LMFDB - Embedded newform 25.3.f.a.12.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			12.4
Character	$\chi$	$=$	25.12
Dual form			25.3.f.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.463000 + 2.92327i) q^{2} +(-0.866921 - 0.441718i) q^{3} +(-4.52691 + 1.47088i) q^{4} +(0.953911 - 4.90816i) q^{5} +(0.889877 - 2.73876i) q^{6} +(4.44588 + 4.44588i) q^{7} +(-1.02103 - 2.00389i) q^{8} +(-4.73363 - 6.51528i) q^{9} +O(q^{10})$	\(q+(0.463000 + 2.92327i) q^{2} +(-0.866921 - 0.441718i) q^{3} +(-4.52691 + 1.47088i) q^{4} +(0.953911 - 4.90816i) q^{5} +(0.889877 - 2.73876i) q^{6} +(4.44588 + 4.44588i) q^{7} +(-1.02103 - 2.00389i) q^{8} +(-4.73363 - 6.51528i) q^{9} +(14.7895 + 0.516059i) q^{10} +(-9.24763 - 6.71880i) q^{11} +(4.57419 + 0.724481i) q^{12} +(0.202120 - 1.27614i) q^{13} +(-10.9381 + 15.0550i) q^{14} +(-2.99499 + 3.83363i) q^{15} +(-10.0181 + 7.27859i) q^{16} +(-22.3384 + 11.3820i) q^{17} +(16.8543 - 16.8543i) q^{18} +(31.7059 + 10.3019i) q^{19} +(2.90106 + 23.6219i) q^{20} +(-1.89040 - 5.81805i) q^{21} +(15.3592 - 30.1441i) q^{22} +(9.63343 - 1.52579i) q^{23} +2.18822i q^{24} +(-23.1801 - 9.36390i) q^{25} +3.82407 q^{26} +(2.59562 + 16.3881i) q^{27} +(-26.6655 - 13.5867i) q^{28} +(13.6325 - 4.42946i) q^{29} +(-12.5934 - 6.98019i) q^{30} +(-3.95492 + 12.1720i) q^{31} +(-32.2769 - 32.2769i) q^{32} +(5.04915 + 9.90952i) q^{33} +(-43.6153 - 60.0314i) q^{34} +(26.0621 - 17.5801i) q^{35} +(31.0120 + 22.5315i) q^{36} +(32.7301 + 5.18393i) q^{37} +(-15.4353 + 97.4547i) q^{38} +(-0.738915 + 1.01703i) q^{39} +(-10.8094 + 3.09986i) q^{40} +(34.5187 - 25.0793i) q^{41} +(16.1325 - 8.21991i) q^{42} +(-10.6048 + 10.6048i) q^{43} +(51.7458 + 16.8132i) q^{44} +(-36.4935 + 17.0184i) q^{45} +(8.92057 + 27.4547i) q^{46} +(-17.0518 + 33.4660i) q^{47} +(11.9000 - 1.88478i) q^{48} -9.46829i q^{49} +(16.6408 - 72.0972i) q^{50} +24.3933 q^{51} +(0.962067 + 6.07425i) q^{52} +(-66.4615 - 33.8638i) q^{53} +(-46.7050 + 15.1754i) q^{54} +(-41.7984 + 38.9797i) q^{55} +(4.36966 - 13.4484i) q^{56} +(-22.9360 - 22.9360i) q^{57} +(19.2603 + 37.8005i) q^{58} +(21.1412 + 29.0983i) q^{59} +(7.91924 - 21.7598i) q^{60} +(-9.86967 - 7.17074i) q^{61} +(-37.4132 - 5.92567i) q^{62} +(7.92102 - 50.0113i) q^{63} +(50.2954 - 69.2257i) q^{64} +(-6.07068 - 2.20936i) q^{65} +(-26.6304 + 19.3481i) q^{66} +(42.3694 - 21.5883i) q^{67} +(84.3825 - 84.3825i) q^{68} +(-9.02539 - 2.93253i) q^{69} +(63.4582 + 68.0469i) q^{70} +(-18.5901 - 57.2145i) q^{71} +(-8.22271 + 16.1380i) q^{72} +(40.6475 - 6.43794i) q^{73} +98.0790i q^{74} +(15.9591 + 18.3568i) q^{75} -158.683 q^{76} +(-11.2429 - 70.9849i) q^{77} +(-3.31517 - 1.68916i) q^{78} +(-66.7175 + 21.6778i) q^{79} +(26.1681 + 56.1137i) q^{80} +(-17.4088 + 53.5789i) q^{81} +(89.2958 + 89.2958i) q^{82} +(-14.9586 - 29.3580i) q^{83} +(17.1154 + 23.5573i) q^{84} +(34.5558 + 120.498i) q^{85} +(-35.9108 - 26.0907i) q^{86} +(-13.7748 - 2.18172i) q^{87} +(-4.02159 + 25.3913i) q^{88} +(23.3194 - 32.0965i) q^{89} +(-66.6460 - 98.8009i) q^{90} +(6.57215 - 4.77495i) q^{91} +(-41.3655 + 21.0768i) q^{92} +(8.80520 - 8.80520i) q^{93} +(-105.725 - 34.3521i) q^{94} +(80.8079 - 145.791i) q^{95} +(13.7242 + 42.2388i) q^{96} +(-16.1345 + 31.6657i) q^{97} +(27.6784 - 4.38382i) q^{98} +92.0553i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

Coefficient data

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

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

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

$2$	0.463000	+	2.92327i	0.231500	+	1.46164i	0.780155	+	0.625586i	$0.215140\pi$
$2$	0.463000	+	2.92327i	0.231500	+	1.46164i	−0.548655	+	0.836049i	$0.684860\pi$
$3$	−0.866921	−	0.441718i	−0.288974	−	0.147239i	0.303495	−	0.952833i	$-0.401847\pi$
$3$	−0.866921	−	0.441718i	−0.288974	−	0.147239i	−0.592468	+	0.805594i	$0.701847\pi$
$4$	−4.52691	+	1.47088i	−1.13173	+	0.367721i
$5$	0.953911	−	4.90816i	0.190782	−	0.981632i
$5$	0.953911	−	4.90816i	0.190782	−	0.981632i
$6$	0.889877	−	2.73876i	0.148313	−	0.456460i
$7$	4.44588	+	4.44588i	0.635126	+	0.635126i	0.949349	−	0.314223i	$-0.101744\pi$
$7$	4.44588	+	4.44588i	0.635126	+	0.635126i	−0.314223	+	0.949349i	$0.601744\pi$
$8$	−1.02103	−	2.00389i	−0.127629	−	0.250486i
$9$	−4.73363	−	6.51528i	−0.525959	−	0.723920i
$10$	14.7895	+	0.516059i	1.47895	+	0.0516059i
$11$	−9.24763	−	6.71880i	−0.840694	−	0.610800i	0.0818704	−	0.996643i	$-0.473911\pi$
$11$	−9.24763	−	6.71880i	−0.840694	−	0.610800i	−0.922564	+	0.385843i	$0.873911\pi$
$12$	4.57419	+	0.724481i	0.381183	+	0.0603734i
$13$	0.202120	−	1.27614i	0.0155477	−	0.0981644i	−0.978694	−	0.205323i	$-0.934175\pi$
$13$	0.202120	−	1.27614i	0.0155477	−	0.0981644i	0.994242	+	0.107159i	$0.0341754\pi$
$14$	−10.9381	+	15.0550i	−0.781290	+	1.07535i
$15$	−2.99499	+	3.83363i	−0.199666	+	0.255575i
$16$	−10.0181	+	7.27859i	−0.626132	+	0.454912i
$17$	−22.3384	+	11.3820i	−1.31402	+	0.669529i	−0.963672	−	0.267089i	$-0.913938\pi$
$17$	−22.3384	+	11.3820i	−1.31402	+	0.669529i	−0.350353	+	0.936618i	$0.613938\pi$
$18$	16.8543	−	16.8543i	0.936348	−	0.936348i
$19$	31.7059	+	10.3019i	1.66873	+	0.542204i	0.982674	−	0.185343i	$-0.0593397\pi$
$19$	31.7059	+	10.3019i	1.66873	+	0.542204i	0.686058	+	0.727547i	$0.259340\pi$
$20$	2.90106	+	23.6219i	0.145053	+	1.18110i
$21$	−1.89040	−	5.81805i	−0.0900191	−	0.277050i
$22$	15.3592	−	30.1441i	0.698146	−	1.37019i
$23$	9.63343	−	1.52579i	0.418845	−	0.0663385i	0.0565449	−	0.998400i	$-0.481992\pi$
$23$	9.63343	−	1.52579i	0.418845	−	0.0663385i	0.362300	+	0.932062i	$0.381992\pi$
$24$			2.18822i			0.0911759i
$25$	−23.1801	−	9.36390i	−0.927204	−	0.374556i
$26$	3.82407			0.147080
$27$	2.59562	+	16.3881i	0.0961339	+	0.606966i
$28$	−26.6655	−	13.5867i	−0.952339	−	0.485241i
$29$	13.6325	−	4.42946i	0.470085	−	0.152740i	−0.0643888	−	0.997925i	$-0.520510\pi$
$29$	13.6325	−	4.42946i	0.470085	−	0.152740i	0.534474	+	0.845185i	$0.320510\pi$
$30$	−12.5934	−	6.98019i	−0.419780	−	0.232673i
$31$	−3.95492	+	12.1720i	−0.127578	+	0.392645i	−0.994362	−	0.106039i	$-0.966183\pi$
$31$	−3.95492	+	12.1720i	−0.127578	+	0.392645i	0.866784	+	0.498684i	$0.166183\pi$
$32$	−32.2769	−	32.2769i	−1.00865	−	1.00865i
$33$	5.04915	+	9.90952i	0.153005	+	0.300288i
$34$	−43.6153	−	60.0314i	−1.28280	−	1.76563i
$35$	26.0621	−	17.5801i	0.744631	−	0.502289i
$36$	31.0120	+	22.5315i	0.861443	+	0.625875i
$37$	32.7301	+	5.18393i	0.884597	+	0.140106i	0.582171	−	0.813067i	$-0.302204\pi$
$37$	32.7301	+	5.18393i	0.884597	+	0.140106i	0.302426	+	0.953173i	$0.402204\pi$
$38$	−15.4353	+	97.4547i	−0.406192	+	2.56460i
$39$	−0.738915	+	1.01703i	−0.0189465	+	0.0260777i
$40$	−10.8094	+	3.09986i	−0.270235	+	0.0774965i
$41$	34.5187	−	25.0793i	0.841920	−	0.611690i	−0.0809866	−	0.996715i	$-0.525807\pi$
$41$	34.5187	−	25.0793i	0.841920	−	0.611690i	0.922906	+	0.385025i	$0.125807\pi$
$42$	16.1325	−	8.21991i	0.384107	−	0.195712i
$43$	−10.6048	+	10.6048i	−0.246624	+	0.246624i	−0.819583	−	0.572960i	$-0.805795\pi$
$43$	−10.6048	+	10.6048i	−0.246624	+	0.246624i	0.572960	+	0.819583i	$0.305795\pi$
$44$	51.7458	+	16.8132i	1.17604	+	0.382119i
$45$	−36.4935	+	17.0184i	−0.810967	+	0.378187i
$46$	8.92057	+	27.4547i	0.193925	+	0.596841i
$47$	−17.0518	+	33.4660i	−0.362803	+	0.712042i	−0.998189	−	0.0601533i	$-0.980841\pi$
$47$	−17.0518	+	33.4660i	−0.362803	+	0.712042i	0.635386	+	0.772195i	$0.280841\pi$
$48$	11.9000	−	1.88478i	0.247917	−	0.0392662i
$49$		−	9.46829i		−	0.193230i
$50$	16.6408	−	72.0972i	0.332816	−	1.44194i
$51$	24.3933			0.478300
$52$	0.962067	+	6.07425i	0.0185013	+	0.116813i
$53$	−66.4615	−	33.8638i	−1.25399	−	0.638940i	−0.304434	−	0.952534i	$-0.598467\pi$
$53$	−66.4615	−	33.8638i	−1.25399	−	0.638940i	−0.949557	+	0.313593i	$0.898467\pi$
$54$	−46.7050	+	15.1754i	−0.864907	+	0.281025i
$55$	−41.7984	+	38.9797i	−0.759971	+	0.708723i
$56$	4.36966	−	13.4484i	0.0780297	−	0.240151i
$57$	−22.9360	−	22.9360i	−0.402386	−	0.402386i
$58$	19.2603	+	37.8005i	0.332075	+	0.651733i
$59$	21.1412	+	29.0983i	0.358325	+	0.493192i	0.949681	−	0.313218i	$-0.101407\pi$
$59$	21.1412	+	29.0983i	0.358325	+	0.493192i	−0.591356	+	0.806411i	$0.701407\pi$
$60$	7.91924	−	21.7598i	0.131987	−	0.362663i
$61$	−9.86967	−	7.17074i	−0.161798	−	0.117553i	0.503940	−	0.863739i	$-0.331883\pi$
$61$	−9.86967	−	7.17074i	−0.161798	−	0.117553i	−0.665738	+	0.746185i	$0.731883\pi$
$62$	−37.4132	−	5.92567i	−0.603438	−	0.0955753i
$63$	7.92102	−	50.0113i	0.125730	−	0.793831i
$64$	50.2954	−	69.2257i	0.785866	−	1.08165i
$65$	−6.07068	−	2.20936i	−0.0933951	−	0.0339901i
$66$	−26.6304	+	19.3481i	−0.403491	+	0.293154i
$67$	42.3694	−	21.5883i	0.632380	−	0.322213i	−0.108253	−	0.994123i	$-0.534526\pi$
$67$	42.3694	−	21.5883i	0.632380	−	0.322213i	0.740633	+	0.671910i	$0.234526\pi$
$68$	84.3825	−	84.3825i	1.24092	−	1.24092i
$69$	−9.02539	−	2.93253i	−0.130803	−	0.0425004i
$70$	63.4582	+	68.0469i	0.906546	+	0.972098i
$71$	−18.5901	−	57.2145i	−0.261833	−	0.805839i	−0.992406	−	0.123004i	$-0.960747\pi$
$71$	−18.5901	−	57.2145i	−0.261833	−	0.805839i	0.730573	−	0.682834i	$-0.239253\pi$
$72$	−8.22271	+	16.1380i	−0.114204	+	0.224139i
$73$	40.6475	−	6.43794i	0.556816	−	0.0881909i	0.128317	−	0.991733i	$-0.459043\pi$
$73$	40.6475	−	6.43794i	0.556816	−	0.0881909i	0.428499	+	0.903542i	$0.359043\pi$
$74$			98.0790i			1.32539i
$75$	15.9591	+	18.3568i	0.212788	+	0.244758i
$76$	−158.683			−2.08793
$77$	−11.2429	−	70.9849i	−0.146012	−	0.921881i
$78$	−3.31517	−	1.68916i	−0.0425022	−	0.0216559i
$79$	−66.7175	+	21.6778i	−0.844525	+	0.274403i	−0.699151	−	0.714974i	$-0.746439\pi$
$79$	−66.7175	+	21.6778i	−0.844525	+	0.274403i	−0.145374	+	0.989377i	$0.546439\pi$
$80$	26.1681	+	56.1137i	0.327101	+	0.701421i
$81$	−17.4088	+	53.5789i	−0.214924	+	0.661468i
$82$	89.2958	+	89.2958i	1.08897	+	1.08897i
$83$	−14.9586	−	29.3580i	−0.180225	−	0.353711i	0.783166	−	0.621813i	$-0.213604\pi$
$83$	−14.9586	−	29.3580i	−0.180225	−	0.353711i	−0.963390	+	0.268102i	$0.913604\pi$
$84$	17.1154	+	23.5573i	0.203754	+	0.280444i
$85$	34.5558	+	120.498i	0.406539	+	1.41762i
$86$	−35.9108	−	26.0907i	−0.417567	−	0.303380i
$87$	−13.7748	−	2.18172i	−0.158332	−	0.0250772i
$88$	−4.02159	+	25.3913i	−0.0456999	+	0.288538i
$89$	23.3194	−	32.0965i	0.262016	−	0.360634i	−0.657658	−	0.753317i	$-0.728453\pi$
$89$	23.3194	−	32.0965i	0.262016	−	0.360634i	0.919674	+	0.392682i	$0.128453\pi$
$90$	−66.6460	−	98.8009i	−0.740511	−	1.09779i
$91$	6.57215	−	4.77495i	0.0722215	−	0.0524720i
$92$	−41.3655	+	21.0768i	−0.449625	+	0.229095i
$93$	8.80520	−	8.80520i	0.0946796	−	0.0946796i
$94$	−105.725	−	34.3521i	−1.12473	−	0.365448i
$95$	80.8079	−	145.791i	0.850609	−	1.53464i
$96$	13.7242	+	42.2388i	0.142960	+	0.439987i
$97$	−16.1345	+	31.6657i	−0.166335	+	0.326450i	−0.959096	−	0.283083i	$-0.908643\pi$
$97$	−16.1345	+	31.6657i	−0.166335	+	0.326450i	0.792761	+	0.609533i	$0.208643\pi$
$98$	27.6784	−	4.38382i	0.282432	−	0.0447329i
$99$			92.0553i			0.929851i
$100$	118.708	+	8.29434i	1.18708	+	0.0829434i
$101$	157.435			1.55876			0.779382	−	0.626549i	$-0.215533\pi$
$101$	157.435			1.55876			0.779382	+	0.626549i	$0.215533\pi$
$102$	11.2941	+	71.3081i	0.110726	+	0.699099i
$103$	−66.4229	−	33.8441i	−0.644882	−	0.328584i	0.100779	−	0.994909i	$-0.467866\pi$
$103$	−66.4229	−	33.8441i	−0.644882	−	0.328584i	−0.745661	+	0.666325i	$0.767866\pi$
$104$	−2.76361	+	0.897950i	−0.0265731	+	0.00863414i
$105$	−30.3592	+	3.72848i	−0.289135	+	0.0355094i
$106$	68.2214	−	209.964i	0.643598	−	1.98079i
$107$	104.689	+	104.689i	0.978397	+	0.978397i	0.999772	−	0.0213742i	$-0.00680414\pi$
$107$	104.689	+	104.689i	0.978397	+	0.978397i	−0.0213742	+	0.999772i	$0.506804\pi$
$108$	−35.8551	−	70.3695i	−0.331991	−	0.651569i
$109$	−1.19918	−	1.65053i	−0.0110016	−	0.0151424i	0.803481	−	0.595331i	$-0.202979\pi$
$109$	−1.19918	−	1.65053i	−0.0110016	−	0.0151424i	−0.814482	+	0.580188i	$0.802979\pi$
$110$	−133.301	−	104.140i	−1.21183	−	0.946730i
$111$	−26.0845	−	18.9515i	−0.234996	−	0.170735i
$112$	−76.8991	−	12.1796i	−0.686599	−	0.108747i
$113$	−11.2756	+	71.1912i	−0.0997839	+	0.630011i	0.886217	+	0.463270i	$0.153324\pi$
$113$	−11.2756	+	71.1912i	−0.0997839	+	0.630011i	−0.986001	+	0.166740i	$0.946676\pi$
$114$	56.4287	−	77.6674i	0.494989	−	0.681293i
$115$	1.70064	−	48.7379i	0.0147881	−	0.423808i
$116$	−55.1978	+	40.1035i	−0.475843	+	0.345720i
$117$	−9.27115	+	4.72389i	−0.0792406	+	0.0403751i
$118$	−75.2739	+	75.2739i	−0.637915	+	0.637915i
$119$	−149.917	−	48.7110i	−1.25981	−	0.409336i
$120$	10.7401	+	2.08737i	0.0895012	+	0.0173947i
$121$	2.98542	+	9.18817i	0.0246729	+	0.0759353i
$122$	16.3923	−	32.1718i	0.134363	−	0.263703i
$123$	−41.0030	+	6.49423i	−0.333357	+	0.0527986i
$124$		−	60.9188i		−	0.491281i
$125$	−68.0713	+	104.839i	−0.544570	+	0.838715i
$126$	149.864			1.18940
$127$	−19.4506	−	122.806i	−0.153154	−	0.966979i	−0.937836	−	0.347079i	$-0.887173\pi$
$127$	−19.4506	−	122.806i	−0.153154	−	0.966979i	0.784681	−	0.619899i	$-0.212827\pi$
$128$	62.9673	+	32.0835i	0.491932	+	0.250652i
$129$	13.8779	−	4.50919i	0.107580	−	0.0349550i
$130$	3.64783	−	18.7692i	0.0280602	−	0.144378i
$131$	−68.1028	+	209.599i	−0.519869	+	1.59999i	0.254377	+	0.967105i	$0.418130\pi$
$131$	−68.1028	+	209.599i	−0.519869	+	1.59999i	−0.774245	+	0.632886i	$0.781870\pi$
$132$	−37.4328	−	37.4328i	−0.283582	−	0.283582i
$133$	95.1598	+	186.762i	0.715487	+	1.40422i
$134$	82.7255	+	113.862i	0.617354	+	0.849716i
$135$	82.9113	+	2.89306i	0.614158	+	0.0214301i
$136$	45.6165	+	33.1423i	0.335415	+	0.243693i
$137$	20.6277	+	3.26711i	0.150567	+	0.0238475i	0.231263	−	0.972891i	$-0.425714\pi$
$137$	20.6277	+	3.26711i	0.150567	+	0.0238475i	−0.0806958	+	0.996739i	$0.525714\pi$
$138$	4.39381	−	27.7414i	0.0318392	−	0.201025i
$139$	36.2719	−	49.9240i	0.260949	−	0.359165i	−0.658359	−	0.752704i	$-0.728749\pi$
$139$	36.2719	−	49.9240i	0.260949	−	0.359165i	0.919308	+	0.393539i	$0.128749\pi$
$140$	−92.1224	+	117.918i	−0.658017	+	0.842271i
$141$	29.5650	−	21.4803i	0.209681	−	0.152342i
$142$	158.646	−	80.8343i	1.11723	−	0.569256i
$143$	−10.4432	+	10.4432i	−0.0730297	+	0.0730297i
$144$	94.8442	+	30.8167i	0.658640	+	0.214005i
$145$	−8.73633	−	71.1357i	−0.0602505	−	0.490591i
$146$	37.6397	+	115.843i	0.257806	+	0.793445i
$147$	−4.18232	+	8.20826i	−0.0284511	+	0.0558385i
$148$	−155.791	+	24.6749i	−1.05264	+	0.166722i
$149$		−	179.133i		−	1.20223i	−0.799161	−	0.601117i	$-0.794722\pi$
$149$		−	179.133i		−	1.20223i	0.799161	−	0.601117i	$-0.205278\pi$
$150$	−46.2729	+	55.1520i	−0.308486	+	0.367680i
$151$	−253.849			−1.68112			−0.840560	−	0.541719i	$-0.817774\pi$
$151$	−253.849			−1.68112			−0.840560	+	0.541719i	$0.817774\pi$
$152$	−11.7289	−	74.0536i	−0.0771641	−	0.487195i
$153$	179.899	+	91.6630i	1.17581	+	0.599105i
$154$	202.302	−	65.7321i	1.31365	−	0.426832i
$155$	55.9695	+	31.0224i	0.361094	+	0.200145i
$156$	1.84907	−	5.69086i	0.0118530	−	0.0364799i
$157$	−186.193	−	186.193i	−1.18594	−	1.18594i	−0.978179	−	0.207766i	$-0.933381\pi$
$157$	−186.193	−	186.193i	−1.18594	−	1.18594i	−0.207766	−	0.978179i	$-0.566619\pi$
$158$	−94.2604	−	184.996i	−0.596585	−	1.17086i
$159$	42.6586	+	58.7145i	0.268293	+	0.369274i
$160$	−189.209	+	127.631i	−1.18256	+	0.797692i
$161$	49.6126	+	36.0456i	0.308153	+	0.223886i
$162$	−164.686	−	26.0837i	−1.01658	−	0.161010i
$163$	24.3502	−	153.741i	0.149388	−	0.943197i	−0.793133	−	0.609049i	$-0.791551\pi$
$163$	24.3502	−	153.741i	0.149388	−	0.943197i	0.942521	−	0.334148i	$-0.108449\pi$
$164$	−119.374	+	164.305i	−0.727893	+	1.00186i
$165$	53.4540	−	15.3293i	0.323963	−	0.0929046i
$166$	78.8954	−	57.3209i	0.475274	−	0.345307i
$167$	−85.4318	+	43.5297i	−0.511567	+	0.260657i	−0.690665	−	0.723175i	$-0.742682\pi$
$167$	−85.4318	+	43.5297i	−0.511567	+	0.260657i	0.179098	+	0.983831i	$0.442682\pi$
$168$	−9.72857	+	9.72857i	−0.0579081	+	0.0579081i
$169$	159.141	+	51.7080i	0.941662	+	0.305965i
$170$	−336.249	+	156.807i	−1.97793	+	0.922392i
$171$	−82.9644	−	255.338i	−0.485172	−	1.49321i
$172$	32.4086	−	63.6055i	0.188422	−	0.369799i
$173$	152.191	−	24.1046i	0.879715	−	0.139333i	0.299792	−	0.954004i	$-0.403083\pi$
$173$	152.191	−	24.1046i	0.879715	−	0.139333i	0.579923	+	0.814671i	$0.303083\pi$
$174$		−	41.2777i		−	0.237228i
$175$	−61.4252	−	144.687i	−0.351001	−	0.826782i
$176$	141.547			0.804246
$177$	−5.47447	−	34.5644i	−0.0309292	−	0.195279i
$178$	104.624	+	53.3084i	0.587773	+	0.299485i
$179$	32.0276	−	10.4064i	0.178925	−	0.0581363i	−0.218184	−	0.975908i	$-0.570013\pi$
$179$	32.0276	−	10.4064i	0.178925	−	0.0581363i	0.397109	+	0.917771i	$0.370013\pi$
$180$	140.171	−	130.719i	0.778727	−	0.726215i
$181$	−40.1690	+	123.628i	−0.221928	+	0.683025i	0.776661	+	0.629919i	$0.216912\pi$
$181$	−40.1690	+	123.628i	−0.221928	+	0.683025i	−0.998589	+	0.0531057i	$0.983088\pi$
$182$	17.0014	+	17.0014i	0.0934142	+	0.0934142i
$183$	5.38878	+	10.5761i	0.0294469	+	0.0577928i
$184$	−12.8935	−	17.7464i	−0.0700736	−	0.0964481i
$185$	56.6652	−	155.699i	0.306298	−	0.841619i
$186$	29.8168	+	21.6632i	0.160305	+	0.116469i
$187$	283.051	+	44.8309i	1.51364	+	0.239737i
$188$	27.9673	−	176.579i	0.148762	−	0.939248i
$189$	−61.3196	+	84.3992i	−0.324442	+	0.446557i
$190$	463.599	+	168.722i	2.44000	+	0.888011i
$191$	−69.2996	+	50.3491i	−0.362825	+	0.263608i	−0.754229	−	0.656611i	$-0.771989\pi$
$191$	−69.2996	+	50.3491i	−0.362825	+	0.263608i	0.391404	+	0.920219i	$0.371989\pi$
$192$	−74.1804	+	37.7968i	−0.386356	+	0.196858i
$193$	−236.560	+	236.560i	−1.22570	+	1.22570i	−0.260121	+	0.965576i	$0.583762\pi$
$193$	−236.560	+	236.560i	−1.22570	+	1.22570i	−0.965576	+	0.260121i	$0.916238\pi$
$194$	−100.038	−	32.5042i	−0.515658	−	0.167547i
$195$	4.28689	+	4.59687i	0.0219840	+	0.0235737i
$196$	13.9267	+	42.8621i	0.0710548	+	0.218684i
$197$	−66.5213	+	130.555i	−0.337671	+	0.662718i	−0.995935	−	0.0900696i	$-0.971291\pi$
$197$	−66.5213	+	130.555i	−0.337671	+	0.662718i	0.658264	+	0.752787i	$0.271291\pi$
$198$	−269.102	+	42.6216i	−1.35910	+	0.215261i
$199$			14.0128i			0.0704163i	0.999380	+	0.0352081i	$0.0112094\pi$
$199$			14.0128i			0.0704163i	−0.999380	+	0.0352081i	$0.988791\pi$
$200$	4.90342	+	56.0112i	0.0245171	+	0.280056i
$201$	−46.2669			−0.230184
$202$	72.8926	+	460.226i	0.360854	+	2.27834i
$203$	80.3012	+	40.9155i	0.395572	+	0.201554i
$204$	−110.426	+	35.8797i	−0.541305	+	0.175881i
$205$	−90.1655	−	193.347i	−0.439832	−	0.943155i
$206$	68.1817	−	209.842i	0.330979	−	1.01865i
$207$	−55.5420	−	55.5420i	−0.268319	−	0.268319i
$208$	7.26361	+	14.2556i	0.0349212	+	0.0685367i
$209$	−223.988	−	308.294i	−1.07171	−	1.47509i
$210$	−24.9557	−	87.0219i	−0.118837	−	0.414390i
$211$	8.19415	+	5.95340i	0.0388348	+	0.0282151i	0.607033	−	0.794676i	$-0.292359\pi$
$211$	8.19415	+	5.95340i	0.0388348	+	0.0282151i	−0.568199	+	0.822892i	$0.692359\pi$
$212$	350.675	+	55.5415i	1.65413	+	0.261988i
$213$	−9.15653	+	57.8121i	−0.0429884	+	0.271418i
$214$	−257.562	+	354.504i	−1.20356	+	1.65656i
$215$	41.9341	+	62.1662i	0.195042	+	0.289145i
$216$	30.1896	−	21.9341i	0.139767	−	0.101547i
$217$	−71.6984	+	36.5322i	−0.330407	+	0.168351i
$218$	4.26971	−	4.26971i	0.0195858	−	0.0195858i
$219$	−38.0819	−	12.3736i	−0.173890	−	0.0565003i
$220$	131.883	−	237.938i	0.599468	−	1.08154i
$221$	10.0099	+	30.8074i	0.0452938	+	0.139400i
$222$	43.3233	−	85.0267i	0.195150	−	0.383003i
$223$	49.4226	−	7.82777i	0.221626	−	0.0351021i	−0.0446338	−	0.999003i	$-0.514212\pi$
$223$	49.4226	−	7.82777i	0.221626	−	0.0351021i	0.266260	+	0.963901i	$0.414212\pi$
$224$		−	286.998i		−	1.28124i
$225$	48.7176	+	195.350i	0.216523	+	0.868223i
$226$	−213.332			−0.943945
$227$	11.3853	+	71.8839i	0.0501555	+	0.316669i	0.999992	+	0.00392328i	$0.00124882\pi$
$227$	11.3853	+	71.8839i	0.0501555	+	0.316669i	−0.949837	+	0.312746i	$0.898751\pi$
$228$	137.565	+	70.0930i	0.603357	+	0.307426i
$229$	65.0698	−	21.1425i	0.284148	−	0.0923251i	−0.163476	−	0.986547i	$-0.552271\pi$
$229$	65.0698	−	21.1425i	0.284148	−	0.0923251i	0.447623	+	0.894222i	$0.352271\pi$
$230$	143.261	−	17.5943i	0.622876	−	0.0764968i
$231$	−21.6086	+	66.5045i	−0.0935437	+	0.287898i
$232$	−22.7953	−	22.7953i	−0.0982557	−	0.0982557i
$233$	−71.7766	−	140.869i	−0.308054	−	0.604590i	0.684132	−	0.729358i	$-0.260181\pi$
$233$	−71.7766	−	140.869i	−0.308054	−	0.604590i	−0.992186	+	0.124768i	$0.960181\pi$
$234$	−18.1018	−	24.9149i	−0.0773579	−	0.106474i
$235$	147.990	+	115.616i	0.629747	+	0.491984i
$236$	−138.505	−	100.629i	−0.586884	−	0.426396i
$237$	67.4143	+	10.6774i	0.284448	+	0.0450522i
$238$	72.9837	−	460.801i	0.306654	−	1.93614i
$239$	−257.267	+	354.097i	−1.07643	+	1.48158i	−0.213039	+	0.977044i	$0.568336\pi$
$239$	−257.267	+	354.097i	−1.07643	+	1.48158i	−0.863391	+	0.504535i	$0.831664\pi$
$240$	2.10076	−	60.2050i	0.00875318	−	0.250854i
$241$	232.488	−	168.912i	0.964679	−	0.700880i	0.0104463	−	0.999945i	$-0.496675\pi$
$241$	232.488	−	168.912i	0.964679	−	0.700880i	0.954233	+	0.299065i	$0.0966748\pi$
$242$	−25.4773	+	12.9813i	−0.105278	+	0.0536418i
$243$	144.352	−	144.352i	0.594041	−	0.594041i
$244$	55.2265	+	17.9442i	0.226338	+	0.0735417i
$245$	−46.4719	−	9.03191i	−0.189681	−	0.0368649i
$246$	−37.9688	−	116.856i	−0.154345	−	0.475024i
$247$	19.5550	−	38.3788i	0.0791700	−	0.155380i
$248$	28.4294	−	4.50278i	0.114635	−	0.0181564i
$249$			32.0585i			0.128749i
$250$	−337.991	−	150.450i	−1.35196	−	0.601801i
$251$	99.2278			0.395330			0.197665	−	0.980270i	$-0.436664\pi$
$251$	99.2278			0.395330			0.197665	+	0.980270i	$0.436664\pi$
$252$	37.7031	+	238.048i	0.149615	+	0.944634i
$253$	−99.3379	−	50.6152i	−0.392640	−	0.200060i
$254$	349.990	−	113.719i	1.37791	−	0.447712i
$255$	23.2690	−	119.726i	0.0912511	−	0.469514i
$256$	41.1327	−	126.594i	0.160675	−	0.494506i
$257$	31.4553	+	31.4553i	0.122394	+	0.122394i	0.765651	−	0.643257i	$-0.222417\pi$
$257$	31.4553	+	31.4553i	0.122394	+	0.122394i	−0.643257	+	0.765651i	$0.722417\pi$
$258$	19.6071	+	38.4810i	0.0759963	+	0.149151i
$259$	122.467	+	168.561i	0.472845	+	0.650815i
$260$	30.7311	+	1.07232i	0.118197	+	0.00412429i
$261$	−93.3902	−	67.8520i	−0.357817	−	0.259969i
$262$	−644.246	−	102.038i	−2.45895	−	0.389460i
$263$	15.1586	−	95.7079i	0.0576374	−	0.363909i	−0.941965	−	0.335711i	$-0.891023\pi$
$263$	15.1586	−	95.7079i	0.0576374	−	0.363909i	0.999602	−	0.0281972i	$-0.00897665\pi$
$264$	14.7022	−	20.2359i	0.0556902	−	0.0766510i
$265$	−229.608	+	293.901i	−0.866444	+	1.10906i
$266$	−501.895	+	364.648i	−1.88682	+	1.37086i
$267$	−34.3937	+	17.5245i	−0.128815	+	0.0656347i
$268$	−160.049	+	160.049i	−0.597197	+	0.597197i
$269$	111.956	+	36.3767i	0.416193	+	0.135229i	0.509626	−	0.860396i	$-0.329784\pi$
$269$	111.956	+	36.3767i	0.416193	+	0.135229i	−0.0934323	+	0.995626i	$0.529784\pi$
$270$	29.9308	+	243.712i	0.110855	+	0.902635i
$271$	129.678	+	399.108i	0.478517	+	1.47272i	0.841156	+	0.540793i	$0.181876\pi$
$271$	129.678	+	399.108i	0.478517	+	1.47272i	−0.362639	+	0.931930i	$0.618124\pi$
$272$	140.944	−	276.618i	0.518177	−	1.01698i
$273$	−7.80672	+	1.23646i	−0.0285960	+	0.00452917i
$274$			61.8130i			0.225595i
$275$	151.447	+	242.336i	0.550716	+	0.881223i
$276$	45.1706			0.163661
$277$	−51.2617	−	323.654i	−0.185060	−	1.16842i	−0.888912	−	0.458078i	$-0.848538\pi$
$277$	−51.2617	−	323.654i	−0.185060	−	1.16842i	0.703852	−	0.710347i	$-0.251462\pi$
$278$	162.735	+	82.9177i	0.585378	+	0.298265i
$279$	98.0252	−	31.8503i	0.351345	−	0.114159i
$280$	−61.8388	−	34.2756i	−0.220853	−	0.122413i
$281$	67.9073	−	208.997i	0.241663	−	0.743762i	−0.754505	−	0.656295i	$-0.772123\pi$
$281$	67.9073	−	208.997i	0.241663	−	0.743762i	0.996167	−	0.0874670i	$-0.0278772\pi$
$282$	76.4812	+	76.4812i	0.271210	+	0.271210i
$283$	−14.4152	−	28.2914i	−0.0509371	−	0.0999698i	0.864135	−	0.503260i	$-0.167866\pi$
$283$	−14.4152	−	28.2914i	−0.0509371	−	0.0999698i	−0.915072	+	0.403291i	$0.867866\pi$
$284$	168.312	+	231.661i	0.592647	+	0.815709i
$285$	−134.452	+	90.6946i	−0.471763	+	0.318227i
$286$	−35.3636	−	25.6932i	−0.123649	−	0.0898363i
$287$	264.966	+	41.9664i	0.923225	+	0.146225i
$288$	−57.5062	+	363.080i	−0.199674	+	1.26069i
$289$	199.585	−	274.706i	0.690607	−	0.950538i
$290$	203.904	−	58.4745i	0.703117	−	0.201636i
$291$	27.9746	−	20.3248i	0.0961327	−	0.0698445i
$292$	−174.538	+	88.9317i	−0.597734	+	0.304561i
$293$	11.7880	−	11.7880i	0.0402321	−	0.0402321i	−0.686705	−	0.726937i	$-0.740943\pi$
$293$	11.7880	−	11.7880i	0.0402321	−	0.0402321i	0.726937	+	0.686705i	$0.240943\pi$
$294$	−25.9314	−	8.42561i	−0.0882019	−	0.0286585i
$295$	162.986	−	76.0071i	0.552496	−	0.257651i
$296$	−23.0304	−	70.8804i	−0.0778055	−	0.239461i
$297$	86.1049	−	168.990i	0.289915	−	0.568991i
$298$	523.654	−	82.9387i	1.75723	−	0.278318i
$299$		−	12.6020i		−	0.0421471i
$300$	−99.2463	−	59.6258i	−0.330821	−	0.198753i
$301$	−94.2955			−0.313274
$302$	−117.532	−	742.069i	−0.389180	−	2.45718i
$303$	−136.484	−	69.5420i	−0.450442	−	0.229512i
$304$	−392.617	+	127.569i	−1.29150	+	0.419634i
$305$	−44.6099	+	41.6017i	−0.146262	+	0.136399i
$306$	−184.662	+	568.333i	−0.603472	+	1.85730i
$307$	87.7352	+	87.7352i	0.285782	+	0.285782i	0.835410	−	0.549628i	$-0.185230\pi$
$307$	87.7352	+	87.7352i	0.285782	+	0.285782i	−0.549628	+	0.835410i	$0.685230\pi$
$308$	155.306	+	304.805i	0.504240	+	0.989627i
$309$	42.6338	+	58.6804i	0.137973	+	0.189904i
$310$	−64.7730	+	177.977i	−0.208945	+	0.574121i
$311$	174.750	+	126.963i	0.561897	+	0.408242i	0.832153	−	0.554547i	$-0.187108\pi$
$311$	174.750	+	126.963i	0.561897	+	0.408242i	−0.270256	+	0.962789i	$0.587108\pi$
$312$	2.79247	+	0.442284i	0.00895022	+	0.00141758i
$313$	−13.2801	+	83.8475i	−0.0424286	+	0.267883i	−0.999778	−	0.0210477i	$-0.993300\pi$
$313$	−13.2801	+	83.8475i	−0.0424286	+	0.267883i	0.957350	+	0.288931i	$0.0932998\pi$
$314$	458.086	−	630.501i	1.45887	−	2.00796i
$315$	−237.908	−	86.5840i	−0.755263	−	0.274870i
$316$	270.139	−	196.267i	0.854869	−	0.621099i
$317$	−198.670	+	101.227i	−0.626718	+	0.319329i	−0.738347	−	0.674421i	$-0.764393\pi$
$317$	−198.670	+	101.227i	−0.626718	+	0.319329i	0.111629	+	0.993750i	$0.464393\pi$
$318$	−151.887	+	151.887i	−0.477634	+	0.477634i
$319$	−155.829	−	50.6318i	−0.488491	−	0.158720i
$320$	−291.794	−	312.893i	−0.911855	−	0.977791i
$321$	−44.5138	−	136.999i	−0.138672	−	0.426790i
$322$	−82.4005	+	161.720i	−0.255902	+	0.502236i
$323$	−825.516	+	130.749i	−2.55578	+	0.404795i
$324$		−	268.153i		−	0.827634i
$325$	−16.6348	+	27.6884i	−0.0511840	+	0.0851949i
$326$	460.701			1.41319
$327$	0.310524	+	1.96057i	0.000949616	+	0.00599564i
$328$	−85.5008	−	43.5648i	−0.260673	−	0.132820i
$329$	−224.596	+	72.9756i	−0.682662	+	0.221810i
$330$	69.5607	+	149.163i	0.210790	+	0.452009i
$331$	152.582	−	469.600i	0.460974	−	1.41873i	−0.403002	−	0.915199i	$-0.632033\pi$
$331$	152.582	−	469.600i	0.460974	−	1.41873i	0.863976	−	0.503533i	$-0.167967\pi$
$332$	110.899	+	110.899i	0.334032	+	0.334032i
$333$	−121.157	−	237.785i	−0.363836	−	0.714068i
$334$	−166.804	−	229.586i	−0.499413	−	0.687383i
$335$	−65.5422	−	228.549i	−0.195648	−	0.682237i
$336$	61.2855	+	44.5265i	0.182397	+	0.132519i
$337$	−226.455	−	35.8669i	−0.671972	−	0.106430i	−0.188881	−	0.982000i	$-0.560486\pi$
$337$	−226.455	−	35.8669i	−0.671972	−	0.106430i	−0.483091	+	0.875570i	$0.660486\pi$
$338$	−77.4742	+	489.153i	−0.229213	+	1.44720i
$339$	41.2215	−	56.7365i	0.121597	−	0.167364i
$340$	−333.670	−	494.656i	−0.981381	−	1.45487i
$341$	118.355	−	85.9899i	0.347082	−	0.252170i
$342$	708.010	−	360.749i	2.07020	−	1.05482i
$343$	259.943	−	259.943i	0.757851	−	0.757851i
$344$	32.0787	+	10.4230i	0.0932521	+	0.0302994i
$345$	−23.0027	+	41.5007i	−0.0666746	+	0.120292i
$346$	140.929	+	433.734i	0.407309	+	1.25357i
$347$	−272.870	+	535.538i	−0.786369	+	1.54334i	0.0522598	+	0.998634i	$0.483358\pi$
$347$	−272.870	+	535.538i	−0.786369	+	1.54334i	−0.838629	+	0.544703i	$0.816642\pi$
$348$	65.5666	−	10.3847i	0.188410	−	0.0298412i
$349$			328.447i			0.941109i	0.882371	+	0.470555i	$0.155946\pi$
$349$			328.447i			0.941109i	−0.882371	+	0.470555i	$0.844054\pi$
$350$	394.519	−	246.553i	1.12720	−	0.704436i
$351$	21.4380			0.0610770
$352$	81.6228	+	515.346i	0.231883	+	1.46405i
$353$	−46.9367	−	23.9154i	−0.132965	−	0.0677491i	0.386242	−	0.922397i	$-0.373773\pi$
$353$	−46.9367	−	23.9154i	−0.132965	−	0.0677491i	−0.519208	+	0.854648i	$0.673773\pi$
$354$	98.5064	−	32.0067i	0.278267	−	0.0904144i
$355$	−298.552	+	36.6658i	−0.840990	+	0.103284i
$356$	−58.3549	+	179.598i	−0.163918	+	0.504489i
$357$	108.450	+	108.450i	0.303780	+	0.303780i
$358$	45.2495	+	88.8071i	0.126395	+	0.248065i
$359$	58.3554	+	80.3193i	0.162550	+	0.223731i	0.882521	−	0.470274i	$-0.155845\pi$
$359$	58.3554	+	80.3193i	0.162550	+	0.223731i	−0.719971	+	0.694004i	$0.755845\pi$
$360$	71.3641	+	55.7526i	0.198234	+	0.154868i
$361$	607.081	+	441.070i	1.68166	+	1.22180i
$362$	−379.995	−	60.1853i	−1.04971	−	0.166258i
$363$	1.47046	−	9.28413i	0.00405086	−	0.0255761i
$364$	−22.7282	+	31.2826i	−0.0624400	+	0.0859413i
$365$	7.17570	−	205.646i	0.0196595	−	0.563413i
$366$	−28.4217	+	20.6496i	−0.0776550	+	0.0564196i
$367$	353.730	−	180.234i	0.963841	−	0.491101i	0.100067	−	0.994981i	$-0.468094\pi$
$367$	353.730	−	180.234i	0.963841	−	0.491101i	0.863774	+	0.503879i	$0.168094\pi$
$368$	−85.4033	+	85.4033i	−0.232074	+	0.232074i
$369$	−326.798	−	106.183i	−0.885630	−	0.287759i
$370$	481.388	+	93.5587i	1.30105	+	0.252861i
$371$	−144.925	−	446.035i	−0.390635	−	1.20225i
$372$	−26.9090	+	52.8118i	−0.0723359	+	0.141967i
$373$	322.660	−	51.1043i	0.865039	−	0.137009i	0.291882	−	0.956454i	$-0.405718\pi$
$373$	322.660	−	51.1043i	0.865039	−	0.137009i	0.573157	+	0.819446i	$0.305718\pi$
$374$			848.191i			2.26789i
$375$	105.322	−	60.8191i	0.280858	−	0.162184i
$376$	84.4724			0.224661
$377$	−2.89720	−	18.2922i	−0.00768487	−	0.0485204i
$378$	−275.113	−	140.177i	−0.727811	−	0.370838i
$379$	205.318	−	66.7119i	0.541737	−	0.176021i	−0.0253507	−	0.999679i	$-0.508070\pi$
$379$	205.318	−	66.7119i	0.541737	−	0.176021i	0.567087	+	0.823658i	$0.308070\pi$
$380$	−151.369	+	778.840i	−0.398340	+	2.04958i
$381$	−37.3836	+	115.055i	−0.0981198	+	0.301982i
$382$	−179.270	−	179.270i	−0.469293	−	0.469293i
$383$	131.906	+	258.880i	0.344402	+	0.675928i	0.996624	−	0.0821004i	$-0.0261628\pi$
$383$	131.906	+	258.880i	0.344402	+	0.675928i	−0.652222	+	0.758028i	$0.726163\pi$
$384$	−40.4159	−	55.6276i	−0.105250	−	0.144864i
$385$	−359.130	−	12.5313i	−0.932805	−	0.0325488i
$386$	−801.055	−	582.000i	−2.07527	−	1.50777i
$387$	119.293	+	18.8941i	0.308250	+	0.0488220i
$388$	26.4628	−	167.080i	0.0682032	−	0.430618i
$389$	324.417	−	446.521i	0.833976	−	1.14787i	−0.153194	−	0.988196i	$-0.548956\pi$
$389$	324.417	−	446.521i	0.833976	−	1.14787i	0.987170	−	0.159674i	$-0.0510442\pi$
$390$	−11.4531	+	14.6601i	−0.0293668	+	0.0375899i
$391$	−197.829	+	143.731i	−0.505957	+	0.367599i
$392$	−18.9734	+	9.66743i	−0.0484015	+	0.0246618i
$393$	151.623	−	151.623i	0.385810	−	0.385810i
$394$	−412.448	−	134.012i	−1.04682	−	0.340133i
$395$	42.7557	+	348.139i	0.108242	+	0.881365i
$396$	−135.403	−	416.726i	−0.341926	−	1.05234i
$397$	−104.265	+	204.632i	−0.262633	+	0.515446i	−0.984236	−	0.176861i	$-0.943406\pi$
$397$	−104.265	+	204.632i	−0.262633	+	0.515446i	0.721603	+	0.692307i	$0.243406\pi$
$398$	−40.9633	+	6.48795i	−0.102923	+	0.0163014i
$399$		−	203.941i		−	0.511131i
$400$	300.377	−	74.9098i	0.750943	−	0.187275i
$401$	−592.400			−1.47731			−0.738653	−	0.674086i	$-0.764538\pi$
$401$	−592.400			−1.47731			−0.738653	+	0.674086i	$0.764538\pi$
$402$	−21.4216	−	135.251i	−0.0532875	−	0.336444i
$403$	14.7338	+	7.50723i	0.0365602	+	0.0186284i
$404$	−712.695	+	231.569i	−1.76410	+	0.573190i
$405$	246.367	+	136.555i	0.608314	+	0.337173i
$406$	−82.4275	+	253.686i	−0.203023	+	0.624842i
$407$	−267.846	−	267.846i	−0.658098	−	0.658098i
$408$	−24.9063	−	48.8814i	−0.0610449	−	0.119807i
$409$	315.617	+	434.410i	0.771680	+	1.06213i	0.996152	+	0.0876456i	$0.0279343\pi$
$409$	315.617	+	434.410i	0.771680	+	1.06213i	−0.224472	+	0.974481i	$0.572066\pi$
$410$	523.458	−	353.098i	1.27673	−	0.861214i
$411$	−16.4394	−	11.9439i	−0.0399986	−	0.0290607i
$412$	350.471	+	55.5092i	0.850658	+	0.134731i
$413$	−35.3766	+	223.359i	−0.0856576	+	0.540821i
$414$	136.648	−	188.080i	0.330069	−	0.454300i
$415$	−158.363	+	45.4145i	−0.381597	+	0.109433i
$416$	−47.7135	+	34.6659i	−0.114696	+	0.0833314i
$417$	−53.4972	+	27.2582i	−0.128291	+	0.0653674i
$418$	797.519	−	797.519i	1.90794	−	1.90794i
$419$	469.941	+	152.693i	1.12158	+	0.364423i	0.810370	−	0.585919i	$-0.199266\pi$
$419$	469.941	+	152.693i	1.12158	+	0.364423i	0.311208	+	0.950342i	$0.399266\pi$
$420$	131.949	−	61.5334i	0.314165	−	0.146508i
$421$	−24.9277	−	76.7195i	−0.0592107	−	0.182232i	0.917076	−	0.398711i	$-0.130542\pi$
$421$	−24.9277	−	76.7195i	−0.0592107	−	0.182232i	−0.976287	+	0.216480i	$0.930542\pi$
$422$	−13.6095	+	26.7101i	−0.0322500	+	0.0632941i
$423$	298.757	−	47.3184i	0.706281	−	0.111864i
$424$			167.758i			0.395654i
$425$	624.387	−	54.6611i	1.46915	−	0.128614i
$426$	−173.240			−0.406666
$427$	−11.9991	−	75.7596i	−0.0281010	−	0.177423i
$428$	−627.900	−	319.931i	−1.46706	−	0.747503i
$429$	13.6664	−	4.44049i	0.0318565	−	0.0103508i
$430$	−162.313	+	151.368i	−0.377472	+	0.352018i
$431$	65.8440	−	202.647i	0.152770	−	0.470179i	−0.845158	−	0.534517i	$-0.820494\pi$
$431$	65.8440	−	202.647i	0.152770	−	0.470179i	0.997928	+	0.0643381i	$0.0204936\pi$
$432$	−145.285	−	145.285i	−0.336308	−	0.336308i
$433$	−261.013	−	512.267i	−0.602802	−	1.18306i	−0.967721	−	0.252025i	$-0.918903\pi$
$433$	−261.013	−	512.267i	−0.602802	−	1.18306i	0.364919	−	0.931039i	$-0.381097\pi$
$434$	−139.990	−	192.679i	−0.322557	−	0.443962i
$435$	−23.8482	+	65.5280i	−0.0548235	+	0.150639i
$436$	7.85630	+	5.70794i	0.0180190	+	0.0130916i
$437$	321.155	+	50.8660i	0.734909	+	0.116398i
$438$	18.5393	−	117.053i	0.0423273	−	0.267244i
$439$	−82.7547	+	113.902i	−0.188507	+	0.259458i	−0.892802	−	0.450450i	$-0.851264\pi$
$439$	−82.7547	+	113.902i	−0.188507	+	0.259458i	0.704294	+	0.709908i	$0.251264\pi$
$440$	120.789	+	43.9597i	0.274519	+	0.0999084i
$441$	−61.6886	+	44.8194i	−0.139883	+	0.101631i
$442$	−85.4238	+	43.5256i	−0.193266	+	0.0984742i
$443$	60.8675	−	60.8675i	0.137399	−	0.137399i	−0.635062	−	0.772461i	$-0.719026\pi$
$443$	60.8675	−	60.8675i	0.137399	−	0.137399i	0.772461	+	0.635062i	$0.219026\pi$
$444$	145.958	+	47.4246i	0.328734	+	0.106812i
$445$	−135.290	−	145.073i	−0.304022	−	0.326006i
$446$	45.7654	+	140.851i	0.102613	+	0.315810i
$447$	−79.1263	+	155.294i	−0.177016	+	0.347414i
$448$	531.377	−	84.1618i	1.18611	−	0.187861i
$449$			545.863i			1.21573i	0.794040	+	0.607865i	$0.207974\pi$
$449$			545.863i			1.21573i	−0.794040	+	0.607865i	$0.792026\pi$
$450$	−548.505	+	232.862i	−1.21890	+	0.517471i
$451$	−487.719			−1.08142
$452$	−53.6704	−	338.861i	−0.118740	−	0.749693i
$453$	220.067	+	112.130i	0.485799	+	0.247527i
$454$	−204.865	+	66.5646i	−0.451244	+	0.146618i
$455$	−17.1670	−	36.8121i	−0.0377296	−	0.0809056i
$456$	−22.5428	+	69.3795i	−0.0494359	+	0.152148i
$457$	454.070	+	454.070i	0.993589	+	0.993589i	0.999980	−	0.00639082i	$-0.00203427\pi$
$457$	454.070	+	454.070i	0.993589	+	0.993589i	−0.00639082	+	0.999980i	$0.502034\pi$
$458$	91.9325	+	180.428i	0.200726	+	0.393947i
$459$	−244.511	−	336.540i	−0.532703	−	0.733203i
$460$	63.9891	+	223.134i	0.139107	+	0.485073i
$461$	−263.053	−	191.119i	−0.570614	−	0.414576i	0.264714	−	0.964327i	$-0.414722\pi$
$461$	−263.053	−	191.119i	−0.570614	−	0.414576i	−0.835328	+	0.549751i	$0.814722\pi$
$462$	−204.415	−	32.3762i	−0.442457	−	0.0700783i
$463$	−92.8711	+	586.365i	−0.200586	+	1.26645i	0.657702	+	0.753278i	$0.271529\pi$
$463$	−92.8711	+	586.365i	−0.200586	+	1.26645i	−0.858288	+	0.513169i	$0.828471\pi$
$464$	−104.331	+	143.600i	−0.224852	+	0.309483i
$465$	−34.8180	−	51.6167i	−0.0748774	−	0.111004i
$466$	378.567	−	275.045i	0.812375	−	0.590225i
$467$	−403.365	+	205.525i	−0.863736	+	0.440095i	−0.828965	−	0.559300i	$-0.811070\pi$
$467$	−403.365	+	205.525i	−0.863736	+	0.440095i	−0.0347704	+	0.999395i	$0.511070\pi$
$468$	35.0214	−	35.0214i	0.0748321	−	0.0748321i
$469$	284.348	+	92.3904i	0.606287	+	0.196994i
$470$	−269.458	+	486.146i	−0.573315	+	1.03435i
$471$	79.1699	+	243.660i	0.168089	+	0.517324i
$472$	36.7240	−	72.0749i	0.0778051	−	0.152701i
$473$	169.321	−	26.8178i	0.357973	−	0.0566973i
$474$			202.014i			0.426189i
$475$	−638.480	−	535.689i	−1.34417	−	1.12777i
$476$	750.309			1.57628
$477$	93.9718	+	593.315i	0.197006	+	1.24385i
$478$	−1154.24	−	588.113i	−2.41472	−	1.23036i
$479$	30.4026	−	9.87842i	0.0634711	−	0.0206230i	−0.277109	−	0.960838i	$-0.589376\pi$
$479$	30.4026	−	9.87842i	0.0634711	−	0.0206230i	0.340580	+	0.940215i	$0.389376\pi$
$480$	220.406	−	27.0686i	0.459180	−	0.0563929i
$481$	13.2308	−	40.7203i	0.0275069	−	0.0846575i
$482$	601.418	+	601.418i	1.24775	+	1.24775i
$483$	−27.0881	−	53.1635i	−0.0560831	−	0.110069i
$484$	−27.0294	−	37.2028i	−0.0558460	−	0.0768654i
$485$	140.029	+	109.397i	0.288721	+	0.225561i
$486$	488.815	+	355.145i	1.00579	+	0.730750i
$487$	−811.083	−	128.463i	−1.66547	−	0.263784i	−0.748614	−	0.663006i	$-0.769280\pi$
$487$	−811.083	−	128.463i	−1.66547	−	0.263784i	−0.916854	+	0.399222i	$0.869280\pi$
$488$	−4.29210	+	27.0993i	−0.00879529	+	0.0555313i
$489$	−89.0199	+	122.525i	−0.182045	+	0.250563i
$490$	4.88619	−	140.032i	0.00997182	−	0.285779i
$491$	−37.1025	+	26.9565i	−0.0755651	+	0.0549013i	−0.624926	−	0.780684i	$-0.714871\pi$
$491$	−37.1025	+	26.9565i	−0.0755651	+	0.0549013i	0.549361	+	0.835585i	$0.314871\pi$
$492$	176.065	−	89.7094i	0.357855	−	0.182336i
$493$	−254.112	+	254.112i	−0.515440	+	0.515440i
$494$	121.246	+	39.3951i	0.245437	+	0.0797472i
$495$	451.822	+	87.8126i	0.912772	+	0.177399i
$496$	−48.9741	−	150.727i	−0.0987381	−	0.303885i
$497$	171.720	−	337.019i	0.345512	−	0.678106i
$498$	−93.7158	+	14.8431i	−0.188184	+	0.0298055i
$499$		−	841.721i		−	1.68681i	−0.537275	−	0.843407i	$-0.680546\pi$
$499$		−	841.721i		−	1.68681i	0.537275	−	0.843407i	$-0.319454\pi$
$500$	153.946	−	574.724i	0.307893	−	1.14945i
$501$	93.2904			0.186208
$502$	45.9425	+	290.070i	0.0915189	+	0.577828i
$503$	805.721	+	410.535i	1.60183	+	0.816174i	0.999844	+	0.0176677i	$0.00562411\pi$
$503$	805.721	+	410.535i	1.60183	+	0.816174i	0.601987	+	0.798506i	$0.294376\pi$
$504$	−108.305	+	35.1903i	−0.214890	+	0.0698221i
$505$	150.179	−	772.717i	0.297385	−	1.53013i
$506$	101.968	−	313.826i	0.201519	−	0.620210i
$507$	−115.122	−	115.122i	−0.227065	−	0.227065i
$508$	268.685	+	527.324i	0.528907	+	1.03804i
$509$	−418.463	−	575.964i	−0.822127	−	1.13156i	−0.989338	−	0.145640i	$-0.953476\pi$
$509$	−418.463	−	575.964i	−0.822127	−	1.13156i	0.167211	−	0.985921i	$-0.446524\pi$
$510$	360.765	+	12.5884i	0.707383	+	0.0246831i
$511$	209.336	+	152.092i	0.409660	+	0.297636i
$512$	668.311	+	105.850i	1.30529	+	0.206738i
$513$	−86.5315	+	546.338i	−0.168677	+	1.06499i
$514$	−77.3885	+	106.516i	−0.150561	+	0.207230i
$515$	−229.474	+	293.730i	−0.445581	+	0.570349i
$516$	−56.1914	+	40.8255i	−0.108898	+	0.0791191i
$517$	382.539	−	194.914i	0.739921	−	0.377009i
$518$	−436.048	+	436.048i	−0.841791	+	0.841791i
$519$	−142.585	−	46.3286i	−0.274730	−	0.0892652i
$520$	1.77105	+	14.4208i	0.00340586	+	0.0277323i
$521$	159.970	+	492.338i	0.307045	+	0.944987i	0.978906	+	0.204310i	$0.0654951\pi$
$521$	159.970	+	492.338i	0.307045	+	0.944987i	−0.671861	+	0.740677i	$0.734505\pi$
$522$	155.110	−	304.420i	0.297145	−	0.583181i
$523$	−735.179	+	116.441i	−1.40570	+	0.222640i	−0.812755	−	0.582605i	$-0.802033\pi$
$523$	−735.179	+	116.441i	−1.40570	+	0.222640i	−0.592941	+	0.805246i	$0.702033\pi$
$524$		−	1049.01i		−	2.00192i
$525$	−10.6600	+	152.565i	−0.0203048	+	0.290599i
$526$	286.799			0.545245
$527$	−50.1949	−	316.918i	−0.0952465	−	0.601363i
$528$	−122.710	−	62.5240i	−0.232406	−	0.118417i
$529$	−412.634	+	134.073i	−0.780026	+	0.253446i
$530$	−965.460	−	535.129i	−1.82162	−	1.00968i
$531$	89.5094	−	275.482i	0.168568	−	0.518798i
$532$	−705.484	−	705.484i	−1.32610	−	1.32610i
$533$	−25.0277	−	49.1196i	−0.0469563	−	0.0921569i
$534$	−67.1531	−	92.4283i	−0.125755	−	0.173087i
$535$	613.692	−	413.965i	1.14709	−	0.773766i
$536$	−86.5211	−	62.8612i	−0.161420	−	0.117278i
$537$	−32.3621	−	5.12565i	−0.0602646	−	0.00954497i
$538$	−54.5033	+	344.120i	−0.101307	+	0.639629i
$539$	−63.6155	+	87.5593i	−0.118025	+	0.162448i
$540$	−379.587	+	108.856i	−0.702940	+	0.201585i
$541$	−309.500	+	224.865i	−0.572089	+	0.415647i	−0.835863	−	0.548937i	$-0.815033\pi$
$541$	−309.500	+	224.865i	−0.572089	+	0.415647i	0.263775	+	0.964584i	$0.415033\pi$
$542$	−1106.66	+	563.871i	−2.04181	+	1.04035i
$543$	89.4319	−	89.4319i	0.164700	−	0.164700i
$544$	1088.39	+	353.639i	2.00072	+	0.650072i
$545$	−9.24496	+	4.31130i	−0.0169632	+	0.00791065i
$546$	−7.22903	−	22.2487i	−0.0132400	−	0.0407485i
$547$	480.598	−	943.226i	0.878607	−	1.72436i	0.214501	−	0.976724i	$-0.431188\pi$
$547$	480.598	−	943.226i	0.878607	−	1.72436i	0.664106	−	0.747639i	$-0.268812\pi$
$548$	−98.1853	+	15.5510i	−0.179170	+	0.0283778i
$549$			98.2473i			0.178957i
$550$	−638.295	+	554.922i	−1.16054	+	1.00895i
$551$	477.861			0.867262
$552$	3.33876	+	21.0801i	0.00604847	+	0.0381885i
$553$	−392.995	−	200.241i	−0.710660	−	0.362099i
$554$	922.393	−	299.704i	1.66497	−	0.540981i
$555$	−117.900	+	109.949i	−0.212432	+	0.198106i
$556$	−90.7674	+	279.353i	−0.163251	+	0.502434i
$557$	−229.778	−	229.778i	−0.412528	−	0.412528i	0.470090	−	0.882618i	$-0.344221\pi$
$557$	−229.778	−	229.778i	−0.412528	−	0.412528i	−0.882618	+	0.470090i	$0.844221\pi$
$558$	138.493	+	271.807i	0.248195	+	0.487110i
$559$	11.3897	+	15.6766i	0.0203752	+	0.0280441i
$560$	−133.134	+	365.815i	−0.237740	+	0.653241i
$561$	−225.580	−	163.894i	−0.402104	−	0.292145i
$562$	642.396	+	101.746i	1.14305	+	0.181042i
$563$	149.292	−	942.595i	0.265173	−	1.67424i	−0.391590	−	0.920140i	$-0.628075\pi$
$563$	149.292	−	942.595i	0.265173	−	1.67424i	0.656763	−	0.754097i	$-0.271925\pi$
$564$	−102.243	+	140.726i	−0.181283	+	0.249514i
$565$	338.662	+	123.252i	0.599402	+	0.218146i
$566$	76.0293	−	55.2385i	0.134327	−	0.0975945i
$567$	−315.603	+	160.808i	−0.556619	+	0.283612i
$568$	−95.6704	+	95.6704i	−0.168434	+	0.168434i
$569$	118.610	+	38.5387i	0.208453	+	0.0677305i	0.411382	−	0.911463i	$-0.365046\pi$
$569$	118.610	+	38.5387i	0.208453	+	0.0677305i	−0.202929	+	0.979193i	$0.565046\pi$
$570$	−327.376	−	351.049i	−0.574345	−	0.615876i
$571$	82.0724	+	252.593i	0.143734	+	0.442369i	0.996846	−	0.0793593i	$-0.0252874\pi$
$571$	82.0724	+	252.593i	0.143734	+	0.442369i	−0.853112	+	0.521728i	$0.825287\pi$
$572$	31.9148	−	62.6364i	0.0557952	−	0.109504i
$573$	82.3174	−	13.0378i	0.143660	−	0.0227536i
$574$			793.997i			1.38327i
$575$	−237.591	−	54.8386i	−0.413202	−	0.0953715i
$576$	−689.105			−1.19636
$577$	11.1911	+	70.6581i	0.0193954	+	0.122458i	0.995486	−	0.0949047i	$-0.0302547\pi$
$577$	11.1911	+	70.6581i	0.0193954	+	0.122458i	−0.976091	+	0.217362i	$0.930255\pi$
$578$	895.447	+	456.253i	1.54922	+	0.789365i
$579$	309.571	−	100.586i	0.534665	−	0.173723i
$580$	144.181	+	309.175i	0.248588	+	0.533060i
$581$	64.0177	−	197.026i	0.110185	−	0.339116i
$582$	72.3670	+	72.3670i	0.124342	+	0.124342i
$583$	387.088	+	759.702i	0.663958	+	1.30309i
$584$	−54.4033	−	74.8798i	−0.0931564	−	0.128219i
$585$	14.3418	+	50.0105i	0.0245158	+	0.0854880i
$586$	39.9174	+	29.0017i	0.0681183	+	0.0494909i
$587$	153.272	+	24.2758i	0.261110	+	0.0413558i	0.285617	−	0.958344i	$-0.407802\pi$
$587$	153.272	+	24.2758i	0.261110	+	0.0413558i	−0.0245068	+	0.999700i	$0.507802\pi$
$588$	6.85959	−	43.3098i	0.0116660	−	0.0736561i
$589$	−250.789	+	345.181i	−0.425788	+	0.586046i
$590$	297.652	+	441.261i	0.504495	+	0.747901i
$591$	115.337	−	83.7975i	0.195156	−	0.141789i
$592$	−365.626	+	186.296i	−0.617611	+	0.314688i
$593$	537.487	−	537.487i	0.906386	−	0.906386i	−0.0895921	−	0.995979i	$-0.528556\pi$
$593$	537.487	−	537.487i	0.906386	−	0.906386i	0.995979	+	0.0895921i	$0.0285564\pi$
$594$	533.871	+	173.465i	0.898772	+	0.292029i
$595$	−382.089	+	689.351i	−0.642166	+	1.15857i
$596$	263.484	+	810.919i	0.442087	+	1.36060i
$597$	6.18973	−	12.1480i	0.0103681	−	0.0203484i
$598$	36.8390	−	5.83472i	0.0616036	−	0.00975705i
$599$			15.1629i			0.0253137i	0.999920	+	0.0126568i	$0.00402891\pi$
$599$			15.1629i			0.0253137i	−0.999920	+	0.0126568i	$0.995971\pi$
$600$	20.4903	−	50.7232i	0.0341505	−	0.0845387i
$601$	164.547			0.273789			0.136895	−	0.990586i	$-0.456288\pi$
$601$	164.547			0.273789			0.136895	+	0.990586i	$0.456288\pi$
$602$	−43.6588	−	275.651i	−0.0725230	−	0.457892i
$603$	−341.215	−	173.858i	−0.565863	−	0.288321i
$604$	1149.15	−	373.382i	1.90257	−	0.618183i
$605$	47.9449	−	5.88821i	0.0792477	−	0.00973259i
$606$	140.098	−	431.177i	0.231185	−	0.711513i
$607$	−428.540	−	428.540i	−0.705998	−	0.705998i	0.259694	−	0.965691i	$-0.416378\pi$
$607$	−428.540	−	428.540i	−0.705998	−	0.705998i	−0.965691	+	0.259694i	$0.916378\pi$
$608$	−690.855	−	1355.88i	−1.13627	−	2.23006i
$609$	−51.5416	−	70.9410i	−0.0846332	−	0.116488i
$610$	−142.267	−	111.145i	−0.233225	−	0.182205i
$611$	39.2606	+	28.5245i	0.0642563	+	0.0466850i
$612$	−949.211	−	150.340i	−1.55100	−	0.245654i
$613$	50.7849	−	320.643i	0.0828465	−	0.523072i	−0.911009	−	0.412386i	$-0.864695\pi$
$613$	50.7849	−	320.643i	0.0828465	−	0.523072i	0.993855	−	0.110686i	$-0.0353046\pi$
$614$	−215.852	+	297.095i	−0.351551	+	0.483868i
$615$	−7.23845	+	207.444i	−0.0117698	+	0.337308i
$616$	−130.766	+	95.0073i	−0.212283	+	0.154233i
$617$	689.629	−	351.383i	1.11771	−	0.569503i	0.205269	−	0.978706i	$-0.434193\pi$
$617$	689.629	−	351.383i	1.11771	−	0.569503i	0.912444	+	0.409202i	$0.134193\pi$
$618$	−151.799	+	151.799i	−0.245630	+	0.245630i
$619$	−202.582	−	65.8227i	−0.327272	−	0.106337i	0.140772	−	0.990042i	$-0.455041\pi$
$619$	−202.582	−	65.8227i	−0.327272	−	0.106337i	−0.468045	+	0.883705i	$0.655041\pi$
$620$	−298.999	−	58.1111i	−0.482257	−	0.0937277i
$621$	50.0094	+	153.913i	0.0805304	+	0.247847i
$622$	−290.239	+	569.625i	−0.466621	+	0.915796i
$623$	246.373	−	39.0216i	0.395461	−	0.0626349i
$624$		−	15.5670i		−	0.0249471i
$625$	449.635	+	434.112i	0.719416	+	0.694580i
$626$	−251.258			−0.401370
$627$	58.0013	+	366.206i	0.0925061	+	0.584060i
$628$	1116.75	+	569.012i	1.77826	+	0.906070i
$629$	−790.142	+	256.733i	−1.25619	+	0.408160i
$630$	142.957	−	735.557i	0.226916	−	1.16755i
$631$	−285.551	+	878.834i	−0.452537	+	1.39276i	0.421467	+	0.906844i	$0.361515\pi$
$631$	−285.551	+	878.834i	−0.452537	+	1.39276i	−0.874003	+	0.485920i	$0.838485\pi$
$632$	111.561	+	111.561i	0.176520	+	0.176520i
$633$	−4.47395	−	8.78063i	−0.00706786	−	0.0138714i
$634$	−387.899	−	533.897i	−0.611828	−	0.842109i
$635$	−621.307	−	21.6796i	−0.978437	−	0.0341411i
$636$	−279.474	−	203.050i	−0.439425	−	0.319261i
$637$	−12.0828	−	1.91373i	−0.0189683	−	0.00300429i
$638$	75.8617	−	478.972i	0.118905	−	0.750740i
$639$	−284.770	+	391.952i	−0.445650	+	0.613384i
$640$	217.536	−	278.449i	0.339900	−	0.435077i
$641$	−508.952	+	369.776i	−0.793998	+	0.576873i	−0.909147	−	0.416475i	$-0.863265\pi$
$641$	−508.952	+	369.776i	−0.793998	+	0.576873i	0.115150	+	0.993348i	$0.463265\pi$
$642$	379.877	−	193.557i	0.591708	−	0.301490i
$643$	−802.840	+	802.840i	−1.24858	+	1.24858i	−0.292239	+	0.956345i	$0.594400\pi$
$643$	−802.840	+	802.840i	−1.24858	+	1.24858i	−0.956345	+	0.292239i	$0.905600\pi$
$644$	−277.611	−	90.2012i	−0.431072	−	0.140064i
$645$	−8.89360	−	72.4162i	−0.0137885	−	0.112273i
$646$	−764.428	−	2352.67i	−1.18333	−	3.64190i
$647$	334.566	−	656.622i	0.517103	−	1.01487i	−0.473843	−	0.880610i	$-0.657133\pi$
$647$	334.566	−	656.622i	0.517103	−	1.01487i	0.990946	−	0.134263i	$-0.0428666\pi$
$648$	125.141	−	19.8204i	0.193119	−	0.0305870i
$649$		−	411.134i		−	0.633489i
$650$	−88.6424	−	35.8082i	−0.136373	−	0.0550896i
$651$	78.2938			0.120267
$652$	115.904	+	731.789i	0.177767	+	1.12238i
$653$	−709.575	−	361.547i	−1.08664	−	0.553670i	−0.183500	−	0.983020i	$-0.558743\pi$
$653$	−709.575	−	361.547i	−1.08664	−	0.553670i	−0.903138	+	0.429349i	$0.858743\pi$
$654$	−5.58751	+	1.81549i	−0.00854360	+	0.00277598i
$655$	963.781	+	534.198i	1.47142	+	0.815570i
$656$	−163.271	+	502.495i	−0.248888	+	0.765998i
$657$	−234.355	−	234.355i	−0.356705	−	0.356705i
$658$	−317.315	−	622.766i	−0.482242	−	0.946453i
$659$	92.3925	+	127.167i	0.140201	+	0.192970i	0.873343	−	0.487105i	$-0.161947\pi$
$659$	92.3925	+	127.167i	0.140201	+	0.192970i	−0.733142	+	0.680075i	$0.761947\pi$
$660$	−219.434	+	148.019i	−0.332476	+	0.224271i
$661$	−349.210	−	253.716i	−0.528305	−	0.383836i	0.291418	−	0.956596i	$-0.405873\pi$
$661$	−349.210	−	253.716i	−0.528305	−	0.383836i	−0.819723	+	0.572760i	$0.805873\pi$
$662$	1443.41	+	228.614i	2.18038	+	0.345339i
$663$	4.93037	−	31.1292i	0.00743646	−	0.0469520i
$664$	−43.5568	+	59.9509i	−0.0655977	+	0.0902874i
$665$	1007.43	−	288.906i	1.51493	−	0.434445i
$666$	639.013	−	464.270i	0.959478	−	0.697102i
$667$	124.569	−	63.4711i	0.186760	−	0.0951591i
$668$	322.715	−	322.715i	0.483106	−	0.483106i
$669$	−46.3031	−	15.0448i	−0.0692125	−	0.0224885i
$670$	637.765	−	297.416i	0.951889	−	0.443905i
$671$	43.0924	+	132.625i	0.0642211	+	0.197652i
$672$	−126.772	+	248.805i	−0.188649	+	0.370245i
$673$	317.505	−	50.2878i	0.471775	−	0.0747219i	0.0839802	−	0.996467i	$-0.473237\pi$
$673$	317.505	−	50.2878i	0.471775	−	0.0747219i	0.387795	+	0.921746i	$0.373237\pi$
$674$		−	678.594i		−	1.00682i
$675$	93.2896	−	404.182i	0.138207	−	0.598789i
$676$	−796.473			−1.17821
$677$	−23.3571	−	147.471i	−0.0345009	−	0.217830i	0.964414	−	0.264395i	$-0.0851724\pi$
$677$	−23.3571	−	147.471i	−0.0345009	−	0.217830i	−0.998915	+	0.0465654i	$0.985172\pi$
$678$	184.942	+	94.2325i	0.272775	+	0.138986i
$679$	−212.514	+	69.0499i	−0.312981	+	0.101694i
$680$	206.182	−	192.278i	0.303209	−	0.282762i
$681$	21.8823	−	67.3467i	0.0321326	−	0.0988939i
$682$	306.170	+	306.170i	0.448930	+	0.448930i
$683$	334.734	+	656.953i	0.490094	+	0.961864i	0.995112	+	0.0987551i	$0.0314861\pi$
$683$	334.734	+	656.953i	0.490094	+	0.961864i	−0.505017	+	0.863109i	$0.668514\pi$
$684$	751.145	+	1033.86i	1.09817	+	1.51150i
$685$	35.7125	−	98.1275i	0.0521350	−	0.143252i
$686$	880.237	+	639.530i	1.28314	+	0.932259i
$687$	−65.7494	−	10.4137i	−0.0957050	−	0.0151582i
$688$	29.0522	−	183.428i	0.0422270	−	0.266611i
$689$	−56.6481	+	77.9694i	−0.0822178	+	0.113163i
$690$	−131.968	−	48.0284i	−0.191258	−	0.0696063i
$691$	763.534	−	554.740i	1.10497	−	0.802807i	0.123105	−	0.992394i	$-0.460715\pi$
$691$	763.534	−	554.740i	1.10497	−	0.802807i	0.981864	+	0.189587i	$0.0607148\pi$
$692$	−653.499	+	332.974i	−0.944363	+	0.481177i
$693$	−409.267	+	409.267i	−0.590573	+	0.590573i
$694$	−1691.86	−	549.719i	−2.43784	−	0.792102i
$695$	−210.435	−	225.651i	−0.302784	−	0.324678i
$696$	9.69263	+	29.8308i	0.0139262	+	0.0428604i
$697$	−485.641	+	953.124i	−0.696759	+	1.36747i
$698$	−960.140	+	152.071i	−1.37556	+	0.217867i
$699$			153.828i			0.220068i
$700$	490.884	+	564.635i	0.701263	+	0.806622i
$701$	−56.1217			−0.0800595			−0.0400297	−	0.999198i	$-0.512745\pi$
$701$	−56.1217			−0.0800595			−0.0400297	+	0.999198i	$0.512745\pi$
$702$	9.92582	+	62.6692i	0.0141393	+	0.0892723i
$703$	984.332	+	501.542i	1.40019	+	0.713431i
$704$	−930.227	+	302.249i	−1.32135	+	0.429331i
$705$	−77.2262	−	165.600i	−0.109541	−	0.234894i
$706$	48.1796	−	148.282i	0.0682430	−	0.210031i
$707$	699.938	+	699.938i	0.990011	+	0.990011i
$708$	75.6226	+	148.418i	0.106812	+	0.209630i
$709$	271.095	+	373.130i	0.382362	+	0.526276i	0.956208	−	0.292687i	$-0.0945494\pi$
$709$	271.095	+	373.130i	0.382362	+	0.526276i	−0.573846	+	0.818963i	$0.694549\pi$
$710$	−245.414	−	855.771i	−0.345653	−	1.20531i
$711$	457.053	+	332.069i	0.642831	+	0.467044i
$712$	−88.1276	−	13.9580i	−0.123775	−	0.0196040i
$713$	−19.5276	+	123.293i	−0.0273880	+	0.172921i
$714$	−266.815	+	367.240i	−0.373691	+	0.514341i
$715$	41.2952	+	61.2190i	0.0577555	+	0.0856210i
$716$	−129.679	+	94.2177i	−0.181117	+	0.131589i
$717$	379.441	−	193.335i	0.529207	−	0.269644i
$718$	−207.776	+	207.776i	−0.289382	+	0.289382i
$719$	−1015.95	−	330.102i	−1.41300	−	0.459112i	−0.499631	−	0.866238i	$-0.666531\pi$
$719$	−1015.95	−	330.102i	−1.41300	−	0.459112i	−0.913372	+	0.407126i	$0.866531\pi$
$720$	241.726	−	436.114i	0.335731	−	0.605714i
$721$	−144.841	−	445.775i	−0.200889	−	0.618273i
$722$	−1008.29	+	1978.88i	−1.39652	+	2.74083i
$723$	−276.160	+	43.7394i	−0.381964	+	0.0604971i
$724$		−	618.735i		−	0.854606i
$725$	−357.479	−	24.9778i	−0.493075	−	0.0344521i
$726$	27.8208			0.0383207
$727$	7.78088	+	49.1265i	0.0107027	+	0.0675743i	0.992462	−	0.122556i	$-0.0391090\pi$
$727$	7.78088	+	49.1265i	0.0107027	+	0.0675743i	−0.981759	+	0.190130i	$0.939109\pi$
$728$	−16.2788	−	8.29448i	−0.0223610	−	0.0113935i
$729$	293.305	−	95.3007i	0.402339	−	0.130728i
$730$	604.481	−	74.2376i	0.828056	−	0.101695i
$731$	116.191	−	357.599i	0.158948	−	0.489191i
$732$	−39.9507	−	39.9507i	−0.0545775	−	0.0545775i
$733$	−644.551	−	1265.00i	−0.879333	−	1.72579i	−0.661718	−	0.749753i	$-0.730172\pi$
$733$	−644.551	−	1265.00i	−0.879333	−	1.72579i	−0.217615	−	0.976035i	$-0.569828\pi$
$734$	690.650	+	950.598i	0.940940	+	1.29509i
$735$	36.2979	+	28.3574i	0.0493849	+	0.0385815i
$736$	−360.185	−	261.689i	−0.489381	−	0.355556i
$737$	−536.864	−	85.0310i	−0.728446	−	0.115374i
$738$	159.094	−	1004.48i	0.215575	−	1.36108i
$739$	611.437	−	841.571i	0.827385	−	1.13880i	−0.161019	−	0.986951i	$-0.551478\pi$
$739$	611.437	−	841.571i	0.827385	−	1.13880i	0.988404	−	0.151846i	$-0.0485218\pi$
$740$	−27.5025	+	788.186i	−0.0371656	+	1.06512i
$741$	−33.9053	+	24.6336i	−0.0457561	+	0.0332438i
$742$	1236.78	−	630.170i	1.66682	−	0.849286i
$743$	458.649	−	458.649i	0.617293	−	0.617293i	−0.327543	−	0.944836i	$-0.606221\pi$
$743$	458.649	−	458.649i	0.617293	−	0.617293i	0.944836	+	0.327543i	$0.106221\pi$
$744$	−26.6350	−	8.65425i	−0.0357998	−	0.0116321i
$745$	−879.214	−	170.877i	−1.18015	−	0.229365i
$746$	298.783	+	919.560i	0.400514	+	1.23265i
$747$	−120.467	+	236.430i	−0.161268	+	0.316505i
$748$	−1347.29	+	213.389i	−1.80119	+	0.285280i
$749$			930.865i			1.24281i
$750$	226.555	+	279.725i	0.302073	+	0.372967i
$751$	1230.15			1.63801			0.819006	−	0.573784i	$-0.194525\pi$
$751$	1230.15			1.63801			0.819006	+	0.573784i	$0.194525\pi$
$752$	−72.7584	−	459.379i	−0.0967532	−	0.610876i
$753$	−86.0226	−	43.8307i	−0.114240	−	0.0582081i
$754$	52.1316	−	16.9386i	0.0691400	−	0.0224649i
$755$	−242.149	+	1245.93i	−0.320728	+	1.65024i
$756$	153.447	−	472.262i	0.202972	−	0.624685i
$757$	416.379	+	416.379i	0.550039	+	0.550039i	0.926452	−	0.376413i	$-0.122843\pi$
$757$	416.379	+	416.379i	0.550039	+	0.550039i	−0.376413	+	0.926452i	$0.622843\pi$
$758$	290.079	+	569.313i	0.382690	+	0.751072i
$759$	63.7605	+	87.7587i	0.0840059	+	0.115624i
$760$	−374.656	−	13.0730i	−0.492968	−	0.0172014i
$761$	−1100.67	−	799.682i	−1.44634	−	1.05083i	−0.986668	−	0.162745i	$-0.947965\pi$
$761$	−1100.67	−	799.682i	−1.44634	−	1.05083i	−0.459677	−	0.888086i	$-0.652035\pi$
$762$	−353.646	−	56.0119i	−0.464102	−	0.0735065i
$763$	2.00664	−	12.6694i	0.00262994	−	0.0166048i
$764$	239.656	−	329.858i	0.313685	−	0.431751i
$765$	621.504	−	795.534i	0.812424	−	1.03991i
$766$	−695.705	+	505.459i	−0.908231	+	0.659868i
$767$	41.4065	−	21.0977i	0.0539850	−	0.0275068i
$768$	−91.5775	+	91.5775i	−0.119242	+	0.119242i
$769$	173.436	+	56.3528i	0.225535	+	0.0732807i	0.419604	−	0.907707i	$-0.362169\pi$
$769$	173.436	+	56.3528i	0.225535	+	0.0732807i	−0.194070	+	0.980988i	$0.562169\pi$
$770$	−129.645	−	1055.64i	−0.168370	−	1.37096i
$771$	−13.3749	−	41.1636i	−0.0173474	−	0.0533899i
$772$	722.933	−	1418.84i	0.936442	−	1.83787i
$773$	1077.04	−	170.587i	1.39333	−	0.220681i	0.585773	−	0.810475i	$-0.300791\pi$
$773$	1077.04	−	170.587i	1.39333	−	0.220681i	0.807554	+	0.589794i	$0.200791\pi$
$774$			357.473i			0.461851i
$775$	205.653	−	245.115i	0.265359	−	0.316277i
$776$	79.9283			0.103000
$777$	−31.7125	−	200.225i	−0.0408141	−	0.257690i
$778$	1455.51	+	741.618i	1.87083	+	0.953237i
$779$	1352.81	−	439.555i	1.73660	−	0.564255i
$780$	−26.1678	−	14.5041i	−0.0335485	−	0.0185950i
$781$	−212.498	+	654.003i	−0.272085	+	0.837391i
$782$	−511.761	−	511.761i	−0.654425	−	0.654425i
$783$	107.975	+	211.913i	0.137899	+	0.270642i
$784$	68.9158	+	94.8545i	0.0879028	+	0.120988i
$785$	−1091.48	+	736.255i	−1.39042	+	0.937904i
$786$	513.438	+	373.034i	0.653229	+	0.474598i
$787$	−909.702	−	144.083i	−1.15591	−	0.183078i	−0.451100	−	0.892473i	$-0.648968\pi$
$787$	−909.702	−	144.083i	−1.15591	−	0.183078i	−0.704811	+	0.709395i	$0.748968\pi$
$788$	109.104	−	688.858i	0.138457	−	0.874185i
$789$	−55.4173	+	76.2754i	−0.0702374	+	0.0966735i
$790$	−997.908	+	286.175i	−1.26318	+	0.362247i
$791$	−366.637	+	266.378i	−0.463511	+	0.336761i
$792$	184.468	−	93.9914i	0.232915	−	0.118676i
$793$	−11.1457	+	11.1457i	−0.0140551	+	0.0140551i
$794$	−646.470	−	210.051i	−0.814194	−	0.264548i
$795$	328.873	−	153.367i	0.413677	−	0.192914i
$796$	−20.6112	−	63.4349i	−0.0258935	−	0.0796921i
$797$	427.244	−	838.514i	0.536065	−	1.05209i	−0.451113	−	0.892467i	$-0.648973\pi$
$797$	427.244	−	838.514i	0.536065	−	1.05209i	0.987178	−	0.159621i	$-0.0510271\pi$
$798$	596.175	−	94.4249i	0.747087	−	0.118327i
$799$		−	941.659i		−	1.17855i
$800$	445.944	+	1050.42i	0.557430	+	1.31302i
$801$	−319.503			−0.398880
$802$	−274.281	−	1731.74i	−0.341997	−	2.15928i
$803$	−419.149	−	213.567i	−0.521978	−	0.265961i
$804$	209.446	−	68.0532i	0.260505	−	0.0846433i
$805$	224.244	−	209.122i	0.278564	−	0.259779i
$806$	−15.1239	+	46.5466i	−0.0187642	+	0.0577502i
$807$	−80.9888	−	80.9888i	−0.100358	−	0.100358i
$808$	−160.746	−	315.483i	−0.198944	−	0.390449i
$809$	302.235	+	415.991i	0.373591	+	0.514203i	0.953872	−	0.300212i	$-0.0970576\pi$
$809$	302.235	+	415.991i	0.373591	+	0.514203i	−0.580282	+	0.814416i	$0.697058\pi$
$810$	−285.119	+	783.423i	−0.351998	+	0.967189i
$811$	−749.585	−	544.605i	−0.924272	−	0.671523i	0.0203115	−	0.999794i	$-0.493534\pi$
$811$	−749.585	−	544.605i	−0.924272	−	0.671523i	−0.944584	+	0.328271i	$0.893534\pi$
$812$	−423.698	−	67.1072i	−0.521796	−	0.0826443i
$813$	63.8727	−	403.276i	0.0785642	−	0.496035i
$814$	658.973	−	906.999i	0.809549	−	1.11425i
$815$	−731.358	−	266.170i	−0.897372	−	0.326589i
$816$	−244.375	+	177.549i	−0.299479	+	0.217584i
$817$	−445.485	+	226.986i	−0.545269	+	0.277828i
$818$	−1123.77	+	1123.77i	−1.37380	+	1.37380i
$819$	−62.2203	−	20.2166i	−0.0759711	−	0.0246845i
$820$	692.562	+	742.641i	0.844588	+	0.905660i
$821$	39.2745	+	120.874i	0.0478374	+	0.147228i	0.972122	−	0.234476i	$-0.0753374\pi$
$821$	39.2745	+	120.874i	0.0478374	+	0.147228i	−0.924285	+	0.381704i	$0.875337\pi$
$822$	27.3039	−	53.5870i	0.0332165	−	0.0651910i
$823$	−953.197	+	150.972i	−1.15820	+	0.183441i	−0.705824	−	0.708388i	$-0.749423\pi$
$823$	−953.197	+	150.972i	−1.15820	+	0.183441i	−0.452374	+	0.891828i	$0.649423\pi$
$824$			167.660i			0.203471i
$825$	−24.2481	−	276.983i	−0.0293917	−	0.335737i
$826$	−669.318			−0.810312
$827$	25.6122	+	161.709i	0.0309700	+	0.195537i	0.998323	−	0.0578978i	$-0.0184397\pi$
$827$	25.6122	+	161.709i	0.0309700	+	0.195537i	−0.967353	+	0.253435i	$0.918440\pi$
$828$	333.130	+	169.738i	0.402331	+	0.204998i
$829$	−313.938	+	102.005i	−0.378695	+	0.123045i	−0.492178	−	0.870495i	$-0.663799\pi$
$829$	−313.938	+	102.005i	−0.378695	+	0.123045i	0.113483	+	0.993540i	$0.463799\pi$
$830$	−206.081	−	441.911i	−0.248290	−	0.532422i
$831$	−98.5239	+	303.225i	−0.118561	+	0.364892i
$832$	−78.1757	−	78.1757i	−0.0939612	−	0.0939612i
$833$	107.768	+	211.507i	0.129373	+	0.253910i
$834$	−104.452	−	143.766i	−0.125243	−	0.172382i
$835$	132.156	+	460.836i	0.158271	+	0.551900i
$836$	1467.44	+	1066.16i	1.75531	+	1.27531i
$837$	−209.741	−	33.2197i	−0.250587	−	0.0396890i
$838$	−228.780	+	1444.46i	−0.273008	+	1.72370i
$839$	164.243	−	226.060i	0.195760	−	0.269440i	−0.699841	−	0.714299i	$-0.746746\pi$
$839$	164.243	−	226.060i	0.195760	−	0.269440i	0.895601	+	0.444858i	$0.146746\pi$
$840$	38.4692	+	57.0296i	0.0457967	+	0.0678924i
$841$	−514.159	+	373.559i	−0.611367	+	0.444184i
$842$	212.730	−	108.392i	0.252649	−	0.128731i
$843$	−151.188	+	151.188i	−0.179345	+	0.179345i
$844$	−45.8509	−	14.8979i	−0.0543257	−	0.0176515i
$845$	405.598	−	731.764i	0.479997	−	0.865993i
$846$	276.649	+	851.439i	0.327008	+	1.00643i
$847$	−27.5767	+	54.1223i	−0.0325581	+	0.0638988i
$848$	912.300	−	144.494i	1.07583	−	0.170394i
$849$			30.8939i			0.0363886i
$850$	448.880	+	1799.94i	0.528095	+	2.11758i
$851$	323.213			0.379803
$852$	−43.5840	−	275.178i	−0.0511549	−	0.322979i
$853$	178.653	+	91.0281i	0.209441	+	0.106715i	0.555564	−	0.831474i	$-0.312502\pi$
$853$	178.653	+	91.0281i	0.209441	+	0.106715i	−0.346124	+	0.938189i	$0.612502\pi$
$854$	215.910	−	70.1535i	0.252822	−	0.0821469i
$855$	−1332.38	+	163.633i	−1.55834	+	0.191383i
$856$	102.894	−	316.674i	0.120203	−	0.369947i
$857$	434.770	+	434.770i	0.507316	+	0.507316i	0.913702	−	0.406385i	$-0.133211\pi$
$857$	434.770	+	434.770i	0.507316	+	0.507316i	−0.406385	+	0.913702i	$0.633211\pi$
$858$	19.3083	+	37.8947i	0.0225039	+	0.0441663i
$859$	692.552	+	953.216i	0.806231	+	1.10968i	0.991894	+	0.127068i	$0.0405566\pi$
$859$	692.552	+	953.216i	0.806231	+	1.10968i	−0.185664	+	0.982613i	$0.559443\pi$
$860$	−281.271	−	219.741i	−0.327059	−	0.255512i
$861$	−211.167	−	153.422i	−0.245258	−	0.178190i
$862$	622.878	+	98.6542i	0.722596	+	0.114448i
$863$	115.970	−	732.207i	0.134380	−	0.848444i	−0.824754	−	0.565492i	$-0.808686\pi$
$863$	115.970	−	732.207i	0.134380	−	0.848444i	0.959134	−	0.282952i	$-0.0913137\pi$
$864$	445.177	−	612.734i	0.515251	−	0.709182i
$865$	26.8670	−	769.971i	0.0310601	−	0.890139i
$866$	1376.65	−	1000.19i	1.58966	−	1.15496i
$867$	−294.367	+	149.988i	−0.339524	+	0.172996i
$868$	270.838	−	270.838i	0.312025	−	0.312025i
$869$	762.628	+	247.793i	0.877593	+	0.285147i
$870$	−202.598	−	39.3753i	−0.232871	−	0.0452589i
$871$	−18.9859	−	58.4326i	−0.0217978	−	0.0670868i
$872$	−2.08307	+	4.08826i	−0.00238884	+	0.00468837i
$873$	282.686	−	44.7730i	0.323809	−	0.0512864i
$874$			962.374i			1.10111i
$875$	−768.740	+	163.467i	−0.878560	+	0.186819i
$876$	190.594			0.217573
$877$	156.821	+	990.130i	0.178816	+	1.12900i	0.899883	+	0.436132i	$0.143652\pi$
$877$	156.821	+	990.130i	0.178816	+	1.12900i	−0.721067	+	0.692865i	$0.756348\pi$
$878$	−371.282	−	189.178i	−0.422872	−	0.215464i
$879$	−15.4262	+	5.01229i	−0.0175498	+	0.00570226i
$880$	135.024	−	694.737i	0.153436	−	0.789474i
$881$	216.789	−	667.209i	0.246072	−	0.757331i	−0.749386	−	0.662133i	$-0.769651\pi$
$881$	216.789	−	667.209i	0.246072	−	0.757331i	0.995458	−	0.0951985i	$-0.0303486\pi$
$882$	−159.581	−	159.581i	−0.180931	−	0.180931i
$883$	401.099	+	787.201i	0.454246	+	0.891507i	0.998613	+	0.0526599i	$0.0167699\pi$
$883$	401.099	+	787.201i	0.454246	+	0.891507i	−0.544367	+	0.838847i	$0.683230\pi$
$884$	−90.6282	−	124.739i	−0.102521	−	0.141107i
$885$	−174.870	−	6.10182i	−0.197593	−	0.00689471i
$886$	206.114	+	149.751i	0.232634	+	0.169019i
$887$	−1115.98	−	176.754i	−1.25815	−	0.199272i	−0.508476	−	0.861076i	$-0.669791\pi$
$887$	−1115.98	−	176.754i	−1.25815	−	0.199272i	−0.749677	+	0.661804i	$0.769791\pi$
$888$	−11.3436	+	71.6206i	−0.0127743	+	0.0806539i
$889$	459.507	−	632.457i	0.516881	−	0.711425i
$890$	361.448	−	462.658i	0.406121	−	0.519840i
$891$	520.976	−	378.511i	0.584710	−	0.424816i
$892$	−212.218	+	108.130i	−0.237913	+	0.121222i
$893$	−885.403	+	885.403i	−0.991493	+	0.991493i
$894$	−490.602	−	159.406i	−0.548772	−	0.178307i
$895$	−20.5248	−	167.123i	−0.0229327	−	0.186730i
$896$	137.306	+	422.585i	0.153243	+	0.471635i
$897$	−5.56652	+	10.9249i	−0.00620571	+	0.0121794i
$898$	−1595.71	+	252.735i	−1.77695	+	0.281442i
$899$			183.453i			0.204063i
$900$	−507.878	−	812.675i	−0.564308	−	0.902973i
$901$	1870.08			2.07556
$902$	−225.814	−	1425.73i	−0.250348	−	1.58064i
$903$	81.7467	+	41.6520i	0.0905279	+	0.0461263i
$904$	154.172	−	50.0935i	0.170544	−	0.0554131i
$905$	568.466	+	315.086i	0.628139	+	0.348161i
$906$	−225.894	+	695.232i	−0.249332	+	0.767364i
$907$	806.814	+	806.814i	0.889542	+	0.889542i	0.994479	−	0.104937i	$-0.0334641\pi$
$907$	806.814	+	806.814i	0.889542	+	0.889542i	−0.104937	+	0.994479i	$0.533464\pi$
$908$	−157.273	−	308.666i	−0.173208	−	0.339940i
$909$	−745.240	−	1025.73i	−0.819846	−	1.12842i
$910$	99.6633	−	67.2277i	0.109520	−	0.0738766i
$911$	−635.376	−	461.628i	−0.697449	−	0.506726i	0.181652	−	0.983363i	$-0.441856\pi$
$911$	−635.376	−	461.628i	−0.697449	−	0.506726i	−0.879100	+	0.476637i	$0.841856\pi$
$912$	396.717	+	62.8338i	0.434997	+	0.0688967i
$913$	−58.9184	+	371.996i	−0.0645327	+	0.407443i
$914$	−1117.13	+	1537.60i	−1.22225	+	1.68228i
$915$	57.0495	−	16.3604i	0.0623492	−	0.0178802i
$916$	−263.467	+	191.420i	−0.287628	+	0.208974i
$917$	−1234.63	+	629.074i	−1.34638	+	0.686014i
$918$	870.590	−	870.590i	0.948355	−	0.948355i
$919$	−280.254	−	91.0602i	−0.304956	−	0.0990862i	0.152542	−	0.988297i	$-0.451254\pi$
$919$	−280.254	−	91.0602i	−0.304956	−	0.0990862i	−0.457498	+	0.889211i	$0.651254\pi$
$920$	−99.4017	+	46.3551i	−0.108045	+	0.0503860i
$921$	−37.3052	−	114.814i	−0.0405051	−	0.124662i
$922$	436.900	−	857.464i	0.473861	−	0.930004i
$923$	−76.7710	+	12.1593i	−0.0831755	+	0.0131737i
$924$		−	332.844i		−	0.360220i
$925$	−710.145	−	426.645i	−0.767724	−	0.461238i
$926$	−1757.10			−1.89752
$927$	93.9171	+	592.969i	0.101313	+	0.639665i
$928$	−582.982	−	297.044i	−0.628213	−	0.320091i
$929$	653.589	−	212.364i	0.703540	−	0.228594i	0.0646677	−	0.997907i	$-0.479401\pi$
$929$	653.589	−	212.364i	0.703540	−	0.228594i	0.638872	+	0.769313i	$0.279401\pi$
$930$	134.769	−	125.681i	0.144913	−	0.135141i
$931$	97.5411	−	300.201i	0.104770	−	0.322450i
$932$	532.129	+	532.129i	0.570953	+	0.570953i
$933$	−95.4124	−	187.257i	−0.102264	−	0.200705i
$934$	−787.562	−	1083.99i	−0.843214	−	1.16058i
$935$	490.043	−	1346.49i	0.524110	−	1.44010i
$936$	18.9323	+	13.7551i	0.0202268	+	0.0146956i
$937$	1103.24	+	174.736i	1.17742	+	0.186485i	0.714318	−	0.699821i	$-0.246737\pi$
$937$	1103.24	+	174.736i	1.17742	+	0.186485i	0.463100	+	0.886306i	$0.346737\pi$
$938$	−138.429	+	874.004i	−0.147579	+	0.931774i
$939$	48.5498	−	66.8231i	0.0517037	−	0.0711641i
$940$	−839.998	−	305.708i	−0.893615	−	0.325222i
$941$	92.8259	−	67.4420i	0.0986460	−	0.0716705i	−0.537369	−	0.843347i	$-0.680582\pi$
$941$	92.8259	−	67.4420i	0.0986460	−	0.0716705i	0.636015	+	0.771677i	$0.280582\pi$
$942$	−675.628	+	344.250i	−0.717227	+	0.365445i
$943$	294.268	−	294.268i	0.312055	−	0.312055i
$944$	−423.590	−	137.633i	−0.448718	−	0.145797i
$945$	355.751	+	381.476i	0.376457	+	0.403678i
$946$	156.791	+	482.554i	0.165741	+	0.510100i
$947$	−116.685	+	229.007i	−0.123215	+	0.241823i	−0.944372	−	0.328879i	$-0.893329\pi$
$947$	−116.685	+	229.007i	−0.123215	+	0.241823i	0.821157	+	0.570703i	$0.193329\pi$
$948$	−320.884	+	50.8230i	−0.338485	+	0.0536107i
$949$		−	53.1730i		−	0.0560306i
$950$	1270.35	−	2114.48i	1.33721	−	2.22576i
$951$	216.945			0.228123
$952$	55.4587	+	350.152i	0.0582549	+	0.367807i
$953$	−351.899	−	179.301i	−0.369254	−	0.188144i	0.259510	−	0.965740i	$-0.416439\pi$
$953$	−351.899	−	179.301i	−0.369254	−	0.188144i	−0.628764	+	0.777596i	$0.716439\pi$
$954$	−1690.91	+	549.410i	−1.77244	+	0.575901i
$955$	181.016	+	388.162i	0.189545	+	0.406453i
$956$	643.788	−	1981.38i	0.673419	−	2.07257i
$957$	112.726	+	112.726i	0.117791	+	0.117791i
$958$	42.9537	+	84.3014i	0.0448369	+	0.0879973i
$959$	77.1831	+	106.233i	0.0804829	+	0.110775i
$960$	114.751	+	400.144i	0.119533	+	0.416817i
$961$	644.949	+	468.583i	0.671123	+	0.487599i
$962$	125.162	+	19.8237i	0.130106	+	0.0206068i
$963$	186.519	−	1177.63i	0.193685	−	1.22288i
$964$	−804.001	+	1106.61i	−0.834026	+	1.14794i
$965$	935.416	+	1386.73i	0.969343	+	1.43703i
$966$	142.869	−	103.801i	0.147898	−	0.107454i
$967$	1526.20	−	777.637i	1.57828	−	0.804175i	0.578350	−	0.815789i	$-0.303697\pi$
$967$	1526.20	−	777.637i	1.57828	−	0.804175i	0.999933	+	0.0116133i	$0.00369671\pi$
$968$	15.3639	−	15.3639i	0.0158718	−	0.0158718i
$969$	773.411	+	251.296i	0.798154	+	0.259336i
$970$	−254.963	+	459.995i	−0.262848	+	0.474221i
$971$	−120.537	−	370.976i	−0.124137	−	0.382055i	0.869606	−	0.493747i	$-0.164373\pi$
$971$	−120.537	−	370.976i	−0.124137	−	0.382055i	−0.993743	+	0.111692i	$0.964373\pi$
$972$	−441.144	+	865.793i	−0.453852	+	0.890734i
$973$	383.217	−	60.6956i	0.393851	−	0.0623798i
$974$		−	2430.49i		−	2.49537i
$975$	26.6515	−	16.6557i	0.0273349	−	0.0170828i
$976$	151.068			0.154783
$977$	236.117	+	1490.79i	0.241676	+	1.52588i	0.748093	+	0.663593i	$0.230970\pi$
$977$	236.117	+	1490.79i	0.241676	+	1.52588i	−0.506417	+	0.862288i	$0.669030\pi$
$978$	−399.391	−	203.500i	−0.408375	−	0.208078i
$979$	−431.299	+	140.138i	−0.440551	+	0.143144i
$980$	223.659	−	27.4681i	0.228224	−	0.0280286i
$981$	−5.07718	+	15.6260i	−0.00517552	+	0.0159286i
$982$	−95.9797	−	95.9797i	−0.0977390	−	0.0977390i
$983$	309.637	+	607.696i	0.314991	+	0.618206i	0.993168	−	0.116694i	$-0.0372295\pi$
$983$	309.637	+	607.696i	0.314991	+	0.618206i	−0.678177	+	0.734899i	$0.737230\pi$
$984$	54.8791	+	75.5345i	0.0557714	+	0.0767627i
$985$	577.332	+	451.035i	0.586123	+	0.457904i
$986$	−860.491	−	625.183i	−0.872709	−	0.634060i
$987$	226.941	+	35.9440i	0.229930	+	0.0364174i
$988$	−32.0730	+	202.501i	−0.0324625	+	0.204960i
$989$	−85.9801	+	118.341i	−0.0869364	+	0.119658i
$990$	−47.5059	+	1361.46i	−0.0479858	+	1.37521i
$991$	−1309.84	+	951.656i	−1.32174	+	0.960298i	−0.321828	+	0.946798i	$0.604297\pi$
$991$	−1309.84	+	951.656i	−1.32174	+	0.960298i	−0.999909	+	0.0135001i	$0.995703\pi$
$992$	520.526	−	265.221i	0.524724	−	0.267360i
$993$	−339.708	+	339.708i	−0.342103	+	0.342103i
$994$	1064.70	+	345.943i	1.07113	+	0.348031i
$995$	68.7773	+	13.3670i	0.0691229	+	0.0134342i
$996$	−47.1544	−	145.126i	−0.0473437	−	0.145709i
$997$	38.4223	−	75.4081i	0.0385380	−	0.0756350i	−0.870935	−	0.491399i	$-0.836486\pi$
$997$	38.4223	−	75.4081i	0.0385380	−	0.0756350i	0.909473	+	0.415764i	$0.136486\pi$
$998$	2460.58	−	389.717i	2.46551	−	0.390498i
$999$			549.838i			0.550389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.12.4	✓	32
3.2	odd	2		225.3.r.a.37.1		32
4.3	odd	2		400.3.bg.c.337.3		32
5.2	odd	4		125.3.f.b.43.1		32
5.3	odd	4		125.3.f.a.43.4		32
5.4	even	2		125.3.f.c.82.1		32
25.2	odd	20		125.3.f.c.93.1		32
25.11	even	5		125.3.f.a.32.4		32
25.14	even	10		125.3.f.b.32.1		32
25.23	odd	20	inner	25.3.f.a.23.4	yes	32
75.23	even	20		225.3.r.a.73.1		32
100.23	even	20		400.3.bg.c.273.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.4	✓	32	1.1	even	1	trivial
25.3.f.a.23.4	yes	32	25.23	odd	20	inner
125.3.f.a.32.4		32	25.11	even	5
125.3.f.a.43.4		32	5.3	odd	4
125.3.f.b.32.1		32	25.14	even	10
125.3.f.b.43.1		32	5.2	odd	4
125.3.f.c.82.1		32	5.4	even	2
125.3.f.c.93.1		32	25.2	odd	20
225.3.r.a.37.1		32	3.2	odd	2
225.3.r.a.73.1		32	75.23	even	20
400.3.bg.c.273.3		32	100.23	even	20
400.3.bg.c.337.3		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.463000 + 2.92327i) q^{2} +(-0.866921 - 0.441718i) q^{3} +(-4.52691 + 1.47088i) q^{4} +(0.953911 - 4.90816i) q^{5} +(0.889877 - 2.73876i) q^{6} +(4.44588 + 4.44588i) q^{7} +(-1.02103 - 2.00389i) q^{8} +(-4.73363 - 6.51528i) q^{9} +O(q^{10})\)	\(q+(0.463000 + 2.92327i) q^{2} +(-0.866921 - 0.441718i) q^{3} +(-4.52691 + 1.47088i) q^{4} +(0.953911 - 4.90816i) q^{5} +(0.889877 - 2.73876i) q^{6} +(4.44588 + 4.44588i) q^{7} +(-1.02103 - 2.00389i) q^{8} +(-4.73363 - 6.51528i) q^{9} +(14.7895 + 0.516059i) q^{10} +(-9.24763 - 6.71880i) q^{11} +(4.57419 + 0.724481i) q^{12} +(0.202120 - 1.27614i) q^{13} +(-10.9381 + 15.0550i) q^{14} +(-2.99499 + 3.83363i) q^{15} +(-10.0181 + 7.27859i) q^{16} +(-22.3384 + 11.3820i) q^{17} +(16.8543 - 16.8543i) q^{18} +(31.7059 + 10.3019i) q^{19} +(2.90106 + 23.6219i) q^{20} +(-1.89040 - 5.81805i) q^{21} +(15.3592 - 30.1441i) q^{22} +(9.63343 - 1.52579i) q^{23} +2.18822i q^{24} +(-23.1801 - 9.36390i) q^{25} +3.82407 q^{26} +(2.59562 + 16.3881i) q^{27} +(-26.6655 - 13.5867i) q^{28} +(13.6325 - 4.42946i) q^{29} +(-12.5934 - 6.98019i) q^{30} +(-3.95492 + 12.1720i) q^{31} +(-32.2769 - 32.2769i) q^{32} +(5.04915 + 9.90952i) q^{33} +(-43.6153 - 60.0314i) q^{34} +(26.0621 - 17.5801i) q^{35} +(31.0120 + 22.5315i) q^{36} +(32.7301 + 5.18393i) q^{37} +(-15.4353 + 97.4547i) q^{38} +(-0.738915 + 1.01703i) q^{39} +(-10.8094 + 3.09986i) q^{40} +(34.5187 - 25.0793i) q^{41} +(16.1325 - 8.21991i) q^{42} +(-10.6048 + 10.6048i) q^{43} +(51.7458 + 16.8132i) q^{44} +(-36.4935 + 17.0184i) q^{45} +(8.92057 + 27.4547i) q^{46} +(-17.0518 + 33.4660i) q^{47} +(11.9000 - 1.88478i) q^{48} -9.46829i q^{49} +(16.6408 - 72.0972i) q^{50} +24.3933 q^{51} +(0.962067 + 6.07425i) q^{52} +(-66.4615 - 33.8638i) q^{53} +(-46.7050 + 15.1754i) q^{54} +(-41.7984 + 38.9797i) q^{55} +(4.36966 - 13.4484i) q^{56} +(-22.9360 - 22.9360i) q^{57} +(19.2603 + 37.8005i) q^{58} +(21.1412 + 29.0983i) q^{59} +(7.91924 - 21.7598i) q^{60} +(-9.86967 - 7.17074i) q^{61} +(-37.4132 - 5.92567i) q^{62} +(7.92102 - 50.0113i) q^{63} +(50.2954 - 69.2257i) q^{64} +(-6.07068 - 2.20936i) q^{65} +(-26.6304 + 19.3481i) q^{66} +(42.3694 - 21.5883i) q^{67} +(84.3825 - 84.3825i) q^{68} +(-9.02539 - 2.93253i) q^{69} +(63.4582 + 68.0469i) q^{70} +(-18.5901 - 57.2145i) q^{71} +(-8.22271 + 16.1380i) q^{72} +(40.6475 - 6.43794i) q^{73} +98.0790i q^{74} +(15.9591 + 18.3568i) q^{75} -158.683 q^{76} +(-11.2429 - 70.9849i) q^{77} +(-3.31517 - 1.68916i) q^{78} +(-66.7175 + 21.6778i) q^{79} +(26.1681 + 56.1137i) q^{80} +(-17.4088 + 53.5789i) q^{81} +(89.2958 + 89.2958i) q^{82} +(-14.9586 - 29.3580i) q^{83} +(17.1154 + 23.5573i) q^{84} +(34.5558 + 120.498i) q^{85} +(-35.9108 - 26.0907i) q^{86} +(-13.7748 - 2.18172i) q^{87} +(-4.02159 + 25.3913i) q^{88} +(23.3194 - 32.0965i) q^{89} +(-66.6460 - 98.8009i) q^{90} +(6.57215 - 4.77495i) q^{91} +(-41.3655 + 21.0768i) q^{92} +(8.80520 - 8.80520i) q^{93} +(-105.725 - 34.3521i) q^{94} +(80.8079 - 145.791i) q^{95} +(13.7242 + 42.2388i) q^{96} +(-16.1345 + 31.6657i) q^{97} +(27.6784 - 4.38382i) q^{98} +92.0553i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

Modular forms

Varieties

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