LMFDB - Embedded newform 1148.2.k.b.729.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, degree $2$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			729.9
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.197445 + 0.197445i) q^{3} +3.12585i q^{5} +(0.707107 - 0.707107i) q^{7} +2.92203i q^{9} +O(q^{10})$	\(q+(-0.197445 + 0.197445i) q^{3} +3.12585i q^{5} +(0.707107 - 0.707107i) q^{7} +2.92203i q^{9} +(-0.0441522 + 0.0441522i) q^{11} +(-3.40539 + 3.40539i) q^{13} +(-0.617183 - 0.617183i) q^{15} +(2.97395 + 2.97395i) q^{17} +(-5.33738 - 5.33738i) q^{19} +0.279229i q^{21} -0.780656 q^{23} -4.77096 q^{25} +(-1.16927 - 1.16927i) q^{27} +(4.24444 - 4.24444i) q^{29} -4.87513 q^{31} -0.0174352i q^{33} +(2.21031 + 2.21031i) q^{35} -1.50079 q^{37} -1.34475i q^{39} +(3.85343 + 5.11381i) q^{41} +2.42062i q^{43} -9.13384 q^{45} +(-4.29984 - 4.29984i) q^{47} -1.00000i q^{49} -1.17438 q^{51} +(-4.07903 + 4.07903i) q^{53} +(-0.138013 - 0.138013i) q^{55} +2.10767 q^{57} -5.85555 q^{59} +8.77946i q^{61} +(2.06619 + 2.06619i) q^{63} +(-10.6447 - 10.6447i) q^{65} +(7.81463 + 7.81463i) q^{67} +(0.154136 - 0.154136i) q^{69} +(6.22855 - 6.22855i) q^{71} -13.3469i q^{73} +(0.942001 - 0.942001i) q^{75} +0.0624407i q^{77} +(-5.78541 + 5.78541i) q^{79} -8.30436 q^{81} -7.21760 q^{83} +(-9.29615 + 9.29615i) q^{85} +1.67608i q^{87} +(-9.01579 + 9.01579i) q^{89} +4.81595i q^{91} +(0.962567 - 0.962567i) q^{93} +(16.6839 - 16.6839i) q^{95} +(11.0205 + 11.0205i) q^{97} +(-0.129014 - 0.129014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.197445	+	0.197445i	−0.113995	+	0.113995i	−0.761803	−	0.647809i	$-0.775686\pi$
$3$	−0.197445	+	0.197445i	−0.113995	+	0.113995i	0.647809	+	0.761803i	$0.275686\pi$
$4$		0			0
$5$			3.12585i			1.39792i	0.715159	+	0.698962i	$0.246354\pi$
$5$			3.12585i			1.39792i	−0.715159	+	0.698962i	$0.753646\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$			2.92203i			0.974010i
$10$		0			0
$11$	−0.0441522	+	0.0441522i	−0.0133124	+	0.0133124i	−0.713732	−	0.700419i	$-0.752996\pi$
$11$	−0.0441522	+	0.0441522i	−0.0133124	+	0.0133124i	0.700419	+	0.713732i	$0.252996\pi$
$12$		0			0
$13$	−3.40539	+	3.40539i	−0.944485	+	0.944485i	−0.998538	−	0.0540535i	$-0.982786\pi$
$13$	−3.40539	+	3.40539i	−0.944485	+	0.944485i	0.0540535	+	0.998538i	$0.482786\pi$
$14$		0			0
$15$	−0.617183	−	0.617183i	−0.159356	−	0.159356i
$16$		0			0
$17$	2.97395	+	2.97395i	0.721290	+	0.721290i	0.968868	−	0.247578i	$-0.0796347\pi$
$17$	2.97395	+	2.97395i	0.721290	+	0.721290i	−0.247578	+	0.968868i	$0.579635\pi$
$18$		0			0
$19$	−5.33738	−	5.33738i	−1.22448	−	1.22448i	−0.966023	−	0.258455i	$-0.916787\pi$
$19$	−5.33738	−	5.33738i	−1.22448	−	1.22448i	−0.258455	−	0.966023i	$-0.583213\pi$
$20$		0			0
$21$			0.279229i			0.0609327i
$22$		0			0
$23$	−0.780656			−0.162778			−0.0813890	−	0.996682i	$-0.525936\pi$
$23$	−0.780656			−0.162778			−0.0813890	+	0.996682i	$0.525936\pi$
$24$		0			0
$25$	−4.77096			−0.954193
$26$		0			0
$27$	−1.16927	−	1.16927i	−0.225027	−	0.225027i
$28$		0			0
$29$	4.24444	−	4.24444i	0.788172	−	0.788172i	−0.193022	−	0.981194i	$-0.561829\pi$
$29$	4.24444	−	4.24444i	0.788172	−	0.788172i	0.981194	+	0.193022i	$0.0618289\pi$
$30$		0			0
$31$	−4.87513			−0.875598			−0.437799	−	0.899073i	$-0.644242\pi$
$31$	−4.87513			−0.875598			−0.437799	+	0.899073i	$0.644242\pi$
$32$		0			0
$33$		−	0.0174352i		−	0.00303509i
$34$		0			0
$35$	2.21031	+	2.21031i	0.373611	+	0.373611i
$36$		0			0
$37$	−1.50079			−0.246729			−0.123364	−	0.992361i	$-0.539368\pi$
$37$	−1.50079			−0.246729			−0.123364	+	0.992361i	$0.539368\pi$
$38$		0			0
$39$		−	1.34475i		−	0.215332i
$40$		0			0
$41$	3.85343	+	5.11381i	0.601805	+	0.798643i
$41$	3.85343	+	5.11381i	0.601805	+	0.798643i
$42$		0			0
$43$			2.42062i			0.369141i	0.982819	+	0.184571i	$0.0590894\pi$
$43$			2.42062i			0.369141i	−0.982819	+	0.184571i	$0.940911\pi$
$44$		0			0
$45$	−9.13384			−1.36159
$46$		0			0
$47$	−4.29984	−	4.29984i	−0.627196	−	0.627196i	0.320166	−	0.947361i	$-0.396261\pi$
$47$	−4.29984	−	4.29984i	−0.627196	−	0.627196i	−0.947361	+	0.320166i	$0.896261\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−1.17438			−0.164446
$52$		0			0
$53$	−4.07903	+	4.07903i	−0.560298	+	0.560298i	−0.929392	−	0.369094i	$-0.879668\pi$
$53$	−4.07903	+	4.07903i	−0.560298	+	0.560298i	0.369094	+	0.929392i	$0.379668\pi$
$54$		0			0
$55$	−0.138013	−	0.138013i	−0.0186097	−	0.0186097i
$56$		0			0
$57$	2.10767			0.279168
$58$		0			0
$59$	−5.85555			−0.762328			−0.381164	−	0.924507i	$-0.624477\pi$
$59$	−5.85555			−0.762328			−0.381164	+	0.924507i	$0.624477\pi$
$60$		0			0
$61$			8.77946i			1.12409i	0.827105	+	0.562047i	$0.189986\pi$
$61$			8.77946i			1.12409i	−0.827105	+	0.562047i	$0.810014\pi$
$62$		0			0
$63$	2.06619	+	2.06619i	0.260315	+	0.260315i
$64$		0			0
$65$	−10.6447	−	10.6447i	−1.32032	−	1.32032i
$66$		0			0
$67$	7.81463	+	7.81463i	0.954709	+	0.954709i	0.999018	−	0.0443091i	$-0.0141086\pi$
$67$	7.81463	+	7.81463i	0.954709	+	0.954709i	−0.0443091	+	0.999018i	$0.514109\pi$
$68$		0			0
$69$	0.154136	−	0.154136i	0.0185558	−	0.0185558i
$70$		0			0
$71$	6.22855	−	6.22855i	0.739193	−	0.739193i	−0.233229	−	0.972422i	$-0.574929\pi$
$71$	6.22855	−	6.22855i	0.739193	−	0.739193i	0.972422	+	0.233229i	$0.0749292\pi$
$72$		0			0
$73$		−	13.3469i		−	1.56213i	−0.624447	−	0.781067i	$-0.714676\pi$
$73$		−	13.3469i		−	1.56213i	0.624447	−	0.781067i	$-0.285324\pi$
$74$		0			0
$75$	0.942001	−	0.942001i	0.108773	−	0.108773i
$76$		0			0
$77$			0.0624407i			0.00711578i
$78$		0			0
$79$	−5.78541	+	5.78541i	−0.650910	+	0.650910i	−0.953212	−	0.302302i	$-0.902245\pi$
$79$	−5.78541	+	5.78541i	−0.650910	+	0.650910i	0.302302	+	0.953212i	$0.402245\pi$
$80$		0			0
$81$	−8.30436			−0.922707
$82$		0			0
$83$	−7.21760			−0.792234			−0.396117	−	0.918200i	$-0.629643\pi$
$83$	−7.21760			−0.792234			−0.396117	+	0.918200i	$0.629643\pi$
$84$		0			0
$85$	−9.29615	+	9.29615i	−1.00831	+	1.00831i
$86$		0			0
$87$			1.67608i			0.179695i
$88$		0			0
$89$	−9.01579	+	9.01579i	−0.955672	+	0.955672i	−0.999058	−	0.0433862i	$-0.986185\pi$
$89$	−9.01579	+	9.01579i	−0.955672	+	0.955672i	0.0433862	+	0.999058i	$0.486185\pi$
$90$		0			0
$91$			4.81595i			0.504848i
$92$		0			0
$93$	0.962567	−	0.962567i	0.0998136	−	0.0998136i
$94$		0			0
$95$	16.6839	−	16.6839i	1.71173	−	1.71173i
$96$		0			0
$97$	11.0205	+	11.0205i	1.11896	+	1.11896i	0.991895	+	0.127063i	$0.0405552\pi$
$97$	11.0205	+	11.0205i	1.11896	+	1.11896i	0.127063	+	0.991895i	$0.459445\pi$
$98$		0			0
$99$	−0.129014	−	0.129014i	−0.0129664	−	0.0129664i
$100$		0			0
$101$	−10.6473	−	10.6473i	−1.05945	−	1.05945i	−0.998117	−	0.0613309i	$-0.980466\pi$
$101$	−10.6473	−	10.6473i	−1.05945	−	1.05945i	−0.0613309	−	0.998117i	$-0.519534\pi$
$102$		0			0
$103$			19.6105i			1.93228i	0.258026	+	0.966138i	$0.416928\pi$
$103$			19.6105i			1.93228i	−0.258026	+	0.966138i	$0.583072\pi$
$104$		0			0
$105$	−0.872829			−0.0851794
$106$		0			0
$107$	1.95499			0.188996			0.0944980	−	0.995525i	$-0.469875\pi$
$107$	1.95499			0.188996			0.0944980	+	0.995525i	$0.469875\pi$
$108$		0			0
$109$	−4.08789	−	4.08789i	−0.391549	−	0.391549i	0.483690	−	0.875239i	$-0.339296\pi$
$109$	−4.08789	−	4.08789i	−0.391549	−	0.391549i	−0.875239	+	0.483690i	$0.839296\pi$
$110$		0			0
$111$	0.296323	−	0.296323i	0.0281258	−	0.0281258i
$112$		0			0
$113$	6.31266			0.593845			0.296922	−	0.954902i	$-0.404040\pi$
$113$	6.31266			0.593845			0.296922	+	0.954902i	$0.404040\pi$
$114$		0			0
$115$		−	2.44022i		−	0.227551i
$116$		0			0
$117$	−9.95065	−	9.95065i	−0.919938	−	0.919938i
$118$		0			0
$119$	4.20581			0.385546
$120$		0			0
$121$			10.9961i			0.999646i
$122$		0			0
$123$	−1.77053	−	0.248855i	−0.159644	−	0.0224385i
$124$		0			0
$125$			0.715936i			0.0640353i
$126$		0			0
$127$	10.0950			0.895783			0.447892	−	0.894088i	$-0.352175\pi$
$127$	10.0950			0.895783			0.447892	+	0.894088i	$0.352175\pi$
$128$		0			0
$129$	−0.477939	−	0.477939i	−0.0420801	−	0.0420801i
$130$		0			0
$131$			0.491225i			0.0429185i	0.999770	+	0.0214592i	$0.00683121\pi$
$131$			0.491225i			0.0429185i	−0.999770	+	0.0214592i	$0.993169\pi$
$132$		0			0
$133$	−7.54819			−0.654511
$134$		0			0
$135$	3.65498	−	3.65498i	0.314570	−	0.314570i
$136$		0			0
$137$	11.8411	+	11.8411i	1.01165	+	1.01165i	0.999931	+	0.0117200i	$0.00373069\pi$
$137$	11.8411	+	11.8411i	1.01165	+	1.01165i	0.0117200	+	0.999931i	$0.496269\pi$
$138$		0			0
$139$	20.0107			1.69729			0.848644	−	0.528964i	$-0.177420\pi$
$139$	20.0107			1.69729			0.848644	+	0.528964i	$0.177420\pi$
$140$		0			0
$141$	1.69796			0.142994
$142$		0			0
$143$		−	0.300711i		−	0.0251467i
$144$		0			0
$145$	13.2675	+	13.2675i	1.10181	+	1.10181i
$146$		0			0
$147$	0.197445	+	0.197445i	0.0162850	+	0.0162850i
$148$		0			0
$149$	4.08115	+	4.08115i	0.334341	+	0.334341i	0.854232	−	0.519891i	$-0.174028\pi$
$149$	4.08115	+	4.08115i	0.334341	+	0.334341i	−0.519891	+	0.854232i	$0.674028\pi$
$150$		0			0
$151$	6.52725	−	6.52725i	0.531180	−	0.531180i	−0.389743	−	0.920923i	$-0.627436\pi$
$151$	6.52725	−	6.52725i	0.531180	−	0.531180i	0.920923	+	0.389743i	$0.127436\pi$
$152$		0			0
$153$	−8.68999	+	8.68999i	−0.702544	+	0.702544i
$154$		0			0
$155$		−	15.2389i		−	1.22402i
$156$		0			0
$157$	3.69698	−	3.69698i	0.295051	−	0.295051i	−0.544021	−	0.839072i	$-0.683099\pi$
$157$	3.69698	−	3.69698i	0.295051	−	0.295051i	0.839072	+	0.544021i	$0.183099\pi$
$158$		0			0
$159$		−	1.61076i		−	0.127742i
$160$		0			0
$161$	−0.552007	+	0.552007i	−0.0435042	+	0.0435042i
$162$		0			0
$163$	−19.6546			−1.53947			−0.769734	−	0.638365i	$-0.779611\pi$
$163$	−19.6546			−1.53947			−0.769734	+	0.638365i	$0.779611\pi$
$164$		0			0
$165$	0.0545000			0.00424282
$166$		0			0
$167$	−5.13425	+	5.13425i	−0.397300	+	0.397300i	−0.877280	−	0.479980i	$-0.840644\pi$
$167$	−5.13425	+	5.13425i	−0.397300	+	0.397300i	0.479980	+	0.877280i	$0.340644\pi$
$168$		0			0
$169$		−	10.1933i		−	0.784102i
$170$		0			0
$171$	15.5960	−	15.5960i	1.19265	−	1.19265i
$172$		0			0
$173$		−	3.93744i		−	0.299358i	−0.988735	−	0.149679i	$-0.952176\pi$
$173$		−	3.93744i		−	0.299358i	0.988735	−	0.149679i	$-0.0478241\pi$
$174$		0			0
$175$	−3.37358	+	3.37358i	−0.255019	+	0.255019i
$176$		0			0
$177$	1.15615	−	1.15615i	0.0869013	−	0.0869013i
$178$		0			0
$179$	11.7303	+	11.7303i	0.876765	+	0.876765i	0.993198	−	0.116434i	$-0.0371463\pi$
$179$	11.7303	+	11.7303i	0.876765	+	0.876765i	−0.116434	+	0.993198i	$0.537146\pi$
$180$		0			0
$181$	−11.0472	−	11.0472i	−0.821134	−	0.821134i	0.165136	−	0.986271i	$-0.447194\pi$
$181$	−11.0472	−	11.0472i	−0.821134	−	0.821134i	−0.986271	+	0.165136i	$0.947194\pi$
$182$		0			0
$183$	−1.73346	−	1.73346i	−0.128141	−	0.128141i
$184$		0			0
$185$		−	4.69126i		−	0.344908i
$186$		0			0
$187$	−0.262613			−0.0192042
$188$		0			0
$189$	−1.65360			−0.120282
$190$		0			0
$191$	10.8724	+	10.8724i	0.786697	+	0.786697i	0.980951	−	0.194254i	$-0.0622286\pi$
$191$	10.8724	+	10.8724i	0.786697	+	0.786697i	−0.194254	+	0.980951i	$0.562229\pi$
$192$		0			0
$193$	14.6058	−	14.6058i	1.05135	−	1.05135i	0.0527383	−	0.998608i	$-0.483205\pi$
$193$	14.6058	−	14.6058i	1.05135	−	1.05135i	0.998608	−	0.0527383i	$-0.0167949\pi$
$194$		0			0
$195$	4.20350			0.301019
$196$		0			0
$197$		−	25.8248i		−	1.83994i	−0.391985	−	0.919972i	$-0.628211\pi$
$197$		−	25.8248i		−	1.83994i	0.391985	−	0.919972i	$-0.371789\pi$
$198$		0			0
$199$	16.4368	+	16.4368i	1.16517	+	1.16517i	0.983327	+	0.181847i	$0.0582076\pi$
$199$	16.4368	+	16.4368i	1.16517	+	1.16517i	0.181847	+	0.983327i	$0.441792\pi$
$200$		0			0
$201$	−3.08591			−0.217664
$202$		0			0
$203$		−	6.00254i		−	0.421296i
$204$		0			0
$205$	−15.9850	+	12.0453i	−1.11644	+	0.841278i
$206$		0			0
$207$		−	2.28110i		−	0.158547i
$208$		0			0
$209$	0.471314			0.0326015
$210$		0			0
$211$	−9.17726	−	9.17726i	−0.631788	−	0.631788i	0.316728	−	0.948516i	$-0.397416\pi$
$211$	−9.17726	−	9.17726i	−0.631788	−	0.631788i	−0.948516	+	0.316728i	$0.897416\pi$
$212$		0			0
$213$			2.45959i			0.168528i
$214$		0			0
$215$	−7.56651			−0.516031
$216$		0			0
$217$	−3.44723	+	3.44723i	−0.234013	+	0.234013i
$218$		0			0
$219$	2.63527	+	2.63527i	0.178075	+	0.178075i
$220$		0			0
$221$	−20.2549			−1.36249
$222$		0			0
$223$	−10.6366			−0.712279			−0.356140	−	0.934433i	$-0.615907\pi$
$223$	−10.6366			−0.712279			−0.356140	+	0.934433i	$0.615907\pi$
$224$		0			0
$225$		−	13.9409i		−	0.929394i
$226$		0			0
$227$	−0.181481	−	0.181481i	−0.0120453	−	0.0120453i	0.701058	−	0.713104i	$-0.252711\pi$
$227$	−0.181481	−	0.181481i	−0.0120453	−	0.0120453i	−0.713104	+	0.701058i	$0.752711\pi$
$228$		0			0
$229$	14.8821	+	14.8821i	0.983438	+	0.983438i	0.999865	−	0.0164271i	$-0.00522915\pi$
$229$	14.8821	+	14.8821i	0.983438	+	0.983438i	−0.0164271	+	0.999865i	$0.505229\pi$
$230$		0			0
$231$	−0.0123286	−	0.0123286i	−0.000811161	−	0.000811161i
$232$		0			0
$233$	13.8210	−	13.8210i	0.905441	−	0.905441i	−0.0904593	−	0.995900i	$-0.528834\pi$
$233$	13.8210	−	13.8210i	0.905441	−	0.905441i	0.995900	+	0.0904593i	$0.0288335\pi$
$234$		0			0
$235$	13.4407	−	13.4407i	0.876772	−	0.876772i
$236$		0			0
$237$		−	2.28460i		−	0.148401i
$238$		0			0
$239$	1.24022	−	1.24022i	0.0802230	−	0.0802230i	−0.665857	−	0.746080i	$-0.731934\pi$
$239$	1.24022	−	1.24022i	0.0802230	−	0.0802230i	0.746080	+	0.665857i	$0.231934\pi$
$240$		0			0
$241$			5.11244i			0.329321i	0.986350	+	0.164661i	$0.0526529\pi$
$241$			5.11244i			0.329321i	−0.986350	+	0.164661i	$0.947347\pi$
$242$		0			0
$243$	5.14747	−	5.14747i	0.330210	−	0.330210i
$244$		0			0
$245$	3.12585			0.199703
$246$		0			0
$247$	36.3517			2.31300
$248$		0			0
$249$	1.42508	−	1.42508i	0.0903105	−	0.0903105i
$250$		0			0
$251$			6.33802i			0.400052i	0.979791	+	0.200026i	$0.0641027\pi$
$251$			6.33802i			0.400052i	−0.979791	+	0.200026i	$0.935897\pi$
$252$		0			0
$253$	0.0344677	−	0.0344677i	0.00216697	−	0.00216697i
$254$		0			0
$255$		−	3.67095i		−	0.229884i
$256$		0			0
$257$	18.1608	−	18.1608i	1.13284	−	1.13284i	0.143135	−	0.989703i	$-0.454282\pi$
$257$	18.1608	−	18.1608i	1.13284	−	1.13284i	0.989703	−	0.143135i	$-0.0457182\pi$
$258$		0			0
$259$	−1.06122	+	1.06122i	−0.0659410	+	0.0659410i
$260$		0			0
$261$	12.4024	+	12.4024i	0.767688	+	0.767688i
$262$		0			0
$263$	−8.59438	−	8.59438i	−0.529952	−	0.529952i	0.390606	−	0.920558i	$-0.372266\pi$
$263$	−8.59438	−	8.59438i	−0.529952	−	0.529952i	−0.920558	+	0.390606i	$0.872266\pi$
$264$		0			0
$265$	−12.7504	−	12.7504i	−0.783254	−	0.783254i
$266$		0			0
$267$		−	3.56024i		−	0.217883i
$268$		0			0
$269$	−2.49990			−0.152422			−0.0762108	−	0.997092i	$-0.524282\pi$
$269$	−2.49990			−0.152422			−0.0762108	+	0.997092i	$0.524282\pi$
$270$		0			0
$271$	−20.9761			−1.27420			−0.637102	−	0.770779i	$-0.719867\pi$
$271$	−20.9761			−1.27420			−0.637102	+	0.770779i	$0.719867\pi$
$272$		0			0
$273$	−0.950883	−	0.950883i	−0.0575500	−	0.0575500i
$274$		0			0
$275$	0.210649	−	0.210649i	0.0127026	−	0.0127026i
$276$		0			0
$277$	1.54775			0.0929953			0.0464977	−	0.998918i	$-0.485194\pi$
$277$	1.54775			0.0929953			0.0464977	+	0.998918i	$0.485194\pi$
$278$		0			0
$279$		−	14.2453i		−	0.852842i
$280$		0			0
$281$	−0.574366	−	0.574366i	−0.0342638	−	0.0342638i	0.689767	−	0.724031i	$-0.257713\pi$
$281$	−0.574366	−	0.574366i	−0.0342638	−	0.0342638i	−0.724031	+	0.689767i	$0.757713\pi$
$282$		0			0
$283$	21.4316			1.27397			0.636987	−	0.770875i	$-0.280180\pi$
$283$	21.4316			1.27397			0.636987	+	0.770875i	$0.280180\pi$
$284$		0			0
$285$			6.58828i			0.390256i
$286$		0			0
$287$	6.34080	+	0.891222i	0.374285	+	0.0526072i
$288$		0			0
$289$			0.688802i			0.0405178i
$290$		0			0
$291$	−4.35186			−0.255111
$292$		0			0
$293$	2.66303	+	2.66303i	0.155576	+	0.155576i	0.780603	−	0.625027i	$-0.214912\pi$
$293$	2.66303	+	2.66303i	0.155576	+	0.155576i	−0.625027	+	0.780603i	$0.714912\pi$
$294$		0			0
$295$		−	18.3036i		−	1.06568i
$296$		0			0
$297$	0.103252			0.00599129
$298$		0			0
$299$	2.65844	−	2.65844i	0.153741	−	0.153741i
$300$		0			0
$301$	1.71164	+	1.71164i	0.0986571	+	0.0986571i
$302$		0			0
$303$	4.20451			0.241543
$304$		0			0
$305$	−27.4433			−1.57140
$306$		0			0
$307$			14.9715i			0.854466i	0.904141	+	0.427233i	$0.140512\pi$
$307$			14.9715i			0.854466i	−0.904141	+	0.427233i	$0.859488\pi$
$308$		0			0
$309$	−3.87198	−	3.87198i	−0.220269	−	0.220269i
$310$		0			0
$311$	22.4001	+	22.4001i	1.27019	+	1.27019i	0.945987	+	0.324205i	$0.105097\pi$
$311$	22.4001	+	22.4001i	1.27019	+	1.27019i	0.324205	+	0.945987i	$0.394903\pi$
$312$		0			0
$313$	16.5977	+	16.5977i	0.938155	+	0.938155i	0.998196	−	0.0600412i	$-0.0191232\pi$
$313$	16.5977	+	16.5977i	0.938155	+	0.938155i	−0.0600412	+	0.998196i	$0.519123\pi$
$314$		0			0
$315$	−6.45860	+	6.45860i	−0.363901	+	0.363901i
$316$		0			0
$317$	3.17288	−	3.17288i	0.178207	−	0.178207i	−0.612367	−	0.790574i	$-0.709783\pi$
$317$	3.17288	−	3.17288i	0.178207	−	0.178207i	0.790574	+	0.612367i	$0.209783\pi$
$318$		0			0
$319$			0.374803i			0.0209849i
$320$		0			0
$321$	−0.386002	+	0.386002i	−0.0215445	+	0.0215445i
$322$		0			0
$323$		−	31.7462i		−	1.76641i
$324$		0			0
$325$	16.2470	−	16.2470i	0.901220	−	0.901220i
$326$		0			0
$327$	1.61427			0.0892691
$328$		0			0
$329$	−6.08089			−0.335250
$330$		0			0
$331$	0.432919	−	0.432919i	0.0237954	−	0.0237954i	−0.695109	−	0.718904i	$-0.744644\pi$
$331$	0.432919	−	0.432919i	0.0237954	−	0.0237954i	0.718904	+	0.695109i	$0.244644\pi$
$332$		0			0
$333$		−	4.38536i		−	0.240316i
$334$		0			0
$335$	−24.4274	+	24.4274i	−1.33461	+	1.33461i
$336$		0			0
$337$			14.6117i			0.795948i	0.917397	+	0.397974i	$0.130287\pi$
$337$			14.6117i			0.795948i	−0.917397	+	0.397974i	$0.869713\pi$
$338$		0			0
$339$	−1.24640	+	1.24640i	−0.0676952	+	0.0676952i
$340$		0			0
$341$	0.215248	−	0.215248i	0.0116563	−	0.0116563i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	0.481807	+	0.481807i	0.0259396	+	0.0259396i
$346$		0			0
$347$	−0.944092	−	0.944092i	−0.0506815	−	0.0506815i	0.681312	−	0.731993i	$-0.261410\pi$
$347$	−0.944092	−	0.944092i	−0.0506815	−	0.0506815i	−0.731993	+	0.681312i	$0.761410\pi$
$348$		0			0
$349$			8.79145i			0.470596i	0.971923	+	0.235298i	$0.0756066\pi$
$349$			8.79145i			0.470596i	−0.971923	+	0.235298i	$0.924393\pi$
$350$		0			0
$351$	7.96366			0.425069
$352$		0			0
$353$	3.42474			0.182280			0.0911401	−	0.995838i	$-0.470949\pi$
$353$	3.42474			0.182280			0.0911401	+	0.995838i	$0.470949\pi$
$354$		0			0
$355$	19.4695	+	19.4695i	1.03334	+	1.03334i
$356$		0			0
$357$	−0.830414	+	0.830414i	−0.0439502	+	0.0439502i
$358$		0			0
$359$	−0.293669			−0.0154992			−0.00774962	−	0.999970i	$-0.502467\pi$
$359$	−0.293669			−0.0154992			−0.00774962	+	0.999970i	$0.502467\pi$
$360$		0			0
$361$			37.9752i			1.99870i
$362$		0			0
$363$	−2.17112	−	2.17112i	−0.113954	−	0.113954i
$364$		0			0
$365$	41.7204			2.18375
$366$		0			0
$367$		−	27.2960i		−	1.42484i	−0.701754	−	0.712419i	$-0.747600\pi$
$367$		−	27.2960i		−	1.42484i	0.701754	−	0.712419i	$-0.252400\pi$
$368$		0			0
$369$	−14.9427	+	11.2599i	−0.777887	+	0.586164i
$370$		0			0
$371$			5.76862i			0.299492i
$372$		0			0
$373$	−8.02826			−0.415688			−0.207844	−	0.978162i	$-0.566645\pi$
$373$	−8.02826			−0.415688			−0.207844	+	0.978162i	$0.566645\pi$
$374$		0			0
$375$	−0.141358	−	0.141358i	−0.00729968	−	0.00729968i
$376$		0			0
$377$			28.9079i			1.48883i
$378$		0			0
$379$	10.1054			0.519080			0.259540	−	0.965732i	$-0.416429\pi$
$379$	10.1054			0.519080			0.259540	+	0.965732i	$0.416429\pi$
$380$		0			0
$381$	−1.99320	+	1.99320i	−0.102115	+	0.102115i
$382$		0			0
$383$	3.77147	+	3.77147i	0.192713	+	0.192713i	0.796867	−	0.604154i	$-0.206489\pi$
$383$	3.77147	+	3.77147i	0.192713	+	0.192713i	−0.604154	+	0.796867i	$0.706489\pi$
$384$		0			0
$385$	−0.195180			−0.00994732
$386$		0			0
$387$	−7.07313			−0.359547
$388$		0			0
$389$			3.68798i			0.186988i	0.995620	+	0.0934940i	$0.0298036\pi$
$389$			3.68798i			0.186988i	−0.995620	+	0.0934940i	$0.970196\pi$
$390$		0			0
$391$	−2.32163	−	2.32163i	−0.117410	−	0.117410i
$392$		0			0
$393$	−0.0969897	−	0.0969897i	−0.00489248	−	0.00489248i
$394$		0			0
$395$	−18.0844	−	18.0844i	−0.909923	−	0.909923i
$396$		0			0
$397$	−25.4075	+	25.4075i	−1.27517	+	1.27517i	−0.331824	+	0.943341i	$0.607664\pi$
$397$	−25.4075	+	25.4075i	−1.27517	+	1.27517i	−0.943341	+	0.331824i	$0.892336\pi$
$398$		0			0
$399$	1.49035	−	1.49035i	0.0746108	−	0.0746108i
$400$		0			0
$401$			14.5249i			0.725337i	0.931918	+	0.362669i	$0.118134\pi$
$401$			14.5249i			0.725337i	−0.931918	+	0.362669i	$0.881866\pi$
$402$		0			0
$403$	16.6017	−	16.6017i	0.826989	−	0.826989i
$404$		0			0
$405$		−	25.9582i		−	1.28987i
$406$		0			0
$407$	0.0662633	−	0.0662633i	0.00328455	−	0.00328455i
$408$		0			0
$409$	−0.302043			−0.0149351			−0.00746754	−	0.999972i	$-0.502377\pi$
$409$	−0.302043			−0.0149351			−0.00746754	+	0.999972i	$0.502377\pi$
$410$		0			0
$411$	−4.67591			−0.230646
$412$		0			0
$413$	−4.14050	+	4.14050i	−0.203741	+	0.203741i
$414$		0			0
$415$		−	22.5612i		−	1.10748i
$416$		0			0
$417$	−3.95101	+	3.95101i	−0.193482	+	0.193482i
$418$		0			0
$419$			33.1732i			1.62062i	0.586002	+	0.810309i	$0.300701\pi$
$419$			33.1732i			1.62062i	−0.586002	+	0.810309i	$0.699299\pi$
$420$		0			0
$421$	−4.15792	+	4.15792i	−0.202645	+	0.202645i	−0.801132	−	0.598488i	$-0.795769\pi$
$421$	−4.15792	+	4.15792i	−0.202645	+	0.202645i	0.598488	+	0.801132i	$0.295769\pi$
$422$		0			0
$423$	12.5643	−	12.5643i	0.610895	−	0.610895i
$424$		0			0
$425$	−14.1886	−	14.1886i	−0.688249	−	0.688249i
$426$		0			0
$427$	6.20801	+	6.20801i	0.300427	+	0.300427i
$428$		0			0
$429$	0.0593738	+	0.0593738i	0.00286659	+	0.00286659i
$430$		0			0
$431$		−	13.0184i		−	0.627074i	−0.949576	−	0.313537i	$-0.898486\pi$
$431$		−	13.0184i		−	0.627074i	0.949576	−	0.313537i	$-0.101514\pi$
$432$		0			0
$433$	25.3433			1.21792			0.608961	−	0.793200i	$-0.291587\pi$
$433$	25.3433			1.21792			0.608961	+	0.793200i	$0.291587\pi$
$434$		0			0
$435$	−5.23919			−0.251200
$436$		0			0
$437$	4.16665	+	4.16665i	0.199318	+	0.199318i
$438$		0			0
$439$	7.34677	−	7.34677i	0.350642	−	0.350642i	−0.509706	−	0.860348i	$-0.670246\pi$
$439$	7.34677	−	7.34677i	0.350642	−	0.350642i	0.860348	+	0.509706i	$0.170246\pi$
$440$		0			0
$441$	2.92203			0.139144
$442$		0			0
$443$		−	14.7528i		−	0.700929i	−0.936576	−	0.350464i	$-0.886024\pi$
$443$		−	14.7528i		−	0.700929i	0.936576	−	0.350464i	$-0.113976\pi$
$444$		0			0
$445$	−28.1821	−	28.1821i	−1.33596	−	1.33596i
$446$		0			0
$447$	−1.61160			−0.0762262
$448$		0			0
$449$		−	26.6232i		−	1.25643i	−0.778040	−	0.628214i	$-0.783786\pi$
$449$		−	26.6232i		−	1.25643i	0.778040	−	0.628214i	$-0.216214\pi$
$450$		0			0
$451$	−0.395924	−	0.0556485i	−0.0186433	−	0.00262039i
$452$		0			0
$453$			2.57754i			0.121103i
$454$		0			0
$455$	−15.0539			−0.705740
$456$		0			0
$457$	0.826739	+	0.826739i	0.0386732	+	0.0386732i	0.726179	−	0.687506i	$-0.241294\pi$
$457$	0.826739	+	0.826739i	0.0386732	+	0.0386732i	−0.687506	+	0.726179i	$0.741294\pi$
$458$		0			0
$459$		−	6.95473i		−	0.324619i
$460$		0			0
$461$	−22.4479			−1.04550			−0.522751	−	0.852485i	$-0.675094\pi$
$461$	−22.4479			−1.04550			−0.522751	+	0.852485i	$0.675094\pi$
$462$		0			0
$463$	−10.0147	+	10.0147i	−0.465421	+	0.465421i	−0.900427	−	0.435006i	$-0.856746\pi$
$463$	−10.0147	+	10.0147i	−0.465421	+	0.465421i	0.435006	+	0.900427i	$0.356746\pi$
$464$		0			0
$465$	3.00884	+	3.00884i	0.139532	+	0.139532i
$466$		0			0
$467$	−4.21327			−0.194967			−0.0974835	−	0.995237i	$-0.531079\pi$
$467$	−4.21327			−0.194967			−0.0974835	+	0.995237i	$0.531079\pi$
$468$		0			0
$469$	11.0516			0.510313
$470$		0			0
$471$			1.45990i			0.0672685i
$472$		0			0
$473$	−0.106876	−	0.106876i	−0.00491415	−	0.00491415i
$474$		0			0
$475$	25.4644	+	25.4644i	1.16839	+	1.16839i
$476$		0			0
$477$	−11.9190	−	11.9190i	−0.545736	−	0.545736i
$478$		0			0
$479$	10.8672	−	10.8672i	0.496536	−	0.496536i	−0.413822	−	0.910358i	$-0.635806\pi$
$479$	10.8672	−	10.8672i	0.496536	−	0.496536i	0.910358	+	0.413822i	$0.135806\pi$
$480$		0			0
$481$	5.11078	−	5.11078i	0.233032	−	0.233032i
$482$		0			0
$483$		−	0.217982i		−	0.00991851i
$484$		0			0
$485$	−34.4483	+	34.4483i	−1.56422	+	1.56422i
$486$		0			0
$487$		−	12.9944i		−	0.588833i	−0.955677	−	0.294416i	$-0.904875\pi$
$487$		−	12.9944i		−	0.588833i	0.955677	−	0.294416i	$-0.0951252\pi$
$488$		0			0
$489$	3.88070	−	3.88070i	0.175491	−	0.175491i
$490$		0			0
$491$	−38.3827			−1.73219			−0.866094	−	0.499880i	$-0.833377\pi$
$491$	−38.3827			−1.73219			−0.866094	+	0.499880i	$0.833377\pi$
$492$		0			0
$493$	25.2455			1.13700
$494$		0			0
$495$	0.403280	−	0.403280i	0.0181261	−	0.0181261i
$496$		0			0
$497$		−	8.80850i		−	0.395115i
$498$		0			0
$499$	−22.8653	+	22.8653i	−1.02359	+	1.02359i	−0.0238770	+	0.999715i	$0.507601\pi$
$499$	−22.8653	+	22.8653i	−1.02359	+	1.02359i	−0.999715	+	0.0238770i	$0.992399\pi$
$500$		0			0
$501$		−	2.02746i		−	0.0905802i
$502$		0			0
$503$	−27.1861	+	27.1861i	−1.21217	+	1.21217i	−0.241853	+	0.970313i	$0.577755\pi$
$503$	−27.1861	+	27.1861i	−1.21217	+	1.21217i	−0.970313	+	0.241853i	$0.922245\pi$
$504$		0			0
$505$	33.2820	−	33.2820i	1.48103	−	1.48103i
$506$		0			0
$507$	2.01262	+	2.01262i	0.0893835	+	0.0893835i
$508$		0			0
$509$	2.86448	+	2.86448i	0.126966	+	0.126966i	0.767734	−	0.640768i	$-0.221384\pi$
$509$	2.86448	+	2.86448i	0.126966	+	0.126966i	−0.640768	+	0.767734i	$0.721384\pi$
$510$		0			0
$511$	−9.43767	−	9.43767i	−0.417498	−	0.417498i
$512$		0			0
$513$			12.4817i			0.551081i
$514$		0			0
$515$	−61.2994			−2.70118
$516$		0			0
$517$	0.379695			0.0166990
$518$		0			0
$519$	0.777427	+	0.777427i	0.0341253	+	0.0341253i
$520$		0			0
$521$	6.47356	−	6.47356i	0.283612	−	0.283612i	−0.550936	−	0.834548i	$-0.685729\pi$
$521$	6.47356	−	6.47356i	0.283612	−	0.283612i	0.834548	+	0.550936i	$0.185729\pi$
$522$		0			0
$523$	5.07244			0.221802			0.110901	−	0.993831i	$-0.464626\pi$
$523$	5.07244			0.221802			0.110901	+	0.993831i	$0.464626\pi$
$524$		0			0
$525$		−	1.33219i		−	0.0581416i
$526$		0			0
$527$	−14.4984	−	14.4984i	−0.631560	−	0.631560i
$528$		0			0
$529$	−22.3906			−0.973503
$530$		0			0
$531$		−	17.1101i		−	0.742515i
$532$		0			0
$533$	−30.5369	−	4.29208i	−1.32270	−	0.185910i
$534$		0			0
$535$			6.11101i			0.264202i
$536$		0			0
$537$	−4.63217			−0.199893
$538$		0			0
$539$	0.0441522	+	0.0441522i	0.00190177	+	0.00190177i
$540$		0			0
$541$			23.3720i			1.00484i	0.864623	+	0.502421i	$0.167557\pi$
$541$			23.3720i			1.00484i	−0.864623	+	0.502421i	$0.832443\pi$
$542$		0			0
$543$	4.36243			0.187210
$544$		0			0
$545$	12.7782	−	12.7782i	0.547356	−	0.547356i
$546$		0			0
$547$	4.86406	+	4.86406i	0.207972	+	0.207972i	0.803405	−	0.595433i	$-0.203019\pi$
$547$	4.86406	+	4.86406i	0.207972	+	0.207972i	−0.595433	+	0.803405i	$0.703019\pi$
$548$		0			0
$549$	−25.6538			−1.09488
$550$		0			0
$551$	−45.3083			−1.93020
$552$		0			0
$553$			8.18181i			0.347926i
$554$		0			0
$555$	0.926264	+	0.926264i	0.0393177	+	0.0393177i
$556$		0			0
$557$	−3.76253	−	3.76253i	−0.159424	−	0.159424i	0.622888	−	0.782311i	$-0.285959\pi$
$557$	−3.76253	−	3.76253i	−0.159424	−	0.159424i	−0.782311	+	0.622888i	$0.785959\pi$
$558$		0			0
$559$	−8.24315	−	8.24315i	−0.348648	−	0.348648i
$560$		0			0
$561$	0.0518516	−	0.0518516i	0.00218918	−	0.00218918i
$562$		0			0
$563$	−14.0660	+	14.0660i	−0.592809	+	0.592809i	−0.938389	−	0.345580i	$-0.887682\pi$
$563$	−14.0660	+	14.0660i	−0.592809	+	0.592809i	0.345580	+	0.938389i	$0.387682\pi$
$564$		0			0
$565$			19.7324i			0.830150i
$566$		0			0
$567$	−5.87207	+	5.87207i	−0.246604	+	0.246604i
$568$		0			0
$569$		−	15.8567i		−	0.664747i	−0.943148	−	0.332374i	$-0.892151\pi$
$569$		−	15.8567i		−	0.664747i	0.943148	−	0.332374i	$-0.107849\pi$
$570$		0			0
$571$	−5.86553	+	5.86553i	−0.245465	+	0.245465i	−0.819106	−	0.573642i	$-0.805530\pi$
$571$	−5.86553	+	5.86553i	−0.245465	+	0.245465i	0.573642	+	0.819106i	$0.305530\pi$
$572$		0			0
$573$	−4.29338			−0.179359
$574$		0			0
$575$	3.72448			0.155322
$576$		0			0
$577$	14.9767	−	14.9767i	0.623489	−	0.623489i	−0.322933	−	0.946422i	$-0.604669\pi$
$577$	14.9767	−	14.9767i	0.623489	−	0.623489i	0.946422	+	0.322933i	$0.104669\pi$
$578$		0			0
$579$			5.76766i			0.239696i
$580$		0			0
$581$	−5.10361	+	5.10361i	−0.211733	+	0.211733i
$582$		0			0
$583$		−	0.360196i		−	0.0149178i
$584$		0			0
$585$	31.1043	−	31.1043i	1.28600	−	1.28600i
$586$		0			0
$587$	17.3988	−	17.3988i	0.718123	−	0.718123i	−0.250097	−	0.968221i	$-0.580463\pi$
$587$	17.3988	−	17.3988i	0.718123	−	0.718123i	0.968221	+	0.250097i	$0.0804626\pi$
$588$		0			0
$589$	26.0204	+	26.0204i	1.07215	+	1.07215i
$590$		0			0
$591$	5.09898	+	5.09898i	0.209744	+	0.209744i
$592$		0			0
$593$	26.0399	+	26.0399i	1.06933	+	1.06933i	0.997410	+	0.0719204i	$0.0229128\pi$
$593$	26.0399	+	26.0399i	1.06933	+	1.06933i	0.0719204	+	0.997410i	$0.477087\pi$
$594$		0			0
$595$			13.1467i			0.538964i
$596$		0			0
$597$	−6.49072			−0.265647
$598$		0			0
$599$	32.2062			1.31591			0.657956	−	0.753057i	$-0.271421\pi$
$599$	32.2062			1.31591			0.657956	+	0.753057i	$0.271421\pi$
$600$		0			0
$601$	−5.54445	−	5.54445i	−0.226163	−	0.226163i	0.584925	−	0.811088i	$-0.301124\pi$
$601$	−5.54445	−	5.54445i	−0.226163	−	0.226163i	−0.811088	+	0.584925i	$0.801124\pi$
$602$		0			0
$603$	−22.8346	+	22.8346i	−0.929896	+	0.929896i
$604$		0			0
$605$	−34.3722			−1.39743
$606$		0			0
$607$			0.212677i			0.00863230i	0.999991	+	0.00431615i	$0.00137388\pi$
$607$			0.212677i			0.00863230i	−0.999991	+	0.00431615i	$0.998626\pi$
$608$		0			0
$609$	1.18517	+	1.18517i	0.0480255	+	0.0480255i
$610$		0			0
$611$	29.2852			1.18475
$612$		0			0
$613$			40.2498i			1.62568i	0.582490	+	0.812838i	$0.302079\pi$
$613$			40.2498i			1.62568i	−0.582490	+	0.812838i	$0.697921\pi$
$614$		0			0
$615$	0.777884	−	5.53443i	0.0313673	−	0.223170i
$616$		0			0
$617$		−	41.6968i		−	1.67865i	−0.543631	−	0.839324i	$-0.682951\pi$
$617$		−	41.6968i		−	1.67865i	0.543631	−	0.839324i	$-0.317049\pi$
$618$		0			0
$619$	−36.7221			−1.47599			−0.737993	−	0.674809i	$-0.764226\pi$
$619$	−36.7221			−1.47599			−0.737993	+	0.674809i	$0.764226\pi$
$620$		0			0
$621$	0.912800	+	0.912800i	0.0366294	+	0.0366294i
$622$		0			0
$623$			12.7503i			0.510828i
$624$		0			0
$625$	−26.0927			−1.04371
$626$		0			0
$627$	−0.0930585	+	0.0930585i	−0.00371640	+	0.00371640i
$628$		0			0
$629$	−4.46329	−	4.46329i	−0.177963	−	0.177963i
$630$		0			0
$631$	−9.01872			−0.359030			−0.179515	−	0.983755i	$-0.557453\pi$
$631$	−9.01872			−0.359030			−0.179515	+	0.983755i	$0.557453\pi$
$632$		0			0
$633$	3.62400			0.144041
$634$		0			0
$635$			31.5554i			1.25224i
$636$		0			0
$637$	3.40539	+	3.40539i	0.134926	+	0.134926i
$638$		0			0
$639$	18.2000	+	18.2000i	0.719982	+	0.719982i
$640$		0			0
$641$	27.3192	+	27.3192i	1.07904	+	1.07904i	0.996595	+	0.0824465i	$0.0262734\pi$
$641$	27.3192	+	27.3192i	1.07904	+	1.07904i	0.0824465	+	0.996595i	$0.473727\pi$
$642$		0			0
$643$	27.8634	−	27.8634i	1.09882	−	1.09882i	0.104275	−	0.994548i	$-0.466748\pi$
$643$	27.8634	−	27.8634i	1.09882	−	1.09882i	0.994548	−	0.104275i	$-0.0332524\pi$
$644$		0			0
$645$	1.49397	−	1.49397i	0.0588249	−	0.0588249i
$646$		0			0
$647$			24.6332i			0.968430i	0.874949	+	0.484215i	$0.160895\pi$
$647$			24.6332i			0.968430i	−0.874949	+	0.484215i	$0.839105\pi$
$648$		0			0
$649$	0.258536	−	0.258536i	0.0101484	−	0.0101484i
$650$		0			0
$651$		−	1.36128i		−	0.0533526i
$652$		0			0
$653$	6.70523	−	6.70523i	0.262396	−	0.262396i	−0.563631	−	0.826027i	$-0.690596\pi$
$653$	6.70523	−	6.70523i	0.262396	−	0.262396i	0.826027	+	0.563631i	$0.190596\pi$
$654$		0			0
$655$	−1.53550			−0.0599968
$656$		0			0
$657$	39.0000			1.52154
$658$		0			0
$659$	13.5120	−	13.5120i	0.526351	−	0.526351i	−0.393131	−	0.919482i	$-0.628608\pi$
$659$	13.5120	−	13.5120i	0.526351	−	0.526351i	0.919482	+	0.393131i	$0.128608\pi$
$660$		0			0
$661$			46.4896i			1.80823i	0.427285	+	0.904117i	$0.359470\pi$
$661$			46.4896i			1.80823i	−0.427285	+	0.904117i	$0.640530\pi$
$662$		0			0
$663$	3.99923	−	3.99923i	0.155317	−	0.155317i
$664$		0			0
$665$		−	23.5945i		−	0.914957i
$666$		0			0
$667$	−3.31344	+	3.31344i	−0.128297	+	0.128297i
$668$		0			0
$669$	2.10014	−	2.10014i	0.0811961	−	0.0811961i
$670$		0			0
$671$	−0.387633	−	0.387633i	−0.0149644	−	0.0149644i
$672$		0			0
$673$	7.17202	+	7.17202i	0.276461	+	0.276461i	0.831695	−	0.555233i	$-0.187371\pi$
$673$	7.17202	+	7.17202i	0.276461	+	0.276461i	−0.555233	+	0.831695i	$0.687371\pi$
$674$		0			0
$675$	5.57856	+	5.57856i	0.214719	+	0.214719i
$676$		0			0
$677$		−	17.3396i		−	0.666415i	−0.942854	−	0.333208i	$-0.891869\pi$
$677$		−	17.3396i		−	0.666415i	0.942854	−	0.333208i	$-0.108131\pi$
$678$		0			0
$679$	15.5853			0.598108
$680$		0			0
$681$	0.0716649			0.00274621
$682$		0			0
$683$	9.30935	+	9.30935i	0.356212	+	0.356212i	0.862415	−	0.506202i	$-0.168951\pi$
$683$	9.30935	+	9.30935i	0.356212	+	0.356212i	−0.506202	+	0.862415i	$0.668951\pi$
$684$		0			0
$685$	−37.0135	+	37.0135i	−1.41421	+	1.41421i
$686$		0			0
$687$	−5.87679			−0.224213
$688$		0			0
$689$		−	27.7813i		−	1.05838i
$690$		0			0
$691$	−22.1097	−	22.1097i	−0.841094	−	0.841094i	0.147908	−	0.989001i	$-0.452746\pi$
$691$	−22.1097	−	22.1097i	−0.841094	−	0.841094i	−0.989001	+	0.147908i	$0.952746\pi$
$692$		0			0
$693$	−0.182454			−0.00693084
$694$		0			0
$695$			62.5506i			2.37268i
$696$		0			0
$697$	−3.74831	+	26.6682i	−0.141977	+	1.01013i
$698$		0			0
$699$			5.45775i			0.206431i
$700$		0			0
$701$	−7.47646			−0.282382			−0.141191	−	0.989982i	$-0.545093\pi$
$701$	−7.47646			−0.282382			−0.141191	+	0.989982i	$0.545093\pi$
$702$		0			0
$703$	8.01030	+	8.01030i	0.302114	+	0.302114i
$704$		0			0
$705$			5.30757i			0.199895i
$706$		0			0
$707$	−15.0576			−0.566299
$708$		0			0
$709$	1.87895	−	1.87895i	0.0705656	−	0.0705656i	−0.670943	−	0.741509i	$-0.734111\pi$
$709$	1.87895	−	1.87895i	0.0705656	−	0.0705656i	0.741509	+	0.670943i	$0.234111\pi$
$710$		0			0
$711$	−16.9052	−	16.9052i	−0.633993	−	0.633993i
$712$		0			0
$713$	3.80579			0.142528
$714$		0			0
$715$	0.939978			0.0351532
$716$		0			0
$717$			0.489748i			0.0182900i
$718$		0			0
$719$	−33.9733	−	33.9733i	−1.26699	−	1.26699i	−0.947636	−	0.319353i	$-0.896534\pi$
$719$	−33.9733	−	33.9733i	−1.26699	−	1.26699i	−0.319353	−	0.947636i	$-0.603466\pi$
$720$		0			0
$721$	13.8667	+	13.8667i	0.516422	+	0.516422i
$722$		0			0
$723$	−1.00942	−	1.00942i	−0.0375409	−	0.0375409i
$724$		0			0
$725$	−20.2501	+	20.2501i	−0.752068	+	0.752068i
$726$		0			0
$727$	−25.5286	+	25.5286i	−0.946802	+	0.946802i	−0.998655	−	0.0518532i	$-0.983487\pi$
$727$	−25.5286	+	25.5286i	−0.946802	+	0.946802i	0.0518532	+	0.998655i	$0.483487\pi$
$728$		0			0
$729$		−	22.8804i		−	0.847422i
$730$		0			0
$731$	−7.19881	+	7.19881i	−0.266258	+	0.266258i
$732$		0			0
$733$			25.3586i			0.936639i	0.883559	+	0.468320i	$0.155140\pi$
$733$			25.3586i			0.936639i	−0.883559	+	0.468320i	$0.844860\pi$
$734$		0			0
$735$	−0.617183	+	0.617183i	−0.0227651	+	0.0227651i
$736$		0			0
$737$	−0.690067			−0.0254189
$738$		0			0
$739$	30.2470			1.11265			0.556327	−	0.830964i	$-0.312210\pi$
$739$	30.2470			1.11265			0.556327	+	0.830964i	$0.312210\pi$
$740$		0			0
$741$	−7.17744	+	7.17744i	−0.263670	+	0.263670i
$742$		0			0
$743$			40.3795i			1.48138i	0.671848	+	0.740689i	$0.265501\pi$
$743$			40.3795i			1.48138i	−0.671848	+	0.740689i	$0.734499\pi$
$744$		0			0
$745$	−12.7571	+	12.7571i	−0.467383	+	0.467383i
$746$		0			0
$747$		−	21.0900i		−	0.771644i
$748$		0			0
$749$	1.38239	−	1.38239i	0.0505113	−	0.0505113i
$750$		0			0
$751$	−22.1052	+	22.1052i	−0.806628	+	0.806628i	−0.984122	−	0.177494i	$-0.943201\pi$
$751$	−22.1052	+	22.1052i	−0.806628	+	0.806628i	0.177494	+	0.984122i	$0.443201\pi$
$752$		0			0
$753$	−1.25141	−	1.25141i	−0.0456039	−	0.0456039i
$754$		0			0
$755$	20.4032	+	20.4032i	0.742549	+	0.742549i
$756$		0			0
$757$	−2.38191	−	2.38191i	−0.0865719	−	0.0865719i	0.662495	−	0.749067i	$-0.269498\pi$
$757$	−2.38191	−	2.38191i	−0.0865719	−	0.0865719i	−0.749067	+	0.662495i	$0.769498\pi$
$758$		0			0
$759$			0.0136109i			0.000494045i
$760$		0			0
$761$	−22.9273			−0.831114			−0.415557	−	0.909567i	$-0.636413\pi$
$761$	−22.9273			−0.831114			−0.415557	+	0.909567i	$0.636413\pi$
$762$		0			0
$763$	−5.78115			−0.209292
$764$		0			0
$765$	−27.1636	−	27.1636i	−0.982103	−	0.982103i
$766$		0			0
$767$	19.9404	−	19.9404i	0.720007	−	0.720007i
$768$		0			0
$769$	−6.07809			−0.219182			−0.109591	−	0.993977i	$-0.534954\pi$
$769$	−6.07809			−0.219182			−0.109591	+	0.993977i	$0.534954\pi$
$770$		0			0
$771$			7.17149i			0.258275i
$772$		0			0
$773$	−32.7106	−	32.7106i	−1.17652	−	1.17652i	−0.980625	−	0.195894i	$-0.937239\pi$
$773$	−32.7106	−	32.7106i	−1.17652	−	1.17652i	−0.195894	−	0.980625i	$-0.562761\pi$
$774$		0			0
$775$	23.2590			0.835489
$776$		0			0
$777$		−	0.419065i		−	0.0150339i
$778$		0			0
$779$	6.72711	−	47.8616i	0.241024	−	1.71482i
$780$		0			0
$781$			0.550009i			0.0196809i
$782$		0			0
$783$	−9.92582			−0.354720
$784$		0			0
$785$	11.5562	+	11.5562i	0.412459	+	0.412459i
$786$		0			0
$787$			23.5774i			0.840442i	0.907422	+	0.420221i	$0.138047\pi$
$787$			23.5774i			0.840442i	−0.907422	+	0.420221i	$0.861953\pi$
$788$		0			0
$789$	3.39383			0.120823
$790$		0			0
$791$	4.46372	−	4.46372i	0.158712	−	0.158712i
$792$		0			0
$793$	−29.8975	−	29.8975i	−1.06169	−	1.06169i
$794$		0			0
$795$	5.03501			0.178574
$796$		0			0
$797$	5.77084			0.204414			0.102207	−	0.994763i	$-0.467410\pi$
$797$	5.77084			0.204414			0.102207	+	0.994763i	$0.467410\pi$
$798$		0			0
$799$		−	25.5750i		−	0.904779i
$800$		0			0
$801$	−26.3444	−	26.3444i	−0.930835	−	0.930835i
$802$		0			0
$803$	0.589295	+	0.589295i	0.0207958	+	0.0207958i
$804$		0			0
$805$	−1.72549	−	1.72549i	−0.0608156	−	0.0608156i
$806$		0			0
$807$	0.493592	−	0.493592i	0.0173753	−	0.0173753i
$808$		0			0
$809$	21.8270	−	21.8270i	0.767398	−	0.767398i	−0.210250	−	0.977648i	$-0.567428\pi$
$809$	21.8270	−	21.8270i	0.767398	−	0.767398i	0.977648	+	0.210250i	$0.0674278\pi$
$810$		0			0
$811$			7.60631i			0.267094i	0.991042	+	0.133547i	$0.0426367\pi$
$811$			7.60631i			0.267094i	−0.991042	+	0.133547i	$0.957363\pi$
$812$		0			0
$813$	4.14161	−	4.14161i	0.145253	−	0.145253i
$814$		0			0
$815$		−	61.4374i		−	2.15206i
$816$		0			0
$817$	12.9198	−	12.9198i	0.452005	−	0.452005i
$818$		0			0
$819$	−14.0723			−0.491727
$820$		0			0
$821$	5.66749			0.197797			0.0988983	−	0.995098i	$-0.468468\pi$
$821$	5.66749			0.197797			0.0988983	+	0.995098i	$0.468468\pi$
$822$		0			0
$823$	5.33364	−	5.33364i	0.185919	−	0.185919i	−0.608010	−	0.793929i	$-0.708032\pi$
$823$	5.33364	−	5.33364i	0.185919	−	0.185919i	0.793929	+	0.608010i	$0.208032\pi$
$824$		0			0
$825$			0.0831829i			0.00289606i
$826$		0			0
$827$	37.4764	−	37.4764i	1.30318	−	1.30318i	0.376949	−	0.926234i	$-0.376973\pi$
$827$	37.4764	−	37.4764i	1.30318	−	1.30318i	0.926234	−	0.376949i	$-0.123027\pi$
$828$		0			0
$829$		−	24.4575i		−	0.849444i	−0.905324	−	0.424722i	$-0.860372\pi$
$829$		−	24.4575i		−	0.849444i	0.905324	−	0.424722i	$-0.139628\pi$
$830$		0			0
$831$	−0.305595	+	0.305595i	−0.0106010	+	0.0106010i
$832$		0			0
$833$	2.97395	−	2.97395i	0.103041	−	0.103041i
$834$		0			0
$835$	−16.0489	−	16.0489i	−0.555396	−	0.555396i
$836$		0			0
$837$	5.70035	+	5.70035i	0.197033	+	0.197033i
$838$		0			0
$839$	−40.8896	−	40.8896i	−1.41167	−	1.41167i	−0.748248	−	0.663419i	$-0.769105\pi$
$839$	−40.8896	−	40.8896i	−1.41167	−	1.41167i	−0.663419	−	0.748248i	$-0.730895\pi$
$840$		0			0
$841$		−	7.03050i		−	0.242431i
$842$		0			0
$843$	0.226811			0.00781178
$844$		0			0
$845$	31.8629			1.09612
$846$		0			0
$847$	7.77542	+	7.77542i	0.267167	+	0.267167i
$848$		0			0
$849$	−4.23155	+	4.23155i	−0.145226	+	0.145226i
$850$		0			0
$851$	1.17160			0.0401620
$852$		0			0
$853$		−	24.3034i		−	0.832134i	−0.909334	−	0.416067i	$-0.863408\pi$
$853$		−	24.3034i		−	0.832134i	0.909334	−	0.416067i	$-0.136592\pi$
$854$		0			0
$855$	48.7508	+	48.7508i	1.66724	+	1.66724i
$856$		0			0
$857$	33.3674			1.13981			0.569905	−	0.821711i	$-0.306980\pi$
$857$	33.3674			1.13981			0.569905	+	0.821711i	$0.306980\pi$
$858$		0			0
$859$		−	9.59218i		−	0.327281i	−0.986520	−	0.163640i	$-0.947676\pi$
$859$		−	9.59218i		−	0.327281i	0.986520	−	0.163640i	$-0.0523237\pi$
$860$		0			0
$861$	−1.42792	+	1.07599i	−0.0486635	+	0.0366696i
$862$		0			0
$863$		−	9.45642i		−	0.321900i	−0.986963	−	0.160950i	$-0.948544\pi$
$863$		−	9.45642i		−	0.321900i	0.986963	−	0.160950i	$-0.0514558\pi$
$864$		0			0
$865$	12.3079			0.418480
$866$		0			0
$867$	−0.136000	−	0.136000i	−0.00461881	−	0.00461881i
$868$		0			0
$869$		−	0.510878i		−	0.0173303i
$870$		0			0
$871$	−53.2237			−1.80342
$872$		0			0
$873$	−32.2021	+	32.2021i	−1.08988	+	1.08988i
$874$		0			0
$875$	0.506243	+	0.506243i	0.0171141	+	0.0171141i
$876$		0			0
$877$	27.7642			0.937531			0.468766	−	0.883323i	$-0.344699\pi$
$877$	27.7642			0.937531			0.468766	+	0.883323i	$0.344699\pi$
$878$		0			0
$879$	−1.05160			−0.0354696
$880$		0			0
$881$		−	11.5441i		−	0.388930i	−0.980909	−	0.194465i	$-0.937703\pi$
$881$		−	11.5441i		−	0.388930i	0.980909	−	0.194465i	$-0.0622971\pi$
$882$		0			0
$883$	−11.0676	−	11.0676i	−0.372453	−	0.372453i	0.495917	−	0.868370i	$-0.334832\pi$
$883$	−11.0676	−	11.0676i	−0.372453	−	0.372453i	−0.868370	+	0.495917i	$0.834832\pi$
$884$		0			0
$885$	3.61395	+	3.61395i	0.121482	+	0.121482i
$886$		0			0
$887$	31.9764	+	31.9764i	1.07366	+	1.07366i	0.997062	+	0.0766007i	$0.0244067\pi$
$887$	31.9764	+	31.9764i	1.07366	+	1.07366i	0.0766007	+	0.997062i	$0.475593\pi$
$888$		0			0
$889$	7.13822	−	7.13822i	0.239408	−	0.239408i
$890$		0			0
$891$	0.366656	−	0.366656i	0.0122834	−	0.0122834i
$892$		0			0
$893$			45.8997i			1.53598i
$894$		0			0
$895$	−36.6672	+	36.6672i	−1.22565	+	1.22565i
$896$		0			0
$897$			1.04979i			0.0350514i
$898$		0			0
$899$	−20.6922	+	20.6922i	−0.690122	+	0.690122i
$900$		0			0
$901$	−24.2617			−0.808274
$902$		0			0
$903$	−0.675907			−0.0224928
$904$		0			0
$905$	34.5320	−	34.5320i	1.14788	−	1.14788i
$906$		0			0
$907$		−	12.2822i		−	0.407825i	−0.978989	−	0.203912i	$-0.934634\pi$
$907$		−	12.2822i		−	0.407825i	0.978989	−	0.203912i	$-0.0653658\pi$
$908$		0			0
$909$	31.1118	−	31.1118i	1.03191	−	1.03191i
$910$		0			0
$911$			18.3599i			0.608291i	0.952626	+	0.304146i	$0.0983709\pi$
$911$			18.3599i			0.608291i	−0.952626	+	0.304146i	$0.901629\pi$
$912$		0			0
$913$	0.318673	−	0.318673i	0.0105465	−	0.0105465i
$914$		0			0
$915$	5.41853	−	5.41853i	0.179131	−	0.179131i
$916$		0			0
$917$	0.347348	+	0.347348i	0.0114704	+	0.0114704i
$918$		0			0
$919$	10.2017	+	10.2017i	0.336524	+	0.336524i	0.855057	−	0.518534i	$-0.173522\pi$
$919$	10.2017	+	10.2017i	0.336524	+	0.336524i	−0.518534	+	0.855057i	$0.673522\pi$
$920$		0			0
$921$	−2.95603	−	2.95603i	−0.0974046	−	0.0974046i
$922$		0			0
$923$			42.4213i			1.39631i
$924$		0			0
$925$	7.16023			0.235427
$926$		0			0
$927$	−57.3024			−1.88206
$928$		0			0
$929$	−35.2565	−	35.2565i	−1.15673	−	1.15673i	−0.985175	−	0.171555i	$-0.945121\pi$
$929$	−35.2565	−	35.2565i	−1.15673	−	1.15673i	−0.171555	−	0.985175i	$-0.554879\pi$
$930$		0			0
$931$	−5.33738	+	5.33738i	−0.174926	+	0.174926i
$932$		0			0
$933$	−8.84555			−0.289590
$934$		0			0
$935$		−	0.820891i		−	0.0268460i
$936$		0			0
$937$	−27.0764	−	27.0764i	−0.884548	−	0.884548i	0.109445	−	0.993993i	$-0.465093\pi$
$937$	−27.0764	−	27.0764i	−0.884548	−	0.884548i	−0.993993	+	0.109445i	$0.965093\pi$
$938$		0			0
$939$	−6.55423			−0.213889
$940$		0			0
$941$		−	53.8999i		−	1.75709i	−0.477664	−	0.878543i	$-0.658516\pi$
$941$		−	53.8999i		−	1.75709i	0.477664	−	0.878543i	$-0.341484\pi$
$942$		0			0
$943$	−3.00820	−	3.99213i	−0.0979606	−	0.130001i
$944$		0			0
$945$		−	5.16892i		−	0.168145i
$946$		0			0
$947$	40.7842			1.32531			0.662654	−	0.748925i	$-0.269430\pi$
$947$	40.7842			1.32531			0.662654	+	0.748925i	$0.269430\pi$
$948$		0			0
$949$	45.4513	+	45.4513i	1.47541	+	1.47541i
$950$		0			0
$951$			1.25293i			0.0406292i
$952$		0			0
$953$	30.3796			0.984092			0.492046	−	0.870569i	$-0.336249\pi$
$953$	30.3796			0.984092			0.492046	+	0.870569i	$0.336249\pi$
$954$		0			0
$955$	−33.9854	+	33.9854i	−1.09974	+	1.09974i
$956$		0			0
$957$	−0.0740028	−	0.0740028i	−0.00239217	−	0.00239217i
$958$		0			0
$959$	16.7458			0.540750
$960$		0			0
$961$	−7.23316			−0.233328
$962$		0			0
$963$			5.71254i			0.184084i
$964$		0			0
$965$	45.6555	+	45.6555i	1.46970	+	1.46970i
$966$		0			0
$967$	17.0024	+	17.0024i	0.546761	+	0.546761i	0.925503	−	0.378741i	$-0.123643\pi$
$967$	17.0024	+	17.0024i	0.546761	+	0.546761i	−0.378741	+	0.925503i	$0.623643\pi$
$968$		0			0
$969$	6.26812	+	6.26812i	0.201361	+	0.201361i
$970$		0			0
$971$	12.7973	−	12.7973i	0.410685	−	0.410685i	−0.471292	−	0.881977i	$-0.656212\pi$
$971$	12.7973	−	12.7973i	0.410685	−	0.410685i	0.881977	+	0.471292i	$0.156212\pi$
$972$		0			0
$973$	14.1497	−	14.1497i	0.453619	−	0.453619i
$974$		0			0
$975$			6.41576i			0.205469i
$976$		0			0
$977$	43.6468	−	43.6468i	1.39639	−	1.39639i	0.586267	−	0.810118i	$-0.300597\pi$
$977$	43.6468	−	43.6468i	1.39639	−	1.39639i	0.810118	−	0.586267i	$-0.199403\pi$
$978$		0			0
$979$		−	0.796135i		−	0.0254446i
$980$		0			0
$981$	11.9450	−	11.9450i	0.381373	−	0.381373i
$982$		0			0
$983$	27.3898			0.873598			0.436799	−	0.899559i	$-0.356112\pi$
$983$	27.3898			0.873598			0.436799	+	0.899559i	$0.356112\pi$
$984$		0			0
$985$	80.7247			2.57210
$986$		0			0
$987$	1.20064	−	1.20064i	0.0382167	−	0.0382167i
$988$		0			0
$989$		−	1.88967i		−	0.0600880i
$990$		0			0
$991$	−34.8514	+	34.8514i	−1.10709	+	1.10709i	−0.113559	+	0.993531i	$0.536225\pi$
$991$	−34.8514	+	34.8514i	−1.10709	+	1.10709i	−0.993531	+	0.113559i	$0.963775\pi$
$992$		0			0
$993$			0.170955i			0.00542509i
$994$		0			0
$995$	−51.3790	+	51.3790i	−1.62883	+	1.62883i
$996$		0			0
$997$	21.5574	−	21.5574i	0.682729	−	0.682729i	−0.277886	−	0.960614i	$-0.589634\pi$
$997$	21.5574	−	21.5574i	0.682729	−	0.682729i	0.960614	+	0.277886i	$0.0896336\pi$
$998$		0			0
$999$	1.75484	+	1.75484i	0.0555206	+	0.0555206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.9	yes	36
41.9	even	4	inner	1148.2.k.b.337.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.9	✓	36	41.9	even	4	inner
1148.2.k.b.729.9	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.197445 + 0.197445i) q^{3} +3.12585i q^{5} +(0.707107 - 0.707107i) q^{7} +2.92203i q^{9} +O(q^{10})\)	\(q+(-0.197445 + 0.197445i) q^{3} +3.12585i q^{5} +(0.707107 - 0.707107i) q^{7} +2.92203i q^{9} +(-0.0441522 + 0.0441522i) q^{11} +(-3.40539 + 3.40539i) q^{13} +(-0.617183 - 0.617183i) q^{15} +(2.97395 + 2.97395i) q^{17} +(-5.33738 - 5.33738i) q^{19} +0.279229i q^{21} -0.780656 q^{23} -4.77096 q^{25} +(-1.16927 - 1.16927i) q^{27} +(4.24444 - 4.24444i) q^{29} -4.87513 q^{31} -0.0174352i q^{33} +(2.21031 + 2.21031i) q^{35} -1.50079 q^{37} -1.34475i q^{39} +(3.85343 + 5.11381i) q^{41} +2.42062i q^{43} -9.13384 q^{45} +(-4.29984 - 4.29984i) q^{47} -1.00000i q^{49} -1.17438 q^{51} +(-4.07903 + 4.07903i) q^{53} +(-0.138013 - 0.138013i) q^{55} +2.10767 q^{57} -5.85555 q^{59} +8.77946i q^{61} +(2.06619 + 2.06619i) q^{63} +(-10.6447 - 10.6447i) q^{65} +(7.81463 + 7.81463i) q^{67} +(0.154136 - 0.154136i) q^{69} +(6.22855 - 6.22855i) q^{71} -13.3469i q^{73} +(0.942001 - 0.942001i) q^{75} +0.0624407i q^{77} +(-5.78541 + 5.78541i) q^{79} -8.30436 q^{81} -7.21760 q^{83} +(-9.29615 + 9.29615i) q^{85} +1.67608i q^{87} +(-9.01579 + 9.01579i) q^{89} +4.81595i q^{91} +(0.962567 - 0.962567i) q^{93} +(16.6839 - 16.6839i) q^{95} +(11.0205 + 11.0205i) q^{97} +(-0.129014 - 0.129014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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