LMFDB - Embedded newform 225.2.u.a.34.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(4,225)]

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([10, 3]))

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

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

chi := DirichletCharacter("225.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.u (of order $30$, 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 $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			34.19
Character	$\chi$	$=$	225.34
Dual form			225.2.u.a.139.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368139 + 0.826853i) q^{2} +(-1.62579 - 0.597338i) q^{3} +(0.790101 - 0.877497i) q^{4} +(0.553337 + 2.16652i) q^{5} +(-0.104605 - 1.56419i) q^{6} +(-0.726180 - 0.419260i) q^{7} +(2.73804 + 0.889642i) q^{8} +(2.28637 + 1.94229i) q^{9} +O(q^{10})$	\(q+(0.368139 + 0.826853i) q^{2} +(-1.62579 - 0.597338i) q^{3} +(0.790101 - 0.877497i) q^{4} +(0.553337 + 2.16652i) q^{5} +(-0.104605 - 1.56419i) q^{6} +(-0.726180 - 0.419260i) q^{7} +(2.73804 + 0.889642i) q^{8} +(2.28637 + 1.94229i) q^{9} +(-1.58769 + 1.25511i) q^{10} +(4.08525 - 1.81887i) q^{11} +(-1.80870 + 0.954666i) q^{12} +(-0.899624 + 2.02059i) q^{13} +(0.0793317 - 0.754790i) q^{14} +(0.394537 - 3.85284i) q^{15} +(0.0255220 + 0.242826i) q^{16} +(6.96914 + 2.26441i) q^{17} +(-0.764286 + 2.60553i) q^{18} +(-0.145865 + 0.448925i) q^{19} +(2.33831 + 1.22622i) q^{20} +(0.930175 + 1.11540i) q^{21} +(3.00787 + 2.70830i) q^{22} +(-7.60995 - 0.799838i) q^{23} +(-3.92005 - 3.08190i) q^{24} +(-4.38764 + 2.39764i) q^{25} -2.00192 q^{26} +(-2.55696 - 4.52349i) q^{27} +(-0.941656 + 0.305963i) q^{28} +(-3.70358 - 0.787221i) q^{29} +(3.33097 - 1.09215i) q^{30} +(5.21984 - 1.10951i) q^{31} +(4.79509 - 2.76845i) q^{32} +(-7.72823 + 0.516822i) q^{33} +(0.693275 + 6.59607i) q^{34} +(0.506514 - 1.80528i) q^{35} +(3.51082 - 0.471679i) q^{36} +(-1.78330 - 2.45450i) q^{37} +(-0.424893 + 0.0446581i) q^{38} +(2.66957 - 2.74767i) q^{39} +(-0.412371 + 6.42429i) q^{40} +(-5.98463 - 2.66453i) q^{41} +(-0.579842 + 1.17974i) q^{42} +(-8.54237 - 4.93194i) q^{43} +(1.63171 - 5.02188i) q^{44} +(-2.94288 + 6.02822i) q^{45} +(-2.14017 - 6.58676i) q^{46} +(-1.73285 + 8.15243i) q^{47} +(0.103556 - 0.410029i) q^{48} +(-3.14844 - 5.45326i) q^{49} +(-3.59775 - 2.74527i) q^{50} +(-9.97772 - 7.84438i) q^{51} +(1.06227 + 2.38589i) q^{52} +(5.86521 - 1.90572i) q^{53} +(2.79895 - 3.77950i) q^{54} +(6.20114 + 7.84433i) q^{55} +(-1.61532 - 1.79399i) q^{56} +(0.505305 - 0.642727i) q^{57} +(-0.712517 - 3.35213i) q^{58} +(7.09978 + 3.16103i) q^{59} +(-3.06913 - 3.39034i) q^{60} +(-1.71496 + 0.763551i) q^{61} +(2.83903 + 3.90759i) q^{62} +(-0.845995 - 2.36904i) q^{63} +(4.44942 + 3.23269i) q^{64} +(-4.87545 - 0.830988i) q^{65} +(-3.27239 - 6.19984i) q^{66} +(-2.49215 - 11.7246i) q^{67} +(7.49334 - 4.32628i) q^{68} +(11.8944 + 5.84608i) q^{69} +(1.67917 - 0.245780i) q^{70} +(1.16473 + 3.58468i) q^{71} +(4.53223 + 7.35212i) q^{72} +(-4.42494 + 6.09040i) q^{73} +(1.37301 - 2.37812i) q^{74} +(8.56556 - 1.27714i) q^{75} +(0.278682 + 0.482692i) q^{76} +(-3.72921 - 0.391955i) q^{77} +(3.25469 + 1.19582i) q^{78} +(-5.43332 - 1.15489i) q^{79} +(-0.511965 + 0.189659i) q^{80} +(1.45501 + 8.88161i) q^{81} -5.92933i q^{82} +(4.71769 - 4.24783i) q^{83} +(1.71370 + 0.0650567i) q^{84} +(-1.04961 + 16.3518i) q^{85} +(0.933212 - 8.87892i) q^{86} +(5.55101 + 3.49215i) q^{87} +(12.8037 - 1.34572i) q^{88} +(-4.63408 - 3.36685i) q^{89} +(-6.06784 - 0.214107i) q^{90} +(1.50044 - 1.09014i) q^{91} +(-6.71449 + 6.04575i) q^{92} +(-9.14911 - 1.31418i) q^{93} +(-7.37879 + 1.56841i) q^{94} +(-1.05332 - 0.0676119i) q^{95} +(-9.44949 + 1.63662i) q^{96} +(-0.634563 + 2.98538i) q^{97} +(3.34998 - 4.61085i) q^{98} +(12.8732 + 3.77612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.368139	+	0.826853i	0.260313	+	0.584673i	0.995665	−	0.0930124i	$-0.0296496\pi$
$2$	0.368139	+	0.826853i	0.260313	+	0.584673i	−0.735352	+	0.677686i	$0.762983\pi$
$3$	−1.62579	−	0.597338i	−0.938649	−	0.344873i
$3$	−1.62579	−	0.597338i	−0.938649	−	0.344873i
$4$	0.790101	−	0.877497i	0.395051	−	0.438748i
$5$	0.553337	+	2.16652i	0.247460	+	0.968898i
$5$	0.553337	+	2.16652i	0.247460	+	0.968898i
$6$	−0.104605	−	1.56419i	−0.0427047	−	0.638578i
$7$	−0.726180	−	0.419260i	−0.274470	−	0.158466i	0.356447	−	0.934316i	$-0.383988\pi$
$7$	−0.726180	−	0.419260i	−0.274470	−	0.158466i	−0.630917	+	0.775850i	$0.717321\pi$
$8$	2.73804	+	0.889642i	0.968042	+	0.314536i
$9$	2.28637	+	1.94229i	0.762125	+	0.647430i
$10$	−1.58769	+	1.25511i	−0.502072	+	0.396900i
$11$	4.08525	−	1.81887i	1.23175	−	0.548410i	0.315464	−	0.948938i	$-0.397840\pi$
$11$	4.08525	−	1.81887i	1.23175	−	0.548410i	0.916285	+	0.400528i	$0.131173\pi$
$12$	−1.80870	+	0.954666i	−0.522127	+	0.275588i
$13$	−0.899624	+	2.02059i	−0.249511	+	0.560411i	−0.994267	−	0.106926i	$-0.965899\pi$
$13$	−0.899624	+	2.02059i	−0.249511	+	0.560411i	0.744756	+	0.667337i	$0.232566\pi$
$14$	0.0793317	−	0.754790i	0.0212023	−	0.201726i
$15$	0.394537	−	3.85284i	0.101869	−	0.994798i
$16$	0.0255220	+	0.242826i	0.00638050	+	0.0607064i
$17$	6.96914	+	2.26441i	1.69026	+	0.549200i	0.986858	−	0.161588i	$-0.0516617\pi$
$17$	6.96914	+	2.26441i	1.69026	+	0.549200i	0.703406	+	0.710788i	$0.251662\pi$
$18$	−0.764286	+	2.60553i	−0.180144	+	0.614129i
$19$	−0.145865	+	0.448925i	−0.0334636	+	0.102990i	−0.966393	−	0.257068i	$-0.917243\pi$
$19$	−0.145865	+	0.448925i	−0.0334636	+	0.102990i	0.932930	+	0.360059i	$0.117243\pi$
$20$	2.33831	+	1.22622i	0.522862	+	0.274191i
$21$	0.930175	+	1.11540i	0.202981	+	0.243401i
$22$	3.00787	+	2.70830i	0.641281	+	0.577412i
$23$	−7.60995	−	0.799838i	−1.58678	−	0.166778i	−0.730364	−	0.683058i	$-0.760650\pi$
$23$	−7.60995	−	0.799838i	−1.58678	−	0.166778i	−0.856420	+	0.516280i	$0.827316\pi$
$24$	−3.92005	−	3.08190i	−0.800177	−	0.629091i
$25$	−4.38764	+	2.39764i	−0.877527	+	0.479527i
$26$	−2.00192			−0.392608
$27$	−2.55696	−	4.52349i	−0.492086	−	0.870546i
$28$	−0.941656	+	0.305963i	−0.177956	+	0.0578215i
$29$	−3.70358	−	0.787221i	−0.687738	−	0.146183i	−0.149229	−	0.988803i	$-0.547679\pi$
$29$	−3.70358	−	0.787221i	−0.687738	−	0.146183i	−0.538510	+	0.842619i	$0.681012\pi$
$30$	3.33097	−	1.09215i	0.608150	−	0.199399i
$31$	5.21984	−	1.10951i	0.937511	−	0.199274i	0.286273	−	0.958148i	$-0.407584\pi$
$31$	5.21984	−	1.10951i	0.937511	−	0.199274i	0.651238	+	0.758874i	$0.274250\pi$
$32$	4.79509	−	2.76845i	0.847660	−	0.489397i
$33$	−7.72823	+	0.516822i	−1.34531	+	0.0899672i
$34$	0.693275	+	6.59607i	0.118896	+	1.13122i
$35$	0.506514	−	1.80528i	0.0856165	−	0.305148i
$36$	3.51082	−	0.471679i	0.585137	−	0.0786132i
$37$	−1.78330	−	2.45450i	−0.293173	−	0.403518i	0.636869	−	0.770972i	$-0.280229\pi$
$37$	−1.78330	−	2.45450i	−0.293173	−	0.403518i	−0.930041	+	0.367455i	$0.880229\pi$
$38$	−0.424893	+	0.0446581i	−0.0689268	+	0.00724450i
$39$	2.66957	−	2.74767i	0.427474	−	0.439979i
$40$	−0.412371	+	6.42429i	−0.0652016	+	1.01577i
$41$	−5.98463	−	2.66453i	−0.934642	−	0.416130i	−0.117830	−	0.993034i	$-0.537594\pi$
$41$	−5.98463	−	2.66453i	−0.934642	−	0.416130i	−0.816812	+	0.576904i	$0.804261\pi$
$42$	−0.579842	+	1.17974i	−0.0894715	+	0.182038i
$43$	−8.54237	−	4.93194i	−1.30270	−	0.752113i	−0.321833	−	0.946797i	$-0.604299\pi$
$43$	−8.54237	−	4.93194i	−1.30270	−	0.752113i	−0.980866	+	0.194683i	$0.937632\pi$
$44$	1.63171	−	5.02188i	0.245989	−	0.757077i
$45$	−2.94288	+	6.02822i	−0.438699	+	0.898634i
$46$	−2.14017	−	6.58676i	−0.315551	−	0.971165i
$47$	−1.73285	+	8.15243i	−0.252763	+	1.18915i	0.650311	+	0.759668i	$0.274639\pi$
$47$	−1.73285	+	8.15243i	−0.252763	+	1.18915i	−0.903073	+	0.429486i	$0.858695\pi$
$48$	0.103556	−	0.410029i	0.0149470	−	0.0591825i
$49$	−3.14844	−	5.45326i	−0.449777	−	0.779037i
$50$	−3.59775	−	2.74527i	−0.508799	−	0.388239i
$51$	−9.97772	−	7.84438i	−1.39716	−	1.09843i
$52$	1.06227	+	2.38589i	0.147310	+	0.330863i
$53$	5.86521	−	1.90572i	0.805648	−	0.261771i	0.122895	−	0.992420i	$-0.460782\pi$
$53$	5.86521	−	1.90572i	0.805648	−	0.261771i	0.682754	+	0.730649i	$0.260782\pi$
$54$	2.79895	−	3.77950i	0.380889	−	0.514325i
$55$	6.20114	+	7.84433i	0.836162	+	1.05773i
$56$	−1.61532	−	1.79399i	−0.215856	−	0.239732i
$57$	0.505305	−	0.642727i	0.0669293	−	0.0851312i
$58$	−0.712517	−	3.35213i	−0.0935580	−	0.440156i
$59$	7.09978	+	3.16103i	0.924313	+	0.411531i	0.813006	−	0.582255i	$-0.197830\pi$
$59$	7.09978	+	3.16103i	0.924313	+	0.411531i	0.111307	+	0.993786i	$0.464496\pi$
$60$	−3.06913	−	3.39034i	−0.396222	−	0.437690i
$61$	−1.71496	+	0.763551i	−0.219578	+	0.0977626i	−0.513578	−	0.858043i	$-0.671680\pi$
$61$	−1.71496	+	0.763551i	−0.219578	+	0.0977626i	0.293999	+	0.955806i	$0.405014\pi$
$62$	2.83903	+	3.90759i	0.360557	+	0.496264i
$63$	−0.845995	−	2.36904i	−0.106585	−	0.298471i
$64$	4.44942	+	3.23269i	0.556177	+	0.404087i
$65$	−4.87545	−	0.830988i	−0.604725	−	0.103071i
$66$	−3.27239	−	6.19984i	−0.402804	−	0.763148i
$67$	−2.49215	−	11.7246i	−0.304464	−	1.43239i	−0.818443	−	0.574588i	$-0.805162\pi$
$67$	−2.49215	−	11.7246i	−0.304464	−	1.43239i	0.513979	−	0.857803i	$-0.328171\pi$
$68$	7.49334	−	4.32628i	0.908701	−	0.524639i
$69$	11.8944	+	5.84608i	1.43192	+	0.703785i
$70$	1.67917	−	0.245780i	0.200699	−	0.0293763i
$71$	1.16473	+	3.58468i	0.138228	+	0.425423i	0.996078	−	0.0884771i	$-0.0282000\pi$
$71$	1.16473	+	3.58468i	0.138228	+	0.425423i	−0.857850	+	0.513901i	$0.828200\pi$
$72$	4.53223	+	7.35212i	0.534129	+	0.866455i
$73$	−4.42494	+	6.09040i	−0.517900	+	0.712828i	−0.985226	−	0.171257i	$-0.945217\pi$
$73$	−4.42494	+	6.09040i	−0.517900	+	0.712828i	0.467327	+	0.884085i	$0.345217\pi$
$74$	1.37301	−	2.37812i	0.159609	−	0.276451i
$75$	8.56556	−	1.27714i	0.989066	−	0.147472i
$76$	0.278682	+	0.482692i	0.0319671	+	0.0553686i
$77$	−3.72921	−	0.391955i	−0.424983	−	0.0446675i
$78$	3.25469	+	1.19582i	0.368521	+	0.135400i
$79$	−5.43332	−	1.15489i	−0.611296	−	0.129935i	−0.108148	−	0.994135i	$-0.534492\pi$
$79$	−5.43332	−	1.15489i	−0.611296	−	0.129935i	−0.503149	+	0.864200i	$0.667825\pi$
$80$	−0.511965	+	0.189659i	−0.0572394	+	0.0212045i
$81$	1.45501	+	8.88161i	0.161668	+	0.986845i
$82$		−	5.92933i		−	0.654784i
$83$	4.71769	−	4.24783i	0.517834	−	0.466259i	−0.368288	−	0.929712i	$-0.620056\pi$
$83$	4.71769	−	4.24783i	0.517834	−	0.466259i	0.886122	+	0.463452i	$0.153389\pi$
$84$	1.71370	+	0.0650567i	0.186980	+	0.00709827i
$85$	−1.04961	+	16.3518i	−0.113846	+	1.77360i
$86$	0.933212	−	8.87892i	0.100631	−	0.957438i
$87$	5.55101	+	3.49215i	0.595130	+	0.374398i
$88$	12.8037	−	1.34572i	1.36488	−	0.143455i
$89$	−4.63408	−	3.36685i	−0.491211	−	0.356886i	0.314439	−	0.949278i	$-0.398184\pi$
$89$	−4.63408	−	3.36685i	−0.491211	−	0.356886i	−0.805650	+	0.592392i	$0.798184\pi$
$90$	−6.06784	−	0.214107i	−0.639607	−	0.0225688i
$91$	1.50044	−	1.09014i	0.157289	−	0.114277i
$92$	−6.71449	+	6.04575i	−0.700034	+	0.630313i
$93$	−9.14911	−	1.31418i	−0.948718	−	0.136274i
$94$	−7.37879	+	1.56841i	−0.761064	+	0.161769i
$95$	−1.05332	−	0.0676119i	−0.108068	−	0.00693683i
$96$	−9.44949	+	1.63662i	−0.964435	+	0.167036i
$97$	−0.634563	+	2.98538i	−0.0644301	+	0.303120i	−0.998550	−	0.0538409i	$-0.982854\pi$
$97$	−0.634563	+	2.98538i	−0.0644301	+	0.303120i	0.934119	+	0.356961i	$0.116187\pi$
$98$	3.34998	−	4.61085i	0.338399	−	0.465767i
$99$	12.8732	+	3.77612i	1.29380	+	0.379514i
$100$	−1.36276	+	5.74451i	−0.136276	+	0.574451i
$101$	−8.64613	+	14.9755i	−0.860322	+	1.49012i	0.0112956	+	0.999936i	$0.496404\pi$
$101$	−8.64613	+	14.9755i	−0.860322	+	1.49012i	−0.871618	+	0.490186i	$0.836929\pi$
$102$	2.81297	−	11.1379i	0.278525	−	1.10282i
$103$	−2.12760	−	1.91570i	−0.209638	−	0.188759i	0.557622	−	0.830095i	$-0.311714\pi$
$103$	−2.12760	−	1.91570i	−0.209638	−	0.188759i	−0.767260	+	0.641336i	$0.778381\pi$
$104$	−4.26080	+	4.73210i	−0.417806	+	0.464021i
$105$	−1.90185	+	2.63244i	−0.185601	+	0.256900i
$106$	3.73496	+	4.14809i	0.362771	+	0.402899i
$107$			8.04871i			0.778098i	0.921217	+	0.389049i	$0.127196\pi$
$107$			8.04871i			0.778098i	−0.921217	+	0.389049i	$0.872804\pi$
$108$	−5.98960	−	1.33030i	−0.576350	−	0.128008i
$109$	2.53605	−	1.84255i	0.242909	−	0.176484i	−0.459669	−	0.888090i	$-0.652032\pi$
$109$	2.53605	−	1.84255i	0.242909	−	0.176484i	0.702578	+	0.711606i	$0.252032\pi$
$110$	−4.20323	+	8.01523i	−0.400762	+	0.764222i
$111$	1.43310	+	5.05573i	0.136024	+	0.479869i
$112$	0.0832737	−	0.187036i	0.00786862	−	0.0176732i
$113$	−1.08610	+	2.43942i	−0.102172	+	0.229481i	−0.957397	−	0.288775i	$-0.906752\pi$
$113$	−1.08610	+	2.43942i	−0.102172	+	0.229481i	0.855225	+	0.518256i	$0.173419\pi$
$114$	0.717463	+	0.181200i	0.0671965	+	0.0169710i
$115$	−2.47800	−	16.9297i	−0.231075	−	1.57870i
$116$	−3.61699	+	2.62790i	−0.335829	+	0.243994i
$117$	−5.98145	+	2.87249i	−0.552985	+	0.265562i
$118$			7.03417i			0.647548i
$119$	−4.11147	−	4.56625i	−0.376898	−	0.418588i
$120$	4.50790	−	10.1982i	0.411513	−	0.930965i
$121$	6.02052	−	6.68647i	0.547320	−	0.607861i
$122$	−1.26269	−	1.13693i	−0.114318	−	0.102933i
$123$	8.13812	+	7.90681i	0.733789	+	0.712933i
$124$	3.15061	−	5.45702i	0.282933	−	0.490055i
$125$	−7.62237	−	8.17921i	−0.681766	−	0.731571i
$126$	1.64740	−	1.57165i	0.146762	−	0.140014i
$127$	4.79732	−	6.60294i	0.425693	−	0.585916i	−0.541265	−	0.840852i	$-0.682054\pi$
$127$	4.79732	−	6.60294i	0.425693	−	0.585916i	0.966958	+	0.254936i	$0.0820544\pi$
$128$	1.26741	−	5.96270i	0.112024	−	0.527033i
$129$	10.9420	+	13.1210i	0.963393	+	1.15524i
$130$	−1.10774	−	4.33720i	−0.0971548	−	0.380397i
$131$	−3.36565	+	0.715391i	−0.294058	+	0.0625040i	−0.352579	−	0.935782i	$-0.614695\pi$
$131$	−3.36565	+	0.715391i	−0.294058	+	0.0625040i	0.0585203	+	0.998286i	$0.481362\pi$
$132$	−5.65257	+	7.18983i	−0.491993	+	0.625795i
$133$	0.294141	−	0.264845i	0.0255052	−	0.0229650i
$134$	8.77708	−	6.37692i	0.758225	−	0.550882i
$135$	8.38538	−	8.04272i	0.721699	−	0.692207i
$136$	17.0672	+	12.4001i	1.46350	+	1.06330i
$137$	16.1020	−	1.69239i	1.37568	−	0.144590i	0.612346	−	0.790590i	$-0.290226\pi$
$137$	16.1020	−	1.69239i	1.37568	−	0.144590i	0.763338	+	0.645999i	$0.223559\pi$
$138$	−0.455063	+	11.9871i	−0.0387376	+	1.02041i
$139$	0.643843	−	6.12576i	0.0546101	−	0.519580i	−0.932686	−	0.360689i	$-0.882541\pi$
$139$	0.643843	−	6.12576i	0.0546101	−	0.519580i	0.987296	−	0.158891i	$-0.0507918\pi$
$140$	−1.18393	−	1.87082i	−0.100060	−	0.158113i
$141$	7.68701	−	12.2190i	0.647363	−	1.02903i
$142$	−2.53522	+	2.28272i	−0.212751	+	0.191562i
$143$			9.89090i			0.827119i
$144$	−0.413285	+	0.604762i	−0.0344404	+	0.0503968i
$145$	−0.343800	−	8.45950i	−0.0285510	−	0.702523i
$146$	−6.66486	−	1.41666i	−0.551588	−	0.117244i
$147$	1.86126	+	10.7465i	0.153514	+	0.886359i
$148$	−3.56280	−	0.374466i	−0.292861	−	0.0307809i
$149$	−4.82813	−	8.36257i	−0.395536	−	0.685088i	0.597634	−	0.801769i	$-0.296108\pi$
$149$	−4.82813	−	8.36257i	−0.395536	−	0.685088i	−0.993169	+	0.116681i	$0.962774\pi$
$150$	4.20933	+	6.61230i	0.343690	+	0.539892i
$151$	−1.32884	+	2.30163i	−0.108140	+	0.187304i	−0.915017	−	0.403416i	$-0.867823\pi$
$151$	−1.32884	+	2.30163i	−0.108140	+	0.187304i	0.806877	+	0.590720i	$0.201156\pi$
$152$	−0.798765	+	1.09941i	−0.0647884	+	0.0891736i
$153$	11.5359	+	18.7134i	0.932623	+	1.51289i
$154$	−1.04878	−	3.22780i	−0.0845127	−	0.260103i
$155$	5.29211	+	10.6950i	0.425073	+	0.859040i
$156$	−0.301837	−	4.51348i	−0.0241663	−	0.361368i
$157$	6.90836	−	3.98854i	0.551347	−	0.318320i	−0.198318	−	0.980138i	$-0.563548\pi$
$157$	6.90836	−	3.98854i	0.551347	−	0.318320i	0.749665	+	0.661817i	$0.230215\pi$
$158$	−1.04529	−	4.91772i	−0.0831591	−	0.391233i
$159$	−10.6739	−	0.405213i	−0.846499	−	0.0321355i
$160$	8.65120	+	8.85678i	0.683937	+	0.700190i
$161$	5.19086	+	3.77138i	0.409097	+	0.297226i
$162$	−6.80814	+	4.47275i	−0.534898	+	0.351412i
$163$	−8.62175	−	11.8668i	−0.675307	−	0.929481i	0.324558	−	0.945866i	$-0.394784\pi$
$163$	−8.62175	−	11.8668i	−0.675307	−	0.929481i	−0.999866	+	0.0163847i	$0.994784\pi$
$164$	−7.06658	+	3.14624i	−0.551807	+	0.245680i
$165$	−5.39602	−	16.4574i	−0.420080	−	1.28121i
$166$	5.24909	+	2.33705i	0.407408	+	0.181390i
$167$	0.169963	+	0.799611i	0.0131521	+	0.0618758i	0.984234	−	0.176870i	$-0.0565971\pi$
$167$	0.169963	+	0.799611i	0.0131521	+	0.0618758i	−0.971082	+	0.238746i	$0.923264\pi$
$168$	1.55454	+	3.88154i	0.119936	+	0.299467i
$169$	5.42524	+	6.02534i	0.417326	+	0.463488i
$170$	−13.9069	+	5.15185i	−1.06661	+	0.395129i
$171$	−1.20544	+	0.743099i	−0.0921826	+	0.0568262i
$172$	−11.0771	+	3.59917i	−0.844621	+	0.274434i
$173$	−4.25495	−	9.55678i	−0.323498	−	0.726588i	0.676453	−	0.736486i	$-0.263516\pi$
$173$	−4.25495	−	9.55678i	−0.323498	−	0.726588i	−0.999951	+	0.00989748i	$0.996849\pi$
$174$	−0.843952	+	5.87546i	−0.0639799	+	0.445418i
$175$	4.19145	+	0.0984464i	0.316844	+	0.00744185i
$176$	0.545932	+	0.945582i	0.0411512	+	0.0712759i
$177$	−9.65454	−	9.38013i	−0.725680	−	0.705054i
$178$	1.07791	−	5.07117i	0.0807928	−	0.380100i
$179$	−3.61753	−	11.1336i	−0.270387	−	0.832165i	−0.990403	−	0.138208i	$-0.955866\pi$
$179$	−3.61753	−	11.1336i	−0.270387	−	0.832165i	0.720016	−	0.693957i	$-0.244134\pi$
$180$	2.96457	+	7.34527i	0.220966	+	0.547484i
$181$	6.64568	−	20.4533i	0.493970	−	1.52028i	−0.324587	−	0.945856i	$-0.605225\pi$
$181$	6.64568	−	20.4533i	0.493970	−	1.52028i	0.818556	−	0.574426i	$-0.194775\pi$
$182$	1.45375	+	0.839324i	0.107759	+	0.0622149i
$183$	3.24426	−	0.216959i	0.239823	−	0.0160381i
$184$	−20.1247	−	8.96012i	−1.48362	−	0.660549i
$185$	4.33097	−	5.22173i	0.318419	−	0.383909i
$186$	−2.28151	−	8.04876i	−0.167288	−	0.590164i
$187$	32.5893	−	3.42527i	2.38317	−	0.250481i
$188$	5.78460	+	7.96182i	0.421885	+	0.580675i
$189$	−0.0397098	+	4.35690i	−0.00288846	+	0.316918i
$190$	−0.331862	−	0.895830i	−0.0240758	−	0.0649903i
$191$	2.58593	+	24.6035i	0.187112	+	1.78025i	0.537125	+	0.843503i	$0.319511\pi$
$191$	2.58593	+	24.6035i	0.187112	+	1.78025i	−0.350013	+	0.936745i	$0.613823\pi$
$192$	−5.30280	−	7.91348i	−0.382697	−	0.571106i
$193$	15.8698	−	9.16246i	1.14234	−	0.659528i	0.195328	−	0.980738i	$-0.437423\pi$
$193$	15.8698	−	9.16246i	1.14234	−	0.659528i	0.947008	+	0.321210i	$0.104090\pi$
$194$	−2.70208	+	0.574345i	−0.193998	+	0.0412355i
$195$	7.43006	+	4.26330i	0.532078	+	0.305301i
$196$	−7.27281	−	1.54588i	−0.519486	−	0.110420i
$197$	−4.55604	+	1.48035i	−0.324605	+	0.105470i	−0.466786	−	0.884370i	$-0.654588\pi$
$197$	−4.55604	+	1.48035i	−0.324605	+	0.105470i	0.142182	+	0.989841i	$0.454588\pi$
$198$	1.61682	+	12.0344i	0.114902	+	0.855245i
$199$	−6.90314			−0.489350			−0.244675	−	0.969605i	$-0.578681\pi$
$199$	−6.90314			−0.489350			−0.244675	+	0.969605i	$0.578681\pi$
$200$	−14.1465	+	2.66139i	−1.00031	+	0.188189i
$201$	−2.95186	+	20.5504i	−0.208208	+	1.44951i
$202$	−15.5655	−	1.63600i	−1.09519	−	0.115109i
$203$	2.35942	+	2.12443i	0.165599	+	0.149106i
$204$	−14.7668	+	2.55756i	−1.03389	+	0.179065i
$205$	2.46124	−	14.4402i	0.171901	−	1.00855i
$206$	0.800749	−	2.46445i	0.0557908	−	0.171707i
$207$	−15.8457	−	16.6095i	−1.10135	−	1.15444i
$208$	−0.513611	−	0.166882i	−0.0356125	−	0.0115712i
$209$	0.220643	+	2.09928i	0.0152622	+	0.145210i
$210$	−2.87678	−	0.603445i	−0.198517	−	0.0416416i
$211$	−1.04097	+	9.90421i	−0.0716637	+	0.681834i	0.898432	+	0.439112i	$0.144707\pi$
$211$	−1.04097	+	9.90421i	−0.0716637	+	0.681834i	−0.970096	+	0.242722i	$0.921960\pi$
$212$	2.96184	−	6.65241i	0.203420	−	0.456890i
$213$	0.247657	−	6.52367i	0.0169692	−	0.446995i
$214$	−6.65510	+	2.96304i	−0.454933	+	0.202549i
$215$	5.95834	−	21.2363i	0.406355	−	1.44830i
$216$	−2.97675	−	14.6603i	−0.202542	−	0.997504i
$217$	−4.25572	−	1.38277i	−0.288897	−	0.0938683i
$218$	2.45713	+	1.41863i	0.166418	+	0.0960814i
$219$	10.8320	−	7.25852i	0.731961	−	0.490485i
$220$	11.7829	+	0.756337i	0.794403	+	0.0509922i
$221$	−10.8450	+	12.0446i	−0.729517	+	0.810210i
$222$	−3.65277	+	3.04617i	−0.245158	+	0.204446i
$223$	−1.40660	−	3.15927i	−0.0941928	−	0.211560i	0.860304	−	0.509781i	$-0.170274\pi$
$223$	−1.40660	−	3.15927i	−0.0941928	−	0.211560i	−0.954497	+	0.298221i	$0.903607\pi$
$224$	−4.64280			−0.310210
$225$	−14.6887	−	3.04017i	−0.979245	−	0.202678i
$226$	−2.41687			−0.160768
$227$	−7.15471	−	16.0697i	−0.474875	−	1.06659i	−0.979168	−	0.203053i	$-0.934914\pi$
$227$	−7.15471	−	16.0697i	−0.474875	−	1.06659i	0.504293	−	0.863533i	$-0.331753\pi$
$228$	−0.164748	−	0.951223i	−0.0109107	−	0.0629963i
$229$	−15.3645	+	17.0641i	−1.01532	+	1.12762i	−0.0235306	+	0.999723i	$0.507491\pi$
$229$	−15.3645	+	17.0641i	−1.01532	+	1.12762i	−0.991787	+	0.127901i	$0.959176\pi$
$230$	13.0861	−	8.28142i	0.862874	−	0.546061i
$231$	5.82877	+	2.86483i	0.383505	+	0.188492i
$232$	−9.44020	−	5.45030i	−0.619780	−	0.357830i
$233$	0.713827	+	0.231936i	0.0467643	+	0.0151947i	0.332306	−	0.943172i	$-0.392173\pi$
$233$	0.713827	+	0.231936i	0.0467643	+	0.0151947i	−0.285541	+	0.958366i	$0.592173\pi$
$234$	−4.57713	−	3.88830i	−0.299216	−	0.254186i
$235$	−18.6213	+	0.756781i	−1.21472	+	0.0493670i
$236$	8.38334	−	3.73250i	0.545709	−	0.242965i
$237$	8.14357	+	5.12313i	0.528982	+	0.332783i
$238$	2.26203	−	5.08060i	0.146626	−	0.329326i
$239$	−0.0646270	+	0.614885i	−0.00418037	+	0.0397736i	−0.996413	−	0.0846208i	$-0.973032\pi$
$239$	−0.0646270	+	0.614885i	−0.00418037	+	0.0397736i	0.992233	+	0.124394i	$0.0396988\pi$
$240$	0.945637	−	0.00252839i	0.0610406	−	0.000163207i
$241$	−0.837721	−	7.97038i	−0.0539624	−	0.513417i	−0.987801	−	0.155723i	$-0.950229\pi$
$241$	−0.837721	−	7.97038i	−0.0539624	−	0.513417i	0.933838	−	0.357695i	$-0.116437\pi$
$242$	7.74511	+	2.51654i	0.497875	+	0.161769i
$243$	2.93978	−	15.3087i	0.188587	−	0.982057i
$244$	−0.684981	+	2.10816i	−0.0438514	+	0.134961i
$245$	10.0725	−	9.83866i	0.643506	−	0.628569i
$246$	−3.54181	+	9.63983i	−0.225818	+	0.614613i
$247$	−0.775870	−	0.698596i	−0.0493674	−	0.0444506i
$248$	15.2792	+	1.60591i	0.970229	+	0.101975i
$249$	−10.2073	+	4.08801i	−0.646865	+	0.259067i
$250$	3.95691	−	9.31366i	0.250257	−	0.589048i
$251$	−12.4316			−0.784678			−0.392339	−	0.919821i	$-0.628334\pi$
$251$	−12.4316			−0.784678			−0.392339	+	0.919821i	$0.628334\pi$
$252$	−2.74725	−	1.12942i	−0.173060	−	0.0711470i
$253$	−32.5433	+	10.5740i	−2.04598	+	0.664780i
$254$	7.22574	+	1.53588i	0.453383	+	0.0963695i
$255$	11.4740	−	25.9575i	0.718529	−	1.62552i
$256$	16.1561	−	3.43408i	1.00975	−	0.214630i
$257$	−19.3884	+	11.1939i	−1.20941	+	0.698255i	−0.962631	−	0.270816i	$-0.912707\pi$
$257$	−19.3884	+	11.1939i	−1.20941	+	0.698255i	−0.246782	+	0.969071i	$0.579373\pi$
$258$	−6.82092	+	13.8778i	−0.424652	+	0.863994i
$259$	0.265922	+	2.53008i	0.0165236	+	0.157211i
$260$	−4.58129	+	3.62162i	−0.284119	+	0.224603i
$261$	−6.93877	−	8.99332i	−0.429499	−	0.556673i
$262$	−1.83055	−	2.51954i	−0.113092	−	0.155657i
$263$	−15.2147	+	1.59913i	−0.938179	+	0.0986065i	−0.561260	−	0.827640i	$-0.689683\pi$
$263$	−15.2147	+	1.59913i	−0.938179	+	0.0986065i	−0.376919	+	0.926246i	$0.623016\pi$
$264$	−21.6200	−	5.46028i	−1.33062	−	0.336057i
$265$	7.37423	+	11.6526i	0.452995	+	0.715813i
$266$	0.327273	+	0.145711i	0.0200664	+	0.00893413i
$267$	5.52287	+	8.24190i	0.337994	+	0.504396i
$268$	−12.2574	−	7.07679i	−0.748738	−	0.432284i
$269$	−4.29161	+	13.2082i	−0.261664	+	0.805320i	0.730779	+	0.682614i	$0.239157\pi$
$269$	−4.29161	+	13.2082i	−0.261664	+	0.805320i	−0.992443	+	0.122706i	$0.960843\pi$
$270$	9.73713	+	3.97264i	0.592583	+	0.241767i
$271$	7.08531	+	21.8064i	0.430402	+	1.32464i	0.897725	+	0.440555i	$0.145218\pi$
$271$	7.08531	+	21.8064i	0.430402	+	1.32464i	−0.467323	+	0.884087i	$0.654782\pi$
$272$	−0.371991	+	1.75008i	−0.0225552	+	0.106114i
$273$	−3.09058	+	0.876058i	−0.187050	+	0.0530214i
$274$	7.32711	+	12.6909i	0.442647	+	0.766687i
$275$	−13.5636	+	17.7755i	−0.817915	+	1.07190i
$276$	14.5277	−	5.81829i	0.874464	−	0.350220i
$277$	1.31737	+	2.95886i	0.0791531	+	0.177781i	0.948787	−	0.315916i	$-0.102312\pi$
$277$	1.31737	+	2.95886i	0.0791531	+	0.177781i	−0.869634	+	0.493697i	$0.835645\pi$
$278$	5.30213	−	1.72277i	0.318000	−	0.103325i
$279$	14.0895	+	7.60169i	0.843516	+	0.455101i
$280$	2.99291	−	4.49230i	0.178860	−	0.268466i
$281$	9.91871	+	11.0158i	0.591701	+	0.657150i	0.962411	−	0.271599i	$-0.0875523\pi$
$281$	9.91871	+	11.0158i	0.591701	+	0.657150i	−0.370710	+	0.928749i	$0.620886\pi$
$282$	12.9332	+	1.85773i	0.770162	+	0.110626i
$283$	4.16230	+	19.5821i	0.247423	+	1.16403i	0.909860	+	0.414916i	$0.136189\pi$
$283$	4.16230	+	19.5821i	0.247423	+	1.16403i	−0.662436	+	0.749118i	$0.730478\pi$
$284$	4.06580	+	1.81021i	0.241261	+	0.107416i
$285$	1.67209	+	0.739110i	0.0990458	+	0.0437811i
$286$	−8.17832	+	3.64122i	−0.483594	+	0.215310i
$287$	3.22879	+	4.44405i	0.190589	+	0.262324i
$288$	16.3405	+	2.98375i	0.962873	+	0.175819i
$289$	29.6880	+	21.5696i	1.74636	+	1.26880i
$290$	6.86819	−	3.39854i	0.403314	−	0.199569i
$291$	2.81495	−	4.47455i	0.165015	−	0.262303i
$292$	1.84816	+	8.69490i	0.108155	+	0.508831i
$293$	22.9491	−	13.2497i	1.34070	−	0.774053i	0.353789	−	0.935325i	$-0.384893\pi$
$293$	22.9491	−	13.2497i	1.34070	−	0.774053i	0.986910	+	0.161272i	$0.0515598\pi$
$294$	−8.20060	+	5.49520i	−0.478269	+	0.320487i
$295$	−2.91986	+	17.1310i	−0.170001	+	0.997403i
$296$	−2.69911	−	8.30701i	−0.156883	−	0.482835i
$297$	−18.6734	−	13.8288i	−1.08354	−	0.802429i
$298$	5.13719	−	7.07074i	0.297590	−	0.409597i
$299$	8.46224	−	14.6570i	0.489384	−	0.847638i
$300$	5.64698	−	8.52533i	0.326028	−	0.492210i
$301$	4.13553	+	7.16295i	0.238368	+	0.412866i
$302$	−2.39231	−	0.251441i	−0.137662	−	0.0144688i
$303$	23.0022	−	19.1824i	1.32144	−	1.10200i
$304$	−0.112733	−	0.0239622i	−0.00646570	−	0.00137433i
$305$	−2.60320	−	3.29300i	−0.149059	−	0.188557i
$306$	−11.2264	+	16.4276i	−0.641770	+	0.939105i
$307$		−	13.8202i		−	0.788759i	−0.918948	−	0.394379i	$-0.870960\pi$
$307$		−	13.8202i		−	0.788759i	0.918948	−	0.394379i	$-0.129040\pi$
$308$	−3.29039	+	2.96268i	−0.187487	+	0.168814i
$309$	2.31470	+	4.38541i	0.131679	+	0.249477i
$310$	−6.89493	+	8.31303i	−0.391606	+	0.472148i
$311$	0.274114	−	2.60802i	0.0155436	−	0.147887i	−0.983997	−	0.178183i	$-0.942978\pi$
$311$	0.274114	−	2.60802i	0.0155436	−	0.147887i	0.999541	+	0.0302955i	$0.00964484\pi$
$312$	9.75383	−	5.14826i	0.552202	−	0.291463i
$313$	−4.13888	+	0.435013i	−0.233943	+	0.0245884i	−0.220775	−	0.975325i	$-0.570858\pi$
$313$	−4.13888	+	0.435013i	−0.233943	+	0.0245884i	−0.0131686	+	0.999913i	$0.504192\pi$
$314$	5.84117	+	4.24386i	0.329636	+	0.239495i
$315$	4.66446	−	3.14374i	0.262812	−	0.177130i
$316$	−5.30629	+	3.85524i	−0.298502	+	0.216874i
$317$	6.47159	−	5.82704i	0.363481	−	0.327279i	−0.467072	−	0.884219i	$-0.654691\pi$
$317$	6.47159	−	5.82704i	0.363481	−	0.327279i	0.830553	+	0.556940i	$0.188025\pi$
$318$	−3.59444	−	8.97496i	−0.201566	−	0.503291i
$319$	−16.5619	+	3.52034i	−0.927289	+	0.197101i
$320$	−4.54167	+	11.4285i	−0.253887	+	0.638874i
$321$	4.80780	−	13.0855i	0.268345	−	0.730361i
$322$	−1.20742	+	5.68047i	−0.0672869	+	0.316560i
$323$	−2.03310	+	2.79832i	−0.113125	+	0.155703i
$324$	8.94319	+	5.74060i	0.496844	+	0.318922i
$325$	−0.897412	−	11.0226i	−0.0497795	−	0.611423i
$326$	6.63812	−	11.4976i	0.367651	−	0.636791i
$327$	−5.22370	+	1.48071i	−0.288871	+	0.0818835i
$328$	−14.0157	−	12.6198i	−0.773885	−	0.696809i
$329$	4.67636	−	5.19362i	0.257816	−	0.286334i
$330$	11.6214	−	10.5203i	0.639735	−	0.579125i
$331$	8.01109	+	8.89722i	0.440329	+	0.489035i	0.921931	−	0.387355i	$-0.126611\pi$
$331$	8.01109	+	8.89722i	0.440329	+	0.489035i	−0.481601	+	0.876391i	$0.659945\pi$
$332$		−	7.49597i		−	0.411395i
$333$	0.690065	−	9.07560i	0.0378153	−	0.497340i
$334$	−0.598591	+	0.434902i	−0.0327534	+	0.0237968i
$335$	24.0227	−	11.8870i	1.31250	−	0.649454i
$336$	−0.247109	+	0.254338i	−0.0134809	+	0.0138753i
$337$	1.91631	−	4.30411i	0.104388	−	0.234460i	−0.853798	−	0.520604i	$-0.825707\pi$
$337$	1.91631	−	4.30411i	0.104388	−	0.234460i	0.958187	+	0.286144i	$0.0923735\pi$
$338$	−2.98483	+	6.70404i	−0.162353	+	0.364652i
$339$	3.22292	−	3.31721i	0.175045	−	0.180166i
$340$	13.5193	+	13.8406i	0.733188	+	0.750611i
$341$	19.3063	−	14.0268i	1.04549	−	0.759595i
$342$	−1.05820	−	0.723161i	−0.0572211	−	0.0391041i
$343$			11.1497i			0.602028i
$344$	−19.0017	−	21.1035i	−1.02450	−	1.13782i
$345$	−6.08405	+	29.0043i	−0.327554	+	1.56154i
$346$	6.33564	−	7.03644i	0.340606	−	0.378281i
$347$	0.455107	+	0.409780i	0.0244314	+	0.0219982i	0.681256	−	0.732045i	$-0.261434\pi$
$347$	0.455107	+	0.409780i	0.0244314	+	0.0219982i	−0.656824	+	0.754044i	$0.728101\pi$
$348$	7.45021	−	2.11184i	0.399373	−	0.113206i
$349$	−16.1011	+	27.8879i	−0.861873	+	1.49281i	0.00824622	+	0.999966i	$0.497375\pi$
$349$	−16.1011	+	27.8879i	−0.861873	+	1.49281i	−0.870119	+	0.492842i	$0.835958\pi$
$350$	1.46163	+	3.50195i	0.0781276	+	0.187187i
$351$	11.4404	−	1.09711i	0.610644	−	0.0585596i
$352$	14.5537	−	20.0314i	0.775714	−	1.06768i
$353$	1.90647	−	8.96923i	0.101471	−	0.477384i	−0.897842	−	0.440318i	$-0.854866\pi$
$353$	1.90647	−	8.96923i	0.101471	−	0.477384i	0.999313	−	0.0370656i	$-0.0118010\pi$
$354$	4.20178	−	11.4361i	0.223322	−	0.607821i
$355$	−7.12180	+	4.50696i	−0.377986	+	0.239205i
$356$	−6.61579	+	1.40623i	−0.350636	+	0.0745300i
$357$	3.95679	+	9.87970i	0.209415	+	0.522889i
$358$	7.87410	−	7.08988i	0.416159	−	0.374712i
$359$	−2.75016	+	1.99811i	−0.145148	+	0.105456i	−0.657990	−	0.753027i	$-0.728593\pi$
$359$	−2.75016	+	1.99811i	−0.145148	+	0.105456i	0.512841	+	0.858483i	$0.328593\pi$
$360$	−13.4207	+	13.8874i	−0.707331	+	0.731929i
$361$	15.1911	+	11.0370i	0.799530	+	0.580892i
$362$	19.3584	−	2.03465i	1.01746	−	0.106939i
$363$	−13.7822	+	7.27449i	−0.723377	+	0.381812i
$364$	0.228912	−	2.17795i	0.0119982	−	0.114156i
$365$	−15.6435	−	6.21667i	−0.818817	−	0.325396i
$366$	1.37373	+	2.60266i	0.0718061	+	0.136043i
$367$	−4.65488	+	4.19127i	−0.242983	+	0.218783i	−0.781620	−	0.623755i	$-0.785606\pi$
$367$	−4.65488	+	4.19127i	−0.242983	+	0.218783i	0.538637	+	0.842538i	$0.318939\pi$
$368$		−	1.86831i		−	0.0973922i
$369$	−8.50781	−	17.7160i	−0.442899	−	0.922258i
$370$	5.91200	+	1.65875i	0.307350	+	0.0862344i
$371$	−5.05819	−	1.07515i	−0.262608	−	0.0558191i
$372$	−8.38191	+	6.98997i	−0.434582	+	0.362413i
$373$	32.7403	+	3.44114i	1.69523	+	0.178176i	0.902290	−	0.431129i	$-0.141884\pi$
$373$	32.7403	+	3.44114i	1.69523	+	0.178176i	0.792937	+	0.609304i	$0.208551\pi$
$374$	14.8296	+	25.6856i	0.766820	+	1.32817i
$375$	7.50661	+	17.8508i	0.387640	+	0.921811i
$376$	−11.9974	+	20.7800i	−0.618717	+	1.07165i
$377$	4.92248	−	6.77522i	0.253521	−	0.348942i
$378$	−3.61714	+	1.57111i	−0.186045	+	0.0808092i
$379$	−7.76357	−	23.8938i	−0.398788	−	1.22734i	−0.925972	−	0.377592i	$-0.876752\pi$
$379$	−7.76357	−	23.8938i	−0.398788	−	1.22734i	0.527184	−	0.849751i	$-0.323248\pi$
$380$	−0.891558	+	0.870863i	−0.0457359	+	0.0446743i
$381$	−11.7436	+	7.86936i	−0.601643	+	0.403159i
$382$	−19.3915	+	11.1957i	−0.992156	+	0.572821i
$383$	6.91221	+	32.5194i	0.353197	+	1.66166i	0.692827	+	0.721104i	$0.256365\pi$
$383$	6.91221	+	32.5194i	0.353197	+	1.66166i	−0.339630	+	0.940559i	$0.610302\pi$
$384$	−5.62229	+	8.93701i	−0.286911	+	0.456065i
$385$	−1.21433	−	8.29629i	−0.0618879	−	0.422818i
$386$	13.4183	+	9.74897i	0.682974	+	0.496209i
$387$	−9.95179	−	27.8680i	−0.505878	−	1.41661i
$388$	2.11829	+	2.91558i	0.107540	+	0.148016i
$389$	3.78655	−	1.68588i	0.191986	−	0.0854776i	−0.308492	−	0.951227i	$-0.599824\pi$
$389$	3.78655	−	1.68588i	0.191986	−	0.0854776i	0.500478	+	0.865749i	$0.333158\pi$
$390$	−0.789830	+	7.71305i	−0.0399946	+	0.390566i
$391$	−51.2236	−	22.8062i	−2.59049	−	1.15336i
$392$	−3.76910	−	17.7322i	−0.190368	−	0.895612i
$393$	5.89917	+	0.847357i	0.297574	+	0.0427435i
$394$	−2.90129	−	3.22220i	−0.146165	−	0.162332i
$395$	−0.504369	−	12.4105i	−0.0253776	−	0.624438i
$396$	13.4846	−	8.31265i	0.677629	−	0.417726i
$397$	9.19710	−	2.98832i	0.461589	−	0.149979i	−0.0689854	−	0.997618i	$-0.521976\pi$
$397$	9.19710	−	2.98832i	0.461589	−	0.149979i	0.530575	+	0.847638i	$0.321976\pi$
$398$	−2.54131	−	5.70788i	−0.127384	−	0.286110i
$399$	−0.636413	+	0.254881i	−0.0318605	+	0.0127600i
$400$	−0.694189	−	1.00424i	−0.0347094	−	0.0502119i
$401$	6.85771	+	11.8779i	0.342458	+	0.593154i	0.984889	−	0.173189i	$-0.0554073\pi$
$401$	6.85771	+	11.8779i	0.342458	+	0.593154i	−0.642431	+	0.766344i	$0.722074\pi$
$402$	−18.0789	+	5.12464i	−0.901691	+	0.255594i
$403$	−2.45403	+	11.5453i	−0.122244	+	0.575112i
$404$	6.30966	+	19.4191i	0.313918	+	0.966139i
$405$	−18.4371	+	8.06685i	−0.916146	+	0.400845i
$406$	−0.887999	+	2.73298i	−0.0440706	+	0.135635i
$407$	−11.7496	−	6.78366i	−0.582408	−	0.336253i
$408$	−20.3407	−	30.3548i	−1.00701	−	1.50279i
$409$	11.6290	+	5.17756i	0.575017	+	0.256014i	0.673577	−	0.739117i	$-0.264757\pi$
$409$	11.6290	+	5.17756i	0.575017	+	0.256014i	−0.0985600	+	0.995131i	$0.531424\pi$
$410$	12.8460	−	3.28092i	0.634419	−	0.162033i
$411$	−27.1893	−	6.86686i	−1.34115	−	0.338717i
$412$	−3.36204	+	0.353364i	−0.165636	+	0.0174090i
$413$	−3.83043	−	5.27214i	−0.188483	−	0.259425i
$414$	7.90018	−	19.2166i	0.388273	−	0.944446i
$415$	11.8135	+	7.87049i	0.579901	+	0.386347i
$416$	1.28011	+	12.1795i	0.0627627	+	0.597147i
$417$	−4.70590	+	9.57460i	−0.230449	+	0.468870i
$418$	−1.65457	+	0.955265i	−0.0809275	+	0.0467235i
$419$	16.6996	−	3.54961i	0.815830	−	0.173410i	0.218945	−	0.975737i	$-0.429738\pi$
$419$	16.6996	−	3.54961i	0.815830	−	0.173410i	0.596885	+	0.802327i	$0.296405\pi$
$420$	0.807305	+	3.74876i	0.0393925	+	0.182921i
$421$	−37.6190	−	7.99617i	−1.83344	−	0.389710i	−0.844202	−	0.536025i	$-0.819925\pi$
$421$	−37.6190	−	7.99617i	−1.83344	−	0.389710i	−0.989238	+	0.146316i	$0.953258\pi$
$422$	−8.57255	+	2.78539i	−0.417305	+	0.135591i
$423$	−19.7963	+	15.2738i	−0.962531	+	0.742638i
$424$	17.7546			0.862238
$425$	−36.0073	+	6.77404i	−1.74661	+	0.328589i
$426$	5.48529	−	2.19684i	0.265763	−	0.106437i
$427$	1.56550	+	0.164541i	0.0757598	+	0.00796268i
$428$	7.06272	+	6.35930i	0.341389	+	0.307388i
$429$	5.90821	−	16.0805i	0.285251	−	0.776375i
$430$	19.7528	−	2.89121i	0.952562	−	0.139427i
$431$	−6.54202	+	20.1343i	−0.315118	+	0.969834i	0.660588	+	0.750749i	$0.270307\pi$
$431$	−6.54202	+	20.1343i	−0.315118	+	0.969834i	−0.975706	+	0.219085i	$0.929693\pi$
$432$	1.03316	−	0.736343i	0.0497080	−	0.0354273i
$433$	32.3863	+	10.5229i	1.55638	+	0.505700i	0.955839	−	0.293891i	$-0.0949502\pi$
$433$	32.3863	+	10.5229i	1.55638	+	0.505700i	0.600545	+	0.799591i	$0.294950\pi$
$434$	−0.423350	−	4.02790i	−0.0203214	−	0.193346i
$435$	−4.49423	+	13.9587i	−0.215482	+	0.669269i
$436$	0.386907	−	3.68117i	0.0185295	−	0.176296i
$437$	1.46909	−	3.29963i	0.0702761	−	0.157843i
$438$	9.98942	+	6.28436i	0.477313	+	0.300278i
$439$	−2.57712	+	1.14741i	−0.122999	+	0.0547628i	−0.467314	−	0.884092i	$-0.654778\pi$
$439$	−2.57712	+	1.14741i	−0.122999	+	0.0547628i	0.344314	+	0.938854i	$0.388111\pi$
$440$	10.0003	+	26.9949i	0.476746	+	1.28693i
$441$	3.39330	−	18.5834i	0.161586	−	0.884923i
$442$	−13.9516	−	4.53316i	−0.663611	−	0.215620i
$443$	19.8764	+	11.4756i	0.944354	+	0.545223i	0.891323	−	0.453370i	$-0.149778\pi$
$443$	19.8764	+	11.4756i	0.944354	+	0.545223i	0.0530318	+	0.998593i	$0.483112\pi$
$444$	5.56868	+	2.73700i	0.264278	+	0.129892i
$445$	4.73015	−	11.9028i	0.224231	−	0.564248i
$446$	2.09443	−	2.32610i	0.0991741	−	0.110144i
$447$	2.85424	+	16.4798i	0.135001	+	0.779467i
$448$	−1.87574	−	4.21298i	−0.0886204	−	0.199045i
$449$	−5.18972			−0.244918			−0.122459	−	0.992474i	$-0.539078\pi$
$449$	−5.18972			−0.244918			−0.122459	+	0.992474i	$0.539078\pi$
$450$	−2.89370	−	13.2646i	−0.136410	−	0.625299i
$451$	−29.2951			−1.37945
$452$	1.28245	+	2.88044i	0.0603215	+	0.135484i
$453$	3.53527	−	2.94819i	0.166101	−	0.138518i
$454$	10.6534	−	11.8318i	0.499988	−	0.555293i
$455$	3.19205	+	2.64753i	0.149646	+	0.124118i
$456$	1.95534	−	1.31027i	0.0915672	−	0.0613589i
$457$	21.7514	+	12.5582i	1.01749	+	0.587447i	0.913375	−	0.407119i	$-0.133466\pi$
$457$	21.7514	+	12.5582i	1.01749	+	0.587447i	0.104112	+	0.994566i	$0.466800\pi$
$458$	−19.7657	−	6.42228i	−0.923593	−	0.300093i
$459$	−7.57674	−	37.3148i	−0.353652	−	1.74171i
$460$	−16.8136	−	11.2017i	−0.783940	−	0.522284i
$461$	35.9821	−	16.0203i	1.67585	−	0.746138i	0.675895	−	0.736998i	$-0.263757\pi$
$461$	35.9821	−	16.0203i	1.67585	−	0.746138i	0.999958	−	0.00913973i	$-0.00290931\pi$
$462$	−0.223001	+	5.87419i	−0.0103749	+	0.273292i
$463$	7.23651	−	16.2535i	0.336309	−	0.755363i	−0.663664	−	0.748031i	$-0.731000\pi$
$463$	7.23651	−	16.2535i	0.336309	−	0.755363i	0.999973	−	0.00733177i	$-0.00233379\pi$
$464$	0.0966347	−	0.919417i	0.00448615	−	0.0426829i
$465$	−2.21534	−	20.5489i	−0.102734	−	0.952933i
$466$	0.0710100	+	0.675615i	0.00328947	+	0.0312972i
$467$	−10.7738	−	3.50061i	−0.498550	−	0.161989i	0.0489385	−	0.998802i	$-0.484416\pi$
$467$	−10.7738	−	3.50061i	−0.498550	−	0.161989i	−0.547489	+	0.836813i	$0.684416\pi$
$468$	−2.20535	+	7.51826i	−0.101942	+	0.347532i
$469$	−3.10592	+	9.55905i	−0.143418	+	0.441396i
$470$	−7.48096	−	15.1185i	−0.345071	−	0.697362i
$471$	−13.6140	+	2.35790i	−0.627302	+	0.108646i
$472$	16.6273	+	14.9713i	0.765333	+	0.689109i
$473$	−43.8682	−	4.61074i	−2.01706	−	0.212002i
$474$	−1.23812	+	8.61956i	−0.0568685	+	0.395910i
$475$	−0.436358	−	2.31945i	−0.0200215	−	0.106424i
$476$	−7.25535			−0.332549
$477$	17.1115	+	7.03474i	0.783483	+	0.322099i
$478$	−0.532211	+	0.172926i	−0.0243428	+	0.00790944i
$479$	25.0863	+	5.33226i	1.14622	+	0.243637i	0.741597	−	0.670845i	$-0.234069\pi$
$479$	25.0863	+	5.33226i	1.14622	+	0.243637i	0.404626	+	0.914482i	$0.367402\pi$
$480$	−8.77452	−	19.5669i	−0.400500	−	0.893104i
$481$	6.56384	−	1.39519i	0.299285	−	0.0636151i
$482$	6.28194	−	3.62688i	0.286134	−	0.165200i
$483$	−6.18645	−	9.23216i	−0.281493	−	0.420078i
$484$	−1.11053	−	10.5660i	−0.0504786	−	0.480272i
$485$	−6.81902	+	0.277130i	−0.309636	+	0.0125838i
$486$	13.7403	−	3.20498i	0.623274	−	0.145381i
$487$	5.42092	+	7.46126i	0.245645	+	0.338102i	0.913980	−	0.405759i	$-0.132993\pi$
$487$	5.42092	+	7.46126i	0.245645	+	0.338102i	−0.668335	+	0.743861i	$0.732993\pi$
$488$	−5.37492	+	0.564926i	−0.243311	+	0.0255730i
$489$	6.92863	+	24.4430i	0.313324	+	1.10535i
$490$	11.8432	+	4.70645i	0.535021	+	0.212616i
$491$	36.2576	+	16.1429i	1.63628	+	0.728519i	0.999109	−	0.0422022i	$-0.0134374\pi$
$491$	36.2576	+	16.1429i	1.63628	+	0.728519i	0.637172	+	0.770722i	$0.280104\pi$
$492$	13.3681	−	0.893989i	0.602682	−	0.0403041i
$493$	−24.0282	−	13.8727i	−1.08218	−	0.624794i
$494$	0.292009	−	0.898711i	0.0131381	−	0.0404349i
$495$	−1.05784	+	29.9795i	−0.0475464	+	1.34748i
$496$	0.402639	+	1.23919i	0.0180790	+	0.0556415i
$497$	0.657108	−	3.09145i	0.0294753	−	0.138671i
$498$	−7.13790	−	6.93502i	−0.319857	−	0.310766i
$499$	−18.0331	−	31.2343i	−0.807273	−	1.39824i	−0.914746	−	0.404029i	$-0.867609\pi$
$499$	−18.0331	−	31.2343i	−0.807273	−	1.39824i	0.107474	−	0.994208i	$-0.465724\pi$
$500$	−13.1997	+	0.226201i	−0.590307	+	0.0101160i
$501$	0.201315	−	1.40152i	0.00899409	−	0.0626154i
$502$	−4.57657	−	10.2791i	−0.204262	−	0.458780i
$503$	−35.0283	+	11.3814i	−1.56184	+	0.507471i	−0.957298	−	0.289105i	$-0.906642\pi$
$503$	−35.0283	+	11.3814i	−1.56184	+	0.507471i	−0.604539	+	0.796576i	$0.706642\pi$
$504$	−0.208767	−	7.23915i	−0.00929921	−	0.322457i
$505$	−37.2291	−	10.4455i	−1.65667	−	0.464819i
$506$	−20.7236	−	23.0159i	−0.921275	−	1.02318i
$507$	−5.22113	−	13.0366i	−0.231878	−	0.578977i
$508$	−2.00369	−	9.42662i	−0.0888994	−	0.418239i
$509$	−18.3752	−	8.18115i	−0.814464	−	0.362623i	−0.0431431	−	0.999069i	$-0.513737\pi$
$509$	−18.3752	−	8.18115i	−0.814464	−	0.362623i	−0.771321	+	0.636446i	$0.780404\pi$
$510$	25.6871	−	0.0686807i	1.13744	−	0.00304123i
$511$	5.76677	−	2.56753i	0.255107	−	0.113581i
$512$	1.62098	+	2.23108i	0.0716377	+	0.0986008i
$513$	2.40368	−	0.488064i	0.106125	−	0.0215486i
$514$	−16.3933	−	11.9104i	−0.723077	−	0.525347i
$515$	2.97312	−	5.66951i	0.131011	−	0.249829i
$516$	20.1589	+	0.765289i	0.887447	+	0.0336900i
$517$	7.74908	+	36.4565i	0.340804	+	1.60336i
$518$	−1.99411	+	1.15130i	−0.0876160	+	0.0505851i
$519$	1.20902	+	18.0789i	0.0530702	+	0.793577i
$520$	−12.6099	−	6.61268i	−0.552979	−	0.289985i
$521$	−10.9309	−	33.6419i	−0.478892	−	1.47388i	−0.840636	−	0.541601i	$-0.817818\pi$
$521$	−10.9309	−	33.6419i	−0.478892	−	1.47388i	0.361744	−	0.932278i	$-0.382182\pi$
$522$	4.88172	−	9.04813i	0.213667	−	0.396026i
$523$	−12.6736	+	17.4437i	−0.554177	+	0.762759i	−0.990572	−	0.136997i	$-0.956255\pi$
$523$	−12.6736	+	17.4437i	−0.554177	+	0.762759i	0.436395	+	0.899755i	$0.356255\pi$
$524$	−2.03145	+	3.51858i	−0.0887444	+	0.153710i
$525$	−6.75560	−	2.66377i	−0.294839	−	0.116256i
$526$	−6.92336	−	11.9916i	−0.301873	−	0.522859i
$527$	38.8902	+	4.08752i	1.69408	+	0.178055i
$528$	−0.322738	−	1.86342i	−0.0140454	−	0.0810950i
$529$	34.7742	+	7.39149i	1.51192	+	0.321369i
$530$	−6.92024	+	10.3872i	−0.300596	+	0.451190i
$531$	10.0931	+	21.0171i	0.438005	+	0.912066i
$532$		−	0.467362i		−	0.0202627i
$533$	10.7678	−	9.69540i	0.466407	−	0.419955i
$534$	−4.78165	+	7.60077i	−0.206922	+	0.328917i
$535$	−17.4377	+	4.45365i	−0.753898	+	0.192548i
$536$	3.60713	−	34.3196i	0.155804	−	1.48238i
$537$	−0.769194	+	20.2618i	−0.0331932	+	0.874360i
$538$	−12.5012	+	1.31393i	−0.538964	+	0.0566474i
$539$	−22.7809	−	16.5513i	−0.981244	−	0.712916i
$540$	−0.432153	−	13.7127i	−0.0185969	−	0.590101i
$541$	−4.45342	+	3.23560i	−0.191467	+	0.139109i	−0.679389	−	0.733778i	$-0.737755\pi$
$541$	−4.45342	+	3.23560i	−0.191467	+	0.139109i	0.487922	+	0.872887i	$0.337755\pi$
$542$	−15.4223	+	13.8863i	−0.662443	+	0.596467i
$543$	−23.0220	+	29.2830i	−0.987969	+	1.25665i
$544$	39.6865	−	8.43563i	1.70155	−	0.361675i
$545$	5.39521	+	4.47485i	0.231105	+	0.191682i
$546$	−1.86213	−	2.23295i	−0.0796919	−	0.0955612i
$547$	−0.799854	+	3.76302i	−0.0341993	+	0.160895i	−0.991933	−	0.126760i	$-0.959542\pi$
$547$	−0.799854	+	3.76302i	−0.0341993	+	0.160895i	0.957734	+	0.287655i	$0.0928756\pi$
$548$	11.2371	−	15.4666i	0.480026	−	0.660700i
$549$	−5.40408	−	1.58519i	−0.230641	−	0.0676544i
$550$	−19.6910	−	4.67126i	−0.839626	−	0.199183i
$551$	0.893625	−	1.54780i	0.0380697	−	0.0659387i
$552$	27.3664	+	26.5885i	1.16479	+	1.13168i
$553$	3.46137	+	3.11663i	0.147193	+	0.132533i
$554$	−1.96157	+	2.17854i	−0.0833391	+	0.0925574i
$555$	−10.1604	+	5.90237i	−0.431284	+	0.250542i
$556$	−4.86663	−	5.40494i	−0.206391	−	0.229221i
$557$			13.2726i			0.562377i	0.959653	+	0.281188i	$0.0907286\pi$
$557$			13.2726i			0.562377i	−0.959653	+	0.281188i	$0.909271\pi$
$558$	−1.09859	+	14.4484i	−0.0465069	+	0.611650i
$559$	17.6503	−	12.8237i	0.746530	−	0.542386i
$560$	0.451295	+	0.0769204i	0.0190707	+	0.00325048i
$561$	−55.0294	−	13.8981i	−2.32334	−	0.586777i
$562$	−5.45702	+	12.2567i	−0.230191	+	0.517017i
$563$	−0.0319966	+	0.0718656i	−0.00134850	+	0.00302877i	−0.914218	−	0.405222i	$-0.867194\pi$
$563$	−0.0319966	+	0.0718656i	−0.00134850	+	0.00302877i	0.912870	+	0.408250i	$0.133861\pi$
$564$	−4.64864	−	16.3996i	−0.195743	−	0.690548i
$565$	−5.88603	−	1.00324i	−0.247627	−	0.0422065i
$566$	−14.6592	+	10.6505i	−0.616172	+	0.447675i
$567$	2.66710	−	7.05968i	0.112008	−	0.296479i
$568$			10.8512i			0.455306i
$569$	8.80492	+	9.77886i	0.369122	+	0.409951i	0.898878	−	0.438199i	$-0.144383\pi$
$569$	8.80492	+	9.77886i	0.369122	+	0.409951i	−0.529757	+	0.848150i	$0.677717\pi$
$570$	0.00442415	+	1.65466i	0.000185307	+	0.0693062i
$571$	27.8854	−	30.9699i	1.16697	−	1.29605i	0.219716	−	0.975564i	$-0.429487\pi$
$571$	27.8854	−	30.9699i	1.16697	−	1.29605i	0.947253	−	0.320486i	$-0.103846\pi$
$572$	8.67923	+	7.81482i	0.362897	+	0.326754i
$573$	10.4924	−	41.5448i	0.438328	−	1.73556i
$574$	−2.48593	+	4.30576i	−0.103761	+	0.179719i
$575$	35.3074	−	14.7365i	1.47242	−	0.614554i
$576$	3.89421	+	16.0332i	0.162259	+	0.668050i
$577$	−7.07463	+	9.73739i	−0.294521	+	0.405373i	−0.930476	−	0.366353i	$-0.880606\pi$
$577$	−7.07463	+	9.73739i	−0.294521	+	0.405373i	0.635955	+	0.771726i	$0.280606\pi$
$578$	−6.90559	+	32.4883i	−0.287235	+	1.35133i
$579$	−31.2741	+	5.41655i	−1.29971	+	0.225104i
$580$	−7.69482	−	6.38218i	−0.319510	−	0.265006i
$581$	−5.20684	+	1.10675i	−0.216016	+	0.0459156i
$582$	4.73609	+	0.680292i	0.196317	+	0.0281990i
$583$	20.4946	−	18.4534i	0.848798	−	0.764261i
$584$	−17.5339	+	12.7391i	−0.725558	+	0.527149i
$585$	−9.53307	−	11.3695i	−0.394144	−	0.470070i
$586$	19.4040	+	14.0978i	0.801570	+	0.582375i
$587$	−30.1731	+	3.17132i	−1.24538	+	0.130894i	−0.704191	−	0.710010i	$-0.748690\pi$
$587$	−30.1731	+	3.17132i	−1.24538	+	0.130894i	−0.541184	+	0.840904i	$0.682024\pi$
$588$	10.9006	+	6.85760i	0.449534	+	0.282803i
$589$	−0.263302	+	2.50516i	−0.0108492	+	0.103223i
$590$	−15.2397	+	3.89227i	−0.627408	+	0.160242i
$591$	8.29143	+	0.314766i	0.341064	+	0.0129477i
$592$	0.550503	−	0.495675i	0.0226255	−	0.0203721i
$593$			29.9806i			1.23115i	0.788077	+	0.615577i	$0.211077\pi$
$593$			29.9806i			1.23115i	−0.788077	+	0.615577i	$0.788923\pi$
$594$	4.55998	−	20.5311i	0.187098	−	0.842402i
$595$	7.61786	−	11.4343i	0.312302	−	0.468760i
$596$	−11.1528	−	2.37061i	−0.456838	−	0.0971039i
$597$	11.2230	+	4.12351i	0.459328	+	0.168764i
$598$	15.2345	+	1.60121i	0.622984	+	0.0654783i
$599$	−8.11907	−	14.0626i	−0.331736	−	0.574584i	0.651116	−	0.758978i	$-0.274301\pi$
$599$	−8.11907	−	14.0626i	−0.331736	−	0.574584i	−0.982852	+	0.184394i	$0.940968\pi$
$600$	24.5890	+	4.12342i	1.00384	+	0.168338i
$601$	20.1259	−	34.8591i	0.820953	−	1.42193i	−0.0840201	−	0.996464i	$-0.526776\pi$
$601$	20.1259	−	34.8591i	0.820953	−	1.42193i	0.904973	−	0.425468i	$-0.139891\pi$
$602$	−4.40026	+	6.05644i	−0.179341	+	0.246842i
$603$	17.0746	−	31.6473i	0.695333	−	1.28878i
$604$	0.969747	+	2.98457i	0.0394584	+	0.121441i
$605$	17.8178	+	9.34372i	0.724395	+	0.379876i
$606$	24.3290	+	11.9577i	0.988299	+	0.485748i
$607$	−6.31935	+	3.64848i	−0.256494	+	0.148087i	−0.622734	−	0.782433i	$-0.713978\pi$
$607$	−6.31935	+	3.64848i	−0.256494	+	0.148087i	0.366240	+	0.930520i	$0.380645\pi$
$608$	0.543391	+	2.55645i	0.0220374	+	0.103678i
$609$	−2.56691	−	4.86325i	−0.104017	−	0.197069i
$610$	1.76449	−	3.36475i	0.0714421	−	0.136235i
$611$	−14.9138	−	10.8355i	−0.603348	−	0.438358i
$612$	25.5355	+	4.66274i	1.03221	+	0.188480i
$613$	−0.622220	−	0.856413i	−0.0251312	−	0.0345902i	0.796266	−	0.604946i	$-0.206805\pi$
$613$	−0.622220	−	0.856413i	−0.0251312	−	0.0345902i	−0.821398	+	0.570356i	$0.806805\pi$
$614$	11.4273	−	5.08774i	0.461166	−	0.205324i
$615$	−12.6271	+	22.0065i	−0.509176	+	0.887389i
$616$	−9.86200	−	4.39085i	−0.397351	−	0.176912i
$617$	3.66891	+	17.2609i	0.147705	+	0.694896i	0.988211	+	0.153095i	$0.0489241\pi$
$617$	3.66891	+	17.2609i	0.147705	+	0.694896i	−0.840507	+	0.541801i	$0.817743\pi$
$618$	−2.77396	+	3.52836i	−0.111585	+	0.141931i
$619$	−2.13614	−	2.37242i	−0.0858588	−	0.0953558i	0.698684	−	0.715430i	$-0.253769\pi$
$619$	−2.13614	−	2.37242i	−0.0858588	−	0.0953558i	−0.784543	+	0.620074i	$0.787102\pi$
$620$	13.5661	+	3.80630i	0.544828	+	0.152864i
$621$	15.8402	+	36.4687i	0.635647	+	1.46344i
$622$	2.25736	−	0.733461i	0.0905119	−	0.0294091i
$623$	1.95359	+	4.38783i	0.0782688	+	0.175795i
$624$	0.735338	+	0.578115i	0.0294371	+	0.0231431i
$625$	13.5027	−	21.0399i	0.540108	−	0.841596i
$626$	−1.88337	−	3.26210i	−0.0752747	−	0.130380i
$627$	0.895260	−	3.54478i	0.0357533	−	0.141565i
$628$	1.95837	−	9.21342i	0.0781476	−	0.367655i
$629$	−6.87006	−	21.1439i	−0.273927	−	0.843062i
$630$	4.31658	+	2.69949i	0.171977	+	0.107550i
$631$	−4.80577	+	14.7907i	−0.191315	+	0.588807i	0.808685	+	0.588242i	$0.200180\pi$
$631$	−4.80577	+	14.7907i	−0.191315	+	0.588807i	−1.00000		0.000564672i	$0.999820\pi$
$632$	−13.8492	−	7.99584i	−0.550891	−	0.318057i
$633$	7.60857	−	15.4803i	0.302413	−	0.615288i
$634$	7.20055	+	3.20589i	0.285970	+	0.127322i
$635$	16.9599	+	6.73984i	0.673035	+	0.267462i
$636$	−8.78907	+	9.04619i	−0.348509	+	0.358705i
$637$	13.8512	−	1.45582i	0.548805	−	0.0576817i
$638$	−9.00789	−	12.3983i	−0.356626	−	0.490853i
$639$	−4.29948	+	10.4582i	−0.170085	+	0.413719i
$640$	13.6196	−	0.553511i	0.538363	−	0.0218794i
$641$	−2.14205	−	20.3802i	−0.0846059	−	0.804971i	−0.951742	−	0.306900i	$-0.900708\pi$
$641$	−2.14205	−	20.3802i	−0.0846059	−	0.804971i	0.867136	−	0.498071i	$-0.165958\pi$
$642$	12.5897	−	0.841933i	0.496877	−	0.0332284i
$643$	−31.3554	+	18.1031i	−1.23654	+	0.713915i	−0.968385	−	0.249461i	$-0.919746\pi$
$643$	−31.3554	+	18.1031i	−1.23654	+	0.713915i	−0.268152	+	0.963376i	$0.586413\pi$
$644$	7.41067	−	1.57519i	0.292021	−	0.0620711i
$645$	−22.3722	+	30.9665i	−0.880905	+	1.21930i
$646$	−3.06227	−	0.650905i	−0.120483	−	0.0256095i
$647$	20.1587	−	6.54997i	0.792522	−	0.257506i	0.115344	−	0.993326i	$-0.463203\pi$
$647$	20.1587	−	6.54997i	0.792522	−	0.257506i	0.677178	+	0.735820i	$0.263203\pi$
$648$	−3.91757	+	25.6126i	−0.153897	+	1.00616i
$649$	34.7539			1.36421
$650$	8.78368	−	4.79987i	0.344524	−	0.188266i
$651$	6.09292	+	4.79019i	0.238800	+	0.187742i
$652$	−17.2251	−	1.81044i	−0.674589	−	0.0709022i
$653$	−15.1333	−	13.6261i	−0.592211	−	0.533229i	0.317615	−	0.948220i	$-0.397118\pi$
$653$	−15.1333	−	13.6261i	−0.592211	−	0.533229i	−0.909826	+	0.414991i	$0.863785\pi$
$654$	−3.14738	−	3.77412i	−0.123072	−	0.147580i
$655$	−3.41225	−	6.89591i	−0.133328	−	0.269445i
$656$	0.494277	−	1.52123i	0.0192983	−	0.0593939i
$657$	−21.9464	+	5.33043i	−0.856210	+	0.207960i
$658$	6.01591	+	1.95469i	0.234525	+	0.0762016i
$659$	4.35148	+	41.4016i	0.169510	+	1.61278i	0.666830	+	0.745210i	$0.267651\pi$
$659$	4.35148	+	41.4016i	0.169510	+	1.61278i	−0.497320	+	0.867567i	$0.665683\pi$
$660$	−18.7047	−	8.26802i	−0.728080	−	0.321832i
$661$	0.110203	−	1.04851i	0.00428640	−	0.0407823i	−0.992170	−	0.124898i	$-0.960140\pi$
$661$	0.110203	−	1.04851i	0.00428640	−	0.0407823i	0.996456	+	0.0841153i	$0.0268064\pi$
$662$	−4.40750	+	9.89941i	−0.171302	+	0.384751i
$663$	24.8265	−	13.1039i	0.964180	−	0.508913i
$664$	16.6962	−	7.43365i	0.647940	−	0.288481i
$665$	0.736552	+	0.490713i	0.0285623	+	0.0190290i
$666$	7.75822	−	2.77050i	0.300625	−	0.107355i
$667$	27.5544	+	8.95298i	1.06691	+	0.346661i
$668$	0.835944	+	0.482632i	0.0323436	+	0.0186736i
$669$	0.399677	+	5.97652i	0.0154524	+	0.231066i
$670$	18.6724	+	15.4872i	0.721379	+	0.598321i
$671$	−5.61725	+	6.23859i	−0.216851	+	0.240838i
$672$	7.54821	+	2.77332i	0.291178	+	0.106983i
$673$	4.37115	+	9.81776i	0.168495	+	0.378447i	0.977981	−	0.208692i	$-0.0669208\pi$
$673$	4.37115	+	9.81776i	0.168495	+	0.378447i	−0.809486	+	0.587139i	$0.800254\pi$
$674$	4.26434			0.164256
$675$	22.0647	+	13.7168i	0.849270	+	0.527959i
$676$	9.57371			0.368220
$677$	−3.63410	−	8.16233i	−0.139670	−	0.313704i	0.830144	−	0.557548i	$-0.188258\pi$
$677$	−3.63410	−	8.16233i	−0.139670	−	0.313704i	−0.969814	+	0.243845i	$0.921591\pi$
$678$	3.92933	+	1.44369i	0.150905	+	0.0554446i
$679$	1.71246	−	1.90188i	0.0657182	−	0.0729874i
$680$	−17.4211	+	43.8380i	−0.668068	+	1.68111i
$681$	2.03297	+	30.3998i	0.0779037	+	1.16492i
$682$	18.7055	+	10.7996i	0.716271	+	0.413539i
$683$	−17.0510	−	5.54019i	−0.652437	−	0.211990i	−0.0359484	−	0.999354i	$-0.511445\pi$
$683$	−17.0510	−	5.54019i	−0.652437	−	0.211990i	−0.616488	+	0.787364i	$0.711445\pi$
$684$	−0.300356	+	1.64490i	−0.0114844	+	0.0628942i
$685$	12.5764	+	33.9488i	0.480520	+	1.29712i
$686$	−9.21917	+	4.10464i	−0.351990	+	0.156716i
$687$	35.1725	−	18.5647i	1.34191	−	0.708288i
$688$	0.979583	−	2.20018i	0.0373463	−	0.0838811i
$689$	−1.42580	+	13.5656i	−0.0543188	+	0.516808i
$690$	−26.2221	+	5.64700i	−0.998258	+	0.214977i
$691$	−2.44521	−	23.2646i	−0.0930201	−	0.885027i	−0.937159	−	0.348903i	$-0.886554\pi$
$691$	−2.44521	−	23.2646i	−0.0930201	−	0.885027i	0.844139	−	0.536125i	$-0.180112\pi$
$692$	−11.7479	−	3.81712i	−0.446587	−	0.145105i
$693$	−7.76507	−	8.13936i	−0.294971	−	0.309189i
$694$	−0.171286	+	0.527163i	−0.00650191	+	0.0200108i
$695$	13.6279	−	1.99471i	0.516934	−	0.0756637i
$696$	12.0921	+	14.5000i	0.458350	+	0.549622i
$697$	−35.6741	−	32.1211i	−1.35125	−	1.21667i
$698$	−28.9867	−	3.04662i	−1.09716	−	0.115316i
$699$	−1.02199	−	0.803475i	−0.0386551	−	0.0303902i
$700$	3.39806	−	3.60020i	0.128434	−	0.136075i
$701$	28.7012			1.08403			0.542014	−	0.840369i	$-0.317662\pi$
$701$	28.7012			1.08403			0.542014	+	0.840369i	$0.317662\pi$
$702$	5.11881	+	9.05565i	0.193197	+	0.341784i
$703$	1.36201	−	0.442543i	0.0513691	−	0.0166908i
$704$	24.0568	+	5.11343i	0.906675	+	0.192720i
$705$	30.7263	+	9.89283i	1.15722	+	0.372586i
$706$	8.11808	−	1.72555i	0.305528	−	0.0649420i
$707$	12.5573	−	7.24996i	0.472266	−	0.272663i
$708$	−15.8591	+	1.06057i	−0.596022	+	0.0398587i
$709$	−1.02491	−	9.75136i	−0.0384913	−	0.366220i	−0.996765	−	0.0803685i	$-0.974390\pi$
$709$	−1.02491	−	9.75136i	−0.0384913	−	0.366220i	0.958274	−	0.285851i	$-0.0922764\pi$
$710$	−6.34840	−	4.22950i	−0.238251	−	0.158730i
$711$	−10.1795	−	13.1936i	−0.381760	−	0.494799i
$712$	−9.69297	−	13.3412i	−0.363260	−	0.499984i
$713$	−40.6101	+	4.26830i	−1.52086	+	0.159849i
$714$	−6.71241	+	6.90878i	−0.251206	+	0.258555i
$715$	−21.4289	+	5.47301i	−0.801394	+	0.204679i
$716$	−12.6279	−	5.62231i	−0.471927	−	0.210116i
$717$	0.472364	−	0.961068i	0.0176408	−	0.0358917i
$718$	−2.66459	−	1.53840i	−0.0994415	−	0.0574126i
$719$	−8.76828	+	26.9860i	−0.327002	+	1.00641i	0.643528	+	0.765423i	$0.277470\pi$
$719$	−8.76828	+	26.9860i	−0.327002	+	1.00641i	−0.970529	+	0.240984i	$0.922530\pi$
$720$	−1.53892	−	0.560755i	−0.0573520	−	0.0208981i
$721$	0.741844	+	2.28316i	0.0276277	+	0.0850293i
$722$	−3.53352	+	16.6239i	−0.131504	+	0.618678i
$723$	−3.39906	+	13.4586i	−0.126412	+	0.500529i
$724$	−12.6969	−	21.9918i	−0.471878	−	0.817317i
$725$	18.1374	−	5.42581i	0.673608	−	0.201509i
$726$	−11.0887	−	8.71781i	−0.411540	−	0.323548i
$727$	12.0187	+	26.9944i	0.445748	+	1.00117i	0.987061	+	0.160345i	$0.0512606\pi$
$727$	12.0187	+	26.9944i	0.445748	+	1.00117i	−0.541313	+	0.840821i	$0.682073\pi$
$728$	5.07810	−	1.64997i	0.188207	−	0.0611521i
$729$	−13.9240	+	23.1327i	−0.515702	+	0.856768i
$730$	−0.618691	−	15.2235i	−0.0228988	−	0.563445i
$731$	−48.3650	−	53.7148i	−1.78884	−	1.98671i
$732$	2.37292	−	3.01825i	0.0877055	−	0.111558i
$733$	9.34275	+	43.9542i	0.345082	+	1.62348i	0.718295	+	0.695739i	$0.244923\pi$
$733$	9.34275	+	43.9542i	0.345082	+	1.62348i	−0.373213	+	0.927746i	$0.621744\pi$
$734$	−5.17920	−	2.30593i	−0.191168	−	0.0851134i
$735$	−22.2527	+	9.97891i	−0.820803	+	0.368078i
$736$	−38.7047	+	17.2324i	−1.42667	+	0.635196i
$737$	−31.5066	−	43.3651i	−1.16056	−	1.59737i
$738$	11.5165	−	13.5567i	0.423927	−	0.499027i
$739$	−22.5119	−	16.3558i	−0.828113	−	0.601659i	0.0909119	−	0.995859i	$-0.471022\pi$
$739$	−22.5119	−	16.3558i	−0.828113	−	0.601659i	−0.919025	+	0.394200i	$0.871022\pi$
$740$	−1.16014	−	7.92610i	−0.0426478	−	0.291369i
$741$	0.844102	+	1.59923i	0.0310089	+	0.0587490i
$742$	−0.973124	−	4.57819i	−0.0357245	−	0.168071i
$743$	25.3004	−	14.6072i	0.928181	−	0.535886i	0.0419454	−	0.999120i	$-0.486644\pi$
$743$	25.3004	−	14.6072i	0.928181	−	0.535886i	0.886236	+	0.463234i	$0.153311\pi$
$744$	−23.8814	−	11.7377i	−0.875536	−	0.430325i
$745$	15.4461	−	15.0876i	0.565901	−	0.552766i
$746$	9.20764	+	28.3382i	0.337116	+	1.03754i
$747$	19.0369	−	0.548998i	0.696524	−	0.0200868i
$748$	22.7432	−	31.3033i	0.831574	−	1.14456i
$749$	3.37451	−	5.84482i	0.123302	−	0.213565i
$750$	−11.9965	+	12.7784i	−0.438051	+	0.466602i
$751$	−12.0975	−	20.9535i	−0.441445	−	0.764605i	0.556352	−	0.830947i	$-0.312201\pi$
$751$	−12.0975	−	20.9535i	−0.441445	−	0.764605i	−0.997797	+	0.0663417i	$0.978867\pi$
$752$	−2.02385	−	0.212715i	−0.0738021	−	0.00775691i
$753$	20.2112	+	7.42589i	0.736538	+	0.270615i
$754$	7.41427	+	1.57595i	0.270012	+	0.0573928i
$755$	−5.72182	−	1.60539i	−0.208238	−	0.0584263i
$756$	3.79179	+	3.47724i	0.137906	+	0.126466i
$757$			8.79376i			0.319615i	0.987148	+	0.159807i	$0.0510873\pi$
$757$			8.79376i			0.319615i	−0.987148	+	0.159807i	$0.948913\pi$
$758$	16.8986	−	15.2156i	0.613785	−	0.552655i
$759$	59.2248	+	2.24834i	2.14972	+	0.0816095i
$760$	−2.82387	−	1.12220i	−0.102433	−	0.0407065i
$761$	1.68020	−	15.9861i	0.0609073	−	0.579494i	−0.920925	−	0.389741i	$-0.872565\pi$
$761$	1.68020	−	15.9861i	0.0609073	−	0.579494i	0.981832	−	0.189753i	$-0.0607688\pi$
$762$	−10.8301	−	6.81322i	−0.392332	−	0.246817i
$763$	−2.61413	+	0.274757i	−0.0946380	+	0.00994686i
$764$	23.6326	+	17.1701i	0.854999	+	0.621193i
$765$	−34.1597	+	35.3476i	−1.23505	+	1.27800i
$766$	−24.3441	+	17.6870i	−0.879588	+	0.639058i
$767$	−12.7743	+	11.5020i	−0.461252	+	0.415313i
$768$	−28.3176	−	4.06755i	−1.02182	−	0.146775i
$769$	10.2458	−	2.17780i	0.369471	−	0.0785336i	−0.0194343	−	0.999811i	$-0.506187\pi$
$769$	10.2458	−	2.17780i	0.369471	−	0.0785336i	0.388906	+	0.921278i	$0.372853\pi$
$770$	6.41277	−	4.05826i	0.231100	−	0.146249i
$771$	38.2079	−	6.61746i	1.37602	−	0.238322i
$772$	4.49876	−	21.1650i	0.161914	−	0.761745i
$773$	7.92951	−	10.9140i	0.285205	−	0.392551i	−0.642244	−	0.766500i	$-0.721997\pi$
$773$	7.92951	−	10.9140i	0.285205	−	0.392551i	0.927449	+	0.373949i	$0.121997\pi$
$774$	19.3791	−	18.4880i	0.696568	−	0.664536i
$775$	−20.2425	+	17.3834i	−0.727134	+	0.624430i
$776$	−4.39338	+	7.60955i	−0.157713	+	0.273167i
$777$	1.07898	−	4.27222i	0.0387082	−	0.153265i
$778$	2.78795	+	2.51028i	0.0999529	+	0.0899980i
$779$	2.06912	−	2.29799i	0.0741339	−	0.0823340i
$780$	9.61153	−	3.15141i	0.344148	−	0.112839i
$781$	11.2783	+	12.5258i	0.403569	+	0.448209i
$782$		−	50.7503i		−	1.81483i
$783$	5.90891	+	18.7660i	0.211167	+	0.670643i
$784$	1.24384	−	0.903701i	0.0444228	−	0.0322750i
$785$	12.4639	+	12.7601i	0.444856	+	0.455428i
$786$	1.47107	+	5.18969i	0.0524714	+	0.185110i
$787$	−15.8943	+	35.6992i	−0.566571	+	1.27254i	0.372249	+	0.928133i	$0.378587\pi$
$787$	−15.8943	+	35.6992i	−0.566571	+	1.27254i	−0.938820	+	0.344407i	$0.888080\pi$
$788$	−2.30074	+	5.16754i	−0.0819603	+	0.184086i
$789$	25.6911	+	6.48847i	0.914627	+	0.230996i
$790$	10.0759	−	4.98581i	0.358486	−	0.177387i
$791$	1.81146	−	1.31610i	0.0644079	−	0.0467951i
$792$	31.8878	+	21.7917i	1.13308	+	0.774333i
$793$		−	4.15214i		−	0.147447i
$794$	5.85671	+	6.50453i	0.207847	+	0.230837i
$795$	−5.02839	−	23.3496i	−0.178339	−	0.828123i
$796$	−5.45418	+	6.05748i	−0.193318	+	0.214702i
$797$	−18.8840	−	17.0033i	−0.668907	−	0.602287i	0.263082	−	0.964774i	$-0.415261\pi$
$797$	−18.8840	−	17.0033i	−0.668907	−	0.602287i	−0.931989	+	0.362487i	$0.881928\pi$
$798$	−0.445037	−	0.432388i	−0.0157541	−	0.0153064i
$799$	−30.5369	+	52.8915i	−1.08032	+	1.87117i
$800$	−14.4014	+	23.6438i	−0.509166	+	0.835935i
$801$	−4.05582	−	16.6986i	−0.143305	−	0.590016i
$802$	−7.29669	+	10.0430i	−0.257655	+	0.354632i
$803$	−6.99931	+	32.9292i	−0.247000	+	1.16205i
$804$	15.7006	+	18.8272i	0.553719	+	0.663983i
$805$	−5.29848	+	13.3329i	−0.186747	+	0.469925i
$806$	−10.4497	+	2.22115i	−0.368074	+	0.0782366i
$807$	14.8670	−	18.9102i	0.523344	−	0.665672i
$808$	−36.9963	+	33.3116i	−1.30153	+	1.17190i
$809$	32.8381	−	23.8583i	1.15453	−	0.838813i	0.165451	−	0.986218i	$-0.447092\pi$
$809$	32.8381	−	23.8583i	1.15453	−	0.838813i	0.989076	+	0.147405i	$0.0470921\pi$
$810$	−13.4575	−	12.2750i	−0.472848	−	0.431301i
$811$	−0.0969202	−	0.0704166i	−0.00340333	−	0.00247266i	0.586082	−	0.810252i	$-0.300670\pi$
$811$	−0.0969202	−	0.0704166i	−0.00340333	−	0.00247266i	−0.589486	+	0.807779i	$0.700670\pi$
$812$	3.72836	−	0.391867i	0.130840	−	0.0137518i
$813$	1.50655	−	39.6848i	0.0528369	−	1.39181i
$814$	1.28359	−	12.2126i	0.0449898	−	0.428050i
$815$	20.9390	−	25.2456i	0.733461	−	0.884314i
$816$	1.65017	−	2.62305i	0.0577674	−	0.0918252i
$817$	3.46010	−	3.11549i	0.121054	−	0.108997i
$818$			11.5215i			0.402841i
$819$	5.54793	+	0.421838i	0.193860	+	0.0147402i
$820$	−10.7266	−	13.5690i	−0.374589	−	0.473849i
$821$	22.5029	+	4.78313i	0.785355	+	0.166932i	0.583100	−	0.812400i	$-0.301840\pi$
$821$	22.5029	+	4.78313i	0.785355	+	0.166932i	0.202255	+	0.979333i	$0.435173\pi$
$822$	−4.33155	−	25.0095i	−0.151080	−	0.872307i
$823$	24.1373	+	2.53693i	0.841372	+	0.0884318i	0.515402	−	0.856948i	$-0.327643\pi$
$823$	24.1373	+	2.53693i	0.841372	+	0.0884318i	0.325970	+	0.945380i	$0.394309\pi$
$824$	−4.12115	−	7.13805i	−0.143567	−	0.248666i
$825$	32.6695	−	20.7971i	1.13741	−	0.724062i
$826$	2.94915	−	5.10808i	0.102614	−	0.177733i
$827$	−3.67598	+	5.05956i	−0.127827	+	0.175938i	−0.868133	−	0.496331i	$-0.834680\pi$
$827$	−3.67598	+	5.05956i	−0.127827	+	0.175938i	0.740307	+	0.672269i	$0.234680\pi$
$828$	−27.0944	+	0.781365i	−0.941597	+	0.0271543i
$829$	−15.6182	−	48.0679i	−0.542442	−	1.66947i	−0.726994	−	0.686643i	$-0.759083\pi$
$829$	−15.6182	−	48.0679i	−0.542442	−	1.66947i	0.184552	−	0.982823i	$-0.440917\pi$
$830$	−2.15874	+	12.6654i	−0.0749311	+	0.439624i
$831$	−0.374324	−	5.59740i	−0.0129851	−	0.194172i
$832$	−10.5347	+	6.08224i	−0.365227	+	0.210864i
$833$	−9.59350	−	45.1339i	−0.332395	−	1.56380i
$834$	−9.64921	−	0.366311i	−0.334125	−	0.0126843i
$835$	−1.63833	+	0.810682i	−0.0566967	+	0.0280548i
$836$	2.01644	+	1.46503i	0.0697400	+	0.0506691i
$837$	−18.3658	−	20.7749i	−0.634814	−	0.718086i
$838$	9.08279	+	12.5014i	0.313760	+	0.431853i
$839$	−42.3973	+	18.8765i	−1.46372	+	0.651688i	−0.975292	−	0.220918i	$-0.929095\pi$
$839$	−42.3973	+	18.8765i	−1.46372	+	0.651688i	−0.488424	+	0.872607i	$0.662428\pi$
$840$	−7.54925	+	5.51575i	−0.260474	+	0.190312i
$841$	−13.3960	−	5.96428i	−0.461931	−	0.205665i
$842$	−7.23736	−	34.0491i	−0.249416	−	1.17341i
$843$	−9.54554	−	23.8343i	−0.328766	−	0.820895i
$844$	7.86844	+	8.73879i	0.270843	+	0.300801i
$845$	−10.0520	+	15.0880i	−0.345801	+	0.519041i
$846$	−19.9170	−	10.7458i	−0.684760	−	0.369448i
$847$	−7.17536	+	2.33141i	−0.246548	+	0.0801084i
$848$	0.612450	+	1.37559i	0.0210316	+	0.0472378i
$849$	4.93011	−	34.3226i	0.169201	−	1.17795i
$850$	−18.8568	−	27.2789i	−0.646783	−	0.935659i
$851$	11.6076	+	20.1050i	0.397904	+	0.689190i
$852$	−5.52883	−	5.37168i	−0.189414	−	0.184031i
$853$	1.61253	−	7.58634i	0.0552119	−	0.259751i	−0.941881	−	0.335947i	$-0.890944\pi$
$853$	1.61253	−	7.58634i	0.0552119	−	0.259751i	0.997093	+	0.0761951i	$0.0242772\pi$
$854$	0.440270	+	1.35501i	0.0150657	+	0.0463675i
$855$	−2.27696	−	2.20044i	−0.0778703	−	0.0752533i
$856$	−7.16047	+	22.0377i	−0.244740	+	0.753232i
$857$	40.1490	+	23.1800i	1.37146	+	0.791815i	0.991112	−	0.133027i	$-0.0424697\pi$
$857$	40.1490	+	23.1800i	1.37146	+	0.791815i	0.380351	+	0.924842i	$0.375803\pi$
$858$	15.4713	−	1.03463i	0.528180	−	0.0353218i
$859$	31.2963	+	13.9340i	1.06782	+	0.475423i	0.863951	−	0.503576i	$-0.167983\pi$
$859$	31.2963	+	13.9340i	1.06782	+	0.475423i	0.203866	+	0.978999i	$0.434649\pi$
$860$	−13.9270	−	22.0072i	−0.474908	−	0.750440i
$861$	−2.59473	−	9.15376i	−0.0884281	−	0.311959i
$862$	−19.0564	+	2.00291i	−0.649065	+	0.0682195i
$863$	0.806258	+	1.10972i	0.0274453	+	0.0377753i	0.822519	−	0.568737i	$-0.192568\pi$
$863$	0.806258	+	1.10972i	0.0274453	+	0.0377753i	−0.795074	+	0.606513i	$0.792568\pi$
$864$	−24.7839	−	14.6117i	−0.843164	−	0.497102i
$865$	18.3505	−	14.5066i	0.623937	−	0.493238i
$866$	3.22172	+	30.6526i	0.109478	+	1.04162i
$867$	−35.3821	−	52.8014i	−1.20164	−	1.79323i
$868$	−4.57582	+	2.64185i	−0.155314	+	0.0896703i
$869$	−24.2971	+	5.16450i	−0.824221	+	0.175194i
$870$	−13.1963	+	1.42267i	−0.447397	+	0.0482331i
$871$	25.9326	+	5.51215i	0.878694	+	0.186772i
$872$	8.58299	−	2.78878i	0.290657	−	0.0944401i
$873$	−7.24933	+	5.59320i	−0.245353	+	0.189301i
$874$	3.26914			0.110580
$875$	2.10600	+	9.13534i	0.0711958	+	0.308831i
$876$	2.18908	−	15.2400i	0.0739622	−	0.514913i
$877$	−11.3165	−	1.18941i	−0.382131	−	0.0401636i	−0.0884844	−	0.996078i	$-0.528202\pi$
$877$	−11.3165	−	1.18941i	−0.382131	−	0.0401636i	−0.293647	+	0.955914i	$0.594869\pi$
$878$	−1.89748	−	1.70849i	−0.0640367	−	0.0576589i
$879$	−45.2248	+	7.83277i	−1.52540	+	0.264193i
$880$	−1.74654	+	1.70600i	−0.0588758	+	0.0575092i
$881$	16.7728	−	51.6212i	0.565088	−	1.73916i	−0.102600	−	0.994723i	$-0.532716\pi$
$881$	16.7728	−	51.6212i	0.565088	−	1.73916i	0.667689	−	0.744441i	$-0.267284\pi$
$882$	16.6149	−	4.03550i	0.559454	−	0.135882i
$883$	27.4009	+	8.90310i	0.922115	+	0.299613i	0.731334	−	0.682019i	$-0.238898\pi$
$883$	27.4009	+	8.90310i	0.922115	+	0.299613i	0.190781	+	0.981633i	$0.438898\pi$
$884$	2.00045	+	19.0330i	0.0672823	+	0.640148i
$885$	14.9800	−	26.1072i	0.503549	−	0.877582i
$886$	−2.17140	+	20.6594i	−0.0729495	+	0.694068i
$887$	−23.2248	+	52.1637i	−0.779812	+	1.75149i	−0.129832	+	0.991536i	$0.541444\pi$
$887$	−23.2248	+	52.1637i	−0.779812	+	1.75149i	−0.649980	+	0.759951i	$0.725223\pi$
$888$	−0.573911	+	15.1177i	−0.0192592	+	0.507318i
$889$	−6.25207	+	2.78360i	−0.209688	+	0.0933589i
$890$	11.5832	−	0.470751i	0.388271	−	0.0157796i
$891$	22.0986	+	33.6371i	0.740330	+	1.12688i
$892$	−3.88360	−	1.26186i	−0.130033	−	0.0422502i
$893$	−3.40707	−	1.96707i	−0.114013	−	0.0658256i
$894$	−12.5756	+	8.42688i	−0.420591	+	0.281837i
$895$	22.1195	−	13.9981i	0.739373	−	0.467905i
$896$	−3.42029	+	3.79862i	−0.114264	+	0.126903i
$897$	−22.5130	+	18.7744i	−0.751688	+	0.626859i
$898$	−1.91054	−	4.29114i	−0.0637555	−	0.143197i
$899$	−20.2055			−0.673893
$900$	−14.2733	+	10.4872i	−0.475776	+	0.349574i
$901$	45.1908			1.50552
$902$	−10.7847	−	24.2228i	−0.359090	−	0.806530i
$903$	−2.44480	−	14.1158i	−0.0813577	−	0.469743i
$904$	−5.14399	+	5.71298i	−0.171086	+	0.190011i
$905$	47.9898	+	3.08044i	1.59524	+	0.102397i
$906$	3.73919	+	1.83781i	0.124226	+	0.0610570i
$907$	−29.9476	−	17.2902i	−0.994393	−	0.574113i	−0.0878082	−	0.996137i	$-0.527986\pi$
$907$	−29.9476	−	17.2902i	−0.994393	−	0.574113i	−0.906584	+	0.422025i	$0.861320\pi$
$908$	−19.7541	−	6.41849i	−0.655562	−	0.213005i
$909$	−48.8551	+	17.4464i	−1.62042	+	0.578660i
$910$	−1.01400	+	3.61402i	−0.0336137	+	0.119803i
$911$	16.0871	−	7.16246i	0.532991	−	0.237303i	−0.122550	−	0.992462i	$-0.539107\pi$
$911$	16.0871	−	7.16246i	0.532991	−	0.237303i	0.655541	+	0.755159i	$0.272441\pi$
$912$	0.168967	+	0.106297i	0.00559506	+	0.00351986i
$913$	11.5467	−	25.9343i	0.382139	−	0.858299i
$914$	−2.37623	+	22.6084i	−0.0785989	+	0.747818i
$915$	2.26522	+	6.90872i	0.0748858	+	0.228395i
$916$	2.83410	+	26.9647i	0.0936413	+	0.890938i
$917$	2.74401	+	0.891581i	0.0906150	+	0.0294426i
$918$	28.0646	−	20.0019i	0.926269	−	0.660160i
$919$	9.62779	−	29.6313i	0.317591	−	0.977446i	−0.657083	−	0.753818i	$-0.728210\pi$
$919$	9.62779	−	29.6313i	0.317591	−	0.977446i	0.974675	−	0.223628i	$-0.0717900\pi$
$920$	8.27651	−	48.5587i	0.272869	−	1.60093i
$921$	−8.25532	+	22.4687i	−0.272022	+	0.740368i
$922$	26.4928	+	23.8542i	0.872494	+	0.785597i
$923$	−8.29099	−	0.871418i	−0.272901	−	0.0286831i
$924$	7.11920	−	2.85122i	0.234205	−	0.0937981i
$925$	13.7095	+	6.49376i	0.450765	+	0.213513i
$926$	16.1033			0.529186
$927$	−1.14364	−	8.51241i	−0.0375622	−	0.279584i
$928$	−19.9384	+	6.47838i	−0.654510	+	0.212663i
$929$	−29.4655	−	6.26309i	−0.966733	−	0.205485i	−0.302615	−	0.953113i	$-0.597860\pi$
$929$	−29.4655	−	6.26309i	−0.966733	−	0.205485i	−0.664118	+	0.747627i	$0.731193\pi$
$930$	16.1754	−	9.39662i	0.530412	−	0.308127i
$931$	2.90735	−	0.617977i	0.0952846	−	0.0202534i
$932$	0.767519	−	0.443127i	0.0251409	−	0.0145151i
$933$	−2.00352	+	4.07635i	−0.0655923	+	0.133454i
$934$	−1.07175	−	10.1970i	−0.0350688	−	0.333657i
$935$	25.4538	+	68.7101i	0.832429	+	2.24706i
$936$	−18.9329	+	2.54364i	−0.618842	+	0.0831414i
$937$	−19.0857	−	26.2692i	−0.623501	−	0.858176i	0.374101	−	0.927388i	$-0.377951\pi$
$937$	−19.0857	−	26.2692i	−0.623501	−	0.858176i	−0.997602	+	0.0692121i	$0.977951\pi$
$938$	−9.04734	+	0.950914i	−0.295406	+	0.0310484i
$939$	6.98879	+	1.76507i	0.228070	+	0.0576008i
$940$	−14.0486	+	16.9380i	−0.458216	+	0.552458i
$941$	32.4727	+	14.4578i	1.05858	+	0.471311i	0.860804	−	0.508936i	$-0.169961\pi$
$941$	32.4727	+	14.4578i	1.05858	+	0.471311i	0.197777	+	0.980247i	$0.436628\pi$
$942$	−6.96149	−	10.3888i	−0.226818	−	0.338485i
$943$	43.4115	+	25.0637i	1.41367	+	0.816185i
$944$	−0.586378	+	1.80469i	−0.0190850	+	0.0587375i
$945$	−9.46130	+	2.32480i	−0.307776	+	0.0756259i
$946$	−12.3372	−	37.9700i	−0.401117	−	1.23451i
$947$	1.06378	−	5.00471i	0.0345684	−	0.162631i	−0.957478	−	0.288508i	$-0.906841\pi$
$947$	1.06378	−	5.00471i	0.0345684	−	0.162631i	0.992046	+	0.125876i	$0.0401743\pi$
$948$	10.9298	−	3.09816i	0.354983	−	0.100624i
$949$	−8.32542	−	14.4200i	−0.270255	−	0.468095i
$950$	1.75720	−	1.21468i	0.0570112	−	0.0394095i
$951$	−14.0021	+	5.60781i	−0.454051	+	0.181846i
$952$	−7.19503	−	16.1603i	−0.233192	−	0.523759i
$953$	34.6153	−	11.2472i	1.12130	−	0.364333i	0.311037	−	0.950398i	$-0.399324\pi$
$953$	34.6153	−	11.2472i	1.12130	−	0.364333i	0.810264	+	0.586065i	$0.199324\pi$
$954$	0.482714	+	16.7385i	0.0156284	+	0.541928i
$955$	−51.8732	+	19.2165i	−1.67858	+	0.621832i
$956$	0.488497	+	0.542531i	0.0157991	+	0.0175467i
$957$	29.0290	+	4.16973i	0.938374	+	0.134788i
$958$	4.82625	+	22.7057i	0.155929	+	0.733588i
$959$	−12.4025	−	5.52194i	−0.400497	−	0.178313i
$960$	14.2105	−	15.8675i	0.458642	−	0.512120i
$961$	−2.30421	+	1.02590i	−0.0743293	+	0.0330935i
$962$	3.57002	+	4.91371i	0.115102	+	0.158424i
$963$	−15.6329	+	18.4024i	−0.503764	+	0.593008i
$964$	−7.65587	−	5.56231i	−0.246579	−	0.179150i
$965$	28.6320	+	29.3124i	0.921698	+	0.943600i
$966$	5.35617	−	8.51399i	0.172332	−	0.273933i
$967$	−9.91464	−	46.6447i	−0.318833	−	1.49999i	−0.787332	−	0.616529i	$-0.788538\pi$
$967$	−9.91464	−	46.6447i	−0.318833	−	1.49999i	0.468499	−	0.883464i	$-0.344795\pi$
$968$	22.4330	−	12.9517i	0.721023	−	0.416283i
$969$	4.97694	−	3.33503i	0.159882	−	0.107137i
$970$	−2.73949	−	5.53631i	−0.0879598	−	0.177760i
$971$	1.13873	+	3.50467i	0.0365437	+	0.112470i	0.967664	−	0.252241i	$-0.0811677\pi$
$971$	1.13873	+	3.50467i	0.0365437	+	0.112470i	−0.931121	+	0.364711i	$0.881168\pi$
$972$	−11.1107	−	14.6751i	−0.356374	−	0.470704i
$973$	−3.03584	+	4.17847i	−0.0973244	+	0.133956i
$974$	−4.17371	+	7.22908i	−0.133734	+	0.231635i
$975$	−5.12520	+	18.4564i	−0.164138	+	0.591079i
$976$	−0.229179	−	0.396950i	−0.00733584	−	0.0127061i
$977$	−50.5042	−	5.30820i	−1.61577	−	0.169824i	−0.746926	−	0.664908i	$-0.768471\pi$
$977$	−50.5042	−	5.30820i	−1.61577	−	0.169824i	−0.868846	+	0.495083i	$0.835138\pi$
$978$	−17.6601	+	14.7274i	−0.564708	+	0.470930i
$979$	−25.0552	−	5.32565i	−0.800768	−	0.170208i
$980$	−0.675126	−	16.6121i	−0.0215661	−	0.530654i
$981$	9.37711	+	0.712990i	0.299388	+	0.0227640i
$982$			35.9225i			1.14633i
$983$	42.0562	−	37.8675i	1.34138	−	1.20779i	0.382510	−	0.923951i	$-0.375060\pi$
$983$	42.0562	−	37.8675i	1.34138	−	1.20779i	0.958873	−	0.283835i	$-0.0916069\pi$
$984$	15.2482	+	28.8891i	0.486096	+	0.920952i
$985$	−5.72824	−	9.05164i	−0.182517	−	0.288409i
$986$	2.62496	−	24.9749i	0.0835959	−	0.795362i
$987$	−10.7051	+	5.65036i	−0.340747	+	0.179853i
$988$	−1.22603	+	0.128861i	−0.0390053	+	0.00409962i
$989$	61.0622	+	44.3643i	1.94167	+	1.41070i
$990$	−25.1781	+	10.1619i	−0.800211	+	0.322967i
$991$	−31.0872	+	22.5862i	−0.987518	+	0.717473i	−0.959376	−	0.282130i	$-0.908959\pi$
$991$	−31.0872	+	22.5862i	−0.987518	+	0.717473i	−0.0281415	+	0.999604i	$0.508959\pi$
$992$	21.9580	−	19.7710i	0.697166	−	0.627731i
$993$	−7.70969	−	19.2503i	−0.244660	−	0.610891i
$994$	2.79808	−	0.594751i	0.0887498	−	0.0188644i
$995$	−3.81976	−	14.9558i	−0.121095	−	0.474131i
$996$	−4.47763	+	12.1869i	−0.141879	+	0.386155i
$997$	−3.88767	+	18.2901i	−0.123124	+	0.579252i	0.872724	+	0.488214i	$0.162352\pi$
$997$	−3.88767	+	18.2901i	−0.123124	+	0.579252i	−0.995847	+	0.0910374i	$0.970982\pi$
$998$	19.1875	−	26.4093i	0.607368	−	0.835971i
$999$	−6.54310	+	14.3428i	−0.207014	+	0.453786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.u.a.34.19	✓	224
3.2	odd	2		675.2.y.a.559.10		224
9.4	even	3	inner	225.2.u.a.184.10	yes	224
9.5	odd	6		675.2.y.a.334.19		224
25.14	even	10	inner	225.2.u.a.214.10	yes	224
75.14	odd	10		675.2.y.a.289.19		224
225.14	odd	30		675.2.y.a.64.10		224
225.139	even	30	inner	225.2.u.a.139.19	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.34.19	✓	224	1.1	even	1	trivial
225.2.u.a.139.19	yes	224	225.139	even	30	inner
225.2.u.a.184.10	yes	224	9.4	even	3	inner
225.2.u.a.214.10	yes	224	25.14	even	10	inner
675.2.y.a.64.10		224	225.14	odd	30
675.2.y.a.289.19		224	75.14	odd	10
675.2.y.a.334.19		224	9.5	odd	6
675.2.y.a.559.10		224	3.2	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.368139 + 0.826853i) q^{2} +(-1.62579 - 0.597338i) q^{3} +(0.790101 - 0.877497i) q^{4} +(0.553337 + 2.16652i) q^{5} +(-0.104605 - 1.56419i) q^{6} +(-0.726180 - 0.419260i) q^{7} +(2.73804 + 0.889642i) q^{8} +(2.28637 + 1.94229i) q^{9} +O(q^{10})\)	\(q+(0.368139 + 0.826853i) q^{2} +(-1.62579 - 0.597338i) q^{3} +(0.790101 - 0.877497i) q^{4} +(0.553337 + 2.16652i) q^{5} +(-0.104605 - 1.56419i) q^{6} +(-0.726180 - 0.419260i) q^{7} +(2.73804 + 0.889642i) q^{8} +(2.28637 + 1.94229i) q^{9} +(-1.58769 + 1.25511i) q^{10} +(4.08525 - 1.81887i) q^{11} +(-1.80870 + 0.954666i) q^{12} +(-0.899624 + 2.02059i) q^{13} +(0.0793317 - 0.754790i) q^{14} +(0.394537 - 3.85284i) q^{15} +(0.0255220 + 0.242826i) q^{16} +(6.96914 + 2.26441i) q^{17} +(-0.764286 + 2.60553i) q^{18} +(-0.145865 + 0.448925i) q^{19} +(2.33831 + 1.22622i) q^{20} +(0.930175 + 1.11540i) q^{21} +(3.00787 + 2.70830i) q^{22} +(-7.60995 - 0.799838i) q^{23} +(-3.92005 - 3.08190i) q^{24} +(-4.38764 + 2.39764i) q^{25} -2.00192 q^{26} +(-2.55696 - 4.52349i) q^{27} +(-0.941656 + 0.305963i) q^{28} +(-3.70358 - 0.787221i) q^{29} +(3.33097 - 1.09215i) q^{30} +(5.21984 - 1.10951i) q^{31} +(4.79509 - 2.76845i) q^{32} +(-7.72823 + 0.516822i) q^{33} +(0.693275 + 6.59607i) q^{34} +(0.506514 - 1.80528i) q^{35} +(3.51082 - 0.471679i) q^{36} +(-1.78330 - 2.45450i) q^{37} +(-0.424893 + 0.0446581i) q^{38} +(2.66957 - 2.74767i) q^{39} +(-0.412371 + 6.42429i) q^{40} +(-5.98463 - 2.66453i) q^{41} +(-0.579842 + 1.17974i) q^{42} +(-8.54237 - 4.93194i) q^{43} +(1.63171 - 5.02188i) q^{44} +(-2.94288 + 6.02822i) q^{45} +(-2.14017 - 6.58676i) q^{46} +(-1.73285 + 8.15243i) q^{47} +(0.103556 - 0.410029i) q^{48} +(-3.14844 - 5.45326i) q^{49} +(-3.59775 - 2.74527i) q^{50} +(-9.97772 - 7.84438i) q^{51} +(1.06227 + 2.38589i) q^{52} +(5.86521 - 1.90572i) q^{53} +(2.79895 - 3.77950i) q^{54} +(6.20114 + 7.84433i) q^{55} +(-1.61532 - 1.79399i) q^{56} +(0.505305 - 0.642727i) q^{57} +(-0.712517 - 3.35213i) q^{58} +(7.09978 + 3.16103i) q^{59} +(-3.06913 - 3.39034i) q^{60} +(-1.71496 + 0.763551i) q^{61} +(2.83903 + 3.90759i) q^{62} +(-0.845995 - 2.36904i) q^{63} +(4.44942 + 3.23269i) q^{64} +(-4.87545 - 0.830988i) q^{65} +(-3.27239 - 6.19984i) q^{66} +(-2.49215 - 11.7246i) q^{67} +(7.49334 - 4.32628i) q^{68} +(11.8944 + 5.84608i) q^{69} +(1.67917 - 0.245780i) q^{70} +(1.16473 + 3.58468i) q^{71} +(4.53223 + 7.35212i) q^{72} +(-4.42494 + 6.09040i) q^{73} +(1.37301 - 2.37812i) q^{74} +(8.56556 - 1.27714i) q^{75} +(0.278682 + 0.482692i) q^{76} +(-3.72921 - 0.391955i) q^{77} +(3.25469 + 1.19582i) q^{78} +(-5.43332 - 1.15489i) q^{79} +(-0.511965 + 0.189659i) q^{80} +(1.45501 + 8.88161i) q^{81} -5.92933i q^{82} +(4.71769 - 4.24783i) q^{83} +(1.71370 + 0.0650567i) q^{84} +(-1.04961 + 16.3518i) q^{85} +(0.933212 - 8.87892i) q^{86} +(5.55101 + 3.49215i) q^{87} +(12.8037 - 1.34572i) q^{88} +(-4.63408 - 3.36685i) q^{89} +(-6.06784 - 0.214107i) q^{90} +(1.50044 - 1.09014i) q^{91} +(-6.71449 + 6.04575i) q^{92} +(-9.14911 - 1.31418i) q^{93} +(-7.37879 + 1.56841i) q^{94} +(-1.05332 - 0.0676119i) q^{95} +(-9.44949 + 1.63662i) q^{96} +(-0.634563 + 2.98538i) q^{97} +(3.34998 - 4.61085i) q^{98} +(12.8732 + 3.77612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9	\( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) 224 * q - 5 * q^2 - 10 * q^3 - 29 * q^4 - 2 * q^6 - 20 * q^8 - 8 * q^9 - 12 * q^10 + 5 * q^11 - 30 * q^12 - 5 * q^13 - 23 * q^14 + 18 * q^15 + 15 * q^16 - 20 * q^17 - 12 * q^19 - 17 * q^20 - 27 * q^21 - 5 * q^22 - 5 * q^23 - 46 * q^24 - 16 * q^25 + 72 * q^26 - 25 * q^27 - 60 * q^28 - 15 * q^29 + 2 * q^30 - 9 * q^31 - 35 * q^33 - 7 * q^34 - 46 * q^35 - 66 * q^36 - 20 * q^37 - 75 * q^38 + 32 * q^39 - q^40 + 13 * q^41 - 140 * q^42 + 20 * q^44 + 90 * q^45 - 4 * q^46 + 20 * q^47 + 165 * q^48 + 56 * q^49 - 29 * q^50 - 6 * q^51 - 15 * q^52 - 20 * q^53 + 61 * q^54 - 44 * q^55 + 22 * q^56 - 5 * q^58 - 30 * q^59 - 149 * q^60 - 3 * q^61 + 40 * q^62 - 12 * q^64 + 45 * q^65 + 98 * q^66 + 10 * q^67 - 14 * q^69 - 12 * q^70 - 106 * q^71 + 40 * q^72 - 20 * q^73 + 82 * q^74 + 43 * q^75 + 8 * q^76 - 115 * q^77 + 110 * q^78 - 15 * q^79 - 22 * q^80 + 72 * q^81 + 65 * q^83 + 57 * q^84 - 21 * q^85 - 15 * q^86 + 115 * q^87 - 5 * q^88 + 26 * q^89 - 29 * q^90 - 54 * q^91 + 95 * q^92 + 41 * q^94 - 17 * q^95 - 47 * q^96 - 5 * q^97 - 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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