LMFDB - Embedded newform 136.2.h.a.101.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(101,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.h (of order $2$, degree $1$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 20x^{12} + 36x^{10} + 240x^{8} - 156x^{6} + 268x^{4} + 136x^{2} + 64 $ x^16 + 8x^14 + 20x^12 + 36x^10 + 240x^8 - 156x^6 + 268x^4 + 136*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.13
Root			$1.32216 - 1.07919i$ of defining polynomial
Character	$\chi$	$=$	136.101
Dual form			136.2.h.a.101.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09558 - 0.894257i) q^{2} -1.88797 q^{3} +(0.400610 - 1.95947i) q^{4} +2.41361 q^{5} +(-2.06843 + 1.68833i) q^{6} -2.57100i q^{7} +(-1.31336 - 2.50501i) q^{8} +0.564439 q^{9} +O(q^{10})$	\(q+(1.09558 - 0.894257i) q^{2} -1.88797 q^{3} +(0.400610 - 1.95947i) q^{4} +2.41361 q^{5} +(-2.06843 + 1.68833i) q^{6} -2.57100i q^{7} +(-1.31336 - 2.50501i) q^{8} +0.564439 q^{9} +(2.64431 - 2.15839i) q^{10} +0.736213 q^{11} +(-0.756340 + 3.69942i) q^{12} +4.07497i q^{13} +(-2.29914 - 2.81675i) q^{14} -4.55683 q^{15} +(-3.67902 - 1.56996i) q^{16} +(3.99239 + 1.02997i) q^{17} +(0.618390 - 0.504753i) q^{18} +0.853468i q^{19} +(0.966916 - 4.72939i) q^{20} +4.85398i q^{21} +(0.806583 - 0.658363i) q^{22} +8.20450i q^{23} +(2.47960 + 4.72939i) q^{24} +0.825510 q^{25} +(3.64407 + 4.46448i) q^{26} +4.59827 q^{27} +(-5.03779 - 1.02997i) q^{28} -5.86012 q^{29} +(-4.99239 + 4.07497i) q^{30} +3.51111i q^{31} +(-5.43463 + 1.56996i) q^{32} -1.38995 q^{33} +(5.29505 - 2.44180i) q^{34} -6.20539i q^{35} +(0.226120 - 1.10600i) q^{36} +4.38770 q^{37} +(0.763219 + 0.935046i) q^{38} -7.69344i q^{39} +(-3.16995 - 6.04611i) q^{40} -11.7156i q^{41} +(4.34070 + 5.31794i) q^{42} +1.09108i q^{43} +(0.294934 - 1.44258i) q^{44} +1.36234 q^{45} +(7.33693 + 8.98872i) q^{46} -5.42795 q^{47} +(6.94589 + 2.96405i) q^{48} +0.389949 q^{49} +(0.904416 - 0.738218i) q^{50} +(-7.53752 - 1.94455i) q^{51} +(7.98478 + 1.63247i) q^{52} -4.66811i q^{53} +(5.03779 - 4.11204i) q^{54} +1.77693 q^{55} +(-6.44038 + 3.37666i) q^{56} -1.61132i q^{57} +(-6.42026 + 5.24045i) q^{58} -12.5060i q^{59} +(-1.82551 + 8.92895i) q^{60} -8.16364 q^{61} +(3.13983 + 3.84672i) q^{62} -1.45117i q^{63} +(-4.55015 + 6.57998i) q^{64} +9.83539i q^{65} +(-1.52281 + 1.24297i) q^{66} +10.5614i q^{67} +(3.61758 - 7.41034i) q^{68} -15.4899i q^{69} +(-5.54922 - 6.79853i) q^{70} +0.511064i q^{71} +(-0.741314 - 1.41392i) q^{72} +13.3269i q^{73} +(4.80709 - 3.92373i) q^{74} -1.55854 q^{75} +(1.67234 + 0.341908i) q^{76} -1.89280i q^{77} +(-6.87991 - 8.42881i) q^{78} -1.45117i q^{79} +(-8.87973 - 3.78928i) q^{80} -10.3747 q^{81} +(-10.4768 - 12.8354i) q^{82} -4.35603i q^{83} +(9.51121 + 1.94455i) q^{84} +(9.63607 + 2.48594i) q^{85} +(0.975710 + 1.19538i) q^{86} +11.0637 q^{87} +(-0.966916 - 1.84422i) q^{88} +5.72371 q^{89} +(1.49255 - 1.21828i) q^{90} +10.4768 q^{91} +(16.0765 + 3.28680i) q^{92} -6.62888i q^{93} +(-5.94678 + 4.85398i) q^{94} +2.05994i q^{95} +(10.2604 - 2.96405i) q^{96} -11.8953i q^{97} +(0.427222 - 0.348714i) q^{98} +0.415547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9 - 8 * q^15 - 14 * q^16 - 2 * q^18 - 16 * q^30 - 2 * q^32 - 8 * q^33 + 18 * q^34 - 22 * q^36 + 36 * q^38 - 24 * q^47 - 8 * q^49 + 34 * q^50 - 8 * q^55 - 16 * q^60 - 30 * q^64 - 32 * q^66 + 38 * q^68 + 40 * q^70 + 70 * q^72 + 4 * q^76 - 24 * q^81 + 72 * q^84 + 4 * q^86 - 40 * q^87 - 24 * q^89 - 16 * q^94 + 34 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.09558	−	0.894257i	0.774695	−	0.632335i
$2$	1.09558	−	0.894257i	0.774695	−	0.632335i
$3$	−1.88797			−1.09002			−0.545011	−	0.838429i	$-0.683474\pi$
$3$	−1.88797			−1.09002			−0.545011	+	0.838429i	$0.683474\pi$
$4$	0.400610	−	1.95947i	0.200305	−	0.979734i
$5$	2.41361			1.07940			0.539699	−	0.841858i	$-0.318538\pi$
$5$	2.41361			1.07940			0.539699	+	0.841858i	$0.318538\pi$
$6$	−2.06843	+	1.68833i	−0.844434	+	0.689259i
$7$		−	2.57100i		−	0.971747i	−0.874029	−	0.485874i	$-0.838501\pi$
$7$		−	2.57100i		−	0.971747i	0.874029	−	0.485874i	$-0.161499\pi$
$8$	−1.31336	−	2.50501i	−0.464345	−	0.885655i
$9$	0.564439			0.188146
$10$	2.64431	−	2.15839i	0.836205	−	0.682542i
$11$	0.736213			0.221976			0.110988	−	0.993822i	$-0.464598\pi$
$11$	0.736213			0.221976			0.110988	+	0.993822i	$0.464598\pi$
$12$	−0.756340	+	3.69942i	−0.218337	+	1.06793i
$13$			4.07497i			1.13019i	0.825024	+	0.565097i	$0.191161\pi$
$13$			4.07497i			1.13019i	−0.825024	+	0.565097i	$0.808839\pi$
$14$	−2.29914	−	2.81675i	−0.614470	−	0.752808i
$15$	−4.55683			−1.17657
$16$	−3.67902	−	1.56996i	−0.919756	−	0.392491i
$17$	3.99239	+	1.02997i	0.968296	+	0.249804i
$17$	3.99239	+	1.02997i	0.968296	+	0.249804i
$18$	0.618390	−	0.504753i	0.145756	−	0.118971i
$19$			0.853468i			0.195799i	0.995196	+	0.0978995i	$0.0312124\pi$
$19$			0.853468i			0.195799i	−0.995196	+	0.0978995i	$0.968788\pi$
$20$	0.966916	−	4.72939i	0.216209	−	1.05752i
$21$			4.85398i			1.05923i
$22$	0.806583	−	0.658363i	0.171964	−	0.140363i
$23$			8.20450i			1.71076i	0.518004	+	0.855378i	$0.326675\pi$
$23$			8.20450i			1.71076i	−0.518004	+	0.855378i	$0.673325\pi$
$24$	2.47960	+	4.72939i	0.506145	+	0.965382i
$25$	0.825510			0.165102
$26$	3.64407	+	4.46448i	0.714661	+	0.875556i
$27$	4.59827			0.884938
$28$	−5.03779	−	1.02997i	−0.952054	−	0.194646i
$29$	−5.86012			−1.08820			−0.544099	−	0.839021i	$-0.683128\pi$
$29$	−5.86012			−1.08820			−0.544099	+	0.839021i	$0.683128\pi$
$30$	−4.99239	+	4.07497i	−0.911481	+	0.743985i
$31$			3.51111i			0.630614i	0.948990	+	0.315307i	$0.102108\pi$
$31$			3.51111i			0.630614i	−0.948990	+	0.315307i	$0.897892\pi$
$32$	−5.43463	+	1.56996i	−0.960716	+	0.277533i
$33$	−1.38995			−0.241959
$34$	5.29505	−	2.44180i	0.908094	−	0.418766i
$35$		−	6.20539i		−	1.04890i
$36$	0.226120	−	1.10600i	0.0376866	−	0.184333i
$37$	4.38770			0.721333			0.360666	−	0.932695i	$-0.382549\pi$
$37$	4.38770			0.721333			0.360666	+	0.932695i	$0.382549\pi$
$38$	0.763219	+	0.935046i	0.123811	+	0.151684i
$39$		−	7.69344i		−	1.23194i
$40$	−3.16995	−	6.04611i	−0.501213	−	0.955975i
$41$		−	11.7156i		−	1.82967i	−0.403827	−	0.914836i	$-0.632320\pi$
$41$		−	11.7156i		−	1.82967i	0.403827	−	0.914836i	$-0.367680\pi$
$42$	4.34070	+	5.31794i	0.669785	+	0.820577i
$43$			1.09108i			0.166389i	0.996533	+	0.0831944i	$0.0265123\pi$
$43$			1.09108i			0.166389i	−0.996533	+	0.0831944i	$0.973488\pi$
$44$	0.294934	−	1.44258i	0.0444630	−	0.217478i
$45$	1.36234			0.203085
$46$	7.33693	+	8.98872i	1.08177	+	1.32531i
$47$	−5.42795			−0.791748			−0.395874	−	0.918305i	$-0.629558\pi$
$47$	−5.42795			−0.791748			−0.395874	+	0.918305i	$0.629558\pi$
$48$	6.94589	+	2.96405i	1.00255	+	0.427823i
$49$	0.389949			0.0557070
$50$	0.904416	−	0.738218i	0.127904	−	0.104400i
$51$	−7.53752	−	1.94455i	−1.05546	−	0.272292i
$52$	7.98478	+	1.63247i	1.10729	+	0.226383i
$53$		−	4.66811i		−	0.641214i	−0.947212	−	0.320607i	$-0.896113\pi$
$53$		−	4.66811i		−	0.641214i	0.947212	−	0.320607i	$-0.103887\pi$
$54$	5.03779	−	4.11204i	0.685557	−	0.559577i
$55$	1.77693			0.239601
$56$	−6.44038	+	3.37666i	−0.860633	+	0.451226i
$57$		−	1.61132i		−	0.213425i
$58$	−6.42026	+	5.24045i	−0.843021	+	0.688105i
$59$		−	12.5060i		−	1.62814i	−0.580767	−	0.814070i	$-0.697247\pi$
$59$		−	12.5060i		−	1.62814i	0.580767	−	0.814070i	$-0.302753\pi$
$60$	−1.82551	+	8.92895i	−0.235672	+	1.15272i
$61$	−8.16364			−1.04525			−0.522624	−	0.852564i	$-0.675047\pi$
$61$	−8.16364			−1.04525			−0.522624	+	0.852564i	$0.675047\pi$
$62$	3.13983	+	3.84672i	0.398759	+	0.488534i
$63$		−	1.45117i		−	0.182831i
$64$	−4.55015	+	6.57998i	−0.568768	+	0.822498i
$65$			9.83539i			1.21993i
$66$	−1.52281	+	1.24297i	−0.187444	+	0.152999i
$67$			10.5614i			1.29028i	0.764063	+	0.645142i	$0.223202\pi$
$67$			10.5614i			1.29028i	−0.764063	+	0.645142i	$0.776798\pi$
$68$	3.61758	−	7.41034i	0.438696	−	0.898636i
$69$		−	15.4899i		−	1.86476i
$70$	−5.54922	−	6.79853i	−0.663258	−	0.812580i
$71$			0.511064i			0.0606522i	0.999540	+	0.0303261i	$0.00965458\pi$
$71$			0.511064i			0.0606522i	−0.999540	+	0.0303261i	$0.990345\pi$
$72$	−0.741314	−	1.41392i	−0.0873647	−	0.166633i
$73$			13.3269i			1.55980i	0.625904	+	0.779900i	$0.284730\pi$
$73$			13.3269i			1.55980i	−0.625904	+	0.779900i	$0.715270\pi$
$74$	4.80709	−	3.92373i	0.558813	−	0.456124i
$75$	−1.55854			−0.179965
$76$	1.67234	+	0.341908i	0.191831	+	0.0392195i
$77$		−	1.89280i		−	0.215705i
$78$	−6.87991	−	8.42881i	−0.778996	−	0.954375i
$79$		−	1.45117i		−	0.163270i	−0.996662	−	0.0816349i	$-0.973986\pi$
$79$		−	1.45117i		−	0.163270i	0.996662	−	0.0816349i	$-0.0260141\pi$
$80$	−8.87973	−	3.78928i	−0.992783	−	0.423654i
$81$	−10.3747			−1.15275
$82$	−10.4768	−	12.8354i	−1.15697	−	1.41744i
$83$		−	4.35603i		−	0.478137i	−0.971003	−	0.239068i	$-0.923158\pi$
$83$		−	4.35603i		−	0.478137i	0.971003	−	0.239068i	$-0.0768420\pi$
$84$	9.51121	+	1.94455i	1.03776	+	0.212168i
$85$	9.63607	+	2.48594i	1.04518	+	0.269638i
$86$	0.975710	+	1.19538i	0.105213	+	0.128901i
$87$	11.0637			1.18616
$88$	−0.966916	−	1.84422i	−0.103074	−	0.196594i
$89$	5.72371			0.606712			0.303356	−	0.952877i	$-0.401893\pi$
$89$	5.72371			0.606712			0.303356	+	0.952877i	$0.401893\pi$
$90$	1.49255	−	1.21828i	0.157329	−	0.128418i
$91$	10.4768			1.09826
$92$	16.0765	+	3.28680i	1.67609	+	0.342673i
$93$		−	6.62888i		−	0.687383i
$94$	−5.94678	+	4.85398i	−0.613363	+	0.500650i
$95$			2.05994i			0.211345i
$96$	10.2604	−	2.96405i	1.04720	−	0.302517i
$97$		−	11.8953i		−	1.20779i	−0.797065	−	0.603894i	$-0.793615\pi$
$97$		−	11.8953i		−	1.20779i	0.797065	−	0.603894i	$-0.206385\pi$
$98$	0.427222	−	0.348714i	0.0431559	−	0.0352255i
$99$	0.415547			0.0417640
$100$	0.330707	−	1.61756i	0.0330707	−	0.161756i
$101$			8.33582i			0.829445i	0.909948	+	0.414722i	$0.136121\pi$
$101$			8.33582i			0.829445i	−0.909948	+	0.414722i	$0.863879\pi$
$102$	−9.99692	+	4.61006i	−0.989842	+	0.456463i
$103$	15.5446			1.53165			0.765826	−	0.643048i	$-0.222330\pi$
$103$	15.5446			1.53165			0.765826	+	0.643048i	$0.222330\pi$
$104$	10.2078	−	5.35193i	1.00096	−	0.524800i
$105$			11.7156i			1.14333i
$106$	−4.17449	−	5.11431i	−0.405462	−	0.496746i
$107$	−14.9889			−1.44903			−0.724517	−	0.689257i	$-0.757937\pi$
$107$	−14.9889			−1.44903			−0.724517	+	0.689257i	$0.757937\pi$
$108$	1.84211	−	9.01016i	0.177257	−	0.867003i
$109$	−0.941184			−0.0901491			−0.0450745	−	0.998984i	$-0.514353\pi$
$109$	−0.941184			−0.0901491			−0.0450745	+	0.998984i	$0.514353\pi$
$110$	1.94678	−	1.58903i	0.185618	−	0.151508i
$111$	−8.28385			−0.786268
$112$	−4.03638	+	9.45878i	−0.381402	+	0.893770i
$113$		−	9.83539i		−	0.925236i	−0.886558	−	0.462618i	$-0.846910\pi$
$113$		−	9.83539i		−	0.925236i	0.886558	−	0.462618i	$-0.153090\pi$
$114$	−1.44094	−	1.76534i	−0.134956	−	0.165339i
$115$			19.8025i			1.84659i
$116$	−2.34762	+	11.4827i	−0.217971	+	1.06614i
$117$			2.30007i			0.212642i
$118$	−11.1836	−	13.7014i	−1.02953	−	1.26131i
$119$	2.64805	−	10.2644i	0.242747	−	0.940940i
$120$	5.98478	+	11.4149i	0.546333	+	1.04203i
$121$	−10.4580			−0.950726
$122$	−8.94396	+	7.30039i	−0.809748	+	0.660946i
$123$			22.1187i			1.99438i
$124$	6.87991	+	1.40659i	0.617834	+	0.126315i
$125$	−10.0756			−0.901188
$126$	−1.29772	−	1.58988i	−0.115610	−	0.141638i
$127$	−11.0984			−0.984827			−0.492413	−	0.870362i	$-0.663885\pi$
$127$	−11.0984			−0.984827			−0.492413	+	0.870362i	$0.663885\pi$
$128$	0.899126	+	11.2779i	0.0794722	+	0.996837i
$129$		−	2.05994i		−	0.181367i
$130$	8.79537	+	10.7755i	0.771405	+	0.945074i
$131$	18.4354			1.61071			0.805356	−	0.592792i	$-0.201974\pi$
$131$	18.4354			1.61071			0.805356	+	0.592792i	$0.201974\pi$
$132$	−0.556827	+	2.72356i	−0.0484656	+	0.237055i
$133$	2.19427			0.190267
$134$	9.44463	+	11.5709i	0.815892	+	0.999577i
$135$	11.0984			0.955201
$136$	−2.66338	−	11.3537i	−0.228383	−	0.973571i
$137$	−13.5340			−1.15629			−0.578143	−	0.815935i	$-0.696223\pi$
$137$	−13.5340			−1.15629			−0.578143	+	0.815935i	$0.696223\pi$
$138$	−13.8519	−	16.9705i	−1.17915	−	1.44462i
$139$	−2.71030			−0.229885			−0.114942	−	0.993372i	$-0.536668\pi$
$139$	−2.71030			−0.229885			−0.114942	+	0.993372i	$0.536668\pi$
$140$	−12.1593	−	2.48594i	−1.02765	−	0.210100i
$141$	10.2478			0.863022
$142$	0.457023	+	0.559914i	0.0383525	+	0.0469870i
$143$			3.00005i			0.250876i
$144$	−2.07658	−	0.886149i	−0.173049	−	0.0738457i
$145$	−14.1440			−1.17460
$146$	11.9177	+	14.6008i	0.986316	+	1.20837i
$147$	−0.736213			−0.0607218
$148$	1.75775	−	8.59755i	0.144487	−	0.706714i
$149$		−	1.70694i		−	0.139838i	−0.997553	−	0.0699188i	$-0.977726\pi$
$149$		−	1.70694i		−	0.139838i	0.997553	−	0.0699188i	$-0.0222740\pi$
$150$	−1.70751	+	1.39373i	−0.139418	+	0.113798i
$151$	3.47786			0.283024			0.141512	−	0.989937i	$-0.454804\pi$
$151$	3.47786			0.283024			0.141512	+	0.989937i	$0.454804\pi$
$152$	2.13794	−	1.12091i	0.173410	−	0.0909182i
$153$	2.25346	+	0.581354i	0.182181	+	0.0469997i
$154$	−1.69265	−	2.07373i	−0.136398	−	0.167106i
$155$			8.47445i			0.680684i
$156$	−15.0750	−	3.08207i	−1.20697	−	0.246763i
$157$			22.0508i			1.75984i	0.475118	+	0.879922i	$0.342405\pi$
$157$			22.0508i			1.75984i	−0.475118	+	0.879922i	$0.657595\pi$
$158$	−1.29772	−	1.58988i	−0.103241	−	0.126484i
$159$			8.81326i			0.698937i
$160$	−13.1171	+	3.78928i	−1.03700	+	0.299569i
$161$	21.0938			1.66242
$162$	−11.3664	+	9.27767i	−0.893028	+	0.728922i
$163$	6.94414			0.543907			0.271953	−	0.962310i	$-0.412330\pi$
$163$	6.94414			0.543907			0.271953	+	0.962310i	$0.412330\pi$
$164$	−22.9564	−	4.69339i	−1.79259	−	0.366492i
$165$	−3.35479			−0.261170
$166$	−3.89541	−	4.77240i	−0.302343	−	0.370410i
$167$		−	11.3843i		−	0.880941i	−0.897767	−	0.440470i	$-0.854812\pi$
$167$		−	11.3843i		−	0.880941i	0.897767	−	0.440470i	$-0.145188\pi$
$168$	12.1593	−	6.37505i	0.938108	−	0.491846i
$169$	−3.60541			−0.277339
$170$	12.7802	−	5.89356i	0.980196	−	0.452015i
$171$			0.481730i			0.0368388i
$172$	2.13794	+	0.437099i	0.163017	+	0.0333285i
$173$	5.68789			0.432442			0.216221	−	0.976344i	$-0.430627\pi$
$173$	5.68789			0.432442			0.216221	+	0.976344i	$0.430627\pi$
$174$	12.1213	−	9.89383i	0.918911	−	0.750049i
$175$		−	2.12239i		−	0.160437i
$176$	−2.70854	−	1.15583i	−0.204164	−	0.0871237i
$177$			23.6109i			1.77471i
$178$	6.27080	−	5.11846i	0.470016	−	0.383645i
$179$		−	16.5292i		−	1.23545i	−0.786394	−	0.617725i	$-0.788054\pi$
$179$		−	16.5292i		−	1.23545i	0.786394	−	0.617725i	$-0.211946\pi$
$180$	0.545765	−	2.66945i	0.0406789	−	0.198969i
$181$	−20.6345			−1.53375			−0.766874	−	0.641798i	$-0.778189\pi$
$181$	−20.6345			−1.53375			−0.766874	+	0.641798i	$0.778189\pi$
$182$	11.4782	−	9.36892i	0.850819	−	0.694470i
$183$	15.4127			1.13934
$184$	20.5524	−	10.7755i	1.51514	−	0.794381i
$185$	10.5902			0.778606
$186$	−5.92792	−	7.26250i	−0.434656	−	0.532512i
$187$	2.93925	+	0.758276i	0.214939	+	0.0554506i
$188$	−2.17449	+	10.6359i	−0.158591	+	0.775702i
$189$		−	11.8222i		−	0.859936i
$190$	1.84211	+	2.25684i	0.133641	+	0.163728i
$191$	−17.3215			−1.25334			−0.626670	−	0.779285i	$-0.715583\pi$
$191$	−17.3215			−1.25334			−0.626670	+	0.779285i	$0.715583\pi$
$192$	8.59055	−	12.4228i	0.619969	−	0.896540i
$193$		−	12.3439i		−	0.888537i	−0.895894	−	0.444268i	$-0.853464\pi$
$193$		−	12.3439i		−	0.888537i	0.895894	−	0.444268i	$-0.146536\pi$
$194$	−10.6375	−	13.0323i	−0.763727	−	0.935667i
$195$		−	18.5689i		−	1.32975i
$196$	0.156217	−	0.764092i	0.0111584	−	0.0545780i
$197$	5.96937			0.425300			0.212650	−	0.977128i	$-0.431791\pi$
$197$	5.96937			0.425300			0.212650	+	0.977128i	$0.431791\pi$
$198$	0.455267	−	0.371606i	0.0323544	−	0.0264089i
$199$			12.8979i			0.914307i	0.889388	+	0.457154i	$0.151131\pi$
$199$			12.8979i			0.914307i	−0.889388	+	0.457154i	$0.848869\pi$
$200$	−1.08420	−	2.06791i	−0.0766642	−	0.146223i
$201$		−	19.9397i		−	1.40644i
$202$	7.45436	+	9.13259i	0.524487	+	0.642567i
$203$			15.0664i			1.05745i
$204$	−6.82989	+	13.9905i	−0.478188	+	0.979532i
$205$		−	28.2769i		−	1.97495i
$206$	17.0304	−	13.9008i	1.18656	−	0.968517i
$207$			4.63094i			0.321873i
$208$	6.39756	−	14.9919i	0.443591	−	1.03950i
$209$			0.628334i			0.0434627i
$210$	10.4768	+	12.8354i	0.722965	+	0.885730i
$211$	−4.31995			−0.297398			−0.148699	−	0.988883i	$-0.547509\pi$
$211$	−4.31995			−0.297398			−0.148699	+	0.988883i	$0.547509\pi$
$212$	−9.14701	−	1.87009i	−0.628219	−	0.128438i
$213$		−	0.964875i		−	0.0661122i
$214$	−16.4216	+	13.4039i	−1.12256	+	0.916275i
$215$			2.63345i			0.179600i
$216$	−6.03921	−	11.5187i	−0.410916	−	0.783749i
$217$	9.02707			0.612798
$218$	−1.03115	+	0.841660i	−0.0698381	+	0.0570044i
$219$		−	25.1609i		−	1.70021i
$220$	0.711855	−	3.48184i	0.0479933	−	0.234745i
$221$	−4.19710	+	16.2689i	−0.282327	+	1.09436i
$222$	−9.07565	+	7.40789i	−0.609118	+	0.497185i
$223$	15.5793			1.04326			0.521632	−	0.853171i	$-0.325323\pi$
$223$	15.5793			1.04326			0.521632	+	0.853171i	$0.325323\pi$
$224$	4.03638	+	13.9724i	0.269692	+	0.933573i
$225$	0.465950			0.0310633
$226$	−8.79537	−	10.7755i	−0.585059	−	0.716776i
$227$	−5.47171			−0.363170			−0.181585	−	0.983375i	$-0.558123\pi$
$227$	−5.47171			−0.363170			−0.181585	+	0.983375i	$0.558123\pi$
$228$	−3.15733	−	0.645512i	−0.209100	−	0.0427501i
$229$		−	2.88870i		−	0.190890i	−0.995435	−	0.0954452i	$-0.969573\pi$
$229$		−	2.88870i		−	0.190890i	0.995435	−	0.0954452i	$-0.0304275\pi$
$230$	17.7085	+	21.6953i	1.16766	+	1.43054i
$231$			3.57356i			0.235123i
$232$	7.69648	+	14.6797i	0.505298	+	0.963767i
$233$			8.67268i			0.568166i	0.958800	+	0.284083i	$0.0916892\pi$
$233$			8.67268i			0.568166i	−0.958800	+	0.284083i	$0.908311\pi$
$234$	2.05686	+	2.51992i	0.134461	+	0.164733i
$235$	−13.1009			−0.854612
$236$	−24.5051	−	5.01002i	−1.59514	−	0.326124i
$237$			2.73978i			0.177968i
$238$	−6.27788	−	13.6136i	−0.406934	−	0.882438i
$239$	−16.1107			−1.04211			−0.521057	−	0.853522i	$-0.674462\pi$
$239$	−16.1107			−1.04211			−0.521057	+	0.853522i	$0.674462\pi$
$240$	16.7647	+	7.15405i	1.08216	+	0.461792i
$241$		−	9.65567i		−	0.621977i	−0.950414	−	0.310988i	$-0.899340\pi$
$241$		−	9.65567i		−	0.621977i	0.950414	−	0.310988i	$-0.100660\pi$
$242$	−11.4576	+	9.35213i	−0.736523	+	0.601178i
$243$	5.79238			0.371581
$244$	−3.27043	+	15.9964i	−0.209368	+	1.02406i
$245$	0.941184			0.0601301
$246$	19.7798	+	24.2330i	1.26112	+	1.54504i
$247$	−3.47786			−0.221291
$248$	8.79537	−	4.61137i	0.558506	−	0.292822i
$249$			8.22407i			0.521179i
$250$	−11.0387	+	9.01016i	−0.698146	+	0.569853i
$251$		−	19.7073i		−	1.24391i	−0.783052	−	0.621956i	$-0.786338\pi$
$251$		−	19.7073i		−	1.24391i	0.783052	−	0.621956i	$-0.213662\pi$
$252$	−2.84353	−	0.581354i	−0.179125	−	0.0366219i
$253$			6.04026i			0.379748i
$254$	−12.1593	+	9.92485i	−0.762940	+	0.622740i
$255$	−18.1926	−	4.69339i	−1.13927	−	0.293911i
$256$	11.0704	+	11.5519i	0.691902	+	0.721992i
$257$	6.33840			0.395379			0.197689	−	0.980265i	$-0.436656\pi$
$257$	6.33840			0.395379			0.197689	+	0.980265i	$0.436656\pi$
$258$	−1.84211	−	2.25684i	−0.114685	−	0.140504i
$259$		−	11.2808i		−	0.700953i
$260$	19.2721	+	3.94016i	1.19521	+	0.244358i
$261$	−3.30768			−0.204740
$262$	20.1976	−	16.4860i	1.24781	−	1.01851i
$263$	−15.5446			−0.958519			−0.479260	−	0.877673i	$-0.659095\pi$
$263$	−15.5446			−0.958519			−0.479260	+	0.877673i	$0.659095\pi$
$264$	1.82551	+	3.48184i	0.112352	+	0.214292i
$265$		−	11.2670i		−	0.692126i
$266$	2.40400	−	1.96224i	0.147399	−	0.120313i
$267$	−10.8062			−0.661329
$268$	20.6948	+	4.23101i	1.26413	+	0.258450i
$269$	22.8463			1.39296			0.696481	−	0.717575i	$-0.254748\pi$
$269$	22.8463			1.39296			0.696481	+	0.717575i	$0.254748\pi$
$270$	12.1593	−	9.92485i	0.739989	−	0.604007i
$271$	7.17019			0.435558			0.217779	−	0.975998i	$-0.430119\pi$
$271$	7.17019			0.435558			0.217779	+	0.975998i	$0.430119\pi$
$272$	−13.0711	−	10.0572i	−0.792550	−	0.609806i
$273$	−19.7798			−1.19713
$274$	−14.8276	+	12.1029i	−0.895770	+	0.731161i
$275$	0.607751			0.0366488
$276$	−30.3519	−	6.20539i	−1.82697	−	0.373521i
$277$	6.61070			0.397199			0.198599	−	0.980081i	$-0.436361\pi$
$277$	6.61070			0.397199			0.198599	+	0.980081i	$0.436361\pi$
$278$	−2.96936	+	2.42370i	−0.178090	+	0.145364i
$279$			1.98181i			0.118648i
$280$	−15.5446	+	8.14995i	−0.928966	+	0.487052i
$281$	14.8479			0.885754			0.442877	−	0.896582i	$-0.353958\pi$
$281$	14.8479			0.885754			0.442877	+	0.896582i	$0.353958\pi$
$282$	11.2273	−	9.16418i	0.668579	−	0.545719i
$283$	14.3388			0.852355			0.426177	−	0.904640i	$-0.359860\pi$
$283$	14.3388			0.852355			0.426177	+	0.904640i	$0.359860\pi$
$284$	1.00141	+	0.204737i	0.0594230	+	0.0121489i
$285$		−	3.88910i		−	0.230371i
$286$	2.68281	+	3.28680i	0.158638	+	0.194353i
$287$	−30.1209			−1.77798
$288$	−3.06752	+	0.886149i	−0.180755	+	0.0522168i
$289$	14.8783	+	8.22407i	0.875196	+	0.483769i
$290$	−15.4960	+	12.6484i	−0.909956	+	0.742740i
$291$			22.4581i			1.31651i
$292$	26.1137	+	5.33890i	1.52819	+	0.312436i
$293$			19.5648i			1.14299i	0.820605	+	0.571495i	$0.193636\pi$
$293$			19.5648i			1.14299i	−0.820605	+	0.571495i	$0.806364\pi$
$294$	−0.806583	+	0.658363i	−0.0470409	+	0.0383965i
$295$		−	30.1846i		−	1.75741i
$296$	−5.76265	−	10.9912i	−0.334947	−	0.638852i
$297$	3.38531			0.196435
$298$	−1.52644	−	1.87009i	−0.0884242	−	0.108331i
$299$	−33.4331			−1.93349
$300$	−0.624366	+	3.05391i	−0.0360478	+	0.176317i
$301$	2.80518			0.161688
$302$	3.81029	−	3.11010i	0.219257	−	0.178966i
$303$		−	15.7378i		−	0.904112i
$304$	1.33991	−	3.13993i	0.0768493	−	0.180087i
$305$	−19.7038			−1.12824
$306$	2.98873	−	1.37825i	0.170855	−	0.0787892i
$307$		−	10.6087i		−	0.605468i	−0.953075	−	0.302734i	$-0.902101\pi$
$307$		−	10.6087i		−	0.605468i	0.953075	−	0.302734i	$-0.0978994\pi$
$308$	−3.70889	−	0.758276i	−0.211333	−	0.0432068i
$309$	−29.3477			−1.66953
$310$	7.57833	+	9.28447i	0.430420	+	0.527323i
$311$			15.2696i			0.865860i	0.901428	+	0.432930i	$0.142520\pi$
$311$			15.2696i			0.865860i	−0.901428	+	0.432930i	$0.857480\pi$
$312$	−19.2721	+	10.1043i	−1.09107	+	0.572043i
$313$			13.1472i			0.743125i	0.928408	+	0.371562i	$0.121178\pi$
$313$			13.1472i			0.743125i	−0.928408	+	0.371562i	$0.878822\pi$
$314$	19.7191	+	24.1585i	1.11281	+	1.36334i
$315$		−	3.50257i		−	0.197347i
$316$	−2.84353	−	0.581354i	−0.159961	−	0.0327037i
$317$	25.7911			1.44857			0.724287	−	0.689499i	$-0.242169\pi$
$317$	25.7911			1.44857			0.724287	+	0.689499i	$0.242169\pi$
$318$	7.88132	+	9.65567i	0.441963	+	0.541463i
$319$	−4.31429			−0.241554
$320$	−10.9823	+	15.8815i	−0.613928	+	0.887803i
$321$	28.2987			1.57948
$322$	23.1100	−	18.8633i	1.28787	−	1.05121i
$323$	−0.879045	+	3.40737i	−0.0489114	+	0.189591i
$324$	−4.15622	+	20.3289i	−0.230901	+	1.12939i
$325$			3.36393i			0.186597i
$326$	7.60789	−	6.20984i	0.421362	−	0.343931i
$327$	1.77693			0.0982644
$328$	−29.3477	+	15.3869i	−1.62046	+	0.849598i
$329$			13.9553i			0.769379i
$330$	−3.67546	+	3.00005i	−0.202327	+	0.165147i
$331$		−	17.4779i		−	0.960670i	−0.877085	−	0.480335i	$-0.840515\pi$
$331$		−	17.4779i		−	0.960670i	0.877085	−	0.480335i	$-0.159485\pi$
$332$	−8.53551	−	1.74507i	−0.468447	−	0.0957732i
$333$	2.47659			0.135716
$334$	−10.1805	−	12.4724i	−0.557050	−	0.682461i
$335$			25.4912i			1.39273i
$336$	7.62057	−	17.8579i	0.415736	−	0.974229i
$337$			26.1195i			1.42282i	0.702777	+	0.711410i	$0.251943\pi$
$337$			26.1195i			1.42282i	−0.702777	+	0.711410i	$0.748057\pi$
$338$	−3.95003	+	3.22416i	−0.214853	+	0.175371i
$339$			18.5689i			1.00853i
$340$	8.73143	−	17.8857i	0.473528	−	0.969986i
$341$			2.58492i			0.139981i
$342$	0.430791	+	0.527776i	0.0232945	+	0.0285389i
$343$		−	18.9996i		−	1.02588i
$344$	2.73318	−	1.43299i	0.147363	−	0.0772618i
$345$		−	37.3865i		−	2.01282i
$346$	6.23157	−	5.08644i	0.335011	−	0.273448i
$347$	17.9138			0.961663			0.480832	−	0.876813i	$-0.340335\pi$
$347$	17.9138			0.961663			0.480832	+	0.876813i	$0.340335\pi$
$348$	4.43225	−	21.6790i	0.237593	−	1.16212i
$349$		−	22.5260i		−	1.20579i	−0.797820	−	0.602895i	$-0.794014\pi$
$349$		−	22.5260i		−	1.20579i	0.797820	−	0.602895i	$-0.205986\pi$
$350$	−1.89796	−	2.32525i	−0.101450	−	0.124290i
$351$			18.7378i			1.00015i
$352$	−4.00104	+	1.15583i	−0.213256	+	0.0616058i
$353$	5.56775			0.296342			0.148171	−	0.988962i	$-0.452661\pi$
$353$	5.56775			0.296342			0.148171	+	0.988962i	$0.452661\pi$
$354$	21.1142	+	25.8678i	1.12221	+	1.37486i
$355$			1.23351i			0.0654679i
$356$	2.29297	−	11.2154i	0.121527	−	0.594416i
$357$	−4.99945	+	19.3790i	−0.264599	+	1.02564i
$358$	−14.7814	−	18.1091i	−0.781219	−	0.957098i
$359$	22.1622			1.16967			0.584837	−	0.811150i	$-0.301158\pi$
$359$	22.1622			1.16967			0.584837	+	0.811150i	$0.301158\pi$
$360$	−1.78924	−	3.41266i	−0.0943014	−	0.179863i
$361$	18.2716			0.961663
$362$	−22.6068	+	18.4525i	−1.18819	+	0.969842i
$363$	19.7444			1.03631
$364$	4.19710	−	20.5289i	0.219988	−	1.07601i
$365$			32.1660i			1.68365i
$366$	16.8859	−	13.7829i	0.882642	−	0.720445i
$367$			2.12239i			0.110788i	0.998465	+	0.0553939i	$0.0176414\pi$
$367$			2.12239i			0.110788i	−0.998465	+	0.0553939i	$0.982359\pi$
$368$	12.8808	−	30.1846i	0.671456	−	1.57348i
$369$		−	6.61275i		−	0.344246i
$370$	11.6024	−	9.47034i	0.603182	−	0.492340i
$371$	−12.0017			−0.623098
$372$	−12.9891	−	2.65559i	−0.673452	−	0.137686i
$373$		−	17.6720i		−	0.915023i	−0.889204	−	0.457512i	$-0.848741\pi$
$373$		−	17.6720i		−	0.915023i	0.889204	−	0.457512i	$-0.151259\pi$
$374$	3.89829	−	1.79769i	0.201576	−	0.0929561i
$375$	19.0224			0.982314
$376$	7.12888	+	13.5971i	0.367644	+	0.701215i
$377$		−	23.8798i		−	1.22987i
$378$	−10.5721	−	12.9522i	−0.543768	−	0.666188i
$379$	3.23194			0.166013			0.0830067	−	0.996549i	$-0.473548\pi$
$379$	3.23194			0.166013			0.0830067	+	0.996549i	$0.473548\pi$
$380$	4.03638	+	0.825231i	0.207062	+	0.0423335i
$381$	20.9535			1.07348
$382$	−18.9772	+	15.4899i	−0.970956	+	0.792531i
$383$	7.92400			0.404897			0.202449	−	0.979293i	$-0.435110\pi$
$383$	7.92400			0.404897			0.202449	+	0.979293i	$0.435110\pi$
$384$	−1.69752	−	21.2924i	−0.0866264	−	1.08657i
$385$		−	4.56849i		−	0.232832i
$386$	−11.0387	−	13.5238i	−0.561853	−	0.688345i
$387$			0.615851i			0.0313054i
$388$	−23.3085	−	4.76539i	−1.18331	−	0.241926i
$389$			4.78602i			0.242661i	0.992612	+	0.121330i	$0.0387160\pi$
$389$			4.78602i			0.242661i	−0.992612	+	0.121330i	$0.961284\pi$
$390$	−16.6054	−	20.3438i	−0.840848	−	1.03015i
$391$	−8.45038	+	32.7556i	−0.427354	+	1.65652i
$392$	−0.512145	−	0.976826i	−0.0258672	−	0.0493371i
$393$	−34.8056			−1.75571
$394$	6.53995	−	5.33815i	0.329478	−	0.268932i
$395$		−	3.50257i		−	0.176233i
$396$	0.166472	−	0.814251i	0.00836554	−	0.0409176i
$397$	−5.00982			−0.251436			−0.125718	−	0.992066i	$-0.540123\pi$
$397$	−5.00982			−0.251436			−0.125718	+	0.992066i	$0.540123\pi$
$398$	11.5340	+	14.1307i	0.578148	+	0.708309i
$399$	−4.14272			−0.207395
$400$	−3.03707	−	1.29602i	−0.151854	−	0.0648010i
$401$			7.61142i			0.380096i	0.981775	+	0.190048i	$0.0608644\pi$
$401$			7.61142i			0.380096i	−0.981775	+	0.190048i	$0.939136\pi$
$402$	−17.8312	−	21.8456i	−0.889339	−	1.08956i
$403$	−14.3077			−0.712717
$404$	16.3338	+	3.33941i	0.812635	+	0.166142i
$405$	−25.0405			−1.24427
$406$	13.4732	+	16.5065i	0.668664	+	0.819203i
$407$	3.23028			0.160119
$408$	5.02839	+	21.4355i	0.248942	+	1.06121i
$409$	−18.6582			−0.922590			−0.461295	−	0.887247i	$-0.652615\pi$
$409$	−18.6582			−0.922590			−0.461295	+	0.887247i	$0.652615\pi$
$410$	−25.2868	−	30.9797i	−1.24883	−	1.52998i
$411$	25.5518			1.26038
$412$	6.22731	−	30.4591i	0.306797	−	1.50061i
$413$	−32.1529			−1.58214
$414$	4.14125	+	5.07358i	0.203531	+	0.249353i
$415$		−	10.5138i		−	0.516100i
$416$	−6.39756	−	22.1460i	−0.313666	−	1.08580i
$417$	5.11697			0.250579
$418$	0.561892	+	0.688392i	0.0274830	+	0.0336704i
$419$	1.05688			0.0516319			0.0258159	−	0.999667i	$-0.491782\pi$
$419$	1.05688			0.0516319			0.0258159	+	0.999667i	$0.491782\pi$
$420$	22.9564	+	4.69339i	1.12016	+	0.229014i
$421$		−	1.37215i		−	0.0668743i	−0.999441	−	0.0334371i	$-0.989355\pi$
$421$		−	1.37215i		−	0.0668743i	0.999441	−	0.0334371i	$-0.0106454\pi$
$422$	−4.73287	+	3.86315i	−0.230393	+	0.188055i
$423$	−3.06375			−0.148964
$424$	−11.6937	+	6.13093i	−0.567895	+	0.297744i
$425$	3.29576	+	0.850249i	0.159868	+	0.0412432i
$426$	−0.862846	−	1.05710i	−0.0418050	−	0.0512168i
$427$			20.9887i			1.01572i
$428$	−6.00471	+	29.3703i	−0.290249	+	1.41967i
$429$		−	5.66400i		−	0.273461i
$430$	2.35498	+	2.88517i	0.113567	+	0.139135i
$431$		−	14.9578i		−	0.720493i	−0.932857	−	0.360247i	$-0.882693\pi$
$431$		−	14.9578i		−	0.720493i	0.932857	−	0.360247i	$-0.117307\pi$
$432$	−16.9171	−	7.21912i	−0.813927	−	0.347330i
$433$	−1.48117			−0.0711806			−0.0355903	−	0.999366i	$-0.511331\pi$
$433$	−1.48117			−0.0711806			−0.0355903	+	0.999366i	$0.511331\pi$
$434$	9.88992	−	8.07252i	0.474731	−	0.387493i
$435$	26.7036			1.28034
$436$	−0.377048	+	1.84422i	−0.0180573	+	0.0883221i
$437$	−7.00228			−0.334964
$438$	−22.5003	−	27.5659i	−1.07511	−	1.31715i
$439$			19.6083i			0.935855i	0.883767	+	0.467927i	$0.154999\pi$
$439$			19.6083i			0.935855i	−0.883767	+	0.467927i	$0.845001\pi$
$440$	−2.33376	−	4.45123i	−0.111257	−	0.212204i
$441$	0.220102			0.0104811
$442$	9.95028	+	21.5772i	0.473287	+	1.02632i
$443$			32.3084i			1.53502i	0.641037	+	0.767510i	$0.278505\pi$
$443$			32.3084i			1.53502i	−0.641037	+	0.767510i	$0.721495\pi$
$444$	−3.31859	+	16.2319i	−0.157493	+	0.770333i
$445$	13.8148			0.654884
$446$	17.0684	−	13.9319i	0.808212	−	0.659692i
$447$			3.22265i			0.152426i
$448$	16.9171	+	11.6984i	0.799260	+	0.552699i
$449$		−	17.4468i		−	0.823366i	−0.911327	−	0.411683i	$-0.864941\pi$
$449$		−	17.4468i		−	0.823366i	0.911327	−	0.411683i	$-0.135059\pi$
$450$	0.510487	−	0.416679i	0.0240646	−	0.0196424i
$451$		−	8.62518i		−	0.406144i
$452$	−19.2721	−	3.94016i	−0.906485	−	0.185329i
$453$	−6.56610			−0.308502
$454$	−5.99472	+	4.89312i	−0.281346	+	0.229645i
$455$	25.2868			1.18546
$456$	−4.03638	+	2.11626i	−0.189021	+	0.0991027i
$457$	−2.35230			−0.110036			−0.0550179	−	0.998485i	$-0.517522\pi$
$457$	−2.35230			−0.110036			−0.0550179	+	0.998485i	$0.517522\pi$
$458$	−2.58324	−	3.16481i	−0.120707	−	0.147882i
$459$	18.3581	+	4.73608i	0.856882	+	0.221061i
$460$	38.8023	+	7.93306i	1.80917	+	0.369881i
$461$			4.32881i			0.201613i	0.994906	+	0.100806i	$0.0321422\pi$
$461$			4.32881i			0.201613i	−0.994906	+	0.100806i	$0.967858\pi$
$462$	3.19568	+	3.91514i	0.148677	+	0.182149i
$463$	5.29610			0.246131			0.123065	−	0.992399i	$-0.460728\pi$
$463$	5.29610			0.246131			0.123065	+	0.992399i	$0.460728\pi$
$464$	21.5595	+	9.20018i	1.00088	+	0.427108i
$465$		−	15.9995i		−	0.741960i
$466$	7.75561	+	9.50166i	0.359272	+	0.440156i
$467$			4.40327i			0.203759i	0.994797	+	0.101879i	$0.0324856\pi$
$467$			4.40327i			0.203759i	−0.994797	+	0.101879i	$0.967514\pi$
$468$	4.50692	+	0.921432i	0.208332	+	0.0425932i
$469$	27.1535			1.25383
$470$	−14.3532	+	11.7156i	−0.662063	+	0.540401i
$471$		−	41.6313i		−	1.91827i
$472$	−31.3276	+	16.4249i	−1.44197	+	0.756018i
$473$			0.803270i			0.0369344i
$474$	2.45006	+	3.00165i	0.112535	+	0.137871i
$475$			0.704546i			0.0323268i
$476$	−19.0520	−	9.30081i	−0.873247	−	0.426302i
$477$		−	2.63486i		−	0.120642i
$478$	−17.6506	+	14.4071i	−0.807320	+	0.658965i
$479$		−	16.4286i		−	0.750641i	−0.926895	−	0.375320i	$-0.877533\pi$
$479$		−	16.4286i		−	0.750641i	0.926895	−	0.375320i	$-0.122467\pi$
$480$	24.7647	−	7.15405i	1.13035	−	0.326536i
$481$			17.8797i			0.815246i
$482$	−8.63465	−	10.5786i	−0.393298	−	0.481842i
$483$	−39.8245			−1.81208
$484$	−4.18957	+	20.4921i	−0.190435	+	0.931459i
$485$		−	28.7107i		−	1.30368i
$486$	6.34604	−	5.17987i	0.287862	−	0.234964i
$487$		−	4.75584i		−	0.215508i	−0.994178	−	0.107754i	$-0.965634\pi$
$487$		−	4.75584i		−	0.215508i	0.994178	−	0.107754i	$-0.0343658\pi$
$488$	10.7218	+	20.4500i	0.485355	+	0.925728i
$489$	−13.1103			−0.592870
$490$	1.03115	−	0.841660i	0.0465825	−	0.0380223i
$491$		−	1.89082i		−	0.0853316i	−0.999089	−	0.0426658i	$-0.986415\pi$
$491$		−	1.89082i		−	0.0853316i	0.999089	−	0.0426658i	$-0.0135851\pi$
$492$	43.3410	+	8.86099i	1.95396	+	0.399484i
$493$	−23.3959	−	6.03574i	−1.05370	−	0.271836i
$494$	−3.81029	+	3.11010i	−0.171433	+	0.139930i
$495$	1.00297			0.0450801
$496$	5.51232	−	12.9175i	0.247510	−	0.580011i
$497$	1.31395			0.0589386
$498$	7.35443	+	9.01016i	0.329560	+	0.403755i
$499$	−36.9132			−1.65246			−0.826231	−	0.563331i	$-0.809520\pi$
$499$	−36.9132			−1.65246			−0.826231	+	0.563331i	$0.809520\pi$
$500$	−4.03638	+	19.7428i	−0.180512	+	0.882924i
$501$			21.4932i			0.960244i
$502$	−17.6234	−	21.5910i	−0.786569	−	0.963652i
$503$		−	17.3295i		−	0.772686i	−0.922355	−	0.386343i	$-0.873738\pi$
$503$		−	17.3295i		−	0.772686i	0.922355	−	0.386343i	$-0.126262\pi$
$504$	−3.63520	+	1.90592i	−0.161925	+	0.0848964i
$505$			20.1194i			0.895302i
$506$	5.40154	+	6.61761i	0.240128	+	0.294189i
$507$	6.80691			0.302305
$508$	−4.44614	+	21.7470i	−0.197266	+	0.964868i
$509$		−	10.2701i		−	0.455213i	−0.973753	−	0.227607i	$-0.926910\pi$
$509$		−	10.2701i		−	0.455213i	0.973753	−	0.227607i	$-0.0730900\pi$
$510$	−24.1286	+	11.1269i	−1.06843	+	0.492706i
$511$	34.2636			1.51573
$512$	22.4589	+	2.75624i	0.992553	+	0.121810i
$513$			3.92448i			0.173270i
$514$	6.94425	−	5.66816i	0.306298	−	0.250012i
$515$	37.5185			1.65326
$516$	−4.03638	−	0.825231i	−0.177692	−	0.0363288i
$517$	−3.99612			−0.175749
$518$	−10.0879	−	12.3590i	−0.443237	−	0.543025i
$519$	−10.7386			−0.471371
$520$	24.6378	−	12.9175i	1.08044	−	0.566468i
$521$			26.1195i			1.14432i	0.820143	+	0.572158i	$0.193894\pi$
$521$			26.1195i			1.14432i	−0.820143	+	0.572158i	$0.806106\pi$
$522$	−3.62384	+	2.95792i	−0.158611	+	0.129464i
$523$			14.8223i			0.648133i	0.946034	+	0.324066i	$0.105050\pi$
$523$			14.8223i			0.648133i	−0.946034	+	0.324066i	$0.894950\pi$
$524$	7.38542	−	36.1236i	0.322633	−	1.57807i
$525$			4.00701i			0.174880i
$526$	−17.0304	+	13.9008i	−0.742560	+	0.606105i
$527$	−3.61633	+	14.0177i	−0.157530	+	0.610621i
$528$	5.11365	+	2.18217i	0.222543	+	0.0949667i
$529$	−44.3138			−1.92669
$530$	−10.0756	−	12.3439i	−0.437656	−	0.536187i
$531$		−	7.05886i		−	0.306329i
$532$	0.879045	−	4.29959i	0.0381114	−	0.186411i
$533$	47.7408			2.06788
$534$	−11.8391	+	9.66351i	−0.512328	+	0.418181i
$535$	−36.1774			−1.56409
$536$	26.4565	−	13.8710i	1.14275	−	0.599136i
$537$			31.2067i			1.34667i
$538$	25.0300	−	20.4304i	1.07912	−	0.880818i
$539$	0.287085			0.0123656
$540$	4.44614	−	21.7470i	0.191331	−	0.935842i
$541$	9.11519			0.391893			0.195946	−	0.980615i	$-0.437222\pi$
$541$	9.11519			0.391893			0.195946	+	0.980615i	$0.437222\pi$
$542$	7.85555	−	6.41199i	0.337425	−	0.275419i
$543$	38.9573			1.67182
$544$	−23.3142	+	0.670405i	−0.999587	+	0.0287434i
$545$	−2.27165			−0.0973068
$546$	−21.6705	+	17.6883i	−0.927411	+	0.756987i
$547$	−26.1596			−1.11850			−0.559251	−	0.828999i	$-0.688911\pi$
$547$	−26.1596			−1.11850			−0.559251	+	0.828999i	$0.688911\pi$
$548$	−5.42185	+	26.5194i	−0.231610	+	1.13285i
$549$	−4.60788			−0.196659
$550$	0.665842	−	0.543485i	0.0283916	−	0.0231743i
$551$		−	5.00142i		−	0.213068i
$552$	−38.8023	+	20.3438i	−1.65153	+	0.865892i
$553$	−3.73097			−0.158657
$554$	7.24258	−	5.91167i	0.307708	−	0.251163i
$555$	−19.9940			−0.848697
$556$	−1.08577	+	5.31074i	−0.0460470	+	0.225226i
$557$		−	41.3488i		−	1.75200i	−0.482307	−	0.876002i	$-0.660201\pi$
$557$		−	41.3488i		−	1.75200i	0.482307	−	0.876002i	$-0.339799\pi$
$558$	1.77224	+	2.17124i	0.0750251	+	0.0919158i
$559$	−4.44614			−0.188052
$560$	−9.74224	+	22.8298i	−0.411685	+	0.964735i
$561$	−5.54922	−	1.43160i	−0.234288	−	0.0604424i
$562$	16.2672	−	13.2779i	0.686189	−	0.560093i
$563$			37.5179i			1.58119i	0.612338	+	0.790596i	$0.290229\pi$
$563$			37.5179i			1.58119i	−0.612338	+	0.790596i	$0.709771\pi$
$564$	4.10538	−	20.0803i	0.172868	−	0.845532i
$565$		−	23.7388i		−	0.998699i
$566$	15.7094	−	12.8226i	0.660315	−	0.538974i
$567$			26.6734i			1.12018i
$568$	1.28022	−	0.671214i	0.0537169	−	0.0281635i
$569$	18.1288			0.760000			0.380000	−	0.924987i	$-0.375924\pi$
$569$	18.1288			0.760000			0.380000	+	0.924987i	$0.375924\pi$
$570$	−3.47786	−	4.26084i	−0.145671	−	0.178467i
$571$	−15.4181			−0.645226			−0.322613	−	0.946531i	$-0.604561\pi$
$571$	−15.4181			−0.645226			−0.322613	+	0.946531i	$0.604561\pi$
$572$	5.87849	+	1.20185i	0.245792	+	0.0502518i
$573$	32.7025			1.36617
$574$	−32.9999	+	26.9358i	−1.37739	+	1.12428i
$575$			6.77290i			0.282449i
$576$	−2.56828	+	3.71400i	−0.107012	+	0.154750i
$577$	18.4051			0.766215			0.383107	−	0.923704i	$-0.374854\pi$
$577$	18.4051			0.766215			0.383107	+	0.923704i	$0.374854\pi$
$578$	23.6549	−	4.29488i	0.983914	−	0.178644i
$579$			23.3050i			0.968524i
$580$	−5.66624	+	27.7148i	−0.235278	+	1.15079i
$581$	−11.1994			−0.464628
$582$	20.0833	+	24.6047i	0.832478	+	1.01990i
$583$		−	3.43672i		−	0.142334i
$584$	33.3841	−	17.5031i	1.38144	−	0.724285i
$585$			5.55148i			0.229525i
$586$	17.4960	+	21.4349i	0.722753	+	0.885469i
$587$		−	28.5683i		−	1.17914i	−0.807718	−	0.589569i	$-0.799298\pi$
$587$		−	28.5683i		−	1.17914i	0.807718	−	0.589569i	$-0.200702\pi$
$588$	−0.294934	+	1.44258i	−0.0121629	+	0.0594912i
$589$	−2.99662			−0.123474
$590$	−26.9927	−	33.0697i	−1.11127	−	1.36146i
$591$	−11.2700			−0.463586
$592$	−16.1424	−	6.88852i	−0.663450	−	0.283117i
$593$	−21.7131			−0.891651			−0.445826	−	0.895120i	$-0.647090\pi$
$593$	−21.7131			−0.891651			−0.445826	+	0.895120i	$0.647090\pi$
$594$	3.70889	−	3.02733i	0.152177	−	0.124213i
$595$	6.39136	−	24.7743i	0.262020	−	1.01565i
$596$	−3.34468	−	0.683815i	−0.137004	−	0.0280102i
$597$		−	24.3509i		−	0.996614i
$598$	−36.6288	+	29.8978i	−1.49786	+	1.22261i
$599$	4.44614			0.181664			0.0908322	−	0.995866i	$-0.471047\pi$
$599$	4.44614			0.181664			0.0908322	+	0.995866i	$0.471047\pi$
$600$	2.04693	+	3.90416i	0.0835656	+	0.159387i
$601$			31.5661i			1.28761i	0.765190	+	0.643804i	$0.222645\pi$
$601$			31.5661i			1.28761i	−0.765190	+	0.643804i	$0.777355\pi$
$602$	3.07331	−	2.50855i	0.125259	−	0.102241i
$603$			5.96128i			0.242762i
$604$	1.39326	−	6.81475i	0.0566911	−	0.277288i
$605$	−25.2415			−1.02621
$606$	−14.0736	−	17.2421i	−0.571702	−	0.700411i
$607$		−	32.8533i		−	1.33347i	−0.745294	−	0.666736i	$-0.767691\pi$
$607$		−	32.8533i		−	1.33347i	0.745294	−	0.666736i	$-0.232309\pi$
$608$	−1.33991	−	4.63828i	−0.0543407	−	0.188107i
$609$		−	28.4449i		−	1.15265i
$610$	−21.5872	+	17.6203i	−0.874041	+	0.713425i
$611$		−	22.1187i		−	0.894829i
$612$	2.04190	−	4.18268i	0.0825390	−	0.169075i
$613$		−	32.7902i		−	1.32438i	−0.749335	−	0.662191i	$-0.769627\pi$
$613$		−	32.7902i		−	1.32438i	0.749335	−	0.662191i	$-0.230373\pi$
$614$	−9.48687	−	11.6227i	−0.382859	−	0.469053i
$615$			53.3860i			2.15273i
$616$	−4.74149	+	2.48594i	−0.191040	+	0.100161i
$617$		−	33.4463i		−	1.34650i	−0.739415	−	0.673249i	$-0.764898\pi$
$617$		−	33.4463i		−	1.34650i	0.739415	−	0.673249i	$-0.235102\pi$
$618$	−32.1529	+	26.2444i	−1.29338	+	1.05570i
$619$	29.0694			1.16840			0.584199	−	0.811610i	$-0.301409\pi$
$619$	29.0694			1.16840			0.584199	+	0.811610i	$0.301409\pi$
$620$	16.6054	+	3.39495i	0.666889	+	0.136344i
$621$			37.7265i			1.51391i
$622$	13.6549	+	16.7291i	0.547513	+	0.670777i
$623$		−	14.7157i		−	0.589570i
$624$	−12.0784	+	28.3043i	−0.483524	+	1.13308i
$625$	−28.4461			−1.13784
$626$	11.7570	+	14.4039i	0.469904	+	0.575695i
$627$		−	1.18628i		−	0.0473753i
$628$	43.2078	+	8.83376i	1.72418	+	0.352505i
$629$	17.5174	+	4.51919i	0.698464	+	0.180192i
$630$	−3.13219	−	3.83736i	−0.124790	−	0.152884i
$631$	−35.3823			−1.40855			−0.704273	−	0.709929i	$-0.748727\pi$
$631$	−35.3823			−1.40855			−0.704273	+	0.709929i	$0.748727\pi$
$632$	−3.63520	+	1.90592i	−0.144601	+	0.0758134i
$633$	8.15595			0.324170
$634$	28.2563	−	23.0639i	1.12220	−	0.915984i
$635$	−26.7873			−1.06302
$636$	17.2693	+	3.53068i	0.684772	+	0.140001i
$637$			1.58903i			0.0629597i
$638$	−4.72667	+	3.85809i	−0.187131	+	0.152743i
$639$			0.288465i			0.0114115i
$640$	2.17014	+	27.2205i	0.0857823	+	1.07598i
$641$		−	3.40578i		−	0.134520i	−0.997735	−	0.0672601i	$-0.978574\pi$
$641$		−	3.40578i		−	0.134520i	0.997735	−	0.0672601i	$-0.0214257\pi$
$642$	31.0036	−	25.3063i	1.22361	−	0.998759i
$643$	39.7622			1.56807			0.784033	−	0.620719i	$-0.213159\pi$
$643$	39.7622			1.56807			0.784033	+	0.620719i	$0.213159\pi$
$644$	8.45038	−	41.3326i	0.332992	−	1.62873i
$645$		−	4.97188i		−	0.195768i
$646$	2.08400	+	4.51916i	0.0819939	+	0.177804i
$647$	19.5885			0.770105			0.385053	−	0.922895i	$-0.374183\pi$
$647$	19.5885			0.770105			0.385053	+	0.922895i	$0.374183\pi$
$648$	13.6258	+	25.9888i	0.535272	+	1.02094i
$649$		−	9.20706i		−	0.361409i
$650$	3.00822	+	3.68547i	0.117992	+	0.144556i
$651$	−17.0429			−0.667962
$652$	2.78189	−	13.6068i	0.108947	−	0.532884i
$653$	−47.0453			−1.84103			−0.920513	−	0.390712i	$-0.872229\pi$
$653$	−47.0453			−1.84103			−0.920513	+	0.390712i	$0.872229\pi$
$654$	1.94678	−	1.58903i	0.0761250	−	0.0621360i
$655$	44.4959			1.73860
$656$	−18.3931	+	43.1020i	−0.718129	+	1.68285i
$657$			7.52224i			0.293471i
$658$	12.4796	+	15.2892i	0.486505	+	0.596034i
$659$		−	26.4748i		−	1.03131i	−0.856796	−	0.515656i	$-0.827548\pi$
$659$		−	26.4748i		−	1.03131i	0.856796	−	0.515656i	$-0.172452\pi$
$660$	−1.34396	+	6.57361i	−0.0523137	+	0.255877i
$661$			34.0089i			1.32279i	0.750037	+	0.661396i	$0.230036\pi$
$661$			34.0089i			1.32279i	−0.750037	+	0.661396i	$0.769964\pi$
$662$	−15.6297	−	19.1485i	−0.607465	−	0.744227i
$663$	7.92400	−	30.7152i	0.307743	−	1.19288i
$664$	−10.9119	+	5.72106i	−0.423464	+	0.222020i
$665$	5.29610			0.205374
$666$	2.71331	−	2.21470i	0.105139	−	0.0858180i
$667$		−	48.0794i		−	1.86164i
$668$	−22.3071	−	4.56065i	−0.863088	−	0.176457i
$669$	−29.4132			−1.13718
$670$	22.7956	+	27.9277i	0.880672	+	1.07894i
$671$	−6.01017			−0.232020
$672$	−7.62057	−	26.3796i	−0.293970	−	1.01761i
$673$		−	14.2242i		−	0.548301i	−0.961687	−	0.274151i	$-0.911603\pi$
$673$		−	14.2242i		−	0.548301i	0.961687	−	0.274151i	$-0.0883967\pi$
$674$	23.3575	+	28.6161i	0.899699	+	1.10225i
$675$	3.79592			0.146105
$676$	−1.44436	+	7.06468i	−0.0555524	+	0.271718i
$677$	−16.1654			−0.621288			−0.310644	−	0.950526i	$-0.600545\pi$
$677$	−16.1654			−0.621288			−0.310644	+	0.950526i	$0.600545\pi$
$678$	16.6054	+	20.3438i	0.637727	+	0.781301i
$679$	−30.5829			−1.17366
$680$	−6.42836	−	27.4034i	−0.246516	−	1.05087i
$681$	10.3304			0.395863
$682$	2.31159	+	2.83200i	0.0885152	+	0.108443i
$683$	15.6478			0.598746			0.299373	−	0.954136i	$-0.403223\pi$
$683$	15.6478			0.598746			0.299373	+	0.954136i	$0.403223\pi$
$684$	0.943935	+	0.192986i	0.0360923	+	0.00737900i
$685$	−32.6658			−1.24809
$686$	−16.9905	−	20.8156i	−0.648700	−	0.794745i
$687$			5.45378i			0.208075i
$688$	1.71296	−	4.01413i	0.0653061	−	0.153037i
$689$	19.0224			0.724697
$690$	−33.4331	−	40.9601i	−1.27278	−	1.55932i
$691$	−2.33710			−0.0889075			−0.0444537	−	0.999011i	$-0.514155\pi$
$691$	−2.33710			−0.0889075			−0.0444537	+	0.999011i	$0.514155\pi$
$692$	2.27863	−	11.1452i	0.0866203	−	0.423678i
$693$		−	1.06837i		−	0.0405841i
$694$	19.6261	−	16.0195i	0.744996	−	0.608093i
$695$	−6.54160			−0.248137
$696$	−14.5307	−	27.7148i	−0.550786	−	1.05053i
$697$	12.0667	−	46.7733i	0.457059	−	1.77166i
$698$	−20.1440	−	24.6792i	−0.762463	−	0.934120i
$699$		−	16.3738i		−	0.619314i
$700$	−4.15875	−	0.850249i	−0.157186	−	0.0321364i
$701$		−	30.6904i		−	1.15916i	−0.814916	−	0.579580i	$-0.803217\pi$
$701$		−	30.6904i		−	1.15916i	0.814916	−	0.579580i	$-0.196783\pi$
$702$	16.7564	+	20.5289i	0.632431	+	0.774813i
$703$			3.74476i			0.141236i
$704$	−3.34987	+	4.84427i	−0.126253	+	0.182575i
$705$	24.7342			0.931545
$706$	6.09994	−	4.97900i	0.229574	−	0.187387i
$707$	21.4314			0.806011
$708$	46.2649	+	9.45878i	1.73874	+	0.355483i
$709$	11.4092			0.428481			0.214240	−	0.976781i	$-0.431272\pi$
$709$	11.4092			0.428481			0.214240	+	0.976781i	$0.431272\pi$
$710$	1.10307	+	1.35141i	0.0413977	+	0.0507177i
$711$		−	0.819099i		−	0.0307186i
$712$	−7.51731	−	14.3379i	−0.281723	−	0.537337i
$713$	−28.8069			−1.07883
$714$	11.8525	+	25.7021i	0.443567	+	0.961877i
$715$			7.24094i			0.270796i
$716$	−32.3884	−	6.62176i	−1.21041	−	0.247467i
$717$	30.4165			1.13593
$718$	24.2805	−	19.8187i	0.906141	−	0.739626i
$719$			7.71301i			0.287647i	0.989603	+	0.143823i	$0.0459397\pi$
$719$			7.71301i			0.287647i	−0.989603	+	0.143823i	$0.954060\pi$
$720$	−5.01206	−	2.13882i	−0.186789	−	0.0797090i
$721$		−	39.9651i		−	1.48838i
$722$	20.0181	−	16.3395i	0.744995	−	0.608093i
$723$			18.2296i			0.677968i
$724$	−8.26637	+	40.4326i	−0.307217	+	1.50266i
$725$	−4.83759			−0.179664
$726$	21.6317	−	17.6566i	0.802826	−	0.655296i
$727$	−13.2911			−0.492938			−0.246469	−	0.969151i	$-0.579270\pi$
$727$	−13.2911			−0.492938			−0.246469	+	0.969151i	$0.579270\pi$
$728$	−13.7598	−	26.2444i	−0.509973	−	0.972682i
$729$	20.1883			0.747716
$730$	28.7647	+	35.2406i	1.06463	+	1.30431i
$731$	−1.12378	+	4.35603i	−0.0415646	+	0.161114i
$732$	6.17449	−	30.2007i	0.228216	−	1.11625i
$733$			4.51326i			0.166701i	0.996520	+	0.0833505i	$0.0265621\pi$
$733$			4.51326i			0.166701i	−0.996520	+	0.0833505i	$0.973438\pi$
$734$	1.89796	+	2.32525i	0.0700550	+	0.0858267i
$735$	−1.77693			−0.0655430
$736$	−12.8808	−	44.5884i	−0.474791	−	1.64355i
$737$			7.77546i			0.286413i
$738$	−5.91349	−	7.24482i	−0.217679	−	0.266686i
$739$			14.4505i			0.531571i	0.964032	+	0.265786i	$0.0856314\pi$
$739$			14.4505i			0.531571i	−0.964032	+	0.265786i	$0.914369\pi$
$740$	4.24253	−	20.7511i	0.155959	−	0.762826i
$741$	6.56610			0.241212
$742$	−13.1489	+	10.7326i	−0.482711	+	0.394007i
$743$			17.2867i			0.634186i	0.948394	+	0.317093i	$0.102707\pi$
$743$			17.2867i			0.634186i	−0.948394	+	0.317093i	$0.897293\pi$
$744$	−16.6054	+	8.70614i	−0.608784	+	0.319182i
$745$		−	4.11988i		−	0.150941i
$746$	−15.8033	−	19.3612i	−0.578601	−	0.708864i
$747$		−	2.45871i		−	0.0899597i
$748$	2.66331	−	5.45558i	0.0973802	−	0.199476i
$749$			38.5365i			1.40809i
$750$	20.8407	−	17.0109i	0.760994	−	0.621152i
$751$			27.5979i			1.00706i	0.863978	+	0.503530i	$0.167966\pi$
$751$			27.5979i			1.00706i	−0.863978	+	0.503530i	$0.832034\pi$
$752$	19.9696	+	8.52168i	0.728215	+	0.310754i
$753$			37.2068i			1.35589i
$754$	−21.3547	−	26.1624i	−0.777692	−	0.952778i
$755$	8.39419			0.305496
$756$	−23.1651	−	4.73608i	−0.842508	−	0.172249i
$757$			29.2683i			1.06377i	0.846815	+	0.531887i	$0.178517\pi$
$757$			29.2683i			1.06377i	−0.846815	+	0.531887i	$0.821483\pi$
$758$	3.54086	−	2.89018i	0.128610	−	0.104976i
$759$		−	11.4038i		−	0.413933i
$760$	5.16016	−	2.70545i	0.187179	−	0.0981370i
$761$	5.48844			0.198956			0.0994779	−	0.995040i	$-0.468283\pi$
$761$	5.48844			0.198956			0.0994779	+	0.995040i	$0.468283\pi$
$762$	22.9564	−	18.7378i	0.831621	−	0.678800i
$763$			2.41979i			0.0876021i
$764$	−6.93916	+	33.9409i	−0.251050	+	1.22794i
$765$	5.43897	+	1.40316i	0.196646	+	0.0507314i
$766$	8.68141	−	7.08609i	0.313672	−	0.256031i
$767$	50.9615			1.84011
$768$	−20.9007	−	21.8096i	−0.754188	−	0.786986i
$769$	41.5703			1.49906			0.749531	−	0.661969i	$-0.230279\pi$
$769$	41.5703			1.49906			0.749531	+	0.661969i	$0.230279\pi$
$770$	−4.08540	−	5.00517i	−0.147228	−	0.180374i
$771$	−11.9667			−0.430971
$772$	−24.1876	−	4.94511i	−0.870529	−	0.177978i
$773$			24.0984i			0.866761i	0.901211	+	0.433380i	$0.142679\pi$
$773$			24.0984i			0.866761i	−0.901211	+	0.433380i	$0.857321\pi$
$774$	0.550729	+	0.674716i	0.0197955	+	0.0242522i
$775$			2.89846i			0.104116i
$776$	−29.7979	+	15.6229i	−1.06968	+	0.560830i
$777$			21.2978i			0.764054i
$778$	4.27993	+	5.24348i	0.153443	+	0.187988i
$779$	9.99890			0.358248
$780$	−36.3852	−	7.43890i	−1.30280	−	0.266356i
$781$			0.376252i			0.0134634i
$782$	20.0338	+	43.4433i	0.716406	+	1.55353i
$783$	−26.9464			−0.962987
$784$	−1.43463	−	0.612206i	−0.0512368	−	0.0218645i
$785$			53.2220i			1.89957i
$786$	−38.1325	+	31.1251i	−1.36014	+	1.11020i
$787$	14.1491			0.504360			0.252180	−	0.967680i	$-0.418853\pi$
$787$	14.1491			0.504360			0.252180	+	0.967680i	$0.418853\pi$
$788$	2.39139	−	11.6968i	0.0851897	−	0.416681i
$789$	29.3477			1.04481
$790$	−3.13219	−	3.83736i	−0.111438	−	0.136527i
$791$	−25.2868			−0.899096
$792$	−0.545765	−	1.04095i	−0.0193929	−	0.0369885i
$793$		−	33.2666i		−	1.18133i
$794$	−5.48868	+	4.48006i	−0.194786	+	0.158991i
$795$			21.2718i			0.754432i
$796$	25.2730	+	5.16702i	0.895777	+	0.183140i
$797$			19.0896i			0.676189i	0.941112	+	0.338094i	$0.109782\pi$
$797$			19.0896i			0.676189i	−0.941112	+	0.338094i	$0.890218\pi$
$798$	−4.53869	+	3.70465i	−0.160668	+	0.131143i
$799$	−21.6705	−	5.59062i	−0.766647	−	0.197782i
$800$	−4.48634	+	1.29602i	−0.158616	+	0.0458213i
$801$	3.23068			0.114151
$802$	6.80656	+	8.33895i	0.240348	+	0.294458i
$803$			9.81146i			0.346239i
$804$	−39.0712	−	7.98803i	−1.37793	−	0.281716i
$805$	50.9122			1.79442
$806$	−15.6753	+	12.7947i	−0.552138	+	0.450676i
$807$	−43.1331			−1.51836
$808$	20.8813	−	10.9480i	0.734601	−	0.385148i
$809$			24.7737i			0.870995i	0.900190	+	0.435498i	$0.143428\pi$
$809$			24.7737i			0.870995i	−0.900190	+	0.435498i	$0.856572\pi$
$810$	−27.4340	+	22.3927i	−0.963933	+	0.786798i
$811$	−28.7575			−1.00981			−0.504906	−	0.863174i	$-0.668473\pi$
$811$	−28.7575			−1.00981			−0.504906	+	0.863174i	$0.668473\pi$
$812$	29.5221	+	6.03574i	1.03602	+	0.211813i
$813$	−13.5371			−0.474768
$814$	3.53904	−	2.88870i	0.124043	−	0.101249i
$815$	16.7604			0.587092
$816$	24.6778	+	18.9877i	0.863897	+	0.664702i
$817$	−0.931205			−0.0325788
$818$	−20.4417	+	16.6852i	−0.714726	+	0.583386i
$819$	5.91349			0.206634
$820$	−55.4077	−	11.3280i	−1.93492	−	0.395591i
$821$	28.6880			1.00122			0.500609	−	0.865673i	$-0.333109\pi$
$821$	28.6880			1.00122			0.500609	+	0.865673i	$0.333109\pi$
$822$	27.9942	−	22.8499i	0.976408	−	0.796981i
$823$			35.5415i			1.23890i	0.785036	+	0.619450i	$0.212644\pi$
$823$			35.5415i			1.23890i	−0.785036	+	0.619450i	$0.787356\pi$
$824$	−20.4157	−	38.9393i	−0.711214	−	1.35651i
$825$	−1.14742			−0.0399479
$826$	−35.2262	+	28.7529i	−1.22568	+	1.00044i
$827$	−35.4846			−1.23392			−0.616959	−	0.786995i	$-0.711636\pi$
$827$	−35.4846			−1.23392			−0.616959	+	0.786995i	$0.711636\pi$
$828$	9.07417	+	1.85520i	0.315349	+	0.0644727i
$829$			54.8280i			1.90425i	0.305703	+	0.952127i	$0.401109\pi$
$829$			54.8280i			1.90425i	−0.305703	+	0.952127i	$0.598891\pi$
$830$	−9.40200	−	11.5187i	−0.326348	−	0.399820i
$831$	−12.4808			−0.432955
$832$	−26.8133	−	18.5417i	−0.929582	−	0.642819i
$833$	1.55683	+	0.401635i	0.0539409	+	0.0139158i
$834$	5.60607	−	4.57588i	0.194122	−	0.158450i
$835$		−	27.4772i		−	0.950887i
$836$	1.23120	+	0.251717i	0.0425819	+	0.00870580i
$837$			16.1450i			0.558054i
$838$	1.15790	−	0.945120i	0.0399990	−	0.0326486i
$839$			2.66018i			0.0918395i	0.998945	+	0.0459198i	$0.0146219\pi$
$839$			2.66018i			0.0918395i	−0.998945	+	0.0459198i	$0.985378\pi$
$840$	29.3477	−	15.3869i	1.01259	−	0.530898i
$841$	5.34102			0.184173
$842$	−1.22705	−	1.50330i	−0.0422869	−	0.0518072i
$843$	−28.0325			−0.965490
$844$	−1.73062	+	8.46481i	−0.0595703	+	0.291371i
$845$	−8.70205			−0.299359
$846$	−3.35659	+	2.73978i	−0.115402	+	0.0941954i
$847$			26.8875i			0.923866i
$848$	−7.32877	+	17.1741i	−0.251671	+	0.589761i
$849$	−27.0713			−0.929085
$850$	4.37112	−	2.01573i	0.149928	−	0.0691390i
$851$			35.9989i			1.23402i
$852$	−1.89064	−	0.386539i	−0.0647723	−	0.0132426i
$853$	−3.49362			−0.119619			−0.0598097	−	0.998210i	$-0.519049\pi$
$853$	−3.49362			−0.119619			−0.0598097	+	0.998210i	$0.519049\pi$
$854$	18.7693	+	22.9949i	0.642273	+	0.786870i
$855$			1.16271i			0.0397638i
$856$	19.6859	+	37.5474i	0.672851	+	1.28334i
$857$		−	32.6540i		−	1.11544i	−0.830030	−	0.557719i	$-0.811677\pi$
$857$		−	32.6540i		−	1.11544i	0.830030	−	0.557719i	$-0.188323\pi$
$858$	−5.06507	−	6.20539i	−0.172919	−	0.211849i
$859$			44.7174i			1.52574i	0.646553	+	0.762869i	$0.276210\pi$
$859$			44.7174i			1.52574i	−0.646553	+	0.762869i	$0.723790\pi$
$860$	5.16016	+	1.05499i	0.175960	+	0.0359748i
$861$	56.8673			1.93803
$862$	−13.3761	−	16.3876i	−0.455593	−	0.558163i
$863$	−2.12167			−0.0722225			−0.0361113	−	0.999348i	$-0.511497\pi$
$863$	−2.12167			−0.0722225			−0.0361113	+	0.999348i	$0.511497\pi$
$864$	−24.9899	+	7.21912i	−0.850174	+	0.245599i
$865$	13.7283			0.466778
$866$	−1.62275	+	1.32455i	−0.0551433	+	0.0450100i
$867$	−28.0899	−	15.5268i	−0.953982	−	0.527318i
$868$	3.61633	−	17.6883i	0.122746	−	0.600378i
$869$		−	1.06837i		−	0.0362420i
$870$	29.2560	−	23.8798i	0.991871	−	0.809602i
$871$	−43.0375			−1.45827
$872$	1.23612	+	2.35768i	0.0418602	+	0.0798410i
$873$		−	6.71419i		−	0.227241i
$874$	−7.67158	+	6.26183i	−0.259495	+	0.211810i
$875$			25.9044i			0.875727i
$876$	−49.3019	−	10.0797i	−1.66576	−	0.340561i
$877$	−48.3375			−1.63224			−0.816121	−	0.577881i	$-0.803880\pi$
$877$	−48.3375			−1.63224			−0.816121	+	0.577881i	$0.803880\pi$
$878$	17.5349	+	21.4826i	0.591774	+	0.725002i
$879$		−	36.9379i		−	1.24588i
$880$	−6.53737	−	2.78971i	−0.220375	−	0.0940413i
$881$		−	12.6986i		−	0.427827i	−0.976853	−	0.213913i	$-0.931379\pi$
$881$		−	12.6986i		−	0.427827i	0.976853	−	0.213913i	$-0.0686210\pi$
$882$	0.241141	−	0.196828i	0.00811963	−	0.00662754i
$883$		−	33.2423i		−	1.11869i	−0.828934	−	0.559346i	$-0.811052\pi$
$883$		−	33.2423i		−	1.11869i	0.828934	−	0.559346i	$-0.188948\pi$
$884$	30.1969	+	14.7415i	1.01563	+	0.495812i
$885$			56.9876i			1.91562i
$886$	28.8920	+	35.3966i	0.970647	+	1.18917i
$887$		−	39.5909i		−	1.32933i	−0.747140	−	0.664666i	$-0.768574\pi$
$887$		−	39.5909i		−	1.32933i	0.747140	−	0.664666i	$-0.231426\pi$
$888$	10.8797	+	20.7511i	0.365099	+	0.696362i
$889$			28.5341i			0.957003i
$890$	15.1353	−	12.3540i	0.507335	−	0.414106i
$891$	−7.63800			−0.255883
$892$	6.24120	−	30.5270i	0.208971	−	1.02212i
$893$		−	4.63258i		−	0.155023i
$894$	2.88187	+	3.53068i	0.0963843	+	0.118084i
$895$		−	39.8950i		−	1.33354i
$896$	28.9956	−	2.31165i	0.968674	−	0.0772269i
$897$	63.1208			2.10754
$898$	−15.6019	−	19.1145i	−0.520643	−	0.637857i
$899$		−	20.5755i		−	0.686233i
$900$	0.186664	−	0.913014i	0.00622214	−	0.0304338i
$901$	4.80801	−	18.6369i	0.160178	−	0.620886i
$902$	−7.71313	−	9.44961i	−0.256819	−	0.314638i
$903$	−5.29610			−0.176243
$904$	−24.6378	+	12.9175i	−0.819440	+	0.429628i
$905$	−49.8035			−1.65553
$906$	−7.19371	+	5.87178i	−0.238995	+	0.195077i
$907$	52.1980			1.73321			0.866603	−	0.498998i	$-0.166299\pi$
$907$	52.1980			1.73321			0.866603	+	0.498998i	$0.166299\pi$
$908$	−2.19202	+	10.7216i	−0.0727448	+	0.355810i
$909$			4.70506i			0.156057i
$910$	27.7038	−	22.6129i	0.918373	−	0.749611i
$911$		−	33.2042i		−	1.10010i	−0.835131	−	0.550052i	$-0.814608\pi$
$911$		−	33.2042i		−	1.10010i	0.835131	−	0.550052i	$-0.185392\pi$
$912$	−2.52972	+	5.92810i	−0.0837674	+	0.196299i
$913$		−	3.20697i		−	0.106135i
$914$	−2.57714	+	2.10356i	−0.0852441	+	0.0695794i
$915$	37.2003			1.22980
$916$	−5.66031	−	1.15724i	−0.187022	−	0.0382363i
$917$		−	47.3975i		−	1.56520i
$918$	24.3481	−	11.2281i	0.803607	−	0.370582i
$919$	2.50268			0.0825558			0.0412779	−	0.999148i	$-0.486857\pi$
$919$	2.50268			0.0825558			0.0412779	+	0.999148i	$0.486857\pi$
$920$	49.6053	−	26.0079i	1.63544	−	0.857454i
$921$			20.0289i			0.659973i
$922$	3.87106	+	4.74257i	0.127487	+	0.156188i
$923$	−2.08257			−0.0685488
$924$	7.00228	+	1.43160i	0.230358	+	0.0470963i
$925$	3.62209			0.119093
$926$	5.80233	−	4.73608i	0.190676	−	0.155637i
$927$	8.77396			0.288175
$928$	31.8476	−	9.20018i	1.04545	−	0.302011i
$929$		−	20.2991i		−	0.665993i	−0.942928	−	0.332996i	$-0.891940\pi$
$929$		−	20.2991i		−	0.665993i	0.942928	−	0.332996i	$-0.108060\pi$
$930$	−14.3077	−	17.5288i	−0.469167	−	0.574793i
$931$			0.332809i			0.0109074i
$932$	16.9938	+	3.47436i	0.556652	+	0.113807i
$933$		−	28.8286i		−	0.943806i
$934$	3.93765	+	4.82415i	0.128844	+	0.157851i
$935$	7.09419	+	1.83018i	0.232005	+	0.0598533i
$936$	5.76171	−	3.02084i	0.188327	−	0.0987391i
$937$	36.2874			1.18546			0.592729	−	0.805402i	$-0.298051\pi$
$937$	36.2874			1.18546			0.592729	+	0.805402i	$0.298051\pi$
$938$	29.7489	−	24.2822i	0.971336	−	0.792841i
$939$		−	24.8216i		−	0.810022i
$940$	−5.24837	+	25.6709i	−0.171183	+	0.837292i
$941$	13.6402			0.444658			0.222329	−	0.974972i	$-0.428634\pi$
$941$	13.6402			0.444658			0.222329	+	0.974972i	$0.428634\pi$
$942$	−37.2290	−	45.6106i	−1.21299	−	1.48607i
$943$	96.1207			3.13012
$944$	−19.6339	+	46.0098i	−0.639030	+	1.49749i
$945$		−	28.5341i		−	0.928214i
$946$	0.718330	+	0.880050i	0.0233549	+	0.0286129i
$947$	9.92155			0.322407			0.161203	−	0.986921i	$-0.448462\pi$
$947$	9.92155			0.322407			0.161203	+	0.986921i	$0.448462\pi$
$948$	5.36850	+	1.09758i	0.174361	+	0.0356478i
$949$	−54.3069			−1.76288
$950$	0.630045	+	0.771890i	0.0204414	+	0.0250434i
$951$	−48.6929			−1.57898
$952$	−29.1904	+	6.84756i	−0.946065	+	0.221931i
$953$	4.30663			0.139505			0.0697526	−	0.997564i	$-0.477779\pi$
$953$	4.30663			0.139505			0.0697526	+	0.997564i	$0.477779\pi$
$954$	−2.35624	−	2.88672i	−0.0762862	−	0.0934609i
$955$	−41.8073			−1.35285
$956$	−6.45410	+	31.5684i	−0.208741	+	1.02099i
$957$	8.14527			0.263299
$958$	−14.6914	−	17.9989i	−0.474656	−	0.581518i
$959$			34.7959i			1.12362i
$960$	20.7342	−	29.9838i	0.669194	−	0.967724i
$961$	18.6721			0.602326
$962$	15.9891	+	19.5888i	0.515509	+	0.631567i
$963$	−8.46033			−0.272630
$964$	−18.9200	−	3.86816i	−0.609371	−	0.124585i
$965$		−	29.7935i		−	0.959085i
$966$	−43.6311	+	35.6133i	−1.40381	+	1.14584i
$967$	−17.6400			−0.567265			−0.283633	−	0.958933i	$-0.591540\pi$
$967$	−17.6400			−0.567265			−0.283633	+	0.958933i	$0.591540\pi$
$968$	13.7352	+	26.1974i	0.441465	+	0.842015i
$969$	1.65961	−	6.43303i	0.0533144	−	0.206659i
$970$	−25.6747	−	31.4550i	−0.824366	−	1.00996i
$971$		−	10.5762i		−	0.339407i	−0.985495	−	0.169704i	$-0.945719\pi$
$971$		−	10.5762i		−	0.339407i	0.985495	−	0.169704i	$-0.0542811\pi$
$972$	2.32048	−	11.3500i	0.0744296	−	0.364051i
$973$			6.96819i			0.223390i
$974$	−4.25294	−	5.21042i	−0.136273	−	0.166953i
$975$		−	6.35101i		−	0.203395i
$976$	30.0342	+	12.8166i	0.961372	+	0.410250i
$977$	−40.2041			−1.28624			−0.643122	−	0.765764i	$-0.722361\pi$
$977$	−40.2041			−1.28624			−0.643122	+	0.765764i	$0.722361\pi$
$978$	−14.3635	+	11.7240i	−0.459293	+	0.374892i
$979$	4.21386			0.134676
$980$	0.377048	−	1.84422i	0.0120443	−	0.0589114i
$981$	−0.531241			−0.0169612
$982$	−1.69088	−	2.07156i	−0.0539582	−	0.0661060i
$983$			20.5056i			0.654026i	0.945020	+	0.327013i	$0.106042\pi$
$983$			20.5056i			0.654026i	−0.945020	+	0.327013i	$0.893958\pi$
$984$	55.4077	−	29.0500i	1.76633	−	0.926080i
$985$	14.4077			0.459069
$986$	−31.0297	+	14.3093i	−0.988186	+	0.455700i
$987$		−	26.3472i		−	0.838639i
$988$	−1.39326	+	6.81475i	−0.0443256	+	0.216806i
$989$	−8.95180			−0.284651
$990$	1.09884	−	0.896911i	0.0349233	−	0.0285057i
$991$		−	4.64662i		−	0.147605i	−0.997273	−	0.0738024i	$-0.976487\pi$
$991$		−	4.64662i		−	0.147605i	0.997273	−	0.0738024i	$-0.0235134\pi$
$992$	−5.51232	−	19.0816i	−0.175016	−	0.605841i
$993$			32.9977i			1.04715i
$994$	1.43954	−	1.17501i	0.0456595	−	0.0372689i
$995$			31.1305i			0.986902i
$996$	16.1148	+	3.29464i	0.510617	+	0.104395i
$997$	−32.7934			−1.03858			−0.519289	−	0.854599i	$-0.673803\pi$
$997$	−32.7934			−1.03858			−0.519289	+	0.854599i	$0.673803\pi$
$998$	−40.4415	+	33.0099i	−1.28015	+	1.04491i
$999$	20.1758			0.638335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.h.a.101.13	✓	16
3.2	odd	2		1224.2.l.b.1189.3		16
4.3	odd	2		544.2.h.a.305.14		16
8.3	odd	2		544.2.h.a.305.4		16
8.5	even	2	inner	136.2.h.a.101.16	yes	16
12.11	even	2		4896.2.l.b.3025.4		16
17.16	even	2	inner	136.2.h.a.101.14	yes	16
24.5	odd	2		1224.2.l.b.1189.2		16
24.11	even	2		4896.2.l.b.3025.14		16
51.50	odd	2		1224.2.l.b.1189.4		16
68.67	odd	2		544.2.h.a.305.3		16
136.67	odd	2		544.2.h.a.305.13		16
136.101	even	2	inner	136.2.h.a.101.15	yes	16
204.203	even	2		4896.2.l.b.3025.13		16
408.101	odd	2		1224.2.l.b.1189.1		16
408.203	even	2		4896.2.l.b.3025.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.h.a.101.13	✓	16	1.1	even	1	trivial
136.2.h.a.101.14	yes	16	17.16	even	2	inner
136.2.h.a.101.15	yes	16	136.101	even	2	inner
136.2.h.a.101.16	yes	16	8.5	even	2	inner
544.2.h.a.305.3		16	68.67	odd	2
544.2.h.a.305.4		16	8.3	odd	2
544.2.h.a.305.13		16	136.67	odd	2
544.2.h.a.305.14		16	4.3	odd	2
1224.2.l.b.1189.1		16	408.101	odd	2
1224.2.l.b.1189.2		16	24.5	odd	2
1224.2.l.b.1189.3		16	3.2	odd	2
1224.2.l.b.1189.4		16	51.50	odd	2
4896.2.l.b.3025.3		16	408.203	even	2
4896.2.l.b.3025.4		16	12.11	even	2
4896.2.l.b.3025.13		16	204.203	even	2
4896.2.l.b.3025.14		16	24.11	even	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09558 - 0.894257i) q^{2} -1.88797 q^{3} +(0.400610 - 1.95947i) q^{4} +2.41361 q^{5} +(-2.06843 + 1.68833i) q^{6} -2.57100i q^{7} +(-1.31336 - 2.50501i) q^{8} +0.564439 q^{9} +O(q^{10})\)	\(q+(1.09558 - 0.894257i) q^{2} -1.88797 q^{3} +(0.400610 - 1.95947i) q^{4} +2.41361 q^{5} +(-2.06843 + 1.68833i) q^{6} -2.57100i q^{7} +(-1.31336 - 2.50501i) q^{8} +0.564439 q^{9} +(2.64431 - 2.15839i) q^{10} +0.736213 q^{11} +(-0.756340 + 3.69942i) q^{12} +4.07497i q^{13} +(-2.29914 - 2.81675i) q^{14} -4.55683 q^{15} +(-3.67902 - 1.56996i) q^{16} +(3.99239 + 1.02997i) q^{17} +(0.618390 - 0.504753i) q^{18} +0.853468i q^{19} +(0.966916 - 4.72939i) q^{20} +4.85398i q^{21} +(0.806583 - 0.658363i) q^{22} +8.20450i q^{23} +(2.47960 + 4.72939i) q^{24} +0.825510 q^{25} +(3.64407 + 4.46448i) q^{26} +4.59827 q^{27} +(-5.03779 - 1.02997i) q^{28} -5.86012 q^{29} +(-4.99239 + 4.07497i) q^{30} +3.51111i q^{31} +(-5.43463 + 1.56996i) q^{32} -1.38995 q^{33} +(5.29505 - 2.44180i) q^{34} -6.20539i q^{35} +(0.226120 - 1.10600i) q^{36} +4.38770 q^{37} +(0.763219 + 0.935046i) q^{38} -7.69344i q^{39} +(-3.16995 - 6.04611i) q^{40} -11.7156i q^{41} +(4.34070 + 5.31794i) q^{42} +1.09108i q^{43} +(0.294934 - 1.44258i) q^{44} +1.36234 q^{45} +(7.33693 + 8.98872i) q^{46} -5.42795 q^{47} +(6.94589 + 2.96405i) q^{48} +0.389949 q^{49} +(0.904416 - 0.738218i) q^{50} +(-7.53752 - 1.94455i) q^{51} +(7.98478 + 1.63247i) q^{52} -4.66811i q^{53} +(5.03779 - 4.11204i) q^{54} +1.77693 q^{55} +(-6.44038 + 3.37666i) q^{56} -1.61132i q^{57} +(-6.42026 + 5.24045i) q^{58} -12.5060i q^{59} +(-1.82551 + 8.92895i) q^{60} -8.16364 q^{61} +(3.13983 + 3.84672i) q^{62} -1.45117i q^{63} +(-4.55015 + 6.57998i) q^{64} +9.83539i q^{65} +(-1.52281 + 1.24297i) q^{66} +10.5614i q^{67} +(3.61758 - 7.41034i) q^{68} -15.4899i q^{69} +(-5.54922 - 6.79853i) q^{70} +0.511064i q^{71} +(-0.741314 - 1.41392i) q^{72} +13.3269i q^{73} +(4.80709 - 3.92373i) q^{74} -1.55854 q^{75} +(1.67234 + 0.341908i) q^{76} -1.89280i q^{77} +(-6.87991 - 8.42881i) q^{78} -1.45117i q^{79} +(-8.87973 - 3.78928i) q^{80} -10.3747 q^{81} +(-10.4768 - 12.8354i) q^{82} -4.35603i q^{83} +(9.51121 + 1.94455i) q^{84} +(9.63607 + 2.48594i) q^{85} +(0.975710 + 1.19538i) q^{86} +11.0637 q^{87} +(-0.966916 - 1.84422i) q^{88} +5.72371 q^{89} +(1.49255 - 1.21828i) q^{90} +10.4768 q^{91} +(16.0765 + 3.28680i) q^{92} -6.62888i q^{93} +(-5.94678 + 4.85398i) q^{94} +2.05994i q^{95} +(10.2604 - 2.96405i) q^{96} -11.8953i q^{97} +(0.427222 - 0.348714i) q^{98} +0.415547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9 - 8 * q^15 - 14 * q^16 - 2 * q^18 - 16 * q^30 - 2 * q^32 - 8 * q^33 + 18 * q^34 - 22 * q^36 + 36 * q^38 - 24 * q^47 - 8 * q^49 + 34 * q^50 - 8 * q^55 - 16 * q^60 - 30 * q^64 - 32 * q^66 + 38 * q^68 + 40 * q^70 + 70 * q^72 + 4 * q^76 - 24 * q^81 + 72 * q^84 + 4 * q^86 - 40 * q^87 - 24 * q^89 - 16 * q^94 + 34 * q^98

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