LMFDB - Embedded newform 1674.2.h.b.253.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(253,1674)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1674, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1674.253"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3669572984$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 558)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			253.10
Character	$\chi$	$=$	1674.253
Dual form			1674.2.h.b.397.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +0.562790 q^{5} -1.00505 q^{7} -1.00000 q^{8} +(0.281395 + 0.487391i) q^{10} +(-0.0722513 + 0.125143i) q^{11} -4.71641 q^{13} +(-0.502527 - 0.870402i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.900123 + 1.55906i) q^{17} +(1.19266 - 2.06575i) q^{19} +(-0.281395 + 0.487391i) q^{20} -0.144503 q^{22} +(-1.87458 + 3.24686i) q^{23} -4.68327 q^{25} +(-2.35820 - 4.08453i) q^{26} +(0.502527 - 0.870402i) q^{28} +(0.145225 + 0.251538i) q^{29} +(-4.88891 - 2.66430i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.80025 q^{34} -0.565634 q^{35} +(1.95794 - 3.39125i) q^{37} +2.38532 q^{38} -0.562790 q^{40} -1.52633 q^{41} -9.11103 q^{43} +(-0.0722513 - 0.125143i) q^{44} -3.74915 q^{46} +(5.11631 + 8.86171i) q^{47} -5.98987 q^{49} +(-2.34163 - 4.05583i) q^{50} +(2.35820 - 4.08453i) q^{52} +(-2.18202 - 3.77937i) q^{53} +(-0.0406623 + 0.0704292i) q^{55} +1.00505 q^{56} +(-0.145225 + 0.251538i) q^{58} +(-0.586070 - 1.01510i) q^{59} +(1.68911 + 2.92562i) q^{61} +(-0.137103 - 5.56608i) q^{62} +1.00000 q^{64} -2.65435 q^{65} -11.7407 q^{67} +(-0.900123 - 1.55906i) q^{68} +(-0.282817 - 0.489854i) q^{70} +(-2.93897 - 5.09045i) q^{71} +(2.10808 + 3.65130i) q^{73} +3.91588 q^{74} +(1.19266 + 2.06575i) q^{76} +(0.0726165 - 0.125775i) q^{77} +5.85031 q^{79} +(-0.281395 - 0.487391i) q^{80} +(-0.763164 - 1.32184i) q^{82} +(3.08762 - 5.34792i) q^{83} +(-0.506580 + 0.877423i) q^{85} +(-4.55551 - 7.89038i) q^{86} +(0.0722513 - 0.125143i) q^{88} +6.44167 q^{89} +4.74024 q^{91} +(-1.87458 - 3.24686i) q^{92} +(-5.11631 + 8.86171i) q^{94} +(0.671217 - 1.16258i) q^{95} +(2.71229 + 4.69783i) q^{97} +(-2.99493 - 5.18738i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 2 q^{5} - 2 q^{7} - 32 q^{8} - q^{10} + 2 q^{11} + 20 q^{13} - q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} + q^{20} + 4 q^{22} + q^{23} + 38 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 2 * q^5 - 2 * q^7 - 32 * q^8 - q^10 + 2 * q^11 + 20 * q^13 - q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 + q^20 + 4 * q^22 + q^23 + 38 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - 10 * q^31 + 16 * q^32 + 8 * q^34 - 19 * q^37 + 8 * q^38 + 2 * q^40 + 20 * q^41 + 26 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 + 26 * q^49 + 19 * q^50 - 10 * q^52 + 7 * q^53 - 11 * q^55 + 2 * q^56 - 3 * q^58 + 6 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 - 16 * q^65 + 16 * q^67 + 4 * q^68 - 7 * q^71 + 7 * q^73 - 38 * q^74 + 4 * q^76 + q^77 + 68 * q^79 + q^80 + 10 * q^82 - 14 * q^83 + 13 * q^85 + 13 * q^86 - 2 * q^88 - 2 * q^89 + 24 * q^91 + q^92 - 6 * q^94 - 21 * q^95 + 10 * q^97 + 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.562790			0.251687			0.125844	−	0.992050i	$-0.459836\pi$
$5$	0.562790			0.251687			0.125844	+	0.992050i	$0.459836\pi$
$6$		0			0
$7$	−1.00505			−0.379875			−0.189937	−	0.981796i	$-0.560828\pi$
$7$	−1.00505			−0.379875			−0.189937	+	0.981796i	$0.560828\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.281395	+	0.487391i	0.0889849	+	0.154126i
$11$	−0.0722513	+	0.125143i	−0.0217846	+	0.0377320i	−0.876712	−	0.481015i	$-0.840268\pi$
$11$	−0.0722513	+	0.125143i	−0.0217846	+	0.0377320i	0.854928	+	0.518747i	$0.173601\pi$
$12$		0			0
$13$	−4.71641			−1.30810			−0.654048	−	0.756453i	$-0.726931\pi$
$13$	−4.71641			−1.30810			−0.654048	+	0.756453i	$0.726931\pi$
$14$	−0.502527	−	0.870402i	−0.134306	−	0.232625i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.900123	+	1.55906i	−0.218312	+	0.378127i	−0.954292	−	0.298876i	$-0.903388\pi$
$17$	−0.900123	+	1.55906i	−0.218312	+	0.378127i	0.735980	+	0.677003i	$0.236722\pi$
$18$		0			0
$19$	1.19266	−	2.06575i	0.273615	−	0.473915i	−0.696170	−	0.717877i	$-0.745114\pi$
$19$	1.19266	−	2.06575i	0.273615	−	0.473915i	0.969785	+	0.243962i	$0.0784472\pi$
$20$	−0.281395	+	0.487391i	−0.0629218	+	0.108984i
$21$		0			0
$22$	−0.144503			−0.0308081
$23$	−1.87458	+	3.24686i	−0.390876	+	0.677017i	−0.992565	−	0.121713i	$-0.961161\pi$
$23$	−1.87458	+	3.24686i	−0.390876	+	0.677017i	0.601689	+	0.798730i	$0.294495\pi$
$24$		0			0
$25$	−4.68327			−0.936653
$26$	−2.35820	−	4.08453i	−0.462482	−	0.801042i
$27$		0			0
$28$	0.502527	−	0.870402i	0.0949687	−	0.164491i
$29$	0.145225	+	0.251538i	0.0269677	+	0.0467093i	0.879194	−	0.476463i	$-0.158082\pi$
$29$	0.145225	+	0.251538i	0.0269677	+	0.0467093i	−0.852227	+	0.523173i	$0.824748\pi$
$30$		0			0
$31$	−4.88891	−	2.66430i	−0.878075	−	0.478523i
$31$	−4.88891	−	2.66430i	−0.878075	−	0.478523i
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.80025			−0.308740
$35$	−0.565634			−0.0956097
$36$		0			0
$37$	1.95794	−	3.39125i	0.321883	−	0.557518i	−0.658994	−	0.752149i	$-0.729018\pi$
$37$	1.95794	−	3.39125i	0.321883	−	0.557518i	0.980877	+	0.194631i	$0.0623509\pi$
$38$	2.38532			0.386950
$39$		0			0
$40$	−0.562790			−0.0889849
$41$	−1.52633			−0.238372			−0.119186	−	0.992872i	$-0.538029\pi$
$41$	−1.52633			−0.238372			−0.119186	+	0.992872i	$0.538029\pi$
$42$		0			0
$43$	−9.11103			−1.38942			−0.694709	−	0.719290i	$-0.744467\pi$
$43$	−9.11103			−1.38942			−0.694709	+	0.719290i	$0.744467\pi$
$44$	−0.0722513	−	0.125143i	−0.0108923	−	0.0188660i
$45$		0			0
$46$	−3.74915			−0.552782
$47$	5.11631	+	8.86171i	0.746291	+	1.29261i	0.949589	+	0.313496i	$0.101500\pi$
$47$	5.11631	+	8.86171i	0.746291	+	1.29261i	−0.203299	+	0.979117i	$0.565166\pi$
$48$		0			0
$49$	−5.98987			−0.855695
$50$	−2.34163	−	4.05583i	−0.331157	−	0.573581i
$51$		0			0
$52$	2.35820	−	4.08453i	0.327024	−	0.566422i
$53$	−2.18202	−	3.77937i	−0.299723	−	0.519136i	0.676349	−	0.736581i	$-0.263561\pi$
$53$	−2.18202	−	3.77937i	−0.299723	−	0.519136i	−0.976073	+	0.217445i	$0.930228\pi$
$54$		0			0
$55$	−0.0406623	+	0.0704292i	−0.00548291	+	0.00949667i
$56$	1.00505			0.134306
$57$		0			0
$58$	−0.145225	+	0.251538i	−0.0190690	+	0.0330285i
$59$	−0.586070	−	1.01510i	−0.0762998	−	0.132155i	0.825351	−	0.564620i	$-0.190977\pi$
$59$	−0.586070	−	1.01510i	−0.0762998	−	0.132155i	−0.901651	+	0.432465i	$0.857644\pi$
$60$		0			0
$61$	1.68911	+	2.92562i	0.216268	+	0.374588i	0.953664	−	0.300873i	$-0.0972781\pi$
$61$	1.68911	+	2.92562i	0.216268	+	0.374588i	−0.737396	+	0.675461i	$0.763945\pi$
$62$	−0.137103	−	5.56608i	−0.0174121	−	0.706892i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.65435			−0.329231
$66$		0			0
$67$	−11.7407			−1.43435			−0.717176	−	0.696893i	$-0.754565\pi$
$67$	−11.7407			−1.43435			−0.717176	+	0.696893i	$0.754565\pi$
$68$	−0.900123	−	1.55906i	−0.109156	−	0.189064i
$69$		0			0
$70$	−0.282817	−	0.489854i	−0.0338031	−	0.0585487i
$71$	−2.93897	−	5.09045i	−0.348792	−	0.604125i	0.637243	−	0.770663i	$-0.280075\pi$
$71$	−2.93897	−	5.09045i	−0.348792	−	0.604125i	−0.986035	+	0.166537i	$0.946741\pi$
$72$		0			0
$73$	2.10808	+	3.65130i	0.246732	+	0.427352i	0.962617	−	0.270866i	$-0.0873099\pi$
$73$	2.10808	+	3.65130i	0.246732	+	0.427352i	−0.715885	+	0.698218i	$0.753977\pi$
$74$	3.91588			0.455211
$75$		0			0
$76$	1.19266	+	2.06575i	0.136808	+	0.236958i
$77$	0.0726165	−	0.125775i	0.00827541	−	0.0143334i
$78$		0			0
$79$	5.85031			0.658212			0.329106	−	0.944293i	$-0.393253\pi$
$79$	5.85031			0.658212			0.329106	+	0.944293i	$0.393253\pi$
$80$	−0.281395	−	0.487391i	−0.0314609	−	0.0544919i
$81$		0			0
$82$	−0.763164	−	1.32184i	−0.0842774	−	0.145973i
$83$	3.08762	−	5.34792i	0.338911	−	0.587011i	−0.645317	−	0.763915i	$-0.723275\pi$
$83$	3.08762	−	5.34792i	0.338911	−	0.587011i	0.984228	+	0.176904i	$0.0566082\pi$
$84$		0			0
$85$	−0.506580	+	0.877423i	−0.0549463	+	0.0951698i
$86$	−4.55551	−	7.89038i	−0.491234	−	0.850842i
$87$		0			0
$88$	0.0722513	−	0.125143i	0.00770202	−	0.0133403i
$89$	6.44167			0.682815			0.341408	−	0.939915i	$-0.389096\pi$
$89$	6.44167			0.682815			0.341408	+	0.939915i	$0.389096\pi$
$90$		0			0
$91$	4.74024			0.496913
$92$	−1.87458	−	3.24686i	−0.195438	−	0.338509i
$93$		0			0
$94$	−5.11631	+	8.86171i	−0.527707	+	0.914016i
$95$	0.671217	−	1.16258i	0.0688655	−	0.119278i
$96$		0			0
$97$	2.71229	+	4.69783i	0.275392	+	0.476992i	0.970234	−	0.242170i	$-0.0778592\pi$
$97$	2.71229	+	4.69783i	0.275392	+	0.476992i	−0.694842	+	0.719162i	$0.744526\pi$
$98$	−2.99493	−	5.18738i	−0.302534	−	0.524004i
$99$		0			0
$100$	2.34163	−	4.05583i	0.234163	−	0.405583i
$101$	−5.63378	−	9.75799i	−0.560582	−	0.970956i	−0.997446	−	0.0714286i	$-0.977244\pi$
$101$	−5.63378	−	9.75799i	−0.560582	−	0.970956i	0.436864	−	0.899528i	$-0.356089\pi$
$102$		0			0
$103$	−11.3556			−1.11890			−0.559450	−	0.828864i	$-0.688988\pi$
$103$	−11.3556			−1.11890			−0.559450	+	0.828864i	$0.688988\pi$
$104$	4.71641			0.462482
$105$		0			0
$106$	2.18202	−	3.77937i	0.211936	−	0.367085i
$107$	−7.45699	+	12.9159i	−0.720895	+	1.24863i	0.239747	+	0.970835i	$0.422936\pi$
$107$	−7.45699	+	12.9159i	−0.720895	+	1.24863i	−0.960642	+	0.277791i	$0.910398\pi$
$108$		0			0
$109$	−3.27184			−0.313386			−0.156693	−	0.987647i	$-0.550083\pi$
$109$	−3.27184			−0.313386			−0.156693	+	0.987647i	$0.550083\pi$
$110$	−0.0813246			−0.00775400
$111$		0			0
$112$	0.502527	+	0.870402i	0.0474843	+	0.0822453i
$113$	6.21456			0.584617			0.292308	−	0.956324i	$-0.405577\pi$
$113$	6.21456			0.584617			0.292308	+	0.956324i	$0.405577\pi$
$114$		0			0
$115$	−1.05499	+	1.82730i	−0.0983786	+	0.170397i
$116$	−0.290450			−0.0269677
$117$		0			0
$118$	0.586070	−	1.01510i	0.0539521	−	0.0934477i
$119$	0.904672	−	1.56694i	0.0829311	−	0.143641i
$120$		0			0
$121$	5.48956	+	9.50820i	0.499051	+	0.864381i
$122$	−1.68911	+	2.92562i	−0.152925	+	0.264874i
$123$		0			0
$124$	4.75181	−	2.90177i	0.426725	−	0.260587i
$125$	−5.44965			−0.487431
$126$		0			0
$127$	1.36027	−	2.35605i	0.120704	−	0.209066i	−0.799341	−	0.600877i	$-0.794818\pi$
$127$	1.36027	−	2.35605i	0.120704	−	0.209066i	0.920046	+	0.391812i	$0.128151\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.32717	−	2.29873i	−0.116401	−	0.201612i
$131$	−6.30206	−	10.9155i	−0.550613	−	0.953690i	−0.998230	−	0.0594646i	$-0.981061\pi$
$131$	−6.30206	−	10.9155i	−0.550613	−	0.953690i	0.447617	−	0.894225i	$-0.352273\pi$
$132$		0			0
$133$	−1.19869	+	2.07619i	−0.103939	+	0.180028i
$134$	−5.87033	−	10.1677i	−0.507120	−	0.878357i
$135$		0			0
$136$	0.900123	−	1.55906i	0.0771849	−	0.133688i
$137$	3.18632	−	5.51886i	0.272226	−	0.471508i	−0.697206	−	0.716871i	$-0.745574\pi$
$137$	3.18632	−	5.51886i	0.272226	−	0.471508i	0.969431	+	0.245363i	$0.0789070\pi$
$138$		0			0
$139$	2.25964	−	3.91382i	0.191660	−	0.331966i	−0.754140	−	0.656713i	$-0.771946\pi$
$139$	2.25964	−	3.91382i	0.191660	−	0.331966i	0.945801	+	0.324748i	$0.105279\pi$
$140$	0.282817	−	0.489854i	0.0239024	−	0.0414002i
$141$		0			0
$142$	2.93897	−	5.09045i	0.246633	−	0.427181i
$143$	0.340767	−	0.590225i	0.0284963	−	0.0493571i
$144$		0			0
$145$	0.0817313	+	0.141563i	0.00678742	+	0.0117562i
$146$	−2.10808	+	3.65130i	−0.174466	+	0.302184i
$147$		0			0
$148$	1.95794	+	3.39125i	0.160942	+	0.278759i
$149$	2.44593	+	4.23647i	0.200378	+	0.347066i	0.948650	−	0.316327i	$-0.102450\pi$
$149$	2.44593	+	4.23647i	0.200378	+	0.347066i	−0.748272	+	0.663392i	$0.769116\pi$
$150$		0			0
$151$	−12.0587	−	20.8862i	−0.981320	−	1.69970i	−0.657269	−	0.753656i	$-0.728288\pi$
$151$	−12.0587	−	20.8862i	−0.981320	−	1.69970i	−0.324051	−	0.946039i	$-0.605045\pi$
$152$	−1.19266	+	2.06575i	−0.0967375	+	0.167554i
$153$		0			0
$154$	0.145233			0.0117032
$155$	−2.75143	−	1.49944i	−0.221000	−	0.120438i
$156$		0			0
$157$	−2.71077	+	4.69520i	−0.216343	+	0.374717i	−0.953687	−	0.300800i	$-0.902746\pi$
$157$	−2.71077	+	4.69520i	−0.216343	+	0.374717i	0.737344	+	0.675517i	$0.236080\pi$
$158$	2.92516	+	5.06652i	0.232713	+	0.403071i
$159$		0			0
$160$	0.281395	−	0.487391i	0.0222462	−	0.0385316i
$161$	1.88405	−	3.26327i	0.148484	−	0.257182i
$162$		0			0
$163$	12.9586			1.01500			0.507498	−	0.861653i	$-0.330571\pi$
$163$	12.9586			1.01500			0.507498	+	0.861653i	$0.330571\pi$
$164$	0.763164	−	1.32184i	0.0595931	−	0.103218i
$165$		0			0
$166$	6.17525			0.479292
$167$	2.63275	+	4.56006i	0.203729	+	0.352868i	0.949727	−	0.313079i	$-0.101361\pi$
$167$	2.63275	+	4.56006i	0.203729	+	0.352868i	−0.745998	+	0.665948i	$0.768027\pi$
$168$		0			0
$169$	9.24451			0.711116
$170$	−1.01316			−0.0777059
$171$		0			0
$172$	4.55551	−	7.89038i	0.347355	−	0.601636i
$173$	−5.98983	+	10.3747i	−0.455398	+	0.788773i	−0.998711	−	0.0507573i	$-0.983837\pi$
$173$	−5.98983	+	10.3747i	−0.455398	+	0.788773i	0.543313	+	0.839530i	$0.317170\pi$
$174$		0			0
$175$	4.70694			0.355811
$176$	0.144503			0.0108923
$177$		0			0
$178$	3.22083	+	5.57865i	0.241412	+	0.418137i
$179$	6.85731	−	11.8772i	0.512539	−	0.887744i	−0.487355	−	0.873204i	$-0.662038\pi$
$179$	6.85731	−	11.8772i	0.512539	−	0.887744i	0.999894	−	0.0145400i	$-0.00462837\pi$
$180$		0			0
$181$	11.0891	+	19.2069i	0.824247	+	1.42764i	0.902493	+	0.430704i	$0.141735\pi$
$181$	11.0891	+	19.2069i	0.824247	+	1.42764i	−0.0782463	+	0.996934i	$0.524932\pi$
$182$	2.37012	+	4.10517i	0.175685	+	0.304296i
$183$		0			0
$184$	1.87458	−	3.24686i	0.138196	−	0.239362i
$185$	1.10191	−	1.90856i	0.0810139	−	0.140320i
$186$		0			0
$187$	−0.130070	−	0.225288i	−0.00951167	−	0.0164747i
$188$	−10.2326			−0.746291
$189$		0			0
$190$	1.34243			0.0973905
$191$	−7.44184	+	12.8897i	−0.538473	+	0.932662i	0.460514	+	0.887653i	$0.347665\pi$
$191$	−7.44184	+	12.8897i	−0.538473	+	0.932662i	−0.998987	+	0.0450098i	$0.985668\pi$
$192$		0			0
$193$	9.35593	+	16.2050i	0.673455	+	1.16646i	0.976918	+	0.213615i	$0.0685237\pi$
$193$	9.35593	+	16.2050i	0.673455	+	1.16646i	−0.303463	+	0.952843i	$0.598143\pi$
$194$	−2.71229	+	4.69783i	−0.194731	+	0.337284i
$195$		0			0
$196$	2.99493	−	5.18738i	0.213924	−	0.370527i
$197$	7.08002	+	12.2629i	0.504430	+	0.873699i	0.999987	+	0.00512323i	$0.00163078\pi$
$197$	7.08002	+	12.2629i	0.504430	+	0.873699i	−0.495557	+	0.868576i	$0.665036\pi$
$198$		0			0
$199$	−4.65872	−	8.06915i	−0.330248	−	0.572007i	0.652312	−	0.757950i	$-0.273799\pi$
$199$	−4.65872	−	8.06915i	−0.330248	−	0.572007i	−0.982560	+	0.185944i	$0.940466\pi$
$200$	4.68327			0.331157
$201$		0			0
$202$	5.63378	−	9.75799i	0.396391	−	0.686570i
$203$	−0.145959	−	0.252809i	−0.0102443	−	0.0177437i
$204$		0			0
$205$	−0.859003			−0.0599953
$206$	−5.67780	−	9.83424i	−0.395591	−	0.685184i
$207$		0			0
$208$	2.35820	+	4.08453i	0.163512	+	0.283211i
$209$	0.172343	+	0.298506i	0.0119212	+	0.0206481i
$210$		0			0
$211$	4.01230	+	6.94950i	0.276218	+	0.478423i	0.970442	−	0.241336i	$-0.0775856\pi$
$211$	4.01230	+	6.94950i	0.276218	+	0.478423i	−0.694224	+	0.719759i	$0.744252\pi$
$212$	4.36404			0.299723
$213$		0			0
$214$	−14.9140			−1.01950
$215$	−5.12760			−0.349699
$216$		0			0
$217$	4.91362	+	2.67777i	0.333558	+	0.181779i
$218$	−1.63592	−	2.83350i	−0.110799	−	0.191909i
$219$		0			0
$220$	−0.0406623	−	0.0704292i	−0.00274145	−	0.00474834i
$221$	4.24535	−	7.35316i	0.285573	−	0.494627i
$222$		0			0
$223$	−14.5273			−0.972817			−0.486409	−	0.873731i	$-0.661693\pi$
$223$	−14.5273			−0.972817			−0.486409	+	0.873731i	$0.661693\pi$
$224$	−0.502527	+	0.870402i	−0.0335765	+	0.0581562i
$225$		0			0
$226$	3.10728	+	5.38197i	0.206693	+	0.358003i
$227$	9.41079	−	16.3000i	0.624616	−	1.08187i	−0.363999	−	0.931399i	$-0.618589\pi$
$227$	9.41079	−	16.3000i	0.624616	−	1.08187i	0.988615	−	0.150467i	$-0.0480779\pi$
$228$		0			0
$229$	−0.879392	−	1.52315i	−0.0581119	−	0.100653i	0.835506	−	0.549481i	$-0.185175\pi$
$229$	−0.879392	−	1.52315i	−0.0581119	−	0.100653i	−0.893618	+	0.448829i	$0.851841\pi$
$230$	−2.10999			−0.139128
$231$		0			0
$232$	−0.145225	−	0.251538i	−0.00953450	−	0.0165142i
$233$	23.2370			1.52231			0.761154	−	0.648571i	$-0.224633\pi$
$233$	23.2370			1.52231			0.761154	+	0.648571i	$0.224633\pi$
$234$		0			0
$235$	2.87941	+	4.98728i	0.187832	+	0.325334i
$236$	1.17214			0.0762998
$237$		0			0
$238$	1.80934			0.117282
$239$	−8.88915			−0.574991			−0.287496	−	0.957782i	$-0.592823\pi$
$239$	−8.88915			−0.574991			−0.287496	+	0.957782i	$0.592823\pi$
$240$		0			0
$241$	−14.7318			−0.948957			−0.474479	−	0.880267i	$-0.657363\pi$
$241$	−14.7318			−0.948957			−0.474479	+	0.880267i	$0.657363\pi$
$242$	−5.48956	+	9.50820i	−0.352882	+	0.611210i
$243$		0			0
$244$	−3.37822			−0.216268
$245$	−3.37104			−0.215368
$246$		0			0
$247$	−5.62507	+	9.74291i	−0.357915	+	0.619927i
$248$	4.88891	+	2.66430i	0.310446	+	0.169183i
$249$		0			0
$250$	−2.72482	−	4.71953i	−0.172333	−	0.298489i
$251$	−1.91785	+	3.32181i	−0.121053	+	0.209671i	−0.920183	−	0.391488i	$-0.871961\pi$
$251$	−1.91785	+	3.32181i	−0.121053	+	0.209671i	0.799130	+	0.601158i	$0.205294\pi$
$252$		0			0
$253$	−0.270881	−	0.469180i	−0.0170302	−	0.0294971i
$254$	2.72053			0.170701
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.62606			0.538079			0.269039	−	0.963129i	$-0.413294\pi$
$257$	8.62606			0.538079			0.269039	+	0.963129i	$0.413294\pi$
$258$		0			0
$259$	−1.96783	+	3.40839i	−0.122275	+	0.211787i
$260$	1.32717	−	2.29873i	0.0823078	−	0.142561i
$261$		0			0
$262$	6.30206	−	10.9155i	0.389342	−	0.674361i
$263$	11.0513	+	19.1415i	0.681455	+	1.18031i	0.974537	+	0.224227i	$0.0719858\pi$
$263$	11.0513	+	19.1415i	0.681455	+	1.18031i	−0.293082	+	0.956087i	$0.594681\pi$
$264$		0			0
$265$	−1.22802	−	2.12699i	−0.0754366	−	0.130660i
$266$	−2.39738			−0.146993
$267$		0			0
$268$	5.87033	−	10.1677i	0.358588	−	0.621092i
$269$	7.76488	+	13.4492i	0.473433	+	0.820010i	0.999538	−	0.0304096i	$-0.00968118\pi$
$269$	7.76488	+	13.4492i	0.473433	+	0.820010i	−0.526104	+	0.850420i	$0.676348\pi$
$270$		0			0
$271$	−24.5909			−1.49379			−0.746894	−	0.664943i	$-0.768456\pi$
$271$	−24.5909			−1.49379			−0.746894	+	0.664943i	$0.768456\pi$
$272$	1.80025			0.109156
$273$		0			0
$274$	6.37264			0.384985
$275$	0.338372	−	0.586078i	0.0204046	−	0.0353418i
$276$		0			0
$277$	−2.42178	−	4.19464i	−0.145510	−	0.252031i	0.784053	−	0.620694i	$-0.213149\pi$
$277$	−2.42178	−	4.19464i	−0.145510	−	0.252031i	−0.929563	+	0.368663i	$0.879816\pi$
$278$	4.51929			0.271049
$279$		0			0
$280$	0.565634			0.0338031
$281$	−1.76336	−	3.05424i	−0.105194	−	0.182201i	0.808624	−	0.588326i	$-0.200213\pi$
$281$	−1.76336	−	3.05424i	−0.105194	−	0.182201i	−0.913817	+	0.406126i	$0.866880\pi$
$282$		0			0
$283$	−0.972049	+	1.68364i	−0.0577823	+	0.100082i	−0.893470	−	0.449124i	$-0.851736\pi$
$283$	−0.972049	+	1.68364i	−0.0577823	+	0.100082i	0.835687	+	0.549206i	$0.185070\pi$
$284$	5.87794			0.348792
$285$		0			0
$286$	0.681533			0.0402999
$287$	1.53404			0.0905517
$288$		0			0
$289$	6.87956	+	11.9157i	0.404680	+	0.700926i
$290$	−0.0817313	+	0.141563i	−0.00479943	+	0.00831285i
$291$		0			0
$292$	−4.21616			−0.246732
$293$	11.0367	+	19.1162i	0.644773	+	1.11678i	0.984354	+	0.176203i	$0.0563814\pi$
$293$	11.0367	+	19.1162i	0.644773	+	1.11678i	−0.339581	+	0.940577i	$0.610285\pi$
$294$		0			0
$295$	−0.329834	−	0.571289i	−0.0192037	−	0.0332618i
$296$	−1.95794	+	3.39125i	−0.113803	+	0.197112i
$297$		0			0
$298$	−2.44593	+	4.23647i	−0.141689	+	0.245412i
$299$	8.84127	−	15.3135i	0.511304	−	0.885604i
$300$		0			0
$301$	9.15708			0.527805
$302$	12.0587	−	20.8862i	0.693898	−	1.20187i
$303$		0			0
$304$	−2.38532			−0.136808
$305$	0.950614	+	1.64651i	0.0544320	+	0.0942790i
$306$		0			0
$307$	−8.51193	+	14.7431i	−0.485801	+	0.841433i	−0.999867	−	0.0163183i	$-0.994805\pi$
$307$	−8.51193	+	14.7431i	−0.485801	+	0.841433i	0.514066	+	0.857751i	$0.328139\pi$
$308$	0.0726165	+	0.125775i	0.00413771	+	0.00716672i
$309$		0			0
$310$	−0.0771603	−	3.13253i	−0.00438241	−	0.177916i
$311$	−4.84163	+	8.38595i	−0.274544	+	0.475523i	−0.970020	−	0.243026i	$-0.921860\pi$
$311$	−4.84163	+	8.38595i	−0.274544	+	0.475523i	0.695476	+	0.718549i	$0.255193\pi$
$312$		0			0
$313$	0.773372			0.0437136			0.0218568	−	0.999761i	$-0.493042\pi$
$313$	0.773372			0.0437136			0.0218568	+	0.999761i	$0.493042\pi$
$314$	−5.42155			−0.305955
$315$		0			0
$316$	−2.92516	+	5.06652i	−0.164553	+	0.285014i
$317$	−14.4868			−0.813660			−0.406830	−	0.913504i	$-0.633366\pi$
$317$	−14.4868			−0.813660			−0.406830	+	0.913504i	$0.633366\pi$
$318$		0			0
$319$	−0.0419709			−0.00234992
$320$	0.562790			0.0314609
$321$		0			0
$322$	3.76810			0.209988
$323$	2.14708	+	3.71885i	0.119467	+	0.206923i
$324$		0			0
$325$	22.0882			1.22523
$326$	6.47930	+	11.2225i	0.358855	+	0.621555i
$327$		0			0
$328$	1.52633			0.0842774
$329$	−5.14217	−	8.90650i	−0.283497	−	0.491031i
$330$		0			0
$331$	10.9088	−	18.8945i	0.599600	−	1.03854i	−0.393280	−	0.919419i	$-0.628660\pi$
$331$	10.9088	−	18.8945i	0.599600	−	1.03854i	0.992880	−	0.119119i	$-0.0380070\pi$
$332$	3.08762	+	5.34792i	0.169455	+	0.293505i
$333$		0			0
$334$	−2.63275	+	4.56006i	−0.144058	+	0.249516i
$335$	−6.60753			−0.361008
$336$		0			0
$337$	6.85960	−	11.8812i	0.373666	−	0.647209i	−0.616460	−	0.787386i	$-0.711434\pi$
$337$	6.85960	−	11.8812i	0.373666	−	0.647209i	0.990126	+	0.140177i	$0.0447673\pi$
$338$	4.62225	+	8.00598i	0.251417	+	0.435468i
$339$		0			0
$340$	−0.506580	−	0.877423i	−0.0274732	−	0.0475849i
$341$	0.686649	−	0.419314i	0.0371841	−	0.0227071i
$342$		0			0
$343$	13.0555			0.704932
$344$	9.11103			0.491234
$345$		0			0
$346$	−11.9797			−0.644031
$347$	7.16616	+	12.4122i	0.384700	+	0.666319i	0.991727	−	0.128361i	$-0.0409717\pi$
$347$	7.16616	+	12.4122i	0.384700	+	0.666319i	−0.607028	+	0.794681i	$0.707638\pi$
$348$		0			0
$349$	7.33248	+	12.7002i	0.392498	+	0.679827i	0.992778	−	0.119963i	$-0.0382775\pi$
$349$	7.33248	+	12.7002i	0.392498	+	0.679827i	−0.600280	+	0.799790i	$0.704944\pi$
$350$	2.35347	+	4.07633i	0.125798	+	0.217889i
$351$		0			0
$352$	0.0722513	+	0.125143i	0.00385101	+	0.00667014i
$353$	12.5009			0.665357			0.332678	−	0.943040i	$-0.392048\pi$
$353$	12.5009			0.665357			0.332678	+	0.943040i	$0.392048\pi$
$354$		0			0
$355$	−1.65402	−	2.86485i	−0.0877865	−	0.152051i
$356$	−3.22083	+	5.57865i	−0.170704	+	0.295668i
$357$		0			0
$358$	13.7146			0.724840
$359$	16.2102	+	28.0769i	0.855543	+	1.48184i	0.876140	+	0.482057i	$0.160110\pi$
$359$	16.2102	+	28.0769i	0.855543	+	1.48184i	−0.0205965	+	0.999788i	$0.506557\pi$
$360$		0			0
$361$	6.65512	+	11.5270i	0.350270	+	0.606685i
$362$	−11.0891	+	19.2069i	−0.582831	+	1.00949i
$363$		0			0
$364$	−2.37012	+	4.10517i	−0.124228	+	0.215169i
$365$	1.18641	+	2.05492i	0.0620993	+	0.107559i
$366$		0			0
$367$	3.87593	−	6.71330i	0.202322	−	0.350431i	−0.746954	−	0.664875i	$-0.768485\pi$
$367$	3.87593	−	6.71330i	0.202322	−	0.350431i	0.949276	+	0.314444i	$0.101818\pi$
$368$	3.74915			0.195438
$369$		0			0
$370$	2.20382			0.114571
$371$	2.19305	+	3.79847i	0.113857	+	0.197207i
$372$		0			0
$373$	4.35411	−	7.54154i	0.225447	−	0.390486i	−0.731006	−	0.682371i	$-0.760949\pi$
$373$	4.35411	−	7.54154i	0.225447	−	0.390486i	0.956454	+	0.291885i	$0.0942823\pi$
$374$	0.130070	−	0.225288i	0.00672577	−	0.0116494i
$375$		0			0
$376$	−5.11631	−	8.86171i	−0.263854	−	0.457008i
$377$	−0.684942	−	1.18635i	−0.0352763	−	0.0611003i
$378$		0			0
$379$	12.2708	−	21.2536i	0.630307	−	1.09172i	−0.357182	−	0.934035i	$-0.616263\pi$
$379$	12.2708	−	21.2536i	0.630307	−	1.09172i	0.987489	−	0.157688i	$-0.0504041\pi$
$380$	0.671217	+	1.16258i	0.0344327	+	0.0596392i
$381$		0			0
$382$	−14.8837			−0.761516
$383$	−11.9253			−0.609356			−0.304678	−	0.952455i	$-0.598549\pi$
$383$	−11.9253			−0.609356			−0.304678	+	0.952455i	$0.598549\pi$
$384$		0			0
$385$	0.0408678	−	0.0707852i	0.00208282	−	0.00360755i
$386$	−9.35593	+	16.2050i	−0.476204	+	0.824810i
$387$		0			0
$388$	−5.42458			−0.275392
$389$	−35.2837			−1.78896			−0.894478	−	0.447113i	$-0.852452\pi$
$389$	−35.2837			−1.78896			−0.894478	+	0.447113i	$0.852452\pi$
$390$		0			0
$391$	−3.37470	−	5.84515i	−0.170666	−	0.295602i
$392$	5.98987			0.302534
$393$		0			0
$394$	−7.08002	+	12.2629i	−0.356686	+	0.617798i
$395$	3.29250			0.165664
$396$		0			0
$397$	−5.24729	+	9.08858i	−0.263354	+	0.456143i	−0.967131	−	0.254278i	$-0.918162\pi$
$397$	−5.24729	+	9.08858i	−0.263354	+	0.456143i	0.703777	+	0.710421i	$0.251495\pi$
$398$	4.65872	−	8.06915i	0.233521	−	0.404470i
$399$		0			0
$400$	2.34163	+	4.05583i	0.117082	+	0.202791i
$401$	−17.4404	+	30.2077i	−0.870933	+	1.50850i	−0.00989984	+	0.999951i	$0.503151\pi$
$401$	−17.4404	+	30.2077i	−0.870933	+	1.50850i	−0.861033	+	0.508549i	$0.830182\pi$
$402$		0			0
$403$	23.0581	+	12.5659i	1.14861	+	0.625954i
$404$	11.2676			0.560582
$405$		0			0
$406$	0.145959	−	0.252809i	0.00724383	−	0.0125467i
$407$	0.282927	+	0.490044i	0.0140242	+	0.0242906i
$408$		0			0
$409$	2.06271	+	3.57272i	0.101994	+	0.176660i	0.912506	−	0.409063i	$-0.134144\pi$
$409$	2.06271	+	3.57272i	0.101994	+	0.176660i	−0.810512	+	0.585722i	$0.800811\pi$
$410$	−0.429501	−	0.743918i	−0.0212116	−	0.0367395i
$411$		0			0
$412$	5.67780	−	9.83424i	0.279725	−	0.484498i
$413$	0.589032	+	1.02023i	0.0289843	+	0.0502024i
$414$		0			0
$415$	1.73768	−	3.00976i	0.0852996	−	0.147743i
$416$	−2.35820	+	4.08453i	−0.115620	+	0.200261i
$417$		0			0
$418$	−0.172343	+	0.298506i	−0.00842955	+	0.0146004i
$419$	4.66325	−	8.07699i	0.227815	−	0.394587i	−0.729345	−	0.684146i	$-0.760175\pi$
$419$	4.66325	−	8.07699i	0.227815	−	0.394587i	0.957160	+	0.289559i	$0.0935086\pi$
$420$		0			0
$421$	13.5827	−	23.5260i	0.661982	−	1.14659i	−0.318112	−	0.948053i	$-0.603049\pi$
$421$	13.5827	−	23.5260i	0.661982	−	1.14659i	0.980094	−	0.198534i	$-0.0636179\pi$
$422$	−4.01230	+	6.94950i	−0.195315	+	0.338296i
$423$		0			0
$424$	2.18202	+	3.77937i	0.105968	+	0.183542i
$425$	4.21552	−	7.30149i	0.204483	−	0.354174i
$426$		0			0
$427$	−1.69765	−	2.94041i	−0.0821549	−	0.142296i
$428$	−7.45699	−	12.9159i	−0.360447	−	0.624313i
$429$		0			0
$430$	−2.56380	−	4.44063i	−0.123637	−	0.214146i
$431$	12.0917	−	20.9434i	0.582435	−	1.00881i	−0.412755	−	0.910842i	$-0.635433\pi$
$431$	12.0917	−	20.9434i	0.582435	−	1.00881i	0.995190	−	0.0979652i	$-0.0312334\pi$
$432$		0			0
$433$	−12.9103			−0.620429			−0.310215	−	0.950667i	$-0.600401\pi$
$433$	−12.9103			−0.620429			−0.310215	+	0.950667i	$0.600401\pi$
$434$	0.137796	+	5.59421i	0.00661442	+	0.268531i
$435$		0			0
$436$	1.63592	−	2.83350i	0.0783464	−	0.135700i
$437$	4.47147	+	7.74481i	0.213899	+	0.370484i
$438$		0			0
$439$	−2.14079	+	3.70795i	−0.102174	+	0.176971i	−0.912580	−	0.408898i	$-0.865913\pi$
$439$	−2.14079	+	3.70795i	−0.102174	+	0.176971i	0.810406	+	0.585869i	$0.199247\pi$
$440$	0.0406623	−	0.0704292i	0.00193850	−	0.00335758i
$441$		0			0
$442$	8.49069			0.403861
$443$	−11.5049	+	19.9272i	−0.546616	+	0.946767i	0.451887	+	0.892075i	$0.350751\pi$
$443$	−11.5049	+	19.9272i	−0.546616	+	0.946767i	−0.998503	+	0.0546922i	$0.982582\pi$
$444$		0			0
$445$	3.62531			0.171856
$446$	−7.26363	−	12.5810i	−0.343943	−	0.595727i
$447$		0			0
$448$	−1.00505			−0.0474843
$449$	0.738049			0.0348307			0.0174153	−	0.999848i	$-0.494456\pi$
$449$	0.738049			0.0348307			0.0174153	+	0.999848i	$0.494456\pi$
$450$		0			0
$451$	0.110279	−	0.191009i	0.00519285	−	0.00899427i
$452$	−3.10728	+	5.38197i	−0.146154	+	0.253147i
$453$		0			0
$454$	18.8216			0.883341
$455$	2.66776			0.125067
$456$		0			0
$457$	−18.3750	−	31.8265i	−0.859548	−	1.48878i	−0.872361	−	0.488863i	$-0.837412\pi$
$457$	−18.3750	−	31.8265i	−0.859548	−	1.48878i	0.0128131	−	0.999918i	$-0.495921\pi$
$458$	0.879392	−	1.52315i	0.0410913	−	0.0711722i
$459$		0			0
$460$	−1.05499	−	1.82730i	−0.0491893	−	0.0851984i
$461$	−12.6047	−	21.8321i	−0.587062	−	1.01682i	−0.994615	−	0.103639i	$-0.966951\pi$
$461$	−12.6047	−	21.8321i	−0.587062	−	1.01682i	0.407553	−	0.913181i	$-0.366382\pi$
$462$		0			0
$463$	1.36131	−	2.35786i	0.0632655	−	0.109579i	−0.832658	−	0.553788i	$-0.813182\pi$
$463$	1.36131	−	2.35786i	0.0632655	−	0.109579i	0.895923	+	0.444209i	$0.146515\pi$
$464$	0.145225	−	0.251538i	0.00674191	−	0.0116773i
$465$		0			0
$466$	11.6185	+	20.1239i	0.538217	+	0.932219i
$467$	−2.41485			−0.111746			−0.0558730	−	0.998438i	$-0.517794\pi$
$467$	−2.41485			−0.111746			−0.0558730	+	0.998438i	$0.517794\pi$
$468$		0			0
$469$	11.8000			0.544874
$470$	−2.87941	+	4.98728i	−0.132817	+	0.230046i
$471$		0			0
$472$	0.586070	+	1.01510i	0.0269760	+	0.0467239i
$473$	0.658284	−	1.14018i	0.0302679	−	0.0524256i
$474$		0			0
$475$	−5.58555	+	9.67445i	−0.256282	+	0.443894i
$476$	0.904672	+	1.56694i	0.0414656	+	0.0718205i
$477$		0			0
$478$	−4.44457	−	7.69823i	−0.203290	−	0.352109i
$479$	−32.6616			−1.49235			−0.746173	−	0.665752i	$-0.768111\pi$
$479$	−32.6616			−1.49235			−0.746173	+	0.665752i	$0.768111\pi$
$480$		0			0
$481$	−9.23444	+	15.9945i	−0.421054	+	0.729287i
$482$	−7.36589	−	12.7581i	−0.335507	−	0.581115i
$483$		0			0
$484$	−10.9791			−0.499051
$485$	1.52645	+	2.64389i	0.0693126	+	0.120053i
$486$		0			0
$487$	−18.4595	−	31.9728i	−0.836480	−	1.44883i	−0.892819	−	0.450415i	$-0.851276\pi$
$487$	−18.4595	−	31.9728i	−0.836480	−	1.44883i	0.0563390	−	0.998412i	$-0.482057\pi$
$488$	−1.68911	−	2.92562i	−0.0764624	−	0.132437i
$489$		0			0
$490$	−1.68552	−	2.91940i	−0.0761440	−	0.131885i
$491$	−14.1020			−0.636415			−0.318207	−	0.948021i	$-0.603081\pi$
$491$	−14.1020			−0.636415			−0.318207	+	0.948021i	$0.603081\pi$
$492$		0			0
$493$	−0.522882			−0.0235494
$494$	−11.2501			−0.506168
$495$		0			0
$496$	0.137103	+	5.56608i	0.00615611	+	0.249924i
$497$	2.95383	+	5.11618i	0.132497	+	0.229492i
$498$		0			0
$499$	17.1482	+	29.7016i	0.767659	+	1.32962i	0.938829	+	0.344383i	$0.111912\pi$
$499$	17.1482	+	29.7016i	0.767659	+	1.32962i	−0.171170	+	0.985241i	$0.554755\pi$
$500$	2.72482	−	4.71953i	0.121858	−	0.211064i
$501$		0			0
$502$	−3.83569			−0.171195
$503$	−9.19335	+	15.9234i	−0.409911	+	0.709987i	−0.994879	−	0.101069i	$-0.967774\pi$
$503$	−9.19335	+	15.9234i	−0.409911	+	0.709987i	0.584968	+	0.811056i	$0.301107\pi$
$504$		0			0
$505$	−3.17063	−	5.49170i	−0.141091	−	0.244377i
$506$	0.270881	−	0.469180i	0.0120421	−	0.0208576i
$507$		0			0
$508$	1.36027	+	2.35605i	0.0603520	+	0.104533i
$509$	26.3867			1.16957			0.584786	−	0.811188i	$-0.301178\pi$
$509$	26.3867			1.16957			0.584786	+	0.811188i	$0.301178\pi$
$510$		0			0
$511$	−2.11873	−	3.66975i	−0.0937273	−	0.162340i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.31303	+	7.47039i	0.190240	+	0.329505i
$515$	−6.39082			−0.281613
$516$		0			0
$517$	−1.47864			−0.0650305
$518$	−3.93567			−0.172923
$519$		0			0
$520$	2.65435			0.116401
$521$	−16.4542	+	28.4995i	−0.720871	+	1.24859i	0.239780	+	0.970827i	$0.422925\pi$
$521$	−16.4542	+	28.4995i	−0.720871	+	1.24859i	−0.960651	+	0.277758i	$0.910409\pi$
$522$		0			0
$523$	−22.4005			−0.979506			−0.489753	−	0.871861i	$-0.662913\pi$
$523$	−22.4005			−0.979506			−0.489753	+	0.871861i	$0.662913\pi$
$524$	12.6041			0.550613
$525$		0			0
$526$	−11.0513	+	19.1415i	−0.481861	+	0.834608i
$527$	8.55443	−	5.22390i	0.372637	−	0.227557i
$528$		0			0
$529$	4.47193	+	7.74560i	0.194432	+	0.336765i
$530$	1.22802	−	2.12699i	0.0533417	−	0.0923906i
$531$		0			0
$532$	−1.19869	−	2.07619i	−0.0519697	−	0.0900142i
$533$	7.19879			0.311814
$534$		0			0
$535$	−4.19672	+	7.26894i	−0.181440	+	0.314264i
$536$	11.7407			0.507120
$537$		0			0
$538$	−7.76488	+	13.4492i	−0.334768	+	0.579835i
$539$	0.432776	−	0.749590i	0.0186410	−	0.0322871i
$540$		0			0
$541$	7.32005	−	12.6787i	0.314714	−	0.545100i	−0.664663	−	0.747143i	$-0.731425\pi$
$541$	7.32005	−	12.6787i	0.314714	−	0.545100i	0.979377	+	0.202043i	$0.0647582\pi$
$542$	−12.2954	−	21.2963i	−0.528134	−	0.914755i
$543$		0			0
$544$	0.900123	+	1.55906i	0.0385924	+	0.0668441i
$545$	−1.84136			−0.0788752
$546$		0			0
$547$	5.27049	−	9.12876i	0.225350	−	0.390318i	−0.731074	−	0.682298i	$-0.760981\pi$
$547$	5.27049	−	9.12876i	0.225350	−	0.390318i	0.956424	+	0.291980i	$0.0943141\pi$
$548$	3.18632	+	5.51886i	0.136113	+	0.235754i
$549$		0			0
$550$	0.676744			0.0288565
$551$	0.692818			0.0295150
$552$		0			0
$553$	−5.87988			−0.250038
$554$	2.42178	−	4.19464i	0.102891	−	0.178213i
$555$		0			0
$556$	2.25964	+	3.91382i	0.0958302	+	0.165983i
$557$	20.9081			0.885905			0.442952	−	0.896545i	$-0.353931\pi$
$557$	20.9081			0.885905			0.442952	+	0.896545i	$0.353931\pi$
$558$		0			0
$559$	42.9713			1.81749
$560$	0.282817	+	0.489854i	0.0119512	+	0.0207001i
$561$		0			0
$562$	1.76336	−	3.05424i	0.0743830	−	0.128835i
$563$	−23.7565			−1.00122			−0.500608	−	0.865674i	$-0.666890\pi$
$563$	−23.7565			−1.00122			−0.500608	+	0.865674i	$0.666890\pi$
$564$		0			0
$565$	3.49749			0.147141
$566$	−1.94410			−0.0817165
$567$		0			0
$568$	2.93897	+	5.09045i	0.123317	+	0.213591i
$569$	17.2022	−	29.7950i	0.721152	−	1.24907i	−0.239386	−	0.970924i	$-0.576946\pi$
$569$	17.2022	−	29.7950i	0.721152	−	1.24907i	0.960538	−	0.278148i	$-0.0897205\pi$
$570$		0			0
$571$	3.81450			0.159632			0.0798159	−	0.996810i	$-0.474567\pi$
$571$	3.81450			0.159632			0.0798159	+	0.996810i	$0.474567\pi$
$572$	0.340767	+	0.590225i	0.0142482	+	0.0246786i
$573$		0			0
$574$	0.767021	+	1.32852i	0.0320148	+	0.0554513i
$575$	8.77914	−	15.2059i	0.366116	−	0.634131i
$576$		0			0
$577$	−15.1861	+	26.3032i	−0.632207	+	1.09502i	0.354892	+	0.934907i	$0.384518\pi$
$577$	−15.1861	+	26.3032i	−0.632207	+	1.09502i	−0.987100	+	0.160108i	$0.948816\pi$
$578$	−6.87956	+	11.9157i	−0.286152	+	0.495630i
$579$		0			0
$580$	−0.163463			−0.00678742
$581$	−3.10323	+	5.37495i	−0.128744	+	0.222991i
$582$		0			0
$583$	0.630615			0.0261174
$584$	−2.10808	−	3.65130i	−0.0872330	−	0.151092i
$585$		0			0
$586$	−11.0367	+	19.1162i	−0.455923	+	0.789682i
$587$	−5.22247	−	9.04558i	−0.215554	−	0.373351i	0.737890	−	0.674921i	$-0.235822\pi$
$587$	−5.22247	−	9.04558i	−0.215554	−	0.373351i	−0.953444	+	0.301570i	$0.902489\pi$
$588$		0			0
$589$	−11.3346	+	6.92166i	−0.467034	+	0.285202i
$590$	0.329834	−	0.571289i	0.0135791	−	0.0235196i
$591$		0			0
$592$	−3.91588			−0.160942
$593$	37.7447			1.54999			0.774995	−	0.631968i	$-0.217753\pi$
$593$	37.7447			1.54999			0.774995	+	0.631968i	$0.217753\pi$
$594$		0			0
$595$	0.509140	−	0.881857i	0.0208727	−	0.0361526i
$596$	−4.89186			−0.200378
$597$		0			0
$598$	17.6825			0.723093
$599$	−38.8992			−1.58938			−0.794690	−	0.607016i	$-0.792367\pi$
$599$	−38.8992			−1.58938			−0.794690	+	0.607016i	$0.792367\pi$
$600$		0			0
$601$	−19.9963			−0.815667			−0.407834	−	0.913056i	$-0.633716\pi$
$601$	−19.9963			−0.815667			−0.407834	+	0.913056i	$0.633716\pi$
$602$	4.57854	+	7.93026i	0.186607	+	0.323213i
$603$		0			0
$604$	24.1173			0.981320
$605$	3.08947	+	5.35112i	0.125605	+	0.217554i
$606$		0			0
$607$	−26.8055			−1.08800			−0.544000	−	0.839085i	$-0.683091\pi$
$607$	−26.8055			−1.08800			−0.544000	+	0.839085i	$0.683091\pi$
$608$	−1.19266	−	2.06575i	−0.0483688	−	0.0837772i
$609$		0			0
$610$	−0.950614	+	1.64651i	−0.0384893	+	0.0666653i
$611$	−24.1306	−	41.7954i	−0.976220	−	1.69086i
$612$		0			0
$613$	−0.164854	+	0.285536i	−0.00665840	+	0.0115327i	−0.869335	−	0.494223i	$-0.835453\pi$
$613$	−0.164854	+	0.285536i	−0.00665840	+	0.0115327i	0.862677	+	0.505755i	$0.168786\pi$
$614$	−17.0239			−0.687027
$615$		0			0
$616$	−0.0726165	+	0.125775i	−0.00292580	+	0.00506764i
$617$	−17.0312	−	29.4990i	−0.685652	−	1.18758i	−0.973232	−	0.229827i	$-0.926184\pi$
$617$	−17.0312	−	29.4990i	−0.685652	−	1.18758i	0.287580	−	0.957757i	$-0.407149\pi$
$618$		0			0
$619$	10.7938	+	18.6954i	0.433838	+	0.751430i	0.997200	−	0.0747805i	$-0.0238256\pi$
$619$	10.7938	+	18.6954i	0.433838	+	0.751430i	−0.563362	+	0.826210i	$0.690492\pi$
$620$	2.67427	−	1.63309i	0.107401	−	0.0655864i
$621$		0			0
$622$	−9.68326			−0.388263
$623$	−6.47422			−0.259384
$624$		0			0
$625$	20.3493			0.813973
$626$	0.386686	+	0.669760i	0.0154551	+	0.0267690i
$627$		0			0
$628$	−2.71077	−	4.69520i	−0.108172	−	0.187359i
$629$	3.52477	+	6.10508i	0.140542	+	0.243425i
$630$		0			0
$631$	−1.47927	−	2.56218i	−0.0588889	−	0.101999i	0.835078	−	0.550132i	$-0.185422\pi$
$631$	−1.47927	−	2.56218i	−0.0588889	−	0.101999i	−0.893967	+	0.448133i	$0.852089\pi$
$632$	−5.85031			−0.232713
$633$		0			0
$634$	−7.24340	−	12.5459i	−0.287672	−	0.498263i
$635$	0.765544	−	1.32596i	0.0303797	−	0.0526192i
$636$		0			0
$637$	28.2507			1.11933
$638$	−0.0209854	−	0.0363478i	−0.000830821	−	0.00143902i
$639$		0			0
$640$	0.281395	+	0.487391i	0.0111231	+	0.0192658i
$641$	13.5699	−	23.5037i	0.535978	−	0.928341i	−0.463137	−	0.886287i	$-0.653276\pi$
$641$	13.5699	−	23.5037i	0.535978	−	0.928341i	0.999115	−	0.0420546i	$-0.0133903\pi$
$642$		0			0
$643$	21.2148	−	36.7450i	0.836628	−	1.44908i	−0.0560698	−	0.998427i	$-0.517857\pi$
$643$	21.2148	−	36.7450i	0.836628	−	1.44908i	0.892698	−	0.450656i	$-0.148810\pi$
$644$	1.88405	+	3.26327i	0.0742420	+	0.128591i
$645$		0			0
$646$	−2.14708	+	3.71885i	−0.0844758	+	0.146316i
$647$	23.6612			0.930219			0.465109	−	0.885253i	$-0.346015\pi$
$647$	23.6612			0.930219			0.465109	+	0.885253i	$0.346015\pi$
$648$		0			0
$649$	0.169377			0.00664864
$650$	11.0441	+	19.1289i	0.433185	+	0.750299i
$651$		0			0
$652$	−6.47930	+	11.2225i	−0.253749	+	0.439506i
$653$	−21.6145	+	37.4374i	−0.845840	+	1.46504i	0.0390505	+	0.999237i	$0.487567\pi$
$653$	−21.6145	+	37.4374i	−0.845840	+	1.46504i	−0.884890	+	0.465800i	$0.845767\pi$
$654$		0			0
$655$	−3.54673	−	6.14312i	−0.138582	−	0.240032i
$656$	0.763164	+	1.32184i	0.0297966	+	0.0516092i
$657$		0			0
$658$	5.14217	−	8.90650i	0.200463	−	0.347211i
$659$	11.6466	+	20.1725i	0.453686	+	0.785807i	0.998612	−	0.0526770i	$-0.0167754\pi$
$659$	11.6466	+	20.1725i	0.453686	+	0.785807i	−0.544925	+	0.838485i	$0.683442\pi$
$660$		0			0
$661$	17.1907			0.668640			0.334320	−	0.942460i	$-0.391493\pi$
$661$	17.1907			0.668640			0.334320	+	0.942460i	$0.391493\pi$
$662$	21.8175			0.847962
$663$		0			0
$664$	−3.08762	+	5.34792i	−0.119823	+	0.207540i
$665$	−0.674610	+	1.16846i	−0.0261602	+	0.0453109i
$666$		0			0
$667$	−1.08894			−0.0421641
$668$	−5.26551			−0.203729
$669$		0			0
$670$	−3.30377	−	5.72229i	−0.127636	−	0.221071i
$671$	−0.488162			−0.0188453
$672$		0			0
$673$	−21.1913	+	36.7044i	−0.816865	+	1.41485i	0.0911157	+	0.995840i	$0.470957\pi$
$673$	−21.1913	+	36.7044i	−0.816865	+	1.41485i	−0.907981	+	0.419012i	$0.862377\pi$
$674$	13.7192			0.528444
$675$		0			0
$676$	−4.62225	+	8.00598i	−0.177779	+	0.307922i
$677$	21.1735	−	36.6736i	0.813764	−	1.40948i	−0.0964477	−	0.995338i	$-0.530748\pi$
$677$	21.1735	−	36.6736i	0.813764	−	1.40948i	0.910212	−	0.414143i	$-0.135919\pi$
$678$		0			0
$679$	−2.72600	−	4.72157i	−0.104614	−	0.181197i
$680$	0.506580	−	0.877423i	0.0194265	−	0.0336476i
$681$		0			0
$682$	0.706461	+	0.384999i	0.0270518	+	0.0147424i
$683$	−7.88799			−0.301825			−0.150913	−	0.988547i	$-0.548221\pi$
$683$	−7.88799			−0.301825			−0.150913	+	0.988547i	$0.548221\pi$
$684$		0			0
$685$	1.79323	−	3.10596i	0.0685157	−	0.118673i
$686$	6.52776	+	11.3064i	0.249231	+	0.431681i
$687$		0			0
$688$	4.55551	+	7.89038i	0.173677	+	0.300818i
$689$	10.2913	+	17.8250i	0.392067	+	0.679080i
$690$		0			0
$691$	21.9346	−	37.9919i	0.834433	−	1.44528i	−0.0600577	−	0.998195i	$-0.519128\pi$
$691$	21.9346	−	37.9919i	0.834433	−	1.44528i	0.894491	−	0.447086i	$-0.147538\pi$
$692$	−5.98983	−	10.3747i	−0.227699	−	0.394387i
$693$		0			0
$694$	−7.16616	+	12.4122i	−0.272024	+	0.471159i
$695$	1.27170	−	2.20266i	0.0482385	−	0.0835516i
$696$		0			0
$697$	1.37388	−	2.37964i	0.0520395	−	0.0901351i
$698$	−7.33248	+	12.7002i	−0.277538	+	0.480710i
$699$		0			0
$700$	−2.35347	+	4.07633i	−0.0889527	+	0.154071i
$701$	0.0214641	−	0.0371768i	0.000810686	−	0.00140415i	−0.865620	−	0.500702i	$-0.833075\pi$
$701$	0.0214641	−	0.0371768i	0.000810686	−	0.00140415i	0.866430	+	0.499298i	$0.166409\pi$
$702$		0			0
$703$	−4.67031	−	8.08922i	−0.176144	−	0.305091i
$704$	−0.0722513	+	0.125143i	−0.00272307	+	0.00471650i
$705$		0			0
$706$	6.25046	+	10.8261i	0.235239	+	0.407446i
$707$	5.66225	+	9.80731i	0.212951	+	0.368842i
$708$		0			0
$709$	−14.5464	−	25.1950i	−0.546300	−	0.946220i	−0.998524	−	0.0543151i	$-0.982702\pi$
$709$	−14.5464	−	25.1950i	−0.546300	−	0.946220i	0.452224	−	0.891905i	$-0.350631\pi$
$710$	1.65402	−	2.86485i	0.0620744	−	0.107516i
$711$		0			0
$712$	−6.44167			−0.241412
$713$	17.8153	−	10.8792i	0.667187	−	0.407429i
$714$		0			0
$715$	0.191780	−	0.332173i	0.00717217	−	0.0124226i
$716$	6.85731	+	11.8772i	0.256270	+	0.443872i
$717$		0			0
$718$	−16.2102	+	28.0769i	−0.604961	+	1.04782i
$719$	2.08236	−	3.60676i	0.0776590	−	0.134509i	−0.824580	−	0.565745i	$-0.808589\pi$
$719$	2.08236	−	3.60676i	0.0776590	−	0.134509i	0.902240	+	0.431235i	$0.141922\pi$
$720$		0			0
$721$	11.4130			0.425042
$722$	−6.65512	+	11.5270i	−0.247678	+	0.428991i
$723$		0			0
$724$	−22.1782			−0.824247
$725$	−0.680129	−	1.17802i	−0.0252593	−	0.0437505i
$726$		0			0
$727$	−2.44996			−0.0908641			−0.0454320	−	0.998967i	$-0.514466\pi$
$727$	−2.44996			−0.0908641			−0.0454320	+	0.998967i	$0.514466\pi$
$728$	−4.74024			−0.175685
$729$		0			0
$730$	−1.18641	+	2.05492i	−0.0439109	+	0.0760559i
$731$	8.20105	−	14.2046i	0.303327	−	0.525377i
$732$		0			0
$733$	12.0610			0.445484			0.222742	−	0.974877i	$-0.428499\pi$
$733$	12.0610			0.445484			0.222742	+	0.974877i	$0.428499\pi$
$734$	7.75185			0.286126
$735$		0			0
$736$	1.87458	+	3.24686i	0.0690978	+	0.119681i
$737$	0.848279	−	1.46926i	0.0312468	−	0.0541210i
$738$		0			0
$739$	−22.3007	−	38.6259i	−0.820343	−	1.42088i	−0.905427	−	0.424502i	$-0.860449\pi$
$739$	−22.3007	−	38.6259i	−0.820343	−	1.42088i	0.0850836	−	0.996374i	$-0.472884\pi$
$740$	1.10191	+	1.90856i	0.0405070	+	0.0701601i
$741$		0			0
$742$	−2.19305	+	3.79847i	−0.0805093	+	0.139446i
$743$	−4.26426	+	7.38592i	−0.156441	+	0.270963i	−0.933583	−	0.358362i	$-0.883335\pi$
$743$	−4.26426	+	7.38592i	−0.156441	+	0.270963i	0.777142	+	0.629325i	$0.216669\pi$
$744$		0			0
$745$	1.37654	+	2.38425i	0.0504327	+	0.0873520i
$746$	8.70822			0.318831
$747$		0			0
$748$	0.260140			0.00951167
$749$	7.49468	−	12.9812i	0.273850	−	0.474322i
$750$		0			0
$751$	12.4273	+	21.5247i	0.453477	+	0.785446i	0.998599	−	0.0529110i	$-0.0168500\pi$
$751$	12.4273	+	21.5247i	0.453477	+	0.785446i	−0.545122	+	0.838357i	$0.683517\pi$
$752$	5.11631	−	8.86171i	0.186573	−	0.323153i
$753$		0			0
$754$	0.684942	−	1.18635i	0.0249441	−	0.0432044i
$755$	−6.78649	−	11.7546i	−0.246986	−	0.427792i
$756$		0			0
$757$	−0.273055	−	0.472945i	−0.00992435	−	0.0171895i	0.861021	−	0.508570i	$-0.169826\pi$
$757$	−0.273055	−	0.472945i	−0.00992435	−	0.0171895i	−0.870945	+	0.491381i	$0.836492\pi$
$758$	24.5415			0.891388
$759$		0			0
$760$	−0.671217	+	1.16258i	−0.0243476	+	0.0421713i
$761$	−11.0381	−	19.1186i	−0.400133	−	0.693050i	0.593609	−	0.804754i	$-0.297703\pi$
$761$	−11.0381	−	19.1186i	−0.400133	−	0.693050i	−0.993742	+	0.111704i	$0.964369\pi$
$762$		0			0
$763$	3.28838			0.119047
$764$	−7.44184	−	12.8897i	−0.269236	−	0.466331i
$765$		0			0
$766$	−5.96267	−	10.3276i	−0.215440	−	0.373153i
$767$	2.76414	+	4.78764i	0.0998074	+	0.172872i
$768$		0			0
$769$	−20.9975	−	36.3687i	−0.757188	−	1.31149i	−0.944279	−	0.329146i	$-0.893239\pi$
$769$	−20.9975	−	36.3687i	−0.757188	−	1.31149i	0.187091	−	0.982343i	$-0.440094\pi$
$770$	0.0817357			0.00294555
$771$		0			0
$772$	−18.7119			−0.673455
$773$	−46.8946			−1.68668			−0.843341	−	0.537379i	$-0.819415\pi$
$773$	−46.8946			−1.68668			−0.843341	+	0.537379i	$0.819415\pi$
$774$		0			0
$775$	22.8961	+	12.4776i	0.822452	+	0.448210i
$776$	−2.71229	−	4.69783i	−0.0973656	−	0.168642i
$777$		0			0
$778$	−17.6419	−	30.5566i	−0.632491	−	1.09551i
$779$	−1.82039	+	3.15301i	−0.0652223	+	0.112968i
$780$		0			0
$781$	0.849379			0.0303932
$782$	3.37470	−	5.84515i	0.120679	−	0.209022i
$783$		0			0
$784$	2.99493	+	5.18738i	0.106962	+	0.185263i
$785$	−1.52560	+	2.64241i	−0.0544509	+	0.0943116i
$786$		0			0
$787$	2.96881	+	5.14212i	0.105826	+	0.183297i	0.914076	−	0.405544i	$-0.132918\pi$
$787$	2.96881	+	5.14212i	0.105826	+	0.183297i	−0.808249	+	0.588841i	$0.799585\pi$
$788$	−14.1600			−0.504430
$789$		0			0
$790$	1.64625	+	2.85139i	0.0585709	+	0.101448i
$791$	−6.24597			−0.222081
$792$		0			0
$793$	−7.96653	−	13.7984i	−0.282900	−	0.489997i
$794$	−10.4946			−0.372439
$795$		0			0
$796$	9.31745			0.330248
$797$	−8.83594			−0.312985			−0.156492	−	0.987679i	$-0.550019\pi$
$797$	−8.83594			−0.312985			−0.156492	+	0.987679i	$0.550019\pi$
$798$		0			0
$799$	−18.4212			−0.651696
$800$	−2.34163	+	4.05583i	−0.0827893	+	0.143395i
$801$		0			0
$802$	−34.8808			−1.23169
$803$	−0.609246			−0.0214998
$804$		0			0
$805$	1.06032	−	1.83654i	0.0373715	−	0.0647294i
$806$	0.646634	+	26.2519i	0.0227767	+	0.924683i
$807$		0			0
$808$	5.63378	+	9.75799i	0.198196	+	0.343285i
$809$	−0.882494	+	1.52852i	−0.0310268	+	0.0537401i	−0.881122	−	0.472889i	$-0.843211\pi$
$809$	−0.882494	+	1.52852i	−0.0310268	+	0.0537401i	0.850095	+	0.526629i	$0.176544\pi$
$810$		0			0
$811$	−7.05458	−	12.2189i	−0.247720	−	0.429063i	0.715173	−	0.698947i	$-0.246348\pi$
$811$	−7.05458	−	12.2189i	−0.247720	−	0.429063i	−0.962893	+	0.269884i	$0.913015\pi$
$812$	0.291918			0.0102443
$813$		0			0
$814$	−0.282927	+	0.490044i	−0.00991659	+	0.0171760i
$815$	7.29297			0.255462
$816$		0			0
$817$	−10.8664	+	18.8211i	−0.380166	+	0.658467i
$818$	−2.06271	+	3.57272i	−0.0721210	+	0.124917i
$819$		0			0
$820$	0.429501	−	0.743918i	0.0149988	−	0.0259787i
$821$	−4.58364	−	7.93910i	−0.159970	−	0.277076i	0.774888	−	0.632099i	$-0.217806\pi$
$821$	−4.58364	−	7.93910i	−0.159970	−	0.277076i	−0.934858	+	0.355023i	$0.884473\pi$
$822$		0			0
$823$	−18.3062	−	31.7073i	−0.638114	−	1.10525i	−0.985846	−	0.167652i	$-0.946381\pi$
$823$	−18.3062	−	31.7073i	−0.638114	−	1.10525i	0.347732	−	0.937594i	$-0.386952\pi$
$824$	11.3556			0.395591
$825$		0			0
$826$	−0.589032	+	1.02023i	−0.0204950	+	0.0354984i
$827$	−23.9647	−	41.5081i	−0.833335	−	1.44338i	−0.895379	−	0.445306i	$-0.853095\pi$
$827$	−23.9647	−	41.5081i	−0.833335	−	1.44338i	0.0620432	−	0.998073i	$-0.480238\pi$
$828$		0			0
$829$	−41.7758			−1.45093			−0.725467	−	0.688257i	$-0.758376\pi$
$829$	−41.7758			−1.45093			−0.725467	+	0.688257i	$0.758376\pi$
$830$	3.47537			0.120632
$831$		0			0
$832$	−4.71641			−0.163512
$833$	5.39162	−	9.33855i	0.186808	−	0.323562i
$834$		0			0
$835$	1.48169	+	2.56636i	0.0512759	+	0.0888125i
$836$	−0.344685			−0.0119212
$837$		0			0
$838$	9.32651			0.322179
$839$	−10.7603	−	18.6374i	−0.371487	−	0.643435i	0.618307	−	0.785936i	$-0.287819\pi$
$839$	−10.7603	−	18.6374i	−0.371487	−	0.643435i	−0.989795	+	0.142502i	$0.954485\pi$
$840$		0			0
$841$	14.4578	−	25.0417i	0.498545	−	0.863506i
$842$	27.1655			0.936184
$843$		0			0
$844$	−8.02459			−0.276218
$845$	5.20272			0.178979
$846$		0			0
$847$	−5.51730	−	9.55625i	−0.189577	−	0.328357i
$848$	−2.18202	+	3.77937i	−0.0749309	+	0.129784i
$849$		0			0
$850$	8.43103			0.289182
$851$	7.34061	+	12.7143i	0.251633	+	0.435841i
$852$		0			0
$853$	16.3170	+	28.2618i	0.558682	+	0.967666i	0.997607	+	0.0691423i	$0.0220263\pi$
$853$	16.3170	+	28.2618i	0.558682	+	0.967666i	−0.438924	+	0.898524i	$0.644640\pi$
$854$	1.69765	−	2.94041i	0.0580923	−	0.100619i
$855$		0			0
$856$	7.45699	−	12.9159i	0.254875	−	0.441456i
$857$	26.6693	−	46.1927i	0.911007	−	1.57791i	0.0983637	−	0.995151i	$-0.468639\pi$
$857$	26.6693	−	46.1927i	0.911007	−	1.57791i	0.812644	−	0.582761i	$-0.198028\pi$
$858$		0			0
$859$	−4.57793			−0.156197			−0.0780985	−	0.996946i	$-0.524885\pi$
$859$	−4.57793			−0.156197			−0.0780985	+	0.996946i	$0.524885\pi$
$860$	2.56380	−	4.44063i	0.0874248	−	0.151424i
$861$		0			0
$862$	24.1833			0.823688
$863$	−25.5424	−	44.2408i	−0.869475	−	1.50597i	−0.862534	−	0.505999i	$-0.831124\pi$
$863$	−25.5424	−	44.2408i	−0.869475	−	1.50597i	−0.00694067	−	0.999976i	$-0.502209\pi$
$864$		0			0
$865$	−3.37102	+	5.83877i	−0.114618	+	0.198524i
$866$	−6.45515	−	11.1806i	−0.219355	−	0.379934i
$867$		0			0
$868$	−4.77583	+	2.91644i	−0.162102	+	0.0989904i
$869$	−0.422693	+	0.732126i	−0.0143389	+	0.0248357i
$870$		0			0
$871$	55.3738			1.87627
$872$	3.27184			0.110799
$873$		0			0
$874$	−4.47147	+	7.74481i	−0.151250	+	0.261972i
$875$	5.47719			0.185163
$876$		0			0
$877$	−17.7699			−0.600045			−0.300023	−	0.953932i	$-0.596994\pi$
$877$	−17.7699			−0.600045			−0.300023	+	0.953932i	$0.596994\pi$
$878$	−4.28157			−0.144496
$879$		0			0
$880$	0.0813246			0.00274145
$881$	−14.3083	−	24.7828i	−0.482060	−	0.834952i	0.517728	−	0.855545i	$-0.326778\pi$
$881$	−14.3083	−	24.7828i	−0.482060	−	0.834952i	−0.999788	+	0.0205930i	$0.993445\pi$
$882$		0			0
$883$	0.842196			0.0283421			0.0141711	−	0.999900i	$-0.495489\pi$
$883$	0.842196			0.0283421			0.0141711	+	0.999900i	$0.495489\pi$
$884$	4.24535	+	7.35316i	0.142786	+	0.247313i
$885$		0			0
$886$	−23.0099			−0.773032
$887$	−27.8755	−	48.2818i	−0.935968	−	1.62114i	−0.772899	−	0.634529i	$-0.781194\pi$
$887$	−27.8755	−	48.2818i	−0.935968	−	1.62114i	−0.163069	−	0.986615i	$-0.552139\pi$
$888$		0			0
$889$	−1.36714	+	2.36796i	−0.0458524	+	0.0794187i
$890$	1.81265	+	3.13961i	0.0607603	+	0.105240i
$891$		0			0
$892$	7.26363	−	12.5810i	0.243204	−	0.421242i
$893$	24.4081			0.816785
$894$		0			0
$895$	3.85922	−	6.68437i	0.129000	−	0.223434i
$896$	−0.502527	−	0.870402i	−0.0167882	−	0.0290781i
$897$		0			0
$898$	0.369024	+	0.639169i	0.0123145	+	0.0213293i
$899$	−0.0398217	−	1.61667i	−0.00132813	−	0.0539189i
$900$		0			0
$901$	7.85634			0.261733
$902$	0.220558			0.00734379
$903$		0			0
$904$	−6.21456			−0.206693
$905$	6.24084	+	10.8095i	0.207453	+	0.359318i
$906$		0			0
$907$	−13.9039	−	24.0823i	−0.461672	−	0.799640i	0.537372	−	0.843345i	$-0.319417\pi$
$907$	−13.9039	−	24.0823i	−0.461672	−	0.799640i	−0.999044	+	0.0437054i	$0.986084\pi$
$908$	9.41079	+	16.3000i	0.312308	+	0.540933i
$909$		0			0
$910$	1.33388	+	2.31035i	0.0442177	+	0.0765874i
$911$	3.19200			0.105756			0.0528778	−	0.998601i	$-0.483161\pi$
$911$	3.19200			0.105756			0.0528778	+	0.998601i	$0.483161\pi$
$912$		0			0
$913$	0.446170	+	0.772789i	0.0147661	+	0.0255756i
$914$	18.3750	−	31.8265i	0.607792	−	1.05273i
$915$		0			0
$916$	1.75878			0.0581119
$917$	6.33391	+	10.9706i	0.209164	+	0.362283i
$918$		0			0
$919$	−5.31857	−	9.21203i	−0.175443	−	0.303877i	0.764871	−	0.644183i	$-0.222803\pi$
$919$	−5.31857	−	9.21203i	−0.175443	−	0.303877i	−0.940315	+	0.340306i	$0.889469\pi$
$920$	1.05499	−	1.82730i	0.0347821	−	0.0602444i
$921$		0			0
$922$	12.6047	−	21.8321i	0.415115	−	0.719001i
$923$	13.8614	+	24.0086i	0.456253	+	0.790254i
$924$		0			0
$925$	−9.16955	+	15.8821i	−0.301493	+	0.522201i
$926$	2.72262			0.0894710
$927$		0			0
$928$	0.290450			0.00953450
$929$	12.4243	+	21.5195i	0.407628	+	0.706032i	0.994623	−	0.103558i	$-0.0330227\pi$
$929$	12.4243	+	21.5195i	0.407628	+	0.706032i	−0.586995	+	0.809590i	$0.699689\pi$
$930$		0			0
$931$	−7.14388	+	12.3736i	−0.234131	+	0.405527i
$932$	−11.6185	+	20.1239i	−0.380577	+	0.659179i
$933$		0			0
$934$	−1.20742	−	2.09132i	−0.0395081	−	0.0684301i
$935$	−0.0732022	−	0.126790i	−0.00239397	−	0.00414647i
$936$		0			0
$937$	−18.2775	+	31.6576i	−0.597100	+	1.03421i	0.396147	+	0.918187i	$0.370347\pi$
$937$	−18.2775	+	31.6576i	−0.597100	+	1.03421i	−0.993247	+	0.116020i	$0.962986\pi$
$938$	5.90000	+	10.2191i	0.192642	+	0.333666i
$939$		0			0
$940$	−5.75882			−0.187832
$941$	−8.79709			−0.286777			−0.143389	−	0.989666i	$-0.545800\pi$
$941$	−8.79709			−0.286777			−0.143389	+	0.989666i	$0.545800\pi$
$942$		0			0
$943$	2.86122	−	4.95578i	0.0931741	−	0.161382i
$944$	−0.586070	+	1.01510i	−0.0190749	+	0.0330388i
$945$		0			0
$946$	1.31657			0.0428053
$947$	12.1166			0.393737			0.196869	−	0.980430i	$-0.436923\pi$
$947$	12.1166			0.393737			0.196869	+	0.980430i	$0.436923\pi$
$948$		0			0
$949$	−9.94256	−	17.2210i	−0.322749	−	0.559018i
$950$	−11.1711			−0.362438
$951$		0			0
$952$	−0.904672	+	1.56694i	−0.0293206	+	0.0507848i
$953$	55.8909			1.81048			0.905242	−	0.424897i	$-0.139690\pi$
$953$	55.8909			1.81048			0.905242	+	0.424897i	$0.139690\pi$
$954$		0			0
$955$	−4.18820	+	7.25417i	−0.135527	+	0.234739i
$956$	4.44457	−	7.69823i	0.143748	−	0.248979i
$957$		0			0
$958$	−16.3308	−	28.2858i	−0.527624	−	0.913872i
$959$	−3.20242	+	5.54676i	−0.103412	+	0.179114i
$960$		0			0
$961$	16.8030	+	26.0511i	0.542031	+	0.840358i
$962$	−18.4689			−0.595460
$963$		0			0
$964$	7.36589	−	12.7581i	0.237239	−	0.410911i
$965$	5.26543	+	9.11999i	0.169500	+	0.293583i
$966$		0			0
$967$	−16.2203	−	28.0944i	−0.521611	−	0.903456i	−0.999684	−	0.0251363i	$-0.991998\pi$
$967$	−16.2203	−	28.0944i	−0.521611	−	0.903456i	0.478073	−	0.878320i	$-0.341335\pi$
$968$	−5.48956	−	9.50820i	−0.176441	−	0.305605i
$969$		0			0
$970$	−1.52645	+	2.64389i	−0.0490114	+	0.0848902i
$971$	−22.2476	−	38.5340i	−0.713960	−	1.23662i	−0.963359	−	0.268215i	$-0.913566\pi$
$971$	−22.2476	−	38.5340i	−0.713960	−	1.23662i	0.249399	−	0.968401i	$-0.419767\pi$
$972$		0			0
$973$	−2.27106	+	3.93360i	−0.0728070	+	0.126105i
$974$	18.4595	−	31.9728i	0.591481	−	1.02448i
$975$		0			0
$976$	1.68911	−	2.92562i	0.0540671	−	0.0936470i
$977$	−16.0697	+	27.8336i	−0.514117	+	0.890476i	0.485749	+	0.874098i	$0.338547\pi$
$977$	−16.0697	+	27.8336i	−0.514117	+	0.890476i	−0.999866	+	0.0163780i	$0.994786\pi$
$978$		0			0
$979$	−0.465419	+	0.806129i	−0.0148748	+	0.0257640i
$980$	1.68552	−	2.91940i	0.0538419	−	0.0932569i
$981$		0			0
$982$	−7.05101	−	12.2127i	−0.225007	−	0.389723i
$983$	−28.3851	+	49.1645i	−0.905345	+	1.56810i	−0.0848916	+	0.996390i	$0.527054\pi$
$983$	−28.3851	+	49.1645i	−0.905345	+	1.56810i	−0.820453	+	0.571713i	$0.806279\pi$
$984$		0			0
$985$	3.98456	+	6.90147i	0.126959	+	0.219899i
$986$	−0.261441	−	0.452829i	−0.00832598	−	0.0144210i
$987$		0			0
$988$	−5.62507	−	9.74291i	−0.178957	−	0.309963i
$989$	17.0793	−	29.5823i	0.543091	−	0.940661i
$990$		0			0
$991$	−39.3750			−1.25079			−0.625394	−	0.780309i	$-0.715062\pi$
$991$	−39.3750			−1.25079			−0.625394	+	0.780309i	$0.715062\pi$
$992$	−4.75181	+	2.90177i	−0.150870	+	0.0921314i
$993$		0			0
$994$	−2.95383	+	5.11618i	−0.0936897	+	0.162275i
$995$	−2.62188	−	4.54124i	−0.0831193	−	0.143967i
$996$		0			0
$997$	−29.2868	+	50.7263i	−0.927524	+	1.60652i	−0.140073	+	0.990141i	$0.544734\pi$
$997$	−29.2868	+	50.7263i	−0.927524	+	1.60652i	−0.787451	+	0.616377i	$0.788600\pi$
$998$	−17.1482	+	29.7016i	−0.542817	+	0.940186i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.h.b.253.10		32
3.2	odd	2		558.2.h.a.67.8	yes	32
9.2	odd	6		558.2.g.a.439.4	yes	32
9.7	even	3		1674.2.g.b.1369.7		32
31.25	even	3		1674.2.g.b.955.7		32
93.56	odd	6		558.2.g.a.211.4	✓	32
279.25	even	3	inner	1674.2.h.b.397.10		32
279.56	odd	6		558.2.h.a.25.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.g.a.211.4	✓	32	93.56	odd	6
558.2.g.a.439.4	yes	32	9.2	odd	6
558.2.h.a.25.8	yes	32	279.56	odd	6
558.2.h.a.67.8	yes	32	3.2	odd	2
1674.2.g.b.955.7		32	31.25	even	3
1674.2.g.b.1369.7		32	9.7	even	3
1674.2.h.b.253.10		32	1.1	even	1	trivial
1674.2.h.b.397.10		32	279.25	even	3	inner

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:	\( N \)	\(=\)	\( 1674 = 2 \cdot 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1674.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +0.562790 q^{5} -1.00505 q^{7} -1.00000 q^{8} +(0.281395 + 0.487391i) q^{10} +(-0.0722513 + 0.125143i) q^{11} -4.71641 q^{13} +(-0.502527 - 0.870402i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.900123 + 1.55906i) q^{17} +(1.19266 - 2.06575i) q^{19} +(-0.281395 + 0.487391i) q^{20} -0.144503 q^{22} +(-1.87458 + 3.24686i) q^{23} -4.68327 q^{25} +(-2.35820 - 4.08453i) q^{26} +(0.502527 - 0.870402i) q^{28} +(0.145225 + 0.251538i) q^{29} +(-4.88891 - 2.66430i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.80025 q^{34} -0.565634 q^{35} +(1.95794 - 3.39125i) q^{37} +2.38532 q^{38} -0.562790 q^{40} -1.52633 q^{41} -9.11103 q^{43} +(-0.0722513 - 0.125143i) q^{44} -3.74915 q^{46} +(5.11631 + 8.86171i) q^{47} -5.98987 q^{49} +(-2.34163 - 4.05583i) q^{50} +(2.35820 - 4.08453i) q^{52} +(-2.18202 - 3.77937i) q^{53} +(-0.0406623 + 0.0704292i) q^{55} +1.00505 q^{56} +(-0.145225 + 0.251538i) q^{58} +(-0.586070 - 1.01510i) q^{59} +(1.68911 + 2.92562i) q^{61} +(-0.137103 - 5.56608i) q^{62} +1.00000 q^{64} -2.65435 q^{65} -11.7407 q^{67} +(-0.900123 - 1.55906i) q^{68} +(-0.282817 - 0.489854i) q^{70} +(-2.93897 - 5.09045i) q^{71} +(2.10808 + 3.65130i) q^{73} +3.91588 q^{74} +(1.19266 + 2.06575i) q^{76} +(0.0726165 - 0.125775i) q^{77} +5.85031 q^{79} +(-0.281395 - 0.487391i) q^{80} +(-0.763164 - 1.32184i) q^{82} +(3.08762 - 5.34792i) q^{83} +(-0.506580 + 0.877423i) q^{85} +(-4.55551 - 7.89038i) q^{86} +(0.0722513 - 0.125143i) q^{88} +6.44167 q^{89} +4.74024 q^{91} +(-1.87458 - 3.24686i) q^{92} +(-5.11631 + 8.86171i) q^{94} +(0.671217 - 1.16258i) q^{95} +(2.71229 + 4.69783i) q^{97} +(-2.99493 - 5.18738i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 2 q^{5} - 2 q^{7} - 32 q^{8} - q^{10} + 2 q^{11} + 20 q^{13} - q^{14} - 16 q^{16} + 4 q^{17} + 4 q^{19} + q^{20} + 4 q^{22} + q^{23} + 38 q^{25} + 10 q^{26} + q^{28} + 3 q^{29}+ \cdots + 13 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 2 * q^5 - 2 * q^7 - 32 * q^8 - q^10 + 2 * q^11 + 20 * q^13 - q^14 - 16 * q^16 + 4 * q^17 + 4 * q^19 + q^20 + 4 * q^22 + q^23 + 38 * q^25 + 10 * q^26 + q^28 + 3 * q^29 - 10 * q^31 + 16 * q^32 + 8 * q^34 - 19 * q^37 + 8 * q^38 + 2 * q^40 + 20 * q^41 + 26 * q^43 + 2 * q^44 + 2 * q^46 + 6 * q^47 + 26 * q^49 + 19 * q^50 - 10 * q^52 + 7 * q^53 - 11 * q^55 + 2 * q^56 - 3 * q^58 + 6 * q^59 + 7 * q^61 - 11 * q^62 + 32 * q^64 - 16 * q^65 + 16 * q^67 + 4 * q^68 - 7 * q^71 + 7 * q^73 - 38 * q^74 + 4 * q^76 + q^77 + 68 * q^79 + q^80 + 10 * q^82 - 14 * q^83 + 13 * q^85 + 13 * q^86 - 2 * q^88 - 2 * q^89 + 24 * q^91 + q^92 - 6 * q^94 - 21 * q^95 + 10 * q^97 + 13 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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