LMFDB - Embedded newform 1815.2.c.k.364.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, 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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.15
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.k.364.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.488299i q^{2} -1.00000i q^{3} +1.76156 q^{4} +(2.10928 + 0.742259i) q^{5} +0.488299 q^{6} +5.10895i q^{7} +1.83677i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.488299i q^{2} -1.00000i q^{3} +1.76156 q^{4} +(2.10928 + 0.742259i) q^{5} +0.488299 q^{6} +5.10895i q^{7} +1.83677i q^{8} -1.00000 q^{9} +(-0.362444 + 1.02996i) q^{10} -1.76156i q^{12} -1.81774i q^{13} -2.49469 q^{14} +(0.742259 - 2.10928i) q^{15} +2.62624 q^{16} +0.639966i q^{17} -0.488299i q^{18} -4.39788 q^{19} +(3.71563 + 1.30754i) q^{20} +5.10895 q^{21} -4.37977i q^{23} +1.83677 q^{24} +(3.89810 + 3.13126i) q^{25} +0.887599 q^{26} +1.00000i q^{27} +8.99974i q^{28} +7.56018 q^{29} +(1.02996 + 0.362444i) q^{30} +2.20501 q^{31} +4.95592i q^{32} -0.312494 q^{34} +(-3.79216 + 10.7762i) q^{35} -1.76156 q^{36} +5.97194i q^{37} -2.14748i q^{38} -1.81774 q^{39} +(-1.36336 + 3.87425i) q^{40} +2.23182 q^{41} +2.49469i q^{42} -3.38068i q^{43} +(-2.10928 - 0.742259i) q^{45} +2.13864 q^{46} -1.51581i q^{47} -2.62624i q^{48} -19.1013 q^{49} +(-1.52899 + 1.90344i) q^{50} +0.639966 q^{51} -3.20206i q^{52} +9.17695i q^{53} -0.488299 q^{54} -9.38395 q^{56} +4.39788i q^{57} +3.69163i q^{58} -5.37174 q^{59} +(1.30754 - 3.71563i) q^{60} -7.26768 q^{61} +1.07670i q^{62} -5.10895i q^{63} +2.83250 q^{64} +(1.34923 - 3.83411i) q^{65} -7.25598i q^{67} +1.12734i q^{68} -4.37977 q^{69} +(-5.26200 - 1.85171i) q^{70} +5.50864 q^{71} -1.83677i q^{72} +7.14322i q^{73} -2.91609 q^{74} +(3.13126 - 3.89810i) q^{75} -7.74714 q^{76} -0.887599i q^{78} +1.90516 q^{79} +(5.53946 + 1.94935i) q^{80} +1.00000 q^{81} +1.08979i q^{82} -0.161902i q^{83} +8.99974 q^{84} +(-0.475021 + 1.34987i) q^{85} +1.65078 q^{86} -7.56018i q^{87} +1.19539 q^{89} +(0.362444 - 1.02996i) q^{90} +9.28673 q^{91} -7.71525i q^{92} -2.20501i q^{93} +0.740167 q^{94} +(-9.27634 - 3.26436i) q^{95} +4.95592 q^{96} +14.2823i q^{97} -9.32716i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			0.488299i			0.345279i	0.984985	+	0.172640i	$0.0552296\pi$
$2$			0.488299i			0.345279i	−0.984985	+	0.172640i	$0.944770\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.76156			0.880782
$5$	2.10928	+	0.742259i	0.943298	+	0.331948i
$5$	2.10928	+	0.742259i	0.943298	+	0.331948i
$6$	0.488299			0.199347
$7$			5.10895i			1.93100i	0.260403	+	0.965500i	$0.416145\pi$
$7$			5.10895i			1.93100i	−0.260403	+	0.965500i	$0.583855\pi$
$8$			1.83677i			0.649395i
$9$	−1.00000			−0.333333
$10$	−0.362444	+	1.02996i	−0.114615	+	0.325701i
$11$		0			0
$11$		0			0
$12$		−	1.76156i		−	0.508520i
$13$		−	1.81774i		−	0.504150i	−0.967708	−	0.252075i	$-0.918887\pi$
$13$		−	1.81774i		−	0.504150i	0.967708	−	0.252075i	$-0.0811130\pi$
$14$	−2.49469			−0.666735
$15$	0.742259	−	2.10928i	0.191651	−	0.544613i
$16$	2.62624			0.656559
$17$			0.639966i			0.155214i	0.996984	+	0.0776072i	$0.0247280\pi$
$17$			0.639966i			0.155214i	−0.996984	+	0.0776072i	$0.975272\pi$
$18$		−	0.488299i		−	0.115093i
$19$	−4.39788			−1.00894			−0.504471	−	0.863429i	$-0.668312\pi$
$19$	−4.39788			−1.00894			−0.504471	+	0.863429i	$0.668312\pi$
$20$	3.71563	+	1.30754i	0.830840	+	0.292374i
$21$	5.10895			1.11486
$22$		0			0
$23$		−	4.37977i		−	0.913246i	−0.889660	−	0.456623i	$-0.849059\pi$
$23$		−	4.37977i		−	0.913246i	0.889660	−	0.456623i	$-0.150941\pi$
$24$	1.83677			0.374929
$25$	3.89810	+	3.13126i	0.779620	+	0.626252i
$26$	0.887599			0.174073
$27$			1.00000i			0.192450i
$28$			8.99974i			1.70079i
$29$	7.56018			1.40389			0.701945	−	0.712231i	$-0.252315\pi$
$29$	7.56018			1.40389			0.701945	+	0.712231i	$0.252315\pi$
$30$	1.02996	+	0.362444i	0.188044	+	0.0661730i
$31$	2.20501			0.396032			0.198016	−	0.980199i	$-0.436550\pi$
$31$	2.20501			0.396032			0.198016	+	0.980199i	$0.436550\pi$
$32$			4.95592i			0.876092i
$33$		0			0
$34$	−0.312494			−0.0535924
$35$	−3.79216	+	10.7762i	−0.640993	+	1.82151i
$36$	−1.76156			−0.293594
$37$			5.97194i			0.981780i	0.871221	+	0.490890i	$0.163328\pi$
$37$			5.97194i			0.981780i	−0.871221	+	0.490890i	$0.836672\pi$
$38$		−	2.14748i		−	0.348367i
$39$	−1.81774			−0.291071
$40$	−1.36336	+	3.87425i	−0.215566	+	0.612573i
$41$	2.23182			0.348551			0.174276	−	0.984697i	$-0.444242\pi$
$41$	2.23182			0.348551			0.174276	+	0.984697i	$0.444242\pi$
$42$			2.49469i			0.384939i
$43$		−	3.38068i		−	0.515549i	−0.966205	−	0.257775i	$-0.917011\pi$
$43$		−	3.38068i		−	0.515549i	0.966205	−	0.257775i	$-0.0829892\pi$
$44$		0			0
$45$	−2.10928	−	0.742259i	−0.314433	−	0.110649i
$46$	2.13864			0.315325
$47$		−	1.51581i		−	0.221103i	−0.993870	−	0.110552i	$-0.964738\pi$
$47$		−	1.51581i		−	0.221103i	0.993870	−	0.110552i	$-0.0352617\pi$
$48$		−	2.62624i		−	0.379065i
$49$	−19.1013			−2.72876
$50$	−1.52899	+	1.90344i	−0.216232	+	0.269187i
$51$	0.639966			0.0896131
$52$		−	3.20206i		−	0.444046i
$53$			9.17695i			1.26055i	0.776372	+	0.630275i	$0.217058\pi$
$53$			9.17695i			1.26055i	−0.776372	+	0.630275i	$0.782942\pi$
$54$	−0.488299			−0.0664491
$55$		0			0
$56$	−9.38395			−1.25398
$57$			4.39788i			0.582513i
$58$			3.69163i			0.484734i
$59$	−5.37174			−0.699341			−0.349671	−	0.936873i	$-0.613706\pi$
$59$	−5.37174			−0.699341			−0.349671	+	0.936873i	$0.613706\pi$
$60$	1.30754	−	3.71563i	0.168802	−	0.479685i
$61$	−7.26768			−0.930531			−0.465266	−	0.885171i	$-0.654041\pi$
$61$	−7.26768			−0.930531			−0.465266	+	0.885171i	$0.654041\pi$
$62$			1.07670i			0.136742i
$63$		−	5.10895i		−	0.643667i
$64$	2.83250			0.354063
$65$	1.34923	−	3.83411i	0.167352	−	0.475563i
$66$		0			0
$67$		−	7.25598i		−	0.886459i	−0.896408	−	0.443230i	$-0.853833\pi$
$67$		−	7.25598i		−	0.886459i	0.896408	−	0.443230i	$-0.146167\pi$
$68$			1.12734i			0.136710i
$69$	−4.37977			−0.527263
$70$	−5.26200	−	1.85171i	−0.628929	−	0.221322i
$71$	5.50864			0.653756			0.326878	−	0.945067i	$-0.394003\pi$
$71$	5.50864			0.653756			0.326878	+	0.945067i	$0.394003\pi$
$72$		−	1.83677i		−	0.216465i
$73$			7.14322i			0.836051i	0.908435	+	0.418026i	$0.137278\pi$
$73$			7.14322i			0.836051i	−0.908435	+	0.418026i	$0.862722\pi$
$74$	−2.91609			−0.338988
$75$	3.13126	−	3.89810i	0.361567	−	0.450114i
$76$	−7.74714			−0.888658
$77$		0			0
$78$		−	0.887599i		−	0.100501i
$79$	1.90516			0.214347			0.107174	−	0.994240i	$-0.465820\pi$
$79$	1.90516			0.214347			0.107174	+	0.994240i	$0.465820\pi$
$80$	5.53946	+	1.94935i	0.619331	+	0.217944i
$81$	1.00000			0.111111
$82$			1.08979i			0.120348i
$83$		−	0.161902i		−	0.0177710i	−0.999961	−	0.00888551i	$-0.997172\pi$
$83$		−	0.161902i		−	0.0177710i	0.999961	−	0.00888551i	$-0.00282838\pi$
$84$	8.99974			0.981952
$85$	−0.475021	+	1.34987i	−0.0515232	+	0.146413i
$86$	1.65078			0.178009
$87$		−	7.56018i		−	0.810536i
$88$		0			0
$89$	1.19539			0.126711			0.0633554	−	0.997991i	$-0.479820\pi$
$89$	1.19539			0.126711			0.0633554	+	0.997991i	$0.479820\pi$
$90$	0.362444	−	1.02996i	0.0382050	−	0.108567i
$91$	9.28673			0.973514
$92$		−	7.71525i		−	0.804371i
$93$		−	2.20501i		−	0.228649i
$94$	0.740167			0.0763424
$95$	−9.27634	−	3.26436i	−0.951732	−	0.334917i
$96$	4.95592			0.505812
$97$			14.2823i			1.45015i	0.688672	+	0.725073i	$0.258194\pi$
$97$			14.2823i			1.45015i	−0.688672	+	0.725073i	$0.741806\pi$
$98$		−	9.32716i		−	0.942185i
$99$		0			0
$100$	6.86676	+	5.51592i	0.686676	+	0.551592i
$101$	4.29089			0.426960			0.213480	−	0.976947i	$-0.431520\pi$
$101$	4.29089			0.426960			0.213480	+	0.976947i	$0.431520\pi$
$102$			0.312494i			0.0309416i
$103$		−	9.49802i		−	0.935868i	−0.883763	−	0.467934i	$-0.844998\pi$
$103$		−	9.49802i		−	0.935868i	0.883763	−	0.467934i	$-0.155002\pi$
$104$	3.33876			0.327393
$105$	10.7762	+	3.79216i	1.05165	+	0.370077i
$106$	−4.48109			−0.435242
$107$		−	8.27470i		−	0.799945i	−0.916527	−	0.399973i	$-0.869020\pi$
$107$		−	8.27470i		−	0.799945i	0.916527	−	0.399973i	$-0.130980\pi$
$108$			1.76156i			0.169507i
$109$	−12.4980			−1.19709			−0.598546	−	0.801089i	$-0.704255\pi$
$109$	−12.4980			−1.19709			−0.598546	+	0.801089i	$0.704255\pi$
$110$		0			0
$111$	5.97194			0.566831
$112$			13.4173i			1.26782i
$113$			16.2096i			1.52487i	0.647065	+	0.762435i	$0.275996\pi$
$113$			16.2096i			1.52487i	−0.647065	+	0.762435i	$0.724004\pi$
$114$	−2.14748			−0.201130
$115$	3.25093	−	9.23816i	0.303151	−	0.861463i
$116$	13.3177			1.23652
$117$			1.81774i			0.168050i
$118$		−	2.62302i		−	0.241468i
$119$	−3.26955			−0.299719
$120$	3.87425	+	1.36336i	0.353669	+	0.124457i
$121$		0			0
$122$		−	3.54880i		−	0.321293i
$123$		−	2.23182i		−	0.201236i
$124$	3.88427			0.348817
$125$	5.89797	+	9.49810i	0.527530	+	0.849536i
$126$	2.49469			0.222245
$127$		−	9.88086i		−	0.876785i	−0.898784	−	0.438392i	$-0.855548\pi$
$127$		−	9.88086i		−	0.876785i	0.898784	−	0.438392i	$-0.144452\pi$
$128$			11.2950i			0.998342i
$129$	−3.38068			−0.297653
$130$	1.87219	+	0.658829i	0.164202	+	0.0577831i
$131$	12.7829			1.11685			0.558425	−	0.829555i	$-0.311406\pi$
$131$	12.7829			1.11685			0.558425	+	0.829555i	$0.311406\pi$
$132$		0			0
$133$		−	22.4685i		−	1.94827i
$134$	3.54309			0.306076
$135$	−0.742259	+	2.10928i	−0.0638835	+	0.181538i
$136$	−1.17547			−0.100796
$137$		−	19.0589i		−	1.62831i	−0.580645	−	0.814157i	$-0.697200\pi$
$137$		−	19.0589i		−	1.62831i	0.580645	−	0.814157i	$-0.302800\pi$
$138$		−	2.13864i		−	0.182053i
$139$	−11.7146			−0.993622			−0.496811	−	0.867859i	$-0.665496\pi$
$139$	−11.7146			−0.993622			−0.496811	+	0.867859i	$0.665496\pi$
$140$	−6.68014	+	18.9829i	−0.564575	+	1.60435i
$141$	−1.51581			−0.127654
$142$			2.68986i			0.225728i
$143$		0			0
$144$	−2.62624			−0.218853
$145$	15.9465	+	5.61161i	1.32429	+	0.466019i
$146$	−3.48803			−0.288671
$147$			19.1013i			1.57545i
$148$			10.5199i			0.864735i
$149$	7.45724			0.610921			0.305461	−	0.952205i	$-0.401190\pi$
$149$	7.45724			0.610921			0.305461	+	0.952205i	$0.401190\pi$
$150$	1.90344	+	1.52899i	0.155415	+	0.124842i
$151$	4.95905			0.403562			0.201781	−	0.979431i	$-0.435327\pi$
$151$	4.95905			0.403562			0.201781	+	0.979431i	$0.435327\pi$
$152$		−	8.07787i		−	0.655202i
$153$		−	0.639966i		−	0.0517382i
$154$		0			0
$155$	4.65098	+	1.63669i	0.373576	+	0.131462i
$156$	−3.20206			−0.256370
$157$		−	20.5916i		−	1.64339i	−0.569930	−	0.821693i	$-0.693030\pi$
$157$		−	20.5916i		−	1.64339i	0.569930	−	0.821693i	$-0.306970\pi$
$158$			0.930287i			0.0740096i
$159$	9.17695			0.727779
$160$	−3.67858	+	10.4534i	−0.290817	+	0.826415i
$161$	22.3760			1.76348
$162$			0.488299i			0.0383644i
$163$		−	7.22774i		−	0.566120i	−0.959102	−	0.283060i	$-0.908650\pi$
$163$		−	7.22774i		−	0.566120i	0.959102	−	0.283060i	$-0.0913496\pi$
$164$	3.93149			0.306998
$165$		0			0
$166$	0.0790564			0.00613597
$167$		−	18.3130i		−	1.41710i	−0.705660	−	0.708550i	$-0.749349\pi$
$167$		−	18.3130i		−	1.41710i	0.705660	−	0.708550i	$-0.250651\pi$
$168$			9.38395i			0.723987i
$169$	9.69583			0.745833
$170$	−0.659138	−	0.231952i	−0.0505535	−	0.0177899i
$171$	4.39788			0.336314
$172$		−	5.95529i		−	0.454087i
$173$		−	12.0157i		−	0.913536i	−0.889586	−	0.456768i	$-0.849007\pi$
$173$		−	12.0157i		−	0.913536i	0.889586	−	0.456768i	$-0.150993\pi$
$174$	3.69163			0.279862
$175$	−15.9974	+	19.9152i	−1.20929	+	1.50545i
$176$		0			0
$177$			5.37174i			0.403765i
$178$			0.583706i			0.0437506i
$179$	6.71004			0.501532			0.250766	−	0.968048i	$-0.419318\pi$
$179$	6.71004			0.501532			0.250766	+	0.968048i	$0.419318\pi$
$180$	−3.71563	−	1.30754i	−0.276947	−	0.0974581i
$181$	−11.3348			−0.842508			−0.421254	−	0.906943i	$-0.638410\pi$
$181$	−11.3348			−0.842508			−0.421254	+	0.906943i	$0.638410\pi$
$182$			4.53470i			0.336134i
$183$			7.26768i			0.537242i
$184$	8.04463			0.593058
$185$	−4.43273	+	12.5965i	−0.325900	+	0.926111i
$186$	1.07670			0.0789478
$187$		0			0
$188$		−	2.67019i		−	0.194744i
$189$	−5.10895			−0.371621
$190$	1.59399	−	4.52963i	0.115640	−	0.328614i
$191$	11.0864			0.802186			0.401093	−	0.916037i	$-0.368630\pi$
$191$	11.0864			0.802186			0.401093	+	0.916037i	$0.368630\pi$
$192$		−	2.83250i		−	0.204418i
$193$		−	1.19205i		−	0.0858056i	−0.999079	−	0.0429028i	$-0.986339\pi$
$193$		−	1.19205i		−	0.0858056i	0.999079	−	0.0429028i	$-0.0136606\pi$
$194$	−6.97402			−0.500705
$195$	−3.83411	−	1.34923i	−0.274567	−	0.0966206i
$196$	−33.6482			−2.40344
$197$			18.3551i			1.30775i	0.756604	+	0.653873i	$0.226857\pi$
$197$			18.3551i			1.30775i	−0.756604	+	0.653873i	$0.773143\pi$
$198$		0			0
$199$	−22.1761			−1.57202			−0.786011	−	0.618213i	$-0.787857\pi$
$199$	−22.1761			−1.57202			−0.786011	+	0.618213i	$0.787857\pi$
$200$	−5.75140	+	7.15991i	−0.406685	+	0.506282i
$201$	−7.25598			−0.511798
$202$			2.09524i			0.147420i
$203$			38.6246i			2.71091i
$204$	1.12734			0.0789296
$205$	4.70752	+	1.65659i	0.328787	+	0.115701i
$206$	4.63787			0.323136
$207$			4.37977i			0.304415i
$208$		−	4.77381i		−	0.331004i
$209$		0			0
$210$	−1.85171	+	5.26200i	−0.127780	+	0.363112i
$211$	−8.30729			−0.571897			−0.285949	−	0.958245i	$-0.592309\pi$
$211$	−8.30729			−0.571897			−0.285949	+	0.958245i	$0.592309\pi$
$212$			16.1658i			1.11027i
$213$		−	5.50864i		−	0.377446i
$214$	4.04052			0.276205
$215$	2.50934	−	7.13080i	0.171136	−	0.486316i
$216$	−1.83677			−0.124976
$217$			11.2653i			0.764737i
$218$		−	6.10276i		−	0.413331i
$219$	7.14322			0.482694
$220$		0			0
$221$	1.16329			0.0782514
$222$			2.91609i			0.195715i
$223$		−	16.5497i		−	1.10825i	−0.832434	−	0.554124i	$-0.813053\pi$
$223$		−	16.5497i		−	1.10825i	0.832434	−	0.554124i	$-0.186947\pi$
$224$	−25.3195			−1.69173
$225$	−3.89810	−	3.13126i	−0.259873	−	0.208751i
$226$	−7.91513			−0.526506
$227$			8.48300i			0.563036i	0.959556	+	0.281518i	$0.0908380\pi$
$227$			8.48300i			0.563036i	−0.959556	+	0.281518i	$0.909162\pi$
$228$			7.74714i			0.513067i
$229$	3.39892			0.224607			0.112303	−	0.993674i	$-0.464177\pi$
$229$	3.39892			0.224607			0.112303	+	0.993674i	$0.464177\pi$
$230$	4.51098	+	1.58742i	0.297445	+	0.104672i
$231$		0			0
$232$			13.8863i			0.911680i
$233$		−	15.7123i		−	1.02935i	−0.857386	−	0.514675i	$-0.827913\pi$
$233$		−	15.7123i		−	1.02935i	0.857386	−	0.514675i	$-0.172087\pi$
$234$	−0.887599			−0.0580242
$235$	1.12512	−	3.19726i	0.0733949	−	0.208566i
$236$	−9.46267			−0.615967
$237$		−	1.90516i		−	0.123753i
$238$		−	1.59652i		−	0.103487i
$239$	30.6972			1.98564			0.992819	−	0.119624i	$-0.0381689\pi$
$239$	30.6972			1.98564			0.992819	+	0.119624i	$0.0381689\pi$
$240$	1.94935	−	5.53946i	0.125830	−	0.357571i
$241$	−5.59097			−0.360146			−0.180073	−	0.983653i	$-0.557633\pi$
$241$	−5.59097			−0.360146			−0.180073	+	0.983653i	$0.557633\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−12.8025			−0.819595
$245$	−40.2900	−	14.1781i	−2.57403	−	0.905808i
$246$	1.08979			0.0694827
$247$			7.99419i			0.508658i
$248$			4.05009i			0.257181i
$249$	−0.161902			−0.0102601
$250$	−4.63791	+	2.87997i	−0.293327	+	0.182145i
$251$	18.7237			1.18183			0.590915	−	0.806734i	$-0.298767\pi$
$251$	18.7237			1.18183			0.590915	+	0.806734i	$0.298767\pi$
$252$		−	8.99974i		−	0.566930i
$253$		0			0
$254$	4.82481			0.302736
$255$	1.34987	+	0.475021i	0.0845318	+	0.0297469i
$256$	0.149694			0.00935585
$257$		−	4.98215i		−	0.310778i	−0.987853	−	0.155389i	$-0.950337\pi$
$257$		−	4.98215i		−	0.310778i	0.987853	−	0.155389i	$-0.0496631\pi$
$258$		−	1.65078i		−	0.102773i
$259$	−30.5103			−1.89582
$260$	2.37676	−	6.75404i	0.147400	−	0.418868i
$261$	−7.56018			−0.467963
$262$			6.24190i			0.385626i
$263$		−	20.0788i		−	1.23811i	−0.785347	−	0.619055i	$-0.787516\pi$
$263$		−	20.0788i		−	1.23811i	0.785347	−	0.619055i	$-0.212484\pi$
$264$		0			0
$265$	−6.81167	+	19.3567i	−0.418438	+	1.18907i
$266$	10.9713			0.672696
$267$		−	1.19539i		−	0.0731565i
$268$		−	12.7819i		−	0.780778i
$269$	9.53027			0.581071			0.290535	−	0.956864i	$-0.406167\pi$
$269$	9.53027			0.581071			0.290535	+	0.956864i	$0.406167\pi$
$270$	−1.02996	−	0.362444i	−0.0626812	−	0.0220577i
$271$	1.18095			0.0717375			0.0358688	−	0.999357i	$-0.488580\pi$
$271$	1.18095			0.0717375			0.0358688	+	0.999357i	$0.488580\pi$
$272$			1.68070i			0.101908i
$273$		−	9.28673i		−	0.562058i
$274$	9.30645			0.562223
$275$		0			0
$276$	−7.71525			−0.464404
$277$			8.22177i			0.493998i	0.969016	+	0.246999i	$0.0794445\pi$
$277$			8.22177i			0.493998i	−0.969016	+	0.246999i	$0.920556\pi$
$278$		−	5.72024i		−	0.343077i
$279$	−2.20501			−0.132011
$280$	−19.7933	−	6.96532i	−1.18288	−	0.416258i
$281$	−10.4453			−0.623116			−0.311558	−	0.950227i	$-0.600851\pi$
$281$	−10.4453			−0.623116			−0.311558	+	0.950227i	$0.600851\pi$
$282$		−	0.740167i		−	0.0440763i
$283$		−	24.8463i		−	1.47696i	−0.674275	−	0.738480i	$-0.735544\pi$
$283$		−	24.8463i		−	1.47696i	0.674275	−	0.738480i	$-0.264456\pi$
$284$	9.70383			0.575816
$285$	−3.26436	+	9.27634i	−0.193364	+	0.549483i
$286$		0			0
$287$			11.4022i			0.673052i
$288$		−	4.95592i		−	0.292031i
$289$	16.5904			0.975908
$290$	−2.74014	+	7.78666i	−0.160907	+	0.457249i
$291$	14.2823			0.837242
$292$			12.5832i			0.736379i
$293$		−	24.8264i		−	1.45037i	−0.688553	−	0.725186i	$-0.741754\pi$
$293$		−	24.8264i		−	1.45037i	0.688553	−	0.725186i	$-0.258246\pi$
$294$	−9.32716			−0.543971
$295$	−11.3305	−	3.98723i	−0.659687	−	0.232145i
$296$	−10.9691			−0.637563
$297$		0			0
$298$			3.64136i			0.210939i
$299$	−7.96128			−0.460413
$300$	5.51592	−	6.86676i	0.318462	−	0.396452i
$301$	17.2717			0.995526
$302$			2.42150i			0.139342i
$303$		−	4.29089i		−	0.246505i
$304$	−11.5499			−0.662430
$305$	−15.3296	−	5.39450i	−0.877768	−	0.308888i
$306$	0.312494			0.0178641
$307$			12.4687i			0.711624i	0.934557	+	0.355812i	$0.115796\pi$
$307$			12.4687i			0.711624i	−0.934557	+	0.355812i	$0.884204\pi$
$308$		0			0
$309$	−9.49802			−0.540324
$310$	−0.799194	+	2.27107i	−0.0453911	+	0.128988i
$311$	−3.15914			−0.179138			−0.0895692	−	0.995981i	$-0.528549\pi$
$311$	−3.15914			−0.179138			−0.0895692	+	0.995981i	$0.528549\pi$
$312$		−	3.33876i		−	0.189020i
$313$			14.2948i			0.807988i	0.914762	+	0.403994i	$0.132378\pi$
$313$			14.2948i			0.807988i	−0.914762	+	0.403994i	$0.867622\pi$
$314$	10.0548			0.567427
$315$	3.79216	−	10.7762i	0.213664	−	0.607169i
$316$	3.35606			0.188793
$317$		−	26.8771i		−	1.50957i	−0.655974	−	0.754784i	$-0.727742\pi$
$317$		−	26.8771i		−	1.50957i	0.655974	−	0.754784i	$-0.272258\pi$
$318$			4.48109i			0.251287i
$319$		0			0
$320$	5.97453	+	2.10245i	0.333987	+	0.117531i
$321$	−8.27470			−0.461849
$322$			10.9262i			0.608893i
$323$		−	2.81449i		−	0.156602i
$324$	1.76156			0.0978647
$325$	5.69181	−	7.08573i	0.315725	−	0.393046i
$326$	3.52930			0.195470
$327$			12.4980i			0.691141i
$328$			4.09933i			0.226347i
$329$	7.74418			0.426950
$330$		0			0
$331$	19.7763			1.08700			0.543502	−	0.839408i	$-0.317098\pi$
$331$	19.7763			1.08700			0.543502	+	0.839408i	$0.317098\pi$
$332$		−	0.285200i		−	0.0156524i
$333$		−	5.97194i		−	0.327260i
$334$	8.94221			0.489296
$335$	5.38582	−	15.3049i	0.294259	−	0.836195i
$336$	13.4173			0.731974
$337$		−	14.2580i		−	0.776685i	−0.921515	−	0.388343i	$-0.873048\pi$
$337$		−	14.2580i		−	0.776685i	0.921515	−	0.388343i	$-0.126952\pi$
$338$			4.73446i			0.257521i
$339$	16.2096			0.880384
$340$	−0.836779	+	2.37787i	−0.0453807	+	0.128958i
$341$		0			0
$342$			2.14748i			0.116122i
$343$		−	61.8251i		−	3.33824i
$344$	6.20953			0.334795
$345$	−9.23816	−	3.25093i	−0.497366	−	0.175024i
$346$	5.86725			0.315425
$347$		−	15.7954i		−	0.847940i	−0.905676	−	0.423970i	$-0.860636\pi$
$347$		−	15.7954i		−	0.847940i	0.905676	−	0.423970i	$-0.139364\pi$
$348$		−	13.3177i		−	0.713906i
$349$	1.71442			0.0917705			0.0458853	−	0.998947i	$-0.485389\pi$
$349$	1.71442			0.0917705			0.0458853	+	0.998947i	$0.485389\pi$
$350$	−9.72457	−	7.81153i	−0.519800	−	0.417544i
$351$	1.81774			0.0970237
$352$		0			0
$353$		−	13.9610i		−	0.743072i	−0.928419	−	0.371536i	$-0.878831\pi$
$353$		−	13.9610i		−	0.743072i	0.928419	−	0.371536i	$-0.121169\pi$
$354$	−2.62302			−0.139412
$355$	11.6193	+	4.08884i	0.616686	+	0.217013i
$356$	2.10575			0.111605
$357$			3.26955i			0.173043i
$358$			3.27650i			0.173169i
$359$	−34.3062			−1.81061			−0.905306	−	0.424759i	$-0.860359\pi$
$359$	−34.3062			−1.81061			−0.905306	+	0.424759i	$0.860359\pi$
$360$	1.36336	−	3.87425i	0.0718553	−	0.204191i
$361$	0.341312			0.0179638
$362$		−	5.53476i		−	0.290901i
$363$		0			0
$364$	16.3592			0.857453
$365$	−5.30213	+	15.0670i	−0.277526	+	0.788645i
$366$	−3.54880			−0.185499
$367$			3.61245i			0.188569i	0.995545	+	0.0942843i	$0.0300563\pi$
$367$			3.61245i			0.188569i	−0.995545	+	0.0942843i	$0.969944\pi$
$368$		−	11.5023i		−	0.599600i
$369$	−2.23182			−0.116184
$370$	−6.15084	−	2.16449i	−0.319767	−	0.112527i
$371$	−46.8845			−2.43412
$372$		−	3.88427i		−	0.201390i
$373$		−	18.7064i		−	0.968579i	−0.874908	−	0.484290i	$-0.839078\pi$
$373$		−	18.7064i		−	0.968579i	0.874908	−	0.484290i	$-0.160922\pi$
$374$		0			0
$375$	9.49810	−	5.89797i	0.490480	−	0.304570i
$376$	2.78418			0.143583
$377$		−	13.7424i		−	0.707771i
$378$		−	2.49469i		−	0.128313i
$379$	9.37468			0.481545			0.240772	−	0.970582i	$-0.422599\pi$
$379$	9.37468			0.481545			0.240772	+	0.970582i	$0.422599\pi$
$380$	−16.3409	−	5.75039i	−0.838269	−	0.294989i
$381$	−9.88086			−0.506212
$382$			5.41349i			0.276978i
$383$			19.2155i			0.981865i	0.871198	+	0.490932i	$0.163344\pi$
$383$			19.2155i			0.981865i	−0.871198	+	0.490932i	$0.836656\pi$
$384$	11.2950			0.576393
$385$		0			0
$386$	0.582076			0.0296269
$387$			3.38068i			0.171850i
$388$			25.1591i			1.27726i
$389$	9.29700			0.471376			0.235688	−	0.971829i	$-0.424266\pi$
$389$	9.29700			0.471376			0.235688	+	0.971829i	$0.424266\pi$
$390$	0.658829	−	1.87219i	0.0333611	−	0.0948022i
$391$	2.80290			0.141749
$392$		−	35.0847i		−	1.77205i
$393$		−	12.7829i		−	0.644814i
$394$	−8.96277			−0.451538
$395$	4.01851	+	1.41412i	0.202193	+	0.0711522i
$396$		0			0
$397$			13.8693i			0.696078i	0.937480	+	0.348039i	$0.113152\pi$
$397$			13.8693i			0.696078i	−0.937480	+	0.348039i	$0.886848\pi$
$398$		−	10.8286i		−	0.542787i
$399$	−22.4685			−1.12483
$400$	10.2373	+	8.22344i	0.511867	+	0.411172i
$401$	10.6336			0.531015			0.265507	−	0.964109i	$-0.414461\pi$
$401$	10.6336			0.531015			0.265507	+	0.964109i	$0.414461\pi$
$402$		−	3.54309i		−	0.176713i
$403$		−	4.00813i		−	0.199659i
$404$	7.55868			0.376058
$405$	2.10928	+	0.742259i	0.104811	+	0.0368832i
$406$	−18.8603			−0.936022
$407$		0			0
$408$			1.17547i			0.0581943i
$409$	3.71320			0.183606			0.0918030	−	0.995777i	$-0.470737\pi$
$409$	3.71320			0.183606			0.0918030	+	0.995777i	$0.470737\pi$
$410$	−0.808909	+	2.29868i	−0.0399492	+	0.113524i
$411$	−19.0589			−0.940107
$412$		−	16.7314i		−	0.824296i
$413$		−	27.4439i		−	1.35043i
$414$	−2.13864			−0.105108
$415$	0.120173	−	0.341496i	0.00589906	−	0.0167634i
$416$	9.00857			0.441682
$417$			11.7146i			0.573668i
$418$		0			0
$419$	15.8996			0.776745			0.388372	−	0.921503i	$-0.373037\pi$
$419$	15.8996			0.776745			0.388372	+	0.921503i	$0.373037\pi$
$420$	18.9829	+	6.68014i	0.926273	+	0.325957i
$421$	4.36664			0.212817			0.106408	−	0.994323i	$-0.466065\pi$
$421$	4.36664			0.212817			0.106408	+	0.994323i	$0.466065\pi$
$422$		−	4.05644i		−	0.197464i
$423$			1.51581i			0.0737011i
$424$	−16.8559			−0.818596
$425$	−2.00390	+	2.49465i	−0.0972034	+	0.121008i
$426$	2.68986			0.130324
$427$		−	37.1302i		−	1.79686i
$428$		−	14.5764i		−	0.704577i
$429$		0			0
$430$	3.48196	+	1.22531i	0.167915	+	0.0590897i
$431$	−20.1005			−0.968209			−0.484105	−	0.875010i	$-0.660855\pi$
$431$	−20.1005			−0.968209			−0.484105	+	0.875010i	$0.660855\pi$
$432$			2.62624i			0.126355i
$433$			30.7232i			1.47646i	0.674549	+	0.738230i	$0.264338\pi$
$433$			30.7232i			1.47646i	−0.674549	+	0.738230i	$0.735662\pi$
$434$	−5.50082			−0.264048
$435$	5.61161	−	15.9465i	0.269056	−	0.764577i
$436$	−22.0160			−1.05438
$437$			19.2617i			0.921412i
$438$			3.48803i			0.166664i
$439$	−20.6104			−0.983679			−0.491840	−	0.870686i	$-0.663675\pi$
$439$	−20.6104			−0.983679			−0.491840	+	0.870686i	$0.663675\pi$
$440$		0			0
$441$	19.1013			0.909587
$442$			0.568033i			0.0270186i
$443$		−	13.7997i		−	0.655644i	−0.944740	−	0.327822i	$-0.893685\pi$
$443$		−	13.7997i		−	0.655644i	0.944740	−	0.327822i	$-0.106315\pi$
$444$	10.5199			0.499255
$445$	2.52140	+	0.887288i	0.119526	+	0.0420615i
$446$	8.08118			0.382655
$447$		−	7.45724i		−	0.352716i
$448$			14.4711i			0.683696i
$449$	−27.2508			−1.28605			−0.643023	−	0.765847i	$-0.722320\pi$
$449$	−27.2508			−1.28605			−0.643023	+	0.765847i	$0.722320\pi$
$450$	1.52899	−	1.90344i	0.0720773	−	0.0897290i
$451$		0			0
$452$			28.5542i			1.34308i
$453$		−	4.95905i		−	0.232997i
$454$	−4.14224			−0.194405
$455$	19.5883	+	6.89316i	0.918313	+	0.323156i
$456$	−8.07787			−0.378281
$457$		−	4.62255i		−	0.216234i	−0.994138	−	0.108117i	$-0.965518\pi$
$457$		−	4.62255i		−	0.216234i	0.994138	−	0.108117i	$-0.0344821\pi$
$458$			1.65969i			0.0775521i
$459$	−0.639966			−0.0298710
$460$	5.72672	−	16.2736i	0.267010	−	0.758761i
$461$	25.3940			1.18272			0.591359	−	0.806409i	$-0.298592\pi$
$461$	25.3940			1.18272			0.591359	+	0.806409i	$0.298592\pi$
$462$		0			0
$463$			12.8949i			0.599275i	0.954053	+	0.299638i	$0.0968658\pi$
$463$			12.8949i			0.599275i	−0.954053	+	0.299638i	$0.903134\pi$
$464$	19.8548			0.921737
$465$	1.63669	−	4.65098i	0.0758997	−	0.215684i
$466$	7.67231			0.355413
$467$		−	3.81025i		−	0.176317i	−0.996106	−	0.0881587i	$-0.971902\pi$
$467$		−	3.81025i		−	0.176317i	0.996106	−	0.0881587i	$-0.0280983\pi$
$468$			3.20206i			0.148015i
$469$	37.0704			1.71175
$470$	1.56122	+	0.549396i	0.0720136	+	0.0253417i
$471$	−20.5916			−0.948809
$472$		−	9.86664i		−	0.454149i
$473$		0			0
$474$	0.930287			0.0427295
$475$	−17.1434	−	13.7709i	−0.786592	−	0.631852i
$476$	−5.75952			−0.263987
$477$		−	9.17695i		−	0.420184i
$478$			14.9894i			0.685600i
$479$	12.2918			0.561625			0.280812	−	0.959763i	$-0.409396\pi$
$479$	12.2918			0.561625			0.280812	+	0.959763i	$0.409396\pi$
$480$	10.4534	+	3.67858i	0.477131	+	0.167903i
$481$	10.8554			0.494964
$482$		−	2.73006i		−	0.124351i
$483$		−	22.3760i		−	1.01814i
$484$		0			0
$485$	−10.6012	+	30.1253i	−0.481373	+	1.36792i
$486$	0.488299			0.0221497
$487$		−	13.4389i		−	0.608975i	−0.952516	−	0.304488i	$-0.901515\pi$
$487$		−	13.4389i		−	0.608975i	0.952516	−	0.304488i	$-0.0984852\pi$
$488$		−	13.3490i		−	0.604283i
$489$	−7.22774			−0.326850
$490$	6.92317	−	19.6736i	0.312757	−	0.888761i
$491$	6.08182			0.274469			0.137234	−	0.990539i	$-0.456179\pi$
$491$	6.08182			0.274469			0.137234	+	0.990539i	$0.456179\pi$
$492$		−	3.93149i		−	0.177245i
$493$			4.83826i			0.217904i
$494$	−3.90355			−0.175629
$495$		0			0
$496$	5.79088			0.260018
$497$			28.1434i			1.26240i
$498$		−	0.0790564i		−	0.00354260i
$499$	−18.7942			−0.841344			−0.420672	−	0.907213i	$-0.638206\pi$
$499$	−18.7942			−0.841344			−0.420672	+	0.907213i	$0.638206\pi$
$500$	10.3897	+	16.7315i	0.464639	+	0.748256i
$501$	−18.3130			−0.818164
$502$			9.14276i			0.408061i
$503$		−	6.06605i		−	0.270472i	−0.990813	−	0.135236i	$-0.956821\pi$
$503$		−	6.06605i		−	0.270472i	0.990813	−	0.135236i	$-0.0431793\pi$
$504$	9.38395			0.417994
$505$	9.05068	+	3.18495i	0.402750	+	0.141729i
$506$		0			0
$507$		−	9.69583i		−	0.430607i
$508$		−	17.4058i		−	0.772256i
$509$	19.7444			0.875154			0.437577	−	0.899181i	$-0.355837\pi$
$509$	19.7444			0.875154			0.437577	+	0.899181i	$0.355837\pi$
$510$	−0.231952	+	0.659138i	−0.0102710	+	0.0291871i
$511$	−36.4943			−1.61441
$512$			22.6630i			1.00157i
$513$		−	4.39788i		−	0.194171i
$514$	2.43278			0.107305
$515$	7.05000	−	20.0340i	0.310660	−	0.882802i
$516$	−5.95529			−0.262167
$517$		0			0
$518$		−	14.8981i		−	0.654587i
$519$	−12.0157			−0.527430
$520$	7.04238	+	2.47823i	0.308829	+	0.108677i
$521$	−42.1434			−1.84634			−0.923168	−	0.384396i	$-0.874410\pi$
$521$	−42.1434			−1.84634			−0.923168	+	0.384396i	$0.874410\pi$
$522$		−	3.69163i		−	0.161578i
$523$			6.37047i			0.278561i	0.990253	+	0.139281i	$0.0444790\pi$
$523$			6.37047i			0.278561i	−0.990253	+	0.139281i	$0.955521\pi$
$524$	22.5180			0.983702
$525$	19.9152	+	15.9974i	0.869170	+	0.698186i
$526$	9.80445			0.427494
$527$			1.41113i			0.0614698i
$528$		0			0
$529$	3.81758			0.165982
$530$	−9.45187	−	3.32613i	−0.410563	−	0.144478i
$531$	5.37174			0.233114
$532$		−	39.5797i		−	1.71600i
$533$		−	4.05686i		−	0.175722i
$534$	0.583706			0.0252594
$535$	6.14197	−	17.4536i	0.265541	−	0.754586i
$536$	13.3276			0.575663
$537$		−	6.71004i		−	0.289560i
$538$			4.65362i			0.200632i
$539$		0			0
$540$	−1.30754	+	3.71563i	−0.0562675	+	0.159895i
$541$	12.3075			0.529140			0.264570	−	0.964367i	$-0.414770\pi$
$541$	12.3075			0.529140			0.264570	+	0.964367i	$0.414770\pi$
$542$			0.576656i			0.0247695i
$543$			11.3348i			0.486422i
$544$	−3.17162			−0.135982
$545$	−26.3618	−	9.27676i	−1.12921	−	0.397373i
$546$	4.53470			0.194067
$547$			5.48939i			0.234709i	0.993090	+	0.117355i	$0.0374415\pi$
$547$			5.48939i			0.234709i	−0.993090	+	0.117355i	$0.962559\pi$
$548$		−	33.5735i		−	1.43419i
$549$	7.26768			0.310177
$550$		0			0
$551$	−33.2487			−1.41644
$552$		−	8.04463i		−	0.342402i
$553$			9.73335i			0.413904i
$554$	−4.01468			−0.170567
$555$	12.5965	+	4.43273i	0.534690	+	0.188159i
$556$	−20.6361			−0.875165
$557$			25.4636i			1.07893i	0.842009	+	0.539464i	$0.181373\pi$
$557$			25.4636i			1.07893i	−0.842009	+	0.539464i	$0.818627\pi$
$558$		−	1.07670i		−	0.0455805i
$559$	−6.14520			−0.259914
$560$	−9.95912	+	28.3008i	−0.420850	+	1.19593i
$561$		0			0
$562$		−	5.10044i		−	0.215149i
$563$		−	38.3527i		−	1.61638i	−0.588925	−	0.808188i	$-0.700449\pi$
$563$		−	38.3527i		−	1.61638i	0.588925	−	0.808188i	$-0.299551\pi$
$564$	−2.67019			−0.112435
$565$	−12.0317	+	34.1905i	−0.506178	+	1.43841i
$566$	12.1324			0.509964
$567$			5.10895i			0.214556i
$568$			10.1181i			0.424546i
$569$	9.15245			0.383691			0.191845	−	0.981425i	$-0.438553\pi$
$569$	9.15245			0.383691			0.191845	+	0.981425i	$0.438553\pi$
$570$	−4.52963	−	1.59399i	−0.189725	−	0.0667647i
$571$	18.3508			0.767957			0.383978	−	0.923342i	$-0.374554\pi$
$571$	18.3508			0.767957			0.383978	+	0.923342i	$0.374554\pi$
$572$		0			0
$573$		−	11.0864i		−	0.463142i
$574$	−5.56769			−0.232391
$575$	13.7142	−	17.0728i	0.571922	−	0.711985i
$576$	−2.83250			−0.118021
$577$			19.9317i			0.829770i	0.909874	+	0.414885i	$0.136178\pi$
$577$			19.9317i			0.829770i	−0.909874	+	0.414885i	$0.863822\pi$
$578$			8.10109i			0.336961i
$579$	−1.19205			−0.0495399
$580$	28.0908	+	9.88522i	1.16641	+	0.410461i
$581$	0.827147			0.0343158
$582$			6.97402i			0.289082i
$583$		0			0
$584$	−13.1204			−0.542928
$585$	−1.34923	+	3.83411i	−0.0557839	+	0.158521i
$586$	12.1227			0.500784
$587$			39.5465i			1.63226i	0.577870	+	0.816129i	$0.303884\pi$
$587$			39.5465i			1.63226i	−0.577870	+	0.816129i	$0.696116\pi$
$588$			33.6482i			1.38763i
$589$	−9.69736			−0.399573
$590$	1.94696	−	5.53267i	0.0801550	−	0.227776i
$591$	18.3551			0.755028
$592$			15.6837i			0.644597i
$593$			12.3314i			0.506391i	0.967415	+	0.253195i	$0.0814816\pi$
$593$			12.3314i			0.506391i	−0.967415	+	0.253195i	$0.918518\pi$
$594$		0			0
$595$	−6.89639	−	2.42685i	−0.282724	−	0.0994913i
$596$	13.1364			0.538088
$597$			22.1761i			0.907607i
$598$		−	3.88748i		−	0.158971i
$599$	−34.7495			−1.41983			−0.709913	−	0.704289i	$-0.751266\pi$
$599$	−34.7495			−1.41983			−0.709913	+	0.704289i	$0.751266\pi$
$600$	7.15991	+	5.75140i	0.292302	+	0.234800i
$601$	−38.6097			−1.57492			−0.787462	−	0.616364i	$-0.788605\pi$
$601$	−38.6097			−1.57492			−0.787462	+	0.616364i	$0.788605\pi$
$602$			8.43376i			0.343735i
$603$			7.25598i			0.295486i
$604$	8.73569			0.355450
$605$		0			0
$606$	2.09524			0.0851132
$607$			6.26341i			0.254224i	0.991888	+	0.127112i	$0.0405708\pi$
$607$			6.26341i			0.254224i	−0.991888	+	0.127112i	$0.959429\pi$
$608$		−	21.7955i		−	0.883926i
$609$	38.6246			1.56515
$610$	2.63413	−	7.48540i	0.106653	−	0.303075i
$611$	−2.75534			−0.111469
$612$		−	1.12734i		−	0.0455700i
$613$		−	18.9911i		−	0.767042i	−0.923532	−	0.383521i	$-0.874711\pi$
$613$		−	18.9911i		−	0.767042i	0.923532	−	0.383521i	$-0.125289\pi$
$614$	−6.08844			−0.245709
$615$	1.65659	−	4.70752i	0.0668000	−	0.189825i
$616$		0			0
$617$			7.58574i			0.305390i	0.988273	+	0.152695i	$0.0487953\pi$
$617$			7.58574i			0.305390i	−0.988273	+	0.152695i	$0.951205\pi$
$618$		−	4.63787i		−	0.186563i
$619$	−27.9795			−1.12459			−0.562296	−	0.826936i	$-0.690082\pi$
$619$	−27.9795			−1.12459			−0.562296	+	0.826936i	$0.690082\pi$
$620$	8.19300	+	2.88313i	0.329039	+	0.115789i
$621$	4.37977			0.175754
$622$		−	1.54260i		−	0.0618528i
$623$			6.10717i			0.244679i
$624$	−4.77381			−0.191105
$625$	5.39040	+	24.4120i	0.215616	+	0.976478i
$626$	−6.98012			−0.278982
$627$		0			0
$628$		−	36.2734i		−	1.44746i
$629$	−3.82183			−0.152387
$630$	5.26200	+	1.85171i	0.209643	+	0.0737738i
$631$	−25.4321			−1.01244			−0.506218	−	0.862406i	$-0.668957\pi$
$631$	−25.4321			−1.01244			−0.506218	+	0.862406i	$0.668957\pi$
$632$			3.49933i			0.139196i
$633$			8.30729i			0.330185i
$634$	13.1240			0.521223
$635$	7.33416	−	20.8415i	0.291047	−	0.827069i
$636$	16.1658			0.641015
$637$			34.7212i			1.37570i
$638$		0			0
$639$	−5.50864			−0.217919
$640$	−8.38379	+	23.8242i	−0.331398	+	0.941734i
$641$	−8.90150			−0.351588			−0.175794	−	0.984427i	$-0.556249\pi$
$641$	−8.90150			−0.351588			−0.175794	+	0.984427i	$0.556249\pi$
$642$		−	4.04052i		−	0.159467i
$643$			19.4814i			0.768272i	0.923276	+	0.384136i	$0.125501\pi$
$643$			19.4814i			0.768272i	−0.923276	+	0.384136i	$0.874499\pi$
$644$	39.4168			1.55324
$645$	−7.13080	−	2.50934i	−0.280775	−	0.0988053i
$646$	1.37431			0.0540716
$647$			32.8093i			1.28987i	0.764238	+	0.644934i	$0.223115\pi$
$647$			32.8093i			1.28987i	−0.764238	+	0.644934i	$0.776885\pi$
$648$			1.83677i			0.0721550i
$649$		0			0
$650$	3.45995	+	2.77931i	0.135711	+	0.109013i
$651$	11.2653			0.441521
$652$		−	12.7321i		−	0.498629i
$653$		−	14.9010i		−	0.583122i	−0.956552	−	0.291561i	$-0.905825\pi$
$653$		−	14.9010i		−	0.583122i	0.956552	−	0.291561i	$-0.0941747\pi$
$654$	−6.10276			−0.238637
$655$	26.9628	+	9.48826i	1.05352	+	0.370737i
$656$	5.86128			0.228844
$657$		−	7.14322i		−	0.278684i
$658$			3.78147i			0.147417i
$659$	−25.7059			−1.00136			−0.500680	−	0.865633i	$-0.666917\pi$
$659$	−25.7059			−1.00136			−0.500680	+	0.865633i	$0.666917\pi$
$660$		0			0
$661$	−12.4887			−0.485753			−0.242876	−	0.970057i	$-0.578091\pi$
$661$	−12.4887			−0.485753			−0.242876	+	0.970057i	$0.578091\pi$
$662$			9.65675i			0.375320i
$663$		−	1.16329i		−	0.0451784i
$664$	0.297376			0.0115404
$665$	16.6775	−	47.3923i	0.646724	−	1.83780i
$666$	2.91609			0.112996
$667$		−	33.1119i		−	1.28210i
$668$		−	32.2595i		−	1.24816i
$669$	−16.5497			−0.639847
$670$	7.47335	+	2.62989i	0.288721	+	0.101602i
$671$		0			0
$672$			25.3195i			0.976723i
$673$			40.3440i			1.55515i	0.628793	+	0.777573i	$0.283549\pi$
$673$			40.3440i			1.55515i	−0.628793	+	0.777573i	$0.716451\pi$
$674$	6.96219			0.268173
$675$	−3.13126	+	3.89810i	−0.120522	+	0.150038i
$676$	17.0798			0.656916
$677$			5.64803i			0.217071i	0.994093	+	0.108536i	$0.0346162\pi$
$677$			5.64803i			0.217071i	−0.994093	+	0.108536i	$0.965384\pi$
$678$			7.91513i			0.303979i
$679$	−72.9674			−2.80023
$680$	−2.47939	−	0.872502i	−0.0950802	−	0.0334589i
$681$	8.48300			0.325069
$682$		0			0
$683$		−	26.7349i		−	1.02298i	−0.859288	−	0.511492i	$-0.829093\pi$
$683$		−	26.7349i		−	1.02298i	0.859288	−	0.511492i	$-0.170907\pi$
$684$	7.74714			0.296219
$685$	14.1467	−	40.2006i	0.540516	−	1.53598i
$686$	30.1891			1.15263
$687$		−	3.39892i		−	0.129677i
$688$		−	8.87848i		−	0.338489i
$689$	16.6813			0.635506
$690$	1.58742	−	4.51098i	0.0604322	−	0.171730i
$691$	39.2696			1.49389			0.746943	−	0.664888i	$-0.231521\pi$
$691$	39.2696			1.49389			0.746943	+	0.664888i	$0.231521\pi$
$692$		−	21.1664i		−	0.804626i
$693$		0			0
$694$	7.71286			0.292776
$695$	−24.7094	−	8.69530i	−0.937281	−	0.329831i
$696$	13.8863			0.526359
$697$			1.42829i			0.0541002i
$698$			0.837147i			0.0316865i
$699$	−15.7123			−0.594295
$700$	−28.1805	+	35.0819i	−1.06512	+	1.32597i
$701$	7.23493			0.273259			0.136630	−	0.990622i	$-0.456373\pi$
$701$	7.23493			0.273259			0.136630	+	0.990622i	$0.456373\pi$
$702$			0.887599i			0.0335003i
$703$		−	26.2638i		−	0.990559i
$704$		0			0
$705$	−3.19726	−	1.12512i	−0.120416	−	0.0423745i
$706$	6.81716			0.256567
$707$			21.9219i			0.824459i
$708$			9.46267i			0.355629i
$709$	9.96887			0.374389			0.187194	−	0.982323i	$-0.440061\pi$
$709$	9.96887			0.374389			0.187194	+	0.982323i	$0.440061\pi$
$710$	−1.99658	+	5.67367i	−0.0749302	+	0.212929i
$711$	−1.90516			−0.0714490
$712$			2.19565i			0.0822854i
$713$		−	9.65745i		−	0.361674i
$714$	−1.59652			−0.0597482
$715$		0			0
$716$	11.8202			0.441740
$717$		−	30.6972i		−	1.14641i
$718$		−	16.7517i		−	0.625167i
$719$	−33.1006			−1.23445			−0.617223	−	0.786788i	$-0.711742\pi$
$719$	−33.1006			−1.23445			−0.617223	+	0.786788i	$0.711742\pi$
$720$	−5.53946	−	1.94935i	−0.206444	−	0.0726480i
$721$	48.5249			1.80716
$722$			0.166662i			0.00620253i
$723$			5.59097i			0.207930i
$724$	−19.9669			−0.742066
$725$	29.4704	+	23.6729i	1.09450	+	0.879189i
$726$		0			0
$727$		−	18.7123i		−	0.694000i	−0.937865	−	0.347000i	$-0.887200\pi$
$727$		−	18.7123i		−	0.694000i	0.937865	−	0.347000i	$-0.112800\pi$
$728$			17.0576i			0.632195i
$729$	−1.00000			−0.0370370
$730$	−7.35722	−	2.58902i	−0.272303	−	0.0958240i
$731$	2.16352			0.0800207
$732$			12.8025i			0.473193i
$733$			10.9499i			0.404442i	0.979340	+	0.202221i	$0.0648160\pi$
$733$			10.9499i			0.404442i	−0.979340	+	0.202221i	$0.935184\pi$
$734$	−1.76396			−0.0651089
$735$	−14.1781	+	40.2900i	−0.522969	+	1.48612i
$736$	21.7058			0.800087
$737$		0			0
$738$		−	1.08979i		−	0.0401158i
$739$	38.0842			1.40095			0.700474	−	0.713677i	$-0.252972\pi$
$739$	38.0842			1.40095			0.700474	+	0.713677i	$0.252972\pi$
$740$	−7.80853	+	22.1895i	−0.287047	+	0.815702i
$741$	7.99419			0.293674
$742$		−	22.8937i		−	0.840453i
$743$			16.5258i			0.606275i	0.952947	+	0.303137i	$0.0980341\pi$
$743$			16.5258i			0.606275i	−0.952947	+	0.303137i	$0.901966\pi$
$744$	4.05009			0.148484
$745$	15.7294	+	5.53521i	0.576280	+	0.202794i
$746$	9.13430			0.334430
$747$			0.161902i			0.00592367i
$748$		0			0
$749$	42.2750			1.54469
$750$	2.87997	+	4.63791i	0.105162	+	0.169353i
$751$	−17.9317			−0.654336			−0.327168	−	0.944966i	$-0.606094\pi$
$751$	−17.9317			−0.654336			−0.327168	+	0.944966i	$0.606094\pi$
$752$		−	3.98087i		−	0.145167i
$753$		−	18.7237i		−	0.682329i
$754$	6.71041			0.244379
$755$	10.4600	+	3.68090i	0.380679	+	0.133962i
$756$	−8.99974			−0.327317
$757$		−	14.0679i		−	0.511307i	−0.966768	−	0.255653i	$-0.917709\pi$
$757$		−	14.0679i		−	0.511307i	0.966768	−	0.255653i	$-0.0822906\pi$
$758$			4.57764i			0.166267i
$759$		0			0
$760$	5.99588	−	17.0385i	0.217493	−	0.618051i
$761$	−10.1182			−0.366783			−0.183392	−	0.983040i	$-0.558708\pi$
$761$	−10.1182			−0.366783			−0.183392	+	0.983040i	$0.558708\pi$
$762$		−	4.82481i		−	0.174785i
$763$		−	63.8516i		−	2.31158i
$764$	19.5295			0.706551
$765$	0.475021	−	1.34987i	0.0171744	−	0.0488045i
$766$	−9.38289			−0.339018
$767$			9.76442i			0.352573i
$768$		−	0.149694i		−	0.00540160i
$769$	−16.0423			−0.578499			−0.289250	−	0.957254i	$-0.593406\pi$
$769$	−16.0423			−0.578499			−0.289250	+	0.957254i	$0.593406\pi$
$770$		0			0
$771$	−4.98215			−0.179428
$772$		−	2.09987i		−	0.0755760i
$773$			40.4357i			1.45437i	0.686442	+	0.727185i	$0.259172\pi$
$773$			40.4357i			1.45437i	−0.686442	+	0.727185i	$0.740828\pi$
$774$	−1.65078			−0.0593362
$775$	8.59535	+	6.90446i	0.308754	+	0.248016i
$776$	−26.2332			−0.941718
$777$			30.5103i			1.09455i
$778$			4.53971i			0.162757i
$779$	−9.81525			−0.351668
$780$	−6.75404	−	2.37676i	−0.241833	−	0.0851017i
$781$		0			0
$782$			1.36866i			0.0489430i
$783$			7.56018i			0.270179i
$784$	−50.1646			−1.79159
$785$	15.2843	−	43.4333i	0.545519	−	1.55020i
$786$	6.24190			0.222641
$787$			16.4314i			0.585716i	0.956156	+	0.292858i	$0.0946063\pi$
$787$			16.4314i			0.585716i	−0.956156	+	0.292858i	$0.905394\pi$
$788$			32.3337i			1.15184i
$789$	−20.0788			−0.714824
$790$	−0.690514	+	1.96223i	−0.0245674	+	0.0698131i
$791$	−82.8140			−2.94453
$792$		0			0
$793$			13.2107i			0.469127i
$794$	−6.77235			−0.240342
$795$	19.3567	+	6.81167i	0.686512	+	0.241585i
$796$	−39.0646			−1.38461
$797$		−	11.8928i		−	0.421266i	−0.977565	−	0.210633i	$-0.932448\pi$
$797$		−	11.8928i		−	0.421266i	0.977565	−	0.210633i	$-0.0675525\pi$
$798$		−	10.9713i		−	0.388381i
$799$	0.970064			0.0343184
$800$	−15.5183	+	19.3187i	−0.548654	+	0.683019i
$801$	−1.19539			−0.0422370
$802$			5.19236i			0.183349i
$803$		0			0
$804$	−12.7819			−0.450782
$805$	47.1973	+	16.6088i	1.66348	+	0.585384i
$806$	1.95717			0.0689382
$807$		−	9.53027i		−	0.335481i
$808$			7.88137i			0.277266i
$809$	39.7032			1.39589			0.697944	−	0.716152i	$-0.254098\pi$
$809$	39.7032			1.39589			0.697944	+	0.716152i	$0.254098\pi$
$810$	−0.362444	+	1.02996i	−0.0127350	+	0.0361890i
$811$	−29.1509			−1.02363			−0.511814	−	0.859096i	$-0.671026\pi$
$811$	−29.1509			−1.02363			−0.511814	+	0.859096i	$0.671026\pi$
$812$			68.0396i			2.38772i
$813$		−	1.18095i		−	0.0414177i
$814$		0			0
$815$	5.36486	−	15.2453i	0.187923	−	0.534020i
$816$	1.68070			0.0588363
$817$			14.8678i			0.520159i
$818$			1.81315i			0.0633954i
$819$	−9.28673			−0.324505
$820$	8.29260	+	2.91818i	0.289590	+	0.101907i
$821$	−47.6040			−1.66139			−0.830696	−	0.556727i	$-0.812057\pi$
$821$	−47.6040			−1.66139			−0.830696	+	0.556727i	$0.812057\pi$
$822$		−	9.30645i		−	0.324600i
$823$			19.2238i			0.670099i	0.942201	+	0.335049i	$0.108753\pi$
$823$			19.2238i			0.670099i	−0.942201	+	0.335049i	$0.891247\pi$
$824$	17.4457			0.607748
$825$		0			0
$826$	13.4008			0.466275
$827$			30.6312i			1.06515i	0.846382	+	0.532576i	$0.178776\pi$
$827$			30.6312i			1.06515i	−0.846382	+	0.532576i	$0.821224\pi$
$828$			7.71525i			0.268124i
$829$	44.8613			1.55810			0.779048	−	0.626964i	$-0.215703\pi$
$829$	44.8613			1.55810			0.779048	+	0.626964i	$0.215703\pi$
$830$	0.166752	+	0.0586803i	0.00578804	+	0.00203682i
$831$	8.22177			0.285210
$832$		−	5.14875i		−	0.178501i
$833$		−	12.2242i		−	0.423543i
$834$	−5.72024			−0.198076
$835$	13.5930	−	38.6272i	0.470405	−	1.33675i
$836$		0			0
$837$			2.20501i			0.0762163i
$838$			7.76374i			0.268194i
$839$	−4.34435			−0.149984			−0.0749919	−	0.997184i	$-0.523893\pi$
$839$	−4.34435			−0.149984			−0.0749919	+	0.997184i	$0.523893\pi$
$840$	−6.96532	+	19.7933i	−0.240326	+	0.682935i
$841$	28.1563			0.970908
$842$			2.13222i			0.0734813i
$843$			10.4453i			0.359756i
$844$	−14.6338			−0.503717
$845$	20.4512	+	7.19682i	0.703542	+	0.247578i
$846$	−0.740167			−0.0254475
$847$		0			0
$848$			24.1008i			0.827626i
$849$	−24.8463			−0.852724
$850$	−1.21814	−	0.978502i	−0.0417817	−	0.0335623i
$851$	26.1557			0.896607
$852$		−	9.70383i		−	0.332448i
$853$		−	40.3581i		−	1.38183i	−0.722934	−	0.690917i	$-0.757207\pi$
$853$		−	40.3581i		−	1.38183i	0.722934	−	0.690917i	$-0.242793\pi$
$854$	18.1306			0.620417
$855$	9.27634	+	3.26436i	0.317244	+	0.111639i
$856$	15.1987			0.519481
$857$		−	36.6122i		−	1.25065i	−0.780365	−	0.625324i	$-0.784967\pi$
$857$		−	36.6122i		−	1.25065i	0.780365	−	0.625324i	$-0.215033\pi$
$858$		0			0
$859$	−28.5710			−0.974831			−0.487415	−	0.873170i	$-0.662060\pi$
$859$	−28.5710			−0.974831			−0.487415	+	0.873170i	$0.662060\pi$
$860$	4.42037	−	12.5614i	0.150733	−	0.428339i
$861$	11.4022			0.388587
$862$		−	9.81507i		−	0.334303i
$863$			29.3094i			0.997704i	0.866687	+	0.498852i	$0.166245\pi$
$863$			29.3094i			0.997704i	−0.866687	+	0.498852i	$0.833755\pi$
$864$	−4.95592			−0.168604
$865$	8.91876	−	25.3444i	0.303247	−	0.861736i
$866$	−15.0021			−0.509791
$867$		−	16.5904i		−	0.563441i
$868$			19.8445i			0.673567i
$869$		0			0
$870$	7.78666	+	2.74014i	0.263993	+	0.0928996i
$871$	−13.1895			−0.446908
$872$		−	22.9559i		−	0.777386i
$873$		−	14.2823i		−	0.483382i
$874$	−9.40547			−0.318145
$875$	−48.5253	+	30.1324i	−1.64045	+	1.01866i
$876$	12.5832			0.425149
$877$			3.67475i			0.124087i	0.998073	+	0.0620437i	$0.0197618\pi$
$877$			3.67475i			0.124087i	−0.998073	+	0.0620437i	$0.980238\pi$
$878$		−	10.0640i		−	0.339644i
$879$	−24.8264			−0.837373
$880$		0			0
$881$	−11.1723			−0.376403			−0.188202	−	0.982130i	$-0.560266\pi$
$881$	−11.1723			−0.376403			−0.188202	+	0.982130i	$0.560266\pi$
$882$			9.32716i			0.314062i
$883$			42.2570i			1.42206i	0.703161	+	0.711030i	$0.251771\pi$
$883$			42.2570i			1.42206i	−0.703161	+	0.711030i	$0.748229\pi$
$884$	2.04921			0.0689224
$885$	−3.98723	+	11.3305i	−0.134029	+	0.380870i
$886$	6.73838			0.226380
$887$			55.8459i			1.87512i	0.347819	+	0.937562i	$0.386922\pi$
$887$			55.8459i			1.87512i	−0.347819	+	0.937562i	$0.613078\pi$
$888$			10.9691i			0.368097i
$889$	50.4808			1.69307
$890$	−0.433262	+	1.23120i	−0.0145230	+	0.0412699i
$891$		0			0
$892$		−	29.1533i		−	0.976125i
$893$			6.66633i			0.223080i
$894$	3.64136			0.121785
$895$	14.1533	+	4.98059i	0.473094	+	0.166483i
$896$	−57.7053			−1.92780
$897$			7.96128i			0.265819i
$898$		−	13.3066i		−	0.444045i
$899$	16.6703			0.555985
$900$	−6.86676	−	5.51592i	−0.228892	−	0.183864i
$901$	−5.87293			−0.195656
$902$		0			0
$903$		−	17.2717i		−	0.574767i
$904$	−29.7733			−0.990244
$905$	−23.9082	−	8.41335i	−0.794736	−	0.279669i
$906$	2.42150			0.0804490
$907$		−	12.0875i		−	0.401358i	−0.979657	−	0.200679i	$-0.935685\pi$
$907$		−	12.0875i		−	0.401358i	0.979657	−	0.200679i	$-0.0643149\pi$
$908$			14.9433i			0.495912i
$909$	−4.29089			−0.142320
$910$	−3.36592	+	9.56494i	−0.111579	+	0.317075i
$911$	−40.2306			−1.33290			−0.666450	−	0.745550i	$-0.732187\pi$
$911$	−40.2306			−1.33290			−0.666450	+	0.745550i	$0.732187\pi$
$912$			11.5499i			0.382454i
$913$		0			0
$914$	2.25719			0.0746611
$915$	−5.39450	+	15.3296i	−0.178337	+	0.506779i
$916$	5.98741			0.197830
$917$			65.3074i			2.15664i
$918$		−	0.312494i		−	0.0103139i
$919$	3.65013			0.120407			0.0602033	−	0.998186i	$-0.480825\pi$
$919$	3.65013			0.120407			0.0602033	+	0.998186i	$0.480825\pi$
$920$	16.9683	+	5.97120i	0.559430	+	0.196865i
$921$	12.4687			0.410857
$922$			12.3999i			0.408368i
$923$		−	10.0133i		−	0.329591i
$924$		0			0
$925$	−18.6997	+	23.2792i	−0.614842	+	0.765416i
$926$	−6.29655			−0.206917
$927$			9.49802i			0.311956i
$928$			37.4677i			1.22994i
$929$	−10.0510			−0.329762			−0.164881	−	0.986313i	$-0.552724\pi$
$929$	−10.0510			−0.329762			−0.164881	+	0.986313i	$0.552724\pi$
$930$	2.27107	+	0.799194i	0.0744712	+	0.0262066i
$931$	84.0053			2.75316
$932$		−	27.6783i		−	0.906632i
$933$			3.15914i			0.103426i
$934$	1.86054			0.0608788
$935$		0			0
$936$	−3.33876			−0.109131
$937$			28.2337i			0.922355i	0.887308	+	0.461177i	$0.152573\pi$
$937$			28.2337i			0.922355i	−0.887308	+	0.461177i	$0.847427\pi$
$938$			18.1014i			0.591033i
$939$	14.2948			0.466492
$940$	1.98197	−	5.63217i	0.0646449	−	0.183701i
$941$	−32.6668			−1.06491			−0.532453	−	0.846459i	$-0.678730\pi$
$941$	−32.6668			−1.06491			−0.532453	+	0.846459i	$0.678730\pi$
$942$		−	10.0548i		−	0.327604i
$943$		−	9.77485i		−	0.318313i
$944$	−14.1075			−0.459159
$945$	−10.7762	−	3.79216i	−0.350549	−	0.123359i
$946$		0			0
$947$		−	57.1073i		−	1.85574i	−0.372906	−	0.927869i	$-0.621639\pi$
$947$		−	57.1073i		−	1.85574i	0.372906	−	0.927869i	$-0.378361\pi$
$948$		−	3.35606i		−	0.109000i
$949$	12.9845			0.421495
$950$	6.72431	−	8.37109i	0.218166	−	0.271594i
$951$	−26.8771			−0.871549
$952$		−	6.00540i		−	0.194636i
$953$		−	4.51422i		−	0.146230i	−0.997324	−	0.0731150i	$-0.976706\pi$
$953$		−	4.51422i		−	0.146230i	0.997324	−	0.0731150i	$-0.0232940\pi$
$954$	4.48109			0.145081
$955$	23.3843	+	8.22900i	0.756700	+	0.266284i
$956$	54.0751			1.74891
$957$		0			0
$958$			6.00205i			0.193917i
$959$	97.3710			3.14427
$960$	2.10245	−	5.97453i	0.0678563	−	0.192827i
$961$	−26.1379			−0.843159
$962$			5.30069i			0.170901i
$963$			8.27470i			0.266648i
$964$	−9.84886			−0.317210
$965$	0.884810	−	2.51436i	0.0284830	−	0.0809402i
$966$	10.9262			0.351544
$967$		−	1.33608i		−	0.0429654i	−0.999769	−	0.0214827i	$-0.993161\pi$
$967$		−	1.33608i		−	0.0429654i	0.999769	−	0.0214827i	$-0.00683868\pi$
$968$		0			0
$969$	−2.81449			−0.0904144
$970$	−14.7101	−	5.17653i	−0.472314	−	0.166208i
$971$	2.71644			0.0871747			0.0435873	−	0.999050i	$-0.486121\pi$
$971$	2.71644			0.0871747			0.0435873	+	0.999050i	$0.486121\pi$
$972$		−	1.76156i		−	0.0565022i
$973$		−	59.8494i		−	1.91868i
$974$	6.56221			0.210267
$975$	−7.08573	−	5.69181i	−0.226925	−	0.182284i
$976$	−19.0867			−0.610949
$977$		−	16.6829i		−	0.533733i	−0.963734	−	0.266866i	$-0.914012\pi$
$977$		−	16.6829i		−	0.533733i	0.963734	−	0.266866i	$-0.0859882\pi$
$978$		−	3.52930i		−	0.112854i
$979$		0			0
$980$	−70.9734	−	24.9757i	−2.26716	−	0.797820i
$981$	12.4980			0.399031
$982$			2.96975i			0.0947684i
$983$		−	26.2517i		−	0.837298i	−0.908148	−	0.418649i	$-0.862504\pi$
$983$		−	26.2517i		−	0.837298i	0.908148	−	0.418649i	$-0.137496\pi$
$984$	4.09933			0.130682
$985$	−13.6242	+	38.7160i	−0.434105	+	1.23359i
$986$	−2.36251			−0.0752378
$987$		−	7.74418i		−	0.246500i
$988$			14.0823i			0.448017i
$989$	−14.8066			−0.470823
$990$		0			0
$991$	−50.3117			−1.59821			−0.799103	−	0.601195i	$-0.794692\pi$
$991$	−50.3117			−1.59821			−0.799103	+	0.601195i	$0.794692\pi$
$992$			10.9279i			0.346960i
$993$		−	19.7763i		−	0.627583i
$994$	−13.7424			−0.435881
$995$	−46.7755	−	16.4604i	−1.48288	−	0.521830i
$996$	−0.285200			−0.00903691
$997$			45.2449i			1.43292i	0.697628	+	0.716460i	$0.254239\pi$
$997$			45.2449i			1.43292i	−0.697628	+	0.716460i	$0.745761\pi$
$998$		−	9.17719i		−	0.290499i
$999$	−5.97194			−0.188944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.k.364.15		24
5.2	odd	4		9075.2.a.dx.1.6		12
5.3	odd	4		9075.2.a.ea.1.7		12
5.4	even	2	inner	1815.2.c.k.364.10		24
11.7	odd	10		165.2.s.a.49.8	yes	48
11.8	odd	10		165.2.s.a.64.5	yes	48
11.10	odd	2		1815.2.c.j.364.10		24
33.8	even	10		495.2.ba.c.64.8		48
33.29	even	10		495.2.ba.c.379.5		48
55.7	even	20		825.2.n.o.676.4		24
55.8	even	20		825.2.n.p.526.3		24
55.18	even	20		825.2.n.p.676.3		24
55.19	odd	10		165.2.s.a.64.8	yes	48
55.29	odd	10		165.2.s.a.49.5	✓	48
55.32	even	4		9075.2.a.dz.1.7		12
55.43	even	4		9075.2.a.dy.1.6		12
55.52	even	20		825.2.n.o.526.4		24
55.54	odd	2		1815.2.c.j.364.15		24
165.29	even	10		495.2.ba.c.379.8		48
165.74	even	10		495.2.ba.c.64.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.5	✓	48	55.29	odd	10
165.2.s.a.49.8	yes	48	11.7	odd	10
165.2.s.a.64.5	yes	48	11.8	odd	10
165.2.s.a.64.8	yes	48	55.19	odd	10
495.2.ba.c.64.5		48	165.74	even	10
495.2.ba.c.64.8		48	33.8	even	10
495.2.ba.c.379.5		48	33.29	even	10
495.2.ba.c.379.8		48	165.29	even	10
825.2.n.o.526.4		24	55.52	even	20
825.2.n.o.676.4		24	55.7	even	20
825.2.n.p.526.3		24	55.8	even	20
825.2.n.p.676.3		24	55.18	even	20
1815.2.c.j.364.10		24	11.10	odd	2
1815.2.c.j.364.15		24	55.54	odd	2
1815.2.c.k.364.10		24	5.4	even	2	inner
1815.2.c.k.364.15		24	1.1	even	1	trivial
9075.2.a.dx.1.6		12	5.2	odd	4
9075.2.a.dy.1.6		12	55.43	even	4
9075.2.a.dz.1.7		12	55.32	even	4
9075.2.a.ea.1.7		12	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.488299i q^{2} -1.00000i q^{3} +1.76156 q^{4} +(2.10928 + 0.742259i) q^{5} +0.488299 q^{6} +5.10895i q^{7} +1.83677i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.488299i q^{2} -1.00000i q^{3} +1.76156 q^{4} +(2.10928 + 0.742259i) q^{5} +0.488299 q^{6} +5.10895i q^{7} +1.83677i q^{8} -1.00000 q^{9} +(-0.362444 + 1.02996i) q^{10} -1.76156i q^{12} -1.81774i q^{13} -2.49469 q^{14} +(0.742259 - 2.10928i) q^{15} +2.62624 q^{16} +0.639966i q^{17} -0.488299i q^{18} -4.39788 q^{19} +(3.71563 + 1.30754i) q^{20} +5.10895 q^{21} -4.37977i q^{23} +1.83677 q^{24} +(3.89810 + 3.13126i) q^{25} +0.887599 q^{26} +1.00000i q^{27} +8.99974i q^{28} +7.56018 q^{29} +(1.02996 + 0.362444i) q^{30} +2.20501 q^{31} +4.95592i q^{32} -0.312494 q^{34} +(-3.79216 + 10.7762i) q^{35} -1.76156 q^{36} +5.97194i q^{37} -2.14748i q^{38} -1.81774 q^{39} +(-1.36336 + 3.87425i) q^{40} +2.23182 q^{41} +2.49469i q^{42} -3.38068i q^{43} +(-2.10928 - 0.742259i) q^{45} +2.13864 q^{46} -1.51581i q^{47} -2.62624i q^{48} -19.1013 q^{49} +(-1.52899 + 1.90344i) q^{50} +0.639966 q^{51} -3.20206i q^{52} +9.17695i q^{53} -0.488299 q^{54} -9.38395 q^{56} +4.39788i q^{57} +3.69163i q^{58} -5.37174 q^{59} +(1.30754 - 3.71563i) q^{60} -7.26768 q^{61} +1.07670i q^{62} -5.10895i q^{63} +2.83250 q^{64} +(1.34923 - 3.83411i) q^{65} -7.25598i q^{67} +1.12734i q^{68} -4.37977 q^{69} +(-5.26200 - 1.85171i) q^{70} +5.50864 q^{71} -1.83677i q^{72} +7.14322i q^{73} -2.91609 q^{74} +(3.13126 - 3.89810i) q^{75} -7.74714 q^{76} -0.887599i q^{78} +1.90516 q^{79} +(5.53946 + 1.94935i) q^{80} +1.00000 q^{81} +1.08979i q^{82} -0.161902i q^{83} +8.99974 q^{84} +(-0.475021 + 1.34987i) q^{85} +1.65078 q^{86} -7.56018i q^{87} +1.19539 q^{89} +(0.362444 - 1.02996i) q^{90} +9.28673 q^{91} -7.71525i q^{92} -2.20501i q^{93} +0.740167 q^{94} +(-9.27634 - 3.26436i) q^{95} +4.95592 q^{96} +14.2823i q^{97} -9.32716i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Introduction

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