LMFDB - Embedded newform 351.2.l.b.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(127,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("351.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	351.199
Dual form			351.2.l.b.127.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.93463i q^{2} -1.74278 q^{4} +(2.26677 + 1.30872i) q^{5} +(2.01692 + 1.16447i) q^{7} -0.497616i q^{8} +(2.53189 - 4.38536i) q^{10} +5.38716i q^{11} +(3.56568 - 0.534742i) q^{13} +(2.25282 - 3.90199i) q^{14} -4.44827 q^{16} +(-0.835786 - 1.44762i) q^{17} +(1.90355 - 1.09901i) q^{19} +(-3.95050 - 2.28082i) q^{20} +10.4221 q^{22} +(-2.10438 - 3.64489i) q^{23} +(0.925505 + 1.60302i) q^{25} +(-1.03453 - 6.89826i) q^{26} +(-3.51506 - 2.02942i) q^{28} -5.72509 q^{29} +(-7.55059 - 4.35934i) q^{31} +7.61052i q^{32} +(-2.80061 + 1.61693i) q^{34} +(3.04794 + 5.27918i) q^{35} +(-1.22479 - 0.707130i) q^{37} +(-2.12618 - 3.68265i) q^{38} +(0.651240 - 1.12798i) q^{40} +(1.31938 - 0.761744i) q^{41} +(-0.938835 + 1.62611i) q^{43} -9.38866i q^{44} +(-7.05150 + 4.07119i) q^{46} +(-4.47809 + 2.58543i) q^{47} +(-0.788015 - 1.36488i) q^{49} +(3.10125 - 1.79051i) q^{50} +(-6.21421 + 0.931939i) q^{52} +9.81151 q^{53} +(-7.05029 + 12.2115i) q^{55} +(0.579459 - 1.00365i) q^{56} +11.0759i q^{58} +7.61266i q^{59} +(0.467085 - 0.809015i) q^{61} +(-8.43369 + 14.6076i) q^{62} +5.82698 q^{64} +(8.78241 + 3.45434i) q^{65} +(-1.79128 + 1.03420i) q^{67} +(1.45659 + 2.52290i) q^{68} +(10.2133 - 5.89662i) q^{70} +(10.9702 - 6.33363i) q^{71} -12.6627i q^{73} +(-1.36803 + 2.36950i) q^{74} +(-3.31747 + 1.91534i) q^{76} +(-6.27319 + 10.8655i) q^{77} +(3.46731 + 6.00556i) q^{79} +(-10.0832 - 5.82155i) q^{80} +(-1.47369 - 2.55251i) q^{82} +(7.95495 - 4.59279i) q^{83} -4.37524i q^{85} +(3.14592 + 1.81630i) q^{86} +2.68073 q^{88} +(-8.62292 - 4.97845i) q^{89} +(7.81439 + 3.07359i) q^{91} +(3.66748 + 6.35226i) q^{92} +(5.00184 + 8.66343i) q^{94} +5.75321 q^{95} +(2.03695 + 1.17603i) q^{97} +(-2.64054 + 1.52452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) $ 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.93463i		−	1.36799i	−0.729487	−	0.683994i	$-0.760241\pi$
$2$		−	1.93463i		−	1.36799i	0.729487	−	0.683994i	$-0.239759\pi$
$3$		0			0
$3$		0			0
$4$	−1.74278			−0.871392
$5$	2.26677	+	1.30872i	1.01373	+	0.585278i	0.912282	−	0.409563i	$-0.134319\pi$
$5$	2.26677	+	1.30872i	1.01373	+	0.585278i	0.101449	+	0.994841i	$0.467652\pi$
$6$		0			0
$7$	2.01692	+	1.16447i	0.762325	+	0.440129i	0.830130	−	0.557570i	$-0.188266\pi$
$7$	2.01692	+	1.16447i	0.762325	+	0.440129i	−0.0678048	+	0.997699i	$0.521600\pi$
$8$		−	0.497616i		−	0.175934i
$9$		0			0
$10$	2.53189	−	4.38536i	0.800654	−	1.38677i
$11$			5.38716i			1.62429i	0.583456	+	0.812145i	$0.301700\pi$
$11$			5.38716i			1.62429i	−0.583456	+	0.812145i	$0.698300\pi$
$12$		0			0
$13$	3.56568	−	0.534742i	0.988941	−	0.148311i
$13$	3.56568	−	0.534742i	0.988941	−	0.148311i
$14$	2.25282	−	3.90199i	0.602091	−	1.04285i
$15$		0			0
$16$	−4.44827			−1.11207
$17$	−0.835786	−	1.44762i	−0.202708	−	0.351100i	0.746692	−	0.665170i	$-0.231641\pi$
$17$	−0.835786	−	1.44762i	−0.202708	−	0.351100i	−0.949400	+	0.314069i	$0.898308\pi$
$18$		0			0
$19$	1.90355	−	1.09901i	0.436703	−	0.252131i	−0.265495	−	0.964112i	$-0.585535\pi$
$19$	1.90355	−	1.09901i	0.436703	−	0.252131i	0.702198	+	0.711982i	$0.252202\pi$
$20$	−3.95050	−	2.28082i	−0.883358	−	0.510007i
$21$		0			0
$22$	10.4221			2.22201
$23$	−2.10438	−	3.64489i	−0.438793	−	0.760012i	0.558804	−	0.829300i	$-0.311261\pi$
$23$	−2.10438	−	3.64489i	−0.438793	−	0.760012i	−0.997597	+	0.0692882i	$0.977927\pi$
$24$		0			0
$25$	0.925505	+	1.60302i	0.185101	+	0.320604i
$26$	−1.03453	−	6.89826i	−0.202887	−	1.35286i
$27$		0			0
$28$	−3.51506	−	2.02942i	−0.664284	−	0.383525i
$29$	−5.72509			−1.06312			−0.531561	−	0.847020i	$-0.678394\pi$
$29$	−5.72509			−1.06312			−0.531561	+	0.847020i	$0.678394\pi$
$30$		0			0
$31$	−7.55059	−	4.35934i	−1.35613	−	0.782960i	−0.367027	−	0.930210i	$-0.619624\pi$
$31$	−7.55059	−	4.35934i	−1.35613	−	0.782960i	−0.989099	+	0.147251i	$0.952958\pi$
$32$			7.61052i			1.34536i
$33$		0			0
$34$	−2.80061	+	1.61693i	−0.480301	+	0.277302i
$35$	3.04794	+	5.27918i	0.515195	+	0.892344i
$36$		0			0
$37$	−1.22479	−	0.707130i	−0.201354	−	0.116252i	0.395933	−	0.918279i	$-0.370421\pi$
$37$	−1.22479	−	0.707130i	−0.201354	−	0.116252i	−0.597287	+	0.802028i	$0.703755\pi$
$38$	−2.12618	−	3.68265i	−0.344912	−	0.597405i
$39$		0			0
$40$	0.651240	−	1.12798i	0.102970	−	0.178350i
$41$	1.31938	−	0.761744i	0.206052	−	0.118964i	−0.393423	−	0.919358i	$-0.628709\pi$
$41$	1.31938	−	0.761744i	0.206052	−	0.118964i	0.599475	+	0.800393i	$0.295376\pi$
$42$		0			0
$43$	−0.938835	+	1.62611i	−0.143171	+	0.247979i	−0.928689	−	0.370859i	$-0.879063\pi$
$43$	−0.938835	+	1.62611i	−0.143171	+	0.247979i	0.785518	+	0.618839i	$0.212397\pi$
$44$		−	9.38866i		−	1.41539i
$45$		0			0
$46$	−7.05150	+	4.07119i	−1.03969	+	0.600264i
$47$	−4.47809	+	2.58543i	−0.653196	+	0.377123i	−0.789680	−	0.613519i	$-0.789753\pi$
$47$	−4.47809	+	2.58543i	−0.653196	+	0.377123i	0.136483	+	0.990642i	$0.456420\pi$
$48$		0			0
$49$	−0.788015	−	1.36488i	−0.112574	−	0.194983i
$50$	3.10125	−	1.79051i	0.438583	−	0.253216i
$51$		0			0
$52$	−6.21421	+	0.931939i	−0.861756	+	0.129237i
$53$	9.81151			1.34771			0.673857	−	0.738862i	$-0.264636\pi$
$53$	9.81151			1.34771			0.673857	+	0.738862i	$0.264636\pi$
$54$		0			0
$55$	−7.05029	+	12.2115i	−0.950661	+	1.64659i
$56$	0.579459	−	1.00365i	0.0774335	−	0.134119i
$57$		0			0
$58$			11.0759i			1.45434i
$59$			7.61266i			0.991084i	0.868584	+	0.495542i	$0.165031\pi$
$59$			7.61266i			0.991084i	−0.868584	+	0.495542i	$0.834969\pi$
$60$		0			0
$61$	0.467085	−	0.809015i	0.0598041	−	0.103584i	−0.834573	−	0.550897i	$-0.814286\pi$
$61$	0.467085	−	0.809015i	0.0598041	−	0.103584i	0.894377	+	0.447313i	$0.147619\pi$
$62$	−8.43369	+	14.6076i	−1.07108	+	1.85516i
$63$		0			0
$64$	5.82698			0.728372
$65$	8.78241	+	3.45434i	1.08932	+	0.428458i
$66$		0			0
$67$	−1.79128	+	1.03420i	−0.218840	+	0.126347i	−0.605413	−	0.795912i	$-0.706992\pi$
$67$	−1.79128	+	1.03420i	−0.218840	+	0.126347i	0.386573	+	0.922259i	$0.373659\pi$
$68$	1.45659	+	2.52290i	0.176638	+	0.305946i
$69$		0			0
$70$	10.2133	−	5.89662i	1.22072	−	0.704781i
$71$	10.9702	−	6.33363i	1.30192	−	0.751664i	0.321187	−	0.947016i	$-0.395918\pi$
$71$	10.9702	−	6.33363i	1.30192	−	0.751664i	0.980733	+	0.195352i	$0.0625849\pi$
$72$		0			0
$73$		−	12.6627i		−	1.48206i	−0.671473	−	0.741029i	$-0.734338\pi$
$73$		−	12.6627i		−	1.48206i	0.671473	−	0.741029i	$-0.265662\pi$
$74$	−1.36803	+	2.36950i	−0.159031	+	0.275449i
$75$		0			0
$76$	−3.31747	+	1.91534i	−0.380540	+	0.219705i
$77$	−6.27319	+	10.8655i	−0.714896	+	1.23824i
$78$		0			0
$79$	3.46731	+	6.00556i	0.390103	+	0.675678i	0.992463	−	0.122547i	$-0.0391061\pi$
$79$	3.46731	+	6.00556i	0.390103	+	0.675678i	−0.602360	+	0.798225i	$0.705773\pi$
$80$	−10.0832	−	5.82155i	−1.12734	−	0.650869i
$81$		0			0
$82$	−1.47369	−	2.55251i	−0.162742	−	0.281877i
$83$	7.95495	−	4.59279i	0.873169	−	0.504124i	0.00476882	−	0.999989i	$-0.498482\pi$
$83$	7.95495	−	4.59279i	0.873169	−	0.504124i	0.868400	+	0.495864i	$0.165149\pi$
$84$		0			0
$85$		−	4.37524i		−	0.474562i
$86$	3.14592	+	1.81630i	0.339233	+	0.195856i
$87$		0			0
$88$	2.68073			0.285767
$89$	−8.62292	−	4.97845i	−0.914028	−	0.527714i	−0.0323029	−	0.999478i	$-0.510284\pi$
$89$	−8.62292	−	4.97845i	−0.914028	−	0.527714i	−0.881725	+	0.471764i	$0.843617\pi$
$90$		0			0
$91$	7.81439	+	3.07359i	0.819170	+	0.322200i
$92$	3.66748	+	6.35226i	0.382361	+	0.662268i
$93$		0			0
$94$	5.00184	+	8.66343i	0.515900	+	0.893565i
$95$	5.75321			0.590266
$96$		0			0
$97$	2.03695	+	1.17603i	0.206821	+	0.119408i	0.599833	−	0.800125i	$-0.295234\pi$
$97$	2.03695	+	1.17603i	0.206821	+	0.119408i	−0.393012	+	0.919533i	$0.628567\pi$
$98$	−2.64054	+	1.52452i	−0.266735	+	0.153999i
$99$		0			0
$100$	−1.61296	−	2.79372i	−0.161296	−	0.279372i
$101$	−12.2572			−1.21964			−0.609820	−	0.792540i	$-0.708758\pi$
$101$	−12.2572			−1.21964			−0.609820	+	0.792540i	$0.708758\pi$
$102$		0			0
$103$	−5.10150	+	8.83607i	−0.502666	+	0.870643i	0.497329	+	0.867562i	$0.334314\pi$
$103$	−5.10150	+	8.83607i	−0.502666	+	0.870643i	−0.999995	+	0.00308139i	$0.999019\pi$
$104$	−0.266096	−	1.77434i	−0.0260928	−	0.173988i
$105$		0			0
$106$		−	18.9816i		−	1.84366i
$107$	−2.96835	+	5.14133i	−0.286961	+	0.497032i	−0.973083	−	0.230455i	$-0.925978\pi$
$107$	−2.96835	+	5.14133i	−0.286961	+	0.497032i	0.686122	+	0.727487i	$0.259312\pi$
$108$		0			0
$109$			12.1858i			1.16719i	0.812046	+	0.583594i	$0.198354\pi$
$109$			12.1858i			1.16719i	−0.812046	+	0.583594i	$0.801646\pi$
$110$	23.6246	+	13.6397i	2.25252	+	1.30049i
$111$		0			0
$112$	−8.97182	−	5.17988i	−0.847757	−	0.489453i
$113$	0.874510			0.0822670			0.0411335	−	0.999154i	$-0.486903\pi$
$113$	0.874510			0.0822670			0.0411335	+	0.999154i	$0.486903\pi$
$114$		0			0
$115$		−	11.0162i		−	1.02726i
$116$	9.97759			0.926396
$117$		0			0
$118$	14.7277			1.35579
$119$		−	3.89299i		−	0.356870i
$120$		0			0
$121$	−18.0215			−1.63832
$122$	−1.56514	−	0.903635i	−0.141701	−	0.0818113i
$123$		0			0
$124$	13.1591	+	7.59738i	1.18172	+	0.682265i
$125$		−	8.24230i		−	0.737214i
$126$		0			0
$127$	−8.46736	+	14.6659i	−0.751357	+	1.30139i	0.195808	+	0.980642i	$0.437267\pi$
$127$	−8.46736	+	14.6659i	−0.751357	+	1.30139i	−0.947165	+	0.320746i	$0.896066\pi$
$128$			3.94800i			0.348957i
$129$		0			0
$130$	6.68286	−	16.9907i	0.586126	−	1.49018i
$131$	−6.88997	+	11.9338i	−0.601980	+	1.04266i	0.390541	+	0.920585i	$0.372288\pi$
$131$	−6.88997	+	11.9338i	−0.601980	+	1.04266i	−0.992521	+	0.122074i	$0.961045\pi$
$132$		0			0
$133$	5.11907			0.443880
$134$	2.00078	+	3.46546i	0.172841	+	0.299370i
$135$		0			0
$136$	−0.720360	+	0.415900i	−0.0617704	+	0.0356631i
$137$	−5.88782	−	3.39934i	−0.503031	−	0.290425i	0.226933	−	0.973910i	$-0.427130\pi$
$137$	−5.88782	−	3.39934i	−0.503031	−	0.290425i	−0.729964	+	0.683485i	$0.760463\pi$
$138$		0			0
$139$	9.37249			0.794965			0.397482	−	0.917610i	$-0.369884\pi$
$139$	9.37249			0.794965			0.397482	+	0.917610i	$0.369884\pi$
$140$	−5.31190	−	9.20048i	−0.448937	−	0.777582i
$141$		0			0
$142$	−12.2532	−	21.2232i	−1.02827	−	1.78101i
$143$	2.88074	+	19.2089i	0.240899	+	1.60633i
$144$		0			0
$145$	−12.9775	−	7.49254i	−1.07772	−	0.622222i
$146$	−24.4976			−2.02744
$147$		0			0
$148$	2.13454	+	1.23238i	0.175458	+	0.101301i
$149$		−	15.1119i		−	1.23802i	−0.785384	−	0.619009i	$-0.787534\pi$
$149$		−	15.1119i		−	1.23802i	0.785384	−	0.619009i	$-0.212466\pi$
$150$		0			0
$151$	−16.8896	+	9.75122i	−1.37446	+	0.793543i	−0.991486	−	0.130217i	$-0.958433\pi$
$151$	−16.8896	+	9.75122i	−1.37446	+	0.793543i	−0.382972	+	0.923760i	$0.625099\pi$
$152$	−0.546886	−	0.947234i	−0.0443583	−	0.0768308i
$153$		0			0
$154$	21.0207	+	12.1363i	1.69389	+	0.977970i
$155$	−11.4103	−	19.7632i	−0.916498	−	1.58742i
$156$		0			0
$157$	−1.95414	+	3.38466i	−0.155957	+	0.270125i	−0.933407	−	0.358819i	$-0.883179\pi$
$157$	−1.95414	+	3.38466i	−0.155957	+	0.270125i	0.777450	+	0.628945i	$0.216513\pi$
$158$	11.6185	−	6.70796i	0.924320	−	0.533656i
$159$		0			0
$160$	−9.96005	+	17.2513i	−0.787411	+	1.36384i
$161$		−	9.80194i		−	0.772501i
$162$		0			0
$163$	−6.22413	+	3.59350i	−0.487511	+	0.281465i	−0.723541	−	0.690281i	$-0.757487\pi$
$163$	−6.22413	+	3.59350i	−0.487511	+	0.281465i	0.236030	+	0.971746i	$0.424154\pi$
$164$	−2.29939	+	1.32756i	−0.179552	+	0.103665i
$165$		0			0
$166$	−8.88534	−	15.3899i	−0.689636	−	1.19448i
$167$	5.19037	−	2.99666i	0.401643	−	0.231889i	−0.285550	−	0.958364i	$-0.592176\pi$
$167$	5.19037	−	2.99666i	0.401643	−	0.231889i	0.687193	+	0.726475i	$0.258843\pi$
$168$		0			0
$169$	12.4281	−	3.81343i	0.956008	−	0.293341i
$170$	−8.46447			−0.649195
$171$		0			0
$172$	1.63619	−	2.83396i	0.124758	−	0.216087i
$173$	−1.09116	+	1.88994i	−0.0829591	+	0.143689i	−0.904520	−	0.426432i	$-0.859770\pi$
$173$	−1.09116	+	1.88994i	−0.0829591	+	0.143689i	0.821561	+	0.570121i	$0.193104\pi$
$174$		0			0
$175$			4.31089i			0.325873i
$176$		−	23.9635i		−	1.80632i
$177$		0			0
$178$	−9.63144	+	16.6821i	−0.721907	+	1.25038i
$179$	1.46465	−	2.53684i	0.109473	−	0.189612i	−0.806084	−	0.591801i	$-0.798417\pi$
$179$	1.46465	−	2.53684i	0.109473	−	0.189612i	0.915557	+	0.402189i	$0.131750\pi$
$180$		0			0
$181$	23.2244			1.72625			0.863127	−	0.504986i	$-0.168502\pi$
$181$	23.2244			1.72625			0.863127	+	0.504986i	$0.168502\pi$
$182$	5.94626	−	15.1179i	0.440766	−	1.12062i
$183$		0			0
$184$	−1.81375	+	1.04717i	−0.133712	+	0.0771985i
$185$	−1.85087	−	3.20581i	−0.136079	−	0.235696i
$186$		0			0
$187$	7.79858	−	4.50251i	0.570289	−	0.329256i
$188$	7.80434	−	4.50584i	0.569190	−	0.328622i
$189$		0			0
$190$		−	11.1303i		−	0.807478i
$191$	4.81042	−	8.33189i	0.348070	−	0.602874i	−0.637837	−	0.770171i	$-0.720171\pi$
$191$	4.81042	−	8.33189i	0.348070	−	0.602874i	0.985906	+	0.167297i	$0.0535040\pi$
$192$		0			0
$193$	17.4030	−	10.0476i	1.25270	−	0.723245i	0.281052	−	0.959692i	$-0.409317\pi$
$193$	17.4030	−	10.0476i	1.25270	−	0.723245i	0.971644	+	0.236448i	$0.0759832\pi$
$194$	2.27519	−	3.94074i	0.163349	−	0.282929i
$195$		0			0
$196$	1.37334	+	2.37870i	0.0980958	+	0.169907i
$197$	−10.3727	−	5.98869i	−0.739025	−	0.426676i	0.0826895	−	0.996575i	$-0.473649\pi$
$197$	−10.3727	−	5.98869i	−0.739025	−	0.426676i	−0.821715	+	0.569899i	$0.806982\pi$
$198$		0			0
$199$	−8.85181	−	15.3318i	−0.627488	−	1.08684i	−0.988054	−	0.154108i	$-0.950750\pi$
$199$	−8.85181	−	15.3318i	−0.627488	−	1.08684i	0.360566	−	0.932734i	$-0.382584\pi$
$200$	0.797688	−	0.460546i	0.0564051	−	0.0325655i
$201$		0			0
$202$			23.7132i			1.66845i
$203$	−11.5471	−	6.66670i	−0.810444	−	0.467910i
$204$		0			0
$205$	3.98764			0.278509
$206$	17.0945	+	9.86951i	1.19103	+	0.687642i
$207$		0			0
$208$	−15.8611	+	2.37867i	−1.09977	+	0.164931i
$209$	5.92055	+	10.2547i	0.409533	+	0.709333i
$210$		0			0
$211$	−11.0954	−	19.2178i	−0.763840	−	1.32301i	−0.940857	−	0.338803i	$-0.889978\pi$
$211$	−11.0954	−	19.2178i	−0.763840	−	1.32301i	0.177017	−	0.984208i	$-0.443355\pi$
$212$	−17.0993			−1.17439
$213$		0			0
$214$	9.94657	+	5.74265i	0.679933	+	0.392560i
$215$	−4.25625	+	2.45735i	−0.290274	+	0.167590i
$216$		0			0
$217$	−10.1526	−	17.5849i	−0.689206	−	1.19374i
$218$	23.5750			1.59670
$219$		0			0
$220$	12.2871	−	21.2820i	0.828399	−	1.43483i
$221$	−3.75425	−	4.71483i	−0.252538	−	0.317154i
$222$		0			0
$223$			4.33152i			0.290060i	0.989427	+	0.145030i	$0.0463279\pi$
$223$			4.33152i			0.290060i	−0.989427	+	0.145030i	$0.953672\pi$
$224$	−8.86223	+	15.3498i	−0.592132	+	1.02560i
$225$		0			0
$226$		−	1.69185i		−	0.112540i
$227$	2.56338	+	1.47997i	0.170137	+	0.0982289i	0.582651	−	0.812723i	$-0.302016\pi$
$227$	2.56338	+	1.47997i	0.170137	+	0.0982289i	−0.412513	+	0.910952i	$0.635349\pi$
$228$		0			0
$229$	9.82313	+	5.67139i	0.649131	+	0.374776i	0.788123	−	0.615518i	$-0.211053\pi$
$229$	9.82313	+	5.67139i	0.649131	+	0.374776i	−0.138992	+	0.990293i	$0.544386\pi$
$230$	−21.3122			−1.40528
$231$		0			0
$232$			2.84889i			0.187039i
$233$	−2.31530			−0.151680			−0.0758401	−	0.997120i	$-0.524164\pi$
$233$	−2.31530			−0.151680			−0.0758401	+	0.997120i	$0.524164\pi$
$234$		0			0
$235$	−13.5344			−0.882887
$236$		−	13.2672i		−	0.863623i
$237$		0			0
$238$	−7.53149			−0.488194
$239$	17.6746	+	10.2044i	1.14327	+	0.660069i	0.947239	−	0.320528i	$-0.103860\pi$
$239$	17.6746	+	10.2044i	1.14327	+	0.660069i	0.196034	+	0.980597i	$0.437194\pi$
$240$		0			0
$241$	−7.56925	−	4.37011i	−0.487578	−	0.281503i	0.235991	−	0.971755i	$-0.424166\pi$
$241$	−7.56925	−	4.37011i	−0.487578	−	0.281503i	−0.723569	+	0.690252i	$0.757500\pi$
$242$			34.8649i			2.24120i
$243$		0			0
$244$	−0.814028	+	1.40994i	−0.0521128	+	0.0902621i
$245$		−	4.12517i		−	0.263547i
$246$		0			0
$247$	6.19974	−	4.93663i	0.394480	−	0.314110i
$248$	−2.16927	+	3.75729i	−0.137749	+	0.238588i
$249$		0			0
$250$	−15.9458			−1.00850
$251$	9.27060	+	16.0571i	0.585155	+	1.01352i	0.994856	+	0.101298i	$0.0322996\pi$
$251$	9.27060	+	16.0571i	0.585155	+	1.01352i	−0.409701	+	0.912220i	$0.634367\pi$
$252$		0			0
$253$	19.6356	−	11.3366i	1.23448	−	0.712727i
$254$	28.3731	+	16.3812i	1.78028	+	1.02785i
$255$		0			0
$256$	19.2919			1.20574
$257$	7.18835	+	12.4506i	0.448397	+	0.776647i	0.998282	−	0.0585939i	$-0.0186617\pi$
$257$	7.18835	+	12.4506i	0.448397	+	0.776647i	−0.549885	+	0.835241i	$0.685328\pi$
$258$		0			0
$259$	−1.64687	−	2.85245i	−0.102331	−	0.177243i
$260$	−15.3058	−	6.02017i	−0.949228	−	0.373355i
$261$		0			0
$262$	23.0874	+	13.3295i	1.42635	+	0.823501i
$263$	−5.60712			−0.345750			−0.172875	−	0.984944i	$-0.555306\pi$
$263$	−5.60712			−0.345750			−0.172875	+	0.984944i	$0.555306\pi$
$264$		0			0
$265$	22.2405	+	12.8405i	1.36622	+	0.788788i
$266$		−	9.90350i		−	0.607222i
$267$		0			0
$268$	3.12181	−	1.80238i	0.190695	−	0.110098i
$269$	1.16337	+	2.01502i	0.0709319	+	0.122858i	0.899310	−	0.437312i	$-0.144069\pi$
$269$	1.16337	+	2.01502i	0.0709319	+	0.122858i	−0.828378	+	0.560169i	$0.810736\pi$
$270$		0			0
$271$	1.59856	+	0.922926i	0.0971053	+	0.0560638i	0.547766	−	0.836631i	$-0.315478\pi$
$271$	1.59856	+	0.922926i	0.0971053	+	0.0560638i	−0.450661	+	0.892695i	$0.648812\pi$
$272$	3.71780	+	6.43942i	0.225425	+	0.390447i
$273$		0			0
$274$	−6.57645	+	11.3907i	−0.397298	+	0.688140i
$275$	−8.63573	+	4.98584i	−0.520754	+	0.300658i
$276$		0			0
$277$	0.267853	−	0.463934i	0.0160937	−	0.0278751i	−0.857866	−	0.513873i	$-0.828210\pi$
$277$	0.267853	−	0.463934i	0.0160937	−	0.0278751i	0.873960	+	0.485998i	$0.161544\pi$
$278$		−	18.1323i		−	1.08750i
$279$		0			0
$280$	2.62700	−	1.51670i	0.156993	−	0.0906402i
$281$	18.0707	−	10.4331i	1.07801	−	0.622387i	0.147648	−	0.989040i	$-0.452830\pi$
$281$	18.0707	−	10.4331i	1.07801	−	0.622387i	0.930358	+	0.366653i	$0.119496\pi$
$282$		0			0
$283$	4.36529	+	7.56090i	0.259489	+	0.449449i	0.966105	−	0.258149i	$-0.0831124\pi$
$283$	4.36529	+	7.56090i	0.259489	+	0.449449i	−0.706616	+	0.707597i	$0.749779\pi$
$284$	−19.1187	+	11.0382i	−1.13448	+	0.654994i
$285$		0			0
$286$	37.1620	−	5.57316i	2.19744	−	0.329548i
$287$	3.54811			0.209439
$288$		0			0
$289$	7.10292	−	12.3026i	0.417819	−	0.723684i
$290$	−14.4953	+	25.1066i	−0.851192	+	1.47431i
$291$		0			0
$292$			22.0684i			1.29145i
$293$			3.04751i			0.178038i	0.996030	+	0.0890188i	$0.0283731\pi$
$293$			3.04751i			0.178038i	−0.996030	+	0.0890188i	$0.971627\pi$
$294$		0			0
$295$	−9.96286	+	17.2562i	−0.580060	+	1.00469i
$296$	−0.351879	+	0.609473i	−0.0204526	+	0.0354249i
$297$		0			0
$298$	−29.2360			−1.69359
$299$	−9.45260	−	11.8712i	−0.546658	−	0.686529i
$300$		0			0
$301$	−3.78711	+	2.18649i	−0.218286	+	0.126027i
$302$	18.8650	+	32.6751i	1.08556	+	1.88024i
$303$		0			0
$304$	−8.46748	+	4.88870i	−0.485644	+	0.280386i
$305$	2.11755	−	1.22257i	0.121251	−	0.0700040i
$306$		0			0
$307$			22.0214i			1.25683i	0.777880	+	0.628413i	$0.216295\pi$
$307$			22.0214i			1.25683i	−0.777880	+	0.628413i	$0.783705\pi$
$308$	10.9328	−	18.9362i	0.622955	−	1.07899i
$309$		0			0
$310$	−38.2345	+	22.0747i	−2.17157	+	1.25376i
$311$	−3.39883	+	5.88694i	−0.192730	+	0.333818i	−0.946154	−	0.323717i	$-0.895067\pi$
$311$	−3.39883	+	5.88694i	−0.192730	+	0.333818i	0.753424	+	0.657535i	$0.228401\pi$
$312$		0			0
$313$	3.05617	+	5.29344i	0.172745	+	0.299203i	0.939379	−	0.342882i	$-0.111403\pi$
$313$	3.05617	+	5.29344i	0.172745	+	0.299203i	−0.766634	+	0.642085i	$0.778070\pi$
$314$	6.54806	+	3.78052i	0.369528	+	0.213347i
$315$		0			0
$316$	−6.04278	−	10.4664i	−0.339933	−	0.588781i
$317$	−15.0342	+	8.67999i	−0.844404	+	0.487517i	−0.858759	−	0.512380i	$-0.828764\pi$
$317$	−15.0342	+	8.67999i	−0.844404	+	0.487517i	0.0143546	+	0.999897i	$0.495431\pi$
$318$		0			0
$319$		−	30.8420i		−	1.72682i
$320$	13.2084	+	7.62589i	0.738374	+	0.426300i
$321$		0			0
$322$	−18.9631			−1.05677
$323$	−3.18191	−	1.83708i	−0.177046	−	0.102218i
$324$		0			0
$325$	4.15725	+	5.22095i	0.230603	+	0.289606i
$326$	6.95209	+	12.0414i	0.385041	+	0.666910i
$327$		0			0
$328$	−0.379056	−	0.656544i	−0.0209298	−	0.0362516i
$329$	−12.0426			−0.663931
$330$		0			0
$331$	−16.5137	−	9.53421i	−0.907677	−	0.524048i	−0.0279940	−	0.999608i	$-0.508912\pi$
$331$	−16.5137	−	9.53421i	−0.907677	−	0.524048i	−0.879683	+	0.475561i	$0.842245\pi$
$332$	−13.8638	+	8.00425i	−0.760873	+	0.439290i
$333$		0			0
$334$	−5.79743	−	10.0414i	−0.317221	−	0.549443i
$335$	−5.41390			−0.295793
$336$		0			0
$337$	−12.0678	+	20.9020i	−0.657372	+	1.13860i	0.323921	+	0.946084i	$0.394999\pi$
$337$	−12.0678	+	20.9020i	−0.657372	+	1.13860i	−0.981293	+	0.192518i	$0.938335\pi$
$338$	−7.37757	−	24.0438i	−0.401287	−	1.30781i
$339$		0			0
$340$			7.62511i			0.413530i
$341$	23.4844	−	40.6762i	1.27175	−	2.20274i
$342$		0			0
$343$		−	19.9731i		−	1.07844i
$344$	0.809178	+	0.467179i	0.0436279	+	0.0251886i
$345$		0			0
$346$	3.65633	+	2.11098i	0.196565	+	0.113487i
$347$	−1.02919			−0.0552500			−0.0276250	−	0.999618i	$-0.508794\pi$
$347$	−1.02919			−0.0552500			−0.0276250	+	0.999618i	$0.508794\pi$
$348$		0			0
$349$		−	28.3410i		−	1.51706i	−0.651637	−	0.758531i	$-0.725918\pi$
$349$		−	28.3410i		−	1.51706i	0.651637	−	0.758531i	$-0.274082\pi$
$350$	8.33997			0.445790
$351$		0			0
$352$	−40.9991			−2.18526
$353$			7.71417i			0.410584i	0.978701	+	0.205292i	$0.0658144\pi$
$353$			7.71417i			0.410584i	−0.978701	+	0.205292i	$0.934186\pi$
$354$		0			0
$355$	33.1559			1.75973
$356$	15.0279	+	8.67636i	0.796477	+	0.459846i
$357$		0			0
$358$	−4.90784	−	2.83354i	−0.259388	−	0.149757i
$359$		−	6.01669i		−	0.317549i	−0.987315	−	0.158774i	$-0.949246\pi$
$359$		−	6.01669i		−	0.317549i	0.987315	−	0.158774i	$-0.0507543\pi$
$360$		0			0
$361$	−7.08434	+	12.2704i	−0.372860	+	0.645813i
$362$		−	44.9305i		−	2.36150i
$363$		0			0
$364$	−13.6188	−	5.35661i	−0.713819	−	0.280763i
$365$	16.5720	−	28.7035i	0.867416	−	1.50241i
$366$		0			0
$367$	24.3910			1.27320			0.636600	−	0.771194i	$-0.280340\pi$
$367$	24.3910			1.27320			0.636600	+	0.771194i	$0.280340\pi$
$368$	9.36084	+	16.2134i	0.487967	+	0.845184i
$369$		0			0
$370$	−6.20204	+	3.58075i	−0.322429	+	0.186154i
$371$	19.7891	+	11.4252i	1.02740	+	0.593168i
$372$		0			0
$373$	5.37633			0.278376			0.139188	−	0.990266i	$-0.455551\pi$
$373$	5.37633			0.278376			0.139188	+	0.990266i	$0.455551\pi$
$374$	−8.71068	−	15.0873i	−0.450419	−	0.780148i
$375$		0			0
$376$	1.28655	+	2.22837i	0.0663487	+	0.114919i
$377$	−20.4138	+	3.06144i	−1.05136	+	0.157672i
$378$		0			0
$379$	19.7362	+	11.3947i	1.01378	+	0.585305i	0.912296	−	0.409532i	$-0.134308\pi$
$379$	19.7362	+	11.3947i	1.01378	+	0.585305i	0.101482	+	0.994837i	$0.467641\pi$
$380$	−10.0266			−0.514354
$381$		0			0
$382$	−16.1191	−	9.30637i	−0.824725	−	0.476155i
$383$			24.8883i			1.27173i	0.771799	+	0.635866i	$0.219357\pi$
$383$			24.8883i			1.27173i	−0.771799	+	0.635866i	$0.780643\pi$
$384$		0			0
$385$	−28.4398	+	16.4197i	−1.44943	+	0.836826i
$386$	−19.4384	−	33.6684i	−0.989390	−	1.71367i
$387$		0			0
$388$	−3.54996	−	2.04957i	−0.180222	−	0.104051i
$389$	7.53659	+	13.0537i	0.382120	+	0.661851i	0.991365	−	0.131131i	$-0.0418607\pi$
$389$	7.53659	+	13.0537i	0.382120	+	0.661851i	−0.609245	+	0.792982i	$0.708527\pi$
$390$		0			0
$391$	−3.51762	+	6.09269i	−0.177894	+	0.308121i
$392$	−0.679187	+	0.392129i	−0.0343041	+	0.0198055i
$393$		0			0
$394$	−11.5859	+	20.0673i	−0.583688	+	1.01098i
$395$			18.1510i			0.913275i
$396$		0			0
$397$	−2.33549	+	1.34840i	−0.117215	+	0.0676741i	−0.557461	−	0.830203i	$-0.688224\pi$
$397$	−2.33549	+	1.34840i	−0.117215	+	0.0676741i	0.440246	+	0.897877i	$0.354891\pi$
$398$	−29.6613	+	17.1250i	−1.48679	+	0.858397i
$399$		0			0
$400$	−4.11690	−	7.13067i	−0.205845	−	0.356534i
$401$	−1.05376	+	0.608391i	−0.0526225	+	0.0303816i	−0.526080	−	0.850435i	$-0.676339\pi$
$401$	−1.05376	+	0.608391i	−0.0526225	+	0.0303816i	0.473458	+	0.880816i	$0.343006\pi$
$402$		0			0
$403$	−29.2541	−	11.5064i	−1.45725	−	0.573173i
$404$	21.3617			1.06279
$405$		0			0
$406$	−12.8976	+	22.3393i	−0.640096	+	1.10868i
$407$	3.80942	−	6.59812i	0.188826	−	0.327056i
$408$		0			0
$409$			34.4077i			1.70135i	0.525693	+	0.850675i	$0.323806\pi$
$409$			34.4077i			1.70135i	−0.525693	+	0.850675i	$0.676194\pi$
$410$		−	7.71460i		−	0.380997i
$411$		0			0
$412$	8.89082	−	15.3994i	0.438019	−	0.758672i
$413$	−8.86472	+	15.3542i	−0.436205	+	0.755528i
$414$		0			0
$415$	24.0427			1.18021
$416$	4.06966	+	27.1366i	0.199531	+	1.33048i
$417$		0			0
$418$	19.8390	−	11.4541i	0.970359	−	0.560237i
$419$	−10.8961	−	18.8726i	−0.532310	−	0.921988i	−0.999288	−	0.0377193i	$-0.987991\pi$
$419$	−10.8961	−	18.8726i	−0.532310	−	0.921988i	0.466978	−	0.884269i	$-0.345343\pi$
$420$		0			0
$421$	22.4288	−	12.9493i	1.09311	−	0.631109i	0.158710	−	0.987325i	$-0.449267\pi$
$421$	22.4288	−	12.9493i	1.09311	−	0.631109i	0.934404	+	0.356216i	$0.115933\pi$
$422$	−37.1794	+	21.4655i	−1.80986	+	1.04492i
$423$		0			0
$424$		−	4.88236i		−	0.237108i
$425$	1.54705	−	2.67956i	0.0750428	−	0.129978i
$426$		0			0
$427$	1.88415	−	1.08781i	0.0911803	−	0.0526430i
$428$	5.17320	−	8.96024i	0.250056	−	0.433110i
$429$		0			0
$430$	4.75405	+	8.23426i	0.229261	+	0.397091i
$431$	−24.4387	−	14.1097i	−1.17717	−	0.679639i	−0.221812	−	0.975090i	$-0.571197\pi$
$431$	−24.4387	−	14.1097i	−1.17717	−	0.679639i	−0.955358	+	0.295450i	$0.904530\pi$
$432$		0			0
$433$	13.4398	+	23.2784i	0.645874	+	1.11869i	0.984099	+	0.177622i	$0.0568403\pi$
$433$	13.4398	+	23.2784i	0.645874	+	1.11869i	−0.338225	+	0.941065i	$0.609826\pi$
$434$	−34.0202	+	19.6416i	−1.63302	+	0.942826i
$435$		0			0
$436$		−	21.2372i		−	1.01708i
$437$	−8.01155	−	4.62547i	−0.383245	−	0.221266i
$438$		0			0
$439$	1.69589			0.0809402			0.0404701	−	0.999181i	$-0.487114\pi$
$439$	1.69589			0.0809402			0.0404701	+	0.999181i	$0.487114\pi$
$440$	6.07662	+	3.50834i	0.289691	+	0.167253i
$441$		0			0
$442$	−9.12144	+	7.26307i	−0.433863	+	0.345469i
$443$	−1.72899	−	2.99471i	−0.0821470	−	0.142283i	0.822025	−	0.569452i	$-0.192844\pi$
$443$	−1.72899	−	2.99471i	−0.0821470	−	0.142283i	−0.904172	+	0.427169i	$0.859511\pi$
$444$		0			0
$445$	−13.0308	−	22.5700i	−0.617719	−	1.06992i
$446$	8.37988			0.396799
$447$		0			0
$448$	11.7526	+	6.78534i	0.555256	+	0.320577i
$449$	24.3114	−	14.0362i	1.14732	−	0.662408i	0.199090	−	0.979981i	$-0.436201\pi$
$449$	24.3114	−	14.0362i	1.14732	−	0.662408i	0.948234	+	0.317574i	$0.102868\pi$
$450$		0			0
$451$	4.10363	+	7.10770i	0.193233	+	0.334689i
$452$	−1.52408			−0.0716868
$453$		0			0
$454$	2.86319	−	4.95918i	0.134376	−	0.232746i
$455$	13.6910	+	17.1940i	0.641842	+	0.806067i
$456$		0			0
$457$		−	9.85430i		−	0.460965i	−0.973076	−	0.230482i	$-0.925970\pi$
$457$		−	9.85430i		−	0.460965i	0.973076	−	0.230482i	$-0.0740304\pi$
$458$	10.9720	−	19.0041i	0.512689	−	0.888004i
$459$		0			0
$460$			19.1988i			0.895150i
$461$	−3.58315	−	2.06873i	−0.166884	−	0.0963506i	0.414232	−	0.910171i	$-0.364050\pi$
$461$	−3.58315	−	2.06873i	−0.166884	−	0.0963506i	−0.581116	+	0.813821i	$0.697384\pi$
$462$		0			0
$463$	−1.95999	−	1.13160i	−0.0910883	−	0.0525898i	0.453764	−	0.891122i	$-0.350081\pi$
$463$	−1.95999	−	1.13160i	−0.0910883	−	0.0525898i	−0.544852	+	0.838532i	$0.683414\pi$
$464$	25.4667			1.18226
$465$		0			0
$466$			4.47924i			0.207497i
$467$	11.5713			0.535454			0.267727	−	0.963495i	$-0.413727\pi$
$467$	11.5713			0.535454			0.267727	+	0.963495i	$0.413727\pi$
$468$		0			0
$469$	−4.81716			−0.222436
$470$			26.1840i			1.20778i
$471$		0			0
$472$	3.78818			0.174365
$473$	−8.76011	−	5.05765i	−0.402790	−	0.232551i
$474$		0			0
$475$	3.52348	+	2.03428i	0.161668	+	0.0933393i
$476$			6.78465i			0.310974i
$477$		0			0
$478$	19.7417	−	34.1937i	0.902967	−	1.56398i
$479$		−	28.9364i		−	1.32214i	−0.750325	−	0.661069i	$-0.770103\pi$
$479$		−	28.9364i		−	1.32214i	0.750325	−	0.661069i	$-0.229897\pi$
$480$		0			0
$481$	−4.74532	−	1.86645i	−0.216368	−	0.0851030i
$482$	−8.45453	+	14.6437i	−0.385093	+	0.667001i
$483$		0			0
$484$	31.4076			1.42762
$485$	3.07820	+	5.33160i	0.139774	+	0.242095i
$486$		0			0
$487$	3.64815	−	2.10626i	0.165313	−	0.0954438i	−0.415061	−	0.909794i	$-0.636240\pi$
$487$	3.64815	−	2.10626i	0.165313	−	0.0954438i	0.580374	+	0.814350i	$0.302906\pi$
$488$	−0.402578	−	0.232429i	−0.0182239	−	0.0105216i
$489$		0			0
$490$	−7.98067			−0.360530
$491$	6.93597	+	12.0135i	0.313016	+	0.542159i	0.979014	−	0.203794i	$-0.0653274\pi$
$491$	6.93597	+	12.0135i	0.313016	+	0.542159i	−0.665998	+	0.745954i	$0.731994\pi$
$492$		0			0
$493$	4.78495	+	8.28777i	0.215503	+	0.373262i
$494$	−9.55054	−	11.9942i	−0.429699	−	0.539644i
$495$		0			0
$496$	33.5871	+	19.3915i	1.50810	+	0.870704i
$497$	29.5013			1.32332
$498$		0			0
$499$	−9.03377	−	5.21565i	−0.404407	−	0.233484i	0.283977	−	0.958831i	$-0.408346\pi$
$499$	−9.03377	−	5.21565i	−0.404407	−	0.233484i	−0.688384	+	0.725347i	$0.741679\pi$
$500$			14.3646i			0.642403i
$501$		0			0
$502$	31.0646	−	17.9352i	1.38648	−	0.800485i
$503$	13.8296	+	23.9535i	0.616630	+	1.06803i	0.990096	+	0.140390i	$0.0448358\pi$
$503$	13.8296	+	23.9535i	0.616630	+	1.06803i	−0.373466	+	0.927644i	$0.621831\pi$
$504$		0			0
$505$	−27.7844	−	16.0413i	−1.23639	−	0.713829i
$506$	−21.9321	−	37.9876i	−0.975002	−	1.68875i
$507$		0			0
$508$	14.7568	−	25.5595i	0.654727	−	1.13402i
$509$	22.6496	−	13.0768i	1.00393	−	0.579618i	0.0945197	−	0.995523i	$-0.469868\pi$
$509$	22.6496	−	13.0768i	1.00393	−	0.579618i	0.909408	+	0.415905i	$0.136535\pi$
$510$		0			0
$511$	14.7454	−	25.5397i	0.652296	−	1.12981i
$512$		−	29.4266i		−	1.30048i
$513$		0			0
$514$	24.0873	−	13.9068i	1.06244	−	0.613402i
$515$	−23.1279	+	13.3529i	−1.01914	+	0.588399i
$516$		0			0
$517$	−13.9281	−	24.1242i	−0.612557	−	1.06098i
$518$	−5.51844	+	3.18607i	−0.242466	+	0.139988i
$519$		0			0
$520$	1.71893	−	4.37026i	0.0753803	−	0.191649i
$521$	−9.78810			−0.428825			−0.214412	−	0.976743i	$-0.568784\pi$
$521$	−9.78810			−0.428825			−0.214412	+	0.976743i	$0.568784\pi$
$522$		0			0
$523$	17.0184	−	29.4767i	0.744161	−	1.28892i	−0.206425	−	0.978462i	$-0.566183\pi$
$523$	17.0184	−	29.4767i	0.744161	−	1.28892i	0.950586	−	0.310462i	$-0.100484\pi$
$524$	12.0077	−	20.7980i	0.524561	−	0.908566i
$525$		0			0
$526$			10.8477i			0.472982i
$527$			14.5739i			0.634848i
$528$		0			0
$529$	2.64319	−	4.57815i	0.114921	−	0.199050i
$530$	24.8417	−	43.0270i	1.07905	−	1.86897i
$531$		0			0
$532$	−8.92144			−0.386793
$533$	4.29714	−	3.42166i	0.186130	−	0.148208i
$534$		0			0
$535$	−13.4572	+	7.76949i	−0.581803	+	0.335904i
$536$	0.514632	+	0.891369i	0.0222287	+	0.0385013i
$537$		0			0
$538$	3.89831	−	2.25069i	0.168068	−	0.0970340i
$539$	7.35284	−	4.24516i	0.316709	−	0.182852i
$540$		0			0
$541$		−	21.1460i		−	0.909138i	−0.890711	−	0.454569i	$-0.849793\pi$
$541$		−	21.1460i		−	0.909138i	0.890711	−	0.454569i	$-0.150207\pi$
$542$	1.78552	−	3.09261i	0.0766946	−	0.132839i
$543$		0			0
$544$	11.0172	−	6.36076i	0.472357	−	0.272715i
$545$	−15.9478	+	27.6224i	−0.683129	+	1.18321i
$546$		0			0
$547$	0.443127	+	0.767519i	0.0189468	+	0.0328168i	0.875343	−	0.483502i	$-0.160635\pi$
$547$	0.443127	+	0.767519i	0.0189468	+	0.0328168i	−0.856397	+	0.516319i	$0.827302\pi$
$548$	10.2612	+	5.92431i	0.438337	+	0.253074i
$549$		0			0
$550$	9.64575	+	16.7069i	0.411296	+	0.712386i
$551$	−10.8980	+	6.29194i	−0.464269	+	0.268046i
$552$		0			0
$553$			16.1503i			0.686782i
$554$	−0.897540	−	0.518195i	−0.0381328	−	0.0220160i
$555$		0			0
$556$	−16.3342			−0.692726
$557$	−8.55128	−	4.93708i	−0.362329	−	0.209191i	0.307773	−	0.951460i	$-0.400416\pi$
$557$	−8.55128	−	4.93708i	−0.362329	−	0.209191i	−0.670102	+	0.742269i	$0.733750\pi$
$558$		0			0
$559$	−2.47803	+	6.30021i	−0.104810	+	0.266471i
$560$	−13.5580	−	23.4832i	−0.572932	−	0.992347i
$561$		0			0
$562$	−20.1842	−	34.9600i	−0.851418	−	1.47470i
$563$	−5.29479			−0.223149			−0.111574	−	0.993756i	$-0.535589\pi$
$563$	−5.29479			−0.223149			−0.111574	+	0.993756i	$0.535589\pi$
$564$		0			0
$565$	1.98231	+	1.14449i	0.0833966	+	0.0481491i
$566$	14.6275	−	8.44521i	0.614841	−	0.354978i
$567$		0			0
$568$	−3.15172	−	5.45893i	−0.132243	−	0.229052i
$569$	3.83481			0.160764			0.0803818	−	0.996764i	$-0.474386\pi$
$569$	3.83481			0.160764			0.0803818	+	0.996764i	$0.474386\pi$
$570$		0			0
$571$	−20.0761	+	34.7728i	−0.840159	+	1.45520i	0.0496009	+	0.998769i	$0.484205\pi$
$571$	−20.0761	+	34.7728i	−0.840159	+	1.45520i	−0.889760	+	0.456429i	$0.849128\pi$
$572$	−5.02051	−	33.4769i	−0.209918	−	1.39974i
$573$		0			0
$574$		−	6.86428i		−	0.286509i
$575$	3.89522	−	6.74672i	0.162442	−	0.281358i
$576$		0			0
$577$			31.4632i			1.30983i	0.755702	+	0.654915i	$0.227296\pi$
$577$			31.4632i			1.30983i	−0.755702	+	0.654915i	$0.772704\pi$
$578$	−23.8010	−	13.7415i	−0.989991	−	0.571572i
$579$		0			0
$580$	22.6169	+	13.0579i	0.939117	+	0.542199i
$581$	21.3927			0.887518
$582$		0			0
$583$			52.8562i			2.18908i
$584$	−6.30116			−0.260744
$585$		0			0
$586$	5.89580			0.243553
$587$			34.6673i			1.43087i	0.698679	+	0.715436i	$0.253772\pi$
$587$			34.6673i			1.43087i	−0.698679	+	0.715436i	$0.746228\pi$
$588$		0			0
$589$	−19.1639			−0.789633
$590$	33.3843	+	19.2744i	1.37441	+	0.793515i
$591$		0			0
$592$	5.44818	+	3.14551i	0.223919	+	0.129280i
$593$		−	8.17407i		−	0.335669i	−0.985815	−	0.167835i	$-0.946323\pi$
$593$		−	8.17407i		−	0.335669i	0.985815	−	0.167835i	$-0.0536774\pi$
$594$		0			0
$595$	5.09484	−	8.82453i	0.208868	−	0.361770i
$596$			26.3369i			1.07880i
$597$		0			0
$598$	−22.9663	+	18.2873i	−0.939164	+	0.747822i
$599$	20.5243	−	35.5492i	0.838601	−	1.45250i	−0.0524634	−	0.998623i	$-0.516707\pi$
$599$	20.5243	−	35.5492i	0.838601	−	1.45250i	0.891064	−	0.453877i	$-0.149959\pi$
$600$		0			0
$601$	−16.0851			−0.656127			−0.328063	−	0.944656i	$-0.606396\pi$
$601$	−16.0851			−0.656127			−0.328063	+	0.944656i	$0.606396\pi$
$602$	4.23005	+	7.32666i	0.172404	+	0.298612i
$603$		0			0
$604$	29.4350	−	16.9943i	1.19769	−	0.691488i
$605$	−40.8506	−	23.5851i	−1.66081	−	0.958871i
$606$		0			0
$607$	12.3021			0.499328			0.249664	−	0.968333i	$-0.419680\pi$
$607$	12.3021			0.499328			0.249664	+	0.968333i	$0.419680\pi$
$608$	8.36405	+	14.4870i	0.339207	+	0.587524i
$609$		0			0
$610$	−2.36521	−	4.09667i	−0.0957647	−	0.165869i
$611$	−14.5849	+	11.6134i	−0.590041	+	0.469828i
$612$		0			0
$613$	11.2160	+	6.47556i	0.453010	+	0.261546i	0.709101	−	0.705107i	$-0.249101\pi$
$613$	11.2160	+	6.47556i	0.453010	+	0.261546i	−0.256091	+	0.966653i	$0.582435\pi$
$614$	42.6032			1.71932
$615$		0			0
$616$	5.40684	+	3.12164i	0.217848	+	0.125774i
$617$		−	39.4798i		−	1.58940i	−0.607004	−	0.794699i	$-0.707629\pi$
$617$		−	39.4798i		−	1.58940i	0.607004	−	0.794699i	$-0.292371\pi$
$618$		0			0
$619$	0.671784	−	0.387855i	0.0270013	−	0.0155892i	−0.486439	−	0.873715i	$-0.661704\pi$
$619$	0.671784	−	0.387855i	0.0270013	−	0.0155892i	0.513440	+	0.858126i	$0.328371\pi$
$620$	19.8857	+	34.4431i	0.798630	+	1.38327i
$621$		0			0
$622$	11.3890	+	6.57547i	0.456659	+	0.263652i
$623$	−11.5945	−	20.0823i	−0.464524	−	0.804580i
$624$		0			0
$625$	15.4144	−	26.6985i	0.616576	−	1.06794i
$626$	10.2408	−	5.91255i	0.409306	−	0.236313i
$627$		0			0
$628$	3.40564	−	5.89874i	0.135900	−	0.235385i
$629$			2.36404i			0.0942604i
$630$		0			0
$631$	−5.40986	+	3.12338i	−0.215363	+	0.124340i	−0.603801	−	0.797135i	$-0.706348\pi$
$631$	−5.40986	+	3.12338i	−0.215363	+	0.124340i	0.388438	+	0.921475i	$0.373015\pi$
$632$	2.98846	−	1.72539i	0.118875	−	0.0686323i
$633$		0			0
$634$	16.7926	+	29.0856i	0.666918	+	1.15514i
$635$	−38.3872	+	22.1628i	−1.52335	+	0.879506i
$636$		0			0
$637$	−3.53967	−	4.44534i	−0.140247	−	0.176131i
$638$	−59.6677			−2.36227
$639$		0			0
$640$	−5.16684	+	8.94922i	−0.204237	+	0.353749i
$641$	−13.1720	+	22.8145i	−0.520262	+	0.901120i	0.479461	+	0.877563i	$0.340832\pi$
$641$	−13.1720	+	22.8145i	−0.520262	+	0.901120i	−0.999723	+	0.0235565i	$0.992501\pi$
$642$		0			0
$643$		−	22.5012i		−	0.887361i	−0.896185	−	0.443681i	$-0.853672\pi$
$643$		−	22.5012i		−	0.887361i	0.896185	−	0.443681i	$-0.146328\pi$
$644$			17.0827i			0.673152i
$645$		0			0
$646$	−3.55406	+	6.15582i	−0.139833	+	0.242197i
$647$	2.07443	−	3.59302i	0.0815542	−	0.141256i	−0.822363	−	0.568962i	$-0.807345\pi$
$647$	2.07443	−	3.59302i	0.0815542	−	0.141256i	0.903918	+	0.427706i	$0.140678\pi$
$648$		0			0
$649$	−41.0106			−1.60981
$650$	10.1006	−	8.04274i	0.396178	−	0.315462i
$651$		0			0
$652$	10.8473	−	6.26270i	0.424814	−	0.245266i
$653$	−2.22555	−	3.85477i	−0.0870927	−	0.150849i	0.819188	−	0.573525i	$-0.194424\pi$
$653$	−2.22555	−	3.85477i	−0.0870927	−	0.150849i	−0.906281	+	0.422676i	$0.861091\pi$
$654$		0			0
$655$	−31.2360	+	18.0341i	−1.22049	+	0.704651i
$656$	−5.86895	+	3.38844i	−0.229144	+	0.132296i
$657$		0			0
$658$			23.2980i			0.908249i
$659$	6.70705	−	11.6169i	0.261269	−	0.452532i	−0.705310	−	0.708899i	$-0.749192\pi$
$659$	6.70705	−	11.6169i	0.261269	−	0.452532i	0.966580	+	0.256367i	$0.0825256\pi$
$660$		0			0
$661$	−4.79886	+	2.77062i	−0.186654	+	0.107765i	−0.590415	−	0.807100i	$-0.701036\pi$
$661$	−4.79886	+	2.77062i	−0.186654	+	0.107765i	0.403761	+	0.914864i	$0.367703\pi$
$662$	−18.4451	+	31.9479i	−0.716891	+	1.24169i
$663$		0			0
$664$	−2.28544	−	3.95851i	−0.0886924	−	0.153620i
$665$	11.6038	+	6.69944i	0.449975	+	0.259793i
$666$		0			0
$667$	12.0477	+	20.8673i	0.466490	+	0.807985i
$668$	−9.04570	+	5.22254i	−0.349989	+	0.202066i
$669$		0			0
$670$			10.4739i			0.404641i
$671$	4.35829	+	2.51626i	0.168250	+	0.0971392i
$672$		0			0
$673$	13.8135			0.532473			0.266236	−	0.963908i	$-0.414220\pi$
$673$	13.8135			0.532473			0.266236	+	0.963908i	$0.414220\pi$
$674$	40.4375	+	23.3466i	1.55759	+	0.899278i
$675$		0			0
$676$	−21.6595	+	6.64599i	−0.833058	+	0.255615i
$677$	−4.70621	−	8.15139i	−0.180874	−	0.313284i	0.761304	−	0.648395i	$-0.224559\pi$
$677$	−4.70621	−	8.15139i	−0.180874	−	0.313284i	−0.942179	+	0.335111i	$0.891226\pi$
$678$		0			0
$679$	2.73891	+	4.74394i	0.105110	+	0.182056i
$680$	−2.17719			−0.0834914
$681$		0			0
$682$	−78.6934	−	45.4336i	−3.01332	−	1.73974i
$683$	16.9642	−	9.79429i	0.649117	−	0.374768i	−0.139001	−	0.990292i	$-0.544389\pi$
$683$	16.9642	−	9.79429i	0.649117	−	0.374768i	0.788118	+	0.615524i	$0.211056\pi$
$684$		0			0
$685$	−8.89757	−	15.4110i	−0.339959	−	0.588826i
$686$	−38.6405			−1.47530
$687$		0			0
$688$	4.17619	−	7.23337i	0.159216	−	0.275770i
$689$	34.9847	−	5.24662i	1.33281	−	0.199880i
$690$		0			0
$691$		−	1.40342i		−	0.0533886i	−0.999644	−	0.0266943i	$-0.991502\pi$
$691$		−	1.40342i		−	0.0533886i	0.999644	−	0.0266943i	$-0.00849807\pi$
$692$	1.90165	−	3.29375i	0.0722899	−	0.125210i
$693$		0			0
$694$			1.99110i			0.0755813i
$695$	21.2453	+	12.2660i	0.805881	+	0.465275i
$696$		0			0
$697$	−2.20544	−	1.27331i	−0.0835369	−	0.0482300i
$698$	−54.8294			−2.07532
$699$		0			0
$700$		−	7.51296i		−	0.283963i
$701$	−19.4308			−0.733892			−0.366946	−	0.930242i	$-0.619597\pi$
$701$	−19.4308			−0.733892			−0.366946	+	0.930242i	$0.619597\pi$
$702$		0			0
$703$	−3.10858			−0.117242
$704$			31.3909i			1.18309i
$705$		0			0
$706$	14.9241			0.561674
$707$	−24.7219	−	14.2732i	−0.929763	−	0.536799i
$708$		0			0
$709$	−3.16828	−	1.82921i	−0.118987	−	0.0686972i	0.439325	−	0.898328i	$-0.355218\pi$
$709$	−3.16828	−	1.82921i	−0.118987	−	0.0686972i	−0.558312	+	0.829631i	$0.688551\pi$
$710$		−	64.1442i		−	2.40729i
$711$		0			0
$712$	−2.47735	+	4.29090i	−0.0928427	+	0.160808i
$713$			36.6947i			1.37423i
$714$		0			0
$715$	−18.6091	+	47.3122i	−0.695940	+	1.76938i
$716$	−2.55256	+	4.42117i	−0.0953937	+	0.165227i
$717$		0			0
$718$	−11.6401			−0.434403
$719$	−3.56798	−	6.17992i	−0.133063	−	0.230472i	0.791793	−	0.610790i	$-0.209148\pi$
$719$	−3.56798	−	6.17992i	−0.133063	−	0.230472i	−0.924856	+	0.380318i	$0.875815\pi$
$720$		0			0
$721$	−20.5787	+	11.8811i	−0.766390	+	0.442476i
$722$	23.7387	+	13.7056i	0.883464	+	0.510068i
$723$		0			0
$724$	−40.4751			−1.50425
$725$	−5.29859	−	9.17743i	−0.196785	−	0.340841i
$726$		0			0
$727$	−18.8741	−	32.6908i	−0.700000	−	1.21244i	−0.968466	−	0.249146i	$-0.919850\pi$
$727$	−18.8741	−	32.6908i	−0.700000	−	1.21244i	0.268466	−	0.963289i	$-0.413483\pi$
$728$	1.52947	−	3.88856i	0.0566859	−	0.144120i
$729$		0			0
$730$	−55.5305	−	32.0606i	−2.05528	−	1.18662i
$731$	3.13866			0.116088
$732$		0			0
$733$	25.7477	+	14.8654i	0.951012	+	0.549067i	0.893395	−	0.449272i	$-0.148316\pi$
$733$	25.7477	+	14.8654i	0.951012	+	0.549067i	0.0576170	+	0.998339i	$0.481650\pi$
$734$		−	47.1875i		−	1.74172i
$735$		0			0
$736$	27.7395	−	16.0154i	1.02249	−	0.590335i
$737$	−5.57138	−	9.64991i	−0.205224	−	0.355459i
$738$		0			0
$739$	−32.8161	−	18.9464i	−1.20716	−	0.696955i	−0.245023	−	0.969517i	$-0.578795\pi$
$739$	−32.8161	−	18.9464i	−1.20716	−	0.696955i	−0.962138	+	0.272563i	$0.912129\pi$
$740$	3.22567	+	5.58703i	0.118578	+	0.205383i
$741$		0			0
$742$	22.1035	−	38.2845i	0.811447	−	1.40547i
$743$	−4.18486	+	2.41613i	−0.153528	+	0.0886393i	−0.574796	−	0.818297i	$-0.694919\pi$
$743$	−4.18486	+	2.41613i	−0.153528	+	0.0886393i	0.421268	+	0.906936i	$0.361585\pi$
$744$		0			0
$745$	19.7773	−	34.2553i	0.724585	−	1.25502i
$746$		−	10.4012i		−	0.380815i
$747$		0			0
$748$	−13.5912	+	7.84691i	−0.496945	+	0.286911i
$749$	−11.9739	+	6.91312i	−0.437516	+	0.252600i
$750$		0			0
$751$	17.1031	+	29.6234i	0.624100	+	1.08097i	0.988714	+	0.149815i	$0.0478677\pi$
$751$	17.1031	+	29.6234i	0.624100	+	1.08097i	−0.364614	+	0.931159i	$0.618799\pi$
$752$	19.9197	−	11.5007i	0.726398	−	0.419386i
$753$		0			0
$754$	5.92275	+	39.4931i	0.215694	+	1.43825i
$755$	−51.0466			−1.85777
$756$		0			0
$757$	9.88450	−	17.1205i	0.359258	−	0.622253i	−0.628579	−	0.777746i	$-0.716363\pi$
$757$	9.88450	−	17.1205i	0.359258	−	0.622253i	0.987837	+	0.155492i	$0.0496964\pi$
$758$	22.0445	−	38.1821i	0.800690	−	1.38684i
$759$		0			0
$760$		−	2.86289i		−	0.103848i
$761$			17.7648i			0.643972i	0.946744	+	0.321986i	$0.104350\pi$
$761$			17.7648i			0.643972i	−0.946744	+	0.321986i	$0.895650\pi$
$762$		0			0
$763$	−14.1900	+	24.5778i	−0.513712	+	0.889776i
$764$	−8.38352	+	14.5207i	−0.303305	+	0.525340i
$765$		0			0
$766$	48.1496			1.73971
$767$	4.07081	+	27.1443i	0.146988	+	0.980124i
$768$		0			0
$769$	−14.0558	+	8.11511i	−0.506865	+	0.292638i	−0.731544	−	0.681794i	$-0.761200\pi$
$769$	−14.0558	+	8.11511i	−0.506865	+	0.292638i	0.224679	+	0.974433i	$0.427867\pi$
$770$	31.7660	+	55.0204i	1.14477	+	1.98280i
$771$		0			0
$772$	−30.3297	+	17.5109i	−1.09159	+	0.630230i
$773$	−14.3635	+	8.29274i	−0.516617	+	0.298269i	−0.735550	−	0.677471i	$-0.763076\pi$
$773$	−14.3635	+	8.29274i	−0.516617	+	0.298269i	0.218932	+	0.975740i	$0.429743\pi$
$774$		0			0
$775$		−	16.1383i		−	0.579706i
$776$	0.585213	−	1.01362i	0.0210079	−	0.0363868i
$777$		0			0
$778$	25.2541	−	14.5805i	0.905405	−	0.522736i
$779$	1.67433	−	2.90003i	0.0599891	−	0.103904i
$780$		0			0
$781$	34.1203	+	59.0981i	1.22092	+	2.11470i
$782$	11.7871	+	6.80528i	0.421506	+	0.243356i
$783$		0			0
$784$	3.50530	+	6.07137i	0.125189	+	0.216834i
$785$	−8.85916	+	5.11484i	−0.316197	+	0.182556i
$786$		0			0
$787$		−	10.2478i		−	0.365295i	−0.983178	−	0.182648i	$-0.941533\pi$
$787$		−	10.2478i		−	0.365295i	0.983178	−	0.182648i	$-0.0584668\pi$
$788$	18.0774	+	10.4370i	0.643981	+	0.371803i
$789$		0			0
$790$	35.1154			1.24935
$791$	1.76382	+	1.01834i	0.0627142	+	0.0362080i
$792$		0			0
$793$	1.23286	−	3.13445i	0.0437801	−	0.111308i
$794$	2.60865	+	4.51831i	0.0925774	+	0.160349i
$795$		0			0
$796$	15.4268	+	26.7200i	0.546789	+	0.947066i
$797$	20.3566			0.721067			0.360534	−	0.932746i	$-0.382595\pi$
$797$	20.3566			0.721067			0.360534	+	0.932746i	$0.382595\pi$
$798$		0			0
$799$	7.48545	+	4.32172i	0.264816	+	0.152892i
$800$	−12.1998	+	7.04357i	−0.431329	+	0.249028i
$801$		0			0
$802$	1.17701	+	2.03864i	0.0415617	+	0.0719870i
$803$	68.2160			2.40729
$804$		0			0
$805$	12.8280	−	22.2188i	0.452128	−	0.783109i
$806$	−22.2605	+	56.5958i	−0.784094	+	1.99350i
$807$		0			0
$808$			6.09939i			0.214576i
$809$	−18.8460	+	32.6423i	−0.662591	+	1.14764i	0.317342	+	0.948311i	$0.397210\pi$
$809$	−18.8460	+	32.6423i	−0.662591	+	1.14764i	−0.979932	+	0.199330i	$0.936124\pi$
$810$		0			0
$811$		−	28.8949i		−	1.01464i	−0.861758	−	0.507319i	$-0.830637\pi$
$811$		−	28.8949i		−	1.01464i	0.861758	−	0.507319i	$-0.169363\pi$
$812$	20.1240	+	11.6186i	0.706215	+	0.407734i
$813$		0			0
$814$	−12.7649	−	7.36982i	−0.447409	−	0.258312i
$815$	−18.8116			−0.658941
$816$		0			0
$817$			4.12716i			0.144391i
$818$	66.5660			2.32743
$819$		0			0
$820$	−6.94960			−0.242691
$821$		−	5.18436i		−	0.180935i	−0.995899	−	0.0904677i	$-0.971164\pi$
$821$		−	5.18436i		−	0.180935i	0.995899	−	0.0904677i	$-0.0288362\pi$
$822$		0			0
$823$	17.6885			0.616582			0.308291	−	0.951292i	$-0.400243\pi$
$823$	17.6885			0.616582			0.308291	+	0.951292i	$0.400243\pi$
$824$	4.39696	+	2.53859i	0.153176	+	0.0884359i
$825$		0			0
$826$	29.7046	+	17.1499i	1.03355	+	0.596723i
$827$			15.0588i			0.523644i	0.965116	+	0.261822i	$0.0843234\pi$
$827$			15.0588i			0.523644i	−0.965116	+	0.261822i	$0.915677\pi$
$828$		0			0
$829$	4.72035	−	8.17589i	0.163945	−	0.283960i	−0.772335	−	0.635215i	$-0.780911\pi$
$829$	4.72035	−	8.17589i	0.163945	−	0.283960i	0.936280	+	0.351255i	$0.114245\pi$
$830$		−	46.5137i		−	1.61452i
$831$		0			0
$832$	20.7771	−	3.11593i	0.720317	−	0.108025i
$833$	−1.31722	+	2.28150i	−0.0456391	+	0.0790492i
$834$		0			0
$835$	15.6872			0.542877
$836$	−10.3183	−	17.8717i	−0.356864	−	0.618107i
$837$		0			0
$838$	−36.5115	+	21.0799i	−1.26127	+	0.728194i
$839$	−25.9632	−	14.9899i	−0.896350	−	0.517508i	−0.0203361	−	0.999793i	$-0.506474\pi$
$839$	−25.9632	−	14.9899i	−0.896350	−	0.517508i	−0.876014	+	0.482285i	$0.839807\pi$
$840$		0			0
$841$	3.77661			0.130228
$842$	−25.0520	−	43.3914i	−0.863350	−	1.49537i
$843$		0			0
$844$	19.3369	+	33.4926i	0.665605	+	1.15286i
$845$	33.1624	+	7.62075i	1.14082	+	0.262162i
$846$		0			0
$847$	−36.3479	−	20.9855i	−1.24893	−	0.721070i
$848$	−43.6443			−1.49875
$849$		0			0
$850$	−5.18396	−	2.99296i	−0.177808	−	0.102658i
$851$			5.95228i			0.204041i
$852$		0			0
$853$	−45.8672	+	26.4814i	−1.57046	+	0.906706i	−0.574349	+	0.818610i	$0.694745\pi$
$853$	−45.8672	+	26.4814i	−1.57046	+	0.906706i	−0.996112	+	0.0880960i	$0.971922\pi$
$854$	−2.10451	−	3.64513i	−0.0720150	−	0.124734i
$855$		0			0
$856$	2.55841	+	1.47710i	0.0874446	+	0.0504862i
$857$	15.1376	+	26.2190i	0.517089	+	0.895624i	0.999803	+	0.0198464i	$0.00631773\pi$
$857$	15.1376	+	26.2190i	0.517089	+	0.895624i	−0.482714	+	0.875778i	$0.660349\pi$
$858$		0			0
$859$	−24.2634	+	42.0254i	−0.827856	+	1.43389i	0.0718602	+	0.997415i	$0.477106\pi$
$859$	−24.2634	+	42.0254i	−0.827856	+	1.43389i	−0.899717	+	0.436475i	$0.856227\pi$
$860$	7.41773	−	4.28263i	0.252942	−	0.146036i
$861$		0			0
$862$	−27.2970	+	47.2797i	−0.929739	+	1.61035i
$863$		−	21.2534i		−	0.723473i	−0.932280	−	0.361737i	$-0.882184\pi$
$863$		−	21.2534i		−	0.723473i	0.932280	−	0.361737i	$-0.117816\pi$
$864$		0			0
$865$	−4.94680	+	2.85604i	−0.168196	+	0.0971082i
$866$	45.0350	−	26.0010i	1.53035	−	0.883548i
$867$		0			0
$868$	17.6939	+	30.6467i	0.600569	+	1.04022i
$869$	−32.3529	+	18.6790i	−1.09750	+	0.633640i
$870$		0			0
$871$	−5.83409	+	4.64548i	−0.197681	+	0.157406i
$872$	6.06384			0.205348
$873$		0			0
$874$	−8.94857	+	15.4994i	−0.302690	+	0.524274i
$875$	9.59792	−	16.6241i	0.324469	−	0.561997i
$876$		0			0
$877$		−	43.3602i		−	1.46417i	−0.681213	−	0.732085i	$-0.738547\pi$
$877$		−	43.3602i		−	1.46417i	0.681213	−	0.732085i	$-0.261453\pi$
$878$		−	3.28091i		−	0.110725i
$879$		0			0
$880$	31.3616	−	54.3199i	1.05720	−	1.83112i
$881$	−25.4246	+	44.0368i	−0.856578	+	1.48364i	0.0185957	+	0.999827i	$0.494080\pi$
$881$	−25.4246	+	44.0368i	−0.856578	+	1.48364i	−0.875174	+	0.483809i	$0.839253\pi$
$882$		0			0
$883$	29.1681			0.981586			0.490793	−	0.871276i	$-0.336707\pi$
$883$	29.1681			0.981586			0.490793	+	0.871276i	$0.336707\pi$
$884$	6.54284	+	8.21693i	0.220060	+	0.276365i
$885$		0			0
$886$	−5.79364	+	3.34496i	−0.194641	+	0.112376i
$887$	−22.0569	−	38.2037i	−0.740598	−	1.28275i	−0.952223	−	0.305403i	$-0.901209\pi$
$887$	−22.0569	−	38.2037i	−0.740598	−	1.28275i	0.211625	−	0.977351i	$-0.432125\pi$
$888$		0			0
$889$	−34.1560	+	19.7200i	−1.14556	+	0.661387i
$890$	−43.6646	+	25.2097i	−1.46364	+	0.845033i
$891$		0			0
$892$		−	7.54891i		−	0.252756i
$893$	−5.68283	+	9.84295i	−0.190169	+	0.329382i
$894$		0			0
$895$	6.64004	−	3.83363i	0.221952	−	0.128144i
$896$	−4.59734	+	7.96282i	−0.153586	+	0.266019i
$897$		0			0
$898$	−27.1548	−	47.0334i	−0.906166	−	1.56953i
$899$	43.2278	+	24.9576i	1.44173	+	0.832382i
$900$		0			0
$901$	−8.20032	−	14.2034i	−0.273192	−	0.473183i
$902$	13.7508	−	7.93901i	0.457850	−	0.264340i
$903$		0			0
$904$		−	0.435170i		−	0.0144735i
$905$	52.6444	+	30.3942i	1.74996	+	1.01034i
$906$		0			0
$907$	21.2054			0.704113			0.352057	−	0.935979i	$-0.385482\pi$
$907$	21.2054			0.704113			0.352057	+	0.935979i	$0.385482\pi$
$908$	−4.46742	−	2.57926i	−0.148256	−	0.0855959i
$909$		0			0
$910$	33.2640	−	26.4869i	1.10269	−	0.878032i
$911$	18.2141	+	31.5478i	0.603460	+	1.04522i	0.992293	+	0.123915i	$0.0395451\pi$
$911$	18.2141	+	31.5478i	0.603460	+	1.04522i	−0.388833	+	0.921308i	$0.627122\pi$
$912$		0			0
$913$	24.7421	+	42.8546i	0.818844	+	1.41828i
$914$	−19.0644			−0.630594
$915$		0			0
$916$	−17.1196	−	9.88401i	−0.565648	−	0.326577i
$917$	−27.7931	+	16.0463i	−0.917809	+	0.529897i
$918$		0			0
$919$	3.68012	+	6.37415i	0.121396	+	0.210264i	0.920318	−	0.391170i	$-0.127930\pi$
$919$	3.68012	+	6.37415i	0.121396	+	0.210264i	−0.798922	+	0.601434i	$0.794596\pi$
$920$	−5.48182			−0.180730
$921$		0			0
$922$	−4.00223	+	6.93207i	−0.131806	+	0.228296i
$923$	35.7292	−	28.4499i	1.17604	−	0.936440i
$924$		0			0
$925$		−	2.61781i		−	0.0860731i
$926$	−2.18922	+	3.79184i	−0.0719423	+	0.124608i
$927$		0			0
$928$		−	43.5709i		−	1.43028i
$929$	−2.05280	−	1.18519i	−0.0673502	−	0.0388847i	0.465947	−	0.884813i	$-0.345714\pi$
$929$	−2.05280	−	1.18519i	−0.0673502	−	0.0388847i	−0.533297	+	0.845928i	$0.679047\pi$
$930$		0			0
$931$	−3.00004	−	1.73208i	−0.0983225	−	0.0567665i
$932$	4.03506			0.132173
$933$		0			0
$934$		−	22.3861i		−	0.732495i
$935$	23.5701			0.770826
$936$		0			0
$937$	36.8188			1.20282			0.601409	−	0.798941i	$-0.294606\pi$
$937$	36.8188			1.20282			0.601409	+	0.798941i	$0.294606\pi$
$938$			9.31942i			0.304290i
$939$		0			0
$940$	23.5876			0.769341
$941$	42.7909	+	24.7053i	1.39494	+	0.805371i	0.993857	−	0.110669i	$-0.0352995\pi$
$941$	42.7909	+	24.7053i	1.39494	+	0.805371i	0.401086	+	0.916040i	$0.368633\pi$
$942$		0			0
$943$	−5.55294	−	3.20599i	−0.180829	−	0.104401i
$944$		−	33.8632i		−	1.10215i
$945$		0			0
$946$	−9.78467	+	16.9476i	−0.318127	+	0.551012i
$947$		−	27.1891i		−	0.883525i	−0.897132	−	0.441763i	$-0.854353\pi$
$947$		−	27.1891i		−	0.883525i	0.897132	−	0.441763i	$-0.145647\pi$
$948$		0			0
$949$	−6.77128	−	45.1511i	−0.219805	−	1.46567i
$950$	3.93558	−	6.81662i	0.127687	−	0.221160i
$951$		0			0
$952$	−1.93721			−0.0627855
$953$	−27.1090	−	46.9542i	−0.878147	−	1.52100i	−0.853372	−	0.521303i	$-0.825446\pi$
$953$	−27.1090	−	46.9542i	−0.878147	−	1.52100i	−0.0247753	−	0.999693i	$-0.507887\pi$
$954$		0			0
$955$	21.8082	−	12.5910i	0.705698	−	0.407435i
$956$	−30.8030	−	17.7841i	−0.996239	−	0.575179i
$957$		0			0
$958$	−55.9811			−1.80867
$959$	−7.91686	−	13.7124i	−0.255649	−	0.442797i
$960$		0			0
$961$	22.5076	+	38.9843i	0.726052	+	1.25756i
$962$	−3.61090	+	9.18043i	−0.116420	+	0.295989i
$963$		0			0
$964$	13.1916	+	7.61615i	0.424872	+	0.245300i
$965$	52.5982			1.69320
$966$		0			0
$967$	−19.6716	−	11.3574i	−0.632595	−	0.365229i	0.149161	−	0.988813i	$-0.452343\pi$
$967$	−19.6716	−	11.3574i	−0.632595	−	0.365229i	−0.781756	+	0.623584i	$0.785676\pi$
$968$			8.96777i			0.288235i
$969$		0			0
$970$	10.3147	−	5.95517i	0.331184	−	0.191209i
$971$	23.0225	+	39.8762i	0.738828	+	1.27969i	0.953023	+	0.302897i	$0.0979538\pi$
$971$	23.0225	+	39.8762i	0.738828	+	1.27969i	−0.214195	+	0.976791i	$0.568713\pi$
$972$		0			0
$973$	18.9036	+	10.9140i	0.606022	+	0.349887i
$974$	−4.07483	−	7.05781i	−0.130566	−	0.226147i
$975$		0			0
$976$	−2.07772	+	3.59872i	−0.0665062	+	0.115192i
$977$	−27.6584	+	15.9686i	−0.884871	+	0.510881i	−0.872261	−	0.489040i	$-0.837347\pi$
$977$	−27.6584	+	15.9686i	−0.884871	+	0.510881i	−0.0126097	+	0.999920i	$0.504014\pi$
$978$		0			0
$979$	26.8197	−	46.4530i	0.857161	−	1.48465i
$980$			7.18928i			0.229653i
$981$		0			0
$982$	23.2416	−	13.4185i	0.741668	−	0.428202i
$983$	2.20776	−	1.27465i	0.0704167	−	0.0406551i	−0.464378	−	0.885637i	$-0.653722\pi$
$983$	2.20776	−	1.27465i	0.0704167	−	0.0406551i	0.534795	+	0.844982i	$0.320389\pi$
$984$		0			0
$985$	−15.6751	−	27.1500i	−0.499449	−	0.865071i
$986$	16.0338	−	9.25709i	0.510619	−	0.294806i
$987$		0			0
$988$	−10.8048	+	8.60348i	−0.343747	+	0.273713i
$989$	7.90265			0.251290
$990$		0			0
$991$	−24.0678	+	41.6867i	−0.764540	+	1.32422i	0.175949	+	0.984399i	$0.443701\pi$
$991$	−24.0678	+	41.6867i	−0.764540	+	1.32422i	−0.940489	+	0.339824i	$0.889633\pi$
$992$	33.1768	−	57.4639i	1.05336	−	1.82448i
$993$		0			0
$994$		−	57.0741i		−	1.81028i
$995$		−	46.3382i		−	1.46902i
$996$		0			0
$997$	−11.9132	+	20.6343i	−0.377295	+	0.653494i	−0.990668	−	0.136299i	$-0.956479\pi$
$997$	−11.9132	+	20.6343i	−0.377295	+	0.653494i	0.613373	+	0.789794i	$0.289812\pi$
$998$	−10.0903	+	17.4770i	−0.319404	+	0.553224i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.l.b.199.3		22
3.2	odd	2		117.2.l.b.4.9	✓	22
9.2	odd	6		117.2.r.b.43.9	yes	22
9.7	even	3		351.2.r.b.316.3		22
13.10	even	6		351.2.r.b.10.3		22
39.23	odd	6		117.2.r.b.49.9	yes	22
117.88	even	6	inner	351.2.l.b.127.9		22
117.101	odd	6		117.2.l.b.88.3	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.9	✓	22	3.2	odd	2
117.2.l.b.88.3	yes	22	117.101	odd	6
117.2.r.b.43.9	yes	22	9.2	odd	6
117.2.r.b.49.9	yes	22	39.23	odd	6
351.2.l.b.127.9		22	117.88	even	6	inner
351.2.l.b.199.3		22	1.1	even	1	trivial
351.2.r.b.10.3		22	13.10	even	6
351.2.r.b.316.3		22	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.93463i q^{2} -1.74278 q^{4} +(2.26677 + 1.30872i) q^{5} +(2.01692 + 1.16447i) q^{7} -0.497616i q^{8} +(2.53189 - 4.38536i) q^{10} +5.38716i q^{11} +(3.56568 - 0.534742i) q^{13} +(2.25282 - 3.90199i) q^{14} -4.44827 q^{16} +(-0.835786 - 1.44762i) q^{17} +(1.90355 - 1.09901i) q^{19} +(-3.95050 - 2.28082i) q^{20} +10.4221 q^{22} +(-2.10438 - 3.64489i) q^{23} +(0.925505 + 1.60302i) q^{25} +(-1.03453 - 6.89826i) q^{26} +(-3.51506 - 2.02942i) q^{28} -5.72509 q^{29} +(-7.55059 - 4.35934i) q^{31} +7.61052i q^{32} +(-2.80061 + 1.61693i) q^{34} +(3.04794 + 5.27918i) q^{35} +(-1.22479 - 0.707130i) q^{37} +(-2.12618 - 3.68265i) q^{38} +(0.651240 - 1.12798i) q^{40} +(1.31938 - 0.761744i) q^{41} +(-0.938835 + 1.62611i) q^{43} -9.38866i q^{44} +(-7.05150 + 4.07119i) q^{46} +(-4.47809 + 2.58543i) q^{47} +(-0.788015 - 1.36488i) q^{49} +(3.10125 - 1.79051i) q^{50} +(-6.21421 + 0.931939i) q^{52} +9.81151 q^{53} +(-7.05029 + 12.2115i) q^{55} +(0.579459 - 1.00365i) q^{56} +11.0759i q^{58} +7.61266i q^{59} +(0.467085 - 0.809015i) q^{61} +(-8.43369 + 14.6076i) q^{62} +5.82698 q^{64} +(8.78241 + 3.45434i) q^{65} +(-1.79128 + 1.03420i) q^{67} +(1.45659 + 2.52290i) q^{68} +(10.2133 - 5.89662i) q^{70} +(10.9702 - 6.33363i) q^{71} -12.6627i q^{73} +(-1.36803 + 2.36950i) q^{74} +(-3.31747 + 1.91534i) q^{76} +(-6.27319 + 10.8655i) q^{77} +(3.46731 + 6.00556i) q^{79} +(-10.0832 - 5.82155i) q^{80} +(-1.47369 - 2.55251i) q^{82} +(7.95495 - 4.59279i) q^{83} -4.37524i q^{85} +(3.14592 + 1.81630i) q^{86} +2.68073 q^{88} +(-8.62292 - 4.97845i) q^{89} +(7.81439 + 3.07359i) q^{91} +(3.66748 + 6.35226i) q^{92} +(5.00184 + 8.66343i) q^{94} +5.75321 q^{95} +(2.03695 + 1.17603i) q^{97} +(-2.64054 + 1.52452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) \) 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more