LMFDB - Embedded newform 370.2.n.f.359.4

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			359.4
Root			$-0.147520 - 0.550552i$ of defining polynomial
Character	$\chi$	$=$	370.359
Dual form			370.2.n.f.269.4

$q$-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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

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	−0.995116	−	0.0987140i	$-0.968527\pi$
$3$	−2.73346	−	1.57816i	−1.57816	−	0.911153i	−0.583047	−	0.812439i	$-0.698140\pi$
$4$	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	0.200127	−	0.979770i	$-0.435865\pi$
$7$	−1.45071	−	0.837565i	−0.548315	−	0.316570i	−0.748442	+	0.663200i	$0.769198\pi$
$8$		−	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	0.951419	−	0.307900i	$-0.0996264\pi$
$13$	4.18416	+	2.41573i	1.16048	+	0.670002i	0.209060	+	0.977903i	$0.432960\pi$
$14$	−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	−0.737407	−	0.675449i	$-0.763950\pi$
$17$	−2.14878	+	1.24060i	−0.521155	+	0.300889i	0.216252	+	0.976338i	$0.430617\pi$
$18$	6.02961	+	3.48119i	1.42119	+	0.820525i
$19$	2.28726	−	3.96165i	0.524733	−	0.908864i	−0.474852	−	0.880065i	$-0.657499\pi$
$19$	2.28726	−	3.96165i	0.524733	−	0.908864i	0.999585	−	0.0287986i	$-0.00916814\pi$
$20$	−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	$0.0558776\pi$
$23$			1.67513i			0.349289i	−0.984632	+	0.174644i	$0.944122\pi$
$24$	−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	−0.852026	−	0.523499i	$-0.824626\pi$
$41$	0.175131	−	0.303336i	0.0273508	−	0.0473731i	0.879377	+	0.476126i	$0.157960\pi$
$42$	4.57890	+	2.64363i	0.706540	+	0.407921i
$43$		−	3.80606i		−	0.580419i	−0.956963	−	0.290210i	$-0.906275\pi$
$43$		−	3.80606i		−	0.580419i	0.956963	−	0.290210i	$-0.0937250\pi$
$44$	−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	$-0.938386\pi$
$47$		−	2.63752i		−	0.384722i	0.981324	−	0.192361i	$-0.0616144\pi$
$48$			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	−0.195453	−	0.980713i	$-0.562618\pi$
$53$	4.04878	−	2.33757i	0.556143	−	0.321089i	0.751596	+	0.659624i	$0.229284\pi$
$54$	−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	0.985438	+	0.170035i	$0.0543879\pi$
$59$	4.91573	+	8.51429i	0.639973	+	1.10847i	−0.345465	+	0.938432i	$0.612279\pi$
$60$	4.67513	+	5.28726i	0.603557	+	0.682582i
$61$	6.83146	−	11.8324i	0.874678	−	1.51499i	0.0175733	−	0.999846i	$-0.494406\pi$
$61$	6.83146	−	11.8324i	0.874678	−	1.51499i	0.857105	−	0.515142i	$-0.172261\pi$
$62$	−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	−0.342334	−	0.939578i	$-0.611217\pi$
$67$	−10.8636	−	6.27210i	−1.32720	−	0.766259i	−0.984866	+	0.173320i	$0.944551\pi$
$68$			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	−0.983102	−	0.183058i	$-0.941400\pi$
$71$	−2.80606	+	4.86024i	−0.333018	+	0.576805i	0.650084	+	0.759863i	$0.274734\pi$
$72$	6.02961	−	3.48119i	0.710596	−	0.410263i
$73$			7.13093i			0.834613i	0.908766	+	0.417306i	$0.137026\pi$
$73$			7.13093i			0.834613i	−0.908766	+	0.417306i	$0.862974\pi$
$74$	−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	−0.429744	−	0.902951i	$-0.641396\pi$
$79$	5.04055	−	8.73049i	0.567106	−	0.982257i	0.996850	−	0.0793062i	$-0.0252705\pi$
$80$	−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	−0.146493	−	0.989212i	$-0.546799\pi$
$83$	5.80282	−	3.35026i	0.636943	−	0.367739i	0.783436	+	0.621473i	$0.213465\pi$
$84$	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	−0.997594	−	0.0693336i	$-0.977913\pi$
$89$	−5.27210	−	9.13154i	−0.558841	−	0.967942i	0.438752	−	0.898608i	$-0.355421\pi$
$90$	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	$-0.863567\pi$
$97$		−	8.18664i		−	0.831228i	0.909541	−	0.415614i	$-0.136433\pi$
$98$	−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	$0.168494\pi$
$103$			10.2496i			1.00993i	−0.863141	+	0.504964i	$0.831506\pi$
$104$	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	−0.152484	−	0.988306i	$-0.548727\pi$
$107$	−11.2194	−	6.47755i	−1.08462	−	0.626208i	−0.932140	+	0.362098i	$0.882061\pi$
$108$	−10.8310	−	6.25329i	−1.04222	−	0.601723i
$109$	9.92478	+	17.1902i	0.950621	+	1.64652i	0.744085	+	0.668085i	$0.232886\pi$
$109$	9.92478	+	17.1902i	0.950621	+	1.64652i	0.206537	+	0.978439i	$0.433781\pi$
$110$	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	−0.660750	−	0.750606i	$-0.729762\pi$
$113$	−3.62574	+	2.09332i	−0.341081	+	0.196923i	0.319669	+	0.947529i	$0.396428\pi$
$114$	−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	−0.913015	−	0.407926i	$-0.866252\pi$
$127$	−11.4525	+	6.61213i	−1.01625	+	0.586731i	−0.103233	+	0.994657i	$0.532919\pi$
$128$	−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	0.893013	−	0.450031i	$-0.148587\pi$
$131$	0.649738	+	1.12538i	0.0567679	+	0.0983249i	−0.836245	+	0.548356i	$0.815254\pi$
$132$	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	$-0.930709\pi$
$137$		−	5.05571i		−	0.431938i	0.976400	−	0.215969i	$-0.0692911\pi$
$138$		−	5.28726i		−	0.450081i
$139$	−0.565466	−	0.979416i	−0.0479622	−	0.0830730i	0.841048	−	0.540961i	$-0.181939\pi$
$139$	−0.565466	−	0.979416i	−0.0479622	−	0.0830730i	−0.889010	+	0.457888i	$0.848606\pi$
$140$	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	−0.457649	−	0.889133i	$-0.651308\pi$
$151$	6.65022	−	11.5185i	0.541187	−	0.937363i	0.998836	−	0.0482304i	$-0.0153582\pi$
$152$	−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	0.0829621	−	0.996553i	$-0.473562\pi$
$157$	12.3731	−	7.14363i	0.987483	−	0.570124i	0.904521	+	0.426429i	$0.140229\pi$
$158$		−	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	−0.123767	−	0.992311i	$-0.539498\pi$
$163$	8.60143	−	4.96604i	0.673716	−	0.388970i	0.797483	+	0.603341i	$0.206164\pi$
$164$	−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	0.897464	−	0.441087i	$-0.145407\pi$
$167$	12.4603	+	7.19394i	0.964204	+	0.556684i	0.0667397	+	0.997770i	$0.478740\pi$
$168$	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	0.110127	−	0.993918i	$-0.464874\pi$
$173$	13.4942	−	7.79090i	1.02595	−	0.592332i	0.915821	+	0.401586i	$0.131541\pi$
$174$	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	−0.245454	−	0.969408i	$-0.578937\pi$
$181$	9.64363	−	16.7033i	0.716805	−	1.24154i	0.962259	−	0.272135i	$-0.0877297\pi$
$182$	−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	$0.0984444\pi$
$193$			8.45676i			0.608731i	−0.952555	+	0.304365i	$0.901556\pi$
$194$	−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	−0.143067	−	0.989713i	$-0.545696\pi$
$197$	9.01815	−	5.20663i	0.642517	−	0.370957i	0.785583	+	0.618756i	$0.212363\pi$
$198$	−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	$0.0297569\pi$
$223$			2.78797i			0.186696i	−0.995634	+	0.0933480i	$0.970243\pi$
$224$	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	−0.257955	−	0.966157i	$-0.583049\pi$
$227$	−18.4361	−	10.6441i	−1.22365	−	0.706474i	−0.965694	+	0.259683i	$0.916382\pi$
$228$			14.4387i			0.956224i
$229$	−5.30654	+	9.19120i	−0.350666	+	0.607371i	−0.986366	−	0.164565i	$-0.947378\pi$
$229$	−5.30654	+	9.19120i	−0.350666	+	0.607371i	0.635700	+	0.771936i	$0.280711\pi$
$230$	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	$-0.800799\pi$
$233$		−	17.8822i		−	1.17150i	0.810490	−	0.585752i	$-0.199201\pi$
$234$	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	0.939985	−	0.341215i	$-0.110838\pi$
$239$	2.69758	+	4.67235i	0.174492	+	0.302229i	−0.765493	+	0.643444i	$0.777505\pi$
$240$	6.91646	−	1.40515i	0.446456	−	0.0907023i
$241$	−1.06300	+	1.84118i	−0.0684741	+	0.118601i	−0.898230	−	0.439526i	$-0.855146\pi$
$241$	−1.06300	+	1.84118i	−0.0684741	+	0.118601i	0.829756	+	0.558127i	$0.188480\pi$
$242$	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	−0.332631	−	0.943057i	$-0.607936\pi$
$257$	5.09417	−	2.94112i	0.317766	−	0.183462i	0.650396	+	0.759595i	$0.274603\pi$
$258$			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	0.436638	−	0.899637i	$-0.356169\pi$
$263$	−2.01340	−	1.16243i	−0.124151	−	0.0716788i	−0.560790	+	0.827958i	$0.689502\pi$
$264$	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	0.999983	+	0.00590727i	$0.00188035\pi$
$271$	8.31511	+	14.4022i	0.505107	+	0.874871i	−0.494875	+	0.868964i	$0.664786\pi$
$272$	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	0.315293	−	0.948994i	$-0.397897\pi$
$277$	−5.80709	−	3.35272i	−0.348914	−	0.201446i	−0.664207	+	0.747549i	$0.731231\pi$
$278$	−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	−0.997220	−	0.0745120i	$-0.976260\pi$
$281$	−9.43994	−	16.3504i	−0.563139	−	0.975386i	0.434081	−	0.900874i	$-0.357073\pi$
$282$			8.32487i			0.495739i
$283$	27.7293	+	16.0095i	1.64834	+	0.951668i	0.977733	+	0.209851i	$0.0672980\pi$
$283$	27.7293	+	16.0095i	1.64834	+	0.951668i	0.670603	+	0.741816i	$0.266035\pi$
$284$	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	0.0672888	−	0.997734i	$-0.478565\pi$
$293$	−13.0627	−	7.54174i	−0.763129	−	0.440593i	−0.830418	+	0.557141i	$0.811898\pi$
$294$	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	$-0.674329\pi$
$307$		−	29.9175i		−	1.70748i	0.520699	−	0.853740i	$-0.325671\pi$
$308$	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	−0.932332	−	0.361605i	$-0.882229\pi$
$311$	−13.7435	−	23.8045i	−0.779324	−	1.34983i	0.153007	−	0.988225i	$-0.451104\pi$
$312$	−13.2066	+	7.62482i	−0.747675	+	0.431671i
$313$	18.5864	−	10.7308i	1.05056	−	0.606543i	0.127756	−	0.991806i	$-0.459222\pi$
$313$	18.5864	−	10.7308i	1.05056	−	0.606543i	0.922807	+	0.385263i	$0.125889\pi$
$314$	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	−0.956896	−	0.290431i	$-0.906201\pi$
$317$	−21.0774	+	12.1690i	−1.18382	+	0.683480i	−0.226927	+	0.973912i	$0.572868\pi$
$318$	−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	0.989699	+	0.143165i	$0.0457279\pi$
$331$	11.2587	+	19.5006i	0.618834	+	1.07185i	−0.370865	+	0.928687i	$0.620939\pi$
$332$		−	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	0.871158	−	0.491002i	$-0.163369\pi$
$337$	16.1825	+	9.34297i	0.881517	+	0.508944i	0.0103585	+	0.999946i	$0.496703\pi$
$338$	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	$0.0512251\pi$
$347$			5.96968i			0.320469i	−0.987079	+	0.160235i	$0.948775\pi$
$348$	24.8427	−	14.3430i	1.33171	−	0.768864i
$349$	−11.0508	−	19.1405i	−0.591535	−	1.02457i	−0.994026	−	0.109145i	$-0.965189\pi$
$349$	−11.0508	−	19.1405i	−0.591535	−	1.02457i	0.402491	−	0.915424i	$-0.368145\pi$
$350$	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	0.0872191	−	0.996189i	$-0.472202\pi$
$353$	18.6672	−	10.7775i	0.993554	−	0.573629i	0.906335	+	0.422561i	$0.138869\pi$
$354$	−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	0.214277	−	0.976773i	$-0.431260\pi$
$367$	−10.0479	−	5.80114i	−0.524494	−	0.302817i	−0.738772	+	0.673956i	$0.764594\pi$
$368$	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	−0.186908	−	0.982377i	$-0.559847\pi$
$373$	−21.8457	−	12.6126i	−1.13113	−	0.653056i	−0.944218	+	0.329321i	$0.893180\pi$
$374$	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	0.985051	−	0.172261i	$-0.0551072\pi$
$379$	6.68418	+	11.5773i	0.343343	+	0.594688i	−0.641708	+	0.766949i	$0.721774\pi$
$380$	−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	0.671299	−	0.741187i	$-0.265737\pi$
$383$	7.14440	+	4.12482i	0.365062	+	0.210769i	−0.306237	+	0.951955i	$0.599070\pi$
$384$	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	−0.794139	−	0.607736i	$-0.792078\pi$
$389$	2.54912	−	4.41521i	0.129246	−	0.223860i	0.923385	+	0.383876i	$0.125411\pi$
$390$	−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	$-0.833514\pi$
$397$		−	19.9053i		−	0.999017i	0.866309	−	0.499508i	$-0.166486\pi$
$398$	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	0.943184	+	0.332271i	$0.107815\pi$
$409$	15.3568	+	26.5988i	0.759347	+	1.31523i	−0.183837	+	0.982957i	$0.558852\pi$
$410$	−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	0.774772	−	0.632241i	$-0.217865\pi$
$419$	−3.27821	−	5.67802i	−0.160151	−	0.277390i	−0.934923	+	0.354851i	$0.884531\pi$
$420$	−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	0.0331813	+	0.999449i	$0.489436\pi$
$431$	−17.6248	+	30.5271i	−0.848958	+	1.47044i	−0.882139	+	0.470989i	$0.843897\pi$
$432$	−10.8310	+	6.25329i	−0.521108	+	0.300862i
$433$			3.92478i			0.188613i	0.995543	+	0.0943064i	$0.0300633\pi$
$433$			3.92478i			0.188613i	−0.995543	+	0.0943064i	$0.969937\pi$
$434$	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	−0.956262	−	0.292511i	$-0.905509\pi$
$439$	−4.71028	+	8.15844i	−0.224809	+	0.389381i	0.731453	+	0.681892i	$0.238843\pi$
$440$	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	$0.192539\pi$
$443$			23.9380i			1.13733i	−0.822570	+	0.568663i	$0.807461\pi$
$444$	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	−0.257128	−	0.966377i	$-0.582776\pi$
$449$	15.0095	−	25.9973i	0.708343	−	1.22689i	0.965471	−	0.260509i	$-0.0838905\pi$
$450$	−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	0.919031	−	0.394185i	$-0.128973\pi$
$457$	22.1722	+	12.8011i	1.03717	+	0.598812i	0.118142	+	0.992997i	$0.462306\pi$
$458$			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	0.821224	−	0.570606i	$-0.193292\pi$
$461$	−1.79384	−	3.10703i	−0.0835477	−	0.144709i	−0.904771	+	0.425897i	$0.859958\pi$
$462$	−20.5189	−	11.8466i	−0.954627	−	0.551154i
$463$	−18.5212	−	10.6932i	−0.860754	−	0.496957i	0.00351076	−	0.999994i	$-0.498882\pi$
$463$	−18.5212	−	10.6932i	−0.860754	−	0.496957i	−0.864265	+	0.503037i	$0.832216\pi$
$464$	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	$-0.908380\pi$
$467$		−	12.2692i		−	0.567749i	0.958861	−	0.283874i	$-0.0916199\pi$
$468$	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	0.634745	−	0.772722i	$-0.281105\pi$
$479$	−7.70005	−	13.3369i	−0.351824	−	0.609377i	−0.986569	+	0.163344i	$0.947772\pi$
$480$	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	$0.0174912\pi$
$487$			2.42407i			0.109845i	−0.998491	+	0.0549225i	$0.982509\pi$
$488$	−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	0.296945	+	0.954895i	$0.404032\pi$
$499$	−15.1563	+	26.2515i	−0.678490	+	1.17518i	−0.975436	+	0.220285i	$0.929301\pi$
$500$	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	−0.298686	−	0.954351i	$-0.596548\pi$
$503$	8.48804	−	4.90057i	0.378463	−	0.218506i	0.677149	+	0.735846i	$0.263215\pi$
$504$	−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	0.748513	−	0.663120i	$-0.230768\pi$
$509$	−4.51270	−	7.81622i	−0.200022	−	0.346448i	−0.948535	+	0.316672i	$0.897435\pi$
$510$	−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	−0.887173	−	0.461437i	$-0.847334\pi$
$521$	−1.00365	+	1.73837i	−0.0439706	+	0.0761593i	0.843203	+	0.537596i	$0.180667\pi$
$522$	−54.7994	−	31.6385i	−2.39851	−	1.38478i
$523$	−11.8862	−	6.86248i	−0.519746	−	0.300075i	0.217085	−	0.976153i	$-0.430345\pi$
$523$	−11.8862	−	6.86248i	−0.519746	−	0.300075i	−0.736831	+	0.676077i	$0.763678\pi$
$524$	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	$-0.884063\pi$
$547$		−	16.6629i		−	0.712455i	0.934399	−	0.356227i	$-0.115937\pi$
$548$	−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	−0.315734	−	0.948848i	$-0.602251\pi$
$557$	8.21605	−	4.74354i	0.348125	−	0.200990i	0.663859	+	0.747858i	$0.268917\pi$
$558$	−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	$-0.871838\pi$
$563$		−	18.5950i		−	0.783685i	0.920032	−	0.391843i	$-0.128162\pi$
$564$	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	0.991850	+	0.127410i	$0.0406663\pi$
$571$	14.4871	+	25.0923i	0.606265	+	1.05008i	−0.385585	+	0.922672i	$0.626000\pi$
$572$	−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	−0.981922	−	0.189287i	$-0.939382\pi$
$577$	−31.4422	+	18.1532i	−1.30896	+	0.755726i	−0.327034	+	0.945013i	$0.606049\pi$
$578$			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	0.742788	−	0.669527i	$-0.233503\pi$
$587$	12.9464	+	7.47461i	0.534355	+	0.308510i	−0.208433	+	0.978037i	$0.566836\pi$
$588$	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	$0.146927\pi$
$593$			21.6909i			0.890737i	−0.895347	+	0.445368i	$0.853073\pi$
$594$	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	−0.535481	−	0.844547i	$-0.679870\pi$
$599$	11.3478	−	19.6550i	0.463659	−	0.803080i	0.999140	+	0.0414669i	$0.0132031\pi$
$600$	1.93207	−	15.6629i	0.0788765	−	0.639436i
$601$	−8.72956	−	15.1200i	−0.356086	−	0.616760i	0.631217	−	0.775606i	$-0.282556\pi$
$601$	−8.72956	−	15.1200i	−0.356086	−	0.616760i	−0.987303	+	0.158847i	$0.949222\pi$
$602$			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	−0.331927	−	0.943305i	$-0.607699\pi$
$607$	7.86020	−	4.53809i	0.319036	−	0.184195i	0.650963	+	0.759110i	$0.274365\pi$
$608$	−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	−0.538712	+	0.842490i	$0.681089\pi$
$613$	−38.0713	+	21.9805i	−1.53769	+	0.887784i	−0.998974	+	0.0452938i	$0.985578\pi$
$614$	−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	−0.970495	−	0.241122i	$-0.922484\pi$
$617$	−30.9730	+	17.8822i	−1.24692	+	0.719912i	−0.276429	+	0.961034i	$0.589151\pi$
$618$		−	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	−0.887898	−	0.460041i	$-0.847835\pi$
$631$	−21.1597	−	36.6497i	−0.842356	−	1.45900i	0.0455416	−	0.998962i	$-0.485499\pi$
$632$	−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	0.999123	+	0.0418706i	$0.0133317\pi$
$641$	13.5659	+	23.4969i	0.535823	+	0.928072i	−0.463300	+	0.886201i	$0.653335\pi$
$642$	35.4122	+	20.4452i	1.39761	+	0.806909i
$643$		−	21.5745i		−	0.850816i	−0.905002	−	0.425408i	$-0.860131\pi$
$643$		−	21.5745i		−	0.850816i	0.905002	−	0.425408i	$-0.139869\pi$
$644$	−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	0.714737	−	0.699393i	$-0.246546\pi$
$647$	11.8638	+	6.84955i	0.466413	+	0.269284i	−0.248324	+	0.968677i	$0.579880\pi$
$648$	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	0.355291	−	0.934756i	$-0.384382\pi$
$653$	−7.06785	−	4.08062i	−0.276586	−	0.159687i	−0.631877	+	0.775069i	$0.717715\pi$
$654$	−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	−0.807640	−	0.589676i	$-0.799255\pi$
$659$	2.74306	−	4.75112i	0.106854	−	0.185077i	0.914494	+	0.404599i	$0.132589\pi$
$660$	−20.9502	−	23.6932i	−0.815484	−	0.922258i
$661$	−3.31147	+	5.73563i	−0.128801	+	0.223090i	−0.923212	−	0.384290i	$-0.874446\pi$
$661$	−3.31147	+	5.73563i	−0.128801	+	0.223090i	0.794411	+	0.607380i	$0.207780\pi$
$662$	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	0.650249	−	0.759721i	$-0.274665\pi$
$673$	8.23500	+	4.75448i	0.317436	+	0.183272i	−0.332813	+	0.942993i	$0.607998\pi$
$674$	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	$0.181213\pi$
$677$			28.0508i			1.07808i	−0.842280	+	0.539040i	$0.818787\pi$
$678$	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	−0.941811	−	0.336144i	$-0.890877\pi$
$683$	−29.3124	+	16.9235i	−1.12161	+	0.647560i	−0.179796	+	0.983704i	$0.557544\pi$
$684$	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	−0.999940	−	0.0109530i	$-0.996513\pi$
$691$	−13.3920	−	23.1956i	−0.509456	−	0.882403i	0.490484	−	0.871450i	$-0.336820\pi$
$692$		−	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	0.648723	−	0.761024i	$-0.275303\pi$
$701$	−8.86177	−	15.3490i	−0.334705	−	0.579725i	−0.983428	+	0.181299i	$0.941970\pi$
$702$		−	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	0.658062	−	0.752963i	$-0.271376\pi$
$719$	−8.66243	−	15.0038i	−0.323054	−	0.559546i	−0.981117	+	0.193417i	$0.938043\pi$
$720$	−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	0.630814	−	0.775934i	$-0.282721\pi$
$727$	7.39440	+	4.26916i	0.274243	+	0.158334i	−0.356571	+	0.934268i	$0.616054\pi$
$728$	−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	0.686542	−	0.727090i	$-0.259128\pi$
$733$	10.8332	+	6.25457i	0.400135	+	0.231018i	−0.286407	+	0.958108i	$0.592461\pi$
$734$	−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	0.630687	−	0.776037i	$-0.282773\pi$
$743$	7.46768	+	4.31147i	0.273963	+	0.158172i	−0.356725	+	0.934210i	$0.616107\pi$
$744$	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	−0.855357	−	0.518038i	$-0.826663\pi$
$757$	−22.9574	+	13.2545i	−0.834402	+	0.481742i	0.0209555	+	0.999780i	$0.493329\pi$
$758$	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	0.988687	−	0.149991i	$-0.0479246\pi$
$761$	10.0537	+	17.4136i	0.364447	+	0.631241i	−0.624240	+	0.781233i	$0.714591\pi$
$762$	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	0.316752	−	0.948508i	$-0.397408\pi$
$773$	−9.62826	−	5.55888i	−0.346304	−	0.199939i	−0.663056	+	0.748569i	$0.730741\pi$
$774$	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	$0.287664\pi$
$787$			44.0797i			1.57127i	−0.618690	+	0.785636i	$0.712336\pi$
$788$		−	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	−0.900434	−	0.434992i	$-0.856751\pi$
$797$	−27.4954	+	15.8745i	−0.973937	+	0.562303i	−0.0735025	+	0.997295i	$0.523418\pi$
$798$	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	−0.363922	−	0.931429i	$-0.618562\pi$
$809$	17.7677	−	30.7746i	0.624681	−	1.08198i	0.988603	−	0.150549i	$-0.0481042\pi$
$810$	40.7313	−	8.27499i	1.43115	−	0.290753i
$811$	8.20711	−	14.2151i	0.288191	−	0.499161i	−0.685187	−	0.728367i	$-0.740280\pi$
$811$	8.20711	−	14.2151i	0.288191	−	0.499161i	0.973378	+	0.229206i	$0.0736130\pi$
$812$	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	−0.988295	−	0.152556i	$-0.951250\pi$
$821$	−10.3733	+	17.9671i	−0.362030	+	0.627055i	0.626265	+	0.779610i	$0.284583\pi$
$822$			15.9575i			0.556580i
$823$	1.88311	−	1.08721i	0.0656410	−	0.0378978i	−0.466820	−	0.884352i	$-0.654601\pi$
$823$	1.88311	−	1.08721i	0.0656410	−	0.0378978i	0.532461	+	0.846454i	$0.321267\pi$
$824$	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	0.299496	−	0.954097i	$-0.403181\pi$
$827$	−10.8424	−	6.25988i	−0.377028	−	0.217677i	−0.676525	+	0.736420i	$0.736515\pi$
$828$			11.6629i			0.405314i
$829$	−6.42430	−	11.1272i	−0.223125	−	0.386464i	0.732630	−	0.680627i	$-0.238293\pi$
$829$	−6.42430	−	11.1272i	−0.223125	−	0.386464i	−0.955755	+	0.294163i	$0.904959\pi$
$830$	−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	0.997302	−	0.0734032i	$-0.0233860\pi$
$839$	12.6024	+	21.8279i	0.435082	+	0.753584i	−0.562220	+	0.826988i	$0.690053\pi$
$840$	−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	−0.254488	−	0.967076i	$-0.581907\pi$
$853$	13.3116	−	7.68546i	0.455781	−	0.263145i	0.710268	+	0.703931i	$0.248574\pi$
$854$	−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	$0.209295\pi$
$857$			35.7826i			1.22231i	−0.791511	+	0.611155i	$0.790705\pi$
$858$	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	0.138955	−	0.990299i	$-0.455626\pi$
$863$	31.3174	−	18.0811i	1.06606	−	0.615488i	0.927101	+	0.374811i	$0.122292\pi$
$864$	−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	$-0.986076\pi$
$877$		−	2.59006i		−	0.0874601i	0.999043	−	0.0437300i	$-0.0139241\pi$
$878$			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	−0.886186	−	0.463331i	$-0.846654\pi$
$881$	−1.24178	+	2.15083i	−0.0418367	+	0.0724633i	0.844349	+	0.535794i	$0.179988\pi$
$882$		−	29.1998i		−	0.983209i
$883$	30.8313	+	17.8004i	1.03755	+	0.599032i	0.919140	−	0.393932i	$-0.128885\pi$
$883$	30.8313	+	17.8004i	1.03755	+	0.599032i	0.118415	+	0.992964i	$0.462219\pi$
$884$	−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	$-0.914886\pi$
$887$		−	15.7381i		−	0.528435i	0.964463	−	0.264217i	$-0.0851137\pi$
$888$	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	0.687222	−	0.726448i	$-0.258830\pi$
$907$	12.0981	+	6.98484i	0.401711	+	0.231928i	−0.285511	+	0.958375i	$0.592163\pi$
$908$	−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	−0.595848	−	0.803097i	$-0.703184\pi$
$929$	12.1180	−	20.9890i	0.397579	−	0.688627i	0.993427	+	0.114471i	$0.0365172\pi$
$930$	−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	−0.718170	−	0.695868i	$-0.755020\pi$
$937$	−14.5282	+	8.38787i	−0.474616	+	0.274020i	0.243554	+	0.969887i	$0.421687\pi$
$938$	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	0.928416	−	0.371542i	$-0.121171\pi$
$941$	4.36954	+	7.56827i	0.142443	+	0.246719i	−0.785973	+	0.618261i	$0.787838\pi$
$942$	−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	−0.724195	−	0.689595i	$-0.757788\pi$
$947$	−15.0508	+	8.68958i	−0.489085	+	0.282373i	0.235110	+	0.971969i	$0.424455\pi$
$948$			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	0.212034	−	0.977262i	$-0.431991\pi$
$953$	35.9454	−	20.7531i	1.16438	−	0.672258i	0.952351	+	0.305005i	$0.0986580\pi$
$954$	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	0.322873	−	0.946442i	$-0.395351\pi$
$967$	−10.4278	−	6.02047i	−0.335334	−	0.193605i	−0.658207	+	0.752837i	$0.728685\pi$
$968$		−	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	−0.935539	−	0.353224i	$-0.885085\pi$
$971$	−24.1082	−	41.7567i	−0.773671	−	1.34004i	0.161868	−	0.986812i	$-0.448248\pi$
$972$		−	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	0.496893	−	0.867812i	$-0.334474\pi$
$977$	46.7882	−	27.0132i	1.49689	−	0.864228i	0.999994	+	0.00358369i	$0.00114073\pi$
$978$	−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	−0.166656	−	0.986015i	$-0.553297\pi$
$983$	18.9349	−	10.9321i	0.603930	−	0.348679i	0.770586	+	0.637336i	$0.219964\pi$
$984$	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	0.0151212	−	0.999886i	$-0.495187\pi$
$997$	28.0581	−	16.1993i	0.888608	−	0.513038i	0.873487	+	0.486847i	$0.161853\pi$
$998$			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.359.4	yes	12
5.4	even	2	inner	370.2.n.f.359.3	yes	12
37.10	even	3	inner	370.2.n.f.269.3	✓	12
185.84	even	6	inner	370.2.n.f.269.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.f.269.3	✓	12	37.10	even	3	inner
370.2.n.f.269.4	yes	12	185.84	even	6	inner
370.2.n.f.359.3	yes	12	5.4	even	2	inner
370.2.n.f.359.4	yes	12	1.1	even	1	trivial

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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