LMFDB - Embedded newform 525.2.n.b.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 31 x^{18} - 74 x^{17} + 109 x^{16} - 72 x^{15} - 51 x^{14} + 9 x^{13} + 866 x^{12} + \cdots + 3125 $ x^20 - 8x^19 + 31x^18 - 74x^17 + 109x^16 - 72x^15 - 51x^14 + 9x^13 + 866x^12 - 3240x^11 + 6385x^10 - 6775x^9 + 330x^8 + 11325x^7 - 18525x^6 + 12000x^5 + 5875x^4 - 21250x^3 + 22500x^2 - 12500*x + 3125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			316.1
Root			$-1.67866 - 0.894495i$ of defining polynomial
Character	$\chi$	$=$	525.316
Dual form			525.2.n.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02723 - 1.47287i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.32228 + 4.06957i) q^{4} +(2.20175 + 0.390266i) q^{5} +(-0.774332 + 2.38315i) q^{6} -1.00000 q^{7} +(1.76470 - 5.43119i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.02723 - 1.47287i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.32228 + 4.06957i) q^{4} +(2.20175 + 0.390266i) q^{5} +(-0.774332 + 2.38315i) q^{6} -1.00000 q^{7} +(1.76470 - 5.43119i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.88864 - 4.03404i) q^{10} +(1.92222 + 1.39657i) q^{11} +(3.46178 - 2.51513i) q^{12} +(-2.89389 + 2.10254i) q^{13} +(2.02723 + 1.47287i) q^{14} +(-0.309213 - 2.21459i) q^{15} +(-4.65331 + 3.38083i) q^{16} +(0.830504 - 2.55603i) q^{17} +2.50579 q^{18} +(-1.88941 + 5.81501i) q^{19} +(1.32312 + 9.47620i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-1.83981 - 5.66235i) q^{22} +(6.64204 + 4.82572i) q^{23} -5.71069 q^{24} +(4.69539 + 1.71853i) q^{25} +8.96334 q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.32228 - 4.06957i) q^{28} +(1.84399 + 5.67521i) q^{29} +(-2.63495 + 4.94490i) q^{30} +(-0.810665 + 2.49497i) q^{31} +2.99145 q^{32} +(0.734222 - 2.25970i) q^{33} +(-5.44831 + 3.95843i) q^{34} +(-2.20175 - 0.390266i) q^{35} +(-3.46178 - 2.51513i) q^{36} +(1.65989 - 1.20598i) q^{37} +(12.3950 - 9.00550i) q^{38} +(2.89389 + 2.10254i) q^{39} +(6.00503 - 11.2694i) q^{40} +(2.42962 - 1.76522i) q^{41} +(0.774332 - 2.38315i) q^{42} -1.78185 q^{43} +(-3.14173 + 9.66926i) q^{44} +(-2.01064 + 0.978423i) q^{45} +(-6.35728 - 19.5657i) q^{46} +(1.12747 + 3.46998i) q^{47} +(4.65331 + 3.38083i) q^{48} +1.00000 q^{49} +(-6.98745 - 10.3995i) q^{50} -2.68757 q^{51} +(-12.3830 - 8.99674i) q^{52} +(-2.83891 - 8.73725i) q^{53} +(-0.774332 - 2.38315i) q^{54} +(3.68721 + 3.82508i) q^{55} +(-1.76470 + 5.43119i) q^{56} +6.11426 q^{57} +(4.62065 - 14.2209i) q^{58} +(12.2973 - 8.93450i) q^{59} +(8.60353 - 4.18667i) q^{60} +(-4.03874 - 2.93432i) q^{61} +(5.31816 - 3.86387i) q^{62} +(0.809017 - 0.587785i) q^{63} +(3.24225 + 2.35564i) q^{64} +(-7.19217 + 3.49987i) q^{65} +(-4.81668 + 3.49952i) q^{66} +(2.07104 - 6.37402i) q^{67} +11.5001 q^{68} +(2.53703 - 7.80818i) q^{69} +(3.88864 + 4.03404i) q^{70} +(-2.49178 - 7.66890i) q^{71} +(1.76470 + 5.43119i) q^{72} +(6.06145 + 4.40390i) q^{73} -5.14121 q^{74} +(0.183468 - 4.99663i) q^{75} -26.1629 q^{76} +(-1.92222 - 1.39657i) q^{77} +(-2.76982 - 8.52464i) q^{78} +(4.93758 + 15.1963i) q^{79} +(-11.5648 + 5.62770i) q^{80} +(0.309017 - 0.951057i) q^{81} -7.52533 q^{82} +(-5.23139 + 16.1006i) q^{83} +(-3.46178 + 2.51513i) q^{84} +(2.82609 - 5.30361i) q^{85} +(3.61221 + 2.62442i) q^{86} +(4.82763 - 3.50748i) q^{87} +(10.9772 - 7.97540i) q^{88} +(-9.43096 - 6.85199i) q^{89} +(5.51712 + 0.977925i) q^{90} +(2.89389 - 2.10254i) q^{91} +(-10.8559 + 33.4112i) q^{92} +2.62337 q^{93} +(2.82519 - 8.69506i) q^{94} +(-6.42941 + 12.0658i) q^{95} +(-0.924410 - 2.84504i) q^{96} +(0.534940 + 1.64638i) q^{97} +(-2.02723 - 1.47287i) q^{98} -2.37599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.02723	−	1.47287i	−1.43347	−	1.04147i	−0.989358	−	0.145502i	$-0.953520\pi$
$2$	−2.02723	−	1.47287i	−1.43347	−	1.04147i	−0.444109	−	0.895973i	$-0.646480\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.32228	+	4.06957i	0.661141	+	2.03478i
$5$	2.20175	+	0.390266i	0.984651	+	0.174532i
$5$	2.20175	+	0.390266i	0.984651	+	0.174532i
$6$	−0.774332	+	2.38315i	−0.316120	+	0.972917i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.76470	−	5.43119i	0.623915	−	1.92021i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−3.88864	−	4.03404i	−1.22969	−	1.27568i
$11$	1.92222	+	1.39657i	0.579571	+	0.421083i	0.838569	−	0.544795i	$-0.183392\pi$
$11$	1.92222	+	1.39657i	0.579571	+	0.421083i	−0.258999	+	0.965878i	$0.583392\pi$
$12$	3.46178	−	2.51513i	0.999330	−	0.726055i
$13$	−2.89389	+	2.10254i	−0.802621	+	0.583139i	−0.911682	−	0.410896i	$-0.865216\pi$
$13$	−2.89389	+	2.10254i	−0.802621	+	0.583139i	0.109061	+	0.994035i	$0.465216\pi$
$14$	2.02723	+	1.47287i	0.541800	+	0.393640i
$15$	−0.309213	−	2.21459i	−0.0798384	−	0.571803i
$16$	−4.65331	+	3.38083i	−1.16333	+	0.845207i
$17$	0.830504	−	2.55603i	0.201427	−	0.619928i	−0.798415	−	0.602108i	$-0.794328\pi$
$17$	0.830504	−	2.55603i	0.201427	−	0.619928i	0.999841	−	0.0178195i	$-0.00567241\pi$
$18$	2.50579			0.590621
$19$	−1.88941	+	5.81501i	−0.433461	+	1.33405i	0.461195	+	0.887299i	$0.347421\pi$
$19$	−1.88941	+	5.81501i	−0.433461	+	1.33405i	−0.894656	+	0.446756i	$0.852579\pi$
$20$	1.32312	+	9.47620i	0.295859	+	2.11894i
$21$	0.309017	+	0.951057i	0.0674330	+	0.207538i
$22$	−1.83981	−	5.66235i	−0.392249	−	1.20722i
$23$	6.64204	+	4.82572i	1.38496	+	1.00623i	0.996397	+	0.0848110i	$0.0270286\pi$
$23$	6.64204	+	4.82572i	1.38496	+	1.00623i	0.388564	+	0.921422i	$0.372971\pi$
$24$	−5.71069			−1.16569
$25$	4.69539	+	1.71853i	0.939077	+	0.343707i
$26$	8.96334			1.75786
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.32228	−	4.06957i	−0.249888	−	0.769076i
$29$	1.84399	+	5.67521i	0.342420	+	1.05386i	0.962950	+	0.269678i	$0.0869174\pi$
$29$	1.84399	+	5.67521i	0.342420	+	1.05386i	−0.620530	+	0.784182i	$0.713083\pi$
$30$	−2.63495	+	4.94490i	−0.481073	+	0.902811i
$31$	−0.810665	+	2.49497i	−0.145600	+	0.448110i	−0.997088	−	0.0762645i	$-0.975701\pi$
$31$	−0.810665	+	2.49497i	−0.145600	+	0.448110i	0.851488	+	0.524374i	$0.175701\pi$
$32$	2.99145			0.528820
$33$	0.734222	−	2.25970i	0.127812	−	0.393364i
$34$	−5.44831	+	3.95843i	−0.934377	+	0.678865i
$35$	−2.20175	−	0.390266i	−0.372163	−	0.0659669i
$36$	−3.46178	−	2.51513i	−0.576963	−	0.419188i
$37$	1.65989	−	1.20598i	0.272884	−	0.198262i	−0.442924	−	0.896559i	$-0.646059\pi$
$37$	1.65989	−	1.20598i	0.272884	−	0.198262i	0.715807	+	0.698298i	$0.246059\pi$
$38$	12.3950	−	9.00550i	2.01074	−	1.46089i
$39$	2.89389	+	2.10254i	0.463394	+	0.336675i
$40$	6.00503	−	11.2694i	0.949478	−	1.78185i
$41$	2.42962	−	1.76522i	0.379443	−	0.275681i	−0.381673	−	0.924297i	$-0.624652\pi$
$41$	2.42962	−	1.76522i	0.379443	−	0.275681i	0.761116	+	0.648616i	$0.224652\pi$
$42$	0.774332	−	2.38315i	0.119482	−	0.367728i
$43$	−1.78185			−0.271729			−0.135864	−	0.990727i	$-0.543381\pi$
$43$	−1.78185			−0.271729			−0.135864	+	0.990727i	$0.543381\pi$
$44$	−3.14173	+	9.66926i	−0.473634	+	1.45770i
$45$	−2.01064	+	0.978423i	−0.299729	+	0.145855i
$46$	−6.35728	−	19.5657i	−0.937329	−	2.88480i
$47$	1.12747	+	3.46998i	0.164458	+	0.506149i	0.998996	−	0.0448012i	$-0.0142654\pi$
$47$	1.12747	+	3.46998i	0.164458	+	0.506149i	−0.834538	+	0.550950i	$0.814265\pi$
$48$	4.65331	+	3.38083i	0.671647	+	0.487980i
$49$	1.00000			0.142857
$50$	−6.98745	−	10.3995i	−0.988174	−	1.47072i
$51$	−2.68757			−0.376334
$52$	−12.3830	−	8.99674i	−1.71721	−	1.24762i
$53$	−2.83891	−	8.73725i	−0.389954	−	1.20015i	−0.932822	−	0.360336i	$-0.882662\pi$
$53$	−2.83891	−	8.73725i	−0.389954	−	1.20015i	0.542869	−	0.839817i	$-0.317338\pi$
$54$	−0.774332	−	2.38315i	−0.105373	−	0.324306i
$55$	3.68721	+	3.82508i	0.497183	+	0.515774i
$56$	−1.76470	+	5.43119i	−0.235818	+	0.725773i
$57$	6.11426			0.809854
$58$	4.62065	−	14.2209i	0.606721	−	1.86730i
$59$	12.2973	−	8.93450i	1.60097	−	1.16317i	0.715346	−	0.698770i	$-0.246269\pi$
$59$	12.2973	−	8.93450i	1.60097	−	1.16317i	0.885624	−	0.464403i	$-0.153731\pi$
$60$	8.60353	−	4.18667i	1.11071	−	0.540496i
$61$	−4.03874	−	2.93432i	−0.517108	−	0.375701i	0.298405	−	0.954439i	$-0.403545\pi$
$61$	−4.03874	−	2.93432i	−0.517108	−	0.375701i	−0.815513	+	0.578738i	$0.803545\pi$
$62$	5.31816	−	3.86387i	0.675407	−	0.490712i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	3.24225	+	2.35564i	0.405282	+	0.294454i
$65$	−7.19217	+	3.49987i	−0.892079	+	0.434105i
$66$	−4.81668	+	3.49952i	−0.592892	+	0.430762i
$67$	2.07104	−	6.37402i	0.253018	−	0.778710i	−0.741195	−	0.671289i	$-0.765741\pi$
$67$	2.07104	−	6.37402i	0.253018	−	0.778710i	0.994214	−	0.107421i	$-0.0342593\pi$
$68$	11.5001			1.39459
$69$	2.53703	−	7.80818i	0.305423	−	0.939995i
$70$	3.88864	+	4.03404i	0.464781	+	0.482160i
$71$	−2.49178	−	7.66890i	−0.295719	−	0.910130i	−0.982979	−	0.183719i	$-0.941187\pi$
$71$	−2.49178	−	7.66890i	−0.295719	−	0.910130i	0.687260	−	0.726412i	$-0.258813\pi$
$72$	1.76470	+	5.43119i	0.207972	+	0.640071i
$73$	6.06145	+	4.40390i	0.709439	+	0.515437i	0.882993	−	0.469387i	$-0.155525\pi$
$73$	6.06145	+	4.40390i	0.709439	+	0.515437i	−0.173554	+	0.984824i	$0.555525\pi$
$74$	−5.14121			−0.597654
$75$	0.183468	−	4.99663i	0.0211851	−	0.576961i
$76$	−26.1629			−3.00109
$77$	−1.92222	−	1.39657i	−0.219057	−	0.159154i
$78$	−2.76982	−	8.52464i	−0.313621	−	0.965226i
$79$	4.93758	+	15.1963i	0.555521	+	1.70972i	0.694562	+	0.719433i	$0.255598\pi$
$79$	4.93758	+	15.1963i	0.555521	+	1.70972i	−0.139041	+	0.990287i	$0.544402\pi$
$80$	−11.5648	+	5.62770i	−1.29299	+	0.629196i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−7.52533			−0.831034
$83$	−5.23139	+	16.1006i	−0.574220	+	1.76727i	0.0646008	+	0.997911i	$0.479423\pi$
$83$	−5.23139	+	16.1006i	−0.574220	+	1.76727i	−0.638821	+	0.769356i	$0.720577\pi$
$84$	−3.46178	+	2.51513i	−0.377711	+	0.274423i
$85$	2.82609	−	5.30361i	0.306532	−	0.575257i
$86$	3.61221	+	2.62442i	0.389514	+	0.282999i
$87$	4.82763	−	3.50748i	0.517576	−	0.376041i
$88$	10.9772	−	7.97540i	1.17017	−	0.850180i
$89$	−9.43096	−	6.85199i	−0.999679	−	0.726309i	−0.0376599	−	0.999291i	$-0.511990\pi$
$89$	−9.43096	−	6.85199i	−0.999679	−	0.726309i	−0.962019	+	0.272981i	$0.911990\pi$
$90$	5.51712	+	0.977925i	0.581556	+	0.103082i
$91$	2.89389	−	2.10254i	0.303362	−	0.220406i
$92$	−10.8559	+	33.4112i	−1.13181	+	3.48336i
$93$	2.62337			0.272030
$94$	2.82519	−	8.69506i	0.291397	−	0.896827i
$95$	−6.42941	+	12.0658i	−0.659643	+	1.23793i
$96$	−0.924410	−	2.84504i	−0.0943472	−	0.290371i
$97$	0.534940	+	1.64638i	0.0543149	+	0.167164i	0.974534	−	0.224239i	$-0.0719897\pi$
$97$	0.534940	+	1.64638i	0.0543149	+	0.167164i	−0.920219	+	0.391403i	$0.871990\pi$
$98$	−2.02723	−	1.47287i	−0.204781	−	0.148782i
$99$	−2.37599			−0.238796
$100$	−0.785059	+	21.3806i	−0.0785059	+	2.13806i
$101$	4.96536			0.494072			0.247036	−	0.969006i	$-0.420543\pi$
$101$	4.96536			0.494072			0.247036	+	0.969006i	$0.420543\pi$
$102$	5.44831	+	3.95843i	0.539463	+	0.391943i
$103$	3.69272	+	11.3650i	0.363855	+	1.11983i	0.950695	+	0.310127i	$0.100372\pi$
$103$	3.69272	+	11.3650i	0.363855	+	1.11983i	−0.586840	+	0.809703i	$0.699628\pi$
$104$	6.31241	+	19.4276i	0.618983	+	1.90503i
$105$	0.309213	+	2.21459i	0.0301761	+	0.216121i
$106$	−7.11371	+	21.8937i	−0.690944	+	2.12651i
$107$	−7.27060			−0.702876			−0.351438	−	0.936211i	$-0.614307\pi$
$107$	−7.27060			−0.702876			−0.351438	+	0.936211i	$0.614307\pi$
$108$	−1.32228	+	4.06957i	−0.127237	+	0.391594i
$109$	8.89067	−	6.45945i	0.851572	−	0.618703i	−0.0740073	−	0.997258i	$-0.523579\pi$
$109$	8.89067	−	6.45945i	0.851572	−	0.618703i	0.925579	+	0.378555i	$0.123579\pi$
$110$	−1.84097	−	13.1851i	−0.175530	−	1.25715i
$111$	−1.65989	−	1.20598i	−0.157549	−	0.114466i
$112$	4.65331	−	3.38083i	0.439696	−	0.319458i
$113$	0.378143	−	0.274737i	0.0355727	−	0.0258451i	−0.569857	−	0.821744i	$-0.693001\pi$
$113$	0.378143	−	0.274737i	0.0355727	−	0.0258451i	0.605430	+	0.795899i	$0.293001\pi$
$114$	−12.3950	−	9.00550i	−1.16090	−	0.843442i
$115$	12.7408	+	13.2172i	1.18808	+	1.23251i
$116$	−20.6574	+	15.0085i	−1.91799	+	1.39350i
$117$	1.10537	−	3.40198i	0.102191	−	0.314513i
$118$	−38.0887			−3.50635
$119$	−0.830504	+	2.55603i	−0.0761321	+	0.234311i
$120$	−12.5735	−	2.22868i	−1.14780	−	0.203450i
$121$	−1.65468	−	5.09258i	−0.150425	−	0.462962i
$122$	3.86559	+	11.8971i	0.349974	+	1.07711i
$123$	−2.42962	−	1.76522i	−0.219071	−	0.159165i
$124$	−11.2254			−1.00807
$125$	9.66737	+	5.61622i	0.864676	+	0.502330i
$126$	−2.50579			−0.223234
$127$	7.47591	+	5.43156i	0.663379	+	0.481973i	0.867803	−	0.496909i	$-0.165532\pi$
$127$	7.47591	+	5.43156i	0.663379	+	0.481973i	−0.204423	+	0.978883i	$0.565532\pi$
$128$	−4.95207	−	15.2409i	−0.437705	−	1.34712i
$129$	0.550620	+	1.69464i	0.0484794	+	0.149204i
$130$	19.7350	+	3.49808i	1.73088	+	0.306802i
$131$	3.10128	−	9.54476i	0.270960	−	0.833929i	−0.719300	−	0.694699i	$-0.755537\pi$
$131$	3.10128	−	9.54476i	0.270960	−	0.833929i	0.990260	−	0.139230i	$-0.0444626\pi$
$132$	10.1669			0.884912
$133$	1.88941	−	5.81501i	0.163833	−	0.504225i
$134$	−13.5866	+	9.87122i	−1.17370	+	0.852744i
$135$	1.55186	+	1.60989i	0.133563	+	0.138557i
$136$	−12.4167	−	9.02124i	−1.06472	−	0.773565i
$137$	15.3181	−	11.1292i	1.30871	−	0.950835i	0.308713	−	0.951155i	$-0.400102\pi$
$137$	15.3181	−	11.1292i	1.30871	−	0.950835i	1.00000		0.000319898i	$0.000101827\pi$
$138$	−16.6436	+	12.0923i	−1.41679	+	1.02936i
$139$	1.34192	+	0.974961i	0.113820	+	0.0826951i	0.643239	−	0.765665i	$-0.277590\pi$
$139$	1.34192	+	0.974961i	0.113820	+	0.0826951i	−0.529419	+	0.848360i	$0.677590\pi$
$140$	−1.32312	−	9.47620i	−0.111824	−	0.800885i
$141$	2.95174	−	2.14457i	0.248582	−	0.180605i
$142$	−6.24387	+	19.2167i	−0.523974	+	1.61263i
$143$	−8.49904			−0.710726
$144$	1.77741	−	5.47029i	0.148117	−	0.455858i
$145$	1.84516	+	13.2150i	0.153232	+	1.09745i
$146$	−5.80158	−	17.8554i	−0.480142	−	1.47772i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	7.10264	+	5.16037i	0.583834	+	0.424180i
$149$	−2.77607			−0.227424			−0.113712	−	0.993514i	$-0.536274\pi$
$149$	−2.77607			−0.227424			−0.113712	+	0.993514i	$0.536274\pi$
$150$	−7.73131	+	9.85909i	−0.631259	+	0.804991i
$151$	−15.9261			−1.29605			−0.648025	−	0.761619i	$-0.724405\pi$
$151$	−15.9261			−1.29605			−0.648025	+	0.761619i	$0.724405\pi$
$152$	28.2482	+	20.5235i	2.29123	+	1.66467i
$153$	0.830504	+	2.55603i	0.0671422	+	0.206643i
$154$	1.83981	+	5.66235i	0.148256	+	0.456285i
$155$	−2.75858	+	5.17692i	−0.221574	+	0.415820i
$156$	−4.72987	+	14.5570i	−0.378692	+	1.16550i
$157$	−9.56073			−0.763029			−0.381515	−	0.924363i	$-0.624597\pi$
$157$	−9.56073			−0.763029			−0.381515	+	0.924363i	$0.624597\pi$
$158$	12.3726	−	38.0788i	0.984308	−	3.02939i
$159$	−7.43235	+	5.39992i	−0.589424	+	0.428241i
$160$	6.58643	+	1.16746i	0.520703	+	0.0922960i
$161$	−6.64204	−	4.82572i	−0.523466	−	0.380320i
$162$	−2.02723	+	1.47287i	−0.159274	+	0.115719i
$163$	−11.6435	+	8.45947i	−0.911987	+	0.662597i	−0.941517	−	0.336967i	$-0.890599\pi$
$163$	−11.6435	+	8.45947i	−0.911987	+	0.662597i	0.0295299	+	0.999564i	$0.490599\pi$
$164$	10.3963	+	7.55338i	0.811817	+	0.589820i
$165$	2.49846	−	4.68876i	0.194505	−	0.365019i
$166$	34.3192	−	24.9344i	2.66369	−	1.93528i
$167$	−3.78806	+	11.6584i	−0.293129	+	0.902157i	0.690715	+	0.723127i	$0.257296\pi$
$167$	−3.78806	+	11.6584i	−0.293129	+	0.902157i	−0.983844	+	0.179030i	$0.942704\pi$
$168$	5.71069			0.440589
$169$	−0.0632635	+	0.194705i	−0.00486643	+	0.0149773i
$170$	−13.5406	+	6.58917i	−1.03852	+	0.505367i
$171$	−1.88941	−	5.81501i	−0.144487	−	0.444685i
$172$	−2.35610	−	7.25134i	−0.179651	−	0.552909i
$173$	−14.7056	−	10.6842i	−1.11804	−	0.812307i	−0.134133	−	0.990963i	$-0.542825\pi$
$173$	−14.7056	−	10.6842i	−1.11804	−	0.812307i	−0.983911	+	0.178657i	$0.942825\pi$
$174$	−14.9527			−1.13356
$175$	−4.69539	−	1.71853i	−0.354938	−	0.129909i
$176$	−13.6663			−1.03013
$177$	−12.2973	−	8.93450i	−0.924321	−	0.671558i
$178$	9.02663	+	27.7811i	0.676574	+	2.08228i
$179$	6.92329	+	21.3077i	0.517471	+	1.59261i	0.778741	+	0.627346i	$0.215859\pi$
$179$	6.92329	+	21.3077i	0.517471	+	1.59261i	−0.261270	+	0.965266i	$0.584141\pi$
$180$	−6.64040	−	6.88869i	−0.494946	−	0.513453i
$181$	1.31073	−	4.03402i	0.0974261	−	0.299847i	−0.890452	−	0.455077i	$-0.849612\pi$
$181$	1.31073	−	4.03402i	0.0974261	−	0.299847i	0.987878	+	0.155230i	$0.0496119\pi$
$182$	−8.96334			−0.664407
$183$	−1.54266	+	4.74783i	−0.114037	+	0.350969i
$184$	37.9306	−	27.5582i	2.79628	−	2.03162i
$185$	4.12530	−	2.00746i	0.303298	−	0.147592i
$186$	−5.31816	−	3.86387i	−0.389946	−	0.283313i
$187$	5.16609	−	3.75338i	0.377782	−	0.274475i
$188$	−12.6305	+	9.17659i	−0.921174	+	0.669272i
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	30.8052	−	14.9905i	2.23485	−	1.08752i
$191$	19.6721	−	14.2926i	1.42343	−	1.03418i	0.432232	−	0.901762i	$-0.357726\pi$
$191$	19.6721	−	14.2926i	1.42343	−	1.03418i	0.991194	−	0.132418i	$-0.0422740\pi$
$192$	1.23843	−	3.81150i	0.0893760	−	0.275071i
$193$	−4.66994			−0.336150			−0.168075	−	0.985774i	$-0.553755\pi$
$193$	−4.66994			−0.336150			−0.168075	+	0.985774i	$0.553755\pi$
$194$	1.34045	−	4.12548i	0.0962386	−	0.296192i
$195$	5.55107	+	5.75864i	0.397521	+	0.412385i
$196$	1.32228	+	4.06957i	0.0944487	+	0.290683i
$197$	4.69938	+	14.4632i	0.334817	+	1.03046i	0.966812	+	0.255488i	$0.0822362\pi$
$197$	4.69938	+	14.4632i	0.334817	+	1.03046i	−0.631995	+	0.774972i	$0.717764\pi$
$198$	4.81668	+	3.49952i	0.342307	+	0.248700i
$199$	−7.09462			−0.502924			−0.251462	−	0.967867i	$-0.580911\pi$
$199$	−7.09462			−0.502924			−0.251462	+	0.967867i	$0.580911\pi$
$200$	17.6196	−	22.4688i	1.24589	−	1.58879i
$201$	−6.70204			−0.472726
$202$	−10.0659	−	7.31332i	−0.708236	−	0.514563i
$203$	−1.84399	−	5.67521i	−0.129423	−	0.398322i
$204$	−3.55372	−	10.9372i	−0.248810	−	0.765759i
$205$	6.03832	−	2.93838i	0.421734	−	0.205225i
$206$	9.25320	−	28.4784i	0.644701	−	1.98419i
$207$	−8.21001			−0.570635
$208$	6.35787	−	19.5675i	0.440839	−	1.35676i
$209$	−11.7530	+	8.53902i	−0.812969	+	0.590656i
$210$	2.63495	−	4.94490i	0.181829	−	0.341230i
$211$	15.5289	+	11.2824i	1.06906	+	0.776715i	0.975742	−	0.218922i	$-0.0702540\pi$
$211$	15.5289	+	11.2824i	1.06906	+	0.776715i	0.0933137	+	0.995637i	$0.470254\pi$
$212$	31.8030	−	23.1062i	2.18424	−	1.58694i
$213$	−6.52355	+	4.73964i	−0.446986	+	0.324755i
$214$	14.7392	+	10.7086i	1.00755	+	0.732027i
$215$	−3.92317	−	0.695393i	−0.267558	−	0.0474254i
$216$	4.62004	−	3.35666i	0.314354	−	0.228392i
$217$	0.810665	−	2.49497i	0.0550315	−	0.169370i
$218$	−27.5373			−1.86506
$219$	2.31527	−	7.12566i	0.156451	−	0.481507i
$220$	−10.6909	+	20.0632i	−0.720779	+	1.35266i
$221$	2.97075	+	9.14303i	0.199834	+	0.615027i
$222$	1.58872	+	4.88959i	0.106628	+	0.328168i
$223$	−20.7315	−	15.0623i	−1.38829	−	1.00865i	−0.996051	−	0.0887849i	$-0.971702\pi$
$223$	−20.7315	−	15.0623i	−1.38829	−	1.00865i	−0.392236	−	0.919865i	$-0.628298\pi$
$224$	−2.99145			−0.199875
$225$	−4.80877	+	1.36956i	−0.320585	+	0.0913037i
$226$	−1.17123			−0.0779094
$227$	−22.6163	−	16.4317i	−1.50110	−	1.09061i	−0.969942	−	0.243337i	$-0.921758\pi$
$227$	−22.6163	−	16.4317i	−1.50110	−	1.09061i	−0.531155	−	0.847274i	$-0.678242\pi$
$228$	8.08478	+	24.8824i	0.535428	+	1.64788i
$229$	−4.00736	−	12.3334i	−0.264814	−	0.815014i	−0.991736	−	0.128294i	$-0.959050\pi$
$229$	−4.00736	−	12.3334i	−0.264814	−	0.815014i	0.726922	−	0.686720i	$-0.240950\pi$
$230$	−6.36130	−	45.5597i	−0.419452	−	3.00412i
$231$	−0.734222	+	2.25970i	−0.0483083	+	0.148678i
$232$	34.0772			2.23728
$233$	−0.310382	+	0.955259i	−0.0203338	+	0.0625811i	−0.960709	−	0.277559i	$-0.910475\pi$
$233$	−0.310382	+	0.955259i	−0.0203338	+	0.0625811i	0.940375	+	0.340140i	$0.110475\pi$
$234$	−7.25149	+	5.26852i	−0.474045	+	0.344414i
$235$	1.12818	+	8.08004i	0.0735943	+	0.527084i
$236$	52.6200	+	38.2307i	3.42527	+	2.48861i
$237$	12.9268	−	9.39184i	0.839683	−	0.610066i
$238$	5.44831	−	3.95843i	0.353161	−	0.256587i
$239$	8.20230	+	5.95932i	0.530563	+	0.385476i	0.820568	−	0.571549i	$-0.193657\pi$
$239$	8.20230	+	5.95932i	0.530563	+	0.385476i	−0.290005	+	0.957025i	$0.593657\pi$
$240$	8.92599	+	9.25975i	0.576170	+	0.597714i
$241$	−0.460917	+	0.334876i	−0.0296903	+	0.0215712i	−0.602531	−	0.798095i	$-0.705841\pi$
$241$	−0.460917	+	0.334876i	−0.0296903	+	0.0215712i	0.572841	+	0.819666i	$0.305841\pi$
$242$	−4.14628	+	12.7609i	−0.266533	+	0.820305i
$243$	−1.00000			−0.0641500
$244$	6.60104	−	20.3159i	0.422588	−	1.30059i
$245$	2.20175	+	0.390266i	0.140664	+	0.0249332i
$246$	2.32546	+	7.15702i	0.148266	+	0.456315i
$247$	−6.75851	−	20.8006i	−0.430034	−	1.32351i
$248$	12.1201	+	8.80574i	0.769625	+	0.559165i
$249$	16.9291			1.07284
$250$	−11.3260	−	25.6241i	−0.716320	−	1.62061i
$251$	−19.6932			−1.24303			−0.621513	−	0.783404i	$-0.713482\pi$
$251$	−19.6932			−1.24303			−0.621513	+	0.783404i	$0.713482\pi$
$252$	3.46178	+	2.51513i	0.218072	+	0.158438i
$253$	6.02797	+	18.5522i	0.378975	+	1.16637i
$254$	−7.15540	−	22.0220i	−0.448969	−	1.38179i
$255$	−5.91734	−	1.04886i	−0.370558	−	0.0656825i
$256$	−9.93200	+	30.5675i	−0.620750	+	1.91047i
$257$	−11.7592			−0.733520			−0.366760	−	0.930316i	$-0.619533\pi$
$257$	−11.7592			−0.733520			−0.366760	+	0.930316i	$0.619533\pi$
$258$	1.37974	−	4.24640i	0.0858989	−	0.264370i
$259$	−1.65989	+	1.20598i	−0.103140	+	0.0749358i
$260$	−23.7530	−	24.6412i	−1.47310	−	1.52818i
$261$	−4.82763	−	3.50748i	−0.298823	−	0.217107i
$262$	−20.3452	+	14.7816i	−1.25693	+	0.913212i
$263$	4.56559	−	3.31709i	0.281526	−	0.204541i	−0.438057	−	0.898947i	$-0.644333\pi$
$263$	4.56559	−	3.31709i	0.281526	−	0.204541i	0.719583	+	0.694407i	$0.244333\pi$
$264$	−10.9772	−	7.97540i	−0.675599	−	0.490852i
$265$	−2.84070	−	20.3451i	−0.174503	−	1.24979i
$266$	−12.3950	+	9.00550i	−0.759987	+	0.552163i
$267$	−3.60230	+	11.0868i	−0.220457	+	0.678498i
$268$	28.6780			1.75179
$269$	0.455923	−	1.40319i	0.0277981	−	0.0855537i	−0.936195	−	0.351481i	$-0.885678\pi$
$269$	0.455923	−	1.40319i	0.0277981	−	0.0855537i	0.963993	+	0.265927i	$0.0856781\pi$
$270$	−0.774823	−	5.54929i	−0.0471542	−	0.337719i
$271$	0.488206	+	1.50254i	0.0296564	+	0.0912730i	0.964789	−	0.263025i	$-0.0847200\pi$
$271$	0.488206	+	1.50254i	0.0296564	+	0.0912730i	−0.935133	+	0.354298i	$0.884720\pi$
$272$	4.77689	+	14.7018i	0.289642	+	0.891426i
$273$	−2.89389	−	2.10254i	−0.175146	−	0.127251i
$274$	−47.4452			−2.86627
$275$	6.62550	+	9.86085i	0.399533	+	0.594632i
$276$	35.1306			2.11461
$277$	7.05473	+	5.12556i	0.423878	+	0.307965i	0.779196	−	0.626780i	$-0.215628\pi$
$277$	7.05473	+	5.12556i	0.423878	+	0.307965i	−0.355318	+	0.934745i	$0.615628\pi$
$278$	−1.28439	−	3.95294i	−0.0770325	−	0.237082i
$279$	−0.810665	−	2.49497i	−0.0485332	−	0.149370i
$280$	−6.00503	+	11.2694i	−0.358869	+	0.673475i
$281$	5.53528	−	17.0358i	0.330207	−	1.01627i	−0.638828	−	0.769350i	$-0.720580\pi$
$281$	5.53528	−	17.0358i	0.330207	−	1.01627i	0.969035	−	0.246924i	$-0.0794197\pi$
$282$	−9.14252			−0.544429
$283$	0.763091	−	2.34855i	0.0453610	−	0.139607i	−0.925811	−	0.377987i	$-0.876616\pi$
$283$	0.763091	−	2.34855i	0.0453610	−	0.139607i	0.971172	+	0.238380i	$0.0766164\pi$
$284$	27.9142	−	20.2809i	1.65641	−	1.20345i
$285$	13.4621	+	2.38619i	0.797424	+	0.141346i
$286$	17.2295	+	12.5180i	1.01880	+	0.740203i
$287$	−2.42962	+	1.76522i	−0.143416	+	0.104198i
$288$	−2.42014	+	1.75833i	−0.142608	+	0.103611i
$289$	7.90975	+	5.74677i	0.465279	+	0.338045i
$290$	15.7234	−	29.5076i	0.923312	−	1.73274i
$291$	1.40049	−	1.01752i	0.0820983	−	0.0596479i
$292$	−9.90701	+	30.4906i	−0.579764	+	1.78433i
$293$	15.1054			0.882465			0.441233	−	0.897393i	$-0.354541\pi$
$293$	15.1054			0.882465			0.441233	+	0.897393i	$0.354541\pi$
$294$	−0.774332	+	2.38315i	−0.0451600	+	0.138988i
$295$	30.5624	−	14.8723i	1.77941	−	0.865899i
$296$	−3.62069	−	11.1433i	−0.210448	−	0.647693i
$297$	0.734222	+	2.25970i	0.0426039	+	0.131121i
$298$	5.62772	+	4.08878i	0.326005	+	0.236857i
$299$	−29.3676			−1.69837
$300$	20.5767	−	5.86032i	1.18800	−	0.338346i
$301$	1.78185			0.102704
$302$	32.2859	+	23.4571i	1.85785	+	1.34980i
$303$	−1.53438	−	4.72234i	−0.0881479	−	0.271291i
$304$	−10.8675	−	33.4468i	−0.623295	−	1.91831i
$305$	−7.74713	−	8.03681i	−0.443599	−	0.460186i
$306$	2.08107	−	6.40487i	0.118967	−	0.366142i
$307$	13.1365			0.749738			0.374869	−	0.927078i	$-0.377688\pi$
$307$	13.1365			0.749738			0.374869	+	0.927078i	$0.377688\pi$
$308$	3.14173	−	9.66926i	0.179017	−	0.550957i
$309$	9.66768	−	7.02398i	0.549975	−	0.399580i
$310$	13.2172	−	6.43177i	0.750686	−	0.365300i
$311$	13.9434	+	10.1305i	0.790657	+	0.574446i	0.908158	−	0.418627i	$-0.137489\pi$
$311$	13.9434	+	10.1305i	0.790657	+	0.574446i	−0.117502	+	0.993073i	$0.537489\pi$
$312$	16.5261	−	12.0069i	0.935607	−	0.679758i
$313$	−21.0410	+	15.2872i	−1.18931	+	0.864083i	−0.993191	−	0.116498i	$-0.962833\pi$
$313$	−21.0410	+	15.2872i	−1.18931	+	0.864083i	−0.196117	+	0.980580i	$0.562833\pi$
$314$	19.3818	+	14.0817i	1.09378	+	0.794676i
$315$	2.01064	−	0.978423i	0.113287	−	0.0551279i
$316$	−55.3135	+	40.1876i	−3.11163	+	2.26073i
$317$	−5.81011	+	17.8817i	−0.326328	+	1.00434i	0.644509	+	0.764597i	$0.277062\pi$
$317$	−5.81011	+	17.8817i	−0.326328	+	1.00434i	−0.970837	+	0.239739i	$0.922938\pi$
$318$	23.0204			1.29092
$319$	−4.38131	+	13.4843i	−0.245306	+	0.754974i
$320$	6.21930	+	6.45185i	0.347669	+	0.360670i
$321$	2.24674	+	6.91475i	0.125401	+	0.385944i
$322$	6.35728	+	19.5657i	0.354277	+	1.09035i
$323$	13.2942	+	9.65877i	0.739707	+	0.537428i
$324$	4.27899			0.237722
$325$	−17.2012	+	4.89897i	−0.954152	+	0.271746i
$326$	36.0637			1.99738
$327$	−8.89067	−	6.45945i	−0.491655	−	0.357208i
$328$	−5.29970	−	16.3108i	−0.292627	−	0.900613i
$329$	−1.12747	−	3.46998i	−0.0621592	−	0.191306i
$330$	−11.9709	+	5.82528i	−0.658974	+	0.320671i
$331$	−6.35270	+	19.5516i	−0.349176	+	1.07465i	0.610134	+	0.792298i	$0.291116\pi$
$331$	−6.35270	+	19.5516i	−0.349176	+	1.07465i	−0.959310	+	0.282355i	$0.908884\pi$
$332$	−72.4397			−3.97564
$333$	−0.634020	+	1.95131i	−0.0347441	+	0.106931i
$334$	24.8506	−	18.0550i	1.35976	−	0.987926i
$335$	7.04748	−	13.2257i	0.385045	−	0.722599i
$336$	−4.65331	−	3.38083i	−0.253859	−	0.184439i
$337$	20.4095	−	14.8284i	1.11178	−	0.807753i	0.128834	−	0.991666i	$-0.458876\pi$
$337$	20.4095	−	14.8284i	1.11178	−	0.807753i	0.982943	+	0.183913i	$0.0588765\pi$
$338$	0.415025	−	0.301533i	0.0225744	−	0.0164012i
$339$	−0.378143	−	0.274737i	−0.0205379	−	0.0149217i
$340$	25.3203	+	4.48809i	1.37318	+	0.243401i
$341$	−5.04268	+	3.66372i	−0.273077	+	0.198402i
$342$	−4.73447	+	14.5712i	−0.256011	+	0.787921i
$343$	−1.00000			−0.0539949
$344$	−3.14442	+	9.67753i	−0.169536	+	0.521778i
$345$	8.63317	−	16.2015i	0.464794	−	0.872261i
$346$	14.0751	+	43.3187i	0.756683	+	2.32883i
$347$	−3.82041	−	11.7580i	−0.205090	−	0.631203i	−0.999710	−	0.0240951i	$-0.992330\pi$
$347$	−3.82041	−	11.7580i	−0.205090	−	0.631203i	0.794619	−	0.607108i	$-0.207670\pi$
$348$	20.6574	+	15.0085i	1.10735	+	0.804538i
$349$	−19.4486			−1.04106			−0.520530	−	0.853844i	$-0.674266\pi$
$349$	−19.4486			−1.04106			−0.520530	+	0.853844i	$0.674266\pi$
$350$	6.98745	+	10.3995i	0.373495	+	0.555879i
$351$	−3.57705			−0.190929
$352$	5.75023	+	4.17779i	0.306488	+	0.222677i
$353$	0.875811	+	2.69547i	0.0466147	+	0.143465i	0.971655	−	0.236404i	$-0.0759689\pi$
$353$	0.875811	+	2.69547i	0.0466147	+	0.143465i	−0.925040	+	0.379869i	$0.875969\pi$
$354$	11.7701	+	36.2246i	0.625572	+	1.92531i
$355$	−2.49335	−	17.8574i	−0.132333	−	0.947774i
$356$	15.4142	−	47.4402i	0.816953	−	2.51432i
$357$	2.68757			0.142241
$358$	17.3483	−	53.3926i	0.916887	−	2.82189i
$359$	−6.77876	+	4.92506i	−0.357769	+	0.259935i	−0.752121	−	0.659025i	$-0.770969\pi$
$359$	−6.77876	+	4.92506i	−0.357769	+	0.259935i	0.394352	+	0.918960i	$0.370969\pi$
$360$	1.76582	+	12.6468i	0.0930667	+	0.666545i
$361$	−14.8731	−	10.8060i	−0.782797	−	0.568735i
$362$	−8.59874	+	6.24735i	−0.451940	+	0.328353i
$363$	−4.33201	+	3.14739i	−0.227371	+	0.165195i
$364$	12.3830	+	8.99674i	0.649043	+	0.471557i
$365$	11.6271	+	12.0618i	0.608589	+	0.631346i
$366$	10.1202	−	7.35279i	0.528994	−	0.384337i
$367$	6.31741	−	19.4430i	0.329766	−	1.01492i	−0.639477	−	0.768810i	$-0.720849\pi$
$367$	6.31741	−	19.4430i	0.329766	−	1.01492i	0.969243	−	0.246106i	$-0.0791510\pi$
$368$	−47.2224			−2.46164
$369$	−0.928032	+	2.85619i	−0.0483114	+	0.148687i
$370$	−11.3197	−	2.00644i	−0.588481	−	0.104310i
$371$	2.83891	+	8.73725i	0.147389	+	0.453615i
$372$	3.46883	+	10.6760i	0.179850	+	0.553523i
$373$	−9.02435	−	6.55657i	−0.467263	−	0.339487i	0.329111	−	0.944291i	$-0.393251\pi$
$373$	−9.02435	−	6.55657i	−0.467263	−	0.339487i	−0.796374	+	0.604805i	$0.793251\pi$
$374$	−16.0011			−0.827396
$375$	2.35396	−	10.9297i	0.121558	−	0.564408i
$376$	20.8358			1.07452
$377$	−17.2686	−	12.5464i	−0.889381	−	0.646173i
$378$	0.774332	+	2.38315i	0.0398274	+	0.122576i
$379$	−11.0132	−	33.8952i	−0.565711	−	1.74108i	−0.665829	−	0.746104i	$-0.731922\pi$
$379$	−11.0132	−	33.8952i	−0.565711	−	1.74108i	0.100118	−	0.994976i	$-0.468078\pi$
$380$	−57.6041	−	10.2105i	−2.95503	−	0.523787i
$381$	2.85554	−	8.78846i	0.146294	−	0.450246i
$382$	−60.9311			−3.11751
$383$	−10.7977	+	33.2318i	−0.551735	+	1.69807i	0.152677	+	0.988276i	$0.451210\pi$
$383$	−10.7977	+	33.2318i	−0.551735	+	1.69807i	−0.704413	+	0.709791i	$0.748790\pi$
$384$	−12.9647	+	9.41940i	−0.661602	+	0.480682i
$385$	−3.68721	−	3.82508i	−0.187917	−	0.194944i
$386$	9.46703	+	6.87820i	0.481859	+	0.350091i
$387$	1.44154	−	1.04734i	0.0732778	−	0.0532394i
$388$	−5.99269	+	4.35395i	−0.304233	+	0.221038i
$389$	−19.4450	−	14.1276i	−0.985899	−	0.716298i	−0.0268798	−	0.999639i	$-0.508557\pi$
$389$	−19.4450	−	14.1276i	−0.985899	−	0.716298i	−0.959019	+	0.283341i	$0.908557\pi$
$390$	−2.77158	−	19.8501i	−0.140344	−	1.00515i
$391$	17.8509	−	12.9694i	0.902760	−	0.655893i
$392$	1.76470	−	5.43119i	0.0891308	−	0.274316i
$393$	−10.0359			−0.506247
$394$	11.7757	−	36.2418i	0.593250	−	1.82583i
$395$	4.94071	+	35.3854i	0.248594	+	1.78043i
$396$	−3.14173	−	9.66926i	−0.157878	−	0.485899i
$397$	1.27953	+	3.93800i	0.0642179	+	0.197642i	0.978017	−	0.208523i	$-0.0668657\pi$
$397$	1.27953	+	3.93800i	0.0642179	+	0.197642i	−0.913800	+	0.406165i	$0.866866\pi$
$398$	14.3824	+	10.4494i	0.720925	+	0.523783i
$399$	−6.11426			−0.306096
$400$	−27.6591	+	7.87742i	−1.38296	+	0.393871i
$401$	−22.7159			−1.13438			−0.567189	−	0.823587i	$-0.691969\pi$
$401$	−22.7159			−1.13438			−0.567189	+	0.823587i	$0.691969\pi$
$402$	13.5866	+	9.87122i	0.677636	+	0.492332i
$403$	−2.89979	−	8.92462i	−0.144449	−	0.444567i
$404$	6.56561	+	20.2069i	0.326651	+	1.00533i
$405$	1.05154	−	1.97339i	0.0522515	−	0.0980584i
$406$	−4.62065	+	14.2209i	−0.229319	+	0.705772i
$407$	4.87490			0.241640
$408$	−4.74275	+	14.5967i	−0.234801	+	0.722643i
$409$	−10.1978	+	7.40914i	−0.504249	+	0.366358i	−0.810638	−	0.585548i	$-0.800879\pi$
$409$	−10.1978	+	7.40914i	−0.504249	+	0.366358i	0.306389	+	0.951907i	$0.400879\pi$
$410$	−16.5689	−	2.93688i	−0.818279	−	0.145042i
$411$	−15.3181	−	11.1292i	−0.755586	−	0.548965i
$412$	−41.3679	+	30.0556i	−2.03805	+	1.48073i
$413$	−12.2973	+	8.93450i	−0.605110	+	0.439638i
$414$	16.6436	+	12.0923i	0.817987	+	0.594302i
$415$	−17.8017	+	33.4078i	−0.873851	+	1.63992i
$416$	−8.65695	+	6.28964i	−0.424442	+	0.308375i
$417$	0.512568	−	1.57752i	0.0251005	−	0.0772515i
$418$	36.4028			1.78052
$419$	−2.57930	+	7.93827i	−0.126007	+	0.387810i	−0.994083	−	0.108621i	$-0.965356\pi$
$419$	−2.57930	+	7.93827i	−0.126007	+	0.387810i	0.868076	+	0.496431i	$0.165356\pi$
$420$	−8.60353	+	4.18667i	−0.419809	+	0.204288i
$421$	−1.57197	−	4.83803i	−0.0766131	−	0.235791i	0.905414	−	0.424529i	$-0.139560\pi$
$421$	−1.57197	−	4.83803i	−0.0766131	−	0.235791i	−0.982027	+	0.188738i	$0.939560\pi$
$422$	−14.8632	−	45.7441i	−0.723528	−	2.22679i
$423$	−2.95174	−	2.14457i	−0.143519	−	0.104272i
$424$	−52.4634			−2.54785
$425$	8.29215	−	10.5743i	0.402228	−	0.512928i
$426$	20.2056			0.978964
$427$	4.03874	+	2.93432i	0.195448	+	0.142002i
$428$	−9.61379	−	29.5882i	−0.464700	−	1.43020i
$429$	2.62635	+	8.08307i	0.126801	+	0.390254i
$430$	6.92895	+	7.18804i	0.334144	+	0.346638i
$431$	4.63460	−	14.2638i	0.223241	−	0.687064i	−0.775225	−	0.631685i	$-0.782363\pi$
$431$	4.63460	−	14.2638i	0.223241	−	0.687064i	0.998465	−	0.0553785i	$-0.0176366\pi$
$432$	−5.75181			−0.276734
$433$	10.6310	−	32.7187i	0.510891	−	1.57236i	−0.279745	−	0.960074i	$-0.590250\pi$
$433$	10.6310	−	32.7187i	0.510891	−	1.57236i	0.790636	−	0.612286i	$-0.209750\pi$
$434$	−5.31816	+	3.86387i	−0.255280	+	0.185472i
$435$	11.9981	−	5.83852i	0.575263	−	0.279936i
$436$	38.0431	+	27.6399i	1.82194	+	1.32371i
$437$	−40.6112	+	29.5057i	−1.94270	+	1.41145i
$438$	−15.1887	+	11.0353i	−0.725745	+	0.527285i
$439$	−15.3882	−	11.1802i	−0.734440	−	0.533602i	0.156525	−	0.987674i	$-0.449971\pi$
$439$	−15.3882	−	11.1802i	−0.734440	−	0.533602i	−0.890965	+	0.454072i	$0.849971\pi$
$440$	27.2815	−	13.2758i	1.30060	−	0.632898i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	7.44409	−	22.9105i	0.354079	−	1.08974i
$443$	6.53556			0.310514			0.155257	−	0.987874i	$-0.450379\pi$
$443$	6.53556			0.310514			0.155257	+	0.987874i	$0.450379\pi$
$444$	2.71297	−	8.34966i	0.128752	−	0.396257i
$445$	−18.0905	−	18.7669i	−0.857571	−	0.889638i
$446$	19.8427	+	61.0696i	0.939581	+	2.89173i
$447$	0.857852	+	2.64020i	0.0405750	+	0.124877i
$448$	−3.24225	−	2.35564i	−0.153182	−	0.111293i
$449$	2.67268			0.126132			0.0630658	−	0.998009i	$-0.479912\pi$
$449$	2.67268			0.126132			0.0630658	+	0.998009i	$0.479912\pi$
$450$	11.7657	+	4.30629i	0.554639	+	0.203000i
$451$	7.13552			0.335999
$452$	1.61807	+	1.17560i	0.0761078	+	0.0552955i
$453$	4.92145	+	15.1467i	0.231230	+	0.711652i
$454$	21.6467	+	66.6217i	1.01593	+	3.12671i
$455$	7.19217	−	3.49987i	0.337174	−	0.164076i
$456$	10.7898	−	33.2077i	0.505280	−	1.55509i
$457$	34.2422			1.60178			0.800891	−	0.598810i	$-0.204360\pi$
$457$	34.2422			1.60178			0.800891	+	0.598810i	$0.204360\pi$
$458$	−10.0416	+	30.9049i	−0.469214	+	1.44409i
$459$	2.17429	−	1.57971i	0.101487	−	0.0737346i
$460$	−36.9413	+	69.3263i	−1.72240	+	3.23235i
$461$	15.5131	+	11.2709i	0.722517	+	0.524939i	0.887187	−	0.461409i	$-0.152656\pi$
$461$	15.5131	+	11.2709i	0.722517	+	0.524939i	−0.164670	+	0.986349i	$0.552656\pi$
$462$	4.81668	−	3.49952i	0.224092	−	0.162813i
$463$	−10.1404	+	7.36746i	−0.471266	+	0.342395i	−0.797934	−	0.602744i	$-0.794074\pi$
$463$	−10.1404	+	7.36746i	−0.471266	+	0.342395i	0.326669	+	0.945139i	$0.394074\pi$
$464$	−27.7676	−	20.1743i	−1.28908	−	0.936569i
$465$	5.77599	+	1.02381i	0.267855	+	0.0474780i
$466$	2.03619	−	1.47938i	0.0943245	−	0.0685308i
$467$	11.4344	−	35.1913i	0.529119	−	1.62846i	−0.226906	−	0.973917i	$-0.572861\pi$
$467$	11.4344	−	35.1913i	0.529119	−	1.62846i	0.756025	−	0.654543i	$-0.227139\pi$
$468$	15.3062			0.707528
$469$	−2.07104	+	6.37402i	−0.0956320	+	0.294325i
$470$	9.61375	−	18.0417i	0.443449	−	0.832204i
$471$	2.95443	+	9.09279i	0.136133	+	0.418974i
$472$	−26.8239	−	82.5556i	−1.23467	−	3.79993i
$473$	−3.42510	−	2.48848i	−0.157486	−	0.114420i
$474$	−40.0384			−1.83903
$475$	−18.8648	+	24.0567i	−0.865576	+	1.10380i
$476$	−11.5001			−0.527105
$477$	7.43235	+	5.39992i	0.340304	+	0.247245i
$478$	−7.85065	−	24.1618i	−0.359080	−	1.10514i
$479$	−13.3652	−	41.1339i	−0.610672	−	1.87946i	−0.451690	−	0.892175i	$-0.649179\pi$
$479$	−13.3652	−	41.1339i	−0.610672	−	1.87946i	−0.158983	−	0.987281i	$-0.550821\pi$
$480$	−0.924996	−	6.62483i	−0.0422201	−	0.302381i
$481$	−2.26792	+	6.97994i	−0.103408	+	0.318258i
$482$	1.42761			0.0650259
$483$	−2.53703	+	7.80818i	−0.115439	+	0.355285i
$484$	18.5366	−	13.4677i	0.842574	−	0.612166i
$485$	0.535279	+	3.83367i	0.0243058	+	0.174078i
$486$	2.02723	+	1.47287i	0.0919570	+	0.0668106i
$487$	6.32318	−	4.59406i	0.286531	−	0.208177i	−0.435230	−	0.900319i	$-0.643333\pi$
$487$	6.32318	−	4.59406i	0.286531	−	0.208177i	0.721761	+	0.692142i	$0.243333\pi$
$488$	−23.0640	+	16.7570i	−1.04406	+	0.758552i
$489$	11.6435	+	8.45947i	0.526536	+	0.382551i
$490$	−3.88864	−	4.03404i	−0.175671	−	0.182239i
$491$	25.9661	−	18.8654i	1.17183	−	0.851386i	0.180605	−	0.983556i	$-0.442194\pi$
$491$	25.9661	−	18.8654i	1.17183	−	0.851386i	0.991227	+	0.132170i	$0.0421944\pi$
$492$	3.97104	−	12.2216i	0.179029	−	0.550993i
$493$	16.0374			0.722290
$494$	−16.9354	+	52.1219i	−0.761961	+	2.34508i
$495$	−5.23134	−	0.927269i	−0.235131	−	0.0416776i
$496$	−4.66278	−	14.3506i	−0.209365	−	0.644360i
$497$	2.49178	+	7.66890i	0.111771	+	0.343997i
$498$	−34.3192	−	24.9344i	−1.53788	−	1.11734i
$499$	11.2931			0.505548			0.252774	−	0.967525i	$-0.418657\pi$
$499$	11.2931			0.505548			0.252774	+	0.967525i	$0.418657\pi$
$500$	−10.0726	+	46.7682i	−0.450460	+	2.09154i
$501$	12.2584			0.547665
$502$	39.9227	+	29.0055i	1.78184	+	1.29458i
$503$	12.5227	+	38.5408i	0.558359	+	1.71845i	0.686905	+	0.726747i	$0.258969\pi$
$503$	12.5227	+	38.5408i	0.558359	+	1.71845i	−0.128546	+	0.991704i	$0.541031\pi$
$504$	−1.76470	−	5.43119i	−0.0786060	−	0.241924i
$505$	10.9325	+	1.93781i	0.486489	+	0.0862314i
$506$	15.1048	−	46.4879i	0.671492	−	2.06664i
$507$	0.204725			0.00909216
$508$	−12.2188	+	37.6058i	−0.542124	+	1.66849i
$509$	27.6592	−	20.0956i	1.22597	−	0.890722i	0.229392	−	0.973334i	$-0.426326\pi$
$509$	27.6592	−	20.0956i	1.22597	−	0.890722i	0.996582	+	0.0826122i	$0.0263263\pi$
$510$	10.4510	+	10.8418i	0.462777	+	0.480081i
$511$	−6.06145	−	4.40390i	−0.268143	−	0.194817i
$512$	39.2270	−	28.5001i	1.73361	−	1.25954i
$513$	−4.94654	+	3.59387i	−0.218395	+	0.158673i
$514$	23.8386	+	17.3198i	1.05148	+	0.763943i
$515$	3.69506	+	26.4641i	0.162824	+	1.16615i
$516$	−6.16836	+	4.48157i	−0.271547	+	0.197290i
$517$	−2.67885	+	8.24466i	−0.117816	+	0.362600i
$518$	5.14121			0.225892
$519$	−5.61703	+	17.2874i	−0.246560	+	0.758835i
$520$	6.31641	+	45.2382i	0.276993	+	1.98383i
$521$	−3.65380	−	11.2453i	−0.160076	−	0.492664i	0.838564	−	0.544804i	$-0.183396\pi$
$521$	−3.65380	−	11.2453i	−0.160076	−	0.492664i	−0.998640	+	0.0521400i	$0.983396\pi$
$522$	4.62065	+	14.2209i	0.202240	+	0.622432i
$523$	−16.9127	−	12.2878i	−0.739540	−	0.537307i	0.153027	−	0.988222i	$-0.451098\pi$
$523$	−16.9127	−	12.2878i	−0.739540	−	0.537307i	−0.892567	+	0.450915i	$0.851098\pi$
$524$	42.9438			1.87601
$525$	−0.183468	+	4.99663i	−0.00800721	+	0.218071i
$526$	−14.1411			−0.616582
$527$	5.70395	+	4.14416i	0.248468	+	0.180522i
$528$	4.22310	+	12.9974i	0.183787	+	0.565638i
$529$	13.7217	+	42.2310i	0.596595	+	1.83613i
$530$	−24.2070	+	45.4282i	−1.05148	+	1.97328i
$531$	−4.69715	+	14.4563i	−0.203839	+	0.627351i
$532$	26.1629			1.13431
$533$	−3.31962	+	10.2167i	−0.143789	+	0.442536i
$534$	23.6320	−	17.1697i	1.02266	−	0.743004i
$535$	−16.0080	−	2.83747i	−0.692088	−	0.122674i
$536$	−30.9637	−	22.4965i	−1.33743	−	0.971699i
$537$	18.1254	−	13.1689i	0.782169	−	0.568279i
$538$	−2.99097	+	2.17306i	−0.128950	+	0.0936874i
$539$	1.92222	+	1.39657i	0.0827958	+	0.0601547i
$540$	−4.49954	+	8.44412i	−0.193630	+	0.363377i
$541$	9.65440	−	7.01433i	0.415075	−	0.301570i	−0.360578	−	0.932729i	$-0.617421\pi$
$541$	9.65440	−	7.01433i	0.415075	−	0.301570i	0.775653	+	0.631159i	$0.217421\pi$
$542$	1.22334	−	3.76506i	0.0525471	−	0.161723i
$543$	−4.24162			−0.182026
$544$	2.48441	−	7.64624i	0.106518	−	0.327830i
$545$	22.0959	−	10.7524i	0.946485	−	0.460580i
$546$	2.76982	+	8.52464i	0.118538	+	0.364821i
$547$	−14.2026	−	43.7111i	−0.607259	−	1.86895i	−0.480442	−	0.877026i	$-0.659524\pi$
$547$	−14.2026	−	43.7111i	−0.607259	−	1.86895i	−0.126817	−	0.991926i	$-0.540476\pi$
$548$	65.5460	+	47.6220i	2.79999	+	2.03431i
$549$	4.99216			0.213060
$550$	1.09232	−	29.7487i	0.0465768	−	1.26849i
$551$	−36.4855			−1.55433
$552$	−37.9306	−	27.5582i	−1.61443	−	1.17295i
$553$	−4.93758	−	15.1963i	−0.209967	−	0.646213i
$554$	−6.75228	−	20.7814i	−0.286877	−	0.882916i
$555$	−3.18400	−	3.30306i	−0.135153	−	0.140207i
$556$	−2.19327	+	6.75020i	−0.0930155	+	0.286272i
$557$	−20.4683			−0.867271			−0.433635	−	0.901088i	$-0.642769\pi$
$557$	−20.4683			−0.867271			−0.433635	+	0.901088i	$0.642769\pi$
$558$	−2.03136	+	6.25187i	−0.0859942	+	0.264663i
$559$	5.15647	−	3.74639i	0.218095	−	0.158456i
$560$	11.5648	−	5.62770i	0.488703	−	0.237814i
$561$	−5.16609	−	3.75338i	−0.218112	−	0.158468i
$562$	−36.3128	+	26.3828i	−1.53176	+	1.11289i
$563$	10.0983	−	7.33682i	0.425591	−	0.309210i	−0.354292	−	0.935135i	$-0.615278\pi$
$563$	10.0983	−	7.33682i	0.425591	−	0.309210i	0.779884	+	0.625925i	$0.215278\pi$
$564$	12.6305	+	9.17659i	0.531840	+	0.386404i
$565$	0.939797	−	0.457326i	0.0395375	−	0.0192398i
$566$	−5.00607	+	3.63712i	−0.210421	+	0.152880i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	−46.0484			−1.93215
$569$	9.09684	−	27.9972i	0.381360	−	1.17370i	−0.557727	−	0.830024i	$-0.688327\pi$
$569$	9.09684	−	27.9972i	0.381360	−	1.17370i	0.939087	−	0.343680i	$-0.111673\pi$
$570$	−23.7761	−	24.6652i	−0.995873	−	1.03311i
$571$	2.34414	+	7.21452i	0.0980992	+	0.301918i	0.988049	−	0.154140i	$-0.0492608\pi$
$571$	2.34414	+	7.21452i	0.0980992	+	0.301918i	−0.889950	+	0.456059i	$0.849261\pi$
$572$	−11.2381	−	34.5874i	−0.469890	−	1.44617i
$573$	−19.6721	−	14.2926i	−0.821816	−	0.597084i
$574$	7.52533			0.314101
$575$	22.8938	+	34.0732i	0.954736	+	1.42095i
$576$	−4.00765			−0.166985
$577$	25.1203	+	18.2509i	1.04577	+	0.759796i	0.971403	−	0.237435i	$-0.0763066\pi$
$577$	25.1203	+	18.2509i	1.04577	+	0.759796i	0.0743662	+	0.997231i	$0.476307\pi$
$578$	−7.57064	−	23.3000i	−0.314897	−	0.969154i
$579$	1.44309	+	4.44138i	0.0599728	+	0.184577i
$580$	−51.3396	+	24.9830i	−2.13176	+	1.03736i
$581$	5.23139	−	16.1006i	0.217035	−	0.667964i
$582$	−4.33778			−0.179807
$583$	6.74522	−	20.7597i	0.279358	−	0.859777i
$584$	34.6150	−	25.1493i	1.43238	−	1.04068i
$585$	3.76142	−	7.05890i	0.155515	−	0.291850i
$586$	−30.6220	−	22.2482i	−1.26498	−	0.919065i
$587$	−9.80057	+	7.12053i	−0.404513	+	0.293896i	−0.771377	−	0.636379i	$-0.780432\pi$
$587$	−9.80057	+	7.12053i	−0.404513	+	0.293896i	0.366864	+	0.930275i	$0.380432\pi$
$588$	3.46178	−	2.51513i	0.142761	−	0.103722i
$589$	−12.9766	−	9.42804i	−0.534691	−	0.388476i
$590$	−83.8618	−	14.8647i	−3.45254	−	0.611971i
$591$	12.3031	−	8.93875i	0.506083	−	0.367691i
$592$	−3.64676	+	11.2236i	−0.149881	+	0.461286i
$593$	27.1547			1.11511			0.557556	−	0.830139i	$-0.311739\pi$
$593$	27.1547			1.11511			0.557556	+	0.830139i	$0.311739\pi$
$594$	1.83981	−	5.66235i	0.0754883	−	0.232329i
$595$	−2.82609	+	5.30361i	−0.115858	+	0.217427i
$596$	−3.67074	−	11.2974i	−0.150360	−	0.462759i
$597$	2.19236	+	6.74738i	0.0897272	+	0.276152i
$598$	59.5348	+	43.2546i	2.43456	+	1.76881i
$599$	19.1561			0.782695			0.391348	−	0.920243i	$-0.372009\pi$
$599$	19.1561			0.782695			0.391348	+	0.920243i	$0.372009\pi$
$600$	−26.8139	−	9.81400i	−1.09467	−	0.400655i
$601$	−20.6428			−0.842035			−0.421018	−	0.907052i	$-0.638327\pi$
$601$	−20.6428			−0.842035			−0.421018	+	0.907052i	$0.638327\pi$
$602$	−3.61221	−	2.62442i	−0.147223	−	0.106963i
$603$	2.07104	+	6.37402i	0.0843395	+	0.259570i
$604$	−21.0588	−	64.8124i	−0.856872	−	2.63718i
$605$	−1.65573	−	11.8583i	−0.0673149	−	0.482110i
$606$	−3.84484	+	11.8332i	−0.156186	+	0.480691i
$607$	7.67574			0.311549			0.155774	−	0.987793i	$-0.450213\pi$
$607$	7.67574			0.311549			0.155774	+	0.987793i	$0.450213\pi$
$608$	−5.65209	+	17.3953i	−0.229222	+	0.705474i
$609$	−4.82763	+	3.50748i	−0.195625	+	0.142130i
$610$	3.86804	+	27.7029i	0.156612	+	1.12166i
$611$	−10.5585	−	7.67122i	−0.427152	−	0.310344i
$612$	−9.30376	+	6.75958i	−0.376082	+	0.273240i
$613$	17.7871	−	12.9231i	0.718414	−	0.521959i	−0.167463	−	0.985878i	$-0.553557\pi$
$613$	17.7871	−	12.9231i	0.718414	−	0.521959i	0.885877	+	0.463920i	$0.153557\pi$
$614$	−26.6306	−	19.3483i	−1.07472	−	0.780833i
$615$	−4.66050	−	4.83477i	−0.187930	−	0.194957i
$616$	−10.9772	+	7.97540i	−0.442284	+	0.321338i
$617$	14.6372	−	45.0486i	0.589270	−	1.81359i	0.00787011	−	0.999969i	$-0.497495\pi$
$617$	14.6372	−	45.0486i	0.589270	−	1.81359i	0.581400	−	0.813618i	$-0.302505\pi$
$618$	−29.9440			−1.20452
$619$	8.55480	−	26.3290i	0.343846	−	1.05825i	−0.618352	−	0.785901i	$-0.712199\pi$
$619$	8.55480	−	26.3290i	0.343846	−	1.05825i	0.962198	−	0.272349i	$-0.0878006\pi$
$620$	−24.7154	−	4.38088i	−0.992595	−	0.175940i
$621$	2.53703	+	7.80818i	0.101808	+	0.313332i
$622$	−13.3456	−	41.0735i	−0.535110	−	1.64690i
$623$	9.43096	+	6.85199i	0.377843	+	0.274519i
$624$	−20.5745			−0.823639
$625$	19.0933	+	16.1384i	0.763732	+	0.645534i
$626$	65.1709			2.60475
$627$	11.7530	+	8.53902i	0.469368	+	0.341016i
$628$	−12.6420	−	38.9080i	−0.504470	−	1.55260i
$629$	−1.70397	−	5.24428i	−0.0679418	−	0.209103i
$630$	−5.51712	−	0.977925i	−0.219807	−	0.0389615i
$631$	−11.4138	+	35.1281i	−0.454376	+	1.39843i	0.417490	+	0.908682i	$0.362910\pi$
$631$	−11.4138	+	35.1281i	−0.454376	+	1.39843i	−0.871866	+	0.489744i	$0.837090\pi$
$632$	91.2474			3.62963
$633$	5.93153	−	18.2554i	0.235757	−	0.725585i
$634$	38.1158	−	27.6927i	1.51377	−	1.09982i
$635$	14.3403	+	14.8765i	0.569078	+	0.590357i
$636$	−31.8030	−	23.1062i	−1.26107	−	0.916221i
$637$	−2.89389	+	2.10254i	−0.114660	+	0.0833055i
$638$	28.7425	−	20.8826i	1.13792	−	0.826751i
$639$	6.52355	+	4.73964i	0.258068	+	0.187497i
$640$	−4.95521	−	35.4893i	−0.195872	−	1.40284i
$641$	−3.43546	+	2.49601i	−0.135693	+	0.0985864i	−0.653561	−	0.756874i	$-0.726726\pi$
$641$	−3.43546	+	2.49601i	−0.135693	+	0.0985864i	0.517868	+	0.855460i	$0.326726\pi$
$642$	5.62986	−	17.3269i	0.222193	−	0.683840i
$643$	−24.4817			−0.965464			−0.482732	−	0.875768i	$-0.660356\pi$
$643$	−24.4817			−0.965464			−0.482732	+	0.875768i	$0.660356\pi$
$644$	10.8559	−	33.4112i	0.427784	−	1.31658i
$645$	0.550969	+	3.94605i	0.0216944	+	0.155375i
$646$	−12.7242	−	39.1611i	−0.500627	−	1.54077i
$647$	0.932041	+	2.86853i	0.0366423	+	0.112773i	0.967705	−	0.252087i	$-0.0811168\pi$
$647$	0.932041	+	2.86853i	0.0366423	+	0.112773i	−0.931062	+	0.364860i	$0.881117\pi$
$648$	−4.62004	−	3.35666i	−0.181492	−	0.131862i
$649$	36.1158			1.41767
$650$	42.0863	+	15.4038i	1.65076	+	0.604187i
$651$	−2.62337			−0.102818
$652$	−49.8223	−	36.1980i	−1.95119	−	1.41762i
$653$	5.79350	+	17.8305i	0.226717	+	0.697763i	0.998113	+	0.0614075i	$0.0195589\pi$
$653$	5.79350	+	17.8305i	0.226717	+	0.697763i	−0.771396	+	0.636356i	$0.780441\pi$
$654$	8.50950	+	26.1896i	0.332748	+	1.02409i
$655$	10.5532	−	19.8048i	0.412349	−	0.773838i
$656$	−5.33786	+	16.4282i	−0.208408	+	0.641415i
$657$	−7.49236			−0.292305
$658$	−2.82519	+	8.69506i	−0.110138	+	0.338969i
$659$	11.7443	−	8.53272i	0.457492	−	0.332388i	−0.335055	−	0.942199i	$-0.608755\pi$
$659$	11.7443	−	8.53272i	0.457492	−	0.332388i	0.792547	+	0.609811i	$0.208755\pi$
$660$	22.3849	+	3.96778i	0.871330	+	0.154446i
$661$	2.96116	+	2.15141i	0.115176	+	0.0836800i	0.643882	−	0.765125i	$-0.277323\pi$
$661$	2.96116	+	2.15141i	0.115176	+	0.0836800i	−0.528706	+	0.848805i	$0.677323\pi$
$662$	41.6753	−	30.2789i	1.61976	−	1.17682i
$663$	7.77753	−	5.65070i	0.302054	−	0.219455i
$664$	78.2133	+	56.8253i	3.03527	+	2.20525i
$665$	6.42941	−	12.0658i	0.249322	−	0.467892i
$666$	4.15933	−	3.02193i	0.161171	−	0.117097i
$667$	−15.1392	+	46.5936i	−0.586191	+	1.80411i
$668$	−52.4536			−2.02949
$669$	−7.91875	+	24.3714i	−0.306156	+	0.942252i
$670$	−33.7666	+	16.4316i	−1.30452	+	0.634807i
$671$	−3.66535	−	11.2808i	−0.141499	−	0.435491i
$672$	0.924410	+	2.84504i	0.0356599	+	0.109750i
$673$	3.23535	+	2.35062i	0.124714	+	0.0906097i	0.648393	−	0.761305i	$-0.275441\pi$
$673$	3.23535	+	2.35062i	0.124714	+	0.0906097i	−0.523680	+	0.851915i	$0.675441\pi$
$674$	−63.2150			−2.43495
$675$	2.78852	+	4.15020i	0.107330	+	0.159741i
$676$	−0.876018			−0.0336930
$677$	21.1914	+	15.3965i	0.814453	+	0.591735i	0.915118	−	0.403186i	$-0.132097\pi$
$677$	21.1914	+	15.3965i	0.814453	+	0.591735i	−0.100665	+	0.994920i	$0.532097\pi$
$678$	0.361931	+	1.11391i	0.0138999	+	0.0427795i
$679$	−0.534940	−	1.64638i	−0.0205291	−	0.0631821i
$680$	−23.8177	−	24.7083i	−0.913367	−	0.947520i
$681$	−8.63866	+	26.5871i	−0.331034	+	1.01882i
$682$	15.6189			0.598077
$683$	3.47820	−	10.7048i	0.133090	−	0.409608i	−0.862198	−	0.506571i	$-0.830913\pi$
$683$	3.47820	−	10.7048i	0.133090	−	0.409608i	0.995288	+	0.0969631i	$0.0309129\pi$
$684$	21.1662	−	15.3782i	0.809311	−	0.587999i
$685$	38.0699	−	18.5257i	1.45458	−	0.707829i
$686$	2.02723	+	1.47287i	0.0773999	+	0.0562343i
$687$	−10.4914	+	7.62246i	−0.400273	+	0.290815i
$688$	8.29147	−	6.02411i	0.316110	−	0.229667i
$689$	26.5859	+	19.3158i	1.01284	+	0.735872i
$690$	−41.3641	+	20.1287i	−1.57471	+	0.766286i
$691$	−21.8198	+	15.8530i	−0.830064	+	0.603077i	−0.919578	−	0.392909i	$-0.871469\pi$
$691$	−21.8198	+	15.8530i	−0.830064	+	0.603077i	0.0895132	+	0.995986i	$0.471469\pi$
$692$	24.0352	−	73.9729i	0.913683	−	2.81203i
$693$	2.37599			0.0902565
$694$	−9.57315	+	29.4631i	−0.363392	+	1.11841i
$695$	2.57407	+	2.67032i	0.0976402	+	0.101291i
$696$	−10.5304	−	32.4094i	−0.399155	−	1.22847i
$697$	−2.49415	−	7.67620i	−0.0944726	−	0.290757i
$698$	39.4268	+	28.6452i	1.49232	+	1.08424i
$699$	1.00442			0.0379906
$700$	0.785059	−	21.3806i	0.0296725	−	0.808109i
$701$	−43.5452			−1.64468			−0.822340	−	0.568996i	$-0.807332\pi$
$701$	−43.5452			−1.64468			−0.822340	+	0.568996i	$0.807332\pi$
$702$	7.25149	+	5.26852i	0.273690	+	0.198847i
$703$	3.87657	+	11.9308i	0.146207	+	0.449980i
$704$	2.94250	+	9.05609i	0.110900	+	0.341314i
$705$	7.33595	−	3.56983i	0.276288	−	0.134448i
$706$	2.19460	−	6.75428i	0.0825948	−	0.254201i
$707$	−4.96536			−0.186742
$708$	20.0991	−	61.8585i	0.755369	−	2.32479i
$709$	12.2095	−	8.87073i	0.458538	−	0.333147i	−0.334420	−	0.942424i	$-0.608540\pi$
$709$	12.2095	−	8.87073i	0.458538	−	0.333147i	0.792957	+	0.609277i	$0.208540\pi$
$710$	−21.2470	+	39.8735i	−0.797387	+	1.49642i
$711$	−12.9268	−	9.39184i	−0.484791	−	0.352222i
$712$	−53.8572	+	39.1296i	−2.01839	+	1.46644i
$713$	−17.4245	+	12.6596i	−0.652552	+	0.474107i
$714$	−5.44831	−	3.95843i	−0.203898	−	0.148140i
$715$	−18.7127	−	3.31688i	−0.699817	−	0.124044i
$716$	−77.5585	+	56.3495i	−2.89850	+	2.10588i
$717$	3.13300	−	9.64239i	0.117004	−	0.360101i
$718$	20.9961			0.783566
$719$	10.9620	−	33.7375i	0.408813	−	1.25820i	−0.508856	−	0.860851i	$-0.669932\pi$
$719$	10.9620	−	33.7375i	0.408813	−	1.25820i	0.917669	−	0.397345i	$-0.130068\pi$
$720$	6.04827	−	11.3505i	0.225406	−	0.423010i
$721$	−3.69272	−	11.3650i	−0.137524	−	0.423256i
$722$	14.2355	+	43.8123i	0.529790	+	1.63053i
$723$	0.460917	+	0.334876i	0.0171417	+	0.0124542i
$724$	18.1499			0.674535
$725$	−1.09480	+	29.8163i	−0.0406600	+	1.10735i
$726$	13.4177			0.497976
$727$	15.0599	+	10.9417i	0.558541	+	0.405804i	0.830925	−	0.556385i	$-0.187812\pi$
$727$	15.0599	+	10.9417i	0.558541	+	0.405804i	−0.272383	+	0.962189i	$0.587812\pi$
$728$	−6.31241	−	19.4276i	−0.233954	−	0.720035i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−5.80525	−	41.5773i	−0.214862	−	1.53884i
$731$	−1.47983	+	4.55444i	−0.0547334	+	0.168452i
$732$	−21.3614			−0.789541
$733$	5.12269	−	15.7660i	0.189211	−	0.582331i	−0.810785	−	0.585345i	$-0.800959\pi$
$733$	5.12269	−	15.7660i	0.189211	−	0.582331i	0.999995	+	0.00301352i	$0.000959235\pi$
$734$	−41.4438	+	30.1107i	−1.52972	+	1.11141i
$735$	−0.309213	−	2.21459i	−0.0114055	−	0.0816862i
$736$	19.8694	+	14.4359i	0.732394	+	0.532116i
$737$	12.8828	−	9.35990i	0.474544	−	0.344776i
$738$	6.08812	−	4.42328i	0.224107	−	0.162823i
$739$	−41.9201	−	30.4567i	−1.54206	−	1.12037i	−0.949030	−	0.315185i	$-0.897933\pi$
$739$	−41.9201	−	30.4567i	−1.54206	−	1.12037i	−0.593026	−	0.805184i	$-0.702067\pi$
$740$	13.6243	+	14.1338i	0.500840	+	0.519567i
$741$	−17.6940	+	12.8555i	−0.650006	+	0.472257i
$742$	7.11371	−	21.8937i	0.261152	−	0.803744i
$743$	−10.8661			−0.398638			−0.199319	−	0.979935i	$-0.563873\pi$
$743$	−10.8661			−0.398638			−0.199319	+	0.979935i	$0.563873\pi$
$744$	4.62945	−	14.2480i	0.169724	−	0.522356i
$745$	−6.11220	−	1.08340i	−0.223934	−	0.0396929i
$746$	8.63745	+	26.5834i	0.316240	+	0.973286i
$747$	−5.23139	−	16.1006i	−0.191407	−	0.589089i
$748$	22.1057	+	16.0607i	0.808263	+	0.587238i
$749$	7.27060			0.265662
$750$	−20.8701	+	18.6900i	−0.762067	+	0.682461i
$751$	46.3119			1.68994			0.844972	−	0.534810i	$-0.179617\pi$
$751$	46.3119			1.68994			0.844972	+	0.534810i	$0.179617\pi$
$752$	−16.9779	−	12.3351i	−0.619119	−	0.449816i
$753$	6.08554	+	18.7294i	0.221769	+	0.682536i
$754$	16.5283	+	50.8689i	0.601925	+	1.85254i
$755$	−35.0653	−	6.21542i	−1.27616	−	0.226202i
$756$	1.32228	−	4.06957i	0.0480909	−	0.148009i
$757$	39.3726			1.43102			0.715510	−	0.698602i	$-0.246194\pi$
$757$	39.3726			1.43102			0.715510	+	0.698602i	$0.246194\pi$
$758$	−27.5968	+	84.9344i	−1.00236	+	3.08495i
$759$	15.7814	−	11.4659i	0.572830	−	0.416185i
$760$	54.1857	+	56.2118i	1.96552	+	2.03902i
$761$	−38.1719	−	27.7335i	−1.38373	−	1.00534i	−0.996521	−	0.0833465i	$-0.973439\pi$
$761$	−38.1719	−	27.7335i	−1.38373	−	1.00534i	−0.387209	−	0.921992i	$-0.626561\pi$
$762$	−18.7331	+	13.6104i	−0.678627	+	0.493052i
$763$	−8.89067	+	6.45945i	−0.321864	+	0.233848i
$764$	84.1770	+	61.1582i	3.04542	+	2.21262i
$765$	0.831030	+	5.95184i	0.0300459	+	0.215189i
$766$	70.8354	−	51.4650i	2.55939	−	1.85950i
$767$	−16.8019	+	51.7110i	−0.606682	+	1.86718i
$768$	32.1406			1.15977
$769$	10.9726	−	33.7701i	0.395681	−	1.21778i	−0.532748	−	0.846274i	$-0.678841\pi$
$769$	10.9726	−	33.7701i	0.395681	−	1.21778i	0.928430	−	0.371508i	$-0.121159\pi$
$770$	1.84097	+	13.1851i	0.0663441	+	0.475157i
$771$	3.63380	+	11.1837i	0.130868	+	0.402771i
$772$	−6.17498	−	19.0046i	−0.222242	−	0.683991i
$773$	−25.4112	−	18.4623i	−0.913979	−	0.664044i	0.0280392	−	0.999607i	$-0.491074\pi$
$773$	−25.4112	−	18.4623i	−0.913979	−	0.664044i	−0.942018	+	0.335562i	$0.891074\pi$
$774$	−4.46493			−0.160489
$775$	−8.09407	+	10.3217i	−0.290748	+	0.370766i
$776$	9.88578			0.354879
$777$	1.65989	+	1.20598i	0.0595481	+	0.0432642i
$778$	18.6113	+	57.2797i	0.667248	+	2.05358i
$779$	5.67423	+	17.4635i	0.203300	+	0.625695i
$780$	−16.0951	+	30.2050i	−0.576296	+	1.08151i
$781$	5.92044	−	18.2212i	0.211850	−	0.652007i
$782$	−55.2902			−1.97717
$783$	−1.84399	+	5.67521i	−0.0658988	+	0.202816i
$784$	−4.65331	+	3.38083i	−0.166190	+	0.120744i
$785$	−21.0503	−	3.73122i	−0.751318	−	0.133173i
$786$	20.3452	+	14.7816i	0.725688	+	0.527243i
$787$	−4.83522	+	3.51300i	−0.172357	+	0.125225i	−0.670619	−	0.741802i	$-0.733972\pi$
$787$	−4.83522	+	3.51300i	−0.172357	+	0.125225i	0.498262	+	0.867026i	$0.333972\pi$
$788$	−52.6450	+	38.2489i	−1.87540	+	1.36256i
$789$	−4.56559	−	3.31709i	−0.162539	−	0.118092i
$790$	42.1021	−	79.0114i	1.49793	−	2.81110i
$791$	−0.378143	+	0.274737i	−0.0134452	+	0.00976853i
$792$	−4.19291	+	12.9045i	−0.148989	+	0.458540i
$793$	17.8572			0.634128
$794$	3.20624	−	9.86780i	0.113785	−	0.350195i
$795$	−18.4716	+	8.98867i	−0.655119	+	0.318795i
$796$	−9.38109	−	28.8720i	−0.332504	−	1.02334i
$797$	1.75598	+	5.40436i	0.0622002	+	0.191432i	0.977328	−	0.211732i	$-0.0679103\pi$
$797$	1.75598	+	5.40436i	0.0622002	+	0.191432i	−0.915128	+	0.403164i	$0.867910\pi$
$798$	12.3950	+	9.00550i	0.438779	+	0.318791i
$799$	9.80573			0.346902
$800$	14.0460	+	5.14091i	0.496602	+	0.181759i
$801$	11.6573			0.411890
$802$	46.0504	+	33.4575i	1.62609	+	1.18143i
$803$	5.50106	+	16.9305i	0.194128	+	0.597465i
$804$	−8.86199	−	27.2744i	−0.312538	−	0.961894i
$805$	−12.7408	−	13.2172i	−0.449053	−	0.465845i
$806$	−7.26626	+	22.3633i	−0.255943	+	0.787712i
$807$	−1.47540			−0.0519364
$808$	8.76237	−	26.9678i	0.308259	−	0.948724i
$809$	−0.168853	+	0.122679i	−0.00593655	+	0.00431315i	−0.590750	−	0.806855i	$-0.701168\pi$
$809$	−0.168853	+	0.122679i	−0.00593655	+	0.00431315i	0.584813	+	0.811168i	$0.301168\pi$
$810$	−5.03826	+	2.45173i	−0.177026	+	0.0861448i
$811$	−20.0592	−	14.5739i	−0.704373	−	0.511757i	0.176980	−	0.984214i	$-0.443367\pi$
$811$	−20.0592	−	14.5739i	−0.704373	−	0.511757i	−0.881354	+	0.472457i	$0.843367\pi$
$812$	20.6574	−	15.0085i	0.724932	−	0.526694i
$813$	1.27814	−	0.928623i	0.0448263	−	0.0325682i
$814$	−9.88254	−	7.18009i	−0.346383	−	0.251662i
$815$	−28.9374	+	14.0816i	−1.01363	+	0.493256i
$816$	12.5061	−	9.08619i	0.437800	−	0.318080i
$817$	3.36664	−	10.3614i	0.117784	−	0.362501i
$818$	31.5860			1.10438
$819$	−1.10537	+	3.40198i	−0.0386247	+	0.118875i
$820$	19.9423	+	20.6880i	0.696414	+	0.722455i
$821$	−1.00442	−	3.09129i	−0.0350545	−	0.107887i	0.931998	−	0.362463i	$-0.118064\pi$
$821$	−1.00442	−	3.09129i	−0.0350545	−	0.107887i	−0.967053	+	0.254576i	$0.918064\pi$
$822$	14.6614	+	45.1230i	0.511374	+	1.57385i
$823$	6.49102	+	4.71600i	0.226263	+	0.164390i	0.695141	−	0.718873i	$-0.255342\pi$
$823$	6.49102	+	4.71600i	0.226263	+	0.164390i	−0.468878	+	0.883263i	$0.655342\pi$
$824$	68.2422			2.37733
$825$	7.33083	−	9.34840i	0.255227	−	0.325469i
$826$	38.0887			1.32528
$827$	4.16729	+	3.02771i	0.144911	+	0.105284i	0.657879	−	0.753124i	$-0.271454\pi$
$827$	4.16729	+	3.02771i	0.144911	+	0.105284i	−0.512968	+	0.858408i	$0.671454\pi$
$828$	−10.8559	−	33.4112i	−0.377270	−	1.16112i
$829$	−1.11560	−	3.43345i	−0.0387462	−	0.119249i	0.929813	−	0.368033i	$-0.119969\pi$
$829$	−1.11560	−	3.43345i	−0.0387462	−	0.119249i	−0.968559	+	0.248785i	$0.919969\pi$
$830$	85.2933	−	41.5056i	2.96057	−	1.44068i
$831$	2.69467	−	8.29334i	0.0934770	−	0.287693i
$832$	−14.3355			−0.496996
$833$	0.830504	−	2.55603i	0.0287752	−	0.0885611i
$834$	−3.36257	+	2.44305i	−0.116436	+	0.0845959i
$835$	−12.8902	+	24.1906i	−0.446085	+	0.837150i
$836$	−50.2908	−	36.5384i	−1.73934	−	1.26371i
$837$	−2.12235	+	1.54198i	−0.0733591	+	0.0532985i
$838$	16.9209	−	12.2937i	0.584521	−	0.424679i
$839$	−20.5920	−	14.9610i	−0.710916	−	0.516511i	0.172553	−	0.985000i	$-0.444798\pi$
$839$	−20.5920	−	14.9610i	−0.710916	−	0.516511i	−0.883469	+	0.468490i	$0.844798\pi$
$840$	12.5735	+	2.22868i	0.433827	+	0.0768969i
$841$	−5.34627	+	3.88429i	−0.184354	+	0.133941i
$842$	−3.93903	+	12.1231i	−0.135748	+	0.417789i
$843$	−17.9126			−0.616941
$844$	−25.3810	+	78.1146i	−0.873649	+	2.68881i
$845$	−0.215277	+	0.404002i	−0.00740576	+	0.0138981i
$846$	2.82519	+	8.69506i	0.0971322	+	0.298942i
$847$	1.65468	+	5.09258i	0.0568555	+	0.174983i
$848$	42.7494	+	31.0593i	1.46802	+	1.06658i
$849$	−2.46941			−0.0847501
$850$	−32.3846	+	9.22325i	−1.11078	+	0.316355i
$851$	16.8447			0.577430
$852$	−27.9142	−	20.2809i	−0.956326	−	0.694812i
$853$	−11.1012	−	34.1659i	−0.380096	−	1.16982i	−0.939975	−	0.341242i	$-0.889152\pi$
$853$	−11.1012	−	34.1659i	−0.380096	−	1.16982i	0.559879	−	0.828574i	$-0.310848\pi$
$854$	−3.86559	−	11.8971i	−0.132278	−	0.407109i
$855$	−1.89061	−	13.5406i	−0.0646574	−	0.463077i
$856$	−12.8304	+	39.4880i	−0.438535	+	1.34967i
$857$	0.461319			0.0157584			0.00787918	−	0.999969i	$-0.497492\pi$
$857$	0.461319			0.0157584			0.00787918	+	0.999969i	$0.497492\pi$
$858$	6.58108	−	20.2545i	0.224675	−	0.691477i
$859$	−3.39757	+	2.46848i	−0.115924	+	0.0842234i	−0.644237	−	0.764826i	$-0.722825\pi$
$859$	−3.39757	+	2.46848i	−0.115924	+	0.0842234i	0.528313	+	0.849050i	$0.322825\pi$
$860$	−2.35759	−	16.8851i	−0.0803933	−	0.575778i
$861$	2.42962	+	1.76522i	0.0828012	+	0.0601586i
$862$	−30.4041	+	22.0899i	−1.03557	+	0.752384i
$863$	31.4713	−	22.8652i	1.07130	−	0.778342i	0.0951512	−	0.995463i	$-0.469667\pi$
$863$	31.4713	−	22.8652i	1.07130	−	0.778342i	0.976145	+	0.217121i	$0.0696666\pi$
$864$	2.42014	+	1.75833i	0.0823348	+	0.0598197i
$865$	−28.2083	−	29.2631i	−0.959110	−	0.994974i
$866$	−69.7417	+	50.6703i	−2.36992	+	1.72185i
$867$	3.02126	−	9.29847i	0.102607	−	0.315793i
$868$	11.2254			0.381014
$869$	−11.7317	+	36.1063i	−0.397969	+	1.22482i
$870$	−32.9222	−	5.83554i	−1.11617	−	0.197843i
$871$	7.40823	+	22.8002i	0.251018	+	0.772555i
$872$	−19.3931	−	59.6859i	−0.656734	−	2.02122i
$873$	−1.40049	−	1.01752i	−0.0473994	−	0.0344377i
$874$	125.786			4.25478
$875$	−9.66737	−	5.61622i	−0.326817	−	0.189863i
$876$	32.0598			1.08320
$877$	−11.4618	−	8.32751i	−0.387039	−	0.281200i	0.377202	−	0.926131i	$-0.376886\pi$
$877$	−11.4618	−	8.32751i	−0.387039	−	0.281200i	−0.764241	+	0.644931i	$0.776886\pi$
$878$	14.7285	+	45.3296i	0.497062	+	1.52980i
$879$	−4.66782	−	14.3661i	−0.157442	−	0.484555i
$880$	−30.0896	−	5.33347i	−1.01432	−	0.179791i
$881$	−9.02178	+	27.7662i	−0.303952	+	0.935467i	0.676115	+	0.736796i	$0.263662\pi$
$881$	−9.02178	+	27.7662i	−0.303952	+	0.935467i	−0.980066	+	0.198670i	$0.936338\pi$
$882$	2.50579			0.0843744
$883$	−5.87735	+	18.0886i	−0.197788	+	0.608730i	0.802144	+	0.597130i	$0.203692\pi$
$883$	−5.87735	+	18.0886i	−0.197788	+	0.608730i	−0.999933	+	0.0116001i	$0.996308\pi$
$884$	−33.2800	+	24.1793i	−1.11933	+	0.813239i
$885$	−23.5887	−	24.4707i	−0.792925	−	0.822575i
$886$	−13.2491	−	9.62602i	−0.445111	−	0.323392i
$887$	−7.21746	+	5.24379i	−0.242339	+	0.176069i	−0.702325	−	0.711857i	$-0.747854\pi$
$887$	−7.21746	+	5.24379i	−0.242339	+	0.176069i	0.459986	+	0.887926i	$0.347854\pi$
$888$	−9.47909	+	6.88696i	−0.318097	+	0.231111i
$889$	−7.47591	−	5.43156i	−0.250734	−	0.182169i
$890$	9.03234	+	64.6897i	0.302765	+	2.16841i
$891$	1.92222	−	1.39657i	0.0643968	−	0.0467870i
$892$	33.8843	−	104.285i	1.13453	−	3.49172i
$893$	−22.3082			−0.746516
$894$	2.14960	−	6.61579i	0.0718934	−	0.221265i
$895$	6.92767	+	49.6161i	0.231567	+	1.65848i
$896$	4.95207	+	15.2409i	0.165437	+	0.509163i
$897$	9.07509	+	27.9303i	0.303008	+	0.932564i
$898$	−5.41813	−	3.93650i	−0.180805	−	0.131363i
$899$	−15.6543			−0.522101
$900$	−11.9321	−	17.7587i	−0.397735	−	0.591956i
$901$	−24.6904			−0.822556
$902$	−14.4653	−	10.5097i	−0.481643	−	0.349934i
$903$	−0.550620	−	1.69464i	−0.0183235	−	0.0563939i
$904$	−0.824839	−	2.53859i	−0.0274338	−	0.0844324i
$905$	4.46025	−	8.37037i	0.148264	−	0.278240i
$906$	12.3321	−	37.9544i	0.409707	−	1.26095i
$907$	−3.18106			−0.105625			−0.0528126	−	0.998604i	$-0.516819\pi$
$907$	−3.18106			−0.105625			−0.0528126	+	0.998604i	$0.516819\pi$
$908$	36.9648	−	113.766i	1.22672	−	3.77545i
$909$	−4.01706	+	2.91857i	−0.133238	+	0.0968027i
$910$	−19.7350	−	3.49808i	−0.654209	−	0.115960i
$911$	24.8399	+	18.0472i	0.822982	+	0.597931i	0.917565	−	0.397586i	$-0.130152\pi$
$911$	24.8399	+	18.0472i	0.822982	+	0.597931i	−0.0945834	+	0.995517i	$0.530152\pi$
$912$	−28.4515	+	20.6713i	−0.942125	+	0.684494i
$913$	−32.5415	+	23.6428i	−1.07697	+	0.782462i
$914$	−69.4167	−	50.4342i	−2.29610	−	1.66822i
$915$	−5.24947	+	9.85147i	−0.173542	+	0.325679i
$916$	44.8927	−	32.6165i	1.48330	−	1.07768i
$917$	−3.10128	+	9.54476i	−0.102413	+	0.315196i
$918$	−6.73448			−0.222271
$919$	−8.05334	+	24.7856i	−0.265655	+	0.817602i	0.725887	+	0.687814i	$0.241430\pi$
$919$	−8.05334	+	24.7856i	−0.265655	+	0.817602i	−0.991542	+	0.129788i	$0.958570\pi$
$920$	94.2686	−	45.8732i	3.10794	−	1.51239i
$921$	−4.05939	−	12.4935i	−0.133762	−	0.411676i
$922$	−14.8480	−	45.6975i	−0.488993	−	1.50497i
$923$	23.3351	+	16.9539i	0.768083	+	0.558045i
$924$	−10.1669			−0.334465
$925$	9.86632	−	2.80996i	0.324403	−	0.0923910i
$926$	31.4083			1.03214
$927$	−9.66768	−	7.02398i	−0.317528	−	0.230698i
$928$	5.51621	+	16.9771i	0.181078	+	0.557302i
$929$	−5.35890	−	16.4930i	−0.175820	−	0.541118i	0.823850	−	0.566808i	$-0.191822\pi$
$929$	−5.35890	−	16.4930i	−0.175820	−	0.541118i	−0.999670	+	0.0256900i	$0.991822\pi$
$930$	−10.2013	−	10.5828i	−0.334514	−	0.347022i
$931$	−1.88941	+	5.81501i	−0.0619229	+	0.190579i
$932$	−4.29790			−0.140782
$933$	5.32590	−	16.3914i	0.174362	−	0.536631i
$934$	−75.0122	+	54.4995i	−2.45447	+	1.78328i
$935$	12.8392	−	6.24786i	0.419888	−	0.204327i
$936$	−16.5261	−	12.0069i	−0.540173	−	0.392459i
$937$	−10.2667	+	7.45917i	−0.335397	+	0.243680i	−0.742717	−	0.669605i	$-0.766463\pi$
$937$	−10.2667	+	7.45917i	−0.335397	+	0.243680i	0.407320	+	0.913286i	$0.366463\pi$
$938$	13.5866	−	9.87122i	0.443617	−	0.322307i
$939$	21.0410	+	15.2872i	0.686647	+	0.498878i
$940$	−31.3905	+	15.2753i	−1.02384	+	0.498225i
$941$	5.29633	−	3.84801i	0.172655	−	0.125441i	−0.498102	−	0.867119i	$-0.665969\pi$
$941$	5.29633	−	3.84801i	0.172655	−	0.125441i	0.670757	+	0.741677i	$0.265969\pi$
$942$	7.40318	−	22.7847i	0.241209	−	0.742364i
$943$	24.6561			0.802913
$944$	−27.0171	+	83.1500i	−0.879331	+	2.70630i
$945$	−1.55186	−	1.60989i	−0.0504820	−	0.0523696i
$946$	3.27825	+	10.0894i	0.106585	+	0.328036i
$947$	6.46810	+	19.9068i	0.210185	+	0.646883i	0.999461	+	0.0328435i	$0.0104563\pi$
$947$	6.46810	+	19.9068i	0.210185	+	0.646883i	−0.789276	+	0.614039i	$0.789544\pi$
$948$	55.3135	+	40.1876i	1.79650	+	1.30523i
$949$	−26.8005			−0.869982
$950$	73.6756	−	20.9831i	2.39035	−	0.680780i
$951$	18.8019			0.609694
$952$	12.4167	+	9.02124i	0.402427	+	0.292380i
$953$	1.82569	+	5.61891i	0.0591400	+	0.182014i	0.976262	−	0.216592i	$-0.0694941\pi$
$953$	1.82569	+	5.61891i	0.0591400	+	0.182014i	−0.917122	+	0.398606i	$0.869494\pi$
$954$	−7.11371	−	21.8937i	−0.230315	−	0.708836i
$955$	48.8910	−	23.7914i	1.58208	−	0.769873i
$956$	−13.4061	+	41.2597i	−0.433584	+	1.33443i
$957$	14.1782			0.458316
$958$	−33.4905	+	103.073i	−1.08203	+	3.33014i
$959$	−15.3181	+	11.1292i	−0.494647	+	0.359382i
$960$	4.21421	−	7.90864i	0.136013	−	0.255250i
$961$	19.5118	+	14.1762i	0.629414	+	0.457296i
$962$	14.8781	−	10.8096i	0.479690	−	0.348515i
$963$	5.88204	−	4.27355i	0.189546	−	0.137713i
$964$	−1.97226	−	1.43293i	−0.0635223	−	0.0461516i
$965$	−10.2820	−	1.82252i	−0.330990	−	0.0586689i
$966$	16.6436	−	12.0923i	0.535498	−	0.389062i
$967$	2.69344	−	8.28955i	0.0866151	−	0.266574i	−0.898363	−	0.439254i	$-0.855243\pi$
$967$	2.69344	−	8.28955i	0.0866151	−	0.266574i	0.984978	+	0.172680i	$0.0552428\pi$
$968$	−30.5788			−0.982839
$969$	5.07792	−	15.6282i	0.163126	−	0.502051i
$970$	4.56136	−	8.56013i	0.146456	−	0.274849i
$971$	−2.03450	−	6.26153i	−0.0652901	−	0.200942i	0.913090	−	0.407759i	$-0.133690\pi$
$971$	−2.03450	−	6.26153i	−0.0652901	−	0.200942i	−0.978380	+	0.206817i	$0.933690\pi$
$972$	−1.32228	−	4.06957i	−0.0424122	−	0.130531i
$973$	−1.34192	−	0.974961i	−0.0430200	−	0.0312558i
$974$	−19.5850			−0.627543
$975$	9.97466	+	14.8455i	0.319445	+	0.475435i
$976$	28.7139			0.919110
$977$	11.2078	+	8.14292i	0.358568	+	0.260515i	0.752455	−	0.658644i	$-0.228870\pi$
$977$	11.2078	+	8.14292i	0.358568	+	0.260515i	−0.393886	+	0.919159i	$0.628870\pi$
$978$	−11.1443	−	34.2986i	−0.356355	−	1.09675i
$979$	−8.55905	−	26.3421i	−0.273548	−	0.841896i
$980$	1.32312	+	9.47620i	0.0422655	+	0.302706i
$981$	−3.39593	+	10.4516i	−0.108424	+	0.333694i
$982$	−80.4255			−2.56648
$983$	12.0483	−	37.0809i	0.384281	−	1.18270i	−0.552719	−	0.833368i	$-0.686410\pi$
$983$	12.0483	−	37.0809i	0.384281	−	1.18270i	0.937000	−	0.349328i	$-0.113590\pi$
$984$	−13.8748	+	10.0806i	−0.442312	+	0.321359i
$985$	4.70236	+	33.6783i	0.149830	+	1.07308i
$986$	−32.5116	−	23.6210i	−1.03538	−	0.752247i
$987$	−2.95174	+	2.14457i	−0.0939550	+	0.0682623i
$988$	75.7126	−	55.0084i	2.40874	−	1.75005i
$989$	−11.8351	−	8.59869i	−0.376334	−	0.273423i
$990$	9.23937	+	9.58485i	0.293647	+	0.304627i
$991$	34.0768	−	24.7582i	1.08248	−	0.786471i	0.104370	−	0.994539i	$-0.466717\pi$
$991$	34.0768	−	24.7582i	1.08248	−	0.786471i	0.978114	+	0.208067i	$0.0667174\pi$
$992$	−2.42507	+	7.46359i	−0.0769959	+	0.236969i
$993$	20.5578			0.652381
$994$	6.24387	−	19.2167i	0.198044	−	0.609515i
$995$	−15.6206	−	2.76879i	−0.495205	−	0.0877764i
$996$	22.3851	+	68.8942i	0.709299	+	2.18300i
$997$	1.23512	+	3.80132i	0.0391167	+	0.120389i	0.968708	−	0.248203i	$-0.0798400\pi$
$997$	1.23512	+	3.80132i	0.0391167	+	0.120389i	−0.929591	+	0.368592i	$0.879840\pi$
$998$	−22.8937	−	16.6332i	−0.724686	−	0.526515i
$999$	2.05173			0.0649139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.b.316.1	yes	20
25.11	even	5	inner	525.2.n.b.211.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.b.211.1	✓	20	25.11	even	5	inner
525.2.n.b.316.1	yes	20	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02723 - 1.47287i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.32228 + 4.06957i) q^{4} +(2.20175 + 0.390266i) q^{5} +(-0.774332 + 2.38315i) q^{6} -1.00000 q^{7} +(1.76470 - 5.43119i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.02723 - 1.47287i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.32228 + 4.06957i) q^{4} +(2.20175 + 0.390266i) q^{5} +(-0.774332 + 2.38315i) q^{6} -1.00000 q^{7} +(1.76470 - 5.43119i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.88864 - 4.03404i) q^{10} +(1.92222 + 1.39657i) q^{11} +(3.46178 - 2.51513i) q^{12} +(-2.89389 + 2.10254i) q^{13} +(2.02723 + 1.47287i) q^{14} +(-0.309213 - 2.21459i) q^{15} +(-4.65331 + 3.38083i) q^{16} +(0.830504 - 2.55603i) q^{17} +2.50579 q^{18} +(-1.88941 + 5.81501i) q^{19} +(1.32312 + 9.47620i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-1.83981 - 5.66235i) q^{22} +(6.64204 + 4.82572i) q^{23} -5.71069 q^{24} +(4.69539 + 1.71853i) q^{25} +8.96334 q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.32228 - 4.06957i) q^{28} +(1.84399 + 5.67521i) q^{29} +(-2.63495 + 4.94490i) q^{30} +(-0.810665 + 2.49497i) q^{31} +2.99145 q^{32} +(0.734222 - 2.25970i) q^{33} +(-5.44831 + 3.95843i) q^{34} +(-2.20175 - 0.390266i) q^{35} +(-3.46178 - 2.51513i) q^{36} +(1.65989 - 1.20598i) q^{37} +(12.3950 - 9.00550i) q^{38} +(2.89389 + 2.10254i) q^{39} +(6.00503 - 11.2694i) q^{40} +(2.42962 - 1.76522i) q^{41} +(0.774332 - 2.38315i) q^{42} -1.78185 q^{43} +(-3.14173 + 9.66926i) q^{44} +(-2.01064 + 0.978423i) q^{45} +(-6.35728 - 19.5657i) q^{46} +(1.12747 + 3.46998i) q^{47} +(4.65331 + 3.38083i) q^{48} +1.00000 q^{49} +(-6.98745 - 10.3995i) q^{50} -2.68757 q^{51} +(-12.3830 - 8.99674i) q^{52} +(-2.83891 - 8.73725i) q^{53} +(-0.774332 - 2.38315i) q^{54} +(3.68721 + 3.82508i) q^{55} +(-1.76470 + 5.43119i) q^{56} +6.11426 q^{57} +(4.62065 - 14.2209i) q^{58} +(12.2973 - 8.93450i) q^{59} +(8.60353 - 4.18667i) q^{60} +(-4.03874 - 2.93432i) q^{61} +(5.31816 - 3.86387i) q^{62} +(0.809017 - 0.587785i) q^{63} +(3.24225 + 2.35564i) q^{64} +(-7.19217 + 3.49987i) q^{65} +(-4.81668 + 3.49952i) q^{66} +(2.07104 - 6.37402i) q^{67} +11.5001 q^{68} +(2.53703 - 7.80818i) q^{69} +(3.88864 + 4.03404i) q^{70} +(-2.49178 - 7.66890i) q^{71} +(1.76470 + 5.43119i) q^{72} +(6.06145 + 4.40390i) q^{73} -5.14121 q^{74} +(0.183468 - 4.99663i) q^{75} -26.1629 q^{76} +(-1.92222 - 1.39657i) q^{77} +(-2.76982 - 8.52464i) q^{78} +(4.93758 + 15.1963i) q^{79} +(-11.5648 + 5.62770i) q^{80} +(0.309017 - 0.951057i) q^{81} -7.52533 q^{82} +(-5.23139 + 16.1006i) q^{83} +(-3.46178 + 2.51513i) q^{84} +(2.82609 - 5.30361i) q^{85} +(3.61221 + 2.62442i) q^{86} +(4.82763 - 3.50748i) q^{87} +(10.9772 - 7.97540i) q^{88} +(-9.43096 - 6.85199i) q^{89} +(5.51712 + 0.977925i) q^{90} +(2.89389 - 2.10254i) q^{91} +(-10.8559 + 33.4112i) q^{92} +2.62337 q^{93} +(2.82519 - 8.69506i) q^{94} +(-6.42941 + 12.0658i) q^{95} +(-0.924410 - 2.84504i) q^{96} +(0.534940 + 1.64638i) q^{97} +(-2.02723 - 1.47287i) q^{98} -2.37599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9	\( 20 q - 2 q^{2} + 5 q^{3} + 5 q^{5} - 3 q^{6} - 20 q^{7} + 4 q^{8} - 5 q^{9} - 15 q^{10} + 12 q^{11} + 5 q^{12} - 17 q^{13} + 2 q^{14} + 15 q^{15} - 28 q^{16} - 9 q^{17} - 2 q^{18} - 9 q^{19} - 20 q^{20} - 5 q^{21} - 21 q^{22} + 7 q^{23} + 6 q^{24} - 15 q^{25} - 20 q^{26} + 5 q^{27} + 28 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{33} - 5 q^{35} - 5 q^{36} - 5 q^{37} - 6 q^{38} + 17 q^{39} - 10 q^{40} + 11 q^{41} + 3 q^{42} + 28 q^{43} - 17 q^{44} + 5 q^{45} - 43 q^{46} - 24 q^{47} + 28 q^{48} + 20 q^{49} + 10 q^{50} - 36 q^{51} - 9 q^{52} - 26 q^{53} - 3 q^{54} - 25 q^{55} - 4 q^{56} + 24 q^{57} - 16 q^{58} + 64 q^{59} + 5 q^{60} + 8 q^{61} + 27 q^{62} + 5 q^{63} + 26 q^{64} + 25 q^{65} - 4 q^{66} - 3 q^{67} + 80 q^{68} - 2 q^{69} + 15 q^{70} + 19 q^{71} + 4 q^{72} + 31 q^{73} + 8 q^{74} - 5 q^{75} - 72 q^{76} - 12 q^{77} - 30 q^{78} + 43 q^{79} - 25 q^{80} - 5 q^{81} - 6 q^{82} + 32 q^{83} - 5 q^{84} + 35 q^{85} + 53 q^{86} + 17 q^{87} - 61 q^{88} - 47 q^{89} + 10 q^{90} + 17 q^{91} + 41 q^{92} + 4 q^{93} + 12 q^{94} - 40 q^{95} - 6 q^{96} - 45 q^{97} - 2 q^{98} - 18 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 5 * q^3 + 5 * q^5 - 3 * q^6 - 20 * q^7 + 4 * q^8 - 5 * q^9 - 15 * q^10 + 12 * q^11 + 5 * q^12 - 17 * q^13 + 2 * q^14 + 15 * q^15 - 28 * q^16 - 9 * q^17 - 2 * q^18 - 9 * q^19 - 20 * q^20 - 5 * q^21 - 21 * q^22 + 7 * q^23 + 6 * q^24 - 15 * q^25 - 20 * q^26 + 5 * q^27 + 28 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^33 - 5 * q^35 - 5 * q^36 - 5 * q^37 - 6 * q^38 + 17 * q^39 - 10 * q^40 + 11 * q^41 + 3 * q^42 + 28 * q^43 - 17 * q^44 + 5 * q^45 - 43 * q^46 - 24 * q^47 + 28 * q^48 + 20 * q^49 + 10 * q^50 - 36 * q^51 - 9 * q^52 - 26 * q^53 - 3 * q^54 - 25 * q^55 - 4 * q^56 + 24 * q^57 - 16 * q^58 + 64 * q^59 + 5 * q^60 + 8 * q^61 + 27 * q^62 + 5 * q^63 + 26 * q^64 + 25 * q^65 - 4 * q^66 - 3 * q^67 + 80 * q^68 - 2 * q^69 + 15 * q^70 + 19 * q^71 + 4 * q^72 + 31 * q^73 + 8 * q^74 - 5 * q^75 - 72 * q^76 - 12 * q^77 - 30 * q^78 + 43 * q^79 - 25 * q^80 - 5 * q^81 - 6 * q^82 + 32 * q^83 - 5 * q^84 + 35 * q^85 + 53 * q^86 + 17 * q^87 - 61 * q^88 - 47 * q^89 + 10 * q^90 + 17 * q^91 + 41 * q^92 + 4 * q^93 + 12 * q^94 - 40 * q^95 - 6 * q^96 - 45 * q^97 - 2 * q^98 - 18 * q^99

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