LMFDB - Embedded newform 1600.2.q.h.849.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (of order $4$, degree $2$, not 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			849.6
Root			$-0.530822 + 1.31081i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.h.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37027 - 1.37027i) q^{3} -2.73482 q^{7} -0.755274i q^{9} +O(q^{10})$	$q+(1.37027 - 1.37027i) q^{3} -2.73482 q^{7} -0.755274i q^{9} +(-4.12175 + 4.12175i) q^{11} +(1.37919 - 1.37919i) q^{13} +4.94921i q^{17} +(-0.292715 - 0.292715i) q^{19} +(-3.74744 + 3.74744i) q^{21} +1.64818 q^{23} +(3.07588 + 3.07588i) q^{27} +(5.67267 + 5.67267i) q^{29} -3.95550 q^{31} +11.2958i q^{33} +(-2.48772 - 2.48772i) q^{37} -3.77973i q^{39} +8.40843i q^{41} +(3.22713 + 3.22713i) q^{43} -5.19809i q^{47} +0.479225 q^{49} +(6.78176 + 6.78176i) q^{51} +(7.20537 + 7.20537i) q^{53} -0.802198 q^{57} +(-6.41142 + 6.41142i) q^{59} +(-3.82618 - 3.82618i) q^{61} +2.06554i q^{63} +(-5.76044 + 5.76044i) q^{67} +(2.25846 - 2.25846i) q^{69} -7.92245i q^{71} +4.36276 q^{73} +(11.2722 - 11.2722i) q^{77} -5.56087 q^{79} +10.6954 q^{81} +(-0.516191 + 0.516191i) q^{83} +15.5462 q^{87} -6.42236i q^{89} +(-3.77184 + 3.77184i) q^{91} +(-5.42011 + 5.42011i) q^{93} +9.44534i q^{97} +(3.11305 + 3.11305i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.37027	−	1.37027i	0.791125	−	0.791125i	−0.190552	−	0.981677i	$-0.561028\pi$
$3$	1.37027	−	1.37027i	0.791125	−	0.791125i	0.981677	+	0.190552i	$0.0610278\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.73482			−1.03366			−0.516832	−	0.856087i	$-0.672889\pi$
$7$	−2.73482			−1.03366			−0.516832	+	0.856087i	$0.672889\pi$
$8$		0			0
$9$		−	0.755274i		−	0.251758i
$10$		0			0
$11$	−4.12175	+	4.12175i	−1.24275	+	1.24275i	−0.283900	+	0.958854i	$0.591629\pi$
$11$	−4.12175	+	4.12175i	−1.24275	+	1.24275i	−0.958854	+	0.283900i	$0.908371\pi$
$12$		0			0
$13$	1.37919	−	1.37919i	0.382519	−	0.382519i	−0.489490	−	0.872009i	$-0.662817\pi$
$13$	1.37919	−	1.37919i	0.382519	−	0.382519i	0.872009	+	0.489490i	$0.162817\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.94921i			1.20036i	0.799865	+	0.600180i	$0.204905\pi$
$17$			4.94921i			1.20036i	−0.799865	+	0.600180i	$0.795095\pi$
$18$		0			0
$19$	−0.292715	−	0.292715i	−0.0671535	−	0.0671535i	0.672732	−	0.739886i	$-0.265121\pi$
$19$	−0.292715	−	0.292715i	−0.0671535	−	0.0671535i	−0.739886	+	0.672732i	$0.765121\pi$
$20$		0			0
$21$	−3.74744	+	3.74744i	−0.817757	+	0.817757i
$22$		0			0
$23$	1.64818			0.343670			0.171835	−	0.985126i	$-0.445030\pi$
$23$	1.64818			0.343670			0.171835	+	0.985126i	$0.445030\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.07588	+	3.07588i	0.591953	+	0.591953i
$28$		0			0
$29$	5.67267	+	5.67267i	1.05339	+	1.05339i	0.998492	+	0.0548963i	$0.0174828\pi$
$29$	5.67267	+	5.67267i	1.05339	+	1.05339i	0.0548963	+	0.998492i	$0.482517\pi$
$30$		0			0
$31$	−3.95550			−0.710430			−0.355215	−	0.934785i	$-0.615592\pi$
$31$	−3.95550			−0.710430			−0.355215	+	0.934785i	$0.615592\pi$
$32$		0			0
$33$			11.2958i			1.96635i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.48772	−	2.48772i	−0.408979	−	0.408979i	0.472403	−	0.881382i	$-0.343387\pi$
$37$	−2.48772	−	2.48772i	−0.408979	−	0.408979i	−0.881382	+	0.472403i	$0.843387\pi$
$38$		0			0
$39$		−	3.77973i		−	0.605241i
$40$		0			0
$41$			8.40843i			1.31318i	0.754250	+	0.656588i	$0.228001\pi$
$41$			8.40843i			1.31318i	−0.754250	+	0.656588i	$0.771999\pi$
$42$		0			0
$43$	3.22713	+	3.22713i	0.492133	+	0.492133i	0.908978	−	0.416845i	$-0.136864\pi$
$43$	3.22713	+	3.22713i	0.492133	+	0.492133i	−0.416845	+	0.908978i	$0.636864\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	5.19809i		−	0.758219i	−0.925352	−	0.379109i	$-0.876230\pi$
$47$		−	5.19809i		−	0.758219i	0.925352	−	0.379109i	$-0.123770\pi$
$48$		0			0
$49$	0.479225			0.0684607
$50$		0			0
$51$	6.78176	+	6.78176i	0.949636	+	0.949636i
$52$		0			0
$53$	7.20537	+	7.20537i	0.989733	+	0.989733i	0.999948	−	0.0102143i	$-0.00325138\pi$
$53$	7.20537	+	7.20537i	0.989733	+	0.989733i	−0.0102143	+	0.999948i	$0.503251\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.802198			−0.106254
$58$		0			0
$59$	−6.41142	+	6.41142i	−0.834695	+	0.834695i	−0.988155	−	0.153459i	$-0.950959\pi$
$59$	−6.41142	+	6.41142i	−0.834695	+	0.834695i	0.153459	+	0.988155i	$0.450959\pi$
$60$		0			0
$61$	−3.82618	−	3.82618i	−0.489892	−	0.489892i	0.418380	−	0.908272i	$-0.362598\pi$
$61$	−3.82618	−	3.82618i	−0.489892	−	0.489892i	−0.908272	+	0.418380i	$0.862598\pi$
$62$		0			0
$63$			2.06554i			0.260233i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.76044	+	5.76044i	−0.703750	+	0.703750i	−0.965213	−	0.261463i	$-0.915795\pi$
$67$	−5.76044	+	5.76044i	−0.703750	+	0.703750i	0.261463	+	0.965213i	$0.415795\pi$
$68$		0			0
$69$	2.25846	−	2.25846i	0.271886	−	0.271886i
$70$		0			0
$71$		−	7.92245i		−	0.940222i	−0.882607	−	0.470111i	$-0.844214\pi$
$71$		−	7.92245i		−	0.940222i	0.882607	−	0.470111i	$-0.155786\pi$
$72$		0			0
$73$	4.36276			0.510622			0.255311	−	0.966859i	$-0.417822\pi$
$73$	4.36276			0.510622			0.255311	+	0.966859i	$0.417822\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.2722	−	11.2722i	1.28459	−	1.28459i
$78$		0			0
$79$	−5.56087			−0.625647			−0.312824	−	0.949811i	$-0.601275\pi$
$79$	−5.56087			−0.625647			−0.312824	+	0.949811i	$0.601275\pi$
$80$		0			0
$81$	10.6954			1.18838
$82$		0			0
$83$	−0.516191	+	0.516191i	−0.0566594	+	0.0566594i	−0.734869	−	0.678209i	$-0.762756\pi$
$83$	−0.516191	+	0.516191i	−0.0566594	+	0.0566594i	0.678209	+	0.734869i	$0.262756\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	15.5462			1.66672
$88$		0			0
$89$		−	6.42236i		−	0.680768i	−0.940286	−	0.340384i	$-0.889443\pi$
$89$		−	6.42236i		−	0.680768i	0.940286	−	0.340384i	$-0.110557\pi$
$90$		0			0
$91$	−3.77184	+	3.77184i	−0.395396	+	0.395396i
$92$		0			0
$93$	−5.42011	+	5.42011i	−0.562039	+	0.562039i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			9.44534i			0.959029i	0.877534	+	0.479515i	$0.159187\pi$
$97$			9.44534i			0.959029i	−0.877534	+	0.479515i	$0.840813\pi$
$98$		0			0
$99$	3.11305	+	3.11305i	0.312873	+	0.312873i
$100$		0			0
$101$	−11.0542	+	11.0542i	−1.09993	+	1.09993i	−0.105515	+	0.994418i	$0.533649\pi$
$101$	−11.0542	+	11.0542i	−1.09993	+	1.09993i	−0.994418	+	0.105515i	$0.966351\pi$
$102$		0			0
$103$	5.46824			0.538801			0.269401	−	0.963028i	$-0.413174\pi$
$103$	5.46824			0.538801			0.269401	+	0.963028i	$0.413174\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.293704	+	0.293704i	0.0283934	+	0.0283934i	0.721161	−	0.692768i	$-0.243609\pi$
$107$	0.293704	+	0.293704i	0.0283934	+	0.0283934i	−0.692768	+	0.721161i	$0.743609\pi$
$108$		0			0
$109$	−10.4135	−	10.4135i	−0.997429	−	0.997429i	0.00256817	−	0.999997i	$-0.499183\pi$
$109$	−10.4135	−	10.4135i	−0.997429	−	0.997429i	−0.999997	+	0.00256817i	$0.999183\pi$
$110$		0			0
$111$	−6.81770			−0.647107
$112$		0			0
$113$		−	17.4145i		−	1.63822i	−0.573639	−	0.819108i	$-0.694469\pi$
$113$		−	17.4145i		−	1.63822i	0.573639	−	0.819108i	$-0.305531\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.04167	−	1.04167i	−0.0963022	−	0.0963022i
$118$		0			0
$119$		−	13.5352i		−	1.24077i
$120$		0			0
$121$		−	22.9776i		−	2.08888i
$122$		0			0
$123$	11.5218	+	11.5218i	1.03889	+	1.03889i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			10.9793i			0.974254i	0.873331	+	0.487127i	$0.161955\pi$
$127$			10.9793i			0.974254i	−0.873331	+	0.487127i	$0.838045\pi$
$128$		0			0
$129$	8.84407			0.778677
$130$		0			0
$131$	−5.77044	−	5.77044i	−0.504166	−	0.504166i	0.408564	−	0.912730i	$-0.366030\pi$
$131$	−5.77044	−	5.77044i	−0.504166	−	0.504166i	−0.912730	+	0.408564i	$0.866030\pi$
$132$		0			0
$133$	0.800523	+	0.800523i	0.0694142	+	0.0694142i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.18832			0.614139			0.307070	−	0.951687i	$-0.400652\pi$
$137$	7.18832			0.614139			0.307070	+	0.951687i	$0.400652\pi$
$138$		0			0
$139$	4.91327	−	4.91327i	0.416738	−	0.416738i	−0.467340	−	0.884078i	$-0.654788\pi$
$139$	4.91327	−	4.91327i	0.416738	−	0.416738i	0.884078	+	0.467340i	$0.154788\pi$
$140$		0			0
$141$	−7.12278	−	7.12278i	−0.599846	−	0.599846i
$142$		0			0
$143$			11.3694i			0.950754i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.656667	−	0.656667i	0.0541609	−	0.0541609i
$148$		0			0
$149$	−9.76620	+	9.76620i	−0.800078	+	0.800078i	−0.983107	−	0.183029i	$-0.941410\pi$
$149$	−9.76620	+	9.76620i	−0.800078	+	0.800078i	0.183029	+	0.983107i	$0.441410\pi$
$150$		0			0
$151$			1.90755i			0.155234i	0.996983	+	0.0776169i	$0.0247311\pi$
$151$			1.90755i			0.155234i	−0.996983	+	0.0776169i	$0.975269\pi$
$152$		0			0
$153$	3.73801			0.302201
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.41296	+	4.41296i	−0.352192	+	0.352192i	−0.860925	−	0.508732i	$-0.830114\pi$
$157$	−4.41296	+	4.41296i	−0.352192	+	0.352192i	0.508732	+	0.860925i	$0.330114\pi$
$158$		0			0
$159$	19.7466			1.56601
$160$		0			0
$161$	−4.50748			−0.355240
$162$		0			0
$163$	−3.58912	+	3.58912i	−0.281122	+	0.281122i	−0.833556	−	0.552435i	$-0.813699\pi$
$163$	−3.58912	+	3.58912i	−0.281122	+	0.281122i	0.552435	+	0.833556i	$0.313699\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17.5993			1.36188			0.680938	−	0.732341i	$-0.261572\pi$
$167$	17.5993			1.36188			0.680938	+	0.732341i	$0.261572\pi$
$168$		0			0
$169$			9.19566i			0.707359i
$170$		0			0
$171$	−0.221080	+	0.221080i	−0.0169064	+	0.0169064i
$172$		0			0
$173$	7.32377	−	7.32377i	0.556816	−	0.556816i	−0.371584	−	0.928400i	$-0.621185\pi$
$173$	7.32377	−	7.32377i	0.556816	−	0.556816i	0.928400	+	0.371584i	$0.121185\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			17.5707i			1.32070i
$178$		0			0
$179$	6.42849	+	6.42849i	0.480488	+	0.480488i	0.905287	−	0.424800i	$-0.139655\pi$
$179$	6.42849	+	6.42849i	0.480488	+	0.480488i	−0.424800	+	0.905287i	$0.639655\pi$
$180$		0			0
$181$	−3.67884	+	3.67884i	−0.273446	+	0.273446i	−0.830486	−	0.557040i	$-0.811937\pi$
$181$	−3.67884	+	3.67884i	−0.273446	+	0.273446i	0.557040	+	0.830486i	$0.311937\pi$
$182$		0			0
$183$	−10.4858			−0.775131
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−20.3994	−	20.3994i	−1.49175	−	1.49175i
$188$		0			0
$189$	−8.41196	−	8.41196i	−0.611880	−	0.611880i
$190$		0			0
$191$	5.39093			0.390074			0.195037	−	0.980796i	$-0.437517\pi$
$191$	5.39093			0.390074			0.195037	+	0.980796i	$0.437517\pi$
$192$		0			0
$193$		−	3.53818i		−	0.254684i	−0.991859	−	0.127342i	$-0.959355\pi$
$193$		−	3.53818i		−	0.254684i	0.991859	−	0.127342i	$-0.0406446\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.6900	−	10.6900i	−0.761627	−	0.761627i	0.214989	−	0.976616i	$-0.431028\pi$
$197$	−10.6900	−	10.6900i	−0.761627	−	0.761627i	−0.976616	+	0.214989i	$0.931028\pi$
$198$		0			0
$199$			15.6543i			1.10971i	0.831948	+	0.554853i	$0.187226\pi$
$199$			15.6543i			1.10971i	−0.831948	+	0.554853i	$0.812774\pi$
$200$		0			0
$201$			15.7867i			1.11351i
$202$		0			0
$203$	−15.5137	−	15.5137i	−1.08885	−	1.08885i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	1.24483i		−	0.0865218i
$208$		0			0
$209$	2.41300			0.166911
$210$		0			0
$211$	19.9359	+	19.9359i	1.37244	+	1.37244i	0.856809	+	0.515634i	$0.172444\pi$
$211$	19.9359	+	19.9359i	1.37244	+	1.37244i	0.515634	+	0.856809i	$0.327556\pi$
$212$		0			0
$213$	−10.8559	−	10.8559i	−0.743833	−	0.743833i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.8176			0.734345
$218$		0			0
$219$	5.97815	−	5.97815i	0.403966	−	0.403966i
$220$		0			0
$221$	6.82591	+	6.82591i	0.459161	+	0.459161i
$222$		0			0
$223$		−	21.2173i		−	1.42081i	−0.703792	−	0.710406i	$-0.748511\pi$
$223$		−	21.2173i		−	1.42081i	0.703792	−	0.710406i	$-0.251489\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.0356	+	12.0356i	−0.798832	+	0.798832i	−0.982911	−	0.184079i	$-0.941070\pi$
$227$	−12.0356	+	12.0356i	−0.798832	+	0.798832i	0.184079	+	0.982911i	$0.441070\pi$
$228$		0			0
$229$	−6.70809	+	6.70809i	−0.443283	+	0.443283i	−0.893114	−	0.449831i	$-0.851484\pi$
$229$	−6.70809	+	6.70809i	−0.443283	+	0.443283i	0.449831	+	0.893114i	$0.351484\pi$
$230$		0			0
$231$		−	30.8920i		−	2.03254i
$232$		0			0
$233$	−5.40431			−0.354048			−0.177024	−	0.984207i	$-0.556647\pi$
$233$	−5.40431			−0.354048			−0.177024	+	0.984207i	$0.556647\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.61989	+	7.61989i	−0.494965	+	0.494965i
$238$		0			0
$239$	−1.86569			−0.120681			−0.0603406	−	0.998178i	$-0.519219\pi$
$239$	−1.86569			−0.120681			−0.0603406	+	0.998178i	$0.519219\pi$
$240$		0			0
$241$	16.3740			1.05474			0.527369	−	0.849636i	$-0.323178\pi$
$241$	16.3740			1.05474			0.527369	+	0.849636i	$0.323178\pi$
$242$		0			0
$243$	5.42792	−	5.42792i	0.348201	−	0.348201i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.807421			−0.0513750
$248$		0			0
$249$			1.41464i			0.0896493i
$250$		0			0
$251$	−3.01154	+	3.01154i	−0.190087	+	0.190087i	−0.795734	−	0.605647i	$-0.792914\pi$
$251$	−3.01154	+	3.01154i	−0.190087	+	0.190087i	0.605647	+	0.795734i	$0.292914\pi$
$252$		0			0
$253$	−6.79340	+	6.79340i	−0.427098	+	0.427098i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	22.7407i		−	1.41853i	−0.704944	−	0.709263i	$-0.749028\pi$
$257$		−	22.7407i		−	1.41853i	0.704944	−	0.709263i	$-0.250972\pi$
$258$		0			0
$259$	6.80346	+	6.80346i	0.422747	+	0.422747i
$260$		0			0
$261$	4.28442	−	4.28442i	0.265199	−	0.265199i
$262$		0			0
$263$	−12.0300			−0.741805			−0.370902	−	0.928672i	$-0.620952\pi$
$263$	−12.0300			−0.741805			−0.370902	+	0.928672i	$0.620952\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.80035	−	8.80035i	−0.538573	−	0.538573i
$268$		0			0
$269$	−4.90068	−	4.90068i	−0.298800	−	0.298800i	0.541744	−	0.840544i	$-0.317764\pi$
$269$	−4.90068	−	4.90068i	−0.298800	−	0.298800i	−0.840544	+	0.541744i	$0.817764\pi$
$270$		0			0
$271$	4.14616			0.251862			0.125931	−	0.992039i	$-0.459808\pi$
$271$	4.14616			0.251862			0.125931	+	0.992039i	$0.459808\pi$
$272$		0			0
$273$			10.3369i			0.625615i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.4815	+	10.4815i	0.629775	+	0.629775i	0.948011	−	0.318236i	$-0.103091\pi$
$277$	10.4815	+	10.4815i	0.629775	+	0.629775i	−0.318236	+	0.948011i	$0.603091\pi$
$278$		0			0
$279$			2.98749i			0.178856i
$280$		0			0
$281$			3.51927i			0.209942i	0.994475	+	0.104971i	$0.0334750\pi$
$281$			3.51927i			0.209942i	−0.994475	+	0.104971i	$0.966525\pi$
$282$		0			0
$283$	2.88462	+	2.88462i	0.171473	+	0.171473i	0.787626	−	0.616153i	$-0.211310\pi$
$283$	2.88462	+	2.88462i	0.171473	+	0.171473i	−0.616153	+	0.787626i	$0.711310\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	22.9955i		−	1.35738i
$288$		0			0
$289$	−7.49472			−0.440866
$290$		0			0
$291$	12.9427	+	12.9427i	0.758712	+	0.758712i
$292$		0			0
$293$	3.92351	+	3.92351i	0.229214	+	0.229214i	0.812364	−	0.583150i	$-0.198180\pi$
$293$	3.92351	+	3.92351i	0.229214	+	0.229214i	−0.583150	+	0.812364i	$0.698180\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−25.3560			−1.47130
$298$		0			0
$299$	2.27316	−	2.27316i	0.131460	−	0.131460i
$300$		0			0
$301$	−8.82561	−	8.82561i	−0.508700	−	0.508700i
$302$		0			0
$303$			30.2944i			1.74037i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.196482	−	0.196482i	0.0112138	−	0.0112138i	−0.701478	−	0.712691i	$-0.747476\pi$
$307$	0.196482	−	0.196482i	0.0112138	−	0.0112138i	0.712691	+	0.701478i	$0.247476\pi$
$308$		0			0
$309$	7.49296	−	7.49296i	0.426259	−	0.426259i
$310$		0			0
$311$			2.52927i			0.143422i	0.997425	+	0.0717110i	$0.0228459\pi$
$311$			2.52927i			0.143422i	−0.997425	+	0.0717110i	$0.977154\pi$
$312$		0			0
$313$	−3.84874			−0.217543			−0.108772	−	0.994067i	$-0.534692\pi$
$313$	−3.84874			−0.217543			−0.108772	+	0.994067i	$0.534692\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.78901	+	6.78901i	−0.381309	+	0.381309i	−0.871574	−	0.490265i	$-0.836900\pi$
$317$	−6.78901	+	6.78901i	−0.381309	+	0.381309i	0.490265	+	0.871574i	$0.336900\pi$
$318$		0			0
$319$	−46.7627			−2.61821
$320$		0			0
$321$	0.804906			0.0449255
$322$		0			0
$323$	1.44871	−	1.44871i	0.0806085	−	0.0806085i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−28.5385			−1.57818
$328$		0			0
$329$			14.2158i			0.783743i
$330$		0			0
$331$	−1.79195	+	1.79195i	−0.0984944	+	0.0984944i	−0.754637	−	0.656143i	$-0.772187\pi$
$331$	−1.79195	+	1.79195i	−0.0984944	+	0.0984944i	0.656143	+	0.754637i	$0.272187\pi$
$332$		0			0
$333$	−1.87891	+	1.87891i	−0.102964	+	0.102964i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	16.1071i		−	0.877411i	−0.898631	−	0.438706i	$-0.855437\pi$
$337$		−	16.1071i		−	0.877411i	0.898631	−	0.438706i	$-0.144563\pi$
$338$		0			0
$339$	−23.8625	−	23.8625i	−1.29603	−	1.29603i
$340$		0			0
$341$	16.3036	−	16.3036i	0.882889	−	0.882889i
$342$		0			0
$343$	17.8331			0.962898
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.6577	+	12.6577i	0.679502	+	0.679502i	0.959888	−	0.280385i	$-0.0904622\pi$
$347$	12.6577	+	12.6577i	0.679502	+	0.679502i	−0.280385	+	0.959888i	$0.590462\pi$
$348$		0			0
$349$	16.3020	+	16.3020i	0.872627	+	0.872627i	0.992758	−	0.120131i	$-0.0383314\pi$
$349$	16.3020	+	16.3020i	0.872627	+	0.872627i	−0.120131	+	0.992758i	$0.538331\pi$
$350$		0			0
$351$	8.48445			0.452866
$352$		0			0
$353$		−	13.2637i		−	0.705954i	−0.935632	−	0.352977i	$-0.885169\pi$
$353$		−	13.2637i		−	0.705954i	0.935632	−	0.352977i	$-0.114831\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−18.5469	−	18.5469i	−0.981604	−	0.981604i
$358$		0			0
$359$			13.3561i			0.704906i	0.935830	+	0.352453i	$0.114652\pi$
$359$			13.3561i			0.704906i	−0.935830	+	0.352453i	$0.885348\pi$
$360$		0			0
$361$		−	18.8286i		−	0.990981i
$362$		0			0
$363$	−31.4855	−	31.4855i	−1.65256	−	1.65256i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			11.8938i			0.620852i	0.950598	+	0.310426i	$0.100472\pi$
$367$			11.8938i			0.620852i	−0.950598	+	0.310426i	$0.899528\pi$
$368$		0			0
$369$	6.35067			0.330603
$370$		0			0
$371$	−19.7054	−	19.7054i	−1.02305	−	1.02305i
$372$		0			0
$373$	−19.0494	−	19.0494i	−0.986342	−	0.986342i	0.0135655	−	0.999908i	$-0.495682\pi$
$373$	−19.0494	−	19.0494i	−0.986342	−	0.986342i	−0.999908	+	0.0135655i	$0.995682\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.6474			0.805882
$378$		0			0
$379$	−4.64554	+	4.64554i	−0.238625	+	0.238625i	−0.816281	−	0.577655i	$-0.803968\pi$
$379$	−4.64554	+	4.64554i	−0.238625	+	0.238625i	0.577655	+	0.816281i	$0.303968\pi$
$380$		0			0
$381$	15.0446	+	15.0446i	0.770757	+	0.770757i
$382$		0			0
$383$		−	38.5131i		−	1.96793i	−0.178366	−	0.983964i	$-0.557081\pi$
$383$		−	38.5131i		−	1.96793i	0.178366	−	0.983964i	$-0.442919\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.43737	−	2.43737i	0.123898	−	0.123898i
$388$		0			0
$389$	0.903192	−	0.903192i	0.0457937	−	0.0457937i	−0.683839	−	0.729633i	$-0.739691\pi$
$389$	0.903192	−	0.903192i	0.0457937	−	0.0457937i	0.729633	+	0.683839i	$0.239691\pi$
$390$		0			0
$391$			8.15722i			0.412528i
$392$		0			0
$393$	−15.8141			−0.797716
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.44748	−	4.44748i	0.223212	−	0.223212i	−0.586637	−	0.809850i	$-0.699549\pi$
$397$	4.44748	−	4.44748i	0.223212	−	0.223212i	0.809850	+	0.586637i	$0.199549\pi$
$398$		0			0
$399$	2.19386			0.109831
$400$		0			0
$401$	27.3379			1.36519			0.682596	−	0.730796i	$-0.260851\pi$
$401$	27.3379			1.36519			0.682596	+	0.730796i	$0.260851\pi$
$402$		0			0
$403$	−5.45540	+	5.45540i	−0.271753	+	0.271753i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.5075			1.01652
$408$		0			0
$409$		−	38.6889i		−	1.91304i	−0.291661	−	0.956522i	$-0.594208\pi$
$409$		−	38.6889i		−	1.91304i	0.291661	−	0.956522i	$-0.405792\pi$
$410$		0			0
$411$	9.84993	−	9.84993i	0.485861	−	0.485861i
$412$		0			0
$413$	17.5341	−	17.5341i	0.862794	−	0.862794i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	13.4650i		−	0.659384i
$418$		0			0
$419$	7.41439	+	7.41439i	0.362217	+	0.362217i	0.864628	−	0.502412i	$-0.167554\pi$
$419$	7.41439	+	7.41439i	0.362217	+	0.362217i	−0.502412	+	0.864628i	$0.667554\pi$
$420$		0			0
$421$	−10.3279	+	10.3279i	−0.503351	+	0.503351i	−0.912478	−	0.409127i	$-0.865833\pi$
$421$	−10.3279	+	10.3279i	−0.503351	+	0.503351i	0.409127	+	0.912478i	$0.365833\pi$
$422$		0			0
$423$	−3.92598			−0.190888
$424$		0			0
$425$		0			0
$426$		0			0
$427$	10.4639	+	10.4639i	0.506383	+	0.506383i
$428$		0			0
$429$	15.5791	+	15.5791i	0.752165	+	0.752165i
$430$		0			0
$431$	14.8644			0.715991			0.357995	−	0.933723i	$-0.383460\pi$
$431$	14.8644			0.715991			0.357995	+	0.933723i	$0.383460\pi$
$432$		0			0
$433$		−	4.96284i		−	0.238499i	−0.992864	−	0.119249i	$-0.961951\pi$
$433$		−	4.96284i		−	0.238499i	0.992864	−	0.119249i	$-0.0380488\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.482449	−	0.482449i	−0.0230787	−	0.0230787i
$438$		0			0
$439$		−	13.7348i		−	0.655527i	−0.944760	−	0.327763i	$-0.893705\pi$
$439$		−	13.7348i		−	0.655527i	0.944760	−	0.327763i	$-0.106295\pi$
$440$		0			0
$441$		−	0.361946i		−	0.0172355i
$442$		0			0
$443$	7.62584	+	7.62584i	0.362315	+	0.362315i	0.864664	−	0.502350i	$-0.167531\pi$
$443$	7.62584	+	7.62584i	0.362315	+	0.362315i	−0.502350	+	0.864664i	$0.667531\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			26.7646i			1.26592i
$448$		0			0
$449$	15.8544			0.748215			0.374108	−	0.927385i	$-0.377949\pi$
$449$	15.8544			0.748215			0.374108	+	0.927385i	$0.377949\pi$
$450$		0			0
$451$	−34.6574	−	34.6574i	−1.63195	−	1.63195i
$452$		0			0
$453$	2.61385	+	2.61385i	0.122809	+	0.122809i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.1978			−0.664144			−0.332072	−	0.943254i	$-0.607748\pi$
$457$	−14.1978			−0.664144			−0.332072	+	0.943254i	$0.607748\pi$
$458$		0			0
$459$	−15.2232	+	15.2232i	−0.710557	+	0.710557i
$460$		0			0
$461$	−22.8952	−	22.8952i	−1.06634	−	1.06634i	−0.997638	−	0.0686980i	$-0.978116\pi$
$461$	−22.8952	−	22.8952i	−1.06634	−	1.06634i	−0.0686980	−	0.997638i	$-0.521884\pi$
$462$		0			0
$463$		−	25.0175i		−	1.16266i	−0.813668	−	0.581330i	$-0.802533\pi$
$463$		−	25.0175i		−	1.16266i	0.813668	−	0.581330i	$-0.197467\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.5446	−	23.5446i	1.08951	−	1.08951i	0.0939334	−	0.995578i	$-0.470056\pi$
$467$	23.5446	−	23.5446i	1.08951	−	1.08951i	0.995578	−	0.0939334i	$-0.0299441\pi$
$468$		0			0
$469$	15.7538	−	15.7538i	0.727441	−	0.727441i
$470$		0			0
$471$			12.0939i			0.557256i
$472$		0			0
$473$	−26.6028			−1.22320
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.44203	−	5.44203i	0.249173	−	0.249173i
$478$		0			0
$479$	39.3416			1.79756			0.898781	−	0.438398i	$-0.144454\pi$
$479$	39.3416			1.79756			0.898781	+	0.438398i	$0.144454\pi$
$480$		0			0
$481$	−6.86209			−0.312884
$482$		0			0
$483$	−6.17647	+	6.17647i	−0.281039	+	0.281039i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−25.6970			−1.16444			−0.582222	−	0.813030i	$-0.697816\pi$
$487$	−25.6970			−1.16444			−0.582222	+	0.813030i	$0.697816\pi$
$488$		0			0
$489$			9.83612i			0.444805i
$490$		0			0
$491$	29.0344	−	29.0344i	1.31030	−	1.31030i	0.389113	−	0.921190i	$-0.372781\pi$
$491$	29.0344	−	29.0344i	1.31030	−	1.31030i	0.921190	−	0.389113i	$-0.127219\pi$
$492$		0			0
$493$	−28.0753	+	28.0753i	−1.26445	+	1.26445i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			21.6665i			0.971873i
$498$		0			0
$499$	−7.89904	−	7.89904i	−0.353610	−	0.353610i	0.507841	−	0.861451i	$-0.330444\pi$
$499$	−7.89904	−	7.89904i	−0.353610	−	0.353610i	−0.861451	+	0.507841i	$0.830444\pi$
$500$		0			0
$501$	24.1158	−	24.1158i	1.07741	−	1.07741i
$502$		0			0
$503$	9.53668			0.425220			0.212610	−	0.977137i	$-0.431804\pi$
$503$	9.53668			0.425220			0.212610	+	0.977137i	$0.431804\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.6005	+	12.6005i	0.559609	+	0.559609i
$508$		0			0
$509$	4.24956	+	4.24956i	0.188358	+	0.188358i	0.794986	−	0.606628i	$-0.207478\pi$
$509$	4.24956	+	4.24956i	0.188358	+	0.188358i	−0.606628	+	0.794986i	$0.707478\pi$
$510$		0			0
$511$	−11.9313			−0.527812
$512$		0			0
$513$		−	1.80071i		−	0.0795035i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	21.4252	+	21.4252i	0.942280	+	0.942280i
$518$		0			0
$519$		−	20.0711i		−	0.881022i
$520$		0			0
$521$		−	9.71766i		−	0.425739i	−0.977081	−	0.212869i	$-0.931719\pi$
$521$		−	9.71766i		−	0.425739i	0.977081	−	0.212869i	$-0.0682809\pi$
$522$		0			0
$523$	4.62580	+	4.62580i	0.202272	+	0.202272i	0.800973	−	0.598701i	$-0.204316\pi$
$523$	4.62580	+	4.62580i	0.202272	+	0.202272i	−0.598701	+	0.800973i	$0.704316\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	19.5766i		−	0.852772i
$528$		0			0
$529$	−20.2835			−0.881891
$530$		0			0
$531$	4.84238	+	4.84238i	0.210141	+	0.210141i
$532$		0			0
$533$	11.5968	+	11.5968i	0.502314	+	0.502314i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	17.6175			0.760252
$538$		0			0
$539$	−1.97524	+	1.97524i	−0.0850798	+	0.0850798i
$540$		0			0
$541$	24.0206	+	24.0206i	1.03272	+	1.03272i	0.999446	+	0.0332788i	$0.0105949\pi$
$541$	24.0206	+	24.0206i	1.03272	+	1.03272i	0.0332788	+	0.999446i	$0.489405\pi$
$542$		0			0
$543$			10.0820i			0.432660i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.63900	+	4.63900i	−0.198349	+	0.198349i	−0.799292	−	0.600943i	$-0.794792\pi$
$547$	−4.63900	+	4.63900i	−0.198349	+	0.198349i	0.600943	+	0.799292i	$0.294792\pi$
$548$		0			0
$549$	−2.88981	+	2.88981i	−0.123334	+	0.123334i
$550$		0			0
$551$		−	3.32096i		−	0.141477i
$552$		0			0
$553$	15.2080			0.646709
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.6258	−	13.6258i	0.577345	−	0.577345i	−0.356826	−	0.934171i	$-0.616141\pi$
$557$	13.6258	−	13.6258i	0.577345	−	0.577345i	0.934171	+	0.356826i	$0.116141\pi$
$558$		0			0
$559$	8.90166			0.376500
$560$		0			0
$561$	−55.9054			−2.36033
$562$		0			0
$563$	28.0885	−	28.0885i	1.18379	−	1.18379i	0.205035	−	0.978755i	$-0.434269\pi$
$563$	28.0885	−	28.0885i	1.18379	−	1.18379i	0.978755	−	0.205035i	$-0.0657308\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−29.2499			−1.22838
$568$		0			0
$569$			42.3770i			1.77654i	0.459326	+	0.888268i	$0.348091\pi$
$569$			42.3770i			1.77654i	−0.459326	+	0.888268i	$0.651909\pi$
$570$		0			0
$571$	−7.99217	+	7.99217i	−0.334462	+	0.334462i	−0.854278	−	0.519816i	$-0.826000\pi$
$571$	−7.99217	+	7.99217i	−0.334462	+	0.334462i	0.519816	+	0.854278i	$0.326000\pi$
$572$		0			0
$573$	7.38702	−	7.38702i	0.308597	−	0.308597i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			20.4651i			0.851972i	0.904730	+	0.425986i	$0.140073\pi$
$577$			20.4651i			0.851972i	−0.904730	+	0.425986i	$0.859927\pi$
$578$		0			0
$579$	−4.84826	−	4.84826i	−0.201487	−	0.201487i
$580$		0			0
$581$	1.41169	−	1.41169i	0.0585667	−	0.0585667i
$582$		0			0
$583$	−59.3974			−2.45999
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.429976	+	0.429976i	0.0177470	+	0.0177470i	0.715925	−	0.698178i	$-0.246005\pi$
$587$	0.429976	+	0.429976i	0.0177470	+	0.0177470i	−0.698178	+	0.715925i	$0.746005\pi$
$588$		0			0
$589$	1.15784	+	1.15784i	0.0477079	+	0.0477079i
$590$		0			0
$591$	−29.2962			−1.20509
$592$		0			0
$593$			37.9620i			1.55891i	0.626458	+	0.779455i	$0.284504\pi$
$593$			37.9620i			1.55891i	−0.626458	+	0.779455i	$0.715496\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	21.4507	+	21.4507i	0.877917	+	0.877917i
$598$		0			0
$599$			13.7108i			0.560207i	0.959970	+	0.280104i	$0.0903688\pi$
$599$			13.7108i			0.560207i	−0.959970	+	0.280104i	$0.909631\pi$
$600$		0			0
$601$			2.84070i			0.115875i	0.998320	+	0.0579373i	$0.0184523\pi$
$601$			2.84070i			0.115875i	−0.998320	+	0.0579373i	$0.981548\pi$
$602$		0			0
$603$	4.35072	+	4.35072i	0.177175	+	0.177175i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	42.8562i		−	1.73948i	−0.493510	−	0.869740i	$-0.664287\pi$
$607$		−	42.8562i		−	1.73948i	0.493510	−	0.869740i	$-0.335713\pi$
$608$		0			0
$609$	−42.5159			−1.72283
$610$		0			0
$611$	−7.16916	−	7.16916i	−0.290033	−	0.290033i
$612$		0			0
$613$	5.48393	+	5.48393i	0.221494	+	0.221494i	0.809127	−	0.587633i	$-0.199940\pi$
$613$	5.48393	+	5.48393i	0.221494	+	0.221494i	−0.587633	+	0.809127i	$0.699940\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.2539			−0.895908			−0.447954	−	0.894057i	$-0.647847\pi$
$617$	−22.2539			−0.895908			−0.447954	+	0.894057i	$0.647847\pi$
$618$		0			0
$619$	10.0974	−	10.0974i	0.405849	−	0.405849i	−0.474439	−	0.880288i	$-0.657349\pi$
$619$	10.0974	−	10.0974i	0.405849	−	0.405849i	0.880288	+	0.474439i	$0.157349\pi$
$620$		0			0
$621$	5.06962	+	5.06962i	0.203437	+	0.203437i
$622$		0			0
$623$			17.5640i			0.703685i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.30646	−	3.30646i	0.132047	−	0.132047i
$628$		0			0
$629$	12.3123	−	12.3123i	0.490922	−	0.490922i
$630$		0			0
$631$			49.5996i			1.97453i	0.159086	+	0.987265i	$0.449145\pi$
$631$			49.5996i			1.97453i	−0.159086	+	0.987265i	$0.550855\pi$
$632$		0			0
$633$	54.6351			2.17155
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.660942	−	0.660942i	0.0261875	−	0.0261875i
$638$		0			0
$639$	−5.98362			−0.236709
$640$		0			0
$641$	−42.5379			−1.68015			−0.840074	−	0.542472i	$-0.817488\pi$
$641$	−42.5379			−1.68015			−0.840074	+	0.542472i	$0.817488\pi$
$642$		0			0
$643$	−29.3128	+	29.3128i	−1.15598	+	1.15598i	−0.170653	+	0.985331i	$0.554588\pi$
$643$	−29.3128	+	29.3128i	−1.15598	+	1.15598i	−0.985331	+	0.170653i	$0.945412\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.35345			0.171152			0.0855759	−	0.996332i	$-0.472727\pi$
$647$	4.35345			0.171152			0.0855759	+	0.996332i	$0.472727\pi$
$648$		0			0
$649$		−	52.8525i		−	2.07464i
$650$		0			0
$651$	14.8230	−	14.8230i	0.580959	−	0.580959i
$652$		0			0
$653$	12.3460	−	12.3460i	0.483137	−	0.483137i	−0.422995	−	0.906132i	$-0.639021\pi$
$653$	12.3460	−	12.3460i	0.483137	−	0.483137i	0.906132	+	0.422995i	$0.139021\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	3.29508i		−	0.128553i
$658$		0			0
$659$	19.5367	+	19.5367i	0.761040	+	0.761040i	0.976510	−	0.215470i	$-0.0691284\pi$
$659$	19.5367	+	19.5367i	0.761040	+	0.761040i	−0.215470	+	0.976510i	$0.569128\pi$
$660$		0			0
$661$	26.4901	−	26.4901i	1.03035	−	1.03035i	0.0308210	−	0.999525i	$-0.490188\pi$
$661$	26.4901	−	26.4901i	1.03035	−	1.03035i	0.999525	−	0.0308210i	$-0.00981219\pi$
$662$		0			0
$663$	18.7067			0.726507
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.34961	+	9.34961i	0.362018	+	0.362018i
$668$		0			0
$669$	−29.0734	−	29.0734i	−1.12404	−	1.12404i
$670$		0			0
$671$	31.5411			1.21763
$672$		0			0
$673$		−	11.5260i		−	0.444295i	−0.975013	−	0.222148i	$-0.928693\pi$
$673$		−	11.5260i		−	0.444295i	0.975013	−	0.222148i	$-0.0713067\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.8009	+	15.8009i	0.607278	+	0.607278i	0.942234	−	0.334956i	$-0.108721\pi$
$677$	15.8009	+	15.8009i	0.607278	+	0.607278i	−0.334956	+	0.942234i	$0.608721\pi$
$678$		0			0
$679$		−	25.8313i		−	0.991314i
$680$		0			0
$681$			32.9841i			1.26395i
$682$		0			0
$683$	25.1439	+	25.1439i	0.962105	+	0.962105i	0.999308	−	0.0372032i	$-0.0118449\pi$
$683$	25.1439	+	25.1439i	0.962105	+	0.962105i	−0.0372032	+	0.999308i	$0.511845\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			18.3838i			0.701385i
$688$		0			0
$689$	19.8752			0.757183
$690$		0			0
$691$	27.2647	+	27.2647i	1.03720	+	1.03720i	0.999281	+	0.0379162i	$0.0120720\pi$
$691$	27.2647	+	27.2647i	1.03720	+	1.03720i	0.0379162	+	0.999281i	$0.487928\pi$
$692$		0			0
$693$	−8.51363	−	8.51363i	−0.323406	−	0.323406i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−41.6151			−1.57628
$698$		0			0
$699$	−7.40536	+	7.40536i	−0.280096	+	0.280096i
$700$		0			0
$701$	12.5566	+	12.5566i	0.474257	+	0.474257i	0.903289	−	0.429032i	$-0.141145\pi$
$701$	12.5566	+	12.5566i	0.474257	+	0.474257i	−0.429032	+	0.903289i	$0.641145\pi$
$702$		0			0
$703$			1.45639i			0.0549288i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	30.2312	−	30.2312i	1.13696	−	1.13696i
$708$		0			0
$709$	−18.0518	+	18.0518i	−0.677950	+	0.677950i	−0.959536	−	0.281586i	$-0.909140\pi$
$709$	−18.0518	+	18.0518i	−0.677950	+	0.677950i	0.281586	+	0.959536i	$0.409140\pi$
$710$		0			0
$711$			4.19999i			0.157512i
$712$		0			0
$713$	−6.51940			−0.244154
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.55649	+	2.55649i	−0.0954739	+	0.0954739i
$718$		0			0
$719$	−1.68053			−0.0626731			−0.0313366	−	0.999509i	$-0.509976\pi$
$719$	−1.68053			−0.0626731			−0.0313366	+	0.999509i	$0.509976\pi$
$720$		0			0
$721$	−14.9546			−0.556939
$722$		0			0
$723$	22.4367	−	22.4367i	0.834431	−	0.834431i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−15.5235			−0.575735			−0.287867	−	0.957670i	$-0.592946\pi$
$727$	−15.5235			−0.575735			−0.287867	+	0.957670i	$0.592946\pi$
$728$		0			0
$729$			17.2107i			0.637435i
$730$		0			0
$731$	−15.9718	+	15.9718i	−0.590737	+	0.590737i
$732$		0			0
$733$	8.79758	−	8.79758i	0.324946	−	0.324946i	−0.525715	−	0.850661i	$-0.676202\pi$
$733$	8.79758	−	8.79758i	0.324946	−	0.324946i	0.850661	+	0.525715i	$0.176202\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	47.4862i		−	1.74918i
$738$		0			0
$739$	−6.44190	−	6.44190i	−0.236969	−	0.236969i	0.578625	−	0.815594i	$-0.303590\pi$
$739$	−6.44190	−	6.44190i	−0.236969	−	0.236969i	−0.815594	+	0.578625i	$0.803590\pi$
$740$		0			0
$741$	−1.10638	+	1.10638i	−0.0406440	+	0.0406440i
$742$		0			0
$743$	34.8920			1.28006			0.640032	−	0.768348i	$-0.278921\pi$
$743$	34.8920			1.28006			0.640032	+	0.768348i	$0.278921\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.389866	+	0.389866i	0.0142645	+	0.0142645i
$748$		0			0
$749$	−0.803225	−	0.803225i	−0.0293492	−	0.0293492i
$750$		0			0
$751$	−17.4058			−0.635148			−0.317574	−	0.948234i	$-0.602868\pi$
$751$	−17.4058			−0.635148			−0.317574	+	0.948234i	$0.602868\pi$
$752$		0			0
$753$			8.25325i			0.300765i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−20.6521	−	20.6521i	−0.750614	−	0.750614i	0.223980	−	0.974594i	$-0.428095\pi$
$757$	−20.6521	−	20.6521i	−0.750614	−	0.750614i	−0.974594	+	0.223980i	$0.928095\pi$
$758$		0			0
$759$			18.6176i			0.675776i
$760$		0			0
$761$			8.36636i			0.303280i	0.988436	+	0.151640i	$0.0484555\pi$
$761$			8.36636i			0.303280i	−0.988436	+	0.151640i	$0.951545\pi$
$762$		0			0
$763$	28.4789	+	28.4789i	1.03101	+	1.03101i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			17.6851i			0.638574i
$768$		0			0
$769$	−45.1264			−1.62730			−0.813650	−	0.581356i	$-0.802523\pi$
$769$	−45.1264			−1.62730			−0.813650	+	0.581356i	$0.802523\pi$
$770$		0			0
$771$	−31.1609	−	31.1609i	−1.12223	−	1.12223i
$772$		0			0
$773$	−11.1233	−	11.1233i	−0.400076	−	0.400076i	0.478184	−	0.878260i	$-0.341295\pi$
$773$	−11.1233	−	11.1233i	−0.400076	−	0.400076i	−0.878260	+	0.478184i	$0.841295\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	18.6452			0.668891
$778$		0			0
$779$	2.46128	−	2.46128i	0.0881844	−	0.0881844i
$780$		0			0
$781$	32.6544	+	32.6544i	1.16846	+	1.16846i
$782$		0			0
$783$			34.8969i			1.24711i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.41779	+	7.41779i	−0.264416	+	0.264416i	−0.826845	−	0.562430i	$-0.809867\pi$
$787$	−7.41779	+	7.41779i	−0.264416	+	0.264416i	0.562430	+	0.826845i	$0.309867\pi$
$788$		0			0
$789$	−16.4844	+	16.4844i	−0.586860	+	0.586860i
$790$		0			0
$791$			47.6254i			1.69337i
$792$		0			0
$793$	−10.5541			−0.374786
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.05803	+	8.05803i	−0.285430	+	0.285430i	−0.835270	−	0.549840i	$-0.814689\pi$
$797$	−8.05803	+	8.05803i	−0.285430	+	0.285430i	0.549840	+	0.835270i	$0.314689\pi$
$798$		0			0
$799$	25.7264			0.910136
$800$		0			0
$801$	−4.85064			−0.171389
$802$		0			0
$803$	−17.9822	+	17.9822i	−0.634578	+	0.634578i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−13.4305			−0.472776
$808$		0			0
$809$			20.1500i			0.708436i	0.935163	+	0.354218i	$0.115253\pi$
$809$			20.1500i			0.708436i	−0.935163	+	0.354218i	$0.884747\pi$
$810$		0			0
$811$	10.5575	−	10.5575i	0.370723	−	0.370723i	−0.497018	−	0.867741i	$-0.665572\pi$
$811$	10.5575	−	10.5575i	0.370723	−	0.370723i	0.867741	+	0.497018i	$0.165572\pi$
$812$		0			0
$813$	5.68136	−	5.68136i	0.199254	−	0.199254i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	1.88926i		−	0.0660969i
$818$		0			0
$819$	2.84877	+	2.84877i	0.0995441	+	0.0995441i
$820$		0			0
$821$	−24.3826	+	24.3826i	−0.850957	+	0.850957i	−0.990251	−	0.139294i	$-0.955517\pi$
$821$	−24.3826	+	24.3826i	−0.850957	+	0.850957i	0.139294	+	0.990251i	$0.455517\pi$
$822$		0			0
$823$	32.5617			1.13503			0.567515	−	0.823363i	$-0.307905\pi$
$823$	32.5617			1.13503			0.567515	+	0.823363i	$0.307905\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.31121	−	1.31121i	−0.0455952	−	0.0455952i	0.683942	−	0.729537i	$-0.260264\pi$
$827$	−1.31121	−	1.31121i	−0.0455952	−	0.0455952i	−0.729537	+	0.683942i	$0.760264\pi$
$828$		0			0
$829$	20.8346	+	20.8346i	0.723617	+	0.723617i	0.969340	−	0.245723i	$-0.0790255\pi$
$829$	20.8346	+	20.8346i	0.723617	+	0.723617i	−0.245723	+	0.969340i	$0.579025\pi$
$830$		0			0
$831$	28.7251			0.996462
$832$		0			0
$833$			2.37179i			0.0821775i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−12.1666	−	12.1666i	−0.420541	−	0.420541i
$838$		0			0
$839$			54.2029i			1.87129i	0.352939	+	0.935646i	$0.385182\pi$
$839$			54.2029i			1.87129i	−0.352939	+	0.935646i	$0.614818\pi$
$840$		0			0
$841$			35.3584i			1.21925i
$842$		0			0
$843$	4.82234	+	4.82234i	0.166090	+	0.166090i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			62.8396i			2.15920i
$848$		0			0
$849$	7.90541			0.271313
$850$		0			0
$851$	−4.10023	−	4.10023i	−0.140554	−	0.140554i
$852$		0			0
$853$	28.4548	+	28.4548i	0.974274	+	0.974274i	0.999677	−	0.0254034i	$-0.00808702\pi$
$853$	28.4548	+	28.4548i	0.974274	+	0.974274i	−0.0254034	+	0.999677i	$0.508087\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.9592			0.989228			0.494614	−	0.869113i	$-0.335309\pi$
$857$	28.9592			0.989228			0.494614	+	0.869113i	$0.335309\pi$
$858$		0			0
$859$	35.6101	−	35.6101i	1.21500	−	1.21500i	0.245640	−	0.969361i	$-0.421002\pi$
$859$	35.6101	−	35.6101i	1.21500	−	1.21500i	0.969361	−	0.245640i	$-0.0789982\pi$
$860$		0			0
$861$	−31.5100	−	31.5100i	−1.07386	−	1.07386i
$862$		0			0
$863$			31.8081i			1.08276i	0.840778	+	0.541380i	$0.182098\pi$
$863$			31.8081i			1.08276i	−0.840778	+	0.541380i	$0.817902\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−10.2698	+	10.2698i	−0.348780	+	0.348780i
$868$		0			0
$869$	22.9205	−	22.9205i	0.777526	−	0.777526i
$870$		0			0
$871$			15.8895i			0.538396i
$872$		0			0
$873$	7.13382			0.241443
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−29.2864	+	29.2864i	−0.988932	+	0.988932i	−0.999939	−	0.0110076i	$-0.996496\pi$
$877$	−29.2864	+	29.2864i	−0.988932	+	0.988932i	0.0110076	+	0.999939i	$0.496496\pi$
$878$		0			0
$879$	10.7525			0.362673
$880$		0			0
$881$	−6.72061			−0.226423			−0.113212	−	0.993571i	$-0.536114\pi$
$881$	−6.72061			−0.226423			−0.113212	+	0.993571i	$0.536114\pi$
$882$		0			0
$883$	−26.2186	+	26.2186i	−0.882327	+	0.882327i	−0.993771	−	0.111444i	$-0.964453\pi$
$883$	−26.2186	+	26.2186i	−0.882327	+	0.882327i	0.111444	+	0.993771i	$0.464453\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.4628			−0.351307			−0.175654	−	0.984452i	$-0.556204\pi$
$887$	−10.4628			−0.351307			−0.175654	+	0.984452i	$0.556204\pi$
$888$		0			0
$889$		−	30.0263i		−	1.00705i
$890$		0			0
$891$	−44.0837	+	44.0837i	−1.47686	+	1.47686i
$892$		0			0
$893$	−1.52156	+	1.52156i	−0.0509171	+	0.0509171i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	6.22969i		−	0.208003i
$898$		0			0
$899$	−22.4383	−	22.4383i	−0.748358	−	0.748358i
$900$		0			0
$901$	−35.6609	+	35.6609i	−1.18804	+	1.18804i
$902$		0			0
$903$	−24.1869			−0.804890
$904$		0			0
$905$		0			0
$906$		0			0
$907$	12.4762	+	12.4762i	0.414267	+	0.414267i	0.883222	−	0.468955i	$-0.155369\pi$
$907$	12.4762	+	12.4762i	0.414267	+	0.414267i	−0.468955	+	0.883222i	$0.655369\pi$
$908$		0			0
$909$	8.34894	+	8.34894i	0.276917	+	0.276917i
$910$		0			0
$911$	−49.3786			−1.63599			−0.817994	−	0.575227i	$-0.804914\pi$
$911$	−49.3786			−1.63599			−0.817994	+	0.575227i	$0.804914\pi$
$912$		0			0
$913$		−	4.25522i		−	0.140827i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.7811	+	15.7811i	0.521138	+	0.521138i
$918$		0			0
$919$			26.6465i			0.878988i	0.898246	+	0.439494i	$0.144842\pi$
$919$			26.6465i			0.878988i	−0.898246	+	0.439494i	$0.855158\pi$
$920$		0			0
$921$		−	0.538466i		−	0.0177431i
$922$		0			0
$923$	−10.9266	−	10.9266i	−0.359653	−	0.359653i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	4.13002i		−	0.135648i
$928$		0			0
$929$	29.5531			0.969606			0.484803	−	0.874623i	$-0.338891\pi$
$929$	29.5531			0.969606			0.484803	+	0.874623i	$0.338891\pi$
$930$		0			0
$931$	−0.140276	−	0.140276i	−0.00459737	−	0.00459737i
$932$		0			0
$933$	3.46579	+	3.46579i	0.113465	+	0.113465i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.5505			0.998042			0.499021	−	0.866590i	$-0.333693\pi$
$937$	30.5505			0.998042			0.499021	+	0.866590i	$0.333693\pi$
$938$		0			0
$939$	−5.27380	+	5.27380i	−0.172104	+	0.172104i
$940$		0			0
$941$	0.808622	+	0.808622i	0.0263603	+	0.0263603i	0.720164	−	0.693804i	$-0.244067\pi$
$941$	0.808622	+	0.808622i	0.0263603	+	0.0263603i	−0.693804	+	0.720164i	$0.744067\pi$
$942$		0			0
$943$			13.8586i			0.451299i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.7181	−	16.7181i	0.543265	−	0.543265i	−0.381220	−	0.924484i	$-0.624496\pi$
$947$	16.7181	−	16.7181i	0.543265	−	0.543265i	0.924484	+	0.381220i	$0.124496\pi$
$948$		0			0
$949$	6.01708	−	6.01708i	0.195323	−	0.195323i
$950$		0			0
$951$			18.6055i			0.603326i
$952$		0			0
$953$	−5.39705			−0.174828			−0.0874138	−	0.996172i	$-0.527860\pi$
$953$	−5.39705			−0.174828			−0.0874138	+	0.996172i	$0.527860\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−64.0774	+	64.0774i	−2.07133	+	2.07133i
$958$		0			0
$959$	−19.6587			−0.634813
$960$		0			0
$961$	−15.3540			−0.495290
$962$		0			0
$963$	0.221827	−	0.221827i	0.00714827	−	0.00714827i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	14.0430			0.451593			0.225796	−	0.974175i	$-0.427502\pi$
$967$	14.0430			0.451593			0.225796	+	0.974175i	$0.427502\pi$
$968$		0			0
$969$		−	3.97025i		−	0.127543i
$970$		0			0
$971$	−13.5960	+	13.5960i	−0.436316	+	0.436316i	−0.890770	−	0.454454i	$-0.849834\pi$
$971$	−13.5960	+	13.5960i	−0.436316	+	0.436316i	0.454454	+	0.890770i	$0.349834\pi$
$972$		0			0
$973$	−13.4369	+	13.4369i	−0.430767	+	0.430767i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	44.9303i		−	1.43745i	−0.695295	−	0.718724i	$-0.744726\pi$
$977$		−	44.9303i		−	1.43745i	0.695295	−	0.718724i	$-0.255274\pi$
$978$		0			0
$979$	26.4713	+	26.4713i	0.846028	+	0.846028i
$980$		0			0
$981$	−7.86502	+	7.86502i	−0.251111	+	0.251111i
$982$		0			0
$983$	55.7813			1.77915			0.889574	−	0.456791i	$-0.151001\pi$
$983$	55.7813			1.77915			0.889574	+	0.456791i	$0.151001\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	19.4795	+	19.4795i	0.620039	+	0.620039i
$988$		0			0
$989$	5.31891	+	5.31891i	0.169131	+	0.169131i
$990$		0			0
$991$	46.1815			1.46700			0.733502	−	0.679688i	$-0.237885\pi$
$991$	46.1815			1.46700			0.733502	+	0.679688i	$0.237885\pi$
$992$		0			0
$993$			4.91090i			0.155843i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	33.4837	+	33.4837i	1.06044	+	1.06044i	0.998052	+	0.0623860i	$0.0198710\pi$
$997$	33.4837	+	33.4837i	1.06044	+	1.06044i	0.0623860	+	0.998052i	$0.480129\pi$
$998$		0			0
$999$		−	15.3039i		−	0.484193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.h.849.6		16
4.3	odd	2		400.2.q.g.349.4		16
5.2	odd	4		320.2.l.a.81.3		16
5.3	odd	4		1600.2.l.i.401.6		16
5.4	even	2		1600.2.q.g.849.3		16
15.2	even	4		2880.2.t.c.721.5		16
16.5	even	4		1600.2.q.g.49.3		16
16.11	odd	4		400.2.q.h.149.5		16
20.3	even	4		400.2.l.h.301.7		16
20.7	even	4		80.2.l.a.61.2	yes	16
20.19	odd	2		400.2.q.h.349.5		16
40.27	even	4		640.2.l.b.161.3		16
40.37	odd	4		640.2.l.a.161.6		16
60.47	odd	4		720.2.t.c.541.7		16
80.27	even	4		80.2.l.a.21.2	✓	16
80.37	odd	4		320.2.l.a.241.3		16
80.43	even	4		400.2.l.h.101.7		16
80.53	odd	4		1600.2.l.i.1201.6		16
80.59	odd	4		400.2.q.g.149.4		16
80.67	even	4		640.2.l.b.481.3		16
80.69	even	4	inner	1600.2.q.h.49.6		16
80.77	odd	4		640.2.l.a.481.6		16
160.27	even	8		5120.2.a.s.1.3		8
160.37	odd	8		5120.2.a.u.1.6		8
160.107	even	8		5120.2.a.v.1.6		8
160.117	odd	8		5120.2.a.t.1.3		8
240.107	odd	4		720.2.t.c.181.7		16
240.197	even	4		2880.2.t.c.2161.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.2	✓	16	80.27	even	4
80.2.l.a.61.2	yes	16	20.7	even	4
320.2.l.a.81.3		16	5.2	odd	4
320.2.l.a.241.3		16	80.37	odd	4
400.2.l.h.101.7		16	80.43	even	4
400.2.l.h.301.7		16	20.3	even	4
400.2.q.g.149.4		16	80.59	odd	4
400.2.q.g.349.4		16	4.3	odd	2
400.2.q.h.149.5		16	16.11	odd	4
400.2.q.h.349.5		16	20.19	odd	2
640.2.l.a.161.6		16	40.37	odd	4
640.2.l.a.481.6		16	80.77	odd	4
640.2.l.b.161.3		16	40.27	even	4
640.2.l.b.481.3		16	80.67	even	4
720.2.t.c.181.7		16	240.107	odd	4
720.2.t.c.541.7		16	60.47	odd	4
1600.2.l.i.401.6		16	5.3	odd	4
1600.2.l.i.1201.6		16	80.53	odd	4
1600.2.q.g.49.3		16	16.5	even	4
1600.2.q.g.849.3		16	5.4	even	2
1600.2.q.h.49.6		16	80.69	even	4	inner
1600.2.q.h.849.6		16	1.1	even	1	trivial
2880.2.t.c.721.5		16	15.2	even	4
2880.2.t.c.2161.8		16	240.197	even	4
5120.2.a.s.1.3		8	160.27	even	8
5120.2.a.t.1.3		8	160.117	odd	8
5120.2.a.u.1.6		8	160.37	odd	8
5120.2.a.v.1.6		8	160.107	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37027 - 1.37027i) q^{3} -2.73482 q^{7} -0.755274i q^{9} +O(q^{10})\)	\(q+(1.37027 - 1.37027i) q^{3} -2.73482 q^{7} -0.755274i q^{9} +(-4.12175 + 4.12175i) q^{11} +(1.37919 - 1.37919i) q^{13} +4.94921i q^{17} +(-0.292715 - 0.292715i) q^{19} +(-3.74744 + 3.74744i) q^{21} +1.64818 q^{23} +(3.07588 + 3.07588i) q^{27} +(5.67267 + 5.67267i) q^{29} -3.95550 q^{31} +11.2958i q^{33} +(-2.48772 - 2.48772i) q^{37} -3.77973i q^{39} +8.40843i q^{41} +(3.22713 + 3.22713i) q^{43} -5.19809i q^{47} +0.479225 q^{49} +(6.78176 + 6.78176i) q^{51} +(7.20537 + 7.20537i) q^{53} -0.802198 q^{57} +(-6.41142 + 6.41142i) q^{59} +(-3.82618 - 3.82618i) q^{61} +2.06554i q^{63} +(-5.76044 + 5.76044i) q^{67} +(2.25846 - 2.25846i) q^{69} -7.92245i q^{71} +4.36276 q^{73} +(11.2722 - 11.2722i) q^{77} -5.56087 q^{79} +10.6954 q^{81} +(-0.516191 + 0.516191i) q^{83} +15.5462 q^{87} -6.42236i q^{89} +(-3.77184 + 3.77184i) q^{91} +(-5.42011 + 5.42011i) q^{93} +9.44534i q^{97} +(3.11305 + 3.11305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

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