LMFDB - Embedded newform 605.2.b.f.364.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(364,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.364"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-2,4,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1480160000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 $ x^8 + 9x^6 + 27x^4 + 31*x^2 + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.2
Root			$-1.65458i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.f.364.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.65458i q^{2} +1.97479i q^{3} -0.737640 q^{4} +(2.19353 + 0.434096i) q^{5} +3.26745 q^{6} +2.24307i q^{7} -2.08868i q^{8} -0.899788 q^{9} +(0.718246 - 3.62937i) q^{10} -1.45668i q^{12} -3.69976i q^{13} +3.71135 q^{14} +(-0.857247 + 4.33175i) q^{15} -4.93117 q^{16} +2.22461i q^{17} +1.48877i q^{18} +5.28684 q^{19} +(-1.61803 - 0.320206i) q^{20} -4.42960 q^{21} +3.85415i q^{23} +4.12469 q^{24} +(4.62312 + 1.90440i) q^{25} -6.12155 q^{26} +4.14747i q^{27} -1.65458i q^{28} +0.188439 q^{29} +(7.16724 + 1.41838i) q^{30} +0.686867 q^{31} +3.98166i q^{32} +3.68079 q^{34} +(-0.973708 + 4.92024i) q^{35} +0.663720 q^{36} +2.59316i q^{37} -8.74751i q^{38} +7.30624 q^{39} +(0.906685 - 4.58157i) q^{40} -7.91604 q^{41} +7.32913i q^{42} +8.41368i q^{43} +(-1.97371 - 0.390594i) q^{45} +6.37701 q^{46} -12.0132i q^{47} -9.73801i q^{48} +1.96862 q^{49} +(3.15099 - 7.64933i) q^{50} -4.39313 q^{51} +2.72909i q^{52} -12.6566i q^{53} +6.86233 q^{54} +4.68506 q^{56} +10.4404i q^{57} -0.311788i q^{58} +0.343688 q^{59} +(0.632340 - 3.19527i) q^{60} -1.73338 q^{61} -1.13648i q^{62} -2.01829i q^{63} -3.27435 q^{64} +(1.60605 - 8.11552i) q^{65} +0.650461i q^{67} -1.64096i q^{68} -7.61114 q^{69} +(8.14094 + 1.61108i) q^{70} +4.64760 q^{71} +1.87937i q^{72} -8.85841i q^{73} +4.29059 q^{74} +(-3.76079 + 9.12969i) q^{75} -3.89979 q^{76} -12.0888i q^{78} -7.23426 q^{79} +(-10.8166 - 2.14060i) q^{80} -10.8897 q^{81} +13.0977i q^{82} +3.18165i q^{83} +3.26745 q^{84} +(-0.965692 + 4.87974i) q^{85} +13.9211 q^{86} +0.372127i q^{87} -9.92195 q^{89} +(-0.646269 + 3.26566i) q^{90} +8.29883 q^{91} -2.84298i q^{92} +1.35642i q^{93} -19.8768 q^{94} +(11.5968 + 2.29499i) q^{95} -7.86294 q^{96} +2.26811i q^{97} -3.25724i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} + 12 q^{19} - 4 q^{20} - 4 q^{21} + 2 q^{24} - 8 q^{25} + 10 q^{26} + 24 q^{29} + 22 q^{30} + 14 q^{31} - 8 q^{34} + 14 q^{35}+ \cdots + 8 q^{96}+O(q^{100}) $ 8 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 + 12 * q^19 - 4 * q^20 - 4 * q^21 + 2 * q^24 - 8 * q^25 + 10 * q^26 + 24 * q^29 + 22 * q^30 + 14 * q^31 - 8 * q^34 + 14 * q^35 + 20 * q^36 + 30 * q^39 + 24 * q^40 - 34 * q^41 + 6 * q^45 - 24 * q^46 + 30 * q^49 + 16 * q^50 - 54 * q^51 + 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 - 20 * q^61 - 14 * q^64 + 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 - 4 * q^74 - 20 * q^75 - 28 * q^76 + 16 * q^79 - 28 * q^80 - 36 * q^81 - 6 * q^84 - 4 * q^85 + 46 * q^86 + 12 * q^89 + 46 * q^90 + 20 * q^91 - 42 * q^94 + 26 * q^95 + 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.65458i		−	1.16997i	−0.811046	−	0.584983i	$-0.801101\pi$
$2$		−	1.65458i		−	1.16997i	0.811046	−	0.584983i	$-0.198899\pi$
$3$			1.97479i			1.14014i	0.821595	+	0.570072i	$0.193085\pi$
$3$			1.97479i			1.14014i	−0.821595	+	0.570072i	$0.806915\pi$
$4$	−0.737640			−0.368820
$5$	2.19353	+	0.434096i	0.980975	+	0.194133i
$5$	2.19353	+	0.434096i	0.980975	+	0.194133i
$6$	3.26745			1.33393
$7$			2.24307i			0.847802i	0.905708	+	0.423901i	$0.139340\pi$
$7$			2.24307i			0.847802i	−0.905708	+	0.423901i	$0.860660\pi$
$8$		−	2.08868i		−	0.738459i
$9$	−0.899788			−0.299929
$10$	0.718246	−	3.62937i	0.227129	−	1.14771i
$11$		0			0
$11$		0			0
$12$		−	1.45668i		−	0.420508i
$13$		−	3.69976i		−	1.02613i	−0.858350	−	0.513064i	$-0.828510\pi$
$13$		−	3.69976i		−	1.02613i	0.858350	−	0.513064i	$-0.171490\pi$
$14$	3.71135			0.991900
$15$	−0.857247	+	4.33175i	−0.221340	+	1.11845i
$16$	−4.93117			−1.23279
$17$			2.22461i			0.539546i	0.962924	+	0.269773i	$0.0869487\pi$
$17$			2.22461i			0.539546i	−0.962924	+	0.269773i	$0.913051\pi$
$18$			1.48877i			0.350907i
$19$	5.28684			1.21288			0.606442	−	0.795127i	$-0.292596\pi$
$19$	5.28684			1.21288			0.606442	+	0.795127i	$0.292596\pi$
$20$	−1.61803	−	0.320206i	−0.361803	−	0.0716003i
$21$	−4.42960			−0.966617
$22$		0			0
$23$			3.85415i			0.803647i	0.915717	+	0.401823i	$0.131623\pi$
$23$			3.85415i			0.803647i	−0.915717	+	0.401823i	$0.868377\pi$
$24$	4.12469			0.841950
$25$	4.62312	+	1.90440i	0.924624	+	0.380880i
$26$	−6.12155			−1.20053
$27$			4.14747i			0.798182i
$28$		−	1.65458i		−	0.312687i
$29$	0.188439			0.0349922			0.0174961	−	0.999847i	$-0.494431\pi$
$29$	0.188439			0.0349922			0.0174961	+	0.999847i	$0.494431\pi$
$30$	7.16724	+	1.41838i	1.30855	+	0.258960i
$31$	0.686867			0.123365			0.0616824	−	0.998096i	$-0.480353\pi$
$31$	0.686867			0.123365			0.0616824	+	0.998096i	$0.480353\pi$
$32$			3.98166i			0.703866i
$33$		0			0
$34$	3.68079			0.631251
$35$	−0.973708	+	4.92024i	−0.164587	+	0.831673i
$36$	0.663720			0.110620
$37$			2.59316i			0.426313i	0.977018	+	0.213156i	$0.0683744\pi$
$37$			2.59316i			0.426313i	−0.977018	+	0.213156i	$0.931626\pi$
$38$		−	8.74751i		−	1.41903i
$39$	7.30624			1.16993
$40$	0.906685	−	4.58157i	0.143360	−	0.724410i
$41$	−7.91604			−1.23628			−0.618139	−	0.786069i	$-0.712113\pi$
$41$	−7.91604			−1.23628			−0.618139	+	0.786069i	$0.712113\pi$
$42$			7.32913i			1.13091i
$43$			8.41368i			1.28307i	0.767092	+	0.641537i	$0.221703\pi$
$43$			8.41368i			1.28307i	−0.767092	+	0.641537i	$0.778297\pi$
$44$		0			0
$45$	−1.97371	−	0.390594i	−0.294223	−	0.0582263i
$46$	6.37701			0.940239
$47$		−	12.0132i		−	1.75230i	−0.482037	−	0.876151i	$-0.660103\pi$
$47$		−	12.0132i		−	1.75230i	0.482037	−	0.876151i	$-0.339897\pi$
$48$		−	9.73801i		−	1.40556i
$49$	1.96862			0.281231
$50$	3.15099	−	7.64933i	0.445617	−	1.08178i
$51$	−4.39313			−0.615161
$52$			2.72909i			0.378457i
$53$		−	12.6566i		−	1.73851i	−0.494360	−	0.869257i	$-0.664597\pi$
$53$		−	12.6566i		−	1.73851i	0.494360	−	0.869257i	$-0.335403\pi$
$54$	6.86233			0.933845
$55$		0			0
$56$	4.68506			0.626067
$57$			10.4404i			1.38286i
$58$		−	0.311788i		−	0.0409397i
$59$	0.343688			0.0447444			0.0223722	−	0.999750i	$-0.492878\pi$
$59$	0.343688			0.0447444			0.0223722	+	0.999750i	$0.492878\pi$
$60$	0.632340	−	3.19527i	0.0816347	−	0.412508i
$61$	−1.73338			−0.221936			−0.110968	−	0.993824i	$-0.535395\pi$
$61$	−1.73338			−0.221936			−0.110968	+	0.993824i	$0.535395\pi$
$62$		−	1.13648i		−	0.144333i
$63$		−	2.01829i		−	0.254281i
$64$	−3.27435			−0.409293
$65$	1.60605	−	8.11552i	0.199206	−	1.00661i
$66$		0			0
$67$			0.650461i			0.0794664i	0.999210	+	0.0397332i	$0.0126508\pi$
$67$			0.650461i			0.0794664i	−0.999210	+	0.0397332i	$0.987349\pi$
$68$		−	1.64096i		−	0.198996i
$69$	−7.61114			−0.916273
$70$	8.14094	+	1.61108i	0.973029	+	0.192561i
$71$	4.64760			0.551569			0.275785	−	0.961219i	$-0.411062\pi$
$71$	4.64760			0.551569			0.275785	+	0.961219i	$0.411062\pi$
$72$			1.87937i			0.221485i
$73$		−	8.85841i		−	1.03680i	−0.855139	−	0.518399i	$-0.826528\pi$
$73$		−	8.85841i		−	1.03680i	0.855139	−	0.518399i	$-0.173472\pi$
$74$	4.29059			0.498772
$75$	−3.76079	+	9.12969i	−0.434258	+	1.05421i
$76$	−3.89979			−0.447336
$77$		0			0
$78$		−	12.0888i		−	1.36878i
$79$	−7.23426			−0.813918			−0.406959	−	0.913447i	$-0.633411\pi$
$79$	−7.23426			−0.813918			−0.406959	+	0.913447i	$0.633411\pi$
$80$	−10.8166	−	2.14060i	−1.20934	−	0.239326i
$81$	−10.8897			−1.20997
$82$			13.0977i			1.44640i
$83$			3.18165i			0.349232i	0.984637	+	0.174616i	$0.0558684\pi$
$83$			3.18165i			0.349232i	−0.984637	+	0.174616i	$0.944132\pi$
$84$	3.26745			0.356508
$85$	−0.965692	+	4.87974i	−0.104744	+	0.529282i
$86$	13.9211			1.50115
$87$			0.372127i			0.0398962i
$88$		0			0
$89$	−9.92195			−1.05172			−0.525862	−	0.850570i	$-0.676257\pi$
$89$	−9.92195			−1.05172			−0.525862	+	0.850570i	$0.676257\pi$
$90$	−0.646269	+	3.26566i	−0.0681228	+	0.344231i
$91$	8.29883			0.869954
$92$		−	2.84298i		−	0.296401i
$93$			1.35642i			0.140654i
$94$	−19.8768			−2.05013
$95$	11.5968	+	2.29499i	1.18981	+	0.235461i
$96$	−7.86294			−0.802508
$97$			2.26811i			0.230292i	0.993349	+	0.115146i	$0.0367335\pi$
$97$			2.26811i			0.230292i	−0.993349	+	0.115146i	$0.963266\pi$
$98$		−	3.25724i		−	0.329031i
$99$		0			0
$100$	−3.41020	−	1.40476i	−0.341020	−	0.140476i
$101$	−9.89686			−0.984774			−0.492387	−	0.870376i	$-0.663876\pi$
$101$	−9.89686			−0.984774			−0.492387	+	0.870376i	$0.663876\pi$
$102$			7.26879i			0.719717i
$103$		−	10.2411i		−	1.00909i	−0.863386	−	0.504544i	$-0.831661\pi$
$103$		−	10.2411i		−	1.00909i	0.863386	−	0.504544i	$-0.168339\pi$
$104$	−7.72760			−0.757753
$105$	−9.71644	−	1.92287i	−0.948227	−	0.187653i
$106$	−20.9413			−2.03400
$107$		−	10.0468i		−	0.971261i	−0.874164	−	0.485631i	$-0.838590\pi$
$107$		−	10.0468i		−	0.971261i	0.874164	−	0.485631i	$-0.161410\pi$
$108$		−	3.05934i		−	0.294386i
$109$	−8.80173			−0.843053			−0.421527	−	0.906816i	$-0.638506\pi$
$109$	−8.80173			−0.843053			−0.421527	+	0.906816i	$0.638506\pi$
$110$		0			0
$111$	−5.12094			−0.486058
$112$		−	11.0610i		−	1.04516i
$113$		−	0.231352i		−	0.0217638i	−0.999941	−	0.0108819i	$-0.996536\pi$
$113$		−	0.231352i		−	0.0217638i	0.999941	−	0.0108819i	$-0.00346388\pi$
$114$	17.2745			1.61790
$115$	−1.67307	+	8.45419i	−0.156015	+	0.788357i
$116$	−0.139000			−0.0129058
$117$			3.32900i			0.307766i
$118$		−	0.568660i		−	0.0523494i
$119$	−4.98996			−0.457429
$120$	9.04763	+	1.79051i	0.825932	+	0.163451i
$121$		0			0
$122$			2.86801i			0.259658i
$123$		−	15.6325i		−	1.40953i
$124$	−0.506660			−0.0454995
$125$	9.31425	+	6.18423i	0.833092	+	0.553134i
$126$	−3.33943			−0.297500
$127$			2.43034i			0.215658i	0.994169	+	0.107829i	$0.0343899\pi$
$127$			2.43034i			0.215658i	−0.994169	+	0.107829i	$0.965610\pi$
$128$			13.3810i			1.18272i
$129$	−16.6152			−1.46289
$130$	−13.4278	−	2.65734i	−1.17769	−	0.233064i
$131$	−1.58846			−0.138785			−0.0693924	−	0.997589i	$-0.522106\pi$
$131$	−1.58846			−0.138785			−0.0693924	+	0.997589i	$0.522106\pi$
$132$		0			0
$133$			11.8588i			1.02829i
$134$	1.07624			0.0929730
$135$	−1.80040	+	9.09760i	−0.154954	+	0.782997i
$136$	4.64649			0.398433
$137$		−	18.7019i		−	1.59781i	−0.601457	−	0.798905i	$-0.705413\pi$
$137$		−	18.7019i		−	1.59781i	0.601457	−	0.798905i	$-0.294587\pi$
$138$			12.5932i			1.07201i
$139$	11.6274			0.986222			0.493111	−	0.869966i	$-0.335860\pi$
$139$	11.6274			0.986222			0.493111	+	0.869966i	$0.335860\pi$
$140$	0.718246	−	3.62937i	0.0607029	−	0.306738i
$141$	23.7235			1.99788
$142$		−	7.68984i		−	0.645317i
$143$		0			0
$144$	4.43700			0.369750
$145$	0.413346	+	0.0818005i	0.0343265	+	0.00679316i
$146$	−14.6570			−1.21302
$147$			3.88761i			0.320644i
$148$		−	1.91282i		−	0.157233i
$149$	5.91553			0.484619			0.242309	−	0.970199i	$-0.422095\pi$
$149$	5.91553			0.484619			0.242309	+	0.970199i	$0.422095\pi$
$150$	15.1058	+	6.22253i	1.23338	+	0.508067i
$151$	−12.7779			−1.03985			−0.519924	−	0.854213i	$-0.674040\pi$
$151$	−12.7779			−1.03985			−0.519924	+	0.854213i	$0.674040\pi$
$152$		−	11.0425i		−	0.895665i
$153$		−	2.00167i		−	0.161826i
$154$		0			0
$155$	1.50666	+	0.298166i	0.121018	+	0.0239492i
$156$	−5.38937			−0.431495
$157$			14.3487i			1.14515i	0.819853	+	0.572574i	$0.194055\pi$
$157$			14.3487i			1.14515i	−0.819853	+	0.572574i	$0.805945\pi$
$158$			11.9697i			0.952256i
$159$	24.9941			1.98216
$160$	−1.72842	+	8.73389i	−0.136644	+	0.690475i
$161$	−8.64515			−0.681333
$162$			18.0180i			1.41563i
$163$			3.62716i			0.284101i	0.989859	+	0.142051i	$0.0453696\pi$
$163$			3.62716i			0.284101i	−0.989859	+	0.142051i	$0.954630\pi$
$164$	5.83919			0.455964
$165$		0			0
$166$	5.26430			0.408589
$167$			3.82070i			0.295655i	0.989013	+	0.147827i	$0.0472280\pi$
$167$			3.82070i			0.295655i	−0.989013	+	0.147827i	$0.952772\pi$
$168$			9.25199i			0.713807i
$169$	−0.688202			−0.0529386
$170$	8.07392	+	1.59782i	0.619241	+	0.122547i
$171$	−4.75703			−0.363779
$172$		−	6.20627i		−	0.473224i
$173$			2.10714i			0.160203i	0.996787	+	0.0801016i	$0.0255245\pi$
$173$			2.10714i			0.160203i	−0.996787	+	0.0801016i	$0.974476\pi$
$174$	0.615714			0.0466772
$175$	−4.27171	+	10.3700i	−0.322911	+	0.783899i
$176$		0			0
$177$			0.678711i			0.0510151i
$178$			16.4167i			1.23048i
$179$	−5.02397			−0.375509			−0.187755	−	0.982216i	$-0.560121\pi$
$179$	−5.02397			−0.375509			−0.187755	+	0.982216i	$0.560121\pi$
$180$	1.45589	+	0.288118i	0.108515	+	0.0214750i
$181$	−15.6476			−1.16308			−0.581539	−	0.813519i	$-0.697549\pi$
$181$	−15.6476			−1.16308			−0.581539	+	0.813519i	$0.697549\pi$
$182$		−	13.7311i		−	1.01782i
$183$		−	3.42305i		−	0.253039i
$184$	8.05008			0.593460
$185$	−1.12568	+	5.68817i	−0.0827616	+	0.418202i
$186$	2.24430			0.164560
$187$		0			0
$188$			8.86140i			0.646284i
$189$	−9.30309			−0.676700
$190$	3.79726	−	19.1879i	0.275482	−	1.39204i
$191$	3.11585			0.225455			0.112728	−	0.993626i	$-0.464041\pi$
$191$	3.11585			0.225455			0.112728	+	0.993626i	$0.464041\pi$
$192$		−	6.46614i		−	0.466653i
$193$		−	9.63638i		−	0.693642i	−0.937931	−	0.346821i	$-0.887261\pi$
$193$		−	9.63638i		−	0.693642i	0.937931	−	0.346821i	$-0.112739\pi$
$194$	3.75277			0.269433
$195$	16.0264	+	3.17160i	1.14768	+	0.227123i
$196$	−1.45213			−0.103724
$197$		−	14.3974i		−	1.02577i	−0.858457	−	0.512885i	$-0.828577\pi$
$197$		−	14.3974i		−	1.02577i	0.858457	−	0.512885i	$-0.171423\pi$
$198$		0			0
$199$	−14.7978			−1.04899			−0.524493	−	0.851415i	$-0.675745\pi$
$199$	−14.7978			−1.04899			−0.524493	+	0.851415i	$0.675745\pi$
$200$	3.97768	−	9.65621i	0.281264	−	0.682797i
$201$	−1.28452			−0.0906032
$202$			16.3752i			1.15215i
$203$			0.422682i			0.0296665i
$204$	3.24055			0.226884
$205$	−17.3640	−	3.43632i	−1.21276	−	0.240003i
$206$	−16.9448			−1.18060
$207$		−	3.46792i		−	0.241037i
$208$			18.2441i			1.26500i
$209$		0			0
$210$	−3.18154	+	16.0766i	−0.219547	+	1.10939i
$211$	6.77147			0.466167			0.233084	−	0.972457i	$-0.425118\pi$
$211$	6.77147			0.466167			0.233084	+	0.972457i	$0.425118\pi$
$212$			9.33600i			0.641199i
$213$			9.17803i			0.628868i
$214$	−16.6233			−1.13634
$215$	−3.65234	+	18.4556i	−0.249088	+	1.25866i
$216$	8.66273			0.589424
$217$			1.54069i			0.104589i
$218$			14.5632i			0.986344i
$219$	17.4935			1.18210
$220$		0			0
$221$	8.23051			0.553644
$222$			8.47302i			0.568672i
$223$		−	8.71727i		−	0.583752i	−0.956456	−	0.291876i	$-0.905721\pi$
$223$		−	8.71727i		−	0.583752i	0.956456	−	0.291876i	$-0.0942794\pi$
$224$	−8.93117			−0.596739
$225$	−4.15983	−	1.71356i	−0.277322	−	0.114237i
$226$	−0.382791			−0.0254629
$227$			3.80744i			0.252708i	0.991985	+	0.126354i	$0.0403276\pi$
$227$			3.80744i			0.252708i	−0.991985	+	0.126354i	$0.959672\pi$
$228$		−	7.70125i		−	0.510028i
$229$	2.71367			0.179324			0.0896621	−	0.995972i	$-0.471421\pi$
$229$	2.71367			0.179324			0.0896621	+	0.995972i	$0.471421\pi$
$230$	13.9881	+	2.76823i	0.922351	+	0.182532i
$231$		0			0
$232$		−	0.393588i		−	0.0258403i
$233$			10.5108i			0.688584i	0.938863	+	0.344292i	$0.111881\pi$
$233$			10.5108i			0.688584i	−0.938863	+	0.344292i	$0.888119\pi$
$234$	5.50809			0.360075
$235$	5.21486	−	26.3512i	0.340180	−	1.71896i
$236$	−0.253518			−0.0165026
$237$		−	14.2861i		−	0.927984i
$238$			8.25629i			0.535176i
$239$	20.0396			1.29625			0.648127	−	0.761532i	$-0.275552\pi$
$239$	20.0396			1.29625			0.648127	+	0.761532i	$0.275552\pi$
$240$	4.22723	−	21.3606i	0.272866	−	1.37882i
$241$	−28.4450			−1.83230			−0.916152	−	0.400832i	$-0.868721\pi$
$241$	−28.4450			−1.83230			−0.916152	+	0.400832i	$0.868721\pi$
$242$		0			0
$243$		−	9.06251i		−	0.581361i
$244$	1.27861			0.0818545
$245$	4.31822	+	0.854569i	0.275881	+	0.0545964i
$246$	−25.8652			−1.64911
$247$		−	19.5600i		−	1.24457i
$248$		−	1.43464i		−	0.0910999i
$249$	−6.28309			−0.398175
$250$	10.2323	−	15.4112i	0.647148	−	0.974689i
$251$	−23.8370			−1.50458			−0.752289	−	0.658833i	$-0.771050\pi$
$251$	−23.8370			−1.50458			−0.752289	+	0.658833i	$0.771050\pi$
$252$			1.48877i			0.0937838i
$253$		0			0
$254$	4.02120			0.252313
$255$	−9.63644	−	1.90704i	−0.603457	−	0.119423i
$256$	15.5913			0.974454
$257$		−	24.6763i		−	1.53927i	−0.638486	−	0.769633i	$-0.720439\pi$
$257$		−	24.6763i		−	1.53927i	0.638486	−	0.769633i	$-0.279561\pi$
$258$			27.4913i			1.71153i
$259$	−5.81665			−0.361429
$260$	−1.18469	+	5.98633i	−0.0734711	+	0.371257i
$261$	−0.169555			−0.0104952
$262$			2.62824i			0.162373i
$263$		−	5.44098i		−	0.335505i	−0.985829	−	0.167753i	$-0.946349\pi$
$263$		−	5.44098i		−	0.335505i	0.985829	−	0.167753i	$-0.0536510\pi$
$264$		0			0
$265$	5.49416	−	27.7625i	0.337504	−	1.70544i
$266$	19.6213			1.20306
$267$		−	19.5937i		−	1.19912i
$268$		−	0.479806i		−	0.0293088i
$269$	6.70557			0.408846			0.204423	−	0.978883i	$-0.434468\pi$
$269$	6.70557			0.408846			0.204423	+	0.978883i	$0.434468\pi$
$270$	15.0527	+	2.97891i	0.916079	+	0.181291i
$271$	5.05983			0.307363			0.153681	−	0.988120i	$-0.450887\pi$
$271$	5.05983			0.307363			0.153681	+	0.988120i	$0.450887\pi$
$272$		−	10.9699i		−	0.665148i
$273$			16.3884i			0.991873i
$274$	−30.9438			−1.86938
$275$		0			0
$276$	5.61428			0.337940
$277$		−	10.6937i		−	0.642522i	−0.946991	−	0.321261i	$-0.895893\pi$
$277$		−	10.6937i		−	0.642522i	0.946991	−	0.321261i	$-0.104107\pi$
$278$		−	19.2385i		−	1.15385i
$279$	−0.618034			−0.0370007
$280$	10.2768	+	2.03376i	0.614156	+	0.121541i
$281$	13.7197			0.818450			0.409225	−	0.912434i	$-0.365799\pi$
$281$	13.7197			0.818450			0.409225	+	0.912434i	$0.365799\pi$
$282$		−	39.2524i		−	2.33745i
$283$			21.9693i			1.30594i	0.757385	+	0.652969i	$0.226477\pi$
$283$			21.9693i			1.30594i	−0.757385	+	0.652969i	$0.773523\pi$
$284$	−3.42826			−0.203430
$285$	−4.53213	+	22.9013i	−0.268460	+	1.35655i
$286$		0			0
$287$		−	17.7563i		−	1.04812i
$288$		−	3.58265i		−	0.211110i
$289$	12.0511			0.708890
$290$	0.135346	−	0.683915i	0.00794777	−	0.0401608i
$291$	−4.47903			−0.262566
$292$			6.53432i			0.382392i
$293$		−	14.0380i		−	0.820110i	−0.912061	−	0.410055i	$-0.865509\pi$
$293$		−	14.0380i		−	0.820110i	0.912061	−	0.410055i	$-0.134491\pi$
$294$	6.43236			0.375143
$295$	0.753889	+	0.149194i	0.0438931	+	0.00868638i
$296$	5.41627			0.314815
$297$		0			0
$298$		−	9.78772i		−	0.566988i
$299$	14.2594			0.824644
$300$	2.77411	−	6.73442i	0.160163	−	0.388812i
$301$	−18.8725			−1.08779
$302$			21.1420i			1.21659i
$303$		−	19.5442i		−	1.12278i
$304$	−26.0703			−1.49523
$305$	−3.80221	−	0.752451i	−0.217714	−	0.0430852i
$306$	−3.31193			−0.189331
$307$		−	6.86951i		−	0.392064i	−0.980598	−	0.196032i	$-0.937194\pi$
$307$		−	6.86951i		−	0.392064i	0.980598	−	0.196032i	$-0.0628056\pi$
$308$		0			0
$309$	20.2241			1.15051
$310$	0.493340	−	2.49289i	0.0280198	−	0.141587i
$311$	−5.50157			−0.311966			−0.155983	−	0.987760i	$-0.549854\pi$
$311$	−5.50157			−0.311966			−0.155983	+	0.987760i	$0.549854\pi$
$312$		−	15.2604i		−	0.863948i
$313$			14.2320i			0.804440i	0.915543	+	0.402220i	$0.131761\pi$
$313$			14.2320i			0.804440i	−0.915543	+	0.402220i	$0.868239\pi$
$314$	23.7411			1.33979
$315$	0.876131	−	4.42717i	0.0493644	−	0.249443i
$316$	5.33628			0.300189
$317$		−	18.6864i		−	1.04953i	−0.851246	−	0.524767i	$-0.824153\pi$
$317$		−	18.6864i		−	1.04953i	0.851246	−	0.524767i	$-0.175847\pi$
$318$		−	41.3547i		−	2.31906i
$319$		0			0
$320$	−7.18237	−	1.42138i	−0.401506	−	0.0794575i
$321$	19.8403			1.10738
$322$			14.3041i			0.797137i
$323$			11.7611i			0.654408i
$324$	8.03271			0.446262
$325$	7.04582	−	17.1044i	0.390832	−	0.948783i
$326$	6.00143			0.332389
$327$		−	17.3816i		−	0.961202i
$328$			16.5340i			0.912940i
$329$	26.9464			1.48560
$330$		0			0
$331$	0.468249			0.0257373			0.0128686	−	0.999917i	$-0.495904\pi$
$331$	0.468249			0.0257373			0.0128686	+	0.999917i	$0.495904\pi$
$332$		−	2.34691i		−	0.128804i
$333$		−	2.33329i		−	0.127864i
$334$	6.32166			0.345906
$335$	−0.282362	+	1.42680i	−0.0154271	+	0.0779546i
$336$	21.8431			1.19164
$337$			34.0872i			1.85685i	0.371522	+	0.928424i	$0.378836\pi$
$337$			34.0872i			1.85685i	−0.371522	+	0.928424i	$0.621164\pi$
$338$			1.13869i			0.0619363i
$339$	0.456871			0.0248139
$340$	0.712333	−	3.59949i	0.0386317	−	0.195210i
$341$		0			0
$342$			7.87090i			0.425610i
$343$			20.1173i			1.08623i
$344$	17.5735			0.947498
$345$	−16.6952	−	3.30396i	−0.898841	−	0.177879i
$346$	3.48644			0.187432
$347$			3.59292i			0.192878i	0.995339	+	0.0964391i	$0.0307453\pi$
$347$			3.59292i			0.192878i	−0.995339	+	0.0964391i	$0.969255\pi$
$348$		−	0.274496i		−	0.0147145i
$349$	−6.37110			−0.341037			−0.170519	−	0.985354i	$-0.554544\pi$
$349$	−6.37110			−0.341037			−0.170519	+	0.985354i	$0.554544\pi$
$350$	17.1580	+	7.06789i	0.917135	+	0.377795i
$351$	15.3446			0.819037
$352$		0			0
$353$		−	12.1971i		−	0.649186i	−0.945854	−	0.324593i	$-0.894773\pi$
$353$		−	12.1971i		−	0.649186i	0.945854	−	0.324593i	$-0.105227\pi$
$354$	1.12298			0.0596859
$355$	10.1946	+	2.01750i	0.541076	+	0.107078i
$356$	7.31883			0.387897
$357$		−	9.85411i		−	0.521535i
$358$			8.31257i			0.439333i
$359$	24.1149			1.27273			0.636367	−	0.771386i	$-0.280436\pi$
$359$	24.1149			1.27273			0.636367	+	0.771386i	$0.280436\pi$
$360$	−0.815824	+	4.12244i	−0.0429977	+	0.217272i
$361$	8.95069			0.471089
$362$			25.8902i			1.36076i
$363$		0			0
$364$	−6.12155			−0.320856
$365$	3.84539	−	19.4312i	0.201277	−	1.01707i
$366$	−5.66372			−0.296047
$367$			20.3899i			1.06435i	0.846636	+	0.532173i	$0.178624\pi$
$367$			20.3899i			1.06435i	−0.846636	+	0.532173i	$0.821376\pi$
$368$		−	19.0055i		−	0.990729i
$369$	7.12275			0.370796
$370$	9.41154	+	1.86253i	0.489282	+	0.0968282i
$371$	28.3896			1.47392
$372$		−	1.00055i		−	0.0518759i
$373$		−	7.51997i		−	0.389369i	−0.980866	−	0.194685i	$-0.937632\pi$
$373$		−	7.51997i		−	0.389369i	0.980866	−	0.194685i	$-0.0623684\pi$
$374$		0			0
$375$	−12.2125	+	18.3937i	−0.630653	+	0.949845i
$376$	−25.0916			−1.29400
$377$		−	0.697178i		−	0.0359065i
$378$			15.3927i			0.791716i
$379$	−23.1912			−1.19125			−0.595627	−	0.803261i	$-0.703096\pi$
$379$	−23.1912			−1.19125			−0.595627	+	0.803261i	$0.703096\pi$
$380$	−8.55429	−	1.69288i	−0.438826	−	0.0868429i
$381$	−4.79942			−0.245881
$382$		−	5.15543i		−	0.263775i
$383$			2.44039i			0.124698i	0.998054	+	0.0623491i	$0.0198592\pi$
$383$			2.44039i			0.124698i	−0.998054	+	0.0623491i	$0.980141\pi$
$384$	−26.4246			−1.34848
$385$		0			0
$386$	−15.9442			−0.811537
$387$		−	7.57053i		−	0.384832i
$388$		−	1.67305i		−	0.0849362i
$389$	−33.9732			−1.72251			−0.861254	−	0.508175i	$-0.830320\pi$
$389$	−33.9732			−1.72251			−0.861254	+	0.508175i	$0.830320\pi$
$390$	5.24768	−	26.5170i	0.265726	−	1.34274i
$391$	−8.57398			−0.433605
$392$		−	4.11181i		−	0.207678i
$393$		−	3.13688i		−	0.158235i
$394$	−23.8216			−1.20012
$395$	−15.8685	−	3.14036i	−0.798433	−	0.158009i
$396$		0			0
$397$			27.4961i			1.37999i	0.723814	+	0.689995i	$0.242387\pi$
$397$			27.4961i			1.37999i	−0.723814	+	0.689995i	$0.757613\pi$
$398$			24.4841i			1.22728i
$399$	−23.4186			−1.17239
$400$	−22.7974	−	9.39092i	−1.13987	−	0.469546i
$401$	−1.88743			−0.0942535			−0.0471268	−	0.998889i	$-0.515006\pi$
$401$	−1.88743			−0.0942535			−0.0471268	+	0.998889i	$0.515006\pi$
$402$			2.12535i			0.106003i
$403$		−	2.54124i		−	0.126588i
$404$	7.30032			0.363205
$405$	−23.8870	−	4.72719i	−1.18695	−	0.234896i
$406$	0.699363			0.0347088
$407$		0			0
$408$			9.17582i			0.454271i
$409$	13.5575			0.670374			0.335187	−	0.942152i	$-0.391201\pi$
$409$	13.5575			0.670374			0.335187	+	0.942152i	$0.391201\pi$
$410$	−5.68567	+	28.7302i	−0.280795	+	1.41888i
$411$	36.9323			1.82173
$412$			7.55427i			0.372172i
$413$			0.770918i			0.0379344i
$414$	−5.73796			−0.282005
$415$	−1.38114	+	6.97904i	−0.0677975	+	0.342588i
$416$	14.7312			0.722256
$417$			22.9616i			1.12444i
$418$		0			0
$419$	22.1368			1.08145			0.540727	−	0.841198i	$-0.318149\pi$
$419$	22.1368			1.08145			0.540727	+	0.841198i	$0.318149\pi$
$420$	7.16724	+	1.41838i	0.349725	+	0.0692101i
$421$	17.9026			0.872517			0.436259	−	0.899821i	$-0.356303\pi$
$421$	17.9026			0.872517			0.436259	+	0.899821i	$0.356303\pi$
$422$		−	11.2040i		−	0.545400i
$423$			10.8093i			0.525566i
$424$	−26.4355			−1.28382
$425$	−4.23654	+	10.2846i	−0.205503	+	0.498878i
$426$	15.1858			0.735755
$427$		−	3.88809i		−	0.188158i
$428$			7.41093i			0.358221i
$429$		0			0
$430$	30.5364	+	6.04310i	1.47259	+	0.291424i
$431$	−33.4457			−1.61102			−0.805510	−	0.592582i	$-0.798109\pi$
$431$	−33.4457			−1.61102			−0.805510	+	0.592582i	$0.798109\pi$
$432$		−	20.4519i		−	0.983992i
$433$			31.4914i			1.51338i	0.653774	+	0.756690i	$0.273185\pi$
$433$			31.4914i			1.51338i	−0.653774	+	0.756690i	$0.726815\pi$
$434$	2.54920			0.122366
$435$	−0.161539	+	0.816270i	−0.00774518	+	0.0391372i
$436$	6.49251			0.310935
$437$			20.3763i			0.974731i
$438$		−	28.9444i		−	1.38302i
$439$	35.6208			1.70009			0.850045	−	0.526710i	$-0.176575\pi$
$439$	35.6208			1.70009			0.850045	+	0.526710i	$0.176575\pi$
$440$		0			0
$441$	−1.77134			−0.0843495
$442$		−	13.6180i		−	0.647744i
$443$			23.4876i			1.11593i	0.829865	+	0.557964i	$0.188417\pi$
$443$			23.4876i			1.11593i	−0.829865	+	0.557964i	$0.811583\pi$
$444$	3.77741			0.179268
$445$	−21.7641	−	4.30707i	−1.03172	−	0.204175i
$446$	−14.4234			−0.682970
$447$			11.6819i			0.552535i
$448$		−	7.34460i		−	0.347000i
$449$	31.3920			1.48148			0.740740	−	0.671792i	$-0.234475\pi$
$449$	31.3920			1.48148			0.740740	+	0.671792i	$0.234475\pi$
$450$	−2.83522	+	6.88277i	−0.133653	+	0.324457i
$451$		0			0
$452$			0.170655i			0.00802692i
$453$		−	25.2336i		−	1.18558i
$454$	6.29971			0.295660
$455$	18.2037	+	3.60248i	0.853403	+	0.168887i
$456$	21.8066			1.02119
$457$			39.1106i			1.82952i	0.404000	+	0.914759i	$0.367620\pi$
$457$			39.1106i			1.82952i	−0.404000	+	0.914759i	$0.632380\pi$
$458$		−	4.48999i		−	0.209803i
$459$	−9.22650			−0.430656
$460$	1.23412	−	6.23615i	0.0575414	−	0.290762i
$461$	8.88399			0.413769			0.206884	−	0.978365i	$-0.433668\pi$
$461$	8.88399			0.413769			0.206884	+	0.978365i	$0.433668\pi$
$462$		0			0
$463$			4.21081i			0.195693i	0.995202	+	0.0978464i	$0.0311954\pi$
$463$			4.21081i			0.195693i	−0.995202	+	0.0978464i	$0.968805\pi$
$464$	−0.929224			−0.0431381
$465$	−0.588814	+	2.97534i	−0.0273056	+	0.137978i
$466$	17.3909			0.805620
$467$			6.72844i			0.311355i	0.987808	+	0.155677i	$0.0497560\pi$
$467$			6.72844i			0.311355i	−0.987808	+	0.155677i	$0.950244\pi$
$468$		−	2.45560i		−	0.113510i
$469$	−1.45903			−0.0673718
$470$	−43.6002	−	8.62842i	−2.01113	−	0.397999i
$471$	−28.3356			−1.30564
$472$		−	0.717854i		−	0.0330419i
$473$		0			0
$474$	−23.6376			−1.08571
$475$	24.4417	+	10.0683i	1.12146	+	0.461964i
$476$	3.68079			0.168709
$477$			11.3882i			0.521431i
$478$		−	33.1572i		−	1.51657i
$479$	20.8094			0.950806			0.475403	−	0.879768i	$-0.342302\pi$
$479$	20.8094			0.950806			0.475403	+	0.879768i	$0.342302\pi$
$480$	−17.2476	−	3.41327i	−0.787241	−	0.155794i
$481$	9.59406			0.437452
$482$			47.0646i			2.14373i
$483$		−	17.0723i		−	0.776818i
$484$		0			0
$485$	−0.984576	+	4.97516i	−0.0447073	+	0.225910i
$486$	−14.9947			−0.680172
$487$			15.7794i			0.715032i	0.933907	+	0.357516i	$0.116376\pi$
$487$			15.7794i			0.715032i	−0.933907	+	0.357516i	$0.883624\pi$
$488$			3.62047i			0.163891i
$489$	−7.16287			−0.323916
$490$	1.41395	−	7.14485i	0.0638760	−	0.322771i
$491$	−19.3303			−0.872366			−0.436183	−	0.899858i	$-0.643670\pi$
$491$	−19.3303			−0.872366			−0.436183	+	0.899858i	$0.643670\pi$
$492$			11.5312i			0.519865i
$493$			0.419203i			0.0188799i
$494$	−32.3637			−1.45611
$495$		0			0
$496$	−3.38705			−0.152083
$497$			10.4249i			0.467622i
$498$			10.3959i			0.465851i
$499$	41.4596			1.85599			0.927994	−	0.372594i	$-0.121532\pi$
$499$	41.4596			1.85599			0.927994	+	0.372594i	$0.121532\pi$
$500$	−6.87057	−	4.56174i	−0.307261	−	0.204007i
$501$	−7.54507			−0.337089
$502$			39.4403i			1.76031i
$503$			32.6613i			1.45630i	0.685420	+	0.728148i	$0.259619\pi$
$503$			32.6613i			1.45630i	−0.685420	+	0.728148i	$0.740381\pi$
$504$	−4.21556			−0.187776
$505$	−21.7090	−	4.29618i	−0.966039	−	0.191178i
$506$		0			0
$507$		−	1.35905i		−	0.0603576i
$508$		−	1.79272i		−	0.0795391i
$509$	−16.6452			−0.737785			−0.368892	−	0.929472i	$-0.620263\pi$
$509$	−16.6452			−0.737785			−0.368892	+	0.929472i	$0.620263\pi$
$510$	−3.15535	+	15.9443i	−0.139721	+	0.706025i
$511$	19.8701			0.879000
$512$			0.964978i			0.0426464i
$513$			21.9270i			0.968102i
$514$	−40.8290			−1.80089
$515$	4.44563	−	22.4642i	0.195898	−	0.989891i
$516$	12.2561			0.539543
$517$		0			0
$518$			9.62412i			0.422860i
$519$	−4.16116			−0.182655
$520$	−16.9507	−	3.35452i	−0.743337	−	0.147105i
$521$	14.0563			0.615816			0.307908	−	0.951416i	$-0.400371\pi$
$521$	14.0563			0.615816			0.307908	+	0.951416i	$0.400371\pi$
$522$			0.280543i			0.0122790i
$523$			15.6677i			0.685101i	0.939499	+	0.342550i	$0.111291\pi$
$523$			15.6677i			0.685101i	−0.939499	+	0.342550i	$0.888709\pi$
$524$	1.17171			0.0511866
$525$	−20.4786	−	8.43572i	−0.893758	−	0.368165i
$526$	−9.00255			−0.392530
$527$			1.52801i			0.0665611i
$528$		0			0
$529$	8.14550			0.354152
$530$	−45.9354	−	9.09054i	−1.99531	−	0.394868i
$531$	−0.309246			−0.0134202
$532$		−	8.74751i		−	0.379253i
$533$			29.2874i			1.26858i
$534$	−32.4195			−1.40293
$535$	4.36127	−	22.0379i	0.188554	−	0.952783i
$536$	1.35860			0.0586827
$537$		−	9.92128i		−	0.428135i
$538$		−	11.0949i		−	0.478336i
$539$		0			0
$540$	1.32805	−	6.71075i	0.0571501	−	0.288785i
$541$	39.6384			1.70419			0.852094	−	0.523389i	$-0.175333\pi$
$541$	39.6384			1.70419			0.852094	+	0.523389i	$0.175333\pi$
$542$		−	8.37190i		−	0.359604i
$543$		−	30.9007i		−	1.32608i
$544$	−8.85764			−0.379768
$545$	−19.3068	−	3.82079i	−0.827014	−	0.163665i
$546$	27.1160			1.16046
$547$		−	41.1664i		−	1.76015i	−0.474835	−	0.880075i	$-0.657492\pi$
$547$		−	41.1664i		−	1.76015i	0.474835	−	0.880075i	$-0.342508\pi$
$548$			13.7953i			0.589305i
$549$	1.55967			0.0665651
$550$		0			0
$551$	0.996247			0.0424415
$552$			15.8972i			0.676630i
$553$		−	16.2270i		−	0.690041i
$554$	−17.6936			−0.751728
$555$	−11.2329	−	2.22298i	−0.476811	−	0.0943601i
$556$	−8.57683			−0.363739
$557$		−	29.8760i		−	1.26589i	−0.774199	−	0.632943i	$-0.781847\pi$
$557$		−	29.8760i		−	1.26589i	0.774199	−	0.632943i	$-0.218153\pi$
$558$			1.02259i			0.0432896i
$559$	31.1286			1.31660
$560$	4.80152	−	24.2625i	0.202901	−	1.02528i
$561$		0			0
$562$		−	22.7004i		−	0.957558i
$563$			2.15779i			0.0909401i	0.998966	+	0.0454701i	$0.0144786\pi$
$563$			2.15779i			0.0909401i	−0.998966	+	0.0454701i	$0.985521\pi$
$564$	−17.4994			−0.736857
$565$	0.100429	−	0.507477i	0.00422508	−	0.0213497i
$566$	36.3500			1.52790
$567$		−	24.4265i		−	1.02582i
$568$		−	9.70734i		−	0.407311i
$569$	0.717288			0.0300703			0.0150351	−	0.999887i	$-0.495214\pi$
$569$	0.717288			0.0300703			0.0150351	+	0.999887i	$0.495214\pi$
$570$	37.8920	+	7.49877i	1.58712	+	0.314089i
$571$	21.6311			0.905235			0.452617	−	0.891705i	$-0.350490\pi$
$571$	21.6311			0.905235			0.452617	+	0.891705i	$0.350490\pi$
$572$		0			0
$573$			6.15315i			0.257051i
$574$	−29.3792			−1.22626
$575$	−7.33985	+	17.8182i	−0.306093	+	0.743071i
$576$	2.94622			0.122759
$577$			23.4276i			0.975303i	0.873038	+	0.487652i	$0.162146\pi$
$577$			23.4276i			0.975303i	−0.873038	+	0.487652i	$0.837854\pi$
$578$		−	19.9396i		−	0.829377i
$579$	19.0298			0.790852
$580$	−0.304901	−	0.0603393i	−0.0126603	−	0.00250545i
$581$	−7.13668			−0.296079
$582$			7.41093i			0.307193i
$583$		0			0
$584$	−18.5023			−0.765633
$585$	−1.44510	+	7.30224i	−0.0597476	+	0.301911i
$586$	−23.2271			−0.959501
$587$		−	2.24734i		−	0.0927576i	−0.998924	−	0.0463788i	$-0.985232\pi$
$587$		−	2.24734i		−	0.0927576i	0.998924	−	0.0463788i	$-0.0147681\pi$
$588$		−	2.86766i		−	0.118260i
$589$	3.63135			0.149627
$590$	0.246853	−	1.24737i	0.0101628	−	0.0513535i
$591$	28.4318			1.16953
$592$		−	12.7873i		−	0.525555i
$593$			25.4034i			1.04319i	0.853193	+	0.521596i	$0.174663\pi$
$593$			25.4034i			1.04319i	−0.853193	+	0.521596i	$0.825337\pi$
$594$		0			0
$595$	−10.9456	−	2.16612i	−0.448726	−	0.0888022i
$596$	−4.36353			−0.178737
$597$		−	29.2224i		−	1.19600i
$598$		−	23.5934i		−	0.964806i
$599$	18.2253			0.744667			0.372333	−	0.928099i	$-0.378558\pi$
$599$	18.2253			0.744667			0.372333	+	0.928099i	$0.378558\pi$
$600$	19.0690	+	7.85507i	0.778487	+	0.320682i
$601$	34.6398			1.41299			0.706494	−	0.707719i	$-0.250276\pi$
$601$	34.6398			1.41299			0.706494	+	0.707719i	$0.250276\pi$
$602$			31.2261i			1.27268i
$603$		−	0.585276i		−	0.0238343i
$604$	9.42547			0.383517
$605$		0			0
$606$	−32.3375			−1.31362
$607$		−	25.4482i		−	1.03291i	−0.856314	−	0.516456i	$-0.827251\pi$
$607$		−	25.4482i		−	1.03291i	0.856314	−	0.516456i	$-0.172749\pi$
$608$			21.0504i			0.853708i
$609$	−0.834708			−0.0338241
$610$	−1.24499	+	6.29107i	−0.0504083	+	0.254718i
$611$	−44.4458			−1.79809
$612$			1.47652i			0.0596846i
$613$		−	37.0616i		−	1.49690i	−0.663189	−	0.748452i	$-0.730797\pi$
$613$		−	37.0616i		−	1.49690i	0.663189	−	0.748452i	$-0.269203\pi$
$614$	−11.3662			−0.458701
$615$	6.78600	−	34.2903i	0.273638	−	1.38272i
$616$		0			0
$617$		−	27.5937i		−	1.11088i	−0.831557	−	0.555439i	$-0.812550\pi$
$617$		−	27.5937i		−	1.11088i	0.831557	−	0.555439i	$-0.187450\pi$
$618$		−	33.4624i		−	1.34605i
$619$	−20.4435			−0.821694			−0.410847	−	0.911704i	$-0.634767\pi$
$619$	−20.4435			−0.821694			−0.410847	+	0.911704i	$0.634767\pi$
$620$	−1.11137	−	0.219939i	−0.0446338	−	0.00883296i
$621$	−15.9850			−0.641456
$622$			9.10280i			0.364989i
$623$		−	22.2557i		−	0.891654i
$624$	−36.0283			−1.44229
$625$	17.7465	+	17.6086i	0.709861	+	0.704342i
$626$	23.5480			0.941167
$627$		0			0
$628$		−	10.5842i		−	0.422354i
$629$	−5.76876			−0.230016
$630$	−7.32512	−	1.44963i	−0.291840	−	0.0577546i
$631$	0.759137			0.0302208			0.0151104	−	0.999886i	$-0.495190\pi$
$631$	0.759137			0.0302208			0.0151104	+	0.999886i	$0.495190\pi$
$632$			15.1100i			0.601045i
$633$			13.3722i			0.531498i
$634$	−30.9182			−1.22792
$635$	−1.05500	+	5.33103i	−0.0418665	+	0.211555i
$636$	−18.4366			−0.731060
$637$		−	7.28342i		−	0.288579i
$638$		0			0
$639$	−4.18186			−0.165432
$640$	−5.80863	+	29.3516i	−0.229606	+	1.16022i
$641$	−14.9050			−0.588712			−0.294356	−	0.955696i	$-0.595105\pi$
$641$	−14.9050			−0.588712			−0.294356	+	0.955696i	$0.595105\pi$
$642$		−	32.8274i		−	1.29559i
$643$		−	27.6346i		−	1.08980i	−0.838501	−	0.544900i	$-0.816568\pi$
$643$		−	27.6346i		−	1.08980i	0.838501	−	0.544900i	$-0.183432\pi$
$644$	6.37701			0.251289
$645$	−36.4460	−	7.21260i	−1.43506	−	0.283996i
$646$	19.4598			0.765635
$647$			24.9785i			0.982008i	0.871157	+	0.491004i	$0.163370\pi$
$647$			24.9785i			0.982008i	−0.871157	+	0.491004i	$0.836630\pi$
$648$			22.7452i			0.893514i
$649$		0			0
$650$	−28.3007	−	11.6579i	−1.11004	−	0.457260i
$651$	−3.04254			−0.119247
$652$		−	2.67554i		−	0.104782i
$653$		−	27.7630i		−	1.08645i	−0.839587	−	0.543225i	$-0.817203\pi$
$653$		−	27.7630i		−	1.08645i	0.839587	−	0.543225i	$-0.182797\pi$
$654$	−28.7592			−1.12457
$655$	−3.48434	−	0.689545i	−0.136144	−	0.0269428i
$656$	39.0353			1.52407
$657$			7.97068i			0.310966i
$658$		−	44.5851i		−	1.73811i
$659$	−21.5863			−0.840883			−0.420442	−	0.907320i	$-0.638125\pi$
$659$	−21.5863			−0.840883			−0.420442	+	0.907320i	$0.638125\pi$
$660$		0			0
$661$	−16.0174			−0.623003			−0.311502	−	0.950246i	$-0.600832\pi$
$661$	−16.0174			−0.623003			−0.311502	+	0.950246i	$0.600832\pi$
$662$		−	0.774756i		−	0.0301118i
$663$			16.2535i			0.631234i
$664$	6.64544			0.257893
$665$	−5.14784	+	26.0125i	−0.199625	+	1.00872i
$666$	−3.86062			−0.149596
$667$			0.726273i			0.0281214i
$668$		−	2.81830i		−	0.109043i
$669$	17.2148			0.665561
$670$	2.36076	+	0.467191i	0.0912042	+	0.0180492i
$671$		0			0
$672$		−	17.6372i		−	0.680368i
$673$			31.3469i			1.20834i	0.796857	+	0.604168i	$0.206494\pi$
$673$			31.3469i			1.20834i	−0.796857	+	0.604168i	$0.793506\pi$
$674$	56.4001			2.17245
$675$	−7.89845	+	19.1743i	−0.304012	+	0.738018i
$676$	0.507645			0.0195248
$677$			30.6664i			1.17860i	0.807913	+	0.589302i	$0.200597\pi$
$677$			30.6664i			1.17860i	−0.807913	+	0.589302i	$0.799403\pi$
$678$		−	0.755931i		−	0.0290314i
$679$	−5.08754			−0.195242
$680$	10.1922	+	2.01702i	0.390853	+	0.0773491i
$681$	−7.51888			−0.288124
$682$		0			0
$683$			3.27236i			0.125213i	0.998038	+	0.0626066i	$0.0199414\pi$
$683$			3.27236i			0.125213i	−0.998038	+	0.0626066i	$0.980059\pi$
$684$	3.50898			0.134169
$685$	8.11841	−	41.0231i	0.310188	−	1.56741i
$686$	33.2857			1.27085
$687$			5.35892i			0.204456i
$688$		−	41.4893i		−	1.58176i
$689$	−46.8263			−1.78394
$690$	−5.46667	+	27.6236i	−0.208113	+	1.05161i
$691$	−36.4946			−1.38832			−0.694160	−	0.719821i	$-0.744224\pi$
$691$	−36.4946			−1.38832			−0.694160	+	0.719821i	$0.744224\pi$
$692$		−	1.55431i		−	0.0590862i
$693$		0			0
$694$	5.94478			0.225661
$695$	25.5050	+	5.04740i	0.967459	+	0.191459i
$696$	0.777253			0.0294617
$697$		−	17.6101i		−	0.667029i
$698$			10.5415i			0.399002i
$699$	−20.7566			−0.785085
$700$	3.15099	−	7.64933i	0.119096	−	0.289118i
$701$	−46.5607			−1.75857			−0.879286	−	0.476293i	$-0.841980\pi$
$701$	−46.5607			−1.75857			−0.879286	+	0.476293i	$0.841980\pi$
$702$		−	25.3890i		−	0.958245i
$703$			13.7096i			0.517068i
$704$		0			0
$705$	52.0381	+	10.2983i	1.95987	+	0.387855i
$706$	−20.1811			−0.759525
$707$		−	22.1994i		−	0.834894i
$708$		−	0.500645i		−	0.0188154i
$709$	35.5966			1.33686			0.668429	−	0.743776i	$-0.266967\pi$
$709$	35.5966			1.33686			0.668429	+	0.743776i	$0.266967\pi$
$710$	3.33813	−	16.8679i	0.125278	−	0.633040i
$711$	6.50930			0.244118
$712$			20.7237i			0.776655i
$713$			2.64729i			0.0991418i
$714$	−16.3044			−0.610178
$715$		0			0
$716$	3.70588			0.138495
$717$			39.5740i			1.47792i
$718$		−	39.9000i		−	1.48906i
$719$	−22.0913			−0.823866			−0.411933	−	0.911214i	$-0.635146\pi$
$719$	−22.0913			−0.823866			−0.411933	+	0.911214i	$0.635146\pi$
$720$	9.73269	+	1.92608i	0.362716	+	0.0717809i
$721$	22.9716			0.855507
$722$		−	14.8097i		−	0.551158i
$723$		−	56.1728i		−	2.08909i
$724$	11.5423			0.428966
$725$	0.871176	+	0.358863i	0.0323547	+	0.0133278i
$726$		0			0
$727$			45.5415i			1.68904i	0.535522	+	0.844521i	$0.320115\pi$
$727$			45.5415i			1.68904i	−0.535522	+	0.844521i	$0.679885\pi$
$728$		−	17.3336i		−	0.642425i
$729$	−14.7727			−0.547137
$730$	−32.1504	−	6.36252i	−1.18994	−	0.235487i
$731$	−18.7171			−0.692278
$732$			2.52498i			0.0933260i
$733$			11.3789i			0.420289i	0.977670	+	0.210145i	$0.0673935\pi$
$733$			11.3789i			0.420289i	−0.977670	+	0.210145i	$0.932607\pi$
$734$	33.7368			1.24525
$735$	−1.68759	+	8.52757i	−0.0622478	+	0.314544i
$736$	−15.3459			−0.565659
$737$		0			0
$738$		−	11.7852i		−	0.433818i
$739$	−4.33778			−0.159568			−0.0797838	−	0.996812i	$-0.525423\pi$
$739$	−4.33778			−0.159568			−0.0797838	+	0.996812i	$0.525423\pi$
$740$	0.830346	−	4.19582i	0.0305241	−	0.154241i
$741$	38.6269			1.41900
$742$		−	46.9730i		−	1.72443i
$743$			17.2945i			0.634473i	0.948346	+	0.317237i	$0.102755\pi$
$743$			17.2945i			0.634473i	−0.948346	+	0.317237i	$0.897245\pi$
$744$	2.83311			0.103867
$745$	12.9759	+	2.56790i	0.475399	+	0.0940807i
$746$	−12.4424			−0.455549
$747$		−	2.86281i		−	0.104745i
$748$		0			0
$749$	22.5357			0.823437
$750$	30.4338	+	20.2067i	1.11129	+	0.737843i
$751$	−31.5130			−1.14993			−0.574963	−	0.818179i	$-0.694984\pi$
$751$	−31.5130			−1.14993			−0.574963	+	0.818179i	$0.694984\pi$
$752$			59.2390i			2.16022i
$753$		−	47.0730i		−	1.71544i
$754$	−1.15354			−0.0420094
$755$	−28.0286	−	5.54681i	−1.02006	−	0.201869i
$756$	6.86233			0.249581
$757$			9.27739i			0.337192i	0.985685	+	0.168596i	$0.0539234\pi$
$757$			9.27739i			0.337192i	−0.985685	+	0.168596i	$0.946077\pi$
$758$			38.3718i			1.39373i
$759$		0			0
$760$	4.79350	−	24.2220i	0.173879	−	0.878626i
$761$	4.15810			0.150731			0.0753655	−	0.997156i	$-0.475988\pi$
$761$	4.15810			0.150731			0.0753655	+	0.997156i	$0.475988\pi$
$762$			7.94102i			0.287673i
$763$		−	19.7429i		−	0.714742i
$764$	−2.29838			−0.0831524
$765$	0.868918	−	4.39073i	0.0314158	−	0.158747i
$766$	4.03783			0.145893
$767$		−	1.27156i		−	0.0459135i
$768$			30.7894i			1.11102i
$769$	16.8800			0.608709			0.304355	−	0.952559i	$-0.401559\pi$
$769$	16.8800			0.608709			0.304355	+	0.952559i	$0.401559\pi$
$770$		0			0
$771$	48.7305			1.75499
$772$			7.10818i			0.255829i
$773$			8.47760i			0.304918i	0.988310	+	0.152459i	$0.0487192\pi$
$773$			8.47760i			0.304918i	−0.988310	+	0.152459i	$0.951281\pi$
$774$	−12.5261			−0.450240
$775$	3.17547	+	1.30807i	0.114066	+	0.0469872i
$776$	4.73735			0.170061
$777$		−	11.4866i		−	0.412081i
$778$			56.2114i			2.01527i
$779$	−41.8508			−1.49946
$780$	−11.8217	−	2.33950i	−0.423286	−	0.0837676i
$781$		0			0
$782$			14.1863i			0.507303i
$783$			0.781546i			0.0279302i
$784$	−9.70760			−0.346700
$785$	−6.22870	+	31.4742i	−0.222312	+	1.12336i
$786$	−5.19022			−0.185129
$787$		−	53.6166i		−	1.91122i	−0.294628	−	0.955612i	$-0.595196\pi$
$787$		−	53.6166i		−	1.91122i	0.294628	−	0.955612i	$-0.404804\pi$
$788$			10.6201i			0.378325i
$789$	10.7448			0.382525
$790$	−5.19598	+	26.2558i	−0.184865	+	0.934139i
$791$	0.518940			0.0184514
$792$		0			0
$793$			6.41307i			0.227735i
$794$	45.4946			1.61454
$795$	54.8251	+	10.8498i	1.94445	+	0.384803i
$796$	10.9154			0.386887
$797$			28.5448i			1.01111i	0.862795	+	0.505554i	$0.168712\pi$
$797$			28.5448i			1.01111i	−0.862795	+	0.505554i	$0.831288\pi$
$798$			38.7479i			1.37166i
$799$	26.7246			0.945448
$800$	−7.58268	+	18.4077i	−0.268088	+	0.650811i
$801$	8.92765			0.315443
$802$			3.12290i			0.110273i
$803$		0			0
$804$	0.947515			0.0334163
$805$	−18.9634	−	3.75282i	−0.668371	−	0.132270i
$806$	−4.20469			−0.148104
$807$			13.2421i			0.466143i
$808$			20.6713i			0.727215i
$809$	36.9460			1.29895			0.649477	−	0.760382i	$-0.274988\pi$
$809$	36.9460			1.29895			0.649477	+	0.760382i	$0.274988\pi$
$810$	−7.82152	+	39.5229i	−0.274820	+	1.38869i
$811$	38.3768			1.34759			0.673795	−	0.738918i	$-0.264663\pi$
$811$	38.3768			1.34759			0.673795	+	0.738918i	$0.264663\pi$
$812$		−	0.311788i		−	0.0109416i
$813$			9.99209i			0.350438i
$814$		0			0
$815$	−1.57453	+	7.95628i	−0.0551535	+	0.278696i
$816$	21.6632			0.758365
$817$			44.4818i			1.55622i
$818$		−	22.4319i		−	0.784314i
$819$	−7.46718			−0.260924
$820$	12.8084	+	2.53477i	0.447289	+	0.0885178i
$821$	10.2496			0.357715			0.178858	−	0.983875i	$-0.442760\pi$
$821$	10.2496			0.357715			0.178858	+	0.983875i	$0.442760\pi$
$822$		−	61.1074i		−	2.13137i
$823$		−	25.2296i		−	0.879448i	−0.898133	−	0.439724i	$-0.855076\pi$
$823$		−	25.2296i		−	0.879448i	0.898133	−	0.439724i	$-0.144924\pi$
$824$	−21.3904			−0.745170
$825$		0			0
$826$	1.27555			0.0443820
$827$			18.3485i			0.638041i	0.947748	+	0.319020i	$0.103354\pi$
$827$			18.3485i			0.638041i	−0.947748	+	0.319020i	$0.896646\pi$
$828$			2.55808i			0.0888993i
$829$	−24.3826			−0.846842			−0.423421	−	0.905933i	$-0.639171\pi$
$829$	−24.3826			−0.846842			−0.423421	+	0.905933i	$0.639171\pi$
$830$	11.5474	+	2.28521i	0.400816	+	0.0793208i
$831$	21.1178			0.732567
$832$			12.1143i			0.419987i
$833$			4.37941i			0.151737i
$834$	37.9919			1.31555
$835$	−1.65855	+	8.38081i	−0.0573964	+	0.290030i
$836$		0			0
$837$			2.84876i			0.0984676i
$838$		−	36.6272i		−	1.26526i
$839$	42.2808			1.45970			0.729848	−	0.683609i	$-0.239591\pi$
$839$	42.2808			1.45970			0.729848	+	0.683609i	$0.239591\pi$
$840$	−4.01625	+	20.2945i	−0.138574	+	0.700227i
$841$	−28.9645			−0.998776
$842$		−	29.6212i		−	1.02082i
$843$			27.0935i			0.933151i
$844$	−4.99491			−0.171932
$845$	−1.50959	−	0.298745i	−0.0519314	−	0.0102771i
$846$	17.8849			0.614895
$847$		0			0
$848$			62.4117i			2.14323i
$849$	−43.3847			−1.48896
$850$	17.0168	+	7.00971i	0.583670	+	0.240431i
$851$	−9.99444			−0.342605
$852$		−	6.77009i		−	0.231939i
$853$			15.3885i			0.526891i	0.964674	+	0.263445i	$0.0848589\pi$
$853$			15.3885i			0.526891i	−0.964674	+	0.263445i	$0.915141\pi$
$854$	−6.43317			−0.220138
$855$	−10.4347	−	2.06501i	−0.356859	−	0.0706218i
$856$	−20.9845			−0.717236
$857$		−	36.1038i		−	1.23328i	−0.787245	−	0.616641i	$-0.788493\pi$
$857$		−	36.1038i		−	1.23328i	0.787245	−	0.616641i	$-0.211507\pi$
$858$		0			0
$859$	−48.3509			−1.64971			−0.824855	−	0.565344i	$-0.808743\pi$
$859$	−48.3509			−1.64971			−0.824855	+	0.565344i	$0.808743\pi$
$860$	2.69411	−	13.6136i	0.0918685	−	0.464221i
$861$	35.0648			1.19501
$862$			55.3386i			1.88484i
$863$		−	37.1887i		−	1.26592i	−0.774186	−	0.632959i	$-0.781840\pi$
$863$		−	37.1887i		−	1.26592i	0.774186	−	0.632959i	$-0.218160\pi$
$864$	−16.5139			−0.561813
$865$	−0.914702	+	4.62208i	−0.0311008	+	0.157155i
$866$	52.1051			1.77060
$867$			23.7984i			0.808237i
$868$		−	1.13648i		−	0.0385745i
$869$		0			0
$870$	1.35059	+	0.267279i	0.0457892	+	0.00906160i
$871$	2.40655			0.0815427
$872$			18.3840i			0.622560i
$873$		−	2.04082i		−	0.0690712i
$874$	33.7143			1.14040
$875$	−13.8717	+	20.8926i	−0.468949	+	0.706297i
$876$	−12.9039			−0.435982
$877$			25.7932i			0.870976i	0.900195	+	0.435488i	$0.143424\pi$
$877$			25.7932i			0.870976i	−0.900195	+	0.435488i	$0.856576\pi$
$878$		−	58.9376i		−	1.98905i
$879$	27.7221			0.935044
$880$		0			0
$881$	−45.6820			−1.53906			−0.769532	−	0.638608i	$-0.779511\pi$
$881$	−45.6820			−1.53906			−0.769532	+	0.638608i	$0.779511\pi$
$882$			2.93083i			0.0986861i
$883$			4.96631i			0.167130i	0.996502	+	0.0835648i	$0.0266306\pi$
$883$			4.96631i			0.167130i	−0.996502	+	0.0835648i	$0.973369\pi$
$884$	−6.07115			−0.204195
$885$	−0.294626	+	1.48877i	−0.00990373	+	0.0500445i
$886$	38.8621			1.30560
$887$		−	28.9232i		−	0.971147i	−0.874196	−	0.485573i	$-0.838611\pi$
$887$		−	28.9232i		−	0.971147i	0.874196	−	0.485573i	$-0.161389\pi$
$888$			10.6960i			0.358934i
$889$	−5.45144			−0.182836
$890$	−7.12641	+	36.0104i	−0.238878	+	1.20707i
$891$		0			0
$892$			6.43021i			0.215299i
$893$		−	63.5117i		−	2.12534i
$894$	19.3287			0.646448
$895$	−11.0202	−	2.18088i	−0.368365	−	0.0728989i
$896$	−30.0146			−1.00272
$897$			28.1594i			0.940213i
$898$		−	51.9406i		−	1.73328i
$899$	0.129432			0.00431681
$900$	3.06846	+	1.26399i	0.102282	+	0.0421329i
$901$	28.1559			0.938010
$902$		0			0
$903$		−	37.2692i		−	1.24024i
$904$	−0.483220			−0.0160717
$905$	−34.3234	−	6.79255i	−1.14095	−	0.225792i
$906$	−41.7510			−1.38708
$907$		−	13.2527i		−	0.440049i	−0.975494	−	0.220024i	$-0.929386\pi$
$907$		−	13.2527i		−	0.440049i	0.975494	−	0.220024i	$-0.0706137\pi$
$908$		−	2.80852i		−	0.0932040i
$909$	8.90507			0.295363
$910$	5.96060	−	30.1195i	0.197592	−	0.998452i
$911$	13.7326			0.454982			0.227491	−	0.973780i	$-0.426948\pi$
$911$	13.7326			0.454982			0.227491	+	0.973780i	$0.426948\pi$
$912$		−	51.4833i		−	1.70478i
$913$		0			0
$914$	64.7117			2.14047
$915$	1.48593	−	7.50856i	0.0491234	−	0.248225i
$916$	−2.00171			−0.0661384
$917$		−	3.56304i		−	0.117662i
$918$			15.2660i			0.503853i
$919$	59.3800			1.95876			0.979382	−	0.202016i	$-0.0647493\pi$
$919$	59.3800			1.95876			0.979382	+	0.202016i	$0.0647493\pi$
$920$	17.6581	+	3.49450i	0.582169	+	0.115210i
$921$	13.5658			0.447009
$922$		−	14.6993i		−	0.484095i
$923$		−	17.1950i		−	0.565981i
$924$		0			0
$925$	−4.93842	+	11.9885i	−0.162374	+	0.394179i
$926$	6.96713			0.228954
$927$			9.21484i			0.302655i
$928$			0.750301i			0.0246298i
$929$	−19.5881			−0.642664			−0.321332	−	0.946967i	$-0.604131\pi$
$929$	−19.5881			−0.642664			−0.321332	+	0.946967i	$0.604131\pi$
$930$	4.92293	+	0.974241i	0.161429	+	0.0319466i
$931$	10.4078			0.341101
$932$		−	7.75317i		−	0.253964i
$933$		−	10.8644i		−	0.355686i
$934$	11.1327			0.364275
$935$		0			0
$936$	6.95320			0.227272
$937$		−	40.5452i		−	1.32455i	−0.749259	−	0.662277i	$-0.769590\pi$
$937$		−	40.5452i		−	1.32455i	0.749259	−	0.662277i	$-0.230410\pi$
$938$			2.41409i			0.0788227i
$939$	−28.1052			−0.917178
$940$	−3.84669	+	19.4377i	−0.125465	+	0.633989i
$941$	0.409691			0.0133556			0.00667778	−	0.999978i	$-0.497874\pi$
$941$	0.409691			0.0133556			0.00667778	+	0.999978i	$0.497874\pi$
$942$			46.8835i			1.52755i
$943$		−	30.5096i		−	0.993530i
$944$	−1.69478			−0.0551605
$945$	−20.4066	−	4.03843i	−0.663826	−	0.131370i
$946$		0			0
$947$			2.45729i			0.0798511i	0.999203	+	0.0399256i	$0.0127121\pi$
$947$			2.45729i			0.0798511i	−0.999203	+	0.0399256i	$0.987288\pi$
$948$			10.5380i			0.342259i
$949$	−32.7739			−1.06389
$950$	16.6588	−	40.4408i	0.540482	−	1.31207i
$951$	36.9017			1.19662
$952$			10.4224i			0.337792i
$953$			61.0264i			1.97684i	0.151744	+	0.988420i	$0.451511\pi$
$953$			61.0264i			1.97684i	−0.151744	+	0.988420i	$0.548489\pi$
$954$	18.8428			0.610057
$955$	6.83471	+	1.35258i	0.221166	+	0.0437684i
$956$	−14.7820			−0.478085
$957$		0			0
$958$		−	34.4309i		−	1.11241i
$959$	41.9497			1.35463
$960$	2.80692	−	14.1837i	0.0905930	−	0.457775i
$961$	−30.5282			−0.984781
$962$		−	15.8742i		−	0.511803i
$963$			9.03999i			0.291310i
$964$	20.9822			0.675790
$965$	4.18311	−	21.1377i	0.134659	−	0.680445i
$966$	−28.2476			−0.908851
$967$		−	17.1997i		−	0.553106i	−0.960999	−	0.276553i	$-0.910808\pi$
$967$		−	17.1997i		−	0.553106i	0.960999	−	0.276553i	$-0.0891921\pi$
$968$		0			0
$969$	−23.2258			−0.746119
$970$	8.23180	+	1.62906i	0.264307	+	0.0523060i
$971$	27.2090			0.873177			0.436589	−	0.899661i	$-0.356187\pi$
$971$	27.2090			0.873177			0.436589	+	0.899661i	$0.356187\pi$
$972$			6.68488i			0.214417i
$973$			26.0811i			0.836121i
$974$	26.1083			0.836563
$975$	33.7776	+	13.9140i	1.08175	+	0.445605i
$976$	8.54757			0.273601
$977$		−	19.1722i		−	0.613374i	−0.951810	−	0.306687i	$-0.900780\pi$
$977$		−	19.1722i		−	0.613374i	0.951810	−	0.306687i	$-0.0992204\pi$
$978$			11.8516i			0.378971i
$979$		0			0
$980$	−3.18529	−	0.630365i	−0.101750	−	0.0201363i
$981$	7.91969			0.252856
$982$			31.9836i			1.02064i
$983$			24.1305i			0.769642i	0.922991	+	0.384821i	$0.125737\pi$
$983$			24.1305i			0.769642i	−0.922991	+	0.384821i	$0.874263\pi$
$984$	−32.6512			−1.04088
$985$	6.24984	−	31.5810i	0.199136	−	1.00626i
$986$	0.693605			0.0220889
$987$			53.2135i			1.69380i
$988$			14.4283i			0.459024i
$989$	−32.4276			−1.03114
$990$		0			0
$991$	27.7081			0.880177			0.440089	−	0.897954i	$-0.354947\pi$
$991$	27.7081			0.880177			0.440089	+	0.897954i	$0.354947\pi$
$992$			2.73487i			0.0868323i
$993$			0.924692i			0.0293442i
$994$	17.2489			0.547101
$995$	−32.4593	−	6.42364i	−1.02903	−	0.203643i
$996$	4.63466			0.146855
$997$		−	33.4912i		−	1.06068i	−0.847786	−	0.530339i	$-0.822065\pi$
$997$		−	33.4912i		−	1.06068i	0.847786	−	0.530339i	$-0.177935\pi$
$998$		−	68.5984i		−	2.17144i
$999$	−10.7551			−0.340275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.f.364.2		8
5.2	odd	4		3025.2.a.bk.1.7		8
5.3	odd	4		3025.2.a.bk.1.2		8
5.4	even	2	inner	605.2.b.f.364.7		8
11.2	odd	10		605.2.j.h.444.4		16
11.3	even	5		605.2.j.d.9.1		16
11.4	even	5		605.2.j.d.269.4		16
11.5	even	5		605.2.j.g.124.4		16
11.6	odd	10		605.2.j.h.124.1		16
11.7	odd	10		55.2.j.a.49.1	yes	16
11.8	odd	10		55.2.j.a.9.4	yes	16
11.9	even	5		605.2.j.g.444.1		16
11.10	odd	2		605.2.b.g.364.7		8
33.8	even	10		495.2.ba.a.64.1		16
33.29	even	10		495.2.ba.a.379.4		16
44.7	even	10		880.2.cd.c.49.1		16
44.19	even	10		880.2.cd.c.449.4		16
55.4	even	10		605.2.j.d.269.1		16
55.7	even	20		275.2.h.d.126.1		16
55.8	even	20		275.2.h.d.251.4		16
55.9	even	10		605.2.j.g.444.4		16
55.14	even	10		605.2.j.d.9.4		16
55.18	even	20		275.2.h.d.126.4		16
55.19	odd	10		55.2.j.a.9.1	✓	16
55.24	odd	10		605.2.j.h.444.1		16
55.29	odd	10		55.2.j.a.49.4	yes	16
55.32	even	4		3025.2.a.bl.1.2		8
55.39	odd	10		605.2.j.h.124.4		16
55.43	even	4		3025.2.a.bl.1.7		8
55.49	even	10		605.2.j.g.124.1		16
55.52	even	20		275.2.h.d.251.1		16
55.54	odd	2		605.2.b.g.364.2		8
165.29	even	10		495.2.ba.a.379.1		16
165.74	even	10		495.2.ba.a.64.4		16
220.19	even	10		880.2.cd.c.449.1		16
220.139	even	10		880.2.cd.c.49.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	55.19	odd	10
55.2.j.a.9.4	yes	16	11.8	odd	10
55.2.j.a.49.1	yes	16	11.7	odd	10
55.2.j.a.49.4	yes	16	55.29	odd	10
275.2.h.d.126.1		16	55.7	even	20
275.2.h.d.126.4		16	55.18	even	20
275.2.h.d.251.1		16	55.52	even	20
275.2.h.d.251.4		16	55.8	even	20
495.2.ba.a.64.1		16	33.8	even	10
495.2.ba.a.64.4		16	165.74	even	10
495.2.ba.a.379.1		16	165.29	even	10
495.2.ba.a.379.4		16	33.29	even	10
605.2.b.f.364.2		8	1.1	even	1	trivial
605.2.b.f.364.7		8	5.4	even	2	inner
605.2.b.g.364.2		8	55.54	odd	2
605.2.b.g.364.7		8	11.10	odd	2
605.2.j.d.9.1		16	11.3	even	5
605.2.j.d.9.4		16	55.14	even	10
605.2.j.d.269.1		16	55.4	even	10
605.2.j.d.269.4		16	11.4	even	5
605.2.j.g.124.1		16	55.49	even	10
605.2.j.g.124.4		16	11.5	even	5
605.2.j.g.444.1		16	11.9	even	5
605.2.j.g.444.4		16	55.9	even	10
605.2.j.h.124.1		16	11.6	odd	10
605.2.j.h.124.4		16	55.39	odd	10
605.2.j.h.444.1		16	55.24	odd	10
605.2.j.h.444.4		16	11.2	odd	10
880.2.cd.c.49.1		16	44.7	even	10
880.2.cd.c.49.4		16	220.139	even	10
880.2.cd.c.449.1		16	220.19	even	10
880.2.cd.c.449.4		16	44.19	even	10
3025.2.a.bk.1.2		8	5.3	odd	4
3025.2.a.bk.1.7		8	5.2	odd	4
3025.2.a.bl.1.2		8	55.32	even	4
3025.2.a.bl.1.7		8	55.43	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.65458i q^{2} +1.97479i q^{3} -0.737640 q^{4} +(2.19353 + 0.434096i) q^{5} +3.26745 q^{6} +2.24307i q^{7} -2.08868i q^{8} -0.899788 q^{9} +(0.718246 - 3.62937i) q^{10} -1.45668i q^{12} -3.69976i q^{13} +3.71135 q^{14} +(-0.857247 + 4.33175i) q^{15} -4.93117 q^{16} +2.22461i q^{17} +1.48877i q^{18} +5.28684 q^{19} +(-1.61803 - 0.320206i) q^{20} -4.42960 q^{21} +3.85415i q^{23} +4.12469 q^{24} +(4.62312 + 1.90440i) q^{25} -6.12155 q^{26} +4.14747i q^{27} -1.65458i q^{28} +0.188439 q^{29} +(7.16724 + 1.41838i) q^{30} +0.686867 q^{31} +3.98166i q^{32} +3.68079 q^{34} +(-0.973708 + 4.92024i) q^{35} +0.663720 q^{36} +2.59316i q^{37} -8.74751i q^{38} +7.30624 q^{39} +(0.906685 - 4.58157i) q^{40} -7.91604 q^{41} +7.32913i q^{42} +8.41368i q^{43} +(-1.97371 - 0.390594i) q^{45} +6.37701 q^{46} -12.0132i q^{47} -9.73801i q^{48} +1.96862 q^{49} +(3.15099 - 7.64933i) q^{50} -4.39313 q^{51} +2.72909i q^{52} -12.6566i q^{53} +6.86233 q^{54} +4.68506 q^{56} +10.4404i q^{57} -0.311788i q^{58} +0.343688 q^{59} +(0.632340 - 3.19527i) q^{60} -1.73338 q^{61} -1.13648i q^{62} -2.01829i q^{63} -3.27435 q^{64} +(1.60605 - 8.11552i) q^{65} +0.650461i q^{67} -1.64096i q^{68} -7.61114 q^{69} +(8.14094 + 1.61108i) q^{70} +4.64760 q^{71} +1.87937i q^{72} -8.85841i q^{73} +4.29059 q^{74} +(-3.76079 + 9.12969i) q^{75} -3.89979 q^{76} -12.0888i q^{78} -7.23426 q^{79} +(-10.8166 - 2.14060i) q^{80} -10.8897 q^{81} +13.0977i q^{82} +3.18165i q^{83} +3.26745 q^{84} +(-0.965692 + 4.87974i) q^{85} +13.9211 q^{86} +0.372127i q^{87} -9.92195 q^{89} +(-0.646269 + 3.26566i) q^{90} +8.29883 q^{91} -2.84298i q^{92} +1.35642i q^{93} -19.8768 q^{94} +(11.5968 + 2.29499i) q^{95} -7.86294 q^{96} +2.26811i q^{97} -3.25724i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 4 q^{5} - 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} + 12 q^{19} - 4 q^{20} - 4 q^{21} + 2 q^{24} - 8 q^{25} + 10 q^{26} + 24 q^{29} + 22 q^{30} + 14 q^{31} - 8 q^{34} + 14 q^{35}+ \cdots + 8 q^{96}+O(q^{100}) \) 8 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 - 4 * q^9 + 4 * q^14 - 8 * q^15 - 22 * q^16 + 12 * q^19 - 4 * q^20 - 4 * q^21 + 2 * q^24 - 8 * q^25 + 10 * q^26 + 24 * q^29 + 22 * q^30 + 14 * q^31 - 8 * q^34 + 14 * q^35 + 20 * q^36 + 30 * q^39 + 24 * q^40 - 34 * q^41 + 6 * q^45 - 24 * q^46 + 30 * q^49 + 16 * q^50 - 54 * q^51 + 20 * q^54 - 10 * q^56 + 6 * q^59 + 34 * q^60 - 20 * q^61 - 14 * q^64 + 20 * q^65 - 32 * q^69 + 8 * q^70 - 42 * q^71 - 4 * q^74 - 20 * q^75 - 28 * q^76 + 16 * q^79 - 28 * q^80 - 36 * q^81 - 6 * q^84 - 4 * q^85 + 46 * q^86 + 12 * q^89 + 46 * q^90 + 20 * q^91 - 42 * q^94 + 26 * q^95 + 8 * q^96

Introduction

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