LMFDB - Embedded newform 1122.2.l.e.727.4

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			727.4
Root			$-0.245576 - 0.245576i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.e.463.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.16670 + 2.16670i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(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} +(-5.23088 + 5.23088i) 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} +(-4.92547 - 4.92547i) q^{29} +1.41421 q^{30} +(-4.42050 - 4.42050i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(3.75877 - 1.69459i) q^{34} +4.33340 q^{35} -1.00000i q^{36} +(-3.86129 - 3.86129i) q^{37} -3.06418 q^{38} +(-0.694593 - 0.694593i) q^{39} +(-1.00000 + 1.00000i) q^{40} +(3.25153 - 3.25153i) q^{41} -3.06418i q^{42} -0.119961i q^{43} +(-0.707107 + 0.707107i) q^{44} +(1.00000 - 1.00000i) q^{45} +(-5.23088 - 5.23088i) q^{46} +6.58493 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} -0.878384i q^{53} +(-0.707107 - 0.707107i) q^{54} -1.41421 q^{55} +(2.16670 + 2.16670i) q^{56} +(-2.16670 + 2.16670i) q^{57} +(4.92547 - 4.92547i) q^{58} -12.4534i q^{59} +1.41421i q^{60} +(-5.04648 + 5.04648i) q^{61} +(4.42050 - 4.42050i) q^{62} +(-2.16670 - 2.16670i) q^{63} -1.00000 q^{64} +(0.982302 + 0.982302i) q^{65} +1.00000i q^{66} -8.42636 q^{67} +(1.69459 + 3.75877i) q^{68} -7.39758 q^{69} +4.33340i q^{70} +(-1.18440 - 1.18440i) q^{71} +1.00000 q^{72} +(-2.38475 - 2.38475i) q^{73} +(3.86129 - 3.86129i) q^{74} +(2.12132 - 2.12132i) q^{75} -3.06418i q^{76} +3.06418i q^{77} +(0.694593 - 0.694593i) q^{78} +(-10.5466 + 10.5466i) q^{79} +(-1.00000 - 1.00000i) q^{80} -1.00000 q^{81} +(3.25153 + 3.25153i) q^{82} +10.2980i q^{83} +3.06418 q^{84} +(-2.06418 + 5.45336i) q^{85} +0.119961 q^{86} -6.96567i q^{87} +(-0.707107 - 0.707107i) q^{88} -5.72259 q^{89} +(1.00000 + 1.00000i) q^{90} +(2.12836 - 2.12836i) q^{91} +(5.23088 - 5.23088i) q^{92} -6.25153i q^{93} +6.58493i q^{94} +(3.06418 - 3.06418i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(4.31570 + 4.31570i) 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	−0.985954	−	0.167018i	$-0.946586\pi$
$7$	−2.16670	+	2.16670i	−0.818936	+	0.818936i	0.167018	+	0.985954i	$0.446586\pi$
$8$		−	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	$-0.543496\pi$
$13$	−0.982302			−0.272442			−0.136221	+	0.990678i	$0.543496\pi$
$14$	−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
$23$	−5.23088	+	5.23088i	−1.09071	+	1.09071i	−0.0952613	+	0.995452i	$0.530369\pi$
$23$	−5.23088	+	5.23088i	−1.09071	+	1.09071i	−0.995452	+	0.0952613i	$0.969631\pi$
$24$	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
$29$	−4.92547	−	4.92547i	−0.914637	−	0.914637i	0.0819956	−	0.996633i	$-0.473871\pi$
$29$	−4.92547	−	4.92547i	−0.914637	−	0.914637i	−0.996633	+	0.0819956i	$0.973871\pi$
$30$	1.41421			0.258199
$31$	−4.42050	−	4.42050i	−0.793945	−	0.793945i	0.188188	−	0.982133i	$-0.439738\pi$
$31$	−4.42050	−	4.42050i	−0.793945	−	0.793945i	−0.982133	+	0.188188i	$0.939738\pi$
$32$			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
$37$	−3.86129	−	3.86129i	−0.634793	−	0.634793i	0.314473	−	0.949266i	$-0.398172\pi$
$37$	−3.86129	−	3.86129i	−0.634793	−	0.634793i	−0.949266	+	0.314473i	$0.898172\pi$
$38$	−3.06418			−0.497075
$39$	−0.694593	−	0.694593i	−0.111224	−	0.111224i
$40$	−1.00000	+	1.00000i	−0.158114	+	0.158114i
$41$	3.25153	−	3.25153i	0.507803	−	0.507803i	−0.406048	−	0.913852i	$-0.633094\pi$
$41$	3.25153	−	3.25153i	0.507803	−	0.507803i	0.913852	+	0.406048i	$0.133094\pi$
$42$		−	3.06418i		−	0.472813i
$43$		−	0.119961i		−	0.0182939i	−0.999958	−	0.00914697i	$-0.997088\pi$
$43$		−	0.119961i		−	0.0182939i	0.999958	−	0.00914697i	$-0.00291161\pi$
$44$	−0.707107	+	0.707107i	−0.106600	+	0.106600i
$45$	1.00000	−	1.00000i	0.149071	−	0.149071i
$46$	−5.23088	−	5.23088i	−0.771251	−	0.771251i
$47$	6.58493			0.960510			0.480255	−	0.877129i	$-0.340544\pi$
$47$	6.58493			0.960510			0.480255	+	0.877129i	$0.340544\pi$
$48$	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
$53$		−	0.878384i		−	0.120655i	−0.998179	−	0.0603277i	$-0.980785\pi$
$53$		−	0.878384i		−	0.120655i	0.998179	−	0.0603277i	$-0.0192146\pi$
$54$	−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
$58$	4.92547	−	4.92547i	0.646746	−	0.646746i
$59$		−	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
$61$	−5.04648	+	5.04648i	−0.646136	+	0.646136i	−0.952057	−	0.305921i	$-0.901036\pi$
$61$	−5.04648	+	5.04648i	−0.646136	+	0.646136i	0.305921	+	0.952057i	$0.401036\pi$
$62$	4.42050	−	4.42050i	0.561404	−	0.561404i
$63$	−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
$67$	−8.42636			−1.02944			−0.514722	−	0.857357i	$-0.672105\pi$
$67$	−8.42636			−1.02944			−0.514722	+	0.857357i	$0.672105\pi$
$68$	1.69459	+	3.75877i	0.205500	+	0.455818i
$69$	−7.39758			−0.890564
$70$			4.33340i			0.517941i
$71$	−1.18440	−	1.18440i	−0.140562	−	0.140562i	0.633324	−	0.773887i	$-0.281690\pi$
$71$	−1.18440	−	1.18440i	−0.140562	−	0.140562i	−0.773887	+	0.633324i	$0.781690\pi$
$72$	1.00000			0.117851
$73$	−2.38475	−	2.38475i	−0.279114	−	0.279114i	0.553641	−	0.832755i	$-0.313238\pi$
$73$	−2.38475	−	2.38475i	−0.279114	−	0.279114i	−0.832755	+	0.553641i	$0.813238\pi$
$74$	3.86129	−	3.86129i	0.448866	−	0.448866i
$75$	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
$79$	−10.5466	+	10.5466i	−1.18658	+	1.18658i	−0.208577	+	0.978006i	$0.566883\pi$
$79$	−10.5466	+	10.5466i	−1.18658	+	1.18658i	−0.978006	+	0.208577i	$0.933117\pi$
$80$	−1.00000	−	1.00000i	−0.111803	−	0.111803i
$81$	−1.00000			−0.111111
$82$	3.25153	+	3.25153i	0.359071	+	0.359071i
$83$			10.2980i			1.13035i	0.824970	+	0.565177i	$0.191192\pi$
$83$			10.2980i			1.13035i	−0.824970	+	0.565177i	$0.808808\pi$
$84$	3.06418			0.334329
$85$	−2.06418	+	5.45336i	−0.223892	+	0.591500i
$86$	0.119961			0.0129358
$87$		−	6.96567i		−	0.746798i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	−5.72259			−0.606593			−0.303297	−	0.952896i	$-0.598087\pi$
$89$	−5.72259			−0.606593			−0.303297	+	0.952896i	$0.598087\pi$
$90$	1.00000	+	1.00000i	0.105409	+	0.105409i
$91$	2.12836	−	2.12836i	0.223112	−	0.223112i
$92$	5.23088	−	5.23088i	0.545357	−	0.545357i
$93$		−	6.25153i		−	0.648253i
$94$			6.58493i			0.679183i
$95$	3.06418	−	3.06418i	0.314378	−	0.314378i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	4.31570	+	4.31570i	0.438193	+	0.438193i	0.891404	−	0.453210i	$-0.149721\pi$
$97$	4.31570	+	4.31570i	0.438193	+	0.438193i	−0.453210	+	0.891404i	$0.649721\pi$
$98$	2.38919			0.241344
$99$	0.707107	+	0.707107i	0.0710669	+	0.0710669i
$100$			3.00000i			0.300000i
$101$	8.80490			0.876121			0.438060	−	0.898946i	$-0.355666\pi$
$101$	8.80490			0.876121			0.438060	+	0.898946i	$0.355666\pi$
$102$	3.85611	+	1.45959i	0.381812	+	0.144521i
$103$	−7.68719			−0.757442			−0.378721	−	0.925511i	$-0.623636\pi$
$103$	−7.68719			−0.757442			−0.378721	+	0.925511i	$0.623636\pi$
$104$			0.982302i			0.0963227i
$105$	3.06418	+	3.06418i	0.299033	+	0.299033i
$106$	0.878384			0.0853162
$107$	0.746552	+	0.746552i	0.0721719	+	0.0721719i	0.742271	−	0.670099i	$-0.233749\pi$
$107$	0.746552	+	0.746552i	0.0721719	+	0.0721719i	−0.670099	+	0.742271i	$0.733749\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	0.269224	−	0.269224i	0.0257870	−	0.0257870i	−0.694096	−	0.719883i	$-0.744196\pi$
$109$	0.269224	−	0.269224i	0.0257870	−	0.0257870i	0.719883	+	0.694096i	$0.244196\pi$
$110$		−	1.41421i		−	0.134840i
$111$		−	5.46069i		−	0.518306i
$112$	−2.16670	+	2.16670i	−0.204734	+	0.204734i
$113$	4.97743	−	4.97743i	0.468237	−	0.468237i	−0.433106	−	0.901343i	$-0.642582\pi$
$113$	4.97743	−	4.97743i	0.468237	−	0.468237i	0.901343	+	0.433106i	$0.142582\pi$
$114$	−2.16670	−	2.16670i	−0.202930	−	0.202930i
$115$	10.4618			0.975564
$116$	4.92547	+	4.92547i	0.457319	+	0.457319i
$117$		−	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
$122$	−5.04648	−	5.04648i	−0.456887	−	0.456887i
$123$	4.59835			0.414620
$124$	4.42050	+	4.42050i	0.396972	+	0.396972i
$125$	−8.00000	+	8.00000i	−0.715542	+	0.715542i
$126$	2.16670	−	2.16670i	0.193025	−	0.193025i
$127$			10.4359i			0.926034i	0.886349	+	0.463017i	$0.153233\pi$
$127$			10.4359i			0.926034i	−0.886349	+	0.463017i	$0.846767\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.0848255	−	0.0848255i	0.00746847	−	0.00746847i
$130$	−0.982302	+	0.982302i	−0.0861536	+	0.0861536i
$131$	14.3924	+	14.3924i	1.25747	+	1.25747i	0.952295	+	0.305179i	$0.0987163\pi$
$131$	14.3924	+	14.3924i	1.25747	+	1.25747i	0.305179	+	0.952295i	$0.401284\pi$
$132$	−1.00000			−0.0870388
$133$	−6.63916	−	6.63916i	−0.575688	−	0.575688i
$134$		−	8.42636i		−	0.727927i
$135$	1.41421			0.121716
$136$	−3.75877	+	1.69459i	−0.322312	+	0.145310i
$137$	11.9549			1.02137			0.510686	−	0.859767i	$-0.329391\pi$
$137$	11.9549			1.02137			0.510686	+	0.859767i	$0.329391\pi$
$138$		−	7.39758i		−	0.629724i
$139$	−10.8014	−	10.8014i	−0.916165	−	0.916165i	0.0805829	−	0.996748i	$-0.474322\pi$
$139$	−10.8014	−	10.8014i	−0.916165	−	0.916165i	−0.996748	+	0.0805829i	$0.974322\pi$
$140$	−4.33340			−0.366239
$141$	4.65625	+	4.65625i	0.392127	+	0.392127i
$142$	1.18440	−	1.18440i	0.0993925	−	0.0993925i
$143$	−0.694593	+	0.694593i	−0.0580848	+	0.0580848i
$144$			1.00000i			0.0833333i
$145$			9.85094i			0.818076i
$146$	2.38475	−	2.38475i	0.197364	−	0.197364i
$147$	1.68941	−	1.68941i	0.139340	−	0.139340i
$148$	3.86129	+	3.86129i	0.317396	+	0.317396i
$149$	−12.6359			−1.03518			−0.517589	−	0.855630i	$-0.673170\pi$
$149$	−12.6359			−1.03518			−0.517589	+	0.855630i	$0.673170\pi$
$150$	2.12132	+	2.12132i	0.173205	+	0.173205i
$151$			11.6407i			0.947308i	0.880711	+	0.473654i	$0.157065\pi$
$151$			11.6407i			0.947308i	−0.880711	+	0.473654i	$0.842935\pi$
$152$	3.06418			0.248538
$153$	3.75877	−	1.69459i	0.303879	−	0.137000i
$154$	−3.06418			−0.246918
$155$			8.84099i			0.710126i
$156$	0.694593	+	0.694593i	0.0556119	+	0.0556119i
$157$	−9.71284			−0.775169			−0.387585	−	0.921834i	$-0.626691\pi$
$157$	−9.71284			−0.775169			−0.387585	+	0.921834i	$0.626691\pi$
$158$	−10.5466	−	10.5466i	−0.839041	−	0.839041i
$159$	0.621111	−	0.621111i	0.0492573	−	0.0492573i
$160$	1.00000	−	1.00000i	0.0790569	−	0.0790569i
$161$		−	22.6675i		−	1.78645i
$162$		−	1.00000i		−	0.0785674i
$163$	6.29949	−	6.29949i	0.493414	−	0.493414i	−0.415966	−	0.909380i	$-0.636557\pi$
$163$	6.29949	−	6.29949i	0.493414	−	0.493414i	0.909380	+	0.415966i	$0.136557\pi$
$164$	−3.25153	+	3.25153i	−0.253902	+	0.253902i
$165$	−1.00000	−	1.00000i	−0.0778499	−	0.0778499i
$166$	−10.2980			−0.799280
$167$	5.29888	+	5.29888i	0.410040	+	0.410040i	0.881752	−	0.471713i	$-0.156364\pi$
$167$	5.29888	+	5.29888i	0.410040	+	0.410040i	−0.471713	+	0.881752i	$0.656364\pi$
$168$			3.06418i			0.236406i
$169$	−12.0351			−0.925776
$170$	−5.45336	−	2.06418i	−0.418254	−	0.158315i
$171$	−3.06418			−0.234324
$172$			0.119961i			0.00914697i
$173$	2.18519	+	2.18519i	0.166137	+	0.166137i	0.785279	−	0.619142i	$-0.212520\pi$
$173$	2.18519	+	2.18519i	0.166137	+	0.166137i	−0.619142	+	0.785279i	$0.712520\pi$
$174$	6.96567			0.528066
$175$	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
$178$		−	5.72259i		−	0.428926i
$179$		−	1.26922i		−	0.0948663i	−0.998874	−	0.0474331i	$-0.984896\pi$
$179$		−	1.26922i		−	0.0948663i	0.998874	−	0.0474331i	$-0.0151041\pi$
$180$	−1.00000	+	1.00000i	−0.0745356	+	0.0745356i
$181$	3.82590	−	3.82590i	0.284377	−	0.284377i	−0.550475	−	0.834852i	$-0.685553\pi$
$181$	3.82590	−	3.82590i	0.284377	−	0.284377i	0.834852	+	0.550475i	$0.185553\pi$
$182$	2.12836	+	2.12836i	0.157764	+	0.157764i
$183$	−7.13680			−0.527567
$184$	5.23088	+	5.23088i	0.385625	+	0.385625i
$185$			7.72259i			0.567776i
$186$	6.25153			0.458384
$187$	−3.85611	−	1.45959i	−0.281987	−	0.106736i
$188$	−6.58493			−0.480255
$189$		−	3.06418i		−	0.222886i
$190$	3.06418	+	3.06418i	0.222299	+	0.222299i
$191$	16.5495			1.19748			0.598741	−	0.800943i	$-0.295668\pi$
$191$	16.5495			1.19748			0.598741	+	0.800943i	$0.295668\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−15.2290	+	15.2290i	−1.09620	+	1.09620i	−0.101354	+	0.994850i	$0.532317\pi$
$193$	−15.2290	+	15.2290i	−1.09620	+	1.09620i	−0.994850	+	0.101354i	$0.967683\pi$
$194$	−4.31570	+	4.31570i	−0.309850	+	0.309850i
$195$			1.38919i			0.0994816i
$196$			2.38919i			0.170656i
$197$	4.14710	−	4.14710i	0.295469	−	0.295469i	−0.543767	−	0.839236i	$-0.683003\pi$
$197$	4.14710	−	4.14710i	0.295469	−	0.295469i	0.839236	+	0.543767i	$0.183003\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	−9.85937	−	9.85937i	−0.698912	−	0.698912i	0.265264	−	0.964176i	$-0.414541\pi$
$199$	−9.85937	−	9.85937i	−0.698912	−	0.698912i	−0.964176	+	0.265264i	$0.914541\pi$
$200$	−3.00000			−0.212132
$201$	−5.95834	−	5.95834i	−0.420269	−	0.420269i
$202$			8.80490i			0.619511i
$203$	21.3440			1.49806
$204$	−1.45959	+	3.85611i	−0.102192	+	0.269982i
$205$	−6.50305			−0.454193
$206$		−	7.68719i		−	0.535592i
$207$	−5.23088	−	5.23088i	−0.363571	−	0.363571i
$208$	−0.982302			−0.0681104
$209$	2.16670	+	2.16670i	0.149874	+	0.149874i
$210$	−3.06418	+	3.06418i	−0.211448	+	0.211448i
$211$	−0.285440	+	0.285440i	−0.0196505	+	0.0196505i	−0.716864	−	0.697213i	$-0.754423\pi$
$211$	−0.285440	+	0.285440i	−0.0196505	+	0.0196505i	0.697213	+	0.716864i	$0.254423\pi$
$212$			0.878384i			0.0603277i
$213$		−	1.67499i		−	0.114769i
$214$	−0.746552	+	0.746552i	−0.0510332	+	0.0510332i
$215$	−0.119961	+	0.119961i	−0.00818130	+	0.00818130i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	19.1558			1.30038
$218$	0.269224	+	0.269224i	0.0182341	+	0.0182341i
$219$		−	3.37255i		−	0.227896i
$220$	1.41421			0.0953463
$221$	1.66460	+	3.69225i	0.111973	+	0.248368i
$222$	5.46069			0.366498
$223$			5.72259i			0.383213i	0.981472	+	0.191606i	$0.0613697\pi$
$223$			5.72259i			0.383213i	−0.981472	+	0.191606i	$0.938630\pi$
$224$	−2.16670	−	2.16670i	−0.144769	−	0.144769i
$225$	3.00000			0.200000
$226$	4.97743	+	4.97743i	0.331094	+	0.331094i
$227$	−18.5775	+	18.5775i	−1.23304	+	1.23304i	−0.270243	+	0.962792i	$0.587104\pi$
$227$	−18.5775	+	18.5775i	−1.23304	+	1.23304i	−0.962792	+	0.270243i	$0.912896\pi$
$228$	2.16670	−	2.16670i	0.143493	−	0.143493i
$229$			15.9342i			1.05296i	0.850188	+	0.526479i	$0.176488\pi$
$229$			15.9342i			1.05296i	−0.850188	+	0.526479i	$0.823512\pi$
$230$			10.4618i			0.689828i
$231$	−2.16670	+	2.16670i	−0.142558	+	0.142558i
$232$	−4.92547	+	4.92547i	−0.323373	+	0.323373i
$233$	−15.1748	−	15.1748i	−0.994137	−	0.994137i	0.00584637	−	0.999983i	$-0.498139\pi$
$233$	−15.1748	−	15.1748i	−0.994137	−	0.994137i	−0.999983	+	0.00584637i	$0.998139\pi$
$234$	0.982302			0.0642151
$235$	−6.58493	−	6.58493i	−0.429553	−	0.429553i
$236$			12.4534i			0.810645i
$237$	−14.9151			−0.968841
$238$	−4.47246	+	11.8158i	−0.289906	+	0.765905i
$239$	−0.174190			−0.0112674			−0.00563370	−	0.999984i	$-0.501793\pi$
$239$	−0.174190			−0.0112674			−0.00563370	+	0.999984i	$0.501793\pi$
$240$		−	1.41421i		−	0.0912871i
$241$	−0.761299	−	0.761299i	−0.0490396	−	0.0490396i	0.682162	−	0.731201i	$-0.261040\pi$
$241$	−0.761299	−	0.761299i	−0.0490396	−	0.0490396i	−0.731201	+	0.682162i	$0.761040\pi$
$242$	1.00000			0.0642824
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	5.04648	−	5.04648i	0.323068	−	0.323068i
$245$	−2.38919	+	2.38919i	−0.152639	+	0.152639i
$246$			4.59835i			0.293180i
$247$		−	3.00995i		−	0.191518i
$248$	−4.42050	+	4.42050i	−0.280702	+	0.280702i
$249$	−7.28179	+	7.28179i	−0.461465	+	0.461465i
$250$	−8.00000	−	8.00000i	−0.505964	−	0.505964i
$251$	−12.8145			−0.808845			−0.404422	−	0.914572i	$-0.632527\pi$
$251$	−12.8145			−0.808845			−0.404422	+	0.914572i	$0.632527\pi$
$252$	2.16670	+	2.16670i	0.136489	+	0.136489i
$253$			7.39758i			0.465082i
$254$	−10.4359			−0.654805
$255$	−5.31570	+	2.39652i	−0.332882	+	0.150076i
$256$	1.00000			0.0625000
$257$			23.6058i			1.47249i	0.676715	+	0.736245i	$0.263403\pi$
$257$			23.6058i			1.47249i	−0.676715	+	0.736245i	$0.736597\pi$
$258$	0.0848255	+	0.0848255i	0.00528101	+	0.00528101i
$259$	16.7325			1.03971
$260$	−0.982302	−	0.982302i	−0.0609198	−	0.0609198i
$261$	4.92547	−	4.92547i	0.304879	−	0.304879i
$262$	−14.3924	+	14.3924i	−0.889168	+	0.889168i
$263$		−	3.32276i		−	0.204890i	−0.994739	−	0.102445i	$-0.967333\pi$
$263$		−	3.32276i		−	0.204890i	0.994739	−	0.102445i	$-0.0326666\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	−0.878384	+	0.878384i	−0.0539587	+	0.0539587i
$266$	6.63916	−	6.63916i	0.407073	−	0.407073i
$267$	−4.04648	−	4.04648i	−0.247641	−	0.247641i
$268$	8.42636			0.514722
$269$	−12.0383	−	12.0383i	−0.733988	−	0.733988i	0.237420	−	0.971407i	$-0.423698\pi$
$269$	−12.0383	−	12.0383i	−0.733988	−	0.733988i	−0.971407	+	0.237420i	$0.923698\pi$
$270$			1.41421i			0.0860663i
$271$	23.1796			1.40806			0.704030	−	0.710171i	$-0.251382\pi$
$271$	23.1796			1.40806			0.704030	+	0.710171i	$0.251382\pi$
$272$	−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
$276$	7.39758			0.445282
$277$	17.9810	+	17.9810i	1.08037	+	1.08037i	0.996474	+	0.0838962i	$0.0267364\pi$
$277$	17.9810	+	17.9810i	1.08037	+	1.08037i	0.0838962	+	0.996474i	$0.473264\pi$
$278$	10.8014	−	10.8014i	0.647826	−	0.647826i
$279$	4.42050	−	4.42050i	0.264648	−	0.264648i
$280$		−	4.33340i		−	0.258970i
$281$			2.05757i			0.122744i	0.998115	+	0.0613720i	$0.0195476\pi$
$281$			2.05757i			0.122744i	−0.998115	+	0.0613720i	$0.980452\pi$
$282$	−4.65625	+	4.65625i	−0.277275	+	0.277275i
$283$	−13.1264	+	13.1264i	−0.780285	+	0.780285i	−0.979879	−	0.199593i	$-0.936038\pi$
$283$	−13.1264	+	13.1264i	−0.780285	+	0.780285i	0.199593	+	0.979879i	$0.436038\pi$
$284$	1.18440	+	1.18440i	0.0702811	+	0.0702811i
$285$	4.33340			0.256689
$286$	−0.694593	−	0.694593i	−0.0410721	−	0.0410721i
$287$			14.0902i			0.831716i
$288$	−1.00000			−0.0589256
$289$	−11.2567	+	12.7392i	−0.662159	+	0.749363i
$290$	−9.85094			−0.578467
$291$			6.10333i			0.357783i
$292$	2.38475	+	2.38475i	0.139557	+	0.139557i
$293$	−23.5195			−1.37403			−0.687013	−	0.726645i	$-0.741078\pi$
$293$	−23.5195			−1.37403			−0.687013	+	0.726645i	$0.741078\pi$
$294$	1.68941	+	1.68941i	0.0985283	+	0.0985283i
$295$	−12.4534	+	12.4534i	−0.725063	+	0.725063i
$296$	−3.86129	+	3.86129i	−0.224433	+	0.224433i
$297$			1.00000i			0.0580259i
$298$		−	12.6359i		−	0.731981i
$299$	5.13830	−	5.13830i	0.297156	−	0.297156i
$300$	−2.12132	+	2.12132i	−0.122474	+	0.122474i
$301$	0.259921	+	0.259921i	0.0149816	+	0.0149816i
$302$	−11.6407			−0.669848
$303$	6.22601	+	6.22601i	0.357675	+	0.357675i
$304$			3.06418i			0.175743i
$305$	10.0930			0.577921
$306$	1.69459	+	3.75877i	0.0968734	+	0.214875i
$307$	22.6680			1.29373			0.646867	−	0.762603i	$-0.276079\pi$
$307$	22.6680			1.29373			0.646867	+	0.762603i	$0.276079\pi$
$308$		−	3.06418i		−	0.174598i
$309$	−5.43567	−	5.43567i	−0.309224	−	0.309224i
$310$	−8.84099			−0.502135
$311$	−12.0835	−	12.0835i	−0.685191	−	0.685191i	0.275974	−	0.961165i	$-0.411000\pi$
$311$	−12.0835	−	12.0835i	−0.685191	−	0.685191i	−0.961165	+	0.275974i	$0.911000\pi$
$312$	−0.694593	+	0.694593i	−0.0393236	+	0.0393236i
$313$	3.94422	−	3.94422i	0.222940	−	0.222940i	−0.586795	−	0.809735i	$-0.699611\pi$
$313$	3.94422	−	3.94422i	0.222940	−	0.222940i	0.809735	+	0.586795i	$0.199611\pi$
$314$		−	9.71284i		−	0.548127i
$315$			4.33340i			0.244160i
$316$	10.5466	−	10.5466i	0.593292	−	0.593292i
$317$	20.1363	−	20.1363i	1.13097	−	1.13097i	0.140951	−	0.990017i	$-0.454984\pi$
$317$	20.1363	−	20.1363i	1.13097	−	1.13097i	0.990017	−	0.140951i	$-0.0450161\pi$
$318$	0.621111	+	0.621111i	0.0348302	+	0.0348302i
$319$	−6.96567			−0.390003
$320$	1.00000	+	1.00000i	0.0559017	+	0.0559017i
$321$			1.05578i			0.0589281i
$322$	22.6675			1.26321
$323$	11.5175	−	5.19253i	0.640853	−	0.288920i
$324$	1.00000			0.0555556
$325$			2.94691i			0.163465i
$326$	6.29949	+	6.29949i	0.348896	+	0.348896i
$327$	0.380740			0.0210550
$328$	−3.25153	−	3.25153i	−0.179536	−	0.179536i
$329$	−14.2676	+	14.2676i	−0.786597	+	0.786597i
$330$	1.00000	−	1.00000i	0.0550482	−	0.0550482i
$331$		−	21.7028i		−	1.19289i	−0.802653	−	0.596446i	$-0.796579\pi$
$331$		−	21.7028i		−	1.19289i	0.802653	−	0.596446i	$-0.203421\pi$
$332$		−	10.2980i		−	0.565177i
$333$	3.86129	−	3.86129i	0.211598	−	0.211598i
$334$	−5.29888	+	5.29888i	−0.289942	+	0.289942i
$335$	8.42636	+	8.42636i	0.460381	+	0.460381i
$336$	−3.06418			−0.167165
$337$	14.9857	+	14.9857i	0.816324	+	0.816324i	0.985573	−	0.169249i	$-0.0541342\pi$
$337$	14.9857	+	14.9857i	0.816324	+	0.816324i	−0.169249	+	0.985573i	$0.554134\pi$
$338$		−	12.0351i		−	0.654622i
$339$	7.03915			0.382314
$340$	2.06418	−	5.45336i	0.111946	−	0.295750i
$341$	−6.25153			−0.338539
$342$		−	3.06418i		−	0.165692i
$343$	−9.99026	−	9.99026i	−0.539423	−	0.539423i
$344$	−0.119961			−0.00646789
$345$	7.39758	+	7.39758i	0.398272	+	0.398272i
$346$	−2.18519	+	2.18519i	−0.117476	+	0.117476i
$347$	9.38180	−	9.38180i	0.503642	−	0.503642i	−0.408926	−	0.912568i	$-0.634097\pi$
$347$	9.38180	−	9.38180i	0.503642	−	0.503642i	0.912568	+	0.408926i	$0.134097\pi$
$348$			6.96567i			0.373399i
$349$		−	21.5729i		−	1.15477i	−0.816471	−	0.577386i	$-0.804073\pi$
$349$		−	21.5729i		−	1.15477i	0.816471	−	0.577386i	$-0.195927\pi$
$350$	−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
$353$	−18.6778			−0.994117			−0.497058	−	0.867717i	$-0.665587\pi$
$353$	−18.6778			−0.994117			−0.497058	+	0.867717i	$0.665587\pi$
$354$	8.80586	+	8.80586i	0.468026	+	0.468026i
$355$			2.36880i			0.125723i
$356$	5.72259			0.303297
$357$	5.19253	+	11.5175i	0.274818	+	0.609573i
$358$	1.26922			0.0670806
$359$		−	1.42927i		−	0.0754338i	−0.999288	−	0.0377169i	$-0.987991\pi$
$359$		−	1.42927i		−	0.0754338i	0.999288	−	0.0377169i	$-0.0120085\pi$
$360$	−1.00000	−	1.00000i	−0.0527046	−	0.0527046i
$361$	9.61081			0.505832
$362$	3.82590	+	3.82590i	0.201085	+	0.201085i
$363$	0.707107	−	0.707107i	0.0371135	−	0.0371135i
$364$	−2.12836	+	2.12836i	−0.111556	+	0.111556i
$365$			4.76951i			0.249647i
$366$		−	7.13680i		−	0.373047i
$367$	−7.02035	+	7.02035i	−0.366459	+	0.366459i	−0.866184	−	0.499725i	$-0.833434\pi$
$367$	−7.02035	+	7.02035i	−0.366459	+	0.366459i	0.499725	+	0.866184i	$0.333434\pi$
$368$	−5.23088	+	5.23088i	−0.272678	+	0.272678i
$369$	3.25153	+	3.25153i	0.169268	+	0.169268i
$370$	−7.72259			−0.401478
$371$	1.90320	+	1.90320i	0.0988090	+	0.0988090i
$372$			6.25153i			0.324127i
$373$	18.9469			0.981034			0.490517	−	0.871432i	$-0.336808\pi$
$373$	18.9469			0.981034			0.490517	+	0.871432i	$0.336808\pi$
$374$	1.45959	−	3.85611i	0.0754738	−	0.199395i
$375$	−11.3137			−0.584237
$376$		−	6.58493i		−	0.339592i
$377$	4.83830	+	4.83830i	0.249185	+	0.249185i
$378$	3.06418			0.157604
$379$	−15.3256	−	15.3256i	−0.787222	−	0.787222i	0.193816	−	0.981038i	$-0.437914\pi$
$379$	−15.3256	−	15.3256i	−0.787222	−	0.787222i	−0.981038	+	0.193816i	$0.937914\pi$
$380$	−3.06418	+	3.06418i	−0.157189	+	0.157189i
$381$	−7.37928	+	7.37928i	−0.378052	+	0.378052i
$382$			16.5495i			0.846748i
$383$			10.5534i			0.539252i	0.962965	+	0.269626i	$0.0869001\pi$
$383$			10.5534i			0.539252i	−0.962965	+	0.269626i	$0.913100\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	3.06418	−	3.06418i	0.156165	−	0.156165i
$386$	−15.2290	−	15.2290i	−0.775133	−	0.775133i
$387$	0.119961			0.00609798
$388$	−4.31570	−	4.31570i	−0.219097	−	0.219097i
$389$		−	13.2491i		−	0.671756i	−0.941906	−	0.335878i	$-0.890967\pi$
$389$		−	13.2491i		−	0.671756i	0.941906	−	0.335878i	$-0.109033\pi$
$390$	−1.38919			−0.0703441
$391$	28.5259	+	10.7975i	1.44262	+	0.546051i
$392$	−2.38919			−0.120672
$393$			20.3540i			1.02672i
$394$	4.14710	+	4.14710i	0.208928	+	0.208928i
$395$	21.0932			1.06131
$396$	−0.707107	−	0.707107i	−0.0355335	−	0.0355335i
$397$	−21.7554	+	21.7554i	−1.09187	+	1.09187i	−0.0965423	+	0.995329i	$0.530778\pi$
$397$	−21.7554	+	21.7554i	−1.09187	+	1.09187i	−0.995329	+	0.0965423i	$0.969222\pi$
$398$	9.85937	−	9.85937i	0.494206	−	0.494206i
$399$		−	9.38919i		−	0.470047i
$400$		−	3.00000i		−	0.150000i
$401$	−3.68738	+	3.68738i	−0.184139	+	0.184139i	−0.793157	−	0.609018i	$-0.791564\pi$
$401$	−3.68738	+	3.68738i	−0.184139	+	0.184139i	0.609018	+	0.793157i	$0.291564\pi$
$402$	5.95834	−	5.95834i	0.297175	−	0.297175i
$403$	4.34226	+	4.34226i	0.216304	+	0.216304i
$404$	−8.80490			−0.438060
$405$	1.00000	+	1.00000i	0.0496904	+	0.0496904i
$406$			21.3440i			1.05929i
$407$	−5.46069			−0.270677
$408$	−3.85611	−	1.45959i	−0.190906	−	0.0722607i
$409$	3.89939			0.192812			0.0964062	−	0.995342i	$-0.469265\pi$
$409$	3.89939			0.192812			0.0964062	+	0.995342i	$0.469265\pi$
$410$		−	6.50305i		−	0.321163i
$411$	8.45336	+	8.45336i	0.416974	+	0.416974i
$412$	7.68719			0.378721
$413$	26.9827	+	26.9827i	1.32773	+	1.32773i
$414$	5.23088	−	5.23088i	0.257084	−	0.257084i
$415$	10.2980	−	10.2980i	0.505509	−	0.505509i
$416$		−	0.982302i		−	0.0481613i
$417$		−	15.2755i		−	0.748046i
$418$	−2.16670	+	2.16670i	−0.105977	+	0.105977i
$419$	25.3335	−	25.3335i	1.23762	−	1.23762i	0.276649	−	0.960971i	$-0.410776\pi$
$419$	25.3335	−	25.3335i	1.23762	−	1.23762i	0.960971	−	0.276649i	$-0.0892240\pi$
$420$	−3.06418	−	3.06418i	−0.149517	−	0.149517i
$421$	−14.1195			−0.688142			−0.344071	−	0.938944i	$-0.611806\pi$
$421$	−14.1195			−0.688142			−0.344071	+	0.938944i	$0.611806\pi$
$422$	−0.285440	−	0.285440i	−0.0138950	−	0.0138950i
$423$			6.58493i			0.320170i
$424$	−0.878384			−0.0426581
$425$	−11.2763	+	5.08378i	−0.546981	+	0.246599i
$426$	1.67499			0.0811536
$427$		−	21.8684i		−	1.05829i
$428$	−0.746552	−	0.746552i	−0.0360859	−	0.0360859i
$429$	−0.982302			−0.0474260
$430$	−0.119961	−	0.119961i	−0.00578505	−	0.00578505i
$431$	7.28914	−	7.28914i	0.351105	−	0.351105i	−0.509415	−	0.860521i	$-0.670138\pi$
$431$	7.28914	−	7.28914i	0.351105	−	0.351105i	0.860521	+	0.509415i	$0.170138\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$		−	13.9845i		−	0.672052i	−0.941853	−	0.336026i	$-0.890917\pi$
$433$		−	13.9845i		−	0.672052i	0.941853	−	0.336026i	$-0.109083\pi$
$434$			19.1558i			0.919507i
$435$	−6.96567	+	6.96567i	−0.333978	+	0.333978i
$436$	−0.269224	+	0.269224i	−0.0128935	+	0.0128935i
$437$	−16.0283	−	16.0283i	−0.766740	−	0.766740i
$438$	3.37255			0.161147
$439$	−25.7564	−	25.7564i	−1.22928	−	1.22928i	−0.964235	−	0.265050i	$-0.914612\pi$
$439$	−25.7564	−	25.7564i	−1.22928	−	1.22928i	−0.265050	−	0.964235i	$-0.585388\pi$
$440$			1.41421i			0.0674200i
$441$	2.38919			0.113771
$442$	−3.69225	+	1.66460i	−0.175622	+	0.0791771i
$443$	19.5542			0.929047			0.464524	−	0.885561i	$-0.346226\pi$
$443$	19.5542			0.929047			0.464524	+	0.885561i	$0.346226\pi$
$444$			5.46069i			0.259153i
$445$	5.72259	+	5.72259i	0.271277	+	0.271277i
$446$	−5.72259			−0.270972
$447$	−8.93496	−	8.93496i	−0.422609	−	0.422609i
$448$	2.16670	−	2.16670i	0.102367	−	0.102367i
$449$	−17.3657	+	17.3657i	−0.819538	+	0.819538i	−0.986041	−	0.166503i	$-0.946753\pi$
$449$	−17.3657	+	17.3657i	−0.819538	+	0.819538i	0.166503	+	0.986041i	$0.446753\pi$
$450$			3.00000i			0.141421i
$451$		−	4.59835i		−	0.216528i
$452$	−4.97743	+	4.97743i	−0.234119	+	0.234119i
$453$	−8.23123	+	8.23123i	−0.386737	+	0.386737i
$454$	−18.5775	−	18.5775i	−0.871887	−	0.871887i
$455$	−4.25671			−0.199558
$456$	2.16670	+	2.16670i	0.101465	+	0.101465i
$457$			9.53008i			0.445798i	0.974842	+	0.222899i	$0.0715520\pi$
$457$			9.53008i			0.445798i	−0.974842	+	0.222899i	$0.928448\pi$
$458$	−15.9342			−0.744554
$459$	3.85611	+	1.45959i	0.179988	+	0.0681280i
$460$	−10.4618			−0.487782
$461$			41.2567i			1.92152i	0.277385	+	0.960759i	$0.410532\pi$
$461$			41.2567i			1.92152i	−0.277385	+	0.960759i	$0.589468\pi$
$462$	−2.16670	−	2.16670i	−0.100804	−	0.100804i
$463$	1.79949			0.0836295			0.0418148	−	0.999125i	$-0.486686\pi$
$463$	1.79949			0.0836295			0.0418148	+	0.999125i	$0.486686\pi$
$464$	−4.92547	−	4.92547i	−0.228659	−	0.228659i
$465$	−6.25153	+	6.25153i	−0.289908	+	0.289908i
$466$	15.1748	−	15.1748i	0.702961	−	0.702961i
$467$		−	15.1512i		−	0.701116i	−0.936541	−	0.350558i	$-0.885992\pi$
$467$		−	15.1512i		−	0.701116i	0.936541	−	0.350558i	$-0.114008\pi$
$468$			0.982302i			0.0454069i
$469$	18.2574	−	18.2574i	0.843049	−	0.843049i
$470$	6.58493	−	6.58493i	0.303740	−	0.303740i
$471$	−6.86802	−	6.86802i	−0.316462	−	0.316462i
$472$	−12.4534			−0.573213
$473$	−0.0848255	−	0.0848255i	−0.00390028	−	0.00390028i
$474$		−	14.9151i		−	0.685074i
$475$	9.19253			0.421782
$476$	−11.8158	−	4.47246i	−0.541577	−	0.204995i
$477$	0.878384			0.0402185
$478$		−	0.174190i		−	0.00796726i
$479$	25.5711	+	25.5711i	1.16837	+	1.16837i	0.982591	+	0.185783i	$0.0594820\pi$
$479$	25.5711	+	25.5711i	1.16837	+	1.16837i	0.185783	+	0.982591i	$0.440518\pi$
$480$	1.41421			0.0645497
$481$	3.79296	+	3.79296i	0.172944	+	0.172944i
$482$	0.761299	−	0.761299i	0.0346762	−	0.0346762i
$483$	16.0283	−	16.0283i	0.729315	−	0.729315i
$484$			1.00000i			0.0454545i
$485$		−	8.63141i		−	0.391932i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	4.95055	−	4.95055i	0.224331	−	0.224331i	−0.585989	−	0.810319i	$-0.699294\pi$
$487$	4.95055	−	4.95055i	0.224331	−	0.224331i	0.810319	+	0.585989i	$0.199294\pi$
$488$	5.04648	+	5.04648i	0.228443	+	0.228443i
$489$	8.90882			0.402871
$490$	−2.38919	−	2.38919i	−0.107932	−	0.107932i
$491$		−	43.0252i		−	1.94170i	−0.239685	−	0.970851i	$-0.577044\pi$
$491$		−	43.0252i		−	1.94170i	0.239685	−	0.970851i	$-0.422956\pi$
$492$	−4.59835			−0.207310
$493$	−10.1670	+	26.8604i	−0.457901	+	1.20973i
$494$	3.00995			0.135424
$495$		−	1.41421i		−	0.0635642i
$496$	−4.42050	−	4.42050i	−0.198486	−	0.198486i
$497$	5.13247			0.230223
$498$	−7.28179	−	7.28179i	−0.326305	−	0.326305i
$499$	−6.13193	+	6.13193i	−0.274503	+	0.274503i	−0.830910	−	0.556407i	$-0.812180\pi$
$499$	−6.13193	+	6.13193i	−0.274503	+	0.274503i	0.556407	+	0.830910i	$0.312180\pi$
$500$	8.00000	−	8.00000i	0.357771	−	0.357771i
$501$			7.49375i			0.334796i
$502$		−	12.8145i		−	0.571940i
$503$	−8.39671	+	8.39671i	−0.374391	+	0.374391i	−0.869074	−	0.494683i	$-0.835284\pi$
$503$	−8.39671	+	8.39671i	−0.374391	+	0.374391i	0.494683	+	0.869074i	$0.335284\pi$
$504$	−2.16670	+	2.16670i	−0.0965125	+	0.0965125i
$505$	−8.80490	−	8.80490i	−0.391813	−	0.391813i
$506$	−7.39758			−0.328863
$507$	−8.51009	−	8.51009i	−0.377946	−	0.377946i
$508$		−	10.4359i		−	0.463017i
$509$	−3.88449			−0.172177			−0.0860885	−	0.996287i	$-0.527437\pi$
$509$	−3.88449			−0.172177			−0.0860885	+	0.996287i	$0.527437\pi$
$510$	−2.39652	−	5.31570i	−0.106120	−	0.235383i
$511$	10.3341			0.457154
$512$			1.00000i			0.0441942i
$513$	−2.16670	−	2.16670i	−0.0956622	−	0.0956622i
$514$	−23.6058			−1.04121
$515$	7.68719	+	7.68719i	0.338738	+	0.338738i
$516$	−0.0848255	+	0.0848255i	−0.00373424	+	0.00373424i
$517$	4.65625	−	4.65625i	0.204782	−	0.204782i
$518$			16.7325i			0.735185i
$519$			3.09032i			0.135650i
$520$	0.982302	−	0.982302i	0.0430768	−	0.0430768i
$521$	16.7078	−	16.7078i	0.731981	−	0.731981i	−0.239031	−	0.971012i	$-0.576830\pi$
$521$	16.7078	−	16.7078i	0.731981	−	0.731981i	0.971012	+	0.239031i	$0.0768299\pi$
$522$	4.92547	+	4.92547i	0.215582	+	0.215582i
$523$	3.35514			0.146710			0.0733550	−	0.997306i	$-0.476629\pi$
$523$	3.35514			0.146710			0.0733550	+	0.997306i	$0.476629\pi$
$524$	−14.3924	−	14.3924i	−0.628737	−	0.628737i
$525$			9.19253i			0.401195i
$526$	3.32276			0.144879
$527$	−9.12469	+	24.1066i	−0.397478	+	1.05010i
$528$	1.00000			0.0435194
$529$		−	31.7242i		−	1.37931i
$530$	−0.878384	−	0.878384i	−0.0381546	−	0.0381546i
$531$	12.4534			0.540430
$532$	6.63916	+	6.63916i	0.287844	+	0.287844i
$533$	−3.19398	+	3.19398i	−0.138347	+	0.138347i
$534$	4.04648	−	4.04648i	0.175108	−	0.175108i
$535$		−	1.49310i		−	0.0645525i
$536$			8.42636i			0.363963i
$537$	0.897477	−	0.897477i	0.0387290	−	0.0387290i
$538$	12.0383	−	12.0383i	0.519008	−	0.519008i
$539$	−1.68941	−	1.68941i	−0.0727680	−	0.0727680i
$540$	−1.41421			−0.0608581
$541$	−27.1973	−	27.1973i	−1.16930	−	1.16930i	−0.982373	−	0.186929i	$-0.940147\pi$
$541$	−27.1973	−	27.1973i	−1.16930	−	1.16930i	−0.186929	−	0.982373i	$-0.559853\pi$
$542$			23.1796i			0.995648i
$543$	5.41064			0.232193
$544$	3.75877	−	1.69459i	0.161156	−	0.0726551i
$545$	−0.538448			−0.0230646
$546$			3.00995i			0.128814i
$547$	23.4119	+	23.4119i	1.00102	+	1.00102i	0.999999	+	0.00102135i	$0.000325106\pi$
$547$	23.4119	+	23.4119i	1.00102	+	1.00102i	0.00102135	+	0.999999i	$0.499675\pi$
$548$	−11.9549			−0.510686
$549$	−5.04648	−	5.04648i	−0.215379	−	0.215379i
$550$	2.12132	−	2.12132i	0.0904534	−	0.0904534i
$551$	15.0925	−	15.0925i	0.642963	−	0.642963i
$552$			7.39758i			0.314862i
$553$		−	45.7026i		−	1.94347i
$554$	−17.9810	+	17.9810i	−0.763937	+	0.763937i
$555$	−5.46069	+	5.46069i	−0.231794	+	0.231794i
$556$	10.8014	+	10.8014i	0.458083	+	0.458083i
$557$	−38.1399			−1.61604			−0.808020	−	0.589155i	$-0.799461\pi$
$557$	−38.1399			−1.61604			−0.808020	+	0.589155i	$0.799461\pi$
$558$	4.42050	+	4.42050i	0.187135	+	0.187135i
$559$			0.117838i			0.00498403i
$560$	4.33340			0.183120
$561$	−1.69459	−	3.75877i	−0.0715458	−	0.158695i
$562$	−2.05757			−0.0867932
$563$		−	5.22407i		−	0.220168i	−0.993922	−	0.110084i	$-0.964888\pi$
$563$		−	5.22407i		−	0.220168i	0.993922	−	0.110084i	$-0.0351121\pi$
$564$	−4.65625	−	4.65625i	−0.196063	−	0.196063i
$565$	−9.95486			−0.418804
$566$	−13.1264	−	13.1264i	−0.551745	−	0.551745i
$567$	2.16670	−	2.16670i	0.0909929	−	0.0909929i
$568$	−1.18440	+	1.18440i	−0.0496963	+	0.0496963i
$569$		−	38.9988i		−	1.63491i	−0.575989	−	0.817457i	$-0.695383\pi$
$569$		−	38.9988i		−	1.63491i	0.575989	−	0.817457i	$-0.304617\pi$
$570$			4.33340i			0.181506i
$571$	26.0150	−	26.0150i	1.08869	−	1.08869i	0.0930316	−	0.995663i	$-0.470344\pi$
$571$	26.0150	−	26.0150i	1.08869	−	1.08869i	0.995663	−	0.0930316i	$-0.0296558\pi$
$572$	0.694593	−	0.694593i	0.0290424	−	0.0290424i
$573$	11.7023	+	11.7023i	0.488870	+	0.488870i
$574$	−14.0902			−0.588112
$575$	15.6926	+	15.6926i	0.654428	+	0.654428i
$576$		−	1.00000i		−	0.0416667i
$577$	35.0220			1.45799			0.728993	−	0.684521i	$-0.239989\pi$
$577$	35.0220			1.45799			0.728993	+	0.684521i	$0.239989\pi$
$578$	−12.7392	−	11.2567i	−0.529880	−	0.468217i
$579$	−21.5370			−0.895047
$580$		−	9.85094i		−	0.409038i
$581$	−22.3127	−	22.3127i	−0.925687	−	0.925687i
$582$	−6.10333			−0.252991
$583$	−0.621111	−	0.621111i	−0.0257238	−	0.0257238i
$584$	−2.38475	+	2.38475i	−0.0986818	+	0.0986818i
$585$	−0.982302	+	0.982302i	−0.0406132	+	0.0406132i
$586$		−	23.5195i		−	0.971583i
$587$		−	28.4658i		−	1.17491i	−0.809257	−	0.587455i	$-0.800130\pi$
$587$		−	28.4658i		−	1.17491i	0.809257	−	0.587455i	$-0.199870\pi$
$588$	−1.68941	+	1.68941i	−0.0696701	+	0.0696701i
$589$	13.5452	−	13.5452i	0.558120	−	0.558120i
$590$	−12.4534	−	12.4534i	−0.512697	−	0.512697i
$591$	5.86489			0.241249
$592$	−3.86129	−	3.86129i	−0.158698	−	0.158698i
$593$		−	20.3160i		−	0.834278i	−0.908843	−	0.417139i	$-0.863033\pi$
$593$		−	20.3160i		−	0.834278i	0.908843	−	0.417139i	$-0.136967\pi$
$594$	−1.00000			−0.0410305
$595$	−7.34335	−	16.2883i	−0.301048	−	0.667754i
$596$	12.6359			0.517589
$597$		−	13.9433i		−	0.570660i
$598$	5.13830	+	5.13830i	0.210121	+	0.210121i
$599$	35.7804			1.46195			0.730974	−	0.682405i	$-0.239066\pi$
$599$	35.7804			1.46195			0.730974	+	0.682405i	$0.239066\pi$
$600$	−2.12132	−	2.12132i	−0.0866025	−	0.0866025i
$601$	−20.7917	+	20.7917i	−0.848113	+	0.848113i	−0.989897	−	0.141785i	$-0.954716\pi$
$601$	−20.7917	+	20.7917i	−0.848113	+	0.848113i	0.141785	+	0.989897i	$0.454716\pi$
$602$	−0.259921	+	0.259921i	−0.0105936	+	0.0105936i
$603$		−	8.42636i		−	0.343148i
$604$		−	11.6407i		−	0.473654i
$605$	−1.00000	+	1.00000i	−0.0406558	+	0.0406558i
$606$	−6.22601	+	6.22601i	−0.252914	+	0.252914i
$607$	−2.09457	−	2.09457i	−0.0850160	−	0.0850160i	0.663320	−	0.748336i	$-0.269147\pi$
$607$	−2.09457	−	2.09457i	−0.0850160	−	0.0850160i	−0.748336	+	0.663320i	$0.769147\pi$
$608$	−3.06418			−0.124269
$609$	15.0925	+	15.0925i	0.611580	+	0.611580i
$610$			10.0930i			0.408652i
$611$	−6.46839			−0.261683
$612$	−3.75877	+	1.69459i	−0.151939	+	0.0684999i
$613$	−0.905249			−0.0365627			−0.0182813	−	0.999833i	$-0.505819\pi$
$613$	−0.905249			−0.0365627			−0.0182813	+	0.999833i	$0.505819\pi$
$614$			22.6680i			0.914808i
$615$	−4.59835	−	4.59835i	−0.185423	−	0.185423i
$616$	3.06418			0.123459
$617$	−34.1255	−	34.1255i	−1.37384	−	1.37384i	−0.854673	−	0.519167i	$-0.826242\pi$
$617$	−34.1255	−	34.1255i	−1.37384	−	1.37384i	−0.519167	−	0.854673i	$-0.673758\pi$
$618$	5.43567	−	5.43567i	0.218655	−	0.218655i
$619$	−13.2178	+	13.2178i	−0.531269	+	0.531269i	−0.920950	−	0.389681i	$-0.872585\pi$
$619$	−13.2178	+	13.2178i	−0.531269	+	0.531269i	0.389681	+	0.920950i	$0.372585\pi$
$620$		−	8.84099i		−	0.355063i
$621$		−	7.39758i		−	0.296855i
$622$	12.0835	−	12.0835i	0.484503	−	0.484503i
$623$	12.3991	−	12.3991i	0.496761	−	0.496761i
$624$	−0.694593	−	0.694593i	−0.0278060	−	0.0278060i
$625$	1.00000			0.0400000
$626$	3.94422	+	3.94422i	0.157643	+	0.157643i
$627$			3.06418i			0.122371i
$628$	9.71284			0.387585
$629$	−7.97040	+	21.0570i	−0.317801	+	0.839599i
$630$	−4.33340			−0.172647
$631$		−	3.07568i		−	0.122441i	−0.998124	−	0.0612205i	$-0.980501\pi$
$631$		−	3.07568i		−	0.122441i	0.998124	−	0.0612205i	$-0.0194993\pi$
$632$	10.5466	+	10.5466i	0.419521	+	0.419521i
$633$	−0.403674			−0.0160446
$634$	20.1363	+	20.1363i	0.799715	+	0.799715i
$635$	10.4359	−	10.4359i	0.414135	−	0.414135i
$636$	−0.621111	+	0.621111i	−0.0246287	+	0.0246287i
$637$			2.34690i			0.0929877i
$638$		−	6.96567i		−	0.275773i
$639$	1.18440	−	1.18440i	0.0468541	−	0.0468541i
$640$	−1.00000	+	1.00000i	−0.0395285	+	0.0395285i
$641$	−16.4646	−	16.4646i	−0.650314	−	0.650314i	0.302755	−	0.953069i	$-0.402094\pi$
$641$	−16.4646	−	16.4646i	−0.650314	−	0.650314i	−0.953069	+	0.302755i	$0.902094\pi$
$642$	−1.05578			−0.0416685
$643$	2.00617	+	2.00617i	0.0791155	+	0.0791155i	0.745557	−	0.666442i	$-0.232183\pi$
$643$	2.00617	+	2.00617i	0.0791155	+	0.0791155i	−0.666442	+	0.745557i	$0.732183\pi$
$644$			22.6675i			0.893225i
$645$	−0.169651			−0.00668000
$646$	5.19253	+	11.5175i	0.204297	+	0.453152i
$647$	−35.7329			−1.40480			−0.702402	−	0.711780i	$-0.747889\pi$
$647$	−35.7329			−1.40480			−0.702402	+	0.711780i	$0.747889\pi$
$648$			1.00000i			0.0392837i
$649$	−8.80586	−	8.80586i	−0.345660	−	0.345660i
$650$	−2.94691			−0.115587
$651$	13.5452	+	13.5452i	0.530878	+	0.530878i
$652$	−6.29949	+	6.29949i	−0.246707	+	0.246707i
$653$	−5.28062	+	5.28062i	−0.206647	+	0.206647i	−0.802841	−	0.596194i	$-0.796679\pi$
$653$	−5.28062	+	5.28062i	−0.206647	+	0.206647i	0.596194	+	0.802841i	$0.296679\pi$
$654$			0.380740i			0.0148881i
$655$		−	28.7849i		−	1.12472i
$656$	3.25153	−	3.25153i	0.126951	−	0.126951i
$657$	2.38475	−	2.38475i	0.0930381	−	0.0930381i
$658$	−14.2676	−	14.2676i	−0.556208	−	0.556208i
$659$	42.7959			1.66709			0.833546	−	0.552449i	$-0.186307\pi$
$659$	42.7959			1.66709			0.833546	+	0.552449i	$0.186307\pi$
$660$	1.00000	+	1.00000i	0.0389249	+	0.0389249i
$661$		−	9.04029i		−	0.351626i	−0.984424	−	0.175813i	$-0.943745\pi$
$661$		−	9.04029i		−	0.351626i	0.984424	−	0.175813i	$-0.0562555\pi$
$662$	21.7028			0.843502
$663$	−1.43376	+	3.78787i	−0.0556827	+	0.147109i
$664$	10.2980			0.399640
$665$			13.2783i			0.514911i
$666$	3.86129	+	3.86129i	0.149622	+	0.149622i
$667$	51.5291			1.99521
$668$	−5.29888	−	5.29888i	−0.205020	−	0.205020i
$669$	−4.04648	+	4.04648i	−0.156446	+	0.156446i
$670$	−8.42636	+	8.42636i	−0.325539	+	0.325539i
$671$			7.13680i			0.275513i
$672$		−	3.06418i		−	0.118203i
$673$	−20.0693	+	20.0693i	−0.773613	+	0.773613i	−0.978736	−	0.205123i	$-0.934240\pi$
$673$	−20.0693	+	20.0693i	−0.773613	+	0.773613i	0.205123	+	0.978736i	$0.434240\pi$
$674$	−14.9857	+	14.9857i	−0.577229	+	0.577229i
$675$	2.12132	+	2.12132i	0.0816497	+	0.0816497i
$676$	12.0351			0.462888
$677$	18.6038	+	18.6038i	0.715002	+	0.715002i	0.967577	−	0.252575i	$-0.0812775\pi$
$677$	18.6038	+	18.6038i	0.715002	+	0.715002i	−0.252575	+	0.967577i	$0.581277\pi$
$678$			7.03915i			0.270337i
$679$	−18.7017			−0.717705
$680$	5.45336	+	2.06418i	0.209127	+	0.0791576i
$681$	−26.2726			−1.00677
$682$		−	6.25153i		−	0.239383i
$683$	14.9631	+	14.9631i	0.572546	+	0.572546i	0.932839	−	0.360293i	$-0.117323\pi$
$683$	14.9631	+	14.9631i	0.572546	+	0.572546i	−0.360293	+	0.932839i	$0.617323\pi$
$684$	3.06418			0.117162
$685$	−11.9549	−	11.9549i	−0.456772	−	0.456772i
$686$	9.99026	−	9.99026i	0.381430	−	0.381430i
$687$	−11.2672	+	11.2672i	−0.429869	+	0.429869i
$688$		−	0.119961i		−	0.00457349i
$689$			0.862839i			0.0328715i
$690$	−7.39758	+	7.39758i	−0.281621	+	0.281621i
$691$	27.3122	−	27.3122i	1.03901	−	1.03901i	0.0397984	−	0.999208i	$-0.487328\pi$
$691$	27.3122	−	27.3122i	1.03901	−	1.03901i	0.999208	−	0.0397984i	$-0.0126716\pi$
$692$	−2.18519	−	2.18519i	−0.0830683	−	0.0830683i
$693$	−3.06418			−0.116398
$694$	9.38180	+	9.38180i	0.356128	+	0.356128i
$695$			21.6029i			0.819443i
$696$	−6.96567			−0.264033
$697$	−17.7318	−	6.71173i	−0.671638	−	0.254225i
$698$	21.5729			0.816548
$699$		−	21.4605i		−	0.811709i
$700$	−6.50010	−	6.50010i	−0.245681	−	0.245681i
$701$	34.6293			1.30793			0.653966	−	0.756524i	$-0.273104\pi$
$701$	34.6293			1.30793			0.653966	+	0.756524i	$0.273104\pi$
$702$	0.694593	+	0.694593i	0.0262157	+	0.0262157i
$703$	11.8317	−	11.8317i	0.446241	−	0.446241i
$704$	−0.707107	+	0.707107i	−0.0266501	+	0.0266501i
$705$		−	9.31249i		−	0.350729i
$706$		−	18.6778i		−	0.702947i
$707$	−19.0776	+	19.0776i	−0.717487	+	0.717487i
$708$	−8.80586	+	8.80586i	−0.330944	+	0.330944i
$709$	−11.9908	−	11.9908i	−0.450323	−	0.450323i	0.445139	−	0.895462i	$-0.353154\pi$
$709$	−11.9908	−	11.9908i	−0.450323	−	0.450323i	−0.895462	+	0.445139i	$0.853154\pi$
$710$	−2.36880			−0.0888994
$711$	−10.5466	−	10.5466i	−0.395528	−	0.395528i
$712$			5.72259i			0.214463i
$713$	46.2462			1.73193
$714$	−11.5175	+	5.19253i	−0.431033	+	0.194326i
$715$	1.38919			0.0519526
$716$			1.26922i			0.0474331i
$717$	−0.123171	−	0.123171i	−0.00459990	−	0.00459990i
$718$	1.42927			0.0533398
$719$	−34.1523	−	34.1523i	−1.27367	−	1.27367i	−0.944150	−	0.329516i	$-0.893115\pi$
$719$	−34.1523	−	34.1523i	−1.27367	−	1.27367i	−0.329516	−	0.944150i	$-0.606885\pi$
$720$	1.00000	−	1.00000i	0.0372678	−	0.0372678i
$721$	16.6558	−	16.6558i	0.620296	−	0.620296i
$722$			9.61081i			0.357677i
$723$		−	1.07664i		−	0.0400407i
$724$	−3.82590	+	3.82590i	−0.142188	+	0.142188i
$725$	−14.7764	+	14.7764i	−0.548782	+	0.548782i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	26.4637			0.981483			0.490742	−	0.871305i	$-0.336726\pi$
$727$	26.4637			0.981483			0.490742	+	0.871305i	$0.336726\pi$
$728$	−2.12836	−	2.12836i	−0.0788821	−	0.0788821i
$729$		−	1.00000i		−	0.0370370i
$730$	−4.76951			−0.176527
$731$	−0.450907	+	0.203286i	−0.0166774	+	0.00751880i
$732$	7.13680			0.263784
$733$		−	27.8097i		−	1.02718i	−0.858037	−	0.513588i	$-0.828316\pi$
$733$		−	27.8097i		−	1.02718i	0.858037	−	0.513588i	$-0.171684\pi$
$734$	−7.02035	−	7.02035i	−0.259126	−	0.259126i
$735$	−3.37882			−0.124630
$736$	−5.23088	−	5.23088i	−0.192813	−	0.192813i
$737$	−5.95834	+	5.95834i	−0.219478	+	0.219478i
$738$	−3.25153	+	3.25153i	−0.119690	+	0.119690i
$739$			28.9267i			1.06409i	0.846717	+	0.532043i	$0.178576\pi$
$739$			28.9267i			1.06409i	−0.846717	+	0.532043i	$0.821424\pi$
$740$		−	7.72259i		−	0.283888i
$741$	2.12836	−	2.12836i	0.0781871	−	0.0781871i
$742$	−1.90320	+	1.90320i	−0.0698685	+	0.0698685i
$743$	8.48757	+	8.48757i	0.311379	+	0.311379i	0.845444	−	0.534065i	$-0.179336\pi$
$743$	8.48757	+	8.48757i	0.311379	+	0.311379i	−0.534065	+	0.845444i	$0.679336\pi$
$744$	−6.25153			−0.229192
$745$	12.6359	+	12.6359i	0.462945	+	0.462945i
$746$			18.9469i			0.693696i
$747$	−10.2980			−0.376784
$748$	3.85611	+	1.45959i	0.140993	+	0.0533680i
$749$	−3.23511			−0.118208
$750$		−	11.3137i		−	0.413118i
$751$	−25.7806	−	25.7806i	−0.940747	−	0.940747i	0.0575932	−	0.998340i	$-0.481657\pi$
$751$	−25.7806	−	25.7806i	−0.940747	−	0.940747i	−0.998340	+	0.0575932i	$0.981657\pi$
$752$	6.58493			0.240128
$753$	−9.06123	−	9.06123i	−0.330209	−	0.330209i
$754$	−4.83830	+	4.83830i	−0.176201	+	0.176201i
$755$	11.6407	−	11.6407i	0.423649	−	0.423649i
$756$			3.06418i			0.111443i
$757$		−	23.2044i		−	0.843377i	−0.906741	−	0.421689i	$-0.861438\pi$
$757$		−	23.2044i		−	0.843377i	0.906741	−	0.421689i	$-0.138562\pi$
$758$	15.3256	−	15.3256i	0.556650	−	0.556650i
$759$	−5.23088	+	5.23088i	−0.189869	+	0.189869i
$760$	−3.06418	−	3.06418i	−0.111149	−	0.111149i
$761$	−18.8158			−0.682071			−0.341035	−	0.940051i	$-0.610778\pi$
$761$	−18.8158			−0.682071			−0.341035	+	0.940051i	$0.610778\pi$
$762$	−7.37928	−	7.37928i	−0.267323	−	0.267323i
$763$			1.16666i			0.0422358i
$764$	−16.5495			−0.598741
$765$	−5.45336	−	2.06418i	−0.197167	−	0.0746305i
$766$	−10.5534			−0.381309
$767$			12.2330i			0.441707i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	43.2854			1.56091			0.780455	−	0.625212i	$-0.214988\pi$
$769$	43.2854			1.56091			0.780455	+	0.625212i	$0.214988\pi$
$770$	3.06418	+	3.06418i	0.110425	+	0.110425i
$771$	−16.6918	+	16.6918i	−0.601142	+	0.601142i
$772$	15.2290	−	15.2290i	0.548102	−	0.548102i
$773$			38.0254i			1.36768i	0.729632	+	0.683840i	$0.239691\pi$
$773$			38.0254i			1.36768i	−0.729632	+	0.683840i	$0.760309\pi$
$774$			0.119961i			0.00431192i
$775$	−13.2615	+	13.2615i	−0.476367	+	0.476367i
$776$	4.31570	−	4.31570i	0.154925	−	0.154925i
$777$	11.8317	+	11.8317i	0.424460	+	0.424460i
$778$	13.2491			0.475003
$779$	9.96325	+	9.96325i	0.356971	+	0.356971i
$780$		−	1.38919i		−	0.0497408i
$781$	−1.67499			−0.0599359
$782$	−10.7975	+	28.5259i	−0.386117	+	1.02008i
$783$	6.96567			0.248933
$784$		−	2.38919i		−	0.0853281i
$785$	9.71284	+	9.71284i	0.346666	+	0.346666i
$786$	−20.3540			−0.726003
$787$	−4.23627	−	4.23627i	−0.151007	−	0.151007i	0.627561	−	0.778568i	$-0.284053\pi$
$787$	−4.23627	−	4.23627i	−0.151007	−	0.151007i	−0.778568	+	0.627561i	$0.784053\pi$
$788$	−4.14710	+	4.14710i	−0.147734	+	0.147734i
$789$	2.34954	−	2.34954i	0.0836460	−	0.0836460i
$790$			21.0932i			0.750461i
$791$			21.5692i			0.766913i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	4.95717	−	4.95717i	0.176034	−	0.176034i
$794$	−21.7554	−	21.7554i	−0.772070	−	0.772070i
$795$	−1.24222			−0.0440571
$796$	9.85937	+	9.85937i	0.349456	+	0.349456i
$797$		−	37.7271i		−	1.33636i	−0.743998	−	0.668182i	$-0.767073\pi$
$797$		−	37.7271i		−	1.33636i	0.743998	−	0.668182i	$-0.232927\pi$
$798$	9.38919			0.332374
$799$	−11.1588	−	24.7512i	−0.394769	−	0.875636i
$800$	3.00000			0.106066
$801$		−	5.72259i		−	0.202198i
$802$	−3.68738	−	3.68738i	−0.130206	−	0.130206i
$803$	−3.37255			−0.119015
$804$	5.95834	+	5.95834i	0.210134	+	0.210134i
$805$	−22.6675	+	22.6675i	−0.798924	+	0.798924i
$806$	−4.34226	+	4.34226i	−0.152950	+	0.152950i
$807$		−	17.0247i		−	0.599298i
$808$		−	8.80490i		−	0.309755i
$809$	−5.27806	+	5.27806i	−0.185567	+	0.185567i	−0.793776	−	0.608210i	$-0.791888\pi$
$809$	−5.27806	+	5.27806i	−0.185567	+	0.185567i	0.608210	+	0.793776i	$0.291888\pi$
$810$	−1.00000	+	1.00000i	−0.0351364	+	0.0351364i
$811$	6.84151	+	6.84151i	0.240238	+	0.240238i	0.816948	−	0.576711i	$-0.195664\pi$
$811$	6.84151	+	6.84151i	0.240238	+	0.240238i	−0.576711	+	0.816948i	$0.695664\pi$
$812$	−21.3440			−0.749029
$813$	16.3904	+	16.3904i	0.574838	+	0.574838i
$814$		−	5.46069i		−	0.191397i
$815$	−12.5990			−0.441323
$816$	1.45959	−	3.85611i	0.0510960	−	0.134991i
$817$	0.367583			0.0128601
$818$			3.89939i			0.136339i
$819$	2.12836	+	2.12836i	0.0743708	+	0.0743708i
$820$	6.50305			0.227096
$821$	14.3315	+	14.3315i	0.500174	+	0.500174i	0.911492	−	0.411318i	$-0.134931\pi$
$821$	14.3315	+	14.3315i	0.500174	+	0.500174i	−0.411318	+	0.911492i	$0.634931\pi$
$822$	−8.45336	+	8.45336i	−0.294845	+	0.294845i
$823$	−17.9515	+	17.9515i	−0.625750	+	0.625750i	−0.946996	−	0.321246i	$-0.895898\pi$
$823$	−17.9515	+	17.9515i	−0.625750	+	0.625750i	0.321246	+	0.946996i	$0.395898\pi$
$824$			7.68719i			0.267796i
$825$		−	3.00000i		−	0.104447i
$826$	−26.9827	+	26.9827i	−0.938849	+	0.938849i
$827$	−5.19217	+	5.19217i	−0.180549	+	0.180549i	−0.791595	−	0.611046i	$-0.790749\pi$
$827$	−5.19217	+	5.19217i	−0.180549	+	0.180549i	0.611046	+	0.791595i	$0.290749\pi$
$828$	5.23088	+	5.23088i	0.181786	+	0.181786i
$829$	−0.771404			−0.0267920			−0.0133960	−	0.999910i	$-0.504264\pi$
$829$	−0.771404			−0.0267920			−0.0133960	+	0.999910i	$0.504264\pi$
$830$	10.2980	+	10.2980i	0.357449	+	0.357449i
$831$			25.4289i			0.882119i
$832$	0.982302			0.0340552
$833$	−8.98040	+	4.04870i	−0.311152	+	0.140279i
$834$	15.2755			0.528948
$835$		−	10.5978i		−	0.366751i
$836$	−2.16670	−	2.16670i	−0.0749369	−	0.0749369i
$837$	6.25153			0.216084
$838$	25.3335	+	25.3335i	0.875130	+	0.875130i
$839$	−35.8551	+	35.8551i	−1.23786	+	1.23786i	−0.276981	+	0.960875i	$0.589334\pi$
$839$	−35.8551	+	35.8551i	−1.23786	+	1.23786i	−0.960875	+	0.276981i	$0.910666\pi$
$840$	3.06418	−	3.06418i	0.105724	−	0.105724i
$841$			19.5205i			0.673122i
$842$		−	14.1195i		−	0.486590i
$843$	−1.45492	+	1.45492i	−0.0501100	+	0.0501100i
$844$	0.285440	−	0.285440i	0.00982526	−	0.00982526i
$845$	12.0351	+	12.0351i	0.414019	+	0.414019i
$846$	−6.58493			−0.226394
$847$	2.16670	+	2.16670i	0.0744487	+	0.0744487i
$848$		−	0.878384i		−	0.0301638i
$849$	−18.5636			−0.637100
$850$	−5.08378	−	11.2763i	−0.174372	−	0.386774i
$851$	40.3959			1.38475
$852$			1.67499i			0.0573843i
$853$	3.01341	+	3.01341i	0.103177	+	0.103177i	0.756811	−	0.653634i	$-0.226756\pi$
$853$	3.01341	+	3.01341i	0.103177	+	0.103177i	−0.653634	+	0.756811i	$0.726756\pi$
$854$	21.8684			0.748322
$855$	3.06418	+	3.06418i	0.104793	+	0.104793i
$856$	0.746552	−	0.746552i	0.0255166	−	0.0255166i
$857$	−23.8854	+	23.8854i	−0.815909	+	0.815909i	−0.985512	−	0.169603i	$-0.945751\pi$
$857$	−23.8854	+	23.8854i	−0.815909	+	0.815909i	0.169603	+	0.985512i	$0.445751\pi$
$858$		−	0.982302i		−	0.0335353i
$859$			39.5263i			1.34862i	0.738448	+	0.674311i	$0.235559\pi$
$859$			39.5263i			1.34862i	−0.738448	+	0.674311i	$0.764441\pi$
$860$	0.119961	−	0.119961i	0.00409065	−	0.00409065i
$861$	−9.96325	+	9.96325i	−0.339547	+	0.339547i
$862$	7.28914	+	7.28914i	0.248269	+	0.248269i
$863$	−7.62576			−0.259584			−0.129792	−	0.991541i	$-0.541431\pi$
$863$	−7.62576			−0.259584			−0.129792	+	0.991541i	$0.541431\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$		−	4.37037i		−	0.148597i
$866$	13.9845			0.475213
$867$	−16.9677	+	1.04826i	−0.576252	+	0.0356007i
$868$	−19.1558			−0.650190
$869$			14.9151i			0.505961i
$870$	−6.96567	−	6.96567i	−0.236158	−	0.236158i
$871$	8.27724			0.280463
$872$	−0.269224	−	0.269224i	−0.00911707	−	0.00911707i
$873$	−4.31570	+	4.31570i	−0.146064	+	0.146064i
$874$	16.0283	−	16.0283i	0.542167	−	0.542167i
$875$		−	34.6672i		−	1.17197i
$876$			3.37255i			0.113948i
$877$	1.18631	−	1.18631i	0.0400589	−	0.0400589i	−0.686794	−	0.726853i	$-0.740982\pi$
$877$	1.18631	−	1.18631i	0.0400589	−	0.0400589i	0.726853	+	0.686794i	$0.240982\pi$
$878$	25.7564	−	25.7564i	0.869235	−	0.869235i
$879$	−16.6308	−	16.6308i	−0.560944	−	0.560944i
$880$	−1.41421			−0.0476731
$881$	−2.95994	−	2.95994i	−0.0997229	−	0.0997229i	0.655485	−	0.755208i	$-0.272464\pi$
$881$	−2.95994	−	2.95994i	−0.0997229	−	0.0997229i	−0.755208	+	0.655485i	$0.772464\pi$
$882$			2.38919i			0.0804481i
$883$	40.0636			1.34825			0.674123	−	0.738619i	$-0.264522\pi$
$883$	40.0636			1.34825			0.674123	+	0.738619i	$0.264522\pi$
$884$	−1.66460	−	3.69225i	−0.0559866	−	0.124184i
$885$	−17.6117			−0.592011
$886$			19.5542i			0.656935i
$887$	−14.2889	−	14.2889i	−0.479775	−	0.479775i	0.425284	−	0.905060i	$-0.360174\pi$
$887$	−14.2889	−	14.2889i	−0.479775	−	0.479775i	−0.905060	+	0.425284i	$0.860174\pi$
$888$	−5.46069			−0.183249
$889$	−22.6114	−	22.6114i	−0.758362	−	0.758362i
$890$	−5.72259	+	5.72259i	−0.191822	+	0.191822i
$891$	−0.707107	+	0.707107i	−0.0236890	+	0.0236890i
$892$		−	5.72259i		−	0.191606i
$893$			20.1774i			0.675211i
$894$	8.93496	−	8.93496i	0.298830	−	0.298830i
$895$	−1.26922	+	1.26922i	−0.0424255	+	0.0424255i
$896$	2.16670	+	2.16670i	0.0723844	+	0.0723844i
$897$	7.26666			0.242627
$898$	−17.3657	−	17.3657i	−0.579501	−	0.579501i
$899$			43.5461i			1.45234i
$900$	−3.00000			−0.100000
$901$	−3.30164	+	1.48850i	−0.109994	+	0.0495892i
$902$	4.59835			0.153108
$903$			0.367583i			0.0122324i
$904$	−4.97743	−	4.97743i	−0.165547	−	0.165547i
$905$	−7.65180			−0.254354
$906$	−8.23123	−	8.23123i	−0.273464	−	0.273464i
$907$	−29.1417	+	29.1417i	−0.967634	+	0.967634i	−0.999492	−	0.0318583i	$-0.989857\pi$
$907$	−29.1417	+	29.1417i	−0.967634	+	0.967634i	0.0318583	+	0.999492i	$0.489857\pi$
$908$	18.5775	−	18.5775i	0.616518	−	0.616518i
$909$			8.80490i			0.292040i
$910$		−	4.25671i		−	0.141109i
$911$	11.1717	−	11.1717i	0.370135	−	0.370135i	−0.497392	−	0.867526i	$-0.665709\pi$
$911$	11.1717	−	11.1717i	0.370135	−	0.370135i	0.867526	+	0.497392i	$0.165709\pi$
$912$	−2.16670	+	2.16670i	−0.0717466	+	0.0717466i
$913$	7.28179	+	7.28179i	0.240992	+	0.240992i
$914$	−9.53008			−0.315227
$915$	7.13680	+	7.13680i	0.235935	+	0.235935i
$916$		−	15.9342i		−	0.526479i
$917$	−62.3683			−2.05958
$918$	−1.45959	+	3.85611i	−0.0481738	+	0.127271i
$919$	8.66434			0.285810			0.142905	−	0.989736i	$-0.454356\pi$
$919$	8.66434			0.285810			0.142905	+	0.989736i	$0.454356\pi$
$920$		−	10.4618i		−	0.344914i
$921$	16.0287	+	16.0287i	0.528165	+	0.528165i
$922$	−41.2567			−1.35872
$923$	1.16344	+	1.16344i	0.0382950	+	0.0382950i
$924$	2.16670	−	2.16670i	0.0712792	−	0.0712792i
$925$	−11.5839	+	11.5839i	−0.380876	+	0.380876i
$926$			1.79949i			0.0591350i
$927$		−	7.68719i		−	0.252481i
$928$	4.92547	−	4.92547i	0.161687	−	0.161687i
$929$	−18.9567	+	18.9567i	−0.621950	+	0.621950i	−0.946030	−	0.324080i	$-0.894945\pi$
$929$	−18.9567	+	18.9567i	−0.621950	+	0.621950i	0.324080	+	0.946030i	$0.394945\pi$
$930$	−6.25153	−	6.25153i	−0.204996	−	0.204996i
$931$	7.32089			0.239932
$932$	15.1748	+	15.1748i	0.497068	+	0.497068i
$933$		−	17.0886i		−	0.559456i
$934$	15.1512			0.495764
$935$	2.39652	+	5.31570i	0.0783745	+	0.173842i
$936$	−0.982302			−0.0321076
$937$		−	3.72590i		−	0.121720i	−0.998146	−	0.0608599i	$-0.980616\pi$
$937$		−	3.72590i		−	0.121720i	0.998146	−	0.0608599i	$-0.0193843\pi$
$938$	18.2574	+	18.2574i	0.596125	+	0.596125i
$939$	5.57796			0.182030
$940$	6.58493	+	6.58493i	0.214777	+	0.214777i
$941$	1.70325	−	1.70325i	0.0555242	−	0.0555242i	−0.678799	−	0.734324i	$-0.737499\pi$
$941$	1.70325	−	1.70325i	0.0555242	−	0.0555242i	0.734324	+	0.678799i	$0.237499\pi$
$942$	6.86802	−	6.86802i	0.223772	−	0.223772i
$943$			34.0167i			1.10774i
$944$		−	12.4534i		−	0.405322i
$945$	−3.06418	+	3.06418i	−0.0996777	+	0.0996777i
$946$	0.0848255	−	0.0848255i	0.00275792	−	0.00275792i
$947$	−8.40141	−	8.40141i	−0.273009	−	0.273009i	0.557301	−	0.830310i	$-0.311837\pi$
$947$	−8.40141	−	8.40141i	−0.273009	−	0.273009i	−0.830310	+	0.557301i	$0.811837\pi$
$948$	14.9151			0.484421
$949$	2.34255	+	2.34255i	0.0760424	+	0.0760424i
$950$			9.19253i			0.298245i
$951$	28.4770			0.923431
$952$	4.47246	−	11.8158i	0.144953	−	0.382952i
$953$	1.03329			0.0334717			0.0167358	−	0.999860i	$-0.494673\pi$
$953$	1.03329			0.0334717			0.0167358	+	0.999860i	$0.494673\pi$
$954$			0.878384i			0.0284387i
$955$	−16.5495	−	16.5495i	−0.535530	−	0.535530i
$956$	0.174190			0.00563370
$957$	−4.92547	−	4.92547i	−0.159218	−	0.159218i
$958$	−25.5711	+	25.5711i	−0.826165	+	0.826165i
$959$	−25.9026	+	25.9026i	−0.836439	+	0.836439i
$960$			1.41421i			0.0456435i
$961$			8.08158i			0.260696i
$962$	−3.79296	+	3.79296i	−0.122290	+	0.122290i
$963$	−0.746552	+	0.746552i	−0.0240573	+	0.0240573i
$964$	0.761299	+	0.761299i	0.0245198	+	0.0245198i
$965$	30.4579			0.980475
$966$	16.0283	+	16.0283i	0.515703	+	0.515703i
$967$		−	14.9015i		−	0.479199i	−0.970872	−	0.239600i	$-0.922984\pi$
$967$		−	14.9015i		−	0.479199i	0.970872	−	0.239600i	$-0.0770161\pi$
$968$	−1.00000			−0.0321412
$969$	11.8158	+	4.47246i	0.379578	+	0.143676i
$970$	8.63141			0.277138
$971$			31.0421i			0.996188i	0.867123	+	0.498094i	$0.165966\pi$
$971$			31.0421i			0.996188i	−0.867123	+	0.498094i	$0.834034\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	46.8069			1.50056
$974$	4.95055	+	4.95055i	0.158626	+	0.158626i
$975$	−2.08378	+	2.08378i	−0.0667343	+	0.0667343i
$976$	−5.04648	+	5.04648i	−0.161534	+	0.161534i
$977$		−	22.4548i		−	0.718393i	−0.933262	−	0.359196i	$-0.883051\pi$
$977$		−	22.4548i		−	0.718393i	0.933262	−	0.359196i	$-0.116949\pi$
$978$			8.90882i			0.284873i
$979$	−4.04648	+	4.04648i	−0.129326	+	0.129326i
$980$	2.38919	−	2.38919i	0.0763197	−	0.0763197i
$981$	0.269224	+	0.269224i	0.00859566	+	0.00859566i
$982$	43.0252			1.37299
$983$	26.0887	+	26.0887i	0.832099	+	0.832099i	0.987804	−	0.155705i	$-0.0497648\pi$
$983$	26.0887	+	26.0887i	0.832099	+	0.832099i	−0.155705	+	0.987804i	$0.549765\pi$
$984$		−	4.59835i		−	0.146590i
$985$	−8.29420			−0.264275
$986$	−26.8604	−	10.1670i	−0.855409	−	0.323785i
$987$	−20.1774			−0.642253
$988$			3.00995i			0.0957592i
$989$	0.627504	+	0.627504i	0.0199535	+	0.0199535i
$990$	1.41421			0.0449467
$991$	−39.2247	−	39.2247i	−1.24602	−	1.24602i	−0.957465	−	0.288550i	$-0.906827\pi$
$991$	−39.2247	−	39.2247i	−1.24602	−	1.24602i	−0.288550	−	0.957465i	$-0.593173\pi$
$992$	4.42050	−	4.42050i	0.140351	−	0.140351i
$993$	15.3462	−	15.3462i	0.486996	−	0.486996i
$994$			5.13247i			0.162792i
$995$			19.7187i			0.625126i
$996$	7.28179	−	7.28179i	0.230732	−	0.230732i
$997$	6.03783	−	6.03783i	0.191220	−	0.191220i	−0.605003	−	0.796223i	$-0.706828\pi$
$997$	6.03783	−	6.03783i	0.191220	−	0.191220i	0.796223	+	0.605003i	$0.206828\pi$
$998$	−6.13193	−	6.13193i	−0.194103	−	0.194103i
$999$	5.46069			0.172769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.e.727.4	yes	12
17.4	even	4	inner	1122.2.l.e.463.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.e.463.4	✓	12	17.4	even	4	inner
1122.2.l.e.727.4	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} +(-5.23088 + 5.23088i) 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} +(-4.92547 - 4.92547i) q^{29} +1.41421 q^{30} +(-4.42050 - 4.42050i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(3.75877 - 1.69459i) q^{34} +4.33340 q^{35} -1.00000i q^{36} +(-3.86129 - 3.86129i) q^{37} -3.06418 q^{38} +(-0.694593 - 0.694593i) q^{39} +(-1.00000 + 1.00000i) q^{40} +(3.25153 - 3.25153i) q^{41} -3.06418i q^{42} -0.119961i q^{43} +(-0.707107 + 0.707107i) q^{44} +(1.00000 - 1.00000i) q^{45} +(-5.23088 - 5.23088i) q^{46} +6.58493 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} -0.878384i q^{53} +(-0.707107 - 0.707107i) q^{54} -1.41421 q^{55} +(2.16670 + 2.16670i) q^{56} +(-2.16670 + 2.16670i) q^{57} +(4.92547 - 4.92547i) q^{58} -12.4534i q^{59} +1.41421i q^{60} +(-5.04648 + 5.04648i) q^{61} +(4.42050 - 4.42050i) q^{62} +(-2.16670 - 2.16670i) q^{63} -1.00000 q^{64} +(0.982302 + 0.982302i) q^{65} +1.00000i q^{66} -8.42636 q^{67} +(1.69459 + 3.75877i) q^{68} -7.39758 q^{69} +4.33340i q^{70} +(-1.18440 - 1.18440i) q^{71} +1.00000 q^{72} +(-2.38475 - 2.38475i) q^{73} +(3.86129 - 3.86129i) q^{74} +(2.12132 - 2.12132i) q^{75} -3.06418i q^{76} +3.06418i q^{77} +(0.694593 - 0.694593i) q^{78} +(-10.5466 + 10.5466i) q^{79} +(-1.00000 - 1.00000i) q^{80} -1.00000 q^{81} +(3.25153 + 3.25153i) q^{82} +10.2980i q^{83} +3.06418 q^{84} +(-2.06418 + 5.45336i) q^{85} +0.119961 q^{86} -6.96567i q^{87} +(-0.707107 - 0.707107i) q^{88} -5.72259 q^{89} +(1.00000 + 1.00000i) q^{90} +(2.12836 - 2.12836i) q^{91} +(5.23088 - 5.23088i) q^{92} -6.25153i q^{93} +6.58493i q^{94} +(3.06418 - 3.06418i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(4.31570 + 4.31570i) 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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