LMFDB - Embedded newform 325.2.n.e.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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, 5]))

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

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

chi := DirichletCharacter("325.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, 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 $\Q(\zeta_{6})$
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} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 $ x^10 + 16x^8 + 84x^6 + 163x^4 + 118x^2 + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$2.63252i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.e.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27983 + 1.31626i) q^{2} +(-1.34953 - 2.33745i) q^{3} +(2.46508 - 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(2.37354 + 1.37037i) q^{7} +7.71370i q^{8} +(-2.14244 + 3.71081i) q^{9} +O(q^{10})$	\(q+(-2.27983 + 1.31626i) q^{2} +(-1.34953 - 2.33745i) q^{3} +(2.46508 - 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(2.37354 + 1.37037i) q^{7} +7.71370i q^{8} +(-2.14244 + 3.71081i) q^{9} +(-1.59372 + 0.920132i) q^{11} -13.3067 q^{12} +(3.60247 - 0.149035i) q^{13} -7.21503 q^{14} +(-5.22307 - 9.04662i) q^{16} +(1.90847 - 3.30556i) q^{17} -11.2800i q^{18} +(4.91151 + 2.83566i) q^{19} -7.39738i q^{21} +(2.42227 - 4.19549i) q^{22} +(0.0696968 + 0.120718i) q^{23} +(18.0304 - 10.4098i) q^{24} +(-8.01684 + 5.08156i) q^{26} +3.46794 q^{27} +(11.7019 - 6.75612i) q^{28} +(-0.583497 - 1.01065i) q^{29} -5.69034i q^{31} +(10.4549 + 6.03614i) q^{32} +(4.30152 + 2.48348i) q^{33} +10.0481i q^{34} +(10.5626 + 18.2949i) q^{36} +(-2.13121 + 1.23046i) q^{37} -14.9299 q^{38} +(-5.20999 - 8.21945i) q^{39} +(8.01584 - 4.62795i) q^{41} +(9.73687 + 16.8648i) q^{42} +(1.04872 - 1.81644i) q^{43} +9.07280i q^{44} +(-0.317794 - 0.183478i) q^{46} -3.66621i q^{47} +(-14.0973 + 24.4173i) q^{48} +(0.255809 + 0.443075i) q^{49} -10.3021 q^{51} +(8.24405 - 15.7486i) q^{52} +9.97820 q^{53} +(-7.90632 + 4.56471i) q^{54} +(-10.5706 + 18.3088i) q^{56} -15.3072i q^{57} +(2.66055 + 1.53607i) q^{58} +(2.19087 + 1.26490i) q^{59} +(4.17536 - 7.23193i) q^{61} +(7.48996 + 12.9730i) q^{62} +(-10.1703 + 5.87185i) q^{63} -10.8882 q^{64} -13.0756 q^{66} +(-5.18026 + 2.99082i) q^{67} +(-9.40904 - 16.2969i) q^{68} +(0.188115 - 0.325825i) q^{69} +(-7.58786 - 4.38085i) q^{71} +(-28.6241 - 16.5261i) q^{72} -10.7918i q^{73} +(3.23920 - 5.61046i) q^{74} +(24.2145 - 13.9803i) q^{76} -5.04367 q^{77} +(22.6968 + 11.8813i) q^{78} -9.64672 q^{79} +(1.74723 + 3.02630i) q^{81} +(-12.1832 + 21.1018i) q^{82} +15.6113i q^{83} +(-31.5842 - 18.2351i) q^{84} +5.52156i q^{86} +(-1.57489 + 2.72779i) q^{87} +(-7.09762 - 12.2934i) q^{88} +(2.91690 - 1.68407i) q^{89} +(8.75486 + 4.58296i) q^{91} +0.687233 q^{92} +(-13.3009 + 7.67925i) q^{93} +(4.82569 + 8.35833i) q^{94} -32.5837i q^{96} +(-0.271200 - 0.156577i) q^{97} +(-1.16640 - 0.673423i) q^{98} -7.88531i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	$ 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9 - 9 * q^11 - 28 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 8 * q^17 - 12 * q^22 + 13 * q^23 + 42 * q^24 - 17 * q^26 + 30 * q^27 + 33 * q^28 + 7 * q^29 + 3 * q^32 - 6 * q^33 - 3 * q^36 + 3 * q^37 - 62 * q^38 + 8 * q^39 + 12 * q^41 + 32 * q^42 + 4 * q^43 + 39 * q^46 - 26 * q^48 - q^49 + 16 * q^51 + 61 * q^52 + 24 * q^53 - 9 * q^54 - 21 * q^56 + 18 * q^58 - 48 * q^59 + 13 * q^61 + 17 * q^62 - 34 * q^64 - 42 * q^66 + 6 * q^67 - 13 * q^68 + 20 * q^69 - 27 * q^71 - 141 * q^72 - 26 * q^74 - 12 * q^76 - 48 * q^77 + 56 * q^78 + 4 * q^79 - 17 * q^81 - q^82 - 90 * q^84 - 49 * q^87 - 6 * q^88 + 24 * q^89 + 13 * q^91 + 34 * q^92 - 63 * q^93 + 5 * q^94 - 15 * q^97 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.27983	+	1.31626i	−1.61208	+	0.930736i	−0.623195	+	0.782066i	$0.714166\pi$
$2$	−2.27983	+	1.31626i	−1.61208	+	0.930736i	−0.988887	+	0.148670i	$0.952501\pi$
$3$	−1.34953	−	2.33745i	−0.779149	−	1.34953i	−0.932433	−	0.361343i	$-0.882318\pi$
$3$	−1.34953	−	2.33745i	−0.779149	−	1.34953i	0.153284	−	0.988182i	$-0.451015\pi$
$4$	2.46508	−	4.26964i	1.23254	−	2.13482i
$5$		0			0
$5$		0			0
$6$	6.15337	+	3.55265i	2.51210	+	1.45036i
$7$	2.37354	+	1.37037i	0.897116	+	0.517950i	0.876263	−	0.481833i	$-0.160029\pi$
$7$	2.37354	+	1.37037i	0.897116	+	0.517950i	0.0208523	+	0.999783i	$0.493362\pi$
$8$			7.71370i			2.72720i
$9$	−2.14244	+	3.71081i	−0.714146	+	1.23694i
$10$		0			0
$11$	−1.59372	+	0.920132i	−0.480523	+	0.277430i	−0.720635	−	0.693315i	$-0.756149\pi$
$11$	−1.59372	+	0.920132i	−0.480523	+	0.277430i	0.240111	+	0.970745i	$0.422816\pi$
$12$	−13.3067			−3.84133
$13$	3.60247	−	0.149035i	0.999145	−	0.0413349i
$13$	3.60247	−	0.149035i	0.999145	−	0.0413349i
$14$	−7.21503			−1.92830
$15$		0			0
$16$	−5.22307	−	9.04662i	−1.30577	−	2.26166i
$17$	1.90847	−	3.30556i	0.462871	−	0.801716i	−0.536232	−	0.844071i	$-0.680153\pi$
$17$	1.90847	−	3.30556i	0.462871	−	0.801716i	0.999103	+	0.0423549i	$0.0134860\pi$
$18$		−	11.2800i		−	2.65873i
$19$	4.91151	+	2.83566i	1.12678	+	0.650545i	0.943123	−	0.332445i	$-0.107874\pi$
$19$	4.91151	+	2.83566i	1.12678	+	0.650545i	0.183655	+	0.982991i	$0.441207\pi$
$20$		0			0
$21$		−	7.39738i		−	1.61424i
$22$	2.42227	−	4.19549i	0.516429	−	0.894481i
$23$	0.0696968	+	0.120718i	0.0145328	+	0.0251715i	0.873200	−	0.487361i	$-0.162041\pi$
$23$	0.0696968	+	0.120718i	0.0145328	+	0.0251715i	−0.858668	+	0.512533i	$0.828707\pi$
$24$	18.0304	−	10.4098i	3.68043	−	2.12490i
$25$		0			0
$26$	−8.01684	+	5.08156i	−1.57223	+	0.996576i
$27$	3.46794			0.667406
$28$	11.7019	−	6.75612i	2.21146	−	1.27679i
$29$	−0.583497	−	1.01065i	−0.108353	−	0.187672i	0.806750	−	0.590892i	$-0.201224\pi$
$29$	−0.583497	−	1.01065i	−0.108353	−	0.187672i	−0.915103	+	0.403220i	$0.867891\pi$
$30$		0			0
$31$		−	5.69034i		−	1.02201i	−0.859576	−	0.511007i	$-0.829273\pi$
$31$		−	5.69034i		−	1.02201i	0.859576	−	0.511007i	$-0.170727\pi$
$32$	10.4549	+	6.03614i	1.84818	+	1.06705i
$33$	4.30152	+	2.48348i	0.748799	+	0.432319i
$34$			10.0481i			1.72324i
$35$		0			0
$36$	10.5626	+	18.2949i	1.76043	+	3.04915i
$37$	−2.13121	+	1.23046i	−0.350369	+	0.202286i	−0.664848	−	0.746979i	$-0.731504\pi$
$37$	−2.13121	+	1.23046i	−0.350369	+	0.202286i	0.314479	+	0.949265i	$0.398170\pi$
$38$	−14.9299			−2.42194
$39$	−5.20999	−	8.21945i	−0.834265	−	1.31617i
$40$		0			0
$41$	8.01584	−	4.62795i	1.25186	−	0.722764i	0.280384	−	0.959888i	$-0.409538\pi$
$41$	8.01584	−	4.62795i	1.25186	−	0.722764i	0.971479	+	0.237124i	$0.0762048\pi$
$42$	9.73687	+	16.8648i	1.50243	+	2.60229i
$43$	1.04872	−	1.81644i	0.159929	−	0.277004i	−0.774914	−	0.632066i	$-0.782207\pi$
$43$	1.04872	−	1.81644i	0.159929	−	0.277004i	0.934843	+	0.355062i	$0.115540\pi$
$44$			9.07280i			1.36778i
$45$		0			0
$46$	−0.317794	−	0.183478i	−0.0468561	−	0.0270524i
$47$		−	3.66621i		−	0.534772i	−0.963590	−	0.267386i	$-0.913840\pi$
$47$		−	3.66621i		−	0.534772i	0.963590	−	0.267386i	$-0.0861598\pi$
$48$	−14.0973	+	24.4173i	−2.03477	+	3.52433i
$49$	0.255809	+	0.443075i	0.0365442	+	0.0632964i
$50$		0			0
$51$	−10.3021			−1.44258
$52$	8.24405	−	15.7486i	1.14324	−	2.18394i
$53$	9.97820			1.37061			0.685305	−	0.728256i	$-0.259669\pi$
$53$	9.97820			1.37061			0.685305	+	0.728256i	$0.259669\pi$
$54$	−7.90632	+	4.56471i	−1.07591	+	0.621179i
$55$		0			0
$56$	−10.5706	+	18.3088i	−1.41255	+	2.44662i
$57$		−	15.3072i		−	2.02749i
$58$	2.66055	+	1.53607i	0.349347	+	0.201696i
$59$	2.19087	+	1.26490i	0.285227	+	0.164676i	0.635787	−	0.771864i	$-0.280676\pi$
$59$	2.19087	+	1.26490i	0.285227	+	0.164676i	−0.350560	+	0.936540i	$0.614009\pi$
$60$		0			0
$61$	4.17536	−	7.23193i	0.534600	−	0.925954i	−0.464583	−	0.885530i	$-0.653796\pi$
$61$	4.17536	−	7.23193i	0.534600	−	0.925954i	0.999183	−	0.0404240i	$-0.0128709\pi$
$62$	7.48996	+	12.9730i	0.951226	+	1.64757i
$63$	−10.1703	+	5.87185i	−1.28134	+	0.739784i
$64$	−10.8882			−1.36103
$65$		0			0
$66$	−13.0756			−1.60950
$67$	−5.18026	+	2.99082i	−0.632869	+	0.365387i	−0.781862	−	0.623451i	$-0.785730\pi$
$67$	−5.18026	+	2.99082i	−0.632869	+	0.365387i	0.148993	+	0.988838i	$0.452397\pi$
$68$	−9.40904	−	16.2969i	−1.14101	−	1.97629i
$69$	0.188115	−	0.325825i	0.0226464	−	0.0392248i
$70$		0			0
$71$	−7.58786	−	4.38085i	−0.900513	−	0.519912i	−0.0231467	−	0.999732i	$-0.507368\pi$
$71$	−7.58786	−	4.38085i	−0.900513	−	0.519912i	−0.877367	+	0.479820i	$0.840702\pi$
$72$	−28.6241	−	16.5261i	−3.37338	−	1.94762i
$73$		−	10.7918i		−	1.26309i	−0.775340	−	0.631544i	$-0.782422\pi$
$73$		−	10.7918i		−	1.26309i	0.775340	−	0.631544i	$-0.217578\pi$
$74$	3.23920	−	5.61046i	0.376549	−	0.652202i
$75$		0			0
$76$	24.2145	−	13.9803i	2.77760	−	1.60365i
$77$	−5.04367			−0.574780
$78$	22.6968	+	11.8813i	2.56991	+	1.34529i
$79$	−9.64672			−1.08534			−0.542670	−	0.839946i	$-0.682587\pi$
$79$	−9.64672			−1.08534			−0.542670	+	0.839946i	$0.682587\pi$
$80$		0			0
$81$	1.74723	+	3.02630i	0.194137	+	0.336255i
$82$	−12.1832	+	21.1018i	−1.34540	+	2.33031i
$83$			15.6113i			1.71356i	0.515684	+	0.856779i	$0.327538\pi$
$83$			15.6113i			1.71356i	−0.515684	+	0.856779i	$0.672462\pi$
$84$	−31.5842	−	18.2351i	−3.44611	−	1.98961i
$85$		0			0
$86$			5.52156i			0.595405i
$87$	−1.57489	+	2.72779i	−0.168846	+	0.292450i
$88$	−7.09762	−	12.2934i	−0.756609	−	1.31049i
$89$	2.91690	−	1.68407i	0.309190	−	0.178511i	−0.337374	−	0.941371i	$-0.609539\pi$
$89$	2.91690	−	1.68407i	0.309190	−	0.178511i	0.646564	+	0.762860i	$0.276205\pi$
$90$		0			0
$91$	8.75486	+	4.58296i	0.917758	+	0.480425i
$92$	0.687233			0.0716490
$93$	−13.3009	+	7.67925i	−1.37923	+	0.796302i
$94$	4.82569	+	8.35833i	0.497731	+	0.862096i
$95$		0			0
$96$		−	32.5837i		−	3.32556i
$97$	−0.271200	−	0.156577i	−0.0275362	−	0.0158980i	0.486169	−	0.873865i	$-0.338394\pi$
$97$	−0.271200	−	0.156577i	−0.0275362	−	0.0158980i	−0.513705	+	0.857967i	$0.671727\pi$
$98$	−1.16640	−	0.673423i	−0.117824	−	0.0680260i
$99$		−	7.88531i		−	0.792503i
$100$		0			0
$101$	7.91794	+	13.7143i	0.787864	+	1.36462i	0.927273	+	0.374386i	$0.122146\pi$
$101$	7.91794	+	13.7143i	0.787864	+	1.36462i	−0.139409	+	0.990235i	$0.544520\pi$
$102$	23.4870	−	13.5602i	2.32556	−	1.34266i
$103$	−7.37659			−0.726837			−0.363418	−	0.931626i	$-0.618390\pi$
$103$	−7.37659			−0.726837			−0.363418	+	0.931626i	$0.618390\pi$
$104$	1.14961	+	27.7884i	0.112729	+	2.72487i
$105$		0			0
$106$	−22.7486	+	13.1339i	−2.20954	+	1.27568i
$107$	−4.81679	−	8.34292i	−0.465656	−	0.806540i	0.533575	−	0.845753i	$-0.320848\pi$
$107$	−4.81679	−	8.34292i	−0.465656	−	0.806540i	−0.999231	+	0.0392127i	$0.987515\pi$
$108$	8.54876	−	14.8069i	0.822604	−	1.42479i
$109$			8.73514i			0.836674i	0.908292	+	0.418337i	$0.137387\pi$
$109$			8.73514i			0.836674i	−0.908292	+	0.418337i	$0.862613\pi$
$110$		0			0
$111$	5.75225	+	3.32106i	0.545979	+	0.315221i
$112$		−	28.6301i		−	2.70529i
$113$	9.13443	−	15.8213i	0.859295	−	1.48834i	−0.0133068	−	0.999911i	$-0.504236\pi$
$113$	9.13443	−	15.8213i	0.859295	−	1.48834i	0.872602	−	0.488432i	$-0.162431\pi$
$114$	20.1482	+	34.8978i	1.88706	+	3.26848i
$115$		0			0
$116$	−5.75347			−0.534196
$117$	−7.16503	+	13.6874i	−0.662407	+	1.26540i
$118$	−6.65974			−0.613079
$119$	9.05966	−	5.23060i	0.830497	−	0.479488i
$120$		0			0
$121$	−3.80671	+	6.59342i	−0.346065	+	0.599402i
$122$			21.9834i			1.99028i
$123$	−21.6352	−	12.4911i	−1.95078	−	1.12628i
$124$	−24.2957	−	14.0271i	−2.18182	−	1.25967i
$125$		0			0
$126$	15.4578	−	26.7736i	1.37709	−	2.38518i
$127$	5.56769	+	9.64353i	0.494053	+	0.855725i	0.999977	−	0.00685350i	$-0.00218155\pi$
$127$	5.56769	+	9.64353i	0.494053	+	0.855725i	−0.505924	+	0.862578i	$0.668848\pi$
$128$	3.91346	−	2.25944i	0.345904	−	0.199708i
$129$	−5.66111			−0.498433
$130$		0			0
$131$	4.16563			0.363953			0.181976	−	0.983303i	$-0.441751\pi$
$131$	4.16563			0.363953			0.181976	+	0.983303i	$0.441751\pi$
$132$	21.2072	−	12.2440i	1.84585	−	1.06570i
$133$	7.77179	+	13.4611i	0.673900	+	1.16723i
$134$	7.87340	−	13.6371i	0.680158	−	1.17807i
$135$		0			0
$136$	25.4981	+	14.7213i	2.18644	+	1.26234i
$137$	−0.347097	−	0.200396i	−0.0296545	−	0.0171210i	0.485099	−	0.874459i	$-0.338783\pi$
$137$	−0.347097	−	0.200396i	−0.0296545	−	0.0171210i	−0.514754	+	0.857338i	$0.672117\pi$
$138$			0.990434i			0.0843114i
$139$	5.57346	−	9.65351i	0.472735	−	0.818800i	−0.526779	−	0.850003i	$-0.676600\pi$
$139$	5.57346	−	9.65351i	0.472735	−	0.818800i	0.999513	+	0.0312024i	$0.00993363\pi$
$140$		0			0
$141$	−8.56957	+	4.94764i	−0.721688	+	0.416667i
$142$	23.0654			1.93560
$143$	−5.60418	+	3.55227i	−0.468645	+	0.297056i
$144$	44.7604			3.73003
$145$		0			0
$146$	14.2048	+	24.6035i	1.17560	+	2.03620i
$147$	0.690442	−	1.19588i	0.0569467	−	0.0986346i
$148$			12.1327i			0.997300i
$149$	15.4824	+	8.93879i	1.26837	+	0.732294i	0.974680	−	0.223606i	$-0.0717829\pi$
$149$	15.4824	+	8.93879i	1.26837	+	0.732294i	0.293691	+	0.955900i	$0.405116\pi$
$150$		0			0
$151$		−	6.29273i		−	0.512095i	−0.966664	−	0.256048i	$-0.917580\pi$
$151$		−	6.29273i		−	0.512095i	0.966664	−	0.256048i	$-0.0824204\pi$
$152$	−21.8734	+	37.8859i	−1.77417	+	3.07295i
$153$	8.17754	+	14.1639i	0.661115	+	1.14508i
$154$	11.4987	−	6.63879i	0.926593	−	0.534969i
$155$		0			0
$156$	−47.9372	+	1.98317i	−3.83804	+	0.158781i
$157$	16.1516			1.28904			0.644518	−	0.764589i	$-0.277058\pi$
$157$	16.1516			1.28904			0.644518	+	0.764589i	$0.277058\pi$
$158$	21.9929	−	12.6976i	1.74966	−	1.01017i
$159$	−13.4658	−	23.3235i	−1.06791	−	1.84967i
$160$		0			0
$161$			0.382041i			0.0301090i
$162$	−7.96679	−	4.59963i	−0.625930	−	0.361381i
$163$	20.6404	+	11.9167i	1.61668	+	0.933390i	0.987771	+	0.155910i	$0.0498311\pi$
$163$	20.6404	+	11.9167i	1.61668	+	0.933390i	0.628908	+	0.777480i	$0.283502\pi$
$164$		−	45.6330i		−	3.56334i
$165$		0			0
$166$	−20.5485	−	35.5910i	−1.59487	−	2.76240i
$167$	−0.967261	+	0.558448i	−0.0748489	+	0.0432140i	−0.536957	−	0.843609i	$-0.680426\pi$
$167$	−0.967261	+	0.558448i	−0.0748489	+	0.0432140i	0.462108	+	0.886823i	$0.347093\pi$
$168$	57.0611			4.40236
$169$	12.9556	−	1.07379i	0.996583	−	0.0825992i
$170$		0			0
$171$	−21.0452	+	12.1505i	−1.60937	+	0.929169i
$172$	−5.17036	−	8.95533i	−0.394236	−	0.682838i
$173$	1.07541	−	1.86266i	0.0817616	−	0.141615i	−0.822245	−	0.569134i	$-0.807279\pi$
$173$	1.07541	−	1.86266i	0.0817616	−	0.141615i	0.904007	+	0.427518i	$0.140612\pi$
$174$		−	8.29185i		−	0.628604i
$175$		0			0
$176$	16.6482	+	9.61183i	1.25490	+	0.724519i
$177$		−	6.82805i		−	0.513228i
$178$	−4.43335	+	7.67878i	−0.332293	+	0.575549i
$179$	−1.08264	−	1.87518i	−0.0809199	−	0.140157i	0.822725	−	0.568439i	$-0.192452\pi$
$179$	−1.08264	−	1.87518i	−0.0809199	−	0.140157i	−0.903645	+	0.428282i	$0.859119\pi$
$180$		0			0
$181$	−19.8242			−1.47352			−0.736759	−	0.676155i	$-0.763645\pi$
$181$	−19.8242			−1.47352			−0.736759	+	0.676155i	$0.763645\pi$
$182$	−25.9919	+	1.07529i	−1.92665	+	0.0797061i
$183$	−22.5390			−1.66613
$184$	−0.931186	+	0.537620i	−0.0686479	+	0.0396339i
$185$		0			0
$186$	20.2158	−	35.0148i	1.48229	−	2.56741i
$187$			7.02416i			0.513658i
$188$	−15.6534	−	9.03750i	−1.14164	−	0.659127i
$189$	8.23132	+	4.75235i	0.598740	+	0.345683i
$190$		0			0
$191$	1.38158	−	2.39297i	0.0999677	−	0.173149i	−0.811703	−	0.584070i	$-0.801459\pi$
$191$	1.38158	−	2.39297i	0.0999677	−	0.173149i	0.911671	+	0.410921i	$0.134793\pi$
$192$	14.6939	+	25.4506i	1.06044	+	1.83674i
$193$	−1.05896	+	0.611391i	−0.0762257	+	0.0440089i	−0.537628	−	0.843182i	$-0.680680\pi$
$193$	−1.05896	+	0.611391i	−0.0762257	+	0.0440089i	0.461403	+	0.887191i	$0.347346\pi$
$194$	0.824386			0.0591875
$195$		0			0
$196$	2.52236			0.180169
$197$	−14.5872	+	8.42195i	−1.03930	+	0.600039i	−0.919634	−	0.392776i	$-0.871515\pi$
$197$	−14.5872	+	8.42195i	−1.03930	+	0.600039i	−0.119663	+	0.992815i	$0.538182\pi$
$198$	10.3791	+	17.9771i	0.737611	+	1.27758i
$199$	−11.5992	+	20.0904i	−0.822245	+	1.42417i	0.0817623	+	0.996652i	$0.473945\pi$
$199$	−11.5992	+	20.0904i	−0.822245	+	1.42417i	−0.904007	+	0.427518i	$0.859388\pi$
$200$		0			0
$201$	13.9818	+	8.07238i	0.986199	+	0.569382i
$202$	−36.1031	−	20.8441i	−2.54020	−	1.46659i
$203$		−	3.19842i		−	0.224485i
$204$	−25.3955	+	43.9862i	−1.77804	+	3.07965i
$205$		0			0
$206$	16.8174	−	9.70951i	1.17172	−	0.676493i
$207$	−0.597285			−0.0415141
$208$	−20.1642	−	31.8118i	−1.39814	−	2.20575i
$209$	−10.4367			−0.721924
$210$		0			0
$211$	−13.4892	−	23.3639i	−0.928632	−	1.60844i	−0.785614	−	0.618717i	$-0.787653\pi$
$211$	−13.4892	−	23.3639i	−0.928632	−	1.60844i	−0.143017	−	0.989720i	$-0.545680\pi$
$212$	24.5970	−	42.6033i	1.68933	−	2.92601i
$213$			23.6483i			1.62035i
$214$	21.9629	+	12.6803i	1.50135	+	0.866806i
$215$		0			0
$216$			26.7507i			1.82015i
$217$	7.79785	−	13.5063i	0.529352	−	0.916865i
$218$	−11.4977	−	19.9146i	−0.778723	−	1.34879i
$219$	−25.2253	+	14.5638i	−1.70457	+	0.984134i
$220$		0			0
$221$	6.38255	−	12.1926i	0.429336	−	0.820164i
$222$	−17.4855			−1.17355
$223$	0.762699	−	0.440345i	0.0510741	−	0.0294877i	−0.474246	−	0.880393i	$-0.657279\pi$
$223$	0.762699	−	0.440345i	0.0510741	−	0.0294877i	0.525320	+	0.850905i	$0.323946\pi$
$224$	16.5434	+	28.6541i	1.10535	+	1.91453i
$225$		0			0
$226$			48.0931i			3.19911i
$227$	3.01263	+	1.73934i	0.199955	+	0.115444i	0.596635	−	0.802513i	$-0.296504\pi$
$227$	3.01263	+	1.73934i	0.199955	+	0.115444i	−0.396679	+	0.917957i	$0.629838\pi$
$228$	−65.3562	−	37.7334i	−4.32832	−	2.49896i
$229$			7.25190i			0.479219i	0.970869	+	0.239610i	$0.0770194\pi$
$229$			7.25190i			0.479219i	−0.970869	+	0.239610i	$0.922981\pi$
$230$		0			0
$231$	6.80657	+	11.7893i	0.447839	+	0.775680i
$232$	7.79583	−	4.50092i	0.511821	−	0.295500i
$233$	14.3236			0.938371			0.469185	−	0.883100i	$-0.344548\pi$
$233$	14.3236			0.938371			0.469185	+	0.883100i	$0.344548\pi$
$234$	−1.68112	−	40.6359i	−0.109898	−	2.65645i
$235$		0			0
$236$	10.8013	−	6.23615i	0.703107	−	0.405939i
$237$	13.0185	+	22.5487i	0.845642	+	1.46469i
$238$	−13.7696	+	23.8497i	−0.892553	+	1.54595i
$239$		−	3.62106i		−	0.234227i	−0.993119	−	0.117114i	$-0.962636\pi$
$239$		−	3.62106i		−	0.234227i	0.993119	−	0.117114i	$-0.0373642\pi$
$240$		0			0
$241$	2.36360	+	1.36462i	0.152253	+	0.0879031i	0.574191	−	0.818721i	$-0.305317\pi$
$241$	2.36360	+	1.36462i	0.152253	+	0.0879031i	−0.421938	+	0.906625i	$0.638650\pi$
$242$		−	20.0425i		−	1.28838i
$243$	9.91779	−	17.1781i	0.636227	−	1.10198i
$244$	−20.5852	−	35.6545i	−1.31783	−	2.28255i
$245$		0			0
$246$	65.7659			4.19308
$247$	18.1162	+	9.48340i	1.15270	+	0.603414i
$248$	43.8935			2.78724
$249$	36.4905	−	21.0678i	2.31249	−	1.33512i
$250$		0			0
$251$	−5.54338	+	9.60142i	−0.349895	+	0.606036i	−0.986231	−	0.165376i	$-0.947116\pi$
$251$	−5.54338	+	9.60142i	−0.349895	+	0.606036i	0.636335	+	0.771413i	$0.280450\pi$
$252$			57.8983i			3.64725i
$253$	−0.222154	−	0.128261i	−0.0139667	−	0.00806368i
$254$	−25.3868	−	14.6571i	−1.59291	−	0.919666i
$255$		0			0
$256$	4.94020	−	8.55667i	0.308762	−	0.534792i
$257$	−14.6301	−	25.3401i	−0.912601	−	1.58067i	−0.810376	−	0.585910i	$-0.800737\pi$
$257$	−14.6301	−	25.3401i	−0.912601	−	1.58067i	−0.102224	−	0.994761i	$-0.532596\pi$
$258$	12.9064	−	7.45149i	0.803514	−	0.463909i
$259$	−6.74470			−0.419095
$260$		0			0
$261$	5.00043			0.309519
$262$	−9.49692	+	5.48305i	−0.586722	+	0.338744i
$263$	−7.20239	−	12.4749i	−0.444118	−	0.769235i	0.553872	−	0.832602i	$-0.313150\pi$
$263$	−7.20239	−	12.4749i	−0.444118	−	0.769235i	−0.997990	+	0.0633665i	$0.979816\pi$
$264$	−19.1568	+	33.1806i	−1.17902	+	2.04213i
$265$		0			0
$266$	−35.4367	−	20.4594i	−2.17276	−	1.25445i
$267$	−7.87285	−	4.54539i	−0.481810	−	0.278173i
$268$			29.4905i			1.80142i
$269$	−6.56252	+	11.3666i	−0.400124	+	0.693035i	−0.993741	−	0.111713i	$-0.964366\pi$
$269$	−6.56252	+	11.3666i	−0.400124	+	0.693035i	0.593616	+	0.804748i	$0.297700\pi$
$270$		0			0
$271$	−1.64683	+	0.950797i	−0.100038	+	0.0577568i	−0.549184	−	0.835701i	$-0.685061\pi$
$271$	−1.64683	+	0.950797i	−0.100038	+	0.0577568i	0.449147	+	0.893458i	$0.351728\pi$
$272$	−39.8722			−2.41761
$273$	−1.10247	−	26.6488i	−0.0667245	−	1.61286i
$274$	1.05509			0.0637406
$275$		0			0
$276$	−0.927438	−	1.60637i	−0.0558252	−	0.0966921i
$277$	−14.3095	+	24.7847i	−0.859772	+	1.48917i	0.0123732	+	0.999923i	$0.496061\pi$
$277$	−14.3095	+	24.7847i	−0.859772	+	1.48917i	−0.872146	+	0.489246i	$0.837272\pi$
$278$			29.3445i			1.75996i
$279$	21.1158	+	12.1912i	1.26417	+	0.729868i
$280$		0			0
$281$			0.841175i			0.0501803i	0.999685	+	0.0250901i	$0.00798728\pi$
$281$			0.841175i			0.0501803i	−0.999685	+	0.0250901i	$0.992013\pi$
$282$	13.0248	−	22.5596i	0.775614	−	1.34340i
$283$	−1.63943	−	2.83957i	−0.0974538	−	0.168795i	0.813176	−	0.582018i	$-0.197736\pi$
$283$	−1.63943	−	2.83957i	−0.0974538	−	0.168795i	−0.910630	+	0.413223i	$0.864403\pi$
$284$	−37.4094	+	21.5983i	−2.21984	+	1.28162i
$285$		0			0
$286$	8.10087	−	15.4751i	0.479014	−	0.915063i
$287$	25.3679			1.49742
$288$	−44.7979	+	25.8641i	−2.63974	+	1.52406i
$289$	1.21552	+	2.10534i	0.0715010	+	0.123843i
$290$		0			0
$291$			0.845221i			0.0495477i
$292$	−46.0772	−	26.6027i	−2.69647	−	1.55681i
$293$	−7.27496	−	4.20020i	−0.425008	−	0.245378i	0.272210	−	0.962238i	$-0.412245\pi$
$293$	−7.27496	−	4.20020i	−0.425008	−	0.245378i	−0.697217	+	0.716860i	$0.745579\pi$
$294$			3.63521i			0.212010i
$295$		0			0
$296$	−9.49136	−	16.4395i	−0.551674	−	0.955528i
$297$	−5.52692	+	3.19097i	−0.320704	+	0.185159i
$298$	−47.0631			−2.72629
$299$	0.269072	+	0.424497i	0.0155608	+	0.0245493i
$300$		0			0
$301$	4.97838	−	2.87427i	0.286949	−	0.165670i
$302$	8.28287	+	14.3464i	0.476626	+	0.825540i
$303$	21.3709	−	37.0155i	1.22773	−	2.12649i
$304$		−	59.2434i		−	3.39784i
$305$		0			0
$306$	−37.2868	−	21.5275i	−2.13154	−	1.23065i
$307$			32.8251i			1.87343i	0.350095	+	0.936714i	$0.386149\pi$
$307$			32.8251i			1.87343i	−0.350095	+	0.936714i	$0.613851\pi$
$308$	−12.4331	+	21.5347i	−0.708439	+	1.22705i
$309$	9.95489	+	17.2424i	0.566314	+	0.980885i
$310$		0			0
$311$	18.5990			1.05465			0.527327	−	0.849662i	$-0.323194\pi$
$311$	18.5990			1.05465			0.527327	+	0.849662i	$0.323194\pi$
$312$	63.4024	−	40.1883i	3.58945	−	2.27521i
$313$	−6.55565			−0.370547			−0.185274	−	0.982687i	$-0.559317\pi$
$313$	−6.55565			−0.370547			−0.185274	+	0.982687i	$0.559317\pi$
$314$	−36.8228	+	21.2597i	−2.07803	+	1.19975i
$315$		0			0
$316$	−23.7799	+	41.1880i	−1.33772	+	2.31701i
$317$		−	28.3918i		−	1.59464i	−0.603555	−	0.797321i	$-0.706250\pi$
$317$		−	28.3918i		−	1.59464i	0.603555	−	0.797321i	$-0.293750\pi$
$318$	61.3996	+	35.4491i	3.44312	+	1.98788i
$319$	1.85986	+	1.07379i	0.104132	+	0.0601207i
$320$		0			0
$321$	−13.0008	+	22.5180i	−0.725631	+	1.25683i
$322$	−0.502865	−	0.870988i	−0.0280236	−	0.0485382i
$323$	18.7469	−	10.8235i	1.04311	−	0.602237i
$324$	17.2283			0.957127
$325$		0			0
$326$	−62.7420			−3.47496
$327$	20.4179	−	11.7883i	1.12911	−	0.651894i
$328$	35.6986	+	61.8317i	1.97112	+	3.41409i
$329$	5.02405	−	8.70191i	0.276985	−	0.479752i
$330$		0			0
$331$	−2.08424	−	1.20334i	−0.114560	−	0.0661413i	0.441625	−	0.897200i	$-0.354402\pi$
$331$	−2.08424	−	1.20334i	−0.114560	−	0.0661413i	−0.556185	+	0.831058i	$0.687735\pi$
$332$	66.6545	+	38.4830i	3.65814	+	2.11203i
$333$		−	10.5447i		−	0.577846i
$334$	1.47013	−	2.54633i	0.0804417	−	0.139329i
$335$		0			0
$336$	−66.9213	+	38.6370i	−3.65086	+	2.10782i
$337$	−3.33555			−0.181699			−0.0908496	−	0.995865i	$-0.528958\pi$
$337$	−3.33555			−0.181699			−0.0908496	+	0.995865i	$0.528958\pi$
$338$	−28.1231	+	19.5010i	−1.52970	+	1.06071i
$339$	−49.3086			−2.67808
$340$		0			0
$341$	5.23586	+	9.06878i	0.283538	+	0.491102i
$342$	31.9863	−	55.4019i	1.72962	−	2.99579i
$343$		−	17.7829i		−	0.960188i
$344$	14.0115	+	8.08952i	0.755447	+	0.436158i
$345$		0			0
$346$			5.66206i			0.304394i
$347$	−10.0224	+	17.3593i	−0.538031	+	0.931897i	0.460979	+	0.887411i	$0.347498\pi$
$347$	−10.0224	+	17.3593i	−0.538031	+	0.931897i	−0.999010	+	0.0444861i	$0.985835\pi$
$348$	7.76445	+	13.4484i	0.416218	+	0.720911i
$349$	12.8911	−	7.44270i	0.690047	−	0.398399i	−0.113583	−	0.993529i	$-0.536233\pi$
$349$	12.8911	−	7.44270i	0.690047	−	0.398399i	0.803630	+	0.595130i	$0.202899\pi$
$350$		0			0
$351$	12.4932	−	0.516846i	0.666836	−	0.0275872i
$352$	−22.2162			−1.18413
$353$	−16.6003	+	9.58417i	−0.883543	+	0.510114i	−0.871825	−	0.489818i	$-0.837063\pi$
$353$	−16.6003	+	9.58417i	−0.883543	+	0.510114i	−0.0117179	+	0.999931i	$0.503730\pi$
$354$	8.98749	+	15.5668i	0.477680	+	0.827365i
$355$		0			0
$356$		−	16.6055i		−	0.880088i
$357$	−24.4525	−	14.1176i	−1.29416	−	0.747185i
$358$	4.93645	+	2.85006i	0.260899	+	0.150630i
$359$			15.1897i			0.801683i	0.916147	+	0.400842i	$0.131282\pi$
$359$			15.1897i			0.801683i	−0.916147	+	0.400842i	$0.868718\pi$
$360$		0			0
$361$	6.58195	+	11.4003i	0.346419	+	0.600014i
$362$	45.1957	−	26.0937i	2.37543	−	1.37146i
$363$	20.5490			1.07854
$364$	41.1490	−	26.0827i	2.15679	−	1.36711i
$365$		0			0
$366$	51.3850	−	29.6672i	2.68594	−	1.55073i
$367$	−2.13354	−	3.69540i	−0.111370	−	0.192898i	0.804953	−	0.593339i	$-0.202190\pi$
$367$	−2.13354	−	3.69540i	−0.111370	−	0.192898i	−0.916323	+	0.400440i	$0.868857\pi$
$368$	0.728063	−	1.26104i	0.0379529	−	0.0657364i
$369$			39.6603i			2.06463i
$370$		0			0
$371$	23.6837	+	13.6738i	1.22960	+	0.709908i
$372$			75.7199i			3.92589i
$373$	−6.85171	+	11.8675i	−0.354768	+	0.614476i	−0.987078	−	0.160239i	$-0.948773\pi$
$373$	−6.85171	+	11.8675i	−0.354768	+	0.614476i	0.632310	+	0.774715i	$0.282107\pi$
$374$	−9.24562	−	16.0139i	−0.478080	−	0.828059i
$375$		0			0
$376$	28.2800			1.45843
$377$	−2.25265	−	3.55386i	−0.116018	−	0.183033i
$378$	−25.0213			−1.28696
$379$	−16.5632	+	9.56275i	−0.850792	+	0.491205i	−0.860918	−	0.508744i	$-0.830110\pi$
$379$	−16.5632	+	9.56275i	−0.850792	+	0.491205i	0.0101257	+	0.999949i	$0.496777\pi$
$380$		0			0
$381$	15.0275	−	26.0284i	0.769882	−	1.33347i
$382$			7.27408i			0.372174i
$383$	8.57619	+	4.95147i	0.438223	+	0.253008i	0.702844	−	0.711344i	$-0.251913\pi$
$383$	8.57619	+	4.95147i	0.438223	+	0.253008i	−0.264621	+	0.964353i	$0.585247\pi$
$384$	−10.5626	−	6.09833i	−0.539022	−	0.311204i
$385$		0			0
$386$	1.60950	−	2.78773i	0.0819213	−	0.141892i
$387$	4.49364	+	7.78322i	0.228425	+	0.395643i
$388$	−1.33706	+	0.771951i	−0.0678789	+	0.0391899i
$389$	−19.3750			−0.982350			−0.491175	−	0.871061i	$-0.663432\pi$
$389$	−19.3750			−0.982350			−0.491175	+	0.871061i	$0.663432\pi$
$390$		0			0
$391$	0.532056			0.0269072
$392$	−3.41774	+	1.97324i	−0.172622	+	0.0996635i
$393$	−5.62162	−	9.73693i	−0.283573	−	0.491163i
$394$	22.1709	−	38.4012i	1.11696	−	1.93462i
$395$		0			0
$396$	−33.6674	−	19.4379i	−1.69185	−	0.976791i
$397$	16.9557	+	9.78940i	0.850984	+	0.491316i	0.860983	−	0.508634i	$-0.169849\pi$
$397$	16.9557	+	9.78940i	0.850984	+	0.491316i	−0.00999849	+	0.999950i	$0.503183\pi$
$398$		−	61.0702i		−	3.06117i
$399$	20.9765	−	36.3323i	1.05014	−	1.81889i
$400$		0			0
$401$	−27.1719	+	15.6877i	−1.35690	+	0.783406i	−0.989205	−	0.146541i	$-0.953186\pi$
$401$	−27.1719	+	15.6877i	−1.35690	+	0.783406i	−0.367694	+	0.929947i	$0.619852\pi$
$402$	−42.5014			−2.11978
$403$	−0.848060	−	20.4993i	−0.0422449	−	1.02114i
$404$	78.0734			3.88429
$405$		0			0
$406$	4.20995	+	7.29185i	0.208936	+	0.361889i
$407$	2.26436	−	3.92199i	0.112240	−	0.194406i
$408$		−	79.4672i		−	3.93421i
$409$	−16.8069	−	9.70347i	−0.831048	−	0.479806i	0.0231636	−	0.999732i	$-0.492626\pi$
$409$	−16.8069	−	9.70347i	−0.831048	−	0.479806i	−0.854211	+	0.519926i	$0.825959\pi$
$410$		0			0
$411$			1.08176i			0.0533593i
$412$	−18.1839	+	31.4954i	−0.895855	+	1.55167i
$413$	3.46675	+	6.00459i	0.170588	+	0.295466i
$414$	1.36171	−	0.786182i	0.0669242	−	0.0386387i
$415$		0			0
$416$	38.5630	+	20.1868i	1.89071	+	0.989742i
$417$	−30.0861			−1.47332
$418$	23.7940	−	13.7375i	1.16380	−	0.671921i
$419$	−4.07630	−	7.06036i	−0.199140	−	0.344921i	0.749110	−	0.662446i	$-0.230482\pi$
$419$	−4.07630	−	7.06036i	−0.199140	−	0.344921i	−0.948250	+	0.317525i	$0.897148\pi$
$420$		0			0
$421$		−	15.3225i		−	0.746771i	−0.927676	−	0.373385i	$-0.878197\pi$
$421$		−	15.3225i		−	0.746771i	0.927676	−	0.373385i	$-0.121803\pi$
$422$	61.5059	+	35.5105i	2.99406	+	1.72862i
$423$	13.6046	+	7.85463i	0.661479	+	0.381905i
$424$			76.9688i			3.73793i
$425$		0			0
$426$	−31.1273	−	53.9141i	−1.50812	−	2.61214i
$427$	19.8208	−	11.4435i	0.959195	−	0.553792i
$428$	−47.4950			−2.29576
$429$	15.8662	+	8.30560i	0.766029	+	0.400998i
$430$		0			0
$431$	12.4274	−	7.17495i	0.598606	−	0.345605i	−0.169887	−	0.985464i	$-0.554340\pi$
$431$	12.4274	−	7.17495i	0.598606	−	0.345605i	0.768493	+	0.639858i	$0.221007\pi$
$432$	−18.1133	−	31.3732i	−0.871477	−	1.50944i
$433$	−7.64462	+	13.2409i	−0.367377	+	0.636316i	−0.989155	−	0.146878i	$-0.953077\pi$
$433$	−7.64462	+	13.2409i	−0.367377	+	0.636316i	0.621778	+	0.783194i	$0.286411\pi$
$434$			41.0560i			1.97075i
$435$		0			0
$436$	37.2959	+	21.5328i	1.78615	+	1.03123i
$437$			0.790547i			0.0378170i
$438$	38.3396	−	66.4061i	1.83194	−	3.17301i
$439$	0.394002	+	0.682432i	0.0188047	+	0.0325707i	0.875275	−	0.483626i	$-0.160681\pi$
$439$	0.394002	+	0.682432i	0.0188047	+	0.0325707i	−0.856470	+	0.516197i	$0.827347\pi$
$440$		0			0
$441$	−2.19222			−0.104392
$442$	1.49753	+	36.1981i	0.0712301	+	1.72177i
$443$	−16.1718			−0.768343			−0.384172	−	0.923262i	$-0.625513\pi$
$443$	−16.1718			−0.768343			−0.384172	+	0.923262i	$0.625513\pi$
$444$	28.3595	−	16.3734i	1.34588	−	0.777045i
$445$		0			0
$446$	−1.15922	+	2.00782i	−0.0548905	+	0.0950731i
$447$		−	48.2525i		−	2.28227i
$448$	−25.8436	−	14.9208i	−1.22100	−	0.704943i
$449$	−5.14701	−	2.97163i	−0.242903	−	0.140240i	0.373607	−	0.927587i	$-0.378121\pi$
$449$	−5.14701	−	2.97163i	−0.242903	−	0.140240i	−0.616510	+	0.787347i	$0.711454\pi$
$450$		0			0
$451$	−8.51665	+	14.7513i	−0.401033	+	0.694610i
$452$	−45.0342	−	78.0015i	−2.11823	−	3.66888i
$453$	−14.7089	+	8.49221i	−0.691086	+	0.398999i
$454$	−9.15770			−0.429792
$455$		0			0
$456$	118.075			5.52937
$457$	7.49289	−	4.32602i	0.350503	−	0.202363i	−0.314404	−	0.949289i	$-0.601805\pi$
$457$	7.49289	−	4.32602i	0.350503	−	0.202363i	0.664907	+	0.746926i	$0.268471\pi$
$458$	−9.54539	−	16.5331i	−0.446027	−	0.772541i
$459$	6.61845	−	11.4635i	0.308923	−	0.535070i
$460$		0			0
$461$	−0.600268	−	0.346565i	−0.0279573	−	0.0161411i	0.485956	−	0.873983i	$-0.338471\pi$
$461$	−0.600268	−	0.346565i	−0.0279573	−	0.0161411i	−0.513913	+	0.857842i	$0.671805\pi$
$462$	−31.0356	−	17.9184i	−1.44391	−	0.833640i
$463$			33.6025i			1.56164i	0.624754	+	0.780821i	$0.285199\pi$
$463$			33.6025i			1.56164i	−0.624754	+	0.780821i	$0.714801\pi$
$464$	−6.09530	+	10.5574i	−0.282967	+	0.490113i
$465$		0			0
$466$	−32.6554	+	18.8536i	−1.51273	+	0.873375i
$467$	−2.48505			−0.114995			−0.0574973	−	0.998346i	$-0.518312\pi$
$467$	−2.48505			−0.114995			−0.0574973	+	0.998346i	$0.518312\pi$
$468$	40.7779	+	64.3326i	1.88496	+	2.97377i
$469$	−16.3941			−0.757009
$470$		0			0
$471$	−21.7970	−	37.7534i	−1.00435	−	1.73959i
$472$	−9.75704	+	16.8997i	−0.449104	+	0.777872i
$473$			3.85985i			0.177476i
$474$	−59.3598	−	34.2714i	−2.72649	−	1.57414i
$475$		0			0
$476$		−	51.5753i		−	2.36395i
$477$	−21.3777	+	37.0272i	−0.978816	+	1.69536i
$478$	4.76626	+	8.25541i	0.218004	+	0.377593i
$479$	−29.0171	+	16.7530i	−1.32583	+	0.765465i	−0.984651	−	0.174535i	$-0.944158\pi$
$479$	−29.0171	+	16.7530i	−1.32583	+	0.765465i	−0.341174	+	0.940000i	$0.610825\pi$
$480$		0			0
$481$	−7.49424	+	4.75030i	−0.341708	+	0.216595i
$482$	−7.18479			−0.327258
$483$	0.893000	−	0.515574i	0.0406329	−	0.0234594i
$484$	18.7677	+	32.5066i	0.853077	+	1.47757i
$485$		0			0
$486$			52.2176i			2.36864i
$487$	0.0175926	+	0.0101571i	0.000797199	+	0.000460263i	0.500399	−	0.865795i	$-0.333187\pi$
$487$	0.0175926	+	0.0101571i	0.000797199	+	0.000460263i	−0.499601	+	0.866255i	$0.666520\pi$
$488$	55.7849	+	32.2074i	2.52526	+	1.45796i
$489$		−	64.3277i		−	2.90900i
$490$		0			0
$491$	−5.50075	−	9.52758i	−0.248245	−	0.429974i	0.714794	−	0.699335i	$-0.246521\pi$
$491$	−5.50075	−	9.52758i	−0.248245	−	0.429974i	−0.963039	+	0.269362i	$0.913187\pi$
$492$	−106.665	+	61.5829i	−4.80882	+	2.77637i
$493$	−4.45434			−0.200613
$494$	−53.7844	+	2.22508i	−2.41987	+	0.100111i
$495$		0			0
$496$	−51.4783	+	29.7210i	−2.31145	+	1.33451i
$497$	−12.0068	−	20.7963i	−0.538576	−	0.932842i
$498$	−55.4613	+	96.0619i	−2.48528	+	4.30464i
$499$			8.95832i			0.401030i	0.979691	+	0.200515i	$0.0642615\pi$
$499$			8.95832i			0.401030i	−0.979691	+	0.200515i	$0.935739\pi$
$500$		0			0
$501$	2.61069	+	1.50728i	0.116637	+	0.0673403i
$502$		−	29.1861i		−	1.30264i
$503$	−10.0881	+	17.4732i	−0.449808	+	0.779090i	−0.998373	−	0.0570180i	$-0.981841\pi$
$503$	−10.0881	+	17.4732i	−0.449808	+	0.779090i	0.548566	+	0.836108i	$0.315174\pi$
$504$	−45.2937	−	78.4509i	−2.01754	−	3.49448i
$505$		0			0
$506$	0.675297			0.0300206
$507$	−19.9938	−	28.8339i	−0.887956	−	1.28056i
$508$	54.8992			2.43576
$509$	1.99934	−	1.15432i	0.0886193	−	0.0511644i	−0.455035	−	0.890473i	$-0.650373\pi$
$509$	1.99934	−	1.15432i	0.0886193	−	0.0511644i	0.543655	+	0.839309i	$0.317040\pi$
$510$		0			0
$511$	14.7888	−	25.6149i	0.654216	−	1.13314i
$512$			35.0481i			1.54892i
$513$	17.0328	+	9.83391i	0.752018	+	0.434178i
$514$	66.7083	+	38.5140i	2.94238	+	1.69878i
$515$		0			0
$516$	−13.9551	+	24.1709i	−0.614338	+	1.06406i
$517$	3.37340	+	5.84290i	0.148362	+	0.256970i
$518$	15.3768	−	8.87778i	0.675616	−	0.390067i
$519$	−5.80515			−0.254818
$520$		0			0
$521$	−9.00049			−0.394319			−0.197159	−	0.980371i	$-0.563172\pi$
$521$	−9.00049			−0.394319			−0.197159	+	0.980371i	$0.563172\pi$
$522$	−11.4001	+	6.58186i	−0.498970	+	0.288080i
$523$	−20.1347	−	34.8743i	−0.880428	−	1.52495i	−0.850866	−	0.525383i	$-0.823922\pi$
$523$	−20.1347	−	34.8743i	−0.880428	−	1.52495i	−0.0295625	−	0.999563i	$-0.509411\pi$
$524$	10.2686	−	17.7857i	0.448586	−	0.776974i
$525$		0			0
$526$	32.8404	+	18.9604i	1.43191	+	0.826714i
$527$	−18.8097	−	10.8598i	−0.819365	−	0.473061i
$528$		−	51.8856i		−	2.25803i
$529$	11.4903	−	19.9018i	0.499578	−	0.865294i
$530$		0			0
$531$	−9.38760	+	5.41993i	−0.407387	+	0.235205i
$532$	76.6323			3.32243
$533$	28.1871	−	17.8667i	1.22092	−	0.773892i
$534$	23.9317			1.03562
$535$		0			0
$536$	−23.0703	−	39.9589i	−0.996485	−	1.72596i
$537$	−2.92209	+	5.06120i	−0.126097	+	0.218407i
$538$		−	34.5519i		−	1.48964i
$539$	−0.815375	−	0.470757i	−0.0351207	−	0.0202769i
$540$		0			0
$541$		−	18.4257i		−	0.792185i	−0.918211	−	0.396092i	$-0.870366\pi$
$541$		−	18.4257i		−	0.792185i	0.918211	−	0.396092i	$-0.129634\pi$
$542$	2.50299	−	4.33531i	0.107513	−	0.186217i
$543$	26.7532	+	46.3379i	1.14809	+	1.98855i
$544$	39.9056	−	23.0395i	1.71094	−	0.987811i
$545$		0			0
$546$	37.5902	+	59.3036i	1.60871	+	2.53796i
$547$	31.9538			1.36625			0.683123	−	0.730303i	$-0.260621\pi$
$547$	31.9538			1.36625			0.683123	+	0.730303i	$0.260621\pi$
$548$	−1.71124	+	0.987985i	−0.0731006	+	0.0422046i
$549$	17.8909	+	30.9879i	0.763564	+	1.32253i
$550$		0			0
$551$		−	6.61840i		−	0.281953i
$552$	2.51332	+	1.45106i	0.106974	+	0.0617614i
$553$	−22.8969	−	13.2195i	−0.973676	−	0.562152i
$554$		−	75.3399i		−	3.20089i
$555$		0			0
$556$	−27.4780	−	47.5933i	−1.16533	−	2.01841i
$557$	−17.9054	+	10.3377i	−0.758677	+	0.438022i	−0.828820	−	0.559515i	$-0.810988\pi$
$557$	−17.9054	+	10.3377i	−0.758677	+	0.438022i	0.0701438	+	0.997537i	$0.477654\pi$
$558$	−64.1871			−2.71726
$559$	3.50727	−	6.69996i	0.148342	−	0.283378i
$560$		0			0
$561$	16.4186	−	9.47929i	0.693194	−	0.400216i
$562$	−1.10720	−	1.91773i	−0.0467046	−	0.0808948i
$563$	−16.9429	+	29.3459i	−0.714056	+	1.23678i	0.249266	+	0.968435i	$0.419811\pi$
$563$	−16.9429	+	29.3459i	−0.714056	+	1.23678i	−0.963322	+	0.268346i	$0.913523\pi$
$564$			48.7853i			2.05423i
$565$		0			0
$566$	7.47523	+	4.31582i	0.314207	+	0.181408i
$567$			9.57741i			0.402213i
$568$	33.7926	−	58.5305i	1.41790	−	2.45588i
$569$	16.4578	+	28.5058i	0.689949	+	1.19503i	0.971854	+	0.235584i	$0.0757003\pi$
$569$	16.4578	+	28.5058i	0.689949	+	1.19503i	−0.281905	+	0.959442i	$0.590966\pi$
$570$		0			0
$571$	−33.3623			−1.39617			−0.698085	−	0.716015i	$-0.745964\pi$
$571$	−33.3623			−1.39617			−0.698085	+	0.716015i	$0.745964\pi$
$572$	1.35217	+	32.6845i	0.0565369	+	1.36661i
$573$	−7.45792			−0.311559
$574$	−57.8345	+	33.3908i	−2.41397	+	1.39370i
$575$		0			0
$576$	23.3273	−	40.4041i	0.971971	−	1.68350i
$577$		−	6.68771i		−	0.278413i	−0.990263	−	0.139206i	$-0.955545\pi$
$577$		−	6.68771i		−	0.278413i	0.990263	−	0.139206i	$-0.0444552\pi$
$578$	−5.54234	−	3.19987i	−0.230531	−	0.133097i
$579$	2.85819	+	1.65018i	0.118782	+	0.0685790i
$580$		0			0
$581$	−21.3931	+	37.0540i	−0.887537	+	1.53726i
$582$	−1.11253	−	1.92696i	−0.0461158	−	0.0798750i
$583$	−15.9024	+	9.18126i	−0.658611	+	0.380249i
$584$	83.2449			3.44470
$585$		0			0
$586$	22.1142			0.913530
$587$	−20.2791	+	11.7081i	−0.837008	+	0.483247i	−0.856246	−	0.516568i	$-0.827209\pi$
$587$	−20.2791	+	11.7081i	−0.837008	+	0.483247i	0.0192383	+	0.999815i	$0.493876\pi$
$588$	−3.40399	−	5.89588i	−0.140378	−	0.243142i
$589$	16.1359	−	27.9481i	0.664867	−	1.15158i
$590$		0			0
$591$	39.3717	+	22.7313i	1.61954	+	0.935039i
$592$	22.2629	+	12.8535i	0.915001	+	0.528276i
$593$		−	7.21585i		−	0.296319i	−0.988963	−	0.148160i	$-0.952665\pi$
$593$		−	7.21585i		−	0.296319i	0.988963	−	0.148160i	$-0.0473349\pi$
$594$	8.40028	−	14.5497i	0.344668	−	0.596982i
$595$		0			0
$596$	76.3309	−	44.0697i	3.12663	−	1.80516i
$597$	62.6136			2.56260
$598$	−1.17219	−	0.613612i	−0.0479343	−	0.0250925i
$599$	37.7682			1.54317			0.771584	−	0.636127i	$-0.219465\pi$
$599$	37.7682			1.54317			0.771584	+	0.636127i	$0.219465\pi$
$600$		0			0
$601$	14.1912	+	24.5800i	0.578873	+	1.00264i	0.995609	+	0.0936099i	$0.0298406\pi$
$601$	14.1912	+	24.5800i	0.578873	+	1.00264i	−0.416736	+	0.909028i	$0.636826\pi$
$602$	−7.56656	+	13.1057i	−0.308390	+	0.534147i
$603$		−	25.6306i		−	1.04376i
$604$	−26.8677	−	15.5121i	−1.09323	−	0.631178i
$605$		0			0
$606$			112.519i			4.57076i
$607$	−13.3253	+	23.0801i	−0.540857	+	0.936792i	0.457998	+	0.888953i	$0.348567\pi$
$607$	−13.3253	+	23.0801i	−0.540857	+	0.936792i	−0.998855	+	0.0478390i	$0.984767\pi$
$608$	34.2329	+	59.2931i	1.38833	+	2.40465i
$609$	−7.47614	+	4.31635i	−0.302948	+	0.174907i
$610$		0			0
$611$	−0.546394	−	13.2074i	−0.0221048	−	0.534315i
$612$	80.6331			3.25940
$613$	3.98537	−	2.30095i	0.160967	−	0.0929346i	−0.417352	−	0.908745i	$-0.637042\pi$
$613$	3.98537	−	2.30095i	0.160967	−	0.0929346i	0.578320	+	0.815810i	$0.303709\pi$
$614$	−43.2064	−	74.8356i	−1.74367	−	3.02012i
$615$		0			0
$616$		−	38.9054i		−	1.56754i
$617$	24.1223	+	13.9270i	0.971126	+	0.560680i	0.899579	−	0.436757i	$-0.143873\pi$
$617$	24.1223	+	13.9270i	0.971126	+	0.560680i	0.0715470	+	0.997437i	$0.477206\pi$
$618$	−45.3909	−	26.2064i	−1.82589	−	1.05418i
$619$			30.3338i			1.21922i	0.792703	+	0.609608i	$0.208673\pi$
$619$			30.3338i			1.21922i	−0.792703	+	0.609608i	$0.791327\pi$
$620$		0			0
$621$	0.241705	+	0.418645i	0.00969928	+	0.0167996i
$622$	−42.4026	+	24.4812i	−1.70019	+	0.981605i
$623$	9.23117			0.369839
$624$	−47.1462	+	90.0636i	−1.88736	+	3.60543i
$625$		0			0
$626$	14.9458	−	8.62894i	0.597353	−	0.344882i
$627$	14.0846	+	24.3953i	0.562486	+	0.974255i
$628$	39.8149	−	68.9614i	1.58879	−	2.75186i
$629$			9.39313i			0.374529i
$630$		0			0
$631$	−2.94868	−	1.70242i	−0.117385	−	0.0677723i	0.440158	−	0.897920i	$-0.354922\pi$
$631$	−2.94868	−	1.70242i	−0.117385	−	0.0677723i	−0.557543	+	0.830148i	$0.688256\pi$
$632$		−	74.4118i		−	2.95994i
$633$	−36.4079	+	63.0603i	−1.44708	+	2.50642i
$634$	37.3710	+	64.7285i	1.48419	+	2.57070i
$635$		0			0
$636$	−132.777			−5.26496
$637$	0.987579	+	1.55804i	0.0391293	+	0.0617318i
$638$	−5.65354			−0.223826
$639$	32.5130	−	18.7714i	1.28620	−	0.742586i
$640$		0			0
$641$	−3.54843	+	6.14606i	−0.140155	+	0.242755i	−0.927555	−	0.373687i	$-0.878093\pi$
$641$	−3.54843	+	6.14606i	−0.140155	+	0.242755i	0.787400	+	0.616442i	$0.211427\pi$
$642$		−	68.4495i		−	2.70148i
$643$	23.2936	+	13.4485i	0.918608	+	0.530359i	0.883191	−	0.469014i	$-0.155391\pi$
$643$	23.2936	+	13.4485i	0.918608	+	0.530359i	0.0354176	+	0.999373i	$0.488724\pi$
$644$	1.63118	+	0.941761i	0.0642774	+	0.0371106i
$645$		0			0
$646$	−28.4931	+	49.3516i	−1.12105	+	1.94171i
$647$	−0.874779	−	1.51516i	−0.0343911	−	0.0595672i	0.848318	−	0.529488i	$-0.177616\pi$
$647$	−0.874779	−	1.51516i	−0.0343911	−	0.0595672i	−0.882709	+	0.469921i	$0.844283\pi$
$648$	−23.3440	+	13.4776i	−0.917037	+	0.529452i
$649$	−4.65550			−0.182744
$650$		0			0
$651$	−42.0936			−1.64978
$652$	101.760	−	58.7513i	3.98524	−	2.30088i
$653$	−0.404850	−	0.701221i	−0.0158430	−	0.0274409i	0.857995	−	0.513658i	$-0.171710\pi$
$653$	−0.404850	−	0.701221i	−0.0158430	−	0.0274409i	−0.873838	+	0.486217i	$0.838377\pi$
$654$	−31.0329	+	53.7505i	−1.21348	+	2.10181i
$655$		0			0
$656$	−83.7346	−	48.3442i	−3.26929	−	1.88752i
$657$	40.0464	+	23.1208i	1.56236	+	0.902029i
$658$			26.4518i			1.03120i
$659$	19.4927	−	33.7623i	0.759327	−	1.31519i	−0.183867	−	0.982951i	$-0.558862\pi$
$659$	19.4927	−	33.7623i	0.759327	−	1.31519i	0.943194	−	0.332242i	$-0.107805\pi$
$660$		0			0
$661$	−13.5955	+	7.84937i	−0.528804	+	0.305305i	−0.740529	−	0.672024i	$-0.765425\pi$
$661$	−13.5955	+	7.84937i	−0.528804	+	0.305305i	0.211725	+	0.977329i	$0.432092\pi$
$662$	6.33561			0.246240
$663$	−37.1130	+	1.53537i	−1.44135	+	0.0596290i
$664$	−120.420			−4.67322
$665$		0			0
$666$	13.8796	+	24.0401i	0.537822	+	0.931535i
$667$	0.0813358	−	0.140878i	0.00314934	−	0.00545481i
$668$			5.50648i			0.213052i
$669$	−2.05856	−	1.18851i	−0.0795887	−	0.0459506i
$670$		0			0
$671$			15.3675i			0.593257i
$672$	44.6516	−	77.3388i	1.72247	−	2.98341i
$673$	16.5267	+	28.6251i	0.637057	+	1.10342i	0.986075	+	0.166300i	$0.0531819\pi$
$673$	16.5267	+	28.6251i	0.637057	+	1.10342i	−0.349018	+	0.937116i	$0.613485\pi$
$674$	7.60449	−	4.39045i	0.292914	−	0.169114i
$675$		0			0
$676$	27.3518	−	57.9627i	1.05199	−	2.22933i
$677$	9.32729			0.358477			0.179238	−	0.983806i	$-0.442637\pi$
$677$	9.32729			0.358477			0.179238	+	0.983806i	$0.442637\pi$
$678$	112.415	−	64.9029i	4.31728	−	2.49258i
$679$	−0.429137	−	0.743287i	−0.0164688	−	0.0285247i
$680$		0			0
$681$		−	9.38914i		−	0.359793i
$682$	−23.8737	−	13.7835i	−0.914173	−	0.527798i
$683$	17.7277	+	10.2351i	0.678331	+	0.391634i	0.799226	−	0.601031i	$-0.205243\pi$
$683$	17.7277	+	10.2351i	0.678331	+	0.391634i	−0.120895	+	0.992665i	$0.538576\pi$
$684$			119.807i			4.58095i
$685$		0			0
$686$	23.4069	+	40.5420i	0.893681	+	1.54790i
$687$	16.9509	−	9.78663i	0.646719	−	0.373383i
$688$	−21.9102			−0.835318
$689$	35.9462	−	1.48710i	1.36944	−	0.0566541i
$690$		0			0
$691$	−3.86449	+	2.23116i	−0.147012	+	0.0848774i	−0.571702	−	0.820462i	$-0.693717\pi$
$691$	−3.86449	+	2.23116i	−0.147012	+	0.0848774i	0.424690	+	0.905339i	$0.360383\pi$
$692$	−5.30192	−	9.18320i	−0.201549	−	0.349093i
$693$	10.8058	−	18.7161i	0.410477	−	0.710967i
$694$		−	52.7684i		−	2.00306i
$695$		0			0
$696$	−21.0413	−	12.1482i	−0.797569	−	0.460477i
$697$		−	35.3291i		−	1.33819i
$698$	−19.5931	+	33.9362i	−0.741608	+	1.28450i
$699$	−19.3301	−	33.4807i	−0.731130	−	1.26635i
$700$		0			0
$701$	41.2801			1.55913			0.779564	−	0.626323i	$-0.215441\pi$
$701$	41.2801			1.55913			0.779564	+	0.626323i	$0.215441\pi$
$702$	−27.8020	+	17.6226i	−1.04932	+	0.665121i
$703$	−13.9566			−0.526384
$704$	17.3527	−	10.0186i	0.654005	−	0.377590i
$705$		0			0
$706$	25.2305	−	43.7005i	0.949562	−	1.64469i
$707$			43.4019i			1.63230i
$708$	−29.1533	−	16.8317i	−1.09565	−	0.632573i
$709$	−24.3714	−	14.0708i	−0.915287	−	0.528441i	−0.0331583	−	0.999450i	$-0.510557\pi$
$709$	−24.3714	−	14.0708i	−0.915287	−	0.528441i	−0.882128	+	0.471009i	$0.843890\pi$
$710$		0			0
$711$	20.6675	−	35.7971i	0.775091	−	1.34250i
$712$	12.9904	+	22.5000i	0.486836	+	0.843225i
$713$	0.686929	−	0.396598i	0.0257257	−	0.0148527i
$714$	74.3299			2.78173
$715$		0			0
$716$	−10.6751			−0.398948
$717$	−8.46404	+	4.88672i	−0.316096	+	0.182498i
$718$	−19.9936	−	34.6300i	−0.746156	−	1.29238i
$719$	−5.50910	+	9.54204i	−0.205455	+	0.355858i	−0.950278	−	0.311404i	$-0.899201\pi$
$719$	−5.50910	+	9.54204i	−0.205455	+	0.355858i	0.744823	+	0.667262i	$0.232534\pi$
$720$		0			0
$721$	−17.5087	−	10.1086i	−0.652057	−	0.376465i
$722$	−30.0114	−	17.3271i	−1.11691	−	0.644848i
$723$		−	7.36637i		−	0.273958i
$724$	−48.8681	+	84.6421i	−1.81617	+	3.14570i
$725$		0			0
$726$	−46.8482	+	27.0478i	−1.73870	+	1.00384i
$727$	−21.0896			−0.782168			−0.391084	−	0.920355i	$-0.627900\pi$
$727$	−21.0896			−0.782168			−0.391084	+	0.920355i	$0.627900\pi$
$728$	−35.3516	+	67.5323i	−1.31022	+	2.50291i
$729$	−43.0538			−1.59459
$730$		0			0
$731$	−4.00290	−	6.93322i	−0.148053	−	0.256435i
$732$	−55.5604	+	96.2334i	−2.05357	+	3.55689i
$733$		−	9.50914i		−	0.351228i	−0.984459	−	0.175614i	$-0.943809\pi$
$733$		−	9.50914i		−	0.351228i	0.984459	−	0.175614i	$-0.0561911\pi$
$734$	9.72820	+	5.61658i	0.359075	+	0.207312i
$735$		0			0
$736$			1.68280i			0.0620288i
$737$	5.50391	−	9.53305i	0.202739	−	0.351154i
$738$	−52.2033	−	90.4188i	−1.92163	−	3.32836i
$739$	−2.97018	+	1.71484i	−0.109260	+	0.0630813i	−0.553634	−	0.832760i	$-0.686759\pi$
$739$	−2.97018	+	1.71484i	−0.109260	+	0.0630813i	0.444374	+	0.895841i	$0.353426\pi$
$740$		0			0
$741$	−2.28131	−	55.1437i	−0.0838060	−	2.02575i
$742$	−71.9930			−2.64295
$743$	−27.3032	+	15.7635i	−1.00166	+	0.578307i	−0.908738	−	0.417367i	$-0.862953\pi$
$743$	−27.3032	+	15.7635i	−1.00166	+	0.578307i	−0.0929188	+	0.995674i	$0.529620\pi$
$744$	−59.2354	−	102.599i	−2.17168	−	3.76145i
$745$		0			0
$746$		−	36.0745i		−	1.32078i
$747$	−57.9304	−	33.4461i	−2.11956	−	1.22373i
$748$	29.9907	+	17.3151i	1.09657	+	0.633103i
$749$		−	26.4031i		−	0.964747i
$750$		0			0
$751$	4.49261	+	7.78143i	0.163938	+	0.283948i	0.936278	−	0.351261i	$-0.114247\pi$
$751$	4.49261	+	7.78143i	0.163938	+	0.283948i	−0.772340	+	0.635210i	$0.780914\pi$
$752$	−33.1668	+	19.1489i	−1.20947	+	0.698288i
$753$	29.9238			1.09048
$754$	9.81347	+	5.13712i	0.357386	+	0.187083i
$755$		0			0
$756$	40.5817	−	23.4299i	1.47594	−	0.852136i
$757$	−16.7711	−	29.0485i	−0.609558	−	1.05578i	−0.991313	−	0.131521i	$-0.958014\pi$
$757$	−16.7711	−	29.0485i	−0.609558	−	1.05578i	0.381756	−	0.924263i	$-0.375320\pi$
$758$	25.1741	−	43.6028i	0.914365	−	1.58373i
$759$			0.692364i			0.0251312i
$760$		0			0
$761$	−39.0273	−	22.5324i	−1.41474	−	0.816800i	−0.418909	−	0.908028i	$-0.637587\pi$
$761$	−39.0273	−	22.5324i	−1.41474	−	0.816800i	−0.995830	+	0.0912283i	$0.970921\pi$
$762$			79.1203i			2.86623i
$763$	−11.9703	+	20.7332i	−0.433355	+	0.750593i
$764$	−6.81141	−	11.7977i	−0.246428	−	0.426826i
$765$		0			0
$766$	−26.0697			−0.941935
$767$	8.08105	+	4.23024i	0.291790	+	0.152745i
$768$	−26.6677			−0.962287
$769$	−13.7521	+	7.93979i	−0.495914	+	0.286316i	−0.727025	−	0.686611i	$-0.759097\pi$
$769$	−13.7521	+	7.93979i	−0.495914	+	0.286316i	0.231110	+	0.972928i	$0.425764\pi$
$770$		0			0
$771$	−39.4874	+	68.3942i	−1.42210	+	2.46316i
$772$			6.02851i			0.216971i
$773$	14.4726	+	8.35573i	0.520542	+	0.300535i	0.737156	−	0.675722i	$-0.236168\pi$
$773$	14.4726	+	8.35573i	0.520542	+	0.300535i	−0.216615	+	0.976257i	$0.569502\pi$
$774$	−20.4895	−	11.8296i	−0.736479	−	0.425206i
$775$		0			0
$776$	1.20779	−	2.09195i	0.0433571	−	0.0750968i
$777$	9.10214	+	15.7654i	0.326538	+	0.565580i
$778$	44.1716	−	25.5025i	1.58363	−	0.914309i
$779$	52.4931			1.88076
$780$		0			0
$781$	16.1239			0.576957
$782$	−1.21300	+	0.700324i	−0.0433767	+	0.0250435i
$783$	−2.02354	−	3.50487i	−0.0723153	−	0.125254i
$784$	2.67222	−	4.62842i	0.0954364	−	0.165301i
$785$		0			0
$786$	25.6327	+	14.7990i	0.914287	+	0.527864i
$787$	−42.7875	−	24.7034i	−1.52521	−	0.880580i	−0.999553	−	0.0298831i	$-0.990487\pi$
$787$	−42.7875	−	24.7034i	−1.52521	−	0.880580i	−0.525656	−	0.850697i	$-0.676180\pi$
$788$			83.0430i			2.95829i
$789$	−19.4396	+	33.6704i	−0.692068	+	1.19870i
$790$		0			0
$791$	43.3620	−	25.0350i	1.54177	−	0.890144i
$792$	60.8249			2.16132
$793$	13.9638	−	26.6751i	0.495868	−	0.947260i
$794$	−51.5416			−1.82914
$795$		0			0
$796$	57.1858	+	99.0488i	2.02690	+	3.51069i
$797$	9.70631	−	16.8118i	0.343815	−	0.595505i	−0.641323	−	0.767271i	$-0.721614\pi$
$797$	9.70631	−	16.8118i	0.343815	−	0.595505i	0.985138	+	0.171766i	$0.0549473\pi$
$798$			110.442i			3.90960i
$799$	−12.1189	−	6.99684i	−0.428735	−	0.247530i
$800$		0			0
$801$			14.4321i			0.509932i
$802$	41.2981	−	71.5305i	1.45829	−	2.52583i
$803$	9.92991	+	17.1991i	0.350419	+	0.606943i
$804$	68.9324	−	39.7981i	2.43106	−	1.40357i
$805$		0			0
$806$	28.9158	+	45.6185i	1.01852	+	1.60684i
$807$	35.4252			1.24702
$808$	−105.788	+	61.0766i	−3.72160	+	2.14867i
$809$	−11.0486	−	19.1368i	−0.388450	−	0.672814i	0.603792	−	0.797142i	$-0.293656\pi$
$809$	−11.0486	−	19.1368i	−0.388450	−	0.672814i	−0.992241	+	0.124328i	$0.960323\pi$
$810$		0			0
$811$		−	13.7950i		−	0.484407i	−0.970225	−	0.242203i	$-0.922130\pi$
$811$		−	13.7950i		−	0.484407i	0.970225	−	0.242203i	$-0.0778702\pi$
$812$	−13.6561	−	7.88436i	−0.479236	−	0.276687i
$813$	4.44487	+	2.56625i	0.155888	+	0.0900022i
$814$			11.9220i			0.417865i
$815$		0			0
$816$	53.8085	+	93.1991i	1.88368	+	3.26262i
$817$	10.3016	−	5.94764i	0.360408	−	0.208082i
$818$	51.0891			1.78629
$819$	−35.7632	+	22.6689i	−1.24967	+	0.792116i
$820$		0			0
$821$	−20.2706	+	11.7032i	−0.707450	+	0.408446i	−0.810116	−	0.586270i	$-0.800596\pi$
$821$	−20.2706	+	11.7032i	−0.707450	+	0.408446i	0.102666	+	0.994716i	$0.467263\pi$
$822$	−1.42388	−	2.46623i	−0.0496634	−	0.0860195i
$823$	−7.92379	+	13.7244i	−0.276206	+	0.478402i	−0.970439	−	0.241348i	$-0.922410\pi$
$823$	−7.92379	+	13.7244i	−0.276206	+	0.478402i	0.694233	+	0.719750i	$0.255744\pi$
$824$		−	56.9008i		−	1.98223i
$825$		0			0
$826$	−15.8072	−	9.12628i	−0.550002	−	0.317544i
$827$			4.85361i			0.168777i	0.996433	+	0.0843883i	$0.0268936\pi$
$827$			4.85361i			0.168777i	−0.996433	+	0.0843883i	$0.973106\pi$
$828$	−1.47235	+	2.55019i	−0.0511678	+	0.0886253i
$829$	−7.58395	−	13.1358i	−0.263401	−	0.456225i	0.703742	−	0.710455i	$-0.251511\pi$
$829$	−7.58395	−	13.1358i	−0.263401	−	0.456225i	−0.967144	+	0.254231i	$0.918178\pi$
$830$		0			0
$831$	77.2440			2.67956
$832$	−39.2244	+	1.62273i	−1.35986	+	0.0562579i
$833$	1.95281			0.0676610
$834$	68.5911	−	39.6011i	2.37512	−	1.37127i
$835$		0			0
$836$	−25.7274	+	44.5611i	−0.889800	+	1.54118i
$837$		−	19.7338i		−	0.682099i
$838$	18.5865	+	10.7309i	0.642061	+	0.370694i
$839$	37.8349	+	21.8440i	1.30620	+	0.754138i	0.981461	−	0.191664i	$-0.0613884\pi$
$839$	37.8349	+	21.8440i	1.30620	+	0.754138i	0.324744	+	0.945802i	$0.394722\pi$
$840$		0			0
$841$	13.8191	−	23.9353i	0.476519	−	0.825356i
$842$	20.1683	+	34.9326i	0.695046	+	1.20386i
$843$	1.96620	−	1.13519i	0.0677196	−	0.0390979i
$844$	−133.007			−4.57830
$845$		0			0
$846$	−41.3549			−1.42181
$847$	−18.0708	+	10.4332i	−0.620920	+	0.358488i
$848$	−52.1168	−	90.2690i	−1.78970	−	3.09985i
$849$	−4.42490	+	7.66415i	−0.151862	+	0.263033i
$850$		0			0
$851$	−0.297077	−	0.171518i	−0.0101837	−	0.00587955i
$852$	100.970	+	58.2949i	3.45917	+	1.99715i
$853$			5.18588i			0.177561i	0.996051	+	0.0887806i	$0.0282970\pi$
$853$			5.18588i			0.177561i	−0.996051	+	0.0887806i	$0.971703\pi$
$854$	−30.1253	+	52.1786i	−1.03087	+	1.78552i
$855$		0			0
$856$	64.3547	−	37.1552i	2.19960	−	1.26994i
$857$	−12.8688			−0.439589			−0.219795	−	0.975546i	$-0.570539\pi$
$857$	−12.8688			−0.439589			−0.219795	+	0.975546i	$0.570539\pi$
$858$	−47.1046	+	1.94873i	−1.60812	+	0.0665286i
$859$	15.7252			0.536538			0.268269	−	0.963344i	$-0.413548\pi$
$859$	15.7252			0.536538			0.268269	+	0.963344i	$0.413548\pi$
$860$		0			0
$861$	−34.2347	−	59.2962i	−1.16671	−	2.02081i
$862$	−18.8882	+	32.7153i	−0.643335	+	1.11429i
$863$		−	16.0465i		−	0.546230i	−0.961981	−	0.273115i	$-0.911946\pi$
$863$		−	16.0465i		−	0.546230i	0.961981	−	0.273115i	$-0.0880539\pi$
$864$	36.2570	+	20.9330i	1.23349	+	0.712154i
$865$		0			0
$866$		−	40.2492i		−	1.36772i
$867$	3.28074	−	5.68241i	0.111420	−	0.192985i
$868$	−38.4446	−	66.5880i	−1.30490	−	2.26015i
$869$	15.3741	−	8.87626i	0.521532	−	0.301106i
$870$		0			0
$871$	−18.2160	+	11.5464i	−0.617225	+	0.391235i
$872$	−67.3802			−2.28178
$873$	1.16206	−	0.670915i	0.0393297	−	0.0227070i
$874$	−1.04056	−	1.80231i	−0.0351976	−	0.0609641i
$875$		0			0
$876$			143.604i			4.85193i
$877$	4.74612	+	2.74017i	0.160265	+	0.0925290i	0.577987	−	0.816046i	$-0.303838\pi$
$877$	4.74612	+	2.74017i	0.160265	+	0.0925290i	−0.417723	+	0.908575i	$0.637172\pi$
$878$	−1.79652	−	1.03722i	−0.0606295	−	0.0350044i
$879$			22.6731i			0.764745i
$880$		0			0
$881$	−4.78231	−	8.28321i	−0.161120	−	0.279068i	0.774151	−	0.633002i	$-0.218177\pi$
$881$	−4.78231	−	8.28321i	−0.161120	−	0.279068i	−0.935271	+	0.353933i	$0.884844\pi$
$882$	4.99789	−	2.88553i	0.168288	−	0.0971610i
$883$	32.6927			1.10020			0.550098	−	0.835100i	$-0.314590\pi$
$883$	32.6927			1.10020			0.550098	+	0.835100i	$0.314590\pi$
$884$	−36.3246	−	57.3069i	−1.22173	−	1.92744i
$885$		0			0
$886$	36.8688	−	21.2862i	1.23863	−	0.715125i
$887$	−22.8984	−	39.6612i	−0.768854	−	1.33169i	−0.938185	−	0.346135i	$-0.887494\pi$
$887$	−22.8984	−	39.6612i	−0.768854	−	1.33169i	0.169331	−	0.985559i	$-0.445839\pi$
$888$	−25.6177	+	44.3711i	−0.859673	+	1.48900i
$889$			30.5191i			1.02358i
$890$		0			0
$891$	−5.56919	−	3.21537i	−0.186575	−	0.107719i
$892$		−	4.34194i		−	0.145379i
$893$	10.3961	−	18.0066i	0.347893	−	0.602569i
$894$	63.5128	+	110.007i	2.12419	+	3.67920i
$895$		0			0
$896$	12.3850			0.413755
$897$	0.629120	−	1.20181i	0.0210057	−	0.0401273i
$898$	15.6457			0.522105
$899$	−5.75092	+	3.32030i	−0.191804	+	0.110738i
$900$		0			0
$901$	19.0430	−	32.9835i	0.634416	−	1.09884i
$902$		−	44.8405i		−	1.49302i
$903$	−13.4369	−	7.75779i	−0.447152	−	0.258163i
$904$	122.041	+	70.4603i	4.05901	+	2.34347i
$905$		0			0
$906$	22.3559	−	38.7215i	0.742725	−	1.28644i
$907$	−6.20272	−	10.7434i	−0.205958	−	0.356729i	0.744480	−	0.667645i	$-0.232698\pi$
$907$	−6.20272	−	10.7434i	−0.205958	−	0.356729i	−0.950437	+	0.310916i	$0.899364\pi$
$908$	14.8527	−	8.57523i	0.492905	−	0.284579i
$909$	−67.8547			−2.25060
$910$		0			0
$911$	−13.8486			−0.458826			−0.229413	−	0.973329i	$-0.573681\pi$
$911$	−13.8486			−0.458826			−0.229413	+	0.973329i	$0.573681\pi$
$912$	−138.478	+	79.9505i	−4.58548	+	2.64743i
$913$	−14.3644	−	24.8799i	−0.475393	−	0.823405i
$914$	−11.3883	+	19.7252i	−0.376693	+	0.652451i
$915$		0			0
$916$	30.9630	+	17.8765i	1.02305	+	0.590657i
$917$	9.88730	+	5.70844i	0.326508	+	0.188509i
$918$			34.8464i			1.15010i
$919$	24.2075	−	41.9287i	0.798533	−	1.38310i	−0.122038	−	0.992525i	$-0.538943\pi$
$919$	24.2075	−	41.9287i	0.798533	−	1.38310i	0.920571	−	0.390575i	$-0.127724\pi$
$920$		0			0
$921$	76.7269	−	44.2983i	2.52824	−	1.45968i
$922$	1.82468			0.0600925
$923$	−27.9879	−	14.6510i	−0.921234	−	0.482245i
$924$	67.1149			2.20792
$925$		0			0
$926$	−44.2297	−	76.6080i	−1.45348	−	2.51750i
$927$	15.8039	−	27.3731i	0.519068	−	0.899051i
$928$		−	14.0883i		−	0.462470i
$929$	16.1983	+	9.35210i	0.531450	+	0.306833i	0.741607	−	0.670835i	$-0.234064\pi$
$929$	16.1983	+	9.35210i	0.531450	+	0.306833i	−0.210157	+	0.977668i	$0.567397\pi$
$930$		0			0
$931$			2.90156i			0.0950946i
$932$	35.3088	−	61.1567i	1.15658	−	2.00325i
$933$	−25.0999	−	43.4743i	−0.821733	−	1.42328i
$934$	5.66549	−	3.27097i	0.185381	−	0.107030i
$935$		0			0
$936$	−105.580	−	55.2688i	−3.45100	−	1.80652i
$937$	−32.9941			−1.07787			−0.538935	−	0.842347i	$-0.681173\pi$
$937$	−32.9941			−1.07787			−0.538935	+	0.842347i	$0.681173\pi$
$938$	37.3757	−	21.5789i	1.22036	−	0.704576i
$939$	8.84702	+	15.3235i	0.288712	+	0.500063i
$940$		0			0
$941$			30.1625i			0.983270i	0.870801	+	0.491635i	$0.163601\pi$
$941$			30.1625i			0.983270i	−0.870801	+	0.491635i	$0.836399\pi$
$942$	99.3866	+	57.3809i	3.23819	+	1.86957i
$943$	1.11736	+	0.645106i	0.0363861	+	0.0210076i
$944$		−	26.4266i		−	0.860113i
$945$		0			0
$946$	−5.08057	−	8.79980i	−0.165183	−	0.286106i
$947$	9.04154	−	5.22013i	0.293810	−	0.169632i	−0.345849	−	0.938290i	$-0.612409\pi$
$947$	9.04154	−	5.22013i	0.293810	−	0.169632i	0.639659	+	0.768659i	$0.279076\pi$
$948$	128.366			4.16915
$949$	−1.60836	−	38.8772i	−0.0522097	−	1.26201i
$950$		0			0
$951$	−66.3643	+	38.3155i	−2.15201	+	1.24246i
$952$	40.3472	+	69.8834i	1.30766	+	2.26494i
$953$	17.6291	−	30.5345i	0.571062	−	0.989108i	−0.425396	−	0.905008i	$-0.639865\pi$
$953$	17.6291	−	30.5345i	0.571062	−	0.989108i	0.996457	−	0.0841005i	$-0.0268017\pi$
$954$		−	112.554i		−	3.64408i
$955$		0			0
$956$	−15.4606	−	8.92621i	−0.500033	−	0.288694i
$957$		−	5.79643i		−	0.187372i
$958$	44.1027	−	76.3881i	1.42489	−	2.46799i
$959$	−0.549233	−	0.951299i	−0.0177357	−	0.0307191i
$960$		0			0
$961$	−1.37993			−0.0445139
$962$	10.8330	−	20.6942i	0.349269	−	0.667209i
$963$	41.2787			1.33019
$964$	11.6529	−	6.72781i	0.375315	−	0.216688i
$965$		0			0
$966$	−1.35726	+	2.35084i	−0.0436691	+	0.0756370i
$967$			36.8535i			1.18513i	0.805523	+	0.592564i	$0.201884\pi$
$967$			36.8535i			1.18513i	−0.805523	+	0.592564i	$0.798116\pi$
$968$	−50.8596	−	29.3638i	−1.63469	−	0.943789i
$969$	−50.5988	−	29.2132i	−1.62547	−	0.938465i
$970$		0			0
$971$	−3.00764	+	5.20939i	−0.0965199	+	0.167177i	−0.910242	−	0.414077i	$-0.864104\pi$
$971$	−3.00764	+	5.20939i	−0.0965199	+	0.167177i	0.813722	+	0.581254i	$0.197438\pi$
$972$	−48.8963	−	84.6908i	−1.56835	−	2.71646i
$973$	26.4577	−	15.2754i	0.848195	−	0.489706i
$974$	−0.0534776			−0.00171353
$975$		0			0
$976$	−87.2327			−2.79225
$977$	−30.9702	+	17.8807i	−0.990826	+	0.572054i	−0.905521	−	0.424301i	$-0.860520\pi$
$977$	−30.9702	+	17.8807i	−0.990826	+	0.572054i	−0.0853050	+	0.996355i	$0.527186\pi$
$978$	84.6720	+	146.656i	2.70751	+	4.68955i
$979$	−3.09913	+	5.36786i	−0.0990488	+	0.171558i
$980$		0			0
$981$	−32.4144	−	18.7145i	−1.03491	−	0.597507i
$982$	25.0815	+	14.4808i	0.800384	+	0.462102i
$983$		−	3.54764i		−	0.113152i	−0.998398	−	0.0565760i	$-0.981982\pi$
$983$		−	3.54764i		−	0.113152i	0.998398	−	0.0565760i	$-0.0180183\pi$
$984$	96.3523	−	166.887i	3.07160	−	5.32016i
$985$		0			0
$986$	10.1551	−	5.86307i	0.323405	−	0.186718i
$987$	−27.1203			−0.863250
$988$	85.1485	−	53.9723i	2.70894	−	1.71709i
$989$	0.292370			0.00929684
$990$		0			0
$991$	24.3549	+	42.1839i	0.773658	+	1.34002i	0.935545	+	0.353206i	$0.114909\pi$
$991$	24.3549	+	42.1839i	0.773658	+	1.34002i	−0.161887	+	0.986809i	$0.551758\pi$
$992$	34.3476	−	59.4919i	1.09054	−	1.88887i
$993$			6.49573i			0.206136i
$994$	54.7467	+	31.6080i	1.73646	+	1.00254i
$995$		0			0
$996$		−	207.735i		−	6.58234i
$997$	17.0874	−	29.5962i	0.541162	−	0.937320i	−0.457676	−	0.889119i	$-0.651318\pi$
$997$	17.0874	−	29.5962i	0.541162	−	0.937320i	0.998838	−	0.0482007i	$-0.0153487\pi$
$998$	−11.7915	−	20.4234i	−0.373253	−	0.646493i
$999$	−7.39092	+	4.26715i	−0.233838	+	0.135007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.e.101.1	✓	10
5.2	odd	4		325.2.m.d.49.1		20
5.3	odd	4		325.2.m.d.49.10		20
5.4	even	2		325.2.n.f.101.5	yes	10
13.2	odd	12		4225.2.a.bv.1.1		10
13.4	even	6	inner	325.2.n.e.251.1	yes	10
13.11	odd	12		4225.2.a.bv.1.10		10
65.4	even	6		325.2.n.f.251.5	yes	10
65.17	odd	12		325.2.m.d.199.10		20
65.24	odd	12		4225.2.a.bu.1.1		10
65.43	odd	12		325.2.m.d.199.1		20
65.54	odd	12		4225.2.a.bu.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.1		20	5.2	odd	4
325.2.m.d.49.10		20	5.3	odd	4
325.2.m.d.199.1		20	65.43	odd	12
325.2.m.d.199.10		20	65.17	odd	12
325.2.n.e.101.1	✓	10	1.1	even	1	trivial
325.2.n.e.251.1	yes	10	13.4	even	6	inner
325.2.n.f.101.5	yes	10	5.4	even	2
325.2.n.f.251.5	yes	10	65.4	even	6
4225.2.a.bu.1.1		10	65.24	odd	12
4225.2.a.bu.1.10		10	65.54	odd	12
4225.2.a.bv.1.1		10	13.2	odd	12
4225.2.a.bv.1.10		10	13.11	odd	12

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27983 + 1.31626i) q^{2} +(-1.34953 - 2.33745i) q^{3} +(2.46508 - 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(2.37354 + 1.37037i) q^{7} +7.71370i q^{8} +(-2.14244 + 3.71081i) q^{9} +O(q^{10})\)	\(q+(-2.27983 + 1.31626i) q^{2} +(-1.34953 - 2.33745i) q^{3} +(2.46508 - 4.26964i) q^{4} +(6.15337 + 3.55265i) q^{6} +(2.37354 + 1.37037i) q^{7} +7.71370i q^{8} +(-2.14244 + 3.71081i) q^{9} +(-1.59372 + 0.920132i) q^{11} -13.3067 q^{12} +(3.60247 - 0.149035i) q^{13} -7.21503 q^{14} +(-5.22307 - 9.04662i) q^{16} +(1.90847 - 3.30556i) q^{17} -11.2800i q^{18} +(4.91151 + 2.83566i) q^{19} -7.39738i q^{21} +(2.42227 - 4.19549i) q^{22} +(0.0696968 + 0.120718i) q^{23} +(18.0304 - 10.4098i) q^{24} +(-8.01684 + 5.08156i) q^{26} +3.46794 q^{27} +(11.7019 - 6.75612i) q^{28} +(-0.583497 - 1.01065i) q^{29} -5.69034i q^{31} +(10.4549 + 6.03614i) q^{32} +(4.30152 + 2.48348i) q^{33} +10.0481i q^{34} +(10.5626 + 18.2949i) q^{36} +(-2.13121 + 1.23046i) q^{37} -14.9299 q^{38} +(-5.20999 - 8.21945i) q^{39} +(8.01584 - 4.62795i) q^{41} +(9.73687 + 16.8648i) q^{42} +(1.04872 - 1.81644i) q^{43} +9.07280i q^{44} +(-0.317794 - 0.183478i) q^{46} -3.66621i q^{47} +(-14.0973 + 24.4173i) q^{48} +(0.255809 + 0.443075i) q^{49} -10.3021 q^{51} +(8.24405 - 15.7486i) q^{52} +9.97820 q^{53} +(-7.90632 + 4.56471i) q^{54} +(-10.5706 + 18.3088i) q^{56} -15.3072i q^{57} +(2.66055 + 1.53607i) q^{58} +(2.19087 + 1.26490i) q^{59} +(4.17536 - 7.23193i) q^{61} +(7.48996 + 12.9730i) q^{62} +(-10.1703 + 5.87185i) q^{63} -10.8882 q^{64} -13.0756 q^{66} +(-5.18026 + 2.99082i) q^{67} +(-9.40904 - 16.2969i) q^{68} +(0.188115 - 0.325825i) q^{69} +(-7.58786 - 4.38085i) q^{71} +(-28.6241 - 16.5261i) q^{72} -10.7918i q^{73} +(3.23920 - 5.61046i) q^{74} +(24.2145 - 13.9803i) q^{76} -5.04367 q^{77} +(22.6968 + 11.8813i) q^{78} -9.64672 q^{79} +(1.74723 + 3.02630i) q^{81} +(-12.1832 + 21.1018i) q^{82} +15.6113i q^{83} +(-31.5842 - 18.2351i) q^{84} +5.52156i q^{86} +(-1.57489 + 2.72779i) q^{87} +(-7.09762 - 12.2934i) q^{88} +(2.91690 - 1.68407i) q^{89} +(8.75486 + 4.58296i) q^{91} +0.687233 q^{92} +(-13.3009 + 7.67925i) q^{93} +(4.82569 + 8.35833i) q^{94} -32.5837i q^{96} +(-0.271200 - 0.156577i) q^{97} +(-1.16640 - 0.673423i) q^{98} -7.88531i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9 - 9 * q^11 - 28 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 8 * q^17 - 12 * q^22 + 13 * q^23 + 42 * q^24 - 17 * q^26 + 30 * q^27 + 33 * q^28 + 7 * q^29 + 3 * q^32 - 6 * q^33 - 3 * q^36 + 3 * q^37 - 62 * q^38 + 8 * q^39 + 12 * q^41 + 32 * q^42 + 4 * q^43 + 39 * q^46 - 26 * q^48 - q^49 + 16 * q^51 + 61 * q^52 + 24 * q^53 - 9 * q^54 - 21 * q^56 + 18 * q^58 - 48 * q^59 + 13 * q^61 + 17 * q^62 - 34 * q^64 - 42 * q^66 + 6 * q^67 - 13 * q^68 + 20 * q^69 - 27 * q^71 - 141 * q^72 - 26 * q^74 - 12 * q^76 - 48 * q^77 + 56 * q^78 + 4 * q^79 - 17 * q^81 - q^82 - 90 * q^84 - 49 * q^87 - 6 * q^88 + 24 * q^89 + 13 * q^91 + 34 * q^92 - 63 * q^93 + 5 * q^94 - 15 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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