LMFDB - Embedded newform 414.2.i.h.271.1

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.1
Root			$-0.303441 + 2.11048i$ of defining polynomial
Character	$\chi$	$=$	414.271
Dual form			414.2.i.h.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.0234248 + 0.162923i) q^{5} +(1.32938 + 2.91093i) q^{7} +(0.654861 + 0.755750i) q^{8} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.0234248 + 0.162923i) q^{5} +(1.32938 + 2.91093i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.0683767 + 0.149724i) q^{10} +(-0.321474 + 0.0943934i) q^{11} +(-0.942704 + 2.06423i) q^{13} +(0.455424 + 3.16754i) q^{14} +(0.415415 + 0.909632i) q^{16} +(3.44273 - 2.21251i) q^{17} +(1.09624 + 0.704511i) q^{19} +(-0.107789 + 0.124395i) q^{20} -0.335046 q^{22} +(-2.70351 - 3.96119i) q^{23} +(4.77147 + 1.40103i) q^{25} +(-1.48608 + 1.71503i) q^{26} +(-0.455424 + 3.16754i) q^{28} +(-1.71069 + 1.09939i) q^{29} +(-0.206606 - 0.238436i) q^{31} +(0.142315 + 0.989821i) q^{32} +(3.92661 - 1.15296i) q^{34} +(-0.505398 + 0.148398i) q^{35} +(0.261437 + 1.81833i) q^{37} +(0.853352 + 0.984821i) q^{38} +(-0.138469 + 0.0889887i) q^{40} +(1.06307 - 7.39384i) q^{41} +(1.34856 - 1.55633i) q^{43} +(-0.321474 - 0.0943934i) q^{44} +(-1.47800 - 4.56240i) q^{46} -7.23723 q^{47} +(-2.12223 + 2.44919i) q^{49} +(4.18348 + 2.68856i) q^{50} +(-1.90906 + 1.22688i) q^{52} +(-5.41917 - 11.8663i) q^{53} +(-0.00784839 - 0.0545868i) q^{55} +(-1.32938 + 2.91093i) q^{56} +(-1.95113 + 0.572903i) q^{58} +(-2.58317 + 5.65636i) q^{59} +(-6.20162 - 7.15706i) q^{61} +(-0.131062 - 0.286985i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(-0.314229 - 0.201943i) q^{65} +(-2.68500 - 0.788387i) q^{67} +4.09238 q^{68} -0.526734 q^{70} +(4.09461 + 1.20229i) q^{71} +(-4.66734 - 2.99952i) q^{73} +(-0.261437 + 1.81833i) q^{74} +(0.541329 + 1.18535i) q^{76} +(-0.702133 - 0.810304i) q^{77} +(4.47779 - 9.80499i) q^{79} +(-0.157931 + 0.0463728i) q^{80} +(3.10310 - 6.79483i) q^{82} +(1.67357 + 11.6399i) q^{83} +(0.279823 + 0.612728i) q^{85} +(1.73241 - 1.11335i) q^{86} +(-0.281859 - 0.181140i) q^{88} +(8.17617 - 9.43580i) q^{89} -7.26204 q^{91} +(-0.132754 - 4.79399i) q^{92} +(-6.94407 - 2.03896i) q^{94} +(-0.140461 + 0.162100i) q^{95} +(1.90815 - 13.2715i) q^{97} +(-2.72628 + 1.75208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$		0			0
$3$		0			0
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.0234248	+	0.162923i	−0.0104759	+	0.0728615i	−0.994389	−	0.105788i	$-0.966264\pi$
$5$	−0.0234248	+	0.162923i	−0.0104759	+	0.0728615i	0.983913	+	0.178649i	$0.0571727\pi$
$6$		0			0
$7$	1.32938	+	2.91093i	0.502457	+	1.10023i	0.975663	+	0.219275i	$0.0703693\pi$
$7$	1.32938	+	2.91093i	0.502457	+	1.10023i	−0.473206	+	0.880952i	$0.656903\pi$
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$		0			0
$10$	−0.0683767	+	0.149724i	−0.0216226	+	0.0473469i
$11$	−0.321474	+	0.0943934i	−0.0969282	+	0.0284607i	−0.329837	−	0.944038i	$-0.606994\pi$
$11$	−0.321474	+	0.0943934i	−0.0969282	+	0.0284607i	0.232909	+	0.972499i	$0.425176\pi$
$12$		0			0
$13$	−0.942704	+	2.06423i	−0.261459	+	0.572515i	−0.994145	−	0.108051i	$-0.965539\pi$
$13$	−0.942704	+	2.06423i	−0.261459	+	0.572515i	0.732686	+	0.680567i	$0.238266\pi$
$14$	0.455424	+	3.16754i	0.121717	+	0.846561i
$15$		0			0
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	3.44273	−	2.21251i	0.834984	−	0.536612i	−0.0518739	−	0.998654i	$-0.516519\pi$
$17$	3.44273	−	2.21251i	0.834984	−	0.536612i	0.886858	+	0.462042i	$0.152883\pi$
$18$		0			0
$19$	1.09624	+	0.704511i	0.251495	+	0.161626i	0.660314	−	0.750989i	$-0.270423\pi$
$19$	1.09624	+	0.704511i	0.251495	+	0.161626i	−0.408819	+	0.912615i	$0.634059\pi$
$20$	−0.107789	+	0.124395i	−0.0241024	+	0.0278156i
$21$		0			0
$22$	−0.335046			−0.0714321
$23$	−2.70351	−	3.96119i	−0.563721	−	0.825966i
$23$	−2.70351	−	3.96119i	−0.563721	−	0.825966i
$24$		0			0
$25$	4.77147	+	1.40103i	0.954294	+	0.280206i
$26$	−1.48608	+	1.71503i	−0.291444	+	0.336345i
$27$		0			0
$28$	−0.455424	+	3.16754i	−0.0860670	+	0.598609i
$29$	−1.71069	+	1.09939i	−0.317667	+	0.204152i	−0.689751	−	0.724047i	$-0.742280\pi$
$29$	−1.71069	+	1.09939i	−0.317667	+	0.204152i	0.372084	+	0.928199i	$0.378643\pi$
$30$		0			0
$31$	−0.206606	−	0.238436i	−0.0371075	−	0.0428243i	0.736892	−	0.676010i	$-0.236292\pi$
$31$	−0.206606	−	0.238436i	−0.0371075	−	0.0428243i	−0.774000	+	0.633186i	$0.781747\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$		0			0
$34$	3.92661	−	1.15296i	0.673408	−	0.197730i
$35$	−0.505398	+	0.148398i	−0.0854279	+	0.0250839i
$36$		0			0
$37$	0.261437	+	1.81833i	0.0429800	+	0.298932i	0.999961	+	0.00878316i	$0.00279580\pi$
$37$	0.261437	+	1.81833i	0.0429800	+	0.298932i	−0.956981	+	0.290149i	$0.906295\pi$
$38$	0.853352	+	0.984821i	0.138432	+	0.159759i
$39$		0			0
$40$	−0.138469	+	0.0889887i	−0.0218939	+	0.0140704i
$41$	1.06307	−	7.39384i	0.166024	−	1.15472i	−0.720978	−	0.692958i	$-0.756307\pi$
$41$	1.06307	−	7.39384i	0.166024	−	1.15472i	0.887002	−	0.461765i	$-0.152784\pi$
$42$		0			0
$43$	1.34856	−	1.55633i	0.205654	−	0.237338i	−0.643548	−	0.765406i	$-0.722538\pi$
$43$	1.34856	−	1.55633i	0.205654	−	0.237338i	0.849202	+	0.528069i	$0.177084\pi$
$44$	−0.321474	−	0.0943934i	−0.0484641	−	0.0142303i
$45$		0			0
$46$	−1.47800	−	4.56240i	−0.217919	−	0.672689i
$47$	−7.23723			−1.05566			−0.527829	−	0.849350i	$-0.676994\pi$
$47$	−7.23723			−1.05566			−0.527829	+	0.849350i	$0.676994\pi$
$48$		0			0
$49$	−2.12223	+	2.44919i	−0.303176	+	0.349884i
$50$	4.18348	+	2.68856i	0.591633	+	0.380219i
$51$		0			0
$52$	−1.90906	+	1.22688i	−0.264739	+	0.170138i
$53$	−5.41917	−	11.8663i	−0.744381	−	1.62997i	−0.776211	−	0.630473i	$-0.782861\pi$
$53$	−5.41917	−	11.8663i	−0.744381	−	1.62997i	0.0318305	−	0.999493i	$-0.489866\pi$
$54$		0			0
$55$	−0.00784839	−	0.0545868i	−0.00105828	−	0.00736048i
$56$	−1.32938	+	2.91093i	−0.177645	+	0.388989i
$57$		0			0
$58$	−1.95113	+	0.572903i	−0.256196	+	0.0752259i
$59$	−2.58317	+	5.65636i	−0.336300	+	0.736395i	−0.999932	−	0.0116646i	$-0.996287\pi$
$59$	−2.58317	+	5.65636i	−0.336300	+	0.736395i	0.663632	+	0.748059i	$0.269014\pi$
$60$		0			0
$61$	−6.20162	−	7.15706i	−0.794037	−	0.916367i	0.204002	−	0.978971i	$-0.434605\pi$
$61$	−6.20162	−	7.15706i	−0.794037	−	0.916367i	−0.998038	+	0.0626034i	$0.980060\pi$
$62$	−0.131062	−	0.286985i	−0.0166448	−	0.0364471i
$63$		0			0
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.314229	−	0.201943i	−0.0389753	−	0.0250479i
$66$		0			0
$67$	−2.68500	−	0.788387i	−0.328025	−	0.0963169i	0.113573	−	0.993530i	$-0.463770\pi$
$67$	−2.68500	−	0.788387i	−0.328025	−	0.0963169i	−0.441599	+	0.897213i	$0.645588\pi$
$68$	4.09238			0.496274
$69$		0			0
$70$	−0.526734			−0.0629568
$71$	4.09461	+	1.20229i	0.485941	+	0.142685i	0.515520	−	0.856877i	$-0.327599\pi$
$71$	4.09461	+	1.20229i	0.485941	+	0.142685i	−0.0295796	+	0.999562i	$0.509417\pi$
$72$		0			0
$73$	−4.66734	−	2.99952i	−0.546271	−	0.351067i	0.238216	−	0.971212i	$-0.423437\pi$
$73$	−4.66734	−	2.99952i	−0.546271	−	0.351067i	−0.784487	+	0.620145i	$0.787074\pi$
$74$	−0.261437	+	1.81833i	−0.0303914	+	0.211377i
$75$		0			0
$76$	0.541329	+	1.18535i	0.0620947	+	0.135968i
$77$	−0.702133	−	0.810304i	−0.0800154	−	0.0923427i
$78$		0			0
$79$	4.47779	−	9.80499i	0.503791	−	1.10315i	−0.471428	−	0.881905i	$-0.656261\pi$
$79$	4.47779	−	9.80499i	0.503791	−	1.10315i	0.975219	−	0.221243i	$-0.0710115\pi$
$80$	−0.157931	+	0.0463728i	−0.0176572	+	0.00518463i
$81$		0			0
$82$	3.10310	−	6.79483i	0.342680	−	0.750364i
$83$	1.67357	+	11.6399i	0.183698	+	1.27765i	0.847924	+	0.530118i	$0.177852\pi$
$83$	1.67357	+	11.6399i	0.183698	+	1.27765i	−0.664225	+	0.747532i	$0.731239\pi$
$84$		0			0
$85$	0.279823	+	0.612728i	0.0303511	+	0.0664597i
$86$	1.73241	−	1.11335i	0.186810	−	0.120056i
$87$		0			0
$88$	−0.281859	−	0.181140i	−0.0300462	−	0.0193095i
$89$	8.17617	−	9.43580i	0.866672	−	1.00019i	−0.133286	−	0.991078i	$-0.542553\pi$
$89$	8.17617	−	9.43580i	0.866672	−	1.00019i	0.999958	−	0.00911558i	$-0.00290162\pi$
$90$		0			0
$91$	−7.26204			−0.761269
$92$	−0.132754	−	4.79399i	−0.0138406	−	0.499808i
$93$		0			0
$94$	−6.94407	−	2.03896i	−0.716226	−	0.210303i
$95$	−0.140461	+	0.162100i	−0.0144109	+	0.0166311i
$96$		0			0
$97$	1.90815	−	13.2715i	0.193743	−	1.34751i	−0.628247	−	0.778014i	$-0.716227\pi$
$97$	1.90815	−	13.2715i	0.193743	−	1.34751i	0.821991	−	0.569501i	$-0.192864\pi$
$98$	−2.72628	+	1.75208i	−0.275396	+	0.176986i
$99$		0			0
$100$	3.25656	+	3.75827i	0.325656	+	0.375827i
$101$	0.459558	+	3.19630i	0.0457278	+	0.318044i	0.999828	+	0.0185556i	$0.00590677\pi$
$101$	0.459558	+	3.19630i	0.0457278	+	0.318044i	−0.954100	+	0.299488i	$0.903184\pi$
$102$		0			0
$103$	−12.5026	+	3.67110i	−1.23192	+	0.361724i	−0.831974	−	0.554815i	$-0.812789\pi$
$103$	−12.5026	+	3.67110i	−1.23192	+	0.361724i	−0.399945	+	0.916539i	$0.630971\pi$
$104$	−2.17738	+	0.639338i	−0.213510	+	0.0626922i
$105$		0			0
$106$	−1.85653	−	12.9124i	−0.180322	−	1.25417i
$107$	8.96709	+	10.3486i	0.866882	+	1.00043i	0.999956	+	0.00932887i	$0.00296952\pi$
$107$	8.96709	+	10.3486i	0.866882	+	1.00043i	−0.133075	+	0.991106i	$0.542485\pi$
$108$		0			0
$109$	6.59727	−	4.23981i	0.631904	−	0.406100i	−0.185110	−	0.982718i	$-0.559264\pi$
$109$	6.59727	−	4.23981i	0.631904	−	0.406100i	0.817014	+	0.576618i	$0.195628\pi$
$110$	0.00784839	−	0.0545868i	0.000748315	−	0.00520465i
$111$		0			0
$112$	−2.09563	+	2.41849i	−0.198018	+	0.228525i
$113$	−5.33952	−	1.56783i	−0.502300	−	0.147489i	0.0207599	−	0.999784i	$-0.493391\pi$
$113$	−5.33952	−	1.56783i	−0.502300	−	0.147489i	−0.523060	+	0.852296i	$0.675210\pi$
$114$		0			0
$115$	0.708699	−	0.347674i	0.0660866	−	0.0324208i
$116$	−2.03350			−0.188806
$117$		0			0
$118$	−4.07211	+	4.69947i	−0.374868	+	0.432621i
$119$	11.0171	+	7.08028i	1.00994	+	0.649048i
$120$		0			0
$121$	−9.15935	+	5.88636i	−0.832668	+	0.535124i
$122$	−3.93404	−	8.61434i	−0.356171	−	0.779906i
$123$		0			0
$124$	−0.0448997	−	0.312284i	−0.00403211	−	0.0280440i
$125$	−0.681915	+	1.49318i	−0.0609923	+	0.133555i
$126$		0			0
$127$	−2.97524	+	0.873610i	−0.264010	+	0.0775204i	−0.411059	−	0.911609i	$-0.634841\pi$
$127$	−2.97524	+	0.873610i	−0.264010	+	0.0775204i	0.147048	+	0.989129i	$0.453023\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$		0			0
$130$	−0.244607	−	0.282291i	−0.0214534	−	0.0247586i
$131$	3.14451	+	6.88551i	0.274737	+	0.601590i	0.995828	−	0.0912504i	$-0.0290864\pi$
$131$	3.14451	+	6.88551i	0.274737	+	0.601590i	−0.721091	+	0.692840i	$0.756359\pi$
$132$		0			0
$133$	−0.593465	+	4.12764i	−0.0514599	+	0.357912i
$134$	−2.35413	−	1.51290i	−0.203365	−	0.130695i
$135$		0			0
$136$	3.92661	+	1.15296i	0.336704	+	0.0988652i
$137$	−1.58993			−0.135837			−0.0679186	−	0.997691i	$-0.521636\pi$
$137$	−1.58993			−0.135837			−0.0679186	+	0.997691i	$0.521636\pi$
$138$		0			0
$139$	−5.21524			−0.442351			−0.221175	−	0.975234i	$-0.570989\pi$
$139$	−5.21524			−0.442351			−0.221175	+	0.975234i	$0.570989\pi$
$140$	−0.505398	−	0.148398i	−0.0427139	−	0.0125419i
$141$		0			0
$142$	3.59003	+	2.30717i	0.301268	+	0.193613i
$143$	0.108205	−	0.752583i	0.00904857	−	0.0629342i
$144$		0			0
$145$	−0.139044	−	0.304464i	−0.0115470	−	0.0252844i
$146$	−3.63322	−	4.19296i	−0.300687	−	0.347012i
$147$		0			0
$148$	−0.763131	+	1.67102i	−0.0627290	+	0.137357i
$149$	9.30410	−	2.73193i	0.762222	−	0.223809i	0.122556	−	0.992462i	$-0.460891\pi$
$149$	9.30410	−	2.73193i	0.762222	−	0.223809i	0.639666	+	0.768653i	$0.279073\pi$
$150$		0			0
$151$	7.19512	−	15.7551i	0.585530	−	1.28213i	−0.352575	−	0.935783i	$-0.614694\pi$
$151$	7.19512	−	15.7551i	0.585530	−	1.28213i	0.938106	−	0.346349i	$-0.112579\pi$
$152$	0.185451	+	1.28984i	0.0150421	+	0.104620i
$153$		0			0
$154$	−0.445402	−	0.975295i	−0.0358915	−	0.0785915i
$155$	0.0436864	−	0.0280756i	0.00350898	−	0.00225508i
$156$		0			0
$157$	7.49407	+	4.81615i	0.598092	+	0.384370i	0.804375	−	0.594122i	$-0.202500\pi$
$157$	7.49407	+	4.81615i	0.598092	+	0.384370i	−0.206283	+	0.978492i	$0.566137\pi$
$158$	7.05879	−	8.14628i	0.561568	−	0.648083i
$159$		0			0
$160$	−0.164599			−0.0130127
$161$	7.93676	−	13.1356i	0.625504	−	1.03523i
$162$		0			0
$163$	22.6652	+	6.65511i	1.77528	+	0.521268i	0.994611	−	0.103680i	$-0.0330619\pi$
$163$	22.6652	+	6.65511i	1.77528	+	0.521268i	0.780666	+	0.624949i	$0.214880\pi$
$164$	4.89172	−	5.64535i	0.381979	−	0.440828i
$165$		0			0
$166$	−1.67357	+	11.6399i	−0.129894	+	0.903435i
$167$	−19.4159	+	12.4779i	−1.50245	+	0.965566i	−0.507888	+	0.861423i	$0.669574\pi$
$167$	−19.4159	+	12.4779i	−1.50245	+	0.965566i	−0.994562	+	0.104143i	$0.966790\pi$
$168$		0			0
$169$	5.14082	+	5.93282i	0.395448	+	0.456371i
$170$	0.0958632	+	0.666744i	0.00735238	+	0.0511369i
$171$		0			0
$172$	1.97590	−	0.580176i	0.150661	−	0.0442380i
$173$	−16.1284	+	4.73572i	−1.22622	+	0.360050i	−0.829822	−	0.558029i	$-0.811558\pi$
$173$	−16.1284	+	4.73572i	−1.22622	+	0.360050i	−0.396397	+	0.918079i	$0.629740\pi$
$174$		0			0
$175$	2.26478	+	15.7519i	0.171201	+	1.19073i
$176$	−0.219409	−	0.253211i	−0.0165385	−	0.0190865i
$177$		0			0
$178$	10.5034	−	6.75009i	0.787259	−	0.505941i
$179$	−2.81762	+	19.5970i	−0.210599	+	1.46475i	0.560564	+	0.828111i	$0.310584\pi$
$179$	−2.81762	+	19.5970i	−0.210599	+	1.46475i	−0.771163	+	0.636637i	$0.780325\pi$
$180$		0			0
$181$	2.85856	−	3.29896i	0.212475	−	0.245210i	−0.639501	−	0.768791i	$-0.720859\pi$
$181$	2.85856	−	3.29896i	0.212475	−	0.245210i	0.851976	+	0.523581i	$0.175404\pi$
$182$	−6.96788	−	2.04595i	−0.516494	−	0.151656i
$183$		0			0
$184$	1.22325	−	4.63720i	0.0901790	−	0.341859i
$185$	−0.302373			−0.0222309
$186$		0			0
$187$	−0.897903	+	1.03624i	−0.0656612	+	0.0757770i
$188$	−6.08835	−	3.91274i	−0.444038	−	0.285366i
$189$		0			0
$190$	−0.180440	+	0.115962i	−0.0130905	+	0.00841274i
$191$	−2.52499	−	5.52896i	−0.182702	−	0.400062i	0.796015	−	0.605277i	$-0.206938\pi$
$191$	−2.52499	−	5.52896i	−0.182702	−	0.400062i	−0.978717	+	0.205216i	$0.934210\pi$
$192$		0			0
$193$	2.46415	+	17.1385i	0.177373	+	1.23366i	0.862811	+	0.505527i	$0.168702\pi$
$193$	2.46415	+	17.1385i	0.177373	+	1.23366i	−0.685437	+	0.728132i	$0.740389\pi$
$194$	5.56987	−	12.1963i	0.399893	−	0.875644i
$195$		0			0
$196$	−3.10947	+	0.913022i	−0.222105	+	0.0652158i
$197$	1.86065	−	4.07425i	0.132566	−	0.290278i	−0.831695	−	0.555232i	$-0.812629\pi$
$197$	1.86065	−	4.07425i	0.132566	−	0.290278i	0.964261	+	0.264954i	$0.0853567\pi$
$198$		0			0
$199$	−1.56996	−	1.81183i	−0.111291	−	0.128437i	0.697370	−	0.716711i	$-0.254353\pi$
$199$	−1.56996	−	1.81183i	−0.111291	−	0.128437i	−0.808662	+	0.588274i	$0.799808\pi$
$200$	2.06582	+	4.52352i	0.146076	+	0.319861i
$201$		0			0
$202$	−0.459558	+	3.19630i	−0.0323344	+	0.224891i
$203$	−5.47440	−	3.51819i	−0.384228	−	0.246928i
$204$		0			0
$205$	1.17973	+	0.346399i	0.0823956	+	0.0241935i
$206$	−13.0304			−0.907873
$207$		0			0
$208$	−2.26931			−0.157348
$209$	−0.418915	−	0.123004i	−0.0289769	−	0.00850839i
$210$		0			0
$211$	−2.43886	−	1.56736i	−0.167898	−	0.107902i	0.453993	−	0.891005i	$-0.349999\pi$
$211$	−2.43886	−	1.56736i	−0.167898	−	0.107902i	−0.621891	+	0.783104i	$0.713635\pi$
$212$	1.85653	−	12.9124i	0.127507	−	0.886829i
$213$		0			0
$214$	5.68833	+	12.4557i	0.388846	+	0.851455i
$215$	0.221972	+	0.256169i	0.0151383	+	0.0174706i
$216$		0			0
$217$	0.419412	−	0.918385i	0.0284716	−	0.0623440i
$218$	7.52452	−	2.20940i	0.509625	−	0.149639i
$219$		0			0
$220$	0.0229094	−	0.0501645i	0.00154455	−	0.00338209i
$221$	1.32166	+	9.19234i	0.0889044	+	0.618343i
$222$		0			0
$223$	9.44237	+	20.6759i	0.632308	+	1.38456i	0.906220	+	0.422806i	$0.138955\pi$
$223$	9.44237	+	20.6759i	0.632308	+	1.38456i	−0.273913	+	0.961755i	$0.588318\pi$
$224$	−2.69211	+	1.73011i	−0.179874	+	0.115598i
$225$		0			0
$226$	−4.68153	−	3.00863i	−0.311411	−	0.200131i
$227$	5.43659	−	6.27416i	0.360839	−	0.416431i	−0.546081	−	0.837732i	$-0.683881\pi$
$227$	5.43659	−	6.27416i	0.360839	−	0.416431i	0.906921	+	0.421301i	$0.138427\pi$
$228$		0			0
$229$	−21.7085			−1.43454			−0.717269	−	0.696796i	$-0.754608\pi$
$229$	−21.7085			−1.43454			−0.717269	+	0.696796i	$0.754608\pi$
$230$	0.777943	−	0.133927i	0.0512960	−	0.00883090i
$231$		0			0
$232$	−1.95113	−	0.572903i	−0.128098	−	0.0376129i
$233$	17.1483	−	19.7902i	1.12342	−	1.29650i	0.173216	−	0.984884i	$-0.444584\pi$
$233$	17.1483	−	19.7902i	1.12342	−	1.29650i	0.950208	−	0.311617i	$-0.100871\pi$
$234$		0			0
$235$	0.169531	−	1.17911i	0.0110590	−	0.0769168i
$236$	−5.23116	+	3.36186i	−0.340519	+	0.218839i
$237$		0			0
$238$	8.57611	+	9.89736i	0.555907	+	0.641551i
$239$	3.35419	+	23.3289i	0.216965	+	1.50902i	0.749153	+	0.662397i	$0.230461\pi$
$239$	3.35419	+	23.3289i	0.216965	+	1.50902i	−0.532188	+	0.846626i	$0.678630\pi$
$240$		0			0
$241$	7.76459	−	2.27989i	0.500161	−	0.146861i	−0.0219142	−	0.999760i	$-0.506976\pi$
$241$	7.76459	−	2.27989i	0.500161	−	0.146861i	0.522076	+	0.852899i	$0.325158\pi$
$242$	−10.4467	+	3.06743i	−0.671540	+	0.197182i
$243$		0			0
$244$	−1.34774	−	9.37375i	−0.0862803	−	0.600093i
$245$	−0.349316	−	0.403133i	−0.0223170	−	0.0257552i
$246$		0			0
$247$	−2.48771	+	1.59875i	−0.158289	+	0.101726i
$248$	0.0448997	−	0.312284i	0.00285114	−	0.0198301i
$249$		0			0
$250$	−1.07497	+	1.24058i	−0.0679871	+	0.0784614i
$251$	−27.3012	−	8.01637i	−1.72324	−	0.505989i	−0.737655	−	0.675177i	$-0.764067\pi$
$251$	−27.3012	−	8.01637i	−1.72324	−	0.505989i	−0.985584	+	0.169189i	$0.945885\pi$
$252$		0			0
$253$	1.24302	+	1.01823i	0.0781479	+	0.0640155i
$254$	−3.10085			−0.194565
$255$		0			0
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	25.0424	+	16.0938i	1.56210	+	1.00390i	0.981893	+	0.189436i	$0.0606659\pi$
$257$	25.0424	+	16.0938i	1.56210	+	1.00390i	0.580210	+	0.814467i	$0.302970\pi$
$258$		0			0
$259$	−4.94549	+	3.17827i	−0.307298	+	0.197488i
$260$	−0.155168	−	0.339770i	−0.00962310	−	0.0210716i
$261$		0			0
$262$	1.07726	+	7.49251i	0.0665534	+	0.462889i
$263$	2.27898	−	4.99028i	0.140528	−	0.307714i	−0.826262	−	0.563286i	$-0.809537\pi$
$263$	2.27898	−	4.99028i	0.140528	−	0.307714i	0.966790	+	0.255573i	$0.0822640\pi$
$264$		0			0
$265$	2.06024	−	0.604942i	0.126560	−	0.0371613i
$266$	−1.73232	+	3.79324i	−0.106215	+	0.232579i
$267$		0			0
$268$	−1.83253	−	2.11485i	−0.111940	−	0.129185i
$269$	8.82453	+	19.3230i	0.538041	+	1.17815i	0.962147	+	0.272533i	$0.0878613\pi$
$269$	8.82453	+	19.3230i	0.538041	+	1.17815i	−0.424105	+	0.905613i	$0.639411\pi$
$270$		0			0
$271$	1.78129	−	12.3891i	0.108205	−	0.752585i	−0.861403	−	0.507923i	$-0.830414\pi$
$271$	1.78129	−	12.3891i	0.108205	−	0.752585i	0.969608	−	0.244663i	$-0.0786773\pi$
$272$	3.44273	+	2.21251i	0.208746	+	0.134153i
$273$		0			0
$274$	−1.52553	−	0.447936i	−0.0921607	−	0.0270608i
$275$	−1.66615			−0.100473
$276$		0			0
$277$	27.3690			1.64444			0.822221	−	0.569168i	$-0.192735\pi$
$277$	27.3690			1.64444			0.822221	+	0.569168i	$0.192735\pi$
$278$	−5.00398	−	1.46930i	−0.300119	−	0.0881229i
$279$		0			0
$280$	−0.443117	−	0.284774i	−0.0264813	−	0.0170185i
$281$	2.94533	−	20.4852i	0.175704	−	1.22205i	−0.690863	−	0.722985i	$-0.742769\pi$
$281$	2.94533	−	20.4852i	0.175704	−	1.22205i	0.866567	−	0.499061i	$-0.166321\pi$
$282$		0			0
$283$	9.23295	+	20.2173i	0.548842	+	1.20180i	0.957321	+	0.289028i	$0.0933322\pi$
$283$	9.23295	+	20.2173i	0.548842	+	1.20180i	−0.408479	+	0.912768i	$0.633941\pi$
$284$	2.79460	+	3.22514i	0.165829	+	0.191377i
$285$		0			0
$286$	0.315849	−	0.691613i	0.0186766	−	0.0408960i
$287$	22.9361	−	6.73466i	1.35388	−	0.397534i
$288$		0			0
$289$	−0.104865	+	0.229622i	−0.00616852	+	0.0135072i
$290$	−0.0476344	−	0.331304i	−0.00279719	−	0.0194549i
$291$		0			0
$292$	−2.30476	−	5.04671i	−0.134876	−	0.295336i
$293$	−12.8694	+	8.27063i	−0.751836	+	0.483176i	−0.859579	−	0.511003i	$-0.829274\pi$
$293$	−12.8694	+	8.27063i	−0.751836	+	0.483176i	0.107743	+	0.994179i	$0.465638\pi$
$294$		0			0
$295$	−0.861041	−	0.553358i	−0.0501318	−	0.0322177i
$296$	−1.20300	+	1.38834i	−0.0699230	+	0.0806954i
$297$		0			0
$298$	9.69690			0.561726
$299$	10.7254	−	1.84644i	0.620268	−	0.106783i
$300$		0			0
$301$	6.32310	+	1.85663i	0.364457	+	0.107014i
$302$	11.3424	−	13.0898i	0.652681	−	0.753234i
$303$		0			0
$304$	−0.185451	+	1.28984i	−0.0106363	+	0.0739774i
$305$	1.31132	−	0.842736i	0.0750861	−	0.0482549i
$306$		0			0
$307$	−16.8228	−	19.4145i	−0.960126	−	1.10804i	−0.994083	−	0.108622i	$-0.965356\pi$
$307$	−16.8228	−	19.4145i	−0.960126	−	1.10804i	0.0339568	−	0.999423i	$-0.489189\pi$
$308$	−0.152588	−	1.06127i	−0.00869451	−	0.0604716i
$309$		0			0
$310$	0.0498266	−	0.0146304i	0.00282996	−	0.000830952i
$311$	−19.4228	+	5.70306i	−1.10137	+	0.323391i	−0.781395	−	0.624036i	$-0.785492\pi$
$311$	−19.4228	+	5.70306i	−1.10137	+	0.323391i	−0.319972	+	0.947427i	$0.603674\pi$
$312$		0			0
$313$	0.804173	+	5.59315i	0.0454546	+	0.316143i	0.999845	+	0.0175833i	$0.00559724\pi$
$313$	0.804173	+	5.59315i	0.0454546	+	0.316143i	−0.954391	+	0.298560i	$0.903494\pi$
$314$	5.83364	+	6.73238i	0.329211	+	0.379930i
$315$		0			0
$316$	9.06794	−	5.82761i	0.510111	−	0.327829i
$317$	−2.73866	+	19.0478i	−0.153818	+	1.06983i	0.755925	+	0.654658i	$0.227187\pi$
$317$	−2.73866	+	19.0478i	−0.153818	+	1.06983i	−0.909743	+	0.415171i	$0.863722\pi$
$318$		0			0
$319$	0.446167	−	0.514905i	0.0249806	−	0.0288291i
$320$	−0.157931	−	0.0463728i	−0.00882862	−	0.00259232i
$321$		0			0
$322$	11.3160	−	10.3675i	0.630616	−	0.577758i
$323$	5.33280			0.296725
$324$		0			0
$325$	−7.39014	+	8.52867i	−0.409931	+	0.473086i
$326$	19.8722	+	12.7711i	1.10062	+	0.707323i
$327$		0			0
$328$	6.28405	−	4.03852i	0.346979	−	0.222990i
$329$	−9.62100	−	21.0671i	−0.530423	−	1.16146i
$330$		0			0
$331$	−2.87785	−	20.0159i	−0.158181	−	1.10017i	−0.901983	−	0.431772i	$-0.857889\pi$
$331$	−2.87785	−	20.0159i	−0.158181	−	1.10017i	0.743802	−	0.668400i	$-0.233020\pi$
$332$	−4.88513	+	10.6969i	−0.268107	+	0.587071i
$333$		0			0
$334$	−22.1449	+	6.50232i	−1.21171	+	0.355791i
$335$	0.191342	−	0.418981i	0.0104541	−	0.0228914i
$336$		0			0
$337$	−18.2175	−	21.0241i	−0.992371	−	1.14526i	−0.989393	−	0.145262i	$-0.953597\pi$
$337$	−18.2175	−	21.0241i	−0.992371	−	1.14526i	−0.00297825	−	0.999996i	$-0.500948\pi$
$338$	3.26111	+	7.14084i	0.177381	+	0.388410i
$339$		0			0
$340$	−0.0958632	+	0.666744i	−0.00519891	+	0.0361592i
$341$	0.0889252	+	0.0571488i	0.00481557	+	0.00309478i
$342$		0			0
$343$	11.5428	+	3.38926i	0.623251	+	0.183003i
$344$	2.05931			0.111031
$345$		0			0
$346$	−16.8093			−0.903673
$347$	−20.2078	−	5.93355i	−1.08481	−	0.318530i	−0.310010	−	0.950733i	$-0.600332\pi$
$347$	−20.2078	−	5.93355i	−1.08481	−	0.318530i	−0.774802	+	0.632204i	$0.782151\pi$
$348$		0			0
$349$	−12.3468	−	7.93479i	−0.660908	−	0.424740i	0.166730	−	0.986003i	$-0.446679\pi$
$349$	−12.3468	−	7.93479i	−0.660908	−	0.424740i	−0.827637	+	0.561263i	$0.810316\pi$
$350$	−2.26478	+	15.7519i	−0.121058	+	0.841974i
$351$		0			0
$352$	−0.139183	−	0.304769i	−0.00741849	−	0.0162442i
$353$	−6.35639	−	7.33567i	−0.338317	−	0.390438i	0.560942	−	0.827855i	$-0.310439\pi$
$353$	−6.35639	−	7.33567i	−0.338317	−	0.390438i	−0.899259	+	0.437417i	$0.855893\pi$
$354$		0			0
$355$	−0.291796	+	0.638944i	−0.0154869	+	0.0339116i
$356$	11.9796	−	3.51753i	0.634918	−	0.186429i
$357$		0			0
$358$	−8.22460	+	18.0094i	−0.434684	+	0.951824i
$359$	3.65264	+	25.4047i	0.192779	+	1.34081i	0.824610	+	0.565702i	$0.191395\pi$
$359$	3.65264	+	25.4047i	0.192779	+	1.34081i	−0.631830	+	0.775107i	$0.717696\pi$
$360$		0			0
$361$	−7.18748	−	15.7384i	−0.378288	−	0.828336i
$362$	3.67219	−	2.35998i	0.193006	−	0.124038i
$363$		0			0
$364$	−6.10922	−	3.92616i	−0.320210	−	0.205787i
$365$	0.598023	−	0.690155i	0.0313019	−	0.0361244i
$366$		0			0
$367$	−14.7857			−0.771805			−0.385902	−	0.922540i	$-0.626110\pi$
$367$	−14.7857			−0.771805			−0.385902	+	0.922540i	$0.626110\pi$
$368$	2.48015	−	4.10474i	0.129287	−	0.213974i
$369$		0			0
$370$	−0.290125	−	0.0851883i	−0.0150829	−	0.00442873i
$371$	27.3379	−	31.5496i	1.41931	−	1.63798i
$372$		0			0
$373$	0.405472	−	2.82012i	0.0209945	−	0.146020i	−0.976628	−	0.214937i	$-0.931045\pi$
$373$	0.405472	−	2.82012i	0.0209945	−	0.146020i	0.997622	+	0.0689171i	$0.0219544\pi$
$374$	−1.15347	+	0.741292i	−0.0596446	+	0.0383313i
$375$		0			0
$376$	−4.73938	−	5.46953i	−0.244415	−	0.282070i
$377$	−0.656731	−	4.56767i	−0.0338234	−	0.235247i
$378$		0			0
$379$	−2.39569	+	0.703438i	−0.123058	+	0.0361332i	−0.342682	−	0.939452i	$-0.611335\pi$
$379$	−2.39569	+	0.703438i	−0.123058	+	0.0361332i	0.219624	+	0.975585i	$0.429517\pi$
$380$	−0.205801	+	0.0604286i	−0.0105574	+	0.00309992i
$381$		0			0
$382$	−0.865024	−	6.01637i	−0.0442585	−	0.307824i
$383$	−4.81630	−	5.55830i	−0.246101	−	0.284016i	0.619237	−	0.785204i	$-0.287442\pi$
$383$	−4.81630	−	5.55830i	−0.246101	−	0.284016i	−0.865338	+	0.501188i	$0.832897\pi$
$384$		0			0
$385$	0.148465	−	0.0954125i	0.00756646	−	0.00486267i
$386$	−2.46415	+	17.1385i	−0.125422	+	0.872329i
$387$		0			0
$388$	8.78034	−	10.1331i	0.445754	−	0.514428i
$389$	−31.3792	−	9.21377i	−1.59099	−	0.467156i	−0.637968	−	0.770063i	$-0.720225\pi$
$389$	−31.3792	−	9.21377i	−1.59099	−	0.467156i	−0.953020	+	0.302906i	$0.902043\pi$
$390$		0			0
$391$	−18.0716	−	7.65577i	−0.913921	−	0.387169i
$392$	−3.24074			−0.163682
$393$		0			0
$394$	2.93313	−	3.38501i	0.147769	−	0.170534i
$395$	1.49257	+	0.959216i	0.0750993	+	0.0482634i
$396$		0			0
$397$	−23.0583	+	14.8187i	−1.15726	+	0.743728i	−0.971072	−	0.238786i	$-0.923251\pi$
$397$	−23.0583	+	14.8187i	−1.15726	+	0.743728i	−0.186191	+	0.982514i	$0.559614\pi$
$398$	−0.995913	−	2.18075i	−0.0499206	−	0.109311i
$399$		0			0
$400$	0.707718	+	4.92229i	0.0353859	+	0.246115i
$401$	6.07478	−	13.3019i	0.303360	−	0.664266i	−0.695148	−	0.718867i	$-0.744661\pi$
$401$	6.07478	−	13.3019i	0.303360	−	0.664266i	0.998508	+	0.0546003i	$0.0173885\pi$
$402$		0			0
$403$	0.686955	−	0.201708i	0.0342197	−	0.0100478i
$404$	−1.34144	+	2.93735i	−0.0667394	+	0.146139i
$405$		0			0
$406$	−4.26146	−	4.91799i	−0.211493	−	0.244076i
$407$	−0.255684	−	0.559870i	−0.0126738	−	0.0277517i
$408$		0			0
$409$	2.19133	−	15.2410i	0.108354	−	0.753620i	−0.861116	−	0.508409i	$-0.830234\pi$
$409$	2.19133	−	15.2410i	0.108354	−	0.753620i	0.969470	−	0.245211i	$-0.0788572\pi$
$410$	1.03435	+	0.664734i	0.0510827	+	0.0328289i
$411$		0			0
$412$	−12.5026	−	3.67110i	−0.615959	−	0.180862i
$413$	−19.8992			−0.979178
$414$		0			0
$415$	−1.93562			−0.0950159
$416$	−2.17738	−	0.639338i	−0.106755	−	0.0313461i
$417$		0			0
$418$	−0.367291	−	0.236044i	−0.0179648	−	0.0115453i
$419$	1.04616	−	7.27619i	0.0511081	−	0.355465i	−0.948180	−	0.317734i	$-0.897078\pi$
$419$	1.04616	−	7.27619i	0.0511081	−	0.355465i	0.999288	−	0.0377307i	$-0.0120129\pi$
$420$		0			0
$421$	−10.3111	−	22.5782i	−0.502533	−	1.10039i	−0.975638	−	0.219388i	$-0.929594\pi$
$421$	−10.3111	−	22.5782i	−0.502533	−	1.10039i	0.473105	−	0.881006i	$-0.343133\pi$
$422$	−1.89849	−	2.19098i	−0.0924173	−	0.106655i
$423$		0			0
$424$	5.41917	−	11.8663i	0.263178	−	0.576280i
$425$	19.5267	−	5.73355i	0.947182	−	0.278118i
$426$		0			0
$427$	12.5894	−	27.5669i	0.609243	−	1.33406i
$428$	1.94874	+	13.5538i	0.0941957	+	0.655146i
$429$		0			0
$430$	0.140809	+	0.308329i	0.00679042	+	0.0148689i
$431$	15.1697	−	9.74895i	0.730697	−	0.469590i	−0.121646	−	0.992574i	$-0.538817\pi$
$431$	15.1697	−	9.74895i	0.730697	−	0.469590i	0.852343	+	0.522983i	$0.175181\pi$
$432$		0			0
$433$	22.1161	+	14.2131i	1.06283	+	0.683039i	0.950529	−	0.310635i	$-0.100542\pi$
$433$	22.1161	+	14.2131i	1.06283	+	0.683039i	0.112301	+	0.993674i	$0.464178\pi$
$434$	0.661162	−	0.763022i	0.0317368	−	0.0366262i
$435$		0			0
$436$	7.84219			0.375573
$437$	−0.172993	−	6.24707i	−0.00827536	−	0.298838i
$438$		0			0
$439$	−7.06867	−	2.07555i	−0.337369	−	0.0990606i	0.108660	−	0.994079i	$-0.465344\pi$
$439$	−7.06867	−	2.07555i	−0.337369	−	0.0990606i	−0.446029	+	0.895018i	$0.647162\pi$
$440$	0.0361143	−	0.0416782i	0.00172168	−	0.00198693i
$441$		0			0
$442$	−1.32166	+	9.19234i	−0.0628649	+	0.437235i
$443$	−8.42814	+	5.41644i	−0.400433	+	0.257343i	−0.725322	−	0.688409i	$-0.758309\pi$
$443$	−8.42814	+	5.41644i	−0.400433	+	0.257343i	0.324889	+	0.945752i	$0.394673\pi$
$444$		0			0
$445$	1.34579	+	1.55312i	0.0637964	+	0.0736249i
$446$	3.23481	+	22.4986i	0.153173	+	1.06534i
$447$		0			0
$448$	−3.07049	+	0.901577i	−0.145067	+	0.0425955i
$449$	−10.1015	+	2.96608i	−0.476721	+	0.139978i	−0.511261	−	0.859426i	$-0.670821\pi$
$449$	−10.1015	+	2.96608i	−0.476721	+	0.139978i	0.0345404	+	0.999403i	$0.489003\pi$
$450$		0			0
$451$	0.356178	+	2.47728i	0.0167718	+	0.116650i
$452$	−3.64426	−	4.20570i	−0.171412	−	0.197820i
$453$		0			0
$454$	6.98401	−	4.48835i	0.327776	−	0.210649i
$455$	0.170112	−	1.18316i	0.00797498	−	0.0554672i
$456$		0			0
$457$	−4.48806	+	5.17950i	−0.209943	+	0.242287i	−0.850948	−	0.525249i	$-0.823972\pi$
$457$	−4.48806	+	5.17950i	−0.209943	+	0.242287i	0.641006	+	0.767536i	$0.278518\pi$
$458$	−20.8292	−	6.11599i	−0.973282	−	0.285782i
$459$		0			0
$460$	0.784163	+	0.0906697i	0.0365618	+	0.00422750i
$461$	−37.9395			−1.76702			−0.883510	−	0.468413i	$-0.844826\pi$
$461$	−37.9395			−1.76702			−0.883510	+	0.468413i	$0.844826\pi$
$462$		0			0
$463$	4.79167	−	5.52988i	0.222688	−	0.256995i	−0.633402	−	0.773823i	$-0.718342\pi$
$463$	4.79167	−	5.52988i	0.222688	−	0.256995i	0.856089	+	0.516828i	$0.172887\pi$
$464$	−1.71069	−	1.09939i	−0.0794168	−	0.0510381i
$465$		0			0
$466$	22.0292	−	14.1573i	1.02049	−	0.655826i
$467$	−12.9128	−	28.2750i	−0.597532	−	1.30841i	−0.930782	−	0.365575i	$-0.880873\pi$
$467$	−12.9128	−	28.2750i	−0.597532	−	1.30841i	0.333250	−	0.942839i	$-0.391855\pi$
$468$		0			0
$469$	−1.27444	−	8.86391i	−0.0588480	−	0.409297i
$470$	0.494858	−	1.08359i	0.0228261	−	0.0499822i
$471$		0			0
$472$	−5.96641	+	1.75189i	−0.274626	+	0.0806375i
$473$	−0.286622	+	0.627614i	−0.0131789	+	0.0288577i
$474$		0			0
$475$	4.24364	+	4.89742i	0.194712	+	0.224709i
$476$	5.44031	+	11.9126i	0.249356	+	0.546014i
$477$		0			0
$478$	−3.35419	+	23.3289i	−0.153417	+	1.06704i
$479$	8.83773	+	5.67966i	0.403806	+	0.259510i	0.726742	−	0.686910i	$-0.241034\pi$
$479$	8.83773	+	5.67966i	0.403806	+	0.259510i	−0.322936	+	0.946421i	$0.604670\pi$
$480$		0			0
$481$	−3.99992	−	1.17448i	−0.182381	−	0.0535518i
$482$	8.09239			0.368598
$483$		0			0
$484$	−10.8877			−0.494897
$485$	2.11753	+	0.621764i	0.0961523	+	0.0282329i
$486$		0			0
$487$	16.0482	+	10.3136i	0.727214	+	0.467352i	0.851140	−	0.524940i	$-0.175912\pi$
$487$	16.0482	+	10.3136i	0.727214	+	0.467352i	−0.123926	+	0.992292i	$0.539548\pi$
$488$	1.34774	−	9.37375i	0.0610094	−	0.424330i
$489$		0			0
$490$	−0.221591	−	0.485217i	−0.0100105	−	0.0219199i
$491$	−10.7526	−	12.4091i	−0.485257	−	0.560016i	0.459335	−	0.888263i	$-0.348088\pi$
$491$	−10.7526	−	12.4091i	−0.485257	−	0.560016i	−0.944592	+	0.328247i	$0.893542\pi$
$492$		0			0
$493$	−3.45702	+	7.56983i	−0.155697	+	0.340928i
$494$	−2.83736	+	0.833124i	−0.127659	+	0.0374840i
$495$		0			0
$496$	0.131062	−	0.286985i	0.00588484	−	0.0128860i
$497$	1.94351	+	13.5174i	0.0871783	+	0.606338i
$498$		0			0
$499$	7.32422	+	16.0378i	0.327877	+	0.717951i	0.999742	−	0.0227230i	$-0.00723357\pi$
$499$	7.32422	+	16.0378i	0.327877	+	0.717951i	−0.671865	+	0.740674i	$0.734506\pi$
$500$	−1.38094	+	0.887476i	−0.0617575	+	0.0396891i
$501$		0			0
$502$	−23.9369	−	15.3833i	−1.06836	−	0.686590i
$503$	11.9472	−	13.7878i	0.532697	−	0.614766i	−0.424067	−	0.905631i	$-0.639398\pi$
$503$	11.9472	−	13.7878i	0.532697	−	0.614766i	0.956764	+	0.290865i	$0.0939432\pi$
$504$		0			0
$505$	−0.531516			−0.0236522
$506$	0.905800	+	1.32718i	0.0402677	+	0.0590004i
$507$		0			0
$508$	−2.97524	−	0.873610i	−0.132005	−	0.0387602i
$509$	5.35907	−	6.18470i	0.237537	−	0.274132i	−0.624448	−	0.781066i	$-0.714676\pi$
$509$	5.35907	−	6.18470i	0.237537	−	0.274132i	0.861985	+	0.506935i	$0.169221\pi$
$510$		0			0
$511$	2.52673	−	17.5738i	0.111776	−	0.777418i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$		0			0
$514$	19.4939	+	22.4971i	0.859838	+	0.992306i
$515$	−0.305236	−	2.12296i	−0.0134503	−	0.0935488i
$516$		0			0
$517$	2.32658	−	0.683147i	0.102323	−	0.0300448i
$518$	−5.64059	+	1.65623i	−0.247833	+	0.0727704i
$519$		0			0
$520$	−0.0531581	−	0.369723i	−0.00233114	−	0.0162134i
$521$	4.84974	+	5.59690i	0.212471	+	0.245204i	0.851974	−	0.523584i	$-0.175405\pi$
$521$	4.84974	+	5.59690i	0.212471	+	0.245204i	−0.639503	+	0.768788i	$0.720860\pi$
$522$		0			0
$523$	−29.8969	+	19.2136i	−1.30730	+	0.840152i	−0.993987	−	0.109497i	$-0.965076\pi$
$523$	−29.8969	+	19.2136i	−1.30730	+	0.840152i	−0.313315	+	0.949649i	$0.601440\pi$
$524$	−1.07726	+	7.49251i	−0.0470603	+	0.327312i
$525$		0			0
$526$	3.59259	−	4.14607i	0.156644	−	0.180777i
$527$	−1.23883	−	0.363753i	−0.0539642	−	0.0158453i
$528$		0			0
$529$	−8.38208	+	21.4182i	−0.364438	+	0.931228i
$530$	2.14722			0.0932694
$531$		0			0
$532$	−2.73082	+	3.15154i	−0.118396	+	0.136637i
$533$	14.2604	+	9.16463i	0.617688	+	0.396964i
$534$		0			0
$535$	−1.89608	+	1.21853i	−0.0819745	+	0.0526818i
$536$	−1.16248	−	2.54547i	−0.0502114	−	0.109948i
$537$		0			0
$538$	3.02315	+	21.0265i	0.130337	+	0.906515i
$539$	0.451056	−	0.987675i	0.0194284	−	0.0425422i
$540$		0			0
$541$	14.8495	−	4.36020i	0.638429	−	0.187460i	0.0535305	−	0.998566i	$-0.482953\pi$
$541$	14.8495	−	4.36020i	0.638429	−	0.187460i	0.584898	+	0.811107i	$0.301134\pi$
$542$	5.19955	−	11.3854i	0.223340	−	0.489046i
$543$		0			0
$544$	2.67994	+	3.09281i	0.114901	+	0.132603i
$545$	0.536223	+	1.17416i	0.0229693	+	0.0502957i
$546$		0			0
$547$	−1.80947	+	12.5851i	−0.0773672	+	0.538101i	0.913870	+	0.406007i	$0.133079\pi$
$547$	−1.80947	+	12.5851i	−0.0773672	+	0.538101i	−0.991237	+	0.132094i	$0.957830\pi$
$548$	−1.33754	−	0.859584i	−0.0571368	−	0.0367196i
$549$		0			0
$550$	−1.59866	−	0.469410i	−0.0681672	−	0.0200157i
$551$	−2.64986			−0.112888
$552$		0			0
$553$	34.4943			1.46685
$554$	26.2603	+	7.71073i	1.11570	+	0.327598i
$555$		0			0
$556$	−4.38734	−	2.81957i	−0.186065	−	0.119576i
$557$	−4.91802	+	34.2056i	−0.208383	+	1.44934i	0.570050	+	0.821610i	$0.306924\pi$
$557$	−4.91802	+	34.2056i	−0.208383	+	1.44934i	−0.778434	+	0.627727i	$0.783985\pi$
$558$		0			0
$559$	1.94132	+	4.25091i	0.0821093	+	0.179794i
$560$	−0.344938	−	0.398079i	−0.0145763	−	0.0168219i
$561$		0			0
$562$	8.59738	−	18.8256i	0.362658	−	0.794111i
$563$	28.2881	−	8.30614i	1.19220	−	0.350062i	0.375335	−	0.926889i	$-0.377528\pi$
$563$	28.2881	−	8.30614i	1.19220	−	0.350062i	0.816866	+	0.576827i	$0.195709\pi$
$564$		0			0
$565$	0.380512	−	0.833206i	0.0160083	−	0.0350532i
$566$	3.16307	+	21.9996i	0.132954	+	0.924713i
$567$		0			0
$568$	1.77277	+	3.88183i	0.0743838	+	0.162878i
$569$	24.4009	−	15.6815i	1.02294	−	0.657403i	0.0822282	−	0.996614i	$-0.473796\pi$
$569$	24.4009	−	15.6815i	1.02294	−	0.657403i	0.940710	+	0.339211i	$0.110160\pi$
$570$		0			0
$571$	16.6739	+	10.7156i	0.697779	+	0.448435i	0.840844	−	0.541278i	$-0.182059\pi$
$571$	16.6739	+	10.7156i	0.697779	+	0.448435i	−0.143065	+	0.989713i	$0.545696\pi$
$572$	0.497905	−	0.574613i	0.0208185	−	0.0240258i
$573$		0			0
$574$	23.9044			0.997752
$575$	−7.34996	−	22.6884i	−0.306515	−	0.946172i
$576$		0			0
$577$	1.52111	+	0.446639i	0.0633248	+	0.0185938i	0.313242	−	0.949673i	$-0.398585\pi$
$577$	1.52111	+	0.446639i	0.0633248	+	0.0185938i	−0.249917	+	0.968267i	$0.580403\pi$
$578$	−0.165309	+	0.190777i	−0.00687595	+	0.00793526i
$579$		0			0
$580$	0.0476344	−	0.331304i	0.00197791	−	0.0137567i
$581$	−31.6582	+	20.3455i	−1.31341	+	0.844074i
$582$		0			0
$583$	2.86223	+	3.30319i	0.118541	+	0.136804i
$584$	−0.789574	−	5.49161i	−0.0326728	−	0.227244i
$585$		0			0
$586$	−14.6782	+	4.30990i	−0.606349	+	0.178040i
$587$	−16.3825	+	4.81034i	−0.676179	+	0.198544i	−0.601753	−	0.798683i	$-0.705531\pi$
$587$	−16.3825	+	4.81034i	−0.676179	+	0.198544i	−0.0744261	+	0.997227i	$0.523712\pi$
$588$		0			0
$589$	−0.0585090	−	0.406939i	−0.00241082	−	0.0167676i
$590$	−0.670264	−	0.773526i	−0.0275943	−	0.0318456i
$591$		0			0
$592$	−1.54541	+	0.993175i	−0.0635159	+	0.0408192i
$593$	−2.18001	+	15.1623i	−0.0895225	+	0.622642i	0.894827	+	0.446414i	$0.147299\pi$
$593$	−2.18001	+	15.1623i	−0.0895225	+	0.622642i	−0.984349	+	0.176229i	$0.943610\pi$
$594$		0			0
$595$	−1.41162	+	1.62909i	−0.0578706	+	0.0667862i
$596$	9.30410	+	2.73193i	0.381111	+	0.111904i
$597$		0			0
$598$	10.8112	+	1.25006i	0.442102	+	0.0511186i
$599$	−43.3961			−1.77312			−0.886558	−	0.462617i	$-0.846911\pi$
$599$	−43.3961			−1.77312			−0.886558	+	0.462617i	$0.846911\pi$
$600$		0			0
$601$	−7.36193	+	8.49612i	−0.300299	+	0.346564i	−0.885766	−	0.464133i	$-0.846366\pi$
$601$	−7.36193	+	8.49612i	−0.300299	+	0.346564i	0.585466	+	0.810697i	$0.300911\pi$
$602$	5.54390	+	3.56285i	0.225952	+	0.145211i
$603$		0			0
$604$	14.5708	−	9.36407i	0.592876	−	0.381019i
$605$	−0.744468	−	1.63016i	−0.0302669	−	0.0662754i
$606$		0			0
$607$	−2.97761	−	20.7097i	−0.120858	−	0.840583i	−0.956588	−	0.291443i	$-0.905865\pi$
$607$	−2.97761	−	20.7097i	−0.120858	−	0.840583i	0.835731	−	0.549140i	$-0.185044\pi$
$608$	−0.541329	+	1.18535i	−0.0219538	+	0.0480721i
$609$		0			0
$610$	1.49563	−	0.439157i	0.0605563	−	0.0177809i
$611$	6.82257	−	14.9393i	0.276012	−	0.604381i
$612$		0			0
$613$	27.7383	+	32.0117i	1.12034	+	1.29294i	0.951621	+	0.307275i	$0.0994170\pi$
$613$	27.7383	+	32.0117i	1.12034	+	1.29294i	0.168717	+	0.985664i	$0.446038\pi$
$614$	−10.6716	−	23.3676i	−0.430672	−	0.943040i
$615$		0			0
$616$	0.152588	−	1.06127i	0.00614795	−	0.0427599i
$617$	24.4065	+	15.6851i	0.982571	+	0.631460i	0.930156	−	0.367166i	$-0.119672\pi$
$617$	24.4065	+	15.6851i	0.982571	+	0.631460i	0.0524150	+	0.998625i	$0.483308\pi$
$618$		0			0
$619$	22.5623	+	6.62489i	0.906855	+	0.266277i	0.701716	−	0.712456i	$-0.252417\pi$
$619$	22.5623	+	6.62489i	0.906855	+	0.266277i	0.205139	+	0.978733i	$0.434236\pi$
$620$	0.0519302			0.00208557
$621$		0			0
$622$	−20.2428			−0.811662
$623$	38.3361	+	11.2565i	1.53591	+	0.450982i
$624$		0			0
$625$	20.6901	+	13.2967i	0.827603	+	0.531868i
$626$	−0.804173	+	5.59315i	−0.0321412	+	0.223547i
$627$		0			0
$628$	3.70061	+	8.10320i	0.147670	+	0.323353i
$629$	4.92313	+	5.68160i	0.196298	+	0.226540i
$630$		0			0
$631$	−10.7263	+	23.4874i	−0.427009	+	0.935018i	0.566794	+	0.823859i	$0.308184\pi$
$631$	−10.7263	+	23.4874i	−0.427009	+	0.935018i	−0.993803	+	0.111159i	$0.964544\pi$
$632$	10.3424	−	3.03682i	0.411401	−	0.120798i
$633$		0			0
$634$	−7.99410	+	17.5046i	−0.317486	+	0.695198i
$635$	−0.0726368	−	0.505200i	−0.00288251	−	0.0200483i
$636$		0			0
$637$	−3.05506	−	6.68964i	−0.121046	−	0.265053i
$638$	0.573160	−	0.368347i	0.0226916	−	0.0145830i
$639$		0			0
$640$	−0.138469	−	0.0889887i	−0.00547347	−	0.00351759i
$641$	9.35718	−	10.7988i	0.369586	−	0.426526i	−0.540242	−	0.841510i	$-0.681667\pi$
$641$	9.35718	−	10.7988i	0.369586	−	0.426526i	0.909829	+	0.414984i	$0.136213\pi$
$642$		0			0
$643$	−8.97463			−0.353925			−0.176962	−	0.984218i	$-0.556627\pi$
$643$	−8.97463			−0.353925			−0.176962	+	0.984218i	$0.556627\pi$
$644$	13.7785	−	6.75946i	0.542948	−	0.266360i
$645$		0			0
$646$	5.11678	+	1.50242i	0.201317	+	0.0591120i
$647$	0.925440	−	1.06801i	0.0363828	−	0.0419880i	−0.737267	−	0.675602i	$-0.763884\pi$
$647$	0.925440	−	1.06801i	0.0363828	−	0.0419880i	0.773649	+	0.633614i	$0.218429\pi$
$648$		0			0
$649$	0.296501	−	2.06221i	0.0116387	−	0.0809487i
$650$	−9.49359	+	6.10116i	−0.372369	+	0.239307i
$651$		0			0
$652$	15.4692	+	17.8524i	0.605819	+	0.699153i
$653$	4.66126	+	32.4198i	0.182409	+	1.26868i	0.851044	+	0.525094i	$0.175970\pi$
$653$	4.66126	+	32.4198i	0.182409	+	1.26868i	−0.668635	+	0.743591i	$0.733121\pi$
$654$		0			0
$655$	−1.19547	+	0.351021i	−0.0467108	+	0.0137155i
$656$	7.16729	−	2.10451i	0.279836	−	0.0821671i
$657$		0			0
$658$	−3.29601	−	22.9242i	−0.128492	−	0.893680i
$659$	2.73057	+	3.15124i	0.106368	+	0.122755i	0.806437	−	0.591320i	$-0.201393\pi$
$659$	2.73057	+	3.15124i	0.106368	+	0.122755i	−0.700069	+	0.714075i	$0.746848\pi$
$660$		0			0
$661$	17.0887	−	10.9823i	0.664674	−	0.427160i	−0.164328	−	0.986406i	$-0.552546\pi$
$661$	17.0887	−	10.9823i	0.664674	−	0.427160i	0.829002	+	0.559246i	$0.188909\pi$
$662$	2.87785	−	20.0159i	0.111851	−	0.777939i
$663$		0			0
$664$	−7.70093	+	8.88735i	−0.298854	+	0.344896i
$665$	−0.658586	−	0.193378i	−0.0255389	−	0.00749889i
$666$		0			0
$667$	8.97977	+	3.80415i	0.347698	+	0.147297i
$668$	−23.0798			−0.892983
$669$		0			0
$670$	0.301632	−	0.348102i	0.0116531	−	0.0134484i
$671$	2.66924	+	1.71542i	0.103045	+	0.0662230i
$672$		0			0
$673$	−34.1127	+	21.9229i	−1.31495	+	0.845065i	−0.994755	−	0.102288i	$-0.967384\pi$
$673$	−34.1127	+	21.9229i	−1.31495	+	0.845065i	−0.320192	+	0.947353i	$0.603747\pi$
$674$	−11.5564	−	25.3050i	−0.445136	−	0.974711i
$675$		0			0
$676$	1.11721	+	7.77034i	0.0429695	+	0.298859i
$677$	−14.8680	+	32.5564i	−0.571425	+	1.25125i	0.374611	+	0.927182i	$0.377776\pi$
$677$	−14.8680	+	32.5564i	−0.571425	+	1.25125i	−0.946035	+	0.324063i	$0.894951\pi$
$678$		0			0
$679$	41.1690	−	12.0883i	1.57992	−	0.463906i
$680$	−0.279823	+	0.612728i	−0.0107307	+	0.0234970i
$681$		0			0
$682$	0.0692224	+	0.0798870i	0.00265066	+	0.00305903i
$683$	6.82062	+	14.9351i	0.260984	+	0.571475i	0.994080	−	0.108650i	$-0.0346528\pi$
$683$	6.82062	+	14.9351i	0.260984	+	0.571475i	−0.733096	+	0.680125i	$0.761925\pi$
$684$		0			0
$685$	0.0372439	−	0.259037i	0.00142302	−	0.00989731i
$686$	10.1203	+	6.50395i	0.386396	+	0.248322i
$687$		0			0
$688$	1.97590	+	0.580176i	0.0753304	+	0.0221190i
$689$	29.6036			1.12781
$690$		0			0
$691$	−39.3617			−1.49739			−0.748696	−	0.662914i	$-0.769320\pi$
$691$	−39.3617			−1.49739			−0.748696	+	0.662914i	$0.769320\pi$
$692$	−16.1284	−	4.73572i	−0.613109	−	0.180025i
$693$		0			0
$694$	−17.7176	−	11.3864i	−0.672550	−	0.432222i
$695$	0.122166	−	0.849683i	0.00463402	−	0.0322303i
$696$		0			0
$697$	−12.6990	−	27.8070i	−0.481011	−	1.05327i
$698$	−9.61115	−	11.0919i	−0.363788	−	0.419833i
$699$		0			0
$700$	−6.61086	+	14.4758i	−0.249867	+	0.547133i
$701$	2.73549	−	0.803213i	0.103318	−	0.0303369i	−0.229665	−	0.973270i	$-0.573763\pi$
$701$	2.73549	−	0.803213i	0.103318	−	0.0303369i	0.332983	+	0.942933i	$0.391945\pi$
$702$		0			0
$703$	−0.994439	+	2.17752i	−0.0375060	+	0.0821266i
$704$	−0.0476820	−	0.331636i	−0.00179708	−	0.0124990i
$705$		0			0
$706$	−4.03222	−	8.82932i	−0.151755	−	0.332296i
$707$	−8.69327	+	5.58682i	−0.326944	+	0.210114i
$708$		0			0
$709$	31.5060	+	20.2477i	1.18323	+	0.760418i	0.975978	−	0.217869i	$-0.0699104\pi$
$709$	31.5060	+	20.2477i	1.18323	+	0.760418i	0.207256	+	0.978287i	$0.433547\pi$
$710$	−0.459987	+	0.530853i	−0.0172630	+	0.0199226i
$711$		0			0
$712$	12.4854			0.467909
$713$	−0.385929	+	1.46302i	−0.0144532	+	0.0547905i
$714$		0			0
$715$	0.120079	+	0.0352583i	0.00449068	+	0.00131858i
$716$	−12.9653	+	14.9627i	−0.484535	+	0.559183i
$717$		0			0
$718$	−3.65264	+	25.4047i	−0.136315	+	0.948095i
$719$	30.8866	−	19.8496i	1.15188	−	0.740266i	0.181864	−	0.983324i	$-0.441787\pi$
$719$	30.8866	−	19.8496i	1.15188	−	0.740266i	0.970012	+	0.243058i	$0.0781505\pi$
$720$		0			0
$721$	−27.3070	−	31.5139i	−1.01696	−	1.17364i
$722$	−2.46232	−	17.1258i	−0.0916381	−	0.637357i
$723$		0			0
$724$	4.18833	−	1.22980i	0.155658	−	0.0457053i
$725$	−9.70279	+	2.84900i	−0.360352	+	0.105809i
$726$		0			0
$727$	4.50409	+	31.3267i	0.167048	+	1.16184i	0.884946	+	0.465693i	$0.154195\pi$
$727$	4.50409	+	31.3267i	0.167048	+	1.16184i	−0.717899	+	0.696148i	$0.754896\pi$
$728$	−4.75563	−	5.48829i	−0.176255	−	0.203409i
$729$		0			0
$730$	0.768238	−	0.493717i	0.0284338	−	0.0182733i
$731$	1.19936	−	8.34172i	0.0443598	−	0.308530i
$732$		0			0
$733$	−20.7193	+	23.9114i	−0.765287	+	0.883188i	−0.995956	−	0.0898444i	$-0.971363\pi$
$733$	−20.7193	+	23.9114i	−0.765287	+	0.883188i	0.230669	+	0.973032i	$0.425908\pi$
$734$	−14.1867	−	4.16560i	−0.523642	−	0.153755i
$735$		0			0
$736$	3.53612	−	3.23973i	0.130343	−	0.119418i
$737$	0.937577			0.0345361
$738$		0			0
$739$	14.5512	−	16.7930i	0.535276	−	0.617741i	−0.422113	−	0.906543i	$-0.638711\pi$
$739$	14.5512	−	16.7930i	0.535276	−	0.617741i	0.957389	+	0.288802i	$0.0932569\pi$
$740$	−0.254372	−	0.163475i	−0.00935091	−	0.00600947i
$741$		0			0
$742$	35.1191	−	22.5697i	1.28926	−	0.828559i
$743$	−19.2474	−	42.1459i	−0.706119	−	1.54618i	−0.832391	−	0.554189i	$-0.813029\pi$
$743$	−19.2474	−	42.1459i	−0.706119	−	1.54618i	0.126272	−	0.991996i	$-0.459699\pi$
$744$		0			0
$745$	0.227148	+	1.57985i	0.00832206	+	0.0578812i
$746$	1.18357	−	2.59165i	0.0433334	−	0.0948870i
$747$		0			0
$748$	−1.31559	+	0.386293i	−0.0481029	+	0.0141243i
$749$	−18.2033	+	39.8597i	−0.665135	+	1.45644i
$750$		0			0
$751$	7.39499	+	8.53428i	0.269847	+	0.311420i	0.874458	−	0.485100i	$-0.161217\pi$
$751$	7.39499	+	8.53428i	0.269847	+	0.311420i	−0.604611	+	0.796521i	$0.706672\pi$
$752$	−3.00645	−	6.58322i	−0.109634	−	0.240065i
$753$		0			0
$754$	0.656731	−	4.56767i	0.0239167	−	0.166345i
$755$	2.39833	+	1.54131i	0.0872841	+	0.0560941i
$756$		0			0
$757$	−31.2231	−	9.16792i	−1.13482	−	0.333214i	−0.340221	−	0.940346i	$-0.610502\pi$
$757$	−31.2231	−	9.16792i	−1.13482	−	0.333214i	−0.794601	+	0.607132i	$0.792320\pi$
$758$	−2.49683			−0.0906888
$759$		0			0
$760$	−0.214489			−0.00778034
$761$	17.0976	+	5.02030i	0.619786	+	0.181986i	0.576527	−	0.817078i	$-0.304408\pi$
$761$	17.0976	+	5.02030i	0.619786	+	0.181986i	0.0432593	+	0.999064i	$0.486226\pi$
$762$		0			0
$763$	21.1120	+	13.5679i	0.764306	+	0.491190i
$764$	0.865024	−	6.01637i	0.0312955	−	0.217665i
$765$		0			0
$766$	−3.05525	−	6.69006i	−0.110391	−	0.241722i
$767$	−9.24088	−	10.6645i	−0.333669	−	0.385074i
$768$		0			0
$769$	2.35590	−	5.15871i	0.0849560	−	0.186028i	−0.862386	−	0.506251i	$-0.831031\pi$
$769$	2.35590	−	5.15871i	0.0849560	−	0.186028i	0.947342	+	0.320224i	$0.103758\pi$
$770$	0.169332	−	0.0497202i	0.00610229	−	0.00179179i
$771$		0			0
$772$	−7.19282	+	15.7501i	−0.258875	+	0.566858i
$773$	7.15654	+	49.7748i	0.257403	+	1.79028i	0.551163	+	0.834398i	$0.314184\pi$
$773$	7.15654	+	49.7748i	0.257403	+	1.79028i	−0.293760	+	0.955879i	$0.594907\pi$
$774$		0			0
$775$	−0.651757	−	1.42715i	−0.0234118	−	0.0512647i
$776$	11.2795	−	7.24889i	0.404910	−	0.260220i
$777$		0			0
$778$	−27.5123	−	17.6811i	−0.986364	−	0.633898i
$779$	6.37443	−	7.35648i	0.228388	−	0.263573i
$780$		0			0
$781$	−1.42980			−0.0511622
$782$	−15.1827	−	12.4370i	−0.542932	−	0.444747i
$783$		0			0
$784$	−3.10947	−	0.913022i	−0.111052	−	0.0326079i
$785$	−0.960209	+	1.10814i	−0.0342713	+	0.0395512i
$786$		0			0
$787$	4.53041	−	31.5097i	0.161492	−	1.12320i	−0.734332	−	0.678790i	$-0.762504\pi$
$787$	4.53041	−	31.5097i	0.161492	−	1.12320i	0.895824	−	0.444409i	$-0.146586\pi$
$788$	3.76798	−	2.42154i	0.134229	−	0.0862637i
$789$		0			0
$790$	1.16187	+	1.34087i	0.0413374	+	0.0477059i
$791$	−2.53441	−	17.6272i	−0.0901132	−	0.626751i
$792$		0			0
$793$	20.6201	−	6.05462i	0.732242	−	0.215006i
$794$	−26.2992	+	7.72214i	−0.933323	+	0.274048i
$795$		0			0
$796$	−0.341185	−	2.37299i	−0.0120930	−	0.0841085i
$797$	13.3852	+	15.4473i	0.474127	+	0.547172i	0.941555	−	0.336859i	$-0.109365\pi$
$797$	13.3852	+	15.4473i	0.474127	+	0.547172i	−0.467428	+	0.884031i	$0.654819\pi$
$798$		0			0
$799$	−24.9158	+	16.0124i	−0.881458	+	0.566479i
$800$	−0.707718	+	4.92229i	−0.0250216	+	0.174029i
$801$		0			0
$802$	9.57630	−	11.0516i	0.338151	−	0.390247i
$803$	1.78357	+	0.523702i	0.0629407	+	0.0184810i
$804$		0			0
$805$	1.95418	+	1.60078i	0.0688759	+	0.0564202i
$806$	0.715957			0.0252185
$807$		0			0
$808$	−2.11465	+	2.44044i	−0.0743933	+	0.0858544i
$809$	−20.5455	−	13.2038i	−0.722341	−	0.464220i	0.127110	−	0.991889i	$-0.459430\pi$
$809$	−20.5455	−	13.2038i	−0.722341	−	0.464220i	−0.849450	+	0.527668i	$0.823066\pi$
$810$		0			0
$811$	4.71928	−	3.03290i	0.165716	−	0.106499i	−0.455154	−	0.890413i	$-0.650416\pi$
$811$	4.71928	−	3.03290i	0.165716	−	0.106499i	0.620870	+	0.783913i	$0.286779\pi$
$812$	−2.70329	−	5.91937i	−0.0948668	−	0.207729i
$813$		0			0
$814$	−0.0875934	−	0.609226i	−0.00307015	−	0.0213533i
$815$	−1.61520	+	3.53679i	−0.0565780	+	0.123889i
$816$		0			0
$817$	2.57480	−	0.756030i	0.0900809	−	0.0264501i
$818$	6.39646	−	14.0063i	0.223647	−	0.489718i
$819$		0			0
$820$	0.805171	+	0.929217i	0.0281178	+	0.0324497i
$821$	−8.22009	−	17.9995i	−0.286883	−	0.628186i	0.710242	−	0.703957i	$-0.248585\pi$
$821$	−8.22009	−	17.9995i	−0.286883	−	0.628186i	−0.997125	+	0.0757713i	$0.975858\pi$
$822$		0			0
$823$	4.58782	−	31.9090i	0.159921	−	1.11228i	−0.738854	−	0.673866i	$-0.764633\pi$
$823$	4.58782	−	31.9090i	0.159921	−	1.11228i	0.898775	−	0.438411i	$-0.144458\pi$
$824$	−10.9619	−	7.04479i	−0.381876	−	0.245417i
$825$		0			0
$826$	−19.0932	−	5.60627i	−0.664337	−	0.195067i
$827$	−7.99830			−0.278128			−0.139064	−	0.990283i	$-0.544409\pi$
$827$	−7.99830			−0.278128			−0.139064	+	0.990283i	$0.544409\pi$
$828$		0			0
$829$	50.1879			1.74310			0.871548	−	0.490310i	$-0.163116\pi$
$829$	50.1879			1.74310			0.871548	+	0.490310i	$0.163116\pi$
$830$	−1.85721	−	0.545327i	−0.0644649	−	0.0189286i
$831$		0			0
$832$	−1.90906	−	1.22688i	−0.0661848	−	0.0425344i
$833$	−1.88743	+	13.1273i	−0.0653955	+	0.454835i
$834$		0			0
$835$	−1.57812	−	3.45560i	−0.0546131	−	0.119586i
$836$	−0.285912	−	0.329960i	−0.00988848	−	0.0114119i
$837$		0			0
$838$	3.05372	−	6.68671i	0.105489	−	0.230989i
$839$	−26.7616	+	7.85792i	−0.923913	+	0.271285i	−0.708886	−	0.705323i	$-0.750802\pi$
$839$	−26.7616	+	7.85792i	−0.923913	+	0.271285i	−0.215027	+	0.976608i	$0.568984\pi$
$840$		0			0
$841$	−10.3292	+	22.6179i	−0.356181	+	0.779927i
$842$	−3.53243	−	24.5686i	−0.121736	−	0.846690i
$843$		0			0
$844$	−1.20432	−	2.63710i	−0.0414545	−	0.0907726i
$845$	−1.08702	+	0.698583i	−0.0373945	+	0.0240320i
$846$		0			0
$847$	−29.3110	−	18.8370i	−1.00714	−	0.647248i
$848$	8.54279	−	9.85891i	0.293361	−	0.338556i
$849$		0			0
$850$	20.3510			0.698034
$851$	6.49597	−	5.95148i	0.222679	−	0.204014i
$852$		0			0
$853$	−33.2530	−	9.76397i	−1.13856	−	0.334312i	−0.342494	−	0.939520i	$-0.611272\pi$
$853$	−33.2530	−	9.76397i	−1.13856	−	0.334312i	−0.796067	+	0.605208i	$0.793090\pi$
$854$	19.8459	−	22.9034i	0.679113	−	0.783738i
$855$		0			0
$856$	−1.94874	+	13.5538i	−0.0666064	+	0.463258i
$857$	−22.4282	+	14.4137i	−0.766132	+	0.492363i	−0.864405	−	0.502797i	$-0.832304\pi$
$857$	−22.4282	+	14.4137i	−0.766132	+	0.492363i	0.0982731	+	0.995159i	$0.468668\pi$
$858$		0			0
$859$	−30.6380	−	35.3582i	−1.04536	−	1.20641i	−0.977985	−	0.208677i	$-0.933084\pi$
$859$	−30.6380	−	35.3582i	−1.04536	−	1.20641i	−0.0673716	−	0.997728i	$-0.521461\pi$
$860$	0.0482391	+	0.335510i	0.00164494	+	0.0114408i
$861$		0			0
$862$	17.3018	−	5.08026i	0.589301	−	0.173034i
$863$	18.8234	−	5.52705i	0.640756	−	0.188143i	0.0548148	−	0.998497i	$-0.482543\pi$
$863$	18.8234	−	5.52705i	0.640756	−	0.188143i	0.585941	+	0.810354i	$0.300725\pi$
$864$		0			0
$865$	−0.393754	−	2.73862i	−0.0133881	−	0.0931160i
$866$	17.2159	+	19.8682i	0.585020	+	0.675149i
$867$		0			0
$868$	0.849349	−	0.545843i	0.0288288	−	0.0185271i
$869$	−0.513968	+	3.57473i	−0.0174352	+	0.121264i
$870$		0			0
$871$	4.15858	−	4.79925i	0.140908	−	0.162617i
$872$	7.52452	+	2.20940i	0.254812	+	0.0748197i
$873$		0			0
$874$	1.59402	−	6.04276i	0.0539185	−	0.204399i
$875$	−5.25307			−0.177586
$876$		0			0
$877$	23.4025	−	27.0079i	0.790246	−	0.911993i	−0.207558	−	0.978223i	$-0.566552\pi$
$877$	23.4025	−	27.0079i	0.790246	−	0.911993i	0.997804	+	0.0662299i	$0.0210971\pi$
$878$	−6.19759	−	3.98295i	−0.209159	−	0.134418i
$879$		0			0
$880$	0.0463935	−	0.0298153i	0.00156393	−	0.00100507i
$881$	−2.39648	−	5.24756i	−0.0807394	−	0.176795i	0.864957	−	0.501846i	$-0.167346\pi$
$881$	−2.39648	−	5.24756i	−0.0807394	−	0.176795i	−0.945696	+	0.325051i	$0.894618\pi$
$882$		0			0
$883$	−4.81367	−	33.4798i	−0.161993	−	1.12668i	−0.894871	−	0.446325i	$-0.852733\pi$
$883$	−4.81367	−	33.4798i	−0.161993	−	1.12668i	0.732878	−	0.680360i	$-0.238176\pi$
$884$	−3.85790	+	8.44763i	−0.129755	+	0.284124i
$885$		0			0
$886$	−9.61273	+	2.82255i	−0.322946	+	0.0948255i
$887$	−0.692651	+	1.51669i	−0.0232570	+	0.0509256i	−0.920904	−	0.389789i	$-0.872548\pi$
$887$	−0.692651	+	1.51669i	−0.0232570	+	0.0509256i	0.897647	+	0.440715i	$0.145275\pi$
$888$		0			0
$889$	−6.49823	−	7.49936i	−0.217944	−	0.251520i
$890$	0.853708	+	1.86936i	0.0286164	+	0.0626611i
$891$		0			0
$892$	−3.23481	+	22.4986i	−0.108309	+	0.753309i
$893$	−7.93375	−	5.09871i	−0.265493	−	0.170622i
$894$		0			0
$895$	−3.12680	−	0.918112i	−0.104518	−	0.0306891i
$896$	−3.20012			−0.106908
$897$		0			0
$898$	−10.5280			−0.351323
$899$	0.615573	+	0.180749i	0.0205305	+	0.00602830i
$900$		0			0
$901$	−44.9111	−	28.8626i	−1.49621	−	0.961553i
$902$	−0.356178	+	2.47728i	−0.0118594	+	0.0824843i
$903$		0			0
$904$	−2.31176	−	5.06205i	−0.0768880	−	0.168361i
$905$	0.470515	+	0.543004i	0.0156405	+	0.0180501i
$906$		0			0
$907$	−10.4870	+	22.9633i	−0.348215	+	0.762485i	0.651776	+	0.758411i	$0.274024\pi$
$907$	−10.4870	+	22.9633i	−0.348215	+	0.762485i	−0.999992	+	0.00407406i	$0.998703\pi$
$908$	7.96562	−	2.33892i	0.264348	−	0.0776197i
$909$		0			0
$910$	0.496555	−	1.08730i	0.0164606	−	0.0360438i
$911$	0.0411855	+	0.286451i	0.00136454	+	0.00949056i	0.990492	−	0.137568i	$-0.0439285\pi$
$911$	0.0411855	+	0.286451i	0.00136454	+	0.00949056i	−0.989128	+	0.147058i	$0.953019\pi$
$912$		0			0
$913$	−1.63674	−	3.58397i	−0.0541683	−	0.118612i
$914$	−5.76550	+	3.70526i	−0.190706	+	0.122559i
$915$		0			0
$916$	−18.2624	−	11.7365i	−0.603405	−	0.387785i
$917$	−15.8630	+	18.3069i	−0.523842	+	0.604546i
$918$		0			0
$919$	−25.1986			−0.831226			−0.415613	−	0.909542i	$-0.636433\pi$
$919$	−25.1986			−0.831226			−0.415613	+	0.909542i	$0.636433\pi$
$920$	0.726854	+	0.307921i	0.0239637	+	0.0101519i
$921$		0			0
$922$	−36.4027	−	10.6888i	−1.19886	−	0.352017i
$923$	−6.34180	+	7.31883i	−0.208743	+	0.240902i
$924$		0			0
$925$	−1.30010	+	9.04241i	−0.0427471	+	0.297312i
$926$	6.15552	−	3.95591i	0.202283	−	0.129999i
$927$		0			0
$928$	−1.33166	−	1.53682i	−0.0437139	−	0.0504485i
$929$	0.266643	+	1.85454i	0.00874826	+	0.0608455i	0.993728	−	0.111825i	$-0.0356696\pi$
$929$	0.266643	+	1.85454i	0.00874826	+	0.0608455i	−0.984980	+	0.172670i	$0.944760\pi$
$930$		0			0
$931$	−4.05196	+	1.18976i	−0.132798	+	0.0389929i
$932$	25.1255	−	7.37751i	0.823013	−	0.241658i
$933$		0			0
$934$	−4.42372	−	30.7677i	−0.144749	−	1.00675i
$935$	−0.147794	−	0.170563i	−0.00483337	−	0.00557800i
$936$		0			0
$937$	−44.3286	+	28.4883i	−1.44815	+	0.930671i	−0.448840	+	0.893612i	$0.648163\pi$
$937$	−44.3286	+	28.4883i	−1.44815	+	0.930671i	−0.999313	+	0.0370593i	$0.988201\pi$
$938$	1.27444	−	8.86391i	0.0416119	−	0.289417i
$939$		0			0
$940$	0.780095	−	0.900278i	0.0254439	−	0.0293638i
$941$	13.8604	+	4.06978i	0.451836	+	0.132671i	0.499730	−	0.866181i	$-0.333433\pi$
$941$	13.8604	+	4.06978i	0.451836	+	0.132671i	−0.0478937	+	0.998852i	$0.515251\pi$
$942$		0			0
$943$	−32.1624	+	15.7783i	−1.04735	+	0.513811i
$944$	−6.21829			−0.202388
$945$		0			0
$946$	−0.451831	+	0.521441i	−0.0146903	+	0.0169535i
$947$	47.1319	+	30.2898i	1.53158	+	0.984287i	0.989592	+	0.143900i	$0.0459644\pi$
$947$	47.1319	+	30.2898i	1.53158	+	0.984287i	0.541988	+	0.840387i	$0.317672\pi$
$948$		0			0
$949$	10.5916	−	6.80683i	0.343819	−	0.220959i
$950$	2.69198	+	5.89461i	0.0873393	+	0.191246i
$951$		0			0
$952$	1.86377	+	12.9628i	0.0604050	+	0.420126i
$953$	2.58173	−	5.65320i	0.0836304	−	0.183125i	−0.863197	−	0.504868i	$-0.831541\pi$
$953$	2.58173	−	5.65320i	0.0836304	−	0.183125i	0.946827	+	0.321743i	$0.104269\pi$
$954$		0			0
$955$	0.959944	−	0.281865i	0.0310630	−	0.00912093i
$956$	−9.79085	+	21.4390i	−0.316659	+	0.693386i
$957$		0			0
$958$	6.87959	+	7.93947i	0.222270	+	0.256513i
$959$	−2.11362	−	4.62818i	−0.0682524	−	0.149452i
$960$		0			0
$961$	4.39759	−	30.5859i	0.141858	−	0.986643i
$962$	−3.50701	−	2.25382i	−0.113070	−	0.0726660i
$963$		0			0
$964$	7.76459	+	2.27989i	0.250081	+	0.0734303i
$965$	−2.84999			−0.0917444
$966$		0			0
$967$	10.4615			0.336419			0.168209	−	0.985751i	$-0.446202\pi$
$967$	10.4615			0.336419			0.168209	+	0.985751i	$0.446202\pi$
$968$	−10.4467	−	3.06743i	−0.335770	−	0.0985910i
$969$		0			0
$970$	1.85659	+	1.19316i	0.0596115	+	0.0383100i
$971$	1.02231	−	7.11029i	0.0328073	−	0.228180i	−0.966821	−	0.255456i	$-0.917774\pi$
$971$	1.02231	−	7.11029i	0.0328073	−	0.228180i	0.999628	+	0.0272763i	$0.00868339\pi$
$972$		0			0
$973$	−6.93301	−	15.1812i	−0.222262	−	0.486686i
$974$	12.4925	+	14.4171i	0.400285	+	0.461953i
$975$		0			0
$976$	3.93404	−	8.61434i	0.125926	−	0.275738i
$977$	25.7672	−	7.56592i	0.824364	−	0.242055i	0.157770	−	0.987476i	$-0.449570\pi$
$977$	25.7672	−	7.56592i	0.824364	−	0.242055i	0.666594	+	0.745421i	$0.267751\pi$
$978$		0			0
$979$	−1.73775	+	3.80515i	−0.0555388	+	0.121613i
$980$	−0.0759137	−	0.527992i	−0.00242498	−	0.0168661i
$981$		0			0
$982$	−6.82096	−	14.9358i	−0.217666	−	0.476621i
$983$	8.70959	−	5.59731i	0.277793	−	0.178527i	−0.394325	−	0.918971i	$-0.629021\pi$
$983$	8.70959	−	5.59731i	0.277793	−	0.178527i	0.672117	+	0.740445i	$0.265385\pi$
$984$		0			0
$985$	0.620205	+	0.398581i	0.0197614	+	0.0126999i
$986$	−5.44966	+	6.28924i	−0.173552	+	0.200290i
$987$		0			0
$988$	−2.95714			−0.0940793
$989$	−9.81076	−	1.13438i	−0.311964	−	0.0360712i
$990$		0			0
$991$	30.4115	+	8.92963i	0.966054	+	0.283659i	0.726456	−	0.687213i	$-0.241166\pi$
$991$	30.4115	+	8.92963i	0.966054	+	0.283659i	0.239598	+	0.970872i	$0.422984\pi$
$992$	0.206606	−	0.238436i	0.00655974	−	0.00757034i
$993$		0			0
$994$	−1.94351	+	13.5174i	−0.0616443	+	0.428746i
$995$	0.331965	−	0.213341i	0.0105240	−	0.00676336i
$996$		0			0
$997$	−11.1067	−	12.8178i	−0.351753	−	0.405945i	0.552107	−	0.833774i	$-0.313824\pi$
$997$	−11.1067	−	12.8178i	−0.351753	−	0.405945i	−0.903860	+	0.427829i	$0.859279\pi$
$998$	2.50917	+	17.4516i	0.0794263	+	0.552422i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.271.1	yes	20
3.2	odd	2		414.2.i.g.271.2	yes	20
23.3	even	11		9522.2.a.cg.1.7		10
23.9	even	11	inner	414.2.i.h.55.1	yes	20
23.20	odd	22		9522.2.a.ch.1.4		10
69.20	even	22		9522.2.a.ci.1.7		10
69.26	odd	22		9522.2.a.cj.1.4		10
69.32	odd	22		414.2.i.g.55.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.55.2	✓	20	69.32	odd	22
414.2.i.g.271.2	yes	20	3.2	odd	2
414.2.i.h.55.1	yes	20	23.9	even	11	inner
414.2.i.h.271.1	yes	20	1.1	even	1	trivial
9522.2.a.cg.1.7		10	23.3	even	11
9522.2.a.ch.1.4		10	23.20	odd	22
9522.2.a.ci.1.7		10	69.20	even	22
9522.2.a.cj.1.4		10	69.26	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)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.0234248 + 0.162923i) q^{5} +(1.32938 + 2.91093i) q^{7} +(0.654861 + 0.755750i) q^{8} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(0.841254 + 0.540641i) q^{4} +(-0.0234248 + 0.162923i) q^{5} +(1.32938 + 2.91093i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.0683767 + 0.149724i) q^{10} +(-0.321474 + 0.0943934i) q^{11} +(-0.942704 + 2.06423i) q^{13} +(0.455424 + 3.16754i) q^{14} +(0.415415 + 0.909632i) q^{16} +(3.44273 - 2.21251i) q^{17} +(1.09624 + 0.704511i) q^{19} +(-0.107789 + 0.124395i) q^{20} -0.335046 q^{22} +(-2.70351 - 3.96119i) q^{23} +(4.77147 + 1.40103i) q^{25} +(-1.48608 + 1.71503i) q^{26} +(-0.455424 + 3.16754i) q^{28} +(-1.71069 + 1.09939i) q^{29} +(-0.206606 - 0.238436i) q^{31} +(0.142315 + 0.989821i) q^{32} +(3.92661 - 1.15296i) q^{34} +(-0.505398 + 0.148398i) q^{35} +(0.261437 + 1.81833i) q^{37} +(0.853352 + 0.984821i) q^{38} +(-0.138469 + 0.0889887i) q^{40} +(1.06307 - 7.39384i) q^{41} +(1.34856 - 1.55633i) q^{43} +(-0.321474 - 0.0943934i) q^{44} +(-1.47800 - 4.56240i) q^{46} -7.23723 q^{47} +(-2.12223 + 2.44919i) q^{49} +(4.18348 + 2.68856i) q^{50} +(-1.90906 + 1.22688i) q^{52} +(-5.41917 - 11.8663i) q^{53} +(-0.00784839 - 0.0545868i) q^{55} +(-1.32938 + 2.91093i) q^{56} +(-1.95113 + 0.572903i) q^{58} +(-2.58317 + 5.65636i) q^{59} +(-6.20162 - 7.15706i) q^{61} +(-0.131062 - 0.286985i) q^{62} +(-0.142315 + 0.989821i) q^{64} +(-0.314229 - 0.201943i) q^{65} +(-2.68500 - 0.788387i) q^{67} +4.09238 q^{68} -0.526734 q^{70} +(4.09461 + 1.20229i) q^{71} +(-4.66734 - 2.99952i) q^{73} +(-0.261437 + 1.81833i) q^{74} +(0.541329 + 1.18535i) q^{76} +(-0.702133 - 0.810304i) q^{77} +(4.47779 - 9.80499i) q^{79} +(-0.157931 + 0.0463728i) q^{80} +(3.10310 - 6.79483i) q^{82} +(1.67357 + 11.6399i) q^{83} +(0.279823 + 0.612728i) q^{85} +(1.73241 - 1.11335i) q^{86} +(-0.281859 - 0.181140i) q^{88} +(8.17617 - 9.43580i) q^{89} -7.26204 q^{91} +(-0.132754 - 4.79399i) q^{92} +(-6.94407 - 2.03896i) q^{94} +(-0.140461 + 0.162100i) q^{95} +(1.90815 - 13.2715i) q^{97} +(-2.72628 + 1.75208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

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