LMFDB - Embedded newform 225.2.q.a.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.254613 - 0.113361i) q^{2} +(-0.427801 - 1.67839i) q^{3} +(-1.28628 + 1.42856i) q^{4} +(0.148962 + 2.23110i) q^{5} +(-0.299187 - 0.378844i) q^{6} +(-1.97470 + 3.42027i) q^{7} +(-0.337813 + 1.03968i) q^{8} +(-2.63397 + 1.43603i) q^{9} +O(q^{10})$	\(q+(0.254613 - 0.113361i) q^{2} +(-0.427801 - 1.67839i) q^{3} +(-1.28628 + 1.42856i) q^{4} +(0.148962 + 2.23110i) q^{5} +(-0.299187 - 0.378844i) q^{6} +(-1.97470 + 3.42027i) q^{7} +(-0.337813 + 1.03968i) q^{8} +(-2.63397 + 1.43603i) q^{9} +(0.290848 + 0.551181i) q^{10} +(1.53404 - 0.682997i) q^{11} +(2.94796 + 1.54774i) q^{12} +(0.961615 + 0.428138i) q^{13} +(-0.115058 + 1.09470i) q^{14} +(3.68093 - 1.20448i) q^{15} +(-0.370027 - 3.52057i) q^{16} +(-1.25351 + 3.85792i) q^{17} +(-0.507854 + 0.664222i) q^{18} +(1.85242 - 5.70117i) q^{19} +(-3.37888 - 2.65703i) q^{20} +(6.58532 + 1.85111i) q^{21} +(0.313161 - 0.347800i) q^{22} +(-0.564211 + 5.36811i) q^{23} +(1.88950 + 0.122205i) q^{24} +(-4.95562 + 0.664700i) q^{25} +0.293374 q^{26} +(3.53703 + 3.80649i) q^{27} +(-2.34606 - 7.22042i) q^{28} +(6.99712 + 1.48728i) q^{29} +(0.800671 - 0.723951i) q^{30} +(-4.81399 + 1.02325i) q^{31} +(-1.58649 - 2.74789i) q^{32} +(-1.80260 - 2.28252i) q^{33} +(0.118177 + 1.12438i) q^{34} +(-7.92513 - 3.89625i) q^{35} +(1.33658 - 5.60994i) q^{36} +(-3.92983 + 2.85519i) q^{37} +(-0.174640 - 1.66158i) q^{38} +(0.307203 - 1.79712i) q^{39} +(-2.36995 - 0.598821i) q^{40} +(-1.14861 - 0.511393i) q^{41} +(1.88655 - 0.275202i) q^{42} +(4.99451 - 8.65075i) q^{43} +(-0.997503 + 3.07000i) q^{44} +(-3.59629 - 5.66275i) q^{45} +(0.464879 + 1.43075i) q^{46} +(4.62748 + 0.983601i) q^{47} +(-5.75059 + 2.12715i) q^{48} +(-4.29885 - 7.44583i) q^{49} +(-1.18641 + 0.731016i) q^{50} +(7.01134 + 0.453463i) q^{51} +(-1.84853 + 0.823020i) q^{52} +(2.76942 + 8.52341i) q^{53} +(1.33208 + 0.568222i) q^{54} +(1.75235 + 3.32085i) q^{55} +(-2.88892 - 3.20847i) q^{56} +(-10.3612 - 0.670120i) q^{57} +(1.95016 - 0.414519i) q^{58} +(5.63502 + 2.50887i) q^{59} +(-3.01404 + 6.80774i) q^{60} +(-2.58041 + 1.14887i) q^{61} +(-1.10971 + 0.806250i) q^{62} +(0.289678 - 11.8446i) q^{63} +(5.01233 + 3.64167i) q^{64} +(-0.811976 + 2.20924i) q^{65} +(-0.717714 - 0.376816i) q^{66} +(11.9904 - 2.54863i) q^{67} +(-3.89891 - 6.75310i) q^{68} +(9.25114 - 1.34951i) q^{69} +(-2.45953 - 0.0936360i) q^{70} +(-2.15288 - 6.62590i) q^{71} +(-0.603224 - 3.22360i) q^{72} +(-4.42300 - 3.21350i) q^{73} +(-0.676918 + 1.17246i) q^{74} +(3.23564 + 8.03310i) q^{75} +(5.76174 + 9.97962i) q^{76} +(-0.693219 + 6.59554i) q^{77} +(-0.125506 - 0.492395i) q^{78} +(11.5363 + 2.45211i) q^{79} +(7.79963 - 1.35000i) q^{80} +(4.87563 - 7.56493i) q^{81} -0.350423 q^{82} +(-3.65812 - 4.06275i) q^{83} +(-11.1150 + 7.02650i) q^{84} +(-8.79413 - 2.22203i) q^{85} +(0.291010 - 2.76878i) q^{86} +(-0.497133 - 12.3801i) q^{87} +(0.191882 + 1.82563i) q^{88} +(12.2123 + 8.87274i) q^{89} +(-1.55760 - 1.03413i) q^{90} +(-3.36325 + 2.44354i) q^{91} +(-6.94294 - 7.71092i) q^{92} +(3.77683 + 7.64200i) q^{93} +(1.28972 - 0.274138i) q^{94} +(12.9958 + 3.28368i) q^{95} +(-3.93332 + 3.83830i) q^{96} +(-3.26984 - 0.695025i) q^{97} +(-1.93861 - 1.40848i) q^{98} +(-3.05981 + 4.00192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.254613	−	0.113361i	0.180039	−	0.0801584i	−0.314738	−	0.949179i	$-0.601917\pi$
$2$	0.254613	−	0.113361i	0.180039	−	0.0801584i	0.494776	+	0.869020i	$0.335250\pi$
$3$	−0.427801	−	1.67839i	−0.246991	−	0.969018i
$3$	−0.427801	−	1.67839i	−0.246991	−	0.969018i
$4$	−1.28628	+	1.42856i	−0.643142	+	0.714282i
$5$	0.148962	+	2.23110i	0.0666180	+	0.997779i
$5$	0.148962	+	2.23110i	0.0666180	+	0.997779i
$6$	−0.299187	−	0.378844i	−0.122143	−	0.154662i
$7$	−1.97470	+	3.42027i	−0.746365	+	1.29274i	0.203189	+	0.979140i	$0.434869\pi$
$7$	−1.97470	+	3.42027i	−0.746365	+	1.29274i	−0.949554	+	0.313603i	$0.898464\pi$
$8$	−0.337813	+	1.03968i	−0.119435	+	0.367583i
$9$	−2.63397	+	1.43603i	−0.877991	+	0.478677i
$10$	0.290848	+	0.551181i	0.0919741	+	0.174299i
$11$	1.53404	−	0.682997i	0.462530	−	0.205931i	−0.162223	−	0.986754i	$-0.551866\pi$
$11$	1.53404	−	0.682997i	0.462530	−	0.205931i	0.624753	+	0.780823i	$0.285200\pi$
$12$	2.94796	+	1.54774i	0.851002	+	0.446795i
$13$	0.961615	+	0.428138i	0.266704	+	0.118744i	0.535732	−	0.844388i	$-0.320036\pi$
$13$	0.961615	+	0.428138i	0.266704	+	0.118744i	−0.269028	+	0.963132i	$0.586702\pi$
$14$	−0.115058	+	1.09470i	−0.0307504	+	0.292571i
$15$	3.68093	−	1.20448i	0.950411	−	0.310996i
$16$	−0.370027	−	3.52057i	−0.0925067	−	0.880143i
$17$	−1.25351	+	3.85792i	−0.304022	+	0.935683i	0.676019	+	0.736884i	$0.263704\pi$
$17$	−1.25351	+	3.85792i	−0.304022	+	0.935683i	−0.980040	+	0.198798i	$0.936296\pi$
$18$	−0.507854	+	0.664222i	−0.119702	+	0.156559i
$19$	1.85242	−	5.70117i	0.424975	−	1.30794i	−0.478044	−	0.878336i	$-0.658654\pi$
$19$	1.85242	−	5.70117i	0.424975	−	1.30794i	0.903019	−	0.429602i	$-0.141346\pi$
$20$	−3.37888	−	2.65703i	−0.755540	−	0.594129i
$21$	6.58532	+	1.85111i	1.43704	+	0.403946i
$22$	0.313161	−	0.347800i	0.0667661	−	0.0741512i
$23$	−0.564211	+	5.36811i	−0.117646	+	1.11933i	0.763278	+	0.646070i	$0.223589\pi$
$23$	−0.564211	+	5.36811i	−0.117646	+	1.11933i	−0.880924	+	0.473257i	$0.843078\pi$
$24$	1.88950	+	0.122205i	0.385693	+	0.0249450i
$25$	−4.95562	+	0.664700i	−0.991124	+	0.132940i
$26$	0.293374			0.0575354
$27$	3.53703	+	3.80649i	0.680702	+	0.732560i
$28$	−2.34606	−	7.22042i	−0.443363	−	1.36453i
$29$	6.99712	+	1.48728i	1.29933	+	0.276182i	0.805096	−	0.593145i	$-0.202114\pi$
$29$	6.99712	+	1.48728i	1.29933	+	0.276182i	0.494238	+	0.869327i	$0.335447\pi$
$30$	0.800671	−	0.723951i	0.146182	−	0.132175i
$31$	−4.81399	+	1.02325i	−0.864618	+	0.183780i	−0.618812	−	0.785539i	$-0.712386\pi$
$31$	−4.81399	+	1.02325i	−0.864618	+	0.183780i	−0.245806	+	0.969319i	$0.579053\pi$
$32$	−1.58649	−	2.74789i	−0.280455	−	0.485763i
$33$	−1.80260	−	2.28252i	−0.313792	−	0.397336i
$34$	0.118177	+	1.12438i	0.0202671	+	0.192829i
$35$	−7.92513	−	3.89625i	−1.33959	−	0.658587i
$36$	1.33658	−	5.60994i	0.222763	−	0.934990i
$37$	−3.92983	+	2.85519i	−0.646059	+	0.469390i	−0.861927	−	0.507033i	$-0.830742\pi$
$37$	−3.92983	+	2.85519i	−0.646059	+	0.469390i	0.215867	+	0.976423i	$0.430742\pi$
$38$	−0.174640	−	1.66158i	−0.0283303	−	0.269545i
$39$	0.307203	−	1.79712i	0.0491919	−	0.287770i
$40$	−2.36995	−	0.598821i	−0.374723	−	0.0946819i
$41$	−1.14861	−	0.511393i	−0.179382	−	0.0798662i	0.315080	−	0.949065i	$-0.397969\pi$
$41$	−1.14861	−	0.511393i	−0.179382	−	0.0798662i	−0.494463	+	0.869199i	$0.664635\pi$
$42$	1.88655	−	0.275202i	0.291102	−	0.0424646i
$43$	4.99451	−	8.65075i	0.761656	−	1.31923i	−0.180341	−	0.983604i	$-0.557720\pi$
$43$	4.99451	−	8.65075i	0.761656	−	1.31923i	0.941997	−	0.335623i	$-0.108947\pi$
$44$	−0.997503	+	3.07000i	−0.150379	+	0.462820i
$45$	−3.59629	−	5.66275i	−0.536104	−	0.844152i
$46$	0.464879	+	1.43075i	0.0685426	+	0.210952i
$47$	4.62748	+	0.983601i	0.674987	+	0.143473i	0.532638	−	0.846343i	$-0.321201\pi$
$47$	4.62748	+	0.983601i	0.674987	+	0.143473i	0.142350	+	0.989816i	$0.454534\pi$
$48$	−5.75059	+	2.12715i	−0.830026	+	0.307028i
$49$	−4.29885	−	7.44583i	−0.614122	−	1.06369i
$50$	−1.18641	+	0.731016i	−0.167784	+	0.103381i
$51$	7.01134	+	0.453463i	0.981784	+	0.0634975i
$52$	−1.84853	+	0.823020i	−0.256345	+	0.114132i
$53$	2.76942	+	8.52341i	0.380410	+	1.17078i	0.939756	+	0.341846i	$0.111052\pi$
$53$	2.76942	+	8.52341i	0.380410	+	1.17078i	−0.559346	+	0.828934i	$0.688948\pi$
$54$	1.33208	+	0.568222i	0.181274	+	0.0773252i
$55$	1.75235	+	3.32085i	0.236287	+	0.447783i
$56$	−2.88892	−	3.20847i	−0.386048	−	0.428749i
$57$	−10.3612	−	0.670120i	−1.37238	−	0.0887595i
$58$	1.95016	−	0.414519i	0.256068	−	0.0544290i
$59$	5.63502	+	2.50887i	0.733618	+	0.326628i	0.739318	−	0.673356i	$-0.235148\pi$
$59$	5.63502	+	2.50887i	0.733618	+	0.326628i	−0.00570072	+	0.999984i	$0.501815\pi$
$60$	−3.01404	+	6.80774i	−0.389111	+	0.878876i
$61$	−2.58041	+	1.14887i	−0.330388	+	0.147098i	−0.565225	−	0.824937i	$-0.691211\pi$
$61$	−2.58041	+	1.14887i	−0.330388	+	0.147098i	0.234838	+	0.972035i	$0.424544\pi$
$62$	−1.10971	+	0.806250i	−0.140933	+	0.102394i
$63$	0.289678	−	11.8446i	0.0364960	−	1.49228i
$64$	5.01233	+	3.64167i	0.626542	+	0.455209i
$65$	−0.811976	+	2.20924i	−0.100713	+	0.274022i
$66$	−0.717714	−	0.376816i	−0.0883445	−	0.0463828i
$67$	11.9904	−	2.54863i	1.46486	−	0.311365i	0.594623	−	0.804005i	$-0.297301\pi$
$67$	11.9904	−	2.54863i	1.46486	−	0.311365i	0.870233	+	0.492640i	$0.163968\pi$
$68$	−3.89891	−	6.75310i	−0.472812	−	0.818934i
$69$	9.25114	−	1.34951i	1.11371	−	0.162462i
$70$	−2.45953	−	0.0936360i	−0.293970	−	0.0111916i
$71$	−2.15288	−	6.62590i	−0.255500	−	0.786349i	−0.993731	−	0.111801i	$-0.964338\pi$
$71$	−2.15288	−	6.62590i	−0.255500	−	0.786349i	0.738230	−	0.674549i	$-0.235662\pi$
$72$	−0.603224	−	3.22360i	−0.0710906	−	0.379905i
$73$	−4.42300	−	3.21350i	−0.517673	−	0.376112i	0.298053	−	0.954549i	$-0.403663\pi$
$73$	−4.42300	−	3.21350i	−0.517673	−	0.376112i	−0.815727	+	0.578437i	$0.803663\pi$
$74$	−0.676918	+	1.17246i	−0.0786901	+	0.136295i
$75$	3.23564	+	8.03310i	0.373620	+	0.927582i
$76$	5.76174	+	9.97962i	0.660917	+	1.14474i
$77$	−0.693219	+	6.59554i	−0.0789997	+	0.751632i
$78$	−0.125506	−	0.492395i	−0.0142107	−	0.0557528i
$79$	11.5363	+	2.45211i	1.29793	+	0.275884i	0.804526	−	0.593917i	$-0.202419\pi$
$79$	11.5363	+	2.45211i	1.29793	+	0.275884i	0.493404	+	0.869800i	$0.335753\pi$
$80$	7.79963	−	1.35000i	0.872025	−	0.150935i
$81$	4.87563	−	7.56493i	0.541737	−	0.840548i
$82$	−0.350423			−0.0386977
$83$	−3.65812	−	4.06275i	−0.401531	−	0.445945i	0.508140	−	0.861274i	$-0.330333\pi$
$83$	−3.65812	−	4.06275i	−0.401531	−	0.445945i	−0.909671	+	0.415329i	$0.863666\pi$
$84$	−11.1150	+	7.02650i	−1.21275	+	0.766654i
$85$	−8.79413	−	2.22203i	−0.953857	−	0.241013i
$86$	0.291010	−	2.76878i	0.0313804	−	0.298565i
$87$	−0.497133	−	12.3801i	−0.0532982	−	1.32729i
$88$	0.191882	+	1.82563i	0.0204547	+	0.194613i
$89$	12.2123	+	8.87274i	1.29450	+	0.940508i	0.999886	−	0.0151087i	$-0.00480943\pi$
$89$	12.2123	+	8.87274i	1.29450	+	0.940508i	0.294612	+	0.955617i	$0.404809\pi$
$90$	−1.55760	−	1.03413i	−0.164185	−	0.109007i
$91$	−3.36325	+	2.44354i	−0.352564	+	0.256153i
$92$	−6.94294	−	7.71092i	−0.723852	−	0.803919i
$93$	3.77683	+	7.64200i	0.391639	+	0.792438i
$94$	1.28972	−	0.274138i	0.133024	−	0.0282752i
$95$	12.9958	+	3.28368i	1.33334	+	0.336898i
$96$	−3.93332	+	3.83830i	−0.401443	+	0.391745i
$97$	−3.26984	−	0.695025i	−0.332002	−	0.0705691i	0.0388949	−	0.999243i	$-0.487616\pi$
$97$	−3.26984	−	0.695025i	−0.332002	−	0.0705691i	−0.370897	+	0.928674i	$0.620950\pi$
$98$	−1.93861	−	1.40848i	−0.195829	−	0.142278i
$99$	−3.05981	+	4.00192i	−0.307522	+	0.402208i
$100$	5.42477	−	7.93441i	0.542477	−	0.793441i
$101$	3.60857	−	6.25022i	0.359066	−	0.621920i	−0.628739	−	0.777616i	$-0.716429\pi$
$101$	3.60857	−	6.25022i	0.359066	−	0.621920i	0.987805	+	0.155696i	$0.0497620\pi$
$102$	1.83658	−	0.679355i	0.181849	−	0.0672662i
$103$	−3.13282	+	3.47934i	−0.308685	+	0.342830i	−0.877448	−	0.479672i	$-0.840756\pi$
$103$	−3.13282	+	3.47934i	−0.308685	+	0.342830i	0.568762	+	0.822502i	$0.307422\pi$
$104$	−0.769973	+	0.855142i	−0.0755021	+	0.0838535i
$105$	−3.14905	+	14.9683i	−0.307316	+	1.46075i
$106$	1.67135	+	1.85623i	0.162336	+	0.180293i
$107$	−19.3140			−1.86715			−0.933577	−	0.358378i	$-0.883330\pi$
$107$	−19.3140			−1.86715			−0.933577	+	0.358378i	$0.883330\pi$
$108$	−9.98745	+	0.156640i	−0.961043	+	0.0150727i
$109$	−8.78758	+	6.38455i	−0.841698	+	0.611529i	−0.922844	−	0.385173i	$-0.874142\pi$
$109$	−8.78758	+	6.38455i	−0.841698	+	0.611529i	0.0811466	+	0.996702i	$0.474142\pi$
$110$	0.822626	+	0.646884i	0.0784343	+	0.0616779i
$111$	6.47329	+	5.37432i	0.614418	+	0.510108i
$112$	12.7720	+	5.68646i	1.20684	+	0.537320i
$113$	6.21807	+	2.76846i	0.584947	+	0.260435i	0.677802	−	0.735245i	$-0.262933\pi$
$113$	6.21807	+	2.76846i	0.584947	+	0.260435i	−0.0928552	+	0.995680i	$0.529599\pi$
$114$	−2.71407	+	1.00394i	−0.254196	+	0.0940275i
$115$	−12.0608	−	0.459165i	−1.12468	−	0.0428173i
$116$	−11.1250	+	8.08276i	−1.03293	+	0.750466i
$117$	−3.14769	+	0.253203i	−0.291004	+	0.0234086i
$118$	1.71916			0.158261
$119$	−10.7198	−	11.9056i	−0.982685	−	1.09138i
$120$	0.00881367	+	4.23388i	0.000804574	+	0.386498i
$121$	−5.47365	+	6.07911i	−0.497605	+	0.552646i
$122$	−0.526769	+	0.585036i	−0.0476914	+	0.0529667i
$123$	−0.366941	+	2.14658i	−0.0330860	+	0.193551i
$124$	4.73039	−	8.19327i	0.424801	−	0.735778i
$125$	−2.22121	−	10.9575i	−0.198671	−	0.980066i
$126$	−1.26896	−	3.04864i	−0.113048	−	0.271594i
$127$	10.7288	+	7.79490i	0.952024	+	0.691686i	0.951285	−	0.308314i	$-0.0997647\pi$
$127$	10.7288	+	7.79490i	0.952024	+	0.691686i	0.000739229		1.00000i	$0.499765\pi$
$128$	7.89633	+	1.67842i	0.697944	+	0.148353i
$129$	−16.6560	−	4.68193i	−1.46648	−	0.412221i
$130$	0.0437017	+	0.654547i	0.00383289	+	0.0574075i
$131$	13.9228	−	2.95937i	1.21644	−	0.258562i	0.445388	−	0.895338i	$-0.353066\pi$
$131$	13.9228	−	2.95937i	1.21644	−	0.258562i	0.771049	+	0.636776i	$0.219732\pi$
$132$	5.57938	+	0.360850i	0.485623	+	0.0314080i
$133$	15.8416	+	17.5939i	1.37364	+	1.52558i
$134$	2.76399	−	2.00815i	0.238772	−	0.173478i
$135$	−7.96579	+	8.45850i	−0.685586	+	0.727992i
$136$	−3.58755	−	2.60651i	−0.307630	−	0.223506i
$137$	1.01433	+	9.65072i	0.0866602	+	0.824516i	0.948381	+	0.317134i	$0.102720\pi$
$137$	1.01433	+	9.65072i	0.0866602	+	0.824516i	−0.861721	+	0.507383i	$0.830613\pi$
$138$	2.20248	−	1.39232i	0.187487	−	0.118522i
$139$	0.170258	−	1.61990i	0.0144411	−	0.137398i	−0.984926	−	0.172978i	$-0.944661\pi$
$139$	0.170258	−	1.61990i	0.0144411	−	0.137398i	0.999367	+	0.0355797i	$0.0113278\pi$
$140$	15.7600	−	6.30986i	1.33196	−	0.533281i
$141$	−0.328774	−	8.18749i	−0.0276878	−	0.689511i
$142$	−1.29927	−	1.44299i	−0.109032	−	0.121093i
$143$	1.76757			0.147812
$144$	6.03029	+	8.74172i	0.502524	+	0.728477i
$145$	−2.27597	+	15.8328i	−0.189009	+	1.31485i
$146$	−1.49044	−	0.316803i	−0.123350	−	0.0262188i
$147$	−10.6579	+	10.4005i	−0.879052	+	0.857817i
$148$	0.976060	−	9.28659i	0.0802316	−	0.763353i
$149$	5.52553	+	9.57050i	0.452669	+	0.784046i	0.998551	−	0.0538166i	$-0.0171386\pi$
$149$	5.52553	+	9.57050i	0.452669	+	0.784046i	−0.545882	+	0.837862i	$0.683805\pi$
$150$	1.73448	+	1.67854i	0.141619	+	0.137052i
$151$	−2.90413	+	5.03011i	−0.236335	+	0.409344i	−0.959660	−	0.281164i	$-0.909280\pi$
$151$	−2.90413	+	5.03011i	−0.236335	+	0.409344i	0.723325	+	0.690508i	$0.242613\pi$
$152$	5.30162	+	3.85185i	0.430018	+	0.312427i
$153$	−2.23837	−	11.9617i	−0.180961	−	0.967049i
$154$	0.571175	+	1.75790i	0.0460266	+	0.141655i
$155$	−3.00007	−	10.5881i	−0.240971	−	0.850454i
$156$	2.17215	+	2.75047i	0.173911	+	0.220214i
$157$	−1.84071	−	3.18821i	−0.146905	−	0.254447i	0.783177	−	0.621799i	$-0.213598\pi$
$157$	−1.84071	−	3.18821i	−0.146905	−	0.254447i	−0.930082	+	0.367352i	$0.880264\pi$
$158$	3.21525	−	0.683423i	0.255792	−	0.0543703i
$159$	13.1208	−	8.29449i	1.04055	−	0.657796i
$160$	5.89449	−	3.94896i	0.466000	−	0.312193i
$161$	−17.2463	−	12.5301i	−1.35920	−	0.987513i
$162$	0.383831	−	2.47884i	0.0301566	−	0.194756i
$163$	−0.304317	+	0.221099i	−0.0238360	+	0.0173178i	−0.599639	−	0.800270i	$-0.704689\pi$
$163$	−0.304317	+	0.221099i	−0.0238360	+	0.0173178i	0.575803	+	0.817588i	$0.304689\pi$
$164$	2.20799	−	0.983062i	0.172415	−	0.0767642i
$165$	4.82402	−	4.36179i	0.375549	−	0.339565i
$166$	−1.39196	−	0.619742i	−0.108037	−	0.0481013i
$167$	8.56276	−	1.82007i	0.662606	−	0.140841i	0.135681	−	0.990753i	$-0.456678\pi$
$167$	8.56276	−	1.82007i	0.662606	−	0.140841i	0.526926	+	0.849911i	$0.323345\pi$
$168$	−4.14917	+	6.22131i	−0.320116	+	0.479984i
$169$	−7.95730	−	8.83747i	−0.612100	−	0.679806i
$170$	−2.49099	+	0.431154i	−0.191050	+	0.0330680i
$171$	3.30782	+	17.6769i	0.252956	+	1.35178i
$172$	5.93378	+	18.2623i	0.452447	+	1.39249i
$173$	−1.96220	+	0.873627i	−0.149183	+	0.0664206i	−0.479970	−	0.877285i	$-0.659353\pi$
$173$	−1.96220	+	0.873627i	−0.149183	+	0.0664206i	0.330787	+	0.943705i	$0.392686\pi$
$174$	−1.53000	−	3.09579i	−0.115989	−	0.234691i
$175$	7.51239	−	18.2622i	0.567883	−	1.38049i
$176$	−2.97218	−	5.14796i	−0.224036	−	0.388042i
$177$	1.80020	−	10.5311i	0.135311	−	0.791562i
$178$	4.11523	+	0.874718i	0.308449	+	0.0655629i
$179$	−6.01883	−	18.5241i	−0.449869	−	1.38455i	−0.877055	−	0.480390i	$-0.840495\pi$
$179$	−6.01883	−	18.5241i	−0.449869	−	1.38455i	0.427187	−	0.904164i	$-0.359505\pi$
$180$	12.7154	+	2.14637i	0.947753	+	0.159981i
$181$	4.60344	−	14.1679i	0.342171	−	1.05309i	−0.620910	−	0.783882i	$-0.713237\pi$
$181$	4.60344	−	14.1679i	0.342171	−	1.05309i	0.963081	−	0.269212i	$-0.0867632\pi$
$182$	−0.579324	+	1.00342i	−0.0429424	+	0.0743784i
$183$	3.03216	+	3.83944i	0.224143	+	0.283820i
$184$	−5.39052	−	2.40001i	−0.397394	−	0.176931i
$185$	−6.95560	−	8.34252i	−0.511386	−	0.613354i
$186$	1.82794	+	1.51761i	0.134031	+	0.111276i
$187$	0.712012	+	6.77434i	0.0520674	+	0.495389i
$188$	−7.35739	+	5.34546i	−0.536593	+	0.389858i
$189$	−20.0038	+	4.58095i	−1.45506	+	0.333215i
$190$	3.68115	−	0.637152i	0.267058	−	0.0462239i
$191$	0.852384	+	8.10990i	0.0616764	+	0.586811i	0.981094	+	0.193530i	$0.0619936\pi$
$191$	0.852384	+	8.10990i	0.0616764	+	0.586811i	−0.919418	+	0.393282i	$0.871340\pi$
$192$	3.96786	−	9.97055i	0.286356	−	0.719563i
$193$	2.38184	+	4.12547i	0.171449	+	0.296958i	0.938927	−	0.344117i	$-0.111822\pi$
$193$	2.38184	+	4.12547i	0.171449	+	0.296958i	−0.767478	+	0.641076i	$0.778488\pi$
$194$	−0.911332	+	0.193710i	−0.0654298	+	0.0139075i
$195$	4.05532	+	0.417698i	0.290407	+	0.0299120i
$196$	16.1664	+	3.43627i	1.15474	+	0.245448i
$197$	−1.66876	−	5.13592i	−0.118894	−	0.365919i	0.873845	−	0.486205i	$-0.161619\pi$
$197$	−1.66876	−	5.13592i	−0.118894	−	0.365919i	−0.992739	+	0.120286i	$0.961619\pi$
$198$	−0.325405	+	1.36580i	−0.0231255	+	0.0970635i
$199$	−21.6479			−1.53458			−0.767291	−	0.641299i	$-0.778396\pi$
$199$	−21.6479			−1.53458			−0.767291	+	0.641299i	$0.778396\pi$
$200$	0.982996	−	5.37681i	0.0695083	−	0.380198i
$201$	−9.40707	−	19.0342i	−0.663524	−	1.34257i
$202$	0.210257	−	2.00046i	0.0147936	−	0.140752i
$203$	−18.9041	+	20.9951i	−1.32681	+	1.47357i
$204$	−9.66637	+	9.43286i	−0.676781	+	0.660432i
$205$	0.969870	−	2.63884i	0.0677387	−	0.184304i
$206$	−0.403234	+	1.24103i	−0.0280946	+	0.0864663i
$207$	−6.22265	−	14.9497i	−0.432504	−	1.03907i
$208$	1.15147	−	3.54386i	0.0798400	−	0.245722i
$209$	−1.05220	−	10.0110i	−0.0727821	−	0.692476i
$210$	0.895029	+	4.16810i	0.0617629	+	0.287626i
$211$	−1.60139	+	15.2362i	−0.110244	+	1.04891i	0.789877	+	0.613266i	$0.210145\pi$
$211$	−1.60139	+	15.2362i	−0.110244	+	1.04891i	−0.900121	+	0.435640i	$0.856522\pi$
$212$	−15.7385	−	7.00723i	−1.08092	−	0.481259i
$213$	−10.1998	+	6.44794i	−0.698880	+	0.441805i
$214$	−4.91759	+	2.18945i	−0.336160	+	0.149668i
$215$	20.0447	+	9.85462i	1.36704	+	0.672080i
$216$	−5.15239	+	2.39150i	−0.350576	+	0.162721i
$217$	6.00639	−	18.4858i	0.407740	−	1.25490i
$218$	−1.51367	+	2.62176i	−0.102519	+	0.177568i
$219$	−3.50134	+	8.79825i	−0.236598	+	0.594531i
$220$	−6.99807	−	1.76822i	−0.471809	−	0.119213i
$221$	−2.85712	+	3.17315i	−0.192191	+	0.213449i
$222$	2.25742	+	0.634554i	0.151508	+	0.0425885i
$223$	18.7205	−	8.33491i	1.25362	−	0.558147i	0.330916	−	0.943660i	$-0.392642\pi$
$223$	18.7205	−	8.33491i	1.25362	−	0.558147i	0.922702	+	0.385513i	$0.125976\pi$
$224$	12.5314			0.837288
$225$	12.0984	−	8.86723i	0.806563	−	0.591148i
$226$	1.89704			0.126189
$227$	−2.16300	+	0.963030i	−0.143563	+	0.0639186i	−0.477261	−	0.878762i	$-0.658370\pi$
$227$	−2.16300	+	0.963030i	−0.143563	+	0.0639186i	0.333697	+	0.942680i	$0.391704\pi$
$228$	14.2848	−	13.9397i	0.946034	−	0.923180i
$229$	2.18473	−	2.42639i	0.144371	−	0.160341i	−0.666622	−	0.745396i	$-0.732261\pi$
$229$	2.18473	−	2.42639i	0.144371	−	0.160341i	0.810993	+	0.585055i	$0.198927\pi$
$230$	−3.12290	+	1.25032i	−0.205918	+	0.0824436i
$231$	11.3664	−	1.65809i	0.747857	−	0.109094i
$232$	−3.91002	+	6.77235i	−0.256705	+	0.444627i
$233$	0.388396	−	1.19536i	0.0254446	−	0.0783106i	−0.937528	−	0.347910i	$-0.886891\pi$
$233$	0.388396	−	1.19536i	0.0254446	−	0.0783106i	0.962972	+	0.269600i	$0.0868914\pi$
$234$	−0.772739	+	0.421294i	−0.0505155	+	0.0275408i
$235$	−1.50519	+	10.4709i	−0.0981880	+	0.683046i
$236$	−10.8323	+	4.82286i	−0.705124	+	0.313942i
$237$	−0.819630	−	20.4113i	−0.0532407	−	1.32586i
$238$	−4.07904	−	1.81610i	−0.264405	−	0.117721i
$239$	1.36041	−	12.9434i	0.0879974	−	0.837240i	−0.858127	−	0.513437i	$-0.828372\pi$
$239$	1.36041	−	12.9434i	0.0879974	−	0.837240i	0.946125	−	0.323802i	$-0.104961\pi$
$240$	−5.60251	−	12.5133i	−0.361640	−	0.807728i
$241$	−0.129158	−	1.22886i	−0.00831982	−	0.0791578i	0.989574	−	0.144025i	$-0.0460044\pi$
$241$	−0.129158	−	1.22886i	−0.00831982	−	0.0791578i	−0.997894	+	0.0648668i	$0.979338\pi$
$242$	−0.704529	+	2.16832i	−0.0452889	+	0.139385i
$243$	−14.7827	−	4.94692i	−0.948310	−	0.317345i
$244$	1.67790	−	5.16406i	0.107417	−	0.330595i
$245$	15.9720	−	10.7003i	1.02042	−	0.683618i
$246$	0.149911	+	0.588145i	0.00955797	+	0.0374988i
$247$	4.22220	−	4.68923i	0.268652	−	0.298369i
$248$	0.562379	−	5.35068i	0.0357111	−	0.339768i
$249$	−5.25393	+	7.87780i	−0.332954	+	0.499235i
$250$	−1.80770	−	2.53812i	−0.114329	−	0.160525i
$251$	16.1915			1.02200			0.511000	−	0.859581i	$-0.329275\pi$
$251$	16.1915			1.02200			0.511000	+	0.859581i	$0.329275\pi$
$252$	16.5482	+	15.6494i	1.04244	+	0.985819i
$253$	2.80088	+	8.62023i	0.176090	+	0.541949i
$254$	3.61532	+	0.768460i	0.226845	+	0.0482175i
$255$	0.0327047	+	15.7105i	0.00204805	+	0.983833i
$256$	−9.91962	+	2.10848i	−0.619976	+	0.131780i
$257$	−12.5307	−	21.7037i	−0.781641	−	1.35384i	−0.930986	−	0.365056i	$-0.881050\pi$
$257$	−12.5307	−	21.7037i	−0.781641	−	1.35384i	0.149345	−	0.988785i	$-0.452284\pi$
$258$	−4.77158	+	0.696056i	−0.297065	+	0.0433346i
$259$	−2.00531	−	19.0792i	−0.124604	−	1.18552i
$260$	−2.11160	−	4.00166i	−0.130956	−	0.248173i
$261$	−20.5660	+	6.13062i	−1.27300	+	0.379476i
$262$	3.20944	−	2.33179i	0.198280	−	0.144059i
$263$	2.02669	+	19.2826i	0.124971	+	1.18902i	0.859751	+	0.510713i	$0.170618\pi$
$263$	2.02669	+	19.2826i	0.124971	+	1.18902i	−0.734781	+	0.678305i	$0.762715\pi$
$264$	2.98204	−	1.10306i	0.183532	−	0.0678886i
$265$	−18.6041	+	7.44853i	−1.14284	+	0.457560i
$266$	6.02793	+	2.68381i	0.369596	+	0.164555i
$267$	9.66748	−	24.2927i	0.591640	−	1.48669i
$268$	−11.7821	+	20.4073i	−0.719708	+	1.24657i
$269$	−1.15306	+	3.54876i	−0.0703034	+	0.216372i	−0.980035	−	0.198825i	$-0.936287\pi$
$269$	−1.15306	+	3.54876i	−0.0703034	+	0.216372i	0.909732	+	0.415197i	$0.136287\pi$
$270$	−1.06933	+	3.05665i	−0.0650773	+	0.186022i
$271$	−6.82902	−	21.0175i	−0.414833	−	1.27673i	−0.912400	−	0.409300i	$-0.865773\pi$
$271$	−6.82902	−	21.0175i	−0.414833	−	1.27673i	0.497567	−	0.867426i	$-0.334227\pi$
$272$	14.0459	+	2.98555i	0.851658	+	0.181026i
$273$	5.54001	+	4.59949i	0.335297	+	0.278374i
$274$	1.35228	+	2.34221i	0.0816941	+	0.141498i
$275$	−7.14812	+	4.40435i	−0.431048	+	0.265592i
$276$	−9.97172	+	14.9517i	−0.600227	+	0.899986i
$277$	−10.9247	+	4.86399i	−0.656401	+	0.292249i	−0.707782	−	0.706431i	$-0.750304\pi$
$277$	−10.9247	+	4.86399i	−0.656401	+	0.292249i	0.0513814	+	0.998679i	$0.483638\pi$
$278$	−0.140284	−	0.431748i	−0.00841365	−	0.0258945i
$279$	11.2105	−	9.60824i	0.671156	−	0.575230i
$280$	6.72807	−	6.92340i	0.402079	−	0.413752i
$281$	18.2979	+	20.3219i	1.09156	+	1.21230i	0.975717	+	0.219034i	$0.0702904\pi$
$281$	18.2979	+	20.3219i	1.09156	+	1.21230i	0.115843	+	0.993267i	$0.463043\pi$
$282$	−1.01185	−	2.04737i	−0.0602550	−	0.121919i
$283$	3.04324	−	0.646861i	0.180902	−	0.0384519i	−0.116570	−	0.993182i	$-0.537190\pi$
$283$	3.04324	−	0.646861i	0.180902	−	0.0384519i	0.297472	+	0.954731i	$0.403857\pi$
$284$	12.2347	+	5.44725i	0.725998	+	0.323235i
$285$	−0.0483304	−	23.2168i	−0.00286285	−	1.37524i
$286$	0.450047	−	0.200374i	0.0266118	−	0.0118483i
$287$	4.01726	−	2.91871i	0.237131	−	0.172286i
$288$	8.12484	+	4.95961i	0.478761	+	0.292248i
$289$	0.441053	+	0.320444i	0.0259443	+	0.0188496i
$290$	1.21533	+	4.28925i	0.0713669	+	0.251874i
$291$	0.232316	+	5.78539i	0.0136186	+	0.339145i
$292$	10.2799	−	2.18507i	0.601587	−	0.127871i
$293$	1.08652	+	1.88191i	0.0634752	+	0.109942i	0.896017	−	0.444021i	$-0.146448\pi$
$293$	1.08652	+	1.88191i	0.0634752	+	0.109942i	−0.832541	+	0.553963i	$0.813115\pi$
$294$	−1.53464	+	3.85629i	−0.0895022	+	0.224903i
$295$	−4.75814	+	12.9460i	−0.277030	+	0.753747i
$296$	−1.64094	−	5.05028i	−0.0953775	−	0.293542i
$297$	8.02577	+	3.42352i	0.465702	+	0.198653i
$298$	2.49179	+	1.81039i	0.144346	+	0.104873i
$299$	−2.84085	+	4.92049i	−0.164290	+	0.284559i
$300$	−15.6377	−	5.71052i	−0.902845	−	0.329697i
$301$	19.7253	+	34.1652i	1.13695	+	1.96925i
$302$	−0.169212	+	1.60995i	−0.00973707	+	0.0926420i
$303$	−12.0340	−	3.38273i	−0.691338	−	0.194333i
$304$	−20.7568	−	4.41200i	−1.19048	−	0.253045i
$305$	−2.94763	−	5.58602i	−0.168781	−	0.319854i
$306$	−1.92591	−	2.79187i	−0.110097	−	0.159601i
$307$	6.16436			0.351818			0.175909	−	0.984406i	$-0.443713\pi$
$307$	6.16436			0.351818			0.175909	+	0.984406i	$0.443713\pi$
$308$	−8.53047	−	9.47405i	−0.486069	−	0.539834i
$309$	7.17991	+	3.76961i	0.408451	+	0.214446i
$310$	−1.96413	−	2.35577i	−0.111555	−	0.133799i
$311$	0.412568	−	3.92532i	0.0233946	−	0.222584i	−0.976578	−	0.215164i	$-0.930971\pi$
$311$	0.412568	−	3.92532i	0.0233946	−	0.222584i	0.999972	−	0.00742028i	$-0.00236197\pi$
$312$	1.76465	+	0.926484i	0.0999039	+	0.0524518i
$313$	−0.256506	−	2.44049i	−0.0144986	−	0.137945i	0.984878	−	0.173249i	$-0.0554266\pi$
$313$	−0.256506	−	2.44049i	−0.0144986	−	0.137945i	−0.999377	+	0.0353045i	$0.988760\pi$
$314$	−0.830088	−	0.603094i	−0.0468446	−	0.0340346i
$315$	26.4697	−	1.11810i	1.49140	−	0.0629980i
$316$	−18.3419	+	13.3262i	−1.03181	+	0.749655i
$317$	−6.30981	−	7.00775i	−0.354394	−	0.393594i	0.539417	−	0.842039i	$-0.318645\pi$
$317$	−6.30981	−	7.00775i	−0.354394	−	0.393594i	−0.893811	+	0.448445i	$0.851978\pi$
$318$	2.40046	−	3.59928i	0.134611	−	0.201837i
$319$	11.7497	−	2.49747i	0.657855	−	0.139831i
$320$	−7.37829	+	11.7255i	−0.412459	+	0.655475i
$321$	8.26253	+	32.4164i	0.461170	+	1.80930i
$322$	−5.81155	−	1.23528i	−0.323865	−	0.0688396i
$323$	19.6726	+	14.2930i	1.09461	+	0.795283i
$324$	4.53554	+	16.6958i	0.251974	+	0.927545i
$325$	−5.04998	−	1.48251i	−0.280123	−	0.0822346i
$326$	−0.0524191	+	0.0907925i	−0.00290323	+	0.00502853i
$327$	14.4751	+	12.0177i	0.800474	+	0.664578i
$328$	0.919700	−	1.02143i	0.0507819	−	0.0563990i
$329$	−12.5021	+	13.8849i	−0.689261	+	0.765501i
$330$	0.733802	−	1.65742i	0.0403945	−	0.0912382i
$331$	−13.8019	−	15.3285i	−0.758619	−	0.842531i	0.232899	−	0.972501i	$-0.425179\pi$
$331$	−13.8019	−	15.3285i	−0.758619	−	0.842531i	−0.991518	+	0.129970i	$0.958512\pi$
$332$	10.5093			0.576772
$333$	6.25092	−	13.1638i	0.342548	−	0.721374i
$334$	1.97387	−	1.43410i	0.108005	−	0.0784703i
$335$	7.47236	+	26.3721i	0.408259	+	1.44086i
$336$	4.08022	−	23.8691i	0.222594	−	1.30216i
$337$	−24.7265	−	11.0089i	−1.34694	−	0.599695i	−0.398649	−	0.917104i	$-0.630521\pi$
$337$	−24.7265	−	11.0089i	−1.34694	−	0.599695i	−0.948289	+	0.317409i	$0.897187\pi$
$338$	−3.02786	−	1.34809i	−0.164694	−	0.0733264i
$339$	1.98646	−	11.6207i	0.107890	−	0.631149i
$340$	14.4861	−	9.70481i	0.785617	−	0.526317i
$341$	−6.68597	+	4.85764i	−0.362065	+	0.263056i
$342$	2.84608	+	4.12578i	0.153898	+	0.223097i
$343$	6.30996			0.340706
$344$	7.30681	+	8.11503i	0.393957	+	0.437533i
$345$	4.38897	+	20.4392i	0.236294	+	1.10041i
$346$	−0.400566	+	0.444874i	−0.0215346	+	0.0239166i
$347$	−22.5406	+	25.0339i	−1.21004	+	1.34389i	−0.287603	+	0.957750i	$0.592858\pi$
$347$	−22.5406	+	25.0339i	−1.21004	+	1.34389i	−0.922441	+	0.386139i	$0.873808\pi$
$348$	18.3253	+	15.2142i	0.982338	+	0.815567i
$349$	2.68244	−	4.64613i	0.143588	−	0.248702i	−0.785257	−	0.619170i	$-0.787469\pi$
$349$	2.68244	−	4.64613i	0.143588	−	0.248702i	0.928845	+	0.370468i	$0.120803\pi$
$350$	−0.157466	−	5.50140i	−0.00841689	−	0.294062i
$351$	1.77156	+	5.17472i	0.0945586	+	0.276206i
$352$	−4.31054	−	3.13179i	−0.229753	−	0.166925i
$353$	22.9425	+	4.87657i	1.22110	+	0.259554i	0.772988	−	0.634421i	$-0.218761\pi$
$353$	22.9425	+	4.87657i	1.22110	+	0.259554i	0.448117	+	0.893975i	$0.352095\pi$
$354$	−0.735457	−	2.88542i	−0.0390891	−	0.153358i
$355$	14.4623	−	5.79031i	0.767582	−	0.307318i
$356$	−28.3837	+	6.03315i	−1.50433	+	0.319756i
$357$	−15.3962	+	23.0852i	−0.814855	+	1.22180i
$358$	−3.63238	−	4.03417i	−0.191977	−	0.213212i
$359$	−12.6673	+	9.20330i	−0.668552	+	0.485732i	−0.869540	−	0.493862i	$-0.835585\pi$
$359$	−12.6673	+	9.20330i	−0.668552	+	0.485732i	0.200988	+	0.979594i	$0.435585\pi$
$360$	7.10232	−	1.82605i	0.374325	−	0.0962412i
$361$	−13.7005	−	9.95401i	−0.721080	−	0.523895i
$362$	−0.433995	−	4.12919i	−0.0228103	−	0.217025i
$363$	12.5447	+	6.58627i	0.658428	+	0.345689i
$364$	0.835337	−	7.94770i	0.0437836	−	0.416573i
$365$	6.51078	−	10.3469i	0.340790	−	0.541579i
$366$	1.20727	+	0.633844i	0.0631050	+	0.0331315i
$367$	−12.2743	−	13.6320i	−0.640713	−	0.711584i	0.332082	−	0.943251i	$-0.392249\pi$
$367$	−12.2743	−	13.6320i	−0.640713	−	0.711584i	−0.972795	+	0.231666i	$0.925582\pi$
$368$	19.1076			0.996051
$369$	3.75978	−	0.302440i	0.195726	−	0.0157444i
$370$	−2.71670	−	1.33562i	−0.141235	−	0.0694356i
$371$	−34.6212	−	7.35896i	−1.79744	−	0.382058i
$372$	−15.7752	−	4.43434i	−0.817904	−	0.229910i
$373$	1.53017	−	14.5586i	0.0792291	−	0.753815i	−0.880719	−	0.473638i	$-0.842940\pi$
$373$	1.53017	−	14.5586i	0.0792291	−	0.753815i	0.959949	−	0.280176i	$-0.0903930\pi$
$374$	0.949233	+	1.64412i	0.0490837	+	0.0850154i
$375$	−17.4407	+	8.41567i	−0.900632	+	0.434583i
$376$	−2.58585	+	4.47883i	−0.133355	+	0.230978i
$377$	6.09177	+	4.42593i	0.313742	+	0.227947i
$378$	−4.57393	+	3.43402i	−0.235258	+	0.176627i
$379$	1.91579	+	5.89620i	0.0984077	+	0.302868i	0.988127	−	0.153641i	$-0.0490998\pi$
$379$	1.91579	+	5.89620i	0.0984077	+	0.302868i	−0.889719	+	0.456508i	$0.849100\pi$
$380$	−21.4073	+	14.3416i	−1.09817	+	0.735709i
$381$	8.49310	−	21.3417i	0.435115	−	1.09337i
$382$	1.13637	+	1.96826i	0.0581420	+	0.100705i
$383$	−11.7942	+	2.50693i	−0.602654	+	0.128098i	−0.499127	−	0.866529i	$-0.666346\pi$
$383$	−11.7942	+	2.50693i	−0.602654	+	0.128098i	−0.103527	+	0.994627i	$0.533013\pi$
$384$	−0.561020	−	13.9711i	−0.0286294	−	0.712962i
$385$	−14.8186	−	0.564154i	−0.755225	−	0.0287520i
$386$	1.07412	+	0.780391i	0.0546711	+	0.0397209i
$387$	−0.732670	+	29.9581i	−0.0372437	+	1.52286i
$388$	5.19883	−	3.77717i	0.263930	−	0.191757i
$389$	−27.9727	+	12.4542i	−1.41827	+	0.631455i	−0.965555	−	0.260200i	$-0.916211\pi$
$389$	−27.9727	+	12.4542i	−1.41827	+	0.631455i	−0.452716	+	0.891655i	$0.649545\pi$
$390$	1.07989	−	0.353364i	0.0546822	−	0.0178933i
$391$	−20.0025	−	8.90567i	−1.01157	−	0.450379i
$392$	9.19349	−	1.95414i	0.464342	−	0.0986988i
$393$	−10.9231	−	22.1018i	−0.550999	−	1.11489i
$394$	−1.00710	−	1.11850i	−0.0507370	−	0.0563492i
$395$	−3.75243	+	26.1038i	−0.188805	+	1.31343i
$396$	−1.78122	−	9.51874i	−0.0895095	−	0.478335i
$397$	4.04467	+	12.4482i	0.202996	+	0.624758i	0.999790	+	0.0205064i	$0.00652785\pi$
$397$	4.04467	+	12.4482i	0.202996	+	0.624758i	−0.796794	+	0.604252i	$0.793472\pi$
$398$	−5.51185	+	2.45403i	−0.276284	+	0.123010i
$399$	22.7523	−	34.1150i	1.13904	−	1.70789i
$400$	4.17384	+	17.2007i	0.208692	+	0.860033i
$401$	−1.28841	−	2.23159i	−0.0643399	−	0.111440i	0.832061	−	0.554684i	$-0.187161\pi$
$401$	−1.28841	−	2.23159i	−0.0643399	−	0.111440i	−0.896401	+	0.443244i	$0.853828\pi$
$402$	−4.55290	−	3.77995i	−0.227078	−	0.188527i
$403$	−5.06729	−	1.07709i	−0.252420	−	0.0536535i
$404$	4.28719	+	13.1946i	0.213296	+	0.656457i
$405$	17.6044	+	9.75113i	0.874770	+	0.484538i
$406$	−2.43320	+	7.48863i	−0.120758	+	0.371654i
$407$	−4.07842	+	7.06402i	−0.202160	+	0.350151i
$408$	−2.83998	+	7.13637i	−0.140600	+	0.353303i
$409$	36.2080	+	16.1208i	1.79037	+	0.797124i	0.976321	+	0.216325i	$0.0694072\pi$
$409$	36.2080	+	16.1208i	1.79037	+	0.797124i	0.814048	+	0.580798i	$0.197259\pi$
$410$	−0.0521998	−	0.781828i	−0.00257796	−	0.0386117i
$411$	15.7637	−	5.83102i	0.777567	−	0.287623i
$412$	−0.940772	−	8.95085i	−0.0463485	−	0.440977i
$413$	−19.7085	+	14.3191i	−0.969792	+	0.704595i
$414$	−3.27908	−	3.10098i	−0.161158	−	0.152405i
$415$	8.51949	−	8.76683i	0.418205	−	0.430347i
$416$	−0.349119	−	3.32165i	−0.0171170	−	0.162857i
$417$	−2.79166	+	0.407234i	−0.136708	+	0.0199424i
$418$	−1.40276	−	2.42965i	−0.0686113	−	0.118838i
$419$	−15.7915	+	3.35660i	−0.771468	+	0.163981i	−0.576796	−	0.816888i	$-0.695697\pi$
$419$	−15.7915	+	3.35660i	−0.771468	+	0.163981i	−0.194671	+	0.980869i	$0.562364\pi$
$420$	−17.3325	−	23.7521i	−0.845742	−	1.15898i
$421$	29.8599	+	6.34692i	1.45528	+	0.309330i	0.866588	−	0.499025i	$-0.166308\pi$
$421$	29.8599	+	6.34692i	1.45528	+	0.309330i	0.588696	+	0.808355i	$0.299642\pi$
$422$	1.31946	+	4.06088i	0.0642303	+	0.197681i
$423$	−13.6011	+	4.05442i	−0.661310	+	0.197133i
$424$	−9.79717			−0.475793
$425$	3.64758	−	19.9516i	0.176934	−	0.967794i
$426$	−1.86606	+	2.79799i	−0.0904110	+	0.135563i
$427$	1.16607	−	11.0944i	0.0564299	−	0.536895i
$428$	24.8433	−	27.5912i	1.20084	−	1.33367i
$429$	−0.756168	−	2.96667i	−0.0365081	−	0.143232i
$430$	6.22077	+	0.236829i	0.299992	+	0.0114209i
$431$	4.75754	−	14.6422i	0.229162	−	0.705290i	−0.768680	−	0.639634i	$-0.779086\pi$
$431$	4.75754	−	14.6422i	0.229162	−	0.705290i	0.997842	−	0.0656558i	$-0.0209139\pi$
$432$	12.0922	−	13.8609i	0.581788	−	0.666882i
$433$	12.3339	−	37.9599i	0.592730	−	1.82424i	0.0270144	−	0.999635i	$-0.491400\pi$
$433$	12.3339	−	37.9599i	0.592730	−	1.82424i	0.565716	−	0.824600i	$-0.308600\pi$
$434$	−0.566260	−	5.38761i	−0.0271814	−	0.258613i
$435$	27.5473	−	2.95333i	1.32079	−	0.141601i
$436$	2.18259	−	20.7660i	0.104527	−	0.994509i
$437$	29.5593	+	13.1607i	1.41401	+	0.629559i
$438$	0.105893	+	2.63707i	0.00505976	+	0.126004i
$439$	21.8459	−	9.72643i	1.04265	−	0.464217i	0.187318	−	0.982299i	$-0.440021\pi$
$439$	21.8459	−	9.72643i	1.04265	−	0.464217i	0.855331	+	0.518082i	$0.173354\pi$
$440$	−4.04459	+	0.700059i	−0.192818	+	0.0333740i
$441$	22.0155	+	13.4388i	1.04836	+	0.639944i
$442$	−0.367748	+	1.13181i	−0.0174920	+	0.0538348i
$443$	10.1099	−	17.5109i	0.480337	−	0.831968i	−0.519409	−	0.854526i	$-0.673848\pi$
$443$	10.1099	−	17.5109i	0.480337	−	0.831968i	0.999746	+	0.0225580i	$0.00718106\pi$
$444$	−16.0041	+	2.33460i	−0.759519	+	0.110795i
$445$	−17.9768	+	28.5685i	−0.852182	+	1.35428i
$446$	3.82163	−	4.24436i	0.180960	−	0.200976i
$447$	13.6992	−	13.3682i	0.647949	−	0.632296i
$448$	−22.3534	+	9.95236i	−1.05610	+	0.470205i
$449$	7.79598			0.367915			0.183957	−	0.982934i	$-0.441109\pi$
$449$	7.79598			0.367915			0.183957	+	0.982934i	$0.441109\pi$
$450$	2.07522	−	3.62920i	0.0978270	−	0.171082i
$451$	−2.11129			−0.0994166
$452$	−11.9531	+	5.32188i	−0.562228	+	0.250320i
$453$	9.68486	+	2.72238i	0.455035	+	0.127909i
$454$	−0.441558	+	0.490400i	−0.0207234	+	0.0230156i
$455$	−5.95279	−	7.13975i	−0.279071	−	0.334717i
$456$	4.19687	−	10.5460i	0.196536	−	0.493862i
$457$	5.97766	−	10.3536i	0.279623	−	0.484321i	−0.691668	−	0.722216i	$-0.743124\pi$
$457$	5.97766	−	10.3536i	0.279623	−	0.484321i	0.971291	+	0.237894i	$0.0764572\pi$
$458$	0.281204	−	0.865455i	0.0131398	−	0.0404401i
$459$	−19.1189	+	8.87409i	−0.892392	+	0.414207i
$460$	16.1696	−	16.6390i	0.753912	−	0.775799i
$461$	21.0765	−	9.38384i	0.981629	−	0.437049i	0.147767	−	0.989022i	$-0.452792\pi$
$461$	21.0765	−	9.38384i	0.981629	−	0.437049i	0.833862	+	0.551973i	$0.186125\pi$
$462$	2.70608	−	1.71068i	0.125898	−	0.0795881i
$463$	−17.7625	−	7.90838i	−0.825494	−	0.367534i	−0.0498910	−	0.998755i	$-0.515887\pi$
$463$	−17.7625	−	7.90838i	−0.825494	−	0.367534i	−0.775603	+	0.631221i	$0.782554\pi$
$464$	2.64697	−	25.1842i	0.122882	−	1.16915i
$465$	−16.4875	+	9.56486i	−0.764588	+	0.443560i
$466$	−0.0366165	−	0.348383i	−0.00169623	−	0.0161385i
$467$	4.78120	−	14.7150i	0.221248	−	0.680931i	−0.777403	−	0.629003i	$-0.783463\pi$
$467$	4.78120	−	14.7150i	0.221248	−	0.680931i	0.998651	−	0.0519278i	$-0.0165366\pi$
$468$	3.68710	−	4.82236i	0.170436	−	0.222914i
$469$	−14.9603	+	46.0431i	−0.690803	+	2.12607i
$470$	0.803750	+	2.83666i	0.0370742	+	0.130845i
$471$	−4.56359	+	4.45335i	−0.210279	+	0.205199i
$472$	−4.51201	+	5.01110i	−0.207682	+	0.230654i
$473$	1.75333	−	16.6818i	0.0806182	−	0.767030i
$474$	−2.52254	−	5.10408i	−0.115864	−	0.234438i
$475$	−5.39033	+	29.4841i	−0.247325	+	1.35282i
$476$	30.7966			1.41156
$477$	−19.5345	−	18.4735i	−0.894422	−	0.845842i
$478$	−1.12090	−	3.44978i	−0.0512688	−	0.157789i
$479$	29.8968	+	6.35475i	1.36602	+	0.290356i	0.831840	−	0.555016i	$-0.187288\pi$
$479$	29.8968	+	6.35475i	1.36602	+	0.290356i	0.534178	+	0.845372i	$0.320621\pi$
$480$	−9.14955	−	8.20387i	−0.417618	−	0.374454i
$481$	−5.00139	+	1.06308i	−0.228044	+	0.0484722i
$482$	−0.172190	−	0.298242i	−0.00784305	−	0.0135846i
$483$	−13.6525	+	34.3063i	−0.621209	+	1.56099i
$484$	−1.64372	−	15.6389i	−0.0747144	−	0.710860i
$485$	1.06359	−	7.39887i	0.0482951	−	0.335965i
$486$	−4.32465	+	0.416231i	−0.196170	+	0.0188806i
$487$	−7.57800	+	5.50574i	−0.343392	+	0.249489i	−0.746092	−	0.665843i	$-0.768072\pi$
$487$	−7.57800	+	5.50574i	−0.343392	+	0.249489i	0.402700	+	0.915332i	$0.368072\pi$
$488$	−0.322765	−	3.07091i	−0.0146109	−	0.139013i
$489$	0.501278	+	0.416176i	0.0226686	+	0.0188201i
$490$	2.85369	−	4.53505i	0.128916	−	0.204873i
$491$	−16.8465	−	7.50055i	−0.760273	−	0.338495i	−0.0102850	−	0.999947i	$-0.503274\pi$
$491$	−16.8465	−	7.50055i	−0.760273	−	0.338495i	−0.749988	+	0.661452i	$0.769941\pi$
$492$	−2.59454	−	3.28531i	−0.116971	−	0.148113i
$493$	−14.5088	+	25.1300i	−0.653444	+	1.13180i
$494$	0.543452	−	1.67257i	0.0244511	−	0.0752526i
$495$	−9.38449	−	6.23060i	−0.421801	−	0.280045i
$496$	5.38371	+	16.5694i	0.241736	+	0.743986i
$497$	26.9137	+	5.72068i	1.20724	+	0.256608i
$498$	−0.444685	+	2.60138i	−0.0199268	+	0.116571i
$499$	13.8809	+	24.0424i	0.621393	+	1.07628i	0.989227	+	0.146393i	$0.0467664\pi$
$499$	13.8809	+	24.0424i	0.621393	+	1.07628i	−0.367833	+	0.929892i	$0.619900\pi$
$500$	18.5106	+	10.9213i	0.827817	+	0.488414i
$501$	−6.71794	−	13.5930i	−0.300135	−	0.607291i
$502$	4.12258	−	1.83549i	0.184000	−	0.0819219i
$503$	−12.4716	−	38.3835i	−0.556080	−	1.71144i	−0.693075	−	0.720865i	$-0.743745\pi$
$503$	−12.4716	−	38.3835i	−0.556080	−	1.71144i	0.136996	−	0.990572i	$-0.456255\pi$
$504$	12.2168	+	4.30244i	0.544179	+	0.191646i
$505$	14.4824	+	7.12003i	0.644459	+	0.316837i
$506$	1.69034	+	1.87731i	0.0751448	+	0.0834567i
$507$	−11.4286	+	17.1361i	−0.507561	+	0.761041i
$508$	−24.9358	+	5.30026i	−1.10635	+	0.235161i
$509$	−16.6460	−	7.41126i	−0.737819	−	0.328498i	0.00318840	−	0.999995i	$-0.498985\pi$
$509$	−16.6460	−	7.41126i	−0.737819	−	0.328498i	−0.741008	+	0.671497i	$0.765652\pi$
$510$	1.78929	+	3.99640i	0.0792311	+	0.176964i
$511$	19.7251	−	8.78220i	0.872589	−	0.388502i
$512$	−15.3486	+	11.1514i	−0.678319	+	0.492828i
$513$	28.2535	−	13.1140i	1.24742	−	0.578996i
$514$	−5.65082	−	4.10556i	−0.249247	−	0.181089i
$515$	−8.22944	−	6.47133i	−0.362632	−	0.285161i
$516$	28.1127	−	17.7718i	1.23759	−	0.782360i
$517$	7.77052	−	1.65168i	0.341747	−	0.0726406i
$518$	−2.67342	−	4.63049i	−0.117463	−	0.203452i
$519$	2.30571	+	2.91959i	0.101210	+	0.128156i
$520$	−2.02260	−	1.59050i	−0.0886971	−	0.0697482i
$521$	5.30810	+	16.3367i	0.232552	+	0.715722i	0.997437	+	0.0715548i	$0.0227961\pi$
$521$	5.30810	+	16.3367i	0.232552	+	0.715722i	−0.764884	+	0.644168i	$0.777204\pi$
$522$	−4.54140	+	3.89232i	−0.198772	+	0.170362i
$523$	−9.32851	−	6.77756i	−0.407907	−	0.296362i	0.364847	−	0.931068i	$-0.381121\pi$
$523$	−9.32851	−	6.77756i	−0.407907	−	0.296362i	−0.772754	+	0.634706i	$0.781121\pi$
$524$	−13.6810	+	23.6961i	−0.597656	+	1.03517i
$525$	−33.8648	−	4.79614i	−1.47798	−	0.209321i
$526$	2.70192	+	4.67986i	0.117809	+	0.204052i
$527$	2.08681	−	19.8546i	0.0909027	−	0.864881i
$528$	−7.36878	+	7.19076i	−0.320685	+	0.312938i
$529$	−6.00083	−	1.27552i	−0.260906	−	0.0554572i
$530$	−3.89246	+	4.00547i	−0.169078	+	0.173986i
$531$	−18.4453	+	1.48376i	−0.800459	+	0.0643897i
$532$	−45.5107			−1.97314
$533$	−0.885571	−	0.983526i	−0.0383583	−	0.0426012i
$534$	−0.292379	−	7.28115i	−0.0126525	−	0.315086i
$535$	−2.87706	−	43.0914i	−0.124386	−	1.86301i
$536$	−1.40074	+	13.3271i	−0.0605026	+	0.575643i
$537$	−28.5157	+	18.0265i	−1.23054	+	0.777903i
$538$	0.108706	+	1.03427i	0.00468666	+	0.0445906i
$539$	−11.6801	−	8.48608i	−0.503097	−	0.365521i
$540$	−1.83723	−	22.2597i	−0.0790620	−	0.957904i
$541$	15.1965	−	11.0409i	0.653350	−	0.474687i	−0.211061	−	0.977473i	$-0.567692\pi$
$541$	15.1965	−	11.0409i	0.653350	−	0.474687i	0.864411	+	0.502786i	$0.167692\pi$
$542$	−4.12133	−	4.57720i	−0.177026	−	0.196607i
$543$	−25.7486	−	1.66531i	−1.10498	−	0.0714653i
$544$	12.5898	−	2.67605i	0.539784	−	0.114735i
$545$	−15.5536	−	18.6549i	−0.666243	−	0.799089i
$546$	1.93196	+	0.543068i	0.0826804	+	0.0232412i
$547$	5.71030	+	1.21376i	0.244155	+	0.0518967i	0.328364	−	0.944551i	$-0.393503\pi$
$547$	5.71030	+	1.21376i	0.244155	+	0.0518967i	−0.0842086	+	0.996448i	$0.526836\pi$
$548$	−15.0914	−	10.9645i	−0.644672	−	0.468381i
$549$	5.14692	−	6.73165i	0.219665	−	0.287300i
$550$	−1.32072	+	1.93172i	−0.0563158	+	0.0823690i
$551$	21.4409	−	37.1367i	0.913412	−	1.58208i
$552$	−1.72209	+	10.0741i	−0.0732969	+	0.428783i
$553$	−31.1675	+	34.6150i	−1.32538	+	1.47198i
$554$	−2.23018	+	2.47687i	−0.0947514	+	0.105232i
$555$	−11.0264	+	15.2431i	−0.468044	+	0.647035i
$556$	2.09513	+	2.32688i	0.0888532	+	0.0986815i
$557$	21.0555			0.892151			0.446076	−	0.894995i	$-0.352821\pi$
$557$	21.0555			0.892151			0.446076	+	0.894995i	$0.352821\pi$
$558$	1.76514	−	3.71722i	0.0747244	−	0.157362i
$559$	8.50652	−	6.18034i	0.359787	−	0.261401i
$560$	−10.7845	+	29.3427i	−0.455729	+	1.23996i
$561$	11.0654	−	4.09310i	0.467180	−	0.172811i
$562$	6.96259	+	3.09995i	0.293699	+	0.130763i
$563$	12.1123	+	5.39273i	0.510471	+	0.227277i	0.645775	−	0.763528i	$-0.276534\pi$
$563$	12.1123	+	5.39273i	0.510471	+	0.227277i	−0.135304	+	0.990804i	$0.543201\pi$
$564$	12.1192	+	10.0618i	0.510312	+	0.423677i
$565$	−5.25046	+	14.2855i	−0.220889	+	0.600997i
$566$	0.701520	−	0.509684i	0.0294871	−	0.0214236i
$567$	16.2463	+	31.6144i	0.682279	+	1.32768i
$568$	7.61609			0.319564
$569$	−7.07709	−	7.85990i	−0.296687	−	0.329504i	0.576309	−	0.817232i	$-0.304493\pi$
$569$	−7.07709	−	7.85990i	−0.296687	−	0.329504i	−0.872996	+	0.487728i	$0.837826\pi$
$570$	−2.64418	−	5.90582i	−0.110753	−	0.247368i
$571$	27.0260	−	30.0154i	1.13100	−	1.25610i	0.168241	−	0.985746i	$-0.446191\pi$
$571$	27.0260	−	30.0154i	1.13100	−	1.25610i	0.962760	−	0.270358i	$-0.0871421\pi$
$572$	−2.27360	+	2.52509i	−0.0950639	+	0.105579i
$573$	13.2469	−	4.90005i	0.553397	−	0.204703i
$574$	0.691978	−	1.19854i	0.0288826	−	0.0500261i
$575$	−0.772167	−	26.9773i	−0.0322016	−	1.12503i
$576$	−18.4319	−	2.39421i	−0.767996	−	0.0997586i
$577$	11.4589	+	8.32536i	0.477039	+	0.346589i	0.800178	−	0.599762i	$-0.204738\pi$
$577$	11.4589	+	8.32536i	0.477039	+	0.346589i	−0.323139	+	0.946351i	$0.604738\pi$
$578$	0.148624	+	0.0315910i	0.00618193	+	0.00131401i
$579$	5.90519	−	5.76254i	0.245411	−	0.239483i
$580$	−19.6907	−	23.6169i	−0.817610	−	0.980638i
$581$	21.1194	−	4.48907i	0.876181	−	0.186238i
$582$	0.714988	+	1.44670i	0.0296372	+	0.0599676i
$583$	10.0699	+	11.1837i	0.417051	+	0.463182i
$584$	4.83516	−	3.51295i	0.200080	−	0.145367i
$585$	−1.03381	−	6.98509i	−0.0427427	−	0.288798i
$586$	0.489977	+	0.355989i	0.0202408	+	0.0147058i
$587$	1.08785	+	10.3502i	0.0449003	+	0.427198i	0.993763	+	0.111510i	$0.0355686\pi$
$587$	1.08785	+	10.3502i	0.0449003	+	0.427198i	−0.948863	+	0.315688i	$0.897765\pi$
$588$	−1.14859	−	28.6035i	−0.0473671	−	1.17959i
$589$	−3.08385	+	29.3408i	−0.127068	+	1.20897i
$590$	0.256090	+	3.83562i	0.0105431	+	0.157910i
$591$	−7.90617	+	4.99798i	−0.325216	+	0.205589i
$592$	11.5060	+	12.7787i	0.472895	+	0.525203i
$593$	33.1998			1.36335			0.681676	−	0.731654i	$-0.261251\pi$
$593$	33.1998			1.36335			0.681676	+	0.731654i	$0.261251\pi$
$594$	2.43156	−	0.0381359i	0.0997681	−	0.00156474i
$595$	24.9657	−	25.6905i	1.02349	−	1.05321i
$596$	−20.7795	−	4.41681i	−0.851160	−	0.180920i
$597$	9.26100	+	36.3336i	0.379027	+	1.48704i
$598$	−0.165525	+	1.57486i	−0.00676881	+	0.0644009i
$599$	−16.0799	−	27.8512i	−0.657007	−	1.13797i	−0.981387	−	0.192043i	$-0.938489\pi$
$599$	−16.0799	−	27.8512i	−0.657007	−	1.13797i	0.324379	−	0.945927i	$-0.394845\pi$
$600$	−9.44490	+	0.650353i	−0.385586	+	0.0265505i
$601$	3.24834	−	5.62629i	0.132503	−	0.229501i	−0.792138	−	0.610342i	$-0.791032\pi$
$601$	3.24834	−	5.62629i	0.132503	−	0.229501i	0.924641	+	0.380841i	$0.124365\pi$
$602$	8.89532	+	6.46283i	0.362546	+	0.263405i
$603$	−27.9224	+	23.9316i	−1.13709	+	0.974568i
$604$	−3.45029	−	10.6189i	−0.140390	−	0.432076i
$605$	−14.3785	−	11.3067i	−0.584568	−	0.459683i
$606$	−3.44749	+	0.502905i	−0.140045	+	0.0204291i
$607$	−4.92697	−	8.53376i	−0.199979	−	0.346375i	0.748542	−	0.663087i	$-0.230754\pi$
$607$	−4.92697	−	8.53376i	−0.199979	−	0.346375i	−0.948521	+	0.316713i	$0.897421\pi$
$608$	−18.6050	+	3.95462i	−0.754534	+	0.160381i
$609$	43.3252	+	22.7467i	1.75563	+	0.921743i
$610$	−1.38374	−	1.08813i	−0.0560261	−	0.0440569i
$611$	4.02874	+	2.92705i	0.162985	+	0.118416i
$612$	19.9673	+	12.1885i	0.807129	+	0.492693i
$613$	21.3372	−	15.5024i	0.861801	−	0.626135i	−0.0665732	−	0.997782i	$-0.521207\pi$
$613$	21.3372	−	15.5024i	0.861801	−	0.626135i	0.928374	+	0.371646i	$0.121207\pi$
$614$	1.56953	−	0.698798i	0.0633409	−	0.0282012i
$615$	−4.84390	−	0.498922i	−0.195325	−	0.0201185i
$616$	−6.62308	−	2.94878i	−0.266851	−	0.118810i
$617$	16.5737	−	3.52285i	0.667232	−	0.141825i	0.138171	−	0.990408i	$-0.455878\pi$
$617$	16.5737	−	3.52285i	0.667232	−	0.141825i	0.529061	+	0.848584i	$0.322544\pi$
$618$	2.25543	+	0.145871i	0.0907265	+	0.00586780i
$619$	18.2999	+	20.3241i	0.735536	+	0.816896i	0.988602	−	0.150553i	$-0.0481055\pi$
$619$	18.2999	+	20.3241i	0.735536	+	0.816896i	−0.253066	+	0.967449i	$0.581439\pi$
$620$	18.9847	+	9.33348i	0.762443	+	0.374842i
$621$	−22.4293	+	16.8395i	−0.900057	+	0.675746i
$622$	−0.339933	−	1.04621i	−0.0136301	−	0.0419491i
$623$	−54.4627	+	24.2484i	−2.18200	+	0.971490i
$624$	−6.44056	−	0.416548i	−0.257829	−	0.0166752i
$625$	24.1163	−	6.58800i	0.964654	−	0.263520i
$626$	−0.341966	−	0.592303i	−0.0136677	−	0.0236732i
$627$	−16.3522	+	6.04871i	−0.653045	+	0.241562i
$628$	6.92223	+	1.47137i	0.276227	+	0.0587139i
$629$	−6.08898	−	18.7400i	−0.242784	−	0.747211i
$630$	6.61279	−	3.28532i	0.263460	−	0.130890i
$631$	−6.22922	+	19.1716i	−0.247981	+	0.763208i	0.747151	+	0.664655i	$0.231421\pi$
$631$	−6.22922	+	19.1716i	−0.247981	+	0.763208i	−0.995132	+	0.0985529i	$0.968579\pi$
$632$	−6.44650	+	11.1657i	−0.256428	+	0.444147i
$633$	26.2574	−	3.83031i	1.04364	−	0.152241i
$634$	−2.40096	−	1.06898i	−0.0953545	−	0.0424546i
$635$	−15.7930	+	25.0981i	−0.626727	+	0.995988i
$636$	−5.02792	+	29.4130i	−0.199370	+	1.16630i
$637$	−0.945993	−	9.00052i	−0.0374816	−	0.356614i
$638$	2.70850	−	1.96784i	0.107231	−	0.0779076i
$639$	15.1856	+	14.3608i	0.600734	+	0.568106i
$640$	−2.56846	+	17.8675i	−0.101527	+	0.706276i
$641$	2.51268	+	23.9066i	0.0992450	+	0.944253i	0.924934	+	0.380128i	$0.124120\pi$
$641$	2.51268	+	23.9066i	0.0992450	+	0.944253i	−0.825689	+	0.564126i	$0.809213\pi$
$642$	5.77850	+	7.31698i	0.228059	+	0.288778i
$643$	6.17193	+	10.6901i	0.243397	+	0.421576i	0.961680	−	0.274175i	$-0.0884048\pi$
$643$	6.17193	+	10.6901i	0.243397	+	0.421576i	−0.718283	+	0.695752i	$0.755071\pi$
$644$	40.0837	−	8.52005i	1.57952	−	0.335737i
$645$	7.96475	−	37.8586i	0.313612	−	1.49068i
$646$	6.62917	+	1.40907i	0.260821	+	0.0554392i
$647$	−13.9688	−	42.9917i	−0.549172	−	1.69018i	−0.710858	−	0.703335i	$-0.751693\pi$
$647$	−13.9688	−	42.9917i	−0.549172	−	1.69018i	0.161687	−	0.986842i	$-0.448307\pi$
$648$	6.21807	+	7.62463i	0.244269	+	0.299524i
$649$	10.3579			0.406583
$650$	−1.45385	+	0.195006i	−0.0570247	+	0.00764875i
$651$	−33.5958	−	2.17283i	−1.31672	−	0.0851600i
$652$	0.0755840	−	0.719133i	0.00296010	−	0.0281634i
$653$	−6.72082	+	7.46423i	−0.263006	+	0.292098i	−0.860155	−	0.510032i	$-0.829633\pi$
$653$	−6.72082	+	7.46423i	−0.263006	+	0.292098i	0.597149	+	0.802130i	$0.296300\pi$
$654$	5.04788	+	1.41894i	0.197388	+	0.0554850i
$655$	8.67662	+	30.6222i	0.339024	+	1.19651i
$656$	−1.37538	+	4.23298i	−0.0536996	+	0.165270i
$657$	16.2648	+	2.11270i	0.634549	+	0.0824245i
$658$	−1.60918	+	4.95253i	−0.0627322	+	0.193070i
$659$	3.83346	+	36.4729i	0.149330	+	1.42078i	0.770666	+	0.637239i	$0.219924\pi$
$659$	3.83346	+	36.4729i	0.149330	+	1.42078i	−0.621336	+	0.783545i	$0.713410\pi$
$660$	0.0260252	+	12.5019i	0.00101303	+	0.486636i
$661$	−1.19894	+	11.4072i	−0.0466334	+	0.443687i	0.946147	+	0.323738i	$0.104940\pi$
$661$	−1.19894	+	11.4072i	−0.0466334	+	0.443687i	−0.992780	+	0.119949i	$0.961727\pi$
$662$	−5.25179	−	2.33825i	−0.204117	−	0.0908785i
$663$	6.54806	+	3.43788i	0.254306	+	0.133516i
$664$	5.45973	−	2.43083i	0.211879	−	0.0943344i
$665$	−36.8939	+	37.9650i	−1.43068	+	1.47222i
$666$	0.0993006	−	4.06030i	0.00384782	−	0.157333i
$667$	−11.9318	+	36.7222i	−0.461999	+	1.42189i
$668$	−8.41406	+	14.5736i	−0.325550	+	0.563869i
$669$	−21.9979	−	27.8546i	−0.850487	−	1.07692i
$670$	4.89212	+	5.86759i	0.188999	+	0.226685i
$671$	−3.17377	+	3.52483i	−0.122522	+	0.136074i
$672$	−5.36093	−	21.0325i	−0.206802	−	0.811347i
$673$	32.2055	−	14.3388i	1.24143	−	0.552721i	0.322288	−	0.946642i	$-0.395548\pi$
$673$	32.2055	−	14.3388i	1.24143	−	0.552721i	0.919144	+	0.393921i	$0.128882\pi$
$674$	−7.54367			−0.290571
$675$	−20.0584	−	16.5125i	−0.772047	−	0.635566i
$676$	22.8602			0.879240
$677$	1.28253	−	0.571021i	0.0492918	−	0.0219461i	−0.381943	−	0.924186i	$-0.624745\pi$
$677$	1.28253	−	0.571021i	0.0492918	−	0.0219461i	0.431234	+	0.902240i	$0.358078\pi$
$678$	−0.811554	−	3.18396i	−0.0311675	−	0.122279i
$679$	8.83411	−	9.81128i	0.339022	−	0.376522i
$680$	5.28097	−	8.39246i	0.202516	−	0.321836i
$681$	2.54167	+	3.21837i	0.0973971	+	0.123328i
$682$	−1.15167	+	1.99475i	−0.0440996	+	0.0763828i
$683$	13.5005	−	41.5502i	0.516582	−	1.58987i	−0.263804	−	0.964576i	$-0.584977\pi$
$683$	13.5005	−	41.5502i	0.516582	−	1.58987i	0.780386	−	0.625298i	$-0.215023\pi$
$684$	−29.5073	−	18.0120i	−1.12824	−	0.688707i
$685$	−21.3806	+	3.70067i	−0.816912	+	0.141395i
$686$	1.60660	−	0.715304i	0.0613402	−	0.0273104i
$687$	−5.00706	−	2.62882i	−0.191031	−	0.100296i
$688$	−32.3037	−	14.3825i	−1.23157	−	0.548329i
$689$	−0.986081	+	9.38194i	−0.0375667	+	0.357423i
$690$	3.43450	+	4.70655i	0.130749	+	0.179175i
$691$	−4.73461	−	45.0468i	−0.180113	−	1.71366i	−0.594947	−	0.803765i	$-0.702827\pi$
$691$	−4.73461	−	45.0468i	−0.180113	−	1.71366i	0.414834	−	0.909897i	$-0.363840\pi$
$692$	1.27591	−	3.92686i	0.0485029	−	0.149277i
$693$	−7.64548	−	18.3680i	−0.290428	−	0.697741i
$694$	−2.90127	+	8.92918i	−0.110131	+	0.338947i
$695$	3.63952	+	0.138559i	0.138055	+	0.00525585i
$696$	13.0393	+	3.66531i	0.494255	+	0.138933i
$697$	3.41271	−	3.79020i	0.129266	−	0.143564i
$698$	0.156295	−	1.48705i	0.00591586	−	0.0562857i
$699$	−2.17243	−	0.140503i	−0.0821689	−	0.00531433i
$700$	16.4256	+	34.2223i	0.620829	+	1.29348i
$701$	29.7825			1.12487			0.562435	−	0.826841i	$-0.309864\pi$
$701$	29.7825			1.12487			0.562435	+	0.826841i	$0.309864\pi$
$702$	1.03767	+	1.11673i	0.0391644	+	0.0421481i
$703$	8.99820	+	27.6936i	0.339373	+	1.04448i
$704$	10.1764	+	2.16305i	0.383536	+	0.0815231i
$705$	18.2181	−	1.95316i	0.686135	−	0.0735601i
$706$	6.39427	−	1.35914i	0.240651	−	0.0511520i
$707$	14.2516	+	24.6846i	0.535988	+	0.928359i
$708$	12.7287	+	16.1176i	0.478374	+	0.605737i
$709$	2.20660	+	20.9944i	0.0828707	+	0.788462i	0.954483	+	0.298266i	$0.0964083\pi$
$709$	2.20660	+	20.9944i	0.0828707	+	0.788462i	−0.871612	+	0.490196i	$0.836925\pi$
$710$	3.02591	−	3.11376i	0.113560	−	0.116857i
$711$	−33.9075	+	10.1076i	−1.27163	+	0.379066i
$712$	−13.3503	+	9.69954i	−0.500323	+	0.363506i
$713$	−2.77678	−	26.4193i	−0.103991	−	0.989412i
$714$	−1.30311	+	7.62314i	−0.0487678	+	0.285289i
$715$	0.263302	+	3.94363i	0.00984692	+	0.147483i
$716$	34.2047	+	15.2289i	1.27829	+	0.569132i
$717$	−22.3060	+	3.25391i	−0.833035	+	0.121519i
$718$	−2.18195	+	3.77925i	−0.0814298	+	0.141040i
$719$	−3.25698	+	10.0240i	−0.121465	+	0.373831i	−0.993240	−	0.116075i	$-0.962969\pi$
$719$	−3.25698	+	10.0240i	−0.121465	+	0.373831i	0.871775	+	0.489906i	$0.162969\pi$
$720$	−18.6054	+	14.7564i	−0.693381	+	0.549937i
$721$	−5.71395	−	17.5857i	−0.212799	−	0.654927i
$722$	−4.61673	−	0.981316i	−0.171817	−	0.0365208i
$723$	−2.00725	+	0.742484i	−0.0746504	+	0.0276133i
$724$	14.3184	+	24.8003i	0.532141	+	0.921695i
$725$	−35.6637	−	2.71943i	−1.32452	−	0.100997i
$726$	3.94068	+	0.254866i	0.146252	+	0.00945896i
$727$	−5.05053	+	2.24864i	−0.187314	+	0.0833974i	−0.498250	−	0.867033i	$-0.666024\pi$
$727$	−5.05053	+	2.24864i	−0.187314	+	0.0833974i	0.310937	+	0.950431i	$0.399357\pi$
$728$	−1.40436	−	4.32216i	−0.0520489	−	0.160190i
$729$	−1.97881	+	26.9274i	−0.0732891	+	0.997311i
$730$	0.484800	−	3.37251i	0.0179432	−	0.124822i
$731$	27.1132	+	30.1123i	1.00282	+	1.11374i
$732$	−9.38510	−	0.606987i	−0.346883	−	0.0224349i
$733$	8.41306	−	1.78825i	0.310744	−	0.0660506i	−0.0499002	−	0.998754i	$-0.515890\pi$
$733$	8.41306	−	1.78825i	0.310744	−	0.0660506i	0.360644	+	0.932704i	$0.382557\pi$
$734$	−4.67053	−	2.07946i	−0.172393	−	0.0767541i
$735$	−24.7921	−	22.2297i	−0.914472	−	0.819953i
$736$	15.6461	−	6.96608i	0.576722	−	0.256773i
$737$	16.6530	−	12.0991i	0.613419	−	0.445675i
$738$	0.923004	−	0.503218i	0.0339762	−	0.0185237i
$739$	−5.63541	−	4.09436i	−0.207302	−	0.150614i	0.479290	−	0.877656i	$-0.340894\pi$
$739$	−5.63541	−	4.09436i	−0.207302	−	0.150614i	−0.686592	+	0.727043i	$0.740894\pi$
$740$	20.8647	+	0.794335i	0.767002	+	0.0292003i
$741$	−9.67662	−	5.08044i	−0.355479	−	0.186635i
$742$	−9.64922	+	2.05101i	−0.354234	+	0.0752948i
$743$	−1.69867	−	2.94218i	−0.0623180	−	0.107938i	0.833183	−	0.552997i	$-0.186516\pi$
$743$	−1.69867	−	2.94218i	−0.0623180	−	0.107938i	−0.895501	+	0.445059i	$0.853183\pi$
$744$	−9.22110	+	1.34513i	−0.338062	+	0.0493150i
$745$	−20.5296	+	13.7537i	−0.752148	+	0.503895i
$746$	−1.26078	−	3.88027i	−0.0461603	−	0.142067i
$747$	15.4696	+	5.44801i	0.566004	+	0.199332i
$748$	−10.5934	−	7.69657i	−0.387334	−	0.281414i
$749$	38.1393	−	66.0591i	1.39358	−	2.41375i
$750$	−3.48661	+	4.11983i	−0.127313	+	0.150435i
$751$	−8.22782	−	14.2510i	−0.300238	−	0.520027i	0.675952	−	0.736946i	$-0.263733\pi$
$751$	−8.22782	−	14.2510i	−0.300238	−	0.520027i	−0.976190	+	0.216919i	$0.930399\pi$
$752$	1.75055	−	16.6553i	0.0638358	−	0.607357i
$753$	−6.92675	−	27.1757i	−0.252425	−	0.990337i
$754$	2.05277	+	0.436330i	0.0747576	+	0.0158902i
$755$	−11.6553	−	5.73012i	−0.424179	−	0.208540i
$756$	19.1864	−	34.4691i	0.697803	−	1.25363i
$757$	32.9922			1.19912			0.599560	−	0.800330i	$-0.295342\pi$
$757$	32.9922			1.19912			0.599560	+	0.800330i	$0.295342\pi$
$758$	1.15619	+	1.28407i	0.0419946	+	0.0466397i
$759$	13.2699	−	8.38871i	0.481666	−	0.304491i
$760$	−7.80413	+	12.4022i	−0.283086	+	0.449876i
$761$	−2.66928	+	25.3965i	−0.0967614	+	0.920624i	0.833201	+	0.552970i	$0.186506\pi$
$761$	−2.66928	+	25.3965i	−0.0967614	+	0.920624i	−0.929963	+	0.367654i	$0.880161\pi$
$762$	−0.256862	−	6.39666i	−0.00930513	−	0.231727i
$763$	−4.48411	−	42.6635i	−0.162336	−	1.54452i
$764$	−12.6819	−	9.21394i	−0.458815	−	0.333349i
$765$	26.3544	−	6.77587i	0.952846	−	0.244982i
$766$	−2.71876	+	1.97530i	−0.0982328	+	0.0713703i
$767$	4.34458	+	4.82514i	0.156874	+	0.174226i
$768$	7.78247	+	15.7470i	0.280826	+	0.568220i
$769$	−26.2553	+	5.58075i	−0.946792	+	0.201247i	−0.655336	−	0.755337i	$-0.727473\pi$
$769$	−26.2553	+	5.58075i	−0.946792	+	0.201247i	−0.291456	+	0.956584i	$0.594140\pi$
$770$	−3.83696	+	1.53621i	−0.138274	+	0.0553611i
$771$	−31.0667	+	30.3162i	−1.11884	+	1.09181i
$772$	−8.95723	−	1.90392i	−0.322378	−	0.0685235i
$773$	−33.5830	−	24.3995i	−1.20790	−	0.877588i	−0.212858	−	0.977083i	$-0.568277\pi$
$773$	−33.5830	−	24.3995i	−1.20790	−	0.877588i	−0.995038	+	0.0994950i	$0.968277\pi$
$774$	3.20954	+	7.71078i	0.115364	+	0.277158i
$775$	23.1762	−	8.27067i	0.832512	−	0.297091i
$776$	1.82720	−	3.16480i	0.0655926	−	0.113610i
$777$	−31.1644	+	11.5278i	−1.11802	+	0.413557i
$778$	−5.71038	+	6.34202i	−0.204727	+	0.227372i
$779$	−5.04324	+	5.60109i	−0.180693	+	0.200680i
$780$	−5.81300	+	5.25600i	−0.208139	+	0.188195i
$781$	−7.82808	−	8.69396i	−0.280111	−	0.311094i
$782$	−6.10245			−0.218223
$783$	19.0877	+	31.8951i	0.682139	+	1.13984i
$784$	−24.6229	+	17.8896i	−0.879389	+	0.638913i
$785$	6.83901	−	4.58174i	0.244095	−	0.163529i
$786$	−5.28665	−	4.38914i	−0.188569	−	0.156555i
$787$	13.4214	+	5.97558i	0.478420	+	0.213006i	0.631755	−	0.775168i	$-0.282335\pi$
$787$	13.4214	+	5.97558i	0.478420	+	0.213006i	−0.153335	+	0.988174i	$0.549001\pi$
$788$	9.48349	+	4.22232i	0.337835	+	0.150414i
$789$	31.4967	−	11.6507i	1.12131	−	0.414775i
$790$	2.00374	+	7.07175i	0.0712898	+	0.251602i
$791$	−21.7477	+	15.8006i	−0.773259	+	0.561806i
$792$	−3.12708	−	4.53312i	−0.111116	−	0.161078i
$793$	−2.97324			−0.105583
$794$	2.44097	+	2.71097i	0.0866267	+	0.0962087i
$795$	20.4604	+	28.0383i	0.725654	+	0.994417i
$796$	27.8454	−	30.9254i	0.986954	−	1.09612i
$797$	−6.10534	+	6.78067i	−0.216262	+	0.240184i	−0.841508	−	0.540244i	$-0.818332\pi$
$797$	−6.10534	+	6.78067i	−0.216262	+	0.240184i	0.625246	+	0.780428i	$0.284999\pi$
$798$	1.92572	−	11.2653i	0.0681697	−	0.398789i
$799$	−9.59526	+	16.6195i	−0.339456	+	0.587955i
$800$	9.68859	+	12.5629i	0.342543	+	0.444167i
$801$	−44.9083	−	5.83335i	−1.58676	−	0.206111i
$802$	−0.581020	−	0.422136i	−0.0205165	−	0.0149061i
$803$	−8.97987	−	1.90873i	−0.316893	−	0.0673576i
$804$	39.2917	+	11.0448i	1.38571	+	0.389519i
$805$	25.3870	−	40.3446i	0.894772	−	1.42196i
$806$	−1.41230	+	0.300193i	−0.0497461	+	0.0105739i
$807$	6.44947	+	0.417124i	0.227032	+	0.0146834i
$808$	5.27921	+	5.86316i	0.185722	+	0.206265i
$809$	−19.4810	+	14.1538i	−0.684916	+	0.497621i	−0.874985	−	0.484150i	$-0.839129\pi$
$809$	−19.4810	+	14.1538i	−0.684916	+	0.497621i	0.190069	+	0.981771i	$0.439129\pi$
$810$	5.58771	+	0.487111i	0.196332	+	0.0171153i
$811$	−16.5638	−	12.0343i	−0.581635	−	0.422582i	0.257678	−	0.966231i	$-0.417043\pi$
$811$	−16.5638	−	12.0343i	−0.581635	−	0.422582i	−0.839313	+	0.543648i	$0.817043\pi$
$812$	−5.67683	−	54.0114i	−0.199218	−	1.89543i
$813$	−32.3541	+	20.4531i	−1.13471	+	0.717320i
$814$	−0.237633	+	2.26093i	−0.00832903	+	0.0792454i
$815$	−0.538627	−	0.646027i	−0.0188673	−	0.0226293i
$816$	−0.997936	−	24.8517i	−0.0349347	−	0.869984i
$817$	−40.0674	−	44.4994i	−1.40178	−	1.55684i
$818$	11.0465			0.386232
$819$	5.34970	−	11.2660i	0.186934	−	0.393664i
$820$	2.52222	+	4.77982i	0.0880797	+	0.166918i
$821$	−26.5774	−	5.64921i	−0.927559	−	0.197159i	−0.280724	−	0.959789i	$-0.590575\pi$
$821$	−26.5774	−	5.64921i	−0.927559	−	0.197159i	−0.646835	+	0.762630i	$0.723908\pi$
$822$	3.35264	−	3.27165i	0.116937	−	0.114112i
$823$	−1.82685	+	17.3813i	−0.0636799	+	0.605874i	0.915421	+	0.402498i	$0.131858\pi$
$823$	−1.82685	+	17.3813i	−0.0636799	+	0.605874i	−0.979101	+	0.203376i	$0.934809\pi$
$824$	−2.55910	−	4.43249i	−0.0891505	−	0.154413i
$825$	10.4502	+	10.1131i	0.363829	+	0.352094i
$826$	−3.39482	+	5.88000i	−0.118121	+	0.204591i
$827$	10.7163	+	7.78583i	0.372641	+	0.270740i	0.758305	−	0.651900i	$-0.226028\pi$
$827$	10.7163	+	7.78583i	0.372641	+	0.270740i	−0.385664	+	0.922639i	$0.626028\pi$
$828$	29.3606	+	10.3401i	1.02035	+	0.359343i
$829$	0.853479	+	2.62674i	0.0296425	+	0.0912304i	0.964783	−	0.263046i	$-0.0847272\pi$
$829$	0.853479	+	2.62674i	0.0296425	+	0.0912304i	−0.935141	+	0.354277i	$0.884727\pi$
$830$	1.17536	−	3.19793i	0.0407972	−	0.111002i
$831$	12.8372	+	16.2551i	0.445319	+	0.563882i
$832$	3.26079	+	5.64786i	0.113048	+	0.195804i
$833$	34.1141	−	7.25117i	1.18198	−	0.251238i
$834$	−0.664628	+	0.420152i	−0.0230142	+	0.0145487i
$835$	5.33629	+	18.8333i	0.184670	+	0.651752i
$836$	15.6548	+	11.3739i	0.541432	+	0.393373i
$837$	−20.9222	−	14.7052i	−0.723178	−	0.508285i
$838$	−3.64023	+	2.64478i	−0.125750	+	0.0913624i
$839$	1.85839	−	0.827407i	0.0641587	−	0.0285653i	−0.374406	−	0.927265i	$-0.622154\pi$
$839$	1.85839	−	0.827407i	0.0641587	−	0.0285653i	0.438565	+	0.898699i	$0.355487\pi$
$840$	−14.4984	−	8.33048i	−0.500243	−	0.287429i
$841$	20.2549	+	9.01806i	0.698445	+	0.310968i
$842$	8.32222	−	1.76894i	0.286803	−	0.0609618i
$843$	26.2801	−	39.4047i	0.905136	−	1.35717i
$844$	−19.7061	−	21.8858i	−0.678311	−	0.753341i
$845$	18.5320	−	19.0700i	0.637519	−	0.656027i
$846$	−3.00341	+	2.57415i	−0.103260	+	0.0885011i
$847$	−9.98341	−	30.7258i	−0.343034	−	1.05575i
$848$	28.9825	−	12.9038i	0.995264	−	0.443120i
$849$	−2.38758	−	4.83101i	−0.0819416	−	0.165800i
$850$	−1.33301	−	5.49343i	−0.0457219	−	0.188423i
$851$	−13.1097	−	22.7067i	−0.449394	−	0.778374i
$852$	3.90858	−	22.8650i	0.133906	−	0.783341i
$853$	−26.3288	−	5.59636i	−0.901481	−	0.191616i	−0.266219	−	0.963913i	$-0.585775\pi$
$853$	−26.3288	−	5.59636i	−0.901481	−	0.191616i	−0.635262	+	0.772297i	$0.719108\pi$
$854$	−0.960775	−	2.95696i	−0.0328771	−	0.101185i
$855$	−38.9461	+	10.0133i	−1.33193	+	0.342447i
$856$	6.52451	−	20.0804i	0.223003	−	0.686333i
$857$	−0.867885	+	1.50322i	−0.0296464	+	0.0513490i	−0.880468	−	0.474106i	$-0.842771\pi$
$857$	−0.867885	+	1.50322i	−0.0296464	+	0.0513490i	0.850822	+	0.525455i	$0.176105\pi$
$858$	−0.528835	−	0.669633i	−0.0180541	−	0.0228609i
$859$	−15.3532	−	6.83571i	−0.523846	−	0.233231i	0.127738	−	0.991808i	$-0.459228\pi$
$859$	−15.3532	−	6.83571i	−0.523846	−	0.233231i	−0.651584	+	0.758577i	$0.725895\pi$
$860$	−39.8611	+	15.9593i	−1.35925	+	0.544206i
$861$	−6.61731	−	5.49389i	−0.225517	−	0.187231i
$862$	−0.448523	−	4.26741i	−0.0152768	−	0.145349i
$863$	−37.0757	+	26.9371i	−1.26207	+	0.916949i	−0.998857	−	0.0477885i	$-0.984783\pi$
$863$	−37.0757	+	26.9371i	−1.26207	+	0.916949i	−0.263214	+	0.964737i	$0.584783\pi$
$864$	4.84834	−	15.7584i	0.164944	−	0.536110i
$865$	−2.24144	−	4.24772i	−0.0762113	−	0.144427i
$866$	−1.16280	−	11.0633i	−0.0395134	−	0.375945i
$867$	0.349146	−	0.877345i	0.0118576	−	0.0297962i
$868$	18.6822	+	32.3585i	0.634114	+	1.09832i
$869$	19.3718	−	4.11761i	0.657144	−	0.139680i
$870$	6.67911	−	3.87475i	0.226443	−	0.131366i
$871$	12.6213	+	2.68273i	0.427656	+	0.0909010i
$872$	−3.66934	−	11.2931i	−0.124260	−	0.382431i
$873$	9.61074	−	2.86491i	0.325274	−	0.0969625i
$874$	9.01809			0.305042
$875$	41.8638	+	14.0405i	1.41525	+	0.474656i
$876$	−8.06515	−	16.3189i	−0.272496	−	0.551366i
$877$	−0.595243	+	5.66336i	−0.0200999	+	0.191238i	−0.999965	−	0.00842524i	$-0.997318\pi$
$877$	−0.595243	+	5.66336i	−0.0200999	+	0.191238i	0.979865	+	0.199663i	$0.0639848\pi$
$878$	4.45966	−	4.95295i	0.150506	−	0.167154i
$879$	2.69376	−	2.62868i	0.0908582	−	0.0886633i
$880$	11.0429	−	7.39808i	0.372255	−	0.249389i
$881$	−15.5751	+	47.9353i	−0.524739	+	1.61498i	0.240093	+	0.970750i	$0.422822\pi$
$881$	−15.5751	+	47.9353i	−0.524739	+	1.61498i	−0.764832	+	0.644230i	$0.777178\pi$
$882$	7.12887	+	0.926002i	0.240042	+	0.0311801i
$883$	−11.3213	+	34.8432i	−0.380990	+	1.17257i	0.558357	+	0.829601i	$0.311432\pi$
$883$	−11.3213	+	34.8432i	−0.380990	+	1.17257i	−0.939347	+	0.342967i	$0.888568\pi$
$884$	−0.857982	−	8.16315i	−0.0288571	−	0.274557i
$885$	23.7640	+	2.44769i	0.798818	+	0.0822783i
$886$	0.589065	−	5.60458i	0.0197900	−	0.188289i
$887$	17.7941	+	7.92244i	0.597467	+	0.266010i	0.683109	−	0.730316i	$-0.260627\pi$
$887$	17.7941	+	7.92244i	0.597467	+	0.266010i	−0.0856417	+	0.996326i	$0.527294\pi$
$888$	−7.77434	+	4.91464i	−0.260890	+	0.164925i
$889$	−47.8468	+	21.3028i	−1.60473	+	0.714471i
$890$	−1.33857	+	9.31179i	−0.0448690	+	0.312132i
$891$	2.31257	−	14.9349i	0.0774740	−	0.500339i
$892$	−12.1730	+	37.4645i	−0.407581	+	1.25440i
$893$	14.1797	−	24.5600i	0.474506	−	0.821869i
$894$	1.97255	−	4.95668i	0.0659720	−	0.165776i
$895$	40.4325	−	16.1880i	1.35151	−	0.541105i
$896$	−21.3335	+	23.6933i	−0.712702	+	0.791536i
$897$	9.47381	+	2.66305i	0.316321	+	0.0889168i
$898$	1.98496	−	0.883760i	0.0662389	−	0.0294914i
$899$	−35.2059			−1.17418
$900$	−2.89464	+	28.6892i	−0.0964880	+	0.956305i
$901$	−36.3541			−1.21113
$902$	−0.537561	+	0.239338i	−0.0178988	+	0.00796907i
$903$	48.9040	−	47.7226i	1.62742	−	1.58811i
$904$	−4.97886	+	5.52958i	−0.165594	+	0.183911i
$905$	32.2958	+	8.16025i	1.07355	+	0.271256i
$906$	2.77450	−	0.404732i	0.0921767	−	0.0134463i
$907$	14.8967	−	25.8019i	0.494638	−	0.856738i	−0.505343	−	0.862919i	$-0.668634\pi$
$907$	14.8967	−	25.8019i	0.494638	−	0.856738i	0.999981	+	0.00618063i	$0.00196737\pi$
$908$	1.40648	−	4.32871i	0.0466758	−	0.143653i
$909$	−0.529359	+	21.6449i	−0.0175577	+	0.717917i
$910$	−2.32503	−	1.14306i	−0.0770739	−	0.0378920i
$911$	21.1134	−	9.40029i	0.699518	−	0.311446i	−0.0259870	−	0.999662i	$-0.508273\pi$
$911$	21.1134	−	9.40029i	0.699518	−	0.311446i	0.725505	+	0.688217i	$0.241606\pi$
$912$	1.47473	+	36.7254i	0.0488333	+	1.21610i
$913$	−8.38655	−	3.73393i	−0.277554	−	0.123575i
$914$	0.348294	−	3.31380i	0.0115205	−	0.109611i
$915$	−8.11450	+	7.33698i	−0.268257	+	0.242553i
$916$	0.656067	+	6.24206i	0.0216771	+	0.206244i
$917$	−17.3713	+	53.4635i	−0.573652	+	1.76552i
$918$	−3.86194	+	4.42679i	−0.127463	+	0.146106i
$919$	15.8586	−	48.8077i	0.523126	−	1.61002i	−0.244865	−	0.969557i	$-0.578744\pi$
$919$	15.8586	−	48.8077i	0.523126	−	1.61002i	0.767992	−	0.640460i	$-0.221256\pi$
$920$	4.55169	−	12.3843i	0.150065	−	0.408298i
$921$	−2.63712	−	10.3462i	−0.0868959	−	0.340918i
$922$	4.30258	−	4.77850i	0.141698	−	0.157371i
$923$	0.766556	−	7.29329i	0.0252315	−	0.240062i
$924$	−12.2518	+	18.3704i	−0.403054	+	0.604343i
$925$	17.5769	−	16.7614i	0.577924	−	0.551111i
$926$	−5.41907			−0.178082
$927$	3.25531	−	13.6633i	0.106918	−	0.448762i
$928$	−7.01400	−	21.5869i	−0.230246	−	0.708624i
$929$	−53.4901	−	11.3697i	−1.75495	−	0.373027i	−0.785607	−	0.618726i	$-0.787649\pi$
$929$	−53.4901	−	11.3697i	−1.75495	−	0.373027i	−0.969346	+	0.245700i	$0.920982\pi$
$930$	−3.11364	+	4.30437i	−0.102100	+	0.141146i
$931$	−50.4132	+	10.7157i	−1.65223	+	0.351192i
$932$	1.20806	+	2.09242i	0.0395713	+	0.0685395i
$933$	−6.76470	+	0.986805i	−0.221466	+	0.0323065i
$934$	−0.450754	−	4.28864i	−0.0147491	−	0.140329i
$935$	−15.0082	+	2.59769i	−0.490819	+	0.0849536i
$936$	0.800079	−	3.35813i	0.0261514	−	0.109764i
$937$	44.5714	−	32.3830i	1.45608	−	1.05791i	0.471722	−	0.881747i	$-0.343632\pi$
$937$	44.5714	−	32.3830i	1.45608	−	1.05791i	0.984362	−	0.176160i	$-0.0563675\pi$
$938$	1.41040	+	13.4191i	0.0460513	+	0.438149i
$939$	−3.98635	+	1.47456i	−0.130090	+	0.0481204i
$940$	−13.0222	−	15.6188i	−0.424738	−	0.509429i
$941$	32.5595	+	14.4964i	1.06141	+	0.472569i	0.861769	−	0.507300i	$-0.169357\pi$
$941$	32.5595	+	14.4964i	1.06141	+	0.472569i	0.199639	+	0.979870i	$0.436023\pi$
$942$	−0.657114	+	1.65121i	−0.0214099	+	0.0537994i
$943$	3.39327	−	5.87731i	0.110500	−	0.191392i
$944$	6.74756	−	20.7668i	0.219614	−	0.675903i
$945$	−13.2004	−	43.9482i	−0.429408	−	1.42963i
$946$	−1.44465	−	4.44617i	−0.0469695	−	0.144557i
$947$	−41.6883	−	8.86113i	−1.35469	−	0.287948i	−0.527348	−	0.849649i	$-0.676814\pi$
$947$	−41.6883	−	8.86113i	−1.35469	−	0.287948i	−0.827340	+	0.561701i	$0.810147\pi$
$948$	30.2131	+	25.0839i	0.981277	+	0.814686i
$949$	−2.87740	−	4.98381i	−0.0934044	−	0.161781i
$950$	1.96990	+	8.11810i	0.0639121	+	0.263386i
$951$	−9.06239	+	13.5882i	−0.293868	+	0.440628i
$952$	15.9993	−	7.12335i	0.518540	−	0.230869i
$953$	6.79715	+	20.9195i	0.220181	+	0.677649i	0.998745	+	0.0500831i	$0.0159486\pi$
$953$	6.79715	+	20.9195i	0.220181	+	0.677649i	−0.778564	+	0.627566i	$0.784051\pi$
$954$	−7.06790	−	2.48914i	−0.228832	−	0.0805888i
$955$	−17.9670	+	3.10982i	−0.581399	+	0.100632i
$956$	16.7406	+	18.5923i	0.541430	+	0.601319i
$957$	−9.21823	−	18.6521i	−0.297983	−	0.602936i
$958$	8.33249	−	1.77113i	0.269210	−	0.0572225i
$959$	−35.0111	−	15.5879i	−1.13057	−	0.503361i
$960$	22.8364	+	7.36746i	0.737041	+	0.237784i
$961$	−6.19244	+	2.75705i	−0.199756	+	0.0889372i
$962$	−1.15291	+	0.837637i	−0.0371713	+	0.0270065i
$963$	50.8725	−	27.7355i	1.63934	−	0.893763i
$964$	1.92164	+	1.39615i	0.0618918	+	0.0449670i
$965$	−8.84954	+	5.92867i	−0.284877	+	0.190851i
$966$	0.412900	+	10.2825i	0.0132848	+	0.330834i
$967$	−21.1184	+	4.48886i	−0.679122	+	0.144352i	−0.534543	−	0.845141i	$-0.679516\pi$
$967$	−21.1184	+	4.48886i	−0.679122	+	0.144352i	−0.144579	+	0.989493i	$0.546183\pi$
$968$	−4.47126	−	7.74445i	−0.143712	−	0.248916i
$969$	15.5732	−	39.1328i	0.500284	−	1.25713i
$970$	−0.567940	−	2.00442i	−0.0182355	−	0.0643580i
$971$	−11.5867	−	35.6601i	−0.371834	−	1.14439i	−0.945590	−	0.325360i	$-0.894514\pi$
$971$	−11.5867	−	35.6601i	−0.371834	−	1.14439i	0.573757	−	0.819026i	$-0.305486\pi$
$972$	26.0817	−	14.7549i	0.836572	−	0.473263i
$973$	5.20429	+	3.78114i	0.166842	+	0.121218i
$974$	−1.30532	+	2.26088i	−0.0418252	+	0.0724434i
$975$	−0.327836	+	9.11005i	−0.0104992	+	0.291755i
$976$	4.99951	+	8.65940i	0.160030	+	0.277181i
$977$	−2.57745	+	24.5228i	−0.0824601	+	0.784555i	0.872658	+	0.488331i	$0.162394\pi$
$977$	−2.57745	+	24.5228i	−0.0824601	+	0.784555i	−0.955119	+	0.296224i	$0.904273\pi$
$978$	0.174810	+	0.0491385i	0.00558981	+	0.00157128i
$979$	24.7941	+	5.27016i	0.792424	+	0.168435i
$980$	−5.25848	+	36.5807i	−0.167976	+	1.16853i
$981$	13.9778	−	29.4360i	0.446278	−	0.939819i
$982$	−5.13961			−0.164012
$983$	−17.5110	−	19.4479i	−0.558514	−	0.620293i	0.396075	−	0.918218i	$-0.370372\pi$
$983$	−17.5110	−	19.4479i	−0.558514	−	0.620293i	−0.954589	+	0.297925i	$0.903705\pi$
$984$	−2.10780	−	1.10664i	−0.0671943	−	0.0352786i
$985$	11.2102	−	4.48823i	0.357186	−	0.143007i
$986$	−0.845370	+	8.04316i	−0.0269221	+	0.256146i
$987$	28.6527	+	15.0433i	0.912026	+	0.478834i
$988$	1.26791	+	12.0634i	0.0403376	+	0.383787i
$989$	43.6202	+	31.6919i	1.38704	+	1.00774i
$990$	−3.09572	−	0.522558i	−0.0983885	−	0.0166080i
$991$	−24.1262	+	17.5287i	−0.766396	+	0.556819i	−0.900865	−	0.434099i	$-0.857067\pi$
$991$	−24.1262	+	17.5287i	−0.766396	+	0.556819i	0.134470	+	0.990918i	$0.457067\pi$
$992$	10.4491	+	11.6049i	0.331760	+	0.368457i
$993$	−19.8228	+	29.7224i	−0.629056	+	0.943212i
$994$	7.50108	−	1.59440i	0.237920	−	0.0505714i
$995$	−3.22473	−	48.2987i	−0.102231	−	1.53117i
$996$	−4.49588	−	17.6387i	−0.142457	−	0.558902i
$997$	−5.99911	−	1.27515i	−0.189994	−	0.0403844i	0.111932	−	0.993716i	$-0.464296\pi$
$997$	−5.99911	−	1.27515i	−0.189994	−	0.0403844i	−0.301926	+	0.953331i	$0.597629\pi$
$998$	6.25972	+	4.54795i	0.198148	+	0.143963i
$999$	−24.7682	−	4.85998i	−0.783630	−	0.153763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.15	✓	224
3.2	odd	2		675.2.r.a.316.14		224
9.4	even	3	inner	225.2.q.a.166.14	yes	224
9.5	odd	6		675.2.r.a.91.15		224
25.11	even	5	inner	225.2.q.a.61.14	yes	224
75.11	odd	10		675.2.r.a.586.15		224
225.86	odd	30		675.2.r.a.361.14		224
225.211	even	15	inner	225.2.q.a.211.15	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.15	✓	224	1.1	even	1	trivial
225.2.q.a.61.14	yes	224	25.11	even	5	inner
225.2.q.a.166.14	yes	224	9.4	even	3	inner
225.2.q.a.211.15	yes	224	225.211	even	15	inner
675.2.r.a.91.15		224	9.5	odd	6
675.2.r.a.316.14		224	3.2	odd	2
675.2.r.a.361.14		224	225.86	odd	30
675.2.r.a.586.15		224	75.11	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.254613 - 0.113361i) q^{2} +(-0.427801 - 1.67839i) q^{3} +(-1.28628 + 1.42856i) q^{4} +(0.148962 + 2.23110i) q^{5} +(-0.299187 - 0.378844i) q^{6} +(-1.97470 + 3.42027i) q^{7} +(-0.337813 + 1.03968i) q^{8} +(-2.63397 + 1.43603i) q^{9} +O(q^{10})\)	\(q+(0.254613 - 0.113361i) q^{2} +(-0.427801 - 1.67839i) q^{3} +(-1.28628 + 1.42856i) q^{4} +(0.148962 + 2.23110i) q^{5} +(-0.299187 - 0.378844i) q^{6} +(-1.97470 + 3.42027i) q^{7} +(-0.337813 + 1.03968i) q^{8} +(-2.63397 + 1.43603i) q^{9} +(0.290848 + 0.551181i) q^{10} +(1.53404 - 0.682997i) q^{11} +(2.94796 + 1.54774i) q^{12} +(0.961615 + 0.428138i) q^{13} +(-0.115058 + 1.09470i) q^{14} +(3.68093 - 1.20448i) q^{15} +(-0.370027 - 3.52057i) q^{16} +(-1.25351 + 3.85792i) q^{17} +(-0.507854 + 0.664222i) q^{18} +(1.85242 - 5.70117i) q^{19} +(-3.37888 - 2.65703i) q^{20} +(6.58532 + 1.85111i) q^{21} +(0.313161 - 0.347800i) q^{22} +(-0.564211 + 5.36811i) q^{23} +(1.88950 + 0.122205i) q^{24} +(-4.95562 + 0.664700i) q^{25} +0.293374 q^{26} +(3.53703 + 3.80649i) q^{27} +(-2.34606 - 7.22042i) q^{28} +(6.99712 + 1.48728i) q^{29} +(0.800671 - 0.723951i) q^{30} +(-4.81399 + 1.02325i) q^{31} +(-1.58649 - 2.74789i) q^{32} +(-1.80260 - 2.28252i) q^{33} +(0.118177 + 1.12438i) q^{34} +(-7.92513 - 3.89625i) q^{35} +(1.33658 - 5.60994i) q^{36} +(-3.92983 + 2.85519i) q^{37} +(-0.174640 - 1.66158i) q^{38} +(0.307203 - 1.79712i) q^{39} +(-2.36995 - 0.598821i) q^{40} +(-1.14861 - 0.511393i) q^{41} +(1.88655 - 0.275202i) q^{42} +(4.99451 - 8.65075i) q^{43} +(-0.997503 + 3.07000i) q^{44} +(-3.59629 - 5.66275i) q^{45} +(0.464879 + 1.43075i) q^{46} +(4.62748 + 0.983601i) q^{47} +(-5.75059 + 2.12715i) q^{48} +(-4.29885 - 7.44583i) q^{49} +(-1.18641 + 0.731016i) q^{50} +(7.01134 + 0.453463i) q^{51} +(-1.84853 + 0.823020i) q^{52} +(2.76942 + 8.52341i) q^{53} +(1.33208 + 0.568222i) q^{54} +(1.75235 + 3.32085i) q^{55} +(-2.88892 - 3.20847i) q^{56} +(-10.3612 - 0.670120i) q^{57} +(1.95016 - 0.414519i) q^{58} +(5.63502 + 2.50887i) q^{59} +(-3.01404 + 6.80774i) q^{60} +(-2.58041 + 1.14887i) q^{61} +(-1.10971 + 0.806250i) q^{62} +(0.289678 - 11.8446i) q^{63} +(5.01233 + 3.64167i) q^{64} +(-0.811976 + 2.20924i) q^{65} +(-0.717714 - 0.376816i) q^{66} +(11.9904 - 2.54863i) q^{67} +(-3.89891 - 6.75310i) q^{68} +(9.25114 - 1.34951i) q^{69} +(-2.45953 - 0.0936360i) q^{70} +(-2.15288 - 6.62590i) q^{71} +(-0.603224 - 3.22360i) q^{72} +(-4.42300 - 3.21350i) q^{73} +(-0.676918 + 1.17246i) q^{74} +(3.23564 + 8.03310i) q^{75} +(5.76174 + 9.97962i) q^{76} +(-0.693219 + 6.59554i) q^{77} +(-0.125506 - 0.492395i) q^{78} +(11.5363 + 2.45211i) q^{79} +(7.79963 - 1.35000i) q^{80} +(4.87563 - 7.56493i) q^{81} -0.350423 q^{82} +(-3.65812 - 4.06275i) q^{83} +(-11.1150 + 7.02650i) q^{84} +(-8.79413 - 2.22203i) q^{85} +(0.291010 - 2.76878i) q^{86} +(-0.497133 - 12.3801i) q^{87} +(0.191882 + 1.82563i) q^{88} +(12.2123 + 8.87274i) q^{89} +(-1.55760 - 1.03413i) q^{90} +(-3.36325 + 2.44354i) q^{91} +(-6.94294 - 7.71092i) q^{92} +(3.77683 + 7.64200i) q^{93} +(1.28972 - 0.274138i) q^{94} +(12.9958 + 3.28368i) q^{95} +(-3.93332 + 3.83830i) q^{96} +(-3.26984 - 0.695025i) q^{97} +(-1.93861 - 1.40848i) q^{98} +(-3.05981 + 4.00192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more