LMFDB - Embedded newform 176.4.m.d.113.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [176,4,Mod(49,176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			113.3
Root			$3.41047 - 2.47785i$ of defining polynomial
Character	$\chi$	$=$	176.113
Dual form			176.4.m.d.81.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30268 + 4.00925i) q^{3} +(-13.7488 - 9.98909i) q^{5} +(-1.14865 + 3.53519i) q^{7} +(7.46635 - 5.42462i) q^{9} +(35.9801 + 6.03578i) q^{11} +(50.6891 - 36.8278i) q^{13} +(22.1384 - 68.1350i) q^{15} +(67.4838 + 49.0299i) q^{17} +(-15.3707 - 47.3060i) q^{19} -15.6698 q^{21} +42.7247 q^{23} +(50.6205 + 155.794i) q^{25} +(123.558 + 89.7700i) q^{27} +(47.8637 - 147.309i) q^{29} +(-163.585 + 118.852i) q^{31} +(22.6718 + 152.116i) q^{33} +(51.1060 - 37.1306i) q^{35} +(29.6386 - 91.2183i) q^{37} +(213.684 + 155.250i) q^{39} +(-139.139 - 428.225i) q^{41} +343.078 q^{43} -156.840 q^{45} +(-121.252 - 373.175i) q^{47} +(266.315 + 193.489i) q^{49} +(-108.663 + 334.430i) q^{51} +(155.884 - 113.257i) q^{53} +(-434.392 - 442.393i) q^{55} +(169.639 - 123.250i) q^{57} +(163.707 - 503.838i) q^{59} +(273.040 + 198.375i) q^{61} +(10.6008 + 32.6260i) q^{63} -1064.79 q^{65} -831.356 q^{67} +(55.6568 + 171.294i) q^{69} +(546.910 + 397.354i) q^{71} +(-375.494 + 1155.65i) q^{73} +(-558.674 + 405.900i) q^{75} +(-62.6663 + 120.264i) q^{77} +(-867.501 + 630.277i) q^{79} +(-121.952 + 375.331i) q^{81} +(-65.4403 - 47.5452i) q^{83} +(-438.058 - 1348.20i) q^{85} +652.951 q^{87} -30.9863 q^{89} +(71.9691 + 221.498i) q^{91} +(-689.606 - 501.028i) q^{93} +(-261.216 + 803.940i) q^{95} +(-73.7338 + 53.5708i) q^{97} +(301.382 - 150.113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.30268	+	4.00925i	0.250702	+	0.771581i	0.994646	+	0.103339i	$0.0329527\pi$
$3$	1.30268	+	4.00925i	0.250702	+	0.771581i	−0.743944	+	0.668242i	$0.767047\pi$
$4$		0			0
$5$	−13.7488	−	9.98909i	−1.22973	−	0.893451i	−0.232860	−	0.972510i	$-0.574808\pi$
$5$	−13.7488	−	9.98909i	−1.22973	−	0.893451i	−0.996870	+	0.0790592i	$0.974808\pi$
$6$		0			0
$7$	−1.14865	+	3.53519i	−0.0620215	+	0.190882i	−0.977266	−	0.212016i	$-0.931997\pi$
$7$	−1.14865	+	3.53519i	−0.0620215	+	0.190882i	0.915245	+	0.402898i	$0.131997\pi$
$8$		0			0
$9$	7.46635	−	5.42462i	0.276531	−	0.200912i
$10$		0			0
$11$	35.9801	+	6.03578i	0.986220	+	0.165441i
$11$	35.9801	+	6.03578i	0.986220	+	0.165441i
$12$		0			0
$13$	50.6891	−	36.8278i	1.08143	−	0.785707i	0.103501	−	0.994629i	$-0.466996\pi$
$13$	50.6891	−	36.8278i	1.08143	−	0.785707i	0.977932	+	0.208922i	$0.0669955\pi$
$14$		0			0
$15$	22.1384	−	68.1350i	0.381074	−	1.17283i
$16$		0			0
$17$	67.4838	+	49.0299i	0.962778	+	0.699499i	0.953794	−	0.300460i	$-0.0971403\pi$
$17$	67.4838	+	49.0299i	0.962778	+	0.699499i	0.00898393	+	0.999960i	$0.497140\pi$
$18$		0			0
$19$	−15.3707	−	47.3060i	−0.185593	−	0.571197i	0.814365	−	0.580353i	$-0.197086\pi$
$19$	−15.3707	−	47.3060i	−0.185593	−	0.571197i	−0.999958	+	0.00915592i	$0.997086\pi$
$20$		0			0
$21$	−15.6698			−0.162830
$22$		0			0
$23$	42.7247			0.387335			0.193668	−	0.981067i	$-0.437962\pi$
$23$	42.7247			0.387335			0.193668	+	0.981067i	$0.437962\pi$
$24$		0			0
$25$	50.6205	+	155.794i	0.404964	+	1.24635i
$26$		0			0
$27$	123.558	+	89.7700i	0.880693	+	0.639861i
$28$		0			0
$29$	47.8637	−	147.309i	0.306485	−	0.943263i	−0.672634	−	0.739975i	$-0.734837\pi$
$29$	47.8637	−	147.309i	0.306485	−	0.943263i	0.979119	−	0.203288i	$-0.0651628\pi$
$30$		0			0
$31$	−163.585	+	118.852i	−0.947767	+	0.688593i	−0.950278	−	0.311404i	$-0.899201\pi$
$31$	−163.585	+	118.852i	−0.947767	+	0.688593i	0.00251102	+	0.999997i	$0.499201\pi$
$32$		0			0
$33$	22.6718	+	152.116i	0.119596	+	0.802425i
$34$		0			0
$35$	51.1060	−	37.1306i	0.246814	−	0.179321i
$36$		0			0
$37$	29.6386	−	91.2183i	0.131691	−	0.405303i	−0.863370	−	0.504572i	$-0.831650\pi$
$37$	29.6386	−	91.2183i	0.131691	−	0.405303i	0.995061	+	0.0992690i	$0.0316504\pi$
$38$		0			0
$39$	213.684	+	155.250i	0.877354	+	0.637435i
$40$		0			0
$41$	−139.139	−	428.225i	−0.529995	−	1.63116i	−0.754221	−	0.656620i	$-0.771985\pi$
$41$	−139.139	−	428.225i	−0.529995	−	1.63116i	0.224226	−	0.974537i	$-0.428015\pi$
$42$		0			0
$43$	343.078			1.21672			0.608360	−	0.793661i	$-0.291828\pi$
$43$	343.078			1.21672			0.608360	+	0.793661i	$0.291828\pi$
$44$		0			0
$45$	−156.840			−0.519564
$46$		0			0
$47$	−121.252	−	373.175i	−0.376306	−	1.15815i	−0.942593	−	0.333943i	$-0.891621\pi$
$47$	−121.252	−	373.175i	−0.376306	−	1.15815i	0.566287	−	0.824208i	$-0.308379\pi$
$48$		0			0
$49$	266.315	+	193.489i	0.776428	+	0.564108i
$50$		0			0
$51$	−108.663	+	334.430i	−0.298350	+	0.918227i
$52$		0			0
$53$	155.884	−	113.257i	0.404007	−	0.293528i	−0.367164	−	0.930156i	$-0.619671\pi$
$53$	155.884	−	113.257i	0.404007	−	0.293528i	0.771171	+	0.636628i	$0.219671\pi$
$54$		0			0
$55$	−434.392	−	442.393i	−1.06497	−	1.08459i
$56$		0			0
$57$	169.639	−	123.250i	0.394196	−	0.286400i
$58$		0			0
$59$	163.707	−	503.838i	0.361235	−	1.11177i	−0.591071	−	0.806619i	$-0.701295\pi$
$59$	163.707	−	503.838i	0.361235	−	1.11177i	0.952306	−	0.305146i	$-0.0987053\pi$
$60$		0			0
$61$	273.040	+	198.375i	0.573102	+	0.416383i	0.836231	−	0.548378i	$-0.184754\pi$
$61$	273.040	+	198.375i	0.573102	+	0.416383i	−0.263129	+	0.964761i	$0.584754\pi$
$62$		0			0
$63$	10.6008	+	32.6260i	0.0211997	+	0.0652459i
$64$		0			0
$65$	−1064.79			−2.03186
$66$		0			0
$67$	−831.356			−1.51591			−0.757957	−	0.652304i	$-0.773803\pi$
$67$	−831.356			−1.51591			−0.757957	+	0.652304i	$0.773803\pi$
$68$		0			0
$69$	55.6568	+	171.294i	0.0971056	+	0.298860i
$70$		0			0
$71$	546.910	+	397.354i	0.914173	+	0.664186i	0.942067	−	0.335425i	$-0.108880\pi$
$71$	546.910	+	397.354i	0.914173	+	0.664186i	−0.0278936	+	0.999611i	$0.508880\pi$
$72$		0			0
$73$	−375.494	+	1155.65i	−0.602030	+	1.85286i	−0.0859871	+	0.996296i	$0.527404\pi$
$73$	−375.494	+	1155.65i	−0.602030	+	1.85286i	−0.516043	+	0.856563i	$0.672596\pi$
$74$		0			0
$75$	−558.674	+	405.900i	−0.860135	+	0.624925i
$76$		0			0
$77$	−62.6663	+	120.264i	−0.0927467	+	0.177991i
$78$		0			0
$79$	−867.501	+	630.277i	−1.23546	+	0.897616i	−0.997287	−	0.0736062i	$-0.976549\pi$
$79$	−867.501	+	630.277i	−1.23546	+	0.897616i	−0.238175	+	0.971222i	$0.576549\pi$
$80$		0			0
$81$	−121.952	+	375.331i	−0.167287	+	0.514857i
$82$		0			0
$83$	−65.4403	−	47.5452i	−0.0865423	−	0.0628766i	0.543673	−	0.839297i	$-0.317033\pi$
$83$	−65.4403	−	47.5452i	−0.0865423	−	0.0628766i	−0.630215	+	0.776421i	$0.717033\pi$
$84$		0			0
$85$	−438.058	−	1348.20i	−0.558989	−	1.72039i
$86$		0			0
$87$	652.951			0.804640
$88$		0			0
$89$	−30.9863			−0.0369049			−0.0184525	−	0.999830i	$-0.505874\pi$
$89$	−30.9863			−0.0369049			−0.0184525	+	0.999830i	$0.505874\pi$
$90$		0			0
$91$	71.9691	+	221.498i	0.0829057	+	0.255157i
$92$		0			0
$93$	−689.606	−	501.028i	−0.768912	−	0.558647i
$94$		0			0
$95$	−261.216	+	803.940i	−0.282107	+	0.868237i
$96$		0			0
$97$	−73.7338	+	53.5708i	−0.0771808	+	0.0560751i	−0.625707	−	0.780059i	$-0.715189\pi$
$97$	−73.7338	+	53.5708i	−0.0771808	+	0.0560751i	0.548526	+	0.836134i	$0.315189\pi$
$98$		0			0
$99$	301.382	−	150.113i	0.305960	−	0.152393i
$100$		0			0
$101$	973.926	−	707.598i	0.959497	−	0.697116i	0.00646329	−	0.999979i	$-0.497943\pi$
$101$	973.926	−	707.598i	0.959497	−	0.697116i	0.953034	+	0.302864i	$0.0979427\pi$
$102$		0			0
$103$	257.794	−	793.408i	0.246613	−	0.758998i	−0.748754	−	0.662849i	$-0.769347\pi$
$103$	257.794	−	793.408i	0.246613	−	0.758998i	0.995367	−	0.0961494i	$-0.0306527\pi$
$104$		0			0
$105$	215.441	+	156.527i	0.200237	+	0.145481i
$106$		0			0
$107$	−123.997	−	381.623i	−0.112030	−	0.344794i	0.879286	−	0.476295i	$-0.158020\pi$
$107$	−123.997	−	381.623i	−0.112030	−	0.344794i	−0.991316	+	0.131501i	$0.958020\pi$
$108$		0			0
$109$	−1195.49			−1.05052			−0.525262	−	0.850941i	$-0.676033\pi$
$109$	−1195.49			−1.05052			−0.525262	+	0.850941i	$0.676033\pi$
$110$		0			0
$111$	404.327			0.345739
$112$		0			0
$113$	269.208	+	828.538i	0.224115	+	0.689755i	0.998380	+	0.0568936i	$0.0181196\pi$
$113$	269.208	+	828.538i	0.224115	+	0.689755i	−0.774265	+	0.632861i	$0.781880\pi$
$114$		0			0
$115$	−587.413	−	426.780i	−0.476318	−	0.346065i
$116$		0			0
$117$	178.686	−	549.938i	0.141192	−	0.434546i
$118$		0			0
$119$	−250.846	+	182.250i	−0.193235	+	0.140394i
$120$		0			0
$121$	1258.14	+	434.336i	0.945258	+	0.326323i
$122$		0			0
$123$	1535.61	−	1115.68i	1.12570	−	0.817868i
$124$		0			0
$125$	203.820	−	627.295i	0.145842	−	0.448855i
$126$		0			0
$127$	699.947	+	508.541i	0.489057	+	0.355321i	0.804822	−	0.593517i	$-0.202261\pi$
$127$	699.947	+	508.541i	0.489057	+	0.355321i	−0.315764	+	0.948838i	$0.602261\pi$
$128$		0			0
$129$	446.923	+	1375.49i	0.305034	+	0.938798i
$130$		0			0
$131$	−2598.55			−1.73310			−0.866551	−	0.499088i	$-0.833668\pi$
$131$	−2598.55			−1.73310			−0.866551	+	0.499088i	$0.833668\pi$
$132$		0			0
$133$	184.892			0.120542
$134$		0			0
$135$	−802.051	−	2468.46i	−0.511330	−	1.57371i
$136$		0			0
$137$	683.314	+	496.457i	0.426127	+	0.309600i	0.780098	−	0.625657i	$-0.215169\pi$
$137$	683.314	+	496.457i	0.426127	+	0.309600i	−0.353971	+	0.935256i	$0.615169\pi$
$138$		0			0
$139$	−385.565	+	1186.65i	−0.235275	+	0.724101i	0.761810	+	0.647800i	$0.224311\pi$
$139$	−385.565	+	1186.65i	−0.235275	+	0.724101i	−0.997085	+	0.0763004i	$0.975689\pi$
$140$		0			0
$141$	1338.20	−	972.258i	0.799267	−	0.580701i
$142$		0			0
$143$	2046.09	−	1019.12i	1.19652	−	0.595966i
$144$		0			0
$145$	−2129.55	+	1547.21i	−1.21965	+	0.886130i
$146$		0			0
$147$	−428.822	+	1319.78i	−0.240603	+	0.740499i
$148$		0			0
$149$	262.444	+	190.677i	0.144297	+	0.104838i	0.657592	−	0.753375i	$-0.271575\pi$
$149$	262.444	+	190.677i	0.144297	+	0.104838i	−0.513295	+	0.858212i	$0.671575\pi$
$150$		0			0
$151$	568.606	+	1749.99i	0.306440	+	0.943126i	0.979136	+	0.203207i	$0.0651364\pi$
$151$	568.606	+	1749.99i	0.306440	+	0.943126i	−0.672695	+	0.739919i	$0.734864\pi$
$152$		0			0
$153$	769.826			0.406776
$154$		0			0
$155$	3436.32			1.78072
$156$		0			0
$157$	−800.616	−	2464.04i	−0.406981	−	1.25256i	−0.919229	−	0.393722i	$-0.871187\pi$
$157$	−800.616	−	2464.04i	−0.406981	−	1.25256i	0.512248	−	0.858838i	$-0.328813\pi$
$158$		0			0
$159$	657.142	+	477.442i	0.327766	+	0.238136i
$160$		0			0
$161$	−49.0758	+	151.040i	−0.0240231	+	0.0739355i
$162$		0			0
$163$	2380.47	−	1729.51i	1.14388	−	0.831079i	0.156227	−	0.987721i	$-0.450067\pi$
$163$	2380.47	−	1729.51i	1.14388	−	0.831079i	0.987655	+	0.156642i	$0.0500668\pi$
$164$		0			0
$165$	1207.79	−	2317.88i	0.569857	−	1.09362i
$166$		0			0
$167$	−1533.32	+	1114.02i	−0.710489	+	0.516201i	−0.883332	−	0.468749i	$-0.844705\pi$
$167$	−1533.32	+	1114.02i	−0.710489	+	0.516201i	0.172842	+	0.984950i	$0.444705\pi$
$168$		0			0
$169$	534.190	−	1644.07i	0.243145	−	0.748323i
$170$		0			0
$171$	−371.380	−	269.823i	−0.166083	−	0.120666i
$172$		0			0
$173$	628.110	+	1933.12i	0.276037	+	0.849553i	0.988943	+	0.148294i	$0.0473783\pi$
$173$	628.110	+	1933.12i	0.276037	+	0.849553i	−0.712907	+	0.701259i	$0.752622\pi$
$174$		0			0
$175$	−608.906			−0.263023
$176$		0			0
$177$	2233.27			0.948379
$178$		0			0
$179$	610.245	+	1878.14i	0.254815	+	0.784239i	0.993866	+	0.110590i	$0.0352741\pi$
$179$	610.245	+	1878.14i	0.254815	+	0.784239i	−0.739051	+	0.673649i	$0.764726\pi$
$180$		0			0
$181$	734.395	+	533.569i	0.301586	+	0.219115i	0.728278	−	0.685282i	$-0.240321\pi$
$181$	734.395	+	533.569i	0.301586	+	0.219115i	−0.426692	+	0.904397i	$0.640321\pi$
$182$		0			0
$183$	−439.651	+	1353.11i	−0.177595	+	0.546583i
$184$		0			0
$185$	−1318.68	+	958.079i	−0.524062	+	0.380753i
$186$		0			0
$187$	2132.14	+	2171.42i	0.833785	+	0.849143i
$188$		0			0
$189$	−459.279	+	333.686i	−0.176760	+	0.128424i
$190$		0			0
$191$	516.342	−	1589.14i	0.195608	−	0.602021i	−0.804361	−	0.594141i	$-0.797492\pi$
$191$	516.342	−	1589.14i	0.195608	−	0.602021i	0.999969	−	0.00787928i	$-0.00250808\pi$
$192$		0			0
$193$	−1950.48	−	1417.11i	−0.727455	−	0.528527i	0.161302	−	0.986905i	$-0.448431\pi$
$193$	−1950.48	−	1417.11i	−0.727455	−	0.528527i	−0.888757	+	0.458378i	$0.848431\pi$
$194$		0			0
$195$	−1387.09	−	4269.01i	−0.509391	−	1.56775i
$196$		0			0
$197$	1966.58			0.711234			0.355617	−	0.934632i	$-0.384271\pi$
$197$	1966.58			0.711234			0.355617	+	0.934632i	$0.384271\pi$
$198$		0			0
$199$	−136.896			−0.0487653			−0.0243827	−	0.999703i	$-0.507762\pi$
$199$	−136.896			−0.0487653			−0.0243827	+	0.999703i	$0.507762\pi$
$200$		0			0
$201$	−1082.99	−	3333.12i	−0.380043	−	1.16965i
$202$		0			0
$203$	465.788	+	338.414i	0.161044	+	0.117005i
$204$		0			0
$205$	−2364.58	+	7277.44i	−0.805608	+	2.47941i
$206$		0			0
$207$	318.997	−	231.765i	0.107110	−	0.0778202i
$208$		0			0
$209$	−267.510	−	1794.85i	−0.0885360	−	0.594031i
$210$		0			0
$211$	−732.412	+	532.129i	−0.238964	+	0.173617i	−0.700821	−	0.713337i	$-0.747183\pi$
$211$	−732.412	+	532.129i	−0.238964	+	0.173617i	0.461858	+	0.886954i	$0.347183\pi$
$212$		0			0
$213$	−880.639	+	2710.33i	−0.283288	+	0.871871i
$214$		0			0
$215$	−4716.91	−	3427.04i	−1.49624	−	1.08708i
$216$		0			0
$217$	−232.261	−	714.824i	−0.0726584	−	0.223620i
$218$		0			0
$219$	−5122.44			−1.58056
$220$		0			0
$221$	5226.36			1.59078
$222$		0			0
$223$	338.973	+	1043.25i	0.101791	+	0.313280i	0.988964	−	0.148157i	$-0.0473341\pi$
$223$	338.973	+	1043.25i	0.101791	+	0.313280i	−0.887173	+	0.461437i	$0.847334\pi$
$224$		0			0
$225$	1223.07	+	888.614i	0.362392	+	0.263293i
$226$		0			0
$227$	1053.66	−	3242.85i	0.308080	−	0.948173i	−0.670430	−	0.741973i	$-0.733890\pi$
$227$	1053.66	−	3242.85i	0.308080	−	0.948173i	0.978510	−	0.206200i	$-0.0661097\pi$
$228$		0			0
$229$	−4478.03	+	3253.48i	−1.29221	+	0.938846i	−0.999848	−	0.0174614i	$-0.994442\pi$
$229$	−4478.03	+	3253.48i	−1.29221	+	0.938846i	−0.292363	+	0.956307i	$0.594442\pi$
$230$		0			0
$231$	−563.802	−	94.5795i	−0.160586	−	0.0269389i
$232$		0			0
$233$	−193.071	+	140.274i	−0.0542854	+	0.0394407i	−0.614597	−	0.788841i	$-0.710681\pi$
$233$	−193.071	+	140.274i	−0.0542854	+	0.0394407i	0.560312	+	0.828282i	$0.310681\pi$
$234$		0			0
$235$	−2060.61	+	6341.90i	−0.571997	+	1.76042i
$236$		0			0
$237$	−3657.02	−	2656.98i	−1.00232	−	0.728225i
$238$		0			0
$239$	−8.27965	−	25.4821i	−0.00224086	−	0.00689667i	0.949930	−	0.312463i	$-0.101154\pi$
$239$	−8.27965	−	25.4821i	−0.00224086	−	0.00689667i	−0.952171	+	0.305567i	$0.901154\pi$
$240$		0			0
$241$	−440.617			−0.117770			−0.0588851	−	0.998265i	$-0.518755\pi$
$241$	−440.617			−0.117770			−0.0588851	+	0.998265i	$0.518755\pi$
$242$		0			0
$243$	2459.93			0.649402
$244$		0			0
$245$	−1728.73	−	5320.48i	−0.450794	−	1.38740i
$246$		0			0
$247$	−2521.30	−	1831.83i	−0.649501	−	0.471890i
$248$		0			0
$249$	105.372	−	324.303i	0.0268181	−	0.0825376i
$250$		0			0
$251$	858.998	−	624.099i	0.216014	−	0.156943i	−0.474517	−	0.880247i	$-0.657377\pi$
$251$	858.998	−	624.099i	0.216014	−	0.156943i	0.690531	+	0.723303i	$0.257377\pi$
$252$		0			0
$253$	1537.24	+	257.877i	0.381997	+	0.0640813i
$254$		0			0
$255$	4834.64	−	3512.57i	1.18728	−	0.862610i
$256$		0			0
$257$	845.449	−	2602.03i	0.205205	−	0.631556i	−0.794500	−	0.607264i	$-0.792267\pi$
$257$	845.449	−	2602.03i	0.205205	−	0.631556i	0.999705	−	0.0242918i	$-0.00773307\pi$
$258$		0			0
$259$	288.430	+	209.557i	0.0691975	+	0.0502749i
$260$		0			0
$261$	−441.730	−	1359.50i	−0.104760	−	0.322418i
$262$		0			0
$263$	−165.974			−0.0389140			−0.0194570	−	0.999811i	$-0.506194\pi$
$263$	−165.974			−0.0389140			−0.0194570	+	0.999811i	$0.506194\pi$
$264$		0			0
$265$	−3274.55			−0.759072
$266$		0			0
$267$	−40.3653	−	124.232i	−0.00925213	−	0.0284751i
$268$		0			0
$269$	1679.93	+	1220.54i	0.380770	+	0.276645i	0.761663	−	0.647974i	$-0.224383\pi$
$269$	1679.93	+	1220.54i	0.380770	+	0.276645i	−0.380893	+	0.924619i	$0.624383\pi$
$270$		0			0
$271$	−2603.52	+	8012.80i	−0.583588	+	1.79610i	0.0212804	+	0.999774i	$0.493226\pi$
$271$	−2603.52	+	8012.80i	−0.583588	+	1.79610i	−0.604868	+	0.796326i	$0.706774\pi$
$272$		0			0
$273$	−794.289	+	577.085i	−0.176090	+	0.127937i
$274$		0			0
$275$	880.994	+	5911.01i	0.193185	+	1.29617i
$276$		0			0
$277$	−1947.27	+	1414.78i	−0.422384	+	0.306880i	−0.778596	−	0.627525i	$-0.784068\pi$
$277$	−1947.27	+	1414.78i	−0.422384	+	0.306880i	0.356213	+	0.934405i	$0.384068\pi$
$278$		0			0
$279$	−576.659	+	1774.77i	−0.123741	+	0.380835i
$280$		0			0
$281$	−2707.68	−	1967.25i	−0.574828	−	0.417637i	0.262028	−	0.965060i	$-0.415609\pi$
$281$	−2707.68	−	1967.25i	−0.574828	−	0.417637i	−0.836856	+	0.547423i	$0.815609\pi$
$282$		0			0
$283$	−1480.10	−	4555.27i	−0.310893	−	0.956830i	−0.977412	−	0.211342i	$-0.932217\pi$
$283$	−1480.10	−	4555.27i	−0.310893	−	0.956830i	0.666519	−	0.745488i	$-0.267783\pi$
$284$		0			0
$285$	−3563.48			−0.740640
$286$		0			0
$287$	1673.68			0.344230
$288$		0			0
$289$	631.938	+	1944.90i	0.128626	+	0.395869i
$290$		0			0
$291$	−310.831	−	225.832i	−0.0626159	−	0.0454931i
$292$		0			0
$293$	−948.897	+	2920.41i	−0.189199	+	0.582293i	−0.999995	−	0.00303441i	$-0.999034\pi$
$293$	−948.897	+	2920.41i	−0.189199	+	0.582293i	0.810797	+	0.585328i	$0.199034\pi$
$294$		0			0
$295$	−7283.66	+	5291.89i	−1.43753	+	1.04443i
$296$		0			0
$297$	3903.79	+	3975.70i	0.762697	+	0.776746i
$298$		0			0
$299$	2165.68	−	1573.46i	0.418877	−	0.304332i
$300$		0			0
$301$	−394.078	+	1212.85i	−0.0754627	+	0.232250i
$302$		0			0
$303$	4105.66	+	2982.93i	0.778429	+	0.565562i
$304$		0			0
$305$	−1772.39	−	5454.85i	−0.332743	−	1.02408i
$306$		0			0
$307$	−9278.28			−1.72488			−0.862442	−	0.506156i	$-0.831066\pi$
$307$	−9278.28			−1.72488			−0.862442	+	0.506156i	$0.831066\pi$
$308$		0			0
$309$	3516.80			0.647455
$310$		0			0
$311$	−2152.99	−	6626.22i	−0.392556	−	1.20816i	−0.930849	−	0.365405i	$-0.880931\pi$
$311$	−2152.99	−	6626.22i	−0.392556	−	1.20816i	0.538293	−	0.842758i	$-0.319069\pi$
$312$		0			0
$313$	4325.63	+	3142.75i	0.781147	+	0.567536i	0.905323	−	0.424724i	$-0.139629\pi$
$313$	4325.63	+	3142.75i	0.781147	+	0.567536i	−0.124176	+	0.992260i	$0.539629\pi$
$314$		0			0
$315$	180.155	−	554.461i	0.0322241	−	0.0991756i
$316$		0			0
$317$	−6487.01	+	4713.09i	−1.14936	+	0.835058i	−0.988396	−	0.151902i	$-0.951460\pi$
$317$	−6487.01	+	4713.09i	−1.14936	+	0.835058i	−0.160963	+	0.986960i	$0.551460\pi$
$318$		0			0
$319$	2611.27	−	5011.31i	0.458316	−	0.879559i
$320$		0			0
$321$	1368.50	−	994.270i	0.237950	−	0.172881i
$322$		0			0
$323$	1282.14	−	3946.01i	0.220867	−	0.679759i
$324$		0			0
$325$	8303.45	+	6032.81i	1.41721	+	1.02966i
$326$		0			0
$327$	−1557.35	−	4793.02i	−0.263368	−	0.810564i
$328$		0			0
$329$	1458.52			0.244410
$330$		0			0
$331$	6738.30			1.11894			0.559472	−	0.828849i	$-0.311004\pi$
$331$	6738.30			1.11894			0.559472	+	0.828849i	$0.311004\pi$
$332$		0			0
$333$	−273.532	−	841.846i	−0.0450135	−	0.138537i
$334$		0			0
$335$	11430.1	+	8304.49i	1.86417	+	1.35440i
$336$		0			0
$337$	1854.56	−	5707.74i	0.299775	−	0.922612i	−0.681801	−	0.731538i	$-0.738803\pi$
$337$	1854.56	−	5707.74i	0.299775	−	0.922612i	0.981576	−	0.191074i	$-0.0611971\pi$
$338$		0			0
$339$	−2971.12	+	2158.65i	−0.476015	+	0.345845i
$340$		0			0
$341$	−6603.18	+	3288.93i	−1.04863	+	0.522304i
$342$		0			0
$343$	−2021.40	+	1468.63i	−0.318208	+	0.231191i
$344$		0			0
$345$	945.856	−	2911.05i	0.147603	−	0.454277i
$346$		0			0
$347$	−5631.84	−	4091.77i	−0.871277	−	0.633020i	0.0596522	−	0.998219i	$-0.481001\pi$
$347$	−5631.84	−	4091.77i	−0.871277	−	0.633020i	−0.930929	+	0.365199i	$0.881001\pi$
$348$		0			0
$349$	71.3186	+	219.496i	0.0109387	+	0.0336658i	0.956377	−	0.292136i	$-0.0943659\pi$
$349$	71.3186	+	219.496i	0.0109387	+	0.0336658i	−0.945438	+	0.325801i	$0.894366\pi$
$350$		0			0
$351$	9569.06			1.45515
$352$		0			0
$353$	6730.46			1.01481			0.507403	−	0.861709i	$-0.330606\pi$
$353$	6730.46			1.01481			0.507403	+	0.861709i	$0.330606\pi$
$354$		0			0
$355$	−3550.16	−	10926.3i	−0.530769	−	1.63354i
$356$		0			0
$357$	−1057.46	−	768.289i	−0.156769	−	0.113900i
$358$		0			0
$359$	−246.333	+	758.137i	−0.0362144	+	0.111457i	−0.967530	−	0.252758i	$-0.918662\pi$
$359$	−246.333	+	758.137i	−0.0362144	+	0.111457i	0.931315	+	0.364214i	$0.118662\pi$
$360$		0			0
$361$	3547.44	−	2577.37i	0.517195	−	0.375764i
$362$		0			0
$363$	−102.405	+	5610.00i	−0.0148068	+	0.811153i
$364$		0			0
$365$	16706.5	−	12138.0i	2.39577	−	1.74063i
$366$		0			0
$367$	3306.07	−	10175.0i	0.470233	−	1.44723i	−0.382048	−	0.924143i	$-0.624781\pi$
$367$	3306.07	−	10175.0i	0.470233	−	1.44723i	0.852281	−	0.523085i	$-0.175219\pi$
$368$		0			0
$369$	−3361.81	−	2442.50i	−0.474279	−	0.344584i
$370$		0			0
$371$	221.327	+	681.173i	0.0309723	+	0.0953228i
$372$		0			0
$373$	−748.042			−0.103839			−0.0519197	−	0.998651i	$-0.516534\pi$
$373$	−748.042			−0.103839			−0.0519197	+	0.998651i	$0.516534\pi$
$374$		0			0
$375$	2780.50			0.382891
$376$		0			0
$377$	−2998.91	−	9229.69i	−0.409686	−	1.26088i
$378$		0			0
$379$	7285.94	+	5293.55i	0.987477	+	0.717444i	0.959367	−	0.282161i	$-0.0910512\pi$
$379$	7285.94	+	5293.55i	0.987477	+	0.717444i	0.0281097	+	0.999605i	$0.491051\pi$
$380$		0			0
$381$	−1127.06	+	3468.73i	−0.151551	+	0.466427i
$382$		0			0
$383$	−5460.78	+	3967.49i	−0.728545	+	0.529319i	−0.889103	−	0.457708i	$-0.848671\pi$
$383$	−5460.78	+	3967.49i	−0.728545	+	0.529319i	0.160558	+	0.987026i	$0.448671\pi$
$384$		0			0
$385$	2062.91	−	1027.50i	0.273080	−	0.136016i
$386$		0			0
$387$	2561.54	−	1861.07i	0.336461	−	0.244453i
$388$		0			0
$389$	−3363.63	+	10352.2i	−0.438413	+	1.34930i	0.451136	+	0.892455i	$0.351019\pi$
$389$	−3363.63	+	10352.2i	−0.438413	+	1.34930i	−0.889548	+	0.456841i	$0.848981\pi$
$390$		0			0
$391$	2883.22	+	2094.78i	0.372918	+	0.270941i
$392$		0			0
$393$	−3385.09	−	10418.2i	−0.434492	−	1.33723i
$394$		0			0
$395$	18223.0			2.32126
$396$		0			0
$397$	−2715.71			−0.343318			−0.171659	−	0.985156i	$-0.554913\pi$
$397$	−2715.71			−0.343318			−0.171659	+	0.985156i	$0.554913\pi$
$398$		0			0
$399$	240.855	+	741.277i	0.0302202	+	0.0930082i
$400$		0			0
$401$	−279.955	−	203.399i	−0.0348636	−	0.0253299i	0.570217	−	0.821494i	$-0.306859\pi$
$401$	−279.955	−	203.399i	−0.0348636	−	0.0253299i	−0.605081	+	0.796164i	$0.706859\pi$
$402$		0			0
$403$	−3914.95	+	12049.0i	−0.483914	+	1.48933i
$404$		0			0
$405$	5425.91	−	3942.16i	0.665718	−	0.483673i
$406$		0			0
$407$	1616.98	−	3103.15i	0.196930	−	0.377930i
$408$		0			0
$409$	−3753.25	+	2726.90i	−0.453756	+	0.329673i	−0.791077	−	0.611716i	$-0.790479\pi$
$409$	−3753.25	+	2726.90i	−0.453756	+	0.329673i	0.337321	+	0.941390i	$0.390479\pi$
$410$		0			0
$411$	−1100.28	+	3386.30i	−0.132050	+	0.406409i
$412$		0			0
$413$	1593.12	+	1157.47i	0.189812	+	0.137907i
$414$		0			0
$415$	424.793	+	1307.38i	0.0502464	+	0.154643i
$416$		0			0
$417$	−5259.83			−0.617686
$418$		0			0
$419$	−4439.38			−0.517609			−0.258804	−	0.965930i	$-0.583328\pi$
$419$	−4439.38			−0.517609			−0.258804	+	0.965930i	$0.583328\pi$
$420$		0			0
$421$	4358.13	+	13412.9i	0.504518	+	1.55275i	0.801579	+	0.597889i	$0.203994\pi$
$421$	4358.13	+	13412.9i	0.504518	+	1.55275i	−0.297060	+	0.954859i	$0.596006\pi$
$422$		0			0
$423$	−2929.64	−	2128.51i	−0.336747	−	0.244661i
$424$		0			0
$425$	−4222.49	+	12995.5i	−0.481931	+	1.48323i
$426$		0			0
$427$	−1014.92	+	737.385i	−0.115025	+	0.0835704i
$428$		0			0
$429$	6751.31	+	6875.68i	0.759805	+	0.773802i
$430$		0			0
$431$	−10016.6	+	7277.51i	−1.11945	+	0.813330i	−0.984126	−	0.177471i	$-0.943209\pi$
$431$	−10016.6	+	7277.51i	−1.11945	+	0.813330i	−0.135327	+	0.990801i	$0.543209\pi$
$432$		0			0
$433$	1908.49	−	5873.72i	0.211815	−	0.651901i	−0.787549	−	0.616252i	$-0.788650\pi$
$433$	1908.49	−	5873.72i	0.211815	−	0.651901i	0.999364	−	0.0356488i	$-0.0113498\pi$
$434$		0			0
$435$	−8977.29	−	6522.38i	−0.989490	−	0.718906i
$436$		0			0
$437$	−656.706	−	2021.13i	−0.0718868	−	0.221245i
$438$		0			0
$439$	−6768.55			−0.735867			−0.367933	−	0.929852i	$-0.619935\pi$
$439$	−6768.55			−0.735867			−0.367933	+	0.929852i	$0.619935\pi$
$440$		0			0
$441$	3038.00			0.328043
$442$		0			0
$443$	425.088	+	1308.29i	0.0455904	+	0.140313i	0.971261	−	0.238019i	$-0.0764980\pi$
$443$	425.088	+	1308.29i	0.0455904	+	0.140313i	−0.925670	+	0.378331i	$0.876498\pi$
$444$		0			0
$445$	426.024	+	309.524i	0.0453831	+	0.0329727i
$446$		0			0
$447$	−422.589	+	1300.60i	−0.0447154	+	0.137620i
$448$		0			0
$449$	712.335	−	517.542i	0.0748712	−	0.0543971i	−0.549720	−	0.835349i	$-0.685266\pi$
$449$	712.335	−	517.542i	0.0748712	−	0.0543971i	0.624591	+	0.780952i	$0.285266\pi$
$450$		0			0
$451$	−2421.56	−	16247.4i	−0.252831	−	1.69636i
$452$		0			0
$453$	−6275.43	+	4559.37i	−0.650873	+	0.472887i
$454$		0			0
$455$	1223.08	−	3764.24i	0.126019	−	0.387847i
$456$		0			0
$457$	−7593.09	−	5516.70i	−0.777221	−	0.564684i	0.126923	−	0.991913i	$-0.459490\pi$
$457$	−7593.09	−	5516.70i	−0.777221	−	0.564684i	−0.904144	+	0.427229i	$0.859490\pi$
$458$		0			0
$459$	3936.74	+	12116.0i	0.400330	+	1.23209i
$460$		0			0
$461$	−14837.4			−1.49902			−0.749508	−	0.661996i	$-0.769710\pi$
$461$	−14837.4			−1.49902			−0.749508	+	0.661996i	$0.769710\pi$
$462$		0			0
$463$	−8010.57			−0.804067			−0.402033	−	0.915625i	$-0.631696\pi$
$463$	−8010.57			−0.804067			−0.402033	+	0.915625i	$0.631696\pi$
$464$		0			0
$465$	4476.44	+	13777.1i	0.446430	+	1.37397i
$466$		0			0
$467$	−4635.28	−	3367.73i	−0.459305	−	0.333704i	0.333954	−	0.942589i	$-0.391617\pi$
$467$	−4635.28	−	3367.73i	−0.459305	−	0.333704i	−0.793258	+	0.608885i	$0.791617\pi$
$468$		0			0
$469$	954.940	−	2939.00i	0.0940193	−	0.289362i
$470$		0			0
$471$	8836.01	−	6419.74i	0.864420	−	0.628038i
$472$		0			0
$473$	12344.0	+	2070.74i	1.19995	+	0.201296i
$474$		0			0
$475$	6591.92	−	4789.31i	0.636754	−	0.462629i
$476$		0			0
$477$	549.513	−	1691.23i	0.0527473	−	0.162339i
$478$		0			0
$479$	6818.88	+	4954.21i	0.650444	+	0.472575i	0.863422	−	0.504482i	$-0.168316\pi$
$479$	6818.88	+	4954.21i	0.650444	+	0.472575i	−0.212978	+	0.977057i	$0.568316\pi$
$480$		0			0
$481$	−1857.01	−	5715.30i	−0.176034	−	0.541778i
$482$		0			0
$483$	−669.487			−0.0630698
$484$		0			0
$485$	1548.87			0.145012
$486$		0			0
$487$	−545.237	−	1678.07i	−0.0507332	−	0.156141i	0.922480	−	0.386044i	$-0.126159\pi$
$487$	−545.237	−	1678.07i	−0.0507332	−	0.156141i	−0.973213	+	0.229904i	$0.926159\pi$
$488$		0			0
$489$	10035.1	+	7290.90i	0.928018	+	0.674245i
$490$		0			0
$491$	1604.32	−	4937.60i	0.147458	−	0.453830i	−0.849861	−	0.527008i	$-0.823314\pi$
$491$	1604.32	−	4937.60i	0.147458	−	0.453830i	0.997319	+	0.0731775i	$0.0233139\pi$
$492$		0			0
$493$	10452.6	−	7594.24i	0.954889	−	0.693767i
$494$		0			0
$495$	−5643.13	−	946.654i	−0.512404	−	0.0859574i
$496$		0			0
$497$	−2032.93	+	1477.01i	−0.183480	+	0.133306i
$498$		0			0
$499$	−1406.92	+	4330.05i	−0.126217	+	0.388456i	−0.994121	−	0.108276i	$-0.965467\pi$
$499$	−1406.92	+	4330.05i	−0.126217	+	0.388456i	0.867904	+	0.496732i	$0.165467\pi$
$500$		0			0
$501$	−6463.82	−	4696.24i	−0.576412	−	0.418787i
$502$		0			0
$503$	−1848.60	−	5689.40i	−0.163867	−	0.504330i	0.835084	−	0.550122i	$-0.185419\pi$
$503$	−1848.60	−	5689.40i	−0.163867	−	0.504330i	−0.998951	+	0.0457921i	$0.985419\pi$
$504$		0			0
$505$	−20458.6			−1.80276
$506$		0			0
$507$	7287.36			0.638349
$508$		0			0
$509$	−4576.25	−	14084.2i	−0.398504	−	1.22647i	−0.926199	−	0.377035i	$-0.876944\pi$
$509$	−4576.25	−	14084.2i	−0.398504	−	1.22647i	0.527695	−	0.849434i	$-0.323056\pi$
$510$		0			0
$511$	−3654.14	−	2654.89i	−0.316339	−	0.229834i
$512$		0			0
$513$	2347.50	−	7224.85i	0.202036	−	0.621803i
$514$		0			0
$515$	−11469.8	+	8333.28i	−0.981395	+	0.713025i
$516$		0			0
$517$	−2110.25	−	14158.7i	−0.179514	−	1.20445i
$518$		0			0
$519$	−6932.15	+	5036.50i	−0.586296	+	0.425969i
$520$		0			0
$521$	−4348.29	+	13382.7i	−0.365647	+	1.12535i	0.583928	+	0.811806i	$0.301515\pi$
$521$	−4348.29	+	13382.7i	−0.365647	+	1.12535i	−0.949575	+	0.313541i	$0.898485\pi$
$522$		0			0
$523$	6521.51	+	4738.15i	0.545250	+	0.396147i	0.826031	−	0.563625i	$-0.190594\pi$
$523$	6521.51	+	4738.15i	0.545250	+	0.396147i	−0.280781	+	0.959772i	$0.590594\pi$
$524$		0			0
$525$	−793.213	−	2441.26i	−0.0659403	−	0.202943i
$526$		0			0
$527$	−16866.6			−1.39416
$528$		0			0
$529$	−10341.6			−0.849972
$530$		0			0
$531$	−1510.84	−	4649.88i	−0.123474	−	0.380014i
$532$		0			0
$533$	−22823.4	−	16582.2i	−1.85477	−	1.34757i
$534$		0			0
$535$	−2107.26	+	6485.48i	−0.170289	+	0.524097i
$536$		0			0
$537$	−6734.98	+	4893.25i	−0.541222	+	0.393221i
$538$		0			0
$539$	8414.18	+	8569.17i	0.672401	+	0.684787i
$540$		0			0
$541$	−1873.12	+	1360.90i	−0.148857	+	0.108151i	−0.659721	−	0.751510i	$-0.729326\pi$
$541$	−1873.12	+	1360.90i	−0.148857	+	0.108151i	0.510864	+	0.859662i	$0.329326\pi$
$542$		0			0
$543$	−1182.53	+	3639.45i	−0.0934569	+	0.287631i
$544$		0			0
$545$	16436.5	+	11941.8i	1.29186	+	0.938592i
$546$		0			0
$547$	3071.91	+	9454.38i	0.240120	+	0.739013i	0.996401	+	0.0847660i	$0.0270143\pi$
$547$	3071.91	+	9454.38i	0.240120	+	0.739013i	−0.756281	+	0.654247i	$0.772986\pi$
$548$		0			0
$549$	3114.73			0.242137
$550$		0			0
$551$	−7704.31			−0.595671
$552$		0			0
$553$	−1231.69	−	3790.75i	−0.0947140	−	0.291500i
$554$		0			0
$555$	−5559.01	−	4038.86i	−0.425165	−	0.308901i
$556$		0			0
$557$	−2116.69	+	6514.50i	−0.161018	+	0.495563i	−0.998721	−	0.0505638i	$-0.983898\pi$
$557$	−2116.69	+	6514.50i	−0.161018	+	0.495563i	0.837703	+	0.546126i	$0.183898\pi$
$558$		0			0
$559$	17390.3	−	12634.8i	1.31580	−	0.955985i
$560$		0			0
$561$	−5928.25	+	11377.0i	−0.446151	+	0.856214i
$562$		0			0
$563$	−19117.2	+	13889.5i	−1.43107	+	1.03974i	−0.441260	+	0.897379i	$0.645468\pi$
$563$	−19117.2	+	13889.5i	−1.43107	+	1.03974i	−0.989815	+	0.142357i	$0.954532\pi$
$564$		0			0
$565$	4575.05	−	14080.5i	0.340661	−	1.04845i
$566$		0			0
$567$	−1186.79	−	862.251i	−0.0879018	−	0.0638644i
$568$		0			0
$569$	8055.13	+	24791.1i	0.593477	+	1.82654i	0.562164	+	0.827026i	$0.309969\pi$
$569$	8055.13	+	24791.1i	0.593477	+	1.82654i	0.0313131	+	0.999510i	$0.490031\pi$
$570$		0			0
$571$	10583.8			0.775688			0.387844	−	0.921725i	$-0.373220\pi$
$571$	10583.8			0.775688			0.387844	+	0.921725i	$0.373220\pi$
$572$		0			0
$573$	7043.88			0.513547
$574$		0			0
$575$	2162.74	+	6656.24i	0.156857	+	0.482755i
$576$		0			0
$577$	−8646.18	−	6281.82i	−0.623822	−	0.453233i	0.230433	−	0.973088i	$-0.425986\pi$
$577$	−8646.18	−	6281.82i	−0.623822	−	0.453233i	−0.854254	+	0.519855i	$0.825986\pi$
$578$		0			0
$579$	3140.68	−	9666.02i	0.225427	−	0.693793i
$580$		0			0
$581$	243.250	−	176.731i	0.0173695	−	0.0126197i
$582$		0			0
$583$	6292.33	−	3134.10i	0.447001	−	0.222644i
$584$		0			0
$585$	−7950.10	+	5776.08i	−0.561874	+	0.408225i
$586$		0			0
$587$	2908.07	−	8950.13i	0.204479	−	0.629321i	−0.795256	−	0.606274i	$-0.792663\pi$
$587$	2908.07	−	8950.13i	0.204479	−	0.629321i	0.999734	−	0.0230465i	$-0.00733658\pi$
$588$		0			0
$589$	8136.81	+	5911.74i	0.569221	+	0.413564i
$590$		0			0
$591$	2561.83	+	7884.51i	0.178308	+	0.548774i
$592$		0			0
$593$	21740.9			1.50555			0.752776	−	0.658277i	$-0.228714\pi$
$593$	21740.9			1.50555			0.752776	+	0.658277i	$0.228714\pi$
$594$		0			0
$595$	5269.34			0.363062
$596$		0			0
$597$	−178.332	−	548.850i	−0.0122255	−	0.0376264i
$598$		0			0
$599$	794.385	+	577.154i	0.0541864	+	0.0393687i	0.614549	−	0.788879i	$-0.289338\pi$
$599$	794.385	+	577.154i	0.0541864	+	0.0393687i	−0.560362	+	0.828248i	$0.689338\pi$
$600$		0			0
$601$	−2222.06	+	6838.80i	−0.150815	+	0.464161i	−0.997713	−	0.0675949i	$-0.978467\pi$
$601$	−2222.06	+	6838.80i	−0.150815	+	0.464161i	0.846898	+	0.531756i	$0.178467\pi$
$602$		0			0
$603$	−6207.19	+	4509.79i	−0.419198	+	0.304565i
$604$		0			0
$605$	−12959.3	−	18539.3i	−0.870859	−	1.24583i
$606$		0			0
$607$	11261.9	−	8182.23i	0.753057	−	0.547128i	−0.143716	−	0.989619i	$-0.545905\pi$
$607$	11261.9	−	8182.23i	0.753057	−	0.547128i	0.896773	+	0.442491i	$0.145905\pi$
$608$		0			0
$609$	−750.014	+	2308.31i	−0.0499050	+	0.153592i
$610$		0			0
$611$	−19889.3	−	14450.5i	−1.31692	−	0.956797i
$612$		0			0
$613$	8192.67	+	25214.4i	0.539802	+	1.66134i	0.733038	+	0.680188i	$0.238102\pi$
$613$	8192.67	+	25214.4i	0.539802	+	1.66134i	−0.193236	+	0.981152i	$0.561898\pi$
$614$		0			0
$615$	−32257.4			−2.11503
$616$		0			0
$617$	808.541			0.0527563			0.0263782	−	0.999652i	$-0.491603\pi$
$617$	808.541			0.0527563			0.0263782	+	0.999652i	$0.491603\pi$
$618$		0			0
$619$	1530.60	+	4710.72i	0.0993864	+	0.305880i	0.988372	−	0.152055i	$-0.0485892\pi$
$619$	1530.60	+	4710.72i	0.0993864	+	0.305880i	−0.888986	+	0.457935i	$0.848589\pi$
$620$		0			0
$621$	5278.96	+	3835.39i	0.341123	+	0.247840i
$622$		0			0
$623$	35.5925	−	109.542i	0.00228890	−	0.00704450i
$624$		0			0
$625$	7497.38	−	5447.17i	0.479832	−	0.348619i
$626$		0			0
$627$	6847.53	−	3410.64i	0.436147	−	0.217237i
$628$		0			0
$629$	6472.55	−	4702.58i	0.410298	−	0.298099i
$630$		0			0
$631$	3789.00	−	11661.3i	0.239045	−	0.735706i	−0.757513	−	0.652820i	$-0.773586\pi$
$631$	3789.00	−	11661.3i	0.239045	−	0.735706i	0.996559	−	0.0828869i	$-0.0264140\pi$
$632$		0			0
$633$	−3087.54	−	2243.23i	−0.193868	−	0.140854i
$634$		0			0
$635$	−4543.57	−	13983.7i	−0.283946	−	0.873897i
$636$		0			0
$637$	20625.0			1.28288
$638$		0			0
$639$	6238.91			0.386240
$640$		0			0
$641$	3083.17	+	9489.02i	0.189981	+	0.584702i	0.999999	−	0.00170413i	$-0.000542441\pi$
$641$	3083.17	+	9489.02i	0.189981	+	0.584702i	−0.810017	+	0.586406i	$0.800542\pi$
$642$		0			0
$643$	−2639.71	−	1917.86i	−0.161897	−	0.117625i	0.503887	−	0.863770i	$-0.331903\pi$
$643$	−2639.71	−	1917.86i	−0.161897	−	0.117625i	−0.665784	+	0.746144i	$0.731903\pi$
$644$		0			0
$645$	7595.21	−	23375.6i	0.463660	−	1.42700i
$646$		0			0
$647$	20476.9	−	14877.3i	1.24425	−	0.903999i	0.246374	−	0.969175i	$-0.420761\pi$
$647$	20476.9	−	14877.3i	1.24425	−	0.903999i	0.997874	+	0.0651758i	$0.0207608\pi$
$648$		0			0
$649$	8931.26	−	17140.1i	0.540189	−	1.03668i
$650$		0			0
$651$	2563.35	−	1862.38i	0.154325	−	0.112124i
$652$		0			0
$653$	−793.250	+	2441.37i	−0.0475379	+	0.146307i	−0.972008	−	0.234948i	$-0.924508\pi$
$653$	−793.250	+	2441.37i	−0.0475379	+	0.146307i	0.924470	+	0.381255i	$0.124508\pi$
$654$		0			0
$655$	35726.9	+	25957.1i	2.13125	+	1.54844i
$656$		0			0
$657$	3465.40	+	10665.4i	0.205781	+	0.633329i
$658$		0			0
$659$	21712.9			1.28348			0.641742	−	0.766920i	$-0.278212\pi$
$659$	21712.9			1.28348			0.641742	+	0.766920i	$0.278212\pi$
$660$		0			0
$661$	−9544.46			−0.561629			−0.280814	−	0.959762i	$-0.590605\pi$
$661$	−9544.46			−0.561629			−0.280814	+	0.959762i	$0.590605\pi$
$662$		0			0
$663$	6808.30	+	20953.8i	0.398812	+	1.22742i
$664$		0			0
$665$	−2542.04	−	1846.90i	−0.148235	−	0.107699i
$666$		0			0
$667$	2044.96	−	6293.73i	0.118712	−	0.365359i
$668$		0			0
$669$	−3741.09	+	2718.06i	−0.216202	+	0.157080i
$670$		0			0
$671$	8626.67	+	8785.58i	0.496318	+	0.505460i
$672$		0			0
$673$	−18897.8	+	13730.1i	−1.08240	+	0.786411i	−0.978100	−	0.208135i	$-0.933261\pi$
$673$	−18897.8	+	13730.1i	−1.08240	+	0.786411i	−0.104302	+	0.994546i	$0.533261\pi$
$674$		0			0
$675$	−7731.05	+	23793.7i	−0.440842	+	1.35677i
$676$		0			0
$677$	277.971	+	201.958i	0.0157803	+	0.0114651i	0.595647	−	0.803246i	$-0.296896\pi$
$677$	277.971	+	201.958i	0.0157803	+	0.0114651i	−0.579867	+	0.814711i	$0.696896\pi$
$678$		0			0
$679$	−104.688	−	322.198i	−0.00591689	−	0.0182103i
$680$		0			0
$681$	14374.0			0.808828
$682$		0			0
$683$	−1268.81			−0.0710831			−0.0355415	−	0.999368i	$-0.511316\pi$
$683$	−1268.81			−0.0710831			−0.0355415	+	0.999368i	$0.511316\pi$
$684$		0			0
$685$	−4435.60	−	13651.4i	−0.247409	−	0.761448i
$686$		0			0
$687$	−18877.5	−	13715.3i	−1.04836	−	0.761675i
$688$		0			0
$689$	3730.65	−	11481.7i	0.206279	−	0.634862i
$690$		0			0
$691$	5281.83	−	3837.47i	0.290782	−	0.211265i	−0.432825	−	0.901478i	$-0.642483\pi$
$691$	5281.83	−	3837.47i	0.290782	−	0.211265i	0.723607	+	0.690213i	$0.242483\pi$
$692$		0			0
$693$	184.496	+	1237.87i	0.0101132	+	0.0678540i
$694$		0			0
$695$	17154.6	−	12463.5i	0.936273	−	0.680242i
$696$		0			0
$697$	11606.2	−	35720.2i	0.630726	−	1.94117i
$698$		0			0
$699$	−813.905	−	591.337i	−0.0440411	−	0.0319977i
$700$		0			0
$701$	−7743.51	−	23832.1i	−0.417216	−	1.28406i	−0.910254	−	0.414051i	$-0.864113\pi$
$701$	−7743.51	−	23832.1i	−0.417216	−	1.28406i	0.493038	−	0.870008i	$-0.335887\pi$
$702$		0			0
$703$	−4770.74			−0.255949
$704$		0			0
$705$	−28110.6			−1.50171
$706$		0			0
$707$	1382.79	+	4255.80i	0.0735577	+	0.226387i
$708$		0			0
$709$	23680.2	+	17204.7i	1.25434	+	0.911334i	0.998466	−	0.0553756i	$-0.0176356\pi$
$709$	23680.2	+	17204.7i	1.25434	+	0.911334i	0.255877	+	0.966709i	$0.417636\pi$
$710$		0			0
$711$	−3058.06	+	9411.73i	−0.161303	+	0.496438i
$712$		0			0
$713$	−6989.12	+	5077.89i	−0.367103	+	0.266716i
$714$		0			0
$715$	−38311.3	−	6426.84i	−2.00386	−	0.336154i
$716$		0			0
$717$	91.3786	−	66.3904i	0.00475955	−	0.00345801i
$718$		0			0
$719$	−4497.67	+	13842.4i	−0.233289	+	0.717990i	0.764055	+	0.645152i	$0.223206\pi$
$719$	−4497.67	+	13842.4i	−0.233289	+	0.717990i	−0.997344	+	0.0728387i	$0.976794\pi$
$720$		0			0
$721$	2508.73	+	1822.70i	0.129584	+	0.0941483i
$722$		0			0
$723$	−573.985	−	1766.54i	−0.0295252	−	0.0908693i
$724$		0			0
$725$	25372.7			1.29975
$726$		0			0
$727$	−25556.6			−1.30377			−0.651887	−	0.758316i	$-0.726022\pi$
$727$	−25556.6			−1.30377			−0.651887	+	0.758316i	$0.726022\pi$
$728$		0			0
$729$	6497.23	+	19996.4i	0.330094	+	1.01592i
$730$		0			0
$731$	23152.2	+	16821.1i	1.17143	+	0.851095i
$732$		0			0
$733$	−7073.64	+	21770.4i	−0.356441	+	1.09701i	0.598729	+	0.800952i	$0.295673\pi$
$733$	−7073.64	+	21770.4i	−0.356441	+	1.09701i	−0.955170	+	0.296059i	$0.904327\pi$
$734$		0			0
$735$	19079.2	−	13861.8i	0.957476	−	0.695647i
$736$		0			0
$737$	−29912.3	−	5017.88i	−1.49503	−	0.250795i
$738$		0			0
$739$	19150.8	−	13913.9i	0.953282	−	0.692600i	0.00170110	−	0.999999i	$-0.499459\pi$
$739$	19150.8	−	13913.9i	0.953282	−	0.692600i	0.951581	+	0.307399i	$0.0994585\pi$
$740$		0			0
$741$	4059.82	−	12494.8i	0.201270	−	0.619446i
$742$		0			0
$743$	6506.66	+	4727.37i	0.321274	+	0.233419i	0.736719	−	0.676199i	$-0.236374\pi$
$743$	6506.66	+	4727.37i	0.321274	+	0.233419i	−0.415445	+	0.909618i	$0.636374\pi$
$744$		0			0
$745$	−1703.60	−	5243.15i	−0.0837787	−	0.257844i
$746$		0			0
$747$	−746.515			−0.0365643
$748$		0			0
$749$	1491.54			0.0727634
$750$		0			0
$751$	9594.40	+	29528.5i	0.466185	+	1.43477i	0.857487	+	0.514506i	$0.172025\pi$
$751$	9594.40	+	29528.5i	0.466185	+	1.43477i	−0.391302	+	0.920262i	$0.627975\pi$
$752$		0			0
$753$	3621.17	+	2630.94i	0.175249	+	0.127326i
$754$		0			0
$755$	9663.14	−	29740.1i	0.465798	−	1.43358i
$756$		0			0
$757$	−2013.15	+	1462.64i	−0.0966569	+	0.0702253i	−0.635064	−	0.772460i	$-0.719026\pi$
$757$	−2013.15	+	1462.64i	−0.0966569	+	0.0702253i	0.538407	+	0.842685i	$0.319026\pi$
$758$		0			0
$759$	968.645	+	6499.11i	0.0463236	+	0.310807i
$760$		0			0
$761$	12625.9	−	9173.25i	0.601430	−	0.436965i	−0.244956	−	0.969534i	$-0.578774\pi$
$761$	12625.9	−	9173.25i	0.601430	−	0.436965i	0.846386	+	0.532570i	$0.178774\pi$
$762$		0			0
$763$	1373.20	−	4226.28i	0.0651550	−	0.200527i
$764$		0			0
$765$	−10584.2	−	7689.86i	−0.500225	−	0.363435i
$766$		0			0
$767$	−10257.1	−	31568.1i	−0.482871	−	1.48612i
$768$		0			0
$769$	17212.1			0.807129			0.403565	−	0.914951i	$-0.367771\pi$
$769$	17212.1			0.807129			0.403565	+	0.914951i	$0.367771\pi$
$770$		0			0
$771$	11533.5			0.538742
$772$		0			0
$773$	−386.582	−	1189.78i	−0.0179876	−	0.0553601i	0.941660	−	0.336566i	$-0.109266\pi$
$773$	−386.582	−	1189.78i	−0.0179876	−	0.0553601i	−0.959647	+	0.281206i	$0.909266\pi$
$774$		0			0
$775$	−26797.1	−	19469.2i	−1.24204	−	0.902394i
$776$		0			0
$777$	−464.432	+	1429.37i	−0.0214432	+	0.0659955i
$778$		0			0
$779$	−18119.0	+	13164.2i	−0.833349	+	0.605464i
$780$		0			0
$781$	17279.6	+	17597.9i	0.791692	+	0.806275i
$782$		0			0
$783$	19137.9	−	13904.5i	0.873476	−	0.634617i
$784$		0			0
$785$	−13606.0	+	41875.0i	−0.618624	+	1.90393i
$786$		0			0
$787$	−11669.1	−	8478.07i	−0.528535	−	0.384003i	0.291274	−	0.956640i	$-0.405921\pi$
$787$	−11669.1	−	8478.07i	−0.528535	−	0.384003i	−0.819810	+	0.572636i	$0.805921\pi$
$788$		0			0
$789$	−216.211	−	665.430i	−0.00975580	−	0.0300253i
$790$		0			0
$791$	−3238.27			−0.145562
$792$		0			0
$793$	21145.9			0.946927
$794$		0			0
$795$	−4265.71	−	13128.5i	−0.190301	−	0.585685i
$796$		0			0
$797$	1092.84	+	793.998i	0.0485703	+	0.0352884i	0.611806	−	0.791008i	$-0.290444\pi$
$797$	1092.84	+	793.998i	0.0485703	+	0.0352884i	−0.563235	+	0.826297i	$0.690444\pi$
$798$		0			0
$799$	10114.2	−	31128.2i	0.447827	−	1.37827i
$800$		0			0
$801$	−231.354	+	168.089i	−0.0102054	+	0.00741463i
$802$		0			0
$803$	−20485.6	+	39314.1i	−0.900274	+	1.72772i
$804$		0			0
$805$	2183.48	−	1586.39i	0.0955996	−	0.0694572i
$806$		0			0
$807$	−2705.03	+	8325.23i	−0.117995	+	0.363150i
$808$		0			0
$809$	5626.46	+	4087.86i	0.244519	+	0.177653i	0.703294	−	0.710899i	$-0.251712\pi$
$809$	5626.46	+	4087.86i	0.244519	+	0.177653i	−0.458775	+	0.888552i	$0.651712\pi$
$810$		0			0
$811$	5301.42	+	16316.1i	0.229541	+	0.706456i	0.997799	+	0.0663147i	$0.0211241\pi$
$811$	5301.42	+	16316.1i	0.229541	+	0.706456i	−0.768257	+	0.640141i	$0.778876\pi$
$812$		0			0
$813$	−35516.9			−1.53214
$814$		0			0
$815$	−50004.9			−2.14920
$816$		0			0
$817$	−5273.34	−	16229.7i	−0.225815	−	0.694987i
$818$		0			0
$819$	1738.89	+	1263.38i	0.0741902	+	0.0539023i
$820$		0			0
$821$	6697.05	−	20611.4i	0.284688	−	0.876178i	−0.701805	−	0.712370i	$-0.747622\pi$
$821$	6697.05	−	20611.4i	0.284688	−	0.876178i	0.986492	−	0.163809i	$-0.0523780\pi$
$822$		0			0
$823$	6412.00	−	4658.59i	0.271577	−	0.197313i	−0.443658	−	0.896196i	$-0.646319\pi$
$823$	6412.00	−	4658.59i	0.271577	−	0.197313i	0.715235	+	0.698884i	$0.246319\pi$
$824$		0			0
$825$	−22551.1	+	11232.3i	−0.951670	+	0.474011i
$826$		0			0
$827$	−31189.0	+	22660.2i	−1.31143	+	0.952807i	−0.311429	+	0.950269i	$0.600808\pi$
$827$	−31189.0	+	22660.2i	−1.31143	+	0.952807i	−0.999997	+	0.00253737i	$0.999192\pi$
$828$		0			0
$829$	−2050.74	+	6311.54i	−0.0859171	+	0.264426i	−0.984780	−	0.173804i	$-0.944394\pi$
$829$	−2050.74	+	6311.54i	−0.0859171	+	0.264426i	0.898863	+	0.438229i	$0.144394\pi$
$830$		0			0
$831$	−8208.88	−	5964.10i	−0.342675	−	0.248968i
$832$		0			0
$833$	8485.19	+	26114.7i	0.352935	+	1.08622i
$834$		0			0
$835$	32209.3			1.33491
$836$		0			0
$837$	−30881.5			−1.27529
$838$		0			0
$839$	14486.0	+	44583.3i	0.596081	+	1.83455i	0.549270	+	0.835645i	$0.314906\pi$
$839$	14486.0	+	44583.3i	0.596081	+	1.83455i	0.0468105	+	0.998904i	$0.485094\pi$
$840$		0			0
$841$	322.049	+	233.983i	0.0132047	+	0.00959378i
$842$		0			0
$843$	4359.93	−	13418.5i	0.178130	−	0.548229i
$844$		0			0
$845$	−23767.2	+	17267.9i	−0.967593	+	0.702998i
$846$		0			0
$847$	−2980.63	+	3948.86i	−0.120916	+	0.160194i
$848$		0			0
$849$	16335.1	−	11868.2i	0.660330	−	0.479758i
$850$		0			0
$851$	1266.30	−	3897.27i	0.0510085	−	0.156988i
$852$		0			0
$853$	1375.00	+	998.996i	0.0551924	+	0.0400996i	0.615039	−	0.788496i	$-0.289140\pi$
$853$	1375.00	+	998.996i	0.0551924	+	0.0400996i	−0.559847	+	0.828596i	$0.689140\pi$
$854$		0			0
$855$	2410.74	+	7419.50i	0.0964276	+	0.296774i
$856$		0			0
$857$	1506.84			0.0600615			0.0300308	−	0.999549i	$-0.490439\pi$
$857$	1506.84			0.0600615			0.0300308	+	0.999549i	$0.490439\pi$
$858$		0			0
$859$	−11830.1			−0.469892			−0.234946	−	0.972008i	$-0.575491\pi$
$859$	−11830.1			−0.469892			−0.234946	+	0.972008i	$0.575491\pi$
$860$		0			0
$861$	2180.28	+	6710.20i	0.0862992	+	0.265602i
$862$		0			0
$863$	32602.8	+	23687.3i	1.28599	+	0.934330i	0.999716	−	0.0238166i	$-0.00758178\pi$
$863$	32602.8	+	23687.3i	1.28599	+	0.934330i	0.286278	+	0.958146i	$0.407582\pi$
$864$		0			0
$865$	10674.4	−	32852.4i	0.419584	−	1.29135i
$866$		0			0
$867$	−6974.39	+	5067.19i	−0.273198	+	0.198490i
$868$		0			0
$869$	−35017.0	+	17441.4i	−1.36694	+	0.680850i
$870$		0			0
$871$	−42140.7	+	30617.0i	−1.63936	+	1.19107i
$872$		0			0
$873$	−259.922	+	799.956i	−0.0100768	+	0.0310131i
$874$		0			0
$875$	1983.49	+	1441.09i	0.0766333	+	0.0556774i
$876$		0			0
$877$	−3976.31	−	12237.8i	−0.153102	−	0.471200i	0.844862	−	0.534985i	$-0.179683\pi$
$877$	−3976.31	−	12237.8i	−0.153102	−	0.471200i	−0.997964	+	0.0637852i	$0.979683\pi$
$878$		0			0
$879$	−12944.8			−0.496719
$880$		0			0
$881$	−31803.0			−1.21620			−0.608098	−	0.793862i	$-0.708067\pi$
$881$	−31803.0			−1.21620			−0.608098	+	0.793862i	$0.708067\pi$
$882$		0			0
$883$	−10237.6	−	31508.1i	−0.390174	−	1.20083i	−0.932657	−	0.360764i	$-0.882516\pi$
$883$	−10237.6	−	31508.1i	−0.390174	−	1.20083i	0.542484	−	0.840066i	$-0.317484\pi$
$884$		0			0
$885$	−30704.8	−	22308.4i	−1.16625	−	0.847330i
$886$		0			0
$887$	3440.61	−	10589.1i	0.130242	−	0.400843i	−0.864578	−	0.502499i	$-0.832414\pi$
$887$	3440.61	−	10589.1i	0.130242	−	0.400843i	0.994820	+	0.101656i	$0.0324142\pi$
$888$		0			0
$889$	−2601.79	+	1890.31i	−0.0981565	+	0.0713149i
$890$		0			0
$891$	−6653.28	+	12768.4i	−0.250161	+	0.480086i
$892$		0			0
$893$	−15789.7	+	11471.9i	−0.591693	+	0.429890i
$894$		0			0
$895$	10370.8	−	31918.0i	0.387326	−	1.19207i
$896$		0			0
$897$	9129.57	+	6633.02i	0.339830	+	0.246901i
$898$		0			0
$899$	9678.15	+	29786.3i	0.359048	+	1.10504i
$900$		0			0
$901$	16072.6			0.594291
$902$		0			0
$903$	−5375.97			−0.198119
$904$		0			0
$905$	−4767.18	−	14671.9i	−0.175101	−	0.538905i
$906$		0			0
$907$	−12857.6	−	9341.62i	−0.470706	−	0.341988i	0.327010	−	0.945021i	$-0.393959\pi$
$907$	−12857.6	−	9341.62i	−0.470706	−	0.341988i	−0.797717	+	0.603033i	$0.793959\pi$
$908$		0			0
$909$	3433.22	−	10566.4i	0.125272	−	0.385549i
$910$		0			0
$911$	−36053.9	+	26194.7i	−1.31122	+	0.952655i	−0.311220	+	0.950338i	$0.600738\pi$
$911$	−36053.9	+	26194.7i	−1.31122	+	0.952655i	−0.999997	+	0.00231766i	$0.999262\pi$
$912$		0			0
$913$	−2067.58	−	2105.66i	−0.0749473	−	0.0763279i
$914$		0			0
$915$	19561.0	−	14211.9i	0.706739	−	0.513476i
$916$		0			0
$917$	2984.83	−	9186.38i	0.107490	−	0.330819i
$918$		0			0
$919$	13800.7	+	10026.8i	0.495369	+	0.359907i	0.807245	−	0.590216i	$-0.200957\pi$
$919$	13800.7	+	10026.8i	0.495369	+	0.359907i	−0.311876	+	0.950123i	$0.600957\pi$
$920$		0			0
$921$	−12086.7	−	37199.0i	−0.432432	−	1.33089i
$922$		0			0
$923$	42356.1			1.51047
$924$		0			0
$925$	15711.6			0.558479
$926$		0			0
$927$	−2379.16	−	7322.29i	−0.0842953	−	0.259434i
$928$		0			0
$929$	−22236.8	−	16156.0i	−0.785325	−	0.570572i	0.121247	−	0.992622i	$-0.461311\pi$
$929$	−22236.8	−	16156.0i	−0.785325	−	0.570572i	−0.906572	+	0.422050i	$0.861311\pi$
$930$		0			0
$931$	5059.76	−	15572.3i	0.178117	−	0.548188i
$932$		0			0
$933$	23761.5	−	17263.8i	0.833781	−	0.605777i
$934$		0			0
$935$	−7623.92	−	51152.5i	−0.266662	−	1.78916i
$936$		0			0
$937$	1747.29	−	1269.48i	0.0609195	−	0.0442606i	−0.556909	−	0.830574i	$-0.688013\pi$
$937$	1747.29	−	1269.48i	0.0609195	−	0.0442606i	0.617828	+	0.786313i	$0.288013\pi$
$938$		0			0
$939$	−6965.16	+	21436.5i	−0.242065	+	0.745000i
$940$		0			0
$941$	16088.4	+	11688.9i	0.557352	+	0.404940i	0.830489	−	0.557035i	$-0.188061\pi$
$941$	16088.4	+	11688.9i	0.557352	+	0.404940i	−0.273137	+	0.961975i	$0.588061\pi$
$942$		0			0
$943$	−5944.65	−	18295.8i	−0.205286	−	0.631805i
$944$		0			0
$945$	9647.75			0.332107
$946$		0			0
$947$	22957.8			0.787780			0.393890	−	0.919158i	$-0.371129\pi$
$947$	22957.8			0.787780			0.393890	+	0.919158i	$0.371129\pi$
$948$		0			0
$949$	23526.6	+	72407.5i	0.804749	+	2.47676i
$950$		0			0
$951$	−27346.5	−	19868.4i	−0.932461	−	0.677473i
$952$		0			0
$953$	896.033	−	2757.71i	0.0304568	−	0.0937365i	−0.934673	−	0.355510i	$-0.884307\pi$
$953$	896.033	−	2757.71i	0.0304568	−	0.0937365i	0.965129	+	0.261773i	$0.0843073\pi$
$954$		0			0
$955$	−22973.1	+	16690.9i	−0.778422	+	0.565556i
$956$		0			0
$957$	23493.3	+	3941.07i	0.793552	+	0.133121i
$958$		0			0
$959$	−2539.96	+	1845.39i	−0.0855262	+	0.0621384i
$960$		0			0
$961$	3428.48	−	10551.8i	0.115085	−	0.354194i
$962$		0			0
$963$	−2995.97	−	2176.70i	−0.100253	−	0.0728381i
$964$		0			0
$965$	12661.2	+	38967.1i	0.422360	+	1.29989i
$966$		0			0
$967$	33626.4			1.11825			0.559127	−	0.829082i	$-0.311136\pi$
$967$	33626.4			1.11825			0.559127	+	0.829082i	$0.311136\pi$
$968$		0			0
$969$	17490.8			0.579861
$970$		0			0
$971$	−14579.3	−	44870.5i	−0.481846	−	1.48297i	−0.836498	−	0.547970i	$-0.815401\pi$
$971$	−14579.3	−	44870.5i	−0.481846	−	1.48297i	0.354652	−	0.934998i	$-0.384599\pi$
$972$		0			0
$973$	−3752.14	−	2726.09i	−0.123626	−	0.0898196i
$974$		0			0
$975$	−13370.3	+	41149.5i	−0.439171	+	1.35163i
$976$		0			0
$977$	8221.34	−	5973.15i	0.269216	−	0.195597i	−0.444984	−	0.895538i	$-0.646791\pi$
$977$	8221.34	−	5973.15i	0.269216	−	0.195597i	0.714200	+	0.699942i	$0.246791\pi$
$978$		0			0
$979$	−1114.89	−	187.026i	−0.0363963	−	0.00610560i
$980$		0			0
$981$	−8925.94	+	6485.07i	−0.290503	+	0.211063i
$982$		0			0
$983$	12867.2	−	39601.1i	0.417496	−	1.28492i	−0.492502	−	0.870311i	$-0.663918\pi$
$983$	12867.2	−	39601.1i	0.417496	−	1.28492i	0.909999	−	0.414611i	$-0.136082\pi$
$984$		0			0
$985$	−27038.1	−	19644.3i	−0.874625	−	0.635452i
$986$		0			0
$987$	1899.99	+	5847.57i	0.0612740	+	0.188582i
$988$		0			0
$989$	14657.9			0.471278
$990$		0			0
$991$	23893.3			0.765888			0.382944	−	0.923772i	$-0.374910\pi$
$991$	23893.3			0.765888			0.382944	+	0.923772i	$0.374910\pi$
$992$		0			0
$993$	8777.88	+	27015.5i	0.280521	+	0.863355i
$994$		0			0
$995$	1882.15	+	1367.47i	0.0599681	+	0.0435694i
$996$		0			0
$997$	18377.8	−	56561.1i	0.583782	−	1.79670i	−0.0203240	−	0.999793i	$-0.506470\pi$
$997$	18377.8	−	56561.1i	0.583782	−	1.79670i	0.604106	−	0.796904i	$-0.293530\pi$
$998$		0			0
$999$	11850.7	−	8610.07i	0.375316	−	0.272683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.d.113.3		12
4.3	odd	2		44.4.e.a.25.1	✓	12
11.2	odd	10		1936.4.a.bs.1.5		6
11.4	even	5	inner	176.4.m.d.81.3		12
11.9	even	5		1936.4.a.br.1.5		6
12.11	even	2		396.4.j.d.289.3		12
44.15	odd	10		44.4.e.a.37.1	yes	12
44.31	odd	10		484.4.a.i.1.2		6
44.35	even	10		484.4.a.h.1.2		6
132.59	even	10		396.4.j.d.37.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.4.e.a.25.1	✓	12	4.3	odd	2
44.4.e.a.37.1	yes	12	44.15	odd	10
176.4.m.d.81.3		12	11.4	even	5	inner
176.4.m.d.113.3		12	1.1	even	1	trivial
396.4.j.d.37.3		12	132.59	even	10
396.4.j.d.289.3		12	12.11	even	2
484.4.a.h.1.2		6	44.35	even	10
484.4.a.i.1.2		6	44.31	odd	10
1936.4.a.br.1.5		6	11.9	even	5
1936.4.a.bs.1.5		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.30268 + 4.00925i) q^{3} +(-13.7488 - 9.98909i) q^{5} +(-1.14865 + 3.53519i) q^{7} +(7.46635 - 5.42462i) q^{9} +(35.9801 + 6.03578i) q^{11} +(50.6891 - 36.8278i) q^{13} +(22.1384 - 68.1350i) q^{15} +(67.4838 + 49.0299i) q^{17} +(-15.3707 - 47.3060i) q^{19} -15.6698 q^{21} +42.7247 q^{23} +(50.6205 + 155.794i) q^{25} +(123.558 + 89.7700i) q^{27} +(47.8637 - 147.309i) q^{29} +(-163.585 + 118.852i) q^{31} +(22.6718 + 152.116i) q^{33} +(51.1060 - 37.1306i) q^{35} +(29.6386 - 91.2183i) q^{37} +(213.684 + 155.250i) q^{39} +(-139.139 - 428.225i) q^{41} +343.078 q^{43} -156.840 q^{45} +(-121.252 - 373.175i) q^{47} +(266.315 + 193.489i) q^{49} +(-108.663 + 334.430i) q^{51} +(155.884 - 113.257i) q^{53} +(-434.392 - 442.393i) q^{55} +(169.639 - 123.250i) q^{57} +(163.707 - 503.838i) q^{59} +(273.040 + 198.375i) q^{61} +(10.6008 + 32.6260i) q^{63} -1064.79 q^{65} -831.356 q^{67} +(55.6568 + 171.294i) q^{69} +(546.910 + 397.354i) q^{71} +(-375.494 + 1155.65i) q^{73} +(-558.674 + 405.900i) q^{75} +(-62.6663 + 120.264i) q^{77} +(-867.501 + 630.277i) q^{79} +(-121.952 + 375.331i) q^{81} +(-65.4403 - 47.5452i) q^{83} +(-438.058 - 1348.20i) q^{85} +652.951 q^{87} -30.9863 q^{89} +(71.9691 + 221.498i) q^{91} +(-689.606 - 501.028i) q^{93} +(-261.216 + 803.940i) q^{95} +(-73.7338 + 53.5708i) q^{97} +(301.382 - 150.113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 4 q^{5} - 6 q^{7} + 47 q^{9} - 39 q^{11} - 10 q^{13} - 74 q^{15} - 56 q^{17} + 141 q^{19} - 304 q^{21} + 388 q^{23} - 203 q^{25} + 331 q^{27} + 772 q^{29} - 882 q^{31} + 981 q^{33} - 412 q^{35}+ \cdots - 3563 q^{99}+O(q^{100}) \) 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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