LMFDB - Embedded newform 195.2.v.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(4,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("195.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.v (of order $6$, degree $2$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	195.4
Dual form			195.2.v.a.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173693 - 0.300844i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.939662 + 1.62754i) q^{4} +(0.956446 - 2.02119i) q^{5} +(0.300844 - 0.173693i) q^{6} +(-2.09191 - 3.62329i) q^{7} +1.34762 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.173693 - 0.300844i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.939662 + 1.62754i) q^{4} +(0.956446 - 2.02119i) q^{5} +(0.300844 - 0.173693i) q^{6} +(-2.09191 - 3.62329i) q^{7} +1.34762 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.441936 - 0.638807i) q^{10} +(4.15617 + 2.39957i) q^{11} +1.87932i q^{12} +(-2.38462 + 2.70436i) q^{13} -1.45339 q^{14} +(1.83890 - 1.27218i) q^{15} +(-1.64525 + 2.84966i) q^{16} +(-0.309305 + 0.178577i) q^{17} +0.347385 q^{18} +(-3.15847 + 1.82354i) q^{19} +(4.18831 - 0.342579i) q^{20} -4.18381i q^{21} +(1.44379 - 0.833575i) q^{22} +(-2.49983 - 1.44328i) q^{23} +(1.16707 + 0.673810i) q^{24} +(-3.17042 - 3.86632i) q^{25} +(0.399401 + 1.18713i) q^{26} +1.00000i q^{27} +(3.93137 - 6.80933i) q^{28} +(-0.583893 + 1.01133i) q^{29} +(-0.0633244 - 0.774192i) q^{30} -9.22100i q^{31} +(1.91916 + 3.32408i) q^{32} +(2.39957 + 4.15617i) q^{33} +0.124070i q^{34} +(-9.32415 + 0.762662i) q^{35} +(-0.939662 + 1.62754i) q^{36} +(-3.42076 + 5.92494i) q^{37} +1.26694i q^{38} +(-3.41733 + 1.14973i) q^{39} +(1.28893 - 2.72380i) q^{40} +(-9.54637 - 5.51160i) q^{41} +(-1.25868 - 0.726697i) q^{42} +(-3.05473 + 1.76365i) q^{43} +9.01913i q^{44} +(2.22863 - 0.182289i) q^{45} +(-0.868404 + 0.501373i) q^{46} +12.7136 q^{47} +(-2.84966 + 1.64525i) q^{48} +(-5.25214 + 9.09698i) q^{49} +(-1.71384 + 0.282253i) q^{50} -0.357154 q^{51} +(-6.64220 - 1.33989i) q^{52} -0.595736i q^{53} +(0.300844 + 0.173693i) q^{54} +(8.82514 - 6.10536i) q^{55} +(-2.81909 - 4.88282i) q^{56} -3.64709 q^{57} +(0.202836 + 0.351322i) q^{58} +(1.79899 - 1.03865i) q^{59} +(3.79847 + 1.79747i) q^{60} +(3.16166 + 5.47616i) q^{61} +(-2.77409 - 1.60162i) q^{62} +(2.09191 - 3.62329i) q^{63} -5.24763 q^{64} +(3.18526 + 7.40635i) q^{65} +1.66715 q^{66} +(-1.80005 + 3.11778i) q^{67} +(-0.581283 - 0.335604i) q^{68} +(-1.44328 - 2.49983i) q^{69} +(-1.39009 + 2.93759i) q^{70} +(8.05442 - 4.65022i) q^{71} +(0.673810 + 1.16707i) q^{72} -0.473298 q^{73} +(1.18832 + 2.05824i) q^{74} +(-0.812506 - 4.93354i) q^{75} +(-5.93579 - 3.42703i) q^{76} -20.0787i q^{77} +(-0.247673 + 1.22778i) q^{78} +5.50429 q^{79} +(4.18611 + 6.05091i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.31627 + 1.91465i) q^{82} -10.1038 q^{83} +(6.80933 - 3.93137i) q^{84} +(0.0651052 + 0.795963i) q^{85} +1.22533i q^{86} +(-1.01133 + 0.583893i) q^{87} +(5.60094 + 3.23371i) q^{88} +(-1.35558 - 0.782643i) q^{89} +(0.332255 - 0.702132i) q^{90} +(14.7871 + 2.98291i) q^{91} -5.42477i q^{92} +(4.61050 - 7.98562i) q^{93} +(2.20827 - 3.82483i) q^{94} +(0.664823 + 8.12799i) q^{95} +3.83831i q^{96} +(4.36294 + 7.55683i) q^{97} +(1.82452 + 3.16016i) q^{98} +4.79914i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q - 20 * q^4 + 16 * q^9	$ 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) $ 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.173693	−	0.300844i	0.122819	−	0.212729i	−0.798059	−	0.602579i	$-0.794140\pi$
$2$	0.173693	−	0.300844i	0.122819	−	0.212729i	0.920878	+	0.389850i	$0.127473\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.939662	+	1.62754i	0.469831	+	0.813771i
$5$	0.956446	−	2.02119i	0.427736	−	0.903904i
$5$	0.956446	−	2.02119i	0.427736	−	0.903904i
$6$	0.300844	−	0.173693i	0.122819	−	0.0709097i
$7$	−2.09191	−	3.62329i	−0.790666	−	1.36947i	−0.925555	−	0.378613i	$-0.876401\pi$
$7$	−2.09191	−	3.62329i	−0.790666	−	1.36947i	0.134889	−	0.990861i	$-0.456932\pi$
$8$	1.34762			0.476456
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.441936	−	0.638807i	−0.139753	−	0.202009i
$11$	4.15617	+	2.39957i	1.25313	+	0.723497i	0.971731	−	0.236092i	$-0.0758668\pi$
$11$	4.15617	+	2.39957i	1.25313	+	0.723497i	0.281403	+	0.959590i	$0.409200\pi$
$12$			1.87932i			0.542514i
$13$	−2.38462	+	2.70436i	−0.661376	+	0.750055i
$13$	−2.38462	+	2.70436i	−0.661376	+	0.750055i
$14$	−1.45339			−0.388436
$15$	1.83890	−	1.27218i	0.474802	−	0.328475i
$16$	−1.64525	+	2.84966i	−0.411313	+	0.712415i
$17$	−0.309305	+	0.178577i	−0.0750174	+	0.0433113i	−0.537040	−	0.843557i	$-0.680457\pi$
$17$	−0.309305	+	0.178577i	−0.0750174	+	0.0433113i	0.462022	+	0.886868i	$0.347124\pi$
$18$	0.347385			0.0818795
$19$	−3.15847	+	1.82354i	−0.724603	+	0.418350i	−0.816444	−	0.577424i	$-0.804058\pi$
$19$	−3.15847	+	1.82354i	−0.724603	+	0.418350i	0.0918417	+	0.995774i	$0.470725\pi$
$20$	4.18831	−	0.342579i	0.936534	−	0.0766031i
$21$		−	4.18381i		−	0.912983i
$22$	1.44379	−	0.833575i	0.307818	−	0.177719i
$23$	−2.49983	−	1.44328i	−0.521250	−	0.300944i	0.216196	−	0.976350i	$-0.430635\pi$
$23$	−2.49983	−	1.44328i	−0.521250	−	0.300944i	−0.737446	+	0.675406i	$0.763968\pi$
$24$	1.16707	+	0.673810i	0.238228	+	0.137541i
$25$	−3.17042	−	3.86632i	−0.634084	−	0.773264i
$26$	0.399401	+	1.18713i	0.0783289	+	0.232815i
$27$			1.00000i			0.192450i
$28$	3.93137	−	6.80933i	0.742959	−	1.28684i
$29$	−0.583893	+	1.01133i	−0.108426	+	0.187800i	−0.915133	−	0.403152i	$-0.867914\pi$
$29$	−0.583893	+	1.01133i	−0.108426	+	0.187800i	0.806707	+	0.590952i	$0.201248\pi$
$30$	−0.0633244	−	0.774192i	−0.0115614	−	0.141347i
$31$		−	9.22100i		−	1.65614i	−0.560624	−	0.828070i	$-0.689439\pi$
$31$		−	9.22100i		−	1.65614i	0.560624	−	0.828070i	$-0.310561\pi$
$32$	1.91916	+	3.32408i	0.339262	+	0.587619i
$33$	2.39957	+	4.15617i	0.417711	+	0.723497i
$34$			0.124070i			0.0212778i
$35$	−9.32415	+	0.762662i	−1.57607	+	0.128913i
$36$	−0.939662	+	1.62754i	−0.156610	+	0.271257i
$37$	−3.42076	+	5.92494i	−0.562370	+	0.974054i	0.434919	+	0.900470i	$0.356777\pi$
$37$	−3.42076	+	5.92494i	−0.562370	+	0.974054i	−0.997289	+	0.0735840i	$0.976556\pi$
$38$			1.26694i			0.205526i
$39$	−3.41733	+	1.14973i	−0.547210	+	0.184105i
$40$	1.28893	−	2.72380i	0.203797	−	0.430670i
$41$	−9.54637	−	5.51160i	−1.49089	−	0.860767i	−0.490947	−	0.871190i	$-0.663349\pi$
$41$	−9.54637	−	5.51160i	−1.49089	−	0.860767i	−0.999946	+	0.0104227i	$0.996682\pi$
$42$	−1.25868	−	0.726697i	−0.194218	−	0.112132i
$43$	−3.05473	+	1.76365i	−0.465841	+	0.268954i	−0.714497	−	0.699638i	$-0.753345\pi$
$43$	−3.05473	+	1.76365i	−0.465841	+	0.268954i	0.248656	+	0.968592i	$0.420011\pi$
$44$			9.01913i			1.35969i
$45$	2.22863	−	0.182289i	0.332224	−	0.0271740i
$46$	−0.868404	+	0.501373i	−0.128039	+	0.0739234i
$47$	12.7136			1.85448			0.927238	−	0.374472i	$-0.122176\pi$
$47$	12.7136			1.85448			0.927238	+	0.374472i	$0.122176\pi$
$48$	−2.84966	+	1.64525i	−0.411313	+	0.237472i
$49$	−5.25214	+	9.09698i	−0.750306	+	1.29957i
$50$	−1.71384	+	0.282253i	−0.242374	+	0.0399166i
$51$	−0.357154			−0.0500116
$52$	−6.64220	−	1.33989i	−0.921108	−	0.185809i
$53$		−	0.595736i		−	0.0818307i	−0.999163	−	0.0409153i	$-0.986973\pi$
$53$		−	0.595736i		−	0.0818307i	0.999163	−	0.0409153i	$-0.0130274\pi$
$54$	0.300844	+	0.173693i	0.0409398	+	0.0236366i
$55$	8.82514	−	6.10536i	1.18998	−	0.823247i
$56$	−2.81909	−	4.88282i	−0.376717	−	0.652494i
$57$	−3.64709			−0.483068
$58$	0.202836	+	0.351322i	0.0266337	+	0.0461308i
$59$	1.79899	−	1.03865i	0.234208	−	0.135220i	−0.378304	−	0.925682i	$-0.623492\pi$
$59$	1.79899	−	1.03865i	0.234208	−	0.135220i	0.612512	+	0.790461i	$0.290159\pi$
$60$	3.79847	+	1.79747i	0.490380	+	0.232053i
$61$	3.16166	+	5.47616i	0.404809	+	0.701150i	0.994299	−	0.106625i	$-0.0340045\pi$
$61$	3.16166	+	5.47616i	0.404809	+	0.701150i	−0.589490	+	0.807776i	$0.700671\pi$
$62$	−2.77409	−	1.60162i	−0.352309	−	0.203406i
$63$	2.09191	−	3.62329i	0.263555	−	0.456491i
$64$	−5.24763			−0.655954
$65$	3.18526	+	7.40635i	0.395083	+	0.918645i
$66$	1.66715			0.205212
$67$	−1.80005	+	3.11778i	−0.219911	+	0.380898i	−0.954781	−	0.297311i	$-0.903910\pi$
$67$	−1.80005	+	3.11778i	−0.219911	+	0.380898i	0.734869	+	0.678209i	$0.237243\pi$
$68$	−0.581283	−	0.335604i	−0.0704910	−	0.0406980i
$69$	−1.44328	−	2.49983i	−0.173750	−	0.300944i
$70$	−1.39009	+	2.93759i	−0.166148	+	0.351109i
$71$	8.05442	−	4.65022i	0.955884	−	0.551880i	0.0609802	−	0.998139i	$-0.480577\pi$
$71$	8.05442	−	4.65022i	0.955884	−	0.551880i	0.894904	+	0.446259i	$0.147244\pi$
$72$	0.673810	+	1.16707i	0.0794093	+	0.137541i
$73$	−0.473298			−0.0553954			−0.0276977	−	0.999616i	$-0.508818\pi$
$73$	−0.473298			−0.0553954			−0.0276977	+	0.999616i	$0.508818\pi$
$74$	1.18832	+	2.05824i	0.138140	+	0.239265i
$75$	−0.812506	−	4.93354i	−0.0938201	−	0.569676i
$76$	−5.93579	−	3.42703i	−0.680881	−	0.393107i
$77$		−	20.0787i		−	2.28818i
$78$	−0.247673	+	1.22778i	−0.0280435	+	0.139019i
$79$	5.50429			0.619281			0.309640	−	0.950854i	$-0.399791\pi$
$79$	5.50429			0.619281			0.309640	+	0.950854i	$0.399791\pi$
$80$	4.18611	+	6.05091i	0.468021	+	0.676513i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.31627	+	1.91465i	−0.366221	+	0.211438i
$83$	−10.1038			−1.10903			−0.554516	−	0.832173i	$-0.687097\pi$
$83$	−10.1038			−1.10903			−0.554516	+	0.832173i	$0.687097\pi$
$84$	6.80933	−	3.93137i	0.742959	−	0.428947i
$85$	0.0651052	+	0.795963i	0.00706165	+	0.0863343i
$86$			1.22533i			0.132131i
$87$	−1.01133	+	0.583893i	−0.108426	+	0.0625999i
$88$	5.60094	+	3.23371i	0.597063	+	0.344714i
$89$	−1.35558	−	0.782643i	−0.143691	−	0.0829600i	0.426431	−	0.904520i	$-0.359771\pi$
$89$	−1.35558	−	0.782643i	−0.143691	−	0.0829600i	−0.570122	+	0.821560i	$0.693104\pi$
$90$	0.332255	−	0.702132i	0.0350228	−	0.0740112i
$91$	14.7871	+	2.98291i	1.55011	+	0.312694i
$92$		−	5.42477i		−	0.565571i
$93$	4.61050	−	7.98562i	0.478087	−	0.828070i
$94$	2.20827	−	3.82483i	0.227765	−	0.394501i
$95$	0.664823	+	8.12799i	0.0682094	+	0.833914i
$96$			3.83831i			0.391746i
$97$	4.36294	+	7.55683i	0.442989	+	0.767280i	0.997910	−	0.0646237i	$-0.0205847\pi$
$97$	4.36294	+	7.55683i	0.442989	+	0.767280i	−0.554921	+	0.831903i	$0.687251\pi$
$98$	1.82452	+	3.16016i	0.184304	+	0.319224i
$99$			4.79914i			0.482331i
$100$	3.31347	−	8.79303i	0.331347	−	0.879303i
$101$	−0.533103	+	0.923361i	−0.0530457	+	0.0918779i	−0.891329	−	0.453357i	$-0.850226\pi$
$101$	−0.533103	+	0.923361i	−0.0530457	+	0.0918779i	0.838283	+	0.545235i	$0.183560\pi$
$102$	−0.0620351	+	0.107448i	−0.00614239	+	0.0106389i
$103$		−	10.5471i		−	1.03924i	−0.854398	−	0.519619i	$-0.826074\pi$
$103$		−	10.5471i		−	1.03924i	0.854398	−	0.519619i	$-0.173926\pi$
$104$	−3.21357	+	3.64445i	−0.315116	+	0.357368i
$105$	−8.45628	−	4.00159i	−0.825249	−	0.390515i
$106$	−0.179224	−	0.103475i	−0.0174078	−	0.0100504i
$107$	8.23481	+	4.75437i	0.796090	+	0.459623i	0.842102	−	0.539318i	$-0.181318\pi$
$107$	8.23481	+	4.75437i	0.796090	+	0.459623i	−0.0460124	+	0.998941i	$0.514651\pi$
$108$	−1.62754	+	0.939662i	−0.156610	+	0.0904190i
$109$			2.19476i			0.210220i	0.994461	+	0.105110i	$0.0335194\pi$
$109$			2.19476i			0.210220i	−0.994461	+	0.105110i	$0.966481\pi$
$110$	−0.303903	−	3.71545i	−0.0289760	−	0.354254i
$111$	−5.92494	+	3.42076i	−0.562370	+	0.324685i
$112$	13.7668			1.30085
$113$	10.3836	−	5.99497i	0.976806	−	0.563959i	0.0755020	−	0.997146i	$-0.475944\pi$
$113$	10.3836	−	5.99497i	0.976806	−	0.563959i	0.901304	+	0.433186i	$0.142611\pi$
$114$	−0.633472	+	1.09721i	−0.0593301	+	0.102763i
$115$	−5.30809	+	3.67221i	−0.494982	+	0.342436i
$116$	−2.19465			−0.203768
$117$	−3.53436	−	0.712964i	−0.326751	−	0.0659136i
$118$		−	0.721621i		−	0.0664306i
$119$	1.29407	+	0.747133i	0.118627	+	0.0684896i
$120$	2.47814	−	1.71441i	0.226222	−	0.156504i
$121$	6.01586	+	10.4198i	0.546896	+	0.947252i
$122$	2.19663			0.198874
$123$	−5.51160	−	9.54637i	−0.496964	−	0.860767i
$124$	15.0076	−	8.66462i	1.34772	−	0.778106i
$125$	−10.8469	+	2.71010i	−0.970177	+	0.242399i
$126$	−0.726697	−	1.25868i	−0.0647394	−	0.112132i
$127$	2.48735	+	1.43607i	0.220717	+	0.127431i	0.606282	−	0.795250i	$-0.292660\pi$
$127$	2.48735	+	1.43607i	0.220717	+	0.127431i	−0.385565	+	0.922681i	$0.625994\pi$
$128$	−4.74979	+	8.22687i	−0.419826	+	0.727160i
$129$	−3.52729			−0.310561
$130$	2.78142	+	0.328160i	0.243947	+	0.0287815i
$131$	7.04982			0.615946			0.307973	−	0.951395i	$-0.400349\pi$
$131$	7.04982			0.615946			0.307973	+	0.951395i	$0.400349\pi$
$132$	−4.50957	+	7.81080i	−0.392507	+	0.679843i
$133$	13.2144	+	7.62936i	1.14584	+	0.661550i
$134$	0.625312	+	1.08307i	0.0540187	+	0.0935631i
$135$	2.02119	+	0.956446i	0.173956	+	0.0823178i
$136$	−0.416825	+	0.240654i	−0.0357424	+	0.0206359i
$137$	1.61595	+	2.79891i	0.138060	+	0.239127i	0.926762	−	0.375648i	$-0.122580\pi$
$137$	1.61595	+	2.79891i	0.138060	+	0.239127i	−0.788702	+	0.614775i	$0.789247\pi$
$138$	−1.00275			−0.0853594
$139$	−1.83438	−	3.17724i	−0.155590	−	0.269490i	0.777684	−	0.628656i	$-0.216395\pi$
$139$	−1.83438	−	3.17724i	−0.155590	−	0.269490i	−0.933274	+	0.359166i	$0.883061\pi$
$140$	−10.0028	−	14.4588i	−0.845392	−	1.22199i
$141$	11.0103	+	6.35682i	0.927238	+	0.535341i
$142$		−	3.23084i		−	0.271126i
$143$	−16.4002	+	5.51773i	−1.37145	+	0.461416i
$144$	−3.29050			−0.274209
$145$	1.48563	+	2.14744i	0.123375	+	0.178336i
$146$	−0.0822084	+	0.142389i	−0.00680362	+	0.0117842i
$147$	−9.09698	+	5.25214i	−0.750306	+	0.433189i
$148$	−12.8574			−1.05688
$149$	−2.91224	+	1.68138i	−0.238580	+	0.137744i	−0.614524	−	0.788898i	$-0.710652\pi$
$149$	−2.91224	+	1.68138i	−0.238580	+	0.137744i	0.375944	+	0.926642i	$0.377318\pi$
$150$	−1.62536	−	0.612482i	−0.132710	−	0.0500089i
$151$		−	11.9614i		−	0.973409i	−0.873567	−	0.486704i	$-0.838199\pi$
$151$		−	11.9614i		−	0.973409i	0.873567	−	0.486704i	$-0.161801\pi$
$152$	−4.25642	+	2.45744i	−0.345241	+	0.199325i
$153$	−0.309305	−	0.178577i	−0.0250058	−	0.0144371i
$154$	−6.04056	−	3.48752i	−0.486762	−	0.281032i
$155$	−18.6374	−	8.81939i	−1.49699	−	0.708390i
$156$	−5.08237	−	4.48148i	−0.406915	−	0.358806i
$157$			7.63140i			0.609052i	0.952504	+	0.304526i	$0.0984981\pi$
$157$			7.63140i			0.609052i	−0.952504	+	0.304526i	$0.901502\pi$
$158$	0.956054	−	1.65593i	0.0760596	−	0.131739i
$159$	0.297868	−	0.515923i	0.0236225	−	0.0409153i
$160$	8.55416	−	0.699681i	0.676266	−	0.0553146i
$161$			12.0768i			0.951785i
$162$	0.173693	+	0.300844i	0.0136466	+	0.0236366i
$163$	9.73676	+	16.8646i	0.762642	+	1.32093i	0.941484	+	0.337056i	$0.109431\pi$
$163$	9.73676	+	16.8646i	0.762642	+	1.32093i	−0.178843	+	0.983878i	$0.557235\pi$
$164$		−	20.7162i		−	1.61766i
$165$	10.6955	−	0.874828i	0.832642	−	0.0681053i
$166$	−1.75495	+	3.03966i	−0.136211	+	0.235924i
$167$	12.0698	−	20.9055i	0.933987	−	1.61771i	0.157558	−	0.987510i	$-0.449638\pi$
$167$	12.0698	−	20.9055i	0.933987	−	1.61771i	0.776430	−	0.630204i	$-0.217029\pi$
$168$		−	5.63819i		−	0.434996i
$169$	−1.62714	−	12.8978i	−0.125164	−	0.992136i
$170$	0.250769	+	0.118666i	0.0192331	+	0.00910129i
$171$	−3.15847	−	1.82354i	−0.241534	−	0.139450i
$172$	−5.74082	−	3.31446i	−0.437733	−	0.252725i
$173$	−4.65531	+	2.68774i	−0.353936	+	0.204345i	−0.666418	−	0.745579i	$-0.732173\pi$
$173$	−4.65531	+	2.68774i	−0.353936	+	0.204345i	0.312481	+	0.949924i	$0.398840\pi$
$174$			0.405672i			0.0307539i
$175$	−7.37656	+	19.5753i	−0.557616	+	1.47976i
$176$	−13.6759	+	7.89579i	−1.03086	+	0.595167i
$177$	2.07729			0.156139
$178$	−0.470908	+	0.271879i	−0.0352960	+	0.0203782i
$179$	8.66244	−	15.0038i	0.647461	−	1.12144i	−0.336266	−	0.941767i	$-0.609164\pi$
$179$	8.66244	−	15.0038i	0.647461	−	1.12144i	0.983727	−	0.179669i	$-0.0575025\pi$
$180$	2.39084	+	3.45589i	0.178202	+	0.257587i
$181$	−5.30343			−0.394201			−0.197100	−	0.980383i	$-0.563152\pi$
$181$	−5.30343			−0.394201			−0.197100	+	0.980383i	$0.563152\pi$
$182$	3.46580	−	3.93050i	0.256902	−	0.291348i
$183$			6.32332i			0.467434i
$184$	−3.36882	−	1.94499i	−0.248353	−	0.143386i
$185$	8.70365	+	12.5809i	0.639905	+	0.924966i
$186$	−1.60162	−	2.77409i	−0.117436	−	0.203406i
$187$	−1.71403			−0.125342
$188$	11.9465	+	20.6920i	0.871290	+	1.50912i
$189$	3.62329	−	2.09191i	0.263555	−	0.152164i
$190$	2.56074	+	1.21176i	0.185775	+	0.0879106i
$191$	−0.781506	−	1.35361i	−0.0565478	−	0.0979437i	0.836366	−	0.548172i	$-0.184676\pi$
$191$	−0.781506	−	1.35361i	−0.0565478	−	0.0979437i	−0.892914	+	0.450228i	$0.851343\pi$
$192$	−4.54458	−	2.62382i	−0.327977	−	0.189358i
$193$	−1.77436	+	3.07328i	−0.127721	+	0.221219i	−0.922793	−	0.385295i	$-0.874100\pi$
$193$	−1.77436	+	3.07328i	−0.127721	+	0.221219i	0.795072	+	0.606515i	$0.207433\pi$
$194$	3.03124			0.217630
$195$	−0.944657	+	8.00672i	−0.0676483	+	0.573373i
$196$	−19.7410			−1.41007
$197$	−0.606245	+	1.05005i	−0.0431932	+	0.0748128i	−0.886814	−	0.462127i	$-0.847086\pi$
$197$	−0.606245	+	1.05005i	−0.0431932	+	0.0748128i	0.843621	+	0.536940i	$0.180420\pi$
$198$	1.44379	+	0.833575i	0.102606	+	0.0592396i
$199$	3.60957	+	6.25195i	0.255875	+	0.443189i	0.965133	−	0.261760i	$-0.0843030\pi$
$199$	3.60957	+	6.25195i	0.255875	+	0.443189i	−0.709258	+	0.704949i	$0.750970\pi$
$200$	−4.27252	−	5.21033i	−0.302113	−	0.368426i
$201$	−3.11778	+	1.80005i	−0.219911	+	0.126966i
$202$	0.185192	+	0.320762i	0.0130301	+	0.0225687i
$203$	4.88580			0.342916
$204$	−0.335604	−	0.581283i	−0.0234970	−	0.0406980i
$205$	−20.2706	+	14.0235i	−1.41576	+	0.979442i
$206$	−3.17304	−	1.83196i	−0.221076	−	0.127638i
$207$		−	2.88655i		−	0.200629i
$208$	−3.78320	−	11.2447i	−0.262318	−	0.779681i
$209$	−17.5029			−1.21070
$210$	−2.67265	+	1.84898i	−0.184430	+	0.127592i
$211$	−3.89803	+	6.75158i	−0.268351	+	0.464798i	−0.968436	−	0.249261i	$-0.919812\pi$
$211$	−3.89803	+	6.75158i	−0.268351	+	0.464798i	0.700085	+	0.714060i	$0.253145\pi$
$212$	0.969586	−	0.559791i	0.0665914	−	0.0384466i
$213$	9.30045			0.637256
$214$	2.86065	−	1.65160i	0.195550	−	0.112901i
$215$	0.642986	+	7.86102i	0.0438513	+	0.536117i
$216$			1.34762i			0.0916939i
$217$	−33.4103	+	19.2895i	−2.26804	+	1.30945i
$218$	0.660281	+	0.381213i	0.0447199	+	0.0258190i
$219$	−0.409888	−	0.236649i	−0.0276977	−	0.0159913i
$220$	18.2294	+	8.62631i	1.22902	+	0.581586i
$221$	0.254638	−	1.26231i	0.0171288	−	0.0849122i
$222$			2.37665i			0.159510i
$223$	9.35609	−	16.2052i	0.626530	−	1.08518i	−0.361713	−	0.932290i	$-0.617808\pi$
$223$	9.35609	−	16.2052i	0.626530	−	1.08518i	0.988243	−	0.152892i	$-0.0488587\pi$
$224$	8.02939	−	13.9073i	0.536486	−	0.929221i
$225$	1.76312	−	4.67883i	0.117541	−	0.311922i
$226$		−	4.16513i		−	0.277060i
$227$	−12.8417	−	22.2424i	−0.852331	−	1.47628i	−0.879099	−	0.476640i	$-0.841855\pi$
$227$	−12.8417	−	22.2424i	−0.852331	−	1.47628i	0.0267675	−	0.999642i	$-0.491479\pi$
$228$	−3.42703	−	5.93579i	−0.226960	−	0.393107i
$229$		−	15.9050i		−	1.05103i	−0.850784	−	0.525515i	$-0.823873\pi$
$229$		−	15.9050i		−	1.05103i	0.850784	−	0.525515i	$-0.176127\pi$
$230$	0.182789	+	2.23475i	0.0120528	+	0.147355i
$231$	10.0393	−	17.3887i	0.660540	−	1.14409i
$232$	−0.786866	+	1.36289i	−0.0516603	+	0.0894782i
$233$			16.7189i			1.09529i	0.836709	+	0.547647i	$0.184476\pi$
$233$			16.7189i			1.09529i	−0.836709	+	0.547647i	$0.815524\pi$
$234$	−0.828383	+	0.939455i	−0.0541531	+	0.0614141i
$235$	12.1599	−	25.6967i	0.793226	−	1.67627i
$236$	3.38088	+	1.95195i	0.220077	+	0.127061i
$237$	4.76685	+	2.75214i	0.309640	+	0.178771i
$238$	0.449542	−	0.259543i	0.0291395	−	0.0168237i
$239$		−	2.73543i		−	0.176940i	−0.996079	−	0.0884702i	$-0.971802\pi$
$239$		−	2.73543i		−	0.176940i	0.996079	−	0.0884702i	$-0.0281978\pi$
$240$	0.599821	+	7.33330i	0.0387183	+	0.473362i
$241$	12.5930	−	7.27056i	0.811185	−	0.468338i	−0.0361820	−	0.999345i	$-0.511520\pi$
$241$	12.5930	−	7.27056i	0.811185	−	0.468338i	0.847367	+	0.531007i	$0.178186\pi$
$242$	4.17964			0.268678
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−5.94179	+	10.2915i	−0.380384	+	0.658844i
$245$	13.3633	+	19.3164i	0.853752	+	1.23408i
$246$	−3.82930			−0.244147
$247$	2.60024	−	12.8901i	0.165449	−	0.820178i
$248$		−	12.4264i		−	0.789077i
$249$	−8.75012	−	5.05188i	−0.554516	−	0.320150i
$250$	−1.06871	+	3.73396i	−0.0675911	+	0.236156i
$251$	5.05966	+	8.76358i	0.319363	+	0.553152i	0.980355	−	0.197240i	$-0.0631979\pi$
$251$	5.05966	+	8.76358i	0.319363	+	0.553152i	−0.660993	+	0.750392i	$0.729865\pi$
$252$	7.86274			0.495306
$253$	−6.92648	−	11.9970i	−0.435464	−	0.754246i
$254$	0.864070	−	0.498871i	0.0542166	−	0.0313020i
$255$	−0.341599	+	0.721877i	−0.0213917	+	0.0452057i
$256$	−3.59763	−	6.23127i	−0.224852	−	0.389455i
$257$	12.3548	+	7.13305i	0.770671	+	0.444947i	0.833114	−	0.553101i	$-0.186556\pi$
$257$	12.3548	+	7.13305i	0.770671	+	0.444947i	−0.0624427	+	0.998049i	$0.519889\pi$
$258$	−0.612665	+	1.06117i	−0.0381429	+	0.0660654i
$259$	28.6237			1.77859
$260$	−9.06108	+	12.1436i	−0.561944	+	0.753115i
$261$	−1.16779			−0.0722841
$262$	1.22450	−	2.12090i	0.0756500	−	0.131030i
$263$	−18.2489	−	10.5360i	−1.12528	−	0.649678i	−0.182533	−	0.983200i	$-0.558430\pi$
$263$	−18.2489	−	10.5360i	−1.12528	−	0.649678i	−0.942742	+	0.333522i	$0.891763\pi$
$264$	3.23371	+	5.60094i	0.199021	+	0.344714i
$265$	−1.20410	−	0.569790i	−0.0739671	−	0.0350019i
$266$	4.59050	−	2.65033i	0.281462	−	0.162502i
$267$	−0.782643	−	1.35558i	−0.0478970	−	0.0829600i
$268$	−6.76576			−0.413285
$269$	12.7906	+	22.1539i	0.779855	+	1.35075i	0.932025	+	0.362394i	$0.118041\pi$
$269$	12.7906	+	22.1539i	0.779855	+	1.35075i	−0.152170	+	0.988354i	$0.548626\pi$
$270$	0.638807	−	0.441936i	0.0388766	−	0.0268954i
$271$	−10.6709	−	6.16086i	−0.648213	−	0.374246i	0.139559	−	0.990214i	$-0.455432\pi$
$271$	−10.6709	−	6.16086i	−0.648213	−	0.374246i	−0.787771	+	0.615968i	$0.788765\pi$
$272$		−	1.17522i		−	0.0712580i
$273$	11.3145	+	9.97682i	0.684787	+	0.603825i
$274$	1.12272			0.0678257
$275$	−3.89933	−	23.6767i	−0.235138	−	1.42776i
$276$	2.71238	−	4.69799i	0.163266	−	0.282786i
$277$	1.52044	−	0.877827i	0.0913545	−	0.0527435i	−0.453627	−	0.891192i	$-0.649870\pi$
$277$	1.52044	−	0.877827i	0.0913545	−	0.0527435i	0.544981	+	0.838448i	$0.316537\pi$
$278$	−1.27447			−0.0764378
$279$	7.98562	−	4.61050i	0.478087	−	0.276023i
$280$	−12.5654	+	1.02778i	−0.750927	+	0.0614215i
$281$			17.5533i			1.04714i	0.851982	+	0.523572i	$0.175401\pi$
$281$			17.5533i			1.04714i	−0.851982	+	0.523572i	$0.824599\pi$
$282$	3.82483	−	2.20827i	0.227765	−	0.131500i
$283$	−2.44245	−	1.41015i	−0.145189	−	0.0838247i	0.425646	−	0.904890i	$-0.360047\pi$
$283$	−2.44245	−	1.41015i	−0.145189	−	0.0838247i	−0.570835	+	0.821065i	$0.693380\pi$
$284$	15.1369	+	8.73927i	0.898208	+	0.518580i
$285$	−3.48824	+	7.37146i	−0.206626	+	0.436647i
$286$	−1.18862	+	5.89230i	−0.0702845	+	0.348419i
$287$			46.1190i			2.72232i
$288$	−1.91916	+	3.32408i	−0.113087	+	0.195873i
$289$	−8.43622	+	14.6120i	−0.496248	+	0.859527i
$290$	0.904090	−	0.0739494i	0.0530900	−	0.00434246i
$291$			8.72587i			0.511520i
$292$	−0.444740	−	0.770313i	−0.0260264	−	0.0450791i
$293$	−2.36311	−	4.09302i	−0.138054	−	0.239117i	0.788706	−	0.614771i	$-0.210751\pi$
$293$	−2.36311	−	4.09302i	−0.138054	−	0.239117i	−0.926760	+	0.375654i	$0.877418\pi$
$294$			3.64903i			0.212816i
$295$	−0.378667	−	4.62951i	−0.0220468	−	0.269540i
$296$	−4.60989	+	7.98456i	−0.267944	+	0.464093i
$297$	−2.39957	+	4.15617i	−0.139237	+	0.241166i
$298$			1.16817i			0.0676705i
$299$	9.86429	−	3.31877i	0.570467	−	0.191929i
$300$	7.26606	−	5.95825i	0.419506	−	0.344000i
$301$	12.7804	+	7.37877i	0.736650	+	0.425305i
$302$	−3.59853	−	2.07762i	−0.207072	−	0.119553i
$303$	−0.923361	+	0.533103i	−0.0530457	+	0.0306260i
$304$		−	12.0008i		−	0.688290i
$305$	14.0923	−	1.15267i	0.806924	−	0.0660017i
$306$	−0.107448	+	0.0620351i	−0.00614239	+	0.00354631i
$307$	12.1350			0.692578			0.346289	−	0.938128i	$-0.387442\pi$
$307$	12.1350			0.692578			0.346289	+	0.938128i	$0.387442\pi$
$308$	32.6789	−	18.8672i	1.86205	−	1.07506i
$309$	5.27355	−	9.13406i	0.300002	−	0.519619i
$310$	−5.89044	+	4.07510i	−0.334555	+	0.231450i
$311$	4.43699			0.251598			0.125799	−	0.992056i	$-0.459850\pi$
$311$	4.43699			0.251598			0.125799	+	0.992056i	$0.459850\pi$
$312$	−4.60526	+	1.54940i	−0.260721	+	0.0877177i
$313$		−	7.75147i		−	0.438139i	−0.975709	−	0.219069i	$-0.929698\pi$
$313$		−	7.75147i		−	0.438139i	0.975709	−	0.219069i	$-0.0703021\pi$
$314$	2.29587	+	1.32552i	0.129563	+	0.0748034i
$315$	−5.32256	−	7.69362i	−0.299892	−	0.433486i
$316$	5.17217	+	8.95846i	0.290957	+	0.503953i
$317$	22.1234			1.24258			0.621288	−	0.783582i	$-0.286610\pi$
$317$	22.1234			1.24258			0.621288	+	0.783582i	$0.286610\pi$
$318$	−0.103475	−	0.179224i	−0.00580259	−	0.0100504i
$319$	−4.85352	+	2.80218i	−0.271745	+	0.156892i
$320$	−5.01908	+	10.6065i	−0.280575	+	0.592920i
$321$	4.75437	+	8.23481i	0.265363	+	0.459623i
$322$	3.63324	+	2.09765i	0.202472	+	0.116898i
$323$	0.651286	−	1.12806i	0.0362385	−	0.0627670i
$324$	−1.87932			−0.104407
$325$	18.0162	+	0.645751i	0.999358	+	0.0358198i
$326$	6.76481			0.374668
$327$	−1.09738	+	1.90072i	−0.0606852	+	0.105110i
$328$	−12.8649	−	7.42754i	−0.710344	−	0.410117i
$329$	−26.5958	−	46.0652i	−1.46627	−	2.53966i
$330$	1.59454	−	3.36963i	0.0877765	−	0.185492i
$331$	−17.6048	+	10.1642i	−0.967650	+	0.558673i	−0.898519	−	0.438935i	$-0.855356\pi$
$331$	−17.6048	+	10.1642i	−0.967650	+	0.558673i	−0.0691308	+	0.997608i	$0.522023\pi$
$332$	−9.49412	−	16.4443i	−0.521058	−	0.902498i
$333$	−6.84153			−0.374913
$334$	−4.19286	−	7.26225i	−0.229423	−	0.397373i
$335$	4.57998	+	6.62024i	0.250231	+	0.361702i
$336$	11.9224	+	6.88342i	0.650423	+	0.375522i
$337$		−	24.9627i		−	1.35981i	−0.733302	−	0.679903i	$-0.762022\pi$
$337$		−	24.9627i		−	1.35981i	0.733302	−	0.679903i	$-0.237978\pi$
$338$	−4.16284	−	1.75073i	−0.226429	−	0.0952273i
$339$	11.9899			0.651204
$340$	−1.23429	+	0.853897i	−0.0669386	+	0.0463091i
$341$	22.1264	−	38.3241i	1.19821	−	2.07537i
$342$	−1.09721	+	0.633472i	−0.0593301	+	0.0342543i
$343$	14.6613			0.791635
$344$	−4.11661	+	2.37673i	−0.221953	+	0.128144i
$345$	−6.43305	+	0.526186i	−0.346344	+	0.0283289i
$346$			1.86736i			0.100390i
$347$	−8.65324	+	4.99595i	−0.464530	+	0.268197i	−0.713947	−	0.700199i	$-0.753094\pi$
$347$	−8.65324	+	4.99595i	−0.464530	+	0.268197i	0.249417	+	0.968396i	$0.419761\pi$
$348$	−1.90062	−	1.09732i	−0.101884	−	0.0588227i
$349$	−23.6807	−	13.6721i	−1.26760	−	0.731850i	−0.293067	−	0.956092i	$-0.594676\pi$
$349$	−23.6807	−	13.6721i	−1.26760	−	0.731850i	−0.974533	+	0.224242i	$0.928009\pi$
$350$	4.60788	+	5.61929i	0.246301	+	0.300364i
$351$	−2.70436	−	2.38462i	−0.144348	−	0.127282i
$352$			18.4206i			0.981821i
$353$	−1.90531	+	3.30009i	−0.101409	+	0.175646i	−0.912265	−	0.409599i	$-0.865668\pi$
$353$	−1.90531	+	3.30009i	−0.101409	+	0.175646i	0.810856	+	0.585245i	$0.199002\pi$
$354$	0.360810	−	0.624942i	0.0191769	−	0.0332153i
$355$	−1.69537	−	20.7272i	−0.0899807	−	1.10009i
$356$		−	2.94168i		−	0.155909i
$357$	0.747133	+	1.29407i	0.0395425	+	0.0684896i
$358$	−3.00920	−	5.21209i	−0.159041	−	0.275468i
$359$			21.4046i			1.12969i	0.825196	+	0.564846i	$0.191064\pi$
$359$			21.4046i			1.12969i	−0.825196	+	0.564846i	$0.808936\pi$
$360$	3.00334	−	0.245656i	0.158290	−	0.0129472i
$361$	−2.84938	+	4.93527i	−0.149967	+	0.259751i
$362$	−0.921166	+	1.59551i	−0.0484154	+	0.0838580i
$363$			12.0317i			0.631501i
$364$	9.04005	+	26.8695i	0.473827	+	1.40835i
$365$	−0.452684	+	0.956626i	−0.0236946	+	0.0500721i
$366$	1.90234	+	1.09831i	0.0994368	+	0.0574098i
$367$	−11.5242	−	6.65351i	−0.601560	−	0.347311i	0.168095	−	0.985771i	$-0.446238\pi$
$367$	−11.5242	−	6.65351i	−0.601560	−	0.347311i	−0.769655	+	0.638460i	$0.779572\pi$
$368$	8.22569	−	4.74911i	0.428794	−	0.247564i
$369$		−	11.0232i		−	0.573845i
$370$	5.29665	−	0.433236i	0.275360	−	0.0225228i
$371$	−2.15852	+	1.24622i	−0.112065	+	0.0647007i
$372$	17.3292			0.898479
$373$	−24.1327	+	13.9330i	−1.24954	+	0.721423i	−0.971018	−	0.239006i	$-0.923178\pi$
$373$	−24.1327	+	13.9330i	−1.24954	+	0.721423i	−0.278524	+	0.960429i	$0.589845\pi$
$374$	−0.297715	+	0.515657i	−0.0153945	+	0.0266640i
$375$	−10.7487	−	3.07644i	−0.555063	−	0.158867i
$376$	17.1332			0.883576
$377$	−1.34264	−	3.99071i	−0.0691496	−	0.205532i
$378$		−	1.45339i		−	0.0747546i
$379$	4.74070	+	2.73705i	0.243514	+	0.140593i	0.616791	−	0.787127i	$-0.288433\pi$
$379$	4.74070	+	2.73705i	0.243514	+	0.140593i	−0.373277	+	0.927720i	$0.621766\pi$
$380$	−12.6039	+	8.71959i	−0.646568	+	0.447305i
$381$	1.43607	+	2.48735i	0.0735723	+	0.127431i
$382$	−0.542968			−0.0277806
$383$	−6.67559	−	11.5625i	−0.341107	−	0.590814i	0.643532	−	0.765419i	$-0.277468\pi$
$383$	−6.67559	−	11.5625i	−0.341107	−	0.590814i	−0.984639	+	0.174605i	$0.944135\pi$
$384$	−8.22687	+	4.74979i	−0.419826	+	0.242387i
$385$	−40.5829	−	19.2042i	−2.06829	−	0.978736i
$386$	0.616386	+	1.06761i	0.0313732	+	0.0543400i
$387$	−3.05473	−	1.76365i	−0.155280	−	0.0896512i
$388$	−8.19937	+	14.2017i	−0.416260	+	0.720983i
$389$	−13.9669			−0.708149			−0.354075	−	0.935217i	$-0.615204\pi$
$389$	−13.9669			−0.708149			−0.354075	+	0.935217i	$0.615204\pi$
$390$	2.24470	+	1.67490i	0.113665	+	0.0848121i
$391$	1.03094			0.0521371
$392$	−7.07789	+	12.2593i	−0.357488	+	0.619187i
$393$	6.10532	+	3.52491i	0.307973	+	0.177808i
$394$	0.210601	+	0.364771i	0.0106099	+	0.0183769i
$395$	5.26455	−	11.1252i	0.264888	−	0.559770i
$396$	−7.81080	+	4.50957i	−0.392507	+	0.226614i
$397$	−15.0188	−	26.0133i	−0.753772	−	1.30557i	−0.945982	−	0.324218i	$-0.894899\pi$
$397$	−15.0188	−	26.0133i	−0.753772	−	1.30557i	0.192210	−	0.981354i	$-0.438435\pi$
$398$	2.50782			0.125706
$399$	7.62936	+	13.2144i	0.381946	+	0.661550i
$400$	16.2338	−	2.67355i	0.811692	−	0.133678i
$401$	−27.9730	−	16.1502i	−1.39691	−	0.806504i	−0.402839	−	0.915271i	$-0.631977\pi$
$401$	−27.9730	−	16.1502i	−1.39691	−	0.806504i	−0.994067	+	0.108766i	$0.965310\pi$
$402$			1.25062i			0.0623754i
$403$	24.9369	+	21.9886i	1.24220	+	1.09533i
$404$	−2.00375			−0.0996901
$405$	1.27218	+	1.83890i	0.0632151	+	0.0913758i
$406$	0.848627	−	1.46987i	0.0421167	−	0.0729482i
$407$	−28.4346	+	16.4167i	−1.40945	+	0.813746i
$408$	−0.481308			−0.0238283
$409$	1.02563	−	0.592148i	0.0507142	−	0.0292798i	−0.474429	−	0.880294i	$-0.657345\pi$
$409$	1.02563	−	0.592148i	0.0507142	−	0.0292798i	0.525143	+	0.851014i	$0.324012\pi$
$410$	0.698037	+	8.53407i	0.0344736	+	0.421468i
$411$			3.23190i			0.159418i
$412$	17.1659	−	9.91071i	0.845701	−	0.488266i
$413$	−7.52663	−	4.34550i	−0.370361	−	0.213828i
$414$	−0.868404	−	0.501373i	−0.0426797	−	0.0246411i
$415$	−9.66371	+	20.4216i	−0.474373	+	1.00246i
$416$	−13.5660	−	2.73658i	−0.665126	−	0.134172i
$417$		−	3.66876i		−	0.179660i
$418$	−3.04012	+	5.26564i	−0.148697	+	0.257551i
$419$	−18.2869	+	31.6738i	−0.893372	+	1.54737i	−0.0575661	+	0.998342i	$0.518334\pi$
$419$	−18.2869	+	31.6738i	−0.893372	+	1.54737i	−0.835806	+	0.549025i	$0.814999\pi$
$420$	−1.43329	−	17.5231i	−0.0699373	−	0.855039i
$421$			16.3670i			0.797677i	0.917021	+	0.398838i	$0.130587\pi$
$421$			16.3670i			0.797677i	−0.917021	+	0.398838i	$0.869413\pi$
$422$	1.35412	+	2.34540i	0.0659174	+	0.114172i
$423$	6.35682	+	11.0103i	0.309079	+	0.535341i
$424$		−	0.802826i		−	0.0389887i
$425$	1.67106	+	0.629706i	0.0810584	+	0.0305452i
$426$	1.61542	−	2.79799i	0.0782673	−	0.135563i
$427$	13.2278	−	22.9112i	0.640138	−	1.10875i
$428$			17.8700i			0.863779i
$429$	−16.9619	−	3.42161i	−0.818927	−	0.165197i
$430$	2.47663	+	1.17196i	0.119433	+	0.0565170i
$431$	4.01136	+	2.31596i	0.193220	+	0.111556i	0.593489	−	0.804842i	$-0.297750\pi$
$431$	4.01136	+	2.31596i	0.193220	+	0.111556i	−0.400269	+	0.916398i	$0.631083\pi$
$432$	−2.84966	−	1.64525i	−0.137104	−	0.0791572i
$433$	16.4065	−	9.47228i	0.788445	−	0.455209i	−0.0509701	−	0.998700i	$-0.516231\pi$
$433$	16.4065	−	9.47228i	0.788445	−	0.455209i	0.839415	+	0.543491i	$0.182898\pi$
$434$			13.4018i			0.643305i
$435$	0.212874	+	2.60256i	0.0102065	+	0.124783i
$436$	−3.57206	+	2.06233i	−0.171071	+	0.0987677i
$437$	10.5275			0.503599
$438$	−0.142389	+	0.0822084i	−0.00680362	+	0.00392807i
$439$	−16.1387	+	27.9530i	−0.770257	+	1.33413i	0.167164	+	0.985929i	$0.446539\pi$
$439$	−16.1387	+	27.9530i	−0.770257	+	1.33413i	−0.937422	+	0.348196i	$0.886794\pi$
$440$	11.8929	−	8.22771i	0.566974	−	0.392241i
$441$	−10.5043			−0.500204
$442$	−0.335530	−	0.295861i	−0.0159596	−	0.0140727i
$443$		−	14.0848i		−	0.669188i	−0.942362	−	0.334594i	$-0.891401\pi$
$443$		−	14.0848i		−	0.669188i	0.942362	−	0.334594i	$-0.108599\pi$
$444$	−11.1349	−	6.42872i	−0.528438	−	0.305094i
$445$	−2.87841	+	1.99133i	−0.136450	+	0.0943979i
$446$	−3.25017	−	5.62945i	−0.153900	−	0.266562i
$447$	−3.36276			−0.159053
$448$	10.9776	+	19.0137i	0.518641	+	0.898312i
$449$	9.28506	−	5.36073i	0.438189	−	0.252989i	−0.264640	−	0.964347i	$-0.585253\pi$
$449$	9.28506	−	5.36073i	0.438189	−	0.252989i	0.702829	+	0.711359i	$0.251920\pi$
$450$	−1.10136	−	1.34310i	−0.0519185	−	0.0633145i
$451$	−26.4509	−	45.8143i	−1.24552	−	2.15731i
$452$	19.5141	+	11.2665i	0.917868	+	0.529931i
$453$	5.98072	−	10.3589i	0.280999	−	0.486704i
$454$	−8.92201			−0.418731
$455$	20.1721	−	27.0345i	0.945682	−	1.26740i
$456$	−4.91489			−0.230161
$457$	−10.7559	+	18.6297i	−0.503138	+	0.871460i	0.496856	+	0.867833i	$0.334488\pi$
$457$	−10.7559	+	18.6297i	−0.503138	+	0.871460i	−0.999993	+	0.00362688i	$0.998846\pi$
$458$	−4.78492	−	2.76258i	−0.223585	−	0.129087i
$459$	−0.178577	−	0.309305i	−0.00833526	−	0.0144371i
$460$	−10.9645	−	5.18850i	−0.511222	−	0.241915i
$461$	10.9341	−	6.31278i	0.509250	−	0.294015i	−0.223275	−	0.974755i	$-0.571675\pi$
$461$	10.9341	−	6.31278i	0.509250	−	0.294015i	0.732525	+	0.680740i	$0.238342\pi$
$462$	−3.48752	−	6.04056i	−0.162254	−	0.281032i
$463$	−30.4930			−1.41713			−0.708565	−	0.705646i	$-0.750657\pi$
$463$	−30.4930			−1.41713			−0.708565	+	0.705646i	$0.750657\pi$
$464$	−1.92130	−	3.32779i	−0.0891942	−	0.154489i
$465$	−11.7308	−	16.9565i	−0.544001	−	0.786339i
$466$	5.02980	+	2.90396i	0.233001	+	0.134523i
$467$			23.4712i			1.08612i	0.839695	+	0.543059i	$0.182734\pi$
$467$			23.4712i			1.08612i	−0.839695	+	0.543059i	$0.817266\pi$
$468$	−2.16072	−	6.42226i	−0.0998794	−	0.296869i
$469$	15.0622			0.695506
$470$	−5.61862	−	8.12157i	−0.259168	−	0.374620i
$471$	−3.81570	+	6.60899i	−0.175818	+	0.304526i
$472$	2.42435	−	1.39970i	0.111590	−	0.0644264i
$473$	−16.9280			−0.778349
$474$	1.65593	−	0.956054i	0.0760596	−	0.0439130i
$475$	17.0641	+	6.43025i	0.782954	+	0.295040i
$476$			2.80821i			0.128714i
$477$	0.515923	−	0.297868i	0.0236225	−	0.0136384i
$478$	−0.822940	−	0.475125i	−0.0376404	−	0.0217317i
$479$	22.1855	+	12.8088i	1.01368	+	0.585248i	0.912267	−	0.409596i	$-0.134330\pi$
$479$	22.1855	+	12.8088i	1.01368	+	0.585248i	0.101413	+	0.994844i	$0.467664\pi$
$480$	7.75796	+	3.67114i	0.354101	+	0.167564i
$481$	−7.86593	−	23.3797i	−0.358656	−	1.06602i
$482$		−	5.05137i		−	0.230084i
$483$	−6.03840	+	10.4588i	−0.274757	+	0.475892i
$484$	−11.3057	+	19.5821i	−0.513898	+	0.890097i
$485$	19.4467	−	1.59063i	0.883029	−	0.0722267i
$486$			0.347385i			0.0157577i
$487$	−2.78346	−	4.82110i	−0.126131	−	0.218465i	0.796044	−	0.605239i	$-0.206923\pi$
$487$	−2.78346	−	4.82110i	−0.126131	−	0.218465i	−0.922174	+	0.386774i	$0.873589\pi$
$488$	4.26072	+	7.37978i	0.192874	+	0.334067i
$489$			19.4735i			0.880623i
$490$	8.13233	−	0.665178i	0.367381	−	0.0300497i
$491$	12.0276	−	20.8325i	0.542799	−	0.940156i	−0.455942	−	0.890009i	$-0.650698\pi$
$491$	12.0276	−	20.8325i	0.542799	−	0.940156i	0.998742	−	0.0501468i	$-0.0159689\pi$
$492$	10.3581	−	17.9407i	0.466978	−	0.808830i
$493$		−	0.417080i		−	0.0187843i
$494$	−3.42628	−	3.02119i	−0.154155	−	0.135930i
$495$	9.69997	+	4.59012i	0.435981	+	0.206310i
$496$	26.2767	+	15.1709i	1.17986	+	0.681192i
$497$	−33.6982	−	19.4557i	−1.51157	−	0.872706i
$498$	−3.03966	+	1.75495i	−0.136211	+	0.0786412i
$499$		−	12.1758i		−	0.545065i	−0.962147	−	0.272532i	$-0.912139\pi$
$499$		−	12.1758i		−	0.545065i	0.962147	−	0.272532i	$-0.0878612\pi$
$500$	−14.6032	−	15.1072i	−0.653076	−	0.675615i
$501$	20.9055	−	12.0698i	0.933987	−	0.539238i
$502$	3.51530			0.156896
$503$	−10.2568	+	5.92178i	−0.457329	+	0.264039i	−0.710920	−	0.703272i	$-0.751721\pi$
$503$	−10.2568	+	5.92178i	−0.457329	+	0.264039i	0.253592	+	0.967311i	$0.418388\pi$
$504$	2.81909	−	4.88282i	0.125572	−	0.217498i
$505$	1.35640	+	1.96065i	0.0603592	+	0.0872477i
$506$	−4.81232			−0.213934
$507$	5.03974	−	11.9834i	0.223823	−	0.532200i
$508$			5.39770i			0.239484i
$509$	21.8930	+	12.6399i	0.970390	+	0.560255i	0.899355	−	0.437219i	$-0.144036\pi$
$509$	21.8930	+	12.6399i	0.970390	+	0.560255i	0.0710352	+	0.997474i	$0.477370\pi$
$510$	0.157839	+	0.228153i	0.00698925	+	0.0101028i
$511$	0.990095	+	1.71490i	0.0437992	+	0.0758625i
$512$	−21.4987			−0.950116
$513$	−1.82354	−	3.15847i	−0.0805114	−	0.139450i
$514$	4.29188	−	2.47792i	0.189307	−	0.109296i
$515$	−21.3177	−	10.0877i	−0.939371	−	0.444519i
$516$	−3.31446	−	5.74082i	−0.145911	−	0.252725i
$517$	52.8401	+	30.5073i	2.32391	+	1.34171i
$518$	4.97172	−	8.61127i	0.218445	−	0.378358i
$519$	−5.37548			−0.235958
$520$	4.29253	+	9.98095i	0.188240	+	0.437694i
$521$	−5.54173			−0.242788			−0.121394	−	0.992604i	$-0.538736\pi$
$521$	−5.54173			−0.242788			−0.121394	+	0.992604i	$0.538736\pi$
$522$	−0.202836	+	0.351322i	−0.00887788	+	0.0153769i
$523$	29.9378	+	17.2846i	1.30909	+	0.755803i	0.981944	−	0.189171i	$-0.0605801\pi$
$523$	29.9378	+	17.2846i	1.30909	+	0.755803i	0.327145	+	0.944974i	$0.393913\pi$
$524$	6.62445	+	11.4739i	0.289390	+	0.501239i
$525$	−16.1760	+	13.2645i	−0.705977	+	0.578908i
$526$	−6.33940	+	3.66005i	−0.276411	+	0.159586i
$527$	1.64666	+	2.85210i	0.0717296	+	0.124239i
$528$	−15.7916			−0.687240
$529$	−7.33391	−	12.7027i	−0.318865	−	0.552291i
$530$	−0.380561	+	0.263278i	−0.0165305	+	0.0114360i
$531$	1.79899	+	1.03865i	0.0780694	+	0.0450734i
$532$			28.6761i			1.24327i
$533$	37.6698	−	12.6737i	1.63166	−	0.548961i
$534$	−0.543758			−0.0235307
$535$	17.4856	−	12.0968i	0.755971	−	0.522991i
$536$	−2.42579	+	4.20159i	−0.104778	+	0.181481i
$537$	15.0038	−	8.66244i	0.647461	−	0.373812i
$538$	8.88652			0.383125
$539$	−43.6577	+	25.2058i	−1.88047	+	1.08569i
$540$	0.342579	+	4.18831i	0.0147423	+	0.180236i
$541$		−	7.28747i		−	0.313313i	−0.987653	−	0.156656i	$-0.949928\pi$
$541$		−	7.28747i		−	0.313313i	0.987653	−	0.156656i	$-0.0500715\pi$
$542$	−3.70692	+	2.14019i	−0.159226	+	0.0919291i
$543$	−4.59290	−	2.65171i	−0.197100	−	0.113796i
$544$	−1.18721	−	0.685435i	−0.0509011	−	0.0293878i
$545$	4.43603	+	2.09917i	0.190018	+	0.0899185i
$546$	4.96672	−	1.67102i	0.212556	−	0.0715129i
$547$			19.7322i			0.843690i	0.906668	+	0.421845i	$0.138617\pi$
$547$			19.7322i			0.843690i	−0.906668	+	0.421845i	$0.861383\pi$
$548$	−3.03690	+	5.26006i	−0.129730	+	0.224699i
$549$	−3.16166	+	5.47616i	−0.134936	+	0.233717i
$550$	−7.80030	−	2.93938i	−0.332606	−	0.125336i
$551$		−	4.25902i		−	0.181440i
$552$	−1.94499	−	3.36882i	−0.0827842	−	0.143386i
$553$	−11.5145	−	19.9436i	−0.489644	−	0.848089i
$554$		−	0.609889i		−	0.0259117i
$555$	1.24713	+	15.2472i	0.0529378	+	0.647208i
$556$	3.44739	−	5.97106i	0.146202	−	0.253229i
$557$	12.2536	−	21.2238i	0.519200	−	0.899281i	−0.480551	−	0.876967i	$-0.659563\pi$
$557$	12.2536	−	21.2238i	0.519200	−	0.899281i	0.999751	−	0.0223140i	$-0.00710335\pi$
$558$		−	3.20324i		−	0.135604i
$559$	2.51483	−	12.4667i	0.106366	−	0.527286i
$560$	13.1672	−	27.8254i	0.556418	−	1.17584i
$561$	−1.48440	−	0.857016i	−0.0626712	−	0.0361832i
$562$	5.28082	+	3.04888i	0.222758	+	0.128609i
$563$	25.5857	−	14.7719i	1.07831	−	0.622562i	0.147870	−	0.989007i	$-0.452758\pi$
$563$	25.5857	−	14.7719i	1.07831	−	0.622562i	0.930440	+	0.366444i	$0.119425\pi$
$564$			23.8931i			1.00608i
$565$	−2.18563	−	26.7211i	−0.0919502	−	1.12416i
$566$	−0.848471	+	0.489865i	−0.0356639	+	0.0205906i
$567$	4.18381			0.175704
$568$	10.8543	−	6.26673i	0.455436	−	0.262946i
$569$	9.05432	−	15.6825i	0.379577	−	0.657446i	−0.611424	−	0.791303i	$-0.709403\pi$
$569$	9.05432	−	15.6825i	0.379577	−	0.657446i	0.991001	+	0.133857i	$0.0427362\pi$
$570$	1.61178	+	2.32979i	0.0675101	+	0.0975840i
$571$	25.7155			1.07616			0.538081	−	0.842893i	$-0.319150\pi$
$571$	25.7155			1.07616			0.538081	+	0.842893i	$0.319150\pi$
$572$	−24.3910	−	21.5072i	−1.01984	−	0.899263i
$573$		−	1.56301i		−	0.0652958i
$574$	13.8746	+	8.01053i	0.579116	+	0.334353i
$575$	2.34534	+	14.2409i	0.0978075	+	0.593888i
$576$	−2.62382	−	4.54458i	−0.109326	−	0.189358i
$577$	31.6602			1.31803			0.659015	−	0.752130i	$-0.270973\pi$
$577$	31.6602			1.31803			0.659015	+	0.752130i	$0.270973\pi$
$578$	2.93062	+	5.07598i	0.121898	+	0.211133i
$579$	−3.07328	+	1.77436i	−0.127721	+	0.0737398i
$580$	−2.09906	+	4.43580i	−0.0871588	+	0.184187i
$581$	21.1361	+	36.6089i	0.876875	+	1.51879i
$582$	2.62513	+	1.51562i	0.108815	+	0.0628245i
$583$	1.42951	−	2.47598i	0.0592043	−	0.102545i
$584$	−0.637826			−0.0263934
$585$	−4.82146	+	6.46170i	−0.199343	+	0.267158i
$586$	−1.64182			−0.0678229
$587$	−22.8076	+	39.5040i	−0.941372	+	1.63050i	−0.178516	+	0.983937i	$0.557130\pi$
$587$	−22.8076	+	39.5040i	−0.941372	+	1.63050i	−0.762857	+	0.646568i	$0.776204\pi$
$588$	−17.0962	−	9.87048i	−0.705034	−	0.407052i
$589$	16.8149	+	29.1243i	0.692846	+	1.20004i
$590$	−1.45853	−	0.690191i	−0.0600468	−	0.0284147i
$591$	−1.05005	+	0.606245i	−0.0431932	+	0.0249376i
$592$	−11.2560	−	19.4960i	−0.462620	−	0.801282i
$593$	−37.4569			−1.53817			−0.769085	−	0.639146i	$-0.779288\pi$
$593$	−37.4569			−1.53817			−0.769085	+	0.639146i	$0.779288\pi$
$594$	0.833575	+	1.44379i	0.0342020	+	0.0592396i
$595$	2.74781	−	1.90097i	0.112649	−	0.0779323i
$596$	−5.47303	−	3.15986i	−0.224184	−	0.129433i
$597$			7.21913i			0.295459i
$598$	0.714922	−	3.54406i	0.0292353	−	0.144928i
$599$	2.93358			0.119863			0.0599315	−	0.998202i	$-0.480912\pi$
$599$	2.93358			0.119863			0.0599315	+	0.998202i	$0.480912\pi$
$600$	−1.09495	−	6.64854i	−0.0447011	−	0.271425i
$601$	0.687940	−	1.19155i	0.0280617	−	0.0486042i	−0.851654	−	0.524105i	$-0.824400\pi$
$601$	0.687940	−	1.19155i	0.0280617	−	0.0486042i	0.879715	+	0.475501i	$0.157733\pi$
$602$	4.43972	−	2.56328i	0.180950	−	0.104471i
$603$	−3.60010			−0.146608
$604$	19.4678	−	11.2397i	0.792132	−	0.457337i
$605$	26.8142	−	2.19325i	1.09015	−	0.0891681i
$606$			0.370384i			0.0150458i
$607$	16.5634	−	9.56289i	0.672288	−	0.388146i	−0.124655	−	0.992200i	$-0.539782\pi$
$607$	16.5634	−	9.56289i	0.672288	−	0.388146i	0.796943	+	0.604054i	$0.206449\pi$
$608$	−12.1232	−	6.99933i	−0.491660	−	0.283860i
$609$	4.23123	+	2.44290i	0.171458	+	0.0989913i
$610$	2.10096	−	4.43981i	0.0850653	−	0.179763i
$611$	−30.3173	+	34.3823i	−1.22651	+	1.39096i
$612$		−	0.671208i		−	0.0271320i
$613$	−8.03111	+	13.9103i	−0.324374	+	0.561832i	−0.981385	−	0.192049i	$-0.938487\pi$
$613$	−8.03111	+	13.9103i	−0.324374	+	0.561832i	0.657012	+	0.753880i	$0.271820\pi$
$614$	2.10775	−	3.65073i	0.0850619	−	0.147332i
$615$	−24.5666	+	2.00940i	−0.990620	+	0.0810270i
$616$		−	27.0584i		−	1.09022i
$617$	0.130614	+	0.226230i	0.00525831	+	0.00910766i	0.868643	−	0.495439i	$-0.164993\pi$
$617$	0.130614	+	0.226230i	0.00525831	+	0.00910766i	−0.863384	+	0.504547i	$0.831660\pi$
$618$	−1.83196	−	3.17304i	−0.0736920	−	0.127638i
$619$			40.4349i			1.62521i	0.582812	+	0.812607i	$0.301953\pi$
$619$			40.4349i			1.62521i	−0.582812	+	0.812607i	$0.698047\pi$
$620$	−3.15892	−	38.6204i	−0.126865	−	1.55103i
$621$	1.44328	−	2.49983i	0.0579167	−	0.100315i
$622$	0.770672	−	1.33484i	0.0309011	−	0.0535223i
$623$			6.54887i			0.262375i
$624$	2.34601	−	11.6298i	0.0939156	−	0.465565i
$625$	−4.89685	+	24.5157i	−0.195874	+	0.980629i
$626$	−2.33199	−	1.34637i	−0.0932049	−	0.0538119i
$627$	−15.1579	−	8.75144i	−0.605349	−	0.349499i
$628$	−12.4204	+	7.17094i	−0.495629	+	0.286152i
$629$		−	2.44348i		−	0.0974279i
$630$	−3.23907	+	0.264937i	−0.129048	+	0.0105554i
$631$	5.05608	−	2.91913i	0.201279	−	0.116209i	−0.395973	−	0.918262i	$-0.629593\pi$
$631$	5.05608	−	2.91913i	0.201279	−	0.116209i	0.597252	+	0.802054i	$0.296259\pi$
$632$	7.41769			0.295060
$633$	−6.75158	+	3.89803i	−0.268351	+	0.154933i
$634$	3.84268	−	6.65571i	0.152612	−	0.264332i
$635$	5.28160	−	3.65389i	0.209594	−	0.145000i
$636$	1.11958			0.0443943
$637$	−12.0771	−	35.8966i	−0.478513	−	1.42227i
$638$			1.94687i			0.0770775i
$639$	8.05442	+	4.65022i	0.318628	+	0.183960i
$640$	12.0852	+	17.4688i	0.477708	+	0.690514i
$641$	0.0342903	+	0.0593926i	0.00135439	+	0.00234587i	0.866702	−	0.498827i	$-0.166236\pi$
$641$	0.0342903	+	0.0593926i	0.00135439	+	0.00234587i	−0.865347	+	0.501172i	$0.832902\pi$
$642$	3.30320			0.130367
$643$	−5.79514	−	10.0375i	−0.228538	−	0.395839i	0.728837	−	0.684687i	$-0.240061\pi$
$643$	−5.79514	−	10.0375i	−0.228538	−	0.395839i	−0.957375	+	0.288848i	$0.906728\pi$
$644$	−19.6555	+	11.3481i	−0.774535	+	0.447178i
$645$	−3.37367	+	7.12933i	−0.132838	+	0.280717i
$646$	−0.226247	−	0.391872i	−0.00890158	−	0.0154180i
$647$	−20.0142	−	11.5552i	−0.786838	−	0.454281i	0.0520099	−	0.998647i	$-0.483437\pi$
$647$	−20.0142	−	11.5552i	−0.786838	−	0.454281i	−0.838848	+	0.544365i	$0.816771\pi$
$648$	−0.673810	+	1.16707i	−0.0264698	+	0.0458470i
$649$	9.96921			0.391326
$650$	3.32355	−	5.30791i	0.130360	−	0.208193i
$651$	−38.5789			−1.51203
$652$	−18.2985	+	31.6940i	−0.716625	+	1.24123i
$653$	30.6118	+	17.6738i	1.19793	+	0.691628i	0.960094	−	0.279677i	$-0.0902273\pi$
$653$	30.6118	+	17.6738i	1.19793	+	0.691628i	0.237840	+	0.971304i	$0.423561\pi$
$654$	0.381213	+	0.660281i	0.0149066	+	0.0258190i
$655$	6.74277	−	14.2490i	0.263462	−	0.556756i
$656$	31.4124	−	18.1359i	1.22645	−	0.708089i
$657$	−0.236649	−	0.409888i	−0.00923256	−	0.0159913i
$658$	−18.4780			−0.720346
$659$	−6.05476	−	10.4872i	−0.235860	−	0.408522i	0.723662	−	0.690154i	$-0.242457\pi$
$659$	−6.05476	−	10.4872i	−0.235860	−	0.408522i	−0.959522	+	0.281633i	$0.909124\pi$
$660$	11.4740	+	16.5853i	0.446623	+	0.645582i
$661$	22.5000	+	12.9904i	0.875150	+	0.505268i	0.869056	−	0.494713i	$-0.164727\pi$
$661$	22.5000	+	12.9904i	0.875150	+	0.505268i	0.00609372	+	0.999981i	$0.498060\pi$
$662$			7.06176i			0.274463i
$663$	0.851678	−	0.965874i	0.0330764	−	0.0375114i
$664$	−13.6160			−0.528405
$665$	28.0593	−	19.4118i	1.08809	−	0.752759i
$666$	−1.18832	+	2.05824i	−0.0460466	+	0.0797550i
$667$	2.91926	−	1.68544i	0.113034	−	0.0652604i
$668$	45.3660			1.75526
$669$	16.2052	−	9.35609i	0.626530	−	0.361727i
$670$	2.78717	−	0.227974i	0.107678	−	0.00880742i
$671$			30.3465i			1.17151i
$672$	13.9073	−	8.02939i	0.536486	−	0.309740i
$673$	25.1355	+	14.5120i	0.968902	+	0.559396i	0.898901	−	0.438151i	$-0.144366\pi$
$673$	25.1355	+	14.5120i	0.968902	+	0.559396i	0.0700008	+	0.997547i	$0.477700\pi$
$674$	−7.50990	−	4.33584i	−0.289270	−	0.167010i
$675$	3.86632	−	3.17042i	0.148815	−	0.122030i
$676$	19.4627	−	14.7678i	0.748565	−	0.567991i
$677$			18.9263i			0.727395i	0.931517	+	0.363698i	$0.118486\pi$
$677$			18.9263i			0.727395i	−0.931517	+	0.363698i	$0.881514\pi$
$678$	2.08256	−	3.60711i	0.0799804	−	0.138530i
$679$	18.2537	−	31.6164i	0.700513	−	1.21332i
$680$	0.0877370	+	1.07266i	0.00336456	+	0.0411345i
$681$		−	25.6833i		−	0.984187i
$682$	−7.68639	−	13.3132i	−0.294327	−	0.509790i
$683$	−15.1366	−	26.2173i	−0.579186	−	1.00318i	−0.995573	−	0.0939915i	$-0.970037\pi$
$683$	−15.1366	−	26.2173i	−0.579186	−	1.00318i	0.416387	−	0.909187i	$-0.363296\pi$
$684$		−	6.85406i		−	0.262071i
$685$	7.20270	−	0.589139i	0.275201	−	0.0225099i
$686$	2.54656	−	4.41076i	0.0972280	−	0.168404i
$687$	7.95249	−	13.7741i	0.303406	−	0.525515i
$688$		−	11.6066i		−	0.442497i
$689$	1.61109	+	1.42061i	0.0613775	+	0.0541208i
$690$	−0.959073	+	2.02674i	−0.0365113	+	0.0771567i
$691$	−26.9294	−	15.5477i	−1.02444	−	0.591463i	−0.109056	−	0.994036i	$-0.534783\pi$
$691$	−26.9294	−	15.5477i	−1.02444	−	0.591463i	−0.915388	+	0.402573i	$0.868116\pi$
$692$	−8.74883	−	5.05114i	−0.332580	−	0.192015i
$693$	17.3887	−	10.0393i	0.660540	−	0.381363i
$694$			3.47104i			0.131759i
$695$	−8.17629	+	0.668773i	−0.310144	+	0.0253680i
$696$	−1.36289	+	0.786866i	−0.0516603	+	0.0298261i
$697$	3.93698			0.149124
$698$	−8.22634	+	4.74948i	−0.311371	+	0.179770i
$699$	−8.35947	+	14.4790i	−0.316184	+	0.547647i
$700$	−38.7911	+	6.38852i	−1.46617	+	0.241463i
$701$	10.9978			0.415381			0.207690	−	0.978195i	$-0.433405\pi$
$701$	10.9978			0.415381			0.207690	+	0.978195i	$0.433405\pi$
$702$	−1.18713	+	0.399401i	−0.0448053	+	0.0150744i
$703$		−	24.9516i		−	0.941069i
$704$	−21.8101	−	12.5921i	−0.821998	−	0.474581i
$705$	23.3792	−	16.1740i	0.880510	−	0.609150i
$706$	0.661875	+	1.14640i	0.0249100	+	0.0431454i
$707$	4.46080			0.167766
$708$	1.95195	+	3.38088i	0.0733588	+	0.127061i
$709$	−37.7066	+	21.7699i	−1.41610	+	0.817587i	−0.995954	−	0.0898683i	$-0.971355\pi$
$709$	−37.7066	+	21.7699i	−1.41610	+	0.817587i	−0.420149	+	0.907455i	$0.638022\pi$
$710$	−6.53014	−	3.09012i	−0.245072	−	0.115970i
$711$	2.75214	+	4.76685i	0.103213	+	0.178771i
$712$	−1.82680	−	1.05471i	−0.0684624	−	0.0395268i
$713$	−13.3085	+	23.0509i	−0.498405	+	0.863264i
$714$	0.519086			0.0194263
$715$	−4.53354	+	38.4254i	−0.169545	+	1.43703i
$716$	32.5590			1.21679
$717$	1.36772	−	2.36896i	0.0510783	−	0.0884702i
$718$	6.43946	+	3.71782i	0.240319	+	0.138748i
$719$	10.4827	+	18.1566i	0.390940	+	0.677127i	0.992574	−	0.121645i	$-0.0388168\pi$
$719$	10.4827	+	18.1566i	0.390940	+	0.677127i	−0.601634	+	0.798772i	$0.705483\pi$
$720$	−3.14719	+	6.65073i	−0.117289	+	0.247858i
$721$	−38.2152	+	22.0636i	−1.42321	+	0.821690i
$722$	0.989832	+	1.71444i	0.0368377	+	0.0638048i
$723$	14.5411			0.540790
$724$	−4.98343	−	8.63155i	−0.185208	−	0.320789i
$725$	5.76132	−	0.948834i	0.213970	−	0.0352388i
$726$	3.61968	+	2.08982i	0.134339	+	0.0775605i
$727$		−	2.09966i		−	0.0778720i	−0.999242	−	0.0389360i	$-0.987603\pi$
$727$		−	2.09966i		−	0.0778720i	0.999242	−	0.0389360i	$-0.0123968\pi$
$728$	19.9274	+	4.01983i	0.738558	+	0.148985i
$729$	−1.00000			−0.0370370
$730$	0.209168	+	0.302346i	0.00774164	+	0.0111903i
$731$	0.629894	−	1.09101i	0.0232975	−	0.0403524i
$732$	−10.2915	+	5.94179i	−0.380384	+	0.219615i
$733$	−29.2214			−1.07932			−0.539658	−	0.841885i	$-0.681446\pi$
$733$	−29.2214			−1.07932			−0.539658	+	0.841885i	$0.681446\pi$
$734$	−4.00335	+	2.31133i	−0.147766	+	0.0853129i
$735$	1.91481	+	23.4101i	0.0706289	+	0.863495i
$736$		−	11.0795i		−	0.408396i
$737$	−14.9627	+	8.63870i	−0.551157	+	0.318211i
$738$	−3.31627	−	1.91465i	−0.122074	−	0.0704792i
$739$	−16.8442	−	9.72501i	−0.619624	−	0.357740i	0.157099	−	0.987583i	$-0.449786\pi$
$739$	−16.8442	−	9.72501i	−0.619624	−	0.357740i	−0.776723	+	0.629843i	$0.783119\pi$
$740$	−12.2975	+	25.9873i	−0.452063	+	0.955314i
$741$	8.69693	−	9.86304i	0.319490	−	0.362328i
$742$			0.865840i			0.0317860i
$743$	−10.4012	+	18.0154i	−0.381583	+	0.660921i	−0.991289	−	0.131707i	$-0.957954\pi$
$743$	−10.4012	+	18.0154i	−0.381583	+	0.660921i	0.609706	+	0.792628i	$0.291288\pi$
$744$	6.21320	−	10.7616i	0.227787	−	0.394539i
$745$	0.612993	+	7.49433i	0.0224583	+	0.274571i
$746$			9.68024i			0.354419i
$747$	−5.05188	−	8.75012i	−0.184839	−	0.320150i
$748$	−1.61061	−	2.78966i	−0.0588897	−	0.102000i
$749$		−	39.7828i		−	1.45363i
$750$	−2.79251	+	2.69935i	−0.101968	+	0.0985662i
$751$	−23.6765	+	41.0089i	−0.863967	+	1.49644i	0.00410163	+	0.999992i	$0.498694\pi$
$751$	−23.6765	+	41.0089i	−0.863967	+	1.49644i	−0.868069	+	0.496444i	$0.834639\pi$
$752$	−20.9172	+	36.2296i	−0.762770	+	1.32116i
$753$			10.1193i			0.368768i
$754$	−1.43379	−	0.289229i	−0.0522155	−	0.0105331i
$755$	−24.1764	−	11.4405i	−0.879868	−	0.416362i
$756$	6.80933	+	3.93137i	0.247653	+	0.142982i
$757$	−33.9413	−	19.5960i	−1.23362	−	0.712230i	−0.265836	−	0.964018i	$-0.585648\pi$
$757$	−33.9413	−	19.5960i	−1.23362	−	0.712230i	−0.967782	+	0.251788i	$0.918981\pi$
$758$	1.64685	−	0.950809i	0.0598163	−	0.0345350i
$759$		−	13.8530i		−	0.502831i
$760$	0.895928	+	10.9534i	0.0324987	+	0.397323i
$761$	−33.8725	+	19.5563i	−1.22788	+	0.708916i	−0.966586	−	0.256344i	$-0.917482\pi$
$761$	−33.8725	+	19.5563i	−1.22788	+	0.708916i	−0.261292	+	0.965260i	$0.584149\pi$
$762$	0.997742			0.0361444
$763$	7.95224	−	4.59123i	0.287891	−	0.166214i
$764$	1.46870	−	2.54387i	0.0531358	−	0.0920340i
$765$	−0.656771	+	0.454364i	−0.0237456	+	0.0164276i
$766$	−4.63801			−0.167578
$767$	−1.48103	+	7.34189i	−0.0534771	+	0.265100i
$768$		−	7.19525i		−	0.259636i
$769$	−24.4633	−	14.1239i	−0.882168	−	0.509320i	−0.0107957	−	0.999942i	$-0.503436\pi$
$769$	−24.4633	−	14.1239i	−0.882168	−	0.509320i	−0.871373	+	0.490622i	$0.836770\pi$
$770$	−12.8264	+	8.87350i	−0.462232	+	0.319779i
$771$	7.13305	+	12.3548i	0.256890	+	0.444947i
$772$	−6.66919			−0.240029
$773$	−10.2560	−	17.7639i	−0.368882	−	0.638922i	0.620509	−	0.784199i	$-0.286926\pi$
$773$	−10.2560	−	17.7639i	−0.368882	−	0.638922i	−0.989391	+	0.145277i	$0.953593\pi$
$774$	−1.06117	+	0.612665i	−0.0381429	+	0.0220218i
$775$	−35.6513	+	29.2345i	−1.28063	+	1.05013i
$776$	5.87958	+	10.1837i	0.211065	+	0.365575i
$777$	24.7888	+	14.3118i	0.889294	+	0.513434i
$778$	−2.42595	+	4.20186i	−0.0869744	+	0.150644i
$779$	40.2026			1.44041
$780$	−13.9189	+	5.98614i	−0.498378	+	0.214338i
$781$	44.6341			1.59713
$782$	0.179067	−	0.310154i	0.00640344	−	0.0110911i
$783$	−1.01133	−	0.583893i	−0.0361421	−	0.0208666i
$784$	−17.2822	−	29.9336i	−0.617221	−	1.06906i
$785$	15.4245	+	7.29903i	0.550525	+	0.260513i
$786$	2.12090	−	1.22450i	0.0756500	−	0.0436765i
$787$	11.0836	+	19.1973i	0.395086	+	0.684310i	0.993112	−	0.117167i	$-0.0373813\pi$
$787$	11.0836	+	19.1973i	0.395086	+	0.684310i	−0.598026	+	0.801477i	$0.704048\pi$
$788$	−2.27866			−0.0811740
$789$	−10.5360	−	18.2489i	−0.375092	−	0.649678i
$790$	−2.43254	−	3.51618i	−0.0865460	−	0.125100i
$791$	−43.4430	−	25.0818i	−1.54466	−	0.891807i
$792$			6.46741i			0.229810i
$793$	−22.3489	−	4.50830i	−0.793632	−	0.160095i
$794$	−10.4346			−0.370311
$795$	−0.757883	−	1.09550i	−0.0268794	−	0.0388534i
$796$	−6.78354	+	11.7494i	−0.240436	+	0.416448i
$797$	−30.2426	+	17.4606i	−1.07125	+	0.618485i	−0.928522	−	0.371278i	$-0.878920\pi$
$797$	−30.2426	+	17.4606i	−1.07125	+	0.618485i	−0.142725	+	0.989762i	$0.545586\pi$
$798$	5.30066			0.187641
$799$	−3.93239	+	2.27037i	−0.139118	+	0.0803198i
$800$	6.76740	−	17.9588i	0.239264	−	0.634939i
$801$		−	1.56529i		−	0.0553067i
$802$	−9.71742	+	5.61036i	−0.343134	+	0.198109i
$803$	−1.96711	−	1.13571i	−0.0694178	−	0.0400784i
$804$	−5.85932	−	3.38288i	−0.206642	−	0.119305i
$805$	24.4095	+	11.5508i	0.860322	+	0.407112i
$806$	10.9465	−	3.68287i	0.385574	−	0.129724i
$807$			25.5812i			0.900499i
$808$	−0.718420	+	1.24434i	−0.0252739	+	0.0437757i
$809$	20.5193	−	35.5404i	0.721418	−	1.24953i	−0.239013	−	0.971016i	$-0.576824\pi$
$809$	20.5193	−	35.5404i	0.721418	−	1.24953i	0.960431	−	0.278517i	$-0.0898429\pi$
$810$	0.774192	−	0.0633244i	0.0272023	−	0.00222499i
$811$			35.0965i			1.23240i	0.787588	+	0.616202i	$0.211329\pi$
$811$			35.0965i			1.23240i	−0.787588	+	0.616202i	$0.788671\pi$
$812$	4.59100	+	7.95184i	0.161112	+	0.279055i
$813$	−6.16086	−	10.6709i	−0.216071	−	0.374246i
$814$			11.4059i			0.399775i
$815$	43.3992	−	3.54980i	1.52021	−	0.124344i
$816$	0.587608	−	1.01777i	0.0205704	−	0.0356290i
$817$	6.43217	−	11.1409i	0.225033	−	0.389769i
$818$		−	0.411407i		−	0.0143845i
$819$	4.81027	+	14.2974i	0.168084	+	0.499593i
$820$	−41.8713	−	19.8139i	−1.46221	−	0.691931i
$821$	−42.4562	−	24.5121i	−1.48173	−	0.855477i	−0.481945	−	0.876201i	$-0.660070\pi$
$821$	−42.4562	−	24.5121i	−1.48173	−	0.855477i	−0.999785	+	0.0207240i	$0.993403\pi$
$822$	0.972300	+	0.561358i	0.0339129	+	0.0195796i
$823$	11.1992	−	6.46588i	0.390381	−	0.225386i	−0.291944	−	0.956435i	$-0.594302\pi$
$823$	11.1992	−	6.46588i	0.390381	−	0.225386i	0.682325	+	0.731049i	$0.260969\pi$
$824$		−	14.2135i		−	0.495150i
$825$	8.46145	−	22.4543i	0.294590	−	0.781759i
$826$	−2.61464	+	1.50956i	−0.0909749	+	0.0525244i
$827$	43.9084			1.52684			0.763422	−	0.645901i	$-0.223518\pi$
$827$	43.9084			1.52684			0.763422	+	0.645901i	$0.223518\pi$
$828$	4.69799	−	2.71238i	0.163266	−	0.0942618i
$829$	17.3009	−	29.9660i	0.600885	−	1.04076i	−0.391802	−	0.920049i	$-0.628148\pi$
$829$	17.3009	−	29.9660i	0.600885	−	1.04076i	0.992687	−	0.120714i	$-0.0385184\pi$
$830$	4.46522	+	6.45436i	0.154990	+	0.224034i
$831$	1.75565			0.0609030
$832$	12.5136	−	14.1915i	0.433832	−	0.492002i
$833$		−	3.75165i		−	0.129987i
$834$	−1.10373	−	0.637236i	−0.0382189	−	0.0220657i
$835$	−30.7098	−	44.3903i	−1.06276	−	1.53619i
$836$	−16.4468	−	28.4867i	−0.568824	−	0.985232i
$837$	9.22100			0.318724
$838$	6.35259	+	11.0030i	0.219447	+	0.380093i
$839$	−2.81603	+	1.62584i	−0.0972202	+	0.0561301i	−0.547822	−	0.836595i	$-0.684543\pi$
$839$	−2.81603	+	1.62584i	−0.0972202	+	0.0561301i	0.450602	+	0.892725i	$0.351209\pi$
$840$	−11.3959	−	5.39262i	−0.393194	−	0.186063i
$841$	13.8181	+	23.9337i	0.476488	+	0.825301i
$842$	4.92391	+	2.84282i	0.169689	+	0.0979700i
$843$	−8.77666	+	15.2016i	−0.302284	+	0.523572i
$844$	−14.6513			−0.504319
$845$	−27.6251	−	9.04726i	−0.950333	−	0.311235i
$846$	4.41653			0.151844
$847$	25.1692	−	43.5944i	0.864825	−	1.49792i
$848$	1.69765	+	0.980136i	0.0582974	+	0.0336580i
$849$	−1.41015	−	2.44245i	−0.0483962	−	0.0838247i
$850$	0.479695	−	0.393355i	0.0164534	−	0.0134920i
$851$	17.1026	−	9.87422i	0.586271	−	0.338484i
$852$	8.73927	+	15.1369i	0.299403	+	0.518580i
$853$	45.5253			1.55876			0.779378	−	0.626554i	$-0.215535\pi$
$853$	45.5253			1.55876			0.779378	+	0.626554i	$0.215535\pi$
$854$	−4.59514	−	7.95902i	−0.157243	−	0.272352i
$855$	−6.70663	+	4.63975i	−0.229362	+	0.158676i
$856$	11.0974	+	6.40709i	0.379301	+	0.218990i
$857$		−	7.81423i		−	0.266929i	−0.991054	−	0.133464i	$-0.957390\pi$
$857$		−	7.81423i		−	0.266929i	0.991054	−	0.133464i	$-0.0426102\pi$
$858$	−3.97553	+	4.50858i	−0.135722	+	0.153920i
$859$	19.4846			0.664807			0.332404	−	0.943137i	$-0.392140\pi$
$859$	19.4846			0.664807			0.332404	+	0.943137i	$0.392140\pi$
$860$	−12.1899	+	8.43318i	−0.415674	+	0.287569i
$861$	−23.0595	+	39.9402i	−0.785865	+	1.36116i
$862$	1.39349	−	0.804530i	0.0474623	−	0.0274024i
$863$	45.7202			1.55633			0.778167	−	0.628058i	$-0.216150\pi$
$863$	45.7202			1.55633			0.778167	+	0.628058i	$0.216150\pi$
$864$	−3.32408	+	1.91916i	−0.113087	+	0.0652910i
$865$	0.979890	+	11.9799i	0.0333173	+	0.407330i
$866$		−	6.58106i		−	0.223634i
$867$	−14.6120	+	8.43622i	−0.496248	+	0.286509i
$868$	−62.7888	−	36.2511i	−2.13119	−	1.23044i
$869$	22.8768	+	13.2079i	0.776041	+	0.448048i
$870$	0.819940	+	0.388003i	0.0277986	+	0.0131545i
$871$	−4.13916	−	12.3027i	−0.140250	−	0.416862i
$872$			2.95770i			0.100160i
$873$	−4.36294	+	7.55683i	−0.147663	+	0.255760i
$874$	1.82855	−	3.16714i	0.0618517	−	0.107130i
$875$	32.5102	+	33.6322i	1.09904	+	1.13698i
$876$		−	0.889480i		−	0.0300528i
$877$	−6.94847	−	12.0351i	−0.234633	−	0.406396i	0.724533	−	0.689240i	$-0.242056\pi$
$877$	−6.94847	−	12.0351i	−0.234633	−	0.406396i	−0.959166	+	0.282844i	$0.908722\pi$
$878$	5.60634	+	9.71047i	0.189205	+	0.327712i
$879$		−	4.72621i		−	0.159411i
$880$	2.87863	+	35.1935i	0.0970385	+	1.18637i
$881$	−4.97729	+	8.62092i	−0.167689	+	0.290446i	−0.937607	−	0.347697i	$-0.886964\pi$
$881$	−4.97729	+	8.62092i	−0.167689	+	0.290446i	0.769918	+	0.638143i	$0.220297\pi$
$882$	−1.82452	+	3.16016i	−0.0614347	+	0.106408i
$883$			13.1934i			0.443993i	0.975047	+	0.221997i	$0.0712574\pi$
$883$			13.1934i			0.443993i	−0.975047	+	0.221997i	$0.928743\pi$
$884$	2.29374	−	0.771711i	0.0771467	−	0.0259554i
$885$	1.98682	−	4.19860i	0.0667861	−	0.141134i
$886$	−4.23733	−	2.44642i	−0.142356	−	0.0821892i
$887$	25.2599	+	14.5838i	0.848143	+	0.489676i	0.860024	−	0.510254i	$-0.170449\pi$
$887$	25.2599	+	14.5838i	0.848143	+	0.489676i	−0.0118809	+	0.999929i	$0.503782\pi$
$888$	−7.98456	+	4.60989i	−0.267944	+	0.154698i
$889$		−	12.0165i		−	0.403022i
$890$	0.0991208	+	1.21183i	0.00332254	+	0.0406207i
$891$	−4.15617	+	2.39957i	−0.139237	+	0.0803886i
$892$	35.1662			1.17745
$893$	−40.1557	+	23.1839i	−1.34376	+	0.775819i
$894$	−0.584087	+	1.01167i	−0.0195348	+	0.0338352i
$895$	−22.0404	−	31.8588i	−0.736728	−	1.06492i
$896$	39.7444			1.32777
$897$	10.2021	+	2.05801i	0.340639	+	0.0687149i
$898$		−	3.72448i		−	0.124288i
$899$	9.32550	+	5.38408i	0.311023	+	0.179569i
$900$	9.27172	−	1.52696i	0.309057	−	0.0508987i
$901$	0.106385	+	0.184264i	0.00354419	+	0.00613872i
$902$	−18.3773			−0.611898
$903$	7.37877	+	12.7804i	0.245550	+	0.425305i
$904$	13.9931	−	8.07894i	0.465405	−	0.268702i
$905$	−5.07244	+	10.7192i	−0.168614	+	0.356320i
$906$	−2.07762	−	3.59853i	−0.0690241	−	0.119553i
$907$	−4.72241	−	2.72648i	−0.156805	−	0.0905313i	0.419544	−	0.907735i	$-0.362190\pi$
$907$	−4.72241	−	2.72648i	−0.156805	−	0.0905313i	−0.576349	+	0.817203i	$0.695523\pi$
$908$	24.1336	−	41.8007i	0.800903	−	1.38720i
$909$	−1.06621			−0.0353638
$910$	−4.62945	−	10.7644i	−0.153465	−	0.356835i
$911$	−8.32918			−0.275958			−0.137979	−	0.990435i	$-0.544061\pi$
$911$	−8.32918			−0.275958			−0.137979	+	0.990435i	$0.544061\pi$
$912$	6.00038	−	10.3930i	0.198692	−	0.344145i
$913$	−41.9930	−	24.2447i	−1.38977	−	0.802382i
$914$	3.73643	+	6.47168i	0.123590	+	0.214064i
$915$	12.7806	+	6.04792i	0.422515	+	0.199938i
$916$	25.8860	−	14.9453i	0.855298	−	0.493807i
$917$	−14.7476	−	25.5435i	−0.487007	−	0.843522i
$918$	−0.124070			−0.00409492
$919$	18.3769	+	31.8298i	0.606199	+	1.04997i	0.991861	+	0.127328i	$0.0406399\pi$
$919$	18.3769	+	31.8298i	0.606199	+	1.04997i	−0.385661	+	0.922640i	$0.626027\pi$
$920$	−7.15328	+	4.94875i	−0.235837	+	0.163155i
$921$	10.5092	+	6.06748i	0.346289	+	0.199930i
$922$		−	4.38593i		−	0.144443i
$923$	−6.63089	+	32.8711i	−0.218258	+	1.08197i
$924$	37.7344			1.24137
$925$	33.7530	−	5.55878i	1.10979	−	0.182772i
$926$	−5.29641	+	9.17365i	−0.174051	+	0.301465i
$927$	9.13406	−	5.27355i	0.300002	−	0.173206i
$928$	−4.48233			−0.147140
$929$	17.4624	−	10.0819i	0.572924	−	0.330778i	−0.185392	−	0.982665i	$-0.559356\pi$
$929$	17.4624	−	10.0819i	0.572924	−	0.330778i	0.758316	+	0.651887i	$0.226022\pi$
$930$	−7.13882	+	0.583914i	−0.234091	+	0.0191473i
$931$		−	38.3100i		−	1.25556i
$932$	−27.2108	+	15.7101i	−0.891318	+	0.514603i
$933$	3.84254	+	2.21849i	0.125799	+	0.0726302i
$934$	7.06118	+	4.07677i	0.231049	+	0.133396i
$935$	−1.63938	+	3.46438i	−0.0536134	+	0.113297i
$936$	−4.76297	−	0.960805i	−0.155683	−	0.0314049i
$937$			16.3524i			0.534210i	0.963667	+	0.267105i	$0.0860671\pi$
$937$			16.3524i			0.534210i	−0.963667	+	0.267105i	$0.913933\pi$
$938$	2.61619	−	4.53137i	0.0854215	−	0.147954i
$939$	3.87573	−	6.71297i	0.126480	−	0.219069i
$940$	53.2487	−	4.35543i	1.73678	−	0.142059i
$941$		−	39.7698i		−	1.29646i	−0.761446	−	0.648228i	$-0.775510\pi$
$941$		−	39.7698i		−	1.29646i	0.761446	−	0.648228i	$-0.224490\pi$
$942$	1.32552	+	2.29587i	0.0431877	+	0.0748034i
$943$	15.9095	+	27.5561i	0.518085	+	0.897350i
$944$			6.83534i			0.222471i
$945$	−0.762662	−	9.32415i	−0.0248094	−	0.303315i
$946$	−2.94026	+	5.09269i	−0.0955962	+	0.165578i
$947$	5.01172	−	8.68055i	0.162859	−	0.282080i	−0.773034	−	0.634365i	$-0.781262\pi$
$947$	5.01172	−	8.68055i	0.162859	−	0.282080i	0.935893	+	0.352285i	$0.114595\pi$
$948$			10.3443i			0.335968i
$949$	1.12864	−	1.27997i	0.0366371	−	0.0415496i
$950$	4.89841	−	4.01675i	0.158925	−	0.130321i
$951$	19.1595	+	11.0617i	0.621288	+	0.358701i
$952$	1.74392	+	1.00685i	0.0565207	+	0.0326322i
$953$	15.8837	−	9.17044i	0.514522	−	0.297060i	−0.220168	−	0.975462i	$-0.570661\pi$
$953$	15.8837	−	9.17044i	0.514522	−	0.297060i	0.734691	+	0.678402i	$0.237327\pi$
$954$		−	0.206950i		−	0.00670025i
$955$	−3.48337	+	0.284920i	−0.112719	+	0.00921978i
$956$	4.45203	−	2.57038i	0.143989	−	0.0831321i
$957$	−5.60437			−0.181163
$958$	7.70690	−	4.44958i	0.248999	−	0.143759i
$959$	6.76084	−	11.7101i	0.218319	−	0.378139i
$960$	−9.64988	+	6.67593i	−0.311449	+	0.215465i
$961$	−54.0268			−1.74280
$962$	−8.39992	−	1.69446i	−0.270824	−	0.0546317i
$963$			9.50874i			0.306415i
$964$	23.6663	+	13.6637i	0.762240	+	0.440079i
$965$	4.51460	+	6.52574i	0.145330	+	0.210071i
$966$	2.09765	+	3.63324i	0.0674908	+	0.116898i
$967$	−23.1393			−0.744109			−0.372055	−	0.928211i	$-0.621347\pi$
$967$	−23.1393			−0.744109			−0.372055	+	0.928211i	$0.621347\pi$
$968$	8.10709	+	14.0419i	0.260572	+	0.451324i
$969$	1.12806	−	0.651286i	0.0362385	−	0.0209223i
$970$	2.89922	−	6.12671i	0.0930883	−	0.196717i
$971$	−11.7553	−	20.3607i	−0.377245	−	0.653407i	0.613415	−	0.789760i	$-0.289795\pi$
$971$	−11.7553	−	20.3607i	−0.377245	−	0.653407i	−0.990660	+	0.136353i	$0.956462\pi$
$972$	−1.62754	−	0.939662i	−0.0522034	−	0.0301397i
$973$	−7.67470	+	13.2930i	−0.246040	+	0.426153i
$974$	−1.93387			−0.0619651
$975$	15.2796	+	9.56733i	0.489339	+	0.306400i
$976$	−20.8069			−0.666013
$977$	7.78231	−	13.4794i	0.248978	−	0.431243i	−0.714264	−	0.699876i	$-0.753239\pi$
$977$	7.78231	−	13.4794i	0.248978	−	0.431243i	0.963243	+	0.268633i	$0.0865719\pi$
$978$	5.85850	+	3.38241i	0.187334	+	0.108157i
$979$	−3.75601	−	6.50560i	−0.120043	−	0.207920i
$980$	−18.8812	+	39.9002i	−0.603136	+	1.27457i
$981$	−1.90072	+	1.09738i	−0.0606852	+	0.0350366i
$982$	−4.17822	−	7.23689i	−0.133332	−	0.230939i
$983$	−24.7575			−0.789641			−0.394821	−	0.918758i	$-0.629193\pi$
$983$	−24.7575			−0.789641			−0.394821	+	0.918758i	$0.629193\pi$
$984$	−7.42754	−	12.8649i	−0.236781	−	0.410117i
$985$	1.54251	+	2.22965i	0.0491483	+	0.0710426i
$986$	−0.125476	−	0.0724437i	−0.00399597	−	0.00230708i
$987$		−	53.1915i		−	1.69310i
$988$	23.4225	−	7.88034i	0.745170	−	0.250707i
$989$	10.1817			0.323760
$990$	3.06572	−	2.12091i	0.0974351	−	0.0674071i
$991$	−23.5183	+	40.7349i	−0.747083	+	1.29399i	0.202133	+	0.979358i	$0.435213\pi$
$991$	−23.5183	+	40.7349i	−0.747083	+	1.29399i	−0.949215	+	0.314627i	$0.898121\pi$
$992$	30.6513	−	17.6965i	0.973180	−	0.561866i
$993$	−20.3283			−0.645100
$994$	−11.7063	+	6.75861i	−0.371300	+	0.214370i
$995$	16.0887	−	1.31597i	0.510047	−	0.0417189i
$996$		−	18.9882i		−	0.601666i
$997$	−26.1426	+	15.0934i	−0.827945	+	0.478014i	−0.853148	−	0.521668i	$-0.825310\pi$
$997$	−26.1426	+	15.0934i	−0.827945	+	0.478014i	0.0252037	+	0.999682i	$0.491977\pi$
$998$	−3.66303	−	2.11485i	−0.115951	−	0.0669445i
$999$	−5.92494	−	3.42076i	−0.187457	−	0.108228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.v.a.4.9	yes	32
3.2	odd	2		585.2.bf.c.199.8		32
5.2	odd	4		975.2.bc.n.901.5		16
5.3	odd	4		975.2.bc.m.901.4		16
5.4	even	2	inner	195.2.v.a.4.8	✓	32
13.10	even	6	inner	195.2.v.a.49.8	yes	32
15.14	odd	2		585.2.bf.c.199.9		32
39.23	odd	6		585.2.bf.c.244.9		32
65.23	odd	12		975.2.bc.m.751.4		16
65.49	even	6	inner	195.2.v.a.49.9	yes	32
65.62	odd	12		975.2.bc.n.751.5		16
195.179	odd	6		585.2.bf.c.244.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.8	✓	32	5.4	even	2	inner
195.2.v.a.4.9	yes	32	1.1	even	1	trivial
195.2.v.a.49.8	yes	32	13.10	even	6	inner
195.2.v.a.49.9	yes	32	65.49	even	6	inner
585.2.bf.c.199.8		32	3.2	odd	2
585.2.bf.c.199.9		32	15.14	odd	2
585.2.bf.c.244.8		32	195.179	odd	6
585.2.bf.c.244.9		32	39.23	odd	6
975.2.bc.m.751.4		16	65.23	odd	12
975.2.bc.m.901.4		16	5.3	odd	4
975.2.bc.n.751.5		16	65.62	odd	12
975.2.bc.n.901.5		16	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173693 - 0.300844i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.939662 + 1.62754i) q^{4} +(0.956446 - 2.02119i) q^{5} +(0.300844 - 0.173693i) q^{6} +(-2.09191 - 3.62329i) q^{7} +1.34762 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.173693 - 0.300844i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.939662 + 1.62754i) q^{4} +(0.956446 - 2.02119i) q^{5} +(0.300844 - 0.173693i) q^{6} +(-2.09191 - 3.62329i) q^{7} +1.34762 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.441936 - 0.638807i) q^{10} +(4.15617 + 2.39957i) q^{11} +1.87932i q^{12} +(-2.38462 + 2.70436i) q^{13} -1.45339 q^{14} +(1.83890 - 1.27218i) q^{15} +(-1.64525 + 2.84966i) q^{16} +(-0.309305 + 0.178577i) q^{17} +0.347385 q^{18} +(-3.15847 + 1.82354i) q^{19} +(4.18831 - 0.342579i) q^{20} -4.18381i q^{21} +(1.44379 - 0.833575i) q^{22} +(-2.49983 - 1.44328i) q^{23} +(1.16707 + 0.673810i) q^{24} +(-3.17042 - 3.86632i) q^{25} +(0.399401 + 1.18713i) q^{26} +1.00000i q^{27} +(3.93137 - 6.80933i) q^{28} +(-0.583893 + 1.01133i) q^{29} +(-0.0633244 - 0.774192i) q^{30} -9.22100i q^{31} +(1.91916 + 3.32408i) q^{32} +(2.39957 + 4.15617i) q^{33} +0.124070i q^{34} +(-9.32415 + 0.762662i) q^{35} +(-0.939662 + 1.62754i) q^{36} +(-3.42076 + 5.92494i) q^{37} +1.26694i q^{38} +(-3.41733 + 1.14973i) q^{39} +(1.28893 - 2.72380i) q^{40} +(-9.54637 - 5.51160i) q^{41} +(-1.25868 - 0.726697i) q^{42} +(-3.05473 + 1.76365i) q^{43} +9.01913i q^{44} +(2.22863 - 0.182289i) q^{45} +(-0.868404 + 0.501373i) q^{46} +12.7136 q^{47} +(-2.84966 + 1.64525i) q^{48} +(-5.25214 + 9.09698i) q^{49} +(-1.71384 + 0.282253i) q^{50} -0.357154 q^{51} +(-6.64220 - 1.33989i) q^{52} -0.595736i q^{53} +(0.300844 + 0.173693i) q^{54} +(8.82514 - 6.10536i) q^{55} +(-2.81909 - 4.88282i) q^{56} -3.64709 q^{57} +(0.202836 + 0.351322i) q^{58} +(1.79899 - 1.03865i) q^{59} +(3.79847 + 1.79747i) q^{60} +(3.16166 + 5.47616i) q^{61} +(-2.77409 - 1.60162i) q^{62} +(2.09191 - 3.62329i) q^{63} -5.24763 q^{64} +(3.18526 + 7.40635i) q^{65} +1.66715 q^{66} +(-1.80005 + 3.11778i) q^{67} +(-0.581283 - 0.335604i) q^{68} +(-1.44328 - 2.49983i) q^{69} +(-1.39009 + 2.93759i) q^{70} +(8.05442 - 4.65022i) q^{71} +(0.673810 + 1.16707i) q^{72} -0.473298 q^{73} +(1.18832 + 2.05824i) q^{74} +(-0.812506 - 4.93354i) q^{75} +(-5.93579 - 3.42703i) q^{76} -20.0787i q^{77} +(-0.247673 + 1.22778i) q^{78} +5.50429 q^{79} +(4.18611 + 6.05091i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.31627 + 1.91465i) q^{82} -10.1038 q^{83} +(6.80933 - 3.93137i) q^{84} +(0.0651052 + 0.795963i) q^{85} +1.22533i q^{86} +(-1.01133 + 0.583893i) q^{87} +(5.60094 + 3.23371i) q^{88} +(-1.35558 - 0.782643i) q^{89} +(0.332255 - 0.702132i) q^{90} +(14.7871 + 2.98291i) q^{91} -5.42477i q^{92} +(4.61050 - 7.98562i) q^{93} +(2.20827 - 3.82483i) q^{94} +(0.664823 + 8.12799i) q^{95} +3.83831i q^{96} +(4.36294 + 7.55683i) q^{97} +(1.82452 + 3.16016i) q^{98} +4.79914i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q - 20 * q^4 + 16 * q^9	\( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Introduction

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