LMFDB - Embedded newform 1100.2.cb.b.949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(49,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("1100.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.cb (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:	$8.78354422234$
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} - 11x^{14} + 56x^{12} - 141x^{10} + 551x^{8} - 1245x^{6} + 1400x^{4} + 125x^{2} + 625 $ x^16 - 11x^14 + 56x^12 - 141x^10 + 551x^8 - 1245x^6 + 1400x^4 + 125*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			949.1
Root			$1.04478 + 1.43801i$ of defining polynomial
Character	$\chi$	$=$	1100.949
Dual form			1100.2.cb.b.1049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27827 + 0.740256i) q^{3} +(4.42575 + 1.43801i) q^{7} +(2.21550 - 1.60965i) q^{9} +O(q^{10})$	\(q+(-2.27827 + 0.740256i) q^{3} +(4.42575 + 1.43801i) q^{7} +(2.21550 - 1.60965i) q^{9} +(-3.31404 - 0.130791i) q^{11} +(3.54757 + 4.88281i) q^{13} +(1.95207 - 2.68680i) q^{17} +(-0.846245 - 2.60448i) q^{19} -11.1476 q^{21} -1.97807i q^{23} +(0.368194 - 0.506776i) q^{27} +(-0.708723 + 2.18123i) q^{29} +(5.62481 - 4.08666i) q^{31} +(7.64712 - 2.15526i) q^{33} +(3.64925 + 1.18571i) q^{37} +(-11.6969 - 8.49826i) q^{39} +(1.17216 + 3.60755i) q^{41} +7.98463i q^{43} +(-11.5639 + 3.75733i) q^{47} +(11.8563 + 8.61411i) q^{49} +(-2.45844 + 7.56629i) q^{51} +(6.76068 + 9.30528i) q^{53} +(3.85596 + 5.30727i) q^{57} +(-2.19357 + 6.75112i) q^{59} +(1.08255 + 0.786521i) q^{61} +(12.1200 - 3.93801i) q^{63} +7.18872i q^{67} +(1.46428 + 4.50659i) q^{69} +(-5.45576 - 3.96384i) q^{71} +(-8.28996 - 2.69357i) q^{73} +(-14.4791 - 5.34450i) q^{77} +(4.43801 - 3.22441i) q^{79} +(-3.00244 + 9.24056i) q^{81} +(-4.82815 + 6.64538i) q^{83} -5.49406i q^{87} +11.4213 q^{89} +(8.67911 + 26.7116i) q^{91} +(-9.78968 + 13.4743i) q^{93} +(3.84880 + 5.29742i) q^{97} +(-7.55279 + 5.04470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} + 10 q^{11} + 14 q^{19} - 56 q^{21} + 2 q^{29} + 44 q^{31} - 54 q^{39} + 48 q^{41} + 54 q^{49} - 94 q^{51} + 18 q^{59} + 44 q^{61} - 22 q^{69} - 44 q^{71} + 50 q^{79} - 56 q^{81} - 16 q^{89} + 28 q^{91} - 120 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 10 * q^11 + 14 * q^19 - 56 * q^21 + 2 * q^29 + 44 * q^31 - 54 * q^39 + 48 * q^41 + 54 * q^49 - 94 * q^51 + 18 * q^59 + 44 * q^61 - 22 * q^69 - 44 * q^71 + 50 * q^79 - 56 * q^81 - 16 * q^89 + 28 * q^91 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	−2.27827	+	0.740256i	−1.31536	+	0.427387i	−0.880900	−	0.473303i	$-0.843062\pi$
$3$	−2.27827	+	0.740256i	−1.31536	+	0.427387i	−0.434462	+	0.900690i	$0.643062\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.42575	+	1.43801i	1.67278	+	0.543519i	0.983489	−	0.180968i	$-0.0579230\pi$
$7$	4.42575	+	1.43801i	1.67278	+	0.543519i	0.689289	+	0.724486i	$0.257923\pi$
$8$		0			0
$9$	2.21550	−	1.60965i	0.738500	−	0.536551i
$10$		0			0
$11$	−3.31404	−	0.130791i	−0.999222	−	0.0394351i
$11$	−3.31404	−	0.130791i	−0.999222	−	0.0394351i
$12$		0			0
$13$	3.54757	+	4.88281i	0.983918	+	1.35425i	0.934692	+	0.355459i	$0.115675\pi$
$13$	3.54757	+	4.88281i	0.983918	+	1.35425i	0.0492260	+	0.998788i	$0.484325\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.95207	−	2.68680i	0.473447	−	0.651644i	−0.503782	−	0.863831i	$-0.668059\pi$
$17$	1.95207	−	2.68680i	0.473447	−	0.651644i	0.977229	+	0.212187i	$0.0680586\pi$
$18$		0			0
$19$	−0.846245	−	2.60448i	−0.194142	−	0.597508i	−0.999986	−	0.00537912i	$-0.998288\pi$
$19$	−0.846245	−	2.60448i	−0.194142	−	0.597508i	0.805844	−	0.592129i	$-0.201712\pi$
$20$		0			0
$21$	−11.1476			−2.43260
$22$		0			0
$23$		−	1.97807i		−	0.412457i	−0.978504	−	0.206228i	$-0.933881\pi$
$23$		−	1.97807i		−	0.412457i	0.978504	−	0.206228i	$-0.0661189\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.368194	−	0.506776i	0.0708590	−	0.0975291i
$28$		0			0
$29$	−0.708723	+	2.18123i	−0.131607	+	0.405043i	−0.995047	−	0.0994078i	$-0.968305\pi$
$29$	−0.708723	+	2.18123i	−0.131607	+	0.405043i	0.863440	+	0.504451i	$0.168305\pi$
$30$		0			0
$31$	5.62481	−	4.08666i	1.01025	−	0.733986i	0.0459851	−	0.998942i	$-0.485357\pi$
$31$	5.62481	−	4.08666i	1.01025	−	0.733986i	0.964261	+	0.264956i	$0.0853573\pi$
$32$		0			0
$33$	7.64712	−	2.15526i	1.33119	−	0.375183i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.64925	+	1.18571i	0.599934	+	0.194930i	0.593211	−	0.805047i	$-0.297860\pi$
$37$	3.64925	+	1.18571i	0.599934	+	0.194930i	0.00672287	+	0.999977i	$0.497860\pi$
$38$		0			0
$39$	−11.6969	−	8.49826i	−1.87300	−	1.36081i
$40$		0			0
$41$	1.17216	+	3.60755i	0.183061	+	0.563404i	0.999910	−	0.0134483i	$-0.00428086\pi$
$41$	1.17216	+	3.60755i	0.183061	+	0.563404i	−0.816849	+	0.576852i	$0.804281\pi$
$42$		0			0
$43$			7.98463i			1.21764i	0.793307	+	0.608822i	$0.208358\pi$
$43$			7.98463i			1.21764i	−0.793307	+	0.608822i	$0.791642\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11.5639	+	3.75733i	−1.68676	+	0.548063i	−0.986204	−	0.165532i	$-0.947066\pi$
$47$	−11.5639	+	3.75733i	−1.68676	+	0.548063i	−0.700559	+	0.713595i	$0.747066\pi$
$48$		0			0
$49$	11.8563	+	8.61411i	1.69376	+	1.23059i
$50$		0			0
$51$	−2.45844	+	7.56629i	−0.344250	+	1.05949i
$52$		0			0
$53$	6.76068	+	9.30528i	0.928651	+	1.27818i	0.960383	+	0.278682i	$0.0898976\pi$
$53$	6.76068	+	9.30528i	0.928651	+	1.27818i	−0.0317323	+	0.999496i	$0.510102\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.85596	+	5.30727i	0.510734	+	0.702965i
$58$		0			0
$59$	−2.19357	+	6.75112i	−0.285579	+	0.878921i	0.700646	+	0.713509i	$0.252895\pi$
$59$	−2.19357	+	6.75112i	−0.285579	+	0.878921i	−0.986225	+	0.165412i	$0.947105\pi$
$60$		0			0
$61$	1.08255	+	0.786521i	0.138607	+	0.100704i	0.654928	−	0.755691i	$-0.272699\pi$
$61$	1.08255	+	0.786521i	0.138607	+	0.100704i	−0.516321	+	0.856395i	$0.672699\pi$
$62$		0			0
$63$	12.1200	−	3.93801i	1.52697	−	0.496143i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			7.18872i			0.878241i	0.898428	+	0.439121i	$0.144710\pi$
$67$			7.18872i			0.878241i	−0.898428	+	0.439121i	$0.855290\pi$
$68$		0			0
$69$	1.46428	+	4.50659i	0.176279	+	0.542530i
$70$		0			0
$71$	−5.45576	−	3.96384i	−0.647479	−	0.470421i	0.214932	−	0.976629i	$-0.431047\pi$
$71$	−5.45576	−	3.96384i	−0.647479	−	0.470421i	−0.862411	+	0.506208i	$0.831047\pi$
$72$		0			0
$73$	−8.28996	−	2.69357i	−0.970266	−	0.315259i	−0.219343	−	0.975648i	$-0.570391\pi$
$73$	−8.28996	−	2.69357i	−0.970266	−	0.315259i	−0.750924	+	0.660389i	$0.770391\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−14.4791	−	5.34450i	−1.65004	−	0.609062i
$78$		0			0
$79$	4.43801	−	3.22441i	0.499316	−	0.362774i	−0.309440	−	0.950919i	$-0.600142\pi$
$79$	4.43801	−	3.22441i	0.499316	−	0.362774i	0.808756	+	0.588145i	$0.200142\pi$
$80$		0			0
$81$	−3.00244	+	9.24056i	−0.333604	+	1.02673i
$82$		0			0
$83$	−4.82815	+	6.64538i	−0.529958	+	0.729425i	−0.987124	−	0.159956i	$-0.948865\pi$
$83$	−4.82815	+	6.64538i	−0.529958	+	0.729425i	0.457166	+	0.889382i	$0.348865\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	5.49406i		−	0.589025i
$88$		0			0
$89$	11.4213			1.21065			0.605327	−	0.795977i	$-0.293042\pi$
$89$	11.4213			1.21065			0.605327	+	0.795977i	$0.293042\pi$
$90$		0			0
$91$	8.67911	+	26.7116i	0.909818	+	2.80013i
$92$		0			0
$93$	−9.78968	+	13.4743i	−1.01514	+	1.39722i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.84880	+	5.29742i	0.390787	+	0.537872i	0.958402	−	0.285422i	$-0.0921338\pi$
$97$	3.84880	+	5.29742i	0.390787	+	0.537872i	−0.567615	+	0.823294i	$0.692134\pi$
$98$		0			0
$99$	−7.55279	+	5.04470i	−0.759084	+	0.507011i
$100$		0			0
$101$	0.220768	−	0.160397i	0.0219672	−	0.0159601i	−0.576747	−	0.816922i	$-0.695678\pi$
$101$	0.220768	−	0.160397i	0.0219672	−	0.0159601i	0.598715	+	0.800962i	$0.295678\pi$
$102$		0			0
$103$	7.79126	+	2.53153i	0.767695	+	0.249439i	0.666578	−	0.745435i	$-0.267758\pi$
$103$	7.79126	+	2.53153i	0.767695	+	0.249439i	0.101117	+	0.994875i	$0.467758\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.26530	−	2.03572i	0.605690	−	0.196801i	0.00991335	−	0.999951i	$-0.496844\pi$
$107$	6.26530	−	2.03572i	0.605690	−	0.196801i	0.595776	+	0.803150i	$0.296844\pi$
$108$		0			0
$109$	−3.06258			−0.293342			−0.146671	−	0.989185i	$-0.546856\pi$
$109$	−3.06258			−0.293342			−0.146671	+	0.989185i	$0.546856\pi$
$110$		0			0
$111$	−9.19173			−0.872441
$112$		0			0
$113$	5.50268	−	1.78793i	0.517649	−	0.168194i	−0.0385293	−	0.999257i	$-0.512267\pi$
$113$	5.50268	−	1.78793i	0.517649	−	0.168194i	0.556178	+	0.831063i	$0.312267\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	15.7193	+	5.10750i	1.45325	+	0.472188i
$118$		0			0
$119$	12.5030	−	9.08399i	1.14615	−	0.832728i
$120$		0			0
$121$	10.9658	+	0.866898i	0.996890	+	0.0788089i
$122$		0			0
$123$	−5.34101	−	7.35127i	−0.481583	−	0.662842i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.03062	+	1.41853i	−0.0914527	+	0.125874i	−0.852292	−	0.523067i	$-0.824788\pi$
$127$	−1.03062	+	1.41853i	−0.0914527	+	0.125874i	0.760839	+	0.648941i	$0.224788\pi$
$128$		0			0
$129$	−5.91067	−	18.1912i	−0.520405	−	1.60164i
$130$		0			0
$131$	−12.7047			−1.11002			−0.555008	−	0.831845i	$-0.687285\pi$
$131$	−12.7047			−1.11002			−0.555008	+	0.831845i	$0.687285\pi$
$132$		0			0
$133$		−	12.7437i		−	1.10502i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.02060	−	1.40473i	0.0871957	−	0.120015i	−0.763191	−	0.646173i	$-0.776368\pi$
$137$	1.02060	−	1.40473i	0.0871957	−	0.120015i	0.850386	+	0.526159i	$0.176368\pi$
$138$		0			0
$139$	−1.99933	+	6.15331i	−0.169581	+	0.521917i	−0.999345	−	0.0361981i	$-0.988475\pi$
$139$	−1.99933	+	6.15331i	−0.169581	+	0.521917i	0.829763	+	0.558115i	$0.188475\pi$
$140$		0			0
$141$	23.5643	−	17.1204i	1.98447	−	1.44180i
$142$		0			0
$143$	−11.1182	−	16.6458i	−0.929748	−	1.39199i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−33.3885	−	10.8486i	−2.75384	−	0.894777i
$148$		0			0
$149$	1.05849	+	0.769037i	0.0867148	+	0.0630020i	0.630298	−	0.776353i	$-0.282933\pi$
$149$	1.05849	+	0.769037i	0.0867148	+	0.0630020i	−0.543583	+	0.839355i	$0.682933\pi$
$150$		0			0
$151$	−6.19819	−	19.0761i	−0.504401	−	1.55239i	−0.801775	−	0.597626i	$-0.796111\pi$
$151$	−6.19819	−	19.0761i	−0.504401	−	1.55239i	0.297374	−	0.954761i	$-0.403889\pi$
$152$		0			0
$153$		−	9.09475i		−	0.735267i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	16.7970	−	5.45768i	1.34055	−	0.435570i	0.451045	−	0.892501i	$-0.351052\pi$
$157$	16.7970	−	5.45768i	1.34055	−	0.435570i	0.889502	+	0.456932i	$0.151052\pi$
$158$		0			0
$159$	−22.2910	−	16.1953i	−1.76779	−	1.28437i
$160$		0			0
$161$	2.84450	−	8.75446i	0.224178	−	0.689948i
$162$		0			0
$163$	−2.71807	−	3.74110i	−0.212895	−	0.293025i	0.689192	−	0.724579i	$-0.257966\pi$
$163$	−2.71807	−	3.74110i	−0.212895	−	0.293025i	−0.902087	+	0.431553i	$0.857966\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.1827	+	18.1445i	1.02011	+	1.40406i	0.912127	+	0.409909i	$0.134439\pi$
$167$	13.1827	+	18.1445i	1.02011	+	1.40406i	0.107984	+	0.994153i	$0.465561\pi$
$168$		0			0
$169$	−7.23935	+	22.2804i	−0.556873	+	1.71388i
$170$		0			0
$171$	−6.06716	−	4.40805i	−0.463967	−	0.337092i
$172$		0			0
$173$	6.76241	−	2.19724i	0.514136	−	0.167053i	−0.0404462	−	0.999182i	$-0.512878\pi$
$173$	6.76241	−	2.19724i	0.514136	−	0.167053i	0.554583	+	0.832129i	$0.312878\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	17.0047i		−	1.27815i
$178$		0			0
$179$	−1.54508	−	4.75528i	−0.115485	−	0.355427i	0.876563	−	0.481287i	$-0.159831\pi$
$179$	−1.54508	−	4.75528i	−0.115485	−	0.355427i	−0.992048	+	0.125861i	$0.959831\pi$
$180$		0			0
$181$	−13.7404	−	9.98299i	−1.02132	−	0.742030i	−0.0547639	−	0.998499i	$-0.517441\pi$
$181$	−13.7404	−	9.98299i	−1.02132	−	0.742030i	−0.966552	+	0.256470i	$0.917441\pi$
$182$		0			0
$183$	−3.04858	−	0.990544i	−0.225358	−	0.0732231i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.82066	+	8.64885i	−0.498776	+	0.632466i
$188$		0			0
$189$	2.35829	−	1.71340i	0.171540	−	0.124631i
$190$		0			0
$191$	1.41853	−	4.36578i	0.102641	−	0.315896i	−0.886529	−	0.462674i	$-0.846890\pi$
$191$	1.41853	−	4.36578i	0.102641	−	0.315896i	0.989170	+	0.146777i	$0.0468901\pi$
$192$		0			0
$193$	−5.14540	+	7.08203i	−0.370374	+	0.509776i	−0.953002	−	0.302963i	$-0.902024\pi$
$193$	−5.14540	+	7.08203i	−0.370374	+	0.509776i	0.582629	+	0.812739i	$0.302024\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	13.4511i		−	0.958352i	−0.877719	−	0.479176i	$-0.840936\pi$
$197$		−	13.4511i		−	0.958352i	0.877719	−	0.479176i	$-0.159064\pi$
$198$		0			0
$199$	−4.55665			−0.323012			−0.161506	−	0.986872i	$-0.551635\pi$
$199$	−4.55665			−0.323012			−0.161506	+	0.986872i	$0.551635\pi$
$200$		0			0
$201$	−5.32149	−	16.3779i	−0.375349	−	1.15521i
$202$		0			0
$203$	−6.27327	+	8.63441i	−0.440297	+	0.606017i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.18401	−	4.38242i	−0.221304	−	0.304599i
$208$		0			0
$209$	2.46385	+	8.74203i	0.170428	+	0.604699i
$210$		0			0
$211$	0.166677	−	0.121098i	0.0114745	−	0.00833675i	−0.582033	−	0.813165i	$-0.697743\pi$
$211$	0.166677	−	0.121098i	0.0114745	−	0.00833675i	0.593508	+	0.804828i	$0.297743\pi$
$212$		0			0
$213$	15.3640	+	4.99205i	1.05272	+	0.342050i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	30.7707	−	9.99801i	2.08885	−	0.678709i
$218$		0			0
$219$	20.8807			1.41099
$220$		0			0
$221$	20.0442			1.34832
$222$		0			0
$223$	−22.8069	+	7.41041i	−1.52726	+	0.496237i	−0.947828	−	0.318782i	$-0.896726\pi$
$223$	−22.8069	+	7.41041i	−1.52726	+	0.496237i	−0.579434	+	0.815019i	$0.696726\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−22.2655	−	7.23449i	−1.47781	−	0.480170i	−0.544353	−	0.838856i	$-0.683225\pi$
$227$	−22.2655	−	7.23449i	−1.47781	−	0.480170i	−0.933458	+	0.358686i	$0.883225\pi$
$228$		0			0
$229$	−16.1473	+	11.7317i	−1.06705	+	0.775254i	−0.975379	−	0.220535i	$-0.929220\pi$
$229$	−16.1473	+	11.7317i	−1.06705	+	0.775254i	−0.0916671	+	0.995790i	$0.529220\pi$
$230$		0			0
$231$	36.9436	+	1.45801i	2.43071	+	0.0959299i
$232$		0			0
$233$	0.768207	+	1.05735i	0.0503269	+	0.0692690i	0.833439	−	0.552612i	$-0.186369\pi$
$233$	0.768207	+	1.05735i	0.0503269	+	0.0692690i	−0.783112	+	0.621881i	$0.786369\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.72412	+	10.6313i	−0.501736	+	0.690580i
$238$		0			0
$239$	3.74662	+	11.5309i	0.242349	+	0.745872i	0.996061	+	0.0886682i	$0.0282611\pi$
$239$	3.74662	+	11.5309i	0.242349	+	0.745872i	−0.753713	+	0.657204i	$0.771739\pi$
$240$		0			0
$241$	−18.3095			−1.17942			−0.589709	−	0.807616i	$-0.700758\pi$
$241$	−18.3095			−1.17942			−0.589709	+	0.807616i	$0.700758\pi$
$242$		0			0
$243$		−	21.3959i		−	1.37255i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.71504	−	13.3716i	0.618153	−	0.850815i
$248$		0			0
$249$	6.08057	−	18.7141i	0.385340	−	1.18596i
$250$		0			0
$251$	21.6733	−	15.7466i	1.36801	−	0.993916i	0.370118	−	0.928985i	$-0.379317\pi$
$251$	21.6733	−	15.7466i	1.36801	−	0.993916i	0.997890	−	0.0649314i	$-0.0206829\pi$
$252$		0			0
$253$	−0.258715	+	6.55542i	−0.0162653	+	0.412136i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.84976	+	2.22562i	0.427277	+	0.138831i	0.514758	−	0.857336i	$-0.327882\pi$
$257$	6.84976	+	2.22562i	0.427277	+	0.138831i	−0.0874814	+	0.996166i	$0.527882\pi$
$258$		0			0
$259$	14.4456	+	10.4954i	0.897608	+	0.652150i
$260$		0			0
$261$	1.94084	+	5.97330i	0.120135	+	0.369738i
$262$		0			0
$263$			11.7870i			0.726816i	0.931630	+	0.363408i	$0.118387\pi$
$263$			11.7870i			0.726816i	−0.931630	+	0.363408i	$0.881613\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−26.0208	+	8.45467i	−1.59245	+	0.517418i
$268$		0			0
$269$	11.9730	+	8.69888i	0.730005	+	0.530380i	0.889565	−	0.456808i	$-0.151008\pi$
$269$	11.9730	+	8.69888i	0.730005	+	0.530380i	−0.159560	+	0.987188i	$0.551008\pi$
$270$		0			0
$271$	7.19508	−	22.1442i	0.437070	−	1.34516i	−0.453881	−	0.891063i	$-0.649961\pi$
$271$	7.19508	−	22.1442i	0.437070	−	1.34516i	0.890951	−	0.454100i	$-0.150039\pi$
$272$		0			0
$273$	−39.5468	−	54.4315i	−2.39348	−	3.29434i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.10304	−	12.5293i	−0.546949	−	0.752811i	0.442645	−	0.896697i	$-0.354040\pi$
$277$	−9.10304	−	12.5293i	−0.546949	−	0.752811i	−0.989594	+	0.143886i	$0.954040\pi$
$278$		0			0
$279$	5.88365	−	18.1080i	0.352245	−	1.08410i
$280$		0			0
$281$	12.1529	+	8.82959i	0.724980	+	0.526729i	0.887971	−	0.459898i	$-0.152114\pi$
$281$	12.1529	+	8.82959i	0.724980	+	0.526729i	−0.162991	+	0.986628i	$0.552114\pi$
$282$		0			0
$283$	13.7741	−	4.47548i	0.818787	−	0.266040i	0.130472	−	0.991452i	$-0.458351\pi$
$283$	13.7741	−	4.47548i	0.818787	−	0.266040i	0.688315	+	0.725412i	$0.258351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			17.6517i			1.04195i
$288$		0			0
$289$	1.84500	+	5.67833i	0.108530	+	0.334019i
$290$		0			0
$291$	−12.6901	−	9.21988i	−0.743905	−	0.540479i
$292$		0			0
$293$	−15.8601	−	5.15326i	−0.926557	−	0.301057i	−0.193403	−	0.981119i	$-0.561953\pi$
$293$	−15.8601	−	5.15326i	−0.926557	−	0.301057i	−0.733154	+	0.680063i	$0.761953\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.28649	+	1.63132i	−0.0746500	+	0.0946589i
$298$		0			0
$299$	9.65854	−	7.01734i	0.558568	−	0.405823i
$300$		0			0
$301$	−11.4820	+	35.3380i	−0.661813	+	2.03685i
$302$		0			0
$303$	−0.384234	+	0.528853i	−0.0220737	+	0.0303818i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	0.537575i		−	0.0306810i	−0.999882	−	0.0153405i	$-0.995117\pi$
$307$		−	0.537575i		−	0.0306810i	0.999882	−	0.0153405i	$-0.00488323\pi$
$308$		0			0
$309$	−19.6246			−1.11640
$310$		0			0
$311$	3.86105	+	11.8831i	0.218940	+	0.673828i	0.998850	+	0.0479370i	$0.0152647\pi$
$311$	3.86105	+	11.8831i	0.218940	+	0.673828i	−0.779910	+	0.625891i	$0.784735\pi$
$312$		0			0
$313$	11.0722	−	15.2396i	0.625837	−	0.861391i	−0.371925	−	0.928263i	$-0.621302\pi$
$313$	11.0722	−	15.2396i	0.625837	−	0.861391i	0.997762	+	0.0668722i	$0.0213020\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.15030	−	5.71239i	−0.233104	−	0.320840i	0.676401	−	0.736534i	$-0.263539\pi$
$317$	−4.15030	−	5.71239i	−0.233104	−	0.320840i	−0.909505	+	0.415694i	$0.863539\pi$
$318$		0			0
$319$	2.63403	−	7.13598i	0.147477	−	0.399538i
$320$		0			0
$321$	−12.7671	+	9.27586i	−0.712591	+	0.517728i
$322$		0			0
$323$	−8.64962	−	2.81043i	−0.481278	−	0.156377i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.97740	−	2.26710i	0.385851	−	0.125371i
$328$		0			0
$329$	−56.5819			−3.11946
$330$		0			0
$331$	7.83433			0.430614			0.215307	−	0.976546i	$-0.430925\pi$
$331$	7.83433			0.430614			0.215307	+	0.976546i	$0.430925\pi$
$332$		0			0
$333$	9.99351	−	3.24709i	0.547641	−	0.177939i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.95173	−	2.25876i	−0.378685	−	0.123042i	0.113489	−	0.993539i	$-0.463797\pi$
$337$	−6.95173	−	2.25876i	−0.378685	−	0.123042i	−0.492174	+	0.870497i	$0.663797\pi$
$338$		0			0
$339$	−11.2131	+	8.14678i	−0.609011	+	0.442472i
$340$		0			0
$341$	−19.1754	+	12.8077i	−1.03840	+	0.693576i
$342$		0			0
$343$	20.9390	+	28.8201i	1.13060	+	1.55614i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.3301	−	14.2181i	0.554548	−	0.763270i	−0.436072	−	0.899912i	$-0.643631\pi$
$347$	10.3301	−	14.2181i	0.554548	−	0.763270i	0.990621	+	0.136641i	$0.0436308\pi$
$348$		0			0
$349$	6.60659	+	20.3330i	0.353643	+	1.08840i	0.956792	+	0.290772i	$0.0939121\pi$
$349$	6.60659	+	20.3330i	0.353643	+	1.08840i	−0.603150	+	0.797628i	$0.706088\pi$
$350$		0			0
$351$	3.78068			0.201798
$352$		0			0
$353$			7.59779i			0.404389i	0.979345	+	0.202195i	$0.0648074\pi$
$353$			7.59779i			0.404389i	−0.979345	+	0.202195i	$0.935193\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−21.7609	+	29.9513i	−1.15171	+	1.58519i
$358$		0			0
$359$	10.7124	−	32.9695i	0.565380	−	1.74006i	−0.101438	−	0.994842i	$-0.532344\pi$
$359$	10.7124	−	32.9695i	0.565380	−	1.74006i	0.666818	−	0.745220i	$-0.267656\pi$
$360$		0			0
$361$	9.30416	−	6.75987i	0.489693	−	0.355783i
$362$		0			0
$363$	−25.6248	+	6.14246i	−1.34495	+	0.322395i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	14.2947	+	4.64462i	0.746176	+	0.242447i	0.657335	−	0.753599i	$-0.271684\pi$
$367$	14.2947	+	4.64462i	0.746176	+	0.242447i	0.0888408	+	0.996046i	$0.471684\pi$
$368$		0			0
$369$	8.40383	+	6.10574i	0.437486	+	0.317852i
$370$		0			0
$371$	16.5400	+	50.9049i	0.858713	+	2.64285i
$372$		0			0
$373$		−	13.5055i		−	0.699286i	−0.936883	−	0.349643i	$-0.886303\pi$
$373$		−	13.5055i		−	0.699286i	0.936883	−	0.349643i	$-0.113697\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−13.1647	+	4.27748i	−0.678019	+	0.220302i
$378$		0			0
$379$	−18.7641	−	13.6329i	−0.963846	−	0.700275i	−0.00980504	−	0.999952i	$-0.503121\pi$
$379$	−18.7641	−	13.6329i	−0.963846	−	0.700275i	−0.954041	+	0.299677i	$0.903121\pi$
$380$		0			0
$381$	1.29796	−	3.99471i	0.0664966	−	0.204655i
$382$		0			0
$383$	−20.6543	−	28.4282i	−1.05539	−	1.45261i	−0.884045	−	0.467402i	$-0.845190\pi$
$383$	−20.6543	−	28.4282i	−1.05539	−	1.45261i	−0.171341	−	0.985212i	$-0.554810\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.8525	+	17.6899i	0.653329	+	0.899230i
$388$		0			0
$389$	11.0505	−	34.0101i	0.560285	−	1.72438i	−0.121278	−	0.992619i	$-0.538699\pi$
$389$	11.0505	−	34.0101i	0.560285	−	1.72438i	0.681562	−	0.731760i	$-0.261301\pi$
$390$		0			0
$391$	−5.31467	−	3.86134i	−0.268775	−	0.195276i
$392$		0			0
$393$	28.9448	−	9.40473i	1.46007	−	0.474406i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			3.62347i			0.181857i	0.995857	+	0.0909284i	$0.0289834\pi$
$397$			3.62347i			0.181857i	−0.995857	+	0.0909284i	$0.971017\pi$
$398$		0			0
$399$	9.43359	+	29.0336i	0.472270	+	1.45350i
$400$		0			0
$401$	−0.851903	−	0.618944i	−0.0425420	−	0.0309086i	0.566311	−	0.824192i	$-0.308370\pi$
$401$	−0.851903	−	0.618944i	−0.0425420	−	0.0309086i	−0.608853	+	0.793283i	$0.708370\pi$
$402$		0			0
$403$	39.9088	+	12.9671i	1.98800	+	0.645940i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.9387	−	4.40680i	−0.591780	−	0.218437i
$408$		0			0
$409$	−9.29498	+	6.75320i	−0.459607	+	0.333924i	−0.793377	−	0.608730i	$-0.791679\pi$
$409$	−9.29498	+	6.75320i	−0.459607	+	0.333924i	0.333770	+	0.942655i	$0.391679\pi$
$410$		0			0
$411$	−1.28534	+	3.95587i	−0.0634012	+	0.195129i
$412$		0			0
$413$	−19.4164	+	26.7244i	−0.955419	+	1.31502i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	15.4989i		−	0.758987i
$418$		0			0
$419$	−9.12829			−0.445946			−0.222973	−	0.974825i	$-0.571576\pi$
$419$	−9.12829			−0.445946			−0.222973	+	0.974825i	$0.571576\pi$
$420$		0			0
$421$	−7.77517	−	23.9295i	−0.378939	−	1.16625i	−0.940783	−	0.339010i	$-0.889908\pi$
$421$	−7.77517	−	23.9295i	−0.378939	−	1.16625i	0.561844	−	0.827243i	$-0.310092\pi$
$422$		0			0
$423$	−19.5717	+	26.9382i	−0.951610	+	1.30978i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.66009	+	5.03768i	0.177124	+	0.243790i
$428$		0			0
$429$	37.6524	+	29.6935i	1.81787	+	1.43361i
$430$		0			0
$431$	12.7836	−	9.28785i	0.615766	−	0.447380i	−0.235674	−	0.971832i	$-0.575730\pi$
$431$	12.7836	−	9.28785i	0.615766	−	0.447380i	0.851440	+	0.524452i	$0.175730\pi$
$432$		0			0
$433$	−2.55526	−	0.830254i	−0.122798	−	0.0398994i	0.246973	−	0.969022i	$-0.420564\pi$
$433$	−2.55526	−	0.830254i	−0.122798	−	0.0398994i	−0.369771	+	0.929123i	$0.620564\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.15184	+	1.67393i	−0.246446	+	0.0800751i
$438$		0			0
$439$	18.0888			0.863333			0.431666	−	0.902033i	$-0.357926\pi$
$439$	18.0888			0.863333			0.431666	+	0.902033i	$0.357926\pi$
$440$		0			0
$441$	40.1334			1.91111
$442$		0			0
$443$	31.0956	−	10.1036i	1.47740	−	0.480035i	0.544063	−	0.839045i	$-0.316885\pi$
$443$	31.0956	−	10.1036i	1.47740	−	0.480035i	0.933334	+	0.359009i	$0.116885\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.98081	−	0.968524i	−0.140987	−	0.0458096i
$448$		0			0
$449$	7.33308	−	5.32780i	0.346070	−	0.251434i	−0.401149	−	0.916013i	$-0.631389\pi$
$449$	7.33308	−	5.32780i	0.346070	−	0.251434i	0.747218	+	0.664579i	$0.231389\pi$
$450$		0			0
$451$	−3.41276	−	12.1089i	−0.160701	−	0.570185i
$452$		0			0
$453$	28.2423	+	38.8722i	1.32694	+	1.82638i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.25773	+	12.7422i	−0.433058	+	0.596054i	−0.968652	−	0.248422i	$-0.920088\pi$
$457$	−9.25773	+	12.7422i	−0.433058	+	0.596054i	0.535593	+	0.844476i	$0.320088\pi$
$458$		0			0
$459$	−0.642862	−	1.97853i	−0.0300062	−	0.0923497i
$460$		0			0
$461$	−33.2263			−1.54750			−0.773751	−	0.633489i	$-0.781622\pi$
$461$	−33.2263			−1.54750			−0.773751	+	0.633489i	$0.781622\pi$
$462$		0			0
$463$			6.68368i			0.310617i	0.987866	+	0.155309i	$0.0496372\pi$
$463$			6.68368i			0.310617i	−0.987866	+	0.155309i	$0.950363\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.5401	+	17.2600i	−0.580286	+	0.798695i	−0.993727	−	0.111836i	$-0.964327\pi$
$467$	−12.5401	+	17.2600i	−0.580286	+	0.798695i	0.413440	+	0.910531i	$0.364327\pi$
$468$		0			0
$469$	−10.3375	+	31.8155i	−0.477341	+	1.46910i
$470$		0			0
$471$	−34.2281	+	24.8682i	−1.57715	+	1.14586i
$472$		0			0
$473$	1.04432	−	26.4614i	0.0480180	−	1.21670i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	29.9566	+	9.73348i	1.37162	+	0.445665i
$478$		0			0
$479$	31.7666	+	23.0798i	1.45145	+	1.05454i	0.985489	+	0.169739i	$0.0542924\pi$
$479$	31.7666	+	23.0798i	1.45145	+	1.05454i	0.465964	+	0.884804i	$0.345708\pi$
$480$		0			0
$481$	7.15636	+	22.0250i	0.326302	+	1.00425i
$482$		0			0
$483$			22.0507i			1.00334i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	12.1066	−	3.93368i	0.548603	−	0.178252i	−0.0215836	−	0.999767i	$-0.506871\pi$
$487$	12.1066	−	3.93368i	0.548603	−	0.178252i	0.570187	+	0.821515i	$0.306871\pi$
$488$		0			0
$489$	8.96186	+	6.51117i	0.405269	+	0.294446i
$490$		0			0
$491$	−1.67052	+	5.14133i	−0.0753895	+	0.232025i	−0.981649	−	0.190697i	$-0.938925\pi$
$491$	−1.67052	+	5.14133i	−0.0753895	+	0.232025i	0.906259	+	0.422722i	$0.138925\pi$
$492$		0			0
$493$	4.47703	+	6.16210i	0.201635	+	0.277527i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.4458	−	25.3884i	−0.827406	−	1.13883i
$498$		0			0
$499$	1.47238	−	4.53151i	0.0659126	−	0.202858i	−0.912676	−	0.408684i	$-0.865988\pi$
$499$	1.47238	−	4.53151i	0.0659126	−	0.202858i	0.978589	+	0.205826i	$0.0659879\pi$
$500$		0			0
$501$	−43.4654	−	31.5795i	−1.94189	−	1.41087i
$502$		0			0
$503$	−15.5978	+	5.06803i	−0.695471	+	0.225972i	−0.635356	−	0.772219i	$-0.719147\pi$
$503$	−15.5978	+	5.06803i	−0.695471	+	0.225972i	−0.0601146	+	0.998191i	$0.519147\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	56.1199i		−	2.49237i
$508$		0			0
$509$	−12.6919	−	39.0615i	−0.562557	−	1.73137i	−0.675101	−	0.737725i	$-0.735900\pi$
$509$	−12.6919	−	39.0615i	−0.562557	−	1.73137i	0.112544	−	0.993647i	$-0.464100\pi$
$510$		0			0
$511$	−32.8159	−	23.8422i	−1.45169	−	1.05472i
$512$		0			0
$513$	−1.63147	−	0.530096i	−0.0720311	−	0.0234043i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	38.8146	−	10.9395i	1.70706	−	0.481119i
$518$		0			0
$519$	−13.7801	+	10.0118i	−0.604879	+	0.439470i
$520$		0			0
$521$	12.1745	−	37.4694i	0.533376	−	1.64156i	−0.213756	−	0.976887i	$-0.568570\pi$
$521$	12.1745	−	37.4694i	0.533376	−	1.64156i	0.747132	−	0.664676i	$-0.231430\pi$
$522$		0			0
$523$	−9.83898	+	13.5422i	−0.430228	+	0.592159i	−0.968006	−	0.250928i	$-0.919264\pi$
$523$	−9.83898	+	13.5422i	−0.430228	+	0.592159i	0.537777	+	0.843087i	$0.319264\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	23.0902i		−	1.00582i
$528$		0			0
$529$	19.0872			0.829880
$530$		0			0
$531$	6.00711	+	18.4880i	0.260686	+	0.802310i
$532$		0			0
$533$	−13.4566	+	18.5214i	−0.582871	+	0.802253i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.04025	+	9.69007i	0.303809	+	0.418158i
$538$		0			0
$539$	−38.1657	−	30.0982i	−1.64391	−	1.29642i
$540$		0			0
$541$	7.27260	−	5.28386i	0.312674	−	0.227171i	−0.420369	−	0.907353i	$-0.638099\pi$
$541$	7.27260	−	5.28386i	0.312674	−	0.227171i	0.733043	+	0.680182i	$0.238099\pi$
$542$		0			0
$543$	38.6944	+	12.5726i	1.66053	+	0.539540i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	19.9346	−	6.47715i	0.852343	−	0.276943i	0.149916	−	0.988699i	$-0.452100\pi$
$547$	19.9346	−	6.47715i	0.852343	−	0.276943i	0.702427	+	0.711756i	$0.252100\pi$
$548$		0			0
$549$	3.66442			0.156394
$550$		0			0
$551$	6.28070			0.267567
$552$		0			0
$553$	24.2783	−	7.88850i	1.03242	−	0.335453i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.4878	+	4.70739i	0.613870	+	0.199458i	0.599417	−	0.800437i	$-0.295399\pi$
$557$	14.4878	+	4.70739i	0.613870	+	0.199458i	0.0144532	+	0.999896i	$0.495399\pi$
$558$		0			0
$559$	−38.9874	+	28.3260i	−1.64899	+	1.19806i
$560$		0			0
$561$	9.13697	−	24.7535i	0.385763	−	1.04509i
$562$		0			0
$563$	−8.94059	−	12.3057i	−0.376801	−	0.518622i	0.577932	−	0.816085i	$-0.303860\pi$
$563$	−8.94059	−	12.3057i	−0.376801	−	0.518622i	−0.954734	+	0.297462i	$0.903860\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−26.5761	+	36.5789i	−1.11609	+	1.53617i
$568$		0			0
$569$	−11.8935	−	36.6045i	−0.498602	−	1.53454i	−0.811267	−	0.584676i	$-0.801222\pi$
$569$	−11.8935	−	36.6045i	−0.498602	−	1.53454i	0.312665	−	0.949864i	$-0.398778\pi$
$570$		0			0
$571$	17.3549			0.726282			0.363141	−	0.931734i	$-0.381704\pi$
$571$	17.3549			0.726282			0.363141	+	0.931734i	$0.381704\pi$
$572$		0			0
$573$			10.9965i			0.459386i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−2.92728	+	4.02905i	−0.121864	+	0.167732i	−0.865590	−	0.500753i	$-0.833057\pi$
$577$	−2.92728	+	4.02905i	−0.121864	+	0.167732i	0.743726	+	0.668484i	$0.233057\pi$
$578$		0			0
$579$	6.48011	−	19.9437i	0.269304	−	0.828833i
$580$		0			0
$581$	−30.9244	+	22.4679i	−1.28296	+	0.932124i
$582$		0			0
$583$	−21.1882	−	31.7224i	−0.877524	−	1.31381i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.2356	+	12.0986i	1.53688	+	0.499362i	0.950513	−	0.310685i	$-0.100558\pi$
$587$	37.2356	+	12.0986i	1.53688	+	0.499362i	0.586365	+	0.810047i	$0.300558\pi$
$588$		0			0
$589$	−15.4036	−	11.1914i	−0.634694	−	0.461132i
$590$		0			0
$591$	9.95726	+	30.6453i	0.409587	+	1.26058i
$592$		0			0
$593$			36.2454i			1.48842i	0.667945	+	0.744211i	$0.267174\pi$
$593$			36.2454i			1.48842i	−0.667945	+	0.744211i	$0.732826\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	10.3813	−	3.37309i	0.424878	−	0.138051i
$598$		0			0
$599$	9.75622	+	7.08831i	0.398628	+	0.289620i	0.768982	−	0.639270i	$-0.220764\pi$
$599$	9.75622	+	7.08831i	0.398628	+	0.289620i	−0.370354	+	0.928891i	$0.620764\pi$
$600$		0			0
$601$	−8.60875	+	26.4950i	−0.351158	+	1.08075i	0.607045	+	0.794667i	$0.292355\pi$
$601$	−8.60875	+	26.4950i	−0.351158	+	1.08075i	−0.958204	+	0.286087i	$0.907645\pi$
$602$		0			0
$603$	11.5713	+	15.9266i	0.471222	+	0.648581i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	24.4037	+	33.5888i	0.990517	+	1.36333i	0.930967	+	0.365104i	$0.118966\pi$
$607$	24.4037	+	33.5888i	0.990517	+	1.36333i	0.0595497	+	0.998225i	$0.481034\pi$
$608$		0			0
$609$	7.90055	−	24.3154i	0.320146	−	0.985309i
$610$		0			0
$611$	−59.3699	−	43.1347i	−2.40185	−	1.74505i
$612$		0			0
$613$	41.3175	−	13.4249i	1.66880	−	0.542226i	0.686111	−	0.727497i	$-0.259316\pi$
$613$	41.3175	−	13.4249i	1.66880	−	0.542226i	0.982687	+	0.185271i	$0.0593163\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			18.9692i			0.763672i	0.924230	+	0.381836i	$0.124708\pi$
$617$			18.9692i			0.763672i	−0.924230	+	0.381836i	$0.875292\pi$
$618$		0			0
$619$	−0.867212	−	2.66900i	−0.0348562	−	0.107276i	0.932115	−	0.362163i	$-0.117962\pi$
$619$	−0.867212	−	2.66900i	−0.0348562	−	0.107276i	−0.966971	+	0.254887i	$0.917962\pi$
$620$		0			0
$621$	−1.00244	−	0.728315i	−0.0402265	−	0.0292263i
$622$		0			0
$623$	50.5478	+	16.4240i	2.02516	+	0.658013i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−12.0847	−	18.0929i	−0.482615	−	0.722559i
$628$		0			0
$629$	10.3094	−	7.49020i	0.411062	−	0.298654i
$630$		0			0
$631$	−7.30552	+	22.4841i	−0.290828	+	0.895077i	0.693763	+	0.720204i	$0.255952\pi$
$631$	−7.30552	+	22.4841i	−0.290828	+	0.895077i	−0.984591	+	0.174873i	$0.944048\pi$
$632$		0			0
$633$	−0.290093	+	0.399279i	−0.0115302	+	0.0158699i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			88.4511i			3.50456i
$638$		0			0
$639$	−18.4676			−0.730568
$640$		0			0
$641$	−1.67959	−	5.16925i	−0.0663399	−	0.204173i	0.912392	−	0.409318i	$-0.134233\pi$
$641$	−1.67959	−	5.16925i	−0.0663399	−	0.204173i	−0.978732	+	0.205145i	$0.934233\pi$
$642$		0			0
$643$	8.57909	−	11.8081i	0.338326	−	0.465666i	−0.605625	−	0.795750i	$-0.707077\pi$
$643$	8.57909	−	11.8081i	0.338326	−	0.465666i	0.943952	+	0.330084i	$0.107077\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.73473	−	9.26956i	−0.264770	−	0.364424i	0.655846	−	0.754895i	$-0.272312\pi$
$647$	−6.73473	−	9.26956i	−0.264770	−	0.364424i	−0.920615	+	0.390471i	$0.872312\pi$
$648$		0			0
$649$	8.15258	−	22.0866i	0.320017	−	0.866975i
$650$		0			0
$651$	−62.7030	+	45.5564i	−2.45752	+	1.78550i
$652$		0			0
$653$	−6.74163	−	2.19049i	−0.263820	−	0.0857204i	0.174120	−	0.984724i	$-0.444292\pi$
$653$	−6.74163	−	2.19049i	−0.263820	−	0.0857204i	−0.437940	+	0.899004i	$0.644292\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−22.7021	+	7.37637i	−0.885694	+	0.287779i
$658$		0			0
$659$	−10.2209			−0.398150			−0.199075	−	0.979984i	$-0.563794\pi$
$659$	−10.2209			−0.398150			−0.199075	+	0.979984i	$0.563794\pi$
$660$		0			0
$661$	−15.7641			−0.613151			−0.306575	−	0.951846i	$-0.599183\pi$
$661$	−15.7641			−0.613151			−0.306575	+	0.951846i	$0.599183\pi$
$662$		0			0
$663$	−45.6662	+	14.8378i	−1.77353	+	0.576254i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.31462	+	1.40191i	0.167063	+	0.0542820i
$668$		0			0
$669$	46.4747	−	33.7659i	1.79682	−	1.30546i
$670$		0			0
$671$	−3.48476	−	2.74816i	−0.134528	−	0.106091i
$672$		0			0
$673$	6.98959	+	9.62034i	0.269429	+	0.370837i	0.922197	−	0.386721i	$-0.126392\pi$
$673$	6.98959	+	9.62034i	0.269429	+	0.370837i	−0.652768	+	0.757558i	$0.726392\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.1462	−	16.7178i	0.466816	−	0.642518i	−0.509088	−	0.860714i	$-0.670017\pi$
$677$	12.1462	−	16.7178i	0.466816	−	0.642518i	0.975905	+	0.218197i	$0.0700174\pi$
$678$		0			0
$679$	9.41609	+	28.9797i	0.361356	+	1.11214i
$680$		0			0
$681$	56.0822			2.14908
$682$		0			0
$683$		−	22.8239i		−	0.873331i	−0.899624	−	0.436666i	$-0.856159\pi$
$683$		−	22.8239i		−	0.873331i	0.899624	−	0.436666i	$-0.143841\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	28.1036	−	38.6812i	1.07222	−	1.47578i
$688$		0			0
$689$	−21.4519	+	66.0222i	−0.817253	+	2.51525i
$690$		0			0
$691$	33.1464	−	24.0823i	1.26095	−	0.916132i	0.262144	−	0.965029i	$-0.415570\pi$
$691$	33.1464	−	24.0823i	1.26095	−	0.916132i	0.998804	+	0.0488962i	$0.0155704\pi$
$692$		0			0
$693$	−40.6812	+	11.4656i	−1.54535	+	0.435541i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	11.9809	+	3.89282i	0.453808	+	0.147451i
$698$		0			0
$699$	−2.53289	−	1.84025i	−0.0958028	−	0.0696048i
$700$		0			0
$701$	10.3083	+	31.7258i	0.389341	+	1.19827i	0.933282	+	0.359145i	$0.116932\pi$
$701$	10.3083	+	31.7258i	0.389341	+	1.19827i	−0.543941	+	0.839124i	$0.683068\pi$
$702$		0			0
$703$		−	10.5078i		−	0.396309i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.20772	−	0.392411i	0.0454208	−	0.0147581i
$708$		0			0
$709$	−12.9697	−	9.42305i	−0.487088	−	0.353890i	0.316975	−	0.948434i	$-0.397333\pi$
$709$	−12.9697	−	9.42305i	−0.487088	−	0.353890i	−0.804063	+	0.594544i	$0.797333\pi$
$710$		0			0
$711$	4.64224	−	14.2873i	0.174098	−	0.535817i
$712$		0			0
$713$	−8.08372	−	11.1263i	−0.302738	−	0.416682i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.0716	−	23.4971i	−0.637552	−	0.877515i
$718$		0			0
$719$	−4.08192	+	12.5628i	−0.152230	+	0.468515i	−0.997870	−	0.0652388i	$-0.979219\pi$
$719$	−4.08192	+	12.5628i	−0.152230	+	0.468515i	0.845640	+	0.533754i	$0.179219\pi$
$720$		0			0
$721$	30.8418	+	22.4079i	1.14861	+	0.834513i
$722$		0			0
$723$	41.7140	−	13.5537i	1.55136	−	0.504068i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	21.9855i		−	0.815395i	−0.913117	−	0.407698i	$-0.866332\pi$
$727$		−	21.9855i		−	0.815395i	0.913117	−	0.407698i	$-0.133668\pi$
$728$		0			0
$729$	6.83109	+	21.0239i	0.253003	+	0.778665i
$730$		0			0
$731$	21.4531	+	15.5866i	0.793470	+	0.576490i
$732$		0			0
$733$	−32.1447	−	10.4444i	−1.18729	−	0.385774i	−0.352221	−	0.935917i	$-0.614573\pi$
$733$	−32.1447	−	10.4444i	−1.18729	−	0.385774i	−0.835071	+	0.550143i	$0.814573\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.940223	−	23.8237i	0.0346335	−	0.877558i
$738$		0			0
$739$	11.9360	−	8.67203i	0.439074	−	0.319006i	−0.346193	−	0.938163i	$-0.612526\pi$
$739$	11.9360	−	8.67203i	0.439074	−	0.319006i	0.785267	+	0.619158i	$0.212526\pi$
$740$		0			0
$741$	−12.2351	+	37.6558i	−0.449468	+	1.38332i
$742$		0			0
$743$	14.3122	−	19.6991i	0.525064	−	0.722688i	−0.461304	−	0.887242i	$-0.652618\pi$
$743$	14.3122	−	19.6991i	0.525064	−	0.722688i	0.986368	+	0.164554i	$0.0526184\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			22.4945i			0.823030i
$748$		0			0
$749$	30.6561			1.12015
$750$		0			0
$751$	−11.6284	−	35.7884i	−0.424325	−	1.30594i	−0.903639	−	0.428295i	$-0.859114\pi$
$751$	−11.6284	−	35.7884i	−0.424325	−	1.30594i	0.479314	−	0.877644i	$-0.340886\pi$
$752$		0			0
$753$	−37.7212	+	51.9188i	−1.37464	+	1.89203i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−25.8273	−	35.5483i	−0.938710	−	1.29202i	−0.956363	−	0.292180i	$-0.905619\pi$
$757$	−25.8273	−	35.5483i	−0.938710	−	1.29202i	0.0176531	−	0.999844i	$-0.494381\pi$
$758$		0			0
$759$	−4.26326	−	15.1266i	−0.154747	−	0.549059i
$760$		0			0
$761$	−33.3417	+	24.2242i	−1.20864	+	0.878126i	−0.995106	−	0.0988110i	$-0.968496\pi$
$761$	−33.3417	+	24.2242i	−1.20864	+	0.878126i	−0.213530	+	0.976937i	$0.568496\pi$
$762$		0			0
$763$	−13.5542	−	4.40404i	−0.490697	−	0.159437i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−40.7462	+	13.2393i	−1.47126	+	0.478042i
$768$		0			0
$769$	21.4283			0.772724			0.386362	−	0.922347i	$-0.373732\pi$
$769$	21.4283			0.772724			0.386362	+	0.922347i	$0.373732\pi$
$770$		0			0
$771$	−17.2532			−0.621358
$772$		0			0
$773$	−5.51590	+	1.79222i	−0.198393	+	0.0644618i	−0.406528	−	0.913638i	$-0.633261\pi$
$773$	−5.51590	+	1.79222i	−0.198393	+	0.0644618i	0.208135	+	0.978100i	$0.433261\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−40.6804	−	13.2178i	−1.45940	−	0.474188i
$778$		0			0
$779$	8.40383	−	6.10574i	0.301098	−	0.218761i
$780$		0			0
$781$	17.5622	+	13.8499i	0.628424	+	0.495589i
$782$		0			0
$783$	0.844445	+	1.16228i	0.0301780	+	0.0415365i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−14.8192	+	20.3969i	−0.528248	+	0.727072i	−0.986862	−	0.161564i	$-0.948346\pi$
$787$	−14.8192	+	20.3969i	−0.528248	+	0.727072i	0.458614	+	0.888636i	$0.348346\pi$
$788$		0			0
$789$	−8.72538	−	26.8540i	−0.310632	−	0.956027i
$790$		0			0
$791$	26.9246			0.957328
$792$		0			0
$793$			8.07614i			0.286792i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.8429	+	14.9240i	−0.384075	+	0.528635i	−0.956658	−	0.291212i	$-0.905941\pi$
$797$	−10.8429	+	14.9240i	−0.384075	+	0.528635i	0.572583	+	0.819847i	$0.305941\pi$
$798$		0			0
$799$	−12.4783	+	38.4043i	−0.441451	+	1.35865i
$800$		0			0
$801$	25.3039	−	18.3843i	0.894068	−	0.649578i
$802$		0			0
$803$	27.1210	+	10.0109i	0.957079	+	0.353276i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−33.7171	−	10.9554i	−1.18690	−	0.385647i
$808$		0			0
$809$	4.21369	+	3.06142i	0.148145	+	0.107634i	0.659389	−	0.751802i	$-0.270815\pi$
$809$	4.21369	+	3.06142i	0.148145	+	0.107634i	−0.511244	+	0.859436i	$0.670815\pi$
$810$		0			0
$811$	−2.40728	−	7.40885i	−0.0845310	−	0.260160i	0.899853	−	0.436193i	$-0.143673\pi$
$811$	−2.40728	−	7.40885i	−0.0845310	−	0.260160i	−0.984384	+	0.176033i	$0.943673\pi$
$812$		0			0
$813$			55.7767i			1.95617i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	20.7958	−	6.75696i	0.727552	−	0.236396i
$818$		0			0
$819$	62.2249	+	45.2091i	2.17432	+	1.57973i
$820$		0			0
$821$	−2.95534	+	9.09561i	−0.103142	+	0.317439i	−0.989290	−	0.145964i	$-0.953372\pi$
$821$	−2.95534	+	9.09561i	−0.103142	+	0.317439i	0.886148	+	0.463403i	$0.153372\pi$
$822$		0			0
$823$	7.92788	+	10.9118i	0.276348	+	0.380361i	0.924520	−	0.381133i	$-0.124466\pi$
$823$	7.92788	+	10.9118i	0.276348	+	0.380361i	−0.648172	+	0.761494i	$0.724466\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.0689	+	15.2351i	0.384905	+	0.529776i	0.956876	−	0.290498i	$-0.0938209\pi$
$827$	11.0689	+	15.2351i	0.384905	+	0.529776i	−0.571971	+	0.820274i	$0.693821\pi$
$828$		0			0
$829$	−9.04366	+	27.8335i	−0.314099	+	0.966698i	0.662024	+	0.749482i	$0.269698\pi$
$829$	−9.04366	+	27.8335i	−0.314099	+	0.966698i	−0.976124	+	0.217216i	$0.930302\pi$
$830$		0			0
$831$	30.0141	+	21.8065i	1.04118	+	0.756459i
$832$		0			0
$833$	46.2887	−	15.0401i	1.60381	−	0.521109i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	4.35521i		−	0.150538i
$838$		0			0
$839$	−3.85178	−	11.8546i	−0.132978	−	0.409265i	0.862292	−	0.506412i	$-0.169028\pi$
$839$	−3.85178	−	11.8546i	−0.132978	−	0.409265i	−0.995270	+	0.0971469i	$0.969028\pi$
$840$		0			0
$841$	19.2060	+	13.9540i	0.662277	+	0.481173i
$842$		0			0
$843$	−34.2237	−	11.1200i	−1.17873	−	0.382992i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	47.2853	+	19.6056i	1.62474	+	0.673658i
$848$		0			0
$849$	−28.0682	+	20.3927i	−0.963299	+	0.699877i
$850$		0			0
$851$	2.34543	−	7.21849i	0.0804003	−	0.247447i
$852$		0			0
$853$	20.1968	−	27.7985i	0.691524	−	0.951802i	−0.308475	−	0.951232i	$-0.599819\pi$
$853$	20.1968	−	27.7985i	0.691524	−	0.951802i	1.00000		0.000569334i	$-0.000181225\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			14.9439i			0.510474i	0.966879	+	0.255237i	$0.0821535\pi$
$857$			14.9439i			0.510474i	−0.966879	+	0.255237i	$0.917847\pi$
$858$		0			0
$859$	−26.2500			−0.895640			−0.447820	−	0.894124i	$-0.647799\pi$
$859$	−26.2500			−0.895640			−0.447820	+	0.894124i	$0.647799\pi$
$860$		0			0
$861$	−13.0668	−	40.2154i	−0.445314	−	1.37054i
$862$		0			0
$863$	11.7954	−	16.2350i	0.401520	−	0.552645i	−0.559604	−	0.828760i	$-0.689047\pi$
$863$	11.7954	−	16.2350i	0.401520	−	0.552645i	0.961125	+	0.276115i	$0.0890469\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−8.40684	−	11.5710i	−0.285511	−	0.392972i
$868$		0			0
$869$	−15.1295	+	10.1054i	−0.513233	+	0.342801i
$870$		0			0
$871$	−35.1011	+	25.5024i	−1.18936	+	0.864117i
$872$		0			0
$873$	17.0540	+	5.54119i	0.577192	+	0.187541i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−34.5141	+	11.2143i	−1.16546	+	0.378680i	−0.826946	−	0.562281i	$-0.809924\pi$
$877$	−34.5141	+	11.2143i	−1.16546	+	0.378680i	−0.338513	+	0.940962i	$0.609924\pi$
$878$		0			0
$879$	39.9484			1.34743
$880$		0			0
$881$	26.3513			0.887796			0.443898	−	0.896077i	$-0.353595\pi$
$881$	26.3513			0.887796			0.443898	+	0.896077i	$0.353595\pi$
$882$		0			0
$883$	−51.3619	+	16.6885i	−1.72847	+	0.561612i	−0.993226	−	0.116196i	$-0.962930\pi$
$883$	−51.3619	+	16.6885i	−1.72847	+	0.561612i	−0.735239	+	0.677808i	$0.762930\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.1684	+	3.95375i	0.408575	+	0.132754i	0.506091	−	0.862480i	$-0.331090\pi$
$887$	12.1684	+	3.95375i	0.408575	+	0.132754i	−0.0975164	+	0.995234i	$0.531090\pi$
$888$		0			0
$889$	−6.60113	+	4.79600i	−0.221395	+	0.160853i
$890$		0			0
$891$	11.1588	−	30.2309i	0.373834	−	1.01277i
$892$		0			0
$893$	19.5717	+	26.9382i	0.654943	+	0.901452i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−16.8102	+	23.1372i	−0.561275	+	0.772529i
$898$		0			0
$899$	4.92750	+	15.1653i	0.164341	+	0.505791i
$900$		0			0
$901$	38.1987			1.27258
$902$		0			0
$903$		−	89.0093i		−	2.96204i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−29.9827	+	41.2677i	−0.995559	+	1.37027i	−0.0675488	+	0.997716i	$0.521518\pi$
$907$	−29.9827	+	41.2677i	−0.995559	+	1.37027i	−0.928011	+	0.372554i	$0.878482\pi$
$908$		0			0
$909$	0.230927	−	0.710719i	0.00765935	−	0.0235731i
$910$		0			0
$911$	1.25100	−	0.908907i	0.0414476	−	0.0301134i	−0.566869	−	0.823808i	$-0.691845\pi$
$911$	1.25100	−	0.908907i	0.0414476	−	0.0301134i	0.608316	+	0.793695i	$0.291845\pi$
$912$		0			0
$913$	16.8699	−	21.3916i	0.558311	−	0.707959i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−56.2279	−	18.2696i	−1.85681	−	0.603314i
$918$		0			0
$919$	−20.4935	−	14.8894i	−0.676018	−	0.491156i	0.196016	−	0.980601i	$-0.437200\pi$
$919$	−20.4935	−	14.8894i	−0.676018	−	0.491156i	−0.872034	+	0.489445i	$0.837200\pi$
$920$		0			0
$921$	0.397943	+	1.22474i	0.0131127	+	0.0403567i
$922$		0			0
$923$		−	40.7014i		−	1.33970i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	21.3364	−	6.93262i	0.700780	−	0.227697i
$928$		0			0
$929$	−44.3317	−	32.2089i	−1.45448	−	1.05674i	−0.984760	−	0.173921i	$-0.944356\pi$
$929$	−44.3317	−	32.2089i	−1.45448	−	1.05674i	−0.469716	−	0.882818i	$-0.655644\pi$
$930$		0			0
$931$	12.4019	−	38.1691i	0.406456	−	1.25094i
$932$		0			0
$933$	−17.5931	−	24.2148i	−0.575971	−	0.792756i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−18.9930	−	26.1416i	−0.620473	−	0.854008i	0.376914	−	0.926248i	$-0.376985\pi$
$937$	−18.9930	−	26.1416i	−0.620473	−	0.854008i	−0.997387	+	0.0722402i	$0.976985\pi$
$938$		0			0
$939$	−13.9443	+	42.9161i	−0.455055	+	1.40051i
$940$		0			0
$941$	−15.8392	−	11.5078i	−0.516342	−	0.375144i	0.298882	−	0.954290i	$-0.403386\pi$
$941$	−15.8392	−	11.5078i	−0.516342	−	0.375144i	−0.815224	+	0.579146i	$0.803386\pi$
$942$		0			0
$943$	7.13598	−	2.31862i	0.232380	−	0.0755047i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			22.1674i			0.720345i	0.932886	+	0.360172i	$0.117282\pi$
$947$			22.1674i			0.720345i	−0.932886	+	0.360172i	$0.882718\pi$
$948$		0			0
$949$	−16.2570	−	50.0339i	−0.527724	−	1.62417i
$950$		0			0
$951$	13.6841	+	9.94211i	0.443739	+	0.322395i
$952$		0			0
$953$	−49.8633	−	16.2016i	−1.61523	−	0.524820i	−0.644420	−	0.764672i	$-0.722901\pi$
$953$	−49.8633	−	16.2016i	−1.61523	−	0.524820i	−0.970810	+	0.239852i	$0.922901\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.718577	+	18.2076i	−0.0232283	+	0.588567i
$958$		0			0
$959$	6.53695	−	4.74937i	0.211089	−	0.153365i
$960$		0			0
$961$	5.35814	−	16.4907i	0.172843	−	0.531957i
$962$		0			0
$963$	10.6040	−	14.5951i	0.341708	−	0.470321i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	9.72125i		−	0.312614i	−0.987709	−	0.156307i	$-0.950041\pi$
$967$		−	9.72125i		−	0.312614i	0.987709	−	0.156307i	$-0.0499590\pi$
$968$		0			0
$969$	21.7866			0.699888
$970$		0			0
$971$	−14.6007	−	44.9362i	−0.468557	−	1.44207i	−0.854453	−	0.519529i	$-0.826108\pi$
$971$	−14.6007	−	44.9362i	−0.468557	−	1.44207i	0.385896	−	0.922542i	$-0.373892\pi$
$972$		0			0
$973$	−17.6971	+	24.3580i	−0.567343	+	0.780881i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−24.6021	−	33.8619i	−0.787092	−	1.08334i	−0.994464	−	0.105077i	$-0.966491\pi$
$977$	−24.6021	−	33.8619i	−0.787092	−	1.08334i	0.207372	−	0.978262i	$-0.433509\pi$
$978$		0			0
$979$	−37.8507	−	1.49381i	−1.20971	−	0.0477423i
$980$		0			0
$981$	−6.78515	+	4.92970i	−0.216633	+	0.157393i
$982$		0			0
$983$	−34.2287	−	11.1216i	−1.09173	−	0.354723i	−0.292813	−	0.956170i	$-0.594591\pi$
$983$	−34.2287	−	11.1216i	−1.09173	−	0.354723i	−0.798913	+	0.601447i	$0.794591\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	128.909	−	41.8851i	4.10322	−	1.33322i
$988$		0			0
$989$	15.7942			0.502226
$990$		0			0
$991$	0.548830			0.0174342			0.00871709	−	0.999962i	$-0.497225\pi$
$991$	0.548830			0.0174342			0.00871709	+	0.999962i	$0.497225\pi$
$992$		0			0
$993$	−17.8488	+	5.79941i	−0.566413	+	0.184039i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.79740	+	2.85845i	0.278616	+	0.0905279i	0.444992	−	0.895534i	$-0.353206\pi$
$997$	8.79740	+	2.85845i	0.278616	+	0.0905279i	−0.166376	+	0.986062i	$0.553206\pi$
$998$		0			0
$999$	1.94453	−	1.41278i	0.0615221	−	0.0446984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.cb.b.949.1		16
5.2	odd	4		220.2.m.b.201.2	yes	8
5.3	odd	4		1100.2.n.b.201.1		8
5.4	even	2	inner	1100.2.cb.b.949.4		16
11.4	even	5	inner	1100.2.cb.b.1049.4		16
15.2	even	4		1980.2.z.d.1081.1		8
20.7	even	4		880.2.bo.c.641.1		8
55.2	even	20		2420.2.a.l.1.4		4
55.4	even	10	inner	1100.2.cb.b.1049.1		16
55.37	odd	20		220.2.m.b.81.2	✓	8
55.42	odd	20		2420.2.a.k.1.4		4
55.48	odd	20		1100.2.n.b.301.1		8
165.92	even	20		1980.2.z.d.1621.1		8
220.147	even	20		880.2.bo.c.81.1		8
220.167	odd	20		9680.2.a.co.1.1		4
220.207	even	20		9680.2.a.cp.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.b.81.2	✓	8	55.37	odd	20
220.2.m.b.201.2	yes	8	5.2	odd	4
880.2.bo.c.81.1		8	220.147	even	20
880.2.bo.c.641.1		8	20.7	even	4
1100.2.n.b.201.1		8	5.3	odd	4
1100.2.n.b.301.1		8	55.48	odd	20
1100.2.cb.b.949.1		16	1.1	even	1	trivial
1100.2.cb.b.949.4		16	5.4	even	2	inner
1100.2.cb.b.1049.1		16	55.4	even	10	inner
1100.2.cb.b.1049.4		16	11.4	even	5	inner
1980.2.z.d.1081.1		8	15.2	even	4
1980.2.z.d.1621.1		8	165.92	even	20
2420.2.a.k.1.4		4	55.42	odd	20
2420.2.a.l.1.4		4	55.2	even	20
9680.2.a.co.1.1		4	220.167	odd	20
9680.2.a.cp.1.1		4	220.207	even	20

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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.27827 + 0.740256i) q^{3} +(4.42575 + 1.43801i) q^{7} +(2.21550 - 1.60965i) q^{9} +O(q^{10})\)	\(q+(-2.27827 + 0.740256i) q^{3} +(4.42575 + 1.43801i) q^{7} +(2.21550 - 1.60965i) q^{9} +(-3.31404 - 0.130791i) q^{11} +(3.54757 + 4.88281i) q^{13} +(1.95207 - 2.68680i) q^{17} +(-0.846245 - 2.60448i) q^{19} -11.1476 q^{21} -1.97807i q^{23} +(0.368194 - 0.506776i) q^{27} +(-0.708723 + 2.18123i) q^{29} +(5.62481 - 4.08666i) q^{31} +(7.64712 - 2.15526i) q^{33} +(3.64925 + 1.18571i) q^{37} +(-11.6969 - 8.49826i) q^{39} +(1.17216 + 3.60755i) q^{41} +7.98463i q^{43} +(-11.5639 + 3.75733i) q^{47} +(11.8563 + 8.61411i) q^{49} +(-2.45844 + 7.56629i) q^{51} +(6.76068 + 9.30528i) q^{53} +(3.85596 + 5.30727i) q^{57} +(-2.19357 + 6.75112i) q^{59} +(1.08255 + 0.786521i) q^{61} +(12.1200 - 3.93801i) q^{63} +7.18872i q^{67} +(1.46428 + 4.50659i) q^{69} +(-5.45576 - 3.96384i) q^{71} +(-8.28996 - 2.69357i) q^{73} +(-14.4791 - 5.34450i) q^{77} +(4.43801 - 3.22441i) q^{79} +(-3.00244 + 9.24056i) q^{81} +(-4.82815 + 6.64538i) q^{83} -5.49406i q^{87} +11.4213 q^{89} +(8.67911 + 26.7116i) q^{91} +(-9.78968 + 13.4743i) q^{93} +(3.84880 + 5.29742i) q^{97} +(-7.55279 + 5.04470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} + 10 q^{11} + 14 q^{19} - 56 q^{21} + 2 q^{29} + 44 q^{31} - 54 q^{39} + 48 q^{41} + 54 q^{49} - 94 q^{51} + 18 q^{59} + 44 q^{61} - 22 q^{69} - 44 q^{71} + 50 q^{79} - 56 q^{81} - 16 q^{89} + 28 q^{91} - 120 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 10 * q^11 + 14 * q^19 - 56 * q^21 + 2 * q^29 + 44 * q^31 - 54 * q^39 + 48 * q^41 + 54 * q^49 - 94 * q^51 + 18 * q^59 + 44 * q^61 - 22 * q^69 - 44 * q^71 + 50 * q^79 - 56 * q^81 - 16 * q^89 + 28 * q^91 - 120 * q^99

Introduction

L-functions

Modular forms

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Database

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