LMFDB - Embedded newform 124.3.o.a.21.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			21.3
Character	$\chi$	$=$	124.21
Dual form			124.3.o.a.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0268627 + 0.00282338i) q^{3} +(-4.16141 - 7.20777i) q^{5} +(0.359013 + 0.0763106i) q^{7} +(-8.80261 + 1.87105i) q^{9} +O(q^{10})$	\(q+(-0.0268627 + 0.00282338i) q^{3} +(-4.16141 - 7.20777i) q^{5} +(0.359013 + 0.0763106i) q^{7} +(-8.80261 + 1.87105i) q^{9} +(-7.33727 - 6.60651i) q^{11} +(6.15947 - 13.8344i) q^{13} +(0.132137 + 0.181871i) q^{15} +(-3.02500 + 2.72373i) q^{17} +(27.6755 - 12.3219i) q^{19} +(-0.00985951 - 0.00103628i) q^{21} +(-8.65905 - 2.81349i) q^{23} +(-22.1346 + 38.3382i) q^{25} +(0.462377 - 0.150235i) q^{27} +(-15.4109 + 21.2112i) q^{29} +(9.16037 - 29.6157i) q^{31} +(0.215751 + 0.156753i) q^{33} +(-0.943971 - 2.90524i) q^{35} +(44.9064 + 25.9267i) q^{37} +(-0.126400 + 0.389019i) q^{39} +(-3.28694 + 31.2731i) q^{41} +(20.2731 + 45.5342i) q^{43} +(50.1174 + 55.6610i) q^{45} +(49.5686 - 36.0137i) q^{47} +(-44.6407 - 19.8753i) q^{49} +(0.0735696 - 0.0817073i) q^{51} +(-12.9955 - 61.1390i) q^{53} +(-17.0848 + 80.3777i) q^{55} +(-0.708648 + 0.409138i) q^{57} +(-6.01893 - 57.2663i) q^{59} +17.5916i q^{61} -3.30304 q^{63} +(-125.347 + 13.1745i) q^{65} +(-11.9566 - 20.7094i) q^{67} +(0.240549 + 0.0511302i) q^{69} +(101.756 - 21.6289i) q^{71} +(-80.1088 - 72.1302i) q^{73} +(0.486351 - 1.09236i) q^{75} +(-2.13003 - 2.93174i) q^{77} +(19.3551 - 17.4275i) q^{79} +(73.9792 - 32.9377i) q^{81} +(-51.4214 - 5.40461i) q^{83} +(32.2202 + 10.4690i) q^{85} +(0.354090 - 0.613301i) q^{87} +(68.1857 - 22.1549i) q^{89} +(3.26704 - 4.49669i) q^{91} +(-0.162456 + 0.821419i) q^{93} +(-203.983 - 148.202i) q^{95} +(-25.6322 - 78.8877i) q^{97} +(76.9483 + 44.4261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9	$ 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9 + 2 * q^11 - 18 * q^13 + 35 * q^15 + 25 * q^17 - 11 * q^19 + 54 * q^21 + 25 * q^23 - 75 * q^25 + 225 * q^27 + 20 * q^29 + 59 * q^31 - 303 * q^33 - 66 * q^35 - 222 * q^37 - 169 * q^39 + q^41 + 122 * q^43 + 54 * q^45 - 120 * q^47 - 118 * q^49 - 515 * q^51 + 61 * q^53 - 121 * q^55 - 201 * q^57 - 257 * q^59 - 158 * q^63 + 182 * q^65 - q^67 + 510 * q^69 + 459 * q^71 + 253 * q^73 + 651 * q^75 + 670 * q^77 + 385 * q^79 + 974 * q^81 + 375 * q^83 - 370 * q^85 - 344 * q^87 + 245 * q^89 + 960 * q^91 - 212 * q^93 - 851 * q^95 - 797 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{29}{30}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0268627	+	0.00282338i	−0.00895422	+	0.000941127i	−0.109005	−	0.994041i	$-0.534766\pi$
$3$	−0.0268627	+	0.00282338i	−0.00895422	+	0.000941127i	0.100050	+	0.994982i	$0.468100\pi$
$4$		0			0
$5$	−4.16141	−	7.20777i	−0.832281	−	1.44155i	−0.896225	−	0.443600i	$-0.853701\pi$
$5$	−4.16141	−	7.20777i	−0.832281	−	1.44155i	0.0639439	−	0.997953i	$-0.479632\pi$
$6$		0			0
$7$	0.359013	+	0.0763106i	0.0512876	+	0.0109015i	0.233484	−	0.972361i	$-0.424987\pi$
$7$	0.359013	+	0.0763106i	0.0512876	+	0.0109015i	−0.182196	+	0.983262i	$0.558321\pi$
$8$		0			0
$9$	−8.80261	+	1.87105i	−0.978068	+	0.207895i
$10$		0			0
$11$	−7.33727	−	6.60651i	−0.667025	−	0.600592i	0.264449	−	0.964400i	$-0.414810\pi$
$11$	−7.33727	−	6.60651i	−0.667025	−	0.600592i	−0.931474	+	0.363808i	$0.881477\pi$
$12$		0			0
$13$	6.15947	−	13.8344i	0.473805	−	1.06418i	−0.505690	−	0.862715i	$-0.668762\pi$
$13$	6.15947	−	13.8344i	0.473805	−	1.06418i	0.979495	−	0.201468i	$-0.0645713\pi$
$14$		0			0
$15$	0.132137	+	0.181871i	0.00880911	+	0.0121247i
$16$		0			0
$17$	−3.02500	+	2.72373i	−0.177941	+	0.160219i	−0.753289	−	0.657690i	$-0.771534\pi$
$17$	−3.02500	+	2.72373i	−0.177941	+	0.160219i	0.575347	+	0.817909i	$0.304867\pi$
$18$		0			0
$19$	27.6755	−	12.3219i	1.45661	−	0.648523i	0.482764	−	0.875750i	$-0.339633\pi$
$19$	27.6755	−	12.3219i	1.45661	−	0.648523i	0.973842	+	0.227228i	$0.0729662\pi$
$20$		0			0
$21$	−0.00985951	−	0.00103628i	−0.000469500	−	4.93465e-5i
$22$		0			0
$23$	−8.65905	−	2.81349i	−0.376480	−	0.122326i	0.114663	−	0.993404i	$-0.463421\pi$
$23$	−8.65905	−	2.81349i	−0.376480	−	0.122326i	−0.491144	+	0.871079i	$0.663421\pi$
$24$		0			0
$25$	−22.1346	+	38.3382i	−0.885384	+	1.53353i
$26$		0			0
$27$	0.462377	−	0.150235i	0.0171251	−	0.00556427i
$28$		0			0
$29$	−15.4109	+	21.2112i	−0.531409	+	0.731422i	−0.987344	−	0.158591i	$-0.949305\pi$
$29$	−15.4109	+	21.2112i	−0.531409	+	0.731422i	0.455935	+	0.890013i	$0.349305\pi$
$30$		0			0
$31$	9.16037	−	29.6157i	0.295496	−	0.955344i
$31$	9.16037	−	29.6157i	0.295496	−	0.955344i
$32$		0			0
$33$	0.215751	+	0.156753i	0.00653792	+	0.00475008i
$34$		0			0
$35$	−0.943971	−	2.90524i	−0.0269706	−	0.0830069i
$36$		0			0
$37$	44.9064	+	25.9267i	1.21369	+	0.700723i	0.963560	−	0.267491i	$-0.0861944\pi$
$37$	44.9064	+	25.9267i	1.21369	+	0.700723i	0.250127	+	0.968213i	$0.419528\pi$
$38$		0			0
$39$	−0.126400	+	0.389019i	−0.00324102	+	0.00997485i
$40$		0			0
$41$	−3.28694	+	31.2731i	−0.0801693	+	0.762760i	0.878405	+	0.477917i	$0.158608\pi$
$41$	−3.28694	+	31.2731i	−0.0801693	+	0.762760i	−0.958574	+	0.284843i	$0.908059\pi$
$42$		0			0
$43$	20.2731	+	45.5342i	0.471468	+	1.05893i	0.980200	+	0.198009i	$0.0634476\pi$
$43$	20.2731	+	45.5342i	0.471468	+	1.05893i	−0.508732	+	0.860925i	$0.669886\pi$
$44$		0			0
$45$	50.1174	+	55.6610i	1.11372	+	1.23691i
$46$		0			0
$47$	49.5686	−	36.0137i	1.05465	−	0.766249i	0.0815598	−	0.996668i	$-0.474010\pi$
$47$	49.5686	−	36.0137i	1.05465	−	0.766249i	0.973091	+	0.230420i	$0.0740099\pi$
$48$		0			0
$49$	−44.6407	−	19.8753i	−0.911034	−	0.405618i
$50$		0			0
$51$	0.0735696	−	0.0817073i	0.00144254	−	0.00160210i
$52$		0			0
$53$	−12.9955	−	61.1390i	−0.245198	−	1.15357i	−0.912595	−	0.408864i	$-0.865925\pi$
$53$	−12.9955	−	61.1390i	−0.245198	−	1.15357i	0.667397	−	0.744702i	$-0.267408\pi$
$54$		0			0
$55$	−17.0848	+	80.3777i	−0.310633	+	1.46141i
$56$		0			0
$57$	−0.708648	+	0.409138i	−0.0124324	+	0.00717787i
$58$		0			0
$59$	−6.01893	−	57.2663i	−0.102016	−	0.970615i	−0.919081	−	0.394069i	$-0.871067\pi$
$59$	−6.01893	−	57.2663i	−0.102016	−	0.970615i	0.817065	−	0.576546i	$-0.195600\pi$
$60$		0			0
$61$			17.5916i			0.288387i	0.989550	+	0.144194i	$0.0460588\pi$
$61$			17.5916i			0.288387i	−0.989550	+	0.144194i	$0.953941\pi$
$62$		0			0
$63$	−3.30304			−0.0524291
$64$		0			0
$65$	−125.347	+	13.1745i	−1.92842	+	0.202685i
$66$		0			0
$67$	−11.9566	−	20.7094i	−0.178456	−	0.309096i	0.762896	−	0.646522i	$-0.223777\pi$
$67$	−11.9566	−	20.7094i	−0.178456	−	0.309096i	−0.941352	+	0.337426i	$0.890444\pi$
$68$		0			0
$69$	0.240549	+	0.0511302i	0.00348621	+	0.000741017i
$70$		0			0
$71$	101.756	−	21.6289i	1.43318	−	0.304632i	0.575073	−	0.818102i	$-0.304973\pi$
$71$	101.756	−	21.6289i	1.43318	−	0.304632i	0.858108	+	0.513470i	$0.171640\pi$
$72$		0			0
$73$	−80.1088	−	72.1302i	−1.09738	−	0.988086i	−0.0974058	−	0.995245i	$-0.531054\pi$
$73$	−80.1088	−	72.1302i	−1.09738	−	0.988086i	−0.999974	+	0.00715918i	$0.997721\pi$
$74$		0			0
$75$	0.486351	−	1.09236i	0.00648468	−	0.0145648i
$76$		0			0
$77$	−2.13003	−	2.93174i	−0.0276627	−	0.0380745i
$78$		0			0
$79$	19.3551	−	17.4275i	0.245002	−	0.220601i	−0.537476	−	0.843279i	$-0.680622\pi$
$79$	19.3551	−	17.4275i	0.245002	−	0.220601i	0.782478	+	0.622678i	$0.213955\pi$
$80$		0			0
$81$	73.9792	−	32.9377i	0.913323	−	0.406638i
$82$		0			0
$83$	−51.4214	−	5.40461i	−0.619535	−	0.0651158i	−0.210439	−	0.977607i	$-0.567489\pi$
$83$	−51.4214	−	5.40461i	−0.619535	−	0.0651158i	−0.409096	+	0.912491i	$0.634156\pi$
$84$		0			0
$85$	32.2202	+	10.4690i	0.379062	+	0.123165i
$86$		0			0
$87$	0.354090	−	0.613301i	0.00407000	−	0.00704944i
$88$		0			0
$89$	68.1857	−	22.1549i	0.766131	−	0.248931i	0.100223	−	0.994965i	$-0.468044\pi$
$89$	68.1857	−	22.1549i	0.766131	−	0.248931i	0.665908	+	0.746034i	$0.268044\pi$
$90$		0			0
$91$	3.26704	−	4.49669i	0.0359015	−	0.0494142i
$92$		0			0
$93$	−0.162456	+	0.821419i	−0.00174683	+	0.00883246i
$94$		0			0
$95$	−203.983	−	148.202i	−2.14719	−	1.56002i
$96$		0			0
$97$	−25.6322	−	78.8877i	−0.264249	−	0.813275i	−0.991865	−	0.127291i	$-0.959372\pi$
$97$	−25.6322	−	78.8877i	−0.264249	−	0.813275i	0.727616	−	0.685984i	$-0.240628\pi$
$98$		0			0
$99$	76.9483	+	44.4261i	0.777256	+	0.448749i
$100$		0			0
$101$	−3.26893	+	10.0607i	−0.0323657	+	0.0996114i	−0.965934	−	0.258787i	$-0.916677\pi$
$101$	−3.26893	+	10.0607i	−0.0323657	+	0.0996114i	0.933569	+	0.358399i	$0.116677\pi$
$102$		0			0
$103$	−13.6992	+	130.339i	−0.133001	+	1.26542i	0.700799	+	0.713359i	$0.252827\pi$
$103$	−13.6992	+	130.339i	−0.133001	+	1.26542i	−0.833801	+	0.552066i	$0.813840\pi$
$104$		0			0
$105$	0.0335602	+	0.0753774i	0.000319621	+	0.000717880i
$106$		0			0
$107$	−120.622	−	133.964i	−1.12731	−	1.25200i	−0.964138	−	0.265403i	$-0.914495\pi$
$107$	−120.622	−	133.964i	−1.12731	−	1.25200i	−0.163170	−	0.986598i	$-0.552172\pi$
$108$		0			0
$109$	7.26438	−	5.27788i	0.0666457	−	0.0484209i	−0.553964	−	0.832541i	$-0.686885\pi$
$109$	7.26438	−	5.27788i	0.0666457	−	0.0484209i	0.620609	+	0.784120i	$0.286885\pi$
$110$		0			0
$111$	−1.27951	−	0.569673i	−0.0115271	−	0.00513219i
$112$		0			0
$113$	−37.7757	+	41.9541i	−0.334298	+	0.371276i	−0.886734	−	0.462280i	$-0.847032\pi$
$113$	−37.7757	+	41.9541i	−0.334298	+	0.371276i	0.552436	+	0.833555i	$0.313698\pi$
$114$		0			0
$115$	15.7548	+	74.1205i	0.136998	+	0.644526i
$116$		0			0
$117$	−28.3345	+	133.303i	−0.242175	+	1.13935i
$118$		0			0
$119$	−1.29387	+	0.747014i	−0.0108728	+	0.00627743i
$120$		0			0
$121$	−2.45834	−	23.3896i	−0.0203169	−	0.193302i
$122$		0			0
$123$		−	0.849360i		−	0.00690537i
$124$		0			0
$125$	160.374			1.28299
$126$		0			0
$127$	38.4789	−	4.04429i	0.302983	−	0.0318448i	0.0481830	−	0.998839i	$-0.484657\pi$
$127$	38.4789	−	4.04429i	0.302983	−	0.0318448i	0.254800	+	0.966994i	$0.417990\pi$
$128$		0			0
$129$	−0.673150	−	1.16593i	−0.00521822	−	0.00903822i
$130$		0			0
$131$	167.627	+	35.6302i	1.27960	+	0.271986i	0.797065	−	0.603893i	$-0.206385\pi$
$131$	167.627	+	35.6302i	1.27960	+	0.271986i	0.482530	+	0.875879i	$0.339718\pi$
$132$		0			0
$133$	10.8762	−	2.31180i	0.0817757	−	0.0173820i
$134$		0			0
$135$	−3.00700	−	2.70751i	−0.0222741	−	0.0200557i
$136$		0			0
$137$	12.0031	−	26.9594i	0.0876140	−	0.196784i	−0.864424	−	0.502763i	$-0.832317\pi$
$137$	12.0031	−	26.9594i	0.0876140	−	0.196784i	0.952038	+	0.305979i	$0.0989836\pi$
$138$		0			0
$139$	127.438	+	175.404i	0.916821	+	1.26190i	0.964783	+	0.263047i	$0.0847274\pi$
$139$	127.438	+	175.404i	0.916821	+	1.26190i	−0.0479620	+	0.998849i	$0.515273\pi$
$140$		0			0
$141$	−1.22986	+	1.10737i	−0.00872244	+	0.00785372i
$142$		0			0
$143$	−136.591	+	60.8141i	−0.955180	+	0.425273i
$144$		0			0
$145$	217.017	+	22.8094i	1.49667	+	0.157306i
$146$		0			0
$147$	1.25528	+	0.407866i	0.00853934	+	0.00277460i
$148$		0			0
$149$	−45.6561	+	79.0787i	−0.306417	+	0.530730i	−0.977576	−	0.210584i	$-0.932464\pi$
$149$	−45.6561	+	79.0787i	−0.306417	+	0.530730i	0.671159	+	0.741314i	$0.265797\pi$
$150$		0			0
$151$	41.6268	−	13.5254i	0.275674	−	0.0895720i	−0.167917	−	0.985801i	$-0.553704\pi$
$151$	41.6268	−	13.5254i	0.275674	−	0.0895720i	0.443592	+	0.896229i	$0.353704\pi$
$152$		0			0
$153$	21.5317	−	29.6359i	0.140730	−	0.193698i
$154$		0			0
$155$	−251.583	+	57.2170i	−1.62311	+	0.369142i
$156$		0			0
$157$	77.6519	+	56.4174i	0.494598	+	0.359346i	0.806950	−	0.590620i	$-0.201117\pi$
$157$	77.6519	+	56.4174i	0.494598	+	0.359346i	−0.312352	+	0.949966i	$0.601117\pi$
$158$		0			0
$159$	0.521712	+	1.60566i	0.00328121	+	0.0100985i
$160$		0			0
$161$	−2.89401	−	1.67086i	−0.0179752	−	0.0103780i
$162$		0			0
$163$	10.3873	−	31.9689i	0.0637259	−	0.196128i	−0.914124	−	0.405434i	$-0.867120\pi$
$163$	10.3873	−	31.9689i	0.0637259	−	0.196128i	0.977850	+	0.209306i	$0.0671204\pi$
$164$		0			0
$165$	0.232007	−	2.20740i	0.00140610	−	0.0133782i
$166$		0			0
$167$	119.950	+	269.412i	0.718263	+	1.61324i	0.787997	+	0.615679i	$0.211118\pi$
$167$	119.950	+	269.412i	0.718263	+	1.61324i	−0.0697340	+	0.997566i	$0.522215\pi$
$168$		0			0
$169$	−40.3681	−	44.8334i	−0.238865	−	0.265286i
$170$		0			0
$171$	−220.562	+	160.248i	−1.28984	+	0.937120i
$172$		0			0
$173$	−190.201	−	84.6828i	−1.09943	−	0.489496i	−0.224855	−	0.974392i	$-0.572191\pi$
$173$	−190.201	−	84.6828i	−1.09943	−	0.489496i	−0.874572	+	0.484896i	$0.838857\pi$
$174$		0			0
$175$	−10.8722	+	12.0748i	−0.0621270	+	0.0689990i
$176$		0			0
$177$	0.323369	+	1.52133i	0.00182694	+	0.00859509i
$178$		0			0
$179$	36.6076	−	172.225i	0.204512	−	0.962153i	−0.749412	−	0.662104i	$-0.769664\pi$
$179$	36.6076	−	172.225i	0.204512	−	0.962153i	0.953924	−	0.300049i	$-0.0970030\pi$
$180$		0			0
$181$	225.310	−	130.083i	1.24481	−	0.718691i	0.274739	−	0.961519i	$-0.411408\pi$
$181$	225.310	−	130.083i	1.24481	−	0.718691i	0.970069	+	0.242828i	$0.0780752\pi$
$182$		0			0
$183$	−0.0496678	−	0.472557i	−0.000271409	−	0.00258228i
$184$		0			0
$185$		−	431.567i		−	2.33279i
$186$		0			0
$187$	40.1896			0.214918
$188$		0			0
$189$	0.177464	−	0.0186522i	0.000938962	−	9.86889e-5i
$190$		0			0
$191$	5.72174	+	9.91035i	0.0299568	+	0.0518866i	0.880615	−	0.473832i	$-0.157130\pi$
$191$	5.72174	+	9.91035i	0.0299568	+	0.0518866i	−0.850658	+	0.525719i	$0.823796\pi$
$192$		0			0
$193$	−179.616	−	38.1787i	−0.930655	−	0.197817i	−0.282450	−	0.959282i	$-0.591147\pi$
$193$	−179.616	−	38.1787i	−0.930655	−	0.197817i	−0.648206	+	0.761465i	$0.724480\pi$
$194$		0			0
$195$	3.32996	−	0.707805i	0.0170767	−	0.00362977i
$196$		0			0
$197$	204.596	+	184.219i	1.03856	+	0.935123i	0.997947	−	0.0640522i	$-0.0204024\pi$
$197$	204.596	+	184.219i	1.03856	+	0.935123i	0.0406125	+	0.999175i	$0.487069\pi$
$198$		0			0
$199$	−144.955	+	325.575i	−0.728419	+	1.63606i	0.0424801	+	0.999097i	$0.486474\pi$
$199$	−144.955	+	325.575i	−0.728419	+	1.63606i	−0.770899	+	0.636958i	$0.780193\pi$
$200$		0			0
$201$	0.379656	+	0.522552i	0.00188884	+	0.00259976i
$202$		0			0
$203$	−7.15135	+	6.43910i	−0.0352283	+	0.0317197i
$204$		0			0
$205$	239.088	−	106.449i	1.16628	−	0.519262i
$206$		0			0
$207$	81.4864	+	8.56457i	0.393654	+	0.0413747i
$208$		0			0
$209$	−284.468	−	92.4292i	−1.36109	−	0.442245i
$210$		0			0
$211$	18.7811	−	32.5298i	0.0890098	−	0.154169i	−0.818083	−	0.575100i	$-0.804963\pi$
$211$	18.7811	−	32.5298i	0.0890098	−	0.154169i	0.907093	+	0.420931i	$0.138296\pi$
$212$		0			0
$213$	−2.67237	+	0.868305i	−0.0125463	+	0.00407655i
$214$		0			0
$215$	243.835	−	335.610i	1.13412	−	1.56098i
$216$		0			0
$217$	5.54868	−	9.93338i	0.0255700	−	0.0457760i
$218$		0			0
$219$	2.35559	+	1.71143i	0.0107561	+	0.00781476i
$220$		0			0
$221$	19.0487	+	58.6258i	0.0861931	+	0.265275i
$222$		0			0
$223$	−334.678	−	193.226i	−1.50080	−	0.866486i	−1.00000		0.000921617i	$-0.999707\pi$
$223$	−334.678	−	193.226i	−1.50080	−	0.866486i	−0.500798	−	0.865564i	$-0.666960\pi$
$224$		0			0
$225$	123.109	−	378.892i	0.547153	−	1.68396i
$226$		0			0
$227$	−14.1600	+	134.723i	−0.0623787	+	0.593494i	0.918029	+	0.396514i	$0.129780\pi$
$227$	−14.1600	+	134.723i	−0.0623787	+	0.593494i	−0.980407	+	0.196980i	$0.936887\pi$
$228$		0			0
$229$	−104.395	−	234.474i	−0.455871	−	1.02390i	−0.984554	−	0.175084i	$-0.943980\pi$
$229$	−104.395	−	234.474i	−0.455871	−	1.02390i	0.528682	−	0.848820i	$-0.322686\pi$
$230$		0			0
$231$	0.0654957	+	0.0727404i	0.000283531	+	0.000314893i
$232$		0			0
$233$	−351.966	+	255.718i	−1.51058	+	1.09750i	−0.544663	+	0.838655i	$0.683343\pi$
$233$	−351.966	+	255.718i	−1.51058	+	1.09750i	−0.965918	+	0.258847i	$0.916657\pi$
$234$		0			0
$235$	−465.853	−	207.411i	−1.98235	−	0.882601i
$236$		0			0
$237$	−0.470726	+	0.522795i	−0.00198619	+	0.00220588i
$238$		0			0
$239$	−47.2482	−	222.285i	−0.197691	−	0.930064i	−0.959379	−	0.282120i	$-0.908962\pi$
$239$	−47.2482	−	222.285i	−0.197691	−	0.930064i	0.761688	−	0.647944i	$-0.224371\pi$
$240$		0			0
$241$	−73.9431	+	347.875i	−0.306818	+	1.44346i	0.506800	+	0.862064i	$0.330828\pi$
$241$	−73.9431	+	347.875i	−0.306818	+	1.44346i	−0.813617	+	0.581401i	$0.802505\pi$
$242$		0			0
$243$	−5.68362	+	3.28144i	−0.0233894	+	0.0135039i
$244$		0			0
$245$	42.5114	+	404.469i	0.173516	+	1.65089i
$246$		0			0
$247$		−	458.770i		−	1.85737i
$248$		0			0
$249$	1.39658			0.00560874
$250$		0			0
$251$	331.559	−	34.8482i	1.32095	−	0.138838i	0.582327	−	0.812955i	$-0.302142\pi$
$251$	331.559	−	34.8482i	1.32095	−	0.138838i	0.738625	+	0.674117i	$0.235476\pi$
$252$		0			0
$253$	44.9464	+	77.8495i	0.177654	+	0.307705i
$254$		0			0
$255$	−0.895080	−	0.190255i	−0.00351012	−	0.000746098i
$256$		0			0
$257$	−155.248	+	32.9989i	−0.604076	+	0.128400i	−0.499789	−	0.866147i	$-0.666589\pi$
$257$	−155.248	+	32.9989i	−0.604076	+	0.128400i	−0.104287	+	0.994547i	$0.533256\pi$
$258$		0			0
$259$	14.1435	+	12.7349i	0.0546082	+	0.0491694i
$260$		0			0
$261$	95.9686	−	215.549i	0.367696	−	0.825858i
$262$		0			0
$263$	116.692	+	160.612i	0.443694	+	0.610693i	0.971028	−	0.238965i	$-0.0768083\pi$
$263$	116.692	+	160.612i	0.443694	+	0.610693i	−0.527334	+	0.849658i	$0.676808\pi$
$264$		0			0
$265$	−386.596	+	348.093i	−1.45885	+	1.31356i
$266$		0			0
$267$	−1.76910	+	0.787653i	−0.00662583	+	0.00295001i
$268$		0			0
$269$	462.080	+	48.5666i	1.71777	+	0.180545i	0.911583	−	0.411116i	$-0.134861\pi$
$269$	462.080	+	48.5666i	1.71777	+	0.180545i	0.806187	+	0.591661i	$0.201528\pi$
$270$		0			0
$271$	126.761	+	41.1872i	0.467753	+	0.151982i	0.533404	−	0.845860i	$-0.320912\pi$
$271$	126.761	+	41.1872i	0.467753	+	0.151982i	−0.0656511	+	0.997843i	$0.520912\pi$
$272$		0			0
$273$	−0.0750655	+	0.130017i	−0.000274965	+	0.000476254i
$274$		0			0
$275$	415.690	−	135.066i	1.51160	−	0.491148i
$276$		0			0
$277$	254.950	−	350.908i	0.920396	−	1.26682i	−0.0430936	−	0.999071i	$-0.513721\pi$
$277$	254.950	−	350.908i	0.920396	−	1.26682i	0.963490	−	0.267746i	$-0.0862786\pi$
$278$		0			0
$279$	−25.2227	+	277.835i	−0.0904039	+	0.995824i
$280$		0			0
$281$	121.253	+	88.0953i	0.431504	+	0.313506i	0.782250	−	0.622964i	$-0.214072\pi$
$281$	121.253	+	88.0953i	0.431504	+	0.313506i	−0.350746	+	0.936471i	$0.614072\pi$
$282$		0			0
$283$	−60.0198	−	184.722i	−0.212084	−	0.652728i	−0.999348	−	0.0361112i	$-0.988503\pi$
$283$	−60.0198	−	184.722i	−0.212084	−	0.652728i	0.787264	−	0.616616i	$-0.211497\pi$
$284$		0			0
$285$	5.89795	+	3.40518i	0.0206946	+	0.0119480i
$286$		0			0
$287$	−3.56653	+	10.9766i	−0.0124269	+	0.0382461i
$288$		0			0
$289$	−28.4768	+	270.938i	−0.0985355	+	0.937503i
$290$		0			0
$291$	0.911278	+	2.04676i	0.00313154	+	0.00703356i
$292$		0			0
$293$	34.4741	+	38.2874i	0.117659	+	0.130674i	0.799097	−	0.601203i	$-0.205312\pi$
$293$	34.4741	+	38.2874i	0.117659	+	0.130674i	−0.681437	+	0.731876i	$0.738645\pi$
$294$		0			0
$295$	−387.715	+	281.691i	−1.31429	+	0.954886i
$296$		0			0
$297$	−4.38512	−	1.95238i	−0.0147647	−	0.00657367i
$298$		0			0
$299$	−92.2581	+	102.463i	−0.308555	+	0.342685i
$300$		0			0
$301$	3.80358	+	17.8944i	0.0126365	+	0.0594499i
$302$		0			0
$303$	0.0594070	−	0.279488i	0.000196063	−	0.000922402i
$304$		0			0
$305$	126.796	−	73.2058i	0.415725	−	0.240019i
$306$		0			0
$307$	26.4548	+	251.701i	0.0861720	+	0.819872i	0.949191	+	0.314701i	$0.101904\pi$
$307$	26.4548	+	251.701i	0.0861720	+	0.819872i	−0.863019	+	0.505172i	$0.831429\pi$
$308$		0			0
$309$		−	3.53992i		−	0.0114561i
$310$		0			0
$311$	410.913			1.32126			0.660632	−	0.750710i	$-0.270288\pi$
$311$	410.913			1.32126			0.660632	+	0.750710i	$0.270288\pi$
$312$		0			0
$313$	−475.930	+	50.0222i	−1.52054	+	0.159815i	−0.827658	−	0.561233i	$-0.810327\pi$
$313$	−475.930	+	50.0222i	−1.52054	+	0.159815i	−0.692884	+	0.721049i	$0.743660\pi$
$314$		0			0
$315$	13.7453	+	23.8075i	0.0436358	+	0.0755794i
$316$		0			0
$317$	−344.321	−	73.1877i	−1.08619	−	0.230876i	−0.370173	−	0.928963i	$-0.620702\pi$
$317$	−344.321	−	73.1877i	−1.08619	−	0.230876i	−0.716013	+	0.698087i	$0.754035\pi$
$318$		0			0
$319$	253.206	−	53.8206i	0.793750	−	0.168717i
$320$		0			0
$321$	3.61846	+	3.25807i	0.0112724	+	0.0101498i
$322$		0			0
$323$	−50.1570	+	112.654i	−0.155285	+	0.348775i
$324$		0			0
$325$	394.049	+	542.362i	1.21246	+	1.66880i
$326$		0			0
$327$	−0.180239	+	0.162288i	−0.000551190	+	0.000496294i
$328$		0			0
$329$	20.5440	−	9.14678i	0.0624438	−	0.0278018i
$330$		0			0
$331$	461.930	+	48.5508i	1.39556	+	0.146679i	0.772261	−	0.635305i	$-0.219126\pi$
$331$	461.930	+	48.5508i	1.39556	+	0.146679i	0.623298	+	0.781984i	$0.285792\pi$
$332$		0			0
$333$	−443.804	−	144.201i	−1.33275	−	0.433035i
$334$		0			0
$335$	−99.5124	+	172.361i	−0.297052	+	0.514509i
$336$		0			0
$337$	−125.593	+	40.8075i	−0.372679	+	0.121091i	−0.489367	−	0.872078i	$-0.662772\pi$
$337$	−125.593	+	40.8075i	−0.372679	+	0.121091i	0.116688	+	0.993169i	$0.462772\pi$
$338$		0			0
$339$	0.896303	−	1.23365i	0.00264396	−	0.00363910i
$340$		0			0
$341$	−262.868	+	156.780i	−0.770875	+	0.459766i
$342$		0			0
$343$	−29.0598	−	21.1132i	−0.0847224	−	0.0615544i
$344$		0			0
$345$	−0.632486	−	1.94659i	−0.00183329	−	0.00564229i
$346$		0			0
$347$	577.310	+	333.310i	1.66372	+	0.960548i	0.970916	+	0.239420i	$0.0769572\pi$
$347$	577.310	+	333.310i	1.66372	+	0.960548i	0.692802	+	0.721128i	$0.256376\pi$
$348$		0			0
$349$	107.209	−	329.954i	0.307188	−	0.945427i	−0.671664	−	0.740856i	$-0.734420\pi$
$349$	107.209	−	329.954i	0.307188	−	0.945427i	0.978852	−	0.204571i	$-0.0655799\pi$
$350$		0			0
$351$	0.769580	−	7.32207i	0.00219254	−	0.0208606i
$352$		0			0
$353$	4.42700	+	9.94321i	0.0125411	+	0.0281677i	0.919707	−	0.392604i	$-0.128426\pi$
$353$	4.42700	+	9.94321i	0.0125411	+	0.0281677i	−0.907166	+	0.420772i	$0.861759\pi$
$354$		0			0
$355$	−579.343	−	643.426i	−1.63195	−	1.81247i
$356$		0			0
$357$	0.0326476	−	0.0237199i	9.14498e−5	−	6.64422e-5i
$358$		0			0
$359$	−101.134	−	45.0276i	−0.281709	−	0.125425i	0.261018	−	0.965334i	$-0.415942\pi$
$359$	−101.134	−	45.0276i	−0.281709	−	0.125425i	−0.542728	+	0.839909i	$0.682608\pi$
$360$		0			0
$361$	372.548	−	413.756i	1.03199	−	1.14614i
$362$		0			0
$363$	0.132075	+	0.621365i	0.000363844	+	0.00171175i
$364$		0			0
$365$	−186.533	+	877.568i	−0.511049	+	2.40430i
$366$		0			0
$367$	537.146	−	310.121i	1.46361	−	0.845017i	0.464436	−	0.885607i	$-0.346257\pi$
$367$	537.146	−	310.121i	1.46361	−	0.845017i	0.999176	+	0.0405899i	$0.0129237\pi$
$368$		0			0
$369$	−29.5801	−	281.435i	−0.0801628	−	0.762698i
$370$		0			0
$371$		−	22.9414i		−	0.0618366i
$372$		0			0
$373$	142.814			0.382878			0.191439	−	0.981504i	$-0.438685\pi$
$373$	142.814			0.382878			0.191439	+	0.981504i	$0.438685\pi$
$374$		0			0
$375$	−4.30807	+	0.452796i	−0.0114882	+	0.00120746i
$376$		0			0
$377$	198.522	+	343.850i	0.526583	+	0.912069i
$378$		0			0
$379$	319.551	+	67.9226i	0.843142	+	0.179215i	0.609182	−	0.793031i	$-0.291498\pi$
$379$	319.551	+	67.9226i	0.843142	+	0.179215i	0.233960	+	0.972246i	$0.424831\pi$
$380$		0			0
$381$	−1.02223	+	0.217281i	−0.00268301	+	0.000570291i
$382$		0			0
$383$	−61.5085	−	55.3825i	−0.160597	−	0.144602i	0.584915	−	0.811095i	$-0.301128\pi$
$383$	−61.5085	−	55.3825i	−0.160597	−	0.144602i	−0.745511	+	0.666493i	$0.767795\pi$
$384$		0			0
$385$	−12.2673	+	27.5529i	−0.0318632	+	0.0715660i
$386$		0			0
$387$	−263.653	−	362.888i	−0.681274	−	0.937694i
$388$		0			0
$389$	80.8324	−	72.7818i	0.207795	−	0.187100i	−0.558661	−	0.829396i	$-0.688685\pi$
$389$	80.8324	−	72.7818i	0.207795	−	0.187100i	0.766456	+	0.642296i	$0.222018\pi$
$390$		0			0
$391$	33.8568	−	15.0740i	0.0865904	−	0.0385525i
$392$		0			0
$393$	−4.60351	−	0.483848i	−0.0117138	−	0.00123117i
$394$		0			0
$395$	−206.158	−	66.9847i	−0.521918	−	0.169581i
$396$		0			0
$397$	−72.9836	+	126.411i	−0.183838	+	0.318416i	−0.943184	−	0.332270i	$-0.892185\pi$
$397$	−72.9836	+	126.411i	−0.183838	+	0.318416i	0.759347	+	0.650686i	$0.225519\pi$
$398$		0			0
$399$	−0.285636	+	0.0928087i	−0.000715879	+	0.000232603i
$400$		0			0
$401$	−55.1468	+	75.9031i	−0.137523	+	0.189285i	−0.872224	−	0.489107i	$-0.837323\pi$
$401$	−55.1468	+	75.9031i	−0.137523	+	0.189285i	0.734700	+	0.678392i	$0.237323\pi$
$402$		0			0
$403$	−353.292	−	309.145i	−0.876654	−	0.767109i
$404$		0			0
$405$	−545.264	−	396.158i	−1.34633	−	0.978167i
$406$		0			0
$407$	−158.205	−	486.906i	−0.388711	−	1.19633i
$408$		0			0
$409$	−121.790	−	70.3157i	−0.297776	−	0.171921i	0.343667	−	0.939091i	$-0.388331\pi$
$409$	−121.790	−	70.3157i	−0.297776	−	0.171921i	−0.641443	+	0.767170i	$0.721664\pi$
$410$		0			0
$411$	−0.246319	+	0.758092i	−0.000599316	+	0.00184451i
$412$		0			0
$413$	2.20915	−	21.0187i	0.00534903	−	0.0508926i
$414$		0			0
$415$	175.030	+	393.124i	0.421760	+	0.947288i
$416$		0			0
$417$	−3.91856	−	4.35200i	−0.00939702	−	0.0104365i
$418$		0			0
$419$	−66.0004	+	47.9521i	−0.157519	+	0.114444i	−0.663753	−	0.747952i	$-0.731037\pi$
$419$	−66.0004	+	47.9521i	−0.157519	+	0.114444i	0.506234	+	0.862396i	$0.331037\pi$
$420$		0			0
$421$	−735.012	−	327.249i	−1.74587	−	0.777313i	−0.992857	−	0.119310i	$-0.961932\pi$
$421$	−735.012	−	327.249i	−1.74587	−	0.777313i	−0.753016	−	0.658003i	$-0.771402\pi$
$422$		0			0
$423$	−368.950	+	409.760i	−0.872222	+	0.968700i
$424$		0			0
$425$	−37.4656	−	176.262i	−0.0881544	−	0.414734i
$426$		0			0
$427$	−1.34243	+	6.31562i	−0.00314386	+	0.0147907i
$428$		0			0
$429$	3.49749	−	2.01928i	0.00815266	−	0.00470694i
$430$		0			0
$431$	−56.0929	−	533.688i	−0.130146	−	1.23825i	−0.843376	−	0.537325i	$-0.819435\pi$
$431$	−56.0929	−	533.688i	−0.130146	−	1.23825i	0.713230	−	0.700930i	$-0.247232\pi$
$432$		0			0
$433$		−	36.4789i		−	0.0842469i	−0.999112	−	0.0421234i	$-0.986588\pi$
$433$		−	36.4789i		−	0.0842469i	0.999112	−	0.0421234i	$-0.0134123\pi$
$434$		0			0
$435$	−5.89404			−0.0135495
$436$		0			0
$437$	−274.311	+	28.8313i	−0.627714	+	0.0659754i
$438$		0			0
$439$	−319.611	−	553.582i	−0.728043	−	1.26101i	−0.957709	−	0.287738i	$-0.907097\pi$
$439$	−319.611	−	553.582i	−0.728043	−	1.26101i	0.229667	−	0.973269i	$-0.426236\pi$
$440$		0			0
$441$	430.142	+	91.4296i	0.975379	+	0.207323i
$442$		0			0
$443$	648.294	−	137.799i	1.46342	−	0.311059i	0.593731	−	0.804664i	$-0.297654\pi$
$443$	648.294	−	137.799i	1.46342	−	0.311059i	0.869686	+	0.493605i	$0.164321\pi$
$444$		0			0
$445$	−443.436	−	399.271i	−0.996484	−	0.897238i
$446$		0			0
$447$	1.00318	−	2.25317i	0.00224424	−	0.00504065i
$448$		0			0
$449$	427.827	+	588.854i	0.952844	+	1.31148i	0.950252	+	0.311481i	$0.100825\pi$
$449$	427.827	+	588.854i	0.952844	+	1.31148i	0.00259215	+	0.999997i	$0.499175\pi$
$450$		0			0
$451$	230.724	−	207.744i	0.511582	−	0.460631i
$452$		0			0
$453$	−1.08002	+	0.480856i	−0.00238415	+	0.00106149i
$454$		0			0
$455$	−46.0066	−	4.83549i	−0.101113	−	0.0106274i
$456$		0			0
$457$	686.995	+	223.218i	1.50327	+	0.488442i	0.940970	−	0.338490i	$-0.109916\pi$
$457$	686.995	+	223.218i	1.50327	+	0.488442i	0.562301	+	0.826932i	$0.309916\pi$
$458$		0			0
$459$	−0.989492	+	1.71385i	−0.00215576	+	0.00373388i
$460$		0			0
$461$	402.607	−	130.815i	0.873335	−	0.283764i	0.162148	−	0.986767i	$-0.448158\pi$
$461$	402.607	−	130.815i	0.873335	−	0.283764i	0.711187	+	0.703003i	$0.248158\pi$
$462$		0			0
$463$	47.7486	−	65.7203i	0.103129	−	0.141944i	−0.754334	−	0.656491i	$-0.772040\pi$
$463$	47.7486	−	65.7203i	0.103129	−	0.141944i	0.857462	+	0.514547i	$0.172040\pi$
$464$		0			0
$465$	6.59664	−	2.24731i	0.0141863	−	0.00483294i
$466$		0			0
$467$	−567.516	−	412.325i	−1.21524	−	0.882922i	−0.219542	−	0.975603i	$-0.570456\pi$
$467$	−567.516	−	412.325i	−1.21524	−	0.882922i	−0.995696	+	0.0926807i	$0.970456\pi$
$468$		0			0
$469$	−2.71222	−	8.34737i	−0.00578299	−	0.0177982i
$470$		0			0
$471$	−2.24522	−	1.29628i	−0.00476693	−	0.00275219i
$472$		0			0
$473$	152.073	−	468.031i	0.321506	−	0.989495i
$474$		0			0
$475$	−140.185	+	1333.77i	−0.295126	+	2.80794i
$476$		0			0
$477$	228.789	+	513.868i	0.479641	+	1.07729i
$478$		0			0
$479$	394.568	+	438.212i	0.823733	+	0.914849i	0.997552	−	0.0699291i	$-0.0222773\pi$
$479$	394.568	+	438.212i	0.823733	+	0.914849i	−0.173819	+	0.984778i	$0.555611\pi$
$480$		0			0
$481$	635.280	−	461.558i	1.32075	−	0.959580i
$482$		0			0
$483$	0.0824583	+	0.0367128i	0.000170721	+	7.60100e-5i
$484$		0			0
$485$	−461.938	+	513.035i	−0.952450	+	1.05780i
$486$		0			0
$487$	37.7510	+	177.604i	0.0775174	+	0.364691i	0.999760	−	0.0219217i	$-0.00697845\pi$
$487$	37.7510	+	177.604i	0.0775174	+	0.364691i	−0.922242	+	0.386612i	$0.873645\pi$
$488$		0			0
$489$	−0.188771	+	0.888097i	−0.000386035	+	0.00181615i
$490$		0			0
$491$	−588.260	+	339.632i	−1.19809	+	0.691715i	−0.960128	−	0.279560i	$-0.909811\pi$
$491$	−588.260	+	339.632i	−1.19809	+	0.691715i	−0.237958	+	0.971276i	$0.576478\pi$
$492$		0			0
$493$	−11.1557	−	106.139i	−0.0226281	−	0.215292i
$494$		0			0
$495$		−	739.501i		−	1.49394i
$496$		0			0
$497$	38.1822			0.0768254
$498$		0			0
$499$	−473.274	+	49.7431i	−0.948444	+	0.0996855i	−0.566102	−	0.824335i	$-0.691549\pi$
$499$	−473.274	+	49.7431i	−0.948444	+	0.0996855i	−0.382342	+	0.924021i	$0.624883\pi$
$500$		0			0
$501$	−3.98283	−	6.89846i	−0.00794975	−	0.0137694i
$502$		0			0
$503$	23.5556	+	5.00689i	0.0468302	+	0.00995406i	0.231267	−	0.972890i	$-0.425713\pi$
$503$	23.5556	+	5.00689i	0.0468302	+	0.00995406i	−0.184437	+	0.982844i	$0.559046\pi$
$504$		0			0
$505$	86.1189	−	18.3051i	0.170532	−	0.0362478i
$506$		0			0
$507$	1.21098	+	1.09037i	0.00238852	+	0.00215063i
$508$		0			0
$509$	127.152	−	285.589i	0.249808	−	0.561078i	−0.744500	−	0.667622i	$-0.767312\pi$
$509$	127.152	−	285.589i	0.249808	−	0.561078i	0.994308	+	0.106545i	$0.0339787\pi$
$510$		0			0
$511$	−23.2558	−	32.0089i	−0.0455104	−	0.0626396i
$512$		0			0
$513$	10.9453	−	9.85521i	0.0213359	−	0.0192109i
$514$		0			0
$515$	996.459	−	443.652i	1.93487	−	0.861460i
$516$		0			0
$517$	−601.623	−	63.2332i	−1.16368	−	0.122308i
$518$		0			0
$519$	5.34839	+	1.73780i	0.0103052	+	0.00334836i
$520$		0			0
$521$	−223.018	+	386.279i	−0.428058	+	0.741418i	−0.996701	−	0.0811668i	$-0.974135\pi$
$521$	−223.018	+	386.279i	−0.428058	+	0.741418i	0.568643	+	0.822585i	$0.307469\pi$
$522$		0			0
$523$	−105.325	+	34.2222i	−0.201386	+	0.0654343i	−0.407973	−	0.912994i	$-0.633764\pi$
$523$	−105.325	+	34.2222i	−0.201386	+	0.0654343i	0.206587	+	0.978428i	$0.433764\pi$
$524$		0			0
$525$	0.257965	−	0.355059i	0.000491362	−	0.000676302i
$526$		0			0
$527$	52.9548	+	114.538i	0.100483	+	0.217339i
$528$		0			0
$529$	−360.907	−	262.214i	−0.682243	−	0.495679i
$530$		0			0
$531$	160.131	+	492.831i	0.301564	+	0.928119i
$532$		0			0
$533$	412.399	+	238.099i	0.773732	+	0.446714i
$534$		0			0
$535$	−463.626	+	1426.89i	−0.866590	+	2.66709i
$536$		0			0
$537$	−0.497121	+	4.72979i	−0.000925737	+	0.00880780i
$538$		0			0
$539$	196.234	+	440.750i	0.364071	+	0.817717i
$540$		0			0
$541$	46.3918	+	51.5233i	0.0857518	+	0.0952371i	0.784494	−	0.620137i	$-0.212923\pi$
$541$	46.3918	+	51.5233i	0.0857518	+	0.0952371i	−0.698742	+	0.715374i	$0.746256\pi$
$542$		0			0
$543$	−5.68516	+	4.13051i	−0.0104699	+	0.00760684i
$544$		0			0
$545$	−68.2718	−	30.3966i	−0.125269	−	0.0557735i
$546$		0			0
$547$	187.024	−	207.711i	0.341908	−	0.379728i	−0.547528	−	0.836788i	$-0.684431\pi$
$547$	187.024	−	207.711i	0.341908	−	0.379728i	0.889436	+	0.457060i	$0.151098\pi$
$548$		0			0
$549$	−32.9148	−	154.852i	−0.0599542	−	0.282062i
$550$		0			0
$551$	−165.140	+	776.924i	−0.299710	+	1.41003i
$552$		0			0
$553$	8.27865	−	4.77968i	0.0149704	−	0.00864319i
$554$		0			0
$555$	1.21848	+	11.5930i	0.00219545	+	0.0208883i
$556$		0			0
$557$		−	209.491i		−	0.376106i	−0.982159	−	0.188053i	$-0.939782\pi$
$557$		−	209.491i		−	0.376106i	0.982159	−	0.188053i	$-0.0602177\pi$
$558$		0			0
$559$	754.809			1.35028
$560$		0			0
$561$	−1.07960	+	0.113471i	−0.00192442	+	0.000202265i
$562$		0			0
$563$	−173.453	−	300.429i	−0.308087	−	0.533622i	0.669857	−	0.742490i	$-0.266355\pi$
$563$	−173.453	−	300.429i	−0.308087	−	0.533622i	−0.977944	+	0.208868i	$0.933022\pi$
$564$		0			0
$565$	459.596	+	97.6900i	0.813443	+	0.172903i
$566$		0			0
$567$	29.0730	−	6.17966i	0.0512751	−	0.0108989i
$568$		0			0
$569$	−4.45445	−	4.01080i	−0.00782855	−	0.00704886i	0.665207	−	0.746659i	$-0.268343\pi$
$569$	−4.45445	−	4.01080i	−0.00782855	−	0.00704886i	−0.673036	+	0.739610i	$0.735010\pi$
$570$		0			0
$571$	−319.554	+	717.729i	−0.559639	+	1.25697i	0.383184	+	0.923672i	$0.374828\pi$
$571$	−319.554	+	717.729i	−0.559639	+	1.25697i	−0.942822	+	0.333296i	$0.891839\pi$
$572$		0			0
$573$	−0.181682	−	0.250064i	−0.000317071	−	0.000436411i
$574$		0			0
$575$	299.529	−	269.697i	0.520920	−	0.469038i
$576$		0			0
$577$	575.342	−	256.159i	0.997127	−	0.443949i	0.157738	−	0.987481i	$-0.449580\pi$
$577$	575.342	−	256.159i	0.997127	−	0.443949i	0.839389	+	0.543532i	$0.182913\pi$
$578$		0			0
$579$	4.93277	+	0.518455i	0.00851946	+	0.000895432i
$580$		0			0
$581$	−18.0485	−	5.86433i	−0.0310646	−	0.0100935i
$582$		0			0
$583$	−308.564	+	534.448i	−0.529269	+	0.916721i
$584$		0			0
$585$	1078.73	−	350.501i	1.84399	−	0.599147i
$586$		0			0
$587$	−67.8088	+	93.3309i	−0.115518	+	0.158996i	−0.862860	−	0.505442i	$-0.831329\pi$
$587$	−67.8088	+	93.3309i	−0.115518	+	0.158996i	0.747343	+	0.664439i	$0.231329\pi$
$588$		0			0
$589$	−111.404	−	932.502i	−0.189141	−	1.58320i
$590$		0			0
$591$	−6.01612	−	4.37097i	−0.0101796	−	0.00739588i
$592$		0			0
$593$	75.0351	+	230.934i	0.126535	+	0.389434i	0.994178	−	0.107754i	$-0.0343659\pi$
$593$	75.0351	+	230.934i	0.126535	+	0.389434i	−0.867643	+	0.497188i	$0.834366\pi$
$594$		0			0
$595$	10.7686	+	6.21725i	0.0180985	+	0.0104492i
$596$		0			0
$597$	2.97466	−	9.15507i	0.00498269	−	0.0153351i
$598$		0			0
$599$	−24.9603	+	237.481i	−0.0416699	+	0.396463i	0.953731	+	0.300662i	$0.0972078\pi$
$599$	−24.9603	+	237.481i	−0.0416699	+	0.396463i	−0.995401	+	0.0958005i	$0.969459\pi$
$600$		0			0
$601$	204.301	+	458.867i	0.339935	+	0.763506i	0.999925	+	0.0122318i	$0.00389360\pi$
$601$	204.301	+	458.867i	0.339935	+	0.763506i	−0.659991	+	0.751274i	$0.729440\pi$
$602$		0			0
$603$	143.998	+	159.926i	0.238802	+	0.265217i
$604$		0			0
$605$	−158.356	+	115.053i	−0.261746	+	0.190170i
$606$		0			0
$607$	−215.417	−	95.9096i	−0.354887	−	0.158006i	0.221547	−	0.975150i	$-0.428889\pi$
$607$	−215.417	−	95.9096i	−0.354887	−	0.158006i	−0.576434	+	0.817144i	$0.695556\pi$
$608$		0			0
$609$	0.173924	−	0.193162i	0.000285590	−	0.000317180i
$610$		0			0
$611$	−192.911	−	907.576i	−0.315730	−	1.48539i
$612$		0			0
$613$	137.994	−	649.210i	0.225112	−	1.05907i	−0.709858	−	0.704344i	$-0.751241\pi$
$613$	137.994	−	649.210i	0.225112	−	1.05907i	0.934971	−	0.354725i	$-0.115426\pi$
$614$		0			0
$615$	−6.12199	+	3.53453i	−0.00995446	+	0.00574721i
$616$		0			0
$617$	−31.8230	−	302.776i	−0.0515770	−	0.490723i	−0.989568	−	0.144064i	$-0.953983\pi$
$617$	−31.8230	−	302.776i	−0.0515770	−	0.490723i	0.937991	−	0.346659i	$-0.112684\pi$
$618$		0			0
$619$			676.424i			1.09277i	0.837534	+	0.546385i	$0.183996\pi$
$619$			676.424i			1.09277i	−0.837534	+	0.546385i	$0.816004\pi$
$620$		0			0
$621$	−4.42643			−0.00712790
$622$		0			0
$623$	26.1702	−	2.75060i	0.0420068	−	0.00441509i
$624$		0			0
$625$	−114.016	−	197.481i	−0.182425	−	0.315969i
$626$		0			0
$627$	7.90253	+	1.67973i	0.0126037	+	0.00267900i
$628$		0			0
$629$	−206.459	+	43.8843i	−0.328234	+	0.0697684i
$630$		0			0
$631$	−387.313	−	348.738i	−0.613809	−	0.552676i	0.302500	−	0.953150i	$-0.402179\pi$
$631$	−387.313	−	348.738i	−0.613809	−	0.552676i	−0.916308	+	0.400474i	$0.868846\pi$
$632$		0			0
$633$	−0.412666	+	0.926862i	−0.000651920	+	0.00146424i
$634$		0			0
$635$	−189.277	−	260.517i	−0.298073	−	0.410263i
$636$		0			0
$637$	−549.925	+	495.155i	−0.863305	+	0.777323i
$638$		0			0
$639$	−855.249	+	380.781i	−1.33842	+	0.595902i
$640$		0			0
$641$	−20.1837	−	2.12139i	−0.0314878	−	0.00330951i	0.0887714	−	0.996052i	$-0.471706\pi$
$641$	−20.1837	−	2.12139i	−0.0314878	−	0.00330951i	−0.120259	+	0.992743i	$0.538373\pi$
$642$		0			0
$643$	−213.158	−	69.2592i	−0.331505	−	0.107713i	0.138535	−	0.990358i	$-0.455761\pi$
$643$	−213.158	−	69.2592i	−0.331505	−	0.107713i	−0.470040	+	0.882645i	$0.655761\pi$
$644$		0			0
$645$	−5.60250	+	9.70381i	−0.00868605	+	0.0150447i
$646$		0			0
$647$	−919.515	+	298.768i	−1.42120	+	0.461775i	−0.915982	−	0.401218i	$-0.868587\pi$
$647$	−919.515	+	298.768i	−1.42120	+	0.461775i	−0.505215	+	0.862993i	$0.668587\pi$
$648$		0			0
$649$	−334.168	+	459.943i	−0.514896	+	0.708694i
$650$		0			0
$651$	−0.121007	+	0.282503i	−0.000185878	+	0.000433953i
$652$		0			0
$653$	−254.910	−	185.203i	−0.390367	−	0.283618i	0.375239	−	0.926928i	$-0.377561\pi$
$653$	−254.910	−	185.203i	−0.390367	−	0.283618i	−0.765606	+	0.643310i	$0.777561\pi$
$654$		0			0
$655$	−440.750	−	1356.49i	−0.672900	−	2.07097i
$656$		0			0
$657$	840.126	+	485.047i	1.27873	+	0.738276i
$658$		0			0
$659$	361.634	−	1112.99i	0.548761	−	1.68891i	−0.163114	−	0.986607i	$-0.552154\pi$
$659$	361.634	−	1112.99i	0.548761	−	1.68891i	0.711875	−	0.702306i	$-0.247846\pi$
$660$		0			0
$661$	70.4990	−	670.753i	0.106655	−	1.01476i	−0.802033	−	0.597280i	$-0.796248\pi$
$661$	70.4990	−	670.753i	0.106655	−	1.01476i	0.908688	−	0.417476i	$-0.137085\pi$
$662$		0			0
$663$	−0.677221	−	1.52106i	−0.00102145	−	0.00229421i
$664$		0			0
$665$	−61.9231	−	68.7725i	−0.0931174	−	0.103417i
$666$		0			0
$667$	193.121	−	140.311i	0.289537	−	0.210361i
$668$		0			0
$669$	9.53589	+	4.24565i	0.0142539	+	0.00634627i
$670$		0			0
$671$	116.219	−	129.074i	0.173203	−	0.192361i
$672$		0			0
$673$	159.009	+	748.081i	0.236270	+	1.11156i	0.923045	+	0.384692i	$0.125692\pi$
$673$	159.009	+	748.081i	0.236270	+	1.11156i	−0.686776	+	0.726870i	$0.740974\pi$
$674$		0			0
$675$	−4.47476	+	21.0521i	−0.00662928	+	0.0311883i
$676$		0			0
$677$	954.513	−	551.088i	1.40992	−	0.814015i	0.414536	−	0.910033i	$-0.363944\pi$
$677$	954.513	−	551.088i	1.40992	−	0.814015i	0.995380	+	0.0960180i	$0.0306106\pi$
$678$		0			0
$679$	−3.18232	−	30.2777i	−0.00468677	−	0.0445917i
$680$		0			0
$681$		−	3.65900i		−	0.00537298i
$682$		0			0
$683$	−1228.53			−1.79873			−0.899366	−	0.437197i	$-0.855971\pi$
$683$	−1228.53			−1.79873			−0.899366	+	0.437197i	$0.855971\pi$
$684$		0			0
$685$	−244.267	+	25.6735i	−0.356594	+	0.0374796i
$686$		0			0
$687$	3.46632	+	6.00385i	0.00504560	+	0.00873923i
$688$		0			0
$689$	−925.865	−	196.799i	−1.34378	−	0.285630i
$690$		0			0
$691$	82.6631	−	17.5706i	0.119628	−	0.0254277i	−0.147709	−	0.989031i	$-0.547190\pi$
$691$	82.6631	−	17.5706i	0.119628	−	0.0254277i	0.267337	+	0.963603i	$0.413856\pi$
$692$		0			0
$693$	24.2353	+	21.8215i	0.0349716	+	0.0314885i
$694$		0			0
$695$	733.946	−	1648.47i	1.05604	−	2.37190i
$696$		0			0
$697$	−75.2365	−	103.554i	−0.107943	−	0.148571i
$698$		0			0
$699$	8.73274	−	7.86300i	0.0124932	−	0.0112489i
$700$		0			0
$701$	−278.461	+	123.979i	−0.397234	+	0.176860i	−0.595624	−	0.803263i	$-0.703095\pi$
$701$	−278.461	+	123.979i	−0.397234	+	0.176860i	0.198390	+	0.980123i	$0.436429\pi$
$702$		0			0
$703$	1562.28	+	164.202i	2.22230	+	0.233573i
$704$		0			0
$705$	13.0997	+	4.25634i	0.0185811	+	0.00603736i
$706$		0			0
$707$	−1.94133	+	3.36249i	−0.00274587	+	0.00475599i
$708$		0			0
$709$	36.3050	−	11.7962i	0.0512059	−	0.0166378i	−0.283302	−	0.959031i	$-0.591430\pi$
$709$	36.3050	−	11.7962i	0.0512059	−	0.0166378i	0.334508	+	0.942393i	$0.391430\pi$
$710$		0			0
$711$	−137.768	+	189.622i	−0.193767	+	0.266697i
$712$		0			0
$713$	−162.644	+	230.671i	−0.228112	+	0.323521i
$714$		0			0
$715$	1006.74	+	731.442i	1.40803	+	1.02300i
$716$		0			0
$717$	1.89681	+	5.83778i	0.00264548	+	0.00814195i
$718$		0			0
$719$	−40.4790	−	23.3706i	−0.0562990	−	0.0325043i	0.471586	−	0.881820i	$-0.343682\pi$
$719$	−40.4790	−	23.3706i	−0.0562990	−	0.0325043i	−0.527885	+	0.849316i	$0.677015\pi$
$720$		0			0
$721$	−14.8644	+	45.7479i	−0.0206164	+	0.0634507i
$722$		0			0
$723$	1.00413	−	9.55362i	0.00138883	−	0.0132139i
$724$		0			0
$725$	−472.088	−	1060.33i	−0.651157	−	1.46252i
$726$		0			0
$727$	−163.068	−	181.105i	−0.224303	−	0.249113i	0.620481	−	0.784222i	$-0.286937\pi$
$727$	−163.068	−	181.105i	−0.224303	−	0.249113i	−0.844783	+	0.535108i	$0.820271\pi$
$728$		0			0
$729$	−589.487	+	428.287i	−0.808624	+	0.587499i
$730$		0			0
$731$	−185.349	−	82.5226i	−0.253555	−	0.112890i
$732$		0			0
$733$	676.936	−	751.813i	0.923514	−	1.02567i	−0.0760782	−	0.997102i	$-0.524240\pi$
$733$	676.936	−	751.813i	0.923514	−	1.02567i	0.999592	−	0.0285641i	$-0.00909348\pi$
$734$		0			0
$735$	−2.28394	−	10.7451i	−0.00310740	−	0.0146192i
$736$		0			0
$737$	−49.0882	+	230.942i	−0.0666055	+	0.313354i
$738$		0			0
$739$	−424.080	+	244.843i	−0.573857	+	0.331316i	−0.758688	−	0.651454i	$-0.774159\pi$
$739$	−424.080	+	244.843i	−0.573857	+	0.331316i	0.184831	+	0.982770i	$0.440826\pi$
$740$		0			0
$741$	1.29528	+	12.3238i	0.00174802	+	0.0166313i
$742$		0			0
$743$			554.237i			0.745945i	0.927842	+	0.372973i	$0.121661\pi$
$743$			554.237i			0.745945i	−0.927842	+	0.372973i	$0.878339\pi$
$744$		0			0
$745$	759.975			1.02010
$746$		0			0
$747$	462.755	−	48.6375i	0.619485	−	0.0651105i
$748$		0			0
$749$	−33.0820	−	57.2996i	−0.0441682	−	0.0765015i
$750$		0			0
$751$	−237.948	−	50.5773i	−0.316841	−	0.0673466i	0.0467462	−	0.998907i	$-0.485115\pi$
$751$	−237.948	−	50.5773i	−0.316841	−	0.0673466i	−0.363587	+	0.931560i	$0.618448\pi$
$752$		0			0
$753$	−8.80816	+	1.87223i	−0.0116974	+	0.00248637i
$754$		0			0
$755$	−270.714	−	243.752i	−0.358561	−	0.322850i
$756$		0			0
$757$	−543.116	+	1219.86i	−0.717459	+	1.61144i	0.0718296	+	0.997417i	$0.477116\pi$
$757$	−543.116	+	1219.86i	−0.717459	+	1.61144i	−0.789289	+	0.614022i	$0.789550\pi$
$758$		0			0
$759$	−1.42718	−	1.96434i	−0.00188034	−	0.00258807i
$760$		0			0
$761$	−272.830	+	245.658i	−0.358516	+	0.322809i	−0.828630	−	0.559797i	$-0.810879\pi$
$761$	−272.830	+	245.658i	−0.358516	+	0.322809i	0.470114	+	0.882605i	$0.344213\pi$
$762$		0			0
$763$	3.01077	−	1.34048i	0.00394596	−	0.00175685i
$764$		0			0
$765$	−303.210	−	31.8687i	−0.396354	−	0.0416584i
$766$		0			0
$767$	−829.317	−	269.461i	−1.08125	−	0.351319i
$768$		0			0
$769$	414.500	−	717.935i	0.539012	−	0.933596i	−0.459946	−	0.887947i	$-0.652131\pi$
$769$	414.500	−	717.935i	0.539012	−	0.933596i	0.998958	−	0.0456487i	$-0.0145355\pi$
$770$		0			0
$771$	4.07719	−	1.32476i	0.00528819	−	0.00171824i
$772$		0			0
$773$	−176.514	+	242.950i	−0.228349	+	0.314295i	−0.907782	−	0.419442i	$-0.862226\pi$
$773$	−176.514	+	242.950i	−0.228349	+	0.314295i	0.679433	+	0.733737i	$0.262226\pi$
$774$		0			0
$775$	932.652	+	1006.72i	1.20342	+	1.29900i
$776$		0			0
$777$	−0.415888	−	0.302160i	−0.000535248	−	0.000388881i
$778$		0			0
$779$	294.378	+	906.002i	0.377892	+	1.16303i
$780$		0			0
$781$	−889.502	−	513.554i	−1.13893	−	0.657560i
$782$		0			0
$783$	−3.93895	+	12.1228i	−0.00503059	+	0.0154826i
$784$		0			0
$785$	83.5024	−	794.472i	0.106372	−	1.01207i
$786$		0			0
$787$	−429.319	−	964.267i	−0.545514	−	1.22524i	−0.950444	−	0.310896i	$-0.899371\pi$
$787$	−429.319	−	964.267i	−0.545514	−	1.22524i	0.404930	−	0.914347i	$-0.367296\pi$
$788$		0			0
$789$	−3.58812	−	3.98501i	−0.00454768	−	0.00505070i
$790$		0			0
$791$	−16.7635	+	12.1794i	−0.0211928	+	0.0153975i
$792$		0			0
$793$	243.369	+	108.355i	0.306897	+	0.136639i
$794$		0			0
$795$	9.40220	−	10.4422i	0.0118267	−	0.0131348i
$796$		0			0
$797$	128.313	+	603.667i	0.160995	+	0.757424i	0.982357	+	0.187016i	$0.0598816\pi$
$797$	128.313	+	603.667i	0.160995	+	0.757424i	−0.821362	+	0.570408i	$0.806785\pi$
$798$		0			0
$799$	−51.8538	+	243.953i	−0.0648984	+	0.305323i
$800$		0			0
$801$	−558.759	+	322.600i	−0.697577	+	0.402746i
$802$		0			0
$803$	111.251	+	1058.48i	0.138544	+	1.31816i
$804$		0			0
$805$			27.8125i			0.0345497i
$806$		0			0
$807$	−12.5498			−0.0155512
$808$		0			0
$809$	423.845	−	44.5479i	0.523912	−	0.0550654i	0.161119	−	0.986935i	$-0.448490\pi$
$809$	423.845	−	44.5479i	0.523912	−	0.0550654i	0.362793	+	0.931870i	$0.381823\pi$
$810$		0			0
$811$	707.993	+	1226.28i	0.872988	+	1.51206i	0.858891	+	0.512159i	$0.171154\pi$
$811$	707.993	+	1226.28i	0.872988	+	1.51206i	0.0140969	+	0.999901i	$0.495513\pi$
$812$		0			0
$813$	−3.52143	−	0.748503i	−0.00433140	−	0.000920668i
$814$		0			0
$815$	−273.650	+	58.1662i	−0.335767	+	0.0713695i
$816$		0			0
$817$	1122.14	+	1010.38i	1.37349	+	1.23669i
$818$		0			0
$819$	−20.3449	+	45.6955i	−0.0248412	+	0.0557942i
$820$		0			0
$821$	−402.089	−	553.428i	−0.489755	−	0.674090i	0.490588	−	0.871392i	$-0.336782\pi$
$821$	−402.089	−	553.428i	−0.489755	−	0.674090i	−0.980343	+	0.197302i	$0.936782\pi$
$822$		0			0
$823$	177.716	−	160.016i	0.215936	−	0.194430i	−0.554063	−	0.832475i	$-0.686923\pi$
$823$	177.716	−	160.016i	0.215936	−	0.194430i	0.769999	+	0.638045i	$0.220257\pi$
$824$		0			0
$825$	−10.7852	+	4.80188i	−0.0130730	+	0.00582046i
$826$		0			0
$827$	−1207.34	−	126.897i	−1.45990	−	0.153442i	−0.658958	−	0.752179i	$-0.729003\pi$
$827$	−1207.34	−	126.897i	−1.45990	−	0.153442i	−0.800945	+	0.598737i	$0.795669\pi$
$828$		0			0
$829$	906.239	+	294.455i	1.09317	+	0.355193i	0.799471	−	0.600705i	$-0.205113\pi$
$829$	906.239	+	294.455i	1.09317	+	0.355193i	0.293700	+	0.955898i	$0.405113\pi$
$830$		0			0
$831$	−5.85788	+	10.1461i	−0.00704920	+	0.0122096i
$832$		0			0
$833$	189.173	−	61.4660i	0.227098	−	0.0737888i
$834$		0			0
$835$	1442.70	−	1985.70i	1.72778	−	2.37809i
$836$		0			0
$837$	−0.213777	−	15.0698i	−0.000255409	−	0.0180045i
$838$		0			0
$839$	936.494	+	680.403i	1.11620	+	0.810969i	0.983629	−	0.180205i	$-0.0576760\pi$
$839$	936.494	+	680.403i	1.11620	+	0.810969i	0.132573	+	0.991173i	$0.457676\pi$
$840$		0			0
$841$	47.4613	+	146.071i	0.0564344	+	0.173687i
$842$		0			0
$843$	−3.50590	−	2.02413i	−0.00415883	−	0.00240110i
$844$		0			0
$845$	−155.160	+	477.534i	−0.183622	+	0.565129i
$846$		0			0
$847$	0.902295	−	8.58476i	0.00106528	−	0.0101355i
$848$		0			0
$849$	2.13383	+	4.79266i	0.00251335	+	0.00564507i
$850$		0			0
$851$	−315.902	−	350.845i	−0.371213	−	0.412274i
$852$		0			0
$853$	114.101	−	82.8990i	0.133764	−	0.0971852i	−0.518891	−	0.854840i	$-0.673655\pi$
$853$	114.101	−	82.8990i	0.133764	−	0.0971852i	0.652655	+	0.757655i	$0.273655\pi$
$854$		0			0
$855$	2072.87	+	922.903i	2.42441	+	1.07942i
$856$		0			0
$857$	−925.524	+	1027.90i	−1.07996	+	1.19941i	−0.101099	+	0.994876i	$0.532236\pi$
$857$	−925.524	+	1027.90i	−1.07996	+	1.19941i	−0.978859	+	0.204538i	$0.934431\pi$
$858$		0			0
$859$	−94.6869	−	445.467i	−0.110229	−	0.518588i	−0.998269	−	0.0588203i	$-0.981266\pi$
$859$	−94.6869	−	445.467i	−0.110229	−	0.518588i	0.888039	−	0.459767i	$-0.152067\pi$
$860$		0			0
$861$	0.0648152	−	0.304932i	7.52790e−5	−	0.000354160i
$862$		0			0
$863$	1105.00	−	637.970i	1.28041	−	0.739247i	0.303489	−	0.952835i	$-0.401848\pi$
$863$	1105.00	−	637.970i	1.28041	−	0.739247i	0.976924	+	0.213588i	$0.0685150\pi$
$864$		0			0
$865$	181.128	+	1723.32i	0.209397	+	1.99228i
$866$		0			0
$867$		−	7.35852i		−	0.00848734i
$868$		0			0
$869$	−257.149			−0.295913
$870$		0			0
$871$	−360.148	+	37.8531i	−0.413488	+	0.0434594i
$872$		0			0
$873$	373.233	+	646.459i	0.427530	+	0.740503i
$874$		0			0
$875$	57.5763	+	12.2382i	0.0658015	+	0.0139865i
$876$		0			0
$877$	−956.329	+	203.274i	−1.09046	+	0.231783i	−0.717844	−	0.696204i	$-0.754871\pi$
$877$	−956.329	+	203.274i	−1.09046	+	0.231783i	−0.372611	+	0.927987i	$0.621538\pi$
$878$		0			0
$879$	−1.03417	−	0.931168i	−0.00117653	−	0.00105935i
$880$		0			0
$881$	−9.50060	+	21.3387i	−0.0107839	+	0.0242210i	−0.918857	−	0.394590i	$-0.870886\pi$
$881$	−9.50060	+	21.3387i	−0.0107839	+	0.0242210i	0.908073	+	0.418811i	$0.137553\pi$
$882$		0			0
$883$	865.303	+	1190.99i	0.979958	+	1.34880i	0.936852	+	0.349726i	$0.113725\pi$
$883$	865.303	+	1190.99i	0.979958	+	1.34880i	0.0431057	+	0.999071i	$0.486275\pi$
$884$		0			0
$885$	9.61973	−	8.66164i	0.0108697	−	0.00978717i
$886$		0			0
$887$	−241.258	+	107.415i	−0.271994	+	0.121099i	−0.538201	−	0.842816i	$-0.680896\pi$
$887$	−241.258	+	107.415i	−0.271994	+	0.121099i	0.266208	+	0.963916i	$0.414229\pi$
$888$		0			0
$889$	14.1230	+	1.48439i	0.0158864	+	0.00166973i
$890$		0			0
$891$	−760.409	−	247.072i	−0.853433	−	0.277297i
$892$		0			0
$893$	928.078	−	1607.48i	1.03928	−	1.80009i
$894$		0			0
$895$	−1393.70	+	452.840i	−1.55721	+	0.505967i
$896$		0			0
$897$	2.18901	−	3.01291i	0.00244036	−	0.00335887i
$898$		0			0
$899$	487.016	+	650.706i	0.541731	+	0.723811i
$900$		0			0
$901$	205.837	+	149.549i	0.228454	+	0.165982i
$902$		0			0
$903$	−0.152697	−	0.469953i	−0.000169100	−	0.000520435i
$904$		0			0
$905$	−1875.22	−	1082.66i	−2.07206	−	1.19631i
$906$		0			0
$907$	315.013	−	969.510i	0.347313	−	1.06892i	−0.613021	−	0.790067i	$-0.710046\pi$
$907$	315.013	−	969.510i	0.347313	−	1.06892i	0.960334	−	0.278853i	$-0.0899541\pi$
$908$		0			0
$909$	9.95098	−	94.6772i	0.0109472	−	0.104155i
$910$		0			0
$911$	−386.178	−	867.369i	−0.423905	−	0.952107i	−0.991657	−	0.128907i	$-0.958853\pi$
$911$	−386.178	−	867.369i	−0.423905	−	0.952107i	0.567752	−	0.823200i	$-0.307813\pi$
$912$		0			0
$913$	341.588	+	379.371i	0.374137	+	0.415522i
$914$		0			0
$915$	−3.19940	+	2.32450i	−0.00349661	+	0.00254043i
$916$		0			0
$917$	57.4613	+	25.5834i	0.0626623	+	0.0278991i
$918$		0			0
$919$	532.799	−	591.733i	0.579760	−	0.643888i	−0.379908	−	0.925024i	$-0.624045\pi$
$919$	532.799	−	591.733i	0.579760	−	0.643888i	0.959668	+	0.281136i	$0.0907112\pi$
$920$		0			0
$921$	−1.42129	−	6.68666i	−0.00154321	−	0.00726022i
$922$		0			0
$923$	327.539	−	1540.95i	0.354864	−	1.66950i
$924$		0			0
$925$	−1987.97	+	1147.76i	−2.14916	+	1.24082i
$926$		0			0
$927$	−123.282	−	1172.95i	−0.132991	−	1.26532i
$928$		0			0
$929$		−	151.389i		−	0.162959i	−0.996675	−	0.0814794i	$-0.974036\pi$
$929$		−	151.389i		−	0.162959i	0.996675	−	0.0814794i	$-0.0259645\pi$
$930$		0			0
$931$	−1480.36			−1.59007
$932$		0			0
$933$	−11.0382	+	1.16016i	−0.0118309	+	0.00124348i
$934$		0			0
$935$	−167.245	−	289.677i	−0.178872	−	0.309815i
$936$		0			0
$937$	−236.488	−	50.2670i	−0.252388	−	0.0536468i	0.0799800	−	0.996796i	$-0.474514\pi$
$937$	−236.488	−	50.2670i	−0.252388	−	0.0536468i	−0.332368	+	0.943150i	$0.607848\pi$
$938$		0			0
$939$	12.6435	−	2.68746i	0.0134649	−	0.00286204i
$940$		0			0
$941$	1108.70	+	998.280i	1.17822	+	1.06087i	0.996998	+	0.0774281i	$0.0246708\pi$
$941$	1108.70	+	998.280i	1.17822	+	1.06087i	0.181219	+	0.983443i	$0.441996\pi$
$942$		0			0
$943$	116.449	−	261.548i	0.123487	−	0.277357i
$944$		0			0
$945$	−0.872940	−	1.20150i	−0.000923746	−	0.00127143i
$946$		0			0
$947$	−308.660	+	277.918i	−0.325934	+	0.293472i	−0.815810	−	0.578320i	$-0.803709\pi$
$947$	−308.660	+	277.918i	−0.325934	+	0.293472i	0.489876	+	0.871792i	$0.337042\pi$
$948$		0			0
$949$	−1491.30	+	663.972i	−1.57145	+	0.699654i
$950$		0			0
$951$	9.45602	+	0.993867i	0.00994324	+	0.00104508i
$952$		0			0
$953$	907.376	+	294.824i	0.952126	+	0.309365i	0.743579	−	0.668648i	$-0.233127\pi$
$953$	907.376	+	294.824i	0.952126	+	0.309365i	0.208547	+	0.978012i	$0.433127\pi$
$954$		0			0
$955$	47.6210	−	82.4819i	0.0498649	−	0.0863685i
$956$		0			0
$957$	−6.64984	+	2.16066i	−0.00694863	+	0.00225775i
$958$		0			0
$959$	6.36657	−	8.76283i	0.00663876	−	0.00913747i
$960$		0			0
$961$	−793.175	−	542.581i	−0.825365	−	0.564600i
$962$		0			0
$963$	1312.44	+	953.545i	1.36287	+	0.990181i
$964$		0			0
$965$	472.274	+	1453.51i	0.489403	+	1.50623i
$966$		0			0
$967$	−778.872	−	449.682i	−0.805452	−	0.465028i	0.0399222	−	0.999203i	$-0.487289\pi$
$967$	−778.872	−	449.682i	−0.805452	−	0.465028i	−0.845374	+	0.534175i	$0.820622\pi$
$968$		0			0
$969$	1.02928	−	3.16781i	0.00106221	−	0.00326915i
$970$		0			0
$971$	74.0742	−	704.769i	0.0762865	−	0.725817i	−0.887800	−	0.460229i	$-0.847767\pi$
$971$	74.0742	−	704.769i	0.0762865	−	0.725817i	0.964087	−	0.265588i	$-0.0855661\pi$
$972$		0			0
$973$	32.3668	+	72.6971i	0.0332650	+	0.0747144i
$974$		0			0
$975$	−12.1165	−	13.4567i	−0.0124272	−	0.0138018i
$976$		0			0
$977$	179.568	−	130.464i	0.183796	−	0.133535i	−0.492083	−	0.870548i	$-0.663764\pi$
$977$	179.568	−	130.464i	0.183796	−	0.133535i	0.675879	+	0.737013i	$0.263764\pi$
$978$		0			0
$979$	−646.664	−	287.913i	−0.660535	−	0.294089i
$980$		0			0
$981$	−54.0704	+	60.0512i	−0.0551176	+	0.0612143i
$982$		0			0
$983$	−84.9108	−	399.474i	−0.0863792	−	0.406382i	0.913621	−	0.406567i	$-0.133274\pi$
$983$	−84.9108	−	399.474i	−0.0863792	−	0.406382i	−1.00000		0.000185160i	$0.999941\pi$
$984$		0			0
$985$	476.401	−	2241.29i	0.483656	−	2.27542i
$986$		0			0
$987$	−0.526042	+	0.303711i	−0.000532971	+	0.000307711i
$988$		0			0
$989$	−47.4357	−	451.321i	−0.0479633	−	0.456340i
$990$		0			0
$991$		−	197.969i		−	0.199767i	−0.994999	−	0.0998836i	$-0.968153\pi$
$991$		−	197.969i		−	0.199767i	0.994999	−	0.0998836i	$-0.0318470\pi$
$992$		0			0
$993$	−12.5458			−0.0126342
$994$		0			0
$995$	2949.89	−	310.045i	2.96471	−	0.311604i
$996$		0			0
$997$	8.63399	+	14.9545i	0.00865997	+	0.0149995i	0.870323	−	0.492481i	$-0.163910\pi$
$997$	8.63399	+	14.9545i	0.00865997	+	0.0149995i	−0.861663	+	0.507481i	$0.830577\pi$
$998$		0			0
$999$	24.6588	+	5.24139i	0.0246835	+	0.00524664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.o.a.21.3	✓	40
31.3	odd	30	inner	124.3.o.a.65.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.o.a.21.3	✓	40	1.1	even	1	trivial
124.3.o.a.65.3	yes	40	31.3	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0268627 + 0.00282338i) q^{3} +(-4.16141 - 7.20777i) q^{5} +(0.359013 + 0.0763106i) q^{7} +(-8.80261 + 1.87105i) q^{9} +O(q^{10})\)	\(q+(-0.0268627 + 0.00282338i) q^{3} +(-4.16141 - 7.20777i) q^{5} +(0.359013 + 0.0763106i) q^{7} +(-8.80261 + 1.87105i) q^{9} +(-7.33727 - 6.60651i) q^{11} +(6.15947 - 13.8344i) q^{13} +(0.132137 + 0.181871i) q^{15} +(-3.02500 + 2.72373i) q^{17} +(27.6755 - 12.3219i) q^{19} +(-0.00985951 - 0.00103628i) q^{21} +(-8.65905 - 2.81349i) q^{23} +(-22.1346 + 38.3382i) q^{25} +(0.462377 - 0.150235i) q^{27} +(-15.4109 + 21.2112i) q^{29} +(9.16037 - 29.6157i) q^{31} +(0.215751 + 0.156753i) q^{33} +(-0.943971 - 2.90524i) q^{35} +(44.9064 + 25.9267i) q^{37} +(-0.126400 + 0.389019i) q^{39} +(-3.28694 + 31.2731i) q^{41} +(20.2731 + 45.5342i) q^{43} +(50.1174 + 55.6610i) q^{45} +(49.5686 - 36.0137i) q^{47} +(-44.6407 - 19.8753i) q^{49} +(0.0735696 - 0.0817073i) q^{51} +(-12.9955 - 61.1390i) q^{53} +(-17.0848 + 80.3777i) q^{55} +(-0.708648 + 0.409138i) q^{57} +(-6.01893 - 57.2663i) q^{59} +17.5916i q^{61} -3.30304 q^{63} +(-125.347 + 13.1745i) q^{65} +(-11.9566 - 20.7094i) q^{67} +(0.240549 + 0.0511302i) q^{69} +(101.756 - 21.6289i) q^{71} +(-80.1088 - 72.1302i) q^{73} +(0.486351 - 1.09236i) q^{75} +(-2.13003 - 2.93174i) q^{77} +(19.3551 - 17.4275i) q^{79} +(73.9792 - 32.9377i) q^{81} +(-51.4214 - 5.40461i) q^{83} +(32.2202 + 10.4690i) q^{85} +(0.354090 - 0.613301i) q^{87} +(68.1857 - 22.1549i) q^{89} +(3.26704 - 4.49669i) q^{91} +(-0.162456 + 0.821419i) q^{93} +(-203.983 - 148.202i) q^{95} +(-25.6322 - 78.8877i) q^{97} +(76.9483 + 44.4261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9 + 2 * q^11 - 18 * q^13 + 35 * q^15 + 25 * q^17 - 11 * q^19 + 54 * q^21 + 25 * q^23 - 75 * q^25 + 225 * q^27 + 20 * q^29 + 59 * q^31 - 303 * q^33 - 66 * q^35 - 222 * q^37 - 169 * q^39 + q^41 + 122 * q^43 + 54 * q^45 - 120 * q^47 - 118 * q^49 - 515 * q^51 + 61 * q^53 - 121 * q^55 - 201 * q^57 - 257 * q^59 - 158 * q^63 + 182 * q^65 - q^67 + 510 * q^69 + 459 * q^71 + 253 * q^73 + 651 * q^75 + 670 * q^77 + 385 * q^79 + 974 * q^81 + 375 * q^83 - 370 * q^85 - 344 * q^87 + 245 * q^89 + 960 * q^91 - 212 * q^93 - 851 * q^95 - 797 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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