$	74.8406			3.63458
$425$	−6.21575	−	3.00512i	−0.301508	−	0.145770i
$426$	−53.0990			−2.57265
$427$		−	1.68781i		−	0.0816789i
$428$			72.9054i			3.52402i
$429$	−13.4133			−0.647599
$430$	−48.5128	+	30.4307i	−2.33950	+	1.46750i
$431$	−18.9022			−0.910489			−0.455244	−	0.890366i	$-0.650448\pi$
$431$	−18.9022			−0.910489			−0.455244	+	0.890366i	$0.650448\pi$
$432$			33.8087i			1.62662i
$433$			6.57598i			0.316021i	0.987437	+	0.158011i	$0.0505080\pi$
$433$			6.57598i			0.316021i	−0.987437	+	0.158011i	$0.949492\pi$
$434$	60.6939			2.91340
$435$	18.2624	+	29.1140i	0.875614	+	1.39591i
$436$	13.6761			0.654964
$437$			2.22531i			0.106451i
$438$			73.7632i			3.52454i
$439$	−33.2995			−1.58930			−0.794649	−	0.607069i	$-0.792345\pi$
$439$	−33.2995			−1.58930			−0.794649	+	0.607069i	$0.792345\pi$
$440$	−11.5012	−	18.3352i	−0.548296	−	0.874098i
$441$	25.1944			1.19973
$442$		−	19.4384i		−	0.924591i
$443$		−	32.8591i		−	1.56118i	−0.625043	−	0.780591i	$-0.714918\pi$
$443$		−	32.8591i		−	1.56118i	0.625043	−	0.780591i	$-0.285082\pi$
$444$	−145.547			−6.90735
$445$	33.2531	−	20.8587i	1.57635	−	0.988798i
$446$	−25.4272			−1.20401
$447$			20.0574i			0.948680i
$448$			120.008i			5.66984i
$449$	37.4890			1.76922			0.884608	−	0.466335i	$-0.154426\pi$
$449$	37.4890			1.76922			0.884608	+	0.466335i	$0.154426\pi$
$450$	47.3561	+	22.8952i	2.23239	+	1.07929i
$451$	−1.40525			−0.0661707
$452$		−	20.4500i		−	0.961885i
$453$		−	38.5204i		−	1.80984i
$454$	62.2570			2.92187
$455$	35.8038	−	22.4587i	1.67851	−	1.05288i
$456$	25.3044			1.18499
$457$		−	32.4391i		−	1.51744i	−0.651419	−	0.758718i	$-0.725826\pi$
$457$		−	32.4391i		−	1.51744i	0.651419	−	0.758718i	$-0.274174\pi$
$458$		−	26.0854i		−	1.21889i
$459$	3.01151			0.140565
$460$	−14.6164	−	23.3016i	−0.681494	−	1.08644i
$461$	−11.4559			−0.533557			−0.266778	−	0.963758i	$-0.585959\pi$
$461$	−11.4559			−0.533557			−0.266778	+	0.963758i	$0.585959\pi$
$462$		−	26.4232i		−	1.22932i
$463$		−	38.3366i		−	1.78166i	−0.454342	−	0.890828i	$-0.650125\pi$
$463$		−	38.3366i		−	1.78166i	0.454342	−	0.890828i	$-0.349875\pi$
$464$	−91.1380			−4.23098
$465$	18.6527	+	29.7363i	0.865000	+	1.37899i
$466$	56.5659			2.62037
$467$			15.5597i			0.720019i	0.932949	+	0.360009i	$0.117226\pi$
$467$			15.5597i			0.720019i	−0.932949	+	0.360009i	$0.882774\pi$
$468$			108.750i			5.02697i
$469$	−40.2742			−1.85969
$470$	−22.6235	+	14.1911i	−1.04354	+	0.654585i
$471$	27.9104			1.28605
$472$			8.96352i			0.412579i
$473$			9.33434i			0.429193i
$474$	108.674			4.99158
$475$	2.17634	−	4.50151i	0.0998572	−	0.206543i
$476$	28.1189			1.28883
$477$			29.6462i			1.35741i
$478$		−	33.7589i		−	1.54410i
$479$	−4.30544			−0.196720			−0.0983602	−	0.995151i	$-0.531360\pi$
$479$	−4.30544			−0.196720			−0.0983602	+	0.995151i	$0.531360\pi$
$480$	−114.754	+	71.9816i	−5.23776	+	3.28550i
$481$	−51.6758			−2.35621
$482$			2.33615i			0.106408i
$483$		−	21.4309i		−	0.975139i
$484$	−5.52788			−0.251267
$485$	−2.13300	−	3.40045i	−0.0968546	−	0.154406i
$486$	59.5621			2.70179
$487$		−	32.6089i		−	1.47765i	−0.673897	−	0.738826i	$-0.735381\pi$
$487$		−	32.6089i		−	1.47765i	0.673897	−	0.738826i	$-0.264619\pi$
$488$			4.43476i			0.200752i
$489$	−42.7862			−1.93486
$490$	21.4215	+	34.1503i	0.967724	+	1.54275i
$491$	−20.4803			−0.924265			−0.462132	−	0.886811i	$-0.652915\pi$
$491$	−20.4803			−0.924265			−0.462132	+	0.886811i	$0.652915\pi$
$492$			20.3076i			0.915537i
$493$			8.11813i			0.365622i
$494$	14.0775			0.633376
$495$	7.26304	−	4.55589i	0.326449	−	0.204772i
$496$	−93.0860			−4.17969
$497$		−	27.2714i		−	1.22329i
$498$			16.0134i			0.717578i
$499$	16.7531			0.749971			0.374986	−	0.927031i	$-0.377648\pi$
$499$	16.7531			0.749971			0.374986	+	0.927031i	$0.377648\pi$
$500$	6.77827	+	61.4308i	0.303134	+	2.74727i
$501$	45.8190			2.04704
$502$			44.3091i			1.97761i
$503$			28.4700i			1.26941i	0.772753	+	0.634707i	$0.218879\pi$
$503$			28.4700i			1.26941i	−0.772753	+	0.634707i	$0.781121\pi$
$504$	−136.721			−6.09004
$505$	−22.6220	+	14.1901i	−1.00667	+	0.631453i
$506$	−6.10558			−0.271426
$507$			34.8363i			1.54713i
$508$		−	65.0536i		−	2.88629i
$509$	16.3538			0.724869			0.362435	−	0.932009i	$-0.381946\pi$
$509$	16.3538			0.724869			0.362435	+	0.932009i	$0.381946\pi$
$510$	11.7682	+	18.7609i	0.521104	+	0.830748i
$511$	−37.8845			−1.67591
$512$		−	59.1270i		−	2.61307i
$513$			2.18097i			0.0962920i
$514$	35.6256			1.57138
$515$	−5.27839	−	8.41485i	−0.232594	−	0.370802i
$516$	134.893			5.93832
$517$			4.35299i			0.191444i
$518$		−	101.798i		−	4.47274i
$519$	9.00840			0.395425
$520$	−94.0753	+	59.0107i	−4.12547	+	2.58779i
$521$	1.21891			0.0534013			0.0267007	−	0.999643i	$-0.491500\pi$
$521$	1.21891			0.0534013			0.0267007	+	0.999643i	$0.491500\pi$
$522$		−	61.8498i		−	2.70709i
$523$			21.0637i			0.921052i	0.887646	+	0.460526i	$0.152339\pi$
$523$			21.0637i			0.921052i	−0.887646	+	0.460526i	$0.847661\pi$
$524$	−71.7169			−3.13297
$525$	−20.9592	+	43.3518i	−0.914736	+	1.89203i
$526$	34.8720			1.52049
$527$			8.29165i			0.361190i
$528$			40.5252i			1.76363i
$529$	18.0480			0.784695
$530$	−40.1846	+	25.2066i	−1.74551	+	1.09491i
$531$	−3.55067			−0.154086
$532$			20.3640i			0.882889i
$533$			7.21013i			0.312305i
$534$	−125.915			−5.44888
$535$	−15.6709	−	24.9826i	−0.677510	−	1.08009i
$536$	105.821			4.57079
$537$			3.21648i			0.138801i
$538$		−	17.4529i		−	0.752447i
$539$	6.57085			0.283027
$540$	−14.3251	−	22.8373i	−0.616456	−	0.982759i
$541$	−3.02607			−0.130101			−0.0650504	−	0.997882i	$-0.520721\pi$
$541$	−3.02607			−0.130101			−0.0650504	+	0.997882i	$0.520721\pi$
$542$		−	20.5451i		−	0.882489i
$543$		−	40.0249i		−	1.71763i
$544$	−31.9978			−1.37189
$545$	−4.68639	+	2.93964i	−0.200743	+	0.125920i
$546$	−135.573			−5.80201
$547$		−	19.4630i		−	0.832179i	−0.909324	−	0.416090i	$-0.863400\pi$
$547$		−	19.4630i		−	0.832179i	0.909324	−	0.416090i	$-0.136600\pi$
$548$			9.05906i			0.386984i
$549$	−1.75672			−0.0749749
$550$	12.3508	+	5.97121i	0.526639	+	0.254613i
$551$	−5.87923			−0.250463
$552$			56.3102i			2.39672i
$553$			55.8147i			2.37348i
$554$	33.4872			1.42274
$555$	49.8747	−	31.2850i	2.11707	−	1.32797i
$556$	−33.2925			−1.41192
$557$			45.8141i			1.94121i	0.240686	+	0.970603i	$0.422628\pi$
$557$			45.8141i			1.94121i	−0.240686	+	0.970603i	$0.577372\pi$
$558$		−	63.1718i		−	2.67428i
$559$	47.8931			2.02566
$560$	−67.8538	−	108.173i	−2.86735	−	4.57115i
$561$	3.60979			0.152405
$562$			32.4719i			1.36974i
$563$			21.4273i			0.903051i	0.892258	+	0.451526i	$0.149120\pi$
$563$			21.4273i			0.903051i	−0.892258	+	0.451526i	$0.850880\pi$
$564$	62.9059			2.64882
$565$	4.39567	+	7.00761i	0.184927	+	0.294812i
$566$	5.03824			0.211773
$567$			21.3709i			0.897493i
$568$			71.6563i			3.00663i
$569$	−8.69206			−0.364390			−0.182195	−	0.983262i	$-0.558320\pi$
$569$	−8.69206			−0.364390			−0.182195	+	0.983262i	$0.558320\pi$
$570$	−13.5868	+	8.52263i	−0.569090	+	0.356974i
$571$	4.55197			0.190494			0.0952469	−	0.995454i	$-0.469636\pi$
$571$	4.55197			0.190494			0.0952469	+	0.995454i	$0.469636\pi$
$572$			28.3627i			1.18590i
$573$		−	61.3633i		−	2.56349i
$574$	−14.2034			−0.592841
$575$	10.0173	+	4.84303i	0.417748	+	0.201968i
$576$	124.907			5.20447
$577$			5.54669i			0.230912i	0.993313	+	0.115456i	$0.0368329\pi$
$577$			5.54669i			0.230912i	−0.993313	+	0.115456i	$0.963167\pi$
$578$		−	41.4116i		−	1.72250i
$579$	13.2498			0.550642
$580$	61.5624	−	38.6163i	2.55624	−	1.60345i
$581$	−8.22442			−0.341206
$582$			12.8760i			0.533728i
$583$			7.73192i			0.320223i
$584$	99.5423			4.11909
$585$	−23.3756	−	37.2655i	−0.966461	−	1.54074i
$586$	−89.7968			−3.70947
$587$			34.8885i			1.44000i	0.693974	+	0.720001i	$0.255858\pi$
$587$			34.8885i			1.44000i	−0.693974	+	0.720001i	$0.744142\pi$
$588$		−	94.9568i		−	3.91595i
$589$	−6.00489			−0.247427
$590$	−3.01895	−	4.81284i	−0.124288	−	0.198141i
$591$	−22.3896			−0.920984
$592$			156.127i			6.41678i
$593$			18.2906i			0.751106i	0.926801	+	0.375553i	$0.122547\pi$
$593$			18.2906i			0.751106i	−0.926801	+	0.375553i	$0.877453\pi$
$594$	−5.98391			−0.245523
$595$	−9.63553	+	6.04409i	−0.395018	+	0.247783i
$596$	42.4118			1.73725
$597$			50.4926i			2.06652i
$598$			31.3268i			1.28105i
$599$	13.5695			0.554434			0.277217	−	0.960807i	$-0.410588\pi$
$599$	13.5695			0.554434			0.277217	+	0.960807i	$0.410588\pi$
$600$	55.0709	−	113.908i	2.24826	−	4.65027i
$601$	31.3666			1.27947			0.639736	−	0.768595i	$-0.279044\pi$
$601$	31.3666			1.27947			0.639736	+	0.768595i	$0.279044\pi$
$602$			94.3460i			3.84526i
$603$			41.9184i			1.70705i
$604$	−81.4523			−3.31425
$605$	1.89425	−	1.18821i	0.0770121	−	0.0483074i
$606$	85.6598			3.47969
$607$			17.2702i			0.700978i	0.936567	+	0.350489i	$0.113985\pi$
$607$			17.2702i			0.700978i	−0.936567	+	0.350489i	$0.886015\pi$
$608$		−	23.1731i		−	0.939794i
$609$	56.6200			2.29436
$610$	−1.49365	−	2.38118i	−0.0604760	−	0.0964113i
$611$	22.3345			0.903557
$612$		−	29.2669i		−	1.18304i
$613$			16.3778i			0.661494i	0.943719	+	0.330747i	$0.107301\pi$
$613$			16.3778i			0.661494i	−0.943719	+	0.330747i	$0.892699\pi$
$614$	4.01740			0.162129
$615$	−4.36507	−	6.95883i	−0.176017	−	0.280607i
$616$	−35.6577			−1.43669
$617$			21.3808i			0.860759i	0.902648	+	0.430379i	$0.141620\pi$
$617$			21.3808i			0.860759i	−0.902648	+	0.430379i	$0.858380\pi$
$618$			31.8634i			1.28173i
$619$	−14.2876			−0.574267			−0.287134	−	0.957891i	$-0.592702\pi$
$619$	−14.2876			−0.574267			−0.287134	+	0.957891i	$0.592702\pi$
$620$	62.8782	−	39.4417i	2.52525	−	1.58402i
$621$	−4.85333			−0.194757
$622$			4.82115i			0.193310i
$623$		−	64.6695i		−	2.59093i
$624$	207.929			8.32380
$625$	−15.5271	−	19.5936i	−0.621085	−	0.783743i
$626$	4.89385			0.195598
$627$			2.61424i			0.104403i
$628$		−	59.0173i		−	2.35505i
$629$	13.9070			0.554509
$630$	73.4105	−	46.0483i	2.92474	−	1.83461i
$631$	24.8052			0.987478			0.493739	−	0.869610i	$-0.335630\pi$
$631$	24.8052			0.987478			0.493739	+	0.869610i	$0.335630\pi$
$632$		−	146.655i		−	5.83360i
$633$		−	49.3802i		−	1.96269i
$634$	−22.0871			−0.877190
$635$	13.9831	+	22.2920i	0.554903	+	0.884631i
$636$	111.736			4.43061
$637$		−	33.7140i		−	1.33580i
$638$		−	16.1308i		−	0.638625i
$639$	−28.3848			−1.12289
$640$	51.1335	+	81.5173i	2.02123	+	3.22226i
$641$	13.8659			0.547671			0.273836	−	0.961776i	$-0.411708\pi$
$641$	13.8659			0.547671			0.273836	+	0.961776i	$0.411708\pi$
$642$			94.5983i			3.73350i
$643$		−	44.4939i		−	1.75467i	−0.479879	−	0.877335i	$-0.659319\pi$
$643$		−	44.4939i		−	1.75467i	0.479879	−	0.877335i	$-0.340681\pi$
$644$	−45.3161			−1.78571
$645$	−46.2238	+	28.9949i	−1.82006	+	1.14167i
$646$	−3.78854			−0.149058
$647$			30.6621i			1.20545i	0.797949	+	0.602726i	$0.205919\pi$
$647$			30.6621i			1.20545i	−0.797949	+	0.602726i	$0.794081\pi$
$648$		−	56.1525i		−	2.20588i
$649$	−0.926037			−0.0363501
$650$	30.6374	−	63.3699i	1.20170	−	2.48557i
$651$	57.8302			2.26654
$652$			90.4726i			3.54318i
$653$			7.31907i			0.286417i	0.989693	+	0.143209i	$0.0457420\pi$
$653$			7.31907i			0.286417i	−0.989693	+	0.143209i	$0.954258\pi$
$654$	17.7453			0.693898
$655$	24.5753	−	15.4154i	0.960238	−	0.602329i
$656$	21.7838			0.850514
$657$			39.4312i			1.53836i
$658$			43.9974i			1.71520i
$659$	24.0735			0.937771			0.468886	−	0.883259i	$-0.344656\pi$
$659$	24.0735			0.937771			0.468886	+	0.883259i	$0.344656\pi$
$660$	−17.1710	−	27.3742i	−0.668381	−	1.06554i
$661$	−3.55333			−0.138208			−0.0691042	−	0.997609i	$-0.522014\pi$
$661$	−3.55333			−0.138208			−0.0691042	+	0.997609i	$0.522014\pi$
$662$		−	67.3604i		−	2.61804i
$663$		−	18.5213i		−	0.719306i
$664$	21.6099			0.838625
$665$	−4.37719	−	6.97814i	−0.169740	−	0.270601i
$666$	−105.954			−4.10563
$667$		−	13.0831i		−	0.506580i
$668$		−	96.8855i		−	3.74861i
$669$	−24.2275			−0.936688
$670$	−56.8193	+	35.6411i	−2.19512	+	1.37694i
$671$	−0.458163			−0.0176872
$672$			223.169i			8.60893i
$673$		−	16.4213i		−	0.632993i	−0.948594	−	0.316496i	$-0.897493\pi$
$673$		−	16.4213i		−	0.632993i	0.948594	−	0.316496i	$-0.102507\pi$
$674$	−42.5556			−1.63918
$675$	9.81763	+	4.74652i	0.377881	+	0.182693i
$676$	73.6622			2.83316
$677$			8.95903i			0.344324i	0.985069	+	0.172162i	$0.0550752\pi$
$677$			8.95903i			0.344324i	−0.985069	+	0.172162i	$0.944925\pi$
$678$		−	26.5348i		−	1.01906i
$679$	−6.61307			−0.253786
$680$	25.3176	−	15.8810i	0.970885	−	0.609008i
$681$	59.3195			2.27313
$682$		−	16.4756i		−	0.630884i
$683$		−	16.7624i		−	0.641395i	−0.947182	−	0.320698i	$-0.896083\pi$
$683$		−	16.7624i		−	0.641395i	0.947182	−	0.320698i	$-0.103917\pi$
$684$	21.1953			0.810424
$685$	−1.94722	−	3.10428i	−0.0743996	−	0.118608i
$686$	−4.33760			−0.165610
$687$		−	24.8546i		−	0.948263i
$688$		−	144.698i		−	5.51656i
$689$	39.6713			1.51136
$690$	−18.9655	−	30.2350i	−0.722005	−	1.15103i
$691$	−24.2063			−0.920853			−0.460426	−	0.887698i	$-0.652303\pi$
$691$	−24.2063			−0.920853			−0.460426	+	0.887698i	$0.652303\pi$
$692$		−	19.0485i		−	0.724115i
$693$		−	14.1249i		−	0.536561i
$694$	19.4713			0.739119
$695$	11.4084	−	7.15616i	0.432745	−	0.271448i
$696$	−148.770			−5.63912
$697$		−	1.94039i		−	0.0734976i
$698$			50.1761i			1.89919i
$699$	53.8970			2.03857
$700$	91.6685	+	44.3188i	3.46474	+	1.67509i
$701$	−45.1047			−1.70358			−0.851791	−	0.523881i	$-0.824484\pi$
$701$	−45.1047			−1.70358			−0.851791	+	0.523881i	$0.824484\pi$
$702$			30.7025i			1.15879i
$703$			10.0716i			0.379858i
$704$	32.5766			1.22778
$705$	−21.5561	+	13.5215i	−0.811848	+	0.509249i
$706$	−73.1805			−2.75418
$707$			43.9945i			1.65458i
$708$			13.3824i			0.502940i
$709$	6.93377			0.260403			0.130202	−	0.991488i	$-0.458438\pi$
$709$	6.93377			0.260403			0.130202	+	0.991488i	$0.458438\pi$
$710$	−24.1341	−	38.4748i	−0.905738	−	1.44393i
$711$	58.0935			2.17867
$712$			169.921i			6.36805i
$713$		−	13.3628i		−	0.500439i
$714$	36.4856			1.36544
$715$	−6.09650	−	9.71908i	−0.227996	−	0.363473i
$716$	6.80132			0.254177
$717$		−	32.1661i		−	1.20126i
$718$			22.4548i			0.838005i
$719$	37.4443			1.39644			0.698218	−	0.715885i	$-0.253976\pi$
$719$	37.4443			1.39644			0.698218	+	0.715885i	$0.253976\pi$
$720$	−112.589	+	70.6241i	−4.19596	+	2.63200i
$721$	−16.3649			−0.609461
$722$		−	2.74370i		−	0.102110i
$723$			2.22592i			0.0827828i
$724$	−84.6336			−3.14538
$725$	−12.7952	+	26.4654i	−0.475201	+	0.982899i
$726$	−7.17269			−0.266204
$727$		−	26.9348i		−	0.998955i	−0.866327	−	0.499478i	$-0.833525\pi$
$727$		−	26.9348i		−	0.998955i	0.866327	−	0.499478i	$-0.166475\pi$
$728$			182.954i			6.78074i
$729$	39.3481			1.45734
$730$	−53.4479	+	33.5263i	−1.97819	+	1.24086i
$731$	−12.8890			−0.476717
$732$			6.62102i			0.244720i
$733$			14.8914i			0.550028i	0.961440	+	0.275014i	$0.0886825\pi$
$733$			14.8914i			0.550028i	−0.961440	+	0.275014i	$0.911318\pi$
$734$	−67.4644			−2.49015
$735$	20.4107	+	32.5390i	0.752862	+	1.20022i
$736$	51.5674			1.90080
$737$			10.9326i			0.402707i
$738$			14.7833i			0.544182i
$739$	21.0072			0.772764			0.386382	−	0.922339i	$-0.373725\pi$
$739$	21.0072			0.772764			0.386382	+	0.922339i	$0.373725\pi$
$740$	−66.1529	−	105.461i	−2.43183	−	3.87684i
$741$	13.4133			0.492749
$742$			78.1496i			2.86896i
$743$			15.6396i			0.573761i	0.957966	+	0.286880i	$0.0926182\pi$
$743$			15.6396i			0.573761i	−0.957966	+	0.286880i	$0.907382\pi$
$744$	−151.950			−5.57076
$745$	−14.5333	+	9.11631i	−0.532459	+	0.333996i
$746$	−81.9304			−2.99968
$747$			8.56020i			0.313201i
$748$		−	7.63298i		−	0.279089i
$749$	−48.5853			−1.77527
$750$	8.79514	+	79.7094i	0.321153	+	2.91057i
$751$	22.7663			0.830755			0.415377	−	0.909649i	$-0.363650\pi$
$751$	22.7663			0.830755			0.415377	+	0.909649i	$0.363650\pi$
$752$		−	67.4787i		−	2.46069i
$753$			42.2184i			1.53853i
$754$	−82.7648			−3.01412
$755$	27.9114	−	17.5080i	1.01580	−	0.637181i
$756$	−44.4131			−1.61529
$757$			14.0431i			0.510406i	0.966888	+	0.255203i	$0.0821423\pi$
$757$			14.0431i			0.510406i	−0.966888	+	0.255203i	$0.917858\pi$
$758$			8.14826i			0.295958i
$759$	−5.81750			−0.211162
$760$	11.5012	+	18.3352i	0.417191	+	0.665089i
$761$	−13.3330			−0.483321			−0.241661	−	0.970361i	$-0.577692\pi$
$761$	−13.3330			−0.483321			−0.241661	+	0.970361i	$0.577692\pi$
$762$		−	84.4102i		−	3.05786i
$763$			9.11393i			0.329946i
$764$	−129.754			−4.69434
$765$	6.29084	+	10.0289i	0.227446	+	0.362596i
$766$	−25.2245			−0.911397
$767$			4.75135i			0.171561i
$768$		−	138.345i		−	4.99208i
$769$	47.1669			1.70088			0.850442	−	0.526069i	$-0.176335\pi$
$769$	47.1669			1.70088			0.850442	+	0.526069i	$0.176335\pi$
$770$	19.1459	−	12.0097i	0.689971	−	0.432799i
$771$	33.9447			1.22249
$772$		−	28.0170i		−	1.00835i
$773$			4.84839i			0.174384i	0.996192	+	0.0871922i	$0.0277894\pi$
$773$			4.84839i			0.174384i	−0.996192	+	0.0871922i	$0.972211\pi$
$774$	98.1978			3.52965
$775$	−13.0687	+	27.0311i	−0.469440	+	0.970984i
$776$	17.3760			0.623762
$777$		−	96.9947i		−	3.47966i
$778$			4.01103i			0.143802i
$779$	1.40525			0.0503484
$780$	−140.453	+	88.1018i	−5.02901	+	3.15455i
$781$	−7.40293			−0.264898
$782$		−	8.43068i		−	0.301481i
$783$		−	12.8224i		−	0.458235i
$784$	−101.859			−3.63783
$785$	12.6856	+	20.2235i	0.452770	+	0.721809i
$786$	−93.0562			−3.31920
$787$		−	36.2292i		−	1.29143i	−0.763578	−	0.645716i	$-0.776559\pi$
$787$		−	36.2292i		−	1.29143i	0.763578	−	0.645716i	$-0.223441\pi$
$788$			47.3433i			1.68654i
$789$	33.2266			1.18290
$790$	49.3939	+	78.7441i	1.75736	+	2.80159i
$791$	13.6282			0.484562
$792$			37.1135i			1.31877i
$793$			2.35076i			0.0834781i
$794$	−2.54771			−0.0904150
$795$	−38.2886	+	24.0173i	−1.35796	+	0.851806i
$796$	106.768			3.78429
$797$		−	2.57188i		−	0.0911007i	−0.998962	−	0.0455504i	$-0.985496\pi$
$797$		−	2.57188i		−	0.0911007i	0.998962	−	0.0455504i	$-0.0145041\pi$
$798$			26.4232i			0.935372i
$799$	−6.01067			−0.212642
$800$	−104.314	−	50.4325i	−3.68805	−	1.78306i
$801$	−67.3098			−2.37827
$802$		−	38.7320i		−	1.36767i
$803$			10.2839i			0.362911i
$804$	157.989			5.57185
$805$	15.5285	−	9.74060i	0.547309	−	0.343311i
$806$	−84.5338			−2.97758
$807$		−	16.6294i		−	0.585383i
$808$		−	115.597i		−	4.06668i
$809$	14.5842			0.512752			0.256376	−	0.966577i	$-0.417471\pi$
$809$	14.5842			0.512752			0.256376	+	0.966577i	$0.417471\pi$
$810$	18.9124	+	30.1503i	0.664514	+	1.05937i
$811$	−5.63124			−0.197740			−0.0988699	−	0.995100i	$-0.531523\pi$
$811$	−5.63124			−0.197740			−0.0988699	+	0.995100i	$0.531523\pi$
$812$		−	119.724i		−	4.20150i
$813$		−	19.5758i		−	0.686552i
$814$	−27.6334			−0.968551
$815$	−19.4469	−	31.0024i	−0.681194	−	1.08597i
$816$	−55.9578			−1.95892
$817$		−	9.33434i		−	0.326567i
$818$		−	0.853764i		−	0.0298512i
$819$	−72.4727			−2.53240
$820$	−14.7146	+	9.23005i	−0.513857	+	0.322327i
$821$	−18.9191			−0.660280			−0.330140	−	0.943932i	$-0.607096\pi$
$821$	−18.9191			−0.660280			−0.330140	+	0.943932i	$0.607096\pi$
$822$			11.7546i			0.409988i
$823$		−	21.2697i		−	0.741414i	−0.928750	−	0.370707i	$-0.879115\pi$
$823$		−	21.2697i		−	0.741414i	0.928750	−	0.370707i	$-0.120885\pi$
$824$	42.9992			1.49795
$825$	11.7680	+	5.68947i	0.409710	+	0.198082i
$826$	−9.35984			−0.325670
$827$			31.7156i			1.10286i	0.834221	+	0.551430i	$0.185917\pi$
$827$			31.7156i			1.10286i	−0.834221	+	0.551430i	$0.814083\pi$
$828$			47.1663i			1.63914i
$829$	−54.7328			−1.90095			−0.950474	−	0.310804i	$-0.899402\pi$
$829$	−54.7328			−1.90095			−0.950474	+	0.310804i	$0.899402\pi$
$830$	−11.6031	+	7.27830i	−0.402750	+	0.252633i
$831$	31.9072			1.10685
$832$		−	167.146i		−	5.79473i
$833$			9.07313i			0.314365i
$834$	−43.1987			−1.49585
$835$	20.8253	+	33.1999i	0.720690	+	1.14893i
$836$	5.52788			0.191186
$837$		−	13.0965i		−	0.452680i
$838$		−	74.7870i		−	2.58347i
$839$	−1.80551			−0.0623330			−0.0311665	−	0.999514i	$-0.509922\pi$
$839$	−1.80551			−0.0623330			−0.0311665	+	0.999514i	$0.509922\pi$
$840$	−110.762	−	176.578i	−3.82165	−	6.09251i
$841$	5.56531			0.191907
$842$			24.1606i			0.832628i
$843$			30.9398i			1.06562i
$844$	−104.416			−3.59413
$845$	−25.2419	+	15.8335i	−0.868349	+	0.544690i
$846$	45.7937			1.57442
$847$		−	3.68386i		−	0.126579i
$848$		−	119.858i		−	4.11594i
$849$	4.80052			0.164753
$850$	−8.24514	+	17.0541i	−0.282806	+	0.584952i
$851$	−22.4125			−0.768289
$852$			106.981i			3.66512i
$853$		−	1.16463i		−	0.0398761i	−0.999801	−	0.0199380i	$-0.993653\pi$
$853$		−	1.16463i		−	0.0398761i	0.999801	−	0.0199380i	$-0.00634689\pi$
$854$	−4.63084			−0.158464
$855$	−7.26304	+	4.55589i	−0.248391	+	0.155808i
$856$	127.659			4.36329
$857$			20.5156i			0.700799i	0.936600	+	0.350400i	$0.113954\pi$
$857$			20.5156i			0.700799i	−0.936600	+	0.350400i	$0.886046\pi$
$858$			36.8020i			1.25640i
$859$	−42.0393			−1.43436			−0.717181	−	0.696887i	$-0.754568\pi$
$859$	−42.0393			−1.43436			−0.717181	+	0.696887i	$0.754568\pi$
$860$	61.3103	+	97.7414i	2.09067	+	3.33295i
$861$	−13.5333			−0.461213
$862$			51.8620i			1.76643i
$863$			34.5403i			1.17577i	0.808946	+	0.587883i	$0.200038\pi$
$863$			34.5403i			1.17577i	−0.808946	+	0.587883i	$0.799962\pi$
$864$	50.5398			1.71940
$865$	4.09443	+	6.52737i	0.139215	+	0.221937i
$866$	18.0425			0.613109
$867$		−	39.4577i		−	1.34005i
$868$		−	122.283i		−	4.15057i
$869$	15.1511			0.513967
$870$	79.8801	−	50.1065i	2.70819	−	1.69877i
$871$	56.0935			1.90065
$872$		−	23.9471i		−	0.810950i
$873$			6.88306i			0.232956i
$874$	6.10558			0.206524
$875$	−40.9384	+	4.51714i	−1.38397	+	0.152707i
$876$	148.615			5.02123
$877$		−	3.22408i		−	0.108870i	−0.998517	−	0.0544348i	$-0.982664\pi$
$877$		−	3.22408i		−	0.108870i	0.998517	−	0.0544348i	$-0.0173357\pi$
$878$			91.3638i			3.08338i
$879$	−85.5599			−2.88586
$880$	−29.3640	+	18.4192i	−0.989861	+	0.620911i
$881$	12.1500			0.409342			0.204671	−	0.978831i	$-0.434388\pi$
$881$	12.1500			0.409342			0.204671	+	0.978831i	$0.434388\pi$
$882$		−	69.1257i		−	2.32758i
$883$		−	12.2591i		−	0.412552i	−0.978494	−	0.206276i	$-0.933866\pi$
$883$		−	12.2591i		−	0.412552i	0.978494	−	0.206276i	$-0.0661344\pi$
$884$	−39.1636			−1.31722
$885$	−2.87651	−	4.58575i	−0.0966928	−	0.154148i
$886$	−90.1553			−3.02883
$887$		−	5.97278i		−	0.200546i	−0.994960	−	0.100273i	$-0.968028\pi$
$887$		−	5.97278i		−	0.200546i	0.994960	−	0.100273i	$-0.0319717\pi$
$888$			254.856i			8.55240i
$889$	43.3527			1.45400
$890$	−57.2300	−	91.2365i	−1.91835	−	3.05826i
$891$	5.80122			0.194348
$892$			51.2296i			1.71529i
$893$		−	4.35299i		−	0.145667i
$894$	55.0313			1.84052
$895$	−2.33062	+	1.46193i	−0.0779040	+	0.0488669i
$896$	158.532			5.29618
$897$			29.8487i			0.996620i
$898$		−	102.859i		−	3.43244i
$899$	35.3041			1.17746
$900$	46.1282	−	95.4110i	1.53761	−	3.18037i
$901$	−10.6763			−0.355681
$902$			3.85559i			0.128377i
$903$			89.8945i			2.99150i
$904$	−35.8083			−1.19097
$905$	29.0015	−	18.1918i	0.964043	−	0.604716i
$906$	−105.688			−3.51126
$907$			49.2353i			1.63483i	0.576049	+	0.817415i	$0.304594\pi$
$907$			49.2353i			1.63483i	−0.576049	+	0.817415i	$0.695406\pi$
$908$		−	125.433i		−	4.16263i
$909$	45.7907			1.51878
$910$	−61.6198	−	98.2348i	−2.04268	−	3.25645i
$911$	−4.26265			−0.141228			−0.0706139	−	0.997504i	$-0.522496\pi$
$911$	−4.26265			−0.141228			−0.0706139	+	0.997504i	$0.522496\pi$
$912$		−	40.5252i		−	1.34192i
$913$			2.23255i			0.0738867i
$914$	−89.0030			−2.94396
$915$	−1.42317	−	2.26883i	−0.0470486	−	0.0750053i
$916$	−52.5557			−1.73649
$917$		−	47.7933i		−	1.57827i
$918$		−	8.26268i		−	0.272709i
$919$	−57.0538			−1.88203			−0.941016	−	0.338361i	$-0.890127\pi$
$919$	−57.0538			−1.88203			−0.941016	+	0.338361i	$0.890127\pi$
$920$	−40.8016	+	25.5937i	−1.34519	+	0.843798i
$921$	3.82785			0.126132
$922$			31.4317i			1.03515i
$923$			37.9833i			1.25024i
$924$	−53.2363			−1.75135
$925$	45.3374	+	21.9192i	1.49068	+	0.720699i
$926$	−105.184			−3.45657
$927$			17.0330i			0.559438i
$928$			136.240i			4.47230i
$929$	4.73196			0.155251			0.0776253	−	0.996983i	$-0.475266\pi$
$929$	4.73196			0.155251			0.0776253	+	0.996983i	$0.475266\pi$
$930$	81.5875	−	51.1775i	2.67536	−	1.67818i
$931$	−6.57085			−0.215351
$932$		−	113.967i		−	3.73310i
$933$			4.59367i			0.150390i
$934$	42.6912			1.39690
$935$	1.64069	+	2.61560i	0.0536564	+	0.0855394i
$936$	190.424			6.22419
$937$		−	53.7204i		−	1.75497i	−0.479605	−	0.877485i	$-0.659220\pi$
$937$		−	53.7204i		−	1.75497i	0.479605	−	0.877485i	$-0.340780\pi$
$938$			110.500i			3.60796i
$939$	4.66294			0.152169
$940$	28.5915	+	45.5808i	0.932553	+	1.48668i
$941$	−13.6878			−0.446208			−0.223104	−	0.974795i	$-0.571619\pi$
$941$	−13.6878			−0.446208			−0.223104	+	0.974795i	$0.571619\pi$
$942$		−	76.5778i		−	2.49504i
$943$			3.12712i			0.101833i
$944$	14.3551			0.467220
$945$	15.2191	−	9.54649i	0.495077	−	0.310547i
$946$	25.6106			0.832673
$947$			44.3802i			1.44216i	0.692850	+	0.721082i	$0.256355\pi$
$947$			44.3802i			1.44216i	−0.692850	+	0.721082i	$0.743645\pi$
$948$		−	218.952i		−	7.11124i
$949$	52.7651			1.71283
$950$	−12.3508	−	5.97121i	−0.400712	−	0.193732i
$951$	−21.0449			−0.682429
$952$		−	49.2367i		−	1.59577i
$953$			42.8836i			1.38914i	0.719427	+	0.694568i	$0.244404\pi$
$953$			42.8836i			1.38914i	−0.719427	+	0.694568i	$0.755596\pi$
$954$	81.3402			2.63349
$955$	44.4630	−	27.8904i	1.43879	−	0.902511i
$956$	−68.0160			−2.19979
$957$		−	15.3697i		−	0.496833i
$958$			11.8128i			0.381655i
$959$	−6.03710			−0.194948
$960$	101.191	+	161.320i	3.26594	+	5.20658i
$961$	5.05871			0.163184
$962$			141.783i			4.57126i
$963$			50.5689i			1.62956i
$964$	4.70676			0.151595
$965$	6.02218	+	9.60061i	0.193861	+	0.309055i
$966$	−58.7999			−1.89186
$967$		−	17.6917i		−	0.568927i	−0.958687	−	0.284463i	$-0.908185\pi$
$967$		−	17.6917i		−	0.568927i	0.958687	−	0.284463i	$-0.0918154\pi$
$968$			9.67944i			0.311109i
$969$	−3.60979			−0.115963
$970$	−9.32980	+	5.85231i	−0.299562	+	0.187906i
$971$	28.1838			0.904461			0.452231	−	0.891901i	$-0.350628\pi$
$971$	28.1838			0.904461			0.452231	+	0.891901i	$0.350628\pi$
$972$		−	120.003i		−	3.84910i
$973$		−	22.1867i		−	0.711271i
$974$	−89.4690			−2.86677
$975$	29.1918	−	60.3799i	0.934886	−	1.93371i
$976$	7.10231			0.227339
$977$		−	17.2693i		−	0.552495i	−0.961087	−	0.276248i	$-0.910909\pi$
$977$		−	17.2693i		−	0.552495i	0.961087	−	0.276248i	$-0.0890910\pi$
$978$			117.393i			3.75380i
$979$	−17.5548			−0.561054
$980$	68.8044	−	43.1590i	2.19788	−	1.37866i
$981$	9.48602			0.302865
$982$			56.1919i			1.79315i
$983$		−	32.7854i		−	1.04569i	−0.852427	−	0.522846i	$-0.824870\pi$
$983$		−	32.7854i		−	1.04569i	0.852427	−	0.522846i	$-0.175130\pi$
$984$	35.5590			1.13358
$985$	−10.1763	−	16.2232i	−0.324245	−	0.516914i
$986$	22.2737			0.709339
$987$			41.9215i			1.33438i
$988$		−	28.3627i		−	0.902338i
$989$	20.7718			0.660505
$990$	−12.5000	−	19.9276i	−0.397276	−	0.633340i
$991$	37.2868			1.18446			0.592228	−	0.805771i	$-0.298249\pi$
$991$	37.2868			1.18446			0.592228	+	0.805771i	$0.298249\pi$
$992$			139.152i			4.41808i
$993$		−	64.1821i		−	2.03676i
$994$	−74.8245			−2.37329
$995$	−36.5863	+	22.9495i	−1.15986	+	0.727548i
$996$	32.2631			1.02230
$997$		−	38.8581i		−	1.23065i	−0.788274	−	0.615324i	$-0.789025\pi$
$997$		−	38.8581i		−	1.23065i	0.788274	−	0.615324i	$-0.210975\pi$
$998$		−	45.9654i		−	1.45501i
$999$	−21.9658			−0.694968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.d.419.1	✓	22
5.2	odd	4		5225.2.a.bb.1.22		22
5.3	odd	4		5225.2.a.bb.1.1		22
5.4	even	2	inner	1045.2.b.d.419.22	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.d.419.1	✓	22	1.1	even	1	trivial
1045.2.b.d.419.22	yes	22	5.4	even	2	inner
5225.2.a.bb.1.1		22	5.3	odd	4
5225.2.a.bb.1.22		22	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.74370i q^{2} -2.61424i q^{3} -5.52788 q^{4} +(1.89425 - 1.18821i) q^{5} -7.17269 q^{6} -3.68386i q^{7} +9.67944i q^{8} -3.83426 q^{9} +O(q^{10})\)	\(q-2.74370i q^{2} -2.61424i q^{3} -5.52788 q^{4} +(1.89425 - 1.18821i) q^{5} -7.17269 q^{6} -3.68386i q^{7} +9.67944i q^{8} -3.83426 q^{9} +(-3.26008 - 5.19724i) q^{10} -1.00000 q^{11} +14.4512i q^{12} +5.13085i q^{13} -10.1074 q^{14} +(-3.10626 - 4.95202i) q^{15} +15.5017 q^{16} -1.38082i q^{17} +10.5201i q^{18} +1.00000 q^{19} +(-10.4712 + 6.56826i) q^{20} -9.63051 q^{21} +2.74370i q^{22} +2.22531i q^{23} +25.3044 q^{24} +(2.17634 - 4.50151i) q^{25} +14.0775 q^{26} +2.18097i q^{27} +20.3640i q^{28} -5.87923 q^{29} +(-13.5868 + 8.52263i) q^{30} -6.00489 q^{31} -23.1731i q^{32} +2.61424i q^{33} -3.78854 q^{34} +(-4.37719 - 6.97814i) q^{35} +21.1953 q^{36} +10.0716i q^{37} -2.74370i q^{38} +13.4133 q^{39} +(11.5012 + 18.3352i) q^{40} +1.40525 q^{41} +26.4232i q^{42} -9.33434i q^{43} +5.52788 q^{44} +(-7.26304 + 4.55589i) q^{45} +6.10558 q^{46} -4.35299i q^{47} -40.5252i q^{48} -6.57085 q^{49} +(-12.3508 - 5.97121i) q^{50} -3.60979 q^{51} -28.3627i q^{52} -7.73192i q^{53} +5.98391 q^{54} +(-1.89425 + 1.18821i) q^{55} +35.6577 q^{56} -2.61424i q^{57} +16.1308i q^{58} +0.926037 q^{59} +(17.1710 + 27.3742i) q^{60} +0.458163 q^{61} +16.4756i q^{62} +14.1249i q^{63} -32.5766 q^{64} +(6.09650 + 9.71908i) q^{65} +7.17269 q^{66} -10.9326i q^{67} +7.63298i q^{68} +5.81750 q^{69} +(-19.1459 + 12.0097i) q^{70} +7.40293 q^{71} -37.1135i q^{72} -10.2839i q^{73} +27.6334 q^{74} +(-11.7680 - 5.68947i) q^{75} -5.52788 q^{76} +3.68386i q^{77} -36.8020i q^{78} -15.1511 q^{79} +(29.3640 - 18.4192i) q^{80} -5.80122 q^{81} -3.85559i q^{82} -2.23255i q^{83} +53.2363 q^{84} +(-1.64069 - 2.61560i) q^{85} -25.6106 q^{86} +15.3697i q^{87} -9.67944i q^{88} +17.5548 q^{89} +(12.5000 + 19.9276i) q^{90} +18.9013 q^{91} -12.3013i q^{92} +15.6982i q^{93} -11.9433 q^{94} +(1.89425 - 1.18821i) q^{95} -60.5801 q^{96} -1.79515i q^{97} +18.0284i q^{98} +3.83426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9}+O(q^{10}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9	\( 22 q - 32 q^{4} + 7 q^{5} - 12 q^{6} - 34 q^{9} + 2 q^{10} - 22 q^{11} + 8 q^{14} - 23 q^{15} + 40 q^{16} + 22 q^{19} - 22 q^{20} - 22 q^{21} + 22 q^{24} + 13 q^{25} + 16 q^{26} + 10 q^{29} - 22 q^{30} + 76 q^{31} - 56 q^{34} - 2 q^{35} + 104 q^{36} + 8 q^{39} - 20 q^{40} + 6 q^{41} + 32 q^{44} - 12 q^{45} + 88 q^{46} - 28 q^{49} - 20 q^{50} + 8 q^{51} - 38 q^{54} - 7 q^{55} + 44 q^{56} - 40 q^{59} + 78 q^{60} - 6 q^{61} - 140 q^{64} - 22 q^{65} + 12 q^{66} - 74 q^{69} - 24 q^{70} + 62 q^{71} + 26 q^{74} + 13 q^{75} - 32 q^{76} - 102 q^{79} + 142 q^{80} + 94 q^{81} + 38 q^{84} + 26 q^{85} + 28 q^{86} - 54 q^{89} + 118 q^{90} + 88 q^{91} - 36 q^{94} + 7 q^{95} + 2 q^{96} + 34 q^{99}+O(q^{100}) \) 22 * q - 32 * q^4 + 7 * q^5 - 12 * q^6 - 34 * q^9 + 2 * q^10 - 22 * q^11 + 8 * q^14 - 23 * q^15 + 40 * q^16 + 22 * q^19 - 22 * q^20 - 22 * q^21 + 22 * q^24 + 13 * q^25 + 16 * q^26 + 10 * q^29 - 22 * q^30 + 76 * q^31 - 56 * q^34 - 2 * q^35 + 104 * q^36 + 8 * q^39 - 20 * q^40 + 6 * q^41 + 32 * q^44 - 12 * q^45 + 88 * q^46 - 28 * q^49 - 20 * q^50 + 8 * q^51 - 38 * q^54 - 7 * q^55 + 44 * q^56 - 40 * q^59 + 78 * q^60 - 6 * q^61 - 140 * q^64 - 22 * q^65 + 12 * q^66 - 74 * q^69 - 24 * q^70 + 62 * q^71 + 26 * q^74 + 13 * q^75 - 32 * q^76 - 102 * q^79 + 142 * q^80 + 94 * q^81 + 38 * q^84 + 26 * q^85 + 28 * q^86 - 54 * q^89 + 118 * q^90 + 88 * q^91 - 36 * q^94 + 7 * q^95 + 2 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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