LMFDB - Embedded newform 187.2.e.b.166.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (of order $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			166.1
Character	$\chi$	$=$	187.166
Dual form			187.2.e.b.89.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44021i q^{2} +(1.95471 + 1.95471i) q^{3} -3.95461 q^{4} +(-2.54760 - 2.54760i) q^{5} +(4.76990 - 4.76990i) q^{6} +(2.90400 - 2.90400i) q^{7} +4.76964i q^{8} +4.64179i q^{9} +O(q^{10})$	\(q-2.44021i q^{2} +(1.95471 + 1.95471i) q^{3} -3.95461 q^{4} +(-2.54760 - 2.54760i) q^{5} +(4.76990 - 4.76990i) q^{6} +(2.90400 - 2.90400i) q^{7} +4.76964i q^{8} +4.64179i q^{9} +(-6.21666 + 6.21666i) q^{10} +(0.707107 - 0.707107i) q^{11} +(-7.73011 - 7.73011i) q^{12} +2.89464 q^{13} +(-7.08636 - 7.08636i) q^{14} -9.95963i q^{15} +3.72970 q^{16} +(-2.37753 + 3.36858i) q^{17} +11.3269 q^{18} +1.89140i q^{19} +(10.0747 + 10.0747i) q^{20} +11.3530 q^{21} +(-1.72549 - 1.72549i) q^{22} +(-2.10664 + 2.10664i) q^{23} +(-9.32327 + 9.32327i) q^{24} +7.98049i q^{25} -7.06352i q^{26} +(-3.20922 + 3.20922i) q^{27} +(-11.4842 + 11.4842i) q^{28} +(0.555364 + 0.555364i) q^{29} -24.3035 q^{30} +(2.41226 + 2.41226i) q^{31} +0.438048i q^{32} +2.76438 q^{33} +(8.22003 + 5.80167i) q^{34} -14.7964 q^{35} -18.3564i q^{36} +(5.49794 + 5.49794i) q^{37} +4.61540 q^{38} +(5.65818 + 5.65818i) q^{39} +(12.1511 - 12.1511i) q^{40} +(0.450757 - 0.450757i) q^{41} -27.7036i q^{42} +2.06706i q^{43} +(-2.79633 + 2.79633i) q^{44} +(11.8254 - 11.8254i) q^{45} +(5.14062 + 5.14062i) q^{46} +0.294091 q^{47} +(7.29049 + 7.29049i) q^{48} -9.86643i q^{49} +19.4741 q^{50} +(-11.2320 + 1.93721i) q^{51} -11.4472 q^{52} -2.92820i q^{53} +(7.83116 + 7.83116i) q^{54} -3.60285 q^{55} +(13.8510 + 13.8510i) q^{56} +(-3.69714 + 3.69714i) q^{57} +(1.35520 - 1.35520i) q^{58} -12.3477i q^{59} +39.3864i q^{60} +(-3.71940 + 3.71940i) q^{61} +(5.88640 - 5.88640i) q^{62} +(13.4797 + 13.4797i) q^{63} +8.52833 q^{64} +(-7.37437 - 7.37437i) q^{65} -6.74565i q^{66} -12.4245 q^{67} +(9.40221 - 13.3214i) q^{68} -8.23572 q^{69} +36.1064i q^{70} +(-4.28995 - 4.28995i) q^{71} -22.1397 q^{72} +(-2.42620 - 2.42620i) q^{73} +(13.4161 - 13.4161i) q^{74} +(-15.5996 + 15.5996i) q^{75} -7.47974i q^{76} -4.10688i q^{77} +(13.8071 - 13.8071i) q^{78} +(6.97385 - 6.97385i) q^{79} +(-9.50177 - 9.50177i) q^{80} +1.37917 q^{81} +(-1.09994 - 1.09994i) q^{82} +14.3336i q^{83} -44.8965 q^{84} +(14.6388 - 2.52478i) q^{85} +5.04405 q^{86} +2.17115i q^{87} +(3.37265 + 3.37265i) q^{88} -7.23419 q^{89} +(-28.8564 - 28.8564i) q^{90} +(8.40603 - 8.40603i) q^{91} +(8.33091 - 8.33091i) q^{92} +9.43053i q^{93} -0.717641i q^{94} +(4.81852 - 4.81852i) q^{95} +(-0.856257 + 0.856257i) q^{96} +(-5.53105 - 5.53105i) q^{97} -24.0761 q^{98} +(3.28224 + 3.28224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	2.44021i		−	1.72549i	−0.505642	−	0.862743i	$-0.668744\pi$
$2$		−	2.44021i		−	1.72549i	0.505642	−	0.862743i	$-0.331256\pi$
$3$	1.95471	+	1.95471i	1.12855	+	1.12855i	0.990413	+	0.138140i	$0.0441124\pi$
$3$	1.95471	+	1.95471i	1.12855	+	1.12855i	0.138140	+	0.990413i	$0.455888\pi$
$4$	−3.95461			−1.97730
$5$	−2.54760	−	2.54760i	−1.13932	−	1.13932i	−0.988572	−	0.150747i	$-0.951832\pi$
$5$	−2.54760	−	2.54760i	−1.13932	−	1.13932i	−0.150747	−	0.988572i	$-0.548168\pi$
$6$	4.76990	−	4.76990i	1.94730	−	1.94730i
$7$	2.90400	−	2.90400i	1.09761	−	1.09761i	0.102919	−	0.994690i	$-0.467182\pi$
$7$	2.90400	−	2.90400i	1.09761	−	1.09761i	0.994690	−	0.102919i	$-0.0328182\pi$
$8$			4.76964i			1.68632i
$9$			4.64179i			1.54726i
$10$	−6.21666	+	6.21666i	−1.96588	+	1.96588i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	−7.73011	−	7.73011i	−2.23149	−	2.23149i
$13$	2.89464			0.802829			0.401414	−	0.915897i	$-0.368519\pi$
$13$	2.89464			0.802829			0.401414	+	0.915897i	$0.368519\pi$
$14$	−7.08636	−	7.08636i	−1.89391	−	1.89391i
$15$		−	9.95963i		−	2.57156i
$16$	3.72970			0.932425
$17$	−2.37753	+	3.36858i	−0.576637	+	0.817001i
$17$	−2.37753	+	3.36858i	−0.576637	+	0.817001i
$18$	11.3269			2.66978
$19$			1.89140i			0.433917i	0.976181	+	0.216958i	$0.0696136\pi$
$19$			1.89140i			0.433917i	−0.976181	+	0.216958i	$0.930386\pi$
$20$	10.0747	+	10.0747i	2.25278	+	2.25278i
$21$	11.3530			2.47742
$22$	−1.72549	−	1.72549i	−0.367875	−	0.367875i
$23$	−2.10664	+	2.10664i	−0.439264	+	0.439264i	−0.891764	−	0.452500i	$-0.850532\pi$
$23$	−2.10664	+	2.10664i	−0.439264	+	0.439264i	0.452500	+	0.891764i	$0.350532\pi$
$24$	−9.32327	+	9.32327i	−1.90311	+	1.90311i
$25$			7.98049i			1.59610i
$26$		−	7.06352i		−	1.38527i
$27$	−3.20922	+	3.20922i	−0.617615	+	0.617615i
$28$	−11.4842	+	11.4842i	−2.17031	+	2.17031i
$29$	0.555364	+	0.555364i	0.103128	+	0.103128i	0.756788	−	0.653660i	$-0.226767\pi$
$29$	0.555364	+	0.555364i	0.103128	+	0.103128i	−0.653660	+	0.756788i	$0.726767\pi$
$30$	−24.3035			−4.43720
$31$	2.41226	+	2.41226i	0.433254	+	0.433254i	0.889734	−	0.456480i	$-0.150890\pi$
$31$	2.41226	+	2.41226i	0.433254	+	0.433254i	−0.456480	+	0.889734i	$0.650890\pi$
$32$			0.438048i			0.0774367i
$33$	2.76438			0.481217
$34$	8.22003	+	5.80167i	1.40972	+	0.994979i
$35$	−14.7964			−2.50105
$36$		−	18.3564i		−	3.05941i
$37$	5.49794	+	5.49794i	0.903855	+	0.903855i	0.995767	−	0.0919118i	$-0.0292978\pi$
$37$	5.49794	+	5.49794i	0.903855	+	0.903855i	−0.0919118	+	0.995767i	$0.529298\pi$
$38$	4.61540			0.748717
$39$	5.65818	+	5.65818i	0.906034	+	0.906034i
$40$	12.1511	−	12.1511i	1.92126	−	1.92126i
$41$	0.450757	−	0.450757i	0.0703965	−	0.0703965i	−0.671032	−	0.741428i	$-0.734149\pi$
$41$	0.450757	−	0.450757i	0.0703965	−	0.0703965i	0.741428	+	0.671032i	$0.234149\pi$
$42$		−	27.7036i		−	4.27475i
$43$			2.06706i			0.315223i	0.987501	+	0.157612i	$0.0503794\pi$
$43$			2.06706i			0.315223i	−0.987501	+	0.157612i	$0.949621\pi$
$44$	−2.79633	+	2.79633i	−0.421562	+	0.421562i
$45$	11.8254	−	11.8254i	1.76283	−	1.76283i
$46$	5.14062	+	5.14062i	0.757944	+	0.757944i
$47$	0.294091			0.0428975			0.0214488	−	0.999770i	$-0.493172\pi$
$47$	0.294091			0.0428975			0.0214488	+	0.999770i	$0.493172\pi$
$48$	7.29049	+	7.29049i	1.05229	+	1.05229i
$49$		−	9.86643i		−	1.40949i
$50$	19.4741			2.75405
$51$	−11.2320	+	1.93721i	−1.57279	+	0.271263i
$52$	−11.4472			−1.58744
$53$		−	2.92820i		−	0.402219i	−0.979569	−	0.201110i	$-0.935545\pi$
$53$		−	2.92820i		−	0.402219i	0.979569	−	0.201110i	$-0.0644548\pi$
$54$	7.83116	+	7.83116i	1.06569	+	1.06569i
$55$	−3.60285			−0.485808
$56$	13.8510	+	13.8510i	1.85092	+	1.85092i
$57$	−3.69714	+	3.69714i	−0.489698	+	0.489698i
$58$	1.35520	−	1.35520i	0.177947	−	0.177947i
$59$		−	12.3477i		−	1.60753i	−0.594948	−	0.803764i	$-0.702827\pi$
$59$		−	12.3477i		−	1.60753i	0.594948	−	0.803764i	$-0.297173\pi$
$60$			39.3864i			5.08476i
$61$	−3.71940	+	3.71940i	−0.476221	+	0.476221i	−0.903921	−	0.427700i	$-0.859324\pi$
$61$	−3.71940	+	3.71940i	−0.476221	+	0.476221i	0.427700	+	0.903921i	$0.359324\pi$
$62$	5.88640	−	5.88640i	0.747574	−	0.747574i
$63$	13.4797	+	13.4797i	1.69829	+	1.69829i
$64$	8.52833			1.06604
$65$	−7.37437	−	7.37437i	−0.914679	−	0.914679i
$66$		−	6.74565i		−	0.830333i
$67$	−12.4245			−1.51790			−0.758949	−	0.651150i	$-0.774287\pi$
$67$	−12.4245			−1.51790			−0.758949	+	0.651150i	$0.774287\pi$
$68$	9.40221	−	13.3214i	1.14019	−	1.61546i
$69$	−8.23572			−0.991465
$70$			36.1064i			4.31554i
$71$	−4.28995	−	4.28995i	−0.509124	−	0.509124i	0.405134	−	0.914257i	$-0.367225\pi$
$71$	−4.28995	−	4.28995i	−0.509124	−	0.509124i	−0.914257	+	0.405134i	$0.867225\pi$
$72$	−22.1397			−2.60919
$73$	−2.42620	−	2.42620i	−0.283965	−	0.283965i	0.550723	−	0.834688i	$-0.314352\pi$
$73$	−2.42620	−	2.42620i	−0.283965	−	0.283965i	−0.834688	+	0.550723i	$0.814352\pi$
$74$	13.4161	−	13.4161i	1.55959	−	1.55959i
$75$	−15.5996	+	15.5996i	−1.80128	+	1.80128i
$76$		−	7.47974i		−	0.857985i
$77$		−	4.10688i		−	0.468022i
$78$	13.8071	−	13.8071i	1.56335	−	1.56335i
$79$	6.97385	−	6.97385i	0.784619	−	0.784619i	−0.195987	−	0.980606i	$-0.562791\pi$
$79$	6.97385	−	6.97385i	0.784619	−	0.784619i	0.980606	+	0.195987i	$0.0627911\pi$
$80$	−9.50177	−	9.50177i	−1.06233	−	1.06233i
$81$	1.37917			0.153241
$82$	−1.09994	−	1.09994i	−0.121468	−	0.121468i
$83$			14.3336i			1.57332i	0.617386	+	0.786661i	$0.288192\pi$
$83$			14.3336i			1.57332i	−0.617386	+	0.786661i	$0.711808\pi$
$84$	−44.8965			−4.89861
$85$	14.6388	−	2.52478i	1.58780	−	0.273851i
$86$	5.04405			0.543914
$87$			2.17115i			0.232772i
$88$	3.37265	+	3.37265i	0.359525	+	0.359525i
$89$	−7.23419			−0.766822			−0.383411	−	0.923578i	$-0.625251\pi$
$89$	−7.23419			−0.766822			−0.383411	+	0.923578i	$0.625251\pi$
$90$	−28.8564	−	28.8564i	−3.04173	−	3.04173i
$91$	8.40603	−	8.40603i	0.881192	−	0.881192i
$92$	8.33091	−	8.33091i	0.868558	−	0.868558i
$93$			9.43053i			0.977900i
$94$		−	0.717641i		−	0.0740191i
$95$	4.81852	−	4.81852i	0.494370	−	0.494370i
$96$	−0.856257	+	0.856257i	−0.0873914	+	0.0873914i
$97$	−5.53105	−	5.53105i	−0.561593	−	0.561593i	0.368167	−	0.929760i	$-0.379985\pi$
$97$	−5.53105	−	5.53105i	−0.561593	−	0.561593i	−0.929760	+	0.368167i	$0.879985\pi$
$98$	−24.0761			−2.43206
$99$	3.28224	+	3.28224i	0.329877	+	0.329877i
$100$		−	31.5597i		−	3.15597i
$101$	−2.07428			−0.206399			−0.103199	−	0.994661i	$-0.532908\pi$
$101$	−2.07428			−0.206399			−0.103199	+	0.994661i	$0.532908\pi$
$102$	4.72719	+	27.4084i	0.468061	+	2.71383i
$103$	−10.4346			−1.02815			−0.514075	−	0.857745i	$-0.671865\pi$
$103$	−10.4346			−1.02815			−0.514075	+	0.857745i	$0.671865\pi$
$104$			13.8064i			1.35383i
$105$	−28.9228	−	28.9228i	−2.82257	−	2.82257i
$106$	−7.14541			−0.694024
$107$	7.72678	+	7.72678i	0.746976	+	0.746976i	0.973910	−	0.226934i	$-0.0728702\pi$
$107$	7.72678	+	7.72678i	0.746976	+	0.746976i	−0.226934	+	0.973910i	$0.572870\pi$
$108$	12.6912	−	12.6912i	1.22121	−	1.22121i
$109$	−6.68664	+	6.68664i	−0.640464	+	0.640464i	−0.950669	−	0.310206i	$-0.899602\pi$
$109$	−6.68664	+	6.68664i	−0.640464	+	0.640464i	0.310206	+	0.950669i	$0.399602\pi$
$110$			8.79169i			0.838254i
$111$			21.4938i			2.04010i
$112$	10.8310	−	10.8310i	1.02344	−	1.02344i
$113$	3.63825	−	3.63825i	0.342258	−	0.342258i	−0.514958	−	0.857216i	$-0.672192\pi$
$113$	3.63825	−	3.63825i	0.342258	−	0.342258i	0.857216	+	0.514958i	$0.172192\pi$
$114$	9.02178	+	9.02178i	0.844967	+	0.844967i
$115$	10.7337			1.00092
$116$	−2.19625	−	2.19625i	−0.203916	−	0.203916i
$117$			13.4363i			1.24219i
$118$	−30.1308			−2.77377
$119$	2.87800	+	16.6867i	0.263825	+	1.52967i
$120$	47.5039			4.33649
$121$		−	1.00000i		−	0.0909091i
$122$	9.07611	+	9.07611i	0.821713	+	0.821713i
$123$	1.76220			0.158892
$124$	−9.53953	−	9.53953i	−0.856675	−	0.856675i
$125$	7.59310	−	7.59310i	0.679147	−	0.679147i
$126$	32.8934	−	32.8934i	2.93037	−	2.93037i
$127$		−	20.7701i		−	1.84305i	−0.388321	−	0.921524i	$-0.626945\pi$
$127$		−	20.7701i		−	1.84305i	0.388321	−	0.921524i	$-0.373055\pi$
$128$		−	19.9348i		−	1.76200i
$129$	−4.04050	+	4.04050i	−0.355746	+	0.355746i
$130$	−17.9950	+	17.9950i	−1.57827	+	1.57827i
$131$	1.28622	+	1.28622i	0.112377	+	0.112377i	0.761059	−	0.648682i	$-0.224680\pi$
$131$	1.28622	+	1.28622i	0.112377	+	0.112377i	−0.648682	+	0.761059i	$0.724680\pi$
$132$	−10.9320			−0.951511
$133$	5.49262	+	5.49262i	0.476271	+	0.476271i
$134$			30.3184i			2.61911i
$135$	16.3516			1.40732
$136$	−16.0669	−	11.3400i	−1.37773	−	0.972396i
$137$	3.52692			0.301325			0.150663	−	0.988585i	$-0.451859\pi$
$137$	3.52692			0.301325			0.150663	+	0.988585i	$0.451859\pi$
$138$			20.0969i			1.71076i
$139$	10.3228	+	10.3228i	0.875565	+	0.875565i	0.993072	−	0.117507i	$-0.0374904\pi$
$139$	10.3228	+	10.3228i	0.875565	+	0.875565i	−0.117507	+	0.993072i	$0.537490\pi$
$140$	58.5141			4.94534
$141$	0.574862	+	0.574862i	0.0484121	+	0.0484121i
$142$	−10.4684	+	10.4684i	−0.878486	+	0.878486i
$143$	2.04682	−	2.04682i	0.171164	−	0.171164i
$144$			17.3125i			1.44271i
$145$		−	2.82969i		−	0.234993i
$146$	−5.92042	+	5.92042i	−0.489977	+	0.489977i
$147$	19.2860	−	19.2860i	1.59068	−	1.59068i
$148$	−21.7422	−	21.7422i	−1.78720	−	1.78720i
$149$	10.0386			0.822390			0.411195	−	0.911547i	$-0.365111\pi$
$149$	10.0386			0.822390			0.411195	+	0.911547i	$0.365111\pi$
$150$	38.0661	+	38.0661i	3.10809	+	3.10809i
$151$		−	9.55616i		−	0.777670i	−0.921308	−	0.388835i	$-0.872878\pi$
$151$		−	9.55616i		−	0.777670i	0.921308	−	0.388835i	$-0.127122\pi$
$152$	−9.02130			−0.731724
$153$	−15.6362	−	11.0360i	−1.26411	−	0.892208i
$154$	−10.0216			−0.807565
$155$		−	12.2909i		−	0.987230i
$156$	−22.3759	−	22.3759i	−1.79150	−	1.79150i
$157$	−14.9849			−1.19593			−0.597963	−	0.801524i	$-0.704023\pi$
$157$	−14.9849			−1.19593			−0.597963	+	0.801524i	$0.704023\pi$
$158$	−17.0176	−	17.0176i	−1.35385	−	1.35385i
$159$	5.72379	−	5.72379i	0.453926	−	0.453926i
$160$	1.11597	−	1.11597i	0.0882252	−	0.0882252i
$161$			12.2353i			0.964280i
$162$		−	3.36546i		−	0.264415i
$163$	4.90566	−	4.90566i	0.384241	−	0.384241i	−0.488387	−	0.872627i	$-0.662414\pi$
$163$	4.90566	−	4.90566i	0.384241	−	0.384241i	0.872627	+	0.488387i	$0.162414\pi$
$164$	−1.78257	+	1.78257i	−0.139195	+	0.139195i
$165$	−7.04252	−	7.04252i	−0.548259	−	0.548259i
$166$	34.9770			2.71474
$167$	14.3614	+	14.3614i	1.11132	+	1.11132i	0.992973	+	0.118343i	$0.0377583\pi$
$167$	14.3614	+	14.3614i	1.11132	+	1.11132i	0.118343	+	0.992973i	$0.462242\pi$
$168$			54.1496i			4.17773i
$169$	−4.62106			−0.355466
$170$	−6.16099	−	35.7216i	−0.472527	−	2.73972i
$171$	−8.77947			−0.671383
$172$		−	8.17440i		−	0.623292i
$173$	−7.79922	−	7.79922i	−0.592964	−	0.592964i	0.345467	−	0.938431i	$-0.387721\pi$
$173$	−7.79922	−	7.79922i	−0.592964	−	0.592964i	−0.938431	+	0.345467i	$0.887721\pi$
$174$	5.29806			0.401645
$175$	23.1754	+	23.1754i	1.75189	+	1.75189i
$176$	2.63730	−	2.63730i	0.198794	−	0.198794i
$177$	24.1361	−	24.1361i	1.81418	−	1.81418i
$178$			17.6529i			1.32314i
$179$			20.4522i			1.52867i	0.644818	+	0.764336i	$0.276933\pi$
$179$			20.4522i			1.52867i	−0.644818	+	0.764336i	$0.723067\pi$
$180$	−46.7648	+	46.7648i	−3.48564	+	3.48564i
$181$	−14.5013	+	14.5013i	−1.07787	+	1.07787i	−0.0811722	+	0.996700i	$0.525866\pi$
$181$	−14.5013	+	14.5013i	−1.07787	+	1.07787i	−0.996700	+	0.0811722i	$0.974134\pi$
$182$	−20.5125	−	20.5125i	−1.52048	−	1.52048i
$183$	−14.5407			−1.07488
$184$	−10.0479	−	10.0479i	−0.740741	−	0.740741i
$185$		−	28.0131i		−	2.05956i
$186$	23.0124			1.68735
$187$	0.700775	+	4.06312i	0.0512457	+	0.297124i
$188$	−1.16301			−0.0848214
$189$			18.6391i			1.35580i
$190$	−11.7582	−	11.7582i	−0.853028	−	0.853028i
$191$	−13.2000			−0.955122			−0.477561	−	0.878599i	$-0.658479\pi$
$191$	−13.2000			−0.955122			−0.477561	+	0.878599i	$0.658479\pi$
$192$	16.6704	+	16.6704i	1.20308	+	1.20308i
$193$	−1.61738	+	1.61738i	−0.116422	+	0.116422i	−0.762918	−	0.646496i	$-0.776234\pi$
$193$	−1.61738	+	1.61738i	−0.116422	+	0.116422i	0.646496	+	0.762918i	$0.276234\pi$
$194$	−13.4969	+	13.4969i	−0.969021	+	0.969021i
$195$		−	28.8295i		−	2.06453i
$196$			39.0178i			2.78699i
$197$	13.7226	−	13.7226i	0.977693	−	0.977693i	−0.0220639	−	0.999757i	$-0.507024\pi$
$197$	13.7226	−	13.7226i	0.977693	−	0.977693i	0.999757	+	0.0220639i	$0.00702374\pi$
$198$	8.00934	−	8.00934i	0.569199	−	0.569199i
$199$	0.165942	+	0.165942i	0.0117634	+	0.0117634i	0.712964	−	0.701201i	$-0.247352\pi$
$199$	0.165942	+	0.165942i	0.0117634	+	0.0117634i	−0.701201	+	0.712964i	$0.747352\pi$
$200$	−38.0641			−2.69154
$201$	−24.2864	−	24.2864i	−1.71303	−	1.71303i
$202$			5.06168i			0.356138i
$203$	3.22555			0.226389
$204$	44.4181	−	7.66089i	3.10989	−	0.536370i
$205$	−2.29669			−0.160408
$206$			25.4625i			1.77406i
$207$	−9.77855	−	9.77855i	−0.679656	−	0.679656i
$208$	10.7961			0.748578
$209$	1.33742	+	1.33742i	0.0925113	+	0.0925113i
$210$	−70.5775	+	70.5775i	−4.87031	+	4.87031i
$211$	−9.70146	+	9.70146i	−0.667876	+	0.667876i	−0.957224	−	0.289348i	$-0.906562\pi$
$211$	−9.70146	+	9.70146i	−0.667876	+	0.667876i	0.289348	+	0.957224i	$0.406562\pi$
$212$			11.5799i			0.795310i
$213$		−	16.7712i		−	1.14915i
$214$	18.8549	−	18.8549i	1.28890	−	1.28890i
$215$	5.26603	−	5.26603i	0.359140	−	0.359140i
$216$	−15.3068	−	15.3068i	−1.04150	−	1.04150i
$217$	14.0104			0.951087
$218$	16.3168	+	16.3168i	1.10511	+	1.10511i
$219$		−	9.48502i		−	0.640938i
$220$	14.2478			0.960589
$221$	−6.88211	+	9.75083i	−0.462941	+	0.655912i
$222$	52.4492			3.52016
$223$		−	22.7152i		−	1.52112i	−0.649265	−	0.760562i	$-0.724923\pi$
$223$		−	22.7152i		−	1.52112i	0.649265	−	0.760562i	$-0.275077\pi$
$224$	1.27209	+	1.27209i	0.0849952	+	0.0849952i
$225$	−37.0438			−2.46958
$226$	−8.87809	−	8.87809i	−0.590561	−	0.590561i
$227$	−6.92198	+	6.92198i	−0.459428	+	0.459428i	−0.898468	−	0.439040i	$-0.855319\pi$
$227$	−6.92198	+	6.92198i	−0.459428	+	0.459428i	0.439040	+	0.898468i	$0.355319\pi$
$228$	14.6207	−	14.6207i	0.968281	−	0.968281i
$229$		−	8.13452i		−	0.537544i	−0.963204	−	0.268772i	$-0.913382\pi$
$229$		−	8.13452i		−	0.537544i	0.963204	−	0.268772i	$-0.0866179\pi$
$230$		−	26.1925i		−	1.72708i
$231$	8.02775	−	8.02775i	0.528187	−	0.528187i
$232$	−2.64889	+	2.64889i	−0.173908	+	0.173908i
$233$	−5.63686	−	5.63686i	−0.369283	−	0.369283i	0.497933	−	0.867216i	$-0.334093\pi$
$233$	−5.63686	−	5.63686i	−0.369283	−	0.369283i	−0.867216	+	0.497933i	$0.834093\pi$
$234$	32.7874			2.14338
$235$	−0.749224	−	0.749224i	−0.0488740	−	0.0488740i
$236$			48.8301i			3.17857i
$237$	27.2637			1.77097
$238$	40.7190	−	7.02290i	2.63942	−	0.455227i
$239$	−6.63910			−0.429448			−0.214724	−	0.976675i	$-0.568885\pi$
$239$	−6.63910			−0.429448			−0.214724	+	0.976675i	$0.568885\pi$
$240$		−	37.1464i		−	2.39779i
$241$	15.0875	+	15.0875i	0.971869	+	0.971869i	0.999615	−	0.0277464i	$-0.00883309\pi$
$241$	15.0875	+	15.0875i	0.971869	+	0.971869i	−0.0277464	+	0.999615i	$0.508833\pi$
$242$	−2.44021			−0.156862
$243$	12.3235	+	12.3235i	0.790555	+	0.790555i
$244$	14.7088	−	14.7088i	0.941633	−	0.941633i
$245$	−25.1357	+	25.1357i	−1.60586	+	1.60586i
$246$		−	4.30013i		−	0.274166i
$247$			5.47492i			0.348361i
$248$	−11.5056	+	11.5056i	−0.730607	+	0.730607i
$249$	−28.0181	+	28.0181i	−1.77558	+	1.77558i
$250$	−18.5287	−	18.5287i	−1.17186	−	1.17186i
$251$	−29.0623			−1.83440			−0.917198	−	0.398431i	$-0.869555\pi$
$251$	−29.0623			−1.83440			−0.917198	+	0.398431i	$0.869555\pi$
$252$	−53.3071	−	53.3071i	−3.35803	−	3.35803i
$253$			2.97923i			0.187303i
$254$	−50.6833			−3.18015
$255$	33.5498	+	23.6794i	2.10097	+	1.48286i
$256$	−31.5883			−1.97427
$257$		−	0.967508i		−	0.0603515i	−0.999545	−	0.0301757i	$-0.990393\pi$
$257$		−	0.967508i		−	0.0603515i	0.999545	−	0.0301757i	$-0.00960669\pi$
$258$	9.85965	+	9.85965i	0.613835	+	0.613835i
$259$	31.9320			1.98416
$260$	29.1627	+	29.1627i	1.80860	+	1.80860i
$261$	−2.57788	+	2.57788i	−0.159567	+	0.159567i
$262$	3.13863	−	3.13863i	0.193905	−	0.193905i
$263$		−	12.1043i		−	0.746384i	−0.927754	−	0.373192i	$-0.878263\pi$
$263$		−	12.1043i		−	0.746384i	0.927754	−	0.373192i	$-0.121737\pi$
$264$			13.1851i			0.811487i
$265$	−7.45987	+	7.45987i	−0.458256	+	0.458256i
$266$	13.4031	−	13.4031i	0.821799	−	0.821799i
$267$	−14.1407	−	14.1407i	−0.865399	−	0.865399i
$268$	49.1341			3.00134
$269$	8.20327	+	8.20327i	0.500162	+	0.500162i	0.911488	−	0.411326i	$-0.134934\pi$
$269$	8.20327	+	8.20327i	0.500162	+	0.500162i	−0.411326	+	0.911488i	$0.634934\pi$
$270$		−	39.9013i		−	2.42831i
$271$	23.5490			1.43050			0.715251	−	0.698867i	$-0.246312\pi$
$271$	23.5490			1.43050			0.715251	+	0.698867i	$0.246312\pi$
$272$	−8.86749	+	12.5638i	−0.537671	+	0.761792i
$273$	32.8627			1.98894
$274$		−	8.60641i		−	0.519932i
$275$	5.64306	+	5.64306i	0.340289	+	0.340289i
$276$	32.5691			1.96043
$277$	0.949749	+	0.949749i	0.0570649	+	0.0570649i	0.735063	−	0.677998i	$-0.237152\pi$
$277$	0.949749	+	0.949749i	0.0570649	+	0.0570649i	−0.677998	+	0.735063i	$0.737152\pi$
$278$	25.1896	−	25.1896i	1.51077	−	1.51077i
$279$	−11.1972	+	11.1972i	−0.670358	+	0.670358i
$280$		−	70.5737i		−	4.21759i
$281$		−	18.8010i		−	1.12157i	−0.827961	−	0.560786i	$-0.810499\pi$
$281$		−	18.8010i		−	1.12157i	0.827961	−	0.560786i	$-0.189501\pi$
$282$	1.40278	−	1.40278i	0.0835344	−	0.0835344i
$283$	−8.06617	+	8.06617i	−0.479484	+	0.479484i	−0.904967	−	0.425483i	$-0.860104\pi$
$283$	−8.06617	+	8.06617i	−0.479484	+	0.479484i	0.425483	+	0.904967i	$0.360104\pi$
$284$	16.9651	+	16.9651i	1.00669	+	1.00669i
$285$	18.8376			1.11584
$286$	−4.99466	−	4.99466i	−0.295341	−	0.295341i
$287$		−	2.61800i		−	0.154536i
$288$	−2.03333			−0.119815
$289$	−5.69466	−	16.0178i	−0.334980	−	0.942225i
$290$	−6.90502			−0.405476
$291$		−	21.6232i		−	1.26757i
$292$	9.59465	+	9.59465i	0.561484	+	0.561484i
$293$	−19.5854			−1.14419			−0.572094	−	0.820188i	$-0.693869\pi$
$293$	−19.5854			−1.14419			−0.572094	+	0.820188i	$0.693869\pi$
$294$	−47.0618	−	47.0618i	−2.74470	−	2.74470i
$295$	−31.4569	+	31.4569i	−1.83149	+	1.83149i
$296$	−26.2232	+	26.2232i	−1.52419	+	1.52419i
$297$			4.53852i			0.263352i
$298$		−	24.4961i		−	1.41902i
$299$	−6.09795	+	6.09795i	−0.352654	+	0.352654i
$300$	61.6901	−	61.6901i	3.56168	−	3.56168i
$301$	6.00274	+	6.00274i	0.345992	+	0.345992i
$302$	−23.3190			−1.34186
$303$	−4.05462	−	4.05462i	−0.232932	−	0.232932i
$304$			7.05435i			0.404595i
$305$	18.9511			1.08514
$306$	−26.9301	+	38.1556i	−1.53949	+	2.18121i
$307$	−16.0121			−0.913862			−0.456931	−	0.889502i	$-0.651051\pi$
$307$	−16.0121			−0.913862			−0.456931	+	0.889502i	$0.651051\pi$
$308$			16.2411i			0.925421i
$309$	−20.3966	−	20.3966i	−1.16032	−	1.16032i
$310$	−29.9924			−1.70345
$311$	5.54644	+	5.54644i	0.314509	+	0.314509i	0.846654	−	0.532144i	$-0.178614\pi$
$311$	5.54644	+	5.54644i	0.314509	+	0.314509i	−0.532144	+	0.846654i	$0.678614\pi$
$312$	−26.9875	+	26.9875i	−1.52787	+	1.52787i
$313$	18.9737	−	18.9737i	1.07245	−	1.07245i	0.0752935	−	0.997161i	$-0.476011\pi$
$313$	18.9737	−	18.9737i	1.07245	−	1.07245i	0.997161	−	0.0752935i	$-0.0239894\pi$
$314$			36.5662i			2.06355i
$315$		−	68.6819i		−	3.86979i
$316$	−27.5788	+	27.5788i	−1.55143	+	1.55143i
$317$	22.2112	−	22.2112i	1.24751	−	1.24751i	0.290691	−	0.956817i	$-0.406115\pi$
$317$	22.2112	−	22.2112i	1.24751	−	1.24751i	0.956817	−	0.290691i	$-0.0938852\pi$
$318$	−13.9672	−	13.9672i	−0.783243	−	0.783243i
$319$	0.785403			0.0439741
$320$	−21.7267	−	21.7267i	−1.21456	−	1.21456i
$321$			30.2072i			1.68600i
$322$	29.8567			1.66385
$323$	−6.37133	−	4.49687i	−0.354510	−	0.250212i
$324$	−5.45408			−0.303004
$325$			23.1007i			1.28139i
$326$	−11.9708	−	11.9708i	−0.663002	−	0.663002i
$327$	−26.1409			−1.44559
$328$	2.14995	+	2.14995i	0.118711	+	0.118711i
$329$	0.854039	−	0.854039i	0.0470847	−	0.0470847i
$330$	−17.1852	+	17.1852i	−0.946014	+	0.946014i
$331$			22.8948i			1.25841i	0.777238	+	0.629206i	$0.216620\pi$
$331$			22.8948i			1.25841i	−0.777238	+	0.629206i	$0.783380\pi$
$332$		−	56.6839i		−	3.11093i
$333$	−25.5203	+	25.5203i	−1.39850	+	1.39850i
$334$	35.0447	−	35.0447i	1.91756	−	1.91756i
$335$	31.6527	+	31.6527i	1.72937	+	1.72937i
$336$	42.3431			2.31001
$337$	1.05413	+	1.05413i	0.0574219	+	0.0574219i	0.735235	−	0.677813i	$-0.237072\pi$
$337$	1.05413	+	1.05413i	0.0574219	+	0.0574219i	−0.677813	+	0.735235i	$0.737072\pi$
$338$			11.2763i			0.613352i
$339$	14.2235			0.772512
$340$	−57.8906	+	9.98453i	−3.13956	+	0.541487i
$341$	3.41145			0.184740
$342$			21.4237i			1.15846i
$343$	−8.32410	−	8.32410i	−0.449459	−	0.449459i
$344$	−9.85913			−0.531569
$345$	20.9813	+	20.9813i	1.12960	+	1.12960i
$346$	−19.0317	+	19.0317i	−1.02315	+	1.02315i
$347$	−12.7723	+	12.7723i	−0.685651	+	0.685651i	−0.961268	−	0.275617i	$-0.911118\pi$
$347$	−12.7723	+	12.7723i	−0.685651	+	0.685651i	0.275617	+	0.961268i	$0.411118\pi$
$348$		−	8.58605i		−	0.460260i
$349$			11.8565i			0.634666i	0.948314	+	0.317333i	$0.102787\pi$
$349$			11.8565i			0.634666i	−0.948314	+	0.317333i	$0.897213\pi$
$350$	56.5526	−	56.5526i	3.02287	−	3.02287i
$351$	−9.28954	+	9.28954i	−0.495839	+	0.495839i
$352$	0.309747	+	0.309747i	0.0165096	+	0.0165096i
$353$	7.94877			0.423070			0.211535	−	0.977370i	$-0.432154\pi$
$353$	7.94877			0.423070			0.211535	+	0.977370i	$0.432154\pi$
$354$	−58.8971	−	58.8971i	−3.13034	−	3.13034i
$355$			21.8581i			1.16011i
$356$	28.6084			1.51624
$357$	−26.9920	+	38.2433i	−1.42857	+	2.02405i
$358$	49.9077			2.63770
$359$			22.8982i			1.20852i	0.796787	+	0.604260i	$0.206531\pi$
$359$			22.8982i			1.20852i	−0.796787	+	0.604260i	$0.793469\pi$
$360$	56.4029	+	56.4029i	2.97270	+	2.97270i
$361$	15.4226			0.811716
$362$	35.3861	+	35.3861i	1.85985	+	1.85985i
$363$	1.95471	−	1.95471i	0.102596	−	0.102596i
$364$	−33.2426	+	33.2426i	−1.74238	+	1.74238i
$365$			12.3619i			0.647053i
$366$			35.4823i			1.85469i
$367$	−12.4367	+	12.4367i	−0.649191	+	0.649191i	−0.952798	−	0.303607i	$-0.901809\pi$
$367$	−12.4367	+	12.4367i	−0.649191	+	0.649191i	0.303607	+	0.952798i	$0.401809\pi$
$368$	−7.85712	+	7.85712i	−0.409581	+	0.409581i
$369$	2.09232	+	2.09232i	0.108922	+	0.108922i
$370$	−68.3576			−3.55374
$371$	−8.50349	−	8.50349i	−0.441479	−	0.441479i
$372$		−	37.2940i		−	1.93361i
$373$	5.41804			0.280536			0.140268	−	0.990114i	$-0.455204\pi$
$373$	5.41804			0.280536			0.140268	+	0.990114i	$0.455204\pi$
$374$	9.91484	−	1.71004i	0.512684	−	0.0884238i
$375$	29.6846			1.53291
$376$			1.40271i			0.0723391i
$377$	1.60758	+	1.60758i	0.0827945	+	0.0827945i
$378$	45.4834			2.33941
$379$	−21.9120	−	21.9120i	−1.12555	−	1.12555i	−0.990893	−	0.134654i	$-0.957008\pi$
$379$	−21.9120	−	21.9120i	−1.12555	−	1.12555i	−0.134654	−	0.990893i	$-0.542992\pi$
$380$	−19.0554	+	19.0554i	−0.977519	+	0.977519i
$381$	40.5995	−	40.5995i	2.07998	−	2.07998i
$382$			32.2108i			1.64805i
$383$			7.99040i			0.408290i	0.978941	+	0.204145i	$0.0654414\pi$
$383$			7.99040i			0.408290i	−0.978941	+	0.204145i	$0.934559\pi$
$384$	38.9667	−	38.9667i	1.98851	−	1.98851i
$385$	−10.4627	+	10.4627i	−0.533227	+	0.533227i
$386$	3.94675	+	3.94675i	0.200884	+	0.200884i
$387$	−9.59484			−0.487733
$388$	21.8731	+	21.8731i	1.11044	+	1.11044i
$389$		−	24.2381i		−	1.22892i	−0.788947	−	0.614461i	$-0.789374\pi$
$389$		−	24.2381i		−	1.22892i	0.788947	−	0.614461i	$-0.210626\pi$
$390$	−70.3500			−3.56231
$391$	−2.08777	−	12.1050i	−0.105583	−	0.612174i
$392$	47.0593			2.37686
$393$			5.02836i			0.253647i
$394$	−33.4859	−	33.4859i	−1.68700	−	1.68700i
$395$	−35.5331			−1.78786
$396$	−12.9800	−	12.9800i	−0.652268	−	0.652268i
$397$	25.5957	−	25.5957i	1.28461	−	1.28461i	0.346598	−	0.938014i	$-0.387337\pi$
$397$	25.5957	−	25.5957i	1.28461	−	1.28461i	0.938014	−	0.346598i	$-0.112663\pi$
$398$	0.404934	−	0.404934i	0.0202975	−	0.0202975i
$399$			21.4730i			1.07499i
$400$			29.7649i			1.48824i
$401$	15.0933	−	15.0933i	0.753724	−	0.753724i	−0.221448	−	0.975172i	$-0.571078\pi$
$401$	15.0933	−	15.0933i	0.753724	−	0.753724i	0.975172	+	0.221448i	$0.0710784\pi$
$402$	−59.2637	+	59.2637i	−2.95581	+	2.95581i
$403$	6.98261	+	6.98261i	0.347829	+	0.347829i
$404$	8.20297			0.408113
$405$	−3.51357	−	3.51357i	−0.174591	−	0.174591i
$406$		−	7.87101i		−	0.390632i
$407$	7.77526			0.385405
$408$	−9.23979	−	53.5726i	−0.457438	−	2.65224i
$409$	3.58657			0.177344			0.0886721	−	0.996061i	$-0.471738\pi$
$409$	3.58657			0.177344			0.0886721	+	0.996061i	$0.471738\pi$
$410$			5.60441i			0.276782i
$411$	6.89411	+	6.89411i	0.340061	+	0.340061i
$412$	41.2647			2.03296
$413$	−35.8576	−	35.8576i	−1.76444	−	1.76444i
$414$	−23.8617	+	23.8617i	−1.17274	+	1.17274i
$415$	36.5163	−	36.5163i	1.79252	−	1.79252i
$416$			1.26799i			0.0621684i
$417$			40.3560i			1.97624i
$418$	3.26358	−	3.26358i	0.159627	−	0.159627i
$419$	−18.9304	+	18.9304i	−0.924811	+	0.924811i	−0.997364	−	0.0725540i	$-0.976885\pi$
$419$	−18.9304	+	18.9304i	−0.924811	+	0.924811i	0.0725540	+	0.997364i	$0.476885\pi$
$420$	114.378	+	114.378i	5.58108	+	5.58108i
$421$	−7.37047			−0.359215			−0.179607	−	0.983738i	$-0.557483\pi$
$421$	−7.37047			−0.359215			−0.179607	+	0.983738i	$0.557483\pi$
$422$	23.6736	+	23.6736i	1.15241	+	1.15241i
$423$			1.36511i			0.0663737i
$424$	13.9665			0.678272
$425$	−26.8829	−	18.9739i	−1.30401	−	0.920369i
$426$	−40.9253			−1.98284
$427$			21.6023i			1.04541i
$428$	−30.5564	−	30.5564i	−1.47700	−	1.47700i
$429$	8.00188			0.386334
$430$	−12.8502	−	12.8502i	−0.619692	−	0.619692i
$431$	24.9198	−	24.9198i	1.20034	−	1.20034i	0.226283	−	0.974062i	$-0.427343\pi$
$431$	24.9198	−	24.9198i	1.20034	−	1.20034i	0.974062	−	0.226283i	$-0.0726573\pi$
$432$	−11.9694	+	11.9694i	−0.575879	+	0.575879i
$433$		−	25.3663i		−	1.21903i	−0.792775	−	0.609514i	$-0.791365\pi$
$433$		−	25.3663i		−	1.21903i	0.792775	−	0.609514i	$-0.208635\pi$
$434$		−	34.1882i		−	1.64109i
$435$	5.53122	−	5.53122i	0.265202	−	0.265202i
$436$	26.4430	−	26.4430i	1.26639	−	1.26639i
$437$	−3.98449	−	3.98449i	−0.190604	−	0.190604i
$438$	−23.1454			−1.10593
$439$	0.812873	+	0.812873i	0.0387963	+	0.0387963i	0.726239	−	0.687442i	$-0.241267\pi$
$439$	0.812873	+	0.812873i	0.0387963	+	0.0387963i	−0.687442	+	0.726239i	$0.741267\pi$
$440$		−	17.1843i		−	0.819229i
$441$	45.7979			2.18085
$442$	23.7940	+	16.7938i	1.13177	+	0.798798i
$443$	11.3923			0.541262			0.270631	−	0.962683i	$-0.412768\pi$
$443$	11.3923			0.541262			0.270631	+	0.962683i	$0.412768\pi$
$444$		−	84.9993i		−	4.03389i
$445$	18.4298	+	18.4298i	0.873656	+	0.873656i
$446$	−55.4299			−2.62468
$447$	19.6225	+	19.6225i	0.928111	+	0.928111i
$448$	24.7663	−	24.7663i	1.17010	−	1.17010i
$449$	−9.11281	+	9.11281i	−0.430060	+	0.430060i	−0.888649	−	0.458589i	$-0.848355\pi$
$449$	−9.11281	+	9.11281i	−0.430060	+	0.430060i	0.458589	+	0.888649i	$0.348355\pi$
$450$			90.3944i			4.26123i
$451$		−	0.637467i		−	0.0300171i
$452$	−14.3879	+	14.3879i	−0.676748	+	0.676748i
$453$	18.6795	−	18.6795i	0.877641	−	0.877641i
$454$	16.8911	+	16.8911i	0.792737	+	0.792737i
$455$	−42.8304			−2.00792
$456$	−17.6340	−	17.6340i	−0.825789	−	0.825789i
$457$		−	39.6546i		−	1.85496i	−0.373869	−	0.927481i	$-0.621969\pi$
$457$		−	39.6546i		−	1.85496i	0.373869	−	0.927481i	$-0.378031\pi$
$458$	−19.8499			−0.927526
$459$	−3.18048	−	18.4405i	−0.148452	−	0.860731i
$460$	−42.4476			−1.97913
$461$			8.50190i			0.395973i	0.980205	+	0.197987i	$0.0634402\pi$
$461$			8.50190i			0.395973i	−0.980205	+	0.197987i	$0.936560\pi$
$462$	−19.5894	−	19.5894i	−0.911380	−	0.911380i
$463$	−23.6849			−1.10073			−0.550364	−	0.834925i	$-0.685511\pi$
$463$	−23.6849			−1.10073			−0.550364	+	0.834925i	$0.685511\pi$
$464$	2.07134	+	2.07134i	0.0961596	+	0.0961596i
$465$	24.0252	−	24.0252i	1.11414	−	1.11414i
$466$	−13.7551	+	13.7551i	−0.637193	+	0.637193i
$467$			26.3832i			1.22087i	0.792066	+	0.610435i	$0.209006\pi$
$467$			26.3832i			1.22087i	−0.792066	+	0.610435i	$0.790994\pi$
$468$		−	53.1353i		−	2.45618i
$469$	−36.0808	+	36.0808i	−1.66606	+	1.66606i
$470$	−1.82826	+	1.82826i	−0.0843314	+	0.0843314i
$471$	−29.2911	−	29.2911i	−1.34966	−	1.34966i
$472$	58.8939			2.71081
$473$	1.46163	+	1.46163i	0.0672058	+	0.0672058i
$474$		−	66.5291i		−	3.05578i
$475$	−15.0943			−0.692574
$476$	−11.3813	−	65.9894i	−0.521663	−	3.02462i
$477$	13.5921			0.622339
$478$			16.2008i			0.741007i
$479$	−0.752961	−	0.752961i	−0.0344037	−	0.0344037i	0.689696	−	0.724099i	$-0.257744\pi$
$479$	−0.752961	−	0.752961i	−0.0344037	−	0.0344037i	−0.724099	+	0.689696i	$0.757744\pi$
$480$	4.36280			0.199134
$481$	15.9145	+	15.9145i	0.725641	+	0.725641i
$482$	36.8165	−	36.8165i	1.67695	−	1.67695i
$483$	−23.9165	+	23.9165i	−1.08824	+	1.08824i
$484$			3.95461i			0.179755i
$485$			28.1818i			1.27967i
$486$	30.0720	−	30.0720i	1.36409	−	1.36409i
$487$	2.41841	−	2.41841i	0.109589	−	0.109589i	−0.650186	−	0.759775i	$-0.725309\pi$
$487$	2.41841	−	2.41841i	0.109589	−	0.109589i	0.759775	+	0.650186i	$0.225309\pi$
$488$	−17.7402	−	17.7402i	−0.803062	−	0.803062i
$489$	19.1783			0.867272
$490$	61.3362	+	61.3362i	2.77089	+	2.77089i
$491$		−	37.8743i		−	1.70924i	−0.519252	−	0.854621i	$-0.673789\pi$
$491$		−	37.8743i		−	1.70924i	0.519252	−	0.854621i	$-0.326211\pi$
$492$	−6.96881			−0.314178
$493$	−3.19118	+	0.550391i	−0.143724	+	0.0247884i
$494$	13.3599			0.601092
$495$		−	16.7236i		−	0.751672i
$496$	8.99699	+	8.99699i	0.403977	+	0.403977i
$497$	−24.9160			−1.11764
$498$	68.3700	+	68.3700i	3.06373	+	3.06373i
$499$	−18.6751	+	18.6751i	−0.836012	+	0.836012i	−0.988331	−	0.152319i	$-0.951326\pi$
$499$	−18.6751	+	18.6751i	−0.836012	+	0.836012i	0.152319	+	0.988331i	$0.451326\pi$
$500$	−30.0277	+	30.0277i	−1.34288	+	1.34288i
$501$			56.1446i			2.50836i
$502$			70.9180i			3.16523i
$503$	−6.98348	+	6.98348i	−0.311378	+	0.311378i	−0.845443	−	0.534065i	$-0.820664\pi$
$503$	−6.98348	+	6.98348i	−0.311378	+	0.311378i	0.534065	+	0.845443i	$0.320664\pi$
$504$	−64.2936	+	64.2936i	−2.86386	+	2.86386i
$505$	5.28443	+	5.28443i	0.235154	+	0.235154i
$506$	7.26994			0.323188
$507$	−9.03284	−	9.03284i	−0.401162	−	0.401162i
$508$			82.1376i			3.64427i
$509$	23.2596			1.03096			0.515482	−	0.856901i	$-0.327613\pi$
$509$	23.2596			1.03096			0.515482	+	0.856901i	$0.327613\pi$
$510$	57.7825	−	81.8684i	2.55865	−	3.62520i
$511$	−14.0913			−0.623364
$512$			37.2125i			1.64457i
$513$	−6.06991	−	6.06991i	−0.267993	−	0.267993i
$514$	−2.36092			−0.104136
$515$	26.5831	+	26.5831i	1.17139	+	1.17139i
$516$	15.9786	−	15.9786i	0.703418	−	0.703418i
$517$	0.207953	−	0.207953i	0.00914578	−	0.00914578i
$518$		−	77.9207i		−	3.42364i
$519$		−	30.4904i		−	1.33838i
$520$	35.1731	−	35.1731i	1.54244	−	1.54244i
$521$	−18.0059	+	18.0059i	−0.788854	+	0.788854i	−0.981306	−	0.192452i	$-0.938356\pi$
$521$	−18.0059	+	18.0059i	−0.788854	+	0.788854i	0.192452	+	0.981306i	$0.438356\pi$
$522$	6.29056	+	6.29056i	0.275330	+	0.275330i
$523$	17.7330			0.775412			0.387706	−	0.921783i	$-0.373268\pi$
$523$	17.7330			0.775412			0.387706	+	0.921783i	$0.373268\pi$
$524$	−5.08648	−	5.08648i	−0.222204	−	0.222204i
$525$			90.6022i			3.95421i
$526$	−29.5370			−1.28788
$527$	−13.8611	+	2.39066i	−0.603799	+	0.104139i
$528$	10.3103			0.448698
$529$			14.1242i			0.614095i
$530$	18.2036	+	18.2036i	0.790715	+	0.790715i
$531$	57.3152			2.48727
$532$	−21.7212	−	21.7212i	−0.941732	−	0.941732i
$533$	1.30478	−	1.30478i	0.0565163	−	0.0565163i
$534$	−34.5063	+	34.5063i	−1.49323	+	1.49323i
$535$		−	39.3694i		−	1.70209i
$536$		−	59.2606i		−	2.55967i
$537$	−39.9782	+	39.9782i	−1.72519	+	1.72519i
$538$	20.0177	−	20.0177i	0.863024	−	0.863024i
$539$	−6.97662	−	6.97662i	−0.300504	−	0.300504i
$540$	−64.6641			−2.78270
$541$	11.6459	+	11.6459i	0.500696	+	0.500696i	0.911654	−	0.410958i	$-0.134806\pi$
$541$	11.6459	+	11.6459i	0.500696	+	0.500696i	−0.410958	+	0.911654i	$0.634806\pi$
$542$		−	57.4645i		−	2.46831i
$543$	−56.6916			−2.43287
$544$	−1.47560	−	1.04147i	−0.0632658	−	0.0446529i
$545$	34.0697			1.45939
$546$		−	80.1918i		−	3.43189i
$547$	−2.05822	−	2.05822i	−0.0880033	−	0.0880033i	0.661735	−	0.749738i	$-0.269821\pi$
$547$	−2.05822	−	2.05822i	−0.0880033	−	0.0880033i	−0.749738	+	0.661735i	$0.769821\pi$
$548$	−13.9476			−0.595811
$549$	−17.2647	−	17.2647i	−0.736839	−	0.736839i
$550$	13.7702	−	13.7702i	0.587165	−	0.587165i
$551$	−1.05041	+	1.05041i	−0.0447492	+	0.0447492i
$552$		−	39.2815i		−	1.67193i
$553$		−	40.5041i		−	1.72241i
$554$	2.31758	−	2.31758i	0.0984647	−	0.0984647i
$555$	54.7574	−	54.7574i	2.32432	−	2.32432i
$556$	−40.8224	−	40.8224i	−1.73126	−	1.73126i
$557$	−25.4999			−1.08046			−0.540232	−	0.841516i	$-0.681664\pi$
$557$	−25.4999			−1.08046			−0.540232	+	0.841516i	$0.681664\pi$
$558$	27.3234	+	27.3234i	1.15669	+	1.15669i
$559$			5.98339i			0.253070i
$560$	−55.1863			−2.33205
$561$	−6.57240	+	9.31203i	−0.277487	+	0.393154i
$562$	−45.8783			−1.93526
$563$		−	0.554846i		−	0.0233840i	−0.999932	−	0.0116920i	$-0.996278\pi$
$563$		−	0.554846i		−	0.0233840i	0.999932	−	0.0116920i	$-0.00372176\pi$
$564$	−2.27335	−	2.27335i	−0.0957254	−	0.0957254i
$565$	−18.5376			−0.779882
$566$	19.6831	+	19.6831i	0.827343	+	0.827343i
$567$	4.00511	−	4.00511i	0.168199	−	0.168199i
$568$	20.4615	−	20.4615i	0.858547	−	0.858547i
$569$		−	8.14402i		−	0.341415i	−0.985322	−	0.170708i	$-0.945395\pi$
$569$		−	8.14402i		−	0.341415i	0.985322	−	0.170708i	$-0.0546054\pi$
$570$		−	45.9677i		−	1.92537i
$571$	28.4491	−	28.4491i	1.19056	−	1.19056i	0.213646	−	0.976911i	$-0.431466\pi$
$571$	28.4491	−	28.4491i	1.19056	−	1.19056i	0.976911	−	0.213646i	$-0.0685338\pi$
$572$	−8.09437	+	8.09437i	−0.338442	+	0.338442i
$573$	−25.8023	−	25.8023i	−1.07790	−	1.07790i
$574$	−6.38845			−0.266649
$575$	−16.8120	−	16.8120i	−0.701109	−	0.701109i
$576$			39.5867i			1.64945i
$577$	−39.0089			−1.62396			−0.811981	−	0.583684i	$-0.801611\pi$
$577$	−39.0089			−1.62396			−0.811981	+	0.583684i	$0.801611\pi$
$578$	−39.0868	+	13.8961i	−1.62580	+	0.578004i
$579$	−6.32303			−0.262776
$580$			11.1903i			0.464652i
$581$	41.6249	+	41.6249i	1.72689	+	1.72689i
$582$	−52.7651			−2.18718
$583$	−2.07055	−	2.07055i	−0.0857535	−	0.0857535i
$584$	11.5721	−	11.5721i	0.478856	−	0.478856i
$585$	34.2303	−	34.2303i	1.41525	−	1.41525i
$586$			47.7923i			1.97428i
$587$			6.80480i			0.280864i	0.990090	+	0.140432i	$0.0448491\pi$
$587$			6.80480i			0.280864i	−0.990090	+	0.140432i	$0.955151\pi$
$588$	−76.2686	+	76.2686i	−3.14526	+	3.14526i
$589$	−4.56254	+	4.56254i	−0.187996	+	0.187996i
$590$	76.7612	+	76.7612i	3.16021	+	3.16021i
$591$	53.6473			2.20676
$592$	20.5057	+	20.5057i	0.842777	+	0.842777i
$593$			2.33369i			0.0958331i	0.998851	+	0.0479165i	$0.0152581\pi$
$593$			2.33369i			0.0958331i	−0.998851	+	0.0479165i	$0.984742\pi$
$594$	11.0749			0.454410
$595$	35.1790	−	49.8430i	1.44220	−	2.04336i
$596$	−39.6985			−1.62612
$597$			0.648739i			0.0265511i
$598$	14.8803	+	14.8803i	0.608499	+	0.608499i
$599$	26.5857			1.08626			0.543132	−	0.839648i	$-0.317238\pi$
$599$	26.5857			1.08626			0.543132	+	0.839648i	$0.317238\pi$
$600$	−74.4043	−	74.4043i	−3.03754	−	3.03754i
$601$	17.4991	−	17.4991i	0.713804	−	0.713804i	−0.253525	−	0.967329i	$-0.581590\pi$
$601$	17.4991	−	17.4991i	0.713804	−	0.713804i	0.967329	+	0.253525i	$0.0815899\pi$
$602$	14.6479	−	14.6479i	0.597004	−	0.597004i
$603$		−	57.6720i		−	2.34859i
$604$			37.7909i			1.53769i
$605$	−2.54760	+	2.54760i	−0.103575	+	0.103575i
$606$	−9.89411	+	9.89411i	−0.401921	+	0.401921i
$607$	−15.4305	−	15.4305i	−0.626305	−	0.626305i	0.320831	−	0.947136i	$-0.396038\pi$
$607$	−15.4305	−	15.4305i	−0.626305	−	0.626305i	−0.947136	+	0.320831i	$0.896038\pi$
$608$	−0.828524			−0.0336011
$609$	6.30502	+	6.30502i	0.255492	+	0.255492i
$610$		−	46.2445i		−	1.87239i
$611$	0.851286			0.0344393
$612$	61.8351	+	43.6431i	2.49954	+	1.76417i
$613$	3.27703			0.132358			0.0661790	−	0.997808i	$-0.478919\pi$
$613$	3.27703			0.132358			0.0661790	+	0.997808i	$0.478919\pi$
$614$			39.0729i			1.57686i
$615$	−4.48937	−	4.48937i	−0.181029	−	0.181029i
$616$	19.5883			0.789236
$617$	0.456795	+	0.456795i	0.0183899	+	0.0183899i	0.716242	−	0.697852i	$-0.245861\pi$
$617$	0.456795	+	0.456795i	0.0183899	+	0.0183899i	−0.697852	+	0.716242i	$0.745861\pi$
$618$	−49.7719	+	49.7719i	−2.00212	+	2.00212i
$619$	12.7125	−	12.7125i	0.510958	−	0.510958i	−0.403862	−	0.914820i	$-0.632332\pi$
$619$	12.7125	−	12.7125i	0.510958	−	0.510958i	0.914820	+	0.403862i	$0.132332\pi$
$620$			48.6057i			1.95205i
$621$		−	13.5213i		−	0.542592i
$622$	13.5344	−	13.5344i	0.542682	−	0.542682i
$623$	−21.0081	+	21.0081i	−0.841671	+	0.841671i
$624$	21.1033	+	21.1033i	0.844809	+	0.844809i
$625$	1.21418			0.0485671
$626$	−46.2997	−	46.2997i	−1.85051	−	1.85051i
$627$			5.22854i			0.208808i
$628$	59.2594			2.36471
$629$	−31.5918	+	5.44871i	−1.25965	+	0.217254i
$630$	−167.598			−6.67727
$631$			28.4826i			1.13388i	0.823761	+	0.566938i	$0.191872\pi$
$631$			28.4826i			1.13388i	−0.823761	+	0.566938i	$0.808128\pi$
$632$	33.2628	+	33.2628i	1.32312	+	1.32312i
$633$	−37.9271			−1.50747
$634$	−54.2000	−	54.2000i	−2.15256	−	2.15256i
$635$	−52.9138	+	52.9138i	−2.09982	+	2.09982i
$636$	−22.6353	+	22.6353i	−0.897549	+	0.897549i
$637$		−	28.5598i		−	1.13158i
$638$		−	1.91655i		−	0.0758767i
$639$	19.9130	−	19.9130i	0.787748	−	0.787748i
$640$	−50.7858	+	50.7858i	−2.00748	+	2.00748i
$641$	19.8500	+	19.8500i	0.784028	+	0.784028i	0.980508	−	0.196480i	$-0.0629511\pi$
$641$	19.8500	+	19.8500i	0.784028	+	0.784028i	−0.196480	+	0.980508i	$0.562951\pi$
$642$	73.7119			2.90918
$643$	11.8154	+	11.8154i	0.465955	+	0.465955i	0.900601	−	0.434647i	$-0.143127\pi$
$643$	11.8154	+	11.8154i	0.465955	+	0.465955i	−0.434647	+	0.900601i	$0.643127\pi$
$644$		−	48.3859i		−	1.90667i
$645$	20.5871			0.810617
$646$	−10.9733	+	15.5474i	−0.431738	+	0.611702i
$647$	−7.15999			−0.281488			−0.140744	−	0.990046i	$-0.544949\pi$
$647$	−7.15999			−0.281488			−0.140744	+	0.990046i	$0.544949\pi$
$648$			6.57815i			0.258414i
$649$	−8.73112	−	8.73112i	−0.342726	−	0.342726i
$650$	56.3704			2.21103
$651$	27.3862	+	27.3862i	1.07335	+	1.07335i
$652$	−19.3999	+	19.3999i	−0.759761	+	0.759761i
$653$	29.3547	−	29.3547i	1.14874	−	1.14874i	0.161936	−	0.986801i	$-0.448226\pi$
$653$	29.3547	−	29.3547i	1.14874	−	1.14874i	0.986801	−	0.161936i	$-0.0517737\pi$
$654$			63.7891i			2.49435i
$655$		−	6.55352i		−	0.256067i
$656$	1.68119	−	1.68119i	0.0656394	−	0.0656394i
$657$	11.2619	−	11.2619i	0.439368	−	0.439368i
$658$	−2.08403	−	2.08403i	−0.0812440	−	0.0812440i
$659$	45.7467			1.78204			0.891020	−	0.453964i	$-0.149991\pi$
$659$	45.7467			1.78204			0.891020	+	0.453964i	$0.149991\pi$
$660$	27.8504	+	27.8504i	1.08408	+	1.08408i
$661$			27.3684i			1.06451i	0.846585	+	0.532254i	$0.178655\pi$
$661$			27.3684i			1.06451i	−0.846585	+	0.532254i	$0.821345\pi$
$662$	55.8681			2.17137
$663$	−32.5126	+	5.60752i	−1.26268	+	0.217778i
$664$	−68.3663			−2.65313
$665$		−	27.9860i		−	1.08525i
$666$	62.2747	+	62.2747i	2.41310	+	2.41310i
$667$	−2.33990			−0.0906012
$668$	−56.7936	−	56.7936i	−2.19741	−	2.19741i
$669$	44.4017	−	44.4017i	1.71667	−	1.71667i
$670$	77.2391	−	77.2391i	2.98401	−	2.98401i
$671$			5.26003i			0.203061i
$672$			4.97314i			0.191843i
$673$	2.32455	−	2.32455i	0.0896048	−	0.0896048i	−0.660884	−	0.750488i	$-0.729818\pi$
$673$	2.32455	−	2.32455i	0.0896048	−	0.0896048i	0.750488	+	0.660884i	$0.229818\pi$
$674$	2.57229	−	2.57229i	0.0990807	−	0.0990807i
$675$	−25.6112	−	25.6112i	−0.985774	−	0.985774i
$676$	18.2745			0.702864
$677$	25.1061	+	25.1061i	0.964907	+	0.964907i	0.999405	−	0.0344977i	$-0.0109832\pi$
$677$	25.1061	+	25.1061i	0.964907	+	0.964907i	−0.0344977	+	0.999405i	$0.510983\pi$
$678$		−	34.7082i		−	1.33296i
$679$	−32.1243			−1.23282
$680$	12.0423	+	69.8218i	0.461802	+	2.67754i
$681$	−27.0609			−1.03698
$682$		−	8.32463i		−	0.318767i
$683$	−8.54940	−	8.54940i	−0.327134	−	0.327134i	0.524362	−	0.851495i	$-0.324304\pi$
$683$	−8.54940	−	8.54940i	−0.327134	−	0.327134i	−0.851495	+	0.524362i	$0.824304\pi$
$684$	34.7194			1.32753
$685$	−8.98517	−	8.98517i	−0.343306	−	0.343306i
$686$	−20.3125	+	20.3125i	−0.775536	+	0.775536i
$687$	15.9006	−	15.9006i	0.606647	−	0.606647i
$688$			7.70951i			0.293922i
$689$		−	8.47609i		−	0.322913i
$690$	51.1987	−	51.1987i	1.94910	−	1.94910i
$691$	14.6564	−	14.6564i	0.557554	−	0.557554i	−0.371056	−	0.928610i	$-0.621004\pi$
$691$	14.6564	−	14.6564i	0.557554	−	0.557554i	0.928610	+	0.371056i	$0.121004\pi$
$692$	30.8429	+	30.8429i	1.17247	+	1.17247i
$693$	19.0632			0.724153
$694$	31.1669	+	31.1669i	1.18308	+	1.18308i
$695$		−	52.5964i		−	1.99510i
$696$	−10.3556			−0.392529
$697$	0.446721	+	2.59010i	0.0169208	+	0.0981071i
$698$	28.9324			1.09511
$699$		−	22.0369i		−	0.833511i
$700$	−91.6494	−	91.6494i	−3.46402	−	3.46402i
$701$	18.4338			0.696237			0.348118	−	0.937451i	$-0.386821\pi$
$701$	18.4338			0.696237			0.348118	+	0.937451i	$0.386821\pi$
$702$	22.6684	+	22.6684i	0.855563	+	0.855563i
$703$	−10.3988	+	10.3988i	−0.392198	+	0.392198i
$704$	6.03044	−	6.03044i	0.227281	−	0.227281i
$705$		−	2.92903i		−	0.110314i
$706$		−	19.3966i		−	0.730002i
$707$	−6.02372	+	6.02372i	−0.226545	+	0.226545i
$708$	−95.4488	+	95.4488i	−3.58719	+	3.58719i
$709$	−14.2171	−	14.2171i	−0.533935	−	0.533935i	0.387806	−	0.921741i	$-0.373233\pi$
$709$	−14.2171	−	14.2171i	−0.533935	−	0.533935i	−0.921741	+	0.387806i	$0.873233\pi$
$710$	53.3384			2.00175
$711$	32.3711	+	32.3711i	1.21401	+	1.21401i
$712$		−	34.5045i		−	1.29311i
$713$	−10.1635			−0.380626
$714$	93.3217	+	65.8662i	3.49248	+	2.46498i
$715$	−10.4289			−0.390020
$716$		−	80.8806i		−	3.02265i
$717$	−12.9775	−	12.9775i	−0.484655	−	0.484655i
$718$	55.8763			2.08528
$719$	−10.4968	−	10.4968i	−0.391465	−	0.391465i	0.483744	−	0.875209i	$-0.339276\pi$
$719$	−10.4968	−	10.4968i	−0.391465	−	0.391465i	−0.875209	+	0.483744i	$0.839276\pi$
$720$	44.1052	−	44.1052i	1.64370	−	1.64370i
$721$	−30.3020	+	30.3020i	−1.12851	+	1.12851i
$722$		−	37.6344i		−	1.40061i
$723$			58.9832i			2.19361i
$724$	57.3469	−	57.3469i	2.13128	−	2.13128i
$725$	−4.43208	+	4.43208i	−0.164603	+	0.164603i
$726$	−4.76990	−	4.76990i	−0.177027	−	0.177027i
$727$	8.29841			0.307771			0.153885	−	0.988089i	$-0.450821\pi$
$727$	8.29841			0.307771			0.153885	+	0.988089i	$0.450821\pi$
$728$	40.0938	+	40.0938i	1.48597	+	1.48597i
$729$			44.0404i			1.63113i
$730$	30.1657			1.11648
$731$	−6.96305	−	4.91450i	−0.257538	−	0.181769i
$732$	57.5028			2.12537
$733$			1.46325i			0.0540465i	0.999635	+	0.0270233i	$0.00860282\pi$
$733$			1.46325i			0.0540465i	−0.999635	+	0.0270233i	$0.991397\pi$
$734$	30.3481	+	30.3481i	1.12017	+	1.12017i
$735$	−98.2659			−3.62459
$736$	−0.922808	−	0.922808i	−0.0340151	−	0.0340151i
$737$	−8.78547	+	8.78547i	−0.323617	+	0.323617i
$738$	5.10569	−	5.10569i	0.187943	−	0.187943i
$739$		−	24.9425i		−	0.917526i	−0.888559	−	0.458763i	$-0.848293\pi$
$739$		−	24.9425i		−	0.917526i	0.888559	−	0.458763i	$-0.151707\pi$
$740$			110.781i			4.07238i
$741$	−10.7019	+	10.7019i	−0.393143	+	0.393143i
$742$	−20.7503	+	20.7503i	−0.761767	+	0.761767i
$743$	31.9577	+	31.9577i	1.17242	+	1.17242i	0.981632	+	0.190784i	$0.0611030\pi$
$743$	31.9577	+	31.9577i	1.17242	+	1.17242i	0.190784	+	0.981632i	$0.438897\pi$
$744$	−44.9803			−1.64906
$745$	−25.5742	−	25.5742i	−0.936965	−	0.936965i
$746$		−	13.2211i		−	0.484060i
$747$	−66.5337			−2.43434
$748$	−2.77129	−	16.0680i	−0.101328	−	0.587505i
$749$	44.8771			1.63977
$750$		−	72.4366i		−	2.64501i
$751$	−15.2901	−	15.2901i	−0.557944	−	0.557944i	0.370778	−	0.928722i	$-0.379091\pi$
$751$	−15.2901	−	15.2901i	−0.557944	−	0.557944i	−0.928722	+	0.370778i	$0.879091\pi$
$752$	1.09687			0.0399987
$753$	−56.8084	−	56.8084i	−2.07021	−	2.07021i
$754$	3.92282	−	3.92282i	0.142861	−	0.142861i
$755$	−24.3452	+	24.3452i	−0.886014	+	0.886014i
$756$		−	73.7105i		−	2.68082i
$757$		−	2.66533i		−	0.0968731i	−0.998826	−	0.0484366i	$-0.984576\pi$
$757$		−	2.66533i		−	0.0968731i	0.998826	−	0.0484366i	$-0.0154239\pi$
$758$	−53.4699	+	53.4699i	−1.94211	+	1.94211i
$759$	−5.82354	+	5.82354i	−0.211381	+	0.211381i
$760$	22.9826	+	22.9826i	0.833667	+	0.833667i
$761$	26.2153			0.950303			0.475151	−	0.879904i	$-0.342393\pi$
$761$	26.2153			0.950303			0.475151	+	0.879904i	$0.342393\pi$
$762$	−99.0712	−	99.0712i	−3.58897	−	3.58897i
$763$			38.8360i			1.40596i
$764$	52.2010			1.88856
$765$	11.7195	+	67.9501i	0.423720	+	2.45674i
$766$	19.4982			0.704499
$767$		−	35.7420i		−	1.29057i
$768$	−61.7460	−	61.7460i	−2.22807	−	2.22807i
$769$	−4.05079			−0.146075			−0.0730375	−	0.997329i	$-0.523269\pi$
$769$	−4.05079			−0.146075			−0.0730375	+	0.997329i	$0.523269\pi$
$770$	25.5311	+	25.5311i	0.920075	+	0.920075i
$771$	1.89120	−	1.89120i	0.0681098	−	0.0681098i
$772$	6.39611	−	6.39611i	0.230201	−	0.230201i
$773$		−	31.1775i		−	1.12138i	−0.828027	−	0.560688i	$-0.810537\pi$
$773$		−	31.1775i		−	1.12138i	0.828027	−	0.560688i	$-0.189463\pi$
$774$			23.4134i			0.841577i
$775$	−19.2510	+	19.2510i	−0.691516	+	0.691516i
$776$	26.3811	−	26.3811i	0.947027	−	0.947027i
$777$	62.4179	+	62.4179i	2.23923	+	2.23923i
$778$	−59.1460			−2.12049
$779$	0.852562	+	0.852562i	0.0305462	+	0.0305462i
$780$			114.009i			4.08219i
$781$	−6.06691			−0.217091
$782$	−29.5386	+	5.09459i	−1.05630	+	0.182182i
$783$	−3.56457			−0.127387
$784$		−	36.7988i		−	1.31424i
$785$	38.1755	+	38.1755i	1.36254	+	1.36254i
$786$	12.2702			0.437665
$787$	26.2366	+	26.2366i	0.935235	+	0.935235i	0.998027	−	0.0627912i	$-0.0200002\pi$
$787$	26.2366	+	26.2366i	0.935235	+	0.935235i	−0.0627912	+	0.998027i	$0.520000\pi$
$788$	−54.2674	+	54.2674i	−1.93319	+	1.93319i
$789$	23.6604	−	23.6604i	0.842334	−	0.842334i
$790$			86.7081i			3.08494i
$791$		−	21.1310i		−	0.751331i
$792$	−15.6551	+	15.6551i	−0.556280	+	0.556280i
$793$	−10.7663	+	10.7663i	−0.382324	+	0.382324i
$794$	−62.4588	−	62.4588i	−2.21658	−	2.21658i
$795$	−29.1638			−1.03433
$796$	−0.656237	−	0.656237i	−0.0232597	−	0.0232597i
$797$			27.3444i			0.968589i	0.874905	+	0.484295i	$0.160924\pi$
$797$			27.3444i			0.968589i	−0.874905	+	0.484295i	$0.839076\pi$
$798$	52.3985			1.85489
$799$	−0.699210	+	0.990667i	−0.0247363	+	0.0350473i
$800$	−3.49584			−0.123597
$801$		−	33.5796i		−	1.18648i
$802$	−36.8308	−	36.8308i	−1.30054	−	1.30054i
$803$	−3.43116			−0.121083
$804$	96.0430	+	96.0430i	3.38718	+	3.38718i
$805$	31.1707	−	31.1707i	1.09862	−	1.09862i
$806$	17.0390	−	17.0390i	0.600174	−	0.600174i
$807$			32.0701i			1.12892i
$808$		−	9.89359i		−	0.348055i
$809$	−32.4293	+	32.4293i	−1.14015	+	1.14015i	−0.151732	+	0.988422i	$0.548485\pi$
$809$	−32.4293	+	32.4293i	−1.14015	+	1.14015i	−0.988422	+	0.151732i	$0.951515\pi$
$810$	−8.57383	+	8.57383i	−0.301254	+	0.301254i
$811$	16.2387	+	16.2387i	0.570217	+	0.570217i	0.932189	−	0.361972i	$-0.117896\pi$
$811$	16.2387	+	16.2387i	0.570217	+	0.570217i	−0.361972	+	0.932189i	$0.617896\pi$
$812$	−12.7558			−0.447640
$813$	46.0316	+	46.0316i	1.61440	+	1.61440i
$814$		−	18.9732i		−	0.665011i
$815$	−24.9953			−0.875546
$816$	−41.8920	+	7.22520i	−1.46651	+	0.252933i
$817$	−3.90963			−0.136781
$818$		−	8.75196i		−	0.306005i
$819$	39.0190	+	39.0190i	1.36343	+	1.36343i
$820$	9.08253			0.317176
$821$	−7.99253	−	7.99253i	−0.278941	−	0.278941i	0.553745	−	0.832686i	$-0.313198\pi$
$821$	−7.99253	−	7.99253i	−0.278941	−	0.278941i	−0.832686	+	0.553745i	$0.813198\pi$
$822$	16.8230	−	16.8230i	0.586771	−	0.586771i
$823$	−2.61960	+	2.61960i	−0.0913134	+	0.0913134i	−0.751288	−	0.659975i	$-0.770567\pi$
$823$	−2.61960	+	2.61960i	−0.0913134	+	0.0913134i	0.659975	+	0.751288i	$0.270567\pi$
$824$		−	49.7692i		−	1.73379i
$825$			22.0611i			0.768069i
$826$	−87.5000	+	87.5000i	−3.04451	+	3.04451i
$827$	−28.1435	+	28.1435i	−0.978644	+	0.978644i	−0.999777	−	0.0211324i	$-0.993273\pi$
$827$	−28.1435	+	28.1435i	−0.978644	+	0.978644i	0.0211324	+	0.999777i	$0.493273\pi$
$828$	38.6703	+	38.6703i	1.34389	+	1.34389i
$829$	−51.0934			−1.77455			−0.887274	−	0.461243i	$-0.847403\pi$
$829$	−51.0934			−1.77455			−0.887274	+	0.461243i	$0.847403\pi$
$830$	−89.1074	−	89.1074i	−3.09296	−	3.09296i
$831$			3.71297i			0.128802i
$832$	24.6864			0.855848
$833$	33.2358	+	23.4578i	1.15155	+	0.812764i
$834$	98.4769			3.40998
$835$		−	73.1739i		−	2.53229i
$836$	−5.28897	−	5.28897i	−0.182923	−	0.182923i
$837$	−15.4829			−0.535168
$838$	46.1941	+	46.1941i	1.59575	+	1.59575i
$839$	−18.8383	+	18.8383i	−0.650370	+	0.650370i	−0.953082	−	0.302712i	$-0.902108\pi$
$839$	−18.8383	+	18.8383i	−0.650370	+	0.650370i	0.302712	+	0.953082i	$0.402108\pi$
$840$	137.951	−	137.951i	4.75977	−	4.75977i
$841$		−	28.3831i		−	0.978729i
$842$			17.9855i			0.619820i
$843$	36.7505	−	36.7505i	1.26575	−	1.26575i
$844$	38.3655	−	38.3655i	1.32059	−	1.32059i
$845$	11.7726	+	11.7726i	0.404990	+	0.404990i
$846$	3.33114			0.114527
$847$	−2.90400	−	2.90400i	−0.0997826	−	0.0997826i
$848$		−	10.9213i		−	0.375039i
$849$	−31.5341			−1.08225
$850$	−46.3002	+	65.5999i	−1.58808	+	2.25006i
$851$	−23.1643			−0.794062
$852$			66.3236i			2.27221i
$853$	−17.2147	−	17.2147i	−0.589422	−	0.589422i	0.348053	−	0.937475i	$-0.386843\pi$
$853$	−17.2147	−	17.2147i	−0.589422	−	0.589422i	−0.937475	+	0.348053i	$0.886843\pi$
$854$	52.7140			1.80384
$855$	22.3666	+	22.3666i	0.764920	+	0.764920i
$856$	−36.8540	+	36.8540i	−1.25964	+	1.25964i
$857$	−3.53629	+	3.53629i	−0.120797	+	0.120797i	−0.764921	−	0.644124i	$-0.777222\pi$
$857$	−3.53629	+	3.53629i	−0.120797	+	0.120797i	0.644124	+	0.764921i	$0.277222\pi$
$858$		−	19.5262i		−	0.666615i
$859$			35.6419i			1.21608i	0.793905	+	0.608042i	$0.208045\pi$
$859$			35.6419i			1.21608i	−0.793905	+	0.608042i	$0.791955\pi$
$860$	−20.8251	+	20.8251i	−0.710129	+	0.710129i
$861$	5.11743	−	5.11743i	0.174401	−	0.174401i
$862$	−60.8094	−	60.8094i	−2.07118	−	2.07118i
$863$	−27.2003			−0.925908			−0.462954	−	0.886382i	$-0.653210\pi$
$863$	−27.2003			−0.925908			−0.462954	+	0.886382i	$0.653210\pi$
$864$	−1.40579	−	1.40579i	−0.0478260	−	0.0478260i
$865$			39.7385i			1.35115i
$866$	−61.8991			−2.10342
$867$	20.1788	−	42.4416i	0.685308	−	1.44139i
$868$	−55.4056			−1.88059
$869$		−	9.86251i		−	0.334563i
$870$	−13.4973	−	13.4973i	−0.457602	−	0.457602i
$871$	−35.9645			−1.21861
$872$	−31.8929	−	31.8929i	−1.08003	−	1.08003i
$873$	25.6739	−	25.6739i	0.868931	−	0.868931i
$874$	−9.72297	+	9.72297i	−0.328884	+	0.328884i
$875$		−	44.1007i		−	1.49088i
$876$			37.5095i			1.26733i
$877$	16.3360	−	16.3360i	0.551627	−	0.551627i	−0.375283	−	0.926910i	$-0.622455\pi$
$877$	16.3360	−	16.3360i	0.551627	−	0.551627i	0.926910	+	0.375283i	$0.122455\pi$
$878$	1.98358	−	1.98358i	0.0669425	−	0.0669425i
$879$	−38.2837	−	38.2837i	−1.29128	−	1.29128i
$880$	−13.4375			−0.452979
$881$	15.2840	+	15.2840i	0.514932	+	0.514932i	0.916034	−	0.401101i	$-0.131372\pi$
$881$	15.2840	+	15.2840i	0.514932	+	0.514932i	−0.401101	+	0.916034i	$0.631372\pi$
$882$		−	111.756i		−	3.76303i
$883$	−3.95285			−0.133024			−0.0665120	−	0.997786i	$-0.521187\pi$
$883$	−3.95285			−0.133024			−0.0665120	+	0.997786i	$0.521187\pi$
$884$	27.2160	−	38.5607i	0.915374	−	1.29694i
$885$	−122.978			−4.13386
$886$		−	27.7994i		−	0.933940i
$887$	−15.4932	−	15.4932i	−0.520210	−	0.520210i	0.397425	−	0.917635i	$-0.369904\pi$
$887$	−15.4932	−	15.4932i	−0.520210	−	0.520210i	−0.917635	+	0.397425i	$0.869904\pi$
$888$	−102.518			−3.44026
$889$	−60.3164	−	60.3164i	−2.02295	−	2.02295i
$890$	44.9725	−	44.9725i	1.50748	−	1.50748i
$891$	0.975221	−	0.975221i	0.0326711	−	0.0326711i
$892$			89.8298i			3.00773i
$893$			0.556242i			0.0186139i
$894$	47.8829	−	47.8829i	1.60144	−	1.60144i
$895$	52.1041	−	52.1041i	1.74165	−	1.74165i
$896$	−57.8906	−	57.8906i	−1.93399	−	1.93399i
$897$	−23.8395			−0.795976
$898$	22.2371	+	22.2371i	0.742063	+	0.742063i
$899$			2.67936i			0.0893616i
$900$	146.494			4.88312
$901$	9.86388	+	6.96190i	0.328613	+	0.231934i
$902$	−1.55555			−0.0517942
$903$			23.4672i			0.780940i
$904$	17.3532	+	17.3532i	0.577158	+	0.577158i
$905$	73.8869			2.45608
$906$	−45.5819	−	45.5819i	−1.51436	−	1.51436i
$907$	13.8933	−	13.8933i	0.461318	−	0.461318i	−0.437769	−	0.899087i	$-0.644231\pi$
$907$	13.8933	−	13.8933i	0.461318	−	0.461318i	0.899087	+	0.437769i	$0.144231\pi$
$908$	27.3737	−	27.3737i	0.908428	−	0.908428i
$909$		−	9.62838i		−	0.319353i
$910$			104.515i			3.46464i
$911$	28.5392	−	28.5392i	0.945547	−	0.945547i	−0.0530450	−	0.998592i	$-0.516893\pi$
$911$	28.5392	−	28.5392i	0.945547	−	0.945547i	0.998592	+	0.0530450i	$0.0168927\pi$
$912$	−13.7892	+	13.7892i	−0.456607	+	0.456607i
$913$	10.1354	+	10.1354i	0.335433	+	0.335433i
$914$	−96.7653			−3.20071
$915$	37.0439	+	37.0439i	1.22463	+	1.22463i
$916$			32.1688i			1.06289i
$917$	7.47034			0.246692
$918$	−44.9987	+	7.76103i	−1.48518	+	0.256152i
$919$	−2.73130			−0.0900973			−0.0450486	−	0.998985i	$-0.514344\pi$
$919$	−2.73130			−0.0900973			−0.0450486	+	0.998985i	$0.514344\pi$
$920$			51.1960i			1.68788i
$921$	−31.2991	−	31.2991i	−1.03134	−	1.03134i
$922$	20.7464			0.683246
$923$	−12.4179	−	12.4179i	−0.408739	−	0.408739i
$924$	−31.7466	+	31.7466i	−1.04439	+	1.04439i
$925$	−43.8763	+	43.8763i	−1.44264	+	1.44264i
$926$			57.7959i			1.89929i
$927$		−	48.4351i		−	1.59082i
$928$	−0.243276	+	0.243276i	−0.00798593	+	0.00798593i
$929$	7.54652	−	7.54652i	0.247593	−	0.247593i	−0.572389	−	0.819982i	$-0.693983\pi$
$929$	7.54652	−	7.54652i	0.247593	−	0.247593i	0.819982	+	0.572389i	$0.193983\pi$
$930$	−58.6264	−	58.6264i	−1.92243	−	1.92243i
$931$	18.6613			0.611601
$932$	22.2916	+	22.2916i	0.730185	+	0.730185i
$933$			21.6834i			0.709881i
$934$	64.3806			2.10660
$935$	8.56589	−	12.1365i	0.280135	−	0.396905i
$936$	−64.0864			−2.09473
$937$		−	14.2826i		−	0.466591i	−0.972406	−	0.233296i	$-0.925049\pi$
$937$		−	14.2826i		−	0.466591i	0.972406	−	0.233296i	$-0.0749510\pi$
$938$	88.0447	+	88.0447i	2.87476	+	2.87476i
$939$	74.1761			2.42064
$940$	2.96289	+	2.96289i	0.0966387	+	0.0966387i
$941$	26.8262	−	26.8262i	0.874511	−	0.874511i	−0.118450	−	0.992960i	$-0.537792\pi$
$941$	26.8262	−	26.8262i	0.874511	−	0.874511i	0.992960	+	0.118450i	$0.0377924\pi$
$942$	−71.4764	+	71.4764i	−2.32883	+	2.32883i
$943$			1.89916i			0.0618452i
$944$		−	46.0531i		−	1.49890i
$945$	47.4850	−	47.4850i	1.54469	−	1.54469i
$946$	3.56668	−	3.56668i	0.115963	−	0.115963i
$947$	11.4211	+	11.4211i	0.371136	+	0.371136i	0.867891	−	0.496755i	$-0.165475\pi$
$947$	11.4211	+	11.4211i	0.371136	+	0.371136i	−0.496755	+	0.867891i	$0.665475\pi$
$948$	−107.817			−3.50174
$949$	−7.02296	−	7.02296i	−0.227975	−	0.227975i
$950$			36.8332i			1.19503i
$951$	86.8331			2.81576
$952$	−79.5897	+	13.7270i	−2.57952	+	0.444895i
$953$	−34.8736			−1.12967			−0.564834	−	0.825205i	$-0.691060\pi$
$953$	−34.8736			−1.12967			−0.564834	+	0.825205i	$0.691060\pi$
$954$		−	33.1675i		−	1.07384i
$955$	33.6284	+	33.6284i	1.08819	+	1.08819i
$956$	26.2550			0.849149
$957$	1.53524	+	1.53524i	0.0496271	+	0.0496271i
$958$	−1.83738	+	1.83738i	−0.0593631	+	0.0593631i
$959$	10.2422	−	10.2422i	0.330737	−	0.330737i
$960$		−	84.9390i		−	2.74139i
$961$		−	19.3620i		−	0.624582i
$962$	38.8348	−	38.8348i	1.25208	−	1.25208i
$963$	−35.8661	+	35.8661i	−1.15577	+	1.15577i
$964$	−59.6650	−	59.6650i	−1.92168	−	1.92168i
$965$	8.24088			0.265283
$966$	58.3613	+	58.3613i	1.87774	+	1.87774i
$967$		−	29.5306i		−	0.949639i	−0.880083	−	0.474820i	$-0.842513\pi$
$967$		−	29.5306i		−	0.949639i	0.880083	−	0.474820i	$-0.157487\pi$
$968$	4.76964			0.153302
$969$	−3.66403	−	21.2442i	−0.117706	−	0.682461i
$970$	68.7693			2.20805
$971$			12.1527i			0.389997i	0.980804	+	0.194999i	$0.0624702\pi$
$971$			12.1527i			0.389997i	−0.980804	+	0.194999i	$0.937530\pi$
$972$	−48.7347	−	48.7347i	−1.56317	−	1.56317i
$973$	59.9545			1.92205
$974$	−5.90142	−	5.90142i	−0.189094	−	0.189094i
$975$	−45.1551	+	45.1551i	−1.44612	+	1.44612i
$976$	−13.8723	+	13.8723i	−0.444040	+	0.444040i
$977$			37.4267i			1.19739i	0.800978	+	0.598693i	$0.204313\pi$
$977$			37.4267i			1.19739i	−0.800978	+	0.598693i	$0.795687\pi$
$978$		−	46.7990i		−	1.49647i
$979$	−5.11534	+	5.11534i	−0.163487	+	0.163487i
$980$	99.4017	−	99.4017i	3.17527	−	3.17527i
$981$	−31.0379	−	31.0379i	−0.990965	−	0.990965i
$982$	−92.4211			−2.94928
$983$	−11.9409	−	11.9409i	−0.380857	−	0.380857i	0.490554	−	0.871411i	$-0.336794\pi$
$983$	−11.9409	−	11.9409i	−0.380857	−	0.380857i	−0.871411	+	0.490554i	$0.836794\pi$
$984$			8.40507i			0.267944i
$985$	−69.9191			−2.22781
$986$	1.34307	+	7.78715i	0.0427720	+	0.247993i
$987$	3.33880			0.106275
$988$		−	21.6511i		−	0.688815i
$989$	−4.35454	−	4.35454i	−0.138466	−	0.138466i
$990$	−40.8091			−1.29700
$991$	−27.6939	−	27.6939i	−0.879726	−	0.879726i	0.113780	−	0.993506i	$-0.463704\pi$
$991$	−27.6939	−	27.6939i	−0.879726	−	0.879726i	−0.993506	+	0.113780i	$0.963704\pi$
$992$	−1.05668	+	1.05668i	−0.0335498	+	0.0335498i
$993$	−44.7527	+	44.7527i	−1.42019	+	1.42019i
$994$			60.8003i			1.92847i
$995$		−	0.845509i		−	0.0268044i
$996$	110.801	−	110.801i	3.51085	−	3.51085i
$997$	14.7081	−	14.7081i	0.465809	−	0.465809i	−0.434744	−	0.900554i	$-0.643161\pi$
$997$	14.7081	−	14.7081i	0.465809	−	0.465809i	0.900554	+	0.434744i	$0.143161\pi$
$998$	45.5711	+	45.5711i	1.44253	+	1.44253i
$999$	−35.2882			−1.11647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.166.1	yes	28
17.2	even	8		3179.2.a.be.1.14		14
17.4	even	4	inner	187.2.e.b.89.14	✓	28
17.15	even	8		3179.2.a.bd.1.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.14	✓	28	17.4	even	4	inner
187.2.e.b.166.1	yes	28	1.1	even	1	trivial
3179.2.a.bd.1.14		14	17.15	even	8
3179.2.a.be.1.14		14	17.2	even	8

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.44021i q^{2} +(1.95471 + 1.95471i) q^{3} -3.95461 q^{4} +(-2.54760 - 2.54760i) q^{5} +(4.76990 - 4.76990i) q^{6} +(2.90400 - 2.90400i) q^{7} +4.76964i q^{8} +4.64179i q^{9} +O(q^{10})\)	\(q-2.44021i q^{2} +(1.95471 + 1.95471i) q^{3} -3.95461 q^{4} +(-2.54760 - 2.54760i) q^{5} +(4.76990 - 4.76990i) q^{6} +(2.90400 - 2.90400i) q^{7} +4.76964i q^{8} +4.64179i q^{9} +(-6.21666 + 6.21666i) q^{10} +(0.707107 - 0.707107i) q^{11} +(-7.73011 - 7.73011i) q^{12} +2.89464 q^{13} +(-7.08636 - 7.08636i) q^{14} -9.95963i q^{15} +3.72970 q^{16} +(-2.37753 + 3.36858i) q^{17} +11.3269 q^{18} +1.89140i q^{19} +(10.0747 + 10.0747i) q^{20} +11.3530 q^{21} +(-1.72549 - 1.72549i) q^{22} +(-2.10664 + 2.10664i) q^{23} +(-9.32327 + 9.32327i) q^{24} +7.98049i q^{25} -7.06352i q^{26} +(-3.20922 + 3.20922i) q^{27} +(-11.4842 + 11.4842i) q^{28} +(0.555364 + 0.555364i) q^{29} -24.3035 q^{30} +(2.41226 + 2.41226i) q^{31} +0.438048i q^{32} +2.76438 q^{33} +(8.22003 + 5.80167i) q^{34} -14.7964 q^{35} -18.3564i q^{36} +(5.49794 + 5.49794i) q^{37} +4.61540 q^{38} +(5.65818 + 5.65818i) q^{39} +(12.1511 - 12.1511i) q^{40} +(0.450757 - 0.450757i) q^{41} -27.7036i q^{42} +2.06706i q^{43} +(-2.79633 + 2.79633i) q^{44} +(11.8254 - 11.8254i) q^{45} +(5.14062 + 5.14062i) q^{46} +0.294091 q^{47} +(7.29049 + 7.29049i) q^{48} -9.86643i q^{49} +19.4741 q^{50} +(-11.2320 + 1.93721i) q^{51} -11.4472 q^{52} -2.92820i q^{53} +(7.83116 + 7.83116i) q^{54} -3.60285 q^{55} +(13.8510 + 13.8510i) q^{56} +(-3.69714 + 3.69714i) q^{57} +(1.35520 - 1.35520i) q^{58} -12.3477i q^{59} +39.3864i q^{60} +(-3.71940 + 3.71940i) q^{61} +(5.88640 - 5.88640i) q^{62} +(13.4797 + 13.4797i) q^{63} +8.52833 q^{64} +(-7.37437 - 7.37437i) q^{65} -6.74565i q^{66} -12.4245 q^{67} +(9.40221 - 13.3214i) q^{68} -8.23572 q^{69} +36.1064i q^{70} +(-4.28995 - 4.28995i) q^{71} -22.1397 q^{72} +(-2.42620 - 2.42620i) q^{73} +(13.4161 - 13.4161i) q^{74} +(-15.5996 + 15.5996i) q^{75} -7.47974i q^{76} -4.10688i q^{77} +(13.8071 - 13.8071i) q^{78} +(6.97385 - 6.97385i) q^{79} +(-9.50177 - 9.50177i) q^{80} +1.37917 q^{81} +(-1.09994 - 1.09994i) q^{82} +14.3336i q^{83} -44.8965 q^{84} +(14.6388 - 2.52478i) q^{85} +5.04405 q^{86} +2.17115i q^{87} +(3.37265 + 3.37265i) q^{88} -7.23419 q^{89} +(-28.8564 - 28.8564i) q^{90} +(8.40603 - 8.40603i) q^{91} +(8.33091 - 8.33091i) q^{92} +9.43053i q^{93} -0.717641i q^{94} +(4.81852 - 4.81852i) q^{95} +(-0.856257 + 0.856257i) q^{96} +(-5.53105 - 5.53105i) q^{97} -24.0761 q^{98} +(3.28224 + 3.28224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Introduction

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