LMFDB - Embedded newform 176.4.m.d.81.3

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			81.3
Root			$3.41047 + 2.47785i$ of defining polynomial
Character	$\chi$	$=$	176.81
Dual form			176.4.m.d.113.3

$q$-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 $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

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

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	−0.743944	−	0.668242i	$-0.767047\pi$
$3$	1.30268	−	4.00925i	0.250702	−	0.771581i	0.994646	−	0.103339i	$-0.0329527\pi$
$4$		0			0
$5$	−13.7488	+	9.98909i	−1.22973	+	0.893451i	−0.996870	−	0.0790592i	$-0.974808\pi$
$5$	−13.7488	+	9.98909i	−1.22973	+	0.893451i	−0.232860	+	0.972510i	$0.574808\pi$
$6$		0			0
$7$	−1.14865	−	3.53519i	−0.0620215	−	0.190882i	0.915245	−	0.402898i	$-0.131997\pi$
$7$	−1.14865	−	3.53519i	−0.0620215	−	0.190882i	−0.977266	+	0.212016i	$0.931997\pi$
$8$		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	0.977932	−	0.208922i	$-0.0669955\pi$
$13$	50.6891	+	36.8278i	1.08143	+	0.785707i	0.103501	+	0.994629i	$0.466996\pi$
$14$		0			0
$15$	22.1384	+	68.1350i	0.381074	+	1.17283i
$16$		0			0
$17$	67.4838	−	49.0299i	0.962778	−	0.699499i	0.00898393	−	0.999960i	$-0.497140\pi$
$17$	67.4838	−	49.0299i	0.962778	−	0.699499i	0.953794	+	0.300460i	$0.0971403\pi$
$18$		0			0
$19$	−15.3707	+	47.3060i	−0.185593	+	0.571197i	−0.999958	−	0.00915592i	$-0.997086\pi$
$19$	−15.3707	+	47.3060i	−0.185593	+	0.571197i	0.814365	+	0.580353i	$0.197086\pi$
$20$		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	0.979119	+	0.203288i	$0.0651628\pi$
$29$	47.8637	+	147.309i	0.306485	+	0.943263i	−0.672634	+	0.739975i	$0.734837\pi$
$30$		0			0
$31$	−163.585	−	118.852i	−0.947767	−	0.688593i	0.00251102	−	0.999997i	$-0.499201\pi$
$31$	−163.585	−	118.852i	−0.947767	−	0.688593i	−0.950278	+	0.311404i	$0.899201\pi$
$32$		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	0.995061	−	0.0992690i	$-0.0316504\pi$
$37$	29.6386	+	91.2183i	0.131691	+	0.405303i	−0.863370	+	0.504572i	$0.831650\pi$
$38$		0			0
$39$	213.684	−	155.250i	0.877354	−	0.637435i
$40$		0			0
$41$	−139.139	+	428.225i	−0.529995	+	1.63116i	0.224226	+	0.974537i	$0.428015\pi$
$41$	−139.139	+	428.225i	−0.529995	+	1.63116i	−0.754221	+	0.656620i	$0.771985\pi$
$42$		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	0.566287	+	0.824208i	$0.308379\pi$
$47$	−121.252	+	373.175i	−0.376306	+	1.15815i	−0.942593	+	0.333943i	$0.891621\pi$
$48$		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	0.771171	−	0.636628i	$-0.219671\pi$
$53$	155.884	+	113.257i	0.404007	+	0.293528i	−0.367164	+	0.930156i	$0.619671\pi$
$54$		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	0.952306	+	0.305146i	$0.0987053\pi$
$59$	163.707	+	503.838i	0.361235	+	1.11177i	−0.591071	+	0.806619i	$0.701295\pi$
$60$		0			0
$61$	273.040	−	198.375i	0.573102	−	0.416383i	−0.263129	−	0.964761i	$-0.584754\pi$
$61$	273.040	−	198.375i	0.573102	−	0.416383i	0.836231	+	0.548378i	$0.184754\pi$
$62$		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	−0.0278936	−	0.999611i	$-0.508880\pi$
$71$	546.910	−	397.354i	0.914173	−	0.664186i	0.942067	+	0.335425i	$0.108880\pi$
$72$		0			0
$73$	−375.494	−	1155.65i	−0.602030	−	1.85286i	−0.516043	−	0.856563i	$-0.672596\pi$
$73$	−375.494	−	1155.65i	−0.602030	−	1.85286i	−0.0859871	−	0.996296i	$-0.527404\pi$
$74$		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	−0.238175	−	0.971222i	$-0.576549\pi$
$79$	−867.501	−	630.277i	−1.23546	−	0.897616i	−0.997287	+	0.0736062i	$0.976549\pi$
$80$		0			0
$81$	−121.952	−	375.331i	−0.167287	−	0.514857i
$82$		0			0
$83$	−65.4403	+	47.5452i	−0.0865423	+	0.0628766i	−0.630215	−	0.776421i	$-0.717033\pi$
$83$	−65.4403	+	47.5452i	−0.0865423	+	0.0628766i	0.543673	+	0.839297i	$0.317033\pi$
$84$		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	0.548526	−	0.836134i	$-0.315189\pi$
$97$	−73.7338	−	53.5708i	−0.0771808	−	0.0560751i	−0.625707	+	0.780059i	$0.715189\pi$
$98$		0			0
$99$	301.382	+	150.113i	0.305960	+	0.152393i
$100$		0			0
$101$	973.926	+	707.598i	0.959497	+	0.697116i	0.953034	−	0.302864i	$-0.0979427\pi$
$101$	973.926	+	707.598i	0.959497	+	0.697116i	0.00646329	+	0.999979i	$0.497943\pi$
$102$		0			0
$103$	257.794	+	793.408i	0.246613	+	0.758998i	0.995367	+	0.0961494i	$0.0306527\pi$
$103$	257.794	+	793.408i	0.246613	+	0.758998i	−0.748754	+	0.662849i	$0.769347\pi$
$104$		0			0
$105$	215.441	−	156.527i	0.200237	−	0.145481i
$106$		0			0
$107$	−123.997	+	381.623i	−0.112030	+	0.344794i	−0.991316	−	0.131501i	$-0.958020\pi$
$107$	−123.997	+	381.623i	−0.112030	+	0.344794i	0.879286	+	0.476295i	$0.158020\pi$
$108$		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	−0.774265	−	0.632861i	$-0.781880\pi$
$113$	269.208	−	828.538i	0.224115	−	0.689755i	0.998380	−	0.0568936i	$-0.0181196\pi$
$114$		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	−0.315764	−	0.948838i	$-0.602261\pi$
$127$	699.947	−	508.541i	0.489057	−	0.355321i	0.804822	+	0.593517i	$0.202261\pi$
$128$		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	−0.353971	−	0.935256i	$-0.615169\pi$
$137$	683.314	−	496.457i	0.426127	−	0.309600i	0.780098	+	0.625657i	$0.215169\pi$
$138$		0			0
$139$	−385.565	−	1186.65i	−0.235275	−	0.724101i	−0.997085	−	0.0763004i	$-0.975689\pi$
$139$	−385.565	−	1186.65i	−0.235275	−	0.724101i	0.761810	−	0.647800i	$-0.224311\pi$
$140$		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	−0.513295	−	0.858212i	$-0.671575\pi$
$149$	262.444	−	190.677i	0.144297	−	0.104838i	0.657592	+	0.753375i	$0.271575\pi$
$150$		0			0
$151$	568.606	−	1749.99i	0.306440	−	0.943126i	−0.672695	−	0.739919i	$-0.734864\pi$
$151$	568.606	−	1749.99i	0.306440	−	0.943126i	0.979136	−	0.203207i	$-0.0651364\pi$
$152$		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	0.512248	+	0.858838i	$0.328813\pi$
$157$	−800.616	+	2464.04i	−0.406981	+	1.25256i	−0.919229	+	0.393722i	$0.871187\pi$
$158$		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	0.987655	−	0.156642i	$-0.0500668\pi$
$163$	2380.47	+	1729.51i	1.14388	+	0.831079i	0.156227	+	0.987721i	$0.450067\pi$
$164$		0			0
$165$	1207.79	+	2317.88i	0.569857	+	1.09362i
$166$		0			0
$167$	−1533.32	−	1114.02i	−0.710489	−	0.516201i	0.172842	−	0.984950i	$-0.444705\pi$
$167$	−1533.32	−	1114.02i	−0.710489	−	0.516201i	−0.883332	+	0.468749i	$0.844705\pi$
$168$		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	−0.712907	−	0.701259i	$-0.752622\pi$
$173$	628.110	−	1933.12i	0.276037	−	0.849553i	0.988943	−	0.148294i	$-0.0473783\pi$
$174$		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	−0.739051	−	0.673649i	$-0.764726\pi$
$179$	610.245	−	1878.14i	0.254815	−	0.784239i	0.993866	−	0.110590i	$-0.0352741\pi$
$180$		0			0
$181$	734.395	−	533.569i	0.301586	−	0.219115i	−0.426692	−	0.904397i	$-0.640321\pi$
$181$	734.395	−	533.569i	0.301586	−	0.219115i	0.728278	+	0.685282i	$0.240321\pi$
$182$		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	0.999969	+	0.00787928i	$0.00250808\pi$
$191$	516.342	+	1589.14i	0.195608	+	0.602021i	−0.804361	+	0.594141i	$0.797492\pi$
$192$		0			0
$193$	−1950.48	+	1417.11i	−0.727455	+	0.528527i	−0.888757	−	0.458378i	$-0.848431\pi$
$193$	−1950.48	+	1417.11i	−0.727455	+	0.528527i	0.161302	+	0.986905i	$0.448431\pi$
$194$		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	0.461858	−	0.886954i	$-0.347183\pi$
$211$	−732.412	−	532.129i	−0.238964	−	0.173617i	−0.700821	+	0.713337i	$0.747183\pi$
$212$		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	−0.887173	−	0.461437i	$-0.847334\pi$
$223$	338.973	−	1043.25i	0.101791	−	0.313280i	0.988964	+	0.148157i	$0.0473341\pi$
$224$		0			0
$225$	1223.07	−	888.614i	0.362392	−	0.263293i
$226$		0			0
$227$	1053.66	+	3242.85i	0.308080	+	0.948173i	0.978510	+	0.206200i	$0.0661097\pi$
$227$	1053.66	+	3242.85i	0.308080	+	0.948173i	−0.670430	+	0.741973i	$0.733890\pi$
$228$		0			0
$229$	−4478.03	−	3253.48i	−1.29221	−	0.938846i	−0.292363	−	0.956307i	$-0.594442\pi$
$229$	−4478.03	−	3253.48i	−1.29221	−	0.938846i	−0.999848	+	0.0174614i	$0.994442\pi$
$230$		0			0
$231$	−563.802	+	94.5795i	−0.160586	+	0.0269389i
$232$		0			0
$233$	−193.071	−	140.274i	−0.0542854	−	0.0394407i	0.560312	−	0.828282i	$-0.310681\pi$
$233$	−193.071	−	140.274i	−0.0542854	−	0.0394407i	−0.614597	+	0.788841i	$0.710681\pi$
$234$		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	−0.952171	−	0.305567i	$-0.901154\pi$
$239$	−8.27965	+	25.4821i	−0.00224086	+	0.00689667i	0.949930	+	0.312463i	$0.101154\pi$
$240$		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	0.690531	−	0.723303i	$-0.257377\pi$
$251$	858.998	+	624.099i	0.216014	+	0.156943i	−0.474517	+	0.880247i	$0.657377\pi$
$252$		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	0.999705	+	0.0242918i	$0.00773307\pi$
$257$	845.449	+	2602.03i	0.205205	+	0.631556i	−0.794500	+	0.607264i	$0.792267\pi$
$258$		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	−0.380893	−	0.924619i	$-0.624383\pi$
$269$	1679.93	−	1220.54i	0.380770	−	0.276645i	0.761663	+	0.647974i	$0.224383\pi$
$270$		0			0
$271$	−2603.52	−	8012.80i	−0.583588	−	1.79610i	−0.604868	−	0.796326i	$-0.706774\pi$
$271$	−2603.52	−	8012.80i	−0.583588	−	1.79610i	0.0212804	−	0.999774i	$-0.493226\pi$
$272$		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	0.356213	−	0.934405i	$-0.384068\pi$
$277$	−1947.27	−	1414.78i	−0.422384	−	0.306880i	−0.778596	+	0.627525i	$0.784068\pi$
$278$		0			0
$279$	−576.659	−	1774.77i	−0.123741	−	0.380835i
$280$		0			0
$281$	−2707.68	+	1967.25i	−0.574828	+	0.417637i	−0.836856	−	0.547423i	$-0.815609\pi$
$281$	−2707.68	+	1967.25i	−0.574828	+	0.417637i	0.262028	+	0.965060i	$0.415609\pi$
$282$		0			0
$283$	−1480.10	+	4555.27i	−0.310893	+	0.956830i	0.666519	+	0.745488i	$0.267783\pi$
$283$	−1480.10	+	4555.27i	−0.310893	+	0.956830i	−0.977412	+	0.211342i	$0.932217\pi$
$284$		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	0.810797	−	0.585328i	$-0.199034\pi$
$293$	−948.897	−	2920.41i	−0.189199	−	0.582293i	−0.999995	+	0.00303441i	$0.999034\pi$
$294$		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	0.538293	+	0.842758i	$0.319069\pi$
$311$	−2152.99	+	6626.22i	−0.392556	+	1.20816i	−0.930849	+	0.365405i	$0.880931\pi$
$312$		0			0
$313$	4325.63	−	3142.75i	0.781147	−	0.567536i	−0.124176	−	0.992260i	$-0.539629\pi$
$313$	4325.63	−	3142.75i	0.781147	−	0.567536i	0.905323	+	0.424724i	$0.139629\pi$
$314$		0			0
$315$	180.155	+	554.461i	0.0322241	+	0.0991756i
$316$		0			0
$317$	−6487.01	−	4713.09i	−1.14936	−	0.835058i	−0.160963	−	0.986960i	$-0.551460\pi$
$317$	−6487.01	−	4713.09i	−1.14936	−	0.835058i	−0.988396	+	0.151902i	$0.951460\pi$
$318$		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	0.981576	+	0.191074i	$0.0611971\pi$
$337$	1854.56	+	5707.74i	0.299775	+	0.922612i	−0.681801	+	0.731538i	$0.738803\pi$
$338$		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	−0.930929	−	0.365199i	$-0.881001\pi$
$347$	−5631.84	+	4091.77i	−0.871277	+	0.633020i	0.0596522	+	0.998219i	$0.481001\pi$
$348$		0			0
$349$	71.3186	−	219.496i	0.0109387	−	0.0336658i	−0.945438	−	0.325801i	$-0.894366\pi$
$349$	71.3186	−	219.496i	0.0109387	−	0.0336658i	0.956377	+	0.292136i	$0.0943659\pi$
$350$		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	0.931315	−	0.364214i	$-0.118662\pi$
$359$	−246.333	−	758.137i	−0.0362144	−	0.111457i	−0.967530	+	0.252758i	$0.918662\pi$
$360$		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	0.852281	+	0.523085i	$0.175219\pi$
$367$	3306.07	+	10175.0i	0.470233	+	1.44723i	−0.382048	+	0.924143i	$0.624781\pi$
$368$		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	0.0281097	−	0.999605i	$-0.491051\pi$
$379$	7285.94	−	5293.55i	0.987477	−	0.717444i	0.959367	+	0.282161i	$0.0910512\pi$
$380$		0			0
$381$	−1127.06	−	3468.73i	−0.151551	−	0.466427i
$382$		0			0
$383$	−5460.78	−	3967.49i	−0.728545	−	0.529319i	0.160558	−	0.987026i	$-0.448671\pi$
$383$	−5460.78	−	3967.49i	−0.728545	−	0.529319i	−0.889103	+	0.457708i	$0.848671\pi$
$384$		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	−0.889548	−	0.456841i	$-0.848981\pi$
$389$	−3363.63	−	10352.2i	−0.438413	−	1.34930i	0.451136	−	0.892455i	$-0.351019\pi$
$390$		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	−0.605081	−	0.796164i	$-0.706859\pi$
$401$	−279.955	+	203.399i	−0.0348636	+	0.0253299i	0.570217	+	0.821494i	$0.306859\pi$
$402$		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	0.337321	−	0.941390i	$-0.390479\pi$
$409$	−3753.25	−	2726.90i	−0.453756	−	0.329673i	−0.791077	+	0.611716i	$0.790479\pi$
$410$		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	−0.297060	−	0.954859i	$-0.596006\pi$
$421$	4358.13	−	13412.9i	0.504518	−	1.55275i	0.801579	−	0.597889i	$-0.203994\pi$
$422$		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	−0.135327	−	0.990801i	$-0.543209\pi$
$431$	−10016.6	−	7277.51i	−1.11945	−	0.813330i	−0.984126	+	0.177471i	$0.943209\pi$
$432$		0			0
$433$	1908.49	+	5873.72i	0.211815	+	0.651901i	0.999364	+	0.0356488i	$0.0113498\pi$
$433$	1908.49	+	5873.72i	0.211815	+	0.651901i	−0.787549	+	0.616252i	$0.788650\pi$
$434$		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	−0.925670	−	0.378331i	$-0.876498\pi$
$443$	425.088	−	1308.29i	0.0455904	−	0.140313i	0.971261	+	0.238019i	$0.0764980\pi$
$444$		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	0.624591	−	0.780952i	$-0.285266\pi$
$449$	712.335	+	517.542i	0.0748712	+	0.0543971i	−0.549720	+	0.835349i	$0.685266\pi$
$450$		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	−0.904144	−	0.427229i	$-0.859490\pi$
$457$	−7593.09	+	5516.70i	−0.777221	+	0.564684i	0.126923	+	0.991913i	$0.459490\pi$
$458$		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	−0.793258	−	0.608885i	$-0.791617\pi$
$467$	−4635.28	+	3367.73i	−0.459305	+	0.333704i	0.333954	+	0.942589i	$0.391617\pi$
$468$		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	−0.212978	−	0.977057i	$-0.568316\pi$
$479$	6818.88	−	4954.21i	0.650444	−	0.472575i	0.863422	+	0.504482i	$0.168316\pi$
$480$		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	−0.973213	−	0.229904i	$-0.926159\pi$
$487$	−545.237	+	1678.07i	−0.0507332	+	0.156141i	0.922480	+	0.386044i	$0.126159\pi$
$488$		0			0
$489$	10035.1	−	7290.90i	0.928018	−	0.674245i
$490$		0			0
$491$	1604.32	+	4937.60i	0.147458	+	0.453830i	0.997319	−	0.0731775i	$-0.0233139\pi$
$491$	1604.32	+	4937.60i	0.147458	+	0.453830i	−0.849861	+	0.527008i	$0.823314\pi$
$492$		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	0.867904	−	0.496732i	$-0.165467\pi$
$499$	−1406.92	−	4330.05i	−0.126217	−	0.388456i	−0.994121	+	0.108276i	$0.965467\pi$
$500$		0			0
$501$	−6463.82	+	4696.24i	−0.576412	+	0.418787i
$502$		0			0
$503$	−1848.60	+	5689.40i	−0.163867	+	0.504330i	−0.998951	−	0.0457921i	$-0.985419\pi$
$503$	−1848.60	+	5689.40i	−0.163867	+	0.504330i	0.835084	+	0.550122i	$0.185419\pi$
$504$		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	0.527695	+	0.849434i	$0.323056\pi$
$509$	−4576.25	+	14084.2i	−0.398504	+	1.22647i	−0.926199	+	0.377035i	$0.876944\pi$
$510$		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	−0.949575	−	0.313541i	$-0.898485\pi$
$521$	−4348.29	−	13382.7i	−0.365647	−	1.12535i	0.583928	−	0.811806i	$-0.301515\pi$
$522$		0			0
$523$	6521.51	−	4738.15i	0.545250	−	0.396147i	−0.280781	−	0.959772i	$-0.590594\pi$
$523$	6521.51	−	4738.15i	0.545250	−	0.396147i	0.826031	+	0.563625i	$0.190594\pi$
$524$		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	0.510864	−	0.859662i	$-0.329326\pi$
$541$	−1873.12	−	1360.90i	−0.148857	−	0.108151i	−0.659721	+	0.751510i	$0.729326\pi$
$542$		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	−0.756281	−	0.654247i	$-0.772986\pi$
$547$	3071.91	−	9454.38i	0.240120	−	0.739013i	0.996401	−	0.0847660i	$-0.0270143\pi$
$548$		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	0.837703	−	0.546126i	$-0.183898\pi$
$557$	−2116.69	−	6514.50i	−0.161018	−	0.495563i	−0.998721	+	0.0505638i	$0.983898\pi$
$558$		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	−0.989815	−	0.142357i	$-0.954532\pi$
$563$	−19117.2	−	13889.5i	−1.43107	−	1.03974i	−0.441260	−	0.897379i	$-0.645468\pi$
$564$		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	0.0313131	−	0.999510i	$-0.490031\pi$
$569$	8055.13	−	24791.1i	0.593477	−	1.82654i	0.562164	−	0.827026i	$-0.309969\pi$
$570$		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	−0.854254	−	0.519855i	$-0.825986\pi$
$577$	−8646.18	+	6281.82i	−0.623822	+	0.453233i	0.230433	+	0.973088i	$0.425986\pi$
$578$		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	0.999734	+	0.0230465i	$0.00733658\pi$
$587$	2908.07	+	8950.13i	0.204479	+	0.629321i	−0.795256	+	0.606274i	$0.792663\pi$
$588$		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	−0.560362	−	0.828248i	$-0.689338\pi$
$599$	794.385	−	577.154i	0.0541864	−	0.0393687i	0.614549	+	0.788879i	$0.289338\pi$
$600$		0			0
$601$	−2222.06	−	6838.80i	−0.150815	−	0.464161i	0.846898	−	0.531756i	$-0.178467\pi$
$601$	−2222.06	−	6838.80i	−0.150815	−	0.464161i	−0.997713	+	0.0675949i	$0.978467\pi$
$602$		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	0.896773	−	0.442491i	$-0.145905\pi$
$607$	11261.9	+	8182.23i	0.753057	+	0.547128i	−0.143716	+	0.989619i	$0.545905\pi$
$608$		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	−0.193236	−	0.981152i	$-0.561898\pi$
$613$	8192.67	−	25214.4i	0.539802	−	1.66134i	0.733038	−	0.680188i	$-0.238102\pi$
$614$		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	−0.888986	−	0.457935i	$-0.848589\pi$
$619$	1530.60	−	4710.72i	0.0993864	−	0.305880i	0.988372	+	0.152055i	$0.0485892\pi$
$620$		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	0.996559	+	0.0828869i	$0.0264140\pi$
$631$	3789.00	+	11661.3i	0.239045	+	0.735706i	−0.757513	+	0.652820i	$0.773586\pi$
$632$		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	−0.810017	−	0.586406i	$-0.800542\pi$
$641$	3083.17	−	9489.02i	0.189981	−	0.584702i	0.999999	+	0.00170413i	$0.000542441\pi$
$642$		0			0
$643$	−2639.71	+	1917.86i	−0.161897	+	0.117625i	−0.665784	−	0.746144i	$-0.731903\pi$
$643$	−2639.71	+	1917.86i	−0.161897	+	0.117625i	0.503887	+	0.863770i	$0.331903\pi$
$644$		0			0
$645$	7595.21	+	23375.6i	0.463660	+	1.42700i
$646$		0			0
$647$	20476.9	+	14877.3i	1.24425	+	0.903999i	0.997874	−	0.0651758i	$-0.0207608\pi$
$647$	20476.9	+	14877.3i	1.24425	+	0.903999i	0.246374	+	0.969175i	$0.420761\pi$
$648$		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	0.924470	−	0.381255i	$-0.124508\pi$
$653$	−793.250	−	2441.37i	−0.0475379	−	0.146307i	−0.972008	+	0.234948i	$0.924508\pi$
$654$		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	−0.104302	−	0.994546i	$-0.533261\pi$
$673$	−18897.8	−	13730.1i	−1.08240	−	0.786411i	−0.978100	+	0.208135i	$0.933261\pi$
$674$		0			0
$675$	−7731.05	−	23793.7i	−0.440842	−	1.35677i
$676$		0			0
$677$	277.971	−	201.958i	0.0157803	−	0.0114651i	−0.579867	−	0.814711i	$-0.696896\pi$
$677$	277.971	−	201.958i	0.0157803	−	0.0114651i	0.595647	+	0.803246i	$0.296896\pi$
$678$		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	0.723607	−	0.690213i	$-0.242483\pi$
$691$	5281.83	+	3837.47i	0.290782	+	0.211265i	−0.432825	+	0.901478i	$0.642483\pi$
$692$		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	0.493038	+	0.870008i	$0.335887\pi$
$701$	−7743.51	+	23832.1i	−0.417216	+	1.28406i	−0.910254	+	0.414051i	$0.864113\pi$
$702$		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	0.255877	−	0.966709i	$-0.417636\pi$
$709$	23680.2	−	17204.7i	1.25434	−	0.911334i	0.998466	+	0.0553756i	$0.0176356\pi$
$710$		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	−0.997344	−	0.0728387i	$-0.976794\pi$
$719$	−4497.67	−	13842.4i	−0.233289	−	0.717990i	0.764055	−	0.645152i	$-0.223206\pi$
$720$		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	−0.955170	−	0.296059i	$-0.904327\pi$
$733$	−7073.64	−	21770.4i	−0.356441	−	1.09701i	0.598729	−	0.800952i	$-0.295673\pi$
$734$		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	0.951581	−	0.307399i	$-0.0994585\pi$
$739$	19150.8	+	13913.9i	0.953282	+	0.692600i	0.00170110	+	0.999999i	$0.499459\pi$
$740$		0			0
$741$	4059.82	+	12494.8i	0.201270	+	0.619446i
$742$		0			0
$743$	6506.66	−	4727.37i	0.321274	−	0.233419i	−0.415445	−	0.909618i	$-0.636374\pi$
$743$	6506.66	−	4727.37i	0.321274	−	0.233419i	0.736719	+	0.676199i	$0.236374\pi$
$744$		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	−0.391302	−	0.920262i	$-0.627975\pi$
$751$	9594.40	−	29528.5i	0.466185	−	1.43477i	0.857487	−	0.514506i	$-0.172025\pi$
$752$		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	0.538407	−	0.842685i	$-0.319026\pi$
$757$	−2013.15	−	1462.64i	−0.0966569	−	0.0702253i	−0.635064	+	0.772460i	$0.719026\pi$
$758$		0			0
$759$	968.645	−	6499.11i	0.0463236	−	0.310807i
$760$		0			0
$761$	12625.9	+	9173.25i	0.601430	+	0.436965i	0.846386	−	0.532570i	$-0.178774\pi$
$761$	12625.9	+	9173.25i	0.601430	+	0.436965i	−0.244956	+	0.969534i	$0.578774\pi$
$762$		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	−0.959647	−	0.281206i	$-0.909266\pi$
$773$	−386.582	+	1189.78i	−0.0179876	+	0.0553601i	0.941660	+	0.336566i	$0.109266\pi$
$774$		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	−0.819810	−	0.572636i	$-0.805921\pi$
$787$	−11669.1	+	8478.07i	−0.528535	+	0.384003i	0.291274	+	0.956640i	$0.405921\pi$
$788$		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	−0.563235	−	0.826297i	$-0.690444\pi$
$797$	1092.84	−	793.998i	0.0485703	−	0.0352884i	0.611806	+	0.791008i	$0.290444\pi$
$798$		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	−0.458775	−	0.888552i	$-0.651712\pi$
$809$	5626.46	−	4087.86i	0.244519	−	0.177653i	0.703294	+	0.710899i	$0.251712\pi$
$810$		0			0
$811$	5301.42	−	16316.1i	0.229541	−	0.706456i	−0.768257	−	0.640141i	$-0.778876\pi$
$811$	5301.42	−	16316.1i	0.229541	−	0.706456i	0.997799	−	0.0663147i	$-0.0211241\pi$
$812$		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	0.986492	+	0.163809i	$0.0523780\pi$
$821$	6697.05	+	20611.4i	0.284688	+	0.876178i	−0.701805	+	0.712370i	$0.747622\pi$
$822$		0			0
$823$	6412.00	+	4658.59i	0.271577	+	0.197313i	0.715235	−	0.698884i	$-0.246319\pi$
$823$	6412.00	+	4658.59i	0.271577	+	0.197313i	−0.443658	+	0.896196i	$0.646319\pi$
$824$		0			0
$825$	−22551.1	−	11232.3i	−0.951670	−	0.474011i
$826$		0			0
$827$	−31189.0	−	22660.2i	−1.31143	−	0.952807i	−0.999997	−	0.00253737i	$-0.999192\pi$
$827$	−31189.0	−	22660.2i	−1.31143	−	0.952807i	−0.311429	−	0.950269i	$-0.600808\pi$
$828$		0			0
$829$	−2050.74	−	6311.54i	−0.0859171	−	0.264426i	0.898863	−	0.438229i	$-0.144394\pi$
$829$	−2050.74	−	6311.54i	−0.0859171	−	0.264426i	−0.984780	+	0.173804i	$0.944394\pi$
$830$		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	0.0468105	−	0.998904i	$-0.485094\pi$
$839$	14486.0	−	44583.3i	0.596081	−	1.83455i	0.549270	−	0.835645i	$-0.314906\pi$
$840$		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	−0.559847	−	0.828596i	$-0.689140\pi$
$853$	1375.00	−	998.996i	0.0551924	−	0.0400996i	0.615039	+	0.788496i	$0.289140\pi$
$854$		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	0.286278	−	0.958146i	$-0.407582\pi$
$863$	32602.8	−	23687.3i	1.28599	−	0.934330i	0.999716	+	0.0238166i	$0.00758178\pi$
$864$		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	−0.997964	−	0.0637852i	$-0.979683\pi$
$877$	−3976.31	+	12237.8i	−0.153102	+	0.471200i	0.844862	+	0.534985i	$0.179683\pi$
$878$		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	0.542484	+	0.840066i	$0.317484\pi$
$883$	−10237.6	+	31508.1i	−0.390174	+	1.20083i	−0.932657	+	0.360764i	$0.882516\pi$
$884$		0			0
$885$	−30704.8	+	22308.4i	−1.16625	+	0.847330i
$886$		0			0
$887$	3440.61	+	10589.1i	0.130242	+	0.400843i	0.994820	−	0.101656i	$-0.0324142\pi$
$887$	3440.61	+	10589.1i	0.130242	+	0.400843i	−0.864578	+	0.502499i	$0.832414\pi$
$888$		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	−0.797717	−	0.603033i	$-0.793959\pi$
$907$	−12857.6	+	9341.62i	−0.470706	+	0.341988i	0.327010	+	0.945021i	$0.393959\pi$
$908$		0			0
$909$	3433.22	+	10566.4i	0.125272	+	0.385549i
$910$		0			0
$911$	−36053.9	−	26194.7i	−1.31122	−	0.952655i	−0.999997	−	0.00231766i	$-0.999262\pi$
$911$	−36053.9	−	26194.7i	−1.31122	−	0.952655i	−0.311220	−	0.950338i	$-0.600738\pi$
$912$		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	−0.311876	−	0.950123i	$-0.600957\pi$
$919$	13800.7	−	10026.8i	0.495369	−	0.359907i	0.807245	+	0.590216i	$0.200957\pi$
$920$		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	−0.906572	−	0.422050i	$-0.861311\pi$
$929$	−22236.8	+	16156.0i	−0.785325	+	0.570572i	0.121247	+	0.992622i	$0.461311\pi$
$930$		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	0.617828	−	0.786313i	$-0.288013\pi$
$937$	1747.29	+	1269.48i	0.0609195	+	0.0442606i	−0.556909	+	0.830574i	$0.688013\pi$
$938$		0			0
$939$	−6965.16	−	21436.5i	−0.242065	−	0.745000i
$940$		0			0
$941$	16088.4	−	11688.9i	0.557352	−	0.404940i	−0.273137	−	0.961975i	$-0.588061\pi$
$941$	16088.4	−	11688.9i	0.557352	−	0.404940i	0.830489	+	0.557035i	$0.188061\pi$
$942$		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	0.965129	−	0.261773i	$-0.0843073\pi$
$953$	896.033	+	2757.71i	0.0304568	+	0.0937365i	−0.934673	+	0.355510i	$0.884307\pi$
$954$		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	0.354652	+	0.934998i	$0.384599\pi$
$971$	−14579.3	+	44870.5i	−0.481846	+	1.48297i	−0.836498	+	0.547970i	$0.815401\pi$
$972$		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	0.714200	−	0.699942i	$-0.246791\pi$
$977$	8221.34	+	5973.15i	0.269216	+	0.195597i	−0.444984	+	0.895538i	$0.646791\pi$
$978$		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	0.909999	+	0.414611i	$0.136082\pi$
$983$	12867.2	+	39601.1i	0.417496	+	1.28492i	−0.492502	+	0.870311i	$0.663918\pi$
$984$		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	0.604106	+	0.796904i	$0.293530\pi$
$997$	18377.8	+	56561.1i	0.583782	+	1.79670i	−0.0203240	+	0.999793i	$0.506470\pi$
$998$		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.81.3		12
4.3	odd	2		44.4.e.a.37.1	yes	12
11.3	even	5	inner	176.4.m.d.113.3		12
11.5	even	5		1936.4.a.br.1.5		6
11.6	odd	10		1936.4.a.bs.1.5		6
12.11	even	2		396.4.j.d.37.3		12
44.3	odd	10		44.4.e.a.25.1	✓	12
44.27	odd	10		484.4.a.i.1.2		6
44.39	even	10		484.4.a.h.1.2		6
132.47	even	10		396.4.j.d.289.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.4.e.a.25.1	✓	12	44.3	odd	10
44.4.e.a.37.1	yes	12	4.3	odd	2
176.4.m.d.81.3		12	1.1	even	1	trivial
176.4.m.d.113.3		12	11.3	even	5	inner
396.4.j.d.37.3		12	12.11	even	2
396.4.j.d.289.3		12	132.47	even	10
484.4.a.h.1.2		6	44.39	even	10
484.4.a.i.1.2		6	44.27	odd	10
1936.4.a.br.1.5		6	11.5	even	5
1936.4.a.bs.1.5		6	11.6	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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