LMFDB - Embedded newform 450.2.s.b.233.2

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			233.2
Root			$0.891007 + 0.453990i$ of defining polynomial
Character	$\chi$	$=$	450.233
Dual form			450.2.s.b.197.2

$q$-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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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	−0.906831	−	0.421495i	$-0.861506\pi$
$7$	−1.28408	+	1.28408i	−0.485336	+	0.485336i	0.421495	+	0.906831i	$0.361506\pi$
$8$	−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	0.318220	−	0.948017i	$-0.396915\pi$
$11$	3.75739	−	1.22085i	1.13290	−	0.368100i	0.814676	+	0.579917i	$0.196915\pi$
$12$		0			0
$13$	4.45434	−	2.26960i	1.23541	−	0.629473i	0.290524	−	0.956868i	$-0.406171\pi$
$13$	4.45434	−	2.26960i	1.23541	−	0.629473i	0.944888	+	0.327394i	$0.106171\pi$
$14$	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	0.555430	+	0.831563i	$0.312554\pi$
$17$	1.17159	+	7.39712i	0.284152	+	1.79406i	−0.271278	+	0.962501i	$0.587446\pi$
$18$		0			0
$19$	2.22358	−	3.06050i	0.510125	−	0.702126i	−0.473816	−	0.880624i	$-0.657124\pi$
$19$	2.22358	−	3.06050i	0.510125	−	0.702126i	0.983940	+	0.178498i	$0.0571237\pi$
$20$	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	0.964685	+	0.263407i	$0.0848463\pi$
$23$	8.36783	+	4.26362i	1.74481	+	0.889027i	0.780128	+	0.625619i	$0.215154\pi$
$24$		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	−0.900695	−	0.434451i	$-0.856942\pi$
$29$	−4.12416	+	2.99638i	−0.765838	+	0.556414i	0.134858	+	0.990865i	$0.456942\pi$
$30$		0			0
$31$	−2.17557	−	1.58064i	−0.390744	−	0.283892i	0.375016	−	0.927018i	$-0.377637\pi$
$31$	−2.17557	−	1.58064i	−0.390744	−	0.283892i	−0.765760	+	0.643126i	$0.777637\pi$
$32$	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	−0.954873	−	0.297014i	$-0.904009\pi$
$37$	−3.85588	−	7.56758i	−0.633902	−	1.24410i	0.320971	−	0.947089i	$-0.395991\pi$
$38$	−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	−0.393979	−	0.919120i	$-0.628902\pi$
$41$	−8.02285	−	2.60678i	−1.25296	−	0.407111i	−0.858980	+	0.512008i	$0.828902\pi$
$42$		0			0
$43$	0.0913225	+	0.0913225i	0.0139265	+	0.0139265i	0.714036	−	0.700109i	$-0.246865\pi$
$43$	0.0913225	+	0.0913225i	0.0139265	+	0.0139265i	−0.700109	+	0.714036i	$0.746865\pi$
$44$	−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	0.126628	−	0.991950i	$-0.459584\pi$
$47$	−0.407709	−	0.0645747i	−0.0594705	−	0.00941919i	−0.186099	+	0.982531i	$0.559584\pi$
$48$		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	−0.747860	−	0.663857i	$-0.768918\pi$
$53$	1.22699	−	7.74691i	0.168540	−	1.06412i	0.916400	−	0.400264i	$-0.131082\pi$
$54$		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	−0.983490	−	0.180960i	$-0.942079\pi$
$59$	−0.625738	+	1.92582i	−0.0814641	+	0.250721i	0.902026	+	0.431681i	$0.142079\pi$
$60$		0			0
$61$	1.33245	+	4.10085i	0.170602	+	0.525060i	0.999405	−	0.0344806i	$-0.0109777\pi$
$61$	1.33245	+	4.10085i	0.170602	+	0.525060i	−0.828803	+	0.559540i	$0.810978\pi$
$62$	−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	−0.0549704	−	0.998488i	$-0.517506\pi$
$67$	1.64771	−	0.260971i	0.201299	−	0.0318827i	0.256270	+	0.966605i	$0.417506\pi$
$68$	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	−0.997139	−	0.0755839i	$-0.975918\pi$
$71$	−6.41138	−	8.82451i	−0.760891	−	1.04728i	0.236249	−	0.971693i	$-0.424082\pi$
$72$		0			0
$73$	−0.183899	+	0.360921i	−0.0215237	+	0.0422427i	−0.901518	−	0.432742i	$-0.857546\pi$
$73$	−0.183899	+	0.360921i	−0.0215237	+	0.0422427i	0.879994	+	0.474984i	$0.157546\pi$
$74$	−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	−0.963309	−	0.268395i	$-0.913507\pi$
$79$	−8.18504	−	11.2657i	−0.920889	−	1.26749i	0.0424201	−	0.999100i	$-0.486493\pi$
$80$	−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	−0.118966	−	0.992898i	$-0.537958\pi$
$83$	0.680668	−	0.107807i	0.0747131	−	0.0118334i	0.193679	+	0.981065i	$0.437958\pi$
$84$		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	0.881325	−	0.472511i	$-0.156652\pi$
$89$	−1.03224	−	3.17691i	−0.109417	−	0.336751i	−0.990742	+	0.135760i	$0.956652\pi$
$90$		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	−0.999832	−	0.0183468i	$-0.994160\pi$
$97$	−0.426119	+	2.69041i	−0.0432658	+	0.273169i	0.956566	+	0.291516i	$0.0941597\pi$
$98$	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	$-0.932921\pi$
$101$		−	4.20442i		−	0.418356i	0.977878	−	0.209178i	$-0.0670788\pi$
$102$		0			0
$103$	13.4999	+	2.13818i	1.33019	+	0.210681i	0.780745	−	0.624849i	$-0.214840\pi$
$103$	13.4999	+	2.13818i	1.33019	+	0.210681i	0.549444	+	0.835531i	$0.314840\pi$
$104$	−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	0.691986	−	0.721911i	$-0.256736\pi$
$107$	−0.309546	−	0.309546i	−0.0299249	−	0.0299249i	−0.721911	+	0.691986i	$0.756736\pi$
$108$		0			0
$109$	−8.68806	−	2.82292i	−0.832165	−	0.270387i	−0.138208	−	0.990403i	$-0.544134\pi$
$109$	−8.68806	−	2.82292i	−0.832165	−	0.270387i	−0.693957	+	0.720016i	$0.744134\pi$
$110$	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	0.982965	+	0.183794i	$0.0588381\pi$
$113$	5.88788	+	11.5556i	0.553885	+	1.08706i	−0.429079	+	0.903267i	$0.641162\pi$
$114$		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	0.106727	−	0.994288i	$-0.465963\pi$
$127$	−7.15537	−	3.64584i	−0.634936	−	0.323516i	−0.741663	+	0.670772i	$0.765963\pi$
$128$	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	−0.240011	−	0.970770i	$-0.577151\pi$
$131$	8.66900	−	11.9319i	0.757414	−	1.04249i	0.997425	−	0.0717208i	$-0.0228491\pi$
$132$		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	−0.825319	−	0.564667i	$-0.809005\pi$
$137$	−9.99117	+	5.09076i	−0.853604	+	0.434933i	−0.0282849	+	0.999600i	$0.509005\pi$
$138$		0			0
$139$	10.8137	−	3.51358i	0.917206	−	0.298018i	0.187886	−	0.982191i	$-0.439837\pi$
$139$	10.8137	−	3.51358i	0.917206	−	0.298018i	0.729320	+	0.684173i	$0.239837\pi$
$140$			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	−0.398288	−	0.917260i	$-0.630396\pi$
$157$	6.50271	−	6.50271i	0.518972	−	0.518972i	0.917260	+	0.398288i	$0.130396\pi$
$158$	−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	−0.913603	−	0.406607i	$-0.866712\pi$
$163$	−14.3203	+	7.29657i	−1.12165	+	0.571511i	−0.208051	+	0.978118i	$0.566712\pi$
$164$	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	0.869410	+	0.494092i	$0.164499\pi$
$167$	2.52299	+	15.9295i	0.195235	+	1.23266i	−0.674175	+	0.738572i	$0.735501\pi$
$168$		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	0.644787	−	0.764362i	$-0.276946\pi$
$173$	5.33223	+	2.71690i	0.405402	+	0.206562i	−0.239386	+	0.970925i	$0.576946\pi$
$174$		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	−0.242159	−	0.970237i	$-0.577856\pi$
$179$	8.10451	−	5.88827i	0.605760	−	0.440110i	0.847919	+	0.530126i	$0.177856\pi$
$180$		0			0
$181$	−3.84011	−	2.79000i	−0.285433	−	0.207379i	0.435851	−	0.900019i	$-0.356448\pi$
$181$	−3.84011	−	2.79000i	−0.285433	−	0.207379i	−0.721284	+	0.692640i	$0.756448\pi$
$182$	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	−0.721235	−	0.692690i	$-0.756425\pi$
$191$	−23.6587	−	7.68716i	−1.71188	−	0.556223i	−0.990645	+	0.136467i	$0.956425\pi$
$192$		0			0
$193$	−9.55217	−	9.55217i	−0.687580	−	0.687580i	0.274116	−	0.961697i	$-0.411615\pi$
$193$	−9.55217	−	9.55217i	−0.687580	−	0.687580i	−0.961697	+	0.274116i	$0.911615\pi$
$194$	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	0.0300428	−	0.999549i	$-0.490436\pi$
$197$	−3.51260	−	0.556341i	−0.250262	−	0.0396377i	−0.280305	+	0.959911i	$0.590436\pi$
$198$		0			0
$199$		−	11.7236i		−	0.831067i	−0.909578	−	0.415533i	$-0.863595\pi$
$199$		−	11.7236i		−	0.831067i	0.909578	−	0.415533i	$-0.136405\pi$
$200$	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	0.681866	+	0.731477i	$0.261169\pi$
$211$	8.13703	+	25.0432i	0.560176	+	1.72404i	−0.121690	+	0.992568i	$0.538831\pi$
$212$	−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	−0.0576344	−	0.998338i	$-0.518356\pi$
$223$	11.7063	−	22.9750i	0.783914	−	1.53852i	0.841549	−	0.540181i	$-0.181644\pi$
$224$	−1.81596			−0.121334
$225$		0			0
$226$	12.9692			0.862697
$227$	−0.0662680	+	0.130058i	−0.00439836	+	0.00863227i	−0.893195	−	0.449669i	$-0.851542\pi$
$227$	−0.0662680	+	0.130058i	−0.00439836	+	0.00863227i	0.888797	+	0.458301i	$0.151542\pi$
$228$		0			0
$229$	−11.1985	−	15.4134i	−0.740015	−	1.01854i	−0.998618	−	0.0525595i	$-0.983262\pi$
$229$	−11.1985	−	15.4134i	−0.740015	−	1.01854i	0.258603	−	0.965984i	$-0.416738\pi$
$230$	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	−0.425413	−	0.904999i	$-0.639871\pi$
$233$	−8.40064	+	1.33053i	−0.550344	+	0.0871660i	−0.124931	+	0.992165i	$0.539871\pi$
$234$		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	0.990679	+	0.136219i	$0.0434952\pi$
$239$	4.16282	+	12.8118i	0.269271	+	0.828730i	−0.721408	+	0.692510i	$0.756505\pi$
$240$		0			0
$241$	3.14111	−	9.66733i	0.202336	−	0.622728i	−0.797476	−	0.603351i	$-0.793832\pi$
$241$	3.14111	−	9.66733i	0.202336	−	0.622728i	0.999812	−	0.0193767i	$-0.00616819\pi$
$242$	−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	$0.0956683\pi$
$251$			9.38052i			0.592093i	−0.955174	+	0.296047i	$0.904332\pi$
$252$		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	0.634174	−	0.773190i	$-0.281340\pi$
$257$	−2.22859	−	2.22859i	−0.139016	−	0.139016i	−0.773190	+	0.634174i	$0.781340\pi$
$258$		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	−0.947728	−	0.319080i	$-0.896626\pi$
$263$	−10.5219	−	20.6504i	−0.648809	−	1.27336i	0.298919	−	0.954279i	$-0.403374\pi$
$264$		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	0.400394	−	0.916343i	$-0.368873\pi$
$269$	−5.69732	−	4.13934i	−0.347372	−	0.252380i	−0.747766	+	0.663963i	$0.768873\pi$
$270$		0			0
$271$	11.6553	−	8.46808i	0.708010	−	0.514399i	−0.174521	−	0.984653i	$-0.555838\pi$
$271$	11.6553	−	8.46808i	0.708010	−	0.514399i	0.882531	+	0.470254i	$0.155838\pi$
$272$	−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	0.873597	−	0.486649i	$-0.161781\pi$
$277$	16.5331	+	8.42403i	0.993378	+	0.506151i	0.119780	+	0.992800i	$0.461781\pi$
$278$	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	−0.311262	−	0.950324i	$-0.600752\pi$
$281$	11.5453	−	15.8908i	0.688735	−	0.947963i	0.999997	+	0.00236125i	$0.000751611\pi$
$282$		0			0
$283$	−1.11102	−	7.01468i	−0.0660430	−	0.416979i	−0.998454	−	0.0555802i	$-0.982299\pi$
$283$	−1.11102	−	7.01468i	−0.0660430	−	0.416979i	0.932411	−	0.361399i	$-0.117701\pi$
$284$	−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	−0.996100	−	0.0882312i	$-0.971879\pi$
$293$	−15.5402	+	15.5402i	−0.907869	+	0.907869i	0.0882312	+	0.996100i	$0.471879\pi$
$294$		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	−0.756592	−	0.653887i	$-0.773137\pi$
$307$	−1.79953	+	1.79953i	−0.102704	+	0.102704i	0.653887	+	0.756592i	$0.273137\pi$
$308$	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	−0.391219	−	0.920297i	$-0.627947\pi$
$311$	−2.94129	+	0.955682i	−0.166785	+	0.0541917i	0.224434	+	0.974489i	$0.427947\pi$
$312$		0			0
$313$	−12.9683	+	6.60767i	−0.733010	+	0.373487i	−0.780310	−	0.625393i	$-0.784939\pi$
$313$	−12.9683	+	6.60767i	−0.733010	+	0.373487i	0.0472993	+	0.998881i	$0.484939\pi$
$314$	−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	0.999678	−	0.0253807i	$-0.00807980\pi$
$317$	0.731491	+	4.61845i	0.0410846	+	0.259398i	−0.958593	+	0.284779i	$0.908080\pi$
$318$		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	−0.236393	−	0.971658i	$-0.575965\pi$
$331$	−22.4424	−	16.3053i	−1.23354	−	0.896222i	−0.997151	+	0.0754361i	$0.975965\pi$
$332$	−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	0.997165	+	0.0752430i	$0.0239732\pi$
$337$	8.66328	+	17.0026i	0.471919	+	0.926193i	−0.525246	+	0.850950i	$0.676027\pi$
$338$	−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	−0.0635027	−	0.997982i	$-0.520227\pi$
$347$	−8.05268	−	1.27542i	−0.432291	−	0.0684681i	−0.368788	+	0.929514i	$0.620227\pi$
$348$		0			0
$349$			5.60220i			0.299879i	0.988695	+	0.149940i	$0.0479079\pi$
$349$			5.60220i			0.299879i	−0.988695	+	0.149940i	$0.952092\pi$
$350$	−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	0.861277	+	0.508136i	$0.169665\pi$
$353$	−2.15819	+	13.6263i	−0.114869	+	0.725253i	−0.976146	+	0.217117i	$0.930335\pi$
$354$		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	−0.478958	−	0.877838i	$-0.658985\pi$
$359$	8.04326	−	24.7546i	0.424507	−	1.30650i	0.903465	−	0.428661i	$-0.141015\pi$
$360$		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	−0.287546	−	0.957767i	$-0.592840\pi$
$367$	−5.07768	+	0.804226i	−0.265053	+	0.0419803i	0.0224934	+	0.999747i	$0.492840\pi$
$368$	−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	−0.994334	−	0.106299i	$-0.966100\pi$
$373$	−6.25519	+	12.2765i	−0.323882	+	0.635653i	0.670453	+	0.741952i	$0.266100\pi$
$374$	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	0.870572	−	0.492042i	$-0.163749\pi$
$379$	2.60074	+	3.57960i	0.133591	+	0.183872i	−0.736981	+	0.675914i	$0.763749\pi$
$380$	−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	−0.719618	−	0.694370i	$-0.755683\pi$
$383$	−23.2779	+	3.68685i	−1.18944	+	0.188389i	−0.469826	+	0.882759i	$0.655683\pi$
$384$		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	0.999773	−	0.0213032i	$-0.00678155\pi$
$389$	3.51895	+	10.8302i	0.178418	+	0.549114i	−0.821355	+	0.570417i	$0.806782\pi$
$390$		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	0.814579	+	0.580053i	$0.196968\pi$
$397$	−2.77709	+	17.5338i	−0.139378	+	0.879998i	−0.953957	+	0.299945i	$0.903032\pi$
$398$	−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	$-0.964279\pi$
$401$		−	4.48497i		−	0.223969i	0.993710	−	0.111984i	$-0.0357207\pi$
$402$		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	−0.0575771	−	0.998341i	$-0.518338\pi$
$409$	−13.9740	−	4.54042i	−0.690968	−	0.224509i	−0.633391	+	0.773832i	$0.718338\pi$
$410$	−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	0.837009	−	0.547190i	$-0.184302\pi$
$419$	11.7751	+	8.55510i	0.575250	+	0.417944i	−0.261758	+	0.965133i	$0.584302\pi$
$420$		0			0
$421$	19.4271	−	14.1146i	0.946818	−	0.687904i	−0.00323396	−	0.999995i	$-0.501029\pi$
$421$	19.4271	−	14.1146i	0.946818	−	0.687904i	0.950052	+	0.312091i	$0.101029\pi$
$422$	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	−0.0640277	+	0.997948i	$0.520395\pi$
$431$	−20.6224	+	28.3843i	−0.993347	+	1.36723i	−0.929319	+	0.369277i	$0.879605\pi$
$432$		0			0
$433$	0.494242	+	3.12052i	0.0237517	+	0.149963i	0.996714	−	0.0810017i	$-0.0258119\pi$
$433$	0.494242	+	3.12052i	0.0237517	+	0.149963i	−0.972962	+	0.230964i	$0.925812\pi$
$434$	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	0.0865201	−	0.996250i	$-0.472425\pi$
$439$	15.5487	−	5.05207i	0.742097	−	0.241122i	0.655577	+	0.755128i	$0.272425\pi$
$440$	−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	−0.719606	−	0.694382i	$-0.755678\pi$
$443$	−0.530898	+	0.530898i	−0.0252237	+	0.0252237i	0.694382	+	0.719606i	$0.255678\pi$
$444$		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	−0.117554	−	0.993066i	$-0.537505\pi$
$457$	18.7163	−	18.7163i	0.875512	−	0.875512i	0.993066	+	0.117554i	$0.0375053\pi$
$458$	−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	0.257923	−	0.966165i	$-0.416962\pi$
$461$	22.2113	−	7.21690i	1.03448	−	0.336125i	0.776562	+	0.630041i	$0.216962\pi$
$462$		0			0
$463$	−9.41860	+	4.79902i	−0.437719	+	0.223029i	−0.658941	−	0.752194i	$-0.728995\pi$
$463$	−9.41860	+	4.79902i	−0.437719	+	0.223029i	0.221222	+	0.975223i	$0.428995\pi$
$464$	−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	−0.733534	−	0.679653i	$-0.762131\pi$
$467$	−5.31450	−	33.5545i	−0.245926	−	1.55272i	0.487608	−	0.873063i	$-0.337869\pi$
$468$		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	−0.438914	+	0.898529i	$0.644637\pi$
$479$	−31.2773	+	22.7243i	−1.42910	+	1.03830i	−0.990184	+	0.139771i	$0.955363\pi$
$480$		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	0.596073	−	0.802931i	$-0.296727\pi$
$487$	−8.91273	−	17.4922i	−0.403875	−	0.792648i	−0.999947	+	0.0102821i	$0.996727\pi$
$488$	−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	0.134116	−	0.990966i	$-0.457180\pi$
$491$	−7.53071	−	2.44688i	−0.339856	−	0.110426i	−0.473973	+	0.880540i	$0.657180\pi$
$492$		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	$0.0498578\pi$
$499$			6.96924i			0.311986i	−0.987758	+	0.155993i	$0.950142\pi$
$500$	−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	0.369543	+	0.929214i	$0.379514\pi$
$503$	−6.03430	+	38.0991i	−0.269056	+	1.69875i	−0.638599	+	0.769539i	$0.720486\pi$
$504$		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	−0.936677	−	0.350195i	$-0.886115\pi$
$509$	0.608017	−	1.87128i	0.0269499	−	0.0829432i	0.963627	+	0.267251i	$0.0861154\pi$
$510$		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	0.991354	+	0.131218i	$0.0418888\pi$
$521$	18.4841	+	25.4412i	0.809804	+	1.11460i	−0.181549	+	0.983382i	$0.558111\pi$
$522$		0			0
$523$	13.8578	−	27.1975i	0.605961	−	1.18926i	−0.360574	−	0.932730i	$-0.617419\pi$
$523$	13.8578	−	27.1975i	0.605961	−	1.18926i	0.966535	−	0.256534i	$-0.0825807\pi$
$524$	−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	0.695905	+	0.718134i	$0.255003\pi$
$541$	−6.72668	+	20.7026i	−0.289202	+	0.890074i	−0.985107	+	0.171940i	$0.944997\pi$
$542$	−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	0.871488	+	0.490417i	$0.163155\pi$
$547$	−2.54680	+	16.0799i	−0.108893	+	0.687526i	−0.980382	+	0.197109i	$0.936845\pi$
$548$	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	0.914971	−	0.403520i	$-0.132214\pi$
$557$	12.0707	+	12.0707i	0.511450	+	0.511450i	−0.403520	+	0.914971i	$0.632214\pi$
$558$		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	0.991994	−	0.126285i	$-0.0403052\pi$
$563$	7.27841	+	14.2847i	0.306748	+	0.602027i	−0.685246	+	0.728312i	$0.740305\pi$
$564$		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	0.992181	−	0.124805i	$-0.0398306\pi$
$569$	28.1494	+	20.4518i	1.18009	+	0.857382i	0.187904	+	0.982187i	$0.439831\pi$
$570$		0			0
$571$	−1.17087	+	0.850687i	−0.0489994	+	0.0356002i	−0.612015	−	0.790846i	$-0.709641\pi$
$571$	−1.17087	+	0.850687i	−0.0489994	+	0.0356002i	0.563016	+	0.826446i	$0.309641\pi$
$572$	−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	0.785551	−	0.618797i	$-0.212380\pi$
$577$	17.9356	+	9.13864i	0.746668	+	0.380446i	−0.0388824	+	0.999244i	$0.512380\pi$
$578$	−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	0.272215	−	0.962236i	$-0.412244\pi$
$587$	29.3326	−	14.9457i	1.21069	−	0.616875i	0.938470	+	0.345361i	$0.112244\pi$
$588$		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	−0.380756	−	0.924676i	$-0.624336\pi$
$593$	13.2453	−	13.2453i	0.543920	−	0.543920i	0.924676	+	0.380756i	$0.124336\pi$
$594$		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	−0.659473	−	0.751729i	$-0.729220\pi$
$607$	2.27295	−	2.27295i	0.0922561	−	0.0922561i	0.751729	+	0.659473i	$0.229220\pi$
$608$	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	−0.589459	−	0.807798i	$-0.700659\pi$
$613$	−6.99219	+	3.56270i	−0.282412	+	0.143896i	0.307047	+	0.951694i	$0.400659\pi$
$614$	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	0.988880	+	0.148714i	$0.0475135\pi$
$617$	2.34372	+	14.7976i	0.0943545	+	0.595731i	−0.894526	+	0.447017i	$0.852487\pi$
$618$		0			0
$619$	16.8199	−	23.1506i	0.676047	−	0.930499i	−0.323831	−	0.946115i	$-0.604971\pi$
$619$	16.8199	−	23.1506i	0.676047	−	0.930499i	0.999878	+	0.0156157i	$0.00497083\pi$
$620$	−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	−0.0876449	−	0.996152i	$-0.527934\pi$
$631$	−26.6803	−	19.3844i	−1.06213	−	0.771679i	−0.974480	+	0.224473i	$0.927934\pi$
$632$	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	0.234840	−	0.972034i	$-0.424543\pi$
$641$	−3.70952	−	1.20529i	−0.146517	−	0.0476063i	−0.381357	+	0.924428i	$0.624543\pi$
$642$		0			0
$643$	24.3761	+	24.3761i	0.961300	+	0.961300i	0.999279	−	0.0379785i	$-0.0120918\pi$
$643$	24.3761	+	24.3761i	0.961300	+	0.961300i	−0.0379785	+	0.999279i	$0.512092\pi$
$644$	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	−0.171408	−	0.985200i	$-0.554831\pi$
$647$	−16.2504	−	2.57381i	−0.638869	−	0.101187i	−0.467462	+	0.884013i	$0.654831\pi$
$648$		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	−0.988518	−	0.151103i	$-0.951718\pi$
$653$	−0.0431419	+	0.272387i	−0.00168827	+	0.0106593i	0.986830	+	0.161762i	$0.0517176\pi$
$654$		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	0.306806	+	0.951772i	$0.400740\pi$
$659$	−12.8571	+	39.5702i	−0.500843	+	1.54144i	−0.807649	+	0.589664i	$0.799260\pi$
$660$		0			0
$661$	−8.76974	−	26.9905i	−0.341103	−	1.04981i	−0.963637	−	0.267215i	$-0.913897\pi$
$661$	−8.76974	−	26.9905i	−0.341103	−	1.04981i	0.622533	−	0.782593i	$-0.286103\pi$
$662$	−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	−0.965168	−	0.261631i	$-0.915740\pi$
$673$	−4.83026	+	9.47992i	−0.186193	+	0.365424i	0.778975	+	0.627055i	$0.215740\pi$
$674$	19.0825			0.735031
$675$		0			0
$676$	−11.9922			−0.461239
$677$	15.3677	−	30.1608i	0.590628	−	1.15917i	−0.381423	−	0.924401i	$-0.624566\pi$
$677$	15.3677	−	30.1608i	0.590628	−	1.15917i	0.972051	−	0.234772i	$-0.0754342\pi$
$678$		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	0.259470	−	0.965751i	$-0.416452\pi$
$683$	21.0295	−	3.33075i	0.804673	−	0.127448i	0.545204	+	0.838304i	$0.316452\pi$
$684$		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	−0.570733	−	0.821136i	$-0.693341\pi$
$691$	9.82212	−	30.2294i	0.373651	−	1.14998i	0.944384	−	0.328844i	$-0.106659\pi$
$692$	−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	$0.0389123\pi$
$701$			6.45719i			0.243885i	−0.992537	+	0.121942i	$0.961088\pi$
$702$		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	0.970168	−	0.242436i	$-0.0779463\pi$
$709$	42.9374	+	13.9512i	1.61255	+	0.523949i	0.642382	+	0.766385i	$0.277946\pi$
$710$	−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	0.781242	−	0.624228i	$-0.214587\pi$
$719$	11.5028	+	8.35728i	0.428982	+	0.311674i	−0.352260	+	0.935902i	$0.614587\pi$
$720$		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	0.270024	−	0.962854i	$-0.412968\pi$
$727$	−9.44311	−	4.81150i	−0.350225	−	0.178449i	−0.620249	+	0.784405i	$0.712968\pi$
$728$	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	0.513047	+	0.858360i	$0.328517\pi$
$733$	7.86115	+	49.6334i	0.290358	+	1.83325i	−0.222689	+	0.974890i	$0.571483\pi$
$734$	−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	−0.224881	−	0.974386i	$-0.572199\pi$
$739$	4.51035	−	1.46550i	0.165916	−	0.0539094i	0.390797	+	0.920477i	$0.372199\pi$
$740$	−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	−0.601435	−	0.798922i	$-0.705404\pi$
$743$	5.38309	−	5.38309i	0.197486	−	0.197486i	0.798922	+	0.601435i	$0.205404\pi$
$744$		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	0.338914	−	0.940817i	$-0.389940\pi$
$757$	35.2101	−	35.2101i	1.27973	−	1.27973i	0.940817	−	0.338914i	$-0.110060\pi$
$758$	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	0.348552	−	0.937290i	$-0.386674\pi$
$761$	32.5920	−	10.5898i	1.18146	−	0.383880i	0.832909	+	0.553410i	$0.186674\pi$
$762$		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	−0.996638	−	0.0819364i	$-0.973890\pi$
$769$	−16.9362	+	23.3106i	−0.610733	+	0.840603i	0.385904	+	0.922539i	$0.373890\pi$
$770$	−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	0.362644	−	0.931928i	$-0.381874\pi$
$773$	−4.95291	−	2.52363i	−0.178144	−	0.0907688i	−0.540788	+	0.841159i	$0.681874\pi$
$774$		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	0.782284	−	0.622922i	$-0.214055\pi$
$787$	−5.09132	−	9.99228i	−0.181486	−	0.356186i	−0.963770	+	0.266736i	$0.914055\pi$
$788$	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	−0.239221	−	0.970965i	$-0.576892\pi$
$797$	−21.6471	−	3.42856i	−0.766779	−	0.121446i	−0.527558	+	0.849519i	$0.676892\pi$
$798$		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	0.374510	+	0.927223i	$0.377811\pi$
$809$	−13.4672	+	41.4479i	−0.473483	+	1.45723i	−0.847993	+	0.530007i	$0.822189\pi$
$810$		0			0
$811$	17.3078	+	53.2679i	0.607759	+	1.87049i	0.476583	+	0.879129i	$0.341875\pi$
$811$	17.3078	+	53.2679i	0.607759	+	1.87049i	0.131175	+	0.991359i	$0.458125\pi$
$812$	−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	0.629207	−	0.777238i	$-0.283380\pi$
$821$	−8.72276	−	12.0058i	−0.304426	−	0.419007i	−0.933633	+	0.358231i	$0.883380\pi$
$822$		0			0
$823$	9.74444	−	19.1245i	0.339670	−	0.666640i	−0.656476	−	0.754347i	$-0.727954\pi$
$823$	9.74444	−	19.1245i	0.339670	−	0.666640i	0.996146	+	0.0877069i	$0.0279539\pi$
$824$	−13.6682			−0.476155
$825$		0			0
$826$	−3.67720			−0.127946
$827$	−10.2597	+	20.1358i	−0.356765	+	0.700190i	−0.997727	−	0.0673818i	$-0.978535\pi$
$827$	−10.2597	+	20.1358i	−0.356765	+	0.700190i	0.640962	+	0.767572i	$0.278535\pi$
$828$		0			0
$829$	−7.34963	−	10.1159i	−0.255263	−	0.351339i	0.662083	−	0.749431i	$-0.269673\pi$
$829$	−7.34963	−	10.1159i	−0.255263	−	0.351339i	−0.917346	+	0.398091i	$0.869673\pi$
$830$	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	−0.990506	−	0.137468i	$-0.956104\pi$
$839$	−7.81986	−	24.0670i	−0.269971	−	0.830887i	0.720535	−	0.693419i	$-0.243896\pi$
$840$		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	0.192555	−	0.981286i	$-0.438323\pi$
$853$	2.11601	+	0.335142i	0.0724506	+	0.0114751i	−0.120104	+	0.992761i	$0.538323\pi$
$854$	−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	−0.953322	−	0.301957i	$-0.902360\pi$
$857$	−36.7477	−	36.7477i	−1.25528	−	1.25528i	−0.301957	−	0.953322i	$-0.597640\pi$
$858$		0			0
$859$	−8.24700	−	2.67961i	−0.281384	−	0.0914273i	0.164925	−	0.986306i	$-0.447262\pi$
$859$	−8.24700	−	2.67961i	−0.281384	−	0.0914273i	−0.446309	+	0.894879i	$0.647262\pi$
$860$	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	0.713483	−	0.700673i	$-0.247117\pi$
$863$	−8.01248	−	15.7254i	−0.272748	−	0.535298i	−0.986231	+	0.165375i	$0.947117\pi$
$864$		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	0.164247	−	0.986419i	$-0.447480\pi$
$877$	−15.9099	−	8.10651i	−0.537240	−	0.273738i	−0.701488	+	0.712682i	$0.747480\pi$
$878$	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	0.165471	−	0.986215i	$-0.447086\pi$
$881$	31.2335	−	42.9892i	1.05228	−	1.44834i	0.886813	−	0.462129i	$-0.152914\pi$
$882$		0			0
$883$	5.81503	+	36.7147i	0.195691	+	1.23555i	0.868485	+	0.495716i	$0.165094\pi$
$883$	5.81503	+	36.7147i	0.195691	+	1.23555i	−0.672793	+	0.739830i	$0.734906\pi$
$884$	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	−0.520420	−	0.853910i	$-0.674225\pi$
$887$	−4.03516	+	2.05602i	−0.135488	+	0.0690344i	0.384933	+	0.922945i	$0.374225\pi$
$888$		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	−0.409893	+	0.912134i	$0.634434\pi$
$907$	−39.8147	+	39.8147i	−1.32203	+	1.32203i	−0.912134	+	0.409893i	$0.865566\pi$
$908$	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	−0.543377	−	0.839489i	$-0.682855\pi$
$911$	−14.7757	+	4.80090i	−0.489540	+	0.159061i	0.0538376	+	0.998550i	$0.482855\pi$
$912$		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	−0.472956	−	0.881086i	$-0.656813\pi$
$919$	15.4958	−	21.3281i	0.511158	−	0.703549i	0.984114	+	0.177537i	$0.0568129\pi$
$920$	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	−0.737771	−	0.675051i	$-0.764122\pi$
$929$	−9.86752	+	7.16917i	−0.323743	+	0.235213i	0.414028	+	0.910264i	$0.364122\pi$
$930$		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	0.962247	+	0.272179i	$0.0877442\pi$
$937$	18.8820	+	37.0581i	0.616850	+	1.21064i	−0.345397	+	0.938457i	$0.612256\pi$
$938$	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	0.450177	−	0.892939i	$-0.351361\pi$
$941$	8.88126	+	2.88570i	0.289521	+	0.0940710i	−0.160656	+	0.987010i	$0.551361\pi$
$942$		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	0.198925	−	0.980015i	$-0.436255\pi$
$947$	2.62415	+	0.415625i	0.0852734	+	0.0135060i	−0.113652	+	0.993521i	$0.536255\pi$
$948$		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	−0.769627	−	0.638494i	$-0.779558\pi$
$953$	4.92811	−	31.1149i	0.159637	−	1.00791i	0.929264	−	0.369416i	$-0.120442\pi$
$954$		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	−0.588699	−	0.808352i	$-0.700360\pi$
$967$	−27.9494	+	4.42675i	−0.898791	+	0.142355i	−0.310092	+	0.950707i	$0.600360\pi$
$968$	−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	0.947997	−	0.318280i	$-0.103105\pi$
$971$	10.9794	+	15.1119i	0.352347	+	0.484964i	−0.595650	+	0.803244i	$0.703105\pi$
$972$		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	−0.868768	−	0.495218i	$-0.835088\pi$
$977$	1.32908	−	2.60846i	0.0425210	−	0.0834521i	0.911289	+	0.411766i	$0.135088\pi$
$978$		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	0.374662	−	0.927161i	$-0.377759\pi$
$983$	31.9014	−	5.05268i	1.01750	−	0.161156i	0.642834	+	0.766006i	$0.277759\pi$
$984$		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	−0.551932	−	0.833889i	$-0.686109\pi$
$991$	12.1116	−	37.2757i	0.384738	−	1.18410i	0.936670	−	0.350213i	$-0.113891\pi$
$992$	−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	0.449842	+	0.893108i	$0.351480\pi$
$997$	−8.01914	+	50.6308i	−0.253969	+	1.60350i	−0.703811	+	0.710387i	$0.748520\pi$
$998$	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.233.2	yes	16
3.2	odd	2	inner	450.2.s.b.233.1	yes	16
25.22	odd	20	inner	450.2.s.b.197.1	✓	16
75.47	even	20	inner	450.2.s.b.197.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.s.b.197.1	✓	16	25.22	odd	20	inner
450.2.s.b.197.2	yes	16	75.47	even	20	inner
450.2.s.b.233.1	yes	16	3.2	odd	2	inner
450.2.s.b.233.2	yes	16	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.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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more