LMFDB - Embedded newform 325.2.e.e.126.1

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 54x^{8} + 78x^{6} + 92x^{4} + 10x^{2} + 1 $ x^12 + 8x^10 + 54x^8 + 78x^6 + 92x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			126.1
Root			$-1.27287 - 2.20467i$ of defining polynomial
Character	$\chi$	$=$	325.126
Dual form			325.2.e.e.276.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27287 + 2.20467i) q^{2} +(-1.07646 + 1.86449i) q^{3} +(-2.24039 - 3.88048i) q^{4} +(-2.74039 - 4.74650i) q^{6} +(-1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(-0.817544 - 1.41603i) q^{9} +O(q^{10})$	\(q+(-1.27287 + 2.20467i) q^{2} +(-1.07646 + 1.86449i) q^{3} +(-2.24039 - 3.88048i) q^{4} +(-2.74039 - 4.74650i) q^{6} +(-1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(-0.817544 - 1.41603i) q^{9} +(0.317544 - 0.550003i) q^{11} +9.64680 q^{12} +(-0.0716710 - 3.60484i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(-0.611979 - 1.05998i) q^{17} +4.16251 q^{18} +(-0.682456 - 1.18205i) q^{19} +6.32648 q^{21} +(0.808385 + 1.40016i) q^{22} +(1.07646 - 1.86449i) q^{23} +(-6.79833 + 11.7751i) q^{24} +(8.03872 + 4.43048i) q^{26} -2.93855 q^{27} +(-6.58351 + 11.4030i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(-2.74215 - 4.74954i) q^{32} +(0.683650 + 1.18412i) q^{33} +3.11588 q^{34} +(-3.66324 + 6.34492i) q^{36} +(0.611979 - 1.05998i) q^{37} +3.47471 q^{38} +(6.79833 + 3.74685i) q^{39} +(4.98079 - 8.62698i) q^{41} +(-8.05279 + 13.9478i) q^{42} +(-0.683650 - 1.18412i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} +6.16379 q^{47} +(-7.65998 - 13.2675i) q^{48} +(-0.817544 + 1.41603i) q^{49} +2.63509 q^{51} +(-13.8279 + 8.35437i) q^{52} -0.642285 q^{53} +(3.74039 - 6.47855i) q^{54} +(-9.27912 - 16.0719i) q^{56} +2.93855 q^{57} +(-3.81861 - 6.61402i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(11.4069 - 19.7574i) q^{62} +(-2.40240 + 4.16107i) q^{63} -0.270178 q^{64} -3.48079 q^{66} +(4.01502 - 6.95421i) q^{67} +(-2.74215 + 4.74954i) q^{68} +(2.31754 + 4.01410i) q^{69} +(-1.31754 - 2.28205i) q^{71} +(-5.16315 - 8.94284i) q^{72} +10.3263 q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} -1.86624 q^{77} +(-16.9140 + 10.2189i) q^{78} +1.03843 q^{79} +(5.61588 - 9.72698i) q^{81} +(12.6798 + 21.9620i) q^{82} -11.8452 q^{83} +(-14.1738 - 24.5498i) q^{84} +3.48079 q^{86} +(-3.22939 - 5.59346i) q^{87} +(2.00543 - 3.47351i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} -9.64680 q^{92} +(9.64680 - 16.7087i) q^{93} +(-7.84570 + 13.5891i) q^{94} +11.8073 q^{96} +(-7.39190 - 12.8031i) q^{97} +(-2.08125 - 3.60484i) q^{98} -1.03843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9	$ 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99}+O(q^{100}) $ 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9 + 44 * q^14 - 16 * q^16 - 12 * q^19 - 8 * q^21 - 32 * q^24 + 24 * q^26 - 18 * q^29 - 16 * q^31 - 16 * q^34 - 2 * q^36 + 32 * q^39 + 14 * q^41 + 4 * q^44 + 10 * q^46 - 6 * q^49 + 24 * q^51 + 22 * q^54 - 16 * q^56 + 4 * q^59 + 6 * q^61 + 12 * q^64 + 4 * q^66 + 24 * q^69 - 12 * q^71 - 8 * q^74 - 10 * q^76 + 104 * q^79 + 14 * q^81 - 90 * q^84 - 4 * q^86 - 20 * q^89 - 44 * q^91 - 56 * q^94 + 12 * q^96 - 104 * 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 $

$2$	−1.27287	+	2.20467i	−0.900055	+	1.55894i	−0.0726333	+	0.997359i	$0.523140\pi$
$2$	−1.27287	+	2.20467i	−0.900055	+	1.55894i	−0.827421	+	0.561582i	$0.810193\pi$
$3$	−1.07646	+	1.86449i	−0.621496	+	1.07646i	0.367711	+	0.929940i	$0.380142\pi$
$3$	−1.07646	+	1.86449i	−0.621496	+	1.07646i	−0.989207	+	0.146523i	$0.953192\pi$
$4$	−2.24039	−	3.88048i	−1.12020	−	1.94024i
$5$		0			0
$5$		0			0
$6$	−2.74039	−	4.74650i	−1.11876	−	1.93775i
$7$	−1.46928	−	2.54486i	−0.555334	−	0.961867i	−0.997877	−	0.0651198i	$-0.979257\pi$
$7$	−1.46928	−	2.54486i	−0.555334	−	0.961867i	0.442543	−	0.896747i	$-0.354076\pi$
$8$	6.31544			2.23284
$9$	−0.817544	−	1.41603i	−0.272515	−	0.472010i
$10$		0			0
$11$	0.317544	−	0.550003i	0.0957433	−	0.165832i	−0.814175	−	0.580619i	$-0.802811\pi$
$11$	0.317544	−	0.550003i	0.0957433	−	0.165832i	0.909919	+	0.414787i	$0.136144\pi$
$12$	9.64680			2.78479
$13$	−0.0716710	−	3.60484i	−0.0198779	−	0.999802i
$13$	−0.0716710	−	3.60484i	−0.0198779	−	0.999802i
$14$	7.48079			1.99932
$15$		0			0
$16$	−3.55794	+	6.16253i	−0.889484	+	1.54063i
$17$	−0.611979	−	1.05998i	−0.148427	−	0.257082i	0.782220	−	0.623003i	$-0.214088\pi$
$17$	−0.611979	−	1.05998i	−0.148427	−	0.257082i	−0.930646	+	0.365920i	$0.880754\pi$
$18$	4.16251			0.981113
$19$	−0.682456	−	1.18205i	−0.156566	−	0.271180i	0.777062	−	0.629424i	$-0.216709\pi$
$19$	−0.682456	−	1.18205i	−0.156566	−	0.271180i	−0.933628	+	0.358244i	$0.883376\pi$
$20$		0			0
$21$	6.32648			1.38055
$22$	0.808385	+	1.40016i	0.172348	+	0.298516i
$23$	1.07646	−	1.86449i	0.224458	−	0.388773i	−0.731699	−	0.681628i	$-0.761272\pi$
$23$	1.07646	−	1.86449i	0.224458	−	0.388773i	0.956157	+	0.292856i	$0.0946055\pi$
$24$	−6.79833	+	11.7751i	−1.38770	+	2.40357i
$25$		0			0
$26$	8.03872	+	4.43048i	1.57652	+	0.868888i
$27$	−2.93855			−0.565525
$28$	−6.58351	+	11.4030i	−1.24417	+	2.15496i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−8.96157			−1.60955			−0.804773	−	0.593583i	$-0.797713\pi$
$31$	−8.96157			−1.60955			−0.804773	+	0.593583i	$0.797713\pi$
$32$	−2.74215	−	4.74954i	−0.484747	−	0.839607i
$33$	0.683650	+	1.18412i	0.119008	+	0.206128i
$34$	3.11588			0.534368
$35$		0			0
$36$	−3.66324	+	6.34492i	−0.610540	+	1.05749i
$37$	0.611979	−	1.05998i	0.100609	−	0.174259i	−0.811327	−	0.584593i	$-0.801254\pi$
$37$	0.611979	−	1.05998i	0.100609	−	0.174259i	0.911936	+	0.410333i	$0.134588\pi$
$38$	3.47471			0.563672
$39$	6.79833	+	3.74685i	1.08860	+	0.599975i
$40$		0			0
$41$	4.98079	−	8.62698i	0.777868	−	1.34731i	−0.155300	−	0.987867i	$-0.549634\pi$
$41$	4.98079	−	8.62698i	0.777868	−	1.34731i	0.933168	−	0.359440i	$-0.117032\pi$
$42$	−8.05279	+	13.9478i	−1.24257	+	2.15220i
$43$	−0.683650	−	1.18412i	−0.104256	−	0.180576i	0.809178	−	0.587563i	$-0.199913\pi$
$43$	−0.683650	−	1.18412i	−0.104256	−	0.180576i	−0.913434	+	0.406987i	$0.866579\pi$
$44$	−2.84570			−0.429005
$45$		0			0
$46$	2.74039	+	4.74650i	0.404049	+	0.699833i
$47$	6.16379			0.899081			0.449540	−	0.893260i	$-0.351588\pi$
$47$	6.16379			0.899081			0.449540	+	0.893260i	$0.351588\pi$
$48$	−7.65998	−	13.2675i	−1.10562	−	1.91499i
$49$	−0.817544	+	1.41603i	−0.116792	+	0.202290i
$50$		0			0
$51$	2.63509			0.368986
$52$	−13.8279	+	8.35437i	−1.91759	+	1.15854i
$53$	−0.642285			−0.0882246			−0.0441123	−	0.999027i	$-0.514046\pi$
$53$	−0.642285			−0.0882246			−0.0441123	+	0.999027i	$0.514046\pi$
$54$	3.74039	−	6.47855i	0.509003	−	0.881619i
$55$		0			0
$56$	−9.27912	−	16.0719i	−1.23997	−	2.14770i
$57$	2.93855			0.389221
$58$	−3.81861	−	6.61402i	−0.501408	−	0.868464i
$59$	−3.79833	−	6.57890i	−0.494501	−	0.856500i	0.505479	−	0.862839i	$-0.331316\pi$
$59$	−3.79833	−	6.57890i	−0.494501	−	0.856500i	−0.999980	+	0.00633858i	$0.997982\pi$
$60$		0			0
$61$	1.13509	+	1.96603i	0.145333	+	0.251725i	0.929497	−	0.368829i	$-0.120241\pi$
$61$	1.13509	+	1.96603i	0.145333	+	0.251725i	−0.784164	+	0.620554i	$0.786908\pi$
$62$	11.4069	−	19.7574i	1.44868	−	2.50919i
$63$	−2.40240	+	4.16107i	−0.302674	+	0.524246i
$64$	−0.270178			−0.0337722
$65$		0			0
$66$	−3.48079			−0.428455
$67$	4.01502	−	6.95421i	0.490512	−	0.849592i	−0.509428	−	0.860513i	$-0.670143\pi$
$67$	4.01502	−	6.95421i	0.490512	−	0.849592i	0.999940	+	0.0109212i	$0.00347639\pi$
$68$	−2.74215	+	4.74954i	−0.332534	+	0.575966i
$69$	2.31754	+	4.01410i	0.279000	+	0.483241i
$70$		0			0
$71$	−1.31754	−	2.28205i	−0.156364	−	0.270830i	0.777191	−	0.629265i	$-0.216644\pi$
$71$	−1.31754	−	2.28205i	−0.156364	−	0.270830i	−0.933555	+	0.358435i	$0.883311\pi$
$72$	−5.16315	−	8.94284i	−0.608483	−	1.05392i
$73$	10.3263			1.20860			0.604301	−	0.796756i	$-0.293453\pi$
$73$	10.3263			1.20860			0.604301	+	0.796756i	$0.293453\pi$
$74$	1.55794	+	2.69843i	0.181107	+	0.313686i
$75$		0			0
$76$	−3.05794	+	5.29650i	−0.350770	+	0.607551i
$77$	−1.86624			−0.212678
$78$	−16.9140	+	10.2189i	−1.91513	+	1.15706i
$79$	1.03843			0.116832			0.0584161	−	0.998292i	$-0.481395\pi$
$79$	1.03843			0.116832			0.0584161	+	0.998292i	$0.481395\pi$
$80$		0			0
$81$	5.61588	−	9.72698i	0.623986	−	1.08078i
$82$	12.6798	+	21.9620i	1.40025	+	2.42530i
$83$	−11.8452			−1.30018			−0.650092	−	0.759855i	$-0.725270\pi$
$83$	−11.8452			−1.30018			−0.650092	+	0.759855i	$0.725270\pi$
$84$	−14.1738	−	24.5498i	−1.54649	−	2.67860i
$85$		0			0
$86$	3.48079			0.375343
$87$	−3.22939	−	5.59346i	−0.346227	−	0.599682i
$88$	2.00543	−	3.47351i	0.213780	−	0.370277i
$89$	6.27912	−	10.8758i	0.665585	−	1.15283i	−0.313541	−	0.949575i	$-0.601515\pi$
$89$	6.27912	−	10.8758i	0.665585	−	1.15283i	0.979126	−	0.203253i	$-0.0651513\pi$
$90$		0			0
$91$	−9.06851	+	5.47890i	−0.950638	+	0.574344i
$92$	−9.64680			−1.00575
$93$	9.64680	−	16.7087i	1.00033	−	1.73262i
$94$	−7.84570	+	13.5891i	−0.809222	+	1.40161i
$95$		0			0
$96$	11.8073			1.20507
$97$	−7.39190	−	12.8031i	−0.750534	−	1.29996i	−0.947564	−	0.319565i	$-0.896463\pi$
$97$	−7.39190	−	12.8031i	−0.750534	−	1.29996i	0.197031	−	0.980397i	$-0.436870\pi$
$98$	−2.08125	−	3.60484i	−0.210238	−	0.364144i
$99$	−1.03843			−0.104366
$100$		0			0
$101$	−6.61588	+	11.4590i	−0.658304	+	1.14022i	0.322750	+	0.946484i	$0.395393\pi$
$101$	−6.61588	+	11.4590i	−0.658304	+	1.14022i	−0.981054	+	0.193732i	$0.937941\pi$
$102$	−3.35412	+	5.80951i	−0.332108	+	0.575228i
$103$	−10.9686			−1.08077			−0.540383	−	0.841419i	$-0.681721\pi$
$103$	−10.9686			−1.08077			−0.540383	+	0.841419i	$0.681721\pi$
$104$	−0.452633	−	22.7661i	−0.0443843	−	2.23240i
$105$		0			0
$106$	0.817544	−	1.41603i	0.0794069	−	0.137537i
$107$	−5.33680	+	9.24360i	−0.515928	+	0.893613i	0.483901	+	0.875123i	$0.339219\pi$
$107$	−5.33680	+	9.24360i	−0.515928	+	0.893613i	−0.999829	+	0.0184903i	$0.994114\pi$
$108$	6.58351	+	11.4030i	0.633499	+	1.09725i
$109$	−3.27018			−0.313226			−0.156613	−	0.987660i	$-0.550058\pi$
$109$	−3.27018			−0.313226			−0.156613	+	0.987660i	$0.550058\pi$
$110$		0			0
$111$	1.31754	+	2.28205i	0.125056	+	0.216603i
$112$	20.9104			1.97584
$113$	−2.76490	−	4.78895i	−0.260100	−	0.450507i	0.706168	−	0.708044i	$-0.250422\pi$
$113$	−2.76490	−	4.78895i	−0.260100	−	0.450507i	−0.966268	+	0.257537i	$0.917089\pi$
$114$	−3.74039	+	6.47855i	−0.350320	+	0.606772i
$115$		0			0
$116$	13.4424			1.24809
$117$	−5.04596	+	3.04860i	−0.466499	+	0.281844i
$118$	19.3391			1.78031
$119$	−1.79833	+	3.11480i	−0.164853	+	0.285533i
$120$		0			0
$121$	5.29833	+	9.17698i	0.481666	+	0.834271i
$122$	−5.77928			−0.523231
$123$	10.7233	+	18.5732i	0.966884	+	1.67469i
$124$	20.0774	+	34.7752i	1.80301	+	3.12290i
$125$		0			0
$126$	−6.11588	−	10.5930i	−0.544845	−	0.943700i
$127$	−8.61586	+	14.9231i	−0.764534	+	1.32421i	0.175959	+	0.984397i	$0.443697\pi$
$127$	−8.61586	+	14.9231i	−0.764534	+	1.32421i	−0.940493	+	0.339813i	$0.889636\pi$
$128$	5.82819	−	10.0947i	0.515144	−	0.892256i
$129$	2.94369			0.259178
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	3.06329	−	5.30577i	0.266625	−	0.461808i
$133$	−2.00543	+	3.47351i	−0.173893	+	0.301191i
$134$	10.2212	+	17.7036i	0.882975	+	1.52936i
$135$		0			0
$136$	−3.86491	−	6.69422i	−0.331413	−	0.574025i
$137$	−4.33616	−	7.51044i	−0.370463	−	0.641661i	0.619174	−	0.785254i	$-0.287468\pi$
$137$	−4.33616	−	7.51044i	−0.370463	−	0.641661i	−0.989637	+	0.143593i	$0.954134\pi$
$138$	−11.7997			−1.00446
$139$	−7.16324	−	12.4071i	−0.607578	−	1.05236i	−0.991638	−	0.129048i	$-0.958808\pi$
$139$	−7.16324	−	12.4071i	−0.607578	−	1.05236i	0.384060	−	0.923308i	$-0.374526\pi$
$140$		0			0
$141$	−6.63509	+	11.4923i	−0.558775	+	0.967827i
$142$	6.70825			0.562944
$143$	−2.00543	−	1.10528i	−0.167703	−	0.0924279i
$144$	11.6351			0.969591
$145$		0			0
$146$	−13.1440	+	22.7661i	−1.08781	+	1.88414i
$147$	−1.76011	−	3.04860i	−0.145172	−	0.251445i
$148$	−5.48429			−0.450806
$149$	8.57745	+	14.8566i	0.702692	+	1.21710i	0.967518	+	0.252802i	$0.0813521\pi$
$149$	8.57745	+	14.8566i	0.702692	+	1.21710i	−0.264826	+	0.964296i	$0.585315\pi$
$150$		0			0
$151$	−21.3828			−1.74011			−0.870053	−	0.492957i	$-0.835916\pi$
$151$	−21.3828			−1.74011			−0.870053	+	0.492957i	$0.835916\pi$
$152$	−4.31000	−	7.46515i	−0.349587	−	0.605503i
$153$	−1.00064	+	1.73316i	−0.0808969	+	0.140118i
$154$	2.37548	−	4.11446i	0.191422	−	0.331552i
$155$		0			0
$156$	−0.691395	−	34.7752i	−0.0553559	−	2.78424i
$157$	18.3646			1.46566			0.732829	−	0.680413i	$-0.238200\pi$
$157$	18.3646			1.46566			0.732829	+	0.680413i	$0.238200\pi$
$158$	−1.32178	+	2.28939i	−0.105155	+	0.182134i
$159$	0.691395	−	1.19753i	0.0548312	−	0.0949705i
$160$		0			0
$161$	−6.32648			−0.498597
$162$	14.2966	+	24.7624i	1.12324	+	1.94551i
$163$	−2.00543	−	3.47351i	−0.157078	−	0.272066i	0.776736	−	0.629826i	$-0.216874\pi$
$163$	−2.00543	−	3.47351i	−0.157078	−	0.272066i	−0.933814	+	0.357760i	$0.883541\pi$
$164$	−44.6357			−3.48546
$165$		0			0
$166$	15.0774	−	26.1149i	1.17024	−	2.02691i
$167$	1.46928	−	2.54486i	0.113696	−	0.196927i	−0.803562	−	0.595221i	$-0.797064\pi$
$167$	1.46928	−	2.54486i	0.113696	−	0.196927i	0.917258	+	0.398294i	$0.130398\pi$
$168$	39.9545			3.08256
$169$	−12.9897	+	0.516725i	−0.999210	+	0.0397480i
$170$		0			0
$171$	−1.11588	+	1.93275i	−0.0853331	+	0.147801i
$172$	−3.06329	+	5.30577i	−0.233574	+	0.404561i
$173$	0.683650	+	1.18412i	0.0519769	+	0.0900267i	0.890843	−	0.454311i	$-0.150114\pi$
$173$	0.683650	+	1.18412i	0.0519769	+	0.0900267i	−0.838866	+	0.544337i	$0.816781\pi$
$174$	16.4424			1.24649
$175$		0			0
$176$	2.25961	+	3.91375i	0.170324	+	0.295010i
$177$	16.3550			1.22932
$178$	15.9850	+	27.6868i	1.19813	+	2.07522i
$179$	−3.89306	+	6.74299i	−0.290981	+	0.503994i	−0.974042	−	0.226367i	$-0.927315\pi$
$179$	−3.89306	+	6.74299i	−0.290981	+	0.503994i	0.683061	+	0.730362i	$0.260648\pi$
$180$		0			0
$181$	−3.86684			−0.287420			−0.143710	−	0.989620i	$-0.545903\pi$
$181$	−3.86684			−0.287420			−0.143710	+	0.989620i	$0.545903\pi$
$182$	−0.536155	−	26.9670i	−0.0397425	−	1.99893i
$183$	−4.88752			−0.361296
$184$	6.79833	−	11.7751i	0.501180	−	0.868069i
$185$		0			0
$186$	24.5582	+	42.5361i	1.80070	+	3.11890i
$187$	−0.777322			−0.0568434
$188$	−13.8093	−	23.9184i	−1.00715	−	1.74443i
$189$	4.31754	+	7.47821i	0.314055	+	0.543959i
$190$		0			0
$191$	−2.47185	−	4.28136i	−0.178857	−	0.309789i	0.762633	−	0.646832i	$-0.223906\pi$
$191$	−2.47185	−	4.28136i	−0.178857	−	0.309789i	−0.941489	+	0.337043i	$0.890573\pi$
$192$	0.290836	−	0.503743i	0.0209893	−	0.0363545i
$193$	2.47822	−	4.29240i	0.178386	−	0.308974i	−0.762942	−	0.646467i	$-0.776246\pi$
$193$	2.47822	−	4.29240i	0.178386	−	0.308974i	0.941328	+	0.337493i	$0.109579\pi$
$194$	37.6357			2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	3.37273	−	5.84174i	0.240297	−	0.416207i	−0.720502	−	0.693453i	$-0.756088\pi$
$197$	3.37273	−	5.84174i	0.240297	−	0.416207i	0.960799	+	0.277246i	$0.0894218\pi$
$198$	1.32178	−	2.28939i	0.0939349	−	0.162700i
$199$	−2.58772	−	4.48207i	−0.183439	−	0.317725i	0.759611	−	0.650378i	$-0.225390\pi$
$199$	−2.58772	−	4.48207i	−0.183439	−	0.317725i	−0.943049	+	0.332653i	$0.892056\pi$
$200$		0			0
$201$	8.64403	+	14.9719i	0.609703	+	1.05604i
$202$	−16.8423	−	29.1717i	−1.18502	−	2.05251i
$203$	8.81566			0.618738
$204$	−5.90364	−	10.2254i	−0.413337	−	0.715921i
$205$		0			0
$206$	13.9616	−	24.1822i	0.972749	−	1.68485i
$207$	−3.52022			−0.244673
$208$	22.4699	+	12.3841i	1.55801	+	0.858684i
$209$	−0.866840			−0.0599606
$210$		0			0
$211$	7.00894	−	12.1398i	0.482515	−	0.835741i	−0.517283	−	0.855814i	$-0.673057\pi$
$211$	7.00894	−	12.1398i	0.482515	−	0.835741i	0.999799	+	0.0200732i	$0.00638994\pi$
$212$	1.43897	+	2.49237i	0.0988289	+	0.171177i
$213$	5.67315			0.388718
$214$	−13.5861	−	23.5318i	−0.928726	−	1.60860i
$215$		0			0
$216$	−18.5582			−1.26273
$217$	13.1670	+	22.8060i	0.893836	+	1.54817i
$218$	4.16251	−	7.20968i	0.281921	−	0.488301i
$219$	−11.1159	+	19.2533i	−0.751141	+	1.30101i
$220$		0			0
$221$	−3.77719	+	2.28205i	−0.254081	+	0.153508i
$222$	−6.70825			−0.450228
$223$	−0.00415245	+	0.00719226i	−0.000278069	+	0.000481629i	−0.866164	−	0.499759i	$-0.833422\pi$
$223$	−0.00415245	+	0.00719226i	−0.000278069	+	0.000481629i	0.865886	+	0.500241i	$0.166755\pi$
$224$	−8.05794	+	13.9568i	−0.538394	+	0.932525i
$225$		0			0
$226$	14.0774			0.936418
$227$	5.63179	+	9.75454i	0.373795	+	0.647431i	0.990146	−	0.140040i	$-0.0447231\pi$
$227$	5.63179	+	9.75454i	0.373795	+	0.647431i	−0.616351	+	0.787471i	$0.711390\pi$
$228$	−6.58351	−	11.4030i	−0.436004	−	0.755181i
$229$	−16.5404			−1.09302			−0.546509	−	0.837453i	$-0.684043\pi$
$229$	−16.5404			−1.09302			−0.546509	+	0.837453i	$0.684043\pi$
$230$		0			0
$231$	2.00894	−	3.47959i	0.132179	−	0.228940i
$232$	−9.47315	+	16.4080i	−0.621943	+	1.07724i
$233$	−6.94941			−0.455271			−0.227636	−	0.973746i	$-0.573100\pi$
$233$	−6.94941			−0.455271			−0.227636	+	0.973746i	$0.573100\pi$
$234$	−0.298331	−	15.0052i	−0.0195025	−	0.980919i
$235$		0			0
$236$	−17.0195	+	29.4787i	−1.10788	+	1.91890i
$237$	−1.11783	+	1.93613i	−0.0726107	+	0.125765i
$238$	−4.57808	−	7.92947i	−0.296753	−	0.513991i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	−9.88605	−	17.1231i	−0.636817	−	1.10300i	−0.986127	−	0.165992i	$-0.946917\pi$
$241$	−9.88605	−	17.1231i	−0.636817	−	1.10300i	0.349310	−	0.937007i	$-0.386416\pi$
$242$	−26.9763			−1.73410
$243$	7.68273	+	13.3069i	0.492848	+	0.853637i
$244$	5.08609	−	8.80937i	0.325604	−	0.563962i
$245$		0			0
$246$	−54.5973			−3.48099
$247$	−4.21218	+	2.54486i	−0.268015	+	0.161926i
$248$	−56.5962			−3.59386
$249$	12.7510	−	22.0853i	0.808060	−	1.39960i
$250$		0			0
$251$	−1.83676	−	3.18136i	−0.115935	−	0.200806i	0.802218	−	0.597031i	$-0.203653\pi$
$251$	−1.83676	−	3.18136i	−0.115935	−	0.200806i	−0.918153	+	0.396226i	$0.870320\pi$
$252$	21.5293			1.35622
$253$	−0.683650	−	1.18412i	−0.0429807	−	0.0744447i
$254$	−21.9337	−	37.9903i	−1.37624	−	2.38372i
$255$		0			0
$256$	14.5669	+	25.2306i	0.910430	+	1.57691i
$257$	−6.63242	+	11.4877i	−0.413719	+	0.716583i	−0.995293	−	0.0969108i	$-0.969104\pi$
$257$	−6.63242	+	11.4877i	−0.413719	+	0.716583i	0.581574	+	0.813494i	$0.302437\pi$
$258$	−3.74694	+	6.48989i	−0.233274	+	0.404043i
$259$	−3.59666			−0.223486
$260$		0			0
$261$	4.90527			0.303628
$262$	−12.7287	+	22.0467i	−0.786381	+	1.36205i
$263$	−15.1352	+	26.2150i	−0.933279	+	1.61649i	−0.155605	+	0.987819i	$0.549733\pi$
$263$	−15.1352	+	26.2150i	−0.933279	+	1.61649i	−0.777674	+	0.628667i	$0.783601\pi$
$264$	4.31754	+	7.47821i	0.265726	+	0.460252i
$265$		0			0
$266$	−5.10530	−	8.84265i	−0.313026	−	0.542177i
$267$	13.5185	+	23.4147i	0.827317	+	1.43296i
$268$	−35.9809			−2.19788
$269$	11.1248	+	19.2687i	0.678292	+	1.17484i	0.975495	+	0.220022i	$0.0706129\pi$
$269$	11.1248	+	19.2687i	0.678292	+	1.17484i	−0.297203	+	0.954814i	$0.596054\pi$
$270$		0			0
$271$	5.91421	−	10.2437i	0.359262	−	0.622261i	−0.628575	−	0.777749i	$-0.716362\pi$
$271$	5.91421	−	10.2437i	0.359262	−	0.622261i	0.987838	+	0.155488i	$0.0496950\pi$
$272$	8.70953			0.528093
$273$	−0.453425	−	22.8060i	−0.0274425	−	1.38028i
$274$	22.0774			1.33375
$275$		0			0
$276$	10.3844	−	17.9863i	0.625069	−	1.08265i
$277$	−8.39254	−	14.5363i	−0.504259	−	0.873402i	−0.999988	−	0.00492452i	$-0.998432\pi$
$277$	−8.39254	−	14.5363i	−0.504259	−	0.873402i	0.495729	−	0.868477i	$-0.334901\pi$
$278$	36.4715			2.18741
$279$	7.32648	+	12.6898i	0.438625	+	0.759721i
$280$		0			0
$281$	−10.5967			−0.632144			−0.316072	−	0.948735i	$-0.602364\pi$
$281$	−10.5967			−0.632144			−0.316072	+	0.948735i	$0.602364\pi$
$282$	−16.8912	−	29.2564i	−1.00586	−	1.74219i
$283$	4.40783	−	7.63458i	0.262018	−	0.453829i	−0.704760	−	0.709446i	$-0.748945\pi$
$283$	4.40783	−	7.63458i	0.262018	−	0.453829i	0.966778	+	0.255617i	$0.0822786\pi$
$284$	−5.90364	+	10.2254i	−0.350316	+	0.606766i
$285$		0			0
$286$	4.98943	−	3.01445i	0.295031	−	0.178248i
$287$	−29.2726			−1.72791
$288$	−4.48365	+	7.76591i	−0.264202	+	0.457611i
$289$	7.75096	−	13.4251i	0.455939	−	0.789710i
$290$		0			0
$291$	31.8284			1.86581
$292$	−23.1350	−	40.0709i	−1.35387	−	2.34497i
$293$	14.1263	+	24.4675i	0.825267	+	1.42940i	0.901715	+	0.432331i	$0.142309\pi$
$293$	14.1263	+	24.4675i	0.825267	+	1.42940i	−0.0764476	+	0.997074i	$0.524358\pi$
$294$	8.96157			0.522650
$295$		0			0
$296$	3.86491	−	6.69422i	0.224643	−	0.389094i
$297$	−0.933121	+	1.61621i	−0.0541452	+	0.0937822i
$298$	−43.6719			−2.52984
$299$	−6.79833	−	3.74685i	−0.393158	−	0.216686i
$300$		0			0
$301$	−2.00894	+	3.47959i	−0.115793	+	0.200560i
$302$	27.2175	−	47.1421i	1.56619	−	2.71272i
$303$	−14.2435	−	24.6704i	−0.818267	−	1.41728i
$304$	9.71254			0.557052
$305$		0			0
$306$	−2.54737	−	4.41217i	−0.145623	−	0.252227i
$307$	12.7219			0.726077			0.363039	−	0.931774i	$-0.381739\pi$
$307$	12.7219			0.726077			0.363039	+	0.931774i	$0.381739\pi$
$308$	4.18112	+	7.24190i	0.238241	+	0.412646i
$309$	11.8073	−	20.4508i	0.671692	−	1.16340i
$310$		0			0
$311$	27.9231			1.58338			0.791688	−	0.610925i	$-0.209202\pi$
$311$	27.9231			1.58338			0.791688	+	0.610925i	$0.209202\pi$
$312$	42.9344	+	23.6630i	2.43068	+	1.33965i
$313$	24.5807			1.38938			0.694692	−	0.719307i	$-0.255540\pi$
$313$	24.5807			1.38938			0.694692	+	0.719307i	$0.255540\pi$
$314$	−23.3758	+	40.4880i	−1.31917	+	2.28487i
$315$		0			0
$316$	−2.32648	−	4.02959i	−0.130875	−	0.226682i
$317$	−0.234377			−0.0131639			−0.00658196	−	0.999978i	$-0.502095\pi$
$317$	−0.234377			−0.0131639			−0.00658196	+	0.999978i	$0.502095\pi$
$318$	1.76011	+	3.04860i	0.0987022	+	0.170957i
$319$	0.952633	+	1.65001i	0.0533372	+	0.0923828i
$320$		0			0
$321$	−11.4897	−	19.9008i	−0.641294	−	1.11075i
$322$	8.05279	−	13.9478i	0.448764	−	0.777283i
$323$	−0.835296	+	1.44678i	−0.0464771	+	0.0805008i
$324$	−50.3271			−2.79595
$325$		0			0
$326$	10.2106			0.565513
$327$	3.52022	−	6.09721i	0.194669	−	0.337176i
$328$	31.4558	−	54.4831i	1.73686	−	3.00833i
$329$	−9.05631	−	15.6860i	−0.499290	−	0.864796i
$330$		0			0
$331$	9.16324	+	15.8712i	0.503657	+	0.872360i	0.999991	+	0.00422829i	$0.00134591\pi$
$331$	9.16324	+	15.8712i	0.503657	+	0.872360i	−0.496334	+	0.868132i	$0.665321\pi$
$332$	26.5380	+	45.9652i	1.45646	+	2.52267i
$333$	−2.00128			−0.109669
$334$	3.74039	+	6.47855i	0.204665	+	0.354491i
$335$		0			0
$336$	−22.5092	+	38.9871i	−1.22798	+	2.12692i
$337$	−21.2949			−1.16001			−0.580003	−	0.814614i	$-0.696949\pi$
$337$	−21.2949			−1.16001			−0.580003	+	0.814614i	$0.696949\pi$
$338$	15.3950	−	29.2958i	0.837379	−	1.59348i
$339$	11.9053			0.646605
$340$		0			0
$341$	−2.84570	+	4.92889i	−0.154103	+	0.266915i
$342$	−2.84073	−	4.92028i	−0.153609	−	0.266059i
$343$	−15.7651			−0.851234
$344$	−4.31754	−	7.47821i	−0.232786	−	0.403198i
$345$		0			0
$346$	−3.48079			−0.187128
$347$	1.90761	+	3.30407i	0.102406	+	0.177372i	0.912675	−	0.408685i	$-0.134013\pi$
$347$	1.90761	+	3.30407i	0.102406	+	0.177372i	−0.810270	+	0.586057i	$0.800679\pi$
$348$	−14.4702	+	25.0631i	−0.775684	+	1.34352i
$349$	−12.1632	+	21.0674i	−0.651083	+	1.12771i	0.331777	+	0.943358i	$0.392352\pi$
$349$	−12.1632	+	21.0674i	−0.651083	+	1.12771i	−0.982860	+	0.184352i	$0.940981\pi$
$350$		0			0
$351$	0.210609	+	10.5930i	0.0112415	+	0.565413i
$352$	−3.48301			−0.185645
$353$	13.5295	−	23.4338i	0.720104	−	1.24726i	−0.240853	−	0.970562i	$-0.577427\pi$
$353$	13.5295	−	23.4338i	0.720104	−	1.24726i	0.960958	−	0.276696i	$-0.0892394\pi$
$354$	−20.8178	+	36.0576i	−1.10646	+	1.91644i
$355$		0			0
$356$	−56.2708			−2.98235
$357$	−3.87167	−	6.70593i	−0.204911	−	0.354916i
$358$	−9.91073	−	17.1659i	−0.523798	−	0.907245i
$359$	27.0039			1.42521			0.712605	−	0.701566i	$-0.247515\pi$
$359$	27.0039			1.42521			0.712605	+	0.701566i	$0.247515\pi$
$360$		0			0
$361$	8.56851	−	14.8411i	0.450974	−	0.781110i
$362$	4.92198	−	8.52512i	0.258694	−	0.448071i
$363$	−22.8138			−1.19742
$364$	41.5777	+	22.9152i	2.17927	+	1.20108i
$365$		0			0
$366$	6.22118	−	10.7754i	0.325186	−	0.563239i
$367$	3.47055	−	6.01118i	0.181161	−	0.313781i	−0.761115	−	0.648617i	$-0.775348\pi$
$367$	3.47055	−	6.01118i	0.181161	−	0.313781i	0.942276	+	0.334836i	$0.108681\pi$
$368$	7.65998	+	13.2675i	0.399304	+	0.691615i
$369$	−16.2881			−0.847922
$370$		0			0
$371$	0.943693	+	1.63452i	0.0489941	+	0.0848603i
$372$	−86.4505			−4.48225
$373$	−1.15644	−	2.00301i	−0.0598781	−	0.103712i	0.834532	−	0.550959i	$-0.185738\pi$
$373$	−1.15644	−	2.00301i	−0.0598781	−	0.103712i	−0.894411	+	0.447247i	$0.852405\pi$
$374$	0.989429	−	1.71374i	0.0511622	−	0.0886154i
$375$		0			0
$376$	38.9270			2.00751
$377$	9.47315	+	5.22105i	0.487892	+	0.268898i
$378$	−21.9827			−1.13067
$379$	−2.58772	+	4.48207i	−0.132922	+	0.230228i	−0.924802	−	0.380449i	$-0.875769\pi$
$379$	−2.58772	+	4.48207i	−0.132922	+	0.230228i	0.791880	+	0.610677i	$0.209103\pi$
$380$		0			0
$381$	−18.5493	−	32.1283i	−0.950309	−	1.64598i
$382$	12.5854			0.643923
$383$	10.3305	+	17.8929i	0.527861	+	0.914283i	0.999473	+	0.0324760i	$0.0103393\pi$
$383$	10.3305	+	17.8929i	0.527861	+	0.914283i	−0.471611	+	0.881807i	$0.656327\pi$
$384$	12.5477	+	21.7332i	0.640320	+	1.10907i
$385$		0			0
$386$	6.30890	+	10.9273i	0.321115	+	0.556187i
$387$	−1.11783	+	1.93613i	−0.0568224	+	0.0984193i
$388$	−33.1215	+	57.3682i	−1.68149	+	2.91243i
$389$	19.7477			1.00125			0.500624	−	0.865665i	$-0.333104\pi$
$389$	19.7477			1.00125			0.500624	+	0.865665i	$0.333104\pi$
$390$		0			0
$391$	−2.63509			−0.133262
$392$	−5.16315	+	8.94284i	−0.260778	+	0.451681i
$393$	−10.7646	+	18.6449i	−0.543004	+	0.940510i
$394$	8.58609	+	14.8715i	0.432561	+	0.749218i
$395$		0			0
$396$	2.32648	+	4.02959i	0.116910	+	0.202494i
$397$	4.69451	+	8.13113i	0.235611	+	0.408090i	0.959450	−	0.281879i	$-0.0909576\pi$
$397$	4.69451	+	8.13113i	0.235611	+	0.408090i	−0.723839	+	0.689969i	$0.757624\pi$
$398$	13.1753			0.660420
$399$	−4.31754	−	7.47821i	−0.216148	−	0.374379i
$400$		0			0
$401$	−12.2510	+	21.2193i	−0.611784	+	1.05964i	0.379156	+	0.925333i	$0.376214\pi$
$401$	−12.2510	+	21.2193i	−0.611784	+	1.05964i	−0.990940	+	0.134308i	$0.957119\pi$
$402$	−44.0109			−2.19506
$403$	0.642285	+	32.3050i	0.0319945	+	1.60923i
$404$	59.2887			2.94972
$405$		0			0
$406$	−11.2212	+	19.4357i	−0.556898	+	0.964575i
$407$	−0.388661	−	0.673180i	−0.0192652	−	0.0333683i
$408$	16.6417			0.823889
$409$	−18.0582	−	31.2778i	−0.892922	−	1.54659i	−0.836355	−	0.548188i	$-0.815318\pi$
$409$	−18.0582	−	31.2778i	−0.892922	−	1.54659i	−0.0565671	−	0.998399i	$-0.518015\pi$
$410$		0			0
$411$	18.6708			0.920965
$412$	24.5739	+	42.5633i	1.21067	+	2.09694i
$413$	−11.1616	+	19.3324i	−0.549226	+	0.951288i
$414$	4.48079	−	7.76095i	0.220219	−	0.381430i
$415$		0			0
$416$	−16.9248	+	10.2254i	−0.829805	+	0.501341i
$417$	30.8439			1.51043
$418$	1.10337	−	1.91110i	0.0539678	−	0.0934749i
$419$	3.43342	−	5.94686i	0.167734	−	0.290523i	−0.769889	−	0.638178i	$-0.779689\pi$
$419$	3.43342	−	5.94686i	0.167734	−	0.290523i	0.937623	+	0.347655i	$0.113022\pi$
$420$		0			0
$421$	33.9795			1.65606			0.828029	−	0.560686i	$-0.189462\pi$
$421$	33.9795			1.65606			0.828029	+	0.560686i	$0.189462\pi$
$422$	17.8429	+	30.9049i	0.868580	+	1.50443i
$423$	−5.03917	−	8.72810i	−0.245013	−	0.424375i
$424$	−4.05631			−0.196992
$425$		0			0
$426$	−7.22118	+	12.5075i	−0.349867	+	0.605988i
$427$	3.33552	−	5.77729i	0.161417	−	0.279582i
$428$	47.8261			2.31176
$429$	4.21955	−	2.54931i	0.203722	−	0.123082i
$430$		0			0
$431$	8.12482	−	14.0726i	0.391359	−	0.677853i	−0.601270	−	0.799046i	$-0.705339\pi$
$431$	8.12482	−	14.0726i	0.391359	−	0.677853i	0.992629	+	0.121193i	$0.0386719\pi$
$432$	10.4552	−	18.1089i	0.503025	−	0.871265i
$433$	−0.128130	−	0.221929i	−0.00615756	−	0.0106652i	0.862930	−	0.505323i	$-0.168627\pi$
$433$	−0.128130	−	0.221929i	−0.00615756	−	0.0106652i	−0.869088	+	0.494658i	$0.835293\pi$
$434$	−67.0396			−3.21800
$435$		0			0
$436$	7.32648	+	12.6898i	0.350875	+	0.607733i
$437$	−2.93855			−0.140570
$438$	−28.2981	−	49.0138i	−1.35214	−	2.34197i
$439$	3.79833	−	6.57890i	0.181284	−	0.313994i	−0.761034	−	0.648712i	$-0.775308\pi$
$439$	3.79833	−	6.57890i	0.181284	−	0.313994i	0.942318	+	0.334718i	$0.108641\pi$
$440$		0			0
$441$	2.67352			0.127310
$442$	−0.223318	−	11.2322i	−0.0106221	−	0.534263i
$443$	4.32246			0.205366			0.102683	−	0.994714i	$-0.467257\pi$
$443$	4.32246			0.205366			0.102683	+	0.994714i	$0.467257\pi$
$444$	5.90364	−	10.2254i	0.280174	−	0.485276i
$445$		0			0
$446$	−0.0105711	−	0.0183096i	−0.000500554	−	0.000866986i
$447$	−36.9332			−1.74688
$448$	0.396966	+	0.687565i	0.0187549	+	0.0324844i
$449$	−1.64403	−	2.84754i	−0.0775865	−	0.134384i	0.824622	−	0.565685i	$-0.191388\pi$
$449$	−1.64403	−	2.84754i	−0.0775865	−	0.134384i	−0.902208	+	0.431301i	$0.858055\pi$
$450$		0			0
$451$	−3.16324	−	5.47890i	−0.148951	−	0.257991i
$452$	−12.3889	+	21.4583i	−0.582727	+	1.00931i
$453$	23.0178	−	39.8680i	1.08147	−	1.87316i
$454$	−28.6741			−1.34574
$455$		0			0
$456$	18.5582			0.869069
$457$	7.71304	−	13.3594i	0.360801	−	0.624925i	−0.627292	−	0.778784i	$-0.715837\pi$
$457$	7.71304	−	13.3594i	0.360801	−	0.624925i	0.988093	+	0.153859i	$0.0491701\pi$
$458$	21.0537	−	36.4661i	0.983775	−	1.70395i
$459$	1.79833	+	3.11480i	0.0839389	+	0.145386i
$460$		0			0
$461$	−12.9424	−	22.4168i	−0.602786	−	1.04406i	−0.992397	−	0.123076i	$-0.960724\pi$
$461$	−12.9424	−	22.4168i	−0.602786	−	1.04406i	0.389611	−	0.920979i	$-0.372609\pi$
$462$	5.11424	+	8.85812i	0.237936	+	0.412117i
$463$	7.04045			0.327197			0.163599	−	0.986527i	$-0.447690\pi$
$463$	7.04045			0.327197			0.163599	+	0.986527i	$0.447690\pi$
$464$	−10.6738	−	18.4876i	−0.495519	−	0.858265i
$465$		0			0
$466$	8.84570	−	15.3212i	0.409769	−	0.709741i
$467$	18.8113			0.870482			0.435241	−	0.900314i	$-0.356663\pi$
$467$	18.8113			0.870482			0.435241	+	0.900314i	$0.356663\pi$
$468$	23.1350	+	12.7507i	1.06941	+	0.589399i
$469$	−23.5967			−1.08959
$470$		0			0
$471$	−19.7688	+	34.2406i	−0.910900	+	1.57773i
$472$	−23.9881	−	41.5486i	−1.10414	−	1.91243i
$473$	−0.868356			−0.0399271
$474$	−2.84570	−	4.92889i	−0.130707	−	0.226392i
$475$		0			0
$476$	16.1159			0.738670
$477$	0.525096	+	0.909493i	0.0240425	+	0.0416428i
$478$	−5.09148	+	8.81870i	−0.232879	+	0.403358i
$479$	9.73876	−	16.8680i	0.444975	−	0.770720i	−0.553075	−	0.833131i	$-0.686546\pi$
$479$	9.73876	−	16.8680i	0.444975	−	0.770720i	0.998051	+	0.0624114i	$0.0198791\pi$
$480$		0			0
$481$	−3.86491	−	2.13011i	−0.176225	−	0.0971249i
$482$	50.3346			2.29268
$483$	6.81023	−	11.7957i	0.309876	−	0.536721i
$484$	23.7407	−	41.1201i	1.07912	−	1.86909i
$485$		0			0
$486$	−39.1165			−1.77436
$487$	16.1620	+	27.9935i	0.732372	+	1.26851i	0.955867	+	0.293800i	$0.0949200\pi$
$487$	16.1620	+	27.9935i	0.732372	+	1.26851i	−0.223495	+	0.974705i	$0.571747\pi$
$488$	7.16858	+	12.4163i	0.324506	+	0.562062i
$489$	8.63509			0.390492
$490$		0			0
$491$	−14.3354	+	24.8297i	−0.646949	+	1.12055i	0.336899	+	0.941541i	$0.390622\pi$
$491$	−14.3354	+	24.8297i	−0.646949	+	1.12055i	−0.983848	+	0.179007i	$0.942711\pi$
$492$	48.0487	−	83.2227i	2.16620	−	3.75197i
$493$	3.67187			0.165373
$494$	−0.249036	−	12.5258i	−0.0112046	−	0.563561i
$495$		0			0
$496$	31.8847	−	55.2260i	1.43167	−	2.47972i
$497$	−3.87167	+	6.70593i	−0.173668	+	0.300802i
$498$	32.4606	+	56.2235i	1.45460	+	2.51943i
$499$	28.9616			1.29650			0.648249	−	0.761428i	$-0.275502\pi$
$499$	28.9616			1.29650			0.648249	+	0.761428i	$0.275502\pi$
$500$		0			0
$501$	3.16324	+	5.47890i	0.141323	+	0.244779i
$502$	9.35181			0.417392
$503$	14.0546	+	24.3433i	0.626665	+	1.08542i	0.988216	+	0.153063i	$0.0489138\pi$
$503$	14.0546	+	24.3433i	0.626665	+	1.08542i	−0.361551	+	0.932352i	$0.617753\pi$
$504$	−15.1722	+	26.2790i	−0.675823	+	1.17056i
$505$		0			0
$506$	3.48079			0.154740
$507$	13.0195	−	24.7754i	0.578218	−	1.10032i
$508$	77.2116			3.42571
$509$	−10.5563	+	18.2841i	−0.467900	+	0.810427i	−0.999327	−	0.0366773i	$-0.988323\pi$
$509$	−10.5563	+	18.2841i	−0.467900	+	0.810427i	0.531427	+	0.847104i	$0.321656\pi$
$510$		0			0
$511$	−15.1722	−	26.2790i	−0.671178	−	1.16251i
$512$	−50.8542			−2.24746
$513$	2.00543	+	3.47351i	0.0885420	+	0.153359i
$514$	−16.8844	−	29.2447i	−0.744740	−	1.28993i
$515$		0			0
$516$	−6.59503	−	11.4229i	−0.290330	−	0.502866i
$517$	1.95728	−	3.39010i	0.0860809	−	0.149097i
$518$	4.57808	−	7.92947i	0.201149	−	0.348401i
$519$	−2.94369			−0.129214
$520$		0			0
$521$	0.673516			0.0295073			0.0147536	−	0.999891i	$-0.495304\pi$
$521$	0.673516			0.0295073			0.0147536	+	0.999891i	$0.495304\pi$
$522$	−6.24376	+	10.8145i	−0.273282	+	0.473339i
$523$	14.9313	−	25.8618i	0.652900	−	1.13086i	−0.329516	−	0.944150i	$-0.606886\pi$
$523$	14.9313	−	25.8618i	0.652900	−	1.13086i	0.982416	−	0.186706i	$-0.0597810\pi$
$524$	−22.4039	−	38.8048i	−0.978720	−	1.69519i
$525$		0			0
$526$	−38.5304	−	66.7366i	−1.68000	−	2.90985i
$527$	5.48429	+	9.49907i	0.238899	+	0.413786i
$528$	−9.72953			−0.423423
$529$	9.18246	+	15.9045i	0.399237	+	0.691499i
$530$		0			0
$531$	−6.21061	+	10.7571i	−0.269517	+	0.466818i
$532$	17.9718			0.779177
$533$	−31.4558	−	17.3366i	−1.36250	−	0.750933i
$534$	−68.8290			−2.97852
$535$		0			0
$536$	25.3566	−	43.9189i	1.09524	−	1.89701i
$537$	−8.38148	−	14.5171i	−0.361687	−	0.626461i
$538$	−56.6418			−2.44200
$539$	0.519213	+	0.899304i	0.0223641	+	0.0387358i
$540$		0			0
$541$	6.28806			0.270345			0.135172	−	0.990822i	$-0.456841\pi$
$541$	6.28806			0.270345			0.135172	+	0.990822i	$0.456841\pi$
$542$	15.0560	+	26.0778i	0.646712	+	1.12014i
$543$	4.16251	−	7.20968i	0.178630	−	0.309397i
$544$	−3.35627	+	5.81323i	−0.143899	+	0.249240i
$545$		0			0
$546$	50.8569	+	28.0294i	2.17647	+	1.19955i
$547$	−3.03789			−0.129891			−0.0649454	−	0.997889i	$-0.520687\pi$
$547$	−3.03789			−0.129891			−0.0649454	+	0.997889i	$0.520687\pi$
$548$	−19.4294	+	33.6527i	−0.829983	+	1.43757i
$549$	1.85597	−	3.21464i	0.0792109	−	0.137197i
$550$		0			0
$551$	4.09473			0.174442
$552$	14.6363	+	25.3508i	0.622962	+	1.07900i
$553$	−1.52574	−	2.64265i	−0.0648809	−	0.112377i
$554$	42.7304			1.81544
$555$		0			0
$556$	−32.0970	+	55.5936i	−1.36121	+	2.35769i
$557$	−10.3498	+	17.9264i	−0.438536	+	0.759566i	−0.997577	−	0.0695738i	$-0.977836\pi$
$557$	−10.3498	+	17.9264i	−0.438536	+	0.759566i	0.559041	+	0.829140i	$0.311169\pi$
$558$	−37.3026			−1.57915
$559$	−4.21955	+	2.54931i	−0.178468	+	0.107824i
$560$		0			0
$561$	0.836758	−	1.44931i	0.0353279	−	0.0611898i
$562$	13.4882	−	23.3622i	0.568964	−	0.985475i
$563$	−5.48014	−	9.49188i	−0.230960	−	0.400035i	0.727131	−	0.686499i	$-0.240853\pi$
$563$	−5.48014	−	9.49188i	−0.230960	−	0.400035i	−0.958091	+	0.286464i	$0.907520\pi$
$564$	59.4608			2.50375
$565$		0			0
$566$	11.2212	+	19.4357i	0.471661	+	0.816941i
$567$	−33.0051			−1.38608
$568$	−8.32087	−	14.4122i	−0.349136	−	0.604721i
$569$	−21.3566	+	36.9907i	−0.895314	+	1.55073i	−0.0618981	+	0.998082i	$0.519715\pi$
$569$	−21.3566	+	36.9907i	−0.895314	+	1.55073i	−0.833416	+	0.552647i	$0.813618\pi$
$570$		0			0
$571$	−23.6145			−0.988238			−0.494119	−	0.869394i	$-0.664509\pi$
$571$	−23.6145			−0.988238			−0.494119	+	0.869394i	$0.664509\pi$
$572$	0.203954	+	10.2583i	0.00852774	+	0.428920i
$573$	10.6434			0.444635
$574$	37.2602	−	64.5366i	1.55521	−	2.69370i
$575$		0			0
$576$	0.220882	+	0.382579i	0.00920343	+	0.0159408i
$577$	−18.3646			−0.764530			−0.382265	−	0.924053i	$-0.624856\pi$
$577$	−18.3646			−0.764530			−0.382265	+	0.924053i	$0.624856\pi$
$578$	19.7319	+	34.1767i	0.820740	+	1.42156i
$579$	5.33542	+	9.24123i	0.221733	+	0.384052i
$580$		0			0
$581$	17.4039	+	30.1445i	0.722037	+	1.25060i
$582$	−40.5134	+	70.1713i	−1.67934	+	2.90869i
$583$	−0.203954	+	0.353259i	−0.00844691	+	0.0146305i
$584$	65.2151			2.69862
$585$		0			0
$586$	−71.9237			−2.97114
$587$	0.351448	−	0.608726i	0.0145058	−	0.0251248i	−0.858681	−	0.512510i	$-0.828716\pi$
$587$	0.351448	−	0.608726i	0.0145058	−	0.0251248i	0.873187	+	0.487385i	$0.162049\pi$
$588$	−7.88669	+	13.6601i	−0.325242	+	0.563335i
$589$	6.11588	+	10.5930i	0.252000	+	0.436477i
$590$		0			0
$591$	7.26124	+	12.5768i	0.298687	+	0.517342i
$592$	4.35476	+	7.54267i	0.178980	+	0.310002i
$593$	−37.1593			−1.52595			−0.762975	−	0.646428i	$-0.776262\pi$
$593$	−37.1593			−1.52595			−0.762975	+	0.646428i	$0.776262\pi$
$594$	−2.37548	−	4.11446i	−0.0974672	−	0.168818i
$595$		0			0
$596$	38.4337	−	66.5692i	1.57431	−	2.72678i
$597$	11.1423			0.456026
$598$	16.9140	−	10.2189i	0.691663	−	0.417880i
$599$	−15.6914			−0.641133			−0.320567	−	0.947226i	$-0.603873\pi$
$599$	−15.6914			−0.641133			−0.320567	+	0.947226i	$0.603873\pi$
$600$		0			0
$601$	−6.00193	+	10.3956i	−0.244824	+	0.424047i	−0.962082	−	0.272760i	$-0.912063\pi$
$601$	−6.00193	+	10.3956i	−0.244824	+	0.424047i	0.717258	+	0.696807i	$0.245397\pi$
$602$	−5.11424	−	8.85812i	−0.208441	−	0.361030i
$603$	−13.1298			−0.534687
$604$	47.9059	+	82.9754i	1.94926	+	3.37622i
$605$		0			0
$606$	72.5204			2.94594
$607$	−19.3433	−	33.5035i	−0.785119	−	1.35987i	−0.928928	−	0.370261i	$-0.879268\pi$
$607$	−19.3433	−	33.5035i	−0.785119	−	1.35987i	0.143809	−	0.989606i	$-0.454065\pi$
$608$	−3.74278	+	6.48269i	−0.151790	+	0.262908i
$609$	−9.48973	+	16.4367i	−0.384543	+	0.666048i
$610$		0			0
$611$	−0.441765	−	22.2195i	−0.0178719	−	0.898903i
$612$	8.96730			0.362482
$613$	8.64201	−	14.9684i	0.349047	−	0.604568i	−0.637033	−	0.770836i	$-0.719839\pi$
$613$	8.64201	−	14.9684i	0.349047	−	0.604568i	0.986081	+	0.166269i	$0.0531719\pi$
$614$	−16.1933	+	28.0477i	−0.653509	+	1.13191i
$615$		0			0
$616$	−11.7861			−0.474877
$617$	−13.2345	−	22.9229i	−0.532803	−	0.922841i	−0.999266	−	0.0383009i	$-0.987805\pi$
$617$	−13.2345	−	22.9229i	−0.532803	−	0.922841i	0.466464	−	0.884540i	$-0.345528\pi$
$618$	30.0582	+	52.0624i	1.20912	+	2.09426i
$619$	−31.0039			−1.24615			−0.623075	−	0.782162i	$-0.714117\pi$
$619$	−31.0039			−1.24615			−0.623075	+	0.782162i	$0.714117\pi$
$620$		0			0
$621$	−3.16324	+	5.47890i	−0.126937	+	0.219861i
$622$	−35.5425	+	61.5615i	−1.42513	+	2.46839i
$623$	−36.9030			−1.47849
$624$	−47.2781	+	28.5639i	−1.89264	+	1.14347i
$625$		0			0
$626$	−31.2881	+	54.1925i	−1.25052	+	2.16597i
$627$	0.933121	−	1.61621i	0.0372653	−	0.0645453i
$628$	−41.1440	−	71.2635i	−1.64182	−	2.84372i
$629$	−1.49807			−0.0597320
$630$		0			0
$631$	10.3566	+	17.9381i	0.412288	+	0.714104i	0.995140	−	0.0984745i	$-0.0313963\pi$
$631$	10.3566	+	17.9381i	0.412288	+	0.714104i	−0.582851	+	0.812579i	$0.698063\pi$
$632$	6.55812			0.260868
$633$	15.0897	+	26.1362i	0.599763	+	1.03882i
$634$	0.298331	−	0.516725i	0.0118482	−	0.0205218i
$635$		0			0
$636$	−6.19599			−0.245687
$637$	5.16315	+	2.84563i	0.204571	+	0.112748i
$638$	−4.85031			−0.192026
$639$	−2.15430	+	3.73136i	−0.0852229	+	0.147610i
$640$		0			0
$641$	−10.5947	−	18.3506i	−0.418467	−	0.724806i	0.577319	−	0.816519i	$-0.304099\pi$
$641$	−10.5947	−	18.3506i	−0.418467	−	0.724806i	−0.995785	+	0.0917132i	$0.970766\pi$
$642$	58.4997			2.30880
$643$	5.76682	+	9.98843i	0.227421	+	0.393905i	0.957043	−	0.289946i	$-0.0936372\pi$
$643$	5.76682	+	9.98843i	0.227421	+	0.393905i	−0.729622	+	0.683851i	$0.760304\pi$
$644$	14.1738	+	24.5498i	0.558526	+	0.967396i
$645$		0			0
$646$	−2.12645	−	3.68311i	−0.0836639	−	0.144910i
$647$	17.4232	−	30.1779i	0.684977	−	1.18641i	−0.288467	−	0.957490i	$-0.593146\pi$
$647$	17.4232	−	30.1779i	0.684977	−	1.18641i	0.973444	−	0.228925i	$-0.0735211\pi$
$648$	35.4667	−	61.4301i	1.39326	−	2.41320i
$649$	−4.82456			−0.189380
$650$		0			0
$651$	−56.6953			−2.22206
$652$	−8.98591	+	15.5641i	−0.351915	+	0.609535i
$653$	−11.1616	+	19.3324i	−0.436787	+	0.756537i	−0.997440	−	0.0715139i	$-0.977217\pi$
$653$	−11.1616	+	19.3324i	−0.436787	+	0.756537i	0.560653	+	0.828051i	$0.310550\pi$
$654$	8.96157	+	15.5219i	0.350425	+	0.606954i
$655$		0			0
$656$	35.4427	+	61.3885i	1.38380	+	2.39682i
$657$	−8.44221	−	14.6223i	−0.329362	−	0.570471i
$658$	46.1100			1.79755
$659$	0.433420	+	0.750705i	0.0168836	+	0.0292433i	0.874344	−	0.485307i	$-0.161292\pi$
$659$	0.433420	+	0.750705i	0.0168836	+	0.0292433i	−0.857460	+	0.514550i	$0.827959\pi$
$660$		0			0
$661$	−6.65430	+	11.5256i	−0.258822	+	0.448293i	−0.965927	−	0.258816i	$-0.916668\pi$
$661$	−6.65430	+	11.5256i	−0.258822	+	0.448293i	0.707104	+	0.707109i	$0.250001\pi$
$662$	−46.6544			−1.81328
$663$	−0.188859	−	9.49907i	−0.00733469	−	0.368913i
$664$	−74.8079			−2.90311
$665$		0			0
$666$	2.54737	−	4.41217i	0.0987085	−	0.170968i
$667$	3.22939	+	5.59346i	0.125042	+	0.216580i
$668$	−13.1670			−0.509448
$669$	−0.00893993	−	0.0154844i	−0.000345637	−	0.000598662i
$670$		0			0
$671$	1.44176			0.0556587
$672$	−17.3481	−	30.0479i	−0.669219	−	1.15912i
$673$	2.75660	−	4.77457i	0.106259	−	0.184046i	−0.807993	−	0.589192i	$-0.799446\pi$
$673$	2.75660	−	4.77457i	0.106259	−	0.184046i	0.914252	+	0.405146i	$0.132779\pi$
$674$	27.1056	−	46.9483i	1.04407	−	1.80838i
$675$		0			0
$676$	31.1072	+	49.2486i	1.19643	+	1.89418i
$677$	−4.80479			−0.184663			−0.0923316	−	0.995728i	$-0.529432\pi$
$677$	−4.80479			−0.184663			−0.0923316	+	0.995728i	$0.529432\pi$
$678$	−15.1539	+	26.2472i	−0.581980	+	1.00802i
$679$	−21.7215	+	37.6227i	−0.833594	+	1.44383i
$680$		0			0
$681$	−24.2496			−0.929248
$682$	−7.24440	−	12.5477i	−0.277403	−	0.480475i
$683$	−5.88126	−	10.1866i	−0.225040	−	0.389781i	0.731291	−	0.682065i	$-0.238918\pi$
$683$	−5.88126	−	10.1866i	−0.225040	−	0.389781i	−0.956331	+	0.292284i	$0.905585\pi$
$684$	10.0000			0.382360
$685$		0			0
$686$	20.0669	−	34.7569i	0.766157	−	1.32702i
$687$	17.8051	−	30.8393i	0.679306	−	1.17659i
$688$	9.72953			0.370935
$689$	0.0460332	+	2.31533i	0.00175372	+	0.0882071i
$690$		0			0
$691$	−2.43342	+	4.21481i	−0.0925717	+	0.160339i	−0.908593	−	0.417684i	$-0.862842\pi$
$691$	−2.43342	+	4.21481i	−0.0925717	+	0.160339i	0.816021	+	0.578022i	$0.196175\pi$
$692$	3.06329	−	5.30577i	0.116449	−	0.201695i
$693$	1.52574	+	2.64265i	0.0579579	+	0.100386i
$694$	−9.71254			−0.368683
$695$		0			0
$696$	−20.3950	−	35.3252i	−0.773070	−	1.33900i
$697$	−12.1925			−0.461825
$698$	−30.9644	−	53.6320i	−1.17202	−	2.03000i
$699$	7.48079	−	12.9571i	0.282949	−	0.490083i
$700$		0			0
$701$	21.3828			0.807617			0.403808	−	0.914844i	$-0.367686\pi$
$701$	21.3828			0.807617			0.403808	+	0.914844i	$0.367686\pi$
$702$	−23.6222	−	13.0192i	−0.891563	−	0.491378i
$703$	−1.67059			−0.0630076
$704$	−0.0857934	+	0.148599i	−0.00323346	+	0.00560052i
$705$		0			0
$706$	34.4427	+	59.6564i	1.29627	+	2.24520i
$707$	38.8822			1.46232
$708$	−36.6417	−	63.4654i	−1.37708	−	2.38517i
$709$	13.0582	+	22.6175i	0.490412	+	0.849419i	0.999939	−	0.0110357i	$-0.00351286\pi$
$709$	13.0582	+	22.6175i	0.490412	+	0.849419i	−0.509527	+	0.860455i	$0.670180\pi$
$710$		0			0
$711$	−0.848960	−	1.47044i	−0.0318385	−	0.0551459i
$712$	39.6554	−	68.6851i	1.48615	−	2.57408i
$713$	−9.64680	+	16.7087i	−0.361276	+	0.625748i
$714$	19.7125			0.737723
$715$		0			0
$716$	34.8880			1.30383
$717$	−4.30585	+	7.45795i	−0.160805	+	0.278522i
$718$	−34.3724	+	59.5347i	−1.28277	+	2.22182i
$719$	−18.3387	−	31.7635i	−0.683918	−	1.18458i	−0.973776	−	0.227510i	$-0.926941\pi$
$719$	−18.3387	−	31.7635i	−0.683918	−	1.18458i	0.289858	−	0.957070i	$-0.406392\pi$
$720$		0			0
$721$	16.1159	+	27.9135i	0.600187	+	1.03955i
$722$	21.8132	+	37.7815i	0.811803	+	1.40608i
$723$	42.5679			1.58312
$724$	8.66324	+	15.0052i	0.321967	+	0.557663i
$725$		0			0
$726$	29.0390	−	50.2971i	1.07774	−	1.86670i
$727$	−26.2596			−0.973916			−0.486958	−	0.873425i	$-0.661893\pi$
$727$	−26.2596			−0.973916			−0.486958	+	0.873425i	$0.661893\pi$
$728$	−57.2716	+	34.6016i	−2.12263	+	1.28242i
$729$	0.614542			0.0227608
$730$		0			0
$731$	−0.836758	+	1.44931i	−0.0309486	+	0.0536046i
$732$	10.9500	+	18.9659i	0.404723	+	0.701000i
$733$	31.7811			1.17386			0.586931	−	0.809637i	$-0.300336\pi$
$733$	31.7811			1.17386			0.586931	+	0.809637i	$0.300336\pi$
$734$	8.83513	+	15.3029i	0.326110	+	0.564840i
$735$		0			0
$736$	−11.8073			−0.435222
$737$	−2.54989	−	4.41654i	−0.0939265	−	0.162685i
$738$	20.7326	−	35.9099i	0.763176	−	1.32186i
$739$	17.0685	−	29.5635i	0.627875	−	1.08751i	−0.360102	−	0.932913i	$-0.617258\pi$
$739$	17.0685	−	29.5635i	0.627875	−	1.08751i	0.987977	−	0.154599i	$-0.0494085\pi$
$740$		0			0
$741$	−0.210609	−	10.5930i	−0.00773691	−	0.389144i
$742$	−4.80479			−0.176390
$743$	−1.56031	+	2.70254i	−0.0572423	+	0.0991465i	−0.893227	−	0.449607i	$-0.851564\pi$
$743$	−1.56031	+	2.70254i	−0.0572423	+	0.0991465i	0.835984	+	0.548753i	$0.184897\pi$
$744$	60.9237	−	105.523i	2.23357	−	3.86866i
$745$		0			0
$746$	5.88798			0.215574
$747$	9.68401	+	16.7732i	0.354320	+	0.613699i
$748$	1.74151	+	3.01638i	0.0636758	+	0.110290i
$749$	31.3649			1.14605
$750$		0			0
$751$	−0.742024	+	1.28522i	−0.0270769	+	0.0468985i	−0.879246	−	0.476367i	$-0.841953\pi$
$751$	−0.742024	+	1.28522i	−0.0270769	+	0.0468985i	0.852169	+	0.523266i	$0.175287\pi$
$752$	−21.9304	+	37.9845i	−0.799718	+	1.38515i
$753$	7.90881			0.288213
$754$	−23.5688	+	14.2395i	−0.858325	+	0.518572i
$755$		0			0
$756$	19.3460	−	33.5082i	0.703607	−	1.21868i
$757$	−2.54989	+	4.41654i	−0.0926774	+	0.160522i	−0.908637	−	0.417587i	$-0.862876\pi$
$757$	−2.54989	+	4.41654i	−0.0926774	+	0.160522i	0.815960	+	0.578109i	$0.196209\pi$
$758$	−6.58767	−	11.4102i	−0.239275	−	0.414436i
$759$	2.94369			0.106849
$760$		0			0
$761$	14.8931	+	25.7955i	0.539873	+	0.935088i	0.998910	+	0.0466707i	$0.0148611\pi$
$761$	14.8931	+	25.7955i	0.539873	+	0.935088i	−0.459037	+	0.888417i	$0.651806\pi$
$762$	94.4433			3.42132
$763$	4.80479	+	8.32215i	0.173945	+	0.301282i
$764$	−11.0758	+	19.1839i	−0.400709	+	0.694048i
$765$		0			0
$766$	−52.5973			−1.90042
$767$	−23.4437	+	14.1639i	−0.846501	+	0.511428i
$768$	−62.7228			−2.26331
$769$	−9.54930	+	16.5399i	−0.344356	+	0.596443i	−0.985237	−	0.171198i	$-0.945236\pi$
$769$	−9.54930	+	16.5399i	−0.344356	+	0.596443i	0.640880	+	0.767641i	$0.278570\pi$
$770$		0			0
$771$	−14.2791	−	24.7322i	−0.514250	−	0.890707i
$772$	−22.2088			−0.799311
$773$	−24.6153	−	42.6350i	−0.885351	−	1.53347i	−0.845311	−	0.534275i	$-0.820585\pi$
$773$	−24.6153	−	42.6350i	−0.885351	−	1.53347i	−0.0400400	−	0.999198i	$-0.512749\pi$
$774$	−2.84570	−	4.92889i	−0.102286	−	0.177165i
$775$		0			0
$776$	−46.6831	−	80.8574i	−1.67582	−	2.90261i
$777$	3.87167	−	6.70593i	0.138895	−	0.240574i
$778$	−25.1362	+	43.5373i	−0.901178	+	1.56089i
$779$	−13.5967			−0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$	3.35412	−	5.80951i	0.119943	−	0.207748i
$783$	4.40783	−	7.63458i	0.157523	−	0.272838i
$784$	−5.81754	−	10.0763i	−0.207769	−	0.359867i
$785$		0			0
$786$	−27.4039	−	47.4650i	−0.977466	−	1.69302i
$787$	4.89168	+	8.47263i	0.174369	+	0.302017i	0.939943	−	0.341332i	$-0.110878\pi$
$787$	4.89168	+	8.47263i	0.174369	+	0.302017i	−0.765573	+	0.643349i	$0.777545\pi$
$788$	−30.2250			−1.07672
$789$	−32.5851	−	56.4390i	−1.16006	−	2.00928i
$790$		0			0
$791$	−8.12482	+	14.0726i	−0.288885	+	0.500364i
$792$	−6.55812			−0.233033
$793$	7.00587	−	4.23272i	0.248786	−	0.150308i
$794$	−23.9020			−0.848250
$795$		0			0
$796$	−11.5950	+	20.0832i	−0.410975	+	0.711830i
$797$	−8.26856	−	14.3216i	−0.292887	−	0.507296i	0.681604	−	0.731721i	$-0.261283\pi$
$797$	−8.26856	−	14.3216i	−0.292887	−	0.507296i	−0.974491	+	0.224426i	$0.927949\pi$
$798$	21.9827			0.778178
$799$	−3.77211	−	6.53348i	−0.133448	−	0.231138i
$800$		0			0
$801$	−20.5338			−0.725527
$802$	−31.1878	−	54.0188i	−1.10128	−	1.90747i
$803$	3.27906	−	5.67950i	0.115715	−	0.200425i
$804$	38.7320	−	67.0859i	1.36597	−	2.36594i
$805$		0			0
$806$	−72.0396	−	39.7041i	−2.53749	−	1.39852i
$807$	−47.9018			−1.68622
$808$	−41.7821	+	72.3688i	−1.46989	+	2.54592i
$809$	15.9212	−	27.5764i	0.559760	−	0.969533i	−0.437756	−	0.899094i	$-0.644227\pi$
$809$	15.9212	−	27.5764i	0.559760	−	0.969533i	0.997516	−	0.0704392i	$-0.0224401\pi$
$810$		0			0
$811$	13.3470			0.468678			0.234339	−	0.972155i	$-0.424707\pi$
$811$	13.3470			0.468678			0.234339	+	0.972155i	$0.424707\pi$
$812$	−19.7505	−	34.2089i	−0.693108	−	1.20050i
$813$	12.7328	+	22.0539i	0.446560	+	0.773465i
$814$	1.97886			0.0693589
$815$		0			0
$816$	−9.37548	+	16.2388i	−0.328208	+	0.568472i
$817$	−0.933121	+	1.61621i	−0.0326458	+	0.0565441i
$818$	91.9431			3.21472
$819$	15.1722	+	8.36203i	0.530159	+	0.292193i
$820$		0			0
$821$	−5.83676	+	10.1096i	−0.203704	+	0.352826i	−0.949719	−	0.313103i	$-0.898631\pi$
$821$	−5.83676	+	10.1096i	−0.203704	+	0.352826i	0.746015	+	0.665929i	$0.231965\pi$
$822$	−23.7656	+	41.1631i	−0.828919	+	1.43573i
$823$	−16.2159	−	28.0867i	−0.565249	−	0.979041i	−0.997026	−	0.0770602i	$-0.975447\pi$
$823$	−16.2159	−	28.0867i	−0.565249	−	0.979041i	0.431777	−	0.901980i	$-0.357887\pi$
$824$	−69.2714			−2.41318
$825$		0			0
$826$	−28.4145	−	49.2154i	−0.988667	−	1.71242i
$827$	27.3319			0.950425			0.475212	−	0.879871i	$-0.342371\pi$
$827$	27.3319			0.950425			0.475212	+	0.879871i	$0.342371\pi$
$828$	7.88669	+	13.6601i	0.274081	+	0.474723i
$829$	−1.77018	+	3.06604i	−0.0614808	+	0.106488i	−0.895128	−	0.445810i	$-0.852916\pi$
$829$	−1.77018	+	3.06604i	−0.0614808	+	0.106488i	0.833647	+	0.552298i	$0.186249\pi$
$830$		0			0
$831$	36.1370			1.25358
$832$	0.0193639	+	0.973947i	0.000671322	+	0.0337655i
$833$	2.00128			0.0693402
$834$	−39.2602	+	68.0007i	−1.35947	+	2.35467i
$835$		0			0
$836$	1.94206	+	3.36375i	0.0671676	+	0.116338i
$837$	26.3341			0.910238
$838$	8.74059	+	15.1391i	0.301939	+	0.522973i
$839$	−22.3950	−	38.7893i	−0.773161	−	1.33915i	−0.935822	−	0.352472i	$-0.885341\pi$
$839$	−22.3950	−	38.7893i	−0.773161	−	1.33915i	0.162661	−	0.986682i	$-0.447992\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−43.2514	+	74.9136i	−1.49054	+	2.58169i
$843$	11.4069	−	19.7574i	0.392875	−	0.680479i
$844$	−62.8111			−2.16205
$845$		0			0
$846$	25.6568			0.882100
$847$	15.5694	−	26.9670i	0.534972	−	0.926598i
$848$	2.28521	−	3.95810i	0.0784744	−	0.135922i
$849$	9.48973	+	16.4367i	0.325687	+	0.564106i
$850$		0			0
$851$	−1.31754	−	2.28205i	−0.0451648	−	0.0782278i
$852$	−12.7101	−	22.0145i	−0.435440	−	0.754205i
$853$	−31.3732			−1.07420			−0.537099	−	0.843519i	$-0.680480\pi$
$853$	−31.3732			−1.07420			−0.537099	+	0.843519i	$0.680480\pi$
$854$	8.49136	+	14.7075i	0.290568	+	0.503279i
$855$		0			0
$856$	−33.7042	+	58.3774i	−1.15199	+	1.99530i
$857$	−21.2813			−0.726955			−0.363478	−	0.931603i	$-0.618411\pi$
$857$	−21.2813			−0.726955			−0.363478	+	0.931603i	$0.618411\pi$
$858$	0.249471	+	12.5477i	0.00851681	+	0.428371i
$859$	56.8502			1.93970			0.969851	−	0.243698i	$-0.0783607\pi$
$859$	56.8502			1.93970			0.969851	+	0.243698i	$0.0783607\pi$
$860$		0			0
$861$	31.5109	−	54.5784i	1.07389	−	1.86003i
$862$	20.6837	+	35.8251i	0.704488	+	1.22021i
$863$	32.8011			1.11656			0.558282	−	0.829651i	$-0.311461\pi$
$863$	32.8011			1.11656			0.558282	+	0.829651i	$0.311461\pi$
$864$	8.05794	+	13.9568i	0.274137	+	0.474819i
$865$		0			0
$866$	0.652374			0.0221686
$867$	16.6873	+	28.9032i	0.566729	+	0.981603i
$868$	58.9986	−	102.189i	2.00254	−	3.46851i
$869$	0.329747	−	0.571138i	0.0111859	−	0.0193745i
$870$		0			0
$871$	−25.3566	−	13.9751i	−0.859174	−	0.473527i
$872$	−20.6526			−0.699385
$873$	−12.0864	+	20.9343i	−0.409063	+	0.708518i
$874$	3.74039	−	6.47855i	0.126521	−	0.219140i
$875$		0			0
$876$	99.6157			3.36570
$877$	18.0325	+	31.2333i	0.608916	+	1.05467i	0.991419	+	0.130719i	$0.0417286\pi$
$877$	18.0325	+	31.2333i	0.608916	+	1.05467i	−0.382504	+	0.923954i	$0.624938\pi$
$878$	9.66956	+	16.7482i	0.326332	+	0.565223i
$879$	−60.8257			−2.05160
$880$		0			0
$881$	23.0198	−	39.8715i	0.775557	−	1.34330i	−0.158924	−	0.987291i	$-0.550802\pi$
$881$	23.0198	−	39.8715i	0.775557	−	1.34330i	0.934481	−	0.356013i	$-0.115864\pi$
$882$	−3.40304	+	5.89423i	−0.114586	+	0.198469i
$883$	0.802236			0.0269974			0.0134987	−	0.999909i	$-0.495703\pi$
$883$	0.802236			0.0269974			0.0134987	+	0.999909i	$0.495703\pi$
$884$	17.3178	+	9.54459i	0.582462	+	0.321019i
$885$		0			0
$886$	−5.50193	+	9.52962i	−0.184841	+	0.320154i
$887$	−4.11284	+	7.12365i	−0.138096	+	0.239189i	−0.926776	−	0.375615i	$-0.877431\pi$
$887$	−4.11284	+	7.12365i	−0.138096	+	0.239189i	0.788680	+	0.614804i	$0.210765\pi$
$888$	8.32087	+	14.4122i	0.279230	+	0.483641i
$889$	50.6363			1.69829
$890$		0			0
$891$	−3.56658	−	6.17750i	−0.119485	−	0.206954i
$892$	0.0372125			0.00124597
$893$	−4.20651	−	7.28589i	−0.140766	−	0.243813i
$894$	47.0112	−	81.4257i	1.57229	−	2.72328i
$895$		0			0
$896$	−34.2529			−1.14431
$897$	14.3041	−	8.64207i	0.477600	−	0.288550i
$898$	8.37054			0.279328
$899$	13.4424	−	23.2829i	0.448328	−	0.776527i
$900$		0			0
$901$	0.393064	+	0.680808i	0.0130949	+	0.0226810i
$902$	16.1056			0.536257
$903$	−4.32510	−	7.49129i	−0.143930	−	0.249295i
$904$	−17.4616	−	30.2443i	−0.580763	−	1.00591i
$905$		0			0
$906$	58.5973	+	101.493i	1.94676	+	3.37189i
$907$	15.2180	−	26.3583i	0.505305	−	0.875213i	−0.494677	−	0.869077i	$-0.664714\pi$
$907$	15.2180	−	26.3583i	0.505305	−	0.875213i	0.999981	−	0.00613601i	$-0.00195317\pi$
$908$	25.2348	−	43.7080i	0.837447	−	1.45050i
$909$	21.6351			0.717591
$910$		0			0
$911$	43.6145			1.44501			0.722507	−	0.691363i	$-0.242990\pi$
$911$	43.6145			1.44501			0.722507	+	0.691363i	$0.242990\pi$
$912$	−10.4552	+	18.1089i	−0.346206	+	0.599646i
$913$	−3.76139	+	6.51492i	−0.124484	+	0.215612i
$914$	19.6354	+	34.0095i	0.649481	+	1.12493i
$915$		0			0
$916$	37.0569	+	64.1844i	1.22439	+	2.12071i
$917$	−14.6928	−	25.4486i	−0.485198	−	0.840387i
$918$	−9.15616			−0.302198
$919$	18.5109	+	32.0618i	0.610617	+	1.05762i	0.991137	+	0.132847i	$0.0424119\pi$
$919$	18.5109	+	32.0618i	0.610617	+	1.05762i	−0.380519	+	0.924773i	$0.624255\pi$
$920$		0			0
$921$	−13.6947	+	23.7198i	−0.451254	+	0.781595i
$922$	65.8957			2.17016
$923$	−8.13201	+	4.91309i	−0.267668	+	0.161716i
$924$	−18.0033			−0.592264
$925$		0			0
$926$	−8.96157	+	15.5219i	−0.294496	+	0.510081i
$927$	8.96730	+	15.5318i	0.294525	+	0.510132i
$928$	16.4529			0.540092
$929$	2.38412	+	4.12942i	0.0782206	+	0.135482i	0.902482	−	0.430727i	$-0.141743\pi$
$929$	2.38412	+	4.12942i	0.0782206	+	0.135482i	−0.824262	+	0.566209i	$0.808409\pi$
$930$		0			0
$931$	2.23175			0.0731427
$932$	15.5694	+	26.9670i	0.509993	+	0.883334i
$933$	−30.0582	+	52.0624i	−0.984062	+	1.70445i
$934$	−23.9443	+	41.4727i	−0.783481	+	1.35703i
$935$		0			0
$936$	−31.8674	+	19.2533i	−1.04162	+	0.629313i
$937$	43.6264			1.42521			0.712606	−	0.701565i	$-0.247515\pi$
$937$	43.6264			1.42521			0.712606	+	0.701565i	$0.247515\pi$
$938$	30.0355	−	52.0230i	0.980693	−	1.69861i
$939$	−26.4602	+	45.8305i	−0.863497	+	1.49562i
$940$		0			0
$941$	18.2675			0.595504			0.297752	−	0.954643i	$-0.403763\pi$
$941$	18.2675			0.595504			0.297752	+	0.954643i	$0.403763\pi$
$942$	−50.3263	−	87.1677i	−1.63972	−	2.84008i
$943$	−10.7233	−	18.5732i	−0.349197	−	0.604828i
$944$	54.0569			1.75940
$945$		0			0
$946$	1.10530	−	1.91444i	0.0359365	−	0.0622439i
$947$	9.99146	−	17.3057i	0.324679	−	0.562360i	−0.656769	−	0.754092i	$-0.728077\pi$
$947$	9.99146	−	17.3057i	0.324679	−	0.562360i	0.981447	+	0.191732i	$0.0614105\pi$
$948$	10.0175			0.325353
$949$	−0.740096	−	37.2246i	−0.0240245	−	1.20836i
$950$		0			0
$951$	0.252298	−	0.436993i	0.00818132	−	0.0141705i
$952$	−11.3572	+	19.6713i	−0.368090	+	0.637551i
$953$	19.9317	+	34.5228i	0.645652	+	1.11830i	0.984150	+	0.177335i	$0.0567477\pi$
$953$	19.9317	+	34.5228i	0.645652	+	1.11830i	−0.338498	+	0.940967i	$0.609919\pi$
$954$	−2.67352			−0.0865583
$955$		0			0
$956$	−8.96157	−	15.5219i	−0.289838	−	0.502014i
$957$	−4.10190			−0.132596
$958$	24.7923	+	42.9416i	0.801004	+	1.38738i
$959$	−12.7420	+	22.0698i	−0.411461	+	0.712672i
$960$		0			0
$961$	49.3098			1.59064
$962$	9.61574	−	5.80951i	0.310024	−	0.187306i
$963$	17.4523			0.562392
$964$	−44.2973	+	76.7252i	−1.42672	+	2.47115i
$965$		0			0
$966$	17.3371	+	30.0287i	0.557811	+	0.966156i
$967$	−43.8607			−1.41047			−0.705233	−	0.708975i	$-0.749158\pi$
$967$	−43.8607			−1.41047			−0.705233	+	0.708975i	$0.749158\pi$
$968$	33.4613	+	57.9566i	1.07549	+	1.86280i
$969$	−1.79833	−	3.11480i	−0.0577707	−	0.100062i
$970$		0			0
$971$	−30.4897	−	52.8098i	−0.978462	−	1.69475i	−0.668002	−	0.744159i	$-0.732850\pi$
$971$	−30.4897	−	52.8098i	−0.978462	−	1.69475i	−0.310459	−	0.950587i	$-0.600483\pi$
$972$	34.4247	−	59.6253i	1.10417	−	1.91248i
$973$	−21.0496	+	36.4589i	−0.674818	+	1.16882i
$974$	−82.2887			−2.63670
$975$		0			0
$976$	−16.1543			−0.517087
$977$	−25.6849	+	44.4875i	−0.821731	+	1.42328i	0.0826604	+	0.996578i	$0.473658\pi$
$977$	−25.6849	+	44.4875i	−0.821731	+	1.42328i	−0.904392	+	0.426703i	$0.859675\pi$
$978$	−10.9913	+	19.0376i	−0.351464	+	0.608754i
$979$	−3.98780	−	6.90707i	−0.127451	−	0.220751i
$980$		0			0
$981$	2.67352	+	4.63066i	0.0853588	+	0.147846i
$982$	−36.4942	−	63.2099i	−1.16458	−	2.01711i
$983$	37.3026			1.18977			0.594885	−	0.803811i	$-0.297198\pi$
$983$	37.3026			1.18977			0.594885	+	0.803811i	$0.297198\pi$
$984$	67.7221	+	117.298i	2.15890	+	3.73933i
$985$		0			0
$986$	−4.67381	+	8.09528i	−0.148845	+	0.257806i
$987$	38.9951			1.24123
$988$	19.3122	+	10.6438i	0.614403	+	0.338623i
$989$	−2.94369			−0.0936040
$990$		0			0
$991$	25.7810	−	44.6541i	0.818962	−	1.41848i	−0.0874859	−	0.996166i	$-0.527883\pi$
$991$	25.7810	−	44.6541i	0.818962	−	1.41848i	0.906448	−	0.422318i	$-0.138783\pi$
$992$	24.5739	+	42.5633i	0.780223	+	1.35139i
$993$	−39.4556			−1.25208
$994$	−9.85627	−	17.0716i	−0.312622	−	0.541477i
$995$		0			0
$996$	−114.269			−3.62074
$997$	−11.4744	−	19.8743i	−0.363399	−	0.629425i	0.625119	−	0.780529i	$-0.285050\pi$
$997$	−11.4744	−	19.8743i	−0.363399	−	0.629425i	−0.988518	+	0.151104i	$0.951717\pi$
$998$	−36.8643	+	63.8508i	−1.16692	+	2.02116i
$999$	−1.79833	+	3.11480i	−0.0568967	+	0.0985479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.e.126.1		12
5.2	odd	4		65.2.n.a.9.1	✓	12
5.3	odd	4		65.2.n.a.9.6	yes	12
5.4	even	2	inner	325.2.e.e.126.6		12
13.3	even	3	inner	325.2.e.e.276.1		12
13.4	even	6		4225.2.a.bq.1.1		6
13.9	even	3		4225.2.a.br.1.6		6
15.2	even	4		585.2.bs.a.334.6		12
15.8	even	4		585.2.bs.a.334.1		12
20.3	even	4		1040.2.dh.a.529.5		12
20.7	even	4		1040.2.dh.a.529.2		12
65.2	even	12		845.2.l.f.699.1		24
65.3	odd	12		65.2.n.a.29.1	yes	12
65.4	even	6		4225.2.a.bq.1.6		6
65.7	even	12		845.2.d.d.844.1		12
65.8	even	4		845.2.l.f.654.1		24
65.9	even	6		4225.2.a.br.1.1		6
65.12	odd	4		845.2.n.e.529.6		12
65.17	odd	12		845.2.b.e.339.1		6
65.18	even	4		845.2.l.f.654.11		24
65.22	odd	12		845.2.b.d.339.6		6
65.23	odd	12		845.2.n.e.484.6		12
65.28	even	12		845.2.l.f.699.12		24
65.29	even	6	inner	325.2.e.e.276.6		12
65.32	even	12		845.2.d.d.844.11		12
65.33	even	12		845.2.d.d.844.12		12
65.37	even	12		845.2.l.f.699.11		24
65.38	odd	4		845.2.n.e.529.1		12
65.42	odd	12		65.2.n.a.29.6	yes	12
65.43	odd	12		845.2.b.e.339.6		6
65.47	even	4		845.2.l.f.654.12		24
65.48	odd	12		845.2.b.d.339.1		6
65.57	even	4		845.2.l.f.654.2		24
65.58	even	12		845.2.d.d.844.2		12
65.62	odd	12		845.2.n.e.484.1		12
65.63	even	12		845.2.l.f.699.2		24
195.68	even	12		585.2.bs.a.289.6		12
195.107	even	12		585.2.bs.a.289.1		12
260.3	even	12		1040.2.dh.a.289.2		12
260.107	even	12		1040.2.dh.a.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	5.2	odd	4
65.2.n.a.9.6	yes	12	5.3	odd	4
65.2.n.a.29.1	yes	12	65.3	odd	12
65.2.n.a.29.6	yes	12	65.42	odd	12
325.2.e.e.126.1		12	1.1	even	1	trivial
325.2.e.e.126.6		12	5.4	even	2	inner
325.2.e.e.276.1		12	13.3	even	3	inner
325.2.e.e.276.6		12	65.29	even	6	inner
585.2.bs.a.289.1		12	195.107	even	12
585.2.bs.a.289.6		12	195.68	even	12
585.2.bs.a.334.1		12	15.8	even	4
585.2.bs.a.334.6		12	15.2	even	4
845.2.b.d.339.1		6	65.48	odd	12
845.2.b.d.339.6		6	65.22	odd	12
845.2.b.e.339.1		6	65.17	odd	12
845.2.b.e.339.6		6	65.43	odd	12
845.2.d.d.844.1		12	65.7	even	12
845.2.d.d.844.2		12	65.58	even	12
845.2.d.d.844.11		12	65.32	even	12
845.2.d.d.844.12		12	65.33	even	12
845.2.l.f.654.1		24	65.8	even	4
845.2.l.f.654.2		24	65.57	even	4
845.2.l.f.654.11		24	65.18	even	4
845.2.l.f.654.12		24	65.47	even	4
845.2.l.f.699.1		24	65.2	even	12
845.2.l.f.699.2		24	65.63	even	12
845.2.l.f.699.11		24	65.37	even	12
845.2.l.f.699.12		24	65.28	even	12
845.2.n.e.484.1		12	65.62	odd	12
845.2.n.e.484.6		12	65.23	odd	12
845.2.n.e.529.1		12	65.38	odd	4
845.2.n.e.529.6		12	65.12	odd	4
1040.2.dh.a.289.2		12	260.3	even	12
1040.2.dh.a.289.5		12	260.107	even	12
1040.2.dh.a.529.2		12	20.7	even	4
1040.2.dh.a.529.5		12	20.3	even	4
4225.2.a.bq.1.1		6	13.4	even	6
4225.2.a.bq.1.6		6	65.4	even	6
4225.2.a.br.1.1		6	65.9	even	6
4225.2.a.br.1.6		6	13.9	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.27287 + 2.20467i) q^{2} +(-1.07646 + 1.86449i) q^{3} +(-2.24039 - 3.88048i) q^{4} +(-2.74039 - 4.74650i) q^{6} +(-1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(-0.817544 - 1.41603i) q^{9} +O(q^{10})\)	\(q+(-1.27287 + 2.20467i) q^{2} +(-1.07646 + 1.86449i) q^{3} +(-2.24039 - 3.88048i) q^{4} +(-2.74039 - 4.74650i) q^{6} +(-1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(-0.817544 - 1.41603i) q^{9} +(0.317544 - 0.550003i) q^{11} +9.64680 q^{12} +(-0.0716710 - 3.60484i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(-0.611979 - 1.05998i) q^{17} +4.16251 q^{18} +(-0.682456 - 1.18205i) q^{19} +6.32648 q^{21} +(0.808385 + 1.40016i) q^{22} +(1.07646 - 1.86449i) q^{23} +(-6.79833 + 11.7751i) q^{24} +(8.03872 + 4.43048i) q^{26} -2.93855 q^{27} +(-6.58351 + 11.4030i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(-2.74215 - 4.74954i) q^{32} +(0.683650 + 1.18412i) q^{33} +3.11588 q^{34} +(-3.66324 + 6.34492i) q^{36} +(0.611979 - 1.05998i) q^{37} +3.47471 q^{38} +(6.79833 + 3.74685i) q^{39} +(4.98079 - 8.62698i) q^{41} +(-8.05279 + 13.9478i) q^{42} +(-0.683650 - 1.18412i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} +6.16379 q^{47} +(-7.65998 - 13.2675i) q^{48} +(-0.817544 + 1.41603i) q^{49} +2.63509 q^{51} +(-13.8279 + 8.35437i) q^{52} -0.642285 q^{53} +(3.74039 - 6.47855i) q^{54} +(-9.27912 - 16.0719i) q^{56} +2.93855 q^{57} +(-3.81861 - 6.61402i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(11.4069 - 19.7574i) q^{62} +(-2.40240 + 4.16107i) q^{63} -0.270178 q^{64} -3.48079 q^{66} +(4.01502 - 6.95421i) q^{67} +(-2.74215 + 4.74954i) q^{68} +(2.31754 + 4.01410i) q^{69} +(-1.31754 - 2.28205i) q^{71} +(-5.16315 - 8.94284i) q^{72} +10.3263 q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} -1.86624 q^{77} +(-16.9140 + 10.2189i) q^{78} +1.03843 q^{79} +(5.61588 - 9.72698i) q^{81} +(12.6798 + 21.9620i) q^{82} -11.8452 q^{83} +(-14.1738 - 24.5498i) q^{84} +3.48079 q^{86} +(-3.22939 - 5.59346i) q^{87} +(2.00543 - 3.47351i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} -9.64680 q^{92} +(9.64680 - 16.7087i) q^{93} +(-7.84570 + 13.5891i) q^{94} +11.8073 q^{96} +(-7.39190 - 12.8031i) q^{97} +(-2.08125 - 3.60484i) q^{98} -1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9	\( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99}+O(q^{100}) \) 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9 + 44 * q^14 - 16 * q^16 - 12 * q^19 - 8 * q^21 - 32 * q^24 + 24 * q^26 - 18 * q^29 - 16 * q^31 - 16 * q^34 - 2 * q^36 + 32 * q^39 + 14 * q^41 + 4 * q^44 + 10 * q^46 - 6 * q^49 + 24 * q^51 + 22 * q^54 - 16 * q^56 + 4 * q^59 + 6 * q^61 + 12 * q^64 + 4 * q^66 + 24 * q^69 - 12 * q^71 - 8 * q^74 - 10 * q^76 + 104 * q^79 + 14 * q^81 - 90 * q^84 - 4 * q^86 - 20 * q^89 - 44 * q^91 - 56 * q^94 + 12 * q^96 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more