LMFDB - Embedded newform 1700.2.o.e.1101.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1700,2,Mod(701,1700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1700.701"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1700, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1700 = 2^{2} \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1700.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.5745683436$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 2 x^{10} + 2 x^{9} + 55 x^{8} - 106 x^{7} + 104 x^{6} + 102 x^{5} + 187 x^{4} + \cdots + 1 $ x^12 - 2x^11 + 2x^10 + 2x^9 + 55x^8 - 106x^7 + 104x^6 + 102x^5 + 187x^4 - 172x^3 + 72x^2 - 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1101.5
Root			$-0.816234 + 0.816234i$ of defining polynomial
Character	$\chi$	$=$	1700.1101
Dual form			1700.2.o.e.701.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.816234 + 0.816234i) q^{3} +(-1.61257 + 1.61257i) q^{7} -1.66752i q^{9} +(-0.266636 + 0.266636i) q^{11} -3.60102 q^{13} +(-2.19722 - 3.48887i) q^{17} -6.27876i q^{19} -2.63247 q^{21} +(-0.733364 + 0.733364i) q^{23} +(3.80979 - 3.80979i) q^{27} +(-2.82135 - 2.82135i) q^{29} +(1.78478 + 1.78478i) q^{31} -0.435275 q^{33} +(-5.08154 - 5.08154i) q^{37} +(-2.93927 - 2.93927i) q^{39} +(4.70378 - 4.70378i) q^{41} -5.09923i q^{43} +4.28454 q^{47} +1.79924i q^{49} +(1.05429 - 4.64118i) q^{51} +12.5437i q^{53} +(5.12494 - 5.12494i) q^{57} -12.7130i q^{59} +(-1.34082 + 1.34082i) q^{61} +(2.68900 + 2.68900i) q^{63} -1.64269 q^{67} -1.19719 q^{69} +(-6.26361 - 6.26361i) q^{71} +(4.58807 + 4.58807i) q^{73} -0.859938i q^{77} +(3.25218 - 3.25218i) q^{79} +1.21679 q^{81} +6.23585i q^{83} -4.60576i q^{87} -6.37439 q^{89} +(5.80689 - 5.80689i) q^{91} +2.91360i q^{93} +(-10.8602 - 10.8602i) q^{97} +(0.444622 + 0.444622i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 4 q^{13} + 2 q^{17} - 8 q^{21} - 12 q^{23} - 2 q^{27} - 14 q^{29} - 14 q^{31} + 12 q^{33} - 2 q^{37} - 10 q^{41} + 4 q^{47} + 12 q^{51} - 30 q^{57} - 8 q^{61} - 38 q^{63} + 20 q^{67} - 8 q^{69}+ \cdots + 26 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 4 * q^13 + 2 * q^17 - 8 * q^21 - 12 * q^23 - 2 * q^27 - 14 * q^29 - 14 * q^31 + 12 * q^33 - 2 * q^37 - 10 * q^41 + 4 * q^47 + 12 * q^51 - 30 * q^57 - 8 * q^61 - 38 * q^63 + 20 * q^67 - 8 * q^69 + 16 * q^71 - 6 * q^73 + 6 * q^79 + 8 * q^81 + 40 * q^89 + 20 * q^91 + 4 * q^97 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1700\mathbb{Z}\right)^\times$.

$n$	$477$	$851$	$1601$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.816234	+	0.816234i	0.471253	+	0.471253i	0.902320	−	0.431067i	$-0.141863\pi$
$3$	0.816234	+	0.816234i	0.471253	+	0.471253i	−0.431067	+	0.902320i	$0.641863\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.61257	+	1.61257i	−0.609494	+	0.609494i	−0.942814	−	0.333320i	$-0.891831\pi$
$7$	−1.61257	+	1.61257i	−0.609494	+	0.609494i	0.333320	+	0.942814i	$0.391831\pi$
$8$		0			0
$9$		−	1.66752i		−	0.555841i
$10$		0			0
$11$	−0.266636	+	0.266636i	−0.0803938	+	0.0803938i	−0.746160	−	0.665766i	$-0.768105\pi$
$11$	−0.266636	+	0.266636i	−0.0803938	+	0.0803938i	0.665766	+	0.746160i	$0.268105\pi$
$12$		0			0
$13$	−3.60102			−0.998742			−0.499371	−	0.866388i	$-0.666436\pi$
$13$	−3.60102			−0.998742			−0.499371	+	0.866388i	$0.666436\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.19722	−	3.48887i	−0.532905	−	0.846175i
$17$	−2.19722	−	3.48887i	−0.532905	−	0.846175i
$18$		0			0
$19$		−	6.27876i		−	1.44045i	−0.693742	−	0.720224i	$-0.744039\pi$
$19$		−	6.27876i		−	1.44045i	0.693742	−	0.720224i	$-0.255961\pi$
$20$		0			0
$21$	−2.63247			−0.574452
$22$		0			0
$23$	−0.733364	+	0.733364i	−0.152917	+	0.152917i	−0.779419	−	0.626502i	$-0.784486\pi$
$23$	−0.733364	+	0.733364i	−0.152917	+	0.152917i	0.626502	+	0.779419i	$0.284486\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.80979	−	3.80979i	0.733195	−	0.733195i
$28$		0			0
$29$	−2.82135	−	2.82135i	−0.523911	−	0.523911i	0.394839	−	0.918750i	$-0.370800\pi$
$29$	−2.82135	−	2.82135i	−0.523911	−	0.523911i	−0.918750	+	0.394839i	$0.870800\pi$
$30$		0			0
$31$	1.78478	+	1.78478i	0.320556	+	0.320556i	0.848980	−	0.528424i	$-0.177217\pi$
$31$	1.78478	+	1.78478i	0.320556	+	0.320556i	−0.528424	+	0.848980i	$0.677217\pi$
$32$		0			0
$33$	−0.435275			−0.0757716
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.08154	−	5.08154i	−0.835400	−	0.835400i	0.152849	−	0.988249i	$-0.451155\pi$
$37$	−5.08154	−	5.08154i	−0.835400	−	0.835400i	−0.988249	+	0.152849i	$0.951155\pi$
$38$		0			0
$39$	−2.93927	−	2.93927i	−0.470660	−	0.470660i
$40$		0			0
$41$	4.70378	−	4.70378i	0.734608	−	0.734608i	−0.236921	−	0.971529i	$-0.576138\pi$
$41$	4.70378	−	4.70378i	0.734608	−	0.734608i	0.971529	+	0.236921i	$0.0761383\pi$
$42$		0			0
$43$		−	5.09923i		−	0.777626i	−0.921317	−	0.388813i	$-0.872885\pi$
$43$		−	5.09923i		−	0.777626i	0.921317	−	0.388813i	$-0.127115\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.28454			0.624964			0.312482	−	0.949924i	$-0.398840\pi$
$47$	4.28454			0.624964			0.312482	+	0.949924i	$0.398840\pi$
$48$		0			0
$49$			1.79924i			0.257034i
$50$		0			0
$51$	1.05429	−	4.64118i	0.147630	−	0.649896i
$52$		0			0
$53$			12.5437i			1.72301i	0.507749	+	0.861505i	$0.330478\pi$
$53$			12.5437i			1.72301i	−0.507749	+	0.861505i	$0.669522\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.12494	−	5.12494i	0.678815	−	0.678815i
$58$		0			0
$59$		−	12.7130i		−	1.65509i	−0.561398	−	0.827546i	$-0.689736\pi$
$59$		−	12.7130i		−	1.65509i	0.561398	−	0.827546i	$-0.310264\pi$
$60$		0			0
$61$	−1.34082	+	1.34082i	−0.171675	+	0.171675i	−0.787715	−	0.616040i	$-0.788736\pi$
$61$	−1.34082	+	1.34082i	−0.171675	+	0.171675i	0.616040	+	0.787715i	$0.288736\pi$
$62$		0			0
$63$	2.68900	+	2.68900i	0.338782	+	0.338782i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.64269			−0.200687			−0.100343	−	0.994953i	$-0.531994\pi$
$67$	−1.64269			−0.200687			−0.100343	+	0.994953i	$0.531994\pi$
$68$		0			0
$69$	−1.19719			−0.144125
$70$		0			0
$71$	−6.26361	−	6.26361i	−0.743353	−	0.743353i	0.229868	−	0.973222i	$-0.426170\pi$
$71$	−6.26361	−	6.26361i	−0.743353	−	0.743353i	−0.973222	+	0.229868i	$0.926170\pi$
$72$		0			0
$73$	4.58807	+	4.58807i	0.536992	+	0.536992i	0.922644	−	0.385652i	$-0.126023\pi$
$73$	4.58807	+	4.58807i	0.536992	+	0.536992i	−0.385652	+	0.922644i	$0.626023\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	0.859938i		−	0.0979991i
$78$		0			0
$79$	3.25218	−	3.25218i	0.365899	−	0.365899i	−0.500080	−	0.865979i	$-0.666696\pi$
$79$	3.25218	−	3.25218i	0.365899	−	0.365899i	0.865979	+	0.500080i	$0.166696\pi$
$80$		0			0
$81$	1.21679			0.135199
$82$		0			0
$83$			6.23585i			0.684474i	0.939614	+	0.342237i	$0.111185\pi$
$83$			6.23585i			0.684474i	−0.939614	+	0.342237i	$0.888815\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	4.60576i		−	0.493789i
$88$		0			0
$89$	−6.37439			−0.675684			−0.337842	−	0.941203i	$-0.609697\pi$
$89$	−6.37439			−0.675684			−0.337842	+	0.941203i	$0.609697\pi$
$90$		0			0
$91$	5.80689	−	5.80689i	0.608727	−	0.608727i
$92$		0			0
$93$			2.91360i			0.302126i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.8602	−	10.8602i	−1.10268	−	1.10268i	−0.994086	−	0.108598i	$-0.965364\pi$
$97$	−10.8602	−	10.8602i	−1.10268	−	1.10268i	−0.108598	−	0.994086i	$-0.534636\pi$
$98$		0			0
$99$	0.444622	+	0.444622i	0.0446862	+	0.0446862i
$100$		0			0
$101$	−13.7141			−1.36460			−0.682301	−	0.731072i	$-0.739020\pi$
$101$	−13.7141			−1.36460			−0.682301	+	0.731072i	$0.739020\pi$
$102$		0			0
$103$	−3.79821			−0.374249			−0.187124	−	0.982336i	$-0.559917\pi$
$103$	−3.79821			−0.374249			−0.187124	+	0.982336i	$0.559917\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.55320	+	2.55320i	0.246827	+	0.246827i	0.819667	−	0.572840i	$-0.194158\pi$
$107$	2.55320	+	2.55320i	0.246827	+	0.246827i	−0.572840	+	0.819667i	$0.694158\pi$
$108$		0			0
$109$	11.3394	−	11.3394i	1.08611	−	1.08611i	0.0901897	−	0.995925i	$-0.471253\pi$
$109$	11.3394	−	11.3394i	1.08611	−	1.08611i	0.995925	−	0.0901897i	$-0.0287473\pi$
$110$		0			0
$111$		−	8.29545i		−	0.787370i
$112$		0			0
$113$	1.83069	−	1.83069i	0.172217	−	0.172217i	−0.615736	−	0.787953i	$-0.711141\pi$
$113$	1.83069	−	1.83069i	0.172217	−	0.172217i	0.787953	+	0.615736i	$0.211141\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			6.00478i			0.555142i
$118$		0			0
$119$	9.16922	+	2.08287i	0.840541	+	0.190936i
$120$		0			0
$121$			10.8578i			0.987074i
$122$		0			0
$123$	7.67878			0.692372
$124$		0			0
$125$		0			0
$126$		0			0
$127$			8.13686i			0.722029i	0.932560	+	0.361015i	$0.117570\pi$
$127$			8.13686i			0.722029i	−0.932560	+	0.361015i	$0.882430\pi$
$128$		0			0
$129$	4.16217	−	4.16217i	0.366458	−	0.366458i
$130$		0			0
$131$	6.32213	+	6.32213i	0.552367	+	0.552367i	0.927123	−	0.374756i	$-0.122274\pi$
$131$	6.32213	+	6.32213i	0.552367	+	0.552367i	−0.374756	+	0.927123i	$0.622274\pi$
$132$		0			0
$133$	10.1249	+	10.1249i	0.877944	+	0.877944i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.17700			−0.100558			−0.0502788	−	0.998735i	$-0.516011\pi$
$137$	−1.17700			−0.100558			−0.0502788	+	0.998735i	$0.516011\pi$
$138$		0			0
$139$	−15.9211	−	15.9211i	−1.35041	−	1.35041i	−0.885199	−	0.465213i	$-0.845978\pi$
$139$	−15.9211	−	15.9211i	−1.35041	−	1.35041i	−0.465213	−	0.885199i	$-0.654022\pi$
$140$		0			0
$141$	3.49719	+	3.49719i	0.294516	+	0.294516i
$142$		0			0
$143$	0.960161	−	0.960161i	0.0802927	−	0.0802927i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.46860	+	1.46860i	−0.121128	+	0.121128i
$148$		0			0
$149$	11.0596			0.906041			0.453020	−	0.891500i	$-0.350346\pi$
$149$	11.0596			0.906041			0.453020	+	0.891500i	$0.350346\pi$
$150$		0			0
$151$		−	10.7888i		−	0.877983i	−0.898491	−	0.438991i	$-0.855336\pi$
$151$		−	10.7888i		−	0.877983i	0.898491	−	0.438991i	$-0.144664\pi$
$152$		0			0
$153$	−5.81777	+	3.66392i	−0.470339	+	0.296210i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.512300			0.0408860			0.0204430	−	0.999791i	$-0.493492\pi$
$157$	0.512300			0.0408860			0.0204430	+	0.999791i	$0.493492\pi$
$158$		0			0
$159$	−10.2386	+	10.2386i	−0.811973	+	0.811973i
$160$		0			0
$161$		−	2.36520i		−	0.186404i
$162$		0			0
$163$	−2.48022	+	2.48022i	−0.194266	+	0.194266i	−0.797537	−	0.603271i	$-0.793864\pi$
$163$	−2.48022	+	2.48022i	−0.194266	+	0.194266i	0.603271	+	0.797537i	$0.293864\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.02501	+	2.02501i	0.156700	+	0.156700i	0.781103	−	0.624403i	$-0.214658\pi$
$167$	2.02501	+	2.02501i	0.156700	+	0.156700i	−0.624403	+	0.781103i	$0.714658\pi$
$168$		0			0
$169$	−0.0326878			−0.00251445
$170$		0			0
$171$	−10.4700			−0.800660
$172$		0			0
$173$	−1.49153	−	1.49153i	−0.113399	−	0.113399i	0.648130	−	0.761529i	$-0.275551\pi$
$173$	−1.49153	−	1.49153i	−0.113399	−	0.113399i	−0.761529	+	0.648130i	$0.775551\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.3768	−	10.3768i	0.779967	−	0.779967i
$178$		0			0
$179$			2.32437i			0.173732i	0.996220	+	0.0868658i	$0.0276851\pi$
$179$			2.32437i			0.173732i	−0.996220	+	0.0868658i	$0.972315\pi$
$180$		0			0
$181$	−0.640639	+	0.640639i	−0.0476183	+	0.0476183i	−0.730515	−	0.682897i	$-0.760720\pi$
$181$	−0.640639	+	0.640639i	−0.0476183	+	0.0476183i	0.682897	+	0.730515i	$0.260720\pi$
$182$		0			0
$183$	−2.18885			−0.161804
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.51612	+	0.344400i	0.110869	+	0.0251850i
$188$		0			0
$189$			12.2871i			0.893756i
$190$		0			0
$191$	−22.4809			−1.62666			−0.813330	−	0.581802i	$-0.802348\pi$
$191$	−22.4809			−1.62666			−0.813330	+	0.581802i	$0.802348\pi$
$192$		0			0
$193$	−5.64538	+	5.64538i	−0.406363	+	0.406363i	−0.880468	−	0.474105i	$-0.842772\pi$
$193$	−5.64538	+	5.64538i	−0.406363	+	0.406363i	0.474105	+	0.880468i	$0.342772\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.52513	−	7.52513i	0.536143	−	0.536143i	−0.386251	−	0.922394i	$-0.626230\pi$
$197$	7.52513	−	7.52513i	0.536143	−	0.536143i	0.922394	+	0.386251i	$0.126230\pi$
$198$		0			0
$199$	0.360058	+	0.360058i	0.0255238	+	0.0255238i	0.719754	−	0.694230i	$-0.244255\pi$
$199$	0.360058	+	0.360058i	0.0255238	+	0.0255238i	−0.694230	+	0.719754i	$0.744255\pi$
$200$		0			0
$201$	−1.34082	−	1.34082i	−0.0945742	−	0.0945742i
$202$		0			0
$203$	9.09923			0.638641
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.22290	+	1.22290i	0.0849975	+	0.0849975i
$208$		0			0
$209$	1.67414	+	1.67414i	0.115803	+	0.115803i
$210$		0			0
$211$	17.2509	−	17.2509i	1.18760	−	1.18760i	0.209872	−	0.977729i	$-0.432695\pi$
$211$	17.2509	−	17.2509i	1.18760	−	1.18760i	0.977729	−	0.209872i	$-0.0673047\pi$
$212$		0			0
$213$		−	10.2251i		−	0.700615i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.75617			−0.390754
$218$		0			0
$219$			7.48987i			0.506119i
$220$		0			0
$221$	7.91223	+	12.5635i	0.532234	+	0.845111i
$222$		0			0
$223$			1.50211i			0.100589i	0.998734	+	0.0502944i	$0.0160160\pi$
$223$			1.50211i			0.100589i	−0.998734	+	0.0502944i	$0.983984\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.30160	+	8.30160i	−0.550996	+	0.550996i	−0.926728	−	0.375732i	$-0.877391\pi$
$227$	−8.30160	+	8.30160i	−0.550996	+	0.550996i	0.375732	+	0.926728i	$0.377391\pi$
$228$		0			0
$229$			14.6217i			0.966227i	0.875558	+	0.483113i	$0.160494\pi$
$229$			14.6217i			0.966227i	−0.875558	+	0.483113i	$0.839506\pi$
$230$		0			0
$231$	0.701911	−	0.701911i	0.0461824	−	0.0461824i
$232$		0			0
$233$	−13.1202	−	13.1202i	−0.859533	−	0.859533i	0.131750	−	0.991283i	$-0.457940\pi$
$233$	−13.1202	−	13.1202i	−0.859533	−	0.859533i	−0.991283	+	0.131750i	$0.957940\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.30908			0.344862
$238$		0			0
$239$	−15.7493			−1.01874			−0.509370	−	0.860548i	$-0.670121\pi$
$239$	−15.7493			−1.01874			−0.509370	+	0.860548i	$0.670121\pi$
$240$		0			0
$241$	13.1072	+	13.1072i	0.844312	+	0.844312i	0.989416	−	0.145104i	$-0.0463518\pi$
$241$	13.1072	+	13.1072i	0.844312	+	0.844312i	−0.145104	+	0.989416i	$0.546352\pi$
$242$		0			0
$243$	−10.4362	−	10.4362i	−0.669482	−	0.669482i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			22.6099i			1.43863i
$248$		0			0
$249$	−5.08991	+	5.08991i	−0.322560	+	0.322560i
$250$		0			0
$251$	−10.0712			−0.635688			−0.317844	−	0.948143i	$-0.602959\pi$
$251$	−10.0712			−0.635688			−0.317844	+	0.948143i	$0.602959\pi$
$252$		0			0
$253$		−	0.391083i		−	0.0245872i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	6.55870i		−	0.409121i	−0.978854	−	0.204560i	$-0.934424\pi$
$257$		−	6.55870i		−	0.409121i	0.978854	−	0.204560i	$-0.0655764\pi$
$258$		0			0
$259$	16.3887			1.01834
$260$		0			0
$261$	−4.70466	+	4.70466i	−0.291211	+	0.291211i
$262$		0			0
$263$		−	18.2703i		−	1.12660i	−0.826254	−	0.563298i	$-0.809532\pi$
$263$		−	18.2703i		−	1.12660i	0.826254	−	0.563298i	$-0.190468\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.20300	−	5.20300i	−0.318418	−	0.318418i
$268$		0			0
$269$	0.684858	+	0.684858i	0.0417565	+	0.0417565i	0.727677	−	0.685920i	$-0.240600\pi$
$269$	0.684858	+	0.684858i	0.0417565	+	0.0417565i	−0.685920	+	0.727677i	$0.740600\pi$
$270$		0			0
$271$	29.6803			1.80295			0.901474	−	0.432833i	$-0.142486\pi$
$271$	29.6803			1.80295			0.901474	+	0.432833i	$0.142486\pi$
$272$		0			0
$273$	9.47956			0.573729
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.9208	−	15.9208i	−0.956587	−	0.956587i	0.0425090	−	0.999096i	$-0.486465\pi$
$277$	−15.9208	−	15.9208i	−0.956587	−	0.956587i	−0.999096	+	0.0425090i	$0.986465\pi$
$278$		0			0
$279$	2.97617	−	2.97617i	0.178178	−	0.178178i
$280$		0			0
$281$			22.6112i			1.34887i	0.738334	+	0.674435i	$0.235613\pi$
$281$			22.6112i			1.34887i	−0.738334	+	0.674435i	$0.764387\pi$
$282$		0			0
$283$	17.5527	−	17.5527i	1.04340	−	1.04340i	0.0443860	−	0.999014i	$-0.485867\pi$
$283$	17.5527	−	17.5527i	1.04340	−	1.04340i	0.999014	−	0.0443860i	$-0.0141331\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			15.1704i			0.895478i
$288$		0			0
$289$	−7.34442	+	15.3316i	−0.432025	+	0.901862i
$290$		0			0
$291$		−	17.7289i		−	1.03929i
$292$		0			0
$293$	1.77021			0.103417			0.0517083	−	0.998662i	$-0.483533\pi$
$293$	1.77021			0.103417			0.0517083	+	0.998662i	$0.483533\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			2.03166i			0.117889i
$298$		0			0
$299$	2.64085	−	2.64085i	0.152725	−	0.152725i
$300$		0			0
$301$	8.22287	+	8.22287i	0.473958	+	0.473958i
$302$		0			0
$303$	−11.1939	−	11.1939i	−0.643072	−	0.643072i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	13.9310			0.795083			0.397541	−	0.917584i	$-0.369864\pi$
$307$	13.9310			0.795083			0.397541	+	0.917584i	$0.369864\pi$
$308$		0			0
$309$	−3.10023	−	3.10023i	−0.176366	−	0.176366i
$310$		0			0
$311$	11.0907	+	11.0907i	0.628897	+	0.628897i	0.947791	−	0.318893i	$-0.103311\pi$
$311$	11.0907	+	11.0907i	0.628897	+	0.628897i	−0.318893	+	0.947791i	$0.603311\pi$
$312$		0			0
$313$	15.6881	−	15.6881i	0.886746	−	0.886746i	−0.107463	−	0.994209i	$-0.534273\pi$
$313$	15.6881	−	15.6881i	0.886746	−	0.886746i	0.994209	+	0.107463i	$0.0342726\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.47602	+	8.47602i	−0.476061	+	0.476061i	−0.903869	−	0.427809i	$-0.859286\pi$
$317$	−8.47602	+	8.47602i	−0.476061	+	0.476061i	0.427809	+	0.903869i	$0.359286\pi$
$318$		0			0
$319$	1.50455			0.0842384
$320$		0			0
$321$			4.16802i			0.232636i
$322$		0			0
$323$	−21.9058	+	13.7958i	−1.21887	+	0.767621i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	18.5112			1.02367
$328$		0			0
$329$	−6.90911	+	6.90911i	−0.380912	+	0.380912i
$330$		0			0
$331$			10.7049i			0.588394i	0.955745	+	0.294197i	$0.0950521\pi$
$331$			10.7049i			0.588394i	−0.955745	+	0.294197i	$0.904948\pi$
$332$		0			0
$333$	−8.47359	+	8.47359i	−0.464350	+	0.464350i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.41211	+	7.41211i	0.403763	+	0.403763i	0.879557	−	0.475794i	$-0.157839\pi$
$337$	7.41211	+	7.41211i	0.403763	+	0.403763i	−0.475794	+	0.879557i	$0.657839\pi$
$338$		0			0
$339$	2.98855			0.162316
$340$		0			0
$341$	−0.951774			−0.0515415
$342$		0			0
$343$	−14.1894	−	14.1894i	−0.766155	−	0.766155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.1775	+	12.1775i	−0.653722	+	0.653722i	−0.953887	−	0.300165i	$-0.902958\pi$
$347$	−12.1775	+	12.1775i	−0.653722	+	0.653722i	0.300165	+	0.953887i	$0.402958\pi$
$348$		0			0
$349$			14.3753i			0.769492i	0.923022	+	0.384746i	$0.125711\pi$
$349$			14.3753i			0.769492i	−0.923022	+	0.384746i	$0.874289\pi$
$350$		0			0
$351$	−13.7191	+	13.7191i	−0.732272	+	0.732272i
$352$		0			0
$353$	−32.8821			−1.75014			−0.875069	−	0.483999i	$-0.839184\pi$
$353$	−32.8821			−1.75014			−0.875069	+	0.483999i	$0.839184\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.78412	+	9.18434i	0.306128	+	0.486087i
$358$		0			0
$359$			16.1610i			0.852944i	0.904501	+	0.426472i	$0.140244\pi$
$359$			16.1610i			0.852944i	−0.904501	+	0.426472i	$0.859756\pi$
$360$		0			0
$361$	−20.4229			−1.07489
$362$		0			0
$363$	−8.86252	+	8.86252i	−0.465161	+	0.465161i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−18.2469	+	18.2469i	−0.952478	+	0.952478i	−0.998921	−	0.0464430i	$-0.985211\pi$
$367$	−18.2469	+	18.2469i	−0.952478	+	0.952478i	0.0464430	+	0.998921i	$0.485211\pi$
$368$		0			0
$369$	−7.84367	−	7.84367i	−0.408325	−	0.408325i
$370$		0			0
$371$	−20.2276	−	20.2276i	−1.05016	−	1.05016i
$372$		0			0
$373$	32.7051			1.69340			0.846702	−	0.532067i	$-0.178585\pi$
$373$	32.7051			1.69340			0.846702	+	0.532067i	$0.178585\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.1597	+	10.1597i	0.523252	+	0.523252i
$378$		0			0
$379$	11.8849	+	11.8849i	0.610486	+	0.610486i	0.943073	−	0.332587i	$-0.107922\pi$
$379$	11.8849	+	11.8849i	0.610486	+	0.610486i	−0.332587	+	0.943073i	$0.607922\pi$
$380$		0			0
$381$	−6.64158	+	6.64158i	−0.340259	+	0.340259i
$382$		0			0
$383$		−	28.8458i		−	1.47395i	−0.675920	−	0.736975i	$-0.736253\pi$
$383$		−	28.8458i		−	1.47395i	0.675920	−	0.736975i	$-0.263747\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.50309			−0.432236
$388$		0			0
$389$			21.2797i			1.07892i	0.842011	+	0.539461i	$0.181372\pi$
$389$			21.2797i			1.07892i	−0.842011	+	0.539461i	$0.818628\pi$
$390$		0			0
$391$	4.16997	+	0.947247i	0.210885	+	0.0479044i
$392$		0			0
$393$			10.3207i			0.520609i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−21.6953	+	21.6953i	−1.08886	+	1.08886i	−0.0932105	+	0.995646i	$0.529713\pi$
$397$	−21.6953	+	21.6953i	−1.08886	+	1.08886i	−0.995646	+	0.0932105i	$0.970287\pi$
$398$		0			0
$399$			16.5286i			0.827467i
$400$		0			0
$401$	−11.5961	+	11.5961i	−0.579083	+	0.579083i	−0.934650	−	0.355568i	$-0.884287\pi$
$401$	−11.5961	+	11.5961i	−0.579083	+	0.579083i	0.355568	+	0.934650i	$0.384287\pi$
$402$		0			0
$403$	−6.42703	−	6.42703i	−0.320153	−	0.320153i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.70984			0.134322
$408$		0			0
$409$	17.9990			0.889991			0.444995	−	0.895533i	$-0.353205\pi$
$409$	17.9990			0.889991			0.444995	+	0.895533i	$0.353205\pi$
$410$		0			0
$411$	−0.960704	−	0.960704i	−0.0473880	−	0.0473880i
$412$		0			0
$413$	20.5006	+	20.5006i	1.00877	+	1.00877i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	25.9907i		−	1.27277i
$418$		0			0
$419$	9.67880	−	9.67880i	0.472840	−	0.472840i	−0.429992	−	0.902833i	$-0.641484\pi$
$419$	9.67880	−	9.67880i	0.472840	−	0.472840i	0.902833	+	0.429992i	$0.141484\pi$
$420$		0			0
$421$	23.1730			1.12938			0.564691	−	0.825302i	$-0.308995\pi$
$421$	23.1730			1.12938			0.564691	+	0.825302i	$0.308995\pi$
$422$		0			0
$423$		−	7.14457i		−	0.347381i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	4.32433i		−	0.209269i
$428$		0			0
$429$	1.56743			0.0756763
$430$		0			0
$431$	10.6226	−	10.6226i	0.511672	−	0.511672i	−0.403367	−	0.915038i	$-0.632160\pi$
$431$	10.6226	−	10.6226i	0.511672	−	0.511672i	0.915038	+	0.403367i	$0.132160\pi$
$432$		0			0
$433$		−	3.81820i		−	0.183491i	−0.995782	−	0.0917456i	$-0.970755\pi$
$433$		−	3.81820i		−	0.183491i	0.995782	−	0.0917456i	$-0.0292446\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.60462	+	4.60462i	0.220269	+	0.220269i
$438$		0			0
$439$	21.4033	+	21.4033i	1.02153	+	1.02153i	0.999763	+	0.0217625i	$0.00692776\pi$
$439$	21.4033	+	21.4033i	1.02153	+	1.02153i	0.0217625	+	0.999763i	$0.493072\pi$
$440$		0			0
$441$	3.00028			0.142870
$442$		0			0
$443$	−23.0057			−1.09303			−0.546517	−	0.837448i	$-0.684047\pi$
$443$	−23.0057			−1.09303			−0.546517	+	0.837448i	$0.684047\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	9.02725	+	9.02725i	0.426974	+	0.426974i
$448$		0			0
$449$	−20.5309	+	20.5309i	−0.968912	+	0.968912i	−0.999531	−	0.0306189i	$-0.990252\pi$
$449$	−20.5309	+	20.5309i	−0.968912	+	0.968912i	0.0306189	+	0.999531i	$0.490252\pi$
$450$		0			0
$451$			2.50840i			0.118116i
$452$		0			0
$453$	8.80621	−	8.80621i	0.413752	−	0.413752i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			29.0219i			1.35759i	0.734329	+	0.678794i	$0.237497\pi$
$457$			29.0219i			1.35759i	−0.734329	+	0.678794i	$0.762503\pi$
$458$		0			0
$459$	−21.6628	−	4.92091i	−1.01113	−	0.229688i
$460$		0			0
$461$			19.2857i			0.898226i	0.893475	+	0.449113i	$0.148260\pi$
$461$			19.2857i			0.898226i	−0.893475	+	0.449113i	$0.851740\pi$
$462$		0			0
$463$	25.9058			1.20394			0.601972	−	0.798517i	$-0.294382\pi$
$463$	25.9058			1.20394			0.601972	+	0.798517i	$0.294382\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	19.3658i		−	0.896144i	−0.893997	−	0.448072i	$-0.852111\pi$
$467$		−	19.3658i		−	0.896144i	0.893997	−	0.448072i	$-0.147889\pi$
$468$		0			0
$469$	2.64895	−	2.64895i	0.122317	−	0.122317i
$470$		0			0
$471$	0.418156	+	0.418156i	0.0192676	+	0.0192676i
$472$		0			0
$473$	1.35964	+	1.35964i	0.0625163	+	0.0625163i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	20.9169			0.957720
$478$		0			0
$479$	−3.36973	−	3.36973i	−0.153967	−	0.153967i	0.625920	−	0.779887i	$-0.284724\pi$
$479$	−3.36973	−	3.36973i	−0.153967	−	0.153967i	−0.779887	+	0.625920i	$0.784724\pi$
$480$		0			0
$481$	18.2987	+	18.2987i	0.834349	+	0.834349i
$482$		0			0
$483$	1.93056	−	1.93056i	0.0878434	−	0.0878434i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.87583	−	4.87583i	0.220945	−	0.220945i	−0.587951	−	0.808896i	$-0.700065\pi$
$487$	4.87583	−	4.87583i	0.220945	−	0.220945i	0.808896	+	0.587951i	$0.200065\pi$
$488$		0			0
$489$	−4.04888			−0.183097
$490$		0			0
$491$		−	35.3825i		−	1.59679i	−0.602135	−	0.798394i	$-0.705683\pi$
$491$		−	35.3825i		−	1.59679i	0.602135	−	0.798394i	$-0.294317\pi$
$492$		0			0
$493$	−3.64418	+	16.0424i	−0.164126	+	0.722515i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.2010			0.906139
$498$		0			0
$499$	0.0682505	−	0.0682505i	0.00305531	−	0.00305531i	−0.705577	−	0.708633i	$-0.749312\pi$
$499$	0.0682505	−	0.0682505i	0.00305531	−	0.00305531i	0.708633	+	0.705577i	$0.249312\pi$
$500$		0			0
$501$			3.30577i			0.147691i
$502$		0			0
$503$	31.1989	−	31.1989i	1.39109	−	1.39109i	0.568205	−	0.822887i	$-0.307638\pi$
$503$	31.1989	−	31.1989i	1.39109	−	1.39109i	0.822887	−	0.568205i	$-0.192362\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0266809	−	0.0266809i	−0.00118494	−	0.00118494i
$508$		0			0
$509$	7.67923			0.340376			0.170188	−	0.985412i	$-0.445563\pi$
$509$	7.67923			0.340376			0.170188	+	0.985412i	$0.445563\pi$
$510$		0			0
$511$	−14.7971			−0.654587
$512$		0			0
$513$	−23.9208	−	23.9208i	−1.05613	−	1.05613i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.14241	+	1.14241i	−0.0502432	+	0.0502432i
$518$		0			0
$519$		−	2.43488i		−	0.106879i
$520$		0			0
$521$	13.3081	−	13.3081i	0.583038	−	0.583038i	−0.352699	−	0.935737i	$-0.614736\pi$
$521$	13.3081	−	13.3081i	0.583038	−	0.583038i	0.935737	+	0.352699i	$0.114736\pi$
$522$		0			0
$523$	39.0256			1.70647			0.853235	−	0.521527i	$-0.174637\pi$
$523$	39.0256			1.70647			0.853235	+	0.521527i	$0.174637\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.30531	−	10.1484i	0.100421	−	0.442073i
$528$		0			0
$529$			21.9244i			0.953233i
$530$		0			0
$531$	−21.1992			−0.919969
$532$		0			0
$533$	−16.9384	+	16.9384i	−0.733684	+	0.733684i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.89723	+	1.89723i	−0.0818716	+	0.0818716i
$538$		0			0
$539$	−0.479742	−	0.479742i	−0.0206640	−	0.0206640i
$540$		0			0
$541$	−7.61871	−	7.61871i	−0.327554	−	0.327554i	0.524102	−	0.851656i	$-0.324401\pi$
$541$	−7.61871	−	7.61871i	−0.327554	−	0.327554i	−0.851656	+	0.524102i	$0.824401\pi$
$542$		0			0
$543$	−1.04582			−0.0448806
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−5.03846	−	5.03846i	−0.215429	−	0.215429i	0.591140	−	0.806569i	$-0.298678\pi$
$547$	−5.03846	−	5.03846i	−0.215429	−	0.215429i	−0.806569	+	0.591140i	$0.798678\pi$
$548$		0			0
$549$	2.23585	+	2.23585i	0.0954238	+	0.0954238i
$550$		0			0
$551$	−17.7146	+	17.7146i	−0.754666	+	0.754666i
$552$		0			0
$553$			10.4887i			0.446026i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.0436			1.01876			0.509379	−	0.860542i	$-0.329875\pi$
$557$	24.0436			1.01876			0.509379	+	0.860542i	$0.329875\pi$
$558$		0			0
$559$			18.3624i			0.776647i
$560$		0			0
$561$	0.956396	+	1.51862i	0.0403791	+	0.0641161i
$562$		0			0
$563$			18.2858i			0.770656i	0.922780	+	0.385328i	$0.125912\pi$
$563$			18.2858i			0.770656i	−0.922780	+	0.385328i	$0.874088\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.96216	+	1.96216i	−0.0824031	+	0.0824031i
$568$		0			0
$569$		−	30.0101i		−	1.25809i	−0.777369	−	0.629045i	$-0.783446\pi$
$569$		−	30.0101i		−	1.25809i	0.777369	−	0.629045i	$-0.216554\pi$
$570$		0			0
$571$	5.90936	−	5.90936i	0.247299	−	0.247299i	−0.572562	−	0.819861i	$-0.694050\pi$
$571$	5.90936	−	5.90936i	0.247299	−	0.247299i	0.819861	+	0.572562i	$0.194050\pi$
$572$		0			0
$573$	−18.3497	−	18.3497i	−0.766569	−	0.766569i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−25.2147			−1.04970			−0.524851	−	0.851194i	$-0.675879\pi$
$577$	−25.2147			−1.04970			−0.524851	+	0.851194i	$0.675879\pi$
$578$		0			0
$579$	−9.21591			−0.383000
$580$		0			0
$581$	−10.0557	−	10.0557i	−0.417183	−	0.417183i
$582$		0			0
$583$	−3.34460	−	3.34460i	−0.138519	−	0.138519i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			4.21200i			0.173848i	0.996215	+	0.0869240i	$0.0277037\pi$
$587$			4.21200i			0.173848i	−0.996215	+	0.0869240i	$0.972296\pi$
$588$		0			0
$589$	11.2062	−	11.2062i	0.461744	−	0.461744i
$590$		0			0
$591$	12.2845			0.505318
$592$		0			0
$593$			45.2887i			1.85979i	0.367831	+	0.929893i	$0.380101\pi$
$593$			45.2887i			1.85979i	−0.367831	+	0.929893i	$0.619899\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			0.587784i			0.0240564i
$598$		0			0
$599$	14.8532			0.606884			0.303442	−	0.952850i	$-0.401864\pi$
$599$	14.8532			0.606884			0.303442	+	0.952850i	$0.401864\pi$
$600$		0			0
$601$	20.1364	−	20.1364i	0.821380	−	0.821380i	−0.164926	−	0.986306i	$-0.552739\pi$
$601$	20.1364	−	20.1364i	0.821380	−	0.821380i	0.986306	+	0.164926i	$0.0527386\pi$
$602$		0			0
$603$			2.73923i			0.111550i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.62836	−	6.62836i	−0.269037	−	0.269037i	0.559675	−	0.828712i	$-0.310926\pi$
$607$	−6.62836	−	6.62836i	−0.269037	−	0.269037i	−0.828712	+	0.559675i	$0.810926\pi$
$608$		0			0
$609$	7.42710	+	7.42710i	0.300961	+	0.300961i
$610$		0			0
$611$	−15.4287			−0.624178
$612$		0			0
$613$	8.34020			0.336858			0.168429	−	0.985714i	$-0.446131\pi$
$613$	8.34020			0.336858			0.168429	+	0.985714i	$0.446131\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.1428	−	14.1428i	−0.569366	−	0.569366i	0.362584	−	0.931951i	$-0.381894\pi$
$617$	−14.1428	−	14.1428i	−0.569366	−	0.569366i	−0.931951	+	0.362584i	$0.881894\pi$
$618$		0			0
$619$	22.6764	−	22.6764i	0.911443	−	0.911443i	−0.0849425	−	0.996386i	$-0.527071\pi$
$619$	22.6764	−	22.6764i	0.911443	−	0.911443i	0.996386	+	0.0849425i	$0.0270706\pi$
$620$		0			0
$621$			5.58793i			0.224236i
$622$		0			0
$623$	10.2791	−	10.2791i	0.411825	−	0.411825i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			2.73299i			0.109145i
$628$		0			0
$629$	−6.56356	+	28.8941i	−0.261706	+	1.15208i
$630$		0			0
$631$		−	6.82832i		−	0.271831i	−0.990720	−	0.135916i	$-0.956602\pi$
$631$		−	6.82832i		−	0.271831i	0.990720	−	0.135916i	$-0.0433976\pi$
$632$		0			0
$633$	28.1615			1.11932
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	6.47909i		−	0.256711i
$638$		0			0
$639$	−10.4447	+	10.4447i	−0.413186	+	0.413186i
$640$		0			0
$641$	32.6491	+	32.6491i	1.28956	+	1.28956i	0.935053	+	0.354508i	$0.115352\pi$
$641$	32.6491	+	32.6491i	1.28956	+	1.28956i	0.354508	+	0.935053i	$0.384648\pi$
$642$		0			0
$643$	8.88296	+	8.88296i	0.350310	+	0.350310i	0.860225	−	0.509915i	$-0.170323\pi$
$643$	8.88296	+	8.88296i	0.350310	+	0.350310i	−0.509915	+	0.860225i	$0.670323\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.6477			−0.575860			−0.287930	−	0.957651i	$-0.592967\pi$
$647$	−14.6477			−0.575860			−0.287930	+	0.957651i	$0.592967\pi$
$648$		0			0
$649$	3.38975	+	3.38975i	0.133059	+	0.133059i
$650$		0			0
$651$	−4.69838	−	4.69838i	−0.184144	−	0.184144i
$652$		0			0
$653$	−7.51545	+	7.51545i	−0.294102	+	0.294102i	−0.838698	−	0.544596i	$-0.816683\pi$
$653$	−7.51545	+	7.51545i	−0.294102	+	0.294102i	0.544596	+	0.838698i	$0.316683\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	7.65071	−	7.65071i	0.298483	−	0.298483i
$658$		0			0
$659$	−28.9747			−1.12870			−0.564348	−	0.825537i	$-0.690872\pi$
$659$	−28.9747			−1.12870			−0.564348	+	0.825537i	$0.690872\pi$
$660$		0			0
$661$		−	35.4711i		−	1.37966i	−0.723969	−	0.689832i	$-0.757684\pi$
$661$		−	35.4711i		−	1.37966i	0.723969	−	0.689832i	$-0.242316\pi$
$662$		0			0
$663$	−3.79650	+	16.7130i	−0.147444	+	0.649078i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.13815			0.160230
$668$		0			0
$669$	−1.22608	+	1.22608i	−0.0474028	+	0.0474028i
$670$		0			0
$671$		−	0.715023i		−	0.0276031i
$672$		0			0
$673$	15.7165	−	15.7165i	0.605828	−	0.605828i	−0.336025	−	0.941853i	$-0.609083\pi$
$673$	15.7165	−	15.7165i	0.605828	−	0.605828i	0.941853	+	0.336025i	$0.109083\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.5308	+	29.5308i	1.13496	+	1.13496i	0.989340	+	0.145621i	$0.0465180\pi$
$677$	29.5308	+	29.5308i	1.13496	+	1.13496i	0.145621	+	0.989340i	$0.453482\pi$
$678$		0			0
$679$	35.0256			1.34416
$680$		0			0
$681$	−13.5521			−0.519317
$682$		0			0
$683$	−5.14596	−	5.14596i	−0.196905	−	0.196905i	0.601767	−	0.798672i	$-0.294464\pi$
$683$	−5.14596	−	5.14596i	−0.196905	−	0.196905i	−0.798672	+	0.601767i	$0.794464\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−11.9347	+	11.9347i	−0.455337	+	0.455337i
$688$		0			0
$689$		−	45.1701i		−	1.72084i
$690$		0			0
$691$	14.4178	−	14.4178i	0.548479	−	0.548479i	−0.377522	−	0.926001i	$-0.623224\pi$
$691$	14.4178	−	14.4178i	0.548479	−	0.548479i	0.926001	+	0.377522i	$0.123224\pi$
$692$		0			0
$693$	−1.43397			−0.0544719
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−26.7462	−	6.07563i	−1.01308	−	0.230131i
$698$		0			0
$699$		−	21.4183i		−	0.810115i
$700$		0			0
$701$	−26.7058			−1.00866			−0.504332	−	0.863510i	$-0.668261\pi$
$701$	−26.7058			−1.00866			−0.504332	+	0.863510i	$0.668261\pi$
$702$		0			0
$703$	−31.9058	+	31.9058i	−1.20335	+	1.20335i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.1149	−	22.1149i	0.831716	−	0.831716i
$708$		0			0
$709$	−35.9994	−	35.9994i	−1.35198	−	1.35198i	−0.883439	−	0.468546i	$-0.844778\pi$
$709$	−35.9994	−	35.9994i	−1.35198	−	1.35198i	−0.468546	−	0.883439i	$-0.655222\pi$
$710$		0			0
$711$	−5.42308	−	5.42308i	−0.203381	−	0.203381i
$712$		0			0
$713$	−2.61779			−0.0980369
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−12.8551	−	12.8551i	−0.480084	−	0.480084i
$718$		0			0
$719$	7.06826	+	7.06826i	0.263602	+	0.263602i	0.826515	−	0.562914i	$-0.190320\pi$
$719$	7.06826	+	7.06826i	0.263602	+	0.263602i	−0.562914	+	0.826515i	$0.690320\pi$
$720$		0			0
$721$	6.12487	−	6.12487i	0.228102	−	0.228102i
$722$		0			0
$723$			21.3972i			0.795769i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−17.8024			−0.660254			−0.330127	−	0.943936i	$-0.607092\pi$
$727$	−17.8024			−0.660254			−0.330127	+	0.943936i	$0.607092\pi$
$728$		0			0
$729$		−	20.6871i		−	0.766190i
$730$		0			0
$731$	−17.7906	+	11.2041i	−0.658008	+	0.414400i
$732$		0			0
$733$			28.6002i			1.05637i	0.849128	+	0.528186i	$0.177128\pi$
$733$			28.6002i			1.05637i	−0.849128	+	0.528186i	$0.822872\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.438001	−	0.438001i	0.0161340	−	0.0161340i
$738$		0			0
$739$		−	36.9400i		−	1.35886i	−0.733741	−	0.679430i	$-0.762227\pi$
$739$		−	36.9400i		−	1.35886i	0.733741	−	0.679430i	$-0.237773\pi$
$740$		0			0
$741$	−18.4550	+	18.4550i	−0.677961	+	0.677961i
$742$		0			0
$743$	−32.9181	−	32.9181i	−1.20765	−	1.20765i	−0.971787	−	0.235861i	$-0.924209\pi$
$743$	−32.9181	−	32.9181i	−1.20765	−	1.20765i	−0.235861	−	0.971787i	$-0.575791\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	10.3984			0.380459
$748$		0			0
$749$	−8.23443			−0.300879
$750$		0			0
$751$	19.6807	+	19.6807i	0.718160	+	0.718160i	0.968228	−	0.250069i	$-0.0804532\pi$
$751$	19.6807	+	19.6807i	0.718160	+	0.718160i	−0.250069	+	0.968228i	$0.580453\pi$
$752$		0			0
$753$	−8.22046	−	8.22046i	−0.299570	−	0.299570i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	40.6172i		−	1.47626i	−0.674660	−	0.738129i	$-0.735710\pi$
$757$		−	40.6172i		−	1.47626i	0.674660	−	0.738129i	$-0.264290\pi$
$758$		0			0
$759$	0.319215	−	0.319215i	0.0115868	−	0.0115868i
$760$		0			0
$761$	−16.8521			−0.610887			−0.305443	−	0.952210i	$-0.598805\pi$
$761$	−16.8521			−0.610887			−0.305443	+	0.952210i	$0.598805\pi$
$762$		0			0
$763$			36.5710i			1.32396i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			45.7797i			1.65301i
$768$		0			0
$769$	4.42825			0.159687			0.0798433	−	0.996807i	$-0.474558\pi$
$769$	4.42825			0.159687			0.0798433	+	0.996807i	$0.474558\pi$
$770$		0			0
$771$	5.35344	−	5.35344i	0.192799	−	0.192799i
$772$		0			0
$773$		−	28.4828i		−	1.02446i	−0.858850	−	0.512228i	$-0.828820\pi$
$773$		−	28.4828i		−	1.02446i	0.858850	−	0.512228i	$-0.171180\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	13.3770	+	13.3770i	0.479897	+	0.479897i
$778$		0			0
$779$	−29.5339	−	29.5339i	−1.05816	−	1.05816i
$780$		0			0
$781$	3.34021			0.119522
$782$		0			0
$783$	−21.4975			−0.768257
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.20267	−	7.20267i	−0.256747	−	0.256747i	0.566982	−	0.823730i	$-0.308111\pi$
$787$	−7.20267	−	7.20267i	−0.256747	−	0.256747i	−0.823730	+	0.566982i	$0.808111\pi$
$788$		0			0
$789$	14.9129	−	14.9129i	0.530912	−	0.530912i
$790$		0			0
$791$			5.90424i			0.209931i
$792$		0			0
$793$	4.82832	−	4.82832i	0.171459	−	0.171459i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	43.8770i		−	1.55420i	−0.629375	−	0.777102i	$-0.716689\pi$
$797$		−	43.8770i		−	1.55420i	0.629375	−	0.777102i	$-0.283311\pi$
$798$		0			0
$799$	−9.41408	−	14.9482i	−0.333046	−	0.528829i
$800$		0			0
$801$			10.6295i			0.375573i
$802$		0			0
$803$	−2.44669			−0.0863417
$804$		0			0
$805$		0			0
$806$		0			0
$807$			1.11801i			0.0393558i
$808$		0			0
$809$	6.67006	−	6.67006i	0.234507	−	0.234507i	−0.580064	−	0.814571i	$-0.696972\pi$
$809$	6.67006	−	6.67006i	0.234507	−	0.234507i	0.814571	+	0.580064i	$0.196972\pi$
$810$		0			0
$811$	28.1387	+	28.1387i	0.988082	+	0.988082i	0.999930	−	0.0118476i	$-0.00377129\pi$
$811$	28.1387	+	28.1387i	0.988082	+	0.988082i	−0.0118476	+	0.999930i	$0.503771\pi$
$812$		0			0
$813$	24.2261	+	24.2261i	0.849645	+	0.849645i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−32.0169			−1.12013
$818$		0			0
$819$	−9.68312	−	9.68312i	−0.338356	−	0.338356i
$820$		0			0
$821$	−13.6305	−	13.6305i	−0.475706	−	0.475706i	0.428049	−	0.903756i	$-0.359201\pi$
$821$	−13.6305	−	13.6305i	−0.475706	−	0.475706i	−0.903756	+	0.428049i	$0.859201\pi$
$822$		0			0
$823$	25.6787	−	25.6787i	0.895104	−	0.895104i	−0.0998945	−	0.994998i	$-0.531851\pi$
$823$	25.6787	−	25.6787i	0.895104	−	0.895104i	0.994998	+	0.0998945i	$0.0318505\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.2622	−	36.2622i	1.26096	−	1.26096i	0.310333	−	0.950628i	$-0.399560\pi$
$827$	36.2622	−	36.2622i	1.26096	−	1.26096i	0.950628	−	0.310333i	$-0.100440\pi$
$828$		0			0
$829$	−16.3954			−0.569436			−0.284718	−	0.958611i	$-0.591900\pi$
$829$	−16.3954			−0.569436			−0.284718	+	0.958611i	$0.591900\pi$
$830$		0			0
$831$		−	25.9902i		−	0.901589i
$832$		0			0
$833$	6.27731	−	3.95333i	0.217496	−	0.136975i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.5993			0.470060
$838$		0			0
$839$	−36.4895	+	36.4895i	−1.25976	+	1.25976i	−0.308549	+	0.951208i	$0.599844\pi$
$839$	−36.4895	+	36.4895i	−1.25976	+	1.25976i	−0.951208	+	0.308549i	$0.900156\pi$
$840$		0			0
$841$		−	13.0800i		−	0.451035i
$842$		0			0
$843$	−18.4560	+	18.4560i	−0.635659	+	0.635659i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−17.5090	−	17.5090i	−0.601615	−	0.601615i
$848$		0			0
$849$	28.6542			0.983411
$850$		0			0
$851$	7.45324			0.255494
$852$		0			0
$853$	−31.1948	−	31.1948i	−1.06809	−	1.06809i	−0.997506	−	0.0705838i	$-0.977514\pi$
$853$	−31.1948	−	31.1948i	−1.06809	−	1.06809i	−0.0705838	−	0.997506i	$-0.522486\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.4997	+	12.4997i	−0.426982	+	0.426982i	−0.887599	−	0.460617i	$-0.847628\pi$
$857$	−12.4997	+	12.4997i	−0.426982	+	0.426982i	0.460617	+	0.887599i	$0.347628\pi$
$858$		0			0
$859$		−	55.5538i		−	1.89547i	−0.319058	−	0.947735i	$-0.603366\pi$
$859$		−	55.5538i		−	1.89547i	0.319058	−	0.947735i	$-0.396634\pi$
$860$		0			0
$861$	−12.3826	+	12.3826i	−0.421997	+	0.421997i
$862$		0			0
$863$	−16.8178			−0.572485			−0.286242	−	0.958157i	$-0.592406\pi$
$863$	−16.8178			−0.572485			−0.286242	+	0.958157i	$0.592406\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.5090	+	6.51945i	−0.628598	+	0.221412i
$868$		0			0
$869$			1.73430i			0.0588320i
$870$		0			0
$871$	5.91536			0.200434
$872$		0			0
$873$	−18.1096	+	18.1096i	−0.612917	+	0.612917i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	26.4783	−	26.4783i	0.894110	−	0.894110i	−0.100797	−	0.994907i	$-0.532139\pi$
$877$	26.4783	−	26.4783i	0.894110	−	0.894110i	0.994907	+	0.100797i	$0.0321392\pi$
$878$		0			0
$879$	1.44490	+	1.44490i	0.0487354	+	0.0487354i
$880$		0			0
$881$	−18.4141	−	18.4141i	−0.620388	−	0.620388i	0.325243	−	0.945631i	$-0.394554\pi$
$881$	−18.4141	−	18.4141i	−0.620388	−	0.620388i	−0.945631	+	0.325243i	$0.894554\pi$
$882$		0			0
$883$	24.2331			0.815509			0.407754	−	0.913092i	$-0.366312\pi$
$883$	24.2331			0.815509			0.407754	+	0.913092i	$0.366312\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.4698	−	26.4698i	−0.888770	−	0.888770i	0.105635	−	0.994405i	$-0.466313\pi$
$887$	−26.4698	−	26.4698i	−0.888770	−	0.888770i	−0.994405	+	0.105635i	$0.966313\pi$
$888$		0			0
$889$	−13.1212	−	13.1212i	−0.440073	−	0.440073i
$890$		0			0
$891$	−0.324441	+	0.324441i	−0.0108692	+	0.0108692i
$892$		0			0
$893$		−	26.9016i		−	0.900227i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	4.31111			0.143944
$898$		0			0
$899$		−	10.0710i		−	0.335886i
$900$		0			0
$901$	43.7633	−	27.5613i	1.45797	−	0.918200i
$902$		0			0
$903$			13.4236i			0.446708i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	22.3536	−	22.3536i	0.742240	−	0.742240i	−0.230768	−	0.973009i	$-0.574124\pi$
$907$	22.3536	−	22.3536i	0.742240	−	0.742240i	0.973009	+	0.230768i	$0.0741239\pi$
$908$		0			0
$909$			22.8685i			0.758502i
$910$		0			0
$911$	12.3031	−	12.3031i	0.407621	−	0.407621i	−0.473287	−	0.880908i	$-0.656933\pi$
$911$	12.3031	−	12.3031i	0.407621	−	0.407621i	0.880908	+	0.473287i	$0.156933\pi$
$912$		0			0
$913$	−1.66270	−	1.66270i	−0.0550274	−	0.0550274i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.3897			−0.673329
$918$		0			0
$919$	11.9651			0.394691			0.197345	−	0.980334i	$-0.436768\pi$
$919$	11.9651			0.394691			0.197345	+	0.980334i	$0.436768\pi$
$920$		0			0
$921$	11.3709	+	11.3709i	0.374685	+	0.374685i
$922$		0			0
$923$	22.5553	+	22.5553i	0.742418	+	0.742418i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			6.33360i			0.208023i
$928$		0			0
$929$	38.9758	−	38.9758i	1.27876	−	1.27876i	0.337390	−	0.941365i	$-0.390456\pi$
$929$	38.9758	−	38.9758i	1.27876	−	1.27876i	0.941365	−	0.337390i	$-0.109544\pi$
$930$		0			0
$931$	11.2970			0.370244
$932$		0			0
$933$			18.1053i			0.592739i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			2.10631i			0.0688100i	0.999408	+	0.0344050i	$0.0109536\pi$
$937$			2.10631i			0.0688100i	−0.999408	+	0.0344050i	$0.989046\pi$
$938$		0			0
$939$	25.6104			0.835764
$940$		0			0
$941$	32.7357	−	32.7357i	1.06715	−	1.06715i	0.0695764	−	0.997577i	$-0.477835\pi$
$941$	32.7357	−	32.7357i	1.06715	−	1.06715i	0.997577	−	0.0695764i	$-0.0221648\pi$
$942$		0			0
$943$			6.89917i			0.224668i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36.0970	−	36.0970i	−1.17299	−	1.17299i	−0.981492	−	0.191501i	$-0.938664\pi$
$947$	−36.0970	−	36.0970i	−1.17299	−	1.17299i	−0.191501	−	0.981492i	$-0.561336\pi$
$948$		0			0
$949$	−16.5217	−	16.5217i	−0.536317	−	0.536317i
$950$		0			0
$951$	−13.8368			−0.448690
$952$		0			0
$953$	−13.8488			−0.448607			−0.224303	−	0.974519i	$-0.572011\pi$
$953$	−13.8488			−0.448607			−0.224303	+	0.974519i	$0.572011\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.22806	+	1.22806i	0.0396976	+	0.0396976i
$958$		0			0
$959$	1.89799	−	1.89799i	0.0612892	−	0.0612892i
$960$		0			0
$961$		−	24.6291i		−	0.794487i
$962$		0			0
$963$	4.25752	−	4.25752i	0.137197	−	0.137197i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	4.28463i		−	0.137784i	−0.997624	−	0.0688922i	$-0.978054\pi$
$967$		−	4.28463i		−	0.137784i	0.997624	−	0.0688922i	$-0.0219465\pi$
$968$		0			0
$969$	−29.1409	−	6.61961i	−0.936140	−	0.212653i
$970$		0			0
$971$		−	19.4100i		−	0.622896i	−0.950263	−	0.311448i	$-0.899186\pi$
$971$		−	19.4100i		−	0.622896i	0.950263	−	0.311448i	$-0.100814\pi$
$972$		0			0
$973$	51.3478			1.64614
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	19.7209i		−	0.630927i	−0.948938	−	0.315464i	$-0.897840\pi$
$977$		−	19.7209i		−	0.630927i	0.948938	−	0.315464i	$-0.102160\pi$
$978$		0			0
$979$	1.69964	−	1.69964i	0.0543208	−	0.0543208i
$980$		0			0
$981$	−18.9087	−	18.9087i	−0.603707	−	0.603707i
$982$		0			0
$983$	40.7504	+	40.7504i	1.29974	+	1.29974i	0.928565	+	0.371170i	$0.121043\pi$
$983$	40.7504	+	40.7504i	1.29974	+	1.29974i	0.371170	+	0.928565i	$0.378957\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−11.2789			−0.359012
$988$		0			0
$989$	3.73959	+	3.73959i	0.118912	+	0.118912i
$990$		0			0
$991$	16.9380	+	16.9380i	0.538052	+	0.538052i	0.922957	−	0.384904i	$-0.125765\pi$
$991$	16.9380	+	16.9380i	0.538052	+	0.538052i	−0.384904	+	0.922957i	$0.625765\pi$
$992$		0			0
$993$	−8.73769	+	8.73769i	−0.277282	+	0.277282i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−9.30278	+	9.30278i	−0.294622	+	0.294622i	−0.838903	−	0.544281i	$-0.816803\pi$
$997$	−9.30278	+	9.30278i	−0.294622	+	0.294622i	0.544281	+	0.838903i	$0.316803\pi$
$998$		0			0
$999$	−38.7192			−1.22502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1700.2.o.e.1101.5	yes	12
5.2	odd	4		1700.2.m.d.149.5		12
5.3	odd	4		1700.2.m.e.149.2		12
5.4	even	2		1700.2.o.g.1101.2	yes	12
17.4	even	4	inner	1700.2.o.e.701.5	✓	12
85.4	even	4		1700.2.o.g.701.2	yes	12
85.38	odd	4		1700.2.m.d.1449.5		12
85.72	odd	4		1700.2.m.e.1449.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1700.2.m.d.149.5		12	5.2	odd	4
1700.2.m.d.1449.5		12	85.38	odd	4
1700.2.m.e.149.2		12	5.3	odd	4
1700.2.m.e.1449.2		12	85.72	odd	4
1700.2.o.e.701.5	✓	12	17.4	even	4	inner
1700.2.o.e.1101.5	yes	12	1.1	even	1	trivial
1700.2.o.g.701.2	yes	12	85.4	even	4
1700.2.o.g.1101.2	yes	12	5.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1700 = 2^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1700.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.816234 + 0.816234i) q^{3} +(-1.61257 + 1.61257i) q^{7} -1.66752i q^{9} +(-0.266636 + 0.266636i) q^{11} -3.60102 q^{13} +(-2.19722 - 3.48887i) q^{17} -6.27876i q^{19} -2.63247 q^{21} +(-0.733364 + 0.733364i) q^{23} +(3.80979 - 3.80979i) q^{27} +(-2.82135 - 2.82135i) q^{29} +(1.78478 + 1.78478i) q^{31} -0.435275 q^{33} +(-5.08154 - 5.08154i) q^{37} +(-2.93927 - 2.93927i) q^{39} +(4.70378 - 4.70378i) q^{41} -5.09923i q^{43} +4.28454 q^{47} +1.79924i q^{49} +(1.05429 - 4.64118i) q^{51} +12.5437i q^{53} +(5.12494 - 5.12494i) q^{57} -12.7130i q^{59} +(-1.34082 + 1.34082i) q^{61} +(2.68900 + 2.68900i) q^{63} -1.64269 q^{67} -1.19719 q^{69} +(-6.26361 - 6.26361i) q^{71} +(4.58807 + 4.58807i) q^{73} -0.859938i q^{77} +(3.25218 - 3.25218i) q^{79} +1.21679 q^{81} +6.23585i q^{83} -4.60576i q^{87} -6.37439 q^{89} +(5.80689 - 5.80689i) q^{91} +2.91360i q^{93} +(-10.8602 - 10.8602i) q^{97} +(0.444622 + 0.444622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 4 q^{13} + 2 q^{17} - 8 q^{21} - 12 q^{23} - 2 q^{27} - 14 q^{29} - 14 q^{31} + 12 q^{33} - 2 q^{37} - 10 q^{41} + 4 q^{47} + 12 q^{51} - 30 q^{57} - 8 q^{61} - 38 q^{63} + 20 q^{67} - 8 q^{69}+ \cdots + 26 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 4 * q^13 + 2 * q^17 - 8 * q^21 - 12 * q^23 - 2 * q^27 - 14 * q^29 - 14 * q^31 + 12 * q^33 - 2 * q^37 - 10 * q^41 + 4 * q^47 + 12 * q^51 - 30 * q^57 - 8 * q^61 - 38 * q^63 + 20 * q^67 - 8 * q^69 + 16 * q^71 - 6 * q^73 + 6 * q^79 + 8 * q^81 + 40 * q^89 + 20 * q^91 + 4 * q^97 + 26 * q^99

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