LMFDB - Embedded newform 1575.2.bc.c.899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(899,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1575.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.2
Character	$\chi$	$=$	1575.899
Dual form			1575.2.bc.c.1349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23340 - 2.13631i) q^{2} +(-2.04255 + 3.53780i) q^{4} +(1.88881 - 1.85267i) q^{7} +5.14351 q^{8} +O(q^{10})$	\(q+(-1.23340 - 2.13631i) q^{2} +(-2.04255 + 3.53780i) q^{4} +(1.88881 - 1.85267i) q^{7} +5.14351 q^{8} +(-2.50111 - 1.44401i) q^{11} +5.72888 q^{13} +(-6.28754 - 1.75000i) q^{14} +(-2.25891 - 3.91255i) q^{16} +(-2.54323 - 1.46833i) q^{17} +(3.13742 - 1.81139i) q^{19} +7.12419i q^{22} +(3.96929 + 6.87502i) q^{23} +(-7.06600 - 12.2387i) q^{26} +(2.69640 + 10.4664i) q^{28} +5.38933i q^{29} +(0.435528 + 0.251452i) q^{31} +(-0.428765 + 0.742643i) q^{32} +7.24416i q^{34} +(2.82425 - 1.63058i) q^{37} +(-7.73938 - 4.46833i) q^{38} +3.54303 q^{41} +10.1033i q^{43} +(10.2173 - 5.89894i) q^{44} +(9.79145 - 16.9593i) q^{46} +(6.55830 - 3.78644i) q^{47} +(0.135204 - 6.99869i) q^{49} +(-11.7015 + 20.2676i) q^{52} +(5.03756 - 8.72531i) q^{53} +(9.71512 - 9.52925i) q^{56} +(11.5133 - 6.64719i) q^{58} +(3.28754 - 5.69419i) q^{59} +(-9.67067 + 5.58337i) q^{61} -1.24057i q^{62} -6.92029 q^{64} +(2.39171 + 1.38086i) q^{67} +(10.3893 - 5.99828i) q^{68} +3.14129i q^{71} +(-0.284088 + 0.492054i) q^{73} +(-6.96685 - 4.02231i) q^{74} +14.7994i q^{76} +(-7.39940 + 1.90626i) q^{77} +(-4.58164 - 7.93563i) q^{79} +(-4.36997 - 7.56901i) q^{82} -15.0860i q^{83} +(21.5837 - 12.4614i) q^{86} +(-12.8645 - 7.42731i) q^{88} +(1.76354 + 3.05453i) q^{89} +(10.8208 - 10.6137i) q^{91} -32.4299 q^{92} +(-16.1780 - 9.34037i) q^{94} +17.6929 q^{97} +(-15.1181 + 8.34335i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{4}+O(q^{10}) $ 24 * q - 16 * q^4	$ 24 q - 16 q^{4} - 24 q^{11} - 24 q^{14} - 32 q^{16} - 12 q^{19} + 12 q^{31} - 48 q^{41} + 24 q^{44} - 8 q^{46} - 12 q^{49} + 120 q^{56} - 48 q^{59} + 112 q^{64} + 168 q^{74} - 36 q^{79} + 168 q^{86} + 24 q^{89} - 36 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q - 16 * q^4 - 24 * q^11 - 24 * q^14 - 32 * q^16 - 12 * q^19 + 12 * q^31 - 48 * q^41 + 24 * q^44 - 8 * q^46 - 12 * q^49 + 120 * q^56 - 48 * q^59 + 112 * q^64 + 168 * q^74 - 36 * q^79 + 168 * q^86 + 24 * q^89 - 36 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.23340	−	2.13631i	−0.872145	−	1.51060i	−0.859773	−	0.510676i	$-0.829395\pi$
$2$	−1.23340	−	2.13631i	−0.872145	−	1.51060i	−0.0123720	−	0.999923i	$-0.503938\pi$
$3$		0			0
$3$		0			0
$4$	−2.04255	+	3.53780i	−1.02127	+	1.76890i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.88881	−	1.85267i	0.713903	−	0.700245i
$7$	1.88881	−	1.85267i	0.713903	−	0.700245i
$8$	5.14351			1.81851
$9$		0			0
$10$		0			0
$11$	−2.50111	−	1.44401i	−0.754112	−	0.435387i	0.0730657	−	0.997327i	$-0.476722\pi$
$11$	−2.50111	−	1.44401i	−0.754112	−	0.435387i	−0.827178	+	0.561940i	$0.810055\pi$
$12$		0			0
$13$	5.72888			1.58891			0.794453	−	0.607326i	$-0.207758\pi$
$13$	5.72888			1.58891			0.794453	+	0.607326i	$0.207758\pi$
$14$	−6.28754	−	1.75000i	−1.68042	−	0.467707i
$15$		0			0
$16$	−2.25891	−	3.91255i	−0.564728	−	0.978137i
$17$	−2.54323	−	1.46833i	−0.616823	−	0.356123i	0.158808	−	0.987309i	$-0.449235\pi$
$17$	−2.54323	−	1.46833i	−0.616823	−	0.356123i	−0.775631	+	0.631187i	$0.782568\pi$
$18$		0			0
$19$	3.13742	−	1.81139i	0.719773	−	0.415561i	−0.0948962	−	0.995487i	$-0.530252\pi$
$19$	3.13742	−	1.81139i	0.719773	−	0.415561i	0.814669	+	0.579926i	$0.196919\pi$
$20$		0			0
$21$		0			0
$22$			7.12419i			1.51888i
$23$	3.96929	+	6.87502i	0.827655	+	1.43354i	0.899873	+	0.436151i	$0.143659\pi$
$23$	3.96929	+	6.87502i	0.827655	+	1.43354i	−0.0722186	+	0.997389i	$0.523008\pi$
$24$		0			0
$25$		0			0
$26$	−7.06600	−	12.2387i	−1.38576	−	2.40020i
$27$		0			0
$28$	2.69640	+	10.4664i	0.509571	+	1.97796i
$29$			5.38933i			1.00077i	0.865802	+	0.500386i	$0.166809\pi$
$29$			5.38933i			1.00077i	−0.865802	+	0.500386i	$0.833191\pi$
$30$		0			0
$31$	0.435528	+	0.251452i	0.0782232	+	0.0451622i	0.538601	−	0.842561i	$-0.318953\pi$
$31$	0.435528	+	0.251452i	0.0782232	+	0.0451622i	−0.460378	+	0.887723i	$0.652286\pi$
$32$	−0.428765	+	0.742643i	−0.0757957	+	0.131282i
$33$		0			0
$34$			7.24416i			1.24236i
$35$		0			0
$36$		0			0
$37$	2.82425	−	1.63058i	0.464303	−	0.268066i	−0.249549	−	0.968362i	$-0.580282\pi$
$37$	2.82425	−	1.63058i	0.464303	−	0.268066i	0.713852	+	0.700297i	$0.246949\pi$
$38$	−7.73938	−	4.46833i	−1.25549	−	0.724859i
$39$		0			0
$40$		0			0
$41$	3.54303			0.553328			0.276664	−	0.960967i	$-0.410771\pi$
$41$	3.54303			0.553328			0.276664	+	0.960967i	$0.410771\pi$
$42$		0			0
$43$			10.1033i			1.54073i	0.637601	+	0.770367i	$0.279927\pi$
$43$			10.1033i			1.54073i	−0.637601	+	0.770367i	$0.720073\pi$
$44$	10.2173	−	5.89894i	1.54031	−	0.889299i
$45$		0			0
$46$	9.79145	−	16.9593i	1.44367	−	2.50051i
$47$	6.55830	−	3.78644i	0.956626	−	0.552308i	0.0614931	−	0.998108i	$-0.480414\pi$
$47$	6.55830	−	3.78644i	0.956626	−	0.552308i	0.895133	+	0.445799i	$0.147080\pi$
$48$		0			0
$49$	0.135204	−	6.99869i	0.0193148	−	0.999813i
$50$		0			0
$51$		0			0
$52$	−11.7015	+	20.2676i	−1.62271	+	2.81061i
$53$	5.03756	−	8.72531i	0.691962	−	1.19851i	−0.279232	−	0.960224i	$-0.590080\pi$
$53$	5.03756	−	8.72531i	0.691962	−	1.19851i	0.971194	−	0.238290i	$-0.0765869\pi$
$54$		0			0
$55$		0			0
$56$	9.71512	−	9.52925i	1.29824	−	1.27340i
$57$		0			0
$58$	11.5133	−	6.64719i	1.51177	−	0.872819i
$59$	3.28754	−	5.69419i	0.428002	−	0.741320i	−0.568694	−	0.822549i	$-0.692551\pi$
$59$	3.28754	−	5.69419i	0.428002	−	0.741320i	0.996695	+	0.0812288i	$0.0258845\pi$
$60$		0			0
$61$	−9.67067	+	5.58337i	−1.23820	+	0.714877i	−0.968727	−	0.248130i	$-0.920184\pi$
$61$	−9.67067	+	5.58337i	−1.23820	+	0.714877i	−0.269476	+	0.963007i	$0.586851\pi$
$62$		−	1.24057i		−	0.157552i
$63$		0			0
$64$	−6.92029			−0.865036
$65$		0			0
$66$		0			0
$67$	2.39171	+	1.38086i	0.292194	+	0.168699i	0.638931	−	0.769264i	$-0.279377\pi$
$67$	2.39171	+	1.38086i	0.292194	+	0.168699i	−0.346737	+	0.937963i	$0.612710\pi$
$68$	10.3893	−	5.99828i	1.25989	−	0.727398i
$69$		0			0
$70$		0			0
$71$			3.14129i			0.372803i	0.982474	+	0.186401i	$0.0596824\pi$
$71$			3.14129i			0.372803i	−0.982474	+	0.186401i	$0.940318\pi$
$72$		0			0
$73$	−0.284088	+	0.492054i	−0.0332499	+	0.0575906i	−0.882172	−	0.470928i	$-0.843919\pi$
$73$	−0.284088	+	0.492054i	−0.0332499	+	0.0575906i	0.848922	+	0.528519i	$0.177252\pi$
$74$	−6.96685	−	4.02231i	−0.809880	−	0.467584i
$75$		0			0
$76$			14.7994i			1.69761i
$77$	−7.39940	+	1.90626i	−0.843240	+	0.217239i
$78$		0			0
$79$	−4.58164	−	7.93563i	−0.515475	−	0.892828i	−0.999839	−	0.0179618i	$-0.994282\pi$
$79$	−4.58164	−	7.93563i	−0.515475	−	0.892828i	0.484364	−	0.874867i	$-0.339051\pi$
$80$		0			0
$81$		0			0
$82$	−4.36997	−	7.56901i	−0.482582	−	0.835857i
$83$		−	15.0860i		−	1.65590i	−0.560800	−	0.827951i	$-0.689506\pi$
$83$		−	15.0860i		−	1.65590i	0.560800	−	0.827951i	$-0.310494\pi$
$84$		0			0
$85$		0			0
$86$	21.5837	−	12.4614i	2.32743	−	1.34374i
$87$		0			0
$88$	−12.8645	−	7.42731i	−1.37136	−	0.791754i
$89$	1.76354	+	3.05453i	0.186934	+	0.323780i	0.944227	−	0.329296i	$-0.106811\pi$
$89$	1.76354	+	3.05453i	0.186934	+	0.323780i	−0.757292	+	0.653076i	$0.773478\pi$
$90$		0			0
$91$	10.8208	−	10.6137i	1.13432	−	1.11262i
$92$	−32.4299			−3.38105
$93$		0			0
$94$	−16.1780	−	9.34037i	−1.66863	−	0.963386i
$95$		0			0
$96$		0			0
$97$	17.6929			1.79644			0.898220	−	0.439546i	$-0.144861\pi$
$97$	17.6929			1.79644			0.898220	+	0.439546i	$0.144861\pi$
$98$	−15.1181	+	8.34335i	−1.52716	+	0.842805i
$99$		0			0
$100$		0			0
$101$	−3.27956	+	5.68037i	−0.326329	+	0.565218i	−0.981780	−	0.190019i	$-0.939145\pi$
$101$	−3.27956	+	5.68037i	−0.326329	+	0.565218i	0.655452	+	0.755237i	$0.272478\pi$
$102$		0			0
$103$	−9.27998	−	16.0734i	−0.914383	−	1.58376i	−0.807801	−	0.589455i	$-0.799343\pi$
$103$	−9.27998	−	16.0734i	−0.914383	−	1.58376i	−0.106582	−	0.994304i	$-0.533991\pi$
$104$	29.4666			2.88944
$105$		0			0
$106$	−24.8533			−2.41397
$107$	−5.01102	−	8.67934i	−0.484433	−	0.839063i	0.515407	−	0.856946i	$-0.327641\pi$
$107$	−5.01102	−	8.67934i	−0.484433	−	0.839063i	−0.999840	+	0.0178824i	$0.994308\pi$
$108$		0			0
$109$	9.11317	−	15.7845i	0.872883	−	1.51188i	0.0138831	−	0.999904i	$-0.495581\pi$
$109$	9.11317	−	15.7845i	0.872883	−	1.51188i	0.859000	−	0.511975i	$-0.171086\pi$
$110$		0			0
$111$		0			0
$112$	−11.5153	−	3.20504i	−1.08810	−	0.302847i
$113$	−1.88734			−0.177546			−0.0887730	−	0.996052i	$-0.528295\pi$
$113$	−1.88734			−0.177546			−0.0887730	+	0.996052i	$0.528295\pi$
$114$		0			0
$115$		0			0
$116$	−19.0663	−	11.0080i	−1.77027	−	1.02206i
$117$		0			0
$118$	−16.2194			−1.49312
$119$	−7.52401	+	1.93837i	−0.689725	+	0.177690i
$120$		0			0
$121$	−1.32964	−	2.30301i	−0.120877	−	0.209365i
$122$	23.8556	+	13.7730i	2.15979	+	1.24695i
$123$		0			0
$124$	−1.77918	+	1.02721i	−0.159775	+	0.0922460i
$125$		0			0
$126$		0			0
$127$		−	6.01472i		−	0.533721i	−0.963735	−	0.266860i	$-0.914014\pi$
$127$		−	6.01472i		−	0.533721i	0.963735	−	0.266860i	$-0.0859862\pi$
$128$	9.39301	+	16.2692i	0.830233	+	1.43801i
$129$		0			0
$130$		0			0
$131$	2.65237	+	4.59404i	0.231739	+	0.401383i	0.958320	−	0.285697i	$-0.0922252\pi$
$131$	2.65237	+	4.59404i	0.231739	+	0.401383i	−0.726581	+	0.687081i	$0.758892\pi$
$132$		0			0
$133$	2.57007	−	9.23398i	0.222854	−	0.800687i
$134$		−	6.81259i		−	0.588518i
$135$		0			0
$136$	−13.0811	−	7.55239i	−1.12170	−	0.647612i
$137$	−3.79626	+	6.57532i	−0.324337	+	0.561768i	−0.981378	−	0.192087i	$-0.938474\pi$
$137$	−3.79626	+	6.57532i	−0.324337	+	0.561768i	0.657041	+	0.753855i	$0.271808\pi$
$138$		0			0
$139$			8.61081i			0.730359i	0.930937	+	0.365180i	$0.118992\pi$
$139$			8.61081i			0.730359i	−0.930937	+	0.365180i	$0.881008\pi$
$140$		0			0
$141$		0			0
$142$	6.71077	−	3.87447i	0.563155	−	0.325138i
$143$	−14.3285	−	8.27259i	−1.19821	−	0.691789i
$144$		0			0
$145$		0			0
$146$	1.40157			0.115995
$147$		0			0
$148$			13.3221i			1.09507i
$149$	−10.7472	+	6.20492i	−0.880448	+	0.508327i	−0.870806	−	0.491626i	$-0.836403\pi$
$149$	−10.7472	+	6.20492i	−0.880448	+	0.508327i	−0.00964212	+	0.999954i	$0.503069\pi$
$150$		0			0
$151$	−1.06679	+	1.84774i	−0.0868145	+	0.150367i	−0.906163	−	0.422929i	$-0.861002\pi$
$151$	−1.06679	+	1.84774i	−0.0868145	+	0.150367i	0.819348	+	0.573296i	$0.194335\pi$
$152$	16.1374	−	9.31690i	1.30891	−	0.755701i
$153$		0			0
$154$	13.1988	+	13.4562i	1.06359	+	1.08433i
$155$		0			0
$156$		0			0
$157$	−2.57830	+	4.46574i	−0.205771	+	0.356405i	−0.950378	−	0.311098i	$-0.899303\pi$
$157$	−2.57830	+	4.46574i	−0.205771	+	0.356405i	0.744607	+	0.667503i	$0.232637\pi$
$158$	−11.3020	+	19.5756i	−0.899137	+	1.55735i
$159$		0			0
$160$		0			0
$161$	20.2344	+	5.63180i	1.59469	+	0.443848i
$162$		0			0
$163$	1.80090	−	1.03975i	0.141057	−	0.0814395i	−0.427810	−	0.903868i	$-0.640715\pi$
$163$	1.80090	−	1.03975i	0.141057	−	0.0814395i	0.568868	+	0.822429i	$0.307382\pi$
$164$	−7.23681	+	12.5345i	−0.565100	+	0.978781i
$165$		0			0
$166$	−32.2284	+	18.6071i	−2.50141	+	1.44419i
$167$		−	10.1175i		−	0.782914i	−0.920196	−	0.391457i	$-0.871971\pi$
$167$		−	10.1175i		−	0.782914i	0.920196	−	0.391457i	$-0.128029\pi$
$168$		0			0
$169$	19.8201			1.52462
$170$		0			0
$171$		0			0
$172$	−35.7433	−	20.6364i	−2.72540	−	1.57351i
$173$	10.4119	−	6.01133i	0.791604	−	0.457033i	−0.0489230	−	0.998803i	$-0.515579\pi$
$173$	10.4119	−	6.01133i	0.791604	−	0.457033i	0.840527	+	0.541770i	$0.182246\pi$
$174$		0			0
$175$		0			0
$176$			13.0476i			0.983500i
$177$		0			0
$178$	4.35029	−	7.53492i	0.326068	−	0.564766i
$179$	4.07580	+	2.35316i	0.304639	+	0.175884i	0.644525	−	0.764583i	$-0.277055\pi$
$179$	4.07580	+	2.35316i	0.304639	+	0.175884i	−0.339886	+	0.940467i	$0.610388\pi$
$180$		0			0
$181$			12.8230i			0.953127i	0.879140	+	0.476564i	$0.158118\pi$
$181$			12.8230i			0.953127i	−0.879140	+	0.476564i	$0.841882\pi$
$182$	−36.0206	−	10.0255i	−2.67002	−	0.743142i
$183$		0			0
$184$	20.4161	+	35.3617i	1.50510	+	2.60690i
$185$		0			0
$186$		0			0
$187$	4.24058	+	7.34491i	0.310102	+	0.537113i
$188$			30.9359i			2.25623i
$189$		0			0
$190$		0			0
$191$	0.0649619	−	0.0375058i	0.00470048	−	0.00271382i	−0.497648	−	0.867379i	$-0.665803\pi$
$191$	0.0649619	−	0.0375058i	0.00470048	−	0.00271382i	0.502348	+	0.864665i	$0.332469\pi$
$192$		0			0
$193$	0.975492	+	0.563201i	0.0702174	+	0.0405401i	0.534698	−	0.845043i	$-0.320425\pi$
$193$	0.975492	+	0.563201i	0.0702174	+	0.0405401i	−0.464480	+	0.885583i	$0.653759\pi$
$194$	−21.8224	−	37.7975i	−1.56676	−	2.71370i
$195$		0			0
$196$	24.4838	+	14.7735i	1.74884	+	1.05525i
$197$	16.2618			1.15860			0.579302	−	0.815113i	$-0.303325\pi$
$197$	16.2618			1.15860			0.579302	+	0.815113i	$0.303325\pi$
$198$		0			0
$199$	−7.48902	−	4.32379i	−0.530882	−	0.306505i	0.210493	−	0.977595i	$-0.432493\pi$
$199$	−7.48902	−	4.32379i	−0.530882	−	0.306505i	−0.741376	+	0.671090i	$0.765826\pi$
$200$		0			0
$201$		0			0
$202$	16.1800			1.13842
$203$	9.98466	+	10.1794i	0.700786	+	0.714454i
$204$		0			0
$205$		0			0
$206$	−22.8918	+	39.6498i	−1.59495	+	2.76253i
$207$		0			0
$208$	−12.9410	−	22.4145i	−0.897299	−	1.55417i
$209$	−10.4627			−0.723719
$210$		0			0
$211$	4.13586			0.284724			0.142362	−	0.989815i	$-0.454530\pi$
$211$	4.13586			0.284724			0.142362	+	0.989815i	$0.454530\pi$
$212$	20.5789	+	35.6437i	1.41337	+	2.44802i
$213$		0			0
$214$	−12.3612	+	21.4102i	−0.844993	+	1.46357i
$215$		0			0
$216$		0			0
$217$	1.28849	−	0.331946i	0.0874684	−	0.0225340i
$218$	−44.9607			−3.04512
$219$		0			0
$220$		0			0
$221$	−14.5698	−	8.41190i	−0.980073	−	0.565845i
$222$		0			0
$223$	−9.82385			−0.657854			−0.328927	−	0.944355i	$-0.606687\pi$
$223$	−9.82385			−0.657854			−0.328927	+	0.944355i	$0.606687\pi$
$224$	0.566019	+	2.19707i	0.0378187	+	0.146798i
$225$		0			0
$226$	2.32784	+	4.03194i	0.154846	+	0.268201i
$227$	−17.0332	−	9.83413i	−1.13053	−	0.652714i	−0.186465	−	0.982462i	$-0.559703\pi$
$227$	−17.0332	−	9.83413i	−1.13053	−	0.652714i	−0.944069	+	0.329747i	$0.893036\pi$
$228$		0			0
$229$	−21.6203	+	12.4825i	−1.42871	+	0.824864i	−0.997019	−	0.0771585i	$-0.975415\pi$
$229$	−21.6203	+	12.4825i	−1.42871	+	0.824864i	−0.431688	+	0.902023i	$0.642082\pi$
$230$		0			0
$231$		0			0
$232$			27.7201i			1.81991i
$233$	10.3756	+	17.9710i	0.679726	+	1.17732i	0.975063	+	0.221926i	$0.0712345\pi$
$233$	10.3756	+	17.9710i	0.679726	+	1.17732i	−0.295338	+	0.955393i	$0.595432\pi$
$234$		0			0
$235$		0			0
$236$	13.4299	+	23.2613i	0.874214	+	1.51418i
$237$		0			0
$238$	13.4211	+	13.6828i	0.869958	+	0.886926i
$239$			10.3699i			0.670773i	0.942081	+	0.335387i	$0.108867\pi$
$239$			10.3699i			0.670773i	−0.942081	+	0.335387i	$0.891133\pi$
$240$		0			0
$241$	−5.41173	−	3.12446i	−0.348600	−	0.201264i	0.315468	−	0.948936i	$-0.397838\pi$
$241$	−5.41173	−	3.12446i	−0.348600	−	0.201264i	−0.664069	+	0.747672i	$0.731172\pi$
$242$	−3.27996	+	5.68106i	−0.210844	+	0.365193i
$243$		0			0
$244$		−	45.6172i		−	2.92034i
$245$		0			0
$246$		0			0
$247$	17.9739	−	10.3772i	1.14365	−	0.660287i
$248$	2.24015	+	1.29335i	0.142249	+	0.0821278i
$249$		0			0
$250$		0			0
$251$	16.4369			1.03749			0.518743	−	0.854930i	$-0.326400\pi$
$251$	16.4369			1.03749			0.518743	+	0.854930i	$0.326400\pi$
$252$		0			0
$253$		−	22.9269i		−	1.44140i
$254$	−12.8493	+	7.41856i	−0.806238	+	0.465482i
$255$		0			0
$256$	16.2504	−	28.1465i	1.01565	−	1.75916i
$257$	5.94035	−	3.42966i	0.370549	−	0.213936i	−0.303150	−	0.952943i	$-0.598038\pi$
$257$	5.94035	−	3.42966i	0.370549	−	0.213936i	0.673698	+	0.739007i	$0.264705\pi$
$258$		0			0
$259$	2.31353	−	8.31226i	0.143756	−	0.516499i
$260$		0			0
$261$		0			0
$262$	6.54287	−	11.3326i	0.404220	−	0.700129i
$263$	1.98815	−	3.44358i	0.122595	−	0.212340i	−0.798196	−	0.602398i	$-0.794212\pi$
$263$	1.98815	−	3.44358i	0.122595	−	0.212340i	0.920790	+	0.390058i	$0.127545\pi$
$264$		0			0
$265$		0			0
$266$	−22.8966	+	5.89871i	−1.40388	+	0.361673i
$267$		0			0
$268$	−9.77039	+	5.64093i	−0.596821	+	0.344575i
$269$	−5.69326	+	9.86101i	−0.347124	+	0.601236i	−0.985737	−	0.168291i	$-0.946175\pi$
$269$	−5.69326	+	9.86101i	−0.347124	+	0.601236i	0.638613	+	0.769528i	$0.279508\pi$
$270$		0			0
$271$	12.2565	−	7.07629i	0.744529	−	0.429854i	−0.0791845	−	0.996860i	$-0.525232\pi$
$271$	12.2565	−	7.07629i	0.744529	−	0.429854i	0.823714	+	0.567006i	$0.191898\pi$
$272$			13.2673i			0.804450i
$273$		0			0
$274$	18.7292			1.13147
$275$		0			0
$276$		0			0
$277$	−15.7117	−	9.07118i	−0.944027	−	0.545034i	−0.0528068	−	0.998605i	$-0.516817\pi$
$277$	−15.7117	−	9.07118i	−0.944027	−	0.545034i	−0.891220	+	0.453570i	$0.850150\pi$
$278$	18.3954	−	10.6206i	1.10328	−	0.636979i
$279$		0			0
$280$		0			0
$281$		−	11.9229i		−	0.711262i	−0.934626	−	0.355631i	$-0.884266\pi$
$281$		−	11.9229i		−	0.711262i	0.934626	−	0.355631i	$-0.115734\pi$
$282$		0			0
$283$	6.06939	−	10.5125i	0.360788	−	0.624903i	−0.627303	−	0.778775i	$-0.715841\pi$
$283$	6.06939	−	10.5125i	0.360788	−	0.624903i	0.988091	+	0.153872i	$0.0491745\pi$
$284$	−11.1132	−	6.41624i	−0.659450	−	0.380734i
$285$		0			0
$286$			40.8136i			2.41336i
$287$	6.69211	−	6.56407i	0.395023	−	0.387465i
$288$		0			0
$289$	−4.18800	−	7.25384i	−0.246353	−	0.426696i
$290$		0			0
$291$		0			0
$292$	−1.16053	−	2.01009i	−0.0679146	−	0.117632i
$293$		−	12.3945i		−	0.724096i	−0.932159	−	0.362048i	$-0.882078\pi$
$293$		−	12.3945i		−	0.724096i	0.932159	−	0.362048i	$-0.117922\pi$
$294$		0			0
$295$		0			0
$296$	14.5266	−	8.38691i	0.844339	−	0.487479i
$297$		0			0
$298$	26.5113	+	15.3063i	1.53576	+	0.886670i
$299$	22.7396	+	39.3862i	1.31507	+	2.27776i
$300$		0			0
$301$	18.7181	+	19.0832i	1.07889	+	1.09993i
$302$	5.26313			0.302859
$303$		0			0
$304$	−14.1743	−	8.18353i	−0.812951	−	0.469358i
$305$		0			0
$306$		0			0
$307$	8.70136			0.496613			0.248306	−	0.968682i	$-0.420126\pi$
$307$	8.70136			0.496613			0.248306	+	0.968682i	$0.420126\pi$
$308$	8.36966	−	30.0712i	0.476906	−	1.71347i
$309$		0			0
$310$		0			0
$311$	−3.07995	+	5.33463i	−0.174648	+	0.302499i	−0.940039	−	0.341066i	$-0.889212\pi$
$311$	−3.07995	+	5.33463i	−0.174648	+	0.302499i	0.765391	+	0.643565i	$0.222545\pi$
$312$		0			0
$313$	16.0901	+	27.8688i	0.909465	+	1.57524i	0.814809	+	0.579730i	$0.196842\pi$
$313$	16.0901	+	27.8688i	0.909465	+	1.57524i	0.0946564	+	0.995510i	$0.469825\pi$
$314$	12.7203			0.717847
$315$		0			0
$316$	37.4329			2.10576
$317$	−3.23829	−	5.60889i	−0.181881	−	0.315027i	0.760640	−	0.649174i	$-0.224885\pi$
$317$	−3.23829	−	5.60889i	−0.181881	−	0.315027i	−0.942521	+	0.334147i	$0.891552\pi$
$318$		0			0
$319$	7.78226	−	13.4793i	0.435723	−	0.754695i
$320$		0			0
$321$		0			0
$322$	−12.9258	−	50.1732i	−0.720328	−	2.79604i
$323$	−10.6389			−0.591963
$324$		0			0
$325$		0			0
$326$	−4.44246	−	2.56485i	−0.246045	−	0.142054i
$327$		0			0
$328$	18.2236			1.00623
$329$	5.37235	−	19.3022i	0.296187	−	1.06417i
$330$		0			0
$331$	−9.84155	−	17.0461i	−0.540941	−	0.936937i	−0.998850	−	0.0479380i	$-0.984735\pi$
$331$	−9.84155	−	17.0461i	−0.540941	−	0.936937i	0.457910	−	0.888999i	$-0.348598\pi$
$332$	53.3712	+	30.8139i	2.92912	+	1.69113i
$333$		0			0
$334$	−21.6141	+	12.4789i	−1.18267	+	0.682815i
$335$		0			0
$336$		0			0
$337$		−	2.87090i		−	0.156388i	−0.996938	−	0.0781941i	$-0.975085\pi$
$337$		−	2.87090i		−	0.156388i	0.996938	−	0.0781941i	$-0.0249154\pi$
$338$	−24.4461	−	42.3418i	−1.32969	−	2.30309i
$339$		0			0
$340$		0			0
$341$	−0.726202	−	1.25782i	−0.0393261	−	0.0681147i
$342$		0			0
$343$	−12.7109	−	13.4697i	−0.686325	−	0.727295i
$344$			51.9663i			2.80184i
$345$		0			0
$346$	−25.6841	−	14.8287i	−1.38079	−	0.797198i
$347$	6.96080	−	12.0565i	0.373675	−	0.647224i	−0.616453	−	0.787392i	$-0.711431\pi$
$347$	6.96080	−	12.0565i	0.373675	−	0.647224i	0.990128	+	0.140168i	$0.0447642\pi$
$348$		0			0
$349$		−	28.6678i		−	1.53455i	−0.641318	−	0.767276i	$-0.721612\pi$
$349$		−	28.6678i		−	1.53455i	0.641318	−	0.767276i	$-0.278388\pi$
$350$		0			0
$351$		0			0
$352$	2.14477	−	1.23829i	0.114317	−	0.0660009i
$353$	1.99135	+	1.14970i	0.105989	+	0.0611926i	0.552057	−	0.833806i	$-0.313843\pi$
$353$	1.99135	+	1.14970i	0.105989	+	0.0611926i	−0.446069	+	0.894999i	$0.647176\pi$
$354$		0			0
$355$		0			0
$356$	−14.4084			−0.763645
$357$		0			0
$358$		−	11.6096i		−	0.613584i
$359$	18.9385	−	10.9341i	0.999534	−	0.577081i	0.0914239	−	0.995812i	$-0.470858\pi$
$359$	18.9385	−	10.9341i	0.999534	−	0.577081i	0.908111	+	0.418731i	$0.137525\pi$
$360$		0			0
$361$	−2.93774	+	5.08832i	−0.154618	+	0.267806i
$362$	27.3939	−	15.8159i	1.43979	−	0.831265i
$363$		0			0
$364$	15.4473	+	59.9608i	0.809661	+	3.14280i
$365$		0			0
$366$		0			0
$367$	−15.1630	+	26.2632i	−0.791504	+	1.37093i	0.133531	+	0.991045i	$0.457368\pi$
$367$	−15.1630	+	26.2632i	−0.791504	+	1.37093i	−0.925035	+	0.379881i	$0.875965\pi$
$368$	17.9326	−	31.0601i	0.934799	−	1.61912i
$369$		0			0
$370$		0			0
$371$	−6.65016	−	25.8134i	−0.345259	−	1.34017i
$372$		0			0
$373$	−17.2442	+	9.95594i	−0.892871	+	0.515499i	−0.874880	−	0.484339i	$-0.839060\pi$
$373$	−17.2442	+	9.95594i	−0.892871	+	0.515499i	−0.0179903	+	0.999838i	$0.505727\pi$
$374$	10.4607	−	18.1184i	0.540908	−	0.936881i
$375$		0			0
$376$	33.7327	−	19.4756i	1.73963	−	1.00438i
$377$			30.8748i			1.59013i
$378$		0			0
$379$	7.37049			0.378597			0.189298	−	0.981920i	$-0.439379\pi$
$379$	7.37049			0.378597			0.189298	+	0.981920i	$0.439379\pi$
$380$		0			0
$381$		0			0
$382$	−0.160248	−	0.0925192i	−0.00819900	−	0.00473369i
$383$	11.8139	−	6.82077i	0.603663	−	0.348525i	−0.166818	−	0.985988i	$-0.553349\pi$
$383$	11.8139	−	6.82077i	0.603663	−	0.348525i	0.770481	+	0.637463i	$0.220016\pi$
$384$		0			0
$385$		0			0
$386$		−	2.77860i		−	0.141427i
$387$		0			0
$388$	−36.1386	+	62.5938i	−1.83466	+	3.17772i
$389$	9.27011	+	5.35210i	0.470013	+	0.271362i	0.716245	−	0.697849i	$-0.245859\pi$
$389$	9.27011	+	5.35210i	0.470013	+	0.271362i	−0.246232	+	0.969211i	$0.579193\pi$
$390$		0			0
$391$		−	23.3130i		−	1.17899i
$392$	0.695423	−	35.9979i	0.0351241	−	1.81817i
$393$		0			0
$394$	−20.0573	−	34.7402i	−1.01047	−	1.75019i
$395$		0			0
$396$		0			0
$397$	5.86896	+	10.1653i	0.294555	+	0.510184i	0.974881	−	0.222725i	$-0.0714953\pi$
$397$	5.86896	+	10.1653i	0.294555	+	0.510184i	−0.680326	+	0.732909i	$0.738162\pi$
$398$			21.3318i			1.06927i
$399$		0			0
$400$		0			0
$401$	−33.8210	+	19.5265i	−1.68894	+	0.975109i	−0.733607	+	0.679574i	$0.762165\pi$
$401$	−33.8210	+	19.5265i	−1.68894	+	0.975109i	−0.955332	+	0.295535i	$0.904502\pi$
$402$		0			0
$403$	2.49509	+	1.44054i	0.124289	+	0.0717585i
$404$	−13.3973	−	23.2049i	−0.666542	−	1.15449i
$405$		0			0
$406$	9.43131	−	33.8856i	0.468068	−	1.68171i
$407$	−9.41832			−0.466849
$408$		0			0
$409$	21.9953	+	12.6990i	1.08760	+	0.627926i	0.932936	−	0.360041i	$-0.117237\pi$
$409$	21.9953	+	12.6990i	1.08760	+	0.627926i	0.154663	+	0.987967i	$0.450571\pi$
$410$		0			0
$411$		0			0
$412$	75.8192			3.73534
$413$	−4.33993	−	16.8460i	−0.213554	−	0.828937i
$414$		0			0
$415$		0			0
$416$	−2.45634	+	4.25451i	−0.120432	+	0.208595i
$417$		0			0
$418$	12.9047	+	22.3515i	0.631188	+	1.09325i
$419$	31.6839			1.54786			0.773929	−	0.633272i	$-0.218289\pi$
$419$	31.6839			1.54786			0.773929	+	0.633272i	$0.218289\pi$
$420$		0			0
$421$	−0.238492			−0.0116234			−0.00581170	−	0.999983i	$-0.501850\pi$
$421$	−0.238492			−0.0116234			−0.00581170	+	0.999983i	$0.501850\pi$
$422$	−5.10117	−	8.83548i	−0.248321	−	0.430104i
$423$		0			0
$424$	25.9108	−	44.8788i	1.25834	−	2.17951i
$425$		0			0
$426$		0			0
$427$	−7.92191	+	28.4625i	−0.383368	+	1.37740i
$428$	40.9410			1.97896
$429$		0			0
$430$		0			0
$431$	9.93154	+	5.73398i	0.478386	+	0.276196i	0.719743	−	0.694240i	$-0.244259\pi$
$431$	9.93154	+	5.73398i	0.478386	+	0.276196i	−0.241358	+	0.970436i	$0.577593\pi$
$432$		0			0
$433$	11.3234			0.544167			0.272084	−	0.962274i	$-0.412287\pi$
$433$	11.3234			0.544167			0.272084	+	0.962274i	$0.412287\pi$
$434$	−2.29836	−	2.34319i	−0.110325	−	0.112477i
$435$		0			0
$436$	37.2282	+	64.4811i	1.78291	+	3.08809i
$437$	24.9067	+	14.3799i	1.19145	+	0.687882i
$438$		0			0
$439$	−1.93190	+	1.11538i	−0.0922045	+	0.0532343i	−0.545393	−	0.838180i	$-0.683620\pi$
$439$	−1.93190	+	1.11538i	−0.0922045	+	0.0532343i	0.453189	+	0.891415i	$0.350286\pi$
$440$		0			0
$441$		0			0
$442$			41.5009i			1.97400i
$443$	−6.45510	−	11.1806i	−0.306691	−	0.531204i	0.670945	−	0.741507i	$-0.265888\pi$
$443$	−6.45510	−	11.1806i	−0.306691	−	0.531204i	−0.977636	+	0.210302i	$0.932555\pi$
$444$		0			0
$445$		0			0
$446$	12.1167	+	20.9868i	0.573744	+	0.993754i
$447$		0			0
$448$	−13.0711	+	12.8210i	−0.617552	+	0.605737i
$449$		−	8.50547i		−	0.401398i	−0.979653	−	0.200699i	$-0.935679\pi$
$449$		−	8.50547i		−	0.401398i	0.979653	−	0.200699i	$-0.0643213\pi$
$450$		0			0
$451$	−8.86149	−	5.11619i	−0.417271	−	0.240912i
$452$	3.85498	−	6.67703i	0.181323	−	0.314061i
$453$		0			0
$454$			48.5176i			2.27705i
$455$		0			0
$456$		0			0
$457$	8.13477	−	4.69661i	0.380528	−	0.219698i	−0.297520	−	0.954716i	$-0.596159\pi$
$457$	8.13477	−	4.69661i	0.380528	−	0.219698i	0.678048	+	0.735017i	$0.262826\pi$
$458$	53.3328	+	30.7917i	2.49208	+	1.43880i
$459$		0			0
$460$		0			0
$461$	16.6535			0.775630			0.387815	−	0.921737i	$-0.373230\pi$
$461$	16.6535			0.775630			0.387815	+	0.921737i	$0.373230\pi$
$462$		0			0
$463$			16.5752i			0.770316i	0.922851	+	0.385158i	$0.125853\pi$
$463$			16.5752i			0.770316i	−0.922851	+	0.385158i	$0.874147\pi$
$464$	21.0860	−	12.1740i	0.978893	−	0.565164i
$465$		0			0
$466$	25.5944	−	44.3308i	1.18564	−	2.05359i
$467$	−12.1740	+	7.02866i	−0.563345	+	0.325247i	−0.754487	−	0.656315i	$-0.772114\pi$
$467$	−12.1740	+	7.02866i	−0.563345	+	0.325247i	0.191142	+	0.981562i	$0.438781\pi$
$468$		0			0
$469$	7.07577	−	1.82289i	0.326729	−	0.0841732i
$470$		0			0
$471$		0			0
$472$	16.9095	−	29.2881i	0.778324	−	1.34810i
$473$	14.5893	−	25.2694i	0.670815	−	1.16189i
$474$		0			0
$475$		0			0
$476$	8.51060	−	30.5776i	0.390083	−	1.40152i
$477$		0			0
$478$	22.1533	−	12.7902i	1.01327	−	0.585012i
$479$	0.557501	−	0.965621i	0.0254729	−	0.0441203i	−0.853008	−	0.521898i	$-0.825224\pi$
$479$	0.557501	−	0.965621i	0.0254729	−	0.0441203i	0.878481	+	0.477778i	$0.158558\pi$
$480$		0			0
$481$	16.1798	−	9.34140i	0.737734	−	0.425931i
$482$			15.4149i			0.702127i
$483$		0			0
$484$	10.8634			0.493793
$485$		0			0
$486$		0			0
$487$	−14.6393	−	8.45200i	−0.663370	−	0.382997i	0.130190	−	0.991489i	$-0.458441\pi$
$487$	−14.6393	−	8.45200i	−0.663370	−	0.382997i	−0.793560	+	0.608492i	$0.791775\pi$
$488$	−49.7413	+	28.7181i	−2.25168	+	1.30001i
$489$		0			0
$490$		0			0
$491$			18.6159i			0.840125i	0.907495	+	0.420063i	$0.137992\pi$
$491$			18.6159i			0.840125i	−0.907495	+	0.420063i	$0.862008\pi$
$492$		0			0
$493$	7.91332	−	13.7063i	0.356398	−	0.617299i
$494$	−44.3380	−	25.5985i	−1.99486	−	1.15173i
$495$		0			0
$496$		−	2.27204i		−	0.102017i
$497$	5.81978	+	5.93330i	0.261053	+	0.266145i
$498$		0			0
$499$	−6.35357	−	11.0047i	−0.284425	−	0.492639i	0.688045	−	0.725668i	$-0.258469\pi$
$499$	−6.35357	−	11.0047i	−0.284425	−	0.492639i	−0.972470	+	0.233030i	$0.925136\pi$
$500$		0			0
$501$		0			0
$502$	−20.2732	−	35.1143i	−0.904839	−	1.56723i
$503$			33.0973i			1.47573i	0.674946	+	0.737867i	$0.264167\pi$
$503$			33.0973i			1.47573i	−0.674946	+	0.737867i	$0.735833\pi$
$504$		0			0
$505$		0			0
$506$	−48.9789	+	28.2780i	−2.17738	+	1.25711i
$507$		0			0
$508$	21.2789	+	12.2854i	0.944098	+	0.545075i
$509$	9.54582	+	16.5338i	0.423111	+	0.732850i	0.996242	−	0.0866140i	$-0.0276047\pi$
$509$	9.54582	+	16.5338i	0.423111	+	0.732850i	−0.573131	+	0.819464i	$0.694271\pi$
$510$		0			0
$511$	0.375028	+	1.45572i	0.0165903	+	0.0643972i
$512$	−42.6008			−1.88271
$513$		0			0
$514$	−14.6536	−	8.46028i	−0.646344	−	0.373167i
$515$		0			0
$516$		0			0
$517$	−21.8707			−0.961871
$518$	−20.6111	+	5.30991i	−0.905599	+	0.233304i
$519$		0			0
$520$		0			0
$521$	−13.8068	+	23.9141i	−0.604888	+	1.04770i	0.387181	+	0.922004i	$0.373449\pi$
$521$	−13.8068	+	23.9141i	−0.604888	+	1.04770i	−0.992069	+	0.125693i	$0.959885\pi$
$522$		0			0
$523$	6.91472	+	11.9767i	0.302360	+	0.523703i	0.976670	−	0.214746i	$-0.0688923\pi$
$523$	6.91472	+	11.9767i	0.302360	+	0.523703i	−0.674310	+	0.738448i	$0.735559\pi$
$524$	−21.6704			−0.946675
$525$		0			0
$526$	−9.80873			−0.427681
$527$	−0.738431	−	1.27900i	−0.0321666	−	0.0557141i
$528$		0			0
$529$	−20.0106	+	34.6593i	−0.870025	+	1.50693i
$530$		0			0
$531$		0			0
$532$	27.4184	+	27.9532i	1.18874	+	1.21193i
$533$	20.2976			0.879186
$534$		0			0
$535$		0			0
$536$	12.3018	+	7.10246i	0.531358	+	0.306779i
$537$		0			0
$538$	28.0882			1.21097
$539$	−10.4444	+	17.3092i	−0.449871	+	0.745562i
$540$		0			0
$541$	8.50784	+	14.7360i	0.365781	+	0.633551i	0.988901	−	0.148575i	$-0.0474687\pi$
$541$	8.50784	+	14.7360i	0.365781	+	0.633551i	−0.623120	+	0.782126i	$0.714135\pi$
$542$	−30.2343	−	17.4558i	−1.29868	−	0.749791i
$543$		0			0
$544$	2.18089	−	1.25914i	0.0935050	−	0.0539851i
$545$		0			0
$546$		0			0
$547$			2.71466i			0.116071i	0.998315	+	0.0580353i	$0.0184836\pi$
$547$			2.71466i			0.116071i	−0.998315	+	0.0580353i	$0.981516\pi$
$548$	−15.5081	−	26.8608i	−0.662474	−	1.14744i
$549$		0			0
$550$		0			0
$551$	9.76216	+	16.9086i	0.415882	+	0.720329i
$552$		0			0
$553$	−23.3560	−	6.50062i	−0.993197	−	0.276434i
$554$			44.7536i			1.90140i
$555$		0			0
$556$	−30.4633	−	17.5880i	−1.29193	−	0.745897i
$557$	−22.3329	+	38.6817i	−0.946275	+	1.63900i	−0.193098	+	0.981179i	$0.561854\pi$
$557$	−22.3329	+	38.6817i	−0.946275	+	1.63900i	−0.753177	+	0.657818i	$0.771480\pi$
$558$		0			0
$559$			57.8804i			2.44808i
$560$		0			0
$561$		0			0
$562$	−25.4711	+	14.7057i	−1.07443	+	0.620324i
$563$	11.1237	+	6.42229i	0.468810	+	0.270667i	0.715741	−	0.698366i	$-0.246089\pi$
$563$	11.1237	+	6.42229i	0.468810	+	0.270667i	−0.246932	+	0.969033i	$0.579422\pi$
$564$		0			0
$565$		0			0
$566$	−29.9439			−1.25864
$567$		0			0
$568$			16.1573i			0.677944i
$569$	−10.9327	+	6.31198i	−0.458321	+	0.264612i	−0.711338	−	0.702850i	$-0.751911\pi$
$569$	−10.9327	+	6.31198i	−0.458321	+	0.264612i	0.253017	+	0.967462i	$0.418577\pi$
$570$		0			0
$571$	−5.21105	+	9.02581i	−0.218076	+	0.377718i	−0.954220	−	0.299107i	$-0.903311\pi$
$571$	−5.21105	+	9.02581i	−0.218076	+	0.377718i	0.736144	+	0.676825i	$0.236645\pi$
$572$	58.5335	−	33.7943i	2.44741	−	1.41301i
$573$		0			0
$574$	−22.2769	−	6.20029i	−0.929822	−	0.258795i
$575$		0			0
$576$		0			0
$577$	15.8359	−	27.4286i	0.659257	−	1.14187i	−0.321551	−	0.946892i	$-0.604204\pi$
$577$	15.8359	−	27.4286i	0.659257	−	1.14187i	0.980808	−	0.194975i	$-0.0624626\pi$
$578$	−10.3310	+	17.8938i	−0.429711	+	0.744282i
$579$		0			0
$580$		0			0
$581$	−27.9494	−	28.4946i	−1.15954	−	1.18215i
$582$		0			0
$583$	−25.1990	+	14.5486i	−1.04363	+	0.602542i
$584$	−1.46121	+	2.53089i	−0.0604652	+	0.104729i
$585$		0			0
$586$	−26.4786	+	15.2874i	−1.09382	+	0.631517i
$587$			1.10922i			0.0457824i	0.999738	+	0.0228912i	$0.00728714\pi$
$587$			1.10922i			0.0457824i	−0.999738	+	0.0228912i	$0.992713\pi$
$588$		0			0
$589$	1.82191			0.0750706
$590$		0			0
$591$		0			0
$592$	−12.7594	−	7.36667i	−0.524410	−	0.302768i
$593$	−31.0638	+	17.9347i	−1.27564	+	0.736490i	−0.976043	−	0.217577i	$-0.930185\pi$
$593$	−31.0638	+	17.9347i	−1.27564	+	0.736490i	−0.299595	+	0.954067i	$0.596851\pi$
$594$		0			0
$595$		0			0
$596$		−	50.6954i		−	2.07657i
$597$		0			0
$598$	56.0940	−	97.1577i	2.29386	−	3.97307i
$599$	−22.8752	−	13.2070i	−0.934656	−	0.539624i	−0.0463752	−	0.998924i	$-0.514767\pi$
$599$	−22.8752	−	13.2070i	−0.934656	−	0.539624i	−0.888281	+	0.459300i	$0.848100\pi$
$600$		0			0
$601$		−	5.01841i		−	0.204705i	−0.994748	−	0.102353i	$-0.967363\pi$
$601$		−	5.01841i		−	0.204705i	0.994748	−	0.102353i	$-0.0326370\pi$
$602$	17.6807	−	63.5247i	0.720611	−	2.58907i
$603$		0			0
$604$	−4.35796	−	7.54821i	−0.177323	−	0.307132i
$605$		0			0
$606$		0			0
$607$	−8.37411	−	14.5044i	−0.339895	−	0.588715i	0.644518	−	0.764589i	$-0.277058\pi$
$607$	−8.37411	−	14.5044i	−0.339895	−	0.588715i	−0.984413	+	0.175874i	$0.943725\pi$
$608$			3.10664i			0.125991i
$609$		0			0
$610$		0			0
$611$	37.5717	−	21.6920i	1.51999	−	0.877566i
$612$		0			0
$613$	−23.7909	−	13.7357i	−0.960904	−	0.554778i	−0.0644531	−	0.997921i	$-0.520530\pi$
$613$	−23.7909	−	13.7357i	−0.960904	−	0.554778i	−0.896451	+	0.443142i	$0.853864\pi$
$614$	−10.7323	−	18.5888i	−0.433119	−	0.750183i
$615$		0			0
$616$	−38.0589	+	9.80490i	−1.53344	+	0.395051i
$617$	−15.8169			−0.636764			−0.318382	−	0.947963i	$-0.603139\pi$
$617$	−15.8169			−0.636764			−0.318382	+	0.947963i	$0.603139\pi$
$618$		0			0
$619$	34.4277	+	19.8769i	1.38377	+	0.798919i	0.992603	−	0.121402i	$-0.0387391\pi$
$619$	34.4277	+	19.8769i	1.38377	+	0.798919i	0.391164	+	0.920321i	$0.372072\pi$
$620$		0			0
$621$		0			0
$622$	15.1952			0.609273
$623$	8.99003	+	2.50218i	0.360178	+	0.100248i
$624$		0			0
$625$		0			0
$626$	39.6910	−	68.7468i	1.58637	−	2.74768i
$627$		0			0
$628$	−10.5326	−	18.2430i	−0.420296	−	0.727974i
$629$	−9.57693			−0.381857
$630$		0			0
$631$	−26.9454			−1.07268			−0.536339	−	0.844002i	$-0.680193\pi$
$631$	−26.9454			−1.07268			−0.536339	+	0.844002i	$0.680193\pi$
$632$	−23.5657	−	40.8170i	−0.937394	−	1.62361i
$633$		0			0
$634$	−7.98822	+	13.8360i	−0.317253	+	0.549498i
$635$		0			0
$636$		0			0
$637$	0.774566	−	40.0947i	0.0306894	−	1.58861i
$638$	−38.3946			−1.52006
$639$		0			0
$640$		0			0
$641$	2.26913	+	1.31008i	0.0896251	+	0.0517450i	0.544143	−	0.838993i	$-0.316855\pi$
$641$	2.26913	+	1.31008i	0.0896251	+	0.0517450i	−0.454518	+	0.890738i	$0.650188\pi$
$642$		0			0
$643$	18.7983			0.741334			0.370667	−	0.928766i	$-0.379129\pi$
$643$	18.7983			0.741334			0.370667	+	0.928766i	$0.379129\pi$
$644$	−61.2539	+	60.0820i	−2.41374	+	2.36756i
$645$		0			0
$646$	13.1220	+	22.7279i	0.516278	+	0.894219i
$647$	20.3131	+	11.7278i	0.798590	+	0.461066i	0.842978	−	0.537948i	$-0.180800\pi$
$647$	20.3131	+	11.7278i	0.798590	+	0.461066i	−0.0443882	+	0.999014i	$0.514134\pi$
$648$		0			0
$649$	−16.4450	+	9.49452i	−0.645522	+	0.372692i
$650$		0			0
$651$		0			0
$652$			8.49496i			0.332688i
$653$	7.80530	+	13.5192i	0.305445	+	0.529046i	0.977360	−	0.211582i	$-0.0678614\pi$
$653$	7.80530	+	13.5192i	0.305445	+	0.529046i	−0.671915	+	0.740628i	$0.734528\pi$
$654$		0			0
$655$		0			0
$656$	−8.00339	−	13.8623i	−0.312480	−	0.541231i
$657$		0			0
$658$	−47.8618	+	12.3304i	−1.86585	+	0.480688i
$659$		−	23.5221i		−	0.916289i	−0.888878	−	0.458145i	$-0.848514\pi$
$659$		−	23.5221i		−	0.916289i	0.888878	−	0.458145i	$-0.151486\pi$
$660$		0			0
$661$	36.6881	+	21.1819i	1.42700	+	0.823879i	0.996883	−	0.0788937i	$-0.0251388\pi$
$661$	36.6881	+	21.1819i	1.42700	+	0.823879i	0.430118	+	0.902773i	$0.358472\pi$
$662$	−24.2771	+	42.0492i	−0.943558	+	1.63429i
$663$		0			0
$664$		−	77.5950i		−	3.01127i
$665$		0			0
$666$		0			0
$667$	−37.0517	+	21.3918i	−1.43465	+	0.828294i
$668$	35.7936	+	20.6654i	1.38490	+	0.799570i
$669$		0			0
$670$		0			0
$671$	32.2498			1.24499
$672$		0			0
$673$		−	7.61191i		−	0.293417i	−0.989180	−	0.146709i	$-0.953132\pi$
$673$		−	7.61191i		−	0.293417i	0.989180	−	0.146709i	$-0.0468680\pi$
$674$	−6.13314	+	3.54097i	−0.236240	+	0.136393i
$675$		0			0
$676$	−40.4835	+	70.1194i	−1.55706	+	2.69690i
$677$	−21.3044	+	12.3001i	−0.818793	+	0.472730i	−0.850000	−	0.526783i	$-0.823398\pi$
$677$	−21.3044	+	12.3001i	−0.818793	+	0.472730i	0.0312070	+	0.999513i	$0.490065\pi$
$678$		0			0
$679$	33.4185	−	32.7791i	1.28248	−	1.25795i
$680$		0			0
$681$		0			0
$682$	−1.79139	+	3.10279i	−0.0685960	+	0.118812i
$683$	−4.93402	+	8.54597i	−0.188795	+	0.327002i	−0.944849	−	0.327507i	$-0.893791\pi$
$683$	−4.93402	+	8.54597i	−0.188795	+	0.327002i	0.756054	+	0.654509i	$0.227125\pi$
$684$		0			0
$685$		0			0
$686$	−13.0978	+	43.7680i	−0.500076	+	1.67107i
$687$		0			0
$688$	39.5295	−	22.8224i	1.50705	−	0.870095i
$689$	28.8596	−	49.9863i	1.09946	−	1.90433i
$690$		0			0
$691$	−5.20637	+	3.00590i	−0.198060	+	0.114350i	−0.595750	−	0.803170i	$-0.703145\pi$
$691$	−5.20637	+	3.00590i	−0.198060	+	0.114350i	0.397690	+	0.917520i	$0.369812\pi$
$692$			49.1137i			1.86702i
$693$		0			0
$694$	−34.3418			−1.30360
$695$		0			0
$696$		0			0
$697$	−9.01072	−	5.20234i	−0.341305	−	0.197053i
$698$	−61.2433	+	35.3588i	−2.31809	+	1.33835i
$699$		0			0
$700$		0			0
$701$			29.2421i			1.10446i	0.833692	+	0.552229i	$0.186223\pi$
$701$			29.2421i			1.10446i	−0.833692	+	0.552229i	$0.813777\pi$
$702$		0			0
$703$	5.90723	−	10.2316i	0.222795	−	0.385893i
$704$	17.3084	+	9.99300i	0.652334	+	0.376625i
$705$		0			0
$706$		−	5.67218i		−	0.213475i
$707$	4.32940	+	16.8051i	0.162824	+	0.632021i
$708$		0			0
$709$	11.5891	+	20.0729i	0.435237	+	0.753853i	0.997315	−	0.0732317i	$-0.0233313\pi$
$709$	11.5891	+	20.0729i	0.435237	+	0.753853i	−0.562078	+	0.827084i	$0.689998\pi$
$710$		0			0
$711$		0			0
$712$	9.07077	+	15.7110i	0.339941	+	0.588796i
$713$			3.99235i			0.149515i
$714$		0			0
$715$		0			0
$716$	−16.6500	+	9.61290i	−0.622241	+	0.359251i
$717$		0			0
$718$	−46.7174	−	26.9723i	−1.74348	−	1.00660i
$719$	−8.72594	−	15.1138i	−0.325423	−	0.563649i	0.656175	−	0.754609i	$-0.272173\pi$
$719$	−8.72594	−	15.1138i	−0.325423	−	0.563649i	−0.981598	+	0.190960i	$0.938840\pi$
$720$		0			0
$721$	−47.3069	−	13.1668i	−1.76180	−	0.490358i
$722$	14.4936			0.539397
$723$		0			0
$724$	−45.3652	−	26.1916i	−1.68599	−	0.973404i
$725$		0			0
$726$		0			0
$727$	−43.5007			−1.61335			−0.806676	−	0.590993i	$-0.798736\pi$
$727$	−43.5007			−1.61335			−0.806676	+	0.590993i	$0.798736\pi$
$728$	55.6568	−	54.5919i	2.06278	−	2.02331i
$729$		0			0
$730$		0			0
$731$	14.8349	−	25.6949i	0.548690	−	0.950360i
$732$		0			0
$733$	3.08007	+	5.33484i	0.113765	+	0.197047i	0.917285	−	0.398230i	$-0.130376\pi$
$733$	3.08007	+	5.33484i	0.113765	+	0.197047i	−0.803520	+	0.595277i	$0.797042\pi$
$734$	74.8084			2.76123
$735$		0			0
$736$	−6.80757			−0.250931
$737$	−3.98796	−	6.90734i	−0.146898	−	0.254435i
$738$		0			0
$739$	3.46772	−	6.00626i	0.127562	−	0.220944i	−0.795170	−	0.606387i	$-0.792618\pi$
$739$	3.46772	−	6.00626i	0.127562	−	0.220944i	0.922731	+	0.385443i	$0.125951\pi$
$740$		0			0
$741$		0			0
$742$	−46.9432	+	46.0450i	−1.72334	+	1.69037i
$743$	31.6185			1.15997			0.579984	−	0.814628i	$-0.303059\pi$
$743$	31.6185			1.15997			0.579984	+	0.814628i	$0.303059\pi$
$744$		0			0
$745$		0			0
$746$	42.5380	+	24.5593i	1.55743	+	0.899180i
$747$		0			0
$748$	−34.6464			−1.26680
$749$	−25.5448	−	7.10984i	−0.933388	−	0.259788i
$750$		0			0
$751$	−12.8034	−	22.1761i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$751$	−12.8034	−	22.1761i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$752$	−29.6292	−	17.1064i	−1.08047	−	0.623808i
$753$		0			0
$754$	65.9582	−	38.0810i	2.40205	−	1.38683i
$755$		0			0
$756$		0			0
$757$			34.4494i			1.25209i	0.779788	+	0.626043i	$0.215327\pi$
$757$			34.4494i			1.25209i	−0.779788	+	0.626043i	$0.784673\pi$
$758$	−9.09076	−	15.7457i	−0.330191	−	0.571908i
$759$		0			0
$760$		0			0
$761$	−4.47010	−	7.74244i	−0.162041	−	0.280663i	0.773560	−	0.633724i	$-0.218474\pi$
$761$	−4.47010	−	7.74244i	−0.162041	−	0.280663i	−0.935601	+	0.353060i	$0.885141\pi$
$762$		0			0
$763$	−12.0304	−	46.6976i	−0.435531	−	1.69057i
$764$			0.306429i			0.0110862i
$765$		0			0
$766$	−29.1426	−	16.8255i	−1.05296	−	0.607929i
$767$	18.8339	−	32.6213i	0.680054	−	1.17789i
$768$		0			0
$769$			5.35789i			0.193210i	0.995323	+	0.0966052i	$0.0307984\pi$
$769$			5.35789i			0.193210i	−0.995323	+	0.0966052i	$0.969202\pi$
$770$		0			0
$771$		0			0
$772$	−3.98498	+	2.30073i	−0.143423	+	0.0828050i
$773$	−34.2116	−	19.7521i	−1.23051	−	0.710433i	−0.263370	−	0.964695i	$-0.584834\pi$
$773$	−34.2116	−	19.7521i	−1.23051	−	0.710433i	−0.967135	+	0.254262i	$0.918167\pi$
$774$		0			0
$775$		0			0
$776$	91.0036			3.26684
$777$		0			0
$778$		−	26.4051i		−	0.946669i
$779$	11.1160	−	6.41780i	0.398271	−	0.229942i
$780$		0			0
$781$	4.53607	−	7.85670i	0.162313	−	0.281135i
$782$	−49.8037	+	28.7542i	−1.78098	+	1.02825i
$783$		0			0
$784$	−27.6881	+	15.2804i	−0.988862	+	0.545730i
$785$		0			0
$786$		0			0
$787$	7.63353	−	13.2217i	0.272106	−	0.471301i	−0.697295	−	0.716784i	$-0.745613\pi$
$787$	7.63353	−	13.2217i	0.272106	−	0.471301i	0.969401	+	0.245483i	$0.0789466\pi$
$788$	−33.2155	+	57.5309i	−1.18325	+	2.04945i
$789$		0			0
$790$		0			0
$791$	−3.56483	+	3.49662i	−0.126751	+	0.124326i
$792$		0			0
$793$	−55.4021	+	31.9864i	−1.96739	+	1.13587i
$794$	14.4775	−	25.0758i	0.513789	−	0.889909i
$795$		0			0
$796$	30.5934	−	17.6631i	1.08435	−	0.626052i
$797$			6.45665i			0.228706i	0.993440	+	0.114353i	$0.0364795\pi$
$797$			6.45665i			0.228706i	−0.993440	+	0.114353i	$0.963520\pi$
$798$		0			0
$799$	−22.2390			−0.786758
$800$		0			0
$801$		0			0
$802$	83.4295	+	48.1681i	2.94600	+	1.70087i
$803$	1.42107	−	0.820453i	0.0501484	−	0.0289532i
$804$		0			0
$805$		0			0
$806$		−	7.10705i		−	0.250335i
$807$		0			0
$808$	−16.8685	+	29.2171i	−0.593431	+	1.02785i
$809$	42.6190	+	24.6061i	1.49841	+	0.865105i	0.999998	−	0.00183874i	$-0.000585290\pi$
$809$	42.6190	+	24.6061i	1.49841	+	0.865105i	0.498407	+	0.866943i	$0.333919\pi$
$810$		0			0
$811$			18.9745i			0.666286i	0.942876	+	0.333143i	$0.108109\pi$
$811$			18.9745i			0.666286i	−0.942876	+	0.333143i	$0.891891\pi$
$812$	−56.4068	+	14.5318i	−1.97949	+	0.509965i
$813$		0			0
$814$	11.6166	+	20.1205i	0.407160	+	0.705222i
$815$		0			0
$816$		0			0
$817$	18.3009	+	31.6982i	0.640269	+	1.10898i
$818$		−	62.6519i		−	2.19057i
$819$		0			0
$820$		0			0
$821$	−37.7912	+	21.8188i	−1.31892	+	0.761480i	−0.983555	−	0.180608i	$-0.942194\pi$
$821$	−37.7912	+	21.8188i	−1.31892	+	0.761480i	−0.335367	+	0.942088i	$0.608860\pi$
$822$		0			0
$823$	30.8143	+	17.7906i	1.07412	+	0.620143i	0.929304	−	0.369316i	$-0.120408\pi$
$823$	30.8143	+	17.7906i	1.07412	+	0.620143i	0.144815	+	0.989459i	$0.453741\pi$
$824$	−47.7317	−	82.6737i	−1.66281	−	2.88008i
$825$		0			0
$826$	−30.6354	+	30.0493i	−1.06594	+	1.04555i
$827$	−24.8460			−0.863980			−0.431990	−	0.901878i	$-0.642188\pi$
$827$	−24.8460			−0.863980			−0.431990	+	0.901878i	$0.642188\pi$
$828$		0			0
$829$	42.8211	+	24.7228i	1.48724	+	0.858658i	0.999894	−	0.0145507i	$-0.00463180\pi$
$829$	42.8211	+	24.7228i	1.48724	+	0.858658i	0.487346	+	0.873209i	$0.337965\pi$
$830$		0			0
$831$		0			0
$832$	−39.6455			−1.37446
$833$	−10.6203	+	17.6007i	−0.367970	+	0.609829i
$834$		0			0
$835$		0			0
$836$	21.3705	−	37.0149i	0.739116	−	1.28019i
$837$		0			0
$838$	−39.0789	−	67.6866i	−1.34996	−	2.33819i
$839$	37.9265			1.30937			0.654684	−	0.755902i	$-0.272801\pi$
$839$	37.9265			1.30937			0.654684	+	0.755902i	$0.272801\pi$
$840$		0			0
$841$	−0.0448246			−0.00154567
$842$	0.294156	+	0.509493i	0.0101373	+	0.0175583i
$843$		0			0
$844$	−8.44769	+	14.6318i	−0.290782	+	0.503648i
$845$		0			0
$846$		0			0
$847$	−6.77817	−	1.88655i	−0.232901	−	0.0648227i
$848$	−45.5176			−1.56308
$849$		0			0
$850$		0			0
$851$	22.4205	+	12.9445i	0.768566	+	0.443732i
$852$		0			0
$853$	28.8931			0.989282			0.494641	−	0.869097i	$-0.335300\pi$
$853$	28.8931			0.989282			0.494641	+	0.869097i	$0.335300\pi$
$854$	70.5756	−	18.1820i	2.41505	−	0.622175i
$855$		0			0
$856$	−25.7742	−	44.6423i	−0.880946	−	1.52584i
$857$	3.68491	+	2.12748i	0.125874	+	0.0726734i	0.561615	−	0.827399i	$-0.310180\pi$
$857$	3.68491	+	2.12748i	0.125874	+	0.0726734i	−0.435741	+	0.900072i	$0.643514\pi$
$858$		0			0
$859$	−45.0935	+	26.0348i	−1.53857	+	0.888294i	−0.539648	+	0.841891i	$0.681443\pi$
$859$	−45.0935	+	26.0348i	−1.53857	+	0.888294i	−0.998923	+	0.0464036i	$0.985224\pi$
$860$		0			0
$861$		0			0
$862$		−	28.2891i		−	0.963532i
$863$	9.64266	+	16.7016i	0.328240	+	0.568528i	0.982163	−	0.188033i	$-0.0602112\pi$
$863$	9.64266	+	16.7016i	0.328240	+	0.568528i	−0.653923	+	0.756561i	$0.726878\pi$
$864$		0			0
$865$		0			0
$866$	−13.9663	−	24.1903i	−0.474593	−	0.822019i
$867$		0			0
$868$	−1.45744	+	5.23643i	−0.0494689	+	0.177736i
$869$			26.4638i			0.897723i
$870$		0			0
$871$	13.7018	+	7.91077i	0.464269	+	0.268046i
$872$	46.8737	−	81.1877i	1.58734	−	2.74936i
$873$		0			0
$874$		−	70.9445i		−	2.39973i
$875$		0			0
$876$		0			0
$877$	11.2717	−	6.50771i	0.380617	−	0.219750i	−0.297469	−	0.954731i	$-0.596143\pi$
$877$	11.2717	−	6.50771i	0.380617	−	0.219750i	0.678087	+	0.734982i	$0.262809\pi$
$878$	4.76561	+	2.75142i	0.160831	+	0.0928561i
$879$		0			0
$880$		0			0
$881$	−41.8412			−1.40967			−0.704833	−	0.709373i	$-0.748978\pi$
$881$	−41.8412			−1.40967			−0.704833	+	0.709373i	$0.748978\pi$
$882$		0			0
$883$		−	12.0409i		−	0.405210i	−0.979261	−	0.202605i	$-0.935059\pi$
$883$		−	12.0409i		−	0.405210i	0.979261	−	0.202605i	$-0.0649408\pi$
$884$	59.5192	−	34.3634i	2.00185	−	1.15577i
$885$		0			0
$886$	−15.9234	+	27.5802i	−0.534958	+	0.926575i
$887$	0.693707	−	0.400512i	0.0232924	−	0.0134479i	−0.488309	−	0.872671i	$-0.662386\pi$
$887$	0.693707	−	0.400512i	0.0232924	−	0.0134479i	0.511601	+	0.859223i	$0.329053\pi$
$888$		0			0
$889$	−11.1433	−	11.3607i	−0.373735	−	0.381025i
$890$		0			0
$891$		0			0
$892$	20.0657	−	34.7548i	0.671849	−	1.16368i
$893$	13.7174	−	23.7593i	0.459036	−	0.795073i
$894$		0			0
$895$		0			0
$896$	47.8831	+	13.3272i	1.59966	+	0.445230i
$897$		0			0
$898$	−18.1703	+	10.4906i	−0.606352	+	0.350077i
$899$	−1.35516	+	2.34720i	−0.0451971	+	0.0782837i
$900$		0			0
$901$	−25.6233	+	14.7936i	−0.853636	+	0.492847i
$902$			25.2412i			0.840440i
$903$		0			0
$904$	−9.70756			−0.322869
$905$		0			0
$906$		0			0
$907$	−31.1895	−	18.0073i	−1.03563	−	0.597922i	−0.117038	−	0.993127i	$-0.537340\pi$
$907$	−31.1895	−	18.0073i	−1.03563	−	0.597922i	−0.918593	+	0.395206i	$0.870673\pi$
$908$	69.5823	−	40.1734i	2.30917	−	1.33320i
$909$		0			0
$910$		0			0
$911$		−	50.1511i		−	1.66158i	−0.556585	−	0.830791i	$-0.687889\pi$
$911$		−	50.1511i		−	1.66158i	0.556585	−	0.830791i	$-0.312111\pi$
$912$		0			0
$913$	−21.7844	+	37.7317i	−0.720958	+	1.24874i
$914$	−20.0668	−	11.5856i	−0.663752	−	0.383217i
$915$		0			0
$916$		−	101.984i		−	3.36965i
$917$	13.5211	+	3.76329i	0.446506	+	0.124275i
$918$		0			0
$919$	−27.4891	−	47.6126i	−0.906783	−	1.57059i	−0.818506	−	0.574497i	$-0.805198\pi$
$919$	−27.4891	−	47.6126i	−0.906783	−	1.57059i	−0.0882762	−	0.996096i	$-0.528136\pi$
$920$		0			0
$921$		0			0
$922$	−20.5404	−	35.5770i	−0.676461	−	1.17167i
$923$			17.9961i			0.592348i
$924$		0			0
$925$		0			0
$926$	35.4098	−	20.4439i	1.16364	−	0.671827i
$927$		0			0
$928$	−4.00234	−	2.31075i	−0.131383	−	0.0758542i
$929$	−0.0879279	−	0.152296i	−0.00288482	−	0.00499666i	0.864579	−	0.502496i	$-0.167585\pi$
$929$	−0.0879279	−	0.152296i	−0.00288482	−	0.00499666i	−0.867464	+	0.497500i	$0.834252\pi$
$930$		0			0
$931$	−12.2532	−	22.2027i	−0.401581	−	0.727665i
$932$	−84.7703			−2.77674
$933$		0			0
$934$	30.0308	+	17.3383i	0.982638	+	0.567326i
$935$		0			0
$936$		0			0
$937$	−3.70490			−0.121034			−0.0605169	−	0.998167i	$-0.519275\pi$
$937$	−3.70490			−0.121034			−0.0605169	+	0.998167i	$0.519275\pi$
$938$	−12.6215	−	12.8677i	−0.412107	−	0.420145i
$939$		0			0
$940$		0			0
$941$	−2.09077	+	3.62132i	−0.0681571	+	0.118052i	−0.898090	−	0.439811i	$-0.855045\pi$
$941$	−2.09077	+	3.62132i	−0.0681571	+	0.118052i	0.829933	+	0.557863i	$0.188379\pi$
$942$		0			0
$943$	14.0633	+	24.3584i	0.457965	+	0.793218i
$944$	−29.7051			−0.966817
$945$		0			0
$946$	−71.9776			−2.34019
$947$	23.2719	+	40.3081i	0.756235	+	1.30984i	0.944758	+	0.327769i	$0.106297\pi$
$947$	23.2719	+	40.3081i	0.756235	+	1.30984i	−0.188523	+	0.982069i	$0.560370\pi$
$948$		0			0
$949$	−1.62750	+	2.81892i	−0.0528310	+	0.0915060i
$950$		0			0
$951$		0			0
$952$	−38.6998	+	9.97001i	−1.25427	+	0.323130i
$953$	−45.4488			−1.47223			−0.736115	−	0.676856i	$-0.763342\pi$
$953$	−45.4488			−1.47223			−0.736115	+	0.676856i	$0.763342\pi$
$954$		0			0
$955$		0			0
$956$	−36.6866	−	21.1810i	−1.18653	−	0.685044i
$957$		0			0
$958$	−2.75049			−0.0888642
$959$	5.01150	+	19.4528i	0.161830	+	0.628163i
$960$		0			0
$961$	−15.3735	−	26.6278i	−0.495921	−	0.858960i
$962$	−39.9122	−	23.0433i	−1.28682	−	0.742947i
$963$		0			0
$964$	22.1074	−	12.7637i	0.712033	−	0.411092i
$965$		0			0
$966$		0			0
$967$		−	38.7687i		−	1.24672i	−0.781937	−	0.623358i	$-0.785768\pi$
$967$		−	38.7687i		−	1.24672i	0.781937	−	0.623358i	$-0.214232\pi$
$968$	−6.83904	−	11.8456i	−0.219815	−	0.380731i
$969$		0			0
$970$		0			0
$971$	29.5433	+	51.1705i	0.948089	+	1.64214i	0.749445	+	0.662067i	$0.230320\pi$
$971$	29.5433	+	51.1705i	0.948089	+	1.64214i	0.198644	+	0.980072i	$0.436346\pi$
$972$		0			0
$973$	15.9530	+	16.2642i	0.511430	+	0.521406i
$974$			41.6988i			1.33612i
$975$		0			0
$976$	43.6904	+	25.2247i	1.39850	+	0.807422i
$977$	18.5725	−	32.1686i	0.594188	−	1.02916i	−0.399473	−	0.916745i	$-0.630807\pi$
$977$	18.5725	−	32.1686i	0.594188	−	1.02916i	0.993661	−	0.112419i	$-0.0358598\pi$
$978$		0			0
$979$		−	10.1863i		−	0.325555i
$980$		0			0
$981$		0			0
$982$	39.7694	−	22.9609i	1.26909	−	0.732711i
$983$	−33.4864	−	19.3334i	−1.06805	−	0.616639i	−0.140402	−	0.990095i	$-0.544840\pi$
$983$	−33.4864	−	19.3334i	−1.06805	−	0.616639i	−0.927648	+	0.373455i	$0.878173\pi$
$984$		0			0
$985$		0			0
$986$	−39.0411			−1.24332
$987$		0			0
$988$			84.7840i			2.69734i
$989$	−69.4601	+	40.1028i	−2.20870	+	1.27520i
$990$		0			0
$991$	1.57347	−	2.72533i	0.0499829	−	0.0865729i	−0.839951	−	0.542661i	$-0.817417\pi$
$991$	1.57347	−	2.72533i	0.0499829	−	0.0865729i	0.889934	+	0.456089i	$0.150750\pi$
$992$	−0.373479	+	0.215628i	−0.0118580	+	0.00684620i
$993$		0			0
$994$	5.49725	−	19.7510i	0.174362	−	0.626463i
$995$		0			0
$996$		0			0
$997$	−30.2936	+	52.4700i	−0.959407	+	1.66174i	−0.235462	+	0.971883i	$0.575660\pi$
$997$	−30.2936	+	52.4700i	−0.959407	+	1.66174i	−0.723945	+	0.689858i	$0.757673\pi$
$998$	−15.6730	+	27.1464i	−0.496120	+	0.859305i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.bc.c.899.2		24
3.2	odd	2		1575.2.bc.d.899.11		24
5.2	odd	4		1575.2.bk.e.1151.6		12
5.3	odd	4		315.2.bj.b.206.1	yes	12
5.4	even	2	inner	1575.2.bc.c.899.11		24
7.5	odd	6		1575.2.bc.d.1349.2		24
15.2	even	4		1575.2.bk.f.1151.1		12
15.8	even	4		315.2.bj.a.206.6	yes	12
15.14	odd	2		1575.2.bc.d.899.2		24
21.5	even	6	inner	1575.2.bc.c.1349.11		24
35.3	even	12		2205.2.b.b.881.2		12
35.12	even	12		1575.2.bk.f.26.1		12
35.18	odd	12		2205.2.b.a.881.2		12
35.19	odd	6		1575.2.bc.d.1349.11		24
35.33	even	12		315.2.bj.a.26.6	✓	12
105.38	odd	12		2205.2.b.a.881.11		12
105.47	odd	12		1575.2.bk.e.26.6		12
105.53	even	12		2205.2.b.b.881.11		12
105.68	odd	12		315.2.bj.b.26.1	yes	12
105.89	even	6	inner	1575.2.bc.c.1349.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bj.a.26.6	✓	12	35.33	even	12
315.2.bj.a.206.6	yes	12	15.8	even	4
315.2.bj.b.26.1	yes	12	105.68	odd	12
315.2.bj.b.206.1	yes	12	5.3	odd	4
1575.2.bc.c.899.2		24	1.1	even	1	trivial
1575.2.bc.c.899.11		24	5.4	even	2	inner
1575.2.bc.c.1349.2		24	105.89	even	6	inner
1575.2.bc.c.1349.11		24	21.5	even	6	inner
1575.2.bc.d.899.2		24	15.14	odd	2
1575.2.bc.d.899.11		24	3.2	odd	2
1575.2.bc.d.1349.2		24	7.5	odd	6
1575.2.bc.d.1349.11		24	35.19	odd	6
1575.2.bk.e.26.6		12	105.47	odd	12
1575.2.bk.e.1151.6		12	5.2	odd	4
1575.2.bk.f.26.1		12	35.12	even	12
1575.2.bk.f.1151.1		12	15.2	even	4
2205.2.b.a.881.2		12	35.18	odd	12
2205.2.b.a.881.11		12	105.38	odd	12
2205.2.b.b.881.2		12	35.3	even	12
2205.2.b.b.881.11		12	105.53	even	12

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23340 - 2.13631i) q^{2} +(-2.04255 + 3.53780i) q^{4} +(1.88881 - 1.85267i) q^{7} +5.14351 q^{8} +O(q^{10})\)	\(q+(-1.23340 - 2.13631i) q^{2} +(-2.04255 + 3.53780i) q^{4} +(1.88881 - 1.85267i) q^{7} +5.14351 q^{8} +(-2.50111 - 1.44401i) q^{11} +5.72888 q^{13} +(-6.28754 - 1.75000i) q^{14} +(-2.25891 - 3.91255i) q^{16} +(-2.54323 - 1.46833i) q^{17} +(3.13742 - 1.81139i) q^{19} +7.12419i q^{22} +(3.96929 + 6.87502i) q^{23} +(-7.06600 - 12.2387i) q^{26} +(2.69640 + 10.4664i) q^{28} +5.38933i q^{29} +(0.435528 + 0.251452i) q^{31} +(-0.428765 + 0.742643i) q^{32} +7.24416i q^{34} +(2.82425 - 1.63058i) q^{37} +(-7.73938 - 4.46833i) q^{38} +3.54303 q^{41} +10.1033i q^{43} +(10.2173 - 5.89894i) q^{44} +(9.79145 - 16.9593i) q^{46} +(6.55830 - 3.78644i) q^{47} +(0.135204 - 6.99869i) q^{49} +(-11.7015 + 20.2676i) q^{52} +(5.03756 - 8.72531i) q^{53} +(9.71512 - 9.52925i) q^{56} +(11.5133 - 6.64719i) q^{58} +(3.28754 - 5.69419i) q^{59} +(-9.67067 + 5.58337i) q^{61} -1.24057i q^{62} -6.92029 q^{64} +(2.39171 + 1.38086i) q^{67} +(10.3893 - 5.99828i) q^{68} +3.14129i q^{71} +(-0.284088 + 0.492054i) q^{73} +(-6.96685 - 4.02231i) q^{74} +14.7994i q^{76} +(-7.39940 + 1.90626i) q^{77} +(-4.58164 - 7.93563i) q^{79} +(-4.36997 - 7.56901i) q^{82} -15.0860i q^{83} +(21.5837 - 12.4614i) q^{86} +(-12.8645 - 7.42731i) q^{88} +(1.76354 + 3.05453i) q^{89} +(10.8208 - 10.6137i) q^{91} -32.4299 q^{92} +(-16.1780 - 9.34037i) q^{94} +17.6929 q^{97} +(-15.1181 + 8.34335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{4}+O(q^{10}) \) 24 * q - 16 * q^4	\( 24 q - 16 q^{4} - 24 q^{11} - 24 q^{14} - 32 q^{16} - 12 q^{19} + 12 q^{31} - 48 q^{41} + 24 q^{44} - 8 q^{46} - 12 q^{49} + 120 q^{56} - 48 q^{59} + 112 q^{64} + 168 q^{74} - 36 q^{79} + 168 q^{86} + 24 q^{89} - 36 q^{91} - 24 q^{94}+O(q^{100}) \) 24 * q - 16 * q^4 - 24 * q^11 - 24 * q^14 - 32 * q^16 - 12 * q^19 + 12 * q^31 - 48 * q^41 + 24 * q^44 - 8 * q^46 - 12 * q^49 + 120 * q^56 - 48 * q^59 + 112 * q^64 + 168 * q^74 - 36 * q^79 + 168 * q^86 + 24 * q^89 - 36 * q^91 - 24 * q^94

Introduction

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