LMFDB - Embedded newform 1045.2.b.e.419.17

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:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.17
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.379302i q^{2} -2.60759i q^{3} +1.85613 q^{4} +(2.20907 + 0.346449i) q^{5} +0.989065 q^{6} +4.15654i q^{7} +1.46264i q^{8} -3.79954 q^{9} +O(q^{10})$	\(q+0.379302i q^{2} -2.60759i q^{3} +1.85613 q^{4} +(2.20907 + 0.346449i) q^{5} +0.989065 q^{6} +4.15654i q^{7} +1.46264i q^{8} -3.79954 q^{9} +(-0.131409 + 0.837903i) q^{10} +1.00000 q^{11} -4.84003i q^{12} -0.808855i q^{13} -1.57658 q^{14} +(0.903398 - 5.76035i) q^{15} +3.15748 q^{16} +5.26829i q^{17} -1.44117i q^{18} -1.00000 q^{19} +(4.10031 + 0.643055i) q^{20} +10.8386 q^{21} +0.379302i q^{22} -2.49456i q^{23} +3.81396 q^{24} +(4.75995 + 1.53066i) q^{25} +0.306800 q^{26} +2.08489i q^{27} +7.71508i q^{28} +2.90329 q^{29} +(2.18491 + 0.342661i) q^{30} +2.50775 q^{31} +4.12291i q^{32} -2.60759i q^{33} -1.99827 q^{34} +(-1.44003 + 9.18207i) q^{35} -7.05245 q^{36} -2.11138i q^{37} -0.379302i q^{38} -2.10917 q^{39} +(-0.506729 + 3.23106i) q^{40} -11.9805 q^{41} +4.11109i q^{42} -1.42063i q^{43} +1.85613 q^{44} +(-8.39344 - 1.31635i) q^{45} +0.946192 q^{46} +4.28038i q^{47} -8.23342i q^{48} -10.2768 q^{49} +(-0.580581 + 1.80546i) q^{50} +13.7376 q^{51} -1.50134i q^{52} -7.81180i q^{53} -0.790801 q^{54} +(2.20907 + 0.346449i) q^{55} -6.07951 q^{56} +2.60759i q^{57} +1.10122i q^{58} +9.86819 q^{59} +(1.67683 - 10.6920i) q^{60} -1.27005 q^{61} +0.951193i q^{62} -15.7930i q^{63} +4.75113 q^{64} +(0.280227 - 1.78682i) q^{65} +0.989065 q^{66} -7.58859i q^{67} +9.77863i q^{68} -6.50480 q^{69} +(-3.48277 - 0.546205i) q^{70} -8.49943 q^{71} -5.55735i q^{72} -6.86804i q^{73} +0.800850 q^{74} +(3.99133 - 12.4120i) q^{75} -1.85613 q^{76} +4.15654i q^{77} -0.800010i q^{78} -3.74373 q^{79} +(6.97508 + 1.09391i) q^{80} -5.96210 q^{81} -4.54421i q^{82} -15.8542i q^{83} +20.1178 q^{84} +(-1.82519 + 11.6380i) q^{85} +0.538847 q^{86} -7.57060i q^{87} +1.46264i q^{88} +1.09693 q^{89} +(0.499293 - 3.18365i) q^{90} +3.36204 q^{91} -4.63023i q^{92} -6.53919i q^{93} -1.62356 q^{94} +(-2.20907 - 0.346449i) q^{95} +10.7509 q^{96} +9.76079i q^{97} -3.89801i q^{98} -3.79954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * 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 $

$2$			0.379302i			0.268207i	0.990967	+	0.134103i	$0.0428154\pi$
$2$			0.379302i			0.268207i	−0.990967	+	0.134103i	$0.957185\pi$
$3$		−	2.60759i		−	1.50549i	−0.658309	−	0.752747i	$-0.728728\pi$
$3$		−	2.60759i		−	1.50549i	0.658309	−	0.752747i	$-0.271272\pi$
$4$	1.85613			0.928065
$5$	2.20907	+	0.346449i	0.987924	+	0.154937i
$5$	2.20907	+	0.346449i	0.987924	+	0.154937i
$6$	0.989065			0.403784
$7$			4.15654i			1.57102i	0.618847	+	0.785512i	$0.287600\pi$
$7$			4.15654i			1.57102i	−0.618847	+	0.785512i	$0.712400\pi$
$8$			1.46264i			0.517120i
$9$	−3.79954			−1.26651
$10$	−0.131409	+	0.837903i	−0.0415551	+	0.264968i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	4.84003i		−	1.39720i
$13$		−	0.808855i		−	0.224336i	−0.993689	−	0.112168i	$-0.964220\pi$
$13$		−	0.808855i		−	0.224336i	0.993689	−	0.112168i	$-0.0357795\pi$
$14$	−1.57658			−0.421359
$15$	0.903398	−	5.76035i	0.233256	−	1.48732i
$16$	3.15748			0.789370
$17$			5.26829i			1.27775i	0.769311	+	0.638874i	$0.220599\pi$
$17$			5.26829i			1.27775i	−0.769311	+	0.638874i	$0.779401\pi$
$18$		−	1.44117i		−	0.339688i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	4.10031	+	0.643055i	0.916858	+	0.143791i
$21$	10.8386			2.36517
$22$			0.379302i			0.0808674i
$23$		−	2.49456i		−	0.520152i	−0.965588	−	0.260076i	$-0.916252\pi$
$23$		−	2.49456i		−	0.520152i	0.965588	−	0.260076i	$-0.0837476\pi$
$24$	3.81396			0.778522
$25$	4.75995	+	1.53066i	0.951989	+	0.306132i
$26$	0.306800			0.0601685
$27$			2.08489i			0.401237i
$28$			7.71508i			1.45801i
$29$	2.90329			0.539127			0.269564	−	0.962983i	$-0.413121\pi$
$29$	2.90329			0.539127			0.269564	+	0.962983i	$0.413121\pi$
$30$	2.18491	+	0.342661i	0.398908	+	0.0625610i
$31$	2.50775			0.450405			0.225202	−	0.974312i	$-0.427696\pi$
$31$	2.50775			0.450405			0.225202	+	0.974312i	$0.427696\pi$
$32$			4.12291i			0.728835i
$33$		−	2.60759i		−	0.453924i
$34$	−1.99827			−0.342701
$35$	−1.44003	+	9.18207i	−0.243409	+	1.55205i
$36$	−7.05245			−1.17541
$37$		−	2.11138i		−	0.347109i	−0.984824	−	0.173554i	$-0.944475\pi$
$37$		−	2.11138i		−	0.347109i	0.984824	−	0.173554i	$-0.0555252\pi$
$38$		−	0.379302i		−	0.0615309i
$39$	−2.10917			−0.337737
$40$	−0.506729	+	3.23106i	−0.0801209	+	0.510876i
$41$	−11.9805			−1.87104			−0.935518	−	0.353280i	$-0.885066\pi$
$41$	−11.9805			−1.87104			−0.935518	+	0.353280i	$0.885066\pi$
$42$			4.11109i			0.634354i
$43$		−	1.42063i		−	0.216644i	−0.994116	−	0.108322i	$-0.965452\pi$
$43$		−	1.42063i		−	0.216644i	0.994116	−	0.108322i	$-0.0345478\pi$
$44$	1.85613			0.279822
$45$	−8.39344	−	1.31635i	−1.25122	−	0.196230i
$46$	0.946192			0.139508
$47$			4.28038i			0.624358i	0.950023	+	0.312179i	$0.101059\pi$
$47$			4.28038i			0.624358i	−0.950023	+	0.312179i	$0.898941\pi$
$48$		−	8.23342i		−	1.18839i
$49$	−10.2768			−1.46812
$50$	−0.580581	+	1.80546i	−0.0821066	+	0.255330i
$51$	13.7376			1.92364
$52$		−	1.50134i		−	0.208199i
$53$		−	7.81180i		−	1.07303i	−0.843890	−	0.536517i	$-0.819740\pi$
$53$		−	7.81180i		−	1.07303i	0.843890	−	0.536517i	$-0.180260\pi$
$54$	−0.790801			−0.107614
$55$	2.20907	+	0.346449i	0.297870	+	0.0467152i
$56$	−6.07951			−0.812408
$57$			2.60759i			0.345384i
$58$			1.10122i			0.144598i
$59$	9.86819			1.28473			0.642365	−	0.766399i	$-0.277953\pi$
$59$	9.86819			1.28473			0.642365	+	0.766399i	$0.277953\pi$
$60$	1.67683	−	10.6920i	0.216477	−	1.38033i
$61$	−1.27005			−0.162613			−0.0813063	−	0.996689i	$-0.525909\pi$
$61$	−1.27005			−0.162613			−0.0813063	+	0.996689i	$0.525909\pi$
$62$			0.951193i			0.120802i
$63$		−	15.7930i		−	1.98972i
$64$	4.75113			0.593892
$65$	0.280227	−	1.78682i	0.0347579	−	0.221627i
$66$	0.989065			0.121745
$67$		−	7.58859i		−	0.927094i	−0.886072	−	0.463547i	$-0.846577\pi$
$67$		−	7.58859i		−	0.927094i	0.886072	−	0.463547i	$-0.153423\pi$
$68$			9.77863i			1.18583i
$69$	−6.50480			−0.783086
$70$	−3.48277	−	0.546205i	−0.416271	−	0.0652840i
$71$	−8.49943			−1.00870			−0.504348	−	0.863500i	$-0.668267\pi$
$71$	−8.49943			−1.00870			−0.504348	+	0.863500i	$0.668267\pi$
$72$		−	5.55735i		−	0.654940i
$73$		−	6.86804i		−	0.803844i	−0.915674	−	0.401922i	$-0.868342\pi$
$73$		−	6.86804i		−	0.803844i	0.915674	−	0.401922i	$-0.131658\pi$
$74$	0.800850			0.0930969
$75$	3.99133	−	12.4120i	0.460880	−	1.43321i
$76$	−1.85613			−0.212913
$77$			4.15654i			0.473681i
$78$		−	0.800010i		−	0.0905833i
$79$	−3.74373			−0.421202			−0.210601	−	0.977572i	$-0.567542\pi$
$79$	−3.74373			−0.421202			−0.210601	+	0.977572i	$0.567542\pi$
$80$	6.97508	+	1.09391i	0.779838	+	0.122302i
$81$	−5.96210			−0.662455
$82$		−	4.54421i		−	0.501824i
$83$		−	15.8542i		−	1.74022i	−0.492857	−	0.870110i	$-0.664048\pi$
$83$		−	15.8542i		−	1.74022i	0.492857	−	0.870110i	$-0.335952\pi$
$84$	20.1178			2.19503
$85$	−1.82519	+	11.6380i	−0.197970	+	1.26232i
$86$	0.538847			0.0581054
$87$		−	7.57060i		−	0.811653i
$88$			1.46264i			0.155918i
$89$	1.09693			0.116274			0.0581369	−	0.998309i	$-0.481484\pi$
$89$	1.09693			0.116274			0.0581369	+	0.998309i	$0.481484\pi$
$90$	0.499293	−	3.18365i	0.0526301	−	0.335586i
$91$	3.36204			0.352437
$92$		−	4.63023i		−	0.482735i
$93$		−	6.53919i		−	0.678082i
$94$	−1.62356			−0.167457
$95$	−2.20907	−	0.346449i	−0.226645	−	0.0355449i
$96$	10.7509			1.09726
$97$			9.76079i			0.991058i	0.868591	+	0.495529i	$0.165026\pi$
$97$			9.76079i			0.991058i	−0.868591	+	0.495529i	$0.834974\pi$
$98$		−	3.89801i		−	0.393759i
$99$	−3.79954			−0.381869
$100$	8.83508	+	2.84110i	0.883508	+	0.284110i
$101$	−15.2672			−1.51915			−0.759573	−	0.650423i	$-0.774592\pi$
$101$	−15.2672			−1.51915			−0.759573	+	0.650423i	$0.774592\pi$
$102$			5.21068i			0.515934i
$103$		−	9.87892i		−	0.973399i	−0.873570	−	0.486699i	$-0.838201\pi$
$103$		−	9.87892i		−	0.973399i	0.873570	−	0.486699i	$-0.161799\pi$
$104$	1.18306			0.116009
$105$	23.9431	+	3.75501i	2.33661	+	0.366451i
$106$	2.96303			0.287795
$107$		−	1.88410i		−	0.182143i	−0.995844	−	0.0910713i	$-0.970971\pi$
$107$		−	1.88410i		−	0.182143i	0.995844	−	0.0910713i	$-0.0290291\pi$
$108$			3.86982i			0.372374i
$109$	2.50045			0.239499			0.119750	−	0.992804i	$-0.461791\pi$
$109$	2.50045			0.239499			0.119750	+	0.992804i	$0.461791\pi$
$110$	−0.131409	+	0.837903i	−0.0125293	+	0.0798909i
$111$	−5.50562			−0.522570
$112$			13.1242i			1.24012i
$113$		−	0.200129i		−	0.0188266i	−0.999956	−	0.00941328i	$-0.997004\pi$
$113$		−	0.200129i		−	0.0188266i	0.999956	−	0.00941328i	$-0.00299638\pi$
$114$	−0.989065			−0.0926344
$115$	0.864239	−	5.51065i	0.0805907	−	0.513871i
$116$	5.38888			0.500345
$117$			3.07328i			0.284125i
$118$			3.74302i			0.344573i
$119$	−21.8978			−2.00737
$120$	8.42530	+	1.32134i	0.769121	+	0.120622i
$121$	1.00000			0.0909091
$122$		−	0.481730i		−	0.0436138i
$123$			31.2402i			2.81683i
$124$	4.65471			0.418005
$125$	9.98474	+	5.03040i	0.893062	+	0.449933i
$126$	5.99029			0.533658
$127$		−	9.37956i		−	0.832301i	−0.909296	−	0.416151i	$-0.863379\pi$
$127$		−	9.37956i		−	0.832301i	0.909296	−	0.416151i	$-0.136621\pi$
$128$			10.0479i			0.888120i
$129$	−3.70442			−0.326156
$130$	0.677742	+	0.106291i	0.0594419	+	0.00932231i
$131$	10.0207			0.875513			0.437756	−	0.899094i	$-0.355773\pi$
$131$	10.0207			0.875513			0.437756	+	0.899094i	$0.355773\pi$
$132$		−	4.84003i		−	0.421271i
$133$		−	4.15654i		−	0.360418i
$134$	2.87836			0.248653
$135$	−0.722307	+	4.60565i	−0.0621663	+	0.396392i
$136$	−7.70559			−0.660749
$137$			14.3772i			1.22833i	0.789178	+	0.614165i	$0.210507\pi$
$137$			14.3772i			1.22833i	−0.789178	+	0.614165i	$0.789493\pi$
$138$		−	2.46728i		−	0.210029i
$139$	11.9706			1.01533			0.507665	−	0.861555i	$-0.330509\pi$
$139$	11.9706			1.01533			0.507665	+	0.861555i	$0.330509\pi$
$140$	−2.67288	+	17.0431i	−0.225900	+	1.44041i
$141$	11.1615			0.939968
$142$		−	3.22385i		−	0.270539i
$143$		−	0.808855i		−	0.0676399i
$144$	−11.9970			−0.999749
$145$	6.41356	+	1.00584i	0.532617	+	0.0835306i
$146$	2.60506			0.215596
$147$			26.7977i			2.21024i
$148$		−	3.91900i		−	0.322139i
$149$	−19.0313			−1.55911			−0.779554	−	0.626335i	$-0.784554\pi$
$149$	−19.0313			−1.55911			−0.779554	+	0.626335i	$0.784554\pi$
$150$	4.70789	+	1.51392i	0.384398	+	0.123611i
$151$	−9.88955			−0.804800			−0.402400	−	0.915464i	$-0.631824\pi$
$151$	−9.88955			−0.804800			−0.402400	+	0.915464i	$0.631824\pi$
$152$		−	1.46264i		−	0.118636i
$153$		−	20.0171i		−	1.61829i
$154$	−1.57658			−0.127045
$155$	5.53978	+	0.868807i	0.444966	+	0.0697842i
$156$	−3.91489			−0.313442
$157$			18.4940i			1.47598i	0.674811	+	0.737991i	$0.264225\pi$
$157$			18.4940i			1.47598i	−0.674811	+	0.737991i	$0.735775\pi$
$158$		−	1.42000i		−	0.112969i
$159$	−20.3700			−1.61545
$160$	−1.42838	+	9.10778i	−0.112923	+	0.720033i
$161$	10.3687			0.817171
$162$		−	2.26143i		−	0.177675i
$163$		−	20.3815i		−	1.59640i	−0.602390	−	0.798202i	$-0.705785\pi$
$163$		−	20.3815i		−	1.59640i	0.602390	−	0.798202i	$-0.294215\pi$
$164$	−22.2373			−1.73644
$165$	0.903398	−	5.76035i	0.0703295	−	0.448442i
$166$	6.01351			0.466739
$167$			6.53284i			0.505526i	0.967528	+	0.252763i	$0.0813394\pi$
$167$			6.53284i			0.505526i	−0.967528	+	0.252763i	$0.918661\pi$
$168$			15.8529i			1.22308i
$169$	12.3458			0.949673
$170$	−4.41431	−	0.692299i	−0.338562	−	0.0530969i
$171$	3.79954			0.290558
$172$		−	2.63687i		−	0.201060i
$173$		−	6.56825i		−	0.499375i	−0.968327	−	0.249687i	$-0.919672\pi$
$173$		−	6.56825i		−	0.499375i	0.968327	−	0.249687i	$-0.0803278\pi$
$174$	2.87154			0.217691
$175$	−6.36224	+	19.7849i	−0.480940	+	1.49560i
$176$	3.15748			0.238004
$177$		−	25.7322i		−	1.93415i
$178$			0.416066i			0.0311854i
$179$	−19.1738			−1.43312			−0.716560	−	0.697525i	$-0.754284\pi$
$179$	−19.1738			−1.43312			−0.716560	+	0.697525i	$0.754284\pi$
$180$	−15.5793	−	2.44331i	−1.16121	−	0.182114i
$181$	−7.26851			−0.540264			−0.270132	−	0.962823i	$-0.587067\pi$
$181$	−7.26851			−0.540264			−0.270132	+	0.962823i	$0.587067\pi$
$182$			1.27523i			0.0945261i
$183$			3.31176i			0.244813i
$184$	3.64864			0.268981
$185$	0.731486	−	4.66418i	0.0537799	−	0.342917i
$186$	2.48032			0.181866
$187$			5.26829i			0.385255i
$188$			7.94495i			0.579445i
$189$	−8.66591			−0.630352
$190$	0.131409	−	0.837903i	0.00953339	−	0.0607878i
$191$	−17.1715			−1.24249			−0.621244	−	0.783617i	$-0.713372\pi$
$191$	−17.1715			−1.24249			−0.621244	+	0.783617i	$0.713372\pi$
$192$		−	12.3890i		−	0.894101i
$193$		−	1.24791i		−	0.0898268i	−0.998991	−	0.0449134i	$-0.985699\pi$
$193$		−	1.24791i		−	0.0898268i	0.998991	−	0.0449134i	$-0.0143012\pi$
$194$	−3.70228			−0.265808
$195$	−4.65929	−	0.730719i	−0.333659	−	0.0523279i
$196$	−19.0751			−1.36251
$197$		−	15.8699i		−	1.13068i	−0.824857	−	0.565341i	$-0.808745\pi$
$197$		−	15.8699i		−	1.13068i	0.824857	−	0.565341i	$-0.191255\pi$
$198$		−	1.44117i		−	0.102420i
$199$	−16.5207			−1.17112			−0.585560	−	0.810629i	$-0.699125\pi$
$199$	−16.5207			−1.17112			−0.585560	+	0.810629i	$0.699125\pi$
$200$	−2.23880	+	6.96207i	−0.158307	+	0.492293i
$201$	−19.7880			−1.39573
$202$		−	5.79088i		−	0.407445i
$203$			12.0676i			0.846982i
$204$	25.4987			1.78527
$205$	−26.4657	−	4.15062i	−1.84844	−	0.289892i
$206$	3.74709			0.261072
$207$			9.47820i			0.658780i
$208$		−	2.55394i		−	0.177084i
$209$	−1.00000			−0.0691714
$210$	−1.42428	+	9.08166i	−0.0982848	+	0.626694i
$211$	16.4238			1.13066			0.565330	−	0.824865i	$-0.308749\pi$
$211$	16.4238			1.13066			0.565330	+	0.824865i	$0.308749\pi$
$212$		−	14.4997i		−	0.995845i
$213$			22.1631i			1.51859i
$214$	0.714642			0.0488519
$215$	0.492176	−	3.13826i	0.0335661	−	0.214028i
$216$	−3.04943			−0.207488
$217$			10.4235i			0.707596i
$218$			0.948424i			0.0642353i
$219$	−17.9091			−1.21018
$220$	4.10031	+	0.643055i	0.276443	+	0.0433547i
$221$	4.26128			0.286645
$222$		−	2.08829i		−	0.140157i
$223$			21.2434i			1.42256i	0.702908	+	0.711281i	$0.251884\pi$
$223$			21.2434i			1.42256i	−0.702908	+	0.711281i	$0.748116\pi$
$224$	−17.1370			−1.14502
$225$	−18.0856	−	5.81580i	−1.20571	−	0.387720i
$226$	0.0759093			0.00504941
$227$		−	29.4936i		−	1.95756i	−0.204913	−	0.978780i	$-0.565691\pi$
$227$		−	29.4936i		−	1.95756i	0.204913	−	0.978780i	$-0.434309\pi$
$228$			4.84003i			0.320539i
$229$	25.8556			1.70859			0.854293	−	0.519792i	$-0.173991\pi$
$229$	25.8556			1.70859			0.854293	+	0.519792i	$0.173991\pi$
$230$	2.09020	+	0.327807i	0.137824	+	0.0216150i
$231$	10.8386			0.713125
$232$			4.24646i			0.278794i
$233$			9.22686i			0.604472i	0.953233	+	0.302236i	$0.0977330\pi$
$233$			9.22686i			0.604472i	−0.953233	+	0.302236i	$0.902267\pi$
$234$	−1.16570			−0.0762043
$235$	−1.48293	+	9.45565i	−0.0967360	+	0.616818i
$236$	18.3167			1.19231
$237$			9.76212i			0.634118i
$238$		−	8.30589i		−	0.538391i
$239$	12.3546			0.799151			0.399575	−	0.916700i	$-0.369158\pi$
$239$	12.3546			0.799151			0.399575	+	0.916700i	$0.369158\pi$
$240$	2.85246	−	18.1882i	0.184126	−	1.17404i
$241$	15.2993			0.985511			0.492756	−	0.870168i	$-0.335990\pi$
$241$	15.2993			0.985511			0.492756	+	0.870168i	$0.335990\pi$
$242$			0.379302i			0.0243824i
$243$			21.8014i			1.39856i
$244$	−2.35737			−0.150915
$245$	−22.7021	−	3.56039i	−1.45039	−	0.227465i
$246$	−11.8495			−0.755494
$247$			0.808855i			0.0514662i
$248$			3.66792i			0.232913i
$249$	−41.3412			−2.61989
$250$	−1.90804	+	3.78723i	−0.120675	+	0.239525i
$251$	−14.6172			−0.922631			−0.461316	−	0.887236i	$-0.652622\pi$
$251$	−14.6172			−0.922631			−0.461316	+	0.887236i	$0.652622\pi$
$252$		−	29.3138i		−	1.84659i
$253$		−	2.49456i		−	0.156832i
$254$	3.55768			0.223229
$255$	30.3472	+	4.75936i	1.90041	+	0.298043i
$256$	5.69107			0.355692
$257$			27.7037i			1.72811i	0.503397	+	0.864055i	$0.332083\pi$
$257$			27.7037i			1.72811i	−0.503397	+	0.864055i	$0.667917\pi$
$258$		−	1.40509i		−	0.0874774i
$259$	8.77603			0.545316
$260$	0.520138	−	3.31656i	0.0322576	−	0.205684i
$261$	−11.0312			−0.682813
$262$			3.80087i			0.234818i
$263$		−	21.3961i		−	1.31934i	−0.751556	−	0.659669i	$-0.770697\pi$
$263$		−	21.3961i		−	1.31934i	0.751556	−	0.659669i	$-0.229303\pi$
$264$	3.81396			0.234733
$265$	2.70639	−	17.2568i	0.166252	−	1.06008i
$266$	1.57658			0.0966664
$267$		−	2.86034i		−	0.175050i
$268$		−	14.0854i		−	0.860403i
$269$	11.8616			0.723214			0.361607	−	0.932331i	$-0.382228\pi$
$269$	11.8616			0.723214			0.361607	+	0.932331i	$0.382228\pi$
$270$	−1.74693	−	0.273972i	−0.106315	−	0.0166734i
$271$	28.2159			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$271$	28.2159			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$272$			16.6345i			1.00862i
$273$		−	8.76683i		−	0.530593i
$274$	−5.45331			−0.329446
$275$	4.75995	+	1.53066i	0.287036	+	0.0923021i
$276$	−12.0738			−0.726755
$277$		−	14.9525i		−	0.898407i	−0.893430	−	0.449203i	$-0.851708\pi$
$277$		−	14.9525i		−	0.898407i	0.893430	−	0.449203i	$-0.148292\pi$
$278$			4.54045i			0.272318i
$279$	−9.52830			−0.570444
$280$	−13.4300	−	2.10624i	−0.802598	−	0.125872i
$281$	−18.8813			−1.12637			−0.563183	−	0.826332i	$-0.690423\pi$
$281$	−18.8813			−1.12637			−0.563183	+	0.826332i	$0.690423\pi$
$282$			4.23358i			0.252106i
$283$			9.06589i			0.538912i	0.963013	+	0.269456i	$0.0868438\pi$
$283$			9.06589i			0.538912i	−0.963013	+	0.269456i	$0.913156\pi$
$284$	−15.7760			−0.936136
$285$	−0.903398	+	5.76035i	−0.0535127	+	0.341213i
$286$	0.306800			0.0181415
$287$		−	49.7973i		−	2.93944i
$288$		−	15.6652i		−	0.923080i
$289$	−10.7549			−0.632639
$290$	−0.381518	+	2.43267i	−0.0224035	+	0.142851i
$291$	25.4522			1.49203
$292$		−	12.7480i		−	0.746019i
$293$			23.4422i			1.36951i	0.728774	+	0.684754i	$0.240091\pi$
$293$			23.4422i			1.36951i	−0.728774	+	0.684754i	$0.759909\pi$
$294$	−10.1644			−0.592801
$295$	21.7995	+	3.41883i	1.26922	+	0.199052i
$296$	3.08818			0.179497
$297$			2.08489i			0.120977i
$298$		−	7.21862i		−	0.418163i
$299$	−2.01774			−0.116689
$300$	7.40844	−	23.0383i	0.427726	−	1.33012i
$301$	5.90490			0.340353
$302$		−	3.75112i		−	0.215853i
$303$			39.8107i			2.28707i
$304$	−3.15748			−0.181094
$305$	−2.80561	−	0.440006i	−0.160649	−	0.0251947i
$306$	7.59252			0.434035
$307$			6.48182i			0.369937i	0.982744	+	0.184969i	$0.0592183\pi$
$307$			6.48182i			0.369937i	−0.982744	+	0.184969i	$0.940782\pi$
$308$			7.71508i			0.439607i
$309$	−25.7602			−1.46545
$310$	−0.329540	+	2.10125i	−0.0187166	+	0.119343i
$311$	−19.0114			−1.07804			−0.539018	−	0.842295i	$-0.681204\pi$
$311$	−19.0114			−1.07804			−0.539018	+	0.842295i	$0.681204\pi$
$312$		−	3.08494i		−	0.174651i
$313$			23.6268i			1.33547i	0.744400	+	0.667733i	$0.232735\pi$
$313$			23.6268i			1.33547i	−0.744400	+	0.667733i	$0.767265\pi$
$314$	−7.01480			−0.395868
$315$	5.47145	−	34.8877i	0.308281	−	1.96570i
$316$	−6.94885			−0.390903
$317$			8.90271i			0.500026i	0.968242	+	0.250013i	$0.0804349\pi$
$317$			8.90271i			0.500026i	−0.968242	+	0.250013i	$0.919565\pi$
$318$		−	7.72638i		−	0.433274i
$319$	2.90329			0.162553
$320$	10.4956	+	1.64603i	0.586720	+	0.0920156i
$321$	−4.91296			−0.274215
$322$			3.93288i			0.219171i
$323$		−	5.26829i		−	0.293135i
$324$	−11.0664			−0.614801
$325$	1.23808	−	3.85011i	0.0686764	−	0.213566i
$326$	7.73074			0.428166
$327$		−	6.52015i		−	0.360565i
$328$		−	17.5231i		−	0.967550i
$329$	−17.7916			−0.980881
$330$	2.18491	+	0.342661i	0.120275	+	0.0188628i
$331$	26.3865			1.45033			0.725167	−	0.688573i	$-0.241763\pi$
$331$	26.3865			1.45033			0.725167	+	0.688573i	$0.241763\pi$
$332$		−	29.4274i		−	1.61504i
$333$			8.02228i			0.439618i
$334$	−2.47792			−0.135586
$335$	2.62906	−	16.7637i	0.143641	−	0.915899i
$336$	34.2225			1.86699
$337$			16.0943i			0.876712i	0.898801	+	0.438356i	$0.144439\pi$
$337$			16.0943i			0.876712i	−0.898801	+	0.438356i	$0.855561\pi$
$338$			4.68277i			0.254709i
$339$	−0.521855			−0.0283433
$340$	−3.38780	+	21.6016i	−0.183729	+	1.17151i
$341$	2.50775			0.135802
$342$			1.44117i			0.0779298i
$343$		−	13.6202i		−	0.735420i
$344$	2.07787			0.112031
$345$	−14.3695	−	2.25358i	−0.773630	−	0.121329i
$346$	2.49135			0.133936
$347$		−	5.88918i		−	0.316148i	−0.987427	−	0.158074i	$-0.949472\pi$
$347$		−	5.88918i		−	0.316148i	0.987427	−	0.158074i	$-0.0505284\pi$
$348$		−	14.0520i		−	0.753267i
$349$	−12.9912			−0.695405			−0.347702	−	0.937605i	$-0.613038\pi$
$349$	−12.9912			−0.695405			−0.347702	+	0.937605i	$0.613038\pi$
$350$	−7.50444	−	2.41321i	−0.401129	−	0.128991i
$351$	1.68637			0.0900119
$352$			4.12291i			0.219752i
$353$			4.89707i			0.260645i	0.991472	+	0.130322i	$0.0416012\pi$
$353$			4.89707i			0.260645i	−0.991472	+	0.130322i	$0.958399\pi$
$354$	9.76028			0.518753
$355$	−18.7758	−	2.94462i	−0.996516	−	0.156284i
$356$	2.03604			0.107910
$357$			57.1007i			3.02209i
$358$		−	7.27267i		−	0.384373i
$359$	−7.98358			−0.421357			−0.210679	−	0.977555i	$-0.567567\pi$
$359$	−7.98358			−0.421357			−0.210679	+	0.977555i	$0.567567\pi$
$360$	1.92534	−	12.2766i	0.101474	−	0.647032i
$361$	1.00000			0.0526316
$362$		−	2.75696i		−	0.144903i
$363$		−	2.60759i		−	0.136863i
$364$	6.24038			0.327085
$365$	2.37943	−	15.1720i	0.124545	−	0.794137i
$366$	−1.25616			−0.0656604
$367$			29.4369i			1.53659i	0.640095	+	0.768296i	$0.278895\pi$
$367$			29.4369i			1.53659i	−0.640095	+	0.768296i	$0.721105\pi$
$368$		−	7.87653i		−	0.410592i
$369$	45.5203			2.36969
$370$	1.76913	+	0.277454i	0.0919727	+	0.0144241i
$371$	32.4700			1.68576
$372$		−	12.1376i		−	0.629304i
$373$			30.5927i			1.58403i	0.610500	+	0.792016i	$0.290968\pi$
$373$			30.5927i			1.58403i	−0.610500	+	0.792016i	$0.709032\pi$
$374$	−1.99827			−0.103328
$375$	13.1172	−	26.0361i	0.677372	−	1.34450i
$376$	−6.26064			−0.322868
$377$		−	2.34834i		−	0.120946i
$378$		−	3.28700i		−	0.169065i
$379$	22.1797			1.13930			0.569648	−	0.821889i	$-0.307080\pi$
$379$	22.1797			1.13930			0.569648	+	0.821889i	$0.307080\pi$
$380$	−4.10031	−	0.643055i	−0.210342	−	0.0329880i
$381$	−24.4581			−1.25303
$382$		−	6.51319i		−	0.333244i
$383$		−	13.7921i		−	0.704743i	−0.935860	−	0.352371i	$-0.885375\pi$
$383$		−	13.7921i		−	0.704743i	0.935860	−	0.352371i	$-0.114625\pi$
$384$	26.2009			1.33706
$385$	−1.44003	+	9.18207i	−0.0733907	+	0.467961i
$386$	0.473336			0.0240922
$387$			5.39775i			0.274383i
$388$			18.1173i			0.919766i
$389$	−35.3099			−1.79029			−0.895143	−	0.445780i	$-0.852926\pi$
$389$	−35.3099			−1.79029			−0.895143	+	0.445780i	$0.852926\pi$
$390$	0.277163	−	1.76728i	0.0140347	−	0.0894895i
$391$	13.1421			0.664623
$392$		−	15.0312i		−	0.759192i
$393$		−	26.1299i		−	1.31808i
$394$	6.01947			0.303257
$395$	−8.27014	−	1.29701i	−0.416116	−	0.0652597i
$396$	−7.05245			−0.354399
$397$			23.0739i			1.15805i	0.815311	+	0.579024i	$0.196566\pi$
$397$			23.0739i			1.15805i	−0.815311	+	0.579024i	$0.803434\pi$
$398$		−	6.26632i		−	0.314102i
$399$	−10.8386			−0.542607
$400$	15.0294	+	4.83302i	0.751472	+	0.241651i
$401$	−34.5824			−1.72696			−0.863480	−	0.504382i	$-0.831720\pi$
$401$	−34.5824			−1.72696			−0.863480	+	0.504382i	$0.831720\pi$
$402$		−	7.50561i		−	0.374346i
$403$		−	2.02841i		−	0.101042i
$404$	−28.3379			−1.40987
$405$	−13.1707	−	2.06556i	−0.654455	−	0.102639i
$406$	−4.57727			−0.227166
$407$		−	2.11138i		−	0.104657i
$408$			20.0931i			0.994755i
$409$	−15.3598			−0.759492			−0.379746	−	0.925091i	$-0.623989\pi$
$409$	−15.3598			−0.759492			−0.379746	+	0.925091i	$0.623989\pi$
$410$	1.57434	−	10.0385i	0.0777511	−	0.495765i
$411$	37.4900			1.84924
$412$		−	18.3366i		−	0.903377i
$413$			41.0175i			2.01834i
$414$	−3.59510			−0.176689
$415$	5.49266	−	35.0229i	0.269624	−	1.71921i
$416$	3.33484			0.163504
$417$		−	31.2143i		−	1.52857i
$418$		−	0.379302i		−	0.0185523i
$419$	−8.90005			−0.434796			−0.217398	−	0.976083i	$-0.569757\pi$
$419$	−8.90005			−0.434796			−0.217398	+	0.976083i	$0.569757\pi$
$420$	44.4415	+	6.96979i	2.16852	+	0.340091i
$421$	−8.72937			−0.425443			−0.212722	−	0.977113i	$-0.568233\pi$
$421$	−8.72937			−0.425443			−0.212722	+	0.977113i	$0.568233\pi$
$422$			6.22957i			0.303251i
$423$		−	16.2635i		−	0.790759i
$424$	11.4258			0.554887
$425$	−8.06395	+	25.0768i	−0.391159	+	1.21640i
$426$	−8.40648			−0.407296
$427$		−	5.27899i		−	0.255468i
$428$		−	3.49713i		−	0.169040i
$429$	−2.10917			−0.101832
$430$	1.19035	+	0.186683i	0.0574037	+	0.00900266i
$431$	−24.5037			−1.18030			−0.590150	−	0.807293i	$-0.700932\pi$
$431$	−24.5037			−1.18030			−0.590150	+	0.807293i	$0.700932\pi$
$432$			6.58299i			0.316724i
$433$		−	34.3038i		−	1.64853i	−0.566201	−	0.824267i	$-0.691587\pi$
$433$		−	34.3038i		−	1.64853i	0.566201	−	0.824267i	$-0.308413\pi$
$434$	−3.95367			−0.189782
$435$	2.62283	−	16.7240i	0.125755	−	0.801852i
$436$	4.64115			0.222271
$437$			2.49456i			0.119331i
$438$		−	6.79294i		−	0.324579i
$439$	1.73839			0.0829686			0.0414843	−	0.999139i	$-0.486791\pi$
$439$	1.73839			0.0829686			0.0414843	+	0.999139i	$0.486791\pi$
$440$	−0.506729	+	3.23106i	−0.0241574	+	0.154035i
$441$	39.0472			1.85939
$442$			1.61631i			0.0768801i
$443$		−	3.00190i		−	0.142624i	−0.997454	−	0.0713122i	$-0.977281\pi$
$443$		−	3.00190i		−	0.142624i	0.997454	−	0.0713122i	$-0.0227187\pi$
$444$	−10.2191			−0.484979
$445$	2.42318	+	0.380029i	0.114870	+	0.0180151i
$446$	−8.05765			−0.381541
$447$			49.6260i			2.34723i
$448$			19.7483i			0.933018i
$449$	38.5044			1.81713			0.908567	−	0.417740i	$-0.137178\pi$
$449$	38.5044			1.81713			0.908567	+	0.417740i	$0.137178\pi$
$450$	2.20594	−	6.85991i	0.103989	−	0.323379i
$451$	−11.9805			−0.564138
$452$		−	0.371466i		−	0.0174723i
$453$			25.7879i			1.21162i
$454$	11.1870			0.525031
$455$	7.42696	+	1.16478i	0.348181	+	0.0546055i
$456$	−3.81396			−0.178605
$457$			0.420486i			0.0196695i	0.999952	+	0.00983476i	$0.00313055\pi$
$457$			0.420486i			0.0196695i	−0.999952	+	0.00983476i	$0.996869\pi$
$458$			9.80707i			0.458254i
$459$	−10.9838			−0.512679
$460$	1.60414	−	10.2285i	0.0747934	−	0.476906i
$461$	21.4596			0.999471			0.499736	−	0.866178i	$-0.333430\pi$
$461$	21.4596			0.999471			0.499736	+	0.866178i	$0.333430\pi$
$462$			4.11109i			0.191265i
$463$			0.392364i			0.0182347i	0.999958	+	0.00911735i	$0.00290218\pi$
$463$			0.392364i			0.0182347i	−0.999958	+	0.00911735i	$0.997098\pi$
$464$	9.16708			0.425571
$465$	2.26549	−	14.4455i	0.105060	−	0.669894i
$466$	−3.49976			−0.162123
$467$			2.01666i			0.0933201i	0.998911	+	0.0466600i	$0.0148577\pi$
$467$			2.01666i			0.0933201i	−0.998911	+	0.0466600i	$0.985142\pi$
$468$			5.70441i			0.263687i
$469$	31.5423			1.45649
$470$	−3.58654	−	0.562480i	−0.165435	−	0.0259452i
$471$	48.2248			2.22208
$472$			14.4336i			0.664359i
$473$		−	1.42063i		−	0.0653206i
$474$	−3.70279			−0.170075
$475$	−4.75995	−	1.53066i	−0.218401	−	0.0702314i
$476$	−40.6452			−1.86297
$477$			29.6813i			1.35901i
$478$			4.68611i			0.214338i
$479$	26.7805			1.22363			0.611817	−	0.790999i	$-0.290439\pi$
$479$	26.7805			1.22363			0.611817	+	0.790999i	$0.290439\pi$
$480$	23.7494	+	3.72463i	1.08401	+	0.170005i
$481$	−1.70780			−0.0778690
$482$			5.80303i			0.264321i
$483$		−	27.0375i		−	1.23025i
$484$	1.85613			0.0843696
$485$	−3.38162	+	21.5622i	−0.153551	+	0.979090i
$486$	−8.26930			−0.375103
$487$		−	28.2429i		−	1.27981i	−0.768454	−	0.639905i	$-0.778974\pi$
$487$		−	28.2429i		−	1.27981i	0.768454	−	0.639905i	$-0.221026\pi$
$488$		−	1.85762i		−	0.0840903i
$489$	−53.1467			−2.40338
$490$	1.35046	−	8.61096i	0.0610077	−	0.389004i
$491$	26.3559			1.18943			0.594713	−	0.803938i	$-0.297266\pi$
$491$	26.3559			1.18943			0.594713	+	0.803938i	$0.297266\pi$
$492$			57.9859i			2.61421i
$493$			15.2954i			0.688869i
$494$	−0.306800			−0.0138036
$495$	−8.39344	−	1.31635i	−0.377257	−	0.0591655i
$496$	7.91816			0.355536
$497$		−	35.3282i		−	1.58469i
$498$		−	15.6808i		−	0.702673i
$499$	−7.09609			−0.317665			−0.158832	−	0.987306i	$-0.550773\pi$
$499$	−7.09609			−0.317665			−0.158832	+	0.987306i	$0.550773\pi$
$500$	18.5330	+	9.33708i	0.828820	+	0.417567i
$501$	17.0350			0.761067
$502$		−	5.54434i		−	0.247456i
$503$			22.7720i			1.01535i	0.861548	+	0.507677i	$0.169496\pi$
$503$			22.7720i			1.01535i	−0.861548	+	0.507677i	$0.830504\pi$
$504$	23.0994			1.02893
$505$	−33.7263	−	5.28931i	−1.50080	−	0.235371i
$506$	0.946192			0.0420634
$507$		−	32.1927i		−	1.42973i
$508$		−	17.4097i		−	0.772430i
$509$	26.6561			1.18151			0.590756	−	0.806850i	$-0.298829\pi$
$509$	26.6561			1.18151			0.590756	+	0.806850i	$0.298829\pi$
$510$	−1.80524	+	11.5107i	−0.0799372	+	0.509704i
$511$	28.5473			1.26286
$512$			22.2545i			0.983519i
$513$		−	2.08489i		−	0.0920500i
$514$	−10.5081			−0.463491
$515$	3.42254	−	21.8232i	0.150815	−	0.961644i
$516$	−6.87589			−0.302694
$517$			4.28038i			0.188251i
$518$			3.32876i			0.146257i
$519$	−17.1273			−0.751806
$520$	2.61346	+	0.409871i	0.114608	+	0.0179740i
$521$	−32.0959			−1.40615			−0.703073	−	0.711118i	$-0.748189\pi$
$521$	−32.0959			−1.40615			−0.703073	+	0.711118i	$0.748189\pi$
$522$		−	4.18414i		−	0.183135i
$523$			21.7074i			0.949200i	0.880202	+	0.474600i	$0.157407\pi$
$523$			21.7074i			0.949200i	−0.880202	+	0.474600i	$0.842593\pi$
$524$	18.5997			0.812533
$525$	51.5910	+	16.5901i	2.25161	+	0.724053i
$526$	8.11556			0.353855
$527$			13.2115i			0.575504i
$528$		−	8.23342i		−	0.358314i
$529$	16.7772			0.729442
$530$	6.54553	+	1.02654i	0.284320	+	0.0445900i
$531$	−37.4946			−1.62713
$532$		−	7.71508i		−	0.334491i
$533$			9.69047i			0.419741i
$534$	1.08493			0.0469495
$535$	0.652744	−	4.16210i	0.0282206	−	0.179943i
$536$	11.0994			0.479419
$537$			49.9976i			2.15756i
$538$			4.49912i			0.193971i
$539$	−10.2768			−0.442653
$540$	−1.34070	+	8.54869i	−0.0576944	+	0.367877i
$541$	−22.6922			−0.975615			−0.487808	−	0.872951i	$-0.662203\pi$
$541$	−22.6922			−0.975615			−0.487808	+	0.872951i	$0.662203\pi$
$542$			10.7024i			0.459706i
$543$			18.9533i			0.813365i
$544$	−21.7207			−0.931267
$545$	5.52365	+	0.866277i	0.236607	+	0.0371072i
$546$	3.32527			0.142309
$547$		−	25.9252i		−	1.10848i	−0.832357	−	0.554240i	$-0.813009\pi$
$547$		−	25.9252i		−	1.10848i	0.832357	−	0.554240i	$-0.186991\pi$
$548$			26.6860i			1.13997i
$549$	4.82559			0.205951
$550$	−0.580581	+	1.80546i	−0.0247561	+	0.0769849i
$551$	−2.90329			−0.123684
$552$		−	9.51417i		−	0.404950i
$553$		−	15.5609i		−	0.661719i
$554$	5.67150			0.240959
$555$	−12.1623	−	1.90742i	−0.516260	−	0.0809653i
$556$	22.2189			0.942292
$557$			15.4699i			0.655482i	0.944768	+	0.327741i	$0.106287\pi$
$557$			15.4699i			0.655482i	−0.944768	+	0.327741i	$0.893713\pi$
$558$		−	3.61410i		−	0.152997i
$559$	−1.14908			−0.0486011
$560$	−4.54686	+	28.9922i	−0.192140	+	1.22514i
$561$	13.7376			0.580000
$562$		−	7.16172i		−	0.302099i
$563$			30.6255i			1.29071i	0.763882	+	0.645356i	$0.223291\pi$
$563$			30.6255i			1.29071i	−0.763882	+	0.645356i	$0.776709\pi$
$564$	20.7172			0.872351
$565$	0.0693345	−	0.442098i	0.00291693	−	0.0185992i
$566$	−3.43871			−0.144540
$567$		−	24.7817i		−	1.04073i
$568$		−	12.4316i		−	0.521617i
$569$	−19.1437			−0.802546			−0.401273	−	0.915959i	$-0.631432\pi$
$569$	−19.1437			−0.802546			−0.401273	+	0.915959i	$0.631432\pi$
$570$	−2.18491	−	0.342661i	−0.0915158	−	0.0143525i
$571$	−28.1015			−1.17601			−0.588005	−	0.808858i	$-0.700086\pi$
$571$	−28.1015			−1.17601			−0.588005	+	0.808858i	$0.700086\pi$
$572$		−	1.50134i		−	0.0627742i
$573$			44.7764i			1.87056i
$574$	18.8882			0.788378
$575$	3.81832	−	11.8740i	0.159235	−	0.495179i
$576$	−18.0521			−0.752172
$577$		−	40.6479i		−	1.69219i	−0.533030	−	0.846096i	$-0.678947\pi$
$577$		−	40.6479i		−	1.69219i	0.533030	−	0.846096i	$-0.321053\pi$
$578$		−	4.07934i		−	0.169678i
$579$	−3.25405			−0.135234
$580$	11.9044	+	1.86697i	0.494303	+	0.0775219i
$581$	65.8984			2.73393
$582$			9.65405i			0.400173i
$583$		−	7.81180i		−	0.323532i
$584$	10.0455			0.415684
$585$	−1.06474	+	6.78908i	−0.0440214	+	0.280694i
$586$	−8.89167			−0.367312
$587$		−	21.8347i		−	0.901215i	−0.892722	−	0.450608i	$-0.851207\pi$
$587$		−	21.8347i		−	0.901215i	0.892722	−	0.450608i	$-0.148793\pi$
$588$			49.7401i			2.05125i
$589$	−2.50775			−0.103330
$590$	−1.29677	+	8.26858i	−0.0533870	+	0.340412i
$591$	−41.3822			−1.70224
$592$		−	6.66664i		−	0.273997i
$593$		−	12.4080i		−	0.509536i	−0.967002	−	0.254768i	$-0.918001\pi$
$593$		−	12.4080i		−	0.509536i	0.967002	−	0.254768i	$-0.0819992\pi$
$594$	−0.790801			−0.0324470
$595$	−48.3738	−	7.58649i	−1.98313	−	0.311016i
$596$	−35.3246			−1.44695
$597$			43.0792i			1.76311i
$598$		−	0.765332i		−	0.0312968i
$599$	−10.3034			−0.420987			−0.210493	−	0.977595i	$-0.567507\pi$
$599$	−10.3034			−0.420987			−0.210493	+	0.977595i	$0.567507\pi$
$600$	18.1543	+	5.83787i	0.741144	+	0.238330i
$601$	−5.81116			−0.237042			−0.118521	−	0.992952i	$-0.537815\pi$
$601$	−5.81116			−0.237042			−0.118521	+	0.992952i	$0.537815\pi$
$602$			2.23974i			0.0912850i
$603$			28.8332i			1.17418i
$604$	−18.3563			−0.746907
$605$	2.20907	+	0.346449i	0.0898113	+	0.0140852i
$606$	−15.1003			−0.613407
$607$		−	9.67871i		−	0.392847i	−0.980519	−	0.196423i	$-0.937067\pi$
$607$		−	9.67871i		−	0.392847i	0.980519	−	0.196423i	$-0.0629327\pi$
$608$		−	4.12291i		−	0.167206i
$609$	31.4675			1.27513
$610$	0.166895	−	1.06417i	0.00675738	−	0.0430872i
$611$	3.46221			0.140066
$612$		−	37.1543i		−	1.50188i
$613$		−	39.9792i		−	1.61474i	−0.590043	−	0.807372i	$-0.700889\pi$
$613$		−	39.9792i		−	1.61474i	0.590043	−	0.807372i	$-0.299111\pi$
$614$	−2.45857			−0.0992197
$615$	−10.8231	+	69.0117i	−0.436431	+	2.78282i
$616$	−6.07951			−0.244950
$617$		−	15.4332i		−	0.621317i	−0.950522	−	0.310658i	$-0.899451\pi$
$617$		−	15.4332i		−	0.621317i	0.950522	−	0.310658i	$-0.100549\pi$
$618$		−	9.77089i		−	0.393043i
$619$	47.7611			1.91968			0.959840	−	0.280549i	$-0.0905164\pi$
$619$	47.7611			1.91968			0.959840	+	0.280549i	$0.0905164\pi$
$620$	10.2826	+	1.61262i	0.412957	+	0.0647643i
$621$	5.20088			0.208704
$622$		−	7.21104i		−	0.289136i
$623$			4.55941i			0.182669i
$624$	−6.65965			−0.266599
$625$	20.3142	+	14.5717i	0.812567	+	0.582868i
$626$	−8.96169			−0.358181
$627$			2.60759i			0.104137i
$628$			34.3273i			1.36981i
$629$	11.1234			0.443517
$630$	13.2330	+	2.07533i	0.527213	+	0.0826832i
$631$	−0.352780			−0.0140439			−0.00702197	−	0.999975i	$-0.502235\pi$
$631$	−0.352780			−0.0140439			−0.00702197	+	0.999975i	$0.502235\pi$
$632$		−	5.47572i		−	0.217812i
$633$		−	42.8266i		−	1.70220i
$634$	−3.37681			−0.134110
$635$	3.24954	−	20.7201i	0.128954	−	0.822251i
$636$	−37.8094			−1.49924
$637$			8.31245i			0.329351i
$638$			1.10122i			0.0435978i
$639$	32.2940			1.27753
$640$	−3.48110	+	22.1966i	−0.137602	+	0.877396i
$641$	−9.12385			−0.360370			−0.180185	−	0.983633i	$-0.557670\pi$
$641$	−9.12385			−0.360370			−0.180185	+	0.983633i	$0.557670\pi$
$642$		−	1.86350i		−	0.0735463i
$643$			7.36034i			0.290263i	0.989412	+	0.145132i	$0.0463606\pi$
$643$			7.36034i			0.290263i	−0.989412	+	0.145132i	$0.953639\pi$
$644$	19.2457			0.758388
$645$	−8.18332	−	1.28339i	−0.322218	−	0.0505336i
$646$	1.99827			0.0786209
$647$		−	34.5602i		−	1.35870i	−0.733813	−	0.679352i	$-0.762261\pi$
$647$		−	34.5602i		−	1.35870i	0.733813	−	0.679352i	$-0.237739\pi$
$648$		−	8.72038i		−	0.342569i
$649$	9.86819			0.387360
$650$	1.46035	+	0.469606i	0.0572797	+	0.0184195i
$651$	27.1804			1.06528
$652$		−	37.8307i		−	1.48157i
$653$		−	17.1242i		−	0.670124i	−0.942196	−	0.335062i	$-0.891243\pi$
$653$		−	17.1242i		−	0.670124i	0.942196	−	0.335062i	$-0.108757\pi$
$654$	2.47310			0.0967060
$655$	22.1364	+	3.47166i	0.864940	+	0.135649i
$656$	−37.8281			−1.47694
$657$			26.0954i			1.01808i
$658$		−	6.74837i		−	0.263079i
$659$	32.1685			1.25311			0.626553	−	0.779379i	$-0.284465\pi$
$659$	32.1685			1.25311			0.626553	+	0.779379i	$0.284465\pi$
$660$	1.67683	−	10.6920i	0.0652703	−	0.416184i
$661$	−6.38995			−0.248540			−0.124270	−	0.992248i	$-0.539659\pi$
$661$	−6.38995			−0.248540			−0.124270	+	0.992248i	$0.539659\pi$
$662$			10.0084i			0.388989i
$663$		−	11.1117i		−	0.431543i
$664$	23.1889			0.899903
$665$	1.44003	−	9.18207i	0.0558419	−	0.356065i
$666$	−3.04286			−0.117909
$667$		−	7.24243i		−	0.280428i
$668$			12.1258i			0.469161i
$669$	55.3941			2.14166
$670$	6.35850	+	0.997207i	0.245650	+	0.0385255i
$671$	−1.27005			−0.0490296
$672$			44.6864i			1.72382i
$673$		−	50.2048i		−	1.93525i	−0.252387	−	0.967626i	$-0.581216\pi$
$673$		−	50.2048i		−	1.93525i	0.252387	−	0.967626i	$-0.418784\pi$
$674$	−6.10459			−0.235140
$675$	−3.19125	+	9.92395i	−0.122831	+	0.381973i
$676$	22.9153			0.881359
$677$		−	13.9577i		−	0.536438i	−0.963358	−	0.268219i	$-0.913565\pi$
$677$		−	13.9577i		−	0.536438i	0.963358	−	0.268219i	$-0.0864350\pi$
$678$		−	0.197941i		−	0.00760186i
$679$	−40.5711			−1.55698
$680$	−17.0222	−	2.66960i	−0.652770	−	0.102374i
$681$	−76.9074			−2.94710
$682$			0.951193i			0.0364231i
$683$			10.8435i			0.414916i	0.978244	+	0.207458i	$0.0665190\pi$
$683$			10.8435i			0.414916i	−0.978244	+	0.207458i	$0.933481\pi$
$684$	7.05245			0.269657
$685$	−4.98098	+	31.7602i	−0.190313	+	1.21350i
$686$	5.16615			0.197245
$687$		−	67.4209i		−	2.57227i
$688$		−	4.48561i		−	0.171012i
$689$	−6.31862			−0.240720
$690$	0.854788	−	5.45039i	0.0325412	−	0.207493i
$691$	33.2982			1.26672			0.633361	−	0.773857i	$-0.281675\pi$
$691$	33.2982			1.26672			0.633361	+	0.773857i	$0.281675\pi$
$692$		−	12.1915i		−	0.463452i
$693$		−	15.7930i		−	0.599925i
$694$	2.23378			0.0847930
$695$	26.4438	+	4.14719i	1.00307	+	0.157312i
$696$	11.0730			0.419722
$697$		−	63.1166i		−	2.39071i
$698$		−	4.92760i		−	0.186512i
$699$	24.0599			0.910029
$700$	−11.8091	+	36.7233i	−0.446344	+	1.38801i
$701$	12.9091			0.487568			0.243784	−	0.969830i	$-0.421611\pi$
$701$	12.9091			0.487568			0.243784	+	0.969830i	$0.421611\pi$
$702$			0.639644i			0.0241418i
$703$			2.11138i			0.0796322i
$704$	4.75113			0.179065
$705$	24.6565	+	3.86689i	0.928617	+	0.145636i
$706$	−1.85747			−0.0699067
$707$		−	63.4588i		−	2.38661i
$708$		−	47.7624i		−	1.79502i
$709$	−5.26917			−0.197888			−0.0989438	−	0.995093i	$-0.531546\pi$
$709$	−5.26917			−0.197888			−0.0989438	+	0.995093i	$0.531546\pi$
$710$	1.11690	−	7.12169i	0.0419165	−	0.267272i
$711$	14.2245			0.533459
$712$			1.60440i			0.0601276i
$713$		−	6.25573i		−	0.234279i
$714$	−21.6584			−0.810545
$715$	0.280227	−	1.78682i	0.0104799	−	0.0668231i
$716$	−35.5891			−1.33003
$717$		−	32.2157i		−	1.20312i
$718$		−	3.02818i		−	0.113011i
$719$	2.43393			0.0907703			0.0453851	−	0.998970i	$-0.485548\pi$
$719$	2.43393			0.0907703			0.0453851	+	0.998970i	$0.485548\pi$
$720$	−26.5021	−	4.15634i	−0.987676	−	0.154898i
$721$	41.0621			1.52923
$722$			0.379302i			0.0141161i
$723$		−	39.8942i		−	1.48368i
$724$	−13.4913			−0.501400
$725$	13.8195	+	4.44394i	0.513243	+	0.165044i
$726$	0.989065			0.0367076
$727$			28.7825i			1.06748i	0.845647	+	0.533742i	$0.179215\pi$
$727$			28.7825i			1.06748i	−0.845647	+	0.533742i	$0.820785\pi$
$728$			4.91744i			0.182252i
$729$	38.9629			1.44307
$730$	5.75475	+	0.902521i	0.212993	+	0.0334038i
$731$	7.48429			0.276816
$732$			6.14706i			0.227202i
$733$		−	16.6212i		−	0.613918i	−0.951723	−	0.306959i	$-0.900689\pi$
$733$		−	16.6212i		−	0.613918i	0.951723	−	0.306959i	$-0.0993115\pi$
$734$	−11.1655			−0.412125
$735$	−9.28405	+	59.1980i	−0.342447	+	2.18355i
$736$	10.2849			0.379105
$737$		−	7.58859i		−	0.279529i
$738$			17.2659i			0.635568i
$739$	−8.17863			−0.300856			−0.150428	−	0.988621i	$-0.548065\pi$
$739$	−8.17863			−0.300856			−0.150428	+	0.988621i	$0.548065\pi$
$740$	1.35773	−	8.65732i	0.0499112	−	0.318249i
$741$	2.10917			0.0774822
$742$			12.3159i			0.452133i
$743$		−	33.8950i		−	1.24349i	−0.783221	−	0.621744i	$-0.786425\pi$
$743$		−	33.8950i		−	1.24349i	0.783221	−	0.621744i	$-0.213575\pi$
$744$	9.56445			0.350650
$745$	−42.0415	−	6.59339i	−1.54028	−	0.241563i
$746$	−11.6039			−0.424848
$747$			60.2386i			2.20401i
$748$			9.77863i			0.357542i
$749$	7.83133			0.286150
$750$	9.87555	+	4.97539i	0.360604	+	0.181676i
$751$	46.2851			1.68897			0.844483	−	0.535582i	$-0.179908\pi$
$751$	46.2851			1.68897			0.844483	+	0.535582i	$0.179908\pi$
$752$			13.5152i			0.492849i
$753$			38.1158i			1.38902i
$754$	0.890730			0.0324385
$755$	−21.8467	−	3.42622i	−0.795081	−	0.124693i
$756$	−16.0851			−0.585008
$757$		−	25.3179i		−	0.920196i	−0.887868	−	0.460098i	$-0.847814\pi$
$757$		−	25.3179i		−	0.920196i	0.887868	−	0.460098i	$-0.152186\pi$
$758$			8.41280i			0.305567i
$759$	−6.50480			−0.236109
$760$	0.506729	−	3.23106i	0.0183810	−	0.117203i
$761$	26.4498			0.958805			0.479403	−	0.877595i	$-0.340853\pi$
$761$	26.4498			0.958805			0.479403	+	0.877595i	$0.340853\pi$
$762$		−	9.27699i		−	0.336070i
$763$			10.3932i			0.376259i
$764$	−31.8726			−1.15311
$765$	6.93491	−	44.2191i	0.250732	−	1.59874i
$766$	5.23136			0.189017
$767$		−	7.98194i		−	0.288211i
$768$		−	14.8400i		−	0.535492i
$769$	−5.11765			−0.184547			−0.0922735	−	0.995734i	$-0.529413\pi$
$769$	−5.11765			−0.184547			−0.0922735	+	0.995734i	$0.529413\pi$
$770$	−3.48277	−	0.546205i	−0.125510	−	0.0196839i
$771$	72.2400			2.60166
$772$		−	2.31629i		−	0.0833651i
$773$			8.91322i			0.320586i	0.987069	+	0.160293i	$0.0512439\pi$
$773$			8.91322i			0.320586i	−0.987069	+	0.160293i	$0.948756\pi$
$774$	−2.04737			−0.0735913
$775$	11.9367	+	3.83850i	0.428780	+	0.137883i
$776$	−14.2765			−0.512496
$777$		−	22.8843i		−	0.820970i
$778$		−	13.3931i		−	0.480167i
$779$	11.9805			0.429245
$780$	−8.64824	−	1.35631i	−0.309657	−	0.0485637i
$781$	−8.49943			−0.304133
$782$			4.98481i			0.178256i
$783$			6.05303i			0.216318i
$784$	−32.4488			−1.15889
$785$	−6.40723	+	40.8545i	−0.228684	+	1.45816i
$786$	9.91112			0.353518
$787$		−	32.0672i		−	1.14307i	−0.820577	−	0.571535i	$-0.806348\pi$
$787$		−	32.0672i		−	1.14307i	0.820577	−	0.571535i	$-0.193652\pi$
$788$		−	29.4566i		−	1.04935i
$789$	−55.7922			−1.98626
$790$	0.491959	−	3.13688i	0.0175031	−	0.111605i
$791$	0.831844			0.0295770
$792$		−	5.55735i		−	0.197472i
$793$			1.02728i			0.0364799i
$794$	−8.75198			−0.310596
$795$	−44.9987	−	7.05717i	−1.59594	−	0.250292i
$796$	−30.6645			−1.08687
$797$			25.9956i			0.920811i	0.887709	+	0.460406i	$0.152296\pi$
$797$			25.9956i			0.920811i	−0.887709	+	0.460406i	$0.847704\pi$
$798$		−	4.11109i		−	0.145531i
$799$	−22.5503			−0.797772
$800$	−6.31077	+	19.6248i	−0.223119	+	0.693843i
$801$	−4.16782			−0.147263
$802$		−	13.1172i		−	0.463183i
$803$		−	6.86804i		−	0.242368i
$804$	−36.7290			−1.29533
$805$	22.9052	+	3.59224i	0.807303	+	0.126610i
$806$	0.769378			0.0271002
$807$		−	30.9302i		−	1.08879i
$808$		−	22.3304i		−	0.785581i
$809$	−49.2061			−1.72999			−0.864997	−	0.501776i	$-0.832680\pi$
$809$	−49.2061			−1.72999			−0.864997	+	0.501776i	$0.832680\pi$
$810$	0.783471	−	4.99565i	0.0275284	−	0.175529i
$811$	−44.5693			−1.56504			−0.782520	−	0.622626i	$-0.786066\pi$
$811$	−44.5693			−1.56504			−0.782520	+	0.622626i	$0.786066\pi$
$812$			22.3991i			0.786054i
$813$		−	73.5757i		−	2.58041i
$814$	0.800850			0.0280698
$815$	7.06116	−	45.0241i	0.247342	−	1.57713i
$816$	43.3761			1.51847
$817$			1.42063i			0.0497015i
$818$		−	5.82599i		−	0.203701i
$819$	−12.7742			−0.446367
$820$	−49.1237	−	7.70410i	−1.71547	−	0.269039i
$821$	−9.78163			−0.341381			−0.170691	−	0.985325i	$-0.554600\pi$
$821$	−9.78163			−0.341381			−0.170691	+	0.985325i	$0.554600\pi$
$822$			14.2200i			0.495980i
$823$			21.5392i			0.750809i	0.926861	+	0.375405i	$0.122496\pi$
$823$			21.5392i			0.750809i	−0.926861	+	0.375405i	$0.877504\pi$
$824$	14.4493			0.503364
$825$	3.99133	−	12.4120i	0.138960	−	0.432131i
$826$	−15.5580			−0.541333
$827$		−	35.5256i		−	1.23535i	−0.786435	−	0.617673i	$-0.788075\pi$
$827$		−	35.5256i		−	1.23535i	0.786435	−	0.617673i	$-0.211925\pi$
$828$			17.5928i			0.611391i
$829$	2.59741			0.0902119			0.0451059	−	0.998982i	$-0.485637\pi$
$829$	2.59741			0.0902119			0.0451059	+	0.998982i	$0.485637\pi$
$830$	13.2842	+	2.08338i	0.461103	+	0.0723150i
$831$	−38.9900			−1.35255
$832$		−	3.84298i		−	0.133231i
$833$		−	54.1412i		−	1.87588i
$834$	11.8397			0.409974
$835$	−2.26330	+	14.4315i	−0.0783246	+	0.499422i
$836$	−1.85613			−0.0641956
$837$			5.22837i			0.180719i
$838$		−	3.37580i		−	0.116615i
$839$	1.00128			0.0345680			0.0172840	−	0.999851i	$-0.494498\pi$
$839$	1.00128			0.0345680			0.0172840	+	0.999851i	$0.494498\pi$
$840$	−5.49222	+	35.0201i	−0.189499	+	1.20831i
$841$	−20.5709			−0.709342
$842$		−	3.31106i		−	0.114107i
$843$			49.2348i			1.69574i
$844$	30.4847			1.04933
$845$	27.2726	+	4.27717i	0.938205	+	0.147139i
$846$	6.16877			0.212087
$847$			4.15654i			0.142820i
$848$		−	24.6656i		−	0.847020i
$849$	23.6402			0.811329
$850$	−9.51166	−	3.05867i	−0.326247	−	0.104911i
$851$	−5.26697			−0.180549
$852$			41.1375i			1.40935i
$853$		−	3.93139i		−	0.134608i	−0.997733	−	0.0673042i	$-0.978560\pi$
$853$		−	3.93139i		−	0.134608i	0.997733	−	0.0673042i	$-0.0214398\pi$
$854$	2.00233			0.0685183
$855$	8.39344	+	1.31635i	0.287050	+	0.0450182i
$856$	2.75575			0.0941896
$857$			37.5655i			1.28321i	0.767034	+	0.641606i	$0.221732\pi$
$857$			37.5655i			1.28321i	−0.767034	+	0.641606i	$0.778268\pi$
$858$		−	0.800010i		−	0.0273119i
$859$	−37.8019			−1.28978			−0.644892	−	0.764273i	$-0.723098\pi$
$859$	−37.8019			−1.28978			−0.644892	+	0.764273i	$0.723098\pi$
$860$	0.913542	−	5.82503i	0.0311515	−	0.198632i
$861$	−129.851			−4.42531
$862$		−	9.29429i		−	0.316565i
$863$			23.3269i			0.794057i	0.917806	+	0.397029i	$0.129959\pi$
$863$			23.3269i			0.794057i	−0.917806	+	0.397029i	$0.870041\pi$
$864$	−8.59580			−0.292435
$865$	2.27556	−	14.5097i	0.0773715	−	0.493344i
$866$	13.0115			0.442148
$867$			28.0443i			0.952435i
$868$			19.3475i			0.656696i
$869$	−3.74373			−0.126997
$870$	6.34342	+	0.994843i	0.215062	+	0.0337283i
$871$	−6.13807			−0.207981
$872$			3.65724i			0.123850i
$873$		−	37.0865i		−	1.25519i
$874$	−0.946192			−0.0320054
$875$	−20.9091	+	41.5020i	−0.706855	+	1.40302i
$876$	−33.2416			−1.12313
$877$			20.7999i			0.702361i	0.936308	+	0.351181i	$0.114220\pi$
$877$			20.7999i			0.702361i	−0.936308	+	0.351181i	$0.885780\pi$
$878$			0.659372i			0.0222527i
$879$	61.1278			2.06179
$880$	6.97508	+	1.09391i	0.235130	+	0.0368756i
$881$	52.3897			1.76506			0.882528	−	0.470261i	$-0.155840\pi$
$881$	52.3897			1.76506			0.882528	+	0.470261i	$0.155840\pi$
$882$			14.8107i			0.498701i
$883$			27.1774i			0.914591i	0.889315	+	0.457295i	$0.151182\pi$
$883$			27.1774i			0.914591i	−0.889315	+	0.457295i	$0.848818\pi$
$884$	7.90950			0.266025
$885$	8.91491	−	56.8442i	0.299671	−	1.91080i
$886$	1.13862			0.0382528
$887$			35.2309i			1.18294i	0.806328	+	0.591469i	$0.201452\pi$
$887$			35.2309i			1.18294i	−0.806328	+	0.591469i	$0.798548\pi$
$888$		−	8.05272i		−	0.270232i
$889$	38.9865			1.30757
$890$	−0.144146	+	0.919117i	−0.00483177	+	0.0308089i
$891$	−5.96210			−0.199738
$892$			39.4305i			1.32023i
$893$		−	4.28038i		−	0.143238i
$894$	−18.8232			−0.629543
$895$	−42.3563	−	6.64276i	−1.41581	−	0.222043i
$896$	−41.7646			−1.39526
$897$			5.26145i			0.175675i
$898$			14.6048i			0.487367i
$899$	7.28071			0.242825
$900$	−33.5693	−	10.7949i	−1.11898	−	0.359830i
$901$	41.1548			1.37107
$902$		−	4.54421i		−	0.151306i
$903$		−	15.3976i		−	0.512399i
$904$	0.292716			0.00973559
$905$	−16.0566	−	2.51817i	−0.533740	−	0.0837068i
$906$	−9.78140			−0.324965
$907$			4.04284i			0.134240i	0.997745	+	0.0671201i	$0.0213811\pi$
$907$			4.04284i			0.134240i	−0.997745	+	0.0671201i	$0.978619\pi$
$908$		−	54.7440i		−	1.81674i
$909$	58.0085			1.92402
$910$	−0.441801	+	2.81706i	−0.0146456	+	0.0933846i
$911$	−25.4464			−0.843077			−0.421539	−	0.906810i	$-0.638510\pi$
$911$	−25.4464			−0.843077			−0.421539	+	0.906810i	$0.638510\pi$
$912$			8.23342i			0.272636i
$913$		−	15.8542i		−	0.524696i
$914$	−0.159491			−0.00527550
$915$	−1.14736	+	7.31590i	−0.0379305	+	0.241856i
$916$	47.9913			1.58568
$917$			41.6514i			1.37545i
$918$		−	4.16617i		−	0.137504i
$919$	27.9210			0.921028			0.460514	−	0.887652i	$-0.347665\pi$
$919$	27.9210			0.921028			0.460514	+	0.887652i	$0.347665\pi$
$920$	8.06008	+	1.26407i	0.265733	+	0.0416751i
$921$	16.9020			0.556938
$922$			8.13965i			0.268065i
$923$			6.87481i			0.226287i
$924$	20.1178			0.661826
$925$	3.23180	−	10.0501i	0.106261	−	0.330444i
$926$	−0.148824			−0.00489067
$927$			37.5354i			1.23282i
$928$			11.9700i			0.392935i
$929$	29.7603			0.976405			0.488203	−	0.872730i	$-0.337653\pi$
$929$	29.7603			0.976405			0.488203	+	0.872730i	$0.337653\pi$
$930$	5.47920	+	0.859306i	0.179670	+	0.0281778i
$931$	10.2768			0.336809
$932$			17.1262i			0.560989i
$933$			49.5739i			1.62298i
$934$	−0.764924			−0.0250291
$935$	−1.82519	+	11.6380i	−0.0596902	+	0.380603i
$936$	−4.49510			−0.146927
$937$		−	33.0699i		−	1.08035i	−0.841554	−	0.540173i	$-0.818359\pi$
$937$		−	33.0699i		−	1.08035i	0.841554	−	0.540173i	$-0.181641\pi$
$938$			11.9640i			0.390640i
$939$	61.6092			2.01054
$940$	−2.75252	+	17.5509i	−0.0897773	+	0.572448i
$941$	17.9201			0.584178			0.292089	−	0.956391i	$-0.405650\pi$
$941$	17.9201			0.584178			0.292089	+	0.956391i	$0.405650\pi$
$942$			18.2918i			0.595978i
$943$			29.8860i			0.973223i
$944$	31.1586			1.01413
$945$	−19.1436	−	3.00230i	−0.622740	−	0.0976647i
$946$	0.538847			0.0175194
$947$			13.3998i			0.435434i	0.976012	+	0.217717i	$0.0698609\pi$
$947$			13.3998i			0.435434i	−0.976012	+	0.217717i	$0.930139\pi$
$948$			18.1198i			0.588503i
$949$	−5.55526			−0.180331
$950$	0.580581	−	1.80546i	0.0188365	−	0.0585767i
$951$	23.2147			0.752787
$952$		−	32.0286i		−	1.03805i
$953$			42.3132i			1.37066i	0.728232	+	0.685330i	$0.240342\pi$
$953$			42.3132i			1.37066i	−0.728232	+	0.685330i	$0.759658\pi$
$954$	−11.2582			−0.364496
$955$	−37.9330	−	5.94906i	−1.22748	−	0.192507i
$956$	22.9317			0.741664
$957$		−	7.57060i		−	0.244723i
$958$			10.1579i			0.328187i
$959$	−59.7595			−1.92973
$960$	4.29217	−	27.3682i	0.138529	−	0.883304i
$961$	−24.7112			−0.797136
$962$		−	0.647772i		−	0.0208850i
$963$			7.15871i			0.230686i
$964$	28.3974			0.914619
$965$	0.432339	−	2.75672i	0.0139175	−	0.0887421i
$966$	10.2554			0.329961
$967$			49.4182i			1.58918i	0.607145	+	0.794591i	$0.292315\pi$
$967$			49.4182i			1.58918i	−0.607145	+	0.794591i	$0.707685\pi$
$968$			1.46264i			0.0470109i
$969$	−13.7376			−0.441314
$970$	−8.17859	−	1.28265i	−0.262599	−	0.0411835i
$971$	−46.5589			−1.49415			−0.747074	−	0.664741i	$-0.768542\pi$
$971$	−46.5589			−1.49415			−0.747074	+	0.664741i	$0.768542\pi$
$972$			40.4662i			1.29795i
$973$			49.7561i			1.59511i
$974$	10.7126			0.343254
$975$	−10.0395	−	3.22841i	−0.321522	−	0.103392i
$976$	−4.01014			−0.128362
$977$		−	13.8329i		−	0.442552i	−0.975211	−	0.221276i	$-0.928978\pi$
$977$		−	13.8329i		−	0.442552i	0.975211	−	0.221276i	$-0.0710222\pi$
$978$		−	20.1586i		−	0.644602i
$979$	1.09693			0.0350579
$980$	−42.1381	−	6.60855i	−1.34605	−	0.211102i
$981$	−9.50056			−0.303329
$982$			9.99684i			0.319012i
$983$		−	11.2618i		−	0.359195i	−0.983740	−	0.179598i	$-0.942520\pi$
$983$		−	11.2618i		−	0.359195i	0.983740	−	0.179598i	$-0.0574796\pi$
$984$	−45.6931			−1.45664
$985$	5.49811	−	35.0576i	0.175184	−	1.11703i
$986$	−5.80156			−0.184759
$987$			46.3932i			1.47671i
$988$			1.50134i			0.0477640i
$989$	−3.54385			−0.112688
$990$	0.499293	−	3.18365i	0.0158686	−	0.101183i
$991$	−8.44195			−0.268167			−0.134084	−	0.990970i	$-0.542809\pi$
$991$	−8.44195			−0.268167			−0.134084	+	0.990970i	$0.542809\pi$
$992$			10.3392i			0.328271i
$993$		−	68.8053i		−	2.18347i
$994$	13.4000			0.425024
$995$	−36.4952	−	5.72357i	−1.15698	−	0.181449i
$996$	−76.7347			−2.43143
$997$			16.9634i			0.537236i	0.963247	+	0.268618i	$0.0865669\pi$
$997$			16.9634i			0.537236i	−0.963247	+	0.268618i	$0.913433\pi$
$998$		−	2.69156i		−	0.0851999i
$999$	4.40199			0.139273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.17	yes	30
5.2	odd	4		5225.2.a.bc.1.14		30
5.3	odd	4		5225.2.a.bc.1.17		30
5.4	even	2	inner	1045.2.b.e.419.14	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.14	✓	30	5.4	even	2	inner
1045.2.b.e.419.17	yes	30	1.1	even	1	trivial
5225.2.a.bc.1.14		30	5.2	odd	4
5225.2.a.bc.1.17		30	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.379302i q^{2} -2.60759i q^{3} +1.85613 q^{4} +(2.20907 + 0.346449i) q^{5} +0.989065 q^{6} +4.15654i q^{7} +1.46264i q^{8} -3.79954 q^{9} +O(q^{10})\)	\(q+0.379302i q^{2} -2.60759i q^{3} +1.85613 q^{4} +(2.20907 + 0.346449i) q^{5} +0.989065 q^{6} +4.15654i q^{7} +1.46264i q^{8} -3.79954 q^{9} +(-0.131409 + 0.837903i) q^{10} +1.00000 q^{11} -4.84003i q^{12} -0.808855i q^{13} -1.57658 q^{14} +(0.903398 - 5.76035i) q^{15} +3.15748 q^{16} +5.26829i q^{17} -1.44117i q^{18} -1.00000 q^{19} +(4.10031 + 0.643055i) q^{20} +10.8386 q^{21} +0.379302i q^{22} -2.49456i q^{23} +3.81396 q^{24} +(4.75995 + 1.53066i) q^{25} +0.306800 q^{26} +2.08489i q^{27} +7.71508i q^{28} +2.90329 q^{29} +(2.18491 + 0.342661i) q^{30} +2.50775 q^{31} +4.12291i q^{32} -2.60759i q^{33} -1.99827 q^{34} +(-1.44003 + 9.18207i) q^{35} -7.05245 q^{36} -2.11138i q^{37} -0.379302i q^{38} -2.10917 q^{39} +(-0.506729 + 3.23106i) q^{40} -11.9805 q^{41} +4.11109i q^{42} -1.42063i q^{43} +1.85613 q^{44} +(-8.39344 - 1.31635i) q^{45} +0.946192 q^{46} +4.28038i q^{47} -8.23342i q^{48} -10.2768 q^{49} +(-0.580581 + 1.80546i) q^{50} +13.7376 q^{51} -1.50134i q^{52} -7.81180i q^{53} -0.790801 q^{54} +(2.20907 + 0.346449i) q^{55} -6.07951 q^{56} +2.60759i q^{57} +1.10122i q^{58} +9.86819 q^{59} +(1.67683 - 10.6920i) q^{60} -1.27005 q^{61} +0.951193i q^{62} -15.7930i q^{63} +4.75113 q^{64} +(0.280227 - 1.78682i) q^{65} +0.989065 q^{66} -7.58859i q^{67} +9.77863i q^{68} -6.50480 q^{69} +(-3.48277 - 0.546205i) q^{70} -8.49943 q^{71} -5.55735i q^{72} -6.86804i q^{73} +0.800850 q^{74} +(3.99133 - 12.4120i) q^{75} -1.85613 q^{76} +4.15654i q^{77} -0.800010i q^{78} -3.74373 q^{79} +(6.97508 + 1.09391i) q^{80} -5.96210 q^{81} -4.54421i q^{82} -15.8542i q^{83} +20.1178 q^{84} +(-1.82519 + 11.6380i) q^{85} +0.538847 q^{86} -7.57060i q^{87} +1.46264i q^{88} +1.09693 q^{89} +(0.499293 - 3.18365i) q^{90} +3.36204 q^{91} -4.63023i q^{92} -6.53919i q^{93} -1.62356 q^{94} +(-2.20907 - 0.346449i) q^{95} +10.7509 q^{96} +9.76079i q^{97} -3.89801i q^{98} -3.79954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

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