LMFDB - Embedded newform 450.2.h.g.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} + \cdots + 15625 $ x^12 - x^11 + 6x^10 - 26x^9 + 61x^8 - 120x^7 + 465x^6 - 600x^5 + 1525x^4 - 3250x^3 + 3750x^2 - 3125x + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			271.2
Root			$-1.01542 - 1.99221i$ of defining polynomial
Character	$\chi$	$=$	450.271
Dual form			450.2.h.g.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.01542 + 1.99221i) q^{5} +4.77988 q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.01542 + 1.99221i) q^{5} +4.77988 q^{7} +(0.809017 - 0.587785i) q^{8} +(-2.20849 + 0.350097i) q^{10} +(0.0788401 - 0.242645i) q^{11} +(-1.32444 - 4.07621i) q^{13} +(-1.47707 + 4.54594i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.88650 - 1.37063i) q^{17} +(1.12141 - 0.814750i) q^{19} +(0.349499 - 2.20859i) q^{20} +(0.206406 + 0.149963i) q^{22} +(-2.31110 + 7.11284i) q^{23} +(-2.93783 + 4.04588i) q^{25} +4.28598 q^{26} +(-3.86701 - 2.80955i) q^{28} +(5.13892 + 3.73364i) q^{29} +(-0.143093 + 0.103963i) q^{31} -1.00000 q^{32} +(0.720581 + 2.21772i) q^{34} +(4.85360 + 9.52255i) q^{35} +(1.57499 + 4.84733i) q^{37} +(0.428339 + 1.31829i) q^{38} +(1.99249 + 1.01488i) q^{40} +(0.681411 + 2.09717i) q^{41} -3.60976 q^{43} +(-0.206406 + 0.149963i) q^{44} +(-6.05054 - 4.39598i) q^{46} +(-6.09086 - 4.42527i) q^{47} +15.8473 q^{49} +(-2.94002 - 4.04429i) q^{50} +(-1.32444 + 4.07621i) q^{52} +(-10.9208 - 7.93444i) q^{53} +(0.563457 - 0.0893209i) q^{55} +(3.86701 - 2.80955i) q^{56} +(-5.13892 + 3.73364i) q^{58} +(-2.20360 - 6.78199i) q^{59} +(3.67232 - 11.3022i) q^{61} +(-0.0546567 - 0.168216i) q^{62} +(0.309017 - 0.951057i) q^{64} +(6.77581 - 6.77764i) q^{65} +(-6.44701 + 4.68403i) q^{67} -2.33185 q^{68} +(-10.5563 + 1.67342i) q^{70} +(-8.27651 - 6.01324i) q^{71} +(-2.98300 + 9.18072i) q^{73} -5.09679 q^{74} -1.38614 q^{76} +(0.376847 - 1.15981i) q^{77} +(2.91479 + 2.11772i) q^{79} +(-1.58092 + 1.58135i) q^{80} -2.20509 q^{82} +(12.8830 - 9.36002i) q^{83} +(4.64618 + 2.36656i) q^{85} +(1.11548 - 3.43308i) q^{86} +(-0.0788401 - 0.242645i) q^{88} +(-3.45616 + 10.6370i) q^{89} +(-6.33067 - 19.4838i) q^{91} +(6.05054 - 4.39598i) q^{92} +(6.09086 - 4.42527i) q^{94} +(2.76186 + 1.40677i) q^{95} +(12.7454 + 9.26005i) q^{97} +(-4.89708 + 15.0717i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8 + q^10 - q^11 + 4 * q^13 - 8 * q^14 - 3 * q^16 + 8 * q^17 - 8 * q^19 - q^20 - 4 * q^22 - 11 * q^25 + 16 * q^26 - 7 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 2 * q^34 + 18 * q^35 - 8 * q^37 - 2 * q^38 + q^40 - 20 * q^41 + 32 * q^43 + 4 * q^44 - 10 * q^46 + 34 * q^49 - 9 * q^50 + 4 * q^52 - 2 * q^53 + 44 * q^55 + 7 * q^56 - 6 * q^58 + 19 * q^59 - 26 * q^61 - 2 * q^62 - 3 * q^64 - 16 * q^65 - 16 * q^67 - 12 * q^68 - 23 * q^70 - 48 * q^71 - 30 * q^73 + 8 * q^74 + 12 * q^76 + 39 * q^77 - 18 * q^79 + 4 * q^80 - 40 * q^82 + 29 * q^83 - 4 * q^85 - 12 * q^86 + q^88 - 62 * q^89 - 26 * q^91 + 10 * q^92 - 6 * q^95 + 23 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.01542	+	1.99221i	0.454111	+	0.890945i
$5$	1.01542	+	1.99221i	0.454111	+	0.890945i
$6$		0			0
$7$	4.77988			1.80663			0.903313	−	0.428982i	$-0.141128\pi$
$7$	4.77988			1.80663			0.903313	+	0.428982i	$0.141128\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$	−2.20849	+	0.350097i	−0.698386	+	0.110710i
$11$	0.0788401	−	0.242645i	0.0237712	−	0.0731602i	−0.938467	−	0.345368i	$-0.887754\pi$
$11$	0.0788401	−	0.242645i	0.0237712	−	0.0731602i	0.962238	+	0.272208i	$0.0877540\pi$
$12$		0			0
$13$	−1.32444	−	4.07621i	−0.367334	−	1.13054i	−0.948507	−	0.316757i	$-0.897406\pi$
$13$	−1.32444	−	4.07621i	−0.367334	−	1.13054i	0.581173	−	0.813780i	$-0.302594\pi$
$14$	−1.47707	+	4.54594i	−0.394762	+	1.21495i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.88650	−	1.37063i	0.457545	−	0.332426i	−0.335023	−	0.942210i	$-0.608744\pi$
$17$	1.88650	−	1.37063i	0.457545	−	0.332426i	0.792567	+	0.609784i	$0.208744\pi$
$18$		0			0
$19$	1.12141	−	0.814750i	0.257268	−	0.186916i	−0.451673	−	0.892183i	$-0.649173\pi$
$19$	1.12141	−	0.814750i	0.257268	−	0.186916i	0.708942	+	0.705267i	$0.249173\pi$
$20$	0.349499	−	2.20859i	0.0781504	−	0.493855i
$21$		0			0
$22$	0.206406	+	0.149963i	0.0440059	+	0.0319722i
$23$	−2.31110	+	7.11284i	−0.481898	+	1.48313i	0.354526	+	0.935046i	$0.384642\pi$
$23$	−2.31110	+	7.11284i	−0.481898	+	1.48313i	−0.836424	+	0.548083i	$0.815358\pi$
$24$		0			0
$25$	−2.93783	+	4.04588i	−0.587566	+	0.809176i
$26$	4.28598			0.840549
$27$		0			0
$28$	−3.86701	−	2.80955i	−0.730796	−	0.530954i
$29$	5.13892	+	3.73364i	0.954273	+	0.693320i	0.951814	−	0.306677i	$-0.0992173\pi$
$29$	5.13892	+	3.73364i	0.954273	+	0.693320i	0.00245906	+	0.999997i	$0.499217\pi$
$30$		0			0
$31$	−0.143093	+	0.103963i	−0.0257003	+	0.0186724i	−0.600561	−	0.799579i	$-0.705056\pi$
$31$	−0.143093	+	0.103963i	−0.0257003	+	0.0186724i	0.574861	+	0.818251i	$0.305056\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.720581	+	2.21772i	0.123579	+	0.380336i
$35$	4.85360	+	9.52255i	0.820409	+	1.60960i
$36$		0			0
$37$	1.57499	+	4.84733i	0.258927	+	0.796897i	0.993030	+	0.117859i	$0.0376029\pi$
$37$	1.57499	+	4.84733i	0.258927	+	0.796897i	−0.734103	+	0.679038i	$0.762397\pi$
$38$	0.428339	+	1.31829i	0.0694858	+	0.213855i
$39$		0			0
$40$	1.99249	+	1.01488i	0.315040	+	0.160467i
$41$	0.681411	+	2.09717i	0.106419	+	0.327523i	0.990061	−	0.140640i	$-0.0449161\pi$
$41$	0.681411	+	2.09717i	0.106419	+	0.327523i	−0.883642	+	0.468163i	$0.844916\pi$
$42$		0			0
$43$	−3.60976			−0.550483			−0.275241	−	0.961375i	$-0.588758\pi$
$43$	−3.60976			−0.550483			−0.275241	+	0.961375i	$0.588758\pi$
$44$	−0.206406	+	0.149963i	−0.0311169	+	0.0226077i
$45$		0			0
$46$	−6.05054	−	4.39598i	−0.892104	−	0.648151i
$47$	−6.09086	−	4.42527i	−0.888443	−	0.645491i	0.0470287	−	0.998894i	$-0.485025\pi$
$47$	−6.09086	−	4.42527i	−0.888443	−	0.645491i	−0.935472	+	0.353402i	$0.885025\pi$
$48$		0			0
$49$	15.8473			2.26390
$50$	−2.94002	−	4.04429i	−0.415782	−	0.571949i
$51$		0			0
$52$	−1.32444	+	4.07621i	−0.183667	+	0.565268i
$53$	−10.9208	−	7.93444i	−1.50009	−	1.08988i	−0.970346	−	0.241722i	$-0.922288\pi$
$53$	−10.9208	−	7.93444i	−1.50009	−	1.08988i	−0.529744	−	0.848157i	$-0.677712\pi$
$54$		0			0
$55$	0.563457	−	0.0893209i	0.0759765	−	0.0120440i
$56$	3.86701	−	2.80955i	0.516751	−	0.375441i
$57$		0			0
$58$	−5.13892	+	3.73364i	−0.674773	+	0.490251i
$59$	−2.20360	−	6.78199i	−0.286884	−	0.882940i	−0.985827	−	0.167762i	$-0.946346\pi$
$59$	−2.20360	−	6.78199i	−0.286884	−	0.882940i	0.698943	−	0.715177i	$-0.253654\pi$
$60$		0			0
$61$	3.67232	−	11.3022i	0.470192	−	1.44710i	−0.382141	−	0.924104i	$-0.624813\pi$
$61$	3.67232	−	11.3022i	0.470192	−	1.44710i	0.852333	−	0.522999i	$-0.175187\pi$
$62$	−0.0546567	−	0.168216i	−0.00694141	−	0.0213635i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	6.77581	−	6.77764i	0.840436	−	0.840663i
$66$		0			0
$67$	−6.44701	+	4.68403i	−0.787628	+	0.572245i	−0.907259	−	0.420573i	$-0.861829\pi$
$67$	−6.44701	+	4.68403i	−0.787628	+	0.572245i	0.119631	+	0.992818i	$0.461829\pi$
$68$	−2.33185			−0.282778
$69$		0			0
$70$	−10.5563	+	1.67342i	−1.26172	+	0.200012i
$71$	−8.27651	−	6.01324i	−0.982241	−	0.713640i	−0.0240327	−	0.999711i	$-0.507651\pi$
$71$	−8.27651	−	6.01324i	−0.982241	−	0.713640i	−0.958208	+	0.286071i	$0.907651\pi$
$72$		0			0
$73$	−2.98300	+	9.18072i	−0.349133	+	1.07452i	0.610200	+	0.792247i	$0.291089\pi$
$73$	−2.98300	+	9.18072i	−0.349133	+	1.07452i	−0.959334	+	0.282275i	$0.908911\pi$
$74$	−5.09679			−0.592490
$75$		0			0
$76$	−1.38614			−0.159001
$77$	0.376847	−	1.15981i	0.0429457	−	0.132173i
$78$		0			0
$79$	2.91479	+	2.11772i	0.327940	+	0.238262i	0.739556	−	0.673095i	$-0.235036\pi$
$79$	2.91479	+	2.11772i	0.327940	+	0.238262i	−0.411616	+	0.911357i	$0.635036\pi$
$80$	−1.58092	+	1.58135i	−0.176753	+	0.176801i
$81$		0			0
$82$	−2.20509			−0.243512
$83$	12.8830	−	9.36002i	1.41409	−	1.02740i	0.421376	−	0.906886i	$-0.361547\pi$
$83$	12.8830	−	9.36002i	1.41409	−	1.02740i	0.992712	−	0.120510i	$-0.0384528\pi$
$84$		0			0
$85$	4.64618	+	2.36656i	0.503949	+	0.256689i
$86$	1.11548	−	3.43308i	0.120285	−	0.370199i
$87$		0			0
$88$	−0.0788401	−	0.242645i	−0.00840439	−	0.0258660i
$89$	−3.45616	+	10.6370i	−0.366353	+	1.12752i	0.582777	+	0.812632i	$0.301966\pi$
$89$	−3.45616	+	10.6370i	−0.366353	+	1.12752i	−0.949130	+	0.314885i	$0.898034\pi$
$90$		0			0
$91$	−6.33067	−	19.4838i	−0.663635	−	2.04246i
$92$	6.05054	−	4.39598i	0.630813	−	0.458312i
$93$		0			0
$94$	6.09086	−	4.42527i	0.628224	−	0.456431i
$95$	2.76186	+	1.40677i	0.283361	+	0.144331i
$96$		0			0
$97$	12.7454	+	9.26005i	1.29410	+	0.940215i	0.999880	−	0.0155234i	$-0.00494146\pi$
$97$	12.7454	+	9.26005i	1.29410	+	0.940215i	0.294216	+	0.955739i	$0.404941\pi$
$98$	−4.89708	+	15.0717i	−0.494680	+	1.52247i
$99$		0			0
$100$	4.75486	−	1.54637i	0.475486	−	0.154637i
$101$	3.41302			0.339608			0.169804	−	0.985478i	$-0.445687\pi$
$101$	3.41302			0.339608			0.169804	+	0.985478i	$0.445687\pi$
$102$		0			0
$103$	−11.9975	−	8.71669i	−1.18215	−	0.858881i	−0.189736	−	0.981835i	$-0.560763\pi$
$103$	−11.9975	−	8.71669i	−1.18215	−	0.858881i	−0.992412	+	0.122954i	$0.960763\pi$
$104$	−3.46743	−	2.51923i	−0.340009	−	0.247031i
$105$		0			0
$106$	10.9208	−	7.93444i	1.06072	−	0.770661i
$107$	−13.4355			−1.29886			−0.649430	−	0.760421i	$-0.724992\pi$
$107$	−13.4355			−1.29886			−0.649430	+	0.760421i	$0.724992\pi$
$108$		0			0
$109$	−0.138411	−	0.425985i	−0.0132574	−	0.0408020i	0.944209	−	0.329347i	$-0.106829\pi$
$109$	−0.138411	−	0.425985i	−0.0132574	−	0.0408020i	−0.957466	+	0.288545i	$0.906829\pi$
$110$	−0.0891685	+	0.563481i	−0.00850188	+	0.0537258i
$111$		0			0
$112$	1.47707	+	4.54594i	0.139570	+	0.429551i
$113$	−3.81333	−	11.7362i	−0.358728	−	1.10405i	−0.953816	−	0.300390i	$-0.902883\pi$
$113$	−3.81333	−	11.7362i	−0.358728	−	1.10405i	0.595089	−	0.803660i	$-0.297117\pi$
$114$		0			0
$115$	−16.5170	+	2.61833i	−1.54022	+	0.244161i
$116$	−1.96289	−	6.04116i	−0.182250	−	0.560907i
$117$		0			0
$118$	7.13100			0.656462
$119$	9.01727	−	6.55143i	0.826612	−	0.600569i
$120$		0			0
$121$	8.84653	+	6.42738i	0.804230	+	0.584307i
$122$	9.61426	+	6.98517i	0.870434	+	0.632407i
$123$		0			0
$124$	0.176873			0.0158837
$125$	−11.0434	−	1.74451i	−0.987752	−	0.156034i
$126$		0			0
$127$	−0.934486	+	2.87605i	−0.0829222	+	0.255208i	−0.983918	−	0.178619i	$-0.942837\pi$
$127$	−0.934486	+	2.87605i	−0.0829222	+	0.255208i	0.900996	+	0.433827i	$0.142837\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	4.35208	+	8.53859i	0.381703	+	0.748883i
$131$	7.66726	−	5.57059i	0.669891	−	0.486705i	−0.200097	−	0.979776i	$-0.564126\pi$
$131$	7.66726	−	5.57059i	0.669891	−	0.486705i	0.869989	+	0.493071i	$0.164126\pi$
$132$		0			0
$133$	5.36020	−	3.89441i	0.464788	−	0.337688i
$134$	−2.46254	−	7.57892i	−0.212731	−	0.654719i
$135$		0			0
$136$	0.720581	−	2.21772i	0.0617893	−	0.190168i
$137$	−5.12674	−	15.7785i	−0.438007	−	1.34805i	−0.889973	−	0.456012i	$-0.849277\pi$
$137$	−5.12674	−	15.7785i	−0.438007	−	1.34805i	0.451966	−	0.892035i	$-0.350723\pi$
$138$		0			0
$139$	6.07920	−	18.7099i	0.515631	−	1.58695i	−0.266499	−	0.963835i	$-0.585867\pi$
$139$	6.07920	−	18.7099i	0.515631	−	1.58695i	0.782130	−	0.623115i	$-0.214133\pi$
$140$	1.67057	−	10.5568i	0.141189	−	0.892211i
$141$		0			0
$142$	8.27651	−	6.01324i	0.694549	−	0.504620i
$143$	−1.09349			−0.0914423
$144$		0			0
$145$	−2.22004	+	14.0290i	−0.184364	+	1.16505i
$146$	−7.80959	−	5.67400i	−0.646326	−	0.469583i
$147$		0			0
$148$	1.57499	−	4.84733i	0.129464	−	0.398448i
$149$	9.63897			0.789655			0.394828	−	0.918755i	$-0.370804\pi$
$149$	9.63897			0.789655			0.394828	+	0.918755i	$0.370804\pi$
$150$		0			0
$151$	0.871365			0.0709107			0.0354553	−	0.999371i	$-0.488712\pi$
$151$	0.871365			0.0709107			0.0354553	+	0.999371i	$0.488712\pi$
$152$	0.428339	−	1.31829i	0.0347429	−	0.106928i
$153$		0			0
$154$	0.986597	+	0.716805i	0.0795023	+	0.0577618i
$155$	−0.352417	−	0.179506i	−0.0283068	−	0.0144182i
$156$		0			0
$157$	0.581370			0.0463984			0.0231992	−	0.999731i	$-0.492615\pi$
$157$	0.581370			0.0463984			0.0231992	+	0.999731i	$0.492615\pi$
$158$	−2.91479	+	2.11772i	−0.231888	+	0.168477i
$159$		0			0
$160$	−1.01542	−	1.99221i	−0.0802762	−	0.157498i
$161$	−11.0468	+	33.9985i	−0.870610	+	2.67946i
$162$		0			0
$163$	−6.02188	−	18.5334i	−0.471670	−	1.45165i	−0.850396	−	0.526143i	$-0.823638\pi$
$163$	−6.02188	−	18.5334i	−0.471670	−	1.45165i	0.378726	−	0.925509i	$-0.376362\pi$
$164$	0.681411	−	2.09717i	0.0532093	−	0.163761i
$165$		0			0
$166$	4.92085	+	15.1448i	0.381932	+	1.17547i
$167$	−10.1158	+	7.34954i	−0.782782	+	0.568724i	−0.905813	−	0.423678i	$-0.860739\pi$
$167$	−10.1158	+	7.34954i	−0.782782	+	0.568724i	0.123031	+	0.992403i	$0.460739\pi$
$168$		0			0
$169$	−4.34411	+	3.15618i	−0.334162	+	0.242783i
$170$	−3.68648	+	3.68747i	−0.282740	+	0.282816i
$171$		0			0
$172$	2.92036	+	2.12176i	0.222675	+	0.161783i
$173$	2.18139	−	6.71363i	0.165848	−	0.510428i	−0.833250	−	0.552897i	$-0.813522\pi$
$173$	2.18139	−	6.71363i	0.165848	−	0.510428i	0.999098	+	0.0424690i	$0.0135224\pi$
$174$		0			0
$175$	−14.0425	+	19.3388i	−1.06151	+	1.46188i
$176$	0.255132			0.0192313
$177$		0			0
$178$	−9.04835	−	6.57401i	−0.678203	−	0.492743i
$179$	4.07732	+	2.96235i	0.304753	+	0.221416i	0.729642	−	0.683829i	$-0.239687\pi$
$179$	4.07732	+	2.96235i	0.304753	+	0.221416i	−0.424889	+	0.905246i	$0.639687\pi$
$180$		0			0
$181$	−4.90348	+	3.56259i	−0.364473	+	0.264805i	−0.754915	−	0.655822i	$-0.772322\pi$
$181$	−4.90348	+	3.56259i	−0.364473	+	0.264805i	0.390442	+	0.920627i	$0.372322\pi$
$182$	20.4865			1.51856
$183$		0			0
$184$	2.31110	+	7.11284i	0.170377	+	0.524366i
$185$	−8.05764	+	8.05982i	−0.592409	+	0.592570i
$186$		0			0
$187$	−0.183843	−	0.565811i	−0.0134439	−	0.0413762i
$188$	2.32650	+	7.16023i	0.169677	+	0.522214i
$189$		0			0
$190$	−2.19138	+	2.19197i	−0.158979	+	0.159022i
$191$	3.41938	+	10.5238i	0.247417	+	0.761472i	0.995229	+	0.0975619i	$0.0311044\pi$
$191$	3.41938	+	10.5238i	0.247417	+	0.761472i	−0.747812	+	0.663910i	$0.768896\pi$
$192$		0			0
$193$	−5.05915			−0.364166			−0.182083	−	0.983283i	$-0.558284\pi$
$193$	−5.05915			−0.364166			−0.182083	+	0.983283i	$0.558284\pi$
$194$	−12.7454	+	9.26005i	−0.915064	+	0.664833i
$195$		0			0
$196$	−12.8207	−	9.31480i	−0.915766	−	0.665343i
$197$	11.7506	+	8.53731i	0.837196	+	0.608258i	0.921586	−	0.388174i	$-0.126894\pi$
$197$	11.7506	+	8.53731i	0.837196	+	0.608258i	−0.0843901	+	0.996433i	$0.526894\pi$
$198$		0			0
$199$	−13.3511			−0.946435			−0.473217	−	0.880946i	$-0.656907\pi$
$199$	−13.3511			−0.946435			−0.473217	+	0.880946i	$0.656907\pi$
$200$	0.00135278	+	5.00000i	9.56561e−5	+	0.353553i
$201$		0			0
$202$	−1.05468	+	3.24598i	−0.0742071	+	0.228386i
$203$	24.5634	+	17.8464i	1.72401	+	1.25257i
$204$		0			0
$205$	−3.48609	+	3.48703i	−0.243479	+	0.243545i
$206$	11.9975	−	8.71669i	0.835905	−	0.607320i
$207$		0			0
$208$	3.46743	−	2.51923i	0.240423	−	0.174678i
$209$	−0.109283	−	0.336339i	−0.00755927	−	0.0232650i
$210$		0			0
$211$	−1.71381	+	5.27458i	−0.117984	+	0.363117i	−0.992558	−	0.121776i	$-0.961141\pi$
$211$	−1.71381	+	5.27458i	−0.117984	+	0.363117i	0.874574	+	0.484892i	$0.161141\pi$
$212$	4.17138	+	12.8382i	0.286492	+	0.881731i
$213$		0			0
$214$	4.15180	−	12.7779i	0.283811	−	0.873481i
$215$	−3.66543	−	7.19141i	−0.249980	−	0.490450i
$216$		0			0
$217$	−0.683969	+	0.496932i	−0.0464308	+	0.0337340i
$218$	0.447908			0.0303361
$219$		0			0
$220$	−0.508348	−	0.258929i	−0.0342728	−	0.0174570i
$221$	−8.08552	−	5.87447i	−0.543891	−	0.395160i
$222$		0			0
$223$	−6.70440	+	20.6340i	−0.448960	+	1.38176i	0.429123	+	0.903246i	$0.358823\pi$
$223$	−6.70440	+	20.6340i	−0.448960	+	1.38176i	−0.878082	+	0.478510i	$0.841177\pi$
$224$	−4.77988			−0.319369
$225$		0			0
$226$	12.3402			0.820857
$227$	−5.19025	+	15.9739i	−0.344489	+	1.06023i	0.617368	+	0.786675i	$0.288199\pi$
$227$	−5.19025	+	15.9739i	−0.344489	+	1.06023i	−0.961857	+	0.273554i	$0.911801\pi$
$228$		0			0
$229$	−2.63764	−	1.91635i	−0.174300	−	0.126636i	0.497215	−	0.867627i	$-0.334356\pi$
$229$	−2.63764	−	1.91635i	−0.174300	−	0.126636i	−0.671515	+	0.740991i	$0.734356\pi$
$230$	2.61386	−	16.5178i	0.172353	−	1.08915i
$231$		0			0
$232$	6.35205			0.417032
$233$	11.0981	−	8.06322i	0.727059	−	0.528239i	−0.161573	−	0.986861i	$-0.551657\pi$
$233$	11.0981	−	8.06322i	0.727059	−	0.528239i	0.888632	+	0.458621i	$0.151657\pi$
$234$		0			0
$235$	2.63128	−	16.6278i	0.171646	−	1.08468i
$236$	−2.20360	+	6.78199i	−0.143442	+	0.441470i
$237$		0			0
$238$	3.44429	+	10.6004i	0.223260	+	0.687124i
$239$	5.42303	−	16.6904i	0.350786	−	1.07961i	−0.607626	−	0.794223i	$-0.707878\pi$
$239$	5.42303	−	16.6904i	0.350786	−	1.07961i	0.958413	−	0.285386i	$-0.0921219\pi$
$240$		0			0
$241$	−1.72397	−	5.30582i	−0.111050	−	0.341778i	0.880052	−	0.474877i	$-0.157507\pi$
$241$	−1.72397	−	5.30582i	−0.111050	−	0.341778i	−0.991103	+	0.133099i	$0.957507\pi$
$242$	−8.84653	+	6.42738i	−0.568676	+	0.413167i
$243$		0			0
$244$	−9.61426	+	6.98517i	−0.615490	+	0.447179i
$245$	16.0917	+	31.5712i	1.02806	+	2.01701i
$246$		0			0
$247$	−4.80633	−	3.49200i	−0.305819	−	0.222191i
$248$	−0.0546567	+	0.168216i	−0.00347071	+	0.0106817i
$249$		0			0
$250$	5.07172	−	9.96381i	0.320764	−	0.630167i
$251$	−9.87560			−0.623342			−0.311671	−	0.950190i	$-0.600889\pi$
$251$	−9.87560			−0.623342			−0.311671	+	0.950190i	$0.600889\pi$
$252$		0			0
$253$	1.54369	+	1.12155i	0.0970508	+	0.0705115i
$254$	−2.44652	−	1.77750i	−0.153508	−	0.111530i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	2.86272			0.178572			0.0892859	−	0.996006i	$-0.471542\pi$
$257$	2.86272			0.178572			0.0892859	+	0.996006i	$0.471542\pi$
$258$		0			0
$259$	7.52829	+	23.1697i	0.467785	+	1.43969i
$260$	−9.46554	+	1.50051i	−0.587028	+	0.0930575i
$261$		0			0
$262$	2.92863	+	9.01340i	0.180931	+	0.556850i
$263$	−5.54717	−	17.0724i	−0.342053	−	1.05273i	−0.963143	−	0.268992i	$-0.913310\pi$
$263$	−5.54717	−	17.0724i	−0.342053	−	1.05273i	0.621089	−	0.783740i	$-0.286690\pi$
$264$		0			0
$265$	4.71785	−	29.8134i	0.289815	−	1.83142i
$266$	2.04741	+	6.30129i	0.125535	+	0.386357i
$267$		0			0
$268$	7.96895			0.486781
$269$	0.298397	−	0.216798i	0.0181936	−	0.0132184i	−0.578651	−	0.815575i	$-0.696421\pi$
$269$	0.298397	−	0.216798i	0.0181936	−	0.0132184i	0.596845	+	0.802357i	$0.296421\pi$
$270$		0			0
$271$	−2.64948	−	1.92496i	−0.160945	−	0.116933i	0.504398	−	0.863471i	$-0.331714\pi$
$271$	−2.64948	−	1.92496i	−0.160945	−	0.116933i	−0.665343	+	0.746538i	$0.731714\pi$
$272$	1.88650	+	1.37063i	0.114386	+	0.0831064i
$273$		0			0
$274$	16.5905			1.00227
$275$	0.750093	+	1.03183i	0.0452323	+	0.0622216i
$276$		0			0
$277$	−2.17396	+	6.69077i	−0.130621	+	0.402010i	−0.994883	−	0.101032i	$-0.967786\pi$
$277$	−2.17396	+	6.69077i	−0.130621	+	0.402010i	0.864262	+	0.503041i	$0.167786\pi$
$278$	15.9156	+	11.5633i	0.954552	+	0.693523i
$279$		0			0
$280$	9.52386	+	4.85103i	0.569160	+	0.289904i
$281$	−1.27666	+	0.927548i	−0.0761592	+	0.0553329i	−0.625213	−	0.780454i	$-0.714988\pi$
$281$	−1.27666	+	0.927548i	−0.0761592	+	0.0553329i	0.549054	+	0.835787i	$0.314988\pi$
$282$		0			0
$283$	−7.37009	+	5.35468i	−0.438106	+	0.318303i	−0.784882	−	0.619645i	$-0.787276\pi$
$283$	−7.37009	+	5.35468i	−0.438106	+	0.318303i	0.346776	+	0.937948i	$0.387276\pi$
$284$	3.16135	+	9.72962i	0.187591	+	0.577347i
$285$		0			0
$286$	0.337907	−	1.03997i	0.0199809	−	0.0614948i
$287$	3.25707	+	10.0242i	0.192259	+	0.591711i
$288$		0			0
$289$	−3.57300	+	10.9966i	−0.210177	+	0.646858i
$290$	−12.6564	−	6.44659i	−0.743208	−	0.378557i
$291$		0			0
$292$	7.80959	−	5.67400i	0.457021	−	0.332045i
$293$	−27.7869			−1.62333			−0.811665	−	0.584123i	$-0.801439\pi$
$293$	−27.7869			−1.62333			−0.811665	+	0.584123i	$0.801439\pi$
$294$		0			0
$295$	11.2736	−	11.2766i	0.656373	−	0.656551i
$296$	4.12339	+	2.99582i	0.239667	+	0.174128i
$297$		0			0
$298$	−2.97861	+	9.16721i	−0.172546	+	0.531042i
$299$	32.0543			1.85375
$300$		0			0
$301$	−17.2542			−0.994517
$302$	−0.269267	+	0.828718i	−0.0154946	+	0.0476873i
$303$		0			0
$304$	1.12141	+	0.814750i	0.0643171	+	0.0467291i
$305$	26.2454	−	4.16051i	1.50281	−	0.238230i
$306$		0			0
$307$	−3.43949			−0.196302			−0.0981510	−	0.995172i	$-0.531293\pi$
$307$	−3.43949			−0.196302			−0.0981510	+	0.995172i	$0.531293\pi$
$308$	−0.986597	+	0.716805i	−0.0562166	+	0.0408438i
$309$		0			0
$310$	0.279623	−	0.279698i	0.0158815	−	0.0158858i
$311$	−10.0420	+	30.9062i	−0.569432	+	1.75253i	0.0849705	+	0.996383i	$0.472920\pi$
$311$	−10.0420	+	30.9062i	−0.569432	+	1.75253i	−0.654402	+	0.756147i	$0.727080\pi$
$312$		0			0
$313$	−0.129918	−	0.399848i	−0.00734342	−	0.0226007i	0.947318	−	0.320296i	$-0.103782\pi$
$313$	−0.129918	−	0.399848i	−0.00734342	−	0.0226007i	−0.954661	+	0.297695i	$0.903782\pi$
$314$	−0.179653	+	0.552916i	−0.0101384	+	0.0312028i
$315$		0			0
$316$	−1.11335	−	3.42654i	−0.0626309	−	0.192758i
$317$	10.6230	−	7.71806i	0.596647	−	0.433489i	−0.248040	−	0.968750i	$-0.579787\pi$
$317$	10.6230	−	7.71806i	0.596647	−	0.433489i	0.844687	+	0.535260i	$0.179787\pi$
$318$		0			0
$319$	1.31110	−	0.952571i	0.0734076	−	0.0533337i
$320$	2.20849	−	0.350097i	0.123458	−	0.0195710i
$321$		0			0
$322$	−28.9209	−	21.0123i	−1.61170	−	1.17097i
$323$	0.998822	−	3.07406i	0.0555760	−	0.171045i
$324$		0			0
$325$	20.3828	+	6.61669i	1.13064	+	0.367028i
$326$	19.4872			1.07930
$327$		0			0
$328$	1.78396	+	1.29612i	0.0985026	+	0.0715663i
$329$	−29.1136	−	21.1523i	−1.60508	−	1.16616i
$330$		0			0
$331$	0.934771	−	0.679151i	0.0513796	−	0.0373295i	−0.561799	−	0.827274i	$-0.689891\pi$
$331$	0.934771	−	0.679151i	0.0513796	−	0.0373295i	0.613179	+	0.789944i	$0.289891\pi$
$332$	−15.9242			−0.873955
$333$		0			0
$334$	−3.86388	−	11.8918i	−0.211422	−	0.650691i
$335$	−15.8780	−	8.08756i	−0.867510	−	0.441870i
$336$		0			0
$337$	−10.4411	−	32.1345i	−0.568765	−	1.75048i	−0.656491	−	0.754334i	$-0.727960\pi$
$337$	−10.4411	−	32.1345i	−0.568765	−	1.75048i	0.0877258	−	0.996145i	$-0.472040\pi$
$338$	−1.65930	−	5.10680i	−0.0902541	−	0.277773i
$339$		0			0
$340$	−2.36781	−	4.64554i	−0.128413	−	0.251940i
$341$	0.0139447	+	0.0429173i	0.000755147	+	0.00232410i
$342$		0			0
$343$	42.2890			2.28339
$344$	−2.92036	+	2.12176i	−0.157455	+	0.114398i
$345$		0			0
$346$	5.71096	+	4.14925i	0.307023	+	0.223065i
$347$	−8.02528	−	5.83071i	−0.430820	−	0.313009i	0.351157	−	0.936317i	$-0.385788\pi$
$347$	−8.02528	−	5.83071i	−0.430820	−	0.313009i	−0.781977	+	0.623308i	$0.785788\pi$
$348$		0			0
$349$	25.5394			1.36709			0.683546	−	0.729907i	$-0.260437\pi$
$349$	25.5394			1.36709			0.683546	+	0.729907i	$0.260437\pi$
$350$	−14.0530	−	19.3312i	−0.751162	−	1.03330i
$351$		0			0
$352$	−0.0788401	+	0.242645i	−0.00420219	+	0.0129330i
$353$	26.3730	+	19.1611i	1.40370	+	1.01984i	0.994202	+	0.107531i	$0.0342945\pi$
$353$	26.3730	+	19.1611i	1.40370	+	1.01984i	0.409493	+	0.912313i	$0.365705\pi$
$354$		0			0
$355$	3.57549	−	22.5946i	0.189767	−	1.19919i
$356$	9.04835	−	6.57401i	0.479562	−	0.348422i
$357$		0			0
$358$	−4.07732	+	2.96235i	−0.215493	+	0.156565i
$359$	3.58944	+	11.0472i	0.189444	+	0.583047i	0.999997	−	0.00261791i	$-0.000833308\pi$
$359$	3.58944	+	11.0472i	0.189444	+	0.583047i	−0.810553	+	0.585665i	$0.800833\pi$
$360$		0			0
$361$	−5.27759	+	16.2427i	−0.277768	+	0.854881i
$362$	−1.87296	−	5.76439i	−0.0984407	−	0.302969i
$363$		0			0
$364$	−6.33067	+	19.4838i	−0.331817	+	1.02123i
$365$	−21.3190	+	3.37955i	−1.11589	+	0.176894i
$366$		0			0
$367$	−11.5204	+	8.37006i	−0.601360	+	0.436913i	−0.846361	−	0.532609i	$-0.821212\pi$
$367$	−11.5204	+	8.37006i	−0.601360	+	0.436913i	0.245002	+	0.969523i	$0.421212\pi$
$368$	−7.47888			−0.389864
$369$		0			0
$370$	−5.17540	−	10.1539i	−0.269056	−	0.527876i
$371$	−52.2002	−	37.9257i	−2.71010	−	1.96900i
$372$		0			0
$373$	−3.15760	+	9.71810i	−0.163494	+	0.503184i	−0.998922	−	0.0464163i	$-0.985220\pi$
$373$	−3.15760	+	9.71810i	−0.163494	+	0.503184i	0.835428	+	0.549600i	$0.185220\pi$
$374$	0.594929			0.0307630
$375$		0			0
$376$	−7.52871			−0.388264
$377$	8.41291	−	25.8923i	0.433287	−	1.33352i
$378$		0			0
$379$	−24.4175	−	17.7403i	−1.25424	−	0.911260i	−0.255782	−	0.966734i	$-0.582333\pi$
$379$	−24.4175	−	17.7403i	−1.25424	−	0.911260i	−0.998460	+	0.0554739i	$0.982333\pi$
$380$	−1.40751	−	2.76148i	−0.0722040	−	0.141661i
$381$		0			0
$382$	−11.0653			−0.566152
$383$	−8.71000	+	6.32819i	−0.445060	+	0.323355i	−0.787642	−	0.616133i	$-0.788699\pi$
$383$	−8.71000	+	6.32819i	−0.445060	+	0.323355i	0.342582	+	0.939488i	$0.388699\pi$
$384$		0			0
$385$	2.69326	−	0.426944i	0.137261	−	0.0217591i
$386$	1.56336	−	4.81154i	0.0795732	−	0.244901i
$387$		0			0
$388$	−4.86830	−	14.9831i	−0.247150	−	0.760650i
$389$	7.66626	−	23.5943i	0.388695	−	1.19628i	−0.545070	−	0.838391i	$-0.683497\pi$
$389$	7.66626	−	23.5943i	0.388695	−	1.19628i	0.933764	−	0.357888i	$-0.116503\pi$
$390$		0			0
$391$	5.38914	+	16.5861i	0.272540	+	0.838793i
$392$	12.8207	−	9.31480i	0.647544	−	0.470469i
$393$		0			0
$394$	−11.7506	+	8.53731i	−0.591987	+	0.430104i
$395$	−1.25920	+	7.95727i	−0.0633575	+	0.400374i
$396$		0			0
$397$	15.2212	+	11.0588i	0.763929	+	0.555027i	0.900113	−	0.435657i	$-0.143484\pi$
$397$	15.2212	+	11.0588i	0.763929	+	0.555027i	−0.136184	+	0.990684i	$0.543484\pi$
$398$	4.12572	−	12.6977i	0.206804	−	0.636476i
$399$		0			0
$400$	−4.75570	−	1.54380i	−0.237785	−	0.0771899i
$401$	35.7666			1.78610			0.893048	−	0.449961i	$-0.148562\pi$
$401$	35.7666			1.78610			0.893048	+	0.449961i	$0.148562\pi$
$402$		0			0
$403$	0.613294	+	0.445584i	0.0305504	+	0.0221961i
$404$	−2.76119	−	2.00612i	−0.137374	−	0.0998084i
$405$		0			0
$406$	−24.5634	+	17.8464i	−1.21906	+	0.885700i
$407$	1.30035			0.0644561
$408$		0			0
$409$	−3.83837	−	11.8133i	−0.189795	−	0.584130i	0.810203	−	0.586150i	$-0.199357\pi$
$409$	−3.83837	−	11.8133i	−0.189795	−	0.584130i	−0.999998	+	0.00201985i	$0.999357\pi$
$410$	−2.23910	−	4.39302i	−0.110581	−	0.216956i
$411$		0			0
$412$	4.58263	+	14.1039i	0.225770	+	0.694849i
$413$	−10.5330	−	32.4171i	−0.518293	−	1.59514i
$414$		0			0
$415$	31.7288	+	16.1612i	1.55751	+	0.793324i
$416$	1.32444	+	4.07621i	0.0649360	+	0.199853i
$417$		0			0
$418$	0.353648			0.0172975
$419$	−7.86313	+	5.71290i	−0.384139	+	0.279093i	−0.763050	−	0.646340i	$-0.776299\pi$
$419$	−7.86313	+	5.71290i	−0.384139	+	0.279093i	0.378910	+	0.925433i	$0.376299\pi$
$420$		0			0
$421$	31.0325	+	22.5464i	1.51243	+	1.09885i	0.965084	+	0.261940i	$0.0843623\pi$
$421$	31.0325	+	22.5464i	1.51243	+	1.09885i	0.547347	+	0.836906i	$0.315638\pi$
$422$	−4.48682	−	3.25987i	−0.218415	−	0.158688i
$423$		0			0
$424$	−13.4989			−0.655563
$425$	0.00315448	+	11.6592i	0.000153015	+	0.565556i
$426$		0			0
$427$	17.5533	−	54.0234i	0.849462	−	2.61437i
$428$	10.8696	+	7.89719i	0.525400	+	0.381725i
$429$		0			0
$430$	7.97212	−	1.26376i	0.384450	−	0.0609441i
$431$	8.60869	−	6.25458i	0.414666	−	0.301273i	−0.360822	−	0.932635i	$-0.617504\pi$
$431$	8.60869	−	6.25458i	0.414666	−	0.301273i	0.775488	+	0.631362i	$0.217504\pi$
$432$		0			0
$433$	25.3450	−	18.4142i	1.21800	−	0.884930i	0.222069	−	0.975031i	$-0.428719\pi$
$433$	25.3450	−	18.4142i	1.21800	−	0.884930i	0.995933	+	0.0901010i	$0.0287190\pi$
$434$	−0.261253	−	0.804054i	−0.0125405	−	0.0385958i
$435$		0			0
$436$	−0.138411	+	0.425985i	−0.00662869	+	0.0204010i
$437$	3.20350	+	9.85936i	0.153244	+	0.471637i
$438$		0			0
$439$	−1.24572	+	3.83392i	−0.0594548	+	0.182983i	−0.976373	−	0.216092i	$-0.930669\pi$
$439$	−1.24572	+	3.83392i	−0.0594548	+	0.182983i	0.916918	+	0.399075i	$0.130669\pi$
$440$	0.403345	−	0.403454i	0.0192287	−	0.0192339i
$441$		0			0
$442$	8.08552	−	5.87447i	0.384589	−	0.279420i
$443$	−19.6040			−0.931413			−0.465706	−	0.884939i	$-0.654200\pi$
$443$	−19.6040			−0.931413			−0.465706	+	0.884939i	$0.654200\pi$
$444$		0			0
$445$	−24.7006	+	3.91562i	−1.17092	+	0.185618i
$446$	−17.5523	−	12.7525i	−0.831127	−	0.603849i
$447$		0			0
$448$	1.47707	−	4.54594i	0.0697848	−	0.214775i
$449$	−27.3128			−1.28897			−0.644484	−	0.764617i	$-0.722928\pi$
$449$	−27.3128			−1.28897			−0.644484	+	0.764617i	$0.722928\pi$
$450$		0			0
$451$	0.562590			0.0264913
$452$	−3.81333	+	11.7362i	−0.179364	+	0.552025i
$453$		0			0
$454$	−13.5883	−	9.87244i	−0.637728	−	0.463337i
$455$	32.3876	−	32.3963i	1.51835	−	1.51876i
$456$		0			0
$457$	−15.3527			−0.718171			−0.359085	−	0.933305i	$-0.616911\pi$
$457$	−15.3527			−0.718171			−0.359085	+	0.933305i	$0.616911\pi$
$458$	2.63764	−	1.91635i	0.123249	−	0.0895453i
$459$		0			0
$460$	14.9016	+	7.59020i	0.694790	+	0.353895i
$461$	2.67581	−	8.23529i	0.124625	−	0.383555i	−0.869208	−	0.494447i	$-0.835371\pi$
$461$	2.67581	−	8.23529i	0.124625	−	0.383555i	0.993833	+	0.110892i	$0.0353706\pi$
$462$		0			0
$463$	7.86851	+	24.2168i	0.365680	+	1.12545i	0.949554	+	0.313604i	$0.101536\pi$
$463$	7.86851	+	24.2168i	0.365680	+	1.12545i	−0.583873	+	0.811845i	$0.698464\pi$
$464$	−1.96289	+	6.04116i	−0.0911249	+	0.280454i
$465$		0			0
$466$	4.23909	+	13.0466i	0.196372	+	0.604371i
$467$	−4.12104	+	2.99411i	−0.190699	+	0.138551i	−0.679038	−	0.734103i	$-0.737603\pi$
$467$	−4.12104	+	2.99411i	−0.190699	+	0.138551i	0.488339	+	0.872654i	$0.337603\pi$
$468$		0			0
$469$	−30.8160	+	22.3891i	−1.42295	+	1.03383i
$470$	15.0009	+	7.64077i	0.691939	+	0.352443i
$471$		0			0
$472$	−5.76910	−	4.19150i	−0.265544	−	0.192929i
$473$	−0.284594	+	0.875889i	−0.0130856	+	0.0402734i
$474$		0			0
$475$	0.00187514	+	6.93068i	8.60372e−5	+	0.318001i
$476$	−11.1460			−0.510874
$477$		0			0
$478$	14.1977	+	10.3152i	0.649386	+	0.471807i
$479$	27.4641	+	19.9538i	1.25487	+	0.911713i	0.998494	−	0.0548650i	$-0.0174728\pi$
$479$	27.4641	+	19.9538i	1.25487	+	0.911713i	0.256372	+	0.966578i	$0.417473\pi$
$480$		0			0
$481$	17.6728	−	12.8400i	0.805808	−	0.585454i
$482$	5.57887			0.254111
$483$		0			0
$484$	−3.37907	−	10.3997i	−0.153594	−	0.472714i
$485$	−5.50606	+	34.7944i	−0.250017	+	1.57993i
$486$		0			0
$487$	1.94471	+	5.98522i	0.0881234	+	0.271216i	0.985401	−	0.170252i	$-0.0544580\pi$
$487$	1.94471	+	5.98522i	0.0881234	+	0.271216i	−0.897277	+	0.441468i	$0.854458\pi$
$488$	−3.67232	−	11.3022i	−0.166238	−	0.511628i
$489$		0			0
$490$	−34.9986	+	5.54809i	−1.58108	+	0.250637i
$491$	0.148389	+	0.456694i	0.00669669	+	0.0206103i	0.954349	−	0.298694i	$-0.0965509\pi$
$491$	0.148389	+	0.456694i	0.00669669	+	0.0206103i	−0.947652	+	0.319304i	$0.896551\pi$
$492$		0			0
$493$	14.8120			0.667099
$494$	4.80633	−	3.49200i	0.216247	−	0.157113i
$495$		0			0
$496$	−0.143093	−	0.103963i	−0.00642507	−	0.00466809i
$497$	−39.5608	−	28.7426i	−1.77454	−	1.28928i
$498$		0			0
$499$	−42.8785			−1.91950			−0.959752	−	0.280848i	$-0.909384\pi$
$499$	−42.8785			−1.91950			−0.959752	+	0.280848i	$0.909384\pi$
$500$	7.90890	+	7.90249i	0.353697	+	0.353410i
$501$		0			0
$502$	3.05173	−	9.39225i	0.136205	−	0.419197i
$503$	4.81519	+	3.49844i	0.214699	+	0.155988i	0.689937	−	0.723869i	$-0.257638\pi$
$503$	4.81519	+	3.49844i	0.214699	+	0.155988i	−0.475238	+	0.879857i	$0.657638\pi$
$504$		0			0
$505$	3.46566	+	6.79947i	0.154220	+	0.302572i
$506$	−1.54369	+	1.12155i	−0.0686253	+	0.0498592i
$507$		0			0
$508$	2.44652	−	1.77750i	0.108547	−	0.0788637i
$509$	3.48006	+	10.7105i	0.154251	+	0.474735i	0.998084	−	0.0618700i	$-0.0197064\pi$
$509$	3.48006	+	10.7105i	0.154251	+	0.474735i	−0.843833	+	0.536605i	$0.819706\pi$
$510$		0			0
$511$	−14.2584	+	43.8828i	−0.630753	+	1.94126i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−0.884630	+	2.72261i	−0.0390194	+	0.120089i
$515$	5.18298	−	32.7527i	0.228389	−	1.44326i
$516$		0			0
$517$	−1.55397	+	1.12903i	−0.0683436	+	0.0496546i
$518$	−24.3621			−1.07041
$519$		0			0
$520$	1.49795	−	9.46595i	0.0656893	−	0.415109i
$521$	0.360123	+	0.261644i	0.0157773	+	0.0114629i	0.595646	−	0.803247i	$-0.296896\pi$
$521$	0.360123	+	0.261644i	0.0157773	+	0.0114629i	−0.579869	+	0.814710i	$0.696896\pi$
$522$		0			0
$523$	6.78786	−	20.8909i	0.296812	−	0.913495i	−0.685794	−	0.727796i	$-0.740545\pi$
$523$	6.78786	−	20.8909i	0.296812	−	0.913495i	0.982607	−	0.185699i	$-0.0594550\pi$
$524$	−9.47725			−0.414016
$525$		0			0
$526$	17.9510			0.782702
$527$	−0.127451	+	0.392254i	−0.00555186	+	0.0170869i
$528$		0			0
$529$	−26.6439	−	19.3579i	−1.15843	−	0.841649i
$530$	26.8964	+	13.6998i	1.16830	+	0.595081i
$531$		0			0
$532$	−6.62557			−0.287255
$533$	7.64600	−	5.55515i	0.331185	−	0.240620i
$534$		0			0
$535$	−13.6427	−	26.7664i	−0.589827	−	1.15721i
$536$	−2.46254	+	7.57892i	−0.106366	+	0.327359i
$537$		0			0
$538$	0.113977	+	0.350787i	0.00491392	+	0.0151235i
$539$	1.24940	−	3.84527i	0.0538156	−	0.165627i
$540$		0			0
$541$	3.15639	+	9.71438i	0.135704	+	0.417654i	0.995699	−	0.0926487i	$-0.0295334\pi$
$541$	3.15639	+	9.71438i	0.135704	+	0.417654i	−0.859995	+	0.510303i	$0.829533\pi$
$542$	2.64948	−	1.92496i	0.113805	−	0.0826842i
$543$		0			0
$544$	−1.88650	+	1.37063i	−0.0808832	+	0.0587651i
$545$	0.708108	−	0.708300i	0.0303320	−	0.0303402i
$546$		0			0
$547$	−9.48068	−	6.88812i	−0.405365	−	0.294515i	0.366358	−	0.930474i	$-0.380605\pi$
$547$	−9.48068	−	6.88812i	−0.405365	−	0.294515i	−0.771723	+	0.635959i	$0.780605\pi$
$548$	−5.12674	+	15.7785i	−0.219004	+	0.674024i
$549$		0			0
$550$	−1.21312	+	0.394529i	−0.0517275	+	0.0168228i
$551$	8.80480			0.375097
$552$		0			0
$553$	13.9324	+	10.1225i	0.592465	+	0.430451i
$554$	−5.69151	−	4.13513i	−0.241809	−	0.175685i
$555$		0			0
$556$	−15.9156	+	11.5633i	−0.674970	+	0.490395i
$557$	−3.38123			−0.143267			−0.0716336	−	0.997431i	$-0.522821\pi$
$557$	−3.38123			−0.143267			−0.0716336	+	0.997431i	$0.522821\pi$
$558$		0			0
$559$	4.78091	+	14.7141i	0.202211	+	0.622341i
$560$	−7.55664	+	7.55868i	−0.319326	+	0.319413i
$561$		0			0
$562$	−0.487641	−	1.50080i	−0.0205699	−	0.0633076i
$563$	3.49579	+	10.7589i	0.147330	+	0.453435i	0.997303	−	0.0733910i	$-0.0233821\pi$
$563$	3.49579	+	10.7589i	0.147330	+	0.453435i	−0.849973	+	0.526826i	$0.823382\pi$
$564$		0			0
$565$	19.5089	−	19.5142i	0.820746	−	0.820968i
$566$	−2.81512	−	8.66406i	−0.118328	−	0.364178i
$567$		0			0
$568$	−10.2303			−0.429255
$569$	−19.9941	+	14.5266i	−0.838197	+	0.608986i	−0.921867	−	0.387507i	$-0.873336\pi$
$569$	−19.9941	+	14.5266i	−0.838197	+	0.608986i	0.0836691	+	0.996494i	$0.473336\pi$
$570$		0			0
$571$	0.171950	+	0.124929i	0.00719590	+	0.00522812i	0.591377	−	0.806395i	$-0.298584\pi$
$571$	0.171950	+	0.124929i	0.00719590	+	0.00522812i	−0.584181	+	0.811623i	$0.698584\pi$
$572$	0.884652	+	0.642737i	0.0369892	+	0.0268742i
$573$		0			0
$574$	−10.5401			−0.439935
$575$	−21.9881	−	30.2468i	−0.916966	−	1.26138i
$576$		0			0
$577$	−3.08858	+	9.50568i	−0.128579	+	0.395727i	−0.994536	−	0.104392i	$-0.966710\pi$
$577$	−3.08858	+	9.50568i	−0.128579	+	0.395727i	0.865957	+	0.500119i	$0.166710\pi$
$578$	−9.35425	−	6.79626i	−0.389085	−	0.282687i
$579$		0			0
$580$	10.0421	−	10.0448i	0.416976	−	0.417089i
$581$	61.5790	−	44.7398i	2.55473	−	1.85612i
$582$		0			0
$583$	−2.78625	+	2.02433i	−0.115395	+	0.0838392i
$584$	2.98300	+	9.18072i	0.123437	+	0.379901i
$585$		0			0
$586$	8.58664	−	26.4269i	0.354711	−	1.09169i
$587$	−3.53822	−	10.8895i	−0.146038	−	0.449458i	0.851105	−	0.524995i	$-0.175933\pi$
$587$	−3.53822	−	10.8895i	−0.146038	−	0.449458i	−0.997143	+	0.0755369i	$0.975933\pi$
$588$		0			0
$589$	−0.0757616	+	0.233170i	−0.00312170	+	0.00960762i
$590$	7.24099	+	14.2065i	0.298107	+	0.584872i
$591$		0			0
$592$	−4.12339	+	2.99582i	−0.169470	+	0.123127i
$593$	−5.62288			−0.230904			−0.115452	−	0.993313i	$-0.536832\pi$
$593$	−5.62288			−0.230904			−0.115452	+	0.993313i	$0.536832\pi$
$594$		0			0
$595$	22.2082	+	11.3119i	0.910447	+	0.463741i
$596$	−7.79809	−	5.66565i	−0.319422	−	0.232074i
$597$		0			0
$598$	−9.90533	+	30.4855i	−0.405059	+	1.24664i
$599$	−8.88538			−0.363047			−0.181523	−	0.983387i	$-0.558103\pi$
$599$	−8.88538			−0.363047			−0.181523	+	0.983387i	$0.558103\pi$
$600$		0			0
$601$	−14.8888			−0.607328			−0.303664	−	0.952779i	$-0.598210\pi$
$601$	−14.8888			−0.607328			−0.303664	+	0.952779i	$0.598210\pi$
$602$	5.33185	−	16.4097i	0.217310	−	0.668811i
$603$		0			0
$604$	−0.704949	−	0.512176i	−0.0286840	−	0.0208401i
$605$	−3.82174	+	24.1507i	−0.155376	+	0.981865i
$606$		0			0
$607$	25.5466			1.03690			0.518452	−	0.855107i	$-0.326509\pi$
$607$	25.5466			1.03690			0.518452	+	0.855107i	$0.326509\pi$
$608$	−1.12141	+	0.814750i	−0.0454791	+	0.0330425i
$609$		0			0
$610$	−4.15341	+	26.2466i	−0.168166	+	1.06269i
$611$	−9.97133	+	30.6886i	−0.403397	+	1.24153i
$612$		0			0
$613$	8.59084	+	26.4399i	0.346981	+	1.06790i	0.960515	+	0.278229i	$0.0897474\pi$
$613$	8.59084	+	26.4399i	0.346981	+	1.06790i	−0.613534	+	0.789668i	$0.710253\pi$
$614$	1.06286	−	3.27115i	0.0428936	−	0.132013i
$615$		0			0
$616$	−0.376847	−	1.15981i	−0.0151836	−	0.0467303i
$617$	−3.89334	+	2.82868i	−0.156740	+	0.113878i	−0.663391	−	0.748273i	$-0.730883\pi$
$617$	−3.89334	+	2.82868i	−0.156740	+	0.113878i	0.506651	+	0.862151i	$0.330883\pi$
$618$		0			0
$619$	25.0600	−	18.2072i	1.00725	−	0.731809i	0.0436181	−	0.999048i	$-0.486112\pi$
$619$	25.0600	−	18.2072i	1.00725	−	0.731809i	0.963630	+	0.267240i	$0.0861115\pi$
$620$	0.179601	+	0.352369i	0.00721294	+	0.0141515i
$621$		0			0
$622$	−26.2904	−	19.1011i	−1.05415	−	0.765884i
$623$	−16.5201	+	50.8435i	−0.661862	+	2.03700i
$624$		0			0
$625$	−7.73829	−	23.7722i	−0.309532	−	0.950889i
$626$	0.420425			0.0168036
$627$		0			0
$628$	−0.470338	−	0.341721i	−0.0187685	−	0.0136361i
$629$	9.61511	+	6.98579i	0.383380	+	0.278542i
$630$		0			0
$631$	19.5916	−	14.2342i	0.779931	−	0.566653i	−0.125027	−	0.992153i	$-0.539902\pi$
$631$	19.5916	−	14.2342i	0.779931	−	0.566653i	0.904958	+	0.425500i	$0.139902\pi$
$632$	3.60288			0.143315
$633$		0			0
$634$	4.05762	+	12.4881i	0.161149	+	0.495965i
$635$	−6.67861	+	1.05871i	−0.265032	+	0.0420138i
$636$		0			0
$637$	−20.9888	−	64.5968i	−0.831606	−	2.55942i
$638$	0.500796	+	1.54129i	0.0198267	+	0.0610204i
$639$		0			0
$640$	−0.349499	+	2.20859i	−0.0138152	+	0.0873020i
$641$	11.9865	+	36.8907i	0.473439	+	1.45710i	0.848051	+	0.529914i	$0.177776\pi$
$641$	11.9865	+	36.8907i	0.473439	+	1.45710i	−0.374612	+	0.927182i	$0.622224\pi$
$642$		0			0
$643$	22.6312			0.892487			0.446243	−	0.894912i	$-0.352762\pi$
$643$	22.6312			0.892487			0.446243	+	0.894912i	$0.352762\pi$
$644$	28.9209	−	21.0123i	1.13964	−	0.827999i
$645$		0			0
$646$	2.61495	+	1.89987i	0.102884	+	0.0747495i
$647$	28.4009	+	20.6345i	1.11655	+	0.811224i	0.983683	−	0.179909i	$-0.0575803\pi$
$647$	28.4009	+	20.6345i	1.11655	+	0.811224i	0.132871	+	0.991133i	$0.457580\pi$
$648$		0			0
$649$	−1.81935			−0.0714156
$650$	−12.5915	+	17.3406i	−0.493879	+	0.680152i
$651$		0			0
$652$	−6.02188	+	18.5334i	−0.235835	+	0.725826i
$653$	−11.7901	−	8.56604i	−0.461384	−	0.335215i	0.332690	−	0.943036i	$-0.392044\pi$
$653$	−11.7901	−	8.56604i	−0.461384	−	0.335215i	−0.794074	+	0.607821i	$0.792044\pi$
$654$		0			0
$655$	18.8833	+	9.61831i	0.737832	+	0.375819i
$656$	−1.78396	+	1.29612i	−0.0696518	+	0.0506050i
$657$		0			0
$658$	29.1136	−	21.1523i	1.13497	−	0.824601i
$659$	12.5559	+	38.6430i	0.489107	+	1.50532i	0.825943	+	0.563754i	$0.190643\pi$
$659$	12.5559	+	38.6430i	0.489107	+	1.50532i	−0.336836	+	0.941563i	$0.609357\pi$
$660$		0			0
$661$	−1.93964	+	5.96961i	−0.0754434	+	0.232191i	−0.981666	−	0.190611i	$-0.938953\pi$
$661$	−1.93964	+	5.96961i	−0.0754434	+	0.232191i	0.906222	+	0.422801i	$0.138953\pi$
$662$	0.357051	+	1.09889i	0.0138772	+	0.0427095i
$663$		0			0
$664$	4.92085	−	15.1448i	0.190966	−	0.587733i
$665$	13.2014	+	6.72418i	0.511927	+	0.260753i
$666$		0			0
$667$	−38.4333	+	27.9235i	−1.48814	+	1.08120i
$668$	12.5038			0.483786
$669$		0			0
$670$	12.5983	−	12.6017i	0.486715	−	0.486847i
$671$	−2.45290	−	1.78214i	−0.0946933	−	0.0687987i
$672$		0			0
$673$	5.21059	−	16.0365i	0.200853	−	0.618163i	−0.799005	−	0.601325i	$-0.794640\pi$
$673$	5.21059	−	16.0365i	0.200853	−	0.618163i	0.999858	−	0.0168387i	$-0.00536019\pi$
$674$	33.7882			1.30147
$675$		0			0
$676$	5.36961			0.206523
$677$	−6.81919	+	20.9873i	−0.262083	+	0.806608i	0.730268	+	0.683160i	$0.239395\pi$
$677$	−6.81919	+	20.9873i	−0.262083	+	0.806608i	−0.992351	+	0.123447i	$0.960605\pi$
$678$		0			0
$679$	60.9214	+	44.2620i	2.33795	+	1.69862i
$680$	5.14986	−	0.816373i	0.197488	−	0.0313065i
$681$		0			0
$682$	−0.0451259			−0.00172796
$683$	18.4449	−	13.4010i	0.705776	−	0.512776i	−0.176032	−	0.984384i	$-0.556326\pi$
$683$	18.4449	−	13.4010i	0.705776	−	0.512776i	0.881808	+	0.471608i	$0.156326\pi$
$684$		0			0
$685$	26.2283	−	26.2354i	1.00213	−	1.00240i
$686$	−13.0680	+	40.2192i	−0.498939	+	1.53558i
$687$		0			0
$688$	−1.11548	−	3.43308i	−0.0425271	−	0.130885i
$689$	−17.8785	+	55.0242i	−0.681115	+	2.09626i
$690$		0			0
$691$	2.57510	+	7.92535i	0.0979615	+	0.301495i	0.988014	−	0.154363i	$-0.0493326\pi$
$691$	2.57510	+	7.92535i	0.0979615	+	0.301495i	−0.890053	+	0.455858i	$0.849333\pi$
$692$	−5.71096	+	4.14925i	−0.217098	+	0.157731i
$693$		0			0
$694$	8.02528	−	5.83071i	0.304636	−	0.221331i
$695$	43.4470	−	6.88736i	1.64804	−	0.261252i
$696$		0			0
$697$	4.15992	+	3.02236i	0.157568	+	0.114480i
$698$	−7.89211	+	24.2894i	−0.298721	+	0.919368i
$699$		0			0
$700$	22.7277	−	7.39148i	0.859026	−	0.279372i
$701$	34.5465			1.30480			0.652401	−	0.757874i	$-0.273762\pi$
$701$	34.5465			1.30480			0.652401	+	0.757874i	$0.273762\pi$
$702$		0			0
$703$	5.71557	+	4.15261i	0.215567	+	0.156619i
$704$	−0.206406	−	0.149963i	−0.00777922	−	0.00565194i
$705$		0			0
$706$	−26.3730	+	19.1611i	−0.992562	+	0.721139i
$707$	16.3138			0.613545
$708$		0			0
$709$	−7.06612	−	21.7473i	−0.265374	−	0.816736i	−0.991607	−	0.129288i	$-0.958731\pi$
$709$	−7.06612	−	21.7473i	−0.265374	−	0.816736i	0.726234	−	0.687448i	$-0.241269\pi$
$710$	20.3838	+	10.3826i	0.764991	+	0.389652i
$711$		0			0
$712$	3.45616	+	10.6370i	0.129525	+	0.398638i
$713$	−0.408771	−	1.25807i	−0.0153086	−	0.0471150i
$714$		0			0
$715$	−1.11036	−	2.17847i	−0.0415249	−	0.0814700i
$716$	−1.55740	−	4.79318i	−0.0582027	−	0.179129i
$717$		0			0
$718$	−11.6157			−0.433493
$719$	27.1888	−	19.7539i	1.01397	−	0.736694i	0.0489342	−	0.998802i	$-0.484418\pi$
$719$	27.1888	−	19.7539i	1.01397	−	0.736694i	0.965039	+	0.262108i	$0.0844175\pi$
$720$		0			0
$721$	−57.3466	−	41.6648i	−2.13570	−	1.55168i
$722$	−13.8169	−	10.0386i	−0.514212	−	0.373597i
$723$		0			0
$724$	6.06103			0.225257
$725$	−30.2031	+	9.82263i	−1.12172	+	0.364803i
$726$		0			0
$727$	−5.91374	+	18.2006i	−0.219328	+	0.675023i	0.779490	+	0.626415i	$0.215479\pi$
$727$	−5.91374	+	18.2006i	−0.219328	+	0.675023i	−0.998818	+	0.0486081i	$0.984521\pi$
$728$	−16.5739	−	12.0416i	−0.614270	−	0.446293i
$729$		0			0
$730$	3.37378	−	21.3199i	0.124869	−	0.789084i
$731$	−6.80982	+	4.94763i	−0.251870	+	0.182995i
$732$		0			0
$733$	−34.6916	+	25.2049i	−1.28136	+	0.930964i	−0.999593	−	0.0285186i	$-0.990921\pi$
$733$	−34.6916	+	25.2049i	−1.28136	+	0.930964i	−0.281769	+	0.959482i	$0.590921\pi$
$734$	−4.40040	−	13.5430i	−0.162422	−	0.499883i
$735$		0			0
$736$	2.31110	−	7.11284i	0.0851883	−	0.262183i
$737$	0.628273	+	1.93362i	0.0231427	+	0.0712260i
$738$		0			0
$739$	−0.116966	+	0.359983i	−0.00430265	+	0.0132422i	−0.953185	−	0.302388i	$-0.902216\pi$
$739$	−0.116966	+	0.359983i	−0.00430265	+	0.0132422i	0.948882	+	0.315631i	$0.102216\pi$
$740$	11.2562	−	1.78437i	0.413787	−	0.0655947i
$741$		0			0
$742$	52.2002	−	37.9257i	1.91633	−	1.39230i
$743$	−1.02959			−0.0377720			−0.0188860	−	0.999822i	$-0.506012\pi$
$743$	−1.02959			−0.0377720			−0.0188860	+	0.999822i	$0.506012\pi$
$744$		0			0
$745$	9.78764	+	19.2029i	0.358591	+	0.703540i
$746$	−8.26671	−	6.00611i	−0.302666	−	0.219899i
$747$		0			0
$748$	−0.183843	+	0.565811i	−0.00672197	+	0.0206881i
$749$	−64.2202			−2.34655
$750$		0			0
$751$	−0.274836			−0.0100289			−0.00501445	−	0.999987i	$-0.501596\pi$
$751$	−0.274836			−0.0100289			−0.00501445	+	0.999987i	$0.501596\pi$
$752$	2.32650	−	7.16023i	0.0848387	−	0.261107i
$753$		0			0
$754$	22.0253	+	16.0023i	0.802113	+	0.582769i
$755$	0.884804	+	1.73595i	0.0322013	+	0.0631775i
$756$		0			0
$757$	−29.6425			−1.07737			−0.538687	−	0.842506i	$-0.681079\pi$
$757$	−29.6425			−1.07737			−0.538687	+	0.842506i	$0.681079\pi$
$758$	24.4175	−	17.7403i	0.886883	−	0.644358i
$759$		0			0
$760$	3.06127	−	0.485282i	0.111044	−	0.0176030i
$761$	0.569688	−	1.75332i	0.0206512	−	0.0635578i	−0.940200	−	0.340623i	$-0.889362\pi$
$761$	0.569688	−	1.75332i	0.0206512	−	0.0635578i	0.960851	+	0.277066i	$0.0893619\pi$
$762$		0			0
$763$	−0.661589	−	2.03616i	−0.0239511	−	0.0737140i
$764$	3.41938	−	10.5238i	0.123709	−	0.380736i
$765$		0			0
$766$	−3.32692	−	10.2392i	−0.120207	−	0.369958i
$767$	−24.7263	+	17.9647i	−0.892813	+	0.648667i
$768$		0			0
$769$	−15.7322	+	11.4301i	−0.567317	+	0.412180i	−0.834130	−	0.551569i	$-0.814030\pi$
$769$	−15.7322	+	11.4301i	−0.567317	+	0.412180i	0.266813	+	0.963748i	$0.414030\pi$
$770$	−0.426215	+	2.69337i	−0.0153597	+	0.0970624i
$771$		0			0
$772$	4.09294	+	2.97370i	0.147308	+	0.107026i
$773$	−7.69523	+	23.6835i	−0.276778	+	0.851836i	0.711965	+	0.702215i	$0.247805\pi$
$773$	−7.69523	+	23.6835i	−0.276778	+	0.851836i	−0.988743	+	0.149621i	$0.952195\pi$
$774$		0			0
$775$	−0.000239270	−	0.884365i	−8.59485e−6	−	0.0317673i
$776$	15.7541			0.565541
$777$		0			0
$778$	20.0705	+	14.5821i	0.719563	+	0.522793i
$779$	2.47281	+	1.79660i	0.0885975	+	0.0643699i
$780$		0			0
$781$	−2.11160	+	1.53417i	−0.0755591	+	0.0548969i
$782$	−17.4396			−0.623639
$783$		0			0
$784$	4.89708	+	15.0717i	0.174896	+	0.538274i
$785$	0.590336	+	1.15821i	0.0210700	+	0.0413384i
$786$		0			0
$787$	−3.21146	−	9.88387i	−0.114476	−	0.352322i	0.877361	−	0.479831i	$-0.159302\pi$
$787$	−3.21146	−	9.88387i	−0.114476	−	0.352322i	−0.991837	+	0.127509i	$0.959302\pi$
$788$	−4.48833	−	13.8137i	−0.159890	−	0.492091i
$789$		0			0
$790$	−7.17870	−	3.65651i	−0.255407	−	0.130093i
$791$	−18.2273	−	56.0977i	−0.648087	−	1.99461i
$792$		0			0
$793$	−50.9340			−1.80872
$794$	−15.2212	+	11.0588i	−0.540179	+	0.392463i
$795$		0			0
$796$	10.8013	+	7.84758i	0.382841	+	0.278150i
$797$	24.4435	+	17.7592i	0.865832	+	0.629064i	0.929465	−	0.368910i	$-0.120269\pi$
$797$	24.4435	+	17.7592i	0.865832	+	0.629064i	−0.0636335	+	0.997973i	$0.520269\pi$
$798$		0			0
$799$	−17.5558			−0.621080
$800$	2.93783	−	4.04588i	0.103868	−	0.143043i
$801$		0			0
$802$	−11.0525	+	34.0160i	−0.390276	+	1.20115i
$803$	1.99248	+	1.44762i	0.0703129	+	0.0510853i
$804$		0			0
$805$	−78.9496	+	12.5153i	−2.78261	+	0.441107i
$806$	−0.613294	+	0.445584i	−0.0216024	+	0.0156950i
$807$		0			0
$808$	2.76119	−	2.00612i	0.0971384	−	0.0705752i
$809$	−14.2404	−	43.8276i	−0.500667	−	1.54090i	−0.807935	−	0.589272i	$-0.799415\pi$
$809$	−14.2404	−	43.8276i	−0.500667	−	1.54090i	0.307267	−	0.951623i	$-0.400585\pi$
$810$		0			0
$811$	4.82498	−	14.8498i	0.169428	−	0.521446i	−0.829907	−	0.557901i	$-0.811607\pi$
$811$	4.82498	−	14.8498i	0.169428	−	0.521446i	0.999335	+	0.0364555i	$0.0116067\pi$
$812$	−9.38239	−	28.8760i	−0.329257	−	1.01335i
$813$		0			0
$814$	−0.401831	+	1.23671i	−0.0140842	+	0.0433467i
$815$	30.8078	−	30.8162i	1.07915	−	1.07944i
$816$		0			0
$817$	−4.04801	+	2.94105i	−0.141622	+	0.102894i
$818$	12.4212			0.434298
$819$		0			0
$820$	4.86993	−	0.771996i	0.170065	−	0.0269593i
$821$	−28.0617	−	20.3880i	−0.979359	−	0.711546i	−0.0217941	−	0.999762i	$-0.506938\pi$
$821$	−28.0617	−	20.3880i	−0.979359	−	0.711546i	−0.957565	+	0.288216i	$0.906938\pi$
$822$		0			0
$823$	−5.04410	+	15.5242i	−0.175826	+	0.541138i	−0.999670	−	0.0256788i	$-0.991825\pi$
$823$	−5.04410	+	15.5242i	−0.175826	+	0.541138i	0.823844	+	0.566817i	$0.191825\pi$
$824$	−14.8297			−0.516618
$825$		0			0
$826$	34.0854			1.18598
$827$	10.6836	−	32.8808i	0.371505	−	1.14338i	−0.574301	−	0.818644i	$-0.694726\pi$
$827$	10.6836	−	32.8808i	0.371505	−	1.14338i	0.945806	−	0.324732i	$-0.105274\pi$
$828$		0			0
$829$	−15.7263	−	11.4258i	−0.546198	−	0.396836i	0.280184	−	0.959946i	$-0.409605\pi$
$829$	−15.7263	−	11.4258i	−0.546198	−	0.396836i	−0.826382	+	0.563110i	$0.809605\pi$
$830$	−25.1750	+	25.1818i	−0.873837	+	0.874073i
$831$		0			0
$832$	−4.28598			−0.148590
$833$	29.8960	−	21.7207i	1.03583	−	0.752578i
$834$		0			0
$835$	−24.9136	−	12.6899i	−0.862172	−	0.439152i
$836$	−0.109283	+	0.336339i	−0.00377964	+	0.0116325i
$837$		0			0
$838$	−3.00345	−	9.24367i	−0.103752	−	0.319317i
$839$	−3.29911	+	10.1536i	−0.113898	+	0.350541i	−0.991716	−	0.128453i	$-0.958999\pi$
$839$	−3.29911	+	10.1536i	−0.113898	+	0.350541i	0.877818	+	0.478995i	$0.158999\pi$
$840$		0			0
$841$	3.50689	+	10.7931i	0.120927	+	0.372175i
$842$	−31.0325	+	22.5464i	−1.06945	+	0.777001i
$843$		0			0
$844$	4.48682	−	3.25987i	0.154443	−	0.112209i
$845$	−10.6989	−	5.44953i	−0.368053	−	0.187470i
$846$		0			0
$847$	42.2854	+	30.7221i	1.45294	+	1.05562i
$848$	4.17138	−	12.8382i	0.143246	−	0.440865i
$849$		0			0
$850$	−11.0896	−	3.59990i	−0.380369	−	0.123476i
$851$	−38.1183			−1.30668
$852$		0			0
$853$	−28.8998	−	20.9969i	−0.989509	−	0.718920i	−0.0296955	−	0.999559i	$-0.509454\pi$
$853$	−28.8998	−	20.9969i	−0.989509	−	0.718920i	−0.959814	+	0.280639i	$0.909454\pi$
$854$	45.9550	+	33.3883i	1.57255	+	1.14252i
$855$		0			0
$856$	−10.8696	+	7.89719i	−0.371514	+	0.269921i
$857$	31.2829			1.06860			0.534302	−	0.845294i	$-0.320575\pi$
$857$	31.2829			1.06860			0.534302	+	0.845294i	$0.320575\pi$
$858$		0			0
$859$	−2.38055	−	7.32658i	−0.0812234	−	0.249980i	0.902196	−	0.431327i	$-0.141954\pi$
$859$	−2.38055	−	7.32658i	−0.0812234	−	0.249980i	−0.983419	+	0.181347i	$0.941954\pi$
$860$	−1.26161	+	7.97246i	−0.0430205	+	0.271859i
$861$		0			0
$862$	3.28823	+	10.1201i	0.111998	+	0.344693i
$863$	11.5192	+	35.4524i	0.392118	+	1.20682i	0.931183	+	0.364551i	$0.118778\pi$
$863$	11.5192	+	35.4524i	0.392118	+	1.20682i	−0.539065	+	0.842264i	$0.681222\pi$
$864$		0			0
$865$	15.5900	−	2.47138i	0.530077	−	0.0840294i
$866$	9.68092	+	29.7948i	0.328971	+	1.01247i
$867$		0			0
$868$	0.845432			0.0286958
$869$	0.743657	−	0.540298i	0.0252268	−	0.0183284i
$870$		0			0
$871$	27.6318	+	20.0756i	0.936266	+	0.680237i
$872$	−0.362365	−	0.263273i	−0.0122712	−	0.00891557i
$873$		0			0
$874$	−10.3667			−0.350660
$875$	−52.7862	−	8.33855i	−1.78450	−	0.281894i
$876$		0			0
$877$	7.14903	−	22.0025i	0.241406	−	0.742971i	−0.754801	−	0.655954i	$-0.772267\pi$
$877$	7.14903	−	22.0025i	0.241406	−	0.742971i	0.996207	−	0.0870168i	$-0.0277334\pi$
$878$	−3.26133	−	2.36949i	−0.110064	−	0.0799665i
$879$		0			0
$880$	0.259067	+	0.508278i	0.00873315	+	0.0171340i
$881$	35.0397	−	25.4578i	1.18052	−	0.857697i	0.188288	−	0.982114i	$-0.439706\pi$
$881$	35.0397	−	25.4578i	1.18052	−	0.857697i	0.992230	+	0.124417i	$0.0397061\pi$
$882$		0			0
$883$	−3.84558	+	2.79398i	−0.129414	+	0.0940248i	−0.650609	−	0.759413i	$-0.725486\pi$
$883$	−3.84558	+	2.79398i	−0.129414	+	0.0940248i	0.521195	+	0.853438i	$0.325486\pi$
$884$	3.08839	+	9.50509i	0.103874	+	0.319691i
$885$		0			0
$886$	6.05796	−	18.6445i	0.203521	−	0.626374i
$887$	11.2840	+	34.7286i	0.378879	+	1.16607i	0.940824	+	0.338896i	$0.110053\pi$
$887$	11.2840	+	34.7286i	0.378879	+	1.16607i	−0.561944	+	0.827175i	$0.689947\pi$
$888$		0			0
$889$	−4.46673	+	13.7472i	−0.149809	+	0.461066i
$890$	3.90893	−	24.7017i	0.131028	−	0.828002i
$891$		0			0
$892$	17.5523	−	12.7525i	0.587696	−	0.426986i
$893$	−10.4358			−0.349221
$894$		0			0
$895$	−1.76142	+	11.1309i	−0.0588778	+	0.372066i
$896$	3.86701	+	2.80955i	0.129188	+	0.0938603i
$897$		0			0
$898$	8.44011	−	25.9760i	0.281650	−	0.866830i
$899$	−1.12351			−0.0374710
$900$		0			0
$901$	−31.4773			−1.04866
$902$	−0.173850	+	0.535055i	−0.00578857	+	0.0178154i
$903$		0			0
$904$	−9.98342	−	7.25338i	−0.332044	−	0.241244i
$905$	−12.0765	−	6.15125i	−0.401438	−	0.204474i
$906$		0			0
$907$	54.2897			1.80266			0.901330	−	0.433133i	$-0.142592\pi$
$907$	54.2897			1.80266			0.901330	+	0.433133i	$0.142592\pi$
$908$	13.5883	−	9.87244i	0.450942	−	0.327629i
$909$		0			0
$910$	20.8024	+	40.8134i	0.689594	+	1.35295i
$911$	2.56443	−	7.89251i	0.0849635	−	0.261491i	−0.899545	−	0.436828i	$-0.856102\pi$
$911$	2.56443	−	7.89251i	0.0849635	−	0.261491i	0.984508	+	0.175338i	$0.0561017\pi$
$912$		0			0
$913$	−1.25547	−	3.86393i	−0.0415499	−	0.127877i
$914$	4.74426	−	14.6013i	0.156926	−	0.482969i
$915$		0			0
$916$	1.00749	+	3.10073i	0.0332883	+	0.102451i
$917$	36.6486	−	26.6268i	1.21024	−	0.879293i
$918$		0			0
$919$	−9.89065	+	7.18597i	−0.326262	+	0.237043i	−0.738843	−	0.673878i	$-0.764627\pi$
$919$	−9.89065	+	7.18597i	−0.326262	+	0.237043i	0.412581	+	0.910921i	$0.364627\pi$
$920$	−11.8236	+	11.8268i	−0.389811	+	0.389916i
$921$		0			0
$922$	7.00535	+	5.08969i	0.230709	+	0.167620i
$923$	−13.5495	+	41.7009i	−0.445986	+	1.37260i
$924$		0			0
$925$	−24.2388	−	7.86841i	−0.796967	−	0.258712i
$926$	−25.4630			−0.836767
$927$		0			0
$928$	−5.13892	−	3.73364i	−0.168693	−	0.122563i
$929$	−6.96620	−	5.06124i	−0.228553	−	0.166054i	0.467615	−	0.883932i	$-0.345113\pi$
$929$	−6.96620	−	5.06124i	−0.228553	−	0.166054i	−0.696169	+	0.717878i	$0.745113\pi$
$930$		0			0
$931$	17.7713	−	12.9116i	0.582430	−	0.423160i
$932$	−13.7180			−0.449347
$933$		0			0
$934$	−1.57410	−	4.84457i	−0.0515060	−	0.158519i
$935$	0.940538	−	0.940793i	0.0307589	−	0.0307672i
$936$		0			0
$937$	13.6897	+	42.1325i	0.447222	+	1.37641i	0.880028	+	0.474922i	$0.157524\pi$
$937$	13.6897	+	42.1325i	0.447222	+	1.37641i	−0.432806	+	0.901487i	$0.642476\pi$
$938$	−11.7707	−	36.2263i	−0.384325	−	1.18283i
$939$		0			0
$940$	−11.9023	+	11.9056i	−0.388211	+	0.388316i
$941$	8.33251	+	25.6448i	0.271632	+	0.835997i	0.990091	+	0.140428i	$0.0448478\pi$
$941$	8.33251	+	25.6448i	0.271632	+	0.835997i	−0.718459	+	0.695569i	$0.755152\pi$
$942$		0			0
$943$	−16.4916			−0.537041
$944$	5.76910	−	4.19150i	0.187768	−	0.136422i
$945$		0			0
$946$	−0.745076	−	0.541329i	−0.0242245	−	0.0176001i
$947$	9.24006	+	6.71330i	0.300262	+	0.218153i	0.727707	−	0.685889i	$-0.240586\pi$
$947$	9.24006	+	6.71330i	0.300262	+	0.218153i	−0.427445	+	0.904041i	$0.640586\pi$
$948$		0			0
$949$	41.3733			1.34303
$950$	−6.59205	−	2.13991i	−0.213874	−	0.0694280i
$951$		0			0
$952$	3.44429	−	10.6004i	0.111630	−	0.343562i
$953$	−25.6659	−	18.6474i	−0.831401	−	0.604048i	0.0885547	−	0.996071i	$-0.471775\pi$
$953$	−25.6659	−	18.6474i	−0.831401	−	0.604048i	−0.919955	+	0.392023i	$0.871775\pi$
$954$		0			0
$955$	−17.4935	+	17.4982i	−0.566075	+	0.566228i
$956$	−14.1977	+	10.3152i	−0.459185	+	0.333618i
$957$		0			0
$958$	−27.4641	+	19.9538i	−0.887324	+	0.644679i
$959$	−24.5052	−	75.4193i	−0.791315	−	2.43542i
$960$		0			0
$961$	−9.56986	+	29.4530i	−0.308705	+	0.950097i
$962$	6.75039	+	20.7756i	0.217641	+	0.669831i
$963$		0			0
$964$	−1.72397	+	5.30582i	−0.0555252	+	0.170889i
$965$	−5.13718	−	10.0789i	−0.165372	−	0.324452i
$966$		0			0
$967$	−17.0823	+	12.4110i	−0.549330	+	0.399112i	−0.827538	−	0.561409i	$-0.810259\pi$
$967$	−17.0823	+	12.4110i	−0.549330	+	0.399112i	0.278208	+	0.960521i	$0.410259\pi$
$968$	10.9349			0.351461
$969$		0			0
$970$	−31.3899	−	15.9886i	−1.00787	−	0.513364i
$971$	1.12518	+	0.817492i	0.0361088	+	0.0262346i	0.605693	−	0.795698i	$-0.292896\pi$
$971$	1.12518	+	0.817492i	0.0361088	+	0.0262346i	−0.569584	+	0.821933i	$0.692896\pi$
$972$		0			0
$973$	29.0579	−	89.4310i	0.931553	−	2.86703i
$974$	−6.29323			−0.201648
$975$		0			0
$976$	11.8839			0.380394
$977$	11.1047	−	34.1767i	0.355270	−	1.09341i	−0.600583	−	0.799563i	$-0.705065\pi$
$977$	11.1047	−	34.1767i	0.355270	−	1.09341i	0.955853	−	0.293846i	$-0.0949353\pi$
$978$		0			0
$979$	2.30852	+	1.67724i	0.0737808	+	0.0536049i
$980$	5.53862	−	35.0001i	0.176925	−	1.11804i
$981$		0			0
$982$	−0.480196			−0.0153237
$983$	−14.6863	+	10.6702i	−0.468420	+	0.340327i	−0.796825	−	0.604210i	$-0.793489\pi$
$983$	−14.6863	+	10.6702i	−0.468420	+	0.340327i	0.328405	+	0.944537i	$0.393489\pi$
$984$		0			0
$985$	−5.07632	+	32.0787i	−0.161745	+	1.02211i
$986$	−4.57716	+	14.0871i	−0.145767	+	0.448623i
$987$		0			0
$988$	1.83585	+	5.65018i	0.0584063	+	0.179756i
$989$	8.34252	−	25.6756i	0.265277	−	0.816437i
$990$		0			0
$991$	−9.75115	−	30.0110i	−0.309756	−	0.953329i	−0.977860	−	0.209262i	$-0.932894\pi$
$991$	−9.75115	−	30.0110i	−0.309756	−	0.953329i	0.668104	−	0.744068i	$-0.267106\pi$
$992$	0.143093	−	0.103963i	0.00454321	−	0.00330084i
$993$		0			0
$994$	39.5608	−	28.7426i	1.25479	−	0.911659i
$995$	−13.5570	−	26.5983i	−0.429786	−	0.843221i
$996$		0			0
$997$	26.4297	+	19.2023i	0.837037	+	0.608143i	0.921541	−	0.388280i	$-0.126931\pi$
$997$	26.4297	+	19.2023i	0.837037	+	0.608143i	−0.0845046	+	0.996423i	$0.526931\pi$
$998$	13.2502	−	40.7799i	0.419427	−	1.29086i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.g.271.2	yes	12
3.2	odd	2		450.2.h.f.271.2	yes	12
25.6	even	5	inner	450.2.h.g.181.2	yes	12
75.56	odd	10		450.2.h.f.181.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.h.f.181.2	✓	12	75.56	odd	10
450.2.h.f.271.2	yes	12	3.2	odd	2
450.2.h.g.181.2	yes	12	25.6	even	5	inner
450.2.h.g.271.2	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.01542 + 1.99221i) q^{5} +4.77988 q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.01542 + 1.99221i) q^{5} +4.77988 q^{7} +(0.809017 - 0.587785i) q^{8} +(-2.20849 + 0.350097i) q^{10} +(0.0788401 - 0.242645i) q^{11} +(-1.32444 - 4.07621i) q^{13} +(-1.47707 + 4.54594i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.88650 - 1.37063i) q^{17} +(1.12141 - 0.814750i) q^{19} +(0.349499 - 2.20859i) q^{20} +(0.206406 + 0.149963i) q^{22} +(-2.31110 + 7.11284i) q^{23} +(-2.93783 + 4.04588i) q^{25} +4.28598 q^{26} +(-3.86701 - 2.80955i) q^{28} +(5.13892 + 3.73364i) q^{29} +(-0.143093 + 0.103963i) q^{31} -1.00000 q^{32} +(0.720581 + 2.21772i) q^{34} +(4.85360 + 9.52255i) q^{35} +(1.57499 + 4.84733i) q^{37} +(0.428339 + 1.31829i) q^{38} +(1.99249 + 1.01488i) q^{40} +(0.681411 + 2.09717i) q^{41} -3.60976 q^{43} +(-0.206406 + 0.149963i) q^{44} +(-6.05054 - 4.39598i) q^{46} +(-6.09086 - 4.42527i) q^{47} +15.8473 q^{49} +(-2.94002 - 4.04429i) q^{50} +(-1.32444 + 4.07621i) q^{52} +(-10.9208 - 7.93444i) q^{53} +(0.563457 - 0.0893209i) q^{55} +(3.86701 - 2.80955i) q^{56} +(-5.13892 + 3.73364i) q^{58} +(-2.20360 - 6.78199i) q^{59} +(3.67232 - 11.3022i) q^{61} +(-0.0546567 - 0.168216i) q^{62} +(0.309017 - 0.951057i) q^{64} +(6.77581 - 6.77764i) q^{65} +(-6.44701 + 4.68403i) q^{67} -2.33185 q^{68} +(-10.5563 + 1.67342i) q^{70} +(-8.27651 - 6.01324i) q^{71} +(-2.98300 + 9.18072i) q^{73} -5.09679 q^{74} -1.38614 q^{76} +(0.376847 - 1.15981i) q^{77} +(2.91479 + 2.11772i) q^{79} +(-1.58092 + 1.58135i) q^{80} -2.20509 q^{82} +(12.8830 - 9.36002i) q^{83} +(4.64618 + 2.36656i) q^{85} +(1.11548 - 3.43308i) q^{86} +(-0.0788401 - 0.242645i) q^{88} +(-3.45616 + 10.6370i) q^{89} +(-6.33067 - 19.4838i) q^{91} +(6.05054 - 4.39598i) q^{92} +(6.09086 - 4.42527i) q^{94} +(2.76186 + 1.40677i) q^{95} +(12.7454 + 9.26005i) q^{97} +(-4.89708 + 15.0717i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8 + q^10 - q^11 + 4 * q^13 - 8 * q^14 - 3 * q^16 + 8 * q^17 - 8 * q^19 - q^20 - 4 * q^22 - 11 * q^25 + 16 * q^26 - 7 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 2 * q^34 + 18 * q^35 - 8 * q^37 - 2 * q^38 + q^40 - 20 * q^41 + 32 * q^43 + 4 * q^44 - 10 * q^46 + 34 * q^49 - 9 * q^50 + 4 * q^52 - 2 * q^53 + 44 * q^55 + 7 * q^56 - 6 * q^58 + 19 * q^59 - 26 * q^61 - 2 * q^62 - 3 * q^64 - 16 * q^65 - 16 * q^67 - 12 * q^68 - 23 * q^70 - 48 * q^71 - 30 * q^73 + 8 * q^74 + 12 * q^76 + 39 * q^77 - 18 * q^79 + 4 * q^80 - 40 * q^82 + 29 * q^83 - 4 * q^85 - 12 * q^86 + q^88 - 62 * q^89 - 26 * q^91 + 10 * q^92 - 6 * q^95 + 23 * q^97 + 6 * q^98

Introduction

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