LMFDB - Embedded newform 336.4.bc.f.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.24856 + 4.05547i) q^{3} +(3.20701 + 5.55470i) q^{5} +(-14.8103 + 11.1200i) q^{7} +(-5.89369 - 26.3489i) q^{9} +O(q^{10})$	\(q+(-3.24856 + 4.05547i) q^{3} +(3.20701 + 5.55470i) q^{5} +(-14.8103 + 11.1200i) q^{7} +(-5.89369 - 26.3489i) q^{9} +(-16.2748 - 9.39624i) q^{11} -3.82794i q^{13} +(-32.9451 - 5.03886i) q^{15} +(-8.12865 + 14.0792i) q^{17} +(-129.810 + 74.9457i) q^{19} +(3.01540 - 96.1868i) q^{21} +(109.660 - 63.3124i) q^{23} +(41.9302 - 72.6252i) q^{25} +(126.003 + 61.6944i) q^{27} -168.029i q^{29} +(43.4021 + 25.0582i) q^{31} +(90.9757 - 35.4776i) q^{33} +(-109.265 - 46.6050i) q^{35} +(24.7303 + 42.8341i) q^{37} +(15.5241 + 12.4353i) q^{39} -19.9421 q^{41} -5.14899 q^{43} +(127.459 - 117.239i) q^{45} +(-308.507 - 534.350i) q^{47} +(95.6911 - 329.382i) q^{49} +(-30.6915 - 78.7028i) q^{51} +(242.707 + 140.127i) q^{53} -120.535i q^{55} +(117.755 - 769.905i) q^{57} +(274.552 - 475.538i) q^{59} +(-507.857 + 293.212i) q^{61} +(380.287 + 324.698i) q^{63} +(21.2631 - 12.2762i) q^{65} +(378.715 - 655.954i) q^{67} +(-99.4768 + 650.399i) q^{69} -351.397i q^{71} +(-530.937 - 306.537i) q^{73} +(158.317 + 405.974i) q^{75} +(345.521 - 41.8141i) q^{77} +(-505.776 - 876.030i) q^{79} +(-659.529 + 310.584i) q^{81} +1015.91 q^{83} -104.275 q^{85} +(681.436 + 545.852i) q^{87} +(178.762 + 309.625i) q^{89} +(42.5667 + 56.6931i) q^{91} +(-242.617 + 94.6128i) q^{93} +(-832.601 - 480.703i) q^{95} +228.442i q^{97} +(-151.662 + 484.201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) $ 48 * q - 12 * q^7 + 14 * q^9	$ 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) $ 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−3.24856	+	4.05547i	−0.625186	+	0.780476i
$3$	−3.24856	+	4.05547i	−0.625186	+	0.780476i
$4$		0			0
$5$	3.20701	+	5.55470i	0.286843	+	0.496827i	0.973055	−	0.230575i	$-0.0740607\pi$
$5$	3.20701	+	5.55470i	0.286843	+	0.496827i	−0.686211	+	0.727402i	$0.740727\pi$
$6$		0			0
$7$	−14.8103	+	11.1200i	−0.799682	+	0.600424i
$7$	−14.8103	+	11.1200i	−0.799682	+	0.600424i
$8$		0			0
$9$	−5.89369	−	26.3489i	−0.218285	−	0.975885i
$10$		0			0
$11$	−16.2748	−	9.39624i	−0.446093	−	0.257552i	0.260086	−	0.965586i	$-0.416249\pi$
$11$	−16.2748	−	9.39624i	−0.446093	−	0.257552i	−0.706179	+	0.708034i	$0.749583\pi$
$12$		0			0
$13$		−	3.82794i		−	0.0816677i	−0.999166	−	0.0408339i	$-0.986999\pi$
$13$		−	3.82794i		−	0.0816677i	0.999166	−	0.0408339i	$-0.0130014\pi$
$14$		0			0
$15$	−32.9451	−	5.03886i	−0.567092	−	0.0867353i
$16$		0			0
$17$	−8.12865	+	14.0792i	−0.115970	+	0.200866i	−0.918167	−	0.396193i	$-0.870331\pi$
$17$	−8.12865	+	14.0792i	−0.115970	+	0.200866i	0.802197	+	0.597059i	$0.203664\pi$
$18$		0			0
$19$	−129.810	+	74.9457i	−1.56739	+	0.904932i	−0.570917	+	0.821008i	$0.693412\pi$
$19$	−129.810	+	74.9457i	−1.56739	+	0.904932i	−0.996472	+	0.0839243i	$0.973255\pi$
$20$		0			0
$21$	3.01540	−	96.1868i	0.0313341	−	0.999509i
$22$		0			0
$23$	109.660	−	63.3124i	0.994164	−	0.573981i	0.0876474	−	0.996152i	$-0.472065\pi$
$23$	109.660	−	63.3124i	0.994164	−	0.573981i	0.906516	+	0.422171i	$0.138732\pi$
$24$		0			0
$25$	41.9302	−	72.6252i	0.335442	−	0.581002i
$26$		0			0
$27$	126.003	+	61.6944i	0.898123	+	0.439744i
$28$		0			0
$29$		−	168.029i		−	1.07594i	−0.842965	−	0.537969i	$-0.819192\pi$
$29$		−	168.029i		−	1.07594i	0.842965	−	0.537969i	$-0.180808\pi$
$30$		0			0
$31$	43.4021	+	25.0582i	0.251460	+	0.145180i	0.620432	−	0.784260i	$-0.286957\pi$
$31$	43.4021	+	25.0582i	0.251460	+	0.145180i	−0.368973	+	0.929440i	$0.620290\pi$
$32$		0			0
$33$	90.9757	−	35.4776i	0.479904	−	0.187147i
$34$		0			0
$35$	−109.265	−	46.6050i	−0.527691	−	0.225076i
$36$		0			0
$37$	24.7303	+	42.8341i	0.109882	+	0.190321i	0.915722	−	0.401812i	$-0.131619\pi$
$37$	24.7303	+	42.8341i	0.109882	+	0.190321i	−0.805840	+	0.592133i	$0.798286\pi$
$38$		0			0
$39$	15.5241	+	12.4353i	0.0637397	+	0.0510575i
$40$		0			0
$41$	−19.9421			−0.0759616			−0.0379808	−	0.999278i	$-0.512093\pi$
$41$	−19.9421			−0.0759616			−0.0379808	+	0.999278i	$0.512093\pi$
$42$		0			0
$43$	−5.14899			−0.0182608			−0.00913039	−	0.999958i	$-0.502906\pi$
$43$	−5.14899			−0.0182608			−0.00913039	+	0.999958i	$0.502906\pi$
$44$		0			0
$45$	127.459	−	117.239i	0.422233	−	0.388376i
$46$		0			0
$47$	−308.507	−	534.350i	−0.957455	−	1.65836i	−0.728647	−	0.684889i	$-0.759851\pi$
$47$	−308.507	−	534.350i	−0.957455	−	1.65836i	−0.228808	−	0.973472i	$-0.573483\pi$
$48$		0			0
$49$	95.6911	−	329.382i	0.278983	−	0.960296i
$50$		0			0
$51$	−30.6915	−	78.7028i	−0.0842681	−	0.216090i
$52$		0			0
$53$	242.707	+	140.127i	0.629027	+	0.363169i	0.780375	−	0.625312i	$-0.215028\pi$
$53$	242.707	+	140.127i	0.629027	+	0.363169i	−0.151348	+	0.988481i	$0.548361\pi$
$54$		0			0
$55$		−	120.535i		−	0.295508i
$56$		0			0
$57$	117.755	−	769.905i	0.273632	−	1.78906i
$58$		0			0
$59$	274.552	−	475.538i	0.605824	−	1.04932i	−0.386097	−	0.922458i	$-0.626177\pi$
$59$	274.552	−	475.538i	0.605824	−	1.04932i	0.991921	−	0.126859i	$-0.0404896\pi$
$60$		0			0
$61$	−507.857	+	293.212i	−1.06597	+	0.615441i	−0.927079	−	0.374866i	$-0.877689\pi$
$61$	−507.857	+	293.212i	−1.06597	+	0.615441i	−0.138896	+	0.990307i	$0.544355\pi$
$62$		0			0
$63$	380.287	+	324.698i	0.760503	+	0.649335i
$64$		0			0
$65$	21.2631	−	12.2762i	0.0405748	−	0.0234259i
$66$		0			0
$67$	378.715	−	655.954i	0.690558	−	1.19608i	−0.281097	−	0.959679i	$-0.590698\pi$
$67$	378.715	−	655.954i	0.690558	−	1.19608i	0.971655	−	0.236403i	$-0.0759685\pi$
$68$		0			0
$69$	−99.4768	+	650.399i	−0.173559	+	1.13477i
$70$		0			0
$71$		−	351.397i		−	0.587369i	−0.955902	−	0.293684i	$-0.905119\pi$
$71$		−	351.397i		−	0.587369i	0.955902	−	0.293684i	$-0.0948814\pi$
$72$		0			0
$73$	−530.937	−	306.537i	−0.851253	−	0.491471i	0.00982022	−	0.999952i	$-0.496874\pi$
$73$	−530.937	−	306.537i	−0.851253	−	0.491471i	−0.861074	+	0.508480i	$0.830207\pi$
$74$		0			0
$75$	158.317	+	405.974i	0.243744	+	0.625038i
$76$		0			0
$77$	345.521	−	41.8141i	0.511373	−	0.0618852i
$78$		0			0
$79$	−505.776	−	876.030i	−0.720307	−	1.24761i	−0.960877	−	0.276976i	$-0.910668\pi$
$79$	−505.776	−	876.030i	−0.720307	−	1.24761i	0.240570	−	0.970632i	$-0.422666\pi$
$80$		0			0
$81$	−659.529	+	310.584i	−0.904704	+	0.426042i
$82$		0			0
$83$	1015.91			1.34350			0.671751	−	0.740777i	$-0.265542\pi$
$83$	1015.91			1.34350			0.671751	+	0.740777i	$0.265542\pi$
$84$		0			0
$85$	−104.275			−0.133061
$86$		0			0
$87$	681.436	+	545.852i	0.839743	+	0.672661i
$88$		0			0
$89$	178.762	+	309.625i	0.212907	+	0.368766i	0.952623	−	0.304153i	$-0.0983735\pi$
$89$	178.762	+	309.625i	0.212907	+	0.368766i	−0.739716	+	0.672919i	$0.765040\pi$
$90$		0			0
$91$	42.5667	+	56.6931i	0.0490352	+	0.0653082i
$92$		0			0
$93$	−242.617	+	94.6128i	−0.270519	+	0.105493i
$94$		0			0
$95$	−832.601	−	480.703i	−0.899190	−	0.519148i
$96$		0			0
$97$			228.442i			0.239121i	0.992827	+	0.119561i	$0.0381486\pi$
$97$			228.442i			0.239121i	−0.992827	+	0.119561i	$0.961851\pi$
$98$		0			0
$99$	−151.662	+	484.201i	−0.153966	+	0.491555i
$100$		0			0
$101$	−369.946	+	640.766i	−0.364466	+	0.631273i	−0.988690	−	0.149972i	$-0.952082\pi$
$101$	−369.946	+	640.766i	−0.364466	+	0.631273i	0.624225	+	0.781245i	$0.285415\pi$
$102$		0			0
$103$	−1097.89	+	633.865i	−1.05027	+	0.606374i	−0.922725	−	0.385459i	$-0.874043\pi$
$103$	−1097.89	+	633.865i	−1.05027	+	0.606374i	−0.127546	+	0.991833i	$0.540710\pi$
$104$		0			0
$105$	543.959	−	291.722i	0.505571	−	0.271135i
$106$		0			0
$107$	−1210.72	+	699.008i	−1.09387	+	0.631548i	−0.934605	−	0.355687i	$-0.884247\pi$
$107$	−1210.72	+	699.008i	−1.09387	+	0.631548i	−0.159269	+	0.987235i	$0.550914\pi$
$108$		0			0
$109$	−689.394	+	1194.07i	−0.605798	+	1.04927i	0.386127	+	0.922446i	$0.373813\pi$
$109$	−689.394	+	1194.07i	−0.605798	+	1.04927i	−0.991925	+	0.126827i	$0.959521\pi$
$110$		0			0
$111$	−254.050	−	38.8563i	−0.217238	−	0.0332259i
$112$		0			0
$113$			753.627i			0.627392i	0.949523	+	0.313696i	$0.101567\pi$
$113$			753.627i			0.627392i	−0.949523	+	0.313696i	$0.898433\pi$
$114$		0			0
$115$	703.363	+	406.087i	0.570339	+	0.329285i
$116$		0			0
$117$	−100.862	+	22.5607i	−0.0796983	+	0.0178268i
$118$		0			0
$119$	−36.1732	−	298.909i	−0.0278655	−	0.230260i
$120$		0			0
$121$	−488.921	−	846.837i	−0.367334	−	0.636241i
$122$		0			0
$123$	64.7830	−	80.8744i	0.0474901	−	0.0592862i
$124$		0			0
$125$	1339.63			0.958564
$126$		0			0
$127$	−1495.09			−1.04463			−0.522314	−	0.852753i	$-0.674931\pi$
$127$	−1495.09			−1.04463			−0.522314	+	0.852753i	$0.674931\pi$
$128$		0			0
$129$	16.7268	−	20.8816i	0.0114164	−	0.0142521i
$130$		0			0
$131$	1016.07	+	1759.88i	0.677667	+	1.17375i	0.975682	+	0.219192i	$0.0703422\pi$
$131$	1016.07	+	1759.88i	0.677667	+	1.17375i	−0.298015	+	0.954561i	$0.596324\pi$
$132$		0			0
$133$	1089.13	−	2553.45i	0.710070	−	1.66476i
$134$		0			0
$135$	61.3995	+	897.764i	0.0391439	+	0.572350i
$136$		0			0
$137$	−493.918	−	285.163i	−0.308016	−	0.177833i	0.338022	−	0.941138i	$-0.390242\pi$
$137$	−493.918	−	285.163i	−0.308016	−	0.177833i	−0.646038	+	0.763305i	$0.723575\pi$
$138$		0			0
$139$			926.505i			0.565361i	0.959214	+	0.282680i	$0.0912236\pi$
$139$			926.505i			0.565361i	−0.959214	+	0.282680i	$0.908776\pi$
$140$		0			0
$141$	3169.25	+	484.728i	1.89290	+	0.289514i
$142$		0			0
$143$	−35.9683	+	62.2989i	−0.0210337	+	0.0364314i
$144$		0			0
$145$	933.350	−	538.870i	0.534555	−	0.308626i
$146$		0			0
$147$	1024.94	+	1458.09i	0.575072	+	0.818103i
$148$		0			0
$149$	−1927.70	+	1112.96i	−1.05989	+	0.611926i	−0.925401	−	0.378989i	$-0.876272\pi$
$149$	−1927.70	+	1112.96i	−1.05989	+	0.611926i	−0.134486	+	0.990915i	$0.542938\pi$
$150$		0			0
$151$	563.616	−	976.211i	0.303751	−	0.526112i	−0.673231	−	0.739432i	$-0.735094\pi$
$151$	563.616	−	976.211i	0.303751	−	0.526112i	0.976982	+	0.213320i	$0.0684275\pi$
$152$		0			0
$153$	418.880	+	131.202i	0.221336	+	0.0693274i
$154$		0			0
$155$			321.447i			0.166576i
$156$		0			0
$157$	−1589.18	−	917.514i	−0.807837	−	0.466405i	0.0383670	−	0.999264i	$-0.487784\pi$
$157$	−1589.18	−	917.514i	−0.807837	−	0.466405i	−0.846204	+	0.532859i	$0.821118\pi$
$158$		0			0
$159$	−1356.73	+	529.081i	−0.676703	+	0.263892i
$160$		0			0
$161$	−920.071	+	2157.10i	−0.450383	+	1.05592i
$162$		0			0
$163$	−1595.98	−	2764.32i	−0.766912	−	1.32833i	−0.939230	−	0.343290i	$-0.888459\pi$
$163$	−1595.98	−	2764.32i	−0.766912	−	1.32833i	0.172317	−	0.985042i	$-0.444875\pi$
$164$		0			0
$165$	488.827	+	391.566i	0.230637	+	0.184748i
$166$		0			0
$167$	−911.629			−0.422419			−0.211209	−	0.977441i	$-0.567740\pi$
$167$	−911.629			−0.422419			−0.211209	+	0.977441i	$0.567740\pi$
$168$		0			0
$169$	2182.35			0.993330
$170$		0			0
$171$	2739.79	+	2978.64i	1.22525	+	1.33206i
$172$		0			0
$173$	−1260.60	−	2183.42i	−0.553997	−	0.959550i	−0.997981	−	0.0635158i	$-0.979769\pi$
$173$	−1260.60	−	2183.42i	−0.553997	−	0.959550i	0.443984	−	0.896035i	$-0.353565\pi$
$174$		0			0
$175$	186.593	+	1541.87i	0.0806006	+	0.666024i
$176$		0			0
$177$	1036.63	+	2658.25i	0.440214	+	1.12885i
$178$		0			0
$179$	2321.13	+	1340.10i	0.969214	+	0.559576i	0.898997	−	0.437956i	$-0.144297\pi$
$179$	2321.13	+	1340.10i	0.969214	+	0.559576i	0.0702175	+	0.997532i	$0.477631\pi$
$180$		0			0
$181$		−	1777.93i		−	0.730126i	−0.930983	−	0.365063i	$-0.881047\pi$
$181$		−	1777.93i		−	0.730126i	0.930983	−	0.365063i	$-0.118953\pi$
$182$		0			0
$183$	460.695	−	3012.12i	0.186096	−	1.21673i
$184$		0			0
$185$	−158.620	+	274.738i	−0.0630378	+	0.109185i
$186$		0			0
$187$	264.584	−	152.758i	0.103467	−	0.0597366i
$188$		0			0
$189$	−2552.19	+	487.443i	−0.982246	+	0.187599i
$190$		0			0
$191$	−4038.21	+	2331.46i	−1.52982	+	0.883240i	−0.530447	+	0.847718i	$0.677976\pi$
$191$	−4038.21	+	2331.46i	−1.52982	+	0.883240i	−0.999369	+	0.0355219i	$0.988691\pi$
$192$		0			0
$193$	−1332.94	+	2308.72i	−0.497135	+	0.861062i	−0.999995	−	0.00330549i	$-0.998948\pi$
$193$	−1332.94	+	2308.72i	−0.497135	+	0.861062i	0.502860	+	0.864368i	$0.332281\pi$
$194$		0			0
$195$	−19.2885	+	126.112i	−0.00708347	+	0.0463132i
$196$		0			0
$197$		−	2482.37i		−	0.897776i	−0.893588	−	0.448888i	$-0.851820\pi$
$197$		−	2482.37i		−	0.897776i	0.893588	−	0.448888i	$-0.148180\pi$
$198$		0			0
$199$	2148.68	+	1240.54i	0.765407	+	0.441908i	0.831234	−	0.555923i	$-0.187635\pi$
$199$	2148.68	+	1240.54i	0.765407	+	0.441908i	−0.0658268	+	0.997831i	$0.520968\pi$
$200$		0			0
$201$	1429.92	+	3666.77i	0.501786	+	1.28674i
$202$		0			0
$203$	1868.48	+	2488.56i	0.646018	+	0.860408i
$204$		0			0
$205$	−63.9543	−	110.772i	−0.0217891	−	0.0377398i
$206$		0			0
$207$	−2314.52	−	2516.29i	−0.777150	−	0.844898i
$208$		0			0
$209$	2816.83			0.932269
$210$		0			0
$211$	−4644.74			−1.51544			−0.757718	−	0.652582i	$-0.773686\pi$
$211$	−4644.74			−1.51544			−0.757718	+	0.652582i	$0.773686\pi$
$212$		0			0
$213$	1425.08	+	1141.54i	0.458427	+	0.367215i
$214$		0			0
$215$	−16.5129	−	28.6011i	−0.00523799	−	0.00907246i
$216$		0			0
$217$	−921.446	+	111.511i	−0.288257	+	0.0348842i
$218$		0			0
$219$	2967.93	−	1157.40i	0.915773	−	0.357122i
$220$		0			0
$221$	53.8946	+	31.1160i	0.0164043	+	0.00947100i
$222$		0			0
$223$		−	4540.41i		−	1.36344i	−0.731611	−	0.681722i	$-0.761231\pi$
$223$		−	4540.41i		−	1.36344i	0.731611	−	0.681722i	$-0.238769\pi$
$224$		0			0
$225$	−2160.72	−	676.784i	−0.640213	−	0.200529i
$226$		0			0
$227$	−1556.40	+	2695.76i	−0.455074	+	0.788211i	−0.998692	−	0.0511214i	$-0.983720\pi$
$227$	−1556.40	+	2695.76i	−0.455074	+	0.788211i	0.543619	+	0.839332i	$0.317054\pi$
$228$		0			0
$229$	−2408.82	+	1390.73i	−0.695105	+	0.401319i	−0.805522	−	0.592566i	$-0.798115\pi$
$229$	−2408.82	+	1390.73i	−0.695105	+	0.401319i	0.110417	+	0.993885i	$0.464782\pi$
$230$		0			0
$231$	−952.869	+	1537.08i	−0.271403	+	0.437804i
$232$		0			0
$233$	752.864	−	434.666i	0.211681	−	0.122214i	−0.390411	−	0.920641i	$-0.627667\pi$
$233$	752.864	−	434.666i	0.211681	−	0.122214i	0.602093	+	0.798426i	$0.294334\pi$
$234$		0			0
$235$	1978.77	−	3427.33i	0.549279	−	0.951380i
$236$		0			0
$237$	5195.76	+	794.677i	1.42405	+	0.217805i
$238$		0			0
$239$		−	5664.29i		−	1.53302i	−0.642230	−	0.766512i	$-0.721991\pi$
$239$		−	5664.29i		−	1.53302i	0.642230	−	0.766512i	$-0.278009\pi$
$240$		0			0
$241$	−3937.58	−	2273.37i	−1.05246	−	0.607636i	−0.129121	−	0.991629i	$-0.541215\pi$
$241$	−3937.58	−	2273.37i	−1.05246	−	0.607636i	−0.923336	+	0.383993i	$0.874549\pi$
$242$		0			0
$243$	882.955	−	3683.65i	0.233093	−	0.972454i
$244$		0			0
$245$	2136.50	−	524.794i	0.557126	−	0.136848i
$246$		0			0
$247$	286.888	+	496.904i	0.0739038	+	0.128005i
$248$		0			0
$249$	−3300.25	+	4120.00i	−0.839939	+	1.04857i
$250$		0			0
$251$	7851.99			1.97455			0.987277	−	0.159009i	$-0.0508300\pi$
$251$	7851.99			1.97455			0.987277	+	0.159009i	$0.0508300\pi$
$252$		0			0
$253$	−2379.59			−0.591320
$254$		0			0
$255$	338.743	−	422.883i	0.0831878	−	0.103851i
$256$		0			0
$257$	−3467.17	−	6005.31i	−0.841541	−	1.45759i	−0.888592	−	0.458699i	$-0.848316\pi$
$257$	−3467.17	−	6005.31i	−0.841541	−	1.45759i	0.0470512	−	0.998892i	$-0.485018\pi$
$258$		0			0
$259$	−842.578	−	359.386i	−0.202144	−	0.0862206i
$260$		0			0
$261$	−4427.38	+	990.310i	−1.04999	+	0.234861i
$262$		0			0
$263$	−2180.19	−	1258.73i	−0.511165	−	0.295121i	0.222147	−	0.975013i	$-0.428693\pi$
$263$	−2180.19	−	1258.73i	−0.511165	−	0.295121i	−0.733312	+	0.679892i	$0.762027\pi$
$264$		0			0
$265$			1797.56i			0.416690i
$266$		0			0
$267$	−1836.39	−	280.871i	−0.420919	−	0.0643785i
$268$		0			0
$269$	−1837.15	+	3182.03i	−0.416405	+	0.721234i	−0.995575	−	0.0939727i	$-0.970043\pi$
$269$	−1837.15	+	3182.03i	−0.416405	+	0.721234i	0.579170	+	0.815207i	$0.303377\pi$
$270$		0			0
$271$	−1393.48	+	804.526i	−0.312354	+	0.180338i	−0.647979	−	0.761658i	$-0.724386\pi$
$271$	−1393.48	+	804.526i	−0.312354	+	0.180338i	0.335625	+	0.941996i	$0.391052\pi$
$272$		0			0
$273$	−368.198	−	11.5428i	−0.0816276	−	0.00255898i
$274$		0			0
$275$	−1364.81	+	787.972i	−0.299276	+	0.172787i
$276$		0			0
$277$	−662.678	+	1147.79i	−0.143742	+	0.248968i	−0.928903	−	0.370324i	$-0.879247\pi$
$277$	−662.678	+	1147.79i	−0.143742	+	0.248968i	0.785161	+	0.619292i	$0.212580\pi$
$278$		0			0
$279$	404.458	−	1291.28i	0.0867895	−	0.277086i
$280$		0			0
$281$		−	7368.35i		−	1.56427i	−0.623111	−	0.782133i	$-0.714132\pi$
$281$		−	7368.35i		−	1.56427i	0.623111	−	0.782133i	$-0.285868\pi$
$282$		0			0
$283$	611.270	+	352.917i	0.128397	+	0.0741298i	0.562823	−	0.826578i	$-0.309715\pi$
$283$	611.270	+	352.917i	0.128397	+	0.0741298i	−0.434426	+	0.900708i	$0.643049\pi$
$284$		0			0
$285$	4654.23	−	1815.00i	0.967344	−	0.377232i
$286$		0			0
$287$	295.348	−	221.756i	0.0607451	−	0.0456091i
$288$		0			0
$289$	2324.35	+	4025.89i	0.473102	+	0.819437i
$290$		0			0
$291$	−926.439	−	742.107i	−0.186628	−	0.149495i
$292$		0			0
$293$	−1369.20			−0.273002			−0.136501	−	0.990640i	$-0.543586\pi$
$293$	−1369.20			−0.273002			−0.136501	+	0.990640i	$0.543586\pi$
$294$		0			0
$295$	3521.96			0.695106
$296$		0			0
$297$	−1470.98	−	2188.02i	−0.287390	−	0.427480i
$298$		0			0
$299$	−242.356	−	419.774i	−0.0468757	−	0.0811911i
$300$		0			0
$301$	76.2582	−	57.2568i	0.0146028	−	0.0109642i
$302$		0			0
$303$	−1396.81	−	3581.87i	−0.264834	−	0.679120i
$304$		0			0
$305$	−3257.40	−	1880.66i	−0.611536	−	0.353070i
$306$		0			0
$307$			378.804i			0.0704217i	0.999380	+	0.0352109i	$0.0112103\pi$
$307$			378.804i			0.0704217i	−0.999380	+	0.0352109i	$0.988790\pi$
$308$		0			0
$309$	995.931	−	6511.59i	0.183354	−	1.19881i
$310$		0			0
$311$	3124.80	−	5412.32i	0.569747	−	0.986830i	−0.426844	−	0.904325i	$-0.640375\pi$
$311$	3124.80	−	5412.32i	0.569747	−	0.986830i	0.996591	−	0.0825051i	$-0.0262921\pi$
$312$		0			0
$313$	6621.79	−	3823.09i	1.19580	−	0.690396i	0.236185	−	0.971708i	$-0.424103\pi$
$313$	6621.79	−	3823.09i	1.19580	−	0.690396i	0.959616	+	0.281312i	$0.0907695\pi$
$314$		0			0
$315$	−584.015	+	3153.69i	−0.104462	+	0.564096i
$316$		0			0
$317$	5158.32	−	2978.16i	0.913944	−	0.527666i	0.0322462	−	0.999480i	$-0.489734\pi$
$317$	5158.32	−	2978.16i	0.913944	−	0.527666i	0.881698	+	0.471814i	$0.156401\pi$
$318$		0			0
$319$	−1578.84	+	2734.63i	−0.277110	+	0.479968i
$320$		0			0
$321$	1098.28	−	7180.80i	0.190967	−	1.24858i
$322$		0			0
$323$		−	2436.83i		−	0.419780i
$324$		0			0
$325$	−278.005	−	160.506i	−0.0474491	−	0.0273948i
$326$		0			0
$327$	−2602.96	−	6674.81i	−0.440195	−	1.12880i
$328$		0			0
$329$	10511.1	+	4483.29i	1.76138	+	0.751283i
$330$		0			0
$331$	5441.26	+	9424.54i	0.903561	+	1.56501i	0.822837	+	0.568278i	$0.192390\pi$
$331$	5441.26	+	9424.54i	0.903561	+	1.56501i	0.0807243	+	0.996736i	$0.474277\pi$
$332$		0			0
$333$	982.878	−	904.066i	0.161746	−	0.148776i
$334$		0			0
$335$	4858.17			0.792329
$336$		0			0
$337$	4801.91			0.776192			0.388096	−	0.921619i	$-0.373133\pi$
$337$	4801.91			0.776192			0.388096	+	0.921619i	$0.373133\pi$
$338$		0			0
$339$	−3056.31	−	2448.21i	−0.489664	−	0.392237i
$340$		0			0
$341$	−470.906	−	815.633i	−0.0747829	−	0.129528i
$342$		0			0
$343$	2245.51	+	5942.33i	0.353487	+	0.935440i
$344$		0			0
$345$	−3931.79	+	1533.27i	−0.613567	+	0.239271i
$346$		0			0
$347$	−2767.90	−	1598.05i	−0.428209	−	0.247227i	0.270374	−	0.962755i	$-0.412853\pi$
$347$	−2767.90	−	1598.05i	−0.428209	−	0.247227i	−0.698584	+	0.715529i	$0.746186\pi$
$348$		0			0
$349$			3496.39i			0.536268i	0.963382	+	0.268134i	$0.0864070\pi$
$349$			3496.39i			0.536268i	−0.963382	+	0.268134i	$0.913593\pi$
$350$		0			0
$351$	236.163	−	482.333i	0.0359129	−	0.0733477i
$352$		0			0
$353$	−793.536	+	1374.44i	−0.119648	+	0.207236i	−0.919628	−	0.392790i	$-0.871510\pi$
$353$	−793.536	+	1374.44i	−0.119648	+	0.207236i	0.799980	+	0.600026i	$0.204843\pi$
$354$		0			0
$355$	1951.91	−	1126.93i	0.291821	−	0.168483i
$356$		0			0
$357$	1329.73	+	824.324i	0.197133	+	0.122207i
$358$		0			0
$359$	−4461.30	+	2575.73i	−0.655873	+	0.378668i	−0.790703	−	0.612200i	$-0.790285\pi$
$359$	−4461.30	+	2575.73i	−0.655873	+	0.378668i	0.134830	+	0.990869i	$0.456951\pi$
$360$		0			0
$361$	7804.20	−	13517.3i	1.13781	−	1.97074i
$362$		0			0
$363$	5022.61	+	768.195i	0.726223	+	0.111074i
$364$		0			0
$365$		−	3932.26i		−	0.563901i
$366$		0			0
$367$	−10702.1	−	6178.85i	−1.52219	−	0.878837i	−0.999656	−	0.0262197i	$-0.991653\pi$
$367$	−10702.1	−	6178.85i	−1.52219	−	0.878837i	−0.522535	−	0.852618i	$-0.675014\pi$
$368$		0			0
$369$	117.532	+	525.451i	0.0165813	+	0.0741298i
$370$		0			0
$371$	−5152.79	+	623.578i	−0.721077	+	0.0872630i
$372$		0			0
$373$	2199.66	+	3809.93i	0.305346	+	0.528876i	0.977338	−	0.211683i	$-0.0678944\pi$
$373$	2199.66	+	3809.93i	0.305346	+	0.528876i	−0.671992	+	0.740558i	$0.734561\pi$
$374$		0			0
$375$	−4351.88	+	5432.85i	−0.599281	+	0.748136i
$376$		0			0
$377$	−643.205			−0.0878694
$378$		0			0
$379$	−5985.48			−0.811223			−0.405611	−	0.914046i	$-0.632941\pi$
$379$	−5985.48			−0.811223			−0.405611	+	0.914046i	$0.632941\pi$
$380$		0			0
$381$	4856.89	−	6063.29i	0.653086	−	0.815306i
$382$		0			0
$383$	499.156	+	864.563i	0.0665944	+	0.115345i	0.897400	−	0.441218i	$-0.145453\pi$
$383$	499.156	+	864.563i	0.0665944	+	0.115345i	−0.830806	+	0.556563i	$0.812120\pi$
$384$		0			0
$385$	1340.35	+	1785.17i	0.177430	+	0.236313i
$386$		0			0
$387$	30.3465	+	135.670i	0.00398605	+	0.0178204i
$388$		0			0
$389$	−2807.41	−	1620.86i	−0.365915	−	0.211261i	0.305757	−	0.952110i	$-0.401090\pi$
$389$	−2807.41	−	1620.86i	−0.365915	−	0.211261i	−0.671673	+	0.740848i	$0.734424\pi$
$390$		0			0
$391$			2058.58i			0.266258i
$392$		0			0
$393$	−10437.9	−	1596.45i	−1.33975	−	0.204912i
$394$		0			0
$395$	3244.05	−	5618.87i	0.413231	−	0.715737i
$396$		0			0
$397$	−4941.23	+	2852.82i	−0.624668	+	0.360652i	−0.778684	−	0.627416i	$-0.784113\pi$
$397$	−4941.23	+	2852.82i	−0.624668	+	0.360652i	0.154016	+	0.988068i	$0.450779\pi$
$398$		0			0
$399$	6817.36	+	12712.0i	0.855375	+	1.59497i
$400$		0			0
$401$	−8593.43	+	4961.42i	−1.07016	+	0.617859i	−0.928226	−	0.372017i	$-0.878666\pi$
$401$	−8593.43	+	4961.42i	−1.07016	+	0.617859i	−0.141937	+	0.989876i	$0.545333\pi$
$402$		0			0
$403$	95.9214	−	166.141i	0.0118565	−	0.0205361i
$404$		0			0
$405$	−3840.32	−	2667.44i	−0.471177	−	0.327274i
$406$		0			0
$407$		−	929.486i		−	0.113201i
$408$		0			0
$409$	3086.33	+	1781.89i	0.373128	+	0.215425i	0.674824	−	0.737979i	$-0.264220\pi$
$409$	3086.33	+	1781.89i	0.373128	+	0.215425i	−0.301696	+	0.953404i	$0.597553\pi$
$410$		0			0
$411$	2760.99	−	1076.70i	0.331362	−	0.129220i
$412$		0			0
$413$	1221.78	+	10095.9i	0.145569	+	1.20287i
$414$		0			0
$415$	3258.03	+	5643.08i	0.385375	+	0.667489i
$416$		0			0
$417$	−3757.41	−	3009.81i	−0.441250	−	0.353456i
$418$		0			0
$419$	6476.33			0.755106			0.377553	−	0.925988i	$-0.376766\pi$
$419$	6476.33			0.755106			0.377553	+	0.925988i	$0.376766\pi$
$420$		0			0
$421$	−9730.34			−1.12643			−0.563216	−	0.826310i	$-0.690436\pi$
$421$	−9730.34			−1.12643			−0.563216	+	0.826310i	$0.690436\pi$
$422$		0			0
$423$	−12261.3	+	11278.1i	−1.40937	+	1.29636i
$424$		0			0
$425$	681.672	+	1180.69i	0.0778023	+	0.134757i
$426$		0			0
$427$	4261.02	−	9989.93i	0.482916	−	1.13219i
$428$		0			0
$429$	−135.806	−	348.250i	−0.0152839	−	0.0391927i
$430$		0			0
$431$	−710.320	−	410.104i	−0.0793850	−	0.0458329i	0.459782	−	0.888032i	$-0.347928\pi$
$431$	−710.320	−	410.104i	−0.0793850	−	0.0458329i	−0.539167	+	0.842199i	$0.681261\pi$
$432$		0			0
$433$		−	2649.84i		−	0.294095i	−0.989129	−	0.147047i	$-0.953023\pi$
$433$		−	2649.84i		−	0.294095i	0.989129	−	0.147047i	$-0.0469770\pi$
$434$		0			0
$435$	−846.675	+	5535.73i	−0.0933217	+	0.610156i
$436$		0			0
$437$	−9489.98	+	16437.1i	−1.03883	+	1.79930i
$438$		0			0
$439$	−749.263	+	432.587i	−0.0814587	+	0.0470302i	−0.540176	−	0.841552i	$-0.681642\pi$
$439$	−749.263	+	432.587i	−0.0814587	+	0.0470302i	0.458717	+	0.888582i	$0.348309\pi$
$440$		0			0
$441$	−9242.81	−	580.084i	−0.998036	−	0.0626373i
$442$		0			0
$443$	−13816.2	+	7976.78i	−1.48178	+	0.855504i	−0.999786	−	0.0206723i	$-0.993419\pi$
$443$	−13816.2	+	7976.78i	−1.48178	+	0.855504i	−0.481990	+	0.876176i	$0.660086\pi$
$444$		0			0
$445$	−1146.58	+	1985.94i	−0.122142	+	0.211556i
$446$		0			0
$447$	1748.68	−	11433.2i	0.185033	−	1.20978i
$448$		0			0
$449$			12434.9i			1.30699i	0.756929	+	0.653497i	$0.226699\pi$
$449$			12434.9i			1.30699i	−0.756929	+	0.653497i	$0.773301\pi$
$450$		0			0
$451$	324.552	+	187.380i	0.0338860	+	0.0195641i
$452$		0			0
$453$	2128.06	+	5457.01i	0.220717	+	0.565988i
$454$		0			0
$455$	−178.401	+	418.261i	−0.0183815	+	0.0430953i
$456$		0			0
$457$	4221.48	+	7311.82i	0.432106	+	0.748430i	0.997054	−	0.0766964i	$-0.0244372\pi$
$457$	4221.48	+	7311.82i	0.432106	+	0.748430i	−0.564948	+	0.825126i	$0.691104\pi$
$458$		0			0
$459$	−1892.85	+	1272.54i	−0.192485	+	0.129405i
$460$		0			0
$461$	15084.5			1.52398			0.761990	−	0.647589i	$-0.224222\pi$
$461$	15084.5			1.52398			0.761990	+	0.647589i	$0.224222\pi$
$462$		0			0
$463$	14516.8			1.45713			0.728565	−	0.684977i	$-0.240188\pi$
$463$	14516.8			1.45713			0.728565	+	0.684977i	$0.240188\pi$
$464$		0			0
$465$	−1303.62	−	1044.24i	−0.130009	−	0.104141i
$466$		0			0
$467$	−112.021	−	194.026i	−0.0111000	−	0.0192258i	0.860422	−	0.509582i	$-0.170200\pi$
$467$	−112.021	−	194.026i	−0.0111000	−	0.0192258i	−0.871522	+	0.490356i	$0.836867\pi$
$468$		0			0
$469$	1685.32	+	13926.2i	0.165929	+	1.37111i
$470$		0			0
$471$	8883.50	−	3464.28i	0.869066	−	0.338907i
$472$		0			0
$473$	83.7986	+	48.3811i	0.00814601	+	0.00470310i
$474$		0			0
$475$			12569.9i			1.21421i
$476$		0			0
$477$	2261.76	−	7220.94i	0.217104	−	0.693132i
$478$		0			0
$479$	−6518.94	+	11291.1i	−0.621833	+	1.07705i	0.367311	+	0.930098i	$0.380279\pi$
$479$	−6518.94	+	11291.1i	−0.621833	+	1.07705i	−0.989144	+	0.146949i	$0.953055\pi$
$480$		0			0
$481$	163.966	−	94.6661i	0.0155431	−	0.00897381i
$482$		0			0
$483$	−5759.15	−	10738.8i	−0.542548	−	1.01166i
$484$		0			0
$485$	−1268.93	+	732.614i	−0.118802	+	0.0685903i
$486$		0			0
$487$	2627.47	−	4550.91i	0.244481	−	0.423453i	−0.717505	−	0.696553i	$-0.754716\pi$
$487$	2627.47	−	4550.91i	0.244481	−	0.423453i	0.961985	+	0.273101i	$0.0880492\pi$
$488$		0			0
$489$	16395.2	+	2507.61i	1.51619	+	0.231898i
$490$		0			0
$491$		−	18062.2i		−	1.66015i	−0.557649	−	0.830077i	$-0.688296\pi$
$491$		−	18062.2i		−	1.66015i	0.557649	−	0.830077i	$-0.311704\pi$
$492$		0			0
$493$	2365.72	+	1365.85i	0.216119	+	0.124776i
$494$		0			0
$495$	−3175.97	+	710.397i	−0.288382	+	0.0645050i
$496$		0			0
$497$	3907.54	+	5204.30i	0.352670	+	0.469708i
$498$		0			0
$499$	3863.05	+	6691.01i	0.346561	+	0.600262i	0.985636	−	0.168883i	$-0.0540159\pi$
$499$	3863.05	+	6691.01i	0.346561	+	0.600262i	−0.639075	+	0.769145i	$0.720683\pi$
$500$		0			0
$501$	2961.48	−	3697.08i	0.264090	−	0.329688i
$502$		0			0
$503$	2728.48			0.241862			0.120931	−	0.992661i	$-0.461412\pi$
$503$	2728.48			0.241862			0.120931	+	0.992661i	$0.461412\pi$
$504$		0			0
$505$	−4745.68			−0.418178
$506$		0			0
$507$	−7089.49	+	8850.44i	−0.621016	+	0.775270i
$508$		0			0
$509$	−350.269	−	606.685i	−0.0305018	−	0.0528307i	0.850372	−	0.526183i	$-0.176377\pi$
$509$	−350.269	−	606.685i	−0.0305018	−	0.0528307i	−0.880873	+	0.473352i	$0.843044\pi$
$510$		0			0
$511$	11272.0	−	1364.12i	0.975823	−	0.118092i
$512$		0			0
$513$	−20980.2	+	1434.87i	−1.80565	+	0.123491i
$514$		0			0
$515$	−7041.86	−	4065.62i	−0.602527	−	0.347869i
$516$		0			0
$517$			11595.2i			0.986378i
$518$		0			0
$519$	12949.9	+	1980.66i	1.09526	+	0.167517i
$520$		0			0
$521$	2238.40	−	3877.02i	0.188227	−	0.326018i	−0.756432	−	0.654072i	$-0.773059\pi$
$521$	2238.40	−	3877.02i	0.188227	−	0.326018i	0.944659	+	0.328054i	$0.106393\pi$
$522$		0			0
$523$	14233.4	−	8217.67i	1.19003	−	0.687062i	0.231714	−	0.972784i	$-0.425567\pi$
$523$	14233.4	−	8217.67i	1.19003	−	0.687062i	0.958313	+	0.285722i	$0.0922333\pi$
$524$		0			0
$525$	−6859.16	−	4252.13i	−0.570206	−	0.353482i
$526$		0			0
$527$	−705.601	+	407.379i	−0.0583235	+	0.0336731i
$528$		0			0
$529$	1933.43	−	3348.80i	0.158908	−	0.275236i
$530$		0			0
$531$	−14148.0	−	4431.47i	−1.15626	−	0.362164i
$532$		0			0
$533$			76.3371i			0.00620361i
$534$		0			0
$535$	−7765.56	−	4483.45i	−0.627541	−	0.362311i
$536$		0			0
$537$	−12975.1	+	5059.86i	−1.04267	+	0.406609i
$538$		0			0
$539$	−4652.30	+	4461.47i	−0.371779	+	0.356529i
$540$		0			0
$541$	−7508.79	−	13005.6i	−0.596725	−	1.03356i	−0.993301	−	0.115556i	$-0.963135\pi$
$541$	−7508.79	−	13005.6i	−0.596725	−	1.03356i	0.396576	−	0.918002i	$-0.370198\pi$
$542$		0			0
$543$	7210.36	+	5775.73i	0.569846	+	0.456465i
$544$		0			0
$545$	−8843.57			−0.695077
$546$		0			0
$547$	6210.19			0.485427			0.242713	−	0.970098i	$-0.421963\pi$
$547$	6210.19			0.485427			0.242713	+	0.970098i	$0.421963\pi$
$548$		0			0
$549$	10719.0	+	11653.4i	0.833285	+	0.905928i
$550$		0			0
$551$	12593.0	+	21811.8i	0.973650	+	1.68641i
$552$		0			0
$553$	17232.2	+	7350.05i	1.32511	+	0.565201i
$554$		0			0
$555$	−598.906	−	1535.78i	−0.0458056	−	0.117460i
$556$		0			0
$557$	1954.64	+	1128.51i	0.148691	+	0.0858468i	0.572500	−	0.819905i	$-0.305974\pi$
$557$	1954.64	+	1128.51i	0.148691	+	0.0858468i	−0.423809	+	0.905752i	$0.639307\pi$
$558$		0			0
$559$			19.7100i			0.00149132i
$560$		0			0
$561$	−240.013	+	1569.25i	−0.0180630	+	0.118100i
$562$		0			0
$563$	3041.83	−	5268.60i	0.227705	−	0.394396i	−0.729423	−	0.684063i	$-0.760211\pi$
$563$	3041.83	−	5268.60i	0.227705	−	0.394396i	0.957127	+	0.289667i	$0.0935446\pi$
$564$		0			0
$565$	−4186.17	+	2416.89i	−0.311706	+	0.179963i
$566$		0			0
$567$	6314.14	−	11933.8i	0.467670	−	0.883903i
$568$		0			0
$569$	14453.8	−	8344.92i	1.06491	−	0.614828i	0.138126	−	0.990415i	$-0.455892\pi$
$569$	14453.8	−	8344.92i	1.06491	−	0.614828i	0.926787	+	0.375587i	$0.122559\pi$
$570$		0			0
$571$	−8262.11	+	14310.4i	−0.605532	+	1.04881i	0.386436	+	0.922316i	$0.373706\pi$
$571$	−8262.11	+	14310.4i	−0.605532	+	1.04881i	−0.991967	+	0.126495i	$0.959627\pi$
$572$		0			0
$573$	3663.21	−	23950.8i	0.267073	−	1.74617i
$574$		0			0
$575$		−	10618.8i		−	0.770148i
$576$		0			0
$577$	21924.0	+	12657.8i	1.58182	+	0.913263i	0.994594	+	0.103839i	$0.0331127\pi$
$577$	21924.0	+	12657.8i	1.58182	+	0.913263i	0.587224	+	0.809424i	$0.300221\pi$
$578$		0			0
$579$	−5032.80	−	12905.7i	−0.361237	−	0.926326i
$580$		0			0
$581$	−15046.0	+	11296.9i	−1.07438	+	0.806671i
$582$		0			0
$583$	−2633.34	−	4561.07i	−0.187070	−	0.324014i
$584$		0			0
$585$	−448.783	−	487.906i	−0.0317178	−	0.0344828i
$586$		0			0
$587$	−3690.67			−0.259507			−0.129753	−	0.991546i	$-0.541419\pi$
$587$	−3690.67			−0.259507			−0.129753	+	0.991546i	$0.541419\pi$
$588$		0			0
$589$	−7512.02			−0.525513
$590$		0			0
$591$	10067.2	+	8064.14i	0.700692	+	0.561277i
$592$		0			0
$593$	−5974.61	−	10348.3i	−0.413740	−	0.716618i	0.581555	−	0.813507i	$-0.302444\pi$
$593$	−5974.61	−	10348.3i	−0.413740	−	0.716618i	−0.995295	+	0.0968883i	$0.969111\pi$
$594$		0			0
$595$	1544.34	−	1159.53i	0.106406	−	0.0798929i
$596$		0			0
$597$	−12011.1	+	4683.94i	−0.823420	+	0.321107i
$598$		0			0
$599$	24525.5	+	14159.8i	1.67293	+	0.965867i	0.965984	+	0.258601i	$0.0832615\pi$
$599$	24525.5	+	14159.8i	1.67293	+	0.965867i	0.706947	+	0.707266i	$0.250072\pi$
$600$		0			0
$601$		−	7283.94i		−	0.494373i	−0.968968	−	0.247186i	$-0.920494\pi$
$601$		−	7283.94i		−	0.494373i	0.968968	−	0.247186i	$-0.0795060\pi$
$602$		0			0
$603$	−19515.7	−	6112.74i	−1.31798	−	0.412819i
$604$		0			0
$605$	3135.95	−	5431.62i	0.210735	−	0.365003i
$606$		0			0
$607$	−11997.0	+	6926.47i	−0.802213	+	0.463158i	−0.844244	−	0.535959i	$-0.819950\pi$
$607$	−11997.0	+	6926.47i	−0.802213	+	0.463158i	0.0420315	+	0.999116i	$0.486617\pi$
$608$		0			0
$609$	−16162.2	−	506.675i	−1.07541	−	0.0337135i
$610$		0			0
$611$	−2045.46	+	1180.95i	−0.135435	+	0.0781932i
$612$		0			0
$613$	12258.6	−	21232.5i	0.807701	−	1.39898i	−0.106752	−	0.994286i	$-0.534045\pi$
$613$	12258.6	−	21232.5i	0.807701	−	1.39898i	0.914453	−	0.404693i	$-0.132622\pi$
$614$		0			0
$615$	656.993	+	100.485i	0.0430772	+	0.00658855i
$616$		0			0
$617$			7547.59i			0.492471i	0.969210	+	0.246235i	$0.0791936\pi$
$617$			7547.59i			0.492471i	−0.969210	+	0.246235i	$0.920806\pi$
$618$		0			0
$619$	−7574.37	−	4373.06i	−0.491825	−	0.283955i	0.233506	−	0.972355i	$-0.424980\pi$
$619$	−7574.37	−	4373.06i	−0.491825	−	0.283955i	−0.725331	+	0.688400i	$0.758313\pi$
$620$		0			0
$621$	17723.6	−	1212.14i	1.14529	−	0.0783279i
$622$		0			0
$623$	−6090.55	−	2597.81i	−0.391674	−	0.167061i
$624$		0			0
$625$	−945.060	−	1636.89i	−0.0604838	−	0.104761i
$626$		0			0
$627$	−9150.64	+	11423.6i	−0.582841	+	0.727613i
$628$		0			0
$629$	−804.095			−0.0509720
$630$		0			0
$631$	496.823			0.0313442			0.0156721	−	0.999877i	$-0.495011\pi$
$631$	496.823			0.0313442			0.0156721	+	0.999877i	$0.495011\pi$
$632$		0			0
$633$	15088.7	−	18836.6i	0.947430	−	1.18276i
$634$		0			0
$635$	−4794.76	−	8304.77i	−0.299645	−	0.519000i
$636$		0			0
$637$	−1260.85	−	366.300i	−0.0784252	−	0.0227839i
$638$		0			0
$639$	−9258.93	+	2071.02i	−0.573204	+	0.128214i
$640$		0			0
$641$	−14230.8	−	8216.15i	−0.876883	−	0.506269i	−0.00725375	−	0.999974i	$-0.502309\pi$
$641$	−14230.8	−	8216.15i	−0.876883	−	0.506269i	−0.869629	+	0.493705i	$0.835642\pi$
$642$		0			0
$643$			26894.9i			1.64950i	0.565495	+	0.824752i	$0.308685\pi$
$643$			26894.9i			1.64950i	−0.565495	+	0.824752i	$0.691315\pi$
$644$		0			0
$645$	169.634	+	25.9451i	0.0103555	+	0.00158385i
$646$		0			0
$647$	8063.38	−	13966.2i	0.489960	−	0.848636i	−0.509973	−	0.860190i	$-0.670345\pi$
$647$	8063.38	−	13966.2i	0.489960	−	0.848636i	0.999933	+	0.0115546i	$0.00367803\pi$
$648$		0			0
$649$	−8936.53	+	5159.51i	−0.540508	+	0.312062i
$650$		0			0
$651$	2541.14	−	4099.15i	0.152988	−	0.246787i
$652$		0			0
$653$	22832.2	−	13182.2i	1.36829	−	0.789982i	0.377579	−	0.925977i	$-0.376757\pi$
$653$	22832.2	−	13182.2i	1.36829	−	0.789982i	0.990709	+	0.135995i	$0.0434232\pi$
$654$		0			0
$655$	−6517.08	+	11287.9i	−0.388769	+	0.673367i
$656$		0			0
$657$	−4947.73	+	15796.2i	−0.293804	+	0.938006i
$658$		0			0
$659$			3730.15i			0.220495i	0.993904	+	0.110247i	$0.0351643\pi$
$659$			3730.15i			0.220495i	−0.993904	+	0.110247i	$0.964836\pi$
$660$		0			0
$661$	−10046.2	−	5800.18i	−0.591153	−	0.341302i	0.174400	−	0.984675i	$-0.444201\pi$
$661$	−10046.2	−	5800.18i	−0.591153	−	0.341302i	−0.765553	+	0.643373i	$0.777535\pi$
$662$		0			0
$663$	−301.270	+	117.485i	−0.0176476	+	0.00688198i
$664$		0			0
$665$	17676.5	−	2139.17i	1.03078	−	0.124742i
$666$		0			0
$667$	−10638.3	−	18426.1i	−0.617567	−	1.06966i
$668$		0			0
$669$	18413.5	+	14749.8i	1.06414	+	0.852407i
$670$		0			0
$671$	11020.3			0.634032
$672$		0			0
$673$	4490.54			0.257203			0.128601	−	0.991696i	$-0.458951\pi$
$673$	4490.54			0.257203			0.128601	+	0.991696i	$0.458951\pi$
$674$		0			0
$675$	9763.91	−	6564.16i	0.556760	−	0.374303i
$676$		0			0
$677$	−16112.9	−	27908.4i	−0.914726	−	1.58435i	−0.807302	−	0.590139i	$-0.799073\pi$
$677$	−16112.9	−	27908.4i	−0.914726	−	1.58435i	−0.107424	−	0.994213i	$-0.534260\pi$
$678$		0			0
$679$	−2540.27	−	3383.29i	−0.143574	−	0.191221i
$680$		0			0
$681$	−5876.52	−	15069.3i	−0.330674	−	0.847952i
$682$		0			0
$683$	−14858.4	−	8578.47i	−0.832414	−	0.480595i	0.0222642	−	0.999752i	$-0.492913\pi$
$683$	−14858.4	−	8578.47i	−0.832414	−	0.480595i	−0.854679	+	0.519157i	$0.826246\pi$
$684$		0			0
$685$		−	3658.08i		−	0.204041i
$686$		0			0
$687$	2185.12	−	14286.8i	0.121350	−	0.793412i
$688$		0			0
$689$	536.399	−	929.070i	0.0296592	−	0.0513712i
$690$		0			0
$691$	−16962.0	+	9792.99i	−0.933811	+	0.539136i	−0.888015	−	0.459815i	$-0.847916\pi$
$691$	−16962.0	+	9792.99i	−0.933811	+	0.539136i	−0.0457962	+	0.998951i	$0.514582\pi$
$692$		0			0
$693$	−3138.15	−	8857.65i	−0.172018	−	0.485533i
$694$		0			0
$695$	−5146.46	+	2971.31i	−0.280887	+	0.162170i
$696$		0			0
$697$	162.102	−	280.769i	0.00880926	−	0.0152581i
$698$		0			0
$699$	−682.950	+	4465.26i	−0.0369550	+	0.241619i
$700$		0			0
$701$		−	22197.8i		−	1.19601i	−0.801494	−	0.598003i	$-0.795961\pi$
$701$		−	22197.8i		−	1.19601i	0.801494	−	0.598003i	$-0.204039\pi$
$702$		0			0
$703$	−6420.46	−	3706.85i	−0.344455	−	0.198871i
$704$		0			0
$705$	7471.28	+	19158.7i	0.399127	+	1.02349i
$706$		0			0
$707$	−1646.29	−	13603.8i	−0.0875746	−	0.723652i
$708$		0			0
$709$	−4796.48	−	8307.74i	−0.254070	−	0.440062i	0.710573	−	0.703624i	$-0.248436\pi$
$709$	−4796.48	−	8307.74i	−0.254070	−	0.440062i	−0.964642	+	0.263562i	$0.915103\pi$
$710$		0			0
$711$	−20101.5	+	18489.7i	−1.06029	+	0.975271i
$712$		0			0
$713$	6345.98			0.333323
$714$		0			0
$715$	−461.402			−0.0241335
$716$		0			0
$717$	22971.4	+	18400.8i	1.19649	+	0.958425i
$718$		0			0
$719$	12967.7	+	22460.7i	0.672619	+	1.16501i	0.977159	+	0.212511i	$0.0681640\pi$
$719$	12967.7	+	22460.7i	0.672619	+	1.16501i	−0.304540	+	0.952500i	$0.598503\pi$
$720$		0			0
$721$	9211.46	−	21596.2i	0.475801	−	1.11551i
$722$		0			0
$723$	22011.1	−	8583.59i	1.13223	−	0.441531i
$724$		0			0
$725$	−12203.1	−	7045.48i	−0.625122	−	0.360914i
$726$		0			0
$727$		−	14119.1i		−	0.720287i	−0.932897	−	0.360144i	$-0.882728\pi$
$727$		−	14119.1i		−	0.720287i	0.932897	−	0.360144i	$-0.117272\pi$
$728$		0			0
$729$	12070.6	+	15547.4i	0.613251	+	0.789888i
$730$		0			0
$731$	41.8544	−	72.4939i	0.00211770	−	0.00366797i
$732$		0			0
$733$	−18735.4	+	10816.9i	−0.944078	+	0.545063i	−0.891236	−	0.453540i	$-0.850161\pi$
$733$	−18735.4	+	10816.9i	−0.944078	+	0.545063i	−0.0528413	+	0.998603i	$0.516828\pi$
$734$		0			0
$735$	−4812.26	+	10369.3i	−0.241501	+	0.520379i
$736$		0			0
$737$	−12327.0	+	7116.99i	−0.616107	+	0.355709i
$738$		0			0
$739$	13187.0	−	22840.6i	0.656417	−	1.13695i	−0.325120	−	0.945673i	$-0.605405\pi$
$739$	13187.0	−	22840.6i	0.656417	−	1.13695i	0.981537	−	0.191274i	$-0.0612619\pi$
$740$		0			0
$741$	−2947.15	−	450.759i	−0.146108	−	0.0223469i
$742$		0			0
$743$			26720.0i			1.31933i	0.751559	+	0.659665i	$0.229302\pi$
$743$			26720.0i			1.31933i	−0.751559	+	0.659665i	$0.770698\pi$
$744$		0			0
$745$	−12364.3	−	7138.53i	−0.608044	−	0.351054i
$746$		0			0
$747$	−5987.46	−	26768.1i	−0.293266	−	1.31110i
$748$		0			0
$749$	10158.1	−	23815.7i	0.495555	−	1.16183i
$750$		0			0
$751$	7551.13	+	13078.9i	0.366904	+	0.635496i	0.989080	−	0.147382i	$-0.0470845\pi$
$751$	7551.13	+	13078.9i	0.366904	+	0.635496i	−0.622176	+	0.782877i	$0.713751\pi$
$752$		0			0
$753$	−25507.7	+	31843.5i	−1.23446	+	1.54109i
$754$		0			0
$755$	7230.08			0.348516
$756$		0			0
$757$	−4993.81			−0.239766			−0.119883	−	0.992788i	$-0.538252\pi$
$757$	−4993.81			−0.239766			−0.119883	+	0.992788i	$0.538252\pi$
$758$		0			0
$759$	7730.26	−	9650.38i	0.369685	−	0.461511i
$760$		0			0
$761$	7991.33	+	13841.4i	0.380664	+	0.659330i	0.991157	−	0.132692i	$-0.0423620\pi$
$761$	7991.33	+	13841.4i	0.380664	+	0.659330i	−0.610493	+	0.792022i	$0.709029\pi$
$762$		0			0
$763$	−3067.86	−	25350.6i	−0.145562	−	1.20282i
$764$		0			0
$765$	614.562	+	2747.52i	0.0290451	+	0.129852i
$766$		0			0
$767$	−1820.33	−	1050.97i	−0.0856954	−	0.0494762i
$768$		0			0
$769$			13140.7i			0.616212i	0.951352	+	0.308106i	$0.0996951\pi$
$769$			13140.7i			0.616212i	−0.951352	+	0.308106i	$0.900305\pi$
$770$		0			0
$771$	35617.7	+	5447.63i	1.66373	+	0.254464i
$772$		0			0
$773$	−6058.86	+	10494.2i	−0.281917	+	0.488295i	−0.971857	−	0.235572i	$-0.924304\pi$
$773$	−6058.86	+	10494.2i	−0.281917	+	0.488295i	0.689940	+	0.723867i	$0.257637\pi$
$774$		0			0
$775$	3639.72	−	2101.39i	0.168700	−	0.0973990i
$776$		0			0
$777$	4194.65	−	2249.56i	0.193671	−	0.103864i
$778$		0			0
$779$	2588.67	−	1494.57i	0.119061	−	0.0687401i
$780$		0			0
$781$	−3301.81	+	5718.90i	−0.151278	+	0.262021i
$782$		0			0
$783$	10366.4	−	21172.2i	0.473137	−	0.966324i
$784$		0			0
$785$		−	11769.9i		−	0.535141i
$786$		0			0
$787$	2392.34	+	1381.22i	0.108358	+	0.0625606i	0.553200	−	0.833049i	$-0.313407\pi$
$787$	2392.34	+	1381.22i	0.108358	+	0.0625606i	−0.444842	+	0.895609i	$0.646740\pi$
$788$		0			0
$789$	12187.2	−	4752.63i	0.549908	−	0.214446i
$790$		0			0
$791$	−8380.34	−	11161.5i	−0.376701	−	0.501714i
$792$		0			0
$793$	1122.40	+	1944.05i	0.0502617	+	0.0870557i
$794$		0			0
$795$	−7289.93	−	5839.47i	−0.325217	−	0.260509i
$796$		0			0
$797$	−25951.3			−1.15338			−0.576689	−	0.816964i	$-0.695656\pi$
$797$	−25951.3			−1.15338			−0.576689	+	0.816964i	$0.695656\pi$
$798$		0			0
$799$	10031.0			0.444144
$800$		0			0
$801$	7104.70	−	6535.01i	0.313399	−	0.288269i
$802$		0			0
$803$	5760.58	+	9977.62i	0.253159	+	0.438484i
$804$		0			0
$805$	−14932.7	+	1807.12i	−0.653800	+	0.0791214i
$806$		0			0
$807$	−6936.55	−	17787.5i	−0.302575	−	0.775899i
$808$		0			0
$809$	−13918.8	−	8036.03i	−0.604894	−	0.349236i	0.166070	−	0.986114i	$-0.446892\pi$
$809$	−13918.8	−	8036.03i	−0.604894	−	0.349236i	−0.770965	+	0.636878i	$0.780226\pi$
$810$		0			0
$811$		−	8537.29i		−	0.369648i	−0.982772	−	0.184824i	$-0.940828\pi$
$811$		−	8537.29i		−	0.369648i	0.982772	−	0.184824i	$-0.0591715\pi$
$812$		0			0
$813$	1264.08	−	8264.77i	0.0545302	−	0.356529i
$814$		0			0
$815$	10236.6	−	17730.4i	0.439968	−	0.762046i
$816$		0			0
$817$	668.389	−	385.894i	0.0286217	−	0.0165248i
$818$		0			0
$819$	1242.93	−	1455.72i	0.0530297	−	0.0621086i
$820$		0			0
$821$	13133.1	−	7582.40i	0.558281	−	0.322324i	−0.194174	−	0.980967i	$-0.562203\pi$
$821$	13133.1	−	7582.40i	0.558281	−	0.322324i	0.752455	+	0.658643i	$0.228869\pi$
$822$		0			0
$823$	16177.4	−	28020.1i	0.685188	−	1.18678i	−0.288190	−	0.957573i	$-0.593054\pi$
$823$	16177.4	−	28020.1i	0.685188	−	1.18678i	0.973378	−	0.229206i	$-0.0736131\pi$
$824$		0			0
$825$	1238.07	−	8094.72i	0.0522472	−	0.341602i
$826$		0			0
$827$			215.168i			0.00904732i	0.999990	+	0.00452366i	$0.00143993\pi$
$827$			215.168i			0.00904732i	−0.999990	+	0.00452366i	$0.998560\pi$
$828$		0			0
$829$	−21242.9	−	12264.6i	−0.889984	−	0.513833i	−0.0160470	−	0.999871i	$-0.505108\pi$
$829$	−21242.9	−	12264.6i	−0.889984	−	0.513833i	−0.873937	+	0.486038i	$0.838441\pi$
$830$		0			0
$831$	−2502.09	−	6416.15i	−0.104448	−	0.267838i
$832$		0			0
$833$	3859.60	+	4024.69i	0.160537	+	0.167404i
$834$		0			0
$835$	−2923.60	−	5063.82i	−0.121168	−	0.209869i
$836$		0			0
$837$	3922.85	+	5835.08i	0.162000	+	0.240968i
$838$		0			0
$839$	−23365.3			−0.961453			−0.480727	−	0.876871i	$-0.659627\pi$
$839$	−23365.3			−0.961453			−0.480727	+	0.876871i	$0.659627\pi$
$840$		0			0
$841$	−3844.70			−0.157641
$842$		0			0
$843$	29882.1	+	23936.5i	1.22087	+	0.977958i
$844$		0			0
$845$	6998.80	+	12122.3i	0.284930	+	0.493514i
$846$		0			0
$847$	16657.9	+	7105.12i	0.675764	+	0.288235i
$848$		0			0
$849$	−3416.99	+	1332.52i	−0.138128	+	0.0538655i
$850$		0			0
$851$	5423.86	+	3131.47i	0.218481	+	0.126140i
$852$		0			0
$853$			27229.8i			1.09300i	0.837459	+	0.546500i	$0.184040\pi$
$853$			27229.8i			1.09300i	−0.837459	+	0.546500i	$0.815960\pi$
$854$		0			0
$855$	−7758.89	+	24771.2i	−0.310349	+	0.990829i
$856$		0			0
$857$	19765.3	−	34234.5i	0.787829	−	1.36456i	−0.139465	−	0.990227i	$-0.544538\pi$
$857$	19765.3	−	34234.5i	0.787829	−	1.36456i	0.927294	−	0.374334i	$-0.122128\pi$
$858$		0			0
$859$	−24390.4	+	14081.8i	−0.968791	+	0.559332i	−0.898867	−	0.438221i	$-0.855609\pi$
$859$	−24390.4	+	14081.8i	−0.968791	+	0.559332i	−0.0699234	+	0.997552i	$0.522275\pi$
$860$		0			0
$861$	−60.1333	+	1918.16i	−0.00238018	+	0.0759243i
$862$		0			0
$863$	17044.3	−	9840.52i	0.672299	−	0.388152i	−0.124648	−	0.992201i	$-0.539780\pi$
$863$	17044.3	−	9840.52i	0.672299	−	0.388152i	0.796947	+	0.604049i	$0.206447\pi$
$864$		0			0
$865$	8085.49	−	14004.5i	0.317821	−	0.550482i
$866$		0			0
$867$	−23877.7	−	3652.03i	−0.935327	−	0.143056i
$868$		0			0
$869$			19009.6i			0.742066i
$870$		0			0
$871$	−2510.95	−	1449.70i	−0.0976813	−	0.0563963i
$872$		0			0
$873$	6019.19	−	1346.36i	0.233355	−	0.0521965i
$874$		0			0
$875$	−19840.4	+	14896.7i	−0.766546	+	0.575544i
$876$		0			0
$877$	12787.9	+	22149.3i	0.492380	+	0.852827i	0.999961	−	0.00877670i	$-0.00279375\pi$
$877$	12787.9	+	22149.3i	0.492380	+	0.852827i	−0.507582	+	0.861604i	$0.669460\pi$
$878$		0			0
$879$	4447.93	−	5552.75i	0.170677	−	0.213071i
$880$		0			0
$881$	−50018.6			−1.91279			−0.956395	−	0.292076i	$-0.905654\pi$
$881$	−50018.6			−1.91279			−0.956395	+	0.292076i	$0.905654\pi$
$882$		0			0
$883$	−19732.9			−0.752057			−0.376029	−	0.926608i	$-0.622711\pi$
$883$	−19732.9			−0.752057			−0.376029	+	0.926608i	$0.622711\pi$
$884$		0			0
$885$	−11441.3	+	14283.2i	−0.434571	+	0.542514i
$886$		0			0
$887$	−13101.3	−	22692.1i	−0.495940	−	0.858993i	0.504049	−	0.863675i	$-0.331843\pi$
$887$	−13101.3	−	22692.1i	−0.495940	−	0.858993i	−0.999989	+	0.00468212i	$0.998510\pi$
$888$		0			0
$889$	22142.7	−	16625.4i	0.835370	−	0.627219i
$890$		0			0
$891$	13652.0	+	1142.40i	0.513310	+	0.0429540i
$892$		0			0
$893$	80094.4	+	46242.5i	3.00141	+	1.73286i
$894$		0			0
$895$			17190.9i			0.642043i
$896$		0			0
$897$	2489.69	+	380.791i	0.0926737	+	0.0141742i
$898$		0			0
$899$	4210.50	−	7292.80i	0.156205	−	0.270555i
$900$		0			0
$901$	−3945.77	+	2278.09i	−0.145896	+	0.0842333i
$902$		0			0
$903$	−15.5263	+	495.265i	−0.000572184	+	0.0182518i
$904$		0			0
$905$	9875.89	−	5701.85i	0.362747	−	0.209432i
$906$		0			0
$907$	20423.8	−	35375.1i	0.747697	−	1.29505i	−0.201227	−	0.979545i	$-0.564493\pi$
$907$	20423.8	−	35375.1i	0.747697	−	1.29505i	0.948924	−	0.315505i	$-0.102174\pi$
$908$		0			0
$909$	19063.8	+	5971.20i	0.695607	+	0.217879i
$910$		0			0
$911$			24476.2i			0.890156i	0.895492	+	0.445078i	$0.146824\pi$
$911$			24476.2i			0.890156i	−0.895492	+	0.445078i	$0.853176\pi$
$912$		0			0
$913$	−16533.7	−	9545.74i	−0.599327	−	0.346022i
$914$		0			0
$915$	18208.9	−	7100.86i	0.657887	−	0.256554i
$916$		0			0
$917$	−34618.2	−	14765.7i	−1.24667	−	0.531742i
$918$		0			0
$919$	−10419.4	−	18046.9i	−0.373997	−	0.647782i	0.616179	−	0.787606i	$-0.288680\pi$
$919$	−10419.4	−	18046.9i	−0.373997	−	0.647782i	−0.990176	+	0.139824i	$0.955346\pi$
$920$		0			0
$921$	−1536.23	−	1230.57i	−0.0549624	−	0.0440267i
$922$		0			0
$923$	−1345.13			−0.0479691
$924$		0			0
$925$	4147.78			0.147436
$926$		0			0
$927$	23172.2	+	25192.3i	0.821010	+	0.892582i
$928$		0			0
$929$	17639.8	+	30553.1i	0.622975	+	1.07903i	0.988929	+	0.148392i	$0.0474097\pi$
$929$	17639.8	+	30553.1i	0.622975	+	1.07903i	−0.365953	+	0.930633i	$0.619257\pi$
$930$		0			0
$931$	12264.1	+	49928.6i	0.431728	+	1.75762i
$932$		0			0
$933$	11798.4	+	30254.8i	0.413999	+	1.06163i
$934$		0			0
$935$	1697.04	+	979.789i	0.0593575	+	0.0342701i
$936$		0			0
$937$			5653.25i			0.197101i	0.995132	+	0.0985504i	$0.0314206\pi$
$937$			5653.25i			0.197101i	−0.995132	+	0.0985504i	$0.968579\pi$
$938$		0			0
$939$	−6006.86	+	39274.0i	−0.208761	+	1.36492i
$940$		0			0
$941$	−20526.0	+	35552.1i	−0.711083	+	1.23163i	0.253368	+	0.967370i	$0.418462\pi$
$941$	−20526.0	+	35552.1i	−0.711083	+	1.23163i	−0.964451	+	0.264262i	$0.914872\pi$
$942$		0			0
$943$	−2186.85	+	1262.58i	−0.0755183	+	0.0436005i
$944$		0			0
$945$	−10892.5	−	12613.4i	−0.374955	−	0.434195i
$946$		0			0
$947$	−16741.2	+	9665.54i	−0.574463	+	0.331666i	−0.758930	−	0.651173i	$-0.774277\pi$
$947$	−16741.2	+	9665.54i	−0.574463	+	0.331666i	0.184467	+	0.982839i	$0.440944\pi$
$948$		0			0
$949$	−1173.41	+	2032.40i	−0.0401374	+	0.0695199i
$950$		0			0
$951$	−4679.30	+	30594.2i	−0.159555	+	1.04320i
$952$		0			0
$953$			51705.5i			1.75751i	0.477275	+	0.878754i	$0.341624\pi$
$953$			51705.5i			1.75751i	−0.477275	+	0.878754i	$0.658376\pi$
$954$		0			0
$955$	−25901.2	−	14954.0i	−0.877636	−	0.506703i
$956$		0			0
$957$	−5961.25	−	15286.6i	−0.201358	−	0.516347i
$958$		0			0
$959$	10486.1	−	1269.00i	0.353090	−	0.0427302i
$960$		0			0
$961$	−13639.7	−	23624.6i	−0.457845	−	0.793012i
$962$		0			0
$963$	25553.7	+	27781.3i	0.855095	+	0.929638i
$964$		0			0
$965$	−17099.0			−0.570399
$966$		0			0
$967$	−53682.9			−1.78524			−0.892619	−	0.450811i	$-0.851135\pi$
$967$	−53682.9			−1.78524			−0.892619	+	0.450811i	$0.851135\pi$
$968$		0			0
$969$	9882.49	+	7916.19i	0.327628	+	0.262440i
$970$		0			0
$971$	13699.6	+	23728.5i	0.452773	+	0.784226i	0.998557	−	0.0537000i	$-0.0171015\pi$
$971$	13699.6	+	23728.5i	0.452773	+	0.784226i	−0.545784	+	0.837926i	$0.683768\pi$
$972$		0			0
$973$	−10302.7	−	13721.8i	−0.339456	−	0.452109i
$974$		0			0
$975$	1554.05	−	606.027i	0.0510455	−	0.0199061i
$976$		0			0
$977$	−29158.1	−	16834.4i	−0.954810	−	0.551260i	−0.0602383	−	0.998184i	$-0.519186\pi$
$977$	−29158.1	−	16834.4i	−0.954810	−	0.551260i	−0.894572	+	0.446924i	$0.852519\pi$
$978$		0			0
$979$		−	6718.76i		−	0.219339i
$980$		0			0
$981$	35525.4	+	11127.3i	1.15621	+	0.362149i
$982$		0			0
$983$	−14662.5	+	25396.3i	−0.475750	+	0.824024i	−0.999614	−	0.0277783i	$-0.991157\pi$
$983$	−14662.5	+	25396.3i	−0.475750	+	0.824024i	0.523864	+	0.851802i	$0.324490\pi$
$984$		0			0
$985$	13788.8	−	7960.99i	0.446040	−	0.257521i
$986$		0			0
$987$	−52327.7	+	28063.0i	−1.68755	+	0.905022i
$988$		0			0
$989$	−564.640	+	325.995i	−0.0181542	+	0.0104813i
$990$		0			0
$991$	3969.18	−	6874.83i	0.127230	−	0.220369i	−0.795372	−	0.606121i	$-0.792725\pi$
$991$	3969.18	−	6874.83i	0.127230	−	0.220369i	0.922603	+	0.385752i	$0.126058\pi$
$992$		0			0
$993$	−55897.2	−	8549.33i	−1.78635	−	0.273217i
$994$		0			0
$995$			15913.7i			0.507034i
$996$		0			0
$997$	−51089.1	−	29496.3i	−1.62288	−	0.936968i	−0.986146	−	0.165882i	$-0.946953\pi$
$997$	−51089.1	−	29496.3i	−1.62288	−	0.936968i	−0.636731	−	0.771086i	$-0.719714\pi$
$998$		0			0
$999$	473.471	+	6922.95i	0.0149950	+	0.219252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.8		48
3.2	odd	2	inner	336.4.bc.f.17.16		48
4.3	odd	2		168.4.u.a.17.17	yes	48
7.5	odd	6	inner	336.4.bc.f.257.16		48
12.11	even	2		168.4.u.a.17.9	✓	48
21.5	even	6	inner	336.4.bc.f.257.8		48
28.19	even	6		168.4.u.a.89.9	yes	48
84.47	odd	6		168.4.u.a.89.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.9	✓	48	12.11	even	2
168.4.u.a.17.17	yes	48	4.3	odd	2
168.4.u.a.89.9	yes	48	28.19	even	6
168.4.u.a.89.17	yes	48	84.47	odd	6
336.4.bc.f.17.8		48	1.1	even	1	trivial
336.4.bc.f.17.16		48	3.2	odd	2	inner
336.4.bc.f.257.8		48	21.5	even	6	inner
336.4.bc.f.257.16		48	7.5	odd	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.24856 + 4.05547i) q^{3} +(3.20701 + 5.55470i) q^{5} +(-14.8103 + 11.1200i) q^{7} +(-5.89369 - 26.3489i) q^{9} +O(q^{10})\)	\(q+(-3.24856 + 4.05547i) q^{3} +(3.20701 + 5.55470i) q^{5} +(-14.8103 + 11.1200i) q^{7} +(-5.89369 - 26.3489i) q^{9} +(-16.2748 - 9.39624i) q^{11} -3.82794i q^{13} +(-32.9451 - 5.03886i) q^{15} +(-8.12865 + 14.0792i) q^{17} +(-129.810 + 74.9457i) q^{19} +(3.01540 - 96.1868i) q^{21} +(109.660 - 63.3124i) q^{23} +(41.9302 - 72.6252i) q^{25} +(126.003 + 61.6944i) q^{27} -168.029i q^{29} +(43.4021 + 25.0582i) q^{31} +(90.9757 - 35.4776i) q^{33} +(-109.265 - 46.6050i) q^{35} +(24.7303 + 42.8341i) q^{37} +(15.5241 + 12.4353i) q^{39} -19.9421 q^{41} -5.14899 q^{43} +(127.459 - 117.239i) q^{45} +(-308.507 - 534.350i) q^{47} +(95.6911 - 329.382i) q^{49} +(-30.6915 - 78.7028i) q^{51} +(242.707 + 140.127i) q^{53} -120.535i q^{55} +(117.755 - 769.905i) q^{57} +(274.552 - 475.538i) q^{59} +(-507.857 + 293.212i) q^{61} +(380.287 + 324.698i) q^{63} +(21.2631 - 12.2762i) q^{65} +(378.715 - 655.954i) q^{67} +(-99.4768 + 650.399i) q^{69} -351.397i q^{71} +(-530.937 - 306.537i) q^{73} +(158.317 + 405.974i) q^{75} +(345.521 - 41.8141i) q^{77} +(-505.776 - 876.030i) q^{79} +(-659.529 + 310.584i) q^{81} +1015.91 q^{83} -104.275 q^{85} +(681.436 + 545.852i) q^{87} +(178.762 + 309.625i) q^{89} +(42.5667 + 56.6931i) q^{91} +(-242.617 + 94.6128i) q^{93} +(-832.601 - 480.703i) q^{95} +228.442i q^{97} +(-151.662 + 484.201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) \) 48 * q - 12 * q^7 + 14 * q^9	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) \) 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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