LMFDB - Embedded newform 950.2.e.o.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 10x^{8} - 12x^{7} + 85x^{6} - 70x^{5} + 186x^{4} - 110x^{3} + 285x^{2} - 150x + 100 $ x^10 + 10x^8 - 12x^7 + 85x^6 - 70x^5 + 186x^4 - 110x^3 + 285x^2 - 150x + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.2
Root			$0.741409 - 1.28416i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.o.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.741409 + 1.28416i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.741409 + 1.28416i) q^{6} -0.482818 q^{7} -1.00000 q^{8} +(0.400626 + 0.693904i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.741409 + 1.28416i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.741409 + 1.28416i) q^{6} -0.482818 q^{7} -1.00000 q^{8} +(0.400626 + 0.693904i) q^{9} -4.43782 q^{11} +1.48282 q^{12} +(-2.07118 - 3.58738i) q^{13} +(-0.241409 + 0.418132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.94930 - 6.84039i) q^{17} +0.801252 q^{18} +(4.31875 + 0.590253i) q^{19} +(0.357965 - 0.620014i) q^{21} +(-2.21891 + 3.84326i) q^{22} +(-2.82977 - 4.90130i) q^{23} +(0.741409 - 1.28416i) q^{24} -4.14235 q^{26} -5.63656 q^{27} +(0.241409 + 0.418132i) q^{28} +(-1.91196 - 3.31161i) q^{29} +7.58017 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.29024 - 5.69885i) q^{33} +(-3.94930 - 6.84039i) q^{34} +(0.400626 - 0.693904i) q^{36} -3.50579 q^{37} +(2.67055 - 3.44502i) q^{38} +6.14235 q^{39} +(4.44930 - 7.70641i) q^{41} +(-0.357965 - 0.620014i) q^{42} +(0.318434 - 0.551544i) q^{43} +(2.21891 + 3.84326i) q^{44} -5.65953 q^{46} +(2.13055 + 3.69022i) q^{47} +(-0.741409 - 1.28416i) q^{48} -6.76689 q^{49} +(5.85609 + 10.1430i) q^{51} +(-2.07118 + 3.58738i) q^{52} +(-1.59368 - 2.76033i) q^{53} +(-2.81828 + 4.88141i) q^{54} +0.482818 q^{56} +(-3.95994 + 5.10834i) q^{57} -3.82392 q^{58} +(-0.812584 + 1.40744i) q^{59} +(-0.735243 - 1.27348i) q^{61} +(3.79008 - 6.56462i) q^{62} +(-0.193429 - 0.335029i) q^{63} +1.00000 q^{64} +(-3.29024 - 5.69885i) q^{66} +(-6.59750 - 11.4272i) q^{67} -7.89860 q^{68} +8.39206 q^{69} +(-1.41164 + 2.44504i) q^{71} +(-0.400626 - 0.693904i) q^{72} +(3.43828 - 5.95528i) q^{73} +(-1.75289 + 3.03610i) q^{74} +(-1.64820 - 4.03527i) q^{76} +2.14266 q^{77} +(3.07118 - 5.31943i) q^{78} +(0.576026 - 0.997706i) q^{79} +(2.97712 - 5.15652i) q^{81} +(-4.44930 - 7.70641i) q^{82} -12.4044 q^{83} -0.715931 q^{84} +(-0.318434 - 0.551544i) q^{86} +5.67017 q^{87} +4.43782 q^{88} +(-4.37859 - 7.58395i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-2.82977 + 4.90130i) q^{92} +(-5.62000 + 9.73413i) q^{93} +4.26110 q^{94} -1.48282 q^{96} +(0.476652 - 0.825585i) q^{97} +(-3.38344 + 5.86030i) q^{98} +(-1.77790 - 3.07942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9	$ 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{13} + 5 q^{14} - 5 q^{16} - 4 q^{17} - 10 q^{18} + 11 q^{19} + 20 q^{21} - 3 q^{22} - 13 q^{23} + 4 q^{26} - 36 q^{27} - 5 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} - 2 q^{33} + 4 q^{34} - 5 q^{36} - 10 q^{37} + 13 q^{38} + 16 q^{39} + q^{41} - 20 q^{42} + 3 q^{44} - 26 q^{46} + 10 q^{47} - 20 q^{49} + 4 q^{51} + 2 q^{52} - 5 q^{53} - 18 q^{54} - 10 q^{56} + 10 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{61} - 4 q^{62} - 23 q^{63} + 10 q^{64} + 2 q^{66} - 4 q^{67} + 8 q^{68} - 24 q^{69} - 22 q^{71} + 5 q^{72} - 26 q^{73} - 5 q^{74} + 2 q^{76} - 10 q^{77} + 8 q^{78} + 2 q^{79} - 5 q^{81} - q^{82} - 12 q^{83} - 40 q^{84} + 20 q^{87} + 6 q^{88} - q^{89} + 10 q^{91} - 13 q^{92} - 6 q^{93} + 20 q^{94} - 8 q^{97} - 10 q^{98} + 13 q^{99}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^13 + 5 * q^14 - 5 * q^16 - 4 * q^17 - 10 * q^18 + 11 * q^19 + 20 * q^21 - 3 * q^22 - 13 * q^23 + 4 * q^26 - 36 * q^27 - 5 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 - 2 * q^33 + 4 * q^34 - 5 * q^36 - 10 * q^37 + 13 * q^38 + 16 * q^39 + q^41 - 20 * q^42 + 3 * q^44 - 26 * q^46 + 10 * q^47 - 20 * q^49 + 4 * q^51 + 2 * q^52 - 5 * q^53 - 18 * q^54 - 10 * q^56 + 10 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^61 - 4 * q^62 - 23 * q^63 + 10 * q^64 + 2 * q^66 - 4 * q^67 + 8 * q^68 - 24 * q^69 - 22 * q^71 + 5 * q^72 - 26 * q^73 - 5 * q^74 + 2 * q^76 - 10 * q^77 + 8 * q^78 + 2 * q^79 - 5 * q^81 - q^82 - 12 * q^83 - 40 * q^84 + 20 * q^87 + 6 * q^88 - q^89 + 10 * q^91 - 13 * q^92 - 6 * q^93 + 20 * q^94 - 8 * q^97 - 10 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.741409	+	1.28416i	−0.428053	+	0.741409i	−0.996700	−	0.0811725i	$-0.974134\pi$
$3$	−0.741409	+	1.28416i	−0.428053	+	0.741409i	0.568647	+	0.822581i	$0.307467\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.741409	+	1.28416i	0.302679	+	0.524255i
$7$	−0.482818			−0.182488			−0.0912440	−	0.995829i	$-0.529084\pi$
$7$	−0.482818			−0.182488			−0.0912440	+	0.995829i	$0.529084\pi$
$8$	−1.00000			−0.353553
$9$	0.400626	+	0.693904i	0.133542	+	0.231301i
$10$		0			0
$11$	−4.43782			−1.33805			−0.669026	−	0.743239i	$-0.733288\pi$
$11$	−4.43782			−1.33805			−0.669026	+	0.743239i	$0.733288\pi$
$12$	1.48282			0.428053
$13$	−2.07118	−	3.58738i	−0.574441	−	0.994960i	−0.996102	−	0.0882071i	$-0.971886\pi$
$13$	−2.07118	−	3.58738i	−0.574441	−	0.994960i	0.421661	−	0.906753i	$-0.361447\pi$
$14$	−0.241409	+	0.418132i	−0.0645192	+	0.111751i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.94930	−	6.84039i	0.957846	−	1.65904i	0.230129	−	0.973160i	$-0.426085\pi$
$17$	3.94930	−	6.84039i	0.957846	−	1.65904i	0.727717	−	0.685878i	$-0.240581\pi$
$18$	0.801252			0.188857
$19$	4.31875	+	0.590253i	0.990789	+	0.135413i
$19$	4.31875	+	0.590253i	0.990789	+	0.135413i
$20$		0			0
$21$	0.357965	−	0.620014i	0.0781144	−	0.135298i
$22$	−2.21891	+	3.84326i	−0.473073	+	0.819386i
$23$	−2.82977	−	4.90130i	−0.590047	−	1.02199i	−0.994225	−	0.107311i	$-0.965776\pi$
$23$	−2.82977	−	4.90130i	−0.590047	−	1.02199i	0.404178	−	0.914680i	$-0.367557\pi$
$24$	0.741409	−	1.28416i	0.151339	−	0.262128i
$25$		0			0
$26$	−4.14235			−0.812382
$27$	−5.63656			−1.08476
$28$	0.241409	+	0.418132i	0.0456220	+	0.0790196i
$29$	−1.91196	−	3.31161i	−0.355042	−	0.614950i	0.632083	−	0.774900i	$-0.282200\pi$
$29$	−1.91196	−	3.31161i	−0.355042	−	0.614950i	−0.987125	+	0.159950i	$0.948867\pi$
$30$		0			0
$31$	7.58017			1.36144			0.680719	−	0.732545i	$-0.261667\pi$
$31$	7.58017			1.36144			0.680719	+	0.732545i	$0.261667\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.29024	−	5.69885i	0.572756	−	0.992043i
$34$	−3.94930	−	6.84039i	−0.677299	−	1.17312i
$35$		0			0
$36$	0.400626	−	0.693904i	0.0667710	−	0.115651i
$37$	−3.50579			−0.576348			−0.288174	−	0.957578i	$-0.593048\pi$
$37$	−3.50579			−0.576348			−0.288174	+	0.957578i	$0.593048\pi$
$38$	2.67055	−	3.44502i	0.433220	−	0.558856i
$39$	6.14235			0.983563
$40$		0			0
$41$	4.44930	−	7.70641i	0.694864	−	1.20354i	−0.275363	−	0.961340i	$-0.588798\pi$
$41$	4.44930	−	7.70641i	0.694864	−	1.20354i	0.970227	−	0.242199i	$-0.0778687\pi$
$42$	−0.357965	−	0.620014i	−0.0552352	−	0.0956702i
$43$	0.318434	−	0.551544i	0.0485607	−	0.0841097i	−0.840723	−	0.541465i	$-0.817870\pi$
$43$	0.318434	−	0.551544i	0.0485607	−	0.0841097i	0.889284	+	0.457355i	$0.151203\pi$
$44$	2.21891	+	3.84326i	0.334513	+	0.579393i
$45$		0			0
$46$	−5.65953			−0.834453
$47$	2.13055	+	3.69022i	0.310773	+	0.538274i	0.978530	−	0.206105i	$-0.0660789\pi$
$47$	2.13055	+	3.69022i	0.310773	+	0.538274i	−0.667757	+	0.744379i	$0.732746\pi$
$48$	−0.741409	−	1.28416i	−0.107013	−	0.185352i
$49$	−6.76689			−0.966698
$50$		0			0
$51$	5.85609	+	10.1430i	0.820017	+	1.42031i
$52$	−2.07118	+	3.58738i	−0.287220	+	0.497480i
$53$	−1.59368	−	2.76033i	−0.218908	−	0.379160i	0.735566	−	0.677453i	$-0.236916\pi$
$53$	−1.59368	−	2.76033i	−0.218908	−	0.379160i	−0.954474	+	0.298293i	$0.903583\pi$
$54$	−2.81828	+	4.88141i	−0.383520	+	0.664275i
$55$		0			0
$56$	0.482818			0.0645192
$57$	−3.95994	+	5.10834i	−0.524507	+	0.676616i
$58$	−3.82392			−0.502105
$59$	−0.812584	+	1.40744i	−0.105789	+	0.183233i	−0.914060	−	0.405578i	$-0.867070\pi$
$59$	−0.812584	+	1.40744i	−0.105789	+	0.183233i	0.808271	+	0.588811i	$0.200404\pi$
$60$		0			0
$61$	−0.735243	−	1.27348i	−0.0941382	−	0.163052i	0.815110	−	0.579306i	$-0.196676\pi$
$61$	−0.735243	−	1.27348i	−0.0941382	−	0.163052i	−0.909249	+	0.416253i	$0.863343\pi$
$62$	3.79008	−	6.56462i	0.481341	−	0.833707i
$63$	−0.193429	−	0.335029i	−0.0243698	−	0.0422097i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.29024	−	5.69885i	−0.405000	−	0.701481i
$67$	−6.59750	−	11.4272i	−0.806013	−	1.39606i	−0.915605	−	0.402079i	$-0.868288\pi$
$67$	−6.59750	−	11.4272i	−0.806013	−	1.39606i	0.109592	−	0.993977i	$-0.465046\pi$
$68$	−7.89860			−0.957846
$69$	8.39206			1.01028
$70$		0			0
$71$	−1.41164	+	2.44504i	−0.167531	+	0.290172i	−0.937551	−	0.347847i	$-0.886913\pi$
$71$	−1.41164	+	2.44504i	−0.167531	+	0.290172i	0.770020	+	0.638020i	$0.220246\pi$
$72$	−0.400626	−	0.693904i	−0.0472142	−	0.0817774i
$73$	3.43828	−	5.95528i	0.402421	−	0.697013i	−0.591597	−	0.806234i	$-0.701502\pi$
$73$	3.43828	−	5.95528i	0.402421	−	0.697013i	0.994017	+	0.109221i	$0.0348356\pi$
$74$	−1.75289	+	3.03610i	−0.203770	+	0.352940i
$75$		0			0
$76$	−1.64820	−	4.03527i	−0.189062	−	0.462878i
$77$	2.14266			0.244178
$78$	3.07118	−	5.31943i	0.347742	−	0.602307i
$79$	0.576026	−	0.997706i	0.0648080	−	0.112251i	−0.831801	−	0.555074i	$-0.812690\pi$
$79$	0.576026	−	0.997706i	0.0648080	−	0.112251i	0.896609	+	0.442824i	$0.146023\pi$
$80$		0			0
$81$	2.97712	−	5.15652i	0.330791	−	0.572947i
$82$	−4.44930	−	7.70641i	−0.491343	−	0.851031i
$83$	−12.4044			−1.36156			−0.680779	−	0.732489i	$-0.738359\pi$
$83$	−12.4044			−1.36156			−0.680779	+	0.732489i	$0.738359\pi$
$84$	−0.715931			−0.0781144
$85$		0			0
$86$	−0.318434	−	0.551544i	−0.0343376	−	0.0594745i
$87$	5.67017			0.607906
$88$	4.43782			0.473073
$89$	−4.37859	−	7.58395i	−0.464130	−	0.803897i	0.535032	−	0.844832i	$-0.320300\pi$
$89$	−4.37859	−	7.58395i	−0.464130	−	0.803897i	−0.999162	+	0.0409353i	$0.986966\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−2.82977	+	4.90130i	−0.295024	+	0.510996i
$93$	−5.62000	+	9.73413i	−0.582767	+	1.00938i
$94$	4.26110			0.439499
$95$		0			0
$96$	−1.48282			−0.151339
$97$	0.476652	−	0.825585i	0.0483967	−	0.0838255i	−0.840812	−	0.541327i	$-0.817922\pi$
$97$	0.476652	−	0.825585i	0.0483967	−	0.0838255i	0.889209	+	0.457501i	$0.151256\pi$
$98$	−3.38344	+	5.86030i	−0.341779	+	0.591979i
$99$	−1.77790	−	3.07942i	−0.178686	−	0.309493i
$100$		0			0
$101$	3.32360	+	5.75665i	0.330711	+	0.572808i	0.982651	−	0.185462i	$-0.0593783\pi$
$101$	3.32360	+	5.75665i	0.330711	+	0.572808i	−0.651941	+	0.758270i	$0.726045\pi$
$102$	11.7122			1.15968
$103$	−4.13171			−0.407110			−0.203555	−	0.979064i	$-0.565250\pi$
$103$	−4.13171			−0.407110			−0.203555	+	0.979064i	$0.565250\pi$
$104$	2.07118	+	3.58738i	0.203095	+	0.351772i
$105$		0			0
$106$	−3.18735			−0.309583
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$	2.81828	+	4.88141i	0.271189	+	0.469714i
$109$	−9.10799	+	15.7755i	−0.872387	+	1.51102i	−0.0128662	+	0.999917i	$0.504096\pi$
$109$	−9.10799	+	15.7755i	−0.872387	+	1.51102i	−0.859521	+	0.511101i	$0.829238\pi$
$110$		0			0
$111$	2.59922	−	4.50198i	0.246707	−	0.427309i
$112$	0.241409	−	0.418132i	0.0228110	−	0.0395098i
$113$	8.29703			0.780519			0.390260	−	0.920705i	$-0.372385\pi$
$113$	8.29703			0.780519			0.390260	+	0.920705i	$0.372385\pi$
$114$	2.44398	+	5.98358i	0.228900	+	0.560413i
$115$		0			0
$116$	−1.91196	+	3.31161i	−0.177521	+	0.307475i
$117$	1.65953	−	2.87440i	0.153424	−	0.265738i
$118$	0.812584	+	1.40744i	0.0748044	+	0.129565i
$119$	−1.90679	+	3.30266i	−0.174795	+	0.302754i
$120$		0			0
$121$	8.69420			0.790382
$122$	−1.47049			−0.133132
$123$	6.59750	+	11.4272i	0.594877	+	1.03036i
$124$	−3.79008	−	6.56462i	−0.340359	−	0.589520i
$125$		0			0
$126$	−0.386859			−0.0344641
$127$	7.17384	+	12.4255i	0.636576	+	1.10258i	0.986179	+	0.165683i	$0.0529830\pi$
$127$	7.17384	+	12.4255i	0.636576	+	1.10258i	−0.349603	+	0.936898i	$0.613684\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.472180	+	0.817839i	0.0415731	+	0.0720067i
$130$		0			0
$131$	−5.00032	+	8.66080i	−0.436880	+	0.756698i	−0.997447	−	0.0714111i	$-0.977250\pi$
$131$	−5.00032	+	8.66080i	−0.436880	+	0.756698i	0.560567	+	0.828109i	$0.310583\pi$
$132$	−6.58047			−0.572756
$133$	−2.08517	−	0.284985i	−0.180807	−	0.0247113i
$134$	−13.1950			−1.13987
$135$		0			0
$136$	−3.94930	+	6.84039i	−0.338650	+	0.586558i
$137$	−1.82945	−	3.16870i	−0.156301	−	0.270720i	0.777231	−	0.629215i	$-0.216623\pi$
$137$	−1.82945	−	3.16870i	−0.156301	−	0.270720i	−0.933532	+	0.358495i	$0.883290\pi$
$138$	4.19603	−	7.26773i	0.357190	−	0.618671i
$139$	3.17602	+	5.50103i	0.269387	+	0.466591i	0.968704	−	0.248220i	$-0.0798457\pi$
$139$	3.17602	+	5.50103i	0.269387	+	0.466591i	−0.699317	+	0.714812i	$0.746512\pi$
$140$		0			0
$141$	−6.31843			−0.532108
$142$	1.41164	+	2.44504i	0.118462	+	0.205183i
$143$	9.19149	+	15.9201i	0.768631	+	1.33131i
$144$	−0.801252			−0.0667710
$145$		0			0
$146$	−3.43828	−	5.95528i	−0.284554	−	0.492863i
$147$	5.01703	−	8.68975i	0.413798	−	0.716719i
$148$	1.75289	+	3.03610i	0.144087	+	0.249566i
$149$	6.02101	−	10.4287i	0.493260	−	0.854351i	−0.506710	−	0.862117i	$-0.669138\pi$
$149$	6.02101	−	10.4287i	0.493260	−	0.854351i	0.999970	+	0.00776522i	$0.00247177\pi$
$150$		0			0
$151$	−1.53484			−0.124903			−0.0624516	−	0.998048i	$-0.519892\pi$
$151$	−1.53484			−0.124903			−0.0624516	+	0.998048i	$0.519892\pi$
$152$	−4.31875	−	0.590253i	−0.350297	−	0.0478759i
$153$	6.32877			0.511650
$154$	1.07133	−	1.85559i	0.0863300	−	0.149528i
$155$		0			0
$156$	−3.07118	−	5.31943i	−0.245891	−	0.425895i
$157$	−9.52664	+	16.5006i	−0.760309	+	1.31689i	0.182383	+	0.983228i	$0.441619\pi$
$157$	−9.52664	+	16.5006i	−0.760309	+	1.31689i	−0.942691	+	0.333666i	$0.891714\pi$
$158$	−0.576026	−	0.997706i	−0.0458262	−	0.0793732i
$159$	4.72626			0.374817
$160$		0			0
$161$	1.36626	+	2.36643i	0.107676	+	0.186501i
$162$	−2.97712	−	5.15652i	−0.233905	−	0.405135i
$163$	9.96533			0.780545			0.390272	−	0.920699i	$-0.372381\pi$
$163$	9.96533			0.780545			0.390272	+	0.920699i	$0.372381\pi$
$164$	−8.89860			−0.694864
$165$		0			0
$166$	−6.20219	+	10.7425i	−0.481384	+	0.833781i
$167$	3.70272	+	6.41331i	0.286525	+	0.496277i	0.972978	−	0.230898i	$-0.0741664\pi$
$167$	3.70272	+	6.41331i	0.286525	+	0.496277i	−0.686453	+	0.727175i	$0.740833\pi$
$168$	−0.357965	+	0.620014i	−0.0276176	+	0.0478351i
$169$	−2.07953	+	3.60186i	−0.159964	+	0.277066i
$170$		0			0
$171$	1.32062	+	3.23327i	0.100991	+	0.247254i
$172$	−0.636868			−0.0485607
$173$	7.83274	−	13.5667i	0.595512	−	1.03146i	−0.397962	−	0.917402i	$-0.630282\pi$
$173$	7.83274	−	13.5667i	0.595512	−	1.03146i	0.993474	−	0.114056i	$-0.0363843\pi$
$174$	2.83509	−	4.91051i	0.214927	−	0.372265i
$175$		0			0
$176$	2.21891	−	3.84326i	0.167256	−	0.289697i
$177$	−1.20491	−	2.08697i	−0.0905669	−	0.156866i
$178$	−8.75719			−0.656379
$179$	4.61284			0.344780			0.172390	−	0.985029i	$-0.444851\pi$
$179$	4.61284			0.344780			0.172390	+	0.985029i	$0.444851\pi$
$180$		0			0
$181$	−0.605224	−	1.04828i	−0.0449860	−	0.0779180i	0.842656	−	0.538453i	$-0.180991\pi$
$181$	−0.605224	−	1.04828i	−0.0449860	−	0.0779180i	−0.887642	+	0.460535i	$0.847658\pi$
$182$	2.00000			0.148250
$183$	2.18046			0.161184
$184$	2.82977	+	4.90130i	0.208613	+	0.361329i
$185$		0			0
$186$	5.62000	+	9.73413i	0.412079	+	0.713741i
$187$	−17.5263	+	30.3564i	−1.28165	+	2.21988i
$188$	2.13055	−	3.69022i	0.155386	−	0.269137i
$189$	2.72143			0.197955
$190$		0			0
$191$	−7.64783			−0.553378			−0.276689	−	0.960960i	$-0.589237\pi$
$191$	−7.64783			−0.553378			−0.276689	+	0.960960i	$0.589237\pi$
$192$	−0.741409	+	1.28416i	−0.0535066	+	0.0926761i
$193$	−8.96163	+	15.5220i	−0.645072	+	1.11730i	0.339212	+	0.940710i	$0.389839\pi$
$193$	−8.96163	+	15.5220i	−0.645072	+	1.11730i	−0.984285	+	0.176588i	$0.943494\pi$
$194$	−0.476652	−	0.825585i	−0.0342216	−	0.0592736i
$195$		0			0
$196$	3.38344	+	5.86030i	0.241675	+	0.418593i
$197$	18.5697			1.32304			0.661518	−	0.749929i	$-0.269912\pi$
$197$	18.5697			1.32304			0.661518	+	0.749929i	$0.269912\pi$
$198$	−3.55581			−0.252700
$199$	6.76689	+	11.7206i	0.479692	+	0.830851i	0.999729	−	0.0232931i	$-0.00741510\pi$
$199$	6.76689	+	11.7206i	0.479692	+	0.830851i	−0.520037	+	0.854144i	$0.674082\pi$
$200$		0			0
$201$	19.5658			1.38006
$202$	6.64720			0.467695
$203$	0.923127	+	1.59890i	0.0647908	+	0.112221i
$204$	5.85609	−	10.1430i	0.410008	−	0.710155i
$205$		0			0
$206$	−2.06586	+	3.57817i	−0.143935	+	0.249303i
$207$	2.26736	−	3.92717i	0.157592	−	0.272958i
$208$	4.14235			0.287220
$209$	−19.1658	−	2.61944i	−1.32573	−	0.181190i
$210$		0			0
$211$	6.67055	−	11.5537i	0.459220	−	0.795392i	−0.539700	−	0.841857i	$-0.681462\pi$
$211$	6.67055	−	11.5537i	0.459220	−	0.795392i	0.998920	+	0.0464656i	$0.0147958\pi$
$212$	−1.59368	+	2.76033i	−0.109454	+	0.189580i
$213$	−2.09321	−	3.62554i	−0.143424	−	0.248418i
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$		0			0
$216$	5.63656			0.383520
$217$	−3.65984			−0.248446
$218$	9.10799	+	15.7755i	0.616871	+	1.06845i
$219$	5.09835	+	8.83060i	0.344514	+	0.596716i
$220$		0			0
$221$	−32.7188			−2.20090
$222$	−2.59922	−	4.50198i	−0.174448	−	0.302153i
$223$	2.75859	−	4.77802i	0.184729	−	0.319960i	−0.758756	−	0.651375i	$-0.774193\pi$
$223$	2.75859	−	4.77802i	0.184729	−	0.319960i	0.943485	+	0.331415i	$0.107526\pi$
$224$	−0.241409	−	0.418132i	−0.0161298	−	0.0279376i
$225$		0			0
$226$	4.14852	−	7.18544i	0.275955	−	0.477968i
$227$	−22.2457			−1.47650			−0.738248	−	0.674529i	$-0.764347\pi$
$227$	−22.2457			−1.47650			−0.738248	+	0.674529i	$0.764347\pi$
$228$	6.40392	+	0.875238i	0.424110	+	0.0579641i
$229$	16.4341			1.08599			0.542997	−	0.839735i	$-0.317290\pi$
$229$	16.4341			1.08599			0.542997	+	0.839735i	$0.317290\pi$
$230$		0			0
$231$	−1.58858	+	2.75151i	−0.104521	+	0.181036i
$232$	1.91196	+	3.31161i	0.125526	+	0.217418i
$233$	−5.28454	+	9.15309i	−0.346202	+	0.599639i	−0.985571	−	0.169261i	$-0.945862\pi$
$233$	−5.28454	+	9.15309i	−0.346202	+	0.599639i	0.639370	+	0.768899i	$0.279195\pi$
$234$	−1.65953	−	2.87440i	−0.108487	−	0.187905i
$235$		0			0
$236$	1.62517			0.105789
$237$	0.854141	+	1.47942i	0.0554824	+	0.0960984i
$238$	1.90679	+	3.30266i	0.123599	+	0.214080i
$239$	−15.8625			−1.02606			−0.513031	−	0.858370i	$-0.671478\pi$
$239$	−15.8625			−1.02606			−0.513031	+	0.858370i	$0.671478\pi$
$240$		0			0
$241$	−2.19672	−	3.80483i	−0.141503	−	0.245091i	0.786560	−	0.617514i	$-0.211860\pi$
$241$	−2.19672	−	3.80483i	−0.141503	−	0.245091i	−0.928063	+	0.372423i	$0.878527\pi$
$242$	4.34710	−	7.52940i	0.279442	−	0.484008i
$243$	−4.04032	−	6.99804i	−0.259187	−	0.448924i
$244$	−0.735243	+	1.27348i	−0.0470691	+	0.0815261i
$245$		0			0
$246$	13.1950			0.841283
$247$	−6.82742	−	16.7155i	−0.434419	−	1.06358i
$248$	−7.58017			−0.481341
$249$	9.19672	−	15.9292i	0.582819	−	1.00947i
$250$		0			0
$251$	−7.21853	−	12.5029i	−0.455630	−	0.789173i	0.543095	−	0.839671i	$-0.317252\pi$
$251$	−7.21853	−	12.5029i	−0.455630	−	0.789173i	−0.998724	+	0.0504980i	$0.983919\pi$
$252$	−0.193429	+	0.335029i	−0.0121849	+	0.0211049i
$253$	12.5580	+	21.7511i	0.789513	+	1.36748i
$254$	14.3477			0.900254
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.51765	−	9.55685i	−0.344182	−	0.596140i	0.641023	−	0.767522i	$-0.278510\pi$
$257$	−5.51765	−	9.55685i	−0.344182	−	0.596140i	−0.985205	+	0.171382i	$0.945177\pi$
$258$	0.944359			0.0587933
$259$	1.69266			0.105177
$260$		0			0
$261$	1.53196	−	2.65343i	0.0948259	−	0.164243i
$262$	5.00032	+	8.66080i	0.308921	+	0.535066i
$263$	−10.5630	+	18.2957i	−0.651345	+	1.12816i	0.331451	+	0.943472i	$0.392462\pi$
$263$	−10.5630	+	18.2957i	−0.651345	+	1.12816i	−0.982797	+	0.184691i	$0.940872\pi$
$264$	−3.29024	+	5.69885i	−0.202500	+	0.350740i
$265$		0			0
$266$	−1.28939	+	1.66332i	−0.0790575	+	0.101984i
$267$	12.9853			0.794688
$268$	−6.59750	+	11.4272i	−0.403006	+	0.698028i
$269$	14.1483	−	24.5056i	0.862637	−	1.49413i	−0.00673681	−	0.999977i	$-0.502144\pi$
$269$	14.1483	−	24.5056i	0.862637	−	1.49413i	0.869374	−	0.494154i	$-0.164522\pi$
$270$		0			0
$271$	6.15672	−	10.6638i	0.373994	−	0.647777i	−0.616182	−	0.787604i	$-0.711321\pi$
$271$	6.15672	−	10.6638i	0.373994	−	0.647777i	0.990176	+	0.139827i	$0.0446546\pi$
$272$	3.94930	+	6.84039i	0.239461	+	0.414759i
$273$	−2.96564			−0.179488
$274$	−3.65890			−0.221042
$275$		0			0
$276$	−4.19603	−	7.26773i	−0.252571	−	0.437466i
$277$	27.2677			1.63836			0.819178	−	0.573539i	$-0.194430\pi$
$277$	27.2677			1.63836			0.819178	+	0.573539i	$0.194430\pi$
$278$	6.35204			0.380970
$279$	3.03681	+	5.25991i	0.181809	+	0.314903i
$280$		0			0
$281$	−4.63665	−	8.03092i	−0.276600	−	0.479084i	0.693938	−	0.720035i	$-0.255874\pi$
$281$	−4.63665	−	8.03092i	−0.276600	−	0.479084i	−0.970537	+	0.240950i	$0.922541\pi$
$282$	−3.15922	+	5.47192i	−0.188129	+	0.325848i
$283$	−13.0034	+	22.5226i	−0.772975	+	1.33883i	0.162951	+	0.986634i	$0.447899\pi$
$283$	−13.0034	+	22.5226i	−0.772975	+	1.33883i	−0.935926	+	0.352197i	$0.885435\pi$
$284$	2.82328			0.167531
$285$		0			0
$286$	18.3830			1.08701
$287$	−2.14820	+	3.72079i	−0.126804	+	0.219631i
$288$	−0.400626	+	0.693904i	−0.0236071	+	0.0408887i
$289$	−22.6939	−	39.3071i	−1.33494	−	2.31218i
$290$		0			0
$291$	0.706788	+	1.22419i	0.0414326	+	0.0717634i
$292$	−6.87657			−0.402421
$293$	17.4435			1.01906			0.509529	−	0.860453i	$-0.329820\pi$
$293$	17.4435			1.01906			0.509529	+	0.860453i	$0.329820\pi$
$294$	−5.01703	−	8.68975i	−0.292599	−	0.506797i
$295$		0			0
$296$	3.50579			0.203770
$297$	25.0140			1.45146
$298$	−6.02101	−	10.4287i	−0.348788	−	0.604118i
$299$	−11.7219	+	20.3029i	−0.677894	+	1.17415i
$300$		0			0
$301$	−0.153746	+	0.266295i	−0.00886175	+	0.0153490i
$302$	−0.767418	+	1.32921i	−0.0441600	+	0.0764873i
$303$	−9.85659			−0.566246
$304$	−2.67055	+	3.44502i	−0.153167	+	0.197585i
$305$		0			0
$306$	3.16438	−	5.48087i	0.180896	−	0.313321i
$307$	−0.557182	+	0.965067i	−0.0318000	+	0.0550793i	−0.881487	−	0.472207i	$-0.843457\pi$
$307$	−0.557182	+	0.965067i	−0.0318000	+	0.0550793i	0.849687	+	0.527287i	$0.176791\pi$
$308$	−1.07133	−	1.85559i	−0.0610446	−	0.105732i
$309$	3.06329	−	5.30577i	0.174264	−	0.301835i
$310$		0			0
$311$	33.8032			1.91680			0.958400	−	0.285427i	$-0.0921354\pi$
$311$	33.8032			1.91680			0.958400	+	0.285427i	$0.0921354\pi$
$312$	−6.14235			−0.347742
$313$	−7.38095	−	12.7842i	−0.417196	−	0.722605i	0.578460	−	0.815711i	$-0.303654\pi$
$313$	−7.38095	−	12.7842i	−0.417196	−	0.722605i	−0.995656	+	0.0931060i	$0.970320\pi$
$314$	9.52664	+	16.5006i	0.537619	+	0.931184i
$315$		0			0
$316$	−1.15205			−0.0648080
$317$	−13.0683	−	22.6350i	−0.733989	−	1.27131i	−0.955165	−	0.296072i	$-0.904323\pi$
$317$	−13.0683	−	22.6350i	−0.733989	−	1.27131i	0.221177	−	0.975234i	$-0.429010\pi$
$318$	2.36313	−	4.09306i	0.132518	−	0.229528i
$319$	8.48492	+	14.6963i	0.475064	+	0.822835i
$320$		0			0
$321$	−7.41409	+	12.8416i	−0.413814	+	0.716747i
$322$	2.73252			0.152278
$323$	21.0936	−	27.2108i	1.17368	−	1.51405i
$324$	−5.95424			−0.330791
$325$		0			0
$326$	4.98267	−	8.63023i	0.275964	−	0.477984i
$327$	−13.5055	−	23.3922i	−0.746855	−	1.29359i
$328$	−4.44930	+	7.70641i	−0.245671	+	0.425515i
$329$	−1.02867	−	1.78170i	−0.0567123	−	0.0982285i
$330$		0			0
$331$	2.17127			0.119344			0.0596720	−	0.998218i	$-0.480995\pi$
$331$	2.17127			0.119344			0.0596720	+	0.998218i	$0.480995\pi$
$332$	6.20219	+	10.7425i	0.340390	+	0.589572i
$333$	−1.40451	−	2.43268i	−0.0769666	−	0.133310i
$334$	7.40545			0.405208
$335$		0			0
$336$	0.357965	+	0.620014i	0.0195286	+	0.0338245i
$337$	−6.56430	+	11.3697i	−0.357580	+	0.619347i	−0.987556	−	0.157268i	$-0.949731\pi$
$337$	−6.56430	+	11.3697i	−0.357580	+	0.619347i	0.629976	+	0.776615i	$0.283065\pi$
$338$	2.07953	+	3.60186i	0.113112	+	0.195915i
$339$	−6.15149	+	10.6547i	−0.334103	+	0.578684i
$340$		0			0
$341$	−33.6394			−1.82167
$342$	3.46041	+	0.472942i	0.187117	+	0.0255738i
$343$	6.64690			0.358899
$344$	−0.318434	+	0.551544i	−0.0171688	+	0.0297373i
$345$		0			0
$346$	−7.83274	−	13.5667i	−0.421091	−	0.729351i
$347$	7.46811	−	12.9352i	0.400909	−	0.694395i	−0.592927	−	0.805257i	$-0.702028\pi$
$347$	7.46811	−	12.9352i	0.400909	−	0.694395i	0.993836	+	0.110861i	$0.0353609\pi$
$348$	−2.83509	−	4.91051i	−0.151977	−	0.263231i
$349$	−18.8611			−1.00961			−0.504806	−	0.863233i	$-0.668436\pi$
$349$	−18.8611			−1.00961			−0.504806	+	0.863233i	$0.668436\pi$
$350$		0			0
$351$	11.6743	+	20.2205i	0.623129	+	1.07929i
$352$	−2.21891	−	3.84326i	−0.118268	−	0.204846i
$353$	−2.01172			−0.107073			−0.0535366	−	0.998566i	$-0.517049\pi$
$353$	−2.01172			−0.107073			−0.0535366	+	0.998566i	$0.517049\pi$
$354$	−2.40983			−0.128081
$355$		0			0
$356$	−4.37859	+	7.58395i	−0.232065	+	0.401948i
$357$	−2.82742	−	4.89724i	−0.149643	−	0.259190i
$358$	2.30642	−	3.99483i	0.121898	−	0.211134i
$359$	3.29938	−	5.71469i	0.174135	−	0.301610i	−0.765727	−	0.643166i	$-0.777621\pi$
$359$	3.29938	−	5.71469i	0.174135	−	0.301610i	0.939861	+	0.341556i	$0.110954\pi$
$360$		0			0
$361$	18.3032	+	5.09831i	0.963326	+	0.268332i
$362$	−1.21045			−0.0636197
$363$	−6.44596	+	11.1647i	−0.338325	+	0.585996i
$364$	1.00000	−	1.73205i	0.0524142	−	0.0907841i
$365$		0			0
$366$	1.09023	−	1.88834i	0.0569873	−	0.0987049i
$367$	5.59922	+	9.69814i	0.292277	+	0.506239i	0.974348	−	0.225048i	$-0.0722537\pi$
$367$	5.59922	+	9.69814i	0.292277	+	0.506239i	−0.682071	+	0.731286i	$0.738920\pi$
$368$	5.65953			0.295024
$369$	7.13002			0.371174
$370$		0			0
$371$	0.769455	+	1.33274i	0.0399481	+	0.0691922i
$372$	11.2400			0.582767
$373$	3.19437			0.165398			0.0826991	−	0.996575i	$-0.473646\pi$
$373$	3.19437			0.165398			0.0826991	+	0.996575i	$0.473646\pi$
$374$	17.5263	+	30.3564i	0.906261	+	1.56969i
$375$		0			0
$376$	−2.13055	−	3.69022i	−0.109875	−	0.190309i
$377$	−7.92000	+	13.7178i	−0.407901	+	0.706505i
$378$	1.36072	−	2.35683i	0.0699877	−	0.121222i
$379$	17.2666			0.886927			0.443463	−	0.896292i	$-0.353750\pi$
$379$	17.2666			0.886927			0.443463	+	0.896292i	$0.353750\pi$
$380$		0			0
$381$	−21.2750			−1.08995
$382$	−3.82392	+	6.62322i	−0.195649	+	0.338873i
$383$	16.0924	−	27.8729i	0.822285	−	1.42424i	−0.0816914	−	0.996658i	$-0.526032\pi$
$383$	16.0924	−	27.8729i	0.822285	−	1.42424i	0.903977	−	0.427582i	$-0.140634\pi$
$384$	0.741409	+	1.28416i	0.0378349	+	0.0655319i
$385$		0			0
$386$	8.96163	+	15.5220i	0.456135	+	0.790049i
$387$	0.510292			0.0259396
$388$	−0.953304			−0.0483967
$389$	5.03587	+	8.72239i	0.255329	+	0.442243i	0.964985	−	0.262306i	$-0.0844829\pi$
$389$	5.03587	+	8.72239i	0.255329	+	0.442243i	−0.709656	+	0.704548i	$0.751150\pi$
$390$		0			0
$391$	−44.7024			−2.26070
$392$	6.76689			0.341779
$393$	−7.41456	−	12.8424i	−0.374015	−	0.647813i
$394$	9.28485	−	16.0818i	0.467764	−	0.810191i
$395$		0			0
$396$	−1.77790	+	3.07942i	−0.0893430	+	0.154747i
$397$	−17.7217	+	30.6949i	−0.889428	+	1.54053i	−0.0488757	+	0.998805i	$0.515564\pi$
$397$	−17.7217	+	30.6949i	−0.889428	+	1.54053i	−0.840553	+	0.541730i	$0.817770\pi$
$398$	13.5338			0.678387
$399$	1.91193	−	2.46640i	0.0957161	−	0.123474i
$400$		0			0
$401$	15.4751	−	26.8036i	0.772789	−	1.33851i	−0.163239	−	0.986587i	$-0.552194\pi$
$401$	15.4751	−	26.8036i	0.772789	−	1.33851i	0.936029	−	0.351924i	$-0.114472\pi$
$402$	9.78289	−	16.9445i	0.487926	−	0.845113i
$403$	−15.6999	−	27.1929i	−0.782065	−	1.35458i
$404$	3.32360	−	5.75665i	0.165355	−	0.286404i
$405$		0			0
$406$	1.84625			0.0916281
$407$	15.5580			0.771183
$408$	−5.85609	−	10.1430i	−0.289920	−	0.502156i
$409$	−13.5583	−	23.4837i	−0.670417	−	1.16120i	−0.977786	−	0.209606i	$-0.932782\pi$
$409$	−13.5583	−	23.4837i	−0.670417	−	1.16120i	0.307369	−	0.951590i	$-0.400551\pi$
$410$		0			0
$411$	5.42548			0.267619
$412$	2.06586	+	3.57817i	0.101777	+	0.176284i
$413$	0.392330	−	0.679535i	0.0193053	−	0.0334378i
$414$	−2.26736	−	3.92717i	−0.111434	−	0.193010i
$415$		0			0
$416$	2.07118	−	3.58738i	0.101548	−	0.175886i
$417$	−9.41892			−0.461246
$418$	−11.8514	+	15.2884i	−0.579671	+	0.747778i
$419$	−8.28108			−0.404557			−0.202279	−	0.979328i	$-0.564835\pi$
$419$	−8.28108			−0.404557			−0.202279	+	0.979328i	$0.564835\pi$
$420$		0			0
$421$	−2.95790	+	5.12323i	−0.144159	+	0.249691i	−0.929059	−	0.369932i	$-0.879381\pi$
$421$	−2.95790	+	5.12323i	−0.144159	+	0.249691i	0.784900	+	0.619623i	$0.212714\pi$
$422$	−6.67055	−	11.5537i	−0.324717	−	0.562427i
$423$	−1.70711	+	2.95680i	−0.0830024	+	0.143764i
$424$	1.59368	+	2.76033i	0.0773958	+	0.134053i
$425$		0			0
$426$	−4.18642			−0.202833
$427$	0.354988	+	0.614858i	0.0171791	+	0.0297551i
$428$	−5.00000	−	8.66025i	−0.241684	−	0.418609i
$429$	−27.2586			−1.31606
$430$		0			0
$431$	7.48526	+	12.9649i	0.360552	+	0.624495i	0.988052	−	0.154122i	$-0.0492548\pi$
$431$	7.48526	+	12.9649i	0.360552	+	0.624495i	−0.627499	+	0.778617i	$0.715922\pi$
$432$	2.81828	−	4.88141i	0.135595	−	0.234857i
$433$	1.67587	+	2.90269i	0.0805371	+	0.139494i	0.903481	−	0.428629i	$-0.141003\pi$
$433$	1.67587	+	2.90269i	0.0805371	+	0.139494i	−0.822944	+	0.568123i	$0.807670\pi$
$434$	−1.82992	+	3.16951i	−0.0878389	+	0.152141i
$435$		0			0
$436$	18.2160			0.872387
$437$	−9.32805	−	22.8378i	−0.446221	−	1.09248i
$438$	10.1967			0.487217
$439$	−6.00116	+	10.3943i	−0.286420	+	0.496094i	−0.972953	−	0.231005i	$-0.925799\pi$
$439$	−6.00116	+	10.3943i	−0.286420	+	0.496094i	0.686533	+	0.727099i	$0.259132\pi$
$440$		0			0
$441$	−2.71099	−	4.69557i	−0.129095	−	0.223599i
$442$	−16.3594	+	28.3353i	−0.778137	+	1.34777i
$443$	−13.3972	−	23.2046i	−0.636520	−	1.10248i	−0.986191	−	0.165612i	$-0.947040\pi$
$443$	−13.3972	−	23.2046i	−0.636520	−	1.10248i	0.349671	−	0.936873i	$-0.386293\pi$
$444$	−5.19844			−0.246707
$445$		0			0
$446$	−2.75859	−	4.77802i	−0.130623	−	0.226246i
$447$	8.92805	+	15.4638i	0.422282	+	0.731415i
$448$	−0.482818			−0.0228110
$449$	3.53608			0.166878			0.0834389	−	0.996513i	$-0.473410\pi$
$449$	3.53608			0.166878			0.0834389	+	0.996513i	$0.473410\pi$
$450$		0			0
$451$	−19.7452	+	34.1996i	−0.929764	+	1.61040i
$452$	−4.14852	−	7.18544i	−0.195130	−	0.337975i
$453$	1.13794	−	1.97097i	0.0534651	−	0.0926043i
$454$	−11.1228	+	19.2653i	−0.522020	+	0.904165i
$455$		0			0
$456$	3.95994	−	5.10834i	0.185441	−	0.239220i
$457$	−21.5147			−1.00642			−0.503208	−	0.864166i	$-0.667847\pi$
$457$	−21.5147			−1.00642			−0.503208	+	0.864166i	$0.667847\pi$
$458$	8.21703	−	14.2323i	0.383957	−	0.665033i
$459$	−22.2605	+	38.5563i	−1.03903	+	1.79965i
$460$		0			0
$461$	−20.1971	+	34.9825i	−0.940675	+	1.62930i	−0.176486	+	0.984303i	$0.556473\pi$
$461$	−20.1971	+	34.9825i	−0.940675	+	1.62930i	−0.764188	+	0.644993i	$0.776860\pi$
$462$	1.58858	+	2.75151i	0.0739076	+	0.128012i
$463$	19.6448			0.912972			0.456486	−	0.889731i	$-0.349108\pi$
$463$	19.6448			0.912972			0.456486	+	0.889731i	$0.349108\pi$
$464$	3.82392			0.177521
$465$		0			0
$466$	5.28454	+	9.15309i	0.244801	+	0.424009i
$467$	−15.1929			−0.703042			−0.351521	−	0.936180i	$-0.614335\pi$
$467$	−15.1929			−0.703042			−0.351521	+	0.936180i	$0.614335\pi$
$468$	−3.31907			−0.153424
$469$	3.18539	+	5.51726i	0.147088	+	0.254763i
$470$		0			0
$471$	−14.1263	−	24.4674i	−0.650904	−	1.12740i
$472$	0.812584	−	1.40744i	0.0374022	−	0.0647825i
$473$	−1.41315	+	2.44765i	−0.0649768	+	0.112543i
$474$	1.70828			0.0784640
$475$		0			0
$476$	3.81358			0.174795
$477$	1.27694	−	2.21172i	0.0584669	−	0.101268i
$478$	−7.93127	+	13.7374i	−0.362768	+	0.628332i
$479$	2.12032	+	3.67250i	0.0968798	+	0.167801i	0.910392	−	0.413748i	$-0.135780\pi$
$479$	2.12032	+	3.67250i	0.0968798	+	0.167801i	−0.813512	+	0.581548i	$0.802447\pi$
$480$		0			0
$481$	7.26110	+	12.5766i	0.331078	+	0.573443i
$482$	−4.39344			−0.200116
$483$	−4.05183			−0.184365
$484$	−4.34710	−	7.52940i	−0.197596	−	0.342245i
$485$		0			0
$486$	−8.08064			−0.366545
$487$	8.00831			0.362891			0.181446	−	0.983401i	$-0.441922\pi$
$487$	8.00831			0.362891			0.181446	+	0.983401i	$0.441922\pi$
$488$	0.735243	+	1.27348i	0.0332829	+	0.0576477i
$489$	−7.38838	+	12.7971i	−0.334114	+	0.578703i
$490$		0			0
$491$	8.53834	−	14.7888i	0.385330	−	0.667411i	−0.606485	−	0.795095i	$-0.707421\pi$
$491$	8.53834	−	14.7888i	0.385330	−	0.667411i	0.991815	+	0.127684i	$0.0407543\pi$
$492$	6.59750	−	11.4272i	0.297438	−	0.515178i
$493$	−30.2036			−1.36030
$494$	−17.8898	−	2.44504i	−0.804899	−	0.110007i
$495$		0			0
$496$	−3.79008	+	6.56462i	−0.170180	+	0.294760i
$497$	0.681566	−	1.18051i	0.0305724	−	0.0529530i
$498$	−9.19672	−	15.9292i	−0.412115	−	0.713804i
$499$	−5.63718	+	9.76389i	−0.252355	+	0.437092i	−0.964174	−	0.265272i	$-0.914538\pi$
$499$	−5.63718	+	9.76389i	−0.252355	+	0.437092i	0.711819	+	0.702363i	$0.247872\pi$
$500$		0			0
$501$	−10.9809			−0.490592
$502$	−14.4371			−0.644357
$503$	−4.25268	−	7.36586i	−0.189618	−	0.328427i	0.755505	−	0.655143i	$-0.227391\pi$
$503$	−4.25268	−	7.36586i	−0.189618	−	0.328427i	−0.945123	+	0.326715i	$0.894058\pi$
$504$	0.193429	+	0.335029i	0.00861602	+	0.0149234i
$505$		0			0
$506$	25.1160			1.11654
$507$	−3.08357	−	5.34090i	−0.136946	−	0.237198i
$508$	7.17384	−	12.4255i	0.318288	−	0.551291i
$509$	−15.4306	−	26.7265i	−0.683948	−	1.18463i	−0.973766	−	0.227550i	$-0.926928\pi$
$509$	−15.4306	−	26.7265i	−0.683948	−	1.18463i	0.289819	−	0.957082i	$-0.406405\pi$
$510$		0			0
$511$	−1.66006	+	2.87532i	−0.0734369	+	0.127196i
$512$	−1.00000			−0.0441942
$513$	−24.3429	−	3.32700i	−1.07477	−	0.146891i
$514$	−11.0353			−0.486746
$515$		0			0
$516$	0.472180	−	0.817839i	0.0207866	−	0.0360034i
$517$	−9.45499	−	16.3765i	−0.415830	−	0.720238i
$518$	0.846328	−	1.46588i	0.0371855	−	0.0644072i
$519$	11.6145	+	20.1170i	0.509821	+	0.883036i
$520$		0			0
$521$	−8.09735			−0.354751			−0.177376	−	0.984143i	$-0.556761\pi$
$521$	−8.09735			−0.354751			−0.177376	+	0.984143i	$0.556761\pi$
$522$	−1.53196	−	2.65343i	−0.0670521	−	0.116138i
$523$	−7.35267	−	12.7352i	−0.321510	−	0.556872i	0.659290	−	0.751889i	$-0.270857\pi$
$523$	−7.35267	−	12.7352i	−0.321510	−	0.556872i	−0.980800	+	0.195017i	$0.937524\pi$
$524$	10.0006			0.436880
$525$		0			0
$526$	10.5630	+	18.2957i	0.460571	+	0.797732i
$527$	29.9363	−	51.8513i	1.30405	−	2.25868i
$528$	3.29024	+	5.69885i	0.143189	+	0.248011i
$529$	−4.51516	+	7.82048i	−0.196311	+	0.340021i
$530$		0			0
$531$	−1.30217			−0.0565093
$532$	0.795780	+	1.94830i	0.0345015	+	0.0844696i
$533$	−36.8611			−1.59663
$534$	6.49265	−	11.2456i	0.280965	−	0.486645i
$535$		0			0
$536$	6.59750	+	11.4272i	0.284969	+	0.493580i
$537$	−3.42000	+	5.92361i	−0.147584	+	0.255623i
$538$	−14.1483	−	24.5056i	−0.609977	−	1.05651i
$539$	30.0302			1.29349
$540$		0			0
$541$	−5.50993	−	9.54347i	−0.236890	−	0.410306i	0.722930	−	0.690921i	$-0.242795\pi$
$541$	−5.50993	−	9.54347i	−0.236890	−	0.410306i	−0.959820	+	0.280615i	$0.909462\pi$
$542$	−6.15672	−	10.6638i	−0.264454	−	0.458048i
$543$	1.79487			0.0770254
$544$	7.89860			0.338650
$545$		0			0
$546$	−1.48282	+	2.56832i	−0.0634587	+	0.109914i
$547$	−1.29610	−	2.24490i	−0.0554171	−	0.0959852i	0.836986	−	0.547224i	$-0.184316\pi$
$547$	−1.29610	−	2.24490i	−0.0554171	−	0.0959852i	−0.892403	+	0.451239i	$0.850982\pi$
$548$	−1.82945	+	3.16870i	−0.0781503	+	0.135360i
$549$	0.589115	−	1.02038i	0.0251428	−	0.0435486i
$550$		0			0
$551$	−6.30258	−	15.4305i	−0.268499	−	0.657364i
$552$	−8.39206			−0.357190
$553$	−0.278115	+	0.481710i	−0.0118267	+	0.0204844i
$554$	13.6338	−	23.6145i	0.579246	−	1.00328i
$555$		0			0
$556$	3.17602	−	5.50103i	0.134693	−	0.233296i
$557$	−4.21791	−	7.30563i	−0.178719	−	0.309550i	0.762723	−	0.646725i	$-0.223862\pi$
$557$	−4.21791	−	7.30563i	−0.178719	−	0.309550i	−0.941442	+	0.337175i	$0.890528\pi$
$558$	6.07362			0.257117
$559$	−2.63813			−0.111581
$560$		0			0
$561$	−25.9883	−	45.0130i	−1.09722	−	1.90045i
$562$	−9.27331			−0.391171
$563$	27.9415			1.17760			0.588798	−	0.808280i	$-0.299601\pi$
$563$	27.9415			1.17760			0.588798	+	0.808280i	$0.299601\pi$
$564$	3.15922	+	5.47192i	0.133027	+	0.230410i
$565$		0			0
$566$	13.0034	+	22.5226i	0.546576	+	0.946697i
$567$	−1.43741	+	2.48966i	−0.0603654	+	0.104556i
$568$	1.41164	−	2.44504i	0.0592312	−	0.102591i
$569$	10.7931			0.452472			0.226236	−	0.974072i	$-0.427358\pi$
$569$	10.7931			0.452472			0.226236	+	0.974072i	$0.427358\pi$
$570$		0			0
$571$	6.26581			0.262216			0.131108	−	0.991368i	$-0.458147\pi$
$571$	6.26581			0.262216			0.131108	+	0.991368i	$0.458147\pi$
$572$	9.19149	−	15.9201i	0.384316	−	0.665654i
$573$	5.67017	−	9.82102i	0.236875	−	0.410279i
$574$	2.14820	+	3.72079i	0.0896642	+	0.155303i
$575$		0			0
$576$	0.400626	+	0.693904i	0.0166927	+	0.0289127i
$577$	42.3965			1.76499			0.882494	−	0.470324i	$-0.155863\pi$
$577$	42.3965			1.76499			0.882494	+	0.470324i	$0.155863\pi$
$578$	−45.3879			−1.88789
$579$	−13.2885	−	23.0163i	−0.552250	−	0.956525i
$580$		0			0
$581$	5.98906			0.248468
$582$	1.41358			0.0585946
$583$	7.07244	+	12.2498i	0.292911	+	0.507336i
$584$	−3.43828	+	5.95528i	−0.142277	+	0.246431i
$585$		0			0
$586$	8.72173	−	15.1065i	0.360291	−	0.624043i
$587$	−21.8535	+	37.8513i	−0.901989	+	1.56229i	−0.0770809	+	0.997025i	$0.524560\pi$
$587$	−21.8535	+	37.8513i	−0.901989	+	1.56229i	−0.824908	+	0.565266i	$0.808773\pi$
$588$	−10.0341			−0.413798
$589$	32.7368	+	4.47422i	1.34890	+	0.184357i
$590$		0			0
$591$	−13.7677	+	23.8464i	−0.566329	+	0.980911i
$592$	1.75289	−	3.03610i	0.0720435	−	0.124783i
$593$	14.2795	+	24.7329i	0.586391	+	1.01566i	0.994700	+	0.102815i	$0.0327850\pi$
$593$	14.2795	+	24.7329i	0.586391	+	1.01566i	−0.408310	+	0.912843i	$0.633882\pi$
$594$	12.5070	−	21.6628i	0.513169	−	0.888835i
$595$		0			0
$596$	−12.0420			−0.493260
$597$	−20.0681			−0.821333
$598$	11.7219	+	20.3029i	0.479344	+	0.830247i
$599$	−6.25875	−	10.8405i	−0.255726	−	0.442930i	0.709367	−	0.704840i	$-0.248981\pi$
$599$	−6.25875	−	10.8405i	−0.255726	−	0.442930i	−0.965092	+	0.261910i	$0.915648\pi$
$600$		0			0
$601$	9.44734			0.385365			0.192682	−	0.981261i	$-0.438281\pi$
$601$	9.44734			0.385365			0.192682	+	0.981261i	$0.438281\pi$
$602$	0.153746	+	0.266295i	0.00626620	+	0.0108534i
$603$	5.28626	−	9.15607i	0.215273	−	0.372864i
$604$	0.767418	+	1.32921i	0.0312258	+	0.0540847i
$605$		0			0
$606$	−4.92829	+	8.53606i	−0.200198	+	0.346754i
$607$	15.1486			0.614864			0.307432	−	0.951570i	$-0.400530\pi$
$607$	15.1486			0.614864			0.307432	+	0.951570i	$0.400530\pi$
$608$	1.64820	+	4.03527i	0.0668434	+	0.163652i
$609$	−2.73766			−0.110936
$610$		0			0
$611$	8.82548	−	15.2862i	0.357041	−	0.618413i
$612$	−3.16438	−	5.48087i	−0.127913	−	0.221551i
$613$	3.67718	−	6.36907i	0.148520	−	0.257244i	−0.782161	−	0.623077i	$-0.785882\pi$
$613$	3.67718	−	6.36907i	0.148520	−	0.257244i	0.930681	+	0.365833i	$0.119216\pi$
$614$	0.557182	+	0.965067i	0.0224860	+	0.0389469i
$615$		0			0
$616$	−2.14266			−0.0863300
$617$	15.1038	+	26.1606i	0.608057	+	1.05319i	0.991560	+	0.129646i	$0.0413841\pi$
$617$	15.1038	+	26.1606i	0.608057	+	1.05319i	−0.383504	+	0.923539i	$0.625283\pi$
$618$	−3.06329	−	5.30577i	−0.123224	−	0.213429i
$619$	32.0889			1.28976			0.644881	−	0.764283i	$-0.276907\pi$
$619$	32.0889			1.28976			0.644881	+	0.764283i	$0.276907\pi$
$620$		0			0
$621$	15.9502	+	27.6265i	0.640058	+	1.10861i
$622$	16.9016	−	29.2744i	0.677691	−	1.17380i
$623$	2.11406	+	3.66166i	0.0846981	+	0.146701i
$624$	−3.07118	+	5.31943i	−0.122945	+	0.212948i
$625$		0			0
$626$	−14.7619			−0.590004
$627$	17.5735	−	22.6699i	0.701817	−	0.905347i
$628$	19.0533			0.760309
$629$	−13.8454	+	23.9809i	−0.552052	+	0.956183i
$630$		0			0
$631$	−5.03414	−	8.71938i	−0.200406	−	0.347113i	0.748253	−	0.663413i	$-0.230893\pi$
$631$	−5.03414	−	8.71938i	−0.200406	−	0.347113i	−0.948659	+	0.316300i	$0.897559\pi$
$632$	−0.576026	+	0.997706i	−0.0229131	+	0.0396866i
$633$	9.89121	+	17.1321i	0.393140	+	0.680939i
$634$	−26.1366			−1.03802
$635$		0			0
$636$	−2.36313	−	4.09306i	−0.0937043	−	0.162301i
$637$	14.0154	+	24.2754i	0.555311	+	0.961826i
$638$	16.9698			0.671842
$639$	−2.26216			−0.0894897
$640$		0			0
$641$	15.9198	−	27.5740i	0.628796	−	1.08911i	−0.358997	−	0.933339i	$-0.616881\pi$
$641$	15.9198	−	27.5740i	0.628796	−	1.08911i	0.987794	−	0.155768i	$-0.0497854\pi$
$642$	7.41409	+	12.8416i	0.292611	+	0.506817i
$643$	−20.0270	+	34.6879i	−0.789790	+	1.36796i	0.136306	+	0.990667i	$0.456477\pi$
$643$	−20.0270	+	34.6879i	−0.789790	+	1.36796i	−0.926096	+	0.377289i	$0.876856\pi$
$644$	1.36626	−	2.36643i	0.0538382	−	0.0932506i
$645$		0			0
$646$	−13.0185	−	31.8730i	−0.512205	−	1.25403i
$647$	−5.37891			−0.211467			−0.105733	−	0.994395i	$-0.533719\pi$
$647$	−5.37891			−0.211467			−0.105733	+	0.994395i	$0.533719\pi$
$648$	−2.97712	+	5.15652i	−0.116952	+	0.202567i
$649$	3.60610	−	6.24594i	0.141552	−	0.245175i
$650$		0			0
$651$	2.71344	−	4.69981i	0.106348	−	0.184200i
$652$	−4.98267	−	8.63023i	−0.195136	−	0.337986i
$653$	19.0958			0.747278			0.373639	−	0.927574i	$-0.378110\pi$
$653$	19.0958			0.747278			0.373639	+	0.927574i	$0.378110\pi$
$654$	−27.0110			−1.05621
$655$		0			0
$656$	4.44930	+	7.70641i	0.173716	+	0.300885i
$657$	5.50986			0.214960
$658$	−2.05733			−0.0802032
$659$	−20.3162	−	35.1887i	−0.791407	−	1.37076i	−0.925096	−	0.379733i	$-0.876016\pi$
$659$	−20.3162	−	35.1887i	−0.791407	−	1.37076i	0.133690	−	0.991023i	$-0.457317\pi$
$660$		0			0
$661$	9.76205	+	16.9084i	0.379700	+	0.657659i	0.991018	−	0.133725i	$-0.0426940\pi$
$661$	9.76205	+	16.9084i	0.379700	+	0.657659i	−0.611319	+	0.791384i	$0.709361\pi$
$662$	1.08564	−	1.88038i	0.0421945	−	0.0730830i
$663$	24.2580	−	42.0161i	0.942102	−	1.63177i
$664$	12.4044			0.481384
$665$		0			0
$666$	−2.80902			−0.108847
$667$	−10.8208	+	18.7422i	−0.418983	+	0.725699i
$668$	3.70272	−	6.41331i	0.143263	−	0.248138i
$669$	4.09049	+	7.08493i	0.158147	+	0.273919i
$670$		0			0
$671$	3.26287	+	5.65146i	0.125962	+	0.218172i
$672$	0.715931			0.0276176
$673$	1.79517			0.0691988			0.0345994	−	0.999401i	$-0.488984\pi$
$673$	1.79517			0.0691988			0.0345994	+	0.999401i	$0.488984\pi$
$674$	6.56430	+	11.3697i	0.252847	+	0.437944i
$675$		0			0
$676$	4.15907			0.159964
$677$	6.92605			0.266190			0.133095	−	0.991103i	$-0.457508\pi$
$677$	6.92605			0.266190			0.133095	+	0.991103i	$0.457508\pi$
$678$	6.15149	+	10.6547i	0.236247	+	0.409191i
$679$	−0.230136	+	0.398607i	−0.00883181	+	0.0152971i
$680$		0			0
$681$	16.4931	−	28.5669i	0.632018	−	1.09469i
$682$	−16.8197	+	29.1326i	−0.644059	+	1.11554i
$683$	−11.7972			−0.451407			−0.225704	−	0.974196i	$-0.572468\pi$
$683$	−11.7972			−0.451407			−0.225704	+	0.974196i	$0.572468\pi$
$684$	2.13978	−	2.76033i	0.0818166	−	0.105544i
$685$		0			0
$686$	3.32345	−	5.75638i	0.126890	−	0.219780i
$687$	−12.1844	+	21.1039i	−0.464862	+	0.805165i
$688$	0.318434	+	0.551544i	0.0121402	+	0.0210274i
$689$	−6.60157	+	11.4342i	−0.251500	+	0.435610i
$690$		0			0
$691$	15.3361			0.583413			0.291707	−	0.956508i	$-0.405777\pi$
$691$	15.3361			0.583413			0.291707	+	0.956508i	$0.405777\pi$
$692$	−15.6655			−0.595512
$693$	0.858403	+	1.48680i	0.0326080	+	0.0564788i
$694$	−7.46811	−	12.9352i	−0.283486	−	0.491012i
$695$		0			0
$696$	−5.67017			−0.214927
$697$	−35.1432	−	60.8699i	−1.33115	−	2.30561i
$698$	−9.43056	+	16.3342i	−0.356952	+	0.618259i
$699$	−7.83601	−	13.5724i	−0.296385	−	0.513354i
$700$		0			0
$701$	5.57300	−	9.65272i	0.210489	−	0.364578i	−0.741378	−	0.671087i	$-0.765828\pi$
$701$	5.57300	−	9.65272i	0.210489	−	0.364578i	0.951868	+	0.306509i	$0.0991609\pi$
$702$	23.3486			0.881237
$703$	−15.1406	−	2.06930i	−0.571039	−	0.0780452i
$704$	−4.43782			−0.167256
$705$		0			0
$706$	−1.00586	+	1.74220i	−0.0378561	+	0.0655686i
$707$	−1.60469	−	2.77941i	−0.0603507	−	0.104530i
$708$	−1.20491	+	2.08697i	−0.0452834	+	0.0784332i
$709$	8.65757	+	14.9954i	0.325142	+	0.563162i	0.981541	−	0.191252i	$-0.0612546\pi$
$709$	8.65757	+	14.9954i	0.325142	+	0.563162i	−0.656399	+	0.754414i	$0.727921\pi$
$710$		0			0
$711$	0.923084			0.0346183
$712$	4.37859	+	7.58395i	0.164095	+	0.284220i
$713$	−21.4501	−	37.1527i	−0.803312	−	1.39138i
$714$	−5.65485			−0.211627
$715$		0			0
$716$	−2.30642	−	3.99483i	−0.0861949	−	0.149294i
$717$	11.7606	−	20.3700i	0.439209	−	0.760732i
$718$	−3.29938	−	5.71469i	−0.123132	−	0.213270i
$719$	18.7052	−	32.3983i	0.697585	−	1.20825i	−0.271716	−	0.962377i	$-0.587591\pi$
$719$	18.7052	−	32.3983i	0.697585	−	1.20825i	0.969301	−	0.245875i	$-0.0790754\pi$
$720$		0			0
$721$	1.99486			0.0742926
$722$	13.5669	−	13.3019i	0.504907	−	0.495045i
$723$	6.51468			0.242283
$724$	−0.605224	+	1.04828i	−0.0224930	+	0.0389590i
$725$		0			0
$726$	6.44596	+	11.1647i	0.239232	+	0.414362i
$727$	−17.9095	+	31.0202i	−0.664228	+	1.15048i	0.315266	+	0.949003i	$0.397906\pi$
$727$	−17.9095	+	31.0202i	−0.664228	+	1.15048i	−0.979494	+	0.201474i	$0.935427\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$	29.8448			1.10536
$730$		0			0
$731$	−2.51518	−	4.35643i	−0.0930274	−	0.161128i
$732$	−1.09023	−	1.88834i	−0.0402961	−	0.0697949i
$733$	20.1867			0.745614			0.372807	−	0.927909i	$-0.378395\pi$
$733$	20.1867			0.745614			0.372807	+	0.927909i	$0.378395\pi$
$734$	11.1984			0.413342
$735$		0			0
$736$	2.82977	−	4.90130i	0.104307	−	0.180664i
$737$	29.2785	+	50.7118i	1.07849	+	1.86799i
$738$	3.56501	−	6.17478i	0.131230	−	0.227297i
$739$	19.1178	−	33.1130i	0.703260	−	1.21808i	−0.264056	−	0.964507i	$-0.585060\pi$
$739$	19.1178	−	33.1130i	0.703260	−	1.21808i	0.967316	−	0.253575i	$-0.0816064\pi$
$740$		0			0
$741$	26.5273	+	3.62554i	0.974504	+	0.133188i
$742$	1.53891			0.0564952
$743$	−7.86688	+	13.6258i	−0.288608	+	0.499884i	−0.973478	−	0.228782i	$-0.926526\pi$
$743$	−7.86688	+	13.6258i	−0.288608	+	0.499884i	0.684870	+	0.728665i	$0.259859\pi$
$744$	5.62000	−	9.73413i	0.206039	−	0.356870i
$745$		0			0
$746$	1.59718	−	2.76640i	0.0584771	−	0.101285i
$747$	−4.96952	−	8.60746i	−0.181825	−	0.314930i
$748$	35.0525			1.28165
$749$	−4.82818			−0.176418
$750$		0			0
$751$	12.1150	+	20.9838i	0.442083	+	0.765710i	0.997844	−	0.0656323i	$-0.0209064\pi$
$751$	12.1150	+	20.9838i	0.442083	+	0.765710i	−0.555761	+	0.831342i	$0.687573\pi$
$752$	−4.26110			−0.155386
$753$	21.4075			0.780134
$754$	7.92000	+	13.7178i	0.288429	+	0.499574i
$755$		0			0
$756$	−1.36072	−	2.35683i	−0.0494888	−	0.0857171i
$757$	−7.40312	+	12.8226i	−0.269071	+	0.466045i	−0.968622	−	0.248538i	$-0.920050\pi$
$757$	−7.40312	+	12.8226i	−0.269071	+	0.466045i	0.699551	+	0.714582i	$0.253383\pi$
$758$	8.63331	−	14.9533i	0.313576	−	0.543130i
$759$	−37.2424			−1.35181
$760$		0			0
$761$	−1.98843			−0.0720804			−0.0360402	−	0.999350i	$-0.511474\pi$
$761$	−1.98843			−0.0720804			−0.0360402	+	0.999350i	$0.511474\pi$
$762$	−10.6375	+	18.4247i	−0.385356	+	0.667456i
$763$	4.39750	−	7.61669i	0.159200	−	0.275743i
$764$	3.82392	+	6.62322i	0.138344	+	0.239620i
$765$		0			0
$766$	−16.0924	−	27.8729i	−0.581443	−	1.00709i
$767$	6.73202			0.243079
$768$	1.48282			0.0535066
$769$	14.9388	+	25.8748i	0.538708	+	0.933070i	0.998974	+	0.0452890i	$0.0144209\pi$
$769$	14.9388	+	25.8748i	0.538708	+	0.933070i	−0.460266	+	0.887781i	$0.652246\pi$
$770$		0			0
$771$	16.3633			0.589311
$772$	17.9233			0.645072
$773$	−6.31979	−	10.9462i	−0.227307	−	0.393707i	0.729702	−	0.683765i	$-0.239659\pi$
$773$	−6.31979	−	10.9462i	−0.227307	−	0.393707i	−0.957009	+	0.290058i	$0.906325\pi$
$774$	0.255146	−	0.441926i	0.00917103	−	0.0158847i
$775$		0			0
$776$	−0.476652	+	0.825585i	−0.0171108	+	0.0296368i
$777$	−1.25495	+	2.17364i	−0.0450211	+	0.0779788i
$778$	10.0717			0.361090
$779$	23.7641	−	30.6559i	0.851439	−	1.09836i
$780$		0			0
$781$	6.26461	−	10.8506i	0.224165	−	0.388266i
$782$	−22.3512	+	38.7134i	−0.799277	+	1.38439i
$783$	10.7769	+	18.6661i	0.385134	+	0.667072i
$784$	3.38344	−	5.86030i	0.120837	−	0.209296i
$785$		0			0
$786$	−14.8291			−0.528937
$787$	−46.4316			−1.65511			−0.827554	−	0.561387i	$-0.810268\pi$
$787$	−46.4316			−1.65511			−0.827554	+	0.561387i	$0.810268\pi$
$788$	−9.28485	−	16.0818i	−0.330759	−	0.572892i
$789$	−15.6631	−	27.1292i	−0.557620	−	0.965826i
$790$		0			0
$791$	−4.00595			−0.142435
$792$	1.77790	+	3.07942i	0.0631751	+	0.109422i
$793$	−3.04563	+	5.27519i	−0.108154	+	0.187328i
$794$	17.7217	+	30.6949i	0.628921	+	1.08932i
$795$		0			0
$796$	6.76689	−	11.7206i	0.239846	−	0.415425i
$797$	51.4600			1.82281			0.911404	−	0.411513i	$-0.135000\pi$
$797$	51.4600			1.82281			0.911404	+	0.411513i	$0.135000\pi$
$798$	−1.18000	−	2.88898i	−0.0417714	−	0.102269i
$799$	33.6567			1.19069
$800$		0			0
$801$	3.50836	−	6.07665i	0.123962	−	0.214708i
$802$	−15.4751	−	26.8036i	−0.546445	−	0.946470i
$803$	−15.2585	+	26.4284i	−0.538460	+	0.932639i
$804$	−9.78289	−	16.9445i	−0.345016	−	0.597585i
$805$		0			0
$806$	−31.3997			−1.10601
$807$	20.9794	+	36.3373i	0.738508	+	1.27913i
$808$	−3.32360	−	5.75665i	−0.116924	−	0.202518i
$809$	14.0066			0.492446			0.246223	−	0.969213i	$-0.420811\pi$
$809$	14.0066			0.492446			0.246223	+	0.969213i	$0.420811\pi$
$810$		0			0
$811$	−21.9071	−	37.9442i	−0.769263	−	1.33240i	−0.937963	−	0.346735i	$-0.887290\pi$
$811$	−21.9071	−	37.9442i	−0.769263	−	1.33240i	0.168700	−	0.985667i	$-0.446043\pi$
$812$	0.923127	−	1.59890i	0.0323954	−	0.0561105i
$813$	9.12930	+	15.8124i	0.320178	+	0.554565i
$814$	7.77902	−	13.4737i	0.272654	−	0.472251i
$815$		0			0
$816$	−11.7122			−0.410008
$817$	1.70079	−	2.19402i	0.0595030	−	0.0767592i
$818$	−27.1167			−0.948113
$819$	−0.801252	+	1.38781i	−0.0279980	+	0.0484940i
$820$		0			0
$821$	15.0983	+	26.1510i	0.526934	+	0.912676i	0.999507	+	0.0313848i	$0.00999175\pi$
$821$	15.0983	+	26.1510i	0.526934	+	0.912676i	−0.472574	+	0.881291i	$0.656675\pi$
$822$	2.71274	−	4.69861i	0.0946177	−	0.163883i
$823$	4.78805	+	8.29314i	0.166901	+	0.289081i	0.937329	−	0.348447i	$-0.113291\pi$
$823$	4.78805	+	8.29314i	0.166901	+	0.289081i	−0.770428	+	0.637527i	$0.779957\pi$
$824$	4.13171			0.143935
$825$		0			0
$826$	−0.392330	−	0.679535i	−0.0136509	−	0.0236441i
$827$	−25.4125	−	44.0158i	−0.883681	−	1.53058i	−0.847218	−	0.531245i	$-0.821724\pi$
$827$	−25.4125	−	44.0158i	−0.883681	−	1.53058i	−0.0364625	−	0.999335i	$-0.511609\pi$
$828$	−4.53471			−0.157592
$829$	−40.5305			−1.40768			−0.703841	−	0.710358i	$-0.748533\pi$
$829$	−40.5305			−1.40768			−0.703841	+	0.710358i	$0.748533\pi$
$830$		0			0
$831$	−20.2165	+	35.0160i	−0.701303	+	1.21469i
$832$	−2.07118	−	3.58738i	−0.0718051	−	0.124370i
$833$	−26.7245	+	46.2881i	−0.925948	+	1.60379i
$834$	−4.70946	+	8.15702i	−0.163075	+	0.282455i
$835$		0			0
$836$	7.31441	+	17.9078i	0.252974	+	0.619354i
$837$	−42.7261			−1.47683
$838$	−4.14054	+	7.17162i	−0.143033	+	0.247740i
$839$	−12.9569	+	22.4420i	−0.447322	+	0.774785i	−0.998211	−	0.0597940i	$-0.980956\pi$
$839$	−12.9569	+	22.4420i	−0.447322	+	0.774785i	0.550888	+	0.834579i	$0.314289\pi$
$840$		0			0
$841$	7.18883	−	12.4514i	0.247891	−	0.429359i
$842$	2.95790	+	5.12323i	0.101936	+	0.176558i
$843$	13.7506			0.473597
$844$	−13.3411			−0.459220
$845$		0			0
$846$	1.70711	+	2.95680i	0.0586915	+	0.101657i
$847$	−4.19771			−0.144235
$848$	3.18735			0.109454
$849$	−19.2817	−	33.3970i	−0.661748	−	1.14618i
$850$		0			0
$851$	9.92056	+	17.1829i	0.340072	+	0.589023i
$852$	−2.09321	+	3.62554i	−0.0717121	+	0.124209i
$853$	−10.5760	+	18.3182i	−0.362116	+	0.627204i	−0.988309	−	0.152465i	$-0.951279\pi$
$853$	−10.5760	+	18.3182i	−0.362116	+	0.627204i	0.626193	+	0.779668i	$0.284612\pi$
$854$	0.709977			0.0242949
$855$		0			0
$856$	−10.0000			−0.341793
$857$	−8.72273	+	15.1082i	−0.297963	+	0.516087i	−0.975670	−	0.219245i	$-0.929640\pi$
$857$	−8.72273	+	15.1082i	−0.297963	+	0.516087i	0.677707	+	0.735332i	$0.262974\pi$
$858$	−13.6293	+	23.6067i	−0.465297	+	0.805918i
$859$	21.0863	+	36.5225i	0.719454	+	1.24613i	0.961216	+	0.275796i	$0.0889413\pi$
$859$	21.0863	+	36.5225i	0.719454	+	1.24613i	−0.241762	+	0.970336i	$0.577725\pi$
$860$		0			0
$861$	−3.18539	−	5.51726i	−0.108558	−	0.188028i
$862$	14.9705			0.509898
$863$	29.1252			0.991434			0.495717	−	0.868484i	$-0.334905\pi$
$863$	29.1252			0.991434			0.495717	+	0.868484i	$0.334905\pi$
$864$	−2.81828	−	4.88141i	−0.0958799	−	0.166069i
$865$		0			0
$866$	3.35174			0.113897
$867$	67.3019			2.28569
$868$	1.82992	+	3.16951i	0.0621115	+	0.107580i
$869$	−2.55630	+	4.42764i	−0.0867164	+	0.150197i
$870$		0			0
$871$	−27.3292	+	47.3355i	−0.926013	+	1.60390i
$872$	9.10799	−	15.7755i	0.308435	−	0.534226i
$873$	0.763836			0.0258519
$874$	−24.4421	−	3.34056i	−0.826767	−	0.112996i
$875$		0			0
$876$	5.09835	−	8.83060i	0.172257	−	0.298358i
$877$	5.09781	−	8.82966i	0.172141	−	0.298156i	−0.767027	−	0.641614i	$-0.778265\pi$
$877$	5.09781	−	8.82966i	0.172141	−	0.298156i	0.939168	+	0.343458i	$0.111598\pi$
$878$	6.00116	+	10.3943i	0.202529	+	0.350791i
$879$	−12.9327	+	22.4002i	−0.436210	+	0.755539i
$880$		0			0
$881$	2.18109			0.0734829			0.0367415	−	0.999325i	$-0.488302\pi$
$881$	2.18109			0.0734829			0.0367415	+	0.999325i	$0.488302\pi$
$882$	−5.42198			−0.182568
$883$	3.32626	+	5.76125i	0.111938	+	0.193881i	0.916551	−	0.399917i	$-0.130961\pi$
$883$	3.32626	+	5.76125i	0.111938	+	0.193881i	−0.804614	+	0.593798i	$0.797628\pi$
$884$	16.3594	+	28.3353i	0.550226	+	0.953019i
$885$		0			0
$886$	−26.7944			−0.900175
$887$	0.178225	+	0.308694i	0.00598419	+	0.0103649i	0.869002	−	0.494809i	$-0.164762\pi$
$887$	0.178225	+	0.308694i	0.00598419	+	0.0103649i	−0.863018	+	0.505174i	$0.831428\pi$
$888$	−2.59922	+	4.50198i	−0.0872242	+	0.151077i
$889$	−3.46366	−	5.99923i	−0.116167	−	0.201208i
$890$		0			0
$891$	−13.2119	+	22.8837i	−0.442616	+	0.766633i
$892$	−5.51718			−0.184729
$893$	7.02315	+	17.1947i	0.235021	+	0.575399i
$894$	17.8561			0.597198
$895$		0			0
$896$	−0.241409	+	0.418132i	−0.00806490	+	0.0139688i
$897$	−17.3814	−	30.1055i	−0.580349	−	1.00519i
$898$	1.76804	−	3.06233i	0.0590002	−	0.102191i
$899$	−14.4930	−	25.1025i	−0.483367	−	0.837217i
$900$		0			0
$901$	−25.1756			−0.838722
$902$	19.7452	+	34.1996i	0.657442	+	1.13872i
$903$	−0.227977	−	0.394867i	−0.00758659	−	0.0131404i
$904$	−8.29703			−0.275955
$905$		0			0
$906$	−1.13794	−	1.97097i	−0.0378056	−	0.0654812i
$907$	8.91530	−	15.4418i	0.296028	−	0.512735i	−0.679196	−	0.733957i	$-0.737671\pi$
$907$	8.91530	−	15.4418i	0.296028	−	0.512735i	0.975223	+	0.221222i	$0.0710046\pi$
$908$	11.1228	+	19.2653i	0.369124	+	0.639341i
$909$	−2.66304	+	4.61252i	−0.0883275	+	0.152988i
$910$		0			0
$911$	44.1391			1.46239			0.731196	−	0.682167i	$-0.238962\pi$
$911$	44.1391			1.46239			0.731196	+	0.682167i	$0.238962\pi$
$912$	−2.44398	−	5.98358i	−0.0809283	−	0.198136i
$913$	55.0484			1.82184
$914$	−10.7573	+	18.6323i	−0.355821	+	0.616301i
$915$		0			0
$916$	−8.21703	−	14.2323i	−0.271498	−	0.470249i
$917$	2.41424	−	4.18159i	0.0797253	−	0.138088i
$918$	22.2605	+	38.5563i	0.734705	+	1.27255i
$919$	−19.5399			−0.644563			−0.322281	−	0.946644i	$-0.604450\pi$
$919$	−19.5399			−0.644563			−0.322281	+	0.946644i	$0.604450\pi$
$920$		0			0
$921$	−0.826199	−	1.43102i	−0.0272242	−	0.0471537i
$922$	20.1971	+	34.9825i	0.665157	+	1.15209i
$923$	11.6950			0.384947
$924$	3.17717			0.104521
$925$		0			0
$926$	9.82241	−	17.0129i	0.322784	−	0.559079i
$927$	−1.65527	−	2.86701i	−0.0543662	−	0.0941651i
$928$	1.91196	−	3.31161i	0.0627631	−	0.108709i
$929$	−9.78639	+	16.9505i	−0.321081	+	0.556129i	−0.980711	−	0.195461i	$-0.937380\pi$
$929$	−9.78639	+	16.9505i	−0.321081	+	0.556129i	0.659630	+	0.751590i	$0.270713\pi$
$930$		0			0
$931$	−29.2245	−	3.99418i	−0.957794	−	0.130904i
$932$	10.5691			0.346202
$933$	−25.0620	+	43.4086i	−0.820492	+	1.42113i
$934$	−7.59644	+	13.1574i	−0.248563	+	0.430524i
$935$		0			0
$936$	−1.65953	+	2.87440i	−0.0542435	+	0.0939525i
$937$	4.85875	+	8.41560i	0.158728	+	0.274926i	0.934410	−	0.356198i	$-0.115927\pi$
$937$	4.85875	+	8.41560i	0.158728	+	0.274926i	−0.775682	+	0.631124i	$0.782594\pi$
$938$	6.37078			0.208013
$939$	21.8892			0.714327
$940$		0			0
$941$	20.1536	+	34.9071i	0.656989	+	1.13794i	0.981391	+	0.192019i	$0.0615037\pi$
$941$	20.1536	+	34.9071i	0.656989	+	1.13794i	−0.324402	+	0.945919i	$0.605163\pi$
$942$	−28.2525			−0.920518
$943$	−50.3619			−1.64001
$944$	−0.812584	−	1.40744i	−0.0264474	−	0.0458082i
$945$		0			0
$946$	1.41315	+	2.44765i	0.0459455	+	0.0795800i
$947$	8.00828	−	13.8707i	0.260234	−	0.450739i	−0.706070	−	0.708142i	$-0.749534\pi$
$947$	8.00828	−	13.8707i	0.260234	−	0.450739i	0.966304	+	0.257403i	$0.0828669\pi$
$948$	0.854141	−	1.47942i	0.0277412	−	0.0480492i
$949$	−28.4851			−0.924667
$950$		0			0
$951$	38.7558			1.25674
$952$	1.90679	−	3.30266i	0.0617995	−	0.107040i
$953$	11.9888	−	20.7652i	0.388354	−	0.672649i	−0.603874	−	0.797080i	$-0.706377\pi$
$953$	11.9888	−	20.7652i	0.388354	−	0.672649i	0.992228	+	0.124430i	$0.0397103\pi$
$954$	−1.27694	−	2.21172i	−0.0413423	−	0.0716070i
$955$		0			0
$956$	7.93127	+	13.7374i	0.256516	+	0.444298i
$957$	−25.1632			−0.813410
$958$	4.24064			0.137009
$959$	0.883291	+	1.52991i	0.0285230	+	0.0494032i
$960$		0			0
$961$	26.4589			0.853513
$962$	14.5222			0.468215
$963$	4.00626	+	6.93904i	0.129100	+	0.223608i
$964$	−2.19672	+	3.80483i	−0.0707517	+	0.122545i
$965$		0			0
$966$	−2.02592	+	3.50899i	−0.0651828	+	0.112900i
$967$	11.9386	−	20.6783i	0.383920	−	0.664969i	−0.607699	−	0.794168i	$-0.707907\pi$
$967$	11.9386	−	20.6783i	0.383920	−	0.664969i	0.991619	+	0.129199i	$0.0412405\pi$
$968$	−8.69420			−0.279442
$969$	19.3040	+	47.2619i	0.620135	+	1.51827i
$970$		0			0
$971$	5.71587	−	9.90017i	0.183431	−	0.317712i	−0.759616	−	0.650372i	$-0.774613\pi$
$971$	5.71587	−	9.90017i	0.183431	−	0.317712i	0.943047	+	0.332660i	$0.107946\pi$
$972$	−4.04032	+	6.99804i	−0.129593	+	0.224462i
$973$	−1.53344	−	2.65599i	−0.0491598	−	0.0851473i
$974$	4.00416	−	6.93540i	0.128301	−	0.222225i
$975$		0			0
$976$	1.47049			0.0470691
$977$	−22.3158			−0.713947			−0.356973	−	0.934115i	$-0.616191\pi$
$977$	−22.3158			−0.713947			−0.356973	+	0.934115i	$0.616191\pi$
$978$	7.38838	+	12.7971i	0.236254	+	0.409205i
$979$	19.4314	+	33.6561i	0.621030	+	1.07566i
$980$		0			0
$981$	−14.5956			−0.466001
$982$	−8.53834	−	14.7888i	−0.272469	−	0.471931i
$983$	−18.8948	+	32.7268i	−0.602652	+	1.04382i	0.389766	+	0.920914i	$0.372556\pi$
$983$	−18.8948	+	32.7268i	−0.602652	+	1.04382i	−0.992418	+	0.122910i	$0.960777\pi$
$984$	−6.59750	−	11.4272i	−0.210321	−	0.364286i
$985$		0			0
$986$	−15.1018	+	26.1571i	−0.480939	+	0.833011i
$987$	3.05065			0.0971033
$988$	−11.0624	+	14.2705i	−0.351940	+	0.454005i
$989$	−3.60438			−0.114613
$990$		0			0
$991$	−22.4330	+	38.8551i	−0.712608	+	1.23427i	0.251267	+	0.967918i	$0.419153\pi$
$991$	−22.4330	+	38.8551i	−0.712608	+	1.23427i	−0.963875	+	0.266355i	$0.914181\pi$
$992$	3.79008	+	6.56462i	0.120335	+	0.208427i
$993$	−1.60980	+	2.78826i	−0.0510855	+	0.0884827i
$994$	−0.681566	−	1.18051i	−0.0216180	−	0.0374434i
$995$		0			0
$996$	−18.3934			−0.582819
$997$	28.4034	+	49.1961i	0.899544	+	1.55806i	0.828079	+	0.560612i	$0.189434\pi$
$997$	28.4034	+	49.1961i	0.899544	+	1.55806i	0.0714649	+	0.997443i	$0.477233\pi$
$998$	5.63718	+	9.76389i	0.178442	+	0.309071i
$999$	19.7606			0.625197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.o.201.2		10
5.2	odd	4		190.2.i.a.49.9	yes	20
5.3	odd	4		190.2.i.a.49.2	✓	20
5.4	even	2		950.2.e.n.201.4		10
15.2	even	4		1710.2.t.d.1189.2		20
15.8	even	4		1710.2.t.d.1189.7		20
19.7	even	3	inner	950.2.e.o.501.2		10
95.7	odd	12		190.2.i.a.159.2	yes	20
95.64	even	6		950.2.e.n.501.4		10
95.83	odd	12		190.2.i.a.159.9	yes	20
285.83	even	12		1710.2.t.d.919.2		20
285.197	even	12		1710.2.t.d.919.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.2	✓	20	5.3	odd	4
190.2.i.a.49.9	yes	20	5.2	odd	4
190.2.i.a.159.2	yes	20	95.7	odd	12
190.2.i.a.159.9	yes	20	95.83	odd	12
950.2.e.n.201.4		10	5.4	even	2
950.2.e.n.501.4		10	95.64	even	6
950.2.e.o.201.2		10	1.1	even	1	trivial
950.2.e.o.501.2		10	19.7	even	3	inner
1710.2.t.d.919.2		20	285.83	even	12
1710.2.t.d.919.7		20	285.197	even	12
1710.2.t.d.1189.2		20	15.2	even	4
1710.2.t.d.1189.7		20	15.8	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.741409 + 1.28416i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.741409 + 1.28416i) q^{6} -0.482818 q^{7} -1.00000 q^{8} +(0.400626 + 0.693904i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.741409 + 1.28416i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.741409 + 1.28416i) q^{6} -0.482818 q^{7} -1.00000 q^{8} +(0.400626 + 0.693904i) q^{9} -4.43782 q^{11} +1.48282 q^{12} +(-2.07118 - 3.58738i) q^{13} +(-0.241409 + 0.418132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.94930 - 6.84039i) q^{17} +0.801252 q^{18} +(4.31875 + 0.590253i) q^{19} +(0.357965 - 0.620014i) q^{21} +(-2.21891 + 3.84326i) q^{22} +(-2.82977 - 4.90130i) q^{23} +(0.741409 - 1.28416i) q^{24} -4.14235 q^{26} -5.63656 q^{27} +(0.241409 + 0.418132i) q^{28} +(-1.91196 - 3.31161i) q^{29} +7.58017 q^{31} +(0.500000 + 0.866025i) q^{32} +(3.29024 - 5.69885i) q^{33} +(-3.94930 - 6.84039i) q^{34} +(0.400626 - 0.693904i) q^{36} -3.50579 q^{37} +(2.67055 - 3.44502i) q^{38} +6.14235 q^{39} +(4.44930 - 7.70641i) q^{41} +(-0.357965 - 0.620014i) q^{42} +(0.318434 - 0.551544i) q^{43} +(2.21891 + 3.84326i) q^{44} -5.65953 q^{46} +(2.13055 + 3.69022i) q^{47} +(-0.741409 - 1.28416i) q^{48} -6.76689 q^{49} +(5.85609 + 10.1430i) q^{51} +(-2.07118 + 3.58738i) q^{52} +(-1.59368 - 2.76033i) q^{53} +(-2.81828 + 4.88141i) q^{54} +0.482818 q^{56} +(-3.95994 + 5.10834i) q^{57} -3.82392 q^{58} +(-0.812584 + 1.40744i) q^{59} +(-0.735243 - 1.27348i) q^{61} +(3.79008 - 6.56462i) q^{62} +(-0.193429 - 0.335029i) q^{63} +1.00000 q^{64} +(-3.29024 - 5.69885i) q^{66} +(-6.59750 - 11.4272i) q^{67} -7.89860 q^{68} +8.39206 q^{69} +(-1.41164 + 2.44504i) q^{71} +(-0.400626 - 0.693904i) q^{72} +(3.43828 - 5.95528i) q^{73} +(-1.75289 + 3.03610i) q^{74} +(-1.64820 - 4.03527i) q^{76} +2.14266 q^{77} +(3.07118 - 5.31943i) q^{78} +(0.576026 - 0.997706i) q^{79} +(2.97712 - 5.15652i) q^{81} +(-4.44930 - 7.70641i) q^{82} -12.4044 q^{83} -0.715931 q^{84} +(-0.318434 - 0.551544i) q^{86} +5.67017 q^{87} +4.43782 q^{88} +(-4.37859 - 7.58395i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-2.82977 + 4.90130i) q^{92} +(-5.62000 + 9.73413i) q^{93} +4.26110 q^{94} -1.48282 q^{96} +(0.476652 - 0.825585i) q^{97} +(-3.38344 + 5.86030i) q^{98} +(-1.77790 - 3.07942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9	\( 10 q + 5 q^{2} - 5 q^{4} + 10 q^{7} - 10 q^{8} - 5 q^{9} - 6 q^{11} + 2 q^{13} + 5 q^{14} - 5 q^{16} - 4 q^{17} - 10 q^{18} + 11 q^{19} + 20 q^{21} - 3 q^{22} - 13 q^{23} + 4 q^{26} - 36 q^{27} - 5 q^{28} + 2 q^{29} - 8 q^{31} + 5 q^{32} - 2 q^{33} + 4 q^{34} - 5 q^{36} - 10 q^{37} + 13 q^{38} + 16 q^{39} + q^{41} - 20 q^{42} + 3 q^{44} - 26 q^{46} + 10 q^{47} - 20 q^{49} + 4 q^{51} + 2 q^{52} - 5 q^{53} - 18 q^{54} - 10 q^{56} + 10 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{61} - 4 q^{62} - 23 q^{63} + 10 q^{64} + 2 q^{66} - 4 q^{67} + 8 q^{68} - 24 q^{69} - 22 q^{71} + 5 q^{72} - 26 q^{73} - 5 q^{74} + 2 q^{76} - 10 q^{77} + 8 q^{78} + 2 q^{79} - 5 q^{81} - q^{82} - 12 q^{83} - 40 q^{84} + 20 q^{87} + 6 q^{88} - q^{89} + 10 q^{91} - 13 q^{92} - 6 q^{93} + 20 q^{94} - 8 q^{97} - 10 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 + 10 * q^7 - 10 * q^8 - 5 * q^9 - 6 * q^11 + 2 * q^13 + 5 * q^14 - 5 * q^16 - 4 * q^17 - 10 * q^18 + 11 * q^19 + 20 * q^21 - 3 * q^22 - 13 * q^23 + 4 * q^26 - 36 * q^27 - 5 * q^28 + 2 * q^29 - 8 * q^31 + 5 * q^32 - 2 * q^33 + 4 * q^34 - 5 * q^36 - 10 * q^37 + 13 * q^38 + 16 * q^39 + q^41 - 20 * q^42 + 3 * q^44 - 26 * q^46 + 10 * q^47 - 20 * q^49 + 4 * q^51 + 2 * q^52 - 5 * q^53 - 18 * q^54 - 10 * q^56 + 10 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^61 - 4 * q^62 - 23 * q^63 + 10 * q^64 + 2 * q^66 - 4 * q^67 + 8 * q^68 - 24 * q^69 - 22 * q^71 + 5 * q^72 - 26 * q^73 - 5 * q^74 + 2 * q^76 - 10 * q^77 + 8 * q^78 + 2 * q^79 - 5 * q^81 - q^82 - 12 * q^83 - 40 * q^84 + 20 * q^87 + 6 * q^88 - q^89 + 10 * q^91 - 13 * q^92 - 6 * q^93 + 20 * q^94 - 8 * q^97 - 10 * q^98 + 13 * q^99

Introduction

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