LMFDB - Embedded newform 684.3.be.a.425.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(425,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.425");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.be (of order $6$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.8
Character	$\chi$	$=$	684.425
Dual form			684.3.be.a.581.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59273 - 1.50922i) q^{3} +(-3.90584 - 2.25504i) q^{5} +(1.48435 - 2.57096i) q^{7} +(4.44449 + 7.82601i) q^{9} +O(q^{10})$	\(q+(-2.59273 - 1.50922i) q^{3} +(-3.90584 - 2.25504i) q^{5} +(1.48435 - 2.57096i) q^{7} +(4.44449 + 7.82601i) q^{9} +(-11.7195 - 6.76627i) q^{11} -19.3382 q^{13} +(6.72342 + 11.7415i) q^{15} +(14.3102 - 8.26201i) q^{17} +(-5.09700 + 18.3036i) q^{19} +(-7.72866 + 4.42560i) q^{21} +12.0690i q^{23} +(-2.32963 - 4.03504i) q^{25} +(0.287840 - 26.9985i) q^{27} +(19.6646 - 11.3534i) q^{29} +(-5.26439 - 9.11820i) q^{31} +(20.1737 + 35.2305i) q^{33} +(-11.5952 + 6.69450i) q^{35} -21.0906 q^{37} +(50.1387 + 29.1856i) q^{39} +(38.0358 + 21.9600i) q^{41} -51.2851 q^{43} +(0.288488 - 40.5896i) q^{45} +(0.00833645 - 0.00481305i) q^{47} +(20.0934 + 34.8028i) q^{49} +(-49.5718 - 0.176162i) q^{51} +(66.1093 + 38.1682i) q^{53} +(30.5164 + 52.8559i) q^{55} +(40.8393 - 39.7637i) q^{57} +(71.7998 + 41.4536i) q^{59} +(13.9840 + 24.2210i) q^{61} +(26.7176 + 0.189893i) q^{63} +(75.5318 + 43.6083i) q^{65} +44.8925 q^{67} +(18.2149 - 31.2918i) q^{69} +(-22.7102 + 13.1117i) q^{71} +(67.3825 + 116.710i) q^{73} +(-0.0496722 + 13.9777i) q^{75} +(-34.7917 + 20.0870i) q^{77} +64.2642 q^{79} +(-41.4930 + 69.5653i) q^{81} +(-29.8857 - 17.2545i) q^{83} -74.5245 q^{85} +(-68.1199 - 0.242075i) q^{87} +(12.8249 + 7.40448i) q^{89} +(-28.7046 + 49.7177i) q^{91} +(-0.112247 + 31.5862i) q^{93} +(61.1832 - 59.9968i) q^{95} -8.02290 q^{97} +(0.865612 - 121.790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9	$ 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.59273	−	1.50922i	−0.864243	−	0.503074i
$3$	−2.59273	−	1.50922i	−0.864243	−	0.503074i
$4$		0			0
$5$	−3.90584	−	2.25504i	−0.781167	−	0.451007i	0.0556767	−	0.998449i	$-0.482268\pi$
$5$	−3.90584	−	2.25504i	−0.781167	−	0.451007i	−0.836844	+	0.547442i	$0.815602\pi$
$6$		0			0
$7$	1.48435	−	2.57096i	0.212049	−	0.367280i	−0.740306	−	0.672270i	$-0.765320\pi$
$7$	1.48435	−	2.57096i	0.212049	−	0.367280i	0.952356	+	0.304989i	$0.0986529\pi$
$8$		0			0
$9$	4.44449	+	7.82601i	0.493832	+	0.869557i
$10$		0			0
$11$	−11.7195	−	6.76627i	−1.06541	−	0.615116i	−0.138487	−	0.990364i	$-0.544224\pi$
$11$	−11.7195	−	6.76627i	−1.06541	−	0.615116i	−0.926924	+	0.375248i	$0.877557\pi$
$12$		0			0
$13$	−19.3382			−1.48755			−0.743776	−	0.668429i	$-0.766967\pi$
$13$	−19.3382			−1.48755			−0.743776	+	0.668429i	$0.766967\pi$
$14$		0			0
$15$	6.72342	+	11.7415i	0.448228	+	0.782765i
$16$		0			0
$17$	14.3102	−	8.26201i	0.841778	−	0.486001i	−0.0160902	−	0.999871i	$-0.505122\pi$
$17$	14.3102	−	8.26201i	0.841778	−	0.486001i	0.857868	+	0.513870i	$0.171789\pi$
$18$		0			0
$19$	−5.09700	+	18.3036i	−0.268263	+	0.963346i
$19$	−5.09700	+	18.3036i	−0.268263	+	0.963346i
$20$		0			0
$21$	−7.72866	+	4.42560i	−0.368032	+	0.210743i
$22$		0			0
$23$			12.0690i			0.524741i	0.964967	+	0.262371i	$0.0845043\pi$
$23$			12.0690i			0.524741i	−0.964967	+	0.262371i	$0.915496\pi$
$24$		0			0
$25$	−2.32963	−	4.03504i	−0.0931854	−	0.161402i
$26$		0			0
$27$	0.287840	−	26.9985i	0.0106608	−	0.999943i
$28$		0			0
$29$	19.6646	−	11.3534i	0.678091	−	0.391496i	−0.121045	−	0.992647i	$-0.538624\pi$
$29$	19.6646	−	11.3534i	0.678091	−	0.391496i	0.799135	+	0.601151i	$0.205291\pi$
$30$		0			0
$31$	−5.26439	−	9.11820i	−0.169819	−	0.294135i	0.768537	−	0.639805i	$-0.220985\pi$
$31$	−5.26439	−	9.11820i	−0.169819	−	0.294135i	−0.938356	+	0.345670i	$0.887652\pi$
$32$		0			0
$33$	20.1737	+	35.2305i	0.611326	+	1.06759i
$34$		0			0
$35$	−11.5952	+	6.69450i	−0.331292	+	0.191272i
$36$		0			0
$37$	−21.0906			−0.570015			−0.285008	−	0.958525i	$-0.591996\pi$
$37$	−21.0906			−0.570015			−0.285008	+	0.958525i	$0.591996\pi$
$38$		0			0
$39$	50.1387	+	29.1856i	1.28561	+	0.748350i
$40$		0			0
$41$	38.0358	+	21.9600i	0.927704	+	0.535610i	0.886085	−	0.463524i	$-0.153415\pi$
$41$	38.0358	+	21.9600i	0.927704	+	0.535610i	0.0416190	+	0.999134i	$0.486748\pi$
$42$		0			0
$43$	−51.2851			−1.19268			−0.596339	−	0.802733i	$-0.703378\pi$
$43$	−51.2851			−1.19268			−0.596339	+	0.802733i	$0.703378\pi$
$44$		0			0
$45$	0.288488	−	40.5896i	0.00641084	−	0.901991i
$46$		0			0
$47$	0.00833645	−	0.00481305i	0.000177371	−	0.000102405i	−0.499911	−	0.866077i	$-0.666634\pi$
$47$	0.00833645	−	0.00481305i	0.000177371	−	0.000102405i	0.500089	+	0.865974i	$0.333301\pi$
$48$		0			0
$49$	20.0934	+	34.8028i	0.410070	+	0.710262i
$50$		0			0
$51$	−49.5718	−	0.176162i	−0.971995	−	0.00345415i
$52$		0			0
$53$	66.1093	+	38.1682i	1.24734	+	0.720155i	0.970579	−	0.240783i	$-0.0774042\pi$
$53$	66.1093	+	38.1682i	1.24734	+	0.720155i	0.276765	+	0.960938i	$0.410738\pi$
$54$		0			0
$55$	30.5164	+	52.8559i	0.554843	+	0.961016i
$56$		0			0
$57$	40.8393	−	39.7637i	0.716479	−	0.697609i
$58$		0			0
$59$	71.7998	+	41.4536i	1.21695	+	0.702604i	0.964263	−	0.264946i	$-0.0853540\pi$
$59$	71.7998	+	41.4536i	1.21695	+	0.702604i	0.252682	+	0.967549i	$0.418687\pi$
$60$		0			0
$61$	13.9840	+	24.2210i	0.229246	+	0.397066i	0.957585	−	0.288151i	$-0.0930407\pi$
$61$	13.9840	+	24.2210i	0.229246	+	0.397066i	−0.728339	+	0.685217i	$0.759707\pi$
$62$		0			0
$63$	26.7176	+	0.189893i	0.424088	+	0.00301418i
$64$		0			0
$65$	75.5318	+	43.6083i	1.16203	+	0.670897i
$66$		0			0
$67$	44.8925			0.670037			0.335018	−	0.942212i	$-0.391257\pi$
$67$	44.8925			0.670037			0.335018	+	0.942212i	$0.391257\pi$
$68$		0			0
$69$	18.2149	−	31.2918i	0.263984	−	0.453504i
$70$		0			0
$71$	−22.7102	+	13.1117i	−0.319862	+	0.184672i	−0.651331	−	0.758794i	$-0.725789\pi$
$71$	−22.7102	+	13.1117i	−0.319862	+	0.184672i	0.331469	+	0.943466i	$0.392456\pi$
$72$		0			0
$73$	67.3825	+	116.710i	0.923048	+	1.59877i	0.794672	+	0.607040i	$0.207643\pi$
$73$	67.3825	+	116.710i	0.923048	+	1.59877i	0.128376	+	0.991726i	$0.459024\pi$
$74$		0			0
$75$	−0.0496722	+	13.9777i	−0.000662296	+	0.186370i
$76$		0			0
$77$	−34.7917	+	20.0870i	−0.451840	+	0.260870i
$78$		0			0
$79$	64.2642			0.813471			0.406735	−	0.913546i	$-0.366667\pi$
$79$	64.2642			0.813471			0.406735	+	0.913546i	$0.366667\pi$
$80$		0			0
$81$	−41.4930	+	69.5653i	−0.512259	+	0.858831i
$82$		0			0
$83$	−29.8857	−	17.2545i	−0.360069	−	0.207886i	0.309042	−	0.951048i	$-0.399992\pi$
$83$	−29.8857	−	17.2545i	−0.360069	−	0.207886i	−0.669111	+	0.743162i	$0.733325\pi$
$84$		0			0
$85$	−74.5245			−0.876759
$86$		0			0
$87$	−68.1199	−	0.242075i	−0.782987	−	0.00278248i
$88$		0			0
$89$	12.8249	+	7.40448i	0.144100	+	0.0831964i	0.570317	−	0.821425i	$-0.306820\pi$
$89$	12.8249	+	7.40448i	0.144100	+	0.0831964i	−0.426216	+	0.904621i	$0.640154\pi$
$90$		0			0
$91$	−28.7046	+	49.7177i	−0.315435	+	0.546349i
$92$		0			0
$93$	−0.112247	+	31.5862i	−0.00120695	+	0.339636i
$94$		0			0
$95$	61.1832	−	59.9968i	0.644034	−	0.631545i
$96$		0			0
$97$	−8.02290			−0.0827104			−0.0413552	−	0.999145i	$-0.513168\pi$
$97$	−8.02290			−0.0827104			−0.0413552	+	0.999145i	$0.513168\pi$
$98$		0			0
$99$	0.865612	−	121.790i	0.00874356	−	1.23020i
$100$		0			0
$101$	−32.5348	+	18.7840i	−0.322127	+	0.185980i	−0.652340	−	0.757926i	$-0.726213\pi$
$101$	−32.5348	+	18.7840i	−0.322127	+	0.185980i	0.330213	+	0.943906i	$0.392879\pi$
$102$		0			0
$103$	−64.3366	−	111.434i	−0.624627	−	1.08189i	−0.988613	−	0.150481i	$-0.951918\pi$
$103$	−64.3366	−	111.434i	−0.624627	−	1.08189i	0.363986	−	0.931404i	$-0.381416\pi$
$104$		0			0
$105$	40.1668	+	0.142739i	0.382541	+	0.00135942i
$106$		0			0
$107$		−	58.5759i		−	0.547438i	−0.961810	−	0.273719i	$-0.911746\pi$
$107$		−	58.5759i		−	0.547438i	0.961810	−	0.273719i	$-0.0882539\pi$
$108$		0			0
$109$	−16.4767	−	28.5385i	−0.151163	−	0.261821i	0.780493	−	0.625165i	$-0.214968\pi$
$109$	−16.4767	−	28.5385i	−0.151163	−	0.261821i	−0.931655	+	0.363344i	$0.881635\pi$
$110$		0			0
$111$	54.6821	+	31.8304i	0.492632	+	0.286760i
$112$		0			0
$113$	−111.840	+	64.5709i	−0.989735	+	0.571423i	−0.905195	−	0.424997i	$-0.860275\pi$
$113$	−111.840	+	64.5709i	−0.989735	+	0.571423i	−0.0845396	+	0.996420i	$0.526942\pi$
$114$		0			0
$115$	27.2161	−	47.1397i	0.236662	−	0.409911i
$116$		0			0
$117$	−85.9484	−	151.341i	−0.734601	−	1.29351i
$118$		0			0
$119$		−	49.0547i		−	0.412225i
$120$		0			0
$121$	31.0649	+	53.8060i	0.256735	+	0.444677i
$122$		0			0
$123$	−65.4741	−	114.341i	−0.532310	−	0.929601i
$124$		0			0
$125$			133.765i			1.07012i
$126$		0			0
$127$	−77.8768	+	134.887i	−0.613203	+	1.06210i	0.377494	+	0.926012i	$0.376786\pi$
$127$	−77.8768	+	134.887i	−0.613203	+	1.06210i	−0.990697	+	0.136087i	$0.956547\pi$
$128$		0			0
$129$	132.968	+	77.4007i	1.03076	+	0.600005i
$130$		0			0
$131$	50.9607	+	29.4222i	0.389013	+	0.224597i	0.681732	−	0.731602i	$-0.261227\pi$
$131$	50.9607	+	29.4222i	0.389013	+	0.224597i	−0.292719	+	0.956198i	$0.594560\pi$
$132$		0			0
$133$	39.4921	+	40.2730i	0.296933	+	0.302805i
$134$		0			0
$135$	−62.0067	+	104.802i	−0.459309	+	0.776315i
$136$		0			0
$137$	180.626	−	104.285i	1.31844	−	0.761202i	0.334964	−	0.942231i	$-0.391276\pi$
$137$	180.626	−	104.285i	1.31844	−	0.761202i	0.983478	+	0.181029i	$0.0579427\pi$
$138$		0			0
$139$	−119.432			−0.859220			−0.429610	−	0.903014i	$-0.641349\pi$
$139$	−119.432			−0.859220			−0.429610	+	0.903014i	$0.641349\pi$
$140$		0			0
$141$	−0.0288781		0.000102623i	−0.000204809		7.27825e-7i
$142$		0			0
$143$	226.634	+	130.847i	1.58486	+	0.915017i
$144$		0			0
$145$	−102.409			−0.706270
$146$		0			0
$147$	0.428430	−	120.560i	0.00291449	−	0.820135i
$148$		0			0
$149$	−39.8495	−	23.0071i	−0.267446	−	0.154410i	0.360280	−	0.932844i	$-0.382681\pi$
$149$	−39.8495	−	23.0071i	−0.267446	−	0.154410i	−0.627726	+	0.778434i	$0.716014\pi$
$150$		0			0
$151$	39.4447	−	68.3202i	0.261223	−	0.452451i	−0.705344	−	0.708865i	$-0.749208\pi$
$151$	39.4447	−	68.3202i	0.261223	−	0.452451i	0.966567	+	0.256414i	$0.0825409\pi$
$152$		0			0
$153$	128.260	+	75.2716i	0.838303	+	0.491971i
$154$		0			0
$155$			47.4856i			0.306359i
$156$		0			0
$157$	−5.24912	+	9.09174i	−0.0334339	+	0.0579092i	−0.882258	−	0.470766i	$-0.843978\pi$
$157$	−5.24912	+	9.09174i	−0.0334339	+	0.0579092i	0.848824	+	0.528675i	$0.177311\pi$
$158$		0			0
$159$	−113.799	−	198.733i	−0.715717	−	1.24990i
$160$		0			0
$161$	31.0291	+	17.9146i	0.192727	+	0.111271i
$162$		0			0
$163$	−319.167			−1.95808			−0.979041	−	0.203662i	$-0.934716\pi$
$163$	−319.167			−1.95808			−0.979041	+	0.203662i	$0.934716\pi$
$164$		0			0
$165$	0.650666	−	183.097i	0.00394343	−	1.10968i
$166$		0			0
$167$		−	155.812i		−	0.933006i	−0.884520	−	0.466503i	$-0.845514\pi$
$167$		−	155.812i		−	0.933006i	0.884520	−	0.466503i	$-0.154486\pi$
$168$		0			0
$169$	204.965			1.21281
$170$		0			0
$171$	−165.898	+	41.4609i	−0.970161	+	0.242461i
$172$		0			0
$173$			217.529i			1.25739i	0.777650	+	0.628697i	$0.216411\pi$
$173$			217.529i			1.25739i	−0.777650	+	0.628697i	$0.783589\pi$
$174$		0			0
$175$	−13.8319			−0.0790396
$176$		0			0
$177$	−123.595	−	215.840i	−0.698275	−	1.21943i
$178$		0			0
$179$		−	77.6658i		−	0.433887i	−0.976184	−	0.216944i	$-0.930391\pi$
$179$		−	77.6658i		−	0.433887i	0.976184	−	0.216944i	$-0.0696088\pi$
$180$		0			0
$181$	68.2164	−	118.154i	0.376886	−	0.652786i	−0.613721	−	0.789523i	$-0.710328\pi$
$181$	68.2164	−	118.154i	0.376886	−	0.652786i	0.990607	+	0.136737i	$0.0436615\pi$
$182$		0			0
$183$	0.298165	−	83.9035i	0.00162932	−	0.458489i
$184$		0			0
$185$	82.3763	+	47.5600i	0.445277	+	0.257081i
$186$		0			0
$187$	−223.612			−1.19579
$188$		0			0
$189$	−68.9848	−	40.8151i	−0.364999	−	0.215953i
$190$		0			0
$191$	−216.762	−	125.148i	−1.13488	−	0.655223i	−0.189722	−	0.981838i	$-0.560759\pi$
$191$	−216.762	−	125.148i	−1.13488	−	0.655223i	−0.945157	+	0.326615i	$0.894092\pi$
$192$		0			0
$193$	−25.7097	+	44.5305i	−0.133211	+	0.230728i	−0.924913	−	0.380180i	$-0.875862\pi$
$193$	−25.7097	+	44.5305i	−0.133211	+	0.230728i	0.791702	+	0.610908i	$0.209195\pi$
$194$		0			0
$195$	−130.019	−	227.059i	−0.666763	−	1.16440i
$196$		0			0
$197$			239.093i			1.21367i	0.794827	+	0.606836i	$0.207561\pi$
$197$			239.093i			1.21367i	−0.794827	+	0.606836i	$0.792439\pi$
$198$		0			0
$199$	−182.856	+	316.716i	−0.918874	+	1.59154i	−0.117746	+	0.993044i	$0.537567\pi$
$199$	−182.856	+	316.716i	−0.918874	+	1.59154i	−0.801128	+	0.598493i	$0.795767\pi$
$200$		0			0
$201$	−116.394	−	67.7528i	−0.579075	−	0.337078i
$202$		0			0
$203$		−	67.4094i		−	0.332066i
$204$		0			0
$205$	−99.0412	−	171.544i	−0.483128	−	0.836802i
$206$		0			0
$207$	−94.4526	+	53.6408i	−0.456293	+	0.259134i
$208$		0			0
$209$	183.581	−	180.022i	0.878380	−	0.861347i
$210$		0			0
$211$	−25.5191	+	44.2004i	−0.120944	+	0.209481i	−0.920140	−	0.391589i	$-0.871925\pi$
$211$	−25.5191	+	44.2004i	−0.120944	+	0.209481i	0.799196	+	0.601070i	$0.205259\pi$
$212$		0			0
$213$	78.6700	+	0.279567i	0.369343	+	0.00131252i
$214$		0			0
$215$	200.311	+	115.650i	0.931680	+	0.537906i
$216$		0			0
$217$	−31.2567			−0.144040
$218$		0			0
$219$	1.43672	−	404.292i	0.00656037	−	1.84608i
$220$		0			0
$221$	−276.734	+	159.772i	−1.25219	+	0.722952i
$222$		0			0
$223$	−374.908			−1.68120			−0.840600	−	0.541656i	$-0.817797\pi$
$223$	−374.908			−1.68120			−0.840600	+	0.541656i	$0.817797\pi$
$224$		0			0
$225$	21.2243	−	36.1655i	0.0943301	−	0.160735i
$226$		0			0
$227$	−149.616	−	86.3809i	−0.659101	−	0.380532i	0.132833	−	0.991138i	$-0.457593\pi$
$227$	−149.616	−	86.3809i	−0.659101	−	0.380532i	−0.791935	+	0.610606i	$0.790926\pi$
$228$		0			0
$229$	142.530	+	246.869i	0.622400	+	1.07803i	0.989037	+	0.147665i	$0.0471757\pi$
$229$	142.530	+	246.869i	0.622400	+	1.07803i	−0.366637	+	0.930364i	$0.619491\pi$
$230$		0			0
$231$	120.521	+	0.428292i	0.521736	+	0.00185408i
$232$		0			0
$233$	108.955	−	62.9051i	0.467617	−	0.269979i	−0.247624	−	0.968856i	$-0.579650\pi$
$233$	108.955	−	62.9051i	0.467617	−	0.269979i	0.715242	+	0.698877i	$0.246317\pi$
$234$		0			0
$235$	−0.0434144			−0.000184742
$236$		0			0
$237$	−166.620	−	96.9890i	−0.703037	−	0.409236i
$238$		0			0
$239$	51.4738	−	29.7184i	0.215372	−	0.124345i	−0.388434	−	0.921477i	$-0.626984\pi$
$239$	51.4738	−	29.7184i	0.215372	−	0.124345i	0.603805	+	0.797132i	$0.293650\pi$
$240$		0			0
$241$	196.221	+	339.865i	0.814196	+	1.41023i	0.909903	+	0.414820i	$0.136155\pi$
$241$	196.221	+	339.865i	0.814196	+	1.41023i	−0.0957070	+	0.995410i	$0.530511\pi$
$242$		0			0
$243$	212.570	−	117.742i	0.874772	−	0.484534i
$244$		0			0
$245$		−	181.246i		−	0.739778i
$246$		0			0
$247$	98.5666	−	353.958i	0.399055	−	1.43303i
$248$		0			0
$249$	51.4447	+	89.8406i	0.206605	+	0.360806i
$250$		0			0
$251$	404.666	+	233.634i	1.61222	+	0.930813i	0.988856	+	0.148878i	$0.0475661\pi$
$251$	404.666	+	233.634i	1.61222	+	0.930813i	0.623360	+	0.781935i	$0.285767\pi$
$252$		0			0
$253$	81.6625	−	141.444i	0.322777	−	0.559065i
$254$		0			0
$255$	193.222	+	112.474i	0.757733	+	0.441075i
$256$		0			0
$257$		−	111.676i		−	0.434538i	−0.976112	−	0.217269i	$-0.930285\pi$
$257$		−	111.676i		−	0.434538i	0.976112	−	0.217269i	$-0.0697148\pi$
$258$		0			0
$259$	−31.3057	+	54.2231i	−0.120871	+	0.209355i
$260$		0			0
$261$	176.251	+	103.436i	0.675291	+	0.396305i
$262$		0			0
$263$		−	268.779i		−	1.02198i	−0.859588	−	0.510988i	$-0.829280\pi$
$263$		−	268.779i		−	1.02198i	0.859588	−	0.510988i	$-0.170720\pi$
$264$		0			0
$265$	−172.141	−	298.157i	−0.649590	−	1.12512i
$266$		0			0
$267$	−22.0766	−	38.5535i	−0.0826838	−	0.144395i
$268$		0			0
$269$	−446.596	+	257.842i	−1.66021	+	0.958521i	−0.687593	+	0.726096i	$0.741333\pi$
$269$	−446.596	+	257.842i	−1.66021	+	0.958521i	−0.972614	+	0.232425i	$0.925334\pi$
$270$		0			0
$271$	−39.9376	−	69.1739i	−0.147371	−	0.255254i	0.782884	−	0.622168i	$-0.213748\pi$
$271$	−39.9376	−	69.1739i	−0.147371	−	0.255254i	−0.930255	+	0.366914i	$0.880414\pi$
$272$		0			0
$273$	149.458	−	85.5831i	0.547466	−	0.313491i
$274$		0			0
$275$			63.0518i			0.229279i
$276$		0			0
$277$	175.469	−	303.921i	0.633461	−	1.09719i	−0.353378	−	0.935481i	$-0.614967\pi$
$277$	175.469	−	303.921i	0.633461	−	1.09719i	0.986839	−	0.161706i	$-0.0516996\pi$
$278$		0			0
$279$	47.9616	−	81.7250i	0.171905	−	0.292921i
$280$		0			0
$281$	−165.103	+	95.3225i	−0.587556	+	0.339226i	−0.764131	−	0.645061i	$-0.776832\pi$
$281$	−165.103	+	95.3225i	−0.587556	+	0.339226i	0.176574	+	0.984287i	$0.443498\pi$
$282$		0			0
$283$	−171.697	+	297.387i	−0.606702	+	1.05084i	0.385078	+	0.922884i	$0.374174\pi$
$283$	−171.697	+	297.387i	−0.606702	+	1.05084i	−0.991780	+	0.127954i	$0.959159\pi$
$284$		0			0
$285$	−249.180	+	63.2164i	−0.874316	+	0.221812i
$286$		0			0
$287$	112.917	−	65.1925i	0.393438	−	0.227152i
$288$		0			0
$289$	−7.97830	+	13.8188i	−0.0276066	+	0.0478160i
$290$		0			0
$291$	20.8012	+	12.1084i	0.0714819	+	0.0416095i
$292$		0			0
$293$	349.886	−	202.007i	1.19415	−	0.689444i	0.234906	−	0.972018i	$-0.424522\pi$
$293$	349.886	−	202.007i	1.19415	−	0.689444i	0.959245	+	0.282574i	$0.0911883\pi$
$294$		0			0
$295$	−186.959	−	323.822i	−0.633758	−	1.09770i
$296$		0			0
$297$	−186.052	+	314.462i	−0.626439	+	1.05879i
$298$		0			0
$299$		−	233.393i		−	0.780580i
$300$		0			0
$301$	−76.1249	+	131.852i	−0.252907	+	0.438047i
$302$		0			0
$303$	112.703	+	0.400510i	0.371958	+	0.00132181i
$304$		0			0
$305$		−	126.138i		−	0.413566i
$306$		0			0
$307$	−10.9879	−	19.0315i	−0.0357911	−	0.0619920i	0.847575	−	0.530676i	$-0.178062\pi$
$307$	−10.9879	−	19.0315i	−0.0357911	−	0.0619920i	−0.883366	+	0.468684i	$0.844728\pi$
$308$		0			0
$309$	−1.37178	+	386.017i	−0.00443940	+	1.24925i
$310$		0			0
$311$	170.820	−	98.6232i	0.549261	−	0.317116i	−0.199563	−	0.979885i	$-0.563952\pi$
$311$	170.820	−	98.6232i	0.549261	−	0.317116i	0.748824	+	0.662769i	$0.230619\pi$
$312$		0			0
$313$	18.2072	+	31.5358i	0.0581700	+	0.100753i	0.893644	−	0.448777i	$-0.148140\pi$
$313$	18.2072	+	31.5358i	0.0581700	+	0.100753i	−0.835474	+	0.549530i	$0.814807\pi$
$314$		0			0
$315$	−103.926	−	60.9907i	−0.329924	−	0.193621i
$316$		0			0
$317$	448.722	−	259.070i	1.41553	−	0.817254i	0.419624	−	0.907698i	$-0.362162\pi$
$317$	448.722	−	259.070i	1.41553	−	0.817254i	0.995902	+	0.0904438i	$0.0288286\pi$
$318$		0			0
$319$	−307.280			−0.963261
$320$		0			0
$321$	−88.4041	+	151.871i	−0.275402	+	0.473120i
$322$		0			0
$323$	78.2852	+	304.040i	0.242369	+	0.941299i
$324$		0			0
$325$	45.0509	+	78.0304i	0.138618	+	0.240094i
$326$		0			0
$327$	−0.351315	+	98.8597i	−0.00107436	+	0.302323i
$328$		0			0
$329$		−	0.0285769i		−	8.68600e-5i
$330$		0			0
$331$	−142.242	+	246.371i	−0.429735	+	0.744323i	−0.996850	−	0.0793163i	$-0.974726\pi$
$331$	−142.242	+	246.371i	−0.429735	+	0.744323i	0.567115	+	0.823639i	$0.308060\pi$
$332$		0			0
$333$	−93.7368	−	165.055i	−0.281492	−	0.495661i
$334$		0			0
$335$	−175.343	−	101.234i	−0.523411	−	0.302191i
$336$		0			0
$337$	−113.387	+	196.392i	−0.336459	+	0.582764i	−0.983764	−	0.179467i	$-0.942563\pi$
$337$	−113.387	+	196.392i	−0.336459	+	0.582764i	0.647305	+	0.762231i	$0.275896\pi$
$338$		0			0
$339$	387.423	+	1.37677i	1.14284	+	0.00406127i
$340$		0			0
$341$			142.481i			0.417834i
$342$		0			0
$343$	264.768			0.771919
$344$		0			0
$345$	−141.708	+	81.1453i	−0.410749	+	0.235204i
$346$		0			0
$347$	457.101	+	263.907i	1.31729	+	0.760540i	0.983292	−	0.182033i	$-0.0582677\pi$
$347$	457.101	+	263.907i	1.31729	+	0.760540i	0.334001	+	0.942573i	$0.391601\pi$
$348$		0			0
$349$	−252.957	+	438.134i	−0.724805	+	1.25540i	0.234249	+	0.972177i	$0.424737\pi$
$349$	−252.957	+	438.134i	−0.724805	+	1.25540i	−0.959054	+	0.283223i	$0.908597\pi$
$350$		0			0
$351$	−5.56631	+	522.101i	−0.0158584	+	1.48747i
$352$		0			0
$353$	−464.682	−	268.284i	−1.31638	−	0.760012i	−0.333235	−	0.942844i	$-0.608140\pi$
$353$	−464.682	−	268.284i	−1.31638	−	0.760012i	−0.983144	+	0.182832i	$0.941474\pi$
$354$		0			0
$355$	118.270			0.333154
$356$		0			0
$357$	−74.0346	+	127.186i	−0.207380	+	0.356262i
$358$		0			0
$359$	−253.830	+	146.549i	−0.707046	+	0.408213i	−0.809966	−	0.586476i	$-0.800515\pi$
$359$	−253.830	+	146.549i	−0.707046	+	0.408213i	0.102920	+	0.994690i	$0.467181\pi$
$360$		0			0
$361$	−309.041	−	186.586i	−0.856070	−	0.516860i
$362$		0			0
$363$	0.662362	−	186.388i	0.00182469	−	0.513466i
$364$		0			0
$365$		−	607.799i		−	1.66520i
$366$		0			0
$367$	209.393	+	362.679i	0.570552	+	0.988226i	0.996509	+	0.0834821i	$0.0266042\pi$
$367$	209.393	+	362.679i	0.570552	+	0.988226i	−0.425957	+	0.904743i	$0.640063\pi$
$368$		0			0
$369$	−2.80935	+	395.270i	−0.00761342	+	1.07119i
$370$		0			0
$371$	196.258	−	113.310i	0.528997	−	0.305417i
$372$		0			0
$373$	−346.664	−	600.440i	−0.929394	−	1.60976i	−0.784337	−	0.620334i	$-0.786997\pi$
$373$	−346.664	−	600.440i	−0.929394	−	1.60976i	−0.145057	−	0.989423i	$-0.546336\pi$
$374$		0			0
$375$	201.882	−	346.817i	0.538351	−	0.924846i
$376$		0			0
$377$	−380.278	+	219.554i	−1.00870	+	0.582371i
$378$		0			0
$379$	503.292			1.32795			0.663973	−	0.747756i	$-0.268869\pi$
$379$	503.292			1.32795			0.663973	+	0.747756i	$0.268869\pi$
$380$		0			0
$381$	405.487	−	232.191i	1.06427	−	0.609425i
$382$		0			0
$383$	485.982	+	280.582i	1.26888	+	0.732590i	0.974776	−	0.223183i	$-0.0716449\pi$
$383$	485.982	+	280.582i	1.26888	+	0.732590i	0.294106	+	0.955773i	$0.404978\pi$
$384$		0			0
$385$	181.187			0.470617
$386$		0			0
$387$	−227.936	−	401.358i	−0.588983	−	1.03710i
$388$		0			0
$389$	−205.486	+	118.638i	−0.528243	+	0.304981i	−0.740300	−	0.672276i	$-0.765317\pi$
$389$	−205.486	+	118.638i	−0.528243	+	0.304981i	0.212058	+	0.977257i	$0.431983\pi$
$390$		0			0
$391$	99.7146	+	172.711i	0.255025	+	0.441716i
$392$		0			0
$393$	−87.7227	−	153.195i	−0.223213	−	0.389809i
$394$		0			0
$395$	−251.005	−	144.918i	−0.635457	−	0.366881i
$396$		0			0
$397$	203.357	+	352.224i	0.512234	+	0.887215i	0.999899	+	0.0141845i	$0.00451523\pi$
$397$	203.357	+	352.224i	0.512234	+	0.887215i	−0.487666	+	0.873031i	$0.662151\pi$
$398$		0			0
$399$	−41.6113	−	164.019i	−0.104289	−	0.411076i
$400$		0			0
$401$	216.832	+	125.188i	0.540728	+	0.312190i	0.745374	−	0.666647i	$-0.232271\pi$
$401$	216.832	+	125.188i	0.540728	+	0.312190i	−0.204646	+	0.978836i	$0.565604\pi$
$402$		0			0
$403$	101.804	+	176.329i	0.252615	+	0.437542i
$404$		0			0
$405$	318.937	−	178.142i	0.787499	−	0.439858i
$406$		0			0
$407$	247.171	+	142.704i	0.607301	+	0.350625i
$408$		0			0
$409$	85.0094			0.207847			0.103923	−	0.994585i	$-0.466860\pi$
$409$	85.0094			0.207847			0.103923	+	0.994585i	$0.466860\pi$
$410$		0			0
$411$	−625.704	−	2.22355i	−1.52240	−	0.00541009i
$412$		0			0
$413$	213.151	−	123.063i	0.516105	−	0.297973i
$414$		0			0
$415$	77.8192	+	134.787i	0.187516	+	0.324787i
$416$		0			0
$417$	309.654	+	180.249i	0.742575	+	0.432252i
$418$		0			0
$419$	−246.917	+	142.558i	−0.589301	+	0.340233i	−0.764821	−	0.644243i	$-0.777173\pi$
$419$	−246.917	+	142.558i	−0.589301	+	0.340233i	0.175520	+	0.984476i	$0.443839\pi$
$420$		0			0
$421$	279.466			0.663815			0.331907	−	0.943312i	$-0.392308\pi$
$421$	279.466			0.663815			0.331907	+	0.943312i	$0.392308\pi$
$422$		0			0
$423$	0.0747183	+	0.0438496i	0.000176639	+	0.000103663i
$424$		0			0
$425$	−66.6752	−	38.4949i	−0.156883	−	0.0905763i
$426$		0			0
$427$	83.0284			0.194446
$428$		0			0
$429$	−390.124	−	681.294i	−0.909379	−	1.58810i
$430$		0			0
$431$	−85.0816	−	49.1219i	−0.197405	−	0.113972i	0.398039	−	0.917368i	$-0.369691\pi$
$431$	−85.0816	−	49.1219i	−0.197405	−	0.113972i	−0.595445	+	0.803396i	$0.703024\pi$
$432$		0			0
$433$	31.7958	−	55.0719i	0.0734314	−	0.127187i	−0.826972	−	0.562244i	$-0.809938\pi$
$433$	31.7958	−	55.0719i	0.0734314	−	0.127187i	0.900403	+	0.435057i	$0.143272\pi$
$434$		0			0
$435$	265.519	+	154.558i	0.610389	+	0.355306i
$436$		0			0
$437$	−220.907	−	61.5159i	−0.505507	−	0.140769i
$438$		0			0
$439$	322.183			0.733901			0.366951	−	0.930240i	$-0.380402\pi$
$439$	322.183			0.733901			0.366951	+	0.930240i	$0.380402\pi$
$440$		0			0
$441$	−183.063	+	311.932i	−0.415108	+	0.707330i
$442$		0			0
$443$	−701.765	+	405.164i	−1.58412	+	0.914592i	−0.589872	+	0.807497i	$0.700822\pi$
$443$	−701.765	+	405.164i	−1.58412	+	0.914592i	−0.994249	+	0.107095i	$0.965845\pi$
$444$		0			0
$445$	−33.3947	−	57.8413i	−0.0750443	−	0.129981i
$446$		0			0
$447$	68.5960	+	119.793i	0.153459	+	0.267993i
$448$		0			0
$449$			530.050i			1.18051i	0.807216	+	0.590256i	$0.200973\pi$
$449$			530.050i			1.18051i	−0.807216	+	0.590256i	$0.799027\pi$
$450$		0			0
$451$	−297.175	−	514.722i	−0.658924	−	1.14129i
$452$		0			0
$453$	−205.380	+	117.605i	−0.453377	+	0.259613i
$454$		0			0
$455$	224.231	−	129.460i	0.492814	−	0.284526i
$456$		0			0
$457$	−192.374	+	333.201i	−0.420949	+	0.729106i	−0.996033	−	0.0889891i	$-0.971636\pi$
$457$	−192.374	+	333.201i	−0.420949	+	0.729106i	0.575083	+	0.818095i	$0.304970\pi$
$458$		0			0
$459$	−218.943	−	388.732i	−0.476999	−	0.846911i
$460$		0			0
$461$			189.480i			0.411019i	0.978655	+	0.205510i	$0.0658852\pi$
$461$			189.480i			0.411019i	−0.978655	+	0.205510i	$0.934115\pi$
$462$		0			0
$463$	−221.710	−	384.012i	−0.478854	−	0.829400i	0.520852	−	0.853647i	$-0.325615\pi$
$463$	−221.710	−	384.012i	−0.478854	−	0.829400i	−0.999706	+	0.0242470i	$0.992281\pi$
$464$		0			0
$465$	71.6663	−	123.117i	0.154121	−	0.264768i
$466$		0			0
$467$			70.8708i			0.151758i	0.997117	+	0.0758788i	$0.0241762\pi$
$467$			70.8708i			0.151758i	−0.997117	+	0.0758788i	$0.975824\pi$
$468$		0			0
$469$	66.6360	−	115.417i	0.142081	−	0.246091i
$470$		0			0
$471$	27.3310	−	15.6503i	0.0580276	−	0.0332279i
$472$		0			0
$473$	601.038	+	347.009i	1.27069	+	0.733635i
$474$		0			0
$475$	85.7299	−	22.0740i	0.180484	−	0.0464716i
$476$		0			0
$477$	−4.88287	+	687.010i	−0.0102366	+	1.44027i
$478$		0			0
$479$	−782.240	+	451.626i	−1.63307	+	0.942852i	−0.649928	+	0.759995i	$0.725201\pi$
$479$	−782.240	+	451.626i	−1.63307	+	0.942852i	−0.983140	+	0.182857i	$0.941466\pi$
$480$		0			0
$481$	407.853			0.847928
$482$		0			0
$483$	−53.4128	−	93.2776i	−0.110586	−	0.193121i
$484$		0			0
$485$	31.3361	+	18.0919i	0.0646106	+	0.0373029i
$486$		0			0
$487$	73.7299			0.151396			0.0756981	−	0.997131i	$-0.475881\pi$
$487$	73.7299			0.151396			0.0756981	+	0.997131i	$0.475881\pi$
$488$		0			0
$489$	827.515	+	481.695i	1.69226	+	0.985061i
$490$		0			0
$491$	−94.7099	−	54.6808i	−0.192892	−	0.111366i	0.400444	−	0.916321i	$-0.368856\pi$
$491$	−94.7099	−	54.6808i	−0.192892	−	0.111366i	−0.593336	+	0.804955i	$0.702189\pi$
$492$		0			0
$493$	187.604	−	324.939i	0.380535	−	0.659105i
$494$		0			0
$495$	−278.021	+	473.739i	−0.561659	+	0.957049i
$496$		0			0
$497$			77.8495i			0.156639i
$498$		0			0
$499$	−45.3385	+	78.5285i	−0.0908587	+	0.157372i	−0.907873	−	0.419246i	$-0.862294\pi$
$499$	−45.3385	+	78.5285i	−0.0908587	+	0.157372i	0.817014	+	0.576618i	$0.195628\pi$
$500$		0			0
$501$	−235.155	+	403.978i	−0.469371	+	0.806344i
$502$		0			0
$503$	55.0270	+	31.7699i	0.109398	+	0.0631608i	0.553701	−	0.832716i	$-0.313215\pi$
$503$	55.0270	+	31.7699i	0.109398	+	0.0631608i	−0.444303	+	0.895877i	$0.646549\pi$
$504$		0			0
$505$	169.434			0.335513
$506$		0			0
$507$	−531.420	−	309.338i	−1.04816	−	0.610135i
$508$		0			0
$509$		−	273.062i		−	0.536468i	−0.963354	−	0.268234i	$-0.913560\pi$
$509$		−	273.062i		−	0.536468i	0.963354	−	0.268234i	$-0.0864400\pi$
$510$		0			0
$511$	400.076			0.782927
$512$		0			0
$513$	492.701	+	142.880i	0.960431	+	0.278518i
$514$		0			0
$515$			580.325i			1.12684i
$516$		0			0
$517$	−0.130266			−0.000251965
$518$		0			0
$519$	328.300	−	563.994i	0.632563	−	1.08669i
$520$		0			0
$521$			116.661i			0.223918i	0.993713	+	0.111959i	$0.0357126\pi$
$521$			116.661i			0.223918i	−0.993713	+	0.111959i	$0.964287\pi$
$522$		0			0
$523$	314.401	−	544.558i	0.601148	−	1.04122i	−0.391499	−	0.920179i	$-0.628043\pi$
$523$	314.401	−	544.558i	0.601148	−	1.04122i	0.992647	−	0.121041i	$-0.0386233\pi$
$524$		0			0
$525$	35.8625	+	20.8755i	0.0683094	+	0.0397628i
$526$		0			0
$527$	−150.669	−	86.9890i	−0.285900	−	0.165064i
$528$		0			0
$529$	383.338			0.724647
$530$		0			0
$531$	−5.30318	+	746.146i	−0.00998716	+	1.40517i
$532$		0			0
$533$	−735.544	−	424.667i	−1.38001	−	0.796748i
$534$		0			0
$535$	−132.091	+	228.788i	−0.246899	+	0.427641i
$536$		0			0
$537$	−117.215	+	201.366i	−0.218278	+	0.374984i
$538$		0			0
$539$		−	543.831i		−	1.00896i
$540$		0			0
$541$	−102.850	+	178.141i	−0.190111	+	0.329282i	−0.945287	−	0.326241i	$-0.894218\pi$
$541$	−102.850	+	178.141i	−0.190111	+	0.329282i	0.755176	+	0.655522i	$0.227551\pi$
$542$		0			0
$543$	−355.188	+	203.388i	−0.654121	+	0.374564i
$544$		0			0
$545$			148.622i			0.272701i
$546$		0			0
$547$	−215.186	−	372.712i	−0.393392	−	0.681375i	0.599502	−	0.800373i	$-0.295365\pi$
$547$	−215.186	−	372.712i	−0.393392	−	0.681375i	−0.992895	+	0.118998i	$0.962032\pi$
$548$		0			0
$549$	−127.402	+	217.089i	−0.232062	+	0.395426i
$550$		0			0
$551$	107.577	+	417.801i	0.195239	+	0.758260i
$552$		0			0
$553$	95.3903	−	165.221i	0.172496	−	0.298772i
$554$		0			0
$555$	−141.801	−	247.634i	−0.255497	−	0.446188i
$556$		0			0
$557$	−132.823	−	76.6855i	−0.238462	−	0.137676i	0.376008	−	0.926616i	$-0.377297\pi$
$557$	−132.823	−	76.6855i	−0.238462	−	0.137676i	−0.614470	+	0.788941i	$0.710630\pi$
$558$		0			0
$559$	991.761			1.77417
$560$		0			0
$561$	579.766	+	337.481i	1.03345	+	0.601570i
$562$		0			0
$563$	203.274	−	117.360i	0.361055	−	0.208455i	−0.308488	−	0.951228i	$-0.599823\pi$
$563$	203.274	−	117.360i	0.361055	−	0.208455i	0.669543	+	0.742773i	$0.266490\pi$
$564$		0			0
$565$	582.438			1.03086
$566$		0			0
$567$	117.260	+	209.936i	0.206807	+	0.370257i
$568$		0			0
$569$	145.321	+	83.9010i	0.255397	+	0.147453i	0.622233	−	0.782832i	$-0.286226\pi$
$569$	145.321	+	83.9010i	0.255397	+	0.147453i	−0.366836	+	0.930286i	$0.619559\pi$
$570$		0			0
$571$	322.919	+	559.311i	0.565532	+	0.979530i	0.997000	+	0.0774016i	$0.0246624\pi$
$571$	322.919	+	559.311i	0.565532	+	0.979530i	−0.431468	+	0.902128i	$0.642004\pi$
$572$		0			0
$573$	373.129	+	651.616i	0.651186	+	1.13720i
$574$		0			0
$575$	48.6992	−	28.1165i	0.0846942	−	0.0488982i
$576$		0			0
$577$	968.311			1.67818			0.839091	−	0.543991i	$-0.183088\pi$
$577$	968.311			1.67818			0.839091	+	0.543991i	$0.183088\pi$
$578$		0			0
$579$	133.865	−	76.6538i	0.231200	−	0.132390i
$580$		0			0
$581$	−88.7216	+	51.2234i	−0.152705	+	0.0881642i
$582$		0			0
$583$	−516.513	−	894.626i	−0.885957	−	1.53452i
$584$		0			0
$585$	−5.57883	+	784.929i	−0.00953646	+	1.34176i
$586$		0			0
$587$			740.527i			1.26155i	0.775968	+	0.630773i	$0.217262\pi$
$587$			740.527i			1.26155i	−0.775968	+	0.630773i	$0.782738\pi$
$588$		0			0
$589$	193.728	−	49.8818i	0.328910	−	0.0846889i
$590$		0			0
$591$	360.845	−	619.904i	0.610567	−	1.04891i
$592$		0			0
$593$	−355.984	−	205.528i	−0.600311	−	0.346589i	0.168853	−	0.985641i	$-0.445994\pi$
$593$	−355.984	−	205.528i	−0.600311	−	0.346589i	−0.769164	+	0.639052i	$0.779327\pi$
$594$		0			0
$595$	−110.620	+	191.600i	−0.185916	+	0.322016i
$596$		0			0
$597$	952.091	−	545.188i	1.59479	−	0.913212i
$598$		0			0
$599$		−	629.578i		−	1.05105i	−0.850778	−	0.525525i	$-0.823869\pi$
$599$		−	629.578i		−	1.05105i	0.850778	−	0.525525i	$-0.176131\pi$
$600$		0			0
$601$	−431.958	+	748.172i	−0.718731	+	1.24488i	0.242771	+	0.970084i	$0.421944\pi$
$601$	−431.958	+	748.172i	−0.718731	+	1.24488i	−0.961503	+	0.274796i	$0.911390\pi$
$602$		0			0
$603$	199.524	+	351.329i	0.330886	+	0.582635i
$604$		0			0
$605$		−	280.210i		−	0.463157i
$606$		0			0
$607$	499.579	+	865.297i	0.823030	+	1.42553i	0.903415	+	0.428767i	$0.141052\pi$
$607$	499.579	+	865.297i	0.823030	+	1.42553i	−0.0803848	+	0.996764i	$0.525615\pi$
$608$		0			0
$609$	−101.736	+	174.774i	−0.167054	+	0.286986i
$610$		0			0
$611$	−0.161212	+	0.0930757i	−0.000263849	+	0.000152333i
$612$		0			0
$613$	−205.131	−	355.297i	−0.334634	−	0.579603i	0.648780	−	0.760976i	$-0.275279\pi$
$613$	−205.131	−	355.297i	−0.334634	−	0.579603i	−0.983414	+	0.181372i	$0.941946\pi$
$614$		0			0
$615$	−2.11174	+	594.243i	−0.00343373	+	0.966249i
$616$		0			0
$617$		−	213.028i		−	0.345264i	−0.984986	−	0.172632i	$-0.944773\pi$
$617$		−	213.028i		−	0.345264i	0.984986	−	0.172632i	$-0.0552271\pi$
$618$		0			0
$619$	−26.1251	+	45.2500i	−0.0422053	+	0.0731017i	−0.886356	−	0.463004i	$-0.846772\pi$
$619$	−26.1251	+	45.2500i	−0.0422053	+	0.0731017i	0.844151	+	0.536105i	$0.180105\pi$
$620$		0			0
$621$	325.846	+	3.47396i	0.524711	+	0.00559414i
$622$		0			0
$623$	38.0733	−	21.9816i	0.0611128	−	0.0352835i
$624$		0			0
$625$	243.405	−	421.589i	0.389448	−	0.674543i
$626$		0			0
$627$	−747.669	+	189.682i	−1.19246	+	0.302523i
$628$		0			0
$629$	−301.811	+	174.250i	−0.479826	+	0.277028i
$630$		0			0
$631$	−544.386	+	942.904i	−0.862736	+	1.49430i	0.00654256	+	0.999979i	$0.497917\pi$
$631$	−544.386	+	942.904i	−0.862736	+	1.49430i	−0.869278	+	0.494323i	$0.835416\pi$
$632$		0			0
$633$	132.872	−	76.0856i	0.209909	−	0.120198i
$634$		0			0
$635$	608.348	−	351.230i	0.958028	−	0.553118i
$636$		0			0
$637$	−388.570	−	673.024i	−0.610001	−	1.05655i
$638$		0			0
$639$	−203.548	−	119.455i	−0.318542	−	0.186941i
$640$		0			0
$641$		−	776.510i		−	1.21140i	−0.795692	−	0.605702i	$-0.792892\pi$
$641$		−	776.510i		−	1.21140i	0.795692	−	0.605702i	$-0.207108\pi$
$642$		0			0
$643$	−150.352	+	260.418i	−0.233829	+	0.405004i	−0.958932	−	0.283637i	$-0.908459\pi$
$643$	−150.352	+	260.418i	−0.233829	+	0.405004i	0.725103	+	0.688641i	$0.241792\pi$
$644$		0			0
$645$	−344.812	−	602.163i	−0.534592	−	0.933586i
$646$		0			0
$647$		−	310.079i		−	0.479257i	−0.970865	−	0.239629i	$-0.922974\pi$
$647$		−	310.079i		−	0.479257i	0.970865	−	0.239629i	$-0.0770257\pi$
$648$		0			0
$649$	−560.973	−	971.634i	−0.864365	−	1.49712i
$650$		0			0
$651$	81.0402	+	47.1734i	0.124486	+	0.0724630i
$652$		0			0
$653$	761.714	−	439.776i	1.16648	−	0.673469i	0.213634	−	0.976914i	$-0.431470\pi$
$653$	761.714	−	439.776i	1.16648	−	0.673469i	0.952849	+	0.303444i	$0.0981367\pi$
$654$		0			0
$655$	−132.696	−	229.836i	−0.202590	−	0.350895i
$656$		0			0
$657$	−613.892	+	1046.05i	−0.934387	+	1.59216i
$658$		0			0
$659$	375.622	−	216.866i	0.569988	−	0.329083i	−0.187156	−	0.982330i	$-0.559927\pi$
$659$	375.622	−	216.866i	0.569988	−	0.329083i	0.757145	+	0.653247i	$0.226594\pi$
$660$		0			0
$661$	1096.30			1.65855			0.829275	−	0.558840i	$-0.188753\pi$
$661$	1096.30			1.65855			0.829275	+	0.558840i	$0.188753\pi$
$662$		0			0
$663$	958.628	+	3.40665i	1.44589	+	0.00513823i
$664$		0			0
$665$	−63.4325	−	246.356i	−0.0953873	−	0.370460i
$666$		0			0
$667$	137.025	+	237.333i	0.205434	+	0.355822i
$668$		0			0
$669$	972.034	+	565.819i	1.45297	+	0.845769i
$670$		0			0
$671$		−	378.478i		−	0.564051i
$672$		0			0
$673$	200.797	−	347.791i	0.298362	−	0.516778i	−0.677400	−	0.735615i	$-0.736893\pi$
$673$	200.797	−	347.791i	0.298362	−	0.516778i	0.975761	+	0.218838i	$0.0702265\pi$
$674$		0			0
$675$	−109.611	+	61.7351i	−0.162386	+	0.0914594i
$676$		0			0
$677$	−937.807	−	541.443i	−1.38524	−	0.799769i	−0.392466	−	0.919767i	$-0.628378\pi$
$677$	−937.807	−	541.443i	−1.38524	−	0.799769i	−0.992774	+	0.119998i	$0.961711\pi$
$678$		0			0
$679$	−11.9088	+	20.6266i	−0.0175387	+	0.0303779i
$680$		0			0
$681$	257.546	+	449.766i	0.378188	+	0.660450i
$682$		0			0
$683$			1001.27i			1.46598i	0.680238	+	0.732991i	$0.261876\pi$
$683$			1001.27i			1.46598i	−0.680238	+	0.732991i	$0.738124\pi$
$684$		0			0
$685$	−940.663			−1.37323
$686$		0			0
$687$	3.03900	−	855.173i	0.00442358	−	1.24479i
$688$		0			0
$689$	−1278.43	−	738.104i	−1.85549	−	1.07127i
$690$		0			0
$691$	−210.261	+	364.182i	−0.304285	+	0.527036i	−0.977102	−	0.212772i	$-0.931751\pi$
$691$	−210.261	+	364.182i	−0.304285	+	0.527036i	0.672817	+	0.739809i	$0.265084\pi$
$692$		0			0
$693$	−311.832	−	183.004i	−0.449974	−	0.264075i
$694$		0			0
$695$	466.480	+	269.322i	0.671195	+	0.387514i
$696$		0			0
$697$	725.735			1.04123
$698$		0			0
$699$	−377.428	−	1.34126i	−0.539955	−	0.00191882i
$700$		0			0
$701$	−482.253	+	278.429i	−0.687950	+	0.397188i	−0.802844	−	0.596190i	$-0.796681\pi$
$701$	−482.253	+	278.429i	−0.687950	+	0.397188i	0.114893	+	0.993378i	$0.463347\pi$
$702$		0			0
$703$	107.499	−	386.033i	0.152914	−	0.549122i
$704$		0			0
$705$	0.112562	+	0.0655220i	0.000159662	+	9.29391e-5i
$706$		0			0
$707$			111.528i			0.157748i
$708$		0			0
$709$	−209.493	−	362.852i	−0.295476	−	0.511780i	0.679619	−	0.733565i	$-0.262145\pi$
$709$	−209.493	−	362.852i	−0.295476	−	0.511780i	−0.975096	+	0.221785i	$0.928812\pi$
$710$		0			0
$711$	285.622	+	502.932i	0.401718	+	0.707359i
$712$		0			0
$713$	110.048	−	63.5362i	0.154345	−	0.0891111i
$714$		0			0
$715$	−590.131	−	1022.14i	−0.825358	−	1.42956i
$716$		0			0
$717$	−178.309	−	0.633653i	−0.248688	−	0.000883755i
$718$		0			0
$719$	322.130	−	185.982i	0.448025	−	0.258667i	−0.258971	−	0.965885i	$-0.583383\pi$
$719$	322.130	−	185.982i	0.448025	−	0.258667i	0.706996	+	0.707218i	$0.250050\pi$
$720$		0			0
$721$	−381.991			−0.529807
$722$		0			0
$723$	4.18381	−	1177.32i	0.00578673	−	1.62838i
$724$		0			0
$725$	−91.6228	−	52.8984i	−0.126376	−	0.0729634i
$726$		0			0
$727$	−1405.81			−1.93372			−0.966858	−	0.255315i	$-0.917821\pi$
$727$	−1405.81			−1.93372			−0.966858	+	0.255315i	$0.917821\pi$
$728$		0			0
$729$	−728.834	−	15.5425i	−0.999773	−	0.0213203i
$730$		0			0
$731$	−733.902	+	423.718i	−1.00397	+	0.579642i
$732$		0			0
$733$	199.608	+	345.732i	0.272317	+	0.471667i	0.969455	−	0.245270i	$-0.0788768\pi$
$733$	199.608	+	345.732i	0.272317	+	0.471667i	−0.697138	+	0.716937i	$0.745543\pi$
$734$		0			0
$735$	−273.540	+	469.921i	−0.372163	+	0.639348i
$736$		0			0
$737$	−526.119	−	303.755i	−0.713865	−	0.412150i
$738$		0			0
$739$	−277.002	−	479.782i	−0.374834	−	0.649231i	0.615468	−	0.788162i	$-0.288967\pi$
$739$	−277.002	−	479.782i	−0.374834	−	0.649231i	−0.990302	+	0.138930i	$0.955634\pi$
$740$		0			0
$741$	−789.758	+	768.958i	−1.06580	+	1.03773i
$742$		0			0
$743$	−107.182	−	61.8818i	−0.144256	−	0.0832865i	0.426135	−	0.904660i	$-0.359875\pi$
$743$	−107.182	−	61.8818i	−0.144256	−	0.0832865i	−0.570391	+	0.821373i	$0.693208\pi$
$744$		0			0
$745$	103.764	+	179.724i	0.139280	+	0.241240i
$746$		0			0
$747$	2.20738	−	310.574i	0.00295499	−	0.415762i
$748$		0			0
$749$	−150.596	−	86.9469i	−0.201063	−	0.116084i
$750$		0			0
$751$	−265.237			−0.353179			−0.176589	−	0.984285i	$-0.556506\pi$
$751$	−265.237			−0.353179			−0.176589	+	0.984285i	$0.556506\pi$
$752$		0			0
$753$	−696.584	−	1216.48i	−0.925078	−	1.61551i
$754$		0			0
$755$	−308.129	+	177.898i	−0.408118	+	0.235627i
$756$		0			0
$757$	−494.951	−	857.280i	−0.653832	−	1.13247i	−0.982185	−	0.187915i	$-0.939827\pi$
$757$	−494.951	−	857.280i	−0.653832	−	1.13247i	0.328354	−	0.944555i	$-0.393506\pi$
$758$		0			0
$759$	−425.199	+	243.478i	−0.560209	+	0.320788i
$760$		0			0
$761$	−233.081	+	134.570i	−0.306283	+	0.176833i	−0.645262	−	0.763961i	$-0.723252\pi$
$761$	−233.081	+	134.570i	−0.306283	+	0.176833i	0.338979	+	0.940794i	$0.389918\pi$
$762$		0			0
$763$	−97.8286			−0.128216
$764$		0			0
$765$	−331.224	−	583.230i	−0.432972	−	0.762392i
$766$		0			0
$767$	−1388.48	−	801.638i	−1.81027	−	1.04516i
$768$		0			0
$769$	646.262			0.840393			0.420196	−	0.907433i	$-0.361961\pi$
$769$	646.262			0.840393			0.420196	+	0.907433i	$0.361961\pi$
$770$		0			0
$771$	−168.544	+	289.546i	−0.218605	+	0.375546i
$772$		0			0
$773$	−763.455	−	440.781i	−0.987652	−	0.570221i	−0.0830804	−	0.996543i	$-0.526476\pi$
$773$	−763.455	−	440.781i	−0.987652	−	0.570221i	−0.904572	+	0.426322i	$0.859809\pi$
$774$		0			0
$775$	−24.5282	+	42.4841i	−0.0316493	+	0.0548182i
$776$		0			0
$777$	163.002	−	93.3384i	0.209784	−	0.120127i
$778$		0			0
$779$	−595.815	+	584.262i	−0.764846	+	0.750015i
$780$		0			0
$781$	354.871			0.454380
$782$		0			0
$783$	−300.864	−	534.183i	−0.384245	−	0.682226i
$784$		0			0
$785$	41.0044	−	23.6739i	0.0522349	−	0.0301578i
$786$		0			0
$787$	430.142	+	745.028i	0.546559	+	0.946668i	0.998507	+	0.0546236i	$0.0173959\pi$
$787$	430.142	+	745.028i	0.546559	+	0.946668i	−0.451948	+	0.892044i	$0.649271\pi$
$788$		0			0
$789$	−405.648	+	696.872i	−0.514129	+	0.883235i
$790$		0			0
$791$			383.382i			0.484680i
$792$		0			0
$793$	−270.425	−	468.390i	−0.341015	−	0.590656i
$794$		0			0
$795$	−3.67037	+	1032.84i	−0.00461682	+	1.29917i
$796$		0			0
$797$	710.624	−	410.279i	0.891624	−	0.514779i	0.0171506	−	0.999853i	$-0.494541\pi$
$797$	710.624	−	410.279i	0.891624	−	0.514779i	0.874473	+	0.485074i	$0.161207\pi$
$798$		0			0
$799$	0.0795310	−	0.137752i	9.95382e−5	−	0.000172405i
$800$		0			0
$801$	−0.947258	+	133.277i	−0.00118259	+	0.166389i
$802$		0			0
$803$		−	1823.71i		−	2.27112i
$804$		0			0
$805$	−80.7963	−	139.943i	−0.100368	−	0.173843i
$806$		0			0
$807$	1547.04	+	5.49768i	1.91703	+	0.00681249i
$808$		0			0
$809$		−	498.718i		−	0.616463i	−0.951311	−	0.308231i	$-0.900263\pi$
$809$		−	498.718i		−	0.616463i	0.951311	−	0.308231i	$-0.0997371\pi$
$810$		0			0
$811$	389.161	−	674.047i	0.479854	−	0.831131i	−0.519879	−	0.854240i	$-0.674023\pi$
$811$	389.161	−	674.047i	0.479854	−	0.831131i	0.999733	+	0.0231087i	$0.00735637\pi$
$812$		0			0
$813$	−0.851544	+	239.624i	−0.00104741	+	0.294740i
$814$		0			0
$815$	1246.62	+	719.734i	1.52959	+	0.883109i
$816$		0			0
$817$	261.400	−	938.701i	0.319951	−	1.14896i
$818$		0			0
$819$	−516.669	−	3.67219i	−0.630853	−	0.00448374i
$820$		0			0
$821$	−934.046	+	539.272i	−1.13769	+	0.656847i	−0.945858	−	0.324580i	$-0.894777\pi$
$821$	−934.046	+	539.272i	−1.13769	+	0.656847i	−0.191834	+	0.981427i	$0.561444\pi$
$822$		0			0
$823$	398.592			0.484316			0.242158	−	0.970237i	$-0.422145\pi$
$823$	398.592			0.484316			0.242158	+	0.970237i	$0.422145\pi$
$824$		0			0
$825$	95.1592	−	163.476i	0.115344	−	0.198153i
$826$		0			0
$827$	345.075	+	199.229i	0.417261	+	0.240906i	0.693905	−	0.720067i	$-0.255889\pi$
$827$	345.075	+	199.229i	0.417261	+	0.240906i	−0.276644	+	0.960973i	$0.589222\pi$
$828$		0			0
$829$	−104.139			−0.125620			−0.0628101	−	0.998025i	$-0.520006\pi$
$829$	−104.139			−0.125620			−0.0628101	+	0.998025i	$0.520006\pi$
$830$		0			0
$831$	−913.627	+	523.163i	−1.09943	+	0.629558i
$832$		0			0
$833$	575.083	+	332.024i	0.690376	+	0.398589i
$834$		0			0
$835$	−351.361	+	608.576i	−0.420792	+	0.728833i
$836$		0			0
$837$	−247.693	+	139.506i	−0.295929	+	0.166674i
$838$		0			0
$839$		−	1341.01i		−	1.59834i	−0.601103	−	0.799171i	$-0.705272\pi$
$839$		−	1341.01i		−	1.59834i	0.601103	−	0.799171i	$-0.294728\pi$
$840$		0			0
$841$	−162.701	+	281.807i	−0.193462	+	0.335086i
$842$		0			0
$843$	571.931	+	2.03245i	0.678447	+	0.00241098i
$844$		0			0
$845$	−800.561	−	462.204i	−0.947409	−	0.546987i
$846$		0			0
$847$	184.444			0.217762
$848$		0			0
$849$	893.986	−	511.916i	1.05299	−	0.602964i
$850$		0			0
$851$		−	254.543i		−	0.299111i
$852$		0			0
$853$	219.649			0.257502			0.128751	−	0.991677i	$-0.458903\pi$
$853$	219.649			0.257502			0.128751	+	0.991677i	$0.458903\pi$
$854$		0			0
$855$	741.464	+	212.165i	0.867210	+	0.248147i
$856$		0			0
$857$		−	1100.57i		−	1.28421i	−0.766617	−	0.642105i	$-0.778061\pi$
$857$		−	1100.57i		−	1.28421i	0.766617	−	0.642105i	$-0.221939\pi$
$858$		0			0
$859$	581.376			0.676805			0.338403	−	0.941001i	$-0.390113\pi$
$859$	581.376			0.676805			0.338403	+	0.941001i	$0.390113\pi$
$860$		0			0
$861$	−391.152	−	1.39003i	−0.454300	−	0.00161443i
$862$		0			0
$863$		−	329.877i		−	0.382245i	−0.981566	−	0.191122i	$-0.938787\pi$
$863$		−	329.877i		−	0.382245i	0.981566	−	0.191122i	$-0.0612128\pi$
$864$		0			0
$865$	490.536	−	849.633i	0.567094	−	0.982235i
$866$		0			0
$867$	41.5412	−	23.7874i	0.0479138	−	0.0274365i
$868$		0			0
$869$	−753.146	−	434.829i	−0.866681	−	0.500379i
$870$		0			0
$871$	−868.139			−0.996715
$872$		0			0
$873$	−35.6577	−	62.7874i	−0.0408450	−	0.0719214i
$874$		0			0
$875$	343.906	+	198.554i	0.393035	+	0.226919i
$876$		0			0
$877$	731.297	−	1266.64i	0.833862	−	1.44429i	−0.0610915	−	0.998132i	$-0.519458\pi$
$877$	731.297	−	1266.64i	0.833862	−	1.44429i	0.894954	−	0.446159i	$-0.147209\pi$
$878$		0			0
$879$	−1212.03	−	4.30717i	−1.37888	−	0.00490008i
$880$		0			0
$881$			1513.93i			1.71842i	0.511620	+	0.859212i	$0.329045\pi$
$881$			1513.93i			1.71842i	−0.511620	+	0.859212i	$0.670955\pi$
$882$		0			0
$883$	410.220	−	710.522i	0.464575	−	0.804668i	−0.534607	−	0.845101i	$-0.679540\pi$
$883$	410.220	−	710.522i	0.464575	−	0.804668i	0.999182	+	0.0404326i	$0.0128736\pi$
$884$		0			0
$885$	−3.98631	+	1121.75i	−0.00450431	+	1.26751i
$886$		0			0
$887$			523.093i			0.589732i	0.955539	+	0.294866i	$0.0952751\pi$
$887$			523.093i			0.589732i	−0.955539	+	0.294866i	$0.904725\pi$
$888$		0			0
$889$	231.192	+	400.437i	0.260059	+	0.450435i
$890$		0			0
$891$	956.976	−	534.520i	1.07405	−	0.599910i
$892$		0			0
$893$	0.0456052	+	0.177119i	5.10696e−5	+	0.000198341i
$894$		0			0
$895$	−175.139	+	303.350i	−0.195686	+	0.338938i
$896$		0			0
$897$	−352.243	+	605.126i	−0.392690	+	0.674611i
$898$		0			0
$899$	−207.045	−	119.537i	−0.230306	−	0.132967i
$900$		0			0
$901$	1261.38			1.39998
$902$		0			0
$903$	396.366	−	226.968i	0.438943	−	0.251348i
$904$		0			0
$905$	−532.884	+	307.661i	−0.588822	+	0.339957i
$906$		0			0
$907$	287.696			0.317195			0.158598	−	0.987343i	$-0.449303\pi$
$907$	287.696			0.317195			0.158598	+	0.987343i	$0.449303\pi$
$908$		0			0
$909$	−291.604	−	171.133i	−0.320797	−	0.188265i
$910$		0			0
$911$	−619.023	−	357.393i	−0.679498	−	0.392309i	0.120168	−	0.992754i	$-0.461657\pi$
$911$	−619.023	−	357.393i	−0.679498	−	0.392309i	−0.799666	+	0.600445i	$0.794990\pi$
$912$		0			0
$913$	233.498	+	404.430i	0.255748	+	0.442968i
$914$		0			0
$915$	−190.370	+	327.041i	−0.208055	+	0.357422i
$916$		0			0
$917$	151.287	−	87.3454i	0.164980	−	0.0952513i
$918$		0			0
$919$	1003.43			1.09187			0.545935	−	0.837827i	$-0.316175\pi$
$919$	1003.43			1.09187			0.545935	+	0.837827i	$0.316175\pi$
$920$		0			0
$921$	−0.234282	+	65.9268i	−0.000254378	+	0.0715817i
$922$		0			0
$923$	439.174	−	253.557i	0.475812	−	0.274710i
$924$		0			0
$925$	49.1333	+	85.1014i	0.0531171	+	0.0920015i
$926$		0			0
$927$	586.142	−	998.767i	0.632300	−	1.07742i
$928$		0			0
$929$			1418.77i			1.52721i	0.645686	+	0.763603i	$0.276572\pi$
$929$			1418.77i			1.52721i	−0.645686	+	0.763603i	$0.723428\pi$
$930$		0			0
$931$	−739.432	+	190.392i	−0.794235	+	0.204502i
$932$		0			0
$933$	−591.735	−	2.10283i	−0.634228	−	0.00225384i
$934$		0			0
$935$	873.392	+	504.253i	0.934109	+	0.539308i
$936$		0			0
$937$	−838.969	+	1453.14i	−0.895378	+	1.55084i	−0.0620422	+	0.998074i	$0.519761\pi$
$937$	−838.969	+	1453.14i	−0.895378	+	1.55084i	−0.833336	+	0.552767i	$0.813572\pi$
$938$		0			0
$939$	0.388212	−	109.243i	0.000413431	−	0.116339i
$940$		0			0
$941$		−	746.526i		−	0.793333i	−0.917963	−	0.396666i	$-0.870167\pi$
$941$		−	746.526i		−	0.793333i	0.917963	−	0.396666i	$-0.129833\pi$
$942$		0			0
$943$	−265.036	+	459.056i	−0.281057	+	0.486804i
$944$		0			0
$945$	177.404	+	314.980i	0.187729	+	0.333312i
$946$		0			0
$947$			421.184i			0.444756i	0.974961	+	0.222378i	$0.0713819\pi$
$947$			421.184i			0.444756i	−0.974961	+	0.222378i	$0.928618\pi$
$948$		0			0
$949$	−1303.05	−	2256.96i	−1.37308	−	2.37825i
$950$		0			0
$951$	−1554.41	−	5.52385i	−1.63450	−	0.00580846i
$952$		0			0
$953$	−1437.86	+	830.148i	−1.50877	+	0.871090i	−0.508824	+	0.860871i	$0.669919\pi$
$953$	−1437.86	+	830.148i	−1.50877	+	0.871090i	−0.999948	+	0.0102189i	$0.996747\pi$
$954$		0			0
$955$	564.424	+	977.611i	0.591020	+	1.02368i
$956$		0			0
$957$	796.695	+	463.755i	0.832492	+	0.484592i
$958$		0			0
$959$		−	619.179i		−	0.645650i
$960$		0			0
$961$	425.072	−	736.247i	0.442323	−	0.766126i
$962$		0			0
$963$	458.416	−	260.340i	0.476029	−	0.270343i
$964$		0			0
$965$	200.836	−	115.952i	0.208120	−	0.120158i
$966$		0			0
$967$	−479.939	+	831.279i	−0.496318	+	0.859648i	−0.999991	−	0.00424658i	$-0.998648\pi$
$967$	−479.939	+	831.279i	−0.496318	+	0.859648i	0.503673	+	0.863894i	$0.331982\pi$
$968$		0			0
$969$	255.891	−	906.442i	0.264078	−	0.935441i
$970$		0			0
$971$	408.229	−	235.691i	0.420421	−	0.242730i	−0.274836	−	0.961491i	$-0.588624\pi$
$971$	408.229	−	235.691i	0.420421	−	0.242730i	0.695257	+	0.718761i	$0.255290\pi$
$972$		0			0
$973$	−177.278	+	307.054i	−0.182197	+	0.315575i
$974$		0			0
$975$	0.960569	−	270.304i	0.000985199	−	0.277234i
$976$		0			0
$977$	−521.280	+	300.961i	−0.533552	+	0.308046i	−0.742462	−	0.669889i	$-0.766342\pi$
$977$	−521.280	+	300.961i	−0.533552	+	0.308046i	0.208910	+	0.977935i	$0.433009\pi$
$978$		0			0
$979$	−100.201	−	173.554i	−0.102351	−	0.177277i
$980$		0			0
$981$	150.112	−	255.786i	0.153020	−	0.260740i
$982$		0			0
$983$			1468.13i			1.49352i	0.665096	+	0.746758i	$0.268390\pi$
$983$			1468.13i			1.49352i	−0.665096	+	0.746758i	$0.731610\pi$
$984$		0			0
$985$	539.164	−	933.859i	0.547374	−	0.948080i
$986$		0			0
$987$	−0.0431290	+	0.0740923i	−4.36970e−5	+	7.50682e-5i
$988$		0			0
$989$		−	618.963i		−	0.625847i
$990$		0			0
$991$	−96.5775	−	167.277i	−0.0974546	−	0.168796i	0.813176	−	0.582018i	$-0.197737\pi$
$991$	−96.5775	−	167.277i	−0.0974546	−	0.168796i	−0.910630	+	0.413222i	$0.864403\pi$
$992$		0			0
$993$	740.624	−	424.097i	0.745845	−	0.427087i
$994$		0			0
$995$	1428.41	−	824.693i	1.43559	−	0.828837i
$996$		0			0
$997$	−454.248	−	786.781i	−0.455615	−	0.789148i	0.543108	−	0.839663i	$-0.317247\pi$
$997$	−454.248	−	786.781i	−0.455615	−	0.789148i	−0.998723	+	0.0505143i	$0.983914\pi$
$998$		0			0
$999$	−6.07072	+	569.413i	−0.00607679	+	0.569983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.be.a.425.8	yes	80
3.2	odd	2		2052.3.be.a.197.29		80
9.4	even	3		2052.3.m.a.881.29		80
9.5	odd	6		684.3.m.a.653.20	yes	80
19.11	even	3		684.3.m.a.353.20	✓	80
57.11	odd	6		2052.3.m.a.1493.12		80
171.49	even	3		2052.3.be.a.125.29		80
171.68	odd	6	inner	684.3.be.a.581.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.20	✓	80	19.11	even	3
684.3.m.a.653.20	yes	80	9.5	odd	6
684.3.be.a.425.8	yes	80	1.1	even	1	trivial
684.3.be.a.581.8	yes	80	171.68	odd	6	inner
2052.3.m.a.881.29		80	9.4	even	3
2052.3.m.a.1493.12		80	57.11	odd	6
2052.3.be.a.125.29		80	171.49	even	3
2052.3.be.a.197.29		80	3.2	odd	2

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59273 - 1.50922i) q^{3} +(-3.90584 - 2.25504i) q^{5} +(1.48435 - 2.57096i) q^{7} +(4.44449 + 7.82601i) q^{9} +O(q^{10})\)	\(q+(-2.59273 - 1.50922i) q^{3} +(-3.90584 - 2.25504i) q^{5} +(1.48435 - 2.57096i) q^{7} +(4.44449 + 7.82601i) q^{9} +(-11.7195 - 6.76627i) q^{11} -19.3382 q^{13} +(6.72342 + 11.7415i) q^{15} +(14.3102 - 8.26201i) q^{17} +(-5.09700 + 18.3036i) q^{19} +(-7.72866 + 4.42560i) q^{21} +12.0690i q^{23} +(-2.32963 - 4.03504i) q^{25} +(0.287840 - 26.9985i) q^{27} +(19.6646 - 11.3534i) q^{29} +(-5.26439 - 9.11820i) q^{31} +(20.1737 + 35.2305i) q^{33} +(-11.5952 + 6.69450i) q^{35} -21.0906 q^{37} +(50.1387 + 29.1856i) q^{39} +(38.0358 + 21.9600i) q^{41} -51.2851 q^{43} +(0.288488 - 40.5896i) q^{45} +(0.00833645 - 0.00481305i) q^{47} +(20.0934 + 34.8028i) q^{49} +(-49.5718 - 0.176162i) q^{51} +(66.1093 + 38.1682i) q^{53} +(30.5164 + 52.8559i) q^{55} +(40.8393 - 39.7637i) q^{57} +(71.7998 + 41.4536i) q^{59} +(13.9840 + 24.2210i) q^{61} +(26.7176 + 0.189893i) q^{63} +(75.5318 + 43.6083i) q^{65} +44.8925 q^{67} +(18.2149 - 31.2918i) q^{69} +(-22.7102 + 13.1117i) q^{71} +(67.3825 + 116.710i) q^{73} +(-0.0496722 + 13.9777i) q^{75} +(-34.7917 + 20.0870i) q^{77} +64.2642 q^{79} +(-41.4930 + 69.5653i) q^{81} +(-29.8857 - 17.2545i) q^{83} -74.5245 q^{85} +(-68.1199 - 0.242075i) q^{87} +(12.8249 + 7.40448i) q^{89} +(-28.7046 + 49.7177i) q^{91} +(-0.112247 + 31.5862i) q^{93} +(61.1832 - 59.9968i) q^{95} -8.02290 q^{97} +(0.865612 - 121.790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9	\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + q^7 + 4 * q^9 + 18 * q^11 + 10 * q^13 - 11 * q^15 + 9 * q^17 + 20 * q^19 - 30 * q^21 + 200 * q^25 + 25 * q^27 - 27 * q^29 - 8 * q^31 + 23 * q^33 + 22 * q^37 + 39 * q^39 - 54 * q^41 + 88 * q^43 - 196 * q^45 + 198 * q^47 - 267 * q^49 - 56 * q^51 + 36 * q^53 + 78 * q^57 + 171 * q^59 + 7 * q^61 + 82 * q^63 - 144 * q^65 + 154 * q^67 + 44 * q^69 + 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 + 34 * q^79 - 44 * q^81 - 171 * q^83 - 244 * q^87 - 216 * q^89 + 122 * q^91 - 104 * q^93 - 216 * q^95 + 16 * q^97 - 305 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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