LMFDB - Embedded newform 1155.2.k.b.769.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.7
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15215 q^{2} +1.00000 q^{3} +2.63174 q^{4} +(1.03706 - 1.98104i) q^{5} -2.15215 q^{6} +(-2.36665 - 1.18277i) q^{7} -1.35961 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15215 q^{2} +1.00000 q^{3} +2.63174 q^{4} +(1.03706 - 1.98104i) q^{5} -2.15215 q^{6} +(-2.36665 - 1.18277i) q^{7} -1.35961 q^{8} +1.00000 q^{9} +(-2.23191 + 4.26348i) q^{10} +(2.31254 - 2.37743i) q^{11} +2.63174 q^{12} -2.85328i q^{13} +(5.09339 + 2.54550i) q^{14} +(1.03706 - 1.98104i) q^{15} -2.33741 q^{16} +4.53838i q^{17} -2.15215 q^{18} +8.19815 q^{19} +(2.72928 - 5.21358i) q^{20} +(-2.36665 - 1.18277i) q^{21} +(-4.97693 + 5.11657i) q^{22} +3.73805i q^{23} -1.35961 q^{24} +(-2.84901 - 4.10891i) q^{25} +6.14067i q^{26} +1.00000 q^{27} +(-6.22843 - 3.11275i) q^{28} -2.78810i q^{29} +(-2.23191 + 4.26348i) q^{30} -8.30729i q^{31} +7.74967 q^{32} +(2.31254 - 2.37743i) q^{33} -9.76726i q^{34} +(-4.79748 + 3.46182i) q^{35} +2.63174 q^{36} -2.54649i q^{37} -17.6436 q^{38} -2.85328i q^{39} +(-1.40999 + 2.69343i) q^{40} +2.83617 q^{41} +(5.09339 + 2.54550i) q^{42} -4.91602 q^{43} +(6.08602 - 6.25677i) q^{44} +(1.03706 - 1.98104i) q^{45} -8.04484i q^{46} -2.80340 q^{47} -2.33741 q^{48} +(4.20211 + 5.59842i) q^{49} +(6.13149 + 8.84298i) q^{50} +4.53838i q^{51} -7.50909i q^{52} +3.66341i q^{53} -2.15215 q^{54} +(-2.31152 - 7.04676i) q^{55} +(3.21772 + 1.60810i) q^{56} +8.19815 q^{57} +6.00041i q^{58} +2.02737i q^{59} +(2.72928 - 5.21358i) q^{60} -7.23628 q^{61} +17.8785i q^{62} +(-2.36665 - 1.18277i) q^{63} -12.0036 q^{64} +(-5.65244 - 2.95902i) q^{65} +(-4.97693 + 5.11657i) q^{66} -13.7748i q^{67} +11.9438i q^{68} +3.73805i q^{69} +(10.3249 - 7.45036i) q^{70} -5.37459 q^{71} -1.35961 q^{72} -6.09921i q^{73} +5.48043i q^{74} +(-2.84901 - 4.10891i) q^{75} +21.5754 q^{76} +(-8.28494 + 2.89134i) q^{77} +6.14067i q^{78} +9.72038i q^{79} +(-2.42404 + 4.63050i) q^{80} +1.00000 q^{81} -6.10387 q^{82} -1.96837i q^{83} +(-6.22843 - 3.11275i) q^{84} +(8.99069 + 4.70657i) q^{85} +10.5800 q^{86} -2.78810i q^{87} +(-3.14414 + 3.23236i) q^{88} +13.9273i q^{89} +(-2.23191 + 4.26348i) q^{90} +(-3.37477 + 6.75272i) q^{91} +9.83759i q^{92} -8.30729i q^{93} +6.03334 q^{94} +(8.50197 - 16.2408i) q^{95} +7.74967 q^{96} +5.74438 q^{97} +(-9.04355 - 12.0486i) q^{98} +(2.31254 - 2.37743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−2.15215			−1.52180			−0.760899	−	0.648870i	$-0.775242\pi$
$2$	−2.15215			−1.52180			−0.760899	+	0.648870i	$0.775242\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	2.63174			1.31587
$5$	1.03706	−	1.98104i	0.463788	−	0.885946i
$5$	1.03706	−	1.98104i	0.463788	−	0.885946i
$6$	−2.15215			−0.878611
$7$	−2.36665	−	1.18277i	−0.894511	−	0.447045i
$7$	−2.36665	−	1.18277i	−0.894511	−	0.447045i
$8$	−1.35961			−0.480693
$9$	1.00000			0.333333
$10$	−2.23191	+	4.26348i	−0.705791	+	1.34823i
$11$	2.31254	−	2.37743i	0.697257	−	0.716821i
$11$	2.31254	−	2.37743i	0.697257	−	0.716821i
$12$	2.63174			0.759719
$13$		−	2.85328i		−	0.791356i	−0.918389	−	0.395678i	$-0.870510\pi$
$13$		−	2.85328i		−	0.791356i	0.918389	−	0.395678i	$-0.129490\pi$
$14$	5.09339	+	2.54550i	1.36127	+	0.680313i
$15$	1.03706	−	1.98104i	0.267768	−	0.511501i
$16$	−2.33741			−0.584353
$17$			4.53838i			1.10072i	0.834928	+	0.550359i	$0.185509\pi$
$17$			4.53838i			1.10072i	−0.834928	+	0.550359i	$0.814491\pi$
$18$	−2.15215			−0.507266
$19$	8.19815			1.88078			0.940392	−	0.340093i	$-0.110459\pi$
$19$	8.19815			1.88078			0.940392	+	0.340093i	$0.110459\pi$
$20$	2.72928	−	5.21358i	0.610285	−	1.16579i
$21$	−2.36665	−	1.18277i	−0.516446	−	0.258102i
$22$	−4.97693	+	5.11657i	−1.06109	+	1.09086i
$23$			3.73805i			0.779438i	0.920934	+	0.389719i	$0.127428\pi$
$23$			3.73805i			0.779438i	−0.920934	+	0.389719i	$0.872572\pi$
$24$	−1.35961			−0.277528
$25$	−2.84901	−	4.10891i	−0.569802	−	0.821782i
$26$			6.14067i			1.20428i
$27$	1.00000			0.192450
$28$	−6.22843	−	3.11275i	−1.17706	−	0.588254i
$29$		−	2.78810i		−	0.517737i	−0.965913	−	0.258869i	$-0.916650\pi$
$29$		−	2.78810i		−	0.517737i	0.965913	−	0.258869i	$-0.0833497\pi$
$30$	−2.23191	+	4.26348i	−0.407489	+	0.778402i
$31$		−	8.30729i		−	1.49203i	−0.665927	−	0.746017i	$-0.731964\pi$
$31$		−	8.30729i		−	1.49203i	0.665927	−	0.746017i	$-0.268036\pi$
$32$	7.74967			1.36996
$33$	2.31254	−	2.37743i	0.402562	−	0.413857i
$34$		−	9.76726i		−	1.67507i
$35$	−4.79748	+	3.46182i	−0.810922	+	0.585155i
$36$	2.63174			0.438624
$37$		−	2.54649i		−	0.418641i	−0.977847	−	0.209320i	$-0.932875\pi$
$37$		−	2.54649i		−	0.418641i	0.977847	−	0.209320i	$-0.0671251\pi$
$38$	−17.6436			−2.86217
$39$		−	2.85328i		−	0.456890i
$40$	−1.40999	+	2.69343i	−0.222940	+	0.425868i
$41$	2.83617			0.442936			0.221468	−	0.975168i	$-0.428915\pi$
$41$	2.83617			0.442936			0.221468	+	0.975168i	$0.428915\pi$
$42$	5.09339	+	2.54550i	0.785927	+	0.392779i
$43$	−4.91602			−0.749687			−0.374843	−	0.927088i	$-0.622304\pi$
$43$	−4.91602			−0.749687			−0.374843	+	0.927088i	$0.622304\pi$
$44$	6.08602	−	6.25677i	0.917501	−	0.943244i
$45$	1.03706	−	1.98104i	0.154596	−	0.295315i
$46$		−	8.04484i		−	1.18615i
$47$	−2.80340			−0.408918			−0.204459	−	0.978875i	$-0.565544\pi$
$47$	−2.80340			−0.408918			−0.204459	+	0.978875i	$0.565544\pi$
$48$	−2.33741			−0.337377
$49$	4.20211	+	5.59842i	0.600301	+	0.799774i
$50$	6.13149	+	8.84298i	0.867124	+	1.25059i
$51$			4.53838i			0.635500i
$52$		−	7.50909i		−	1.04132i
$53$			3.66341i			0.503208i	0.967830	+	0.251604i	$0.0809581\pi$
$53$			3.66341i			0.503208i	−0.967830	+	0.251604i	$0.919042\pi$
$54$	−2.15215			−0.292870
$55$	−2.31152	−	7.04676i	−0.311685	−	0.950185i
$56$	3.21772	+	1.60810i	0.429986	+	0.214892i
$57$	8.19815			1.08587
$58$			6.00041i			0.787892i
$59$			2.02737i			0.263941i	0.991254	+	0.131970i	$0.0421304\pi$
$59$			2.02737i			0.263941i	−0.991254	+	0.131970i	$0.957870\pi$
$60$	2.72928	−	5.21358i	0.352348	−	0.673070i
$61$	−7.23628			−0.926511			−0.463255	−	0.886225i	$-0.653319\pi$
$61$	−7.23628			−0.926511			−0.463255	+	0.886225i	$0.653319\pi$
$62$			17.8785i			2.27057i
$63$	−2.36665	−	1.18277i	−0.298170	−	0.149015i
$64$	−12.0036			−1.50045
$65$	−5.65244	−	2.95902i	−0.701099	−	0.367021i
$66$	−4.97693	+	5.11657i	−0.612618	+	0.629807i
$67$		−	13.7748i		−	1.68286i	−0.540367	−	0.841429i	$-0.681715\pi$
$67$		−	13.7748i		−	1.68286i	0.540367	−	0.841429i	$-0.318285\pi$
$68$			11.9438i			1.44840i
$69$			3.73805i			0.450009i
$70$	10.3249	−	7.45036i	1.23406	−	0.890488i
$71$	−5.37459			−0.637846			−0.318923	−	0.947781i	$-0.603321\pi$
$71$	−5.37459			−0.637846			−0.318923	+	0.947781i	$0.603321\pi$
$72$	−1.35961			−0.160231
$73$		−	6.09921i		−	0.713859i	−0.934131	−	0.356929i	$-0.883824\pi$
$73$		−	6.09921i		−	0.713859i	0.934131	−	0.356929i	$-0.116176\pi$
$74$			5.48043i			0.637087i
$75$	−2.84901	−	4.10891i	−0.328975	−	0.474456i
$76$	21.5754			2.47487
$77$	−8.28494	+	2.89134i	−0.944156	+	0.329499i
$78$			6.14067i			0.695294i
$79$			9.72038i			1.09363i	0.837254	+	0.546814i	$0.184160\pi$
$79$			9.72038i			1.09363i	−0.837254	+	0.546814i	$0.815840\pi$
$80$	−2.42404	+	4.63050i	−0.271016	+	0.517706i
$81$	1.00000			0.111111
$82$	−6.10387			−0.674060
$83$		−	1.96837i		−	0.216057i	−0.994148	−	0.108029i	$-0.965546\pi$
$83$		−	1.96837i		−	0.216057i	0.994148	−	0.108029i	$-0.0344538\pi$
$84$	−6.22843	−	3.11275i	−0.679577	−	0.339629i
$85$	8.99069	+	4.70657i	0.975177	+	0.510499i
$86$	10.5800			1.14087
$87$		−	2.78810i		−	0.298916i
$88$	−3.14414	+	3.23236i	−0.335167	+	0.344571i
$89$			13.9273i			1.47629i	0.674643	+	0.738144i	$0.264297\pi$
$89$			13.9273i			1.47629i	−0.674643	+	0.738144i	$0.735703\pi$
$90$	−2.23191	+	4.26348i	−0.235264	+	0.449411i
$91$	−3.37477	+	6.75272i	−0.353772	+	0.707877i
$92$			9.83759i			1.02564i
$93$		−	8.30729i		−	0.861426i
$94$	6.03334			0.622291
$95$	8.50197	−	16.2408i	0.872284	−	1.66627i
$96$	7.74967			0.790948
$97$	5.74438			0.583254			0.291627	−	0.956532i	$-0.405803\pi$
$97$	5.74438			0.583254			0.291627	+	0.956532i	$0.405803\pi$
$98$	−9.04355	−	12.0486i	−0.913537	−	1.21710i
$99$	2.31254	−	2.37743i	0.232419	−	0.238940i
$100$	−7.49787	−	10.8136i	−0.749787	−	1.08136i
$101$	0.179936			0.0179043			0.00895216	−	0.999960i	$-0.497150\pi$
$101$	0.179936			0.0179043			0.00895216	+	0.999960i	$0.497150\pi$
$102$		−	9.76726i		−	0.967103i
$103$	−13.1694			−1.29762			−0.648808	−	0.760952i	$-0.724732\pi$
$103$	−13.1694			−1.29762			−0.648808	+	0.760952i	$0.724732\pi$
$104$			3.87933i			0.380400i
$105$	−4.79748	+	3.46182i	−0.468186	+	0.337839i
$106$		−	7.88421i		−	0.765782i
$107$	19.0087			1.83764			0.918822	−	0.394673i	$-0.129142\pi$
$107$	19.0087			1.83764			0.918822	+	0.394673i	$0.129142\pi$
$108$	2.63174			0.253240
$109$		−	20.1826i		−	1.93314i	−0.256405	−	0.966569i	$-0.582538\pi$
$109$		−	20.1826i		−	1.93314i	0.256405	−	0.966569i	$-0.417462\pi$
$110$	4.97474	+	15.1657i	0.474323	+	1.44599i
$111$		−	2.54649i		−	0.241702i
$112$	5.53185	+	2.76462i	0.522711	+	0.261232i
$113$		−	11.9738i		−	1.12640i	−0.826321	−	0.563200i	$-0.809570\pi$
$113$		−	11.9738i		−	1.12640i	0.826321	−	0.563200i	$-0.190430\pi$
$114$	−17.6436			−1.65248
$115$	7.40522	+	3.87659i	0.690540	+	0.361494i
$116$		−	7.33757i		−	0.681276i
$117$		−	2.85328i		−	0.263785i
$118$		−	4.36320i		−	0.401665i
$119$	5.36786	−	10.7408i	0.492071	−	0.984605i
$120$	−1.40999	+	2.69343i	−0.128714	+	0.245875i
$121$	−0.304306	−	10.9958i	−0.0276641	−	0.999617i
$122$	15.5735			1.40996
$123$	2.83617			0.255729
$124$		−	21.8627i		−	1.96332i
$125$	−11.0945	+	1.38281i	−0.992322	+	0.123682i
$126$	5.09339	+	2.54550i	0.453755	+	0.226771i
$127$	3.05790			0.271345			0.135673	−	0.990754i	$-0.456681\pi$
$127$	3.05790			0.271345			0.135673	+	0.990754i	$0.456681\pi$
$128$	10.3342			0.913425
$129$	−4.91602			−0.432832
$130$	12.1649	+	6.36825i	1.06693	+	0.558532i
$131$	−10.3006			−0.899967			−0.449983	−	0.893037i	$-0.648570\pi$
$131$	−10.3006			−0.899967			−0.449983	+	0.893037i	$0.648570\pi$
$132$	6.08602	−	6.25677i	0.529720	−	0.544582i
$133$	−19.4022	−	9.69653i	−1.68238	−	0.840796i
$134$			29.6454i			2.56097i
$135$	1.03706	−	1.98104i	0.0892560	−	0.170500i
$136$		−	6.17040i		−	0.529108i
$137$		−	19.1966i		−	1.64008i	−0.572310	−	0.820038i	$-0.693952\pi$
$137$		−	19.1966i		−	1.64008i	0.572310	−	0.820038i	$-0.306048\pi$
$138$		−	8.04484i		−	0.684823i
$139$	−15.6692			−1.32904			−0.664522	−	0.747268i	$-0.731365\pi$
$139$	−15.6692			−1.32904			−0.664522	+	0.747268i	$0.731365\pi$
$140$	−12.6257	+	9.11063i	−1.06707	+	0.769989i
$141$	−2.80340			−0.236089
$142$	11.5669			0.970674
$143$	−6.78345	−	6.59832i	−0.567261	−	0.551779i
$144$	−2.33741			−0.194784
$145$	−5.52333	−	2.89143i	−0.458688	−	0.240120i
$146$			13.1264i			1.08635i
$147$	4.20211	+	5.59842i	0.346584	+	0.461750i
$148$		−	6.70171i		−	0.550877i
$149$		−	4.88333i		−	0.400058i	−0.979790	−	0.200029i	$-0.935896\pi$
$149$		−	4.88333i		−	0.400058i	0.979790	−	0.200029i	$-0.0641036\pi$
$150$	6.13149	+	8.84298i	0.500634	+	0.722027i
$151$			0.299514i			0.0243741i	0.999926	+	0.0121871i	$0.00387936\pi$
$151$			0.299514i			0.0243741i	−0.999926	+	0.0121871i	$0.996121\pi$
$152$	−11.1462			−0.904080
$153$			4.53838i			0.366906i
$154$	17.8304	−	6.22259i	1.43682	−	0.501430i
$155$	−16.4570	−	8.61516i	−1.32186	−	0.691986i
$156$		−	7.50909i		−	0.601208i
$157$	−1.75520			−0.140080			−0.0700401	−	0.997544i	$-0.522313\pi$
$157$	−1.75520			−0.140080			−0.0700401	+	0.997544i	$0.522313\pi$
$158$		−	20.9197i		−	1.66428i
$159$			3.66341i			0.290528i
$160$	8.03688	−	15.3524i	0.635371	−	1.21371i
$161$	4.42126	−	8.84668i	0.348444	−	0.697216i
$162$	−2.15215			−0.169089
$163$			11.3819i			0.891502i	0.895157	+	0.445751i	$0.147063\pi$
$163$			11.3819i			0.891502i	−0.895157	+	0.445751i	$0.852937\pi$
$164$	7.46408			0.582847
$165$	−2.31152	−	7.04676i	−0.179952	−	0.548590i
$166$			4.23623i			0.328796i
$167$		−	5.43502i		−	0.420575i	−0.977640	−	0.210287i	$-0.932560\pi$
$167$		−	5.43502i		−	0.420575i	0.977640	−	0.210287i	$-0.0674400\pi$
$168$	3.21772	+	1.60810i	0.248252	+	0.124068i
$169$	4.85882			0.373755
$170$	−19.3493	−	10.1292i	−1.48402	−	0.776877i
$171$	8.19815			0.626928
$172$	−12.9377			−0.986492
$173$		−	13.6439i		−	1.03732i	−0.854979	−	0.518662i	$-0.826430\pi$
$173$		−	13.6439i		−	1.03732i	0.854979	−	0.518662i	$-0.173570\pi$
$174$			6.00041i			0.454890i
$175$	1.88272	+	13.0941i	0.142321	+	0.989821i
$176$	−5.40536	+	5.55703i	−0.407445	+	0.418877i
$177$			2.02737i			0.152386i
$178$		−	29.9736i		−	2.24661i
$179$	19.2025			1.43527			0.717633	−	0.696422i	$-0.245226\pi$
$179$	19.2025			1.43527			0.717633	+	0.696422i	$0.245226\pi$
$180$	2.72928	−	5.21358i	0.203428	−	0.388597i
$181$			3.21422i			0.238911i	0.992840	+	0.119456i	$0.0381149\pi$
$181$			3.21422i			0.238911i	−0.992840	+	0.119456i	$0.961885\pi$
$182$	7.26301	−	14.5328i	0.538370	−	1.07725i
$183$	−7.23628			−0.534921
$184$		−	5.08228i		−	0.374671i
$185$	−5.04469	−	2.64087i	−0.370893	−	0.194160i
$186$			17.8785i			1.31092i
$187$	10.7897	+	10.4952i	0.789017	+	0.767484i
$188$	−7.37784			−0.538084
$189$	−2.36665	−	1.18277i	−0.172149	−	0.0860339i
$190$	−18.2975	+	34.9527i	−1.32744	+	2.53573i
$191$	−4.65835			−0.337067			−0.168533	−	0.985696i	$-0.553903\pi$
$191$	−4.65835			−0.337067			−0.168533	+	0.985696i	$0.553903\pi$
$192$	−12.0036			−0.866287
$193$	3.17890			0.228822			0.114411	−	0.993433i	$-0.463502\pi$
$193$	3.17890			0.228822			0.114411	+	0.993433i	$0.463502\pi$
$194$	−12.3628			−0.887595
$195$	−5.65244	−	2.95902i	−0.404780	−	0.211900i
$196$	11.0589	+	14.7336i	0.789919	+	1.05240i
$197$	−3.27099			−0.233048			−0.116524	−	0.993188i	$-0.537175\pi$
$197$	−3.27099			−0.233048			−0.116524	+	0.993188i	$0.537175\pi$
$198$	−4.97693	+	5.11657i	−0.353695	+	0.363619i
$199$		−	3.84002i		−	0.272212i	−0.990694	−	0.136106i	$-0.956541\pi$
$199$		−	3.84002i		−	0.272212i	0.990694	−	0.136106i	$-0.0434587\pi$
$200$	3.87353	+	5.58650i	0.273900	+	0.395025i
$201$		−	13.7748i		−	0.971599i
$202$	−0.387249			−0.0272468
$203$	−3.29768	+	6.59847i	−0.231452	+	0.463122i
$204$			11.9438i			0.836236i
$205$	2.94128	−	5.61857i	0.205428	−	0.392418i
$206$	28.3424			1.97471
$207$			3.73805i			0.259813i
$208$			6.66928i			0.462432i
$209$	18.9586	−	19.4905i	1.31139	−	1.34818i
$210$	10.3249	−	7.45036i	0.712485	−	0.514124i
$211$			15.7083i			1.08140i	0.841215	+	0.540701i	$0.181841\pi$
$211$			15.7083i			1.08140i	−0.841215	+	0.540701i	$0.818159\pi$
$212$			9.64116i			0.662158i
$213$	−5.37459			−0.368261
$214$	−40.9096			−2.79652
$215$	−5.09822	+	9.73882i	−0.347695	+	0.664182i
$216$	−1.35961			−0.0925095
$217$	−9.82562	+	19.6605i	−0.667007	+	1.33464i
$218$			43.4359i			2.94185i
$219$		−	6.09921i		−	0.412147i
$220$	−6.08333	−	18.5453i	−0.410138	−	1.25032i
$221$	12.9492			0.871060
$222$			5.48043i			0.367822i
$223$	14.7511			0.987809			0.493905	−	0.869516i	$-0.335569\pi$
$223$	14.7511			0.987809			0.493905	+	0.869516i	$0.335569\pi$
$224$	−18.3408	−	9.16609i	−1.22545	−	0.612435i
$225$	−2.84901	−	4.10891i	−0.189934	−	0.273927i
$226$			25.7694i			1.71415i
$227$			16.6800i			1.10709i	0.832820	+	0.553544i	$0.186725\pi$
$227$			16.6800i			1.10709i	−0.832820	+	0.553544i	$0.813275\pi$
$228$	21.5754			1.42887
$229$			11.6865i			0.772263i	0.922444	+	0.386131i	$0.126189\pi$
$229$			11.6865i			0.772263i	−0.922444	+	0.386131i	$0.873811\pi$
$230$	−15.9371	−	8.34299i	−1.05086	−	0.550120i
$231$	−8.28494	+	2.89134i	−0.545109	+	0.190236i
$232$			3.79072i			0.248873i
$233$	19.5846			1.28303			0.641516	−	0.767110i	$-0.278306\pi$
$233$	19.5846			1.28303			0.641516	+	0.767110i	$0.278306\pi$
$234$			6.14067i			0.401428i
$235$	−2.90730	+	5.55364i	−0.189651	+	0.362280i
$236$			5.33552i			0.347312i
$237$			9.72038i			0.631407i
$238$	−11.5524	+	23.1157i	−0.748833	+	1.49837i
$239$			22.9246i			1.48287i	0.671026	+	0.741434i	$0.265854\pi$
$239$			22.9246i			1.48287i	−0.671026	+	0.741434i	$0.734146\pi$
$240$	−2.42404	+	4.63050i	−0.156471	+	0.298898i
$241$	0.858653			0.0553107			0.0276553	−	0.999618i	$-0.491196\pi$
$241$	0.858653			0.0553107			0.0276553	+	0.999618i	$0.491196\pi$
$242$	0.654911	+	23.6646i	0.0420993	+	1.52122i
$243$	1.00000			0.0641500
$244$	−19.0440			−1.21917
$245$	15.4485	−	2.51862i	0.986969	−	0.160909i
$246$	−6.10387			−0.389168
$247$		−	23.3916i		−	1.48837i
$248$			11.2946i			0.717210i
$249$		−	1.96837i		−	0.124741i
$250$	23.8770	−	2.97600i	1.51011	−	0.188219i
$251$			16.2067i			1.02296i	0.859296	+	0.511478i	$0.170902\pi$
$251$			16.2067i			1.02296i	−0.859296	+	0.511478i	$0.829098\pi$
$252$	−6.22843	−	3.11275i	−0.392354	−	0.196085i
$253$	8.88694	+	8.64440i	0.558717	+	0.543469i
$254$	−6.58106			−0.412933
$255$	8.99069	+	4.70657i	0.563019	+	0.294737i
$256$	1.76644			0.110403
$257$	12.6011			0.786038			0.393019	−	0.919530i	$-0.371431\pi$
$257$	12.6011			0.786038			0.393019	+	0.919530i	$0.371431\pi$
$258$	10.5800			0.658683
$259$	−3.01192	+	6.02667i	−0.187151	+	0.374479i
$260$	−14.8758	−	7.78738i	−0.922557	−	0.482953i
$261$		−	2.78810i		−	0.172579i
$262$	22.1684			1.36957
$263$	−2.96589			−0.182884			−0.0914422	−	0.995810i	$-0.529148\pi$
$263$	−2.96589			−0.182884			−0.0914422	+	0.995810i	$0.529148\pi$
$264$	−3.14414	+	3.23236i	−0.193509	+	0.198938i
$265$	7.25735	+	3.79918i	0.445816	+	0.233382i
$266$	41.7564	+	20.8684i	2.56025	+	1.27952i
$267$			13.9273i			0.852335i
$268$		−	36.2517i		−	2.21443i
$269$		−	18.9620i		−	1.15613i	−0.815989	−	0.578067i	$-0.803807\pi$
$269$		−	18.9620i		−	1.15613i	0.815989	−	0.578067i	$-0.196193\pi$
$270$	−2.23191	+	4.26348i	−0.135830	+	0.259467i
$271$	12.0999			0.735017			0.367508	−	0.930020i	$-0.380211\pi$
$271$	12.0999			0.735017			0.367508	+	0.930020i	$0.380211\pi$
$272$		−	10.6081i		−	0.643208i
$273$	−3.37477	+	6.75272i	−0.204250	+	0.408693i
$274$			41.3139i			2.49586i
$275$	−16.3571	−	2.72871i	−0.986369	−	0.164547i
$276$			9.83759i			0.592154i
$277$	−29.0875			−1.74770			−0.873849	−	0.486198i	$-0.838383\pi$
$277$	−29.0875			−1.74770			−0.873849	+	0.486198i	$0.838383\pi$
$278$	33.7225			2.02254
$279$		−	8.30729i		−	0.497344i
$280$	6.52268	−	4.70672i	0.389805	−	0.281280i
$281$		−	21.2889i		−	1.26999i	−0.772516	−	0.634995i	$-0.781002\pi$
$281$		−	21.2889i		−	1.26999i	0.772516	−	0.634995i	$-0.218998\pi$
$282$	6.03334			0.359280
$283$			3.54750i			0.210877i	0.994426	+	0.105439i	$0.0336246\pi$
$283$			3.54750i			0.210877i	−0.994426	+	0.105439i	$0.966375\pi$
$284$	−14.1445			−0.839324
$285$	8.50197	−	16.2408i	0.503613	−	0.962023i
$286$	14.5990	+	14.2006i	0.863256	+	0.839697i
$287$	−6.71225	−	3.35455i	−0.396211	−	0.198013i
$288$	7.74967			0.456654
$289$	−3.59686			−0.211580
$290$	11.8870	+	6.22279i	0.698030	+	0.365415i
$291$	5.74438			0.336742
$292$		−	16.0516i		−	0.939347i
$293$			21.7486i			1.27057i	0.772279	+	0.635284i	$0.219117\pi$
$293$			21.7486i			1.27057i	−0.772279	+	0.635284i	$0.780883\pi$
$294$	−9.04355	−	12.0486i	−0.527431	−	0.702691i
$295$	4.01629	+	2.10250i	0.233838	+	0.122413i
$296$			3.46223i			0.201238i
$297$	2.31254	−	2.37743i	0.134187	−	0.137952i
$298$			10.5096i			0.608808i
$299$	10.6657			0.616813
$300$	−7.49787	−	10.8136i	−0.432889	−	0.624323i
$301$	11.6345	+	5.81453i	0.670603	+	0.335144i
$302$		−	0.644599i		−	0.0370925i
$303$	0.179936			0.0103371
$304$	−19.1625			−1.09904
$305$	−7.50446	+	14.3353i	−0.429704	+	0.820839i
$306$		−	9.76726i		−	0.558357i
$307$			14.6920i			0.838516i	0.907867	+	0.419258i	$0.137710\pi$
$307$			14.6920i			0.838516i	−0.907867	+	0.419258i	$0.862290\pi$
$308$	−21.8038	+	7.60926i	−1.24239	+	0.433578i
$309$	−13.1694			−0.749180
$310$	35.4180	+	18.5411i	2.01161	+	1.05306i
$311$			27.5939i			1.56471i	0.622834	+	0.782354i	$0.285981\pi$
$311$			27.5939i			1.56471i	−0.622834	+	0.782354i	$0.714019\pi$
$312$			3.87933i			0.219624i
$313$	15.7642			0.891047			0.445524	−	0.895270i	$-0.353018\pi$
$313$	15.7642			0.891047			0.445524	+	0.895270i	$0.353018\pi$
$314$	3.77745			0.213174
$315$	−4.79748	+	3.46182i	−0.270307	+	0.195052i
$316$			25.5816i			1.43908i
$317$			26.2007i			1.47158i	0.677211	+	0.735789i	$0.263188\pi$
$317$			26.2007i			1.47158i	−0.677211	+	0.735789i	$0.736812\pi$
$318$		−	7.88421i		−	0.442125i
$319$	−6.62850	−	6.44760i	−0.371125	−	0.360996i
$320$	−12.4485	+	23.7796i	−0.695891	+	1.32932i
$321$	19.0087			1.06096
$322$	−9.51521	+	19.0394i	−0.530262	+	1.06102i
$323$			37.2063i			2.07021i
$324$	2.63174			0.146208
$325$	−11.7238	+	8.12901i	−0.650322	+	0.450916i
$326$		−	24.4956i		−	1.35669i
$327$		−	20.1826i		−	1.11610i
$328$	−3.85608			−0.212916
$329$	6.63468	+	3.31578i	0.365782	+	0.182805i
$330$	4.97474	+	15.1657i	0.273850	+	0.834843i
$331$	−3.81467			−0.209673			−0.104837	−	0.994489i	$-0.533432\pi$
$331$	−3.81467			−0.209673			−0.104837	+	0.994489i	$0.533432\pi$
$332$		−	5.18026i		−	0.284304i
$333$		−	2.54649i		−	0.139547i
$334$			11.6970i			0.640030i
$335$	−27.2884	−	14.2853i	−1.49092	−	0.780489i
$336$	5.53185	+	2.76462i	0.301787	+	0.150823i
$337$	11.0317			0.600935			0.300468	−	0.953792i	$-0.402857\pi$
$337$	11.0317			0.600935			0.300468	+	0.953792i	$0.402857\pi$
$338$	−10.4569			−0.568781
$339$		−	11.9738i		−	0.650327i
$340$	23.6612	+	12.3865i	1.28321	+	0.671752i
$341$	−19.7500	−	19.2110i	−1.06952	−	1.04033i
$342$	−17.6436			−0.954058
$343$	−3.32328	−	18.2197i	−0.179440	−	0.983769i
$344$	6.68386			0.360369
$345$	7.40522	+	3.87659i	0.398684	+	0.208708i
$346$			29.3636i			1.57860i
$347$	−4.88339			−0.262154			−0.131077	−	0.991372i	$-0.541844\pi$
$347$	−4.88339			−0.262154			−0.131077	+	0.991372i	$0.541844\pi$
$348$		−	7.33757i		−	0.393335i
$349$	−21.2195			−1.13585			−0.567926	−	0.823080i	$-0.692254\pi$
$349$	−21.2195			−1.13585			−0.567926	+	0.823080i	$0.692254\pi$
$350$	−4.05190	−	28.1804i	−0.216583	−	1.50631i
$351$		−	2.85328i		−	0.152297i
$352$	17.9214	−	18.4243i	0.955216	−	0.982017i
$353$	−30.2275			−1.60885			−0.804423	−	0.594056i	$-0.797526\pi$
$353$	−30.2275			−1.60885			−0.804423	+	0.594056i	$0.797526\pi$
$354$		−	4.36320i		−	0.231901i
$355$	−5.57377	+	10.6473i	−0.295825	+	0.565098i
$356$			36.6530i			1.94261i
$357$	5.36786	−	10.7408i	0.284097	−	0.568462i
$358$	−41.3267			−2.18419
$359$			20.1665i			1.06435i	0.846635	+	0.532174i	$0.178625\pi$
$359$			20.1665i			1.06435i	−0.846635	+	0.532174i	$0.821375\pi$
$360$	−1.40999	+	2.69343i	−0.0743132	+	0.141956i
$361$	48.2096			2.53735
$362$		−	6.91748i		−	0.363575i
$363$	−0.304306	−	10.9958i	−0.0159719	−	0.577129i
$364$	−8.88153	+	17.7714i	−0.465519	+	0.931475i
$365$	−12.0828	−	6.32525i	−0.632441	−	0.331079i
$366$	15.5735			0.814042
$367$	25.8529			1.34951			0.674755	−	0.738042i	$-0.264249\pi$
$367$	25.8529			1.34951			0.674755	+	0.738042i	$0.264249\pi$
$368$		−	8.73737i		−	0.455467i
$369$	2.83617			0.147645
$370$	10.8569	+	5.68354i	0.564425	+	0.295473i
$371$	4.33298	−	8.67003i	0.224957	−	0.450126i
$372$		−	21.8627i		−	1.13353i
$373$	0.526740			0.0272736			0.0136368	−	0.999907i	$-0.495659\pi$
$373$	0.526740			0.0272736			0.0136368	+	0.999907i	$0.495659\pi$
$374$	−23.2209	−	22.5872i	−1.20073	−	1.16796i
$375$	−11.0945	+	1.38281i	−0.572917	+	0.0714078i
$376$	3.81152			0.196564
$377$	−7.95522			−0.409715
$378$	5.09339	+	2.54550i	0.261976	+	0.130926i
$379$	−5.66073			−0.290772			−0.145386	−	0.989375i	$-0.546442\pi$
$379$	−5.66073			−0.290772			−0.145386	+	0.989375i	$0.546442\pi$
$380$	22.3750	−	42.7417i	1.14781	−	2.19260i
$381$	3.05790			0.156661
$382$	10.0255			0.512948
$383$	13.3443			0.681859			0.340930	−	0.940089i	$-0.389258\pi$
$383$	13.3443			0.681859			0.340930	+	0.940089i	$0.389258\pi$
$384$	10.3342			0.527366
$385$	−2.86413	+	19.4113i	−0.145970	+	0.989289i
$386$	−6.84146			−0.348221
$387$	−4.91602			−0.249896
$388$	15.1177			0.767487
$389$	37.0292			1.87746			0.938729	−	0.344657i	$-0.112005\pi$
$389$	37.0292			1.87746			0.938729	+	0.344657i	$0.112005\pi$
$390$	12.1649	+	6.36825i	0.615993	+	0.322469i
$391$	−16.9647			−0.857941
$392$	−5.71321	−	7.61165i	−0.288561	−	0.384446i
$393$	−10.3006			−0.519596
$394$	7.03965			0.354653
$395$	19.2564	+	10.0806i	0.968896	+	0.507211i
$396$	6.08602	−	6.25677i	0.305834	−	0.314415i
$397$	−33.8285			−1.69780			−0.848902	−	0.528551i	$-0.822736\pi$
$397$	−33.8285			−1.69780			−0.848902	+	0.528551i	$0.822736\pi$
$398$			8.26429i			0.414252i
$399$	−19.4022	−	9.69653i	−0.971324	−	0.485434i
$400$	6.65932	+	9.60422i	0.332966	+	0.480211i
$401$	−36.0567			−1.80059			−0.900293	−	0.435284i	$-0.856648\pi$
$401$	−36.0567			−1.80059			−0.900293	+	0.435284i	$0.856648\pi$
$402$			29.6454i			1.47858i
$403$	−23.7030			−1.18073
$404$	0.473546			0.0235598
$405$	1.03706	−	1.98104i	0.0515320	−	0.0984385i
$406$	7.09711	−	14.2009i	0.352224	−	0.704778i
$407$	−6.05410	−	5.88887i	−0.300090	−	0.291900i
$408$		−	6.17040i		−	0.305480i
$409$	−4.07862			−0.201675			−0.100837	−	0.994903i	$-0.532152\pi$
$409$	−4.07862			−0.201675			−0.100837	+	0.994903i	$0.532152\pi$
$410$	−6.33008	+	12.0920i	−0.312620	+	0.597181i
$411$		−	19.1966i		−	0.946898i
$412$	−34.6584			−1.70750
$413$	2.39791	−	4.79808i	0.117994	−	0.236098i
$414$		−	8.04484i		−	0.395383i
$415$	−3.89942	−	2.04132i	−0.191415	−	0.100205i
$416$		−	22.1119i		−	1.08413i
$417$	−15.6692			−0.767324
$418$	−40.8016	+	41.9464i	−1.99567	+	2.05167i
$419$			6.29750i			0.307653i	0.988098	+	0.153827i	$0.0491597\pi$
$419$			6.29750i			0.307653i	−0.988098	+	0.153827i	$0.950840\pi$
$420$	−12.6257	+	9.11063i	−0.616072	+	0.444553i
$421$	12.8233			0.624968			0.312484	−	0.949923i	$-0.398839\pi$
$421$	12.8233			0.624968			0.312484	+	0.949923i	$0.398839\pi$
$422$		−	33.8065i		−	1.64568i
$423$	−2.80340			−0.136306
$424$		−	4.98080i		−	0.241889i
$425$	18.6478	−	12.9299i	0.904550	−	0.627191i
$426$	11.5669			0.560419
$427$	17.1258	+	8.55886i	0.828774	+	0.414192i
$428$	50.0261			2.41810
$429$	−6.78345	−	6.59832i	−0.327508	−	0.318570i
$430$	10.9721	−	20.9594i	0.529122	−	1.01075i
$431$		−	33.6794i		−	1.62228i	−0.584852	−	0.811140i	$-0.698847\pi$
$431$		−	33.6794i		−	1.62228i	0.584852	−	0.811140i	$-0.301153\pi$
$432$	−2.33741			−0.112459
$433$	22.5860			1.08541			0.542707	−	0.839922i	$-0.317399\pi$
$433$	22.5860			1.08541			0.542707	+	0.839922i	$0.317399\pi$
$434$	21.1462	−	42.3123i	1.01505	−	2.03105i
$435$	−5.52333	−	2.89143i	−0.264823	−	0.138633i
$436$		−	53.1153i		−	2.54376i
$437$			30.6451i			1.46595i
$438$			13.1264i			0.627204i
$439$	11.6126			0.554239			0.277120	−	0.960835i	$-0.410620\pi$
$439$	11.6126			0.554239			0.277120	+	0.960835i	$0.410620\pi$
$440$	3.14276	+	9.58082i	0.149825	+	0.456748i
$441$	4.20211	+	5.59842i	0.200100	+	0.266591i
$442$	−27.8687			−1.32558
$443$			2.80338i			0.133193i	0.997780	+	0.0665963i	$0.0212139\pi$
$443$			2.80338i			0.133193i	−0.997780	+	0.0665963i	$0.978786\pi$
$444$		−	6.70171i		−	0.318049i
$445$	27.5904	+	14.4434i	1.30791	+	0.684684i
$446$	−31.7466			−1.50325
$447$		−	4.88333i		−	0.230973i
$448$	28.4084	+	14.1975i	1.34217	+	0.670770i
$449$	17.7897			0.839550			0.419775	−	0.907628i	$-0.362109\pi$
$449$	17.7897			0.839550			0.419775	+	0.907628i	$0.362109\pi$
$450$	6.13149	+	8.84298i	0.289041	+	0.416862i
$451$	6.55877	−	6.74279i	0.308840	−	0.317506i
$452$		−	31.5120i		−	1.48220i
$453$			0.299514i			0.0140724i
$454$		−	35.8977i		−	1.68476i
$455$	9.87753	+	13.6885i	0.463066	+	0.641728i
$456$	−11.1462			−0.521971
$457$	0.848816			0.0397059			0.0198530	−	0.999803i	$-0.493680\pi$
$457$	0.848816			0.0397059			0.0198530	+	0.999803i	$0.493680\pi$
$458$		−	25.1510i		−	1.17523i
$459$			4.53838i			0.211833i
$460$	19.4886	+	10.2022i	0.908662	+	0.475679i
$461$	22.6973			1.05712			0.528559	−	0.848896i	$-0.322732\pi$
$461$	22.6973			1.05712			0.528559	+	0.848896i	$0.322732\pi$
$462$	17.8304	−	6.22259i	0.829546	−	0.289501i
$463$		−	29.6452i		−	1.37773i	−0.724891	−	0.688864i	$-0.758110\pi$
$463$		−	29.6452i		−	1.37773i	0.724891	−	0.688864i	$-0.241890\pi$
$464$			6.51694i			0.302542i
$465$	−16.4570	−	8.61516i	−0.763177	−	0.399519i
$466$	−42.1490			−1.95252
$467$	−8.99890			−0.416419			−0.208210	−	0.978084i	$-0.566764\pi$
$467$	−8.99890			−0.416419			−0.208210	+	0.978084i	$0.566764\pi$
$468$		−	7.50909i		−	0.347108i
$469$	−16.2924	+	32.6002i	−0.752314	+	1.50534i
$470$	6.25694	−	11.9523i	0.288611	−	0.551317i
$471$	−1.75520			−0.0808753
$472$		−	2.75642i		−	0.126875i
$473$	−11.3685	+	11.6875i	−0.522725	+	0.537391i
$474$		−	20.9197i		−	0.960874i
$475$	−23.3566	−	33.6854i	−1.07167	−	1.54559i
$476$	14.1268	−	28.2669i	0.647502	−	1.29561i
$477$			3.66341i			0.167736i
$478$		−	49.3371i		−	2.25663i
$479$	31.3111			1.43064			0.715320	−	0.698797i	$-0.246281\pi$
$479$	31.3111			1.43064			0.715320	+	0.698797i	$0.246281\pi$
$480$	8.03688	−	15.3524i	0.366832	−	0.700737i
$481$	−7.26584			−0.331294
$482$	−1.84795			−0.0841718
$483$	4.42126	−	8.84668i	0.201174	−	0.402538i
$484$	−0.800854	−	28.9381i	−0.0364025	−	1.31537i
$485$	5.95727	−	11.3798i	0.270506	−	0.516731i
$486$	−2.15215			−0.0976234
$487$		−	1.83929i		−	0.0833462i	−0.999131	−	0.0416731i	$-0.986731\pi$
$487$		−	1.83929i		−	0.0833462i	0.999131	−	0.0416731i	$-0.0132688\pi$
$488$	9.83849			0.445367
$489$			11.3819i			0.514709i
$490$	−33.2475	+	5.42045i	−1.50197	+	0.244871i
$491$			3.46665i			0.156448i	0.996936	+	0.0782238i	$0.0249249\pi$
$491$			3.46665i			0.156448i	−0.996936	+	0.0782238i	$0.975075\pi$
$492$	7.46408			0.336507
$493$	12.6534			0.569883
$494$			50.3421i			2.26500i
$495$	−2.31152	−	7.04676i	−0.103895	−	0.316728i
$496$			19.4176i			0.871875i
$497$	12.7198	+	6.35691i	0.570561	+	0.285146i
$498$			4.23623i			0.189830i
$499$	−33.8080			−1.51346			−0.756728	−	0.653730i	$-0.773203\pi$
$499$	−33.8080			−1.51346			−0.756728	+	0.653730i	$0.773203\pi$
$500$	−29.1979	+	3.63919i	−1.30577	+	0.162750i
$501$		−	5.43502i		−	0.242819i
$502$		−	34.8792i		−	1.55673i
$503$			23.8920i			1.06529i	0.846338	+	0.532646i	$0.178802\pi$
$503$			23.8920i			1.06529i	−0.846338	+	0.532646i	$0.821198\pi$
$504$	3.21772	+	1.60810i	0.143329	+	0.0716306i
$505$	0.186605	−	0.356460i	0.00830380	−	0.0158623i
$506$	−19.1260	−	18.6040i	−0.850255	−	0.827050i
$507$	4.85882			0.215788
$508$	8.04762			0.357055
$509$			24.4575i			1.08406i	0.840359	+	0.542031i	$0.182344\pi$
$509$			24.4575i			1.08406i	−0.840359	+	0.542031i	$0.817656\pi$
$510$	−19.3493	−	10.1292i	−0.856801	−	0.448530i
$511$	−7.21397	+	14.4347i	−0.319127	+	0.638555i
$512$	−24.4701			−1.08144
$513$	8.19815			0.361957
$514$	−27.1195			−1.19619
$515$	−13.6574	+	26.0890i	−0.601819	+	1.14962i
$516$	−12.9377			−0.569551
$517$	−6.48298	+	6.66488i	−0.285121	+	0.293121i
$518$	6.48209	−	12.9703i	0.284807	−	0.569881i
$519$		−	13.6439i		−	0.598900i
$520$	7.68509	+	4.02310i	0.337014	+	0.176425i
$521$			20.7027i			0.907002i	0.891256	+	0.453501i	$0.149825\pi$
$521$			20.7027i			0.907002i	−0.891256	+	0.453501i	$0.850175\pi$
$522$			6.00041i			0.262631i
$523$			15.0535i			0.658242i	0.944288	+	0.329121i	$0.106752\pi$
$523$			15.0535i			0.658242i	−0.944288	+	0.329121i	$0.893248\pi$
$524$	−27.1085			−1.18424
$525$	1.88272	+	13.0941i	0.0821688	+	0.571473i
$526$	6.38303			0.278313
$527$	37.7016			1.64231
$528$	−5.40536	+	5.55703i	−0.235238	+	0.241839i
$529$	9.02697			0.392477
$530$	−15.6189	−	8.17640i	−0.678442	−	0.355160i
$531$			2.02737i			0.0879803i
$532$	−51.0616	−	25.5188i	−2.21380	−	1.10638i
$533$		−	8.09239i		−	0.350520i
$534$		−	29.9736i		−	1.29708i
$535$	19.7132	−	37.6570i	0.852276	−	1.62805i
$536$			18.7283i			0.808939i
$537$	19.2025			0.828651
$538$			40.8091i			1.75940i
$539$	23.0274	+	2.95639i	0.991859	+	0.127341i
$540$	2.72928	−	5.21358i	0.117449	−	0.224357i
$541$			20.8138i			0.894855i	0.894320	+	0.447428i	$0.147660\pi$
$541$			20.8138i			0.894855i	−0.894320	+	0.447428i	$0.852340\pi$
$542$	−26.0408			−1.11855
$543$			3.21422i			0.137935i
$544$			35.1709i			1.50794i
$545$	−39.9824	−	20.9305i	−1.71266	−	0.896566i
$546$	7.26301	−	14.5328i	0.310828	−	0.621948i
$547$	17.5198			0.749093			0.374547	−	0.927208i	$-0.377798\pi$
$547$	17.5198			0.749093			0.374547	+	0.927208i	$0.377798\pi$
$548$		−	50.5205i		−	2.15813i
$549$	−7.23628			−0.308837
$550$	35.2029	+	5.87259i	1.50106	+	0.250408i
$551$		−	22.8573i		−	0.973752i
$552$		−	5.08228i		−	0.216316i
$553$	11.4970	−	23.0048i	0.488902	−	0.978263i
$554$	62.6006			2.65964
$555$	−5.04469	−	2.64087i	−0.214135	−	0.112099i
$556$	−41.2373			−1.74885
$557$	−17.8192			−0.755025			−0.377512	−	0.926005i	$-0.623220\pi$
$557$	−17.8192			−0.755025			−0.377512	+	0.926005i	$0.623220\pi$
$558$			17.8785i			0.756858i
$559$			14.0268i			0.593269i
$560$	11.2137	−	8.09171i	0.473865	−	0.341937i
$561$	10.7897	+	10.4952i	0.455539	+	0.443107i
$562$			45.8169i			1.93267i
$563$			23.2385i			0.979385i	0.871895	+	0.489693i	$0.162891\pi$
$563$			23.2385i			0.979385i	−0.871895	+	0.489693i	$0.837109\pi$
$564$	−7.37784			−0.310663
$565$	−23.7205	−	12.4176i	−0.997930	−	0.522410i
$566$		−	7.63475i		−	0.320912i
$567$	−2.36665	−	1.18277i	−0.0993901	−	0.0496717i
$568$	7.30732			0.306608
$569$		−	3.34614i		−	0.140277i	−0.997537	−	0.0701387i	$-0.977656\pi$
$569$		−	3.34614i		−	0.140277i	0.997537	−	0.0701387i	$-0.0223442\pi$
$570$	−18.2975	+	34.9527i	−0.766398	+	1.46401i
$571$			44.3884i			1.85760i	0.370583	+	0.928799i	$0.379158\pi$
$571$			44.3884i			1.85760i	−0.370583	+	0.928799i	$0.620842\pi$
$572$	−17.8523	−	17.3651i	−0.746442	−	0.726070i
$573$	−4.65835			−0.194606
$574$	14.4457	+	7.21948i	0.602954	+	0.301335i
$575$	15.3593	−	10.6498i	0.640528	−	0.444125i
$576$	−12.0036			−0.500151
$577$	35.2687			1.46826			0.734128	−	0.679012i	$-0.237591\pi$
$577$	35.2687			1.46826			0.734128	+	0.679012i	$0.237591\pi$
$578$	7.74097			0.321982
$579$	3.17890			0.132111
$580$	−14.5360	−	7.60950i	−0.603574	−	0.315967i
$581$	−2.32814	+	4.65846i	−0.0965874	+	0.193266i
$582$	−12.3628			−0.512453
$583$	8.70949	+	8.47179i	0.360710	+	0.350866i
$584$			8.29252i			0.343147i
$585$	−5.65244	−	2.95902i	−0.233700	−	0.122340i
$586$		−	46.8062i		−	1.93355i
$587$	25.3894			1.04793			0.523966	−	0.851739i	$-0.324452\pi$
$587$	25.3894			1.04793			0.523966	+	0.851739i	$0.324452\pi$
$588$	11.0589	+	14.7336i	0.456060	+	0.607604i
$589$		−	68.1044i		−	2.80619i
$590$	−8.64366	−	4.52490i	−0.355854	−	0.186287i
$591$	−3.27099			−0.134550
$592$			5.95220i			0.244634i
$593$		−	12.1933i		−	0.500719i	−0.968153	−	0.250360i	$-0.919451\pi$
$593$		−	12.1933i		−	0.500719i	0.968153	−	0.250360i	$-0.0805489\pi$
$594$	−4.97693	+	5.11657i	−0.204206	+	0.209936i
$595$	−15.7111	−	21.7728i	−0.644090	−	0.892596i
$596$		−	12.8517i		−	0.526425i
$597$		−	3.84002i		−	0.157162i
$598$	−22.9542			−0.938665
$599$	0.00928252			0.000379273			0.000189637	−	1.00000i	$-0.499940\pi$
$599$	0.00928252			0.000379273			0.000189637		1.00000i	$0.499940\pi$
$600$	3.87353	+	5.58650i	0.158136	+	0.228068i
$601$	−10.6234			−0.433338			−0.216669	−	0.976245i	$-0.569519\pi$
$601$	−10.6234			−0.433338			−0.216669	+	0.976245i	$0.569519\pi$
$602$	−25.0392	−	12.5137i	−1.02052	−	0.510022i
$603$		−	13.7748i		−	0.560953i
$604$			0.788245i			0.0320732i
$605$	−22.0986	−	10.8005i	−0.898438	−	0.439101i
$606$	−0.387249			−0.0157309
$607$			17.7479i			0.720366i	0.932882	+	0.360183i	$0.117286\pi$
$607$			17.7479i			0.720366i	−0.932882	+	0.360183i	$0.882714\pi$
$608$	63.5329			2.57660
$609$	−3.29768	+	6.59847i	−0.133629	+	0.267384i
$610$	16.1507	−	30.8518i	0.653923	−	1.24915i
$611$			7.99888i			0.323600i
$612$			11.9438i			0.482801i
$613$	3.80169			0.153549			0.0767745	−	0.997048i	$-0.475538\pi$
$613$	3.80169			0.153549			0.0767745	+	0.997048i	$0.475538\pi$
$614$		−	31.6193i		−	1.27605i
$615$	2.94128	−	5.61857i	0.118604	−	0.226562i
$616$	11.2642	−	3.93108i	0.453849	−	0.158388i
$617$		−	20.7212i		−	0.834206i	−0.908859	−	0.417103i	$-0.863046\pi$
$617$		−	20.7212i		−	0.834206i	0.908859	−	0.417103i	$-0.136954\pi$
$618$	28.3424			1.14010
$619$			23.8793i			0.959791i	0.877326	+	0.479896i	$0.159325\pi$
$619$			23.8793i			0.959791i	−0.877326	+	0.479896i	$0.840675\pi$
$620$	−43.3107	−	22.6729i	−1.73940	−	0.910565i
$621$			3.73805i			0.150003i
$622$		−	59.3862i		−	2.38117i
$623$	16.4728	−	32.9610i	0.659968	−	1.32056i
$624$			6.66928i			0.266985i
$625$	−8.76627	+	23.4127i	−0.350651	+	0.936506i
$626$	−33.9270			−1.35599
$627$	18.9586	−	19.4905i	0.757132	−	0.778375i
$628$	−4.61923			−0.184328
$629$	11.5569			0.460805
$630$	10.3249	−	7.45036i	0.411353	−	0.296829i
$631$	11.1610			0.444314			0.222157	−	0.975011i	$-0.428690\pi$
$631$	11.1610			0.444314			0.222157	+	0.975011i	$0.428690\pi$
$632$		−	13.2159i		−	0.525700i
$633$			15.7083i			0.624348i
$634$		−	56.3878i		−	2.23944i
$635$	3.17123	−	6.05782i	0.125846	−	0.240397i
$636$			9.64116i			0.382297i
$637$	15.9738	−	11.9898i	0.632906	−	0.475052i
$638$	14.2655	+	13.8762i	0.564777	+	0.549364i
$639$	−5.37459			−0.212615
$640$	10.7172	−	20.4725i	0.423635	−	0.809246i
$641$	−45.0426			−1.77907			−0.889537	−	0.456862i	$-0.848973\pi$
$641$	−45.0426			−1.77907			−0.889537	+	0.456862i	$0.848973\pi$
$642$	−40.9096			−1.61457
$643$	−6.14189			−0.242213			−0.121106	−	0.992640i	$-0.538644\pi$
$643$	−6.14189			−0.242213			−0.121106	+	0.992640i	$0.538644\pi$
$644$	11.6356	−	23.2822i	0.458508	−	0.917447i
$645$	−5.09822	+	9.73882i	−0.200742	+	0.383466i
$646$		−	80.0734i		−	3.15045i
$647$	−15.8669			−0.623792			−0.311896	−	0.950116i	$-0.600964\pi$
$647$	−15.8669			−0.623792			−0.311896	+	0.950116i	$0.600964\pi$
$648$	−1.35961			−0.0534104
$649$	4.81992	+	4.68837i	0.189198	+	0.184035i
$650$	25.2315	−	17.4948i	0.989659	−	0.686204i
$651$	−9.82562	+	19.6605i	−0.385096	+	0.770555i
$652$			29.9543i			1.17310i
$653$		−	38.4273i		−	1.50378i	−0.659290	−	0.751889i	$-0.729143\pi$
$653$		−	38.4273i		−	1.50378i	0.659290	−	0.751889i	$-0.270857\pi$
$654$			43.4359i			1.69848i
$655$	−10.6823	+	20.4058i	−0.417393	+	0.797322i
$656$	−6.62931			−0.258831
$657$		−	6.09921i		−	0.237953i
$658$	−14.2788	−	7.13606i	−0.556647	−	0.278192i
$659$			8.08533i			0.314960i	0.987522	+	0.157480i	$0.0503370\pi$
$659$			8.08533i			0.314960i	−0.987522	+	0.157480i	$0.949663\pi$
$660$	−6.08333	−	18.5453i	−0.236793	−	0.721874i
$661$		−	44.4153i		−	1.72756i	−0.503873	−	0.863778i	$-0.668092\pi$
$661$		−	44.4153i		−	1.72756i	0.503873	−	0.863778i	$-0.331908\pi$
$662$	8.20973			0.319080
$663$	12.9492			0.502907
$664$			2.67621i			0.103857i
$665$	−39.3304	+	28.3805i	−1.52517	+	1.10055i
$666$			5.48043i			0.212362i
$667$	10.4221			0.403544
$668$		−	14.3036i		−	0.553422i
$669$	14.7511			0.570312
$670$	58.7286	+	30.7441i	2.26888	+	1.18775i
$671$	−16.7342	+	17.2037i	−0.646016	+	0.664142i
$672$	−18.3408	−	9.16609i	−0.707512	−	0.353590i
$673$	−5.55501			−0.214130			−0.107065	−	0.994252i	$-0.534145\pi$
$673$	−5.55501			−0.214130			−0.107065	+	0.994252i	$0.534145\pi$
$674$	−23.7419			−0.914502
$675$	−2.84901	−	4.10891i	−0.109658	−	0.158152i
$676$	12.7872			0.491814
$677$			44.9868i			1.72898i	0.502649	+	0.864491i	$0.332359\pi$
$677$			44.9868i			1.72898i	−0.502649	+	0.864491i	$0.667641\pi$
$678$			25.7694i			0.989668i
$679$	−13.5950	−	6.79429i	−0.521727	−	0.260741i
$680$	−12.2238	−	6.39908i	−0.468761	−	0.245394i
$681$			16.6800i			0.639177i
$682$	42.5049	+	41.3448i	1.62760	+	1.58317i
$683$			16.7196i			0.639758i	0.947458	+	0.319879i	$0.103642\pi$
$683$			16.7196i			0.639758i	−0.947458	+	0.319879i	$0.896358\pi$
$684$	21.5754			0.824957
$685$	−38.0291	−	19.9080i	−1.45302	−	0.760647i
$686$	7.15219	+	39.2114i	0.273072	+	1.49710i
$687$			11.6865i			0.445866i
$688$	11.4908			0.438082
$689$	10.4527			0.398217
$690$	−15.9371	−	8.34299i	−0.606716	−	0.317612i
$691$		−	30.6543i		−	1.16615i	−0.812420	−	0.583073i	$-0.801850\pi$
$691$		−	30.6543i		−	1.16615i	0.812420	−	0.583073i	$-0.198150\pi$
$692$		−	35.9072i		−	1.36499i
$693$	−8.28494	+	2.89134i	−0.314719	+	0.109833i
$694$	10.5098			0.398946
$695$	−16.2499	+	31.0413i	−0.616394	+	1.17746i
$696$			3.79072i			0.143687i
$697$			12.8716i			0.487548i
$698$	45.6674			1.72854
$699$	19.5846			0.740758
$700$	4.95485	+	34.4603i	0.187276	+	1.30248i
$701$		−	36.7998i		−	1.38991i	−0.719054	−	0.694954i	$-0.755425\pi$
$701$		−	36.7998i		−	1.38991i	0.719054	−	0.694954i	$-0.244575\pi$
$702$			6.14067i			0.231765i
$703$		−	20.8765i		−	0.787373i
$704$	−27.7589	+	28.5377i	−1.04620	+	1.07556i
$705$	−2.90730	+	5.55364i	−0.109495	+	0.209162i
$706$	65.0541			2.44834
$707$	−0.425847	−	0.212823i	−0.0160156	−	0.00800404i
$708$			5.33552i			0.200521i
$709$	50.9309			1.91275			0.956375	−	0.292142i	$-0.0943679\pi$
$709$	50.9309			1.91275			0.956375	+	0.292142i	$0.0943679\pi$
$710$	11.9956	−	22.9145i	0.450186	−	0.859965i
$711$			9.72038i			0.364543i
$712$		−	18.9356i		−	0.709641i
$713$	31.0531			1.16295
$714$	−11.5524	+	23.1157i	−0.432339	+	0.865084i
$715$	−20.1064	+	6.59541i	−0.751935	+	0.246654i
$716$	50.5362			1.88863
$717$			22.9246i			0.856134i
$718$		−	43.4013i		−	1.61972i
$719$			7.61059i			0.283827i	0.989879	+	0.141914i	$0.0453255\pi$
$719$			7.61059i			0.283827i	−0.989879	+	0.141914i	$0.954674\pi$
$720$	−2.42404	+	4.63050i	−0.0903386	+	0.172569i
$721$	31.1674	+	15.5764i	1.16073	+	0.580094i
$722$	−103.754			−3.86133
$723$	0.858653			0.0319336
$724$			8.45900i			0.314376i
$725$	−11.4561	+	7.94333i	−0.425467	+	0.295008i
$726$	0.654911	+	23.6646i	0.0243060	+	0.878275i
$727$	43.0012			1.59483			0.797413	−	0.603433i	$-0.206201\pi$
$727$	43.0012			1.59483			0.797413	+	0.603433i	$0.206201\pi$
$728$	4.58836	−	9.18103i	0.170056	−	0.340272i
$729$	1.00000			0.0370370
$730$	26.0039	+	13.6129i	0.962447	+	0.503835i
$731$		−	22.3108i		−	0.825194i
$732$	−19.0440			−0.703888
$733$			38.6181i			1.42639i	0.700965	+	0.713196i	$0.252753\pi$
$733$			38.6181i			1.42639i	−0.700965	+	0.713196i	$0.747247\pi$
$734$	−55.6393			−2.05368
$735$	15.4485	−	2.51862i	0.569827	−	0.0929008i
$736$			28.9687i			1.06780i
$737$	−32.7485	−	31.8548i	−1.20631	−	1.17339i
$738$	−6.10387			−0.224687
$739$		−	46.0178i		−	1.69279i	−0.532553	−	0.846397i	$-0.678767\pi$
$739$		−	46.0178i		−	1.69279i	0.532553	−	0.846397i	$-0.321233\pi$
$740$	−13.2763	−	6.95008i	−0.488048	−	0.255490i
$741$		−	23.3916i		−	0.859311i
$742$	−9.32521	+	18.6592i	−0.342339	+	0.685001i
$743$	−9.77595			−0.358645			−0.179322	−	0.983790i	$-0.557391\pi$
$743$	−9.77595			−0.358645			−0.179322	+	0.983790i	$0.557391\pi$
$744$			11.2946i			0.414082i
$745$	−9.67405	−	5.06431i	−0.354430	−	0.185542i
$746$	−1.13362			−0.0415049
$747$		−	1.96837i		−	0.0720191i
$748$	28.3956	+	27.6206i	1.03825	+	1.00991i
$749$	−44.9871	−	22.4830i	−1.64379	−	0.821510i
$750$	23.8770	−	2.97600i	0.871865	−	0.108668i
$751$	−0.131035			−0.00478154			−0.00239077	−	0.999997i	$-0.500761\pi$
$751$	−0.131035			−0.00478154			−0.00239077	+	0.999997i	$0.500761\pi$
$752$	6.55271			0.238953
$753$			16.2067i			0.590604i
$754$	17.1208			0.623503
$755$	0.593349	+	0.310614i	0.0215942	+	0.0113044i
$756$	−6.22843	−	3.11275i	−0.226526	−	0.113210i
$757$		−	27.1027i		−	0.985065i	−0.870294	−	0.492533i	$-0.836071\pi$
$757$		−	27.1027i		−	0.985065i	0.870294	−	0.492533i	$-0.163929\pi$
$758$	12.1827			0.442497
$759$	8.88694	+	8.64440i	0.322576	+	0.313772i
$760$	−11.5593	+	22.0811i	−0.419301	+	0.800966i
$761$	−14.4283			−0.523025			−0.261512	−	0.965200i	$-0.584221\pi$
$761$	−14.4283			−0.523025			−0.261512	+	0.965200i	$0.584221\pi$
$762$	−6.58106			−0.238407
$763$	−23.8713	+	47.7651i	−0.864201	+	1.72921i
$764$	−12.2596			−0.443537
$765$	8.99069	+	4.70657i	0.325059	+	0.170166i
$766$	−28.7188			−1.03765
$767$	5.78464			0.208871
$768$	1.76644			0.0637410
$769$	47.3642			1.70800			0.853999	−	0.520275i	$-0.174171\pi$
$769$	47.3642			1.70800			0.853999	+	0.520275i	$0.174171\pi$
$770$	6.16404	−	41.7759i	0.222137	−	1.50550i
$771$	12.6011			0.453819
$772$	8.36605			0.301101
$773$	26.2480			0.944075			0.472038	−	0.881578i	$-0.343519\pi$
$773$	26.2480			0.944075			0.472038	+	0.881578i	$0.343519\pi$
$774$	10.5800			0.380291
$775$	−34.1339	+	23.6676i	−1.22613	+	0.850164i
$776$	−7.81009			−0.280366
$777$	−3.01192	+	6.02667i	−0.108052	+	0.216205i
$778$	−79.6924			−2.85711
$779$	23.2514			0.833067
$780$	−14.8758	−	7.78738i	−0.532638	−	0.278833i
$781$	−12.4290	+	12.7777i	−0.444743	+	0.457221i
$782$	36.5105			1.30561
$783$		−	2.78810i		−	0.0996386i
$784$	−9.82206	−	13.0858i	−0.350788	−	0.467351i
$785$	−1.82025	+	3.47711i	−0.0649674	+	0.124104i
$786$	22.1684			0.790721
$787$		−	17.3536i		−	0.618591i	−0.950966	−	0.309295i	$-0.899907\pi$
$787$		−	17.3536i		−	0.618591i	0.950966	−	0.309295i	$-0.100093\pi$
$788$	−8.60840			−0.306662
$789$	−2.96589			−0.105588
$790$	−41.4427	−	21.6950i	−1.47447	−	0.771874i
$791$	−14.1623	+	28.3378i	−0.503552	+	1.00758i
$792$	−3.14414	+	3.23236i	−0.111722	+	0.114857i
$793$			20.6471i			0.733200i
$794$	72.8039			2.58371
$795$	7.25735	+	3.79918i	0.257392	+	0.134743i
$796$		−	10.1059i		−	0.358196i
$797$	7.87005			0.278772			0.139386	−	0.990238i	$-0.455487\pi$
$797$	7.87005			0.278772			0.139386	+	0.990238i	$0.455487\pi$
$798$	41.7564	+	20.8684i	1.47816	+	0.738732i
$799$		−	12.7229i		−	0.450104i
$800$	−22.0789	−	31.8427i	−0.780607	−	1.12581i
$801$			13.9273i			0.492096i
$802$	77.5994			2.74013
$803$	−14.5004	−	14.1047i	−0.511709	−	0.497743i
$804$		−	36.2517i		−	1.27850i
$805$	−12.9405	−	17.9332i	−0.456092	−	0.632063i
$806$	51.0123			1.79683
$807$		−	18.9620i		−	0.667495i
$808$	−0.244642			−0.00860648
$809$		−	26.0847i		−	0.917089i	−0.888671	−	0.458544i	$-0.848371\pi$
$809$		−	26.0847i		−	0.917089i	0.888671	−	0.458544i	$-0.151629\pi$
$810$	−2.23191	+	4.26348i	−0.0784213	+	0.149804i
$811$	36.1842			1.27060			0.635300	−	0.772265i	$-0.280876\pi$
$811$	36.1842			1.27060			0.635300	+	0.772265i	$0.280876\pi$
$812$	−8.67866	+	17.3655i	−0.304561	+	0.609409i
$813$	12.0999			0.424362
$814$	13.0293	+	12.6737i	0.456677	+	0.444214i
$815$	22.5480	+	11.8038i	0.789823	+	0.413468i
$816$		−	10.6081i		−	0.371356i
$817$	−40.3023			−1.41000
$818$	8.77779			0.306908
$819$	−3.37477	+	6.75272i	−0.117924	+	0.235959i
$820$	7.74071	−	14.7866i	0.270317	−	0.516371i
$821$			1.85357i			0.0646899i	0.999477	+	0.0323450i	$0.0102975\pi$
$821$			1.85357i			0.0646899i	−0.999477	+	0.0323450i	$0.989702\pi$
$822$			41.3139i			1.44099i
$823$		−	7.49969i		−	0.261423i	−0.991420	−	0.130711i	$-0.958274\pi$
$823$		−	7.49969i		−	0.261423i	0.991420	−	0.130711i	$-0.0417261\pi$
$824$	17.9052			0.623756
$825$	−16.3571	−	2.72871i	−0.569481	−	0.0950015i
$826$	−5.16067	+	10.3262i	−0.179563	+	0.359294i
$827$	21.7867			0.757599			0.378799	−	0.925479i	$-0.376337\pi$
$827$	21.7867			0.757599			0.378799	+	0.925479i	$0.376337\pi$
$828$			9.83759i			0.341880i
$829$		−	11.8722i		−	0.412337i	−0.978516	−	0.206169i	$-0.933900\pi$
$829$		−	11.8722i		−	0.412337i	0.978516	−	0.206169i	$-0.0660996\pi$
$830$	8.39213	+	4.39323i	0.291295	+	0.152491i
$831$	−29.0875			−1.00903
$832$			34.2496i			1.18739i
$833$	−25.4077	+	19.0707i	−0.880326	+	0.660762i
$834$	33.7225			1.16771
$835$	−10.7670	−	5.63645i	−0.372607	−	0.195057i
$836$	49.8940	−	51.2939i	1.72562	−	1.77404i
$837$		−	8.30729i		−	0.287142i
$838$		−	13.5532i		−	0.468186i
$839$			48.1605i			1.66269i	0.555760	+	0.831343i	$0.312427\pi$
$839$			48.1605i			1.66269i	−0.555760	+	0.831343i	$0.687573\pi$
$840$	6.52268	−	4.70672i	0.225054	−	0.162397i
$841$	21.2265			0.731948
$842$	−27.5976			−0.951076
$843$		−	21.2889i		−	0.733229i
$844$			41.3401i			1.42299i
$845$	5.03889	−	9.62550i	0.173343	−	0.331127i
$846$	6.03334			0.207430
$847$	−12.2853	+	26.3832i	−0.422128	+	0.906536i
$848$		−	8.56291i		−	0.294052i
$849$			3.54750i			0.121750i
$850$	−40.1328	+	27.8270i	−1.37654	+	0.954459i
$851$	9.51892			0.326304
$852$	−14.1445			−0.484584
$853$			35.1012i			1.20184i	0.799309	+	0.600921i	$0.205199\pi$
$853$			35.1012i			1.20184i	−0.799309	+	0.600921i	$0.794801\pi$
$854$	−36.8572	−	18.4199i	−1.26123	−	0.630318i
$855$	8.50197	−	16.2408i	0.290761	−	0.555424i
$856$	−25.8444			−0.883343
$857$		−	20.1174i		−	0.687198i	−0.939117	−	0.343599i	$-0.888354\pi$
$857$		−	20.1174i		−	0.687198i	0.939117	−	0.343599i	$-0.111646\pi$
$858$	14.5990	+	14.2006i	0.498401	+	0.484799i
$859$			39.1281i			1.33503i	0.744595	+	0.667517i	$0.232643\pi$
$859$			39.1281i			1.33503i	−0.744595	+	0.667517i	$0.767357\pi$
$860$	−13.4172	+	25.6301i	−0.457523	+	0.873979i
$861$	−6.71225	−	3.35455i	−0.228753	−	0.114323i
$862$			72.4831i			2.46878i
$863$			42.7624i			1.45565i	0.685763	+	0.727825i	$0.259469\pi$
$863$			42.7624i			1.45565i	−0.685763	+	0.727825i	$0.740531\pi$
$864$	7.74967			0.263649
$865$	−27.0290	−	14.1495i	−0.919014	−	0.481098i
$866$	−48.6085			−1.65178
$867$	−3.59686			−0.122156
$868$	−25.8585	+	51.7413i	−0.877695	+	1.75622i
$869$	23.1095	+	22.4788i	0.783936	+	0.762541i
$870$	11.8870	+	6.22279i	0.403008	+	0.210972i
$871$	−39.3033			−1.33174
$872$			27.4403i			0.929247i
$873$	5.74438			0.194418
$874$		−	65.9528i		−	2.23089i
$875$	27.8924	+	9.84962i	0.942935	+	0.332978i
$876$		−	16.0516i		−	0.542332i
$877$	−5.73388			−0.193619			−0.0968097	−	0.995303i	$-0.530864\pi$
$877$	−5.73388			−0.193619			−0.0968097	+	0.995303i	$0.530864\pi$
$878$	−24.9920			−0.843441
$879$			21.7486i			0.733562i
$880$	5.40298	+	16.4712i	0.182134	+	0.555244i
$881$		−	7.96067i		−	0.268202i	−0.990968	−	0.134101i	$-0.957185\pi$
$881$		−	7.96067i		−	0.268202i	0.990968	−	0.134101i	$-0.0428146\pi$
$882$	−9.04355	−	12.0486i	−0.304512	−	0.405699i
$883$		−	48.6442i		−	1.63701i	−0.574501	−	0.818504i	$-0.694804\pi$
$883$		−	48.6442i		−	1.63701i	0.574501	−	0.818504i	$-0.305196\pi$
$884$	34.0791			1.14620
$885$	4.01629	+	2.10250i	0.135006	+	0.0706749i
$886$		−	6.03329i		−	0.202692i
$887$		−	2.79811i		−	0.0939513i	−0.998896	−	0.0469756i	$-0.985042\pi$
$887$		−	2.79811i		−	0.0939513i	0.998896	−	0.0469756i	$-0.0149583\pi$
$888$			3.46223i			0.116185i
$889$	−7.23700	−	3.61680i	−0.242721	−	0.121304i
$890$	−59.3787	−	31.0844i	−1.99038	−	1.04195i
$891$	2.31254	−	2.37743i	0.0774730	−	0.0796468i
$892$	38.8212			1.29983
$893$	−22.9827			−0.769087
$894$			10.5096i			0.351495i
$895$	19.9142	−	38.0409i	0.665658	−	1.27157i
$896$	−24.4575	−	12.2230i	−0.817069	−	0.408343i
$897$	10.6657			0.356117
$898$	−38.2862			−1.27763
$899$	−23.1616			−0.772481
$900$	−7.49787	−	10.8136i	−0.249929	−	0.360453i
$901$	−16.6259			−0.553891
$902$	−14.1154	+	14.5115i	−0.469993	+	0.483180i
$903$	11.6345	+	5.81453i	0.387173	+	0.193496i
$904$			16.2796i			0.541453i
$905$	6.36749	+	3.33334i	0.211662	+	0.110804i
$906$		−	0.644599i		−	0.0214154i
$907$			7.24461i			0.240553i	0.992740	+	0.120277i	$0.0383782\pi$
$907$			7.24461i			0.240553i	−0.992740	+	0.120277i	$0.961622\pi$
$908$			43.8974i			1.45679i
$909$	0.179936			0.00596810
$910$	−21.2579	−	29.4597i	−0.704693	−	0.976580i
$911$	−52.3144			−1.73325			−0.866626	−	0.498958i	$-0.833716\pi$
$911$	−52.3144			−1.73325			−0.866626	+	0.498958i	$0.833716\pi$
$912$	−19.1625			−0.634532
$913$	−4.67966	−	4.55195i	−0.154874	−	0.150647i
$914$	−1.82678			−0.0604244
$915$	−7.50446	+	14.3353i	−0.248090	+	0.473912i
$916$			30.7557i			1.01620i
$917$	24.3779	+	12.1832i	0.805030	+	0.402326i
$918$		−	9.76726i		−	0.322368i
$919$			9.95202i			0.328287i	0.986436	+	0.164143i	$0.0524860\pi$
$919$			9.95202i			0.328287i	−0.986436	+	0.164143i	$0.947514\pi$
$920$	−10.0682	−	5.27063i	−0.331938	−	0.173768i
$921$			14.6920i			0.484117i
$922$	−48.8480			−1.60872
$923$			15.3352i			0.504764i
$924$	−21.8038	+	7.60926i	−0.717293	+	0.250326i
$925$	−10.4633	+	7.25498i	−0.344031	+	0.238542i
$926$			63.8008i			2.09662i
$927$	−13.1694			−0.432539
$928$		−	21.6069i		−	0.709280i
$929$		−	34.0693i		−	1.11778i	−0.829243	−	0.558889i	$-0.811228\pi$
$929$		−	34.0693i		−	1.11778i	0.829243	−	0.558889i	$-0.188772\pi$
$930$	35.4180	+	18.5411i	1.16140	+	0.607987i
$931$	34.4495	+	45.8967i	1.12904	+	1.50420i
$932$	51.5417			1.68830
$933$			27.5939i			0.903384i
$934$	19.3670			0.633706
$935$	31.9809	−	10.4906i	1.04589	−	0.343078i
$936$			3.87933i			0.126800i
$937$		−	33.3688i		−	1.09011i	−0.838400	−	0.545055i	$-0.816509\pi$
$937$		−	33.3688i		−	1.09011i	0.838400	−	0.545055i	$-0.183491\pi$
$938$	35.0637	−	70.1604i	1.14487	−	2.29082i
$939$	15.7642			0.514446
$940$	−7.65126	+	14.6158i	−0.249557	+	0.476714i
$941$	−51.8151			−1.68912			−0.844562	−	0.535457i	$-0.820139\pi$
$941$	−51.8151			−1.68912			−0.844562	+	0.535457i	$0.820139\pi$
$942$	3.77745			0.123076
$943$			10.6018i			0.345241i
$944$		−	4.73880i		−	0.154235i
$945$	−4.79748	+	3.46182i	−0.156062	+	0.112613i
$946$	24.4667	−	25.1532i	0.795482	−	0.817801i
$947$			30.7207i			0.998290i	0.866518	+	0.499145i	$0.166353\pi$
$947$			30.7207i			0.998290i	−0.866518	+	0.499145i	$0.833647\pi$
$948$			25.5816i			0.830850i
$949$	−17.4027			−0.564917
$950$	50.2669	+	72.4961i	1.63087	+	2.35208i
$951$			26.2007i			0.849616i
$952$	−7.29817	+	14.6032i	−0.236535	+	0.473293i
$953$	46.9921			1.52222			0.761112	−	0.648620i	$-0.224654\pi$
$953$	46.9921			1.52222			0.761112	+	0.648620i	$0.224654\pi$
$954$		−	7.88421i		−	0.255261i
$955$	−4.83100	+	9.22837i	−0.156327	+	0.298623i
$956$			60.3316i			1.95126i
$957$	−6.62850	−	6.44760i	−0.214269	−	0.208421i
$958$	−67.3861			−2.17715
$959$	−22.7052	+	45.4317i	−0.733188	+	1.46707i
$960$	−12.4485	+	23.7796i	−0.401773	+	0.767484i
$961$	−38.0111			−1.22616
$962$	15.6372			0.504163
$963$	19.0087			0.612548
$964$	2.25975			0.0727818
$965$	3.29671	−	6.29752i	0.106125	−	0.202724i
$966$	−9.51521	+	19.0394i	−0.306147	+	0.612582i
$967$	5.03993			0.162073			0.0810367	−	0.996711i	$-0.474177\pi$
$967$	5.03993			0.162073			0.0810367	+	0.996711i	$0.474177\pi$
$968$	0.413736	+	14.9499i	0.0132980	+	0.480509i
$969$			37.2063i			1.19524i
$970$	−12.8209	+	24.4911i	−0.411655	+	0.786361i
$971$		−	11.1250i		−	0.357019i	−0.983938	−	0.178510i	$-0.942872\pi$
$971$		−	11.1250i		−	0.357019i	0.983938	−	0.178510i	$-0.0571276\pi$
$972$	2.63174			0.0844132
$973$	37.0836	+	18.5331i	1.18885	+	0.594143i
$974$			3.95842i			0.126836i
$975$	−11.7238	+	8.12901i	−0.375464	+	0.260337i
$976$	16.9142			0.541410
$977$			27.7532i			0.887904i	0.896050	+	0.443952i	$0.146424\pi$
$977$			27.7532i			0.887904i	−0.896050	+	0.443952i	$0.853576\pi$
$978$		−	24.4956i		−	0.783284i
$979$	33.1110	+	32.2074i	1.05823	+	1.02935i
$980$	40.6565	−	6.62837i	1.29872	−	0.211735i
$981$		−	20.1826i		−	0.644380i
$982$		−	7.46074i		−	0.238082i
$983$	17.6122			0.561743			0.280872	−	0.959745i	$-0.409376\pi$
$983$	17.6122			0.561743			0.280872	+	0.959745i	$0.409376\pi$
$984$	−3.85608			−0.122927
$985$	−3.39221	+	6.47995i	−0.108085	+	0.206468i
$986$	−27.2321			−0.867247
$987$	6.63468	+	3.31578i	0.211184	+	0.105543i
$988$		−	61.5606i		−	1.95850i
$989$		−	18.3764i		−	0.584334i
$990$	4.97474	+	15.1657i	0.158108	+	0.481997i
$991$	−23.4138			−0.743765			−0.371882	−	0.928280i	$-0.621288\pi$
$991$	−23.4138			−0.743765			−0.371882	+	0.928280i	$0.621288\pi$
$992$		−	64.3788i		−	2.04403i
$993$	−3.81467			−0.121055
$994$	−27.3749	−	13.6810i	−0.868279	−	0.433935i
$995$	−7.60722	−	3.98233i	−0.241165	−	0.126248i
$996$		−	5.18026i		−	0.164143i
$997$			5.64428i			0.178756i	0.995998	+	0.0893781i	$0.0284879\pi$
$997$			5.64428i			0.178756i	−0.995998	+	0.0893781i	$0.971512\pi$
$998$	72.7599			2.30318
$999$		−	2.54649i		−	0.0805674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.7	yes	48
5.4	even	2		1155.2.k.a.769.42	yes	48
7.6	odd	2		1155.2.k.a.769.8	yes	48
11.10	odd	2	inner	1155.2.k.b.769.42	yes	48
35.34	odd	2	inner	1155.2.k.b.769.41	yes	48
55.54	odd	2		1155.2.k.a.769.7	✓	48
77.76	even	2		1155.2.k.a.769.41	yes	48
385.384	even	2	inner	1155.2.k.b.769.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.7	✓	48	55.54	odd	2
1155.2.k.a.769.8	yes	48	7.6	odd	2
1155.2.k.a.769.41	yes	48	77.76	even	2
1155.2.k.a.769.42	yes	48	5.4	even	2
1155.2.k.b.769.7	yes	48	1.1	even	1	trivial
1155.2.k.b.769.8	yes	48	385.384	even	2	inner
1155.2.k.b.769.41	yes	48	35.34	odd	2	inner
1155.2.k.b.769.42	yes	48	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.15215 q^{2} +1.00000 q^{3} +2.63174 q^{4} +(1.03706 - 1.98104i) q^{5} -2.15215 q^{6} +(-2.36665 - 1.18277i) q^{7} -1.35961 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15215 q^{2} +1.00000 q^{3} +2.63174 q^{4} +(1.03706 - 1.98104i) q^{5} -2.15215 q^{6} +(-2.36665 - 1.18277i) q^{7} -1.35961 q^{8} +1.00000 q^{9} +(-2.23191 + 4.26348i) q^{10} +(2.31254 - 2.37743i) q^{11} +2.63174 q^{12} -2.85328i q^{13} +(5.09339 + 2.54550i) q^{14} +(1.03706 - 1.98104i) q^{15} -2.33741 q^{16} +4.53838i q^{17} -2.15215 q^{18} +8.19815 q^{19} +(2.72928 - 5.21358i) q^{20} +(-2.36665 - 1.18277i) q^{21} +(-4.97693 + 5.11657i) q^{22} +3.73805i q^{23} -1.35961 q^{24} +(-2.84901 - 4.10891i) q^{25} +6.14067i q^{26} +1.00000 q^{27} +(-6.22843 - 3.11275i) q^{28} -2.78810i q^{29} +(-2.23191 + 4.26348i) q^{30} -8.30729i q^{31} +7.74967 q^{32} +(2.31254 - 2.37743i) q^{33} -9.76726i q^{34} +(-4.79748 + 3.46182i) q^{35} +2.63174 q^{36} -2.54649i q^{37} -17.6436 q^{38} -2.85328i q^{39} +(-1.40999 + 2.69343i) q^{40} +2.83617 q^{41} +(5.09339 + 2.54550i) q^{42} -4.91602 q^{43} +(6.08602 - 6.25677i) q^{44} +(1.03706 - 1.98104i) q^{45} -8.04484i q^{46} -2.80340 q^{47} -2.33741 q^{48} +(4.20211 + 5.59842i) q^{49} +(6.13149 + 8.84298i) q^{50} +4.53838i q^{51} -7.50909i q^{52} +3.66341i q^{53} -2.15215 q^{54} +(-2.31152 - 7.04676i) q^{55} +(3.21772 + 1.60810i) q^{56} +8.19815 q^{57} +6.00041i q^{58} +2.02737i q^{59} +(2.72928 - 5.21358i) q^{60} -7.23628 q^{61} +17.8785i q^{62} +(-2.36665 - 1.18277i) q^{63} -12.0036 q^{64} +(-5.65244 - 2.95902i) q^{65} +(-4.97693 + 5.11657i) q^{66} -13.7748i q^{67} +11.9438i q^{68} +3.73805i q^{69} +(10.3249 - 7.45036i) q^{70} -5.37459 q^{71} -1.35961 q^{72} -6.09921i q^{73} +5.48043i q^{74} +(-2.84901 - 4.10891i) q^{75} +21.5754 q^{76} +(-8.28494 + 2.89134i) q^{77} +6.14067i q^{78} +9.72038i q^{79} +(-2.42404 + 4.63050i) q^{80} +1.00000 q^{81} -6.10387 q^{82} -1.96837i q^{83} +(-6.22843 - 3.11275i) q^{84} +(8.99069 + 4.70657i) q^{85} +10.5800 q^{86} -2.78810i q^{87} +(-3.14414 + 3.23236i) q^{88} +13.9273i q^{89} +(-2.23191 + 4.26348i) q^{90} +(-3.37477 + 6.75272i) q^{91} +9.83759i q^{92} -8.30729i q^{93} +6.03334 q^{94} +(8.50197 - 16.2408i) q^{95} +7.74967 q^{96} +5.74438 q^{97} +(-9.04355 - 12.0486i) q^{98} +(2.31254 - 2.37743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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