LMFDB - Embedded newform 450.2.s.b.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(17,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("450.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.s (of order $20$, degree $8$, 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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			197.2
Root			$0.891007 - 0.453990i$ of defining polynomial
Character	$\chi$	$=$	450.197
Dual form			450.2.s.b.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 + 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(0.349798 - 2.20854i) q^{5} +(-1.28408 - 1.28408i) q^{7} +(-0.987688 - 0.156434i) q^{8} +O(q^{10})$	\(q+(0.453990 + 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(0.349798 - 2.20854i) q^{5} +(-1.28408 - 1.28408i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(2.12663 - 0.690983i) q^{10} +(3.75739 + 1.22085i) q^{11} +(4.45434 + 2.26960i) q^{13} +(0.561163 - 1.72708i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(1.17159 - 7.39712i) q^{17} +(2.22358 + 3.06050i) q^{19} +(1.58114 + 1.58114i) q^{20} +(0.618034 + 3.90211i) q^{22} +(8.36783 - 4.26362i) q^{23} +(-4.75528 - 1.54508i) q^{25} +4.99922i q^{26} +(1.79360 - 0.284079i) q^{28} +(-4.12416 - 2.99638i) q^{29} +(-2.17557 + 1.58064i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.12277 - 2.31433i) q^{34} +(-3.28511 + 2.38677i) q^{35} +(-3.85588 + 7.56758i) q^{37} +(-1.71744 + 3.37066i) q^{38} +(-0.690983 + 2.12663i) q^{40} +(-8.02285 + 2.60678i) q^{41} +(0.0913225 - 0.0913225i) q^{43} +(-3.19623 + 2.32219i) q^{44} +(7.59783 + 5.52015i) q^{46} +(-0.407709 + 0.0645747i) q^{47} -3.70228i q^{49} +(-0.782172 - 4.93844i) q^{50} +(-4.45434 + 2.26960i) q^{52} +(1.22699 + 7.74691i) q^{53} +(4.01062 - 7.87129i) q^{55} +(1.06740 + 1.46914i) q^{56} +(0.797463 - 5.03498i) q^{58} +(-0.625738 - 1.92582i) q^{59} +(1.33245 - 4.10085i) q^{61} +(-2.39605 - 1.22085i) q^{62} +(0.951057 + 0.309017i) q^{64} +(6.57062 - 9.04368i) q^{65} +(1.64771 + 0.260971i) q^{67} +(5.29575 + 5.29575i) q^{68} +(-3.61803 - 1.84348i) q^{70} +(-6.41138 + 8.82451i) q^{71} +(-0.183899 - 0.360921i) q^{73} -8.49330 q^{74} -3.78298 q^{76} +(-3.25712 - 6.39245i) q^{77} +(-8.18504 + 11.2657i) q^{79} +(-2.20854 + 0.349798i) q^{80} +(-5.96496 - 5.96496i) q^{82} +(0.680668 + 0.107807i) q^{83} +(-15.9270 - 5.17499i) q^{85} +(0.122828 + 0.0399094i) q^{86} +(-3.52015 - 1.79360i) q^{88} +(-1.03224 + 3.17691i) q^{89} +(-2.80538 - 8.63407i) q^{91} +(-1.46914 + 9.27581i) q^{92} +(-0.242632 - 0.333955i) q^{94} +(7.53703 - 3.84031i) q^{95} +(-0.426119 - 2.69041i) q^{97} +(3.29876 - 1.68080i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 52 q^{13} + 4 q^{16} + 40 q^{19} - 8 q^{22} - 8 q^{28} - 16 q^{31} + 20 q^{34} + 52 q^{37} - 20 q^{40} + 40 q^{43} + 24 q^{46} - 52 q^{52} + 40 q^{55} + 36 q^{58} - 40 q^{61} - 64 q^{67} - 40 q^{70} - 84 q^{73} - 48 q^{76} + 40 q^{79} - 52 q^{82} - 100 q^{85} - 8 q^{88} - 112 q^{91} + 40 q^{94} + 12 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 52 * q^13 + 4 * q^16 + 40 * q^19 - 8 * q^22 - 8 * q^28 - 16 * q^31 + 20 * q^34 + 52 * q^37 - 20 * q^40 + 40 * q^43 + 24 * q^46 - 52 * q^52 + 40 * q^55 + 36 * q^58 - 40 * q^61 - 64 * q^67 - 40 * q^70 - 84 * q^73 - 48 * q^76 + 40 * q^79 - 52 * q^82 - 100 * q^85 - 8 * q^88 - 112 * q^91 + 40 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	0.453990	+	0.891007i	0.321020	+	0.630037i
$2$	0.453990	+	0.891007i	0.321020	+	0.630037i
$3$		0			0
$3$		0			0
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	0.349798	−	2.20854i	0.156434	−	0.987688i
$5$	0.349798	−	2.20854i	0.156434	−	0.987688i
$6$		0			0
$7$	−1.28408	−	1.28408i	−0.485336	−	0.485336i	0.421495	−	0.906831i	$-0.361506\pi$
$7$	−1.28408	−	1.28408i	−0.485336	−	0.485336i	−0.906831	+	0.421495i	$0.861506\pi$
$8$	−0.987688	−	0.156434i	−0.349201	−	0.0553079i
$9$		0			0
$10$	2.12663	−	0.690983i	0.672499	−	0.218508i
$11$	3.75739	+	1.22085i	1.13290	+	0.368100i	0.814676	−	0.579917i	$-0.196915\pi$
$11$	3.75739	+	1.22085i	1.13290	+	0.368100i	0.318220	+	0.948017i	$0.396915\pi$
$12$		0			0
$13$	4.45434	+	2.26960i	1.23541	+	0.629473i	0.944888	−	0.327394i	$-0.106171\pi$
$13$	4.45434	+	2.26960i	1.23541	+	0.629473i	0.290524	+	0.956868i	$0.406171\pi$
$14$	0.561163	−	1.72708i	0.149977	−	0.461582i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.17159	−	7.39712i	0.284152	−	1.79406i	−0.271278	−	0.962501i	$-0.587446\pi$
$17$	1.17159	−	7.39712i	0.284152	−	1.79406i	0.555430	−	0.831563i	$-0.312554\pi$
$18$		0			0
$19$	2.22358	+	3.06050i	0.510125	+	0.702126i	0.983940	−	0.178498i	$-0.0571237\pi$
$19$	2.22358	+	3.06050i	0.510125	+	0.702126i	−0.473816	+	0.880624i	$0.657124\pi$
$20$	1.58114	+	1.58114i	0.353553	+	0.353553i
$21$		0			0
$22$	0.618034	+	3.90211i	0.131765	+	0.831933i
$23$	8.36783	−	4.26362i	1.74481	−	0.889027i	0.780128	−	0.625619i	$-0.215154\pi$
$23$	8.36783	−	4.26362i	1.74481	−	0.889027i	0.964685	−	0.263407i	$-0.0848463\pi$
$24$		0			0
$25$	−4.75528	−	1.54508i	−0.951057	−	0.309017i
$26$			4.99922i			0.980428i
$27$		0			0
$28$	1.79360	−	0.284079i	0.338959	−	0.0536859i
$29$	−4.12416	−	2.99638i	−0.765838	−	0.556414i	0.134858	−	0.990865i	$-0.456942\pi$
$29$	−4.12416	−	2.99638i	−0.765838	−	0.556414i	−0.900695	+	0.434451i	$0.856942\pi$
$30$		0			0
$31$	−2.17557	+	1.58064i	−0.390744	+	0.283892i	−0.765760	−	0.643126i	$-0.777637\pi$
$31$	−2.17557	+	1.58064i	−0.390744	+	0.283892i	0.375016	+	0.927018i	$0.377637\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	7.12277	−	2.31433i	1.22154	−	0.396904i
$35$	−3.28511	+	2.38677i	−0.555284	+	0.403438i
$36$		0			0
$37$	−3.85588	+	7.56758i	−0.633902	+	1.24410i	0.320971	+	0.947089i	$0.395991\pi$
$37$	−3.85588	+	7.56758i	−0.633902	+	1.24410i	−0.954873	+	0.297014i	$0.904009\pi$
$38$	−1.71744	+	3.37066i	−0.278605	+	0.546794i
$39$		0			0
$40$	−0.690983	+	2.12663i	−0.109254	+	0.336249i
$41$	−8.02285	+	2.60678i	−1.25296	+	0.407111i	−0.858980	−	0.512008i	$-0.828902\pi$
$41$	−8.02285	+	2.60678i	−1.25296	+	0.407111i	−0.393979	+	0.919120i	$0.628902\pi$
$42$		0			0
$43$	0.0913225	−	0.0913225i	0.0139265	−	0.0139265i	−0.700109	−	0.714036i	$-0.746865\pi$
$43$	0.0913225	−	0.0913225i	0.0139265	−	0.0139265i	0.714036	+	0.700109i	$0.246865\pi$
$44$	−3.19623	+	2.32219i	−0.481849	+	0.350084i
$45$		0			0
$46$	7.59783	+	5.52015i	1.12024	+	0.813901i
$47$	−0.407709	+	0.0645747i	−0.0594705	+	0.00941919i	−0.186099	−	0.982531i	$-0.559584\pi$
$47$	−0.407709	+	0.0645747i	−0.0594705	+	0.00941919i	0.126628	+	0.991950i	$0.459584\pi$
$48$		0			0
$49$		−	3.70228i		−	0.528897i
$50$	−0.782172	−	4.93844i	−0.110616	−	0.698401i
$51$		0			0
$52$	−4.45434	+	2.26960i	−0.617706	+	0.314737i
$53$	1.22699	+	7.74691i	0.168540	+	1.06412i	0.916400	+	0.400264i	$0.131082\pi$
$53$	1.22699	+	7.74691i	0.168540	+	1.06412i	−0.747860	+	0.663857i	$0.768918\pi$
$54$		0			0
$55$	4.01062	−	7.87129i	0.540792	−	1.06136i
$56$	1.06740	+	1.46914i	0.142637	+	0.196323i
$57$		0			0
$58$	0.797463	−	5.03498i	0.104712	−	0.661126i
$59$	−0.625738	−	1.92582i	−0.0814641	−	0.250721i	0.902026	−	0.431681i	$-0.142079\pi$
$59$	−0.625738	−	1.92582i	−0.0814641	−	0.250721i	−0.983490	+	0.180960i	$0.942079\pi$
$60$		0			0
$61$	1.33245	−	4.10085i	0.170602	−	0.525060i	−0.828803	−	0.559540i	$-0.810978\pi$
$61$	1.33245	−	4.10085i	0.170602	−	0.525060i	0.999405	+	0.0344806i	$0.0109777\pi$
$62$	−2.39605	−	1.22085i	−0.304299	−	0.155048i
$63$		0			0
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	6.57062	−	9.04368i	0.814985	−	1.12173i
$66$		0			0
$67$	1.64771	+	0.260971i	0.201299	+	0.0318827i	0.256270	−	0.966605i	$-0.417506\pi$
$67$	1.64771	+	0.260971i	0.201299	+	0.0318827i	−0.0549704	+	0.998488i	$0.517506\pi$
$68$	5.29575	+	5.29575i	0.642204	+	0.642204i
$69$		0			0
$70$	−3.61803	−	1.84348i	−0.432438	−	0.220338i
$71$	−6.41138	+	8.82451i	−0.760891	+	1.04728i	0.236249	+	0.971693i	$0.424082\pi$
$71$	−6.41138	+	8.82451i	−0.760891	+	1.04728i	−0.997139	+	0.0755839i	$0.975918\pi$
$72$		0			0
$73$	−0.183899	−	0.360921i	−0.0215237	−	0.0422427i	0.879994	−	0.474984i	$-0.157546\pi$
$73$	−0.183899	−	0.360921i	−0.0215237	−	0.0422427i	−0.901518	+	0.432742i	$0.857546\pi$
$74$	−8.49330			−0.987326
$75$		0			0
$76$	−3.78298			−0.433938
$77$	−3.25712	−	6.39245i	−0.371183	−	0.728488i
$78$		0			0
$79$	−8.18504	+	11.2657i	−0.920889	+	1.26749i	0.0424201	+	0.999100i	$0.486493\pi$
$79$	−8.18504	+	11.2657i	−0.920889	+	1.26749i	−0.963309	+	0.268395i	$0.913507\pi$
$80$	−2.20854	+	0.349798i	−0.246922	+	0.0391086i
$81$		0			0
$82$	−5.96496	−	5.96496i	−0.658720	−	0.658720i
$83$	0.680668	+	0.107807i	0.0747131	+	0.0118334i	0.193679	−	0.981065i	$-0.437958\pi$
$83$	0.680668	+	0.107807i	0.0747131	+	0.0118334i	−0.118966	+	0.992898i	$0.537958\pi$
$84$		0			0
$85$	−15.9270	−	5.17499i	−1.72753	−	0.561307i
$86$	0.122828	+	0.0399094i	0.0132449	+	0.00430354i
$87$		0			0
$88$	−3.52015	−	1.79360i	−0.375249	−	0.191199i
$89$	−1.03224	+	3.17691i	−0.109417	+	0.336751i	−0.990742	−	0.135760i	$-0.956652\pi$
$89$	−1.03224	+	3.17691i	−0.109417	+	0.336751i	0.881325	+	0.472511i	$0.156652\pi$
$90$		0			0
$91$	−2.80538	−	8.63407i	−0.294084	−	0.905096i
$92$	−1.46914	+	9.27581i	−0.153169	+	0.967070i
$93$		0			0
$94$	−0.242632	−	0.333955i	−0.0250256	−	0.0344448i
$95$	7.53703	−	3.84031i	0.773283	−	0.394007i
$96$		0			0
$97$	−0.426119	−	2.69041i	−0.0432658	−	0.273169i	0.956566	−	0.291516i	$-0.0941597\pi$
$97$	−0.426119	−	2.69041i	−0.0432658	−	0.273169i	−0.999832	+	0.0183468i	$0.994160\pi$
$98$	3.29876	−	1.68080i	0.333225	−	0.169787i
$99$		0			0
$100$	4.04508	−	2.93893i	0.404508	−	0.293893i
$101$			4.20442i			0.418356i	0.977878	+	0.209178i	$0.0670788\pi$
$101$			4.20442i			0.418356i	−0.977878	+	0.209178i	$0.932921\pi$
$102$		0			0
$103$	13.4999	−	2.13818i	1.33019	−	0.210681i	0.549444	−	0.835531i	$-0.314840\pi$
$103$	13.4999	−	2.13818i	1.33019	−	0.210681i	0.780745	+	0.624849i	$0.214840\pi$
$104$	−4.04445	−	2.93847i	−0.396591	−	0.288141i
$105$		0			0
$106$	−6.34551	+	4.61028i	−0.616330	+	0.447790i
$107$	−0.309546	+	0.309546i	−0.0299249	+	0.0299249i	−0.721911	−	0.691986i	$-0.756736\pi$
$107$	−0.309546	+	0.309546i	−0.0299249	+	0.0299249i	0.691986	+	0.721911i	$0.256736\pi$
$108$		0			0
$109$	−8.68806	+	2.82292i	−0.832165	+	0.270387i	−0.693957	−	0.720016i	$-0.744134\pi$
$109$	−8.68806	+	2.82292i	−0.832165	+	0.270387i	−0.138208	+	0.990403i	$0.544134\pi$
$110$	8.83415			0.842303
$111$		0			0
$112$	−0.824429	+	1.61803i	−0.0779013	+	0.152890i
$113$	5.88788	−	11.5556i	0.553885	−	1.08706i	−0.429079	−	0.903267i	$-0.641162\pi$
$113$	5.88788	−	11.5556i	0.553885	−	1.08706i	0.982965	−	0.183794i	$-0.0588381\pi$
$114$		0			0
$115$	−6.48932	−	19.9721i	−0.605132	−	1.86241i
$116$	4.84824	−	1.57529i	0.450148	−	0.146262i
$117$		0			0
$118$	1.43184	−	1.43184i	0.131812	−	0.131812i
$119$	−11.0029	+	7.99407i	−1.00863	+	0.732815i
$120$		0			0
$121$	3.72832	+	2.70878i	0.338938	+	0.246253i
$122$	4.25880	−	0.674528i	0.385574	−	0.0610689i
$123$		0			0
$124$		−	2.68915i		−	0.241493i
$125$	−5.07577	+	9.96176i	−0.453990	+	0.891007i
$126$		0			0
$127$	−7.15537	+	3.64584i	−0.634936	+	0.323516i	−0.741663	−	0.670772i	$-0.765963\pi$
$127$	−7.15537	+	3.64584i	−0.634936	+	0.323516i	0.106727	+	0.994288i	$0.465963\pi$
$128$	0.156434	+	0.987688i	0.0138270	+	0.0873001i
$129$		0			0
$130$	11.0410	+	1.74872i	0.968357	+	0.153373i
$131$	8.66900	+	11.9319i	0.757414	+	1.04249i	0.997425	+	0.0717208i	$0.0228491\pi$
$131$	8.66900	+	11.9319i	0.757414	+	1.04249i	−0.240011	+	0.970770i	$0.577151\pi$
$132$		0			0
$133$	1.07467	−	6.78518i	0.0931854	−	0.588349i
$134$	0.515516	+	1.58660i	0.0445338	+	0.137061i
$135$		0			0
$136$	−2.31433	+	7.12277i	−0.198452	+	0.610772i
$137$	−9.99117	−	5.09076i	−0.853604	−	0.434933i	−0.0282849	−	0.999600i	$-0.509005\pi$
$137$	−9.99117	−	5.09076i	−0.853604	−	0.434933i	−0.825319	+	0.564667i	$0.809005\pi$
$138$		0			0
$139$	10.8137	+	3.51358i	0.917206	+	0.298018i	0.729320	−	0.684173i	$-0.239837\pi$
$139$	10.8137	+	3.51358i	0.917206	+	0.298018i	0.187886	+	0.982191i	$0.439837\pi$
$140$		−	4.06061i		−	0.343185i
$141$		0			0
$142$	−10.7734	−	1.70634i	−0.904084	−	0.143193i
$143$	13.9658	+	13.9658i	1.16788	+	1.16788i
$144$		0			0
$145$	−8.06024	+	8.06024i	−0.669367	+	0.669367i
$146$	0.238095	−	0.327710i	0.0197049	−	0.0271215i
$147$		0			0
$148$	−3.85588	−	7.56758i	−0.316951	−	0.622051i
$149$	−10.8708			−0.890569			−0.445285	−	0.895389i	$-0.646897\pi$
$149$	−10.8708			−0.890569			−0.445285	+	0.895389i	$0.646897\pi$
$150$		0			0
$151$	21.0865			1.71600			0.857998	−	0.513653i	$-0.171708\pi$
$151$	21.0865			1.71600			0.857998	+	0.513653i	$0.171708\pi$
$152$	−1.71744	−	3.37066i	−0.139303	−	0.273397i
$153$		0			0
$154$	4.21702	−	5.80423i	0.339817	−	0.467718i
$155$	2.72990	+	5.35774i	0.219271	+	0.430344i
$156$		0			0
$157$	6.50271	+	6.50271i	0.518972	+	0.518972i	0.917260	−	0.398288i	$-0.130396\pi$
$157$	6.50271	+	6.50271i	0.518972	+	0.518972i	−0.398288	+	0.917260i	$0.630396\pi$
$158$	−13.7538	−	2.17838i	−1.09419	−	0.173303i
$159$		0			0
$160$	−1.31433	−	1.80902i	−0.103907	−	0.143015i
$161$	−16.2198	−	5.27013i	−1.27830	−	0.415344i
$162$		0			0
$163$	−14.3203	−	7.29657i	−1.12165	−	0.571511i	−0.208051	−	0.978118i	$-0.566712\pi$
$163$	−14.3203	−	7.29657i	−1.12165	−	0.571511i	−0.913603	+	0.406607i	$0.866712\pi$
$164$	2.60678	−	8.02285i	0.203556	−	0.626480i
$165$		0			0
$166$	0.212960	+	0.655423i	0.0165289	+	0.0508707i
$167$	2.52299	−	15.9295i	0.195235	−	1.23266i	−0.674175	−	0.738572i	$-0.735501\pi$
$167$	2.52299	−	15.9295i	0.195235	−	1.23266i	0.869410	−	0.494092i	$-0.164499\pi$
$168$		0			0
$169$	7.04885	+	9.70190i	0.542219	+	0.746300i
$170$	−2.61975	−	16.5405i	−0.200926	−	1.26859i
$171$		0			0
$172$	0.0202034	+	0.127559i	0.00154050	+	0.00972632i
$173$	5.33223	−	2.71690i	0.405402	−	0.206562i	−0.239386	−	0.970925i	$-0.576946\pi$
$173$	5.33223	−	2.71690i	0.405402	−	0.206562i	0.644787	+	0.764362i	$0.276946\pi$
$174$		0			0
$175$	4.12215	+	8.09017i	0.311605	+	0.611559i
$176$		−	3.95075i		−	0.297799i
$177$		0			0
$178$	−3.29927	+	0.522553i	−0.247291	+	0.0391670i
$179$	8.10451	+	5.88827i	0.605760	+	0.440110i	0.847919	−	0.530126i	$-0.177856\pi$
$179$	8.10451	+	5.88827i	0.605760	+	0.440110i	−0.242159	+	0.970237i	$0.577856\pi$
$180$		0			0
$181$	−3.84011	+	2.79000i	−0.285433	+	0.207379i	−0.721284	−	0.692640i	$-0.756448\pi$
$181$	−3.84011	+	2.79000i	−0.285433	+	0.207379i	0.435851	+	0.900019i	$0.356448\pi$
$182$	6.41940	−	6.41940i	0.475837	−	0.475837i
$183$		0			0
$184$	−8.93179	+	2.90211i	−0.658460	+	0.213947i
$185$	15.3645	+	11.1630i	1.12962	+	0.820718i
$186$		0			0
$187$	13.4329	−	26.3635i	0.982310	−	1.92789i
$188$	0.187403	−	0.367799i	0.0136678	−	0.0268245i
$189$		0			0
$190$	6.84348	+	4.97208i	0.496478	+	0.360713i
$191$	−23.6587	+	7.68716i	−1.71188	+	0.556223i	−0.990645	−	0.136467i	$-0.956425\pi$
$191$	−23.6587	+	7.68716i	−1.71188	+	0.556223i	−0.721235	+	0.692690i	$0.756425\pi$
$192$		0			0
$193$	−9.55217	+	9.55217i	−0.687580	+	0.687580i	−0.961697	−	0.274116i	$-0.911615\pi$
$193$	−9.55217	+	9.55217i	−0.687580	+	0.687580i	0.274116	+	0.961697i	$0.411615\pi$
$194$	2.20372	−	1.60109i	0.158218	−	0.114952i
$195$		0			0
$196$	2.99521	+	2.17615i	0.213944	+	0.155439i
$197$	−3.51260	+	0.556341i	−0.250262	+	0.0396377i	−0.280305	−	0.959911i	$-0.590436\pi$
$197$	−3.51260	+	0.556341i	−0.250262	+	0.0396377i	0.0300428	+	0.999549i	$0.490436\pi$
$198$		0			0
$199$			11.7236i			0.831067i	0.909578	+	0.415533i	$0.136405\pi$
$199$			11.7236i			0.831067i	−0.909578	+	0.415533i	$0.863595\pi$
$200$	4.45503	+	2.26995i	0.315018	+	0.160510i
$201$		0			0
$202$	−3.74617	+	1.90877i	−0.263580	+	0.134301i
$203$	1.44816	+	9.14334i	0.101641	+	0.641737i
$204$		0			0
$205$	2.95080	+	18.6306i	0.206093	+	1.30122i
$206$	8.03398	+	11.0578i	0.559754	+	0.770435i
$207$		0			0
$208$	0.782051	−	4.93767i	0.0542254	−	0.342366i
$209$	4.61845	+	14.2141i	0.319465	+	0.983213i
$210$		0			0
$211$	8.13703	−	25.0432i	0.560176	−	1.72404i	−0.121690	−	0.992568i	$-0.538831\pi$
$211$	8.13703	−	25.0432i	0.560176	−	1.72404i	0.681866	−	0.731477i	$-0.261169\pi$
$212$	−6.98859	−	3.56087i	−0.479978	−	0.244561i
$213$		0			0
$214$	−0.416338	−	0.135276i	−0.0284603	−	0.00924731i
$215$	−0.169745	−	0.233634i	−0.0115765	−	0.0159337i
$216$		0			0
$217$	4.82328	+	0.763932i	0.327425	+	0.0518591i
$218$	−6.45954	−	6.45954i	−0.437495	−	0.437495i
$219$		0			0
$220$	4.01062	+	7.87129i	0.270396	+	0.530682i
$221$	22.0071	−	30.2902i	1.48036	−	2.03754i
$222$		0			0
$223$	11.7063	+	22.9750i	0.783914	+	1.53852i	0.841549	+	0.540181i	$0.181644\pi$
$223$	11.7063	+	22.9750i	0.783914	+	1.53852i	−0.0576344	+	0.998338i	$0.518356\pi$
$224$	−1.81596			−0.121334
$225$		0			0
$226$	12.9692			0.862697
$227$	−0.0662680	−	0.130058i	−0.00439836	−	0.00863227i	0.888797	−	0.458301i	$-0.151542\pi$
$227$	−0.0662680	−	0.130058i	−0.00439836	−	0.00863227i	−0.893195	+	0.449669i	$0.851542\pi$
$228$		0			0
$229$	−11.1985	+	15.4134i	−0.740015	+	1.01854i	0.258603	+	0.965984i	$0.416738\pi$
$229$	−11.1985	+	15.4134i	−0.740015	+	1.01854i	−0.998618	+	0.0525595i	$0.983262\pi$
$230$	14.8492	−	14.8492i	0.979125	−	0.979125i
$231$		0			0
$232$	3.60465	+	3.60465i	0.236657	+	0.236657i
$233$	−8.40064	−	1.33053i	−0.550344	−	0.0871660i	−0.124931	−	0.992165i	$-0.539871\pi$
$233$	−8.40064	−	1.33053i	−0.550344	−	0.0871660i	−0.425413	+	0.904999i	$0.639871\pi$
$234$		0			0
$235$			0.923029i			0.0602118i
$236$	1.92582	+	0.625738i	0.125360	+	0.0407321i
$237$		0			0
$238$	−12.1180	−	6.17442i	−0.785492	−	0.400228i
$239$	4.16282	−	12.8118i	0.269271	−	0.828730i	−0.721408	−	0.692510i	$-0.756505\pi$
$239$	4.16282	−	12.8118i	0.269271	−	0.828730i	0.990679	−	0.136219i	$-0.0434952\pi$
$240$		0			0
$241$	3.14111	+	9.66733i	0.202336	+	0.622728i	0.999812	+	0.0193767i	$0.00616819\pi$
$241$	3.14111	+	9.66733i	0.202336	+	0.622728i	−0.797476	+	0.603351i	$0.793832\pi$
$242$	−0.720921	+	4.55171i	−0.0463425	+	0.292595i
$243$		0			0
$244$	2.53446	+	3.48839i	0.162252	+	0.223321i
$245$	−8.17663	−	1.29505i	−0.522386	−	0.0827378i
$246$		0			0
$247$	2.95848	+	18.6791i	0.188244	+	1.18852i
$248$	2.39605	−	1.22085i	0.152150	−	0.0775240i
$249$		0			0
$250$	−11.1803			−0.707107
$251$		−	9.38052i		−	0.592093i	−0.955174	−	0.296047i	$-0.904332\pi$
$251$		−	9.38052i		−	0.592093i	0.955174	−	0.296047i	$-0.0956683\pi$
$252$		0			0
$253$	36.6464	−	5.80423i	2.30394	−	0.364909i
$254$	−6.49694	−	4.72030i	−0.407654	−	0.296178i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.22859	+	2.22859i	−0.139016	+	0.139016i	−0.773190	−	0.634174i	$-0.781340\pi$
$257$	−2.22859	+	2.22859i	−0.139016	+	0.139016i	0.634174	+	0.773190i	$0.281340\pi$
$258$		0			0
$259$	14.6686	−	4.76612i	0.911464	−	0.296153i
$260$	3.45438	+	10.6315i	0.214231	+	0.659336i
$261$		0			0
$262$	−6.69572	+	13.1411i	−0.413663	+	0.811859i
$263$	−10.5219	+	20.6504i	−0.648809	+	1.27336i	0.298919	+	0.954279i	$0.403374\pi$
$263$	−10.5219	+	20.6504i	−0.648809	+	1.27336i	−0.947728	+	0.319080i	$0.896626\pi$
$264$		0			0
$265$	17.5386			1.07738
$266$	6.53352	−	2.12287i	0.400596	−	0.130162i
$267$		0			0
$268$	−1.17963	+	1.17963i	−0.0720572	+	0.0720572i
$269$	−5.69732	+	4.13934i	−0.347372	+	0.252380i	−0.747766	−	0.663963i	$-0.768873\pi$
$269$	−5.69732	+	4.13934i	−0.347372	+	0.252380i	0.400394	+	0.916343i	$0.368873\pi$
$270$		0			0
$271$	11.6553	+	8.46808i	0.708010	+	0.514399i	0.882531	−	0.470254i	$-0.155838\pi$
$271$	11.6553	+	8.46808i	0.708010	+	0.514399i	−0.174521	+	0.984653i	$0.555838\pi$
$272$	−7.39712	+	1.17159i	−0.448516	+	0.0710380i
$273$		0			0
$274$		−	11.2134i		−	0.677424i
$275$	−15.9811	−	11.6110i	−0.963699	−	0.700168i
$276$		0			0
$277$	16.5331	−	8.42403i	0.993378	−	0.506151i	0.119780	−	0.992800i	$-0.461781\pi$
$277$	16.5331	−	8.42403i	0.993378	−	0.506151i	0.873597	+	0.486649i	$0.161781\pi$
$278$	1.77869	+	11.2302i	0.106679	+	0.673543i
$279$		0			0
$280$	3.61803	−	1.84348i	0.216219	−	0.110169i
$281$	11.5453	+	15.8908i	0.688735	+	0.947963i	0.999997	−	0.00236125i	$-0.000751611\pi$
$281$	11.5453	+	15.8908i	0.688735	+	0.947963i	−0.311262	+	0.950324i	$0.600752\pi$
$282$		0			0
$283$	−1.11102	+	7.01468i	−0.0660430	+	0.416979i	0.932411	+	0.361399i	$0.117701\pi$
$283$	−1.11102	+	7.01468i	−0.0660430	+	0.416979i	−0.998454	+	0.0555802i	$0.982299\pi$
$284$	−3.37066	−	10.3738i	−0.200012	−	0.615574i
$285$		0			0
$286$	−6.10330	+	18.7840i	−0.360896	+	1.11072i
$287$	13.6493	+	6.95466i	0.805692	+	0.410521i
$288$		0			0
$289$	−37.1767	−	12.0795i	−2.18687	−	0.710556i
$290$	−10.8410	−	3.52246i	−0.636606	−	0.206846i
$291$		0			0
$292$	0.400084	+	0.0633672i	0.0234132	+	0.00370828i
$293$	−15.5402	−	15.5402i	−0.907869	−	0.907869i	0.0882312	−	0.996100i	$-0.471879\pi$
$293$	−15.5402	−	15.5402i	−0.907869	−	0.907869i	−0.996100	+	0.0882312i	$0.971879\pi$
$294$		0			0
$295$	−4.47214	+	0.708317i	−0.260378	+	0.0412398i
$296$	4.99223	−	6.87122i	0.290168	−	0.399382i
$297$		0			0
$298$	−4.93523	−	9.68594i	−0.285890	−	0.561091i
$299$	46.9499			2.71518
$300$		0			0
$301$	−0.234531			−0.0135181
$302$	9.57308	+	18.7882i	0.550869	+	1.08114i
$303$		0			0
$304$	2.22358	−	3.06050i	0.127531	−	0.175532i
$305$	−8.59079	−	4.37723i	−0.491907	−	0.250639i
$306$		0			0
$307$	−1.79953	−	1.79953i	−0.102704	−	0.102704i	0.653887	−	0.756592i	$-0.273137\pi$
$307$	−1.79953	−	1.79953i	−0.102704	−	0.102704i	−0.756592	+	0.653887i	$0.773137\pi$
$308$	7.08609	+	1.12233i	0.403767	+	0.0639505i
$309$		0			0
$310$	−3.53443	+	4.86472i	−0.200742	+	0.276298i
$311$	−2.94129	−	0.955682i	−0.166785	−	0.0541917i	0.224434	−	0.974489i	$-0.427947\pi$
$311$	−2.94129	−	0.955682i	−0.166785	−	0.0541917i	−0.391219	+	0.920297i	$0.627947\pi$
$312$		0			0
$313$	−12.9683	−	6.60767i	−0.733010	−	0.373487i	0.0472993	−	0.998881i	$-0.484939\pi$
$313$	−12.9683	−	6.60767i	−0.733010	−	0.373487i	−0.780310	+	0.625393i	$0.784939\pi$
$314$	−2.84179	+	8.74612i	−0.160371	+	0.493572i
$315$		0			0
$316$	−4.30313	−	13.2437i	−0.242070	−	0.745015i
$317$	0.731491	−	4.61845i	0.0410846	−	0.259398i	−0.958593	−	0.284779i	$-0.908080\pi$
$317$	0.731491	−	4.61845i	0.0410846	−	0.259398i	0.999678	+	0.0253807i	$0.00807980\pi$
$318$		0			0
$319$	−11.8380	−	16.2935i	−0.662798	−	0.912264i
$320$	1.01515	−	1.99235i	0.0567488	−	0.111376i
$321$		0			0
$322$	−2.66791	−	16.8445i	−0.148677	−	0.938708i
$323$	25.2440	−	12.8624i	1.40461	−	0.715686i
$324$		0			0
$325$	−17.6749	−	17.6749i	−0.980428	−	0.980428i
$326$		−	16.0721i		−	0.890149i
$327$		0			0
$328$	8.33187	−	1.31964i	0.460051	−	0.0728649i
$329$	0.606449	+	0.440611i	0.0334346	+	0.0242917i
$330$		0			0
$331$	−22.4424	+	16.3053i	−1.23354	+	0.896222i	−0.997151	−	0.0754361i	$-0.975965\pi$
$331$	−22.4424	+	16.3053i	−1.23354	+	0.896222i	−0.236393	+	0.971658i	$0.575965\pi$
$332$	−0.487305	+	0.487305i	−0.0267443	+	0.0267443i
$333$		0			0
$334$	15.3387	−	4.98385i	0.839298	−	0.272704i
$335$	1.15273	−	3.54774i	0.0629803	−	0.193834i
$336$		0			0
$337$	8.66328	−	17.0026i	0.471919	−	0.926193i	−0.525246	−	0.850950i	$-0.676027\pi$
$337$	8.66328	−	17.0026i	0.471919	−	0.926193i	0.997165	−	0.0752430i	$-0.0239732\pi$
$338$	−5.44435	+	10.6851i	−0.296134	+	0.581195i
$339$		0			0
$340$	13.5483	−	9.84342i	0.734760	−	0.533835i
$341$	−10.1042	+	3.28305i	−0.547173	+	0.177787i
$342$		0			0
$343$	−13.7426	+	13.7426i	−0.742029	+	0.742029i
$344$	−0.104484	+	0.0759122i	−0.00563341	+	0.00409291i
$345$		0			0
$346$	4.84156	+	3.51760i	0.260284	+	0.189107i
$347$	−8.05268	+	1.27542i	−0.432291	+	0.0684681i	−0.368788	−	0.929514i	$-0.620227\pi$
$347$	−8.05268	+	1.27542i	−0.432291	+	0.0684681i	−0.0635027	+	0.997982i	$0.520227\pi$
$348$		0			0
$349$		−	5.60220i		−	0.299879i	−0.988695	−	0.149940i	$-0.952092\pi$
$349$		−	5.60220i		−	0.299879i	0.988695	−	0.149940i	$-0.0479079\pi$
$350$	−5.33698	+	7.34572i	−0.285273	+	0.392645i
$351$		0			0
$352$	3.52015	−	1.79360i	0.187624	−	0.0955994i
$353$	−2.15819	−	13.6263i	−0.114869	−	0.725253i	−0.976146	−	0.217117i	$-0.930335\pi$
$353$	−2.15819	−	13.6263i	−0.114869	−	0.725253i	0.861277	−	0.508136i	$-0.169665\pi$
$354$		0			0
$355$	17.2466	+	17.2466i	0.915353	+	0.915353i
$356$	−1.96344	−	2.70244i	−0.104062	−	0.143229i
$357$		0			0
$358$	−1.56712	+	9.89440i	−0.0828248	+	0.522935i
$359$	8.04326	+	24.7546i	0.424507	+	1.30650i	0.903465	+	0.428661i	$0.141015\pi$
$359$	8.04326	+	24.7546i	0.424507	+	1.30650i	−0.478958	+	0.877838i	$0.658985\pi$
$360$		0			0
$361$	1.44899	−	4.45954i	0.0762628	−	0.234713i
$362$	−4.22928	−	2.15493i	−0.222286	−	0.113260i
$363$		0			0
$364$	8.63407	+	2.80538i	0.452548	+	0.147042i
$365$	−0.861436	+	0.279898i	−0.0450896	+	0.0146505i
$366$		0			0
$367$	−5.07768	−	0.804226i	−0.265053	−	0.0419803i	0.0224934	−	0.999747i	$-0.492840\pi$
$367$	−5.07768	−	0.804226i	−0.265053	−	0.0419803i	−0.287546	+	0.957767i	$0.592840\pi$
$368$	−6.64075	−	6.64075i	−0.346173	−	0.346173i
$369$		0			0
$370$	−2.97094	+	18.7578i	−0.154452	+	0.975170i
$371$	8.37210	−	11.5232i	0.434658	−	0.598255i
$372$		0			0
$373$	−6.25519	−	12.2765i	−0.323882	−	0.635653i	0.670453	−	0.741952i	$-0.266100\pi$
$373$	−6.25519	−	12.2765i	−0.323882	−	0.635653i	−0.994334	+	0.106299i	$0.966100\pi$
$374$	29.5885			1.52998
$375$		0			0
$376$	0.412791			0.0212881
$377$	−11.5698	−	22.7071i	−0.595877	−	1.16947i
$378$		0			0
$379$	2.60074	−	3.57960i	0.133591	−	0.183872i	−0.736981	−	0.675914i	$-0.763749\pi$
$379$	2.60074	−	3.57960i	0.133591	−	0.183872i	0.870572	+	0.492042i	$0.163749\pi$
$380$	−1.32328	+	8.35486i	−0.0678828	+	0.428595i
$381$		0			0
$382$	−17.5901	−	17.5901i	−0.899989	−	0.899989i
$383$	−23.2779	−	3.68685i	−1.18944	−	0.188389i	−0.469826	−	0.882759i	$-0.655683\pi$
$383$	−23.2779	−	3.68685i	−1.18944	−	0.188389i	−0.719618	+	0.694370i	$0.755683\pi$
$384$		0			0
$385$	−15.2573	+	4.95740i	−0.777585	+	0.252653i
$386$	−12.8476	−	4.17445i	−0.653928	−	0.212474i
$387$		0			0
$388$	2.42705	+	1.23664i	0.123215	+	0.0627811i
$389$	3.51895	−	10.8302i	0.178418	−	0.549114i	−0.821355	−	0.570417i	$-0.806782\pi$
$389$	3.51895	−	10.8302i	0.178418	−	0.549114i	0.999773	+	0.0213032i	$0.00678155\pi$
$390$		0			0
$391$	−21.7349	−	66.8930i	−1.09918	−	3.38293i
$392$	−0.579165	+	3.65670i	−0.0292522	+	0.184691i
$393$		0			0
$394$	−2.09039	−	2.87718i	−0.105312	−	0.144950i
$395$	22.0177	+	22.0177i	1.10783	+	1.10783i
$396$		0			0
$397$	−2.77709	−	17.5338i	−0.139378	−	0.879998i	−0.953957	−	0.299945i	$-0.903032\pi$
$397$	−2.77709	−	17.5338i	−0.139378	−	0.879998i	0.814579	−	0.580053i	$-0.196968\pi$
$398$	−10.4458	+	5.32242i	−0.523603	+	0.266789i
$399$		0			0
$400$			5.00000i			0.250000i
$401$			4.48497i			0.223969i	0.993710	+	0.111984i	$0.0357207\pi$
$401$			4.48497i			0.223969i	−0.993710	+	0.111984i	$0.964279\pi$
$402$		0			0
$403$	−13.2782	+	2.10305i	−0.661432	+	0.104761i
$404$	−3.40145	−	2.47130i	−0.169229	−	0.122952i
$405$		0			0
$406$	−7.48932	+	5.44131i	−0.371689	+	0.270048i
$407$	−23.7269	+	23.7269i	−1.17610	+	1.17610i
$408$		0			0
$409$	−13.9740	+	4.54042i	−0.690968	+	0.224509i	−0.633391	−	0.773832i	$-0.718338\pi$
$409$	−13.9740	+	4.54042i	−0.690968	+	0.224509i	−0.0575771	+	0.998341i	$0.518338\pi$
$410$	−15.2604	+	11.0873i	−0.753656	+	0.547563i
$411$		0			0
$412$	−6.20524	+	12.1785i	−0.305710	+	0.599990i
$413$	−1.66941	+	3.27641i	−0.0821464	+	0.161221i
$414$		0			0
$415$	0.476193	−	1.46557i	0.0233754	−	0.0719421i
$416$	4.75454	−	1.54484i	0.233111	−	0.0757422i
$417$		0			0
$418$	−10.5682	+	10.5682i	−0.516906	+	0.516906i
$419$	11.7751	−	8.55510i	0.575250	−	0.417944i	−0.261758	−	0.965133i	$-0.584302\pi$
$419$	11.7751	−	8.55510i	0.575250	−	0.417944i	0.837009	+	0.547190i	$0.184302\pi$
$420$		0			0
$421$	19.4271	+	14.1146i	0.946818	+	0.687904i	0.950052	−	0.312091i	$-0.101029\pi$
$421$	19.4271	+	14.1146i	0.946818	+	0.687904i	−0.00323396	+	0.999995i	$0.501029\pi$
$422$	26.0078	−	4.11923i	1.26604	−	0.200521i
$423$		0			0
$424$		−	7.84348i		−	0.380913i
$425$	−17.0004	+	33.3652i	−0.824641	+	1.61845i
$426$		0			0
$427$	−6.97678	+	3.55485i	−0.337630	+	0.172031i
$428$	−0.0684814	−	0.432374i	−0.00331017	−	0.0208996i
$429$		0			0
$430$	0.131107	−	0.257311i	0.00632252	−	0.0124086i
$431$	−20.6224	−	28.3843i	−0.993347	−	1.36723i	−0.929319	−	0.369277i	$-0.879605\pi$
$431$	−20.6224	−	28.3843i	−0.993347	−	1.36723i	−0.0640277	−	0.997948i	$-0.520395\pi$
$432$		0			0
$433$	0.494242	−	3.12052i	0.0237517	−	0.149963i	−0.972962	−	0.230964i	$-0.925812\pi$
$433$	0.494242	−	3.12052i	0.0237517	−	0.149963i	0.996714	+	0.0810017i	$0.0258119\pi$
$434$	1.50905	+	4.64439i	0.0724369	+	0.222938i
$435$		0			0
$436$	2.82292	−	8.68806i	0.135193	−	0.416082i
$437$	31.6554	+	16.1292i	1.51428	+	0.771565i
$438$		0			0
$439$	15.5487	+	5.05207i	0.742097	+	0.241122i	0.655577	−	0.755128i	$-0.272425\pi$
$439$	15.5487	+	5.05207i	0.742097	+	0.241122i	0.0865201	+	0.996250i	$0.472425\pi$
$440$	−5.19258	+	7.14698i	−0.247547	+	0.340719i
$441$		0			0
$442$	36.9798	+	5.85703i	1.75895	+	0.278590i
$443$	−0.530898	−	0.530898i	−0.0252237	−	0.0252237i	0.694382	−	0.719606i	$-0.255678\pi$
$443$	−0.530898	−	0.530898i	−0.0252237	−	0.0252237i	−0.719606	+	0.694382i	$0.755678\pi$
$444$		0			0
$445$	6.65524	+	3.39102i	0.315489	+	0.160750i
$446$	−15.1563	+	20.8608i	−0.717671	+	0.987790i
$447$		0			0
$448$	−0.824429	−	1.61803i	−0.0389506	−	0.0764449i
$449$	−13.4807			−0.636192			−0.318096	−	0.948059i	$-0.603043\pi$
$449$	−13.4807			−0.636192			−0.318096	+	0.948059i	$0.603043\pi$
$450$		0			0
$451$	−33.3275			−1.56933
$452$	5.88788	+	11.5556i	0.276943	+	0.543531i
$453$		0			0
$454$	0.0857977	−	0.118090i	0.00402669	−	0.00554226i
$455$	−20.0500	+	3.17561i	−0.939958	+	0.148875i
$456$		0			0
$457$	18.7163	+	18.7163i	0.875512	+	0.875512i	0.993066	−	0.117554i	$-0.0375053\pi$
$457$	18.7163	+	18.7163i	0.875512	+	0.875512i	−0.117554	+	0.993066i	$0.537505\pi$
$458$	−18.8174	−	2.98038i	−0.879279	−	0.139264i
$459$		0			0
$460$	19.9721	+	6.48932i	0.931203	+	0.302566i
$461$	22.2113	+	7.21690i	1.03448	+	0.336125i	0.776562	−	0.630041i	$-0.216962\pi$
$461$	22.2113	+	7.21690i	1.03448	+	0.336125i	0.257923	+	0.966165i	$0.416962\pi$
$462$		0			0
$463$	−9.41860	−	4.79902i	−0.437719	−	0.223029i	0.221222	−	0.975223i	$-0.428995\pi$
$463$	−9.41860	−	4.79902i	−0.437719	−	0.223029i	−0.658941	+	0.752194i	$0.728995\pi$
$464$	−1.57529	+	4.84824i	−0.0731310	+	0.225074i
$465$		0			0
$466$	−2.62830	−	8.08907i	−0.121754	−	0.374719i
$467$	−5.31450	+	33.5545i	−0.245926	+	1.55272i	0.487608	+	0.873063i	$0.337869\pi$
$467$	−5.31450	+	33.5545i	−0.245926	+	1.55272i	−0.733534	+	0.679653i	$0.762131\pi$
$468$		0			0
$469$	−1.78068	−	2.45089i	−0.0822241	−	0.113172i
$470$	−0.822425	+	0.419046i	−0.0379356	+	0.0193292i
$471$		0			0
$472$	0.316769	+	2.00000i	0.0145805	+	0.0920575i
$473$	0.454625	−	0.231643i	0.0209037	−	0.0106510i
$474$		0			0
$475$	−5.84503	−	17.9892i	−0.268188	−	0.825399i
$476$		−	13.6003i		−	0.623370i
$477$		0			0
$478$	13.3053	−	2.10736i	0.608571	−	0.0963882i
$479$	−31.2773	−	22.7243i	−1.42910	−	1.03830i	−0.990184	−	0.139771i	$-0.955363\pi$
$479$	−31.2773	−	22.7243i	−1.42910	−	1.03830i	−0.438914	−	0.898529i	$-0.644637\pi$
$480$		0			0
$481$	−34.3508	+	24.9573i	−1.56626	+	1.13795i
$482$	−7.18762	+	7.18762i	−0.327387	+	0.327387i
$483$		0			0
$484$	−4.38290	+	1.42409i	−0.199223	+	0.0647314i
$485$	−6.09092			−0.276575
$486$		0			0
$487$	−8.91273	+	17.4922i	−0.403875	+	0.792648i	−0.999947	−	0.0102821i	$-0.996727\pi$
$487$	−8.91273	+	17.4922i	−0.403875	+	0.792648i	0.596073	+	0.802931i	$0.296727\pi$
$488$	−1.95756	+	3.84192i	−0.0886144	+	0.173916i
$489$		0			0
$490$	−2.55821	−	7.87337i	−0.115568	−	0.355683i
$491$	−7.53071	+	2.44688i	−0.339856	+	0.110426i	−0.473973	−	0.880540i	$-0.657180\pi$
$491$	−7.53071	+	2.44688i	−0.339856	+	0.110426i	0.134116	+	0.990966i	$0.457180\pi$
$492$		0			0
$493$	−26.9964	+	26.9964i	−1.21586	+	1.21586i
$494$	−15.3001	+	11.1162i	−0.688384	+	0.500140i
$495$		0			0
$496$	2.17557	+	1.58064i	0.0976860	+	0.0709730i
$497$	19.5641	−	3.09865i	0.877569	−	0.138993i
$498$		0			0
$499$		−	6.96924i		−	0.311986i	−0.987758	−	0.155993i	$-0.950142\pi$
$499$		−	6.96924i		−	0.311986i	0.987758	−	0.155993i	$-0.0498578\pi$
$500$	−5.07577	−	9.96176i	−0.226995	−	0.445503i
$501$		0			0
$502$	8.35810	−	4.25867i	0.373040	−	0.190074i
$503$	−6.03430	−	38.0991i	−0.269056	−	1.69875i	−0.638599	−	0.769539i	$-0.720486\pi$
$503$	−6.03430	−	38.0991i	−0.269056	−	1.69875i	0.369543	−	0.929214i	$-0.379514\pi$
$504$		0			0
$505$	9.28563	+	1.47070i	0.413205	+	0.0654453i
$506$	21.8087	+	30.0172i	0.969517	+	1.33443i
$507$		0			0
$508$	1.25627	−	7.93179i	0.0557380	−	0.351916i
$509$	0.608017	+	1.87128i	0.0269499	+	0.0829432i	0.963627	−	0.267251i	$-0.0861154\pi$
$509$	0.608017	+	1.87128i	0.0269499	+	0.0829432i	−0.936677	+	0.350195i	$0.886115\pi$
$510$		0			0
$511$	−0.227311	+	0.699592i	−0.0100557	+	0.0309481i
$512$	−0.891007	−	0.453990i	−0.0393773	−	0.0200637i
$513$		0			0
$514$	−2.99745	−	0.973931i	−0.132212	−	0.0429583i
$515$		−	30.5631i		−	1.34677i
$516$		0			0
$517$	−1.61076	−	0.255119i	−0.0708410	−	0.0112201i
$518$	10.9061	+	10.9061i	0.479185	+	0.479185i
$519$		0			0
$520$	−7.90446	+	7.90446i	−0.346634	+	0.346634i
$521$	18.4841	−	25.4412i	0.809804	−	1.11460i	−0.181549	−	0.983382i	$-0.558111\pi$
$521$	18.4841	−	25.4412i	0.809804	−	1.11460i	0.991354	−	0.131218i	$-0.0418888\pi$
$522$		0			0
$523$	13.8578	+	27.1975i	0.605961	+	1.18926i	0.966535	+	0.256534i	$0.0825807\pi$
$523$	13.8578	+	27.1975i	0.605961	+	1.18926i	−0.360574	+	0.932730i	$0.617419\pi$
$524$	−14.7486			−0.644295
$525$		0			0
$526$	−23.1765			−1.01054
$527$	9.14334	+	17.9448i	0.398290	+	0.781688i
$528$		0			0
$529$	38.3230	−	52.7471i	1.66622	−	2.29335i
$530$	7.96234	+	15.6270i	0.345862	+	0.678792i
$531$		0			0
$532$	4.85765	+	4.85765i	0.210606	+	0.210606i
$533$	−41.6529	−	6.59717i	−1.80419	−	0.285755i
$534$		0			0
$535$	0.575365	+	0.791922i	0.0248752	+	0.0342378i
$536$	−1.58660	−	0.515516i	−0.0685305	−	0.0222669i
$537$		0			0
$538$	−6.27471	−	3.19713i	−0.270522	−	0.137838i
$539$	4.51993	−	13.9109i	0.194687	−	0.599186i
$540$		0			0
$541$	−6.72668	−	20.7026i	−0.289202	−	0.890074i	−0.985107	−	0.171940i	$-0.944997\pi$
$541$	−6.72668	−	20.7026i	−0.289202	−	0.890074i	0.695905	−	0.718134i	$-0.255003\pi$
$542$	−2.25371	+	14.2294i	−0.0968053	+	0.611204i
$543$		0			0
$544$	−4.40211	−	6.05899i	−0.188739	−	0.259777i
$545$	3.19546	+	20.1754i	0.136879	+	0.864217i
$546$		0			0
$547$	−2.54680	−	16.0799i	−0.108893	−	0.687526i	−0.980382	−	0.197109i	$-0.936845\pi$
$547$	−2.54680	−	16.0799i	−0.108893	−	0.687526i	0.871488	−	0.490417i	$-0.163155\pi$
$548$	9.99117	−	5.09076i	0.426802	−	0.217466i
$549$		0			0
$550$	3.09017	−	19.5106i	0.131765	−	0.831933i
$551$		−	19.2847i		−	0.821555i
$552$		0			0
$553$	24.9763	−	3.95586i	1.06210	−	0.168220i
$554$	15.0117	+	10.9067i	0.637788	+	0.463380i
$555$		0			0
$556$	−9.19868	+	6.68323i	−0.390111	+	0.283432i
$557$	12.0707	−	12.0707i	0.511450	−	0.511450i	−0.403520	−	0.914971i	$-0.632214\pi$
$557$	12.0707	−	12.0707i	0.511450	−	0.511450i	0.914971	+	0.403520i	$0.132214\pi$
$558$		0			0
$559$	0.614047	−	0.199516i	0.0259714	−	0.00843862i
$560$	3.28511	+	2.38677i	0.138821	+	0.100859i
$561$		0			0
$562$	−8.91731	+	17.5012i	−0.376154	+	0.738243i
$563$	7.27841	−	14.2847i	0.306748	−	0.602027i	−0.685246	−	0.728312i	$-0.740305\pi$
$563$	7.27841	−	14.2847i	0.306748	−	0.602027i	0.991994	+	0.126285i	$0.0403052\pi$
$564$		0			0
$565$	−23.4615	−	17.0457i	−0.987031	−	0.717120i
$566$	−6.75452	+	2.19468i	−0.283913	+	0.0922491i
$567$		0			0
$568$	7.71290	−	7.71290i	0.323626	−	0.323626i
$569$	28.1494	−	20.4518i	1.18009	−	0.857382i	0.187904	−	0.982187i	$-0.439831\pi$
$569$	28.1494	−	20.4518i	1.18009	−	0.857382i	0.992181	+	0.124805i	$0.0398306\pi$
$570$		0			0
$571$	−1.17087	−	0.850687i	−0.0489994	−	0.0356002i	0.563016	−	0.826446i	$-0.309641\pi$
$571$	−1.17087	−	0.850687i	−0.0489994	−	0.0356002i	−0.612015	+	0.790846i	$0.709641\pi$
$572$	−19.5075	+	3.08969i	−0.815651	+	0.129186i
$573$		0			0
$574$			15.3190i			0.639401i
$575$	−46.3791	+	7.34572i	−1.93414	+	0.306338i
$576$		0			0
$577$	17.9356	−	9.13864i	0.746668	−	0.380446i	−0.0388824	−	0.999244i	$-0.512380\pi$
$577$	17.9356	−	9.13864i	0.746668	−	0.380446i	0.785551	+	0.618797i	$0.212380\pi$
$578$	−6.11501	−	38.6087i	−0.254351	−	1.60591i
$579$		0			0
$580$	−1.78318	−	11.2586i	−0.0740426	−	0.467486i
$581$	−0.735599	−	1.01247i	−0.0305178	−	0.0420041i
$582$		0			0
$583$	−4.84754	+	30.6061i	−0.200764	+	1.26758i
$584$	0.125174	+	0.385246i	0.00517974	+	0.0159416i
$585$		0			0
$586$	6.79132	−	20.9015i	0.280547	−	0.863435i
$587$	29.3326	+	14.9457i	1.21069	+	0.616875i	0.938470	−	0.345361i	$-0.112244\pi$
$587$	29.3326	+	14.9457i	1.21069	+	0.616875i	0.272215	+	0.962236i	$0.412244\pi$
$588$		0			0
$589$	−9.67512	−	3.14364i	−0.398656	−	0.129531i
$590$	−2.66142	−	3.66313i	−0.109569	−	0.150809i
$591$		0			0
$592$	8.38873	+	1.32864i	0.344775	+	0.0546069i
$593$	13.2453	+	13.2453i	0.543920	+	0.543920i	0.924676	−	0.380756i	$-0.124336\pi$
$593$	13.2453	+	13.2453i	0.543920	+	0.543920i	−0.380756	+	0.924676i	$0.624336\pi$
$594$		0			0
$595$	13.8064	+	27.0966i	0.566008	+	1.11085i
$596$	6.38968	−	8.79465i	0.261732	−	0.360243i
$597$		0			0
$598$	21.3148	+	41.8326i	0.871627	+	1.71066i
$599$	−5.34213			−0.218274			−0.109137	−	0.994027i	$-0.534809\pi$
$599$	−5.34213			−0.218274			−0.109137	+	0.994027i	$0.534809\pi$
$600$		0			0
$601$	30.5114			1.24459			0.622293	−	0.782785i	$-0.286201\pi$
$601$	30.5114			1.24459			0.622293	+	0.782785i	$0.286201\pi$
$602$	−0.106475	−	0.208968i	−0.00433958	−	0.00851691i
$603$		0			0
$604$	−12.3943	+	17.0593i	−0.504319	+	0.694135i
$605$	7.28660	−	7.28660i	0.296243	−	0.296243i
$606$		0			0
$607$	2.27295	+	2.27295i	0.0922561	+	0.0922561i	0.751729	−	0.659473i	$-0.229220\pi$
$607$	2.27295	+	2.27295i	0.0922561	+	0.0922561i	−0.659473	+	0.751729i	$0.729220\pi$
$608$	3.73641	+	0.591789i	0.151531	+	0.0240002i
$609$		0			0
$610$		−	9.64167i		−	0.390380i
$611$	−1.96263	−	0.637698i	−0.0793996	−	0.0257985i
$612$		0			0
$613$	−6.99219	−	3.56270i	−0.282412	−	0.143896i	0.307047	−	0.951694i	$-0.400659\pi$
$613$	−6.99219	−	3.56270i	−0.282412	−	0.143896i	−0.589459	+	0.807798i	$0.700659\pi$
$614$	0.786422	−	2.42036i	0.0317374	−	0.0976777i
$615$		0			0
$616$	2.21702	+	6.82328i	0.0893262	+	0.274918i
$617$	2.34372	−	14.7976i	0.0943545	−	0.595731i	−0.894526	−	0.447017i	$-0.852487\pi$
$617$	2.34372	−	14.7976i	0.0943545	−	0.595731i	0.988880	−	0.148714i	$-0.0475135\pi$
$618$		0			0
$619$	16.8199	+	23.1506i	0.676047	+	0.930499i	0.999878	−	0.0156157i	$-0.00497083\pi$
$619$	16.8199	+	23.1506i	0.676047	+	0.930499i	−0.323831	+	0.946115i	$0.604971\pi$
$620$	−5.93910	−	0.940661i	−0.238520	−	0.0377778i
$621$		0			0
$622$	−0.483797	−	3.05458i	−0.0193985	−	0.122477i
$623$	5.40488	−	2.75392i	0.216542	−	0.110334i
$624$		0			0
$625$	20.2254	+	14.6946i	0.809017	+	0.587785i
$626$		−	14.5546i		−	0.581720i
$627$		0			0
$628$	−9.08299	+	1.43860i	−0.362451	+	0.0574066i
$629$	51.4608	+	37.3884i	2.05188	+	1.49078i
$630$		0			0
$631$	−26.6803	+	19.3844i	−1.06213	+	0.771679i	−0.974480	−	0.224473i	$-0.927934\pi$
$631$	−26.6803	+	19.3844i	−1.06213	+	0.771679i	−0.0876449	+	0.996152i	$0.527934\pi$
$632$	9.84662	−	9.84662i	0.391677	−	0.391677i
$633$		0			0
$634$	4.44716	−	1.44497i	0.176619	−	0.0573871i
$635$	5.54905	+	17.0782i	0.220207	+	0.677728i
$636$		0			0
$637$	8.40270	−	16.4912i	0.332927	−	0.653406i
$638$	9.14334	−	17.9448i	0.361988	−	0.710442i
$639$		0			0
$640$	2.23607			0.0883883
$641$	−3.70952	+	1.20529i	−0.146517	+	0.0476063i	−0.381357	−	0.924428i	$-0.624543\pi$
$641$	−3.70952	+	1.20529i	−0.146517	+	0.0476063i	0.234840	+	0.972034i	$0.424543\pi$
$642$		0			0
$643$	24.3761	−	24.3761i	0.961300	−	0.961300i	−0.0379785	−	0.999279i	$-0.512092\pi$
$643$	24.3761	−	24.3761i	0.961300	−	0.961300i	0.999279	+	0.0379785i	$0.0120918\pi$
$644$	13.7974	−	10.0244i	0.543693	−	0.395016i
$645$		0			0
$646$	22.9211	+	16.6531i	0.901817	+	0.655208i
$647$	−16.2504	+	2.57381i	−0.638869	+	0.101187i	−0.467462	−	0.884013i	$-0.654831\pi$
$647$	−16.2504	+	2.57381i	−0.638869	+	0.101187i	−0.171408	+	0.985200i	$0.554831\pi$
$648$		0			0
$649$		−	8.00000i		−	0.314027i
$650$	7.72422	−	23.7727i	0.302969	−	0.932442i
$651$		0			0
$652$	14.3203	−	7.29657i	0.560827	−	0.285756i
$653$	−0.0431419	−	0.272387i	−0.00168827	−	0.0106593i	0.986830	−	0.161762i	$-0.0517176\pi$
$653$	−0.0431419	−	0.272387i	−0.00168827	−	0.0106593i	−0.988518	+	0.151103i	$0.951718\pi$
$654$		0			0
$655$	29.3844	−	14.9721i	1.14814	−	0.585008i
$656$	4.95840	+	6.82465i	0.193593	+	0.266458i
$657$		0			0
$658$	−0.117265	+	0.740384i	−0.00457148	+	0.0288632i
$659$	−12.8571	−	39.5702i	−0.500843	−	1.54144i	−0.807649	−	0.589664i	$-0.799260\pi$
$659$	−12.8571	−	39.5702i	−0.500843	−	1.54144i	0.306806	−	0.951772i	$-0.400740\pi$
$660$		0			0
$661$	−8.76974	+	26.9905i	−0.341103	+	1.04981i	0.622533	+	0.782593i	$0.286103\pi$
$661$	−8.76974	+	26.9905i	−0.341103	+	1.04981i	−0.963637	+	0.267215i	$0.913897\pi$
$662$	−24.7168	−	12.5938i	−0.960644	−	0.489473i
$663$		0			0
$664$	−0.655423	−	0.212960i	−0.0254354	−	0.00826445i
$665$	−14.6094	−	4.74688i	−0.566528	−	0.184076i
$666$		0			0
$667$	−47.2857	−	7.48932i	−1.83091	−	0.289988i
$668$	11.4043	+	11.4043i	0.441245	+	0.441245i
$669$		0			0
$670$	3.68438	−	0.583549i	0.142340	−	0.0225445i
$671$	10.0130	−	13.7818i	0.386549	−	0.532039i
$672$		0			0
$673$	−4.83026	−	9.47992i	−0.186193	−	0.365424i	0.778975	−	0.627055i	$-0.215740\pi$
$673$	−4.83026	−	9.47992i	−0.186193	−	0.365424i	−0.965168	+	0.261631i	$0.915740\pi$
$674$	19.0825			0.735031
$675$		0			0
$676$	−11.9922			−0.461239
$677$	15.3677	+	30.1608i	0.590628	+	1.15917i	0.972051	+	0.234772i	$0.0754342\pi$
$677$	15.3677	+	30.1608i	0.590628	+	1.15917i	−0.381423	+	0.924401i	$0.624566\pi$
$678$		0			0
$679$	−2.90752	+	4.00186i	−0.111581	+	0.153577i
$680$	14.9214	+	7.60281i	0.572208	+	0.291555i
$681$		0			0
$682$	−7.51243	−	7.51243i	−0.287666	−	0.287666i
$683$	21.0295	+	3.33075i	0.804673	+	0.127448i	0.545204	−	0.838304i	$-0.316452\pi$
$683$	21.0295	+	3.33075i	0.804673	+	0.127448i	0.259470	+	0.965751i	$0.416452\pi$
$684$		0			0
$685$	−14.7380	+	20.2852i	−0.563111	+	0.775056i
$686$	−18.4837	−	6.00573i	−0.705712	−	0.229300i
$687$		0			0
$688$	−0.115073	−	0.0586326i	−0.00438712	−	0.00223535i
$689$	−12.1170	+	37.2922i	−0.461619	+	1.42072i
$690$		0			0
$691$	9.82212	+	30.2294i	0.373651	+	1.14998i	0.944384	+	0.328844i	$0.106659\pi$
$691$	9.82212	+	30.2294i	0.373651	+	1.14998i	−0.570733	+	0.821136i	$0.693341\pi$
$692$	−0.936181	+	5.91082i	−0.0355883	+	0.224696i
$693$		0			0
$694$	−4.79225	−	6.59597i	−0.181911	−	0.250379i
$695$	11.5425	−	22.6534i	0.437832	−	0.859293i
$696$		0			0
$697$	9.88320	+	62.4001i	0.374353	+	2.36357i
$698$	4.99160	−	2.54335i	0.188935	−	0.0962671i
$699$		0			0
$700$	−8.96802	−	1.42040i	−0.338959	−	0.0536859i
$701$		−	6.45719i		−	0.243885i	−0.992537	−	0.121942i	$-0.961088\pi$
$701$		−	6.45719i		−	0.243885i	0.992537	−	0.121942i	$-0.0389123\pi$
$702$		0			0
$703$	−31.7344	+	5.02624i	−1.19689	+	0.189568i
$704$	3.19623	+	2.32219i	0.120462	+	0.0875210i
$705$		0			0
$706$	11.1613	−	8.10915i	0.420061	−	0.305192i
$707$	5.39881	−	5.39881i	0.203043	−	0.203043i
$708$		0			0
$709$	42.9374	−	13.9512i	1.61255	−	0.523949i	0.642382	−	0.766385i	$-0.277946\pi$
$709$	42.9374	−	13.9512i	1.61255	−	0.523949i	0.970168	+	0.242436i	$0.0779463\pi$
$710$	−7.53703	+	23.1966i	−0.282860	+	0.870553i
$711$		0			0
$712$	1.51651	−	2.97632i	0.0568336	−	0.111542i
$713$	−11.4655	+	22.5024i	−0.429388	+	0.842721i
$714$		0			0
$715$	35.7293	−	25.9589i	1.33620	−	0.970807i
$716$	−9.52743	+	3.09565i	−0.356057	+	0.115690i
$717$		0			0
$718$	−18.4050	+	18.4050i	−0.686867	+	0.686867i
$719$	11.5028	−	8.35728i	0.428982	−	0.311674i	−0.352260	−	0.935902i	$-0.614587\pi$
$719$	11.5028	−	8.35728i	0.428982	−	0.311674i	0.781242	+	0.624228i	$0.214587\pi$
$720$		0			0
$721$	−20.0806	−	14.5894i	−0.747840	−	0.543338i
$722$	4.63131	−	0.733527i	0.172360	−	0.0272991i
$723$		0			0
$724$		−	4.74663i		−	0.176407i
$725$	14.9819	+	20.6208i	0.556414	+	0.765838i
$726$		0			0
$727$	−9.44311	+	4.81150i	−0.350225	+	0.178449i	−0.620249	−	0.784405i	$-0.712968\pi$
$727$	−9.44311	+	4.81150i	−0.350225	+	0.178449i	0.270024	+	0.962854i	$0.412968\pi$
$728$	1.42017	+	8.96663i	0.0526352	+	0.332325i
$729$		0			0
$730$	−0.640474	−	0.640474i	−0.0237050	−	0.0237050i
$731$	−0.568531	−	0.782515i	−0.0210279	−	0.0289424i
$732$		0			0
$733$	7.86115	−	49.6334i	0.290358	−	1.83325i	−0.222689	−	0.974890i	$-0.571483\pi$
$733$	7.86115	−	49.6334i	0.290358	−	1.83325i	0.513047	−	0.858360i	$-0.328517\pi$
$734$	−1.58865	−	4.88936i	−0.0586381	−	0.180470i
$735$		0			0
$736$	2.90211	−	8.93179i	0.106973	−	0.329230i
$737$	5.87247	+	2.99217i	0.216315	+	0.110218i
$738$		0			0
$739$	4.51035	+	1.46550i	0.165916	+	0.0539094i	0.390797	−	0.920477i	$-0.372199\pi$
$739$	4.51035	+	1.46550i	0.165916	+	0.0539094i	−0.224881	+	0.974386i	$0.572199\pi$
$740$	−18.0621	+	5.86872i	−0.663975	+	0.215739i
$741$		0			0
$742$	14.0681	+	2.22817i	0.516456	+	0.0817986i
$743$	5.38309	+	5.38309i	0.197486	+	0.197486i	0.798922	−	0.601435i	$-0.205404\pi$
$743$	5.38309	+	5.38309i	0.197486	+	0.197486i	−0.601435	+	0.798922i	$0.705404\pi$
$744$		0			0
$745$	−3.80258	+	24.0085i	−0.139316	+	0.879605i
$746$	8.09865	−	11.1468i	0.296513	−	0.408115i
$747$		0			0
$748$	13.4329	+	26.3635i	0.491155	+	0.963946i
$749$	0.794962			0.0290473
$750$		0			0
$751$	33.6368			1.22742			0.613712	−	0.789530i	$-0.289676\pi$
$751$	33.6368			1.22742			0.613712	+	0.789530i	$0.289676\pi$
$752$	0.187403	+	0.367799i	0.00683389	+	0.0134123i
$753$		0			0
$754$	14.9796	−	20.6176i	0.545524	−	0.750849i
$755$	7.37602	−	46.5704i	0.268441	−	1.69487i
$756$		0			0
$757$	35.2101	+	35.2101i	1.27973	+	1.27973i	0.940817	+	0.338914i	$0.110060\pi$
$757$	35.2101	+	35.2101i	1.27973	+	1.27973i	0.338914	+	0.940817i	$0.389940\pi$
$758$	4.37016	+	0.692165i	0.158731	+	0.0251406i
$759$		0			0
$760$	−8.04499	+	2.61398i	−0.291823	+	0.0948189i
$761$	32.5920	+	10.5898i	1.18146	+	0.383880i	0.832909	−	0.553410i	$-0.186674\pi$
$761$	32.5920	+	10.5898i	1.18146	+	0.383880i	0.348552	+	0.937290i	$0.386674\pi$
$762$		0			0
$763$	14.7810	+	7.53130i	0.535108	+	0.272651i
$764$	7.68716	−	23.6587i	0.278112	−	0.855940i
$765$		0			0
$766$	−7.28293	−	22.4145i	−0.263143	−	0.809870i
$767$	1.58360	−	9.99844i	0.0571804	−	0.361023i
$768$		0			0
$769$	−16.9362	−	23.3106i	−0.610733	−	0.840603i	0.385904	−	0.922539i	$-0.373890\pi$
$769$	−16.9362	−	23.3106i	−0.610733	−	0.840603i	−0.996638	+	0.0819364i	$0.973890\pi$
$770$	−11.3438	−	11.3438i	−0.408800	−	0.408800i
$771$		0			0
$772$	−2.11324	−	13.3425i	−0.0760573	−	0.480207i
$773$	−4.95291	+	2.52363i	−0.178144	+	0.0907688i	−0.540788	−	0.841159i	$-0.681874\pi$
$773$	−4.95291	+	2.52363i	−0.178144	+	0.0907688i	0.362644	+	0.931928i	$0.381874\pi$
$774$		0			0
$775$	12.7877	−	4.15497i	0.459347	−	0.149251i
$776$			2.72394i			0.0977839i
$777$		0			0
$778$	11.2474	−	1.78141i	0.403238	−	0.0638666i
$779$	−25.8175	−	18.7575i	−0.925009	−	0.672058i
$780$		0			0
$781$	−34.8635	+	25.3298i	−1.24751	+	0.906371i
$782$	49.7347	−	49.7347i	1.77851	−	1.77851i
$783$		0			0
$784$	−3.52108	+	1.14407i	−0.125753	+	0.0408596i
$785$	16.6361	−	12.0868i	0.593768	−	0.431398i
$786$		0			0
$787$	−5.09132	+	9.99228i	−0.181486	+	0.356186i	−0.963770	−	0.266736i	$-0.914055\pi$
$787$	−5.09132	+	9.99228i	−0.181486	+	0.356186i	0.782284	+	0.622922i	$0.214055\pi$
$788$	1.61456	−	3.16876i	0.0575165	−	0.112882i
$789$		0			0
$790$	−9.62209	+	29.6138i	−0.342339	+	1.05361i
$791$	−22.3988	+	7.27782i	−0.796411	+	0.258770i
$792$		0			0
$793$	15.2424	−	15.2424i	0.541275	−	0.541275i
$794$	14.3620	−	10.4346i	0.509688	−	0.370310i
$795$		0			0
$796$	−9.48462	−	6.89098i	−0.336174	−	0.244244i
$797$	−21.6471	+	3.42856i	−0.766779	+	0.121446i	−0.527558	−	0.849519i	$-0.676892\pi$
$797$	−21.6471	+	3.42856i	−0.766779	+	0.121446i	−0.239221	+	0.970965i	$0.576892\pi$
$798$		0			0
$799$			3.09152i			0.109370i
$800$	−4.45503	+	2.26995i	−0.157509	+	0.0802549i
$801$		0			0
$802$	−3.99614	+	2.03614i	−0.141109	+	0.0718985i
$803$	−0.250348	−	1.58064i	−0.00883459	−	0.0557794i
$804$		0			0
$805$	−17.3129	+	33.9785i	−0.610200	+	1.19759i
$806$	−7.90199	−	10.8762i	−0.278336	−	0.383096i
$807$		0			0
$808$	0.657717	−	4.15266i	0.0231384	−	0.146090i
$809$	−13.4672	−	41.4479i	−0.473483	−	1.45723i	−0.847993	−	0.530007i	$-0.822189\pi$
$809$	−13.4672	−	41.4479i	−0.473483	−	1.45723i	0.374510	−	0.927223i	$-0.377811\pi$
$810$		0			0
$811$	17.3078	−	53.2679i	0.607759	−	1.87049i	0.131175	−	0.991359i	$-0.458125\pi$
$811$	17.3078	−	53.2679i	0.607759	−	1.87049i	0.476583	−	0.879129i	$-0.341875\pi$
$812$	−8.24832	−	4.20273i	−0.289459	−	0.147487i
$813$		0			0
$814$	−31.9126	−	10.3690i	−1.11854	−	0.363435i
$815$	−21.1240	+	29.0746i	−0.739940	+	1.01844i
$816$		0			0
$817$	0.482555	+	0.0764292i	0.0168825	+	0.00267392i
$818$	−10.3896	−	10.3896i	−0.363263	−	0.363263i
$819$		0			0
$820$	−16.8069	−	8.56356i	−0.586924	−	0.299052i
$821$	−8.72276	+	12.0058i	−0.304426	+	0.419007i	−0.933633	−	0.358231i	$-0.883380\pi$
$821$	−8.72276	+	12.0058i	−0.304426	+	0.419007i	0.629207	+	0.777238i	$0.283380\pi$
$822$		0			0
$823$	9.74444	+	19.1245i	0.339670	+	0.666640i	0.996146	−	0.0877069i	$-0.0279539\pi$
$823$	9.74444	+	19.1245i	0.339670	+	0.666640i	−0.656476	+	0.754347i	$0.727954\pi$
$824$	−13.6682			−0.476155
$825$		0			0
$826$	−3.67720			−0.127946
$827$	−10.2597	−	20.1358i	−0.356765	−	0.700190i	0.640962	−	0.767572i	$-0.278535\pi$
$827$	−10.2597	−	20.1358i	−0.356765	−	0.700190i	−0.997727	+	0.0673818i	$0.978535\pi$
$828$		0			0
$829$	−7.34963	+	10.1159i	−0.255263	+	0.351339i	−0.917346	−	0.398091i	$-0.869673\pi$
$829$	−7.34963	+	10.1159i	−0.255263	+	0.351339i	0.662083	+	0.749431i	$0.269673\pi$
$830$	1.52202	−	0.241064i	0.0528301	−	0.00836747i
$831$		0			0
$832$	3.53498	+	3.53498i	0.122553	+	0.122553i
$833$	−27.3862	−	4.33755i	−0.948876	−	0.150287i
$834$		0			0
$835$	−34.2984	−	11.1442i	−1.18695	−	0.385662i
$836$	−14.2141	−	4.61845i	−0.491606	−	0.159733i
$837$		0			0
$838$	12.9684	+	6.60774i	0.447987	+	0.228261i
$839$	−7.81986	+	24.0670i	−0.269971	+	0.830887i	0.720535	+	0.693419i	$0.243896\pi$
$839$	−7.81986	+	24.0670i	−0.269971	+	0.830887i	−0.990506	+	0.137468i	$0.956104\pi$
$840$		0			0
$841$	−0.931067	−	2.86553i	−0.0321058	−	0.0988114i
$842$	−3.75649	+	23.7176i	−0.129457	+	0.817361i
$843$		0			0
$844$	15.4775	+	21.3030i	0.532759	+	0.733280i
$845$	23.8927	−	12.1739i	0.821934	−	0.418796i
$846$		0			0
$847$	−1.30916	−	8.26574i	−0.0449834	−	0.284014i
$848$	6.98859	−	3.56087i	0.239989	−	0.122281i
$849$		0			0
$850$	−37.4466			−1.28441
$851$			79.7642i			2.73428i
$852$		0			0
$853$	2.11601	−	0.335142i	0.0724506	−	0.0114751i	−0.120104	−	0.992761i	$-0.538323\pi$
$853$	2.11601	−	0.335142i	0.0724506	−	0.0114751i	0.192555	+	0.981286i	$0.438323\pi$
$854$	−6.33478	−	4.60249i	−0.216772	−	0.157494i
$855$		0			0
$856$	0.354158	−	0.257311i	0.0121049	−	0.00879471i
$857$	−36.7477	+	36.7477i	−1.25528	+	1.25528i	−0.301957	+	0.953322i	$0.597640\pi$
$857$	−36.7477	+	36.7477i	−1.25528	+	1.25528i	−0.953322	+	0.301957i	$0.902360\pi$
$858$		0			0
$859$	−8.24700	+	2.67961i	−0.281384	+	0.0914273i	−0.446309	−	0.894879i	$-0.647262\pi$
$859$	−8.24700	+	2.67961i	−0.281384	+	0.0914273i	0.164925	+	0.986306i	$0.447262\pi$
$860$	0.288787			0.00984756
$861$		0			0
$862$	15.9282	−	31.2609i	0.542518	−	1.06475i
$863$	−8.01248	+	15.7254i	−0.272748	+	0.535298i	−0.986231	−	0.165375i	$-0.947117\pi$
$863$	−8.01248	+	15.7254i	−0.272748	+	0.535298i	0.713483	+	0.700673i	$0.247117\pi$
$864$		0			0
$865$	−4.13519	−	12.7268i	−0.140601	−	0.432724i
$866$	3.00478	−	0.976314i	0.102107	−	0.0331765i
$867$		0			0
$868$	−3.45309	+	3.45309i	−0.117205	+	0.117205i
$869$	−44.5082	+	32.3371i	−1.50984	+	1.09696i
$870$		0			0
$871$	6.74714	+	4.90209i	0.228618	+	0.166101i
$872$	9.02269	−	1.42905i	0.305547	−	0.0483939i
$873$		0			0
$874$			35.5276i			1.20174i
$875$	19.3094	−	6.27399i	0.652776	−	0.212100i
$876$		0			0
$877$	−15.9099	+	8.10651i	−0.537240	+	0.273738i	−0.701488	−	0.712682i	$-0.747480\pi$
$877$	−15.9099	+	8.10651i	−0.537240	+	0.273738i	0.164247	+	0.986419i	$0.447480\pi$
$878$	2.55752	+	16.1476i	0.0863122	+	0.544954i
$879$		0			0
$880$	−8.72539	−	1.38197i	−0.294133	−	0.0465861i
$881$	31.2335	+	42.9892i	1.05228	+	1.44834i	0.886813	+	0.462129i	$0.152914\pi$
$881$	31.2335	+	42.9892i	1.05228	+	1.44834i	0.165471	+	0.986215i	$0.447086\pi$
$882$		0			0
$883$	5.81503	−	36.7147i	0.195691	−	1.23555i	−0.672793	−	0.739830i	$-0.734906\pi$
$883$	5.81503	−	36.7147i	0.195691	−	1.23555i	0.868485	−	0.495716i	$-0.165094\pi$
$884$	11.5698	+	35.6083i	0.389136	+	1.19764i
$885$		0			0
$886$	0.232011	−	0.714056i	0.00779456	−	0.0239892i
$887$	−4.03516	−	2.05602i	−0.135488	−	0.0690344i	0.384933	−	0.922945i	$-0.374225\pi$
$887$	−4.03516	−	2.05602i	−0.135488	−	0.0690344i	−0.520420	+	0.853910i	$0.674225\pi$
$888$		0			0
$889$	13.8696	+	4.50651i	0.465172	+	0.151143i
$890$			7.46936i			0.250373i
$891$		0			0
$892$	−25.4680	−	4.03373i	−0.852731	−	0.135059i
$893$	−1.10420	−	1.10420i	−0.0369508	−	0.0369508i
$894$		0			0
$895$	15.8394	−	15.8394i	0.529454	−	0.529454i
$896$	1.06740	−	1.46914i	0.0356592	−	0.0490807i
$897$		0			0
$898$	−6.12009	−	12.0114i	−0.204230	−	0.400824i
$899$	13.7086			0.457208
$900$		0			0
$901$	58.7424			1.95699
$902$	−15.1304	−	29.6950i	−0.503786	−	0.988735i
$903$		0			0
$904$	−7.62309	+	10.4923i	−0.253540	+	0.348968i
$905$	4.81856	+	9.45696i	0.160174	+	0.314360i
$906$		0			0
$907$	−39.8147	−	39.8147i	−1.32203	−	1.32203i	−0.912134	−	0.409893i	$-0.865566\pi$
$907$	−39.8147	−	39.8147i	−1.32203	−	1.32203i	−0.409893	−	0.912134i	$-0.634434\pi$
$908$	0.144171	+	0.0228344i	0.00478447	+	0.000757786i
$909$		0			0
$910$	−11.9320	−	16.4230i	−0.395542	−	0.544416i
$911$	−14.7757	−	4.80090i	−0.489540	−	0.159061i	0.0538376	−	0.998550i	$-0.482855\pi$
$911$	−14.7757	−	4.80090i	−0.489540	−	0.159061i	−0.543377	+	0.839489i	$0.682855\pi$
$912$		0			0
$913$	2.42592	+	1.23607i	0.0802862	+	0.0409079i
$914$	−8.17933	+	25.1734i	−0.270548	+	0.832662i
$915$		0			0
$916$	−5.88738	−	18.1195i	−0.194524	−	0.598685i
$917$	4.18976	−	26.4531i	0.138358	−	0.873559i
$918$		0			0
$919$	15.4958	+	21.3281i	0.511158	+	0.703549i	0.984114	−	0.177537i	$-0.0568129\pi$
$919$	15.4958	+	21.3281i	0.511158	+	0.703549i	−0.472956	+	0.881086i	$0.656813\pi$
$920$	3.28511	+	20.7413i	0.108307	+	0.683822i
$921$		0			0
$922$	3.65343	+	23.0668i	0.120319	+	0.759666i
$923$	−48.5866	+	24.7561i	−1.59925	+	0.814857i
$924$		0			0
$925$	30.0283	−	30.0283i	0.987326	−	0.987326i
$926$		−	10.5707i		−	0.347376i
$927$		0			0
$928$	−5.03498	+	0.797463i	−0.165281	+	0.0261780i
$929$	−9.86752	−	7.16917i	−0.323743	−	0.235213i	0.414028	−	0.910264i	$-0.364122\pi$
$929$	−9.86752	−	7.16917i	−0.323743	−	0.235213i	−0.737771	+	0.675051i	$0.764122\pi$
$930$		0			0
$931$	11.3308	−	8.23233i	0.371353	−	0.269804i
$932$	6.01419	−	6.01419i	0.197001	−	0.197001i
$933$		0			0
$934$	−32.3100	+	10.4981i	−1.05721	+	0.343510i
$935$	−53.5260	−	38.8889i	−1.75049	−	1.27180i
$936$		0			0
$937$	18.8820	−	37.0581i	0.616850	−	1.21064i	−0.345397	−	0.938457i	$-0.612256\pi$
$937$	18.8820	−	37.0581i	0.616850	−	1.21064i	0.962247	−	0.272179i	$-0.0877442\pi$
$938$	1.37535	−	2.69928i	0.0449068	−	0.0881345i
$939$		0			0
$940$	−0.746746	−	0.542543i	−0.0243562	−	0.0176958i
$941$	8.88126	−	2.88570i	0.289521	−	0.0940710i	−0.160656	−	0.987010i	$-0.551361\pi$
$941$	8.88126	−	2.88570i	0.289521	−	0.0940710i	0.450177	+	0.892939i	$0.351361\pi$
$942$		0			0
$943$	−56.0195	+	56.0195i	−1.82425	+	1.82425i
$944$	−1.63820	+	1.19022i	−0.0533190	+	0.0387385i
$945$		0			0
$946$	0.412791	+	0.299910i	0.0134210	+	0.00975092i
$947$	2.62415	−	0.415625i	0.0852734	−	0.0135060i	−0.113652	−	0.993521i	$-0.536255\pi$
$947$	2.62415	−	0.415625i	0.0852734	−	0.0135060i	0.198925	+	0.980015i	$0.436255\pi$
$948$		0			0
$949$		−	2.02504i		−	0.0657357i
$950$	13.3749	−	13.3749i	0.433938	−	0.433938i
$951$		0			0
$952$	12.1180	−	6.17442i	0.392746	−	0.200114i
$953$	4.92811	+	31.1149i	0.159637	+	1.00791i	0.929264	+	0.369416i	$0.120442\pi$
$953$	4.92811	+	31.1149i	0.159637	+	1.00791i	−0.769627	+	0.638494i	$0.779558\pi$
$954$		0			0
$955$	8.70164	+	54.9400i	0.281578	+	1.77782i
$956$	7.91816	+	10.8984i	0.256092	+	0.352480i
$957$		0			0
$958$	6.04790	−	38.1849i	0.195399	−	1.23370i
$959$	6.29252	+	19.3664i	0.203196	+	0.625373i
$960$		0			0
$961$	−7.34486	+	22.6051i	−0.236931	+	0.729198i
$962$	−37.8320	−	19.2764i	−1.21975	−	0.621495i
$963$		0			0
$964$	−9.66733	−	3.14111i	−0.311364	−	0.101168i
$965$	17.7550	+	24.4377i	0.571554	+	0.786676i
$966$		0			0
$967$	−27.9494	−	4.42675i	−0.898791	−	0.142355i	−0.310092	−	0.950707i	$-0.600360\pi$
$967$	−27.9494	−	4.42675i	−0.898791	−	0.142355i	−0.588699	+	0.808352i	$0.700360\pi$
$968$	−3.25867	−	3.25867i	−0.104738	−	0.104738i
$969$		0			0
$970$	−2.76522	−	5.42705i	−0.0887859	−	0.174252i
$971$	10.9794	−	15.1119i	0.352347	−	0.484964i	−0.595650	−	0.803244i	$-0.703105\pi$
$971$	10.9794	−	15.1119i	0.352347	−	0.484964i	0.947997	+	0.318280i	$0.103105\pi$
$972$		0			0
$973$	−9.37392	−	18.3974i	−0.300514	−	0.589792i
$974$	−19.6320			−0.629049
$975$		0			0
$976$	−4.31189			−0.138020
$977$	1.32908	+	2.60846i	0.0425210	+	0.0834521i	0.911289	−	0.411766i	$-0.135088\pi$
$977$	1.32908	+	2.60846i	0.0425210	+	0.0834521i	−0.868768	+	0.495218i	$0.835088\pi$
$978$		0			0
$979$	−7.75705	+	10.6767i	−0.247916	+	0.341228i
$980$	5.85382	−	5.85382i	0.186993	−	0.186993i
$981$		0			0
$982$	−5.59905	−	5.59905i	−0.178673	−	0.178673i
$983$	31.9014	+	5.05268i	1.01750	+	0.161156i	0.642834	−	0.766006i	$-0.277759\pi$
$983$	31.9014	+	5.05268i	1.01750	+	0.161156i	0.374662	+	0.927161i	$0.377759\pi$
$984$		0			0
$985$			7.95232i			0.253382i
$986$	−36.3101	−	11.7979i	−1.15635	−	0.375720i
$987$		0			0
$988$	−16.8507	−	8.58585i	−0.536092	−	0.273152i
$989$	0.374806	−	1.15354i	0.0119182	−	0.0366803i
$990$		0			0
$991$	12.1116	+	37.2757i	0.384738	+	1.18410i	0.936670	+	0.350213i	$0.113891\pi$
$991$	12.1116	+	37.2757i	0.384738	+	1.18410i	−0.551932	+	0.833889i	$0.686109\pi$
$992$	−0.420676	+	2.65605i	−0.0133565	+	0.0843295i
$993$		0			0
$994$	11.6428	+	16.0250i	0.369288	+	0.508281i
$995$	25.8921	+	4.10091i	0.820835	+	0.130007i
$996$		0			0
$997$	−8.01914	−	50.6308i	−0.253969	−	1.60350i	−0.703811	−	0.710387i	$-0.748520\pi$
$997$	−8.01914	−	50.6308i	−0.253969	−	1.60350i	0.449842	−	0.893108i	$-0.351480\pi$
$998$	6.20964	−	3.16397i	0.196563	−	0.100154i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.s.b.197.2	yes	16
3.2	odd	2	inner	450.2.s.b.197.1	✓	16
25.8	odd	20	inner	450.2.s.b.233.1	yes	16
75.8	even	20	inner	450.2.s.b.233.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.s.b.197.1	✓	16	3.2	odd	2	inner
450.2.s.b.197.2	yes	16	1.1	even	1	trivial
450.2.s.b.233.1	yes	16	25.8	odd	20	inner
450.2.s.b.233.2	yes	16	75.8	even	20	inner

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.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 + 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(0.349798 - 2.20854i) q^{5} +(-1.28408 - 1.28408i) q^{7} +(-0.987688 - 0.156434i) q^{8} +O(q^{10})\)	\(q+(0.453990 + 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(0.349798 - 2.20854i) q^{5} +(-1.28408 - 1.28408i) q^{7} +(-0.987688 - 0.156434i) q^{8} +(2.12663 - 0.690983i) q^{10} +(3.75739 + 1.22085i) q^{11} +(4.45434 + 2.26960i) q^{13} +(0.561163 - 1.72708i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(1.17159 - 7.39712i) q^{17} +(2.22358 + 3.06050i) q^{19} +(1.58114 + 1.58114i) q^{20} +(0.618034 + 3.90211i) q^{22} +(8.36783 - 4.26362i) q^{23} +(-4.75528 - 1.54508i) q^{25} +4.99922i q^{26} +(1.79360 - 0.284079i) q^{28} +(-4.12416 - 2.99638i) q^{29} +(-2.17557 + 1.58064i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.12277 - 2.31433i) q^{34} +(-3.28511 + 2.38677i) q^{35} +(-3.85588 + 7.56758i) q^{37} +(-1.71744 + 3.37066i) q^{38} +(-0.690983 + 2.12663i) q^{40} +(-8.02285 + 2.60678i) q^{41} +(0.0913225 - 0.0913225i) q^{43} +(-3.19623 + 2.32219i) q^{44} +(7.59783 + 5.52015i) q^{46} +(-0.407709 + 0.0645747i) q^{47} -3.70228i q^{49} +(-0.782172 - 4.93844i) q^{50} +(-4.45434 + 2.26960i) q^{52} +(1.22699 + 7.74691i) q^{53} +(4.01062 - 7.87129i) q^{55} +(1.06740 + 1.46914i) q^{56} +(0.797463 - 5.03498i) q^{58} +(-0.625738 - 1.92582i) q^{59} +(1.33245 - 4.10085i) q^{61} +(-2.39605 - 1.22085i) q^{62} +(0.951057 + 0.309017i) q^{64} +(6.57062 - 9.04368i) q^{65} +(1.64771 + 0.260971i) q^{67} +(5.29575 + 5.29575i) q^{68} +(-3.61803 - 1.84348i) q^{70} +(-6.41138 + 8.82451i) q^{71} +(-0.183899 - 0.360921i) q^{73} -8.49330 q^{74} -3.78298 q^{76} +(-3.25712 - 6.39245i) q^{77} +(-8.18504 + 11.2657i) q^{79} +(-2.20854 + 0.349798i) q^{80} +(-5.96496 - 5.96496i) q^{82} +(0.680668 + 0.107807i) q^{83} +(-15.9270 - 5.17499i) q^{85} +(0.122828 + 0.0399094i) q^{86} +(-3.52015 - 1.79360i) q^{88} +(-1.03224 + 3.17691i) q^{89} +(-2.80538 - 8.63407i) q^{91} +(-1.46914 + 9.27581i) q^{92} +(-0.242632 - 0.333955i) q^{94} +(7.53703 - 3.84031i) q^{95} +(-0.426119 - 2.69041i) q^{97} +(3.29876 - 1.68080i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 52 q^{13} + 4 q^{16} + 40 q^{19} - 8 q^{22} - 8 q^{28} - 16 q^{31} + 20 q^{34} + 52 q^{37} - 20 q^{40} + 40 q^{43} + 24 q^{46} - 52 q^{52} + 40 q^{55} + 36 q^{58} - 40 q^{61} - 64 q^{67} - 40 q^{70} - 84 q^{73} - 48 q^{76} + 40 q^{79} - 52 q^{82} - 100 q^{85} - 8 q^{88} - 112 q^{91} + 40 q^{94} + 12 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 52 * q^13 + 4 * q^16 + 40 * q^19 - 8 * q^22 - 8 * q^28 - 16 * q^31 + 20 * q^34 + 52 * q^37 - 20 * q^40 + 40 * q^43 + 24 * q^46 - 52 * q^52 + 40 * q^55 + 36 * q^58 - 40 * q^61 - 64 * q^67 - 40 * q^70 - 84 * q^73 - 48 * q^76 + 40 * q^79 - 52 * q^82 - 100 * q^85 - 8 * q^88 - 112 * q^91 + 40 * q^94 + 12 * q^97

Introduction

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