LMFDB - Embedded newform 370.2.n.f.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Root			$-0.147520 + 0.550552i$ of defining polynomial
Character	$\chi$	$=$	370.269
Dual form			370.2.n.f.359.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-2.73346 + 1.57816i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 + 2.19130i) q^{5} -3.15633 q^{6} +(-1.45071 + 0.837565i) q^{7} +1.00000i q^{8} +(3.48119 - 6.02961i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-2.73346 + 1.57816i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 + 2.19130i) q^{5} -3.15633 q^{6} +(-1.45071 + 0.837565i) q^{7} +1.00000i q^{8} +(3.48119 - 6.02961i) q^{9} +(-1.48119 + 1.67513i) q^{10} -4.48119 q^{11} +(-2.73346 - 1.57816i) q^{12} +(4.18416 - 2.41573i) q^{13} -1.67513 q^{14} +(-2.24133 - 6.69241i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.14878 - 1.24060i) q^{17} +(6.02961 - 3.48119i) q^{18} +(2.28726 + 3.96165i) q^{19} +(-2.12032 + 0.710109i) q^{20} +(2.64363 - 4.57890i) q^{21} +(-3.88083 - 2.24060i) q^{22} -1.67513i q^{23} +(-1.57816 - 2.73346i) q^{24} +(-4.60362 - 1.95108i) q^{25} +4.83146 q^{26} +12.5066i q^{27} +(-1.45071 - 0.837565i) q^{28} -9.08840 q^{29} +(1.40515 - 6.91646i) q^{30} -2.83146 q^{31} +(-0.866025 + 0.500000i) q^{32} +(12.2492 - 7.07205i) q^{33} +(-1.24060 - 2.14878i) q^{34} +(-1.18953 - 3.55181i) q^{35} +6.96239 q^{36} +(0.920588 + 6.01270i) q^{37} +4.57452i q^{38} +(-7.62482 + 13.2066i) q^{39} +(-2.19130 - 0.445186i) q^{40} +(0.175131 + 0.303336i) q^{41} +(4.57890 - 2.64363i) q^{42} +3.80606i q^{43} +(-2.24060 - 3.88083i) q^{44} +(11.6629 + 10.3127i) q^{45} +(0.837565 - 1.45071i) q^{46} +2.63752i q^{47} -3.15633i q^{48} +(-2.09697 + 3.63206i) q^{49} +(-3.01131 - 3.99149i) q^{50} +7.83146 q^{51} +(4.18416 + 2.41573i) q^{52} +(4.04878 + 2.33757i) q^{53} +(-6.25329 + 10.8310i) q^{54} +(1.99497 - 9.81965i) q^{55} +(-0.837565 - 1.45071i) q^{56} +(-12.5042 - 7.21933i) q^{57} +(-7.87078 - 4.54420i) q^{58} +(4.91573 - 8.51429i) q^{59} +(4.67513 - 5.28726i) q^{60} +(6.83146 + 11.8324i) q^{61} +(-2.45211 - 1.41573i) q^{62} +11.6629i q^{63} -1.00000 q^{64} +(3.43086 + 10.2442i) q^{65} +14.1441 q^{66} +(-10.8636 + 6.27210i) q^{67} -2.48119i q^{68} +(2.64363 + 4.57890i) q^{69} +(0.745746 - 3.67072i) q^{70} +(-2.80606 - 4.86024i) q^{71} +(6.02961 + 3.48119i) q^{72} -7.13093i q^{73} +(-2.20910 + 5.66744i) q^{74} +(15.6629 - 1.93207i) q^{75} +(-2.28726 + 3.96165i) q^{76} +(6.50089 - 3.75329i) q^{77} +(-13.2066 + 7.62482i) q^{78} +(5.04055 + 8.73049i) q^{79} +(-1.67513 - 1.48119i) q^{80} +(-9.29384 - 16.0974i) q^{81} +0.350262i q^{82} +(5.80282 + 3.35026i) q^{83} +5.28726 q^{84} +(3.67513 - 4.15633i) q^{85} +(-1.90303 + 3.29615i) q^{86} +(24.8427 - 14.3430i) q^{87} -4.48119i q^{88} +(-5.27210 + 9.13154i) q^{89} +(4.94405 + 14.7625i) q^{90} +(-4.04666 + 7.00902i) q^{91} +(1.45071 - 0.837565i) q^{92} +(7.73967 - 4.46850i) q^{93} +(-1.31876 + 2.28416i) q^{94} +(-9.69942 + 3.24840i) q^{95} +(1.57816 - 2.73346i) q^{96} +8.18664i q^{97} +(-3.63206 + 2.09697i) q^{98} +(-15.5999 + 27.0198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9	$ 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9} + 4 q^{10} - 32 q^{11} + 18 q^{15} - 6 q^{16} + 4 q^{19} + 20 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 32 q^{29} - 20 q^{30} + 28 q^{31} - 4 q^{34} + 4 q^{35} + 40 q^{36} - 58 q^{39} + 2 q^{40} - 18 q^{41} - 16 q^{44} + 16 q^{45} - 26 q^{49} - 8 q^{50} + 32 q^{51} - 34 q^{54} - 4 q^{55} + 28 q^{59} + 36 q^{60} + 20 q^{61} - 12 q^{64} - 22 q^{65} + 24 q^{66} + 20 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{74} + 64 q^{75} - 4 q^{76} - 4 q^{79} - 6 q^{81} + 40 q^{84} + 24 q^{85} - 22 q^{86} - 44 q^{89} - 20 q^{90} - 36 q^{91} + 16 q^{94} + 16 q^{95} - 2 q^{96} - 80 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9 + 4 * q^10 - 32 * q^11 + 18 * q^15 - 6 * q^16 + 4 * q^19 + 20 * q^21 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 32 * q^29 - 20 * q^30 + 28 * q^31 - 4 * q^34 + 4 * q^35 + 40 * q^36 - 58 * q^39 + 2 * q^40 - 18 * q^41 - 16 * q^44 + 16 * q^45 - 26 * q^49 - 8 * q^50 + 32 * q^51 - 34 * q^54 - 4 * q^55 + 28 * q^59 + 36 * q^60 + 20 * q^61 - 12 * q^64 - 22 * q^65 + 24 * q^66 + 20 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^74 + 64 * q^75 - 4 * q^76 - 4 * q^79 - 6 * q^81 + 40 * q^84 + 24 * q^85 - 22 * q^86 - 44 * q^89 - 20 * q^90 - 36 * q^91 + 16 * q^94 + 16 * q^95 - 2 * q^96 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−2.73346	+	1.57816i	−1.57816	+	0.911153i	−0.583047	+	0.812439i	$0.698140\pi$
$3$	−2.73346	+	1.57816i	−1.57816	+	0.911153i	−0.995116	+	0.0987140i	$0.968527\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.445186	+	2.19130i	−0.199093	+	0.979981i
$5$	−0.445186	+	2.19130i	−0.199093	+	0.979981i
$6$	−3.15633			−1.28856
$7$	−1.45071	+	0.837565i	−0.548315	+	0.316570i	−0.748442	−	0.663200i	$-0.769198\pi$
$7$	−1.45071	+	0.837565i	−0.548315	+	0.316570i	0.200127	+	0.979770i	$0.435865\pi$
$8$			1.00000i			0.353553i
$9$	3.48119	−	6.02961i	1.16040	−	2.00987i
$10$	−1.48119	+	1.67513i	−0.468395	+	0.529723i
$11$	−4.48119			−1.35113			−0.675565	−	0.737300i	$-0.736100\pi$
$11$	−4.48119			−1.35113			−0.675565	+	0.737300i	$0.736100\pi$
$12$	−2.73346	−	1.57816i	−0.789081	−	0.455576i
$13$	4.18416	−	2.41573i	1.16048	−	0.670002i	0.209060	−	0.977903i	$-0.432960\pi$
$13$	4.18416	−	2.41573i	1.16048	−	0.670002i	0.951419	+	0.307900i	$0.0996264\pi$
$14$	−1.67513			−0.447698
$15$	−2.24133	−	6.69241i	−0.578710	−	1.72797i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.14878	−	1.24060i	−0.521155	−	0.300889i	0.216252	−	0.976338i	$-0.430617\pi$
$17$	−2.14878	−	1.24060i	−0.521155	−	0.300889i	−0.737407	+	0.675449i	$0.763950\pi$
$18$	6.02961	−	3.48119i	1.42119	−	0.820525i
$19$	2.28726	+	3.96165i	0.524733	+	0.908864i	0.999585	+	0.0287986i	$0.00916814\pi$
$19$	2.28726	+	3.96165i	0.524733	+	0.908864i	−0.474852	+	0.880065i	$0.657499\pi$
$20$	−2.12032	+	0.710109i	−0.474117	+	0.158785i
$21$	2.64363	−	4.57890i	0.576887	−	0.999198i
$22$	−3.88083	−	2.24060i	−0.827395	−	0.477697i
$23$		−	1.67513i		−	0.349289i	−0.984632	−	0.174644i	$-0.944122\pi$
$23$		−	1.67513i		−	0.349289i	0.984632	−	0.174644i	$-0.0558776\pi$
$24$	−1.57816	−	2.73346i	−0.322141	−	0.557965i
$25$	−4.60362	−	1.95108i	−0.920724	−	0.390215i
$26$	4.83146			0.947526
$27$			12.5066i			2.40689i
$28$	−1.45071	−	0.837565i	−0.274158	−	0.158285i
$29$	−9.08840			−1.68767			−0.843836	−	0.536600i	$-0.819708\pi$
$29$	−9.08840			−1.68767			−0.843836	+	0.536600i	$0.819708\pi$
$30$	1.40515	−	6.91646i	0.256545	−	1.26277i
$31$	−2.83146			−0.508545			−0.254272	−	0.967133i	$-0.581836\pi$
$31$	−2.83146			−0.508545			−0.254272	+	0.967133i	$0.581836\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	12.2492	−	7.07205i	2.13230	−	1.23109i
$34$	−1.24060	−	2.14878i	−0.212761	−	0.368512i
$35$	−1.18953	−	3.55181i	−0.201066	−	0.600365i
$36$	6.96239			1.16040
$37$	0.920588	+	6.01270i	0.151344	+	0.988481i
$37$	0.920588	+	6.01270i	0.151344	+	0.988481i
$38$			4.57452i			0.742084i
$39$	−7.62482	+	13.2066i	−1.22095	+	2.11475i
$40$	−2.19130	−	0.445186i	−0.346475	−	0.0703902i
$41$	0.175131	+	0.303336i	0.0273508	+	0.0473731i	0.879377	−	0.476126i	$-0.157960\pi$
$41$	0.175131	+	0.303336i	0.0273508	+	0.0473731i	−0.852026	+	0.523499i	$0.824626\pi$
$42$	4.57890	−	2.64363i	0.706540	−	0.407921i
$43$			3.80606i			0.580419i	0.956963	+	0.290210i	$0.0937250\pi$
$43$			3.80606i			0.580419i	−0.956963	+	0.290210i	$0.906275\pi$
$44$	−2.24060	−	3.88083i	−0.337783	−	0.585057i
$45$	11.6629	+	10.3127i	1.73860	+	1.53732i
$46$	0.837565	−	1.45071i	0.123492	−	0.213895i
$47$			2.63752i			0.384722i	0.981324	+	0.192361i	$0.0616144\pi$
$47$			2.63752i			0.384722i	−0.981324	+	0.192361i	$0.938386\pi$
$48$		−	3.15633i		−	0.455576i
$49$	−2.09697	+	3.63206i	−0.299567	+	0.518865i
$50$	−3.01131	−	3.99149i	−0.425864	−	0.564482i
$51$	7.83146			1.09662
$52$	4.18416	+	2.41573i	0.580239	+	0.335001i
$53$	4.04878	+	2.33757i	0.556143	+	0.321089i	0.751596	−	0.659624i	$-0.229284\pi$
$53$	4.04878	+	2.33757i	0.556143	+	0.321089i	−0.195453	+	0.980713i	$0.562618\pi$
$54$	−6.25329	+	10.8310i	−0.850965	+	1.47392i
$55$	1.99497	−	9.81965i	0.269001	−	1.32408i
$56$	−0.837565	−	1.45071i	−0.111924	−	0.193859i
$57$	−12.5042	−	7.21933i	−1.65623	−	0.956224i
$58$	−7.87078	−	4.54420i	−1.03348	−	0.596682i
$59$	4.91573	−	8.51429i	0.639973	−	1.10847i	−0.345465	−	0.938432i	$-0.612279\pi$
$59$	4.91573	−	8.51429i	0.639973	−	1.10847i	0.985438	−	0.170035i	$-0.0543879\pi$
$60$	4.67513	−	5.28726i	0.603557	−	0.682582i
$61$	6.83146	+	11.8324i	0.874678	+	1.51499i	0.857105	+	0.515142i	$0.172261\pi$
$61$	6.83146	+	11.8324i	0.874678	+	1.51499i	0.0175733	+	0.999846i	$0.494406\pi$
$62$	−2.45211	−	1.41573i	−0.311419	−	0.179798i
$63$			11.6629i			1.46939i
$64$	−1.00000			−0.125000
$65$	3.43086	+	10.2442i	0.425546	+	1.27064i
$66$	14.1441			1.74102
$67$	−10.8636	+	6.27210i	−1.32720	+	0.766259i	−0.984866	−	0.173320i	$-0.944551\pi$
$67$	−10.8636	+	6.27210i	−1.32720	+	0.766259i	−0.342334	+	0.939578i	$0.611217\pi$
$68$		−	2.48119i		−	0.300889i
$69$	2.64363	+	4.57890i	0.318256	+	0.551235i
$70$	0.745746	−	3.67072i	0.0891336	−	0.438735i
$71$	−2.80606	−	4.86024i	−0.333018	−	0.576805i	0.650084	−	0.759863i	$-0.274734\pi$
$71$	−2.80606	−	4.86024i	−0.333018	−	0.576805i	−0.983102	+	0.183058i	$0.941400\pi$
$72$	6.02961	+	3.48119i	0.710596	+	0.410263i
$73$		−	7.13093i		−	0.834613i	−0.908766	−	0.417306i	$-0.862974\pi$
$73$		−	7.13093i		−	0.834613i	0.908766	−	0.417306i	$-0.137026\pi$
$74$	−2.20910	+	5.66744i	−0.256802	+	0.658827i
$75$	15.6629	−	1.93207i	1.80860	−	0.223096i
$76$	−2.28726	+	3.96165i	−0.262366	+	0.454432i
$77$	6.50089	−	3.75329i	0.740846	−	0.427727i
$78$	−13.2066	+	7.62482i	−1.49535	+	0.863341i
$79$	5.04055	+	8.73049i	0.567106	+	0.982257i	0.996850	+	0.0793062i	$0.0252705\pi$
$79$	5.04055	+	8.73049i	0.567106	+	0.982257i	−0.429744	+	0.902951i	$0.641396\pi$
$80$	−1.67513	−	1.48119i	−0.187285	−	0.165603i
$81$	−9.29384	−	16.0974i	−1.03265	−	1.78860i
$82$			0.350262i			0.0386799i
$83$	5.80282	+	3.35026i	0.636943	+	0.367739i	0.783436	−	0.621473i	$-0.213465\pi$
$83$	5.80282	+	3.35026i	0.636943	+	0.367739i	−0.146493	+	0.989212i	$0.546799\pi$
$84$	5.28726			0.576887
$85$	3.67513	−	4.15633i	0.398624	−	0.450817i
$86$	−1.90303	+	3.29615i	−0.205209	+	0.355433i
$87$	24.8427	−	14.3430i	2.66342	−	1.53773i
$88$		−	4.48119i		−	0.477697i
$89$	−5.27210	+	9.13154i	−0.558841	+	0.967942i	0.438752	+	0.898608i	$0.355421\pi$
$89$	−5.27210	+	9.13154i	−0.558841	+	0.967942i	−0.997594	+	0.0693336i	$0.977913\pi$
$90$	4.94405	+	14.7625i	0.521149	+	1.55610i
$91$	−4.04666	+	7.00902i	−0.424205	+	0.734745i
$92$	1.45071	−	0.837565i	0.151247	−	0.0873222i
$93$	7.73967	−	4.46850i	0.802566	−	0.463362i
$94$	−1.31876	+	2.28416i	−0.136020	+	0.235593i
$95$	−9.69942	+	3.24840i	−0.995140	+	0.333279i
$96$	1.57816	−	2.73346i	0.161071	−	0.278982i
$97$			8.18664i			0.831228i	0.909541	+	0.415614i	$0.136433\pi$
$97$			8.18664i			0.831228i	−0.909541	+	0.415614i	$0.863567\pi$
$98$	−3.63206	+	2.09697i	−0.366893	+	0.211826i
$99$	−15.5999	+	27.0198i	−1.56785	+	2.71560i
$100$	−0.612127	−	4.96239i	−0.0612127	−	0.496239i
$101$	−16.1744			−1.60942			−0.804708	−	0.593671i	$-0.797678\pi$
$101$	−16.1744			−1.60942			−0.804708	+	0.593671i	$0.797678\pi$
$102$	6.78224	+	3.91573i	0.671542	+	0.387715i
$103$		−	10.2496i		−	1.00993i	−0.863141	−	0.504964i	$-0.831506\pi$
$103$		−	10.2496i		−	1.00993i	0.863141	−	0.504964i	$-0.168494\pi$
$104$	2.41573	+	4.18416i	0.236882	+	0.410291i
$105$	8.85685	+	7.83146i	0.864340	+	0.764272i
$106$	2.33757	+	4.04878i	0.227044	+	0.393252i
$107$	−11.2194	+	6.47755i	−1.08462	+	0.626208i	−0.932140	−	0.362098i	$-0.882061\pi$
$107$	−11.2194	+	6.47755i	−1.08462	+	0.626208i	−0.152484	+	0.988306i	$0.548727\pi$
$108$	−10.8310	+	6.25329i	−1.04222	+	0.601723i
$109$	9.92478	−	17.1902i	0.950621	−	1.64652i	0.206537	−	0.978439i	$-0.433781\pi$
$109$	9.92478	−	17.1902i	0.950621	−	1.64652i	0.744085	−	0.668085i	$-0.232886\pi$
$110$	6.63752	−	7.50659i	0.632863	−	0.715725i
$111$	−12.0054	−	14.9826i	−1.13950	−	1.42209i
$112$		−	1.67513i		−	0.158285i
$113$	−3.62574	−	2.09332i	−0.341081	−	0.196923i	0.319669	−	0.947529i	$-0.396428\pi$
$113$	−3.62574	−	2.09332i	−0.341081	−	0.196923i	−0.660750	+	0.750606i	$0.729762\pi$
$114$	−7.21933	−	12.5042i	−0.676152	−	1.17113i
$115$	3.67072	+	0.745746i	0.342296	+	0.0695411i
$116$	−4.54420	−	7.87078i	−0.421918	−	0.730784i
$117$		−	33.6385i		−	3.10988i
$118$	8.51429	−	4.91573i	0.783804	−	0.452529i
$119$	4.15633			0.381010
$120$	6.69241	−	2.24133i	0.610931	−	0.204605i
$121$	9.08110			0.825555
$122$			13.6629i			1.23698i
$123$	−0.957426	−	0.552770i	−0.0863282	−	0.0498416i
$124$	−1.41573	−	2.45211i	−0.127136	−	0.220206i
$125$	6.32487	−	9.21933i	0.565713	−	0.824602i
$126$	−5.83146	+	10.1004i	−0.519507	+	0.899813i
$127$	−11.4525	−	6.61213i	−1.01625	−	0.586731i	−0.103233	−	0.994657i	$-0.532919\pi$
$127$	−11.4525	−	6.61213i	−1.01625	−	0.586731i	−0.913015	+	0.407926i	$0.866252\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−6.00659	−	10.4037i	−0.528850	−	0.915996i
$130$	−2.15090	+	10.5872i	−0.188646	+	0.928557i
$131$	0.649738	−	1.12538i	0.0567679	−	0.0983249i	−0.836245	−	0.548356i	$-0.815254\pi$
$131$	0.649738	−	1.12538i	0.0567679	−	0.0983249i	0.893013	+	0.450031i	$0.148587\pi$
$132$	12.2492	+	7.07205i	1.06615	+	0.615543i
$133$	−6.63628	−	3.83146i	−0.575438	−	0.332229i
$134$	−12.5442			−1.08365
$135$	−27.4057	−	5.56776i	−2.35871	−	0.479197i
$136$	1.24060	−	2.14878i	0.106380	−	0.184256i
$137$			5.05571i			0.431938i	0.976400	+	0.215969i	$0.0692911\pi$
$137$			5.05571i			0.431938i	−0.976400	+	0.215969i	$0.930709\pi$
$138$			5.28726i			0.450081i
$139$	−0.565466	+	0.979416i	−0.0479622	+	0.0830730i	−0.889010	−	0.457888i	$-0.848606\pi$
$139$	−0.565466	+	0.979416i	−0.0479622	+	0.0830730i	0.841048	+	0.540961i	$0.181939\pi$
$140$	2.48119	−	2.80606i	0.209699	−	0.237156i
$141$	−4.16243	−	7.20955i	−0.350540	−	0.607153i
$142$		−	5.61213i		−	0.470959i
$143$	−18.7501	+	10.8253i	−1.56796	+	0.905261i
$144$	3.48119	+	6.02961i	0.290100	+	0.502467i
$145$	4.04603	−	19.9154i	0.336005	−	1.65389i
$146$	3.56547	−	6.17557i	0.295080	−	0.511094i
$147$		−	13.2374i		−	1.09180i
$148$	−4.74685	+	3.80360i	−0.390189	+	0.312654i
$149$	−3.47627			−0.284787			−0.142394	−	0.989810i	$-0.545480\pi$
$149$	−3.47627			−0.284787			−0.142394	+	0.989810i	$0.545480\pi$
$150$	14.5305	+	6.15823i	1.18641	+	0.502818i
$151$	6.65022	+	11.5185i	0.541187	+	0.937363i	0.998836	+	0.0482304i	$0.0153582\pi$
$151$	6.65022	+	11.5185i	0.541187	+	0.937363i	−0.457649	+	0.889133i	$0.651308\pi$
$152$	−3.96165	+	2.28726i	−0.321332	+	0.185521i
$153$	−14.9606	+	8.63752i	−1.20949	+	0.698302i
$154$	7.50659			0.604898
$155$	1.26053	−	6.20458i	0.101248	−	0.498364i
$156$	−15.2496			−1.22095
$157$	12.3731	+	7.14363i	0.987483	+	0.570124i	0.904521	−	0.426429i	$-0.140229\pi$
$157$	12.3731	+	7.14363i	0.987483	+	0.570124i	0.0829621	+	0.996553i	$0.473562\pi$
$158$			10.0811i			0.802009i
$159$	−14.7562			−1.17025
$160$	−0.710109	−	2.12032i	−0.0561390	−	0.167626i
$161$	1.40303	+	2.43012i	0.110574	+	0.191520i
$162$		−	18.5877i		−	1.46039i
$163$	8.60143	+	4.96604i	0.673716	+	0.388970i	0.797483	−	0.603341i	$-0.206164\pi$
$163$	8.60143	+	4.96604i	0.673716	+	0.388970i	−0.123767	+	0.992311i	$0.539498\pi$
$164$	−0.175131	+	0.303336i	−0.0136754	+	0.0236865i
$165$	10.0439	+	29.9900i	0.781913	+	2.33472i
$166$	3.35026	+	5.80282i	0.260031	+	0.450386i
$167$	12.4603	−	7.19394i	0.964204	−	0.556684i	0.0667397	−	0.997770i	$-0.478740\pi$
$167$	12.4603	−	7.19394i	0.964204	−	0.556684i	0.897464	+	0.441087i	$0.145407\pi$
$168$	4.57890	+	2.64363i	0.353270	+	0.203960i
$169$	5.17148	−	8.95727i	0.397806	−	0.689021i
$170$	5.26092	−	1.76192i	0.403494	−	0.135133i
$171$	31.8496			2.43560
$172$	−3.29615	+	1.90303i	−0.251329	+	0.145105i
$173$	13.4942	+	7.79090i	1.02595	+	0.592332i	0.915821	−	0.401586i	$-0.131541\pi$
$173$	13.4942	+	7.79090i	1.02595	+	0.592332i	0.110127	+	0.993918i	$0.464874\pi$
$174$	28.6859			2.17468
$175$	8.31265	−	1.02539i	0.628377	−	0.0775124i
$176$	2.24060	−	3.88083i	0.168891	−	0.292528i
$177$			31.0313i			2.33245i
$178$	−9.13154	+	5.27210i	−0.684438	+	0.395161i
$179$	13.1490			0.982805			0.491402	−	0.870933i	$-0.336484\pi$
$179$	13.1490			0.982805			0.491402	+	0.870933i	$0.336484\pi$
$180$	−3.09956	+	15.2567i	−0.231028	+	1.13717i
$181$	9.64363	+	16.7033i	0.716805	+	1.24154i	0.962259	+	0.272135i	$0.0877297\pi$
$181$	9.64363	+	16.7033i	0.716805	+	1.24154i	−0.245454	+	0.969408i	$0.578937\pi$
$182$	−7.00902	+	4.04666i	−0.519543	+	0.299958i
$183$	−37.3470	−	21.5623i	−2.76077	−	1.59393i
$184$	1.67513			0.123492
$185$	−13.5855	−	0.659483i	−0.998824	−	0.0484861i
$186$	8.93700			0.655292
$187$	9.62909	+	5.55936i	0.704149	+	0.406540i
$188$	−2.28416	+	1.31876i	−0.166589	+	0.0961804i
$189$	−10.4751	−	18.1434i	−0.761950	−	1.31974i
$190$	−10.0241	−	2.03651i	−0.727228	−	0.147744i
$191$	6.10062			0.441425			0.220713	−	0.975339i	$-0.429162\pi$
$191$	6.10062			0.441425			0.220713	+	0.975339i	$0.429162\pi$
$192$	2.73346	−	1.57816i	0.197270	−	0.113894i
$193$		−	8.45676i		−	0.608731i	−0.952555	−	0.304365i	$-0.901556\pi$
$193$		−	8.45676i		−	0.608731i	0.952555	−	0.304365i	$-0.0984444\pi$
$194$	−4.09332	+	7.08984i	−0.293883	+	0.509021i
$195$	−25.5452	−	22.5877i	−1.82933	−	1.61754i
$196$	−4.19394			−0.299567
$197$	9.01815	+	5.20663i	0.642517	+	0.370957i	0.785583	−	0.618756i	$-0.212363\pi$
$197$	9.01815	+	5.20663i	0.642517	+	0.370957i	−0.143067	+	0.989713i	$0.545696\pi$
$198$	−27.0198	+	15.5999i	−1.92022	+	1.10864i
$199$	4.75035			0.336744			0.168372	−	0.985724i	$-0.446149\pi$
$199$	4.75035			0.336744			0.168372	+	0.985724i	$0.446149\pi$
$200$	1.95108	−	4.60362i	0.137962	−	0.325525i
$201$	19.7968	−	34.2890i	1.39636	−	2.41856i
$202$	−14.0075	−	8.08721i	−0.985562	−	0.569014i
$203$	13.1846	−	7.61213i	0.925377	−	0.534267i
$204$	3.91573	+	6.78224i	0.274156	+	0.474852i
$205$	−0.742666	+	0.248724i	−0.0518700	+	0.0173716i
$206$	5.12482	−	8.87645i	0.357063	−	0.618452i
$207$	−10.1004	−	5.83146i	−0.702025	−	0.405314i
$208$			4.83146i			0.335001i
$209$	−10.2496	−	17.7529i	−0.708983	−	1.22799i
$210$	3.75453	+	11.2107i	0.259087	+	0.773609i
$211$	−6.82653			−0.469958			−0.234979	−	0.972000i	$-0.575502\pi$
$211$	−6.82653			−0.469958			−0.234979	+	0.972000i	$0.575502\pi$
$212$			4.67513i			0.321089i
$213$	15.3405	+	8.85685i	1.05111	+	0.606861i
$214$	−12.9551			−0.885592
$215$	−8.34024	−	1.69441i	−0.568800	−	0.115558i
$216$	−12.5066			−0.850965
$217$	4.10761	−	2.37153i	0.278843	−	0.160990i
$218$	17.1902	−	9.92478i	1.16427	−	0.672191i
$219$	11.2538	+	19.4921i	0.760459	+	1.31715i
$220$	9.50155	−	3.18214i	0.640595	−	0.214540i
$221$	−11.9878			−0.806385
$222$	−2.90568	−	18.9780i	−0.195016	−	1.27372i
$223$		−	2.78797i		−	0.186696i	−0.995634	−	0.0933480i	$-0.970243\pi$
$223$		−	2.78797i		−	0.186696i	0.995634	−	0.0933480i	$-0.0297569\pi$
$224$	0.837565	−	1.45071i	0.0559622	−	0.0969294i
$225$	−27.7903	+	20.9659i	−1.85269	+	1.39773i
$226$	−2.09332	−	3.62574i	−0.139246	−	0.241181i
$227$	−18.4361	+	10.6441i	−1.22365	+	0.706474i	−0.965694	−	0.259683i	$-0.916382\pi$
$227$	−18.4361	+	10.6441i	−1.22365	+	0.706474i	−0.257955	+	0.966157i	$0.583049\pi$
$228$		−	14.4387i		−	0.956224i
$229$	−5.30654	−	9.19120i	−0.350666	−	0.607371i	0.635700	−	0.771936i	$-0.280711\pi$
$229$	−5.30654	−	9.19120i	−0.350666	−	0.607371i	−0.986366	+	0.164565i	$0.947378\pi$
$230$	2.80606	+	2.48119i	0.185026	+	0.163605i
$231$	−11.8466	+	20.5189i	−0.779450	+	1.35005i
$232$		−	9.08840i		−	0.596682i
$233$			17.8822i			1.17150i	0.810490	+	0.585752i	$0.199201\pi$
$233$			17.8822i			1.17150i	−0.810490	+	0.585752i	$0.800799\pi$
$234$	16.8192	−	29.1318i	1.09951	−	1.90440i
$235$	−5.77960	−	1.17419i	−0.377020	−	0.0765956i
$236$	9.83146			0.639973
$237$	−27.5563	−	15.9096i	−1.78997	−	1.03344i
$238$	3.59948	+	2.07816i	0.233320	+	0.134707i
$239$	2.69758	−	4.67235i	0.174492	−	0.302229i	−0.765493	−	0.643444i	$-0.777505\pi$
$239$	2.69758	−	4.67235i	0.174492	−	0.302229i	0.939985	+	0.341215i	$0.110838\pi$
$240$	6.91646	+	1.40515i	0.446456	+	0.0907023i
$241$	−1.06300	−	1.84118i	−0.0684741	−	0.118601i	0.829756	−	0.558127i	$-0.188480\pi$
$241$	−1.06300	−	1.84118i	−0.0684741	−	0.118601i	−0.898230	+	0.439526i	$0.855146\pi$
$242$	7.86447	+	4.54055i	0.505547	+	0.291878i
$243$	18.3156	+	10.5745i	1.17495	+	0.678355i
$244$	−6.83146	+	11.8324i	−0.437339	+	0.757494i
$245$	−7.02539	−	6.21203i	−0.448836	−	0.396872i
$246$	−0.552770	−	0.957426i	−0.0352433	−	0.0610432i
$247$	19.1405	+	11.0508i	1.21788	+	0.703145i
$248$		−	2.83146i		−	0.179798i
$249$	−21.1490			−1.34027
$250$	10.0872	−	4.82174i	0.637968	−	0.304954i
$251$	15.2506			0.962609			0.481305	−	0.876553i	$-0.340163\pi$
$251$	15.2506			0.962609			0.481305	+	0.876553i	$0.340163\pi$
$252$	−10.1004	+	5.83146i	−0.636264	+	0.367347i
$253$			7.50659i			0.471935i
$254$	−6.61213	−	11.4525i	−0.414882	−	0.718596i
$255$	−3.48646	+	17.1611i	−0.218330	+	1.07467i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.09417	+	2.94112i	0.317766	+	0.183462i	0.650396	−	0.759595i	$-0.274603\pi$
$257$	5.09417	+	2.94112i	0.317766	+	0.183462i	−0.332631	+	0.943057i	$0.607936\pi$
$258$		−	12.0132i		−	0.747908i
$259$	−6.37153	−	7.95160i	−0.395908	−	0.494088i
$260$	−7.15633	+	8.09332i	−0.443816	+	0.501926i
$261$	−31.6385	+	54.7994i	−1.95837	+	3.39200i
$262$	1.12538	−	0.649738i	0.0695262	−	0.0401410i
$263$	−2.01340	+	1.16243i	−0.124151	+	0.0716788i	−0.560790	−	0.827958i	$-0.689502\pi$
$263$	−2.01340	+	1.16243i	−0.124151	+	0.0716788i	0.436638	+	0.899637i	$0.356169\pi$
$264$	7.07205	+	12.2492i	0.435255	+	0.753883i
$265$	−6.92478	+	7.83146i	−0.425386	+	0.481083i
$266$	−3.83146	−	6.63628i	−0.234922	−	0.406896i
$267$		−	33.2809i		−	2.03676i
$268$	−10.8636	−	6.27210i	−0.663600	−	0.383129i
$269$	8.13823			0.496196			0.248098	−	0.968735i	$-0.420194\pi$
$269$	8.13823			0.496196			0.248098	+	0.968735i	$0.420194\pi$
$270$	−20.9502	−	18.5247i	−1.27499	−	1.12738i
$271$	8.31511	−	14.4022i	0.505107	−	0.874871i	−0.494875	−	0.868964i	$-0.664786\pi$
$271$	8.31511	−	14.4022i	0.505107	−	0.874871i	0.999983	−	0.00590727i	$-0.00188035\pi$
$272$	2.14878	−	1.24060i	0.130289	−	0.0752223i
$273$		−	25.5452i		−	1.54606i
$274$	−2.52785	+	4.37837i	−0.152713	+	0.264507i
$275$	20.6297	+	8.74315i	1.24402	+	0.527232i
$276$	−2.64363	+	4.57890i	−0.159128	+	0.275617i
$277$	−5.80709	+	3.35272i	−0.348914	+	0.201446i	−0.664207	−	0.747549i	$-0.731231\pi$
$277$	−5.80709	+	3.35272i	−0.348914	+	0.201446i	0.315293	+	0.948994i	$0.397897\pi$
$278$	−0.979416	+	0.565466i	−0.0587415	+	0.0339144i
$279$	−9.85685	+	17.0726i	−0.590114	+	1.02211i
$280$	3.55181	−	1.18953i	0.212261	−	0.0710877i
$281$	−9.43994	+	16.3504i	−0.563139	+	0.975386i	0.434081	+	0.900874i	$0.357073\pi$
$281$	−9.43994	+	16.3504i	−0.563139	+	0.975386i	−0.997220	+	0.0745120i	$0.976260\pi$
$282$		−	8.32487i		−	0.495739i
$283$	27.7293	−	16.0095i	1.64834	−	0.951668i	0.670603	−	0.741816i	$-0.266035\pi$
$283$	27.7293	−	16.0095i	1.64834	−	0.951668i	0.977733	−	0.209851i	$-0.0672980\pi$
$284$	2.80606	−	4.86024i	0.166509	−	0.288402i
$285$	21.3865	−	24.1866i	1.26682	−	1.43269i
$286$	−21.6507			−1.28023
$287$	−0.508127	−	0.293367i	−0.0299938	−	0.0173169i
$288$			6.96239i			0.410263i
$289$	−5.42184	−	9.39090i	−0.318932	−	0.552406i
$290$	13.4617	−	15.2243i	0.790497	−	0.893999i
$291$	−12.9199	−	22.3778i	−0.757375	−	1.31181i
$292$	6.17557	−	3.56547i	0.361398	−	0.208653i
$293$	−13.0627	+	7.54174i	−0.763129	+	0.440593i	−0.830418	−	0.557141i	$-0.811898\pi$
$293$	−13.0627	+	7.54174i	−0.763129	+	0.440593i	0.0672888	+	0.997734i	$0.478565\pi$
$294$	6.61871	−	11.4639i	0.386011	−	0.668591i
$295$	16.4690	+	14.5623i	0.958861	+	0.847850i
$296$	−6.01270	+	0.920588i	−0.349481	+	0.0535081i
$297$		−	56.0444i		−	3.25203i
$298$	−3.01054	−	1.73813i	−0.174396	−	0.100687i
$299$	−4.04666	−	7.00902i	−0.234024	−	0.405342i
$300$	9.50468	+	12.5984i	0.548753	+	0.727372i
$301$	−3.18783	−	5.52148i	−0.183743	−	0.318253i
$302$			13.3004i			0.765354i
$303$	44.2121	−	25.5259i	2.53992	−	1.46642i
$304$	−4.57452			−0.262366
$305$	−28.9697	+	9.70215i	−1.65880	+	0.555544i
$306$	−17.2750			−0.987548
$307$			29.9175i			1.70748i	0.520699	+	0.853740i	$0.325671\pi$
$307$			29.9175i			1.70748i	−0.520699	+	0.853740i	$0.674329\pi$
$308$	6.50089	+	3.75329i	0.370423	+	0.213864i
$309$	16.1756	+	28.0170i	0.920198	+	1.59383i
$310$	4.19394	−	4.74306i	0.238200	−	0.269388i
$311$	−13.7435	+	23.8045i	−0.779324	+	1.34983i	0.153007	+	0.988225i	$0.451104\pi$
$311$	−13.7435	+	23.8045i	−0.779324	+	1.34983i	−0.932332	+	0.361605i	$0.882229\pi$
$312$	−13.2066	−	7.62482i	−0.747675	−	0.431671i
$313$	18.5864	+	10.7308i	1.05056	+	0.606543i	0.922807	−	0.385263i	$-0.125889\pi$
$313$	18.5864	+	10.7308i	1.05056	+	0.606543i	0.127756	+	0.991806i	$0.459222\pi$
$314$	7.14363	+	12.3731i	0.403138	+	0.698256i
$315$	−25.5570	−	5.19217i	−1.43997	−	0.292546i
$316$	−5.04055	+	8.73049i	−0.283553	+	0.491128i
$317$	−21.0774	−	12.1690i	−1.18382	−	0.683480i	−0.226927	−	0.973912i	$-0.572868\pi$
$317$	−21.0774	−	12.1690i	−1.18382	−	0.683480i	−0.956896	+	0.290431i	$0.906201\pi$
$318$	−12.7793	−	7.37812i	−0.716626	−	0.413744i
$319$	40.7269			2.28027
$320$	0.445186	−	2.19130i	0.0248867	−	0.122498i
$321$	20.4452	−	35.4122i	1.14114	−	1.97652i
$322$			2.80606i			0.156376i
$323$		−	11.3503i		−	0.631545i
$324$	9.29384	−	16.0974i	0.516325	−	0.894301i
$325$	−23.9756	+	2.95746i	−1.32992	+	0.164051i
$326$	4.96604	+	8.60143i	0.275043	+	0.476389i
$327$			62.6516i			3.46464i
$328$	−0.303336	+	0.175131i	−0.0167489	+	0.00966998i
$329$	−2.20910	−	3.82627i	−0.121791	−	0.210949i
$330$	−6.29676	+	30.9940i	−0.346625	+	1.70616i
$331$	11.2587	−	19.5006i	0.618834	−	1.07185i	−0.370865	−	0.928687i	$-0.620939\pi$
$331$	11.2587	−	19.5006i	0.618834	−	1.07185i	0.989699	−	0.143165i	$-0.0457279\pi$
$332$			6.70052i			0.367739i
$333$	39.4589	+	15.3806i	2.16234	+	0.842851i
$334$	14.3879			0.787269
$335$	−8.90774	−	26.5977i	−0.486682	−	1.45319i
$336$	2.64363	+	4.57890i	0.144222	+	0.249799i
$337$	16.1825	−	9.34297i	0.881517	−	0.508944i	0.0103585	−	0.999946i	$-0.496703\pi$
$337$	16.1825	−	9.34297i	0.881517	−	0.508944i	0.871158	+	0.491002i	$0.163369\pi$
$338$	8.95727	−	5.17148i	0.487211	−	0.281292i
$339$	13.2144			0.717708
$340$	5.43705	+	1.10459i	0.294865	+	0.0599050i
$341$	12.6883			0.687110
$342$	27.5825	+	15.9248i	1.49149	+	0.861113i
$343$		−	18.7513i		−	1.01248i
$344$	−3.80606			−0.205209
$345$	−11.2107	+	3.75453i	−0.603562	+	0.202137i
$346$	7.79090	+	13.4942i	0.418842	+	0.725455i
$347$		−	5.96968i		−	0.320469i	−0.987079	−	0.160235i	$-0.948775\pi$
$347$		−	5.96968i		−	0.320469i	0.987079	−	0.160235i	$-0.0512251\pi$
$348$	24.8427	+	14.3430i	1.33171	+	0.768864i
$349$	−11.0508	+	19.1405i	−0.591535	+	1.02457i	0.402491	+	0.915424i	$0.368145\pi$
$349$	−11.0508	+	19.1405i	−0.591535	+	1.02457i	−0.994026	+	0.109145i	$0.965189\pi$
$350$	7.71166	+	3.26831i	0.412206	+	0.174698i
$351$	30.2125	+	52.3296i	1.61262	+	2.79315i
$352$	3.88083	−	2.24060i	0.206849	−	0.119424i
$353$	18.6672	+	10.7775i	0.993554	+	0.573629i	0.906335	−	0.422561i	$-0.138869\pi$
$353$	18.6672	+	10.7775i	0.993554	+	0.573629i	0.0872191	+	0.996189i	$0.472202\pi$
$354$	−15.5156	+	26.8739i	−0.824647	+	1.42833i
$355$	11.8995	−	3.98522i	0.631559	−	0.211514i
$356$	−10.5442			−0.558841
$357$	−11.3611	+	6.55936i	−0.601295	+	0.347158i
$358$	11.3874	+	6.57452i	0.601843	+	0.347474i
$359$	−5.38550			−0.284236			−0.142118	−	0.989850i	$-0.545391\pi$
$359$	−5.38550			−0.284236			−0.142118	+	0.989850i	$0.545391\pi$
$360$	−10.3127	+	11.6629i	−0.543524	+	0.614689i
$361$	−0.963096	+	1.66813i	−0.0506893	+	0.0877964i
$362$			19.2873i			1.01372i
$363$	−24.8228	+	14.3315i	−1.30286	+	0.752206i
$364$	−8.09332			−0.424205
$365$	15.6260	+	3.17459i	0.817904	+	0.166166i
$366$	−21.5623	−	37.3470i	−1.12708	−	1.95216i
$367$	−10.0479	+	5.80114i	−0.524494	+	0.302817i	−0.738772	−	0.673956i	$-0.764594\pi$
$367$	−10.0479	+	5.80114i	−0.524494	+	0.302817i	0.214277	+	0.976773i	$0.431260\pi$
$368$	1.45071	+	0.837565i	0.0756233	+	0.0436611i
$369$	2.43866			0.126951
$370$	−11.4356	−	7.36387i	−0.594510	−	0.382829i
$371$	−7.83146			−0.406589
$372$	7.73967	+	4.46850i	0.401283	+	0.231681i
$373$	−21.8457	+	12.6126i	−1.13113	+	0.653056i	−0.944218	−	0.329321i	$-0.893180\pi$
$373$	−21.8457	+	12.6126i	−1.13113	+	0.653056i	−0.186908	+	0.982377i	$0.559847\pi$
$374$	5.55936	+	9.62909i	0.287468	+	0.497908i
$375$	−2.73916	+	35.1823i	−0.141450	+	1.81681i
$376$	−2.63752			−0.136020
$377$	−38.0273	+	21.9551i	−1.95851	+	1.13074i
$378$		−	20.9502i		−	1.07756i
$379$	6.68418	−	11.5773i	0.343343	−	0.594688i	−0.641708	−	0.766949i	$-0.721774\pi$
$379$	6.68418	−	11.5773i	0.343343	−	0.594688i	0.985051	+	0.172261i	$0.0551072\pi$
$380$	−7.66291	−	6.77575i	−0.393099	−	0.347588i
$381$	41.7400			2.13841
$382$	5.28329	+	3.05031i	0.270317	+	0.156067i
$383$	7.14440	−	4.12482i	0.365062	−	0.210769i	−0.306237	−	0.951955i	$-0.599070\pi$
$383$	7.14440	−	4.12482i	0.365062	−	0.210769i	0.671299	+	0.741187i	$0.265737\pi$
$384$	3.15633			0.161071
$385$	5.33049	+	15.9163i	0.271667	+	0.811172i
$386$	4.22838	−	7.32377i	0.215219	−	0.372770i
$387$	22.9491	+	13.2496i	1.16657	+	0.673517i
$388$	−7.08984	+	4.09332i	−0.359932	+	0.207807i
$389$	2.54912	+	4.41521i	0.129246	+	0.223860i	0.923385	−	0.383876i	$-0.125411\pi$
$389$	2.54912	+	4.41521i	0.129246	+	0.223860i	−0.794139	+	0.607736i	$0.792078\pi$
$390$	−10.8289	−	32.3341i	−0.548343	−	1.63730i
$391$	−2.07816	+	3.59948i	−0.105097	+	0.182034i
$392$	−3.63206	−	2.09697i	−0.183447	−	0.105913i
$393$			4.10157i			0.206897i
$394$	5.20663	+	9.01815i	0.262306	+	0.454328i
$395$	−21.3751	+	7.15868i	−1.07550	+	0.360192i
$396$	−31.1998			−1.56785
$397$			19.9053i			0.999017i	0.866309	+	0.499508i	$0.166486\pi$
$397$			19.9053i			0.999017i	−0.866309	+	0.499508i	$0.833514\pi$
$398$	4.11393	+	2.37518i	0.206213	+	0.119057i
$399$	24.1866			1.21085
$400$	3.99149	−	3.01131i	0.199575	−	0.150566i
$401$	16.2170			0.809836			0.404918	−	0.914353i	$-0.367300\pi$
$401$	16.2170			0.809836			0.404918	+	0.914353i	$0.367300\pi$
$402$	34.2890	−	19.7968i	1.71018	−	0.987374i
$403$	−11.8473	+	6.84003i	−0.590155	+	0.340726i
$404$	−8.08721	−	14.0075i	−0.402354	−	0.696897i
$405$	39.4118	−	13.1993i	1.95839	−	0.655878i
$406$	15.2243			0.755567
$407$	−4.12534	−	26.9441i	−0.204485	−	1.33557i
$408$			7.83146i			0.387715i
$409$	15.3568	−	26.5988i	0.759347	−	1.31523i	−0.183837	−	0.982957i	$-0.558852\pi$
$409$	15.3568	−	26.5988i	0.759347	−	1.31523i	0.943184	−	0.332271i	$-0.107815\pi$
$410$	−0.767530	−	0.155932i	−0.0379056	−	0.00770092i
$411$	−7.97873	−	13.8196i	−0.393562	−	0.681669i
$412$	8.87645	−	5.12482i	0.437312	−	0.252482i
$413$			16.4690i			0.810385i
$414$	−5.83146	−	10.1004i	−0.286600	−	0.496407i
$415$	−9.92478	+	11.2243i	−0.487188	+	0.550977i
$416$	−2.41573	+	4.18416i	−0.118441	+	0.205146i
$417$		−	3.56959i		−	0.174804i
$418$		−	20.4993i		−	1.00265i
$419$	−3.27821	+	5.67802i	−0.160151	+	0.277390i	−0.934923	−	0.354851i	$-0.884531\pi$
$419$	−3.27821	+	5.67802i	−0.160151	+	0.277390i	0.774772	+	0.632241i	$0.217865\pi$
$420$	−2.35382	+	11.5860i	−0.114854	+	0.565338i
$421$	−12.8994			−0.628678			−0.314339	−	0.949311i	$-0.601783\pi$
$421$	−12.8994			−0.628678			−0.314339	+	0.949311i	$0.601783\pi$
$422$	−5.91195	−	3.41327i	−0.287789	−	0.166155i
$423$	15.9032	+	9.18172i	0.773240	+	0.446430i
$424$	−2.33757	+	4.04878i	−0.113522	+	0.196626i
$425$	7.47165	+	9.90367i	0.362428	+	0.480398i
$426$	8.85685	+	15.3405i	0.429116	+	0.743250i
$427$	−19.8209	−	11.4436i	−0.959199	−	0.553794i
$428$	−11.2194	−	6.47755i	−0.542312	−	0.313104i
$429$	34.1683	−	59.1813i	1.64966	−	2.85730i
$430$	−6.37565	−	5.63752i	−0.307461	−	0.271865i
$431$	−17.6248	−	30.5271i	−0.848958	−	1.47044i	−0.882139	−	0.470989i	$-0.843897\pi$
$431$	−17.6248	−	30.5271i	−0.848958	−	1.47044i	0.0331813	−	0.999449i	$-0.489436\pi$
$432$	−10.8310	−	6.25329i	−0.521108	−	0.300862i
$433$		−	3.92478i		−	0.188613i	−0.995543	−	0.0943064i	$-0.969937\pi$
$433$		−	3.92478i		−	0.188613i	0.995543	−	0.0943064i	$-0.0300633\pi$
$434$	4.74306			0.227674
$435$	20.3701	+	60.8233i	0.976673	+	2.91625i
$436$	19.8496			0.950621
$437$	6.63628	−	3.83146i	0.317456	−	0.183283i
$438$			22.5075i			1.07545i
$439$	−4.71028	−	8.15844i	−0.224809	−	0.389381i	0.731453	−	0.681892i	$-0.238843\pi$
$439$	−4.71028	−	8.15844i	−0.224809	−	0.389381i	−0.956262	+	0.292511i	$0.905509\pi$
$440$	9.81965	+	1.99497i	0.468134	+	0.0951063i
$441$	14.5999	+	25.2878i	0.695234	+	1.20418i
$442$	−10.3817	−	5.99389i	−0.493808	−	0.285100i
$443$		−	23.9380i		−	1.13733i	−0.822570	−	0.568663i	$-0.807461\pi$
$443$		−	23.9380i		−	1.13733i	0.822570	−	0.568663i	$-0.192539\pi$
$444$	6.97262	−	17.8883i	0.330906	−	0.848941i
$445$	−17.6629	−	15.6180i	−0.837302	−	0.740365i
$446$	1.39398	−	2.41445i	0.0660070	−	0.114327i
$447$	9.50224	−	5.48612i	0.449440	−	0.259485i
$448$	1.45071	−	0.837565i	0.0685394	−	0.0395712i
$449$	15.0095	+	25.9973i	0.708343	+	1.22689i	0.965471	+	0.260509i	$0.0838905\pi$
$449$	15.0095	+	25.9973i	0.708343	+	1.22689i	−0.257128	+	0.966377i	$0.582776\pi$
$450$	−34.5501	+	4.26187i	−1.62871	+	0.200906i
$451$	−0.784795	−	1.35931i	−0.0369546	−	0.0640072i
$452$		−	4.18664i		−	0.196923i
$453$	−36.3562	−	20.9902i	−1.70816	−	0.986208i
$454$	−21.2882			−0.999105
$455$	−13.5574	−	11.9878i	−0.635579	−	0.561996i
$456$	7.21933	−	12.5042i	0.338076	−	0.585565i
$457$	22.1722	−	12.8011i	1.03717	−	0.598812i	0.118142	−	0.992997i	$-0.462306\pi$
$457$	22.1722	−	12.8011i	1.03717	−	0.598812i	0.919031	+	0.394185i	$0.128973\pi$
$458$		−	10.6131i		−	0.495917i
$459$	15.5156	−	26.8739i	0.724208	−	1.25436i
$460$	1.18953	+	3.55181i	0.0554619	+	0.165604i
$461$	−1.79384	+	3.10703i	−0.0835477	+	0.144709i	−0.904771	−	0.425897i	$-0.859958\pi$
$461$	−1.79384	+	3.10703i	−0.0835477	+	0.144709i	0.821224	+	0.570606i	$0.193292\pi$
$462$	−20.5189	+	11.8466i	−0.954627	+	0.551154i
$463$	−18.5212	+	10.6932i	−0.860754	+	0.496957i	−0.864265	−	0.503037i	$-0.832216\pi$
$463$	−18.5212	+	10.6932i	−0.860754	+	0.496957i	0.00351076	+	0.999994i	$0.498882\pi$
$464$	4.54420	−	7.87078i	0.210959	−	0.365392i
$465$	6.34624	+	18.9493i	0.294300	+	0.878751i
$466$	−8.94112	+	15.4865i	−0.414189	+	0.717397i
$467$			12.2692i			0.567749i	0.958861	+	0.283874i	$0.0916199\pi$
$467$			12.2692i			0.567749i	−0.958861	+	0.283874i	$0.908380\pi$
$468$	29.1318	−	16.8192i	1.34662	−	0.777470i
$469$	10.5066	−	18.1979i	0.485149	−	0.840303i
$470$	−4.41819	−	3.90668i	−0.203796	−	0.180202i
$471$	−45.0952			−2.07788
$472$	8.51429	+	4.91573i	0.391902	+	0.226265i
$473$		−	17.0557i		−	0.784222i
$474$	−15.9096	−	27.5563i	−0.730753	−	1.26570i
$475$	−2.80018	−	22.7005i	−0.128481	−	1.04157i
$476$	2.07816	+	3.59948i	0.0952524	+	0.164982i
$477$	28.1892	−	16.2750i	1.29069	−	0.745183i
$478$	4.67235	−	2.69758i	0.213708	−	0.123385i
$479$	−7.70005	+	13.3369i	−0.351824	+	0.609377i	−0.986569	−	0.163344i	$-0.947772\pi$
$479$	−7.70005	+	13.3369i	−0.351824	+	0.609377i	0.634745	+	0.772722i	$0.281105\pi$
$480$	5.28726	+	4.67513i	0.241329	+	0.213390i
$481$	18.3769	+	22.9342i	0.837916	+	1.04571i
$482$		−	2.12601i		−	0.0968370i
$483$	−7.67026	−	4.42842i	−0.349009	−	0.201500i
$484$	4.54055	+	7.86447i	0.206389	+	0.357476i
$485$	−17.9394	−	3.64458i	−0.814587	−	0.165492i
$486$	10.5745	+	18.3156i	0.479670	+	0.830812i
$487$		−	2.42407i		−	0.109845i	−0.998491	−	0.0549225i	$-0.982509\pi$
$487$		−	2.42407i		−	0.109845i	0.998491	−	0.0549225i	$-0.0174912\pi$
$488$	−11.8324	+	6.83146i	−0.535629	+	0.309245i
$489$	−31.3488			−1.41764
$490$	−2.97815	−	8.89248i	−0.134539	−	0.401721i
$491$	28.1949			1.27242			0.636209	−	0.771517i	$-0.280502\pi$
$491$	28.1949			1.27242			0.636209	+	0.771517i	$0.280502\pi$
$492$		−	1.10554i		−	0.0498416i
$493$	19.5289	+	11.2750i	0.879539	+	0.507802i
$494$	11.0508	+	19.1405i	0.497198	+	0.861173i
$495$	−52.2638	−	46.2130i	−2.34908	−	2.07712i
$496$	1.41573	−	2.45211i	0.0635681	−	0.110103i
$497$	8.14155	+	4.70052i	0.365198	+	0.210847i
$498$	−18.3156	−	10.5745i	−0.820742	−	0.473855i
$499$	−15.1563	−	26.2515i	−0.678490	−	1.17518i	−0.975436	−	0.220285i	$-0.929301\pi$
$499$	−15.1563	−	26.2515i	−0.678490	−	1.17518i	0.296945	−	0.954895i	$-0.404032\pi$
$500$	11.1466	+	0.867833i	0.498491	+	0.0388107i
$501$	−22.7064	+	39.3286i	−1.01445	+	1.75707i
$502$	13.2074	+	7.62530i	0.589475	+	0.340334i
$503$	8.48804	+	4.90057i	0.378463	+	0.218506i	0.677149	−	0.735846i	$-0.263215\pi$
$503$	8.48804	+	4.90057i	0.378463	+	0.218506i	−0.298686	+	0.954351i	$0.596548\pi$
$504$	−11.6629			−0.519507
$505$	7.20063	−	35.4431i	0.320424	−	1.57720i
$506$	−3.75329	+	6.50089i	−0.166854	+	0.289000i
$507$			32.6458i			1.44985i
$508$		−	13.2243i		−	0.586731i
$509$	−4.51270	+	7.81622i	−0.200022	+	0.346448i	−0.948535	−	0.316672i	$-0.897435\pi$
$509$	−4.51270	+	7.81622i	−0.200022	+	0.346448i	0.748513	+	0.663120i	$0.230768\pi$
$510$	−11.5999	+	13.1187i	−0.513653	+	0.580906i
$511$	5.97262	+	10.3449i	0.264213	+	0.457631i
$512$		−	1.00000i		−	0.0441942i
$513$	−49.5467	+	28.6058i	−2.18754	+	1.26298i
$514$	2.94112	+	5.09417i	0.129727	+	0.224694i
$515$	22.4601	+	4.56300i	0.989709	+	0.201070i
$516$	6.00659	−	10.4037i	0.264425	−	0.457998i
$517$		−	11.8192i		−	0.519809i
$518$	−1.54211	−	10.0721i	−0.0677563	−	0.442541i
$519$	−49.1813			−2.15882
$520$	−10.2442	+	3.43086i	−0.449239	+	0.150453i
$521$	−1.00365	−	1.73837i	−0.0439706	−	0.0761593i	0.843203	−	0.537596i	$-0.180667\pi$
$521$	−1.00365	−	1.73837i	−0.0439706	−	0.0761593i	−0.887173	+	0.461437i	$0.847334\pi$
$522$	−54.7994	+	31.6385i	−2.39851	+	1.38478i
$523$	−11.8862	+	6.86248i	−0.519746	+	0.300075i	−0.736831	−	0.676077i	$-0.763678\pi$
$523$	−11.8862	+	6.86248i	−0.519746	+	0.300075i	0.217085	+	0.976153i	$0.430345\pi$
$524$	1.29948			0.0567679
$525$	−21.1040	+	15.9216i	−0.921056	+	0.694875i
$526$	−2.32487			−0.101369
$527$	6.08417	+	3.51270i	0.265031	+	0.153015i
$528$			14.1441i			0.615543i
$529$	20.1939			0.877997
$530$	−9.91276	+	3.31985i	−0.430583	+	0.144205i
$531$	−34.2252	−	59.2798i	−1.48525	−	2.57252i
$532$		−	7.66291i		−	0.332229i
$533$	1.46555	+	0.846137i	0.0634801	+	0.0366503i
$534$	16.6405	−	28.8221i	0.720103	−	1.24726i
$535$	−9.19953	−	27.4689i	−0.397730	−	1.18758i
$536$	−6.27210	−	10.8636i	−0.270913	−	0.469236i
$537$	−35.9423	+	20.7513i	−1.55103	+	0.895485i
$538$	7.04791	+	4.06911i	0.303857	+	0.175432i
$539$	9.39692	−	16.2759i	0.404754	−	0.701055i
$540$	−8.88104	−	26.5179i	−0.382179	−	1.14115i
$541$	−44.2130			−1.90086			−0.950432	−	0.310931i	$-0.899359\pi$
$541$	−44.2130			−1.90086			−0.950432	+	0.310931i	$0.899359\pi$
$542$	14.4022	−	8.31511i	0.618627	−	0.357165i
$543$	−52.7209	−	30.4384i	−2.26247	−	1.30624i
$544$	2.48119			0.106380
$545$	33.2506	+	29.4010i	1.42430	+	1.25940i
$546$	12.7726	−	22.1228i	0.546616	−	0.946766i
$547$			16.6629i			0.712455i	0.934399	+	0.356227i	$0.115937\pi$
$547$			16.6629i			0.712455i	−0.934399	+	0.356227i	$0.884063\pi$
$548$	−4.37837	+	2.52785i	−0.187035	+	0.107985i
$549$	95.1265			4.05990
$550$	13.4943	+	17.8866i	0.575398	+	0.762689i
$551$	−20.7875	−	36.0050i	−0.885578	−	1.53387i
$552$	−4.57890	+	2.64363i	−0.194891	+	0.112520i
$553$	−14.6247	−	8.44358i	−0.621906	−	0.359058i
$554$	−6.70545			−0.284887
$555$	38.1761	−	19.6374i	1.62048	−	0.833562i
$556$	−1.13093			−0.0479622
$557$	8.21605	+	4.74354i	0.348125	+	0.200990i	0.663859	−	0.747858i	$-0.268917\pi$
$557$	8.21605	+	4.74354i	0.348125	+	0.200990i	−0.315734	+	0.948848i	$0.602251\pi$
$558$	−17.0726	+	9.85685i	−0.722739	+	0.417274i
$559$	9.19441	+	15.9252i	0.388882	+	0.673564i
$560$	3.67072	+	0.745746i	0.155116	+	0.0315135i
$561$	−35.0943			−1.48168
$562$	−16.3504	+	9.43994i	−0.689702	+	0.398200i
$563$			18.5950i			0.783685i	0.920032	+	0.391843i	$0.128162\pi$
$563$			18.5950i			0.783685i	−0.920032	+	0.391843i	$0.871838\pi$
$564$	4.16243	−	7.20955i	0.175270	−	0.303577i
$565$	6.20123	−	7.01317i	0.260888	−	0.295046i
$566$	32.0191			1.34586
$567$	26.9653	+	15.5684i	1.13243	+	0.653812i
$568$	4.86024	−	2.80606i	0.203931	−	0.117740i
$569$	−5.81194			−0.243649			−0.121825	−	0.992552i	$-0.538875\pi$
$569$	−5.81194			−0.243649			−0.121825	+	0.992552i	$0.538875\pi$
$570$	30.6145	−	10.2530i	1.28230	−	0.429452i
$571$	14.4871	−	25.0923i	0.606265	−	1.05008i	−0.385585	−	0.922672i	$-0.626000\pi$
$571$	14.4871	−	25.0923i	0.606265	−	1.05008i	0.991850	−	0.127410i	$-0.0406663\pi$
$572$	−18.7501	−	10.8253i	−0.783979	−	0.452630i
$573$	−16.6758	+	9.62776i	−0.696640	+	0.402206i
$574$	−0.293367	−	0.508127i	−0.0122449	−	0.0212088i
$575$	−3.26831	+	7.71166i	−0.136298	+	0.321599i
$576$	−3.48119	+	6.02961i	−0.145050	+	0.251234i
$577$	−31.4422	−	18.1532i	−1.30896	−	0.755726i	−0.327034	−	0.945013i	$-0.606049\pi$
$577$	−31.4422	−	18.1532i	−1.30896	−	0.755726i	−0.981922	+	0.189287i	$0.939382\pi$
$578$		−	10.8437i		−	0.451037i
$579$	13.3461	+	23.1162i	0.554647	+	0.960676i
$580$	19.2703	−	6.45375i	0.800155	−	0.267977i
$581$	−11.2243			−0.465661
$582$		−	25.8397i		−	1.07109i
$583$	−18.1434	−	10.4751i	−0.751422	−	0.433834i
$584$	7.13093			0.295080
$585$	73.7121	+	14.9754i	3.04762	+	0.619156i
$586$	−15.0835			−0.623092
$587$	12.9464	−	7.47461i	0.534355	−	0.308510i	−0.208433	−	0.978037i	$-0.566836\pi$
$587$	12.9464	−	7.47461i	0.534355	−	0.308510i	0.742788	+	0.669527i	$0.233503\pi$
$588$	11.4639	−	6.61871i	0.472765	−	0.272951i
$589$	−6.47627	−	11.2172i	−0.266850	−	0.462198i
$590$	6.98140	+	20.8458i	0.287420	+	0.858208i
$591$	−32.8677			−1.35199
$592$	−5.66744	−	2.20910i	−0.232930	−	0.0907933i
$593$		−	21.6909i		−	0.890737i	−0.895347	−	0.445368i	$-0.853073\pi$
$593$		−	21.6909i		−	0.890737i	0.895347	−	0.445368i	$-0.146927\pi$
$594$	28.0222	−	48.5359i	1.14977	−	1.99145i
$595$	−1.85034	+	9.10777i	−0.0758565	+	0.373382i
$596$	−1.73813	−	3.01054i	−0.0711968	−	0.123316i
$597$	−12.9849	+	7.49683i	−0.531436	+	0.306825i
$598$		−	8.09332i		−	0.330961i
$599$	11.3478	+	19.6550i	0.463659	+	0.803080i	0.999140	−	0.0414669i	$-0.0132031\pi$
$599$	11.3478	+	19.6550i	0.463659	+	0.803080i	−0.535481	+	0.844547i	$0.679870\pi$
$600$	1.93207	+	15.6629i	0.0788765	+	0.639436i
$601$	−8.72956	+	15.1200i	−0.356086	+	0.616760i	−0.987303	−	0.158847i	$-0.949222\pi$
$601$	−8.72956	+	15.1200i	−0.356086	+	0.616760i	0.631217	+	0.775606i	$0.282556\pi$
$602$		−	6.37565i		−	0.259852i
$603$			87.3376i			3.55666i
$604$	−6.65022	+	11.5185i	−0.270593	+	0.468682i
$605$	−4.04278	+	19.8994i	−0.164363	+	0.809028i
$606$	51.0517			2.07384
$607$	7.86020	+	4.53809i	0.319036	+	0.184195i	0.650963	−	0.759110i	$-0.274365\pi$
$607$	7.86020	+	4.53809i	0.319036	+	0.184195i	−0.331927	+	0.943305i	$0.607699\pi$
$608$	−3.96165	−	2.28726i	−0.160666	−	0.0927606i
$609$	−24.0263	+	41.6149i	−0.973597	+	1.68632i
$610$	−29.9396	−	6.08254i	−1.21222	−	0.246275i
$611$	6.37153	+	11.0358i	0.257765	+	0.446461i
$612$	−14.9606	−	8.63752i	−0.604747	−	0.349151i
$613$	−38.0713	−	21.9805i	−1.53769	−	0.887784i	−0.998974	−	0.0452938i	$-0.985578\pi$
$613$	−38.0713	−	21.9805i	−1.53769	−	0.887784i	−0.538712	−	0.842490i	$-0.681089\pi$
$614$	−14.9587	+	25.9093i	−0.603686	+	1.04561i
$615$	1.63752	−	1.85192i	0.0660312	−	0.0746768i
$616$	3.75329	+	6.50089i	0.151225	+	0.261929i
$617$	−30.9730	−	17.8822i	−1.24692	−	0.719912i	−0.276429	−	0.961034i	$-0.589151\pi$
$617$	−30.9730	−	17.8822i	−1.24692	−	0.719912i	−0.970495	+	0.241122i	$0.922484\pi$
$618$			32.3512i			1.30136i
$619$	−22.7757			−0.915435			−0.457717	−	0.889098i	$-0.651333\pi$
$619$	−22.7757			−0.915435			−0.457717	+	0.889098i	$0.651333\pi$
$620$	6.00359	−	2.01064i	0.241110	−	0.0807493i
$621$	20.9502			0.840701
$622$	−23.8045	+	13.7435i	−0.954474	+	0.551066i
$623$		−	17.6629i		−	0.707650i
$624$	−7.62482	−	13.2066i	−0.305237	−	0.528686i
$625$	17.3866	+	17.9640i	0.695464	+	0.718561i
$626$	10.7308	+	18.5864i	0.428891	+	0.742860i
$627$	56.0340	+	32.3512i	2.23778	+	1.29198i
$628$			14.2873i			0.570124i
$629$	5.48119	−	14.0620i	0.218550	−	0.560690i
$630$	−19.5369	−	17.2750i	−0.778369	−	0.688254i
$631$	−21.1597	+	36.6497i	−0.842356	+	1.45900i	0.0455416	+	0.998962i	$0.485499\pi$
$631$	−21.1597	+	36.6497i	−0.842356	+	1.45900i	−0.887898	+	0.460041i	$0.847835\pi$
$632$	−8.73049	+	5.04055i	−0.347280	+	0.200502i
$633$	18.6600	−	10.7734i	0.741670	−	0.428203i
$634$	−12.1690	−	21.0774i	−0.483294	−	0.837089i
$635$	19.5877	−	22.1524i	0.777314	−	0.879089i
$636$	−7.37812	−	12.7793i	−0.292561	−	0.506731i
$637$			20.2628i			0.802842i
$638$	35.2705	+	20.3634i	1.39637	+	0.806196i
$639$	−39.0738			−1.54574
$640$	1.48119	−	1.67513i	0.0585493	−	0.0662154i
$641$	13.5659	−	23.4969i	0.535823	−	0.928072i	−0.463300	−	0.886201i	$-0.653335\pi$
$641$	13.5659	−	23.4969i	0.535823	−	0.928072i	0.999123	−	0.0418706i	$-0.0133317\pi$
$642$	35.4122	−	20.4452i	1.39761	−	0.806909i
$643$			21.5745i			0.850816i	0.905002	+	0.425408i	$0.139869\pi$
$643$			21.5745i			0.850816i	−0.905002	+	0.425408i	$0.860131\pi$
$644$	−1.40303	+	2.43012i	−0.0552872	+	0.0957602i
$645$	25.4717	−	8.53066i	1.00295	−	0.335894i
$646$	5.67513	−	9.82962i	0.223285	−	0.386741i
$647$	11.8638	−	6.84955i	0.466413	−	0.269284i	−0.248324	−	0.968677i	$-0.579880\pi$
$647$	11.8638	−	6.84955i	0.466413	−	0.269284i	0.714737	+	0.699393i	$0.246546\pi$
$648$	16.0974	−	9.29384i	0.632366	−	0.365097i
$649$	−22.0283	+	38.1542i	−0.864688	+	1.49768i
$650$	−22.2422	−	9.42654i	−0.872410	−	0.369739i
$651$	−7.48532	+	12.9650i	−0.293373	+	0.508137i
$652$			9.93207i			0.388970i
$653$	−7.06785	+	4.08062i	−0.276586	+	0.159687i	−0.631877	−	0.775069i	$-0.717715\pi$
$653$	−7.06785	+	4.08062i	−0.276586	+	0.159687i	0.355291	+	0.934756i	$0.384382\pi$
$654$	−31.3258	+	54.2579i	−1.22494	+	2.12165i
$655$	2.17679	+	1.92478i	0.0850543	+	0.0752073i
$656$	−0.350262			−0.0136754
$657$	−42.9967	−	24.8242i	−1.67746	−	0.968483i
$658$		−	4.41819i		−	0.172239i
$659$	2.74306	+	4.75112i	0.106854	+	0.185077i	0.914494	−	0.404599i	$-0.132589\pi$
$659$	2.74306	+	4.75112i	0.106854	+	0.185077i	−0.807640	+	0.589676i	$0.799255\pi$
$660$	−20.9502	+	23.6932i	−0.815484	+	0.922258i
$661$	−3.31147	−	5.73563i	−0.128801	−	0.223090i	0.794411	−	0.607380i	$-0.207780\pi$
$661$	−3.31147	−	5.73563i	−0.128801	−	0.223090i	−0.923212	+	0.384290i	$0.874446\pi$
$662$	19.5006	−	11.2587i	0.757914	−	0.437582i
$663$	32.7681	−	18.9187i	1.27261	−	0.734740i
$664$	−3.35026	+	5.80282i	−0.130015	+	0.225193i
$665$	11.3503	−	12.8364i	0.440144	−	0.497773i
$666$	26.4821	+	33.0494i	1.02616	+	1.28064i
$667$			15.2243i			0.589485i
$668$	12.4603	+	7.19394i	0.482102	+	0.278342i
$669$	4.39986	+	7.62078i	0.170108	+	0.294637i
$670$	5.58451	−	27.4881i	0.215748	−	1.06196i
$671$	−30.6131	−	53.0234i	−1.18180	−	2.04695i
$672$			5.28726i			0.203960i
$673$	8.23500	−	4.75448i	0.317436	−	0.183272i	−0.332813	−	0.942993i	$-0.607998\pi$
$673$	8.23500	−	4.75448i	0.317436	−	0.183272i	0.650249	+	0.759721i	$0.274665\pi$
$674$	18.6859			0.719755
$675$	24.4013	−	57.5755i	0.939207	−	2.21608i
$676$	10.3430			0.397806
$677$		−	28.0508i		−	1.07808i	−0.842280	−	0.539040i	$-0.818787\pi$
$677$		−	28.0508i		−	1.07808i	0.842280	−	0.539040i	$-0.181213\pi$
$678$	11.4440	+	6.60720i	0.439505	+	0.253748i
$679$	−6.85685	−	11.8764i	−0.263142	−	0.455775i
$680$	4.15633	+	3.67513i	0.159388	+	0.140935i
$681$	33.5963	−	58.1904i	1.28741	−	2.22986i
$682$	10.9884	+	6.34415i	0.420767	+	0.242930i
$683$	−29.3124	−	16.9235i	−1.12161	−	0.647560i	−0.179796	−	0.983704i	$-0.557544\pi$
$683$	−29.3124	−	16.9235i	−1.12161	−	0.647560i	−0.941811	+	0.336144i	$0.890877\pi$
$684$	15.9248	+	27.5825i	0.608899	+	1.05464i
$685$	−11.0786	−	2.25073i	−0.423291	−	0.0859961i
$686$	9.37565	−	16.2391i	0.357964	−	0.620012i
$687$	29.0104	+	16.7492i	1.10682	+	0.639021i
$688$	−3.29615	−	1.90303i	−0.125664	−	0.0725524i
$689$	22.5877			0.860522
$690$	−11.5860	−	2.35382i	−0.441071	−	0.0896082i
$691$	−13.3920	+	23.1956i	−0.509456	+	0.882403i	0.490484	+	0.871450i	$0.336820\pi$
$691$	−13.3920	+	23.1956i	−0.509456	+	0.882403i	−0.999940	+	0.0109530i	$0.996513\pi$
$692$			15.5818i			0.592332i
$693$		−	52.2638i		−	1.98534i
$694$	2.98484	−	5.16990i	0.113303	−	0.196247i
$695$	−1.89446	−	1.67513i	−0.0718610	−	0.0635413i
$696$	14.3430	+	24.8427i	0.543669	+	0.941662i
$697$		−	0.869067i		−	0.0329183i
$698$	−19.1405	+	11.0508i	−0.724479	+	0.418278i
$699$	−28.2211	−	48.8804i	−1.06742	−	1.84882i
$700$	5.04434	+	6.68627i	0.190658	+	0.252717i
$701$	−8.86177	+	15.3490i	−0.334705	+	0.579725i	−0.983428	−	0.181299i	$-0.941970\pi$
$701$	−8.86177	+	15.3490i	−0.334705	+	0.579725i	0.648723	+	0.761024i	$0.275303\pi$
$702$			60.4250i			2.28060i
$703$	−21.7146	+	17.3996i	−0.818980	+	0.656240i
$704$	4.48119			0.168891
$705$	17.6514	−	5.91156i	0.664789	−	0.222642i
$706$	10.7775	+	18.6672i	0.405617	+	0.702549i
$707$	23.4643	−	13.5471i	0.882467	−	0.509493i
$708$	−26.8739	+	15.5156i	−1.00998	+	0.583113i
$709$	−44.7974			−1.68240			−0.841200	−	0.540724i	$-0.818150\pi$
$709$	−44.7974			−1.68240			−0.841200	+	0.540724i	$0.818150\pi$
$710$	12.2979	+	2.49844i	0.461531	+	0.0937649i
$711$	70.1886			2.63228
$712$	−9.13154	−	5.27210i	−0.342219	−	0.197580i
$713$			4.74306i			0.177629i
$714$	−13.1187			−0.490956
$715$	−15.3743	−	45.9063i	−0.574968	−	1.71680i
$716$	6.57452	+	11.3874i	0.245701	+	0.425567i
$717$			17.0289i			0.635956i
$718$	−4.66398	−	2.69275i	−0.174058	−	0.100493i
$719$	−8.66243	+	15.0038i	−0.323054	+	0.559546i	−0.981117	−	0.193417i	$-0.938043\pi$
$719$	−8.66243	+	15.0038i	−0.323054	+	0.559546i	0.658062	+	0.752963i	$0.271376\pi$
$720$	−14.7625	+	4.94405i	−0.550165	+	0.184254i
$721$	8.58475	+	14.8692i	0.319713	+	0.553759i
$722$	−1.66813	+	0.963096i	−0.0620814	+	0.0358427i
$723$	5.81135	+	3.35519i	0.216127	+	0.124781i
$724$	−9.64363	+	16.7033i	−0.358403	+	0.620772i
$725$	41.8395	+	17.7322i	1.55388	+	0.658556i
$726$	−28.6629			−1.06378
$727$	7.39440	−	4.26916i	0.274243	−	0.158334i	−0.356571	−	0.934268i	$-0.616054\pi$
$727$	7.39440	−	4.26916i	0.274243	−	0.158334i	0.630814	+	0.775934i	$0.282721\pi$
$728$	−7.00902	−	4.04666i	−0.259772	−	0.149979i
$729$	−10.9902			−0.407043
$730$	11.9452	+	10.5623i	0.442113	+	0.390928i
$731$	4.72179	−	8.17838i	0.174642	−	0.302488i
$732$		−	43.1246i		−	1.59393i
$733$	10.8332	−	6.25457i	0.400135	−	0.231018i	−0.286407	−	0.958108i	$-0.592461\pi$
$733$	10.8332	−	6.25457i	0.400135	−	0.231018i	0.686542	+	0.727090i	$0.259128\pi$
$734$	−11.6023			−0.428248
$735$	29.0072	+	5.89312i	1.06995	+	0.217371i
$736$	0.837565	+	1.45071i	0.0308731	+	0.0534737i
$737$	48.6819	−	28.1065i	1.79322	−	1.03532i
$738$	2.11194	+	1.21933i	0.0777416	+	0.0448841i
$739$	43.1935			1.58890			0.794449	−	0.607331i	$-0.207760\pi$
$739$	43.1935			1.58890			0.794449	+	0.607331i	$0.207760\pi$
$740$	−6.22161	−	12.0951i	−0.228711	−	0.444625i
$741$	−69.7597			−2.56269
$742$	−6.78224	−	3.91573i	−0.248984	−	0.143751i
$743$	7.46768	−	4.31147i	0.273963	−	0.158172i	−0.356725	−	0.934210i	$-0.616107\pi$
$743$	7.46768	−	4.31147i	0.273963	−	0.158172i	0.630687	+	0.776037i	$0.282773\pi$
$744$	4.46850	+	7.73967i	0.163823	+	0.283750i
$745$	1.54759	−	7.61756i	0.0566992	−	0.279086i
$746$	−25.2252			−0.923561
$747$	40.4015	−	23.3258i	1.47821	−	0.853447i
$748$			11.1187i			0.406540i
$749$	10.8507	−	18.7940i	0.396477	−	0.686719i
$750$	−19.9633	+	29.0992i	−0.728958	+	1.06255i
$751$	23.4217			0.854670			0.427335	−	0.904093i	$-0.359452\pi$
$751$	23.4217			0.854670			0.427335	+	0.904093i	$0.359452\pi$
$752$	−2.28416	−	1.31876i	−0.0832947	−	0.0480902i
$753$	−41.6869	+	24.0679i	−1.51915	+	0.877084i
$754$	−43.9102			−1.59911
$755$	−28.2011	+	9.44475i	−1.02634	+	0.343730i
$756$	10.4751	−	18.1434i	0.380975	−	0.659868i
$757$	−22.9574	−	13.2545i	−0.834402	−	0.481742i	0.0209555	−	0.999780i	$-0.493329\pi$
$757$	−22.9574	−	13.2545i	−0.834402	−	0.481742i	−0.855357	+	0.518038i	$0.826663\pi$
$758$	11.5773	−	6.68418i	0.420508	−	0.242780i
$759$	−11.8466	−	20.5189i	−0.430005	−	0.744790i
$760$	−3.24840	−	9.69942i	−0.117832	−	0.351835i
$761$	10.0537	−	17.4136i	0.364447	−	0.631241i	−0.624240	−	0.781233i	$-0.714591\pi$
$761$	10.0537	−	17.4136i	0.364447	−	0.631241i	0.988687	+	0.149991i	$0.0479246\pi$
$762$	36.1479	+	20.8700i	1.30950	+	0.756041i
$763$			33.2506i			1.20375i
$764$	3.05031	+	5.28329i	0.110356	+	0.191143i
$765$	−12.2672	−	36.6286i	−0.443520	−	1.32431i
$766$	8.24965			0.298072
$767$		−	47.5002i		−	1.71513i
$768$	2.73346	+	1.57816i	0.0986352	+	0.0569470i
$769$	−46.0567			−1.66085			−0.830423	−	0.557134i	$-0.811901\pi$
$769$	−46.0567			−1.66085			−0.830423	+	0.557134i	$0.811901\pi$
$770$	−3.34183	+	16.4492i	−0.120431	+	0.592788i
$771$	−18.5663			−0.668648
$772$	7.32377	−	4.22838i	0.263588	−	0.152183i
$773$	−9.62826	+	5.55888i	−0.346304	+	0.199939i	−0.663056	−	0.748569i	$-0.730741\pi$
$773$	−9.62826	+	5.55888i	−0.346304	+	0.199939i	0.316752	+	0.948508i	$0.397408\pi$
$774$	13.2496	+	22.9491i	0.476249	+	0.824887i
$775$	13.0349	+	5.52439i	0.468229	+	0.198442i
$776$	−8.18664			−0.293883
$777$	29.9652	+	11.6801i	1.07500	+	0.419020i
$778$			5.09825i			0.182781i
$779$	−0.801139	+	1.38761i	−0.0287038	+	0.0497164i
$780$	6.78894	−	33.4166i	0.243083	−	1.19651i
$781$	12.5745	+	21.7797i	0.449952	+	0.779339i
$782$	−3.59948	+	2.07816i	−0.128717	+	0.0743149i
$783$		−	113.665i		−	4.06205i
$784$	−2.09697	−	3.63206i	−0.0748917	−	0.129716i
$785$	−21.1622	+	23.9330i	−0.755311	+	0.854206i
$786$	−2.05079	+	3.55206i	−0.0731491	+	0.126698i
$787$		−	44.0797i		−	1.57127i	−0.618690	−	0.785636i	$-0.712336\pi$
$787$		−	44.0797i		−	1.57127i	0.618690	−	0.785636i	$-0.287664\pi$
$788$			10.4133i			0.370957i
$789$	3.66902	−	6.35493i	0.130621	−	0.226242i
$790$	−22.0908	−	4.48797i	−0.785954	−	0.159675i
$791$	7.01317			0.249360
$792$	−27.0198	−	15.5999i	−0.960108	−	0.554319i
$793$	57.1679	+	33.0059i	2.03009	+	1.17207i
$794$	−9.95263	+	17.2385i	−0.353206	+	0.611770i
$795$	6.56928	−	32.3354i	0.232988	−	1.14682i
$796$	2.37518	+	4.11393i	0.0841859	+	0.145814i
$797$	−27.4954	−	15.8745i	−0.973937	−	0.562303i	−0.0735025	−	0.997295i	$-0.523418\pi$
$797$	−27.4954	−	15.8745i	−0.973937	−	0.562303i	−0.900434	+	0.434992i	$0.856751\pi$
$798$	20.9462	+	12.0933i	0.741489	+	0.428099i
$799$	3.27210	−	5.66744i	0.115759	−	0.200500i
$800$	4.96239	−	0.612127i	0.175447	−	0.0216420i
$801$	36.7064	+	63.5774i	1.29696	+	2.24640i
$802$	14.0443	+	8.10848i	0.495921	+	0.286320i
$803$			31.9551i			1.12767i
$804$	39.5936			1.39636
$805$	−5.94974	+	1.99261i	−0.209701	+	0.0702303i
$806$	−13.6801			−0.481859
$807$	−22.2455	+	12.8434i	−0.783079	+	0.452111i
$808$		−	16.1744i		−	0.569014i
$809$	17.7677	+	30.7746i	0.624681	+	1.08198i	0.988603	+	0.150549i	$0.0481042\pi$
$809$	17.7677	+	30.7746i	0.624681	+	1.08198i	−0.363922	+	0.931429i	$0.618562\pi$
$810$	40.7313	+	8.27499i	1.43115	+	0.290753i
$811$	8.20711	+	14.2151i	0.288191	+	0.499161i	0.973378	−	0.229206i	$-0.0736130\pi$
$811$	8.20711	+	14.2151i	0.288191	+	0.499161i	−0.685187	+	0.728367i	$0.740280\pi$
$812$	13.1846	+	7.61213i	0.462688	+	0.267133i
$813$			52.4904i			1.84092i
$814$	9.89938	−	25.3969i	0.346973	−	0.890161i
$815$	−14.7113	+	16.6375i	−0.515315	+	0.582787i
$816$	−3.91573	+	6.78224i	−0.137078	+	0.237426i
$817$	−15.0783	+	8.70545i	−0.527522	+	0.304565i
$818$	26.5988	−	15.3568i	0.930007	−	0.536940i
$819$	28.1744	+	48.7995i	0.984494	+	1.70519i
$820$	−0.586734	−	0.518806i	−0.0204896	−	0.0181175i
$821$	−10.3733	−	17.9671i	−0.362030	−	0.627055i	0.626265	−	0.779610i	$-0.284583\pi$
$821$	−10.3733	−	17.9671i	−0.362030	−	0.627055i	−0.988295	+	0.152556i	$0.951250\pi$
$822$		−	15.9575i		−	0.556580i
$823$	1.88311	+	1.08721i	0.0656410	+	0.0378978i	0.532461	−	0.846454i	$-0.321267\pi$
$823$	1.88311	+	1.08721i	0.0656410	+	0.0378978i	−0.466820	+	0.884352i	$0.654601\pi$
$824$	10.2496			0.357063
$825$	−70.1886	+	8.65799i	−2.44365	+	0.301432i
$826$	−8.23449	+	14.2626i	−0.286514	+	0.496258i
$827$	−10.8424	+	6.25988i	−0.377028	+	0.217677i	−0.676525	−	0.736420i	$-0.736515\pi$
$827$	−10.8424	+	6.25988i	−0.377028	+	0.217677i	0.299496	+	0.954097i	$0.403181\pi$
$828$		−	11.6629i		−	0.405314i
$829$	−6.42430	+	11.1272i	−0.223125	+	0.386464i	−0.955755	−	0.294163i	$-0.904959\pi$
$829$	−6.42430	+	11.1272i	−0.223125	+	0.386464i	0.732630	+	0.680627i	$0.238293\pi$
$830$	−14.2072	+	4.75810i	−0.493140	+	0.165156i
$831$	10.5823	−	18.3291i	0.367095	−	0.635828i
$832$	−4.18416	+	2.41573i	−0.145060	+	0.0837503i
$833$	9.01184	−	5.20299i	0.312242	−	0.180273i
$834$	1.78480	−	3.09136i	0.0618024	−	0.107045i
$835$	10.2170	+	30.5069i	0.353572	+	1.05573i
$836$	10.2496	−	17.7529i	0.354491	−	0.613997i
$837$		−	35.4119i		−	1.22401i
$838$	−5.67802	+	3.27821i	−0.196144	+	0.113244i
$839$	12.6024	−	21.8279i	0.435082	−	0.753584i	−0.562220	−	0.826988i	$-0.690053\pi$
$839$	12.6024	−	21.8279i	0.435082	−	0.753584i	0.997302	+	0.0734032i	$0.0233860\pi$
$840$	−7.83146	+	8.85685i	−0.270211	+	0.305590i
$841$	53.5990			1.84824
$842$	−11.1712	−	6.44969i	−0.384985	−	0.222271i
$843$		−	59.5910i		−	2.05242i
$844$	−3.41327	−	5.91195i	−0.117489	−	0.203498i
$845$	17.3258	+	15.3199i	0.596026	+	0.527022i
$846$	9.18172	+	15.9032i	0.315674	+	0.546763i
$847$	−13.1740	+	7.60602i	−0.452664	+	0.261346i
$848$	−4.04878	+	2.33757i	−0.139036	+	0.0802723i
$849$	−50.5313	+	87.5227i	−1.73423	+	3.00377i
$850$	1.51881	+	12.3127i	0.0520946	+	0.422320i
$851$	10.0721	−	1.54211i	0.345266	−	0.0528627i
$852$			17.7137i			0.606861i
$853$	13.3116	+	7.68546i	0.455781	+	0.263145i	0.710268	−	0.703931i	$-0.248574\pi$
$853$	13.3116	+	7.68546i	0.455781	+	0.263145i	−0.254488	+	0.967076i	$0.581907\pi$
$854$	−11.4436	−	19.8209i	−0.391591	−	0.678256i
$855$	−14.1790	+	69.7920i	−0.484911	+	2.38684i
$856$	−6.47755	−	11.2194i	−0.221398	−	0.383473i
$857$		−	35.7826i		−	1.22231i	−0.791511	−	0.611155i	$-0.790705\pi$
$857$		−	35.7826i		−	1.22231i	0.791511	−	0.611155i	$-0.209295\pi$
$858$	59.1813	−	34.1683i	2.02041	−	1.16649i
$859$	20.5237			0.700261			0.350130	−	0.936701i	$-0.386137\pi$
$859$	20.5237			0.700261			0.350130	+	0.936701i	$0.386137\pi$
$860$	−2.70272	−	8.07006i	−0.0921619	−	0.275187i
$861$	1.85192			0.0631134
$862$		−	35.2496i		−	1.20061i
$863$	31.3174	+	18.0811i	1.06606	+	0.615488i	0.927101	−	0.374811i	$-0.122292\pi$
$863$	31.3174	+	18.0811i	1.06606	+	0.615488i	0.138955	+	0.990299i	$0.455626\pi$
$864$	−6.25329	−	10.8310i	−0.212741	−	0.368479i
$865$	−23.0797	+	26.1016i	−0.784733	+	0.887480i
$866$	1.96239	−	3.39896i	0.0666847	−	0.115501i
$867$	29.6407	+	17.1131i	1.00665	+	0.581191i
$868$	4.10761	+	2.37153i	0.139421	+	0.0804950i
$869$	−22.5877	−	39.1230i	−0.766235	−	1.32716i
$870$	−12.7706	+	62.8596i	−0.432964	+	2.13114i
$871$	−30.3034	+	52.4870i	−1.02679	+	1.77845i
$872$	17.1902	+	9.92478i	0.582134	+	0.336095i
$873$	49.3622	+	28.4993i	1.67066	+	0.964555i
$874$	7.66291			0.259202
$875$	−1.45373	+	18.6720i	−0.0491452	+	0.631230i
$876$	−11.2538	+	19.4921i	−0.380230	+	0.658577i
$877$			2.59006i			0.0874601i	0.999043	+	0.0437300i	$0.0139241\pi$
$877$			2.59006i			0.0874601i	−0.999043	+	0.0437300i	$0.986076\pi$
$878$		−	9.42056i		−	0.317928i
$879$	23.8042	−	41.2300i	0.802895	−	1.39065i
$880$	7.50659	+	6.63752i	0.253047	+	0.223751i
$881$	−1.24178	−	2.15083i	−0.0418367	−	0.0724633i	0.844349	−	0.535794i	$-0.179988\pi$
$881$	−1.24178	−	2.15083i	−0.0418367	−	0.0724633i	−0.886186	+	0.463331i	$0.846654\pi$
$882$			29.1998i			0.983209i
$883$	30.8313	−	17.8004i	1.03755	−	0.599032i	0.118415	−	0.992964i	$-0.462219\pi$
$883$	30.8313	−	17.8004i	1.03755	−	0.599032i	0.919140	+	0.393932i	$0.128885\pi$
$884$	−5.99389	−	10.3817i	−0.201596	−	0.349175i
$885$	−67.9989	−	13.8147i	−2.28576	−	0.464376i
$886$	11.9690	−	20.7309i	0.402106	−	0.696467i
$887$			15.7381i			0.528435i	0.964463	+	0.264217i	$0.0851137\pi$
$887$			15.7381i			0.528435i	−0.964463	+	0.264217i	$0.914886\pi$
$888$	14.9826	−	12.0054i	0.502784	−	0.402875i
$889$	22.1524			0.742966
$890$	−7.48753	−	22.3570i	−0.250982	−	0.749410i
$891$	41.6475	+	72.1356i	1.39524	+	2.41663i
$892$	2.41445	−	1.39398i	0.0808417	−	0.0466740i
$893$	−10.4489	+	6.03269i	−0.349660	+	0.201876i
$894$	10.9722			0.366967
$895$	−5.85377	+	28.8135i	−0.195670	+	0.963129i
$896$	1.67513			0.0559622
$897$	22.1228	+	12.7726i	0.738657	+	0.426464i
$898$			30.0191i			1.00175i
$899$	25.7334			0.858257
$900$	−32.0522	−	13.5842i	−1.06841	−	0.452805i
$901$	−5.79995	−	10.0458i	−0.193224	−	0.334675i
$902$		−	1.56959i		−	0.0522617i
$903$	17.4276	+	10.0618i	0.579954	+	0.334836i
$904$	2.09332	−	3.62574i	0.0696228	−	0.120590i
$905$	−40.8951	+	13.6961i	−1.35940	+	0.455272i
$906$	−20.9902	−	36.3562i	−0.697354	−	1.20785i
$907$	12.0981	−	6.98484i	0.401711	−	0.231928i	−0.285511	−	0.958375i	$-0.592163\pi$
$907$	12.0981	−	6.98484i	0.401711	−	0.231928i	0.687222	+	0.726448i	$0.258830\pi$
$908$	−18.4361	−	10.6441i	−0.611825	−	0.353237i
$909$	−56.3063	+	97.5254i	−1.86756	+	3.23471i
$910$	−5.74714	−	17.1604i	−0.190516	−	0.568862i
$911$	37.1850			1.23200			0.615998	−	0.787748i	$-0.288753\pi$
$911$	37.1850			1.23200			0.615998	+	0.787748i	$0.288753\pi$
$912$	12.5042	−	7.21933i	0.414057	−	0.239056i
$913$	−26.0036	−	15.0132i	−0.860593	−	0.496864i
$914$	25.6023			0.846848
$915$	63.8759	−	72.2393i	2.11167	−	2.38816i
$916$	5.30654	−	9.19120i	0.175333	−	0.303686i
$917$			2.17679i			0.0718840i
$918$	26.8739	−	15.5156i	0.886970	−	0.512092i
$919$	−4.43866			−0.146418			−0.0732089	−	0.997317i	$-0.523324\pi$
$919$	−4.43866			−0.146418			−0.0732089	+	0.997317i	$0.523324\pi$
$920$	−0.745746	+	3.67072i	−0.0245865	+	0.121020i
$921$	−47.2147	−	81.7782i	−1.55578	−	2.69468i
$922$	−3.10703	+	1.79384i	−0.102325	+	0.0590771i
$923$	−23.4821	−	13.5574i	−0.772921	−	0.446246i
$924$	−23.6932			−0.779450
$925$	7.49320	−	29.4763i	0.246375	−	0.969175i
$926$	−21.3865			−0.702803
$927$	−61.8013	−	35.6810i	−2.02982	−	1.17192i
$928$	7.87078	−	4.54420i	0.258371	−	0.149171i
$929$	12.1180	+	20.9890i	0.397579	+	0.688627i	0.993427	−	0.114471i	$-0.0365172\pi$
$929$	12.1180	+	20.9890i	0.397579	+	0.688627i	−0.595848	+	0.803097i	$0.703184\pi$
$930$	−3.97863	+	19.5837i	−0.130464	+	0.642174i
$931$	−19.1852			−0.628770
$932$	−15.4865	+	8.94112i	−0.507276	+	0.292876i
$933$		−	86.7581i		−	2.84033i
$934$	−6.13458	+	10.6254i	−0.200730	+	0.347674i
$935$	−16.4690	+	18.6253i	−0.538593	+	0.609112i
$936$	33.6385			1.09951
$937$	−14.5282	−	8.38787i	−0.474616	−	0.274020i	0.243554	−	0.969887i	$-0.421687\pi$
$937$	−14.5282	−	8.38787i	−0.474616	−	0.274020i	−0.718170	+	0.695868i	$0.755020\pi$
$938$	18.1979	−	10.5066i	0.594184	−	0.343052i
$939$	−67.7400			−2.21061
$940$	−1.87293	−	5.59238i	−0.0610881	−	0.182403i
$941$	4.36954	−	7.56827i	0.142443	−	0.246719i	−0.785973	−	0.618261i	$-0.787838\pi$
$941$	4.36954	−	7.56827i	0.142443	−	0.246719i	0.928416	+	0.371542i	$0.121171\pi$
$942$	−39.0536	−	22.5476i	−1.27244	−	0.734641i
$943$	0.508127	−	0.293367i	0.0165469	−	0.00955335i
$944$	4.91573	+	8.51429i	0.159993	+	0.277117i
$945$	44.4210	−	14.8769i	1.44502	−	0.483946i
$946$	8.52785	−	14.7707i	0.277264	−	0.480236i
$947$	−15.0508	−	8.68958i	−0.489085	−	0.282373i	0.235110	−	0.971969i	$-0.424455\pi$
$947$	−15.0508	−	8.68958i	−0.489085	−	0.282373i	−0.724195	+	0.689595i	$0.757788\pi$
$948$		−	31.8192i		−	1.03344i
$949$	−17.2264	−	29.8370i	−0.559192	−	0.968550i
$950$	8.92523	−	21.0593i	0.289573	−	0.683255i
$951$	76.8188			2.49102
$952$			4.15633i			0.134707i
$953$	35.9454	+	20.7531i	1.16438	+	0.672258i	0.952351	−	0.305005i	$-0.0986580\pi$
$953$	35.9454	+	20.7531i	1.16438	+	0.672258i	0.212034	+	0.977262i	$0.431991\pi$
$954$	32.5501			1.05385
$955$	−2.71591	+	13.3683i	−0.0878848	+	0.432588i
$956$	5.39517			0.174492
$957$	−111.325	+	64.2736i	−3.59863	+	2.07767i
$958$	−13.3369	+	7.70005i	−0.430895	+	0.248777i
$959$	−4.23449	−	7.33435i	−0.136739	−	0.236838i
$960$	2.24133	+	6.69241i	0.0723387	+	0.215997i
$961$	−22.9829			−0.741382
$962$	4.44778	+	29.0501i	0.143402	+	0.936612i
$963$			90.1984i			2.90660i
$964$	1.06300	−	1.84118i	0.0342371	−	0.0593003i
$965$	18.5313	+	3.76483i	0.596544	+	0.121194i
$966$	−4.42842	−	7.67026i	−0.142482	−	0.246786i
$967$	−10.4278	+	6.02047i	−0.335334	+	0.193605i	−0.658207	−	0.752837i	$-0.728685\pi$
$967$	−10.4278	+	6.02047i	−0.335334	+	0.193605i	0.322873	+	0.946442i	$0.395351\pi$
$968$			9.08110i			0.291878i
$969$	17.9126	+	31.0255i	0.575434	+	0.996681i
$970$	−13.7137	−	12.1260i	−0.440320	−	0.389343i
$971$	−24.1082	+	41.7567i	−0.773671	+	1.34004i	0.161868	+	0.986812i	$0.448248\pi$
$971$	−24.1082	+	41.7567i	−0.773671	+	1.34004i	−0.935539	+	0.353224i	$0.885085\pi$
$972$			21.1490i			0.678355i
$973$		−	1.89446i		−	0.0607336i
$974$	1.21203	−	2.09931i	0.0388361	−	0.0672661i
$975$	60.8688	−	45.9214i	1.94936	−	1.47066i
$976$	−13.6629			−0.437339
$977$	46.7882	+	27.0132i	1.49689	+	0.864228i	0.999994	−	0.00358369i	$-0.00114073\pi$
$977$	46.7882	+	27.0132i	1.49689	+	0.864228i	0.496893	+	0.867812i	$0.334474\pi$
$978$	−27.1489	−	15.6744i	−0.868126	−	0.501213i
$979$	23.6253	−	40.9202i	0.755068	−	1.30782i
$980$	1.86708	−	9.19019i	0.0596418	−	0.293570i
$981$	−69.1002	−	119.685i	−2.20620	−	3.82125i
$982$	24.4175	+	14.0974i	0.779193	+	0.449868i
$983$	18.9349	+	10.9321i	0.603930	+	0.348679i	0.770586	−	0.637336i	$-0.219964\pi$
$983$	18.9349	+	10.9321i	0.603930	+	0.348679i	−0.166656	+	0.986015i	$0.553297\pi$
$984$	0.552770	−	0.957426i	0.0176217	−	0.0305216i
$985$	−15.4241	+	17.4436i	−0.491452	+	0.555799i
$986$	11.2750	+	19.5289i	0.359070	+	0.621928i
$987$	12.0769	+	6.97262i	0.384413	+	0.221941i
$988$			22.1016i			0.703145i
$989$	6.37565			0.202734
$990$	−22.1553	−	66.1535i	−0.704140	−	2.10250i
$991$	−30.8070			−0.978617			−0.489309	−	0.872111i	$-0.662751\pi$
$991$	−30.8070			−0.978617			−0.489309	+	0.872111i	$0.662751\pi$
$992$	2.45211	−	1.41573i	0.0778547	−	0.0449494i
$993$			71.0722i			2.25541i
$994$	4.70052	+	8.14155i	0.149092	+	0.258234i
$995$	−2.11479	+	10.4095i	−0.0670434	+	0.330002i
$996$	−10.5745	−	18.3156i	−0.335066	−	0.580352i
$997$	28.0581	+	16.1993i	0.888608	+	0.513038i	0.873487	−	0.486847i	$-0.161853\pi$
$997$	28.0581	+	16.1993i	0.888608	+	0.513038i	0.0151212	+	0.999886i	$0.495187\pi$
$998$		−	30.3127i		−	0.959530i
$999$	−75.1983	+	11.5134i	−2.37917	+	0.364268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.f.269.4	yes	12
5.4	even	2	inner	370.2.n.f.269.3	✓	12
37.26	even	3	inner	370.2.n.f.359.3	yes	12
185.174	even	6	inner	370.2.n.f.359.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.f.269.3	✓	12	5.4	even	2	inner
370.2.n.f.269.4	yes	12	1.1	even	1	trivial
370.2.n.f.359.3	yes	12	37.26	even	3	inner
370.2.n.f.359.4	yes	12	185.174	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-2.73346 + 1.57816i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 + 2.19130i) q^{5} -3.15633 q^{6} +(-1.45071 + 0.837565i) q^{7} +1.00000i q^{8} +(3.48119 - 6.02961i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-2.73346 + 1.57816i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.445186 + 2.19130i) q^{5} -3.15633 q^{6} +(-1.45071 + 0.837565i) q^{7} +1.00000i q^{8} +(3.48119 - 6.02961i) q^{9} +(-1.48119 + 1.67513i) q^{10} -4.48119 q^{11} +(-2.73346 - 1.57816i) q^{12} +(4.18416 - 2.41573i) q^{13} -1.67513 q^{14} +(-2.24133 - 6.69241i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.14878 - 1.24060i) q^{17} +(6.02961 - 3.48119i) q^{18} +(2.28726 + 3.96165i) q^{19} +(-2.12032 + 0.710109i) q^{20} +(2.64363 - 4.57890i) q^{21} +(-3.88083 - 2.24060i) q^{22} -1.67513i q^{23} +(-1.57816 - 2.73346i) q^{24} +(-4.60362 - 1.95108i) q^{25} +4.83146 q^{26} +12.5066i q^{27} +(-1.45071 - 0.837565i) q^{28} -9.08840 q^{29} +(1.40515 - 6.91646i) q^{30} -2.83146 q^{31} +(-0.866025 + 0.500000i) q^{32} +(12.2492 - 7.07205i) q^{33} +(-1.24060 - 2.14878i) q^{34} +(-1.18953 - 3.55181i) q^{35} +6.96239 q^{36} +(0.920588 + 6.01270i) q^{37} +4.57452i q^{38} +(-7.62482 + 13.2066i) q^{39} +(-2.19130 - 0.445186i) q^{40} +(0.175131 + 0.303336i) q^{41} +(4.57890 - 2.64363i) q^{42} +3.80606i q^{43} +(-2.24060 - 3.88083i) q^{44} +(11.6629 + 10.3127i) q^{45} +(0.837565 - 1.45071i) q^{46} +2.63752i q^{47} -3.15633i q^{48} +(-2.09697 + 3.63206i) q^{49} +(-3.01131 - 3.99149i) q^{50} +7.83146 q^{51} +(4.18416 + 2.41573i) q^{52} +(4.04878 + 2.33757i) q^{53} +(-6.25329 + 10.8310i) q^{54} +(1.99497 - 9.81965i) q^{55} +(-0.837565 - 1.45071i) q^{56} +(-12.5042 - 7.21933i) q^{57} +(-7.87078 - 4.54420i) q^{58} +(4.91573 - 8.51429i) q^{59} +(4.67513 - 5.28726i) q^{60} +(6.83146 + 11.8324i) q^{61} +(-2.45211 - 1.41573i) q^{62} +11.6629i q^{63} -1.00000 q^{64} +(3.43086 + 10.2442i) q^{65} +14.1441 q^{66} +(-10.8636 + 6.27210i) q^{67} -2.48119i q^{68} +(2.64363 + 4.57890i) q^{69} +(0.745746 - 3.67072i) q^{70} +(-2.80606 - 4.86024i) q^{71} +(6.02961 + 3.48119i) q^{72} -7.13093i q^{73} +(-2.20910 + 5.66744i) q^{74} +(15.6629 - 1.93207i) q^{75} +(-2.28726 + 3.96165i) q^{76} +(6.50089 - 3.75329i) q^{77} +(-13.2066 + 7.62482i) q^{78} +(5.04055 + 8.73049i) q^{79} +(-1.67513 - 1.48119i) q^{80} +(-9.29384 - 16.0974i) q^{81} +0.350262i q^{82} +(5.80282 + 3.35026i) q^{83} +5.28726 q^{84} +(3.67513 - 4.15633i) q^{85} +(-1.90303 + 3.29615i) q^{86} +(24.8427 - 14.3430i) q^{87} -4.48119i q^{88} +(-5.27210 + 9.13154i) q^{89} +(4.94405 + 14.7625i) q^{90} +(-4.04666 + 7.00902i) q^{91} +(1.45071 - 0.837565i) q^{92} +(7.73967 - 4.46850i) q^{93} +(-1.31876 + 2.28416i) q^{94} +(-9.69942 + 3.24840i) q^{95} +(1.57816 - 2.73346i) q^{96} +8.18664i q^{97} +(-3.63206 + 2.09697i) q^{98} +(-15.5999 + 27.0198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9	\( 12 q + 6 q^{4} + 4 q^{6} + 20 q^{9} + 4 q^{10} - 32 q^{11} + 18 q^{15} - 6 q^{16} + 4 q^{19} + 20 q^{21} + 2 q^{24} - 2 q^{25} - 4 q^{26} - 32 q^{29} - 20 q^{30} + 28 q^{31} - 4 q^{34} + 4 q^{35} + 40 q^{36} - 58 q^{39} + 2 q^{40} - 18 q^{41} - 16 q^{44} + 16 q^{45} - 26 q^{49} - 8 q^{50} + 32 q^{51} - 34 q^{54} - 4 q^{55} + 28 q^{59} + 36 q^{60} + 20 q^{61} - 12 q^{64} - 22 q^{65} + 24 q^{66} + 20 q^{69} - 16 q^{70} - 32 q^{71} - 24 q^{74} + 64 q^{75} - 4 q^{76} - 4 q^{79} - 6 q^{81} + 40 q^{84} + 24 q^{85} - 22 q^{86} - 44 q^{89} - 20 q^{90} - 36 q^{91} + 16 q^{94} + 16 q^{95} - 2 q^{96} - 80 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 4 * q^6 + 20 * q^9 + 4 * q^10 - 32 * q^11 + 18 * q^15 - 6 * q^16 + 4 * q^19 + 20 * q^21 + 2 * q^24 - 2 * q^25 - 4 * q^26 - 32 * q^29 - 20 * q^30 + 28 * q^31 - 4 * q^34 + 4 * q^35 + 40 * q^36 - 58 * q^39 + 2 * q^40 - 18 * q^41 - 16 * q^44 + 16 * q^45 - 26 * q^49 - 8 * q^50 + 32 * q^51 - 34 * q^54 - 4 * q^55 + 28 * q^59 + 36 * q^60 + 20 * q^61 - 12 * q^64 - 22 * q^65 + 24 * q^66 + 20 * q^69 - 16 * q^70 - 32 * q^71 - 24 * q^74 + 64 * q^75 - 4 * q^76 - 4 * q^79 - 6 * q^81 + 40 * q^84 + 24 * q^85 - 22 * q^86 - 44 * q^89 - 20 * q^90 - 36 * q^91 + 16 * q^94 + 16 * q^95 - 2 * q^96 - 80 * q^99

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