LMFDB - Embedded newform 3150.2.m.i.1457.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.4
Root			$-0.692297i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.i.2843.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.77786i q^{11} +(-0.692297 + 0.692297i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(2.39327 - 2.39327i) q^{17} +(1.25714 + 1.25714i) q^{22} +(-3.38459 - 3.38459i) q^{23} +0.979056i q^{26} +(-0.707107 + 0.707107i) q^{28} -4.42289 q^{29} -5.77786 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.38459i q^{34} +(-5.91399 - 5.91399i) q^{37} -0.807922i q^{41} +(4.64173 - 4.64173i) q^{43} +1.77786 q^{44} -4.78654 q^{46} +(7.47016 - 7.47016i) q^{47} +1.00000i q^{49} +(0.692297 + 0.692297i) q^{52} +(-3.56484 - 3.56484i) q^{53} +1.00000i q^{56} +(-3.12745 + 3.12745i) q^{58} -5.89887 q^{59} +2.39327 q^{61} +(-4.08557 + 4.08557i) q^{62} +1.00000i q^{64} +(0.641735 + 0.641735i) q^{67} +(-2.39327 - 2.39327i) q^{68} -10.6854i q^{71} +(-5.70097 + 5.70097i) q^{73} -8.36365 q^{74} +(1.25714 - 1.25714i) q^{77} +16.3423i q^{79} +(-0.571287 - 0.571287i) q^{82} +(0.171134 + 0.171134i) q^{83} -6.56440i q^{86} +(1.25714 - 1.25714i) q^{88} -13.2340 q^{89} +0.979056 q^{91} +(-3.38459 + 3.38459i) q^{92} -10.5644i q^{94} +(-12.6413 - 12.6413i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{22} - 8 q^{23} - 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} - 24 q^{44} + 12 q^{47} - 4 q^{52} - 32 q^{53} - 12 q^{58} - 16 q^{59} - 4 q^{62} - 20 q^{67} - 36 q^{73} - 40 q^{74} + 4 q^{77} + 12 q^{82} - 56 q^{83} + 4 q^{88} - 72 q^{89} - 8 q^{92} + 4 q^{97}+O(q^{100}) $ 8 * q + 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^22 - 8 * q^23 - 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 - 24 * q^44 + 12 * q^47 - 4 * q^52 - 32 * q^53 - 12 * q^58 - 16 * q^59 - 4 * q^62 - 20 * q^67 - 36 * q^73 - 40 * q^74 + 4 * q^77 + 12 * q^82 - 56 * q^83 + 4 * q^88 - 72 * q^89 - 8 * q^92 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			1.77786i			0.536046i	0.963412	+	0.268023i	$0.0863704\pi$
$11$			1.77786i			0.536046i	−0.963412	+	0.268023i	$0.913630\pi$
$12$		0			0
$13$	−0.692297	+	0.692297i	−0.192009	+	0.192009i	−0.796564	−	0.604555i	$-0.793351\pi$
$13$	−0.692297	+	0.692297i	−0.192009	+	0.192009i	0.604555	+	0.796564i	$0.293351\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.39327	−	2.39327i	0.580453	−	0.580453i	−0.354575	−	0.935028i	$-0.615374\pi$
$17$	2.39327	−	2.39327i	0.580453	−	0.580453i	0.935028	+	0.354575i	$0.115374\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$	1.25714	+	1.25714i	0.268023	+	0.268023i
$23$	−3.38459	−	3.38459i	−0.705737	−	0.705737i	0.259899	−	0.965636i	$-0.416311\pi$
$23$	−3.38459	−	3.38459i	−0.705737	−	0.705737i	−0.965636	+	0.259899i	$0.916311\pi$
$24$		0			0
$25$		0			0
$26$			0.979056i			0.192009i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−4.42289			−0.821310			−0.410655	−	0.911791i	$-0.634700\pi$
$29$	−4.42289			−0.821310			−0.410655	+	0.911791i	$0.634700\pi$
$30$		0			0
$31$	−5.77786			−1.03774			−0.518868	−	0.854855i	$-0.673646\pi$
$31$	−5.77786			−1.03774			−0.518868	+	0.854855i	$0.673646\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	3.38459i		−	0.580453i
$35$		0			0
$36$		0			0
$37$	−5.91399	−	5.91399i	−0.972255	−	0.972255i	0.0273707	−	0.999625i	$-0.491287\pi$
$37$	−5.91399	−	5.91399i	−0.972255	−	0.972255i	−0.999625	+	0.0273707i	$0.991287\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	0.807922i		−	0.126176i	−0.998008	−	0.0630881i	$-0.979905\pi$
$41$		−	0.807922i		−	0.126176i	0.998008	−	0.0630881i	$-0.0200949\pi$
$42$		0			0
$43$	4.64173	−	4.64173i	0.707858	−	0.707858i	−0.258227	−	0.966084i	$-0.583138\pi$
$43$	4.64173	−	4.64173i	0.707858	−	0.707858i	0.966084	+	0.258227i	$0.0831381\pi$
$44$	1.77786			0.268023
$45$		0			0
$46$	−4.78654			−0.705737
$47$	7.47016	−	7.47016i	1.08964	−	1.08964i	0.0940694	−	0.995566i	$-0.470012\pi$
$47$	7.47016	−	7.47016i	1.08964	−	1.08964i	0.995566	−	0.0940694i	$-0.0299876\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	0.692297	+	0.692297i	0.0960044	+	0.0960044i
$53$	−3.56484	−	3.56484i	−0.489669	−	0.489669i	0.418533	−	0.908202i	$-0.362544\pi$
$53$	−3.56484	−	3.56484i	−0.489669	−	0.489669i	−0.908202	+	0.418533i	$0.862544\pi$
$54$		0			0
$55$		0			0
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−3.12745	+	3.12745i	−0.410655	+	0.410655i
$59$	−5.89887			−0.767968			−0.383984	−	0.923340i	$-0.625448\pi$
$59$	−5.89887			−0.767968			−0.383984	+	0.923340i	$0.625448\pi$
$60$		0			0
$61$	2.39327			0.306427			0.153213	−	0.988193i	$-0.451038\pi$
$61$	2.39327			0.306427			0.153213	+	0.988193i	$0.451038\pi$
$62$	−4.08557	+	4.08557i	−0.518868	+	0.518868i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	0.641735	+	0.641735i	0.0784004	+	0.0784004i	0.745220	−	0.666819i	$-0.232345\pi$
$67$	0.641735	+	0.641735i	0.0784004	+	0.0784004i	−0.666819	+	0.745220i	$0.732345\pi$
$68$	−2.39327	−	2.39327i	−0.290227	−	0.290227i
$69$		0			0
$70$		0			0
$71$		−	10.6854i		−	1.26813i	−0.773282	−	0.634063i	$-0.781386\pi$
$71$		−	10.6854i		−	1.26813i	0.773282	−	0.634063i	$-0.218614\pi$
$72$		0			0
$73$	−5.70097	+	5.70097i	−0.667248	+	0.667248i	−0.957078	−	0.289830i	$-0.906401\pi$
$73$	−5.70097	+	5.70097i	−0.667248	+	0.667248i	0.289830	+	0.957078i	$0.406401\pi$
$74$	−8.36365			−0.972255
$75$		0			0
$76$		0			0
$77$	1.25714	−	1.25714i	0.143264	−	0.143264i
$78$		0			0
$79$			16.3423i			1.83865i	0.393500	+	0.919324i	$0.371264\pi$
$79$			16.3423i			1.83865i	−0.393500	+	0.919324i	$0.628736\pi$
$80$		0			0
$81$		0			0
$82$	−0.571287	−	0.571287i	−0.0630881	−	0.0630881i
$83$	0.171134	+	0.171134i	0.0187844	+	0.0187844i	0.716437	−	0.697652i	$-0.245772\pi$
$83$	0.171134	+	0.171134i	0.0187844	+	0.0187844i	−0.697652	+	0.716437i	$0.745772\pi$
$84$		0			0
$85$		0			0
$86$		−	6.56440i		−	0.707858i
$87$		0			0
$88$	1.25714	−	1.25714i	0.134012	−	0.134012i
$89$	−13.2340			−1.40280			−0.701399	−	0.712769i	$-0.747441\pi$
$89$	−13.2340			−1.40280			−0.701399	+	0.712769i	$0.747441\pi$
$90$		0			0
$91$	0.979056			0.102633
$92$	−3.38459	+	3.38459i	−0.352868	+	0.352868i
$93$		0			0
$94$		−	10.5644i		−	1.08964i
$95$		0			0
$96$		0			0
$97$	−12.6413	−	12.6413i	−1.28353	−	1.28353i	−0.938645	−	0.344884i	$-0.887918\pi$
$97$	−12.6413	−	12.6413i	−1.28353	−	1.28353i	−0.344884	−	0.938645i	$-0.612082\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	12.6778i		−	1.26149i	−0.775991	−	0.630744i	$-0.782750\pi$
$101$		−	12.6778i		−	1.26149i	0.775991	−	0.630744i	$-0.217250\pi$
$102$		0			0
$103$	−7.43472	+	7.43472i	−0.732565	+	0.732565i	−0.971127	−	0.238563i	$-0.923324\pi$
$103$	−7.43472	+	7.43472i	−0.732565	+	0.732565i	0.238563	+	0.971127i	$0.423324\pi$
$104$	0.979056			0.0960044
$105$		0			0
$106$	−5.04145			−0.489669
$107$	−13.5138	+	13.5138i	−1.30643	+	1.30643i	−0.382461	+	0.923972i	$0.624923\pi$
$107$	−13.5138	+	13.5138i	−1.30643	+	1.30643i	−0.923972	+	0.382461i	$0.875077\pi$
$108$		0			0
$109$		−	3.30082i		−	0.316161i	−0.987426	−	0.158081i	$-0.949469\pi$
$109$		−	3.30082i		−	0.316161i	0.987426	−	0.158081i	$-0.0505306\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−5.84937	−	5.84937i	−0.550263	−	0.550263i	0.376254	−	0.926517i	$-0.377212\pi$
$113$	−5.84937	−	5.84937i	−0.550263	−	0.550263i	−0.926517	+	0.376254i	$0.877212\pi$
$114$		0			0
$115$		0			0
$116$			4.42289i			0.410655i
$117$		0			0
$118$	−4.17113	+	4.17113i	−0.383984	+	0.383984i
$119$	−3.38459			−0.310265
$120$		0			0
$121$	7.83920			0.712654
$122$	1.69230	−	1.69230i	0.153213	−	0.153213i
$123$		0			0
$124$			5.77786i			0.518868i
$125$		0			0
$126$		0			0
$127$	0.615405	+	0.615405i	0.0546084	+	0.0546084i	0.733884	−	0.679275i	$-0.237706\pi$
$127$	0.615405	+	0.615405i	0.0546084	+	0.0546084i	−0.679275	+	0.733884i	$0.737706\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	6.52717i		−	0.570281i	−0.958486	−	0.285141i	$-0.907960\pi$
$131$		−	6.52717i		−	0.570281i	0.958486	−	0.285141i	$-0.0920403\pi$
$132$		0			0
$133$		0			0
$134$	0.907550			0.0784004
$135$		0			0
$136$	−3.38459			−0.290227
$137$	0.192517	−	0.192517i	0.0164478	−	0.0164478i	−0.698835	−	0.715283i	$-0.746298\pi$
$137$	0.192517	−	0.192517i	0.0164478	−	0.0164478i	0.715283	+	0.698835i	$0.246298\pi$
$138$		0			0
$139$			14.8694i			1.26121i	0.776104	+	0.630605i	$0.217193\pi$
$139$			14.8694i			1.26121i	−0.776104	+	0.630605i	$0.782807\pi$
$140$		0			0
$141$		0			0
$142$	−7.55573	−	7.55573i	−0.634063	−	0.634063i
$143$	−1.23081	−	1.23081i	−0.102926	−	0.102926i
$144$		0			0
$145$		0			0
$146$			8.06239i			0.667248i
$147$		0			0
$148$	−5.91399	+	5.91399i	−0.486127	+	0.486127i
$149$	20.6467			1.69144			0.845721	−	0.533625i	$-0.179171\pi$
$149$	20.6467			1.69144			0.845721	+	0.533625i	$0.179171\pi$
$150$		0			0
$151$	6.01735			0.489685			0.244843	−	0.969563i	$-0.421264\pi$
$151$	6.01735			0.489685			0.244843	+	0.969563i	$0.421264\pi$
$152$		0			0
$153$		0			0
$154$		−	1.77786i		−	0.143264i
$155$		0			0
$156$		0			0
$157$	0.608522	+	0.608522i	0.0485654	+	0.0485654i	0.730972	−	0.682407i	$-0.239067\pi$
$157$	0.608522	+	0.608522i	0.0485654	+	0.0485654i	−0.682407	+	0.730972i	$0.739067\pi$
$158$	11.5557	+	11.5557i	0.919324	+	0.919324i
$159$		0			0
$160$		0			0
$161$			4.78654i			0.377232i
$162$		0			0
$163$	−6.12745	+	6.12745i	−0.479939	+	0.479939i	−0.905112	−	0.425173i	$-0.860213\pi$
$163$	−6.12745	+	6.12745i	−0.479939	+	0.479939i	0.425173	+	0.905112i	$0.360213\pi$
$164$	−0.807922			−0.0630881
$165$		0			0
$166$	0.242020			0.0187844
$167$	6.18669	−	6.18669i	0.478741	−	0.478741i	−0.425988	−	0.904729i	$-0.640073\pi$
$167$	6.18669	−	6.18669i	0.478741	−	0.478741i	0.904729	+	0.425988i	$0.140073\pi$
$168$		0			0
$169$			12.0414i			0.926265i
$170$		0			0
$171$		0			0
$172$	−4.64173	−	4.64173i	−0.353929	−	0.353929i
$173$	−15.7720	−	15.7720i	−1.19913	−	1.19913i	−0.974429	−	0.224697i	$-0.927861\pi$
$173$	−15.7720	−	15.7720i	−1.19913	−	1.19913i	−0.224697	−	0.974429i	$-0.572139\pi$
$174$		0			0
$175$		0			0
$176$		−	1.77786i		−	0.134012i
$177$		0			0
$178$	−9.35783	+	9.35783i	−0.701399	+	0.701399i
$179$	3.87899			0.289929			0.144965	−	0.989437i	$-0.453693\pi$
$179$	3.87899			0.289929			0.144965	+	0.989437i	$0.453693\pi$
$180$		0			0
$181$	23.6896			1.76084			0.880418	−	0.474198i	$-0.157262\pi$
$181$	23.6896			1.76084			0.880418	+	0.474198i	$0.157262\pi$
$182$	0.692297	−	0.692297i	0.0513165	−	0.0513165i
$183$		0			0
$184$			4.78654i			0.352868i
$185$		0			0
$186$		0			0
$187$	4.25491	+	4.25491i	0.311150	+	0.311150i
$188$	−7.47016	−	7.47016i	−0.544818	−	0.544818i
$189$		0			0
$190$		0			0
$191$		−	23.4720i		−	1.69837i	−0.528095	−	0.849185i	$-0.677093\pi$
$191$		−	23.4720i		−	1.69837i	0.528095	−	0.849185i	$-0.322907\pi$
$192$		0			0
$193$	−18.1288	+	18.1288i	−1.30494	+	1.30494i	−0.379921	+	0.925019i	$0.624049\pi$
$193$	−18.1288	+	18.1288i	−1.30494	+	1.30494i	−0.925019	+	0.379921i	$0.875951\pi$
$194$	−17.8775			−1.28353
$195$		0			0
$196$	1.00000			0.0714286
$197$	−9.58535	+	9.58535i	−0.682928	+	0.682928i	−0.960659	−	0.277731i	$-0.910418\pi$
$197$	−9.58535	+	9.58535i	−0.682928	+	0.682928i	0.277731	+	0.960659i	$0.410418\pi$
$198$		0			0
$199$		−	2.46416i		−	0.174679i	−0.996179	−	0.0873397i	$-0.972163\pi$
$199$		−	2.46416i		−	0.174679i	0.996179	−	0.0873397i	$-0.0278366\pi$
$200$		0			0
$201$		0			0
$202$	−8.96456	−	8.96456i	−0.630744	−	0.630744i
$203$	3.12745	+	3.12745i	0.219504	+	0.219504i
$204$		0			0
$205$		0			0
$206$			10.5143i			0.732565i
$207$		0			0
$208$	0.692297	−	0.692297i	0.0480022	−	0.0480022i
$209$		0			0
$210$		0			0
$211$	−5.57308			−0.383667			−0.191833	−	0.981428i	$-0.561443\pi$
$211$	−5.57308			−0.383667			−0.191833	+	0.981428i	$0.561443\pi$
$212$	−3.56484	+	3.56484i	−0.244834	+	0.244834i
$213$		0			0
$214$			19.1115i			1.30643i
$215$		0			0
$216$		0			0
$217$	4.08557	+	4.08557i	0.277346	+	0.277346i
$218$	−2.33403	−	2.33403i	−0.158081	−	0.158081i
$219$		0			0
$220$		0			0
$221$			3.31371i			0.222904i
$222$		0			0
$223$	14.6854	−	14.6854i	0.983408	−	0.983408i	−0.0164565	−	0.999865i	$-0.505239\pi$
$223$	14.6854	−	14.6854i	0.983408	−	0.983408i	0.999865	+	0.0164565i	$0.00523851\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−8.27226			−0.550263
$227$	19.5557	−	19.5557i	1.29796	−	1.29796i	0.368221	−	0.929738i	$-0.379967\pi$
$227$	19.5557	−	19.5557i	1.29796	−	1.29796i	0.929738	−	0.368221i	$-0.120033\pi$
$228$		0			0
$229$		−	24.3622i		−	1.60990i	−0.593345	−	0.804948i	$-0.702193\pi$
$229$		−	24.3622i		−	1.60990i	0.593345	−	0.804948i	$-0.297807\pi$
$230$		0			0
$231$		0			0
$232$	3.12745	+	3.12745i	0.205327	+	0.205327i
$233$	−14.7692	−	14.7692i	−0.967562	−	0.967562i	0.0319284	−	0.999490i	$-0.489835\pi$
$233$	−14.7692	−	14.7692i	−0.967562	−	0.967562i	−0.999490	+	0.0319284i	$0.989835\pi$
$234$		0			0
$235$		0			0
$236$			5.89887i			0.383984i
$237$		0			0
$238$	−2.39327	+	2.39327i	−0.155133	+	0.155133i
$239$	1.47283			0.0952695			0.0476348	−	0.998865i	$-0.484832\pi$
$239$	1.47283			0.0952695			0.0476348	+	0.998865i	$0.484832\pi$
$240$		0			0
$241$	−21.5557			−1.38853			−0.694263	−	0.719721i	$-0.744270\pi$
$241$	−21.5557			−1.38853			−0.694263	+	0.719721i	$0.744270\pi$
$242$	5.54315	−	5.54315i	0.356327	−	0.356327i
$243$		0			0
$244$		−	2.39327i		−	0.153213i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.08557	+	4.08557i	0.259434	+	0.259434i
$249$		0			0
$250$		0			0
$251$		−	2.68541i		−	0.169502i	−0.996402	−	0.0847509i	$-0.972991\pi$
$251$		−	2.68541i		−	0.169502i	0.996402	−	0.0847509i	$-0.0270095\pi$
$252$		0			0
$253$	6.01735	−	6.01735i	0.378308	−	0.378308i
$254$	0.870315			0.0546084
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.9873	−	10.9873i	0.685368	−	0.685368i	−0.275836	−	0.961205i	$-0.588955\pi$
$257$	10.9873	−	10.9873i	0.685368	−	0.685368i	0.961205	+	0.275836i	$0.0889547\pi$
$258$		0			0
$259$			8.36365i			0.519692i
$260$		0			0
$261$		0			0
$262$	−4.61541	−	4.61541i	−0.285141	−	0.285141i
$263$	7.92911	+	7.92911i	0.488930	+	0.488930i	0.907969	−	0.419038i	$-0.137633\pi$
$263$	7.92911	+	7.92911i	0.488930	+	0.488930i	−0.419038	+	0.907969i	$0.637633\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.641735	−	0.641735i	0.0392002	−	0.0392002i
$269$	7.26420			0.442906			0.221453	−	0.975171i	$-0.428920\pi$
$269$	7.26420			0.442906			0.221453	+	0.975171i	$0.428920\pi$
$270$		0			0
$271$	−17.5756			−1.06764			−0.533821	−	0.845597i	$-0.679244\pi$
$271$	−17.5756			−1.06764			−0.533821	+	0.845597i	$0.679244\pi$
$272$	−2.39327	+	2.39327i	−0.145113	+	0.145113i
$273$		0			0
$274$		−	0.272260i		−	0.0164478i
$275$		0			0
$276$		0			0
$277$	9.81287	+	9.81287i	0.589598	+	0.589598i	0.937523	−	0.347924i	$-0.113113\pi$
$277$	9.81287	+	9.81287i	0.589598	+	0.589598i	−0.347924	+	0.937523i	$0.613113\pi$
$278$	10.5143	+	10.5143i	0.630605	+	0.630605i
$279$		0			0
$280$		0			0
$281$			12.5849i			0.750753i	0.926872	+	0.375376i	$0.122487\pi$
$281$			12.5849i			0.750753i	−0.926872	+	0.375376i	$0.877513\pi$
$282$		0			0
$283$	−4.69918	+	4.69918i	−0.279337	+	0.279337i	−0.832844	−	0.553507i	$-0.813289\pi$
$283$	−4.69918	+	4.69918i	−0.279337	+	0.279337i	0.553507	+	0.832844i	$0.313289\pi$
$284$	−10.6854			−0.634063
$285$		0			0
$286$	−1.74063			−0.102926
$287$	−0.571287	+	0.571287i	−0.0337220	+	0.0337220i
$288$		0			0
$289$			5.54452i			0.326148i
$290$		0			0
$291$		0			0
$292$	5.70097	+	5.70097i	0.333624	+	0.333624i
$293$	−3.39866	−	3.39866i	−0.198552	−	0.198552i	0.600827	−	0.799379i	$-0.294838\pi$
$293$	−3.39866	−	3.39866i	−0.198552	−	0.198552i	−0.799379	+	0.600827i	$0.794838\pi$
$294$		0			0
$295$		0			0
$296$			8.36365i			0.486127i
$297$		0			0
$298$	14.5994	−	14.5994i	0.845721	−	0.845721i
$299$	4.68629			0.271015
$300$		0			0
$301$	−6.56440			−0.378366
$302$	4.25491	−	4.25491i	0.244843	−	0.244843i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	15.5557	+	15.5557i	0.887812	+	0.887812i	0.994313	−	0.106500i	$-0.0339645\pi$
$307$	15.5557	+	15.5557i	0.887812	+	0.887812i	−0.106500	+	0.994313i	$0.533965\pi$
$308$	−1.25714	−	1.25714i	−0.0716322	−	0.0716322i
$309$		0			0
$310$		0			0
$311$			0.773651i			0.0438697i	0.999759	+	0.0219349i	$0.00698264\pi$
$311$			0.773651i			0.0438697i	−0.999759	+	0.0219349i	$0.993017\pi$
$312$		0			0
$313$	11.8548	−	11.8548i	0.670070	−	0.670070i	−0.287662	−	0.957732i	$-0.592878\pi$
$313$	11.8548	−	11.8548i	0.670070	−	0.670070i	0.957732	+	0.287662i	$0.0928779\pi$
$314$	0.860580			0.0485654
$315$		0			0
$316$	16.3423			0.919324
$317$	0.00911383	−	0.00911383i	0.000511884	−	0.000511884i	−0.706851	−	0.707363i	$-0.749885\pi$
$317$	0.00911383	−	0.00911383i	0.000511884	−	0.000511884i	0.707363	+	0.706851i	$0.249885\pi$
$318$		0			0
$319$		−	7.86330i		−	0.440260i
$320$		0			0
$321$		0			0
$322$	3.38459	+	3.38459i	0.188616	+	0.188616i
$323$		0			0
$324$		0			0
$325$		0			0
$326$			8.66553i			0.479939i
$327$		0			0
$328$	−0.571287	+	0.571287i	−0.0315441	+	0.0315441i
$329$	−10.5644			−0.582434
$330$		0			0
$331$	−23.7977			−1.30804			−0.654021	−	0.756476i	$-0.726919\pi$
$331$	−23.7977			−1.30804			−0.654021	+	0.756476i	$0.726919\pi$
$332$	0.171134	−	0.171134i	0.00939221	−	0.00939221i
$333$		0			0
$334$		−	8.74930i		−	0.478741i
$335$		0			0
$336$		0			0
$337$	0.828866	+	0.828866i	0.0451512	+	0.0451512i	0.729322	−	0.684171i	$-0.239836\pi$
$337$	0.828866	+	0.828866i	0.0451512	+	0.0451512i	−0.684171	+	0.729322i	$0.739836\pi$
$338$	8.51459	+	8.51459i	0.463133	+	0.463133i
$339$		0			0
$340$		0			0
$341$		−	10.2723i		−	0.556274i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−6.56440			−0.353929
$345$		0			0
$346$	−22.3050			−1.19913
$347$	5.17157	−	5.17157i	0.277625	−	0.277625i	−0.554535	−	0.832160i	$-0.687104\pi$
$347$	5.17157	−	5.17157i	0.277625	−	0.277625i	0.832160	+	0.554535i	$0.187104\pi$
$348$		0			0
$349$			4.20837i			0.225269i	0.993636	+	0.112634i	$0.0359289\pi$
$349$			4.20837i			0.225269i	−0.993636	+	0.112634i	$0.964071\pi$
$350$		0			0
$351$		0			0
$352$	−1.25714	−	1.25714i	−0.0670058	−	0.0670058i
$353$	2.22214	+	2.22214i	0.118272	+	0.118272i	0.763766	−	0.645493i	$-0.223348\pi$
$353$	2.22214	+	2.22214i	0.118272	+	0.118272i	−0.645493	+	0.763766i	$0.723348\pi$
$354$		0			0
$355$		0			0
$356$			13.2340i			0.701399i
$357$		0			0
$358$	2.74286	−	2.74286i	0.144965	−	0.144965i
$359$	22.7692			1.20171			0.600856	−	0.799357i	$-0.294827\pi$
$359$	22.7692			1.20171			0.600856	+	0.799357i	$0.294827\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	16.7511	−	16.7511i	0.880418	−	0.880418i
$363$		0			0
$364$		−	0.979056i		−	0.0513165i
$365$		0			0
$366$		0			0
$367$	−2.13836	−	2.13836i	−0.111622	−	0.111622i	0.649090	−	0.760712i	$-0.275150\pi$
$367$	−2.13836	−	2.13836i	−0.111622	−	0.111622i	−0.760712	+	0.649090i	$0.775150\pi$
$368$	3.38459	+	3.38459i	0.176434	+	0.176434i
$369$		0			0
$370$		0			0
$371$			5.04145i			0.261739i
$372$		0			0
$373$	−13.0263	+	13.0263i	−0.674478	+	0.674478i	−0.958745	−	0.284267i	$-0.908250\pi$
$373$	−13.0263	+	13.0263i	−0.674478	+	0.674478i	0.284267	+	0.958745i	$0.408250\pi$
$374$	6.01735			0.311150
$375$		0			0
$376$	−10.5644			−0.544818
$377$	3.06195	−	3.06195i	0.157699	−	0.157699i
$378$		0			0
$379$			27.4011i			1.40750i	0.710449	+	0.703749i	$0.248492\pi$
$379$			27.4011i			1.40750i	−0.710449	+	0.703749i	$0.751508\pi$
$380$		0			0
$381$		0			0
$382$	−16.5972	−	16.5972i	−0.849185	−	0.849185i
$383$	−17.6715	−	17.6715i	−0.902973	−	0.902973i	0.0927190	−	0.995692i	$-0.470444\pi$
$383$	−17.6715	−	17.6715i	−0.902973	−	0.902973i	−0.995692	+	0.0927190i	$0.970444\pi$
$384$		0			0
$385$		0			0
$386$			25.6380i			1.30494i
$387$		0			0
$388$	−12.6413	+	12.6413i	−0.641765	+	0.641765i
$389$	15.8356			0.802897			0.401449	−	0.915882i	$-0.368507\pi$
$389$	15.8356			0.802897			0.401449	+	0.915882i	$0.368507\pi$
$390$		0			0
$391$	−16.2005			−0.819294
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$			13.5557i			0.682928i
$395$		0			0
$396$		0			0
$397$	14.5575	+	14.5575i	0.730621	+	0.730621i	0.970743	−	0.240122i	$-0.0771874\pi$
$397$	14.5575	+	14.5575i	0.730621	+	0.730621i	−0.240122	+	0.970743i	$0.577187\pi$
$398$	−1.74242	−	1.74242i	−0.0873397	−	0.0873397i
$399$		0			0
$400$		0			0
$401$			9.78102i			0.488441i	0.969720	+	0.244220i	$0.0785320\pi$
$401$			9.78102i			0.488441i	−0.969720	+	0.244220i	$0.921468\pi$
$402$		0			0
$403$	4.00000	−	4.00000i	0.199254	−	0.199254i
$404$	−12.6778			−0.630744
$405$		0			0
$406$	4.42289			0.219504
$407$	10.5143	−	10.5143i	0.521174	−	0.521174i
$408$		0			0
$409$		−	10.3907i		−	0.513789i	−0.966439	−	0.256894i	$-0.917301\pi$
$409$		−	10.3907i		−	0.513789i	0.966439	−	0.256894i	$-0.0826993\pi$
$410$		0			0
$411$		0			0
$412$	7.43472	+	7.43472i	0.366282	+	0.366282i
$413$	4.17113	+	4.17113i	0.205248	+	0.205248i
$414$		0			0
$415$		0			0
$416$		−	0.979056i		−	0.0480022i
$417$		0			0
$418$		0			0
$419$	32.8521			1.60493			0.802465	−	0.596700i	$-0.203522\pi$
$419$	32.8521			1.60493			0.802465	+	0.596700i	$0.203522\pi$
$420$		0			0
$421$	33.6560			1.64029			0.820146	−	0.572154i	$-0.193892\pi$
$421$	33.6560			1.64029			0.820146	+	0.572154i	$0.193892\pi$
$422$	−3.94076	+	3.94076i	−0.191833	+	0.191833i
$423$		0			0
$424$			5.04145i			0.244834i
$425$		0			0
$426$		0			0
$427$	−1.69230	−	1.69230i	−0.0818960	−	0.0818960i
$428$	13.5138	+	13.5138i	0.653216	+	0.653216i
$429$		0			0
$430$		0			0
$431$			28.4260i			1.36923i	0.728903	+	0.684617i	$0.240031\pi$
$431$			28.4260i			1.36923i	−0.728903	+	0.684617i	$0.759969\pi$
$432$		0			0
$433$	8.84355	−	8.84355i	0.424994	−	0.424994i	−0.461925	−	0.886919i	$-0.652841\pi$
$433$	8.84355	−	8.84355i	0.424994	−	0.424994i	0.886919	+	0.461925i	$0.152841\pi$
$434$	5.77786			0.277346
$435$		0			0
$436$	−3.30082			−0.158081
$437$		0			0
$438$		0			0
$439$		−	0.481506i		−	0.0229810i	−0.999934	−	0.0114905i	$-0.996342\pi$
$439$		−	0.481506i		−	0.0229810i	0.999934	−	0.0114905i	$-0.00365763\pi$
$440$		0			0
$441$		0			0
$442$	2.34315	+	2.34315i	0.111452	+	0.111452i
$443$	15.8570	+	15.8570i	0.753388	+	0.753388i	0.975110	−	0.221722i	$-0.0711677\pi$
$443$	15.8570	+	15.8570i	0.753388	+	0.753388i	−0.221722	+	0.975110i	$0.571168\pi$
$444$		0			0
$445$		0			0
$446$		−	20.7683i		−	0.983408i
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−31.8986			−1.50539			−0.752694	−	0.658370i	$-0.771246\pi$
$449$	−31.8986			−1.50539			−0.752694	+	0.658370i	$0.771246\pi$
$450$		0			0
$451$	1.43638			0.0676363
$452$	−5.84937	+	5.84937i	−0.275131	+	0.275131i
$453$		0			0
$454$		−	27.6560i		−	1.29796i
$455$		0			0
$456$		0			0
$457$	−20.5557	−	20.5557i	−0.961556	−	0.961556i	0.0377315	−	0.999288i	$-0.487987\pi$
$457$	−20.5557	−	20.5557i	−0.961556	−	0.961556i	−0.999288	+	0.0377315i	$0.987987\pi$
$458$	−17.2266	−	17.2266i	−0.804948	−	0.804948i
$459$		0			0
$460$		0			0
$461$		−	35.9849i		−	1.67599i	−0.545682	−	0.837993i	$-0.683729\pi$
$461$		−	35.9849i		−	1.67599i	0.545682	−	0.837993i	$-0.316271\pi$
$462$		0			0
$463$	12.8703	−	12.8703i	0.598134	−	0.598134i	−0.341682	−	0.939816i	$-0.610996\pi$
$463$	12.8703	−	12.8703i	0.598134	−	0.598134i	0.939816	+	0.341682i	$0.110996\pi$
$464$	4.42289			0.205327
$465$		0			0
$466$	−20.8868			−0.967562
$467$	−0.531630	+	0.531630i	−0.0246009	+	0.0246009i	−0.719300	−	0.694699i	$-0.755537\pi$
$467$	−0.531630	+	0.531630i	−0.0246009	+	0.0246009i	0.694699	+	0.719300i	$0.255537\pi$
$468$		0			0
$469$		−	0.907550i		−	0.0419068i
$470$		0			0
$471$		0			0
$472$	4.17113	+	4.17113i	0.191992	+	0.191992i
$473$	8.25237	+	8.25237i	0.379445	+	0.379445i
$474$		0			0
$475$		0			0
$476$			3.38459i			0.155133i
$477$		0			0
$478$	1.04145	−	1.04145i	0.0476348	−	0.0476348i
$479$	23.0588			1.05358			0.526792	−	0.849994i	$-0.323395\pi$
$479$	23.0588			1.05358			0.526792	+	0.849994i	$0.323395\pi$
$480$		0			0
$481$	8.18848			0.373363
$482$	−15.2422	+	15.2422i	−0.694263	+	0.694263i
$483$		0			0
$484$		−	7.83920i		−	0.356327i
$485$		0			0
$486$		0			0
$487$	15.9291	+	15.9291i	0.721817	+	0.721817i	0.968975	−	0.247158i	$-0.0794967\pi$
$487$	15.9291	+	15.9291i	0.721817	+	0.721817i	−0.247158	+	0.968975i	$0.579497\pi$
$488$	−1.69230	−	1.69230i	−0.0766067	−	0.0766067i
$489$		0			0
$490$		0			0
$491$			11.3509i			0.512261i	0.966642	+	0.256130i	$0.0824477\pi$
$491$			11.3509i			0.512261i	−0.966642	+	0.256130i	$0.917552\pi$
$492$		0			0
$493$	−10.5852	+	10.5852i	−0.476732	+	0.476732i
$494$		0			0
$495$		0			0
$496$	5.77786			0.259434
$497$	−7.55573	+	7.55573i	−0.338921	+	0.338921i
$498$		0			0
$499$		−	20.6319i		−	0.923610i	−0.886982	−	0.461805i	$-0.847202\pi$
$499$		−	20.6319i		−	0.923610i	0.886982	−	0.461805i	$-0.152798\pi$
$500$		0			0
$501$		0			0
$502$	−1.89887	−	1.89887i	−0.0847509	−	0.0847509i
$503$	21.2982	+	21.2982i	0.949638	+	0.949638i	0.998791	−	0.0491536i	$-0.0156524\pi$
$503$	21.2982	+	21.2982i	0.949638	+	0.949638i	−0.0491536	+	0.998791i	$0.515652\pi$
$504$		0			0
$505$		0			0
$506$		−	8.50982i		−	0.378308i
$507$		0			0
$508$	0.615405	−	0.615405i	0.0273042	−	0.0273042i
$509$	8.13328			0.360501			0.180251	−	0.983621i	$-0.442309\pi$
$509$	8.13328			0.360501			0.180251	+	0.983621i	$0.442309\pi$
$510$		0			0
$511$	8.06239			0.356659
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	15.5384i		−	0.685368i
$515$		0			0
$516$		0			0
$517$	13.2809	+	13.2809i	0.584095	+	0.584095i
$518$	5.91399	+	5.91399i	0.259846	+	0.259846i
$519$		0			0
$520$		0			0
$521$		−	19.2331i		−	0.842617i	−0.906917	−	0.421308i	$-0.861571\pi$
$521$		−	19.2331i		−	0.842617i	0.906917	−	0.421308i	$-0.138429\pi$
$522$		0			0
$523$	3.22635	−	3.22635i	0.141078	−	0.141078i	−0.633040	−	0.774119i	$-0.718193\pi$
$523$	3.22635	−	3.22635i	0.141078	−	0.141078i	0.774119	+	0.633040i	$0.218193\pi$
$524$	−6.52717			−0.285141
$525$		0			0
$526$	11.2135			0.488930
$527$	−13.8280	+	13.8280i	−0.602357	+	0.602357i
$528$		0			0
$529$		−	0.0890385i		−	0.00387124i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.559322	+	0.559322i	0.0242269	+	0.0242269i
$534$		0			0
$535$		0			0
$536$		−	0.907550i		−	0.0392002i
$537$		0			0
$538$	5.13657	−	5.13657i	0.221453	−	0.221453i
$539$	−1.77786			−0.0765780
$540$		0			0
$541$	−12.9412			−0.556386			−0.278193	−	0.960525i	$-0.589735\pi$
$541$	−12.9412			−0.556386			−0.278193	+	0.960525i	$0.589735\pi$
$542$	−12.4278	+	12.4278i	−0.533821	+	0.533821i
$543$		0			0
$544$			3.38459i			0.145113i
$545$		0			0
$546$		0			0
$547$	−7.15601	−	7.15601i	−0.305969	−	0.305969i	0.537375	−	0.843344i	$-0.319416\pi$
$547$	−7.15601	−	7.15601i	−0.305969	−	0.305969i	−0.843344	+	0.537375i	$0.819416\pi$
$548$	−0.192517	−	0.192517i	−0.00822390	−	0.00822390i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	11.5557	−	11.5557i	0.491400	−	0.491400i
$554$	13.8775			0.589598
$555$		0			0
$556$	14.8694			0.630605
$557$	−19.5648	+	19.5648i	−0.828989	+	0.828989i	−0.987377	−	0.158388i	$-0.949370\pi$
$557$	−19.5648	+	19.5648i	−0.828989	+	0.828989i	0.158388	+	0.987377i	$0.449370\pi$
$558$		0			0
$559$			6.42692i			0.271830i
$560$		0			0
$561$		0			0
$562$	8.89887	+	8.89887i	0.375376	+	0.375376i
$563$	0.0708861	+	0.0708861i	0.00298749	+	0.00298749i	0.708599	−	0.705611i	$-0.249328\pi$
$563$	0.0708861	+	0.0708861i	0.00298749	+	0.00298749i	−0.705611	+	0.708599i	$0.749328\pi$
$564$		0			0
$565$		0			0
$566$			6.64564i			0.279337i
$567$		0			0
$568$	−7.55573	+	7.55573i	−0.317031	+	0.317031i
$569$	−20.2232			−0.847799			−0.423900	−	0.905709i	$-0.639339\pi$
$569$	−20.2232			−0.847799			−0.423900	+	0.905709i	$0.639339\pi$
$570$		0			0
$571$	34.9439			1.46236			0.731179	−	0.682186i	$-0.238971\pi$
$571$	34.9439			1.46236			0.731179	+	0.682186i	$0.238971\pi$
$572$	−1.23081	+	1.23081i	−0.0514628	+	0.0514628i
$573$		0			0
$574$			0.807922i			0.0337220i
$575$		0			0
$576$		0			0
$577$	−32.2853	−	32.2853i	−1.34405	−	1.34405i	−0.891982	−	0.452071i	$-0.850685\pi$
$577$	−32.2853	−	32.2853i	−1.34405	−	1.34405i	−0.452071	−	0.891982i	$-0.649315\pi$
$578$	3.92057	+	3.92057i	0.163074	+	0.163074i
$579$		0			0
$580$		0			0
$581$		−	0.242020i		−	0.0100407i
$582$		0			0
$583$	6.33781	−	6.33781i	0.262485	−	0.262485i
$584$	8.06239			0.333624
$585$		0			0
$586$	−4.80642			−0.198552
$587$	9.40194	−	9.40194i	0.388060	−	0.388060i	−0.485935	−	0.873995i	$-0.661521\pi$
$587$	9.40194	−	9.40194i	0.388060	−	0.388060i	0.873995	+	0.485935i	$0.161521\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	5.91399	+	5.91399i	0.243064	+	0.243064i
$593$	−0.326416	−	0.326416i	−0.0134043	−	0.0134043i	0.700373	−	0.713777i	$-0.253017\pi$
$593$	−0.326416	−	0.326416i	−0.0134043	−	0.0134043i	−0.713777	+	0.700373i	$0.753017\pi$
$594$		0			0
$595$		0			0
$596$		−	20.6467i		−	0.845721i
$597$		0			0
$598$	3.31371	−	3.31371i	0.135508	−	0.135508i
$599$	29.1288			1.19017			0.595085	−	0.803662i	$-0.297118\pi$
$599$	29.1288			1.19017			0.595085	+	0.803662i	$0.297118\pi$
$600$		0			0
$601$	45.0579			1.83795			0.918975	−	0.394315i	$-0.129018\pi$
$601$	45.0579			1.83795			0.918975	+	0.394315i	$0.129018\pi$
$602$	−4.64173	+	4.64173i	−0.189183	+	0.189183i
$603$		0			0
$604$		−	6.01735i		−	0.244843i
$605$		0			0
$606$		0			0
$607$	−6.68541	−	6.68541i	−0.271353	−	0.271353i	0.558292	−	0.829645i	$-0.311457\pi$
$607$	−6.68541	−	6.68541i	−0.271353	−	0.271353i	−0.829645	+	0.558292i	$0.811457\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			10.3431i			0.418439i
$612$		0			0
$613$	20.5112	−	20.5112i	0.828438	−	0.828438i	−0.158862	−	0.987301i	$-0.550783\pi$
$613$	20.5112	−	20.5112i	0.828438	−	0.828438i	0.987301	+	0.158862i	$0.0507826\pi$
$614$	21.9991			0.887812
$615$		0			0
$616$	−1.77786			−0.0716322
$617$	4.29214	−	4.29214i	0.172795	−	0.172795i	−0.615411	−	0.788206i	$-0.711010\pi$
$617$	4.29214	−	4.29214i	0.172795	−	0.172795i	0.788206	+	0.615411i	$0.211010\pi$
$618$		0			0
$619$		−	8.16755i		−	0.328282i	−0.986437	−	0.164141i	$-0.947515\pi$
$619$		−	8.16755i		−	0.328282i	0.986437	−	0.164141i	$-0.0524851\pi$
$620$		0			0
$621$		0			0
$622$	0.547054	+	0.547054i	0.0219349	+	0.0219349i
$623$	9.35783	+	9.35783i	0.374913	+	0.374913i
$624$		0			0
$625$		0			0
$626$		−	16.7652i		−	0.670070i
$627$		0			0
$628$	0.608522	−	0.608522i	0.0242827	−	0.0242827i
$629$	−28.3076			−1.12870
$630$		0			0
$631$	38.8694			1.54737			0.773684	−	0.633572i	$-0.218412\pi$
$631$	38.8694			1.54737			0.773684	+	0.633572i	$0.218412\pi$
$632$	11.5557	−	11.5557i	0.459662	−	0.459662i
$633$		0			0
$634$		−	0.0128889i		−	0.000511884i
$635$		0			0
$636$		0			0
$637$	−0.692297	−	0.692297i	−0.0274298	−	0.0274298i
$638$	−5.56019	−	5.56019i	−0.220130	−	0.220130i
$639$		0			0
$640$		0			0
$641$		−	20.0751i		−	0.792918i	−0.918052	−	0.396459i	$-0.870239\pi$
$641$		−	20.0751i		−	0.792918i	0.918052	−	0.396459i	$-0.129761\pi$
$642$		0			0
$643$	13.6257	−	13.6257i	0.537347	−	0.537347i	−0.385402	−	0.922749i	$-0.625937\pi$
$643$	13.6257	−	13.6257i	0.537347	−	0.537347i	0.922749	+	0.385402i	$0.125937\pi$
$644$	4.78654			0.188616
$645$		0			0
$646$		0			0
$647$	−1.47104	+	1.47104i	−0.0578325	+	0.0578325i	−0.735432	−	0.677599i	$-0.763021\pi$
$647$	−1.47104	+	1.47104i	−0.0578325	+	0.0578325i	0.677599	+	0.735432i	$0.263021\pi$
$648$		0			0
$649$		−	10.4874i		−	0.411666i
$650$		0			0
$651$		0			0
$652$	6.12745	+	6.12745i	0.239970	+	0.239970i
$653$	−4.09647	−	4.09647i	−0.160307	−	0.160307i	0.622396	−	0.782703i	$-0.286160\pi$
$653$	−4.09647	−	4.09647i	−0.160307	−	0.160307i	−0.782703	+	0.622396i	$0.786160\pi$
$654$		0			0
$655$		0			0
$656$			0.807922i			0.0315441i
$657$		0			0
$658$	−7.47016	+	7.47016i	−0.291217	+	0.291217i
$659$	0.683757			0.0266354			0.0133177	−	0.999911i	$-0.495761\pi$
$659$	0.683757			0.0266354			0.0133177	+	0.999911i	$0.495761\pi$
$660$		0			0
$661$	−42.9776			−1.67163			−0.835817	−	0.549009i	$-0.815005\pi$
$661$	−42.9776			−1.67163			−0.835817	+	0.549009i	$0.815005\pi$
$662$	−16.8275	+	16.8275i	−0.654021	+	0.654021i
$663$		0			0
$664$		−	0.242020i		−	0.00939221i
$665$		0			0
$666$		0			0
$667$	14.9697	+	14.9697i	0.579629	+	0.579629i
$668$	−6.18669	−	6.18669i	−0.239370	−	0.239370i
$669$		0			0
$670$		0			0
$671$			4.25491i			0.164259i
$672$		0			0
$673$	24.6569	−	24.6569i	0.950452	−	0.950452i	−0.0483773	−	0.998829i	$-0.515405\pi$
$673$	24.6569	−	24.6569i	0.950452	−	0.950452i	0.998829	+	0.0483773i	$0.0154050\pi$
$674$	1.17219			0.0451512
$675$		0			0
$676$	12.0414			0.463133
$677$	−31.2343	+	31.2343i	−1.20043	+	1.20043i	−0.226394	+	0.974036i	$0.572694\pi$
$677$	−31.2343	+	31.2343i	−1.20043	+	1.20043i	−0.974036	+	0.226394i	$0.927306\pi$
$678$		0			0
$679$			17.8775i			0.686075i
$680$		0			0
$681$		0			0
$682$	−7.26358	−	7.26358i	−0.278137	−	0.278137i
$683$	7.92000	+	7.92000i	0.303050	+	0.303050i	0.842206	−	0.539156i	$-0.181257\pi$
$683$	7.92000	+	7.92000i	0.303050	+	0.303050i	−0.539156	+	0.842206i	$0.681257\pi$
$684$		0			0
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	−4.64173	+	4.64173i	−0.176964	+	0.176964i
$689$	4.93586			0.188041
$690$		0			0
$691$	22.1227			0.841586			0.420793	−	0.907157i	$-0.361752\pi$
$691$	22.1227			0.841586			0.420793	+	0.907157i	$0.361752\pi$
$692$	−15.7720	+	15.7720i	−0.599563	+	0.599563i
$693$		0			0
$694$		−	7.31371i		−	0.277625i
$695$		0			0
$696$		0			0
$697$	−1.93358	−	1.93358i	−0.0732394	−	0.0732394i
$698$	2.97577	+	2.97577i	0.112634	+	0.112634i
$699$		0			0
$700$		0			0
$701$			6.16352i			0.232793i	0.993203	+	0.116396i	$0.0371343\pi$
$701$			6.16352i			0.232793i	−0.993203	+	0.116396i	$0.962866\pi$
$702$		0			0
$703$		0			0
$704$	−1.77786			−0.0670058
$705$		0			0
$706$	3.14257			0.118272
$707$	−8.96456	+	8.96456i	−0.337147	+	0.337147i
$708$		0			0
$709$		−	49.7215i		−	1.86733i	−0.358146	−	0.933666i	$-0.616591\pi$
$709$		−	49.7215i		−	1.86733i	0.358146	−	0.933666i	$-0.383409\pi$
$710$		0			0
$711$		0			0
$712$	9.35783	+	9.35783i	0.350699	+	0.350699i
$713$	19.5557	+	19.5557i	0.732368	+	0.732368i
$714$		0			0
$715$		0			0
$716$		−	3.87899i		−	0.144965i
$717$		0			0
$718$	16.1002	−	16.1002i	0.600856	−	0.600856i
$719$	−16.9706			−0.632895			−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$		0			0
$721$	10.5143			0.391572
$722$	13.4350	−	13.4350i	0.500000	−	0.500000i
$723$		0			0
$724$		−	23.6896i		−	0.880418i
$725$		0			0
$726$		0			0
$727$	15.9162	+	15.9162i	0.590300	+	0.590300i	0.937712	−	0.347412i	$-0.112940\pi$
$727$	15.9162	+	15.9162i	0.590300	+	0.590300i	−0.347412	+	0.937712i	$0.612940\pi$
$728$	−0.692297	−	0.692297i	−0.0256582	−	0.0256582i
$729$		0			0
$730$		0			0
$731$		−	22.2178i		−	0.821757i
$732$		0			0
$733$	15.3578	−	15.3578i	0.567254	−	0.567254i	−0.364104	−	0.931358i	$-0.618625\pi$
$733$	15.3578	−	15.3578i	0.567254	−	0.567254i	0.931358	+	0.364104i	$0.118625\pi$
$734$	−3.02410			−0.111622
$735$		0			0
$736$	4.78654			0.176434
$737$	−1.14092	+	1.14092i	−0.0420262	+	0.0420262i
$738$		0			0
$739$			45.6515i			1.67932i	0.543114	+	0.839659i	$0.317245\pi$
$739$			45.6515i			1.67932i	−0.543114	+	0.839659i	$0.682755\pi$
$740$		0			0
$741$		0			0
$742$	3.56484	+	3.56484i	0.130869	+	0.130869i
$743$	5.67508	+	5.67508i	0.208199	+	0.208199i	0.803501	−	0.595303i	$-0.202968\pi$
$743$	5.67508	+	5.67508i	0.208199	+	0.208199i	−0.595303	+	0.803501i	$0.702968\pi$
$744$		0			0
$745$		0			0
$746$			18.4220i			0.674478i
$747$		0			0
$748$	4.25491	−	4.25491i	0.155575	−	0.155575i
$749$	19.1115			0.698317
$750$		0			0
$751$	−41.4364			−1.51203			−0.756017	−	0.654552i	$-0.772857\pi$
$751$	−41.4364			−1.51203			−0.756017	+	0.654552i	$0.772857\pi$
$752$	−7.47016	+	7.47016i	−0.272409	+	0.272409i
$753$		0			0
$754$		−	4.33026i		−	0.157699i
$755$		0			0
$756$		0			0
$757$	22.4109	+	22.4109i	0.814539	+	0.814539i	0.985311	−	0.170772i	$-0.0546261\pi$
$757$	22.4109	+	22.4109i	0.814539	+	0.814539i	−0.170772	+	0.985311i	$0.554626\pi$
$758$	19.3755	+	19.3755i	0.703749	+	0.703749i
$759$		0			0
$760$		0			0
$761$		−	15.1675i		−	0.549823i	−0.961470	−	0.274911i	$-0.911351\pi$
$761$		−	15.1675i		−	0.549823i	0.961470	−	0.274911i	$-0.0886485\pi$
$762$		0			0
$763$	−2.33403	+	2.33403i	−0.0844976	+	0.0844976i
$764$	−23.4720			−0.849185
$765$		0			0
$766$	−24.9913			−0.902973
$767$	4.08378	−	4.08378i	0.147457	−	0.147457i
$768$		0			0
$769$			19.8686i			0.716481i	0.933629	+	0.358241i	$0.116623\pi$
$769$			19.8686i			0.716481i	−0.933629	+	0.358241i	$0.883377\pi$
$770$		0			0
$771$		0			0
$772$	18.1288	+	18.1288i	0.652470	+	0.652470i
$773$	0.293937	+	0.293937i	0.0105722	+	0.0105722i	0.712373	−	0.701801i	$-0.247620\pi$
$773$	0.293937	+	0.293937i	0.0105722	+	0.0105722i	−0.701801	+	0.712373i	$0.747620\pi$
$774$		0			0
$775$		0			0
$776$			17.8775i			0.641765i
$777$		0			0
$778$	11.1975	−	11.1975i	0.401449	−	0.401449i
$779$		0			0
$780$		0			0
$781$	18.9972			0.679774
$782$	−11.4555	+	11.4555i	−0.409647	+	0.409647i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	−16.3076	−	16.3076i	−0.581302	−	0.581302i	0.353959	−	0.935261i	$-0.384835\pi$
$787$	−16.3076	−	16.3076i	−0.581302	−	0.581302i	−0.935261	+	0.353959i	$0.884835\pi$
$788$	9.58535	+	9.58535i	0.341464	+	0.341464i
$789$		0			0
$790$		0			0
$791$			8.27226i			0.294128i
$792$		0			0
$793$	−1.65685	+	1.65685i	−0.0588366	+	0.0588366i
$794$	20.5874			0.730621
$795$		0			0
$796$	−2.46416			−0.0873397
$797$	22.1562	−	22.1562i	0.784813	−	0.784813i	−0.195826	−	0.980639i	$-0.562739\pi$
$797$	22.1562	−	22.1562i	0.784813	−	0.784813i	0.980639	+	0.195826i	$0.0627388\pi$
$798$		0			0
$799$		−	35.7562i		−	1.26496i
$800$		0			0
$801$		0			0
$802$	6.91622	+	6.91622i	0.244220	+	0.244220i
$803$	−10.1356	−	10.1356i	−0.357676	−	0.357676i
$804$		0			0
$805$		0			0
$806$		−	5.65685i		−	0.199254i
$807$		0			0
$808$	−8.96456	+	8.96456i	−0.315372	+	0.315372i
$809$	−17.0046			−0.597851			−0.298926	−	0.954276i	$-0.596628\pi$
$809$	−17.0046			−0.597851			−0.298926	+	0.954276i	$0.596628\pi$
$810$		0			0
$811$	19.7927			0.695015			0.347508	−	0.937677i	$-0.387028\pi$
$811$	19.7927			0.695015			0.347508	+	0.937677i	$0.387028\pi$
$812$	3.12745	−	3.12745i	0.109752	−	0.109752i
$813$		0			0
$814$		−	14.8694i		−	0.521174i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−7.34736	−	7.34736i	−0.256894	−	0.256894i
$819$		0			0
$820$		0			0
$821$			8.89887i			0.310573i	0.987870	+	0.155286i	$0.0496300\pi$
$821$			8.89887i			0.310573i	−0.987870	+	0.155286i	$0.950370\pi$
$822$		0			0
$823$	−31.0932	+	31.0932i	−1.08384	+	1.08384i	−0.0876944	+	0.996147i	$0.527950\pi$
$823$	−31.0932	+	31.0932i	−1.08384	+	1.08384i	−0.996147	+	0.0876944i	$0.972050\pi$
$824$	10.5143			0.366282
$825$		0			0
$826$	5.89887			0.205248
$827$	−25.5604	+	25.5604i	−0.888822	+	0.888822i	−0.994410	−	0.105588i	$-0.966327\pi$
$827$	−25.5604	+	25.5604i	−0.888822	+	0.888822i	0.105588	+	0.994410i	$0.466327\pi$
$828$		0			0
$829$		−	13.6067i		−	0.472581i	−0.971682	−	0.236291i	$-0.924068\pi$
$829$		−	13.6067i		−	0.472581i	0.971682	−	0.236291i	$-0.0759317\pi$
$830$		0			0
$831$		0			0
$832$	−0.692297	−	0.692297i	−0.0240011	−	0.0240011i
$833$	2.39327	+	2.39327i	0.0829219	+	0.0829219i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	23.2299	−	23.2299i	0.802465	−	0.802465i
$839$	−45.4002			−1.56739			−0.783694	−	0.621147i	$-0.786667\pi$
$839$	−45.4002			−1.56739			−0.783694	+	0.621147i	$0.786667\pi$
$840$		0			0
$841$	−9.43806			−0.325450
$842$	23.7984	−	23.7984i	0.820146	−	0.820146i
$843$		0			0
$844$			5.57308i			0.191833i
$845$		0			0
$846$		0			0
$847$	−5.54315	−	5.54315i	−0.190465	−	0.190465i
$848$	3.56484	+	3.56484i	0.122417	+	0.122417i
$849$		0			0
$850$		0			0
$851$			40.0329i			1.37231i
$852$		0			0
$853$	−4.62841	+	4.62841i	−0.158474	+	0.158474i	−0.781890	−	0.623416i	$-0.785744\pi$
$853$	−4.62841	+	4.62841i	−0.158474	+	0.158474i	0.623416	+	0.781890i	$0.285744\pi$
$854$	−2.39327			−0.0818960
$855$		0			0
$856$	19.1115			0.653216
$857$	−23.4218	+	23.4218i	−0.800074	+	0.800074i	−0.983107	−	0.183032i	$-0.941409\pi$
$857$	−23.4218	+	23.4218i	−0.800074	+	0.800074i	0.183032	+	0.983107i	$0.441409\pi$
$858$		0			0
$859$		−	29.8062i		−	1.01697i	−0.861070	−	0.508487i	$-0.830205\pi$
$859$		−	29.8062i		−	1.01697i	0.861070	−	0.508487i	$-0.169795\pi$
$860$		0			0
$861$		0			0
$862$	20.1002	+	20.1002i	0.684617	+	0.684617i
$863$	−12.8868	−	12.8868i	−0.438671	−	0.438671i	0.452893	−	0.891565i	$-0.350392\pi$
$863$	−12.8868	−	12.8868i	−0.438671	−	0.438671i	−0.891565	+	0.452893i	$0.850392\pi$
$864$		0			0
$865$		0			0
$866$		−	12.5067i		−	0.424994i
$867$		0			0
$868$	4.08557	−	4.08557i	0.138673	−	0.138673i
$869$	−29.0543			−0.985601
$870$		0			0
$871$	−0.888542			−0.0301071
$872$	−2.33403	+	2.33403i	−0.0790403	+	0.0790403i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.6479	−	10.6479i	−0.359553	−	0.359553i	0.504095	−	0.863648i	$-0.331826\pi$
$877$	−10.6479	−	10.6479i	−0.359553	−	0.359553i	−0.863648	+	0.504095i	$0.831826\pi$
$878$	−0.340476	−	0.340476i	−0.0114905	−	0.0114905i
$879$		0			0
$880$		0			0
$881$			59.0706i			1.99014i	0.0991785	+	0.995070i	$0.468379\pi$
$881$			59.0706i			1.99014i	−0.0991785	+	0.995070i	$0.531621\pi$
$882$		0			0
$883$	14.9269	−	14.9269i	0.502330	−	0.502330i	−0.409832	−	0.912161i	$-0.634413\pi$
$883$	14.9269	−	14.9269i	0.502330	−	0.502330i	0.912161	+	0.409832i	$0.134413\pi$
$884$	3.31371			0.111452
$885$		0			0
$886$	22.4252			0.753388
$887$	7.58864	−	7.58864i	0.254802	−	0.254802i	−0.568134	−	0.822936i	$-0.692335\pi$
$887$	7.58864	−	7.58864i	0.254802	−	0.254802i	0.822936	+	0.568134i	$0.192335\pi$
$888$		0			0
$889$		−	0.870315i		−	0.0291894i
$890$		0			0
$891$		0			0
$892$	−14.6854	−	14.6854i	−0.491704	−	0.491704i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−22.5557	+	22.5557i	−0.752694	+	0.752694i
$899$	25.5549			0.852302
$900$		0			0
$901$	−17.0633			−0.568460
$902$	1.01567	−	1.01567i	0.0338181	−	0.0338181i
$903$		0			0
$904$			8.27226i			0.275131i
$905$		0			0
$906$		0			0
$907$	−7.95544	−	7.95544i	−0.264156	−	0.264156i	0.562584	−	0.826740i	$-0.309807\pi$
$907$	−7.95544	−	7.95544i	−0.264156	−	0.264156i	−0.826740	+	0.562584i	$0.809807\pi$
$908$	−19.5557	−	19.5557i	−0.648980	−	0.648980i
$909$		0			0
$910$		0			0
$911$			53.4969i			1.77243i	0.463274	+	0.886215i	$0.346674\pi$
$911$			53.4969i			1.77243i	−0.463274	+	0.886215i	$0.653326\pi$
$912$		0			0
$913$	−0.304253	+	0.304253i	−0.0100693	+	0.0100693i
$914$	−29.0702			−0.961556
$915$		0			0
$916$	−24.3622			−0.804948
$917$	−4.61541	+	4.61541i	−0.152414	+	0.152414i
$918$		0			0
$919$		−	43.3882i		−	1.43124i	−0.698488	−	0.715622i	$-0.746143\pi$
$919$		−	43.3882i		−	1.43124i	0.698488	−	0.715622i	$-0.253857\pi$
$920$		0			0
$921$		0			0
$922$	−25.4452	−	25.4452i	−0.837993	−	0.837993i
$923$	7.39748	+	7.39748i	0.243491	+	0.243491i
$924$		0			0
$925$		0			0
$926$		−	18.2014i		−	0.598134i
$927$		0			0
$928$	3.12745	−	3.12745i	0.102664	−	0.102664i
$929$	12.2024			0.400348			0.200174	−	0.979760i	$-0.435849\pi$
$929$	12.2024			0.400348			0.200174	+	0.979760i	$0.435849\pi$
$930$		0			0
$931$		0			0
$932$	−14.7692	+	14.7692i	−0.483781	+	0.483781i
$933$		0			0
$934$			0.751839i			0.0246009i
$935$		0			0
$936$		0			0
$937$	−2.82978	−	2.82978i	−0.0924449	−	0.0924449i	0.659372	−	0.751817i	$-0.270822\pi$
$937$	−2.82978	−	2.82978i	−0.0924449	−	0.0924449i	−0.751817	+	0.659372i	$0.770822\pi$
$938$	−0.641735	−	0.641735i	−0.0209534	−	0.0209534i
$939$		0			0
$940$		0			0
$941$		−	42.7478i		−	1.39354i	−0.717295	−	0.696769i	$-0.754620\pi$
$941$		−	42.7478i		−	1.39354i	0.717295	−	0.696769i	$-0.245380\pi$
$942$		0			0
$943$	−2.73449	+	2.73449i	−0.0890472	+	0.0890472i
$944$	5.89887			0.191992
$945$		0			0
$946$	11.6706			0.379445
$947$	35.5502	−	35.5502i	1.15523	−	1.15523i	0.169737	−	0.985489i	$-0.445708\pi$
$947$	35.5502	−	35.5502i	1.15523	−	1.15523i	0.985489	−	0.169737i	$-0.0542918\pi$
$948$		0			0
$949$		−	7.89354i		−	0.256235i
$950$		0			0
$951$		0			0
$952$	2.39327	+	2.39327i	0.0775663	+	0.0775663i
$953$	−1.05372	−	1.05372i	−0.0341333	−	0.0341333i	0.689834	−	0.723967i	$-0.257683\pi$
$953$	−1.05372	−	1.05372i	−0.0341333	−	0.0341333i	−0.723967	+	0.689834i	$0.757683\pi$
$954$		0			0
$955$		0			0
$956$		−	1.47283i		−	0.0476348i
$957$		0			0
$958$	16.3050	−	16.3050i	0.526792	−	0.526792i
$959$	−0.272260			−0.00879172
$960$		0			0
$961$	2.38372			0.0768941
$962$	5.79013	−	5.79013i	0.186681	−	0.186681i
$963$		0			0
$964$			21.5557i			0.694263i
$965$		0			0
$966$		0			0
$967$	26.3414	+	26.3414i	0.847082	+	0.847082i	0.989768	−	0.142686i	$-0.0455739\pi$
$967$	26.3414	+	26.3414i	0.847082	+	0.847082i	−0.142686	+	0.989768i	$0.545574\pi$
$968$	−5.54315	−	5.54315i	−0.178164	−	0.178164i
$969$		0			0
$970$		0			0
$971$			30.7692i			0.987430i	0.869624	+	0.493715i	$0.164361\pi$
$971$			30.7692i			0.987430i	−0.869624	+	0.493715i	$0.835639\pi$
$972$		0			0
$973$	10.5143	−	10.5143i	0.337072	−	0.337072i
$974$	22.5272			0.721817
$975$		0			0
$976$	−2.39327			−0.0766067
$977$	−5.55661	+	5.55661i	−0.177772	+	0.177772i	−0.790384	−	0.612612i	$-0.790119\pi$
$977$	−5.55661	+	5.55661i	−0.177772	+	0.177772i	0.612612	+	0.790384i	$0.290119\pi$
$978$		0			0
$979$		−	23.5282i		−	0.751964i
$980$		0			0
$981$		0			0
$982$	8.02633	+	8.02633i	0.256130	+	0.256130i
$983$	−40.8357	−	40.8357i	−1.30246	−	1.30246i	−0.926732	−	0.375723i	$-0.877394\pi$
$983$	−40.8357	−	40.8357i	−1.30246	−	1.30246i	−0.375723	−	0.926732i	$-0.622606\pi$
$984$		0			0
$985$		0			0
$986$			14.9697i			0.476732i
$987$		0			0
$988$		0			0
$989$	−31.4208			−0.999123
$990$		0			0
$991$	−9.67333			−0.307283			−0.153642	−	0.988127i	$-0.549100\pi$
$991$	−9.67333			−0.307283			−0.153642	+	0.988127i	$0.549100\pi$
$992$	4.08557	−	4.08557i	0.129717	−	0.129717i
$993$		0			0
$994$			10.6854i			0.338921i
$995$		0			0
$996$		0			0
$997$	28.1841	+	28.1841i	0.892601	+	0.892601i	0.994767	−	0.102167i	$-0.0325775\pi$
$997$	28.1841	+	28.1841i	0.892601	+	0.892601i	−0.102167	+	0.994767i	$0.532578\pi$
$998$	−14.5889	−	14.5889i	−0.461805	−	0.461805i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.i.1457.4		8
3.2	odd	2		3150.2.m.j.1457.1		8
5.2	odd	4		630.2.m.d.323.4	yes	8
5.3	odd	4		3150.2.m.j.2843.2		8
5.4	even	2		630.2.m.c.197.1	✓	8
15.2	even	4		630.2.m.c.323.1	yes	8
15.8	even	4	inner	3150.2.m.i.2843.3		8
15.14	odd	2		630.2.m.d.197.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.c.197.1	✓	8	5.4	even	2
630.2.m.c.323.1	yes	8	15.2	even	4
630.2.m.d.197.4	yes	8	15.14	odd	2
630.2.m.d.323.4	yes	8	5.2	odd	4
3150.2.m.i.1457.4		8	1.1	even	1	trivial
3150.2.m.i.2843.3		8	15.8	even	4	inner
3150.2.m.j.1457.1		8	3.2	odd	2
3150.2.m.j.2843.2		8	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.77786i q^{11} +(-0.692297 + 0.692297i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(2.39327 - 2.39327i) q^{17} +(1.25714 + 1.25714i) q^{22} +(-3.38459 - 3.38459i) q^{23} +0.979056i q^{26} +(-0.707107 + 0.707107i) q^{28} -4.42289 q^{29} -5.77786 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.38459i q^{34} +(-5.91399 - 5.91399i) q^{37} -0.807922i q^{41} +(4.64173 - 4.64173i) q^{43} +1.77786 q^{44} -4.78654 q^{46} +(7.47016 - 7.47016i) q^{47} +1.00000i q^{49} +(0.692297 + 0.692297i) q^{52} +(-3.56484 - 3.56484i) q^{53} +1.00000i q^{56} +(-3.12745 + 3.12745i) q^{58} -5.89887 q^{59} +2.39327 q^{61} +(-4.08557 + 4.08557i) q^{62} +1.00000i q^{64} +(0.641735 + 0.641735i) q^{67} +(-2.39327 - 2.39327i) q^{68} -10.6854i q^{71} +(-5.70097 + 5.70097i) q^{73} -8.36365 q^{74} +(1.25714 - 1.25714i) q^{77} +16.3423i q^{79} +(-0.571287 - 0.571287i) q^{82} +(0.171134 + 0.171134i) q^{83} -6.56440i q^{86} +(1.25714 - 1.25714i) q^{88} -13.2340 q^{89} +0.979056 q^{91} +(-3.38459 + 3.38459i) q^{92} -10.5644i q^{94} +(-12.6413 - 12.6413i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{22} - 8 q^{23} - 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} - 24 q^{44} + 12 q^{47} - 4 q^{52} - 32 q^{53} - 12 q^{58} - 16 q^{59} - 4 q^{62} - 20 q^{67} - 36 q^{73} - 40 q^{74} + 4 q^{77} + 12 q^{82} - 56 q^{83} + 4 q^{88} - 72 q^{89} - 8 q^{92} + 4 q^{97}+O(q^{100}) \) 8 * q + 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^22 - 8 * q^23 - 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 - 24 * q^44 + 12 * q^47 - 4 * q^52 - 32 * q^53 - 12 * q^58 - 16 * q^59 - 4 * q^62 - 20 * q^67 - 36 * q^73 - 40 * q^74 + 4 * q^77 + 12 * q^82 - 56 * q^83 + 4 * q^88 - 72 * q^89 - 8 * q^92 + 4 * q^97

Introduction

L-functions

Modular forms

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Database

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