LMFDB - Embedded newform 1500.2.o.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Root			$0.132563 - 1.40799i$ of defining polynomial
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.b.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{3} -1.50430i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{3} -1.50430i q^{7} +(0.809017 - 0.587785i) q^{9} +(4.99517 + 3.62921i) q^{11} +(2.09036 + 2.87714i) q^{13} +(-0.471439 - 0.153180i) q^{17} +(-0.0963126 + 0.296420i) q^{19} +(-0.464854 - 1.43067i) q^{21} +(-1.79900 + 2.47611i) q^{23} +(0.587785 - 0.809017i) q^{27} +(0.0378031 + 0.116346i) q^{29} +(-0.909629 + 2.79955i) q^{31} +(5.87218 + 1.90799i) q^{33} +(-2.56686 - 3.53298i) q^{37} +(2.87714 + 2.09036i) q^{39} +(-3.44096 + 2.50001i) q^{41} -3.62663i q^{43} +(5.02362 - 1.63227i) q^{47} +4.73708 q^{49} -0.495700 q^{51} +(8.17888 - 2.65748i) q^{53} +0.311674i q^{57} +(10.4222 - 7.57219i) q^{59} +(9.15882 + 6.65427i) q^{61} +(-0.884205 - 1.21700i) q^{63} +(-12.5933 - 4.09181i) q^{67} +(-0.945790 + 2.91084i) q^{69} +(1.00994 + 3.10827i) q^{71} +(9.38504 - 12.9174i) q^{73} +(5.45941 - 7.51424i) q^{77} +(2.63513 + 8.11010i) q^{79} +(0.309017 - 0.951057i) q^{81} +(10.7832 + 3.50367i) q^{83} +(0.0719058 + 0.0989699i) q^{87} +(11.4335 + 8.30691i) q^{89} +(4.32808 - 3.14453i) q^{91} +2.94362i q^{93} +(-10.9208 + 3.54837i) q^{97} +6.17438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.50430i		−	0.568572i	−0.958740	−	0.284286i	$-0.908244\pi$
$7$		−	1.50430i		−	0.568572i	0.958740	−	0.284286i	$-0.0917565\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	4.99517	+	3.62921i	1.50610	+	1.09425i	0.967870	+	0.251450i	$0.0809074\pi$
$11$	4.99517	+	3.62921i	1.50610	+	1.09425i	0.538231	+	0.842797i	$0.319093\pi$
$12$		0			0
$13$	2.09036	+	2.87714i	0.579763	+	0.797975i	0.993669	−	0.112344i	$-0.0358359\pi$
$13$	2.09036	+	2.87714i	0.579763	+	0.797975i	−0.413906	+	0.910319i	$0.635836\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.471439	−	0.153180i	−0.114341	−	0.0371516i	0.251288	−	0.967912i	$-0.419146\pi$
$17$	−0.471439	−	0.153180i	−0.114341	−	0.0371516i	−0.365629	+	0.930761i	$0.619146\pi$
$18$		0			0
$19$	−0.0963126	+	0.296420i	−0.0220956	+	0.0680034i	−0.961496	−	0.274818i	$-0.911382\pi$
$19$	−0.0963126	+	0.296420i	−0.0220956	+	0.0680034i	0.939401	+	0.342821i	$0.111382\pi$
$20$		0			0
$21$	−0.464854	−	1.43067i	−0.101439	−	0.312199i
$22$		0			0
$23$	−1.79900	+	2.47611i	−0.375117	+	0.516305i	−0.954283	−	0.298905i	$-0.903379\pi$
$23$	−1.79900	+	2.47611i	−0.375117	+	0.516305i	0.579165	+	0.815210i	$0.303379\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$		0			0
$29$	0.0378031	+	0.116346i	0.00701987	+	0.0216049i	0.954505	−	0.298195i	$-0.0963844\pi$
$29$	0.0378031	+	0.116346i	0.00701987	+	0.0216049i	−0.947485	+	0.319800i	$0.896384\pi$
$30$		0			0
$31$	−0.909629	+	2.79955i	−0.163374	+	0.502814i	−0.998913	−	0.0466176i	$-0.985156\pi$
$31$	−0.909629	+	2.79955i	−0.163374	+	0.502814i	0.835539	+	0.549432i	$0.185156\pi$
$32$		0			0
$33$	5.87218	+	1.90799i	1.02222	+	0.332138i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.56686	−	3.53298i	−0.421989	−	0.580818i	0.544102	−	0.839019i	$-0.316870\pi$
$37$	−2.56686	−	3.53298i	−0.421989	−	0.580818i	−0.966091	+	0.258201i	$0.916870\pi$
$38$		0			0
$39$	2.87714	+	2.09036i	0.460711	+	0.334726i
$40$		0			0
$41$	−3.44096	+	2.50001i	−0.537388	+	0.390436i	−0.823114	−	0.567876i	$-0.807765\pi$
$41$	−3.44096	+	2.50001i	−0.537388	+	0.390436i	0.285726	+	0.958311i	$0.407765\pi$
$42$		0			0
$43$		−	3.62663i		−	0.553056i	−0.961006	−	0.276528i	$-0.910816\pi$
$43$		−	3.62663i		−	0.553056i	0.961006	−	0.276528i	$-0.0891839\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.02362	−	1.63227i	0.732770	−	0.238091i	0.0812191	−	0.996696i	$-0.474119\pi$
$47$	5.02362	−	1.63227i	0.732770	−	0.238091i	0.651551	+	0.758605i	$0.274119\pi$
$48$		0			0
$49$	4.73708			0.676726
$50$		0			0
$51$	−0.495700			−0.0694120
$52$		0			0
$53$	8.17888	−	2.65748i	1.12346	−	0.365033i	0.312370	−	0.949960i	$-0.398877\pi$
$53$	8.17888	−	2.65748i	1.12346	−	0.365033i	0.811086	+	0.584928i	$0.198877\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			0.311674i			0.0412823i
$58$		0			0
$59$	10.4222	−	7.57219i	1.35686	−	0.985815i	0.358220	−	0.933637i	$-0.383384\pi$
$59$	10.4222	−	7.57219i	1.35686	−	0.985815i	0.998638	−	0.0521781i	$-0.0166164\pi$
$60$		0			0
$61$	9.15882	+	6.65427i	1.17267	+	0.851992i	0.991326	−	0.131428i	$-0.0419562\pi$
$61$	9.15882	+	6.65427i	1.17267	+	0.851992i	0.181341	+	0.983420i	$0.441956\pi$
$62$		0			0
$63$	−0.884205	−	1.21700i	−0.111399	−	0.153328i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−12.5933	−	4.09181i	−1.53852	−	0.499894i	−0.587550	−	0.809188i	$-0.699908\pi$
$67$	−12.5933	−	4.09181i	−1.53852	−	0.499894i	−0.950967	+	0.309293i	$0.899908\pi$
$68$		0			0
$69$	−0.945790	+	2.91084i	−0.113860	+	0.350424i
$70$		0			0
$71$	1.00994	+	3.10827i	0.119858	+	0.368884i	0.992929	−	0.118708i	$-0.0378753\pi$
$71$	1.00994	+	3.10827i	0.119858	+	0.368884i	−0.873071	+	0.487592i	$0.837875\pi$
$72$		0			0
$73$	9.38504	−	12.9174i	1.09844	−	1.51187i	0.260994	−	0.965340i	$-0.415950\pi$
$73$	9.38504	−	12.9174i	1.09844	−	1.51187i	0.837441	−	0.546527i	$-0.184050\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.45941	−	7.51424i	0.622158	−	0.856327i
$78$		0			0
$79$	2.63513	+	8.11010i	0.296475	+	0.912457i	0.982722	+	0.185088i	$0.0592571\pi$
$79$	2.63513	+	8.11010i	0.296475	+	0.912457i	−0.686247	+	0.727369i	$0.740743\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	10.7832	+	3.50367i	1.18361	+	0.384578i	0.833706	−	0.552208i	$-0.186215\pi$
$83$	10.7832	+	3.50367i	1.18361	+	0.384578i	0.349903	+	0.936786i	$0.386215\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.0719058	+	0.0989699i	0.00770911	+	0.0106107i
$88$		0			0
$89$	11.4335	+	8.30691i	1.21195	+	0.880531i	0.995406	−	0.0957428i	$-0.0305226\pi$
$89$	11.4335	+	8.30691i	1.21195	+	0.880531i	0.216541	+	0.976274i	$0.430523\pi$
$90$		0			0
$91$	4.32808	−	3.14453i	0.453706	−	0.329637i
$92$		0			0
$93$			2.94362i			0.305239i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.9208	+	3.54837i	−1.10884	+	0.360282i	−0.805497	−	0.592601i	$-0.798101\pi$
$97$	−10.9208	+	3.54837i	−1.10884	+	0.360282i	−0.303339	+	0.952883i	$0.598101\pi$
$98$		0			0
$99$	6.17438			0.620548
$100$		0			0
$101$	−14.8359			−1.47622			−0.738111	−	0.674679i	$-0.764282\pi$
$101$	−14.8359			−1.47622			−0.738111	+	0.674679i	$0.764282\pi$
$102$		0			0
$103$	−18.3217	+	5.95307i	−1.80529	+	0.586574i	−0.999980	−	0.00628354i	$-0.998000\pi$
$103$	−18.3217	+	5.95307i	−1.80529	+	0.586574i	−0.805308	+	0.592857i	$0.798000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	8.63523i		−	0.834799i	−0.908723	−	0.417400i	$-0.862942\pi$
$107$		−	8.63523i		−	0.834799i	0.908723	−	0.417400i	$-0.137058\pi$
$108$		0			0
$109$	−15.1200	+	10.9853i	−1.44823	+	1.05220i	−0.461989	+	0.886886i	$0.652864\pi$
$109$	−15.1200	+	10.9853i	−1.44823	+	1.05220i	−0.986241	+	0.165315i	$0.947136\pi$
$110$		0			0
$111$	−3.53298	−	2.56686i	−0.335335	−	0.243635i
$112$		0			0
$113$	−3.55985	−	4.89971i	−0.334883	−	0.460926i	0.608056	−	0.793894i	$-0.291950\pi$
$113$	−3.55985	−	4.89971i	−0.334883	−	0.460926i	−0.942938	+	0.332968i	$0.891950\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.38228	+	1.09897i	0.312692	+	0.101600i
$118$		0			0
$119$	−0.230428	+	0.709186i	−0.0211233	+	0.0650109i
$120$		0			0
$121$	8.38144	+	25.7954i	0.761949	+	2.34504i
$122$		0			0
$123$	−2.50001	+	3.44096i	−0.225418	+	0.310261i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.43445	−	7.47988i	0.482230	−	0.663732i	−0.496702	−	0.867921i	$-0.665456\pi$
$127$	5.43445	−	7.47988i	0.482230	−	0.663732i	0.978931	+	0.204189i	$0.0654557\pi$
$128$		0			0
$129$	−1.12069	−	3.44913i	−0.0986714	−	0.303679i
$130$		0			0
$131$	5.87613	−	18.0849i	0.513399	−	1.58008i	−0.272776	−	0.962078i	$-0.587942\pi$
$131$	5.87613	−	18.0849i	0.513399	−	1.58008i	0.786175	−	0.618003i	$-0.212058\pi$
$132$		0			0
$133$	0.445904	+	0.144883i	0.0386648	+	0.0125630i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.62120	+	6.36053i	0.394816	+	0.543417i	0.959433	−	0.281936i	$-0.0909764\pi$
$137$	4.62120	+	6.36053i	0.394816	+	0.543417i	−0.564618	+	0.825352i	$0.690976\pi$
$138$		0			0
$139$	−11.1647	−	8.11165i	−0.946980	−	0.688021i	0.00311101	−	0.999995i	$-0.499010\pi$
$139$	−11.1647	−	8.11165i	−0.946980	−	0.688021i	−0.950091	+	0.311974i	$0.899010\pi$
$140$		0			0
$141$	4.27335	−	3.10477i	0.359881	−	0.261469i
$142$		0			0
$143$			21.9582i			1.83624i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.50523	−	1.46384i	0.371585	−	0.120735i
$148$		0			0
$149$	−5.12168			−0.419585			−0.209792	−	0.977746i	$-0.567279\pi$
$149$	−5.12168			−0.419585			−0.209792	+	0.977746i	$0.567279\pi$
$150$		0			0
$151$	−12.9476			−1.05366			−0.526829	−	0.849972i	$-0.676619\pi$
$151$	−12.9476			−1.05366			−0.526829	+	0.849972i	$0.676619\pi$
$152$		0			0
$153$	−0.471439	+	0.153180i	−0.0381136	+	0.0123839i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			4.02750i			0.321429i	0.987001	+	0.160715i	$0.0513799\pi$
$157$			4.02750i			0.321429i	−0.987001	+	0.160715i	$0.948620\pi$
$158$		0			0
$159$	6.95737	−	5.05483i	0.551755	−	0.400874i
$160$		0			0
$161$	3.72481	+	2.70623i	0.293556	+	0.213281i
$162$		0			0
$163$	−9.18062	−	12.6360i	−0.719082	−	0.989732i	−0.999554	−	0.0298692i	$-0.990491\pi$
$163$	−9.18062	−	12.6360i	−0.719082	−	0.989732i	0.280472	−	0.959862i	$-0.409509\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.2647	−	3.66014i	−0.871692	−	0.283230i	−0.161189	−	0.986924i	$-0.551533\pi$
$167$	−11.2647	−	3.66014i	−0.871692	−	0.283230i	−0.710503	+	0.703694i	$0.751533\pi$
$168$		0			0
$169$	0.108909	−	0.335187i	0.00837761	−	0.0257836i
$170$		0			0
$171$	0.0963126	+	0.296420i	0.00736521	+	0.0226678i
$172$		0			0
$173$	8.71717	−	11.9982i	0.662754	−	0.912203i	−0.336814	−	0.941571i	$-0.609349\pi$
$173$	8.71717	−	11.9982i	0.662754	−	0.912203i	0.999569	+	0.0293681i	$0.00934950\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	7.57219	−	10.4222i	0.569161	−	0.783382i
$178$		0			0
$179$	0.295895	+	0.910670i	0.0221162	+	0.0680667i	0.961505	−	0.274786i	$-0.0886069\pi$
$179$	0.295895	+	0.910670i	0.0221162	+	0.0680667i	−0.939389	+	0.342852i	$0.888607\pi$
$180$		0			0
$181$	1.27971	−	3.93855i	0.0951202	−	0.292750i	−0.892165	−	0.451710i	$-0.850814\pi$
$181$	1.27971	−	3.93855i	0.0951202	−	0.292750i	0.987285	+	0.158960i	$0.0508141\pi$
$182$		0			0
$183$	10.7668	+	3.49836i	0.795908	+	0.258606i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.79900	−	2.47611i	−0.131556	−	0.181071i
$188$		0			0
$189$	−1.21700	−	0.884205i	−0.0885240	−	0.0643165i
$190$		0			0
$191$	14.2634	−	10.3629i	1.03206	−	0.749836i	0.0633410	−	0.997992i	$-0.479824\pi$
$191$	14.2634	−	10.3629i	1.03206	−	0.749836i	0.968720	+	0.248156i	$0.0798244\pi$
$192$		0			0
$193$			5.25392i			0.378185i	0.981959	+	0.189093i	$0.0605546\pi$
$193$			5.25392i			0.378185i	−0.981959	+	0.189093i	$0.939445\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.01240	+	0.653870i	−0.143378	+	0.0465863i	−0.379827	−	0.925058i	$-0.624016\pi$
$197$	−2.01240	+	0.653870i	−0.143378	+	0.0465863i	0.236449	+	0.971644i	$0.424016\pi$
$198$		0			0
$199$	−9.07029			−0.642976			−0.321488	−	0.946914i	$-0.604183\pi$
$199$	−9.07029			−0.642976			−0.321488	+	0.946914i	$0.604183\pi$
$200$		0			0
$201$	−13.2414			−0.933975
$202$		0			0
$203$	0.175019	−	0.0568672i	0.0122840	−	0.00399130i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			3.06064i			0.212729i
$208$		0			0
$209$	−1.55687	+	1.13113i	−0.107691	+	0.0782419i
$210$		0			0
$211$	16.0306	+	11.6469i	1.10359	+	0.801807i	0.981643	−	0.190729i	$-0.0610853\pi$
$211$	16.0306	+	11.6469i	1.10359	+	0.801807i	0.121950	+	0.992536i	$0.461085\pi$
$212$		0			0
$213$	1.92102	+	2.64405i	0.131626	+	0.181168i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.21136	+	1.36835i	0.285886	+	0.0928900i
$218$		0			0
$219$	4.93401	−	15.1853i	0.333409	−	1.02613i
$220$		0			0
$221$	−0.544760	−	1.67660i	−0.0366445	−	0.112780i
$222$		0			0
$223$	3.86888	−	5.32506i	0.259080	−	0.356593i	−0.659586	−	0.751629i	$-0.729268\pi$
$223$	3.86888	−	5.32506i	0.259080	−	0.356593i	0.918665	+	0.395037i	$0.129268\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.92535	+	9.53193i	−0.459652	+	0.632656i	−0.974436	−	0.224663i	$-0.927872\pi$
$227$	−6.92535	+	9.53193i	−0.459652	+	0.632656i	0.514785	+	0.857319i	$0.327872\pi$
$228$		0			0
$229$	−3.67417	−	11.3079i	−0.242796	−	0.747250i	−0.995991	−	0.0894526i	$-0.971488\pi$
$229$	−3.67417	−	11.3079i	−0.242796	−	0.747250i	0.753195	−	0.657798i	$-0.228512\pi$
$230$		0			0
$231$	2.87018	−	8.83352i	0.188844	−	0.581203i
$232$		0			0
$233$	−4.80285	−	1.56054i	−0.314645	−	0.102234i	0.147437	−	0.989071i	$-0.452898\pi$
$233$	−4.80285	−	1.56054i	−0.314645	−	0.102234i	−0.462082	+	0.886837i	$0.652898\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.01232	+	6.89886i	0.325585	+	0.448129i
$238$		0			0
$239$	2.16762	+	1.57487i	0.140212	+	0.101870i	0.655680	−	0.755039i	$-0.272382\pi$
$239$	2.16762	+	1.57487i	0.140212	+	0.101870i	−0.515468	+	0.856909i	$0.672382\pi$
$240$		0			0
$241$	−10.2390	+	7.43906i	−0.659551	+	0.479192i	−0.866511	−	0.499157i	$-0.833643\pi$
$241$	−10.2390	+	7.43906i	−0.659551	+	0.479192i	0.206960	+	0.978349i	$0.433643\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.05417	+	0.342521i	−0.0670752	+	0.0217941i
$248$		0			0
$249$	11.3381			0.718524
$250$		0			0
$251$	−22.9068			−1.44586			−0.722932	−	0.690919i	$-0.757206\pi$
$251$	−22.9068			−1.44586			−0.722932	+	0.690919i	$0.757206\pi$
$252$		0			0
$253$	−17.9726	+	5.83966i	−1.12993	+	0.367136i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			27.7764i			1.73264i	0.499486	+	0.866322i	$0.333522\pi$
$257$			27.7764i			1.73264i	−0.499486	+	0.866322i	$0.666478\pi$
$258$		0			0
$259$	−5.31466	+	3.86132i	−0.330237	+	0.239931i
$260$		0			0
$261$	0.0989699	+	0.0719058i	0.00612608	+	0.00445086i
$262$		0			0
$263$	−6.88384	−	9.47479i	−0.424476	−	0.584241i	0.542198	−	0.840250i	$-0.317592\pi$
$263$	−6.88384	−	9.47479i	−0.424476	−	0.584241i	−0.966674	+	0.256010i	$0.917592\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	13.4409	+	4.36720i	0.822568	+	0.267268i
$268$		0			0
$269$	−1.29979	+	4.00034i	−0.0792496	+	0.243905i	−0.982830	−	0.184513i	$-0.940929\pi$
$269$	−1.29979	+	4.00034i	−0.0792496	+	0.243905i	0.903580	+	0.428419i	$0.140929\pi$
$270$		0			0
$271$	−3.88308	−	11.9509i	−0.235880	−	0.725965i	−0.997003	−	0.0773578i	$-0.975352\pi$
$271$	−3.88308	−	11.9509i	−0.235880	−	0.725965i	0.761123	−	0.648608i	$-0.224648\pi$
$272$		0			0
$273$	3.14453	−	4.32808i	0.190316	−	0.261947i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.7299	+	25.7795i	−1.12537	+	1.54894i	−0.328800	+	0.944400i	$0.606644\pi$
$277$	−18.7299	+	25.7795i	−1.12537	+	1.54894i	−0.796573	+	0.604543i	$0.793356\pi$
$278$		0			0
$279$	0.909629	+	2.79955i	0.0544581	+	0.167605i
$280$		0			0
$281$	5.03691	−	15.5020i	0.300477	−	0.924773i	−0.680849	−	0.732423i	$-0.738389\pi$
$281$	5.03691	−	15.5020i	0.300477	−	0.924773i	0.981326	−	0.192350i	$-0.0616108\pi$
$282$		0			0
$283$	−12.9634	−	4.21205i	−0.770592	−	0.250381i	−0.102774	−	0.994705i	$-0.532772\pi$
$283$	−12.9634	−	4.21205i	−0.770592	−	0.250381i	−0.667819	+	0.744324i	$0.732772\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.76076	+	5.17624i	0.221991	+	0.305544i
$288$		0			0
$289$	−13.5545	−	9.84792i	−0.797323	−	0.579289i
$290$		0			0
$291$	−9.28975	+	6.74940i	−0.544575	+	0.395657i
$292$		0			0
$293$			25.2652i			1.47601i	0.674796	+	0.738004i	$0.264232\pi$
$293$			25.2652i			1.47601i	−0.674796	+	0.738004i	$0.735768\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	5.87218	−	1.90799i	0.340738	−	0.110713i
$298$		0			0
$299$	−10.8847			−0.629477
$300$		0			0
$301$	−5.45554			−0.314452
$302$		0			0
$303$	−14.1097	+	4.58453i	−0.810583	+	0.263374i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			7.01023i			0.400095i	0.979786	+	0.200047i	$0.0641096\pi$
$307$			7.01023i			0.400095i	−0.979786	+	0.200047i	$0.935890\pi$
$308$		0			0
$309$	−15.5853	+	11.3234i	−0.886619	+	0.644167i
$310$		0			0
$311$	−11.7403	−	8.52985i	−0.665733	−	0.483683i	0.202861	−	0.979208i	$-0.434976\pi$
$311$	−11.7403	−	8.52985i	−0.665733	−	0.483683i	−0.868594	+	0.495524i	$0.834976\pi$
$312$		0			0
$313$	−12.8841	−	17.7334i	−0.728250	−	1.00235i	−0.999209	−	0.0397589i	$-0.987341\pi$
$313$	−12.8841	−	17.7334i	−0.728250	−	1.00235i	0.270960	−	0.962591i	$-0.412659\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	32.0675	+	10.4194i	1.80109	+	0.585210i	0.999913	−	0.0132156i	$-0.00420677\pi$
$317$	32.0675	+	10.4194i	1.80109	+	0.585210i	0.801178	+	0.598426i	$0.204207\pi$
$318$		0			0
$319$	−0.233411	+	0.718364i	−0.0130685	+	0.0402207i
$320$		0			0
$321$	−2.66843	−	8.21259i	−0.148937	−	0.458382i
$322$		0			0
$323$	0.0908111	−	0.124991i	0.00505286	−	0.00695467i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−10.9853	+	15.1200i	−0.607488	+	0.836136i
$328$		0			0
$329$	−2.45543	−	7.55703i	−0.135372	−	0.416632i
$330$		0			0
$331$	10.3814	−	31.9508i	0.570616	−	1.75617i	−0.0800299	−	0.996792i	$-0.525502\pi$
$331$	10.3814	−	31.9508i	0.570616	−	1.75617i	0.650645	−	0.759382i	$-0.274498\pi$
$332$		0			0
$333$	−4.15326	−	1.34948i	−0.227597	−	0.0739509i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.81347	+	2.49603i	0.0987859	+	0.135967i	0.855548	−	0.517723i	$-0.173220\pi$
$337$	1.81347	+	2.49603i	0.0987859	+	0.135967i	−0.756763	+	0.653690i	$0.773220\pi$
$338$		0			0
$339$	−4.89971	−	3.55985i	−0.266116	−	0.193345i
$340$		0			0
$341$	−14.7039	+	10.6830i	−0.796261	+	0.578518i
$342$		0			0
$343$		−	17.6561i		−	0.953339i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.9585	−	3.88556i	0.641967	−	0.208588i	0.0300984	−	0.999547i	$-0.490418\pi$
$347$	11.9585	−	3.88556i	0.641967	−	0.208588i	0.611869	+	0.790959i	$0.290418\pi$
$348$		0			0
$349$	−13.3100			−0.712466			−0.356233	−	0.934397i	$-0.615939\pi$
$349$	−13.3100			−0.712466			−0.356233	+	0.934397i	$0.615939\pi$
$350$		0			0
$351$	3.55634			0.189823
$352$		0			0
$353$	10.7388	−	3.48923i	0.571566	−	0.185713i	−0.00895265	−	0.999960i	$-0.502850\pi$
$353$	10.7388	−	3.48923i	0.571566	−	0.185713i	0.580519	+	0.814247i	$0.302850\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			0.745682i			0.0394657i
$358$		0			0
$359$	15.7007	−	11.4072i	0.828652	−	0.602051i	−0.0905254	−	0.995894i	$-0.528855\pi$
$359$	15.7007	−	11.4072i	0.828652	−	0.602051i	0.919178	+	0.393843i	$0.128855\pi$
$360$		0			0
$361$	15.2927	+	11.1108i	0.804881	+	0.584780i
$362$		0			0
$363$	15.9424	+	21.9429i	0.836761	+	1.15170i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.7103	−	5.42951i	−0.872271	−	0.283418i	−0.161526	−	0.986868i	$-0.551642\pi$
$367$	−16.7103	−	5.42951i	−0.872271	−	0.283418i	−0.710744	+	0.703450i	$0.751642\pi$
$368$		0			0
$369$	−1.31433	+	4.04510i	−0.0684214	+	0.210579i
$370$		0			0
$371$	−3.99764	−	12.3035i	−0.207547	−	0.638765i
$372$		0			0
$373$	−16.5793	+	22.8195i	−0.858446	+	1.18155i	0.123492	+	0.992346i	$0.460591\pi$
$373$	−16.5793	+	22.8195i	−0.858446	+	1.18155i	−0.981938	+	0.189204i	$0.939409\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.255722	+	0.351971i	−0.0131703	+	0.0181274i
$378$		0			0
$379$	−1.12118	−	3.45064i	−0.0575912	−	0.177247i	0.918123	−	0.396296i	$-0.129705\pi$
$379$	−1.12118	−	3.45064i	−0.0575912	−	0.177247i	−0.975714	+	0.219049i	$0.929705\pi$
$380$		0			0
$381$	2.85706	−	8.79313i	0.146372	−	0.450486i
$382$		0			0
$383$	−13.1577	−	4.27519i	−0.672326	−	0.218452i	−0.0470934	−	0.998890i	$-0.514996\pi$
$383$	−13.1577	−	4.27519i	−0.672326	−	0.218452i	−0.625232	+	0.780439i	$0.714996\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.13168	−	2.93401i	−0.108359	−	0.149144i
$388$		0			0
$389$	−16.9096	−	12.2855i	−0.857348	−	0.622900i	0.0698138	−	0.997560i	$-0.477759\pi$
$389$	−16.9096	−	12.2855i	−0.857348	−	0.622900i	−0.927162	+	0.374660i	$0.877759\pi$
$390$		0			0
$391$	1.22741	−	0.891765i	0.0620727	−	0.0450985i
$392$		0			0
$393$		−	19.0155i		−	0.959207i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−14.6959	+	4.77499i	−0.737566	+	0.239650i	−0.653622	−	0.756821i	$-0.726752\pi$
$397$	−14.6959	+	4.77499i	−0.737566	+	0.239650i	−0.0839436	+	0.996471i	$0.526752\pi$
$398$		0			0
$399$	0.468851			0.0234719
$400$		0			0
$401$	2.25590			0.112654			0.0563271	−	0.998412i	$-0.482061\pi$
$401$	2.25590			0.112654			0.0563271	+	0.998412i	$0.482061\pi$
$402$		0			0
$403$	−9.95616	+	3.23495i	−0.495952	+	0.161144i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	26.9635i		−	1.33653i
$408$		0			0
$409$	−1.88712	+	1.37107i	−0.0933119	+	0.0677951i	−0.633463	−	0.773773i	$-0.718367\pi$
$409$	−1.88712	+	1.37107i	−0.0933119	+	0.0677951i	0.540151	+	0.841568i	$0.318367\pi$
$410$		0			0
$411$	6.36053	+	4.62120i	0.313742	+	0.227947i
$412$		0			0
$413$	−11.3908	−	15.6781i	−0.560507	−	0.771471i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−13.1249	−	4.26455i	−0.642730	−	0.208836i
$418$		0			0
$419$	1.55768	−	4.79405i	0.0760977	−	0.234205i	−0.905771	−	0.423768i	$-0.860707\pi$
$419$	1.55768	−	4.79405i	0.0760977	−	0.234205i	0.981869	+	0.189563i	$0.0607072\pi$
$420$		0			0
$421$	3.99823	+	12.3053i	0.194862	+	0.599724i	0.999978	+	0.00660640i	$0.00210290\pi$
$421$	3.99823	+	12.3053i	0.194862	+	0.599724i	−0.805116	+	0.593117i	$0.797897\pi$
$422$		0			0
$423$	3.10477	−	4.27335i	0.150959	−	0.207777i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	10.0100	−	13.7776i	0.484419	−	0.666745i
$428$		0			0
$429$	6.78545	+	20.8835i	0.327605	+	1.00826i
$430$		0			0
$431$	0.483616	−	1.48842i	0.0232950	−	0.0716945i	−0.938733	−	0.344645i	$-0.887999\pi$
$431$	0.483616	−	1.48842i	0.0232950	−	0.0716945i	0.962028	+	0.272950i	$0.0879994\pi$
$432$		0			0
$433$	24.6066	+	7.99517i	1.18252	+	0.384224i	0.833302	−	0.552818i	$-0.186448\pi$
$433$	24.6066	+	7.99517i	1.18252	+	0.384224i	0.349217	+	0.937042i	$0.386448\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.560702	−	0.771740i	−0.0268220	−	0.0369173i
$438$		0			0
$439$	13.2446	+	9.62279i	0.632132	+	0.459271i	0.857138	−	0.515087i	$-0.172240\pi$
$439$	13.2446	+	9.62279i	0.632132	+	0.459271i	−0.225006	+	0.974357i	$0.572240\pi$
$440$		0			0
$441$	3.83238	−	2.78439i	0.182494	−	0.132590i
$442$		0			0
$443$			28.1180i			1.33593i	0.744194	+	0.667963i	$0.232834\pi$
$443$			28.1180i			1.33593i	−0.744194	+	0.667963i	$0.767166\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.87101	+	1.58269i	−0.230391	+	0.0748585i
$448$		0			0
$449$	2.65681			0.125383			0.0626914	−	0.998033i	$-0.480032\pi$
$449$	2.65681			0.125383			0.0626914	+	0.998033i	$0.480032\pi$
$450$		0			0
$451$	−26.2613			−1.23659
$452$		0			0
$453$	−12.3139	+	4.00101i	−0.578556	+	0.187984i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			0.321574i			0.0150426i	0.999972	+	0.00752129i	$0.00239412\pi$
$457$			0.321574i			0.0150426i	−0.999972	+	0.00752129i	$0.997606\pi$
$458$		0			0
$459$	−0.401030	+	0.291365i	−0.0187185	+	0.0135998i
$460$		0			0
$461$	6.21780	+	4.51749i	0.289592	+	0.210401i	0.723090	−	0.690754i	$-0.242721\pi$
$461$	6.21780	+	4.51749i	0.289592	+	0.210401i	−0.433499	+	0.901154i	$0.642721\pi$
$462$		0			0
$463$	−11.2291	−	15.4555i	−0.521860	−	0.718279i	0.464002	−	0.885834i	$-0.346413\pi$
$463$	−11.2291	−	15.4555i	−0.521860	−	0.718279i	−0.985863	+	0.167555i	$0.946413\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.10525	+	1.98372i	0.282517	+	0.0917955i	0.446848	−	0.894610i	$-0.352546\pi$
$467$	6.10525	+	1.98372i	0.282517	+	0.0917955i	−0.164331	+	0.986405i	$0.552546\pi$
$468$		0			0
$469$	−6.15531	+	18.9441i	−0.284226	+	0.874757i
$470$		0			0
$471$	1.24457	+	3.83038i	0.0573466	+	0.176495i
$472$		0			0
$473$	13.1618	−	18.1157i	0.605180	−	0.832959i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	5.05483	−	6.95737i	0.231445	−	0.318556i
$478$		0			0
$479$	−10.3709	−	31.9183i	−0.473858	−	1.45839i	−0.847491	−	0.530810i	$-0.821888\pi$
$479$	−10.3709	−	31.9183i	−0.473858	−	1.45839i	0.373633	−	0.927577i	$-0.378112\pi$
$480$		0			0
$481$	4.79920	−	14.7704i	0.218825	−	0.673473i
$482$		0			0
$483$	4.37878	+	1.42275i	0.199241	+	0.0647374i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−7.00080	−	9.63578i	−0.317237	−	0.436639i	0.620384	−	0.784298i	$-0.286977\pi$
$487$	−7.00080	−	9.63578i	−0.317237	−	0.436639i	−0.937621	+	0.347659i	$0.886977\pi$
$488$		0			0
$489$	−12.6360	−	9.18062i	−0.571422	−	0.415162i
$490$		0			0
$491$	−12.6312	+	9.17712i	−0.570039	+	0.414158i	−0.835119	−	0.550069i	$-0.814602\pi$
$491$	−12.6312	+	9.17712i	−0.570039	+	0.414158i	0.265080	+	0.964226i	$0.414602\pi$
$492$		0			0
$493$		−	0.0606408i		−	0.00273112i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.67577	−	1.51925i	0.209737	−	0.0681477i
$498$		0			0
$499$	−30.9130			−1.38386			−0.691929	−	0.721966i	$-0.743239\pi$
$499$	−30.9130			−1.38386			−0.691929	+	0.721966i	$0.743239\pi$
$500$		0			0
$501$	−11.8445			−0.529171
$502$		0			0
$503$	−29.5204	+	9.59178i	−1.31625	+	0.427676i	−0.881206	−	0.472732i	$-0.843268\pi$
$503$	−29.5204	+	9.59178i	−1.31625	+	0.427676i	−0.435046	+	0.900408i	$0.643268\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	0.352437i		−	0.0156523i
$508$		0			0
$509$	−10.7945	+	7.84269i	−0.478460	+	0.347621i	−0.800729	−	0.599027i	$-0.795554\pi$
$509$	−10.7945	+	7.84269i	−0.478460	+	0.347621i	0.322269	+	0.946648i	$0.395554\pi$
$510$		0			0
$511$	−19.4316	−	14.1179i	−0.859605	−	0.624540i
$512$		0			0
$513$	0.183198	+	0.252150i	0.00808837	+	0.0111327i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	31.0177	+	10.0783i	1.36416	+	0.443242i
$518$		0			0
$519$	4.58289	−	14.1047i	0.201166	−	0.619127i
$520$		0			0
$521$	8.19439	+	25.2197i	0.359003	+	1.10490i	0.953652	+	0.300912i	$0.0972910\pi$
$521$	8.19439	+	25.2197i	0.359003	+	1.10490i	−0.594649	+	0.803985i	$0.702709\pi$
$522$		0			0
$523$	−10.2361	+	14.0888i	−0.447594	+	0.616060i	−0.971878	−	0.235483i	$-0.924333\pi$
$523$	−10.2361	+	14.0888i	−0.447594	+	0.616060i	0.524285	+	0.851543i	$0.324333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.857670	−	1.18048i	0.0373607	−	0.0514226i
$528$		0			0
$529$	4.21267	+	12.9653i	0.183159	+	0.563707i
$530$		0			0
$531$	3.98094	−	12.2521i	0.172758	−	0.531694i
$532$		0			0
$533$	−14.3857	−	4.67421i	−0.623116	−	0.202463i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.562825	+	0.774662i	0.0242877	+	0.0334291i
$538$		0			0
$539$	23.6626	+	17.1919i	1.01922	+	0.740506i
$540$		0			0
$541$	−4.42275	+	3.21332i	−0.190149	+	0.138151i	−0.678787	−	0.734335i	$-0.737494\pi$
$541$	−4.42275	+	3.21332i	−0.190149	+	0.138151i	0.488638	+	0.872487i	$0.337494\pi$
$542$		0			0
$543$		−	4.14123i		−	0.177717i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	20.5864	−	6.68894i	0.880212	−	0.285998i	0.166167	−	0.986098i	$-0.446861\pi$
$547$	20.5864	−	6.68894i	0.880212	−	0.285998i	0.714046	+	0.700099i	$0.246861\pi$
$548$		0			0
$549$	11.3209			0.483165
$550$		0			0
$551$	−0.0381282			−0.00162432
$552$		0			0
$553$	12.2000	−	3.96403i	0.518798	−	0.168568i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			2.58830i			0.109670i	0.998495	+	0.0548349i	$0.0174633\pi$
$557$			2.58830i			0.109670i	−0.998495	+	0.0548349i	$0.982537\pi$
$558$		0			0
$559$	10.4343	−	7.58099i	0.441325	−	0.320642i
$560$		0			0
$561$	−2.47611	−	1.79900i	−0.104541	−	0.0759538i
$562$		0			0
$563$	−11.6933	−	16.0945i	−0.492815	−	0.678301i	0.488089	−	0.872794i	$-0.337694\pi$
$563$	−11.6933	−	16.0945i	−0.492815	−	0.678301i	−0.980904	+	0.194493i	$0.937694\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.43067	−	0.464854i	−0.0600827	−	0.0195220i
$568$		0			0
$569$	−10.0215	+	30.8431i	−0.420124	+	1.29301i	0.487463	+	0.873144i	$0.337923\pi$
$569$	−10.0215	+	30.8431i	−0.420124	+	1.29301i	−0.907587	+	0.419865i	$0.862077\pi$
$570$		0			0
$571$	4.23915	+	13.0468i	0.177403	+	0.545990i	0.999735	−	0.0230176i	$-0.00732739\pi$
$571$	4.23915	+	13.0468i	0.177403	+	0.545990i	−0.822332	+	0.569008i	$0.807327\pi$
$572$		0			0
$573$	10.3629	−	14.2634i	0.432918	−	0.595861i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−14.4849	+	19.9368i	−0.603015	+	0.829979i	−0.995980	−	0.0895741i	$-0.971449\pi$
$577$	−14.4849	+	19.9368i	−0.603015	+	0.829979i	0.392965	+	0.919553i	$0.371449\pi$
$578$		0			0
$579$	1.62355	+	4.99677i	0.0674724	+	0.207659i
$580$		0			0
$581$	5.27057	−	16.2212i	0.218660	−	0.672967i
$582$		0			0
$583$	50.4995	+	16.4083i	2.09147	+	0.679561i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.89134	+	6.73236i	0.201887	+	0.277874i	0.897941	−	0.440115i	$-0.145062\pi$
$587$	4.89134	+	6.73236i	0.201887	+	0.277874i	−0.696054	+	0.717990i	$0.745062\pi$
$588$		0			0
$589$	−0.742234	−	0.539264i	−0.0305832	−	0.0222200i
$590$		0			0
$591$	−1.71185	+	1.24373i	−0.0704162	+	0.0511604i
$592$		0			0
$593$			21.7904i			0.894826i	0.894328	+	0.447413i	$0.147654\pi$
$593$			21.7904i			0.894826i	−0.894328	+	0.447413i	$0.852346\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.62636	+	2.80287i	−0.353053	+	0.114714i
$598$		0			0
$599$	−10.6482			−0.435074			−0.217537	−	0.976052i	$-0.569802\pi$
$599$	−10.6482			−0.435074			−0.217537	+	0.976052i	$0.569802\pi$
$600$		0			0
$601$	2.60740			0.106358			0.0531791	−	0.998585i	$-0.483065\pi$
$601$	2.60740			0.106358			0.0531791	+	0.998585i	$0.483065\pi$
$602$		0			0
$603$	−12.5933	+	4.09181i	−0.512839	+	0.166631i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	32.9820i		−	1.33870i	−0.742948	−	0.669349i	$-0.766573\pi$
$607$		−	32.9820i		−	1.33870i	0.742948	−	0.669349i	$-0.233427\pi$
$608$		0			0
$609$	0.148880	−	0.108168i	0.00603294	−	0.00438318i
$610$		0			0
$611$	15.1975	+	11.0416i	0.614824	+	0.446696i
$612$		0			0
$613$	11.0440	+	15.2007i	0.446062	+	0.613951i	0.971546	−	0.236852i	$-0.0761157\pi$
$613$	11.0440	+	15.2007i	0.446062	+	0.613951i	−0.525484	+	0.850804i	$0.676116\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−37.4030	−	12.1530i	−1.50579	−	0.489260i	−0.564087	−	0.825715i	$-0.690772\pi$
$617$	−37.4030	−	12.1530i	−1.50579	−	0.489260i	−0.941699	+	0.336456i	$0.890772\pi$
$618$		0			0
$619$	4.95554	−	15.2516i	0.199180	−	0.613013i	−0.800722	−	0.599036i	$-0.795551\pi$
$619$	4.95554	−	15.2516i	0.199180	−	0.613013i	0.999902	−	0.0139774i	$-0.00444929\pi$
$620$		0			0
$621$	0.945790	+	2.91084i	0.0379532	+	0.116808i
$622$		0			0
$623$	12.4961	−	17.1994i	0.500645	−	0.689079i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.13113	+	1.55687i	−0.0451730	+	0.0621753i
$628$		0			0
$629$	0.668937	+	2.05878i	0.0266722	+	0.0820887i
$630$		0			0
$631$	1.49158	−	4.59061i	0.0593788	−	0.182749i	−0.916967	−	0.398962i	$-0.869371\pi$
$631$	1.49158	−	4.59061i	0.0593788	−	0.182749i	0.976346	+	0.216213i	$0.0693705\pi$
$632$		0			0
$633$	18.8451	+	6.12315i	0.749026	+	0.243373i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.90223	+	13.6293i	0.392341	+	0.540011i
$638$		0			0
$639$	2.64405	+	1.92102i	0.104597	+	0.0759943i
$640$		0			0
$641$	29.5813	−	21.4921i	1.16839	−	0.848887i	0.177577	−	0.984107i	$-0.443174\pi$
$641$	29.5813	−	21.4921i	1.16839	−	0.848887i	0.990816	+	0.135220i	$0.0431742\pi$
$642$		0			0
$643$		−	18.3769i		−	0.724714i	−0.932039	−	0.362357i	$-0.881972\pi$
$643$		−	18.3769i		−	0.724714i	0.932039	−	0.362357i	$-0.118028\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−39.1206	+	12.7110i	−1.53799	+	0.499723i	−0.950820	−	0.309743i	$-0.899757\pi$
$647$	−39.1206	+	12.7110i	−1.53799	+	0.499723i	−0.587167	+	0.809465i	$0.699757\pi$
$648$		0			0
$649$	79.5419			3.12229
$650$		0			0
$651$	4.42809			0.173550
$652$		0			0
$653$	20.8706	−	6.78128i	0.816731	−	0.265372i	0.129285	−	0.991608i	$-0.458732\pi$
$653$	20.8706	−	6.78128i	0.816731	−	0.265372i	0.687446	+	0.726236i	$0.258732\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	15.9668i		−	0.622924i
$658$		0			0
$659$	17.1550	−	12.4638i	0.668264	−	0.485522i	−0.201179	−	0.979554i	$-0.564477\pi$
$659$	17.1550	−	12.4638i	0.668264	−	0.485522i	0.869444	+	0.494032i	$0.164477\pi$
$660$		0			0
$661$	−14.5172	−	10.5473i	−0.564652	−	0.410244i	0.268507	−	0.963278i	$-0.413470\pi$
$661$	−14.5172	−	10.5473i	−0.564652	−	0.410244i	−0.833159	+	0.553034i	$0.813470\pi$
$662$		0			0
$663$	−1.03619	−	1.42620i	−0.0402425	−	0.0553890i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.356094	−	0.115702i	−0.0137880	−	0.00447999i
$668$		0			0
$669$	2.03399	−	6.25999i	0.0786387	−	0.242025i
$670$		0			0
$671$	21.6002	+	66.4785i	0.833865	+	2.56637i
$672$		0			0
$673$	20.1619	−	27.7504i	0.777183	−	1.06970i	−0.218404	−	0.975858i	$-0.570085\pi$
$673$	20.1619	−	27.7504i	0.777183	−	1.06970i	0.995587	−	0.0938421i	$-0.0299149\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.43752	−	3.35495i	0.0936814	−	0.128941i	−0.759603	−	0.650387i	$-0.774607\pi$
$677$	2.43752	−	3.35495i	0.0936814	−	0.128941i	0.853285	+	0.521445i	$0.174607\pi$
$678$		0			0
$679$	5.33781	+	16.4281i	0.204846	+	0.630452i
$680$		0			0
$681$	−3.64087	+	11.2055i	−0.139519	+	0.429394i
$682$		0			0
$683$	2.01472	+	0.654621i	0.0770910	+	0.0250484i	0.347309	−	0.937751i	$-0.387096\pi$
$683$	2.01472	+	0.654621i	0.0770910	+	0.0250484i	−0.270218	+	0.962799i	$0.587096\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−6.98869	−	9.61911i	−0.266635	−	0.366992i
$688$		0			0
$689$	24.7428	+	17.9767i	0.942625	+	0.684857i
$690$		0			0
$691$	3.21546	−	2.33617i	0.122322	−	0.0888721i	−0.524942	−	0.851138i	$-0.675913\pi$
$691$	3.21546	−	2.33617i	0.122322	−	0.0888721i	0.647264	+	0.762266i	$0.275913\pi$
$692$		0			0
$693$		−	9.28811i		−	0.352826i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.00516	−	0.651515i	0.0759507	−	0.0246779i
$698$		0			0
$699$	−5.05001			−0.191009
$700$		0			0
$701$	−10.1954			−0.385076			−0.192538	−	0.981289i	$-0.561672\pi$
$701$	−10.1954			−0.385076			−0.192538	+	0.981289i	$0.561672\pi$
$702$		0			0
$703$	1.29447	−	0.420597i	0.0488217	−	0.0158631i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			22.3176i			0.839338i
$708$		0			0
$709$	24.1421	−	17.5403i	0.906676	−	0.658739i	−0.0334959	−	0.999439i	$-0.510664\pi$
$709$	24.1421	−	17.5403i	0.906676	−	0.658739i	0.940172	+	0.340700i	$0.110664\pi$
$710$		0			0
$711$	6.89886	+	5.01232i	0.258728	+	0.187977i
$712$		0			0
$713$	−5.29557	−	7.28873i	−0.198321	−	0.272965i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.54819	+	0.827957i	0.0951639	+	0.0309206i
$718$		0			0
$719$	−2.29734	+	7.07047i	−0.0856762	+	0.263684i	−0.984712	−	0.174191i	$-0.944269\pi$
$719$	−2.29734	+	7.07047i	−0.0856762	+	0.263684i	0.899036	+	0.437875i	$0.144269\pi$
$720$		0			0
$721$	8.95520	+	27.5613i	0.333509	+	1.02644i
$722$		0			0
$723$	−7.43906	+	10.2390i	−0.276662	+	0.380792i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	9.35722	−	12.8791i	0.347040	−	0.477660i	−0.599441	−	0.800419i	$-0.704610\pi$
$727$	9.35722	−	12.8791i	0.347040	−	0.477660i	0.946481	+	0.322759i	$0.104610\pi$
$728$		0			0
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−0.555527	+	1.70974i	−0.0205469	+	0.0632369i
$732$		0			0
$733$	29.1121	+	9.45910i	1.07528	+	0.349380i	0.792542	−	0.609817i	$-0.208757\pi$
$733$	29.1121	+	9.45910i	1.07528	+	0.349380i	0.282738	+	0.959197i	$0.408757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−48.0557	−	66.1430i	−1.77015	−	2.43641i
$738$		0			0
$739$	20.9842	+	15.2459i	0.771917	+	0.560830i	0.902542	−	0.430602i	$-0.141699\pi$
$739$	20.9842	+	15.2459i	0.771917	+	0.560830i	−0.130626	+	0.991432i	$0.541699\pi$
$740$		0			0
$741$	−0.896731	+	0.651513i	−0.0329422	+	0.0239339i
$742$		0			0
$743$			17.2136i			0.631504i	0.948842	+	0.315752i	$0.102257\pi$
$743$			17.2136i			0.631504i	−0.948842	+	0.315752i	$0.897743\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	10.7832	−	3.50367i	0.394536	−	0.128193i
$748$		0			0
$749$	−12.9900			−0.474643
$750$		0			0
$751$	10.4020			0.379576			0.189788	−	0.981825i	$-0.439220\pi$
$751$	10.4020			0.379576			0.189788	+	0.981825i	$0.439220\pi$
$752$		0			0
$753$	−21.7857	+	7.07859i	−0.793913	+	0.257958i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			16.9118i			0.614669i	0.951601	+	0.307335i	$0.0994371\pi$
$757$			16.9118i			0.614669i	−0.951601	+	0.307335i	$0.900563\pi$
$758$		0			0
$759$	−15.2884	+	11.1077i	−0.554935	+	0.403184i
$760$		0			0
$761$	−0.422588	−	0.307028i	−0.0153188	−	0.0111297i	0.580100	−	0.814546i	$-0.303014\pi$
$761$	−0.422588	−	0.307028i	−0.0153188	−	0.0111297i	−0.595418	+	0.803416i	$0.703014\pi$
$762$		0			0
$763$	16.5252	+	22.7450i	0.598252	+	0.823423i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	43.5725	+	14.1576i	1.57331	+	0.511200i
$768$		0			0
$769$	11.7671	−	36.2154i	0.424333	−	1.30596i	−0.479299	−	0.877651i	$-0.659109\pi$
$769$	11.7671	−	36.2154i	0.424333	−	1.30596i	0.903632	−	0.428310i	$-0.140891\pi$
$770$		0			0
$771$	8.58338	+	26.4169i	0.309123	+	0.951382i
$772$		0			0
$773$	−13.3376	+	18.3577i	−0.479721	+	0.660280i	−0.978451	−	0.206478i	$-0.933800\pi$
$773$	−13.3376	+	18.3577i	−0.479721	+	0.660280i	0.498730	+	0.866757i	$0.333800\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.86132	+	5.31466i	−0.138524	+	0.190662i
$778$		0			0
$779$	−0.409643	−	1.26075i	−0.0146770	−	0.0451711i
$780$		0			0
$781$	−6.23574	+	19.1916i	−0.223132	+	0.686731i
$782$		0			0
$783$	0.116346	+	0.0378031i	0.00415787	+	0.00135097i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.33963	+	1.84384i	0.0477525	+	0.0657257i	0.832226	−	0.554437i	$-0.187066\pi$
$787$	1.33963	+	1.84384i	0.0477525	+	0.0657257i	−0.784473	+	0.620163i	$0.787066\pi$
$788$		0			0
$789$	−9.47479	−	6.88384i	−0.337312	−	0.245071i
$790$		0			0
$791$	−7.37064	+	5.35508i	−0.262070	+	0.190405i
$792$		0			0
$793$			40.2611i			1.42971i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	18.6796	−	6.06936i	0.661665	−	0.214988i	0.0411143	−	0.999154i	$-0.486909\pi$
$797$	18.6796	−	6.06936i	0.661665	−	0.214988i	0.620550	+	0.784167i	$0.286909\pi$
$798$		0			0
$799$	−2.61836			−0.0926310
$800$		0			0
$801$	14.1326			0.499349
$802$		0			0
$803$	93.7598	−	30.4644i	3.30871	−	1.07507i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			4.20621i			0.148066i
$808$		0			0
$809$	9.05703	−	6.58032i	0.318428	−	0.231352i	−0.417076	−	0.908871i	$-0.636945\pi$
$809$	9.05703	−	6.58032i	0.318428	−	0.231352i	0.735504	+	0.677520i	$0.236945\pi$
$810$		0			0
$811$	15.6132	+	11.3436i	0.548253	+	0.398329i	0.827141	−	0.561995i	$-0.189966\pi$
$811$	15.6132	+	11.3436i	0.548253	+	0.398329i	−0.278888	+	0.960324i	$0.589966\pi$
$812$		0			0
$813$	−7.38606	−	10.1660i	−0.259040	−	0.356539i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.07501	+	0.349291i	0.0376097	+	0.0122201i
$818$		0			0
$819$	1.65318	−	5.08796i	0.0577668	−	0.177788i
$820$		0			0
$821$	−14.8716	−	45.7701i	−0.519023	−	1.59739i	−0.775841	−	0.630928i	$-0.782674\pi$
$821$	−14.8716	−	45.7701i	−0.519023	−	1.59739i	0.256818	−	0.966460i	$-0.417326\pi$
$822$		0			0
$823$	20.5144	−	28.2356i	0.715087	−	0.984232i	−0.284586	−	0.958650i	$-0.591856\pi$
$823$	20.5144	−	28.2356i	0.715087	−	0.984232i	0.999673	−	0.0255817i	$-0.00814380\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.6155	+	18.7401i	−0.473456	+	0.651656i	−0.977231	−	0.212179i	$-0.931944\pi$
$827$	−13.6155	+	18.7401i	−0.473456	+	0.651656i	0.503775	+	0.863835i	$0.331944\pi$
$828$		0			0
$829$	−6.70966	−	20.6502i	−0.233036	−	0.717211i	−0.997376	−	0.0723976i	$-0.976935\pi$
$829$	−6.70966	−	20.6502i	−0.233036	−	0.717211i	0.764340	−	0.644814i	$-0.223065\pi$
$830$		0			0
$831$	−9.84691	+	30.3057i	−0.341585	+	1.05129i
$832$		0			0
$833$	−2.23325	−	0.725626i	−0.0773774	−	0.0251414i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.73022	+	2.38144i	0.0598051	+	0.0823146i
$838$		0			0
$839$	8.40486	+	6.10649i	0.290168	+	0.210819i	0.723340	−	0.690492i	$-0.242606\pi$
$839$	8.40486	+	6.10649i	0.290168	+	0.210819i	−0.433172	+	0.901311i	$0.642606\pi$
$840$		0			0
$841$	23.4494	−	17.0370i	0.808600	−	0.587482i
$842$		0			0
$843$		−	16.2998i		−	0.561395i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	38.8040	−	12.6082i	1.33332	−	0.433223i
$848$		0			0
$849$	−13.6305			−0.467797
$850$		0			0
$851$	13.3658			0.458174
$852$		0			0
$853$	−31.9651	+	10.3861i	−1.09447	+	0.355613i	−0.799970	−	0.600039i	$-0.795152\pi$
$853$	−31.9651	+	10.3861i	−1.09447	+	0.355613i	−0.294495	+	0.955653i	$0.595152\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	46.0078i		−	1.57160i	−0.618482	−	0.785799i	$-0.712252\pi$
$857$		−	46.0078i		−	1.57160i	0.618482	−	0.785799i	$-0.287748\pi$
$858$		0			0
$859$	−24.5549	+	17.8402i	−0.837803	+	0.608700i	−0.921756	−	0.387770i	$-0.873245\pi$
$859$	−24.5549	+	17.8402i	−0.837803	+	0.608700i	0.0839529	+	0.996470i	$0.473245\pi$
$860$		0			0
$861$	5.17624	+	3.76076i	0.176406	+	0.128166i
$862$		0			0
$863$	4.30289	+	5.92243i	0.146472	+	0.201602i	0.875949	−	0.482404i	$-0.160236\pi$
$863$	4.30289	+	5.92243i	0.146472	+	0.201602i	−0.729477	+	0.684006i	$0.760236\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.9343	−	5.17736i	−0.541156	−	0.175832i
$868$		0			0
$869$	−16.2703	+	50.0748i	−0.551932	+	1.69867i
$870$		0			0
$871$	−14.5519	−	44.7861i	−0.493072	−	1.51752i
$872$		0			0
$873$	−6.74940	+	9.28975i	−0.228433	+	0.314410i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	27.3577	−	37.6546i	0.923803	−	1.27151i	−0.0384252	−	0.999261i	$-0.512234\pi$
$877$	27.3577	−	37.6546i	0.923803	−	1.27151i	0.962228	−	0.272244i	$-0.0877659\pi$
$878$		0			0
$879$	7.80737	+	24.0286i	0.263336	+	0.810466i
$880$		0			0
$881$	−4.62663	+	14.2393i	−0.155875	+	0.479735i	−0.998249	−	0.0591598i	$-0.981158\pi$
$881$	−4.62663	+	14.2393i	−0.155875	+	0.479735i	0.842373	+	0.538894i	$0.181158\pi$
$882$		0			0
$883$	−8.31451	−	2.70155i	−0.279806	−	0.0909144i	0.165752	−	0.986167i	$-0.446995\pi$
$883$	−8.31451	−	2.70155i	−0.279806	−	0.0909144i	−0.445558	+	0.895253i	$0.646995\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.69054	+	13.3379i	0.325376	+	0.447842i	0.940099	−	0.340901i	$-0.110732\pi$
$887$	9.69054	+	13.3379i	0.325376	+	0.447842i	−0.614723	+	0.788743i	$0.710732\pi$
$888$		0			0
$889$	−11.2520	−	8.17505i	−0.377379	−	0.274182i
$890$		0			0
$891$	4.99517	−	3.62921i	0.167345	−	0.121583i
$892$		0			0
$893$			1.64631i			0.0550916i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−10.3519	+	3.36355i	−0.345642	+	0.112306i
$898$		0			0
$899$	−0.360104			−0.0120101
$900$		0			0
$901$	−4.26292			−0.142018
$902$		0			0
$903$	−5.18853	+	1.68586i	−0.172663	+	0.0561018i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	26.0243i		−	0.864124i	−0.901844	−	0.432062i	$-0.857786\pi$
$907$		−	26.0243i		−	0.864124i	0.901844	−	0.432062i	$-0.142214\pi$
$908$		0			0
$909$	−12.0025	+	8.72029i	−0.398096	+	0.289234i
$910$		0			0
$911$	41.7815	+	30.3560i	1.38428	+	1.00574i	0.996466	+	0.0840029i	$0.0267705\pi$
$911$	41.7815	+	30.3560i	1.38428	+	1.00574i	0.387816	+	0.921737i	$0.373229\pi$
$912$		0			0
$913$	41.1484	+	56.6359i	1.36181	+	1.87437i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.2050	−	8.83945i	−0.898390	−	0.291904i
$918$		0			0
$919$	8.53835	−	26.2784i	0.281654	−	0.866843i	−0.705727	−	0.708484i	$-0.749380\pi$
$919$	8.53835	−	26.2784i	0.281654	−	0.866843i	0.987382	−	0.158359i	$-0.0506204\pi$
$920$		0			0
$921$	2.16628	+	6.66712i	0.0713813	+	0.219689i
$922$		0			0
$923$	−6.83180	+	9.40316i	−0.224871	+	0.309509i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.3234	+	15.5853i	−0.371910	+	0.511890i
$928$		0			0
$929$	−16.5946	−	51.0728i	−0.544450	−	1.67565i	−0.722294	−	0.691587i	$-0.756912\pi$
$929$	−16.5946	−	51.0728i	−0.544450	−	1.67565i	0.177843	−	0.984059i	$-0.443088\pi$
$930$		0			0
$931$	−0.456241	+	1.40417i	−0.0149527	+	0.0460197i
$932$		0			0
$933$	−13.8016	−	4.48441i	−0.451844	−	0.146813i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−17.8224	−	24.5304i	−0.582232	−	0.801373i	0.411706	−	0.911317i	$-0.364933\pi$
$937$	−17.8224	−	24.5304i	−0.582232	−	0.801373i	−0.993938	+	0.109943i	$0.964933\pi$
$938$		0			0
$939$	−17.7334	−	12.8841i	−0.578707	−	0.420455i
$940$		0			0
$941$	−38.3217	+	27.8423i	−1.24925	+	0.907635i	−0.998178	−	0.0603335i	$-0.980784\pi$
$941$	−38.3217	+	27.8423i	−1.24925	+	0.907635i	−0.251073	+	0.967968i	$0.580784\pi$
$942$		0			0
$943$		−	13.0177i		−	0.423915i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.5826	+	6.68770i	−0.668845	+	0.217321i	−0.623705	−	0.781660i	$-0.714373\pi$
$947$	−20.5826	+	6.68770i	−0.668845	+	0.217321i	−0.0451402	+	0.998981i	$0.514373\pi$
$948$		0			0
$949$	56.7833			1.84327
$950$		0			0
$951$	33.7178			1.09337
$952$		0			0
$953$	43.6456	−	14.1813i	1.41382	−	0.459378i	0.500187	−	0.865918i	$-0.333265\pi$
$953$	43.6456	−	14.1813i	1.41382	−	0.459378i	0.913633	+	0.406540i	$0.133265\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			0.755333i			0.0244164i
$958$		0			0
$959$	9.56815	−	6.95167i	0.308972	−	0.224481i
$960$		0			0
$961$	18.0695	+	13.1282i	0.582886	+	0.423492i
$962$		0			0
$963$	−5.07566	−	6.98605i	−0.163561	−	0.225122i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	14.2370	+	4.62587i	0.457830	+	0.148758i	0.528847	−	0.848717i	$-0.322625\pi$
$967$	14.2370	+	4.62587i	0.457830	+	0.148758i	−0.0710173	+	0.997475i	$0.522625\pi$
$968$		0			0
$969$	0.0477422	−	0.146935i	0.00153370	−	0.00472025i
$970$		0			0
$971$	−6.91563	−	21.2841i	−0.221933	−	0.683040i	−0.998588	−	0.0531143i	$-0.983085\pi$
$971$	−6.91563	−	21.2841i	−0.221933	−	0.683040i	0.776655	−	0.629926i	$-0.216915\pi$
$972$		0			0
$973$	−12.2023	+	16.7951i	−0.391189	+	0.538426i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.7280	−	32.6588i	0.759127	−	1.04485i	−0.238159	−	0.971226i	$-0.576544\pi$
$977$	23.7280	−	32.6588i	0.759127	−	1.04485i	0.997286	−	0.0736229i	$-0.0234561\pi$
$978$		0			0
$979$	26.9647	+	82.9889i	0.861797	+	2.65234i
$980$		0			0
$981$	−5.77531	+	17.7746i	−0.184392	+	0.567499i
$982$		0			0
$983$	−22.2290	−	7.22264i	−0.708995	−	0.230367i	−0.0677498	−	0.997702i	$-0.521582\pi$
$983$	−22.2290	−	7.22264i	−0.708995	−	0.230367i	−0.641245	+	0.767336i	$0.721582\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.67050	−	6.42839i	−0.148664	−	0.204618i
$988$		0			0
$989$	8.97994	+	6.52431i	0.285546	+	0.207461i
$990$		0			0
$991$	−27.3815	+	19.8938i	−0.869803	+	0.631949i	−0.930534	−	0.366205i	$-0.880657\pi$
$991$	−27.3815	+	19.8938i	−0.869803	+	0.631949i	0.0607312	+	0.998154i	$0.480657\pi$
$992$		0			0
$993$		−	33.5950i		−	1.06611i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	5.27364	−	1.71351i	0.167018	−	0.0542674i	−0.224314	−	0.974517i	$-0.572014\pi$
$997$	5.27364	−	1.71351i	0.167018	−	0.0542674i	0.391332	+	0.920249i	$0.372014\pi$
$998$		0			0
$999$	−4.36700			−0.138166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.b.49.3		16
5.2	odd	4		300.2.m.b.241.2	yes	8
5.3	odd	4		1500.2.m.a.1201.1		8
5.4	even	2	inner	1500.2.o.b.49.2		16
15.2	even	4		900.2.n.b.541.1		8
25.2	odd	20		300.2.m.b.61.2	✓	8
25.6	even	5		7500.2.d.c.1249.2		8
25.8	odd	20		7500.2.a.f.1.2		4
25.11	even	5	inner	1500.2.o.b.949.1		16
25.14	even	10	inner	1500.2.o.b.949.4		16
25.17	odd	20		7500.2.a.e.1.3		4
25.19	even	10		7500.2.d.c.1249.7		8
25.23	odd	20		1500.2.m.a.301.1		8
75.2	even	20		900.2.n.b.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.2	✓	8	25.2	odd	20
300.2.m.b.241.2	yes	8	5.2	odd	4
900.2.n.b.361.1		8	75.2	even	20
900.2.n.b.541.1		8	15.2	even	4
1500.2.m.a.301.1		8	25.23	odd	20
1500.2.m.a.1201.1		8	5.3	odd	4
1500.2.o.b.49.2		16	5.4	even	2	inner
1500.2.o.b.49.3		16	1.1	even	1	trivial
1500.2.o.b.949.1		16	25.11	even	5	inner
1500.2.o.b.949.4		16	25.14	even	10	inner
7500.2.a.e.1.3		4	25.17	odd	20
7500.2.a.f.1.2		4	25.8	odd	20
7500.2.d.c.1249.2		8	25.6	even	5
7500.2.d.c.1249.7		8	25.19	even	10

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{3} -1.50430i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{3} -1.50430i q^{7} +(0.809017 - 0.587785i) q^{9} +(4.99517 + 3.62921i) q^{11} +(2.09036 + 2.87714i) q^{13} +(-0.471439 - 0.153180i) q^{17} +(-0.0963126 + 0.296420i) q^{19} +(-0.464854 - 1.43067i) q^{21} +(-1.79900 + 2.47611i) q^{23} +(0.587785 - 0.809017i) q^{27} +(0.0378031 + 0.116346i) q^{29} +(-0.909629 + 2.79955i) q^{31} +(5.87218 + 1.90799i) q^{33} +(-2.56686 - 3.53298i) q^{37} +(2.87714 + 2.09036i) q^{39} +(-3.44096 + 2.50001i) q^{41} -3.62663i q^{43} +(5.02362 - 1.63227i) q^{47} +4.73708 q^{49} -0.495700 q^{51} +(8.17888 - 2.65748i) q^{53} +0.311674i q^{57} +(10.4222 - 7.57219i) q^{59} +(9.15882 + 6.65427i) q^{61} +(-0.884205 - 1.21700i) q^{63} +(-12.5933 - 4.09181i) q^{67} +(-0.945790 + 2.91084i) q^{69} +(1.00994 + 3.10827i) q^{71} +(9.38504 - 12.9174i) q^{73} +(5.45941 - 7.51424i) q^{77} +(2.63513 + 8.11010i) q^{79} +(0.309017 - 0.951057i) q^{81} +(10.7832 + 3.50367i) q^{83} +(0.0719058 + 0.0989699i) q^{87} +(11.4335 + 8.30691i) q^{89} +(4.32808 - 3.14453i) q^{91} +2.94362i q^{93} +(-10.9208 + 3.54837i) q^{97} +6.17438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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