LMFDB - Embedded newform 300.2.x.a.77.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			77.3
Character	$\chi$	$=$	300.77
Dual form			300.2.x.a.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21892 + 1.23054i) q^{3} +(-1.48454 + 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(-0.0284784 - 2.99986i) q^{9} +O(q^{10})$	\(q+(-1.21892 + 1.23054i) q^{3} +(-1.48454 + 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(-0.0284784 - 2.99986i) q^{9} +(0.879848 + 1.21101i) q^{11} +(-5.29990 + 0.839422i) q^{13} +(-0.248153 - 3.86503i) q^{15} +(-6.61182 - 3.36889i) q^{17} +(-3.22097 + 1.04656i) q^{19} +(0.601255 - 0.00285386i) q^{21} +(1.61050 + 0.255078i) q^{23} +(-0.592307 - 4.96479i) q^{25} +(3.72618 + 3.62154i) q^{27} +(0.637623 - 1.96240i) q^{29} +(2.11791 + 6.51825i) q^{31} +(-2.56266 - 0.393426i) q^{33} +(0.774858 - 0.0460576i) q^{35} +(1.18914 + 7.50792i) q^{37} +(5.42720 - 7.54495i) q^{39} +(-2.49942 + 3.44015i) q^{41} +(-3.03773 + 3.03773i) q^{43} +(5.05856 + 4.40579i) q^{45} +(1.43370 + 2.81380i) q^{47} -6.87949i q^{49} +(12.2048 - 4.02974i) q^{51} +(0.212713 - 0.108383i) q^{53} +(-3.33118 - 0.326527i) q^{55} +(2.63826 - 5.23920i) q^{57} +(2.57801 + 1.87303i) q^{59} +(3.40759 - 2.47576i) q^{61} +(-0.729368 + 0.743349i) q^{63} +(6.46424 - 10.1085i) q^{65} +(-5.71895 + 11.2241i) q^{67} +(-2.27695 + 1.67087i) q^{69} +(15.0056 + 4.87563i) q^{71} +(-2.02219 + 12.7676i) q^{73} +(6.83137 + 5.32281i) q^{75} +(0.0812876 - 0.513230i) q^{77} +(-9.94456 - 3.23118i) q^{79} +(-8.99838 + 0.170863i) q^{81} +(6.61756 - 12.9877i) q^{83} +(15.4489 - 6.05486i) q^{85} +(1.63761 + 3.17663i) q^{87} +(-10.2231 + 7.42754i) q^{89} +(1.50698 + 1.09489i) q^{91} +(-10.6025 - 5.33903i) q^{93} +(3.03162 - 6.93965i) q^{95} +(2.73153 - 1.39178i) q^{97} +(3.60780 - 2.67391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.21892	+	1.23054i	−0.703743	+	0.710455i
$3$	−1.21892	+	1.23054i	−0.703743	+	0.710455i
$4$		0			0
$5$	−1.48454	+	1.67217i	−0.663905	+	0.747817i
$5$	−1.48454	+	1.67217i	−0.663905	+	0.747817i
$6$		0			0
$7$	−0.245464	−	0.245464i	−0.0927767	−	0.0927767i	0.659195	−	0.751972i	$-0.270897\pi$
$7$	−0.245464	−	0.245464i	−0.0927767	−	0.0927767i	−0.751972	+	0.659195i	$0.770897\pi$
$8$		0			0
$9$	−0.0284784	−	2.99986i	−0.00949280	−	0.999955i
$10$		0			0
$11$	0.879848	+	1.21101i	0.265284	+	0.365132i	0.920791	−	0.390057i	$-0.127545\pi$
$11$	0.879848	+	1.21101i	0.265284	+	0.365132i	−0.655506	+	0.755190i	$0.727545\pi$
$12$		0			0
$13$	−5.29990	+	0.839422i	−1.46993	+	0.232814i	−0.839469	−	0.543408i	$-0.817134\pi$
$13$	−5.29990	+	0.839422i	−1.46993	+	0.232814i	−0.630460	+	0.776222i	$0.717134\pi$
$14$		0			0
$15$	−0.248153	−	3.86503i	−0.0640727	−	0.997945i
$16$		0			0
$17$	−6.61182	−	3.36889i	−1.60360	−	0.817077i	−0.999801	−	0.0199422i	$-0.993652\pi$
$17$	−6.61182	−	3.36889i	−1.60360	−	0.817077i	−0.603802	−	0.797134i	$-0.706348\pi$
$18$		0			0
$19$	−3.22097	+	1.04656i	−0.738940	+	0.240096i	−0.654215	−	0.756308i	$-0.727001\pi$
$19$	−3.22097	+	1.04656i	−0.738940	+	0.240096i	−0.0847246	+	0.996404i	$0.527001\pi$
$20$		0			0
$21$	0.601255	−	0.00285386i	0.131205	−	0.000622763i
$22$		0			0
$23$	1.61050	+	0.255078i	0.335812	+	0.0531874i	0.322063	−	0.946718i	$-0.395624\pi$
$23$	1.61050	+	0.255078i	0.335812	+	0.0531874i	0.0137486	+	0.999905i	$0.495624\pi$
$24$		0			0
$25$	−0.592307	−	4.96479i	−0.118461	−	0.992959i
$26$		0			0
$27$	3.72618	+	3.62154i	0.717104	+	0.696967i
$28$		0			0
$29$	0.637623	−	1.96240i	0.118404	−	0.364409i	−0.874238	−	0.485497i	$-0.838639\pi$
$29$	0.637623	−	1.96240i	0.118404	−	0.364409i	0.992642	+	0.121089i	$0.0386385\pi$
$30$		0			0
$31$	2.11791	+	6.51825i	0.380387	+	1.17071i	0.939772	+	0.341803i	$0.111038\pi$
$31$	2.11791	+	6.51825i	0.380387	+	1.17071i	−0.559384	+	0.828908i	$0.688962\pi$
$32$		0			0
$33$	−2.56266	−	0.393426i	−0.446102	−	0.0684867i
$34$		0			0
$35$	0.774858	−	0.0460576i	0.130975	−	0.00778515i
$36$		0			0
$37$	1.18914	+	7.50792i	0.195493	+	1.23429i	0.868887	+	0.495010i	$0.164836\pi$
$37$	1.18914	+	7.50792i	0.195493	+	1.23429i	−0.673394	+	0.739284i	$0.735164\pi$
$38$		0			0
$39$	5.42720	−	7.54495i	0.869048	−	1.20816i
$40$		0			0
$41$	−2.49942	+	3.44015i	−0.390343	+	0.537261i	−0.958288	−	0.285806i	$-0.907739\pi$
$41$	−2.49942	+	3.44015i	−0.390343	+	0.537261i	0.567944	+	0.823067i	$0.307739\pi$
$42$		0			0
$43$	−3.03773	+	3.03773i	−0.463250	+	0.463250i	−0.899719	−	0.436469i	$-0.856229\pi$
$43$	−3.03773	+	3.03773i	−0.463250	+	0.463250i	0.436469	+	0.899719i	$0.356229\pi$
$44$		0			0
$45$	5.05856	+	4.40579i	0.754086	+	0.656776i
$46$		0			0
$47$	1.43370	+	2.81380i	0.209127	+	0.410435i	0.971615	−	0.236567i	$-0.0760223\pi$
$47$	1.43370	+	2.81380i	0.209127	+	0.410435i	−0.762488	+	0.647002i	$0.776022\pi$
$48$		0			0
$49$		−	6.87949i		−	0.982785i
$50$		0			0
$51$	12.2048	−	4.02974i	1.70902	−	0.564276i
$52$		0			0
$53$	0.212713	−	0.108383i	0.0292184	−	0.0148875i	−0.439320	−	0.898330i	$-0.644781\pi$
$53$	0.212713	−	0.108383i	0.0292184	−	0.0148875i	0.468539	+	0.883443i	$0.344781\pi$
$54$		0			0
$55$	−3.33118	−	0.326527i	−0.449176	−	0.0440289i
$56$		0			0
$57$	2.63826	−	5.23920i	0.349446	−	0.693950i
$58$		0			0
$59$	2.57801	+	1.87303i	0.335628	+	0.243848i	0.742815	−	0.669497i	$-0.233490\pi$
$59$	2.57801	+	1.87303i	0.335628	+	0.243848i	−0.407187	+	0.913345i	$0.633490\pi$
$60$		0			0
$61$	3.40759	−	2.47576i	0.436297	−	0.316988i	−0.347865	−	0.937545i	$-0.613093\pi$
$61$	3.40759	−	2.47576i	0.436297	−	0.316988i	0.784162	+	0.620556i	$0.213093\pi$
$62$		0			0
$63$	−0.729368	+	0.743349i	−0.0918918	+	0.0936532i
$64$		0			0
$65$	6.46424	−	10.1085i	0.801790	−	1.25380i
$66$		0			0
$67$	−5.71895	+	11.2241i	−0.698681	+	1.37124i	0.219709	+	0.975565i	$0.429489\pi$
$67$	−5.71895	+	11.2241i	−0.698681	+	1.37124i	−0.918391	+	0.395674i	$0.870511\pi$
$68$		0			0
$69$	−2.27695	+	1.67087i	−0.274113	+	0.201149i
$70$		0			0
$71$	15.0056	+	4.87563i	1.78084	+	0.578630i	0.998994	−	0.0448405i	$-0.0142780\pi$
$71$	15.0056	+	4.87563i	1.78084	+	0.578630i	0.781847	+	0.623471i	$0.214278\pi$
$72$		0			0
$73$	−2.02219	+	12.7676i	−0.236679	+	1.49433i	0.527625	+	0.849478i	$0.323083\pi$
$73$	−2.02219	+	12.7676i	−0.236679	+	1.49433i	−0.764304	+	0.644856i	$0.776917\pi$
$74$		0			0
$75$	6.83137	+	5.32281i	0.788819	+	0.614626i
$76$		0			0
$77$	0.0812876	−	0.513230i	0.00926358	−	0.0584879i
$78$		0			0
$79$	−9.94456	−	3.23118i	−1.11885	−	0.363536i	−0.309521	−	0.950892i	$-0.600169\pi$
$79$	−9.94456	−	3.23118i	−1.11885	−	0.363536i	−0.809329	+	0.587356i	$0.800169\pi$
$80$		0			0
$81$	−8.99838	+	0.170863i	−0.999820	+	0.0189847i
$82$		0			0
$83$	6.61756	−	12.9877i	0.726372	−	1.42559i	−0.171434	−	0.985196i	$-0.554840\pi$
$83$	6.61756	−	12.9877i	0.726372	−	1.42559i	0.897807	−	0.440390i	$-0.145160\pi$
$84$		0			0
$85$	15.4489	−	6.05486i	1.67566	−	0.656741i
$86$		0			0
$87$	1.63761	+	3.17663i	0.175570	+	0.340570i
$88$		0			0
$89$	−10.2231	+	7.42754i	−1.08365	+	0.787318i	−0.978316	−	0.207119i	$-0.933591\pi$
$89$	−10.2231	+	7.42754i	−1.08365	+	0.787318i	−0.105335	+	0.994437i	$0.533591\pi$
$90$		0			0
$91$	1.50698	+	1.09489i	0.157975	+	0.114775i
$92$		0			0
$93$	−10.6025	−	5.33903i	−1.09943	−	0.553632i
$94$		0			0
$95$	3.03162	−	6.93965i	0.311038	−	0.711993i
$96$		0			0
$97$	2.73153	−	1.39178i	0.277345	−	0.141314i	−0.309786	−	0.950806i	$-0.600257\pi$
$97$	2.73153	−	1.39178i	0.277345	−	0.141314i	0.587131	+	0.809492i	$0.300257\pi$
$98$		0			0
$99$	3.60780	−	2.67391i	0.362598	−	0.268738i
$100$		0			0
$101$			2.16240i			0.215167i	0.994196	+	0.107584i	$0.0343113\pi$
$101$			2.16240i			0.215167i	−0.994196	+	0.107584i	$0.965689\pi$
$102$		0			0
$103$	−6.42093	−	12.6018i	−0.632673	−	1.24169i	−0.955432	−	0.295210i	$-0.904610\pi$
$103$	−6.42093	−	12.6018i	−0.632673	−	1.24169i	0.322759	−	0.946481i	$-0.395390\pi$
$104$		0			0
$105$	−0.887812	+	1.00964i	−0.0866416	+	0.0985305i
$106$		0			0
$107$	−1.63321	+	1.63321i	−0.157888	+	0.157888i	−0.781630	−	0.623742i	$-0.785612\pi$
$107$	−1.63321	+	1.63321i	−0.157888	+	0.157888i	0.623742	+	0.781630i	$0.285612\pi$
$108$		0			0
$109$	−2.52845	+	3.48012i	−0.242182	+	0.333335i	−0.912754	−	0.408509i	$-0.866049\pi$
$109$	−2.52845	+	3.48012i	−0.242182	+	0.333335i	0.670572	+	0.741844i	$0.266049\pi$
$110$		0			0
$111$	−10.6883	−	7.68825i	−1.01449	−	0.729736i
$112$		0			0
$113$	0.695637	+	4.39208i	0.0654401	+	0.413172i	0.998562	+	0.0536118i	$0.0170733\pi$
$113$	0.695637	+	4.39208i	0.0654401	+	0.413172i	−0.933122	+	0.359560i	$0.882927\pi$
$114$		0			0
$115$	−2.81738	+	2.31436i	−0.262722	+	0.215815i
$116$		0			0
$117$	2.66909	+	15.8751i	0.246757	+	1.46765i
$118$		0			0
$119$	0.796023	+	2.44991i	0.0729713	+	0.224583i
$120$		0			0
$121$	2.70678	−	8.33062i	0.246071	−	0.757329i
$122$		0			0
$123$	−1.18668	−	7.26890i	−0.106999	−	0.655415i
$124$		0			0
$125$	9.18128	+	6.37997i	0.821199	+	0.570642i
$126$		0			0
$127$	9.40727	+	1.48997i	0.834760	+	0.132213i	0.559161	−	0.829059i	$-0.311124\pi$
$127$	9.40727	+	1.48997i	0.834760	+	0.132213i	0.275600	+	0.961272i	$0.411124\pi$
$128$		0			0
$129$	−0.0353179	−	7.44081i	−0.00310956	−	0.655127i
$130$		0			0
$131$	−18.1696	+	5.90366i	−1.58748	+	0.515805i	−0.963971	−	0.266007i	$-0.914295\pi$
$131$	−18.1696	+	5.90366i	−1.58748	+	0.515805i	−0.623514	+	0.781812i	$0.714295\pi$
$132$		0			0
$133$	1.04752	+	0.533739i	0.0908317	+	0.0462811i
$134$		0			0
$135$	−11.5875	+	0.854494i	−0.997292	+	0.0735431i
$136$		0			0
$137$	−13.6830	+	2.16717i	−1.16902	+	0.185154i	−0.710609	−	0.703587i	$-0.751580\pi$
$137$	−13.6830	+	2.16717i	−1.16902	+	0.185154i	−0.458409	+	0.888741i	$0.651580\pi$
$138$		0			0
$139$	−6.20281	−	8.53743i	−0.526115	−	0.724136i	0.460417	−	0.887703i	$-0.347700\pi$
$139$	−6.20281	−	8.53743i	−0.526115	−	0.724136i	−0.986532	+	0.163567i	$0.947700\pi$
$140$		0			0
$141$	−5.21008	−	1.66556i	−0.438768	−	0.140265i
$142$		0			0
$143$	−5.67966	−	5.67966i	−0.474957	−	0.474957i
$144$		0			0
$145$	2.33490	+	3.97947i	0.193903	+	0.330477i
$146$		0			0
$147$	8.46552	+	8.38554i	0.698225	+	0.691628i
$148$		0			0
$149$	−3.21507			−0.263389			−0.131695	−	0.991290i	$-0.542042\pi$
$149$	−3.21507			−0.263389			−0.131695	+	0.991290i	$0.542042\pi$
$150$		0			0
$151$	13.2319			1.07680			0.538400	−	0.842689i	$-0.319029\pi$
$151$	13.2319			1.07680			0.538400	+	0.842689i	$0.319029\pi$
$152$		0			0
$153$	−9.91793	+	19.9305i	−0.801817	+	1.61129i
$154$		0			0
$155$	−14.0437	−	6.13507i	−1.12802	−	0.492781i
$156$		0			0
$157$	−6.70136	−	6.70136i	−0.534827	−	0.534827i	0.387178	−	0.922005i	$-0.373450\pi$
$157$	−6.70136	−	6.70136i	−0.534827	−	0.534827i	−0.922005	+	0.387178i	$0.873450\pi$
$158$		0			0
$159$	−0.125910	+	0.393862i	−0.00998531	+	0.0312353i
$160$		0			0
$161$	−0.332707	−	0.457932i	−0.0262210	−	0.0360901i
$162$		0			0
$163$	9.95274	−	1.57636i	0.779559	−	0.123470i	0.246042	−	0.969259i	$-0.420870\pi$
$163$	9.95274	−	1.57636i	0.779559	−	0.123470i	0.533517	+	0.845789i	$0.320870\pi$
$164$		0			0
$165$	4.46224	−	3.70115i	0.347385	−	0.288134i
$166$		0			0
$167$	−9.23014	−	4.70299i	−0.714249	−	0.363928i	0.0588037	−	0.998270i	$-0.481271\pi$
$167$	−9.23014	−	4.70299i	−0.714249	−	0.363928i	−0.773053	+	0.634341i	$0.781271\pi$
$168$		0			0
$169$	15.0206	−	4.88050i	1.15543	−	0.375423i
$170$		0			0
$171$	3.23125	+	9.63266i	0.247100	+	0.736628i
$172$		0			0
$173$	21.4566	+	3.39839i	1.63132	+	0.258375i	0.903875	−	0.427796i	$-0.140710\pi$
$173$	21.4566	+	3.39839i	1.63132	+	0.258375i	0.727440	+	0.686171i	$0.240710\pi$
$174$		0			0
$175$	−1.07329	+	1.36407i	−0.0811329	+	0.103114i
$176$		0			0
$177$	−5.44722	+	0.889279i	−0.409438	+	0.0668423i
$178$		0			0
$179$	−5.69521	+	17.5280i	−0.425680	+	1.31011i	0.476662	+	0.879087i	$0.341847\pi$
$179$	−5.69521	+	17.5280i	−0.425680	+	1.31011i	−0.902342	+	0.431021i	$0.858153\pi$
$180$		0			0
$181$	−0.883167	−	2.71811i	−0.0656453	−	0.202035i	0.912854	−	0.408287i	$-0.133874\pi$
$181$	−0.883167	−	2.71811i	−0.0656453	−	0.202035i	−0.978499	+	0.206251i	$0.933874\pi$
$182$		0			0
$183$	−1.10704	+	7.21094i	−0.0818349	+	0.533048i
$184$		0			0
$185$	−14.3198	−	9.15733i	−1.05282	−	0.673260i
$186$		0			0
$187$	−1.73765	−	10.9711i	−0.127069	−	0.802285i
$188$		0			0
$189$	−0.0256840	−	1.80360i	−0.00186823	−	0.131193i
$190$		0			0
$191$	−9.19912	+	12.6615i	−0.665625	+	0.916154i	−0.999651	−	0.0264098i	$-0.991593\pi$
$191$	−9.19912	+	12.6615i	−0.665625	+	0.916154i	0.334026	+	0.942564i	$0.391593\pi$
$192$		0			0
$193$	7.21036	−	7.21036i	0.519013	−	0.519013i	−0.398260	−	0.917273i	$-0.630386\pi$
$193$	7.21036	−	7.21036i	0.519013	−	0.519013i	0.917273	+	0.398260i	$0.130386\pi$
$194$		0			0
$195$	4.55957	+	20.2760i	0.326518	+	1.45199i
$196$		0			0
$197$	−6.50774	−	12.7722i	−0.463657	−	0.909979i	−0.997908	−	0.0646527i	$-0.979406\pi$
$197$	−6.50774	−	12.7722i	−0.463657	−	0.909979i	0.534250	−	0.845326i	$-0.320594\pi$
$198$		0			0
$199$			9.24251i			0.655184i	0.944819	+	0.327592i	$0.106237\pi$
$199$			9.24251i			0.655184i	−0.944819	+	0.327592i	$0.893763\pi$
$200$		0			0
$201$	−6.84079	−	20.7187i	−0.482512	−	1.46138i
$202$		0			0
$203$	−0.638212	+	0.325185i	−0.0447937	+	0.0228235i
$204$		0			0
$205$	−2.04205	−	9.28647i	−0.142623	−	0.648596i
$206$		0			0
$207$	0.719335	−	4.83854i	0.0499972	−	0.336302i
$208$		0			0
$209$	−4.10135	−	2.97980i	−0.283696	−	0.206117i
$210$		0			0
$211$	−8.57544	+	6.23042i	−0.590358	+	0.428920i	−0.842443	−	0.538785i	$-0.818884\pi$
$211$	−8.57544	+	6.23042i	−0.590358	+	0.428920i	0.252085	+	0.967705i	$0.418884\pi$
$212$		0			0
$213$	−24.2903	+	12.5221i	−1.66434	+	0.858001i
$214$		0			0
$215$	−0.569984	−	9.58923i	−0.0388726	−	0.653980i
$216$		0			0
$217$	1.08012	−	2.11986i	0.0733237	−	0.143906i
$218$		0			0
$219$	−13.2462	−	18.0510i	−0.895096	−	1.21978i
$220$		0			0
$221$	37.8700	+	12.3047i	2.54741	+	0.827704i
$222$		0			0
$223$	0.952406	−	6.01326i	0.0637778	−	0.402677i	−0.935060	−	0.354488i	$-0.884655\pi$
$223$	0.952406	−	6.01326i	0.0637778	−	0.402677i	0.998838	−	0.0481890i	$-0.0153450\pi$
$224$		0			0
$225$	−14.8768	+	1.91823i	−0.991789	+	0.127882i
$226$		0			0
$227$	−0.651345	+	4.11243i	−0.0432313	+	0.272952i	−0.999830	−	0.0184580i	$-0.994124\pi$
$227$	−0.651345	+	4.11243i	−0.0432313	+	0.272952i	0.956598	+	0.291410i	$0.0941243\pi$
$228$		0			0
$229$	18.6691	+	6.06597i	1.23369	+	0.400851i	0.852051	−	0.523460i	$-0.175359\pi$
$229$	18.6691	+	6.06597i	1.23369	+	0.400851i	0.381642	+	0.924310i	$0.375359\pi$
$230$		0			0
$231$	0.532469	+	0.725613i	0.0350339	+	0.0477418i
$232$		0			0
$233$	6.67158	−	13.0937i	0.437070	−	0.857797i	−0.562451	−	0.826831i	$-0.690141\pi$
$233$	6.67158	−	13.0937i	0.437070	−	0.857797i	0.999520	−	0.0309667i	$-0.00985859\pi$
$234$		0			0
$235$	−6.83354	−	1.77979i	−0.445771	−	0.116101i
$236$		0			0
$237$	16.0977	−	8.29867i	1.04566	−	0.539057i
$238$		0			0
$239$	5.39910	−	3.92267i	0.349239	−	0.253737i	−0.399311	−	0.916816i	$-0.630751\pi$
$239$	5.39910	−	3.92267i	0.349239	−	0.253737i	0.748550	+	0.663079i	$0.230751\pi$
$240$		0			0
$241$	−19.2337	−	13.9741i	−1.23895	−	0.900153i	−0.241426	−	0.970419i	$-0.577615\pi$
$241$	−19.2337	−	13.9741i	−1.23895	−	0.900153i	−0.997528	+	0.0702665i	$0.977615\pi$
$242$		0			0
$243$	10.7580	−	11.2812i	0.690128	−	0.723687i
$244$		0			0
$245$	11.5037	+	10.2129i	0.734944	+	0.652475i
$246$		0			0
$247$	16.1923	−	8.25039i	1.03029	−	0.524960i
$248$		0			0
$249$	7.91567	+	23.9741i	0.501635	+	1.51930i
$250$		0			0
$251$		−	26.5783i		−	1.67761i	−0.544435	−	0.838803i	$-0.683256\pi$
$251$		−	26.5783i		−	1.67761i	0.544435	−	0.838803i	$-0.316744\pi$
$252$		0			0
$253$	1.10809	+	2.17475i	0.0696652	+	0.136726i
$254$		0			0
$255$	−11.3801	+	26.3909i	−0.712650	+	1.65266i
$256$		0			0
$257$	10.0358	−	10.0358i	0.626014	−	0.626014i	−0.321049	−	0.947063i	$-0.604035\pi$
$257$	10.0358	−	10.0358i	0.626014	−	0.626014i	0.947063	+	0.321049i	$0.104035\pi$
$258$		0			0
$259$	1.55103	−	2.13481i	0.0963765	−	0.132651i
$260$		0			0
$261$	−5.90510	−	1.85690i	−0.365516	−	0.114939i
$262$		0			0
$263$	3.61785	+	22.8422i	0.223086	+	1.40851i	0.804040	+	0.594575i	$0.202680\pi$
$263$	3.61785	+	22.8422i	0.223086	+	1.40851i	−0.580954	+	0.813937i	$0.697320\pi$
$264$		0			0
$265$	−0.134546	+	0.516590i	−0.00826508	+	0.0317339i
$266$		0			0
$267$	3.32124	−	21.6336i	0.203257	−	1.32395i
$268$		0			0
$269$	2.60045	+	8.00336i	0.158552	+	0.487974i	0.998503	−	0.0546882i	$-0.0174165\pi$
$269$	2.60045	+	8.00336i	0.158552	+	0.487974i	−0.839951	+	0.542662i	$0.817416\pi$
$270$		0			0
$271$	−7.11567	+	21.8998i	−0.432246	+	1.33032i	0.463636	+	0.886026i	$0.346544\pi$
$271$	−7.11567	+	21.8998i	−0.432246	+	1.33032i	−0.895882	+	0.444291i	$0.853456\pi$
$272$		0			0
$273$	−3.18420	+	0.519832i	−0.192716	+	0.0314617i
$274$		0			0
$275$	5.49126	−	5.08555i	0.331135	−	0.306670i
$276$		0			0
$277$	−11.0819	−	1.75520i	−0.665845	−	0.105459i	−0.185643	−	0.982617i	$-0.559437\pi$
$277$	−11.0819	−	1.75520i	−0.665845	−	0.105459i	−0.480202	+	0.877158i	$0.659437\pi$
$278$		0			0
$279$	19.4935	−	6.53906i	1.16705	−	0.391483i
$280$		0			0
$281$	14.6137	−	4.74827i	0.871778	−	0.283258i	0.161239	−	0.986915i	$-0.448451\pi$
$281$	14.6137	−	4.74827i	0.871778	−	0.283258i	0.710539	+	0.703658i	$0.248451\pi$
$282$		0			0
$283$	7.57810	+	3.86124i	0.450471	+	0.229527i	0.664481	−	0.747305i	$-0.268652\pi$
$283$	7.57810	+	3.86124i	0.450471	+	0.229527i	−0.214010	+	0.976831i	$0.568652\pi$
$284$		0			0
$285$	4.84425	+	12.1894i	0.286949	+	0.722038i
$286$		0			0
$287$	1.45795	−	0.230917i	0.0860600	−	0.0136306i
$288$		0			0
$289$	22.3744	+	30.7958i	1.31614	+	1.81152i
$290$		0			0
$291$	−1.61686	+	5.05774i	−0.0947820	+	0.296490i
$292$		0			0
$293$	3.65414	+	3.65414i	0.213477	+	0.213477i	0.805743	−	0.592266i	$-0.201766\pi$
$293$	3.65414	+	3.65414i	0.213477	+	0.213477i	−0.592266	+	0.805743i	$0.701766\pi$
$294$		0			0
$295$	−6.95917	+	1.53028i	−0.405178	+	0.0890966i
$296$		0			0
$297$	−1.10724	+	7.69884i	−0.0642488	+	0.446732i
$298$		0			0
$299$	−8.74960			−0.506003
$300$		0			0
$301$	1.49131			0.0859575
$302$		0			0
$303$	−2.66093	−	2.63579i	−0.152867	−	0.151422i
$304$		0			0
$305$	−0.918798	+	9.37342i	−0.0526102	+	0.536721i
$306$		0			0
$307$	1.46729	+	1.46729i	0.0837427	+	0.0837427i	0.747737	−	0.663995i	$-0.231140\pi$
$307$	1.46729	+	1.46729i	0.0837427	+	0.0837427i	−0.663995	+	0.747737i	$0.731140\pi$
$308$		0			0
$309$	23.3337	+	7.45931i	1.32741	+	0.424345i
$310$		0			0
$311$	13.3661	+	18.3969i	0.757922	+	1.04319i	0.997384	+	0.0722845i	$0.0230290\pi$
$311$	13.3661	+	18.3969i	0.757922	+	1.04319i	−0.239462	+	0.970906i	$0.576971\pi$
$312$		0			0
$313$	22.0952	−	3.49953i	1.24889	−	0.197805i	0.503245	−	0.864144i	$-0.332139\pi$
$313$	22.0952	−	3.49953i	1.24889	−	0.197805i	0.745649	+	0.666339i	$0.232139\pi$
$314$		0			0
$315$	−0.160233	−	2.32316i	−0.00902811	−	0.130895i
$316$		0			0
$317$	−2.91256	−	1.48402i	−0.163586	−	0.0833510i	0.370281	−	0.928920i	$-0.379261\pi$
$317$	−2.91256	−	1.48402i	−0.163586	−	0.0833510i	−0.533866	+	0.845569i	$0.679261\pi$
$318$		0			0
$319$	2.93749	−	0.954449i	0.164468	−	0.0534389i
$320$		0			0
$321$	−0.0189883	−	4.00049i	−0.00105983	−	0.223285i
$322$		0			0
$323$	24.8222	+	3.93145i	1.38114	+	0.218752i
$324$		0			0
$325$	7.30673	+	25.8157i	0.405305	+	1.43200i
$326$		0			0
$327$	−1.20046	−	7.35335i	−0.0663857	−	0.406641i
$328$		0			0
$329$	0.338764	−	1.04261i	0.0186767	−	0.0574809i
$330$		0			0
$331$	−5.16968	−	15.9106i	−0.284151	−	0.874527i	−0.986652	−	0.162844i	$-0.947933\pi$
$331$	−5.16968	−	15.9106i	−0.284151	−	0.874527i	0.702501	−	0.711683i	$-0.252067\pi$
$332$		0			0
$333$	22.4889	−	3.78107i	1.23238	−	0.207201i
$334$		0			0
$335$	−10.2786	−	26.2256i	−0.561579	−	1.43286i
$336$		0			0
$337$	−3.12579	−	19.7355i	−0.170273	−	1.07506i	−0.913744	−	0.406291i	$-0.866822\pi$
$337$	−3.12579	−	19.7355i	−0.170273	−	1.07506i	0.743471	−	0.668768i	$-0.233178\pi$
$338$		0			0
$339$	−6.25257	−	4.49757i	−0.339593	−	0.244275i
$340$		0			0
$341$	−6.03020	+	8.29986i	−0.326554	+	0.449463i
$342$		0			0
$343$	−3.40692	+	3.40692i	−0.183956	+	0.183956i
$344$		0			0
$345$	0.586233	−	6.28791i	0.0315617	−	0.338530i
$346$		0			0
$347$	−0.905384	−	1.77692i	−0.0486036	−	0.0953899i	0.865427	−	0.501035i	$-0.167047\pi$
$347$	−0.905384	−	1.77692i	−0.0486036	−	0.0953899i	−0.914031	+	0.405645i	$0.867047\pi$
$348$		0			0
$349$		−	19.7345i		−	1.05636i	−0.849132	−	0.528181i	$-0.822874\pi$
$349$		−	19.7345i		−	1.05636i	0.849132	−	0.528181i	$-0.177126\pi$
$350$		0			0
$351$	−22.7884	−	16.0660i	−1.21635	−	0.857540i
$352$		0			0
$353$	−11.2294	+	5.72168i	−0.597682	+	0.304534i	−0.726535	−	0.687129i	$-0.758871\pi$
$353$	−11.2294	+	5.72168i	−0.597682	+	0.304534i	0.128853	+	0.991664i	$0.458871\pi$
$354$		0			0
$355$	−30.4293	+	17.8539i	−1.61502	+	0.947588i
$356$		0			0
$357$	−3.98501	−	2.00669i	−0.210909	−	0.106205i
$358$		0			0
$359$	−14.9247	−	10.8434i	−0.787695	−	0.572294i	0.119583	−	0.992824i	$-0.461844\pi$
$359$	−14.9247	−	10.8434i	−0.787695	−	0.572294i	−0.907279	+	0.420530i	$0.861844\pi$
$360$		0			0
$361$	−6.09198	+	4.42609i	−0.320631	+	0.232952i
$362$		0			0
$363$	6.95185	+	13.4852i	0.364877	+	0.707787i
$364$		0			0
$365$	−18.3476	−	22.3354i	−0.960356	−	1.16909i
$366$		0			0
$367$	13.9237	−	27.3269i	0.726814	−	1.42645i	−0.170636	−	0.985334i	$-0.554582\pi$
$367$	13.9237	−	27.3269i	0.726814	−	1.42645i	0.897449	−	0.441118i	$-0.145418\pi$
$368$		0			0
$369$	10.3912	+	7.39994i	0.540942	+	0.385225i
$370$		0			0
$371$	−0.0788174	−	0.0256093i	−0.00409200	−	0.00132957i
$372$		0			0
$373$	−1.64265	+	10.3713i	−0.0850532	+	0.537005i	0.907965	+	0.419046i	$0.137635\pi$
$373$	−1.64265	+	10.3713i	−0.0850532	+	0.537005i	−0.993018	+	0.117959i	$0.962365\pi$
$374$		0			0
$375$	−19.0421	+	3.52131i	−0.983328	+	0.181840i
$376$		0			0
$377$	−1.73206	+	10.9358i	−0.0892055	+	0.563221i
$378$		0			0
$379$	−18.0985	−	5.88056i	−0.929657	−	0.302064i	−0.195235	−	0.980757i	$-0.562547\pi$
$379$	−18.0985	−	5.88056i	−0.929657	−	0.302064i	−0.734423	+	0.678693i	$0.762547\pi$
$380$		0			0
$381$	−13.3002	+	9.75992i	−0.681388	+	0.500016i
$382$		0			0
$383$	−2.02976	+	3.98364i	−0.103716	+	0.203554i	−0.937033	−	0.349242i	$-0.886439\pi$
$383$	−2.02976	+	3.98364i	−0.103716	+	0.203554i	0.833317	+	0.552796i	$0.186439\pi$
$384$		0			0
$385$	0.737533	+	0.897834i	0.0375882	+	0.0457579i
$386$		0			0
$387$	9.19929	+	9.02628i	0.467626	+	0.458831i
$388$		0			0
$389$	−6.59921	+	4.79461i	−0.334593	+	0.243096i	−0.742377	−	0.669982i	$-0.766302\pi$
$389$	−6.59921	+	4.79461i	−0.334593	+	0.243096i	0.407784	+	0.913079i	$0.366302\pi$
$390$		0			0
$391$	−9.78900	−	7.11213i	−0.495051	−	0.359676i
$392$		0			0
$393$	14.8825	−	29.5546i	0.750724	−	1.49083i
$394$		0			0
$395$	20.1661	−	11.8322i	1.01467	−	0.595342i
$396$		0			0
$397$	−27.6243	+	14.0753i	−1.38642	+	0.706418i	−0.978432	−	0.206568i	$-0.933771\pi$
$397$	−27.6243	+	14.0753i	−1.38642	+	0.706418i	−0.407991	+	0.912986i	$0.633771\pi$
$398$		0			0
$399$	−1.93363	+	0.638438i	−0.0968028	+	0.0319619i
$400$		0			0
$401$		−	30.3238i		−	1.51430i	−0.653241	−	0.757150i	$-0.726591\pi$
$401$		−	30.3238i		−	1.51430i	0.653241	−	0.757150i	$-0.273409\pi$
$402$		0			0
$403$	−16.6963	−	32.7683i	−0.831700	−	1.63230i
$404$		0			0
$405$	13.0727	−	15.3005i	0.649588	−	0.760287i
$406$		0			0
$407$	−8.04588	+	8.04588i	−0.398819	+	0.398819i
$408$		0			0
$409$	−23.2791	+	32.0409i	−1.15108	+	1.58432i	−0.411250	+	0.911523i	$0.634908\pi$
$409$	−23.2791	+	32.0409i	−1.15108	+	1.58432i	−0.739826	+	0.672798i	$0.765092\pi$
$410$		0			0
$411$	14.0117	−	19.4791i	0.691144	−	0.960835i
$412$		0			0
$413$	−0.173046	−	1.09257i	−0.00851503	−	0.0537618i
$414$		0			0
$415$	11.8936	+	30.3464i	0.583836	+	1.48965i
$416$		0			0
$417$	18.0664	+	2.77360i	0.884716	+	0.135824i
$418$		0			0
$419$	5.71751	+	17.5967i	0.279319	+	0.859655i	0.988044	+	0.154171i	$0.0492705\pi$
$419$	5.71751	+	17.5967i	0.279319	+	0.859655i	−0.708725	+	0.705484i	$0.750729\pi$
$420$		0			0
$421$	−6.75964	+	20.8040i	−0.329445	+	1.01393i	0.639949	+	0.768417i	$0.278955\pi$
$421$	−6.75964	+	20.8040i	−0.329445	+	1.01393i	−0.969394	+	0.245510i	$0.921045\pi$
$422$		0			0
$423$	8.40020	−	4.38105i	0.408432	−	0.213014i
$424$		0			0
$425$	−12.8096	+	34.8218i	−0.621358	+	1.68910i
$426$		0			0
$427$	−1.44415	−	0.228731i	−0.0698873	−	0.0110691i
$428$		0			0
$429$	13.9121	−	0.0660339i	0.671683	−	0.00318815i
$430$		0			0
$431$	−25.6284	+	8.32716i	−1.23447	+	0.401105i	−0.852333	−	0.522999i	$-0.824813\pi$
$431$	−25.6284	+	8.32716i	−1.23447	+	0.401105i	−0.382141	+	0.924104i	$0.624813\pi$
$432$		0			0
$433$	0.736984	+	0.375512i	0.0354172	+	0.0180460i	0.471609	−	0.881808i	$-0.343673\pi$
$433$	0.736984	+	0.375512i	0.0354172	+	0.0180460i	−0.436192	+	0.899854i	$0.643673\pi$
$434$		0			0
$435$	−7.74296	−	1.97745i	−0.371246	−	0.0948116i
$436$		0			0
$437$	−5.45431	+	0.863878i	−0.260915	+	0.0413249i
$438$		0			0
$439$	11.6409	+	16.0224i	0.555591	+	0.764705i	0.990758	−	0.135645i	$-0.0433105\pi$
$439$	11.6409	+	16.0224i	0.555591	+	0.764705i	−0.435167	+	0.900350i	$0.643311\pi$
$440$		0			0
$441$	−20.6376	+	0.195917i	−0.982741	+	0.00932938i
$442$		0			0
$443$	−26.4453	−	26.4453i	−1.25645	−	1.25645i	−0.952775	−	0.303677i	$-0.901786\pi$
$443$	−26.4453	−	26.4453i	−1.25645	−	1.25645i	−0.303677	−	0.952775i	$-0.598214\pi$
$444$		0			0
$445$	2.75649	−	28.1213i	0.130670	−	1.33308i
$446$		0			0
$447$	3.91891	−	3.95629i	0.185358	−	0.187126i
$448$		0			0
$449$	−18.7481			−0.884779			−0.442390	−	0.896823i	$-0.645869\pi$
$449$	−18.7481			−0.884779			−0.442390	+	0.896823i	$0.645869\pi$
$450$		0			0
$451$	−6.36515			−0.299723
$452$		0			0
$453$	−16.1286	+	16.2825i	−0.757790	+	0.765018i
$454$		0			0
$455$	−4.06801	+	0.894533i	−0.190711	+	0.0419364i
$456$		0			0
$457$	0.650828	+	0.650828i	0.0304444	+	0.0304444i	0.722165	−	0.691721i	$-0.243147\pi$
$457$	0.650828	+	0.650828i	0.0304444	+	0.0304444i	−0.691721	+	0.722165i	$0.743147\pi$
$458$		0			0
$459$	−12.4362	−	36.4981i	−0.580474	−	1.70359i
$460$		0			0
$461$	−12.6563	−	17.4199i	−0.589464	−	0.811328i	0.405229	−	0.914215i	$-0.367192\pi$
$461$	−12.6563	−	17.4199i	−0.589464	−	0.811328i	−0.994693	+	0.102888i	$0.967192\pi$
$462$		0			0
$463$	27.7819	−	4.40022i	1.29113	−	0.204495i	0.527172	−	0.849758i	$-0.323252\pi$
$463$	27.7819	−	4.40022i	1.29113	−	0.204495i	0.763961	+	0.645263i	$0.223252\pi$
$464$		0			0
$465$	24.6676	−	9.80328i	1.14393	−	0.454616i
$466$		0			0
$467$	26.7269	+	13.6180i	1.23677	+	0.630168i	0.945235	−	0.326391i	$-0.105833\pi$
$467$	26.7269	+	13.6180i	1.23677	+	0.630168i	0.291539	+	0.956559i	$0.405833\pi$
$468$		0			0
$469$	4.15890	−	1.35131i	0.192040	−	0.0623977i
$470$		0			0
$471$	16.4147	−	0.0779126i	0.756351	−	0.00359002i
$472$		0			0
$473$	−6.35146	−	1.00597i	−0.292040	−	0.0462546i
$474$		0			0
$475$	7.10373	+	15.3715i	0.325942	+	0.705295i
$476$		0			0
$477$	−0.331191	−	0.635023i	−0.0151642	−	0.0290757i
$478$		0			0
$479$	−8.94946	+	27.5436i	−0.408911	+	1.25850i	0.508673	+	0.860960i	$0.330136\pi$
$479$	−8.94946	+	27.5436i	−0.408911	+	1.25850i	−0.917585	+	0.397540i	$0.869864\pi$
$480$		0			0
$481$	−12.6046	−	38.7931i	−0.574722	−	1.76881i
$482$		0			0
$483$	0.969048	+	0.148771i	0.0440932	+	0.00676930i
$484$		0			0
$485$	−1.72775	+	6.63374i	−0.0784533	+	0.301223i
$486$		0			0
$487$	2.59886	+	16.4086i	0.117766	+	0.743544i	0.973931	+	0.226842i	$0.0728402\pi$
$487$	2.59886	+	16.4086i	0.117766	+	0.743544i	−0.856166	+	0.516701i	$0.827160\pi$
$488$		0			0
$489$	−10.1918	+	14.1687i	−0.460889	+	0.640732i
$490$		0			0
$491$	−20.7228	+	28.5225i	−0.935207	+	1.28720i	0.0225861	+	0.999745i	$0.492810\pi$
$491$	−20.7228	+	28.5225i	−0.935207	+	1.28720i	−0.957793	+	0.287457i	$0.907190\pi$
$492$		0			0
$493$	−10.8270	+	10.8270i	−0.487622	+	0.487622i
$494$		0			0
$495$	−0.884671	+	10.0024i	−0.0397630	+	0.449573i
$496$		0			0
$497$	−2.48655	−	4.88013i	−0.111537	−	0.218904i
$498$		0			0
$499$		−	3.09564i		−	0.138580i	−0.997597	−	0.0692900i	$-0.977927\pi$
$499$		−	3.09564i		−	0.138580i	0.997597	−	0.0692900i	$-0.0220734\pi$
$500$		0			0
$501$	17.0380	−	5.62553i	0.761202	−	0.251330i
$502$		0			0
$503$	4.58961	−	2.33852i	0.204641	−	0.104270i	−0.348667	−	0.937247i	$-0.613366\pi$
$503$	4.58961	−	2.33852i	0.204641	−	0.104270i	0.553307	+	0.832977i	$0.313366\pi$
$504$		0			0
$505$	−3.61591	−	3.21016i	−0.160906	−	0.142850i
$506$		0			0
$507$	−12.3032	+	24.4325i	−0.546406	+	1.08508i
$508$		0			0
$509$	22.3242	+	16.2195i	0.989502	+	0.718915i	0.959812	−	0.280644i	$-0.0905481\pi$
$509$	22.3242	+	16.2195i	0.989502	+	0.718915i	0.0296898	+	0.999559i	$0.490548\pi$
$510$		0			0
$511$	3.63036	−	2.63761i	0.160598	−	0.116681i
$512$		0			0
$513$	−15.7920	−	7.76522i	−0.697236	−	0.342843i
$514$		0			0
$515$	30.6044	+	7.97091i	1.34859	+	0.351240i
$516$		0			0
$517$	−2.14609	+	4.21194i	−0.0943850	+	0.185241i
$518$		0			0
$519$	−30.3357	+	22.2609i	−1.33159	+	0.977147i
$520$		0			0
$521$	12.0428	+	3.91295i	0.527606	+	0.171430i	0.560694	−	0.828023i	$-0.310534\pi$
$521$	12.0428	+	3.91295i	0.527606	+	0.171430i	−0.0330883	+	0.999452i	$0.510534\pi$
$522$		0			0
$523$	−3.21583	+	20.3040i	−0.140619	+	0.887831i	0.811999	+	0.583659i	$0.198380\pi$
$523$	−3.21583	+	20.3040i	−0.140619	+	0.887831i	−0.952617	+	0.304172i	$0.901620\pi$
$524$		0			0
$525$	−0.370297	−	2.98342i	−0.0161611	−	0.130207i
$526$		0			0
$527$	7.95605	−	50.2325i	0.346571	−	2.18816i
$528$		0			0
$529$	−19.3457	−	6.28579i	−0.841116	−	0.273295i
$530$		0			0
$531$	5.54542	−	7.78701i	0.240651	−	0.337927i
$532$		0			0
$533$	10.3589	−	20.3305i	0.448695	−	0.880613i
$534$		0			0
$535$	−0.306447	−	5.15557i	−0.0132489	−	0.222895i
$536$		0			0
$537$	−14.6270	−	28.3735i	−0.631204	−	1.22440i
$538$		0			0
$539$	8.33112	−	6.05291i	0.358847	−	0.260717i
$540$		0			0
$541$	23.2522	+	16.8937i	0.999689	+	0.726317i	0.962022	−	0.272974i	$-0.0880072\pi$
$541$	23.2522	+	16.8937i	0.999689	+	0.726317i	0.0376677	+	0.999290i	$0.488007\pi$
$542$		0			0
$543$	4.42126	+	2.22638i	0.189735	+	0.0955429i
$544$		0			0
$545$	−2.06577	−	9.39436i	−0.0884879	−	0.402410i
$546$		0			0
$547$	−22.4858	+	11.4571i	−0.961424	+	0.489870i	−0.862961	−	0.505271i	$-0.831393\pi$
$547$	−22.4858	+	11.4571i	−0.961424	+	0.489870i	−0.0984630	+	0.995141i	$0.531393\pi$
$548$		0			0
$549$	−7.52399	−	10.1518i	−0.321116	−	0.433268i
$550$		0			0
$551$			6.98813i			0.297705i
$552$		0			0
$553$	1.64789	+	3.23417i	0.0700755	+	0.137531i
$554$		0			0
$555$	28.7232	−	6.45916i	1.21923	−	0.274176i
$556$		0			0
$557$	−26.1957	+	26.1957i	−1.10995	+	1.10995i	−0.116791	+	0.993157i	$0.537261\pi$
$557$	−26.1957	+	26.1957i	−1.10995	+	1.10995i	−0.993157	+	0.116791i	$0.962739\pi$
$558$		0			0
$559$	13.5497	−	18.6496i	0.573093	−	0.788795i
$560$		0			0
$561$	15.6184	+	11.2346i	0.659411	+	0.474325i
$562$		0			0
$563$	−0.227603	−	1.43703i	−0.00959232	−	0.0605636i	0.982428	−	0.186643i	$-0.0597607\pi$
$563$	−0.227603	−	1.43703i	−0.00959232	−	0.0605636i	−0.992020	+	0.126079i	$0.959761\pi$
$564$		0			0
$565$	−8.37701	−	5.35698i	−0.352423	−	0.225370i
$566$		0			0
$567$	2.25072	+	2.16684i	0.0945213	+	0.0909986i
$568$		0			0
$569$	−7.83577	−	24.1160i	−0.328493	−	1.01100i	−0.969839	−	0.243745i	$-0.921624\pi$
$569$	−7.83577	−	24.1160i	−0.328493	−	1.01100i	0.641347	−	0.767251i	$-0.278376\pi$
$570$		0			0
$571$	−3.23704	+	9.96258i	−0.135466	+	0.416921i	−0.995662	−	0.0930420i	$-0.970341\pi$
$571$	−3.23704	+	9.96258i	−0.135466	+	0.416921i	0.860196	+	0.509963i	$0.170341\pi$
$572$		0			0
$573$	−4.36757	−	26.7532i	−0.182458	−	1.11763i
$574$		0			0
$575$	0.312499	−	8.14687i	0.0130321	−	0.339748i
$576$		0			0
$577$	−12.5173	−	1.98255i	−0.521102	−	0.0825345i	−0.109658	−	0.993969i	$-0.534976\pi$
$577$	−12.5173	−	1.98255i	−0.521102	−	0.0825345i	−0.411444	+	0.911435i	$0.634976\pi$
$578$		0			0
$579$	0.0838305	+	17.6615i	0.00348388	+	0.733987i
$580$		0			0
$581$	−4.81239	+	1.56364i	−0.199651	+	0.0648707i
$582$		0			0
$583$	0.318407	+	0.162237i	0.0131871	+	0.00671915i
$584$		0			0
$585$	−30.5082	−	19.1040i	−1.26136	−	0.789852i
$586$		0			0
$587$	27.7688	−	4.39815i	1.14614	−	0.181531i	0.445661	−	0.895202i	$-0.352969\pi$
$587$	27.7688	−	4.39815i	1.14614	−	0.181531i	0.700481	+	0.713671i	$0.252969\pi$
$588$		0			0
$589$	−13.6434	−	18.7785i	−0.562167	−	0.773756i
$590$		0			0
$591$	23.6491	+	7.56015i	0.972795	+	0.310983i
$592$		0			0
$593$	16.3288	+	16.3288i	0.670545	+	0.670545i	0.957842	−	0.287297i	$-0.0927567\pi$
$593$	16.3288	+	16.3288i	0.670545	+	0.670545i	−0.287297	+	0.957842i	$0.592757\pi$
$594$		0			0
$595$	−5.27839	−	2.30589i	−0.216393	−	0.0945322i
$596$		0			0
$597$	−11.3733	−	11.2659i	−0.465479	−	0.461081i
$598$		0			0
$599$	37.1895			1.51952			0.759761	−	0.650202i	$-0.225316\pi$
$599$	37.1895			1.51952			0.759761	+	0.650202i	$0.225316\pi$
$600$		0			0
$601$	−4.85996			−0.198242			−0.0991209	−	0.995075i	$-0.531603\pi$
$601$	−4.85996			−0.198242			−0.0991209	+	0.995075i	$0.531603\pi$
$602$		0			0
$603$	33.8336	+	16.8364i	1.37781	+	0.685633i
$604$		0			0
$605$	9.91190	+	16.8933i	0.402976	+	0.686810i
$606$		0			0
$607$	17.8944	+	17.8944i	0.726313	+	0.726313i	0.969883	−	0.243570i	$-0.0783187\pi$
$607$	17.8944	+	17.8944i	0.726313	+	0.726313i	−0.243570	+	0.969883i	$0.578319\pi$
$608$		0			0
$609$	0.377773	−	1.18172i	0.0153081	−	0.0478858i
$610$		0			0
$611$	−9.96046	−	13.7094i	−0.402957	−	0.554623i
$612$		0			0
$613$	−9.30092	+	1.47312i	−0.375661	+	0.0594988i	−0.341410	−	0.939914i	$-0.610904\pi$
$613$	−9.30092	+	1.47312i	−0.375661	+	0.0594988i	−0.0342506	+	0.999413i	$0.510904\pi$
$614$		0			0
$615$	13.9165	+	8.80662i	0.561168	+	0.355117i
$616$		0			0
$617$	9.21730	+	4.69645i	0.371075	+	0.189072i	0.629576	−	0.776939i	$-0.283229\pi$
$617$	9.21730	+	4.69645i	0.371075	+	0.189072i	−0.258501	+	0.966011i	$0.583229\pi$
$618$		0			0
$619$	−0.644785	+	0.209503i	−0.0259161	+	0.00842065i	−0.321946	−	0.946758i	$-0.604337\pi$
$619$	−0.644785	+	0.209503i	−0.0259161	+	0.00842065i	0.296030	+	0.955179i	$0.404337\pi$
$620$		0			0
$621$	5.07723	+	6.78296i	0.203742	+	0.272191i
$622$		0			0
$623$	4.33261	+	0.686218i	0.173582	+	0.0274927i
$624$		0			0
$625$	−24.2983	+	5.88137i	−0.971934	+	0.235255i
$626$		0			0
$627$	8.66598	−	1.41475i	0.346086	−	0.0564998i
$628$		0			0
$629$	17.4310	−	53.6471i	0.695020	−	2.13905i
$630$		0			0
$631$	7.71397	+	23.7411i	0.307088	+	0.945120i	0.978890	+	0.204389i	$0.0655207\pi$
$631$	7.71397	+	23.7411i	0.307088	+	0.945120i	−0.671802	+	0.740731i	$0.734479\pi$
$632$		0			0
$633$	2.78595	−	18.1468i	0.110732	−	0.721272i
$634$		0			0
$635$	−16.4569	+	13.5187i	−0.653072	+	0.536471i
$636$		0			0
$637$	5.77480	+	36.4607i	0.228806	+	1.44462i
$638$		0			0
$639$	14.1989	−	45.1537i	0.561699	−	1.78625i
$640$		0			0
$641$	10.2750	−	14.1423i	0.405836	−	0.558586i	−0.556361	−	0.830941i	$-0.687803\pi$
$641$	10.2750	−	14.1423i	0.405836	−	0.558586i	0.962197	+	0.272355i	$0.0878027\pi$
$642$		0			0
$643$	−11.1067	+	11.1067i	−0.438005	+	0.438005i	−0.891340	−	0.453335i	$-0.850234\pi$
$643$	−11.1067	+	11.1067i	−0.438005	+	0.438005i	0.453335	+	0.891340i	$0.350234\pi$
$644$		0			0
$645$	12.4947	+	10.9871i	0.491980	+	0.432616i
$646$		0			0
$647$	10.7527	+	21.1033i	0.422730	+	0.829655i	0.999915	+	0.0130414i	$0.00415134\pi$
$647$	10.7527	+	21.1033i	0.422730	+	0.829655i	−0.577185	+	0.816614i	$0.695849\pi$
$648$		0			0
$649$			4.76996i			0.187237i
$650$		0			0
$651$	1.29200	+	3.91308i	0.0506376	+	0.153366i
$652$		0			0
$653$	−31.4248	+	16.0117i	−1.22975	+	0.626587i	−0.943438	−	0.331550i	$-0.892428\pi$
$653$	−31.4248	+	16.0117i	−1.22975	+	0.626587i	−0.286309	+	0.958137i	$0.592428\pi$
$654$		0			0
$655$	17.1015	−	39.1468i	0.668210	−	1.52959i
$656$		0			0
$657$	38.3586	+	5.70269i	1.49651	+	0.222483i
$658$		0			0
$659$	3.78905	+	2.75290i	0.147600	+	0.107238i	0.659135	−	0.752025i	$-0.270923\pi$
$659$	3.78905	+	2.75290i	0.147600	+	0.107238i	−0.511534	+	0.859263i	$0.670923\pi$
$660$		0			0
$661$	22.2635	−	16.1754i	0.865950	−	0.629149i	−0.0635475	−	0.997979i	$-0.520241\pi$
$661$	22.2635	−	16.1754i	0.865950	−	0.629149i	0.929497	+	0.368830i	$0.120241\pi$
$662$		0			0
$663$	−61.3019	+	31.6023i	−2.38077	+	1.22733i
$664$		0			0
$665$	−2.44759	+	0.959281i	−0.0949134	+	0.0371993i
$666$		0			0
$667$	1.52746	−	2.99780i	0.0591433	−	0.116075i
$668$		0			0
$669$	6.23867	+	8.50164i	0.241201	+	0.328692i
$670$		0			0
$671$	5.99632	+	1.94832i	0.231485	+	0.0752142i
$672$		0			0
$673$	−2.35183	+	14.8489i	−0.0906565	+	0.572383i	0.899988	+	0.435915i	$0.143575\pi$
$673$	−2.35183	+	14.8489i	−0.0906565	+	0.572383i	−0.990644	+	0.136468i	$0.956425\pi$
$674$		0			0
$675$	15.7732	−	20.6448i	0.607110	−	0.794618i
$676$		0			0
$677$	−1.90476	+	12.0262i	−0.0732060	+	0.462204i	0.923668	+	0.383194i	$0.125176\pi$
$677$	−1.90476	+	12.0262i	−0.0732060	+	0.462204i	−0.996874	+	0.0790103i	$0.974824\pi$
$678$		0			0
$679$	−1.01213	−	0.328860i	−0.0388418	−	0.0126205i
$680$		0			0
$681$	−4.26659	−	5.81423i	−0.163496	−	0.222802i
$682$		0			0
$683$	−2.44981	+	4.80802i	−0.0937393	+	0.183974i	−0.933115	−	0.359578i	$-0.882921\pi$
$683$	−2.44981	+	4.80802i	−0.0937393	+	0.183974i	0.839376	+	0.543551i	$0.182921\pi$
$684$		0			0
$685$	16.6890	−	26.0976i	0.637655	−	0.997136i
$686$		0			0
$687$	−30.2206	+	15.5793i	−1.15299	+	0.594387i
$688$		0			0
$689$	−1.03638	+	0.752974i	−0.0394829	+	0.0286860i
$690$		0			0
$691$	16.6980	+	12.1318i	0.635223	+	0.461517i	0.858206	−	0.513306i	$-0.171579\pi$
$691$	16.6980	+	12.1318i	0.635223	+	0.461517i	−0.222983	+	0.974822i	$0.571579\pi$
$692$		0			0
$693$	−1.54193	−	0.229236i	−0.0585732	−	0.00870795i
$694$		0			0
$695$	23.4843	+	2.30197i	0.890811	+	0.0873188i
$696$		0			0
$697$	28.1152	−	14.3254i	1.06494	−	0.542614i
$698$		0			0
$699$	7.98028	+	24.1698i	0.301842	+	0.914187i
$700$		0			0
$701$		−	31.7969i		−	1.20095i	−0.799643	−	0.600475i	$-0.794978\pi$
$701$		−	31.7969i		−	1.20095i	0.799643	−	0.600475i	$-0.205022\pi$
$702$		0			0
$703$	−11.6876	−	22.9382i	−0.440807	−	0.865132i
$704$		0			0
$705$	10.5196	−	6.23955i	0.396193	−	0.234995i
$706$		0			0
$707$	0.530792	−	0.530792i	0.0199625	−	0.0199625i
$708$		0			0
$709$	−3.36185	+	4.62719i	−0.126257	+	0.173778i	−0.867466	−	0.497497i	$-0.834253\pi$
$709$	−3.36185	+	4.62719i	−0.126257	+	0.173778i	0.741209	+	0.671274i	$0.234253\pi$
$710$		0			0
$711$	−9.40991	+	29.9243i	−0.352899	+	1.12225i
$712$		0			0
$713$	1.74822	+	11.0379i	0.0654715	+	0.413371i
$714$		0			0
$715$	17.9290	−	1.06570i	0.670507	−	0.0398549i
$716$		0			0
$717$	−1.75403	+	11.4252i	−0.0655055	+	0.426684i
$718$		0			0
$719$	−10.7159	−	32.9803i	−0.399637	−	1.22996i	−0.925291	−	0.379258i	$-0.876179\pi$
$719$	−10.7159	−	32.9803i	−0.399637	−	1.22996i	0.525654	−	0.850699i	$-0.323821\pi$
$720$		0			0
$721$	−1.51718	+	4.66939i	−0.0565027	+	0.173897i
$722$		0			0
$723$	40.6401	−	6.63465i	1.51142	−	0.246745i
$724$		0			0
$725$	−10.1206	−	2.00332i	−0.375869	−	0.0744015i
$726$		0			0
$727$	1.83595	+	0.290786i	0.0680916	+	0.0107847i	0.190387	−	0.981709i	$-0.439026\pi$
$727$	1.83595	+	0.290786i	0.0680916	+	0.0107847i	−0.122296	+	0.992494i	$0.539026\pi$
$728$		0			0
$729$	0.768825	+	26.9891i	0.0284750	+	0.999595i
$730$		0			0
$731$	30.3187	−	9.85116i	1.12138	−	0.364358i
$732$		0			0
$733$	−35.2924	−	17.9824i	−1.30355	−	0.664194i	−0.342230	−	0.939616i	$-0.611182\pi$
$733$	−35.2924	−	17.9824i	−1.30355	−	0.664194i	−0.961323	+	0.275423i	$0.911182\pi$
$734$		0			0
$735$	−26.5894	+	1.70716i	−0.980766	+	0.0629697i
$736$		0			0
$737$	−18.6242	+	2.94979i	−0.686033	+	0.108657i
$738$		0			0
$739$	−4.54039	−	6.24931i	−0.167021	−	0.229885i	0.717300	−	0.696765i	$-0.245378\pi$
$739$	−4.54039	−	6.24931i	−0.167021	−	0.229885i	−0.884321	+	0.466880i	$0.845378\pi$
$740$		0			0
$741$	−9.58462	+	29.9819i	−0.352100	+	1.10141i
$742$		0			0
$743$	−15.7766	−	15.7766i	−0.578787	−	0.578787i	0.355782	−	0.934569i	$-0.384215\pi$
$743$	−15.7766	−	15.7766i	−0.578787	−	0.578787i	−0.934569	+	0.355782i	$0.884215\pi$
$744$		0			0
$745$	4.77289	−	5.37615i	0.174865	−	0.196967i
$746$		0			0
$747$	−39.1498	−	19.4819i	−1.43242	−	0.712807i
$748$		0			0
$749$	0.801789			0.0292967
$750$		0			0
$751$	21.4943			0.784340			0.392170	−	0.919893i	$-0.371725\pi$
$751$	21.4943			0.784340			0.392170	+	0.919893i	$0.371725\pi$
$752$		0			0
$753$	32.7058	+	32.3967i	1.19186	+	1.18060i
$754$		0			0
$755$	−19.6433	+	22.1261i	−0.714892	+	0.805250i
$756$		0			0
$757$	20.2676	+	20.2676i	0.736638	+	0.736638i	0.971926	−	0.235287i	$-0.0756031\pi$
$757$	20.2676	+	20.2676i	0.736638	+	0.736638i	−0.235287	+	0.971926i	$0.575603\pi$
$758$		0			0
$759$	−4.02680	−	1.28729i	−0.146164	−	0.0467257i
$760$		0			0
$761$	26.5073	+	36.4842i	0.960890	+	1.32255i	0.946517	+	0.322654i	$0.104575\pi$
$761$	26.5073	+	36.4842i	0.960890	+	1.32255i	0.0143726	+	0.999897i	$0.495425\pi$
$762$		0			0
$763$	1.47489	−	0.233599i	0.0533945	−	0.00845686i
$764$		0			0
$765$	−18.6037	−	46.1720i	−0.672618	−	1.66935i
$766$		0			0
$767$	−15.2354	−	7.76285i	−0.550120	−	0.280300i
$768$		0			0
$769$	20.9117	−	6.79462i	0.754095	−	0.245020i	0.0933528	−	0.995633i	$-0.470242\pi$
$769$	20.9117	−	6.79462i	0.754095	−	0.245020i	0.660742	+	0.750613i	$0.270242\pi$
$770$		0			0
$771$	0.116680	+	24.5822i	0.00420212	+	0.885307i
$772$		0			0
$773$	1.94871	+	0.308646i	0.0700904	+	0.0111012i	0.191381	−	0.981516i	$-0.438703\pi$
$773$	1.94871	+	0.308646i	0.0700904	+	0.0111012i	−0.121291	+	0.992617i	$0.538703\pi$
$774$		0			0
$775$	31.1073	−	14.3758i	1.11741	−	0.516393i
$776$		0			0
$777$	0.736401	+	4.51078i	0.0264182	+	0.161823i
$778$		0			0
$779$	4.45022	−	13.6964i	0.159446	−	0.490724i
$780$		0			0
$781$	7.29826	+	22.4617i	0.261152	+	0.803744i
$782$		0			0
$783$	9.48282	−	5.00308i	0.338888	−	0.178795i
$784$		0			0
$785$	21.1542	−	1.25741i	0.755027	−	0.0448788i
$786$		0			0
$787$	−3.81634	−	24.0954i	−0.136038	−	0.858909i	−0.957455	−	0.288582i	$-0.906816\pi$
$787$	−3.81634	−	24.0954i	−0.136038	−	0.858909i	0.821418	−	0.570327i	$-0.193184\pi$
$788$		0			0
$789$	−32.5182	−	23.3909i	−1.15768	−	0.832737i
$790$		0			0
$791$	0.907344	−	1.24885i	0.0322614	−	0.0444041i
$792$		0			0
$793$	−15.9817	+	15.9817i	−0.567527	+	0.567527i
$794$		0			0
$795$	−0.471687	−	0.795245i	−0.0167290	−	0.0282044i
$796$		0			0
$797$	−12.9280	−	25.3725i	−0.457932	−	0.898742i	−0.998354	−	0.0573478i	$-0.981736\pi$
$797$	−12.9280	−	25.3725i	−0.457932	−	0.898742i	0.540423	−	0.841394i	$-0.318264\pi$
$798$		0			0
$799$		−	23.4344i		−	0.829048i
$800$		0			0
$801$	22.5728	+	30.4565i	0.797570	+	1.07613i
$802$		0			0
$803$	−17.2409	+	8.78466i	−0.608417	+	0.310004i
$804$		0			0
$805$	1.25966	+	0.123473i	0.0443970	+	0.00435187i
$806$		0			0
$807$	−13.0182	−	6.55547i	−0.458263	−	0.230764i
$808$		0			0
$809$	6.51664	+	4.73462i	0.229113	+	0.166460i	0.696419	−	0.717635i	$-0.254775\pi$
$809$	6.51664	+	4.73462i	0.229113	+	0.166460i	−0.467306	+	0.884095i	$0.654775\pi$
$810$		0			0
$811$	25.7314	−	18.6950i	0.903552	−	0.656469i	−0.0358236	−	0.999358i	$-0.511405\pi$
$811$	25.7314	−	18.6950i	0.903552	−	0.656469i	0.939376	+	0.342889i	$0.111405\pi$
$812$		0			0
$813$	−18.2752	−	35.4502i	−0.640940	−	1.24329i
$814$		0			0
$815$	−12.1393	+	18.9828i	−0.425220	+	0.664940i
$816$		0			0
$817$	6.60528	−	12.9636i	0.231089	−	0.453538i
$818$		0			0
$819$	3.24160	−	4.55193i	0.113271	−	0.159057i
$820$		0			0
$821$	−30.3635	−	9.86569i	−1.05969	−	0.344315i	−0.273227	−	0.961950i	$-0.588091\pi$
$821$	−30.3635	−	9.86569i	−1.05969	−	0.344315i	−0.786465	+	0.617635i	$0.788091\pi$
$822$		0			0
$823$	−7.65807	+	48.3511i	−0.266943	+	1.68541i	0.381672	+	0.924298i	$0.375348\pi$
$823$	−7.65807	+	48.3511i	−0.266943	+	1.68541i	−0.648615	+	0.761116i	$0.724652\pi$
$824$		0			0
$825$	−0.435396	+	12.9561i	−0.0151585	+	0.451074i
$826$		0			0
$827$	−5.20579	+	32.8681i	−0.181023	+	1.14294i	0.715065	+	0.699058i	$0.246397\pi$
$827$	−5.20579	+	32.8681i	−0.181023	+	1.14294i	−0.896088	+	0.443877i	$0.853603\pi$
$828$		0			0
$829$	−33.6047	−	10.9188i	−1.16714	−	0.379226i	−0.339564	−	0.940583i	$-0.610280\pi$
$829$	−33.6047	−	10.9188i	−1.16714	−	0.379226i	−0.827574	+	0.561357i	$0.810280\pi$
$830$		0			0
$831$	15.6677	−	11.4973i	0.543507	−	0.398836i
$832$		0			0
$833$	−23.1763	+	45.4860i	−0.803011	+	1.57600i
$834$		0			0
$835$	21.5667	−	8.45261i	0.746345	−	0.292514i
$836$		0			0
$837$	−15.7144	+	31.9582i	−0.543170	+	1.10464i
$838$		0			0
$839$	−0.448091	+	0.325557i	−0.0154698	+	0.0112395i	−0.595493	−	0.803360i	$-0.703043\pi$
$839$	−0.448091	+	0.325557i	−0.0154698	+	0.0112395i	0.580023	+	0.814600i	$0.303043\pi$
$840$		0			0
$841$	20.0170	+	14.5432i	0.690243	+	0.501491i
$842$		0			0
$843$	−11.9699	+	23.7705i	−0.412265	+	0.818700i
$844$		0			0
$845$	−14.1376	+	32.3623i	−0.486349	+	1.11330i
$846$		0			0
$847$	−2.70928	+	1.38045i	−0.0930921	+	0.0474328i
$848$		0			0
$849$	−13.9885	+	4.61866i	−0.480084	+	0.158512i
$850$		0			0
$851$			12.3948i			0.424889i
$852$		0			0
$853$	−21.8598	−	42.9023i	−0.748466	−	1.46895i	−0.878654	−	0.477458i	$-0.841558\pi$
$853$	−21.8598	−	42.9023i	−0.748466	−	1.46895i	0.130188	−	0.991489i	$-0.458442\pi$
$854$		0			0
$855$	−20.9044	−	8.89682i	−0.714914	−	0.304265i
$856$		0			0
$857$	20.1939	−	20.1939i	0.689811	−	0.689811i	−0.272379	−	0.962190i	$-0.587810\pi$
$857$	20.1939	−	20.1939i	0.689811	−	0.689811i	0.962190	+	0.272379i	$0.0878104\pi$
$858$		0			0
$859$	−11.6355	+	16.0149i	−0.396998	+	0.546421i	−0.959987	−	0.280043i	$-0.909651\pi$
$859$	−11.6355	+	16.0149i	−0.396998	+	0.546421i	0.562989	+	0.826464i	$0.309651\pi$
$860$		0			0
$861$	−1.49297	+	2.07554i	−0.0508802	+	0.0707342i
$862$		0			0
$863$	−3.15711	−	19.9332i	−0.107469	−	0.678534i	−0.981326	−	0.192351i	$-0.938389\pi$
$863$	−3.15711	−	19.9332i	−0.107469	−	0.678534i	0.873857	−	0.486183i	$-0.161611\pi$
$864$		0			0
$865$	−37.5358	+	30.8341i	−1.27625	+	1.04839i
$866$		0			0
$867$	−65.1682	−	10.0048i	−2.21323	−	0.339780i
$868$		0			0
$869$	−4.83671	−	14.8859i	−0.164074	−	0.504969i
$870$		0			0
$871$	20.8882	−	64.2872i	0.707769	−	2.17829i
$872$		0			0
$873$	−4.25296	−	8.15459i	−0.143941	−	0.275991i
$874$		0			0
$875$	−0.687620	−	3.81973i	−0.0232458	−	0.129130i
$876$		0			0
$877$	−13.4522	−	2.13062i	−0.454249	−	0.0719460i	−0.0748823	−	0.997192i	$-0.523858\pi$
$877$	−13.4522	−	2.13062i	−0.454249	−	0.0719460i	−0.379367	+	0.925246i	$0.623858\pi$
$878$		0			0
$879$	−8.95067	+	0.0424844i	−0.301898	+	0.00143296i
$880$		0			0
$881$	−25.1299	+	8.16520i	−0.846648	+	0.275093i	−0.700041	−	0.714102i	$-0.746835\pi$
$881$	−25.1299	+	8.16520i	−0.846648	+	0.275093i	−0.146607	+	0.989195i	$0.546835\pi$
$882$		0			0
$883$	11.7538	+	5.98887i	0.395547	+	0.201541i	0.640439	−	0.768009i	$-0.278752\pi$
$883$	11.7538	+	5.98887i	0.395547	+	0.201541i	−0.244892	+	0.969550i	$0.578752\pi$
$884$		0			0
$885$	6.59957	−	10.4289i	0.221842	−	0.350562i
$886$		0			0
$887$	46.6702	−	7.39183i	1.56703	−	0.248193i	0.688270	−	0.725455i	$-0.258371\pi$
$887$	46.6702	−	7.39183i	1.56703	−	0.248193i	0.878761	+	0.477261i	$0.158371\pi$
$888$		0			0
$889$	−1.94341	−	2.67488i	−0.0651800	−	0.0897126i
$890$		0			0
$891$	−8.12412	−	10.7468i	−0.272168	−	0.360030i
$892$		0			0
$893$	−7.56271	−	7.56271i	−0.253076	−	0.253076i
$894$		0			0
$895$	−20.8551	−	35.5444i	−0.697111	−	1.18812i
$896$		0			0
$897$	10.6650	−	10.7668i	0.356096	−	0.359492i
$898$		0			0
$899$	14.1418			0.471657
$900$		0			0
$901$	−1.77155			−0.0590189
$902$		0			0
$903$	−1.81778	+	1.83512i	−0.0604920	+	0.0610690i
$904$		0			0
$905$	5.85624	+	2.55832i	0.194668	+	0.0850416i
$906$		0			0
$907$	2.53014	+	2.53014i	0.0840121	+	0.0840121i	0.747864	−	0.663852i	$-0.231079\pi$
$907$	2.53014	+	2.53014i	0.0840121	+	0.0840121i	−0.663852	+	0.747864i	$0.731079\pi$
$908$		0			0
$909$	6.48692	−	0.0615818i	0.215157	−	0.00204254i
$910$		0			0
$911$	−23.4648	−	32.2965i	−0.777424	−	1.07003i	−0.995561	−	0.0941143i	$-0.969998\pi$
$911$	−23.4648	−	32.2965i	−0.777424	−	1.07003i	0.218137	−	0.975918i	$-0.430002\pi$
$912$		0			0
$913$	21.5506	−	3.41329i	0.713222	−	0.112963i
$914$		0			0
$915$	−10.4145	−	12.5561i	−0.344292	−	0.415090i
$916$		0			0
$917$	5.90912	+	3.01085i	0.195136	+	0.0994269i
$918$		0			0
$919$	28.5675	−	9.28213i	0.942354	−	0.306189i	0.202749	−	0.979231i	$-0.435012\pi$
$919$	28.5675	−	9.28213i	0.942354	−	0.306189i	0.739605	+	0.673042i	$0.235012\pi$
$920$		0			0
$921$	−3.59407	+	0.0170593i	−0.118429	+	0.000562123i
$922$		0			0
$923$	−83.6211	−	13.2443i	−2.75242	−	0.435941i
$924$		0			0
$925$	36.5709	−	10.3508i	1.20244	−	0.340333i
$926$		0			0
$927$	−37.6208	+	19.6208i	−1.23563	+	0.644432i
$928$		0			0
$929$	13.5788	−	41.7913i	0.445507	−	1.37113i	−0.436420	−	0.899743i	$-0.643754\pi$
$929$	13.5788	−	41.7913i	0.445507	−	1.37113i	0.881927	−	0.471386i	$-0.156246\pi$
$930$		0			0
$931$	7.19977	+	22.1586i	0.235963	+	0.726219i
$932$		0			0
$933$	−38.9303	−	5.97668i	−1.27452	−	0.195668i
$934$		0			0
$935$	20.9251	+	13.3813i	0.684324	+	0.437616i
$936$		0			0
$937$	0.0688669	+	0.434808i	0.00224978	+	0.0142046i	0.988788	−	0.149328i	$-0.0477111\pi$
$937$	0.0688669	+	0.434808i	0.00224978	+	0.0142046i	−0.986538	+	0.163533i	$0.947711\pi$
$938$		0			0
$939$	−22.6259	+	31.4548i	−0.738368	+	1.02649i
$940$		0			0
$941$	−4.63450	+	6.37884i	−0.151080	+	0.207944i	−0.877848	−	0.478939i	$-0.841022\pi$
$941$	−4.63450	+	6.37884i	−0.151080	+	0.207944i	0.726768	+	0.686883i	$0.241022\pi$
$942$		0			0
$943$	−4.90281	+	4.90281i	−0.159657	+	0.159657i
$944$		0			0
$945$	3.05406	+	2.63456i	0.0993485	+	0.0857023i
$946$		0			0
$947$	15.6899	+	30.7932i	0.509854	+	1.00065i	0.992199	+	0.124664i	$0.0397853\pi$
$947$	15.6899	+	30.7932i	0.509854	+	1.00065i	−0.482345	+	0.875982i	$0.660215\pi$
$948$		0			0
$949$		−	69.3645i		−	2.25167i
$950$		0			0
$951$	5.37633	−	1.77513i	0.174339	−	0.0575626i
$952$		0			0
$953$	40.6912	−	20.7332i	1.31812	−	0.671615i	0.353542	−	0.935419i	$-0.384977\pi$
$953$	40.6912	−	20.7332i	1.31812	−	0.671615i	0.964576	+	0.263804i	$0.0849771\pi$
$954$		0			0
$955$	−7.51576	−	34.1789i	−0.243204	−	1.10600i
$956$		0			0
$957$	−2.40607	+	4.77811i	−0.0777772	+	0.154454i
$958$		0			0
$959$	3.89065	+	2.82672i	0.125636	+	0.0912796i
$960$		0			0
$961$	−12.9225	+	9.38873i	−0.416854	+	0.302862i
$962$		0			0
$963$	4.94592	+	4.85290i	0.159380	+	0.156382i
$964$		0			0
$965$	1.35291	+	22.7610i	0.0435518	+	0.732702i
$966$		0			0
$967$	−24.1811	+	47.4582i	−0.777613	+	1.52615i	0.0712023	+	0.997462i	$0.477316\pi$
$967$	−24.1811	+	47.4582i	−0.777613	+	1.52615i	−0.848815	+	0.528690i	$0.822684\pi$
$968$		0			0
$969$	−35.0940	+	25.7527i	−1.12738	+	0.827296i
$970$		0			0
$971$	−44.7462	−	14.5389i	−1.43597	−	0.466576i	−0.515334	−	0.856989i	$-0.672332\pi$
$971$	−44.7462	−	14.5389i	−1.43597	−	0.466576i	−0.920640	+	0.390413i	$0.872332\pi$
$972$		0			0
$973$	−0.573066	+	3.61820i	−0.0183717	+	0.115994i
$974$		0			0
$975$	−40.6737	−	22.4760i	−1.30260	−	0.719808i
$976$		0			0
$977$	−1.14152	+	7.20725i	−0.0365203	+	0.230580i	−0.999197	−	0.0400750i	$-0.987240\pi$
$977$	−1.14152	+	7.20725i	−0.0365203	+	0.230580i	0.962676	+	0.270655i	$0.0872403\pi$
$978$		0			0
$979$	−17.9896	−	5.84518i	−0.574951	−	0.186813i
$980$		0			0
$981$	10.5119	+	7.48591i	0.335619	+	0.239007i
$982$		0			0
$983$	8.79016	−	17.2517i	0.280363	−	0.550243i	−0.707286	−	0.706928i	$-0.750081\pi$
$983$	8.79016	−	17.2517i	0.280363	−	0.550243i	0.987649	+	0.156685i	$0.0500807\pi$
$984$		0			0
$985$	31.0182	+	8.07868i	0.988322	+	0.257408i
$986$		0			0
$987$	0.870052	+	1.68772i	0.0276940	+	0.0537207i
$988$		0			0
$989$	−5.66712	+	4.11740i	−0.180204	+	0.130926i
$990$		0			0
$991$	−34.6053	−	25.1423i	−1.09927	−	0.798670i	−0.118333	−	0.992974i	$-0.537755\pi$
$991$	−34.6053	−	25.1423i	−1.09927	−	0.798670i	−0.980941	+	0.194304i	$0.937755\pi$
$992$		0			0
$993$	25.8801	+	13.0322i	0.821282	+	0.413565i
$994$		0			0
$995$	−15.4550	−	13.7208i	−0.489958	−	0.434980i
$996$		0			0
$997$	14.6440	−	7.46148i	0.463779	−	0.236307i	−0.206456	−	0.978456i	$-0.566193\pi$
$997$	14.6440	−	7.46148i	0.463779	−	0.236307i	0.670236	+	0.742148i	$0.266193\pi$
$998$		0			0
$999$	−22.7593	+	32.2824i	−0.720073	+	1.02137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.77.3	✓	80
3.2	odd	2	inner	300.2.x.a.77.9	yes	80
25.13	odd	20	inner	300.2.x.a.113.9	yes	80
75.38	even	20	inner	300.2.x.a.113.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.77.3	✓	80	1.1	even	1	trivial
300.2.x.a.77.9	yes	80	3.2	odd	2	inner
300.2.x.a.113.3	yes	80	75.38	even	20	inner
300.2.x.a.113.9	yes	80	25.13	odd	20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21892 + 1.23054i) q^{3} +(-1.48454 + 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(-0.0284784 - 2.99986i) q^{9} +O(q^{10})\)	\(q+(-1.21892 + 1.23054i) q^{3} +(-1.48454 + 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(-0.0284784 - 2.99986i) q^{9} +(0.879848 + 1.21101i) q^{11} +(-5.29990 + 0.839422i) q^{13} +(-0.248153 - 3.86503i) q^{15} +(-6.61182 - 3.36889i) q^{17} +(-3.22097 + 1.04656i) q^{19} +(0.601255 - 0.00285386i) q^{21} +(1.61050 + 0.255078i) q^{23} +(-0.592307 - 4.96479i) q^{25} +(3.72618 + 3.62154i) q^{27} +(0.637623 - 1.96240i) q^{29} +(2.11791 + 6.51825i) q^{31} +(-2.56266 - 0.393426i) q^{33} +(0.774858 - 0.0460576i) q^{35} +(1.18914 + 7.50792i) q^{37} +(5.42720 - 7.54495i) q^{39} +(-2.49942 + 3.44015i) q^{41} +(-3.03773 + 3.03773i) q^{43} +(5.05856 + 4.40579i) q^{45} +(1.43370 + 2.81380i) q^{47} -6.87949i q^{49} +(12.2048 - 4.02974i) q^{51} +(0.212713 - 0.108383i) q^{53} +(-3.33118 - 0.326527i) q^{55} +(2.63826 - 5.23920i) q^{57} +(2.57801 + 1.87303i) q^{59} +(3.40759 - 2.47576i) q^{61} +(-0.729368 + 0.743349i) q^{63} +(6.46424 - 10.1085i) q^{65} +(-5.71895 + 11.2241i) q^{67} +(-2.27695 + 1.67087i) q^{69} +(15.0056 + 4.87563i) q^{71} +(-2.02219 + 12.7676i) q^{73} +(6.83137 + 5.32281i) q^{75} +(0.0812876 - 0.513230i) q^{77} +(-9.94456 - 3.23118i) q^{79} +(-8.99838 + 0.170863i) q^{81} +(6.61756 - 12.9877i) q^{83} +(15.4489 - 6.05486i) q^{85} +(1.63761 + 3.17663i) q^{87} +(-10.2231 + 7.42754i) q^{89} +(1.50698 + 1.09489i) q^{91} +(-10.6025 - 5.33903i) q^{93} +(3.03162 - 6.93965i) q^{95} +(2.73153 - 1.39178i) q^{97} +(3.60780 - 2.67391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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