LMFDB - Embedded newform 114.2.i.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.25
Dual form			114.2.i.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.386659 - 2.19285i) q^{5} +(0.939693 - 0.342020i) q^{6} +(1.32635 - 2.29731i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(1.70574 + 1.43128i) q^{10} +(-1.11334 - 1.92836i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(4.97178 - 1.80958i) q^{13} +(0.460637 + 2.61240i) q^{14} +(-0.386659 + 2.19285i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-2.61334 + 2.19285i) q^{17} -1.00000 q^{18} +(-4.29813 + 0.725293i) q^{19} -2.22668 q^{20} +(-2.03209 + 1.70513i) q^{21} +(2.09240 + 0.761570i) q^{22} +(0.386659 - 2.19285i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(0.0393628 - 0.0143269i) q^{25} +(-2.64543 + 4.58202i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-2.03209 - 1.70513i) q^{28} +(3.68866 + 3.09516i) q^{29} +(-1.11334 - 1.92836i) q^{30} +(-5.15657 + 8.93145i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.386659 + 2.19285i) q^{33} +(0.592396 - 3.35965i) q^{34} +(-5.55051 - 2.02022i) q^{35} +(0.766044 - 0.642788i) q^{36} +2.30541 q^{37} +(2.82635 - 3.31839i) q^{38} -5.29086 q^{39} +(1.70574 - 1.43128i) q^{40} +(6.79813 + 2.47432i) q^{41} +(0.460637 - 2.61240i) q^{42} +(-1.02822 - 5.83132i) q^{43} +(-2.09240 + 0.761570i) q^{44} +(1.11334 - 1.92836i) q^{45} +(1.11334 + 1.92836i) q^{46} +(8.43242 + 7.07564i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-0.0184183 - 0.0319015i) q^{49} +(-0.0209445 + 0.0362770i) q^{50} +(3.20574 - 1.16679i) q^{51} +(-0.918748 - 5.21048i) q^{52} +(1.70574 - 9.67372i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-3.79813 + 3.18701i) q^{55} +2.65270 q^{56} +(4.28699 + 0.788496i) q^{57} -4.81521 q^{58} +(3.79813 - 3.18701i) q^{59} +(2.09240 + 0.761570i) q^{60} +(-0.990200 + 5.61570i) q^{61} +(-1.79086 - 10.1565i) q^{62} +(2.49273 - 0.907278i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.89053 - 10.2027i) q^{65} +(-1.70574 - 1.43128i) q^{66} +(6.56805 + 5.51125i) q^{67} +(1.70574 + 2.95442i) q^{68} +(-1.11334 + 1.92836i) q^{69} +(5.55051 - 2.02022i) q^{70} +(0.764700 + 4.33683i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(2.62701 + 0.956154i) q^{73} +(-1.76604 + 1.48189i) q^{74} -0.0418891 q^{75} +(-0.0320889 + 4.35878i) q^{76} -5.90673 q^{77} +(4.05303 - 3.40090i) q^{78} +(-12.9684 - 4.72010i) q^{79} +(-0.386659 + 2.19285i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-6.79813 + 2.47432i) q^{82} +(5.25150 - 9.09586i) q^{83} +(1.32635 + 2.29731i) q^{84} +(5.81908 + 4.88279i) q^{85} +(4.53596 + 3.80612i) q^{86} +(-2.40760 - 4.17009i) q^{87} +(1.11334 - 1.92836i) q^{88} +(-7.34389 + 2.67296i) q^{89} +(0.386659 + 2.19285i) q^{90} +(2.43717 - 13.8219i) q^{91} +(-2.09240 - 0.761570i) q^{92} +(7.90033 - 6.62916i) q^{93} -11.0077 q^{94} +(3.25237 + 9.14473i) q^{95} -1.00000 q^{96} +(-13.6270 + 11.4344i) q^{97} +(0.0346151 + 0.0125989i) q^{98} +(0.386659 - 2.19285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8} - 3 q^{12} + 15 q^{13} - 6 q^{14} - 9 q^{15} - 9 q^{17} - 6 q^{18} - 12 q^{19} - 3 q^{21} + 9 q^{22} + 9 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{28} - 9 q^{29} - 9 q^{31} + 9 q^{33}+ \cdots + 9 q^{99}+O(q^{100}) $ 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8 - 3 * q^12 + 15 * q^13 - 6 * q^14 - 9 * q^15 - 9 * q^17 - 6 * q^18 - 12 * q^19 - 3 * q^21 + 9 * q^22 + 9 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^28 - 9 * q^29 - 9 * q^31 + 9 * q^33 - 36 * q^35 + 18 * q^37 + 18 * q^38 + 27 * q^41 - 6 * q^42 - 21 * q^43 - 9 * q^44 + 27 * q^47 - 12 * q^49 + 3 * q^50 + 9 * q^51 - 3 * q^52 - 9 * q^55 + 18 * q^56 + 18 * q^57 - 36 * q^58 + 9 * q^59 + 9 * q^60 - 3 * q^61 + 21 * q^62 - 3 * q^63 - 3 * q^64 - 18 * q^65 - 3 * q^67 + 36 * q^70 + 9 * q^71 - 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 18 * q^77 + 12 * q^78 - 21 * q^79 - 9 * q^80 - 27 * q^82 - 9 * q^83 + 9 * q^84 + 18 * q^85 - 6 * q^86 - 18 * q^87 + 9 * q^90 + 24 * q^91 - 9 * q^92 + 33 * q^93 - 18 * q^94 + 36 * q^95 - 6 * q^96 - 54 * q^97 - 24 * q^98 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.386659	−	2.19285i	−0.172919	−	0.980674i	−0.940518	−	0.339743i	$-0.889660\pi$
$5$	−0.386659	−	2.19285i	−0.172919	−	0.980674i	0.767599	−	0.640930i	$-0.221451\pi$
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	1.32635	−	2.29731i	0.501314	−	0.868301i	−0.498685	−	0.866783i	$-0.666184\pi$
$7$	1.32635	−	2.29731i	0.501314	−	0.868301i	0.999999	−	0.00151779i	$-0.000483127\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	1.70574	+	1.43128i	0.539401	+	0.452612i
$11$	−1.11334	−	1.92836i	−0.335685	−	0.581423i	0.647931	−	0.761699i	$-0.275634\pi$
$11$	−1.11334	−	1.92836i	−0.335685	−	0.581423i	−0.983616	+	0.180276i	$0.942301\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	4.97178	−	1.80958i	1.37892	−	0.501887i	0.457072	−	0.889430i	$-0.348898\pi$
$13$	4.97178	−	1.80958i	1.37892	−	0.501887i	0.921852	+	0.387542i	$0.126676\pi$
$14$	0.460637	+	2.61240i	0.123110	+	0.698194i
$15$	−0.386659	+	2.19285i	−0.0998350	+	0.566192i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−2.61334	+	2.19285i	−0.633828	+	0.531845i	−0.902116	−	0.431494i	$-0.857987\pi$
$17$	−2.61334	+	2.19285i	−0.633828	+	0.531845i	0.268288	+	0.963339i	$0.413542\pi$
$18$	−1.00000			−0.235702
$19$	−4.29813	+	0.725293i	−0.986059	+	0.166394i
$19$	−4.29813	+	0.725293i	−0.986059	+	0.166394i
$20$	−2.22668			−0.497901
$21$	−2.03209	+	1.70513i	−0.443438	+	0.372089i
$22$	2.09240	+	0.761570i	0.446100	+	0.162367i
$23$	0.386659	−	2.19285i	0.0806240	−	0.457242i	−0.917591	−	0.397525i	$-0.869869\pi$
$23$	0.386659	−	2.19285i	0.0806240	−	0.457242i	0.998215	−	0.0597166i	$-0.0190197\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	0.0393628	−	0.0143269i	0.00787257	−	0.00286538i
$26$	−2.64543	+	4.58202i	−0.518811	+	0.898608i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−2.03209	−	1.70513i	−0.384029	−	0.322238i
$29$	3.68866	+	3.09516i	0.684968	+	0.574756i	0.917453	−	0.397844i	$-0.130241\pi$
$29$	3.68866	+	3.09516i	0.684968	+	0.574756i	−0.232486	+	0.972600i	$0.574686\pi$
$30$	−1.11334	−	1.92836i	−0.203267	−	0.352069i
$31$	−5.15657	+	8.93145i	−0.926148	+	1.60414i	−0.136444	+	0.990648i	$0.543567\pi$
$31$	−5.15657	+	8.93145i	−0.926148	+	1.60414i	−0.789704	+	0.613488i	$0.789766\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.386659	+	2.19285i	0.0673087	+	0.381727i
$34$	0.592396	−	3.35965i	0.101595	−	0.576175i
$35$	−5.55051	−	2.02022i	−0.938207	−	0.341479i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	2.30541			0.379007			0.189503	−	0.981880i	$-0.439312\pi$
$37$	2.30541			0.379007			0.189503	+	0.981880i	$0.439312\pi$
$38$	2.82635	−	3.31839i	0.458495	−	0.538315i
$39$	−5.29086			−0.847216
$40$	1.70574	−	1.43128i	0.269701	−	0.226306i
$41$	6.79813	+	2.47432i	1.06169	+	0.386424i	0.813063	−	0.582176i	$-0.197798\pi$
$41$	6.79813	+	2.47432i	1.06169	+	0.386424i	0.248627	+	0.968599i	$0.420021\pi$
$42$	0.460637	−	2.61240i	0.0710779	−	0.403103i
$43$	−1.02822	−	5.83132i	−0.156802	−	0.889267i	−0.957120	−	0.289692i	$-0.906447\pi$
$43$	−1.02822	−	5.83132i	−0.156802	−	0.889267i	0.800318	−	0.599576i	$-0.204664\pi$
$44$	−2.09240	+	0.761570i	−0.315441	+	0.114811i
$45$	1.11334	−	1.92836i	0.165967	−	0.287463i
$46$	1.11334	+	1.92836i	0.164153	+	0.284322i
$47$	8.43242	+	7.07564i	1.22999	+	1.03209i	0.998239	+	0.0593140i	$0.0188913\pi$
$47$	8.43242	+	7.07564i	1.22999	+	1.03209i	0.231755	+	0.972774i	$0.425553\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	−0.0184183	−	0.0319015i	−0.00263119	−	0.00455735i
$50$	−0.0209445	+	0.0362770i	−0.00296200	+	0.00513034i
$51$	3.20574	−	1.16679i	0.448893	−	0.163384i
$52$	−0.918748	−	5.21048i	−0.127407	−	0.722563i
$53$	1.70574	−	9.67372i	0.234301	−	1.32879i	−0.609780	−	0.792571i	$-0.708742\pi$
$53$	1.70574	−	9.67372i	0.234301	−	1.32879i	0.844081	−	0.536216i	$-0.180147\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	−3.79813	+	3.18701i	−0.512140	+	0.429737i
$56$	2.65270			0.354482
$57$	4.28699	+	0.788496i	0.567826	+	0.104439i
$58$	−4.81521			−0.632268
$59$	3.79813	−	3.18701i	0.494475	−	0.414914i	−0.361152	−	0.932507i	$-0.617616\pi$
$59$	3.79813	−	3.18701i	0.494475	−	0.414914i	0.855627	+	0.517593i	$0.173172\pi$
$60$	2.09240	+	0.761570i	0.270127	+	0.0983183i
$61$	−0.990200	+	5.61570i	−0.126782	+	0.719017i	0.853451	+	0.521173i	$0.174505\pi$
$61$	−0.990200	+	5.61570i	−0.126782	+	0.719017i	−0.980233	+	0.197844i	$0.936606\pi$
$62$	−1.79086	−	10.1565i	−0.227439	−	1.28987i
$63$	2.49273	−	0.907278i	0.314054	−	0.114306i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−5.89053	−	10.2027i	−0.730630	−	1.26549i
$66$	−1.70574	−	1.43128i	−0.209962	−	0.176179i
$67$	6.56805	+	5.51125i	0.802415	+	0.673306i	0.948784	−	0.315924i	$-0.102314\pi$
$67$	6.56805	+	5.51125i	0.802415	+	0.673306i	−0.146370	+	0.989230i	$0.546759\pi$
$68$	1.70574	+	2.95442i	0.206851	+	0.358276i
$69$	−1.11334	+	1.92836i	−0.134030	+	0.232148i
$70$	5.55051	−	2.02022i	0.663413	−	0.241462i
$71$	0.764700	+	4.33683i	0.0907532	+	0.514687i	0.995966	+	0.0897290i	$0.0286001\pi$
$71$	0.764700	+	4.33683i	0.0907532	+	0.514687i	−0.905213	+	0.424958i	$0.860289\pi$
$72$	−0.173648	+	0.984808i	−0.0204646	+	0.116061i
$73$	2.62701	+	0.956154i	0.307468	+	0.111909i	0.491146	−	0.871077i	$-0.336578\pi$
$73$	2.62701	+	0.956154i	0.307468	+	0.111909i	−0.183678	+	0.982987i	$0.558800\pi$
$74$	−1.76604	+	1.48189i	−0.205298	+	0.172266i
$75$	−0.0418891			−0.00483693
$76$	−0.0320889	+	4.35878i	−0.00368085	+	0.499986i
$77$	−5.90673			−0.673134
$78$	4.05303	−	3.40090i	0.458916	−	0.385076i
$79$	−12.9684	−	4.72010i	−1.45906	−	0.531053i	−0.513951	−	0.857819i	$-0.671819\pi$
$79$	−12.9684	−	4.72010i	−1.45906	−	0.531053i	−0.945105	+	0.326766i	$0.894041\pi$
$80$	−0.386659	+	2.19285i	−0.0432298	+	0.245168i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−6.79813	+	2.47432i	−0.750728	+	0.273243i
$83$	5.25150	−	9.09586i	0.576427	−	0.998400i	−0.419458	−	0.907775i	$-0.637780\pi$
$83$	5.25150	−	9.09586i	0.576427	−	0.998400i	0.995885	−	0.0906256i	$-0.0288867\pi$
$84$	1.32635	+	2.29731i	0.144717	+	0.250657i
$85$	5.81908	+	4.88279i	0.631168	+	0.529613i
$86$	4.53596	+	3.80612i	0.489125	+	0.410425i
$87$	−2.40760	−	4.17009i	−0.258122	−	0.447081i
$88$	1.11334	−	1.92836i	0.118683	−	0.205564i
$89$	−7.34389	+	2.67296i	−0.778451	+	0.283333i	−0.700527	−	0.713626i	$-0.747052\pi$
$89$	−7.34389	+	2.67296i	−0.778451	+	0.283333i	−0.0779244	+	0.996959i	$0.524829\pi$
$90$	0.386659	+	2.19285i	0.0407575	+	0.231147i
$91$	2.43717	−	13.8219i	0.255484	−	1.44892i
$92$	−2.09240	−	0.761570i	−0.218147	−	0.0793992i
$93$	7.90033	−	6.62916i	0.819226	−	0.687412i
$94$	−11.0077			−1.13536
$95$	3.25237	+	9.14473i	0.333687	+	0.938230i
$96$	−1.00000			−0.102062
$97$	−13.6270	+	11.4344i	−1.38361	+	1.16099i	−0.415760	+	0.909474i	$0.636484\pi$
$97$	−13.6270	+	11.4344i	−1.38361	+	1.16099i	−0.967853	+	0.251515i	$0.919071\pi$
$98$	0.0346151	+	0.0125989i	0.00349665	+	0.00127268i
$99$	0.386659	−	2.19285i	0.0388607	−	0.220390i
$100$	−0.00727396	−	0.0412527i	−0.000727396	−	0.00412527i
$101$	−16.8268	+	6.12446i	−1.67433	+	0.609407i	−0.992516	−	0.122118i	$-0.961031\pi$
$101$	−16.8268	+	6.12446i	−1.67433	+	0.609407i	−0.681815	+	0.731524i	$0.738809\pi$
$102$	−1.70574	+	2.95442i	−0.168893	+	0.292531i
$103$	−2.12314	−	3.67739i	−0.209199	−	0.362344i	0.742263	−	0.670108i	$-0.233752\pi$
$103$	−2.12314	−	3.67739i	−0.209199	−	0.362344i	−0.951463	+	0.307765i	$0.900419\pi$
$104$	4.05303	+	3.40090i	0.397433	+	0.333486i
$105$	4.52481	+	3.79677i	0.441577	+	0.370527i
$106$	4.91147	+	8.50692i	0.477045	+	0.826265i
$107$	−7.80200	+	13.5135i	−0.754248	+	1.30640i	0.191499	+	0.981493i	$0.438665\pi$
$107$	−7.80200	+	13.5135i	−0.754248	+	1.30640i	−0.945747	+	0.324903i	$0.894668\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	−0.236482	−	1.34115i	−0.0226508	−	0.128459i	0.971386	−	0.237508i	$-0.0763306\pi$
$109$	−0.236482	−	1.34115i	−0.0226508	−	0.128459i	−0.994036	+	0.109049i	$0.965220\pi$
$110$	0.860967	−	4.88279i	0.0820900	−	0.465555i
$111$	−2.16637	−	0.788496i	−0.205623	−	0.0748407i
$112$	−2.03209	+	1.70513i	−0.192014	+	0.161119i
$113$	17.2003			1.61807			0.809033	−	0.587763i	$-0.199991\pi$
$113$	17.2003			1.61807			0.809033	+	0.587763i	$0.199991\pi$
$114$	−3.79086	+	2.15160i	−0.355047	+	0.201516i
$115$	−4.95811			−0.462346
$116$	3.68866	−	3.09516i	0.342484	−	0.287378i
$117$	4.97178	+	1.80958i	0.459641	+	0.167296i
$118$	−0.860967	+	4.88279i	−0.0792584	+	0.449497i
$119$	1.57145	+	8.91215i	0.144055	+	0.816975i
$120$	−2.09240	+	0.761570i	−0.191009	+	0.0695215i
$121$	3.02094	−	5.23243i	0.274631	−	0.475675i
$122$	−2.85117	−	4.93837i	−0.258133	−	0.447099i
$123$	−5.54189	−	4.65020i	−0.499695	−	0.419294i
$124$	7.90033	+	6.62916i	0.709471	+	0.595316i
$125$	−5.61334	−	9.72259i	−0.502072	−	0.869615i
$126$	−1.32635	+	2.29731i	−0.118161	+	0.204661i
$127$	12.3969	−	4.51211i	1.10005	−	0.400385i	0.272715	−	0.962095i	$-0.412078\pi$
$127$	12.3969	−	4.51211i	1.10005	−	0.400385i	0.827334	+	0.561710i	$0.189856\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−1.02822	+	5.83132i	−0.0905296	+	0.513419i
$130$	11.0706	+	4.02936i	0.970954	+	0.353398i
$131$	5.74763	−	4.82283i	0.502172	−	0.421373i	−0.356192	−	0.934413i	$-0.615925\pi$
$131$	5.74763	−	4.82283i	0.502172	−	0.421373i	0.858365	+	0.513040i	$0.171481\pi$
$132$	2.22668			0.193808
$133$	−4.03462	+	10.8361i	−0.349845	+	0.939612i
$134$	−8.57398			−0.740679
$135$	−1.70574	+	1.43128i	−0.146806	+	0.123185i
$136$	−3.20574	−	1.16679i	−0.274890	−	0.100052i
$137$	1.15136	−	6.52968i	0.0983673	−	0.557869i	−0.895296	−	0.445472i	$-0.853036\pi$
$137$	1.15136	−	6.52968i	0.0983673	−	0.557869i	0.993663	−	0.112397i	$-0.0358528\pi$
$138$	−0.386659	−	2.19285i	−0.0329146	−	0.186668i
$139$	7.99660	−	2.91052i	0.678262	−	0.246867i	0.0201612	−	0.999797i	$-0.493582\pi$
$139$	7.99660	−	2.91052i	0.678262	−	0.246867i	0.658101	+	0.752929i	$0.271360\pi$
$140$	−2.95336	+	5.11538i	−0.249605	+	0.432328i
$141$	−5.50387	−	9.53298i	−0.463510	−	0.802822i
$142$	−3.37346	−	2.83067i	−0.283094	−	0.237544i
$143$	−9.02481	−	7.57272i	−0.754693	−	0.633263i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.36097	−	9.28547i	0.445204	−	0.771116i
$146$	−2.62701	+	0.956154i	−0.217413	+	0.0791319i
$147$	0.00639661	+	0.0362770i	0.000527584	+	0.00299208i
$148$	0.400330	−	2.27038i	0.0329069	−	0.186624i
$149$	3.20574	+	1.16679i	0.262624	+	0.0955874i	0.469976	−	0.882679i	$-0.344262\pi$
$149$	3.20574	+	1.16679i	0.262624	+	0.0955874i	−0.207352	+	0.978266i	$0.566485\pi$
$150$	0.0320889	−	0.0269258i	0.00262005	−	0.00219848i
$151$	3.04189			0.247545			0.123773	−	0.992311i	$-0.460501\pi$
$151$	3.04189			0.247545			0.123773	+	0.992311i	$0.460501\pi$
$152$	−2.77719	−	3.35965i	−0.225260	−	0.272503i
$153$	−3.41147			−0.275801
$154$	4.52481	−	3.79677i	0.364620	−	0.305952i
$155$	21.5792	+	7.85418i	1.73328	+	0.630863i
$156$	−0.918748	+	5.21048i	−0.0735587	+	0.417172i
$157$	−2.69594	−	15.2894i	−0.215159	−	1.22023i	−0.880630	−	0.473805i	$-0.842880\pi$
$157$	−2.69594	−	15.2894i	−0.215159	−	1.22023i	0.665471	−	0.746424i	$-0.268231\pi$
$158$	12.9684	−	4.72010i	1.03171	−	0.375511i
$159$	−4.91147	+	8.50692i	−0.389505	+	0.674643i
$160$	−1.11334	−	1.92836i	−0.0880173	−	0.152450i
$161$	−4.52481	−	3.79677i	−0.356605	−	0.299227i
$162$	−0.766044	−	0.642788i	−0.0601861	−	0.0505022i
$163$	−2.21941	−	3.84413i	−0.173837	−	0.301095i	0.765921	−	0.642935i	$-0.222283\pi$
$163$	−2.21941	−	3.84413i	−0.173837	−	0.301095i	−0.939758	+	0.341840i	$0.888950\pi$
$164$	3.61721	−	6.26519i	0.282457	−	0.489229i
$165$	4.65910	−	1.69577i	0.362710	−	0.132016i
$166$	1.82383	+	10.3434i	0.141556	+	0.802806i
$167$	−1.41534	+	8.02682i	−0.109523	+	0.621134i	0.879794	+	0.475354i	$0.157680\pi$
$167$	−1.41534	+	8.02682i	−0.109523	+	0.621134i	−0.989317	+	0.145779i	$0.953431\pi$
$168$	−2.49273	−	0.907278i	−0.192318	−	0.0699980i
$169$	11.4855	−	9.63744i	0.883496	−	0.741341i
$170$	−7.59627			−0.582607
$171$	−3.75877	−	2.20718i	−0.287440	−	0.168787i
$172$	−5.92127			−0.451493
$173$	−12.2306	+	10.2627i	−0.929872	+	0.780255i	−0.975794	−	0.218690i	$-0.929822\pi$
$173$	−12.2306	+	10.2627i	−0.929872	+	0.780255i	0.0459227	+	0.998945i	$0.485377\pi$
$174$	4.52481	+	1.64690i	0.343025	+	0.124851i
$175$	0.0192957	−	0.109431i	0.00145861	−	0.00827222i
$176$	0.386659	+	2.19285i	0.0291455	+	0.165293i
$177$	−4.65910	+	1.69577i	−0.350199	+	0.127462i
$178$	3.90760	−	6.76817i	0.292887	−	0.507296i
$179$	−0.726682	−	1.25865i	−0.0543147	−	0.0940759i	0.837590	−	0.546300i	$-0.183964\pi$
$179$	−0.726682	−	1.25865i	−0.0543147	−	0.0940759i	−0.891904	+	0.452224i	$0.850631\pi$
$180$	−1.70574	−	1.43128i	−0.127138	−	0.106682i
$181$	−0.862311	−	0.723565i	−0.0640951	−	0.0537822i	0.610177	−	0.792265i	$-0.291098\pi$
$181$	−0.862311	−	0.723565i	−0.0640951	−	0.0537822i	−0.674272	+	0.738483i	$0.735543\pi$
$182$	7.01754	+	12.1547i	0.520175	+	0.900969i
$183$	2.85117	−	4.93837i	0.210764	−	0.365054i
$184$	2.09240	−	0.761570i	0.154253	−	0.0561437i
$185$	−0.891407	−	5.05542i	−0.0655375	−	0.371682i
$186$	−1.79086	+	10.1565i	−0.131312	+	0.744708i
$187$	7.13816	+	2.59808i	0.521994	+	0.189990i
$188$	8.43242	−	7.07564i	0.614997	−	0.516044i
$189$	−2.65270			−0.192956
$190$	−8.36959	−	4.91469i	−0.607194	−	0.356549i
$191$	−1.32770			−0.0960687			−0.0480344	−	0.998846i	$-0.515296\pi$
$191$	−1.32770			−0.0960687			−0.0480344	+	0.998846i	$0.515296\pi$
$192$	0.766044	−	0.642788i	0.0552845	−	0.0463892i
$193$	−14.0817	−	5.12533i	−1.01362	−	0.368929i	−0.218801	−	0.975770i	$-0.570214\pi$
$193$	−14.0817	−	5.12533i	−1.01362	−	0.368929i	−0.794824	+	0.606841i	$0.792437\pi$
$194$	3.08899	−	17.5185i	0.221777	−	1.25776i
$195$	2.04576	+	11.6021i	0.146500	+	0.830842i
$196$	−0.0346151	+	0.0125989i	−0.00247251	+	0.000899919i
$197$	−11.5039	+	19.9253i	−0.819617	+	1.41962i	0.0863480	+	0.996265i	$0.472480\pi$
$197$	−11.5039	+	19.9253i	−0.819617	+	1.41962i	−0.905965	+	0.423353i	$0.860853\pi$
$198$	1.11334	+	1.92836i	0.0791217	+	0.137043i
$199$	7.41740	+	6.22394i	0.525806	+	0.441203i	0.866650	−	0.498916i	$-0.166268\pi$
$199$	7.41740	+	6.22394i	0.525806	+	0.441203i	−0.340844	+	0.940120i	$0.610713\pi$
$200$	0.0320889	+	0.0269258i	0.00226903	+	0.00190394i
$201$	−4.28699	−	7.42528i	−0.302381	−	0.523739i
$202$	8.95336	−	15.5077i	0.629956	−	1.09112i
$203$	12.0030	−	4.36873i	0.842445	−	0.306625i
$204$	−0.592396	−	3.35965i	−0.0414760	−	0.235222i
$205$	2.79726	−	15.8640i	0.195369	−	1.10799i
$206$	3.99020	+	1.45231i	0.278010	+	0.101188i
$207$	1.70574	−	1.43128i	0.118557	−	0.0994811i
$208$	−5.29086			−0.366855
$209$	6.18392	+	7.48086i	0.427750	+	0.517462i
$210$	−5.90673			−0.407603
$211$	−0.847296	+	0.710966i	−0.0583303	+	0.0489449i	−0.671487	−	0.741017i	$-0.734344\pi$
$211$	−0.847296	+	0.710966i	−0.0583303	+	0.0489449i	0.613156	+	0.789962i	$0.289900\pi$
$212$	−9.23055	−	3.35965i	−0.633957	−	0.230741i
$213$	0.764700	−	4.33683i	0.0523964	−	0.297155i
$214$	−2.70961	−	15.3669i	−0.185225	−	1.05046i
$215$	−12.3897	+	4.50946i	−0.844967	+	0.307543i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	13.6789	+	23.6925i	0.928582	+	1.60835i
$218$	1.04323	+	0.875377i	0.0706567	+	0.0592880i
$219$	−2.14156	−	1.79698i	−0.144713	−	0.121429i
$220$	2.47906	+	4.29385i	0.167138	+	0.289491i
$221$	−9.02481	+	15.6314i	−0.607075	+	1.05148i
$222$	2.16637	−	0.788496i	0.145398	−	0.0529204i
$223$	4.39100	+	24.9026i	0.294043	+	1.66760i	0.671067	+	0.741397i	$0.265836\pi$
$223$	4.39100	+	24.9026i	0.294043	+	1.66760i	−0.377024	+	0.926203i	$0.623053\pi$
$224$	0.460637	−	2.61240i	0.0307776	−	0.174549i
$225$	0.0393628	+	0.0143269i	0.00262419	+	0.000955127i
$226$	−13.1762	+	11.0561i	−0.876466	+	0.735442i
$227$	3.42871			0.227572			0.113786	−	0.993505i	$-0.463702\pi$
$227$	3.42871			0.227572			0.113786	+	0.993505i	$0.463702\pi$
$228$	1.52094	−	4.08494i	0.100727	−	0.270532i
$229$	29.9418			1.97861			0.989305	−	0.145860i	$-0.0465950\pi$
$229$	29.9418			1.97861			0.989305	+	0.145860i	$0.0465950\pi$
$230$	3.79813	−	3.18701i	0.250441	−	0.210145i
$231$	5.55051	+	2.02022i	0.365197	+	0.132921i
$232$	−0.836152	+	4.74205i	−0.0548961	+	0.311331i
$233$	−1.80200	−	10.2197i	−0.118053	−	0.669513i	−0.985193	−	0.171448i	$-0.945155\pi$
$233$	−1.80200	−	10.2197i	−0.118053	−	0.669513i	0.867140	−	0.498065i	$-0.165956\pi$
$234$	−4.97178	+	1.80958i	−0.325016	+	0.118296i
$235$	12.2554	−	21.2269i	0.799452	−	1.38469i
$236$	−2.47906	−	4.29385i	−0.161373	−	0.279506i
$237$	10.5719	+	8.87089i	0.686720	+	0.576226i
$238$	−6.93242	−	5.81699i	−0.449362	−	0.377059i
$239$	8.00774	+	13.8698i	0.517978	+	0.897164i	0.999782	+	0.0208848i	$0.00664831\pi$
$239$	8.00774	+	13.8698i	0.517978	+	0.897164i	−0.481804	+	0.876279i	$0.660018\pi$
$240$	1.11334	−	1.92836i	0.0718658	−	0.124475i
$241$	−24.0390	+	8.74946i	−1.54849	+	0.563602i	−0.968062	−	0.250712i	$-0.919335\pi$
$241$	−24.0390	+	8.74946i	−1.54849	+	0.563602i	−0.580423	+	0.814315i	$0.697113\pi$
$242$	1.04916	+	5.95010i	0.0674428	+	0.382487i
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$	5.35844	+	1.95031i	0.343039	+	0.124856i
$245$	−0.0628336	+	0.0527236i	−0.00401429	+	0.00336839i
$246$	7.23442			0.461250
$247$	−20.0569	+	11.3838i	−1.27619	+	0.724335i
$248$	−10.3131			−0.654886
$249$	−8.04576	+	6.75119i	−0.509879	+	0.427840i
$250$	10.5496	+	3.83975i	0.667217	+	0.242847i
$251$	1.85622	−	10.5271i	0.117164	−	0.664467i	−0.868493	−	0.495702i	$-0.834911\pi$
$251$	1.85622	−	10.5271i	0.117164	−	0.664467i	0.985656	−	0.168765i	$-0.0539780\pi$
$252$	−0.460637	−	2.61240i	−0.0290174	−	0.164566i
$253$	−4.65910	+	1.69577i	−0.292915	+	0.106612i
$254$	−6.59627	+	11.4251i	−0.413887	+	0.716873i
$255$	−3.79813	−	6.57856i	−0.237848	−	0.411965i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−23.5783	−	19.7846i	−1.47077	−	1.23413i	−0.915412	−	0.402519i	$-0.868135\pi$
$257$	−23.5783	−	19.7846i	−1.47077	−	1.23413i	−0.555363	−	0.831608i	$-0.687421\pi$
$258$	−2.96064	−	5.12797i	−0.184321	−	0.319254i
$259$	3.05778	−	5.29623i	0.190001	−	0.329092i
$260$	−11.0706	+	4.02936i	−0.686568	+	0.249890i
$261$	0.836152	+	4.74205i	0.0517565	+	0.293526i
$262$	−1.30288	+	7.38901i	−0.0804923	+	0.456494i
$263$	−2.95336	−	1.07494i	−0.182112	−	0.0662834i	0.249355	−	0.968412i	$-0.419782\pi$
$263$	−2.95336	−	1.07494i	−0.182112	−	0.0662834i	−0.431467	+	0.902129i	$0.642004\pi$
$264$	−1.70574	+	1.43128i	−0.104981	+	0.0880894i
$265$	−21.8726			−1.34362
$266$	−3.87464	−	10.8944i	−0.237569	−	0.667976i
$267$	7.81521			0.478283
$268$	6.56805	−	5.51125i	0.401207	−	0.336653i
$269$	−13.9829	−	5.08937i	−0.852554	−	0.310304i	−0.121473	−	0.992595i	$-0.538762\pi$
$269$	−13.9829	−	5.08937i	−0.852554	−	0.310304i	−0.731081	+	0.682290i	$0.760984\pi$
$270$	0.386659	−	2.19285i	0.0235313	−	0.133453i
$271$	2.64543	+	15.0030i	0.160698	+	0.911366i	0.953389	+	0.301742i	$0.0975683\pi$
$271$	2.64543	+	15.0030i	0.160698	+	0.911366i	−0.792691	+	0.609624i	$0.791321\pi$
$272$	3.20574	−	1.16679i	0.194376	−	0.0707472i
$273$	−7.01754	+	12.1547i	−0.424721	+	0.735638i
$274$	3.31521	+	5.74211i	0.200279	+	0.346893i
$275$	−0.0714517	−	0.0599551i	−0.00430870	−	0.00361543i
$276$	1.70574	+	1.43128i	0.102673	+	0.0861531i
$277$	6.10472	+	10.5737i	0.366797	+	0.635311i	0.989063	−	0.147495i	$-0.0471209\pi$
$277$	6.10472	+	10.5737i	0.366797	+	0.635311i	−0.622266	+	0.782806i	$0.713788\pi$
$278$	−4.25490	+	7.36970i	−0.255192	+	0.442005i
$279$	−9.69119	+	3.52730i	−0.580196	+	0.211174i
$280$	−1.02569	−	5.81699i	−0.0612968	−	0.347632i
$281$	−0.389652	+	2.20983i	−0.0232447	+	0.131827i	−0.994222	−	0.107345i	$-0.965765\pi$
$281$	−0.389652	+	2.20983i	−0.0232447	+	0.131827i	0.970977	+	0.239172i	$0.0768761\pi$
$282$	10.3439	+	3.76487i	0.615970	+	0.224195i
$283$	−11.3289	+	9.50606i	−0.673432	+	0.565076i	−0.914079	−	0.405536i	$-0.867085\pi$
$283$	−11.3289	+	9.50606i	−0.673432	+	0.565076i	0.240647	+	0.970613i	$0.422640\pi$
$284$	4.40373			0.261313
$285$	0.0714517	−	9.70562i	0.00423244	−	0.574911i
$286$	11.7811			0.696629
$287$	14.7010	−	12.3356i	0.867772	−	0.728147i
$288$	0.939693	+	0.342020i	0.0553719	+	0.0201537i
$289$	−0.931074	+	5.28039i	−0.0547691	+	0.310611i
$290$	1.86184	+	10.5590i	0.109331	+	0.620048i
$291$	16.7160	−	6.08413i	0.979910	−	0.356658i
$292$	1.39780	−	2.42107i	0.0818003	−	0.141682i
$293$	6.02481	+	10.4353i	0.351973	+	0.609636i	0.986595	−	0.163187i	$-0.0521774\pi$
$293$	6.02481	+	10.4353i	0.351973	+	0.609636i	−0.634622	+	0.772823i	$0.718844\pi$
$294$	−0.0282185	−	0.0236781i	−0.00164574	−	0.00138094i
$295$	−8.45723	−	7.09646i	−0.492399	−	0.413172i
$296$	1.15270	+	1.99654i	0.0669995	+	0.116047i
$297$	−1.11334	+	1.92836i	−0.0646026	+	0.111895i
$298$	−3.20574	+	1.16679i	−0.185703	+	0.0675905i
$299$	−2.04576	−	11.6021i	−0.118309	−	0.670966i
$300$	−0.00727396	+	0.0412527i	−0.000419962	+	0.00238172i
$301$	−14.7601	−	5.37224i	−0.850759	−	0.309651i
$302$	−2.33022	+	1.95529i	−0.134089	+	0.112514i
$303$	17.9067			1.02871
$304$	4.28699	+	0.788496i	0.245876	+	0.0452233i
$305$	12.6973			0.727044
$306$	2.61334	−	2.19285i	0.149395	−	0.125357i
$307$	−21.2319	−	7.72778i	−1.21177	−	0.441048i	−0.344452	−	0.938804i	$-0.611935\pi$
$307$	−21.2319	−	7.72778i	−1.21177	−	0.441048i	−0.867317	+	0.497757i	$0.834157\pi$
$308$	−1.02569	+	5.81699i	−0.0584442	+	0.331454i
$309$	0.737359	+	4.18177i	0.0419469	+	0.237893i
$310$	−21.5792	+	7.85418i	−1.22562	+	0.446088i
$311$	5.66297	−	9.80855i	0.321118	−	0.556192i	−0.659601	−	0.751616i	$-0.729275\pi$
$311$	5.66297	−	9.80855i	0.321118	−	0.556192i	0.980719	+	0.195424i	$0.0626082\pi$
$312$	−2.64543	−	4.58202i	−0.149768	−	0.259406i
$313$	−4.56418	−	3.82980i	−0.257983	−	0.216473i	0.504618	−	0.863343i	$-0.331633\pi$
$313$	−4.56418	−	3.82980i	−0.257983	−	0.216473i	−0.762601	+	0.646870i	$0.776078\pi$
$314$	11.8931	+	9.97946i	0.671164	+	0.563173i
$315$	−2.95336	−	5.11538i	−0.166403	−	0.288219i
$316$	−6.90033	+	11.9517i	−0.388174	+	0.672337i
$317$	8.38578	−	3.05217i	0.470992	−	0.171427i	−0.0956094	−	0.995419i	$-0.530480\pi$
$317$	8.38578	−	3.05217i	0.470992	−	0.171427i	0.566602	+	0.823992i	$0.308258\pi$
$318$	−1.70574	−	9.67372i	−0.0956530	−	0.542475i
$319$	1.86184	−	10.5590i	0.104243	−	0.591193i
$320$	2.09240	+	0.761570i	0.116969	+	0.0425731i
$321$	11.9534	−	10.0301i	0.667172	−	0.559824i
$322$	5.90673			0.329169
$323$	9.64203	−	11.3206i	0.536497	−	0.629896i
$324$	1.00000			0.0555556
$325$	0.169778	−	0.142460i	0.00941758	−	0.00790229i
$326$	4.17112	+	1.51816i	0.231017	+	0.0840833i
$327$	−0.236482	+	1.34115i	−0.0130775	+	0.0741660i
$328$	1.25624	+	7.12452i	0.0693645	+	0.393386i
$329$	27.4393	−	9.98708i	1.51278	−	0.550606i
$330$	−2.47906	+	4.29385i	−0.136468	+	0.236369i
$331$	−3.32976	−	5.76731i	−0.183020	−	0.317000i	0.759888	−	0.650054i	$-0.225254\pi$
$331$	−3.32976	−	5.76731i	−0.183020	−	0.317000i	−0.942908	+	0.333055i	$0.891921\pi$
$332$	−8.04576	−	6.75119i	−0.441568	−	0.370520i
$333$	1.76604	+	1.48189i	0.0967786	+	0.0812069i
$334$	−4.07532	−	7.05866i	−0.222992	−	0.386233i
$335$	9.54576	−	16.5337i	0.521541	−	0.903335i
$336$	2.49273	−	0.907278i	0.135989	−	0.0494961i
$337$	−1.88057	−	10.6652i	−0.102441	−	0.580972i	−0.992212	−	0.124564i	$-0.960247\pi$
$337$	−1.88057	−	10.6652i	−0.102441	−	0.580972i	0.889771	−	0.456408i	$-0.150864\pi$
$338$	−2.60354	+	14.7654i	−0.141614	+	0.803133i
$339$	−16.1630	−	5.88284i	−0.877852	−	0.319512i
$340$	5.81908	−	4.88279i	0.315584	−	0.264806i
$341$	22.9641			1.24358
$342$	4.29813	−	0.725293i	0.232416	−	0.0392194i
$343$	18.4712			0.997352
$344$	4.53596	−	3.80612i	0.244563	−	0.205212i
$345$	4.65910	+	1.69577i	0.250838	+	0.0912974i
$346$	2.77244	−	15.7233i	0.149047	−	0.845290i
$347$	3.58781	+	20.3475i	0.192604	+	1.09231i	0.915790	+	0.401657i	$0.131566\pi$
$347$	3.58781	+	20.3475i	0.192604	+	1.09231i	−0.723186	+	0.690653i	$0.757323\pi$
$348$	−4.52481	+	1.64690i	−0.242556	+	0.0882830i
$349$	1.01976	−	1.76628i	0.0545866	−	0.0945468i	−0.837441	−	0.546528i	$-0.815949\pi$
$349$	1.01976	−	1.76628i	0.0545866	−	0.0945468i	0.892028	+	0.451981i	$0.149283\pi$
$350$	0.0555596	+	0.0962321i	0.00296979	+	0.00514382i
$351$	−4.05303	−	3.40090i	−0.216335	−	0.181527i
$352$	−1.70574	−	1.43128i	−0.0909161	−	0.0762877i
$353$	−15.6506	−	27.1077i	−0.833000	−	1.44280i	−0.895649	−	0.444762i	$-0.853288\pi$
$353$	−15.6506	−	27.1077i	−0.833000	−	1.44280i	0.0626489	−	0.998036i	$-0.480045\pi$
$354$	2.47906	−	4.29385i	0.131760	−	0.228216i
$355$	9.21436	−	3.35375i	0.489047	−	0.177999i
$356$	1.35710	+	7.69648i	0.0719260	+	0.407912i
$357$	1.57145	−	8.91215i	0.0831700	−	0.471681i
$358$	1.36571	+	0.497079i	0.0721803	+	0.0262715i
$359$	−6.82295	+	5.72513i	−0.360101	+	0.302161i	−0.804831	−	0.593504i	$-0.797744\pi$
$359$	−6.82295	+	5.72513i	−0.360101	+	0.302161i	0.444730	+	0.895665i	$0.353300\pi$
$360$	2.22668			0.117356
$361$	17.9479	−	6.23481i	0.944626	−	0.328148i
$362$	1.12567			0.0591638
$363$	−4.62836	+	3.88365i	−0.242926	+	0.203839i
$364$	−13.1887	−	4.80028i	−0.691274	−	0.251603i
$365$	1.08095	−	6.13036i	0.0565794	−	0.320878i
$366$	0.990200	+	5.61570i	0.0517586	+	0.293537i
$367$	−3.23308	+	1.17674i	−0.168765	+	0.0614255i	−0.425021	−	0.905183i	$-0.639733\pi$
$367$	−3.23308	+	1.17674i	−0.168765	+	0.0614255i	0.256256	+	0.966609i	$0.417511\pi$
$368$	−1.11334	+	1.92836i	−0.0580369	+	0.100523i
$369$	3.61721	+	6.26519i	0.188304	+	0.326153i
$370$	3.93242	+	3.29969i	0.204437	+	0.171543i
$371$	−19.9611	−	16.7494i	−1.03633	−	0.869583i
$372$	−5.15657	−	8.93145i	−0.267356	−	0.463074i
$373$	3.15998	−	5.47324i	0.163617	−	0.283394i	−0.772546	−	0.634959i	$-0.781017\pi$
$373$	3.15998	−	5.47324i	0.163617	−	0.283394i	0.936163	+	0.351565i	$0.114350\pi$
$374$	−7.13816	+	2.59808i	−0.369105	+	0.134343i
$375$	1.94949	+	11.0561i	0.100671	+	0.570936i
$376$	−1.91147	+	10.8405i	−0.0985768	+	0.559057i
$377$	23.9402	+	8.71351i	1.23298	+	0.448768i
$378$	2.03209	−	1.70513i	0.104519	−	0.0877022i
$379$	−14.4074			−0.740056			−0.370028	−	0.929021i	$-0.620652\pi$
$379$	−14.4074			−0.740056			−0.370028	+	0.929021i	$0.620652\pi$
$380$	9.57057	−	1.61500i	0.490960	−	0.0828476i
$381$	−13.1925			−0.675874
$382$	1.01707	−	0.853427i	0.0520380	−	0.0436651i
$383$	1.77719	+	0.646844i	0.0908101	+	0.0330522i	0.387026	−	0.922069i	$-0.373502\pi$
$383$	1.77719	+	0.646844i	0.0908101	+	0.0330522i	−0.296216	+	0.955121i	$0.595725\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	2.28389	+	12.9526i	0.116398	+	0.660125i
$386$	14.0817	−	5.12533i	0.716741	−	0.260872i
$387$	2.96064	−	5.12797i	0.150498	−	0.260670i
$388$	8.89440	+	15.4056i	0.451545	+	0.782098i
$389$	−5.65136	−	4.74205i	−0.286535	−	0.240432i	0.488178	−	0.872744i	$-0.337662\pi$
$389$	−5.65136	−	4.74205i	−0.286535	−	0.240432i	−0.774714	+	0.632312i	$0.782106\pi$
$390$	−9.02481	−	7.57272i	−0.456989	−	0.383460i
$391$	3.79813	+	6.57856i	0.192080	+	0.332692i
$392$	0.0184183	−	0.0319015i	0.000930265	−	0.00161127i
$393$	−7.05051	+	2.56617i	−0.355651	+	0.129446i
$394$	−3.99525	−	22.6582i	−0.201278	−	1.14150i
$395$	−5.33615	+	30.2628i	−0.268491	+	1.52269i
$396$	−2.09240	−	0.761570i	−0.105147	−	0.0382703i
$397$	−8.86824	+	7.44134i	−0.445084	+	0.373470i	−0.837608	−	0.546272i	$-0.816047\pi$
$397$	−8.86824	+	7.44134i	−0.445084	+	0.373470i	0.392524	+	0.919742i	$0.371602\pi$
$398$	−9.68273			−0.485352
$399$	7.49747	−	8.80271i	0.375343	−	0.440687i
$400$	−0.0418891			−0.00209445
$401$	11.6514	−	9.77665i	0.581841	−	0.488223i	−0.303710	−	0.952765i	$-0.598225\pi$
$401$	11.6514	−	9.77665i	0.581841	−	0.488223i	0.885551	+	0.464542i	$0.153781\pi$
$402$	8.05690	+	2.93247i	0.401842	+	0.146258i
$403$	−9.47519	+	53.7364i	−0.471993	+	2.67680i
$404$	3.10947	+	17.6347i	0.154702	+	0.877358i
$405$	2.09240	−	0.761570i	0.103972	−	0.0378427i
$406$	−6.38666	+	11.0620i	−0.316965	+	0.548999i
$407$	−2.56670	−	4.44566i	−0.127227	−	0.220363i
$408$	2.61334	+	2.19285i	0.129380	+	0.108562i
$409$	−1.17293	−	0.984208i	−0.0579978	−	0.0486659i	0.613328	−	0.789828i	$-0.289830\pi$
$409$	−1.17293	−	0.984208i	−0.0579978	−	0.0486659i	−0.671326	+	0.741162i	$0.734275\pi$
$410$	8.05438	+	13.9506i	0.397777	+	0.688971i
$411$	−3.31521	+	5.74211i	−0.163527	+	0.283237i
$412$	−3.99020	+	1.45231i	−0.196583	+	0.0715504i
$413$	−2.28389	−	12.9526i	−0.112383	−	0.637355i
$414$	−0.386659	+	2.19285i	−0.0190033	+	0.107773i
$415$	−21.9764	−	7.99876i	−1.07878	−	0.392644i
$416$	4.05303	−	3.40090i	0.198716	−	0.166743i
$417$	−8.50980			−0.416727
$418$	−9.54576	−	1.75573i	−0.466898	−	0.0858755i
$419$	−26.7374			−1.30621			−0.653104	−	0.757268i	$-0.726534\pi$
$419$	−26.7374			−1.30621			−0.653104	+	0.757268i	$0.726534\pi$
$420$	4.52481	−	3.79677i	0.220788	−	0.185263i
$421$	−22.4329	−	8.16490i	−1.09331	−	0.397933i	−0.268465	−	0.963289i	$-0.586516\pi$
$421$	−22.4329	−	8.16490i	−1.09331	−	0.397933i	−0.824847	+	0.565356i	$0.808739\pi$
$422$	0.192066	−	1.08926i	0.00934965	−	0.0530245i
$423$	1.91147	+	10.8405i	0.0929391	+	0.527084i
$424$	9.23055	−	3.35965i	0.448275	−	0.163159i
$425$	−0.0714517	+	0.123758i	−0.00346592	+	0.00600315i
$426$	2.20187	+	3.81374i	0.106681	+	0.184777i
$427$	11.5876	+	9.72319i	0.560766	+	0.470538i
$428$	11.9534	+	10.0301i	0.577788	+	0.484821i
$429$	5.89053	+	10.2027i	0.284397	+	0.492591i
$430$	6.59240	−	11.4184i	0.317914	−	0.550642i
$431$	−14.8277	+	5.39684i	−0.714225	+	0.259957i	−0.673472	−	0.739213i	$-0.735198\pi$
$431$	−14.8277	+	5.39684i	−0.714225	+	0.259957i	−0.0407529	+	0.999169i	$0.512976\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	−2.33006	+	13.2144i	−0.111976	+	0.635045i	0.876228	+	0.481897i	$0.160052\pi$
$433$	−2.33006	+	13.2144i	−0.111976	+	0.635045i	−0.988203	+	0.153148i	$0.951059\pi$
$434$	−25.7079	−	9.35689i	−1.23402	−	0.449145i
$435$	−8.21348	+	6.89193i	−0.393806	+	0.330443i
$436$	−1.36184			−0.0652205
$437$	−0.0714517	+	9.70562i	−0.00341800	+	0.464283i
$438$	2.79561			0.133579
$439$	14.4795	−	12.1498i	0.691070	−	0.579876i	−0.228148	−	0.973627i	$-0.573267\pi$
$439$	14.4795	−	12.1498i	0.691070	−	0.579876i	0.919218	+	0.393750i	$0.128822\pi$
$440$	−4.65910	−	1.69577i	−0.222114	−	0.0808428i
$441$	0.00639661	−	0.0362770i	0.000304601	−	0.00172748i
$442$	−3.13429	−	17.7754i	−0.149083	−	0.845490i
$443$	10.6125	−	3.86262i	0.504213	−	0.183519i	−0.0773747	−	0.997002i	$-0.524654\pi$
$443$	10.6125	−	3.86262i	0.504213	−	0.183519i	0.581588	+	0.813483i	$0.302432\pi$
$444$	−1.15270	+	1.99654i	−0.0547049	+	0.0947517i
$445$	8.70099	+	15.0706i	0.412466	+	0.714413i
$446$	−19.3708	−	16.2540i	−0.917232	−	0.769649i
$447$	−2.61334	−	2.19285i	−0.123607	−	0.103718i
$448$	1.32635	+	2.29731i	0.0626642	+	0.108538i
$449$	4.37733	−	7.58175i	0.206579	−	0.357805i	−0.744056	−	0.668117i	$-0.767100\pi$
$449$	4.37733	−	7.58175i	0.206579	−	0.357805i	0.950635	+	0.310313i	$0.100434\pi$
$450$	−0.0393628	+	0.0143269i	−0.00185558	+	0.000675377i
$451$	−2.79726	−	15.8640i	−0.131718	−	0.747008i
$452$	2.98680	−	16.9390i	0.140487	−	0.796742i
$453$	−2.85844	−	1.04039i	−0.134301	−	0.0488817i
$454$	−2.62654	+	2.20393i	−0.123270	+	0.103436i
$455$	−31.2517			−1.46510
$456$	1.46064	+	4.10689i	0.0684006	+	0.192323i
$457$	23.8334			1.11488			0.557439	−	0.830218i	$-0.311784\pi$
$457$	23.8334			1.11488			0.557439	+	0.830218i	$0.311784\pi$
$458$	−22.9368	+	19.2462i	−1.07176	+	0.899317i
$459$	3.20574	+	1.16679i	0.149631	+	0.0544612i
$460$	−0.860967	+	4.88279i	−0.0401428	+	0.227661i
$461$	2.73442	+	15.5077i	0.127355	+	0.722265i	0.979881	+	0.199581i	$0.0639581\pi$
$461$	2.73442	+	15.5077i	0.127355	+	0.722265i	−0.852527	+	0.522684i	$0.824931\pi$
$462$	−5.55051	+	2.02022i	−0.258233	+	0.0939891i
$463$	2.18732	−	3.78855i	0.101653	−	0.176069i	−0.810713	−	0.585444i	$-0.800920\pi$
$463$	2.18732	−	3.78855i	0.101653	−	0.176069i	0.912366	+	0.409376i	$0.134253\pi$
$464$	−2.40760	−	4.17009i	−0.111770	−	0.193592i
$465$	−17.5915	−	14.7610i	−0.815787	−	0.684527i
$466$	7.94949	+	6.67042i	0.368253	+	0.309001i
$467$	−13.0535	−	22.6093i	−0.604044	−	1.04623i	−0.992202	−	0.124642i	$-0.960222\pi$
$467$	−13.0535	−	22.6093i	−0.604044	−	1.04623i	0.388158	−	0.921593i	$-0.373112\pi$
$468$	2.64543	−	4.58202i	0.122285	−	0.211804i
$469$	21.3726	−	7.77898i	0.986894	−	0.359200i
$470$	4.25624	+	24.1384i	0.196326	+	1.11342i
$471$	−2.69594	+	15.2894i	−0.124222	+	0.704499i
$472$	4.65910	+	1.69577i	0.214452	+	0.0780543i
$473$	−10.1001	+	8.47502i	−0.464405	+	0.389682i
$474$	−13.8007			−0.633885
$475$	−0.158796	+	0.0901285i	−0.00728604	+	0.00413538i
$476$	9.04963			0.414789
$477$	7.52481	−	6.31407i	0.344538	−	0.289101i
$478$	−15.0496	−	5.47762i	−0.688354	−	0.250540i
$479$	−5.92556	+	33.6055i	−0.270746	+	1.53547i	0.481414	+	0.876493i	$0.340123\pi$
$479$	−5.92556	+	33.6055i	−0.270746	+	1.53547i	−0.752160	+	0.658981i	$0.770988\pi$
$480$	0.386659	+	2.19285i	0.0176485	+	0.100090i
$481$	11.4620	−	4.17182i	0.522621	−	0.190219i
$482$	12.7909	−	22.1544i	0.582608	−	1.00911i
$483$	2.95336	+	5.11538i	0.134383	+	0.232758i
$484$	−4.62836	−	3.88365i	−0.210380	−	0.176530i
$485$	30.3430	+	25.4608i	1.37781	+	1.15612i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	7.88191	−	13.6519i	0.357164	−	0.618625i	−0.630322	−	0.776334i	$-0.717077\pi$
$487$	7.88191	−	13.6519i	0.357164	−	0.618625i	0.987486	+	0.157708i	$0.0504106\pi$
$488$	−5.35844	+	1.95031i	−0.242565	+	0.0882865i
$489$	0.770792	+	4.37138i	0.0348564	+	0.197681i
$490$	0.0142432	−	0.0807773i	0.000643443	−	0.00364915i
$491$	−13.0039	−	4.73302i	−0.586856	−	0.213598i	0.0314898	−	0.999504i	$-0.489975\pi$
$491$	−13.0039	−	4.73302i	−0.586856	−	0.213598i	−0.618346	+	0.785906i	$0.712197\pi$
$492$	−5.54189	+	4.65020i	−0.249848	+	0.209647i
$493$	−16.4270			−0.739833
$494$	8.04710	−	21.6128i	0.362056	−	0.972408i
$495$	−4.95811			−0.222851
$496$	7.90033	−	6.62916i	0.354735	−	0.297658i
$497$	10.9773	+	3.99541i	0.492399	+	0.179219i
$498$	1.82383	−	10.3434i	0.0817276	−	0.463500i
$499$	−3.46064	−	19.6262i	−0.154919	−	0.878592i	−0.958859	−	0.283881i	$-0.908378\pi$
$499$	−3.46064	−	19.6262i	−0.154919	−	0.878592i	0.803940	−	0.594710i	$-0.202733\pi$
$500$	−10.5496	+	3.83975i	−0.471794	+	0.171719i
$501$	4.07532	−	7.05866i	0.182072	−	0.315358i
$502$	5.34477	+	9.25741i	0.238549	+	0.413179i
$503$	−11.3990	−	9.56488i	−0.508256	−	0.426477i	0.352259	−	0.935902i	$-0.385414\pi$
$503$	−11.3990	−	9.56488i	−0.508256	−	0.426477i	−0.860515	+	0.509425i	$0.829858\pi$
$504$	2.03209	+	1.70513i	0.0905164	+	0.0759523i
$505$	19.9363	+	34.5307i	0.887153	+	1.53659i
$506$	2.47906	−	4.29385i	0.110207	−	0.190885i
$507$	−14.0890	+	5.12797i	−0.625714	+	0.227741i
$508$	−2.29086	−	12.9921i	−0.101640	−	0.576432i
$509$	−6.37046	+	36.1287i	−0.282366	+	1.60138i	0.432180	+	0.901787i	$0.357744\pi$
$509$	−6.37046	+	36.1287i	−0.282366	+	1.60138i	−0.714546	+	0.699589i	$0.753367\pi$
$510$	7.13816	+	2.59808i	0.316083	+	0.115045i
$511$	5.68092	−	4.76686i	0.251309	−	0.210873i
$512$	−1.00000			−0.0441942
$513$	2.77719	+	3.35965i	0.122616	+	0.148332i
$514$	30.7793			1.35762
$515$	−7.24304	+	6.07763i	−0.319166	+	0.267812i
$516$	5.56418	+	2.02520i	0.244949	+	0.0891542i
$517$	4.25624	−	24.1384i	0.187189	−	1.06160i
$518$	1.06196	+	6.02265i	0.0466597	+	0.264620i
$519$	15.0030	−	5.46064i	0.658558	−	0.239696i
$520$	5.89053	−	10.2027i	0.258317	−	0.447418i
$521$	18.7677	+	32.5066i	0.822228	+	1.42414i	0.904020	+	0.427491i	$0.140602\pi$
$521$	18.7677	+	32.5066i	0.822228	+	1.42414i	−0.0817923	+	0.996649i	$0.526064\pi$
$522$	−3.68866	−	3.09516i	−0.161448	−	0.135471i
$523$	0.304063	+	0.255139i	0.0132958	+	0.0111565i	0.649411	−	0.760437i	$-0.275015\pi$
$523$	0.304063	+	0.255139i	0.0132958	+	0.0111565i	−0.636116	+	0.771594i	$0.719460\pi$
$524$	−3.75150	−	6.49778i	−0.163885	−	0.283857i
$525$	−0.0555596	+	0.0962321i	−0.00242482	+	0.00419991i
$526$	2.95336	−	1.07494i	0.128773	−	0.0468694i
$527$	−6.10947	−	34.6485i	−0.266133	−	1.50931i
$528$	0.386659	−	2.19285i	0.0168272	−	0.0954317i
$529$	16.9538	+	6.17069i	0.737123	+	0.268291i
$530$	16.7554	−	14.0594i	0.727807	−	0.610702i
$531$	4.95811			0.215164
$532$	9.97090	+	5.85499i	0.432294	+	0.253846i
$533$	38.2763			1.65793
$534$	−5.98680	+	5.02352i	−0.259074	+	0.217389i
$535$	32.6498	+	11.8835i	1.41157	+	0.513770i
$536$	−1.48886	+	8.44372i	−0.0643088	+	0.364713i
$537$	0.252374	+	1.43128i	0.0108907	+	0.0617644i
$538$	13.9829	−	5.08937i	0.602847	−	0.219418i
$539$	−0.0410117	+	0.0710344i	−0.00176650	+	0.00305967i
$540$	1.11334	+	1.92836i	0.0479106	+	0.0829835i
$541$	−15.9730	−	13.4029i	−0.686731	−	0.576236i	0.231233	−	0.972898i	$-0.425724\pi$
$541$	−15.9730	−	13.4029i	−0.686731	−	0.576236i	−0.917965	+	0.396662i	$0.870168\pi$
$542$	−11.6702	−	9.79250i	−0.501280	−	0.420624i
$543$	0.562834	+	0.974856i	0.0241535	+	0.0418351i
$544$	−1.70574	+	2.95442i	−0.0731329	+	0.126670i
$545$	−2.84952	+	1.03714i	−0.122060	+	0.0444262i
$546$	−2.43717	−	13.8219i	−0.104301	−	0.591521i
$547$	−0.896926	+	5.08672i	−0.0383498	+	0.217492i	−0.997960	−	0.0638400i	$-0.979665\pi$
$547$	−0.896926	+	5.08672i	−0.0383498	+	0.217492i	0.959610	+	0.281332i	$0.0907764\pi$
$548$	−6.23055	−	2.26774i	−0.266156	−	0.0968729i
$549$	−4.36824	+	3.66539i	−0.186432	+	0.156435i
$550$	0.0932736			0.00397720
$551$	−18.0993	−	10.6280i	−0.771054	−	0.452769i
$552$	−2.22668			−0.0947739
$553$	−28.0442	+	23.5319i	−1.19256	+	1.00068i
$554$	−11.4731	−	4.17588i	−0.487446	−	0.177416i
$555$	−0.891407	+	5.05542i	−0.0378381	+	0.214591i
$556$	−1.47771	−	8.38052i	−0.0626689	−	0.355413i
$557$	−27.2173	+	9.90630i	−1.15324	+	0.419744i	−0.846677	−	0.532108i	$-0.821400\pi$
$557$	−27.2173	+	9.90630i	−1.15324	+	0.419744i	−0.306560	+	0.951851i	$0.599178\pi$
$558$	5.15657	−	8.93145i	0.218295	−	0.378098i
$559$	−15.6643	−	27.1314i	−0.662530	−	1.14754i
$560$	4.52481	+	3.79677i	0.191208	+	0.160443i
$561$	−5.81908	−	4.88279i	−0.245682	−	0.206151i
$562$	−1.12196	−	1.94329i	−0.0473270	−	0.0819727i
$563$	4.37892	−	7.58451i	0.184549	−	0.319649i	−0.758875	−	0.651236i	$-0.774251\pi$
$563$	4.37892	−	7.58451i	0.184549	−	0.319649i	0.943425	+	0.331587i	$0.107584\pi$
$564$	−10.3439	+	3.76487i	−0.435556	+	0.158530i
$565$	−6.65064	−	37.7177i	−0.279795	−	1.58679i
$566$	2.56805	−	14.5641i	0.107943	−	0.612176i
$567$	2.49273	+	0.907278i	0.104685	+	0.0381021i
$568$	−3.37346	+	2.83067i	−0.141547	+	0.118772i
$569$	11.3696			0.476638			0.238319	−	0.971187i	$-0.423404\pi$
$569$	11.3696			0.476638			0.238319	+	0.971187i	$0.423404\pi$
$570$	6.18392	+	7.48086i	0.259016	+	0.313339i
$571$	2.98545			0.124937			0.0624686	−	0.998047i	$-0.480103\pi$
$571$	2.98545			0.124937			0.0624686	+	0.998047i	$0.480103\pi$
$572$	−9.02481	+	7.57272i	−0.377346	+	0.316631i
$573$	1.24763	+	0.454099i	0.0521203	+	0.0189702i
$574$	−3.33244	+	18.8992i	−0.139094	+	0.788839i
$575$	−0.0161968	−	0.0918566i	−0.000675453	−	0.00383068i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	11.3735	−	19.6994i	0.473483	−	0.820097i	−0.526056	−	0.850450i	$-0.676330\pi$
$577$	11.3735	−	19.6994i	0.473483	−	0.820097i	0.999539	+	0.0303530i	$0.00966315\pi$
$578$	−2.68092	−	4.64349i	−0.111512	−	0.193144i
$579$	11.4795	+	9.63246i	0.477073	+	0.400311i
$580$	−8.21348	−	6.89193i	−0.341046	−	0.286172i
$581$	−13.9307	−	24.1286i	−0.577941	−	1.00102i
$582$	−8.89440	+	15.4056i	−0.368685	+	0.638581i
$583$	−20.5535	+	7.48086i	−0.851239	+	0.309826i
$584$	0.485452	+	2.75314i	0.0200882	+	0.113926i
$585$	2.04576	−	11.6021i	0.0845817	−	0.479687i
$586$	−11.3229	−	4.12122i	−0.467747	−	0.170246i
$587$	−12.6552	+	10.6190i	−0.522337	+	0.438293i	−0.865446	−	0.501003i	$-0.832965\pi$
$587$	−12.6552	+	10.6190i	−0.522337	+	0.438293i	0.343108	+	0.939296i	$0.388520\pi$
$588$	0.0368366			0.00151912
$589$	15.6857	−	42.1286i	0.646319	−	1.73588i
$590$	11.0401			0.454515
$591$	17.6250	−	14.7891i	0.724994	−	0.608342i
$592$	−2.16637	−	0.788496i	−0.0890374	−	0.0324070i
$593$	2.62355	−	14.8789i	0.107736	−	0.611003i	−0.882356	−	0.470583i	$-0.844044\pi$
$593$	2.62355	−	14.8789i	0.107736	−	0.611003i	0.990092	−	0.140420i	$-0.0448453\pi$
$594$	−0.386659	−	2.19285i	−0.0158648	−	0.0899739i
$595$	18.9354	−	6.89193i	0.776276	−	0.282541i
$596$	1.70574	−	2.95442i	0.0698697	−	0.121018i
$597$	−4.84137	−	8.38549i	−0.198144	−	0.343195i
$598$	9.02481	+	7.57272i	0.369052	+	0.309672i
$599$	−14.0326	−	11.7747i	−0.573355	−	0.481102i	0.309403	−	0.950931i	$-0.399871\pi$
$599$	−14.0326	−	11.7747i	−0.573355	−	0.481102i	−0.882757	+	0.469829i	$0.844315\pi$
$600$	−0.0209445	−	0.0362770i	−0.000855057	−	0.00148100i
$601$	1.78746	−	3.09596i	0.0729118	−	0.126287i	−0.827264	−	0.561813i	$-0.810104\pi$
$601$	1.78746	−	3.09596i	0.0729118	−	0.126287i	0.900176	+	0.435526i	$0.143437\pi$
$602$	14.7601	−	5.37224i	0.601577	−	0.218956i
$603$	1.48886	+	8.44372i	0.0606309	+	0.343855i
$604$	0.528218	−	2.99568i	0.0214929	−	0.121892i
$605$	−12.6420	−	4.60132i	−0.513971	−	0.187070i
$606$	−13.7173	+	11.5102i	−0.557229	+	0.467571i
$607$	10.9436			0.444186			0.222093	−	0.975026i	$-0.428711\pi$
$607$	10.9436			0.444186			0.222093	+	0.975026i	$0.428711\pi$
$608$	−3.79086	+	2.15160i	−0.153740	+	0.0872589i
$609$	−12.7733			−0.517601
$610$	−9.72668	+	8.16165i	−0.393822	+	0.330456i
$611$	54.7281	+	19.9194i	2.21406	+	0.805852i
$612$	−0.592396	+	3.35965i	−0.0239462	+	0.135806i
$613$	7.74345	+	43.9153i	0.312755	+	1.77372i	0.584541	+	0.811364i	$0.301275\pi$
$613$	7.74345	+	43.9153i	0.312755	+	1.77372i	−0.271786	+	0.962358i	$0.587614\pi$
$614$	21.2319	−	7.72778i	0.856850	−	0.311868i
$615$	−8.05438	+	13.9506i	−0.324784	+	0.562542i
$616$	−2.95336	−	5.11538i	−0.118994	−	0.206104i
$617$	−1.10876	−	0.930356i	−0.0446368	−	0.0374547i	0.620196	−	0.784447i	$-0.287053\pi$
$617$	−1.10876	−	0.930356i	−0.0446368	−	0.0374547i	−0.664833	+	0.746992i	$0.731497\pi$
$618$	−3.25284	−	2.72946i	−0.130848	−	0.109795i
$619$	23.6236	+	40.9173i	0.949513	+	1.64460i	0.746453	+	0.665438i	$0.231755\pi$
$619$	23.6236	+	40.9173i	0.949513	+	1.64460i	0.203060	+	0.979166i	$0.434911\pi$
$620$	11.4820	−	19.8875i	0.461130	−	0.798701i
$621$	−2.09240	+	0.761570i	−0.0839650	+	0.0305607i
$622$	1.96673	+	11.1539i	0.0788587	+	0.447230i
$623$	−3.59997	+	20.4165i	−0.144230	+	0.817969i
$624$	4.97178	+	1.80958i	0.199031	+	0.0724412i
$625$	−18.9893	+	15.9339i	−0.759573	+	0.637357i
$626$	5.95811			0.238134
$627$	−3.25237	−	9.14473i	−0.129887	−	0.365206i
$628$	−15.5253			−0.619526
$629$	−6.02481	+	5.05542i	−0.240225	+	0.201573i
$630$	5.55051	+	2.02022i	0.221138	+	0.0804875i
$631$	6.05010	−	34.3118i	0.240851	−	1.36593i	−0.589085	−	0.808071i	$-0.700512\pi$
$631$	6.05010	−	34.3118i	0.240851	−	1.36593i	0.829935	−	0.557860i	$-0.188377\pi$
$632$	−2.39646	−	13.5910i	−0.0953260	−	0.540621i
$633$	1.03936	−	0.378297i	0.0413110	−	0.0150360i
$634$	−4.46198	+	7.72838i	−0.177208	+	0.306933i
$635$	−14.6878	−	25.4400i	−0.582867	−	1.00956i
$636$	7.52481	+	6.31407i	0.298378	+	0.250369i
$637$	−0.149300	−	0.125278i	−0.00591548	−	0.00496368i
$638$	5.36097	+	9.28547i	0.212243	+	0.367615i
$639$	−2.20187	+	3.81374i	−0.0871045	+	0.150869i
$640$	−2.09240	+	0.761570i	−0.0827092	+	0.0301037i
$641$	1.90286	+	10.7916i	0.0751583	+	0.426244i	0.999050	+	0.0435888i	$0.0138791\pi$
$641$	1.90286	+	10.7916i	0.0751583	+	0.426244i	−0.923891	+	0.382655i	$0.875010\pi$
$642$	−2.70961	+	15.3669i	−0.106940	+	0.606485i
$643$	−3.47683	−	1.26546i	−0.137113	−	0.0499050i	0.272552	−	0.962141i	$-0.412132\pi$
$643$	−3.47683	−	1.26546i	−0.137113	−	0.0499050i	−0.409665	+	0.912236i	$0.634354\pi$
$644$	−4.52481	+	3.79677i	−0.178303	+	0.149614i
$645$	13.1848			0.519151
$646$	−0.109470	+	14.8699i	−0.00430706	+	0.585047i
$647$	26.2671			1.03267			0.516334	−	0.856387i	$-0.327296\pi$
$647$	26.2671			1.03267			0.516334	+	0.856387i	$0.327296\pi$
$648$	−0.766044	+	0.642788i	−0.0300931	+	0.0252511i
$649$	−10.3743	−	3.77595i	−0.407228	−	0.148219i
$650$	−0.0384855	+	0.218262i	−0.00150953	+	0.00856094i
$651$	−4.75062	−	26.9421i	−0.186191	−	1.05594i
$652$	−4.17112	+	1.51816i	−0.163354	+	0.0594559i
$653$	−13.0783	+	22.6523i	−0.511794	+	0.886453i	0.488113	+	0.872781i	$0.337686\pi$
$653$	−13.0783	+	22.6523i	−0.511794	+	0.886453i	−0.999907	+	0.0136725i	$0.995648\pi$
$654$	−0.680922	−	1.17939i	−0.0266262	−	0.0461179i
$655$	−12.7981	−	10.7389i	−0.500064	−	0.419604i
$656$	−5.54189	−	4.65020i	−0.216374	−	0.181560i
$657$	1.39780	+	2.42107i	0.0545335	+	0.0944548i
$658$	−14.6001	+	25.2882i	−0.569173	+	0.985836i
$659$	−25.2592	+	9.19361i	−0.983960	+	0.358132i	−0.783379	−	0.621545i	$-0.786505\pi$
$659$	−25.2592	+	9.19361i	−0.983960	+	0.358132i	−0.200582	+	0.979677i	$0.564283\pi$
$660$	−0.860967	−	4.88279i	−0.0335131	−	0.190062i
$661$	0.972086	−	5.51297i	0.0378098	−	0.214430i	−0.960049	−	0.279831i	$-0.909722\pi$
$661$	0.972086	−	5.51297i	0.0378098	−	0.214430i	0.997859	+	0.0654011i	$0.0208327\pi$
$662$	6.25789	+	2.27769i	0.243220	+	0.0885248i
$663$	13.8268	−	11.6021i	0.536989	−	0.450587i
$664$	10.5030			0.407595
$665$	25.3221	+	4.65743i	0.981948	+	0.180607i
$666$	−2.30541			−0.0893327
$667$	8.21348	−	6.89193i	0.318027	−	0.266856i
$668$	7.65910	+	2.78768i	0.296339	+	0.107859i
$669$	4.39100	−	24.9026i	0.169766	−	0.962789i
$670$	3.31521	+	18.8015i	0.128078	+	0.726364i
$671$	11.9315	−	4.34273i	0.460612	−	0.167649i
$672$	−1.32635	+	2.29731i	−0.0511651	+	0.0886206i
$673$	−11.4966	−	19.9127i	−0.443161	−	0.767578i	0.554761	−	0.832010i	$-0.312810\pi$
$673$	−11.4966	−	19.9127i	−0.443161	−	0.767578i	−0.997922	+	0.0644321i	$0.979476\pi$
$674$	8.29607	+	6.96123i	0.319553	+	0.268137i
$675$	−0.0320889	−	0.0269258i	−0.00123510	−	0.00103637i
$676$	−7.49660	−	12.9845i	−0.288331	−	0.499403i
$677$	−7.66772	+	13.2809i	−0.294694	+	0.510426i	−0.974914	−	0.222583i	$-0.928551\pi$
$677$	−7.66772	+	13.2809i	−0.294694	+	0.510426i	0.680219	+	0.733009i	$0.261885\pi$
$678$	16.1630	−	5.88284i	0.620735	−	0.225929i
$679$	8.19418	+	46.4715i	0.314464	+	1.78341i
$680$	−1.31908	+	7.48086i	−0.0505843	+	0.286878i
$681$	−3.22193	−	1.17269i	−0.123465	−	0.0449375i
$682$	−17.5915	+	14.7610i	−0.673614	+	0.565229i
$683$	−19.6459			−0.751729			−0.375865	−	0.926675i	$-0.622654\pi$
$683$	−19.6459			−0.751729			−0.375865	+	0.926675i	$0.622654\pi$
$684$	−2.82635	+	3.31839i	−0.108068	+	0.126882i
$685$	−14.7638			−0.564097
$686$	−14.1498	+	11.8731i	−0.540241	+	0.453316i
$687$	−28.1361	−	10.2407i	−1.07346	−	0.390707i
$688$	−1.02822	+	5.83132i	−0.0392005	+	0.222317i
$689$	−9.02481	−	51.1823i	−0.343818	−	1.94989i
$690$	−4.65910	+	1.69577i	−0.177369	+	0.0645570i
$691$	−9.73442	+	16.8605i	−0.370315	+	0.641404i	−0.989614	−	0.143751i	$-0.954084\pi$
$691$	−9.73442	+	16.8605i	−0.370315	+	0.641404i	0.619299	+	0.785155i	$0.287417\pi$
$692$	7.98293	+	13.8268i	0.303465	+	0.525617i
$693$	−4.52481	−	3.79677i	−0.171884	−	0.144227i
$694$	−15.8275	−	13.2809i	−0.600805	−	0.504135i
$695$	−9.47431	−	16.4100i	−0.359381	−	0.622466i
$696$	2.40760	−	4.17009i	0.0912600	−	0.158067i
$697$	−23.1917	+	8.44107i	−0.878447	+	0.319728i
$698$	0.354160	+	2.00854i	0.0134051	+	0.0760244i
$699$	−1.80200	+	10.2197i	−0.0681580	+	0.386543i
$700$	−0.104418	−	0.0380050i	−0.00394663	−	0.00143646i
$701$	16.9433	−	14.2171i	0.639940	−	0.536974i	−0.264060	−	0.964506i	$-0.585062\pi$
$701$	16.9433	−	14.2171i	0.639940	−	0.536974i	0.904000	+	0.427533i	$0.140617\pi$
$702$	5.29086			0.199691
$703$	−9.90895	+	1.67210i	−0.373723	+	0.0630643i
$704$	2.22668			0.0839212
$705$	−18.7763	+	15.7552i	−0.707157	+	0.593375i
$706$	29.4136	+	10.7057i	1.10700	+	0.402913i
$707$	−8.24850	+	46.7796i	−0.310217	+	1.75933i
$708$	0.860967	+	4.88279i	0.0323571	+	0.183506i
$709$	−8.96451	+	3.26281i	−0.336669	+	0.122538i	−0.504822	−	0.863223i	$-0.668442\pi$
$709$	−8.96451	+	3.26281i	−0.336669	+	0.122538i	0.168153	+	0.985761i	$0.446220\pi$
$710$	−4.90286	+	8.49200i	−0.184001	+	0.318699i
$711$	−6.90033	−	11.9517i	−0.258783	−	0.448225i
$712$	−5.98680	−	5.02352i	−0.224365	−	0.188264i
$713$	17.5915	+	14.7610i	0.658808	+	0.552805i
$714$	4.52481	+	7.83721i	0.169337	+	0.293300i
$715$	−13.1163	+	22.7182i	−0.490523	+	0.849611i
$716$	−1.36571	+	0.497079i	−0.0510392	+	0.0185767i
$717$	−2.78106	−	15.7722i	−0.103861	−	0.589022i
$718$	1.54664	−	8.77141i	0.0577200	−	0.327346i
$719$	36.4479	+	13.2660i	1.35928	+	0.494736i	0.915831	−	0.401564i	$-0.131533\pi$
$719$	36.4479	+	13.2660i	1.35928	+	0.494736i	0.443447	+	0.896301i	$0.353756\pi$
$720$	−1.70574	+	1.43128i	−0.0635691	+	0.0533408i
$721$	−11.2641			−0.419498
$722$	−9.74123	+	16.3128i	−0.362531	+	0.607101i
$723$	25.5817			0.951394
$724$	−0.862311	+	0.723565i	−0.0320475	+	0.0268911i
$725$	0.189540	+	0.0689870i	0.00703935	+	0.00256211i
$726$	1.04916	−	5.95010i	0.0389381	−	0.220829i
$727$	−6.22446	−	35.3007i	−0.230852	−	1.30923i	−0.851175	−	0.524882i	$-0.824109\pi$
$727$	−6.22446	−	35.3007i	−0.230852	−	1.30923i	0.620322	−	0.784347i	$-0.287002\pi$
$728$	13.1887	−	4.80028i	0.488804	−	0.177910i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	3.11246	+	5.39094i	0.115197	+	0.199528i
$731$	15.4743	+	12.9845i	0.572338	+	0.480249i
$732$	−4.36824	−	3.66539i	−0.161455	−	0.135477i
$733$	−0.201867	−	0.349643i	−0.00745612	−	0.0129144i	0.862273	−	0.506443i	$-0.169040\pi$
$733$	−0.201867	−	0.349643i	−0.00745612	−	0.0129144i	−0.869729	+	0.493529i	$0.835707\pi$
$734$	1.72028	−	2.97962i	0.0634969	−	0.109980i
$735$	0.0770768	−	0.0280537i	0.00284302	−	0.00103478i
$736$	−0.386659	−	2.19285i	−0.0142524	−	0.0808296i
$737$	3.31521	−	18.8015i	0.122117	−	0.692561i
$738$	−6.79813	−	2.47432i	−0.250243	−	0.0910809i
$739$	−0.456052	+	0.382673i	−0.0167761	+	0.0140768i	−0.651137	−	0.758960i	$-0.725708\pi$
$739$	−0.456052	+	0.382673i	−0.0167761	+	0.0140768i	0.634361	+	0.773037i	$0.281263\pi$
$740$	−5.13341			−0.188708
$741$	22.7408	−	3.83742i	0.835405	−	0.140971i
$742$	26.0574			0.956596
$743$	9.09627	−	7.63267i	0.333710	−	0.280016i	−0.460500	−	0.887660i	$-0.652330\pi$
$743$	9.09627	−	7.63267i	0.333710	−	0.280016i	0.794209	+	0.607644i	$0.207885\pi$
$744$	9.69119	+	3.52730i	0.355296	+	0.129317i
$745$	1.31908	−	7.48086i	0.0483273	−	0.274078i
$746$	1.09745	+	6.22394i	0.0401805	+	0.227875i
$747$	9.86959	−	3.59224i	0.361109	−	0.131433i
$748$	3.79813	−	6.57856i	0.138874	−	0.240536i
$749$	20.6964	+	35.8472i	0.756230	+	1.30983i
$750$	−8.60014	−	7.21637i	−0.314033	−	0.263505i
$751$	4.18067	+	3.50800i	0.152555	+	0.128009i	0.715871	−	0.698233i	$-0.246030\pi$
$751$	4.18067	+	3.50800i	0.152555	+	0.128009i	−0.563316	+	0.826242i	$0.690474\pi$
$752$	−5.50387	−	9.53298i	−0.200706	−	0.347632i
$753$	−5.34477	+	9.25741i	−0.194774	+	0.337359i
$754$	−23.9402	+	8.71351i	−0.871849	+	0.317327i
$755$	−1.17617	−	6.67042i	−0.0428054	−	0.242761i
$756$	−0.460637	+	2.61240i	−0.0167532	+	0.0950122i
$757$	−11.3645	−	4.13635i	−0.413051	−	0.150338i	0.127132	−	0.991886i	$-0.459423\pi$
$757$	−11.3645	−	4.13635i	−0.413051	−	0.150338i	−0.540183	+	0.841548i	$0.681645\pi$
$758$	11.0367	−	9.26087i	0.400870	−	0.336370i
$759$	4.95811			0.179968
$760$	−6.29339	+	7.38901i	−0.228285	+	0.268027i
$761$	−18.8726			−0.684130			−0.342065	−	0.939676i	$-0.611126\pi$
$761$	−18.8726			−0.684130			−0.342065	+	0.939676i	$0.611126\pi$
$762$	10.1061	−	8.48000i	0.366104	−	0.307198i
$763$	−3.39470	−	1.23557i	−0.122897	−	0.0447307i
$764$	−0.230552	+	1.30753i	−0.00834108	+	0.0473046i
$765$	1.31908	+	7.48086i	0.0476914	+	0.270471i
$766$	−1.77719	+	0.646844i	−0.0642124	+	0.0233714i
$767$	13.1163	−	22.7182i	0.473603	−	0.820305i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−38.5094	−	32.3132i	−1.38868	−	1.16524i	−0.965870	−	0.259028i	$-0.916598\pi$
$769$	−38.5094	−	32.3132i	−1.38868	−	1.16524i	−0.422814	−	0.906216i	$-0.638958\pi$
$770$	−10.0753	−	8.45420i	−0.363089	−	0.304668i
$771$	15.3897	+	26.6557i	0.554245	+	0.959980i
$772$	−7.49273	+	12.9778i	−0.269669	+	0.467081i
$773$	20.1887	−	7.34807i	0.726136	−	0.264292i	0.0476075	−	0.998866i	$-0.484840\pi$
$773$	20.1887	−	7.34807i	0.726136	−	0.264292i	0.678528	+	0.734574i	$0.262618\pi$
$774$	1.02822	+	5.83132i	0.0369586	+	0.209602i
$775$	−0.0750174	+	0.425445i	−0.00269471	+	0.0152824i
$776$	−16.7160	−	6.08413i	−0.600070	−	0.218407i
$777$	−4.68479	+	3.93101i	−0.168066	+	0.141024i
$778$	7.37733			0.264490
$779$	−31.0139	−	5.70431i	−1.11119	−	0.204378i
$780$	11.7811			0.421830
$781$	7.51161	−	6.30299i	0.268787	−	0.225539i
$782$	−7.13816	−	2.59808i	−0.255260	−	0.0929070i
$783$	0.836152	−	4.74205i	0.0298816	−	0.169467i
$784$	0.00639661	+	0.0362770i	0.000228450	+	0.00129561i
$785$	−32.4850	+	11.8236i	−1.15944	+	0.422002i
$786$	3.75150	−	6.49778i	0.133811	−	0.231768i
$787$	11.2750	+	19.5288i	0.401909	+	0.696127i	0.993956	−	0.109776i	$-0.0350134\pi$
$787$	11.2750	+	19.5288i	0.401909	+	0.696127i	−0.592047	+	0.805903i	$0.701680\pi$
$788$	17.6250	+	14.7891i	0.627863	+	0.526840i
$789$	2.40760	+	2.02022i	0.0857130	+	0.0719217i
$790$	−15.3648	−	26.6127i	−0.546656	−	0.946837i
$791$	22.8136	−	39.5143i	0.811159	−	1.40497i
$792$	2.09240	−	0.761570i	0.0743501	−	0.0270612i
$793$	5.23901	+	29.7119i	0.186043	+	1.05510i
$794$	2.01027	−	11.4008i	0.0713417	−	0.404599i
$795$	20.5535	+	7.48086i	0.728958	+	0.265319i
$796$	7.41740	−	6.22394i	0.262903	−	0.220602i
$797$	−27.2098			−0.963819			−0.481910	−	0.876221i	$-0.660057\pi$
$797$	−27.2098			−0.963819			−0.481910	+	0.876221i	$0.660057\pi$
$798$	−0.0851223	+	11.5626i	−0.00301330	+	0.409310i
$799$	−37.5526			−1.32852
$800$	0.0320889	−	0.0269258i	0.00113451	−	0.000951970i
$801$	−7.34389	−	2.67296i	−0.259484	−	0.0944443i
$802$	−2.64115	+	14.9787i	−0.0932622	+	0.528916i
$803$	−1.08095	−	6.13036i	−0.0381458	−	0.216336i
$804$	−8.05690	+	2.93247i	−0.284145	+	0.103420i
$805$	−6.57620	+	11.3903i	−0.231781	+	0.401456i
$806$	−27.2827	−	47.2550i	−0.960992	−	1.66449i
$807$	11.3990	+	9.56488i	0.401263	+	0.336700i
$808$	−13.7173	−	11.5102i	−0.482575	−	0.404928i
$809$	14.6762	+	25.4199i	0.515987	+	0.893715i	0.999828	+	0.0185594i	$0.00590799\pi$
$809$	14.6762	+	25.4199i	0.515987	+	0.893715i	−0.483841	+	0.875156i	$0.660759\pi$
$810$	−1.11334	+	1.92836i	−0.0391188	+	0.0677558i
$811$	−17.9547	+	6.53498i	−0.630475	+	0.229474i	−0.637438	−	0.770502i	$-0.720006\pi$
$811$	−17.9547	+	6.53498i	−0.630475	+	0.229474i	0.00696301	+	0.999976i	$0.497784\pi$
$812$	−2.21806	−	12.5793i	−0.0778388	−	0.441446i
$813$	2.64543	−	15.0030i	0.0927793	−	0.526177i
$814$	4.82383	+	1.75573i	0.169075	+	0.0615383i
$815$	−7.57145	+	6.35320i	−0.265216	+	0.222543i
$816$	−3.41147			−0.119425
$817$	8.64883	+	24.3180i	0.302584	+	0.850780i
$818$	1.53116			0.0535356
$819$	10.7515	−	9.02158i	0.375688	−	0.315239i
$820$	−15.1373	−	5.50952i	−0.528617	−	0.192401i
$821$	0.0730443	−	0.414255i	0.00254926	−	0.0144576i	−0.983507	−	0.180872i	$-0.942108\pi$
$821$	0.0730443	−	0.414255i	0.00254926	−	0.0144576i	0.986056	+	0.166415i	$0.0532190\pi$
$822$	−1.15136	−	6.52968i	−0.0401583	−	0.227749i
$823$	34.4286	−	12.5310i	1.20011	−	0.436803i	0.336845	−	0.941560i	$-0.390640\pi$
$823$	34.4286	−	12.5310i	1.20011	−	0.436803i	0.863261	+	0.504758i	$0.168418\pi$
$824$	2.12314	−	3.67739i	0.0739631	−	0.128108i
$825$	0.0466368	+	0.0807773i	0.00162369	+	0.00281231i
$826$	10.0753	+	8.45420i	0.350565	+	0.294159i
$827$	22.5876	+	18.9533i	0.785449	+	0.659070i	0.944615	−	0.328182i	$-0.106436\pi$
$827$	22.5876	+	18.9533i	0.785449	+	0.659070i	−0.159165	+	0.987252i	$0.550880\pi$
$828$	−1.11334	−	1.92836i	−0.0386913	−	0.0670152i
$829$	2.81315	−	4.87252i	0.0977047	−	0.169229i	−0.813030	−	0.582222i	$-0.802183\pi$
$829$	2.81315	−	4.87252i	0.0977047	−	0.169229i	0.910734	+	0.412993i	$0.135517\pi$
$830$	21.9764	−	7.99876i	0.762813	−	0.277641i
$831$	−2.12015	−	12.0240i	−0.0735471	−	0.417106i
$832$	−0.918748	+	5.21048i	−0.0318519	+	0.180641i
$833$	0.118089	+	0.0429807i	0.00409153	+	0.00148919i
$834$	6.51889	−	5.46999i	0.225731	−	0.189410i
$835$	18.1489			0.628068
$836$	8.44104	−	4.79093i	0.291939	−	0.165698i
$837$	10.3131			0.356475
$838$	20.4820	−	17.1865i	0.707541	−	0.593697i
$839$	−40.4213	−	14.7122i	−1.39550	−	0.507920i	−0.468660	−	0.883379i	$-0.655263\pi$
$839$	−40.4213	−	14.7122i	−1.39550	−	0.507920i	−0.926839	+	0.375458i	$0.877485\pi$
$840$	−1.02569	+	5.81699i	−0.0353897	+	0.200705i
$841$	−1.00955	−	5.72545i	−0.0348121	−	0.197429i
$842$	22.4329	−	8.16490i	0.773088	−	0.281381i
$843$	1.12196	−	1.94329i	0.0386423	−	0.0669305i
$844$	0.553033	+	0.957882i	0.0190362	+	0.0329717i
$845$	−25.5744	−	21.4595i	−0.879788	−	0.738229i
$846$	−8.43242	−	7.07564i	−0.289913	−	0.243265i
$847$	−8.01367	−	13.8801i	−0.275353	−	0.476925i
$848$	−4.91147	+	8.50692i	−0.168661	+	0.292129i
$849$	13.8969	−	5.05807i	0.476941	−	0.173592i
$850$	−0.0248149	−	0.140732i	−0.000851145	−	0.00482708i
$851$	0.891407	−	5.05542i	0.0305570	−	0.173298i
$852$	−4.13816	−	1.50617i	−0.141771	−	0.0516004i
$853$	18.1480	−	15.2279i	0.621374	−	0.521395i	−0.276861	−	0.960910i	$-0.589294\pi$
$853$	18.1480	−	15.2279i	0.621374	−	0.521395i	0.898235	+	0.439515i	$0.144850\pi$
$854$	−15.1266			−0.517622
$855$	−3.38666	+	9.09586i	−0.115821	+	0.311072i
$856$	−15.6040			−0.533334
$857$	38.6862	−	32.4616i	1.32150	−	1.10887i	0.335509	−	0.942037i	$-0.391092\pi$
$857$	38.6862	−	32.4616i	1.32150	−	1.10887i	0.985986	−	0.166829i	$-0.0533529\pi$
$858$	−11.0706	−	4.02936i	−0.377943	−	0.137560i
$859$	0.864066	−	4.90036i	0.0294815	−	0.167198i	−0.966512	−	0.256620i	$-0.917391\pi$
$859$	0.864066	−	4.90036i	0.0294815	−	0.167198i	0.995994	+	0.0894223i	$0.0285021\pi$
$860$	2.28952	+	12.9845i	0.0780718	+	0.442767i
$861$	−18.0334	+	6.56363i	−0.614578	+	0.223688i
$862$	7.88965	−	13.6653i	0.268723	−	0.465441i
$863$	3.95424	+	6.84895i	0.134604	+	0.233141i	0.925446	−	0.378879i	$-0.123690\pi$
$863$	3.95424	+	6.84895i	0.134604	+	0.233141i	−0.790842	+	0.612020i	$0.790357\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	27.2335	+	22.8517i	0.925968	+	0.776980i
$866$	−6.70914	−	11.6206i	−0.227986	−	0.394883i
$867$	2.68092	−	4.64349i	0.0910489	−	0.157701i
$868$	25.7079	−	9.35689i	0.872581	−	0.317594i
$869$	5.33615	+	30.2628i	0.181017	+	1.02660i
$870$	1.86184	−	10.5590i	0.0631224	−	0.357985i
$871$	42.6279	+	15.5153i	1.44439	+	0.525716i
$872$	1.04323	−	0.875377i	0.0353283	−	0.0296440i
$873$	−17.7888			−0.602060
$874$	−6.18392	−	7.48086i	−0.209174	−	0.253044i
$875$	−29.7811			−1.00678
$876$	−2.14156	+	1.79698i	−0.0723566	+	0.0607144i
$877$	7.17664	+	2.61208i	0.242338	+	0.0882038i	0.460334	−	0.887746i	$-0.347730\pi$
$877$	7.17664	+	2.61208i	0.242338	+	0.0882038i	−0.217996	+	0.975950i	$0.569952\pi$
$878$	−3.28224	+	18.6145i	−0.110770	+	0.628209i
$879$	−2.09240	−	11.8666i	−0.0705748	−	0.400249i
$880$	4.65910	−	1.69577i	0.157058	−	0.0571645i
$881$	−9.44491	+	16.3591i	−0.318207	+	0.551151i	−0.980114	−	0.198435i	$-0.936414\pi$
$881$	−9.44491	+	16.3591i	−0.318207	+	0.551151i	0.661907	+	0.749586i	$0.269747\pi$
$882$	0.0184183	+	0.0319015i	0.000620177	+	0.00107418i
$883$	41.1339	+	34.5154i	1.38427	+	1.16154i	0.967604	+	0.252475i	$0.0812444\pi$
$883$	41.1339	+	34.5154i	1.38427	+	1.16154i	0.416662	+	0.909062i	$0.363200\pi$
$884$	13.8268	+	11.6021i	0.465046	+	0.390220i
$885$	5.52007	+	9.56104i	0.185555	+	0.321391i
$886$	−5.64677	+	9.78050i	−0.189707	+	0.328582i
$887$	45.8680	−	16.6946i	1.54010	−	0.560549i	0.574028	−	0.818836i	$-0.305380\pi$
$887$	45.8680	−	16.6946i	1.54010	−	0.560549i	0.966068	+	0.258286i	$0.0831578\pi$
$888$	−0.400330	−	2.27038i	−0.0134342	−	0.0761891i
$889$	6.07697	−	34.4642i	0.203815	−	1.15589i
$890$	−16.3525	−	5.95183i	−0.548137	−	0.199506i
$891$	1.70574	−	1.43128i	0.0571443	−	0.0479498i
$892$	25.2867			0.846663
$893$	−41.3756	−	24.2961i	−1.38458	−	0.813037i
$894$	3.41147			0.114097
$895$	−2.47906	+	2.08017i	−0.0828657	+	0.0695326i
$896$	−2.49273	−	0.907278i	−0.0832761	−	0.0303100i
$897$	−2.04576	+	11.6021i	−0.0683059	+	0.387382i
$898$	1.52023	+	8.62165i	0.0507307	+	0.287708i
$899$	−46.6651	+	16.9847i	−1.55637	+	0.566472i
$900$	0.0209445	−	0.0362770i	0.000698151	−	0.00120923i
$901$	16.7554	+	29.0211i	0.558202	+	0.966835i
$902$	12.3400	+	10.3545i	0.410878	+	0.344767i
$903$	12.0326	+	10.0965i	0.400418	+	0.335991i
$904$	8.60014	+	14.8959i	0.286036	+	0.495429i
$905$	−1.25325	+	2.17069i	−0.0416595	+	0.0721563i
$906$	2.85844	−	1.04039i	0.0949653	−	0.0345646i
$907$	−7.04623	−	39.9611i	−0.233966	−	1.32689i	−0.844780	−	0.535114i	$-0.820269\pi$
$907$	−7.04623	−	39.9611i	−0.233966	−	1.32689i	0.610814	−	0.791774i	$-0.290842\pi$
$908$	0.595389	−	3.37662i	0.0197587	−	0.112057i
$909$	−16.8268	−	6.12446i	−0.558110	−	0.203136i
$910$	23.9402	−	20.0882i	0.793609	−	0.665917i
$911$	36.0384			1.19400			0.597002	−	0.802239i	$-0.296358\pi$
$911$	36.0384			1.19400			0.597002	+	0.802239i	$0.296358\pi$
$912$	−3.75877	−	2.20718i	−0.124465	−	0.0730870i
$913$	−23.3868			−0.773991
$914$	−18.2574	+	15.3198i	−0.603902	+	0.506734i
$915$	−11.9315	−	4.34273i	−0.394445	−	0.143566i
$916$	5.19934	−	29.4869i	0.171791	−	0.974275i
$917$	−3.45616	−	19.6008i	−0.114132	−	0.647277i
$918$	−3.20574	+	1.16679i	−0.105805	+	0.0385099i
$919$	−13.0959	+	22.6827i	−0.431992	+	0.748233i	−0.997045	−	0.0768222i	$-0.975523\pi$
$919$	−13.0959	+	22.6827i	−0.431992	+	0.748233i	0.565052	+	0.825055i	$0.308856\pi$
$920$	−2.47906	−	4.29385i	−0.0817320	−	0.141564i
$921$	17.3084	+	14.5235i	0.570331	+	0.478565i
$922$	−12.0628	−	10.1219i	−0.397268	−	0.333348i
$923$	11.6498	+	20.1780i	0.383457	+	0.664167i
$924$	2.95336	−	5.11538i	0.0971585	−	0.168283i
$925$	0.0907474	−	0.0330293i	0.00298376	−	0.00108600i
$926$	0.759648	+	4.30818i	0.0249636	+	0.141575i
$927$	0.737359	−	4.18177i	0.0242181	−	0.137347i
$928$	4.52481	+	1.64690i	0.148534	+	0.0540621i
$929$	37.0185	−	31.0622i	1.21454	−	1.01912i	0.215445	−	0.976516i	$-0.430880\pi$
$929$	37.0185	−	31.0622i	1.21454	−	1.01912i	0.999092	−	0.0426013i	$-0.0135645\pi$
$930$	22.9641			0.753022
$931$	0.102302	+	0.123758i	0.00335282	+	0.00405601i
$932$	−10.3773			−0.339921
$933$	−8.67617	+	7.28017i	−0.284045	+	0.238342i
$934$	24.5326	+	8.92912i	0.802730	+	0.292170i
$935$	2.93717	−	16.6575i	0.0960556	−	0.544758i
$936$	0.918748	+	5.21048i	0.0300302	+	0.170310i
$937$	−55.6220	+	20.2448i	−1.81709	+	0.661367i	−0.821219	+	0.570614i	$0.806705\pi$
$937$	−55.6220	+	20.2448i	−1.81709	+	0.661367i	−0.995873	+	0.0907538i	$0.971072\pi$
$938$	−11.3721	+	19.6971i	−0.371313	+	0.643132i
$939$	2.97906	+	5.15988i	0.0972178	+	0.168386i
$940$	−18.7763	−	15.7552i	−0.612416	−	0.513878i
$941$	4.43557	+	3.72189i	0.144596	+	0.121330i	0.712216	−	0.701960i	$-0.247692\pi$
$941$	4.43557	+	3.72189i	0.144596	+	0.121330i	−0.567621	+	0.823290i	$0.692136\pi$
$942$	−7.76264	−	13.4453i	−0.252921	−	0.438071i
$943$	8.05438	−	13.9506i	0.262287	−	0.454294i
$944$	−4.65910	+	1.69577i	−0.151641	+	0.0551927i
$945$	1.02569	+	5.81699i	0.0333658	+	0.189227i
$946$	2.28952	−	12.9845i	0.0744386	−	0.422162i
$947$	43.1441	+	15.7032i	1.40200	+	0.510285i	0.928770	−	0.370656i	$-0.120867\pi$
$947$	43.1441	+	15.7032i	1.40200	+	0.510285i	0.473226	+	0.880941i	$0.343089\pi$
$948$	10.5719	−	8.87089i	0.343360	−	0.288113i
$949$	14.7912			0.480142
$950$	0.0637109	−	0.171114i	0.00206706	−	0.00555168i
$951$	−8.92396			−0.289379
$952$	−6.93242	+	5.81699i	−0.224681	+	0.188530i
$953$	−26.8307	−	9.76557i	−0.869131	−	0.316338i	−0.131316	−	0.991341i	$-0.541920\pi$
$953$	−26.8307	−	9.76557i	−0.869131	−	0.316338i	−0.737815	+	0.675003i	$0.764142\pi$
$954$	−1.70574	+	9.67372i	−0.0552253	+	0.313198i
$955$	0.513366	+	2.91144i	0.0166121	+	0.0942121i
$956$	15.0496	−	5.47762i	0.486740	−	0.177159i
$957$	−5.36097	+	9.28547i	−0.173295	+	0.300157i
$958$	−17.0620	−	29.5522i	−0.551247	−	0.954787i
$959$	−13.4736	−	11.3057i	−0.435085	−	0.365080i
$960$	−1.70574	−	1.43128i	−0.0550524	−	0.0461945i
$961$	−37.6805	−	65.2646i	−1.21550	−	2.10531i
$962$	−6.09879	+	10.5634i	−0.196633	+	0.340578i
$963$	−14.6630	+	5.33688i	−0.472508	+	0.171979i
$964$	4.44222	+	25.1931i	0.143074	+	0.811414i
$965$	−5.79426	+	32.8609i	−0.186524	+	1.05783i
$966$	−5.55051	−	2.02022i	−0.178585	−	0.0649995i
$967$	−16.9140	+	14.1925i	−0.543918	+	0.456401i	−0.872875	−	0.487944i	$-0.837747\pi$
$967$	−16.9140	+	14.1925i	−0.543918	+	0.456401i	0.328958	+	0.944345i	$0.393303\pi$
$968$	6.04189			0.194194
$969$	−12.9324	+	7.34013i	−0.415449	+	0.235799i
$970$	−39.6100			−1.27180
$971$	−9.70645	+	8.14468i	−0.311495	+	0.261375i	−0.785110	−	0.619357i	$-0.787393\pi$
$971$	−9.70645	+	8.14468i	−0.311495	+	0.261375i	0.473615	+	0.880732i	$0.342949\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	3.91993	−	22.2310i	0.125667	−	0.712694i
$974$	2.73736	+	15.5243i	0.0877106	+	0.497432i
$975$	−0.208263	+	0.0758016i	−0.00666976	+	0.00242760i
$976$	2.85117	−	4.93837i	0.0912636	−	0.158073i
$977$	8.62495	+	14.9389i	0.275937	+	0.477936i	0.970371	−	0.241620i	$-0.0776787\pi$
$977$	8.62495	+	14.9389i	0.275937	+	0.477936i	−0.694434	+	0.719556i	$0.744345\pi$
$978$	−3.40033	−	2.85322i	−0.108731	−	0.0912358i
$979$	13.3307	+	11.1858i	0.426051	+	0.357499i
$980$	0.0410117	+	0.0710344i	0.00131007	+	0.00226911i
$981$	0.680922	−	1.17939i	0.0217402	−	0.0376551i
$982$	13.0039	−	4.73302i	0.414970	−	0.151037i
$983$	−1.05509	−	5.98373i	−0.0336522	−	0.190851i	0.963347	−	0.268257i	$-0.0864475\pi$
$983$	−1.05509	−	5.98373i	−0.0336522	−	0.190851i	−0.997000	+	0.0774054i	$0.975336\pi$
$984$	1.25624	−	7.12452i	0.0400476	−	0.227121i
$985$	48.1413	+	17.5220i	1.53391	+	0.558297i
$986$	12.5838	−	10.5590i	0.400749	−	0.336268i
$987$	−29.2003			−0.929455
$988$	7.72803	+	21.7290i	0.245861	+	0.691291i
$989$	−13.1848			−0.419252
$990$	3.79813	−	3.18701i	0.120713	−	0.101290i
$991$	9.37851	+	3.41350i	0.297918	+	0.108433i	0.486655	−	0.873594i	$-0.338217\pi$
$991$	9.37851	+	3.41350i	0.297918	+	0.108433i	−0.188737	+	0.982028i	$0.560439\pi$
$992$	−1.79086	+	10.1565i	−0.0568598	+	0.322468i
$993$	1.15641	+	6.55834i	0.0366976	+	0.208123i
$994$	−10.9773	+	3.99541i	−0.348179	+	0.126727i
$995$	10.7802	−	18.6718i	0.341755	−	0.591937i
$996$	5.25150	+	9.09586i	0.166400	+	0.288213i
$997$	19.3840	+	16.2651i	0.613897	+	0.515120i	0.895878	−	0.444299i	$-0.146547\pi$
$997$	19.3840	+	16.2651i	0.613897	+	0.515120i	−0.281982	+	0.959420i	$0.590992\pi$
$998$	15.2665	+	12.8101i	0.483253	+	0.405497i
$999$	−1.15270	−	1.99654i	−0.0364699	−	0.0631678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.a.25.1	✓	6
3.2	odd	2		342.2.u.e.253.1		6
4.3	odd	2		912.2.bo.a.481.1		6
19.4	even	9		2166.2.a.q.1.1		3
19.15	odd	18		2166.2.a.s.1.1		3
19.16	even	9	inner	114.2.i.a.73.1	yes	6
57.23	odd	18		6498.2.a.br.1.3		3
57.35	odd	18		342.2.u.e.73.1		6
57.53	even	18		6498.2.a.bm.1.3		3
76.35	odd	18		912.2.bo.a.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.25.1	✓	6	1.1	even	1	trivial
114.2.i.a.73.1	yes	6	19.16	even	9	inner
342.2.u.e.73.1		6	57.35	odd	18
342.2.u.e.253.1		6	3.2	odd	2
912.2.bo.a.481.1		6	4.3	odd	2
912.2.bo.a.529.1		6	76.35	odd	18
2166.2.a.q.1.1		3	19.4	even	9
2166.2.a.s.1.1		3	19.15	odd	18
6498.2.a.bm.1.3		3	57.53	even	18
6498.2.a.br.1.3		3	57.23	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.386659 - 2.19285i) q^{5} +(0.939693 - 0.342020i) q^{6} +(1.32635 - 2.29731i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(1.70574 + 1.43128i) q^{10} +(-1.11334 - 1.92836i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(4.97178 - 1.80958i) q^{13} +(0.460637 + 2.61240i) q^{14} +(-0.386659 + 2.19285i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-2.61334 + 2.19285i) q^{17} -1.00000 q^{18} +(-4.29813 + 0.725293i) q^{19} -2.22668 q^{20} +(-2.03209 + 1.70513i) q^{21} +(2.09240 + 0.761570i) q^{22} +(0.386659 - 2.19285i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(0.0393628 - 0.0143269i) q^{25} +(-2.64543 + 4.58202i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-2.03209 - 1.70513i) q^{28} +(3.68866 + 3.09516i) q^{29} +(-1.11334 - 1.92836i) q^{30} +(-5.15657 + 8.93145i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.386659 + 2.19285i) q^{33} +(0.592396 - 3.35965i) q^{34} +(-5.55051 - 2.02022i) q^{35} +(0.766044 - 0.642788i) q^{36} +2.30541 q^{37} +(2.82635 - 3.31839i) q^{38} -5.29086 q^{39} +(1.70574 - 1.43128i) q^{40} +(6.79813 + 2.47432i) q^{41} +(0.460637 - 2.61240i) q^{42} +(-1.02822 - 5.83132i) q^{43} +(-2.09240 + 0.761570i) q^{44} +(1.11334 - 1.92836i) q^{45} +(1.11334 + 1.92836i) q^{46} +(8.43242 + 7.07564i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-0.0184183 - 0.0319015i) q^{49} +(-0.0209445 + 0.0362770i) q^{50} +(3.20574 - 1.16679i) q^{51} +(-0.918748 - 5.21048i) q^{52} +(1.70574 - 9.67372i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-3.79813 + 3.18701i) q^{55} +2.65270 q^{56} +(4.28699 + 0.788496i) q^{57} -4.81521 q^{58} +(3.79813 - 3.18701i) q^{59} +(2.09240 + 0.761570i) q^{60} +(-0.990200 + 5.61570i) q^{61} +(-1.79086 - 10.1565i) q^{62} +(2.49273 - 0.907278i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.89053 - 10.2027i) q^{65} +(-1.70574 - 1.43128i) q^{66} +(6.56805 + 5.51125i) q^{67} +(1.70574 + 2.95442i) q^{68} +(-1.11334 + 1.92836i) q^{69} +(5.55051 - 2.02022i) q^{70} +(0.764700 + 4.33683i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(2.62701 + 0.956154i) q^{73} +(-1.76604 + 1.48189i) q^{74} -0.0418891 q^{75} +(-0.0320889 + 4.35878i) q^{76} -5.90673 q^{77} +(4.05303 - 3.40090i) q^{78} +(-12.9684 - 4.72010i) q^{79} +(-0.386659 + 2.19285i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-6.79813 + 2.47432i) q^{82} +(5.25150 - 9.09586i) q^{83} +(1.32635 + 2.29731i) q^{84} +(5.81908 + 4.88279i) q^{85} +(4.53596 + 3.80612i) q^{86} +(-2.40760 - 4.17009i) q^{87} +(1.11334 - 1.92836i) q^{88} +(-7.34389 + 2.67296i) q^{89} +(0.386659 + 2.19285i) q^{90} +(2.43717 - 13.8219i) q^{91} +(-2.09240 - 0.761570i) q^{92} +(7.90033 - 6.62916i) q^{93} -11.0077 q^{94} +(3.25237 + 9.14473i) q^{95} -1.00000 q^{96} +(-13.6270 + 11.4344i) q^{97} +(0.0346151 + 0.0125989i) q^{98} +(0.386659 - 2.19285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8} - 3 q^{12} + 15 q^{13} - 6 q^{14} - 9 q^{15} - 9 q^{17} - 6 q^{18} - 12 q^{19} - 3 q^{21} + 9 q^{22} + 9 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{28} - 9 q^{29} - 9 q^{31} + 9 q^{33}+ \cdots + 9 q^{99}+O(q^{100}) \) 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8 - 3 * q^12 + 15 * q^13 - 6 * q^14 - 9 * q^15 - 9 * q^17 - 6 * q^18 - 12 * q^19 - 3 * q^21 + 9 * q^22 + 9 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^28 - 9 * q^29 - 9 * q^31 + 9 * q^33 - 36 * q^35 + 18 * q^37 + 18 * q^38 + 27 * q^41 - 6 * q^42 - 21 * q^43 - 9 * q^44 + 27 * q^47 - 12 * q^49 + 3 * q^50 + 9 * q^51 - 3 * q^52 - 9 * q^55 + 18 * q^56 + 18 * q^57 - 36 * q^58 + 9 * q^59 + 9 * q^60 - 3 * q^61 + 21 * q^62 - 3 * q^63 - 3 * q^64 - 18 * q^65 - 3 * q^67 + 36 * q^70 + 9 * q^71 - 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 18 * q^77 + 12 * q^78 - 21 * q^79 - 9 * q^80 - 27 * q^82 - 9 * q^83 + 9 * q^84 + 18 * q^85 - 6 * q^86 - 18 * q^87 + 9 * q^90 + 24 * q^91 - 9 * q^92 + 33 * q^93 - 18 * q^94 + 36 * q^95 - 6 * q^96 - 54 * q^97 - 24 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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