LMFDB - Embedded newform 414.2.i.a.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			307.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.307
Dual form			414.2.i.a.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.81440 + 2.09393i) q^{5} +(0.163423 + 0.105026i) q^{7} +(0.415415 - 0.909632i) q^{8} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.81440 + 2.09393i) q^{5} +(0.163423 + 0.105026i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.33083 + 1.49793i) q^{10} +(0.413293 + 2.87451i) q^{11} +(0.910738 - 0.585296i) q^{13} +(-0.127214 + 0.146813i) q^{14} +(0.841254 + 0.540641i) q^{16} +(-4.45384 + 1.30777i) q^{17} +(4.24593 + 1.24672i) q^{19} +(-1.15098 - 2.52028i) q^{20} -2.90407 q^{22} +(4.73556 + 0.757939i) q^{23} +(-0.380916 + 2.64933i) q^{25} +(0.449727 + 0.984764i) q^{26} +(-0.127214 - 0.146813i) q^{28} +(-8.83766 + 2.59497i) q^{29} +(-2.85525 + 6.25212i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-0.660607 - 4.59462i) q^{34} +(0.0765987 + 0.532755i) q^{35} +(3.17329 - 3.66217i) q^{37} +(-1.83829 + 4.02529i) q^{38} +(2.65843 - 0.780586i) q^{40} +(-3.76214 - 4.34174i) q^{41} +(3.14342 + 6.88313i) q^{43} +(0.413293 - 2.87451i) q^{44} +(-1.42416 + 4.57949i) q^{46} +5.61457 q^{47} +(-2.89223 - 6.33310i) q^{49} +(-2.56815 - 0.754078i) q^{50} +(-1.03874 + 0.305003i) q^{52} +(3.48496 + 2.23965i) q^{53} +(-5.26914 + 6.08092i) q^{55} +(0.163423 - 0.105026i) q^{56} +(-1.31083 - 9.11701i) q^{58} +(9.01685 - 5.79478i) q^{59} +(-1.19623 + 2.61939i) q^{61} +(-5.78214 - 3.71596i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(2.87801 + 0.845060i) q^{65} +(2.08311 - 14.4884i) q^{67} +4.64187 q^{68} -0.538234 q^{70} +(1.81195 - 12.6024i) q^{71} +(-2.86708 - 0.841852i) q^{73} +(3.17329 + 3.66217i) q^{74} +(-3.72270 - 2.39243i) q^{76} +(-0.234356 + 0.513169i) q^{77} +(2.15275 - 1.38349i) q^{79} +(0.394306 + 2.74246i) q^{80} +(4.83295 - 3.10595i) q^{82} +(-0.531462 + 0.613340i) q^{83} +(-10.8194 - 6.95322i) q^{85} +(-7.26043 + 2.13185i) q^{86} +(2.78644 + 0.818172i) q^{88} +(-2.81645 - 6.16716i) q^{89} +0.210307 q^{91} +(-4.33020 - 2.06140i) q^{92} +(-0.799036 + 5.55742i) q^{94} +(5.09327 + 11.1527i) q^{95} +(8.09928 + 9.34707i) q^{97} +(6.68024 - 1.96150i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	1.81440	+	2.09393i	0.811424	+	0.936433i	0.998949	−	0.0458269i	$-0.0145923\pi$
$5$	1.81440	+	2.09393i	0.811424	+	0.936433i	−0.187526	+	0.982260i	$0.560047\pi$
$6$		0			0
$7$	0.163423	+	0.105026i	0.0617682	+	0.0396960i	0.571160	−	0.820838i	$-0.306493\pi$
$7$	0.163423	+	0.105026i	0.0617682	+	0.0396960i	−0.509392	+	0.860534i	$0.670130\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$		0			0
$10$	−2.33083	+	1.49793i	−0.737073	+	0.473688i
$11$	0.413293	+	2.87451i	0.124612	+	0.866698i	0.952225	+	0.305398i	$0.0987896\pi$
$11$	0.413293	+	2.87451i	0.124612	+	0.866698i	−0.827612	+	0.561300i	$0.810301\pi$
$12$		0			0
$13$	0.910738	−	0.585296i	0.252593	−	0.162332i	−0.408217	−	0.912885i	$-0.633849\pi$
$13$	0.910738	−	0.585296i	0.252593	−	0.162332i	0.660810	+	0.750553i	$0.270213\pi$
$14$	−0.127214	+	0.146813i	−0.0339995	+	0.0392375i
$15$		0			0
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−4.45384	+	1.30777i	−1.08022	+	0.317180i	−0.772965	−	0.634449i	$-0.781227\pi$
$17$	−4.45384	+	1.30777i	−1.08022	+	0.317180i	−0.307251	+	0.951629i	$0.599409\pi$
$18$		0			0
$19$	4.24593	+	1.24672i	0.974083	+	0.286017i	0.729780	−	0.683682i	$-0.239623\pi$
$19$	4.24593	+	1.24672i	0.974083	+	0.286017i	0.244303	+	0.969699i	$0.421441\pi$
$20$	−1.15098	−	2.52028i	−0.257366	−	0.563553i
$21$		0			0
$22$	−2.90407			−0.619150
$23$	4.73556	+	0.757939i	0.987433	+	0.158041i
$23$	4.73556	+	0.757939i	0.987433	+	0.158041i
$24$		0			0
$25$	−0.380916	+	2.64933i	−0.0761832	+	0.529866i
$26$	0.449727	+	0.984764i	0.0881987	+	0.193128i
$27$		0			0
$28$	−0.127214	−	0.146813i	−0.0240413	−	0.0277451i
$29$	−8.83766	+	2.59497i	−1.64111	+	0.481874i	−0.966579	−	0.256371i	$-0.917473\pi$
$29$	−8.83766	+	2.59497i	−1.64111	+	0.481874i	−0.674533	+	0.738245i	$0.735655\pi$
$30$		0			0
$31$	−2.85525	+	6.25212i	−0.512818	+	1.12291i	0.459270	+	0.888297i	$0.348111\pi$
$31$	−2.85525	+	6.25212i	−0.512818	+	1.12291i	−0.972088	+	0.234617i	$0.924616\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$		0			0
$34$	−0.660607	−	4.59462i	−0.113293	−	0.787972i
$35$	0.0765987	+	0.532755i	0.0129475	+	0.0900521i
$36$		0			0
$37$	3.17329	−	3.66217i	0.521685	−	0.602057i	−0.432367	−	0.901698i	$-0.642321\pi$
$37$	3.17329	−	3.66217i	0.521685	−	0.602057i	0.954052	+	0.299641i	$0.0968669\pi$
$38$	−1.83829	+	4.02529i	−0.298209	+	0.652988i
$39$		0			0
$40$	2.65843	−	0.780586i	0.420335	−	0.123421i
$41$	−3.76214	−	4.34174i	−0.587547	−	0.678065i	0.381663	−	0.924302i	$-0.375352\pi$
$41$	−3.76214	−	4.34174i	−0.587547	−	0.678065i	−0.969210	+	0.246236i	$0.920806\pi$
$42$		0			0
$43$	3.14342	+	6.88313i	0.479367	+	1.04967i	0.982637	+	0.185538i	$0.0594029\pi$
$43$	3.14342	+	6.88313i	0.479367	+	1.04967i	−0.503270	+	0.864129i	$0.667870\pi$
$44$	0.413293	−	2.87451i	0.0623062	−	0.433349i
$45$		0			0
$46$	−1.42416	+	4.57949i	−0.209982	+	0.675209i
$47$	5.61457			0.818969			0.409484	−	0.912317i	$-0.365709\pi$
$47$	5.61457			0.818969			0.409484	+	0.912317i	$0.365709\pi$
$48$		0			0
$49$	−2.89223	−	6.33310i	−0.413175	−	0.904728i
$50$	−2.56815	−	0.754078i	−0.363192	−	0.106643i
$51$		0			0
$52$	−1.03874	+	0.305003i	−0.144048	+	0.0422963i
$53$	3.48496	+	2.23965i	0.478697	+	0.307640i	0.757645	−	0.652666i	$-0.226350\pi$
$53$	3.48496	+	2.23965i	0.478697	+	0.307640i	−0.278949	+	0.960306i	$0.589986\pi$
$54$		0			0
$55$	−5.26914	+	6.08092i	−0.710491	+	0.819951i
$56$	0.163423	−	0.105026i	0.0218384	−	0.0140347i
$57$		0			0
$58$	−1.31083	−	9.11701i	−0.172120	−	1.19712i
$59$	9.01685	−	5.79478i	1.17389	−	0.754416i	0.199640	−	0.979869i	$-0.436023\pi$
$59$	9.01685	−	5.79478i	1.17389	−	0.754416i	0.974254	+	0.225453i	$0.0723862\pi$
$60$		0			0
$61$	−1.19623	+	2.61939i	−0.153162	+	0.335378i	−0.970623	−	0.240606i	$-0.922654\pi$
$61$	−1.19623	+	2.61939i	−0.153162	+	0.335378i	0.817461	+	0.575984i	$0.195381\pi$
$62$	−5.78214	−	3.71596i	−0.734332	−	0.471927i
$63$		0			0
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	2.87801	+	0.845060i	0.356973	+	0.104817i
$66$		0			0
$67$	2.08311	−	14.4884i	0.254493	−	1.77003i	−0.316027	−	0.948750i	$-0.602349\pi$
$67$	2.08311	−	14.4884i	0.254493	−	1.77003i	0.570519	−	0.821284i	$-0.306742\pi$
$68$	4.64187			0.562910
$69$		0			0
$70$	−0.538234			−0.0643313
$71$	1.81195	−	12.6024i	0.215038	−	1.49563i	−0.540958	−	0.841050i	$-0.681938\pi$
$71$	1.81195	−	12.6024i	0.215038	−	1.49563i	0.755997	−	0.654576i	$-0.227153\pi$
$72$		0			0
$73$	−2.86708	−	0.841852i	−0.335567	−	0.0985313i	0.109608	−	0.993975i	$-0.465040\pi$
$73$	−2.86708	−	0.841852i	−0.335567	−	0.0985313i	−0.445175	+	0.895444i	$0.646859\pi$
$74$	3.17329	+	3.66217i	0.368887	+	0.425718i
$75$		0			0
$76$	−3.72270	−	2.39243i	−0.427023	−	0.274431i
$77$	−0.234356	+	0.513169i	−0.0267074	+	0.0584811i
$78$		0			0
$79$	2.15275	−	1.38349i	0.242203	−	0.155654i	−0.413908	−	0.910319i	$-0.635837\pi$
$79$	2.15275	−	1.38349i	0.242203	−	0.155654i	0.656111	+	0.754664i	$0.272200\pi$
$80$	0.394306	+	2.74246i	0.0440848	+	0.306617i
$81$		0			0
$82$	4.83295	−	3.10595i	0.533710	−	0.342995i
$83$	−0.531462	+	0.613340i	−0.0583356	+	0.0673228i	−0.784167	−	0.620549i	$-0.786910\pi$
$83$	−0.531462	+	0.613340i	−0.0583356	+	0.0673228i	0.725832	+	0.687872i	$0.241455\pi$
$84$		0			0
$85$	−10.8194	−	6.95322i	−1.17353	−	0.754182i
$86$	−7.26043	+	2.13185i	−0.782912	+	0.229884i
$87$		0			0
$88$	2.78644	+	0.818172i	0.297035	+	0.0872174i
$89$	−2.81645	−	6.16716i	−0.298543	−	0.653717i	0.699607	−	0.714528i	$-0.253359\pi$
$89$	−2.81645	−	6.16716i	−0.298543	−	0.653717i	−0.998149	+	0.0608109i	$0.980631\pi$
$90$		0			0
$91$	0.210307			0.0220462
$92$	−4.33020	−	2.06140i	−0.451455	−	0.214916i
$93$		0			0
$94$	−0.799036	+	5.55742i	−0.0824143	+	0.573204i
$95$	5.09327	+	11.1527i	0.522559	+	1.14424i
$96$		0			0
$97$	8.09928	+	9.34707i	0.822357	+	0.949051i	0.999382	−	0.0351554i	$-0.0111926\pi$
$97$	8.09928	+	9.34707i	0.822357	+	0.949051i	−0.177024	+	0.984206i	$0.556647\pi$
$98$	6.68024	−	1.96150i	0.674806	−	0.198141i
$99$		0			0
$100$	1.11189	−	2.43470i	0.111189	−	0.243470i
$101$	10.2791	−	11.8628i	1.02281	−	1.18039i	0.0393592	−	0.999225i	$-0.487468\pi$
$101$	10.2791	−	11.8628i	1.02281	−	1.18039i	0.983453	−	0.181163i	$-0.0579862\pi$
$102$		0			0
$103$	−1.34415	−	9.34877i	−0.132443	−	0.921162i	−0.942356	−	0.334612i	$-0.891395\pi$
$103$	−1.34415	−	9.34877i	−0.132443	−	0.921162i	0.809913	−	0.586550i	$-0.199514\pi$
$104$	−0.154070	−	1.07158i	−0.0151078	−	0.105077i
$105$		0			0
$106$	−2.71282	+	3.13076i	−0.263492	+	0.304086i
$107$	−3.95144	+	8.65244i	−0.382000	+	0.836463i	0.616783	+	0.787133i	$0.288436\pi$
$107$	−3.95144	+	8.65244i	−0.382000	+	0.836463i	−0.998783	+	0.0493295i	$0.984292\pi$
$108$		0			0
$109$	19.4026	−	5.69711i	1.85843	−	0.545684i	0.858998	−	0.511980i	$-0.171088\pi$
$109$	19.4026	−	5.69711i	1.85843	−	0.545684i	0.999432	−	0.0337045i	$-0.0107305\pi$
$110$	−5.26914	−	6.08092i	−0.502393	−	0.579793i
$111$		0			0
$112$	0.0806993	+	0.176707i	0.00762536	+	0.0166972i
$113$	0.187381	−	1.30327i	0.0176274	−	0.122601i	−0.979108	−	0.203342i	$-0.934820\pi$
$113$	0.187381	−	1.30327i	0.0176274	−	0.122601i	0.996735	+	0.0807412i	$0.0257287\pi$
$114$		0			0
$115$	7.00512	+	11.2911i	0.653231	+	1.05290i
$116$	9.21076			0.855197
$117$		0			0
$118$	4.45257	+	9.74976i	0.409892	+	0.897538i
$119$	−0.865212	−	0.254049i	−0.0793138	−	0.0232886i
$120$		0			0
$121$	2.46241	−	0.723028i	0.223855	−	0.0657298i
$122$	−2.42248	−	1.55683i	−0.219321	−	0.140949i
$123$		0			0
$124$	4.50102	−	5.19445i	0.404203	−	0.466475i
$125$	5.41551	−	3.48034i	0.484378	−	0.311291i
$126$		0			0
$127$	0.685740	+	4.76943i	0.0608496	+	0.423218i	0.997362	+	0.0725845i	$0.0231247\pi$
$127$	0.685740	+	4.76943i	0.0608496	+	0.423218i	−0.936513	+	0.350634i	$0.885966\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$		0			0
$130$	−1.24604	+	2.72845i	−0.109285	+	0.239301i
$131$	−13.4413	−	8.63823i	−1.17438	−	0.754725i	−0.200032	−	0.979789i	$-0.564104\pi$
$131$	−13.4413	−	8.63823i	−1.17438	−	0.754725i	−0.974344	+	0.225064i	$0.927741\pi$
$132$		0			0
$133$	0.562947	+	0.649675i	0.0488137	+	0.0563340i
$134$	14.0444	+	4.12382i	1.21325	+	0.356243i
$135$		0			0
$136$	−0.660607	+	4.59462i	−0.0566466	+	0.393986i
$137$	−18.7720			−1.60380			−0.801898	−	0.597460i	$-0.796176\pi$
$137$	−18.7720			−1.60380			−0.801898	+	0.597460i	$0.796176\pi$
$138$		0			0
$139$	17.7540			1.50588			0.752938	−	0.658092i	$-0.228636\pi$
$139$	17.7540			1.50588			0.752938	+	0.658092i	$0.228636\pi$
$140$	0.0765987	−	0.532755i	0.00647377	−	0.0450261i
$141$		0			0
$142$	12.2162	+	3.58701i	1.02516	+	0.301015i
$143$	2.05884	+	2.37603i	0.172169	+	0.198694i
$144$		0			0
$145$	−21.4687	−	13.7971i	−1.78288	−	1.14579i
$146$	1.24131	−	2.71809i	0.102732	−	0.224951i
$147$		0			0
$148$	−4.07650	+	2.61981i	−0.335086	+	0.215347i
$149$	−1.35418	−	9.41852i	−0.110939	−	0.771595i	−0.967010	−	0.254738i	$-0.918011\pi$
$149$	−1.35418	−	9.41852i	−0.110939	−	0.771595i	0.856072	−	0.516857i	$-0.172898\pi$
$150$		0			0
$151$	−7.30101	+	4.69207i	−0.594148	+	0.381835i	−0.802883	−	0.596137i	$-0.796702\pi$
$151$	−7.30101	+	4.69207i	−0.594148	+	0.381835i	0.208735	+	0.977972i	$0.433065\pi$
$152$	2.89788	−	3.34433i	0.235049	−	0.271261i
$153$		0			0
$154$	−0.474593	−	0.305003i	−0.0382438	−	0.0245778i
$155$	−18.2720	+	5.36516i	−1.46765	+	0.430940i
$156$		0			0
$157$	−19.0136	−	5.58290i	−1.51745	−	0.445564i	−0.586270	−	0.810116i	$-0.699404\pi$
$157$	−19.0136	−	5.58290i	−1.51745	−	0.445564i	−0.931183	+	0.364552i	$0.881222\pi$
$158$	1.06304	+	2.32772i	0.0845706	+	0.185184i
$159$		0			0
$160$	−2.77066			−0.219040
$161$	0.694298	+	0.621221i	0.0547184	+	0.0489591i
$162$		0			0
$163$	−2.06377	+	14.3538i	−0.161647	+	1.12428i	0.733883	+	0.679276i	$0.237706\pi$
$163$	−2.06377	+	14.3538i	−0.161647	+	1.12428i	−0.895530	+	0.445001i	$0.853203\pi$
$164$	2.38653	+	5.22578i	0.186357	+	0.408065i
$165$		0			0
$166$	−0.531462	−	0.613340i	−0.0412495	−	0.0476044i
$167$	−9.49053	+	2.78667i	−0.734399	+	0.215639i	−0.627484	−	0.778629i	$-0.715915\pi$
$167$	−9.49053	+	2.78667i	−0.734399	+	0.215639i	−0.106915	+	0.994268i	$0.534097\pi$
$168$		0			0
$169$	−4.91352	+	10.7591i	−0.377963	+	0.827624i
$170$	8.42221	−	9.71974i	0.645954	−	0.745470i
$171$		0			0
$172$	−1.07689	−	7.48992i	−0.0821119	−	0.571101i
$173$	1.88474	+	13.1086i	0.143294	+	0.996631i	0.926883	+	0.375351i	$0.122478\pi$
$173$	1.88474	+	13.1086i	0.143294	+	0.996631i	−0.783589	+	0.621280i	$0.786613\pi$
$174$		0			0
$175$	−0.340499	+	0.392956i	−0.0257393	+	0.0297047i
$176$	−1.20640	+	2.64164i	−0.0909355	+	0.199121i
$177$		0			0
$178$	6.50521	−	1.91010i	0.487586	−	0.143168i
$179$	3.43495	+	3.96414i	0.256740	+	0.296294i	0.869457	−	0.494009i	$-0.164469\pi$
$179$	3.43495	+	3.96414i	0.256740	+	0.296294i	−0.612717	+	0.790302i	$0.709923\pi$
$180$		0			0
$181$	−6.75269	−	14.7863i	−0.501924	−	1.09906i	−0.975839	−	0.218489i	$-0.929887\pi$
$181$	−6.75269	−	14.7863i	−0.501924	−	1.09906i	0.473916	−	0.880570i	$-0.342840\pi$
$182$	−0.0299298	+	0.208166i	−0.00221855	+	0.0154303i
$183$		0			0
$184$	2.65667	−	3.99276i	0.195852	−	0.294350i
$185$	13.4259			0.987093
$186$		0			0
$187$	−5.59993	−	12.2621i	−0.409508	−	0.896697i
$188$	−5.38714	−	1.58181i	−0.392897	−	0.115365i
$189$		0			0
$190$	−11.7640	+	3.45423i	−0.853453	+	0.250596i
$191$	6.47147	+	4.15896i	0.468259	+	0.300932i	0.753410	−	0.657551i	$-0.228407\pi$
$191$	6.47147	+	4.15896i	0.468259	+	0.300932i	−0.285151	+	0.958483i	$0.592044\pi$
$192$		0			0
$193$	0.934780	−	1.07879i	0.0672869	−	0.0776533i	−0.721108	−	0.692823i	$-0.756367\pi$
$193$	0.934780	−	1.07879i	0.0672869	−	0.0776533i	0.788395	+	0.615169i	$0.210912\pi$
$194$	−10.4046	+	6.68662i	−0.747005	+	0.480071i
$195$		0			0
$196$	0.990833	+	6.89140i	0.0707738	+	0.492243i
$197$	−5.26265	+	3.38210i	−0.374948	+	0.240965i	−0.714519	−	0.699616i	$-0.753354\pi$
$197$	−5.26265	+	3.38210i	−0.374948	+	0.240965i	0.339571	+	0.940580i	$0.389718\pi$
$198$		0			0
$199$	0.358560	−	0.785136i	0.0254176	−	0.0556568i	−0.896497	−	0.443049i	$-0.853897\pi$
$199$	0.358560	−	0.785136i	0.0254176	−	0.0556568i	0.921915	+	0.387392i	$0.126624\pi$
$200$	2.25168	+	1.44706i	0.159218	+	0.102323i
$201$		0			0
$202$	10.2791	+	11.8628i	0.723237	+	0.834661i
$203$	−1.71682	−	0.504104i	−0.120497	−	0.0353811i
$204$		0			0
$205$	2.26527	−	15.7553i	0.158213	−	1.10040i
$206$	9.44491			0.658058
$207$		0			0
$208$	1.08260			0.0750646
$209$	−1.82889	+	12.7202i	−0.126507	+	0.879878i
$210$		0			0
$211$	−18.2924	−	5.37114i	−1.25930	−	0.369764i	−0.417067	−	0.908876i	$-0.636942\pi$
$211$	−18.2924	−	5.37114i	−1.25930	−	0.369764i	−0.842234	+	0.539112i	$0.818760\pi$
$212$	−2.71282	−	3.13076i	−0.186317	−	0.215021i
$213$		0			0
$214$	−8.00202	−	5.14259i	−0.547007	−	0.351540i
$215$	−8.70936	+	19.0708i	−0.593973	+	1.30062i
$216$		0			0
$217$	−1.12325	+	0.721868i	−0.0762511	+	0.0490036i
$218$	2.87785	+	20.0159i	0.194912	+	1.35565i
$219$		0			0
$220$	6.76890	−	4.35011i	0.456359	−	0.293284i
$221$	−3.29085	+	3.79785i	−0.221367	+	0.255471i
$222$		0			0
$223$	5.39879	+	3.46959i	0.361529	+	0.232341i	0.708777	−	0.705433i	$-0.249247\pi$
$223$	5.39879	+	3.46959i	0.361529	+	0.232341i	−0.347248	+	0.937774i	$0.612884\pi$
$224$	−0.186393	+	0.0547299i	−0.0124539	+	0.00365679i
$225$		0			0
$226$	1.26333	+	0.370948i	0.0840357	+	0.0246751i
$227$	0.497189	+	1.08869i	0.0329996	+	0.0722590i	0.925414	−	0.378958i	$-0.123717\pi$
$227$	0.497189	+	1.08869i	0.0329996	+	0.0722590i	−0.892414	+	0.451217i	$0.850990\pi$
$228$		0			0
$229$	−28.0856			−1.85595			−0.927974	−	0.372646i	$-0.878451\pi$
$229$	−28.0856			−1.85595			−0.927974	+	0.372646i	$0.878451\pi$
$230$	−12.1731	+	5.32693i	−0.802672	+	0.351247i
$231$		0			0
$232$	−1.31083	+	9.11701i	−0.0860600	+	0.598561i
$233$	6.81811	+	14.9296i	0.446669	+	0.978070i	0.990326	+	0.138762i	$0.0443122\pi$
$233$	6.81811	+	14.9296i	0.446669	+	0.978070i	−0.543656	+	0.839308i	$0.682961\pi$
$234$		0			0
$235$	10.1871	+	11.7565i	0.664531	+	0.766909i
$236$	−10.2842	+	3.01971i	−0.669444	+	0.196566i
$237$		0			0
$238$	0.374596	−	0.820250i	0.0242814	−	0.0531689i
$239$	6.76847	−	7.81123i	0.437816	−	0.505266i	−0.493366	−	0.869822i	$-0.664234\pi$
$239$	6.76847	−	7.81123i	0.437816	−	0.505266i	0.931182	+	0.364556i	$0.118779\pi$
$240$		0			0
$241$	3.12210	+	21.7147i	0.201112	+	1.39877i	0.800991	+	0.598676i	$0.204306\pi$
$241$	3.12210	+	21.7147i	0.201112	+	1.39877i	−0.599879	+	0.800091i	$0.704785\pi$
$242$	0.365231	+	2.54024i	0.0234780	+	0.163293i
$243$		0			0
$244$	1.88574	−	2.17626i	0.120722	−	0.139321i
$245$	8.01339	−	17.5469i	0.511957	−	1.12103i
$246$		0			0
$247$	4.59663	−	1.34969i	0.292476	−	0.0858788i
$248$	4.50102	+	5.19445i	0.285815	+	0.329848i
$249$		0			0
$250$	2.67421	+	5.85569i	0.169132	+	0.370347i
$251$	0.0385613	−	0.268200i	0.00243397	−	0.0169286i	−0.988568	−	0.150774i	$-0.951823\pi$
$251$	0.0385613	−	0.268200i	0.00243397	−	0.0169286i	0.991002	+	0.133845i	$0.0427325\pi$
$252$		0			0
$253$	−0.221534	+	13.9257i	−0.0139277	+	0.875500i
$254$	−4.81847			−0.302338
$255$		0			0
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	14.0118	+	4.11424i	0.874033	+	0.256639i	0.687830	−	0.725872i	$-0.258564\pi$
$257$	14.0118	+	4.11424i	0.874033	+	0.256639i	0.186203	+	0.982511i	$0.440382\pi$
$258$		0			0
$259$	0.903212	−	0.265207i	0.0561228	−	0.0164792i
$260$	−2.52335	−	1.62166i	−0.156491	−	0.100571i
$261$		0			0
$262$	10.4632	−	12.0752i	0.646419	−	0.746007i
$263$	14.3594	−	9.22820i	0.885436	−	0.569035i	−0.0170015	−	0.999855i	$-0.505412\pi$
$263$	14.3594	−	9.22820i	0.885436	−	0.569035i	0.902438	+	0.430820i	$0.141776\pi$
$264$		0			0
$265$	1.63345	+	11.3609i	0.100342	+	0.697893i
$266$	−0.723178	+	0.464758i	−0.0443409	+	0.0284962i
$267$		0			0
$268$	−6.08057	+	13.3146i	−0.371430	+	0.813318i
$269$	−27.1087	−	17.4217i	−1.65284	−	1.06222i	−0.927494	−	0.373837i	$-0.878042\pi$
$269$	−27.1087	−	17.4217i	−1.65284	−	1.06222i	−0.725349	−	0.688381i	$-0.758322\pi$
$270$		0			0
$271$	−2.00662	−	2.31576i	−0.121893	−	0.140672i	0.691523	−	0.722355i	$-0.256940\pi$
$271$	−2.00662	−	2.31576i	−0.121893	−	0.140672i	−0.813416	+	0.581682i	$0.802395\pi$
$272$	−4.45384	−	1.30777i	−0.270054	−	0.0792950i
$273$		0			0
$274$	2.67153	−	18.5809i	0.161393	−	1.12251i
$275$	−7.77296			−0.468727
$276$		0			0
$277$	−5.05736			−0.303867			−0.151934	−	0.988391i	$-0.548550\pi$
$277$	−5.05736			−0.303867			−0.151934	+	0.988391i	$0.548550\pi$
$278$	−2.52666	+	17.5733i	−0.151539	+	1.05398i
$279$		0			0
$280$	0.516432	+	0.151638i	0.0308627	+	0.00906210i
$281$	−5.50042	−	6.34782i	−0.328127	−	0.378679i	0.567584	−	0.823316i	$-0.307878\pi$
$281$	−5.50042	−	6.34782i	−0.328127	−	0.378679i	−0.895711	+	0.444636i	$0.853333\pi$
$282$		0			0
$283$	12.8122	+	8.23389i	0.761605	+	0.489454i	0.862883	−	0.505404i	$-0.168657\pi$
$283$	12.8122	+	8.23389i	0.761605	+	0.489454i	−0.101278	+	0.994858i	$0.532293\pi$
$284$	−5.28905	+	11.5814i	−0.313847	+	0.687229i
$285$		0			0
$286$	−2.64485	+	1.69974i	−0.156393	+	0.100508i
$287$	−0.158827	−	1.10466i	−0.00937524	−	0.0652062i
$288$		0			0
$289$	3.82516	−	2.45828i	0.225010	−	0.144605i
$290$	16.7120	−	19.2867i	0.981361	−	1.13255i
$291$		0			0
$292$	2.51377	+	1.61550i	0.147107	+	0.0945401i
$293$	27.7542	−	8.14937i	1.62142	−	0.476091i	0.660018	−	0.751249i	$-0.270548\pi$
$293$	27.7542	−	8.14937i	1.62142	−	0.476091i	0.961399	+	0.275158i	$0.0887303\pi$
$294$		0			0
$295$	28.4940	+	8.36660i	1.65899	+	0.487122i
$296$	−2.01299	−	4.40784i	−0.117003	−	0.256201i
$297$		0			0
$298$	9.51537			0.551211
$299$	4.75647	−	2.08142i	0.275074	−	0.120372i
$300$		0			0
$301$	−0.209198	+	1.45501i	−0.0120580	+	0.0838651i
$302$	−3.60527	−	7.89445i	−0.207460	−	0.454274i
$303$		0			0
$304$	2.89788	+	3.34433i	0.166205	+	0.191810i
$305$	−7.65525	+	2.24778i	−0.438338	+	0.128708i
$306$		0			0
$307$	−8.96612	+	19.6331i	−0.511724	+	1.12052i	0.460755	+	0.887527i	$0.347579\pi$
$307$	−8.96612	+	19.6331i	−0.511724	+	1.12052i	−0.972479	+	0.232991i	$0.925149\pi$
$308$	0.369440	−	0.426356i	0.0210508	−	0.0242939i
$309$		0			0
$310$	−2.71016	−	18.8496i	−0.153927	−	1.07059i
$311$	0.125077	+	0.869929i	0.00709246	+	0.0493291i	0.993060	−	0.117606i	$-0.0375220\pi$
$311$	0.125077	+	0.869929i	0.00709246	+	0.0493291i	−0.985968	+	0.166935i	$0.946613\pi$
$312$		0			0
$313$	3.57263	−	4.12304i	0.201937	−	0.233048i	−0.645744	−	0.763554i	$-0.723453\pi$
$313$	3.57263	−	4.12304i	0.201937	−	0.233048i	0.847681	+	0.530506i	$0.177998\pi$
$314$	8.23200	−	18.0256i	0.464559	−	1.01724i
$315$		0			0
$316$	−2.45532	+	0.720946i	−0.138122	+	0.0405564i
$317$	−3.33115	−	3.84435i	−0.187096	−	0.215920i	0.654451	−	0.756105i	$-0.272900\pi$
$317$	−3.33115	−	3.84435i	−0.187096	−	0.215920i	−0.841547	+	0.540184i	$0.818355\pi$
$318$		0			0
$319$	−11.1118	−	24.3315i	−0.622142	−	1.36230i
$320$	0.394306	−	2.74246i	0.0220424	−	0.153308i
$321$		0			0
$322$	−0.713707	+	0.598822i	−0.0397733	+	0.0333711i
$323$	−20.5411			−1.14294
$324$		0			0
$325$	1.20373	+	2.63579i	0.0667708	+	0.146208i
$326$	−13.9140	−	4.08552i	−0.770625	−	0.226276i
$327$		0			0
$328$	−5.51223	+	1.61854i	−0.304362	+	0.0893688i
$329$	0.917552	+	0.589675i	0.0505863	+	0.0325098i
$330$		0			0
$331$	23.3216	−	26.9146i	1.28187	−	1.47936i	0.485919	−	0.874004i	$-0.338485\pi$
$331$	23.3216	−	26.9146i	1.28187	−	1.47936i	0.795954	−	0.605356i	$-0.206969\pi$
$332$	0.682732	−	0.438765i	0.0374698	−	0.0240804i
$333$		0			0
$334$	−1.40766	−	9.79051i	−0.0770239	−	0.535713i
$335$	34.1172	−	21.9258i	1.86402	−	1.19793i
$336$		0			0
$337$	4.77911	−	10.4648i	0.260335	−	0.570053i	−0.733656	−	0.679521i	$-0.762187\pi$
$337$	4.77911	−	10.4648i	0.260335	−	0.570053i	0.993990	+	0.109468i	$0.0349147\pi$
$338$	−9.95033	−	6.39469i	−0.541227	−	0.347825i
$339$		0			0
$340$	8.42221	+	9.71974i	0.456758	+	0.527127i
$341$	−19.1519	−	5.62349i	−1.03713	−	0.304529i
$342$		0			0
$343$	0.386005	−	2.68473i	0.0208423	−	0.144962i
$344$	7.56694			0.407982
$345$		0			0
$346$	−13.2434			−0.711972
$347$	−2.24907	+	15.6426i	−0.120736	+	0.839740i	0.835989	+	0.548747i	$0.184895\pi$
$347$	−2.24907	+	15.6426i	−0.120736	+	0.839740i	−0.956725	+	0.290993i	$0.906014\pi$
$348$		0			0
$349$	−11.7351	−	3.44574i	−0.628167	−	0.184446i	−0.0478727	−	0.998853i	$-0.515244\pi$
$349$	−11.7351	−	3.44574i	−0.628167	−	0.184446i	−0.580294	+	0.814407i	$0.697062\pi$
$350$	−0.340499	−	0.392956i	−0.0182004	−	0.0210044i
$351$		0			0
$352$	−2.44306	−	1.57006i	−0.130216	−	0.0836845i
$353$	−1.51906	+	3.32628i	−0.0808514	+	0.177040i	−0.945740	−	0.324923i	$-0.894661\pi$
$353$	−1.51906	+	3.32628i	−0.0808514	+	0.177040i	0.864889	+	0.501963i	$0.167389\pi$
$354$		0			0
$355$	29.6760	−	19.0716i	1.57504	−	1.01222i
$356$	0.964871	+	6.71083i	0.0511381	+	0.355673i
$357$		0			0
$358$	−4.41264	+	2.83583i	−0.233215	+	0.149878i
$359$	−8.61646	+	9.94392i	−0.454759	+	0.524820i	−0.936110	−	0.351708i	$-0.885601\pi$
$359$	−8.61646	+	9.94392i	−0.454759	+	0.524820i	0.481351	+	0.876528i	$0.340146\pi$
$360$		0			0
$361$	0.489802	+	0.314776i	0.0257790	+	0.0165672i
$362$	15.5968	−	4.57965i	0.819752	−	0.240701i
$363$		0			0
$364$	−0.201788	−	0.0592504i	−0.0105766	−	0.00310556i
$365$	−3.43926	−	7.53092i	−0.180019	−	0.394186i
$366$		0			0
$367$	−12.3385			−0.644064			−0.322032	−	0.946729i	$-0.604366\pi$
$367$	−12.3385			−0.644064			−0.322032	+	0.946729i	$0.604366\pi$
$368$	3.57403	+	3.19786i	0.186309	+	0.166700i
$369$		0			0
$370$	−1.91071	+	13.2893i	−0.0993330	+	0.690876i
$371$	0.334303	+	0.732022i	0.0173562	+	0.0380047i
$372$		0			0
$373$	12.1475	+	14.0189i	0.628973	+	0.725873i	0.977385	−	0.211468i	$-0.0678244\pi$
$373$	12.1475	+	14.0189i	0.628973	+	0.725873i	−0.348412	+	0.937341i	$0.613279\pi$
$374$	12.9343	−	3.79785i	0.668816	−	0.196382i
$375$		0			0
$376$	2.33238	−	5.10719i	0.120283	−	0.263383i
$377$	−6.52997	+	7.53598i	−0.336310	+	0.388123i
$378$		0			0
$379$	−0.406982	−	2.83062i	−0.0209053	−	0.145399i	0.976695	−	0.214630i	$-0.0688546\pi$
$379$	−0.406982	−	2.83062i	−0.0209053	−	0.145399i	−0.997601	+	0.0692308i	$0.977946\pi$
$380$	−1.74488	−	12.1359i	−0.0895103	−	0.622558i
$381$		0			0
$382$	−5.03762	+	5.81372i	−0.257747	+	0.297456i
$383$	0.0334270	−	0.0731949i	0.00170804	−	0.00374009i	−0.908776	−	0.417284i	$-0.862982\pi$
$383$	0.0334270	−	0.0731949i	0.00170804	−	0.00374009i	0.910484	+	0.413544i	$0.135709\pi$
$384$		0			0
$385$	−1.49975	+	0.440368i	−0.0764346	+	0.0224432i
$386$	0.934780	+	1.07879i	0.0475791	+	0.0549092i
$387$		0			0
$388$	−5.13783	−	11.2503i	−0.260834	−	0.571146i
$389$	−1.95719	+	13.6126i	−0.0992337	+	0.690185i	0.878099	+	0.478478i	$0.158811\pi$
$389$	−1.95719	+	13.6126i	−0.0992337	+	0.690185i	−0.977333	+	0.211707i	$0.932098\pi$
$390$		0			0
$391$	−22.0827	+	2.81726i	−1.11677	+	0.142475i
$392$	−6.96226			−0.351647
$393$		0			0
$394$	−2.59872	−	5.69041i	−0.130922	−	0.286678i
$395$	6.80286	+	1.99750i	0.342289	+	0.100505i
$396$		0			0
$397$	6.36046	−	1.86760i	0.319222	−	0.0937321i	−0.118196	−	0.992990i	$-0.537711\pi$
$397$	6.36046	−	1.86760i	0.319222	−	0.0937321i	0.437418	+	0.899258i	$0.355893\pi$
$398$	0.726117	+	0.466647i	0.0363969	+	0.0233909i
$399$		0			0
$400$	−1.75278	+	2.02282i	−0.0876391	+	0.101141i
$401$	29.6875	−	19.0790i	1.48252	−	0.952759i	0.485615	−	0.874173i	$-0.338596\pi$
$401$	29.6875	−	19.0790i	1.48252	−	0.952759i	0.996907	−	0.0785860i	$-0.0250405\pi$
$402$		0			0
$403$	1.05896	+	7.36521i	0.0527504	+	0.366887i
$404$	−13.2049	+	8.48626i	−0.656967	+	0.422207i
$405$		0			0
$406$	0.743301	−	1.62760i	0.0368894	−	0.0807766i
$407$	11.8384	+	7.60811i	0.586810	+	0.377120i
$408$		0			0
$409$	19.1568	+	22.1082i	0.947244	+	1.09318i	0.995540	+	0.0943452i	$0.0300757\pi$
$409$	19.1568	+	22.1082i	0.947244	+	1.09318i	−0.0482952	+	0.998833i	$0.515379\pi$
$410$	15.2725	+	4.48442i	0.754257	+	0.221470i
$411$		0			0
$412$	−1.34415	+	9.34877i	−0.0662215	+	0.460581i
$413$	2.08217			0.102457
$414$		0			0
$415$	−2.24857			−0.110378
$416$	−0.154070	+	1.07158i	−0.00755388	+	0.0525384i
$417$		0			0
$418$	−12.3305	−	3.62056i	−0.603104	−	0.177087i
$419$	0.476760	+	0.550210i	0.0232912	+	0.0268795i	0.767276	−	0.641317i	$-0.221612\pi$
$419$	0.476760	+	0.550210i	0.0232912	+	0.0268795i	−0.743984	+	0.668197i	$0.767066\pi$
$420$		0			0
$421$	−28.4791	−	18.3024i	−1.38798	−	0.892004i	−0.388419	−	0.921483i	$-0.626979\pi$
$421$	−28.4791	−	18.3024i	−1.38798	−	0.892004i	−0.999565	+	0.0294793i	$0.990615\pi$
$422$	7.91975	−	17.3418i	0.385527	−	0.844187i
$423$		0			0
$424$	3.48496	−	2.23965i	0.169245	−	0.108767i
$425$	−1.76816	−	12.2979i	−0.0857685	−	0.596533i
$426$		0			0
$427$	−0.470596	+	0.302434i	−0.0227737	+	0.0146358i
$428$	6.22905	−	7.18871i	0.301092	−	0.347479i
$429$		0			0
$430$	−17.6373	−	11.3348i	−0.850544	−	0.546611i
$431$	1.42384	−	0.418077i	0.0685839	−	0.0201381i	−0.247261	−	0.968949i	$-0.579530\pi$
$431$	1.42384	−	0.418077i	0.0685839	−	0.0201381i	0.315845	+	0.948811i	$0.397712\pi$
$432$		0			0
$433$	6.69224	+	1.96502i	0.321608	+	0.0944327i	0.438552	−	0.898706i	$-0.355492\pi$
$433$	6.69224	+	1.96502i	0.321608	+	0.0944327i	−0.116944	+	0.993139i	$0.537310\pi$
$434$	−0.554666	−	1.21455i	−0.0266248	−	0.0583002i
$435$		0			0
$436$	−20.2217			−0.968443
$437$	19.1619	+	9.12206i	0.916639	+	0.436367i
$438$		0			0
$439$	−1.32651	+	9.22605i	−0.0633106	+	0.440335i	0.933369	+	0.358917i	$0.116854\pi$
$439$	−1.32651	+	9.22605i	−0.0633106	+	0.440335i	−0.996680	+	0.0814180i	$0.974055\pi$
$440$	3.34251	+	7.31909i	0.159348	+	0.348924i
$441$		0			0
$442$	−3.29085	−	3.79785i	−0.156530	−	0.180645i
$443$	30.3672	−	8.91661i	1.44279	−	0.423641i	0.535638	−	0.844448i	$-0.320071\pi$
$443$	30.3672	−	8.91661i	1.44279	−	0.423641i	0.907150	+	0.420807i	$0.138253\pi$
$444$		0			0
$445$	7.80342	−	17.0871i	0.369918	−	0.810007i
$446$	−4.20260	+	4.85006i	−0.198999	+	0.229657i
$447$		0			0
$448$	−0.0276463	−	0.192284i	−0.00130617	−	0.00908459i
$449$	−1.36062	−	9.46329i	−0.0642115	−	0.446600i	−0.996410	−	0.0846542i	$-0.973021\pi$
$449$	−1.36062	−	9.46329i	−0.0642115	−	0.446600i	0.932199	−	0.361946i	$-0.117888\pi$
$450$		0			0
$451$	10.9255	−	12.6087i	0.514463	−	0.593721i
$452$	−0.546964	+	1.19768i	−0.0257270	+	0.0563343i
$453$		0			0
$454$	−1.14837	+	0.337191i	−0.0538955	+	0.0158252i
$455$	0.381581	+	0.440368i	0.0178888	+	0.0206448i
$456$		0			0
$457$	−5.34240	−	11.6982i	−0.249907	−	0.547220i	0.742553	−	0.669787i	$-0.233615\pi$
$457$	−5.34240	−	11.6982i	−0.249907	−	0.547220i	−0.992460	+	0.122567i	$0.960887\pi$
$458$	3.99700	−	27.7997i	0.186767	−	1.29900i
$459$		0			0
$460$	−3.54029	−	12.8073i	−0.165067	−	0.597145i
$461$	−18.4038			−0.857151			−0.428575	−	0.903506i	$-0.640984\pi$
$461$	−18.4038			−0.857151			−0.428575	+	0.903506i	$0.640984\pi$
$462$		0			0
$463$	11.4891	+	25.1576i	0.533944	+	1.16917i	0.963885	+	0.266318i	$0.0858070\pi$
$463$	11.4891	+	25.1576i	0.533944	+	1.16917i	−0.429941	+	0.902857i	$0.641466\pi$
$464$	−8.83766	−	2.59497i	−0.410278	−	0.120468i
$465$		0			0
$466$	−15.7479	+	4.62401i	−0.729509	+	0.214203i
$467$	−20.4802	−	13.1618i	−0.947711	−	0.609057i	−0.0271399	−	0.999632i	$-0.508640\pi$
$467$	−20.4802	−	13.1618i	−0.947711	−	0.609057i	−0.920571	+	0.390575i	$0.872276\pi$
$468$		0			0
$469$	1.86208	−	2.14896i	0.0859829	−	0.0992296i
$470$	−13.0866	+	8.41025i	−0.603640	+	0.387936i
$471$		0			0
$472$	−1.52538	−	10.6093i	−0.0702114	−	0.488331i
$473$	−18.4865	+	11.8806i	−0.850010	+	0.546268i
$474$		0			0
$475$	−4.92031	+	10.7740i	−0.225759	+	0.494344i
$476$	0.758591	+	0.487517i	0.0347699	+	0.0223453i
$477$		0			0
$478$	6.76847	+	7.81123i	0.309582	+	0.357277i
$479$	−6.99671	−	2.05442i	−0.319688	−	0.0938689i	0.117952	−	0.993019i	$-0.462367\pi$
$479$	−6.99671	−	2.05442i	−0.319688	−	0.0938689i	−0.437640	+	0.899150i	$0.644185\pi$
$480$		0			0
$481$	0.746581	−	5.19259i	0.0340412	−	0.236762i
$482$	−21.9380			−0.999248
$483$		0			0
$484$	−2.56636			−0.116653
$485$	−4.87676	+	33.9186i	−0.221442	+	1.54016i
$486$		0			0
$487$	−21.5014	−	6.31339i	−0.974323	−	0.286087i	−0.244444	−	0.969663i	$-0.578605\pi$
$487$	−21.5014	−	6.31339i	−0.974323	−	0.286087i	−0.729879	+	0.683576i	$0.760424\pi$
$488$	1.88574	+	2.17626i	0.0853636	+	0.0985149i
$489$		0			0
$490$	16.2279	+	10.4290i	0.733100	+	0.471134i
$491$	−8.18375	+	17.9199i	−0.369328	+	0.808715i	0.630152	+	0.776471i	$0.282992\pi$
$491$	−8.18375	+	17.9199i	−0.369328	+	0.808715i	−0.999480	+	0.0322432i	$0.989735\pi$
$492$		0			0
$493$	35.9679	−	23.1152i	1.61991	−	1.04106i
$494$	0.681786	+	4.74192i	0.0306750	+	0.213349i
$495$		0			0
$496$	−5.78214	+	3.71596i	−0.259626	+	0.166851i
$497$	1.61969	−	1.86922i	0.0726529	−	0.0838460i
$498$		0			0
$499$	−14.5484	−	9.34971i	−0.651277	−	0.418550i	0.172855	−	0.984947i	$-0.444701\pi$
$499$	−14.5484	−	9.34971i	−0.651277	−	0.418550i	−0.824133	+	0.566397i	$0.808337\pi$
$500$	−6.17667	+	1.81363i	−0.276229	+	0.0811082i
$501$		0			0
$502$	0.259982	+	0.0763376i	0.0116036	+	0.00340711i
$503$	−6.82524	−	14.9452i	−0.304323	−	0.666373i	0.694253	−	0.719731i	$-0.255735\pi$
$503$	−6.82524	−	14.9452i	−0.304323	−	0.666373i	−0.998575	+	0.0533577i	$0.983008\pi$
$504$		0			0
$505$	43.4902			1.93529
$506$	−13.7524	−	2.20111i	−0.611369	−	0.0978513i
$507$		0			0
$508$	0.685740	−	4.76943i	0.0304248	−	0.211609i
$509$	−11.2142	−	24.5556i	−0.497059	−	1.08841i	−0.977414	−	0.211334i	$-0.932219\pi$
$509$	−11.2142	−	24.5556i	−0.497059	−	1.08841i	0.480354	−	0.877074i	$-0.340508\pi$
$510$		0			0
$511$	−0.380132	−	0.438696i	−0.0168161	−	0.0194068i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$		0			0
$514$	−6.06645	+	13.2837i	−0.267580	+	0.585918i
$515$	17.1368	−	19.7770i	0.755139	−	0.871477i
$516$		0			0
$517$	2.32046	+	16.1392i	0.102054	+	0.709799i
$518$	0.133967	+	0.931761i	0.00588617	+	0.0409392i
$519$		0			0
$520$	1.96426	−	2.26688i	0.0861386	−	0.0994092i
$521$	−9.75660	+	21.3640i	−0.427444	+	0.935973i	0.566290	+	0.824206i	$0.308378\pi$
$521$	−9.75660	+	21.3640i	−0.427444	+	0.935973i	−0.993734	+	0.111767i	$0.964349\pi$
$522$		0			0
$523$	−28.1477	+	8.26490i	−1.23081	+	0.361399i	−0.831556	−	0.555441i	$-0.812550\pi$
$523$	−28.1477	+	8.26490i	−1.23081	+	0.361399i	−0.399255	+	0.916840i	$0.630731\pi$
$524$	10.4632	+	12.0752i	0.457087	+	0.527507i
$525$		0			0
$526$	7.09072	+	15.5265i	0.309170	+	0.676988i
$527$	4.54051	−	31.5800i	0.197788	−	1.37565i
$528$		0			0
$529$	21.8511	+	7.17853i	0.950046	+	0.312110i
$530$	−11.4777			−0.498560
$531$		0			0
$532$	−0.357109	−	0.781959i	−0.0154826	−	0.0339022i
$533$	−5.96752	−	1.75222i	−0.258482	−	0.0758972i
$534$		0			0
$535$	−25.2871	+	7.42495i	−1.09326	+	0.321009i
$536$	−12.3137	−	7.91354i	−0.531872	−	0.341813i
$537$		0			0
$538$	21.1023	−	24.3534i	0.909785	−	1.04995i
$539$	17.0092	−	10.9312i	0.732640	−	0.470839i
$540$		0			0
$541$	0.682956	+	4.75006i	0.0293626	+	0.204221i	0.999222	−	0.0394449i	$-0.0125590\pi$
$541$	0.682956	+	4.75006i	0.0293626	+	0.204221i	−0.969859	+	0.243666i	$0.921650\pi$
$542$	2.57776	−	1.65662i	0.110724	−	0.0711581i
$543$		0			0
$544$	1.92830	−	4.22240i	0.0826753	−	0.181034i
$545$	47.1333	+	30.2908i	2.01897	+	1.29751i
$546$		0			0
$547$	−18.0000	−	20.7731i	−0.769622	−	0.888192i	0.226692	−	0.973966i	$-0.427209\pi$
$547$	−18.0000	−	20.7731i	−0.769622	−	0.888192i	−0.996315	+	0.0857749i	$0.972663\pi$
$548$	18.0116	+	5.28867i	0.769416	+	0.225921i
$549$		0			0
$550$	1.10621	−	7.69385i	0.0471689	−	0.328067i
$551$	−40.7593			−1.73640
$552$		0			0
$553$	0.497111			0.0211393
$554$	0.719737	−	5.00588i	0.0305787	−	0.212679i
$555$		0			0
$556$	−17.0348	−	5.00188i	−0.722438	−	0.212127i
$557$	−7.86165	−	9.07283i	−0.333109	−	0.384428i	0.564343	−	0.825540i	$-0.309130\pi$
$557$	−7.86165	−	9.07283i	−0.333109	−	0.384428i	−0.897452	+	0.441112i	$0.854584\pi$
$558$		0			0
$559$	6.89150	+	4.42890i	0.291479	+	0.187322i
$560$	−0.223590	+	0.489595i	−0.00944842	+	0.0206892i
$561$		0			0
$562$	7.06600	−	4.54104i	0.298061	−	0.191552i
$563$	−0.869255	−	6.04580i	−0.0366347	−	0.254800i	0.963271	−	0.268531i	$-0.0865382\pi$
$563$	−0.869255	−	6.04580i	−0.0366347	−	0.254800i	−0.999906	+	0.0137310i	$0.995629\pi$
$564$		0			0
$565$	3.06893	−	1.97228i	0.129111	−	0.0829745i
$566$	−9.97344	+	11.5100i	−0.419215	+	0.483800i
$567$		0			0
$568$	−10.7108	−	6.88341i	−0.449415	−	0.288822i
$569$	23.9950	−	7.04556i	1.00592	−	0.295365i	0.263038	−	0.964786i	$-0.415276\pi$
$569$	23.9950	−	7.04556i	1.00592	−	0.295365i	0.742884	+	0.669420i	$0.233457\pi$
$570$		0			0
$571$	22.4009	+	6.57751i	0.937450	+	0.275260i	0.714553	−	0.699582i	$-0.246630\pi$
$571$	22.4009	+	6.57751i	0.937450	+	0.275260i	0.222898	+	0.974842i	$0.428448\pi$
$572$	−1.30604	−	2.85983i	−0.0546082	−	0.119575i
$573$		0			0
$574$	1.11602			0.0465819
$575$	−3.81188	+	12.2573i	−0.158966	+	0.511167i
$576$		0			0
$577$	−5.23379	+	36.4018i	−0.217886	+	1.51543i	0.527937	+	0.849284i	$0.322966\pi$
$577$	−5.23379	+	36.4018i	−0.217886	+	1.51543i	−0.745823	+	0.666145i	$0.767943\pi$
$578$	1.88888	+	4.13608i	0.0785672	+	0.172038i
$579$		0			0
$580$	16.7120	+	19.2867i	0.693927	+	0.800835i
$581$	−0.151270	+	0.0444169i	−0.00627573	+	0.00184272i
$582$		0			0
$583$	−4.99759	+	10.9432i	−0.206979	+	0.453221i
$584$	−1.95680	+	2.25827i	−0.0809731	+	0.0934480i
$585$		0			0
$586$	4.11658	+	28.6315i	0.170055	+	1.18276i
$587$	3.37092	+	23.4453i	0.139133	+	0.967690i	0.933071	+	0.359692i	$0.117118\pi$
$587$	3.37092	+	23.4453i	0.139133	+	0.967690i	−0.793938	+	0.607998i	$0.791973\pi$
$588$		0			0
$589$	−19.9178	+	22.9864i	−0.820699	+	0.947137i
$590$	−12.3366	+	27.0133i	−0.507888	+	1.11212i
$591$		0			0
$592$	4.64946	−	1.36520i	0.191091	−	0.0561095i
$593$	17.0796	+	19.7109i	0.701376	+	0.809431i	0.988938	−	0.148331i	$-0.0473901\pi$
$593$	17.0796	+	19.7109i	0.701376	+	0.809431i	−0.287562	+	0.957762i	$0.592845\pi$
$594$		0			0
$595$	−1.03788	−	2.27264i	−0.0425489	−	0.0931690i
$596$	−1.35418	+	9.41852i	−0.0554693	+	0.385797i
$597$		0			0
$598$	1.38332	+	5.00428i	0.0565680	+	0.204640i
$599$	−11.2311			−0.458891			−0.229445	−	0.973322i	$-0.573691\pi$
$599$	−11.2311			−0.458891			−0.229445	+	0.973322i	$0.573691\pi$
$600$		0			0
$601$	9.43741	+	20.6650i	0.384960	+	0.842945i	0.998576	+	0.0533404i	$0.0169868\pi$
$601$	9.43741	+	20.6650i	0.384960	+	0.842945i	−0.613616	+	0.789604i	$0.710286\pi$
$602$	−1.41042	−	0.414138i	−0.0574846	−	0.0168790i
$603$		0			0
$604$	8.32718	−	2.44508i	0.338828	−	0.0994889i
$605$	5.98175	+	3.84424i	0.243193	+	0.156291i
$606$		0			0
$607$	−10.5182	+	12.1387i	−0.426922	+	0.492694i	−0.927933	−	0.372747i	$-0.878416\pi$
$607$	−10.5182	+	12.1387i	−0.426922	+	0.492694i	0.501011	+	0.865441i	$0.332962\pi$
$608$	−3.72270	+	2.39243i	−0.150975	+	0.0970260i
$609$		0			0
$610$	−1.13545	−	7.89722i	−0.0459730	−	0.319749i
$611$	5.11340	−	3.28618i	0.206866	−	0.132945i
$612$		0			0
$613$	2.61584	−	5.72789i	0.105653	−	0.231347i	−0.849421	−	0.527716i	$-0.823048\pi$
$613$	2.61584	−	5.72789i	0.105653	−	0.231347i	0.955074	+	0.296369i	$0.0957757\pi$
$614$	−18.1572	−	11.6689i	−0.732766	−	0.470920i
$615$		0			0
$616$	0.369440	+	0.426356i	0.0148852	+	0.0171784i
$617$	−9.23760	−	2.71240i	−0.371892	−	0.109197i	0.0904455	−	0.995901i	$-0.471171\pi$
$617$	−9.23760	−	2.71240i	−0.371892	−	0.109197i	−0.462337	+	0.886704i	$0.652989\pi$
$618$		0			0
$619$	−3.51921	+	24.4767i	−0.141449	+	0.983800i	0.788217	+	0.615397i	$0.211004\pi$
$619$	−3.51921	+	24.4767i	−0.141449	+	0.983800i	−0.929666	+	0.368403i	$0.879905\pi$
$620$	19.0434			0.764803
$621$		0			0
$622$	−0.878874			−0.0352396
$623$	0.187438	−	1.30366i	0.00750953	−	0.0522299i
$624$		0			0
$625$	29.9542	+	8.79536i	1.19817	+	0.351814i
$626$	3.57263	+	4.12304i	0.142791	+	0.164790i
$627$		0			0
$628$	16.6706	+	10.7135i	0.665228	+	0.427516i
$629$	−9.34406	+	20.4606i	−0.372572	+	0.815819i
$630$		0			0
$631$	30.1416	−	19.3708i	1.19992	−	0.771141i	0.220977	−	0.975279i	$-0.429076\pi$
$631$	30.1416	−	19.3708i	1.19992	−	0.771141i	0.978942	+	0.204138i	$0.0654391\pi$
$632$	−0.364180	−	2.53293i	−0.0144863	−	0.100754i
$633$		0			0
$634$	4.27930	−	2.75014i	0.169953	−	0.109222i
$635$	−8.74263	+	10.0895i	−0.346941	+	0.400391i
$636$		0			0
$637$	−6.34080	−	4.07498i	−0.251232	−	0.161457i
$638$	25.6652	−	7.53598i	1.01609	−	0.298352i
$639$		0			0
$640$	2.65843	+	0.780586i	0.105084	+	0.0308554i
$641$	5.26851	+	11.5364i	0.208094	+	0.455662i	0.984685	−	0.174343i	$-0.0557802\pi$
$641$	5.26851	+	11.5364i	0.208094	+	0.455662i	−0.776591	+	0.630005i	$0.783053\pi$
$642$		0			0
$643$	−27.3350			−1.07799			−0.538993	−	0.842310i	$-0.681195\pi$
$643$	−27.3350			−1.07799			−0.538993	+	0.842310i	$0.681195\pi$
$644$	−0.491156	−	0.791664i	−0.0193543	−	0.0311959i
$645$		0			0
$646$	2.92331	−	20.3320i	0.115016	−	0.799954i
$647$	1.94623	+	4.26166i	0.0765143	+	0.167543i	0.944024	−	0.329878i	$-0.107008\pi$
$647$	1.94623	+	4.26166i	0.0765143	+	0.167543i	−0.867509	+	0.497421i	$0.834280\pi$
$648$		0			0
$649$	20.3838	+	23.5241i	0.800133	+	0.923403i
$650$	−2.78027	+	0.816362i	−0.109051	+	0.0320204i
$651$		0			0
$652$	6.02410	−	13.1909i	0.235922	−	0.516597i
$653$	−18.8217	+	21.7214i	−0.736550	+	0.850024i	−0.993193	−	0.116482i	$-0.962838\pi$
$653$	−18.8217	+	21.7214i	−0.736550	+	0.850024i	0.256643	+	0.966506i	$0.417384\pi$
$654$		0			0
$655$	−6.30013	−	43.8184i	−0.246167	−	1.71213i
$656$	−0.817590	−	5.68647i	−0.0319215	−	0.222019i
$657$		0			0
$658$	−0.714254	+	0.824293i	−0.0278445	+	0.0321343i
$659$	−1.50370	+	3.29264i	−0.0585758	+	0.128263i	−0.936656	−	0.350250i	$-0.886097\pi$
$659$	−1.50370	+	3.29264i	−0.0585758	+	0.128263i	0.878081	+	0.478513i	$0.158824\pi$
$660$		0			0
$661$	16.3839	−	4.81074i	0.637259	−	0.187116i	0.0528849	−	0.998601i	$-0.483158\pi$
$661$	16.3839	−	4.81074i	0.637259	−	0.187116i	0.584374	+	0.811485i	$0.301340\pi$
$662$	23.3216	+	26.9146i	0.906421	+	1.04607i
$663$		0			0
$664$	0.337136	+	0.738226i	0.0130834	+	0.0286487i
$665$	−0.338963	+	2.35754i	−0.0131444	+	0.0914215i
$666$		0			0
$667$	−43.8181	+	5.59023i	−1.69664	+	0.216455i
$668$	9.89119			0.382702
$669$		0			0
$670$	16.8472	+	36.8903i	0.650865	+	1.42519i
$671$	−8.02385	−	2.35602i	−0.309757	−	0.0909530i
$672$		0			0
$673$	−42.8696	+	12.5877i	−1.65250	+	0.485219i	−0.969478	−	0.245177i	$-0.921154\pi$
$673$	−42.8696	+	12.5877i	−1.65250	+	0.485219i	−0.683025	+	0.730395i	$0.739336\pi$
$674$	9.67814	+	6.21976i	0.372788	+	0.239576i
$675$		0			0
$676$	7.74568	−	8.93899i	0.297911	−	0.343807i
$677$	−17.0221	+	10.9395i	−0.654214	+	0.420438i	−0.825204	−	0.564835i	$-0.808940\pi$
$677$	−17.0221	+	10.9395i	−0.654214	+	0.420438i	0.170990	+	0.985273i	$0.445303\pi$
$678$		0			0
$679$	0.341928	+	2.37816i	0.0131220	+	0.0912655i
$680$	−10.8194	+	6.95322i	−0.414906	+	0.266644i
$681$		0			0
$682$	8.29185	−	18.1566i	0.317511	−	0.695253i
$683$	34.6818	+	22.2886i	1.32706	+	0.852850i	0.995877	−	0.0907163i	$-0.0289156\pi$
$683$	34.6818	+	22.2886i	1.32706	+	0.852850i	0.331184	+	0.943566i	$0.392552\pi$
$684$		0			0
$685$	−34.0598	−	39.3071i	−1.30136	−	1.50185i
$686$	2.60247	+	0.764153i	0.0993626	+	0.0291755i
$687$		0			0
$688$	−1.07689	+	7.48992i	−0.0410560	+	0.285551i
$689$	4.48475			0.170855
$690$		0			0
$691$	−39.4196			−1.49959			−0.749795	−	0.661670i	$-0.769848\pi$
$691$	−39.4196			−1.49959			−0.749795	+	0.661670i	$0.769848\pi$
$692$	1.88474	−	13.1086i	0.0716470	−	0.498316i
$693$		0			0
$694$	−15.1633	−	4.45236i	−0.575592	−	0.169009i
$695$	32.2128	+	37.1756i	1.22190	+	1.41015i
$696$		0			0
$697$	22.4339	+	14.4174i	0.849746	+	0.546099i
$698$	5.08075	−	11.1253i	0.192309	−	0.421099i
$699$		0			0
$700$	0.437415	−	0.281109i	0.0165327	−	0.0106249i
$701$	−6.43057	−	44.7256i	−0.242879	−	1.68926i	−0.637525	−	0.770430i	$-0.720042\pi$
$701$	−6.43057	−	44.7256i	−0.242879	−	1.68926i	0.394645	−	0.918834i	$-0.370868\pi$
$702$		0			0
$703$	18.0392	−	11.5931i	0.680363	−	0.437243i
$704$	1.90176	−	2.19475i	0.0716754	−	0.0827178i
$705$		0			0
$706$	−3.07624	−	1.97698i	−0.115776	−	0.0744045i
$707$	2.92575	−	0.859077i	0.110034	−	0.0323089i
$708$		0			0
$709$	−30.6067	−	8.98694i	−1.14946	−	0.337511i	−0.349131	−	0.937074i	$-0.613523\pi$
$709$	−30.6067	−	8.98694i	−1.14946	−	0.337511i	−0.800328	+	0.599563i	$0.795341\pi$
$710$	14.6542	+	32.0881i	0.549961	+	1.20425i
$711$		0			0
$712$	−6.77984			−0.254085
$713$	−18.2599	+	27.4432i	−0.683840	+	1.02776i
$714$		0			0
$715$	−1.23968	+	8.62213i	−0.0463612	+	0.322449i
$716$	−2.17898	−	4.77130i	−0.0814323	−	0.178312i
$717$		0			0
$718$	−8.61646	−	9.94392i	−0.321563	−	0.371104i
$719$	−24.1545	+	7.09239i	−0.900809	+	0.264502i	−0.699168	−	0.714958i	$-0.746446\pi$
$719$	−24.1545	+	7.09239i	−0.900809	+	0.264502i	−0.201642	+	0.979459i	$0.564628\pi$
$720$		0			0
$721$	0.762197	−	1.66898i	0.0283857	−	0.0621560i
$722$	−0.381279	+	0.440019i	−0.0141897	+	0.0163758i
$723$		0			0
$724$	2.31337	+	16.0898i	0.0859757	+	0.597974i
$725$	−3.50853	−	24.4023i	−0.130303	−	0.906280i
$726$		0			0
$727$	−1.54963	+	1.78836i	−0.0574725	+	0.0663268i	−0.783758	−	0.621067i	$-0.786700\pi$
$727$	−1.54963	+	1.78836i	−0.0574725	+	0.0663268i	0.726285	+	0.687393i	$0.241245\pi$
$728$	0.0873647	−	0.191302i	0.00323795	−	0.00709013i
$729$		0			0
$730$	7.94372	−	2.33249i	0.294010	−	0.0863292i
$731$	−23.0018	−	26.5455i	−0.850754	−	0.981822i
$732$		0			0
$733$	−0.181280	−	0.396947i	−0.00669571	−	0.0146616i	0.906255	−	0.422732i	$-0.138929\pi$
$733$	−0.181280	−	0.396947i	−0.00669571	−	0.0146616i	−0.912950	+	0.408071i	$0.866202\pi$
$734$	1.75595	−	12.2129i	0.0648133	−	0.450786i
$735$		0			0
$736$	−3.67394	+	3.08255i	−0.135423	+	0.113624i
$737$	42.5079			1.56580
$738$		0			0
$739$	−14.5747	−	31.9141i	−0.536138	−	1.17398i	−0.962960	−	0.269643i	$-0.913094\pi$
$739$	−14.5747	−	31.9141i	−0.536138	−	1.17398i	0.426822	−	0.904336i	$-0.359633\pi$
$740$	−12.8821	−	3.78252i	−0.473555	−	0.139048i
$741$		0			0
$742$	−0.772148	+	0.226723i	−0.0283464	+	0.00832327i
$743$	−28.2800	−	18.1745i	−1.03749	−	0.666756i	−0.0931277	−	0.995654i	$-0.529686\pi$
$743$	−28.2800	−	18.1745i	−1.03749	−	0.666756i	−0.944366	+	0.328898i	$0.893323\pi$
$744$		0			0
$745$	17.2647	−	19.9245i	0.632529	−	0.729977i
$746$	−15.6050	+	10.0287i	−0.571340	+	0.367178i
$747$		0			0
$748$	1.91845	+	13.3431i	0.0701455	+	0.487873i
$749$	−1.55449	+	0.999008i	−0.0567997	+	0.0365030i
$750$		0			0
$751$	16.5189	−	36.1713i	0.602782	−	1.31991i	−0.324621	−	0.945844i	$-0.605237\pi$
$751$	16.5189	−	36.1713i	0.602782	−	1.31991i	0.927403	−	0.374064i	$-0.122036\pi$
$752$	4.72328	+	3.03546i	0.172240	+	0.110692i
$753$		0			0
$754$	−6.52997	−	7.53598i	−0.237807	−	0.274444i
$755$	−23.0718	−	6.77449i	−0.839669	−	0.246549i
$756$		0			0
$757$	3.53539	−	24.5892i	0.128496	−	0.893709i	−0.818966	−	0.573842i	$-0.805452\pi$
$757$	3.53539	−	24.5892i	0.128496	−	0.893709i	0.947462	−	0.319868i	$-0.103638\pi$
$758$	2.85973			0.103870
$759$		0			0
$760$	12.2607			0.444742
$761$	−3.46327	+	24.0876i	−0.125543	+	0.873174i	0.825563	+	0.564310i	$0.190858\pi$
$761$	−3.46327	+	24.0876i	−0.125543	+	0.873174i	−0.951106	+	0.308864i	$0.900051\pi$
$762$		0			0
$763$	3.76918	+	1.10673i	0.136453	+	0.0400663i
$764$	−5.03762	−	5.81372i	−0.182255	−	0.210333i
$765$		0			0
$766$	0.0676928	+	0.0435035i	0.00244584	+	0.00157185i
$767$	4.82033	−	10.5551i	0.174052	−	0.381121i
$768$		0			0
$769$	−22.2445	+	14.2957i	−0.802159	+	0.515516i	−0.876320	−	0.481730i	$-0.840009\pi$
$769$	−22.2445	+	14.2957i	−0.802159	+	0.515516i	0.0741608	+	0.997246i	$0.476372\pi$
$770$	−0.222448	−	1.54716i	−0.00801647	−	0.0557558i
$771$		0			0
$772$	−1.20085	+	0.771737i	−0.0432194	+	0.0277754i
$773$	14.4872	−	16.7191i	0.521067	−	0.601343i	−0.432831	−	0.901475i	$-0.642485\pi$
$773$	14.4872	−	16.7191i	0.521067	−	0.601343i	0.953898	+	0.300132i	$0.0970307\pi$
$774$		0			0
$775$	−15.4763	−	9.94603i	−0.555926	−	0.357272i
$776$	11.8670	−	3.48445i	0.425999	−	0.125085i
$777$		0			0
$778$	−13.1955	−	3.87455i	−0.473081	−	0.138909i
$779$	−10.5608	−	23.1250i	−0.378382	−	0.828540i
$780$		0			0
$781$	36.9745			1.32305
$782$	0.354100	−	22.2588i	0.0126626	−	0.795974i
$783$		0			0
$784$	0.990833	−	6.89140i	0.0353869	−	0.246121i
$785$	−22.8081	−	49.9428i	−0.814056	−	1.78253i
$786$		0			0
$787$	−2.95813	−	3.41387i	−0.105446	−	0.121691i	0.700573	−	0.713581i	$-0.252928\pi$
$787$	−2.95813	−	3.41387i	−0.105446	−	0.121691i	−0.806019	+	0.591889i	$0.798382\pi$
$788$	6.00232	−	1.76244i	0.213824	−	0.0627844i
$789$		0			0
$790$	−2.94532	+	6.44934i	−0.104790	+	0.229457i
$791$	0.167499	−	0.193304i	0.00595559	−	0.00687311i
$792$		0			0
$793$	0.443660	+	3.08572i	0.0157548	+	0.109577i
$794$	0.943402	+	6.56150i	0.0334801	+	0.232859i
$795$		0			0
$796$	−0.565234	+	0.652315i	−0.0200342	+	0.0231207i
$797$	12.5900	−	27.5683i	0.445961	−	0.976518i	−0.544505	−	0.838758i	$-0.683282\pi$
$797$	12.5900	−	27.5683i	0.445961	−	0.976518i	0.990466	−	0.137760i	$-0.0439903\pi$
$798$		0			0
$799$	−25.0064	+	7.34255i	−0.884663	+	0.259761i
$800$	−1.75278	−	2.02282i	−0.0619702	−	0.0715175i
$801$		0			0
$802$	14.6598	+	32.1005i	0.517656	+	1.13351i
$803$	1.23497	−	8.58940i	0.0435811	−	0.303113i
$804$		0			0
$805$	−0.0410586	+	2.58095i	−0.00144712	+	0.0909666i
$806$	−7.44095			−0.262096
$807$		0			0
$808$	−6.52063	−	14.2782i	−0.229395	−	0.502305i
$809$	27.2132	+	7.99050i	0.956764	+	0.280931i	0.722600	−	0.691266i	$-0.242947\pi$
$809$	27.2132	+	7.99050i	0.956764	+	0.280931i	0.234163	+	0.972197i	$0.424765\pi$
$810$		0			0
$811$	10.1871	−	2.99120i	0.357718	−	0.105035i	−0.0979355	−	0.995193i	$-0.531224\pi$
$811$	10.1871	−	2.99120i	0.357718	−	0.105035i	0.455653	+	0.890157i	$0.349406\pi$
$812$	1.50525	+	0.967368i	0.0528240	+	0.0339479i
$813$		0			0
$814$	−9.21546	+	10.6352i	−0.323002	+	0.372764i
$815$	−33.8003	+	21.7221i	−1.18397	+	0.760894i
$816$		0			0
$817$	4.76542	+	33.1443i	0.166721	+	1.15957i
$818$	−24.6094	+	15.8155i	−0.860449	+	0.552977i
$819$		0			0
$820$	−6.61228	+	14.4789i	−0.230911	+	0.505625i
$821$	−13.0634	−	8.39532i	−0.455915	−	0.292999i	0.292456	−	0.956279i	$-0.405527\pi$
$821$	−13.0634	−	8.39532i	−0.455915	−	0.292999i	−0.748371	+	0.663280i	$0.769164\pi$
$822$		0			0
$823$	32.8520	+	37.9133i	1.14515	+	1.32157i	0.939342	+	0.342981i	$0.111437\pi$
$823$	32.8520	+	37.9133i	1.14515	+	1.32157i	0.205808	+	0.978592i	$0.434018\pi$
$824$	−9.06232	−	2.66094i	−0.315701	−	0.0926982i
$825$		0			0
$826$	−0.296323	+	2.06097i	−0.0103104	+	0.0717104i
$827$	33.0620			1.14968			0.574839	−	0.818267i	$-0.305065\pi$
$827$	33.0620			1.14968			0.574839	+	0.818267i	$0.305065\pi$
$828$		0			0
$829$	−11.7345			−0.407556			−0.203778	−	0.979017i	$-0.565322\pi$
$829$	−11.7345			−0.407556			−0.203778	+	0.979017i	$0.565322\pi$
$830$	0.320005	−	2.22569i	0.0111076	−	0.0772547i
$831$		0			0
$832$	−1.03874	−	0.305003i	−0.0360120	−	0.0105741i
$833$	21.1637	+	24.4243i	0.733280	+	0.846251i
$834$		0			0
$835$	−23.0547	−	14.8163i	−0.797840	−	0.512741i
$836$	5.33852	−	11.6897i	0.184637	−	0.404298i
$837$		0			0
$838$	−0.612459	+	0.393604i	−0.0211571	+	0.0135968i
$839$	−1.09621	−	7.62430i	−0.0378453	−	0.263220i	0.962110	−	0.272661i	$-0.0879038\pi$
$839$	−1.09621	−	7.62430i	−0.0378453	−	0.263220i	−0.999955	+	0.00944127i	$0.996995\pi$
$840$		0			0
$841$	46.9740	−	30.1883i	1.61979	−	1.04098i
$842$	22.1691	−	25.5845i	0.763997	−	0.881700i
$843$		0			0
$844$	16.0382	+	10.3071i	0.552058	+	0.354786i
$845$	−31.4439	+	9.23276i	−1.08170	+	0.317617i
$846$		0			0
$847$	0.478351	+	0.140457i	0.0164364	+	0.00482615i
$848$	1.72089	+	3.76823i	0.0590957	+	0.129401i
$849$		0			0
$850$	12.4243			0.426150
$851$	17.8030	−	14.9373i	0.610279	−	0.512043i
$852$		0			0
$853$	6.01254	−	41.8181i	0.205865	−	1.43183i	−0.580599	−	0.814190i	$-0.697181\pi$
$853$	6.01254	−	41.8181i	0.205865	−	1.43183i	0.786464	−	0.617636i	$-0.211909\pi$
$854$	−0.232382	−	0.508847i	−0.00795196	−	0.0174124i
$855$		0			0
$856$	6.22905	+	7.18871i	0.212905	+	0.245705i
$857$	−18.5488	+	5.44641i	−0.633613	+	0.186046i	−0.582739	−	0.812659i	$-0.698019\pi$
$857$	−18.5488	+	5.44641i	−0.633613	+	0.186046i	−0.0508744	+	0.998705i	$0.516201\pi$
$858$		0			0
$859$	−8.34241	+	18.2673i	−0.284639	+	0.623273i	−0.996903	−	0.0786387i	$-0.974943\pi$
$859$	−8.34241	+	18.2673i	−0.284639	+	0.623273i	0.712264	+	0.701912i	$0.247670\pi$
$860$	13.7294	−	15.8446i	0.468170	−	0.540297i
$861$		0			0
$862$	0.211188	+	1.46885i	0.00719309	+	0.0500291i
$863$	0.826096	+	5.74562i	0.0281206	+	0.195583i	0.999039	−	0.0438270i	$-0.0139550\pi$
$863$	0.826096	+	5.74562i	0.0281206	+	0.195583i	−0.970919	+	0.239410i	$0.923046\pi$
$864$		0			0
$865$	−24.0289	+	27.7308i	−0.817006	+	0.942875i
$866$	−2.89742	+	6.34447i	−0.0984584	+	0.215594i
$867$		0			0
$868$	1.28112	−	0.376172i	0.0434841	−	0.0127681i
$869$	4.86656	+	5.61631i	0.165087	+	0.190520i
$870$		0			0
$871$	−6.58281	−	14.4143i	−0.223050	−	0.488411i
$872$	2.87785	−	20.0159i	0.0974562	−	0.677823i
$873$		0			0
$874$	−11.7562	+	17.6687i	−0.397661	+	0.597652i
$875$	1.25055			0.0422762
$876$		0			0
$877$	14.9519	+	32.7400i	0.504889	+	1.10555i	0.974849	+	0.222865i	$0.0715410\pi$
$877$	14.9519	+	32.7400i	0.504889	+	1.10555i	−0.469960	+	0.882688i	$0.655732\pi$
$878$	−8.94336	−	2.62601i	−0.301824	−	0.0886234i
$879$		0			0
$880$	−7.72028	+	2.26688i	−0.260251	+	0.0764165i
$881$	−31.4703	−	20.2247i	−1.06026	−	0.681388i	−0.110344	−	0.993893i	$-0.535195\pi$
$881$	−31.4703	−	20.2247i	−1.06026	−	0.681388i	−0.949916	+	0.312506i	$0.898832\pi$
$882$		0			0
$883$	32.9735	−	38.0535i	1.10965	−	1.28060i	0.153361	−	0.988170i	$-0.450990\pi$
$883$	32.9735	−	38.0535i	1.10965	−	1.28060i	0.956287	−	0.292431i	$-0.0944643\pi$
$884$	4.22753	−	2.71687i	0.142187	−	0.0913782i
$885$		0			0
$886$	4.50415	+	31.3270i	0.151320	+	1.05245i
$887$	−25.8216	+	16.5945i	−0.867004	+	0.557190i	−0.896835	−	0.442365i	$-0.854140\pi$
$887$	−25.8216	+	16.5945i	−0.867004	+	0.557190i	0.0298308	+	0.999555i	$0.490503\pi$
$888$		0			0
$889$	−0.388847	+	0.851456i	−0.0130415	+	0.0285569i
$890$	15.8026	+	10.1557i	0.529706	+	0.340421i
$891$		0			0
$892$	−4.20260	−	4.85006i	−0.140713	−	0.162392i
$893$	23.8391	+	6.99978i	0.797744	+	0.234239i
$894$		0			0
$895$	−2.06826	+	14.3851i	−0.0691343	+	0.480840i
$896$	0.194262			0.00648983
$897$		0			0
$898$	9.56061			0.319042
$899$	9.00963	−	62.6634i	0.300488	−	2.08994i
$900$		0			0
$901$	−18.4504	−	5.41753i	−0.614673	−	0.180484i
$902$	10.9255	+	12.6087i	0.363780	+	0.419824i
$903$		0			0
$904$	−1.10765	−	0.711845i	−0.0368400	−	0.0236756i
$905$	18.7094	−	40.9680i	0.621923	−	1.36182i
$906$		0			0
$907$	−4.54974	+	2.92394i	−0.151071	+	0.0970877i	−0.613993	−	0.789312i	$-0.710438\pi$
$907$	−4.54974	+	2.92394i	−0.151071	+	0.0970877i	0.462921	+	0.886399i	$0.346801\pi$
$908$	−0.170329	−	1.18467i	−0.00565257	−	0.0393145i
$909$		0			0
$910$	−0.490190	+	0.315026i	−0.0162496	+	0.0104430i
$911$	−29.6277	+	34.1922i	−0.981610	+	1.13284i	0.00952202	+	0.999955i	$0.496969\pi$
$911$	−29.6277	+	34.1922i	−0.981610	+	1.13284i	−0.991132	+	0.132883i	$0.957576\pi$
$912$		0			0
$913$	−1.98270	−	1.27421i	−0.0656179	−	0.0421701i
$914$	12.3395	−	3.62319i	0.408153	−	0.119845i
$915$		0			0
$916$	26.9479	+	7.91262i	0.890384	+	0.261440i
$917$	−1.28939	−	2.82338i	−0.0425795	−	0.0932361i
$918$		0			0
$919$	10.7793			0.355576			0.177788	−	0.984069i	$-0.443106\pi$
$919$	10.7793			0.355576			0.177788	+	0.984069i	$0.443106\pi$
$920$	13.1808	−	1.68158i	0.434558	−	0.0554401i
$921$		0			0
$922$	2.61914	−	18.2165i	0.0862566	−	0.599928i
$923$	−5.72590	−	12.5380i	−0.188470	−	0.412692i
$924$		0			0
$925$	8.49354	+	9.80206i	0.279266	+	0.322290i
$926$	−26.5366	+	7.79186i	−0.872048	+	0.256056i
$927$		0			0
$928$	3.82629	−	8.37840i	0.125604	−	0.275034i
$929$	−20.5270	+	23.6894i	−0.673470	+	0.777226i	−0.984915	−	0.173038i	$-0.944642\pi$
$929$	−20.5270	+	23.6894i	−0.673470	+	0.777226i	0.311445	+	0.950264i	$0.399187\pi$
$930$		0			0
$931$	−4.38462	−	30.4957i	−0.143700	−	0.999455i
$932$	−2.33578	−	16.2457i	−0.0765111	−	0.532146i
$933$		0			0
$934$	15.9425	−	18.3986i	0.521655	−	0.602022i
$935$	15.5155	−	33.9743i	0.507412	−	1.11108i
$936$		0			0
$937$	−15.5397	+	4.56287i	−0.507661	+	0.149063i	−0.525526	−	0.850778i	$-0.676131\pi$
$937$	−15.5397	+	4.56287i	−0.507661	+	0.149063i	0.0178650	+	0.999840i	$0.494313\pi$
$938$	1.86208	+	2.14896i	0.0607991	+	0.0701659i
$939$		0			0
$940$	−6.46223	−	14.1503i	−0.210775	−	0.461532i
$941$	−3.42607	+	23.8289i	−0.111687	+	0.776798i	0.854592	+	0.519300i	$0.173807\pi$
$941$	−3.42607	+	23.8289i	−0.111687	+	0.776798i	−0.966279	+	0.257498i	$0.917102\pi$
$942$		0			0
$943$	−14.5251	−	23.4120i	−0.473001	−	0.762400i
$944$	10.7184			0.348853
$945$		0			0
$946$	−9.12872	−	19.9891i	−0.296800	−	0.649902i
$947$	4.75553	+	1.39635i	0.154534	+	0.0453753i	0.358085	−	0.933689i	$-0.383430\pi$
$947$	4.75553	+	1.39635i	0.154534	+	0.0453753i	−0.203551	+	0.979064i	$0.565248\pi$
$948$		0			0
$949$	−3.10389	+	0.911386i	−0.100757	+	0.0295848i
$950$	−9.96408	−	6.40352i	−0.323277	−	0.207758i
$951$		0			0
$952$	−0.590513	+	0.681488i	−0.0191386	+	0.0220872i
$953$	32.4534	−	20.8566i	1.05127	−	0.675610i	0.103521	−	0.994627i	$-0.466989\pi$
$953$	32.4534	−	20.8566i	1.05127	−	0.675610i	0.947749	+	0.319017i	$0.103353\pi$
$954$		0			0
$955$	3.03326	+	21.0968i	0.0981541	+	0.682677i
$956$	−8.69497	+	5.58792i	−0.281215	+	0.180726i
$957$		0			0
$958$	3.02925	−	6.63312i	0.0978705	−	0.214306i
$959$	−3.06778	−	1.97154i	−0.0990637	−	0.0636644i
$960$		0			0
$961$	−10.6359	−	12.2745i	−0.343093	−	0.395951i
$962$	5.03349	+	1.47796i	0.162286	+	0.0476515i
$963$		0			0
$964$	3.12210	−	21.7147i	0.100556	−	0.699383i
$965$	3.95498			0.127315
$966$		0			0
$967$	47.2484			1.51940			0.759702	−	0.650271i	$-0.225345\pi$
$967$	47.2484			1.51940			0.759702	+	0.650271i	$0.225345\pi$
$968$	0.365231	−	2.54024i	0.0117390	−	0.0816464i
$969$		0			0
$970$	−32.8793	−	9.65424i	−1.05569	−	0.309979i
$971$	11.2136	+	12.9412i	0.359863	+	0.415304i	0.906594	−	0.422005i	$-0.138673\pi$
$971$	11.2136	+	12.9412i	0.359863	+	0.415304i	−0.546731	+	0.837308i	$0.684128\pi$
$972$		0			0
$973$	2.90142	+	1.86463i	0.0930153	+	0.0597773i
$974$	9.30911	−	20.3841i	0.298283	−	0.653149i
$975$		0			0
$976$	−2.42248	+	1.55683i	−0.0775418	+	0.0498331i
$977$	−3.35123	−	23.3083i	−0.107215	−	0.745699i	−0.970521	−	0.241017i	$-0.922519\pi$
$977$	−3.35123	−	23.3083i	−0.107215	−	0.745699i	0.863306	−	0.504682i	$-0.168390\pi$
$978$		0			0
$979$	16.5636	−	10.6448i	0.529374	−	0.340208i
$980$	−12.6323	+	14.5785i	−0.403525	+	0.465692i
$981$		0			0
$982$	−16.5729	−	10.6507i	−0.528861	−	0.339878i
$983$	−7.70621	+	2.26275i	−0.245790	+	0.0721704i	−0.402307	−	0.915505i	$-0.631792\pi$
$983$	−7.70621	+	2.26275i	−0.245790	+	0.0721704i	0.156517	+	0.987675i	$0.449973\pi$
$984$		0			0
$985$	−16.6304	−	4.88313i	−0.529889	−	0.155589i
$986$	17.7611	+	38.8915i	0.565630	+	1.23856i
$987$		0			0
$988$	−4.79069			−0.152412
$989$	9.66886	+	34.9780i	0.307452	+	1.11224i
$990$		0			0
$991$	7.56451	−	52.6123i	0.240294	−	1.67128i	−0.410370	−	0.911919i	$-0.634600\pi$
$991$	7.56451	−	52.6123i	0.240294	−	1.67128i	0.650664	−	0.759365i	$-0.274490\pi$
$992$	−2.85525	−	6.25212i	−0.0906542	−	0.198505i
$993$		0			0
$994$	1.61969	+	1.86922i	0.0513734	+	0.0592880i
$995$	2.29459	−	0.673752i	0.0727434	−	0.0213594i
$996$		0			0
$997$	−5.98347	+	13.1020i	−0.189498	+	0.414944i	−0.980405	−	0.196993i	$-0.936882\pi$
$997$	−5.98347	+	13.1020i	−0.189498	+	0.414944i	0.790906	+	0.611937i	$0.209610\pi$
$998$	11.3250	−	13.0697i	0.358487	−	0.413716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.a.307.1		10
3.2	odd	2		138.2.e.d.31.1	✓	10
23.3	even	11	inner	414.2.i.a.325.1		10
23.7	odd	22		9522.2.a.by.1.4		5
23.16	even	11		9522.2.a.bx.1.2		5
69.26	odd	22		138.2.e.d.49.1	yes	10
69.53	even	22		3174.2.a.w.1.2		5
69.62	odd	22		3174.2.a.x.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.31.1	✓	10	3.2	odd	2
138.2.e.d.49.1	yes	10	69.26	odd	22
414.2.i.a.307.1		10	1.1	even	1	trivial
414.2.i.a.325.1		10	23.3	even	11	inner
3174.2.a.w.1.2		5	69.53	even	22
3174.2.a.x.1.4		5	69.62	odd	22
9522.2.a.bx.1.2		5	23.16	even	11
9522.2.a.by.1.4		5	23.7	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.81440 + 2.09393i) q^{5} +(0.163423 + 0.105026i) q^{7} +(0.415415 - 0.909632i) q^{8} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(1.81440 + 2.09393i) q^{5} +(0.163423 + 0.105026i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.33083 + 1.49793i) q^{10} +(0.413293 + 2.87451i) q^{11} +(0.910738 - 0.585296i) q^{13} +(-0.127214 + 0.146813i) q^{14} +(0.841254 + 0.540641i) q^{16} +(-4.45384 + 1.30777i) q^{17} +(4.24593 + 1.24672i) q^{19} +(-1.15098 - 2.52028i) q^{20} -2.90407 q^{22} +(4.73556 + 0.757939i) q^{23} +(-0.380916 + 2.64933i) q^{25} +(0.449727 + 0.984764i) q^{26} +(-0.127214 - 0.146813i) q^{28} +(-8.83766 + 2.59497i) q^{29} +(-2.85525 + 6.25212i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-0.660607 - 4.59462i) q^{34} +(0.0765987 + 0.532755i) q^{35} +(3.17329 - 3.66217i) q^{37} +(-1.83829 + 4.02529i) q^{38} +(2.65843 - 0.780586i) q^{40} +(-3.76214 - 4.34174i) q^{41} +(3.14342 + 6.88313i) q^{43} +(0.413293 - 2.87451i) q^{44} +(-1.42416 + 4.57949i) q^{46} +5.61457 q^{47} +(-2.89223 - 6.33310i) q^{49} +(-2.56815 - 0.754078i) q^{50} +(-1.03874 + 0.305003i) q^{52} +(3.48496 + 2.23965i) q^{53} +(-5.26914 + 6.08092i) q^{55} +(0.163423 - 0.105026i) q^{56} +(-1.31083 - 9.11701i) q^{58} +(9.01685 - 5.79478i) q^{59} +(-1.19623 + 2.61939i) q^{61} +(-5.78214 - 3.71596i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(2.87801 + 0.845060i) q^{65} +(2.08311 - 14.4884i) q^{67} +4.64187 q^{68} -0.538234 q^{70} +(1.81195 - 12.6024i) q^{71} +(-2.86708 - 0.841852i) q^{73} +(3.17329 + 3.66217i) q^{74} +(-3.72270 - 2.39243i) q^{76} +(-0.234356 + 0.513169i) q^{77} +(2.15275 - 1.38349i) q^{79} +(0.394306 + 2.74246i) q^{80} +(4.83295 - 3.10595i) q^{82} +(-0.531462 + 0.613340i) q^{83} +(-10.8194 - 6.95322i) q^{85} +(-7.26043 + 2.13185i) q^{86} +(2.78644 + 0.818172i) q^{88} +(-2.81645 - 6.16716i) q^{89} +0.210307 q^{91} +(-4.33020 - 2.06140i) q^{92} +(-0.799036 + 5.55742i) q^{94} +(5.09327 + 11.1527i) q^{95} +(8.09928 + 9.34707i) q^{97} +(6.68024 - 1.96150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

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