LMFDB - Embedded newform 349.2.b.b.348.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(348,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("349.348");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			348.7
Character	$\chi$	$=$	349.348
Dual form			349.2.b.b.348.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82942i q^{2} +3.30797 q^{3} -1.34678 q^{4} -0.842567 q^{5} -6.05168i q^{6} +2.41293i q^{7} -1.19501i q^{8} +7.94269 q^{9} +O(q^{10})$	\(q-1.82942i q^{2} +3.30797 q^{3} -1.34678 q^{4} -0.842567 q^{5} -6.05168i q^{6} +2.41293i q^{7} -1.19501i q^{8} +7.94269 q^{9} +1.54141i q^{10} +4.72131i q^{11} -4.45512 q^{12} -5.49618i q^{13} +4.41427 q^{14} -2.78719 q^{15} -4.87974 q^{16} -5.40474 q^{17} -14.5305i q^{18} -1.88589 q^{19} +1.13475 q^{20} +7.98192i q^{21} +8.63727 q^{22} -0.0997728 q^{23} -3.95306i q^{24} -4.29008 q^{25} -10.0548 q^{26} +16.3503 q^{27} -3.24969i q^{28} -6.54458 q^{29} +5.09894i q^{30} +8.71156 q^{31} +6.53708i q^{32} +15.6180i q^{33} +9.88755i q^{34} -2.03306i q^{35} -10.6971 q^{36} +0.766816 q^{37} +3.45009i q^{38} -18.1812i q^{39} +1.00688i q^{40} -6.82187 q^{41} +14.6023 q^{42} +10.8915i q^{43} -6.35858i q^{44} -6.69225 q^{45} +0.182527i q^{46} -2.74159i q^{47} -16.1421 q^{48} +1.17776 q^{49} +7.84837i q^{50} -17.8787 q^{51} +7.40216i q^{52} -9.40270i q^{53} -29.9116i q^{54} -3.97802i q^{55} +2.88348 q^{56} -6.23848 q^{57} +11.9728i q^{58} -3.01252i q^{59} +3.75374 q^{60} -3.21372i q^{61} -15.9371i q^{62} +19.1652i q^{63} +2.19960 q^{64} +4.63090i q^{65} +28.5719 q^{66} +8.03497 q^{67} +7.27901 q^{68} -0.330046 q^{69} -3.71932 q^{70} +9.76050i q^{71} -9.49160i q^{72} +5.75667 q^{73} -1.40283i q^{74} -14.1915 q^{75} +2.53989 q^{76} -11.3922 q^{77} -33.2611 q^{78} +4.00639i q^{79} +4.11151 q^{80} +30.2583 q^{81} +12.4801i q^{82} +4.95753 q^{83} -10.7499i q^{84} +4.55386 q^{85} +19.9251 q^{86} -21.6493 q^{87} +5.64201 q^{88} +7.56059i q^{89} +12.2429i q^{90} +13.2619 q^{91} +0.134372 q^{92} +28.8176 q^{93} -5.01552 q^{94} +1.58899 q^{95} +21.6245i q^{96} -12.8493i q^{97} -2.15462i q^{98} +37.4999i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$		−	1.82942i		−	1.29360i	−0.762661	−	0.646798i	$-0.776108\pi$
$2$		−	1.82942i		−	1.29360i	0.762661	−	0.646798i	$-0.223892\pi$
$3$	3.30797			1.90986			0.954930	−	0.296831i	$-0.0959299\pi$
$3$	3.30797			1.90986			0.954930	+	0.296831i	$0.0959299\pi$
$4$	−1.34678			−0.673391
$5$	−0.842567			−0.376807			−0.188404	−	0.982092i	$-0.560331\pi$
$5$	−0.842567			−0.376807			−0.188404	+	0.982092i	$0.560331\pi$
$6$		−	6.05168i		−	2.47059i
$7$			2.41293i			0.912003i	0.889979	+	0.456001i	$0.150719\pi$
$7$			2.41293i			0.912003i	−0.889979	+	0.456001i	$0.849281\pi$
$8$		−	1.19501i		−	0.422500i
$9$	7.94269			2.64756
$10$			1.54141i			0.487436i
$11$			4.72131i			1.42353i	0.702418	+	0.711765i	$0.252104\pi$
$11$			4.72131i			1.42353i	−0.702418	+	0.711765i	$0.747896\pi$
$12$	−4.45512			−1.28608
$13$		−	5.49618i		−	1.52437i	−0.647362	−	0.762183i	$-0.724128\pi$
$13$		−	5.49618i		−	1.52437i	0.647362	−	0.762183i	$-0.275872\pi$
$14$	4.41427			1.17976
$15$	−2.78719			−0.719649
$16$	−4.87974			−1.21994
$17$	−5.40474			−1.31084			−0.655421	−	0.755263i	$-0.727509\pi$
$17$	−5.40474			−1.31084			−0.655421	+	0.755263i	$0.727509\pi$
$18$		−	14.5305i		−	3.42488i
$19$	−1.88589			−0.432653			−0.216327	−	0.976321i	$-0.569408\pi$
$19$	−1.88589			−0.432653			−0.216327	+	0.976321i	$0.569408\pi$
$20$	1.13475			0.253739
$21$			7.98192i			1.74180i
$22$	8.63727			1.84147
$23$	−0.0997728			−0.0208041			−0.0104020	−	0.999946i	$-0.503311\pi$
$23$	−0.0997728			−0.0208041			−0.0104020	+	0.999946i	$0.503311\pi$
$24$		−	3.95306i		−	0.806915i
$25$	−4.29008			−0.858016
$26$	−10.0548			−1.97191
$27$	16.3503			3.14662
$28$		−	3.24969i		−	0.614135i
$29$	−6.54458			−1.21530			−0.607649	−	0.794206i	$-0.707887\pi$
$29$	−6.54458			−1.21530			−0.607649	+	0.794206i	$0.707887\pi$
$30$			5.09894i			0.930935i
$31$	8.71156			1.56464			0.782321	−	0.622875i	$-0.214036\pi$
$31$	8.71156			1.56464			0.782321	+	0.622875i	$0.214036\pi$
$32$			6.53708i			1.15560i
$33$			15.6180i			2.71874i
$34$			9.88755i			1.69570i
$35$		−	2.03306i		−	0.343649i
$36$	−10.6971			−1.78285
$37$	0.766816			0.126064			0.0630319	−	0.998012i	$-0.479923\pi$
$37$	0.766816			0.126064			0.0630319	+	0.998012i	$0.479923\pi$
$38$			3.45009i			0.559678i
$39$		−	18.1812i		−	2.91132i
$40$			1.00688i			0.159201i
$41$	−6.82187			−1.06540			−0.532699	−	0.846305i	$-0.678822\pi$
$41$	−6.82187			−1.06540			−0.532699	+	0.846305i	$0.678822\pi$
$42$	14.6023			2.25318
$43$			10.8915i			1.66094i	0.557065	+	0.830469i	$0.311928\pi$
$43$			10.8915i			1.66094i	−0.557065	+	0.830469i	$0.688072\pi$
$44$		−	6.35858i		−	0.958592i
$45$	−6.69225			−0.997622
$46$			0.182527i			0.0269121i
$47$		−	2.74159i		−	0.399902i	−0.979806	−	0.199951i	$-0.935922\pi$
$47$		−	2.74159i		−	0.399902i	0.979806	−	0.199951i	$-0.0640783\pi$
$48$	−16.1421			−2.32991
$49$	1.17776			0.168251
$50$			7.84837i			1.10993i
$51$	−17.8787			−2.50353
$52$			7.40216i			1.02649i
$53$		−	9.40270i		−	1.29156i	−0.763523	−	0.645780i	$-0.776532\pi$
$53$		−	9.40270i		−	1.29156i	0.763523	−	0.645780i	$-0.223468\pi$
$54$		−	29.9116i		−	4.07045i
$55$		−	3.97802i		−	0.536396i
$56$	2.88348			0.385321
$57$	−6.23848			−0.826307
$58$			11.9728i			1.57210i
$59$		−	3.01252i		−	0.392196i	−0.980584	−	0.196098i	$-0.937173\pi$
$59$		−	3.01252i		−	0.392196i	0.980584	−	0.196098i	$-0.0628271\pi$
$60$	3.75374			0.484605
$61$		−	3.21372i		−	0.411475i	−0.978607	−	0.205737i	$-0.934041\pi$
$61$		−	3.21372i		−	0.411475i	0.978607	−	0.205737i	$-0.0659593\pi$
$62$		−	15.9371i		−	2.02402i
$63$			19.1652i			2.41459i
$64$	2.19960			0.274950
$65$			4.63090i			0.574392i
$66$	28.5719			3.51695
$67$	8.03497			0.981627			0.490814	−	0.871265i	$-0.336700\pi$
$67$	8.03497			0.981627			0.490814	+	0.871265i	$0.336700\pi$
$68$	7.27901			0.882710
$69$	−0.330046			−0.0397329
$70$	−3.71932			−0.444543
$71$			9.76050i			1.15836i	0.815200	+	0.579179i	$0.196627\pi$
$71$			9.76050i			1.15836i	−0.815200	+	0.579179i	$0.803373\pi$
$72$		−	9.49160i		−	1.11860i
$73$	5.75667			0.673767			0.336884	−	0.941546i	$-0.390627\pi$
$73$	5.75667			0.673767			0.336884	+	0.941546i	$0.390627\pi$
$74$		−	1.40283i		−	0.163076i
$75$	−14.1915			−1.63869
$76$	2.53989			0.291345
$77$	−11.3922			−1.29826
$78$	−33.2611			−3.76608
$79$			4.00639i			0.450754i	0.974272	+	0.225377i	$0.0723614\pi$
$79$			4.00639i			0.450754i	−0.974272	+	0.225377i	$0.927639\pi$
$80$	4.11151			0.459681
$81$	30.2583			3.36203
$82$			12.4801i			1.37819i
$83$	4.95753			0.544159			0.272080	−	0.962275i	$-0.412289\pi$
$83$	4.95753			0.544159			0.272080	+	0.962275i	$0.412289\pi$
$84$		−	10.7499i		−	1.17291i
$85$	4.55386			0.493935
$86$	19.9251			2.14858
$87$	−21.6493			−2.32105
$88$	5.64201			0.601441
$89$			7.56059i			0.801421i	0.916205	+	0.400711i	$0.131237\pi$
$89$			7.56059i			0.801421i	−0.916205	+	0.400711i	$0.868763\pi$
$90$			12.2429i			1.29052i
$91$	13.2619			1.39023
$92$	0.134372			0.0140093
$93$	28.8176			2.98825
$94$	−5.01552			−0.517312
$95$	1.58899			0.163027
$96$			21.6245i			2.20704i
$97$		−	12.8493i		−	1.30465i	−0.757938	−	0.652326i	$-0.773793\pi$
$97$		−	12.8493i		−	1.30465i	0.757938	−	0.652326i	$-0.226207\pi$
$98$		−	2.15462i		−	0.217649i
$99$			37.4999i			3.76889i
$100$	5.77781			0.577781
$101$			2.79582i			0.278195i	0.990279	+	0.139097i	$0.0444201\pi$
$101$			2.79582i			0.278195i	−0.990279	+	0.139097i	$0.955580\pi$
$102$			32.7078i			3.23855i
$103$		−	6.66076i		−	0.656304i	−0.944625	−	0.328152i	$-0.893574\pi$
$103$		−	6.66076i		−	0.656304i	0.944625	−	0.328152i	$-0.106426\pi$
$104$	−6.56799			−0.644044
$105$		−	6.72530i		−	0.656322i
$106$	−17.2015			−1.67076
$107$			1.41135i			0.136441i	0.997670	+	0.0682204i	$0.0217321\pi$
$107$			1.41135i			0.136441i	−0.997670	+	0.0682204i	$0.978268\pi$
$108$	−22.0203			−2.11890
$109$	12.6747			1.21401			0.607006	−	0.794697i	$-0.292370\pi$
$109$	12.6747			1.21401			0.607006	+	0.794697i	$0.292370\pi$
$110$	−7.27748			−0.693880
$111$	2.53661			0.240764
$112$		−	11.7745i		−	1.11258i
$113$		−	14.9344i		−	1.40491i	−0.711726	−	0.702457i	$-0.752086\pi$
$113$		−	14.9344i		−	1.40491i	0.711726	−	0.702457i	$-0.247914\pi$
$114$			11.4128i			1.06891i
$115$	0.0840653			0.00783913
$116$	8.81412			0.818371
$117$		−	43.6545i		−	4.03586i
$118$	−5.51116			−0.507344
$119$		−	13.0413i		−	1.19549i
$120$			3.33072i			0.304052i
$121$	−11.2908			−1.02644
$122$	−5.87925			−0.532282
$123$	−22.5666			−2.03476
$124$	−11.7326			−1.05362
$125$	7.82751			0.700114
$126$	35.0612			3.12350
$127$			2.29144i			0.203332i	0.994819	+	0.101666i	$0.0324173\pi$
$127$			2.29144i			0.203332i	−0.994819	+	0.101666i	$0.967583\pi$
$128$			9.05018i			0.799930i
$129$			36.0288i			3.17216i
$130$	8.47186			0.743031
$131$			9.11389i			0.796285i	0.917324	+	0.398142i	$0.130345\pi$
$131$			9.11389i			0.796285i	−0.917324	+	0.398142i	$0.869655\pi$
$132$		−	21.0340i		−	1.83078i
$133$		−	4.55053i		−	0.394581i
$134$		−	14.6993i		−	1.26983i
$135$	−13.7762			−1.18567
$136$			6.45872i			0.553831i
$137$			6.75590i			0.577196i	0.957450	+	0.288598i	$0.0931890\pi$
$137$			6.75590i			0.577196i	−0.957450	+	0.288598i	$0.906811\pi$
$138$			0.603793i			0.0513983i
$139$	−12.3804			−1.05009			−0.525045	−	0.851074i	$-0.675952\pi$
$139$	−12.3804			−1.05009			−0.525045	+	0.851074i	$0.675952\pi$
$140$			2.73808i			0.231410i
$141$		−	9.06911i		−	0.763757i
$142$	17.8561			1.49845
$143$	25.9492			2.16998
$144$	−38.7583			−3.22986
$145$	5.51424			0.457933
$146$		−	10.5314i		−	0.871583i
$147$	3.89600			0.321336
$148$	−1.03273			−0.0848903
$149$		−	6.18856i		−	0.506986i	−0.967337	−	0.253493i	$-0.918420\pi$
$149$		−	6.18856i		−	0.506986i	0.967337	−	0.253493i	$-0.0815795\pi$
$150$			25.9622i			2.11980i
$151$	7.89687			0.642638			0.321319	−	0.946971i	$-0.395874\pi$
$151$	7.89687			0.642638			0.321319	+	0.946971i	$0.395874\pi$
$152$			2.25366i			0.182796i
$153$	−42.9282			−3.47054
$154$			20.8411i			1.67943i
$155$	−7.34007			−0.589569
$156$			24.4861i			1.96046i
$157$	−7.76159			−0.619443			−0.309721	−	0.950827i	$-0.600236\pi$
$157$	−7.76159			−0.619443			−0.309721	+	0.950827i	$0.600236\pi$
$158$	7.32938			0.583094
$159$		−	31.1039i		−	2.46670i
$160$		−	5.50793i		−	0.435440i
$161$		−	0.240745i		−	0.0189734i
$162$		−	55.3552i		−	4.34911i
$163$			21.4795i			1.68241i	0.540719	+	0.841203i	$0.318152\pi$
$163$			21.4795i			1.68241i	−0.540719	+	0.841203i	$0.681848\pi$
$164$	9.18758			0.717430
$165$		−	13.1592i		−	1.02444i
$166$		−	9.06941i		−	0.703922i
$167$		−	14.5993i		−	1.12973i	−0.825184	−	0.564865i	$-0.808928\pi$
$167$		−	14.5993i		−	1.12973i	0.825184	−	0.564865i	$-0.191072\pi$
$168$	9.53847			0.735909
$169$	−17.2080			−1.32369
$170$		−	8.33092i		−	0.638953i
$171$	−14.9791			−1.14548
$172$		−	14.6685i		−	1.11846i
$173$			0.0917206i			0.00697339i	0.999994	+	0.00348669i	$0.00110985\pi$
$173$			0.0917206i			0.00697339i	−0.999994	+	0.00348669i	$0.998890\pi$
$174$			39.6057i			3.00250i
$175$		−	10.3517i		−	0.782513i
$176$		−	23.0388i		−	1.73661i
$177$		−	9.96533i		−	0.749040i
$178$	13.8315			1.03672
$179$		−	15.5771i		−	1.16429i	−0.813086	−	0.582144i	$-0.802214\pi$
$179$		−	15.5771i		−	1.16429i	0.813086	−	0.582144i	$-0.197786\pi$
$180$	9.01300			0.671790
$181$	1.63588			0.121594			0.0607971	−	0.998150i	$-0.480636\pi$
$181$	1.63588			0.121594			0.0607971	+	0.998150i	$0.480636\pi$
$182$		−	24.2616i		−	1.79839i
$183$		−	10.6309i		−	0.785859i
$184$			0.119230i			0.00878972i
$185$	−0.646094			−0.0475018
$186$		−	52.7196i		−	3.86559i
$187$		−	25.5175i		−	1.86602i
$188$			3.69233i			0.269291i
$189$			39.4522i			2.86972i
$190$		−	2.90693i		−	0.210891i
$191$	−1.65964			−0.120087			−0.0600437	−	0.998196i	$-0.519124\pi$
$191$	−1.65964			−0.120087			−0.0600437	+	0.998196i	$0.519124\pi$
$192$	7.27622			0.525116
$193$			0.786459i			0.0566106i	0.999599	+	0.0283053i	$0.00901106\pi$
$193$			0.786459i			0.0566106i	−0.999599	+	0.0283053i	$0.990989\pi$
$194$	−23.5068			−1.68769
$195$			15.3189i			1.09701i
$196$	−1.58619			−0.113299
$197$		−	6.86952i		−	0.489433i	−0.969595	−	0.244717i	$-0.921305\pi$
$197$		−	6.86952i		−	0.489433i	0.969595	−	0.244717i	$-0.0786949\pi$
$198$	68.6032			4.87542
$199$		−	18.2926i		−	1.29673i	−0.761330	−	0.648364i	$-0.775453\pi$
$199$		−	18.2926i		−	1.29673i	0.761330	−	0.648364i	$-0.224547\pi$
$200$			5.12669i			0.362512i
$201$	26.5795			1.87477
$202$	5.11474			0.359872
$203$		−	15.7916i		−	1.10835i
$204$	24.0788			1.68585
$205$	5.74788			0.401450
$206$	−12.1853			−0.848993
$207$	−0.792465			−0.0550801
$208$			26.8199i			1.85963i
$209$		−	8.90388i		−	0.615894i
$210$	−12.3034			−0.849015
$211$			16.9166i			1.16459i	0.812979	+	0.582293i	$0.197844\pi$
$211$			16.9166i			1.16459i	−0.812979	+	0.582293i	$0.802156\pi$
$212$			12.6634i			0.869725i
$213$			32.2875i			2.21230i
$214$	2.58196			0.176499
$215$		−	9.17682i		−	0.625854i
$216$		−	19.5388i		−	1.32945i
$217$			21.0204i			1.42696i
$218$		−	23.1873i		−	1.57044i
$219$	19.0429			1.28680
$220$			5.35753i			0.361205i
$221$			29.7054i			1.99820i
$222$		−	4.64053i		−	0.311452i
$223$	−12.6535			−0.847341			−0.423671	−	0.905816i	$-0.639259\pi$
$223$	−12.6535			−0.847341			−0.423671	+	0.905816i	$0.639259\pi$
$224$	−15.7735			−1.05391
$225$	−34.0748			−2.27165
$226$	−27.3214			−1.81739
$227$	5.36712			0.356228			0.178114	−	0.984010i	$-0.443000\pi$
$227$	5.36712			0.356228			0.178114	+	0.984010i	$0.443000\pi$
$228$	8.40188			0.556428
$229$			0.563641i			0.0372464i	0.999827	+	0.0186232i	$0.00592830\pi$
$229$			0.563641i			0.0372464i	−0.999827	+	0.0186232i	$0.994072\pi$
$230$		−	0.153791i		−	0.0101407i
$231$	−37.6851			−2.47950
$232$			7.82083i			0.513463i
$233$	−17.5637			−1.15064			−0.575318	−	0.817929i	$-0.695122\pi$
$233$	−17.5637			−1.15064			−0.575318	+	0.817929i	$0.695122\pi$
$234$	−79.8624			−5.22077
$235$			2.30997i			0.150686i
$236$			4.05721i			0.264102i
$237$			13.2530i			0.860878i
$238$	−23.8580			−1.54648
$239$	−9.27122			−0.599705			−0.299853	−	0.953986i	$-0.596937\pi$
$239$	−9.27122			−0.599705			−0.299853	+	0.953986i	$0.596937\pi$
$240$	13.6008			0.877925
$241$	11.5879			0.746442			0.373221	−	0.927742i	$-0.378253\pi$
$241$	11.5879			0.746442			0.373221	+	0.927742i	$0.378253\pi$
$242$			20.6556i			1.32779i
$243$	51.0428			3.27440
$244$			4.32818i			0.277084i
$245$	−0.992341			−0.0633983
$246$			41.2838i			2.63216i
$247$			10.3652i			0.659521i
$248$		−	10.4104i		−	0.661061i
$249$	16.3994			1.03927
$250$		−	14.3198i		−	0.905665i
$251$			28.8514i			1.82108i	0.413417	+	0.910542i	$0.364335\pi$
$251$			28.8514i			1.82108i	−0.413417	+	0.910542i	$0.635665\pi$
$252$		−	25.8113i		−	1.62596i
$253$		−	0.471059i		−	0.0296152i
$254$	4.19200			0.263030
$255$	15.0640			0.943347
$256$	20.9558			1.30974
$257$	2.82129			0.175987			0.0879937	−	0.996121i	$-0.471954\pi$
$257$	2.82129			0.175987			0.0879937	+	0.996121i	$0.471954\pi$
$258$	65.9119			4.10349
$259$			1.85028i			0.114971i
$260$		−	6.23681i		−	0.386791i
$261$	−51.9816			−3.21758
$262$	16.6732			1.03007
$263$	−17.9956			−1.10966			−0.554828	−	0.831965i	$-0.687216\pi$
$263$	−17.9956			−1.10966			−0.554828	+	0.831965i	$0.687216\pi$
$264$	18.6636			1.14867
$265$			7.92240i			0.486669i
$266$	−8.32483			−0.510428
$267$			25.0102i			1.53060i
$268$	−10.8214			−0.661019
$269$	−11.1771			−0.681481			−0.340741	−	0.940157i	$-0.610678\pi$
$269$	−11.1771			−0.681481			−0.340741	+	0.940157i	$0.610678\pi$
$270$			25.2025i			1.53378i
$271$	−9.54295			−0.579693			−0.289847	−	0.957073i	$-0.593604\pi$
$271$	−9.54295			−0.579693			−0.289847	+	0.957073i	$0.593604\pi$
$272$	26.3737			1.59914
$273$	43.8700			2.65513
$274$	12.3594			0.746658
$275$		−	20.2548i		−	1.22141i
$276$	0.444500			0.0267558
$277$		−	31.0024i		−	1.86275i	−0.364058	−	0.931376i	$-0.618609\pi$
$277$		−	31.0024i		−	1.86275i	0.364058	−	0.931376i	$-0.381391\pi$
$278$			22.6489i			1.35839i
$279$	69.1932			4.14249
$280$	−2.42952			−0.145192
$281$	−15.9949			−0.954177			−0.477089	−	0.878855i	$-0.658308\pi$
$281$	−15.9949			−0.954177			−0.477089	+	0.878855i	$0.658308\pi$
$282$	−16.5912			−0.987993
$283$	14.5680			0.865977			0.432989	−	0.901399i	$-0.357459\pi$
$283$	14.5680			0.865977			0.432989	+	0.901399i	$0.357459\pi$
$284$		−	13.1453i		−	0.780029i
$285$	5.25633			0.311358
$286$		−	47.4720i		−	2.80708i
$287$		−	16.4607i		−	0.971646i
$288$			51.9221i			3.05954i
$289$	12.2112			0.718308
$290$		−	10.0879i		−	0.592380i
$291$		−	42.5053i		−	2.49170i
$292$	−7.75298			−0.453709
$293$	28.4879			1.66428			0.832142	−	0.554563i	$-0.187115\pi$
$293$	28.4879			1.66428			0.832142	+	0.554563i	$0.187115\pi$
$294$		−	7.12742i		−	0.415680i
$295$			2.53825i			0.147782i
$296$		−	0.916353i		−	0.0532619i
$297$			77.1949i			4.47930i
$298$	−11.3215			−0.655836
$299$			0.548369i			0.0317130i
$300$	19.1128			1.10348
$301$	−26.2805			−1.51478
$302$		−	14.4467i		−	0.831314i
$303$			9.24851i			0.531313i
$304$	9.20266			0.527809
$305$			2.70777i			0.155047i
$306$			78.5338i			4.48948i
$307$	−24.9773			−1.42553			−0.712764	−	0.701404i	$-0.752557\pi$
$307$	−24.9773			−1.42553			−0.712764	+	0.701404i	$0.752557\pi$
$308$	15.3428			0.874239
$309$		−	22.0336i		−	1.25345i
$310$			13.4281i			0.762664i
$311$		−	7.43358i		−	0.421520i	−0.977538	−	0.210760i	$-0.932406\pi$
$311$		−	7.43358i		−	0.421520i	0.977538	−	0.210760i	$-0.0675938\pi$
$312$	−21.7267			−1.23003
$313$	−13.2220			−0.747353			−0.373676	−	0.927559i	$-0.621903\pi$
$313$	−13.2220			−0.747353			−0.373676	+	0.927559i	$0.621903\pi$
$314$			14.1992i			0.801309i
$315$		−	16.1479i		−	0.909833i
$316$		−	5.39574i		−	0.303534i
$317$		−	11.8733i		−	0.666871i	−0.942773	−	0.333435i	$-0.891792\pi$
$317$		−	11.8733i		−	0.666871i	0.942773	−	0.333435i	$-0.108208\pi$
$318$	−56.9021			−3.19091
$319$		−	30.8990i		−	1.73001i
$320$	−1.85331			−0.103603
$321$			4.66872i			0.260583i
$322$	−0.440424			−0.0245439
$323$	10.1928			0.567140
$324$	−40.7514			−2.26396
$325$			23.5790i			1.30793i
$326$	39.2951			2.17635
$327$	41.9274			2.31859
$328$			8.15221i			0.450130i
$329$	6.61527			0.364712
$330$	−24.0737			−1.32521
$331$			0.356292i			0.0195836i	0.999952	+	0.00979179i	$0.00311687\pi$
$331$			0.356292i			0.0195836i	−0.999952	+	0.00979179i	$0.996883\pi$
$332$	−6.67671			−0.366432
$333$	6.09059			0.333762
$334$	−26.7083			−1.46141
$335$	−6.76999			−0.369884
$336$		−	38.9497i		−	2.12488i
$337$	23.4259			1.27609			0.638046	−	0.769998i	$-0.279743\pi$
$337$	23.4259			1.27609			0.638046	+	0.769998i	$0.279743\pi$
$338$			31.4806i			1.71232i
$339$		−	49.4027i		−	2.68319i
$340$	−6.13305			−0.332612
$341$			41.1300i			2.22731i
$342$			27.4030i			1.48178i
$343$			19.7324i			1.06545i
$344$	13.0155			0.701746
$345$	0.278086			0.0149716
$346$	0.167796			0.00902075
$347$		−	10.3712i		−	0.556758i	−0.960471	−	0.278379i	$-0.910203\pi$
$347$		−	10.3712i		−	0.556758i	0.960471	−	0.278379i	$-0.0897971\pi$
$348$	29.1569			1.56297
$349$	−2.14956	−	18.5575i	−0.115063	−	0.993358i
$349$	−2.14956	−	18.5575i	−0.115063	−	0.993358i
$350$	−18.9376			−1.01226
$351$		−	89.8642i		−	4.79659i
$352$	−30.8636			−1.64504
$353$	29.9861			1.59600			0.798000	−	0.602658i	$-0.205892\pi$
$353$	29.9861			1.59600			0.798000	+	0.602658i	$0.205892\pi$
$354$	−18.2308			−0.968955
$355$		−	8.22388i		−	0.436478i
$356$		−	10.1825i		−	0.539670i
$357$		−	43.1402i		−	2.28322i
$358$	−28.4971			−1.50612
$359$		−	1.86227i		−	0.0982867i	−0.998792	−	0.0491434i	$-0.984351\pi$
$359$		−	1.86227i		−	0.0982867i	0.998792	−	0.0491434i	$-0.0156491\pi$
$360$			7.99730i			0.421495i
$361$	−15.4434			−0.812811
$362$		−	2.99272i		−	0.157294i
$363$	−37.3496			−1.96035
$364$	−17.8609			−0.936165
$365$	−4.85038			−0.253880
$366$	−19.4484			−1.01658
$367$			23.0189i			1.20158i	0.799407	+	0.600790i	$0.205147\pi$
$367$			23.0189i			1.20158i	−0.799407	+	0.600790i	$0.794853\pi$
$368$	0.486866			0.0253796
$369$	−54.1841			−2.82071
$370$			1.18198i			0.0614481i
$371$	22.6881			1.17791
$372$	−38.8111			−2.01226
$373$		−	9.31858i		−	0.482498i	−0.970463	−	0.241249i	$-0.922443\pi$
$373$		−	9.31858i		−	0.482498i	0.970463	−	0.241249i	$-0.0775570\pi$
$374$	−46.6822			−2.41388
$375$	25.8932			1.33712
$376$	−3.27623			−0.168959
$377$			35.9701i			1.85256i
$378$	72.1746			3.71226
$379$		−	21.3408i		−	1.09620i	−0.836413	−	0.548100i	$-0.815351\pi$
$379$		−	21.3408i		−	1.09620i	0.836413	−	0.548100i	$-0.184649\pi$
$380$	−2.14002			−0.109781
$381$			7.58001i			0.388336i
$382$			3.03618i			0.155345i
$383$			7.61608i			0.389163i	0.980886	+	0.194582i	$0.0623349\pi$
$383$			7.61608i			0.389163i	−0.980886	+	0.194582i	$0.937665\pi$
$384$			29.9378i			1.52775i
$385$	9.59869			0.489195
$386$	1.43877			0.0732312
$387$			86.5079i			4.39744i
$388$			17.3053i			0.878541i
$389$		−	6.62986i		−	0.336147i	−0.985774	−	0.168074i	$-0.946245\pi$
$389$		−	6.62986i		−	0.336147i	0.985774	−	0.168074i	$-0.0537546\pi$
$390$	28.0247			1.41909
$391$	0.539247			0.0272709
$392$		−	1.40743i		−	0.0710862i
$393$			30.1485i			1.52079i
$394$	−12.5672			−0.633129
$395$		−	3.37565i		−	0.169848i
$396$		−	50.5043i		−	2.53793i
$397$	14.0406			0.704676			0.352338	−	0.935873i	$-0.385387\pi$
$397$	14.0406			0.704676			0.352338	+	0.935873i	$0.385387\pi$
$398$	−33.4649			−1.67744
$399$		−	15.0530i		−	0.753594i
$400$	20.9345			1.04672
$401$			16.7868i			0.838295i	0.907918	+	0.419147i	$0.137671\pi$
$401$			16.7868i			0.838295i	−0.907918	+	0.419147i	$0.862329\pi$
$402$		−	48.6250i		−	2.42520i
$403$		−	47.8803i		−	2.38509i
$404$		−	3.76537i		−	0.187334i
$405$	−25.4946			−1.26684
$406$	−28.8895			−1.43376
$407$			3.62038i			0.179456i
$408$			21.3653i			1.05774i
$409$	23.5801			1.16596			0.582981	−	0.812485i	$-0.301886\pi$
$409$	23.5801			1.16596			0.582981	+	0.812485i	$0.301886\pi$
$410$		−	10.5153i		−	0.519314i
$411$			22.3483i			1.10236i
$412$			8.97060i			0.441950i
$413$	7.26900			0.357684
$414$			1.44975i			0.0712515i
$415$	−4.17705			−0.205043
$416$	35.9290			1.76156
$417$	−40.9540			−2.00553
$418$	−16.2890			−0.796719
$419$	−24.6726			−1.20533			−0.602667	−	0.797993i	$-0.705895\pi$
$419$	−24.6726			−1.20533			−0.602667	+	0.797993i	$0.705895\pi$
$420$			9.05751i			0.441961i
$421$			7.41282i			0.361279i	0.983549	+	0.180639i	$0.0578166\pi$
$421$			7.41282i			0.361279i	−0.983549	+	0.180639i	$0.942183\pi$
$422$	30.9476			1.50650
$423$		−	21.7756i		−	1.05877i
$424$	−11.2363			−0.545684
$425$	23.1868			1.12472
$426$	59.0674			2.86183
$427$	7.75449			0.375266
$428$		−	1.90079i		−	0.0918780i
$429$	85.8392			4.14435
$430$	−16.7883			−0.809602
$431$		−	12.1960i		−	0.587462i	−0.955888	−	0.293731i	$-0.905103\pi$
$431$		−	12.1960i		−	0.587462i	0.955888	−	0.293731i	$-0.0948971\pi$
$432$	−79.7853			−3.83867
$433$			14.9651i			0.719175i	0.933111	+	0.359587i	$0.117083\pi$
$433$			14.9651i			0.719175i	−0.933111	+	0.359587i	$0.882917\pi$
$434$	38.4552			1.84591
$435$	18.2410			0.874588
$436$	−17.0700			−0.817505
$437$	0.188161			0.00900095
$438$		−	34.8375i		−	1.66460i
$439$		−	12.6963i		−	0.605962i	−0.952997	−	0.302981i	$-0.902018\pi$
$439$		−	12.6963i		−	0.605962i	0.952997	−	0.302981i	$-0.0979819\pi$
$440$	−4.75377			−0.226627
$441$	9.35458			0.445456
$442$	54.3437			2.58487
$443$	−0.158577			−0.00753420			−0.00376710	−	0.999993i	$-0.501199\pi$
$443$	−0.158577			−0.00753420			−0.00376710	+	0.999993i	$0.501199\pi$
$444$	−3.41626			−0.162129
$445$		−	6.37030i		−	0.301981i
$446$			23.1486i			1.09612i
$447$		−	20.4716i		−	0.968273i
$448$			5.30748i			0.250755i
$449$	22.2598			1.05051			0.525253	−	0.850946i	$-0.323971\pi$
$449$	22.2598			1.05051			0.525253	+	0.850946i	$0.323971\pi$
$450$			62.3372i			2.93860i
$451$		−	32.2082i		−	1.51663i
$452$			20.1134i			0.946057i
$453$	26.1226			1.22735
$454$		−	9.81873i		−	0.460816i
$455$	−11.1740			−0.523847
$456$			7.45504i			0.349114i
$457$	−12.4449			−0.582149			−0.291075	−	0.956700i	$-0.594013\pi$
$457$	−12.4449			−0.582149			−0.291075	+	0.956700i	$0.594013\pi$
$458$	1.03114			0.0481819
$459$	−88.3692			−4.12472
$460$	−0.113218			−0.00527880
$461$			23.3703i			1.08846i	0.838935	+	0.544232i	$0.183179\pi$
$461$			23.3703i			1.08846i	−0.838935	+	0.544232i	$0.816821\pi$
$462$			68.9420i			3.20747i
$463$		−	0.591905i		−	0.0275082i	−0.999905	−	0.0137541i	$-0.995622\pi$
$463$		−	0.591905i		−	0.0275082i	0.999905	−	0.0137541i	$-0.00437820\pi$
$464$	31.9358			1.48258
$465$	−24.2808			−1.12599
$466$			32.1314i			1.48846i
$467$	27.8590			1.28916			0.644581	−	0.764536i	$-0.277032\pi$
$467$	27.8590			1.28916			0.644581	+	0.764536i	$0.277032\pi$
$468$			58.7931i			2.71771i
$469$			19.3878i			0.895247i
$470$	4.22591			0.194927
$471$	−25.6752			−1.18305
$472$	−3.59999			−0.165703
$473$	−51.4222			−2.36439
$474$	24.2454			1.11363
$475$	8.09063			0.371223
$476$			17.5638i			0.805034i
$477$		−	74.6828i		−	3.41949i
$478$			16.9610i			0.775776i
$479$	−8.65654			−0.395527			−0.197764	−	0.980250i	$-0.563368\pi$
$479$	−8.65654			−0.395527			−0.197764	+	0.980250i	$0.563368\pi$
$480$		−	18.2201i		−	0.831629i
$481$		−	4.21456i		−	0.192167i
$482$		−	21.1992i		−	0.965595i
$483$		−	0.796379i		−	0.0362365i
$484$	15.2062			0.691193
$485$			10.8264i			0.491602i
$486$		−	93.3787i		−	4.23575i
$487$			26.2319i			1.18868i	0.804213	+	0.594341i	$0.202587\pi$
$487$			26.2319i			1.18868i	−0.804213	+	0.594341i	$0.797413\pi$
$488$	−3.84043			−0.173848
$489$			71.0537i			3.21316i
$490$			1.81541i			0.0820118i
$491$	32.9975			1.48916			0.744579	−	0.667534i	$-0.232650\pi$
$491$	32.9975			1.48916			0.744579	+	0.667534i	$0.232650\pi$
$492$	30.3923			1.37019
$493$	35.3717			1.59306
$494$	18.9623			0.853154
$495$		−	31.5962i		−	1.42014i
$496$	−42.5102			−1.90876
$497$	−23.5514			−1.05643
$498$		−	30.0014i		−	1.34439i
$499$		−	38.5634i		−	1.72634i	−0.504917	−	0.863168i	$-0.668477\pi$
$499$		−	38.5634i		−	1.72634i	0.504917	−	0.863168i	$-0.331523\pi$
$500$	−10.5420			−0.471451
$501$		−	48.2942i		−	2.15762i
$502$	52.7814			2.35575
$503$			27.5601i			1.22884i	0.788978	+	0.614422i	$0.210611\pi$
$503$			27.5601i			1.22884i	−0.788978	+	0.614422i	$0.789389\pi$
$504$	22.9026			1.02016
$505$		−	2.35567i		−	0.104826i
$506$	−0.861765			−0.0383101
$507$	−56.9235			−2.52806
$508$		−	3.08607i		−	0.136922i
$509$			37.1270i			1.64563i	0.568311	+	0.822814i	$0.307597\pi$
$509$			37.1270i			1.64563i	−0.568311	+	0.822814i	$0.692403\pi$
$510$		−	27.5585i		−	1.22031i
$511$			13.8905i			0.614477i
$512$		−	20.2366i		−	0.894340i
$513$	−30.8349			−1.36139
$514$		−	5.16133i		−	0.227657i
$515$			5.61214i			0.247300i
$516$		−	48.5230i		−	2.13610i
$517$	12.9439			0.569272
$518$	3.38493			0.148725
$519$			0.303409i			0.0133182i
$520$	5.53397			0.242680
$521$		−	6.65009i		−	0.291346i	−0.989333	−	0.145673i	$-0.953465\pi$
$521$		−	6.65009i		−	0.291346i	0.989333	−	0.145673i	$-0.0465347\pi$
$522$			95.0962i			4.16225i
$523$			16.5720i			0.724641i	0.932054	+	0.362320i	$0.118015\pi$
$523$			16.5720i			0.724641i	−0.932054	+	0.362320i	$0.881985\pi$
$524$		−	12.2744i		−	0.536211i
$525$		−	34.2431i		−	1.49449i
$526$			32.9215i			1.43545i
$527$	−47.0837			−2.05100
$528$		−	76.2117i		−	3.31669i
$529$	−22.9900			−0.999567
$530$	14.4934			0.629554
$531$		−	23.9275i		−	1.03837i
$532$			6.12857i			0.265707i
$533$			37.4942i			1.62406i
$534$	45.7543			1.97998
$535$		−	1.18916i		−	0.0514119i
$536$		−	9.60186i		−	0.414737i
$537$		−	51.5287i		−	2.22363i
$538$			20.4477i			0.881562i
$539$			5.56057i			0.239511i
$540$	18.5536			0.798419
$541$	18.5491			0.797489			0.398744	−	0.917062i	$-0.369446\pi$
$541$	18.5491			0.797489			0.398744	+	0.917062i	$0.369446\pi$
$542$			17.4581i			0.749889i
$543$	5.41146			0.232228
$544$		−	35.3313i		−	1.51482i
$545$	−10.6792			−0.457448
$546$		−	80.2568i		−	3.43467i
$547$	2.09575			0.0896078			0.0448039	−	0.998996i	$-0.485734\pi$
$547$	2.09575			0.0896078			0.0448039	+	0.998996i	$0.485734\pi$
$548$		−	9.09873i		−	0.388678i
$549$		−	25.5256i		−	1.08941i
$550$	−37.0546			−1.58001
$551$	12.3424			0.525802
$552$			0.394408i			0.0167871i
$553$	−9.66715			−0.411089
$554$	−56.7164			−2.40965
$555$	−2.13726			−0.0907217
$556$	16.6737			0.707122
$557$			33.5493i			1.42153i	0.703430	+	0.710765i	$0.251651\pi$
$557$			33.5493i			1.42153i	−0.703430	+	0.710765i	$0.748349\pi$
$558$		−	126.584i		−	5.35871i
$559$	59.8616			2.53188
$560$			9.92079i			0.419230i
$561$		−	84.4112i		−	3.56384i
$562$			29.2615i			1.23432i
$563$	−1.64483			−0.0693214			−0.0346607	−	0.999399i	$-0.511035\pi$
$563$	−1.64483			−0.0693214			−0.0346607	+	0.999399i	$0.511035\pi$
$564$			12.2141i			0.514307i
$565$			12.5833i			0.529382i
$566$		−	26.6510i		−	1.12022i
$567$			73.0112i			3.06618i
$568$	11.6639			0.489406
$569$			4.45546i			0.186782i	0.995629	+	0.0933912i	$0.0297707\pi$
$569$			4.45546i			0.186782i	−0.995629	+	0.0933912i	$0.970229\pi$
$570$		−	9.61605i		−	0.402772i
$571$			4.28185i			0.179190i	0.995978	+	0.0895950i	$0.0285573\pi$
$571$			4.28185i			0.179190i	−0.995978	+	0.0895950i	$0.971443\pi$
$572$	−34.9479			−1.46124
$573$	−5.49005			−0.229350
$574$	−30.1136			−1.25692
$575$	0.428034			0.0178502
$576$	17.4707			0.727947
$577$	41.4012			1.72356			0.861778	−	0.507286i	$-0.169351\pi$
$577$	41.4012			1.72356			0.861778	+	0.507286i	$0.169351\pi$
$578$		−	22.3395i		−	0.929201i
$579$			2.60159i			0.108118i
$580$	−7.42648			−0.308368
$581$			11.9622i			0.496275i
$582$	−77.7600			−3.22326
$583$	44.3931			1.83857
$584$		−	6.87928i		−	0.284666i
$585$			36.7818i			1.52074i
$586$		−	52.1165i		−	2.15291i
$587$	25.9905			1.07274			0.536372	−	0.843982i	$-0.319794\pi$
$587$	25.9905			1.07274			0.536372	+	0.843982i	$0.319794\pi$
$588$	−5.24706			−0.216385
$589$	−16.4291			−0.676947
$590$	4.64352			0.191171
$591$		−	22.7242i		−	0.934748i
$592$	−3.74186			−0.153790
$593$		−	26.8864i		−	1.10409i	−0.833814	−	0.552046i	$-0.813847\pi$
$593$		−	26.8864i		−	1.10409i	0.833814	−	0.552046i	$-0.186153\pi$
$594$	141.222			5.79441
$595$			10.9881i			0.450470i
$596$			8.33464i			0.341400i
$597$		−	60.5115i		−	2.47657i
$598$	1.00320			0.0410238
$599$			43.1360i			1.76249i	0.472660	+	0.881245i	$0.343294\pi$
$599$			43.1360i			1.76249i	−0.472660	+	0.881245i	$0.656706\pi$
$600$			16.9590i			0.692346i
$601$		−	6.70002i		−	0.273299i	−0.990619	−	0.136650i	$-0.956367\pi$
$601$		−	6.70002i		−	0.273299i	0.990619	−	0.136650i	$-0.0436335\pi$
$602$			48.0780i			1.95951i
$603$	63.8193			2.59892
$604$	−10.6354			−0.432747
$605$	9.51324			0.386768
$606$	16.9194			0.687305
$607$	24.0104			0.974551			0.487275	−	0.873248i	$-0.337991\pi$
$607$	24.0104			0.974551			0.487275	+	0.873248i	$0.337991\pi$
$608$		−	12.3282i		−	0.499976i
$609$		−	52.2383i		−	2.11680i
$610$	4.95366			0.200568
$611$	−15.0683			−0.609597
$612$	57.8150			2.33703
$613$	−21.5207			−0.869214			−0.434607	−	0.900620i	$-0.643113\pi$
$613$	−21.5207			−0.869214			−0.434607	+	0.900620i	$0.643113\pi$
$614$			45.6940i			1.84406i
$615$	19.0139			0.766713
$616$			13.6138i			0.548516i
$617$	−12.7493			−0.513267			−0.256634	−	0.966509i	$-0.582613\pi$
$617$	−12.7493			−0.513267			−0.256634	+	0.966509i	$0.582613\pi$
$618$	−40.3088			−1.62146
$619$			34.5077i			1.38698i	0.720465	+	0.693491i	$0.243928\pi$
$619$			34.5077i			1.38698i	−0.720465	+	0.693491i	$0.756072\pi$
$620$	9.88548			0.397010
$621$	−1.63132			−0.0654625
$622$	−13.5992			−0.545276
$623$	−18.2432			−0.730898
$624$			88.7196i			3.55163i
$625$	14.8552			0.594208
$626$			24.1887i			0.966773i
$627$		−	29.4538i		−	1.17627i
$628$	10.4532			0.417127
$629$	−4.14444			−0.165250
$630$	−29.5414			−1.17696
$631$	−49.6131			−1.97507			−0.987534	−	0.157408i	$-0.949686\pi$
$631$	−49.6131			−1.97507			−0.987534	+	0.157408i	$0.949686\pi$
$632$	4.78768			0.190444
$633$			55.9597i			2.22420i
$634$	−21.7213			−0.862662
$635$		−	1.93069i		−	0.0766170i
$636$			41.8902i			1.66105i
$637$		−	6.47317i		−	0.256477i
$638$	−56.5273			−2.23794
$639$			77.5247i			3.06683i
$640$		−	7.62538i		−	0.301419i
$641$	−30.1036			−1.18902			−0.594511	−	0.804087i	$-0.702654\pi$
$641$	−30.1036			−1.18902			−0.594511	+	0.804087i	$0.702654\pi$
$642$	8.54106			0.337089
$643$		−	25.7896i		−	1.01704i	−0.861049	−	0.508522i	$-0.830192\pi$
$643$		−	25.7896i		−	1.01704i	0.861049	−	0.508522i	$-0.169808\pi$
$644$			0.324231i			0.0127765i
$645$		−	30.3567i		−	1.19529i
$646$		−	18.6468i		−	0.733650i
$647$	0.161262			0.00633986			0.00316993	−	0.999995i	$-0.498991\pi$
$647$	0.161262			0.00633986			0.00316993	+	0.999995i	$0.498991\pi$
$648$		−	36.1590i		−	1.42046i
$649$	14.2230			0.558303
$650$	43.1360			1.69193
$651$			69.5349i			2.72529i
$652$		−	28.9283i		−	1.13292i
$653$	−28.1542			−1.10176			−0.550880	−	0.834585i	$-0.685708\pi$
$653$	−28.1542			−1.10176			−0.550880	+	0.834585i	$0.685708\pi$
$654$		−	76.7029i		−	2.99932i
$655$		−	7.67906i		−	0.300046i
$656$	33.2890			1.29972
$657$	45.7235			1.78384
$658$		−	12.1021i		−	0.471790i
$659$		−	11.0888i		−	0.431960i	−0.976398	−	0.215980i	$-0.930705\pi$
$659$		−	11.0888i		−	0.431960i	0.976398	−	0.215980i	$-0.0692946\pi$
$660$			17.7226i			0.689850i
$661$	−38.8179			−1.50984			−0.754920	−	0.655817i	$-0.772324\pi$
$661$	−38.8179			−1.50984			−0.754920	+	0.655817i	$0.772324\pi$
$662$	0.651808			0.0253332
$663$			98.2648i			3.81629i
$664$		−	5.92429i		−	0.229907i
$665$			3.83412i			0.148681i
$666$		−	11.1422i		−	0.431753i
$667$	0.652971			0.0252831
$668$			19.6621i			0.760750i
$669$	−41.8575			−1.61830
$670$			12.3852i			0.478481i
$671$	15.1730			0.585746
$672$	−52.1785			−2.01283
$673$	7.96959			0.307205			0.153603	−	0.988133i	$-0.450912\pi$
$673$	7.96959			0.307205			0.153603	+	0.988133i	$0.450912\pi$
$674$		−	42.8559i		−	1.65075i
$675$	−70.1441			−2.69985
$676$	23.1754			0.891361
$677$		−	16.4177i		−	0.630983i	−0.948928	−	0.315491i	$-0.897831\pi$
$677$		−	16.4177i		−	0.630983i	0.948928	−	0.315491i	$-0.102169\pi$
$678$	−90.3784			−3.47096
$679$	31.0046			1.18985
$680$		−	5.44190i		−	0.208687i
$681$	17.7543			0.680346
$682$	75.2441			2.88125
$683$	−30.3940			−1.16299			−0.581497	−	0.813549i	$-0.697533\pi$
$683$	−30.3940			−1.16299			−0.581497	+	0.813549i	$0.697533\pi$
$684$	20.1735			0.771354
$685$		−	5.69230i		−	0.217491i
$686$	36.0988			1.37826
$687$			1.86451i			0.0711355i
$688$		−	53.1477i		−	2.02624i
$689$	−51.6789			−1.96881
$690$		−	0.508736i		−	0.0193673i
$691$			11.4388i			0.435151i	0.976043	+	0.217576i	$0.0698149\pi$
$691$			11.4388i			0.435151i	−0.976043	+	0.217576i	$0.930185\pi$
$692$		−	0.123528i		−	0.00469582i
$693$	−90.4848			−3.43723
$694$	−18.9734			−0.720220
$695$	10.4313			0.395682
$696$			25.8711i			0.980642i
$697$	36.8705			1.39657
$698$	−33.9494	+	3.93245i	−1.28500	+	0.148845i
$699$	−58.1003			−2.19756
$700$			13.9415i			0.526937i
$701$	11.5258			0.435323			0.217661	−	0.976024i	$-0.430157\pi$
$701$	11.5258			0.435323			0.217661	+	0.976024i	$0.430157\pi$
$702$	−164.399			−6.20486
$703$	−1.44613			−0.0545419
$704$			10.3850i			0.391399i
$705$			7.64133i			0.287789i
$706$		−	54.8572i		−	2.06458i
$707$	−6.74613			−0.253714
$708$			13.4211i			0.504397i
$709$			28.4552i			1.06866i	0.845277	+	0.534329i	$0.179435\pi$
$709$			28.4552i			1.06866i	−0.845277	+	0.534329i	$0.820565\pi$
$710$	−15.0449			−0.564626
$711$			31.8215i			1.19340i
$712$	9.03498			0.338600
$713$	−0.869177			−0.0325509
$714$	−78.9216			−2.95357
$715$	−21.8639			−0.817664
$716$			20.9790i			0.784021i
$717$	−30.6689			−1.14535
$718$	−3.40687			−0.127143
$719$		−	10.5726i		−	0.394290i	−0.980374	−	0.197145i	$-0.936833\pi$
$719$		−	10.5726i		−	0.394290i	0.980374	−	0.197145i	$-0.0631670\pi$
$720$	32.6564			1.21703
$721$	16.0720			0.598551
$722$			28.2525i			1.05145i
$723$	38.3325			1.42560
$724$	−2.20318			−0.0818805
$725$	28.0768			1.04274
$726$			68.3282i			2.53590i
$727$	8.68381			0.322065			0.161032	−	0.986949i	$-0.448518\pi$
$727$	8.68381			0.322065			0.161032	+	0.986949i	$0.448518\pi$
$728$		−	15.8481i		−	0.587370i
$729$	78.0733			2.89160
$730$			8.87338i			0.328419i
$731$		−	58.8658i		−	2.17723i
$732$			14.3175i			0.529191i
$733$			25.8142i			0.953469i	0.879047	+	0.476735i	$0.158180\pi$
$733$			25.8142i			0.953469i	−0.879047	+	0.476735i	$0.841820\pi$
$734$	42.1114			1.55436
$735$	−3.28264			−0.121082
$736$		−	0.652223i		−	0.0240413i
$737$			37.9356i			1.39738i
$738$			99.1255i			3.64886i
$739$	−24.3498			−0.895721			−0.447861	−	0.894103i	$-0.647814\pi$
$739$	−24.3498			−0.895721			−0.447861	+	0.894103i	$0.647814\pi$
$740$	0.870148			0.0319873
$741$			34.2878i			1.25959i
$742$		−	41.5060i		−	1.52374i
$743$	12.6260			0.463204			0.231602	−	0.972811i	$-0.425603\pi$
$743$	12.6260			0.463204			0.231602	+	0.972811i	$0.425603\pi$
$744$		−	34.4373i		−	1.26253i
$745$			5.21427i			0.191036i
$746$	−17.0476			−0.624157
$747$	39.3761			1.44070
$748$			34.3665i			1.25656i
$749$	−3.40550			−0.124434
$750$		−	47.3696i		−	1.72969i
$751$			1.16605i			0.0425496i	0.999774	+	0.0212748i	$0.00677249\pi$
$751$			1.16605i			0.0425496i	−0.999774	+	0.0212748i	$0.993228\pi$
$752$			13.3783i			0.487855i
$753$			95.4397i			3.47801i
$754$	65.8046			2.39646
$755$	−6.65364			−0.242151
$756$		−	53.1335i		−	1.93245i
$757$			15.3787i			0.558949i	0.960153	+	0.279475i	$0.0901603\pi$
$757$			15.3787i			0.558949i	−0.960153	+	0.279475i	$0.909840\pi$
$758$	−39.0412			−1.41804
$759$		−	1.55825i		−	0.0565609i
$760$		−	1.89886i		−	0.0688788i
$761$		−	25.9640i		−	0.941194i	−0.882348	−	0.470597i	$-0.844039\pi$
$761$		−	25.9640i		−	0.941194i	0.882348	−	0.470597i	$-0.155961\pi$
$762$	13.8670			0.502350
$763$			30.5831i			1.10718i
$764$	2.23518			0.0808658
$765$	36.1699			1.30772
$766$	13.9330			0.503420
$767$	−16.5573			−0.597851
$768$	69.3212			2.50141
$769$		−	19.8214i		−	0.714776i	−0.933956	−	0.357388i	$-0.883667\pi$
$769$		−	19.8214i		−	0.714776i	0.933956	−	0.357388i	$-0.116333\pi$
$770$		−	17.5601i		−	0.632820i
$771$	9.33277			0.336111
$772$		−	1.05919i		−	0.0381211i
$773$	30.8800			1.11068			0.555338	−	0.831625i	$-0.312589\pi$
$773$	30.8800			1.11068			0.555338	+	0.831625i	$0.312589\pi$
$774$	158.259			5.68851
$775$	−37.3733			−1.34249
$776$	−15.3551			−0.551215
$777$			6.12066i			0.219578i
$778$	−12.1288			−0.434839
$779$	12.8653			0.460948
$780$		−	20.6312i		−	0.738716i
$781$	−46.0824			−1.64896
$782$		−	0.986509i		−	0.0352775i
$783$	−107.006			−3.82408
$784$	−5.74716			−0.205256
$785$	6.53966			0.233410
$786$	55.1544			1.96729
$787$			22.1925i			0.791077i	0.918449	+	0.395539i	$0.129442\pi$
$787$			22.1925i			0.791077i	−0.918449	+	0.395539i	$0.870558\pi$
$788$			9.25175i			0.329580i
$789$	−59.5289			−2.11929
$790$	−6.17549			−0.219714
$791$	36.0358			1.28128
$792$	44.8128			1.59235
$793$	−17.6632			−0.627238
$794$		−	25.6861i		−	0.911566i
$795$			26.2071i			0.929470i
$796$			24.6362i			0.873206i
$797$			16.7974i			0.594995i	0.954723	+	0.297498i	$0.0961520\pi$
$797$			16.7974i			0.594995i	−0.954723	+	0.297498i	$0.903848\pi$
$798$	−27.5383			−0.974846
$799$			14.8176i			0.524209i
$800$		−	28.0446i		−	0.991527i
$801$			60.0515i			2.12181i
$802$	30.7102			1.08442
$803$			27.1790i			0.959127i
$804$	−35.7968			−1.26245
$805$			0.202844i			0.00714930i
$806$	−87.5932			−3.08534
$807$	−36.9736			−1.30153
$808$	3.34104			0.117537
$809$	37.1624			1.30656			0.653280	−	0.757116i	$-0.273392\pi$
$809$	37.1624			1.30656			0.653280	+	0.757116i	$0.273392\pi$
$810$			46.6404i			1.63878i
$811$		−	21.4042i		−	0.751602i	−0.926700	−	0.375801i	$-0.877368\pi$
$811$		−	21.4042i		−	0.751602i	0.926700	−	0.375801i	$-0.122632\pi$
$812$			21.2679i			0.746356i
$813$	−31.5678			−1.10713
$814$	6.62320			0.232143
$815$		−	18.0979i		−	0.633943i
$816$	87.2437			3.05414
$817$		−	20.5402i		−	0.718610i
$818$		−	43.1380i		−	1.50829i
$819$	105.335			3.68071
$820$	−7.74115			−0.270333
$821$	21.8648			0.763086			0.381543	−	0.924351i	$-0.375393\pi$
$821$	21.8648			0.763086			0.381543	+	0.924351i	$0.375393\pi$
$822$	40.8845			1.42601
$823$	−47.5977			−1.65915			−0.829576	−	0.558395i	$-0.811418\pi$
$823$	−47.5977			−1.65915			−0.829576	+	0.558395i	$0.811418\pi$
$824$	−7.95968			−0.277288
$825$		−	67.0024i		−	2.33272i
$826$		−	13.2981i		−	0.462699i
$827$			32.5483i			1.13181i	0.824469	+	0.565907i	$0.191474\pi$
$827$			32.5483i			1.13181i	−0.824469	+	0.565907i	$0.808526\pi$
$828$	1.06728			0.0370905
$829$			27.6730i			0.961122i	0.876961	+	0.480561i	$0.159567\pi$
$829$			27.6730i			0.961122i	−0.876961	+	0.480561i	$0.840433\pi$
$830$			7.64158i			0.265243i
$831$		−	102.555i		−	3.55760i
$832$		−	12.0894i		−	0.419124i
$833$	−6.36549			−0.220551
$834$			74.9221i			2.59434i
$835$			12.3009i			0.425690i
$836$			11.9916i			0.414738i
$837$	142.437			4.92333
$838$			45.1365i			1.55922i
$839$		−	0.413400i		−	0.0142721i	−0.999975	−	0.00713607i	$-0.997728\pi$
$839$		−	0.413400i		−	0.0142721i	0.999975	−	0.00713607i	$-0.00227150\pi$
$840$	−8.03680			−0.277296
$841$	13.8315			0.476947
$842$	13.5612			0.467349
$843$	−52.9108			−1.82235
$844$		−	22.7830i		−	0.784223i
$845$	14.4989			0.498776
$846$	−39.8368			−1.36962
$847$		−	27.2439i		−	0.936112i
$848$			45.8827i			1.57562i
$849$	48.1905			1.65389
$850$		−	42.4184i		−	1.45494i
$851$	−0.0765074			−0.00262264
$852$		−	43.4842i		−	1.48975i
$853$	−54.5059			−1.86625			−0.933123	−	0.359558i	$-0.882928\pi$
$853$	−54.5059			−1.86625			−0.933123	+	0.359558i	$0.882928\pi$
$854$		−	14.1862i		−	0.485443i
$855$	12.6209			0.431624
$856$	1.68658			0.0576462
$857$		−	24.8727i		−	0.849635i	−0.905279	−	0.424818i	$-0.860338\pi$
$857$		−	24.8727i		−	0.849635i	0.905279	−	0.424818i	$-0.139662\pi$
$858$		−	157.036i		−	5.36112i
$859$		−	37.4632i		−	1.27823i	−0.769112	−	0.639114i	$-0.779301\pi$
$859$		−	37.4632i		−	1.27823i	0.769112	−	0.639114i	$-0.220699\pi$
$860$			12.3592i			0.421444i
$861$		−	54.4516i		−	1.85571i
$862$	−22.3117			−0.759939
$863$		−	52.0897i		−	1.77315i	−0.462581	−	0.886577i	$-0.653077\pi$
$863$		−	52.0897i		−	1.77315i	0.462581	−	0.886577i	$-0.346923\pi$
$864$			106.883i			3.63624i
$865$		−	0.0772807i		−	0.00262762i
$866$	27.3774			0.930322
$867$	40.3945			1.37187
$868$		−	28.3099i		−	0.960901i
$869$	−18.9154			−0.641662
$870$		−	33.3704i		−	1.13136i
$871$		−	44.1616i		−	1.49636i
$872$		−	15.1463i		−	0.512920i
$873$		−	102.058i		−	3.45415i
$874$		−	0.344225i		−	0.0116436i
$875$			18.8873i			0.638506i
$876$	−25.6467			−0.866520
$877$			2.98406i			0.100765i	0.998730	+	0.0503823i	$0.0160440\pi$
$877$			2.98406i			0.100765i	−0.998730	+	0.0503823i	$0.983956\pi$
$878$	−23.2269			−0.783870
$879$	94.2374			3.17855
$880$			19.4117i			0.654369i
$881$		−	17.9280i		−	0.604011i	−0.953306	−	0.302005i	$-0.902344\pi$
$881$		−	17.9280i		−	0.604011i	0.953306	−	0.302005i	$-0.0976561\pi$
$882$		−	17.1135i		−	0.576241i
$883$	31.8297			1.07116			0.535578	−	0.844486i	$-0.320094\pi$
$883$	31.8297			1.07116			0.535578	+	0.844486i	$0.320094\pi$
$884$		−	40.0067i		−	1.34557i
$885$			8.39646i			0.282244i
$886$			0.290103i			0.00974621i
$887$			28.5815i			0.959672i	0.877358	+	0.479836i	$0.159304\pi$
$887$			28.5815i			0.959672i	−0.877358	+	0.479836i	$0.840696\pi$
$888$		−	3.03127i		−	0.101723i
$889$	−5.52908			−0.185439
$890$	−11.6540			−0.390642
$891$			142.859i			4.78595i
$892$	17.0415			0.570592
$893$			5.17034i			0.173019i
$894$	−37.4512			−1.25255
$895$			13.1248i			0.438712i
$896$	−21.8375			−0.729538
$897$			1.81399i			0.0605674i
$898$		−	40.7226i		−	1.35893i
$899$	−57.0135			−1.90151
$900$	45.8914			1.52971
$901$			50.8192i			1.69303i
$902$	−58.9224			−1.96190
$903$	−86.9351			−2.89302
$904$	−17.8468			−0.593576
$905$	−1.37834			−0.0458176
$906$		−	47.7893i		−	1.58769i
$907$			27.7022i			0.919836i	0.887961	+	0.459918i	$0.152121\pi$
$907$			27.7022i			0.919836i	−0.887961	+	0.459918i	$0.847879\pi$
$908$	−7.22835			−0.239881
$909$			22.2064i			0.736539i
$910$			20.4420i			0.677646i
$911$		−	54.1658i		−	1.79459i	−0.441430	−	0.897296i	$-0.645529\pi$
$911$		−	54.1658i		−	1.79459i	0.441430	−	0.897296i	$-0.354471\pi$
$912$	30.4422			1.00804
$913$			23.4060i			0.774627i
$914$			22.7670i			0.753066i
$915$			8.95725i			0.296117i
$916$		−	0.759102i		−	0.0250814i
$917$	−21.9912			−0.726214
$918$			161.664i			5.33572i
$919$			40.4643i			1.33480i	0.744702	+	0.667398i	$0.232592\pi$
$919$			40.4643i			1.33480i	−0.744702	+	0.667398i	$0.767408\pi$
$920$		−	0.100459i		−	0.00331203i
$921$	−82.6242			−2.72256
$922$	42.7541			1.40803
$923$	53.6455			1.76576
$924$	50.7537			1.66967
$925$	−3.28970			−0.108165
$926$	−1.08284			−0.0355845
$927$		−	52.9044i		−	1.73761i
$928$		−	42.7824i		−	1.40440i
$929$	−4.85683			−0.159348			−0.0796738	−	0.996821i	$-0.525388\pi$
$929$	−4.85683			−0.159348			−0.0796738	+	0.996821i	$0.525388\pi$
$930$			44.4197i			1.45658i
$931$	−2.22113			−0.0727945
$932$	23.6545			0.774829
$933$		−	24.5901i		−	0.805044i
$934$		−	50.9659i		−	1.66765i
$935$			21.5002i			0.703131i
$936$	−52.1675			−1.70515
$937$	40.3204			1.31721			0.658605	−	0.752489i	$-0.271147\pi$
$937$	40.3204			1.31721			0.658605	+	0.752489i	$0.271147\pi$
$938$	35.4685			1.15809
$939$	−43.7381			−1.42734
$940$		−	3.11103i		−	0.101471i
$941$	−28.6166			−0.932874			−0.466437	−	0.884554i	$-0.654463\pi$
$941$	−28.6166			−0.932874			−0.466437	+	0.884554i	$0.654463\pi$
$942$			46.9707i			1.53039i
$943$	0.680638			0.0221646
$944$			14.7003i			0.478454i
$945$		−	33.2411i		−	1.08133i
$946$			94.0728i			3.05857i
$947$	19.4312			0.631431			0.315715	−	0.948854i	$-0.397756\pi$
$947$	19.4312			0.631431			0.315715	+	0.948854i	$0.397756\pi$
$948$		−	17.8490i		−	0.579708i
$949$		−	31.6397i		−	1.02707i
$950$		−	14.8012i		−	0.480213i
$951$		−	39.2766i		−	1.27363i
$952$	−15.5845			−0.505095
$953$	25.6355			0.830416			0.415208	−	0.909727i	$-0.363709\pi$
$953$	25.6355			0.830416			0.415208	+	0.909727i	$0.363709\pi$
$954$	−136.626			−4.42344
$955$	1.39836			0.0452498
$956$	12.4863			0.403836
$957$		−	102.213i		−	3.30408i
$958$			15.8365i			0.511653i
$959$	−16.3015			−0.526404
$960$	−6.13070			−0.197867
$961$	44.8913			1.44811
$962$	−7.71020			−0.248587
$963$			11.2100i			0.361236i
$964$	−15.6064			−0.502648
$965$		−	0.662644i		−	0.0213313i
$966$	−1.45691			−0.0468754
$967$	−34.6438			−1.11407			−0.557035	−	0.830489i	$-0.688061\pi$
$967$	−34.6438			−1.11407			−0.557035	+	0.830489i	$0.688061\pi$
$968$			13.4926i			0.433669i
$969$	33.7174			1.08316
$970$	19.8061			0.635935
$971$	13.9687			0.448277			0.224139	−	0.974557i	$-0.428043\pi$
$971$	13.9687			0.448277			0.224139	+	0.974557i	$0.428043\pi$
$972$	−68.7435			−2.20495
$973$		−	29.8730i		−	0.957685i
$974$	47.9892			1.53767
$975$			77.9989i			2.49796i
$976$			15.6821i			0.501973i
$977$	−52.0432			−1.66501			−0.832504	−	0.554018i	$-0.813094\pi$
$977$	−52.0432			−1.66501			−0.832504	+	0.554018i	$0.813094\pi$
$978$	129.987			4.15653
$979$	−35.6959			−1.14085
$980$	1.33647			0.0426919
$981$	100.671			3.21417
$982$		−	60.3664i		−	1.92637i
$983$	−38.3595			−1.22348			−0.611738	−	0.791060i	$-0.709529\pi$
$983$	−38.3595			−1.22348			−0.611738	+	0.791060i	$0.709529\pi$
$984$			26.9673i			0.859686i
$985$			5.78803i			0.184422i
$986$		−	64.7098i		−	2.06078i
$987$	21.8831			0.696548
$988$		−	13.9597i		−	0.444116i
$989$		−	1.08668i		−	0.0345543i
$990$	−57.8028			−1.83709
$991$	46.0811			1.46382			0.731908	−	0.681404i	$-0.238630\pi$
$991$	46.0811			1.46382			0.731908	+	0.681404i	$0.238630\pi$
$992$			56.9482i			1.80811i
$993$			1.17860i			0.0374019i
$994$			43.0855i			1.36659i
$995$			15.4127i			0.488617i
$996$	−22.0864			−0.699834
$997$		−	47.4873i		−	1.50394i	−0.659198	−	0.751970i	$-0.729104\pi$
$997$		−	47.4873i		−	1.50394i	0.659198	−	0.751970i	$-0.270896\pi$
$998$	−70.5487			−2.23318
$999$	12.5377			0.396675

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.b.b.348.7	✓	26
349.348	even	2	inner	349.2.b.b.348.20	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.b.b.348.7	✓	26	1.1	even	1	trivial
349.2.b.b.348.20	yes	26	349.348	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.82942i q^{2} +3.30797 q^{3} -1.34678 q^{4} -0.842567 q^{5} -6.05168i q^{6} +2.41293i q^{7} -1.19501i q^{8} +7.94269 q^{9} +O(q^{10})\)	\(q-1.82942i q^{2} +3.30797 q^{3} -1.34678 q^{4} -0.842567 q^{5} -6.05168i q^{6} +2.41293i q^{7} -1.19501i q^{8} +7.94269 q^{9} +1.54141i q^{10} +4.72131i q^{11} -4.45512 q^{12} -5.49618i q^{13} +4.41427 q^{14} -2.78719 q^{15} -4.87974 q^{16} -5.40474 q^{17} -14.5305i q^{18} -1.88589 q^{19} +1.13475 q^{20} +7.98192i q^{21} +8.63727 q^{22} -0.0997728 q^{23} -3.95306i q^{24} -4.29008 q^{25} -10.0548 q^{26} +16.3503 q^{27} -3.24969i q^{28} -6.54458 q^{29} +5.09894i q^{30} +8.71156 q^{31} +6.53708i q^{32} +15.6180i q^{33} +9.88755i q^{34} -2.03306i q^{35} -10.6971 q^{36} +0.766816 q^{37} +3.45009i q^{38} -18.1812i q^{39} +1.00688i q^{40} -6.82187 q^{41} +14.6023 q^{42} +10.8915i q^{43} -6.35858i q^{44} -6.69225 q^{45} +0.182527i q^{46} -2.74159i q^{47} -16.1421 q^{48} +1.17776 q^{49} +7.84837i q^{50} -17.8787 q^{51} +7.40216i q^{52} -9.40270i q^{53} -29.9116i q^{54} -3.97802i q^{55} +2.88348 q^{56} -6.23848 q^{57} +11.9728i q^{58} -3.01252i q^{59} +3.75374 q^{60} -3.21372i q^{61} -15.9371i q^{62} +19.1652i q^{63} +2.19960 q^{64} +4.63090i q^{65} +28.5719 q^{66} +8.03497 q^{67} +7.27901 q^{68} -0.330046 q^{69} -3.71932 q^{70} +9.76050i q^{71} -9.49160i q^{72} +5.75667 q^{73} -1.40283i q^{74} -14.1915 q^{75} +2.53989 q^{76} -11.3922 q^{77} -33.2611 q^{78} +4.00639i q^{79} +4.11151 q^{80} +30.2583 q^{81} +12.4801i q^{82} +4.95753 q^{83} -10.7499i q^{84} +4.55386 q^{85} +19.9251 q^{86} -21.6493 q^{87} +5.64201 q^{88} +7.56059i q^{89} +12.2429i q^{90} +13.2619 q^{91} +0.134372 q^{92} +28.8176 q^{93} -5.01552 q^{94} +1.58899 q^{95} +21.6245i q^{96} -12.8493i q^{97} -2.15462i q^{98} +37.4999i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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