LMFDB - Embedded newform 1122.2.l.e.727.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (of order $4$, 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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.3
Root			$0.245576 + 0.245576i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.e.463.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.16670 - 2.16670i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.16670 - 2.16670i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +0.982302 q^{13} +(2.16670 + 2.16670i) q^{14} +1.41421i q^{15} +1.00000 q^{16} +(-1.69459 - 3.75877i) q^{17} -1.00000 q^{18} +3.06418i q^{19} +(1.00000 + 1.00000i) q^{20} -3.06418 q^{21} +(-0.707107 - 0.707107i) q^{22} +(-0.897477 + 0.897477i) q^{23} +(-0.707107 + 0.707107i) q^{24} -3.00000i q^{25} +0.982302i q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.16670 + 2.16670i) q^{28} +(-0.592070 - 0.592070i) q^{29} -1.41421 q^{30} +(-3.09704 - 3.09704i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(3.75877 - 1.69459i) q^{34} -4.33340 q^{35} -1.00000i q^{36} +(0.472108 + 0.472108i) q^{37} -3.06418 q^{38} +(-0.694593 - 0.694593i) q^{39} +(-1.00000 + 1.00000i) q^{40} +(-7.37988 + 7.37988i) q^{41} -3.06418i q^{42} -8.78676i q^{43} +(0.707107 - 0.707107i) q^{44} +(1.00000 - 1.00000i) q^{45} +(-0.897477 - 0.897477i) q^{46} -12.7133 q^{47} +(-0.707107 - 0.707107i) q^{48} -2.38919i q^{49} +3.00000 q^{50} +(-1.45959 + 3.85611i) q^{51} -0.982302 q^{52} -14.1567i q^{53} +(0.707107 + 0.707107i) q^{54} +1.41421 q^{55} +(-2.16670 - 2.16670i) q^{56} +(2.16670 - 2.16670i) q^{57} +(0.592070 - 0.592070i) q^{58} -12.4534i q^{59} -1.41421i q^{60} +(-3.08188 + 3.08188i) q^{61} +(3.09704 - 3.09704i) q^{62} +(2.16670 + 2.16670i) q^{63} -1.00000 q^{64} +(-0.982302 - 0.982302i) q^{65} +1.00000i q^{66} +4.16965 q^{67} +(1.69459 + 3.75877i) q^{68} +1.26922 q^{69} -4.33340i q^{70} +(1.18440 + 1.18440i) q^{71} +1.00000 q^{72} +(-1.74360 - 1.74360i) q^{73} +(-0.472108 + 0.472108i) q^{74} +(-2.12132 + 2.12132i) q^{75} -3.06418i q^{76} +3.06418i q^{77} +(0.694593 - 0.694593i) q^{78} +(4.41823 - 4.41823i) q^{79} +(-1.00000 - 1.00000i) q^{80} -1.00000 q^{81} +(-7.37988 - 7.37988i) q^{82} -2.29801i q^{83} +3.06418 q^{84} +(-2.06418 + 5.45336i) q^{85} +8.78676 q^{86} +0.837313i q^{87} +(0.707107 + 0.707107i) q^{88} +2.94422 q^{89} +(1.00000 + 1.00000i) q^{90} +(2.12836 - 2.12836i) q^{91} +(0.897477 - 0.897477i) q^{92} +4.37988i q^{93} -12.7133i q^{94} +(3.06418 - 3.06418i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-6.31570 - 6.31570i) q^{97} +2.38919 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 12 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 12 * q^5	$ 12 q - 12 q^{4} - 12 q^{5} + 12 q^{10} + 12 q^{16} - 12 q^{17} - 12 q^{18} + 12 q^{20} + 12 q^{29} + 12 q^{33} - 12 q^{37} - 12 q^{40} + 12 q^{41} + 12 q^{45} + 36 q^{50} - 12 q^{58} - 12 q^{61} - 12 q^{64} + 48 q^{67} + 12 q^{68} + 12 q^{72} + 12 q^{73} + 12 q^{74} - 12 q^{80} - 12 q^{81} + 12 q^{82} + 12 q^{85} + 12 q^{90} - 48 q^{91} - 12 q^{97} + 12 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 12 * q^5 + 12 * q^10 + 12 * q^16 - 12 * q^17 - 12 * q^18 + 12 * q^20 + 12 * q^29 + 12 * q^33 - 12 * q^37 - 12 * q^40 + 12 * q^41 + 12 * q^45 + 36 * q^50 - 12 * q^58 - 12 * q^61 - 12 * q^64 + 48 * q^67 + 12 * q^68 + 12 * q^72 + 12 * q^73 + 12 * q^74 - 12 * q^80 - 12 * q^81 + 12 * q^82 + 12 * q^85 + 12 * q^90 - 48 * q^91 - 12 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	0.447214	−	0.894427i	$-0.352416\pi$
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	−0.894427	+	0.447214i	$0.852416\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	2.16670	−	2.16670i	0.818936	−	0.818936i	−0.167018	−	0.985954i	$-0.553414\pi$
$7$	2.16670	−	2.16670i	0.818936	−	0.818936i	0.985954	+	0.167018i	$0.0534138\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	1.00000	−	1.00000i	0.316228	−	0.316228i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	0.982302			0.272442			0.136221	−	0.990678i	$-0.456504\pi$
$13$	0.982302			0.272442			0.136221	+	0.990678i	$0.456504\pi$
$14$	2.16670	+	2.16670i	0.579075	+	0.579075i
$15$			1.41421i			0.365148i
$16$	1.00000			0.250000
$17$	−1.69459	−	3.75877i	−0.410999	−	0.911636i
$17$	−1.69459	−	3.75877i	−0.410999	−	0.911636i
$18$	−1.00000			−0.235702
$19$			3.06418i			0.702971i	0.936193	+	0.351485i	$0.114323\pi$
$19$			3.06418i			0.702971i	−0.936193	+	0.351485i	$0.885677\pi$
$20$	1.00000	+	1.00000i	0.223607	+	0.223607i
$21$	−3.06418			−0.668658
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	−0.897477	+	0.897477i	−0.187137	+	0.187137i	−0.794457	−	0.607320i	$-0.792244\pi$
$23$	−0.897477	+	0.897477i	−0.187137	+	0.187137i	0.607320	+	0.794457i	$0.292244\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$		−	3.00000i		−	0.600000i
$26$			0.982302i			0.192645i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.16670	+	2.16670i	−0.409468	+	0.409468i
$29$	−0.592070	−	0.592070i	−0.109945	−	0.109945i	0.649994	−	0.759939i	$-0.274771\pi$
$29$	−0.592070	−	0.592070i	−0.109945	−	0.109945i	−0.759939	+	0.649994i	$0.774771\pi$
$30$	−1.41421			−0.258199
$31$	−3.09704	−	3.09704i	−0.556246	−	0.556246i	0.371991	−	0.928236i	$-0.378675\pi$
$31$	−3.09704	−	3.09704i	−0.556246	−	0.556246i	−0.928236	+	0.371991i	$0.878675\pi$
$32$			1.00000i			0.176777i
$33$	1.00000			0.174078
$34$	3.75877	−	1.69459i	0.644624	−	0.290620i
$35$	−4.33340			−0.732479
$36$		−	1.00000i		−	0.166667i
$37$	0.472108	+	0.472108i	0.0776141	+	0.0776141i	0.744848	−	0.667234i	$-0.232522\pi$
$37$	0.472108	+	0.472108i	0.0776141	+	0.0776141i	−0.667234	+	0.744848i	$0.732522\pi$
$38$	−3.06418			−0.497075
$39$	−0.694593	−	0.694593i	−0.111224	−	0.111224i
$40$	−1.00000	+	1.00000i	−0.158114	+	0.158114i
$41$	−7.37988	+	7.37988i	−1.15254	+	1.15254i	−0.166503	+	0.986041i	$0.553248\pi$
$41$	−7.37988	+	7.37988i	−1.15254	+	1.15254i	−0.986041	+	0.166503i	$0.946752\pi$
$42$		−	3.06418i		−	0.472813i
$43$		−	8.78676i		−	1.33997i	−0.742375	−	0.669985i	$-0.766301\pi$
$43$		−	8.78676i		−	1.33997i	0.742375	−	0.669985i	$-0.233699\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	1.00000	−	1.00000i	0.149071	−	0.149071i
$46$	−0.897477	−	0.897477i	−0.132326	−	0.132326i
$47$	−12.7133			−1.85442			−0.927212	−	0.374538i	$-0.877801\pi$
$47$	−12.7133			−1.85442			−0.927212	+	0.374538i	$0.877801\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	2.38919i		−	0.341312i
$50$	3.00000			0.424264
$51$	−1.45959	+	3.85611i	−0.204384	+	0.539963i
$52$	−0.982302			−0.136221
$53$		−	14.1567i		−	1.94457i	−0.233795	−	0.972286i	$-0.575114\pi$
$53$		−	14.1567i		−	1.94457i	0.233795	−	0.972286i	$-0.424886\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	1.41421			0.190693
$56$	−2.16670	−	2.16670i	−0.289538	−	0.289538i
$57$	2.16670	−	2.16670i	0.286987	−	0.286987i
$58$	0.592070	−	0.592070i	0.0777425	−	0.0777425i
$59$		−	12.4534i		−	1.62129i	−0.585538	−	0.810645i	$-0.699117\pi$
$59$		−	12.4534i		−	1.62129i	0.585538	−	0.810645i	$-0.300883\pi$
$60$		−	1.41421i		−	0.182574i
$61$	−3.08188	+	3.08188i	−0.394594	+	0.394594i	−0.876321	−	0.481727i	$-0.840010\pi$
$61$	−3.08188	+	3.08188i	−0.394594	+	0.394594i	0.481727	+	0.876321i	$0.340010\pi$
$62$	3.09704	−	3.09704i	0.393325	−	0.393325i
$63$	2.16670	+	2.16670i	0.272979	+	0.272979i
$64$	−1.00000			−0.125000
$65$	−0.982302	−	0.982302i	−0.121840	−	0.121840i
$66$			1.00000i			0.123091i
$67$	4.16965			0.509404			0.254702	−	0.967020i	$-0.418023\pi$
$67$	4.16965			0.509404			0.254702	+	0.967020i	$0.418023\pi$
$68$	1.69459	+	3.75877i	0.205500	+	0.455818i
$69$	1.26922			0.152797
$70$		−	4.33340i		−	0.517941i
$71$	1.18440	+	1.18440i	0.140562	+	0.140562i	0.773887	−	0.633324i	$-0.218310\pi$
$71$	1.18440	+	1.18440i	0.140562	+	0.140562i	−0.633324	+	0.773887i	$0.718310\pi$
$72$	1.00000			0.117851
$73$	−1.74360	−	1.74360i	−0.204073	−	0.204073i	0.597669	−	0.801743i	$-0.296094\pi$
$73$	−1.74360	−	1.74360i	−0.204073	−	0.204073i	−0.801743	+	0.597669i	$0.796094\pi$
$74$	−0.472108	+	0.472108i	−0.0548815	+	0.0548815i
$75$	−2.12132	+	2.12132i	−0.244949	+	0.244949i
$76$		−	3.06418i		−	0.351485i
$77$			3.06418i			0.349195i
$78$	0.694593	−	0.694593i	0.0786471	−	0.0786471i
$79$	4.41823	−	4.41823i	0.497089	−	0.497089i	−0.413441	−	0.910531i	$-0.635673\pi$
$79$	4.41823	−	4.41823i	0.497089	−	0.497089i	0.910531	+	0.413441i	$0.135673\pi$
$80$	−1.00000	−	1.00000i	−0.111803	−	0.111803i
$81$	−1.00000			−0.111111
$82$	−7.37988	−	7.37988i	−0.814972	−	0.814972i
$83$		−	2.29801i		−	0.252239i	−0.992015	−	0.126119i	$-0.959748\pi$
$83$		−	2.29801i		−	0.252239i	0.992015	−	0.126119i	$-0.0402523\pi$
$84$	3.06418			0.334329
$85$	−2.06418	+	5.45336i	−0.223892	+	0.591500i
$86$	8.78676			0.947501
$87$			0.837313i			0.0897694i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	2.94422			0.312086			0.156043	−	0.987750i	$-0.450126\pi$
$89$	2.94422			0.312086			0.156043	+	0.987750i	$0.450126\pi$
$90$	1.00000	+	1.00000i	0.105409	+	0.105409i
$91$	2.12836	−	2.12836i	0.223112	−	0.223112i
$92$	0.897477	−	0.897477i	0.0935684	−	0.0935684i
$93$			4.37988i			0.454173i
$94$		−	12.7133i		−	1.31128i
$95$	3.06418	−	3.06418i	0.314378	−	0.314378i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−6.31570	−	6.31570i	−0.641263	−	0.641263i	0.309603	−	0.950866i	$-0.399804\pi$
$97$	−6.31570	−	6.31570i	−0.641263	−	0.641263i	−0.950866	+	0.309603i	$0.899804\pi$
$98$	2.38919			0.241344
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$			3.00000i			0.300000i
$101$	11.4518			1.13950			0.569749	−	0.821819i	$-0.307041\pi$
$101$	11.4518			1.13950			0.569749	+	0.821819i	$0.307041\pi$
$102$	−3.85611	−	1.45959i	−0.381812	−	0.144521i
$103$	4.90882			0.483681			0.241840	−	0.970316i	$-0.422249\pi$
$103$	4.90882			0.483681			0.241840	+	0.970316i	$0.422249\pi$
$104$		−	0.982302i		−	0.0963227i
$105$	3.06418	+	3.06418i	0.299033	+	0.299033i
$106$	14.1567			1.37502
$107$	−6.87491	−	6.87491i	−0.664622	−	0.664622i	0.291844	−	0.956466i	$-0.405731\pi$
$107$	−6.87491	−	6.87491i	−0.664622	−	0.664622i	−0.956466	+	0.291844i	$0.905731\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−8.39758	+	8.39758i	−0.804342	+	0.804342i	−0.983771	−	0.179429i	$-0.942575\pi$
$109$	−8.39758	+	8.39758i	−0.804342	+	0.804342i	0.179429	+	0.983771i	$0.442575\pi$
$110$			1.41421i			0.134840i
$111$		−	0.667662i		−	0.0633717i
$112$	2.16670	−	2.16670i	0.204734	−	0.204734i
$113$	−6.97743	+	6.97743i	−0.656381	+	0.656381i	−0.954522	−	0.298141i	$-0.903634\pi$
$113$	−6.97743	+	6.97743i	−0.656381	+	0.656381i	0.298141	+	0.954522i	$0.403634\pi$
$114$	2.16670	+	2.16670i	0.202930	+	0.202930i
$115$	1.79495			0.167380
$116$	0.592070	+	0.592070i	0.0549723	+	0.0549723i
$117$			0.982302i			0.0908139i
$118$	12.4534			1.14643
$119$	−11.8158	−	4.47246i	−1.08315	−	0.409989i
$120$	1.41421			0.129099
$121$		−	1.00000i		−	0.0909091i
$122$	−3.08188	−	3.08188i	−0.279020	−	0.279020i
$123$	10.4367			0.941048
$124$	3.09704	+	3.09704i	0.278123	+	0.278123i
$125$	−8.00000	+	8.00000i	−0.715542	+	0.715542i
$126$	−2.16670	+	2.16670i	−0.193025	+	0.193025i
$127$		−	17.5291i		−	1.55546i	−0.628598	−	0.777730i	$-0.716371\pi$
$127$		−	17.5291i		−	1.55546i	0.628598	−	0.777730i	$-0.283629\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.21318	+	6.21318i	−0.547040	+	0.547040i
$130$	0.982302	−	0.982302i	0.0861536	−	0.0861536i
$131$	6.77099	+	6.77099i	0.591584	+	0.591584i	0.938059	−	0.346475i	$-0.112621\pi$
$131$	6.77099	+	6.77099i	0.591584	+	0.591584i	−0.346475	+	0.938059i	$0.612621\pi$
$132$	−1.00000			−0.0870388
$133$	6.63916	+	6.63916i	0.575688	+	0.575688i
$134$			4.16965i			0.360203i
$135$	−1.41421			−0.121716
$136$	−3.75877	+	1.69459i	−0.322312	+	0.145310i
$137$	−11.9549			−1.02137			−0.510686	−	0.859767i	$-0.670609\pi$
$137$	−11.9549			−1.02137			−0.510686	+	0.859767i	$0.670609\pi$
$138$			1.26922i			0.108044i
$139$	7.45144	+	7.45144i	0.632023	+	0.632023i	0.948575	−	0.316552i	$-0.102525\pi$
$139$	7.45144	+	7.45144i	0.632023	+	0.632023i	−0.316552	+	0.948575i	$0.602525\pi$
$140$	4.33340			0.366239
$141$	8.98965	+	8.98965i	0.757065	+	0.757065i
$142$	−1.18440	+	1.18440i	−0.0993925	+	0.0993925i
$143$	−0.694593	+	0.694593i	−0.0580848	+	0.0580848i
$144$			1.00000i			0.0833333i
$145$			1.18414i			0.0983374i
$146$	1.74360	−	1.74360i	0.144301	−	0.144301i
$147$	−1.68941	+	1.68941i	−0.139340	+	0.139340i
$148$	−0.472108	−	0.472108i	−0.0388071	−	0.0388071i
$149$	−18.6558			−1.52835			−0.764173	−	0.645011i	$-0.776853\pi$
$149$	−18.6558			−1.52835			−0.764173	+	0.645011i	$0.776853\pi$
$150$	−2.12132	−	2.12132i	−0.173205	−	0.173205i
$151$			1.00930i			0.0821360i	0.999156	+	0.0410680i	$0.0130760\pi$
$151$			1.00930i			0.0821360i	−0.999156	+	0.0410680i	$0.986924\pi$
$152$	3.06418			0.248538
$153$	3.75877	−	1.69459i	0.303879	−	0.137000i
$154$	−3.06418			−0.246918
$155$			6.19409i			0.497521i
$156$	0.694593	+	0.694593i	0.0556119	+	0.0556119i
$157$	18.9345			1.51114			0.755568	−	0.655071i	$-0.227361\pi$
$157$	18.9345			1.51114			0.755568	+	0.655071i	$0.227361\pi$
$158$	4.41823	+	4.41823i	0.351495	+	0.351495i
$159$	−10.0103	+	10.0103i	−0.793868	+	0.793868i
$160$	1.00000	−	1.00000i	0.0790569	−	0.0790569i
$161$			3.88913i			0.306506i
$162$		−	1.00000i		−	0.0785674i
$163$	2.60724	−	2.60724i	0.204215	−	0.204215i	−0.597588	−	0.801803i	$-0.703874\pi$
$163$	2.60724	−	2.60724i	0.204215	−	0.204215i	0.801803	+	0.597588i	$0.203874\pi$
$164$	7.37988	−	7.37988i	0.576272	−	0.576272i
$165$	−1.00000	−	1.00000i	−0.0778499	−	0.0778499i
$166$	2.29801			0.178360
$167$	17.2537	+	17.2537i	1.33513	+	1.33513i	0.900706	+	0.434428i	$0.143050\pi$
$167$	17.2537	+	17.2537i	1.33513	+	1.33513i	0.434428	+	0.900706i	$0.356950\pi$
$168$			3.06418i			0.236406i
$169$	−12.0351			−0.925776
$170$	−5.45336	−	2.06418i	−0.418254	−	0.158315i
$171$	−3.06418			−0.234324
$172$			8.78676i			0.669985i
$173$	4.55398	+	4.55398i	0.346233	+	0.346233i	0.858704	−	0.512471i	$-0.171270\pi$
$173$	4.55398	+	4.55398i	0.346233	+	0.346233i	−0.512471	+	0.858704i	$0.671270\pi$
$174$	−0.837313			−0.0634765
$175$	−6.50010	−	6.50010i	−0.491362	−	0.491362i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	−8.80586	+	8.80586i	−0.661889	+	0.661889i
$178$			2.94422i			0.220678i
$179$			7.39758i			0.552921i	0.961025	+	0.276461i	$0.0891615\pi$
$179$			7.39758i			0.552921i	−0.961025	+	0.276461i	$0.910838\pi$
$180$	−1.00000	+	1.00000i	−0.0745356	+	0.0745356i
$181$	−4.43671	+	4.43671i	−0.329778	+	0.329778i	−0.852502	−	0.522724i	$-0.824916\pi$
$181$	−4.43671	+	4.43671i	−0.329778	+	0.329778i	0.522724	+	0.852502i	$0.324916\pi$
$182$	2.12836	+	2.12836i	0.157764	+	0.157764i
$183$	4.35843			0.322184
$184$	0.897477	+	0.897477i	0.0661629	+	0.0661629i
$185$		−	0.944216i		−	0.0694202i
$186$	−4.37988			−0.321149
$187$	3.85611	+	1.45959i	0.281987	+	0.106736i
$188$	12.7133			0.927212
$189$		−	3.06418i		−	0.222886i
$190$	3.06418	+	3.06418i	0.222299	+	0.222299i
$191$	−6.67789			−0.483195			−0.241598	−	0.970377i	$-0.577671\pi$
$191$	−6.67789			−0.483195			−0.241598	+	0.970377i	$0.577671\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	7.35731	−	7.35731i	0.529591	−	0.529591i	−0.390859	−	0.920450i	$-0.627822\pi$
$193$	7.35731	−	7.35731i	0.529591	−	0.529591i	0.920450	+	0.390859i	$0.127822\pi$
$194$	6.31570	−	6.31570i	0.453441	−	0.453441i
$195$			1.38919i			0.0994816i
$196$			2.38919i			0.170656i
$197$	−0.186301	+	0.186301i	−0.0132734	+	0.0132734i	−0.713712	−	0.700439i	$-0.752988\pi$
$197$	−0.186301	+	0.186301i	−0.0132734	+	0.0132734i	0.700439	+	0.713712i	$0.252988\pi$
$198$	0.707107	−	0.707107i	0.0502519	−	0.0502519i
$199$	12.7269	+	12.7269i	0.902186	+	0.902186i	0.995625	−	0.0934392i	$-0.0297861\pi$
$199$	12.7269	+	12.7269i	0.902186	+	0.902186i	−0.0934392	+	0.995625i	$0.529786\pi$
$200$	−3.00000			−0.212132
$201$	−2.94839	−	2.94839i	−0.207963	−	0.207963i
$202$			11.4518i			0.805746i
$203$	−2.56568			−0.180075
$204$	1.45959	−	3.85611i	0.102192	−	0.269982i
$205$	14.7598			1.03087
$206$			4.90882i			0.342014i
$207$	−0.897477	−	0.897477i	−0.0623790	−	0.0623790i
$208$	0.982302			0.0681104
$209$	−2.16670	−	2.16670i	−0.149874	−	0.149874i
$210$	−3.06418	+	3.06418i	−0.211448	+	0.211448i
$211$	15.3205	−	15.3205i	1.05471	−	1.05471i	0.0562940	−	0.998414i	$-0.482072\pi$
$211$	15.3205	−	15.3205i	1.05471	−	1.05471i	0.998414	−	0.0562940i	$-0.0179284\pi$
$212$			14.1567i			0.972286i
$213$		−	1.67499i		−	0.114769i
$214$	6.87491	−	6.87491i	0.469959	−	0.469959i
$215$	−8.78676	+	8.78676i	−0.599252	+	0.599252i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−13.4207			−0.911059
$218$	−8.39758	−	8.39758i	−0.568756	−	0.568756i
$219$			2.46583i			0.166625i
$220$	−1.41421			−0.0953463
$221$	−1.66460	−	3.69225i	−0.111973	−	0.248368i
$222$	0.667662			0.0448105
$223$		−	2.94422i		−	0.197159i	−0.995129	−	0.0985797i	$-0.968570\pi$
$223$		−	2.94422i		−	0.197159i	0.995129	−	0.0985797i	$-0.0314299\pi$
$224$	2.16670	+	2.16670i	0.144769	+	0.144769i
$225$	3.00000			0.200000
$226$	−6.97743	−	6.97743i	−0.464132	−	0.464132i
$227$	−6.90079	+	6.90079i	−0.458022	+	0.458022i	−0.898006	−	0.439984i	$-0.854984\pi$
$227$	−6.90079	+	6.90079i	−0.458022	+	0.458022i	0.439984	+	0.898006i	$0.354984\pi$
$228$	−2.16670	+	2.16670i	−0.143493	+	0.143493i
$229$		−	16.6424i		−	1.09976i	−0.835244	−	0.549879i	$-0.814674\pi$
$229$		−	16.6424i		−	1.09976i	0.835244	−	0.549879i	$-0.185326\pi$
$230$			1.79495i			0.118356i
$231$	2.16670	−	2.16670i	0.142558	−	0.142558i
$232$	−0.592070	+	0.592070i	−0.0388713	+	0.0388713i
$233$	−13.2102	−	13.2102i	−0.865431	−	0.865431i	0.126532	−	0.991963i	$-0.459615\pi$
$233$	−13.2102	−	13.2102i	−0.865431	−	0.865431i	−0.991963	+	0.126532i	$0.959615\pi$
$234$	−0.982302			−0.0642151
$235$	12.7133	+	12.7133i	0.829323	+	0.829323i
$236$			12.4534i			0.810645i
$237$	−6.24832			−0.405872
$238$	4.47246	−	11.8158i	0.289906	−	0.765905i
$239$	−14.8609			−0.961271			−0.480636	−	0.876920i	$-0.659594\pi$
$239$	−14.8609			−0.961271			−0.480636	+	0.876920i	$0.659594\pi$
$240$			1.41421i			0.0912871i
$241$	−3.36706	−	3.36706i	−0.216891	−	0.216891i	0.590296	−	0.807187i	$-0.299011\pi$
$241$	−3.36706	−	3.36706i	−0.216891	−	0.216891i	−0.807187	+	0.590296i	$0.799011\pi$
$242$	1.00000			0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	3.08188	−	3.08188i	0.197297	−	0.197297i
$245$	−2.38919	+	2.38919i	−0.152639	+	0.152639i
$246$			10.4367i			0.665422i
$247$			3.00995i			0.191518i
$248$	−3.09704	+	3.09704i	−0.196663	+	0.196663i
$249$	−1.62494	+	1.62494i	−0.102976	+	0.102976i
$250$	−8.00000	−	8.00000i	−0.505964	−	0.505964i
$251$	24.4996			1.54640			0.773201	−	0.634161i	$-0.218654\pi$
$251$	24.4996			1.54640			0.773201	+	0.634161i	$0.218654\pi$
$252$	−2.16670	−	2.16670i	−0.136489	−	0.136489i
$253$		−	1.26922i		−	0.0797954i
$254$	17.5291			1.09988
$255$	5.31570	−	2.39652i	0.332882	−	0.150076i
$256$	1.00000			0.0625000
$257$			4.90761i			0.306128i	0.988216	+	0.153064i	$0.0489141\pi$
$257$			4.90761i			0.306128i	−0.988216	+	0.153064i	$0.951086\pi$
$258$	−6.21318	−	6.21318i	−0.386816	−	0.386816i
$259$	2.04583			0.127122
$260$	0.982302	+	0.982302i	0.0609198	+	0.0609198i
$261$	0.592070	−	0.592070i	0.0366482	−	0.0366482i
$262$	−6.77099	+	6.77099i	−0.418313	+	0.418313i
$263$		−	9.89887i		−	0.610391i	−0.952290	−	0.305195i	$-0.901278\pi$
$263$		−	9.89887i		−	0.610391i	0.952290	−	0.305195i	$-0.0987217\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	−14.1567	+	14.1567i	−0.869639	+	0.869639i
$266$	−6.63916	+	6.63916i	−0.407073	+	0.407073i
$267$	−2.08188	−	2.08188i	−0.127409	−	0.127409i
$268$	−4.16965			−0.254702
$269$	7.25992	+	7.25992i	0.442645	+	0.442645i	0.892900	−	0.450255i	$-0.148667\pi$
$269$	7.25992	+	7.25992i	0.442645	+	0.442645i	−0.450255	+	0.892900i	$0.648667\pi$
$270$		−	1.41421i		−	0.0860663i
$271$	22.4973			1.36661			0.683306	−	0.730132i	$-0.260541\pi$
$271$	22.4973			1.36661			0.683306	+	0.730132i	$0.260541\pi$
$272$	−1.69459	−	3.75877i	−0.102750	−	0.227909i
$273$	−3.00995			−0.182170
$274$		−	11.9549i		−	0.722220i
$275$	2.12132	+	2.12132i	0.127920	+	0.127920i
$276$	−1.26922			−0.0763983
$277$	−12.6310	−	12.6310i	−0.758921	−	0.758921i	0.217205	−	0.976126i	$-0.430306\pi$
$277$	−12.6310	−	12.6310i	−0.758921	−	0.758921i	−0.976126	+	0.217205i	$0.930306\pi$
$278$	−7.45144	+	7.45144i	−0.446908	+	0.446908i
$279$	3.09704	−	3.09704i	0.185415	−	0.185415i
$280$			4.33340i			0.258970i
$281$		−	5.80085i		−	0.346050i	−0.984917	−	0.173025i	$-0.944646\pi$
$281$		−	5.80085i		−	0.346050i	0.984917	−	0.173025i	$-0.0553541\pi$
$282$	−8.98965	+	8.98965i	−0.535326	+	0.535326i
$283$	5.12643	−	5.12643i	0.304735	−	0.304735i	−0.538128	−	0.842863i	$-0.680868\pi$
$283$	5.12643	−	5.12643i	0.304735	−	0.304735i	0.842863	+	0.538128i	$0.180868\pi$
$284$	−1.18440	−	1.18440i	−0.0702811	−	0.0702811i
$285$	−4.33340			−0.256689
$286$	−0.694593	−	0.694593i	−0.0410721	−	0.0410721i
$287$			31.9800i			1.88772i
$288$	−1.00000			−0.0589256
$289$	−11.2567	+	12.7392i	−0.662159	+	0.749363i
$290$	−1.18414			−0.0695350
$291$			8.93175i			0.523589i
$292$	1.74360	+	1.74360i	0.102037	+	0.102037i
$293$	19.0061			1.11035			0.555174	−	0.831734i	$-0.312652\pi$
$293$	19.0061			1.11035			0.555174	+	0.831734i	$0.312652\pi$
$294$	−1.68941	−	1.68941i	−0.0985283	−	0.0985283i
$295$	−12.4534	+	12.4534i	−0.725063	+	0.725063i
$296$	0.472108	−	0.472108i	0.0274407	−	0.0274407i
$297$			1.00000i			0.0580259i
$298$		−	18.6558i		−	1.08070i
$299$	−0.881594	+	0.881594i	−0.0509839	+	0.0509839i
$300$	2.12132	−	2.12132i	0.122474	−	0.122474i
$301$	−19.0383	−	19.0383i	−1.09735	−	1.09735i
$302$	−1.00930			−0.0580789
$303$	−8.09765	−	8.09765i	−0.465198	−	0.465198i
$304$			3.06418i			0.175743i
$305$	6.16375			0.352935
$306$	1.69459	+	3.75877i	0.0968734	+	0.214875i
$307$	4.05213			0.231267			0.115634	−	0.993292i	$-0.463110\pi$
$307$	4.05213			0.231267			0.115634	+	0.993292i	$0.463110\pi$
$308$		−	3.06418i		−	0.174598i
$309$	−3.47106	−	3.47106i	−0.197462	−	0.197462i
$310$	−6.19409			−0.351801
$311$	22.8618	+	22.8618i	1.29638	+	1.29638i	0.930769	+	0.365607i	$0.119139\pi$
$311$	22.8618	+	22.8618i	1.29638	+	1.29638i	0.365607	+	0.930769i	$0.380861\pi$
$312$	−0.694593	+	0.694593i	−0.0393236	+	0.0393236i
$313$	−4.72259	+	4.72259i	−0.266936	+	0.266936i	−0.827865	−	0.560928i	$-0.810444\pi$
$313$	−4.72259	+	4.72259i	−0.266936	+	0.266936i	0.560928	+	0.827865i	$0.310444\pi$
$314$			18.9345i			1.06853i
$315$		−	4.33340i		−	0.244160i
$316$	−4.41823	+	4.41823i	−0.248545	+	0.248545i
$317$	2.12040	−	2.12040i	0.119094	−	0.119094i	−0.645048	−	0.764142i	$-0.723163\pi$
$317$	2.12040	−	2.12040i	0.119094	−	0.119094i	0.764142	+	0.645048i	$0.223163\pi$
$318$	−10.0103	−	10.0103i	−0.561350	−	0.561350i
$319$	0.837313			0.0468805
$320$	1.00000	+	1.00000i	0.0559017	+	0.0559017i
$321$			9.72259i			0.542662i
$322$	−3.88913			−0.216733
$323$	11.5175	−	5.19253i	0.640853	−	0.288920i
$324$	1.00000			0.0555556
$325$		−	2.94691i		−	0.163465i
$326$	2.60724	+	2.60724i	0.144402	+	0.144402i
$327$	11.8760			0.656743
$328$	7.37988	+	7.37988i	0.407486	+	0.407486i
$329$	−27.5459	+	27.5459i	−1.51865	+	1.51865i
$330$	1.00000	−	1.00000i	0.0550482	−	0.0550482i
$331$		−	23.0674i		−	1.26790i	−0.773375	−	0.633949i	$-0.781433\pi$
$331$		−	23.0674i		−	1.26790i	0.773375	−	0.633949i	$-0.218567\pi$
$332$			2.29801i			0.126119i
$333$	−0.472108	+	0.472108i	−0.0258714	+	0.0258714i
$334$	−17.2537	+	17.2537i	−0.944083	+	0.944083i
$335$	−4.16965	−	4.16965i	−0.227812	−	0.227812i
$336$	−3.06418			−0.167165
$337$	18.9561	+	18.9561i	1.03260	+	1.03260i	0.999450	+	0.0331534i	$0.0105550\pi$
$337$	18.9561	+	18.9561i	1.03260	+	1.03260i	0.0331534	+	0.999450i	$0.489445\pi$
$338$		−	12.0351i		−	0.654622i
$339$	9.86758			0.535933
$340$	2.06418	−	5.45336i	0.111946	−	0.295750i
$341$	4.37988			0.237184
$342$		−	3.06418i		−	0.165692i
$343$	9.99026	+	9.99026i	0.539423	+	0.539423i
$344$	−8.78676			−0.473751
$345$	−1.26922	−	1.26922i	−0.0683327	−	0.0683327i
$346$	−4.55398	+	4.55398i	−0.244824	+	0.244824i
$347$	17.0033	−	17.0033i	0.912783	−	0.912783i	−0.0837074	−	0.996490i	$-0.526676\pi$
$347$	17.0033	−	17.0033i	0.912783	−	0.912783i	0.996490	+	0.0837074i	$0.0266761\pi$
$348$		−	0.837313i		−	0.0448847i
$349$			11.1297i			0.595758i	0.954604	+	0.297879i	$0.0962792\pi$
$349$			11.1297i			0.595758i	−0.954604	+	0.297879i	$0.903721\pi$
$350$	6.50010	−	6.50010i	0.347445	−	0.347445i
$351$	0.694593	−	0.694593i	0.0370746	−	0.0370746i
$352$	−0.707107	−	0.707107i	−0.0376889	−	0.0376889i
$353$	9.96955			0.530626			0.265313	−	0.964162i	$-0.414525\pi$
$353$	9.96955			0.530626			0.265313	+	0.964162i	$0.414525\pi$
$354$	−8.80586	−	8.80586i	−0.468026	−	0.468026i
$355$		−	2.36880i		−	0.125723i
$356$	−2.94422			−0.156043
$357$	5.19253	+	11.5175i	0.274818	+	0.609573i
$358$	−7.39758			−0.390974
$359$		−	20.1275i		−	1.06229i	−0.847282	−	0.531144i	$-0.821762\pi$
$359$		−	20.1275i		−	1.06229i	0.847282	−	0.531144i	$-0.178238\pi$
$360$	−1.00000	−	1.00000i	−0.0527046	−	0.0527046i
$361$	9.61081			0.505832
$362$	−4.43671	−	4.43671i	−0.233188	−	0.233188i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	−2.12836	+	2.12836i	−0.111556	+	0.111556i
$365$			3.48720i			0.182529i
$366$			4.35843i			0.227819i
$367$	−17.0106	+	17.0106i	−0.887947	+	0.887947i	−0.994326	−	0.106379i	$-0.966074\pi$
$367$	−17.0106	+	17.0106i	−0.887947	+	0.887947i	0.106379	+	0.994326i	$0.466074\pi$
$368$	−0.897477	+	0.897477i	−0.0467842	+	0.0467842i
$369$	−7.37988	−	7.37988i	−0.384181	−	0.384181i
$370$	0.944216			0.0490875
$371$	−30.6733	−	30.6733i	−1.59248	−	1.59248i
$372$		−	4.37988i		−	0.227086i
$373$	13.0531			0.675864			0.337932	−	0.941171i	$-0.390273\pi$
$373$	13.0531			0.675864			0.337932	+	0.941171i	$0.390273\pi$
$374$	−1.45959	+	3.85611i	−0.0754738	+	0.199395i
$375$	11.3137			0.584237
$376$			12.7133i			0.655638i
$377$	−0.581591	−	0.581591i	−0.0299535	−	0.0299535i
$378$	3.06418			0.157604
$379$	−4.93113	−	4.93113i	−0.253295	−	0.253295i	0.569025	−	0.822320i	$-0.307321\pi$
$379$	−4.93113	−	4.93113i	−0.253295	−	0.253295i	−0.822320	+	0.569025i	$0.807321\pi$
$380$	−3.06418	+	3.06418i	−0.157189	+	0.157189i
$381$	−12.3950	+	12.3950i	−0.635014	+	0.635014i
$382$		−	6.67789i		−	0.341671i
$383$			23.8317i			1.21774i	0.793269	+	0.608871i	$0.208377\pi$
$383$			23.8317i			1.21774i	−0.793269	+	0.608871i	$0.791623\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	3.06418	−	3.06418i	0.156165	−	0.156165i
$386$	7.35731	+	7.35731i	0.374477	+	0.374477i
$387$	8.78676			0.446656
$388$	6.31570	+	6.31570i	0.320631	+	0.320631i
$389$			18.7274i			0.949518i	0.880116	+	0.474759i	$0.157465\pi$
$389$			18.7274i			0.949518i	−0.880116	+	0.474759i	$0.842535\pi$
$390$	−1.38919			−0.0703441
$391$	4.89427	+	1.85255i	0.247514	+	0.0936876i
$392$	−2.38919			−0.120672
$393$		−	9.57562i		−	0.483026i
$394$	−0.186301	−	0.186301i	−0.00938572	−	0.00938572i
$395$	−8.83645			−0.444610
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	−20.6689	+	20.6689i	−1.03734	+	1.03734i	−0.0380665	+	0.999275i	$0.512120\pi$
$397$	−20.6689	+	20.6689i	−1.03734	+	1.03734i	−0.999275	+	0.0380665i	$0.987880\pi$
$398$	−12.7269	+	12.7269i	−0.637942	+	0.637942i
$399$		−	9.38919i		−	0.470047i
$400$		−	3.00000i		−	0.150000i
$401$	13.6874	−	13.6874i	0.683515	−	0.683515i	−0.277275	−	0.960790i	$-0.589431\pi$
$401$	13.6874	−	13.6874i	0.683515	−	0.683515i	0.960790	+	0.277275i	$0.0894315\pi$
$402$	2.94839	−	2.94839i	0.147052	−	0.147052i
$403$	−3.04223	−	3.04223i	−0.151544	−	0.151544i
$404$	−11.4518			−0.569749
$405$	1.00000	+	1.00000i	0.0496904	+	0.0496904i
$406$		−	2.56568i		−	0.127332i
$407$	−0.667662			−0.0330948
$408$	3.85611	+	1.45959i	0.190906	+	0.0722607i
$409$	−24.7479			−1.22371			−0.611853	−	0.790971i	$-0.709576\pi$
$409$	−24.7479			−1.22371			−0.611853	+	0.790971i	$0.709576\pi$
$410$			14.7598i			0.728933i
$411$	8.45336	+	8.45336i	0.416974	+	0.416974i
$412$	−4.90882			−0.241840
$413$	−26.9827	−	26.9827i	−1.32773	−	1.32773i
$414$	0.897477	−	0.897477i	0.0441086	−	0.0441086i
$415$	−2.29801	+	2.29801i	−0.112805	+	0.112805i
$416$			0.982302i			0.0481613i
$417$		−	10.5379i		−	0.516045i
$418$	2.16670	−	2.16670i	0.105977	−	0.105977i
$419$	28.3434	−	28.3434i	1.38467	−	1.38467i	0.548545	−	0.836121i	$-0.315182\pi$
$419$	28.3434	−	28.3434i	1.38467	−	1.38467i	0.836121	−	0.548545i	$-0.184818\pi$
$420$	−3.06418	−	3.06418i	−0.149517	−	0.149517i
$421$	−12.8372			−0.625646			−0.312823	−	0.949811i	$-0.601275\pi$
$421$	−12.8372			−0.625646			−0.312823	+	0.949811i	$0.601275\pi$
$422$	15.3205	+	15.3205i	0.745791	+	0.745791i
$423$		−	12.7133i		−	0.618141i
$424$	−14.1567			−0.687510
$425$	−11.2763	+	5.08378i	−0.546981	+	0.246599i
$426$	1.67499			0.0811536
$427$			13.3550i			0.646294i
$428$	6.87491	+	6.87491i	0.332311	+	0.332311i
$429$	0.982302			0.0474260
$430$	−8.78676	−	8.78676i	−0.423735	−	0.423735i
$431$	−0.736514	+	0.736514i	−0.0354766	+	0.0354766i	−0.724623	−	0.689146i	$-0.757986\pi$
$431$	−0.736514	+	0.736514i	−0.0354766	+	0.0354766i	0.689146	+	0.724623i	$0.257986\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$			1.98450i			0.0953691i	0.998862	+	0.0476846i	$0.0151842\pi$
$433$			1.98450i			0.0953691i	−0.998862	+	0.0476846i	$0.984816\pi$
$434$		−	13.4207i		−	0.644216i
$435$	0.837313	−	0.837313i	0.0401461	−	0.0401461i
$436$	8.39758	−	8.39758i	0.402171	−	0.402171i
$437$	−2.75003	−	2.75003i	−0.131552	−	0.131552i
$438$	−2.46583			−0.117822
$439$	−3.40706	−	3.40706i	−0.162610	−	0.162610i	0.621112	−	0.783722i	$-0.286681\pi$
$439$	−3.40706	−	3.40706i	−0.162610	−	0.162610i	−0.783722	+	0.621112i	$0.786681\pi$
$440$		−	1.41421i		−	0.0674200i
$441$	2.38919			0.113771
$442$	3.69225	−	1.66460i	0.175622	−	0.0791771i
$443$	22.2011			1.05481			0.527403	−	0.849615i	$-0.323166\pi$
$443$	22.2011			1.05481			0.527403	+	0.849615i	$0.323166\pi$
$444$			0.667662i			0.0316858i
$445$	−2.94422	−	2.94422i	−0.139569	−	0.139569i
$446$	2.94422			0.139413
$447$	13.1917	+	13.1917i	0.623945	+	0.623945i
$448$	−2.16670	+	2.16670i	−0.102367	+	0.102367i
$449$	13.8874	−	13.8874i	0.655385	−	0.655385i	−0.298899	−	0.954285i	$-0.596619\pi$
$449$	13.8874	−	13.8874i	0.655385	−	0.655385i	0.954285	+	0.298899i	$0.0966195\pi$
$450$			3.00000i			0.141421i
$451$		−	10.4367i		−	0.491446i
$452$	6.97743	−	6.97743i	0.328191	−	0.328191i
$453$	0.713685	−	0.713685i	0.0335319	−	0.0335319i
$454$	−6.90079	−	6.90079i	−0.323870	−	0.323870i
$455$	−4.25671			−0.199558
$456$	−2.16670	−	2.16670i	−0.101465	−	0.101465i
$457$			7.69155i			0.359796i	0.983685	+	0.179898i	$0.0575767\pi$
$457$			7.69155i			0.359796i	−0.983685	+	0.179898i	$0.942423\pi$
$458$	16.6424			0.777647
$459$	−3.85611	−	1.45959i	−0.179988	−	0.0681280i
$460$	−1.79495			−0.0836902
$461$		−	12.6649i		−	0.589864i	−0.955518	−	0.294932i	$-0.904703\pi$
$461$		−	12.6649i		−	0.589864i	0.955518	−	0.294932i	$-0.0952969\pi$
$462$	2.16670	+	2.16670i	0.100804	+	0.100804i
$463$	37.7490			1.75435			0.877173	−	0.480175i	$-0.159427\pi$
$463$	37.7490			1.75435			0.877173	+	0.480175i	$0.159427\pi$
$464$	−0.592070	−	0.592070i	−0.0274861	−	0.0274861i
$465$	4.37988	−	4.37988i	0.203112	−	0.203112i
$466$	13.2102	−	13.2102i	0.611952	−	0.611952i
$467$		−	27.7473i		−	1.28399i	−0.766709	−	0.641995i	$-0.778107\pi$
$467$		−	27.7473i		−	1.28399i	0.766709	−	0.641995i	$-0.221893\pi$
$468$		−	0.982302i		−	0.0454069i
$469$	9.03439	−	9.03439i	0.417169	−	0.417169i
$470$	−12.7133	+	12.7133i	−0.586420	+	0.586420i
$471$	−13.3887	−	13.3887i	−0.616918	−	0.616918i
$472$	−12.4534			−0.573213
$473$	6.21318	+	6.21318i	0.285682	+	0.285682i
$474$		−	6.24832i		−	0.286995i
$475$	9.19253			0.421782
$476$	11.8158	+	4.47246i	0.541577	+	0.204995i
$477$	14.1567			0.648191
$478$		−	14.8609i		−	0.679721i
$479$	−18.9603	−	18.9603i	−0.866318	−	0.866318i	0.125745	−	0.992063i	$-0.459868\pi$
$479$	−18.9603	−	18.9603i	−0.866318	−	0.866318i	−0.992063	+	0.125745i	$0.959868\pi$
$480$	−1.41421			−0.0645497
$481$	0.463753	+	0.463753i	0.0211453	+	0.0211453i
$482$	3.36706	−	3.36706i	0.153365	−	0.153365i
$483$	2.75003	−	2.75003i	0.125131	−	0.125131i
$484$			1.00000i			0.0454545i
$485$			12.6314i			0.573563i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−5.03971	+	5.03971i	−0.228371	+	0.228371i	−0.812012	−	0.583641i	$-0.801628\pi$
$487$	−5.03971	+	5.03971i	−0.228371	+	0.228371i	0.583641	+	0.812012i	$0.301628\pi$
$488$	3.08188	+	3.08188i	0.139510	+	0.139510i
$489$	−3.68719			−0.166741
$490$	−2.38919	−	2.38919i	−0.107932	−	0.107932i
$491$			6.88490i			0.310711i	0.987859	+	0.155356i	$0.0496524\pi$
$491$			6.88490i			0.310711i	−0.987859	+	0.155356i	$0.950348\pi$
$492$	−10.4367			−0.470524
$493$	−1.22214	+	3.22877i	−0.0550423	+	0.145417i
$494$	−3.00995			−0.135424
$495$			1.41421i			0.0635642i
$496$	−3.09704	−	3.09704i	−0.139061	−	0.139061i
$497$	5.13247			0.230223
$498$	−1.62494	−	1.62494i	−0.0728151	−	0.0728151i
$499$	−2.43968	+	2.43968i	−0.109215	+	0.109215i	−0.759603	−	0.650387i	$-0.774607\pi$
$499$	−2.43968	+	2.43968i	−0.109215	+	0.109215i	0.650387	+	0.759603i	$0.274607\pi$
$500$	8.00000	−	8.00000i	0.357771	−	0.357771i
$501$		−	24.4005i		−	1.09013i
$502$			24.4996i			1.09347i
$503$	24.8210	−	24.8210i	1.10671	−	1.10671i	0.113133	−	0.993580i	$-0.463912\pi$
$503$	24.8210	−	24.8210i	1.10671	−	1.10671i	0.993580	−	0.113133i	$-0.0360885\pi$
$504$	2.16670	−	2.16670i	0.0965125	−	0.0965125i
$505$	−11.4518	−	11.4518i	−0.509599	−	0.509599i
$506$	1.26922			0.0564239
$507$	8.51009	+	8.51009i	0.377946	+	0.377946i
$508$			17.5291i			0.777730i
$509$	25.3628			1.12419			0.562094	−	0.827073i	$-0.309996\pi$
$509$	25.3628			1.12419			0.562094	+	0.827073i	$0.309996\pi$
$510$	2.39652	+	5.31570i	0.106120	+	0.235383i
$511$	−7.55573			−0.334246
$512$			1.00000i			0.0441942i
$513$	2.16670	+	2.16670i	0.0956622	+	0.0956622i
$514$	−4.90761			−0.216465
$515$	−4.90882	−	4.90882i	−0.216309	−	0.216309i
$516$	6.21318	−	6.21318i	0.273520	−	0.273520i
$517$	8.98965	−	8.98965i	0.395364	−	0.395364i
$518$			2.04583i			0.0898888i
$519$		−	6.44031i		−	0.282698i
$520$	−0.982302	+	0.982302i	−0.0430768	+	0.0430768i
$521$	4.07060	−	4.07060i	0.178336	−	0.178336i	−0.612294	−	0.790630i	$-0.709753\pi$
$521$	4.07060	−	4.07060i	0.178336	−	0.178336i	0.790630	+	0.612294i	$0.209753\pi$
$522$	0.592070	+	0.592070i	0.0259142	+	0.0259142i
$523$	28.0732			1.22756			0.613779	−	0.789478i	$-0.289649\pi$
$523$	28.0732			1.22756			0.613779	+	0.789478i	$0.289649\pi$
$524$	−6.77099	−	6.77099i	−0.295792	−	0.295792i
$525$			9.19253i			0.401195i
$526$	9.89887			0.431611
$527$	−6.39285	+	16.8893i	−0.278477	+	0.735710i
$528$	1.00000			0.0435194
$529$			21.3891i			0.929960i
$530$	−14.1567	−	14.1567i	−0.614928	−	0.614928i
$531$	12.4534			0.540430
$532$	−6.63916	−	6.63916i	−0.287844	−	0.287844i
$533$	−7.24928	+	7.24928i	−0.314001	+	0.314001i
$534$	2.08188	−	2.08188i	0.0900916	−	0.0900916i
$535$			13.7498i			0.594456i
$536$		−	4.16965i		−	0.180101i
$537$	5.23088	−	5.23088i	0.225729	−	0.225729i
$538$	−7.25992	+	7.25992i	−0.312997	+	0.312997i
$539$	1.68941	+	1.68941i	0.0727680	+	0.0727680i
$540$	1.41421			0.0608581
$541$	−28.4796	−	28.4796i	−1.22443	−	1.22443i	−0.966040	−	0.258393i	$-0.916807\pi$
$541$	−28.4796	−	28.4796i	−1.22443	−	1.22443i	−0.258393	−	0.966040i	$-0.583193\pi$
$542$			22.4973i			0.966341i
$543$	6.27446			0.269263
$544$	3.75877	−	1.69459i	0.161156	−	0.0726551i
$545$	16.7952			0.719426
$546$		−	3.00995i		−	0.128814i
$547$	−5.59845	−	5.59845i	−0.239373	−	0.239373i	0.577218	−	0.816590i	$-0.304138\pi$
$547$	−5.59845	−	5.59845i	−0.239373	−	0.239373i	−0.816590	+	0.577218i	$0.804138\pi$
$548$	11.9549			0.510686
$549$	−3.08188	−	3.08188i	−0.131531	−	0.131531i
$550$	−2.12132	+	2.12132i	−0.0904534	+	0.0904534i
$551$	1.81421	−	1.81421i	0.0772878	−	0.0772878i
$552$		−	1.26922i		−	0.0540218i
$553$		−	19.1460i		−	0.814169i
$554$	12.6310	−	12.6310i	0.536638	−	0.536638i
$555$	−0.667662	+	0.667662i	−0.0283407	+	0.0283407i
$556$	−7.45144	−	7.45144i	−0.316012	−	0.316012i
$557$	12.3264			0.522288			0.261144	−	0.965300i	$-0.415900\pi$
$557$	12.3264			0.522288			0.261144	+	0.965300i	$0.415900\pi$
$558$	3.09704	+	3.09704i	0.131108	+	0.131108i
$559$		−	8.63126i		−	0.365063i
$560$	−4.33340			−0.183120
$561$	−1.69459	−	3.75877i	−0.0715458	−	0.158695i
$562$	5.80085			0.244694
$563$		−	45.1028i		−	1.90086i	−0.310944	−	0.950428i	$-0.600645\pi$
$563$		−	45.1028i		−	1.90086i	0.310944	−	0.950428i	$-0.399355\pi$
$564$	−8.98965	−	8.98965i	−0.378533	−	0.378533i
$565$	13.9549			0.587085
$566$	5.12643	+	5.12643i	0.215480	+	0.215480i
$567$	−2.16670	+	2.16670i	−0.0909929	+	0.0909929i
$568$	1.18440	−	1.18440i	0.0496963	−	0.0496963i
$569$		−	16.3714i		−	0.686324i	−0.939276	−	0.343162i	$-0.888502\pi$
$569$		−	16.3714i		−	0.686324i	0.939276	−	0.343162i	$-0.111498\pi$
$570$		−	4.33340i		−	0.181506i
$571$	−3.55155	+	3.55155i	−0.148628	+	0.148628i	−0.777505	−	0.628877i	$-0.783515\pi$
$571$	−3.55155	+	3.55155i	−0.148628	+	0.148628i	0.628877	+	0.777505i	$0.283515\pi$
$572$	0.694593	−	0.694593i	0.0290424	−	0.0290424i
$573$	4.72198	+	4.72198i	0.197264	+	0.197264i
$574$	−31.9800			−1.33482
$575$	2.69243	+	2.69243i	0.112282	+	0.112282i
$576$		−	1.00000i		−	0.0416667i
$577$	−43.5354			−1.81240			−0.906202	−	0.422845i	$-0.861031\pi$
$577$	−43.5354			−1.81240			−0.906202	+	0.422845i	$0.861031\pi$
$578$	−12.7392	−	11.2567i	−0.529880	−	0.468217i
$579$	−10.4048			−0.432409
$580$		−	1.18414i		−	0.0491687i
$581$	−4.97909	−	4.97909i	−0.206568	−	0.206568i
$582$	−8.93175			−0.370233
$583$	10.0103	+	10.0103i	0.414584	+	0.414584i
$584$	−1.74360	+	1.74360i	−0.0721507	+	0.0721507i
$585$	0.982302	−	0.982302i	0.0406132	−	0.0406132i
$586$			19.0061i			0.785135i
$587$		−	37.1326i		−	1.53263i	−0.642466	−	0.766314i	$-0.722089\pi$
$587$		−	37.1326i		−	1.53263i	0.642466	−	0.766314i	$-0.277911\pi$
$588$	1.68941	−	1.68941i	0.0696701	−	0.0696701i
$589$	9.48989	−	9.48989i	0.391024	−	0.391024i
$590$	−12.4534	−	12.4534i	−0.512697	−	0.512697i
$591$	0.263470			0.0108377
$592$	0.472108	+	0.472108i	0.0194035	+	0.0194035i
$593$			40.9078i			1.67988i	0.542677	+	0.839942i	$0.317411\pi$
$593$			40.9078i			1.67988i	−0.542677	+	0.839942i	$0.682589\pi$
$594$	−1.00000			−0.0410305
$595$	7.34335	+	16.2883i	0.301048	+	0.667754i
$596$	18.6558			0.764173
$597$		−	17.9986i		−	0.736632i
$598$	−0.881594	−	0.881594i	−0.0360510	−	0.0360510i
$599$	−38.1655			−1.55940			−0.779700	−	0.626153i	$-0.784628\pi$
$599$	−38.1655			−1.55940			−0.779700	+	0.626153i	$0.784628\pi$
$600$	2.12132	+	2.12132i	0.0866025	+	0.0866025i
$601$	2.47683	−	2.47683i	0.101032	−	0.101032i	−0.654784	−	0.755816i	$-0.727240\pi$
$601$	2.47683	−	2.47683i	0.101032	−	0.101032i	0.755816	+	0.654784i	$0.227240\pi$
$602$	19.0383	−	19.0383i	0.775943	−	0.775943i
$603$			4.16965i			0.169801i
$604$		−	1.00930i		−	0.0410680i
$605$	−1.00000	+	1.00000i	−0.0406558	+	0.0406558i
$606$	8.09765	−	8.09765i	0.328945	−	0.328945i
$607$	−15.7771	−	15.7771i	−0.640372	−	0.640372i	0.310275	−	0.950647i	$-0.399579\pi$
$607$	−15.7771	−	15.7771i	−0.640372	−	0.640372i	−0.950647	+	0.310275i	$0.899579\pi$
$608$	−3.06418			−0.124269
$609$	1.81421	+	1.81421i	0.0735154	+	0.0735154i
$610$			6.16375i			0.249563i
$611$	−12.4883			−0.505222
$612$	−3.75877	+	1.69459i	−0.151939	+	0.0684999i
$613$	33.1620			1.33940			0.669699	−	0.742632i	$-0.266423\pi$
$613$	33.1620			1.33940			0.669699	+	0.742632i	$0.266423\pi$
$614$			4.05213i			0.163531i
$615$	−10.4367	−	10.4367i	−0.420850	−	0.420850i
$616$	3.06418			0.123459
$617$	18.3904	+	18.3904i	0.740370	+	0.740370i	0.972649	−	0.232279i	$-0.0746182\pi$
$617$	18.3904	+	18.3904i	0.740370	+	0.740370i	−0.232279	+	0.972649i	$0.574618\pi$
$618$	3.47106	−	3.47106i	0.139627	−	0.139627i
$619$	18.4394	−	18.4394i	0.741144	−	0.741144i	−0.231654	−	0.972798i	$-0.574414\pi$
$619$	18.4394	−	18.4394i	0.741144	−	0.741144i	0.972798	+	0.231654i	$0.0744138\pi$
$620$		−	6.19409i		−	0.248761i
$621$			1.26922i			0.0509322i
$622$	−22.8618	+	22.8618i	−0.916677	+	0.916677i
$623$	6.37924	−	6.37924i	0.255579	−	0.255579i
$624$	−0.694593	−	0.694593i	−0.0278060	−	0.0278060i
$625$	1.00000			0.0400000
$626$	−4.72259	−	4.72259i	−0.188753	−	0.188753i
$627$			3.06418i			0.122371i
$628$	−18.9345			−0.755568
$629$	0.974515	−	2.57458i	0.0388565	−	0.102655i
$630$	4.33340			0.172647
$631$			0.297311i			0.0118358i	0.999982	+	0.00591789i	$0.00188373\pi$
$631$			0.297311i			0.0118358i	−0.999982	+	0.00591789i	$0.998116\pi$
$632$	−4.41823	−	4.41823i	−0.175748	−	0.175748i
$633$	−21.6665			−0.861166
$634$	2.12040	+	2.12040i	0.0842119	+	0.0842119i
$635$	−17.5291	+	17.5291i	−0.695623	+	0.695623i
$636$	10.0103	−	10.0103i	0.396934	−	0.396934i
$637$		−	2.34690i		−	0.0929877i
$638$			0.837313i			0.0331495i
$639$	−1.18440	+	1.18440i	−0.0468541	+	0.0468541i
$640$	−1.00000	+	1.00000i	−0.0395285	+	0.0395285i
$641$	−5.79208	−	5.79208i	−0.228773	−	0.228773i	0.583407	−	0.812180i	$-0.301719\pi$
$641$	−5.79208	−	5.79208i	−0.228773	−	0.228773i	−0.812180	+	0.583407i	$0.801719\pi$
$642$	−9.72259			−0.383720
$643$	25.6789	+	25.6789i	1.01268	+	1.01268i	0.999919	+	0.0127595i	$0.00406159\pi$
$643$	25.6789	+	25.6789i	1.01268	+	1.01268i	0.0127595	+	0.999919i	$0.495938\pi$
$644$		−	3.88913i		−	0.153253i
$645$	12.4264			0.489288
$646$	5.19253	+	11.5175i	0.204297	+	0.453152i
$647$	−0.465650			−0.0183066			−0.00915330	−	0.999958i	$-0.502914\pi$
$647$	−0.465650			−0.0183066			−0.00915330	+	0.999958i	$0.502914\pi$
$648$			1.00000i			0.0392837i
$649$	8.80586	+	8.80586i	0.345660	+	0.345660i
$650$	2.94691			0.115587
$651$	9.48989	+	9.48989i	0.371938	+	0.371938i
$652$	−2.60724	+	2.60724i	−0.102107	+	0.102107i
$653$	5.35079	−	5.35079i	0.209392	−	0.209392i	−0.594617	−	0.804009i	$-0.702696\pi$
$653$	5.35079	−	5.35079i	0.209392	−	0.209392i	0.804009	+	0.594617i	$0.202696\pi$
$654$			11.8760i			0.464387i
$655$		−	13.5420i		−	0.529129i
$656$	−7.37988	+	7.37988i	−0.288136	+	0.288136i
$657$	1.74360	−	1.74360i	0.0680244	−	0.0680244i
$658$	−27.5459	−	27.5459i	−1.07385	−	1.07385i
$659$	14.2309			0.554358			0.277179	−	0.960818i	$-0.410601\pi$
$659$	14.2309			0.554358			0.277179	+	0.960818i	$0.410601\pi$
$660$	1.00000	+	1.00000i	0.0389249	+	0.0389249i
$661$		−	1.73808i		−	0.0676036i	−0.999429	−	0.0338018i	$-0.989238\pi$
$661$		−	1.73808i		−	0.0676036i	0.999429	−	0.0338018i	$-0.0107615\pi$
$662$	23.0674			0.896539
$663$	−1.43376	+	3.78787i	−0.0556827	+	0.147109i
$664$	−2.29801			−0.0891800
$665$		−	13.2783i		−	0.514911i
$666$	−0.472108	−	0.472108i	−0.0182938	−	0.0182938i
$667$	1.06274			0.0411494
$668$	−17.2537	−	17.2537i	−0.667567	−	0.667567i
$669$	−2.08188	+	2.08188i	−0.0804900	+	0.0804900i
$670$	4.16965	−	4.16965i	0.161088	−	0.161088i
$671$		−	4.35843i		−	0.168255i
$672$		−	3.06418i		−	0.118203i
$673$	−4.05910	+	4.05910i	−0.156467	+	0.156467i	−0.780999	−	0.624532i	$-0.785290\pi$
$673$	−4.05910	+	4.05910i	−0.156467	+	0.156467i	0.624532	+	0.780999i	$0.285290\pi$
$674$	−18.9561	+	18.9561i	−0.730161	+	0.730161i
$675$	−2.12132	−	2.12132i	−0.0816497	−	0.0816497i
$676$	12.0351			0.462888
$677$	0.392081	+	0.392081i	0.0150689	+	0.0150689i	0.714601	−	0.699532i	$-0.246608\pi$
$677$	0.392081	+	0.392081i	0.0150689	+	0.0150689i	−0.699532	+	0.714601i	$0.746608\pi$
$678$			9.86758i			0.378962i
$679$	−27.3685			−1.05031
$680$	5.45336	+	2.06418i	0.209127	+	0.0791576i
$681$	9.75920			0.373973
$682$			4.37988i			0.167714i
$683$	13.2354	+	13.2354i	0.506440	+	0.506440i	0.913432	−	0.406992i	$-0.133422\pi$
$683$	13.2354	+	13.2354i	0.506440	+	0.506440i	−0.406992	+	0.913432i	$0.633422\pi$
$684$	3.06418			0.117162
$685$	11.9549	+	11.9549i	0.456772	+	0.456772i
$686$	−9.99026	+	9.99026i	−0.381430	+	0.381430i
$687$	−11.7679	+	11.7679i	−0.448975	+	0.448975i
$688$		−	8.78676i		−	0.334992i
$689$		−	13.9062i		−	0.529782i
$690$	1.26922	−	1.26922i	0.0483185	−	0.0483185i
$691$	−4.21895	+	4.21895i	−0.160497	+	0.160497i	−0.782787	−	0.622290i	$-0.786202\pi$
$691$	−4.21895	+	4.21895i	−0.160497	+	0.160497i	0.622290	+	0.782787i	$0.286202\pi$
$692$	−4.55398	−	4.55398i	−0.173116	−	0.173116i
$693$	−3.06418			−0.116398
$694$	17.0033	+	17.0033i	0.645435	+	0.645435i
$695$		−	14.9029i		−	0.565299i
$696$	0.837313			0.0317383
$697$	40.2452	+	15.2334i	1.52439	+	0.577006i
$698$	−11.1297			−0.421264
$699$			18.6821i			0.706621i
$700$	6.50010	+	6.50010i	0.245681	+	0.245681i
$701$	25.9625			0.980590			0.490295	−	0.871556i	$-0.336889\pi$
$701$	25.9625			0.980590			0.490295	+	0.871556i	$0.336889\pi$
$702$	0.694593	+	0.694593i	0.0262157	+	0.0262157i
$703$	−1.44662	+	1.44662i	−0.0545604	+	0.0545604i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$		−	17.9793i		−	0.677140i
$706$			9.96955i			0.375209i
$707$	24.8126	−	24.8126i	0.933175	−	0.933175i
$708$	8.80586	−	8.80586i	0.330944	−	0.330944i
$709$	−0.955163	−	0.955163i	−0.0358719	−	0.0358719i	0.688943	−	0.724815i	$-0.258075\pi$
$709$	−0.955163	−	0.955163i	−0.0358719	−	0.0358719i	−0.724815	+	0.688943i	$0.758075\pi$
$710$	2.36880			0.0888994
$711$	4.41823	+	4.41823i	0.165696	+	0.165696i
$712$		−	2.94422i		−	0.110339i
$713$	5.55905			0.208188
$714$	−11.5175	+	5.19253i	−0.431033	+	0.194326i
$715$	1.38919			0.0519526
$716$		−	7.39758i		−	0.276461i
$717$	10.5082	+	10.5082i	0.392437	+	0.392437i
$718$	20.1275			0.751151
$719$	−25.0813	−	25.0813i	−0.935375	−	0.935375i	0.0626602	−	0.998035i	$-0.480042\pi$
$719$	−25.0813	−	25.0813i	−0.935375	−	0.935375i	−0.998035	+	0.0626602i	$0.980042\pi$
$720$	1.00000	−	1.00000i	0.0372678	−	0.0372678i
$721$	10.6359	−	10.6359i	0.396103	−	0.396103i
$722$			9.61081i			0.357677i
$723$			4.76174i			0.177091i
$724$	4.43671	−	4.43671i	0.164889	−	0.164889i
$725$	−1.77621	+	1.77621i	−0.0659667	+	0.0659667i
$726$	−0.707107	−	0.707107i	−0.0262432	−	0.0262432i
$727$	−22.7204			−0.842652			−0.421326	−	0.906909i	$-0.638435\pi$
$727$	−22.7204			−0.842652			−0.421326	+	0.906909i	$0.638435\pi$
$728$	−2.12836	−	2.12836i	−0.0788821	−	0.0788821i
$729$		−	1.00000i		−	0.0370370i
$730$	−3.48720			−0.129067
$731$	−33.0274	+	14.8900i	−1.22156	+	0.550726i
$732$	−4.35843			−0.161092
$733$		−	7.14693i		−	0.263978i	−0.991251	−	0.131989i	$-0.957864\pi$
$733$		−	7.14693i		−	0.263978i	0.991251	−	0.131989i	$-0.0421364\pi$
$734$	−17.0106	−	17.0106i	−0.627873	−	0.627873i
$735$	3.37882			0.124630
$736$	−0.897477	−	0.897477i	−0.0330814	−	0.0330814i
$737$	−2.94839	+	2.94839i	−0.108605	+	0.108605i
$738$	7.37988	−	7.37988i	0.271657	−	0.271657i
$739$			10.2285i			0.376261i	0.982144	+	0.188131i	$0.0602428\pi$
$739$			10.2285i			0.376261i	−0.982144	+	0.188131i	$0.939757\pi$
$740$			0.944216i			0.0347101i
$741$	2.12836	−	2.12836i	0.0781871	−	0.0781871i
$742$	30.6733	−	30.6733i	1.12605	−	1.12605i
$743$	−16.0633	−	16.0633i	−0.589305	−	0.589305i	0.348138	−	0.937443i	$-0.386814\pi$
$743$	−16.0633	−	16.0633i	−0.589305	−	0.589305i	−0.937443	+	0.348138i	$0.886814\pi$
$744$	4.37988			0.160574
$745$	18.6558	+	18.6558i	0.683497	+	0.683497i
$746$			13.0531i			0.477908i
$747$	2.29801			0.0840797
$748$	−3.85611	−	1.45959i	−0.140993	−	0.0533680i
$749$	−29.7917			−1.08857
$750$			11.3137i			0.413118i
$751$	−24.4571	−	24.4571i	−0.892453	−	0.892453i	0.102300	−	0.994754i	$-0.467380\pi$
$751$	−24.4571	−	24.4571i	−0.892453	−	0.892453i	−0.994754	+	0.102300i	$0.967380\pi$
$752$	−12.7133			−0.463606
$753$	−17.3238	−	17.3238i	−0.631316	−	0.631316i
$754$	0.581591	−	0.581591i	0.0211803	−	0.0211803i
$755$	1.00930	−	1.00930i	0.0367323	−	0.0367323i
$756$			3.06418i			0.111443i
$757$			30.1611i			1.09622i	0.836406	+	0.548111i	$0.184653\pi$
$757$			30.1611i			1.09622i	−0.836406	+	0.548111i	$0.815347\pi$
$758$	4.93113	−	4.93113i	0.179107	−	0.179107i
$759$	−0.897477	+	0.897477i	−0.0325763	+	0.0325763i
$760$	−3.06418	−	3.06418i	−0.111149	−	0.111149i
$761$	19.7807			0.717049			0.358524	−	0.933520i	$-0.383280\pi$
$761$	19.7807			0.717049			0.358524	+	0.933520i	$0.383280\pi$
$762$	−12.3950	−	12.3950i	−0.449023	−	0.449023i
$763$			36.3901i			1.31741i
$764$	6.67789			0.241598
$765$	−5.45336	−	2.06418i	−0.197167	−	0.0746305i
$766$	−23.8317			−0.861074
$767$		−	12.2330i		−	0.441707i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−20.5854			−0.742328			−0.371164	−	0.928567i	$-0.621041\pi$
$769$	−20.5854			−0.742328			−0.371164	+	0.928567i	$0.621041\pi$
$770$	3.06418	+	3.06418i	0.110425	+	0.110425i
$771$	3.47020	−	3.47020i	0.124976	−	0.124976i
$772$	−7.35731	+	7.35731i	−0.264795	+	0.264795i
$773$			16.6365i			0.598375i	0.954194	+	0.299187i	$0.0967156\pi$
$773$			16.6365i			0.598375i	−0.954194	+	0.299187i	$0.903284\pi$
$774$			8.78676i			0.315834i
$775$	−9.29113	+	9.29113i	−0.333747	+	0.333747i
$776$	−6.31570	+	6.31570i	−0.226721	+	0.226721i
$777$	−1.44662	−	1.44662i	−0.0518973	−	0.0518973i
$778$	−18.7274			−0.671411
$779$	−22.6133	−	22.6133i	−0.810204	−	0.810204i
$780$		−	1.38919i		−	0.0497408i
$781$	−1.67499			−0.0599359
$782$	−1.85255	+	4.89427i	−0.0662471	+	0.175019i
$783$	−0.837313			−0.0299231
$784$		−	2.38919i		−	0.0853281i
$785$	−18.9345	−	18.9345i	−0.675800	−	0.675800i
$786$	9.57562			0.341551
$787$	12.1781	+	12.1781i	0.434102	+	0.434102i	0.890021	−	0.455919i	$-0.150689\pi$
$787$	12.1781	+	12.1781i	0.434102	+	0.434102i	−0.455919	+	0.890021i	$0.650689\pi$
$788$	0.186301	−	0.186301i	0.00663671	−	0.00663671i
$789$	−6.99956	+	6.99956i	−0.249191	+	0.249191i
$790$		−	8.83645i		−	0.314387i
$791$			30.2360i			1.07507i
$792$	−0.707107	+	0.707107i	−0.0251259	+	0.0251259i
$793$	−3.02733	+	3.02733i	−0.107504	+	0.107504i
$794$	−20.6689	−	20.6689i	−0.733511	−	0.733511i
$795$	20.0206			0.710057
$796$	−12.7269	−	12.7269i	−0.451093	−	0.451093i
$797$		−	1.82139i		−	0.0645168i	−0.999480	−	0.0322584i	$-0.989730\pi$
$797$		−	1.82139i		−	0.0645168i	0.999480	−	0.0322584i	$-0.0102700\pi$
$798$	9.38919			0.332374
$799$	21.5438	+	47.7863i	0.762166	+	1.69056i
$800$	3.00000			0.106066
$801$			2.94422i			0.104029i
$802$	13.6874	+	13.6874i	0.483318	+	0.483318i
$803$	2.46583			0.0870171
$804$	2.94839	+	2.94839i	0.103982	+	0.103982i
$805$	3.88913	−	3.88913i	0.137074	−	0.137074i
$806$	3.04223	−	3.04223i	0.107158	−	0.107158i
$807$		−	10.2671i		−	0.361418i
$808$		−	11.4518i		−	0.402873i
$809$	2.70644	−	2.70644i	0.0951535	−	0.0951535i	−0.657928	−	0.753081i	$-0.728567\pi$
$809$	2.70644	−	2.70644i	0.0951535	−	0.0951535i	0.753081	+	0.657928i	$0.228567\pi$
$810$	−1.00000	+	1.00000i	−0.0351364	+	0.0351364i
$811$	7.28685	+	7.28685i	0.255876	+	0.255876i	0.823374	−	0.567499i	$-0.192089\pi$
$811$	7.28685	+	7.28685i	0.255876	+	0.255876i	−0.567499	+	0.823374i	$0.692089\pi$
$812$	2.56568			0.0900376
$813$	−15.9080	−	15.9080i	−0.557917	−	0.557917i
$814$		−	0.667662i		−	0.0234015i
$815$	−5.21448			−0.182655
$816$	−1.45959	+	3.85611i	−0.0510960	+	0.134991i
$817$	26.9242			0.941959
$818$		−	24.7479i		−	0.865291i
$819$	2.12836	+	2.12836i	0.0743708	+	0.0743708i
$820$	−14.7598			−0.515433
$821$	−31.9275	−	31.9275i	−1.11428	−	1.11428i	−0.992566	−	0.121711i	$-0.961162\pi$
$821$	−31.9275	−	31.9275i	−1.11428	−	1.11428i	−0.121711	−	0.992566i	$-0.538838\pi$
$822$	−8.45336	+	8.45336i	−0.294845	+	0.294845i
$823$	−13.1727	+	13.1727i	−0.459173	+	0.459173i	−0.898384	−	0.439211i	$-0.855258\pi$
$823$	−13.1727	+	13.1727i	−0.459173	+	0.459173i	0.439211	+	0.898384i	$0.355258\pi$
$824$		−	4.90882i		−	0.171007i
$825$		−	3.00000i		−	0.104447i
$826$	26.9827	−	26.9827i	0.938849	−	0.938849i
$827$	10.4138	−	10.4138i	0.362123	−	0.362123i	−0.502471	−	0.864594i	$-0.667576\pi$
$827$	10.4138	−	10.4138i	0.362123	−	0.362123i	0.864594	+	0.502471i	$0.167576\pi$
$828$	0.897477	+	0.897477i	0.0311895	+	0.0311895i
$829$	−36.0771			−1.25301			−0.626505	−	0.779417i	$-0.715515\pi$
$829$	−36.0771			−1.25301			−0.626505	+	0.779417i	$0.715515\pi$
$830$	−2.29801	−	2.29801i	−0.0797650	−	0.0797650i
$831$			17.8629i			0.619657i
$832$	−0.982302			−0.0340552
$833$	−8.98040	+	4.04870i	−0.311152	+	0.140279i
$834$	10.5379			0.364899
$835$		−	34.5075i		−	1.19418i
$836$	2.16670	+	2.16670i	0.0749369	+	0.0749369i
$837$	−4.37988			−0.151391
$838$	28.3434	+	28.3434i	0.979107	+	0.979107i
$839$	−17.6434	+	17.6434i	−0.609118	+	0.609118i	−0.942716	−	0.333597i	$-0.891737\pi$
$839$	−17.6434	+	17.6434i	−0.609118	+	0.609118i	0.333597	+	0.942716i	$0.391737\pi$
$840$	3.06418	−	3.06418i	0.105724	−	0.105724i
$841$		−	28.2989i		−	0.975824i
$842$		−	12.8372i		−	0.442399i
$843$	−4.10182	+	4.10182i	−0.141274	+	0.141274i
$844$	−15.3205	+	15.3205i	−0.527354	+	0.527354i
$845$	12.0351	+	12.0351i	0.414019	+	0.414019i
$846$	12.7133			0.437092
$847$	−2.16670	−	2.16670i	−0.0744487	−	0.0744487i
$848$		−	14.1567i		−	0.486143i
$849$	−7.24987			−0.248815
$850$	−5.08378	−	11.2763i	−0.174372	−	0.386774i
$851$	−0.847412			−0.0290489
$852$			1.67499i			0.0573843i
$853$	−40.8768	−	40.8768i	−1.39960	−	1.39960i	−0.801203	−	0.598393i	$-0.795806\pi$
$853$	−40.8768	−	40.8768i	−1.39960	−	1.39960i	−0.598393	−	0.801203i	$-0.704194\pi$
$854$	−13.3550			−0.456999
$855$	3.06418	+	3.06418i	0.104793	+	0.104793i
$856$	−6.87491	+	6.87491i	−0.234979	+	0.234979i
$857$	−31.8699	+	31.8699i	−1.08865	+	1.08865i	−0.0929871	+	0.995667i	$0.529642\pi$
$857$	−31.8699	+	31.8699i	−1.08865	+	1.08865i	−0.995667	+	0.0929871i	$0.970358\pi$
$858$			0.982302i			0.0335353i
$859$			51.3140i			1.75081i	0.483390	+	0.875405i	$0.339405\pi$
$859$			51.3140i			1.75081i	−0.483390	+	0.875405i	$0.660595\pi$
$860$	8.78676	−	8.78676i	0.299626	−	0.299626i
$861$	22.6133	−	22.6133i	0.770658	−	0.770658i
$862$	−0.736514	−	0.736514i	−0.0250858	−	0.0250858i
$863$	15.6840			0.533888			0.266944	−	0.963712i	$-0.413986\pi$
$863$	15.6840			0.533888			0.266944	+	0.963712i	$0.413986\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$		−	9.10797i		−	0.309680i
$866$	−1.98450			−0.0674362
$867$	16.9677	−	1.04826i	0.576252	−	0.0356007i
$868$	13.4207			0.455529
$869$			6.24832i			0.211960i
$870$	0.837313	+	0.837313i	0.0283876	+	0.0283876i
$871$	4.09586			0.138783
$872$	8.39758	+	8.39758i	0.284378	+	0.284378i
$873$	6.31570	−	6.31570i	0.213754	−	0.213754i
$874$	2.75003	−	2.75003i	0.0930211	−	0.0930211i
$875$			34.6672i			1.17197i
$876$		−	2.46583i		−	0.0833125i
$877$	−34.1632	+	34.1632i	−1.15361	+	1.15361i	−0.167786	+	0.985823i	$0.553662\pi$
$877$	−34.1632	+	34.1632i	−1.15361	+	1.15361i	−0.985823	+	0.167786i	$0.946338\pi$
$878$	3.40706	−	3.40706i	0.114983	−	0.114983i
$879$	−13.4393	−	13.4393i	−0.453298	−	0.453298i
$880$	1.41421			0.0476731
$881$	36.9599	+	36.9599i	1.24521	+	1.24521i	0.957810	+	0.287402i	$0.0927915\pi$
$881$	36.9599	+	36.9599i	1.24521	+	1.24521i	0.287402	+	0.957810i	$0.407208\pi$
$882$			2.38919i			0.0804481i
$883$	−11.2934			−0.380055			−0.190027	−	0.981779i	$-0.560858\pi$
$883$	−11.2934			−0.380055			−0.190027	+	0.981779i	$0.560858\pi$
$884$	1.66460	+	3.69225i	0.0559866	+	0.124184i
$885$	17.6117			0.592011
$886$			22.2011i			0.745860i
$887$	−32.2637	−	32.2637i	−1.08331	−	1.08331i	−0.996199	−	0.0871100i	$-0.972237\pi$
$887$	−32.2637	−	32.2637i	−1.08331	−	1.08331i	−0.0871100	−	0.996199i	$-0.527763\pi$
$888$	−0.667662			−0.0224053
$889$	−37.9804	−	37.9804i	−1.27382	−	1.27382i
$890$	2.94422	−	2.94422i	0.0986904	−	0.0986904i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$			2.94422i			0.0985797i
$893$		−	38.9558i		−	1.30360i
$894$	−13.1917	+	13.1917i	−0.441196	+	0.441196i
$895$	7.39758	−	7.39758i	0.247274	−	0.247274i
$896$	−2.16670	−	2.16670i	−0.0723844	−	0.0723844i
$897$	1.24676			0.0416282
$898$	13.8874	+	13.8874i	0.463427	+	0.463427i
$899$			3.66733i			0.122312i
$900$	−3.00000			−0.100000
$901$	−53.2118	+	23.9898i	−1.77274	+	0.799217i
$902$	10.4367			0.347505
$903$			26.9242i			0.895982i
$904$	6.97743	+	6.97743i	0.232066	+	0.232066i
$905$	8.87343			0.294963
$906$	0.713685	+	0.713685i	0.0237106	+	0.0237106i
$907$	8.49168	−	8.49168i	0.281962	−	0.281962i	−0.551929	−	0.833891i	$-0.686108\pi$
$907$	8.49168	−	8.49168i	0.281962	−	0.281962i	0.833891	+	0.551929i	$0.186108\pi$
$908$	6.90079	−	6.90079i	0.229011	−	0.229011i
$909$			11.4518i			0.379832i
$910$		−	4.25671i		−	0.141109i
$911$	−28.9851	+	28.9851i	−0.960321	+	0.960321i	−0.999242	−	0.0389216i	$-0.987608\pi$
$911$	−28.9851	+	28.9851i	−0.960321	+	0.960321i	0.0389216	+	0.999242i	$0.487608\pi$
$912$	2.16670	−	2.16670i	0.0717466	−	0.0717466i
$913$	1.62494	+	1.62494i	0.0537775	+	0.0537775i
$914$	−7.69155			−0.254414
$915$	−4.35843	−	4.35843i	−0.144085	−	0.144085i
$916$			16.6424i			0.549879i
$917$	29.3414			0.968939
$918$	1.45959	−	3.85611i	0.0481738	−	0.127271i
$919$	−30.6144			−1.00988			−0.504938	−	0.863156i	$-0.668485\pi$
$919$	−30.6144			−1.00988			−0.504938	+	0.863156i	$0.668485\pi$
$920$		−	1.79495i		−	0.0591779i
$921$	−2.86529	−	2.86529i	−0.0944146	−	0.0944146i
$922$	12.6649			0.417096
$923$	1.16344	+	1.16344i	0.0382950	+	0.0382950i
$924$	−2.16670	+	2.16670i	−0.0712792	+	0.0712792i
$925$	1.41632	−	1.41632i	0.0465685	−	0.0465685i
$926$			37.7490i			1.24051i
$927$			4.90882i			0.161227i
$928$	0.592070	−	0.592070i	0.0194356	−	0.0194356i
$929$	1.66494	−	1.66494i	0.0546248	−	0.0546248i	−0.679267	−	0.733891i	$-0.737702\pi$
$929$	1.66494	−	1.66494i	0.0546248	−	0.0546248i	0.733891	+	0.679267i	$0.237702\pi$
$930$	4.37988	+	4.37988i	0.143622	+	0.143622i
$931$	7.32089			0.239932
$932$	13.2102	+	13.2102i	0.432715	+	0.432715i
$933$		−	32.3315i		−	1.05849i
$934$	27.7473			0.907918
$935$	−2.39652	−	5.31570i	−0.0783745	−	0.173842i
$936$	0.982302			0.0321076
$937$			48.8311i			1.59524i	0.603158	+	0.797622i	$0.293909\pi$
$937$			48.8311i			1.59524i	−0.603158	+	0.797622i	$0.706091\pi$
$938$	9.03439	+	9.03439i	0.294983	+	0.294983i
$939$	6.67875			0.217953
$940$	−12.7133	−	12.7133i	−0.414662	−	0.414662i
$941$	−17.9992	+	17.9992i	−0.586756	+	0.586756i	−0.936751	−	0.349996i	$-0.886183\pi$
$941$	−17.9992	+	17.9992i	−0.586756	+	0.586756i	0.349996	+	0.936751i	$0.386183\pi$
$942$	13.3887	−	13.3887i	0.436227	−	0.436227i
$943$		−	13.2465i		−	0.431367i
$944$		−	12.4534i		−	0.405322i
$945$	−3.06418	+	3.06418i	−0.0996777	+	0.0996777i
$946$	−6.21318	+	6.21318i	−0.202008	+	0.202008i
$947$	22.5298	+	22.5298i	0.732119	+	0.732119i	0.971039	−	0.238920i	$-0.0767934\pi$
$947$	22.5298	+	22.5298i	0.732119	+	0.732119i	−0.238920	+	0.971039i	$0.576793\pi$
$948$	6.24832			0.202936
$949$	−1.71274	−	1.71274i	−0.0555980	−	0.0555980i
$950$			9.19253i			0.298245i
$951$	−2.99870			−0.0972395
$952$	−4.47246	+	11.8158i	−0.144953	+	0.382952i
$953$	−5.62512			−0.182215			−0.0911077	−	0.995841i	$-0.529041\pi$
$953$	−5.62512			−0.182215			−0.0911077	+	0.995841i	$0.529041\pi$
$954$			14.1567i			0.458340i
$955$	6.67789	+	6.67789i	0.216091	+	0.216091i
$956$	14.8609			0.480636
$957$	−0.592070	−	0.592070i	−0.0191389	−	0.0191389i
$958$	18.9603	−	18.9603i	0.612579	−	0.612579i
$959$	−25.9026	+	25.9026i	−0.836439	+	0.836439i
$960$		−	1.41421i		−	0.0456435i
$961$		−	11.8166i		−	0.381182i
$962$	−0.463753	+	0.463753i	−0.0149520	+	0.0149520i
$963$	6.87491	−	6.87491i	0.221541	−	0.221541i
$964$	3.36706	+	3.36706i	0.108446	+	0.108446i
$965$	−14.7146			−0.473681
$966$	2.75003	+	2.75003i	0.0884807	+	0.0884807i
$967$		−	14.7754i		−	0.475144i	−0.971370	−	0.237572i	$-0.923648\pi$
$967$		−	14.7754i		−	0.475144i	0.971370	−	0.237572i	$-0.0763516\pi$
$968$	−1.00000			−0.0321412
$969$	−11.8158	−	4.47246i	−0.379578	−	0.143676i
$970$	−12.6314			−0.405570
$971$			25.7483i			0.826301i	0.910663	+	0.413151i	$0.135572\pi$
$971$			25.7483i			0.826301i	−0.910663	+	0.413151i	$0.864428\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	32.2901			1.03517
$974$	−5.03971	−	5.03971i	−0.161483	−	0.161483i
$975$	−2.08378	+	2.08378i	−0.0667343	+	0.0667343i
$976$	−3.08188	+	3.08188i	−0.0986484	+	0.0986484i
$977$			28.0115i			0.896169i	0.893991	+	0.448084i	$0.147894\pi$
$977$			28.0115i			0.896169i	−0.893991	+	0.448084i	$0.852106\pi$
$978$		−	3.68719i		−	0.117903i
$979$	−2.08188	+	2.08188i	−0.0665370	+	0.0665370i
$980$	2.38919	−	2.38919i	0.0763197	−	0.0763197i
$981$	−8.39758	−	8.39758i	−0.268114	−	0.268114i
$982$	−6.88490			−0.219706
$983$	1.77475	+	1.77475i	0.0566056	+	0.0566056i	0.734843	−	0.678237i	$-0.237256\pi$
$983$	1.77475	+	1.77475i	0.0566056	+	0.0566056i	−0.678237	+	0.734843i	$0.737256\pi$
$984$		−	10.4367i		−	0.332711i
$985$	0.372602			0.0118721
$986$	−3.22877	−	1.22214i	−0.102825	−	0.0389208i
$987$	38.9558			1.23998
$988$		−	3.00995i		−	0.0957592i
$989$	7.88592	+	7.88592i	0.250758	+	0.250758i
$990$	−1.41421			−0.0449467
$991$	−2.67786	−	2.67786i	−0.0850651	−	0.0850651i	0.663294	−	0.748359i	$-0.269158\pi$
$991$	−2.67786	−	2.67786i	−0.0850651	−	0.0850651i	−0.748359	+	0.663294i	$0.769158\pi$
$992$	3.09704	−	3.09704i	0.0983313	−	0.0983313i
$993$	−16.3111	+	16.3111i	−0.517617	+	0.517617i
$994$			5.13247i			0.162792i
$995$		−	25.4538i		−	0.806940i
$996$	1.62494	−	1.62494i	0.0514881	−	0.0514881i
$997$	31.3122	−	31.3122i	0.991666	−	0.991666i	−0.00829971	−	0.999966i	$-0.502642\pi$
$997$	31.3122	−	31.3122i	0.991666	−	0.991666i	0.999966	+	0.00829971i	$0.00264191\pi$
$998$	−2.43968	−	2.43968i	−0.0772268	−	0.0772268i
$999$	0.667662			0.0211239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.e.727.3	yes	12
17.4	even	4	inner	1122.2.l.e.463.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.e.463.3	✓	12	17.4	even	4	inner
1122.2.l.e.727.3	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.16670 - 2.16670i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.16670 - 2.16670i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +0.982302 q^{13} +(2.16670 + 2.16670i) q^{14} +1.41421i q^{15} +1.00000 q^{16} +(-1.69459 - 3.75877i) q^{17} -1.00000 q^{18} +3.06418i q^{19} +(1.00000 + 1.00000i) q^{20} -3.06418 q^{21} +(-0.707107 - 0.707107i) q^{22} +(-0.897477 + 0.897477i) q^{23} +(-0.707107 + 0.707107i) q^{24} -3.00000i q^{25} +0.982302i q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.16670 + 2.16670i) q^{28} +(-0.592070 - 0.592070i) q^{29} -1.41421 q^{30} +(-3.09704 - 3.09704i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(3.75877 - 1.69459i) q^{34} -4.33340 q^{35} -1.00000i q^{36} +(0.472108 + 0.472108i) q^{37} -3.06418 q^{38} +(-0.694593 - 0.694593i) q^{39} +(-1.00000 + 1.00000i) q^{40} +(-7.37988 + 7.37988i) q^{41} -3.06418i q^{42} -8.78676i q^{43} +(0.707107 - 0.707107i) q^{44} +(1.00000 - 1.00000i) q^{45} +(-0.897477 - 0.897477i) q^{46} -12.7133 q^{47} +(-0.707107 - 0.707107i) q^{48} -2.38919i q^{49} +3.00000 q^{50} +(-1.45959 + 3.85611i) q^{51} -0.982302 q^{52} -14.1567i q^{53} +(0.707107 + 0.707107i) q^{54} +1.41421 q^{55} +(-2.16670 - 2.16670i) q^{56} +(2.16670 - 2.16670i) q^{57} +(0.592070 - 0.592070i) q^{58} -12.4534i q^{59} -1.41421i q^{60} +(-3.08188 + 3.08188i) q^{61} +(3.09704 - 3.09704i) q^{62} +(2.16670 + 2.16670i) q^{63} -1.00000 q^{64} +(-0.982302 - 0.982302i) q^{65} +1.00000i q^{66} +4.16965 q^{67} +(1.69459 + 3.75877i) q^{68} +1.26922 q^{69} -4.33340i q^{70} +(1.18440 + 1.18440i) q^{71} +1.00000 q^{72} +(-1.74360 - 1.74360i) q^{73} +(-0.472108 + 0.472108i) q^{74} +(-2.12132 + 2.12132i) q^{75} -3.06418i q^{76} +3.06418i q^{77} +(0.694593 - 0.694593i) q^{78} +(4.41823 - 4.41823i) q^{79} +(-1.00000 - 1.00000i) q^{80} -1.00000 q^{81} +(-7.37988 - 7.37988i) q^{82} -2.29801i q^{83} +3.06418 q^{84} +(-2.06418 + 5.45336i) q^{85} +8.78676 q^{86} +0.837313i q^{87} +(0.707107 + 0.707107i) q^{88} +2.94422 q^{89} +(1.00000 + 1.00000i) q^{90} +(2.12836 - 2.12836i) q^{91} +(0.897477 - 0.897477i) q^{92} +4.37988i q^{93} -12.7133i q^{94} +(3.06418 - 3.06418i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-6.31570 - 6.31570i) q^{97} +2.38919 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 12 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 12 * q^5	\( 12 q - 12 q^{4} - 12 q^{5} + 12 q^{10} + 12 q^{16} - 12 q^{17} - 12 q^{18} + 12 q^{20} + 12 q^{29} + 12 q^{33} - 12 q^{37} - 12 q^{40} + 12 q^{41} + 12 q^{45} + 36 q^{50} - 12 q^{58} - 12 q^{61} - 12 q^{64} + 48 q^{67} + 12 q^{68} + 12 q^{72} + 12 q^{73} + 12 q^{74} - 12 q^{80} - 12 q^{81} + 12 q^{82} + 12 q^{85} + 12 q^{90} - 48 q^{91} - 12 q^{97} + 12 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 12 * q^5 + 12 * q^10 + 12 * q^16 - 12 * q^17 - 12 * q^18 + 12 * q^20 + 12 * q^29 + 12 * q^33 - 12 * q^37 - 12 * q^40 + 12 * q^41 + 12 * q^45 + 36 * q^50 - 12 * q^58 - 12 * q^61 - 12 * q^64 + 48 * q^67 + 12 * q^68 + 12 * q^72 + 12 * q^73 + 12 * q^74 - 12 * q^80 - 12 * q^81 + 12 * q^82 + 12 * q^85 + 12 * q^90 - 48 * q^91 - 12 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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