LMFDB - Embedded newform 300.2.x.a.77.9

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			77.9
Character	$\chi$	$=$	300.77
Dual form			300.2.x.a.113.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71199 - 0.262830i) q^{3} +(1.48454 - 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(2.86184 - 0.899925i) q^{9} +O(q^{10})$	\(q+(1.71199 - 0.262830i) q^{3} +(1.48454 - 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(2.86184 - 0.899925i) q^{9} +(-0.879848 - 1.21101i) q^{11} +(-5.29990 + 0.839422i) q^{13} +(2.10202 - 3.25292i) q^{15} +(6.61182 + 3.36889i) q^{17} +(-3.22097 + 1.04656i) q^{19} +(-0.484748 - 0.355717i) q^{21} +(-1.61050 - 0.255078i) q^{23} +(-0.592307 - 4.96479i) q^{25} +(4.66293 - 2.29284i) q^{27} +(-0.637623 + 1.96240i) q^{29} +(2.11791 + 6.51825i) q^{31} +(-1.82458 - 1.84199i) q^{33} +(-0.774858 + 0.0460576i) q^{35} +(1.18914 + 7.50792i) q^{37} +(-8.85278 + 2.83006i) q^{39} +(2.49942 - 3.44015i) q^{41} +(-3.03773 + 3.03773i) q^{43} +(2.74368 - 6.12146i) q^{45} +(-1.43370 - 2.81380i) q^{47} -6.87949i q^{49} +(12.2048 + 4.02974i) q^{51} +(-0.212713 + 0.108383i) q^{53} +(-3.33118 - 0.326527i) q^{55} +(-5.23920 + 2.63826i) q^{57} +(-2.57801 - 1.87303i) q^{59} +(3.40759 - 2.47576i) q^{61} +(-0.923378 - 0.481580i) q^{63} +(-6.46424 + 10.1085i) q^{65} +(-5.71895 + 11.2241i) q^{67} +(-2.82420 - 0.0134051i) q^{69} +(-15.0056 - 4.87563i) q^{71} +(-2.02219 + 12.7676i) q^{73} +(-2.31892 - 8.34402i) q^{75} +(-0.0812876 + 0.513230i) q^{77} +(-9.94456 - 3.23118i) q^{79} +(7.38027 - 5.15088i) q^{81} +(-6.61756 + 12.9877i) q^{83} +(15.4489 - 6.05486i) q^{85} +(-0.575829 + 3.52720i) q^{87} +(10.2231 - 7.42754i) q^{89} +(1.50698 + 1.09489i) q^{91} +(5.33903 + 10.6025i) q^{93} +(-3.03162 + 6.93965i) q^{95} +(2.73153 - 1.39178i) q^{97} +(-3.60780 - 2.67391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.71199	−	0.262830i	0.988420	−	0.151745i
$3$	1.71199	−	0.262830i	0.988420	−	0.151745i
$4$		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
$9$	2.86184	−	0.899925i	0.953947	−	0.299975i
$10$		0			0
$11$	−0.879848	−	1.21101i	−0.265284	−	0.365132i	0.655506	−	0.755190i	$-0.272455\pi$
$11$	−0.879848	−	1.21101i	−0.265284	−	0.365132i	−0.920791	+	0.390057i	$0.872455\pi$
$12$		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
$15$	2.10202	−	3.25292i	0.542739	−	0.839901i
$16$		0			0
$17$	6.61182	+	3.36889i	1.60360	+	0.817077i	0.999801	+	0.0199422i	$0.00634822\pi$
$17$	6.61182	+	3.36889i	1.60360	+	0.817077i	0.603802	+	0.797134i	$0.293652\pi$
$18$		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
$21$	−0.484748	−	0.355717i	−0.105781	−	0.0776239i
$22$		0			0
$23$	−1.61050	−	0.255078i	−0.335812	−	0.0531874i	−0.0137486	−	0.999905i	$-0.504376\pi$
$23$	−1.61050	−	0.255078i	−0.335812	−	0.0531874i	−0.322063	+	0.946718i	$0.604376\pi$
$24$		0			0
$25$	−0.592307	−	4.96479i	−0.118461	−	0.992959i
$26$		0			0
$27$	4.66293	−	2.29284i	0.897381	−	0.441257i
$28$		0			0
$29$	−0.637623	+	1.96240i	−0.118404	+	0.364409i	−0.992642	−	0.121089i	$-0.961361\pi$
$29$	−0.637623	+	1.96240i	−0.118404	+	0.364409i	0.874238	+	0.485497i	$0.161361\pi$
$30$		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
$33$	−1.82458	−	1.84199i	−0.317619	−	0.320649i
$34$		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
$39$	−8.85278	+	2.83006i	−1.41758	+	0.453172i
$40$		0			0
$41$	2.49942	−	3.44015i	0.390343	−	0.537261i	−0.567944	−	0.823067i	$-0.692261\pi$
$41$	2.49942	−	3.44015i	0.390343	−	0.537261i	0.958288	+	0.285806i	$0.0922612\pi$
$42$		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
$45$	2.74368	−	6.12146i	0.409003	−	0.912533i
$46$		0			0
$47$	−1.43370	−	2.81380i	−0.209127	−	0.410435i	0.762488	−	0.647002i	$-0.223978\pi$
$47$	−1.43370	−	2.81380i	−0.209127	−	0.410435i	−0.971615	+	0.236567i	$0.923978\pi$
$48$		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	−0.468539	−	0.883443i	$-0.655219\pi$
$53$	−0.212713	+	0.108383i	−0.0292184	+	0.0148875i	0.439320	+	0.898330i	$0.355219\pi$
$54$		0			0
$55$	−3.33118	−	0.326527i	−0.449176	−	0.0440289i
$56$		0			0
$57$	−5.23920	+	2.63826i	−0.693950	+	0.349446i
$58$		0			0
$59$	−2.57801	−	1.87303i	−0.335628	−	0.243848i	0.407187	−	0.913345i	$-0.366510\pi$
$59$	−2.57801	−	1.87303i	−0.335628	−	0.243848i	−0.742815	+	0.669497i	$0.766510\pi$
$60$		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
$63$	−0.923378	−	0.481580i	−0.116335	−	0.0606734i
$64$		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
$69$	−2.82420	−	0.0134051i	−0.339994	−	0.00161379i
$70$		0			0
$71$	−15.0056	−	4.87563i	−1.78084	−	0.578630i	−0.781847	−	0.623471i	$-0.785722\pi$
$71$	−15.0056	−	4.87563i	−1.78084	−	0.578630i	−0.998994	+	0.0448405i	$0.985722\pi$
$72$		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
$75$	−2.31892	−	8.34402i	−0.267766	−	0.963484i
$76$		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
$81$	7.38027	−	5.15088i	0.820030	−	0.572320i
$82$		0			0
$83$	−6.61756	+	12.9877i	−0.726372	+	1.42559i	0.171434	+	0.985196i	$0.445160\pi$
$83$	−6.61756	+	12.9877i	−0.726372	+	1.42559i	−0.897807	+	0.440390i	$0.854840\pi$
$84$		0			0
$85$	15.4489	−	6.05486i	1.67566	−	0.656741i
$86$		0			0
$87$	−0.575829	+	3.52720i	−0.0617354	+	0.378156i
$88$		0			0
$89$	10.2231	−	7.42754i	1.08365	−	0.787318i	0.105335	−	0.994437i	$-0.466409\pi$
$89$	10.2231	−	7.42754i	1.08365	−	0.787318i	0.978316	+	0.207119i	$0.0664086\pi$
$90$		0			0
$91$	1.50698	+	1.09489i	0.157975	+	0.114775i
$92$		0			0
$93$	5.33903	+	10.6025i	0.553632	+	1.09943i
$94$		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	$-0.965689\pi$
$101$		−	2.16240i		−	0.215167i	0.994196	−	0.107584i	$-0.0343113\pi$
$102$		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
$105$	−1.31445	+	0.282506i	−0.128277	+	0.0275697i
$106$		0			0
$107$	1.63321	−	1.63321i	0.157888	−	0.157888i	−0.623742	−	0.781630i	$-0.714388\pi$
$107$	1.63321	−	1.63321i	0.157888	−	0.157888i	0.781630	+	0.623742i	$0.214388\pi$
$108$		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
$111$	4.00910	+	12.5410i	0.380527	+	1.19034i
$112$		0			0
$113$	−0.695637	−	4.39208i	−0.0654401	−	0.413172i	−0.998562	−	0.0536118i	$-0.982927\pi$
$113$	−0.695637	−	4.39208i	−0.0654401	−	0.413172i	0.933122	−	0.359560i	$-0.117073\pi$
$114$		0			0
$115$	−2.81738	+	2.31436i	−0.262722	+	0.215815i
$116$		0			0
$117$	−14.4121	+	7.17181i	−1.33240	+	0.663034i
$118$		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
$123$	3.37481	−	6.54643i	0.304296	−	0.590272i
$124$		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
$129$	−4.40217	+	5.99898i	−0.387590	+	0.528181i
$130$		0			0
$131$	18.1696	−	5.90366i	1.58748	−	0.515805i	0.623514	−	0.781812i	$-0.285705\pi$
$131$	18.1696	−	5.90366i	1.58748	−	0.515805i	0.963971	+	0.266007i	$0.0857045\pi$
$132$		0			0
$133$	1.04752	+	0.533739i	0.0908317	+	0.0462811i
$134$		0			0
$135$	3.08826	−	11.2010i	0.265795	−	0.964030i
$136$		0			0
$137$	13.6830	−	2.16717i	1.16902	−	0.185154i	0.458409	−	0.888741i	$-0.348420\pi$
$137$	13.6830	−	2.16717i	1.16902	−	0.185154i	0.710609	+	0.703587i	$0.248420\pi$
$138$		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
$141$	−3.19404	−	4.44039i	−0.268987	−	0.373948i
$142$		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
$147$	−1.80813	−	11.7776i	−0.149132	−	0.971404i
$148$		0			0
$149$	3.21507			0.263389			0.131695	−	0.991290i	$-0.457958\pi$
$149$	3.21507			0.263389			0.131695	+	0.991290i	$0.457958\pi$
$150$		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
$153$	21.9537	+	3.69109i	1.77485	+	0.298407i
$154$		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
$159$	−0.335677	+	0.241458i	−0.0266209	+	0.0191488i
$160$		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
$165$	−5.78877	+	0.316519i	−0.450655	+	0.0246410i
$166$		0			0
$167$	9.23014	+	4.70299i	0.714249	+	0.363928i	0.773053	−	0.634341i	$-0.218729\pi$
$167$	9.23014	+	4.70299i	0.714249	+	0.363928i	−0.0588037	+	0.998270i	$0.518729\pi$
$168$		0			0
$169$	15.0206	−	4.88050i	1.15543	−	0.375423i
$170$		0			0
$171$	−8.27607	+	5.89370i	−0.632887	+	0.450703i
$172$		0			0
$173$	−21.4566	−	3.39839i	−1.63132	−	0.258375i	−0.727440	−	0.686171i	$-0.759290\pi$
$173$	−21.4566	−	3.39839i	−1.63132	−	0.258375i	−0.903875	+	0.427796i	$0.859290\pi$
$174$		0			0
$175$	−1.07329	+	1.36407i	−0.0811329	+	0.103114i
$176$		0			0
$177$	−4.90582	−	2.52904i	−0.368744	−	0.190094i
$178$		0			0
$179$	5.69521	−	17.5280i	0.425680	−	1.31011i	−0.476662	−	0.879087i	$-0.658153\pi$
$179$	5.69521	−	17.5280i	0.425680	−	1.31011i	0.902342	−	0.431021i	$-0.141847\pi$
$180$		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
$183$	5.18307	−	5.13410i	0.383143	−	0.379523i
$184$		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
$189$	−1.70739	−	0.581770i	−0.124194	−	0.0423176i
$190$		0			0
$191$	9.19912	−	12.6615i	0.665625	−	0.916154i	−0.334026	−	0.942564i	$-0.608407\pi$
$191$	9.19912	−	12.6615i	0.665625	−	0.916154i	0.999651	+	0.0264098i	$0.00840749\pi$
$192$		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
$195$	−8.40992	+	19.0047i	−0.602247	+	1.36095i
$196$		0			0
$197$	6.50774	+	12.7722i	0.463657	+	0.909979i	0.997908	+	0.0646527i	$0.0205940\pi$
$197$	6.50774	+	12.7722i	0.463657	+	0.909979i	−0.534250	+	0.845326i	$0.679406\pi$
$198$		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
$207$	−4.83854	+	0.719335i	−0.336302	+	0.0499972i
$208$		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
$213$	−26.9710	−	4.40311i	−1.84802	−	0.301696i
$214$		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
$219$	−0.106272	+	22.3895i	−0.00718120	+	1.51294i
$220$		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
$225$	−6.16303	−	13.6754i	−0.410869	−	0.911695i
$226$		0			0
$227$	0.651345	−	4.11243i	0.0432313	−	0.272952i	−0.956598	−	0.291410i	$-0.905876\pi$
$227$	0.651345	−	4.11243i	0.0432313	−	0.272952i	0.999830	+	0.0184580i	$0.00587571\pi$
$228$		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
$231$	−0.00427191	+	0.900010i	−0.000281071	+	0.0592163i
$232$		0			0
$233$	−6.67158	+	13.0937i	−0.437070	+	0.857797i	0.562451	+	0.826831i	$0.309859\pi$
$233$	−6.67158	+	13.0937i	−0.437070	+	0.857797i	−0.999520	+	0.0309667i	$0.990141\pi$
$234$		0			0
$235$	−6.83354	−	1.77979i	−0.445771	−	0.116101i
$236$		0			0
$237$	−17.8743	−	2.91804i	−1.16106	−	0.189547i
$238$		0			0
$239$	−5.39910	+	3.92267i	−0.349239	+	0.253737i	−0.748550	−	0.663079i	$-0.769249\pi$
$239$	−5.39910	+	3.92267i	−0.349239	+	0.253737i	0.399311	+	0.916816i	$0.369249\pi$
$240$		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
$243$	11.2812	−	10.7580i	0.723687	−	0.690128i
$244$		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	$0.316744\pi$
$251$			26.5783i			1.67761i	−0.544435	+	0.838803i	$0.683256\pi$
$252$		0			0
$253$	1.10809	+	2.17475i	0.0696652	+	0.136726i
$254$		0			0
$255$	24.8569	−	14.4263i	1.55660	−	0.903409i
$256$		0			0
$257$	−10.0358	+	10.0358i	−0.626014	+	0.626014i	−0.947063	−	0.321049i	$-0.895965\pi$
$257$	−10.0358	+	10.0358i	−0.626014	+	0.626014i	0.321049	+	0.947063i	$0.395965\pi$
$258$		0			0
$259$	1.55103	−	2.13481i	0.0963765	−	0.132651i
$260$		0			0
$261$	−0.0587621	+	6.18989i	−0.00363728	+	0.383145i
$262$		0			0
$263$	−3.61785	−	22.8422i	−0.223086	−	1.40851i	−0.804040	−	0.594575i	$-0.797320\pi$
$263$	−3.61785	−	22.8422i	−0.223086	−	1.40851i	0.580954	−	0.813937i	$-0.302680\pi$
$264$		0			0
$265$	−0.134546	+	0.516590i	−0.00826508	+	0.0317339i
$266$		0			0
$267$	15.5498	−	15.4028i	0.951630	−	0.942639i
$268$		0			0
$269$	−2.60045	−	8.00336i	−0.158552	−	0.487974i	0.839951	−	0.542662i	$-0.182584\pi$
$269$	−2.60045	−	8.00336i	−0.158552	−	0.487974i	−0.998503	+	0.0546882i	$0.982584\pi$
$270$		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
$273$	2.86771	+	1.47836i	0.173562	+	0.0894744i
$274$		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
$279$	11.9270	+	16.7482i	0.714053	+	1.00269i
$280$		0			0
$281$	−14.6137	+	4.74827i	−0.871778	+	0.283258i	−0.710539	−	0.703658i	$-0.751549\pi$
$281$	−14.6137	+	4.74827i	−0.871778	+	0.283258i	−0.161239	+	0.986915i	$0.551549\pi$
$282$		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
$285$	−3.36617	+	12.6774i	−0.199395	+	0.750946i
$286$		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
$291$	4.31056	−	3.10065i	0.252690	−	0.181764i
$292$		0			0
$293$	−3.65414	−	3.65414i	−0.213477	−	0.213477i	0.592266	−	0.805743i	$-0.298234\pi$
$293$	−3.65414	−	3.65414i	−0.213477	−	0.213477i	−0.805743	+	0.592266i	$0.798234\pi$
$294$		0			0
$295$	−6.95917	+	1.53028i	−0.405178	+	0.0890966i
$296$		0			0
$297$	−6.87931	−	3.62948i	−0.399178	−	0.210604i
$298$		0			0
$299$	8.74960			0.506003
$300$		0			0
$301$	1.49131			0.0859575
$302$		0			0
$303$	−0.568343	−	3.70202i	−0.0326505	−	0.212675i
$304$		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
$309$	−14.3047	−	19.8866i	−0.813767	−	1.13131i
$310$		0			0
$311$	−13.3661	−	18.3969i	−0.757922	−	1.04319i	−0.997384	−	0.0722845i	$-0.976971\pi$
$311$	−13.3661	−	18.3969i	−0.757922	−	1.04319i	0.239462	−	0.970906i	$-0.423029\pi$
$312$		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
$315$	−2.17607	+	0.829123i	−0.122608	+	0.0467158i
$316$		0			0
$317$	2.91256	+	1.48402i	0.163586	+	0.0833510i	0.533866	−	0.845569i	$-0.320739\pi$
$317$	2.91256	+	1.48402i	0.163586	+	0.0833510i	−0.370281	+	0.928920i	$0.620739\pi$
$318$		0			0
$319$	2.93749	−	0.954449i	0.164468	−	0.0534389i
$320$		0			0
$321$	2.36679	−	3.22530i	0.132101	−	0.180019i
$322$		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
$327$	−3.41402	+	6.62249i	−0.188796	+	0.366225i
$328$		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
$333$	10.1597	+	20.4163i	0.556747	+	1.11881i
$334$		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
$339$	−2.34529	−	7.33638i	−0.127379	−	0.398457i
$340$		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
$345$	−4.21505	+	4.70265i	−0.226931	+	0.253182i
$346$		0			0
$347$	0.905384	+	1.77692i	0.0486036	+	0.0953899i	0.914031	−	0.405645i	$-0.132953\pi$
$347$	0.905384	+	1.77692i	0.0486036	+	0.0953899i	−0.865427	+	0.501035i	$0.832953\pi$
$348$		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	−0.128853	−	0.991664i	$-0.541129\pi$
$353$	11.2294	−	5.72168i	0.597682	−	0.304534i	0.726535	+	0.687129i	$0.241129\pi$
$354$		0			0
$355$	−30.4293	+	17.8539i	−1.61502	+	0.947588i
$356$		0			0
$357$	−2.00669	−	3.98501i	−0.106205	−	0.210909i
$358$		0			0
$359$	14.9247	+	10.8434i	0.787695	+	0.572294i	0.907279	−	0.420530i	$-0.138156\pi$
$359$	14.9247	+	10.8434i	0.787695	+	0.572294i	−0.119583	+	0.992824i	$0.538156\pi$
$360$		0			0
$361$	−6.09198	+	4.42609i	−0.320631	+	0.232952i
$362$		0			0
$363$	2.44446	−	14.9734i	0.128301	−	0.785899i
$364$		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
$369$	4.05705	−	12.0945i	0.211202	−	0.629612i
$370$		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
$375$	−17.3951	−	8.50936i	−0.898281	−	0.439421i
$376$		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
$381$	16.4968	+	0.0783022i	0.845156	+	0.00401154i
$382$		0			0
$383$	2.02976	−	3.98364i	0.103716	−	0.203554i	−0.833317	−	0.552796i	$-0.813561\pi$
$383$	2.02976	−	3.98364i	0.103716	−	0.203554i	0.937033	+	0.349242i	$0.113561\pi$
$384$		0			0
$385$	0.737533	+	0.897834i	0.0375882	+	0.0457579i
$386$		0			0
$387$	−5.95978	+	11.4272i	−0.302952	+	0.580879i
$388$		0			0
$389$	6.59921	−	4.79461i	0.334593	−	0.243096i	−0.407784	−	0.913079i	$-0.633698\pi$
$389$	6.59921	−	4.79461i	0.334593	−	0.243096i	0.742377	+	0.669982i	$0.233698\pi$
$390$		0			0
$391$	−9.78900	−	7.11213i	−0.495051	−	0.359676i
$392$		0			0
$393$	29.5546	−	14.8825i	1.49083	−	0.750724i
$394$		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	$0.273409\pi$
$401$			30.3238i			1.51430i	−0.653241	+	0.757150i	$0.726591\pi$
$402$		0			0
$403$	−16.6963	−	32.7683i	−0.831700	−	1.63230i
$404$		0			0
$405$	2.34312	−	19.9877i	0.116431	−	0.993199i
$406$		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
$411$	22.8556	−	7.30648i	1.12738	−	0.360402i
$412$		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
$417$	−12.8631	−	12.9857i	−0.629906	−	0.635915i
$418$		0			0
$419$	−5.71751	−	17.5967i	−0.279319	−	0.859655i	−0.988044	−	0.154171i	$-0.950729\pi$
$419$	−5.71751	−	17.5967i	−0.279319	−	0.859655i	0.708725	−	0.705484i	$-0.249271\pi$
$420$		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
$423$	−6.63524	−	6.76243i	−0.322617	−	0.328801i
$424$		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
$429$	11.2163	+	8.23075i	0.541529	+	0.397384i
$430$		0			0
$431$	25.6284	−	8.32716i	1.23447	−	0.401105i	0.382141	−	0.924104i	$-0.375187\pi$
$431$	25.6284	−	8.32716i	1.23447	−	0.401105i	0.852333	+	0.522999i	$0.175187\pi$
$432$		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
$435$	5.04325	+	6.19914i	0.241805	+	0.297226i
$436$		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
$441$	−6.19103	−	19.6880i	−0.294811	−	0.937525i
$442$		0			0
$443$	26.4453	+	26.4453i	1.25645	+	1.25645i	0.952775	+	0.303677i	$0.0982142\pi$
$443$	26.4453	+	26.4453i	1.25645	+	1.25645i	0.303677	+	0.952775i	$0.401786\pi$
$444$		0			0
$445$	2.75649	−	28.1213i	0.130670	−	1.33308i
$446$		0			0
$447$	5.50418	−	0.845016i	0.260339	−	0.0399679i
$448$		0			0
$449$	18.7481			0.884779			0.442390	−	0.896823i	$-0.354131\pi$
$449$	18.7481			0.884779			0.442390	+	0.896823i	$0.354131\pi$
$450$		0			0
$451$	−6.36515			−0.299723
$452$		0			0
$453$	22.6530	−	3.47774i	1.06433	−	0.163399i
$454$		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
$459$	38.5548	+	0.549035i	1.79958	+	0.0256268i
$460$		0			0
$461$	12.6563	+	17.4199i	0.589464	+	0.811328i	0.994693	−	0.102888i	$-0.0328082\pi$
$461$	12.6563	+	17.4199i	0.589464	+	0.811328i	−0.405229	+	0.914215i	$0.632808\pi$
$462$		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
$465$	25.6552	+	6.81209i	1.18973	+	0.315903i
$466$		0			0
$467$	−26.7269	−	13.6180i	−1.23677	−	0.630168i	−0.291539	−	0.956559i	$-0.594167\pi$
$467$	−26.7269	−	13.6180i	−1.23677	−	0.630168i	−0.945235	+	0.326391i	$0.894167\pi$
$468$		0			0
$469$	4.15890	−	1.35131i	0.192040	−	0.0623977i
$470$		0			0
$471$	−13.2340	−	9.71137i	−0.609790	−	0.447476i
$472$		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
$477$	−0.511214	+	0.501600i	−0.0234069	+	0.0229667i
$478$		0			0
$479$	8.94946	−	27.5436i	0.408911	−	1.25850i	−0.508673	−	0.860960i	$-0.669864\pi$
$479$	8.94946	−	27.5436i	0.408911	−	1.25850i	0.917585	−	0.397540i	$-0.130136\pi$
$480$		0			0
$481$	−12.6046	−	38.7931i	−0.574722	−	1.76881i
$482$		0			0
$483$	0.689950	+	0.696531i	0.0313938	+	0.0316932i
$484$		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
$489$	16.6247	−	5.31459i	0.751795	−	0.240334i
$490$		0			0
$491$	20.7228	−	28.5225i	0.935207	−	1.28720i	−0.0225861	−	0.999745i	$-0.507190\pi$
$491$	20.7228	−	28.5225i	0.935207	−	1.28720i	0.957793	−	0.287457i	$-0.0928100\pi$
$492$		0			0
$493$	−10.8270	+	10.8270i	−0.487622	+	0.487622i
$494$		0			0
$495$	−9.82715	+	2.06334i	−0.441697	+	0.0927401i
$496$		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	−0.553307	−	0.832977i	$-0.686634\pi$
$503$	−4.58961	+	2.33852i	−0.204641	+	0.104270i	0.348667	+	0.937247i	$0.386634\pi$
$504$		0			0
$505$	−3.61591	−	3.21016i	−0.160906	−	0.142850i
$506$		0			0
$507$	24.4325	−	12.3032i	1.08508	−	0.546406i
$508$		0			0
$509$	−22.3242	−	16.2195i	−0.989502	−	0.718915i	−0.0296898	−	0.999559i	$-0.509452\pi$
$509$	−22.3242	−	16.2195i	−0.989502	−	0.718915i	−0.959812	+	0.280644i	$0.909452\pi$
$510$		0			0
$511$	3.63036	−	2.63761i	0.160598	−	0.116681i
$512$		0			0
$513$	−12.6195	+	12.2652i	−0.557166	+	0.541521i
$514$		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
$519$	−37.6268	−	0.178596i	−1.65163	−	0.00783948i
$520$		0			0
$521$	−12.0428	−	3.91295i	−0.527606	−	0.171430i	0.0330883	−	0.999452i	$-0.489466\pi$
$521$	−12.0428	−	3.91295i	−0.527606	−	0.171430i	−0.560694	+	0.828023i	$0.689466\pi$
$522$		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
$525$	−1.47894	+	2.61737i	−0.0645464	+	0.114231i
$526$		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
$531$	−9.06343	−	3.04031i	−0.393319	−	0.131938i
$532$		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
$537$	5.14327	−	31.5048i	0.221948	−	1.35953i
$538$		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
$543$	−2.22638	−	4.42126i	−0.0955429	−	0.189735i
$544$		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
$555$	26.9223	+	11.9136i	1.14279	+	0.505705i
$556$		0			0
$557$	26.1957	−	26.1957i	1.10995	−	1.10995i	0.116791	−	0.993157i	$-0.462739\pi$
$557$	26.1957	−	26.1957i	1.10995	−	1.10995i	0.993157	−	0.116791i	$-0.0372606\pi$
$558$		0			0
$559$	13.5497	−	18.6496i	0.573093	−	0.788795i
$560$		0			0
$561$	−5.85837	−	18.3257i	−0.247340	−	0.773712i
$562$		0			0
$563$	0.227603	+	1.43703i	0.00959232	+	0.0605636i	0.992020	−	0.126079i	$-0.0402393\pi$
$563$	0.227603	+	1.43703i	0.00959232	+	0.0605636i	−0.982428	+	0.186643i	$0.940239\pi$
$564$		0			0
$565$	−8.37701	−	5.35698i	−0.352423	−	0.225370i
$566$		0			0
$567$	−3.07595	−	0.547235i	−0.129178	−	0.0229817i
$568$		0			0
$569$	7.83577	+	24.1160i	0.328493	+	1.01100i	0.969839	+	0.243745i	$0.0783761\pi$
$569$	7.83577	+	24.1160i	0.328493	+	1.01100i	−0.641347	+	0.767251i	$0.721624\pi$
$570$		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
$573$	12.4210	−	24.0942i	0.518895	−	1.00655i
$574$		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
$579$	10.4490	−	14.2392i	0.434245	−	0.591760i
$580$		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
$585$	−9.40274	+	34.7462i	−0.388756	+	1.43658i
$586$		0			0
$587$	−27.7688	+	4.39815i	−1.14614	+	0.181531i	−0.700481	−	0.713671i	$-0.747031\pi$
$587$	−27.7688	+	4.39815i	−1.14614	+	0.181531i	−0.445661	+	0.895202i	$0.647031\pi$
$588$		0			0
$589$	−13.6434	−	18.7785i	−0.562167	−	0.773756i
$590$		0			0
$591$	14.4981	+	20.1554i	0.596373	+	0.829084i
$592$		0			0
$593$	−16.3288	−	16.3288i	−0.670545	−	0.670545i	0.287297	−	0.957842i	$-0.407243\pi$
$593$	−16.3288	−	16.3288i	−0.670545	−	0.670545i	−0.957842	+	0.287297i	$0.907243\pi$
$594$		0			0
$595$	−5.27839	−	2.30589i	−0.216393	−	0.0945322i
$596$		0			0
$597$	2.42920	+	15.8231i	0.0994207	+	0.647597i
$598$		0			0
$599$	−37.1895			−1.51952			−0.759761	−	0.650202i	$-0.774684\pi$
$599$	−37.1895			−1.51952			−0.759761	+	0.650202i	$0.774684\pi$
$600$		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
$603$	−6.26591	+	37.2682i	−0.255168	+	1.51768i
$604$		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
$609$	1.00715	−	0.724456i	0.0408117	−	0.0293565i
$610$		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
$615$	−5.93673	−	15.3617i	−0.239392	−	0.619442i
$616$		0			0
$617$	−9.21730	−	4.69645i	−0.371075	−	0.189072i	0.258501	−	0.966011i	$-0.416771\pi$
$617$	−9.21730	−	4.69645i	−0.371075	−	0.189072i	−0.629576	+	0.776939i	$0.716771\pi$
$618$		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
$621$	−8.09449	+	2.50321i	−0.324821	+	0.100450i
$622$		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
$627$	7.80465	+	4.02345i	0.311688	+	0.160681i
$628$		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
$633$	−13.0436	+	12.9203i	−0.518435	+	0.513537i
$634$		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
$639$	−47.3314	−	0.449328i	−1.87240	−	0.0177751i
$640$		0			0
$641$	−10.2750	+	14.1423i	−0.405836	+	0.558586i	−0.962197	−	0.272355i	$-0.912197\pi$
$641$	−10.2750	+	14.1423i	−0.405836	+	0.558586i	0.556361	+	0.830941i	$0.312197\pi$
$642$		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
$645$	3.49614	+	16.2669i	0.137660	+	0.640508i
$646$		0			0
$647$	−10.7527	−	21.1033i	−0.422730	−	0.829655i	−0.999915	−	0.0130414i	$-0.995849\pi$
$647$	−10.7527	−	21.1033i	−0.422730	−	0.829655i	0.577185	−	0.816614i	$-0.304151\pi$
$648$		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	0.286309	−	0.958137i	$-0.407572\pi$
$653$	31.4248	−	16.0117i	1.22975	−	0.626587i	0.943438	+	0.331550i	$0.107572\pi$
$654$		0			0
$655$	17.1015	−	39.1468i	0.668210	−	1.52959i
$656$		0			0
$657$	5.70269	+	38.3586i	0.222483	+	1.49651i
$658$		0			0
$659$	−3.78905	−	2.75290i	−0.147600	−	0.107238i	0.511534	−	0.859263i	$-0.329077\pi$
$659$	−3.78905	−	2.75290i	−0.147600	−	0.107238i	−0.659135	+	0.752025i	$0.729077\pi$
$660$		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
$663$	−68.0672	−	11.1122i	−2.64351	−	0.431563i
$664$		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
$669$	0.0500518	−	10.5450i	0.00193511	−	0.407692i
$670$		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
$675$	−14.1454	−	21.7924i	−0.544455	−	0.838790i
$676$		0			0
$677$	1.90476	−	12.0262i	0.0732060	−	0.462204i	−0.923668	−	0.383194i	$-0.874824\pi$
$677$	1.90476	−	12.0262i	0.0732060	−	0.462204i	0.996874	−	0.0790103i	$-0.0251760\pi$
$678$		0			0
$679$	−1.01213	−	0.328860i	−0.0388418	−	0.0126205i
$680$		0			0
$681$	0.0342301	−	7.21165i	0.00131170	−	0.276351i
$682$		0			0
$683$	2.44981	−	4.80802i	0.0937393	−	0.183974i	−0.839376	−	0.543551i	$-0.817079\pi$
$683$	2.44981	−	4.80802i	0.0937393	−	0.183974i	0.933115	+	0.359578i	$0.117079\pi$
$684$		0			0
$685$	16.6890	−	26.0976i	0.637655	−	0.997136i
$686$		0			0
$687$	33.5558	+	5.47810i	1.28023	+	0.209003i
$688$		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
$693$	0.229236	+	1.54193i	0.00870795	+	0.0585732i
$694$		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	$0.205022\pi$
$701$			31.7969i			1.20095i	−0.799643	+	0.600475i	$0.794978\pi$
$702$		0			0
$703$	−11.6876	−	22.9382i	−0.440807	−	0.865132i
$704$		0			0
$705$	−12.1668	−	1.25094i	−0.458227	−	0.0471130i
$706$		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
$711$	−31.3676	−	0.297780i	−1.17638	−	0.0111676i
$712$		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
$717$	−8.21222	+	8.13463i	−0.306691	+	0.303793i
$718$		0			0
$719$	10.7159	+	32.9803i	0.399637	+	1.22996i	0.925291	+	0.379258i	$0.123821\pi$
$719$	10.7159	+	32.9803i	0.399637	+	1.22996i	−0.525654	+	0.850699i	$0.676179\pi$
$720$		0			0
$721$	−1.51718	+	4.66939i	−0.0565027	+	0.173897i
$722$		0			0
$723$	−36.6008	−	18.8684i	−1.36120	−	0.701724i
$724$		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
$729$	16.4858	−	21.3827i	0.610584	−	0.791952i
$730$		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
$735$	−22.3785	−	14.4608i	−0.825442	−	0.533396i
$736$		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
$741$	25.5527	−	18.3804i	0.938701	−	0.675222i
$742$		0			0
$743$	15.7766	+	15.7766i	0.578787	+	0.578787i	0.934569	−	0.355782i	$-0.115785\pi$
$743$	15.7766	+	15.7766i	0.578787	+	0.578787i	−0.355782	+	0.934569i	$0.615785\pi$
$744$		0			0
$745$	4.77289	−	5.37615i	0.174865	−	0.196967i
$746$		0			0
$747$	−7.25047	+	43.1241i	−0.265281	+	1.57783i
$748$		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
$753$	6.98556	+	45.5018i	0.254568	+	1.65818i
$754$		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
$759$	2.46864	+	3.43192i	0.0896058	+	0.124571i
$760$		0			0
$761$	−26.5073	−	36.4842i	−0.960890	−	1.32255i	−0.946517	−	0.322654i	$-0.895425\pi$
$761$	−26.5073	−	36.4842i	−0.960890	−	1.32255i	−0.0143726	−	0.999897i	$-0.504575\pi$
$762$		0			0
$763$	1.47489	−	0.233599i	0.0533945	−	0.00845686i
$764$		0			0
$765$	38.7633	−	31.2308i	1.40149	−	1.12915i
$766$		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
$771$	−14.5435	+	19.8189i	−0.523770	+	0.713759i
$772$		0			0
$773$	−1.94871	−	0.308646i	−0.0700904	−	0.0111012i	0.121291	−	0.992617i	$-0.461297\pi$
$773$	−1.94871	−	0.308646i	−0.0700904	−	0.0111012i	−0.191381	+	0.981516i	$0.561297\pi$
$774$		0			0
$775$	31.1073	−	14.3758i	1.11741	−	0.516393i
$776$		0			0
$777$	2.09427	−	4.06244i	0.0751314	−	0.145739i
$778$		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
$783$	1.52629	+	10.6125i	0.0545450	+	0.379260i
$784$		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
$789$	−12.1974	−	38.1549i	−0.434237	−	1.35835i
$790$		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
$795$	−0.0945661	+	0.919761i	−0.00335392	+	0.0326206i
$796$		0			0
$797$	12.9280	+	25.3725i	0.457932	+	0.898742i	0.998354	+	0.0573478i	$0.0182644\pi$
$797$	12.9280	+	25.3725i	0.457932	+	0.898742i	−0.540423	+	0.841394i	$0.681736\pi$
$798$		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
$807$	−6.55547	−	13.0182i	−0.230764	−	0.458263i
$808$		0			0
$809$	−6.51664	−	4.73462i	−0.229113	−	0.166460i	0.467306	−	0.884095i	$-0.345225\pi$
$809$	−6.51664	−	4.73462i	−0.229113	−	0.166460i	−0.696419	+	0.717635i	$0.745225\pi$
$810$		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
$813$	−6.42607	+	39.3625i	−0.225372	+	1.38050i
$814$		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
$819$	5.29806	+	1.77722i	0.185129	+	0.0621012i
$820$		0			0
$821$	30.3635	+	9.86569i	1.05969	+	0.344315i	0.786465	−	0.617635i	$-0.211909\pi$
$821$	30.3635	+	9.86569i	1.05969	+	0.344315i	0.273227	+	0.961950i	$0.411909\pi$
$822$		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
$825$	−8.06436	+	10.1497i	−0.280765	+	0.353367i
$826$		0			0
$827$	5.20579	−	32.8681i	0.181023	−	1.14294i	−0.715065	−	0.699058i	$-0.753603\pi$
$827$	5.20579	−	32.8681i	0.181023	−	1.14294i	0.896088	−	0.443877i	$-0.146397\pi$
$828$		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
$831$	−19.4334	−	0.0922408i	−0.674137	−	0.00319980i
$832$		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
$837$	24.8209	+	25.5381i	0.857937	+	0.882725i
$838$		0			0
$839$	0.448091	−	0.325557i	0.0154698	−	0.0112395i	−0.580023	−	0.814600i	$-0.696957\pi$
$839$	0.448091	−	0.325557i	0.0154698	−	0.0112395i	0.595493	+	0.803360i	$0.296957\pi$
$840$		0			0
$841$	20.0170	+	14.5432i	0.690243	+	0.501491i
$842$		0			0
$843$	−23.7705	+	11.9699i	−0.818700	+	0.412265i
$844$		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
$855$	−2.43085	+	22.5884i	−0.0831334	+	0.772507i
$856$		0			0
$857$	−20.1939	+	20.1939i	−0.689811	+	0.689811i	−0.962190	−	0.272379i	$-0.912190\pi$
$857$	−20.1939	+	20.1939i	−0.689811	+	0.689811i	0.272379	+	0.962190i	$0.412190\pi$
$858$		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
$861$	−2.43531	+	0.778520i	−0.0829951	+	0.0265319i
$862$		0			0
$863$	3.15711	+	19.9332i	0.107469	+	0.678534i	0.981326	+	0.192351i	$0.0616112\pi$
$863$	3.15711	+	19.9332i	0.107469	+	0.678534i	−0.873857	+	0.486183i	$0.838389\pi$
$864$		0			0
$865$	−37.5358	+	30.8341i	−1.27625	+	1.04839i
$866$		0			0
$867$	46.3989	+	46.8415i	1.57579	+	1.59082i
$868$		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
$873$	6.56471	−	6.44124i	0.222182	−	0.218003i
$874$		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
$879$	−7.21627	−	5.29544i	−0.243399	−	0.178611i
$880$		0			0
$881$	25.1299	−	8.16520i	0.846648	−	0.275093i	0.146607	−	0.989195i	$-0.453165\pi$
$881$	25.1299	−	8.16520i	0.846648	−	0.275093i	0.700041	+	0.714102i	$0.253165\pi$
$882$		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
$885$	−11.5118	+	4.44891i	−0.386966	+	0.149548i
$886$		0			0
$887$	−46.6702	+	7.39183i	−1.56703	+	0.248193i	−0.878761	−	0.477261i	$-0.841629\pi$
$887$	−46.6702	+	7.39183i	−1.56703	+	0.248193i	−0.688270	+	0.725455i	$0.741629\pi$
$888$		0			0
$889$	−1.94341	−	2.67488i	−0.0651800	−	0.0897126i
$890$		0			0
$891$	−12.7313	−	4.40557i	−0.426514	−	0.147592i
$892$		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
$897$	14.9793	−	2.29965i	0.500143	−	0.0767832i
$898$		0			0
$899$	−14.1418			−0.471657
$900$		0			0
$901$	−1.77155			−0.0590189
$902$		0			0
$903$	2.55311	−	0.391960i	0.0849621	−	0.0130436i
$904$		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
$909$	−1.94600	−	6.18845i	−0.0645447	−	0.205258i
$910$		0			0
$911$	23.4648	+	32.2965i	0.777424	+	1.07003i	0.995561	+	0.0941143i	$0.0300019\pi$
$911$	23.4648	+	32.2965i	0.777424	+	1.07003i	−0.218137	+	0.975918i	$0.569998\pi$
$912$		0			0
$913$	21.5506	−	3.41329i	0.713222	−	0.112963i
$914$		0			0
$915$	−0.890636	−	16.2887i	−0.0294435	−	0.538489i
$916$		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
$921$	2.89764	+	2.12634i	0.0954804	+	0.0700654i
$922$		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
$927$	−29.7164	−	30.2860i	−0.976013	−	0.994722i
$928$		0			0
$929$	−13.5788	+	41.7913i	−0.445507	+	1.37113i	0.436420	+	0.899743i	$0.356246\pi$
$929$	−13.5788	+	41.7913i	−0.445507	+	1.37113i	−0.881927	+	0.471386i	$0.843754\pi$
$930$		0			0
$931$	7.19977	+	22.1586i	0.235963	+	0.726219i
$932$		0			0
$933$	−27.7179	−	27.9823i	−0.907444	−	0.916099i
$934$		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
$939$	36.9070	−	11.7984i	1.20442	−	0.385028i
$940$		0			0
$941$	4.63450	−	6.37884i	0.151080	−	0.207944i	−0.726768	−	0.686883i	$-0.758978\pi$
$941$	4.63450	−	6.37884i	0.151080	−	0.207944i	0.877848	+	0.478939i	$0.158978\pi$
$942$		0			0
$943$	−4.90281	+	4.90281i	−0.159657	+	0.159657i
$944$		0			0
$945$	−3.50750	+	1.99139i	−0.114099	+	0.0647799i
$946$		0			0
$947$	−15.6899	−	30.7932i	−0.509854	−	1.00065i	−0.992199	−	0.124664i	$-0.960215\pi$
$947$	−15.6899	−	30.7932i	−0.509854	−	1.00065i	0.482345	−	0.875982i	$-0.339785\pi$
$948$		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	−0.964576	−	0.263804i	$-0.915023\pi$
$953$	−40.6912	+	20.7332i	−1.31812	+	0.671615i	−0.353542	+	0.935419i	$0.615023\pi$
$954$		0			0
$955$	−7.51576	−	34.1789i	−0.243204	−	1.10600i
$956$		0			0
$957$	4.77811	−	2.40607i	0.154454	−	0.0777772i
$958$		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
$963$	3.20422	−	6.14376i	0.103255	−	0.197980i
$964$		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
$969$	−43.5287	−	0.206609i	−1.39834	−	0.00663725i
$970$		0			0
$971$	44.7462	+	14.5389i	1.43597	+	0.466576i	0.920640	−	0.390413i	$-0.127668\pi$
$971$	44.7462	+	14.5389i	1.43597	+	0.466576i	0.515334	+	0.856989i	$0.327668\pi$
$972$		0			0
$973$	−0.573066	+	3.61820i	−0.0183717	+	0.115994i
$974$		0			0
$975$	19.2942	+	42.2759i	0.617909	+	1.35391i
$976$		0			0
$977$	1.14152	−	7.20725i	0.0365203	−	0.230580i	−0.962676	−	0.270655i	$-0.912760\pi$
$977$	1.14152	−	7.20725i	0.0365203	−	0.230580i	0.999197	+	0.0400750i	$0.0127597\pi$
$978$		0			0
$979$	−17.9896	−	5.84518i	−0.574951	−	0.186813i
$980$		0			0
$981$	−4.10419	+	12.2350i	−0.131037	+	0.390632i
$982$		0			0
$983$	−8.79016	+	17.2517i	−0.280363	+	0.550243i	−0.987649	−	0.156685i	$-0.949919\pi$
$983$	−8.79016	+	17.2517i	−0.280363	+	0.550243i	0.707286	+	0.706928i	$0.249919\pi$
$984$		0			0
$985$	31.0182	+	8.07868i	0.988322	+	0.257408i
$986$		0			0
$987$	−0.305934	+	1.87398i	−0.00973798	+	0.0596494i
$988$		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
$993$	−13.0322	−	25.8801i	−0.413565	−	0.821282i
$994$		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.77.9	yes	80
3.2	odd	2	inner	300.2.x.a.77.3	✓	80
25.13	odd	20	inner	300.2.x.a.113.3	yes	80
75.38	even	20	inner	300.2.x.a.113.9	yes	80

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

\(f(q)\)	\(=\)	\(q+(1.71199 - 0.262830i) q^{3} +(1.48454 - 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(2.86184 - 0.899925i) q^{9} +O(q^{10})\)	\(q+(1.71199 - 0.262830i) q^{3} +(1.48454 - 1.67217i) q^{5} +(-0.245464 - 0.245464i) q^{7} +(2.86184 - 0.899925i) q^{9} +(-0.879848 - 1.21101i) q^{11} +(-5.29990 + 0.839422i) q^{13} +(2.10202 - 3.25292i) q^{15} +(6.61182 + 3.36889i) q^{17} +(-3.22097 + 1.04656i) q^{19} +(-0.484748 - 0.355717i) q^{21} +(-1.61050 - 0.255078i) q^{23} +(-0.592307 - 4.96479i) q^{25} +(4.66293 - 2.29284i) q^{27} +(-0.637623 + 1.96240i) q^{29} +(2.11791 + 6.51825i) q^{31} +(-1.82458 - 1.84199i) q^{33} +(-0.774858 + 0.0460576i) q^{35} +(1.18914 + 7.50792i) q^{37} +(-8.85278 + 2.83006i) q^{39} +(2.49942 - 3.44015i) q^{41} +(-3.03773 + 3.03773i) q^{43} +(2.74368 - 6.12146i) q^{45} +(-1.43370 - 2.81380i) q^{47} -6.87949i q^{49} +(12.2048 + 4.02974i) q^{51} +(-0.212713 + 0.108383i) q^{53} +(-3.33118 - 0.326527i) q^{55} +(-5.23920 + 2.63826i) q^{57} +(-2.57801 - 1.87303i) q^{59} +(3.40759 - 2.47576i) q^{61} +(-0.923378 - 0.481580i) q^{63} +(-6.46424 + 10.1085i) q^{65} +(-5.71895 + 11.2241i) q^{67} +(-2.82420 - 0.0134051i) q^{69} +(-15.0056 - 4.87563i) q^{71} +(-2.02219 + 12.7676i) q^{73} +(-2.31892 - 8.34402i) q^{75} +(-0.0812876 + 0.513230i) q^{77} +(-9.94456 - 3.23118i) q^{79} +(7.38027 - 5.15088i) q^{81} +(-6.61756 + 12.9877i) q^{83} +(15.4489 - 6.05486i) q^{85} +(-0.575829 + 3.52720i) q^{87} +(10.2231 - 7.42754i) q^{89} +(1.50698 + 1.09489i) q^{91} +(5.33903 + 10.6025i) q^{93} +(-3.03162 + 6.93965i) q^{95} +(2.73153 - 1.39178i) q^{97} +(-3.60780 - 2.67391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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