LMFDB - Embedded newform 136.4.k.a.89.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(81,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("136.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.k (of order $4$, degree $2$, 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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 142x^{12} + 7785x^{10} + 208489x^{8} + 2822686x^{6} + 17977041x^{4} + 45020416x^{2} + 31719424 $ x^14 + 142x^12 + 7785x^10 + 208489x^8 + 2822686x^6 + 17977041x^4 + 45020416x^2 + 31719424
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.7
Root			$5.56386i$ of defining polynomial
Character	$\chi$	$=$	136.89
Dual form			136.4.k.a.81.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.56386 - 5.56386i) q^{3} +(-3.36317 + 3.36317i) q^{5} +(-19.4947 - 19.4947i) q^{7} -34.9130i q^{9} +O(q^{10})$	\(q+(5.56386 - 5.56386i) q^{3} +(-3.36317 + 3.36317i) q^{5} +(-19.4947 - 19.4947i) q^{7} -34.9130i q^{9} +(-39.4297 - 39.4297i) q^{11} +89.7473 q^{13} +37.4244i q^{15} +(-64.9377 + 26.3836i) q^{17} -71.5540i q^{19} -216.931 q^{21} +(33.0711 + 33.0711i) q^{23} +102.378i q^{25} +(-44.0269 - 44.0269i) q^{27} +(208.609 - 208.609i) q^{29} +(46.5325 - 46.5325i) q^{31} -438.762 q^{33} +131.128 q^{35} +(-61.1650 + 61.1650i) q^{37} +(499.341 - 499.341i) q^{39} +(-131.216 - 131.216i) q^{41} +57.3705i q^{43} +(117.418 + 117.418i) q^{45} +280.415 q^{47} +417.083i q^{49} +(-214.510 + 508.099i) q^{51} +239.415i q^{53} +265.217 q^{55} +(-398.116 - 398.116i) q^{57} +1.44991i q^{59} +(411.727 + 411.727i) q^{61} +(-680.617 + 680.617i) q^{63} +(-301.835 + 301.835i) q^{65} +618.610 q^{67} +368.005 q^{69} +(-455.114 + 455.114i) q^{71} +(525.708 - 525.708i) q^{73} +(569.618 + 569.618i) q^{75} +1537.34i q^{77} +(70.9619 + 70.9619i) q^{79} +452.733 q^{81} -399.720i q^{83} +(129.664 - 307.129i) q^{85} -2321.34i q^{87} -616.098 q^{89} +(-1749.59 - 1749.59i) q^{91} -517.800i q^{93} +(240.648 + 240.648i) q^{95} +(877.904 - 877.904i) q^{97} +(-1376.61 + 1376.61i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	5.56386	−	5.56386i	1.07076	−	1.07076i	0.0734672	−	0.997298i	$-0.476594\pi$
$3$	5.56386	−	5.56386i	1.07076	−	1.07076i	0.997298	−	0.0734672i	$-0.0234064\pi$
$4$		0			0
$5$	−3.36317	+	3.36317i	−0.300811	+	0.300811i	−0.841331	−	0.540520i	$-0.818227\pi$
$5$	−3.36317	+	3.36317i	−0.300811	+	0.300811i	0.540520	+	0.841331i	$0.318227\pi$
$6$		0			0
$7$	−19.4947	−	19.4947i	−1.05261	−	1.05261i	−0.998537	−	0.0540756i	$-0.982779\pi$
$7$	−19.4947	−	19.4947i	−1.05261	−	1.05261i	−0.0540756	−	0.998537i	$-0.517221\pi$
$8$		0			0
$9$		−	34.9130i		−	1.29307i
$10$		0			0
$11$	−39.4297	−	39.4297i	−1.08077	−	1.08077i	−0.996437	−	0.0843352i	$-0.973123\pi$
$11$	−39.4297	−	39.4297i	−1.08077	−	1.08077i	−0.0843352	−	0.996437i	$-0.526877\pi$
$12$		0			0
$13$	89.7473			1.91472			0.957362	−	0.288891i	$-0.0932866\pi$
$13$	89.7473			1.91472			0.957362	+	0.288891i	$0.0932866\pi$
$14$		0			0
$15$			37.4244i			0.644196i
$16$		0			0
$17$	−64.9377	+	26.3836i	−0.926453	+	0.376409i
$17$	−64.9377	+	26.3836i	−0.926453	+	0.376409i
$18$		0			0
$19$		−	71.5540i		−	0.863979i	−0.901879	−	0.431990i	$-0.857812\pi$
$19$		−	71.5540i		−	0.863979i	0.901879	−	0.431990i	$-0.142188\pi$
$20$		0			0
$21$	−216.931			−2.25420
$22$		0			0
$23$	33.0711	+	33.0711i	0.299817	+	0.299817i	0.840942	−	0.541125i	$-0.182001\pi$
$23$	33.0711	+	33.0711i	0.299817	+	0.299817i	−0.541125	+	0.840942i	$0.682001\pi$
$24$		0			0
$25$			102.378i			0.819025i
$26$		0			0
$27$	−44.0269	−	44.0269i	−0.313814	−	0.313814i
$28$		0			0
$29$	208.609	−	208.609i	1.33578	−	1.33578i	0.435680	−	0.900102i	$-0.356508\pi$
$29$	208.609	−	208.609i	1.33578	−	1.33578i	0.900102	−	0.435680i	$-0.143492\pi$
$30$		0			0
$31$	46.5325	−	46.5325i	0.269596	−	0.269596i	−0.559341	−	0.828937i	$-0.688946\pi$
$31$	46.5325	−	46.5325i	0.269596	−	0.269596i	0.828937	+	0.559341i	$0.188946\pi$
$32$		0			0
$33$	−438.762			−2.31451
$34$		0			0
$35$	131.128			0.633275
$36$		0			0
$37$	−61.1650	+	61.1650i	−0.271769	+	0.271769i	−0.829812	−	0.558043i	$-0.811552\pi$
$37$	−61.1650	+	61.1650i	−0.271769	+	0.271769i	0.558043	+	0.829812i	$0.311552\pi$
$38$		0			0
$39$	499.341	−	499.341i	2.05022	−	2.05022i
$40$		0			0
$41$	−131.216	−	131.216i	−0.499818	−	0.499818i	0.411563	−	0.911381i	$-0.364983\pi$
$41$	−131.216	−	131.216i	−0.499818	−	0.499818i	−0.911381	+	0.411563i	$0.864983\pi$
$42$		0			0
$43$			57.3705i			0.203463i	0.994812	+	0.101732i	$0.0324383\pi$
$43$			57.3705i			0.203463i	−0.994812	+	0.101732i	$0.967562\pi$
$44$		0			0
$45$	117.418	+	117.418i	0.388971	+	0.388971i
$46$		0			0
$47$	280.415			0.870270			0.435135	−	0.900365i	$-0.356701\pi$
$47$	280.415			0.870270			0.435135	+	0.900365i	$0.356701\pi$
$48$		0			0
$49$			417.083i			1.21599i
$50$		0			0
$51$	−214.510	+	508.099i	−0.588968	+	1.39506i
$52$		0			0
$53$			239.415i			0.620495i	0.950656	+	0.310248i	$0.100412\pi$
$53$			239.415i			0.620495i	−0.950656	+	0.310248i	$0.899588\pi$
$54$		0			0
$55$	265.217			0.650217
$56$		0			0
$57$	−398.116	−	398.116i	−0.925118	−	0.925118i
$58$		0			0
$59$			1.44991i			0.00319937i	0.999999	+	0.00159968i	$0.000509195\pi$
$59$			1.44991i			0.00319937i	−0.999999	+	0.00159968i	$0.999491\pi$
$60$		0			0
$61$	411.727	+	411.727i	0.864201	+	0.864201i	0.991823	−	0.127622i	$-0.0407343\pi$
$61$	411.727	+	411.727i	0.864201	+	0.864201i	−0.127622	+	0.991823i	$0.540734\pi$
$62$		0			0
$63$	−680.617	+	680.617i	−1.36111	+	1.36111i
$64$		0			0
$65$	−301.835	+	301.835i	−0.575970	+	0.575970i
$66$		0			0
$67$	618.610			1.12799			0.563994	−	0.825779i	$-0.309264\pi$
$67$	618.610			1.12799			0.563994	+	0.825779i	$0.309264\pi$
$68$		0			0
$69$	368.005			0.642067
$70$		0			0
$71$	−455.114	+	455.114i	−0.760734	+	0.760734i	−0.976455	−	0.215721i	$-0.930790\pi$
$71$	−455.114	+	455.114i	−0.760734	+	0.760734i	0.215721	+	0.976455i	$0.430790\pi$
$72$		0			0
$73$	525.708	−	525.708i	0.842869	−	0.842869i	−0.146362	−	0.989231i	$-0.546757\pi$
$73$	525.708	−	525.708i	0.842869	−	0.842869i	0.989231	+	0.146362i	$0.0467566\pi$
$74$		0			0
$75$	569.618	+	569.618i	0.876984	+	0.876984i
$76$		0			0
$77$			1537.34i			2.27527i
$78$		0			0
$79$	70.9619	+	70.9619i	0.101061	+	0.101061i	0.755830	−	0.654768i	$-0.227234\pi$
$79$	70.9619	+	70.9619i	0.101061	+	0.101061i	−0.654768	+	0.755830i	$0.727234\pi$
$80$		0			0
$81$	452.733			0.621033
$82$		0			0
$83$		−	399.720i		−	0.528614i	−0.964439	−	0.264307i	$-0.914857\pi$
$83$		−	399.720i		−	0.528614i	0.964439	−	0.264307i	$-0.0851432\pi$
$84$		0			0
$85$	129.664	−	307.129i	0.165459	−	0.391916i
$86$		0			0
$87$		−	2321.34i		−	2.86062i
$88$		0			0
$89$	−616.098			−0.733778			−0.366889	−	0.930265i	$-0.619577\pi$
$89$	−616.098			−0.733778			−0.366889	+	0.930265i	$0.619577\pi$
$90$		0			0
$91$	−1749.59	−	1749.59i	−2.01546	−	2.01546i
$92$		0			0
$93$		−	517.800i		−	0.577348i
$94$		0			0
$95$	240.648	+	240.648i	0.259894	+	0.259894i
$96$		0			0
$97$	877.904	−	877.904i	0.918945	−	0.918945i	−0.0780082	−	0.996953i	$-0.524856\pi$
$97$	877.904	−	877.904i	0.918945	−	0.918945i	0.996953	+	0.0780082i	$0.0248560\pi$
$98$		0			0
$99$	−1376.61	+	1376.61i	−1.39752	+	1.39752i
$100$		0			0
$101$	392.284			0.386472			0.193236	−	0.981152i	$-0.438102\pi$
$101$	392.284			0.386472			0.193236	+	0.981152i	$0.438102\pi$
$102$		0			0
$103$	1187.66			1.13615			0.568077	−	0.822975i	$-0.307687\pi$
$103$	1187.66			1.13615			0.568077	+	0.822975i	$0.307687\pi$
$104$		0			0
$105$	729.576	−	729.576i	0.678088	−	0.678088i
$106$		0			0
$107$	−1097.91	+	1097.91i	−0.991953	+	0.991953i	−0.999968	−	0.00801490i	$-0.997449\pi$
$107$	−1097.91	+	1097.91i	−0.991953	+	0.991953i	0.00801490	+	0.999968i	$0.497449\pi$
$108$		0			0
$109$	−435.083	−	435.083i	−0.382325	−	0.382325i	0.489614	−	0.871939i	$-0.337138\pi$
$109$	−435.083	−	435.083i	−0.382325	−	0.382325i	−0.871939	+	0.489614i	$0.837138\pi$
$110$		0			0
$111$			680.627i			0.582002i
$112$		0			0
$113$	−719.417	−	719.417i	−0.598912	−	0.598912i	0.341111	−	0.940023i	$-0.389197\pi$
$113$	−719.417	−	719.417i	−0.598912	−	0.598912i	−0.940023	+	0.341111i	$0.889197\pi$
$114$		0			0
$115$	−222.447			−0.180377
$116$		0			0
$117$		−	3133.35i		−	2.47588i
$118$		0			0
$119$	1780.28	+	751.599i	1.37141	+	0.578983i
$120$		0			0
$121$			1778.40i			1.33614i
$122$		0			0
$123$	−1460.14			−1.07038
$124$		0			0
$125$	−764.711	−	764.711i	−0.547183	−	0.547183i
$126$		0			0
$127$		−	462.306i		−	0.323016i	−0.986871	−	0.161508i	$-0.948364\pi$
$127$		−	462.306i		−	0.323016i	0.986871	−	0.161508i	$-0.0516358\pi$
$128$		0			0
$129$	319.201	+	319.201i	0.217861	+	0.217861i
$130$		0			0
$131$	−305.039	+	305.039i	−0.203446	+	0.203446i	−0.801474	−	0.598029i	$-0.795951\pi$
$131$	−305.039	+	305.039i	−0.203446	+	0.203446i	0.598029	+	0.801474i	$0.295951\pi$
$132$		0			0
$133$	−1394.92	+	1394.92i	−0.909435	+	0.909435i
$134$		0			0
$135$	296.140			0.188797
$136$		0			0
$137$	−1029.34			−0.641915			−0.320958	−	0.947094i	$-0.604005\pi$
$137$	−1029.34			−0.641915			−0.320958	+	0.947094i	$0.604005\pi$
$138$		0			0
$139$	547.949	−	547.949i	0.334363	−	0.334363i	−0.519878	−	0.854241i	$-0.674023\pi$
$139$	547.949	−	547.949i	0.334363	−	0.334363i	0.854241	+	0.519878i	$0.174023\pi$
$140$		0			0
$141$	1560.19	−	1560.19i	0.931854	−	0.931854i
$142$		0			0
$143$	−3538.71	−	3538.71i	−2.06938	−	2.06938i
$144$		0			0
$145$			1403.17i			0.803636i
$146$		0			0
$147$	2320.59	+	2320.59i	1.30204	+	1.30204i
$148$		0			0
$149$	308.178			0.169442			0.0847212	−	0.996405i	$-0.473000\pi$
$149$	308.178			0.169442			0.0847212	+	0.996405i	$0.473000\pi$
$150$		0			0
$151$			1267.47i			0.683081i	0.939867	+	0.341540i	$0.110949\pi$
$151$			1267.47i			0.683081i	−0.939867	+	0.341540i	$0.889051\pi$
$152$		0			0
$153$	921.131	+	2267.17i	0.486726	+	1.19797i
$154$		0			0
$155$			312.993i			0.162195i
$156$		0			0
$157$	−3005.63			−1.52787			−0.763935	−	0.645293i	$-0.776735\pi$
$157$	−3005.63			−1.52787			−0.763935	+	0.645293i	$0.776735\pi$
$158$		0			0
$159$	1332.07	+	1332.07i	0.664404	+	0.664404i
$160$		0			0
$161$		−	1289.42i		−	0.631182i
$162$		0			0
$163$	−2382.02	−	2382.02i	−1.14463	−	1.14463i	−0.987593	−	0.157037i	$-0.949806\pi$
$163$	−2382.02	−	2382.02i	−1.14463	−	1.14463i	−0.157037	−	0.987593i	$-0.550194\pi$
$164$		0			0
$165$	1475.63	−	1475.63i	0.696229	−	0.696229i
$166$		0			0
$167$	602.583	−	602.583i	0.279217	−	0.279217i	−0.553579	−	0.832796i	$-0.686738\pi$
$167$	602.583	−	602.583i	0.279217	−	0.279217i	0.832796	+	0.553579i	$0.186738\pi$
$168$		0			0
$169$	5857.57			2.66617
$170$		0			0
$171$	−2498.16			−1.11719
$172$		0			0
$173$	−854.543	+	854.543i	−0.375547	+	0.375547i	−0.869493	−	0.493945i	$-0.835554\pi$
$173$	−854.543	+	854.543i	−0.375547	+	0.375547i	0.493945	+	0.869493i	$0.335554\pi$
$174$		0			0
$175$	1995.83	−	1995.83i	0.862116	−	0.862116i
$176$		0			0
$177$	8.06711	+	8.06711i	0.00342577	+	0.00342577i
$178$		0			0
$179$			2466.10i			1.02975i	0.857266	+	0.514874i	$0.172161\pi$
$179$			2466.10i			1.02975i	−0.857266	+	0.514874i	$0.827839\pi$
$180$		0			0
$181$	−1779.29	−	1779.29i	−0.730684	−	0.730684i	0.240071	−	0.970755i	$-0.422829\pi$
$181$	−1779.29	−	1779.29i	−0.730684	−	0.730684i	−0.970755	+	0.240071i	$0.922829\pi$
$182$		0			0
$183$	4581.58			1.85071
$184$		0			0
$185$		−	411.417i		−	0.163502i
$186$		0			0
$187$	3600.77	+	1520.18i	1.40810	+	0.594472i
$188$		0			0
$189$			1716.58i			0.660649i
$190$		0			0
$191$	−1947.44			−0.737757			−0.368879	−	0.929478i	$-0.620258\pi$
$191$	−1947.44			−0.737757			−0.368879	+	0.929478i	$0.620258\pi$
$192$		0			0
$193$	314.980	+	314.980i	0.117476	+	0.117476i	0.763401	−	0.645925i	$-0.223528\pi$
$193$	314.980	+	314.980i	0.117476	+	0.117476i	−0.645925	+	0.763401i	$0.723528\pi$
$194$		0			0
$195$			3358.74i			1.23346i
$196$		0			0
$197$	2530.57	+	2530.57i	0.915207	+	0.915207i	0.996676	−	0.0814692i	$-0.0259612\pi$
$197$	2530.57	+	2530.57i	0.915207	+	0.915207i	−0.0814692	+	0.996676i	$0.525961\pi$
$198$		0			0
$199$	−1665.04	+	1665.04i	−0.593123	+	0.593123i	−0.938474	−	0.345351i	$-0.887760\pi$
$199$	−1665.04	+	1665.04i	−0.593123	+	0.593123i	0.345351	+	0.938474i	$0.387760\pi$
$200$		0			0
$201$	3441.86	−	3441.86i	1.20781	−	1.20781i
$202$		0			0
$203$	−8133.51			−2.81212
$204$		0			0
$205$	882.605			0.300702
$206$		0			0
$207$	1154.61	−	1154.61i	0.387686	−	0.387686i
$208$		0			0
$209$	−2821.35	+	2821.35i	−0.933765	+	0.933765i
$210$		0			0
$211$	−434.097	−	434.097i	−0.141633	−	0.141633i	0.632735	−	0.774368i	$-0.281932\pi$
$211$	−434.097	−	434.097i	−0.141633	−	0.141633i	−0.774368	+	0.632735i	$0.781932\pi$
$212$		0			0
$213$			5064.38i			1.62914i
$214$		0			0
$215$	−192.947	−	192.947i	−0.0612040	−	0.0612040i
$216$		0			0
$217$	−1814.27			−0.567560
$218$		0			0
$219$		−	5849.92i		−	1.80503i
$220$		0			0
$221$	−5827.98	+	2367.86i	−1.77390	+	0.720720i
$222$		0			0
$223$		−	4638.28i		−	1.39284i	−0.717637	−	0.696418i	$-0.754776\pi$
$223$		−	4638.28i		−	1.39284i	0.717637	−	0.696418i	$-0.245224\pi$
$224$		0			0
$225$	3574.33			1.05906
$226$		0			0
$227$	4201.24	+	4201.24i	1.22840	+	1.22840i	0.964570	+	0.263828i	$0.0849852\pi$
$227$	4201.24	+	4201.24i	1.22840	+	1.22840i	0.263828	+	0.964570i	$0.415015\pi$
$228$		0			0
$229$			6620.75i			1.91053i	0.295752	+	0.955265i	$0.404430\pi$
$229$			6620.75i			1.91053i	−0.295752	+	0.955265i	$0.595570\pi$
$230$		0			0
$231$	8553.52	+	8553.52i	2.43628	+	2.43628i
$232$		0			0
$233$	−4203.03	+	4203.03i	−1.18176	+	1.18176i	−0.202469	+	0.979289i	$0.564896\pi$
$233$	−4203.03	+	4203.03i	−1.18176	+	1.18176i	−0.979289	+	0.202469i	$0.935104\pi$
$234$		0			0
$235$	−943.082	+	943.082i	−0.261787	+	0.261787i
$236$		0			0
$237$	789.644			0.216426
$238$		0			0
$239$	2377.46			0.643453			0.321727	−	0.946833i	$-0.395737\pi$
$239$	2377.46			0.643453			0.321727	+	0.946833i	$0.395737\pi$
$240$		0			0
$241$	2254.15	−	2254.15i	0.602499	−	0.602499i	−0.338476	−	0.940975i	$-0.609911\pi$
$241$	2254.15	−	2254.15i	0.602499	−	0.602499i	0.940975	+	0.338476i	$0.109911\pi$
$242$		0			0
$243$	3707.67	−	3707.67i	0.978794	−	0.978794i
$244$		0			0
$245$	−1402.72	−	1402.72i	−0.365782	−	0.365782i
$246$		0			0
$247$		−	6421.77i		−	1.65428i
$248$		0			0
$249$	−2223.98	−	2223.98i	−0.566021	−	0.566021i
$250$		0			0
$251$	−2951.63			−0.742251			−0.371125	−	0.928583i	$-0.621028\pi$
$251$	−2951.63			−0.742251			−0.371125	+	0.928583i	$0.621028\pi$
$252$		0			0
$253$		−	2607.96i		−	0.648068i
$254$		0			0
$255$	−987.390	−	2430.25i	−0.242481	−	0.596817i
$256$		0			0
$257$		−	2076.53i		−	0.504010i	−0.967726	−	0.252005i	$-0.918910\pi$
$257$		−	2076.53i		−	0.504010i	0.967726	−	0.252005i	$-0.0810899\pi$
$258$		0			0
$259$	2384.78			0.572136
$260$		0			0
$261$	−7283.16	−	7283.16i	−1.72727	−	1.72727i
$262$		0			0
$263$			199.955i			0.0468813i	0.999725	+	0.0234406i	$0.00746207\pi$
$263$			199.955i			0.0468813i	−0.999725	+	0.0234406i	$0.992538\pi$
$264$		0			0
$265$	−805.195	−	805.195i	−0.186652	−	0.186652i
$266$		0			0
$267$	−3427.88	+	3427.88i	−0.785704	+	0.785704i
$268$		0			0
$269$	1674.73	−	1674.73i	0.379591	−	0.379591i	−0.491364	−	0.870955i	$-0.663501\pi$
$269$	1674.73	−	1674.73i	0.379591	−	0.379591i	0.870955	+	0.491364i	$0.163501\pi$
$270$		0			0
$271$	2503.39			0.561145			0.280573	−	0.959833i	$-0.409476\pi$
$271$	2503.39			0.561145			0.280573	+	0.959833i	$0.409476\pi$
$272$		0			0
$273$	−19469.0			−4.31617
$274$		0			0
$275$	4036.74	−	4036.74i	0.885180	−	0.885180i
$276$		0			0
$277$	2499.53	−	2499.53i	0.542173	−	0.542173i	−0.381992	−	0.924166i	$-0.624762\pi$
$277$	2499.53	−	2499.53i	0.542173	−	0.542173i	0.924166	+	0.381992i	$0.124762\pi$
$278$		0			0
$279$	−1624.59	−	1624.59i	−0.348608	−	0.348608i
$280$		0			0
$281$		−	4340.20i		−	0.921404i	−0.887555	−	0.460702i	$-0.847598\pi$
$281$		−	4340.20i		−	0.921404i	0.887555	−	0.460702i	$-0.152402\pi$
$282$		0			0
$283$	−719.569	−	719.569i	−0.151145	−	0.151145i	0.627484	−	0.778629i	$-0.284085\pi$
$283$	−719.569	−	719.569i	−0.151145	−	0.151145i	−0.778629	+	0.627484i	$0.784085\pi$
$284$		0			0
$285$	2677.86			0.556572
$286$		0			0
$287$			5116.03i			1.05223i
$288$		0			0
$289$	3520.81	−	3426.58i	0.716632	−	0.697452i
$290$		0			0
$291$		−	9769.06i		−	1.96795i
$292$		0			0
$293$	5903.33			1.17705			0.588526	−	0.808478i	$-0.299709\pi$
$293$	5903.33			1.17705			0.588526	+	0.808478i	$0.299709\pi$
$294$		0			0
$295$	−4.87630	−	4.87630i	−0.000962405	−	0.000962405i
$296$		0			0
$297$			3471.93i			0.678323i
$298$		0			0
$299$	2968.04	+	2968.04i	0.574067	+	0.574067i
$300$		0			0
$301$	1118.42	−	1118.42i	0.214168	−	0.214168i
$302$		0			0
$303$	2182.61	−	2182.61i	0.413821	−	0.413821i
$304$		0			0
$305$	−2769.42			−0.519923
$306$		0			0
$307$	−3468.20			−0.644758			−0.322379	−	0.946611i	$-0.604483\pi$
$307$	−3468.20			−0.644758			−0.322379	+	0.946611i	$0.604483\pi$
$308$		0			0
$309$	6607.99	−	6607.99i	1.21655	−	1.21655i
$310$		0			0
$311$	3384.96	−	3384.96i	0.617181	−	0.617181i	−0.327627	−	0.944807i	$-0.606249\pi$
$311$	3384.96	−	3384.96i	0.617181	−	0.617181i	0.944807	+	0.327627i	$0.106249\pi$
$312$		0			0
$313$	6172.22	+	6172.22i	1.11462	+	1.11462i	0.992518	+	0.122097i	$0.0389619\pi$
$313$	6172.22	+	6172.22i	1.11462	+	1.11462i	0.122097	+	0.992518i	$0.461038\pi$
$314$		0			0
$315$		−	4578.06i		−	0.818872i
$316$		0			0
$317$	−2125.19	−	2125.19i	−0.376539	−	0.376539i	0.493313	−	0.869852i	$-0.335786\pi$
$317$	−2125.19	−	2125.19i	−0.376539	−	0.376539i	−0.869852	+	0.493313i	$0.835786\pi$
$318$		0			0
$319$	−16450.8			−2.88735
$320$		0			0
$321$			12217.2i			2.12430i
$322$		0			0
$323$	1887.85	+	4646.55i	0.325210	+	0.800436i
$324$		0			0
$325$			9188.16i			1.56821i
$326$		0			0
$327$	−4841.48			−0.818760
$328$		0			0
$329$	−5466.59	−	5466.59i	−0.916057	−	0.916057i
$330$		0			0
$331$			10840.9i			1.80022i	0.435668	+	0.900108i	$0.356512\pi$
$331$			10840.9i			1.80022i	−0.435668	+	0.900108i	$0.643488\pi$
$332$		0			0
$333$	2135.46	+	2135.46i	0.351418	+	0.351418i
$334$		0			0
$335$	−2080.49	+	2080.49i	−0.339311	+	0.339311i
$336$		0			0
$337$	766.585	−	766.585i	0.123913	−	0.123913i	−0.642431	−	0.766344i	$-0.722074\pi$
$337$	766.585	−	766.585i	0.123913	−	0.123913i	0.766344	+	0.642431i	$0.222074\pi$
$338$		0			0
$339$	−8005.46			−1.28259
$340$		0			0
$341$	−3669.52			−0.582744
$342$		0			0
$343$	1444.23	−	1444.23i	0.227350	−	0.227350i
$344$		0			0
$345$	−1237.66	+	1237.66i	−0.193141	+	0.193141i
$346$		0			0
$347$	−1040.36	−	1040.36i	−0.160949	−	0.160949i	0.622038	−	0.782987i	$-0.286305\pi$
$347$	−1040.36	−	1040.36i	−0.160949	−	0.160949i	−0.782987	+	0.622038i	$0.786305\pi$
$348$		0			0
$349$			4596.63i			0.705020i	0.935808	+	0.352510i	$0.114672\pi$
$349$			4596.63i			0.705020i	−0.935808	+	0.352510i	$0.885328\pi$
$350$		0			0
$351$	−3951.29	−	3951.29i	−0.600867	−	0.600867i
$352$		0			0
$353$	701.385			0.105753			0.0528767	−	0.998601i	$-0.483161\pi$
$353$	701.385			0.105753			0.0528767	+	0.998601i	$0.483161\pi$
$354$		0			0
$355$		−	3061.25i		−	0.457675i
$356$		0			0
$357$	14087.0	−	5723.42i	2.08841	−	0.848503i
$358$		0			0
$359$			12107.6i			1.77998i	0.455977	+	0.889992i	$0.349290\pi$
$359$			12107.6i			1.77998i	−0.455977	+	0.889992i	$0.650710\pi$
$360$		0			0
$361$	1739.03			0.253540
$362$		0			0
$363$	9894.77	+	9894.77i	1.43069	+	1.43069i
$364$		0			0
$365$			3536.09i			0.507088i
$366$		0			0
$367$	−2164.03	−	2164.03i	−0.307797	−	0.307797i	0.536257	−	0.844055i	$-0.319838\pi$
$367$	−2164.03	−	2164.03i	−0.307797	−	0.307797i	−0.844055	+	0.536257i	$0.819838\pi$
$368$		0			0
$369$	−4581.16	+	4581.16i	−0.646302	+	0.646302i
$370$		0			0
$371$	4667.32	−	4667.32i	0.653141	−	0.653141i
$372$		0			0
$373$	10044.1			1.39427			0.697137	−	0.716938i	$-0.254457\pi$
$373$	10044.1			1.39427			0.697137	+	0.716938i	$0.254457\pi$
$374$		0			0
$375$	−8509.49			−1.17181
$376$		0			0
$377$	18722.1	−	18722.1i	2.55765	−	2.55765i
$378$		0			0
$379$	899.020	−	899.020i	0.121846	−	0.121846i	−0.643555	−	0.765400i	$-0.722541\pi$
$379$	899.020	−	899.020i	0.121846	−	0.121846i	0.765400	+	0.643555i	$0.222541\pi$
$380$		0			0
$381$	−2572.21	−	2572.21i	−0.345874	−	0.345874i
$382$		0			0
$383$		−	37.3656i		−	0.00498510i	−0.999997	−	0.00249255i	$-0.999207\pi$
$383$		−	37.3656i		−	0.00498510i	0.999997	−	0.00249255i	$-0.000793404\pi$
$384$		0			0
$385$	−5170.32	−	5170.32i	−0.684426	−	0.684426i
$386$		0			0
$387$	2002.98			0.263093
$388$		0			0
$389$		−	4192.80i		−	0.546487i	−0.961945	−	0.273244i	$-0.911903\pi$
$389$		−	4192.80i		−	0.546487i	0.961945	−	0.273244i	$-0.0880965\pi$
$390$		0			0
$391$	−3020.09	−	1275.03i	−0.390621	−	0.164913i
$392$		0			0
$393$			3394.38i			0.435685i
$394$		0			0
$395$	−477.314			−0.0608007
$396$		0			0
$397$	10889.7	+	10889.7i	1.37668	+	1.37668i	0.850175	+	0.526500i	$0.176496\pi$
$397$	10889.7	+	10889.7i	1.37668	+	1.37668i	0.526500	+	0.850175i	$0.323504\pi$
$398$		0			0
$399$			15522.3i			1.94758i
$400$		0			0
$401$	5692.40	+	5692.40i	0.708890	+	0.708890i	0.966302	−	0.257412i	$-0.0828696\pi$
$401$	5692.40	+	5692.40i	0.708890	+	0.708890i	−0.257412	+	0.966302i	$0.582870\pi$
$402$		0			0
$403$	4176.16	−	4176.16i	0.516202	−	0.516202i
$404$		0			0
$405$	−1522.62	+	1522.62i	−0.186813	+	0.186813i
$406$		0			0
$407$	4823.43			0.587442
$408$		0			0
$409$	−4530.35			−0.547705			−0.273852	−	0.961772i	$-0.588298\pi$
$409$	−4530.35			−0.547705			−0.273852	+	0.961772i	$0.588298\pi$
$410$		0			0
$411$	−5727.10	+	5727.10i	−0.687340	+	0.687340i
$412$		0			0
$413$	28.2656	−	28.2656i	0.00336769	−	0.00336769i
$414$		0			0
$415$	1344.33	+	1344.33i	0.159013	+	0.159013i
$416$		0			0
$417$		−	6097.42i		−	0.716048i
$418$		0			0
$419$	3743.79	+	3743.79i	0.436506	+	0.436506i	0.890834	−	0.454328i	$-0.150121\pi$
$419$	3743.79	+	3743.79i	0.436506	+	0.436506i	−0.454328	+	0.890834i	$0.650121\pi$
$420$		0			0
$421$	1324.38			0.153317			0.0766583	−	0.997057i	$-0.475575\pi$
$421$	1324.38			0.153317			0.0766583	+	0.997057i	$0.475575\pi$
$422$		0			0
$423$		−	9790.12i		−	1.12532i
$424$		0			0
$425$	−2701.10	−	6648.20i	−0.308289	−	0.758789i
$426$		0			0
$427$		−	16053.0i		−	1.81934i
$428$		0			0
$429$	−39377.7			−4.43164
$430$		0			0
$431$	7269.18	+	7269.18i	0.812399	+	0.812399i	0.984993	−	0.172594i	$-0.0552149\pi$
$431$	7269.18	+	7269.18i	0.812399	+	0.812399i	−0.172594	+	0.984993i	$0.555215\pi$
$432$		0			0
$433$			8776.61i			0.974081i	0.873379	+	0.487040i	$0.161924\pi$
$433$			8776.61i			0.974081i	−0.873379	+	0.487040i	$0.838076\pi$
$434$		0			0
$435$	7807.05	+	7807.05i	0.860505	+	0.860505i
$436$		0			0
$437$	2366.36	−	2366.36i	0.259036	−	0.259036i
$438$		0			0
$439$	−6494.95	+	6494.95i	−0.706121	+	0.706121i	−0.965717	−	0.259596i	$-0.916411\pi$
$439$	−6494.95	+	6494.95i	−0.706121	+	0.706121i	0.259596	+	0.965717i	$0.416411\pi$
$440$		0			0
$441$	14561.6			1.57236
$442$		0			0
$443$	−18104.5			−1.94170			−0.970848	−	0.239697i	$-0.922952\pi$
$443$	−18104.5			−1.94170			−0.970848	+	0.239697i	$0.922952\pi$
$444$		0			0
$445$	2072.04	−	2072.04i	0.220729	−	0.220729i
$446$		0			0
$447$	1714.66	−	1714.66i	0.181433	−	0.181433i
$448$		0			0
$449$	3462.42	+	3462.42i	0.363924	+	0.363924i	0.865255	−	0.501331i	$-0.167156\pi$
$449$	3462.42	+	3462.42i	0.363924	+	0.363924i	−0.501331	+	0.865255i	$0.667156\pi$
$450$		0			0
$451$			10347.6i			1.08038i
$452$		0			0
$453$	7052.02	+	7052.02i	0.731419	+	0.731419i
$454$		0			0
$455$	11768.3			1.21255
$456$		0			0
$457$		−	6625.57i		−	0.678186i	−0.940753	−	0.339093i	$-0.889880\pi$
$457$		−	6625.57i		−	0.678186i	0.940753	−	0.339093i	$-0.110120\pi$
$458$		0			0
$459$	4020.59	+	1697.42i	0.408857	+	0.172612i
$460$		0			0
$461$			1825.62i			0.184442i	0.995739	+	0.0922210i	$0.0293966\pi$
$461$			1825.62i			0.184442i	−0.995739	+	0.0922210i	$0.970603\pi$
$462$		0			0
$463$	11214.4			1.12566			0.562828	−	0.826574i	$-0.309713\pi$
$463$	11214.4			1.12566			0.562828	+	0.826574i	$0.309713\pi$
$464$		0			0
$465$	1741.45	+	1741.45i	0.173673	+	0.173673i
$466$		0			0
$467$		−	5806.23i		−	0.575333i	−0.957731	−	0.287666i	$-0.907121\pi$
$467$		−	5806.23i		−	0.575333i	0.957731	−	0.287666i	$-0.0928794\pi$
$468$		0			0
$469$	−12059.6	−	12059.6i	−1.18733	−	1.18733i
$470$		0			0
$471$	−16722.9	+	16722.9i	−1.63599	+	1.63599i
$472$		0			0
$473$	2262.10	−	2262.10i	0.219898	−	0.219898i
$474$		0			0
$475$	7325.56			0.707621
$476$		0			0
$477$	8358.71			0.802346
$478$		0			0
$479$	−1861.11	+	1861.11i	−0.177529	+	0.177529i	−0.790278	−	0.612749i	$-0.790064\pi$
$479$	−1861.11	+	1861.11i	−0.177529	+	0.177529i	0.612749	+	0.790278i	$0.290064\pi$
$480$		0			0
$481$	−5489.39	+	5489.39i	−0.520363	+	0.520363i
$482$		0			0
$483$	−7174.14	−	7174.14i	−0.675848	−	0.675848i
$484$		0			0
$485$			5905.08i			0.552857i
$486$		0			0
$487$	−159.835	−	159.835i	−0.0148723	−	0.0148723i	0.699632	−	0.714504i	$-0.253348\pi$
$487$	−159.835	−	159.835i	−0.0148723	−	0.0148723i	−0.714504	+	0.699632i	$0.753348\pi$
$488$		0			0
$489$	−26506.5			−2.45126
$490$		0			0
$491$		−	4762.10i		−	0.437700i	−0.975758	−	0.218850i	$-0.929769\pi$
$491$		−	4762.10i		−	0.437700i	0.975758	−	0.218850i	$-0.0702306\pi$
$492$		0			0
$493$	−8042.73	+	19050.4i	−0.734739	+	1.74034i
$494$		0			0
$495$		−	9259.54i		−	0.840779i
$496$		0			0
$497$	17744.6			1.60152
$498$		0			0
$499$	−9754.70	−	9754.70i	−0.875111	−	0.875111i	0.117913	−	0.993024i	$-0.462379\pi$
$499$	−9754.70	−	9754.70i	−0.875111	−	0.875111i	−0.993024	+	0.117913i	$0.962379\pi$
$500$		0			0
$501$		−	6705.37i		−	0.597952i
$502$		0			0
$503$	−4681.44	−	4681.44i	−0.414980	−	0.414980i	0.468489	−	0.883469i	$-0.344799\pi$
$503$	−4681.44	−	4681.44i	−0.414980	−	0.414980i	−0.883469	+	0.468489i	$0.844799\pi$
$504$		0			0
$505$	−1319.32	+	1319.32i	−0.116255	+	0.116255i
$506$		0			0
$507$	32590.7	−	32590.7i	2.85484	−	2.85484i
$508$		0			0
$509$	353.920			0.0308197			0.0154098	−	0.999881i	$-0.495095\pi$
$509$	353.920			0.0308197			0.0154098	+	0.999881i	$0.495095\pi$
$510$		0			0
$511$	−20497.0			−1.77443
$512$		0			0
$513$	−3150.30	+	3150.30i	−0.271129	+	0.271129i
$514$		0			0
$515$	−3994.31	+	3994.31i	−0.341768	+	0.341768i
$516$		0			0
$517$	−11056.7	−	11056.7i	−0.940564	−	0.940564i
$518$		0			0
$519$			9509.11i			0.804246i
$520$		0			0
$521$	3609.78	+	3609.78i	0.303545	+	0.303545i	0.842399	−	0.538854i	$-0.181142\pi$
$521$	3609.78	+	3609.78i	0.303545	+	0.303545i	−0.538854	+	0.842399i	$0.681142\pi$
$522$		0			0
$523$	13245.5			1.10743			0.553715	−	0.832706i	$-0.313210\pi$
$523$	13245.5			1.10743			0.553715	+	0.832706i	$0.313210\pi$
$524$		0			0
$525$		−	22209.0i		−	1.84625i
$526$		0			0
$527$	−1794.02	+	4249.41i	−0.148290	+	0.351247i
$528$		0			0
$529$		−	9979.61i		−	0.820219i
$530$		0			0
$531$	50.6208			0.00413702
$532$		0			0
$533$	−11776.3	−	11776.3i	−0.957014	−	0.957014i
$534$		0			0
$535$		−	7384.92i		−	0.596781i
$536$		0			0
$537$	13721.0	+	13721.0i	1.10262	+	1.10262i
$538$		0			0
$539$	16445.5	−	16445.5i	1.31420	−	1.31420i
$540$		0			0
$541$	−5983.60	+	5983.60i	−0.475518	+	0.475518i	−0.903695	−	0.428177i	$-0.859156\pi$
$541$	−5983.60	+	5983.60i	−0.475518	+	0.475518i	0.428177	+	0.903695i	$0.359156\pi$
$542$		0			0
$543$	−19799.5			−1.56478
$544$		0			0
$545$	2926.52			0.230015
$546$		0			0
$547$	−11488.4	+	11488.4i	−0.898001	+	0.898001i	−0.995259	−	0.0972582i	$-0.968993\pi$
$547$	−11488.4	+	11488.4i	−0.898001	+	0.898001i	0.0972582	+	0.995259i	$0.468993\pi$
$548$		0			0
$549$	14374.6	−	14374.6i	1.11748	−	1.11748i
$550$		0			0
$551$	−14926.8	−	14926.8i	−1.15409	−	1.15409i
$552$		0			0
$553$		−	2766.76i		−	0.212757i
$554$		0			0
$555$	−2289.06	−	2289.06i	−0.175073	−	0.175073i
$556$		0			0
$557$	−12755.9			−0.970351			−0.485176	−	0.874417i	$-0.661244\pi$
$557$	−12755.9			−0.970351			−0.485176	+	0.874417i	$0.661244\pi$
$558$		0			0
$559$			5148.85i			0.389576i
$560$		0			0
$561$	28492.2	−	11576.1i	2.14428	−	0.871202i
$562$		0			0
$563$		−	9012.89i		−	0.674685i	−0.941382	−	0.337343i	$-0.890472\pi$
$563$		−	9012.89i		−	0.674685i	0.941382	−	0.337343i	$-0.109528\pi$
$564$		0			0
$565$	4839.04			0.360319
$566$		0			0
$567$	−8825.87	−	8825.87i	−0.653707	−	0.653707i
$568$		0			0
$569$		−	6993.21i		−	0.515238i	−0.966247	−	0.257619i	$-0.917062\pi$
$569$		−	6993.21i		−	0.515238i	0.966247	−	0.257619i	$-0.0829379\pi$
$570$		0			0
$571$	16206.2	+	16206.2i	1.18776	+	1.18776i	0.977686	+	0.210073i	$0.0673703\pi$
$571$	16206.2	+	16206.2i	1.18776	+	1.18776i	0.210073	+	0.977686i	$0.432630\pi$
$572$		0			0
$573$	−10835.3	+	10835.3i	−0.789965	+	0.789965i
$574$		0			0
$575$	−3385.75	+	3385.75i	−0.245558	+	0.245558i
$576$		0			0
$577$	−17427.8			−1.25742			−0.628708	−	0.777641i	$-0.716416\pi$
$577$	−17427.8			−1.25742			−0.628708	+	0.777641i	$0.716416\pi$
$578$		0			0
$579$	3505.01			0.251577
$580$		0			0
$581$	−7792.40	+	7792.40i	−0.556425	+	0.556425i
$582$		0			0
$583$	9440.08	−	9440.08i	0.670614	−	0.670614i
$584$		0			0
$585$	10538.0	+	10538.0i	0.744772	+	0.744772i
$586$		0			0
$587$			17486.8i			1.22957i	0.788694	+	0.614786i	$0.210757\pi$
$587$			17486.8i			1.22957i	−0.788694	+	0.614786i	$0.789243\pi$
$588$		0			0
$589$	−3329.58	−	3329.58i	−0.232925	−	0.232925i
$590$		0			0
$591$	28159.5			1.95994
$592$		0			0
$593$		−	1329.47i		−	0.0920651i	−0.998940	−	0.0460326i	$-0.985342\pi$
$593$		−	1329.47i		−	0.0920651i	0.998940	−	0.0460326i	$-0.0146578\pi$
$594$		0			0
$595$	−8515.13	+	3459.62i	−0.586700	+	0.238371i
$596$		0			0
$597$			18528.1i			1.27019i
$598$		0			0
$599$	−6284.31			−0.428664			−0.214332	−	0.976761i	$-0.568758\pi$
$599$	−6284.31			−0.428664			−0.214332	+	0.976761i	$0.568758\pi$
$600$		0			0
$601$	7091.46	+	7091.46i	0.481309	+	0.481309i	0.905549	−	0.424241i	$-0.139459\pi$
$601$	7091.46	+	7091.46i	0.481309	+	0.481309i	−0.424241	+	0.905549i	$0.639459\pi$
$602$		0			0
$603$		−	21597.5i		−	1.45857i
$604$		0			0
$605$	−5981.06	−	5981.06i	−0.401925	−	0.401925i
$606$		0			0
$607$	8636.19	−	8636.19i	0.577483	−	0.577483i	−0.356726	−	0.934209i	$-0.616107\pi$
$607$	8636.19	−	8636.19i	0.577483	−	0.577483i	0.934209	+	0.356726i	$0.116107\pi$
$608$		0			0
$609$	−45253.7	+	45253.7i	−3.01112	+	3.01112i
$610$		0			0
$611$	25166.4			1.66633
$612$		0			0
$613$	19917.5			1.31233			0.656166	−	0.754616i	$-0.272177\pi$
$613$	19917.5			1.31233			0.656166	+	0.754616i	$0.272177\pi$
$614$		0			0
$615$	4910.69	−	4910.69i	0.321981	−	0.321981i
$616$		0			0
$617$	4252.29	−	4252.29i	0.277457	−	0.277457i	−0.554636	−	0.832093i	$-0.687143\pi$
$617$	4252.29	−	4252.29i	0.277457	−	0.277457i	0.832093	+	0.554636i	$0.187143\pi$
$618$		0			0
$619$	−11639.2	−	11639.2i	−0.755766	−	0.755766i	0.219783	−	0.975549i	$-0.429465\pi$
$619$	−11639.2	−	11639.2i	−0.755766	−	0.755766i	−0.975549	+	0.219783i	$0.929465\pi$
$620$		0			0
$621$		−	2912.03i		−	0.188174i
$622$		0			0
$623$	12010.6	+	12010.6i	0.772384	+	0.772384i
$624$		0			0
$625$	−7653.56			−0.489828
$626$		0			0
$627$			31395.2i			1.99969i
$628$		0			0
$629$	2358.16	−	5585.67i	0.149485	−	0.354078i
$630$		0			0
$631$		−	18141.3i		−	1.14452i	−0.820071	−	0.572261i	$-0.806066\pi$
$631$		−	18141.3i		−	1.14452i	0.820071	−	0.572261i	$-0.193934\pi$
$632$		0			0
$633$	−4830.51			−0.303310
$634$		0			0
$635$	1554.81	+	1554.81i	0.0971668	+	0.0971668i
$636$		0			0
$637$			37432.1i			2.32828i
$638$		0			0
$639$	15889.4	+	15889.4i	0.983686	+	0.983686i
$640$		0			0
$641$	−2086.05	+	2086.05i	−0.128540	+	0.128540i	−0.768450	−	0.639910i	$-0.778972\pi$
$641$	−2086.05	+	2086.05i	−0.128540	+	0.128540i	0.639910	+	0.768450i	$0.278972\pi$
$642$		0			0
$643$	−20401.6	+	20401.6i	−1.25126	+	1.25126i	−0.296102	+	0.955156i	$0.595687\pi$
$643$	−20401.6	+	20401.6i	−1.25126	+	1.25126i	−0.955156	+	0.296102i	$0.904313\pi$
$644$		0			0
$645$	−2147.06			−0.131070
$646$		0			0
$647$	4851.29			0.294782			0.147391	−	0.989078i	$-0.452912\pi$
$647$	4851.29			0.294782			0.147391	+	0.989078i	$0.452912\pi$
$648$		0			0
$649$	57.1696	−	57.1696i	0.00345779	−	0.00345779i
$650$		0			0
$651$	−10094.3	+	10094.3i	−0.607724	+	0.607724i
$652$		0			0
$653$	6397.27	+	6397.27i	0.383376	+	0.383376i	0.872317	−	0.488941i	$-0.162617\pi$
$653$	6397.27	+	6397.27i	0.383376	+	0.383376i	−0.488941	+	0.872317i	$0.662617\pi$
$654$		0			0
$655$		−	2051.79i		−	0.122397i
$656$		0			0
$657$	−18354.0	−	18354.0i	−1.08989	−	1.08989i
$658$		0			0
$659$	19299.5			1.14082			0.570411	−	0.821359i	$-0.306784\pi$
$659$	19299.5			1.14082			0.570411	+	0.821359i	$0.306784\pi$
$660$		0			0
$661$			14859.0i			0.874353i	0.899376	+	0.437177i	$0.144022\pi$
$661$			14859.0i			0.874353i	−0.899376	+	0.437177i	$0.855978\pi$
$662$		0			0
$663$	−19251.6	+	45600.5i	−1.12771	+	2.67115i
$664$		0			0
$665$		−	9382.70i		−	0.547136i
$666$		0			0
$667$	13797.8			0.800980
$668$		0			0
$669$	−25806.7	−	25806.7i	−1.49140	−	1.49140i
$670$		0			0
$671$		−	32468.6i		−	1.86801i
$672$		0			0
$673$	−9307.60	−	9307.60i	−0.533108	−	0.533108i	0.388388	−	0.921496i	$-0.373032\pi$
$673$	−9307.60	−	9307.60i	−0.533108	−	0.533108i	−0.921496	+	0.388388i	$0.873032\pi$
$674$		0			0
$675$	4507.39	−	4507.39i	0.257022	−	0.257022i
$676$		0			0
$677$	8777.18	−	8777.18i	0.498278	−	0.498278i	−0.412623	−	0.910902i	$-0.635387\pi$
$677$	8777.18	−	8777.18i	0.498278	−	0.498278i	0.910902	+	0.412623i	$0.135387\pi$
$678$		0			0
$679$	−34228.9			−1.93459
$680$		0			0
$681$	46750.2			2.63065
$682$		0			0
$683$	18789.6	−	18789.6i	1.05266	−	1.05266i	0.0541238	−	0.998534i	$-0.482763\pi$
$683$	18789.6	−	18789.6i	1.05266	−	1.05266i	0.998534	−	0.0541238i	$-0.0172366\pi$
$684$		0			0
$685$	3461.84	−	3461.84i	0.193095	−	0.193095i
$686$		0			0
$687$	36836.9	+	36836.9i	2.04573	+	2.04573i
$688$		0			0
$689$			21486.9i			1.18808i
$690$		0			0
$691$	−20565.7	−	20565.7i	−1.13221	−	1.13221i	−0.989810	−	0.142396i	$-0.954519\pi$
$691$	−20565.7	−	20565.7i	−1.13221	−	1.13221i	−0.142396	−	0.989810i	$-0.545481\pi$
$692$		0			0
$693$	53673.1			2.94209
$694$		0			0
$695$			3685.69i			0.201160i
$696$		0			0
$697$	11982.8	+	5058.93i	0.651194	+	0.274922i
$698$		0			0
$699$			46770.1i			2.53077i
$700$		0			0
$701$	−17979.5			−0.968725			−0.484362	−	0.874868i	$-0.660948\pi$
$701$	−17979.5			−0.968725			−0.484362	+	0.874868i	$0.660948\pi$
$702$		0			0
$703$	4376.60	+	4376.60i	0.234803	+	0.234803i
$704$		0			0
$705$			10494.3i			0.560624i
$706$		0			0
$707$	−7647.43	−	7647.43i	−0.406805	−	0.406805i
$708$		0			0
$709$	−4384.10	+	4384.10i	−0.232226	+	0.232226i	−0.813621	−	0.581395i	$-0.802507\pi$
$709$	−4384.10	+	4384.10i	−0.232226	+	0.232226i	0.581395	+	0.813621i	$0.302507\pi$
$710$		0			0
$711$	2477.50	−	2477.50i	0.130680	−	0.130680i
$712$		0			0
$713$	3077.76			0.161659
$714$		0			0
$715$	23802.5			1.24499
$716$		0			0
$717$	13227.9	−	13227.9i	0.688987	−	0.688987i
$718$		0			0
$719$	1358.91	−	1358.91i	0.0704851	−	0.0704851i	−0.670985	−	0.741471i	$-0.734129\pi$
$719$	1358.91	−	1358.91i	0.0704851	−	0.0704851i	0.741471	+	0.670985i	$0.234129\pi$
$720$		0			0
$721$	−23153.1	−	23153.1i	−1.19593	−	1.19593i
$722$		0			0
$723$		−	25083.5i		−	1.29027i
$724$		0			0
$725$	21357.0	+	21357.0i	1.09404	+	1.09404i
$726$		0			0
$727$	−11402.0			−0.581676			−0.290838	−	0.956772i	$-0.593934\pi$
$727$	−11402.0			−0.581676			−0.290838	+	0.956772i	$0.593934\pi$
$728$		0			0
$729$		−	29034.1i		−	1.47508i
$730$		0			0
$731$	−1513.64	−	3725.51i	−0.0765855	−	0.188499i
$732$		0			0
$733$			2813.44i			0.141769i	0.997485	+	0.0708845i	$0.0225822\pi$
$733$			2813.44i			0.141769i	−0.997485	+	0.0708845i	$0.977418\pi$
$734$		0			0
$735$	−15609.1			−0.783333
$736$		0			0
$737$	−24391.6	−	24391.6i	−1.21910	−	1.21910i
$738$		0			0
$739$		−	20976.7i		−	1.04417i	−0.852895	−	0.522083i	$-0.825155\pi$
$739$		−	20976.7i		−	1.04417i	0.852895	−	0.522083i	$-0.174845\pi$
$740$		0			0
$741$	−35729.8	−	35729.8i	−1.77135	−	1.77135i
$742$		0			0
$743$	21164.3	−	21164.3i	1.04501	−	1.04501i	0.0460732	−	0.998938i	$-0.485329\pi$
$743$	21164.3	−	21164.3i	1.04501	−	1.04501i	0.998938	−	0.0460732i	$-0.0146707\pi$
$744$		0			0
$745$	−1036.46	+	1036.46i	−0.0509702	+	0.0509702i
$746$		0			0
$747$	−13955.4			−0.683537
$748$		0			0
$749$	42806.8			2.08828
$750$		0			0
$751$	−14274.1	+	14274.1i	−0.693569	+	0.693569i	−0.963015	−	0.269446i	$-0.913159\pi$
$751$	−14274.1	+	14274.1i	−0.693569	+	0.693569i	0.269446	+	0.963015i	$0.413159\pi$
$752$		0			0
$753$	−16422.4	+	16422.4i	−0.794776	+	0.794776i
$754$		0			0
$755$	−4262.72	−	4262.72i	−0.205478	−	0.205478i
$756$		0			0
$757$		−	383.768i		−	0.0184257i	−0.999958	−	0.00921287i	$-0.997067\pi$
$757$		−	383.768i		−	0.0184257i	0.999958	−	0.00921287i	$-0.00293259\pi$
$758$		0			0
$759$	−14510.3	−	14510.3i	−0.693929	−	0.693929i
$760$		0			0
$761$	−37915.9			−1.80611			−0.903056	−	0.429524i	$-0.858681\pi$
$761$	−37915.9			−1.80611			−0.903056	+	0.429524i	$0.858681\pi$
$762$		0			0
$763$			16963.6i			0.804880i
$764$		0			0
$765$	−10722.8	−	4526.96i	−0.506776	−	0.213951i
$766$		0			0
$767$			130.126i			0.00612590i
$768$		0			0
$769$	8933.81			0.418936			0.209468	−	0.977816i	$-0.432827\pi$
$769$	8933.81			0.418936			0.209468	+	0.977816i	$0.432827\pi$
$770$		0			0
$771$	−11553.5	−	11553.5i	−0.539676	−	0.539676i
$772$		0			0
$773$			35202.0i			1.63794i	0.573835	+	0.818971i	$0.305455\pi$
$773$			35202.0i			1.63794i	−0.573835	+	0.818971i	$0.694545\pi$
$774$		0			0
$775$	4763.91	+	4763.91i	0.220806	+	0.220806i
$776$		0			0
$777$	13268.6	−	13268.6i	0.612623	−	0.612623i
$778$		0			0
$779$	−9389.05	+	9389.05i	−0.431832	+	0.431832i
$780$		0			0
$781$	35890.0			1.64436
$782$		0			0
$783$	−18368.8			−0.838374
$784$		0			0
$785$	10108.5	−	10108.5i	0.459600	−	0.459600i
$786$		0			0
$787$	21860.5	−	21860.5i	0.990142	−	0.990142i	−0.00980983	−	0.999952i	$-0.503123\pi$
$787$	21860.5	−	21860.5i	0.990142	−	0.990142i	0.999952	+	0.00980983i	$0.00312262\pi$
$788$		0			0
$789$	1112.52	+	1112.52i	0.0501988	+	0.0501988i
$790$		0			0
$791$			28049.6i			1.26084i
$792$		0			0
$793$	36951.4	+	36951.4i	1.65471	+	1.65471i
$794$		0			0
$795$	−8959.98			−0.399720
$796$		0			0
$797$			15775.9i			0.701143i	0.936536	+	0.350572i	$0.114013\pi$
$797$			15775.9i			0.701143i	−0.936536	+	0.350572i	$0.885987\pi$
$798$		0			0
$799$	−18209.5	+	7398.34i	−0.806264	+	0.327578i
$800$		0			0
$801$			21509.8i			0.948830i
$802$		0			0
$803$	−41457.0			−1.82190
$804$		0			0
$805$	4336.53	+	4336.53i	0.189867	+	0.189867i
$806$		0			0
$807$		−	18635.9i		−	0.812905i
$808$		0			0
$809$	13505.2	+	13505.2i	0.586918	+	0.586918i	0.936796	−	0.349877i	$-0.113777\pi$
$809$	13505.2	+	13505.2i	0.586918	+	0.586918i	−0.349877	+	0.936796i	$0.613777\pi$
$810$		0			0
$811$	−21019.0	+	21019.0i	−0.910084	+	0.910084i	−0.996278	−	0.0861943i	$-0.972529\pi$
$811$	−21019.0	+	21019.0i	−0.910084	+	0.910084i	0.0861943	+	0.996278i	$0.472529\pi$
$812$		0			0
$813$	13928.5	−	13928.5i	0.600854	−	0.600854i
$814$		0			0
$815$	16022.3			0.688634
$816$		0			0
$817$	4105.09			0.175788
$818$		0			0
$819$	−61083.5	+	61083.5i	−2.60614	+	2.60614i
$820$		0			0
$821$	17789.2	−	17789.2i	0.756209	−	0.756209i	−0.219421	−	0.975630i	$-0.570417\pi$
$821$	17789.2	−	17789.2i	0.756209	−	0.756209i	0.975630	+	0.219421i	$0.0704169\pi$
$822$		0			0
$823$	−6920.23	−	6920.23i	−0.293103	−	0.293103i	0.545202	−	0.838305i	$-0.316453\pi$
$823$	−6920.23	−	6920.23i	−0.293103	−	0.293103i	−0.838305	+	0.545202i	$0.816453\pi$
$824$		0			0
$825$		−	44919.7i		−	1.89564i
$826$		0			0
$827$	−11770.3	−	11770.3i	−0.494915	−	0.494915i	0.414936	−	0.909851i	$-0.363804\pi$
$827$	−11770.3	−	11770.3i	−0.494915	−	0.494915i	−0.909851	+	0.414936i	$0.863804\pi$
$828$		0			0
$829$	−2386.81			−0.0999969			−0.0499985	−	0.998749i	$-0.515922\pi$
$829$	−2386.81			−0.0999969			−0.0499985	+	0.998749i	$0.515922\pi$
$830$		0			0
$831$		−	27814.0i		−	1.16108i
$832$		0			0
$833$	−11004.2	−	27084.4i	−0.457709	−	1.12655i
$834$		0			0
$835$			4053.18i			0.167983i
$836$		0			0
$837$	−4097.36			−0.169206
$838$		0			0
$839$	6939.74	+	6939.74i	0.285562	+	0.285562i	0.835322	−	0.549760i	$-0.185281\pi$
$839$	6939.74	+	6939.74i	0.285562	+	0.285562i	−0.549760	+	0.835322i	$0.685281\pi$
$840$		0			0
$841$		−	62646.2i		−	2.56863i
$842$		0			0
$843$	−24148.3	−	24148.3i	−0.986608	−	0.986608i
$844$		0			0
$845$	−19700.0	+	19700.0i	−0.802013	+	0.802013i
$846$		0			0
$847$	34669.3	−	34669.3i	1.40644	−	1.40644i
$848$		0			0
$849$	−8007.15			−0.323681
$850$		0			0
$851$	−4045.58			−0.162962
$852$		0			0
$853$	−7974.82	+	7974.82i	−0.320109	+	0.320109i	−0.848809	−	0.528700i	$-0.822680\pi$
$853$	−7974.82	+	7974.82i	−0.320109	+	0.320109i	0.528700	+	0.848809i	$0.322680\pi$
$854$		0			0
$855$	8401.75	−	8401.75i	0.336063	−	0.336063i
$856$		0			0
$857$	22470.1	+	22470.1i	0.895640	+	0.895640i	0.995047	−	0.0994073i	$-0.0316947\pi$
$857$	22470.1	+	22470.1i	0.895640	+	0.895640i	−0.0994073	+	0.995047i	$0.531695\pi$
$858$		0			0
$859$			42067.4i			1.67092i	0.549551	+	0.835460i	$0.314799\pi$
$859$			42067.4i			1.67092i	−0.549551	+	0.835460i	$0.685201\pi$
$860$		0			0
$861$	28464.9	+	28464.9i	1.12669	+	1.12669i
$862$		0			0
$863$	−21825.9			−0.860907			−0.430454	−	0.902613i	$-0.641646\pi$
$863$	−21825.9			−0.860907			−0.430454	+	0.902613i	$0.641646\pi$
$864$		0			0
$865$		−	5747.95i		−	0.225938i
$866$		0			0
$867$	524.292	−	38654.3i	0.0205374	−	1.51415i
$868$		0			0
$869$		−	5596.01i		−	0.218449i
$870$		0			0
$871$	55518.5			2.15979
$872$		0			0
$873$	−30650.3	−	30650.3i	−1.18826	−	1.18826i
$874$		0			0
$875$			29815.6i			1.15194i
$876$		0			0
$877$	−35777.3	−	35777.3i	−1.37755	−	1.37755i	−0.848737	−	0.528816i	$-0.822636\pi$
$877$	−35777.3	−	35777.3i	−1.37755	−	1.37755i	−0.528816	−	0.848737i	$-0.677364\pi$
$878$		0			0
$879$	32845.3	−	32845.3i	1.26035	−	1.26035i
$880$		0			0
$881$	−27849.8	+	27849.8i	−1.06502	+	1.06502i	−0.0672881	+	0.997734i	$0.521435\pi$
$881$	−27849.8	+	27849.8i	−1.06502	+	1.06502i	−0.997734	+	0.0672881i	$0.978565\pi$
$882$		0			0
$883$	−870.305			−0.0331689			−0.0165844	−	0.999862i	$-0.505279\pi$
$883$	−870.305			−0.0331689			−0.0165844	+	0.999862i	$0.505279\pi$
$884$		0			0
$885$	−54.2621			−0.00206102
$886$		0			0
$887$	−16666.6	+	16666.6i	−0.630903	+	0.630903i	−0.948294	−	0.317392i	$-0.897193\pi$
$887$	−16666.6	+	16666.6i	−0.630903	+	0.630903i	0.317392	+	0.948294i	$0.397193\pi$
$888$		0			0
$889$	−9012.50	+	9012.50i	−0.340011	+	0.340011i
$890$		0			0
$891$	−17851.1	−	17851.1i	−0.671195	−	0.671195i
$892$		0			0
$893$		−	20064.8i		−	0.751895i
$894$		0			0
$895$	−8293.92	−	8293.92i	−0.309760	−	0.309760i
$896$		0			0
$897$	33027.5			1.22938
$898$		0			0
$899$		−	19414.2i		−	0.720243i
$900$		0			0
$901$	−6316.64	−	15547.1i	−0.233560	−	0.574860i
$902$		0			0
$903$		−	12445.4i		−	0.458647i
$904$		0			0
$905$	11968.1			0.439596
$906$		0			0
$907$	32122.3	+	32122.3i	1.17597	+	1.17597i	0.980762	+	0.195205i	$0.0625372\pi$
$907$	32122.3	+	32122.3i	1.17597	+	1.17597i	0.195205	+	0.980762i	$0.437463\pi$
$908$		0			0
$909$		−	13695.8i		−	0.499737i
$910$		0			0
$911$	3094.72	+	3094.72i	0.112549	+	0.112549i	0.761139	−	0.648589i	$-0.224641\pi$
$911$	3094.72	+	3094.72i	0.112549	+	0.112549i	−0.648589	+	0.761139i	$0.724641\pi$
$912$		0			0
$913$	−15760.8	+	15760.8i	−0.571311	+	0.571311i
$914$		0			0
$915$	−15408.6	+	15408.6i	−0.556715	+	0.556715i
$916$		0			0
$917$	11893.3			0.428299
$918$		0			0
$919$	34895.3			1.25255			0.626273	−	0.779604i	$-0.284580\pi$
$919$	34895.3			1.25255			0.626273	+	0.779604i	$0.284580\pi$
$920$		0			0
$921$	−19296.6	+	19296.6i	−0.690384	+	0.690384i
$922$		0			0
$923$	−40845.3	+	40845.3i	−1.45660	+	1.45660i
$924$		0			0
$925$	−6261.96	−	6261.96i	−0.222586	−	0.222586i
$926$		0			0
$927$		−	41464.9i		−	1.46913i
$928$		0			0
$929$	−13820.1	−	13820.1i	−0.488078	−	0.488078i	0.419621	−	0.907699i	$-0.362163\pi$
$929$	−13820.1	−	13820.1i	−0.488078	−	0.488078i	−0.907699	+	0.419621i	$0.862163\pi$
$930$		0			0
$931$	29844.0			1.05059
$932$		0			0
$933$		−	37666.8i		−	1.32171i
$934$		0			0
$935$	−17222.6	+	6997.39i	−0.602395	+	0.244748i
$936$		0			0
$937$		−	16465.7i		−	0.574079i	−0.957919	−	0.287039i	$-0.907329\pi$
$937$		−	16465.7i		−	0.574079i	0.957919	−	0.287039i	$-0.0926711\pi$
$938$		0			0
$939$	68682.7			2.38698
$940$		0			0
$941$	35502.3	+	35502.3i	1.22991	+	1.22991i	0.963998	+	0.265909i	$0.0856721\pi$
$941$	35502.3	+	35502.3i	1.22991	+	1.22991i	0.265909	+	0.963998i	$0.414328\pi$
$942$		0			0
$943$		−	8678.92i		−	0.299708i
$944$		0			0
$945$	−5773.14	−	5773.14i	−0.198731	−	0.198731i
$946$		0			0
$947$	23603.0	−	23603.0i	0.809919	−	0.809919i	−0.174703	−	0.984621i	$-0.555896\pi$
$947$	23603.0	−	23603.0i	0.809919	−	0.809919i	0.984621	+	0.174703i	$0.0558964\pi$
$948$		0			0
$949$	47180.8	−	47180.8i	1.61386	−	1.61386i
$950$		0			0
$951$	−23648.6			−0.806369
$952$		0			0
$953$	−10840.6			−0.368481			−0.184240	−	0.982881i	$-0.558982\pi$
$953$	−10840.6			−0.368481			−0.184240	+	0.982881i	$0.558982\pi$
$954$		0			0
$955$	6549.56	−	6549.56i	0.221926	−	0.221926i
$956$		0			0
$957$	−91529.7	+	91529.7i	−3.09168	+	3.09168i
$958$		0			0
$959$	20066.6	+	20066.6i	0.675688	+	0.675688i
$960$		0			0
$961$			25460.5i			0.854636i
$962$		0			0
$963$	38331.4	+	38331.4i	1.28267	+	1.28267i
$964$		0			0
$965$	−2118.66			−0.0706759
$966$		0			0
$967$			17109.9i			0.568994i	0.958677	+	0.284497i	$0.0918266\pi$
$967$			17109.9i			0.568994i	−0.958677	+	0.284497i	$0.908173\pi$
$968$		0			0
$969$	36356.5	+	15349.0i	1.20530	+	0.508856i
$970$		0			0
$971$		−	54624.2i		−	1.80533i	−0.430345	−	0.902665i	$-0.641608\pi$
$971$		−	54624.2i		−	1.80533i	0.430345	−	0.902665i	$-0.358392\pi$
$972$		0			0
$973$	−21364.2			−0.703909
$974$		0			0
$975$	51121.6	+	51121.6i	1.67918	+	1.67918i
$976$		0			0
$977$		−	20189.0i		−	0.661110i	−0.943787	−	0.330555i	$-0.892764\pi$
$977$		−	20189.0i		−	0.661110i	0.943787	−	0.330555i	$-0.107236\pi$
$978$		0			0
$979$	24292.6	+	24292.6i	0.793048	+	0.793048i
$980$		0			0
$981$	−15190.1	+	15190.1i	−0.494375	+	0.494375i
$982$		0			0
$983$	3762.59	−	3762.59i	0.122083	−	0.122083i	−0.643425	−	0.765509i	$-0.722487\pi$
$983$	3762.59	−	3762.59i	0.122083	−	0.122083i	0.765509	+	0.643425i	$0.222487\pi$
$984$		0			0
$985$	−17021.5			−0.550609
$986$		0			0
$987$	−60830.6			−1.96176
$988$		0			0
$989$	−1897.30	+	1897.30i	−0.0610018	+	0.0610018i
$990$		0			0
$991$	−22679.7	+	22679.7i	−0.726986	+	0.726986i	−0.970018	−	0.243032i	$-0.921858\pi$
$991$	−22679.7	+	22679.7i	−0.726986	+	0.726986i	0.243032	+	0.970018i	$0.421858\pi$
$992$		0			0
$993$	60317.4	+	60317.4i	1.92761	+	1.92761i
$994$		0			0
$995$		−	11199.6i		−	0.356836i
$996$		0			0
$997$	−16453.3	−	16453.3i	−0.522651	−	0.522651i	0.395720	−	0.918371i	$-0.370495\pi$
$997$	−16453.3	−	16453.3i	−0.522651	−	0.522651i	−0.918371	+	0.395720i	$0.870495\pi$
$998$		0			0
$999$	5385.81			0.170570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.a.89.7	yes	14
4.3	odd	2		272.4.o.g.225.1		14
17.8	even	8		2312.4.a.m.1.2		14
17.9	even	8		2312.4.a.m.1.13		14
17.13	even	4	inner	136.4.k.a.81.7	✓	14
68.47	odd	4		272.4.o.g.81.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.a.81.7	✓	14	17.13	even	4	inner
136.4.k.a.89.7	yes	14	1.1	even	1	trivial
272.4.o.g.81.1		14	68.47	odd	4
272.4.o.g.225.1		14	4.3	odd	2
2312.4.a.m.1.2		14	17.8	even	8
2312.4.a.m.1.13		14	17.9	even	8

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.56386 - 5.56386i) q^{3} +(-3.36317 + 3.36317i) q^{5} +(-19.4947 - 19.4947i) q^{7} -34.9130i q^{9} +O(q^{10})\)	\(q+(5.56386 - 5.56386i) q^{3} +(-3.36317 + 3.36317i) q^{5} +(-19.4947 - 19.4947i) q^{7} -34.9130i q^{9} +(-39.4297 - 39.4297i) q^{11} +89.7473 q^{13} +37.4244i q^{15} +(-64.9377 + 26.3836i) q^{17} -71.5540i q^{19} -216.931 q^{21} +(33.0711 + 33.0711i) q^{23} +102.378i q^{25} +(-44.0269 - 44.0269i) q^{27} +(208.609 - 208.609i) q^{29} +(46.5325 - 46.5325i) q^{31} -438.762 q^{33} +131.128 q^{35} +(-61.1650 + 61.1650i) q^{37} +(499.341 - 499.341i) q^{39} +(-131.216 - 131.216i) q^{41} +57.3705i q^{43} +(117.418 + 117.418i) q^{45} +280.415 q^{47} +417.083i q^{49} +(-214.510 + 508.099i) q^{51} +239.415i q^{53} +265.217 q^{55} +(-398.116 - 398.116i) q^{57} +1.44991i q^{59} +(411.727 + 411.727i) q^{61} +(-680.617 + 680.617i) q^{63} +(-301.835 + 301.835i) q^{65} +618.610 q^{67} +368.005 q^{69} +(-455.114 + 455.114i) q^{71} +(525.708 - 525.708i) q^{73} +(569.618 + 569.618i) q^{75} +1537.34i q^{77} +(70.9619 + 70.9619i) q^{79} +452.733 q^{81} -399.720i q^{83} +(129.664 - 307.129i) q^{85} -2321.34i q^{87} -616.098 q^{89} +(-1749.59 - 1749.59i) q^{91} -517.800i q^{93} +(240.648 + 240.648i) q^{95} +(877.904 - 877.904i) q^{97} +(-1376.61 + 1376.61i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

Introduction

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