LMFDB - Embedded newform 208.4.i.h.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(81,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("208.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.i (of order $3$, 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:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 132 x^{10} - 149 x^{9} + 12792 x^{8} - 16413 x^{7} + 432175 x^{6} + 21798 x^{5} + \cdots + 16842816 $ x^12 - 3x^11 + 132x^10 - 149x^9 + 12792x^8 - 16413x^7 + 432175x^6 + 21798x^5 + 10031364x^4 - 7963488x^3 + 23277456x^2 + 13296960*x + 16842816
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.4
Root			$0.876590 + 1.51830i$ of defining polynomial
Character	$\chi$	$=$	208.81
Dual form			208.4.i.h.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.376590 + 0.652272i) q^{3} -7.26675 q^{5} +(-1.42656 + 2.47088i) q^{7} +(13.2164 - 22.8914i) q^{9} +O(q^{10})$	\(q+(0.376590 + 0.652272i) q^{3} -7.26675 q^{5} +(-1.42656 + 2.47088i) q^{7} +(13.2164 - 22.8914i) q^{9} +(29.0446 + 50.3068i) q^{11} +(-45.4840 - 11.3229i) q^{13} +(-2.73658 - 4.73990i) q^{15} +(-36.5317 + 63.2748i) q^{17} +(-71.4076 + 123.682i) q^{19} -2.14891 q^{21} +(24.4138 + 42.2859i) q^{23} -72.1943 q^{25} +40.2444 q^{27} +(-19.4432 - 33.6766i) q^{29} -153.866 q^{31} +(-21.8758 + 37.8900i) q^{33} +(10.3665 - 17.9553i) q^{35} +(178.123 + 308.518i) q^{37} +(-9.74321 - 33.9320i) q^{39} +(-1.94147 - 3.36272i) q^{41} +(6.09103 - 10.5500i) q^{43} +(-96.0400 + 166.346i) q^{45} -258.312 q^{47} +(167.430 + 289.997i) q^{49} -55.0298 q^{51} -302.642 q^{53} +(-211.060 - 365.567i) q^{55} -107.565 q^{57} +(55.3428 - 95.8566i) q^{59} +(207.568 - 359.518i) q^{61} +(37.7079 + 65.3121i) q^{63} +(330.521 + 82.2804i) q^{65} +(466.960 + 808.799i) q^{67} +(-18.3880 + 31.8489i) q^{69} +(330.950 - 573.221i) q^{71} +436.800 q^{73} +(-27.1876 - 47.0904i) q^{75} -165.736 q^{77} +318.158 q^{79} +(-341.686 - 591.818i) q^{81} -595.656 q^{83} +(265.467 - 459.802i) q^{85} +(14.6442 - 25.3645i) q^{87} +(-573.340 - 993.054i) q^{89} +(92.8632 - 96.2327i) q^{91} +(-57.9445 - 100.363i) q^{93} +(518.901 - 898.763i) q^{95} +(334.920 - 580.099i) q^{97} +1535.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 18 q^{5} + q^{7} - 93 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 18 * q^5 + q^7 - 93 * q^9	$ 12 q - 3 q^{3} + 18 q^{5} + q^{7} - 93 q^{9} + 11 q^{11} + 49 q^{13} + 168 q^{15} - 50 q^{17} + 211 q^{19} - 166 q^{21} - 103 q^{23} + 786 q^{25} + 486 q^{27} + 48 q^{29} - 380 q^{31} + 133 q^{33} - 226 q^{35} - 476 q^{37} - 655 q^{39} - 10 q^{41} + 13 q^{43} + 57 q^{45} - 244 q^{47} + 31 q^{49} + 1490 q^{51} - 966 q^{53} + 1510 q^{55} + 2354 q^{57} - 731 q^{59} + 704 q^{61} - 518 q^{63} + 251 q^{65} + 901 q^{67} - 3479 q^{69} - 673 q^{71} + 3102 q^{73} - 2739 q^{75} + 266 q^{77} + 1680 q^{79} - 3018 q^{81} - 4032 q^{83} + 1373 q^{85} - 1485 q^{87} - 295 q^{89} + 2009 q^{91} - 3220 q^{93} + 3128 q^{95} - 2575 q^{97} - 916 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 18 * q^5 + q^7 - 93 * q^9 + 11 * q^11 + 49 * q^13 + 168 * q^15 - 50 * q^17 + 211 * q^19 - 166 * q^21 - 103 * q^23 + 786 * q^25 + 486 * q^27 + 48 * q^29 - 380 * q^31 + 133 * q^33 - 226 * q^35 - 476 * q^37 - 655 * q^39 - 10 * q^41 + 13 * q^43 + 57 * q^45 - 244 * q^47 + 31 * q^49 + 1490 * q^51 - 966 * q^53 + 1510 * q^55 + 2354 * q^57 - 731 * q^59 + 704 * q^61 - 518 * q^63 + 251 * q^65 + 901 * q^67 - 3479 * q^69 - 673 * q^71 + 3102 * q^73 - 2739 * q^75 + 266 * q^77 + 1680 * q^79 - 3018 * q^81 - 4032 * q^83 + 1373 * q^85 - 1485 * q^87 - 295 * q^89 + 2009 * q^91 - 3220 * q^93 + 3128 * q^95 - 2575 * q^97 - 916 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.376590	+	0.652272i	0.0724747	+	0.125530i	0.899985	−	0.435920i	$-0.143577\pi$
$3$	0.376590	+	0.652272i	0.0724747	+	0.125530i	−0.827511	+	0.561450i	$0.810244\pi$
$4$		0			0
$5$	−7.26675			−0.649958			−0.324979	−	0.945721i	$-0.605357\pi$
$5$	−7.26675			−0.649958			−0.324979	+	0.945721i	$0.605357\pi$
$6$		0			0
$7$	−1.42656	+	2.47088i	−0.0770271	+	0.133415i	−0.901966	−	0.431807i	$-0.857876\pi$
$7$	−1.42656	+	2.47088i	−0.0770271	+	0.133415i	0.824939	+	0.565222i	$0.191209\pi$
$8$		0			0
$9$	13.2164	−	22.8914i	0.489495	−	0.847830i
$10$		0			0
$11$	29.0446	+	50.3068i	0.796117	+	1.37891i	0.922128	+	0.386886i	$0.126449\pi$
$11$	29.0446	+	50.3068i	0.796117	+	1.37891i	−0.126011	+	0.992029i	$0.540217\pi$
$12$		0			0
$13$	−45.4840	−	11.3229i	−0.970384	−	0.241569i
$13$	−45.4840	−	11.3229i	−0.970384	−	0.241569i
$14$		0			0
$15$	−2.73658	−	4.73990i	−0.0471055	−	0.0815891i
$16$		0			0
$17$	−36.5317	+	63.2748i	−0.521190	+	0.902728i	0.478506	+	0.878084i	$0.341179\pi$
$17$	−36.5317	+	63.2748i	−0.521190	+	0.902728i	−0.999696	+	0.0246440i	$0.992155\pi$
$18$		0			0
$19$	−71.4076	+	123.682i	−0.862212	+	1.49339i	0.00757726	+	0.999971i	$0.497588\pi$
$19$	−71.4076	+	123.682i	−0.862212	+	1.49339i	−0.869789	+	0.493424i	$0.835745\pi$
$20$		0			0
$21$	−2.14891			−0.0223301
$22$		0			0
$23$	24.4138	+	42.2859i	0.221332	+	0.383358i	0.955213	−	0.295921i	$-0.0956264\pi$
$23$	24.4138	+	42.2859i	0.221332	+	0.383358i	−0.733881	+	0.679278i	$0.762293\pi$
$24$		0			0
$25$	−72.1943			−0.577555
$26$		0			0
$27$	40.2444			0.286853
$28$		0			0
$29$	−19.4432	−	33.6766i	−0.124500	−	0.215641i	0.797037	−	0.603930i	$-0.206399\pi$
$29$	−19.4432	−	33.6766i	−0.124500	−	0.215641i	−0.921538	+	0.388289i	$0.873066\pi$
$30$		0			0
$31$	−153.866			−0.891459			−0.445730	−	0.895168i	$-0.647056\pi$
$31$	−153.866			−0.891459			−0.445730	+	0.895168i	$0.647056\pi$
$32$		0			0
$33$	−21.8758	+	37.8900i	−0.115397	+	0.199873i
$34$		0			0
$35$	10.3665	−	17.9553i	0.0500644	−	0.0867141i
$36$		0			0
$37$	178.123	+	308.518i	0.791439	+	1.37081i	0.925076	+	0.379782i	$0.124001\pi$
$37$	178.123	+	308.518i	0.791439	+	1.37081i	−0.133637	+	0.991030i	$0.542666\pi$
$38$		0			0
$39$	−9.74321	−	33.9320i	−0.0400042	−	0.139320i
$40$		0			0
$41$	−1.94147	−	3.36272i	−0.00739528	−	0.0128090i	0.862304	−	0.506391i	$-0.169021\pi$
$41$	−1.94147	−	3.36272i	−0.00739528	−	0.0128090i	−0.869699	+	0.493582i	$0.835687\pi$
$42$		0			0
$43$	6.09103	−	10.5500i	0.0216017	−	0.0374152i	−0.855022	−	0.518591i	$-0.826457\pi$
$43$	6.09103	−	10.5500i	0.0216017	−	0.0374152i	0.876624	+	0.481176i	$0.159790\pi$
$44$		0			0
$45$	−96.0400	+	166.346i	−0.318151	+	0.551054i
$46$		0			0
$47$	−258.312			−0.801675			−0.400837	−	0.916149i	$-0.631281\pi$
$47$	−258.312			−0.801675			−0.400837	+	0.916149i	$0.631281\pi$
$48$		0			0
$49$	167.430	+	289.997i	0.488134	+	0.845472i
$50$		0			0
$51$	−55.0298			−0.151092
$52$		0			0
$53$	−302.642			−0.784361			−0.392180	−	0.919888i	$-0.628279\pi$
$53$	−302.642			−0.784361			−0.392180	+	0.919888i	$0.628279\pi$
$54$		0			0
$55$	−211.060	−	365.567i	−0.517443	−	0.896237i
$56$		0			0
$57$	−107.565			−0.249954
$58$		0			0
$59$	55.3428	−	95.8566i	0.122119	−	0.211516i	−0.798484	−	0.602016i	$-0.794364\pi$
$59$	55.3428	−	95.8566i	0.122119	−	0.211516i	0.920603	+	0.390500i	$0.127698\pi$
$60$		0			0
$61$	207.568	−	359.518i	0.435678	−	0.754616i	−0.561673	−	0.827359i	$-0.689842\pi$
$61$	207.568	−	359.518i	0.435678	−	0.754616i	0.997351	+	0.0727435i	$0.0231755\pi$
$62$		0			0
$63$	37.7079	+	65.3121i	0.0754088	+	0.130612i
$64$		0			0
$65$	330.521	+	82.2804i	0.630709	+	0.157010i
$66$		0			0
$67$	466.960	+	808.799i	0.851466	+	1.47478i	0.879885	+	0.475187i	$0.157620\pi$
$67$	466.960	+	808.799i	0.851466	+	1.47478i	−0.0284183	+	0.999596i	$0.509047\pi$
$68$		0			0
$69$	−18.3880	+	31.8489i	−0.0320819	+	0.0555674i
$70$		0			0
$71$	330.950	−	573.221i	0.553190	−	0.958153i	−0.444852	−	0.895604i	$-0.646744\pi$
$71$	330.950	−	573.221i	0.553190	−	0.958153i	0.998042	−	0.0625489i	$-0.0199229\pi$
$72$		0			0
$73$	436.800			0.700323			0.350162	−	0.936689i	$-0.386127\pi$
$73$	436.800			0.700323			0.350162	+	0.936689i	$0.386127\pi$
$74$		0			0
$75$	−27.1876	−	47.0904i	−0.0418581	−	0.0725003i
$76$		0			0
$77$	−165.736			−0.245290
$78$		0			0
$79$	318.158			0.453109			0.226554	−	0.973999i	$-0.427254\pi$
$79$	318.158			0.453109			0.226554	+	0.973999i	$0.427254\pi$
$80$		0			0
$81$	−341.686	−	591.818i	−0.468705	−	0.811821i
$82$		0			0
$83$	−595.656			−0.787732			−0.393866	−	0.919168i	$-0.628863\pi$
$83$	−595.656			−0.787732			−0.393866	+	0.919168i	$0.628863\pi$
$84$		0			0
$85$	265.467	−	459.802i	0.338752	−	0.586736i
$86$		0			0
$87$	14.6442	−	25.3645i	0.0180463	−	0.0312570i
$88$		0			0
$89$	−573.340	−	993.054i	−0.682853	−	1.18274i	−0.974106	−	0.226090i	$-0.927406\pi$
$89$	−573.340	−	993.054i	−0.682853	−	1.18274i	0.291253	−	0.956646i	$-0.405928\pi$
$90$		0			0
$91$	92.8632	−	96.2327i	0.106975	−	0.110856i
$92$		0			0
$93$	−57.9445	−	100.363i	−0.0646082	−	0.111905i
$94$		0			0
$95$	518.901	−	898.763i	0.560402	−	0.970644i
$96$		0			0
$97$	334.920	−	580.099i	0.350577	−	0.607218i	−0.635773	−	0.771876i	$-0.719319\pi$
$97$	334.920	−	580.099i	0.350577	−	0.607218i	0.986351	+	0.164658i	$0.0526521\pi$
$98$		0			0
$99$	1535.46			1.55878
$100$		0			0
$101$	−716.928	−	1241.76i	−0.706307	−	1.22336i	−0.966218	−	0.257727i	$-0.917026\pi$
$101$	−716.928	−	1241.76i	−0.706307	−	1.22336i	0.259911	−	0.965633i	$-0.416307\pi$
$102$		0			0
$103$	−794.312			−0.759863			−0.379931	−	0.925015i	$-0.624052\pi$
$103$	−794.312			−0.759863			−0.379931	+	0.925015i	$0.624052\pi$
$104$		0			0
$105$	15.6156			0.0145136
$106$		0			0
$107$	782.271	+	1354.93i	0.706776	+	1.22417i	0.966047	+	0.258367i	$0.0831843\pi$
$107$	782.271	+	1354.93i	0.706776	+	1.22417i	−0.259271	+	0.965805i	$0.583482\pi$
$108$		0			0
$109$	2083.84			1.83115			0.915575	−	0.402147i	$-0.131736\pi$
$109$	2083.84			1.83115			0.915575	+	0.402147i	$0.131736\pi$
$110$		0			0
$111$	−134.158	+	232.369i	−0.114719	+	0.198698i
$112$		0			0
$113$	−99.1838	+	171.791i	−0.0825701	+	0.143016i	−0.904353	−	0.426785i	$-0.859646\pi$
$113$	−99.1838	+	171.791i	−0.0825701	+	0.143016i	0.821783	+	0.569800i	$0.192980\pi$
$114$		0			0
$115$	−177.409	−	307.281i	−0.143856	−	0.249166i
$116$		0			0
$117$	−860.329	+	891.545i	−0.679807	+	0.704474i
$118$		0			0
$119$	−104.230	−	180.531i	−0.0802916	−	0.139069i
$120$		0			0
$121$	−1021.68	+	1769.60i	−0.767604	+	1.32953i
$122$		0			0
$123$	1.46227	−	2.53273i	0.00107194	−	0.00185666i
$124$		0			0
$125$	1432.96			1.02534
$126$		0			0
$127$	−1083.94	−	1877.44i	−0.757356	−	1.31178i	−0.944195	−	0.329388i	$-0.893158\pi$
$127$	−1083.94	−	1877.44i	−0.757356	−	1.31178i	0.186839	−	0.982391i	$-0.440176\pi$
$128$		0			0
$129$	9.17527			0.00626231
$130$		0			0
$131$	800.420			0.533840			0.266920	−	0.963719i	$-0.413994\pi$
$131$	800.420			0.533840			0.266920	+	0.963719i	$0.413994\pi$
$132$		0			0
$133$	−203.735	−	352.879i	−0.132827	−	0.230064i
$134$		0			0
$135$	−292.446			−0.186443
$136$		0			0
$137$	567.774	−	983.413i	0.354074	−	0.613275i	−0.632885	−	0.774246i	$-0.718129\pi$
$137$	567.774	−	983.413i	0.354074	−	0.613275i	0.986959	+	0.160971i	$0.0514626\pi$
$138$		0			0
$139$	−1003.46	+	1738.04i	−0.612318	+	1.06057i	0.378530	+	0.925589i	$0.376430\pi$
$139$	−1003.46	+	1738.04i	−0.612318	+	1.06057i	−0.990849	+	0.134978i	$0.956904\pi$
$140$		0			0
$141$	−97.2777	−	168.490i	−0.0581011	−	0.100634i
$142$		0			0
$143$	−751.449	−	2617.02i	−0.439436	−	1.53039i
$144$		0			0
$145$	141.289	+	244.720i	0.0809200	+	0.140158i
$146$		0			0
$147$	−126.105	+	218.420i	−0.0707547	+	0.122551i
$148$		0			0
$149$	−1293.57	+	2240.52i	−0.711229	+	1.23189i	0.253167	+	0.967423i	$0.418528\pi$
$149$	−1293.57	+	2240.52i	−0.711229	+	1.23189i	−0.964396	+	0.264463i	$0.914805\pi$
$150$		0			0
$151$	−1582.79			−0.853016			−0.426508	−	0.904484i	$-0.640256\pi$
$151$	−1582.79			−0.853016			−0.426508	+	0.904484i	$0.640256\pi$
$152$		0			0
$153$	965.632	+	1672.52i	0.510240	+	0.883762i
$154$		0			0
$155$	1118.11			0.579411
$156$		0			0
$157$	−270.338			−0.137423			−0.0687113	−	0.997637i	$-0.521889\pi$
$157$	−270.338			−0.137423			−0.0687113	+	0.997637i	$0.521889\pi$
$158$		0			0
$159$	−113.972	−	197.405i	−0.0568463	−	0.0984607i
$160$		0			0
$161$	−139.311			−0.0681942
$162$		0			0
$163$	−71.1015	+	123.151i	−0.0341662	+	0.0591777i	−0.882603	−	0.470119i	$-0.844211\pi$
$163$	−71.1015	+	123.151i	−0.0341662	+	0.0591777i	0.848437	+	0.529297i	$0.177544\pi$
$164$		0			0
$165$	158.966	−	275.337i	0.0750030	−	0.129909i
$166$		0			0
$167$	121.456	+	210.368i	0.0562789	+	0.0974778i	0.892792	−	0.450469i	$-0.148743\pi$
$167$	121.456	+	210.368i	0.0562789	+	0.0974778i	−0.836513	+	0.547946i	$0.815410\pi$
$168$		0			0
$169$	1940.59	+	1030.02i	0.883289	+	0.468829i
$170$		0			0
$171$	1887.50	+	3269.24i	0.844097	+	1.46202i
$172$		0			0
$173$	−1736.08	+	3006.98i	−0.762958	+	1.32148i	0.178362	+	0.983965i	$0.442920\pi$
$173$	−1736.08	+	3006.98i	−0.762958	+	1.32148i	−0.941320	+	0.337517i	$0.890413\pi$
$174$		0			0
$175$	102.990	−	178.383i	0.0444874	−	0.0770544i
$176$		0			0
$177$	83.3661			0.0354022
$178$		0			0
$179$	−417.432	−	723.014i	−0.174304	−	0.301903i	0.765616	−	0.643297i	$-0.222434\pi$
$179$	−417.432	−	723.014i	−0.174304	−	0.301903i	−0.939920	+	0.341395i	$0.889101\pi$
$180$		0			0
$181$	269.143			0.110526			0.0552632	−	0.998472i	$-0.482400\pi$
$181$	269.143			0.110526			0.0552632	+	0.998472i	$0.482400\pi$
$182$		0			0
$183$	312.671			0.126302
$184$		0			0
$185$	−1294.38	−	2241.92i	−0.514402	−	0.890970i
$186$		0			0
$187$	−4244.20			−1.65971
$188$		0			0
$189$	−57.4112	+	99.4391i	−0.0220955	+	0.0382705i
$190$		0			0
$191$	−660.013	+	1143.18i	−0.250036	+	0.433075i	−0.963535	−	0.267581i	$-0.913776\pi$
$191$	−660.013	+	1143.18i	−0.250036	+	0.433075i	0.713499	+	0.700656i	$0.247109\pi$
$192$		0			0
$193$	649.688	+	1125.29i	0.242309	+	0.419691i	0.961371	−	0.275254i	$-0.0887620\pi$
$193$	649.688	+	1125.29i	0.242309	+	0.419691i	−0.719063	+	0.694945i	$0.755429\pi$
$194$		0			0
$195$	70.8015	+	246.575i	0.0260010	+	0.0905520i
$196$		0			0
$197$	−1235.31	−	2139.61i	−0.446761	−	0.773812i	0.551412	−	0.834233i	$-0.314089\pi$
$197$	−1235.31	−	2139.61i	−0.446761	−	0.773812i	−0.998173	+	0.0604206i	$0.980756\pi$
$198$		0			0
$199$	−700.940	+	1214.06i	−0.249690	+	0.432476i	−0.963440	−	0.267925i	$-0.913662\pi$
$199$	−700.940	+	1214.06i	−0.249690	+	0.432476i	0.713750	+	0.700401i	$0.246995\pi$
$200$		0			0
$201$	−351.705	+	609.170i	−0.123420	+	0.213769i
$202$		0			0
$203$	110.948			0.0383596
$204$		0			0
$205$	14.1082	+	24.4361i	0.00480662	+	0.00832531i
$206$		0			0
$207$	1290.65			0.433363
$208$		0			0
$209$	−8296.03			−2.74569
$210$		0			0
$211$	1345.50	+	2330.48i	0.438996	+	0.760363i	0.997612	−	0.0690632i	$-0.0220010\pi$
$211$	1345.50	+	2330.48i	0.438996	+	0.760363i	−0.558617	+	0.829426i	$0.688668\pi$
$212$		0			0
$213$	498.528			0.160369
$214$		0			0
$215$	−44.2620	+	76.6640i	−0.0140402	+	0.0243183i
$216$		0			0
$217$	219.500	−	380.185i	0.0686665	−	0.118934i
$218$		0			0
$219$	164.494	+	284.913i	0.0507557	+	0.0879115i
$220$		0			0
$221$	2378.06	−	2464.34i	0.723826	−	0.750089i
$222$		0			0
$223$	2719.89	+	4710.98i	0.816759	+	1.41467i	0.908058	+	0.418844i	$0.137565\pi$
$223$	2719.89	+	4710.98i	0.816759	+	1.41467i	−0.0912994	+	0.995823i	$0.529102\pi$
$224$		0			0
$225$	−954.146	+	1652.63i	−0.282710	+	0.489668i
$226$		0			0
$227$	−2020.39	+	3499.42i	−0.590740	+	1.02319i	0.403393	+	0.915027i	$0.367831\pi$
$227$	−2020.39	+	3499.42i	−0.590740	+	1.02319i	−0.994133	+	0.108165i	$0.965503\pi$
$228$		0			0
$229$	1072.07			0.309365			0.154682	−	0.987964i	$-0.450565\pi$
$229$	1072.07			0.309365			0.154682	+	0.987964i	$0.450565\pi$
$230$		0			0
$231$	−62.4144	−	108.105i	−0.0177774	−	0.0307913i
$232$		0			0
$233$	4062.66			1.14229			0.571145	−	0.820849i	$-0.306499\pi$
$233$	4062.66			1.14229			0.571145	+	0.820849i	$0.306499\pi$
$234$		0			0
$235$	1877.09			0.521055
$236$		0			0
$237$	119.815	+	207.526i	0.0328389	+	0.0568787i
$238$		0			0
$239$	−4371.13			−1.18303			−0.591516	−	0.806293i	$-0.701470\pi$
$239$	−4371.13			−1.18303			−0.591516	+	0.806293i	$0.701470\pi$
$240$		0			0
$241$	1723.61	−	2985.38i	0.460695	−	0.797948i	−0.538301	−	0.842753i	$-0.680933\pi$
$241$	1723.61	−	2985.38i	0.460695	−	0.797948i	0.998996	+	0.0448054i	$0.0142668\pi$
$242$		0			0
$243$	800.650	−	1386.77i	0.211365	−	0.366095i
$244$		0			0
$245$	−1216.67	−	2107.34i	−0.317266	−	0.549521i
$246$		0			0
$247$	4648.33	−	4816.99i	1.19743	−	1.24088i
$248$		0			0
$249$	−224.318	−	388.530i	−0.0570906	−	0.0988838i
$250$		0			0
$251$	3366.98	−	5831.77i	0.846700	−	1.46653i	−0.0374369	−	0.999299i	$-0.511919\pi$
$251$	3366.98	−	5831.77i	0.846700	−	1.46653i	0.884137	−	0.467228i	$-0.154747\pi$
$252$		0			0
$253$	−1418.18	+	2456.36i	−0.352412	+	0.610395i
$254$		0			0
$255$	399.888			0.0982038
$256$		0			0
$257$	−1500.47	−	2598.90i	−0.364190	−	0.630796i	0.624455	−	0.781060i	$-0.285321\pi$
$257$	−1500.47	−	2598.90i	−0.364190	−	0.630796i	−0.988646	+	0.150264i	$0.951988\pi$
$258$		0			0
$259$	−1016.41			−0.243849
$260$		0			0
$261$	−1027.87			−0.243769
$262$		0			0
$263$	−1580.71	−	2737.88i	−0.370612	−	0.641919i	0.619048	−	0.785353i	$-0.287519\pi$
$263$	−1580.71	−	2737.88i	−0.370612	−	0.641919i	−0.989660	+	0.143434i	$0.954185\pi$
$264$		0			0
$265$	2199.23			0.509802
$266$		0			0
$267$	431.828	−	747.948i	0.0989791	−	0.171437i
$268$		0			0
$269$	2171.34	−	3760.87i	0.492151	−	0.852431i	−0.507808	−	0.861470i	$-0.669544\pi$
$269$	2171.34	−	3760.87i	0.492151	−	0.852431i	0.999959	+	0.00903915i	$0.00287729\pi$
$270$		0			0
$271$	2935.95	+	5085.21i	0.658104	+	1.13987i	0.981106	+	0.193472i	$0.0619748\pi$
$271$	2935.95	+	5085.21i	0.658104	+	1.13987i	−0.323002	+	0.946398i	$0.604692\pi$
$272$		0			0
$273$	97.7412	+	24.3319i	0.0216687	+	0.00539425i
$274$		0			0
$275$	−2096.86	−	3631.86i	−0.459801	−	0.796399i
$276$		0			0
$277$	−2707.15	+	4688.93i	−0.587210	+	1.01708i	0.407386	+	0.913256i	$0.366440\pi$
$277$	−2707.15	+	4688.93i	−0.587210	+	1.01708i	−0.994596	+	0.103821i	$0.966893\pi$
$278$		0			0
$279$	−2033.55	+	3522.22i	−0.436365	+	0.755806i
$280$		0			0
$281$	6679.68			1.41806			0.709032	−	0.705176i	$-0.249132\pi$
$281$	6679.68			1.41806			0.709032	+	0.705176i	$0.249132\pi$
$282$		0			0
$283$	−4122.38	−	7140.17i	−0.865901	−	1.49978i	−0.866150	−	0.499785i	$-0.833412\pi$
$283$	−4122.38	−	7140.17i	−0.865901	−	1.49978i	0.000248651	−	1.00000i	$-0.499921\pi$
$284$		0			0
$285$	781.651			0.162460
$286$		0			0
$287$	11.0785			0.00227855
$288$		0			0
$289$	−212.630	−	368.285i	−0.0432790	−	0.0749614i
$290$		0			0
$291$	504.510			0.101632
$292$		0			0
$293$	269.959	−	467.583i	0.0538265	−	0.0932303i	−0.837857	−	0.545890i	$-0.816192\pi$
$293$	269.959	−	467.583i	0.0538265	−	0.0932303i	0.891683	+	0.452660i	$0.149525\pi$
$294$		0			0
$295$	−402.163	+	696.566i	−0.0793722	+	0.137477i
$296$		0			0
$297$	1168.88	+	2024.57i	0.228369	+	0.395546i
$298$		0			0
$299$	−631.639	−	2199.77i	−0.122169	−	0.425471i
$300$		0			0
$301$	17.3785	+	30.1004i	0.00332783	+	0.00576398i
$302$		0			0
$303$	539.975	−	935.265i	0.102379	−	0.177325i
$304$		0			0
$305$	−1508.34	+	2612.53i	−0.283172	+	0.490469i
$306$		0			0
$307$	4032.04			0.749578			0.374789	−	0.927110i	$-0.377715\pi$
$307$	4032.04			0.749578			0.374789	+	0.927110i	$0.377715\pi$
$308$		0			0
$309$	−299.129	−	518.107i	−0.0550708	−	0.0953854i
$310$		0			0
$311$	4146.61			0.756054			0.378027	−	0.925794i	$-0.376603\pi$
$311$	4146.61			0.756054			0.378027	+	0.925794i	$0.376603\pi$
$312$		0			0
$313$	4998.17			0.902597			0.451299	−	0.892373i	$-0.350961\pi$
$313$	4998.17			0.902597			0.451299	+	0.892373i	$0.350961\pi$
$314$		0			0
$315$	−274.014	−	474.606i	−0.0490125	−	0.0848922i
$316$		0			0
$317$	65.9112			0.0116780			0.00583902	−	0.999983i	$-0.498141\pi$
$317$	65.9112			0.0116780			0.00583902	+	0.999983i	$0.498141\pi$
$318$		0			0
$319$	1129.44	−	1956.25i	0.198234	−	0.343351i
$320$		0			0
$321$	−589.190	+	1020.51i	−0.102447	+	0.177443i
$322$		0			0
$323$	−5217.28	−	9036.60i	−0.898753	−	1.55669i
$324$		0			0
$325$	3283.69	+	817.446i	0.560450	+	0.139519i
$326$		0			0
$327$	784.751	+	1359.23i	0.132712	+	0.229864i
$328$		0			0
$329$	368.499	−	638.258i	0.0617507	−	0.106955i
$330$		0			0
$331$	2036.55	−	3527.40i	0.338184	−	0.585751i	−0.645908	−	0.763416i	$-0.723521\pi$
$331$	2036.55	−	3527.40i	0.338184	−	0.585751i	0.984091	+	0.177665i	$0.0568542\pi$
$332$		0			0
$333$	9416.55			1.54962
$334$		0			0
$335$	−3393.28	−	5877.34i	−0.553417	−	0.958547i
$336$		0			0
$337$	−6440.94			−1.04113			−0.520564	−	0.853822i	$-0.674278\pi$
$337$	−6440.94			−1.04113			−0.520564	+	0.853822i	$0.674278\pi$
$338$		0			0
$339$	−149.406			−0.0239370
$340$		0			0
$341$	−4468.99	−	7740.53i	−0.709706	−	1.22925i
$342$		0			0
$343$	−1934.02			−0.304452
$344$		0			0
$345$	133.621	−	231.438i	0.0208519	−	0.0361165i
$346$		0			0
$347$	−4151.70	+	7190.95i	−0.642291	+	1.11248i	0.342629	+	0.939471i	$0.388683\pi$
$347$	−4151.70	+	7190.95i	−0.642291	+	1.11248i	−0.984920	+	0.173010i	$0.944651\pi$
$348$		0			0
$349$	325.237	+	563.327i	0.0498841	+	0.0864017i	0.889889	−	0.456177i	$-0.150781\pi$
$349$	325.237	+	563.327i	0.0498841	+	0.0864017i	−0.840005	+	0.542578i	$0.817448\pi$
$350$		0			0
$351$	−1830.48	−	455.682i	−0.278358	−	0.0692948i
$352$		0			0
$353$	1521.34	+	2635.03i	0.229384	+	0.397305i	0.957626	−	0.288016i	$-0.0929955\pi$
$353$	1521.34	+	2635.03i	0.229384	+	0.397305i	−0.728242	+	0.685320i	$0.759662\pi$
$354$		0			0
$355$	−2404.93	+	4165.46i	−0.359550	+	0.622759i
$356$		0			0
$357$	78.5035	−	135.972i	0.0116382	−	0.0201580i
$358$		0			0
$359$	13014.1			1.91325			0.956627	−	0.291317i	$-0.0940934\pi$
$359$	13014.1			1.91325			0.956627	+	0.291317i	$0.0940934\pi$
$360$		0			0
$361$	−6768.59	−	11723.5i	−0.986819	−	1.70922i
$362$		0			0
$363$	−1539.02			−0.222528
$364$		0			0
$365$	−3174.12			−0.455181
$366$		0			0
$367$	4425.42	+	7665.05i	0.629441	+	1.09022i	0.987664	+	0.156588i	$0.0500494\pi$
$367$	4425.42	+	7665.05i	0.629441	+	1.09022i	−0.358223	+	0.933636i	$0.616617\pi$
$368$		0			0
$369$	−102.637			−0.0144798
$370$		0			0
$371$	431.738	−	747.793i	0.0604171	−	0.104645i
$372$		0			0
$373$	−5335.83	+	9241.93i	−0.740694	+	1.28292i	0.211486	+	0.977381i	$0.432170\pi$
$373$	−5335.83	+	9241.93i	−0.740694	+	1.28292i	−0.952180	+	0.305538i	$0.901164\pi$
$374$		0			0
$375$	539.639	+	934.681i	0.0743115	+	0.128711i
$376$		0			0
$377$	503.039	+	1751.90i	0.0687210	+	0.239330i
$378$		0			0
$379$	3725.50	+	6452.75i	0.504923	+	0.874553i	0.999984	+	0.00569442i	$0.00181260\pi$
$379$	3725.50	+	6452.75i	0.504923	+	0.874553i	−0.495060	+	0.868859i	$0.664854\pi$
$380$		0			0
$381$	816.401	−	1414.05i	0.109778	−	0.190141i
$382$		0			0
$383$	320.634	−	555.355i	0.0427772	−	0.0740922i	−0.843844	−	0.536588i	$-0.819713\pi$
$383$	320.634	−	555.355i	0.0427772	−	0.0740922i	0.886621	+	0.462496i	$0.153046\pi$
$384$		0			0
$385$	1204.36			0.159428
$386$		0			0
$387$	−161.002	−	278.864i	−0.0211478	−	0.0366291i
$388$		0			0
$389$	4522.54			0.589465			0.294732	−	0.955580i	$-0.404769\pi$
$389$	4522.54			0.589465			0.294732	+	0.955580i	$0.404769\pi$
$390$		0			0
$391$	−3567.51			−0.461424
$392$		0			0
$393$	301.430	+	522.091i	0.0386899	+	0.0670128i
$394$		0			0
$395$	−2311.98			−0.294502
$396$		0			0
$397$	3690.01	−	6391.28i	0.466489	−	0.807983i	−0.532778	−	0.846255i	$-0.678852\pi$
$397$	3690.01	−	6391.28i	0.466489	−	0.807983i	0.999267	+	0.0382722i	$0.0121854\pi$
$398$		0			0
$399$	153.449	−	265.781i	0.0192533	−	0.0333476i
$400$		0			0
$401$	−4885.10	−	8461.24i	−0.608354	−	1.05370i	−0.991512	−	0.130018i	$-0.958497\pi$
$401$	−4885.10	−	8461.24i	−0.608354	−	1.05370i	0.383157	−	0.923683i	$-0.374837\pi$
$402$		0			0
$403$	6998.46	+	1742.21i	0.865057	+	0.215349i
$404$		0			0
$405$	2482.95	+	4300.59i	0.304639	+	0.527650i
$406$		0			0
$407$	−10347.0	+	17921.6i	−1.26016	+	2.18265i
$408$		0			0
$409$	−3962.92	+	6863.97i	−0.479104	+	0.829833i	−0.999713	−	0.0239625i	$-0.992372\pi$
$409$	−3962.92	+	6863.97i	−0.479104	+	0.829833i	0.520609	+	0.853795i	$0.325705\pi$
$410$		0			0
$411$	855.271			0.102646
$412$		0			0
$413$	157.900	+	273.491i	0.0188130	+	0.0325850i
$414$		0			0
$415$	4328.48			0.511992
$416$		0			0
$417$	−1511.57			−0.177510
$418$		0			0
$419$	−7791.62	−	13495.5i	−0.908462	−	1.57350i	−0.816201	−	0.577768i	$-0.803924\pi$
$419$	−7791.62	−	13495.5i	−0.908462	−	1.57350i	−0.0922613	−	0.995735i	$-0.529409\pi$
$420$		0			0
$421$	−15726.7			−1.82060			−0.910298	−	0.413954i	$-0.864148\pi$
$421$	−15726.7			−1.82060			−0.910298	+	0.413954i	$0.864148\pi$
$422$		0			0
$423$	−3413.95	+	5913.13i	−0.392416	+	0.679684i
$424$		0			0
$425$	2637.38	−	4568.08i	0.301016	−	0.521375i
$426$		0			0
$427$	592.217	+	1025.75i	0.0671180	+	0.116252i
$428$		0			0
$429$	1424.02	−	1475.69i	0.160262	−	0.166077i
$430$		0			0
$431$	4922.11	+	8525.35i	0.550093	+	0.952788i	0.998267	+	0.0588422i	$0.0187409\pi$
$431$	4922.11	+	8525.35i	0.550093	+	0.952788i	−0.448175	+	0.893946i	$0.647926\pi$
$432$		0			0
$433$	−6158.71	+	10667.2i	−0.683531	+	1.18391i	0.290365	+	0.956916i	$0.406223\pi$
$433$	−6158.71	+	10667.2i	−0.683531	+	1.18391i	−0.973896	+	0.226995i	$0.927110\pi$
$434$		0			0
$435$	−106.416	+	184.318i	−0.0117293	+	0.0203158i
$436$		0			0
$437$	−6973.32			−0.763339
$438$		0			0
$439$	4591.10	+	7952.02i	0.499137	+	0.864531i	1.00000		0.000995960i	$-0.000317024\pi$
$439$	4591.10	+	7952.02i	0.499137	+	0.864531i	−0.500862	+	0.865527i	$0.666984\pi$
$440$		0			0
$441$	8851.25			0.955756
$442$		0			0
$443$	−8288.47			−0.888933			−0.444466	−	0.895795i	$-0.646607\pi$
$443$	−8288.47			−0.888933			−0.444466	+	0.895795i	$0.646607\pi$
$444$		0			0
$445$	4166.32	+	7216.28i	0.443826	+	0.768729i
$446$		0			0
$447$	−1948.58			−0.206184
$448$		0			0
$449$	−5147.70	+	8916.07i	−0.541058	+	0.937139i	0.457786	+	0.889062i	$0.348643\pi$
$449$	−5147.70	+	8916.07i	−0.541058	+	0.937139i	−0.998844	+	0.0480769i	$0.984691\pi$
$450$		0			0
$451$	112.779	−	195.338i	0.0117750	−	0.0203949i
$452$		0			0
$453$	−596.061	−	1032.41i	−0.0618221	−	0.107079i
$454$		0			0
$455$	−674.814	+	699.299i	−0.0695291	+	0.0720519i
$456$		0			0
$457$	6105.23	+	10574.6i	0.624924	+	1.08240i	0.988555	+	0.150858i	$0.0482035\pi$
$457$	6105.23	+	10574.6i	0.624924	+	1.08240i	−0.363631	+	0.931543i	$0.618463\pi$
$458$		0			0
$459$	−1470.20	+	2546.45i	−0.149505	+	0.258951i
$460$		0			0
$461$	4557.35	−	7893.56i	0.460427	−	0.797483i	−0.538555	−	0.842590i	$-0.681030\pi$
$461$	4557.35	−	7893.56i	0.460427	−	0.797483i	0.998982	+	0.0451071i	$0.0143629\pi$
$462$		0			0
$463$	−0.376664			−3.78079e−5			−1.89040e−5	−	1.00000i	$-0.500006\pi$
$463$	−0.376664			−3.78079e−5			−1.89040e−5		1.00000i	$0.500006\pi$
$464$		0			0
$465$	421.068	+	729.312i	0.0419926	+	0.0727334i
$466$		0			0
$467$	−5771.35			−0.571877			−0.285938	−	0.958248i	$-0.592305\pi$
$467$	−5771.35			−0.571877			−0.285938	+	0.958248i	$0.592305\pi$
$468$		0			0
$469$	−2664.59			−0.262344
$470$		0			0
$471$	−101.807	−	176.334i	−0.00995966	−	0.0172506i
$472$		0			0
$473$	707.647			0.0687899
$474$		0			0
$475$	5155.22	−	8929.11i	0.497974	−	0.862517i
$476$		0			0
$477$	−3999.83	+	6927.91i	−0.383941	+	0.665005i
$478$		0			0
$479$	4304.53	+	7455.67i	0.410604	+	0.711186i	0.994956	−	0.100314i	$-0.0319847\pi$
$479$	4304.53	+	7455.67i	0.410604	+	0.711186i	−0.584352	+	0.811500i	$0.698651\pi$
$480$		0			0
$481$	−4608.44	−	16049.5i	−0.436854	−	1.52140i
$482$		0			0
$483$	−52.4631	−	90.8688i	−0.00494235	−	0.00856040i
$484$		0			0
$485$	−2433.78	+	4215.43i	−0.227860	+	0.394666i
$486$		0			0
$487$	−1817.58	+	3148.14i	−0.169122	+	0.292928i	−0.938111	−	0.346333i	$-0.887427\pi$
$487$	−1817.58	+	3148.14i	−0.169122	+	0.292928i	0.768989	+	0.639262i	$0.220760\pi$
$488$		0			0
$489$	−107.104			−0.00990475
$490$		0			0
$491$	−8693.73	−	15058.0i	−0.799068	−	1.38403i	−0.920224	−	0.391393i	$-0.871993\pi$
$491$	−8693.73	−	15058.0i	−0.799068	−	1.38403i	0.121156	−	0.992633i	$-0.461340\pi$
$492$		0			0
$493$	2841.17			0.259554
$494$		0			0
$495$	−11157.8			−1.01314
$496$		0			0
$497$	944.240	+	1635.47i	0.0852213	+	0.147608i
$498$		0			0
$499$	1174.90			0.105403			0.0527014	−	0.998610i	$-0.483217\pi$
$499$	1174.90			0.105403			0.0527014	+	0.998610i	$0.483217\pi$
$500$		0			0
$501$	−91.4783	+	158.445i	−0.00815758	+	0.0141294i
$502$		0			0
$503$	10786.5	−	18682.7i	0.956155	−	1.65611i	0.224451	−	0.974485i	$-0.427941\pi$
$503$	10786.5	−	18682.7i	0.956155	−	1.65611i	0.731703	−	0.681623i	$-0.238726\pi$
$504$		0			0
$505$	5209.74	+	9023.53i	0.459070	+	0.795133i
$506$		0			0
$507$	58.9526	+	1653.68i	0.00516406	+	0.144857i
$508$		0			0
$509$	10930.1	+	18931.5i	0.951804	+	1.64857i	0.741518	+	0.670932i	$0.234106\pi$
$509$	10930.1	+	18931.5i	0.951804	+	1.64857i	0.210285	+	0.977640i	$0.432561\pi$
$510$		0			0
$511$	−623.123	+	1079.28i	−0.0539439	+	0.0934336i
$512$		0			0
$513$	−2873.76	+	4977.49i	−0.247328	+	0.428385i
$514$		0			0
$515$	5772.07			0.493879
$516$		0			0
$517$	−7502.58	−	12994.9i	−0.638227	−	1.10544i
$518$		0			0
$519$	−2615.16			−0.221180
$520$		0			0
$521$	18858.4			1.58580			0.792899	−	0.609353i	$-0.208571\pi$
$521$	18858.4			1.58580			0.792899	+	0.609353i	$0.208571\pi$
$522$		0			0
$523$	−7216.85	−	12499.9i	−0.603386	−	1.04509i	−0.992304	−	0.123823i	$-0.960485\pi$
$523$	−7216.85	−	12499.9i	−0.603386	−	1.04509i	0.388919	−	0.921272i	$-0.372849\pi$
$524$		0			0
$525$	155.139			0.0128968
$526$		0			0
$527$	5621.00	−	9735.86i	0.464620	−	0.804745i
$528$		0			0
$529$	4891.43	−	8472.21i	0.402025	−	0.696327i
$530$		0			0
$531$	−1462.86	−	2533.75i	−0.119553	−	0.207072i
$532$		0			0
$533$	50.2301	+	174.933i	0.00408200	+	0.0142161i
$534$		0			0
$535$	−5684.57	−	9845.96i	−0.459374	−	0.795660i
$536$		0			0
$537$	314.401	−	544.559i	0.0252652	−	0.0437606i
$538$		0			0
$539$	−9725.88	+	16845.7i	−0.777223	+	1.34619i
$540$		0			0
$541$	9419.76			0.748590			0.374295	−	0.927310i	$-0.377885\pi$
$541$	9419.76			0.748590			0.374295	+	0.927310i	$0.377885\pi$
$542$		0			0
$543$	101.357	+	175.555i	0.00801036	+	0.0138744i
$544$		0			0
$545$	−15142.7			−1.19017
$546$		0			0
$547$	12270.8			0.959162			0.479581	−	0.877498i	$-0.340789\pi$
$547$	12270.8			0.959162			0.479581	+	0.877498i	$0.340789\pi$
$548$		0			0
$549$	−5486.58	−	9503.04i	−0.426524	−	0.738761i
$550$		0			0
$551$	5553.57			0.429383
$552$		0			0
$553$	−453.873	+	786.131i	−0.0349017	+	0.0604515i
$554$		0			0
$555$	974.896	−	1688.57i	0.0745622	−	0.129146i
$556$		0			0
$557$	9139.58	+	15830.2i	0.695254	+	1.20421i	0.970095	+	0.242725i	$0.0780413\pi$
$557$	9139.58	+	15830.2i	0.695254	+	1.20421i	−0.274842	+	0.961490i	$0.588625\pi$
$558$		0			0
$559$	−396.500	+	410.887i	−0.0300003	+	0.0310888i
$560$		0			0
$561$	−1598.32	−	2768.37i	−0.120287	−	0.208344i
$562$		0			0
$563$	−11997.0	+	20779.5i	−0.898073	+	1.55551i	−0.0681174	+	0.997677i	$0.521699\pi$
$563$	−11997.0	+	20779.5i	−0.898073	+	1.55551i	−0.829955	+	0.557830i	$0.811634\pi$
$564$		0			0
$565$	720.744	−	1248.36i	0.0536671	−	0.0929542i
$566$		0			0
$567$	1949.75			0.144412
$568$		0			0
$569$	−5131.80	−	8888.54i	−0.378096	−	0.654881i	0.612690	−	0.790324i	$-0.290088\pi$
$569$	−5131.80	−	8888.54i	−0.378096	−	0.654881i	−0.990785	+	0.135443i	$0.956754\pi$
$570$		0			0
$571$	18173.6			1.33195			0.665974	−	0.745975i	$-0.268016\pi$
$571$	18173.6			1.33195			0.665974	+	0.745975i	$0.268016\pi$
$572$		0			0
$573$	−994.216			−0.0724851
$574$		0			0
$575$	−1762.54	−	3052.80i	−0.127831	−	0.221410i
$576$		0			0
$577$	−21688.8			−1.56484			−0.782422	−	0.622748i	$-0.786016\pi$
$577$	−21688.8			−1.56484			−0.782422	+	0.622748i	$0.786016\pi$
$578$		0			0
$579$	−489.331	+	847.547i	−0.0351225	+	0.0608339i
$580$		0			0
$581$	849.740	−	1471.79i	0.0606767	−	0.105095i
$582$		0			0
$583$	−8790.13	−	15225.0i	−0.624443	−	1.08157i
$584$		0			0
$585$	6251.80	−	6478.64i	0.441846	−	0.457878i
$586$		0			0
$587$	−464.663	−	804.819i	−0.0326724	−	0.0565902i	0.849227	−	0.528028i	$-0.177068\pi$
$587$	−464.663	−	804.819i	−0.0326724	−	0.0565902i	−0.881899	+	0.471438i	$0.843735\pi$
$588$		0			0
$589$	10987.2	−	19030.4i	0.768627	−	1.33130i
$590$		0			0
$591$	930.406	−	1611.51i	0.0647577	−	0.112164i
$592$		0			0
$593$	8355.69			0.578629			0.289315	−	0.957234i	$-0.406573\pi$
$593$	8355.69			0.578629			0.289315	+	0.957234i	$0.406573\pi$
$594$		0			0
$595$	757.410	+	1311.87i	0.0521862	+	0.0903891i
$596$		0			0
$597$	−1055.87			−0.0723848
$598$		0			0
$599$	−241.352			−0.0164631			−0.00823154	−	0.999966i	$-0.502620\pi$
$599$	−241.352			−0.0164631			−0.00823154	+	0.999966i	$0.502620\pi$
$600$		0			0
$601$	4303.51	+	7453.90i	0.292087	+	0.505909i	0.974303	−	0.225242i	$-0.0723171\pi$
$601$	4303.51	+	7453.90i	0.292087	+	0.505909i	−0.682216	+	0.731150i	$0.738984\pi$
$602$		0			0
$603$	24686.1			1.66715
$604$		0			0
$605$	7424.30	−	12859.3i	0.498911	−	0.864138i
$606$		0			0
$607$	−2446.05	+	4236.68i	−0.163562	+	0.283298i	−0.936144	−	0.351618i	$-0.885632\pi$
$607$	−2446.05	+	4236.68i	−0.163562	+	0.283298i	0.772582	+	0.634915i	$0.218965\pi$
$608$		0			0
$609$	41.7818	+	72.3681i	0.00278010	+	0.00481528i
$610$		0			0
$611$	11749.1	+	2924.83i	0.777932	+	0.193660i
$612$		0			0
$613$	−1937.86	−	3356.47i	−0.127682	−	0.221152i	0.795096	−	0.606484i	$-0.207420\pi$
$613$	−1937.86	−	3356.47i	−0.127682	−	0.221152i	−0.922778	+	0.385331i	$0.874087\pi$
$614$		0			0
$615$	−10.6260	+	18.4047i	−0.000696717	+	0.00120675i
$616$		0			0
$617$	4331.88	−	7503.04i	0.282650	−	0.489564i	−0.689387	−	0.724393i	$-0.742120\pi$
$617$	4331.88	−	7503.04i	0.282650	−	0.489564i	0.972037	+	0.234830i	$0.0754532\pi$
$618$		0			0
$619$	3269.09			0.212271			0.106136	−	0.994352i	$-0.466152\pi$
$619$	3269.09			0.212271			0.106136	+	0.994352i	$0.466152\pi$
$620$		0			0
$621$	982.518	+	1701.77i	0.0634897	+	0.109967i
$622$		0			0
$623$	3271.62			0.210393
$624$		0			0
$625$	−1388.69			−0.0888761
$626$		0			0
$627$	−3124.20	−	5411.27i	−0.198993	−	0.344666i
$628$		0			0
$629$	−26028.5			−1.64996
$630$		0			0
$631$	5585.02	−	9673.53i	0.352355	−	0.610297i	−0.634307	−	0.773082i	$-0.718714\pi$
$631$	5585.02	−	9673.53i	0.352355	−	0.610297i	0.986662	+	0.162785i	$0.0520476\pi$
$632$		0			0
$633$	−1013.40	+	1755.27i	−0.0636322	+	0.110214i
$634$		0			0
$635$	7876.73	+	13642.9i	0.492249	+	0.852601i
$636$		0			0
$637$	−4331.78	−	15086.0i	−0.269437	−	0.938350i
$638$		0			0
$639$	−8747.90	−	15151.8i	−0.541567	−	0.938022i
$640$		0			0
$641$	10160.2	−	17597.9i	0.626057	−	1.08436i	−0.362279	−	0.932070i	$-0.618001\pi$
$641$	10160.2	−	17597.9i	0.626057	−	1.08436i	0.988336	−	0.152292i	$-0.0486655\pi$
$642$		0			0
$643$	−5436.78	+	9416.79i	−0.333446	+	0.577546i	−0.983185	−	0.182612i	$-0.941545\pi$
$643$	−5436.78	+	9416.79i	−0.333446	+	0.577546i	0.649739	+	0.760157i	$0.274878\pi$
$644$		0			0
$645$	−66.6744			−0.00407024
$646$		0			0
$647$	3766.86	+	6524.39i	0.228888	+	0.396446i	0.957479	−	0.288504i	$-0.0931577\pi$
$647$	3766.86	+	6524.39i	0.228888	+	0.396446i	−0.728591	+	0.684949i	$0.759824\pi$
$648$		0			0
$649$	6429.65			0.388884
$650$		0			0
$651$	330.646			0.0199063
$652$		0			0
$653$	1919.75	+	3325.10i	0.115047	+	0.199267i	0.917798	−	0.397047i	$-0.129965\pi$
$653$	1919.75	+	3325.10i	0.115047	+	0.199267i	−0.802752	+	0.596314i	$0.796632\pi$
$654$		0			0
$655$	−5816.45			−0.346973
$656$		0			0
$657$	5772.91	−	9998.97i	0.342805	−	0.593755i
$658$		0			0
$659$	−2750.21	+	4763.51i	−0.162569	+	0.281578i	−0.935789	−	0.352560i	$-0.885311\pi$
$659$	−2750.21	+	4763.51i	−0.162569	+	0.281578i	0.773220	+	0.634138i	$0.218645\pi$
$660$		0			0
$661$	−6929.56	−	12002.3i	−0.407759	−	0.706259i	0.586880	−	0.809674i	$-0.300356\pi$
$661$	−6929.56	−	12002.3i	−0.407759	−	0.706259i	−0.994638	+	0.103416i	$0.967023\pi$
$662$		0			0
$663$	2502.98	+	623.095i	0.146618	+	0.0364992i
$664$		0			0
$665$	1480.49	+	2564.28i	0.0863323	+	0.149532i
$666$		0			0
$667$	949.364	−	1644.35i	0.0551117	−	0.0954563i
$668$		0			0
$669$	−2048.56	+	3548.22i	−0.118389	+	0.205055i
$670$		0			0
$671$	24114.9			1.38740
$672$		0			0
$673$	−1034.93	−	1792.55i	−0.0592772	−	0.102671i	0.834864	−	0.550456i	$-0.185546\pi$
$673$	−1034.93	−	1792.55i	−0.0592772	−	0.102671i	−0.894141	+	0.447785i	$0.852213\pi$
$674$		0			0
$675$	−2905.42			−0.165673
$676$		0			0
$677$	7030.18			0.399102			0.199551	−	0.979887i	$-0.436052\pi$
$677$	7030.18			0.399102			0.199551	+	0.979887i	$0.436052\pi$
$678$		0			0
$679$	955.569	+	1655.09i	0.0540079	+	0.0935445i
$680$		0			0
$681$	−3043.43			−0.171255
$682$		0			0
$683$	1915.67	−	3318.03i	0.107322	−	0.185887i	−0.807362	−	0.590056i	$-0.799106\pi$
$683$	1915.67	−	3318.03i	0.107322	−	0.185887i	0.914685	+	0.404168i	$0.132439\pi$
$684$		0			0
$685$	−4125.87	+	7146.22i	−0.230134	+	0.398603i
$686$		0			0
$687$	403.731	+	699.283i	0.0224211	+	0.0388345i
$688$		0			0
$689$	13765.4	+	3426.78i	0.761131	+	0.189477i
$690$		0			0
$691$	4093.47	+	7090.10i	0.225359	+	0.390333i	0.956427	−	0.291971i	$-0.0943112\pi$
$691$	4093.47	+	7090.10i	0.225359	+	0.390333i	−0.731068	+	0.682304i	$0.760978\pi$
$692$		0			0
$693$	−2190.43	+	3793.93i	−0.120068	+	0.207965i
$694$		0			0
$695$	7291.88	−	12629.9i	0.397981	−	0.689324i
$696$		0			0
$697$	283.701			0.0154174
$698$		0			0
$699$	1529.95	+	2649.96i	0.0827871	+	0.143392i
$700$		0			0
$701$	−2297.51			−0.123789			−0.0618943	−	0.998083i	$-0.519714\pi$
$701$	−2297.51			−0.123789			−0.0618943	+	0.998083i	$0.519714\pi$
$702$		0			0
$703$	−50877.3			−2.72955
$704$		0			0
$705$	706.893	+	1224.37i	0.0377633	+	0.0654079i
$706$		0			0
$707$	4090.97			0.217619
$708$		0			0
$709$	−14164.3	+	24533.3i	−0.750285	+	1.29953i	0.197399	+	0.980323i	$0.436751\pi$
$709$	−14164.3	+	24533.3i	−0.750285	+	1.29953i	−0.947684	+	0.319209i	$0.896583\pi$
$710$		0			0
$711$	4204.89	−	7283.09i	0.221794	−	0.384159i
$712$		0			0
$713$	−3756.46	−	6506.38i	−0.197308	−	0.341748i
$714$		0			0
$715$	5460.59	+	19017.2i	0.285615	+	0.994692i
$716$		0			0
$717$	−1646.12	−	2851.17i	−0.0857399	−	0.148506i
$718$		0			0
$719$	585.130	−	1013.48i	0.0303500	−	0.0525678i	−0.850451	−	0.526054i	$-0.823671\pi$
$719$	585.130	−	1013.48i	0.0303500	−	0.0525678i	0.880801	+	0.473486i	$0.157004\pi$
$720$		0			0
$721$	1133.14	−	1962.65i	0.0585301	−	0.101377i
$722$		0			0
$723$	2596.38			0.133555
$724$		0			0
$725$	1403.69	+	2431.26i	0.0719058	+	0.124544i
$726$		0			0
$727$	−30312.6			−1.54640			−0.773201	−	0.634162i	$-0.781345\pi$
$727$	−30312.6			−1.54640			−0.773201	+	0.634162i	$0.781345\pi$
$728$		0			0
$729$	−17245.0			−0.876136
$730$		0			0
$731$	445.031	+	770.817i	0.0225172	+	0.0390009i
$732$		0			0
$733$	27438.1			1.38260			0.691302	−	0.722565i	$-0.257037\pi$
$733$	27438.1			1.38260			0.691302	+	0.722565i	$0.257037\pi$
$734$		0			0
$735$	916.371	−	1587.20i	0.0459876	−	0.0796528i
$736$		0			0
$737$	−27125.4	+	46982.5i	−1.35573	+	2.34820i
$738$		0			0
$739$	−8663.80	−	15006.1i	−0.431263	−	0.746969i	0.565720	−	0.824598i	$-0.308598\pi$
$739$	−8663.80	−	15006.1i	−0.431263	−	0.746969i	−0.996982	+	0.0776287i	$0.975265\pi$
$740$		0			0
$741$	4892.50	+	1217.95i	0.242551	+	0.0603812i
$742$		0			0
$743$	−8647.98	−	14978.7i	−0.427004	−	0.739592i	0.569602	−	0.821921i	$-0.307098\pi$
$743$	−8647.98	−	14978.7i	−0.427004	−	0.739592i	−0.996605	+	0.0823289i	$0.973764\pi$
$744$		0			0
$745$	9400.03	−	16281.3i	0.462269	−	0.800674i
$746$		0			0
$747$	−7872.40	+	13635.4i	−0.385591	+	0.667862i
$748$		0			0
$749$	−4463.83			−0.217764
$750$		0			0
$751$	−5544.79	−	9603.87i	−0.269417	−	0.466645i	0.699294	−	0.714834i	$-0.253498\pi$
$751$	−5544.79	−	9603.87i	−0.269417	−	0.466645i	−0.968712	+	0.248189i	$0.920164\pi$
$752$		0			0
$753$	5071.87			0.245457
$754$		0			0
$755$	11501.7			0.554425
$756$		0			0
$757$	11880.7	+	20578.0i	0.570425	+	0.988005i	0.996522	+	0.0833274i	$0.0265547\pi$
$757$	11880.7	+	20578.0i	0.570425	+	0.988005i	−0.426097	+	0.904677i	$0.640112\pi$
$758$		0			0
$759$	−2136.29			−0.102164
$760$		0			0
$761$	−8844.83	+	15319.7i	−0.421321	+	0.729749i	−0.996069	−	0.0885816i	$-0.971767\pi$
$761$	−8844.83	+	15319.7i	−0.421321	+	0.729749i	0.574748	+	0.818330i	$0.305100\pi$
$762$		0			0
$763$	−2972.72	+	5148.91i	−0.141048	+	0.244303i
$764$		0			0
$765$	−7017.01	−	12153.8i	−0.331635	−	0.574408i
$766$		0			0
$767$	−3602.58	+	3733.30i	−0.169598	+	0.175752i
$768$		0			0
$769$	14366.1	+	24882.8i	0.673673	+	1.16684i	0.976855	+	0.213903i	$0.0686178\pi$
$769$	14366.1	+	24882.8i	0.673673	+	1.16684i	−0.303182	+	0.952933i	$0.598049\pi$
$770$		0			0
$771$	1130.12	−	1957.43i	0.0527892	−	0.0914335i
$772$		0			0
$773$	−2594.14	+	4493.19i	−0.120705	+	0.209067i	−0.920046	−	0.391811i	$-0.871849\pi$
$773$	−2594.14	+	4493.19i	−0.120705	+	0.209067i	0.799341	+	0.600878i	$0.205182\pi$
$774$		0			0
$775$	11108.3			0.514866
$776$		0			0
$777$	−382.771	−	662.979i	−0.0176729	−	0.0306103i
$778$		0			0
$779$	554.543			0.0255052
$780$		0			0
$781$	38449.2			1.76162
$782$		0			0
$783$	−782.480	−	1355.30i	−0.0357134	−	0.0618573i
$784$		0			0
$785$	1964.48			0.0893189
$786$		0			0
$787$	−7903.48	+	13689.2i	−0.357978	+	0.620036i	−0.987623	−	0.156847i	$-0.949867\pi$
$787$	−7903.48	+	13689.2i	−0.357978	+	0.620036i	0.629645	+	0.776883i	$0.283200\pi$
$788$		0			0
$789$	1190.56	−	2062.11i	0.0537200	−	0.0930457i
$790$		0			0
$791$	−282.984	−	490.142i	−0.0127203	−	0.0220322i
$792$		0			0
$793$	−13511.8	+	14002.0i	−0.605066	+	0.627021i
$794$		0			0
$795$	828.206	+	1434.49i	0.0369477	+	0.0639953i
$796$		0			0
$797$	−11301.7	+	19575.1i	−0.502292	+	0.869994i	0.497705	+	0.867346i	$0.334176\pi$
$797$	−11301.7	+	19575.1i	−0.502292	+	0.869994i	−0.999996	+	0.00264807i	$0.999157\pi$
$798$		0			0
$799$	9436.58	−	16344.6i	0.417825	−	0.723694i
$800$		0			0
$801$	−30309.9			−1.33701
$802$		0			0
$803$	12686.7	+	21974.0i	0.557539	+	0.965686i
$804$		0			0
$805$	1012.34			0.0443233
$806$		0			0
$807$	3270.81			0.142674
$808$		0			0
$809$	4951.10	+	8575.56i	0.215169	+	0.372683i	0.953325	−	0.301947i	$-0.0976365\pi$
$809$	4951.10	+	8575.56i	0.215169	+	0.372683i	−0.738156	+	0.674630i	$0.764303\pi$
$810$		0			0
$811$	−3136.80			−0.135818			−0.0679088	−	0.997692i	$-0.521633\pi$
$811$	−3136.80			−0.135818			−0.0679088	+	0.997692i	$0.521633\pi$
$812$		0			0
$813$	−2211.30	+	3830.08i	−0.0953918	+	0.165223i
$814$		0			0
$815$	516.677	−	894.911i	0.0222066	−	0.0384630i
$816$		0			0
$817$	869.891	+	1506.70i	0.0372505	+	0.0645197i
$818$		0			0
$819$	−975.588	−	3397.61i	−0.0416237	−	0.144960i
$820$		0			0
$821$	−386.973	−	670.257i	−0.0164500	−	0.0284922i	0.857683	−	0.514178i	$-0.171903\pi$
$821$	−386.973	−	670.257i	−0.0164500	−	0.0284922i	−0.874133	+	0.485686i	$0.838570\pi$
$822$		0			0
$823$	−6190.87	+	10722.9i	−0.262212	+	0.454164i	−0.966829	−	0.255423i	$-0.917785\pi$
$823$	−6190.87	+	10722.9i	−0.262212	+	0.454164i	0.704618	+	0.709587i	$0.251119\pi$
$824$		0			0
$825$	1579.31	−	2735.44i	0.0666479	−	0.115437i
$826$		0			0
$827$	−39362.3			−1.65509			−0.827545	−	0.561399i	$-0.810263\pi$
$827$	−39362.3			−1.65509			−0.827545	+	0.561399i	$0.810263\pi$
$828$		0			0
$829$	−5833.56	−	10104.0i	−0.244400	−	0.423314i	0.717563	−	0.696494i	$-0.245258\pi$
$829$	−5833.56	−	10104.0i	−0.244400	−	0.423314i	−0.961963	+	0.273180i	$0.911924\pi$
$830$		0			0
$831$	−4077.94			−0.170231
$832$		0			0
$833$	−24466.0			−1.01764
$834$		0			0
$835$	−882.593	−	1528.70i	−0.0365789	−	0.0633565i
$836$		0			0
$837$	−6192.26			−0.255718
$838$		0			0
$839$	−23009.2	+	39853.1i	−0.946801	+	1.63991i	−0.194695	+	0.980864i	$0.562372\pi$
$839$	−23009.2	+	39853.1i	−0.946801	+	1.63991i	−0.752105	+	0.659043i	$0.770962\pi$
$840$		0			0
$841$	11438.4	−	19811.9i	0.468999	−	0.812331i
$842$		0			0
$843$	2515.50	+	4356.97i	0.102774	+	0.178009i
$844$		0			0
$845$	−14101.8	−	7484.88i	−0.574101	−	0.304719i
$846$		0			0
$847$	−2914.99	−	5048.90i	−0.118253	−	0.204820i
$848$		0			0
$849$	3104.89	−	5377.83i	0.125512	−	0.217393i
$850$		0			0
$851$	−8697.31	+	15064.2i	−0.350341	+	0.606808i
$852$		0			0
$853$	−6667.50			−0.267633			−0.133817	−	0.991006i	$-0.542723\pi$
$853$	−6667.50			−0.267633			−0.133817	+	0.991006i	$0.542723\pi$
$854$		0			0
$855$	−13716.0	−	23756.8i	−0.548627	−	0.950250i
$856$		0			0
$857$	23981.7			0.955890			0.477945	−	0.878390i	$-0.341382\pi$
$857$	23981.7			0.955890			0.477945	+	0.878390i	$0.341382\pi$
$858$		0			0
$859$	−4760.36			−0.189082			−0.0945409	−	0.995521i	$-0.530138\pi$
$859$	−4760.36			−0.189082			−0.0945409	+	0.995521i	$0.530138\pi$
$860$		0			0
$861$	4.17205	+	7.22620i	0.000165137	+	0.000286026i
$862$		0			0
$863$	49009.9			1.93316			0.966580	−	0.256363i	$-0.0825244\pi$
$863$	49009.9			1.93316			0.966580	+	0.256363i	$0.0825244\pi$
$864$		0			0
$865$	12615.7	−	21851.0i	0.495890	−	0.858907i
$866$		0			0
$867$	160.148	−	277.385i	0.00627326	−	0.0108656i
$868$		0			0
$869$	9240.79	+	16005.5i	0.360728	+	0.624799i
$870$		0			0
$871$	−12081.3	−	42074.7i	−0.469987	−	1.63679i
$872$		0			0
$873$	−8852.85	−	15333.6i	−0.343211	−	0.594460i
$874$		0			0
$875$	−2044.21	+	3540.68i	−0.0789793	+	0.136796i
$876$		0			0
$877$	−24080.6	+	41708.9i	−0.927189	+	1.60594i	−0.139188	+	0.990266i	$0.544449\pi$
$877$	−24080.6	+	41708.9i	−0.927189	+	1.60594i	−0.788002	+	0.615673i	$0.788884\pi$
$878$		0			0
$879$	406.655			0.0156042
$880$		0			0
$881$	12876.1	+	22302.0i	0.492402	+	0.852865i	0.999962	−	0.00875144i	$-0.00278571\pi$
$881$	12876.1	+	22302.0i	0.492402	+	0.852865i	−0.507560	+	0.861617i	$0.669452\pi$
$882$		0			0
$883$	41104.6			1.56657			0.783285	−	0.621663i	$-0.213543\pi$
$883$	41104.6			1.56657			0.783285	+	0.621663i	$0.213543\pi$
$884$		0			0
$885$	−605.801			−0.0230099
$886$		0			0
$887$	24480.5	+	42401.4i	0.926689	+	1.60507i	0.788822	+	0.614622i	$0.210691\pi$
$887$	24480.5	+	42401.4i	0.926689	+	1.60507i	0.137867	+	0.990451i	$0.455975\pi$
$888$		0			0
$889$	6185.24			0.233348
$890$		0			0
$891$	19848.3	−	34378.3i	0.746288	−	1.29261i
$892$		0			0
$893$	18445.5	−	31948.5i	0.691213	−	1.19722i
$894$		0			0
$895$	3033.38	+	5253.96i	0.113290	+	0.196224i
$896$		0			0
$897$	1196.98	−	1240.41i	0.0445551	−	0.0461718i
$898$		0			0
$899$	2991.66	+	5181.70i	0.110987	+	0.192235i
$900$		0			0
$901$	11056.0	−	19149.6i	0.408801	−	0.708065i
$902$		0			0
$903$	−13.0891	+	22.6710i	−0.000482368	+	0.000835485i
$904$		0			0
$905$	−1955.80			−0.0718375
$906$		0			0
$907$	21199.1	+	36717.9i	0.776081	+	1.34421i	0.934185	+	0.356789i	$0.116128\pi$
$907$	21199.1	+	36717.9i	0.776081	+	1.34421i	−0.158105	+	0.987422i	$0.550538\pi$
$908$		0			0
$909$	−37900.7			−1.38293
$910$		0			0
$911$	8150.26			0.296411			0.148205	−	0.988957i	$-0.452650\pi$
$911$	8150.26			0.296411			0.148205	+	0.988957i	$0.452650\pi$
$912$		0			0
$913$	−17300.6	−	29965.5i	−0.627126	−	1.08621i
$914$		0			0
$915$	−2272.11			−0.0820913
$916$		0			0
$917$	−1141.85	+	1977.74i	−0.0411201	+	0.0712222i
$918$		0			0
$919$	−13507.6	+	23395.8i	−0.484847	+	0.839779i	−0.999848	−	0.0174101i	$-0.994458\pi$
$919$	−13507.6	+	23395.8i	−0.484847	+	0.839779i	0.515002	+	0.857189i	$0.327791\pi$
$920$		0			0
$921$	1518.42	+	2629.99i	0.0543255	+	0.0940944i
$922$		0			0
$923$	−21543.4	+	22325.1i	−0.768266	+	0.796143i
$924$		0			0
$925$	−12859.5	−	22273.2i	−0.457099	−	0.791719i
$926$		0			0
$927$	−10497.9	+	18182.9i	−0.371949	+	0.644234i
$928$		0			0
$929$	9361.47	−	16214.5i	0.330613	−	0.572639i	−0.652019	−	0.758203i	$-0.726078\pi$
$929$	9361.47	−	16214.5i	0.330613	−	0.572639i	0.982632	+	0.185563i	$0.0594110\pi$
$930$		0			0
$931$	−47823.0			−1.68350
$932$		0			0
$933$	1561.57	+	2704.72i	0.0547948	+	0.0949074i
$934$		0			0
$935$	30841.5			1.07874
$936$		0			0
$937$	15955.0			0.556274			0.278137	−	0.960541i	$-0.410283\pi$
$937$	15955.0			0.556274			0.278137	+	0.960541i	$0.410283\pi$
$938$		0			0
$939$	1882.26	+	3260.16i	0.0654155	+	0.113303i
$940$		0			0
$941$	9021.18			0.312521			0.156260	−	0.987716i	$-0.450056\pi$
$941$	9021.18			0.312521			0.156260	+	0.987716i	$0.450056\pi$
$942$		0			0
$943$	94.7972	−	164.194i	0.00327362	−	0.00567007i
$944$		0			0
$945$	417.193	−	722.599i	0.0143611	−	0.0248742i
$946$		0			0
$947$	−6248.95	−	10823.5i	−0.214428	−	0.371401i	0.738667	−	0.674070i	$-0.235456\pi$
$947$	−6248.95	−	10823.5i	−0.214428	−	0.371401i	−0.953096	+	0.302669i	$0.902122\pi$
$948$		0			0
$949$	−19867.4	−	4945.83i	−0.679582	−	0.169176i
$950$		0			0
$951$	24.8215	+	42.9920i	0.000846362	+	0.00146594i
$952$		0			0
$953$	−18167.2	+	31466.5i	−0.617516	+	1.06957i	0.372421	+	0.928064i	$0.378528\pi$
$953$	−18167.2	+	31466.5i	−0.617516	+	1.06957i	−0.989937	+	0.141506i	$0.954806\pi$
$954$		0			0
$955$	4796.15	−	8307.18i	0.162513	−	0.281481i
$956$		0			0
$957$	1701.34			0.0574677
$958$		0			0
$959$	1619.93	+	2805.80i	0.0545467	+	0.0944776i
$960$		0			0
$961$	−6116.11			−0.205301
$962$		0			0
$963$	41355.1			1.38385
$964$		0			0
$965$	−4721.12	−	8177.22i	−0.157490	−	0.272781i
$966$		0			0
$967$	−40930.2			−1.36114			−0.680572	−	0.732681i	$-0.738269\pi$
$967$	−40930.2			−1.36114			−0.680572	+	0.732681i	$0.738269\pi$
$968$		0			0
$969$	3929.55	−	6806.18i	0.130274	−	0.225641i
$970$		0			0
$971$	14721.5	−	25498.4i	0.486546	−	0.842722i	−0.513335	−	0.858189i	$-0.671590\pi$
$971$	14721.5	−	25498.4i	0.486546	−	0.842722i	0.999880	+	0.0154665i	$0.00492335\pi$
$972$		0			0
$973$	−2862.99	−	4958.85i	−0.0943303	−	0.163385i
$974$		0			0
$975$	703.404	+	2449.70i	0.0231046	+	0.0804648i
$976$		0			0
$977$	−13415.6	−	23236.5i	−0.439307	−	0.760902i	0.558329	−	0.829620i	$-0.311443\pi$
$977$	−13415.6	−	23236.5i	−0.439307	−	0.760902i	−0.997636	+	0.0687175i	$0.978109\pi$
$978$		0			0
$979$	33304.9	−	57685.8i	1.08726	−	1.88319i
$980$		0			0
$981$	27540.7	−	47702.0i	0.896339	−	1.55250i
$982$		0			0
$983$	−3409.34			−0.110622			−0.0553108	−	0.998469i	$-0.517615\pi$
$983$	−3409.34			−0.110622			−0.0553108	+	0.998469i	$0.517615\pi$
$984$		0			0
$985$	8976.66	+	15548.0i	0.290376	+	0.502945i
$986$		0			0
$987$	555.091			0.0179015
$988$		0			0
$989$	594.820			0.0191246
$990$		0			0
$991$	−11607.4	−	20104.6i	−0.372069	−	0.644443i	0.617814	−	0.786324i	$-0.288018\pi$
$991$	−11607.4	−	20104.6i	−0.372069	−	0.644443i	−0.989884	+	0.141881i	$0.954685\pi$
$992$		0			0
$993$	3067.77			0.0980390
$994$		0			0
$995$	5093.56	−	8822.30i	0.162288	−	0.281091i
$996$		0			0
$997$	6523.50	−	11299.0i	0.207223	−	0.358921i	−0.743616	−	0.668607i	$-0.766891\pi$
$997$	6523.50	−	11299.0i	0.207223	−	0.358921i	0.950839	+	0.309686i	$0.100224\pi$
$998$		0			0
$999$	7168.45	+	12416.1i	0.227027	+	0.393222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.i.h.81.4		12
4.3	odd	2		104.4.i.c.81.3	yes	12
13.9	even	3	inner	208.4.i.h.113.4		12
52.3	odd	6		1352.4.a.n.1.4		6
52.23	odd	6		1352.4.a.m.1.4		6
52.35	odd	6		104.4.i.c.9.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.4.i.c.9.3	✓	12	52.35	odd	6
104.4.i.c.81.3	yes	12	4.3	odd	2
208.4.i.h.81.4		12	1.1	even	1	trivial
208.4.i.h.113.4		12	13.9	even	3	inner
1352.4.a.m.1.4		6	52.23	odd	6
1352.4.a.n.1.4		6	52.3	odd	6

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.376590 + 0.652272i) q^{3} -7.26675 q^{5} +(-1.42656 + 2.47088i) q^{7} +(13.2164 - 22.8914i) q^{9} +O(q^{10})\)	\(q+(0.376590 + 0.652272i) q^{3} -7.26675 q^{5} +(-1.42656 + 2.47088i) q^{7} +(13.2164 - 22.8914i) q^{9} +(29.0446 + 50.3068i) q^{11} +(-45.4840 - 11.3229i) q^{13} +(-2.73658 - 4.73990i) q^{15} +(-36.5317 + 63.2748i) q^{17} +(-71.4076 + 123.682i) q^{19} -2.14891 q^{21} +(24.4138 + 42.2859i) q^{23} -72.1943 q^{25} +40.2444 q^{27} +(-19.4432 - 33.6766i) q^{29} -153.866 q^{31} +(-21.8758 + 37.8900i) q^{33} +(10.3665 - 17.9553i) q^{35} +(178.123 + 308.518i) q^{37} +(-9.74321 - 33.9320i) q^{39} +(-1.94147 - 3.36272i) q^{41} +(6.09103 - 10.5500i) q^{43} +(-96.0400 + 166.346i) q^{45} -258.312 q^{47} +(167.430 + 289.997i) q^{49} -55.0298 q^{51} -302.642 q^{53} +(-211.060 - 365.567i) q^{55} -107.565 q^{57} +(55.3428 - 95.8566i) q^{59} +(207.568 - 359.518i) q^{61} +(37.7079 + 65.3121i) q^{63} +(330.521 + 82.2804i) q^{65} +(466.960 + 808.799i) q^{67} +(-18.3880 + 31.8489i) q^{69} +(330.950 - 573.221i) q^{71} +436.800 q^{73} +(-27.1876 - 47.0904i) q^{75} -165.736 q^{77} +318.158 q^{79} +(-341.686 - 591.818i) q^{81} -595.656 q^{83} +(265.467 - 459.802i) q^{85} +(14.6442 - 25.3645i) q^{87} +(-573.340 - 993.054i) q^{89} +(92.8632 - 96.2327i) q^{91} +(-57.9445 - 100.363i) q^{93} +(518.901 - 898.763i) q^{95} +(334.920 - 580.099i) q^{97} +1535.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 18 q^{5} + q^{7} - 93 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 18 * q^5 + q^7 - 93 * q^9	\( 12 q - 3 q^{3} + 18 q^{5} + q^{7} - 93 q^{9} + 11 q^{11} + 49 q^{13} + 168 q^{15} - 50 q^{17} + 211 q^{19} - 166 q^{21} - 103 q^{23} + 786 q^{25} + 486 q^{27} + 48 q^{29} - 380 q^{31} + 133 q^{33} - 226 q^{35} - 476 q^{37} - 655 q^{39} - 10 q^{41} + 13 q^{43} + 57 q^{45} - 244 q^{47} + 31 q^{49} + 1490 q^{51} - 966 q^{53} + 1510 q^{55} + 2354 q^{57} - 731 q^{59} + 704 q^{61} - 518 q^{63} + 251 q^{65} + 901 q^{67} - 3479 q^{69} - 673 q^{71} + 3102 q^{73} - 2739 q^{75} + 266 q^{77} + 1680 q^{79} - 3018 q^{81} - 4032 q^{83} + 1373 q^{85} - 1485 q^{87} - 295 q^{89} + 2009 q^{91} - 3220 q^{93} + 3128 q^{95} - 2575 q^{97} - 916 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 18 * q^5 + q^7 - 93 * q^9 + 11 * q^11 + 49 * q^13 + 168 * q^15 - 50 * q^17 + 211 * q^19 - 166 * q^21 - 103 * q^23 + 786 * q^25 + 486 * q^27 + 48 * q^29 - 380 * q^31 + 133 * q^33 - 226 * q^35 - 476 * q^37 - 655 * q^39 - 10 * q^41 + 13 * q^43 + 57 * q^45 - 244 * q^47 + 31 * q^49 + 1490 * q^51 - 966 * q^53 + 1510 * q^55 + 2354 * q^57 - 731 * q^59 + 704 * q^61 - 518 * q^63 + 251 * q^65 + 901 * q^67 - 3479 * q^69 - 673 * q^71 + 3102 * q^73 - 2739 * q^75 + 266 * q^77 + 1680 * q^79 - 3018 * q^81 - 4032 * q^83 + 1373 * q^85 - 1485 * q^87 - 295 * q^89 + 2009 * q^91 - 3220 * q^93 + 3128 * q^95 - 2575 * q^97 - 916 * q^99

Introduction

L-functions

Modular forms

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Database

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