LMFDB - Embedded newform 950.2.e.n.201.4

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			201.4
Root			$0.741409 - 1.28416i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.n.501.4

$q$-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	−0.568647	−	0.822581i	$-0.692533\pi$
$3$	0.741409	−	1.28416i	0.428053	−	0.741409i	0.996700	+	0.0811725i	$0.0258665\pi$
$4$	−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	$-0.470916\pi$
$7$	0.482818			0.182488			0.0912440	+	0.995829i	$0.470916\pi$
$8$	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	$0.0281137\pi$
$13$	2.07118	+	3.58738i	0.574441	+	0.994960i	−0.421661	+	0.906753i	$0.638553\pi$
$14$	−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	$0.573915\pi$
$17$	−3.94930	+	6.84039i	−0.957846	+	1.65904i	−0.727717	+	0.685878i	$0.759419\pi$
$18$	−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	$0.0342242\pi$
$23$	2.82977	+	4.90130i	0.590047	+	1.02199i	−0.404178	+	0.914680i	$0.632443\pi$
$24$	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	$-0.406952\pi$
$37$	3.50579			0.576348			0.288174	+	0.957578i	$0.406952\pi$
$38$	−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	−0.889284	−	0.457355i	$-0.848797\pi$
$43$	−0.318434	+	0.551544i	−0.0485607	+	0.0841097i	0.840723	+	0.541465i	$0.182130\pi$
$44$	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	0.667757	−	0.744379i	$-0.267254\pi$
$47$	−2.13055	−	3.69022i	−0.310773	−	0.538274i	−0.978530	+	0.206105i	$0.933921\pi$
$48$	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	0.954474	−	0.298293i	$-0.0964171\pi$
$53$	1.59368	+	2.76033i	0.218908	+	0.379160i	−0.735566	+	0.677453i	$0.763084\pi$
$54$	−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	$0.131712\pi$
$67$	6.59750	+	11.4272i	0.806013	+	1.39606i	−0.109592	+	0.993977i	$0.534954\pi$
$68$	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	−0.994017	−	0.109221i	$-0.965164\pi$
$73$	−3.43828	+	5.95528i	−0.402421	+	0.697013i	0.591597	+	0.806234i	$0.298498\pi$
$74$	−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	$-0.261641\pi$
$83$	12.4044			1.36156			0.680779	+	0.732489i	$0.261641\pi$
$84$	−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	−0.889209	−	0.457501i	$-0.848744\pi$
$97$	−0.476652	+	0.825585i	−0.0483967	+	0.0838255i	0.840812	+	0.541327i	$0.182078\pi$
$98$	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	$-0.434750\pi$
$103$	4.13171			0.407110			0.203555	+	0.979064i	$0.434750\pi$
$104$	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	$-0.660587\pi$
$107$	−10.0000			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$108$	−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	$-0.627615\pi$
$113$	−8.29703			−0.780519			−0.390260	+	0.920705i	$0.627615\pi$
$114$	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	$-0.947017\pi$
$127$	−7.17384	−	12.4255i	−0.636576	−	1.10258i	0.349603	−	0.936898i	$-0.386316\pi$
$128$	−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	0.933532	−	0.358495i	$-0.116710\pi$
$137$	1.82945	+	3.16870i	0.156301	+	0.270720i	−0.777231	+	0.629215i	$0.783377\pi$
$138$	−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	$-0.558381\pi$
$157$	9.52664	−	16.5006i	0.760309	−	1.31689i	0.942691	−	0.333666i	$-0.108286\pi$
$158$	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	$-0.627619\pi$
$163$	−9.96533			−0.780545			−0.390272	+	0.920699i	$0.627619\pi$
$164$	−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	0.686453	−	0.727175i	$-0.259167\pi$
$167$	−3.70272	−	6.41331i	−0.286525	−	0.496277i	−0.972978	+	0.230898i	$0.925834\pi$
$168$	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	$0.369718\pi$
$173$	−7.83274	+	13.5667i	−0.595512	+	1.03146i	−0.993474	+	0.114056i	$0.963616\pi$
$174$	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	$-0.610161\pi$
$193$	8.96163	−	15.5220i	0.645072	−	1.11730i	0.984285	−	0.176588i	$-0.0565061\pi$
$194$	−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	$-0.730088\pi$
$197$	−18.5697			−1.32304			−0.661518	+	0.749929i	$0.730088\pi$
$198$	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	−0.943485	−	0.331415i	$-0.892474\pi$
$223$	−2.75859	+	4.77802i	−0.184729	+	0.319960i	0.758756	+	0.651375i	$0.225807\pi$
$224$	−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	$-0.235653\pi$
$227$	22.2457			1.47650			0.738248	+	0.674529i	$0.235653\pi$
$228$	−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	−0.639370	−	0.768899i	$-0.720805\pi$
$233$	5.28454	−	9.15309i	0.346202	−	0.599639i	0.985571	+	0.169261i	$0.0541380\pi$
$234$	−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	0.985205	−	0.171382i	$-0.0548231\pi$
$257$	5.51765	+	9.55685i	0.344182	+	0.596140i	−0.641023	+	0.767522i	$0.721490\pi$
$258$	−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	$-0.607538\pi$
$263$	10.5630	−	18.2957i	0.651345	−	1.12816i	0.982797	−	0.184691i	$-0.0591284\pi$
$264$	−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	$-0.805570\pi$
$277$	−27.2677			−1.63836			−0.819178	+	0.573539i	$0.805570\pi$
$278$	−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	$-0.552101\pi$
$283$	13.0034	−	22.5226i	0.772975	−	1.33883i	0.935926	−	0.352197i	$-0.114565\pi$
$284$	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	$-0.670180\pi$
$293$	−17.4435			−1.01906			−0.509529	+	0.860453i	$0.670180\pi$
$294$	−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	−0.849687	−	0.527287i	$-0.823209\pi$
$307$	0.557182	−	0.965067i	0.0318000	−	0.0550793i	0.881487	+	0.472207i	$0.156543\pi$
$308$	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	0.995656	−	0.0931060i	$-0.0296796\pi$
$313$	7.38095	+	12.7842i	0.417196	+	0.722605i	−0.578460	+	0.815711i	$0.696346\pi$
$314$	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	$0.0956770\pi$
$317$	13.0683	+	22.6350i	0.733989	+	1.27131i	−0.221177	+	0.975234i	$0.570990\pi$
$318$	−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	−0.629976	−	0.776615i	$-0.716935\pi$
$337$	6.56430	−	11.3697i	0.357580	−	0.619347i	0.987556	+	0.157268i	$0.0502686\pi$
$338$	−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	−0.993836	−	0.110861i	$-0.964639\pi$
$347$	−7.46811	+	12.9352i	−0.400909	+	0.694395i	0.592927	+	0.805257i	$0.297972\pi$
$348$	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	$-0.482951\pi$
$353$	2.01172			0.107073			0.0535366	+	0.998566i	$0.482951\pi$
$354$	−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	0.682071	−	0.731286i	$-0.261080\pi$
$367$	−5.59922	−	9.69814i	−0.292277	−	0.506239i	−0.974348	+	0.225048i	$0.927746\pi$
$368$	−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	$-0.526354\pi$
$373$	−3.19437			−0.165398			−0.0826991	+	0.996575i	$0.526354\pi$
$374$	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	$0.473968\pi$
$383$	−16.0924	+	27.8729i	−0.822285	+	1.42424i	−0.903977	+	0.427582i	$0.859366\pi$
$384$	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	$-0.484436\pi$
$397$	17.7217	−	30.6949i	0.889428	−	1.54053i	0.840553	−	0.541730i	$-0.182230\pi$
$398$	−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	0.822944	−	0.568123i	$-0.192330\pi$
$433$	−1.67587	−	2.90269i	−0.0805371	−	0.139494i	−0.903481	+	0.428629i	$0.858997\pi$
$434$	−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	$0.0529600\pi$
$443$	13.3972	+	23.2046i	0.636520	+	1.10248i	−0.349671	+	0.936873i	$0.613707\pi$
$444$	−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	$-0.332153\pi$
$457$	21.5147			1.00642			0.503208	+	0.864166i	$0.332153\pi$
$458$	−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	$-0.650892\pi$
$463$	−19.6448			−0.912972			−0.456486	+	0.889731i	$0.650892\pi$
$464$	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	$-0.385665\pi$
$467$	15.1929			0.703042			0.351521	+	0.936180i	$0.385665\pi$
$468$	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	$-0.558078\pi$
$487$	−8.00831			−0.362891			−0.181446	+	0.983401i	$0.558078\pi$
$488$	−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	0.945123	−	0.326715i	$-0.105942\pi$
$503$	4.25268	+	7.36586i	0.189618	+	0.328427i	−0.755505	+	0.655143i	$0.772609\pi$
$504$	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	0.980800	−	0.195017i	$-0.0624763\pi$
$523$	7.35267	+	12.7352i	0.321510	+	0.556872i	−0.659290	+	0.751889i	$0.729143\pi$
$524$	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	0.892403	−	0.451239i	$-0.149018\pi$
$547$	1.29610	+	2.24490i	0.0554171	+	0.0959852i	−0.836986	+	0.547224i	$0.815684\pi$
$548$	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	0.941442	−	0.337175i	$-0.109472\pi$
$557$	4.21791	+	7.30563i	0.178719	+	0.309550i	−0.762723	+	0.646725i	$0.776138\pi$
$558$	−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	$-0.700399\pi$
$563$	−27.9415			−1.17760			−0.588798	+	0.808280i	$0.700399\pi$
$564$	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	$-0.844137\pi$
$577$	−42.3965			−1.76499			−0.882494	+	0.470324i	$0.844137\pi$
$578$	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	$-0.475440\pi$
$587$	21.8535	−	37.8513i	0.901989	−	1.56229i	0.824908	−	0.565266i	$-0.191227\pi$
$588$	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	$-0.967215\pi$
$593$	−14.2795	−	24.7329i	−0.586391	−	1.01566i	0.408310	−	0.912843i	$-0.366118\pi$
$594$	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	$-0.599470\pi$
$607$	−15.1486			−0.614864			−0.307432	+	0.951570i	$0.599470\pi$
$608$	−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	−0.930681	−	0.365833i	$-0.880784\pi$
$613$	−3.67718	+	6.36907i	−0.148520	+	0.257244i	0.782161	+	0.623077i	$0.214118\pi$
$614$	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	$-0.958616\pi$
$617$	−15.1038	−	26.1606i	−0.608057	−	1.05319i	0.383504	−	0.923539i	$-0.374717\pi$
$618$	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	$-0.543523\pi$
$643$	20.0270	−	34.6879i	0.789790	−	1.36796i	0.926096	−	0.377289i	$-0.123144\pi$
$644$	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	$-0.466281\pi$
$647$	5.37891			0.211467			0.105733	+	0.994395i	$0.466281\pi$
$648$	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	$-0.621890\pi$
$653$	−19.0958			−0.747278			−0.373639	+	0.927574i	$0.621890\pi$
$654$	−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	$-0.511016\pi$
$673$	−1.79517			−0.0691988			−0.0345994	+	0.999401i	$0.511016\pi$
$674$	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	$-0.542492\pi$
$677$	−6.92605			−0.266190			−0.133095	+	0.991103i	$0.542492\pi$
$678$	−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	$-0.427532\pi$
$683$	11.7972			0.451407			0.225704	+	0.974196i	$0.427532\pi$
$684$	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	$-0.602094\pi$
$727$	17.9095	−	31.0202i	0.664228	−	1.15048i	0.979494	−	0.201474i	$-0.0645730\pi$
$728$	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	$-0.621605\pi$
$733$	−20.1867			−0.745614			−0.372807	+	0.927909i	$0.621605\pi$
$734$	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	−0.684870	−	0.728665i	$-0.740141\pi$
$743$	7.86688	−	13.6258i	0.288608	−	0.499884i	0.973478	+	0.228782i	$0.0734743\pi$
$744$	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	−0.699551	−	0.714582i	$-0.746617\pi$
$757$	7.40312	−	12.8226i	0.269071	−	0.466045i	0.968622	+	0.248538i	$0.0799500\pi$
$758$	−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	0.957009	−	0.290058i	$-0.0936746\pi$
$773$	6.31979	+	10.9462i	0.227307	+	0.393707i	−0.729702	+	0.683765i	$0.760341\pi$
$774$	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	$-0.189732\pi$
$787$	46.4316			1.65511			0.827554	+	0.561387i	$0.189732\pi$
$788$	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	$-0.865000\pi$
$797$	−51.4600			−1.82281			−0.911404	+	0.411513i	$0.865000\pi$
$798$	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	0.770428	−	0.637527i	$-0.220043\pi$
$823$	−4.78805	−	8.29314i	−0.166901	−	0.289081i	−0.937329	+	0.348447i	$0.886709\pi$
$824$	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	$0.178276\pi$
$827$	25.4125	+	44.0158i	0.883681	+	1.53058i	0.0364625	+	0.999335i	$0.488391\pi$
$828$	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	−0.626193	−	0.779668i	$-0.715388\pi$
$853$	10.5760	−	18.3182i	0.362116	−	0.627204i	0.988309	+	0.152465i	$0.0487210\pi$
$854$	0.709977			0.0242949
$855$		0			0
$856$	−10.0000			−0.341793
$857$	8.72273	−	15.1082i	0.297963	−	0.516087i	−0.677707	−	0.735332i	$-0.737026\pi$
$857$	8.72273	−	15.1082i	0.297963	−	0.516087i	0.975670	+	0.219245i	$0.0703596\pi$
$858$	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	$-0.665095\pi$
$863$	−29.1252			−0.991434			−0.495717	+	0.868484i	$0.665095\pi$
$864$	−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	−0.939168	−	0.343458i	$-0.888402\pi$
$877$	−5.09781	+	8.82966i	−0.172141	+	0.298156i	0.767027	+	0.641614i	$0.221735\pi$
$878$	−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	0.804614	−	0.593798i	$-0.202372\pi$
$883$	−3.32626	−	5.76125i	−0.111938	−	0.193881i	−0.916551	+	0.399917i	$0.869039\pi$
$884$	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	0.863018	−	0.505174i	$-0.168572\pi$
$887$	−0.178225	−	0.308694i	−0.00598419	−	0.0103649i	−0.869002	+	0.494809i	$0.835238\pi$
$888$	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	−0.975223	−	0.221222i	$-0.928995\pi$
$907$	−8.91530	+	15.4418i	−0.296028	+	0.512735i	0.679196	+	0.733957i	$0.262329\pi$
$908$	−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	0.775682	−	0.631124i	$-0.217406\pi$
$937$	−4.85875	−	8.41560i	−0.158728	−	0.274926i	−0.934410	+	0.356198i	$0.884073\pi$
$938$	−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	−0.966304	−	0.257403i	$-0.917133\pi$
$947$	−8.00828	+	13.8707i	−0.260234	+	0.450739i	0.706070	+	0.708142i	$0.250466\pi$
$948$	−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	−0.992228	−	0.124430i	$-0.960290\pi$
$953$	−11.9888	+	20.7652i	−0.388354	+	0.672649i	0.603874	+	0.797080i	$0.293623\pi$
$954$	−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	−0.991619	−	0.129199i	$-0.958759\pi$
$967$	−11.9386	+	20.6783i	−0.383920	+	0.664969i	0.607699	+	0.794168i	$0.292093\pi$
$968$	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	$-0.383809\pi$
$977$	22.3158			0.713947			0.356973	+	0.934115i	$0.383809\pi$
$978$	−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	$-0.627444\pi$
$983$	18.8948	−	32.7268i	0.602652	−	1.04382i	0.992418	−	0.122910i	$-0.0392226\pi$
$984$	−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	$-0.810566\pi$
$997$	−28.4034	−	49.1961i	−0.899544	−	1.55806i	−0.0714649	−	0.997443i	$-0.522767\pi$
$998$	−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.n.201.4		10
5.2	odd	4		190.2.i.a.49.2	✓	20
5.3	odd	4		190.2.i.a.49.9	yes	20
5.4	even	2		950.2.e.o.201.2		10
15.2	even	4		1710.2.t.d.1189.7		20
15.8	even	4		1710.2.t.d.1189.2		20
19.7	even	3	inner	950.2.e.n.501.4		10
95.7	odd	12		190.2.i.a.159.9	yes	20
95.64	even	6		950.2.e.o.501.2		10
95.83	odd	12		190.2.i.a.159.2	yes	20
285.83	even	12		1710.2.t.d.919.7		20
285.197	even	12		1710.2.t.d.919.2		20

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