LMFDB - Embedded newform 176.4.m.d.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,4,Mod(49,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("176.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	176.m (of order $5$, 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:	$10.3843361610$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 70 x^{10} - 84 x^{9} + 2459 x^{8} - 8514 x^{7} + 54995 x^{6} - 432951 x^{5} + \cdots + 40896025 $ x^12 - x^11 + 70x^10 - 84x^9 + 2459x^8 - 8514x^7 + 54995x^6 - 432951x^5 + 3635141x^4 - 13377765x^3 + 34447885x^2 - 51287900x + 40896025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.2
Root			$1.50918 - 1.09648i$ of defining polynomial
Character	$\chi$	$=$	176.113
Dual form			176.4.m.d.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.576456 + 1.77415i) q^{3} +(14.9139 + 10.8356i) q^{5} +(-9.02047 + 27.7622i) q^{7} +(19.0282 - 13.8248i) q^{9} +(-5.54276 - 36.0594i) q^{11} +(-63.1228 + 45.8614i) q^{13} +(-10.6267 + 32.7057i) q^{15} +(-23.1093 - 16.7899i) q^{17} +(13.4717 + 41.4615i) q^{19} -54.4541 q^{21} +104.563 q^{23} +(66.3872 + 204.319i) q^{25} +(76.2440 + 55.3945i) q^{27} +(13.1435 - 40.4515i) q^{29} +(-51.0435 + 37.0853i) q^{31} +(60.7796 - 30.6203i) q^{33} +(-435.349 + 316.300i) q^{35} +(-98.0877 + 301.883i) q^{37} +(-117.752 - 85.5522i) q^{39} +(-21.1199 - 65.0003i) q^{41} +227.116 q^{43} +433.583 q^{45} +(3.32926 + 10.2464i) q^{47} +(-411.875 - 299.245i) q^{49} +(16.4663 - 50.6779i) q^{51} +(402.111 - 292.151i) q^{53} +(308.060 - 597.844i) q^{55} +(-65.7931 + 47.8015i) q^{57} +(130.834 - 402.665i) q^{59} +(154.010 + 111.895i) q^{61} +(212.162 + 652.968i) q^{63} -1438.34 q^{65} +386.223 q^{67} +(60.2760 + 185.511i) q^{69} +(-559.414 - 406.438i) q^{71} +(98.3036 - 302.547i) q^{73} +(-324.223 + 235.562i) q^{75} +(1051.08 + 171.393i) q^{77} +(130.828 - 95.0523i) q^{79} +(141.912 - 436.760i) q^{81} +(318.845 + 231.654i) q^{83} +(-162.721 - 500.804i) q^{85} +79.3436 q^{87} +108.129 q^{89} +(-703.814 - 2166.12i) q^{91} +(-95.2193 - 69.1808i) q^{93} +(-248.344 + 764.325i) q^{95} +(549.111 - 398.952i) q^{97} +(-603.981 - 609.516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 4 q^{5} - 6 q^{7} + 47 q^{9} - 39 q^{11} - 10 q^{13} - 74 q^{15} - 56 q^{17} + 141 q^{19} - 304 q^{21} + 388 q^{23} - 203 q^{25} + 331 q^{27} + 772 q^{29} - 882 q^{31} + 981 q^{33} - 412 q^{35}+ \cdots - 3563 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 4 * q^5 - 6 * q^7 + 47 * q^9 - 39 * q^11 - 10 * q^13 - 74 * q^15 - 56 * q^17 + 141 * q^19 - 304 * q^21 + 388 * q^23 - 203 * q^25 + 331 * q^27 + 772 * q^29 - 882 * q^31 + 981 * q^33 - 412 * q^35 - 192 * q^37 + 154 * q^39 - 180 * q^41 + 2330 * q^43 - 1340 * q^45 - 196 * q^47 - 973 * q^49 - 2969 * q^51 + 2246 * q^53 - 2672 * q^55 + 431 * q^57 + 1099 * q^59 - 470 * q^61 + 2008 * q^63 - 3892 * q^65 + 4394 * q^67 - 1394 * q^69 + 2084 * q^71 + 2824 * q^73 - 4623 * q^75 + 3654 * q^77 - 838 * q^79 + 1518 * q^81 - 789 * q^83 - 2632 * q^85 + 3036 * q^87 - 954 * q^89 - 2460 * q^91 - 808 * q^93 - 4362 * q^95 + 2651 * q^97 - 3563 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.576456	+	1.77415i	0.110939	+	0.341435i	0.991078	−	0.133280i	$-0.0425510\pi$
$3$	0.576456	+	1.77415i	0.110939	+	0.341435i	−0.880139	+	0.474715i	$0.842551\pi$
$4$		0			0
$5$	14.9139	+	10.8356i	1.33394	+	0.969163i	0.999644	+	0.0266942i	$0.00849804\pi$
$5$	14.9139	+	10.8356i	1.33394	+	0.969163i	0.334295	+	0.942469i	$0.391502\pi$
$6$		0			0
$7$	−9.02047	+	27.7622i	−0.487060	+	1.49902i	0.341916	+	0.939731i	$0.388924\pi$
$7$	−9.02047	+	27.7622i	−0.487060	+	1.49902i	−0.828976	+	0.559285i	$0.811076\pi$
$8$		0			0
$9$	19.0282	−	13.8248i	0.704746	−	0.512028i
$10$		0			0
$11$	−5.54276	−	36.0594i	−0.151928	−	0.988392i
$11$	−5.54276	−	36.0594i	−0.151928	−	0.988392i
$12$		0			0
$13$	−63.1228	+	45.8614i	−1.34670	+	0.978435i	−0.347532	+	0.937668i	$0.612980\pi$
$13$	−63.1228	+	45.8614i	−1.34670	+	0.978435i	−0.999169	+	0.0407672i	$0.987020\pi$
$14$		0			0
$15$	−10.6267	+	32.7057i	−0.182921	+	0.562972i
$16$		0			0
$17$	−23.1093	−	16.7899i	−0.329695	−	0.239538i	0.410606	−	0.911813i	$-0.365317\pi$
$17$	−23.1093	−	16.7899i	−0.329695	−	0.239538i	−0.740301	+	0.672275i	$0.765317\pi$
$18$		0			0
$19$	13.4717	+	41.4615i	0.162664	+	0.500628i	0.998857	−	0.0478081i	$-0.0152236\pi$
$19$	13.4717	+	41.4615i	0.162664	+	0.500628i	−0.836193	+	0.548436i	$0.815224\pi$
$20$		0			0
$21$	−54.4541			−0.565851
$22$		0			0
$23$	104.563			0.947952			0.473976	−	0.880538i	$-0.342818\pi$
$23$	104.563			0.947952			0.473976	+	0.880538i	$0.342818\pi$
$24$		0			0
$25$	66.3872	+	204.319i	0.531098	+	1.63455i
$26$		0			0
$27$	76.2440	+	55.3945i	0.543451	+	0.394840i
$28$		0			0
$29$	13.1435	−	40.4515i	0.0841615	−	0.259022i	−0.900116	−	0.435650i	$-0.856519\pi$
$29$	13.1435	−	40.4515i	0.0841615	−	0.259022i	0.984278	+	0.176627i	$0.0565187\pi$
$30$		0			0
$31$	−51.0435	+	37.0853i	−0.295732	+	0.214862i	−0.725750	−	0.687958i	$-0.758507\pi$
$31$	−51.0435	+	37.0853i	−0.295732	+	0.214862i	0.430018	+	0.902820i	$0.358507\pi$
$32$		0			0
$33$	60.7796	−	30.6203i	0.320617	−	0.161525i
$34$		0			0
$35$	−435.349	+	316.300i	−2.10250	+	1.52755i
$36$		0			0
$37$	−98.0877	+	301.883i	−0.435825	+	1.34133i	0.456414	+	0.889768i	$0.349134\pi$
$37$	−98.0877	+	301.883i	−0.435825	+	1.34133i	−0.892239	+	0.451564i	$0.850866\pi$
$38$		0			0
$39$	−117.752	−	85.5522i	−0.483474	−	0.351264i
$40$		0			0
$41$	−21.1199	−	65.0003i	−0.0804481	−	0.247594i	0.902741	−	0.430185i	$-0.141552\pi$
$41$	−21.1199	−	65.0003i	−0.0804481	−	0.247594i	−0.983189	+	0.182591i	$0.941552\pi$
$42$		0			0
$43$	227.116			0.805463			0.402731	−	0.915318i	$-0.368061\pi$
$43$	227.116			0.805463			0.402731	+	0.915318i	$0.368061\pi$
$44$		0			0
$45$	433.583			1.43633
$46$		0			0
$47$	3.32926	+	10.2464i	0.0103324	+	0.0317999i	0.956090	−	0.293074i	$-0.0946782\pi$
$47$	3.32926	+	10.2464i	0.0103324	+	0.0317999i	−0.945757	+	0.324874i	$0.894678\pi$
$48$		0			0
$49$	−411.875	−	299.245i	−1.20080	−	0.872434i
$50$		0			0
$51$	16.4663	−	50.6779i	0.0452105	−	0.139144i
$52$		0			0
$53$	402.111	−	292.151i	1.04215	−	0.757170i	0.0714497	−	0.997444i	$-0.477237\pi$
$53$	402.111	−	292.151i	1.04215	−	0.757170i	0.970705	+	0.240274i	$0.0772375\pi$
$54$		0			0
$55$	308.060	−	597.844i	0.755250	−	1.46570i
$56$		0			0
$57$	−65.7931	+	47.8015i	−0.152886	+	0.111078i
$58$		0			0
$59$	130.834	−	402.665i	0.288697	−	0.888517i	−0.696570	−	0.717489i	$-0.745291\pi$
$59$	130.834	−	402.665i	0.288697	−	0.888517i	0.985266	−	0.171028i	$-0.0547088\pi$
$60$		0			0
$61$	154.010	+	111.895i	0.323262	+	0.234864i	0.737566	−	0.675275i	$-0.235975\pi$
$61$	154.010	+	111.895i	0.323262	+	0.234864i	−0.414304	+	0.910139i	$0.635975\pi$
$62$		0			0
$63$	212.162	+	652.968i	0.424285	+	1.30581i
$64$		0			0
$65$	−1438.34			−2.74468
$66$		0			0
$67$	386.223			0.704248			0.352124	−	0.935953i	$-0.385459\pi$
$67$	386.223			0.704248			0.352124	+	0.935953i	$0.385459\pi$
$68$		0			0
$69$	60.2760	+	185.511i	0.105165	+	0.323664i
$70$		0			0
$71$	−559.414	−	406.438i	−0.935074	−	0.679371i	0.0121559	−	0.999926i	$-0.496131\pi$
$71$	−559.414	−	406.438i	−0.935074	−	0.679371i	−0.947230	+	0.320555i	$0.896131\pi$
$72$		0			0
$73$	98.3036	−	302.547i	0.157610	−	0.485075i	−0.840806	−	0.541337i	$-0.817918\pi$
$73$	98.3036	−	302.547i	0.157610	−	0.485075i	0.998416	+	0.0562620i	$0.0179182\pi$
$74$		0			0
$75$	−324.223	+	235.562i	−0.499174	+	0.362671i
$76$		0			0
$77$	1051.08	+	171.393i	1.55561	+	0.253664i
$78$		0			0
$79$	130.828	−	95.0523i	0.186321	−	0.135370i	−0.490715	−	0.871320i	$-0.663264\pi$
$79$	130.828	−	95.0523i	0.186321	−	0.135370i	0.677035	+	0.735950i	$0.263264\pi$
$80$		0			0
$81$	141.912	−	436.760i	0.194667	−	0.599123i
$82$		0			0
$83$	318.845	+	231.654i	0.421660	+	0.306354i	0.778305	−	0.627886i	$-0.216080\pi$
$83$	318.845	+	231.654i	0.421660	+	0.306354i	−0.356645	+	0.934240i	$0.616080\pi$
$84$		0			0
$85$	−162.721	−	500.804i	−0.207642	−	0.639057i
$86$		0			0
$87$	79.3436			0.0977762
$88$		0			0
$89$	108.129			0.128782			0.0643912	−	0.997925i	$-0.479489\pi$
$89$	108.129			0.128782			0.0643912	+	0.997925i	$0.479489\pi$
$90$		0			0
$91$	−703.814	−	2166.12i	−0.810766	−	2.49528i
$92$		0			0
$93$	−95.2193	−	69.1808i	−0.106170	−	0.0771368i
$94$		0			0
$95$	−248.344	+	764.325i	−0.268206	+	0.825454i
$96$		0			0
$97$	549.111	−	398.952i	0.574781	−	0.417603i	−0.262058	−	0.965052i	$-0.584401\pi$
$97$	549.111	−	398.952i	0.574781	−	0.417603i	0.836839	+	0.547449i	$0.184401\pi$
$98$		0			0
$99$	−603.981	−	609.516i	−0.613155	−	0.618774i
$100$		0			0
$101$	913.347	−	663.585i	0.899816	−	0.653755i	−0.0386027	−	0.999255i	$-0.512291\pi$
$101$	913.347	−	663.585i	0.899816	−	0.653755i	0.938419	+	0.345500i	$0.112291\pi$
$102$		0			0
$103$	30.3811	−	93.5035i	0.0290635	−	0.0894483i	−0.935473	−	0.353399i	$-0.885026\pi$
$103$	30.3811	−	93.5035i	0.0290635	−	0.0894483i	0.964536	+	0.263951i	$0.0850257\pi$
$104$		0			0
$105$	−812.122	−	590.041i	−0.754810	−	0.548401i
$106$		0			0
$107$	168.311	+	518.006i	0.152067	+	0.468015i	0.997852	−	0.0655096i	$-0.0208673\pi$
$107$	168.311	+	518.006i	0.152067	+	0.468015i	−0.845785	+	0.533524i	$0.820867\pi$
$108$		0			0
$109$	367.085			0.322572			0.161286	−	0.986908i	$-0.448436\pi$
$109$	367.085			0.322572			0.161286	+	0.986908i	$0.448436\pi$
$110$		0			0
$111$	−592.129			−0.506328
$112$		0			0
$113$	−172.032	−	529.461i	−0.143216	−	0.440774i	0.853561	−	0.520993i	$-0.174438\pi$
$113$	−172.032	−	529.461i	−0.143216	−	0.440774i	−0.996777	+	0.0802186i	$0.974438\pi$
$114$		0			0
$115$	1559.44	+	1133.00i	1.26451	+	0.918720i
$116$		0			0
$117$	−567.087	+	1745.31i	−0.448096	+	1.37910i
$118$		0			0
$119$	674.579	−	490.110i	0.519652	−	0.377549i
$120$		0			0
$121$	−1269.56	+	399.737i	−0.953836	+	0.300328i
$122$		0			0
$123$	103.146	−	74.9397i	0.0756124	−	0.0549356i
$124$		0			0
$125$	−511.745	+	1574.99i	−0.366175	+	1.12697i
$126$		0			0
$127$	−1050.67	−	763.356i	−0.734109	−	0.533362i	0.156751	−	0.987638i	$-0.449898\pi$
$127$	−1050.67	−	763.356i	−0.734109	−	0.533362i	−0.890861	+	0.454276i	$0.849898\pi$
$128$		0			0
$129$	130.923	+	402.938i	0.0893573	+	0.275013i
$130$		0			0
$131$	1110.64			0.740738			0.370369	−	0.928885i	$-0.379231\pi$
$131$	1110.64			0.740738			0.370369	+	0.928885i	$0.379231\pi$
$132$		0			0
$133$	−1272.58			−0.829675
$134$		0			0
$135$	536.863	+	1652.29i	0.342265	+	1.05338i
$136$		0			0
$137$	960.004	+	697.484i	0.598676	+	0.434964i	0.845409	−	0.534120i	$-0.179357\pi$
$137$	960.004	+	697.484i	0.598676	+	0.434964i	−0.246732	+	0.969084i	$0.579357\pi$
$138$		0			0
$139$	−895.798	+	2756.98i	−0.546623	+	1.68233i	0.170476	+	0.985362i	$0.445469\pi$
$139$	−895.798	+	2756.98i	−0.546623	+	1.68233i	−0.717099	+	0.696971i	$0.754531\pi$
$140$		0			0
$141$	−16.2595	+	11.8132i	−0.00971133	+	0.00705570i
$142$		0			0
$143$	2003.61	+	2021.97i	1.17168	+	1.18242i
$144$		0			0
$145$	634.335	−	460.871i	0.363301	−	0.263954i
$146$		0			0
$147$	293.477	−	903.230i	0.164664	−	0.506784i
$148$		0			0
$149$	2376.18	+	1726.40i	1.30647	+	0.949208i	0.999996	−	0.00267076i	$-0.000850130\pi$
$149$	2376.18	+	1726.40i	1.30647	+	0.949208i	0.306476	+	0.951878i	$0.400850\pi$
$150$		0			0
$151$	−944.489	−	2906.84i	−0.509016	−	1.56659i	−0.793913	−	0.608032i	$-0.791959\pi$
$151$	−944.489	−	2906.84i	−0.509016	−	1.56659i	0.284897	−	0.958558i	$-0.408041\pi$
$152$		0			0
$153$	−671.842			−0.355002
$154$		0			0
$155$	−1163.10			−0.602724
$156$		0			0
$157$	−487.141	−	1499.27i	−0.247631	−	0.762130i	−0.995193	−	0.0979375i	$-0.968775\pi$
$157$	−487.141	−	1499.27i	−0.247631	−	0.762130i	0.747561	−	0.664193i	$-0.231225\pi$
$158$		0			0
$159$	750.119	+	544.993i	0.374140	+	0.271829i
$160$		0			0
$161$	−943.208	+	2902.90i	−0.461709	+	1.42100i
$162$		0			0
$163$	−2290.77	+	1664.34i	−1.10078	+	0.799761i	−0.981187	−	0.193062i	$-0.938158\pi$
$163$	−2290.77	+	1664.34i	−1.10078	+	0.799761i	−0.119590	+	0.992823i	$0.538158\pi$
$164$		0			0
$165$	1238.25	+	201.913i	0.584227	+	0.0952662i
$166$		0			0
$167$	1008.58	−	732.774i	0.467341	−	0.339543i	−0.329063	−	0.944308i	$-0.606733\pi$
$167$	1008.58	−	732.774i	0.467341	−	0.339543i	0.796404	+	0.604765i	$0.206733\pi$
$168$		0			0
$169$	1202.31	−	3700.32i	0.547250	−	1.68426i
$170$		0			0
$171$	829.536	+	602.693i	0.370972	+	0.269527i
$172$		0			0
$173$	−605.621	−	1863.91i	−0.266153	−	0.819136i	−0.991425	−	0.130674i	$-0.958286\pi$
$173$	−605.621	−	1863.91i	−0.266153	−	0.819136i	0.725272	−	0.688462i	$-0.241714\pi$
$174$		0			0
$175$	−6271.17			−2.70889
$176$		0			0
$177$	789.808			0.335399
$178$		0			0
$179$	−197.434	−	607.639i	−0.0824408	−	0.253727i	0.901337	−	0.433119i	$-0.142587\pi$
$179$	−197.434	−	607.639i	−0.0824408	−	0.253727i	−0.983778	+	0.179392i	$0.942587\pi$
$180$		0			0
$181$	2545.77	+	1849.61i	1.04544	+	0.759559i	0.971341	−	0.237691i	$-0.0763907\pi$
$181$	2545.77	+	1849.61i	1.04544	+	0.759559i	0.0741029	+	0.997251i	$0.476391\pi$
$182$		0			0
$183$	−109.738	+	337.740i	−0.0443284	+	0.136429i
$184$		0			0
$185$	−4733.94	+	3439.41i	−1.88133	+	1.36687i
$186$		0			0
$187$	−477.343	+	926.367i	−0.186667	+	0.362260i
$188$		0			0
$189$	−2225.63	+	1617.01i	−0.856564	+	0.622330i
$190$		0			0
$191$	−544.897	+	1677.02i	−0.206426	+	0.635313i	0.793226	+	0.608927i	$0.208400\pi$
$191$	−544.897	+	1677.02i	−0.206426	+	0.635313i	−0.999652	+	0.0263861i	$0.991600\pi$
$192$		0			0
$193$	−3375.40	−	2452.37i	−1.25889	−	0.914639i	−0.260190	−	0.965558i	$-0.583785\pi$
$193$	−3375.40	−	2452.37i	−1.25889	−	0.914639i	−0.998703	+	0.0509185i	$0.983785\pi$
$194$		0			0
$195$	−829.140	−	2551.83i	−0.304492	−	0.937130i
$196$		0			0
$197$	2892.24			1.04601			0.523005	−	0.852330i	$-0.324811\pi$
$197$	2892.24			1.04601			0.523005	+	0.852330i	$0.324811\pi$
$198$		0			0
$199$	4281.26			1.52508			0.762539	−	0.646943i	$-0.223953\pi$
$199$	4281.26			1.52508			0.762539	+	0.646943i	$0.223953\pi$
$200$		0			0
$201$	222.641	+	685.217i	0.0781286	+	0.240455i
$202$		0			0
$203$	1004.46	+	729.783i	0.347287	+	0.252319i
$204$		0			0
$205$	389.336	−	1198.25i	0.132646	−	0.408242i
$206$		0			0
$207$	1989.64	−	1445.56i	0.668066	−	0.485378i
$208$		0			0
$209$	1420.41	−	715.591i	0.470103	−	0.236835i
$210$		0			0
$211$	2222.99	−	1615.09i	0.725293	−	0.526956i	−0.162778	−	0.986663i	$-0.552045\pi$
$211$	2222.99	−	1615.09i	0.725293	−	0.526956i	0.888071	+	0.459707i	$0.152045\pi$
$212$		0			0
$213$	398.604	−	1226.78i	0.128225	−	0.394636i
$214$		0			0
$215$	3387.18	+	2460.93i	1.07444	+	0.780624i
$216$		0			0
$217$	−569.131	−	1751.61i	−0.178042	−	0.547957i
$218$		0			0
$219$	593.432			0.183107
$220$		0			0
$221$	2228.73			0.678373
$222$		0			0
$223$	268.699	+	826.970i	0.0806880	+	0.248332i	0.983260	−	0.182206i	$-0.0583238\pi$
$223$	268.699	+	826.970i	0.0806880	+	0.248332i	−0.902572	+	0.430538i	$0.858324\pi$
$224$		0			0
$225$	4087.88	+	2970.02i	1.21122	+	0.880006i
$226$		0			0
$227$	882.731	−	2716.77i	0.258101	−	0.794353i	−0.735102	−	0.677957i	$-0.762866\pi$
$227$	882.731	−	2716.77i	0.258101	−	0.794353i	0.993203	−	0.116397i	$-0.0371344\pi$
$228$		0			0
$229$	−4269.92	+	3102.28i	−1.23216	+	0.895215i	−0.997050	−	0.0767540i	$-0.975544\pi$
$229$	−4269.92	+	3102.28i	−1.23216	+	0.895215i	−0.235108	+	0.971969i	$0.575544\pi$
$230$		0			0
$231$	301.826	+	1963.58i	0.0859684	+	0.559282i
$232$		0			0
$233$	−740.566	+	538.052i	−0.208223	+	0.151283i	−0.687010	−	0.726648i	$-0.741077\pi$
$233$	−740.566	+	538.052i	−0.208223	+	0.151283i	0.478786	+	0.877932i	$0.341077\pi$
$234$		0			0
$235$	−61.3736	+	188.888i	−0.0170365	+	0.0524329i
$236$		0			0
$237$	244.054	+	177.315i	0.0668903	+	0.0485986i
$238$		0			0
$239$	−1955.53	−	6018.51i	−0.529259	−	1.62889i	−0.755737	−	0.654876i	$-0.772721\pi$
$239$	−1955.53	−	6018.51i	−0.529259	−	1.62889i	0.226477	−	0.974016i	$-0.427279\pi$
$240$		0			0
$241$	−540.257			−0.144403			−0.0722013	−	0.997390i	$-0.523002\pi$
$241$	−540.257			−0.144403			−0.0722013	+	0.997390i	$0.523002\pi$
$242$		0			0
$243$	3401.24			0.897900
$244$		0			0
$245$	−2900.17	−	8925.81i	−0.756266	−	2.32755i
$246$		0			0
$247$	−2751.85	−	1999.34i	−0.708891	−	0.515039i
$248$		0			0
$249$	−227.190	+	699.218i	−0.0578215	+	0.177956i
$250$		0			0
$251$	−4314.83	+	3134.91i	−1.08506	+	0.788341i	−0.978558	−	0.205972i	$-0.933965\pi$
$251$	−4314.83	+	3134.91i	−1.08506	+	0.788341i	−0.106500	+	0.994313i	$0.533965\pi$
$252$		0			0
$253$	−579.568	−	3770.48i	−0.144020	−	0.936948i
$254$		0			0
$255$	794.700	−	577.383i	0.195161	−	0.141793i
$256$		0			0
$257$	425.852	−	1310.64i	0.103362	−	0.318114i	−0.885981	−	0.463722i	$-0.846514\pi$
$257$	425.852	−	1310.64i	0.103362	−	0.318114i	0.989342	+	0.145608i	$0.0465137\pi$
$258$		0			0
$259$	−7496.12	−	5446.25i	−1.79840	−	1.30662i
$260$		0			0
$261$	−309.136	−	951.422i	−0.0733143	−	0.225638i
$262$		0			0
$263$	−7490.14			−1.75613			−0.878064	−	0.478543i	$-0.841165\pi$
$263$	−7490.14			−1.75613			−0.878064	+	0.478543i	$0.841165\pi$
$264$		0			0
$265$	9162.66			2.12399
$266$		0			0
$267$	62.3316	+	191.837i	0.0142870	+	0.0439709i
$268$		0			0
$269$	−5898.73	−	4285.68i	−1.33700	−	0.971384i	−0.999549	−	0.0300390i	$-0.990437\pi$
$269$	−5898.73	−	4285.68i	−1.33700	−	0.971384i	−0.337446	−	0.941345i	$-0.609563\pi$
$270$		0			0
$271$	241.614	−	743.610i	0.0541586	−	0.166683i	−0.920319	−	0.391170i	$-0.872071\pi$
$271$	241.614	−	743.610i	0.0541586	−	0.166683i	0.974477	+	0.224487i	$0.0720705\pi$
$272$		0			0
$273$	3437.30	−	2497.34i	0.762031	−	0.553648i
$274$		0			0
$275$	6999.64	−	3526.37i	1.53489	−	0.773266i
$276$		0			0
$277$	465.219	−	338.001i	0.100911	−	0.0733160i	−0.536186	−	0.844100i	$-0.680135\pi$
$277$	465.219	−	338.001i	0.100911	−	0.0733160i	0.637096	+	0.770784i	$0.280135\pi$
$278$		0			0
$279$	−458.569	+	1411.33i	−0.0984007	+	0.302846i
$280$		0			0
$281$	4532.66	+	3293.17i	0.962262	+	0.699125i	0.953675	−	0.300839i	$-0.0972665\pi$
$281$	4532.66	+	3293.17i	0.962262	+	0.699125i	0.00858736	+	0.999963i	$0.497267\pi$
$282$		0			0
$283$	277.501	+	854.061i	0.0582888	+	0.179395i	0.975962	−	0.217942i	$-0.0699345\pi$
$283$	277.501	+	854.061i	0.0582888	+	0.179395i	−0.917673	+	0.397337i	$0.869934\pi$
$284$		0			0
$285$	−1499.19			−0.311594
$286$		0			0
$287$	1995.06			0.410330
$288$		0			0
$289$	−1266.06	−	3896.54i	−0.257696	−	0.793108i
$290$		0			0
$291$	1024.34	+	744.226i	0.206350	+	0.149922i
$292$		0			0
$293$	−2484.65	+	7646.98i	−0.495410	+	1.52471i	0.320907	+	0.947111i	$0.396012\pi$
$293$	−2484.65	+	7646.98i	−0.495410	+	1.52471i	−0.816317	+	0.577604i	$0.803988\pi$
$294$		0			0
$295$	6314.34	−	4587.64i	1.24622	−	0.905433i
$296$		0			0
$297$	1574.89	−	3056.35i	0.307691	−	0.597129i
$298$		0			0
$299$	−6600.31	+	4795.41i	−1.27661	+	0.927510i
$300$		0			0
$301$	−2048.69	+	6305.23i	−0.392308	+	1.20740i
$302$		0			0
$303$	1703.80	+	1237.89i	0.323040	+	0.234702i
$304$		0			0
$305$	1084.44	+	3337.58i	0.203591	+	0.626587i
$306$		0			0
$307$	5491.51			1.02090			0.510451	−	0.859907i	$-0.329478\pi$
$307$	5491.51			1.02090			0.510451	+	0.859907i	$0.329478\pi$
$308$		0			0
$309$	183.403			0.0337651
$310$		0			0
$311$	−987.327	−	3038.68i	−0.180020	−	0.554044i	0.819807	−	0.572640i	$-0.194081\pi$
$311$	−987.327	−	3038.68i	−0.180020	−	0.554044i	−0.999827	+	0.0185954i	$0.994081\pi$
$312$		0			0
$313$	2522.04	+	1832.37i	0.455445	+	0.330900i	0.791742	−	0.610856i	$-0.209175\pi$
$313$	2522.04	+	1832.37i	0.455445	+	0.330900i	−0.336297	+	0.941756i	$0.609175\pi$
$314$		0			0
$315$	−3911.12	+	12037.2i	−0.699577	+	2.15308i
$316$		0			0
$317$	−194.378	+	141.224i	−0.0344396	+	0.0250219i	−0.604872	−	0.796323i	$-0.706776\pi$
$317$	−194.378	+	141.224i	−0.0344396	+	0.0250219i	0.570432	+	0.821345i	$0.306776\pi$
$318$		0			0
$319$	−1531.51	−	249.733i	−0.268802	−	0.0438318i
$320$		0			0
$321$	−821.997	+	597.216i	−0.142927	+	0.103842i
$322$		0			0
$323$	384.813	−	1184.33i	0.0662897	−	0.204019i
$324$		0			0
$325$	−13560.9	−	9852.56i	−2.31453	−	1.68161i
$326$		0			0
$327$	211.608	+	651.264i	0.0357858	+	0.110138i
$328$		0			0
$329$	−314.494			−0.0527010
$330$		0			0
$331$	9405.79			1.56190			0.780950	−	0.624594i	$-0.214735\pi$
$331$	9405.79			1.56190			0.780950	+	0.624594i	$0.214735\pi$
$332$		0			0
$333$	2307.03	+	7100.31i	0.379653	+	1.16845i
$334$		0			0
$335$	5760.08	+	4184.95i	0.939424	+	0.682531i
$336$		0			0
$337$	−1449.42	+	4460.85i	−0.234288	+	0.721063i	0.762928	+	0.646484i	$0.223761\pi$
$337$	−1449.42	+	4460.85i	−0.234288	+	0.721063i	−0.997215	+	0.0745790i	$0.976239\pi$
$338$		0			0
$339$	840.174	−	610.422i	0.134608	−	0.0977981i
$340$		0			0
$341$	1620.19	+	1635.04i	0.257298	+	0.259656i
$342$		0			0
$343$	3922.74	−	2850.04i	0.617516	−	0.448652i
$344$		0			0
$345$	−1111.16	+	3419.81i	−0.173400	+	0.533670i
$346$		0			0
$347$	−4334.77	−	3149.39i	−0.670612	−	0.487228i	0.199618	−	0.979874i	$-0.436030\pi$
$347$	−4334.77	−	3149.39i	−0.670612	−	0.487228i	−0.870230	+	0.492645i	$0.836030\pi$
$348$		0			0
$349$	−305.037	−	938.808i	−0.0467859	−	0.143992i	0.924935	−	0.380126i	$-0.124120\pi$
$349$	−305.037	−	938.808i	−0.0467859	−	0.143992i	−0.971720	+	0.236134i	$0.924120\pi$
$350$		0			0
$351$	−7353.20			−1.11819
$352$		0			0
$353$	−130.359			−0.0196552			−0.00982762	−	0.999952i	$-0.503128\pi$
$353$	−130.359			−0.0196552			−0.00982762	+	0.999952i	$0.503128\pi$
$354$		0			0
$355$	−3939.05	−	12123.1i	−0.588910	−	1.81248i
$356$		0			0
$357$	1258.39	+	914.277i	0.186558	+	0.135543i
$358$		0			0
$359$	−2852.55	+	8779.23i	−0.419364	+	1.29067i	0.488925	+	0.872326i	$0.337389\pi$
$359$	−2852.55	+	8779.23i	−0.419364	+	1.29067i	−0.908289	+	0.418343i	$0.862611\pi$
$360$		0			0
$361$	4011.48	−	2914.51i	0.584849	−	0.424917i
$362$		0			0
$363$	−1441.04	−	2021.95i	−0.208360	−	0.292355i
$364$		0			0
$365$	4744.36	−	3446.98i	0.680360	−	0.494310i
$366$		0			0
$367$	−2625.81	+	8081.41i	−0.373477	+	1.14944i	0.571023	+	0.820934i	$0.306547\pi$
$367$	−2625.81	+	8081.41i	−0.373477	+	1.14944i	−0.944500	+	0.328510i	$0.893453\pi$
$368$		0			0
$369$	−1300.49	−	944.859i	−0.183471	−	0.133299i
$370$		0			0
$371$	4483.50	+	13798.8i	0.627418	+	1.93099i
$372$		0			0
$373$	−12810.7			−1.77832			−0.889160	−	0.457597i	$-0.848710\pi$
$373$	−12810.7			−1.77832			−0.889160	+	0.457597i	$0.848710\pi$
$374$		0			0
$375$	−3089.27			−0.425411
$376$		0			0
$377$	1025.51	+	3156.19i	0.140096	+	0.431172i
$378$		0			0
$379$	−5475.79	−	3978.39i	−0.742143	−	0.539199i	0.151238	−	0.988497i	$-0.451674\pi$
$379$	−5475.79	−	3978.39i	−0.742143	−	0.539199i	−0.893382	+	0.449299i	$0.851674\pi$
$380$		0			0
$381$	748.643	−	2304.09i	0.100667	−	0.309821i
$382$		0			0
$383$	−9385.29	+	6818.81i	−1.25213	+	0.909726i	−0.998344	−	0.0575338i	$-0.981676\pi$
$383$	−9385.29	+	6818.81i	−1.25213	+	0.909726i	−0.253787	+	0.967260i	$0.581676\pi$
$384$		0			0
$385$	13818.6	+	13945.2i	1.82925	+	1.84601i
$386$		0			0
$387$	4321.60	−	3139.83i	0.567647	−	0.412420i
$388$		0			0
$389$	983.756	−	3027.69i	0.128222	−	0.394627i	−0.866252	−	0.499607i	$-0.833478\pi$
$389$	983.756	−	3027.69i	0.128222	−	0.394627i	0.994474	+	0.104980i	$0.0334778\pi$
$390$		0			0
$391$	−2416.37	−	1755.60i	−0.312535	−	0.227070i
$392$		0			0
$393$	640.233	+	1970.43i	0.0821768	+	0.252914i
$394$		0			0
$395$	2981.10			0.379736
$396$		0			0
$397$	4412.72			0.557854			0.278927	−	0.960312i	$-0.410021\pi$
$397$	4412.72			0.557854			0.278927	+	0.960312i	$0.410021\pi$
$398$		0			0
$399$	−733.588	−	2257.75i	−0.0920434	−	0.283280i
$400$		0			0
$401$	−3050.01	−	2215.96i	−0.379826	−	0.275959i	0.381448	−	0.924390i	$-0.375426\pi$
$401$	−3050.01	−	2215.96i	−0.379826	−	0.275959i	−0.761274	+	0.648431i	$0.775426\pi$
$402$		0			0
$403$	1521.23	−	4681.85i	0.188034	−	0.578709i
$404$		0			0
$405$	6849.01	−	4976.10i	0.840321	−	0.610529i
$406$		0			0
$407$	11429.4	+	1863.72i	1.39197	+	0.226980i
$408$		0			0
$409$	−5154.89	+	3745.25i	−0.623210	+	0.452789i	−0.854041	−	0.520205i	$-0.825856\pi$
$409$	−5154.89	+	3745.25i	−0.623210	+	0.452789i	0.230831	+	0.972994i	$0.425856\pi$
$410$		0			0
$411$	−684.040	+	2105.26i	−0.0820954	+	0.252664i
$412$		0			0
$413$	9998.66	+	7264.45i	1.19129	+	0.865522i
$414$		0			0
$415$	2245.11	+	6909.74i	0.265562	+	0.817315i
$416$		0			0
$417$	−5407.69			−0.635050
$418$		0			0
$419$	−2107.98			−0.245779			−0.122890	−	0.992420i	$-0.539216\pi$
$419$	−2107.98			−0.245779			−0.122890	+	0.992420i	$0.539216\pi$
$420$		0			0
$421$	−2548.58	−	7843.73i	−0.295036	−	0.908029i	−0.983209	−	0.182482i	$-0.941587\pi$
$421$	−2548.58	−	7843.73i	−0.295036	−	0.908029i	0.688173	−	0.725547i	$-0.258413\pi$
$422$		0			0
$423$	205.004	+	148.944i	0.0235642	+	0.0171204i
$424$		0			0
$425$	1896.32	−	5836.29i	0.216436	−	0.666121i
$426$		0			0
$427$	−4495.69	+	3266.31i	−0.509512	+	0.370182i
$428$		0			0
$429$	−2432.28	+	4720.28i	−0.273734	+	0.531229i
$430$		0			0
$431$	−10459.3	+	7599.12i	−1.16892	+	0.849273i	−0.990880	−	0.134749i	$-0.956977\pi$
$431$	−10459.3	+	7599.12i	−1.16892	+	0.849273i	−0.178045	+	0.984022i	$0.556977\pi$
$432$		0			0
$433$	−2413.49	+	7427.96i	−0.267864	+	0.824400i	0.723156	+	0.690685i	$0.242691\pi$
$433$	−2413.49	+	7427.96i	−0.267864	+	0.824400i	−0.991020	+	0.133715i	$0.957309\pi$
$434$		0			0
$435$	1183.32	+	859.733i	0.130427	+	0.0947610i
$436$		0			0
$437$	1408.64	+	4335.34i	0.154197	+	0.474571i
$438$		0			0
$439$	17491.4			1.90163			0.950817	−	0.309752i	$-0.100246\pi$
$439$	17491.4			1.90163			0.950817	+	0.309752i	$0.100246\pi$
$440$		0			0
$441$	−11974.2			−1.29297
$442$		0			0
$443$	−794.117	−	2444.04i	−0.0851685	−	0.262122i	0.899399	−	0.437130i	$-0.144005\pi$
$443$	−794.117	−	2444.04i	−0.0851685	−	0.262122i	−0.984567	+	0.175008i	$0.944005\pi$
$444$		0			0
$445$	1612.62	+	1171.64i	0.171788	+	0.124811i
$446$		0			0
$447$	−1693.12	+	5210.89i	−0.179154	+	0.551380i
$448$		0			0
$449$	−4334.56	+	3149.24i	−0.455591	+	0.331007i	−0.791799	−	0.610781i	$-0.790855\pi$
$449$	−4334.56	+	3149.24i	−0.455591	+	0.331007i	0.336208	+	0.941788i	$0.390855\pi$
$450$		0			0
$451$	−2226.81	+	1121.85i	−0.232497	+	0.117131i
$452$		0			0
$453$	4612.71	−	3351.33i	0.478419	−	0.347592i
$454$		0			0
$455$	12974.5	−	39931.4i	1.33682	−	4.11432i
$456$		0			0
$457$	−3912.81	−	2842.82i	−0.400511	−	0.290988i	0.369238	−	0.929335i	$-0.379619\pi$
$457$	−3912.81	−	2842.82i	−0.400511	−	0.290988i	−0.769749	+	0.638347i	$0.779619\pi$
$458$		0			0
$459$	−831.877	−	2560.25i	−0.0845941	−	0.260354i
$460$		0			0
$461$	−18173.0			−1.83601			−0.918007	−	0.396564i	$-0.870203\pi$
$461$	−18173.0			−1.83601			−0.918007	+	0.396564i	$0.870203\pi$
$462$		0			0
$463$	−13451.4			−1.35019			−0.675095	−	0.737731i	$-0.735897\pi$
$463$	−13451.4			−1.35019			−0.675095	+	0.737731i	$0.735897\pi$
$464$		0			0
$465$	−670.475	−	2063.51i	−0.0668657	−	0.205791i
$466$		0			0
$467$	13010.5	+	9452.69i	1.28920	+	0.936656i	0.999789	−	0.0205495i	$-0.00654158\pi$
$467$	13010.5	+	9452.69i	1.28920	+	0.936656i	0.289408	+	0.957206i	$0.406542\pi$
$468$		0			0
$469$	−3483.91	+	10722.4i	−0.343011	+	1.05568i
$470$		0			0
$471$	2379.11	−	1728.52i	0.232746	−	0.169100i
$472$		0			0
$473$	−1258.85	−	8189.66i	−0.122372	−	0.796112i
$474$		0			0
$475$	−7577.02	+	5505.03i	−0.731911	+	0.531764i
$476$		0			0
$477$	3612.52	−	11118.2i	0.346763	−	1.06723i
$478$		0			0
$479$	2651.17	+	1926.19i	0.252892	+	0.183737i	0.707008	−	0.707206i	$-0.250045\pi$
$479$	2651.17	+	1926.19i	0.252892	+	0.183737i	−0.454116	+	0.890943i	$0.650045\pi$
$480$		0			0
$481$	−7653.20	−	23554.1i	−0.725480	−	2.23280i
$482$		0			0
$483$	−5693.89			−0.536399
$484$		0			0
$485$	12512.3			1.17145
$486$		0			0
$487$	−498.075	−	1532.92i	−0.0463448	−	0.142635i	0.925206	−	0.379464i	$-0.123892\pi$
$487$	−498.075	−	1532.92i	−0.0463448	−	0.142635i	−0.971551	+	0.236830i	$0.923892\pi$
$488$		0			0
$489$	−4273.31	−	3104.74i	−0.395186	−	0.287119i
$490$		0			0
$491$	3326.22	−	10237.0i	0.305723	−	0.940919i	−0.673683	−	0.739020i	$-0.735289\pi$
$491$	3326.22	−	10237.0i	0.305723	−	0.940919i	0.979406	−	0.201899i	$-0.0647112\pi$
$492$		0			0
$493$	−982.911	+	714.126i	−0.0897932	+	0.0652386i
$494$		0			0
$495$	−2403.25	−	15634.7i	−0.218218	−	1.41965i
$496$		0			0
$497$	16329.8	−	11864.3i	1.47382	−	1.07080i
$498$		0			0
$499$	−4149.15	+	12769.8i	−0.372228	+	1.14560i	0.573103	+	0.819484i	$0.305740\pi$
$499$	−4149.15	+	12769.8i	−0.372228	+	1.14560i	−0.945330	+	0.326115i	$0.894260\pi$
$500$		0			0
$501$	1881.45	+	1366.95i	0.167779	+	0.121898i
$502$		0			0
$503$	−5840.89	−	17976.4i	−0.517758	−	1.59350i	−0.778207	−	0.628008i	$-0.783870\pi$
$503$	−5840.89	−	17976.4i	−0.517758	−	1.59350i	0.260448	−	0.965488i	$-0.416130\pi$
$504$		0			0
$505$	20811.9			1.83389
$506$		0			0
$507$	7258.01			0.635778
$508$		0			0
$509$	3253.27	+	10012.5i	0.283298	+	0.871902i	0.986904	+	0.161311i	$0.0515722\pi$
$509$	3253.27	+	10012.5i	0.283298	+	0.871902i	−0.703606	+	0.710591i	$0.748428\pi$
$510$		0			0
$511$	7512.62	+	5458.24i	0.650369	+	0.472521i
$512$		0			0
$513$	−1269.61	+	3907.45i	−0.109268	+	0.336292i
$514$		0			0
$515$	1466.26	−	1065.30i	0.125459	−	0.0911513i
$516$		0			0
$517$	351.026	−	176.845i	0.0298610	−	0.0150437i
$518$		0			0
$519$	2957.74	−	2148.93i	0.250155	−	0.181748i
$520$		0			0
$521$	−573.594	+	1765.34i	−0.0482334	+	0.148447i	−0.972272	−	0.233851i	$-0.924867\pi$
$521$	−573.594	+	1765.34i	−0.0482334	+	0.148447i	0.924039	+	0.382298i	$0.124867\pi$
$522$		0			0
$523$	−1578.10	−	1146.56i	−0.131941	−	0.0958611i	0.519857	−	0.854253i	$-0.325985\pi$
$523$	−1578.10	−	1146.56i	−0.131941	−	0.0958611i	−0.651799	+	0.758392i	$0.725985\pi$
$524$		0			0
$525$	−3615.06	−	11126.0i	−0.300522	−	0.924911i
$526$		0			0
$527$	1802.24			0.148969
$528$		0			0
$529$	−1233.57			−0.101386
$530$		0			0
$531$	−3077.22	−	9470.72i	−0.251488	−	0.774000i
$532$		0			0
$533$	4314.15	+	3134.41i	0.350594	+	0.254721i
$534$		0			0
$535$	−3102.73	+	9549.23i	−0.250734	+	0.771681i
$536$		0			0
$537$	964.230	−	700.554i	0.0774853	−	0.0562964i
$538$		0			0
$539$	−8507.66	+	16510.6i	−0.679872	+	1.31941i
$540$		0			0
$541$	−70.7645	+	51.4135i	−0.00562367	+	0.00408584i	−0.590594	−	0.806969i	$-0.701106\pi$
$541$	−70.7645	+	51.4135i	−0.00562367	+	0.00408584i	0.584970	+	0.811055i	$0.301106\pi$
$542$		0			0
$543$	−1813.96	+	5582.79i	−0.143360	+	0.441216i
$544$		0			0
$545$	5474.66	+	3977.57i	0.430291	+	0.312625i
$546$		0			0
$547$	−4171.58	−	12838.8i	−0.326077	−	1.00356i	−0.970952	−	0.239274i	$-0.923091\pi$
$547$	−4171.58	−	12838.8i	−0.326077	−	1.00356i	0.644875	−	0.764288i	$-0.276909\pi$
$548$		0			0
$549$	4477.45			0.348075
$550$		0			0
$551$	1854.24			0.143364
$552$		0			0
$553$	1458.72	+	4489.49i	0.112172	+	0.345231i
$554$		0			0
$555$	−8830.94	−	6416.05i	−0.675410	−	0.490714i
$556$		0			0
$557$	2141.73	−	6591.58i	0.162923	−	0.501426i	−0.835954	−	0.548799i	$-0.815085\pi$
$557$	2141.73	−	6591.58i	0.162923	−	0.501426i	0.998877	+	0.0473735i	$0.0150851\pi$
$558$		0			0
$559$	−14336.2	+	10415.9i	−1.08472	+	0.788093i
$560$		0			0
$561$	−1918.68	−	312.867i	−0.144397	−	0.0235459i
$562$		0			0
$563$	12283.7	−	8924.65i	0.919534	−	0.668080i	−0.0238741	−	0.999715i	$-0.507600\pi$
$563$	12283.7	−	8924.65i	0.919534	−	0.668080i	0.943408	+	0.331635i	$0.107600\pi$
$564$		0			0
$565$	3171.34	−	9760.38i	0.236140	−	0.726765i
$566$		0			0
$567$	10845.3	+	7879.57i	0.803280	+	0.583617i
$568$		0			0
$569$	−2671.84	−	8223.09i	−0.196853	−	0.605852i	−0.999950	−	0.0100035i	$-0.996816\pi$
$569$	−2671.84	−	8223.09i	−0.196853	−	0.605852i	0.803097	−	0.595849i	$-0.203184\pi$
$570$		0			0
$571$	−306.105			−0.0224345			−0.0112172	−	0.999937i	$-0.503571\pi$
$571$	−306.105			−0.0224345			−0.0112172	+	0.999937i	$0.503571\pi$
$572$		0			0
$573$	−3289.39			−0.239819
$574$		0			0
$575$	6941.65	+	21364.2i	0.503455	+	1.54948i
$576$		0			0
$577$	12018.4	+	8731.90i	0.867130	+	0.630007i	0.929815	−	0.368026i	$-0.119966\pi$
$577$	12018.4	+	8731.90i	0.867130	+	0.630007i	−0.0626853	+	0.998033i	$0.519966\pi$
$578$		0			0
$579$	2405.10	−	7402.14i	0.172630	−	0.531300i
$580$		0			0
$581$	−9307.36	+	6762.19i	−0.664603	+	0.482862i
$582$		0			0
$583$	−12763.6	−	12880.5i	−0.906712	−	0.915022i
$584$		0			0
$585$	−27369.0	+	19884.7i	−1.93430	+	1.40535i
$586$		0			0
$587$	−379.264	+	1167.26i	−0.0266677	+	0.0820746i	−0.963505	−	0.267692i	$-0.913739\pi$
$587$	−379.264	+	1167.26i	−0.0266677	+	0.0820746i	0.936837	+	0.349766i	$0.113739\pi$
$588$		0			0
$589$	−2225.25	−	1616.74i	−0.155671	−	0.113101i
$590$		0			0
$591$	1667.25	+	5131.28i	0.116043	+	0.357145i
$592$		0			0
$593$	−14255.5			−0.987189			−0.493594	−	0.869692i	$-0.664317\pi$
$593$	−14255.5			−0.987189			−0.493594	+	0.869692i	$0.664317\pi$
$594$		0			0
$595$	15371.2			1.05909
$596$		0			0
$597$	2467.96	+	7595.59i	0.169191	+	0.520715i
$598$		0			0
$599$	−12643.3	−	9185.92i	−0.862426	−	0.626589i	0.0661182	−	0.997812i	$-0.478939\pi$
$599$	−12643.3	−	9185.92i	−0.862426	−	0.626589i	−0.928544	+	0.371223i	$0.878939\pi$
$600$		0			0
$601$	7972.25	−	24536.1i	0.541090	−	1.66530i	−0.189020	−	0.981973i	$-0.560531\pi$
$601$	7972.25	−	24536.1i	0.541090	−	1.66530i	0.730110	−	0.683330i	$-0.239469\pi$
$602$		0			0
$603$	7349.11	−	5339.44i	0.496316	−	0.360595i
$604$		0			0
$605$	−23265.4	−	7794.73i	−1.56343	−	0.523803i
$606$		0			0
$607$	17691.2	−	12853.4i	1.18297	−	0.859479i	0.190468	−	0.981693i	$-0.439000\pi$
$607$	17691.2	−	12853.4i	1.18297	−	0.859479i	0.992504	+	0.122215i	$0.0389996\pi$
$608$		0			0
$609$	−715.717	+	2202.75i	−0.0476228	+	0.146568i
$610$		0			0
$611$	−680.067	−	494.098i	−0.0450288	−	0.0327153i
$612$		0			0
$613$	7044.02	+	21679.3i	0.464120	+	1.42841i	0.860086	+	0.510148i	$0.170410\pi$
$613$	7044.02	+	21679.3i	0.464120	+	1.42841i	−0.395967	+	0.918265i	$0.629590\pi$
$614$		0			0
$615$	2350.32			0.154104
$616$		0			0
$617$	−16843.3			−1.09901			−0.549504	−	0.835491i	$-0.685183\pi$
$617$	−16843.3			−1.09901			−0.549504	+	0.835491i	$0.685183\pi$
$618$		0			0
$619$	5621.76	+	17302.0i	0.365037	+	1.12347i	0.949958	+	0.312378i	$0.101125\pi$
$619$	5621.76	+	17302.0i	0.365037	+	1.12347i	−0.584921	+	0.811090i	$0.698875\pi$
$620$		0			0
$621$	7972.31	+	5792.22i	0.515165	+	0.374289i
$622$		0			0
$623$	−975.374	+	3001.89i	−0.0627247	+	0.193047i
$624$		0			0
$625$	−2972.52	+	2159.66i	−0.190241	+	0.138218i
$626$		0			0
$627$	2088.37	+	2107.51i	0.133016	+	0.134236i
$628$		0			0
$629$	7335.31	−	5329.41i	0.464989	−	0.337834i
$630$		0			0
$631$	−4988.01	+	15351.5i	−0.314690	+	0.968516i	0.661192	+	0.750217i	$0.270051\pi$
$631$	−4988.01	+	15351.5i	−0.314690	+	0.968516i	−0.975882	+	0.218299i	$0.929949\pi$
$632$		0			0
$633$	4146.87	+	3012.88i	0.260385	+	0.189181i
$634$		0			0
$635$	−7398.17	−	22769.2i	−0.462342	−	1.42294i
$636$		0			0
$637$	39722.5			2.47074
$638$		0			0
$639$	−16263.5			−1.00685
$640$		0			0
$641$	−6301.60	−	19394.3i	−0.388297	−	1.19506i	−0.934060	−	0.357116i	$-0.883760\pi$
$641$	−6301.60	−	19394.3i	−0.388297	−	1.19506i	0.545763	−	0.837939i	$-0.316240\pi$
$642$		0			0
$643$	9208.86	+	6690.63i	0.564793	+	0.410346i	0.833210	−	0.552957i	$-0.186500\pi$
$643$	9208.86	+	6690.63i	0.564793	+	0.410346i	−0.268417	+	0.963303i	$0.586500\pi$
$644$		0			0
$645$	−2413.50	+	7427.99i	−0.147336	+	0.453453i
$646$		0			0
$647$	10915.7	−	7930.73i	0.663278	−	0.481900i	−0.204490	−	0.978869i	$-0.565554\pi$
$647$	10915.7	−	7930.73i	0.663278	−	0.481900i	0.867768	+	0.496969i	$0.165554\pi$
$648$		0			0
$649$	−15245.0	−	2485.91i	−0.922064	−	0.150355i
$650$		0			0
$651$	2779.53	−	2019.45i	0.167340	−	0.121580i
$652$		0			0
$653$	−2631.59	+	8099.21i	−0.157706	+	0.485370i	−0.998425	−	0.0561021i	$-0.982133\pi$
$653$	−2631.59	+	8099.21i	−0.157706	+	0.485370i	0.840719	+	0.541472i	$0.182133\pi$
$654$		0			0
$655$	16563.9	+	12034.4i	0.988099	+	0.717896i
$656$		0			0
$657$	−2312.11	−	7115.94i	−0.137297	−	0.422556i
$658$		0			0
$659$	−29637.1			−1.75189			−0.875946	−	0.482409i	$-0.839762\pi$
$659$	−29637.1			−1.75189			−0.875946	+	0.482409i	$0.839762\pi$
$660$		0			0
$661$	7113.07			0.418557			0.209279	−	0.977856i	$-0.432888\pi$
$661$	7113.07			0.418557			0.209279	+	0.977856i	$0.432888\pi$
$662$		0			0
$663$	1284.76	+	3954.10i	0.0752580	+	0.231620i
$664$		0			0
$665$	−18979.1	−	13789.1i	−1.10674	−	0.804090i
$666$		0			0
$667$	1374.32	−	4229.73i	0.0797811	−	0.245541i
$668$		0			0
$669$	−1312.28	+	953.425i	−0.0758379	+	0.0550994i
$670$		0			0
$671$	3181.22	−	6173.72i	0.183025	−	0.355192i
$672$		0			0
$673$	−9566.47	+	6950.45i	−0.547935	+	0.398098i	−0.827024	−	0.562167i	$-0.809968\pi$
$673$	−9566.47	+	6950.45i	−0.547935	+	0.398098i	0.279088	+	0.960265i	$0.409968\pi$
$674$		0			0
$675$	−6256.51	+	19255.6i	−0.356760	+	1.09800i
$676$		0			0
$677$	19761.7	+	14357.7i	1.12187	+	0.815083i	0.984491	−	0.175436i	$-0.0561335\pi$
$677$	19761.7	+	14357.7i	1.12187	+	0.815083i	0.137375	+	0.990519i	$0.456133\pi$
$678$		0			0
$679$	6122.54	+	18843.2i	0.346041	+	1.06500i
$680$		0			0
$681$	5328.81			0.299854
$682$		0			0
$683$	−21680.4			−1.21461			−0.607304	−	0.794469i	$-0.707749\pi$
$683$	−21680.4			−1.21461			−0.607304	+	0.794469i	$0.707749\pi$
$684$		0			0
$685$	6759.75	+	20804.4i	0.377047	+	1.16043i
$686$		0			0
$687$	−7965.33	−	5787.15i	−0.442353	−	0.321388i
$688$		0			0
$689$	−11983.9	+	36882.7i	−0.662629	+	2.03936i
$690$		0			0
$691$	5707.55	−	4146.78i	0.314219	−	0.228294i	−0.419485	−	0.907762i	$-0.637789\pi$
$691$	5707.55	−	4146.78i	0.314219	−	0.228294i	0.733705	+	0.679468i	$0.237789\pi$
$692$		0			0
$693$	22369.7	−	11269.7i	1.22619	−	0.617749i
$694$		0			0
$695$	−43233.3	+	31410.8i	−2.35962	+	1.71436i
$696$		0			0
$697$	−603.282	+	1856.71i	−0.0327847	+	0.100901i
$698$		0			0
$699$	−1381.49	−	1003.71i	−0.0747535	−	0.0543116i
$700$		0			0
$701$	9684.94	+	29807.2i	0.521819	+	1.60599i	0.770522	+	0.637414i	$0.219996\pi$
$701$	9684.94	+	29807.2i	0.521819	+	1.60599i	−0.248703	+	0.968580i	$0.580004\pi$
$702$		0			0
$703$	−13837.9			−0.742400
$704$		0			0
$705$	−370.495			−0.0197924
$706$		0			0
$707$	10183.7	+	31342.3i	0.541724	+	1.66726i
$708$		0			0
$709$	−3823.80	−	2778.15i	−0.202547	−	0.147159i	0.481888	−	0.876233i	$-0.339951\pi$
$709$	−3823.80	−	2778.15i	−0.202547	−	0.147159i	−0.684435	+	0.729074i	$0.739951\pi$
$710$		0			0
$711$	1175.34	−	3617.34i	0.0619956	−	0.190803i
$712$		0			0
$713$	−5337.27	+	3877.75i	−0.280340	+	0.203679i
$714$		0			0
$715$	7972.37	+	51865.6i	0.416993	+	2.71282i
$716$		0			0
$717$	9550.46	−	6938.82i	0.497446	−	0.361415i
$718$		0			0
$719$	8402.15	−	25859.2i	0.435810	−	1.34129i	−0.456444	−	0.889752i	$-0.650877\pi$
$719$	8402.15	−	25859.2i	0.435810	−	1.34129i	0.892254	−	0.451533i	$-0.149123\pi$
$720$		0			0
$721$	2321.81	+	1686.89i	0.119929	+	0.0871333i
$722$		0			0
$723$	−311.435	−	958.497i	−0.0160199	−	0.0493042i
$724$		0			0
$725$	9137.55			0.468083
$726$		0			0
$727$	14387.6			0.733986			0.366993	−	0.930224i	$-0.380387\pi$
$727$	14387.6			0.733986			0.366993	+	0.930224i	$0.380387\pi$
$728$		0			0
$729$	−1870.96	−	5758.22i	−0.0950546	−	0.292548i
$730$		0			0
$731$	−5248.49	−	3813.25i	−0.265557	−	0.192939i
$732$		0			0
$733$	9206.38	−	28334.3i	0.463909	−	1.42777i	−0.396440	−	0.918061i	$-0.629754\pi$
$733$	9206.38	−	28334.3i	0.463909	−	1.42777i	0.860349	−	0.509705i	$-0.170246\pi$
$734$		0			0
$735$	14163.9	−	10290.7i	0.710807	−	0.516432i
$736$		0			0
$737$	−2140.74	−	13927.0i	−0.106995	−	0.696073i
$738$		0			0
$739$	18153.6	−	13189.4i	0.903641	−	0.656534i	−0.0357574	−	0.999361i	$-0.511384\pi$
$739$	18153.6	−	13189.4i	0.903641	−	0.656534i	0.939399	+	0.342827i	$0.111384\pi$
$740$		0			0
$741$	1960.80	−	6034.73i	0.0972090	−	0.299178i
$742$		0			0
$743$	5660.31	+	4112.45i	0.279484	+	0.203057i	0.718692	−	0.695328i	$-0.244741\pi$
$743$	5660.31	+	4112.45i	0.279484	+	0.203057i	−0.439208	+	0.898385i	$0.644741\pi$
$744$		0			0
$745$	16731.6	+	51494.6i	0.822817	+	2.53237i
$746$		0			0
$747$	9269.60			0.454025
$748$		0			0
$749$	−15899.2			−0.775627
$750$		0			0
$751$	−8967.71	−	27599.8i	−0.435734	−	1.34105i	−0.892333	−	0.451379i	$-0.850932\pi$
$751$	−8967.71	−	27599.8i	−0.435734	−	1.34105i	0.456599	−	0.889673i	$-0.349068\pi$
$752$		0			0
$753$	−8049.11	−	5848.02i	−0.389543	−	0.283019i
$754$		0			0
$755$	17411.2	−	53586.3i	0.839285	−	2.58305i
$756$		0			0
$757$	−12090.7	+	8784.44i	−0.580509	+	0.421765i	−0.838908	−	0.544274i	$-0.816805\pi$
$757$	−12090.7	+	8784.44i	−0.580509	+	0.421765i	0.258398	+	0.966038i	$0.416805\pi$
$758$		0			0
$759$	6355.30	−	3201.76i	0.303930	−	0.153118i
$760$		0			0
$761$	12571.8	−	9133.92i	0.598852	−	0.435091i	−0.246619	−	0.969112i	$-0.579320\pi$
$761$	12571.8	−	9133.92i	0.598852	−	0.435091i	0.845471	+	0.534021i	$0.179320\pi$
$762$		0			0
$763$	−3311.28	+	10191.1i	−0.157112	+	0.483541i
$764$		0			0
$765$	−10019.8	−	7279.80i	−0.473550	−	0.344054i
$766$		0			0
$767$	10208.2	+	31417.5i	0.480568	+	1.47904i
$768$		0			0
$769$	1512.44			0.0709233			0.0354616	−	0.999371i	$-0.488710\pi$
$769$	1512.44			0.0709233			0.0354616	+	0.999371i	$0.488710\pi$
$770$		0			0
$771$	2570.75			0.120082
$772$		0			0
$773$	−12574.3	−	38699.8i	−0.585081	−	1.80069i	−0.598945	−	0.800790i	$-0.704413\pi$
$773$	−12574.3	−	38699.8i	−0.585081	−	1.80069i	0.0138643	−	0.999904i	$-0.495587\pi$
$774$		0			0
$775$	−10965.9	−	7967.16i	−0.508265	−	0.369276i
$776$		0			0
$777$	5341.28	−	16438.8i	0.246612	−	0.758993i
$778$		0			0
$779$	2410.49	−	1751.32i	0.110866	−	0.0805491i
$780$		0			0
$781$	−11555.2	+	22424.9i	−0.529421	+	1.02743i
$782$		0			0
$783$	3242.90	−	2356.11i	0.148010	−	0.107536i
$784$		0			0
$785$	8980.24	−	27638.3i	0.408304	−	1.25663i
$786$		0			0
$787$	−27079.9	−	19674.7i	−1.22655	−	0.891140i	−0.229923	−	0.973209i	$-0.573847\pi$
$787$	−27079.9	−	19674.7i	−1.22655	−	0.891140i	−0.996627	+	0.0820688i	$0.973847\pi$
$788$		0			0
$789$	−4317.74	−	13288.6i	−0.194823	−	0.599604i
$790$		0			0
$791$	16250.8			0.730482
$792$		0			0
$793$	−14853.2			−0.665136
$794$		0			0
$795$	5281.87	+	16255.9i	0.235634	+	0.725205i
$796$		0			0
$797$	−15215.6	−	11054.8i	−0.676240	−	0.491317i	0.195868	−	0.980630i	$-0.437248\pi$
$797$	−15215.6	−	11054.8i	−0.676240	−	0.491317i	−0.872108	+	0.489313i	$0.837248\pi$
$798$		0			0
$799$	95.0991	−	292.685i	0.00421072	−	0.0129593i
$800$		0			0
$801$	2057.49	−	1494.86i	0.0907590	−	0.0659403i
$802$		0			0
$803$	−11454.5	−	1867.82i	−0.503390	−	0.0820845i
$804$		0			0
$805$	−45521.4	+	33073.2i	−1.99307	+	1.44805i
$806$		0			0
$807$	4203.07	−	12935.7i	0.183340	−	0.564262i
$808$		0			0
$809$	−24141.4	−	17539.8i	−1.04916	−	0.762256i	−0.0771041	−	0.997023i	$-0.524567\pi$
$809$	−24141.4	−	17539.8i	−1.04916	−	0.762256i	−0.972052	+	0.234767i	$0.924567\pi$
$810$		0			0
$811$	6559.41	+	20187.8i	0.284010	+	0.874092i	0.986694	+	0.162590i	$0.0519848\pi$
$811$	6559.41	+	20187.8i	0.284010	+	0.874092i	−0.702684	+	0.711502i	$0.748015\pi$
$812$		0			0
$813$	1458.56			0.0629198
$814$		0			0
$815$	−52198.3			−2.24347
$816$		0			0
$817$	3059.63	+	9416.58i	0.131020	+	0.403237i
$818$		0			0
$819$	−43338.3	−	31487.1i	−1.84904	−	1.34341i
$820$		0			0
$821$	1212.55	−	3731.84i	0.0515447	−	0.158638i	−0.921971	−	0.387260i	$-0.873422\pi$
$821$	1212.55	−	3731.84i	0.0515447	−	0.158638i	0.973515	+	0.228621i	$0.0734217\pi$
$822$		0			0
$823$	16307.8	−	11848.3i	0.690708	−	0.501829i	−0.186185	−	0.982515i	$-0.559612\pi$
$823$	16307.8	−	11848.3i	0.690708	−	0.501829i	0.876893	+	0.480686i	$0.159612\pi$
$824$		0			0
$825$	10291.3	+	10385.6i	0.434299	+	0.438279i
$826$		0			0
$827$	31618.0	−	22971.9i	1.32946	−	0.965912i	0.329703	−	0.944085i	$-0.393051\pi$
$827$	31618.0	−	22971.9i	1.32946	−	0.965912i	0.999762	−	0.0218277i	$-0.00694852\pi$
$828$		0			0
$829$	−5841.62	+	17978.7i	−0.244738	+	0.753226i	0.750941	+	0.660369i	$0.229600\pi$
$829$	−5841.62	+	17978.7i	−0.244738	+	0.753226i	−0.995679	+	0.0928575i	$0.970400\pi$
$830$		0			0
$831$	867.843	+	630.525i	0.0362276	+	0.0263209i
$832$		0			0
$833$	4493.85	+	13830.7i	0.186918	+	0.575275i
$834$		0			0
$835$	22981.8			0.952477
$836$		0			0
$837$	−5946.09			−0.245552
$838$		0			0
$839$	417.741	+	1285.67i	0.0171895	+	0.0529039i	0.959283	−	0.282446i	$-0.0911456\pi$
$839$	417.741	+	1285.67i	0.0171895	+	0.0529039i	−0.942094	+	0.335349i	$0.891146\pi$
$840$		0			0
$841$	18267.5	+	13272.1i	0.749008	+	0.544186i
$842$		0			0
$843$	−3229.70	+	9939.98i	−0.131953	+	0.406111i
$844$		0			0
$845$	58026.2	−	42158.5i	2.36232	−	1.71633i
$846$		0			0
$847$	354.435	−	38851.4i	0.0143784	−	1.57609i
$848$		0			0
$849$	−1355.26	+	984.658i	−0.0547851	+	0.0398037i
$850$		0			0
$851$	−10256.4	+	31565.8i	−0.413141	+	1.27152i
$852$		0			0
$853$	−27556.6	−	20021.0i	−1.10612	−	0.803643i	−0.124071	−	0.992273i	$-0.539595\pi$
$853$	−27556.6	−	20021.0i	−1.10612	−	0.803643i	−0.982048	+	0.188630i	$0.939595\pi$
$854$		0			0
$855$	5841.08	+	17977.0i	0.233638	+	0.719065i
$856$		0			0
$857$	40085.5			1.59778			0.798888	−	0.601480i	$-0.205422\pi$
$857$	40085.5			1.59778			0.798888	+	0.601480i	$0.205422\pi$
$858$		0			0
$859$	20827.3			0.827261			0.413631	−	0.910445i	$-0.364261\pi$
$859$	20827.3			0.827261			0.413631	+	0.910445i	$0.364261\pi$
$860$		0			0
$861$	1150.07	+	3539.54i	0.0455216	+	0.140101i
$862$		0			0
$863$	32530.0	+	23634.4i	1.28312	+	0.932242i	0.999643	−	0.0267360i	$-0.00851135\pi$
$863$	32530.0	+	23634.4i	1.28312	+	0.932242i	0.283479	+	0.958978i	$0.408511\pi$
$864$		0			0
$865$	11164.4	−	34360.4i	0.438844	−	1.35062i
$866$		0			0
$867$	6183.21	−	4492.37i	0.242206	−	0.175973i
$868$		0			0
$869$	−4152.67	−	4190.73i	−0.162106	−	0.163591i
$870$		0			0
$871$	−24379.5	+	17712.7i	−0.948412	+	0.689061i
$872$		0			0
$873$	4933.14	−	15182.7i	0.191250	−	0.588608i
$874$		0			0
$875$	−39108.9	−	28414.3i	−1.51100	−	1.09780i
$876$		0			0
$877$	2172.95	+	6687.64i	0.0836661	+	0.257498i	0.984135	−	0.177423i	$-0.0567762\pi$
$877$	2172.95	+	6687.64i	0.0836661	+	0.257498i	−0.900469	+	0.434921i	$0.856776\pi$
$878$		0			0
$879$	−14999.2			−0.575552
$880$		0			0
$881$	30396.7			1.16242			0.581209	−	0.813754i	$-0.302580\pi$
$881$	30396.7			1.16242			0.581209	+	0.813754i	$0.302580\pi$
$882$		0			0
$883$	582.341	+	1792.26i	0.0221940	+	0.0683063i	0.961540	−	0.274665i	$-0.0885668\pi$
$883$	582.341	+	1792.26i	0.0221940	+	0.0683063i	−0.939346	+	0.342971i	$0.888567\pi$
$884$		0			0
$885$	11779.1	+	8558.02i	0.447401	+	0.325056i
$886$		0			0
$887$	−442.860	+	1362.98i	−0.0167641	+	0.0515947i	−0.959089	−	0.283106i	$-0.908635\pi$
$887$	−442.860	+	1362.98i	−0.0167641	+	0.0515947i	0.942325	+	0.334701i	$0.108635\pi$
$888$		0			0
$889$	30670.0	−	22283.0i	1.15707	−	0.840662i
$890$		0			0
$891$	−16535.9	−	2696.40i	−0.621743	−	0.101384i
$892$		0			0
$893$	−379.981	+	276.073i	−0.0142392	+	0.0103454i
$894$		0			0
$895$	3639.61	−	11201.6i	0.135931	−	0.418354i
$896$		0			0
$897$	−12312.6	−	8945.60i	−0.458310	−	0.332982i
$898$		0			0
$899$	829.265	+	2552.22i	0.0307648	+	0.0946843i
$900$		0			0
$901$	−14197.7			−0.524964
$902$		0			0
$903$	−12367.4			−0.455772
$904$		0			0
$905$	17925.7	+	55169.7i	0.658421	+	2.02641i
$906$		0			0
$907$	−22216.3	−	16141.1i	−0.813319	−	0.590911i	0.101472	−	0.994838i	$-0.467645\pi$
$907$	−22216.3	−	16141.1i	−0.813319	−	0.590911i	−0.914791	+	0.403927i	$0.867645\pi$
$908$		0			0
$909$	8205.40	−	25253.6i	0.299401	−	0.921462i
$910$		0			0
$911$	37947.6	−	27570.5i	1.38009	−	1.00269i	0.383215	−	0.923659i	$-0.374817\pi$
$911$	37947.6	−	27570.5i	1.38009	−	1.00269i	0.996872	−	0.0790330i	$-0.0251833\pi$
$912$		0			0
$913$	6586.03	−	12781.4i	0.238736	−	0.463309i
$914$		0			0
$915$	−5296.23	+	3847.93i	−0.191353	+	0.139026i
$916$		0			0
$917$	−10018.5	+	30833.6i	−0.360784	+	1.11038i
$918$		0			0
$919$	27166.7	+	19737.7i	0.975131	+	0.708474i	0.956615	−	0.291354i	$-0.0941059\pi$
$919$	27166.7	+	19737.7i	0.975131	+	0.708474i	0.0185159	+	0.999829i	$0.494106\pi$
$920$		0			0
$921$	3165.61	+	9742.76i	0.113258	+	0.348572i
$922$		0			0
$923$	53951.6			1.92399
$924$		0			0
$925$	−68192.1			−2.42394
$926$		0			0
$927$	−714.567	−	2199.21i	−0.0253177	−	0.0779197i
$928$		0			0
$929$	−15803.6	−	11482.0i	−0.558127	−	0.405503i	0.272646	−	0.962114i	$-0.412101\pi$
$929$	−15803.6	−	11482.0i	−0.558127	−	0.405503i	−0.830773	+	0.556612i	$0.812101\pi$
$930$		0			0
$931$	6858.50	−	21108.3i	0.241438	−	0.743068i
$932$		0			0
$933$	4821.92	−	3503.33i	0.169199	−	0.122930i
$934$		0			0
$935$	−17156.8	+	8643.46i	−0.600092	+	0.302322i
$936$		0			0
$937$	42555.5	−	30918.4i	1.48370	−	1.07797i	0.507361	−	0.861734i	$-0.330621\pi$
$937$	42555.5	−	30918.4i	1.48370	−	1.07797i	0.976341	−	0.216239i	$-0.0693789\pi$
$938$		0			0
$939$	−1797.05	+	5530.76i	−0.0624543	+	0.192215i
$940$		0			0
$941$	28258.3	+	20530.8i	0.978951	+	0.711250i	0.957474	−	0.288520i	$-0.0931631\pi$
$941$	28258.3	+	20530.8i	0.978951	+	0.711250i	0.0214772	+	0.999769i	$0.493163\pi$
$942$		0			0
$943$	−2208.36	−	6796.63i	−0.0762610	−	0.234707i
$944$		0			0
$945$	−50714.0			−1.74574
$946$		0			0
$947$	−4206.50			−0.144343			−0.0721715	−	0.997392i	$-0.522993\pi$
$947$	−4206.50			−0.144343			−0.0721715	+	0.997392i	$0.522993\pi$
$948$		0			0
$949$	7670.04	+	23606.0i	0.262361	+	0.807463i
$950$		0			0
$951$	−362.603	−	263.447i	−0.0123640	−	0.00898301i
$952$		0			0
$953$	−226.324	+	696.553i	−0.00769291	+	0.0236763i	−0.954829	−	0.297155i	$-0.903962\pi$
$953$	−226.324	+	696.553i	−0.00769291	+	0.0236763i	0.947136	+	0.320831i	$0.103962\pi$
$954$		0			0
$955$	−26298.0	+	19106.6i	−0.891082	+	0.647409i
$956$		0			0
$957$	−439.783	−	2861.08i	−0.0148549	−	0.0966412i
$958$		0			0
$959$	−28023.3	+	20360.1i	−0.943609	+	0.685572i
$960$		0			0
$961$	−7975.80	+	24547.0i	−0.267725	+	0.823973i
$962$		0			0
$963$	10364.0	+	7529.85i	0.346806	+	0.251969i
$964$		0			0
$965$	−23767.4	−	73148.7i	−0.792851	−	2.44014i
$966$		0			0
$967$	6877.86			0.228725			0.114363	−	0.993439i	$-0.463517\pi$
$967$	6877.86			0.228725			0.114363	+	0.993439i	$0.463517\pi$
$968$		0			0
$969$	2323.01			0.0770133
$970$		0			0
$971$	−11642.4	−	35831.6i	−0.384781	−	1.18423i	−0.936639	−	0.350295i	$-0.886081\pi$
$971$	−11642.4	−	35831.6i	−0.384781	−	1.18423i	0.551859	−	0.833938i	$-0.313919\pi$
$972$		0			0
$973$	−68459.3	−	49738.6i	−2.25560	−	1.63879i
$974$		0			0
$975$	9662.66	−	29738.6i	0.317388	−	0.976818i
$976$		0			0
$977$	−25728.6	+	18692.9i	−0.842508	+	0.612118i	−0.923070	−	0.384632i	$-0.874328\pi$
$977$	−25728.6	+	18692.9i	−0.842508	+	0.612118i	0.0805620	+	0.996750i	$0.474328\pi$
$978$		0			0
$979$	−599.333	−	3899.06i	−0.0195656	−	0.127288i
$980$		0			0
$981$	6984.95	−	5074.86i	0.227332	−	0.165166i
$982$		0			0
$983$	10041.4	−	30904.2i	0.325809	−	1.00274i	−0.645265	−	0.763959i	$-0.723253\pi$
$983$	10041.4	−	30904.2i	0.325809	−	1.00274i	0.971074	−	0.238779i	$-0.0767470\pi$
$984$		0			0
$985$	43134.6	+	31339.1i	1.39531	+	1.01375i
$986$		0			0
$987$	−181.292	−	557.960i	−0.00584660	−	0.0179940i
$988$		0			0
$989$	23748.0			0.763540
$990$		0			0
$991$	−3024.29			−0.0969423			−0.0484712	−	0.998825i	$-0.515435\pi$
$991$	−3024.29			−0.0969423			−0.0484712	+	0.998825i	$0.515435\pi$
$992$		0			0
$993$	5422.02	+	16687.3i	0.173276	+	0.533288i
$994$		0			0
$995$	63850.2	+	46389.9i	2.03436	+	1.47805i
$996$		0			0
$997$	−3247.69	+	9995.35i	−0.103165	+	0.317509i	−0.989295	−	0.145927i	$-0.953383\pi$
$997$	−3247.69	+	9995.35i	−0.103165	+	0.317509i	0.886131	+	0.463436i	$0.153383\pi$
$998$		0			0
$999$	−24201.3	+	17583.2i	−0.766461	+	0.556866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.d.113.2		12
4.3	odd	2		44.4.e.a.25.2	✓	12
11.2	odd	10		1936.4.a.bs.1.4		6
11.4	even	5	inner	176.4.m.d.81.2		12
11.9	even	5		1936.4.a.br.1.4		6
12.11	even	2		396.4.j.d.289.1		12
44.15	odd	10		44.4.e.a.37.2	yes	12
44.31	odd	10		484.4.a.i.1.3		6
44.35	even	10		484.4.a.h.1.3		6
132.59	even	10		396.4.j.d.37.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.4.e.a.25.2	✓	12	4.3	odd	2
44.4.e.a.37.2	yes	12	44.15	odd	10
176.4.m.d.81.2		12	11.4	even	5	inner
176.4.m.d.113.2		12	1.1	even	1	trivial
396.4.j.d.37.1		12	132.59	even	10
396.4.j.d.289.1		12	12.11	even	2
484.4.a.h.1.3		6	44.35	even	10
484.4.a.i.1.3		6	44.31	odd	10
1936.4.a.br.1.4		6	11.9	even	5
1936.4.a.bs.1.4		6	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.576456 + 1.77415i) q^{3} +(14.9139 + 10.8356i) q^{5} +(-9.02047 + 27.7622i) q^{7} +(19.0282 - 13.8248i) q^{9} +(-5.54276 - 36.0594i) q^{11} +(-63.1228 + 45.8614i) q^{13} +(-10.6267 + 32.7057i) q^{15} +(-23.1093 - 16.7899i) q^{17} +(13.4717 + 41.4615i) q^{19} -54.4541 q^{21} +104.563 q^{23} +(66.3872 + 204.319i) q^{25} +(76.2440 + 55.3945i) q^{27} +(13.1435 - 40.4515i) q^{29} +(-51.0435 + 37.0853i) q^{31} +(60.7796 - 30.6203i) q^{33} +(-435.349 + 316.300i) q^{35} +(-98.0877 + 301.883i) q^{37} +(-117.752 - 85.5522i) q^{39} +(-21.1199 - 65.0003i) q^{41} +227.116 q^{43} +433.583 q^{45} +(3.32926 + 10.2464i) q^{47} +(-411.875 - 299.245i) q^{49} +(16.4663 - 50.6779i) q^{51} +(402.111 - 292.151i) q^{53} +(308.060 - 597.844i) q^{55} +(-65.7931 + 47.8015i) q^{57} +(130.834 - 402.665i) q^{59} +(154.010 + 111.895i) q^{61} +(212.162 + 652.968i) q^{63} -1438.34 q^{65} +386.223 q^{67} +(60.2760 + 185.511i) q^{69} +(-559.414 - 406.438i) q^{71} +(98.3036 - 302.547i) q^{73} +(-324.223 + 235.562i) q^{75} +(1051.08 + 171.393i) q^{77} +(130.828 - 95.0523i) q^{79} +(141.912 - 436.760i) q^{81} +(318.845 + 231.654i) q^{83} +(-162.721 - 500.804i) q^{85} +79.3436 q^{87} +108.129 q^{89} +(-703.814 - 2166.12i) q^{91} +(-95.2193 - 69.1808i) q^{93} +(-248.344 + 764.325i) q^{95} +(549.111 - 398.952i) q^{97} +(-603.981 - 609.516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 4 q^{5} - 6 q^{7} + 47 q^{9} - 39 q^{11} - 10 q^{13} - 74 q^{15} - 56 q^{17} + 141 q^{19} - 304 q^{21} + 388 q^{23} - 203 q^{25} + 331 q^{27} + 772 q^{29} - 882 q^{31} + 981 q^{33} - 412 q^{35}+ \cdots - 3563 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 4 * q^5 - 6 * q^7 + 47 * q^9 - 39 * q^11 - 10 * q^13 - 74 * q^15 - 56 * q^17 + 141 * q^19 - 304 * q^21 + 388 * q^23 - 203 * q^25 + 331 * q^27 + 772 * q^29 - 882 * q^31 + 981 * q^33 - 412 * q^35 - 192 * q^37 + 154 * q^39 - 180 * q^41 + 2330 * q^43 - 1340 * q^45 - 196 * q^47 - 973 * q^49 - 2969 * q^51 + 2246 * q^53 - 2672 * q^55 + 431 * q^57 + 1099 * q^59 - 470 * q^61 + 2008 * q^63 - 3892 * q^65 + 4394 * q^67 - 1394 * q^69 + 2084 * q^71 + 2824 * q^73 - 4623 * q^75 + 3654 * q^77 - 838 * q^79 + 1518 * q^81 - 789 * q^83 - 2632 * q^85 + 3036 * q^87 - 954 * q^89 - 2460 * q^91 - 808 * q^93 - 4362 * q^95 + 2651 * q^97 - 3563 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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