LMFDB - Embedded newform 144.4.i.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(49,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, 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("144.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.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:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} - 9x + 81 $ x^4 - x^3 - 8x^2 - 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.1
Root			$-2.31174 - 1.91203i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.4.i.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.31174 - 4.00405i) q^{3} +(-5.43521 - 9.41407i) q^{5} +(12.4352 - 21.5384i) q^{7} +(-5.06479 + 26.5207i) q^{9} +O(q^{10})$	\(q+(-3.31174 - 4.00405i) q^{3} +(-5.43521 - 9.41407i) q^{5} +(12.4352 - 21.5384i) q^{7} +(-5.06479 + 26.5207i) q^{9} +(-21.3704 + 37.0147i) q^{11} +(-7.56479 - 13.1026i) q^{13} +(-19.6944 + 52.9398i) q^{15} -13.8704 q^{17} -143.352 q^{19} +(-127.423 + 21.5384i) q^{21} +(9.56479 + 16.5667i) q^{23} +(3.41692 - 5.91828i) q^{25} +(122.963 - 67.5500i) q^{27} +(-113.046 + 195.802i) q^{29} +(29.6944 + 51.4321i) q^{31} +(218.982 - 37.0147i) q^{33} -270.352 q^{35} -84.1860 q^{37} +(-27.4108 + 73.6821i) q^{39} +(-101.630 - 176.028i) q^{41} +(162.945 - 282.229i) q^{43} +(277.196 - 96.4655i) q^{45} +(5.47180 - 9.47744i) q^{47} +(-137.769 - 238.623i) q^{49} +(45.9352 + 55.5378i) q^{51} -140.186 q^{53} +464.611 q^{55} +(474.745 + 573.989i) q^{57} +(57.3704 + 99.3685i) q^{59} +(377.528 - 653.898i) q^{61} +(508.232 + 438.878i) q^{63} +(-82.2325 + 142.431i) q^{65} +(-383.723 - 664.627i) q^{67} +(34.6578 - 93.1624i) q^{69} -335.854 q^{71} +167.279 q^{73} +(-35.0130 + 5.91828i) q^{75} +(531.492 + 920.570i) q^{77} +(-12.6578 + 21.9239i) q^{79} +(-677.696 - 268.643i) q^{81} +(143.861 - 249.174i) q^{83} +(75.3887 + 130.577i) q^{85} +(1158.38 - 195.802i) q^{87} -860.817 q^{89} -376.279 q^{91} +(107.597 - 289.227i) q^{93} +(779.149 + 1349.53i) q^{95} +(201.075 - 348.272i) q^{97} +(-873.418 - 754.230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} + 9 q^{5} + 19 q^{7} - 51 q^{9}+O(q^{10}) $ 4 * q - 3 * q^3 + 9 * q^5 + 19 * q^7 - 51 * q^9	$ 4 q - 3 q^{3} + 9 q^{5} + 19 q^{7} - 51 q^{9} - 24 q^{11} - 61 q^{13} - 171 q^{15} + 6 q^{17} - 266 q^{19} - 315 q^{21} + 69 q^{23} - 263 q^{25} - 237 q^{29} + 211 q^{31} + 630 q^{33} - 774 q^{35} + 524 q^{37} + 249 q^{39} - 468 q^{41} - 86 q^{43} - 459 q^{45} + 483 q^{47} + 33 q^{49} + 153 q^{51} + 300 q^{53} + 1674 q^{55} + 987 q^{57} + 168 q^{59} + 1049 q^{61} + 957 q^{63} + 747 q^{65} - 1166 q^{67} - 261 q^{69} + 624 q^{71} - 622 q^{73} - 2835 q^{75} + 1173 q^{77} + 349 q^{79} - 1143 q^{81} + 1221 q^{83} + 486 q^{85} + 2205 q^{87} - 984 q^{89} - 214 q^{91} - 789 q^{93} + 1764 q^{95} + 128 q^{97} - 1557 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 + 9 * q^5 + 19 * q^7 - 51 * q^9 - 24 * q^11 - 61 * q^13 - 171 * q^15 + 6 * q^17 - 266 * q^19 - 315 * q^21 + 69 * q^23 - 263 * q^25 - 237 * q^29 + 211 * q^31 + 630 * q^33 - 774 * q^35 + 524 * q^37 + 249 * q^39 - 468 * q^41 - 86 * q^43 - 459 * q^45 + 483 * q^47 + 33 * q^49 + 153 * q^51 + 300 * q^53 + 1674 * q^55 + 987 * q^57 + 168 * q^59 + 1049 * q^61 + 957 * q^63 + 747 * q^65 - 1166 * q^67 - 261 * q^69 + 624 * q^71 - 622 * q^73 - 2835 * q^75 + 1173 * q^77 + 349 * q^79 - 1143 * q^81 + 1221 * q^83 + 486 * q^85 + 2205 * q^87 - 984 * q^89 - 214 * q^91 - 789 * q^93 + 1764 * q^95 + 128 * q^97 - 1557 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.31174	−	4.00405i	−0.637344	−	0.770579i
$3$	−3.31174	−	4.00405i	−0.637344	−	0.770579i
$4$		0			0
$5$	−5.43521	−	9.41407i	−0.486140	−	0.842020i	0.513733	−	0.857950i	$-0.328262\pi$
$5$	−5.43521	−	9.41407i	−0.486140	−	0.842020i	−0.999873	+	0.0159306i	$0.994929\pi$
$6$		0			0
$7$	12.4352	−	21.5384i	0.671438	−	1.16297i	−0.306058	−	0.952013i	$-0.599010\pi$
$7$	12.4352	−	21.5384i	0.671438	−	1.16297i	0.977496	−	0.210953i	$-0.0676565\pi$
$8$		0			0
$9$	−5.06479	+	26.5207i	−0.187585	+	0.982248i
$10$		0			0
$11$	−21.3704	+	37.0147i	−0.585766	+	1.01458i	0.409013	+	0.912528i	$0.365873\pi$
$11$	−21.3704	+	37.0147i	−0.585766	+	1.01458i	−0.994779	+	0.102048i	$0.967460\pi$
$12$		0			0
$13$	−7.56479	−	13.1026i	−0.161392	−	0.279539i	0.773976	−	0.633215i	$-0.218265\pi$
$13$	−7.56479	−	13.1026i	−0.161392	−	0.279539i	−0.935368	+	0.353676i	$0.884932\pi$
$14$		0			0
$15$	−19.6944	+	52.9398i	−0.339004	+	0.911266i
$16$		0			0
$17$	−13.8704			−0.197887			−0.0989433	−	0.995093i	$-0.531546\pi$
$17$	−13.8704			−0.197887			−0.0989433	+	0.995093i	$0.531546\pi$
$18$		0			0
$19$	−143.352			−1.73091			−0.865454	−	0.500989i	$-0.832970\pi$
$19$	−143.352			−1.73091			−0.865454	+	0.500989i	$0.832970\pi$
$20$		0			0
$21$	−127.423	+	21.5384i	−1.32409	+	0.223813i
$22$		0			0
$23$	9.56479	+	16.5667i	0.0867129	+	0.150191i	0.906120	−	0.423021i	$-0.139030\pi$
$23$	9.56479	+	16.5667i	0.0867129	+	0.150191i	−0.819407	+	0.573212i	$0.805697\pi$
$24$		0			0
$25$	3.41692	−	5.91828i	0.0273353	−	0.0473462i
$26$		0			0
$27$	122.963	−	67.5500i	0.876456	−	0.481481i
$28$		0			0
$29$	−113.046	+	195.802i	−0.723869	+	1.25378i	0.235569	+	0.971858i	$0.424305\pi$
$29$	−113.046	+	195.802i	−0.723869	+	1.25378i	−0.959438	+	0.281920i	$0.909029\pi$
$30$		0			0
$31$	29.6944	+	51.4321i	0.172041	+	0.297983i	0.939133	−	0.343553i	$-0.111631\pi$
$31$	29.6944	+	51.4321i	0.172041	+	0.297983i	−0.767092	+	0.641537i	$0.778297\pi$
$32$		0			0
$33$	218.982	−	37.0147i	1.15515	−	0.195255i
$34$		0			0
$35$	−270.352			−1.30565
$36$		0			0
$37$	−84.1860			−0.374056			−0.187028	−	0.982355i	$-0.559886\pi$
$37$	−84.1860			−0.374056			−0.187028	+	0.982355i	$0.559886\pi$
$38$		0			0
$39$	−27.4108	+	73.6821i	−0.112545	+	0.302528i
$40$		0			0
$41$	−101.630	−	176.028i	−0.387119	−	0.670510i	0.604942	−	0.796270i	$-0.293196\pi$
$41$	−101.630	−	176.028i	−0.387119	−	0.670510i	−0.992061	+	0.125760i	$0.959863\pi$
$42$		0			0
$43$	162.945	−	282.229i	0.577881	−	1.00092i	−0.417841	−	0.908520i	$-0.637213\pi$
$43$	162.945	−	282.229i	0.577881	−	1.00092i	0.995722	−	0.0923995i	$-0.0294537\pi$
$44$		0			0
$45$	277.196	−	96.4655i	0.918265	−	0.319560i
$46$		0			0
$47$	5.47180	−	9.47744i	0.0169818	−	0.0294133i	−0.857410	−	0.514635i	$-0.827928\pi$
$47$	5.47180	−	9.47744i	0.0169818	−	0.0294133i	0.874391	+	0.485221i	$0.161261\pi$
$48$		0			0
$49$	−137.769	−	238.623i	−0.401659	−	0.695694i
$50$		0			0
$51$	45.9352	+	55.5378i	0.126122	+	0.152487i
$52$		0			0
$53$	−140.186			−0.363321			−0.181661	−	0.983361i	$-0.558147\pi$
$53$	−140.186			−0.363321			−0.181661	+	0.983361i	$0.558147\pi$
$54$		0			0
$55$	464.611			1.13906
$56$		0			0
$57$	474.745	+	573.989i	1.10318	+	1.33380i
$58$		0			0
$59$	57.3704	+	99.3685i	0.126593	+	0.219266i	0.922355	−	0.386345i	$-0.126262\pi$
$59$	57.3704	+	99.3685i	0.126593	+	0.219266i	−0.795761	+	0.605610i	$0.792929\pi$
$60$		0			0
$61$	377.528	−	653.898i	0.792419	−	1.37251i	−0.132047	−	0.991243i	$-0.542155\pi$
$61$	377.528	−	653.898i	0.792419	−	1.37251i	0.924465	−	0.381266i	$-0.124512\pi$
$62$		0			0
$63$	508.232	+	438.878i	1.01637	+	0.877674i
$64$		0			0
$65$	−82.2325	+	142.431i	−0.156918	+	0.271790i
$66$		0			0
$67$	−383.723	−	664.627i	−0.699689	−	1.21190i	−0.968574	−	0.248725i	$-0.919989\pi$
$67$	−383.723	−	664.627i	−0.699689	−	1.21190i	0.268885	−	0.963172i	$-0.413345\pi$
$68$		0			0
$69$	34.6578	−	93.1624i	0.0604682	−	0.162543i
$70$		0			0
$71$	−335.854			−0.561387			−0.280694	−	0.959797i	$-0.590564\pi$
$71$	−335.854			−0.561387			−0.280694	+	0.959797i	$0.590564\pi$
$72$		0			0
$73$	167.279			0.268199			0.134099	−	0.990968i	$-0.457186\pi$
$73$	167.279			0.268199			0.134099	+	0.990968i	$0.457186\pi$
$74$		0			0
$75$	−35.0130	+	5.91828i	−0.0539060	+	0.00911178i
$76$		0			0
$77$	531.492	+	920.570i	0.786612	+	1.36245i
$78$		0			0
$79$	−12.6578	+	21.9239i	−0.0180267	+	0.0312232i	−0.874898	−	0.484307i	$-0.839072\pi$
$79$	−12.6578	+	21.9239i	−0.0180267	+	0.0312232i	0.856871	+	0.515530i	$0.172405\pi$
$80$		0			0
$81$	−677.696	−	268.643i	−0.929624	−	0.368510i
$82$		0			0
$83$	143.861	−	249.174i	0.190250	−	0.329523i	−0.755083	−	0.655629i	$-0.772403\pi$
$83$	143.861	−	249.174i	0.190250	−	0.329523i	0.945333	+	0.326107i	$0.105737\pi$
$84$		0			0
$85$	75.3887	+	130.577i	0.0962006	+	0.166624i
$86$		0			0
$87$	1158.38	−	195.802i	1.42749	−	0.241290i
$88$		0			0
$89$	−860.817			−1.02524			−0.512620	−	0.858615i	$-0.671325\pi$
$89$	−860.817			−1.02524			−0.512620	+	0.858615i	$0.671325\pi$
$90$		0			0
$91$	−376.279			−0.433459
$92$		0			0
$93$	107.597	−	289.227i	0.119971	−	0.322489i
$94$		0			0
$95$	779.149	+	1349.53i	0.841464	+	1.45746i
$96$		0			0
$97$	201.075	−	348.272i	0.210475	−	0.364553i	−0.741389	−	0.671076i	$-0.765832\pi$
$97$	201.075	−	348.272i	0.210475	−	0.364553i	0.951863	+	0.306523i	$0.0991657\pi$
$98$		0			0
$99$	−873.418	−	754.230i	−0.886685	−	0.765687i
$100$		0			0
$101$	665.714	−	1153.05i	0.655852	−	1.13597i	−0.325828	−	0.945429i	$-0.605643\pi$
$101$	665.714	−	1153.05i	0.655852	−	1.13597i	0.981680	−	0.190540i	$-0.0610237\pi$
$102$		0			0
$103$	−259.252	−	449.038i	−0.248009	−	0.429563i	0.714965	−	0.699161i	$-0.246443\pi$
$103$	−259.252	−	449.038i	−0.248009	−	0.429563i	−0.962973	+	0.269597i	$0.913109\pi$
$104$		0			0
$105$	895.335	+	1082.50i	0.832150	+	1.00611i
$106$		0			0
$107$	−1471.87			−1.32982			−0.664912	−	0.746922i	$-0.731531\pi$
$107$	−1471.87			−1.32982			−0.664912	+	0.746922i	$0.731531\pi$
$108$		0			0
$109$	−643.668			−0.565616			−0.282808	−	0.959176i	$-0.591266\pi$
$109$	−643.668			−0.565616			−0.282808	+	0.959176i	$0.591266\pi$
$110$		0			0
$111$	278.802	+	337.085i	0.238403	+	0.288240i
$112$		0			0
$113$	−511.864	−	886.574i	−0.426125	−	0.738069i	0.570400	−	0.821367i	$-0.306788\pi$
$113$	−511.864	−	886.574i	−0.426125	−	0.738069i	−0.996525	+	0.0832976i	$0.973455\pi$
$114$		0			0
$115$	103.973	−	180.087i	0.0843092	−	0.146028i
$116$		0			0
$117$	385.804	−	134.262i	0.304851	−	0.106090i
$118$		0			0
$119$	−172.482	+	298.747i	−0.132869	+	0.230135i
$120$		0			0
$121$	−247.890	−	429.358i	−0.186244	−	0.322583i
$122$		0			0
$123$	−368.252	+	989.887i	−0.269953	+	0.725651i
$124$		0			0
$125$	−1433.09			−1.02544
$126$		0			0
$127$	31.4481			0.0219730			0.0109865	−	0.999940i	$-0.496503\pi$
$127$	31.4481			0.0219730			0.0109865	+	0.999940i	$0.496503\pi$
$128$		0			0
$129$	−1669.69	+	282.229i	−1.13960	+	0.192627i
$130$		0			0
$131$	−968.678	−	1677.80i	−0.646059	−	1.11901i	−0.984056	−	0.177860i	$-0.943083\pi$
$131$	−968.678	−	1677.80i	−0.646059	−	1.11901i	0.337997	−	0.941147i	$-0.390251\pi$
$132$		0			0
$133$	−1782.61	+	3087.58i	−1.16220	+	2.01299i
$134$		0			0
$135$	−1304.25	−	790.437i	−0.831497	−	0.503926i
$136$		0			0
$137$	−579.297	+	1003.37i	−0.361261	+	0.625722i	−0.988169	−	0.153372i	$-0.950987\pi$
$137$	−579.297	+	1003.37i	−0.361261	+	0.625722i	0.626908	+	0.779093i	$0.284320\pi$
$138$		0			0
$139$	1155.80	+	2001.90i	0.705277	+	1.22158i	0.966591	+	0.256323i	$0.0825109\pi$
$139$	1155.80	+	2001.90i	0.705277	+	1.22158i	−0.261314	+	0.965254i	$0.584156\pi$
$140$		0			0
$141$	−56.0693	+	9.47744i	−0.0334886	+	0.00566060i
$142$		0			0
$143$	646.651			0.378151
$144$		0			0
$145$	2457.73			1.40761
$146$		0			0
$147$	−499.203	+	1341.89i	−0.280092	+	0.752907i
$148$		0			0
$149$	1475.11	+	2554.96i	0.811043	+	1.40477i	0.912135	+	0.409890i	$0.134433\pi$
$149$	1475.11	+	2554.96i	0.811043	+	1.40477i	−0.101092	+	0.994877i	$0.532234\pi$
$150$		0			0
$151$	−863.199	+	1495.10i	−0.465206	+	0.805761i	−0.999211	−	0.0397208i	$-0.987353\pi$
$151$	−863.199	+	1495.10i	−0.465206	+	0.805761i	0.534005	+	0.845482i	$0.320686\pi$
$152$		0			0
$153$	70.2508	−	367.854i	0.0371205	−	0.194374i
$154$		0			0
$155$	322.790	−	559.089i	0.167272	−	0.289723i
$156$		0			0
$157$	−641.694	−	1111.45i	−0.326196	−	0.564988i	0.655558	−	0.755145i	$-0.272434\pi$
$157$	−641.694	−	1111.45i	−0.326196	−	0.564988i	−0.981754	+	0.190157i	$0.939100\pi$
$158$		0			0
$159$	464.259	+	561.311i	0.231561	+	0.279968i
$160$		0			0
$161$	475.761			0.232889
$162$		0			0
$163$	−1033.93			−0.496831			−0.248415	−	0.968654i	$-0.579910\pi$
$163$	−1033.93			−0.496831			−0.248415	+	0.968654i	$0.579910\pi$
$164$		0			0
$165$	−1538.67	−	1860.33i	−0.725972	−	0.877734i
$166$		0			0
$167$	−141.309	−	244.754i	−0.0654778	−	0.113411i	0.831428	−	0.555632i	$-0.187524\pi$
$167$	−141.309	−	244.754i	−0.0654778	−	0.113411i	−0.896906	+	0.442222i	$0.854190\pi$
$168$		0			0
$169$	984.048	−	1704.42i	0.447905	−	0.775795i
$170$		0			0
$171$	726.048	−	3801.80i	0.324692	−	1.70018i
$172$		0			0
$173$	1766.36	−	3059.43i	0.776266	−	1.34453i	−0.157814	−	0.987469i	$-0.550445\pi$
$173$	1766.36	−	3059.43i	0.776266	−	1.34453i	0.934080	−	0.357063i	$-0.116222\pi$
$174$		0			0
$175$	−84.9802	−	147.190i	−0.0367080	−	0.0635801i
$176$		0			0
$177$	207.880	−	558.796i	0.0882782	−	0.237298i
$178$		0			0
$179$	4052.74			1.69227			0.846135	−	0.532969i	$-0.178924\pi$
$179$	4052.74			1.69227			0.846135	+	0.532969i	$0.178924\pi$
$180$		0			0
$181$	−2830.97			−1.16257			−0.581283	−	0.813702i	$-0.697449\pi$
$181$	−2830.97			−1.16257			−0.581283	+	0.813702i	$0.697449\pi$
$182$		0			0
$183$	−3868.51	+	653.898i	−1.56267	+	0.264140i
$184$		0			0
$185$	457.569	+	792.532i	0.181844	+	0.314963i
$186$		0			0
$187$	296.417	−	513.409i	0.115915	−	0.200771i
$188$		0			0
$189$	74.1563	−	3488.44i	0.0285401	−	1.34257i
$190$		0			0
$191$	2254.62	−	3905.12i	0.854129	−	1.47940i	−0.0233215	−	0.999728i	$-0.507424\pi$
$191$	2254.62	−	3905.12i	0.854129	−	1.47940i	0.877451	−	0.479667i	$-0.159243\pi$
$192$		0			0
$193$	1610.56	+	2789.58i	0.600678	+	1.04040i	0.992719	+	0.120457i	$0.0384359\pi$
$193$	1610.56	+	2789.58i	0.600678	+	1.04040i	−0.392041	+	0.919948i	$0.628231\pi$
$194$		0			0
$195$	842.632	−	142.431i	0.309447	−	0.0523061i
$196$		0			0
$197$	3784.20			1.36859			0.684297	−	0.729204i	$-0.260109\pi$
$197$	3784.20			1.36859			0.684297	+	0.729204i	$0.260109\pi$
$198$		0			0
$199$	2926.27			1.04240			0.521200	−	0.853435i	$-0.325485\pi$
$199$	2926.27			1.04240			0.521200	+	0.853435i	$0.325485\pi$
$200$		0			0
$201$	−1390.41	+	3737.51i	−0.487920	+	1.31156i
$202$		0			0
$203$	2811.51	+	4869.69i	0.972067	+	1.68367i
$204$		0			0
$205$	−1104.76	+	1913.49i	−0.376388	+	0.651923i
$206$		0			0
$207$	−487.804	+	169.758i	−0.163791	+	0.0570000i
$208$		0			0
$209$	3063.50	−	5306.13i	1.01391	−	1.75614i
$210$		0			0
$211$	156.737	+	271.476i	0.0511385	+	0.0885744i	0.890462	−	0.455059i	$-0.150382\pi$
$211$	156.737	+	271.476i	0.0511385	+	0.0885744i	−0.839323	+	0.543633i	$0.817048\pi$
$212$		0			0
$213$	1112.26	+	1344.77i	0.357797	+	0.432593i
$214$		0			0
$215$	−3542.57			−1.12373
$216$		0			0
$217$	1477.02			0.462059
$218$		0			0
$219$	−553.984	−	669.793i	−0.170935	−	0.206669i
$220$		0			0
$221$	104.927	+	181.739i	0.0319373	+	0.0553170i
$222$		0			0
$223$	−355.193	+	615.212i	−0.106661	+	0.184743i	−0.914416	−	0.404776i	$-0.867349\pi$
$223$	−355.193	+	615.212i	−0.106661	+	0.184743i	0.807754	+	0.589519i	$0.200683\pi$
$224$		0			0
$225$	139.651	+	120.594i	0.0413780	+	0.0357315i
$226$		0			0
$227$	16.3308	−	28.2858i	0.00477496	−	0.00827046i	−0.863628	−	0.504130i	$-0.831813\pi$
$227$	16.3308	−	28.2858i	0.00477496	−	0.00827046i	0.868403	+	0.495859i	$0.165147\pi$
$228$		0			0
$229$	2751.92	+	4766.47i	0.794114	+	1.37545i	0.923400	+	0.383839i	$0.125398\pi$
$229$	2751.92	+	4766.47i	0.794114	+	1.37545i	−0.129286	+	0.991607i	$0.541268\pi$
$230$		0			0
$231$	1925.85	−	5176.81i	0.548534	−	1.47450i
$232$		0			0
$233$	−6788.81			−1.90880			−0.954399	−	0.298534i	$-0.903502\pi$
$233$	−6788.81			−1.90880			−0.954399	+	0.298534i	$0.903502\pi$
$234$		0			0
$235$	−118.962			−0.0330221
$236$		0			0
$237$	129.704	−	21.9239i	0.0355492	−	0.00600890i
$238$		0			0
$239$	−214.694	−	371.862i	−0.0581064	−	0.100643i	0.835509	−	0.549477i	$-0.185173\pi$
$239$	−214.694	−	371.862i	−0.0581064	−	0.100643i	−0.893615	+	0.448834i	$0.851840\pi$
$240$		0			0
$241$	2421.82	−	4194.72i	0.647317	−	1.12119i	−0.336444	−	0.941703i	$-0.609224\pi$
$241$	2421.82	−	4194.72i	0.647317	−	1.12119i	0.983761	−	0.179483i	$-0.0574424\pi$
$242$		0			0
$243$	1168.69	+	3603.20i	0.308525	+	0.951216i
$244$		0			0
$245$	−1497.61	+	2593.93i	−0.390525	+	0.676410i
$246$		0			0
$247$	1084.43	+	1878.28i	0.279354	+	0.483856i
$248$		0			0
$249$	−1474.13	+	249.174i	−0.375178	+	0.0634166i
$250$		0			0
$251$	−2400.87			−0.603752			−0.301876	−	0.953347i	$-0.597613\pi$
$251$	−2400.87			−0.603752			−0.301876	+	0.953347i	$0.597613\pi$
$252$		0			0
$253$	−817.614			−0.203174
$254$		0			0
$255$	273.169	−	734.297i	0.0670844	−	0.180327i
$256$		0			0
$257$	−1490.50	−	2581.62i	−0.361769	−	0.626602i	0.626483	−	0.779435i	$-0.284494\pi$
$257$	−1490.50	−	2581.62i	−0.361769	−	0.626602i	−0.988252	+	0.152833i	$0.951160\pi$
$258$		0			0
$259$	−1046.87	+	1813.23i	−0.251156	+	0.435015i
$260$		0			0
$261$	−4620.26	−	3989.77i	−1.09573	−	0.946209i
$262$		0			0
$263$	2780.41	−	4815.81i	0.651891	−	1.12911i	−0.330773	−	0.943710i	$-0.607309\pi$
$263$	2780.41	−	4815.81i	0.651891	−	1.12911i	0.982664	−	0.185398i	$-0.0593573\pi$
$264$		0			0
$265$	761.941	+	1319.72i	0.176625	+	0.305924i
$266$		0			0
$267$	2850.80	+	3446.75i	0.653431	+	0.790029i
$268$		0			0
$269$	6288.50			1.42534			0.712671	−	0.701499i	$-0.247485\pi$
$269$	6288.50			1.42534			0.712671	+	0.701499i	$0.247485\pi$
$270$		0			0
$271$	−6854.90			−1.53655			−0.768275	−	0.640119i	$-0.778885\pi$
$271$	−6854.90			−1.53655			−0.768275	+	0.640119i	$0.778885\pi$
$272$		0			0
$273$	1246.14	+	1506.64i	0.276262	+	0.334014i
$274$		0			0
$275$	146.042	+	252.952i	0.0320242	+	0.0554676i
$276$		0			0
$277$	−449.086	+	777.840i	−0.0974114	+	0.168722i	−0.910612	−	0.413261i	$-0.864390\pi$
$277$	−449.086	+	777.840i	−0.0974114	+	0.168722i	0.813201	+	0.581983i	$0.197723\pi$
$278$		0			0
$279$	−1514.41	+	527.023i	−0.324966	+	0.113090i
$280$		0			0
$281$	−119.385	+	206.781i	−0.0253448	+	0.0438986i	−0.878420	−	0.477890i	$-0.841402\pi$
$281$	−119.385	+	206.781i	−0.0253448	+	0.0438986i	0.853075	+	0.521789i	$0.174735\pi$
$282$		0			0
$283$	1035.58	+	1793.68i	0.217523	+	0.376760i	0.954050	−	0.299647i	$-0.0968690\pi$
$283$	1035.58	+	1793.68i	0.217523	+	0.376760i	−0.736527	+	0.676408i	$0.763536\pi$
$284$		0			0
$285$	2823.23	−	7589.03i	0.586785	−	1.57732i
$286$		0			0
$287$	−5055.14			−1.03971
$288$		0			0
$289$	−4720.61			−0.960841
$290$		0			0
$291$	−2060.40	+	348.272i	−0.415062	+	0.0701582i
$292$		0			0
$293$	3288.88	+	5696.51i	0.655763	+	1.13581i	0.981702	+	0.190423i	$0.0609861\pi$
$293$	3288.88	+	5696.51i	0.655763	+	1.13581i	−0.325939	+	0.945391i	$0.605681\pi$
$294$		0			0
$295$	623.641	−	1080.18i	0.123084	−	0.213188i
$296$		0			0
$297$	−127.441	+	5995.02i	−0.0248985	+	1.17127i
$298$		0			0
$299$	144.711	−	250.647i	0.0279895	−	0.0484792i
$300$		0			0
$301$	−4052.51	−	7019.16i	−0.776023	−	1.34411i
$302$		0			0
$303$	−6821.54	+	1153.05i	−1.29336	+	0.218617i
$304$		0			0
$305$	−8207.78			−1.54091
$306$		0			0
$307$	5237.30			0.973644			0.486822	−	0.873501i	$-0.338156\pi$
$307$	5237.30			0.973644			0.486822	+	0.873501i	$0.338156\pi$
$308$		0			0
$309$	−939.394	+	2525.15i	−0.172946	+	0.464890i
$310$		0			0
$311$	2852.49	+	4940.67i	0.520097	+	0.900834i	0.999727	+	0.0233635i	$0.00743750\pi$
$311$	2852.49	+	4940.67i	0.520097	+	0.900834i	−0.479630	+	0.877471i	$0.659229\pi$
$312$		0			0
$313$	−2538.74	+	4397.23i	−0.458460	+	0.794076i	−0.998880	−	0.0473193i	$-0.984932\pi$
$313$	−2538.74	+	4397.23i	−0.458460	+	0.794076i	0.540420	+	0.841396i	$0.318265\pi$
$314$		0			0
$315$	1369.28	−	7169.93i	0.244921	−	1.28248i
$316$		0			0
$317$	−1434.46	+	2484.55i	−0.254155	+	0.440209i	−0.964666	−	0.263477i	$-0.915131\pi$
$317$	−1434.46	+	2484.55i	−0.254155	+	0.440209i	0.710511	+	0.703686i	$0.248464\pi$
$318$		0			0
$319$	−4831.70	−	8368.76i	−0.848036	−	1.46884i
$320$		0			0
$321$	4874.45	+	5893.44i	0.847555	+	1.02473i
$322$		0			0
$323$	1988.36			0.342523
$324$		0			0
$325$	−103.393			−0.0176468
$326$		0			0
$327$	2131.66	+	2577.28i	0.360492	+	0.435852i
$328$		0			0
$329$	−136.086	−	235.708i	−0.0228045	−	0.0394985i
$330$		0			0
$331$	1015.67	−	1759.20i	0.168660	−	0.292128i	−0.769289	−	0.638901i	$-0.779389\pi$
$331$	1015.67	−	1759.20i	0.168660	−	0.292128i	0.937949	+	0.346773i	$0.112723\pi$
$332$		0			0
$333$	426.384	−	2232.67i	0.0701673	−	0.367416i
$334$		0			0
$335$	−4171.23	+	7224.78i	−0.680294	+	1.17830i
$336$		0			0
$337$	−4899.14	−	8485.56i	−0.791909	−	1.37163i	−0.924784	−	0.380493i	$-0.875754\pi$
$337$	−4899.14	−	8485.56i	−0.791909	−	1.37163i	0.132875	−	0.991133i	$-0.457579\pi$
$338$		0			0
$339$	−1854.72	+	4985.63i	−0.297153	+	0.798767i
$340$		0			0
$341$	−2538.32			−0.403103
$342$		0			0
$343$	1677.81			0.264120
$344$		0			0
$345$	−1065.41	+	180.087i	−0.166260	+	0.0281031i
$346$		0			0
$347$	−2278.28	−	3946.10i	−0.352463	−	0.610483i	0.634218	−	0.773154i	$-0.281322\pi$
$347$	−2278.28	−	3946.10i	−0.352463	−	0.610483i	−0.986680	+	0.162671i	$0.947989\pi$
$348$		0			0
$349$	−1674.44	+	2900.22i	−0.256822	+	0.444829i	−0.965389	−	0.260815i	$-0.916009\pi$
$349$	−1674.44	+	2900.22i	−0.256822	+	0.444829i	0.708567	+	0.705644i	$0.249342\pi$
$350$		0			0
$351$	−1815.27	−	1100.14i	−0.276046	−	0.167296i
$352$		0			0
$353$	−931.134	+	1612.77i	−0.140395	+	0.243170i	−0.927645	−	0.373463i	$-0.878170\pi$
$353$	−931.134	+	1612.77i	−0.140395	+	0.243170i	0.787251	+	0.616633i	$0.211504\pi$
$354$		0			0
$355$	1825.44	+	3161.75i	0.272913	+	0.472699i
$356$		0			0
$357$	1767.41	−	298.747i	0.262021	−	0.0442896i
$358$		0			0
$359$	−6179.46			−0.908466			−0.454233	−	0.890883i	$-0.650087\pi$
$359$	−6179.46			−0.908466			−0.454233	+	0.890883i	$0.650087\pi$
$360$		0			0
$361$	13690.8			1.99604
$362$		0			0
$363$	−898.224	+	2414.49i	−0.129875	+	0.349112i
$364$		0			0
$365$	−909.197	−	1574.77i	−0.130382	−	0.225829i
$366$		0			0
$367$	3436.98	−	5953.02i	0.488852	−	0.846717i	−0.511066	−	0.859542i	$-0.670749\pi$
$367$	3436.98	−	5953.02i	0.488852	−	0.846717i	0.999918	+	0.0128251i	$0.00408245\pi$
$368$		0			0
$369$	5183.11	−	1803.75i	0.731224	−	0.254470i
$370$		0			0
$371$	−1743.24	+	3019.38i	−0.243948	+	0.422530i
$372$		0			0
$373$	−635.013	−	1099.87i	−0.0881494	−	0.152679i	0.818580	−	0.574393i	$-0.194762\pi$
$373$	−635.013	−	1099.87i	−0.0881494	−	0.152679i	−0.906729	+	0.421714i	$0.861429\pi$
$374$		0			0
$375$	4746.02	+	5738.16i	0.653556	+	0.790179i
$376$		0			0
$377$	3420.69			0.467306
$378$		0			0
$379$	−2490.54			−0.337548			−0.168774	−	0.985655i	$-0.553981\pi$
$379$	−2490.54			−0.337548			−0.168774	+	0.985655i	$0.553981\pi$
$380$		0			0
$381$	−104.148	−	125.920i	−0.0140044	−	0.0169319i
$382$		0			0
$383$	156.213	+	270.568i	0.0208410	+	0.0360976i	0.876258	−	0.481843i	$-0.160032\pi$
$383$	156.213	+	270.568i	0.0208410	+	0.0360976i	−0.855417	+	0.517940i	$0.826699\pi$
$384$		0			0
$385$	5777.54	−	10007.0i	0.764807	−	1.32468i
$386$		0			0
$387$	6659.64	+	5750.85i	0.874750	+	0.755380i
$388$		0			0
$389$	−4821.58	+	8351.23i	−0.628442	+	1.08849i	0.359422	+	0.933175i	$0.382974\pi$
$389$	−4821.58	+	8351.23i	−0.628442	+	1.08849i	−0.987864	+	0.155319i	$0.950360\pi$
$390$		0			0
$391$	−132.668	−	229.787i	−0.0171593	−	0.0297208i
$392$		0			0
$393$	−3509.98	+	9435.06i	−0.450522	+	1.21103i
$394$		0			0
$395$	275.191			0.0350540
$396$		0			0
$397$	−2260.32			−0.285749			−0.142874	−	0.989741i	$-0.545634\pi$
$397$	−2260.32			−0.285749			−0.142874	+	0.989741i	$0.545634\pi$
$398$		0			0
$399$	18266.4	−	3087.58i	2.29188	−	0.387399i
$400$		0			0
$401$	−5084.64	−	8806.85i	−0.633204	−	1.09674i	−0.986893	−	0.161378i	$-0.948406\pi$
$401$	−5084.64	−	8806.85i	−0.633204	−	1.09674i	0.353689	−	0.935363i	$-0.384927\pi$
$402$		0			0
$403$	449.263	−	778.146i	0.0555320	−	0.0961842i
$404$		0			0
$405$	1154.39	+	7840.01i	0.141635	+	0.961909i
$406$		0			0
$407$	1799.09	−	3116.12i	0.219110	−	0.379509i
$408$		0			0
$409$	474.916	+	822.579i	0.0574159	+	0.0994472i	0.893305	−	0.449452i	$-0.148381\pi$
$409$	474.916	+	822.579i	0.0574159	+	0.0994472i	−0.835889	+	0.548899i	$0.815047\pi$
$410$		0			0
$411$	5936.03	−	1003.37i	0.712416	−	0.120420i
$412$		0			0
$413$	2853.65			0.339998
$414$		0			0
$415$	−3127.65			−0.369953
$416$		0			0
$417$	4188.01	−	11257.6i	0.491817	−	1.32204i
$418$		0			0
$419$	−5899.63	−	10218.5i	−0.687866	−	1.19142i	−0.972527	−	0.232791i	$-0.925214\pi$
$419$	−5899.63	−	10218.5i	−0.687866	−	1.19142i	0.284660	−	0.958628i	$-0.408119\pi$
$420$		0			0
$421$	3206.46	−	5553.76i	0.371196	−	0.642930i	−0.618554	−	0.785742i	$-0.712281\pi$
$421$	3206.46	−	5553.76i	0.371196	−	0.642930i	0.989750	+	0.142812i	$0.0456145\pi$
$422$		0			0
$423$	223.635	+	193.117i	0.0257057	+	0.0221978i
$424$		0			0
$425$	−47.3941	+	82.0890i	−0.00540930	+	0.00936918i
$426$		0			0
$427$	−9389.29	−	16262.7i	−1.06412	−	1.84311i
$428$		0			0
$429$	−2141.54	−	2589.22i	−0.241013	−	0.291396i
$430$		0			0
$431$	12042.7			1.34589			0.672945	−	0.739693i	$-0.265029\pi$
$431$	12042.7			1.34589			0.672945	+	0.739693i	$0.265029\pi$
$432$		0			0
$433$	7279.83			0.807959			0.403980	−	0.914768i	$-0.367627\pi$
$433$	7279.83			0.807959			0.403980	+	0.914768i	$0.367627\pi$
$434$		0			0
$435$	−8139.35	−	9840.86i	−0.897131	−	1.08467i
$436$		0			0
$437$	−1371.13	−	2374.87i	−0.150092	−	0.259967i
$438$		0			0
$439$	−1799.35	+	3116.57i	−0.195623	+	0.338828i	−0.947104	−	0.320926i	$-0.896006\pi$
$439$	−1799.35	+	3116.57i	−0.195623	+	0.338828i	0.751482	+	0.659754i	$0.229339\pi$
$440$		0			0
$441$	7026.22	−	2445.16i	0.758689	−	0.264027i
$442$		0			0
$443$	−7393.18	+	12805.4i	−0.792913	+	1.37337i	0.131243	+	0.991350i	$0.458103\pi$
$443$	−7393.18	+	12805.4i	−0.792913	+	1.37337i	−0.924156	+	0.382016i	$0.875230\pi$
$444$		0			0
$445$	4678.72	+	8103.79i	0.498411	+	0.863273i
$446$		0			0
$447$	5345.01	−	14367.7i	0.565571	−	1.52029i
$448$		0			0
$449$	114.489			0.0120336			0.00601681	−	0.999982i	$-0.498085\pi$
$449$	114.489			0.0120336			0.00601681	+	0.999982i	$0.498085\pi$
$450$		0			0
$451$	8687.47			0.907044
$452$		0			0
$453$	8845.16	−	1495.10i	0.917399	−	0.155069i
$454$		0			0
$455$	2045.16	+	3542.31i	0.210722	+	0.364981i
$456$		0			0
$457$	−3155.57	+	5465.60i	−0.323001	+	0.559453i	−0.981106	−	0.193473i	$-0.938025\pi$
$457$	−3155.57	+	5465.60i	−0.323001	+	0.559453i	0.658105	+	0.752926i	$0.271358\pi$
$458$		0			0
$459$	−1705.55	+	936.947i	−0.173439	+	0.0952787i
$460$		0			0
$461$	6872.41	−	11903.4i	0.694317	−	1.20259i	−0.276094	−	0.961131i	$-0.589040\pi$
$461$	6872.41	−	11903.4i	0.694317	−	1.20259i	0.970411	−	0.241461i	$-0.0776266\pi$
$462$		0			0
$463$	7824.30	+	13552.1i	0.785369	+	1.36030i	0.928778	+	0.370636i	$0.120860\pi$
$463$	7824.30	+	13552.1i	0.785369	+	1.36030i	−0.143409	+	0.989664i	$0.545806\pi$
$464$		0			0
$465$	−3307.62	+	559.089i	−0.329865	+	0.0557573i
$466$		0			0
$467$	7395.79			0.732840			0.366420	−	0.930450i	$-0.380583\pi$
$467$	7395.79			0.732840			0.366420	+	0.930450i	$0.380583\pi$
$468$		0			0
$469$	−19086.7			−1.87919
$470$		0			0
$471$	−2325.16	+	6250.20i	−0.227469	+	0.611452i
$472$		0			0
$473$	6964.41	+	12062.7i	0.677006	+	1.17261i
$474$		0			0
$475$	−489.822	+	848.397i	−0.0473149	+	0.0819519i
$476$		0			0
$477$	710.012	−	3717.83i	0.0681535	−	0.356872i
$478$		0			0
$479$	−3130.53	+	5422.24i	−0.298617	+	0.517221i	−0.975820	−	0.218576i	$-0.929859\pi$
$479$	−3130.53	+	5422.24i	−0.298617	+	0.517221i	0.677202	+	0.735797i	$0.263192\pi$
$480$		0			0
$481$	636.849	+	1103.05i	0.0603697	+	0.104563i
$482$		0			0
$483$	−1575.59	−	1904.97i	−0.148431	−	0.179460i
$484$		0			0
$485$	−4371.54			−0.409281
$486$		0			0
$487$	10314.7			0.959763			0.479881	−	0.877333i	$-0.340680\pi$
$487$	10314.7			0.959763			0.479881	+	0.877333i	$0.340680\pi$
$488$		0			0
$489$	3424.09	+	4139.89i	0.316652	+	0.382847i
$490$		0			0
$491$	−1380.45	−	2391.01i	−0.126881	−	0.219765i	0.795585	−	0.605841i	$-0.207163\pi$
$491$	−1380.45	−	2391.01i	−0.126881	−	0.219765i	−0.922467	+	0.386076i	$0.873830\pi$
$492$		0			0
$493$	1568.00	−	2715.86i	0.143244	−	0.248106i
$494$		0			0
$495$	−2353.16	+	12321.8i	−0.213670	+	1.11884i
$496$		0			0
$497$	−4176.41	+	7233.76i	−0.376937	+	0.652874i
$498$		0			0
$499$	−4793.00	−	8301.71i	−0.429988	−	0.744761i	0.566884	−	0.823798i	$-0.308149\pi$
$499$	−4793.00	−	8301.71i	−0.429988	−	0.744761i	−0.996872	+	0.0790369i	$0.974816\pi$
$500$		0			0
$501$	−512.028	+	1376.37i	−0.0456602	+	0.122738i
$502$		0			0
$503$	−8829.60			−0.782689			−0.391344	−	0.920244i	$-0.627990\pi$
$503$	−8829.60			−0.782689			−0.391344	+	0.920244i	$0.627990\pi$
$504$		0			0
$505$	−14473.2			−1.27534
$506$		0			0
$507$	−10083.5	+	1704.42i	−0.883281	+	0.149302i
$508$		0			0
$509$	−2370.87	−	4106.47i	−0.206458	−	0.357595i	0.744138	−	0.668025i	$-0.232860\pi$
$509$	−2370.87	−	4106.47i	−0.206458	−	0.357595i	−0.950596	+	0.310430i	$0.899527\pi$
$510$		0			0
$511$	2080.15	−	3602.92i	0.180079	−	0.311906i
$512$		0			0
$513$	−17627.1	+	9683.43i	−1.51706	+	0.833400i
$514$		0			0
$515$	−2818.18	+	4881.24i	−0.241134	+	0.417656i
$516$		0			0
$517$	233.870	+	405.074i	0.0198947	+	0.0344587i
$518$		0			0
$519$	−18099.8	+	3059.43i	−1.53082	+	0.258755i
$520$		0			0
$521$	−2753.22			−0.231518			−0.115759	−	0.993277i	$-0.536930\pi$
$521$	−2753.22			−0.231518			−0.115759	+	0.993277i	$0.536930\pi$
$522$		0			0
$523$	−17115.3			−1.43098			−0.715489	−	0.698624i	$-0.753796\pi$
$523$	−17115.3			−1.43098			−0.715489	+	0.698624i	$0.753796\pi$
$524$		0			0
$525$	−307.924	+	827.719i	−0.0255979	+	0.0688088i
$526$		0			0
$527$	−411.873	−	713.386i	−0.0340446	−	0.0589669i
$528$		0			0
$529$	5900.53	−	10220.0i	0.484962	−	0.839978i
$530$		0			0
$531$	−2925.89	+	1018.22i	−0.239120	+	0.0832150i
$532$		0			0
$533$	−1537.61	+	2663.22i	−0.124956	+	0.216430i
$534$		0			0
$535$	7999.93	+	13856.3i	0.646481	+	1.11974i
$536$		0			0
$537$	−13421.6	−	16227.4i	−1.07856	−	1.30403i
$538$		0			0
$539$	11776.7			0.941113
$540$		0			0
$541$	17880.1			1.42093			0.710467	−	0.703731i	$-0.248484\pi$
$541$	17880.1			1.42093			0.710467	+	0.703731i	$0.248484\pi$
$542$		0			0
$543$	9375.43	+	11335.3i	0.740954	+	0.895849i
$544$		0			0
$545$	3498.47	+	6059.53i	0.274969	+	0.476260i
$546$		0			0
$547$	−6534.73	+	11318.5i	−0.510795	+	0.884723i	0.489127	+	0.872213i	$0.337316\pi$
$547$	−6534.73	+	11318.5i	−0.510795	+	0.884723i	−0.999922	+	0.0125101i	$0.996018\pi$
$548$		0			0
$549$	15429.7	+	13324.2i	1.19950	+	1.03581i
$550$		0			0
$551$	16205.5	−	28068.7i	1.25295	−	2.17017i
$552$		0			0
$553$	314.804	+	545.257i	0.0242077	+	0.0419289i
$554$		0			0
$555$	1657.99	−	4456.79i	0.126807	−	0.340865i
$556$		0			0
$557$	9507.62			0.723251			0.361626	−	0.932323i	$-0.382222\pi$
$557$	9507.62			0.723251			0.361626	+	0.932323i	$0.382222\pi$
$558$		0			0
$559$	−4930.58			−0.373061
$560$		0			0
$561$	−3037.37	+	513.409i	−0.228588	+	0.0386384i
$562$		0			0
$563$	−10222.3	−	17705.6i	−0.765221	−	1.32540i	−0.940130	−	0.340817i	$-0.889296\pi$
$563$	−10222.3	−	17705.6i	−0.765221	−	1.32540i	0.174909	−	0.984585i	$-0.444037\pi$
$564$		0			0
$565$	−5564.17	+	9637.43i	−0.414313	+	0.717610i
$566$		0			0
$567$	−14213.4	+	11255.9i	−1.05275	+	0.833689i
$568$		0			0
$569$	−1323.03	+	2291.56i	−0.0974770	+	0.168835i	−0.910640	−	0.413201i	$-0.864411\pi$
$569$	−1323.03	+	2291.56i	−0.0974770	+	0.168835i	0.813163	+	0.582036i	$0.197744\pi$
$570$		0			0
$571$	878.514	+	1521.63i	0.0643864	+	0.111521i	0.896422	−	0.443202i	$-0.146158\pi$
$571$	878.514	+	1521.63i	0.0643864	+	0.111521i	−0.832035	+	0.554723i	$0.812824\pi$
$572$		0			0
$573$	−23103.0	+	3905.12i	−1.68437	+	0.284710i
$574$		0			0
$575$	130.728			0.00948130
$576$		0			0
$577$	−7515.43			−0.542238			−0.271119	−	0.962546i	$-0.587394\pi$
$577$	−7515.43			−0.542238			−0.271119	+	0.962546i	$0.587394\pi$
$578$		0			0
$579$	5835.83	−	15687.1i	0.418876	−	1.12597i
$580$		0			0
$581$	−3577.87	−	6197.06i	−0.255482	−	0.442508i
$582$		0			0
$583$	2995.83	−	5188.94i	0.212821	−	0.368617i
$584$		0			0
$585$	−3360.88	−	2902.24i	−0.237530	−	0.205116i
$586$		0			0
$587$	−2476.24	+	4288.98i	−0.174115	+	0.301576i	−0.939855	−	0.341575i	$-0.889040\pi$
$587$	−2476.24	+	4288.98i	−0.174115	+	0.301576i	0.765740	+	0.643151i	$0.222373\pi$
$588$		0			0
$589$	−4256.75	−	7372.91i	−0.297787	−	0.515782i
$590$		0			0
$591$	−12532.3	−	15152.1i	−0.872265	−	1.05461i
$592$		0			0
$593$	17115.3			1.18523			0.592613	−	0.805487i	$-0.298096\pi$
$593$	17115.3			1.18523			0.592613	+	0.805487i	$0.298096\pi$
$594$		0			0
$595$	3749.90			0.258371
$596$		0			0
$597$	−9691.02	−	11716.9i	−0.664367	−	0.803251i
$598$		0			0
$599$	4207.06	+	7286.85i	0.286972	+	0.497049i	0.973085	−	0.230445i	$-0.0740182\pi$
$599$	4207.06	+	7286.85i	0.286972	+	0.497049i	−0.686114	+	0.727494i	$0.740685\pi$
$600$		0			0
$601$	−14047.1	+	24330.3i	−0.953399	+	1.65134i	−0.215409	+	0.976524i	$0.569108\pi$
$601$	−14047.1	+	24330.3i	−0.953399	+	1.65134i	−0.737990	+	0.674812i	$0.764225\pi$
$602$		0			0
$603$	19569.9	−	6810.40i	1.32164	−	0.459935i
$604$		0			0
$605$	−2694.67	+	4667.31i	−0.181081	+	0.313642i
$606$		0			0
$607$	715.423	+	1239.15i	0.0478388	+	0.0828592i	0.888953	−	0.457998i	$-0.151433\pi$
$607$	715.423	+	1239.15i	0.0478388	+	0.0828592i	−0.841114	+	0.540857i	$0.818100\pi$
$608$		0			0
$609$	10187.5	−	27384.6i	0.677860	−	1.82213i
$610$		0			0
$611$	−165.572			−0.0109629
$612$		0			0
$613$	14438.1			0.951306			0.475653	−	0.879633i	$-0.342212\pi$
$613$	14438.1			0.951306			0.475653	+	0.879633i	$0.342212\pi$
$614$		0			0
$615$	11320.4	−	1913.49i	0.742247	−	0.125463i
$616$		0			0
$617$	−12722.5	−	22036.0i	−0.830125	−	1.43782i	−0.897938	−	0.440121i	$-0.854935\pi$
$617$	−12722.5	−	22036.0i	−0.830125	−	1.43782i	0.0678130	−	0.997698i	$-0.478398\pi$
$618$		0			0
$619$	−1739.73	+	3013.30i	−0.112966	+	0.195662i	−0.916965	−	0.398968i	$-0.869368\pi$
$619$	−1739.73	+	3013.30i	−0.112966	+	0.195662i	0.803999	+	0.594631i	$0.202702\pi$
$620$		0			0
$621$	2295.20	+	1391.00i	0.148314	+	0.0898853i
$622$		0			0
$623$	−10704.4	+	18540.6i	−0.688386	+	1.19232i
$624$		0			0
$625$	7362.03	+	12751.4i	0.471170	+	0.816091i
$626$		0			0
$627$	−31391.5	+	5306.13i	−1.99945	+	0.337969i
$628$		0			0
$629$	1167.70			0.0740208
$630$		0			0
$631$	−11151.7			−0.703552			−0.351776	−	0.936084i	$-0.614422\pi$
$631$	−11151.7			−0.703552			−0.351776	+	0.936084i	$0.614422\pi$
$632$		0			0
$633$	567.933	−	1526.64i	0.0356608	−	0.0958587i
$634$		0			0
$635$	−170.927	−	296.055i	−0.0106820	−	0.0185017i
$636$		0			0
$637$	−2084.39	+	3610.26i	−0.129649	+	0.224559i
$638$		0			0
$639$	1701.03	−	8907.08i	0.105308	−	0.551422i
$640$		0			0
$641$	546.388	−	946.373i	0.0336678	−	0.0583143i	−0.848701	−	0.528874i	$-0.822615\pi$
$641$	546.388	−	946.373i	0.0336678	−	0.0583143i	0.882368	+	0.470559i	$0.155948\pi$
$642$		0			0
$643$	15847.0	+	27447.8i	0.971922	+	1.68342i	0.689741	+	0.724056i	$0.257724\pi$
$643$	15847.0	+	27447.8i	0.971922	+	1.68342i	0.282181	+	0.959361i	$0.408942\pi$
$644$		0			0
$645$	11732.0	+	14184.6i	0.716200	+	0.865919i
$646$		0			0
$647$	13719.9			0.833672			0.416836	−	0.908982i	$-0.363139\pi$
$647$	13719.9			0.833672			0.416836	+	0.908982i	$0.363139\pi$
$648$		0			0
$649$	−4904.12			−0.296616
$650$		0			0
$651$	−4891.51	−	5914.07i	−0.294491	−	0.356053i
$652$		0			0
$653$	−6642.59	−	11505.3i	−0.398078	−	0.689491i	0.595411	−	0.803421i	$-0.296989\pi$
$653$	−6642.59	−	11505.3i	−0.398078	−	0.689491i	−0.993489	+	0.113930i	$0.963656\pi$
$654$		0			0
$655$	−10529.9	+	18238.4i	−0.628151	+	1.08799i
$656$		0			0
$657$	−847.232	+	4436.36i	−0.0503100	+	0.263438i
$658$		0			0
$659$	−1296.99	+	2246.45i	−0.0766670	+	0.132791i	−0.901810	−	0.432133i	$-0.857761\pi$
$659$	−1296.99	+	2246.45i	−0.0766670	+	0.132791i	0.825143	+	0.564924i	$0.191095\pi$
$660$		0			0
$661$	7937.67	+	13748.4i	0.467079	+	0.809005i	0.999293	−	0.0376052i	$-0.0119729\pi$
$661$	7937.67	+	13748.4i	0.467079	+	0.809005i	−0.532213	+	0.846610i	$0.678640\pi$
$662$		0			0
$663$	380.200	−	1022.00i	0.0222711	−	0.0598662i
$664$		0			0
$665$	38755.6			2.25996
$666$		0			0
$667$	−4325.06			−0.251075
$668$		0			0
$669$	3639.64	−	615.212i	0.210339	−	0.0355538i
$670$		0			0
$671$	16135.9	+	27948.2i	0.928344	+	1.60794i
$672$		0			0
$673$	−10717.3	+	18563.0i	−0.613853	+	1.06323i	0.376731	+	0.926323i	$0.377048\pi$
$673$	−10717.3	+	18563.0i	−0.613853	+	1.06323i	−0.990585	+	0.136903i	$0.956285\pi$
$674$		0			0
$675$	20.3765	−	958.544i	0.00116191	−	0.0546583i
$676$		0			0
$677$	10166.5	−	17608.9i	0.577150	−	0.999653i	−0.418655	−	0.908146i	$-0.637498\pi$
$677$	10166.5	−	17608.9i	0.577150	−	0.999653i	0.995804	−	0.0915074i	$-0.0291685\pi$
$678$		0			0
$679$	−5000.81	−	8661.66i	−0.282642	−	0.489549i
$680$		0			0
$681$	−167.341	+	28.2858i	−0.00941634	+	0.00159165i
$682$		0			0
$683$	27149.0			1.52097			0.760487	−	0.649353i	$-0.224960\pi$
$683$	27149.0			1.52097			0.760487	+	0.649353i	$0.224960\pi$
$684$		0			0
$685$	12594.4			0.702493
$686$		0			0
$687$	9971.53	−	26804.1i	0.553766	−	1.48856i
$688$		0			0
$689$	1060.48	+	1836.80i	0.0586371	+	0.101562i
$690$		0			0
$691$	11355.1	−	19667.6i	0.625134	−	1.08276i	−0.363381	−	0.931641i	$-0.618378\pi$
$691$	11355.1	−	19667.6i	0.625134	−	1.08276i	0.988515	−	0.151123i	$-0.0482891\pi$
$692$		0			0
$693$	−27106.1	+	9433.04i	−1.48582	+	0.517073i
$694$		0			0
$695$	12564.0	−	21761.5i	0.685728	−	1.18771i
$696$		0			0
$697$	1409.65	+	2441.58i	0.0766056	+	0.132685i
$698$		0			0
$699$	22482.8	+	27182.7i	1.21656	+	1.47088i
$700$		0			0
$701$	−20079.5			−1.08187			−0.540936	−	0.841064i	$-0.681930\pi$
$701$	−20079.5			−1.08187			−0.540936	+	0.841064i	$0.681930\pi$
$702$		0			0
$703$	12068.2			0.647457
$704$		0			0
$705$	393.970	+	476.328i	0.0210465	+	0.0254462i
$706$		0			0
$707$	−16556.6	−	28676.9i	−0.880728	−	1.52547i
$708$		0			0
$709$	14491.8	−	25100.6i	0.767634	−	1.32958i	−0.171209	−	0.985235i	$-0.554767\pi$
$709$	14491.8	−	25100.6i	0.767634	−	1.32958i	0.938843	−	0.344346i	$-0.111899\pi$
$710$		0			0
$711$	−517.328	−	446.733i	−0.0272874	−	0.0235637i
$712$		0			0
$713$	−568.040	+	983.875i	−0.0298363	+	0.0516780i
$714$		0			0
$715$	−3514.69	−	6087.61i	−0.183835	−	0.318411i
$716$		0			0
$717$	−777.940	+	2091.15i	−0.0405198	+	0.108920i
$718$		0			0
$719$	−14496.2			−0.751901			−0.375951	−	0.926640i	$-0.622684\pi$
$719$	−14496.2			−0.751901			−0.375951	+	0.926640i	$0.622684\pi$
$720$		0			0
$721$	−12895.4			−0.666090
$722$		0			0
$723$	−24816.3	+	4194.72i	−1.27653	+	0.215772i
$724$		0			0
$725$	772.541	+	1338.08i	0.0395744	+	0.0685449i
$726$		0			0
$727$	2500.25	−	4330.56i	0.127550	−	0.220924i	−0.795177	−	0.606378i	$-0.792622\pi$
$727$	2500.25	−	4330.56i	0.127550	−	0.220924i	0.922727	+	0.385454i	$0.125955\pi$
$728$		0			0
$729$	10557.0	−	16612.4i	0.536351	−	0.843995i
$730$		0			0
$731$	−2260.12	+	3914.64i	−0.114355	+	0.198069i
$732$		0			0
$733$	−8757.79	−	15168.9i	−0.441305	−	0.764362i	0.556482	−	0.830860i	$-0.312151\pi$
$733$	−8757.79	−	15168.9i	−0.441305	−	0.764362i	−0.997787	+	0.0664977i	$0.978817\pi$
$734$		0			0
$735$	15345.9	−	2593.93i	0.770126	−	0.130175i
$736$		0			0
$737$	32801.3			1.63942
$738$		0			0
$739$	20169.2			1.00397			0.501985	−	0.864876i	$-0.332603\pi$
$739$	20169.2			1.00397			0.501985	+	0.864876i	$0.332603\pi$
$740$		0			0
$741$	3929.40	−	10562.5i	0.194804	−	0.523647i
$742$		0			0
$743$	−18351.3	−	31785.4i	−0.906116	−	1.56944i	−0.819412	−	0.573205i	$-0.805700\pi$
$743$	−18351.3	−	31785.4i	−0.906116	−	1.56944i	−0.0867044	−	0.996234i	$-0.527634\pi$
$744$		0			0
$745$	16035.0	−	27773.5i	0.788561	−	1.36583i
$746$		0			0
$747$	5879.64	+	5077.29i	0.287985	+	0.248686i
$748$		0			0
$749$	−18303.0	+	31701.8i	−0.892894	+	1.54654i
$750$		0			0
$751$	−16660.0	−	28856.0i	−0.809499	−	1.40209i	−0.913212	−	0.407485i	$-0.866406\pi$
$751$	−16660.0	−	28856.0i	−0.809499	−	1.40209i	0.103713	−	0.994607i	$-0.466928\pi$
$752$		0			0
$753$	7951.06	+	9613.21i	0.384798	+	0.465239i
$754$		0			0
$755$	18766.7			0.904622
$756$		0			0
$757$	26515.6			1.27309			0.636543	−	0.771241i	$-0.280364\pi$
$757$	26515.6			1.27309			0.636543	+	0.771241i	$0.280364\pi$
$758$		0			0
$759$	2707.72	+	3273.77i	0.129492	+	0.156562i
$760$		0			0
$761$	2842.17	+	4922.79i	0.135386	+	0.234495i	0.925745	−	0.378149i	$-0.123439\pi$
$761$	2842.17	+	4922.79i	0.135386	+	0.234495i	−0.790359	+	0.612644i	$0.790106\pi$
$762$		0			0
$763$	−8004.14	+	13863.6i	−0.379777	+	0.657792i
$764$		0			0
$765$	−3844.82	+	1338.02i	−0.181712	+	0.0632367i
$766$		0			0
$767$	867.990	−	1503.40i	0.0408622	−	0.0707754i
$768$		0			0
$769$	199.189	+	345.005i	0.00934060	+	0.0161784i	0.870658	−	0.491889i	$-0.163693\pi$
$769$	199.189	+	345.005i	0.00934060	+	0.0161784i	−0.861317	+	0.508067i	$0.830360\pi$
$770$		0			0
$771$	−5400.78	+	14517.7i	−0.252275	+	0.678133i
$772$		0			0
$773$	−8437.17			−0.392579			−0.196290	−	0.980546i	$-0.562889\pi$
$773$	−8437.17			−0.392579			−0.196290	+	0.980546i	$0.562889\pi$
$774$		0			0
$775$	405.853			0.0188112
$776$		0			0
$777$	10727.2	−	1813.23i	0.495286	−	0.0837186i
$778$		0			0
$779$	14568.8	+	25233.9i	0.670067	+	1.16059i
$780$		0			0
$781$	7177.34	−	12431.5i	0.328842	−	0.569570i
$782$		0			0
$783$	−674.142	+	31712.8i	−0.0307687	+	1.44741i
$784$		0			0
$785$	−6975.49	+	12081.9i	−0.317154	+	0.549327i
$786$		0			0
$787$	8138.94	+	14097.1i	0.368643	+	0.638508i	0.989354	−	0.145531i	$-0.0464892\pi$
$787$	8138.94	+	14097.1i	0.368643	+	0.638508i	−0.620711	+	0.784040i	$0.713156\pi$
$788$		0			0
$789$	−28490.7	+	4815.81i	−1.28555	+	0.217297i
$790$		0			0
$791$	−25460.5			−1.14447
$792$		0			0
$793$	−11423.7			−0.511560
$794$		0			0
$795$	2760.87	−	7421.41i	0.123167	−	0.331082i
$796$		0			0
$797$	−2556.06	−	4427.22i	−0.113601	−	0.196763i	0.803619	−	0.595145i	$-0.202905\pi$
$797$	−2556.06	−	4427.22i	−0.113601	−	0.196763i	−0.917220	+	0.398382i	$0.869572\pi$
$798$		0			0
$799$	−75.8963	+	131.456i	−0.00336047	+	0.00582051i
$800$		0			0
$801$	4359.85	−	22829.5i	0.192319	−	1.00704i
$802$		0			0
$803$	−3574.82	+	6191.77i	−0.157102	+	0.272108i
$804$		0			0
$805$	−2585.86	−	4478.84i	−0.113217	−	0.196097i
$806$		0			0
$807$	−20825.9	−	25179.5i	−0.908433	−	1.09834i
$808$		0			0
$809$	−13141.2			−0.571100			−0.285550	−	0.958364i	$-0.592176\pi$
$809$	−13141.2			−0.571100			−0.285550	+	0.958364i	$0.592176\pi$
$810$		0			0
$811$	18614.2			0.805957			0.402979	−	0.915209i	$-0.367975\pi$
$811$	18614.2			0.805957			0.402979	+	0.915209i	$0.367975\pi$
$812$		0			0
$813$	22701.6	+	27447.3i	0.979312	+	1.18403i
$814$		0			0
$815$	5619.61	+	9733.45i	0.241529	+	0.418341i
$816$		0			0
$817$	−23358.5	+	40458.2i	−1.00026	+	1.73250i
$818$		0			0
$819$	1905.77	−	9979.18i	0.0813102	−	0.425764i
$820$		0			0
$821$	5660.01	−	9803.43i	0.240604	−	0.416738i	−0.720283	−	0.693681i	$-0.755988\pi$
$821$	5660.01	−	9803.43i	0.240604	−	0.416738i	0.960886	+	0.276943i	$0.0893212\pi$
$822$		0			0
$823$	5433.29	+	9410.73i	0.230125	+	0.398587i	0.957845	−	0.287287i	$-0.0927533\pi$
$823$	5433.29	+	9410.73i	0.230125	+	0.398587i	−0.727720	+	0.685874i	$0.759420\pi$
$824$		0			0
$825$	529.179	−	1422.47i	0.0223317	−	0.0600292i
$826$		0			0
$827$	13059.3			0.549114			0.274557	−	0.961571i	$-0.411469\pi$
$827$	13059.3			0.549114			0.274557	+	0.961571i	$0.411469\pi$
$828$		0			0
$829$	−21203.7			−0.888341			−0.444171	−	0.895942i	$-0.646502\pi$
$829$	−21203.7			−0.888341			−0.444171	+	0.895942i	$0.646502\pi$
$830$		0			0
$831$	4601.76	−	777.840i	0.192098	−	0.0324705i
$832$		0			0
$833$	1910.92	+	3309.80i	0.0794829	+	0.137669i
$834$		0			0
$835$	−1536.09	+	2660.58i	−0.0636628	+	0.110267i
$836$		0			0
$837$	7125.56	+	4318.42i	0.294260	+	0.178335i
$838$		0			0
$839$	−7240.28	+	12540.5i	−0.297929	+	0.516028i	−0.975662	−	0.219280i	$-0.929629\pi$
$839$	−7240.28	+	12540.5i	−0.297929	+	0.516028i	0.677733	+	0.735308i	$0.262962\pi$
$840$		0			0
$841$	−13364.5	−	23148.0i	−0.547973	−	0.949117i
$842$		0			0
$843$	1223.33	−	206.781i	0.0499807	−	0.00844828i
$844$		0			0
$845$	−21394.0			−0.870979
$846$		0			0
$847$	−12330.3			−0.500204
$848$		0			0
$849$	3752.40	−	10086.7i	0.151687	−	0.407745i
$850$		0			0
$851$	−805.221	−	1394.68i	−0.0324355	−	0.0561799i
$852$		0			0
$853$	3233.61	−	5600.78i	0.129797	−	0.224815i	−0.793801	−	0.608178i	$-0.791901\pi$
$853$	3233.61	−	5600.78i	0.129797	−	0.224815i	0.923598	+	0.383363i	$0.125234\pi$
$854$		0			0
$855$	−39736.6	+	13828.5i	−1.58943	+	0.553130i
$856$		0			0
$857$	−1947.32	+	3372.85i	−0.0776186	+	0.134439i	−0.902222	−	0.431272i	$-0.858065\pi$
$857$	−1947.32	+	3372.85i	−0.0776186	+	0.134439i	0.824603	+	0.565711i	$0.191398\pi$
$858$		0			0
$859$	−18826.9	−	32609.1i	−0.747805	−	1.29524i	−0.948873	−	0.315659i	$-0.897774\pi$
$859$	−18826.9	−	32609.1i	−0.747805	−	1.29524i	0.201067	−	0.979577i	$-0.435559\pi$
$860$		0			0
$861$	16741.3	+	20241.0i	0.662651	+	0.801176i
$862$		0			0
$863$	−47067.5			−1.85654			−0.928271	−	0.371905i	$-0.878705\pi$
$863$	−47067.5			−1.85654			−0.928271	+	0.371905i	$0.878705\pi$
$864$		0			0
$865$	−38402.2			−1.50950
$866$		0			0
$867$	15633.4	+	18901.6i	0.612386	+	0.740404i
$868$		0			0
$869$	−541.004	−	937.046i	−0.0211189	−	0.0365790i
$870$		0			0
$871$	−5805.56	+	10055.5i	−0.225848	+	0.391181i
$872$		0			0
$873$	8218.01	+	7096.56i	0.318600	+	0.275123i
$874$		0			0
$875$	−17820.8	+	30866.5i	−0.688517	+	1.19255i
$876$		0			0
$877$	3721.77	+	6446.29i	0.143301	+	0.248205i	0.928738	−	0.370737i	$-0.120895\pi$
$877$	3721.77	+	6446.29i	0.143301	+	0.248205i	−0.785437	+	0.618942i	$0.787562\pi$
$878$		0			0
$879$	11917.2	−	32034.2i	0.457288	−	1.22922i
$880$		0			0
$881$	−13781.9			−0.527040			−0.263520	−	0.964654i	$-0.584884\pi$
$881$	−13781.9			−0.527040			−0.263520	+	0.964654i	$0.584884\pi$
$882$		0			0
$883$	−12230.3			−0.466119			−0.233060	−	0.972462i	$-0.574874\pi$
$883$	−12230.3			−0.466119			−0.233060	+	0.972462i	$0.574874\pi$
$884$		0			0
$885$	−6390.42	+	1080.18i	−0.242725	+	0.0410280i
$886$		0			0
$887$	−837.437	−	1450.48i	−0.0317005	−	0.0549069i	0.849740	−	0.527202i	$-0.176759\pi$
$887$	−837.437	−	1450.48i	−0.0317005	−	0.0549069i	−0.881440	+	0.472295i	$0.843426\pi$
$888$		0			0
$889$	391.064	−	677.343i	0.0147535	−	0.0255538i
$890$		0			0
$891$	24426.4	−	19343.7i	0.918423	−	0.727314i
$892$		0			0
$893$	−784.395	+	1358.61i	−0.0293939	+	0.0509118i
$894$		0			0
$895$	−22027.5	−	38152.8i	−0.822680	−	1.42492i
$896$		0			0
$897$	−1482.85	+	250.647i	−0.0551960	+	0.00932983i
$898$		0			0
$899$	−13427.4			−0.498140
$900$		0			0
$901$	1944.44			0.0718964
$902$		0			0
$903$	−14684.2	+	39472.1i	−0.541151	+	1.45465i
$904$		0			0
$905$	15386.9	+	26650.9i	0.565170	+	0.978903i
$906$		0			0
$907$	8544.04	−	14798.7i	0.312790	−	0.541768i	−0.666175	−	0.745795i	$-0.732070\pi$
$907$	8544.04	−	14798.7i	0.312790	−	0.541768i	0.978965	+	0.204027i	$0.0654031\pi$
$908$		0			0
$909$	27208.0	+	23495.2i	0.992776	+	0.857300i
$910$		0			0
$911$	10644.2	−	18436.3i	0.387111	−	0.670496i	−0.604949	−	0.796264i	$-0.706806\pi$
$911$	10644.2	−	18436.3i	0.387111	−	0.670496i	0.992060	+	0.125769i	$0.0401397\pi$
$912$		0			0
$913$	6148.72	+	10649.9i	0.222884	+	0.386046i
$914$		0			0
$915$	27182.0	+	32864.4i	0.982088	+	1.18739i
$916$		0			0
$917$	−48182.8			−1.73516
$918$		0			0
$919$	10413.4			0.373784			0.186892	−	0.982380i	$-0.440159\pi$
$919$	10413.4			0.373784			0.186892	+	0.982380i	$0.440159\pi$
$920$		0			0
$921$	−17344.6	−	20970.4i	−0.620546	−	0.750270i
$922$		0			0
$923$	2540.66	+	4400.55i	0.0906033	+	0.156930i
$924$		0			0
$925$	−287.657	+	498.236i	−0.0102250	+	0.0177102i
$926$		0			0
$927$	13221.9	−	4601.27i	0.468461	−	0.163027i
$928$		0			0
$929$	3411.72	−	5909.26i	0.120490	−	0.208694i	−0.799471	−	0.600704i	$-0.794887\pi$
$929$	3411.72	−	5909.26i	0.120490	−	0.208694i	0.919961	+	0.392010i	$0.128220\pi$
$930$		0			0
$931$	19749.5	+	34207.1i	0.695234	+	1.20418i
$932$		0			0
$933$	10335.9	−	27783.7i	0.362683	−	0.974917i
$934$		0			0
$935$	−6444.36			−0.225404
$936$		0			0
$937$	41049.8			1.43120			0.715602	−	0.698508i	$-0.246152\pi$
$937$	41049.8			1.43120			0.715602	+	0.698508i	$0.246152\pi$
$938$		0			0
$939$	26014.3	−	4397.23i	0.904096	−	0.152820i
$940$		0			0
$941$	−1208.06	−	2092.42i	−0.0418508	−	0.0724878i	0.844341	−	0.535806i	$-0.179992\pi$
$941$	−1208.06	−	2092.42i	−0.0418508	−	0.0724878i	−0.886192	+	0.463318i	$0.846659\pi$
$942$		0			0
$943$	1944.13	−	3367.33i	0.0671364	−	0.116284i
$944$		0			0
$945$	−33243.4	+	18262.3i	−1.14435	+	0.628648i
$946$		0			0
$947$	−1197.04	+	2073.33i	−0.0410755	+	0.0711448i	−0.885832	−	0.464006i	$-0.846412\pi$
$947$	−1197.04	+	2073.33i	−0.0410755	+	0.0711448i	0.844757	+	0.535150i	$0.179745\pi$
$948$		0			0
$949$	−1265.43	−	2191.79i	−0.0432851	−	0.0749720i
$950$		0			0
$951$	14698.8	−	2484.55i	0.501200	−	0.0847182i
$952$		0			0
$953$	−50651.3			−1.72168			−0.860838	−	0.508879i	$-0.830060\pi$
$953$	−50651.3			−1.72168			−0.860838	+	0.508879i	$0.830060\pi$
$954$		0			0
$955$	−49017.4			−1.66091
$956$		0			0
$957$	−17507.6	+	47061.5i	−0.591368	+	1.58964i
$958$		0			0
$959$	14407.4	+	24954.3i	0.485128	+	0.840267i
$960$		0			0
$961$	13132.0	−	22745.3i	0.440804	−	0.763495i
$962$		0			0
$963$	7454.71	−	39035.0i	0.249454	−	1.30622i
$964$		0			0
$965$	17507.5	−	30323.9i	0.584027	−	1.01156i
$966$		0			0
$967$	12517.5	+	21680.9i	0.416271	+	0.721003i	0.995561	−	0.0941189i	$-0.0300034\pi$
$967$	12517.5	+	21680.9i	0.416271	+	0.721003i	−0.579290	+	0.815122i	$0.696670\pi$
$968$		0			0
$969$	−6584.91	−	7961.47i	−0.218305	−	0.263941i
$970$		0			0
$971$	−49553.7			−1.63775			−0.818875	−	0.573972i	$-0.805402\pi$
$971$	−49553.7			−1.63775			−0.818875	+	0.573972i	$0.805402\pi$
$972$		0			0
$973$	57490.4			1.89420
$974$		0			0
$975$	342.411	+	413.991i	0.0112471	+	0.0135983i
$976$		0			0
$977$	17588.1	+	30463.5i	0.575939	+	0.997556i	0.995939	+	0.0900320i	$0.0286969\pi$
$977$	17588.1	+	30463.5i	0.575939	+	0.997556i	−0.419999	+	0.907524i	$0.637970\pi$
$978$		0			0
$979$	18396.0	−	31862.9i	0.600551	−	1.04019i
$980$		0			0
$981$	3260.04	−	17070.5i	0.106101	−	0.555576i
$982$		0			0
$983$	16674.6	−	28881.3i	0.541036	−	0.937102i	−0.457809	−	0.889051i	$-0.651366\pi$
$983$	16674.6	−	28881.3i	0.541036	−	0.937102i	0.998845	−	0.0480511i	$-0.0153010\pi$
$984$		0			0
$985$	−20567.9	−	35624.7i	−0.665328	−	1.15238i
$986$		0			0
$987$	−493.105	+	1325.50i	−0.0159024	+	0.0427468i
$988$		0			0
$989$	6234.14			0.200439
$990$		0			0
$991$	−23066.3			−0.739378			−0.369689	−	0.929156i	$-0.620536\pi$
$991$	−23066.3			−0.739378			−0.369689	+	0.929156i	$0.620536\pi$
$992$		0			0
$993$	−10407.6	+	1759.20i	−0.332602	+	0.0562201i
$994$		0			0
$995$	−15904.9	−	27548.1i	−0.506752	−	0.877721i
$996$		0			0
$997$	27884.9	−	48298.1i	0.885782	−	1.53422i	0.0409671	−	0.999160i	$-0.486956\pi$
$997$	27884.9	−	48298.1i	0.885782	−	1.53422i	0.844815	−	0.535059i	$-0.179711\pi$
$998$		0			0
$999$	−10351.8	+	5686.76i	−0.327844	+	0.180101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.i.b.97.1		4
3.2	odd	2		432.4.i.b.289.2		4
4.3	odd	2		18.4.c.b.7.2	✓	4
9.2	odd	6		1296.4.a.r.1.1		2
9.4	even	3	inner	144.4.i.b.49.1		4
9.5	odd	6		432.4.i.b.145.2		4
9.7	even	3		1296.4.a.l.1.2		2
12.11	even	2		54.4.c.b.19.2		4
36.7	odd	6		162.4.a.f.1.2		2
36.11	even	6		162.4.a.g.1.1		2
36.23	even	6		54.4.c.b.37.2		4
36.31	odd	6		18.4.c.b.13.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.4.c.b.7.2	✓	4	4.3	odd	2
18.4.c.b.13.2	yes	4	36.31	odd	6
54.4.c.b.19.2		4	12.11	even	2
54.4.c.b.37.2		4	36.23	even	6
144.4.i.b.49.1		4	9.4	even	3	inner
144.4.i.b.97.1		4	1.1	even	1	trivial
162.4.a.f.1.2		2	36.7	odd	6
162.4.a.g.1.1		2	36.11	even	6
432.4.i.b.145.2		4	9.5	odd	6
432.4.i.b.289.2		4	3.2	odd	2
1296.4.a.l.1.2		2	9.7	even	3
1296.4.a.r.1.1		2	9.2	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.31174 - 4.00405i) q^{3} +(-5.43521 - 9.41407i) q^{5} +(12.4352 - 21.5384i) q^{7} +(-5.06479 + 26.5207i) q^{9} +O(q^{10})\)	\(q+(-3.31174 - 4.00405i) q^{3} +(-5.43521 - 9.41407i) q^{5} +(12.4352 - 21.5384i) q^{7} +(-5.06479 + 26.5207i) q^{9} +(-21.3704 + 37.0147i) q^{11} +(-7.56479 - 13.1026i) q^{13} +(-19.6944 + 52.9398i) q^{15} -13.8704 q^{17} -143.352 q^{19} +(-127.423 + 21.5384i) q^{21} +(9.56479 + 16.5667i) q^{23} +(3.41692 - 5.91828i) q^{25} +(122.963 - 67.5500i) q^{27} +(-113.046 + 195.802i) q^{29} +(29.6944 + 51.4321i) q^{31} +(218.982 - 37.0147i) q^{33} -270.352 q^{35} -84.1860 q^{37} +(-27.4108 + 73.6821i) q^{39} +(-101.630 - 176.028i) q^{41} +(162.945 - 282.229i) q^{43} +(277.196 - 96.4655i) q^{45} +(5.47180 - 9.47744i) q^{47} +(-137.769 - 238.623i) q^{49} +(45.9352 + 55.5378i) q^{51} -140.186 q^{53} +464.611 q^{55} +(474.745 + 573.989i) q^{57} +(57.3704 + 99.3685i) q^{59} +(377.528 - 653.898i) q^{61} +(508.232 + 438.878i) q^{63} +(-82.2325 + 142.431i) q^{65} +(-383.723 - 664.627i) q^{67} +(34.6578 - 93.1624i) q^{69} -335.854 q^{71} +167.279 q^{73} +(-35.0130 + 5.91828i) q^{75} +(531.492 + 920.570i) q^{77} +(-12.6578 + 21.9239i) q^{79} +(-677.696 - 268.643i) q^{81} +(143.861 - 249.174i) q^{83} +(75.3887 + 130.577i) q^{85} +(1158.38 - 195.802i) q^{87} -860.817 q^{89} -376.279 q^{91} +(107.597 - 289.227i) q^{93} +(779.149 + 1349.53i) q^{95} +(201.075 - 348.272i) q^{97} +(-873.418 - 754.230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} + 9 q^{5} + 19 q^{7} - 51 q^{9}+O(q^{10}) \) 4 * q - 3 * q^3 + 9 * q^5 + 19 * q^7 - 51 * q^9	\( 4 q - 3 q^{3} + 9 q^{5} + 19 q^{7} - 51 q^{9} - 24 q^{11} - 61 q^{13} - 171 q^{15} + 6 q^{17} - 266 q^{19} - 315 q^{21} + 69 q^{23} - 263 q^{25} - 237 q^{29} + 211 q^{31} + 630 q^{33} - 774 q^{35} + 524 q^{37} + 249 q^{39} - 468 q^{41} - 86 q^{43} - 459 q^{45} + 483 q^{47} + 33 q^{49} + 153 q^{51} + 300 q^{53} + 1674 q^{55} + 987 q^{57} + 168 q^{59} + 1049 q^{61} + 957 q^{63} + 747 q^{65} - 1166 q^{67} - 261 q^{69} + 624 q^{71} - 622 q^{73} - 2835 q^{75} + 1173 q^{77} + 349 q^{79} - 1143 q^{81} + 1221 q^{83} + 486 q^{85} + 2205 q^{87} - 984 q^{89} - 214 q^{91} - 789 q^{93} + 1764 q^{95} + 128 q^{97} - 1557 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 + 9 * q^5 + 19 * q^7 - 51 * q^9 - 24 * q^11 - 61 * q^13 - 171 * q^15 + 6 * q^17 - 266 * q^19 - 315 * q^21 + 69 * q^23 - 263 * q^25 - 237 * q^29 + 211 * q^31 + 630 * q^33 - 774 * q^35 + 524 * q^37 + 249 * q^39 - 468 * q^41 - 86 * q^43 - 459 * q^45 + 483 * q^47 + 33 * q^49 + 153 * q^51 + 300 * q^53 + 1674 * q^55 + 987 * q^57 + 168 * q^59 + 1049 * q^61 + 957 * q^63 + 747 * q^65 - 1166 * q^67 - 261 * q^69 + 624 * q^71 - 622 * q^73 - 2835 * q^75 + 1173 * q^77 + 349 * q^79 - 1143 * q^81 + 1221 * q^83 + 486 * q^85 + 2205 * q^87 - 984 * q^89 - 214 * q^91 - 789 * q^93 + 1764 * q^95 + 128 * q^97 - 1557 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more