LMFDB - Embedded newform 325.2.e.d.126.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(126,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("325.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.e (of order $3$, degree $2$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 8x^{8} - 2x^{7} + 52x^{6} - 5x^{5} + 97x^{4} + 60x^{3} + 141x^{2} + 36x + 9 $ x^10 + 8x^8 - 2x^7 + 52x^6 - 5x^5 + 97x^4 + 60x^3 + 141x^2 + 36x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			126.4
Root			$-0.547998 + 0.949161i$ of defining polynomial
Character	$\chi$	$=$	325.126
Dual form			325.2.e.d.276.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.547998 - 0.949161i) q^{2} +(1.68234 - 2.91389i) q^{3} +(0.399395 + 0.691773i) q^{4} +(-1.84383 - 3.19362i) q^{6} +(0.795836 + 1.37843i) q^{7} +3.06747 q^{8} +(-4.16051 - 7.20621i) q^{9} +O(q^{10})$	\(q+(0.547998 - 0.949161i) q^{2} +(1.68234 - 2.91389i) q^{3} +(0.399395 + 0.691773i) q^{4} +(-1.84383 - 3.19362i) q^{6} +(0.795836 + 1.37843i) q^{7} +3.06747 q^{8} +(-4.16051 - 7.20621i) q^{9} +(-1.84383 + 3.19362i) q^{11} +2.68767 q^{12} +(-3.21311 - 1.63582i) q^{13} +1.74447 q^{14} +(0.882175 - 1.52797i) q^{16} +(1.49244 + 2.58498i) q^{17} -9.11981 q^{18} +(1.39940 + 2.42382i) q^{19} +5.35546 q^{21} +(2.02084 + 3.50019i) q^{22} +(0.335546 - 0.581184i) q^{23} +(5.16051 - 8.93826i) q^{24} +(-3.31344 + 2.15334i) q^{26} -17.9035 q^{27} +(-0.635707 + 1.10108i) q^{28} +(-1.37894 + 2.38839i) q^{29} -6.43214 q^{31} +(2.10060 + 3.63835i) q^{32} +(6.20390 + 10.7455i) q^{33} +3.27141 q^{34} +(3.32338 - 5.75626i) q^{36} +(0.479163 - 0.829935i) q^{37} +3.06747 q^{38} +(-10.1721 + 6.61067i) q^{39} +(-1.42722 + 2.47202i) q^{41} +(2.93478 - 5.08319i) q^{42} +(-2.44279 - 4.23103i) q^{43} -2.94568 q^{44} +(-0.367758 - 0.636975i) q^{46} +3.83323 q^{47} +(-2.96823 - 5.14113i) q^{48} +(2.23329 - 3.86817i) q^{49} +10.0431 q^{51} +(-0.151689 - 2.87608i) q^{52} +2.70355 q^{53} +(-9.81108 + 16.9933i) q^{54} +(2.44120 + 4.22828i) q^{56} +9.41701 q^{57} +(1.51131 + 2.61767i) q^{58} +(5.17839 + 8.96924i) q^{59} +(-3.71607 - 6.43642i) q^{61} +(-3.52480 + 6.10513i) q^{62} +(6.62217 - 11.4699i) q^{63} +8.13321 q^{64} +13.5989 q^{66} +(5.76308 - 9.98194i) q^{67} +(-1.19215 + 2.06486i) q^{68} +(-1.12900 - 1.95549i) q^{69} +(-4.28885 - 7.42851i) q^{71} +(-12.7622 - 22.1048i) q^{72} +3.72859 q^{73} +(-0.525161 - 0.909606i) q^{74} +(-1.11782 + 1.93613i) q^{76} -5.86956 q^{77} +(0.700282 + 13.2776i) q^{78} +4.33442 q^{79} +(-17.6381 + 30.5501i) q^{81} +(1.56423 + 2.70932i) q^{82} +15.6619 q^{83} +(2.13895 + 3.70476i) q^{84} -5.35457 q^{86} +(4.63967 + 8.03615i) q^{87} +(-5.65590 + 9.79631i) q^{88} +(-0.826615 + 1.43174i) q^{89} +(-0.302256 - 5.73089i) q^{91} +0.536063 q^{92} +(-10.8210 + 18.7426i) q^{93} +(2.10060 - 3.63835i) q^{94} +14.1357 q^{96} +(1.12863 + 1.95484i) q^{97} +(-2.44768 - 4.23950i) q^{98} +30.6852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9	$ 10 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9} - 3 q^{11} - 4 q^{12} - 10 q^{13} - 16 q^{14} - 4 q^{16} + 4 q^{17} + 4 q^{18} + 4 q^{19} - 16 q^{21} + 8 q^{22} + 15 q^{23} + 14 q^{24} - 9 q^{26} - 42 q^{27} - 17 q^{28} + q^{29} + 31 q^{32} - 2 q^{33} + 54 q^{34} + 13 q^{36} + 17 q^{37} - 6 q^{38} - 10 q^{39} - 6 q^{41} + 32 q^{42} + 12 q^{43} - 16 q^{44} + 7 q^{46} + 24 q^{47} - 2 q^{48} - 7 q^{49} - 23 q^{52} - 16 q^{53} - 19 q^{54} + 17 q^{56} + 8 q^{57} + 38 q^{58} + 12 q^{59} - 5 q^{61} + 13 q^{62} + 26 q^{63} - 10 q^{64} + 86 q^{66} - 16 q^{67} + 25 q^{68} - 20 q^{69} - 19 q^{71} - 45 q^{72} + 16 q^{73} - 2 q^{74} - 24 q^{76} - 64 q^{77} - 42 q^{78} - 28 q^{79} - 29 q^{81} - 23 q^{82} + 14 q^{83} + 34 q^{84} - 84 q^{86} + 21 q^{87} + 2 q^{88} + 10 q^{89} + 17 q^{91} - 142 q^{92} - 33 q^{93} + 31 q^{94} + 34 q^{96} + 37 q^{97} - 21 q^{98} + 56 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9 - 3 * q^11 - 4 * q^12 - 10 * q^13 - 16 * q^14 - 4 * q^16 + 4 * q^17 + 4 * q^18 + 4 * q^19 - 16 * q^21 + 8 * q^22 + 15 * q^23 + 14 * q^24 - 9 * q^26 - 42 * q^27 - 17 * q^28 + q^29 + 31 * q^32 - 2 * q^33 + 54 * q^34 + 13 * q^36 + 17 * q^37 - 6 * q^38 - 10 * q^39 - 6 * q^41 + 32 * q^42 + 12 * q^43 - 16 * q^44 + 7 * q^46 + 24 * q^47 - 2 * q^48 - 7 * q^49 - 23 * q^52 - 16 * q^53 - 19 * q^54 + 17 * q^56 + 8 * q^57 + 38 * q^58 + 12 * q^59 - 5 * q^61 + 13 * q^62 + 26 * q^63 - 10 * q^64 + 86 * q^66 - 16 * q^67 + 25 * q^68 - 20 * q^69 - 19 * q^71 - 45 * q^72 + 16 * q^73 - 2 * q^74 - 24 * q^76 - 64 * q^77 - 42 * q^78 - 28 * q^79 - 29 * q^81 - 23 * q^82 + 14 * q^83 + 34 * q^84 - 84 * q^86 + 21 * q^87 + 2 * q^88 + 10 * q^89 + 17 * q^91 - 142 * q^92 - 33 * q^93 + 31 * q^94 + 34 * q^96 + 37 * q^97 - 21 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.547998	−	0.949161i	0.387493	−	0.671158i	−0.604618	−	0.796515i	$-0.706674\pi$
$2$	0.547998	−	0.949161i	0.387493	−	0.671158i	0.992112	+	0.125357i	$0.0400077\pi$
$3$	1.68234	−	2.91389i	0.971297	−	1.68234i	0.279647	−	0.960103i	$-0.409782\pi$
$3$	1.68234	−	2.91389i	0.971297	−	1.68234i	0.691650	−	0.722233i	$-0.256884\pi$
$4$	0.399395	+	0.691773i	0.199698	+	0.345887i
$5$		0			0
$5$		0			0
$6$	−1.84383	−	3.19362i	−0.752742	−	1.30379i
$7$	0.795836	+	1.37843i	0.300798	+	0.520997i	0.976317	−	0.216345i	$-0.0694137\pi$
$7$	0.795836	+	1.37843i	0.300798	+	0.520997i	−0.675519	+	0.737343i	$0.736080\pi$
$8$	3.06747			1.08451
$9$	−4.16051	−	7.20621i	−1.38684	−	2.40207i
$10$		0			0
$11$	−1.84383	+	3.19362i	−0.555937	+	0.962911i	0.441893	+	0.897068i	$0.354307\pi$
$11$	−1.84383	+	3.19362i	−0.555937	+	0.962911i	−0.997830	+	0.0658435i	$0.979026\pi$
$12$	2.68767			0.775863
$13$	−3.21311	−	1.63582i	−0.891158	−	0.453694i
$13$	−3.21311	−	1.63582i	−0.891158	−	0.453694i
$14$	1.74447			0.466229
$15$		0			0
$16$	0.882175	−	1.52797i	0.220544	−	0.381993i
$17$	1.49244	+	2.58498i	0.361969	+	0.626949i	0.988285	−	0.152620i	$-0.0487712\pi$
$17$	1.49244	+	2.58498i	0.361969	+	0.626949i	−0.626316	+	0.779570i	$0.715438\pi$
$18$	−9.11981			−2.14956
$19$	1.39940	+	2.42382i	0.321043	+	0.556063i	0.980704	−	0.195501i	$-0.0626331\pi$
$19$	1.39940	+	2.42382i	0.321043	+	0.556063i	−0.659660	+	0.751564i	$0.729300\pi$
$20$		0			0
$21$	5.35546			1.16866
$22$	2.02084	+	3.50019i	0.430844	+	0.746244i
$23$	0.335546	−	0.581184i	0.0699663	−	0.121185i	−0.828920	−	0.559367i	$-0.811044\pi$
$23$	0.335546	−	0.581184i	0.0699663	−	0.121185i	0.898886	+	0.438182i	$0.144377\pi$
$24$	5.16051	−	8.93826i	1.05338	−	1.82452i
$25$		0			0
$26$	−3.31344	+	2.15334i	−0.649818	+	0.422304i
$27$	−17.9035			−3.44553
$28$	−0.635707	+	1.10108i	−0.120137	+	0.208084i
$29$	−1.37894	+	2.38839i	−0.256062	+	0.443513i	−0.965183	−	0.261574i	$-0.915759\pi$
$29$	−1.37894	+	2.38839i	−0.256062	+	0.443513i	0.709121	+	0.705087i	$0.249092\pi$
$30$		0			0
$31$	−6.43214			−1.15525			−0.577623	−	0.816304i	$-0.696020\pi$
$31$	−6.43214			−1.15525			−0.577623	+	0.816304i	$0.696020\pi$
$32$	2.10060	+	3.63835i	0.371338	+	0.643176i
$33$	6.20390	+	10.7455i	1.07996	+	1.87055i
$34$	3.27141			0.561043
$35$		0			0
$36$	3.32338	−	5.75626i	0.553896	−	0.959376i
$37$	0.479163	−	0.829935i	0.0787739	−	0.136440i	−0.823947	−	0.566666i	$-0.808233\pi$
$37$	0.479163	−	0.829935i	0.0787739	−	0.136440i	0.902721	+	0.430226i	$0.141566\pi$
$38$	3.06747			0.497609
$39$	−10.1721	+	6.61067i	−1.62884	+	1.05855i
$40$		0			0
$41$	−1.42722	+	2.47202i	−0.222894	+	0.386064i	−0.955686	−	0.294389i	$-0.904884\pi$
$41$	−1.42722	+	2.47202i	−0.222894	+	0.386064i	0.732791	+	0.680453i	$0.238217\pi$
$42$	2.93478	−	5.08319i	0.452847	−	0.784353i
$43$	−2.44279	−	4.23103i	−0.372521	−	0.645226i	0.617431	−	0.786625i	$-0.288173\pi$
$43$	−2.44279	−	4.23103i	−0.372521	−	0.645226i	−0.989953	+	0.141399i	$0.954840\pi$
$44$	−2.94568			−0.444078
$45$		0			0
$46$	−0.367758	−	0.636975i	−0.0542229	−	0.0939169i
$47$	3.83323			0.559134			0.279567	−	0.960126i	$-0.409809\pi$
$47$	3.83323			0.559134			0.279567	+	0.960126i	$0.409809\pi$
$48$	−2.96823	−	5.14113i	−0.428427	−	0.742058i
$49$	2.23329	−	3.86817i	0.319041	−	0.552596i
$50$		0			0
$51$	10.0431			1.40632
$52$	−0.151689	−	2.87608i	−0.0210355	−	0.398841i
$53$	2.70355			0.371361			0.185681	−	0.982610i	$-0.440551\pi$
$53$	2.70355			0.371361			0.185681	+	0.982610i	$0.440551\pi$
$54$	−9.81108	+	16.9933i	−1.33512	+	2.31249i
$55$		0			0
$56$	2.44120	+	4.22828i	0.326219	+	0.565028i
$57$	9.41701			1.24731
$58$	1.51131	+	2.61767i	0.198445	+	0.343717i
$59$	5.17839	+	8.96924i	0.674169	+	1.16770i	0.976711	+	0.214559i	$0.0688314\pi$
$59$	5.17839	+	8.96924i	0.674169	+	1.16770i	−0.302542	+	0.953136i	$0.597835\pi$
$60$		0			0
$61$	−3.71607	−	6.43642i	−0.475794	−	0.824099i	0.523822	−	0.851828i	$-0.324506\pi$
$61$	−3.71607	−	6.43642i	−0.475794	−	0.824099i	−0.999615	+	0.0277288i	$0.991173\pi$
$62$	−3.52480	+	6.10513i	−0.447650	+	0.775353i
$63$	6.62217	−	11.4699i	0.834315	−	1.44508i
$64$	8.13321			1.01665
$65$		0			0
$66$	13.5989			1.67391
$67$	5.76308	−	9.98194i	0.704072	−	1.21949i	−0.262954	−	0.964808i	$-0.584697\pi$
$67$	5.76308	−	9.98194i	0.704072	−	1.21949i	0.967025	−	0.254680i	$-0.0819701\pi$
$68$	−1.19215	+	2.06486i	−0.144569	+	0.250401i
$69$	−1.12900	−	1.95549i	−0.135916	−	0.235414i
$70$		0			0
$71$	−4.28885	−	7.42851i	−0.508993	−	0.881601i	−0.999946	−	0.0104153i	$-0.996685\pi$
$71$	−4.28885	−	7.42851i	−0.508993	−	0.881601i	0.490953	−	0.871186i	$-0.336649\pi$
$72$	−12.7622	−	22.1048i	−1.50404	−	2.60508i
$73$	3.72859			0.436398			0.218199	−	0.975904i	$-0.429982\pi$
$73$	3.72859			0.436398			0.218199	+	0.975904i	$0.429982\pi$
$74$	−0.525161	−	0.909606i	−0.0610487	−	0.105740i
$75$		0			0
$76$	−1.11782	+	1.93613i	−0.128223	+	0.222089i
$77$	−5.86956			−0.668899
$78$	0.700282	+	13.2776i	0.0792913	+	1.50340i
$79$	4.33442			0.487661			0.243830	−	0.969818i	$-0.421596\pi$
$79$	4.33442			0.487661			0.243830	+	0.969818i	$0.421596\pi$
$80$		0			0
$81$	−17.6381	+	30.5501i	−1.95979	+	3.39446i
$82$	1.56423	+	2.70932i	0.172740	+	0.299195i
$83$	15.6619			1.71912			0.859559	−	0.511036i	$-0.170738\pi$
$83$	15.6619			1.71912			0.859559	+	0.511036i	$0.170738\pi$
$84$	2.13895	+	3.70476i	0.233378	+	0.404223i
$85$		0			0
$86$	−5.35457			−0.577398
$87$	4.63967	+	8.03615i	0.497425	+	0.861565i
$88$	−5.65590	+	9.79631i	−0.602921	+	1.04429i
$89$	−0.826615	+	1.43174i	−0.0876210	+	0.151764i	−0.906505	−	0.422195i	$-0.861260\pi$
$89$	−0.826615	+	1.43174i	−0.0876210	+	0.151764i	0.818884	+	0.573959i	$0.194593\pi$
$90$		0			0
$91$	−0.302256	−	5.73089i	−0.0316850	−	0.600761i
$92$	0.536063			0.0558884
$93$	−10.8210	+	18.7426i	−1.12209	+	1.94351i
$94$	2.10060	−	3.63835i	0.216661	−	0.375268i
$95$		0			0
$96$	14.1357			1.44272
$97$	1.12863	+	1.95484i	0.114595	+	0.198484i	0.917618	−	0.397464i	$-0.130110\pi$
$97$	1.12863	+	1.95484i	0.114595	+	0.198484i	−0.803023	+	0.595948i	$0.796776\pi$
$98$	−2.44768	−	4.23950i	−0.247253	−	0.428254i
$99$	30.6852			3.08397
$100$		0			0
$101$	−5.64329	+	9.77446i	−0.561528	+	0.972595i	0.435835	+	0.900026i	$0.356453\pi$
$101$	−5.64329	+	9.77446i	−0.561528	+	0.972595i	−0.997363	+	0.0725688i	$0.976880\pi$
$102$	5.50362	−	9.53254i	0.544939	−	0.943863i
$103$	−19.5998			−1.93122			−0.965612	−	0.259986i	$-0.916282\pi$
$103$	−19.5998			−1.93122			−0.965612	+	0.259986i	$0.916282\pi$
$104$	−9.85612	−	5.01781i	−0.966472	−	0.492037i
$105$		0			0
$106$	1.48154	−	2.56611i	0.143900	−	0.249242i
$107$	0.880787	−	1.52557i	0.0851489	−	0.147482i	−0.820306	−	0.571925i	$-0.806197\pi$
$107$	0.880787	−	1.52557i	0.0851489	−	0.147482i	0.905455	+	0.424443i	$0.139530\pi$
$108$	−7.15057	−	12.3851i	−0.688064	−	1.19176i
$109$	−9.33442			−0.894076			−0.447038	−	0.894515i	$-0.647521\pi$
$109$	−9.33442			−0.894076			−0.447038	+	0.894515i	$0.647521\pi$
$110$		0			0
$111$	−1.61223	−	2.79246i	−0.153026	−	0.265048i
$112$	2.80827			0.265357
$113$	−5.66946	−	9.81979i	−0.533338	−	0.923768i	−0.999242	−	0.0389329i	$-0.987604\pi$
$113$	−5.66946	−	9.81979i	−0.533338	−	0.923768i	0.465904	−	0.884835i	$-0.345729\pi$
$114$	5.16051	−	8.93826i	0.483326	−	0.837145i
$115$		0			0
$116$	−2.20297			−0.204540
$117$	1.58015	+	29.9602i	0.146085	+	2.76982i
$118$	11.3510			1.04494
$119$	−2.37547	+	4.11444i	−0.217759	+	0.377170i
$120$		0			0
$121$	−1.29945	−	2.25072i	−0.118132	−	0.204611i
$122$	−8.14560			−0.737468
$123$	4.80212	+	8.31752i	0.432993	+	0.749966i
$124$	−2.56897	−	4.44958i	−0.230700	−	0.399584i
$125$		0			0
$126$	−7.25787	−	12.5710i	−0.646583	−	1.11991i
$127$	5.09996	−	8.83339i	0.452548	−	0.783837i	−0.545995	−	0.837788i	$-0.683848\pi$
$127$	5.09996	−	8.83339i	0.452548	−	0.783837i	0.998544	+	0.0539516i	$0.0171817\pi$
$128$	0.255779	−	0.443022i	0.0226079	−	0.0391580i
$129$	−16.4383			−1.44732
$130$		0			0
$131$	−10.7666			−0.940679			−0.470339	−	0.882486i	$-0.655868\pi$
$131$	−10.7666			−0.940679			−0.470339	+	0.882486i	$0.655868\pi$
$132$	−4.95562	+	8.58338i	−0.431331	+	0.747088i
$133$	−2.22738	+	3.85793i	−0.193138	+	0.334525i
$134$	−6.31631	−	10.9402i	−0.545646	−	0.945087i
$135$		0			0
$136$	4.57800	+	7.92933i	0.392560	+	0.679935i
$137$	−6.37230	−	11.0371i	−0.544422	−	0.942967i	−0.998643	−	0.0520777i	$-0.983416\pi$
$137$	−6.37230	−	11.0371i	−0.544422	−	0.942967i	0.454221	−	0.890889i	$-0.349918\pi$
$138$	−2.47477			−0.210666
$139$	1.95172	+	3.38047i	0.165543	+	0.286728i	0.936848	−	0.349737i	$-0.113729\pi$
$139$	1.95172	+	3.38047i	0.165543	+	0.286728i	−0.771305	+	0.636465i	$0.780396\pi$
$140$		0			0
$141$	6.44878	−	11.1696i	0.543085	−	0.940652i
$142$	−9.40113			−0.788925
$143$	11.1486	−	7.24528i	0.932295	−	0.605880i
$144$	−14.6812			−1.22343
$145$		0			0
$146$	2.04326	−	3.53903i	0.169101	−	0.292892i
$147$	−7.51428	−	13.0151i	−0.619768	−	1.07347i
$148$	0.765502			0.0629239
$149$	0.727708	+	1.26043i	0.0596162	+	0.103258i	0.894293	−	0.447482i	$-0.147679\pi$
$149$	0.727708	+	1.26043i	0.0596162	+	0.103258i	−0.834677	+	0.550740i	$0.814346\pi$
$150$		0			0
$151$	18.4701			1.50308			0.751538	−	0.659690i	$-0.229312\pi$
$151$	18.4701			1.50308			0.751538	+	0.659690i	$0.229312\pi$
$152$	4.29260	+	7.43500i	0.348176	+	0.603058i
$153$	12.4186	−	21.5096i	1.00398	−	1.73895i
$154$	−3.21651	+	5.57116i	−0.259194	+	0.448937i
$155$		0			0
$156$	−8.63579	−	4.39654i	−0.691417	−	0.352005i
$157$	−11.2891			−0.900972			−0.450486	−	0.892784i	$-0.648749\pi$
$157$	−11.2891			−0.900972			−0.450486	+	0.892784i	$0.648749\pi$
$158$	2.37526	−	4.11407i	0.188965	−	0.327297i
$159$	4.54828	−	7.87786i	0.360702	−	0.624755i
$160$		0			0
$161$	1.06816			0.0841828
$162$	19.3313	+	33.4829i	1.51881	+	2.63066i
$163$	−6.24224	−	10.8119i	−0.488930	−	0.846851i	0.510989	−	0.859587i	$-0.329279\pi$
$163$	−6.24224	−	10.8119i	−0.488930	−	0.846851i	−0.999919	+	0.0127358i	$0.995946\pi$
$164$	−2.28010			−0.178046
$165$		0			0
$166$	8.58270	−	14.8657i	0.666147	−	1.15380i
$167$	−6.28642	+	10.8884i	−0.486458	+	0.842570i	−0.999879	−	0.0155669i	$-0.995045\pi$
$167$	−6.28642	+	10.8884i	−0.486458	+	0.842570i	0.513421	+	0.858137i	$0.328378\pi$
$168$	16.4277			1.26742
$169$	7.64821	+	10.5121i	0.588324	+	0.808626i
$170$		0			0
$171$	11.6444	−	20.1687i	0.890469	−	1.54234i
$172$	1.95128	−	3.37971i	0.148783	−	0.257700i
$173$	1.34902	+	2.33657i	0.102564	+	0.177646i	0.912740	−	0.408540i	$-0.133962\pi$
$173$	1.34902	+	2.33657i	0.102564	+	0.177646i	−0.810176	+	0.586186i	$0.800629\pi$
$174$	10.1701			0.770996
$175$		0			0
$176$	3.25317	+	5.63466i	0.245217	+	0.424728i
$177$	34.8472			2.61927
$178$	0.905967	+	1.56918i	0.0679051	+	0.117615i
$179$	1.15559	−	2.00154i	0.0863728	−	0.149602i	−0.819603	−	0.572933i	$-0.805806\pi$
$179$	1.15559	−	2.00154i	0.0863728	−	0.149602i	0.905975	+	0.423330i	$0.139139\pi$
$180$		0			0
$181$	4.80127			0.356875			0.178438	−	0.983951i	$-0.442896\pi$
$181$	4.80127			0.356875			0.178438	+	0.983951i	$0.442896\pi$
$182$	−5.60518	−	2.85363i	−0.415483	−	0.211525i
$183$	−25.0067			−1.84855
$184$	1.02928	−	1.78276i	0.0758793	−	0.131427i
$185$		0			0
$186$	11.8598	+	20.5418i	0.869603	+	1.50620i
$187$	−11.0072			−0.804929
$188$	1.53098	+	2.65173i	0.111658	+	0.193397i
$189$	−14.2482	−	24.6787i	−1.03641	−	1.79511i
$190$		0			0
$191$	8.91168	+	15.4355i	0.644826	+	1.11687i	0.984342	+	0.176272i	$0.0564037\pi$
$191$	8.91168	+	15.4355i	0.644826	+	1.11687i	−0.339515	+	0.940601i	$0.610263\pi$
$192$	13.6828	−	23.6993i	0.987471	−	1.71035i
$193$	−1.25888	+	2.18045i	−0.0906165	+	0.156952i	−0.907771	−	0.419467i	$-0.862217\pi$
$193$	−1.25888	+	2.18045i	−0.0906165	+	0.156952i	0.817154	+	0.576419i	$0.195550\pi$
$194$	2.47394			0.177618
$195$		0			0
$196$	3.56786			0.254847
$197$	−9.25781	+	16.0350i	−0.659591	+	1.14245i	0.321130	+	0.947035i	$0.395937\pi$
$197$	−9.25781	+	16.0350i	−0.659591	+	1.14245i	−0.980721	+	0.195411i	$0.937396\pi$
$198$	16.8154	−	29.1252i	1.19502	−	2.06983i
$199$	−6.60105	−	11.4333i	−0.467936	−	0.810489i	0.531393	−	0.847126i	$-0.321669\pi$
$199$	−6.60105	−	11.4333i	−0.467936	−	0.810489i	−0.999329	+	0.0366369i	$0.988335\pi$
$200$		0			0
$201$	−19.3909	−	33.5860i	−1.36773	−	2.36897i
$202$	6.18503	+	10.7128i	0.435177	+	0.753748i
$203$	−4.38963			−0.308092
$204$	4.01118	+	6.94757i	0.280839	+	0.486427i
$205$		0			0
$206$	−10.7407	+	18.6034i	−0.748337	+	1.29616i
$207$	−5.58418			−0.388127
$208$	−5.33401	+	3.46647i	−0.369847	+	0.240357i
$209$	−10.3210			−0.713920
$210$		0			0
$211$	3.96666	−	6.87046i	0.273076	−	0.472982i	−0.696572	−	0.717487i	$-0.745292\pi$
$211$	3.96666	−	6.87046i	0.273076	−	0.472982i	0.969648	+	0.244505i	$0.0786255\pi$
$212$	1.07979	+	1.87024i	0.0741600	+	0.128449i
$213$	−28.8611			−1.97753
$214$	−0.965340	−	1.67202i	−0.0659893	−	0.114297i
$215$		0			0
$216$	−54.9183			−3.73672
$217$	−5.11893	−	8.86625i	−0.347496	−	0.601880i
$218$	−5.11525	+	8.85987i	−0.346448	+	0.600066i
$219$	6.27273	−	10.8647i	0.423872	−	0.734168i
$220$		0			0
$221$	−0.566823	−	10.7472i	−0.0381286	−	0.722934i
$222$	−3.53399			−0.237186
$223$	1.87499	−	3.24758i	0.125559	−	0.217474i	−0.796392	−	0.604780i	$-0.793261\pi$
$223$	1.87499	−	3.24758i	0.125559	−	0.217474i	0.921951	+	0.387306i	$0.126594\pi$
$224$	−3.34347	+	5.79107i	−0.223395	+	0.386932i
$225$		0			0
$226$	−12.4274			−0.826660
$227$	−6.46171	−	11.1920i	−0.428879	−	0.742840i	0.567895	−	0.823101i	$-0.307758\pi$
$227$	−6.46171	−	11.1920i	−0.428879	−	0.742840i	−0.996774	+	0.0802612i	$0.974425\pi$
$228$	3.76111	+	6.51444i	0.249086	+	0.431429i
$229$	−24.5322			−1.62114			−0.810568	−	0.585645i	$-0.800841\pi$
$229$	−24.5322			−1.62114			−0.810568	+	0.585645i	$0.800841\pi$
$230$		0			0
$231$	−9.87458	+	17.1033i	−0.649699	+	1.12531i
$232$	−4.22984	+	7.32630i	−0.277703	+	0.480995i
$233$	−8.82732			−0.578297			−0.289149	−	0.957284i	$-0.593372\pi$
$233$	−8.82732			−0.578297			−0.289149	+	0.957284i	$0.593372\pi$
$234$	29.3030	+	14.9183i	1.91560	+	0.975242i
$235$		0			0
$236$	−4.13645	+	7.16454i	−0.269260	+	0.466372i
$237$	7.29195	−	12.6300i	0.473663	−	0.820409i
$238$	2.60351	+	4.50941i	0.168760	+	0.292302i
$239$	4.23582			0.273993			0.136996	−	0.990572i	$-0.456255\pi$
$239$	4.23582			0.273993			0.136996	+	0.990572i	$0.456255\pi$
$240$		0			0
$241$	9.06784	+	15.7060i	0.584111	+	1.01171i	0.994986	+	0.100018i	$0.0318902\pi$
$241$	9.06784	+	15.7060i	0.584111	+	1.01171i	−0.410874	+	0.911692i	$0.634777\pi$
$242$	−2.84839			−0.183102
$243$	32.4913	+	56.2766i	2.08432	+	3.61015i
$244$	2.96836	−	5.14135i	0.190030	−	0.329141i
$245$		0			0
$246$	10.5262			0.671128
$247$	−0.531485	−	10.0772i	−0.0338176	−	0.641196i
$248$	−19.7304			−1.25288
$249$	26.3486	−	45.6371i	1.66977	−	2.89213i
$250$		0			0
$251$	0.540917	+	0.936895i	0.0341424	+	0.0591363i	0.882592	−	0.470140i	$-0.155797\pi$
$251$	0.540917	+	0.936895i	0.0341424	+	0.0591363i	−0.848449	+	0.529277i	$0.822463\pi$
$252$	10.5795			0.666443
$253$	1.23738	+	2.14321i	0.0777937	+	0.134743i
$254$	−5.58954	−	9.68137i	−0.350719	−	0.607463i
$255$		0			0
$256$	7.85288	+	13.6016i	0.490805	+	0.850099i
$257$	−4.07280	+	7.05430i	−0.254054	+	0.440035i	−0.964638	−	0.263578i	$-0.915098\pi$
$257$	−4.07280	+	7.05430i	−0.254054	+	0.440035i	0.710584	+	0.703612i	$0.248431\pi$
$258$	−9.00819	+	15.6026i	−0.560825	+	0.971378i
$259$	1.52534			0.0947801
$260$		0			0
$261$	22.9483			1.42047
$262$	−5.90006	+	10.2192i	−0.364507	+	0.631344i
$263$	8.63198	−	14.9510i	0.532271	−	0.921920i	−0.467020	−	0.884247i	$-0.654672\pi$
$263$	8.63198	−	14.9510i	0.532271	−	0.921920i	0.999290	−	0.0376726i	$-0.0119944\pi$
$264$	19.0302	+	32.9614i	1.17123	+	2.02863i
$265$		0			0
$266$	2.44120	+	4.22828i	0.149680	+	0.259253i
$267$	2.78129	+	4.81733i	0.170212	+	0.294816i
$268$	9.20699			0.562406
$269$	9.47829	+	16.4169i	0.577901	+	1.00095i	0.995720	+	0.0924239i	$0.0294615\pi$
$269$	9.47829	+	16.4169i	0.577901	+	1.00095i	−0.417818	+	0.908531i	$0.637205\pi$
$270$		0			0
$271$	−11.6797	+	20.2299i	−0.709492	+	1.22888i	0.255554	+	0.966795i	$0.417742\pi$
$271$	−11.6797	+	20.2299i	−0.709492	+	1.22888i	−0.965046	+	0.262081i	$0.915591\pi$
$272$	5.26637			0.319320
$273$	−17.2077	−	8.76055i	−1.04146	−	0.530212i
$274$	−13.9680			−0.843840
$275$		0			0
$276$	0.901838	−	1.56203i	0.0542843	−	0.0940231i
$277$	−3.00362	−	5.20242i	−0.180470	−	0.312583i	0.761571	−	0.648082i	$-0.224428\pi$
$277$	−3.00362	−	5.20242i	−0.180470	−	0.312583i	−0.942041	+	0.335499i	$0.891095\pi$
$278$	4.27815			0.256587
$279$	26.7610	+	46.3513i	1.60214	+	2.77498i
$280$		0			0
$281$	18.1001			1.07976			0.539881	−	0.841742i	$-0.318469\pi$
$281$	18.1001			1.07976			0.539881	+	0.841742i	$0.318469\pi$
$282$	−7.06784	−	12.2419i	−0.420884	−	0.728993i
$283$	1.19566	−	2.07094i	0.0710743	−	0.123104i	−0.828298	−	0.560288i	$-0.810691\pi$
$283$	1.19566	−	2.07094i	0.0710743	−	0.123104i	0.899372	+	0.437183i	$0.144024\pi$
$284$	3.42589	−	5.93382i	0.203289	−	0.352108i
$285$		0			0
$286$	−0.767507	−	14.5522i	−0.0453836	−	0.860492i
$287$	−4.54333			−0.268184
$288$	17.4792	−	30.2748i	1.02997	−	1.78396i
$289$	4.04526	−	7.00660i	0.237956	−	0.412153i
$290$		0			0
$291$	7.59491			0.445221
$292$	1.48918	+	2.57934i	0.0871477	+	0.150944i
$293$	−7.38780	−	12.7960i	−0.431600	−	0.747553i	0.565411	−	0.824809i	$-0.308717\pi$
$293$	−7.38780	−	12.7960i	−0.431600	−	0.747553i	−0.997011	+	0.0772560i	$0.975384\pi$
$294$	−16.4713			−0.960624
$295$		0			0
$296$	1.46982	−	2.54580i	0.0854313	−	0.147971i
$297$	33.0110	−	57.1768i	1.91550	−	3.31774i
$298$	1.59513			0.0924035
$299$	−2.02886	+	1.31852i	−0.117332	+	0.0762518i
$300$		0			0
$301$	3.88812	−	6.73441i	0.224107	−	0.388165i
$302$	10.1216	−	17.5311i	0.582432	−	1.00880i
$303$	18.9878	+	32.8879i	1.09082	+	1.88936i
$304$	4.93805			0.283217
$305$		0			0
$306$	−13.6107	−	23.5745i	−0.778074	−	1.34766i
$307$	14.6966			0.838781			0.419390	−	0.907806i	$-0.362244\pi$
$307$	14.6966			0.838781			0.419390	+	0.907806i	$0.362244\pi$
$308$	−2.34428	−	4.06041i	−0.133578	−	0.231363i
$309$	−32.9734	+	57.1117i	−1.87579	+	3.24897i
$310$		0			0
$311$	−14.2032			−0.805392			−0.402696	−	0.915334i	$-0.631927\pi$
$311$	−14.2032			−0.805392			−0.402696	+	0.915334i	$0.631927\pi$
$312$	−31.2027	+	20.2780i	−1.76650	+	1.14802i
$313$	21.0319			1.18879			0.594397	−	0.804171i	$-0.297391\pi$
$313$	21.0319			1.18879			0.594397	+	0.804171i	$0.297391\pi$
$314$	−6.18643	+	10.7152i	−0.349121	+	0.604694i
$315$		0			0
$316$	1.73115	+	2.99844i	0.0973847	+	0.168675i
$317$	−22.4641			−1.26171			−0.630854	−	0.775902i	$-0.717295\pi$
$317$	−22.4641			−1.26171			−0.630854	+	0.775902i	$0.717295\pi$
$318$	−4.98490	−	8.63410i	−0.279539	−	0.484177i
$319$	−5.08506	−	8.80759i	−0.284709	−	0.493130i
$320$		0			0
$321$	−2.96356	−	5.13304i	−0.165410	−	0.286498i
$322$	0.585350	−	1.01386i	0.0326203	−	0.0565000i
$323$	−4.17702	+	7.23481i	−0.232416	+	0.402556i
$324$	−28.1784			−1.56546
$325$		0			0
$326$	−13.6829			−0.757828
$327$	−15.7036	+	27.1995i	−0.868413	+	1.50414i
$328$	−4.37795	+	7.58283i	−0.241732	+	0.418692i
$329$	3.05062	+	5.28384i	0.168186	+	0.291307i
$330$		0			0
$331$	4.66419	+	8.07861i	0.256367	+	0.444041i	0.965266	−	0.261269i	$-0.0841411\pi$
$331$	4.66419	+	8.07861i	0.256367	+	0.444041i	−0.708899	+	0.705310i	$0.750808\pi$
$332$	6.25530	+	10.8345i	0.343304	+	0.594620i
$333$	−7.97425			−0.436986
$334$	6.88990	+	11.9337i	0.376999	+	0.652981i
$335$		0			0
$336$	4.72445	−	8.18299i	0.257740	−	0.446419i
$337$	27.6999			1.50891			0.754455	−	0.656352i	$-0.227901\pi$
$337$	27.6999			1.50891			0.754455	+	0.656352i	$0.227901\pi$
$338$	14.1689	−	1.49875i	0.770687	−	0.0815212i
$339$	−38.1517			−2.07212
$340$		0			0
$341$	11.8598	−	20.5418i	0.642244	−	1.11240i
$342$	−12.7622	−	22.1048i	−0.690102	−	1.19529i
$343$	18.2510			0.985464
$344$	−7.49316	−	12.9785i	−0.404004	−	0.699756i
$345$		0			0
$346$	2.95704			0.158971
$347$	−0.156978	−	0.271894i	−0.00842702	−	0.0145960i	0.861781	−	0.507280i	$-0.169349\pi$
$347$	−0.156978	−	0.271894i	−0.00842702	−	0.0145960i	−0.870208	+	0.492684i	$0.836016\pi$
$348$	−3.70613	+	6.41920i	−0.198669	+	0.344105i
$349$	−12.3713	+	21.4278i	−0.662223	+	1.14700i	0.317808	+	0.948155i	$0.397053\pi$
$349$	−12.3713	+	21.4278i	−0.662223	+	1.14700i	−0.980030	+	0.198848i	$0.936280\pi$
$350$		0			0
$351$	57.5259	+	29.2868i	3.07051	+	1.56321i
$352$	−15.4927			−0.825762
$353$	3.12287	−	5.40898i	0.166214	−	0.287891i	−0.770872	−	0.636990i	$-0.780179\pi$
$353$	3.12287	−	5.40898i	0.166214	−	0.287891i	0.937086	+	0.349099i	$0.113512\pi$
$354$	19.0962	−	33.0756i	1.01495	−	1.75795i
$355$		0			0
$356$	−1.32058			−0.0699909
$357$	7.99268	+	13.8437i	0.423018	+	0.732688i
$358$	−1.26652	−	2.19368i	−0.0669378	−	0.115940i
$359$	16.3025			0.860411			0.430205	−	0.902731i	$-0.358441\pi$
$359$	16.3025			0.860411			0.430205	+	0.902731i	$0.358441\pi$
$360$		0			0
$361$	5.58338	−	9.67071i	0.293862	−	0.508985i
$362$	2.63109	−	4.55718i	0.138287	−	0.239520i
$363$	−8.74447			−0.458966
$364$	3.84376	−	2.49799i	0.201468	−	0.130930i
$365$		0			0
$366$	−13.7036	+	23.7354i	−0.716300	+	1.24067i
$367$	1.98854	−	3.44425i	0.103801	−	0.179788i	−0.809447	−	0.587193i	$-0.800233\pi$
$367$	1.98854	−	3.44425i	0.103801	−	0.179788i	0.913248	+	0.407405i	$0.133566\pi$
$368$	−0.592022	−	1.02541i	−0.0308613	−	0.0534533i
$369$	23.7518			1.23647
$370$		0			0
$371$	2.15158	+	3.72665i	0.111705	+	0.193478i
$372$	−17.2875			−0.896313
$373$	−15.1191	−	26.1870i	−0.782837	−	1.35591i	−0.930283	−	0.366844i	$-0.880438\pi$
$373$	−15.1191	−	26.1870i	−0.782837	−	1.35591i	0.147445	−	0.989070i	$-0.452895\pi$
$374$	−6.03195	+	10.4476i	−0.311905	+	0.540235i
$375$		0			0
$376$	11.7583			0.606388
$377$	8.33765	−	5.41848i	0.429411	−	0.279066i
$378$	−31.2320			−1.60640
$379$	4.46836	−	7.73943i	0.229524	−	0.397548i	−0.728143	−	0.685425i	$-0.759616\pi$
$379$	4.46836	−	7.73943i	0.229524	−	0.397548i	0.957667	+	0.287878i	$0.0929496\pi$
$380$		0			0
$381$	−17.1597	−	29.7215i	−0.879118	−	1.52268i
$382$	19.5343			0.999464
$383$	13.4674	+	23.3261i	0.688150	+	1.19191i	0.972436	+	0.233171i	$0.0749101\pi$
$383$	13.4674	+	23.3261i	0.688150	+	1.19191i	−0.284286	+	0.958739i	$0.591757\pi$
$384$	−0.860612	−	1.49062i	−0.0439179	−	0.0760681i
$385$		0			0
$386$	1.37973	+	2.38977i	0.0702266	+	0.121636i
$387$	−20.3265	+	35.2065i	−1.03325	+	1.78965i
$388$	−0.901536	+	1.56151i	−0.0457685	+	0.0792734i
$389$	29.5512			1.49831			0.749153	−	0.662397i	$-0.230461\pi$
$389$	29.5512			1.49831			0.749153	+	0.662397i	$0.230461\pi$
$390$		0			0
$391$	2.00313			0.101303
$392$	6.85054	−	11.8655i	0.346004	−	0.599297i
$393$	−18.1130	+	31.3726i	−0.913679	+	1.58254i
$394$	10.1465	+	17.5743i	0.511175	+	0.885380i
$395$		0			0
$396$	12.2555	+	21.2272i	0.615863	+	1.06671i
$397$	10.1450	+	17.5717i	0.509165	+	0.881899i	0.999944	+	0.0106149i	$0.00337888\pi$
$397$	10.1450	+	17.5717i	0.509165	+	0.881899i	−0.490779	+	0.871284i	$0.663288\pi$
$398$	−14.4695			−0.725288
$399$	7.49440	+	12.9807i	0.375189	+	0.649847i
$400$		0			0
$401$	−5.92420	+	10.2610i	−0.295840	+	0.512410i	−0.975180	−	0.221414i	$-0.928933\pi$
$401$	−5.92420	+	10.2610i	−0.295840	+	0.512410i	0.679340	+	0.733824i	$0.262266\pi$
$402$	−42.5046			−2.11994
$403$	20.6672	+	10.5218i	1.02951	+	0.524128i
$404$	−9.01562			−0.448544
$405$		0			0
$406$	−2.40551	+	4.16647i	−0.119384	+	0.206778i
$407$	1.76699	+	3.06052i	0.0875867	+	0.151705i
$408$	30.8069			1.52517
$409$	−14.2989	−	24.7664i	−0.707033	−	1.22462i	−0.965953	−	0.258718i	$-0.916700\pi$
$409$	−14.2989	−	24.7664i	−0.707033	−	1.22462i	0.258920	−	0.965899i	$-0.416634\pi$
$410$		0			0
$411$	−42.8814			−2.11518
$412$	−7.82807	−	13.5586i	−0.385661	−	0.667985i
$413$	−8.24230	+	14.2761i	−0.405577	+	0.702480i
$414$	−3.06012	+	5.30028i	−0.150397	+	0.260495i
$415$		0			0
$416$	−0.797802	−	15.1267i	−0.0391155	−	0.741645i
$417$	13.1338			0.643164
$418$	−5.65590	+	9.79631i	−0.276639	+	0.479153i
$419$	7.46032	−	12.9217i	0.364461	−	0.631264i	−0.624229	−	0.781242i	$-0.714587\pi$
$419$	7.46032	−	12.9217i	0.364461	−	0.631264i	0.988689	+	0.149977i	$0.0479201\pi$
$420$		0			0
$421$	−31.6984			−1.54489			−0.772443	−	0.635085i	$-0.780965\pi$
$421$	−31.6984			−1.54489			−0.772443	+	0.635085i	$0.780965\pi$
$422$	−4.34745	−	7.53001i	−0.211631	−	0.366555i
$423$	−15.9482	−	27.6231i	−0.775427	−	1.34308i
$424$	8.29305			0.402746
$425$		0			0
$426$	−15.8159	+	27.3939i	−0.766281	+	1.32724i
$427$	5.91477	−	10.2447i	0.286236	−	0.495775i
$428$	1.40713			0.0680162
$429$	−2.35622	−	44.6749i	−0.113759	−	2.15692i
$430$		0			0
$431$	20.1828	−	34.9577i	0.972172	−	1.68385i	0.283204	−	0.959060i	$-0.408603\pi$
$431$	20.1828	−	34.9577i	0.972172	−	1.68385i	0.688968	−	0.724792i	$-0.258064\pi$
$432$	−15.7940	+	27.3560i	−0.759889	+	1.31617i
$433$	−0.559489	−	0.969063i	−0.0268873	−	0.0465702i	0.852269	−	0.523104i	$-0.175226\pi$
$433$	−0.559489	−	0.969063i	−0.0268873	−	0.0465702i	−0.879156	+	0.476534i	$0.841893\pi$
$434$	−11.2207			−0.538609
$435$		0			0
$436$	−3.72813	−	6.45730i	−0.178545	−	0.309249i
$437$	1.87825			0.0898488
$438$	−6.87490	−	11.9077i	−0.328495	−	0.568971i
$439$	17.8611	−	30.9364i	0.852465	−	1.47651i	−0.0265125	−	0.999648i	$-0.508440\pi$
$439$	17.8611	−	30.9364i	0.852465	−	1.47651i	0.878977	−	0.476864i	$-0.158226\pi$
$440$		0			0
$441$	−37.1665			−1.76983
$442$	−10.5114	−	5.35143i	−0.499978	−	0.254542i
$443$	−26.4988			−1.25899			−0.629497	−	0.777003i	$-0.716739\pi$
$443$	−26.4988			−1.25899			−0.629497	+	0.777003i	$0.716739\pi$
$444$	1.28783	−	2.23059i	0.0611178	−	0.105859i
$445$		0			0
$446$	−2.05499	−	3.55934i	−0.0973064	−	0.168540i
$447$	4.89700			0.231620
$448$	6.47271	+	11.2111i	0.305807	+	0.529673i
$449$	17.5306	+	30.3639i	0.827321	+	1.43296i	0.900133	+	0.435616i	$0.143469\pi$
$449$	17.5306	+	30.3639i	0.827321	+	1.43296i	−0.0728122	+	0.997346i	$0.523197\pi$
$450$		0			0
$451$	−5.26311	−	9.11598i	−0.247830	−	0.429255i
$452$	4.52871	−	7.84396i	0.213013	−	0.368949i
$453$	31.0729	−	53.8199i	1.45993	−	2.52868i
$454$	−14.1640			−0.664751
$455$		0			0
$456$	28.8864			1.35273
$457$	−5.86670	+	10.1614i	−0.274433	+	0.475332i	−0.969992	−	0.243137i	$-0.921823\pi$
$457$	−5.86670	+	10.1614i	−0.274433	+	0.475332i	0.695559	+	0.718469i	$0.255157\pi$
$458$	−13.4436	+	23.2850i	−0.628179	+	1.08804i
$459$	−26.7198	−	46.2801i	−1.24717	−	2.16017i
$460$		0			0
$461$	−10.3514	−	17.9292i	−0.482114	−	0.835045i	0.517676	−	0.855577i	$-0.326797\pi$
$461$	−10.3514	−	17.9292i	−0.482114	−	0.835045i	−0.999789	+	0.0205318i	$0.993464\pi$
$462$	10.8225	+	18.7451i	0.503508	+	0.872102i
$463$	10.1342			0.470976			0.235488	−	0.971877i	$-0.424331\pi$
$463$	10.1342			0.470976			0.235488	+	0.971877i	$0.424331\pi$
$464$	2.43293	+	4.21396i	0.112946	+	0.195628i
$465$		0			0
$466$	−4.83736	+	8.37855i	−0.224086	+	0.388129i
$467$	23.3950			1.08259			0.541296	−	0.840832i	$-0.317934\pi$
$467$	23.3950			1.08259			0.541296	+	0.840832i	$0.317934\pi$
$468$	−20.0946	+	13.0591i	−0.928872	+	0.603656i
$469$	18.3459			0.847133
$470$		0			0
$471$	−18.9921	+	32.8953i	−0.875111	+	1.51574i
$472$	15.8845	+	27.5128i	0.731145	+	1.26638i
$473$	18.0164			0.828394
$474$	−7.99196	−	13.8425i	−0.367083	−	0.635806i
$475$		0			0
$476$	−3.79501			−0.173944
$477$	−11.2481	−	19.4824i	−0.515017	−	0.892036i
$478$	2.32122	−	4.02048i	0.106170	−	0.183892i
$479$	13.9714	−	24.1993i	0.638372	−	1.10569i	−0.347418	−	0.937710i	$-0.612942\pi$
$479$	13.9714	−	24.1993i	0.638372	−	1.10569i	0.985790	−	0.167982i	$-0.0537251\pi$
$480$		0			0
$481$	−2.89723	+	1.88285i	−0.132102	+	0.0858507i
$482$	19.8767			0.905357
$483$	1.79700	−	3.11250i	0.0817665	−	0.141624i
$484$	1.03799	−	1.79785i	0.0471814	−	0.0817206i
$485$		0			0
$486$	71.2208			3.23064
$487$	3.69829	+	6.40563i	0.167586	+	0.290267i	0.937570	−	0.347795i	$-0.113070\pi$
$487$	3.69829	+	6.40563i	0.167586	+	0.290267i	−0.769985	+	0.638062i	$0.779736\pi$
$488$	−11.3989	−	19.7435i	−0.516005	−	0.893746i
$489$	−42.0062			−1.89958
$490$		0			0
$491$	4.73425	−	8.19997i	0.213654	−	0.370059i	−0.739201	−	0.673484i	$-0.764797\pi$
$491$	4.73425	−	8.19997i	0.213654	−	0.370059i	0.952855	+	0.303425i	$0.0981302\pi$
$492$	−3.83589	+	6.64396i	−0.172935	+	0.299533i
$493$	−8.23191			−0.370747
$494$	−9.85612	−	5.01781i	−0.443448	−	0.225762i
$495$		0			0
$496$	−5.67427	+	9.82813i	−0.254782	+	0.441296i
$497$	6.82645	−	11.8237i	0.306208	−	0.530368i
$498$	−28.8780	−	50.0181i	−1.29405	−	2.24137i
$499$	−30.6022			−1.36994			−0.684971	−	0.728571i	$-0.740185\pi$
$499$	−30.6022			−1.36994			−0.684971	+	0.728571i	$0.740185\pi$
$500$		0			0
$501$	21.1518	+	36.6359i	0.944991	+	1.63677i
$502$	1.18569			0.0529197
$503$	11.9604	+	20.7161i	0.533290	+	0.923685i	0.999244	+	0.0388762i	$0.0123778\pi$
$503$	11.9604	+	20.7161i	0.533290	+	0.923685i	−0.465954	+	0.884809i	$0.654289\pi$
$504$	20.3133	−	35.1836i	0.904825	−	1.56720i
$505$		0			0
$506$	2.71234			0.120578
$507$	43.4981	−	4.60110i	1.93182	−	0.204342i
$508$	8.14761			0.361492
$509$	−1.72122	+	2.98124i	−0.0762918	+	0.132141i	−0.901647	−	0.432472i	$-0.857641\pi$
$509$	−1.72122	+	2.98124i	−0.0762918	+	0.132141i	0.825356	+	0.564613i	$0.190975\pi$
$510$		0			0
$511$	2.96734	+	5.13959i	0.131268	+	0.227362i
$512$	18.2366			0.805951
$513$	−25.0540	−	43.3949i	−1.10616	−	1.91593i
$514$	4.46378	+	7.73149i	0.196889	+	0.341021i
$515$		0			0
$516$	−6.56540	−	11.3716i	−0.289026	−	0.500607i
$517$	−7.06784	+	12.2419i	−0.310843	+	0.538397i
$518$	0.835885	−	1.44779i	0.0367267	−	0.0636124i
$519$	9.07801			0.398480
$520$		0			0
$521$	−5.33204			−0.233601			−0.116800	−	0.993155i	$-0.537264\pi$
$521$	−5.33204			−0.233601			−0.116800	+	0.993155i	$0.537264\pi$
$522$	12.5756	−	21.7817i	0.550421	−	0.953357i
$523$	−1.57545	+	2.72876i	−0.0688897	+	0.119320i	−0.898413	−	0.439152i	$-0.855279\pi$
$523$	−1.57545	+	2.72876i	−0.0688897	+	0.119320i	0.829523	+	0.558472i	$0.188612\pi$
$524$	−4.30012	−	7.44802i	−0.187851	−	0.325368i
$525$		0			0
$526$	−9.46062	−	16.3863i	−0.412503	−	0.714475i
$527$	−9.59956	−	16.6269i	−0.418164	−	0.724281i
$528$	21.8917			0.952714
$529$	11.2748	+	19.5286i	0.490209	+	0.849068i
$530$		0			0
$531$	43.0895	−	74.6332i	1.86992	−	3.23880i
$532$	−3.55842			−0.154277
$533$	8.62958	−	5.60820i	0.373789	−	0.242918i
$534$	6.09656			0.263824
$535$		0			0
$536$	17.6780	−	30.6193i	0.763575	−	1.32255i
$537$	−3.88818	−	6.73453i	−0.167787	−	0.290616i
$538$	20.7763			0.895732
$539$	8.23563	+	14.2645i	0.354734	+	0.614417i
$540$		0			0
$541$	3.22739			0.138757			0.0693783	−	0.997590i	$-0.477898\pi$
$541$	3.22739			0.138757			0.0693783	+	0.997590i	$0.477898\pi$
$542$	12.8009	+	22.1719i	0.549847	+	0.952363i
$543$	8.07734	−	13.9904i	0.346632	−	0.600384i
$544$	−6.27004	+	10.8600i	−0.268826	+	0.465620i
$545$		0			0
$546$	−17.7450	+	11.5321i	−0.759414	+	0.493529i
$547$	7.09772			0.303476			0.151738	−	0.988421i	$-0.451513\pi$
$547$	7.09772			0.303476			0.151738	+	0.988421i	$0.451513\pi$
$548$	5.09013	−	8.81637i	0.217440	−	0.376617i
$549$	−30.9215	+	53.5576i	−1.31970	+	2.28578i
$550$		0			0
$551$	−7.71871			−0.328828
$552$	−3.46318	−	5.99841i	−0.147403	−	0.255309i
$553$	3.44949	+	5.97469i	0.146687	+	0.254070i
$554$	−6.58391			−0.279724
$555$		0			0
$556$	−1.55901	+	2.70029i	−0.0661170	+	0.114518i
$557$	−19.2037	+	33.2617i	−0.813685	+	1.40934i	0.0965835	+	0.995325i	$0.469209\pi$
$557$	−19.2037	+	33.2617i	−0.813685	+	1.40934i	−0.910268	+	0.414019i	$0.864125\pi$
$558$	58.6599			2.48327
$559$	0.927762	+	17.5907i	0.0392401	+	0.744009i
$560$		0			0
$561$	−18.5179	+	32.0739i	−0.781825	+	1.35416i
$562$	9.91882	−	17.1799i	0.418400	−	0.724691i
$563$	14.1990	+	24.5934i	0.598416	+	1.03649i	0.993055	+	0.117650i	$0.0375362\pi$
$563$	14.1990	+	24.5934i	0.598416	+	1.03649i	−0.394639	+	0.918836i	$0.629130\pi$
$564$	10.3025			0.433812
$565$		0			0
$566$	−1.31043	−	2.26974i	−0.0550817	−	0.0954042i
$567$	−56.1483			−2.35801
$568$	−13.1559	−	22.7867i	−0.552009	−	0.956108i
$569$	12.2675	−	21.2479i	0.514279	−	0.890757i	−0.485584	−	0.874190i	$-0.661393\pi$
$569$	12.2675	−	21.2479i	0.514279	−	0.890757i	0.999863	−	0.0165666i	$-0.00527356\pi$
$570$		0			0
$571$	−35.1010			−1.46893			−0.734465	−	0.678646i	$-0.762567\pi$
$571$	−35.1010			−1.46893			−0.734465	+	0.678646i	$0.762567\pi$
$572$	9.46480	+	4.81859i	0.395743	+	0.201475i
$573$	59.9698			2.50527
$574$	−2.48974	+	4.31235i	−0.103920	+	0.179994i
$575$		0			0
$576$	−33.8383	−	58.6097i	−1.40993	−	2.44207i
$577$	−42.0461			−1.75040			−0.875202	−	0.483758i	$-0.839271\pi$
$577$	−42.0461			−1.75040			−0.875202	+	0.483758i	$0.839271\pi$
$578$	−4.43359	−	7.67921i	−0.184413	−	0.319413i
$579$	4.23573	+	7.33650i	0.176031	+	0.304895i
$580$		0			0
$581$	12.4643	+	21.5888i	0.517107	+	0.895656i
$582$	4.16200	−	7.20879i	0.172520	−	0.298814i
$583$	−4.98490	+	8.63410i	−0.206454	+	0.357588i
$584$	11.4373			0.473279
$585$		0			0
$586$	−16.1940			−0.668969
$587$	20.2428	−	35.0615i	0.835509	−	1.44714i	−0.0581057	−	0.998310i	$-0.518506\pi$
$587$	20.2428	−	35.0615i	0.835509	−	1.44714i	0.893615	−	0.448834i	$-0.148161\pi$
$588$	6.00234	−	10.3964i	0.247532	−	0.428739i
$589$	−9.00110	−	15.5904i	−0.370884	−	0.642390i
$590$		0			0
$591$	31.1495	+	53.9525i	1.28132	+	2.21931i
$592$	−0.845412	−	1.46430i	−0.0347462	−	0.0601822i
$593$	−3.00502			−0.123402			−0.0617008	−	0.998095i	$-0.519652\pi$
$593$	−3.00502			−0.123402			−0.0617008	+	0.998095i	$0.519652\pi$
$594$	−36.1800	−	62.6656i	−1.48448	−	2.57120i
$595$		0			0
$596$	−0.581287	+	1.00682i	−0.0238104	+	0.0412409i
$597$	−44.4207			−1.81802
$598$	0.139673	+	2.64826i	0.00571166	+	0.108295i
$599$	20.3595			0.831865			0.415932	−	0.909396i	$-0.363455\pi$
$599$	20.3595			0.831865			0.415932	+	0.909396i	$0.363455\pi$
$600$		0			0
$601$	19.6123	−	33.9695i	0.800003	−	1.38565i	−0.119611	−	0.992821i	$-0.538165\pi$
$601$	19.6123	−	33.9695i	0.800003	−	1.38565i	0.919613	−	0.392825i	$-0.128502\pi$
$602$	−4.26136	−	7.38090i	−0.173680	−	0.300823i
$603$	−95.9093			−3.90573
$604$	7.37688	+	12.7771i	0.300161	+	0.519894i
$605$		0			0
$606$	41.6212			1.69074
$607$	7.72213	+	13.3751i	0.313432	+	0.542880i	0.979103	−	0.203366i	$-0.0651880\pi$
$607$	7.72213	+	13.3751i	0.313432	+	0.542880i	−0.665671	+	0.746245i	$0.731855\pi$
$608$	−5.87915	+	10.1830i	−0.238431	+	0.412975i
$609$	−7.38484	+	12.7909i	−0.299249	+	0.518314i
$610$		0			0
$611$	−12.3166	−	6.27046i	−0.498277	−	0.253676i
$612$	19.8397			0.801974
$613$	−13.5792	+	23.5198i	−0.548457	+	0.949955i	0.449924	+	0.893067i	$0.351451\pi$
$613$	−13.5792	+	23.5198i	−0.548457	+	0.949955i	−0.998381	+	0.0568882i	$0.981882\pi$
$614$	8.05373	−	13.9495i	0.325022	−	0.562954i
$615$		0			0
$616$	−18.0047			−0.725429
$617$	13.4870	+	23.3601i	0.542964	+	0.940442i	0.998732	+	0.0503430i	$0.0160314\pi$
$617$	13.4870	+	23.3601i	0.542964	+	0.940442i	−0.455768	+	0.890099i	$0.650635\pi$
$618$	36.1388	+	62.5942i	1.45371	+	2.51791i
$619$	38.2116			1.53586			0.767928	−	0.640537i	$-0.221288\pi$
$619$	38.2116			1.53586			0.767928	+	0.640537i	$0.221288\pi$
$620$		0			0
$621$	−6.00745	+	10.4052i	−0.241071	+	0.417546i
$622$	−7.78336	+	13.4812i	−0.312084	+	0.540546i
$623$	−2.63140			−0.105425
$624$	1.12732	+	21.3745i	0.0451291	+	0.855665i
$625$		0			0
$626$	11.5255	−	19.9627i	0.460650	−	0.797870i
$627$	−17.3634	+	30.0743i	−0.693428	+	1.20105i
$628$	−4.50883	−	7.80953i	−0.179922	−	0.311634i
$629$	2.86048			0.114055
$630$		0			0
$631$	5.94887	+	10.3037i	0.236821	+	0.410186i	0.959800	−	0.280684i	$-0.0905613\pi$
$631$	5.94887	+	10.3037i	0.236821	+	0.410186i	−0.722980	+	0.690869i	$0.757228\pi$
$632$	13.2957			0.528874
$633$	−13.3465	−	23.1169i	−0.530477	−	0.918813i
$634$	−12.3103	+	21.3220i	−0.488903	+	0.846806i
$635$		0			0
$636$	7.26625			0.288126
$637$	−13.5034	+	8.77562i	−0.535025	+	0.347703i
$638$	−11.1464			−0.441291
$639$	−35.6876	+	61.8127i	−1.41178	+	2.44527i
$640$		0			0
$641$	23.9587	+	41.4977i	0.946312	+	1.63906i	0.753103	+	0.657903i	$0.228556\pi$
$641$	23.9587	+	41.4977i	0.946312	+	1.63906i	0.193209	+	0.981158i	$0.438110\pi$
$642$	−6.49610			−0.256381
$643$	−15.3849	−	26.6475i	−0.606722	−	1.05087i	−0.991777	−	0.127980i	$-0.959151\pi$
$643$	−15.3849	−	26.6475i	−0.606722	−	1.05087i	0.385054	−	0.922894i	$-0.374183\pi$
$644$	0.426618	+	0.738925i	0.0168111	+	0.0291177i
$645$		0			0
$646$	4.57800	+	7.92933i	0.180119	+	0.311975i
$647$	17.1725	−	29.7436i	0.675121	−	1.16934i	−0.301313	−	0.953525i	$-0.597425\pi$
$647$	17.1725	−	29.7436i	0.675121	−	1.16934i	0.976434	−	0.215818i	$-0.0692418\pi$
$648$	−54.1044	+	93.7115i	−2.12542	+	3.68134i
$649$	−38.1924			−1.49918
$650$		0			0
$651$	−34.4470			−1.35009
$652$	4.98624	−	8.63643i	0.195276	−	0.338229i
$653$	−11.7346	+	20.3250i	−0.459211	+	0.795377i	−0.998919	−	0.0464749i	$-0.985201\pi$
$653$	−11.7346	+	20.3250i	−0.459211	+	0.795377i	0.539708	+	0.841852i	$0.318535\pi$
$654$	17.2111	+	29.8106i	0.673009	+	1.16569i
$655$		0			0
$656$	2.51812	+	4.36150i	0.0983159	+	0.170288i
$657$	−15.5128	−	26.8690i	−0.605212	−	1.04826i
$658$	6.68695			0.260684
$659$	−24.4179	−	42.2931i	−0.951187	−	1.64750i	−0.742862	−	0.669445i	$-0.766532\pi$
$659$	−24.4179	−	42.2931i	−0.951187	−	1.64750i	−0.208325	−	0.978060i	$-0.566801\pi$
$660$		0			0
$661$	−11.9416	+	20.6835i	−0.464476	+	0.804495i	−0.999178	−	0.0405453i	$-0.987090\pi$
$661$	−11.9416	+	20.6835i	−0.464476	+	0.804495i	0.534702	+	0.845041i	$0.320424\pi$
$662$	10.2239			0.397362
$663$	−32.2697	−	16.4287i	−1.25325	−	0.638038i
$664$	48.0424			1.86441
$665$		0			0
$666$	−4.36987	+	7.56884i	−0.169329	+	0.293287i
$667$	0.925395	+	1.60283i	0.0358314	+	0.0620619i
$668$	−10.0431			−0.388578
$669$	−6.30873	−	10.9270i	−0.243910	−	0.422464i
$670$		0			0
$671$	27.4073			1.05805
$672$	11.2497	+	19.4850i	0.433966	+	0.751652i
$673$	14.4017	−	24.9444i	0.555143	−	0.961536i	−0.442749	−	0.896646i	$-0.645997\pi$
$673$	14.4017	−	24.9444i	0.555143	−	0.961536i	0.997892	−	0.0648907i	$-0.0206699\pi$
$674$	15.1795	−	26.2917i	0.584692	−	1.01272i
$675$		0			0
$676$	−4.21735	+	9.48932i	−0.162206	+	0.364974i
$677$	−6.71561			−0.258102			−0.129051	−	0.991638i	$-0.541193\pi$
$677$	−6.71561			−0.258102			−0.129051	+	0.991638i	$0.541193\pi$
$678$	−20.9071	+	36.2121i	−0.802932	+	1.39072i
$679$	−1.79640	+	3.11146i	−0.0689396	+	0.119407i
$680$		0			0
$681$	−43.4831			−1.66627
$682$	−12.9983	−	22.5137i	−0.497731	−	0.862095i
$683$	2.66564	+	4.61703i	0.101998	+	0.176666i	0.912508	−	0.409059i	$-0.134143\pi$
$683$	2.66564	+	4.61703i	0.101998	+	0.176666i	−0.810510	+	0.585725i	$0.800810\pi$
$684$	18.6029			0.711299
$685$		0			0
$686$	10.0015	−	17.3232i	0.381861	−	0.661402i
$687$	−41.2715	+	71.4843i	−1.57460	+	2.72729i
$688$	−8.61986			−0.328629
$689$	−8.68682	−	4.42252i	−0.330942	−	0.168484i
$690$		0			0
$691$	−22.1827	+	38.4216i	−0.843871	+	1.46163i	0.0427272	+	0.999087i	$0.486395\pi$
$691$	−22.1827	+	38.4216i	−0.843871	+	1.46163i	−0.886598	+	0.462541i	$0.846938\pi$
$692$	−1.07758	+	1.86643i	−0.0409636	+	0.0709510i
$693$	24.4204	+	42.2973i	0.927653	+	1.60674i
$694$	−0.344095			−0.0130617
$695$		0			0
$696$	14.2320	+	24.6506i	0.539464	+	0.934379i
$697$	−8.52014			−0.322723
$698$	13.5589	+	23.4848i	0.513214	+	0.888912i
$699$	−14.8505	+	25.7219i	−0.561698	+	0.972890i
$700$		0			0
$701$	40.0973			1.51445			0.757227	−	0.653151i	$-0.226553\pi$
$701$	40.0973			1.51445			0.757227	+	0.653151i	$0.226553\pi$
$702$	59.3220	−	38.5522i	2.23896	−	1.45506i
$703$	2.68215			0.101159
$704$	−14.9963	+	25.9744i	−0.565194	+	0.978945i
$705$		0			0
$706$	−3.42266	−	5.92822i	−0.128814	−	0.223112i
$707$	−17.9645			−0.675626
$708$	13.9178	+	24.1063i	0.523063	+	0.905972i
$709$	0.800778	+	1.38699i	0.0300739	+	0.0520894i	0.880671	−	0.473729i	$-0.157092\pi$
$709$	0.800778	+	1.38699i	0.0300739	+	0.0520894i	−0.850597	+	0.525819i	$0.823759\pi$
$710$		0			0
$711$	−18.0334	−	31.2348i	−0.676305	−	1.17140i
$712$	−2.53561	+	4.39181i	−0.0950261	+	0.164590i
$713$	−2.15828	+	3.73825i	−0.0808283	+	0.139999i
$714$	17.5199			0.655666
$715$		0			0
$716$	1.84615			0.0689938
$717$	7.12608	−	12.3427i	0.266128	−	0.460948i
$718$	8.93372	−	15.4737i	0.333404	−	0.577472i
$719$	0.826615	+	1.43174i	0.0308275	+	0.0533948i	0.881028	−	0.473065i	$-0.156852\pi$
$719$	0.826615	+	1.43174i	0.0308275	+	0.0533948i	−0.850200	+	0.526460i	$0.823519\pi$
$720$		0			0
$721$	−15.5982	−	27.0169i	−0.580908	−	1.00616i
$722$	−6.11937	−	10.5991i	−0.227739	−	0.394456i
$723$	61.0206			2.26938
$724$	1.91760	+	3.32139i	0.0712672	+	0.123438i
$725$		0			0
$726$	−4.79195	+	8.29991i	−0.177846	+	0.308039i
$727$	5.56875			0.206533			0.103267	−	0.994654i	$-0.467070\pi$
$727$	5.56875			0.206533			0.103267	+	0.994654i	$0.467070\pi$
$728$	−0.927159	−	17.5793i	−0.0343628	−	0.651533i
$729$	112.816			4.17839
$730$		0			0
$731$	7.29141	−	12.6291i	0.269683	−	0.467104i
$732$	−9.98757	−	17.2990i	−0.369151	−	0.639388i
$733$	−36.1927			−1.33681			−0.668403	−	0.743799i	$-0.733022\pi$
$733$	−36.1927			−1.33681			−0.668403	+	0.743799i	$0.733022\pi$
$734$	−2.17943	−	3.77488i	−0.0804442	−	0.139334i
$735$		0			0
$736$	2.81940			0.103925
$737$	21.2523	+	36.8101i	0.782839	+	1.35592i
$738$	13.0160	−	22.5443i	0.479124	−	0.829868i
$739$	−13.6967	+	23.7234i	−0.503842	+	0.872680i	0.496148	+	0.868238i	$0.334747\pi$
$739$	−13.6967	+	23.7234i	−0.503842	+	0.872680i	−0.999990	+	0.00444240i	$0.998586\pi$
$740$		0			0
$741$	−30.2579	−	15.4045i	−1.11155	−	0.565899i
$742$	4.71626			0.173139
$743$	15.0123	−	26.0020i	0.550746	−	0.953920i	−0.447475	−	0.894297i	$-0.647677\pi$
$743$	15.0123	−	26.0020i	0.550746	−	0.953920i	0.998221	−	0.0596237i	$-0.0189901\pi$
$744$	−33.1931	+	57.4921i	−1.21692	+	2.10776i
$745$		0			0
$746$	−33.1410			−1.21338
$747$	−65.1615	−	112.863i	−2.38414	−	4.12944i
$748$	−4.39624	−	7.61451i	−0.160742	−	0.278414i
$749$	2.80385			0.102450
$750$		0			0
$751$	−13.2453	+	22.9415i	−0.483328	+	0.837148i	−0.999817	−	0.0191455i	$-0.993905\pi$
$751$	−13.2453	+	22.9415i	−0.483328	+	0.837148i	0.516489	+	0.856294i	$0.327239\pi$
$752$	3.38158	−	5.85707i	0.123314	−	0.213585i
$753$	3.64001			0.132649
$754$	−0.573990	−	10.8831i	−0.0209035	−	0.396339i
$755$		0			0
$756$	11.3814	−	19.7131i	0.413936	−	0.716958i
$757$	5.52919	−	9.57685i	0.200962	−	0.348076i	−0.747877	−	0.663838i	$-0.768927\pi$
$757$	5.52919	−	9.57685i	0.200962	−	0.348076i	0.948839	+	0.315761i	$0.102260\pi$
$758$	−4.89731	−	8.48239i	−0.177878	−	0.308094i
$759$	8.32679			0.302243
$760$		0			0
$761$	5.01890	+	8.69300i	0.181935	+	0.315121i	0.942539	−	0.334095i	$-0.108431\pi$
$761$	5.01890	+	8.69300i	0.181935	+	0.315121i	−0.760604	+	0.649216i	$0.775097\pi$
$762$	−37.6139			−1.36261
$763$	−7.42867	−	12.8668i	−0.268936	−	0.465811i
$764$	−7.11857	+	12.3297i	−0.257541	+	0.446074i
$765$		0			0
$766$	29.5204			1.06661
$767$	−1.96673	−	37.2901i	−0.0710147	−	1.34647i
$768$	52.8447			1.90687
$769$	2.59941	−	4.50232i	0.0937372	−	0.162358i	−0.815344	−	0.578977i	$-0.803452\pi$
$769$	2.59941	−	4.50232i	0.0937372	−	0.162358i	0.909081	+	0.416620i	$0.136785\pi$
$770$		0			0
$771$	13.7036	+	23.7354i	0.493524	+	0.854809i
$772$	−2.01117			−0.0723836
$773$	1.27337	+	2.20553i	0.0457998	+	0.0793275i	0.888017	−	0.459812i	$-0.152083\pi$
$773$	1.27337	+	2.20553i	0.0457998	+	0.0793275i	−0.842217	+	0.539139i	$0.818750\pi$
$774$	22.2777	+	38.5862i	0.800757	+	1.38695i
$775$		0			0
$776$	3.46202	+	5.99639i	0.124279	+	0.215258i
$777$	2.56614	−	4.44468i	0.0920596	−	0.159452i
$778$	16.1940	−	28.0489i	0.580584	−	1.00560i
$779$	−7.98898			−0.286235
$780$		0			0
$781$	31.6317			1.13187
$782$	1.09771	−	1.90129i	0.0392541	−	0.0679901i
$783$	24.6878	−	42.7605i	0.882269	−	1.52813i
$784$	−3.94031	−	6.82481i	−0.140725	−	0.243743i
$785$		0			0
$786$	19.8518	+	34.3843i	0.708089	+	1.22645i
$787$	20.3917	+	35.3195i	0.726886	+	1.25900i	0.958193	+	0.286123i	$0.0923666\pi$
$787$	20.3917	+	35.3195i	0.726886	+	1.25900i	−0.231307	+	0.972881i	$0.574300\pi$
$788$	−14.7901			−0.526876
$789$	−29.0438	−	50.3053i	−1.03399	−	1.79092i
$790$		0			0
$791$	9.02392	−	15.6299i	0.320854	−	0.555735i
$792$	94.1257			3.34461
$793$	1.41135	+	26.7598i	0.0501185	+	0.950267i
$794$	22.2378			0.789192
$795$		0			0
$796$	5.27286	−	9.13286i	0.186891	−	0.323705i
$797$	8.86862	+	15.3609i	0.314143	+	0.544111i	0.979255	−	0.202632i	$-0.0649497\pi$
$797$	8.86862	+	15.3609i	0.314143	+	0.544111i	−0.665112	+	0.746743i	$0.731616\pi$
$798$	16.4277			0.581534
$799$	5.72086	+	9.90882i	0.202389	+	0.350549i
$800$		0			0
$801$	13.7565			0.486064
$802$	6.49290	+	11.2460i	0.229272	+	0.397111i
$803$	−6.87490	+	11.9077i	−0.242610	+	0.420213i
$804$	15.4892	−	26.8282i	0.546264	−	0.946156i
$805$		0			0
$806$	21.3125	−	13.8506i	0.750700	−	0.487865i
$807$	63.7826			2.24526
$808$	−17.3106	+	29.9828i	−0.608985	+	1.05479i
$809$	−17.0104	+	29.4629i	−0.598054	+	1.03586i	0.395054	+	0.918658i	$0.370726\pi$
$809$	−17.0104	+	29.4629i	−0.598054	+	1.03586i	−0.993108	+	0.117202i	$0.962607\pi$
$810$		0			0
$811$	−2.94630			−0.103459			−0.0517294	−	0.998661i	$-0.516473\pi$
$811$	−2.94630			−0.103459			−0.0517294	+	0.998661i	$0.516473\pi$
$812$	−1.75320	−	3.03663i	−0.0615253	−	0.106565i
$813$	39.2984	+	68.0668i	1.37825	+	2.38721i
$814$	3.87324			0.135757
$815$		0			0
$816$	8.85980	−	15.3456i	0.310155	−	0.537204i
$817$	6.83685	−	11.8418i	0.239191	−	0.414291i
$818$	−31.3430			−1.09588
$819$	−40.0405	+	26.0215i	−1.39913	+	0.909266i
$820$		0			0
$821$	4.25553	−	7.37080i	0.148519	−	0.257243i	−0.782161	−	0.623076i	$-0.785883\pi$
$821$	4.25553	−	7.37080i	0.148519	−	0.257243i	0.930680	+	0.365833i	$0.119216\pi$
$822$	−23.4989	+	40.7013i	−0.819619	+	1.41962i
$823$	−18.3511	−	31.7850i	−0.639678	−	1.10796i	−0.985503	−	0.169657i	$-0.945734\pi$
$823$	−18.3511	−	31.7850i	−0.639678	−	1.10796i	0.345825	−	0.938299i	$-0.387599\pi$
$824$	−60.1217			−2.09444
$825$		0			0
$826$	9.03354	+	15.6465i	0.314317	+	0.544413i
$827$	−3.32022			−0.115455			−0.0577277	−	0.998332i	$-0.518386\pi$
$827$	−3.32022			−0.115455			−0.0577277	+	0.998332i	$0.518386\pi$
$828$	−2.23029	−	3.86298i	−0.0775081	−	0.134248i
$829$	18.0712	−	31.3002i	0.627637	−	1.08710i	−0.360387	−	0.932803i	$-0.617355\pi$
$829$	18.0712	−	31.3002i	0.627637	−	1.08710i	0.988025	−	0.154297i	$-0.0493112\pi$
$830$		0			0
$831$	−20.2124			−0.701159
$832$	−26.1329	−	13.3044i	−0.905997	−	0.461249i
$833$	13.3322			0.461933
$834$	7.19729	−	12.4661i	0.249222	−	0.431665i
$835$		0			0
$836$	−4.12217	−	7.13980i	−0.142568	−	0.246935i
$837$	115.158			3.98043
$838$	−8.17649	−	14.1621i	−0.282452	−	0.489221i
$839$	10.8414	+	18.7778i	0.374286	+	0.648283i	0.990220	−	0.139515i	$-0.0445544\pi$
$839$	10.8414	+	18.7778i	0.374286	+	0.648283i	−0.615934	+	0.787798i	$0.711221\pi$
$840$		0			0
$841$	10.6971	+	18.5279i	0.368864	+	0.638892i
$842$	−17.3707	+	30.0869i	−0.598633	+	1.03686i
$843$	30.4504	−	52.7417i	1.04877	−	1.81652i
$844$	6.33707			0.218131
$845$		0			0
$846$	−34.9583			−1.20189
$847$	2.06830	−	3.58241i	0.0710678	−	0.123093i
$848$	2.38501	−	4.13095i	0.0819015	−	0.141858i
$849$	−4.02299	−	6.96802i	−0.138069	−	0.239142i
$850$		0			0
$851$	−0.321563	−	0.556963i	−0.0110230	−	0.0190925i
$852$	−11.5270	−	19.9654i	−0.394909	−	0.684002i
$853$	−12.0199			−0.411553			−0.205776	−	0.978599i	$-0.565972\pi$
$853$	−12.0199			−0.411553			−0.205776	+	0.978599i	$0.565972\pi$
$854$	−6.48256	−	11.2281i	−0.221829	−	0.384219i
$855$		0			0
$856$	2.70178	−	4.67963i	0.0923451	−	0.159946i
$857$	−47.3024			−1.61582			−0.807910	−	0.589306i	$-0.799401\pi$
$857$	−47.3024			−1.61582			−0.807910	+	0.589306i	$0.799401\pi$
$858$	−43.6948	−	22.2453i	−1.49172	−	0.759443i
$859$	−19.5027			−0.665423			−0.332712	−	0.943029i	$-0.607964\pi$
$859$	−19.5027			−0.665423			−0.332712	+	0.943029i	$0.607964\pi$
$860$		0			0
$861$	−7.64341	+	13.2388i	−0.260487	+	0.451176i
$862$	−22.1203	−	38.3135i	−0.753420	−	1.30496i
$863$	31.5568			1.07420			0.537102	−	0.843517i	$-0.319519\pi$
$863$	31.5568			1.07420			0.537102	+	0.843517i	$0.319519\pi$
$864$	−37.6081	−	65.1392i	−1.27945	−	2.21608i
$865$		0			0
$866$	−1.22640			−0.0416746
$867$	−13.6110	−	23.5749i	−0.462253	−	0.800645i
$868$	4.08895	−	7.08228i	0.138788	−	0.240388i
$869$	−7.99196	+	13.8425i	−0.271109	+	0.469574i
$870$		0			0
$871$	−34.8461	+	22.6458i	−1.18071	+	0.767323i
$872$	−28.6330			−0.969637
$873$	9.39131	−	16.2662i	0.317848	−	0.550528i
$874$	1.02928	−	1.78276i	0.0348158	−	0.0603028i
$875$		0			0
$876$	10.0212			0.338585
$877$	−5.20428	−	9.01408i	−0.175736	−	0.304384i	0.764680	−	0.644411i	$-0.222897\pi$
$877$	−5.20428	−	9.01408i	−0.175736	−	0.304384i	−0.940416	+	0.340027i	$0.889564\pi$
$878$	−19.5757	−	33.9062i	−0.660649	−	1.14428i
$879$	−49.7151			−1.67685
$880$		0			0
$881$	3.00838	−	5.21067i	0.101355	−	0.175552i	−0.810888	−	0.585201i	$-0.801016\pi$
$881$	3.00838	−	5.21067i	0.101355	−	0.175552i	0.912243	+	0.409649i	$0.134349\pi$
$882$	−20.3672	+	35.2770i	−0.685798	+	1.18784i
$883$	18.0630			0.607869			0.303934	−	0.952693i	$-0.401700\pi$
$883$	18.0630			0.607869			0.303934	+	0.952693i	$0.401700\pi$
$884$	7.20823	−	4.68449i	0.242439	−	0.157556i
$885$		0			0
$886$	−14.5213	+	25.1516i	−0.487852	+	0.844985i
$887$	6.89386	−	11.9405i	0.231473	−	0.400924i	−0.726769	−	0.686882i	$-0.758979\pi$
$887$	6.89386	−	11.9405i	0.231473	−	0.400924i	0.958242	+	0.285959i	$0.0923121\pi$
$888$	−4.94545	−	8.56577i	−0.165958	−	0.287448i
$889$	16.2349			0.544502
$890$		0			0
$891$	−65.0436	−	112.659i	−2.17904	−	3.77421i
$892$	2.99545			0.100295
$893$	5.36421	+	9.29108i	0.179506	+	0.310914i
$894$	2.68355	−	4.64804i	0.0897512	−	0.155454i
$895$		0			0
$896$	0.814233			0.0272016
$897$	0.428792	+	8.13006i	0.0143169	+	0.271455i
$898$	38.4270			1.28233
$899$	8.86951	−	15.3624i	0.295815	−	0.512366i
$900$		0			0
$901$	4.03488	+	6.98862i	0.134421	+	0.232825i
$902$	−11.5367			−0.384130
$903$	−13.0822	−	22.6591i	−0.435350	−	0.754047i
$904$	−17.3909	−	30.1219i	−0.578412	−	1.00184i
$905$		0			0
$906$	−34.0558	−	58.9864i	−1.13143	−	1.95969i
$907$	−7.81727	+	13.5399i	−0.259568	+	0.449585i	−0.966126	−	0.258070i	$-0.916914\pi$
$907$	−7.81727	+	13.5399i	−0.259568	+	0.449585i	0.706558	+	0.707655i	$0.250247\pi$
$908$	5.16156	−	8.94008i	0.171292	−	0.296687i
$909$	93.9158			3.11499
$910$		0			0
$911$	−34.5627			−1.14511			−0.572557	−	0.819865i	$-0.694048\pi$
$911$	−34.5627			−1.14511			−0.572557	+	0.819865i	$0.694048\pi$
$912$	8.30746	−	14.3889i	0.275087	−	0.476465i
$913$	−28.8780	+	50.0181i	−0.955722	+	1.65536i
$914$	6.42989	+	11.1369i	0.212682	+	0.368376i
$915$		0			0
$916$	−9.79806	−	16.9707i	−0.323737	−	0.560729i
$917$	−8.56842	−	14.8409i	−0.282954	−	0.490091i
$918$	−58.5697			−1.93309
$919$	14.7356	+	25.5229i	0.486084	+	0.841922i	0.999872	−	0.0159954i	$-0.00509170\pi$
$919$	14.7356	+	25.5229i	0.486084	+	0.841922i	−0.513788	+	0.857917i	$0.671758\pi$
$920$		0			0
$921$	24.7247	−	42.8244i	0.814705	−	1.41111i
$922$	−22.6902			−0.747263
$923$	1.62889	+	30.8844i	0.0536156	+	1.01657i
$924$	−15.7754			−0.518974
$925$		0			0
$926$	5.55352	−	9.61898i	0.182500	−	0.316099i
$927$	81.5451	+	141.240i	2.67829	+	4.63894i
$928$	−11.5864			−0.380342
$929$	−14.2382	−	24.6613i	−0.467140	−	0.809110i	0.532155	−	0.846647i	$-0.321382\pi$
$929$	−14.2382	−	24.6613i	−0.467140	−	0.809110i	−0.999295	+	0.0375367i	$0.988049\pi$
$930$		0			0
$931$	12.5010			0.409704
$932$	−3.52559	−	6.10651i	−0.115485	−	0.200025i
$933$	−23.8946	+	41.3867i	−0.782275	+	1.35494i
$934$	12.8204	−	22.2056i	0.419497	−	0.726591i
$935$		0			0
$936$	4.84704	+	91.9019i	0.158431	+	3.00391i
$937$	−36.3202			−1.18653			−0.593264	−	0.805008i	$-0.702161\pi$
$937$	−36.3202			−1.18653			−0.593264	+	0.805008i	$0.702161\pi$
$938$	10.0535	−	17.4132i	0.328259	−	0.568560i
$939$	35.3828	−	61.2848i	1.15467	−	1.99995i
$940$		0			0
$941$	46.7007			1.52240			0.761200	−	0.648517i	$-0.224610\pi$
$941$	46.7007			1.52240			0.761200	+	0.648517i	$0.224610\pi$
$942$	20.8153	+	36.0532i	0.678200	+	1.17468i
$943$	0.957797	+	1.65895i	0.0311902	+	0.0540229i
$944$	18.2730			0.594735
$945$		0			0
$946$	9.87295	−	17.1004i	0.320997	−	0.555983i
$947$	7.48133	−	12.9580i	0.243110	−	0.421080i	−0.718488	−	0.695539i	$-0.755166\pi$
$947$	7.48133	−	12.9580i	0.243110	−	0.421080i	0.961599	+	0.274459i	$0.0884989\pi$
$948$	11.6495			0.378358
$949$	−11.9804	−	6.09928i	−0.388899	−	0.197991i
$950$		0			0
$951$	−37.7921	+	65.4578i	−1.22549	+	2.12262i
$952$	−7.28668	+	12.6209i	−0.236163	+	0.409046i
$953$	14.9792	+	25.9447i	0.485224	+	0.840432i	0.999856	−	0.0169791i	$-0.00540488\pi$
$953$	14.9792	+	25.9447i	0.485224	+	0.840432i	−0.514632	+	0.857411i	$0.672072\pi$
$954$	−24.6559			−0.798263
$955$		0			0
$956$	1.69177	+	2.93023i	0.0547157	+	0.0947704i
$957$	−34.2191			−1.10615
$958$	−15.3127	−	26.5223i	−0.494730	−	0.856897i
$959$	10.1426	−	17.5675i	0.327522	−	0.567285i
$960$		0			0
$961$	10.3724			0.334593
$962$	0.199454	+	3.78173i	0.00643067	+	0.121928i
$963$	−14.6581			−0.472350
$964$	−7.24331	+	12.5458i	−0.233291	+	0.404073i
$965$		0			0
$966$	−1.96951	−	3.41129i	−0.0633680	−	0.109757i
$967$	13.5633			0.436166			0.218083	−	0.975930i	$-0.430020\pi$
$967$	13.5633			0.436166			0.218083	+	0.975930i	$0.430020\pi$
$968$	−3.98603	−	6.90400i	−0.128116	−	0.221903i
$969$	14.0543	+	24.3428i	0.451489	+	0.782002i
$970$		0			0
$971$	18.1715	+	31.4739i	0.583150	+	1.01005i	0.995103	+	0.0988405i	$0.0315134\pi$
$971$	18.1715	+	31.4739i	0.583150	+	1.01005i	−0.411953	+	0.911205i	$0.635153\pi$
$972$	−25.9538	+	44.9532i	−0.832468	+	1.44188i
$973$	−3.10650	+	5.38061i	−0.0995897	+	0.172494i
$974$	8.10663			0.259753
$975$		0			0
$976$	−13.1129			−0.419734
$977$	−1.38358	+	2.39642i	−0.0442645	+	0.0766684i	−0.887309	−	0.461176i	$-0.847428\pi$
$977$	−1.38358	+	2.39642i	−0.0442645	+	0.0766684i	0.843044	+	0.537844i	$0.180761\pi$
$978$	−23.0193	+	39.8706i	−0.736077	+	1.27492i
$979$	−3.04828	−	5.27978i	−0.0974235	−	0.168742i
$980$		0			0
$981$	38.8359	+	67.2658i	1.23994	+	2.14763i
$982$	−5.18873	−	8.98714i	−0.165579	−	0.286791i
$983$	−52.2816			−1.66752			−0.833762	−	0.552124i	$-0.813817\pi$
$983$	−52.2816			−1.66752			−0.833762	+	0.552124i	$0.813817\pi$
$984$	14.7304	+	25.5137i	0.469587	+	0.813348i
$985$		0			0
$986$	−4.51107	+	7.81341i	−0.143662	+	0.248830i
$987$	20.5287			0.653436
$988$	6.75885	−	4.39245i	0.215028	−	0.139742i
$989$	−3.27867			−0.104256
$990$		0			0
$991$	1.29643	−	2.24548i	0.0411825	−	0.0713302i	−0.844699	−	0.535241i	$-0.820221\pi$
$991$	1.29643	−	2.24548i	0.0411825	−	0.0713302i	0.885882	+	0.463911i	$0.153554\pi$
$992$	−13.5114	−	23.4024i	−0.428987	−	0.743027i
$993$	31.3869			0.996034
$994$	−7.48176	−	12.9588i	−0.237307	−	0.411028i
$995$		0			0
$996$	42.0941			1.33380
$997$	−8.58746	−	14.8739i	−0.271968	−	0.471062i	0.697398	−	0.716684i	$-0.254341\pi$
$997$	−8.58746	−	14.8739i	−0.271968	−	0.471062i	−0.969366	+	0.245622i	$0.921008\pi$
$998$	−16.7699	+	29.0464i	−0.530843	+	0.919447i
$999$	−8.57868	+	14.8587i	−0.271417	+	0.470109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.d.126.4	yes	10
5.2	odd	4		325.2.o.c.74.7		20
5.3	odd	4		325.2.o.c.74.4		20
5.4	even	2		325.2.e.c.126.2	✓	10
13.3	even	3	inner	325.2.e.d.276.4	yes	10
13.4	even	6		4225.2.a.bm.1.4		5
13.9	even	3		4225.2.a.bn.1.2		5
65.3	odd	12		325.2.o.c.224.7		20
65.4	even	6		4225.2.a.bo.1.2		5
65.9	even	6		4225.2.a.bp.1.4		5
65.29	even	6		325.2.e.c.276.2	yes	10
65.42	odd	12		325.2.o.c.224.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.e.c.126.2	✓	10	5.4	even	2
325.2.e.c.276.2	yes	10	65.29	even	6
325.2.e.d.126.4	yes	10	1.1	even	1	trivial
325.2.e.d.276.4	yes	10	13.3	even	3	inner
325.2.o.c.74.4		20	5.3	odd	4
325.2.o.c.74.7		20	5.2	odd	4
325.2.o.c.224.4		20	65.42	odd	12
325.2.o.c.224.7		20	65.3	odd	12
4225.2.a.bm.1.4		5	13.4	even	6
4225.2.a.bn.1.2		5	13.9	even	3
4225.2.a.bo.1.2		5	65.4	even	6
4225.2.a.bp.1.4		5	65.9	even	6

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.547998 - 0.949161i) q^{2} +(1.68234 - 2.91389i) q^{3} +(0.399395 + 0.691773i) q^{4} +(-1.84383 - 3.19362i) q^{6} +(0.795836 + 1.37843i) q^{7} +3.06747 q^{8} +(-4.16051 - 7.20621i) q^{9} +O(q^{10})\)	\(q+(0.547998 - 0.949161i) q^{2} +(1.68234 - 2.91389i) q^{3} +(0.399395 + 0.691773i) q^{4} +(-1.84383 - 3.19362i) q^{6} +(0.795836 + 1.37843i) q^{7} +3.06747 q^{8} +(-4.16051 - 7.20621i) q^{9} +(-1.84383 + 3.19362i) q^{11} +2.68767 q^{12} +(-3.21311 - 1.63582i) q^{13} +1.74447 q^{14} +(0.882175 - 1.52797i) q^{16} +(1.49244 + 2.58498i) q^{17} -9.11981 q^{18} +(1.39940 + 2.42382i) q^{19} +5.35546 q^{21} +(2.02084 + 3.50019i) q^{22} +(0.335546 - 0.581184i) q^{23} +(5.16051 - 8.93826i) q^{24} +(-3.31344 + 2.15334i) q^{26} -17.9035 q^{27} +(-0.635707 + 1.10108i) q^{28} +(-1.37894 + 2.38839i) q^{29} -6.43214 q^{31} +(2.10060 + 3.63835i) q^{32} +(6.20390 + 10.7455i) q^{33} +3.27141 q^{34} +(3.32338 - 5.75626i) q^{36} +(0.479163 - 0.829935i) q^{37} +3.06747 q^{38} +(-10.1721 + 6.61067i) q^{39} +(-1.42722 + 2.47202i) q^{41} +(2.93478 - 5.08319i) q^{42} +(-2.44279 - 4.23103i) q^{43} -2.94568 q^{44} +(-0.367758 - 0.636975i) q^{46} +3.83323 q^{47} +(-2.96823 - 5.14113i) q^{48} +(2.23329 - 3.86817i) q^{49} +10.0431 q^{51} +(-0.151689 - 2.87608i) q^{52} +2.70355 q^{53} +(-9.81108 + 16.9933i) q^{54} +(2.44120 + 4.22828i) q^{56} +9.41701 q^{57} +(1.51131 + 2.61767i) q^{58} +(5.17839 + 8.96924i) q^{59} +(-3.71607 - 6.43642i) q^{61} +(-3.52480 + 6.10513i) q^{62} +(6.62217 - 11.4699i) q^{63} +8.13321 q^{64} +13.5989 q^{66} +(5.76308 - 9.98194i) q^{67} +(-1.19215 + 2.06486i) q^{68} +(-1.12900 - 1.95549i) q^{69} +(-4.28885 - 7.42851i) q^{71} +(-12.7622 - 22.1048i) q^{72} +3.72859 q^{73} +(-0.525161 - 0.909606i) q^{74} +(-1.11782 + 1.93613i) q^{76} -5.86956 q^{77} +(0.700282 + 13.2776i) q^{78} +4.33442 q^{79} +(-17.6381 + 30.5501i) q^{81} +(1.56423 + 2.70932i) q^{82} +15.6619 q^{83} +(2.13895 + 3.70476i) q^{84} -5.35457 q^{86} +(4.63967 + 8.03615i) q^{87} +(-5.65590 + 9.79631i) q^{88} +(-0.826615 + 1.43174i) q^{89} +(-0.302256 - 5.73089i) q^{91} +0.536063 q^{92} +(-10.8210 + 18.7426i) q^{93} +(2.10060 - 3.63835i) q^{94} +14.1357 q^{96} +(1.12863 + 1.95484i) q^{97} +(-2.44768 - 4.23950i) q^{98} +30.6852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9	\( 10 q + 3 q^{3} - 6 q^{4} - 3 q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9} - 3 q^{11} - 4 q^{12} - 10 q^{13} - 16 q^{14} - 4 q^{16} + 4 q^{17} + 4 q^{18} + 4 q^{19} - 16 q^{21} + 8 q^{22} + 15 q^{23} + 14 q^{24} - 9 q^{26} - 42 q^{27} - 17 q^{28} + q^{29} + 31 q^{32} - 2 q^{33} + 54 q^{34} + 13 q^{36} + 17 q^{37} - 6 q^{38} - 10 q^{39} - 6 q^{41} + 32 q^{42} + 12 q^{43} - 16 q^{44} + 7 q^{46} + 24 q^{47} - 2 q^{48} - 7 q^{49} - 23 q^{52} - 16 q^{53} - 19 q^{54} + 17 q^{56} + 8 q^{57} + 38 q^{58} + 12 q^{59} - 5 q^{61} + 13 q^{62} + 26 q^{63} - 10 q^{64} + 86 q^{66} - 16 q^{67} + 25 q^{68} - 20 q^{69} - 19 q^{71} - 45 q^{72} + 16 q^{73} - 2 q^{74} - 24 q^{76} - 64 q^{77} - 42 q^{78} - 28 q^{79} - 29 q^{81} - 23 q^{82} + 14 q^{83} + 34 q^{84} - 84 q^{86} + 21 q^{87} + 2 q^{88} + 10 q^{89} + 17 q^{91} - 142 q^{92} - 33 q^{93} + 31 q^{94} + 34 q^{96} + 37 q^{97} - 21 q^{98} + 56 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 - 6 * q^4 - 3 * q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9 - 3 * q^11 - 4 * q^12 - 10 * q^13 - 16 * q^14 - 4 * q^16 + 4 * q^17 + 4 * q^18 + 4 * q^19 - 16 * q^21 + 8 * q^22 + 15 * q^23 + 14 * q^24 - 9 * q^26 - 42 * q^27 - 17 * q^28 + q^29 + 31 * q^32 - 2 * q^33 + 54 * q^34 + 13 * q^36 + 17 * q^37 - 6 * q^38 - 10 * q^39 - 6 * q^41 + 32 * q^42 + 12 * q^43 - 16 * q^44 + 7 * q^46 + 24 * q^47 - 2 * q^48 - 7 * q^49 - 23 * q^52 - 16 * q^53 - 19 * q^54 + 17 * q^56 + 8 * q^57 + 38 * q^58 + 12 * q^59 - 5 * q^61 + 13 * q^62 + 26 * q^63 - 10 * q^64 + 86 * q^66 - 16 * q^67 + 25 * q^68 - 20 * q^69 - 19 * q^71 - 45 * q^72 + 16 * q^73 - 2 * q^74 - 24 * q^76 - 64 * q^77 - 42 * q^78 - 28 * q^79 - 29 * q^81 - 23 * q^82 + 14 * q^83 + 34 * q^84 - 84 * q^86 + 21 * q^87 + 2 * q^88 + 10 * q^89 + 17 * q^91 - 142 * q^92 - 33 * q^93 + 31 * q^94 + 34 * q^96 + 37 * q^97 - 21 * q^98 + 56 * q^99

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