LMFDB - Embedded newform 25.3.f.a.12.1

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			12.1
Character	$\chi$	$=$	25.12
Dual form			25.3.f.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.513943 - 3.24491i) q^{2} +(2.81033 + 1.43193i) q^{3} +(-6.46108 + 2.09933i) q^{4} +(-4.99960 - 0.0628765i) q^{5} +(3.20215 - 9.85519i) q^{6} +(7.51823 + 7.51823i) q^{7} +(4.16668 + 8.17758i) q^{8} +(0.557438 + 0.767248i) q^{9} +O(q^{10})$	\(q+(-0.513943 - 3.24491i) q^{2} +(2.81033 + 1.43193i) q^{3} +(-6.46108 + 2.09933i) q^{4} +(-4.99960 - 0.0628765i) q^{5} +(3.20215 - 9.85519i) q^{6} +(7.51823 + 7.51823i) q^{7} +(4.16668 + 8.17758i) q^{8} +(0.557438 + 0.767248i) q^{9} +(2.36548 + 16.2556i) q^{10} +(-1.41944 - 1.03128i) q^{11} +(-21.1638 - 3.35202i) q^{12} +(0.639079 - 4.03498i) q^{13} +(20.5320 - 28.2599i) q^{14} +(-13.9605 - 7.33580i) q^{15} +(2.40958 - 1.75066i) q^{16} +(-9.09666 + 4.63498i) q^{17} +(2.20316 - 2.20316i) q^{18} +(-23.1149 - 7.51050i) q^{19} +(32.4348 - 10.0896i) q^{20} +(10.3631 + 31.8943i) q^{21} +(-2.61691 + 5.13597i) q^{22} +(24.8384 - 3.93402i) q^{23} +28.9481i q^{24} +(24.9921 + 0.628715i) q^{25} -13.4216 q^{26} +(-3.97276 - 25.0830i) q^{27} +(-64.3591 - 32.7926i) q^{28} +(0.252929 - 0.0821815i) q^{29} +(-16.6291 + 49.0707i) q^{30} +(1.10744 - 3.40835i) q^{31} +(19.0399 + 19.0399i) q^{32} +(-2.51236 - 4.93078i) q^{33} +(19.7153 + 27.1357i) q^{34} +(-37.1155 - 38.0609i) q^{35} +(-5.21236 - 3.78700i) q^{36} +(25.0718 + 3.97099i) q^{37} +(-12.4911 + 78.8659i) q^{38} +(7.57385 - 10.4245i) q^{39} +(-20.3176 - 41.1466i) q^{40} +(-1.53440 + 1.11481i) q^{41} +(98.1681 - 50.0191i) q^{42} +(34.0593 - 34.0593i) q^{43} +(11.3361 + 3.68332i) q^{44} +(-2.73873 - 3.87099i) q^{45} +(-25.5311 - 78.5765i) q^{46} +(-20.9070 + 41.0322i) q^{47} +(9.27854 - 1.46958i) q^{48} +64.0476i q^{49} +(-10.8044 - 81.4202i) q^{50} -32.2016 q^{51} +(4.34163 + 27.4120i) q^{52} +(2.70446 + 1.37799i) q^{53} +(-79.3503 + 25.7825i) q^{54} +(7.03178 + 5.24525i) q^{55} +(-30.1548 + 92.8070i) q^{56} +(-54.2060 - 54.2060i) q^{57} +(-0.396662 - 0.778494i) q^{58} +(-11.7686 - 16.1981i) q^{59} +(105.600 + 18.0895i) q^{60} +(63.6100 + 46.2154i) q^{61} +(-11.6290 - 1.84185i) q^{62} +(-1.57740 + 9.95930i) q^{63} +(59.0000 - 81.2066i) q^{64} +(-3.44885 + 20.1331i) q^{65} +(-14.7087 + 10.6865i) q^{66} +(-72.5829 + 36.9828i) q^{67} +(49.0439 - 49.0439i) q^{68} +(75.4373 + 24.5111i) q^{69} +(-104.429 + 139.997i) q^{70} +(-0.716327 - 2.20463i) q^{71} +(-3.95156 + 7.75537i) q^{72} +(-99.1579 + 15.7051i) q^{73} -83.3967i q^{74} +(69.3357 + 37.5539i) q^{75} +165.114 q^{76} +(-2.91825 - 18.4251i) q^{77} +(-37.7191 - 19.2188i) q^{78} +(16.4258 - 5.33707i) q^{79} +(-12.1570 + 8.60111i) q^{80} +(27.3900 - 84.2978i) q^{81} +(4.40604 + 4.40604i) q^{82} +(-2.03502 - 3.99395i) q^{83} +(-133.913 - 184.316i) q^{84} +(45.7712 - 22.6011i) q^{85} +(-128.024 - 93.0149i) q^{86} +(0.828490 + 0.131220i) q^{87} +(2.51904 - 15.9046i) q^{88} +(-85.4992 + 117.680i) q^{89} +(-11.1535 + 10.8764i) q^{90} +(35.1407 - 25.5312i) q^{91} +(-152.224 + 77.5620i) q^{92} +(7.99280 - 7.99280i) q^{93} +(143.891 + 46.7530i) q^{94} +(115.093 + 39.0029i) q^{95} +(26.2445 + 80.7723i) q^{96} +(63.3499 - 124.331i) q^{97} +(207.829 - 32.9168i) q^{98} -1.66394i 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 $

$2$	−0.513943	−	3.24491i	−0.256972	−	1.62246i	−0.691902	−	0.721991i	$-0.743227\pi$
$2$	−0.513943	−	3.24491i	−0.256972	−	1.62246i	0.434931	−	0.900464i	$-0.356773\pi$
$3$	2.81033	+	1.43193i	0.936776	+	0.477311i	0.854588	−	0.519306i	$-0.173809\pi$
$3$	2.81033	+	1.43193i	0.936776	+	0.477311i	0.0821872	+	0.996617i	$0.473809\pi$
$4$	−6.46108	+	2.09933i	−1.61527	+	0.524833i
$5$	−4.99960	−	0.0628765i	−0.999921	−	0.0125753i
$5$	−4.99960	−	0.0628765i	−0.999921	−	0.0125753i
$6$	3.20215	−	9.85519i	0.533691	−	1.64253i
$7$	7.51823	+	7.51823i	1.07403	+	1.07403i	0.997031	+	0.0770020i	$0.0245348\pi$
$7$	7.51823	+	7.51823i	1.07403	+	1.07403i	0.0770020	+	0.997031i	$0.475465\pi$
$8$	4.16668	+	8.17758i	0.520835	+	1.02220i
$9$	0.557438	+	0.767248i	0.0619376	+	0.0852498i
$10$	2.36548	+	16.2556i	0.236548	+	1.62556i
$11$	−1.41944	−	1.03128i	−0.129040	−	0.0937529i	0.521393	−	0.853317i	$-0.325413\pi$
$11$	−1.41944	−	1.03128i	−0.129040	−	0.0937529i	−0.650433	+	0.759564i	$0.725413\pi$
$12$	−21.1638	−	3.35202i	−1.76365	−	0.279335i
$13$	0.639079	−	4.03498i	0.0491599	−	0.310383i	−0.950840	−	0.309683i	$-0.899777\pi$
$13$	0.639079	−	4.03498i	0.0491599	−	0.310383i	1.00000		0.000700342i	$-0.000222926\pi$
$14$	20.5320	−	28.2599i	1.46657	−	2.01857i
$15$	−13.9605	−	7.33580i	−0.930699	−	0.489054i
$16$	2.40958	−	1.75066i	0.150599	−	0.109416i
$17$	−9.09666	+	4.63498i	−0.535098	+	0.272646i	−0.700589	−	0.713565i	$-0.747079\pi$
$17$	−9.09666	+	4.63498i	−0.535098	+	0.272646i	0.165491	+	0.986211i	$0.447079\pi$
$18$	2.20316	−	2.20316i	0.122398	−	0.122398i
$19$	−23.1149	−	7.51050i	−1.21658	−	0.395289i	−0.370742	−	0.928736i	$-0.620897\pi$
$19$	−23.1149	−	7.51050i	−1.21658	−	0.395289i	−0.845834	+	0.533447i	$0.820897\pi$
$20$	32.4348	−	10.0896i	1.62174	−	0.504479i
$21$	10.3631	+	31.8943i	0.493480	+	1.51878i
$22$	−2.61691	+	5.13597i	−0.118950	+	0.233453i
$23$	24.8384	−	3.93402i	1.07993	−	0.171044i	0.408978	−	0.912544i	$-0.365885\pi$
$23$	24.8384	−	3.93402i	1.07993	−	0.171044i	0.670953	+	0.741500i	$0.265885\pi$
$24$			28.9481i			1.20617i
$25$	24.9921	+	0.628715i	0.999684	+	0.0251486i
$26$	−13.4216			−0.516216
$27$	−3.97276	−	25.0830i	−0.147139	−	0.929000i
$28$	−64.3591	−	32.7926i	−2.29854	−	1.17116i
$29$	0.252929	−	0.0821815i	0.00872167	−	0.00283384i	−0.304653	−	0.952463i	$-0.598540\pi$
$29$	0.252929	−	0.0821815i	0.00872167	−	0.00283384i	0.313375	+	0.949630i	$0.398540\pi$
$30$	−16.6291	+	49.0707i	−0.554304	+	1.63569i
$31$	1.10744	−	3.40835i	0.0357239	−	0.109947i	−0.931604	−	0.363474i	$-0.881591\pi$
$31$	1.10744	−	3.40835i	0.0357239	−	0.109947i	0.967328	+	0.253527i	$0.0815906\pi$
$32$	19.0399	+	19.0399i	0.594997	+	0.594997i
$33$	−2.51236	−	4.93078i	−0.0761320	−	0.149418i
$34$	19.7153	+	27.1357i	0.579861	+	0.798110i
$35$	−37.1155	−	38.0609i	−1.06044	−	1.08745i
$36$	−5.21236	−	3.78700i	−0.144788	−	0.105194i
$37$	25.0718	+	3.97099i	0.677617	+	0.107324i	0.485751	−	0.874097i	$-0.338546\pi$
$37$	25.0718	+	3.97099i	0.677617	+	0.107324i	0.191866	+	0.981421i	$0.438546\pi$
$38$	−12.4911	+	78.8659i	−0.328714	+	2.07542i
$39$	7.57385	−	10.4245i	0.194201	−	0.267295i
$40$	−20.3176	−	41.1466i	−0.507940	−	1.02867i
$41$	−1.53440	+	1.11481i	−0.0374243	+	0.0271904i	−0.606340	−	0.795205i	$-0.707363\pi$
$41$	−1.53440	+	1.11481i	−0.0374243	+	0.0271904i	0.568916	+	0.822396i	$0.307363\pi$
$42$	98.1681	−	50.0191i	2.33733	−	1.19093i
$43$	34.0593	−	34.0593i	0.792078	−	0.792078i	−0.189754	−	0.981832i	$-0.560769\pi$
$43$	34.0593	−	34.0593i	0.792078	−	0.792078i	0.981832	+	0.189754i	$0.0607691\pi$
$44$	11.3361	+	3.68332i	0.257639	+	0.0837119i
$45$	−2.73873	−	3.87099i	−0.0608607	−	0.0860219i
$46$	−25.5311	−	78.5765i	−0.555023	−	1.70818i
$47$	−20.9070	+	41.0322i	−0.444829	+	0.873026i	0.554341	+	0.832290i	$0.312970\pi$
$47$	−20.9070	+	41.0322i	−0.444829	+	0.873026i	−0.999170	+	0.0407366i	$0.987030\pi$
$48$	9.27854	−	1.46958i	0.193303	−	0.0306162i
$49$			64.0476i			1.30709i
$50$	−10.8044	−	81.4202i	−0.216088	−	1.62840i
$51$	−32.2016			−0.631404
$52$	4.34163	+	27.4120i	0.0834929	+	0.527153i
$53$	2.70446	+	1.37799i	0.0510276	+	0.0259998i	0.479318	−	0.877641i	$-0.340884\pi$
$53$	2.70446	+	1.37799i	0.0510276	+	0.0259998i	−0.428291	+	0.903641i	$0.640884\pi$
$54$	−79.3503	+	25.7825i	−1.46945	+	0.477454i
$55$	7.03178	+	5.24525i	0.127851	+	0.0953682i
$56$	−30.1548	+	92.8070i	−0.538479	+	1.65727i
$57$	−54.2060	−	54.2060i	−0.950982	−	0.950982i
$58$	−0.396662	−	0.778494i	−0.00683901	−	0.0134223i
$59$	−11.7686	−	16.1981i	−0.199468	−	0.274544i	0.697552	−	0.716534i	$-0.254273\pi$
$59$	−11.7686	−	16.1981i	−0.199468	−	0.274544i	−0.897020	+	0.441990i	$0.854273\pi$
$60$	105.600	+	18.0895i	1.76000	+	0.301492i
$61$	63.6100	+	46.2154i	1.04279	+	0.757629i	0.970828	−	0.239778i	$-0.0770748\pi$
$61$	63.6100	+	46.2154i	1.04279	+	0.757629i	0.0719595	+	0.997408i	$0.477075\pi$
$62$	−11.6290	−	1.84185i	−0.187564	−	0.0297072i
$63$	−1.57740	+	9.95930i	−0.0250381	+	0.158084i
$64$	59.0000	−	81.2066i	0.921876	−	1.26885i
$65$	−3.44885	+	20.1331i	−0.0530592	+	0.309741i
$66$	−14.7087	+	10.6865i	−0.222859	+	0.161917i
$67$	−72.5829	+	36.9828i	−1.08333	+	0.551982i	−0.902130	−	0.431465i	$-0.857997\pi$
$67$	−72.5829	+	36.9828i	−1.08333	+	0.551982i	−0.181196	+	0.983447i	$0.557997\pi$
$68$	49.0439	−	49.0439i	0.721234	−	0.721234i
$69$	75.4373	+	24.5111i	1.09329	+	0.355233i
$70$	−104.429	+	139.997i	−1.49184	+	1.99996i
$71$	−0.716327	−	2.20463i	−0.0100891	−	0.0310511i	0.945885	−	0.324501i	$-0.105196\pi$
$71$	−0.716327	−	2.20463i	−0.0100891	−	0.0310511i	−0.955974	+	0.293450i	$0.905196\pi$
$72$	−3.95156	+	7.75537i	−0.0548828	+	0.107714i
$73$	−99.1579	+	15.7051i	−1.35833	+	0.215138i	−0.792745	−	0.609553i	$-0.791349\pi$
$73$	−99.1579	+	15.7051i	−1.35833	+	0.215138i	−0.565583	+	0.824691i	$0.691349\pi$
$74$		−	83.3967i		−	1.12698i
$75$	69.3357	+	37.5539i	0.924476	+	0.500719i
$76$	165.114			2.17256
$77$	−2.91825	−	18.4251i	−0.0378993	−	0.239287i
$78$	−37.7191	−	19.2188i	−0.483578	−	0.246395i
$79$	16.4258	−	5.33707i	0.207922	−	0.0675578i	−0.203204	−	0.979136i	$-0.565136\pi$
$79$	16.4258	−	5.33707i	0.207922	−	0.0675578i	0.411126	+	0.911578i	$0.365136\pi$
$80$	−12.1570	+	8.60111i	−0.151963	+	0.107514i
$81$	27.3900	−	84.2978i	0.338148	−	1.04071i
$82$	4.40604	+	4.40604i	0.0537322	+	0.0537322i
$83$	−2.03502	−	3.99395i	−0.0245183	−	0.0481199i	0.878422	−	0.477885i	$-0.158596\pi$
$83$	−2.03502	−	3.99395i	−0.0245183	−	0.0481199i	−0.902941	+	0.429765i	$0.858596\pi$
$84$	−133.913	−	184.316i	−1.59421	−	2.19424i
$85$	45.7712	−	22.6011i	0.538484	−	0.265895i
$86$	−128.024	−	93.0149i	−1.48865	−	1.08157i
$87$	0.828490	+	0.131220i	0.00952288	+	0.00150828i
$88$	2.51904	−	15.9046i	0.0286254	−	0.180734i
$89$	−85.4992	+	117.680i	−0.960665	+	1.32224i	−0.0140418	+	0.999901i	$0.504470\pi$
$89$	−85.4992	+	117.680i	−0.960665	+	1.32224i	−0.946624	+	0.322341i	$0.895530\pi$
$90$	−11.1535	+	10.8764i	−0.123927	+	0.120849i
$91$	35.1407	−	25.5312i	0.386161	−	0.280563i
$92$	−152.224	+	77.5620i	−1.65461	+	0.843065i
$93$	7.99280	−	7.99280i	0.0859441	−	0.0859441i
$94$	143.891	+	46.7530i	1.53075	+	0.497372i
$95$	115.093	+	39.0029i	1.21151	+	0.410557i
$96$	26.2445	+	80.7723i	0.273380	+	0.841378i
$97$	63.3499	−	124.331i	0.653092	−	1.28176i	−0.292455	−	0.956279i	$-0.594472\pi$
$97$	63.3499	−	124.331i	0.653092	−	1.28176i	0.945547	−	0.325485i	$-0.105528\pi$
$98$	207.829	−	32.9168i	2.12070	−	0.335886i
$99$		−	1.66394i		−	0.0168074i
$100$	−162.796	+	48.4045i	−1.62796	+	0.484045i
$101$	−90.5620			−0.896654			−0.448327	−	0.893870i	$-0.647980\pi$
$101$	−90.5620			−0.896654			−0.448327	+	0.893870i	$0.647980\pi$
$102$	16.5498	+	104.491i	0.162253	+	1.02442i
$103$	93.1352	+	47.4548i	0.904226	+	0.460726i	0.843316	−	0.537417i	$-0.180600\pi$
$103$	93.1352	+	47.4548i	0.904226	+	0.460726i	0.0609092	+	0.998143i	$0.480600\pi$
$104$	35.6592	−	11.5864i	0.342877	−	0.111408i
$105$	−49.8059	−	160.110i	−0.474342	−	1.52486i
$106$	3.08152	−	9.48394i	0.0290709	−	0.0894711i
$107$	−2.72254	−	2.72254i	−0.0254443	−	0.0254443i	0.694270	−	0.719714i	$-0.255727\pi$
$107$	−2.72254	−	2.72254i	−0.0254443	−	0.0254443i	−0.719714	+	0.694270i	$0.755727\pi$
$108$	78.3259	+	153.723i	0.725239	+	1.42336i
$109$	−43.6029	−	60.0142i	−0.400026	−	0.550589i	0.560724	−	0.828003i	$-0.310523\pi$
$109$	−43.6029	−	60.0142i	−0.400026	−	0.550589i	−0.960751	+	0.277414i	$0.910523\pi$
$110$	13.4064	−	25.5133i	0.121877	−	0.231939i
$111$	64.7739	+	47.0610i	0.583548	+	0.423973i
$112$	31.2777	+	4.95389i	0.279265	+	0.0442312i
$113$	−32.5292	+	205.381i	−0.287869	+	1.81753i	0.242941	+	0.970041i	$0.421888\pi$
$113$	−32.5292	+	205.381i	−0.287869	+	1.81753i	−0.530810	+	0.847491i	$0.678112\pi$
$114$	−148.035	+	203.752i	−1.29855	+	1.78730i
$115$	−124.430	+	18.1068i	−1.08200	+	0.157450i
$116$	−1.46166	+	1.06196i	−0.0126006	+	0.00915484i
$117$	3.45208	−	1.75892i	0.0295050	−	0.0150335i
$118$	−46.5130	+	46.5130i	−0.394178	+	0.394178i
$119$	−103.238	−	33.5440i	−0.867544	−	0.281882i
$120$	1.82015	−	144.729i	0.0151679	−	1.20607i
$121$	−36.4398	−	112.150i	−0.301155	−	0.926861i
$122$	117.273	−	230.161i	0.961253	−	1.88656i
$123$	−5.90849	+	0.935812i	−0.0480365	+	0.00760823i
$124$			24.3465i			0.196343i
$125$	−124.911	−	4.71474i	−0.999288	−	0.0377179i
$126$	33.1277			0.262918
$127$	14.3730	+	90.7473i	0.113173	+	0.714545i	0.977393	+	0.211431i	$0.0678125\pi$
$127$	14.3730	+	90.7473i	0.113173	+	0.714545i	−0.864220	+	0.503114i	$0.832188\pi$
$128$	−197.864	−	100.817i	−1.54581	−	0.787631i
$129$	144.489	−	46.9472i	1.12007	−	0.363932i
$130$	67.1027	+	0.843904i	0.516175	+	0.00649157i
$131$	43.2439	−	133.091i	0.330106	−	1.01596i	−0.638976	−	0.769226i	$-0.720642\pi$
$131$	43.2439	−	133.091i	0.330106	−	1.01596i	0.969083	−	0.246736i	$-0.0793582\pi$
$132$	26.5839	+	26.5839i	0.201393	+	0.201393i
$133$	−117.318	−	230.249i	−0.882088	−	1.73120i
$134$	157.309	+	216.518i	1.17395	+	1.61580i
$135$	18.2851	+	125.655i	0.135445	+	0.930777i
$136$	−75.8059	−	55.0762i	−0.557396	−	0.404972i
$137$	221.537	+	35.0880i	1.61706	+	0.256117i	0.898378	−	0.439223i	$-0.144746\pi$
$137$	221.537	+	35.0880i	1.61706	+	0.256117i	0.718681	+	0.695340i	$0.244746\pi$
$138$	40.7657	−	257.384i	0.295404	−	1.86510i
$139$	52.6171	−	72.4212i	0.378540	−	0.521016i	−0.576657	−	0.816986i	$-0.695643\pi$
$139$	52.6171	−	72.4212i	0.378540	−	0.521016i	0.955197	+	0.295971i	$0.0956431\pi$
$140$	319.708	+	167.997i	2.28363	+	1.19998i
$141$	−117.511	+	85.3766i	−0.833410	+	0.605508i
$142$	−6.78567	+	3.45747i	−0.0477864	+	0.0243484i
$143$	−5.06834	+	5.06834i	−0.0354429	+	0.0354429i
$144$	2.68638	+	0.872859i	0.0186554	+	0.00606152i
$145$	−1.26971	+	0.394972i	−0.00875662	+	0.00272394i
$146$	101.923	+	313.687i	0.698103	+	2.14854i
$147$	−91.7119	+	179.995i	−0.623890	+	1.22445i
$148$	−170.328	+	26.9772i	−1.15086	+	0.182279i
$149$		−	137.402i		−	0.922164i	−0.887357	−	0.461082i	$-0.847461\pi$
$149$		−	137.402i		−	0.922164i	0.887357	−	0.461082i	$-0.152539\pi$
$150$	86.2244	−	244.289i	0.574830	−	1.62859i
$151$	−224.692			−1.48802			−0.744012	−	0.668166i	$-0.767080\pi$
$151$	−224.692			−1.48802			−0.744012	+	0.668166i	$0.767080\pi$
$152$	−34.8950	−	220.318i	−0.229572	−	1.44946i
$153$	−8.62701	−	4.39568i	−0.0563857	−	0.0287299i
$154$	−58.2879	+	18.9389i	−0.378493	+	0.122980i
$155$	−5.75107	+	16.9708i	−0.0371037	+	0.109489i
$156$	−27.0507	+	83.2536i	−0.173402	+	0.533677i
$157$	23.3931	+	23.3931i	0.149001	+	0.149001i	0.777671	−	0.628671i	$-0.216401\pi$
$157$	23.3931	+	23.3931i	0.149001	+	0.149001i	−0.628671	+	0.777671i	$0.716401\pi$
$158$	−25.7602	−	50.5573i	−0.163040	−	0.319983i
$159$	5.62723	+	7.74521i	0.0353914	+	0.0487120i
$160$	−93.9949	−	96.3892i	−0.587468	−	0.602433i
$161$	216.318	+	157.164i	1.34359	+	0.976174i
$162$	−287.616	−	45.5538i	−1.77541	−	0.281197i
$163$	23.7948	−	150.235i	0.145980	−	0.921684i	−0.800596	−	0.599205i	$-0.795484\pi$
$163$	23.7948	−	150.235i	0.145980	−	0.921684i	0.946576	−	0.322480i	$-0.104516\pi$
$164$	7.57352	−	10.4241i	0.0461800	−	0.0635613i
$165$	12.2508	+	24.8099i	0.0742471	+	0.150363i
$166$	−11.9141	+	8.65612i	−0.0717718	+	0.0521453i
$167$	175.201	−	89.2693i	1.04911	−	0.534547i	0.157576	−	0.987507i	$-0.449632\pi$
$167$	175.201	−	89.2693i	1.04911	−	0.534547i	0.891531	+	0.452960i	$0.149632\pi$
$168$	−217.638	+	217.638i	−1.29547	+	1.29547i
$169$	144.856	+	47.0665i	0.857135	+	0.278500i
$170$	−96.8624	−	136.908i	−0.569779	−	0.805339i
$171$	−7.12274	−	21.9215i	−0.0416534	−	0.128196i
$172$	−148.558	+	291.562i	−0.863710	+	1.69513i
$173$	−71.2599	+	11.2865i	−0.411907	+	0.0652396i	−0.358949	−	0.933357i	$-0.616865\pi$
$173$	−71.2599	+	11.2865i	−0.411907	+	0.0652396i	−0.0529577	+	0.998597i	$0.516865\pi$
$174$		−	2.75582i		−	0.0158380i
$175$	183.169	+	192.623i	1.04668	+	1.10070i
$176$	−5.22568			−0.0296913
$177$	−9.87906	−	62.3739i	−0.0558139	−	0.352395i
$178$	425.801	+	216.957i	2.39214	+	1.21886i
$179$	−162.358	+	52.7534i	−0.907029	+	0.294712i	−0.725135	−	0.688607i	$-0.758223\pi$
$179$	−162.358	+	52.7534i	−0.907029	+	0.294712i	−0.181894	+	0.983318i	$0.558223\pi$
$180$	25.8216	+	19.2612i	0.143453	+	0.107007i
$181$	−104.793	+	322.519i	−0.578965	+	1.78187i	0.0432982	+	0.999062i	$0.486213\pi$
$181$	−104.793	+	322.519i	−0.578965	+	1.78187i	−0.622263	+	0.782808i	$0.713787\pi$
$182$	−100.907	−	100.907i	−0.554433	−	0.554433i
$183$	112.588	+	220.966i	0.615233	+	1.20746i
$184$	135.664	+	186.726i	0.737307	+	1.01482i
$185$	−125.100	−	21.4298i	−0.676214	−	0.115837i
$186$	−30.0438	−	21.8281i	−0.161526	−	0.117355i
$187$	17.6921	+	2.80216i	0.0946103	+	0.0149848i
$188$	48.9413	−	309.003i	0.260326	−	1.64363i
$189$	158.712	−	218.448i	0.839745	−	1.15581i
$190$	67.4095	−	393.513i	0.354787	−	2.07112i
$191$	263.275	−	191.280i	1.37840	−	1.00147i	0.381373	−	0.924421i	$-0.375451\pi$
$191$	263.275	−	191.280i	1.37840	−	1.00147i	0.997028	−	0.0770457i	$-0.0245487\pi$
$192$	282.092	−	143.733i	1.46923	−	0.748609i
$193$	56.2302	−	56.2302i	0.291348	−	0.291348i	−0.546265	−	0.837613i	$-0.683951\pi$
$193$	56.2302	−	56.2302i	0.291348	−	0.291348i	0.837613	+	0.546265i	$0.183951\pi$
$194$	−436.002	−	141.666i	−2.24743	−	0.730235i
$195$	−38.5217	+	51.6422i	−0.197547	+	0.264832i
$196$	−134.457	−	413.816i	−0.686006	−	2.11131i
$197$	−74.3737	+	145.967i	−0.377531	+	0.740947i	−0.999100	−	0.0424126i	$-0.986496\pi$
$197$	−74.3737	+	145.967i	−0.377531	+	0.740947i	0.621569	+	0.783360i	$0.286496\pi$
$198$	−5.39933	+	0.855169i	−0.0272693	+	0.00431904i
$199$		−	1.06434i		−	0.00534845i	−0.999996	−	0.00267423i	$-0.999149\pi$
$199$		−	1.06434i		−	0.00534845i	0.999996	−	0.00267423i	$-0.000851234\pi$
$200$	98.9928	+	206.994i	0.494964	+	1.03497i
$201$	−256.938			−1.27830
$202$	46.5437	+	293.866i	0.230415	+	1.45478i
$203$	2.51943	+	1.28372i	0.0124110	+	0.00632372i
$204$	208.057	−	67.6018i	1.01989	−	0.331381i
$205$	7.74148	−	5.47711i	0.0377633	−	0.0267176i
$206$	106.120	−	326.605i	0.515147	−	1.58546i
$207$	16.8642	+	16.8642i	0.0814698	+	0.0814698i
$208$	−5.52398	−	10.8414i	−0.0265576	−	0.0521222i
$209$	25.0648	+	34.4987i	0.119927	+	0.165066i
$210$	−493.947	+	243.903i	−2.35213	+	1.16144i
$211$	−191.101	−	138.843i	−0.905692	−	0.658024i	0.0342298	−	0.999414i	$-0.489102\pi$
$211$	−191.101	−	138.843i	−0.905692	−	0.658024i	−0.939922	+	0.341390i	$0.889102\pi$
$212$	−20.3666	−	3.22575i	−0.0960688	−	0.0152158i
$213$	1.14377	−	7.22146i	0.00536980	−	0.0339036i
$214$	−7.43516	+	10.2336i	−0.0347438	+	0.0478207i
$215$	−172.425	+	168.142i	−0.801976	+	0.782054i
$216$	188.565	−	137.001i	0.872986	−	0.634262i
$217$	33.9508	−	17.2988i	0.156455	−	0.0797179i
$218$	−172.331	+	172.331i	−0.790510	+	0.790510i
$219$	−301.155	−	97.8511i	−1.37514	−	0.446809i
$220$	−56.4444	−	19.1279i	−0.256566	−	0.0869451i
$221$	12.8886	+	39.6670i	0.0583194	+	0.179489i
$222$	119.419	−	234.372i	0.537921	−	1.05573i
$223$	−65.8376	+	10.4276i	−0.295236	+	0.0467608i	−0.302295	−	0.953214i	$-0.597753\pi$
$223$	−65.8376	+	10.4276i	−0.295236	+	0.0467608i	0.00705953	+	0.999975i	$0.497753\pi$
$224$			286.293i			1.27809i
$225$	13.4492	+	19.5256i	0.0597741	+	0.0867805i
$226$	683.162			3.02284
$227$	−57.9987	−	366.189i	−0.255501	−	1.61317i	−0.697794	−	0.716298i	$-0.745835\pi$
$227$	−57.9987	−	366.189i	−0.255501	−	1.61317i	0.442293	−	0.896870i	$-0.354165\pi$
$228$	464.026	+	236.433i	2.03520	+	1.03699i
$229$	−39.3491	+	12.7853i	−0.171830	+	0.0558310i	−0.393669	−	0.919252i	$-0.628794\pi$
$229$	−39.3491	+	12.7853i	−0.171830	+	0.0558310i	0.221838	+	0.975083i	$0.428794\pi$
$230$	122.705	+	394.457i	0.533498	+	1.71503i
$231$	18.1823	−	55.9592i	0.0787110	−	0.242248i
$232$	1.72592	+	1.72592i	0.00743930	+	0.00743930i
$233$	16.0800	+	31.5588i	0.0690129	+	0.135445i	0.922936	−	0.384955i	$-0.125783\pi$
$233$	16.0800	+	31.5588i	0.0690129	+	0.135445i	−0.853923	+	0.520400i	$0.825783\pi$
$234$	−7.48172	−	10.2977i	−0.0319732	−	0.0440073i
$235$	107.107	−	203.830i	0.455773	−	0.867363i
$236$	110.043	+	79.9511i	0.466285	+	0.338776i
$237$	53.8042	+	8.52175i	0.227022	+	0.0359568i
$238$	−55.7888	+	352.237i	−0.234407	+	1.47999i
$239$	28.4156	−	39.1107i	0.118894	−	0.163643i	−0.745422	−	0.666593i	$-0.767752\pi$
$239$	28.4156	−	39.1107i	0.118894	−	0.163643i	0.864316	+	0.502950i	$0.167752\pi$
$240$	−46.4814	+	6.76390i	−0.193673	+	0.0281829i
$241$	−168.371	+	122.329i	−0.698634	+	0.507587i	−0.879487	−	0.475923i	$-0.842114\pi$
$241$	−168.371	+	122.329i	−0.698634	+	0.507587i	0.180853	+	0.983510i	$0.442114\pi$
$242$	−345.189	+	175.883i	−1.42640	+	0.726788i
$243$	36.0666	−	36.0666i	0.148422	−	0.148422i
$244$	−508.011	−	165.063i	−2.08201	−	0.676486i
$245$	4.02709	−	320.213i	0.0164371	−	1.30699i
$246$	6.07325	+	18.6916i	0.0246880	+	0.0759819i
$247$	−45.0770	+	88.4686i	−0.182498	+	0.358172i
$248$	32.4864	−	5.14534i	0.130994	−	0.0207473i
$249$		−	14.1383i		−	0.0567804i
$250$	48.8983	+	407.748i	0.195593	+	1.63099i
$251$	283.972			1.13136			0.565682	−	0.824623i	$-0.308613\pi$
$251$	283.972			1.13136			0.565682	+	0.824623i	$0.308613\pi$
$252$	−10.7162	−	67.6593i	−0.0425245	−	0.268489i
$253$	−39.3136	−	20.0313i	−0.155390	−	0.0791751i
$254$	287.080	−	93.2779i	1.13024	−	0.367236i
$255$	160.995	+	2.02472i	0.631354	+	0.00794009i
$256$	−101.378	+	312.009i	−0.396007	+	1.21878i
$257$	147.092	+	147.092i	0.572344	+	0.572344i	0.932783	−	0.360439i	$-0.117373\pi$
$257$	147.092	+	147.092i	0.572344	+	0.572344i	−0.360439	+	0.932783i	$0.617373\pi$
$258$	−226.598	−	444.724i	−0.878288	−	1.72374i
$259$	158.641	+	218.351i	0.612514	+	0.843053i
$260$	−19.9829	−	137.322i	−0.0768572	−	0.528162i
$261$	0.204046	+	0.148248i	0.000781784	+	0.000567999i
$262$	−454.094	−	71.9214i	−1.73318	−	0.274509i
$263$	16.9483	−	107.008i	0.0644423	−	0.406873i	−0.934289	−	0.356517i	$-0.883964\pi$
$263$	16.9483	−	107.008i	0.0644423	−	0.406873i	0.998731	−	0.0503562i	$-0.0160357\pi$
$264$	29.8536	−	41.0900i	0.113082	−	0.155644i
$265$	−13.4346	−	7.05946i	−0.0506966	−	0.0266395i
$266$	−686.843	+	499.021i	−2.58212	+	1.87602i
$267$	−408.790	+	208.289i	−1.53105	+	0.780108i
$268$	391.324	−	391.324i	1.46017	−	1.46017i
$269$	229.570	+	74.5918i	0.853419	+	0.277293i	0.702878	−	0.711311i	$-0.251898\pi$
$269$	229.570	+	74.5918i	0.853419	+	0.277293i	0.150542	+	0.988604i	$0.451898\pi$
$270$	398.341	−	123.913i	1.47534	−	0.458937i
$271$	−9.71113	−	29.8878i	−0.0358344	−	0.110287i	0.931539	−	0.363641i	$-0.118466\pi$
$271$	−9.71113	−	29.8878i	−0.0358344	−	0.110287i	−0.967374	+	0.253354i	$0.918466\pi$
$272$	−13.8049	+	27.0935i	−0.0507531	+	0.0996086i
$273$	135.316	−	21.4319i	0.495662	−	0.0785052i
$274$		−	736.901i		−	2.68942i
$275$	−34.8263	−	26.6663i	−0.126641	−	0.0969684i
$276$	−538.863			−1.95240
$277$	−46.3265	−	292.494i	−0.167244	−	1.05594i	−0.918354	−	0.395759i	$-0.870481\pi$
$277$	−46.3265	−	292.494i	−0.167244	−	1.05594i	0.751110	−	0.660177i	$-0.229519\pi$
$278$	−262.042	−	133.517i	−0.942599	−	0.480278i
$279$	3.23238	−	1.05026i	0.0115856	−	0.00376439i
$280$	156.598	−	462.102i	0.559277	−	1.65037i
$281$	70.3842	−	216.620i	0.250477	−	0.770890i	−0.744210	−	0.667946i	$-0.767174\pi$
$281$	70.3842	−	216.620i	0.250477	−	0.770890i	0.994687	−	0.102944i	$-0.0328263\pi$
$282$	337.433	+	337.433i	1.19657	+	1.19657i
$283$	−33.8916	−	66.5161i	−0.119758	−	0.235039i	0.823343	−	0.567544i	$-0.192106\pi$
$283$	−33.8916	−	66.5161i	−0.119758	−	0.235039i	−0.943102	+	0.332505i	$0.892106\pi$
$284$	9.25649	+	12.7405i	0.0325933	+	0.0448608i
$285$	267.600	+	274.417i	0.938948	+	0.962866i
$286$	19.0511	+	13.8415i	0.0666124	+	0.0483967i
$287$	−19.9173	−	3.15459i	−0.0693983	−	0.0109916i
$288$	−3.99476	+	25.2219i	−0.0138707	+	0.0875761i
$289$	−108.604	+	149.480i	−0.375791	+	0.517232i
$290$	1.93421	+	3.91710i	0.00666968	+	0.0135072i
$291$	356.068	−	258.698i	1.22360	−	0.888998i
$292$	607.697	−	309.637i	2.08115	−	1.06040i
$293$	−340.456	+	340.456i	−1.16197	+	1.16197i	−0.177920	+	0.984045i	$0.556937\pi$
$293$	−340.456	+	340.456i	−1.16197	+	1.16197i	−0.984045	+	0.177920i	$0.943063\pi$
$294$	631.201	+	205.090i	2.14694	+	0.697584i
$295$	57.8200	+	81.7242i	0.196000	+	0.277031i
$296$	71.9934	+	221.573i	0.243221	+	0.748557i
$297$	−20.2286	+	39.7008i	−0.0681097	+	0.133673i
$298$	−445.859	+	70.6171i	−1.49617	+	0.236970i
$299$		−	102.737i		−	0.343601i
$300$	−526.821	−	97.0801i	−1.75607	−	0.323600i
$301$	512.132			1.70143
$302$	115.479	+	729.104i	0.382380	+	2.41425i
$303$	−254.509	−	129.679i	−0.839963	−	0.427983i
$304$	−68.8456	+	22.3693i	−0.226466	+	0.0735832i
$305$	−315.119	−	235.058i	−1.03318	−	0.770683i
$306$	−9.82980	+	30.2530i	−0.0321235	+	0.0988660i
$307$	−98.5129	−	98.5129i	−0.320889	−	0.320889i	0.528219	−	0.849108i	$-0.322860\pi$
$307$	−98.5129	−	98.5129i	−0.320889	−	0.320889i	−0.849108	+	0.528219i	$0.822860\pi$
$308$	57.5353	+	112.919i	0.186803	+	0.366622i
$309$	193.788	+	266.727i	0.627147	+	0.863194i
$310$	58.0244	+	9.93969i	0.187175	+	0.0320635i
$311$	−319.500	−	232.130i	−1.02733	−	0.746399i	−0.0595579	−	0.998225i	$-0.518969\pi$
$311$	−319.500	−	232.130i	−1.02733	−	0.746399i	−0.967773	+	0.251825i	$0.918969\pi$
$312$	116.805	+	18.5001i	0.374375	+	0.0592952i
$313$	−34.8118	+	219.793i	−0.111220	+	0.702214i	0.867565	+	0.497323i	$0.165684\pi$
$313$	−34.8118	+	219.793i	−0.111220	+	0.702214i	−0.978785	+	0.204890i	$0.934316\pi$
$314$	63.8858	−	87.9312i	0.203458	−	0.280036i
$315$	8.51257	−	49.6934i	0.0270240	−	0.157757i
$316$	−94.9242	+	68.9664i	−0.300393	+	0.218248i
$317$	−61.6015	+	31.3875i	−0.194326	+	0.0990142i	−0.548446	−	0.836186i	$-0.684780\pi$
$317$	−61.6015	+	31.3875i	−0.194326	+	0.0990142i	0.354120	+	0.935200i	$0.384780\pi$
$318$	22.2404	−	22.2404i	0.0699385	−	0.0699385i
$319$	−0.443769	−	0.144189i	−0.00139112	−	0.000452004i
$320$	−300.083	+	402.291i	−0.937759	+	1.25716i
$321$	−3.75273	−	11.5497i	−0.0116908	−	0.0359804i
$322$	398.808	−	782.705i	1.23853	−	2.43076i
$323$	245.080	−	38.8168i	0.758761	−	0.120176i
$324$			602.155i			1.85850i
$325$	18.5088	−	100.441i	0.0569501	−	0.309049i
$326$	−499.727			−1.53290
$327$	−36.6020	−	231.096i	−0.111933	−	0.706715i
$328$	−15.5098	−	7.90262i	−0.0472859	−	0.0240933i
$329$	−465.673	+	151.306i	−1.41542	+	0.459898i
$330$	74.2097	−	52.5035i	0.224878	−	0.159102i
$331$	−153.868	+	473.558i	−0.464859	+	1.43069i	0.394300	+	0.918982i	$0.370987\pi$
$331$	−153.868	+	473.558i	−0.464859	+	1.43069i	−0.859159	+	0.511708i	$0.829013\pi$
$332$	21.5330	+	21.5330i	0.0648586	+	0.0648586i
$333$	10.9293	+	21.4499i	0.0328206	+	0.0644141i
$334$	−379.714	−	522.632i	−1.13687	−	1.56477i
$335$	365.211	−	180.336i	1.09018	−	0.538315i
$336$	80.8068	+	58.7096i	0.240496	+	0.174731i
$337$	257.701	+	40.8158i	0.764691	+	0.121115i	0.526583	−	0.850124i	$-0.323473\pi$
$337$	257.701	+	40.8158i	0.764691	+	0.121115i	0.238108	+	0.971239i	$0.423473\pi$
$338$	78.2790	−	494.234i	0.231595	−	1.46223i
$339$	−385.510	+	530.609i	−1.13720	+	1.56522i
$340$	−248.284	+	242.116i	−0.730246	+	0.712107i
$341$	−5.08691	+	3.69586i	−0.0149176	+	0.0108383i
$342$	−67.4727	+	34.3791i	−0.197289	+	0.100524i
$343$	−113.131	+	113.131i	−0.329828	+	0.329828i
$344$	420.437	+	136.608i	1.22220	+	0.397117i
$345$	−375.615	−	127.289i	−1.08874	−	0.368953i
$346$	73.2471	+	225.431i	0.211697	+	0.651536i
$347$	−55.3613	+	108.653i	−0.159543	+	0.313120i	−0.956915	−	0.290367i	$-0.906223\pi$
$347$	−55.3613	+	108.653i	−0.159543	+	0.313120i	0.797373	+	0.603487i	$0.206223\pi$
$348$	−5.62841	+	0.891453i	−0.0161736	+	0.00256165i
$349$			610.515i			1.74933i	0.484731	+	0.874663i	$0.338918\pi$
$349$			610.515i			1.74933i	−0.484731	+	0.874663i	$0.661082\pi$
$350$	530.906	−	693.366i	1.51687	−	1.98105i
$351$	−103.748			−0.295580
$352$	−7.39046	−	46.6615i	−0.0209956	−	0.132561i
$353$	318.376	+	162.221i	0.901916	+	0.459549i	0.842508	−	0.538684i	$-0.181078\pi$
$353$	318.376	+	162.221i	0.901916	+	0.459549i	0.0594087	+	0.998234i	$0.481078\pi$
$354$	−197.320	+	64.1133i	−0.557402	+	0.181111i
$355$	3.44273	+	11.0673i	0.00969784	+	0.0311755i
$356$	305.369	−	939.828i	0.857777	−	2.63997i
$357$	−242.099	−	242.099i	−0.678148	−	0.678148i
$358$	254.623	+	499.726i	0.711237	+	1.39588i
$359$	−217.134	−	298.859i	−0.604829	−	0.832476i	0.391310	−	0.920259i	$-0.372022\pi$
$359$	−217.134	−	298.859i	−0.604829	−	0.832476i	−0.996140	+	0.0877825i	$0.972022\pi$
$360$	20.2439	−	38.5253i	0.0562330	−	0.107015i
$361$	185.838	+	135.019i	0.514785	+	0.374013i
$362$	1100.40	+	174.286i	3.03978	+	0.481454i
$363$	58.1838	−	367.358i	0.160286	−	1.01201i
$364$	−173.448	+	238.731i	−0.476506	+	0.655854i
$365$	496.738	−	72.2845i	1.36093	−	0.198040i
$366$	659.150	−	478.900i	1.80096	−	1.30847i
$367$	−104.123	+	53.0534i	−0.283714	+	0.144560i	−0.590057	−	0.807362i	$-0.700895\pi$
$367$	−104.123	+	53.0534i	−0.283714	+	0.144560i	0.306343	+	0.951921i	$0.400895\pi$
$368$	52.9630	−	52.9630i	0.143921	−	0.143921i
$369$	−1.71066	−	0.555829i	−0.00463595	−	0.00150631i
$370$	−5.24369	+	416.951i	−0.0141721	+	1.12689i
$371$	9.97270	+	30.6928i	0.0268806	+	0.0827299i
$372$	−34.8626	+	68.4216i	−0.0937166	+	0.183929i
$373$	283.128	−	44.8431i	0.759057	−	0.120223i	0.235105	−	0.971970i	$-0.424457\pi$
$373$	283.128	−	44.8431i	0.759057	−	0.120223i	0.523953	+	0.851747i	$0.324457\pi$
$374$		−	58.8495i		−	0.157352i
$375$	−344.290	−	192.114i	−0.918106	−	0.512305i
$376$	−422.657			−1.12409
$377$	−0.169960	−	1.07308i	−0.000450821	−	0.00284637i
$378$	−790.413	−	402.735i	−2.09104	−	1.06544i
$379$	350.259	−	113.806i	0.924167	−	0.300280i	0.191992	−	0.981397i	$-0.438505\pi$
$379$	350.259	−	113.806i	0.924167	−	0.300280i	0.732175	+	0.681117i	$0.238505\pi$
$380$	−825.507	−	10.3818i	−2.17239	−	0.0273206i
$381$	−89.5513	+	275.611i	−0.235043	+	0.723387i
$382$	−755.995	−	755.995i	−1.97904	−	1.97904i
$383$	228.265	+	447.995i	0.595992	+	1.16970i	0.970189	+	0.242351i	$0.0779185\pi$
$383$	228.265	+	447.995i	0.595992	+	1.16970i	−0.374197	+	0.927349i	$0.622082\pi$
$384$	−411.700	−	566.656i	−1.07213	−	1.47567i
$385$	13.4316	+	92.3016i	0.0348872	+	0.239744i
$386$	−211.361	−	153.563i	−0.547567	−	0.397831i
$387$	45.1179	+	7.14598i	0.116584	+	0.0184651i
$388$	−148.296	+	936.306i	−0.382207	+	2.41316i
$389$	283.654	−	390.416i	0.729186	−	1.00364i	−0.269982	−	0.962865i	$-0.587018\pi$
$389$	283.654	−	390.416i	0.729186	−	1.00364i	0.999168	−	0.0407737i	$-0.0129823\pi$
$390$	187.372	+	98.4583i	0.480442	+	0.252457i
$391$	−207.712	+	150.912i	−0.531234	+	0.385964i
$392$	−523.754	+	266.866i	−1.33611	+	0.680781i
$393$	312.107	−	312.107i	0.794166	−	0.794166i
$394$	511.872	+	166.317i	1.29917	+	0.422125i
$395$	−82.4581	+	25.6504i	−0.208755	+	0.0649378i
$396$	3.49315	+	10.7508i	0.00882110	+	0.0271485i
$397$	−95.9284	+	188.270i	−0.241633	+	0.474232i	−0.979693	−	0.200503i	$-0.935742\pi$
$397$	−95.9284	+	188.270i	−0.241633	+	0.474232i	0.738060	+	0.674735i	$0.235742\pi$
$398$	−3.45369	+	0.547011i	−0.00867762	+	0.00137440i
$399$		−	815.066i		−	2.04277i
$400$	61.3211	−	42.2378i	0.153303	−	0.105594i
$401$	−33.6091			−0.0838132			−0.0419066	−	0.999122i	$-0.513343\pi$
$401$	−33.6091			−0.0838132			−0.0419066	+	0.999122i	$0.513343\pi$
$402$	132.052	+	833.742i	0.328487	+	2.07399i
$403$	−13.0449	−	6.64671i	−0.0323695	−	0.0164931i
$404$	585.128	−	190.120i	1.44834	−	0.470593i
$405$	−142.240	+	419.733i	−0.351209	+	1.03638i
$406$	2.87070	−	8.83509i	0.00707068	−	0.0217613i
$407$	−31.4927	−	31.4927i	−0.0773777	−	0.0773777i
$408$	−134.174	−	263.331i	−0.328857	−	0.645419i
$409$	−296.632	−	408.279i	−0.725262	−	0.998238i	−0.999333	−	0.0365283i	$-0.988370\pi$
$409$	−296.632	−	408.279i	−0.725262	−	0.998238i	0.274070	−	0.961710i	$-0.411630\pi$
$410$	−21.7514	−	22.3055i	−0.0530522	−	0.0544036i
$411$	572.348	+	415.835i	1.39257	+	1.01176i
$412$	−701.377	−	111.087i	−1.70237	−	0.269629i
$413$	33.3020	−	210.260i	0.0806343	−	0.509105i
$414$	46.0557	−	63.3902i	0.111246	−	0.153116i
$415$	9.92317	+	20.0961i	0.0239112	+	0.0484244i
$416$	88.9938	−	64.6578i	0.213927	−	0.155427i
$417$	251.574	−	128.183i	0.603294	−	0.307394i
$418$	99.0633	−	99.0633i	0.236994	−	0.236994i
$419$	678.992	+	220.618i	1.62051	+	0.526535i	0.972061	−	0.234727i	$-0.0754195\pi$
$419$	678.992	+	220.618i	1.62051	+	0.526535i	0.648445	+	0.761261i	$0.275419\pi$
$420$	657.925	+	929.927i	1.56649	+	2.21411i
$421$	−205.918	−	633.749i	−0.489115	−	1.50534i	−0.825931	−	0.563772i	$-0.809350\pi$
$421$	−205.918	−	633.749i	−0.489115	−	1.50534i	0.336815	−	0.941571i	$-0.390650\pi$
$422$	−352.318	+	691.463i	−0.834877	+	1.63854i
$423$	−43.1363	+	6.83211i	−0.101977	+	0.0161516i
$424$			27.8576i			0.0657019i
$425$	−230.259	+	110.119i	−0.541785	+	0.259103i
$426$	−24.0208			−0.0563869
$427$	130.777	+	825.693i	0.306269	+	1.93371i
$428$	23.3061	+	11.8750i	0.0544534	+	0.0277454i
$429$	−21.5012	+	6.98617i	−0.0501194	+	0.0162848i
$430$	634.221	+	473.088i	1.47493	+	1.10020i
$431$	−208.917	+	642.979i	−0.484725	+	1.49183i	0.347653	+	0.937623i	$0.386979\pi$
$431$	−208.917	+	642.979i	−0.484725	+	1.49183i	−0.832378	+	0.554208i	$0.813021\pi$
$432$	−53.4846	−	53.4846i	−0.123807	−	0.123807i
$433$	−319.506	−	627.066i	−0.737889	−	1.44819i	−0.888156	−	0.459543i	$-0.848013\pi$
$433$	−319.506	−	627.066i	−0.737889	−	1.44819i	0.150267	−	0.988645i	$-0.451987\pi$
$434$	−73.5817	−	101.277i	−0.169543	−	0.233356i
$435$	−4.13387	−	0.708141i	−0.00950316	−	0.00162791i
$436$	407.711	+	296.219i	0.935117	+	0.679402i
$437$	−603.684	−	95.6142i	−1.38143	−	0.218797i
$438$	−162.742	+	1027.51i	−0.371556	+	2.34591i
$439$	−99.5625	+	137.036i	−0.226794	+	0.312155i	−0.907216	−	0.420666i	$-0.861797\pi$
$439$	−99.5625	+	137.036i	−0.226794	+	0.312155i	0.680422	+	0.732821i	$0.261797\pi$
$440$	−13.5942	+	79.3583i	−0.0308960	+	0.180360i
$441$	−49.1404	+	35.7026i	−0.111429	+	0.0809582i
$442$	122.092	−	62.2089i	0.276226	−	0.140744i
$443$	386.504	−	386.504i	0.872469	−	0.872469i	−0.120272	−	0.992741i	$-0.538377\pi$
$443$	386.504	−	386.504i	0.872469	−	0.872469i	0.992741	+	0.120272i	$0.0383767\pi$
$444$	−517.306	−	168.083i	−1.16510	−	0.378565i
$445$	434.862	−	582.975i	0.977217	−	1.31006i
$446$	67.6736	+	208.278i	0.151734	+	0.466991i
$447$	196.751	−	386.146i	0.440159	−	0.863861i
$448$	1054.11	−	166.954i	2.35291	−	0.372665i
$449$			45.5385i			0.101422i	0.998713	+	0.0507110i	$0.0161487\pi$
$449$			45.5385i			0.101422i	−0.998713	+	0.0507110i	$0.983851\pi$
$450$	56.4467	−	53.6764i	0.125437	−	0.119281i
$451$	3.32766			0.00737841
$452$	−220.990	−	1395.27i	−0.488915	−	3.08689i
$453$	−631.457	−	321.743i	−1.39394	−	0.710250i
$454$	−1158.44	+	376.401i	−2.55164	+	0.829077i
$455$	−177.295	+	125.436i	−0.389659	+	0.275684i
$456$	217.414	−	669.133i	0.476786	−	1.46740i
$457$	−133.531	−	133.531i	−0.292190	−	0.292190i	0.545755	−	0.837945i	$-0.316243\pi$
$457$	−133.531	−	133.531i	−0.292190	−	0.292190i	−0.837945	+	0.545755i	$0.816243\pi$
$458$	61.7103	+	121.113i	0.134739	+	0.264440i
$459$	152.398	+	209.758i	0.332022	+	0.456989i
$460$	765.937	−	378.208i	1.66508	−	0.822191i
$461$	−269.252	−	195.623i	−0.584061	−	0.424345i	0.256125	−	0.966644i	$-0.417554\pi$
$461$	−269.252	−	195.623i	−0.584061	−	0.424345i	−0.840186	+	0.542299i	$0.817554\pi$
$462$	−190.927	−	30.2399i	−0.413263	−	0.0654544i
$463$	35.1369	−	221.846i	0.0758896	−	0.479148i	−0.920247	−	0.391337i	$-0.872013\pi$
$463$	35.1369	−	221.846i	0.0758896	−	0.479148i	0.996137	−	0.0878114i	$-0.0279873\pi$
$464$	0.465580	−	0.640815i	0.00100340	−	0.00138107i
$465$	−40.4634	+	39.4583i	−0.0870181	+	0.0848565i
$466$	94.1412	−	68.3976i	0.202020	−	0.146776i
$467$	3.23818	−	1.64993i	0.00693399	−	0.00353305i	−0.450520	−	0.892766i	$-0.648761\pi$
$467$	3.23818	−	1.64993i	0.00693399	−	0.00353305i	0.457454	+	0.889233i	$0.348761\pi$
$468$	−18.6116	+	18.6116i	−0.0397684	+	0.0397684i
$469$	−823.740	−	267.649i	−1.75638	−	0.570681i
$470$	−716.458	−	242.794i	−1.52438	−	0.516583i
$471$	32.2449	+	99.2396i	0.0684605	+	0.210700i
$472$	83.4253	−	163.731i	0.176748	−	0.346888i
$473$	−83.4699	+	13.2203i	−0.176469	+	0.0279500i
$474$		−	178.970i		−	0.377573i
$475$	−572.969	−	202.236i	−1.20625	−	0.425760i
$476$	737.447			1.54926
$477$	0.450309	+	2.84314i	0.000944043	+	0.00596045i
$478$	−141.515	−	72.1053i	−0.296056	−	0.150848i
$479$	125.388	−	40.7412i	0.261771	−	0.0850546i	−0.175191	−	0.984534i	$-0.556054\pi$
$479$	125.388	−	40.7412i	0.261771	−	0.0850546i	0.436962	+	0.899480i	$0.356054\pi$
$480$	−126.133	−	405.480i	−0.262778	−	0.844749i
$481$	32.0457	−	98.6267i	0.0666232	−	0.205045i
$482$	483.478	+	483.478i	1.00307	+	1.00307i
$483$	382.875	+	751.434i	0.792702	+	1.55576i
$484$	470.881	+	648.112i	0.972894	+	1.33907i
$485$	−324.542	+	617.623i	−0.669159	+	1.27345i
$486$	−135.569	−	98.4966i	−0.278949	−	0.202668i
$487$	853.736	+	135.219i	1.75305	+	0.277656i	0.948627	−	0.316398i	$-0.102473\pi$
$487$	853.736	+	135.219i	1.75305	+	0.277656i	0.804425	+	0.594054i	$0.202473\pi$
$488$	−112.887	+	712.741i	−0.231326	+	1.46053i
$489$	281.997	−	388.136i	0.576681	−	0.793733i
$490$	−1041.13	+	151.504i	−2.12476	+	0.309191i
$491$	55.6131	−	40.4053i	0.113265	−	0.0822918i	−0.529711	−	0.848178i	$-0.677700\pi$
$491$	55.6131	−	40.4053i	0.113265	−	0.0822918i	0.642976	+	0.765886i	$0.277700\pi$
$492$	36.2106	−	18.4502i	0.0735988	−	0.0375005i
$493$	−1.91990	+	1.91990i	−0.00389431	+	0.00389431i
$494$	310.240	+	100.803i	0.628015	+	0.204055i
$495$	−0.104623	+	8.31903i	−0.000211359	+	0.0168061i
$496$	−3.29841	−	10.1514i	−0.00665001	−	0.0204666i
$497$	11.1894	−	21.9604i	0.0225139	−	0.0441859i
$498$	−45.8776	+	7.26629i	−0.0921236	+	0.0145909i
$499$			590.105i			1.18257i	0.806461	+	0.591287i	$0.201380\pi$
$499$			590.105i			1.18257i	−0.806461	+	0.591287i	$0.798620\pi$
$500$	816.958	−	231.767i	1.63392	−	0.463535i
$501$	620.199			1.23792
$502$	−145.946	−	921.465i	−0.290729	−	1.83559i
$503$	133.604	+	68.0748i	0.265615	+	0.135337i	0.581726	−	0.813384i	$-0.302377\pi$
$503$	133.604	+	68.0748i	0.265615	+	0.135337i	−0.316112	+	0.948722i	$0.602377\pi$
$504$	−88.0154	+	28.5980i	−0.174634	+	0.0567420i
$505$	452.774	+	5.69422i	0.896583	+	0.0112757i
$506$	−44.7948	+	137.864i	−0.0885272	+	0.272459i
$507$	339.696	+	339.696i	0.670012	+	0.670012i
$508$	−283.373	−	556.152i	−0.557822	−	1.09479i
$509$	−55.2439	−	76.0367i	−0.108534	−	0.149384i	0.751295	−	0.659967i	$-0.229430\pi$
$509$	−55.2439	−	76.0367i	−0.108534	−	0.149384i	−0.859829	+	0.510583i	$0.829430\pi$
$510$	−76.1724	−	523.456i	−0.149358	−	1.02638i
$511$	−863.567	−	627.418i	−1.68995	−	1.22782i
$512$	187.207	+	29.6506i	0.365638	+	0.0579114i
$513$	−96.5558	+	609.630i	−0.188218	+	1.18836i
$514$	401.705	−	552.899i	0.781526	−	1.07568i
$515$	−462.656	−	243.111i	−0.898360	−	0.472060i
$516$	−834.994	+	606.659i	−1.61821	+	1.17570i
$517$	71.9919	−	36.6817i	0.139249	−	0.0709511i
$518$	626.996	−	626.996i	1.21042	−	1.21042i
$519$	−216.425	−	70.3208i	−0.417004	−	0.135493i
$520$	−179.011	+	55.6852i	−0.344251	+	0.107087i
$521$	−9.08811	−	27.9703i	−0.0174436	−	0.0536859i	0.941956	−	0.335737i	$-0.108985\pi$
$521$	−9.08811	−	27.9703i	−0.0174436	−	0.0536859i	−0.959399	+	0.282051i	$0.908985\pi$
$522$	0.376183	−	0.738301i	0.000720657	−	0.00141437i
$523$	−262.167	+	41.5232i	−0.501275	+	0.0793942i	−0.401952	−	0.915661i	$-0.631668\pi$
$523$	−262.167	+	41.5232i	−0.501275	+	0.0793942i	−0.0993239	+	0.995055i	$0.531668\pi$
$524$			950.696i			1.81430i
$525$	238.943	+	803.620i	0.455129	+	1.53071i
$526$	−355.940			−0.676693
$527$	5.72363	+	36.1376i	0.0108608	+	0.0685723i
$528$	−14.6859	−	7.48282i	−0.0278141	−	0.0141720i
$529$	98.3605	−	31.9593i	0.185937	−	0.0604145i
$530$	−16.0027	+	47.2222i	−0.0301938	+	0.0890985i
$531$	5.86769	−	18.0589i	0.0110503	−	0.0340092i
$532$	1241.37	+	1241.37i	2.33340	+	2.33340i
$533$	3.51762	+	6.90372i	0.00659966	+	0.0129526i
$534$	885.974	+	1219.44i	1.65913	+	2.28359i
$535$	13.4404	+	13.7828i	0.0251223	+	0.0257623i
$536$	−604.860	−	439.456i	−1.12847	−	0.819881i
$537$	−531.819	−	84.2319i	−0.990352	−	0.156856i
$538$	124.058	−	783.269i	0.230590	−	1.45589i
$539$	66.0511	−	90.9115i	0.122544	−	0.168667i
$540$	−381.933	−	773.480i	−0.707283	−	1.43237i
$541$	206.758	−	150.219i	0.382178	−	0.277669i	−0.380064	−	0.924960i	$-0.624098\pi$
$541$	206.758	−	150.219i	0.382178	−	0.277669i	0.762243	+	0.647291i	$0.224098\pi$
$542$	−91.9922	+	46.8724i	−0.169727	+	0.0864804i
$543$	−756.327	+	756.327i	−1.39287	+	1.39287i
$544$	−261.449	−	84.9501i	−0.480606	−	0.156158i
$545$	214.224	+	302.789i	0.393071	+	0.555576i
$546$	−139.089	−	428.073i	−0.254742	−	0.784016i
$547$	160.709	−	315.410i	0.293801	−	0.576618i	−0.696171	−	0.717876i	$-0.745115\pi$
$547$	160.709	−	315.410i	0.293801	−	0.576618i	0.989973	+	0.141258i	$0.0451147\pi$
$548$	−1505.03	+	238.373i	−2.74641	+	0.434988i
$549$			74.5669i			0.135823i
$550$	−68.6310	+	126.713i	−0.124784	+	0.230388i
$551$	−6.46365			−0.0117308
$552$	113.882	+	719.024i	0.206308	+	1.30258i
$553$	163.618	+	83.3677i	0.295874	+	0.150755i
$554$	−925.308	+	300.651i	−1.67023	+	0.542691i
$555$	−320.885	−	239.359i	−0.578171	−	0.431278i
$556$	−187.927	+	578.380i	−0.337998	+	1.04025i
$557$	465.228	+	465.228i	0.835239	+	0.835239i	0.988228	−	0.152989i	$-0.0488899\pi$
$557$	465.228	+	465.228i	0.835239	+	0.835239i	−0.152989	+	0.988228i	$0.548890\pi$
$558$	−5.06927	−	9.94901i	−0.00908472	−	0.0178298i
$559$	−115.662	−	159.195i	−0.206909	−	0.284786i
$560$	−156.064	−	26.7341i	−0.278687	−	0.0477395i
$561$	45.7081	+	33.2089i	0.0814762	+	0.0591959i
$562$	−739.086	−	117.060i	−1.31510	−	0.208291i
$563$	73.0207	−	461.034i	0.129699	−	0.818889i	−0.833974	−	0.551804i	$-0.813940\pi$
$563$	73.0207	−	461.034i	0.129699	−	0.818889i	0.963673	−	0.267085i	$-0.0860604\pi$
$564$	580.013	−	798.319i	1.02839	−	1.41546i
$565$	175.547	−	1024.78i	0.310702	−	1.81377i
$566$	−198.420	+	144.161i	−0.350566	+	0.254701i
$567$	839.695	−	427.846i	1.48094	−	0.754578i
$568$	15.0438	−	15.0438i	0.0264856	−	0.0264856i
$569$	165.686	+	53.8347i	0.291188	+	0.0946129i	0.450969	−	0.892540i	$-0.351079\pi$
$569$	165.686	+	53.8347i	0.291188	+	0.0946129i	−0.159780	+	0.987153i	$0.551079\pi$
$570$	752.927	−	1009.37i	1.32092	−	1.77083i
$571$	151.720	+	466.947i	0.265710	+	0.817770i	0.991529	+	0.129885i	$0.0414608\pi$
$571$	151.720	+	466.947i	0.265710	+	0.817770i	−0.725819	+	0.687885i	$0.758539\pi$
$572$	22.1068	−	43.3870i	0.0386483	−	0.0758515i
$573$	1013.79	−	160.568i	1.76926	−	0.280224i
$574$			66.2512i			0.115420i
$575$	623.237	−	82.7030i	1.08389	−	0.143831i
$576$	95.1945			0.165268
$577$	48.6071	+	306.893i	0.0842411	+	0.531877i	0.993333	+	0.115281i	$0.0367770\pi$
$577$	48.6071	+	306.893i	0.0842411	+	0.531877i	−0.909092	+	0.416596i	$0.863223\pi$
$578$	540.866	+	275.585i	0.935754	+	0.476790i
$579$	238.543	−	77.5073i	0.411991	−	0.133864i
$580$	7.37452	−	5.21748i	0.0127147	−	0.00899566i
$581$	14.7277	−	45.3272i	0.0253489	−	0.0780158i
$582$	−1022.45	−	1022.45i	−1.75679	−	1.75679i
$583$	−2.41772	−	4.74503i	−0.00414702	−	0.00813899i
$584$	−541.589	−	745.434i	−0.927379	−	1.27643i
$585$	−17.3696	+	8.57686i	−0.0296917	+	0.0146613i
$586$	1279.72	+	929.773i	2.18383	+	1.58664i
$587$	−558.108	−	88.3956i	−0.950780	−	0.150589i	−0.338268	−	0.941050i	$-0.609841\pi$
$587$	−558.108	−	88.3956i	−0.950780	−	0.150589i	−0.612512	+	0.790461i	$0.709841\pi$
$588$	214.689	−	1355.49i	0.365117	−	2.30526i
$589$	−51.1968	+	70.4664i	−0.0869216	+	0.119637i
$590$	235.471	−	229.622i	0.399104	−	0.389190i
$591$	−418.029	+	303.716i	−0.707324	+	0.513901i
$592$	67.3645	−	34.3239i	0.113791	−	0.0579796i
$593$	−358.764	+	358.764i	−0.604998	+	0.604998i	−0.941635	−	0.336636i	$-0.890711\pi$
$593$	−358.764	+	358.764i	−0.604998	+	0.604998i	0.336636	+	0.941635i	$0.390711\pi$
$594$	139.222	+	45.2359i	0.234380	+	0.0761548i
$595$	514.038	+	174.198i	0.863930	+	0.292769i
$596$	288.453	+	887.768i	0.483982	+	1.48954i
$597$	1.52407	−	2.99115i	0.00255288	−	0.00501030i
$598$	−333.371	+	52.8008i	−0.557477	+	0.0882957i
$599$		−	65.7927i		−	0.109837i	−0.998491	−	0.0549187i	$-0.982510\pi$
$599$		−	65.7927i		−	0.109837i	0.998491	−	0.0549187i	$-0.0174900\pi$
$600$	−18.2001	+	723.473i	−0.0303335	+	1.20579i
$601$	−537.779			−0.894807			−0.447403	−	0.894332i	$-0.647651\pi$
$601$	−537.779			−0.894807			−0.447403	+	0.894332i	$0.647651\pi$
$602$	−263.207	−	1661.82i	−0.437220	−	2.76050i
$603$	−68.8354	−	35.0734i	−0.114155	−	0.0581649i
$604$	1451.75	−	471.702i	2.40356	−	0.780964i
$605$	175.133	+	562.998i	0.289476	+	0.930575i
$606$	−289.993	+	892.506i	−0.478536	+	1.47278i
$607$	−368.560	−	368.560i	−0.607184	−	0.607184i	0.335026	−	0.942209i	$-0.391255\pi$
$607$	−368.560	−	368.560i	−0.607184	−	0.607184i	−0.942209	+	0.335026i	$0.891255\pi$
$608$	−297.107	−	583.106i	−0.488663	−	0.959056i
$609$	5.24224	+	7.21532i	0.00860795	+	0.0118478i
$610$	−600.789	+	1143.34i	−0.984901	+	1.87433i
$611$	152.203	+	110.582i	0.249105	+	0.180985i
$612$	64.9678	+	10.2899i	0.106157	+	0.0168135i
$613$	−96.0244	+	606.274i	−0.156647	+	0.989028i	0.776653	+	0.629929i	$0.216916\pi$
$613$	−96.0244	+	606.274i	−0.156647	+	0.989028i	−0.933299	+	0.359099i	$0.883084\pi$
$614$	−269.035	+	370.295i	−0.438168	+	0.603087i
$615$	29.5989	−	4.30719i	0.0481284	−	0.00700356i
$616$	138.513	−	100.636i	0.224859	−	0.163370i
$617$	−626.986	+	319.465i	−1.01618	+	0.517772i	−0.881034	−	0.473053i	$-0.843152\pi$
$617$	−626.986	+	319.465i	−1.01618	+	0.517772i	−0.135150	+	0.990825i	$0.543152\pi$
$618$	765.908	−	765.908i	1.23933	−	1.23933i
$619$	0.633583	+	0.205864i	0.00102356	+	0.000332575i	0.309529	−	0.950890i	$-0.399829\pi$
$619$	0.633583	+	0.205864i	0.00102356	+	0.000332575i	−0.308505	+	0.951223i	$0.599829\pi$
$620$	1.53082	−	121.723i	0.00246907	−	0.196327i
$621$	−197.354	−	607.393i	−0.317800	−	0.978088i
$622$	−589.037	+	1156.05i	−0.947005	+	1.85860i
$623$	−1527.55	+	241.939i	−2.45192	+	0.388346i
$624$		−	38.3779i		−	0.0615031i
$625$	624.209	+	31.4258i	0.998735	+	0.0502813i
$626$	731.099			1.16789
$627$	21.0404	+	132.844i	0.0335572	+	0.211872i
$628$	−200.254	−	102.035i	−0.318877	−	0.162476i
$629$	−246.476	+	80.0848i	−0.391853	+	0.127321i
$630$	−165.625	−	2.08295i	−0.262898	−	0.00330628i
$631$	240.796	−	741.095i	0.381611	−	1.17448i	−0.557298	−	0.830312i	$-0.688162\pi$
$631$	240.796	−	741.095i	0.381611	−	1.17448i	0.938909	−	0.344165i	$-0.111838\pi$
$632$	112.085	+	112.085i	0.177350	+	0.177350i
$633$	−338.242	−	663.838i	−0.534348	−	1.04872i
$634$	133.509	+	183.760i	0.210583	+	0.289842i
$635$	−66.1532	−	454.604i	−0.104178	−	0.715912i
$636$	−52.6177	−	38.2290i	−0.0827323	−	0.0601085i
$637$	258.431	+	40.9314i	0.405700	+	0.0642566i
$638$	−0.239809	+	1.51409i	−0.000375876	+	0.00237319i
$639$	1.29219	−	1.77854i	0.00202220	−	0.00278333i
$640$	982.903	+	516.485i	1.53579	+	0.807007i
$641$	481.236	−	349.638i	0.750758	−	0.545458i	−0.145304	−	0.989387i	$-0.546416\pi$
$641$	481.236	−	349.638i	0.750758	−	0.545458i	0.896062	+	0.443929i	$0.146416\pi$
$642$	−35.5491	+	18.1132i	−0.0553724	+	0.0282137i
$643$	−175.195	+	175.195i	−0.272465	+	0.272465i	−0.830092	−	0.557627i	$-0.811712\pi$
$643$	−175.195	+	175.195i	−0.272465	+	0.272465i	0.557627	+	0.830092i	$0.311712\pi$
$644$	−1727.58	−	561.326i	−2.68258	−	0.871624i
$645$	−725.338	+	225.632i	−1.12455	+	0.349818i
$646$	−251.914	−	775.312i	−0.389960	−	1.20017i
$647$	188.793	−	370.526i	0.291797	−	0.572684i	−0.697844	−	0.716250i	$-0.745857\pi$
$647$	188.793	−	370.526i	0.291797	−	0.572684i	0.989641	+	0.143566i	$0.0458570\pi$
$648$	803.477	−	127.258i	1.23993	−	0.196386i
$649$			35.1290i			0.0541279i
$650$	−335.434	−	8.43837i	−0.516052	−	0.0129821i
$651$	120.183			0.184614
$652$	161.652	+	1020.63i	0.247932	+	1.56538i
$653$	−154.952	−	78.9520i	−0.237293	−	0.120907i	0.331301	−	0.943525i	$-0.392512\pi$
$653$	−154.952	−	78.9520i	−0.237293	−	0.120907i	−0.568594	+	0.822618i	$0.692512\pi$
$654$	−731.074	+	237.540i	−1.11785	+	0.363211i
$655$	−224.571	+	662.684i	−0.342856	+	1.01173i
$656$	−1.74561	+	5.37243i	−0.00266099	+	0.00818967i
$657$	−67.3241	−	67.3241i	−0.102472	−	0.102472i
$658$	730.305	+	1433.30i	1.10989	+	2.17828i
$659$	475.861	+	654.967i	0.722096	+	0.993880i	0.999452	+	0.0331123i	$0.0105419\pi$
$659$	475.861	+	654.967i	0.722096	+	0.993880i	−0.277356	+	0.960767i	$0.589458\pi$
$660$	−131.237	−	134.580i	−0.198845	−	0.203910i
$661$	−523.116	−	380.066i	−0.791401	−	0.574987i	0.116978	−	0.993135i	$-0.462679\pi$
$661$	−523.116	−	380.066i	−0.791401	−	0.574987i	−0.908379	+	0.418148i	$0.862679\pi$
$662$	1615.73	+	255.907i	2.44069	+	0.386567i
$663$	−20.5793	+	129.933i	−0.0310397	+	0.195977i
$664$	24.1816	−	33.2831i	0.0364180	−	0.0501251i
$665$	572.065	+	1158.53i	0.860248	+	1.74215i
$666$	63.9860	−	46.4885i	0.0960750	−	0.0698026i
$667$	5.95904	−	3.03628i	0.00893409	−	0.00455214i
$668$	−944.581	+	944.581i	−1.41404	+	1.41404i
$669$	−199.957	−	64.9699i	−0.298889	−	0.0971150i
$670$	−772.871	−	1092.39i	−1.15354	−	1.63044i
$671$	−42.6294	−	131.200i	−0.0635311	−	0.195529i
$672$	−409.952	+	804.577i	−0.610048	+	1.19729i
$673$	627.765	−	99.4282i	0.932786	−	0.147739i	0.328498	−	0.944505i	$-0.393458\pi$
$673$	627.765	−	99.4282i	0.932786	−	0.147739i	0.604288	+	0.796766i	$0.293458\pi$
$674$		−	857.193i		−	1.27180i
$675$	−83.5175	−	629.375i	−0.123730	−	0.932407i
$676$	−1034.73			−1.53067
$677$	−4.37313	−	27.6108i	−0.00645957	−	0.0407841i	0.984248	−	0.176793i	$-0.0565724\pi$
$677$	−4.37313	−	27.6108i	−0.00645957	−	0.0407841i	−0.990708	+	0.136009i	$0.956572\pi$
$678$	1919.91	+	978.242i	2.83172	+	1.44283i
$679$	1411.03	−	458.471i	2.07810	−	0.675215i
$680$	375.536	+	280.126i	0.552259	+	0.411949i
$681$	361.363	−	1112.16i	0.530636	−	1.63313i
$682$	14.6071	+	14.6071i	0.0214181	+	0.0214181i
$683$	−142.066	−	278.821i	−0.208004	−	0.408230i	0.763310	−	0.646032i	$-0.223573\pi$
$683$	−142.066	−	278.821i	−0.208004	−	0.408230i	−0.971314	+	0.237802i	$0.923573\pi$
$684$	92.0411	+	126.684i	0.134563	+	0.185210i
$685$	−1105.39	−	189.356i	−1.61371	−	0.276432i
$686$	425.243	+	308.957i	0.619888	+	0.450375i
$687$	−128.891	−	20.4144i	−0.187615	−	0.0297153i
$688$	22.4423	−	141.695i	0.0326196	−	0.205952i
$689$	7.28853	−	10.0318i	0.0105784	−	0.0145600i
$690$	−219.996	+	1284.26i	−0.318834	+	1.86124i
$691$	465.719	−	338.364i	0.673978	−	0.489673i	−0.197377	−	0.980328i	$-0.563242\pi$
$691$	465.719	−	338.364i	0.673978	−	0.489673i	0.871354	+	0.490654i	$0.163242\pi$
$692$	436.722	−	222.521i	0.631101	−	0.321562i
$693$	12.5099	−	12.5099i	0.0180517	−	0.0180517i
$694$	381.021	+	123.801i	0.549021	+	0.178388i
$695$	−267.618	+	358.769i	−0.385062	+	0.516214i
$696$	2.37900	+	7.32180i	0.00341810	+	0.0105198i
$697$	8.79080	−	17.2529i	0.0126123	−	0.0247531i
$698$	1981.07	−	313.770i	2.83820	−	0.449527i
$699$			111.716i			0.159823i
$700$	−1587.85	−	860.020i	−2.26836	−	1.22860i
$701$	−189.634			−0.270520			−0.135260	−	0.990810i	$-0.543187\pi$
$701$	−189.634			−0.270520			−0.135260	+	0.990810i	$0.543187\pi$
$702$	53.3208	+	336.654i	0.0759556	+	0.479565i
$703$	−549.710	−	280.091i	−0.781949	−	0.398423i
$704$	−167.494	+	54.4220i	−0.237917	+	0.0773040i
$705$	592.876	−	419.461i	0.840959	−	0.594980i
$706$	362.765	−	1116.48i	0.513831	−	1.58141i
$707$	−680.866	−	680.866i	−0.963035	−	0.963035i
$708$	194.773	+	382.263i	0.275103	+	0.539920i
$709$	−291.834	−	401.676i	−0.411614	−	0.566538i	0.551997	−	0.833846i	$-0.313866\pi$
$709$	−291.834	−	401.676i	−0.411614	−	0.566538i	−0.963611	+	0.267308i	$0.913866\pi$
$710$	34.1431	−	16.8593i	0.0480888	−	0.0237455i
$711$	13.2512	+	9.62758i	0.0186375	+	0.0135409i
$712$	−1318.58	−	208.843i	−1.85194	−	0.293319i
$713$	14.0985	−	89.0147i	0.0197735	−	0.124845i
$714$	−661.164	+	910.014i	−0.926000	+	1.27453i
$715$	25.6584	−	25.0210i	0.0358858	−	0.0349944i
$716$	938.262	−	681.687i	1.31042	−	0.952077i
$717$	135.861	−	69.2246i	0.189485	−	0.0965475i
$718$	−858.176	+	858.176i	−1.19523	+	1.19523i
$719$	−276.486	−	89.8356i	−0.384542	−	0.124945i	0.110365	−	0.993891i	$-0.464798\pi$
$719$	−276.486	−	89.8356i	−0.384542	−	0.124945i	−0.494907	+	0.868946i	$0.664798\pi$
$720$	−13.3760	−	4.53286i	−0.0185777	−	0.00629564i
$721$	343.436	+	1056.99i	0.476333	+	1.46600i
$722$	342.614	−	672.418i	0.474535	−	0.931327i
$723$	−648.343	+	102.688i	−0.896741	+	0.142030i
$724$		−	2303.81i		−	3.18206i
$725$	6.37288	−	1.89487i	0.00879018	−	0.00261361i
$726$	−1221.95			−1.68312
$727$	−49.3376	−	311.506i	−0.0678647	−	0.428481i	−0.998105	−	0.0615305i	$-0.980402\pi$
$727$	−49.3376	−	311.506i	−0.0678647	−	0.428481i	0.930240	−	0.366950i	$-0.119598\pi$
$728$	355.203	+	180.985i	0.487917	+	0.248606i
$729$	−605.676	+	196.796i	−0.830832	+	0.269954i
$730$	−489.852	−	1574.72i	−0.671030	−	2.15715i
$731$	−151.962	+	467.691i	−0.207882	+	0.639796i
$732$	−1191.32	−	1191.32i	−1.62748	−	1.62748i
$733$	494.423	+	970.360i	0.674520	+	1.32382i	0.933723	+	0.357997i	$0.116540\pi$
$733$	494.423	+	970.360i	0.674520	+	1.32382i	−0.259203	+	0.965823i	$0.583460\pi$
$734$	225.667	+	310.604i	0.307448	+	0.423166i
$735$	469.840	−	894.136i	0.639239	−	1.21651i
$736$	547.824	+	398.018i	0.744327	+	0.540785i
$737$	141.167	+	22.3586i	0.191542	+	0.0303373i
$738$	−0.924429	+	5.83662i	−0.00125261	+	0.00790870i
$739$	−539.948	+	743.174i	−0.730646	+	1.00565i	0.268456	+	0.963292i	$0.413486\pi$
$739$	−539.948	+	743.174i	−0.730646	+	1.00565i	−0.999103	+	0.0423564i	$0.986514\pi$
$740$	853.267	−	124.166i	1.15306	−	0.167792i
$741$	−253.362	+	184.078i	−0.341919	+	0.248419i
$742$	94.4700	−	48.1349i	0.127318	−	0.0648718i
$743$	840.345	−	840.345i	1.13102	−	1.13102i	0.141008	−	0.990008i	$-0.454966\pi$
$743$	840.345	−	840.345i	1.13102	−	1.13102i	0.990008	−	0.141008i	$-0.0450344\pi$
$744$	98.6652	+	32.0583i	0.132615	+	0.0430891i
$745$	−8.63939	+	686.958i	−0.0115965	+	0.922092i
$746$	−291.024	−	895.680i	−0.390112	−	1.20064i
$747$	1.92995	−	3.78774i	0.00258360	−	0.00507061i
$748$	−120.193	+	19.0367i	−0.160686	+	0.0254501i
$749$		−	40.9374i		−	0.0546560i
$750$	−446.448	+	1215.93i	−0.595264	+	1.62123i
$751$	−59.5548			−0.0793007			−0.0396504	−	0.999214i	$-0.512624\pi$
$751$	−59.5548			−0.0793007			−0.0396504	+	0.999214i	$0.512624\pi$
$752$	21.4566	+	135.472i	0.0285327	+	0.180148i
$753$	798.055	+	406.630i	1.05983	+	0.540013i
$754$	−3.39471	+	1.10301i	−0.00450226	+	0.00146287i
$755$	1123.37	+	14.1278i	1.48791	+	0.0187123i
$756$	−566.854	+	1744.60i	−0.749807	+	2.30767i
$757$	466.274	+	466.274i	0.615950	+	0.615950i	0.944490	−	0.328540i	$-0.106557\pi$
$757$	466.274	+	466.274i	0.615950	+	0.615950i	−0.328540	+	0.944490i	$0.606557\pi$
$758$	−549.304	−	1078.07i	−0.724675	−	1.42226i
$759$	−81.8007	−	112.589i	−0.107774	−	0.148339i
$760$	160.608	+	1103.70i	0.211326	+	1.45223i
$761$	−64.3585	−	46.7592i	−0.0845710	−	0.0614444i	0.544696	−	0.838633i	$-0.316645\pi$
$761$	−64.3585	−	46.7592i	−0.0845710	−	0.0614444i	−0.629267	+	0.777189i	$0.716645\pi$
$762$	940.356	+	148.938i	1.23406	+	0.195456i
$763$	123.384	−	779.017i	0.161709	−	1.02099i
$764$	−1299.48	+	1788.58i	−1.70089	+	2.34107i
$765$	42.8553	+	22.5191i	0.0560199	+	0.0294367i
$766$	1336.39	−	970.943i	1.74463	−	1.26755i
$767$	−72.8802	+	37.1343i	−0.0950198	+	0.0484150i
$768$	−731.680	+	731.680i	−0.952708	+	0.952708i
$769$	1320.49	+	429.054i	1.71716	+	0.557938i	0.991498	−	0.130119i	$-0.0415359\pi$
$769$	1320.49	+	429.054i	1.71716	+	0.557938i	0.725657	+	0.688057i	$0.241536\pi$
$770$	292.607	−	91.0220i	0.380009	−	0.118210i
$771$	202.751	+	624.004i	0.262972	+	0.809344i
$772$	−245.262	+	481.353i	−0.317697	+	0.623515i
$773$	759.496	−	120.292i	0.982531	−	0.155618i	0.355554	−	0.934656i	$-0.384292\pi$
$773$	759.496	−	120.292i	0.982531	−	0.155618i	0.626977	+	0.779038i	$0.284292\pi$
$774$		−	150.076i		−	0.193897i
$775$	29.8201	−	84.4856i	0.0384776	−	0.109014i
$776$	1280.69			1.65037
$777$	133.170	+	840.800i	0.171390	+	1.08211i
$778$	−1412.65	−	719.779i	−1.81574	−	0.925165i
$779$	43.8403	−	14.2446i	0.0562776	−	0.0182857i
$780$	140.478	−	414.534i	0.180099	−	0.531454i
$781$	−1.25681	+	3.86807i	−0.00160923	+	0.00495271i
$782$	596.448	+	596.448i	0.762721	+	0.762721i
$783$	−3.06618	−	6.01772i	−0.00391594	−	0.00768547i
$784$	112.126	+	154.328i	0.143017	+	0.196847i
$785$	−115.485	−	118.427i	−0.147115	−	0.150863i
$786$	−1173.17	−	852.354i	−1.49258	−	1.08442i
$787$	−149.730	−	23.7149i	−0.190254	−	0.0301333i	0.0605802	−	0.998163i	$-0.480705\pi$
$787$	−149.730	−	23.7149i	−0.190254	−	0.0301333i	−0.250834	+	0.968030i	$0.580705\pi$
$788$	174.102	−	1099.24i	0.220942	−	1.39497i
$789$	200.858	−	276.457i	0.254573	−	0.350390i
$790$	125.612	+	254.386i	0.159003	+	0.322008i
$791$	−1788.66	+	1299.54i	−2.26127	+	1.64291i
$792$	13.6070	−	6.93310i	0.0171805	−	0.00875391i
$793$	227.130	−	227.130i	0.286419	−	0.286419i
$794$	660.221	+	214.519i	0.831513	+	0.270175i
$795$	−27.6469	−	39.0768i	−0.0347760	−	0.0491532i
$796$	2.23441	+	6.87680i	0.00280704	+	0.00863919i
$797$	−91.0589	+	178.713i	−0.114252	+	0.224232i	−0.941051	−	0.338266i	$-0.890160\pi$
$797$	−91.0589	+	178.713i	−0.114252	+	0.224232i	0.826799	+	0.562498i	$0.190160\pi$
$798$	−2644.82	+	418.898i	−3.31431	+	0.524935i
$799$		−	470.160i		−	0.588435i
$800$	463.877	+	487.818i	0.579846	+	0.609773i
$801$	−137.950			−0.172222
$802$	17.2732	+	109.059i	0.0215376	+	0.135983i
$803$	156.945	+	79.9674i	0.195448	+	0.0995858i
$804$	1660.10	−	539.399i	2.06480	−	0.670894i
$805$	−1071.62	−	799.359i	−1.33121	−	0.992992i
$806$	−14.8636	+	45.7455i	−0.0184412	+	0.0567563i
$807$	538.356	+	538.356i	0.667108	+	0.667108i
$808$	−377.343	−	740.578i	−0.467009	−	0.916557i
$809$	−837.689	−	1152.98i	−1.03546	−	1.42519i	−0.900766	−	0.434304i	$-0.856994\pi$
$809$	−837.689	−	1152.98i	−1.03546	−	1.42519i	−0.134695	−	0.990887i	$-0.543006\pi$
$810$	1435.10	+	245.835i	1.77173	+	0.303501i
$811$	901.333	+	654.857i	1.11138	+	0.807468i	0.982881	−	0.184241i	$-0.0589827\pi$
$811$	901.333	+	654.857i	1.11138	+	0.807468i	0.128503	+	0.991709i	$0.458983\pi$
$812$	−18.9732	−	3.00506i	−0.0233660	−	0.00370081i
$813$	15.5059	−	97.9001i	0.0190724	−	0.120418i
$814$	−86.0055	+	118.376i	−0.105658	+	0.145426i
$815$	−128.411	+	749.617i	−0.157559	+	0.919776i
$816$	−77.5923	+	56.3741i	−0.0950886	+	0.0690859i
$817$	−1043.08	+	531.477i	−1.27672	+	0.650522i
$818$	−1172.38	+	1172.38i	−1.43322	+	1.43322i
$819$	39.1775	+	12.7295i	0.0478358	+	0.0155428i
$820$	−38.5200	+	51.6400i	−0.0469756	+	0.0629756i
$821$	390.798	+	1202.75i	0.476002	+	1.46498i	0.844602	+	0.535395i	$0.179837\pi$
$821$	390.798	+	1202.75i	0.476002	+	1.46498i	−0.368600	+	0.929588i	$0.620163\pi$
$822$	1055.19	−	2070.93i	1.28369	−	2.51938i
$823$	−1141.29	+	180.762i	−1.38674	+	0.219638i	−0.804777	−	0.593577i	$-0.797715\pi$
$823$	−1141.29	+	180.762i	−1.38674	+	0.219638i	−0.581964	+	0.813215i	$0.697715\pi$
$824$			959.350i			1.16426i
$825$	−59.6890	−	124.810i	−0.0723503	−	0.151285i
$826$	−699.392			−0.846721
$827$	−98.0146	−	618.840i	−0.118518	−	0.748295i	−0.973339	−	0.229371i	$-0.926333\pi$
$827$	−98.0146	−	618.840i	−0.118518	−	0.748295i	0.854821	−	0.518923i	$-0.173667\pi$
$828$	−144.365	−	73.5575i	−0.174354	−	0.0888376i
$829$	−671.187	+	218.082i	−0.809634	+	0.263066i	−0.684443	−	0.729067i	$-0.739954\pi$
$829$	−671.187	+	218.082i	−0.809634	+	0.263066i	−0.125191	+	0.992133i	$0.539954\pi$
$830$	60.1102	−	42.5280i	0.0724219	−	0.0512386i
$831$	288.639	−	888.341i	0.347340	−	1.06900i
$832$	−289.962	−	289.962i	−0.348511	−	0.348511i
$833$	−296.859	−	582.619i	−0.356374	−	0.699423i
$834$	−545.237	−	750.455i	−0.653762	−	0.899826i
$835$	−881.548	+	435.295i	−1.05575	+	0.521312i
$836$	−234.370	−	170.280i	−0.280346	−	0.203684i
$837$	−89.8913	−	14.2374i	−0.107397	−	0.0170100i
$838$	366.922	−	2316.65i	0.437854	−	2.76450i
$839$	308.459	−	424.557i	0.367651	−	0.506028i	−0.584610	−	0.811315i	$-0.698752\pi$
$839$	308.459	−	424.557i	0.367651	−	0.506028i	0.952260	+	0.305287i	$0.0987523\pi$
$840$	1101.79	−	1074.42i	1.31165	−	1.27907i
$841$	−680.326	+	494.286i	−0.808949	+	0.587736i
$842$	−1950.63	+	993.895i	−2.31666	+	1.18040i
$843$	507.988	−	507.988i	0.602596	−	0.602596i
$844$	1526.20	+	495.891i	1.80829	+	0.587549i
$845$	−721.263	−	244.422i	−0.853565	−	0.289257i
$846$	44.3392	+	136.462i	0.0524104	+	0.161303i
$847$	569.208	−	1117.13i	0.672028	−	1.31893i
$848$	8.92901	−	1.41422i	0.0105295	−	0.00166771i
$849$		−	235.462i		−	0.277341i
$850$	475.665	+	690.574i	0.559606	+	0.812440i
$851$	638.366			0.750137
$852$	7.77027	+	49.0596i	0.00912004	+	0.0575816i
$853$	1096.28	+	558.582i	1.28520	+	0.654844i	0.957089	−	0.289795i	$-0.0935870\pi$
$853$	1096.28	+	558.582i	1.28520	+	0.654844i	0.328114	+	0.944638i	$0.393587\pi$
$854$	2612.09	−	848.718i	3.05865	−	0.993815i
$855$	34.2325	+	110.047i	0.0400380	+	0.128710i
$856$	10.9198	−	33.6077i	0.0127568	−	0.0392614i
$857$	−306.519	−	306.519i	−0.357665	−	0.357665i	0.505287	−	0.862951i	$-0.331387\pi$
$857$	−306.519	−	306.519i	−0.357665	−	0.357665i	−0.862951	+	0.505287i	$0.831387\pi$
$858$	33.7199	+	66.1790i	0.0393006	+	0.0771317i
$859$	425.400	+	585.513i	0.495228	+	0.681622i	0.981341	−	0.192273i	$-0.0615860\pi$
$859$	425.400	+	585.513i	0.495228	+	0.681622i	−0.486114	+	0.873895i	$0.661586\pi$
$860$	761.065	−	1448.35i	0.884959	−	1.68413i
$861$	−51.4570	−	37.3857i	−0.0597643	−	0.0434213i
$862$	2193.78	+	347.461i	2.54499	+	0.403087i
$863$	−221.984	+	1401.55i	−0.257224	+	1.62405i	0.433657	+	0.901078i	$0.357223\pi$
$863$	−221.984	+	1401.55i	−0.257224	+	1.62405i	−0.690881	+	0.722969i	$0.742777\pi$
$864$	401.938	−	553.220i	0.465205	−	0.640300i
$865$	356.981	−	51.9473i	0.412695	−	0.0600546i
$866$	−1870.56	+	1359.04i	−2.16000	+	1.56933i
$867$	−519.257	+	264.575i	−0.598913	+	0.305161i
$868$	−183.043	+	183.043i	−0.210879	+	0.210879i
$869$	−28.8194	−	9.36400i	−0.0331639	−	0.0107756i
$870$	−0.173276	+	13.7780i	−0.000199168	+	0.0158368i
$871$	102.839	+	316.506i	0.118070	+	0.363382i
$872$	309.091	−	606.626i	0.354463	−	0.695672i
$873$	130.707	−	20.7019i	0.149721	−	0.0237135i
$874$			2008.04i			2.29753i
$875$	−903.664	−	974.557i	−1.03276	−	1.11378i
$876$	2151.21			2.45572
$877$	169.141	+	1067.91i	0.192863	+	1.21769i	0.874144	+	0.485666i	$0.161423\pi$
$877$	169.141	+	1067.91i	0.192863	+	1.21769i	−0.681282	+	0.732021i	$0.738577\pi$
$878$	495.839	+	252.643i	0.564737	+	0.287748i
$879$	−1444.30	+	469.282i	−1.64312	+	0.533882i
$880$	26.1263	+	0.328572i	0.0296890	+	0.000373377i
$881$	147.306	−	453.362i	0.167204	−	0.514600i	−0.831988	−	0.554793i	$-0.812797\pi$
$881$	147.306	−	453.362i	0.167204	−	0.514600i	0.999192	+	0.0401934i	$0.0127974\pi$
$882$	141.107	+	141.107i	0.159985	+	0.159985i
$883$	−364.142	−	714.670i	−0.412392	−	0.809365i	−1.00000		0.000219342i	$-0.999930\pi$
$883$	−364.142	−	714.670i	−0.412392	−	0.809365i	0.587608	−	0.809146i	$-0.300070\pi$
$884$	−166.548	−	229.234i	−0.188403	−	0.259315i
$885$	45.4695	+	312.466i	0.0513780	+	0.353069i
$886$	−1452.81	−	1055.53i	−1.63974	−	1.19134i
$887$	−73.1702	−	11.5890i	−0.0824918	−	0.0130654i	0.115052	−	0.993359i	$-0.463296\pi$
$887$	−73.1702	−	11.5890i	−0.0824918	−	0.0130654i	−0.197544	+	0.980294i	$0.563296\pi$
$888$	−114.953	+	725.782i	−0.129451	+	0.817322i
$889$	−574.200	+	790.318i	−0.645894	+	0.888997i
$890$	−2115.20	−	1111.47i	−2.37663	−	1.24884i
$891$	−125.813	+	91.4086i	−0.141204	+	0.102591i
$892$	403.491	−	205.589i	0.452344	−	0.230481i
$893$	791.436	−	791.436i	0.886266	−	0.886266i
$894$	−1354.13	−	439.983i	−1.51468	−	0.492151i
$895$	815.044	−	253.538i	0.910664	−	0.283282i
$896$	−729.623	−	2245.55i	−0.814312	−	2.50619i
$897$	147.112	−	288.724i	0.164004	−	0.321877i
$898$	147.768	−	23.4042i	0.164553	−	0.0260626i
$899$		−	0.953080i		−	0.00106016i
$900$	−127.887	−	97.9222i	−0.142096	−	0.108802i
$901$	−30.9885			−0.0343935
$902$	−1.71023	−	10.7980i	−0.00189604	−	0.0119711i
$903$	1439.26	+	733.339i	1.59386	+	0.812114i
$904$	−1815.06	+	589.748i	−2.00781	+	0.652377i
$905$	544.201	−	1605.88i	0.601327	−	1.77445i
$906$	−719.495	+	2214.38i	−0.794145	+	2.44413i
$907$	958.275	+	958.275i	1.05653	+	1.05653i	0.998303	+	0.0582292i	$0.0185454\pi$
$907$	958.275	+	958.275i	1.05653	+	1.05653i	0.0582292	+	0.998303i	$0.481455\pi$
$908$	1143.49	+	2244.22i	1.25935	+	2.47161i
$909$	−50.4827	−	69.4835i	−0.0555366	−	0.0764395i
$910$	498.149	+	510.838i	0.547417	+	0.561361i
$911$	477.623	+	347.013i	0.524284	+	0.380915i	0.818215	−	0.574912i	$-0.194964\pi$
$911$	477.623	+	347.013i	0.524284	+	0.380915i	−0.293931	+	0.955827i	$0.594964\pi$
$912$	−225.510	−	35.7173i	−0.247270	−	0.0391637i
$913$	−1.23031	+	7.76784i	−0.00134754	+	0.00850804i
$914$	−364.668	+	501.922i	−0.398980	+	0.549149i
$915$	−549.000	−	1111.82i	−0.600000	−	1.21510i
$916$	227.397	−	165.214i	0.248250	−	0.180364i
$917$	1325.73	−	675.492i	1.44572	−	0.736632i
$918$	602.322	−	602.322i	0.656124	−	0.656124i
$919$	−922.085	−	299.604i	−1.00336	−	0.326011i	−0.239151	−	0.970982i	$-0.576869\pi$
$919$	−922.085	−	299.604i	−1.00336	−	0.326011i	−0.764206	+	0.644972i	$0.776869\pi$
$920$	−666.528	−	942.087i	−0.724487	−	1.02401i
$921$	−135.790	−	417.917i	−0.147437	−	0.453765i
$922$	−496.399	+	974.237i	−0.538393	+	1.05666i
$923$	−9.35343	+	1.48144i	−0.0101337	+	0.00160502i
$924$			399.727i			0.432605i
$925$	624.101	+	115.006i	0.674704	+	0.124331i
$926$	−737.928			−0.796898
$927$	15.5076	+	97.9109i	0.0167288	+	0.105621i
$928$	6.38047	+	3.25101i	0.00687550	+	0.00350324i
$929$	593.663	−	192.893i	0.639035	−	0.207635i	0.0284617	−	0.999595i	$-0.490939\pi$
$929$	593.663	−	192.893i	0.639035	−	0.207635i	0.610573	+	0.791960i	$0.290939\pi$
$930$	148.834	+	111.021i	0.160037	+	0.119377i
$931$	481.029	−	1480.46i	0.516680	−	1.59018i
$932$	−170.147	−	170.147i	−0.182561	−	0.182561i
$933$	−565.504	−	1109.86i	−0.606114	−	1.18957i
$934$	−7.01812	−	9.65962i	−0.00751405	−	0.0103422i
$935$	−88.2774	−	15.1221i	−0.0944144	−	0.0161734i
$936$	28.7674	+	20.9008i	0.0307345	+	0.0223299i
$937$	−1250.38	−	198.040i	−1.33445	−	0.211355i	−0.551880	−	0.833924i	$-0.686089\pi$
$937$	−1250.38	−	198.040i	−1.33445	−	0.211355i	−0.782566	+	0.622568i	$0.786089\pi$
$938$	−445.142	+	2810.52i	−0.474565	+	2.99629i
$939$	−412.561	+	567.842i	−0.439362	+	0.604730i
$940$	−264.116	+	1541.82i	−0.280975	+	1.64023i
$941$	511.738	−	371.799i	0.543823	−	0.395111i	−0.281680	−	0.959508i	$-0.590892\pi$
$941$	511.738	−	371.799i	0.543823	−	0.395111i	0.825503	+	0.564398i	$0.190892\pi$
$942$	305.452	−	155.635i	0.324259	−	0.165218i
$943$	−33.7263	+	33.7263i	−0.0357649	+	0.0357649i
$944$	−56.7149	−	18.4278i	−0.0600793	−	0.0195210i
$945$	−807.231	+	1082.17i	−0.854213	+	1.14516i
$946$	85.7976	+	264.058i	0.0906951	+	0.279131i
$947$	−263.136	+	516.434i	−0.277863	+	0.545336i	−0.987191	−	0.159542i	$-0.948998\pi$
$947$	−263.136	+	516.434i	−0.277863	+	0.545336i	0.709328	+	0.704878i	$0.248998\pi$
$948$	−365.523	+	57.8932i	−0.385573	+	0.0610688i
$949$			410.137i			0.432178i
$950$	−361.764	+	1963.17i	−0.380804	+	2.06649i
$951$	−218.065			−0.229301
$952$	−155.850	−	984.001i	−0.163708	−	1.03361i
$953$	−1558.82	−	794.259i	−1.63570	−	0.833430i	−0.998005	−	0.0631412i	$-0.979888\pi$
$953$	−1558.82	−	794.259i	−1.63570	−	0.833430i	−0.637695	−	0.770289i	$-0.720112\pi$
$954$	8.99429	−	2.92242i	0.00942798	−	0.00306334i
$955$	−1328.30	+	939.771i	−1.39089	+	0.984054i
$956$	−101.489	+	312.351i	−0.106160	+	0.326727i
$957$	−1.04067	−	1.04067i	−0.00108742	−	0.00108742i
$958$	−196.644	−	385.936i	−0.205265	−	0.402855i
$959$	1401.77	+	1929.37i	1.46170	+	2.01185i
$960$	−1419.38	+	700.871i	−1.47853	+	0.730074i
$961$	767.075	+	557.313i	0.798205	+	0.579930i
$962$	−336.504	−	53.2971i	−0.349797	−	0.0554023i
$963$	0.571215	−	3.60651i	0.000593162	−	0.00374508i
$964$	831.049	−	1143.84i	0.862084	−	1.18656i
$965$	−284.664	+	277.593i	−0.294989	+	0.287661i
$966$	2241.56	−	1628.59i	2.32046	−	1.68591i
$967$	1615.87	−	823.328i	1.67102	−	0.851425i	0.677785	−	0.735260i	$-0.262940\pi$
$967$	1615.87	−	823.328i	1.67102	−	0.851425i	0.993230	−	0.116165i	$-0.0370601\pi$
$968$	765.284	−	765.284i	0.790582	−	0.790582i
$969$	744.338	+	241.850i	0.768150	+	0.249587i
$970$	2170.93	+	735.686i	2.23807	+	0.758439i
$971$	−307.744	−	947.139i	−0.316935	−	0.975427i	−0.974950	−	0.222422i	$-0.928604\pi$
$971$	−307.744	−	947.139i	−0.316935	−	0.975427i	0.658015	−	0.753005i	$-0.271396\pi$
$972$	−157.313	+	308.745i	−0.161845	+	0.317639i
$973$	940.067	−	148.892i	0.966153	−	0.153024i
$974$		−	2839.79i		−	2.91560i
$975$	195.840	−	255.768i	0.200862	−	0.262327i
$976$	234.181			0.239939
$977$	34.3026	+	216.578i	0.0351101	+	0.221676i	0.999005	−	0.0446081i	$-0.0142039\pi$
$977$	34.3026	+	216.578i	0.0351101	+	0.221676i	−0.963894	+	0.266285i	$0.914204\pi$
$978$	−1404.40	−	715.575i	−1.43599	−	0.731672i
$979$	242.722	−	78.8650i	0.247928	−	0.0805567i
$980$	646.213	+	2077.37i	0.659401	+	2.11977i
$981$	21.7399	−	66.9084i	0.0221609	−	0.0682043i
$982$	−159.694	−	159.694i	−0.162621	−	0.162621i
$983$	438.146	+	859.910i	0.445723	+	0.874781i	0.999123	+	0.0418655i	$0.0133301\pi$
$983$	438.146	+	859.910i	0.445723	+	0.874781i	−0.553400	+	0.832916i	$0.686670\pi$
$984$	−32.2715	−	44.4179i	−0.0327962	−	0.0451401i
$985$	381.017	−	725.099i	0.386819	−	0.736141i
$986$	7.21661	+	5.24317i	0.00731908	+	0.00531762i
$987$	−1525.35	−	241.592i	−1.54545	−	0.244775i
$988$	105.521	−	666.234i	0.106803	−	0.674326i
$989$	711.989	−	979.969i	0.719908	−	0.990869i
$990$	27.0483	−	3.93602i	0.0273215	−	0.00397577i
$991$	656.840	−	477.222i	0.662805	−	0.481556i	−0.204804	−	0.978803i	$-0.565656\pi$
$991$	656.840	−	477.222i	0.662805	−	0.481556i	0.867609	+	0.497247i	$0.165656\pi$
$992$	85.9803	−	43.8092i	0.0866737	−	0.0441625i
$993$	−1110.52	+	1110.52i	−1.11835	+	1.11835i
$994$	−77.0103	−	25.0222i	−0.0774751	−	0.0251732i
$995$	−0.0669221	+	5.32129i	−6.72584e−5	+	0.00534803i
$996$	29.6810	+	91.3488i	0.0298002	+	0.0917156i
$997$	160.104	−	314.222i	0.160586	−	0.315167i	−0.796668	−	0.604417i	$-0.793406\pi$
$997$	160.104	−	314.222i	0.160586	−	0.315167i	0.957254	+	0.289250i	$0.0934059\pi$
$998$	1914.84	−	303.280i	1.91867	−	0.303888i
$999$		−	644.653i		−	0.645298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.12.1	✓	32
3.2	odd	2		225.3.r.a.37.4		32
4.3	odd	2		400.3.bg.c.337.1		32
5.2	odd	4		125.3.f.b.43.4		32
5.3	odd	4		125.3.f.a.43.1		32
5.4	even	2		125.3.f.c.82.4		32
25.2	odd	20		125.3.f.c.93.4		32
25.11	even	5		125.3.f.a.32.1		32
25.14	even	10		125.3.f.b.32.4		32
25.23	odd	20	inner	25.3.f.a.23.1	yes	32
75.23	even	20		225.3.r.a.73.4		32
100.23	even	20		400.3.bg.c.273.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.1	✓	32	1.1	even	1	trivial
25.3.f.a.23.1	yes	32	25.23	odd	20	inner
125.3.f.a.32.1		32	25.11	even	5
125.3.f.a.43.1		32	5.3	odd	4
125.3.f.b.32.4		32	25.14	even	10
125.3.f.b.43.4		32	5.2	odd	4
125.3.f.c.82.4		32	5.4	even	2
125.3.f.c.93.4		32	25.2	odd	20
225.3.r.a.37.4		32	3.2	odd	2
225.3.r.a.73.4		32	75.23	even	20
400.3.bg.c.273.1		32	100.23	even	20
400.3.bg.c.337.1		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)

\(f(q)\)	\(=\)	\(q+(-0.513943 - 3.24491i) q^{2} +(2.81033 + 1.43193i) q^{3} +(-6.46108 + 2.09933i) q^{4} +(-4.99960 - 0.0628765i) q^{5} +(3.20215 - 9.85519i) q^{6} +(7.51823 + 7.51823i) q^{7} +(4.16668 + 8.17758i) q^{8} +(0.557438 + 0.767248i) q^{9} +O(q^{10})\)	\(q+(-0.513943 - 3.24491i) q^{2} +(2.81033 + 1.43193i) q^{3} +(-6.46108 + 2.09933i) q^{4} +(-4.99960 - 0.0628765i) q^{5} +(3.20215 - 9.85519i) q^{6} +(7.51823 + 7.51823i) q^{7} +(4.16668 + 8.17758i) q^{8} +(0.557438 + 0.767248i) q^{9} +(2.36548 + 16.2556i) q^{10} +(-1.41944 - 1.03128i) q^{11} +(-21.1638 - 3.35202i) q^{12} +(0.639079 - 4.03498i) q^{13} +(20.5320 - 28.2599i) q^{14} +(-13.9605 - 7.33580i) q^{15} +(2.40958 - 1.75066i) q^{16} +(-9.09666 + 4.63498i) q^{17} +(2.20316 - 2.20316i) q^{18} +(-23.1149 - 7.51050i) q^{19} +(32.4348 - 10.0896i) q^{20} +(10.3631 + 31.8943i) q^{21} +(-2.61691 + 5.13597i) q^{22} +(24.8384 - 3.93402i) q^{23} +28.9481i q^{24} +(24.9921 + 0.628715i) q^{25} -13.4216 q^{26} +(-3.97276 - 25.0830i) q^{27} +(-64.3591 - 32.7926i) q^{28} +(0.252929 - 0.0821815i) q^{29} +(-16.6291 + 49.0707i) q^{30} +(1.10744 - 3.40835i) q^{31} +(19.0399 + 19.0399i) q^{32} +(-2.51236 - 4.93078i) q^{33} +(19.7153 + 27.1357i) q^{34} +(-37.1155 - 38.0609i) q^{35} +(-5.21236 - 3.78700i) q^{36} +(25.0718 + 3.97099i) q^{37} +(-12.4911 + 78.8659i) q^{38} +(7.57385 - 10.4245i) q^{39} +(-20.3176 - 41.1466i) q^{40} +(-1.53440 + 1.11481i) q^{41} +(98.1681 - 50.0191i) q^{42} +(34.0593 - 34.0593i) q^{43} +(11.3361 + 3.68332i) q^{44} +(-2.73873 - 3.87099i) q^{45} +(-25.5311 - 78.5765i) q^{46} +(-20.9070 + 41.0322i) q^{47} +(9.27854 - 1.46958i) q^{48} +64.0476i q^{49} +(-10.8044 - 81.4202i) q^{50} -32.2016 q^{51} +(4.34163 + 27.4120i) q^{52} +(2.70446 + 1.37799i) q^{53} +(-79.3503 + 25.7825i) q^{54} +(7.03178 + 5.24525i) q^{55} +(-30.1548 + 92.8070i) q^{56} +(-54.2060 - 54.2060i) q^{57} +(-0.396662 - 0.778494i) q^{58} +(-11.7686 - 16.1981i) q^{59} +(105.600 + 18.0895i) q^{60} +(63.6100 + 46.2154i) q^{61} +(-11.6290 - 1.84185i) q^{62} +(-1.57740 + 9.95930i) q^{63} +(59.0000 - 81.2066i) q^{64} +(-3.44885 + 20.1331i) q^{65} +(-14.7087 + 10.6865i) q^{66} +(-72.5829 + 36.9828i) q^{67} +(49.0439 - 49.0439i) q^{68} +(75.4373 + 24.5111i) q^{69} +(-104.429 + 139.997i) q^{70} +(-0.716327 - 2.20463i) q^{71} +(-3.95156 + 7.75537i) q^{72} +(-99.1579 + 15.7051i) q^{73} -83.3967i q^{74} +(69.3357 + 37.5539i) q^{75} +165.114 q^{76} +(-2.91825 - 18.4251i) q^{77} +(-37.7191 - 19.2188i) q^{78} +(16.4258 - 5.33707i) q^{79} +(-12.1570 + 8.60111i) q^{80} +(27.3900 - 84.2978i) q^{81} +(4.40604 + 4.40604i) q^{82} +(-2.03502 - 3.99395i) q^{83} +(-133.913 - 184.316i) q^{84} +(45.7712 - 22.6011i) q^{85} +(-128.024 - 93.0149i) q^{86} +(0.828490 + 0.131220i) q^{87} +(2.51904 - 15.9046i) q^{88} +(-85.4992 + 117.680i) q^{89} +(-11.1535 + 10.8764i) q^{90} +(35.1407 - 25.5312i) q^{91} +(-152.224 + 77.5620i) q^{92} +(7.99280 - 7.99280i) q^{93} +(143.891 + 46.7530i) q^{94} +(115.093 + 39.0029i) q^{95} +(26.2445 + 80.7723i) q^{96} +(63.3499 - 124.331i) q^{97} +(207.829 - 32.9168i) q^{98} -1.66394i 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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Database

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