LMFDB - Embedded newform 91.2.bc.a.76.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(6,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("91.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.bc (of order $12$, degree $4$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.7
Character	$\chi$	$=$	91.76
Dual form			91.2.bc.a.6.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.612835 - 2.28713i) q^{2} +(-1.04118 + 0.601128i) q^{3} +(-3.12335 - 1.80327i) q^{4} +(2.25527 - 2.25527i) q^{5} +(0.736784 + 2.74971i) q^{6} +(-2.60590 + 0.457468i) q^{7} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 + 1.34631i) q^{9} +O(q^{10})$	\(q+(0.612835 - 2.28713i) q^{2} +(-1.04118 + 0.601128i) q^{3} +(-3.12335 - 1.80327i) q^{4} +(2.25527 - 2.25527i) q^{5} +(0.736784 + 2.74971i) q^{6} +(-2.60590 + 0.457468i) q^{7} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 + 1.34631i) q^{9} +(-3.77599 - 6.54020i) q^{10} +(4.11159 + 1.10170i) q^{11} +4.33597 q^{12} +(3.48609 + 0.920440i) q^{13} +(-0.550697 + 6.24039i) q^{14} +(-0.992444 + 3.70385i) q^{15} +(0.897005 + 1.55366i) q^{16} +(0.721872 - 1.25032i) q^{17} +(2.60283 + 2.60283i) q^{18} +(0.649502 + 2.42397i) q^{19} +(-11.1108 + 2.97714i) q^{20} +(2.43823 - 2.04279i) q^{21} +(5.03945 - 8.72858i) q^{22} +(-4.52952 + 2.61512i) q^{23} +(1.18367 - 4.41750i) q^{24} -5.17247i q^{25} +(4.24156 - 7.40905i) q^{26} -5.47577i q^{27} +(8.96408 + 3.27030i) q^{28} +(1.34350 + 2.32701i) q^{29} +(7.86299 + 4.53970i) q^{30} +(-3.76457 + 3.76457i) q^{31} +(-3.24556 + 0.869646i) q^{32} +(-4.94318 + 1.32452i) q^{33} +(-2.41725 - 2.41725i) q^{34} +(-4.84529 + 6.90872i) q^{35} +(4.85550 - 2.80333i) q^{36} +(-0.599466 - 0.160626i) q^{37} +5.94198 q^{38} +(-4.18296 + 1.13724i) q^{39} +12.1325i q^{40} +(-5.04879 - 1.35282i) q^{41} +(-3.17789 - 6.82843i) q^{42} +(-5.46143 - 3.15316i) q^{43} +(-10.8553 - 10.8553i) q^{44} +(1.28329 + 4.78929i) q^{45} +(3.20527 + 11.9622i) q^{46} +(4.68009 + 4.68009i) q^{47} +(-1.86789 - 1.07843i) q^{48} +(6.58145 - 2.38424i) q^{49} +(-11.8301 - 3.16987i) q^{50} +1.73575i q^{51} +(-9.22846 - 9.16119i) q^{52} -7.58528 q^{53} +(-12.5238 - 3.35574i) q^{54} +(11.7574 - 6.78811i) q^{55} +(5.77888 - 8.23988i) q^{56} +(-2.13337 - 2.13337i) q^{57} +(6.14553 - 1.64669i) q^{58} +(-1.96185 + 0.525675i) q^{59} +(9.77878 - 9.77878i) q^{60} +(4.53851 + 2.62031i) q^{61} +(6.30300 + 10.9171i) q^{62} +(1.40965 - 3.86393i) q^{63} +11.5440i q^{64} +(9.93790 - 5.78622i) q^{65} +12.1174i q^{66} +(2.26854 - 8.46631i) q^{67} +(-4.50931 + 2.60345i) q^{68} +(3.14404 - 5.44564i) q^{69} +(12.8318 + 15.3157i) q^{70} +(8.31929 - 2.22915i) q^{71} +(-1.53055 - 5.71208i) q^{72} +(-11.1801 - 11.1801i) q^{73} +(-0.734747 + 1.27262i) q^{74} +(3.10932 + 5.38549i) q^{75} +(2.34245 - 8.74214i) q^{76} +(-11.2184 - 0.989991i) q^{77} +(0.0375447 + 10.2639i) q^{78} +2.01287 q^{79} +(5.52690 + 1.48093i) q^{80} +(0.959764 + 1.66236i) q^{81} +(-6.18815 + 10.7182i) q^{82} +(5.11623 - 5.11623i) q^{83} +(-11.2991 + 1.98357i) q^{84} +(-1.19179 - 4.44782i) q^{85} +(-10.5586 + 10.5586i) q^{86} +(-2.79766 - 1.61523i) q^{87} +(-14.0227 + 8.09604i) q^{88} +(-1.81184 + 6.76189i) q^{89} +11.7402 q^{90} +(-9.50547 - 0.803801i) q^{91} +18.8630 q^{92} +(1.65662 - 6.18260i) q^{93} +(13.5721 - 7.83586i) q^{94} +(6.93151 + 4.00191i) q^{95} +(2.85646 - 2.85646i) q^{96} +(1.62618 + 6.06897i) q^{97} +(-1.41972 - 16.5138i) q^{98} +(-4.67912 + 4.67912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9	$ 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99}+O(q^{100}) $ 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9 - 4 * q^11 - 32 * q^14 - 8 * q^15 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 4 * q^22 - 12 * q^23 + 24 * q^28 + 4 * q^29 + 12 * q^30 + 4 * q^32 - 20 * q^35 + 4 * q^37 - 36 * q^39 - 28 * q^42 - 48 * q^43 + 24 * q^44 + 84 * q^46 + 24 * q^49 - 44 * q^50 + 72 * q^53 + 60 * q^56 - 92 * q^57 - 16 * q^58 + 76 * q^60 + 48 * q^63 + 4 * q^65 - 56 * q^67 + 56 * q^70 + 84 * q^71 - 128 * q^72 - 24 * q^74 + 148 * q^78 - 80 * q^79 + 28 * q^81 - 64 * q^84 + 36 * q^85 - 48 * q^86 - 228 * q^88 - 48 * q^91 + 24 * q^92 + 108 * q^93 - 84 * q^95 - 32 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	0.612835	−	2.28713i	0.433340	−	1.61725i	−0.311669	−	0.950191i	$-0.600888\pi$
$2$	0.612835	−	2.28713i	0.433340	−	1.61725i	0.745009	−	0.667055i	$-0.232445\pi$
$3$	−1.04118	+	0.601128i	−0.601128	+	0.347061i	−0.769485	−	0.638665i	$-0.779487\pi$
$3$	−1.04118	+	0.601128i	−0.601128	+	0.347061i	0.168357	+	0.985726i	$0.446154\pi$
$4$	−3.12335	−	1.80327i	−1.56167	−	0.901633i
$5$	2.25527	−	2.25527i	1.00859	−	1.00859i	0.00862388	−	0.999963i	$-0.497255\pi$
$5$	2.25527	−	2.25527i	1.00859	−	1.00859i	0.999963	−	0.00862388i	$-0.00274510\pi$
$6$	0.736784	+	2.74971i	0.300791	+	1.12257i
$7$	−2.60590	+	0.457468i	−0.984938	+	0.172907i
$7$	−2.60590	+	0.457468i	−0.984938	+	0.172907i
$8$	−2.68981	+	2.68981i	−0.950991	+	0.950991i
$9$	−0.777291	+	1.34631i	−0.259097	+	0.448769i
$10$	−3.77599	−	6.54020i	−1.19407	−	2.06819i
$11$	4.11159	+	1.10170i	1.23969	+	0.332174i	0.818346	−	0.574726i	$-0.194891\pi$
$11$	4.11159	+	1.10170i	1.23969	+	0.332174i	0.421345	+	0.906900i	$0.361558\pi$
$12$	4.33597			1.25169
$13$	3.48609	+	0.920440i	0.966866	+	0.255284i
$13$	3.48609	+	0.920440i	0.966866	+	0.255284i
$14$	−0.550697	+	6.24039i	−0.147180	+	1.66781i
$15$	−0.992444	+	3.70385i	−0.256248	+	0.956331i
$16$	0.897005	+	1.55366i	0.224251	+	0.388414i
$17$	0.721872	−	1.25032i	0.175080	−	0.303247i	−0.765109	−	0.643901i	$-0.777315\pi$
$17$	0.721872	−	1.25032i	0.175080	−	0.303247i	0.940189	+	0.340654i	$0.110648\pi$
$18$	2.60283	+	2.60283i	0.613493	+	0.613493i
$19$	0.649502	+	2.42397i	0.149006	+	0.556098i	0.999544	+	0.0301847i	$0.00960954\pi$
$19$	0.649502	+	2.42397i	0.149006	+	0.556098i	−0.850538	+	0.525913i	$0.823724\pi$
$20$	−11.1108	+	2.97714i	−2.48446	+	0.665709i
$21$	2.43823	−	2.04279i	0.532064	−	0.445773i
$22$	5.03945	−	8.72858i	1.07441	−	1.86094i
$23$	−4.52952	+	2.61512i	−0.944470	+	0.545290i	−0.891359	−	0.453299i	$-0.850247\pi$
$23$	−4.52952	+	2.61512i	−0.944470	+	0.545290i	−0.0531111	+	0.998589i	$0.516914\pi$
$24$	1.18367	−	4.41750i	0.241615	−	0.901719i
$25$		−	5.17247i		−	1.03449i
$26$	4.24156	−	7.40905i	0.831838	−	1.45304i
$27$		−	5.47577i		−	1.05381i
$28$	8.96408	+	3.27030i	1.69405	+	0.618029i
$29$	1.34350	+	2.32701i	0.249482	+	0.432116i	0.963382	−	0.268132i	$-0.0864063\pi$
$29$	1.34350	+	2.32701i	0.249482	+	0.432116i	−0.713900	+	0.700248i	$0.753073\pi$
$30$	7.86299	+	4.53970i	1.43558	+	0.828832i
$31$	−3.76457	+	3.76457i	−0.676137	+	0.676137i	−0.959124	−	0.282987i	$-0.908675\pi$
$31$	−3.76457	+	3.76457i	−0.676137	+	0.676137i	0.282987	+	0.959124i	$0.408675\pi$
$32$	−3.24556	+	0.869646i	−0.573740	+	0.153733i
$33$	−4.94318	+	1.32452i	−0.860497	+	0.230570i
$34$	−2.41725	−	2.41725i	−0.414555	−	0.414555i
$35$	−4.84529	+	6.90872i	−0.819004	+	1.16779i
$36$	4.85550	−	2.80333i	0.809250	−	0.467221i
$37$	−0.599466	−	0.160626i	−0.0985516	−	0.0264068i	0.209206	−	0.977872i	$-0.432912\pi$
$37$	−0.599466	−	0.160626i	−0.0985516	−	0.0264068i	−0.307758	+	0.951465i	$0.599579\pi$
$38$	5.94198			0.963916
$39$	−4.18296	+	1.13724i	−0.669809	+	0.182103i
$40$			12.1325i			1.91831i
$41$	−5.04879	−	1.35282i	−0.788488	−	0.211275i	−0.157965	−	0.987445i	$-0.550493\pi$
$41$	−5.04879	−	1.35282i	−0.788488	−	0.211275i	−0.630524	+	0.776170i	$0.717160\pi$
$42$	−3.17789	−	6.82843i	−0.490360	−	1.05365i
$43$	−5.46143	−	3.15316i	−0.832860	−	0.480852i	0.0219711	−	0.999759i	$-0.493006\pi$
$43$	−5.46143	−	3.15316i	−0.832860	−	0.480852i	−0.854831	+	0.518907i	$0.826339\pi$
$44$	−10.8553	−	10.8553i	−1.63649	−	1.63649i
$45$	1.28329	+	4.78929i	0.191301	+	0.713944i
$46$	3.20527	+	11.9622i	0.472591	+	1.76374i
$47$	4.68009	+	4.68009i	0.682662	+	0.682662i	0.960599	−	0.277937i	$-0.0896508\pi$
$47$	4.68009	+	4.68009i	0.682662	+	0.682662i	−0.277937	+	0.960599i	$0.589651\pi$
$48$	−1.86789	−	1.07843i	−0.269607	−	0.155658i
$49$	6.58145	−	2.38424i	0.940206	−	0.340605i
$50$	−11.8301	−	3.16987i	−1.67303	−	0.448287i
$51$			1.73575i			0.243053i
$52$	−9.22846	−	9.16119i	−1.27976	−	1.27043i
$53$	−7.58528			−1.04192			−0.520959	−	0.853582i	$-0.674426\pi$
$53$	−7.58528			−1.04192			−0.520959	+	0.853582i	$0.674426\pi$
$54$	−12.5238	−	3.35574i	−1.70427	−	0.456659i
$55$	11.7574	−	6.78811i	1.58536	−	0.915309i
$56$	5.77888	−	8.23988i	0.772235	−	1.10110i
$57$	−2.13337	−	2.13337i	−0.282571	−	0.282571i
$58$	6.14553	−	1.64669i	0.806947	−	0.216221i
$59$	−1.96185	+	0.525675i	−0.255410	+	0.0684370i	−0.384252	−	0.923228i	$-0.625541\pi$
$59$	−1.96185	+	0.525675i	−0.255410	+	0.0684370i	0.128842	+	0.991665i	$0.458874\pi$
$60$	9.77878	−	9.77878i	1.26244	−	1.26244i
$61$	4.53851	+	2.62031i	0.581097	+	0.335496i	0.761569	−	0.648084i	$-0.224429\pi$
$61$	4.53851	+	2.62031i	0.581097	+	0.335496i	−0.180472	+	0.983580i	$0.557763\pi$
$62$	6.30300	+	10.9171i	0.800482	+	1.38648i
$63$	1.40965	−	3.86393i	0.177599	−	0.486810i
$64$			11.5440i			1.44300i
$65$	9.93790	−	5.78622i	1.23264	−	0.717692i
$66$			12.1174i			1.49155i
$67$	2.26854	−	8.46631i	0.277147	−	1.03432i	−0.677243	−	0.735760i	$-0.736825\pi$
$67$	2.26854	−	8.46631i	0.277147	−	1.03432i	0.954389	−	0.298565i	$-0.0965080\pi$
$68$	−4.50931	+	2.60345i	−0.546835	+	0.315715i
$69$	3.14404	−	5.44564i	0.378498	−	0.655578i
$70$	12.8318	+	15.3157i	1.53369	+	1.83058i
$71$	8.31929	−	2.22915i	0.987318	−	0.264551i	0.271194	−	0.962525i	$-0.412581\pi$
$71$	8.31929	−	2.22915i	0.987318	−	0.264551i	0.716124	+	0.697974i	$0.245915\pi$
$72$	−1.53055	−	5.71208i	−0.180377	−	0.673175i
$73$	−11.1801	−	11.1801i	−1.30854	−	1.30854i	−0.922472	−	0.386065i	$-0.873834\pi$
$73$	−11.1801	−	11.1801i	−1.30854	−	1.30854i	−0.386065	−	0.922472i	$-0.626166\pi$
$74$	−0.734747	+	1.27262i	−0.0854126	+	0.147939i
$75$	3.10932	+	5.38549i	0.359033	+	0.621863i
$76$	2.34245	−	8.74214i	0.268697	−	1.00279i
$77$	−11.2184	−	0.989991i	−1.27845	−	0.112820i
$78$	0.0375447	+	10.2639i	0.00425110	+	1.16216i
$79$	2.01287			0.226465			0.113233	−	0.993568i	$-0.463879\pi$
$79$	2.01287			0.226465			0.113233	+	0.993568i	$0.463879\pi$
$80$	5.52690	+	1.48093i	0.617926	+	0.165573i
$81$	0.959764	+	1.66236i	0.106640	+	0.184707i
$82$	−6.18815	+	10.7182i	−0.683367	+	1.18363i
$83$	5.11623	−	5.11623i	0.561579	−	0.561579i	−0.368177	−	0.929756i	$-0.620018\pi$
$83$	5.11623	−	5.11623i	0.561579	−	0.561579i	0.929756	+	0.368177i	$0.120018\pi$
$84$	−11.2991	+	1.98357i	−1.23283	+	0.216425i
$85$	−1.19179	−	4.44782i	−0.129268	−	0.482434i
$86$	−10.5586	+	10.5586i	−1.13857	+	1.13857i
$87$	−2.79766	−	1.61523i	−0.299941	−	0.173171i
$88$	−14.0227	+	8.09604i	−1.49483	+	0.863040i
$89$	−1.81184	+	6.76189i	−0.192055	+	0.716759i	0.800955	+	0.598725i	$0.204326\pi$
$89$	−1.81184	+	6.76189i	−0.192055	+	0.716759i	−0.993010	+	0.118034i	$0.962341\pi$
$90$	11.7402			1.23752
$91$	−9.50547	−	0.803801i	−0.996444	−	0.0842613i
$92$	18.8630			1.96661
$93$	1.65662	−	6.18260i	0.171784	−	0.641105i
$94$	13.5721	−	7.83586i	1.39986	−	0.808207i
$95$	6.93151	+	4.00191i	0.711158	+	0.410587i
$96$	2.85646	−	2.85646i	0.291536	−	0.291536i
$97$	1.62618	+	6.06897i	0.165113	+	0.616211i	0.998026	+	0.0628062i	$0.0200050\pi$
$97$	1.62618	+	6.06897i	0.165113	+	0.616211i	−0.832913	+	0.553405i	$0.813328\pi$
$98$	−1.41972	−	16.5138i	−0.143413	−	1.66814i
$99$	−4.67912	+	4.67912i	−0.470270	+	0.470270i
$100$	−9.32734	+	16.1554i	−0.932734	+	1.61554i
$101$	6.66959	+	11.5521i	0.663649	+	1.14947i	0.979650	+	0.200715i	$0.0643264\pi$
$101$	6.66959	+	11.5521i	0.663649	+	1.14947i	−0.316001	+	0.948759i	$0.602340\pi$
$102$	3.96988	+	1.06373i	0.393077	+	0.105325i
$103$	−6.17453			−0.608395			−0.304197	−	0.952609i	$-0.598388\pi$
$103$	−6.17453			−0.608395			−0.304197	+	0.952609i	$0.598388\pi$
$104$	−11.8527	+	6.90110i	−1.16225	+	0.676708i
$105$	0.891816	−	10.1059i	0.0870324	−	0.986234i
$106$	−4.64852	+	17.3485i	−0.451504	+	1.68504i
$107$	4.27353	+	7.40196i	0.413137	+	0.715575i	0.995231	−	0.0975469i	$-0.0310996\pi$
$107$	4.27353	+	7.40196i	0.413137	+	0.715575i	−0.582094	+	0.813122i	$0.697766\pi$
$108$	−9.87427	+	17.1027i	−0.950152	+	1.64571i
$109$	3.30124	+	3.30124i	0.316201	+	0.316201i	0.847306	−	0.531105i	$-0.178223\pi$
$109$	3.30124	+	3.30124i	0.316201	+	0.316201i	−0.531105	+	0.847306i	$0.678223\pi$
$110$	−8.31998	−	31.0506i	−0.793279	−	2.96056i
$111$	0.720711	−	0.193114i	0.0684069	−	0.0183296i
$112$	−3.04825	−	3.63833i	−0.288033	−	0.343790i
$113$	9.80118	−	16.9761i	0.922018	−	1.59698i	0.125729	−	0.992065i	$-0.459873\pi$
$113$	9.80118	−	16.9761i	0.922018	−	1.59698i	0.796289	−	0.604917i	$-0.206794\pi$
$114$	−6.18669	+	3.57189i	−0.579437	+	0.334538i
$115$	−4.31748	+	16.1131i	−0.402608	+	1.50255i
$116$		−	9.69077i		−	0.899765i
$117$	−3.94890	+	3.97789i	−0.365076	+	0.367756i
$118$			4.80915i			0.442718i
$119$	−1.30915	+	3.58844i	−0.120009	+	0.328952i
$120$	−7.29317	−	12.6321i	−0.665773	−	1.15315i
$121$	6.16515	+	3.55945i	0.560468	+	0.323586i
$122$	8.77435	−	8.77435i	0.794392	−	0.794392i
$123$	6.06993	−	1.62643i	0.547308	−	0.146651i
$124$	18.5466	−	4.96954i	1.66553	−	0.446278i
$125$	−0.388969	−	0.388969i	−0.0347904	−	0.0347904i
$126$	−7.97343	−	5.59201i	−0.710330	−	0.498176i
$127$	1.02476	−	0.591646i	0.0909329	−	0.0525001i	−0.453844	−	0.891081i	$-0.649948\pi$
$127$	1.02476	−	0.591646i	0.0909329	−	0.0525001i	0.544777	+	0.838581i	$0.316614\pi$
$128$	19.9115	+	5.33527i	1.75994	+	0.471576i
$129$	7.58180			0.667540
$130$	−7.14355	−	26.2753i	−0.626531	−	2.30449i
$131$		−	9.67103i		−	0.844962i	−0.906372	−	0.422481i	$-0.861159\pi$
$131$		−	9.67103i		−	0.844962i	0.906372	−	0.422481i	$-0.138841\pi$
$132$	17.8277	+	4.77693i	1.55171	+	0.415778i
$133$	−2.80143	−	6.01951i	−0.242915	−	0.521958i
$134$	−17.9733	−	10.3769i	−1.55266	−	0.896428i
$135$	−12.3493	−	12.3493i	−1.06286	−	1.06286i
$136$	1.42142	+	5.30482i	0.121886	+	0.454884i
$137$	1.70702	+	6.37069i	0.145841	+	0.544285i	0.999717	+	0.0238082i	$0.00757909\pi$
$137$	1.70702	+	6.37069i	0.145841	+	0.544285i	−0.853876	+	0.520477i	$0.825754\pi$
$138$	−10.5281	−	10.5281i	−0.896212	−	0.896212i
$139$	−19.6752	−	11.3595i	−1.66883	−	0.963500i	−0.968269	−	0.249909i	$-0.919599\pi$
$139$	−19.6752	−	11.3595i	−1.66883	−	0.963500i	−0.700562	−	0.713591i	$-0.747067\pi$
$140$	27.5918	−	12.8410i	2.33193	−	1.08526i
$141$	−7.68617	−	2.05950i	−0.647292	−	0.173441i
$142$		−	20.3934i		−	1.71138i
$143$	13.3193	+	7.62508i	1.11382	+	0.637641i
$144$	−2.78893			−0.232411
$145$	8.27800	+	2.21808i	0.687450	+	0.184202i
$146$	−32.4220	+	18.7189i	−2.68327	+	1.54918i
$147$	−5.41926	+	6.43872i	−0.446973	+	0.531056i
$148$	1.58269	+	1.58269i	0.130096	+	0.130096i
$149$	−14.6725	+	3.93148i	−1.20202	+	0.322079i	−0.803625	−	0.595137i	$-0.797098\pi$
$149$	−14.6725	+	3.93148i	−1.20202	+	0.322079i	−0.398391	+	0.917216i	$0.630431\pi$
$150$	14.2228	−	3.81099i	1.16129	−	0.311166i
$151$	−5.08565	+	5.08565i	−0.413864	+	0.413864i	−0.883082	−	0.469218i	$-0.844536\pi$
$151$	−5.08565	+	5.08565i	−0.413864	+	0.413864i	0.469218	+	0.883082i	$0.344536\pi$
$152$	−8.26706	−	4.77299i	−0.670547	−	0.387141i
$153$	1.12221	+	1.94372i	0.0907252	+	0.157141i
$154$	−9.13926	+	25.0512i	−0.736462	+	2.01868i
$155$			16.9802i			1.36389i
$156$	15.1156	+	3.99100i	1.21021	+	0.319536i
$157$		−	19.0028i		−	1.51659i	−0.651911	−	0.758296i	$-0.726032\pi$
$157$		−	19.0028i		−	1.51659i	0.651911	−	0.758296i	$-0.273968\pi$
$158$	1.23356	−	4.60369i	0.0981364	−	0.366250i
$159$	7.89767	−	4.55972i	0.626326	−	0.361609i
$160$	−5.35833	+	9.28090i	−0.423613	+	0.733720i
$161$	10.6071	−	8.88685i	0.835960	−	0.700382i
$162$	4.39021	−	1.17635i	0.344928	−	0.0924231i
$163$	−0.262463	−	0.979525i	−0.0205577	−	0.0767223i	0.954885	−	0.296976i	$-0.0959781\pi$
$163$	−0.262463	−	0.979525i	−0.0205577	−	0.0767223i	−0.975443	+	0.220254i	$0.929311\pi$
$164$	13.3296	+	13.3296i	1.04087	+	1.04087i
$165$	−8.16105	+	14.1353i	−0.635337	+	1.10044i
$166$	−8.56608	−	14.8369i	−0.664857	−	1.15157i
$167$	0.522634	−	1.95050i	0.0404426	−	0.150934i	−0.942752	−	0.333495i	$-0.891772\pi$
$167$	0.522634	−	1.95050i	0.0404426	−	0.150934i	0.983195	+	0.182561i	$0.0584387\pi$
$168$	−1.06365	+	12.0531i	−0.0820624	+	0.929915i
$169$	11.3056	+	6.41746i	0.869660	+	0.493651i
$170$	−10.9031			−0.836230
$171$	−3.76827	−	1.00970i	−0.288166	−	0.0772140i
$172$	11.3720	+	19.6968i	0.867104	+	1.50187i
$173$	−1.22524	+	2.12218i	−0.0931533	+	0.161346i	−0.908836	−	0.417153i	$-0.863028\pi$
$173$	−1.22524	+	2.12218i	−0.0931533	+	0.161346i	0.815683	+	0.578499i	$0.196361\pi$
$174$	−5.40875	+	5.40875i	−0.410037	+	0.410037i
$175$	2.36624	+	13.4790i	0.178871	+	1.01891i
$176$	1.97645	+	7.37623i	0.148981	+	0.556004i
$177$	1.72664	−	1.72664i	0.129782	−	0.129782i
$178$	14.3550	+	8.28784i	1.07595	+	0.621200i
$179$	−6.50355	+	3.75482i	−0.486098	+	0.280649i	−0.722954	−	0.690896i	$-0.757216\pi$
$179$	−6.50355	+	3.75482i	−0.486098	+	0.280649i	0.236856	+	0.971545i	$0.423883\pi$
$180$	4.62821	−	17.2727i	0.344966	−	1.28743i
$181$	−4.93320			−0.366682			−0.183341	−	0.983049i	$-0.558691\pi$
$181$	−4.93320			−0.366682			−0.183341	+	0.983049i	$0.558691\pi$
$182$	−7.66368	+	21.2476i	−0.568070	+	1.57498i
$183$	−6.30057			−0.465751
$184$	5.14937	−	19.2177i	0.379617	−	1.41675i
$185$	−1.71421	+	0.989701i	−0.126031	+	0.0727642i
$186$	−13.1252	−	7.57782i	−0.962384	−	0.555633i
$187$	4.34551	−	4.34551i	0.317775	−	0.317775i
$188$	−6.17811	−	23.0570i	−0.450585	−	1.68161i
$189$	2.50499	+	14.2693i	0.182211	+	1.03794i
$190$	13.4008	−	13.4008i	0.972193	−	0.972193i
$191$	3.04432	−	5.27291i	0.220279	−	0.381534i	−0.734614	−	0.678486i	$-0.762637\pi$
$191$	3.04432	−	5.27291i	0.220279	−	0.381534i	0.954893	+	0.296951i	$0.0959699\pi$
$192$	−6.93941	−	12.0194i	−0.500809	−	0.867427i
$193$	−13.9940	−	3.74968i	−1.00731	−	0.269908i	−0.282805	−	0.959177i	$-0.591265\pi$
$193$	−13.9940	−	3.74968i	−1.00731	−	0.269908i	−0.724505	+	0.689270i	$0.757932\pi$
$194$	14.8771			1.06811
$195$	−6.86892	+	11.9985i	−0.491894	+	0.859228i
$196$	−24.8556	−	4.42130i	−1.77540	−	0.315807i
$197$	−4.33340	+	16.1725i	−0.308742	+	1.15224i	0.620934	+	0.783863i	$0.286754\pi$
$197$	−4.33340	+	16.1725i	−0.308742	+	1.15224i	−0.929676	+	0.368379i	$0.879913\pi$
$198$	7.83424	+	13.5693i	0.556755	+	0.964328i
$199$	9.90747	−	17.1602i	0.702322	−	1.21646i	−0.265328	−	0.964158i	$-0.585480\pi$
$199$	9.90747	−	17.1602i	0.702322	−	1.21646i	0.967649	−	0.252298i	$-0.0811865\pi$
$200$	13.9130	+	13.9130i	0.983795	+	0.983795i
$201$	2.72737	+	10.1787i	0.192374	+	0.717948i
$202$	30.5084	−	8.17471i	2.14657	−	0.575171i
$203$	−4.56557	−	5.44936i	−0.320440	−	0.382470i
$204$	3.13002	−	5.42135i	0.219145	−	0.379570i
$205$	−14.4373	+	8.33541i	−1.00835	+	0.582170i
$206$	−3.78397	+	14.1220i	−0.263641	+	0.983923i
$207$		−	8.13083i		−	0.565132i
$208$	1.69699	+	6.24182i	0.117665	+	0.432792i
$209$			10.6819i			0.738885i
$210$	−22.5669	−	8.23294i	−1.55727	−	0.568127i
$211$	−9.56393	−	16.5652i	−0.658408	−	1.14040i	−0.981028	−	0.193868i	$-0.937897\pi$
$211$	−9.56393	−	16.5652i	−0.658408	−	1.14040i	0.322619	−	0.946529i	$-0.395437\pi$
$212$	23.6915	+	13.6783i	1.62714	+	0.939428i
$213$	−7.32191	+	7.32191i	−0.501689	+	0.501689i
$214$	19.5482	−	5.23793i	1.33629	−	0.358058i
$215$	−19.4282	+	5.20577i	−1.32499	+	0.355031i
$216$	14.7288	+	14.7288i	1.00217	+	1.00217i
$217$	8.08793	−	11.5323i	0.549044	−	0.782862i
$218$	9.57347	−	5.52725i	0.648397	−	0.374352i
$219$	18.3613	+	4.91989i	1.24074	+	0.332455i
$220$	−48.9631			−3.30109
$221$	3.66735	−	3.69428i	0.246693	−	0.248504i
$222$		−	1.76671i		−	0.118574i
$223$	−0.670621	−	0.179692i	−0.0449081	−	0.0120331i	0.236295	−	0.971681i	$-0.424067\pi$
$223$	−0.670621	−	0.179692i	−0.0449081	−	0.0120331i	−0.281203	+	0.959648i	$0.590733\pi$
$224$	8.05978	−	3.75096i	0.538517	−	0.250621i
$225$	6.96374	+	4.02052i	0.464249	+	0.268034i
$226$	−32.8202	−	32.8202i	−2.18316	−	2.18316i
$227$	−1.34886	−	5.03400i	−0.0895267	−	0.334118i	0.906606	−	0.421978i	$-0.138664\pi$
$227$	−1.34886	−	5.03400i	−0.0895267	−	0.334118i	−0.996133	+	0.0878596i	$0.971997\pi$
$228$	2.81622	+	10.5103i	0.186509	+	0.696060i
$229$	0.749026	+	0.749026i	0.0494970	+	0.0494970i	0.731422	−	0.681925i	$-0.238857\pi$
$229$	0.749026	+	0.749026i	0.0494970	+	0.0494970i	−0.681925	+	0.731422i	$0.738857\pi$
$230$	34.2068	+	19.7493i	2.25553	+	1.30223i
$231$	12.2755	−	5.71292i	0.807669	−	0.375883i
$232$	−9.87299	−	2.64546i	−0.648193	−	0.173683i
$233$			1.32103i			0.0865439i	0.999063	+	0.0432719i	$0.0137782\pi$
$233$			1.32103i			0.0865439i	−0.999063	+	0.0432719i	$0.986222\pi$
$234$	6.67794	+	11.4694i	0.436551	+	0.749780i
$235$	21.1097			1.37705
$236$	7.07546	+	1.89586i	0.460573	+	0.123410i
$237$	−2.09577	+	1.20999i	−0.136135	+	0.0785973i
$238$	7.40494	+	5.19331i	0.479991	+	0.336632i
$239$	15.2273	+	15.2273i	0.984972	+	0.984972i	0.999889	−	0.0149168i	$-0.00474835\pi$
$239$	15.2273	+	15.2273i	0.984972	+	0.984972i	−0.0149168	+	0.999889i	$0.504748\pi$
$240$	−6.64475	+	1.78045i	−0.428917	+	0.114928i
$241$	3.38927	−	0.908152i	0.218322	−	0.0584992i	−0.148000	−	0.988987i	$-0.547284\pi$
$241$	3.38927	−	0.908152i	0.218322	−	0.0584992i	0.366322	+	0.930488i	$0.380617\pi$
$242$	11.9191	−	11.9191i	0.766191	−	0.766191i
$243$	12.2279	+	7.05977i	0.784419	+	0.452885i
$244$	−9.45024	−	16.3683i	−0.604989	−	1.04787i
$245$	9.46583	−	20.2200i	0.604750	−	1.29181i
$246$		−	14.8795i		−	0.948680i
$247$	0.0330970	+	9.04800i	0.00210591	+	0.575711i
$248$		−	20.2520i		−	1.28600i
$249$	−2.25143	+	8.40244i	−0.142678	+	0.532483i
$250$	−1.12800	+	0.651249i	−0.0713407	+	0.0411886i
$251$	8.75834	−	15.1699i	0.552822	−	0.957515i	−0.445248	−	0.895407i	$-0.646884\pi$
$251$	8.75834	−	15.1699i	0.552822	−	0.957515i	0.998069	−	0.0621079i	$-0.0197823\pi$
$252$	−11.3705	+	9.52643i	−0.716276	+	0.600109i
$253$	−21.5046	+	5.76214i	−1.35198	+	0.362262i
$254$	−0.725163	−	2.70634i	−0.0455008	−	0.169811i
$255$	3.91458	+	3.91458i	0.245140	+	0.245140i
$256$	12.8609	−	22.2758i	0.803807	−	1.39224i
$257$	3.42559	+	5.93330i	0.213683	+	0.370109i	0.952864	−	0.303397i	$-0.0981208\pi$
$257$	3.42559	+	5.93330i	0.213683	+	0.370109i	−0.739182	+	0.673506i	$0.764788\pi$
$258$	4.64639	−	17.3406i	0.289272	−	1.07958i
$259$	1.63563	+	0.144340i	0.101633	+	0.00896884i
$260$	−41.4736	+	0.151708i	−2.57208	+	0.00940850i
$261$	−4.17717			−0.258560
$262$	−22.1189	−	5.92674i	−1.36651	−	0.366155i
$263$	−8.70849	−	15.0836i	−0.536989	−	0.930092i	−0.999064	−	0.0432511i	$-0.986228\pi$
$263$	−8.70849	−	15.0836i	−0.536989	−	0.930092i	0.462076	−	0.886841i	$-0.347105\pi$
$264$	9.73350	−	16.8589i	0.599056	−	1.03759i
$265$	−17.1068	+	17.1068i	−1.05086	+	1.05086i
$266$	−15.4842	+	2.71827i	−0.949398	+	0.166668i
$267$	−2.17830	−	8.12952i	−0.133310	−	0.497518i
$268$	−22.3525	+	22.3525i	−1.36539	+	1.36539i
$269$	−0.145276	−	0.0838752i	−0.00885764	−	0.00511396i	0.495565	−	0.868571i	$-0.334961\pi$
$269$	−0.145276	−	0.0838752i	−0.00885764	−	0.00511396i	−0.504422	+	0.863457i	$0.668294\pi$
$270$	−35.8126	+	20.6764i	−2.17949	+	1.25833i
$271$	−0.645525	+	2.40913i	−0.0392128	+	0.146344i	−0.982757	−	0.184903i	$-0.940803\pi$
$271$	−0.645525	+	2.40913i	−0.0392128	+	0.146344i	0.943544	+	0.331248i	$0.107470\pi$
$272$	2.59009			0.157047
$273$	10.3801	−	4.87709i	0.628234	−	0.295175i
$274$	15.6167			0.943441
$275$	5.69850	−	21.2671i	0.343632	−	1.28245i
$276$	−19.6399	+	11.3391i	−1.18218	+	0.682532i
$277$	−7.38731	−	4.26506i	−0.443860	−	0.256263i	0.261373	−	0.965238i	$-0.415825\pi$
$277$	−7.38731	−	4.26506i	−0.443860	−	0.256263i	−0.705234	+	0.708975i	$0.749158\pi$
$278$	−38.0383	+	38.0383i	−2.28139	+	2.28139i
$279$	−2.14210	−	7.99444i	−0.128244	−	0.478614i
$280$	−5.55023	−	31.6161i	−0.331690	−	1.88942i
$281$	15.7936	−	15.7936i	0.942166	−	0.942166i	−0.0562508	−	0.998417i	$-0.517915\pi$
$281$	15.7936	−	15.7936i	0.942166	−	0.942166i	0.998417	+	0.0562508i	$0.0179146\pi$
$282$	−9.42071	+	16.3171i	−0.560995	+	0.971672i
$283$	4.79048	+	8.29736i	0.284765	+	0.493227i	0.972552	−	0.232685i	$-0.0747512\pi$
$283$	4.79048	+	8.29736i	0.284765	+	0.493227i	−0.687787	+	0.725912i	$0.741418\pi$
$284$	−30.0038	−	8.03949i	−1.78040	−	0.477056i
$285$	−9.62263			−0.569996
$286$	25.6021	−	25.7901i	1.51388	−	1.52500i
$287$	13.7755	+	1.21565i	0.813143	+	0.0717576i
$288$	1.35194	−	5.04550i	0.0796636	−	0.297309i
$289$	7.45780	+	12.9173i	0.438694	+	0.759841i
$290$	10.1461	−	17.5735i	0.595799	−	1.03195i
$291$	−5.34138	−	5.34138i	−0.313117	−	0.313117i
$292$	14.7587	+	55.0802i	0.863688	+	3.22333i
$293$	−14.5286	+	3.89292i	−0.848769	+	0.227427i	−0.656885	−	0.753991i	$-0.728126\pi$
$293$	−14.5286	+	3.89292i	−0.848769	+	0.227427i	−0.191884	+	0.981418i	$0.561460\pi$
$294$	11.4051	+	16.3404i	0.665157	+	0.952993i
$295$	−3.23895	+	5.61003i	−0.188579	+	0.326628i
$296$	2.04450	−	1.18039i	0.118834	−	0.0686090i
$297$	6.03264	−	22.5141i	0.350049	−	1.30640i
$298$			35.9672i			2.08352i
$299$	−18.1973	+	4.94738i	−1.05238	+	0.286114i
$300$		−	22.4277i		−	1.29486i
$301$	15.6744	+	5.71838i	0.903458	+	0.329602i
$302$	8.51488	+	14.7482i	0.489976	+	0.848663i
$303$	−13.8885	−	8.01855i	−0.797875	−	0.460654i
$304$	−3.18342	+	3.18342i	−0.182582	+	0.182582i
$305$	16.1451	−	4.32606i	0.924464	−	0.247709i
$306$	5.13328	−	1.37546i	0.293450	−	0.0786296i
$307$	15.7439	+	15.7439i	0.898552	+	0.898552i	0.995308	−	0.0967560i	$-0.0308467\pi$
$307$	15.7439	+	15.7439i	0.898552	+	0.898552i	−0.0967560	+	0.995308i	$0.530847\pi$
$308$	33.2537	+	23.3218i	1.89481	+	1.32888i
$309$	6.42882	−	3.71168i	0.365723	−	0.211150i
$310$	38.8360	+	10.4061i	2.20574	+	0.591025i
$311$	−3.89372			−0.220793			−0.110396	−	0.993888i	$-0.535212\pi$
$311$	−3.89372			−0.220793			−0.110396	+	0.993888i	$0.535212\pi$
$312$	8.19241	−	14.3103i	0.463804	−	0.810161i
$313$		−	9.97498i		−	0.563819i	−0.959441	−	0.281910i	$-0.909032\pi$
$313$		−	9.97498i		−	0.563819i	0.959441	−	0.281910i	$-0.0909678\pi$
$314$	−43.4620	−	11.6456i	−2.45270	−	0.657199i
$315$	−5.53506	−	11.8933i	−0.311865	−	0.670114i
$316$	−6.28689	−	3.62974i	−0.353665	−	0.204189i
$317$	10.9787	+	10.9787i	0.616625	+	0.616625i	0.944664	−	0.328039i	$-0.106388\pi$
$317$	10.9787	+	10.9787i	0.616625	+	0.616625i	−0.328039	+	0.944664i	$0.606388\pi$
$318$	−5.58871	−	20.8574i	−0.313399	−	1.16962i
$319$	2.96026	+	11.0479i	0.165743	+	0.618561i
$320$	26.0348	+	26.0348i	1.45539	+	1.45539i
$321$	−8.89905	−	5.13787i	−0.496697	−	0.286768i
$322$	−13.8250	−	29.7061i	−0.770435	−	1.65546i
$323$	3.49959	+	0.937714i	0.194723	+	0.0521758i
$324$		−	6.92284i		−	0.384602i
$325$	4.76095	−	18.0317i	0.264090	−	1.00022i
$326$	−2.40115			−0.132987
$327$	−5.42166	−	1.45273i	−0.299818	−	0.0803361i
$328$	17.2191	−	9.94146i	0.950766	−	0.548925i
$329$	−14.3369	−	10.0549i	−0.790417	−	0.554343i
$330$	27.3280	+	27.3280i	1.50436	+	1.50436i
$331$	14.1453	−	3.79022i	0.777495	−	0.208329i	0.151815	−	0.988409i	$-0.451488\pi$
$331$	14.1453	−	3.79022i	0.777495	−	0.208329i	0.625680	+	0.780080i	$0.284822\pi$
$332$	−25.2057	+	6.75384i	−1.38334	+	0.370665i
$333$	0.682212	−	0.682212i	0.0373850	−	0.0373850i
$334$	−4.14075	−	2.39066i	−0.226572	−	0.130811i
$335$	−13.9776	−	24.2100i	−0.763680	−	1.32273i
$336$	5.36089	+	1.95578i	0.292461	+	0.106696i
$337$			11.8235i			0.644066i	0.946728	+	0.322033i	$0.104366\pi$
$337$			11.8235i			0.644066i	−0.946728	+	0.322033i	$0.895634\pi$
$338$	21.6060	−	21.9245i	1.17521	−	1.19254i
$339$			23.5670i			1.27999i
$340$	−4.29823	+	16.0412i	−0.233104	+	0.869956i
$341$	−19.6258	+	11.3309i	−1.06280	+	0.613605i
$342$	−4.61865	+	7.99973i	−0.249748	+	0.432576i
$343$	−16.0599	+	9.22389i	−0.867152	+	0.498043i
$344$	23.1716	−	6.20881i	1.24933	−	0.334756i
$345$	−5.19072	−	19.3720i	−0.279459	−	1.04295i
$346$	4.10283	+	4.10283i	0.220569	+	0.220569i
$347$	5.00685	−	8.67212i	0.268782	−	0.465544i	−0.699766	−	0.714372i	$-0.746712\pi$
$347$	5.00685	−	8.67212i	0.268782	−	0.465544i	0.968548	+	0.248829i	$0.0800456\pi$
$348$	5.82539	+	10.0899i	0.312274	+	0.540874i
$349$	−4.39634	+	16.4073i	−0.235330	+	0.878265i	0.742669	+	0.669658i	$0.233559\pi$
$349$	−4.39634	+	16.4073i	−0.235330	+	0.878265i	−0.978000	+	0.208607i	$0.933107\pi$
$350$	32.2782	+	2.84846i	1.72534	+	0.152257i
$351$	5.04012	−	19.0890i	0.269022	−	1.01890i
$352$	−14.3025			−0.762326
$353$	34.8505	+	9.33817i	1.85491	+	0.497021i	0.999771	−	0.0213843i	$-0.00680736\pi$
$353$	34.8505	+	9.33817i	1.85491	+	0.497021i	0.855135	+	0.518405i	$0.173474\pi$
$354$	−2.89091	−	5.00721i	−0.153650	−	0.266130i
$355$	13.7349	−	23.7896i	0.728973	−	1.26262i
$356$	17.8525	−	17.8525i	0.946181	−	0.946181i
$357$	−0.794050	−	4.52319i	−0.0420256	−	0.239393i
$358$	4.60217	+	17.1755i	0.243232	+	0.907756i
$359$	−2.44977	+	2.44977i	−0.129294	+	0.129294i	−0.768792	−	0.639498i	$-0.779142\pi$
$359$	−2.44977	+	2.44977i	−0.129294	+	0.129294i	0.639498	+	0.768792i	$0.279142\pi$
$360$	−16.3341	−	9.43047i	−0.860880	−	0.497030i
$361$	11.0007	−	6.35125i	0.578984	−	0.334276i
$362$	−3.02324	+	11.2829i	−0.158898	+	0.593014i
$363$	−8.55873			−0.449217
$364$	28.2394	+	19.6514i	1.48015	+	1.03002i
$365$	−50.4284			−2.63954
$366$	−3.86121	+	14.4102i	−0.201828	+	0.753234i
$367$	−10.9829	+	6.34099i	−0.573303	+	0.330997i	−0.758468	−	0.651711i	$-0.774052\pi$
$367$	−10.9829	+	6.34099i	−0.573303	+	0.330997i	0.185164	+	0.982708i	$0.440718\pi$
$368$	−8.12600	−	4.69155i	−0.423597	−	0.244564i
$369$	5.74569	−	5.74569i	0.299109	−	0.299109i
$370$	1.21305	+	4.52715i	0.0630633	+	0.235355i
$371$	19.7665	−	3.47003i	1.02623	−	0.180155i
$372$	−16.3231	+	16.3231i	−0.846312	+	0.846312i
$373$	−15.0192	+	26.0141i	−0.777667	+	1.34696i	0.155617	+	0.987818i	$0.450264\pi$
$373$	−15.0192	+	26.0141i	−0.777667	+	1.34696i	−0.933283	+	0.359141i	$0.883070\pi$
$374$	−7.27567	−	12.6018i	−0.376216	−	0.651625i
$375$	0.638808	+	0.171168i	0.0329879	+	0.00883908i
$376$	−25.1771			−1.29841
$377$	2.54169	+	9.34878i	0.130904	+	0.481487i
$378$	34.1709	+	3.01549i	1.75756	+	0.155100i
$379$	3.10882	−	11.6023i	0.159689	−	0.595969i	−0.838969	−	0.544180i	$-0.816841\pi$
$379$	3.10882	−	11.6023i	0.159689	−	0.595969i	0.998658	−	0.0517891i	$-0.0164924\pi$
$380$	−14.4330	−	24.9987i	−0.740398	−	1.28241i
$381$	−0.711310	+	1.23202i	−0.0364415	+	0.0631185i
$382$	−10.1942	−	10.1942i	−0.521579	−	0.521579i
$383$	1.48137	+	5.52856i	0.0756947	+	0.282496i	0.993390	−	0.114789i	$-0.0366191\pi$
$383$	1.48137	+	5.52856i	0.0756947	+	0.282496i	−0.917695	+	0.397285i	$0.869952\pi$
$384$	−23.9387	+	6.41436i	−1.22162	+	0.327331i
$385$	−27.5332	+	23.0678i	−1.40322	+	1.17564i
$386$	−17.1520	+	29.7082i	−0.873015	+	1.51211i
$387$	8.49024	−	4.90184i	0.431583	−	0.249175i
$388$	5.86486	−	21.8879i	0.297743	−	1.11119i
$389$		−	16.4483i		−	0.833960i	−0.908916	−	0.416980i	$-0.863088\pi$
$389$		−	16.4483i		−	0.833960i	0.908916	−	0.416980i	$-0.136912\pi$
$390$	23.2325	+	23.0632i	1.17643	+	1.16785i
$391$			7.55112i			0.381877i
$392$	−11.2897	+	24.1160i	−0.570216	+	1.21804i
$393$	5.81352	+	10.0693i	0.293253	+	0.507930i
$394$	34.3329	+	19.8221i	1.72967	+	0.998624i
$395$	4.53956	−	4.53956i	0.228410	−	0.228410i
$396$	23.0522	−	6.17683i	1.15842	−	0.310397i
$397$	10.9116	−	2.92375i	0.547636	−	0.146739i	0.0256162	−	0.999672i	$-0.491845\pi$
$397$	10.9116	−	2.92375i	0.547636	−	0.146739i	0.522020	+	0.852933i	$0.325179\pi$
$398$	−33.1761	−	33.1761i	−1.66297	−	1.66297i
$399$	6.53529	+	4.58340i	0.327174	+	0.229457i
$400$	8.03625	−	4.63973i	0.401812	−	0.231987i
$401$	−23.3830	−	6.26544i	−1.16769	−	0.312881i	−0.377656	−	0.925946i	$-0.623270\pi$
$401$	−23.3830	−	6.26544i	−1.16769	−	0.312881i	−0.790033	+	0.613064i	$0.789937\pi$
$402$	24.9514			1.24446
$403$	−16.5887	+	9.65855i	−0.826341	+	0.481127i
$404$		−	48.1082i		−	2.39347i
$405$	5.91359	+	1.58454i	0.293849	+	0.0787366i
$406$	−15.2613	+	7.10250i	−0.757407	+	0.352491i
$407$	−2.28780	−	1.32086i	−0.113402	−	0.0654726i
$408$	−4.66883	−	4.66883i	−0.231142	−	0.231142i
$409$	0.0933824	+	0.348508i	0.00461746	+	0.0172326i	0.968196	−	0.250192i	$-0.0804939\pi$
$409$	0.0933824	+	0.348508i	0.00461746	+	0.0172326i	−0.963579	+	0.267425i	$0.913827\pi$
$410$	10.2165	+	38.1283i	0.504555	+	1.88302i
$411$	−5.60692	−	5.60692i	−0.276569	−	0.276569i
$412$	19.2852	+	11.1343i	0.950114	+	0.548549i
$413$	4.87190	−	2.26734i	0.239730	−	0.111568i
$414$	−18.5963	−	4.98286i	−0.913957	−	0.244894i
$415$		−	23.0769i		−	1.13280i
$416$	−12.1148	+	0.0443150i	−0.593975	+	0.00217272i
$417$	27.3140			1.33757
$418$	24.4310	+	6.54626i	1.19496	+	0.320188i
$419$	15.9181	−	9.19033i	0.777651	−	0.448977i	−0.0579460	−	0.998320i	$-0.518455\pi$
$419$	15.9181	−	9.19033i	0.777651	−	0.448977i	0.835597	+	0.549343i	$0.185122\pi$
$420$	−21.0091	+	29.9560i	−1.02514	+	1.46170i
$421$	20.7439	+	20.7439i	1.01099	+	1.01099i	0.999939	+	0.0110561i	$0.00351933\pi$
$421$	20.7439	+	20.7439i	1.01099	+	1.01099i	0.0110561	+	0.999939i	$0.496481\pi$
$422$	−43.7479	+	11.7222i	−2.12962	+	0.570629i
$423$	−9.93864	+	2.66305i	−0.483233	+	0.129482i
$424$	20.4030	−	20.4030i	0.990855	−	0.990855i
$425$	−6.46724	−	3.73386i	−0.313707	−	0.181119i
$426$	12.2590	+	21.2333i	0.593952	+	1.02876i
$427$	−13.0256	−	4.75205i	−0.630354	−	0.229968i
$428$		−	30.8252i		−	1.48999i
$429$	−18.4515	+	0.0674943i	−0.890846	+	0.00325865i
$430$			47.6251i			2.29669i
$431$	−2.49781	+	9.32194i	−0.120315	+	0.449022i	−0.999629	−	0.0272197i	$-0.991335\pi$
$431$	−2.49781	+	9.32194i	−0.120315	+	0.449022i	0.879314	+	0.476242i	$0.158001\pi$
$432$	8.50747	−	4.91179i	0.409316	−	0.236319i
$433$	−13.6960	+	23.7221i	−0.658186	+	1.14001i	0.322899	+	0.946433i	$0.395343\pi$
$433$	−13.6960	+	23.7221i	−0.658186	+	1.14001i	−0.981085	+	0.193578i	$0.937991\pi$
$434$	−21.4192	−	25.5655i	−1.02816	−	1.22718i
$435$	−9.95227	+	2.66670i	−0.477175	+	0.127859i
$436$	−4.35791	−	16.2639i	−0.208706	−	0.778901i
$437$	−9.28091	−	9.28091i	−0.443966	−	0.443966i
$438$	22.5048	−	38.9795i	1.07532	−	1.86251i
$439$	−17.2958	−	29.9571i	−0.825481	−	1.42978i	−0.901551	−	0.432673i	$-0.857570\pi$
$439$	−17.2958	−	29.9571i	−0.825481	−	1.42978i	0.0760695	−	0.997103i	$-0.475763\pi$
$440$	−13.3663	+	49.8838i	−0.637214	+	2.37812i
$441$	−1.90578	+	10.7139i	−0.0907516	+	0.510185i
$442$	−6.20181	−	10.6517i	−0.294990	−	0.506649i
$443$	7.97215			0.378768			0.189384	−	0.981903i	$-0.439351\pi$
$443$	7.97215			0.378768			0.189384	+	0.981903i	$0.439351\pi$
$444$	−2.59927	−	0.696472i	−0.123356	−	0.0330531i
$445$	11.1637	+	19.3361i	0.529209	+	0.916617i
$446$	−0.821959	+	1.42368i	−0.0389209	+	0.0674130i
$447$	12.9134	−	12.9134i	0.610784	−	0.610784i
$448$	−5.28101	−	30.0825i	−0.249504	−	1.42127i
$449$	−5.25579	−	19.6149i	−0.248036	−	0.925683i	−0.971833	−	0.235670i	$-0.924271\pi$
$449$	−5.25579	−	19.6149i	−0.248036	−	0.925683i	0.723797	−	0.690013i	$-0.242395\pi$
$450$	13.4631	−	13.4631i	0.634655	−	0.634655i
$451$	−19.2682	−	11.1245i	−0.907302	−	0.523831i
$452$	−61.2250	+	35.3483i	−2.87978	+	1.66264i
$453$	2.23797	−	8.35221i	0.105149	−	0.392421i
$454$	−12.3400			−0.579146
$455$	−23.2502	+	19.6246i	−1.08998	+	0.920015i
$456$	11.4767			0.537446
$457$	0.363747	−	1.35752i	0.0170154	−	0.0635022i	−0.956896	−	0.290430i	$-0.906202\pi$
$457$	0.363747	−	1.35752i	0.0170154	−	0.0635022i	0.973912	+	0.226928i	$0.0728682\pi$
$458$	2.17215	−	1.25409i	0.101498	−	0.0585998i
$459$	−6.84646	−	3.95280i	−0.319565	−	0.184501i
$460$	42.5412	−	42.5412i	1.98349	−	1.98349i
$461$	4.89285	+	18.2604i	0.227883	+	0.850469i	0.981229	+	0.192846i	$0.0617717\pi$
$461$	4.89285	+	18.2604i	0.227883	+	0.850469i	−0.753347	+	0.657624i	$0.771562\pi$
$462$	−5.54333	−	31.5768i	−0.257899	−	1.46908i
$463$	22.4573	−	22.4573i	1.04368	−	1.04368i	0.0446754	−	0.999002i	$-0.485775\pi$
$463$	22.4573	−	22.4573i	1.04368	−	1.04368i	0.999002	−	0.0446754i	$-0.0142253\pi$
$464$	−2.41026	+	4.17468i	−0.111893	+	0.193805i
$465$	−10.2073	−	17.6795i	−0.473352	−	0.819869i
$466$	3.02138	+	0.809576i	0.139963	+	0.0375029i
$467$	28.3889			1.31368			0.656841	−	0.754029i	$-0.271892\pi$
$467$	28.3889			1.31368			0.656841	+	0.754029i	$0.271892\pi$
$468$	19.5070	−	5.30343i	0.901711	−	0.245151i
$469$	−2.03853	+	23.1002i	−0.0941304	+	1.06667i
$470$	12.9368	−	48.2807i	0.596729	−	2.22702i
$471$	11.4231	+	19.7854i	0.526350	+	0.911665i
$472$	3.86302	−	6.69096i	0.177810	−	0.307976i
$473$	−18.9813	−	18.9813i	−0.872762	−	0.872762i
$474$	1.48305	+	5.53481i	0.0681187	+	0.254222i
$475$	12.5379	−	3.35953i	0.575280	−	0.154146i
$476$	10.5598	−	8.84721i	0.484009	−	0.405511i
$477$	5.89597	−	10.2121i	0.269958	−	0.467581i
$478$	44.1586	−	25.4950i	2.01977	−	1.16611i
$479$	−0.905222	+	3.37834i	−0.0413607	+	0.154360i	−0.983518	−	0.180811i	$-0.942128\pi$
$479$	−0.905222	+	3.37834i	−0.0413607	+	0.154360i	0.942157	+	0.335172i	$0.108794\pi$
$480$		−	12.8842i		−	0.588079i
$481$	−1.94194	−	1.11173i	−0.0885449	−	0.0506905i
$482$		−	8.30825i		−	0.378430i
$483$	−5.70185	+	15.6291i	−0.259443	+	0.711148i
$484$	−12.8373	−	22.2348i	−0.583512	−	1.01067i
$485$	17.3546	+	10.0197i	0.788033	+	0.454971i
$486$	23.6403	−	23.6403i	1.07235	−	1.07235i
$487$	−23.4826	+	6.29214i	−1.06410	+	0.285124i	−0.748066	−	0.663625i	$-0.769017\pi$
$487$	−23.4826	+	6.29214i	−1.06410	+	0.285124i	−0.316032	+	0.948749i	$0.602351\pi$
$488$	−19.2559	+	5.15960i	−0.871672	+	0.233564i
$489$	0.862092	+	0.862092i	0.0389851	+	0.0389851i
$490$	−40.4448	−	34.0411i	−1.82711	−	1.53782i
$491$	−5.24444	+	3.02788i	−0.236678	+	0.136646i	−0.613649	−	0.789579i	$-0.710299\pi$
$491$	−5.24444	+	3.02788i	−0.236678	+	0.136646i	0.376971	+	0.926225i	$0.376966\pi$
$492$	−21.8914	−	5.86579i	−0.986941	−	0.264450i
$493$	3.87934			0.174717
$494$	20.7142	+	5.46923i	0.931978	+	0.246072i
$495$			21.1054i			0.948615i
$496$	−9.22569	−	2.47202i	−0.414246	−	0.110997i
$497$	−20.6595	+	9.61475i	−0.926704	+	0.431280i
$498$	17.8377	+	10.2986i	0.799328	+	0.461492i
$499$	12.9362	+	12.9362i	0.579103	+	0.579103i	0.934656	−	0.355553i	$-0.115707\pi$
$499$	12.9362	+	12.9362i	0.579103	+	0.579103i	−0.355553	+	0.934656i	$0.615707\pi$
$500$	0.513471	+	1.91630i	0.0229631	+	0.0856995i
$501$	0.628339	+	2.34499i	0.0280721	+	0.104767i
$502$	−29.3281	−	29.3281i	−1.30898	−	1.30898i
$503$	7.01237	+	4.04859i	0.312666	+	0.180518i	0.648119	−	0.761539i	$-0.275556\pi$
$503$	7.01237	+	4.04859i	0.312666	+	0.180518i	−0.335453	+	0.942057i	$0.608889\pi$
$504$	6.60155	+	14.1849i	0.294056	+	0.631847i
$505$	41.0947	+	11.0113i	1.82869	+	0.489996i
$506$			52.7150i			2.34347i
$507$	−15.6289	+	0.114340i	−0.694104	+	0.00507804i
$508$	−4.26758			−0.189343
$509$	15.6029	+	4.18077i	0.691584	+	0.185309i	0.587458	−	0.809255i	$-0.300129\pi$
$509$	15.6029	+	4.18077i	0.691584	+	0.185309i	0.104126	+	0.994564i	$0.466795\pi$
$510$	11.3521	−	6.55416i	0.502681	−	0.290223i
$511$	34.2489	+	24.0198i	1.51508	+	1.06257i
$512$	−13.9135	−	13.9135i	−0.614896	−	0.614896i
$513$	13.2731	−	3.55652i	0.586023	−	0.157024i
$514$	15.6696	−	4.19864i	0.691154	−	0.185194i
$515$	−13.9252	+	13.9252i	−0.613619	+	0.613619i
$516$	−23.6806	−	13.6720i	−1.04248	−	0.601876i
$517$	14.0866	+	24.3987i	0.619527	+	1.07305i
$518$	1.33250	−	3.65244i	0.0585465	−	0.160479i
$519$		−	2.94610i		−	0.129320i
$520$	−11.1672	+	42.2949i	−0.489715	+	1.85475i
$521$		−	32.3470i		−	1.41715i	−0.705636	−	0.708574i	$-0.749339\pi$
$521$		−	32.3470i		−	1.41715i	0.705636	−	0.708574i	$-0.250661\pi$
$522$	−2.55991	+	9.55373i	−0.112044	+	0.418155i
$523$	18.4602	−	10.6580i	0.807210	−	0.466043i	−0.0387760	−	0.999248i	$-0.512346\pi$
$523$	18.4602	−	10.6580i	0.807210	−	0.466043i	0.845986	+	0.533205i	$0.179013\pi$
$524$	−17.4394	+	30.2060i	−0.761845	+	1.31956i
$525$	−10.5663	−	12.6116i	−0.461150	−	0.550417i
$526$	−39.8349	+	10.6737i	−1.73688	+	0.465397i
$527$	1.98937	+	7.42445i	0.0866585	+	0.323414i
$528$	−6.49191	−	6.49191i	−0.282524	−	0.282524i
$529$	2.17769	−	3.77187i	0.0946821	−	0.163994i
$530$	28.6419	+	49.6092i	1.24413	+	2.15489i
$531$	0.817205	−	3.04985i	0.0354637	−	0.132352i
$532$	−2.10494	+	23.8527i	−0.0912606	+	1.03415i
$533$	−16.3553	−	9.36315i	−0.708428	−	0.405563i
$534$	−19.9282			−0.862378
$535$	26.3314	+	7.05547i	1.13840	+	0.305034i
$536$	16.6708	+	28.8747i	0.720070	+	1.24720i
$537$	4.51426	−	7.81892i	0.194805	−	0.337411i
$538$	−0.280864	+	0.280864i	−0.0121089	+	0.0121089i
$539$	29.6869	−	2.55224i	1.27871	−	0.109933i
$540$	16.3021	+	60.8404i	0.701532	+	2.61815i
$541$	13.0949	−	13.0949i	0.562992	−	0.562992i	−0.367164	−	0.930156i	$-0.619671\pi$
$541$	13.0949	−	13.0949i	0.562992	−	0.562992i	0.930156	+	0.367164i	$0.119671\pi$
$542$	5.11440	+	2.95280i	0.219682	+	0.126834i
$543$	5.13637	−	2.96548i	0.220423	−	0.127261i
$544$	−1.25555	+	4.68576i	−0.0538311	+	0.200900i
$545$	14.8904			0.637833
$546$	−4.79325	−	26.7296i	−0.205132	−	1.14392i
$547$	−35.0943			−1.50053			−0.750263	−	0.661140i	$-0.770073\pi$
$547$	−35.0943			−1.50053			−0.750263	+	0.661140i	$0.770073\pi$
$548$	6.15643	−	22.9761i	0.262990	−	0.981490i
$549$	−7.05549	+	4.07349i	−0.301121	+	0.173852i
$550$	−45.1483	−	26.0664i	−1.92513	−	1.11148i
$551$	−4.76801	+	4.76801i	−0.203124	+	0.203124i
$552$	6.19086	+	23.1046i	0.263500	+	0.983397i
$553$	−5.24534	+	0.920824i	−0.223054	+	0.0391574i
$554$	−14.2820	+	14.2820i	−0.606782	+	0.606782i
$555$	1.18987	−	2.06092i	0.0505073	−	0.0874812i
$556$	40.9684	+	70.9594i	1.73745	+	3.00935i
$557$	9.16086	+	2.45464i	0.388158	+	0.104007i	0.447620	−	0.894224i	$-0.352272\pi$
$557$	9.16086	+	2.45464i	0.388158	+	0.104007i	−0.0594618	+	0.998231i	$0.518938\pi$
$558$	−19.5971			−0.829610
$559$	−16.1367	−	16.0191i	−0.682510	−	0.677535i
$560$	−15.0800	−	1.33077i	−0.637248	−	0.0562354i
$561$	−1.91227	+	7.13668i	−0.0807360	+	0.301311i
$562$	−26.4431	−	45.8008i	−1.11544	−	1.93199i
$563$	−15.8351	+	27.4272i	−0.667369	+	1.15592i	0.311268	+	0.950322i	$0.399246\pi$
$563$	−15.8351	+	27.4272i	−0.667369	+	1.15592i	−0.978637	+	0.205595i	$0.934087\pi$
$564$	20.2928	+	20.2928i	0.854479	+	0.854479i
$565$	−16.1815	−	60.3901i	−0.680760	−	2.54063i
$566$	21.9129	−	5.87155i	0.921069	−	0.246800i
$567$	−3.26153	−	3.89288i	−0.136971	−	0.163486i
$568$	−16.3813	+	28.3733i	−0.687345	+	1.19052i
$569$	−6.05848	+	3.49787i	−0.253985	+	0.146638i	−0.621587	−	0.783345i	$-0.713512\pi$
$569$	−6.05848	+	3.49787i	−0.253985	+	0.146638i	0.367603	+	0.929983i	$0.380179\pi$
$570$	−5.89708	+	22.0082i	−0.247002	+	0.921823i
$571$			15.2998i			0.640277i	0.947371	+	0.320139i	$0.103729\pi$
$571$			15.2998i			0.640277i	−0.947371	+	0.320139i	$0.896271\pi$
$572$	−27.8508	−	47.8340i	−1.16450	−	2.00004i
$573$			7.32009i			0.305801i
$574$	11.2225	−	30.7614i	0.468417	−	1.28396i
$575$	13.5266	+	23.4288i	0.564099	+	0.977049i
$576$	−15.5418	−	8.97304i	−0.647574	−	0.373877i
$577$	−29.5539	+	29.5539i	−1.23035	+	1.23035i	−0.266516	+	0.963831i	$0.585872\pi$
$577$	−29.5539	+	29.5539i	−1.23035	+	1.23035i	−0.963831	+	0.266516i	$0.914128\pi$
$578$	34.1139	−	9.14080i	1.41895	−	0.380207i
$579$	16.8244	−	4.50807i	0.699196	−	0.187349i
$580$	−21.8553	−	21.8553i	−0.907491	−	0.907491i
$581$	−10.9919	+	15.6729i	−0.456020	+	0.650222i
$582$	−15.4898	+	8.94304i	−0.642073	+	0.370701i
$583$	−31.1876	−	8.35668i	−1.29166	−	0.346098i
$584$	60.1449			2.48881
$585$	0.0653930	+	17.8770i	0.00270367	+	0.739125i
$586$			35.6145i			1.47122i
$587$	0.941084	+	0.252163i	0.0388427	+	0.0104079i	0.278188	−	0.960527i	$-0.410266\pi$
$587$	0.941084	+	0.252163i	0.0388427	+	0.0104079i	−0.239345	+	0.970934i	$0.576933\pi$
$588$	28.5370	−	10.3380i	1.17684	−	0.426331i
$589$	−11.5703	−	6.68012i	−0.476746	−	0.275250i
$590$	10.8459	+	10.8459i	0.446519	+	0.446519i
$591$	−5.20986	−	19.4435i	−0.214305	−	0.799797i
$592$	−0.288165	−	1.07545i	−0.0118435	−	0.0442006i
$593$	−27.9207	−	27.9207i	−1.14657	−	1.14657i	−0.987223	−	0.159344i	$-0.949062\pi$
$593$	−27.9207	−	27.9207i	−1.14657	−	1.14657i	−0.159344	−	0.987223i	$-0.550938\pi$
$594$	−47.7957	−	27.5949i	−1.96108	−	1.13223i
$595$	5.14042	+	11.0454i	0.210737	+	0.452816i
$596$	52.9167	+	14.1790i	2.16755	+	0.580794i
$597$			23.8226i			0.974994i
$598$	0.163333	+	44.6516i	0.00667917	+	1.82594i
$599$	16.5488			0.676164			0.338082	−	0.941117i	$-0.390222\pi$
$599$	16.5488			0.676164			0.338082	+	0.941117i	$0.390222\pi$
$600$	−22.8494	−	6.12248i	−0.932824	−	0.249949i
$601$	−9.99562	+	5.77097i	−0.407730	+	0.235403i	−0.689814	−	0.723987i	$-0.742308\pi$
$601$	−9.99562	+	5.77097i	−0.407730	+	0.235403i	0.282084	+	0.959390i	$0.408974\pi$
$602$	22.6845	−	32.3450i	0.924552	−	1.31828i
$603$	9.63495	+	9.63495i	0.392365	+	0.392365i
$604$	25.0550	−	6.71347i	1.01947	−	0.273167i
$605$	21.9316	−	5.87655i	0.891645	−	0.238916i
$606$	−26.8508	+	26.8508i	−1.09074	+	1.09074i
$607$	−18.5137	−	10.6889i	−0.751447	−	0.433848i	0.0747696	−	0.997201i	$-0.476178\pi$
$607$	−18.5137	−	10.6889i	−0.751447	−	0.433848i	−0.826216	+	0.563353i	$0.809511\pi$
$608$	−4.21600	−	7.30232i	−0.170981	−	0.296148i
$609$	8.02936	+	2.92929i	0.325366	+	0.118701i
$610$		−	39.5770i		−	1.60243i
$611$	12.0075	+	20.6230i	0.485770	+	0.834315i
$612$		−	8.09456i		−	0.327203i
$613$	8.07793	−	30.1473i	0.326265	−	1.21764i	−0.586770	−	0.809754i	$-0.699601\pi$
$613$	8.07793	−	30.1473i	0.326265	−	1.21764i	0.913034	−	0.407882i	$-0.133733\pi$
$614$	45.6568	−	26.3600i	1.84256	−	1.06380i
$615$	10.0213	−	17.3574i	0.404097	−	0.699917i
$616$	32.8382	−	27.5124i	1.32309	−	1.10851i
$617$	26.9421	−	7.21911i	1.08465	−	0.290630i	0.328149	−	0.944626i	$-0.393575\pi$
$617$	26.9421	−	7.21911i	1.08465	−	0.290630i	0.756498	+	0.653996i	$0.226909\pi$
$618$	−4.54929	−	16.9782i	−0.182999	−	0.682963i
$619$	34.0406	+	34.0406i	1.36821	+	1.36821i	0.862994	+	0.505214i	$0.168586\pi$
$619$	34.0406	+	34.0406i	1.36821	+	1.36821i	0.505214	+	0.862994i	$0.331414\pi$
$620$	30.6199	−	53.0352i	1.22972	−	2.12994i
$621$	14.3198	+	24.8026i	0.574633	+	0.995294i
$622$	−2.38621	+	8.90546i	−0.0956783	+	0.357076i
$623$	1.62813	−	18.4497i	0.0652298	−	0.739171i
$624$	−5.51901	−	5.47878i	−0.220937	−	0.219327i
$625$	24.1079			0.964316
$626$	−22.8141	−	6.11301i	−0.911834	−	0.244325i
$627$	−6.42121	−	11.1219i	−0.256438	−	0.444164i
$628$	−34.2672	+	59.3525i	−1.36741	+	2.36842i
$629$	−0.633571	+	0.633571i	−0.0252621	+	0.0252621i
$630$	−30.5937	+	5.37075i	−1.21888	+	0.213976i
$631$	−2.94853	−	11.0041i	−0.117379	−	0.438064i	0.882075	−	0.471109i	$-0.156146\pi$
$631$	−2.94853	−	11.0041i	−0.117379	−	0.438064i	−0.999454	+	0.0330448i	$0.989480\pi$
$632$	−5.41423	+	5.41423i	−0.215367	+	0.215367i
$633$	19.9156	+	11.4983i	0.791575	+	0.457016i
$634$	31.8379	−	18.3816i	1.26444	−	0.730026i
$635$	0.976791	−	3.64543i	0.0387628	−	0.144665i
$636$	−32.8896			−1.30416
$637$	25.1380	−	2.25382i	0.996005	−	0.0892998i
$638$	27.0820			1.07219
$639$	−3.46539	+	12.9330i	−0.137089	+	0.511622i
$640$	56.9382	−	32.8733i	2.25068	−	1.29943i
$641$	−16.9100	−	9.76301i	−0.667906	−	0.385616i	0.127377	−	0.991854i	$-0.459344\pi$
$641$	−16.9100	−	9.76301i	−0.667906	−	0.385616i	−0.795283	+	0.606239i	$0.792678\pi$
$642$	−17.2046	+	17.2046i	−0.679012	+	0.679012i
$643$	−9.35047	−	34.8964i	−0.368747	−	1.37618i	−0.862270	−	0.506449i	$-0.830958\pi$
$643$	−9.35047	−	34.8964i	−0.368747	−	1.37618i	0.493524	−	0.869732i	$-0.335709\pi$
$644$	−49.1552	+	8.62924i	−1.93698	+	0.340040i
$645$	17.0990	−	17.0990i	0.673272	−	0.673272i
$646$	4.28935	−	7.42937i	0.168762	−	0.292304i
$647$	2.89695	+	5.01767i	0.113891	+	0.197265i	0.917336	−	0.398114i	$-0.130335\pi$
$647$	2.89695	+	5.01767i	0.113891	+	0.197265i	−0.803445	+	0.595379i	$0.797002\pi$
$648$	−7.05301	−	1.88985i	−0.277069	−	0.0742403i
$649$	−8.64544			−0.339363
$650$	−38.3231	−	21.9393i	−1.50316	−	0.860532i
$651$	−1.48865	+	16.8691i	−0.0583448	+	0.661152i
$652$	−0.946581	+	3.53269i	−0.0370710	+	0.138351i
$653$	−18.1035	−	31.3562i	−0.708445	−	1.22706i	−0.965434	−	0.260648i	$-0.916064\pi$
$653$	−18.1035	−	31.3562i	−0.708445	−	1.22706i	0.256989	−	0.966414i	$-0.417270\pi$
$654$	−6.64516	+	11.5098i	−0.259846	+	0.450067i
$655$	−21.8108	−	21.8108i	−0.852217	−	0.852217i
$656$	−2.42697	−	9.05757i	−0.0947573	−	0.353639i
$657$	23.7421	−	6.36168i	0.926269	−	0.248193i
$658$	−31.7829	+	26.6283i	−1.23903	+	1.03808i
$659$	−10.3685	+	17.9588i	−0.403901	+	0.699576i	−0.994193	−	0.107613i	$-0.965679\pi$
$659$	−10.3685	+	17.9588i	−0.403901	+	0.699576i	0.590292	+	0.807190i	$0.299013\pi$
$660$	50.9796	−	29.4331i	1.98438	−	1.14568i
$661$	8.78410	−	32.7827i	0.341662	−	1.27510i	−0.554801	−	0.831983i	$-0.687206\pi$
$661$	8.78410	−	32.7827i	0.341662	−	1.27510i	0.896464	−	0.443117i	$-0.146128\pi$
$662$		−	34.6749i		−	1.34768i
$663$	−1.59765	+	6.05097i	−0.0620476	+	0.235000i
$664$			27.5234i			1.06811i
$665$	−19.8936	−	7.25763i	−0.771440	−	0.281439i
$666$	−1.14222	−	1.97839i	−0.0442603	−	0.0766611i
$667$	−12.1708	−	7.02683i	−0.471257	−	0.272080i
$668$	−5.14963	+	5.14963i	−0.199245	+	0.199245i
$669$	0.806257	−	0.216036i	0.0311717	−	0.00835243i
$670$	−63.9374	+	17.1320i	−2.47012	+	0.661866i
$671$	15.7737	+	15.7737i	0.608937	+	0.608937i
$672$	−6.13691	+	8.75039i	−0.236737	+	0.337554i
$673$	−35.7571	+	20.6444i	−1.37834	+	0.795783i	−0.991959	−	0.126558i	$-0.959607\pi$
$673$	−35.7571	+	20.6444i	−1.37834	+	0.795783i	−0.386377	+	0.922341i	$0.626274\pi$
$674$	27.0419	+	7.24584i	1.04161	+	0.279099i
$675$	−28.3233			−1.09016
$676$	−23.7389	−	40.4309i	−0.913034	−	1.55504i
$677$			45.2354i			1.73854i	0.494341	+	0.869268i	$0.335410\pi$
$677$			45.2354i			1.73854i	−0.494341	+	0.869268i	$0.664590\pi$
$678$	53.9009	+	14.4427i	2.07005	+	0.554669i
$679$	−7.01402	−	15.0712i	−0.269173	−	0.578380i
$680$	15.1695	+	8.75810i	0.581723	+	0.335858i
$681$	4.43048	+	4.43048i	0.169776	+	0.169776i
$682$	13.8880	+	51.8307i	0.531799	+	1.98470i
$683$	11.2563	+	42.0091i	0.430710	+	1.60743i	0.751129	+	0.660156i	$0.229510\pi$
$683$	11.2563	+	42.0091i	0.430710	+	1.60743i	−0.320419	+	0.947276i	$0.603824\pi$
$684$	9.94884	+	9.94884i	0.380403	+	0.380403i
$685$	18.2174	+	10.5178i	0.696051	+	0.401866i
$686$	11.2542	+	42.3838i	0.429686	+	1.61822i
$687$	−1.23013	−	0.329613i	−0.0469325	−	0.0125755i
$688$		−	11.3136i		−	0.431326i
$689$	−26.4429	−	6.98179i	−1.00740	−	0.265985i
$690$	−47.4874			−1.80781
$691$	−20.7975	−	5.57267i	−0.791174	−	0.211994i	−0.159468	−	0.987203i	$-0.550978\pi$
$691$	−20.7975	−	5.57267i	−0.791174	−	0.211994i	−0.631705	+	0.775209i	$0.717645\pi$
$692$	7.65370	−	4.41887i	0.290950	−	0.167980i
$693$	10.0528	−	14.3339i	0.381874	−	0.544499i
$694$	−16.7659	−	16.7659i	−0.636425	−	0.636425i
$695$	−69.9917	+	18.7542i	−2.65494	+	0.711388i
$696$	11.8699	−	3.18052i	0.449926	−	0.120557i
$697$	−5.33603	+	5.33603i	−0.202117	+	0.202117i
$698$	34.8315	+	20.1100i	1.31839	+	0.761174i
$699$	−0.794111	−	1.37544i	−0.0300360	−	0.0520239i
$700$	16.9155	−	46.3664i	0.639347	−	1.75249i
$701$			8.77295i			0.331350i	0.986180	+	0.165675i	$0.0529803\pi$
$701$			8.77295i			0.331350i	−0.986180	+	0.165675i	$0.947020\pi$
$702$	−40.5703	−	23.2258i	−1.53123	−	0.876602i
$703$		−	1.55742i		−	0.0587391i
$704$	−12.7180	+	47.4642i	−0.479327	+	1.78887i
$705$	−21.9791	+	12.6896i	−0.827781	+	0.477920i
$706$	42.7152	−	73.9850i	1.60761	−	2.78446i
$707$	−22.6650	−	27.0524i	−0.852405	−	1.01741i
$708$	−8.50651	+	2.27931i	−0.319694	+	0.0856618i
$709$	−10.9783	−	40.9718i	−0.412300	−	1.53873i	−0.790182	−	0.612872i	$-0.790014\pi$
$709$	−10.9783	−	40.9718i	−0.412300	−	1.53873i	0.377881	−	0.925854i	$-0.376653\pi$
$710$	−45.9926	−	45.9926i	−1.72607	−	1.72607i
$711$	−1.56458	+	2.70994i	−0.0586765	+	0.101631i
$712$	−13.3147	−	23.0617i	−0.498989	−	0.864274i
$713$	7.20689	−	26.8965i	0.269900	−	1.00728i
$714$	−10.8317	−	0.955871i	−0.405368	−	0.0357726i
$715$	47.2352	−	12.8420i	1.76650	−	0.480264i
$716$	27.0838			1.01217
$717$	−25.0080	−	6.70086i	−0.933939	−	0.250248i
$718$	4.10165	+	7.10426i	0.153072	+	0.265129i
$719$	2.80010	−	4.84991i	0.104426	−	0.180871i	−0.809078	−	0.587702i	$-0.800033\pi$
$719$	2.80010	−	4.84991i	0.104426	−	0.180871i	0.913504	+	0.406831i	$0.133366\pi$
$720$	−6.28980	+	6.28980i	−0.234407	+	0.234407i
$721$	16.0902	−	2.82465i	0.599231	−	0.105196i
$722$	−7.78453	−	29.0523i	−0.289710	−	1.08121i
$723$	−2.98294	+	2.98294i	−0.110937	+	0.110937i
$724$	15.4081	+	8.89587i	0.572637	+	0.330612i
$725$	12.0364	−	6.94923i	0.447021	−	0.258088i
$726$	−5.24509	+	19.5749i	−0.194664	+	0.726494i
$727$	32.0200			1.18756			0.593778	−	0.804629i	$-0.297636\pi$
$727$	32.0200			1.18756			0.593778	+	0.804629i	$0.297636\pi$
$728$	27.7300	−	23.4058i	1.02774	−	0.867478i
$729$	−22.7339			−0.841996
$730$	−30.9043	+	115.336i	−1.14382	+	4.26879i
$731$	−7.88490	+	4.55235i	−0.291633	+	0.168375i
$732$	19.6789	+	11.3616i	0.727352	+	0.419937i
$733$	0.647616	−	0.647616i	0.0239202	−	0.0239202i	−0.695046	−	0.718966i	$-0.744616\pi$
$733$	0.647616	−	0.647616i	0.0239202	−	0.0239202i	0.718966	+	0.695046i	$0.244616\pi$
$734$	7.77195	+	29.0053i	0.286868	+	1.07061i
$735$	2.29914	+	26.7429i	0.0848050	+	0.986428i
$736$	12.4266	−	12.4266i	0.458051	−	0.458051i
$737$	18.6546	−	32.3108i	0.687152	−	1.19018i
$738$	−9.61998	−	16.6623i	−0.354116	−	0.613348i
$739$	−8.47234	−	2.27016i	−0.311660	−	0.0835090i	0.0995988	−	0.995028i	$-0.468244\pi$
$739$	−8.47234	−	2.27016i	−0.311660	−	0.0835090i	−0.411259	+	0.911519i	$0.634911\pi$
$740$	7.13877			0.262427
$741$	−5.47347	−	9.40074i	−0.201073	−	0.345345i
$742$	4.17719	−	47.3351i	0.153349	−	1.73773i
$743$	−9.56609	+	35.7011i	−0.350946	+	1.30975i	0.534564	+	0.845128i	$0.320476\pi$
$743$	−9.56609	+	35.7011i	−0.350946	+	1.30975i	−0.885510	+	0.464620i	$0.846191\pi$
$744$	12.1740	+	21.0860i	0.446321	+	0.773050i
$745$	−24.2238	+	41.9569i	−0.887492	+	1.53718i
$746$	50.2933	+	50.2933i	1.84137	+	1.84137i
$747$	2.91122	+	10.8648i	0.106516	+	0.397523i
$748$	−21.4087	+	5.73643i	−0.782778	+	0.209745i
$749$	−14.5226	−	17.3338i	−0.530643	−	0.633363i
$750$	0.782967	−	1.35614i	0.0285899	−	0.0495192i
$751$	−10.7508	+	6.20698i	−0.392303	+	0.226496i	−0.683157	−	0.730271i	$-0.739394\pi$
$751$	−10.7508	+	6.20698i	−0.392303	+	0.226496i	0.290855	+	0.956767i	$0.406060\pi$
$752$	−3.07320	+	11.4693i	−0.112068	+	0.418243i
$753$			21.0595i			0.767452i
$754$	22.9395	−	0.0839112i	0.835408	−	0.00305586i
$755$			22.9390i			0.834835i
$756$	17.9074	−	49.0852i	0.651286	−	1.78521i
$757$	11.7793	+	20.4023i	0.428124	+	0.741533i	0.996707	−	0.0810934i	$-0.0258412\pi$
$757$	11.7793	+	20.4023i	0.428124	+	0.741533i	−0.568582	+	0.822626i	$0.692508\pi$
$758$	−24.6307	−	14.2206i	−0.894628	−	0.516514i
$759$	18.9264	−	18.9264i	0.686986	−	0.686986i
$760$	−29.4088	+	7.88007i	−1.06677	+	0.285840i
$761$	13.0838	−	3.50579i	0.474286	−	0.127085i	−0.0137545	−	0.999905i	$-0.504378\pi$
$761$	13.0838	−	3.50579i	0.474286	−	0.127085i	0.488041	+	0.872821i	$0.337712\pi$
$762$	2.38189	+	2.38189i	0.0862866	+	0.0862866i
$763$	−10.1129	−	7.09249i	−0.366112	−	0.256765i
$764$	−19.0169	+	10.9794i	−0.688008	+	0.397222i
$765$	6.91450	+	1.85273i	0.249994	+	0.0669857i
$766$	13.5524			0.489667
$767$	−7.32301	+	0.0267871i	−0.264419	+	0.000967225i
$768$			30.9242i			1.11588i
$769$	29.8604	+	8.00107i	1.07679	+	0.288526i	0.753282	−	0.657698i	$-0.228470\pi$
$769$	29.8604	+	8.00107i	1.07679	+	0.288526i	0.323512	+	0.946224i	$0.395136\pi$
$770$	35.8857	+	77.1087i	1.29323	+	2.77880i
$771$	−7.13334	−	4.11844i	−0.256901	−	0.148322i
$772$	36.9465	+	36.9465i	1.32973	+	1.32973i
$773$	5.17138	+	19.2999i	0.186002	+	0.694167i	0.994414	+	0.105551i	$0.0336606\pi$
$773$	5.17138	+	19.2999i	0.186002	+	0.694167i	−0.808412	+	0.588617i	$0.799673\pi$
$774$	−6.00804	−	22.4223i	−0.215954	−	0.805953i
$775$	19.4721	+	19.4721i	0.699460	+	0.699460i
$776$	−20.6985	−	11.9503i	−0.743032	−	0.428990i
$777$	−1.78976	+	0.832938i	−0.0642072	+	0.0298815i
$778$	−37.6193	−	10.0801i	−1.34872	−	0.361388i
$779$		−	13.1168i		−	0.469958i
$780$	43.0904	−	25.0889i	1.54289	−	0.898326i
$781$	36.6613			1.31185
$782$	17.2704	+	4.62759i	0.617588	+	0.165482i
$783$	12.7422	−	7.35671i	0.455369	−	0.262907i
$784$	9.60787	+	8.08664i	0.343138	+	0.288809i
$785$	−42.8565	−	42.8565i	−1.52961	−	1.52961i
$786$	26.5926	−	7.12546i	0.948526	−	0.254157i
$787$	−47.9041	+	12.8359i	−1.70760	+	0.457549i	−0.974834	−	0.222934i	$-0.928437\pi$
$787$	−47.9041	+	12.8359i	−1.70760	+	0.457549i	−0.732764	+	0.680483i	$0.761770\pi$
$788$	42.6980	−	42.6980i	1.52105	−	1.52105i
$789$	18.1343	+	10.4698i	0.645597	+	0.372736i
$790$	−7.60056	−	13.1646i	−0.270416	−	0.468374i
$791$	−17.7749	+	48.7219i	−0.632001	+	1.73235i
$792$		−	25.1719i		−	0.894445i
$793$	13.4098	+	13.3121i	0.476196	+	0.472725i
$794$		−	26.7480i		−	0.949250i
$795$	7.52797	−	28.0948i	0.266990	−	0.996418i
$796$	−61.8889	+	35.7316i	−2.19360	+	1.26647i
$797$	−3.67854	+	6.37141i	−0.130300	+	0.225687i	−0.923792	−	0.382894i	$-0.874928\pi$
$797$	−3.67854	+	6.37141i	−0.130300	+	0.225687i	0.793492	+	0.608581i	$0.208261\pi$
$798$	14.4879	−	12.1382i	0.512866	−	0.429688i
$799$	9.23003	−	2.47318i	0.326535	−	0.0874948i
$800$	4.49822	+	16.7876i	0.159036	+	0.593531i
$801$	−7.69525	−	7.69525i	−0.271898	−	0.271898i
$802$	−28.6598	+	49.6402i	−1.01201	+	1.75286i
$803$	−33.6510	−	58.2853i	−1.18752	−	2.05684i
$804$	9.83634	−	36.7097i	0.346901	−	1.29465i
$805$	3.87972	−	43.9642i	0.136742	−	1.54953i
$806$	11.9243	+	43.8596i	0.420014	+	1.54489i
$807$	0.201679			0.00709943
$808$	−49.0128	−	13.1329i	−1.72426	−	0.462015i
$809$	−20.3898	−	35.3162i	−0.716867	−	1.24165i	−0.962235	−	0.272220i	$-0.912242\pi$
$809$	−20.3898	−	35.3162i	−0.716867	−	1.24165i	0.245368	−	0.969430i	$-0.421091\pi$
$810$	7.24811	−	12.5541i	0.254673	−	0.441106i
$811$	−2.15658	+	2.15658i	−0.0757278	+	0.0757278i	−0.743956	−	0.668228i	$-0.767053\pi$
$811$	−2.15658	+	2.15658i	−0.0757278	+	0.0757278i	0.668228	+	0.743956i	$0.267053\pi$
$812$	4.43322	+	25.2532i	0.155576	+	0.886213i
$813$	−0.776086	−	2.89639i	−0.0272185	−	0.101581i
$814$	−4.42302	+	4.42302i	−0.155027	+	0.155027i
$815$	−2.80102	−	1.61717i	−0.0981153	−	0.0566469i
$816$	−2.69676	+	1.55697i	−0.0944054	+	0.0545050i
$817$	4.09596	−	15.2863i	0.143299	−	0.534801i
$818$	0.854311			0.0298703
$819$	8.47068	−	12.1725i	0.295989	−	0.425341i
$820$	60.1238			2.09961
$821$	9.67009	−	36.0893i	0.337488	−	1.25952i	−0.563658	−	0.826009i	$-0.690606\pi$
$821$	9.67009	−	36.0893i	0.337488	−	1.25952i	0.901146	−	0.433516i	$-0.142727\pi$
$822$	−16.2599	+	9.38764i	−0.567128	+	0.327432i
$823$	31.8883	+	18.4107i	1.11156	+	0.641757i	0.939232	−	0.343283i	$-0.111539\pi$
$823$	31.8883	+	18.4107i	1.11156	+	0.641757i	0.172324	+	0.985040i	$0.444872\pi$
$824$	16.6083	−	16.6083i	0.578578	−	0.578578i
$825$	6.85105	+	25.5685i	0.238523	+	0.890179i
$826$	−2.20003	−	12.5322i	−0.0765490	−	0.436050i
$827$	−16.2525	+	16.2525i	−0.565154	+	0.565154i	−0.930767	−	0.365613i	$-0.880859\pi$
$827$	−16.2525	+	16.2525i	−0.565154	+	0.565154i	0.365613	+	0.930767i	$0.380859\pi$
$828$	−14.6621	+	25.3954i	−0.509542	+	0.882552i
$829$	−6.86086	−	11.8834i	−0.238287	−	0.412726i	0.721936	−	0.691960i	$-0.243253\pi$
$829$	−6.86086	−	11.8834i	−0.238287	−	0.412726i	−0.960223	+	0.279234i	$0.909919\pi$
$830$	−52.7800	−	14.1424i	−1.83202	−	0.490888i
$831$	10.2554			0.355756
$832$	−10.6256	+	40.2434i	−0.368375	+	1.39519i
$833$	1.76991	−	9.95001i	0.0613236	−	0.344748i
$834$	16.7390	−	62.4708i	0.579624	−	2.16319i
$835$	−3.22021	−	5.57757i	−0.111440	−	0.193020i
$836$	19.2624	−	33.3634i	0.666203	−	1.15390i
$837$	20.6139	+	20.6139i	0.712521	+	0.712521i
$838$	−11.2643	−	42.0390i	−0.389119	−	1.45221i
$839$	−4.02716	+	1.07907i	−0.139033	+	0.0372537i	−0.327664	−	0.944794i	$-0.606262\pi$
$839$	−4.02716	+	1.07907i	−0.139033	+	0.0372537i	0.188631	+	0.982048i	$0.439595\pi$
$840$	24.7841	+	29.5817i	0.855133	+	1.02067i
$841$	10.8900	−	18.8620i	0.375517	−	0.650415i
$842$	60.1565	−	34.7314i	2.07313	−	1.19692i
$843$	−6.95006	+	25.9380i	−0.239373	+	0.893351i
$844$			68.9853i			2.37457i
$845$	39.9702	−	11.0240i	1.37502	−	0.379238i
$846$			24.3630i			0.837617i
$847$	−17.6941	−	6.45521i	−0.607977	−	0.221804i
$848$	−6.80403	−	11.7849i	−0.233651	−	0.404696i
$849$	−9.97555	−	5.75939i	−0.342360	−	0.197662i
$850$	−12.5032	+	12.5032i	−0.428855	+	0.428855i
$851$	3.13535	−	0.840114i	0.107478	−	0.0287987i
$852$	36.0722	−	9.66552i	1.23581	−	0.331135i
$853$	−3.44436	−	3.44436i	−0.117933	−	0.117933i	0.645678	−	0.763610i	$-0.276575\pi$
$853$	−3.44436	−	3.44436i	−0.117933	−	0.117933i	−0.763610	+	0.645678i	$0.776575\pi$
$854$	−18.8511	+	26.8791i	−0.645072	+	0.919783i
$855$	−10.7756	+	6.22130i	−0.368518	+	0.212764i
$856$	−31.4048	−	8.41490i	−1.07340	−	0.287615i
$857$	48.6245			1.66098			0.830491	−	0.557032i	$-0.188060\pi$
$857$	48.6245			1.66098			0.830491	+	0.557032i	$0.188060\pi$
$858$	−11.1533	+	42.2423i	−0.380769	+	1.44213i
$859$		−	25.0980i		−	0.856333i	−0.903700	−	0.428167i	$-0.859160\pi$
$859$		−	25.0980i		−	0.856333i	0.903700	−	0.428167i	$-0.140840\pi$
$860$	70.0684	+	18.7748i	2.38931	+	0.640214i
$861$	−15.0736	+	7.01513i	−0.513707	+	0.239075i
$862$	19.7898	+	11.4256i	0.674042	+	0.389158i
$863$	36.7571	+	36.7571i	1.25123	+	1.25123i	0.955170	+	0.296057i	$0.0956718\pi$
$863$	36.7571	+	36.7571i	1.25123	+	1.25123i	0.296057	+	0.955170i	$0.404328\pi$
$864$	4.76198	+	17.7720i	0.162006	+	0.604614i
$865$	2.02284	+	7.54933i	0.0687785	+	0.256685i
$866$	45.8622	+	45.8622i	1.55846	+	1.55846i
$867$	−15.5299	−	8.96618i	−0.527423	−	0.304508i
$868$	−46.0572	+	21.4346i	−1.56328	+	0.727538i
$869$	8.27609	+	2.21757i	0.280747	+	0.0752259i
$870$			24.3964i			0.827115i
$871$	15.7011	−	27.4262i	0.532010	−	0.929303i
$872$	−17.7594			−0.601409
$873$	−9.43472	−	2.52802i	−0.319317	−	0.0855607i
$874$	−26.9143	+	15.5390i	−0.910390	+	0.525614i
$875$	1.19156	+	0.835673i	0.0402819	+	0.0282509i
$876$	−48.4768	−	48.4768i	−1.63788	−	1.63788i
$877$	32.3325	−	8.66346i	1.09179	−	0.292544i	0.332373	−	0.943148i	$-0.392151\pi$
$877$	32.3325	−	8.66346i	1.09179	−	0.292544i	0.759417	+	0.650604i	$0.225484\pi$
$878$	−79.1153	+	21.1989i	−2.67001	+	0.715428i
$879$	12.7868	−	12.7868i	0.431288	−	0.431288i
$880$	21.0928	+	12.1779i	0.711038	+	0.410518i
$881$	−26.0483	−	45.1170i	−0.877590	−	1.52003i	−0.853978	−	0.520309i	$-0.825817\pi$
$881$	−26.0483	−	45.1170i	−0.877590	−	1.52003i	−0.0236116	−	0.999721i	$-0.507517\pi$
$882$	23.3361	+	10.9246i	0.785769	+	0.367851i
$883$			22.4598i			0.755831i	0.925840	+	0.377916i	$0.123359\pi$
$883$			22.4598i			0.755831i	−0.925840	+	0.377916i	$0.876641\pi$
$884$	−18.1162	+	4.92531i	−0.609313	+	0.165656i
$885$		−	7.78809i		−	0.261794i
$886$	4.88561	−	18.2333i	0.164135	−	0.612561i
$887$	10.3759	−	5.99053i	0.348389	−	0.201142i	−0.315587	−	0.948897i	$-0.602201\pi$
$887$	10.3759	−	5.99053i	0.348389	−	0.201142i	0.663975	+	0.747754i	$0.268868\pi$
$888$	−1.41914	+	2.45801i	−0.0476231	+	0.0824856i
$889$	−2.39977	+	2.01057i	−0.0804856	+	0.0674323i
$890$	51.0656	−	13.6830i	1.71172	−	0.458655i
$891$	2.11474	+	7.89231i	0.0708464	+	0.264402i
$892$	1.77055	+	1.77055i	0.0592824	+	0.0592824i
$893$	−8.30469	+	14.3842i	−0.277906	+	0.481347i
$894$	−21.6209	−	37.4485i	−0.723110	−	1.25246i
$895$	−6.19911	+	23.1354i	−0.207213	+	0.773330i
$896$	−54.3281	−	4.79430i	−1.81497	−	0.160166i
$897$	15.9728	−	16.0901i	0.533315	−	0.537231i
$898$	−48.0827			−1.60454
$899$	−13.8179	−	3.70250i	−0.460853	−	0.123485i
$900$	−14.5001	−	25.1149i	−0.483337	−	0.837165i
$901$	−5.47560	+	9.48401i	−0.182419	+	0.315958i
$902$	−37.2513	+	37.2513i	−1.24033	+	1.24033i
$903$	−19.7574	+	3.46843i	−0.657486	+	0.115422i
$904$	19.2993	+	72.0259i	0.641885	+	2.39555i
$905$	−11.1257	+	11.1257i	−0.369830	+	0.369830i
$906$	−17.7311	−	10.2371i	−0.589076	−	0.340103i
$907$	−0.460660	+	0.265962i	−0.0152959	+	0.00883112i	−0.507628	−	0.861576i	$-0.669478\pi$
$907$	−0.460660	+	0.265962i	−0.0152959	+	0.00883112i	0.492333	+	0.870407i	$0.336144\pi$
$908$	−4.86469	+	18.1553i	−0.161440	+	0.602504i
$909$	−20.7368			−0.687798
$910$	30.6355	+	65.2028i	1.01556	+	2.16145i
$911$	2.16430			0.0717065			0.0358532	−	0.999357i	$-0.488585\pi$
$911$	2.16430			0.0717065			0.0358532	+	0.999357i	$0.488585\pi$
$912$	1.40088	−	5.22816i	0.0463878	−	0.173122i
$913$	26.6724	−	15.3993i	0.882727	−	0.509642i
$914$	−2.88191	−	1.66387i	−0.0953252	−	0.0550360i
$915$	−14.2095	+	14.2095i	−0.469750	+	0.469750i
$916$	−0.988776	−	3.69016i	−0.0326701	−	0.121926i
$917$	4.42419	+	25.2018i	0.146100	+	0.832235i
$918$	−13.2363	+	13.2363i	−0.436864	+	0.436864i
$919$	12.9020	−	22.3470i	0.425599	−	0.737158i	−0.570878	−	0.821035i	$-0.693397\pi$
$919$	12.9020	−	22.3470i	0.425599	−	0.737158i	0.996476	+	0.0838769i	$0.0267302\pi$
$920$	−31.7279	−	54.9543i	−1.04604	−	1.81179i
$921$	−25.8564	−	6.92820i	−0.851997	−	0.228292i
$922$	44.7623			1.47417
$923$	31.0535	−	0.113592i	1.02214	−	0.00373892i
$924$	−48.6426	−	4.29258i	−1.60022	−	0.141215i
$925$	−0.830835	+	3.10072i	−0.0273177	+	0.101951i
$926$	−37.6001	−	65.1252i	−1.23562	−	2.14015i
$927$	4.79941	−	8.31282i	0.157633	−	0.273029i
$928$	−6.38410	−	6.38410i	−0.209568	−	0.209568i
$929$	5.37770	+	20.0699i	0.176437	+	0.658470i	0.996302	+	0.0859148i	$0.0273813\pi$
$929$	5.37770	+	20.0699i	0.176437	+	0.658470i	−0.819866	+	0.572556i	$0.805952\pi$
$930$	−46.6908	+	12.5108i	−1.53105	+	0.410244i
$931$	10.0540	+	14.4047i	0.329506	+	0.472094i
$932$	2.38218	−	4.12605i	0.0780308	−	0.135153i
$933$	4.05408	−	2.34063i	0.132725	−	0.0766286i
$934$	17.3977	−	64.9291i	0.569270	−	2.12455i
$935$		−	19.6006i		−	0.641008i
$936$	−0.0779928	−	21.3216i	−0.00254927	−	0.696917i
$937$		−	37.2049i		−	1.21543i	−0.794154	−	0.607716i	$-0.792086\pi$
$937$		−	37.2049i		−	1.21543i	0.794154	−	0.607716i	$-0.207914\pi$
$938$	51.5838	+	18.8190i	1.68427	+	0.614461i
$939$	5.99623	+	10.3858i	0.195680	+	0.338927i
$940$	−65.9331	−	38.0665i	−2.15050	−	1.24159i
$941$	31.5449	−	31.5449i	1.02833	−	1.02833i	0.0287483	−	0.999587i	$-0.490848\pi$
$941$	31.5449	−	31.5449i	1.02833	−	1.02833i	0.999587	−	0.0287483i	$-0.00915212\pi$
$942$	52.2524	−	14.0010i	1.70247	−	0.456177i
$943$	26.4064	−	7.07556i	0.859910	−	0.230412i
$944$	−2.57650	−	2.57650i	−0.0838580	−	0.0838580i
$945$	37.8306	+	26.5317i	1.23063	+	0.863077i
$946$	−55.0452	+	31.7803i	−1.78967	+	1.03327i
$947$	−7.57686	−	2.03021i	−0.246215	−	0.0659731i	0.133601	−	0.991035i	$-0.457346\pi$
$947$	−7.57686	−	2.03021i	−0.246215	−	0.0659731i	−0.379816	+	0.925062i	$0.624013\pi$
$948$	8.72774			0.283464
$949$	−28.6843	−	49.2656i	−0.931131	−	1.59923i
$950$		−	30.7347i		−	0.997166i
$951$	−18.0304	−	4.83124i	−0.584677	−	0.156664i
$952$	−6.13087	−	13.1736i	−0.198703	−	0.426958i
$953$	28.7075	+	16.5743i	0.929926	+	0.536893i	0.886788	−	0.462176i	$-0.152931\pi$
$953$	28.7075	+	16.5743i	0.929926	+	0.536893i	0.0431379	+	0.999069i	$0.486265\pi$
$954$	−19.7432	−	19.7432i	−0.639210	−	0.639210i
$955$	−5.02608	−	18.7576i	−0.162640	−	0.606981i
$956$	−20.1013	−	75.0190i	−0.650122	−	2.42629i
$957$	−9.72335	−	9.72335i	−0.314311	−	0.314311i
$958$	7.17194	+	4.14072i	0.231715	+	0.133781i
$959$	−7.36272	−	15.8205i	−0.237755	−	0.510870i
$960$	−42.7573	−	11.4568i	−1.37998	−	0.369766i
$961$			2.65603i			0.0856782i
$962$	−3.73276	+	3.76017i	−0.120349	+	0.121233i
$963$	−13.2871			−0.428171
$964$	−12.2235	−	3.27528i	−0.393693	−	0.105490i
$965$	−40.0168	+	23.1037i	−1.28818	+	0.743734i
$966$	32.2515	+	22.6189i	1.03767	+	0.727752i
$967$	−21.9068	−	21.9068i	−0.704477	−	0.704477i	0.260892	−	0.965368i	$-0.415984\pi$
$967$	−21.9068	−	21.9068i	−0.704477	−	0.704477i	−0.965368	+	0.260892i	$0.915984\pi$
$968$	−26.1573	+	7.00883i	−0.840728	+	0.225272i
$969$	−4.20741	+	1.12737i	−0.135161	+	0.0362164i
$970$	33.5519	−	33.5519i	1.07729	−	1.07729i
$971$	17.9328	+	10.3535i	0.575490	+	0.332259i	0.759339	−	0.650695i	$-0.225522\pi$
$971$	17.9328	+	10.3535i	0.575490	+	0.332259i	−0.183849	+	0.982954i	$0.558856\pi$
$972$	−25.4613	−	44.1003i	−0.816672	−	1.41452i
$973$	56.4683	+	20.6009i	1.81029	+	0.660436i
$974$			57.5638i			1.84446i
$975$	5.88232	+	21.6362i	0.188385	+	0.692914i
$976$			9.40172i			0.300942i
$977$	−4.63057	+	17.2815i	−0.148145	+	0.552885i	0.851450	+	0.524436i	$0.175724\pi$
$977$	−4.63057	+	17.2815i	−0.148145	+	0.552885i	−0.999595	+	0.0284497i	$0.990943\pi$
$978$	2.50004	−	1.44340i	0.0799423	−	0.0461547i
$979$	−14.8991	+	25.8060i	−0.476177	+	0.824763i
$980$	−66.0272	+	46.0847i	−2.10916	+	1.47212i
$981$	−7.01050	+	1.87846i	−0.223828	+	0.0599746i
$982$	3.71118	+	13.8503i	0.118429	+	0.441981i
$983$	31.6634	+	31.6634i	1.00990	+	1.00990i	0.999950	+	0.00995384i	$0.00316846\pi$
$983$	31.6634	+	31.6634i	1.00990	+	1.00990i	0.00995384	+	0.999950i	$0.496832\pi$
$984$	−11.9522	+	20.7018i	−0.381021	+	0.659948i
$985$	26.7003	+	46.2463i	0.850742	+	1.47353i
$986$	2.37740	−	8.87257i	0.0757117	−	0.282560i
$987$	20.9716	+	1.85068i	0.667532	+	0.0589079i
$988$	16.2126	−	28.3198i	0.515791	−	0.900971i
$989$	32.9835			1.04881
$990$	48.2707	+	12.9341i	1.53414	+	0.411073i
$991$	12.5780	+	21.7857i	0.399553	+	0.692045i	0.993671	−	0.112332i	$-0.0358322\pi$
$991$	12.5780	+	21.7857i	0.399553	+	0.692045i	−0.594118	+	0.804378i	$0.702499\pi$
$992$	8.94431	−	15.4920i	0.283982	−	0.491871i
$993$	−12.4494	+	12.4494i	−0.395071	+	0.395071i
$994$	9.32934	+	53.1432i	0.295909	+	1.68560i
$995$	−16.3569	−	61.0449i	−0.518550	−	1.93525i
$996$	22.1838	−	22.1838i	0.702922	−	0.702922i
$997$	−10.3336	−	5.96610i	−0.327268	−	0.188948i	0.327359	−	0.944900i	$-0.393841\pi$
$997$	−10.3336	−	5.96610i	−0.327268	−	0.188948i	−0.654628	+	0.755952i	$0.727175\pi$
$998$	37.5145	−	21.6590i	1.18750	−	0.685604i
$999$	−0.879553	+	3.28254i	−0.0278278	+	0.103855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.bc.a.76.7	yes	32
3.2	odd	2		819.2.fm.g.622.1		32
7.2	even	3		637.2.x.b.570.1		32
7.3	odd	6		637.2.bb.b.362.7		32
7.4	even	3		637.2.bb.b.362.8		32
7.5	odd	6		637.2.x.b.570.2		32
7.6	odd	2	inner	91.2.bc.a.76.8	yes	32
13.6	odd	12	inner	91.2.bc.a.6.8	yes	32
21.20	even	2		819.2.fm.g.622.2		32
39.32	even	12		819.2.fm.g.370.2		32
91.6	even	12	inner	91.2.bc.a.6.7	✓	32
91.19	even	12		637.2.bb.b.227.8		32
91.32	odd	12		637.2.x.b.19.1		32
91.45	even	12		637.2.x.b.19.2		32
91.58	odd	12		637.2.bb.b.227.7		32
273.188	odd	12		819.2.fm.g.370.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.7	✓	32	91.6	even	12	inner
91.2.bc.a.6.8	yes	32	13.6	odd	12	inner
91.2.bc.a.76.7	yes	32	1.1	even	1	trivial
91.2.bc.a.76.8	yes	32	7.6	odd	2	inner
637.2.x.b.19.1		32	91.32	odd	12
637.2.x.b.19.2		32	91.45	even	12
637.2.x.b.570.1		32	7.2	even	3
637.2.x.b.570.2		32	7.5	odd	6
637.2.bb.b.227.7		32	91.58	odd	12
637.2.bb.b.227.8		32	91.19	even	12
637.2.bb.b.362.7		32	7.3	odd	6
637.2.bb.b.362.8		32	7.4	even	3
819.2.fm.g.370.1		32	273.188	odd	12
819.2.fm.g.370.2		32	39.32	even	12
819.2.fm.g.622.1		32	3.2	odd	2
819.2.fm.g.622.2		32	21.20	even	2

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.612835 - 2.28713i) q^{2} +(-1.04118 + 0.601128i) q^{3} +(-3.12335 - 1.80327i) q^{4} +(2.25527 - 2.25527i) q^{5} +(0.736784 + 2.74971i) q^{6} +(-2.60590 + 0.457468i) q^{7} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 + 1.34631i) q^{9} +O(q^{10})\)	\(q+(0.612835 - 2.28713i) q^{2} +(-1.04118 + 0.601128i) q^{3} +(-3.12335 - 1.80327i) q^{4} +(2.25527 - 2.25527i) q^{5} +(0.736784 + 2.74971i) q^{6} +(-2.60590 + 0.457468i) q^{7} +(-2.68981 + 2.68981i) q^{8} +(-0.777291 + 1.34631i) q^{9} +(-3.77599 - 6.54020i) q^{10} +(4.11159 + 1.10170i) q^{11} +4.33597 q^{12} +(3.48609 + 0.920440i) q^{13} +(-0.550697 + 6.24039i) q^{14} +(-0.992444 + 3.70385i) q^{15} +(0.897005 + 1.55366i) q^{16} +(0.721872 - 1.25032i) q^{17} +(2.60283 + 2.60283i) q^{18} +(0.649502 + 2.42397i) q^{19} +(-11.1108 + 2.97714i) q^{20} +(2.43823 - 2.04279i) q^{21} +(5.03945 - 8.72858i) q^{22} +(-4.52952 + 2.61512i) q^{23} +(1.18367 - 4.41750i) q^{24} -5.17247i q^{25} +(4.24156 - 7.40905i) q^{26} -5.47577i q^{27} +(8.96408 + 3.27030i) q^{28} +(1.34350 + 2.32701i) q^{29} +(7.86299 + 4.53970i) q^{30} +(-3.76457 + 3.76457i) q^{31} +(-3.24556 + 0.869646i) q^{32} +(-4.94318 + 1.32452i) q^{33} +(-2.41725 - 2.41725i) q^{34} +(-4.84529 + 6.90872i) q^{35} +(4.85550 - 2.80333i) q^{36} +(-0.599466 - 0.160626i) q^{37} +5.94198 q^{38} +(-4.18296 + 1.13724i) q^{39} +12.1325i q^{40} +(-5.04879 - 1.35282i) q^{41} +(-3.17789 - 6.82843i) q^{42} +(-5.46143 - 3.15316i) q^{43} +(-10.8553 - 10.8553i) q^{44} +(1.28329 + 4.78929i) q^{45} +(3.20527 + 11.9622i) q^{46} +(4.68009 + 4.68009i) q^{47} +(-1.86789 - 1.07843i) q^{48} +(6.58145 - 2.38424i) q^{49} +(-11.8301 - 3.16987i) q^{50} +1.73575i q^{51} +(-9.22846 - 9.16119i) q^{52} -7.58528 q^{53} +(-12.5238 - 3.35574i) q^{54} +(11.7574 - 6.78811i) q^{55} +(5.77888 - 8.23988i) q^{56} +(-2.13337 - 2.13337i) q^{57} +(6.14553 - 1.64669i) q^{58} +(-1.96185 + 0.525675i) q^{59} +(9.77878 - 9.77878i) q^{60} +(4.53851 + 2.62031i) q^{61} +(6.30300 + 10.9171i) q^{62} +(1.40965 - 3.86393i) q^{63} +11.5440i q^{64} +(9.93790 - 5.78622i) q^{65} +12.1174i q^{66} +(2.26854 - 8.46631i) q^{67} +(-4.50931 + 2.60345i) q^{68} +(3.14404 - 5.44564i) q^{69} +(12.8318 + 15.3157i) q^{70} +(8.31929 - 2.22915i) q^{71} +(-1.53055 - 5.71208i) q^{72} +(-11.1801 - 11.1801i) q^{73} +(-0.734747 + 1.27262i) q^{74} +(3.10932 + 5.38549i) q^{75} +(2.34245 - 8.74214i) q^{76} +(-11.2184 - 0.989991i) q^{77} +(0.0375447 + 10.2639i) q^{78} +2.01287 q^{79} +(5.52690 + 1.48093i) q^{80} +(0.959764 + 1.66236i) q^{81} +(-6.18815 + 10.7182i) q^{82} +(5.11623 - 5.11623i) q^{83} +(-11.2991 + 1.98357i) q^{84} +(-1.19179 - 4.44782i) q^{85} +(-10.5586 + 10.5586i) q^{86} +(-2.79766 - 1.61523i) q^{87} +(-14.0227 + 8.09604i) q^{88} +(-1.81184 + 6.76189i) q^{89} +11.7402 q^{90} +(-9.50547 - 0.803801i) q^{91} +18.8630 q^{92} +(1.65662 - 6.18260i) q^{93} +(13.5721 - 7.83586i) q^{94} +(6.93151 + 4.00191i) q^{95} +(2.85646 - 2.85646i) q^{96} +(1.62618 + 6.06897i) q^{97} +(-1.41972 - 16.5138i) q^{98} +(-4.67912 + 4.67912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9	\( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99}+O(q^{100}) \) 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9 - 4 * q^11 - 32 * q^14 - 8 * q^15 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 4 * q^22 - 12 * q^23 + 24 * q^28 + 4 * q^29 + 12 * q^30 + 4 * q^32 - 20 * q^35 + 4 * q^37 - 36 * q^39 - 28 * q^42 - 48 * q^43 + 24 * q^44 + 84 * q^46 + 24 * q^49 - 44 * q^50 + 72 * q^53 + 60 * q^56 - 92 * q^57 - 16 * q^58 + 76 * q^60 + 48 * q^63 + 4 * q^65 - 56 * q^67 + 56 * q^70 + 84 * q^71 - 128 * q^72 - 24 * q^74 + 148 * q^78 - 80 * q^79 + 28 * q^81 - 64 * q^84 + 36 * q^85 - 48 * q^86 - 228 * q^88 - 48 * q^91 + 24 * q^92 + 108 * q^93 - 84 * q^95 - 32 * q^98 - 60 * q^99

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