LMFDB - Embedded newform 196.6.d.b.195.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, 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:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.31
Character	$\chi$	$=$	196.195
Dual form			196.6.d.b.195.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.22163 + 2.17591i) q^{2} -1.80249 q^{3} +(22.5308 + 22.7236i) q^{4} +47.5545i q^{5} +(-9.41192 - 3.92205i) q^{6} +(68.2033 + 167.679i) q^{8} -239.751 q^{9} +(-103.474 + 248.312i) q^{10} +440.652i q^{11} +(-40.6116 - 40.9590i) q^{12} -283.636i q^{13} -85.7165i q^{15} +(-8.72235 + 1023.96i) q^{16} -1492.26i q^{17} +(-1251.89 - 521.676i) q^{18} -2122.13 q^{19} +(-1080.61 + 1071.44i) q^{20} +(-958.818 + 2300.92i) q^{22} +2282.61i q^{23} +(-122.936 - 302.240i) q^{24} +863.567 q^{25} +(617.166 - 1481.04i) q^{26} +870.153 q^{27} +1844.20 q^{29} +(186.511 - 447.580i) q^{30} -7827.61 q^{31} +(-2273.59 + 5327.78i) q^{32} -794.270i q^{33} +(3247.03 - 7792.05i) q^{34} +(-5401.79 - 5448.00i) q^{36} -4035.42 q^{37} +(-11081.0 - 4617.57i) q^{38} +511.251i q^{39} +(-7973.90 + 3243.37i) q^{40} +1848.03i q^{41} +3423.76i q^{43} +(-10013.2 + 9928.26i) q^{44} -11401.2i q^{45} +(-4966.75 + 11918.9i) q^{46} +15907.9 q^{47} +(15.7219 - 1845.68i) q^{48} +(4509.23 + 1879.04i) q^{50} +2689.79i q^{51} +(6445.23 - 6390.56i) q^{52} -32107.3 q^{53} +(4543.62 + 1893.37i) q^{54} -20955.0 q^{55} +3825.12 q^{57} +(9629.72 + 4012.81i) q^{58} -8022.27 q^{59} +(1947.78 - 1931.26i) q^{60} +46698.1i q^{61} +(-40872.9 - 17032.2i) q^{62} +(-23464.6 + 22872.5i) q^{64} +13488.2 q^{65} +(1728.26 - 4147.38i) q^{66} +53887.8i q^{67} +(33909.6 - 33622.0i) q^{68} -4114.38i q^{69} -16295.5i q^{71} +(-16351.8 - 40201.3i) q^{72} -20384.0i q^{73} +(-21071.5 - 8780.71i) q^{74} -1556.57 q^{75} +(-47813.4 - 48222.4i) q^{76} +(-1112.43 + 2669.56i) q^{78} -44562.4i q^{79} +(-48694.1 - 414.787i) q^{80} +56691.1 q^{81} +(-4021.15 + 9649.73i) q^{82} +44256.0 q^{83} +70963.9 q^{85} +(-7449.80 + 17877.6i) q^{86} -3324.14 q^{87} +(-73888.1 + 30053.9i) q^{88} +39941.0i q^{89} +(24808.1 - 59533.1i) q^{90} +(-51869.1 + 51429.1i) q^{92} +14109.2 q^{93} +(83065.3 + 34614.2i) q^{94} -100917. i q^{95} +(4098.13 - 9603.25i) q^{96} +131224. i q^{97} -105647. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50}+ \cdots + 330324 q^{93}+O(q^{100}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	5.22163	+	2.17591i	0.923063	+	0.384650i
$2$	5.22163	+	2.17591i	0.923063	+	0.384650i
$3$	−1.80249			−0.115630			−0.0578148	−	0.998327i	$-0.518413\pi$
$3$	−1.80249			−0.115630			−0.0578148	+	0.998327i	$0.518413\pi$
$4$	22.5308	+	22.7236i	0.704089	+	0.710112i
$5$			47.5545i			0.850681i	0.905033	+	0.425341i	$0.139846\pi$
$5$			47.5545i			0.850681i	−0.905033	+	0.425341i	$0.860154\pi$
$6$	−9.41192	−	3.92205i	−0.106733	−	0.0444769i
$7$		0			0
$7$		0			0
$8$	68.2033	+	167.679i	0.376773	+	0.926305i
$9$	−239.751			−0.986630
$10$	−103.474	+	248.312i	−0.327215	+	0.785232i
$11$			440.652i			1.09803i	0.835813	+	0.549015i	$0.184997\pi$
$11$			440.652i			1.09803i	−0.835813	+	0.549015i	$0.815003\pi$
$12$	−40.6116	−	40.9590i	−0.0814135	−	0.0821100i
$13$		−	283.636i		−	0.465482i	−0.972539	−	0.232741i	$-0.925230\pi$
$13$		−	283.636i		−	0.465482i	0.972539	−	0.232741i	$-0.0747695\pi$
$14$		0			0
$15$		−	85.7165i		−	0.0983640i
$16$	−8.72235	+	1023.96i	−0.00851792	+	0.999964i
$17$		−	1492.26i		−	1.25234i	−0.779685	−	0.626171i	$-0.784621\pi$
$17$		−	1492.26i		−	1.25234i	0.779685	−	0.626171i	$-0.215379\pi$
$18$	−1251.89	−	521.676i	−0.910721	−	0.379507i
$19$	−2122.13			−1.34862			−0.674308	−	0.738450i	$-0.735558\pi$
$19$	−2122.13			−1.34862			−0.674308	+	0.738450i	$0.735558\pi$
$20$	−1080.61	+	1071.44i	−0.604079	+	0.598955i
$21$		0			0
$22$	−958.818	+	2300.92i	−0.422357	+	1.01355i
$23$			2282.61i			0.899730i	0.893097	+	0.449865i	$0.148528\pi$
$23$			2282.61i			0.899730i	−0.893097	+	0.449865i	$0.851472\pi$
$24$	−122.936	−	302.240i	−0.0435662	−	0.107108i
$25$	863.567			0.276341
$26$	617.166	−	1481.04i	0.179048	−	0.429669i
$27$	870.153			0.229713
$28$		0			0
$29$	1844.20			0.407204			0.203602	−	0.979054i	$-0.434735\pi$
$29$	1844.20			0.407204			0.203602	+	0.979054i	$0.434735\pi$
$30$	186.511	−	447.580i	0.0378357	−	0.0907961i
$31$	−7827.61			−1.46293			−0.731467	−	0.681877i	$-0.761164\pi$
$31$	−7827.61			−1.46293			−0.731467	+	0.681877i	$0.761164\pi$
$32$	−2273.59	+	5327.78i	−0.392499	+	0.919753i
$33$		−	794.270i		−	0.126965i
$34$	3247.03	−	7792.05i	0.481714	−	1.15599i
$35$		0			0
$36$	−5401.79	−	5448.00i	−0.694675	−	0.700618i
$37$	−4035.42			−0.484601			−0.242301	−	0.970201i	$-0.577902\pi$
$37$	−4035.42			−0.484601			−0.242301	+	0.970201i	$0.577902\pi$
$38$	−11081.0	−	4617.57i	−1.24486	−	0.518745i
$39$			511.251i			0.0538236i
$40$	−7973.90	+	3243.37i	−0.787991	+	0.320514i
$41$			1848.03i			0.171692i	0.996308	+	0.0858459i	$0.0273593\pi$
$41$			1848.03i			0.171692i	−0.996308	+	0.0858459i	$0.972641\pi$
$42$		0			0
$43$			3423.76i			0.282379i	0.989983	+	0.141190i	$0.0450927\pi$
$43$			3423.76i			0.282379i	−0.989983	+	0.141190i	$0.954907\pi$
$44$	−10013.2	+	9928.26i	−0.779724	+	0.773110i
$45$		−	11401.2i		−	0.839307i
$46$	−4966.75	+	11918.9i	−0.346081	+	0.830507i
$47$	15907.9			1.05043			0.525217	−	0.850968i	$-0.323984\pi$
$47$	15907.9			1.05043			0.525217	+	0.850968i	$0.323984\pi$
$48$	15.7219	−	1845.68i	0.000984924	−	0.115625i
$49$		0			0
$50$	4509.23	+	1879.04i	0.255080	+	0.106295i
$51$			2689.79i			0.144808i
$52$	6445.23	−	6390.56i	0.330545	−	0.327741i
$53$	−32107.3			−1.57005			−0.785027	−	0.619462i	$-0.787351\pi$
$53$	−32107.3			−1.57005			−0.785027	+	0.619462i	$0.787351\pi$
$54$	4543.62	+	1893.37i	0.212040	+	0.0883592i
$55$	−20955.0			−0.934073
$56$		0			0
$57$	3825.12			0.155940
$58$	9629.72	+	4012.81i	0.375875	+	0.156631i
$59$	−8022.27			−0.300032			−0.150016	−	0.988684i	$-0.547933\pi$
$59$	−8022.27			−0.300032			−0.150016	+	0.988684i	$0.547933\pi$
$60$	1947.78	−	1931.26i	0.0698494	−	0.0692570i
$61$			46698.1i			1.60685i	0.595407	+	0.803424i	$0.296991\pi$
$61$			46698.1i			1.60685i	−0.595407	+	0.803424i	$0.703009\pi$
$62$	−40872.9	−	17032.2i	−1.35038	−	0.562718i
$63$		0			0
$64$	−23464.6	+	22872.5i	−0.716084	+	0.698015i
$65$	13488.2			0.395977
$66$	1728.26	−	4147.38i	0.0488370	−	0.117196i
$67$			53887.8i			1.46657i	0.679921	+	0.733286i	$0.262014\pi$
$67$			53887.8i			1.46657i	−0.679921	+	0.733286i	$0.737986\pi$
$68$	33909.6	−	33622.0i	0.889304	−	0.881761i
$69$		−	4114.38i		−	0.104035i
$70$		0			0
$71$		−	16295.5i		−	0.383639i	−0.981430	−	0.191820i	$-0.938561\pi$
$71$		−	16295.5i		−	0.383639i	0.981430	−	0.191820i	$-0.0614389\pi$
$72$	−16351.8	−	40201.3i	−0.371736	−	0.913921i
$73$		−	20384.0i		−	0.447695i	−0.974624	−	0.223848i	$-0.928138\pi$
$73$		−	20384.0i		−	0.447695i	0.974624	−	0.223848i	$-0.0718618\pi$
$74$	−21071.5	−	8780.71i	−0.447317	−	0.186402i
$75$	−1556.57			−0.0319533
$76$	−47813.4	−	48222.4i	−0.949546	−	0.957669i
$77$		0			0
$78$	−1112.43	+	2669.56i	−0.0207032	+	0.0496825i
$79$		−	44562.4i		−	0.803343i	−0.915784	−	0.401672i	$-0.868429\pi$
$79$		−	44562.4i		−	0.803343i	0.915784	−	0.401672i	$-0.131571\pi$
$80$	−48694.1	−	414.787i	−0.850650	−	0.00724604i
$81$	56691.1			0.960068
$82$	−4021.15	+	9649.73i	−0.0660413	+	0.158482i
$83$	44256.0			0.705143			0.352571	−	0.935785i	$-0.385307\pi$
$83$	44256.0			0.705143			0.352571	+	0.935785i	$0.385307\pi$
$84$		0			0
$85$	70963.9			1.06534
$86$	−7449.80	+	17877.6i	−0.108617	+	0.260654i
$87$	−3324.14			−0.0470849
$88$	−73888.1	+	30053.9i	−1.01711	+	0.413708i
$89$			39941.0i			0.534495i	0.963628	+	0.267248i	$0.0861141\pi$
$89$			39941.0i			0.534495i	−0.963628	+	0.267248i	$0.913886\pi$
$90$	24808.1	−	59533.1i	0.322840	−	0.774733i
$91$		0			0
$92$	−51869.1	+	51429.1i	−0.638909	+	0.633490i
$93$	14109.2			0.169159
$94$	83065.3	+	34614.2i	0.969616	+	0.404049i
$95$		−	100917.i		−	1.14724i
$96$	4098.13	−	9603.25i	0.0453845	−	0.106351i
$97$			131224.i			1.41607i	0.706178	+	0.708034i	$0.250418\pi$
$97$			131224.i			1.41607i	−0.706178	+	0.708034i	$0.749582\pi$
$98$		0			0
$99$		−	105647.i		−	1.08335i
$100$	19456.9	+	19623.3i	0.194569	+	0.196233i
$101$		−	98559.5i		−	0.961380i	−0.876890	−	0.480690i	$-0.840386\pi$
$101$		−	98559.5i		−	0.961380i	0.876890	−	0.480690i	$-0.159614\pi$
$102$	−5852.73	+	14045.1i	−0.0557004	+	0.133667i
$103$	193496.			1.79712			0.898562	−	0.438846i	$-0.144613\pi$
$103$	193496.			1.79712			0.898562	+	0.438846i	$0.144613\pi$
$104$	47559.9	−	19344.9i	0.431179	−	0.175381i
$105$		0			0
$106$	−167653.	−	69862.6i	−1.44926	−	0.603921i
$107$			81994.0i			0.692345i	0.938171	+	0.346173i	$0.112519\pi$
$107$			81994.0i			0.692345i	−0.938171	+	0.346173i	$0.887481\pi$
$108$	19605.3	+	19773.0i	0.161739	+	0.163122i
$109$	−7310.62			−0.0589370			−0.0294685	−	0.999566i	$-0.509381\pi$
$109$	−7310.62			−0.0589370			−0.0294685	+	0.999566i	$0.509381\pi$
$110$	−109419.	−	45596.1i	−0.862208	−	0.359291i
$111$	7273.80			0.0560343
$112$		0			0
$113$	242851.			1.78913			0.894567	−	0.446933i	$-0.147484\pi$
$113$	242851.			1.78913			0.894567	+	0.446933i	$0.147484\pi$
$114$	19973.4	+	8323.11i	0.143942	+	0.0599823i
$115$	−108548.			−0.765383
$116$	41551.3	+	41906.8i	0.286708	+	0.289161i
$117$			68002.1i			0.459259i
$118$	−41889.4	−	17455.7i	−0.276948	−	0.115407i
$119$		0			0
$120$	14372.9	−	5846.14i	0.0911151	−	0.0370609i
$121$	−33123.0			−0.205668
$122$	−101611.	+	243840.i	−0.618074	+	1.48322i
$123$		−	3331.05i		−	0.0198527i
$124$	−176363.	−	177871.i	−1.03004	−	1.03885i
$125$			189674.i			1.08576i
$126$		0			0
$127$			139283.i			0.766280i	0.923690	+	0.383140i	$0.125157\pi$
$127$			139283.i			0.766280i	−0.923690	+	0.383140i	$0.874843\pi$
$128$	−172292.	+	68375.1i	−0.929481	+	0.368870i
$129$		−	6171.29i		−	0.0326514i
$130$	70430.3	+	29349.1i	0.365512	+	0.152313i
$131$	−374276.			−1.90552			−0.952761	−	0.303722i	$-0.901771\pi$
$131$	−374276.			−1.90552			−0.952761	+	0.303722i	$0.901771\pi$
$132$	18048.6	−	17895.6i	0.0901592	−	0.0893944i
$133$		0			0
$134$	−117255.	+	281382.i	−0.564117	+	1.35374i
$135$			41379.7i			0.195413i
$136$	250222.	−	101777.i	1.16005	−	0.471850i
$137$	274838.			1.25105			0.625526	−	0.780204i	$-0.284885\pi$
$137$	274838.			1.25105			0.625526	+	0.780204i	$0.284885\pi$
$138$	8952.51	−	21483.8i	0.0400172	−	0.0960312i
$139$	323870.			1.42178			0.710892	−	0.703301i	$-0.248291\pi$
$139$	323870.			1.42178			0.710892	+	0.703301i	$0.248291\pi$
$140$		0			0
$141$	−28673.8			−0.121461
$142$	35457.6	−	85089.3i	0.147567	−	0.354123i
$143$	124985.			0.511113
$144$	2091.19	−	245496.i	0.00840403	−	0.986594i
$145$			87699.9i			0.346401i
$146$	44353.8	−	106438.i	0.172206	−	0.413251i
$147$		0			0
$148$	−90921.5	−	91699.3i	−0.341202	−	0.344121i
$149$	218474.			0.806185			0.403092	−	0.915159i	$-0.367935\pi$
$149$	218474.			0.806185			0.403092	+	0.915159i	$0.367935\pi$
$150$	−8127.83	−	3386.95i	−0.0294949	−	0.0122908i
$151$		−	161314.i		−	0.575743i	−0.957669	−	0.287872i	$-0.907052\pi$
$151$		−	161314.i		−	0.575743i	0.957669	−	0.287872i	$-0.0929476\pi$
$152$	−144736.	−	355837.i	−0.508123	−	1.24923i
$153$			357772.i			1.23560i
$154$		0			0
$155$		−	372238.i		−	1.24449i
$156$	−11617.4	+	11518.9i	−0.0382208	+	0.0378966i
$157$			319097.i			1.03318i	0.856234	+	0.516588i	$0.172798\pi$
$157$			319097.i			1.03318i	−0.856234	+	0.516588i	$0.827202\pi$
$158$	96963.8	−	232689.i	0.309006	−	0.741536i
$159$	57873.1			0.181545
$160$	−253360.	−	108120.i	−0.782416	−	0.333891i
$161$		0			0
$162$	296020.	+	123355.i	0.886203	+	0.369290i
$163$		−	359129.i		−	1.05872i	−0.848397	−	0.529360i	$-0.822432\pi$
$163$		−	359129.i		−	1.05872i	0.848397	−	0.529360i	$-0.177568\pi$
$164$	−41993.9	+	41637.7i	−0.121920	+	0.120886i
$165$	37771.1			0.108007
$166$	231089.	+	96297.1i	0.650891	+	0.271233i
$167$	99313.1			0.275560			0.137780	−	0.990463i	$-0.456003\pi$
$167$	99313.1			0.275560			0.137780	+	0.990463i	$0.456003\pi$
$168$		0			0
$169$	290844.			0.783326
$170$	370547.	+	154411.i	0.983380	+	0.409785i
$171$	508783.			1.33059
$172$	−77800.2	+	77140.3i	−0.200521	+	0.198820i
$173$			200300.i			0.508823i	0.967096	+	0.254411i	$0.0818817\pi$
$173$			200300.i			0.508823i	−0.967096	+	0.254411i	$0.918118\pi$
$174$	−17357.4	−	7233.03i	−0.0434623	−	0.0181112i
$175$		0			0
$176$	−451211.	−	3843.52i	−1.09799	−	0.00935293i
$177$	14460.1			0.0346926
$178$	−86907.9	+	208557.i	−0.205593	+	0.493372i
$179$			49179.8i			0.114724i	0.998353	+	0.0573620i	$0.0182689\pi$
$179$			49179.8i			0.114724i	−0.998353	+	0.0573620i	$0.981731\pi$
$180$	259077.	−	256880.i	0.596002	−	0.590947i
$181$			211447.i			0.479739i	0.970805	+	0.239869i	$0.0771046\pi$
$181$			211447.i			0.479739i	−0.970805	+	0.239869i	$0.922895\pi$
$182$		0			0
$183$		−	84172.8i		−	0.185799i
$184$	−382746.	+	155681.i	−0.833425	+	0.338994i
$185$		−	191903.i		−	0.412241i
$186$	73672.9	+	30700.3i	0.156144	+	0.0650668i
$187$	657569.			1.37511
$188$	358419.	+	361485.i	0.739599	+	0.745926i
$189$		0			0
$190$	219586.	−	526951.i	0.441287	−	1.05898i
$191$			4755.35i			0.00943189i	0.999989	+	0.00471595i	$0.00150114\pi$
$191$			4755.35i			0.00943189i	−0.999989	+	0.00471595i	$0.998499\pi$
$192$	42294.7	−	41227.5i	0.0828005	−	0.0807112i
$193$	30938.7			0.0597873			0.0298937	−	0.999553i	$-0.490483\pi$
$193$	30938.7			0.0597873			0.0298937	+	0.999553i	$0.490483\pi$
$194$	−285532.	+	685203.i	−0.544690	+	1.30712i
$195$	−24312.3			−0.0457867
$196$		0			0
$197$	55534.5			0.101952			0.0509762	−	0.998700i	$-0.483767\pi$
$197$	55534.5			0.101952			0.0509762	+	0.998700i	$0.483767\pi$
$198$	229878.	−	551648.i	0.416710	−	0.999998i
$199$	−688941.			−1.23324			−0.616622	−	0.787259i	$-0.711499\pi$
$199$	−688941.			−1.23324			−0.616622	+	0.787259i	$0.711499\pi$
$200$	58898.1	+	144802.i	0.104118	+	0.255977i
$201$		−	97132.0i		−	0.169579i
$202$	214457.	−	514641.i	0.369795	−	0.887414i
$203$		0			0
$204$	−61121.6	+	60603.2i	−0.102830	+	0.101958i
$205$	−87882.2			−0.146055
$206$	1.01036e6	+	421029.i	1.65886	+	0.691264i
$207$		−	547258.i		−	0.887700i
$208$	290433.	+	2473.97i	0.465465	+	0.00396494i
$209$		−	935121.i		−	1.48082i
$210$		0			0
$211$			403122.i			0.623348i	0.950189	+	0.311674i	$0.100890\pi$
$211$			403122.i			0.623348i	−0.950189	+	0.311674i	$0.899110\pi$
$212$	−723405.	−	729593.i	−1.10546	−	1.11491i
$213$			29372.5i			0.0443601i
$214$	−178411.	+	428142.i	−0.266311	+	0.639078i
$215$	−162815.			−0.240215
$216$	59347.3	+	145907.i	0.0865499	+	0.212785i
$217$		0			0
$218$	−38173.4	−	15907.3i	−0.0544026	−	0.0226701i
$219$			36741.9i			0.0517669i
$220$	−472134.	−	476172.i	−0.657670	−	0.663296i
$221$	−423260.			−0.582944
$222$	37981.1	+	15827.1i	0.0517232	+	0.0215536i
$223$	−905280.			−1.21905			−0.609524	−	0.792767i	$-0.708640\pi$
$223$	−905280.			−1.21905			−0.609524	+	0.792767i	$0.708640\pi$
$224$		0			0
$225$	−207041.			−0.272647
$226$	1.26808e6	+	528421.i	1.65148	+	0.688191i
$227$	136157.			0.175378			0.0876889	−	0.996148i	$-0.472052\pi$
$227$	136157.			0.175378			0.0876889	+	0.996148i	$0.472052\pi$
$228$	86183.1	+	86920.4i	0.109796	+	0.110735i
$229$		−	106577.i		−	0.134300i	−0.997743	−	0.0671498i	$-0.978609\pi$
$229$		−	106577.i		−	0.134300i	0.997743	−	0.0671498i	$-0.0213905\pi$
$230$	−566800.	−	236191.i	−0.706497	−	0.294405i
$231$		0			0
$232$	125780.	+	309234.i	0.153424	+	0.377196i
$233$	−137442.			−0.165855			−0.0829276	−	0.996556i	$-0.526427\pi$
$233$	−137442.			−0.165855			−0.0829276	+	0.996556i	$0.526427\pi$
$234$	−147966.	+	355082.i	−0.176654	+	0.423925i
$235$			756494.i			0.893585i
$236$	−180749.	−	182295.i	−0.211249	−	0.213056i
$237$			80323.2i			0.0928903i
$238$		0			0
$239$			438994.i			0.497122i	0.968616	+	0.248561i	$0.0799577\pi$
$239$			438994.i			0.497122i	−0.968616	+	0.248561i	$0.920042\pi$
$240$	87770.5	+	747.649i	0.0983604	+	0.000837857i
$241$		−	1.03937e6i		−	1.15273i	−0.817192	−	0.576365i	$-0.804471\pi$
$241$		−	1.03937e6i		−	1.15273i	0.817192	−	0.576365i	$-0.195529\pi$
$242$	−172956.	−	72072.7i	−0.189844	−	0.0791102i
$243$	−313632.			−0.340726
$244$	−1.06115e6	+	1.05215e6i	−1.14104	+	1.13136i
$245$		0			0
$246$	7248.07	−	17393.5i	0.00763633	−	0.0183253i
$247$			601913.i			0.627757i
$248$	−533869.	−	1.31253e6i	−0.551195	−	1.35512i
$249$	−79770.9			−0.0815354
$250$	−412714.	+	990410.i	−0.417637	+	1.00222i
$251$	−856358.			−0.857968			−0.428984	−	0.903312i	$-0.641128\pi$
$251$	−856358.			−0.857968			−0.428984	+	0.903312i	$0.641128\pi$
$252$		0			0
$253$	−1.00584e6			−0.987929
$254$	−303066.	+	727282.i	−0.294749	+	0.707324i
$255$	−127912.			−0.123185
$256$	−1.04842e6	−	17862.7i	−0.999855	−	0.0170352i
$257$		−	1.13713e6i		−	1.07394i	−0.843602	−	0.536968i	$-0.819569\pi$
$257$		−	1.13713e6i		−	1.07394i	0.843602	−	0.536968i	$-0.180431\pi$
$258$	13428.2	−	32224.2i	0.0125594	−	0.0301393i
$259$		0			0
$260$	303900.	+	306500.i	0.278803	+	0.281188i
$261$	−442148.			−0.401760
$262$	−1.95433e6	−	814391.i	−1.75892	−	0.732959i
$263$			1.69566e6i			1.51165i	0.654776	+	0.755823i	$0.272763\pi$
$263$			1.69566e6i			1.51165i	−0.654776	+	0.755823i	$0.727237\pi$
$264$	133182.	−	54171.8i	0.117608	−	0.0478369i
$265$		−	1.52685e6i		−	1.33561i
$266$		0			0
$267$		−	71993.1i		−	0.0618035i
$268$	−1.22452e6	+	1.21414e6i	−1.04143	+	1.03260i
$269$			1.11664e6i			0.940872i	0.882434	+	0.470436i	$0.155903\pi$
$269$			1.11664e6i			0.940872i	−0.882434	+	0.470436i	$0.844097\pi$
$270$	−90038.5	+	216070.i	−0.0751655	+	0.180378i
$271$	−1.22705e6			−1.01494			−0.507470	−	0.861669i	$-0.669419\pi$
$271$	−1.22705e6			−1.01494			−0.507470	+	0.861669i	$0.669419\pi$
$272$	1.52802e6	+	13016.0i	1.25230	+	0.0106674i
$273$		0			0
$274$	1.43510e6	+	598022.i	1.15480	+	0.481217i
$275$			380532.i			0.303431i
$276$	93493.4	−	92700.4i	0.0738768	−	0.0732502i
$277$	−842504.			−0.659740			−0.329870	−	0.944026i	$-0.607005\pi$
$277$	−842504.			−0.659740			−0.329870	+	0.944026i	$0.607005\pi$
$278$	1.69113e6	+	704712.i	1.31240	+	0.546889i
$279$	1.87668e6			1.44337
$280$		0			0
$281$	−2.05076e6			−1.54935			−0.774675	−	0.632359i	$-0.782087\pi$
$281$	−2.05076e6			−1.54935			−0.774675	+	0.632359i	$0.782087\pi$
$282$	−149724.	−	62391.7i	−0.112116	−	0.0467201i
$283$	−1.28614e6			−0.954604			−0.477302	−	0.878739i	$-0.658385\pi$
$283$	−1.28614e6			−0.954604			−0.477302	+	0.878739i	$0.658385\pi$
$284$	370293.	−	367152.i	0.272427	−	0.270116i
$285$			181902.i			0.132655i
$286$	652624.	+	271956.i	0.471789	+	0.196600i
$287$		0			0
$288$	545097.	−	1.27734e6i	0.387251	−	0.907455i
$289$	−806994.			−0.568363
$290$	−190827.	+	457937.i	−0.133243	+	0.319750i
$291$		−	236530.i		−	0.163739i
$292$	463198.	−	459269.i	0.317914	−	0.315217i
$293$		−	1.56244e6i		−	1.06325i	−0.846981	−	0.531623i	$-0.821582\pi$
$293$		−	1.56244e6i		−	1.06325i	0.846981	−	0.531623i	$-0.178418\pi$
$294$		0			0
$295$		−	381495.i		−	0.255232i
$296$	−275229.	−	676656.i	−0.182585	−	0.448889i
$297$			383434.i			0.252232i
$298$	1.14079e6	+	475380.i	0.744159	+	0.310099i
$299$	647431.			0.418808
$300$	−35070.8	−	35370.8i	−0.0224979	−	0.0226904i
$301$		0			0
$302$	351004.	−	842320.i	0.221460	−	0.531447i
$303$			177652.i			0.111164i
$304$	18510.0	−	2.17298e6i	0.0114874	−	1.34857i
$305$	−2.22071e6			−1.36692
$306$	−778479.	+	1.86815e6i	−0.475273	+	1.14054i
$307$	−1.33011e6			−0.805456			−0.402728	−	0.915320i	$-0.631938\pi$
$307$	−1.33011e6			−0.805456			−0.402728	+	0.915320i	$0.631938\pi$
$308$		0			0
$309$	−348774.			−0.207801
$310$	809956.	−	1.94369e6i	0.478693	−	1.14874i
$311$	1.17071e6			0.686357			0.343178	−	0.939270i	$-0.388496\pi$
$311$	1.17071e6			0.686357			0.343178	+	0.939270i	$0.388496\pi$
$312$	−85726.1	+	34869.0i	−0.0498571	+	0.0202793i
$313$			2715.41i			0.00156666i	1.00000		0.000783329i	$0.000249341\pi$
$313$			2715.41i			0.00156666i	−1.00000		0.000783329i	$0.999751\pi$
$314$	−694327.	+	1.66621e6i	−0.397411	+	0.953686i
$315$		0			0
$316$	1.01262e6	−	1.00403e6i	0.570464	−	0.565625i
$317$	698795.			0.390572			0.195286	−	0.980746i	$-0.437436\pi$
$317$	698795.			0.390572			0.195286	+	0.980746i	$0.437436\pi$
$318$	302192.	+	125926.i	0.167577	+	0.0698312i
$319$			812649.i			0.447122i
$320$	−1.08769e6	−	1.11585e6i	−0.593788	−	0.609159i
$321$		−	147793.i		−	0.0800556i
$322$		0			0
$323$			3.16678e6i			1.68893i
$324$	1.27730e6	+	1.28822e6i	0.675973	+	0.681756i
$325$		−	244939.i		−	0.128632i
$326$	781432.	−	1.87524e6i	0.407237	−	0.977265i
$327$	13177.3			0.00681487
$328$	−309876.	+	126042.i	−0.159039	+	0.0646889i
$329$		0			0
$330$	197227.	+	82186.5i	0.0996968	+	0.0415447i
$331$			1.37663e6i			0.690632i	0.938486	+	0.345316i	$0.112228\pi$
$331$			1.37663e6i			0.690632i	−0.938486	+	0.345316i	$0.887772\pi$
$332$	997125.	+	1.00566e6i	0.496483	+	0.500730i
$333$	967497.			0.478122
$334$	518576.	+	216096.i	0.254359	+	0.105994i
$335$	−2.56261e6			−1.24758
$336$		0			0
$337$	−776941.			−0.372660			−0.186330	−	0.982487i	$-0.559659\pi$
$337$	−776941.			−0.372660			−0.186330	+	0.982487i	$0.559659\pi$
$338$	1.51868e6	+	632849.i	0.723059	+	0.301306i
$339$	−437735.			−0.206877
$340$	1.59888e6	+	1.61255e6i	0.750097	+	0.756514i
$341$		−	3.44925e6i		−	1.60634i
$342$	2.65668e6	+	1.10707e6i	1.22821	+	0.511810i
$343$		0			0
$344$	−574094.	+	233512.i	−0.261569	+	0.106393i
$345$	195657.			0.0885010
$346$	−435835.	+	1.04589e6i	−0.195719	+	0.469675i
$347$		−	4.34258e6i		−	1.93608i	−0.250791	−	0.968041i	$-0.580691\pi$
$347$		−	4.34258e6i		−	1.93608i	0.250791	−	0.968041i	$-0.419309\pi$
$348$	−74895.8	−	75536.5i	−0.0331520	−	0.0334356i
$349$			123357.i			0.0542127i	0.999633	+	0.0271063i	$0.00862927\pi$
$349$			123357.i			0.0542127i	−0.999633	+	0.0271063i	$0.991371\pi$
$350$		0			0
$351$		−	246807.i		−	0.106927i
$352$	−2.34769e6	−	1.00186e6i	−1.00992	−	0.430975i
$353$			2.16756e6i			0.925837i	0.886401	+	0.462918i	$0.153198\pi$
$353$			2.16756e6i			0.925837i	−0.886401	+	0.462918i	$0.846802\pi$
$354$	75505.0	+	31463.8i	0.0320234	+	0.0133445i
$355$	774927.			0.326355
$356$	−907602.	+	899904.i	−0.379551	+	0.376332i
$357$		0			0
$358$	−107011.	+	256799.i	−0.0441286	+	0.105897i
$359$		−	4.66927e6i		−	1.91211i	−0.293185	−	0.956056i	$-0.594715\pi$
$359$		−	4.66927e6i		−	1.91211i	0.293185	−	0.956056i	$-0.405285\pi$
$360$	1.91175e6	−	777602.i	0.777455	−	0.316229i
$361$	2.02735e6			0.818766
$362$	−460089.	+	1.10410e6i	−0.184531	+	0.442829i
$363$	59703.8			0.0237813
$364$		0			0
$365$	969352.			0.380846
$366$	183152.	−	439519.i	0.0714677	−	0.171504i
$367$	3.92657e6			1.52177			0.760884	−	0.648888i	$-0.224766\pi$
$367$	3.92657e6			1.52177			0.760884	+	0.648888i	$0.224766\pi$
$368$	−2.33731e6	−	19909.7i	−0.899697	−	0.00766383i
$369$		−	443067.i		−	0.169396i
$370$	417563.	−	1.00204e6i	0.158569	−	0.380525i
$371$		0			0
$372$	317891.	+	320611.i	0.119103	+	0.120122i
$373$	1.19566e6			0.444975			0.222488	−	0.974935i	$-0.428582\pi$
$373$	1.19566e6			0.444975			0.222488	+	0.974935i	$0.428582\pi$
$374$	3.43358e6	+	1.43081e6i	1.26931	+	0.528936i
$375$		−	341886.i		−	0.125546i
$376$	1.08497e6	+	2.66743e6i	0.395776	+	0.973023i
$377$		−	523081.i		−	0.189546i
$378$		0			0
$379$		−	2.70264e6i		−	0.966473i	−0.875490	−	0.483237i	$-0.839461\pi$
$379$		−	2.70264e6i		−	0.966473i	0.875490	−	0.483237i	$-0.160539\pi$
$380$	2.29320e6	−	2.27374e6i	0.814671	−	0.807761i
$381$		−	251055.i		−	0.0886046i
$382$	−10347.2	+	24830.7i	−0.00362798	+	0.00870622i
$383$	−2.02959e6			−0.706986			−0.353493	−	0.935437i	$-0.615006\pi$
$383$	−2.02959e6			−0.706986			−0.353493	+	0.935437i	$0.615006\pi$
$384$	310555.	−	123245.i	0.107476	−	0.0426523i
$385$		0			0
$386$	161551.	+	67319.8i	0.0551874	+	0.0229972i
$387$		−	820851.i		−	0.278604i
$388$	−2.98188e6	+	2.95659e6i	−1.00557	+	0.997037i
$389$	3.88740e6			1.30252			0.651261	−	0.758854i	$-0.274241\pi$
$389$	3.88740e6			1.30252			0.651261	+	0.758854i	$0.274241\pi$
$390$	−126950.	−	52901.3i	−0.0422640	−	0.0176118i
$391$	3.40626e6			1.12677
$392$		0			0
$393$	674628.			0.220335
$394$	289981.	+	120838.i	0.0941084	+	0.0392160i
$395$	2.11915e6			0.683389
$396$	2.40067e6	−	2.38031e6i	0.769298	−	0.762773i
$397$			4.31496e6i			1.37404i	0.726636	+	0.687022i	$0.241083\pi$
$397$			4.31496e6i			1.37404i	−0.726636	+	0.687022i	$0.758917\pi$
$398$	−3.59739e6	−	1.49907e6i	−1.13836	−	0.474367i
$399$		0			0
$400$	−7532.34	+	884261.i	−0.00235385	+	0.276331i
$401$	−2.39818e6			−0.744769			−0.372385	−	0.928079i	$-0.621460\pi$
$401$	−2.39818e6			−0.744769			−0.372385	+	0.928079i	$0.621460\pi$
$402$	211350.	−	507188.i	0.0652286	−	0.156532i
$403$			2.22019e6i			0.680970i
$404$	2.23963e6	−	2.22063e6i	0.682688	−	0.676897i
$405$			2.69592e6i			0.816712i
$406$		0			0
$407$		−	1.77822e6i		−	0.532107i
$408$	−451021.	+	183452.i	−0.134136	+	0.0545598i
$409$			3.21957e6i			0.951678i	0.879532	+	0.475839i	$0.157856\pi$
$409$			3.21957e6i			0.951678i	−0.879532	+	0.475839i	$0.842144\pi$
$410$	−458889.	−	191224.i	−0.134818	−	0.0561801i
$411$	−495392.			−0.144659
$412$	4.35962e6	+	4.39691e6i	1.26534	+	1.27616i
$413$		0			0
$414$	1.19078e6	−	2.85758e6i	0.341454	−	0.819403i
$415$			2.10457e6i			0.599852i
$416$	1.51115e6	+	644874.i	0.428129	+	0.182701i
$417$	−583772.			−0.164400
$418$	2.03474e6	−	4.88286e6i	0.569597	−	1.36689i
$419$	3.84140e6			1.06894			0.534472	−	0.845186i	$-0.320510\pi$
$419$	3.84140e6			1.06894			0.534472	+	0.845186i	$0.320510\pi$
$420$		0			0
$421$	2.57965e6			0.709342			0.354671	−	0.934991i	$-0.384593\pi$
$421$	2.57965e6			0.709342			0.354671	+	0.934991i	$0.384593\pi$
$422$	−877158.	+	2.10496e6i	−0.239771	+	0.575389i
$423$	−3.81394e6			−1.03639
$424$	−2.18982e6	−	5.38373e6i	−0.591554	−	1.45435i
$425$		−	1.28867e6i		−	0.346074i
$426$	−63911.9	+	153372.i	−0.0170631	+	0.0409471i
$427$		0			0
$428$	−1.86320e6	+	1.84739e6i	−0.491643	+	0.487472i
$429$	−225284.			−0.0590998
$430$	−850162.	−	354272.i	−0.221733	−	0.0923986i
$431$		−	837370.i		−	0.217132i	−0.994089	−	0.108566i	$-0.965374\pi$
$431$		−	837370.i		−	0.217132i	0.994089	−	0.108566i	$-0.0346259\pi$
$432$	−7589.78	+	891004.i	−0.00195668	+	0.229705i
$433$			2.31098e6i			0.592348i	0.955134	+	0.296174i	$0.0957108\pi$
$433$			2.31098e6i			0.592348i	−0.955134	+	0.296174i	$0.904289\pi$
$434$		0			0
$435$		−	158078.i		−	0.0400542i
$436$	−164715.	−	166124.i	−0.0414969	−	0.0418519i
$437$		−	4.84400e6i		−	1.21339i
$438$	−79947.1	+	191853.i	−0.0199121	+	0.0477841i
$439$	837534.			0.207416			0.103708	−	0.994608i	$-0.466929\pi$
$439$	837534.			0.207416			0.103708	+	0.994608i	$0.466929\pi$
$440$	−1.42920e6	−	3.51372e6i	−0.351934	−	0.865237i
$441$		0			0
$442$	−2.21011e6	−	920975.i	−0.538093	−	0.224229i
$443$			3.24790e6i			0.786310i	0.919472	+	0.393155i	$0.128616\pi$
$443$			3.24790e6i			0.786310i	−0.919472	+	0.393155i	$0.871384\pi$
$444$	163885.	+	165287.i	0.0394531	+	0.0397906i
$445$	−1.89937e6			−0.454685
$446$	−4.72704e6	−	1.96981e6i	−1.12526	−	0.468907i
$447$	−393797.			−0.0932188
$448$		0			0
$449$	−4.27089e6			−0.999776			−0.499888	−	0.866090i	$-0.666626\pi$
$449$	−4.27089e6			−0.999776			−0.499888	+	0.866090i	$0.666626\pi$
$450$	−1.08109e6	−	450503.i	−0.251670	−	0.104874i
$451$	−814338.			−0.188523
$452$	5.47163e6	+	5.51843e6i	1.25971	+	1.27049i
$453$			290766.i			0.0665730i
$454$	710961.	+	296265.i	0.161885	+	0.0674591i
$455$		0			0
$456$	260886.	+	641393.i	0.0587541	+	0.144448i
$457$	7.91259e6			1.77226			0.886131	−	0.463434i	$-0.153383\pi$
$457$	7.91259e6			1.77226			0.886131	+	0.463434i	$0.153383\pi$
$458$	231902.	−	556505.i	0.0516583	−	0.123967i
$459$		−	1.29850e6i		−	0.287680i
$460$	−2.44569e6	−	2.46661e6i	−0.538898	−	0.543508i
$461$			1.83353e6i			0.401824i	0.979609	+	0.200912i	$0.0643906\pi$
$461$			1.83353e6i			0.401824i	−0.979609	+	0.200912i	$0.935609\pi$
$462$		0			0
$463$		−	218753.i		−	0.0474245i	−0.999719	−	0.0237122i	$-0.992451\pi$
$463$		−	218753.i		−	0.0474245i	0.999719	−	0.0237122i	$-0.00754855\pi$
$464$	−16085.7	+	1.88839e6i	−0.00346853	+	0.407190i
$465$			670955.i			0.143900i
$466$	−717670.	−	299061.i	−0.153095	−	0.0637962i
$467$	−1.75614e6			−0.372621			−0.186310	−	0.982491i	$-0.559653\pi$
$467$	−1.75614e6			−0.372621			−0.186310	+	0.982491i	$0.559653\pi$
$468$	−1.54525e6	+	1.53214e6i	−0.326125	+	0.323359i
$469$		0			0
$470$	−1.64606e6	+	3.95013e6i	−0.343717	+	0.824834i
$471$		−	575169.i		−	0.119466i
$472$	−547145.	−	1.34517e6i	−0.113044	−	0.277921i
$473$	−1.50869e6			−0.310061
$474$	−174776.	+	419418.i	−0.0357303	+	0.0857436i
$475$	−1.83260e6			−0.372679
$476$		0			0
$477$	7.69776e6			1.54906
$478$	−955210.	+	2.29226e6i	−0.191218	+	0.458875i
$479$	−1.45354e6			−0.289459			−0.144730	−	0.989471i	$-0.546231\pi$
$479$	−1.45354e6			−0.289459			−0.144730	+	0.989471i	$0.546231\pi$
$480$	456678.	+	194884.i	0.0904705	+	0.0386077i
$481$			1.14459e6i			0.225573i
$482$	2.26158e6	−	5.42721e6i	0.443398	−	1.06404i
$483$		0			0
$484$	−746290.	−	752674.i	−0.144808	−	0.146047i
$485$	−6.24030e6			−1.20462
$486$	−1.63767e6	−	682435.i	−0.314511	−	0.131060i
$487$		−	3.22703e6i		−	0.616568i	−0.951294	−	0.308284i	$-0.900245\pi$
$487$		−	3.22703e6i		−	0.616568i	0.951294	−	0.308284i	$-0.0997547\pi$
$488$	−7.83030e6	+	3.18496e6i	−1.48843	+	0.605418i
$489$			647325.i			0.122419i
$490$		0			0
$491$			5.93538e6i			1.11108i	0.831490	+	0.555540i	$0.187488\pi$
$491$			5.93538e6i			1.11108i	−0.831490	+	0.555540i	$0.812512\pi$
$492$	75693.5	−	75051.4i	0.0140976	−	0.0139780i
$493$		−	2.75203e6i		−	0.509960i
$494$	−1.30971e6	+	3.14297e6i	−0.241467	+	0.579459i
$495$	5.02398e6			0.921584
$496$	68275.1	−	8.01518e6i	0.0124612	−	1.46288i
$497$		0			0
$498$	−416534.	−	173574.i	−0.0752623	−	0.0313626i
$499$		−	6.13417e6i		−	1.10282i	−0.834235	−	0.551409i	$-0.814090\pi$
$499$		−	6.13417e6i		−	1.10282i	0.834235	−	0.551409i	$-0.185910\pi$
$500$	−4.31008e6	+	4.27352e6i	−0.771011	+	0.764471i
$501$	−179011.			−0.0318629
$502$	−4.47158e6	−	1.86336e6i	−0.791958	−	0.330017i
$503$	−1.32110e6			−0.232818			−0.116409	−	0.993201i	$-0.537138\pi$
$503$	−1.32110e6			−0.232818			−0.116409	+	0.993201i	$0.537138\pi$
$504$		0			0
$505$	4.68695e6			0.817828
$506$	−5.25210e6	−	2.18861e6i	−0.911921	−	0.380007i
$507$	−524242.			−0.0905757
$508$	−3.16500e6	+	3.13815e6i	−0.544144	+	0.539529i
$509$			6.26550e6i			1.07192i	0.844244	+	0.535958i	$0.180050\pi$
$509$			6.26550e6i			1.07192i	−0.844244	+	0.535958i	$0.819950\pi$
$510$	−667907.	−	278324.i	−0.113708	−	0.0473833i
$511$		0			0
$512$	−5.43561e6	−	2.37455e6i	−0.916376	−	0.400319i
$513$	−1.84658e6			−0.309795
$514$	2.47430e6	−	5.93769e6i	0.413090	−	0.991311i
$515$			9.20159e6i			1.52878i
$516$	140234.	−	139044.i	0.0231862	−	0.0229895i
$517$			7.00985e6i			1.15341i
$518$		0			0
$519$		−	361039.i		−	0.0588350i
$520$	919938.	+	2.26169e6i	0.149194	+	0.366796i
$521$			1.14739e6i			0.185190i	0.995704	+	0.0925949i	$0.0295162\pi$
$521$			1.14739e6i			0.185190i	−0.995704	+	0.0925949i	$0.970484\pi$
$522$	−2.30873e6	−	962074.i	−0.370850	−	0.154537i
$523$	5.24592e6			0.838624			0.419312	−	0.907842i	$-0.362271\pi$
$523$	5.24592e6			0.838624			0.419312	+	0.907842i	$0.362271\pi$
$524$	−8.43276e6	−	8.50489e6i	−1.34166	−	1.35313i
$525$		0			0
$526$	−3.68961e6	+	8.85412e6i	−0.581454	+	1.39534i
$527$			1.16809e7i			1.83210i
$528$	813303.	+	6927.90i	0.126960	+	0.00108148i
$529$	1.22604e6			0.190486
$530$	3.32228e6	−	7.97264e6i	0.513744	−	1.23286i
$531$	1.92335e6			0.296020
$532$		0			0
$533$	524168.			0.0799195
$534$	156650.	−	375921.i	0.0237727	−	0.0570485i
$535$	−3.89919e6			−0.588965
$536$	−9.03586e6	+	3.67532e6i	−1.35849	+	0.552565i
$537$		−	88646.0i		−	0.0132655i
$538$	−2.42970e6	+	5.83066e6i	−0.361907	+	0.868484i
$539$		0			0
$540$	−940295.	+	932320.i	−0.138765	+	0.137588i
$541$	3.53916e6			0.519885			0.259943	−	0.965624i	$-0.416296\pi$
$541$	3.53916e6			0.519885			0.259943	+	0.965624i	$0.416296\pi$
$542$	−6.40722e6	−	2.66996e6i	−0.936854	−	0.390397i
$543$		−	381130.i		−	0.0554720i
$544$	7.95045e6	+	3.39280e6i	1.15185	+	0.491543i
$545$		−	347653.i		−	0.0501366i
$546$		0			0
$547$		−	1.25811e7i		−	1.79783i	−0.438121	−	0.898916i	$-0.644356\pi$
$547$		−	1.25811e7i		−	1.79783i	0.438121	−	0.898916i	$-0.355644\pi$
$548$	6.19233e6	+	6.24530e6i	0.880851	+	0.888386i
$549$		−	1.11959e7i		−	1.58536i
$550$	−828004.	+	1.98700e6i	−0.116715	+	0.280086i
$551$	−3.91363e6			−0.549163
$552$	689895.	−	280614.i	0.0963686	−	0.0391978i
$553$		0			0
$554$	−4.39925e6	−	1.83321e6i	−0.608981	−	0.253769i
$555$			345902.i			0.0476673i
$556$	7.29707e6	+	7.35949e6i	1.00106	+	1.00963i
$557$	1.67910e6			0.229318			0.114659	−	0.993405i	$-0.463422\pi$
$557$	1.67910e6			0.229318			0.114659	+	0.993405i	$0.463422\pi$
$558$	9.79931e6	+	4.08348e6i	1.33233	+	0.555194i
$559$	971103.			0.131443
$560$		0			0
$561$	−1.18526e6			−0.159003
$562$	−1.07083e7	−	4.46227e6i	−1.43015	−	0.595958i
$563$	−3.94833e6			−0.524980			−0.262490	−	0.964935i	$-0.584544\pi$
$563$	−3.94833e6			−0.524980			−0.262490	+	0.964935i	$0.584544\pi$
$564$	−646046.	−	651572.i	−0.0855196	−	0.0862511i
$565$			1.15486e7i			1.52198i
$566$	−6.71576e6	−	2.79853e6i	−0.881159	−	0.367188i
$567$		0			0
$568$	2.73242e6	−	1.11141e6i	0.355367	−	0.144545i
$569$	869064.			0.112531			0.0562654	−	0.998416i	$-0.482081\pi$
$569$	869064.			0.112531			0.0562654	+	0.998416i	$0.482081\pi$
$570$	−395801.	+	949823.i	−0.0510258	+	0.122449i
$571$		−	1.87664e6i		−	0.240874i	−0.992721	−	0.120437i	$-0.961570\pi$
$571$		−	1.87664e6i		−	0.240874i	0.992721	−	0.120437i	$-0.0384296\pi$
$572$	2.81601e6	+	2.84010e6i	0.359869	+	0.362948i
$573$		−	8571.45i		−	0.00109061i
$574$		0			0
$575$			1.97119e6i			0.248633i
$576$	5.62567e6	−	5.48372e6i	0.706509	−	0.688682i
$577$		−	3.46225e6i		−	0.432932i	−0.976290	−	0.216466i	$-0.930547\pi$
$577$		−	3.46225e6i		−	0.432932i	0.976290	−	0.216466i	$-0.0694530\pi$
$578$	−4.21382e6	−	1.75595e6i	−0.524635	−	0.218621i
$579$	−55766.7			−0.00691319
$580$	−1.99286e6	+	1.97595e6i	−0.245984	+	0.243897i
$581$		0			0
$582$	514667.	−	1.23507e6i	0.0629824	−	0.151142i
$583$		−	1.41481e7i		−	1.72396i
$584$	3.41798e6	−	1.39026e6i	0.414703	−	0.168680i
$585$	−3.23381e6			−0.390683
$586$	3.39972e6	−	8.15847e6i	0.408977	−	0.981442i
$587$	−3.18312e6			−0.381292			−0.190646	−	0.981659i	$-0.561058\pi$
$587$	−3.18312e6			−0.381292			−0.190646	+	0.981659i	$0.561058\pi$
$588$		0			0
$589$	1.66112e7			1.97294
$590$	830099.	−	1.99203e6i	0.0981748	−	0.235595i
$591$	−100100.			−0.0117887
$592$	35198.4	−	4.13212e6i	0.00412780	−	0.484584i
$593$		−	1.97523e6i		−	0.230665i	−0.993327	−	0.115332i	$-0.963207\pi$
$593$		−	1.97523e6i		−	0.230665i	0.993327	−	0.115332i	$-0.0367933\pi$
$594$	−834318.	+	2.00215e6i	−0.0970210	+	0.232826i
$595$		0			0
$596$	4.92241e6	+	4.96452e6i	0.567626	+	0.572481i
$597$	1.24181e6			0.142600
$598$	3.38064e6	+	1.40875e6i	0.386586	+	0.161095i
$599$			6.42535e6i			0.731695i	0.930675	+	0.365847i	$0.119221\pi$
$599$			6.42535e6i			0.731695i	−0.930675	+	0.365847i	$0.880779\pi$
$600$	−106163.	−	261004.i	−0.0120391	−	0.0295985i
$601$		−	1.27820e7i		−	1.44349i	−0.692159	−	0.721745i	$-0.743340\pi$
$601$		−	1.27820e7i		−	1.44349i	0.692159	−	0.721745i	$-0.256660\pi$
$602$		0			0
$603$		−	1.29196e7i		−	1.44696i
$604$	3.66562e6	−	3.63453e6i	0.408842	−	0.405374i
$605$		−	1.57515e6i		−	0.174958i
$606$	−386555.	+	927635.i	−0.0427593	+	0.102611i
$607$	1.25033e7			1.37737			0.688687	−	0.725059i	$-0.258188\pi$
$607$	1.25033e7			1.37737			0.688687	+	0.725059i	$0.258188\pi$
$608$	4.82487e6	−	1.13062e7i	0.529330	−	1.24039i
$609$		0			0
$610$	−1.15957e7	−	4.83206e6i	−1.26175	−	0.525784i
$611$		−	4.51206e6i		−	0.488959i
$612$	−8.12986e6	+	8.06090e6i	−0.877414	+	0.869971i
$613$	7.68180e6			0.825680			0.412840	−	0.910804i	$-0.364537\pi$
$613$	7.68180e6			0.825680			0.412840	+	0.910804i	$0.364537\pi$
$614$	−6.94534e6	−	2.89420e6i	−0.743486	−	0.309818i
$615$	158407.			0.0168883
$616$		0			0
$617$	−1.48453e7			−1.56991			−0.784956	−	0.619552i	$-0.787314\pi$
$617$	−1.48453e7			−1.56991			−0.784956	+	0.619552i	$0.787314\pi$
$618$	−1.82117e6	−	758900.i	−0.191813	−	0.0799306i
$619$	8.42082e6			0.883340			0.441670	−	0.897178i	$-0.354386\pi$
$619$	8.42082e6			0.883340			0.441670	+	0.897178i	$0.354386\pi$
$620$	8.45859e6	−	8.38684e6i	0.883728	−	0.876232i
$621$			1.98622e6i			0.206680i
$622$	6.11303e6	+	2.54737e6i	0.633550	+	0.264007i
$623$		0			0
$624$	−523502.	−	4459.31i	−0.0538216	−	0.000458465i
$625$	−6.32123e6			−0.647294
$626$	−5908.48	+	14178.8i	−0.000602615	+	0.00144612i
$627$			1.68555e6i			0.171227i
$628$	−7.25104e6	+	7.18953e6i	−0.733670	+	0.727447i
$629$			6.02192e6i			0.606887i
$630$		0			0
$631$			1.38513e7i			1.38489i	0.721470	+	0.692446i	$0.243467\pi$
$631$			1.38513e7i			1.38489i	−0.721470	+	0.692446i	$0.756533\pi$
$632$	7.47219e6	−	3.03930e6i	0.744141	−	0.302678i
$633$		−	726623.i		−	0.0720775i
$634$	3.64885e6	+	1.52051e6i	0.360523	+	0.150234i
$635$	−6.62351e6			−0.651860
$636$	1.30393e6	+	1.31508e6i	0.127824	+	0.128917i
$637$		0			0
$638$	−1.76825e6	+	4.24335e6i	−0.171986	+	0.412722i
$639$			3.90687e6i			0.378510i
$640$	−3.25154e6	−	8.19327e6i	−0.313790	−	0.790692i
$641$	−1.19731e7			−1.15097			−0.575483	−	0.817813i	$-0.695186\pi$
$641$	−1.19731e7			−1.15097			−0.575483	+	0.817813i	$0.695186\pi$
$642$	321584.	−	771721.i	0.0307934	−	0.0738963i
$643$	8.56267e6			0.816736			0.408368	−	0.912817i	$-0.366098\pi$
$643$	8.56267e6			0.816736			0.408368	+	0.912817i	$0.366098\pi$
$644$		0			0
$645$	293473.			0.0277759
$646$	−6.89063e6	+	1.65358e7i	−0.649647	+	1.55899i
$647$	−4.07023e6			−0.382260			−0.191130	−	0.981565i	$-0.561215\pi$
$647$	−4.07023e6			−0.382260			−0.191130	+	0.981565i	$0.561215\pi$
$648$	3.86652e6	+	9.50591e6i	0.361728	+	0.889316i
$649$		−	3.53503e6i		−	0.329444i
$650$	532965.	−	1.27898e6i	0.0494783	−	0.118735i
$651$		0			0
$652$	8.16069e6	−	8.09148e6i	0.751810	−	0.745433i
$653$	2.26308e6			0.207690			0.103845	−	0.994593i	$-0.466885\pi$
$653$	2.26308e6			0.207690			0.103845	+	0.994593i	$0.466885\pi$
$654$	68807.1	+	28672.6i	0.00629055	+	0.00262134i
$655$		−	1.77985e7i		−	1.62099i
$656$	−1.89232e6	−	16119.2i	−0.171686	−	0.00146246i
$657$			4.88709e6i			0.441710i
$658$		0			0
$659$			1.26265e7i			1.13258i	0.824205	+	0.566292i	$0.191623\pi$
$659$			1.26265e7i			1.13258i	−0.824205	+	0.566292i	$0.808377\pi$
$660$	851015.	+	858295.i	0.0760462	+	0.0766967i
$661$			1.92975e7i			1.71790i	0.512060	+	0.858949i	$0.328882\pi$
$661$			1.92975e7i			1.71790i	−0.512060	+	0.858949i	$0.671118\pi$
$662$	−2.99542e6	+	7.18825e6i	−0.265652	+	0.637497i
$663$	762921.			0.0674056
$664$	3.01841e6	+	7.42081e6i	0.265679	+	0.653178i
$665$		0			0
$666$	5.05191e6	+	2.10518e6i	0.441337	+	0.183910i
$667$			4.20958e6i			0.366374i
$668$	2.23761e6	+	2.25675e6i	0.194018	+	0.195678i
$669$	1.63176e6			0.140958
$670$	−1.33810e7	−	5.57600e6i	−1.15160	−	0.479883i
$671$	−2.05776e7			−1.76437
$672$		0			0
$673$	−2.00592e6			−0.170717			−0.0853583	−	0.996350i	$-0.527203\pi$
$673$	−2.00592e6			−0.170717			−0.0853583	+	0.996350i	$0.527203\pi$
$674$	−4.05690e6	−	1.69055e6i	−0.343989	−	0.143344i
$675$	751435.			0.0634793
$676$	6.55295e6	+	6.60901e6i	0.551531	+	0.556249i
$677$		−	1.97697e7i		−	1.65779i	−0.559406	−	0.828894i	$-0.688971\pi$
$677$		−	1.97697e7i		−	1.65779i	0.559406	−	0.828894i	$-0.311029\pi$
$678$	−2.28569e6	−	952472.i	−0.190960	−	0.0795752i
$679$		0			0
$680$	4.83997e6	+	1.18992e7i	0.401394	+	0.986835i
$681$	−245421.			−0.0202789
$682$	7.50525e6	−	1.80107e7i	0.617880	−	1.48276i
$683$		−	3.00078e6i		−	0.246140i	−0.992398	−	0.123070i	$-0.960726\pi$
$683$		−	3.00078e6i		−	0.246140i	0.992398	−	0.123070i	$-0.0392740\pi$
$684$	1.14633e7	+	1.15614e7i	0.936850	+	0.944864i
$685$			1.30698e7i			1.06425i
$686$		0			0
$687$			192104.i			0.0155290i
$688$	−3.50581e6	−	29863.3i	−0.282369	−	0.00240528i
$689$			9.10680e6i			0.730832i
$690$	1.02165e6	+	425732.i	0.0816919	+	0.0340419i
$691$	−1.05751e7			−0.842539			−0.421269	−	0.906936i	$-0.638415\pi$
$691$	−1.05751e7			−0.842539			−0.421269	+	0.906936i	$0.638415\pi$
$692$	−4.55154e6	+	4.51293e6i	−0.361321	+	0.358256i
$693$		0			0
$694$	9.44905e6	−	2.26753e7i	0.744714	−	1.78713i
$695$			1.54015e7i			1.20949i
$696$	−226718.	−	557390.i	−0.0177403	−	0.0436150i
$697$	2.75775e6			0.215017
$698$	−268414.	+	644125.i	−0.0208529	+	0.0500417i
$699$	247737.			0.0191778
$700$		0			0
$701$	−5.89982e6			−0.453465			−0.226733	−	0.973957i	$-0.572804\pi$
$701$	−5.89982e6			−0.453465			−0.226733	+	0.973957i	$0.572804\pi$
$702$	537029.	−	1.28873e6i	0.0411297	−	0.0987008i
$703$	8.56370e6			0.653542
$704$	−1.00788e7	−	1.03397e7i	−0.766440	−	0.786281i
$705$		−	1.36357e6i		−	0.103325i
$706$	−4.71641e6	+	1.13182e7i	−0.356123	+	0.854605i
$707$		0			0
$708$	325797.	+	328584.i	0.0244267	+	0.0246356i
$709$	2.09040e7			1.56176			0.780881	−	0.624680i	$-0.214771\pi$
$709$	2.09040e7			1.56176			0.780881	+	0.624680i	$0.214771\pi$
$710$	4.04638e6	+	1.68617e6i	0.301246	+	0.125532i
$711$			1.06839e7i			0.792602i
$712$	−6.69727e6	+	2.72411e6i	−0.495106	+	0.201384i
$713$		−	1.78674e7i		−	1.31625i
$714$		0			0
$715$			5.94359e6i			0.434794i
$716$	−1.11754e6	+	1.10806e6i	−0.0814669	+	0.0807759i
$717$		−	791280.i		−	0.0574821i
$718$	1.01599e7	−	2.43812e7i	0.735494	−	1.76500i
$719$	−9.04694e6			−0.652648			−0.326324	−	0.945258i	$-0.605810\pi$
$719$	−9.04694e6			−0.652648			−0.326324	+	0.945258i	$0.605810\pi$
$720$	1.16745e7	+	99445.7i	0.839277	+	0.00714915i
$721$		0			0
$722$	1.05861e7	+	4.41132e6i	0.755773	+	0.314938i
$723$			1.87345e6i			0.133290i
$724$	−4.80483e6	+	4.76407e6i	−0.340668	+	0.337779i
$725$	1.59259e6			0.112527
$726$	311751.	+	129910.i	0.0219516	+	0.00914748i
$727$	2.52083e7			1.76892			0.884458	−	0.466621i	$-0.154529\pi$
$727$	2.52083e7			1.76892			0.884458	+	0.466621i	$0.154529\pi$
$728$		0			0
$729$	−1.32106e7			−0.920670
$730$	5.06160e6	+	2.10922e6i	0.351545	+	0.146492i
$731$	5.10916e6			0.353636
$732$	1.91271e6	−	1.89648e6i	0.131938	−	0.130819i
$733$			1.07049e7i			0.735904i	0.929845	+	0.367952i	$0.119941\pi$
$733$			1.07049e7i			0.735904i	−0.929845	+	0.367952i	$0.880059\pi$
$734$	2.05031e7	+	8.54386e6i	1.40469	+	0.585348i
$735$		0			0
$736$	−1.21612e7	−	5.18973e6i	−0.827529	−	0.353143i
$737$	−2.37457e7			−1.61034
$738$	964074.	−	2.31353e6i	0.0651583	−	0.156363i
$739$		−	4.29031e6i		−	0.288987i	−0.989506	−	0.144493i	$-0.953845\pi$
$739$		−	4.29031e6i		−	0.288987i	0.989506	−	0.144493i	$-0.0461552\pi$
$740$	4.36071e6	−	4.32373e6i	0.292738	−	0.290255i
$741$		−	1.08494e6i		−	0.0725873i
$742$		0			0
$743$		−	1.03989e7i		−	0.691062i	−0.938407	−	0.345531i	$-0.887699\pi$
$743$		−	1.03989e7i		−	0.691062i	0.938407	−	0.345531i	$-0.112301\pi$
$744$	962292.	+	2.36581e6i	0.0637345	+	0.156693i
$745$			1.03894e7i			0.685806i
$746$	6.24330e6	+	2.60165e6i	0.410740	+	0.171160i
$747$	−1.06104e7			−0.695715
$748$	1.48156e7	+	1.49423e7i	0.968199	+	0.976481i
$749$		0			0
$750$	743912.	−	1.78520e6i	0.0482913	−	0.115887i
$751$		−	1.42620e7i		−	0.922740i	−0.887208	−	0.461370i	$-0.847358\pi$
$751$		−	1.42620e7i		−	0.922740i	0.887208	−	0.461370i	$-0.152642\pi$
$752$	−138754.	+	1.62891e7i	−0.00894751	+	1.05040i
$753$	1.54357e6			0.0992065
$754$	1.13818e6	−	2.73134e6i	0.0729090	−	0.174963i
$755$	7.67119e6			0.489774
$756$		0			0
$757$	−2.38648e6			−0.151362			−0.0756811	−	0.997132i	$-0.524113\pi$
$757$	−2.38648e6			−0.151362			−0.0756811	+	0.997132i	$0.524113\pi$
$758$	5.88069e6	−	1.41122e7i	0.371754	−	0.892115i
$759$	1.81301e6			0.114234
$760$	1.69217e7	−	6.88287e6i	1.06270	−	0.432251i
$761$		−	2.99799e7i		−	1.87659i	−0.345838	−	0.938294i	$-0.612405\pi$
$761$		−	2.99799e7i		−	1.87659i	0.345838	−	0.938294i	$-0.387595\pi$
$762$	546273.	−	1.31092e6i	0.0340818	−	0.0817876i
$763$		0			0
$764$	−108059.	+	107142.i	−0.00669770	+	0.00664089i
$765$	−1.70137e7			−1.05110
$766$	−1.05978e7	−	4.41620e6i	−0.652592	−	0.271942i
$767$			2.27541e6i			0.139660i
$768$	1.88977e6	+	32197.3i	0.115613	+	0.00196978i
$769$		−	2.85040e7i		−	1.73816i	−0.494673	−	0.869079i	$-0.664712\pi$
$769$		−	2.85040e7i		−	1.73816i	0.494673	−	0.869079i	$-0.335288\pi$
$770$		0			0
$771$			2.04967e6i			0.124179i
$772$	697075.	+	703038.i	0.0420956	+	0.0424557i
$773$		−	7.13489e6i		−	0.429476i	−0.976672	−	0.214738i	$-0.931110\pi$
$773$		−	7.13489e6i		−	0.429476i	0.976672	−	0.214738i	$-0.0688897\pi$
$774$	1.78610e6	−	4.28618e6i	0.107165	−	0.257169i
$775$	−6.75967e6			−0.404269
$776$	−2.20035e7	+	8.94991e6i	−1.31171	+	0.533537i
$777$		0			0
$778$	2.02985e7	+	8.45862e6i	1.20231	+	0.501015i
$779$		−	3.92177e6i		−	0.231546i
$780$	−547776.	−	552462.i	−0.0322379	−	0.0325137i
$781$	7.18066e6			0.421247
$782$	1.77862e7	+	7.41170e6i	1.04008	+	0.433412i
$783$	1.60473e6			0.0935403
$784$		0			0
$785$	−1.51745e7			−0.878903
$786$	3.52266e6	+	1.46793e6i	0.203383	+	0.0847518i
$787$	−1.11677e7			−0.642728			−0.321364	−	0.946956i	$-0.604141\pi$
$787$	−1.11677e7			−0.642728			−0.321364	+	0.946956i	$0.604141\pi$
$788$	1.25124e6	+	1.26194e6i	0.0717835	+	0.0723976i
$789$		−	3.05641e6i		−	0.174791i
$790$	1.10654e7	+	4.61107e6i	0.630811	+	0.262866i
$791$		0			0
$792$	1.77148e7	−	7.20545e6i	1.00351	−	0.408177i
$793$	1.32453e7			0.747959
$794$	−9.38897e6	+	2.25311e7i	−0.528526	+	1.26833i
$795$			2.75213e6i			0.154437i
$796$	−1.55224e7	−	1.56552e7i	−0.868313	−	0.875741i
$797$			3.53833e6i			0.197312i	0.995122	+	0.0986559i	$0.0314543\pi$
$797$			3.53833e6i			0.197312i	−0.995122	+	0.0986559i	$0.968546\pi$
$798$		0			0
$799$		−	2.37388e7i		−	1.31550i
$800$	−1.96340e6	+	4.60089e6i	−0.108464	+	0.254166i
$801$		−	9.57589e6i		−	0.527349i
$802$	−1.25224e7	−	5.21823e6i	−0.687469	−	0.286475i
$803$	8.98226e6			0.491583
$804$	2.20719e6	−	2.18847e6i	0.120420	−	0.119399i
$805$		0			0
$806$	−4.83094e6	+	1.15930e7i	−0.261935	+	0.628578i
$807$		−	2.01272e6i		−	0.108793i
$808$	1.65264e7	−	6.72208e6i	0.890532	−	0.362223i
$809$	8.47199e6			0.455108			0.227554	−	0.973765i	$-0.426927\pi$
$809$	8.47199e6			0.455108			0.227554	+	0.973765i	$0.426927\pi$
$810$	−5.86607e6	+	1.40771e7i	−0.314148	+	0.753876i
$811$	−3.15075e7			−1.68214			−0.841071	−	0.540925i	$-0.818074\pi$
$811$	−3.15075e7			−1.68214			−0.841071	+	0.540925i	$0.818074\pi$
$812$		0			0
$813$	2.21175e6			0.117357
$814$	3.86924e6	−	9.28519e6i	0.204675	−	0.491168i
$815$	1.70782e7			0.900634
$816$	−2.75424e6	−	23461.3i	−0.144803	−	0.00123346i
$817$		−	7.26568e6i		−	0.380821i
$818$	−7.00550e6	+	1.68114e7i	−0.366063	+	0.878459i
$819$		0			0
$820$	−1.98006e6	−	1.99700e6i	−0.102836	−	0.103715i
$821$	1.14106e7			0.590815			0.295408	−	0.955371i	$-0.404545\pi$
$821$	1.14106e7			0.590815			0.295408	+	0.955371i	$0.404545\pi$
$822$	−2.58675e6	−	1.07793e6i	−0.133529	−	0.0556429i
$823$		−	5.67425e6i		−	0.292017i	−0.989283	−	0.146009i	$-0.953357\pi$
$823$		−	5.67425e6i		−	0.292017i	0.989283	−	0.146009i	$-0.0466427\pi$
$824$	1.31970e7	+	3.24452e7i	0.677109	+	1.66469i
$825$		−	685905.i		−	0.0350856i
$826$		0			0
$827$			1.92994e7i			0.981248i	0.871371	+	0.490624i	$0.163231\pi$
$827$			1.92994e7i			0.981248i	−0.871371	+	0.490624i	$0.836769\pi$
$828$	1.24357e7	−	1.23302e7i	0.630367	−	0.625020i
$829$			2.17447e7i			1.09892i	0.835519	+	0.549461i	$0.185167\pi$
$829$			2.17447e7i			1.09892i	−0.835519	+	0.549461i	$0.814833\pi$
$830$	−4.57936e6	+	1.09893e7i	−0.230733	+	0.553701i
$831$	1.51860e6			0.0762855
$832$	6.48748e6	+	6.65542e6i	0.324913	+	0.333324i
$833$		0			0
$834$	−3.04824e6	−	1.27023e6i	−0.151752	−	0.0632366i
$835$			4.72279e6i			0.234413i
$836$	2.12493e7	−	2.10691e7i	1.05155	−	1.04263i
$837$	−6.81122e6			−0.336055
$838$	2.00584e7	+	8.35855e6i	0.986702	+	0.411169i
$839$	−1.73523e7			−0.851046			−0.425523	−	0.904948i	$-0.639910\pi$
$839$	−1.73523e7			−0.851046			−0.425523	+	0.904948i	$0.639910\pi$
$840$		0			0
$841$	−1.71101e7			−0.834185
$842$	1.34700e7	+	5.61308e6i	0.654767	+	0.272848i
$843$	3.69648e6			0.179151
$844$	−9.16038e6	+	9.08269e6i	−0.442647	+	0.438893i
$845$			1.38309e7i			0.666361i
$846$	−1.99150e7	−	8.29879e6i	−0.956652	−	0.398647i
$847$		0			0
$848$	280051.	−	3.28767e7i	0.0133736	−	1.57000i
$849$	2.31826e6			0.110381
$850$	2.80403e6	−	6.72896e6i	0.133117	−	0.319448i
$851$		−	9.21130e6i		−	0.436010i
$852$	−667449.	+	661788.i	−0.0315006	+	0.0312334i
$853$			3.34110e6i			0.157223i	0.996905	+	0.0786117i	$0.0250487\pi$
$853$			3.34110e6i			0.157223i	−0.996905	+	0.0786117i	$0.974951\pi$
$854$		0			0
$855$			2.41950e7i			1.13190i
$856$	−1.37487e7	+	5.59226e6i	−0.641323	+	0.260857i
$857$		−	5.74789e6i		−	0.267336i	−0.991026	−	0.133668i	$-0.957324\pi$
$857$		−	5.74789e6i		−	0.267336i	0.991026	−	0.133668i	$-0.0426755\pi$
$858$	−1.17635e6	−	490196.i	−0.0545528	−	0.0227328i
$859$	2.70940e7			1.25282			0.626411	−	0.779493i	$-0.284523\pi$
$859$	2.70940e7			1.25282			0.626411	+	0.779493i	$0.284523\pi$
$860$	−3.66837e6	−	3.69975e6i	−0.169132	−	0.170579i
$861$		0			0
$862$	1.82204e6	−	4.37244e6i	0.0835199	−	0.200427i
$863$		−	1.13453e7i		−	0.518548i	−0.965804	−	0.259274i	$-0.916517\pi$
$863$		−	1.13453e7i		−	0.518548i	0.965804	−	0.259274i	$-0.0834833\pi$
$864$	−1.97837e6	+	4.63598e6i	−0.0901621	+	0.211279i
$865$	−9.52518e6			−0.432846
$866$	−5.02849e6	+	1.20671e7i	−0.227847	+	0.546774i
$867$	1.45460e6			0.0657196
$868$		0			0
$869$	1.96365e7			0.882094
$870$	343963.	−	825425.i	0.0154069	−	0.0369726i
$871$	1.52845e7			0.682663
$872$	−498609.	−	1.22584e6i	−0.0222059	−	0.0545937i
$873$		−	3.14611e7i		−	1.39713i
$874$	1.05401e7	−	2.52936e7i	0.466731	−	1.12004i
$875$		0			0
$876$	−834909.	+	827827.i	−0.0367603	+	0.0364485i
$877$	−1.14952e7			−0.504682			−0.252341	−	0.967638i	$-0.581200\pi$
$877$	−1.14952e7			−0.504682			−0.252341	+	0.967638i	$0.581200\pi$
$878$	4.37330e6	+	1.82240e6i	0.191458	+	0.0797824i
$879$			2.81627e6i			0.122943i
$880$	182777.	−	2.14571e7i	0.00795636	−	0.934039i
$881$		−	3.70787e7i		−	1.60948i	−0.593630	−	0.804738i	$-0.702306\pi$
$881$		−	3.70787e7i		−	1.60948i	0.593630	−	0.804738i	$-0.297694\pi$
$882$		0			0
$883$			9.49309e6i			0.409738i	0.978789	+	0.204869i	$0.0656768\pi$
$883$			9.49309e6i			0.409738i	−0.978789	+	0.204869i	$0.934323\pi$
$884$	−9.53640e6	−	9.61798e6i	−0.410444	−	0.413955i
$885$			687641.i			0.0295123i
$886$	−7.06714e6	+	1.69594e7i	−0.302454	+	0.725814i
$887$	−7.01372e6			−0.299322			−0.149661	−	0.988737i	$-0.547818\pi$
$887$	−7.01372e6			−0.299322			−0.149661	+	0.988737i	$0.547818\pi$
$888$	496097.	+	1.21967e6i	0.0211122	+	0.0519049i
$889$		0			0
$890$	−9.91783e6	−	4.13287e6i	−0.419703	−	0.174895i
$891$			2.49810e7i			1.05418i
$892$	−2.03967e7	−	2.05712e7i	−0.858318	−	0.865661i
$893$	−3.37587e7			−1.41663
$894$	−2.05626e6	−	856867.i	−0.0860468	−	0.0358566i
$895$	−2.33872e6			−0.0975936
$896$		0			0
$897$	−1.16699e6			−0.0484267
$898$	−2.23010e7	−	9.29307e6i	−0.922856	−	0.384564i
$899$	−1.44357e7			−0.595713
$900$	−4.66481e6	−	4.70472e6i	−0.191968	−	0.193610i
$901$			4.79126e7i			1.96625i
$902$	−4.25217e6	−	1.77193e6i	−0.174018	−	0.0725152i
$903$		0			0
$904$	1.65632e7	+	4.07210e7i	0.674098	+	1.65728i
$905$	−1.00553e7			−0.408105
$906$	−632680.	+	1.51827e6i	−0.0256073	+	0.0614510i
$907$			1.37533e7i			0.555124i	0.960708	+	0.277562i	$0.0895264\pi$
$907$			1.37533e7i			0.555124i	−0.960708	+	0.277562i	$0.910474\pi$
$908$	3.06773e6	+	3.09397e6i	0.123482	+	0.124538i
$909$			2.36298e7i			0.948527i
$910$		0			0
$911$		−	3.60526e6i		−	0.143926i	−0.997407	−	0.0719632i	$-0.977074\pi$
$911$		−	3.60526e6i		−	0.143926i	0.997407	−	0.0719632i	$-0.0229264\pi$
$912$	−33364.0	+	3.91678e6i	−0.00132829	+	0.155934i
$913$			1.95015e7i			0.774267i
$914$	4.13166e7	+	1.72171e7i	1.63591	+	0.681701i
$915$	4.00280e6			0.158056
$916$	2.42181e6	−	2.40127e6i	0.0953677	−	0.0945588i
$917$		0			0
$918$	2.82541e6	−	6.78027e6i	0.110656	−	0.265546i
$919$			386352.i			0.0150902i	0.999972	+	0.00754510i	$0.00240170\pi$
$919$			386352.i			0.0150902i	−0.999972	+	0.00754510i	$0.997598\pi$
$920$	−7.40336e6	−	1.82013e7i	−0.288376	−	0.708979i
$921$	2.39751e6			0.0931346
$922$	−3.98960e6	+	9.57403e6i	−0.154562	+	0.370909i
$923$	−4.62201e6			−0.178577
$924$		0			0
$925$	−3.48486e6			−0.133915
$926$	475988.	−	1.14225e6i	0.0182418	−	0.0437757i
$927$	−4.63908e7			−1.77310
$928$	−4.19296e6	+	9.82547e6i	−0.159827	+	0.374527i
$929$		−	6.18099e6i		−	0.234973i	−0.993074	−	0.117487i	$-0.962516\pi$
$929$		−	6.18099e6i		−	0.234973i	0.993074	−	0.117487i	$-0.0374837\pi$
$930$	−1.45994e6	+	3.50348e6i	−0.0553511	+	0.132829i
$931$		0			0
$932$	−3.09668e6	−	3.12317e6i	−0.116777	−	0.117776i
$933$	−2.11020e6			−0.0793632
$934$	−9.16991e6	−	3.82120e6i	−0.343952	−	0.143328i
$935$			3.12704e7i			1.16978i
$936$	−1.14025e7	+	4.63796e6i	−0.425414	+	0.173037i
$937$		−	1.37458e7i		−	0.511469i	−0.966747	−	0.255735i	$-0.917683\pi$
$937$		−	1.37458e7i		−	0.511469i	0.966747	−	0.255735i	$-0.0823173\pi$
$938$		0			0
$939$		−	4894.49i		−	0.000181152i
$940$	−1.71902e7	+	1.70444e7i	−0.634545	+	0.629163i
$941$		−	3.77179e7i		−	1.38859i	−0.719691	−	0.694294i	$-0.755717\pi$
$941$		−	3.77179e7i		−	1.38859i	0.719691	−	0.694294i	$-0.244283\pi$
$942$	1.25152e6	−	3.00332e6i	0.0459525	−	0.110274i
$943$	−4.21833e6			−0.154476
$944$	69973.1	−	8.21451e6i	0.00255565	−	0.300021i
$945$		0			0
$946$	−7.87781e6	−	3.28277e6i	−0.286205	−	0.119265i
$947$		−	2.68030e7i		−	0.971199i	−0.874181	−	0.485599i	$-0.838601\pi$
$947$		−	2.68030e7i		−	0.971199i	0.874181	−	0.485599i	$-0.161399\pi$
$948$	−1.82523e6	+	1.80975e6i	−0.0659625	+	0.0654030i
$949$	−5.78165e6			−0.208394
$950$	−9.56918e6	−	3.98758e6i	−0.344006	−	0.143351i
$951$	−1.25957e6			−0.0451617
$952$		0			0
$953$	−2.21927e7			−0.791548			−0.395774	−	0.918348i	$-0.629524\pi$
$953$	−2.21927e7			−0.791548			−0.395774	+	0.918348i	$0.629524\pi$
$954$	4.01949e7	+	1.67496e7i	1.42988	+	0.595846i
$955$	−226138.			−0.00802353
$956$	−9.97550e6	+	9.89089e6i	−0.353013	+	0.350018i
$957$		−	1.46479e6i		−	0.0517006i
$958$	−7.58984e6	−	3.16277e6i	−0.267189	−	0.111341i
$959$		0			0
$960$	1.96055e6	+	2.01130e6i	0.0686595	+	0.0704368i
$961$	3.26423e7			1.14018
$962$	−2.49053e6	+	5.97664e6i	−0.0867668	+	0.208218i
$963$		−	1.96581e7i		−	0.683088i
$964$	2.36182e7	−	2.34179e7i	0.818568	−	0.811625i
$965$			1.47128e6i			0.0508599i
$966$		0			0
$967$		−	1.62944e7i		−	0.560366i	−0.959947	−	0.280183i	$-0.909605\pi$
$967$		−	1.62944e7i		−	0.560366i	0.959947	−	0.280183i	$-0.0903952\pi$
$968$	−2.25910e6	−	5.55404e6i	−0.0774902	−	0.190511i
$969$		−	5.70808e6i		−	0.195290i
$970$	−3.25845e7	−	1.35783e7i	−1.11194	−	0.463358i
$971$	238504.			0.00811796			0.00405898	−	0.999992i	$-0.498708\pi$
$971$	238504.			0.00811796			0.00405898	+	0.999992i	$0.498708\pi$
$972$	−7.06640e6	−	7.12684e6i	−0.239901	−	0.241953i
$973$		0			0
$974$	7.02173e6	−	1.68504e7i	0.237163	−	0.569131i
$975$			441499.i			0.0148737i
$976$	−4.78171e7	−	407317.i	−1.60679	−	0.0136870i
$977$	−1.12237e7			−0.376183			−0.188091	−	0.982152i	$-0.560230\pi$
$977$	−1.12237e7			−0.376183			−0.188091	+	0.982152i	$0.560230\pi$
$978$	−1.40852e6	+	3.38009e6i	−0.0470886	+	0.113001i
$979$	−1.76001e7			−0.586891
$980$		0			0
$981$	1.75273e6			0.0581490
$982$	−1.29149e7	+	3.09924e7i	−0.427377	+	1.02560i
$983$	5.72153e6			0.188855			0.0944275	−	0.995532i	$-0.469898\pi$
$983$	5.72153e6			0.188855			0.0944275	+	0.995532i	$0.469898\pi$
$984$	558548.	−	227189.i	0.0183896	−	0.00747996i
$985$			2.64092e6i			0.0867290i
$986$	5.98816e6	−	1.43701e7i	0.196156	−	0.470725i
$987$		0			0
$988$	−1.36776e7	+	1.35616e7i	−0.445778	+	0.441997i
$989$	−7.81512e6			−0.254065
$990$	2.62334e7	+	1.09317e7i	0.850680	+	0.354487i
$991$			4.79274e7i			1.55024i	0.631812	+	0.775122i	$0.282312\pi$
$991$			4.79274e7i			1.55024i	−0.631812	+	0.775122i	$0.717688\pi$
$992$	1.77968e7	−	4.17037e7i	0.574200	−	1.34554i
$993$		−	2.48136e6i		−	0.0798576i
$994$		0			0
$995$		−	3.27622e7i		−	1.04910i
$996$	−1.79731e6	−	1.81268e6i	−0.0574082	−	0.0578993i
$997$		−	3.82882e7i		−	1.21991i	−0.792437	−	0.609954i	$-0.791188\pi$
$997$		−	3.82882e7i		−	1.21991i	0.792437	−	0.609954i	$-0.208812\pi$
$998$	1.33474e7	−	3.20303e7i	0.424199	−	1.01797i
$999$	−3.51143e6			−0.111319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.d.b.195.31		36
4.3	odd	2	inner	196.6.d.b.195.30		36
7.4	even	3		28.6.f.a.19.4	yes	36
7.5	odd	6		28.6.f.a.3.9	yes	36
7.6	odd	2	inner	196.6.d.b.195.32		36
28.11	odd	6		28.6.f.a.19.9	yes	36
28.19	even	6		28.6.f.a.3.4	✓	36
28.27	even	2	inner	196.6.d.b.195.29		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.4	✓	36	28.19	even	6
28.6.f.a.3.9	yes	36	7.5	odd	6
28.6.f.a.19.4	yes	36	7.4	even	3
28.6.f.a.19.9	yes	36	28.11	odd	6
196.6.d.b.195.29		36	28.27	even	2	inner
196.6.d.b.195.30		36	4.3	odd	2	inner
196.6.d.b.195.31		36	1.1	even	1	trivial
196.6.d.b.195.32		36	7.6	odd	2	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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.22163 + 2.17591i) q^{2} -1.80249 q^{3} +(22.5308 + 22.7236i) q^{4} +47.5545i q^{5} +(-9.41192 - 3.92205i) q^{6} +(68.2033 + 167.679i) q^{8} -239.751 q^{9} +(-103.474 + 248.312i) q^{10} +440.652i q^{11} +(-40.6116 - 40.9590i) q^{12} -283.636i q^{13} -85.7165i q^{15} +(-8.72235 + 1023.96i) q^{16} -1492.26i q^{17} +(-1251.89 - 521.676i) q^{18} -2122.13 q^{19} +(-1080.61 + 1071.44i) q^{20} +(-958.818 + 2300.92i) q^{22} +2282.61i q^{23} +(-122.936 - 302.240i) q^{24} +863.567 q^{25} +(617.166 - 1481.04i) q^{26} +870.153 q^{27} +1844.20 q^{29} +(186.511 - 447.580i) q^{30} -7827.61 q^{31} +(-2273.59 + 5327.78i) q^{32} -794.270i q^{33} +(3247.03 - 7792.05i) q^{34} +(-5401.79 - 5448.00i) q^{36} -4035.42 q^{37} +(-11081.0 - 4617.57i) q^{38} +511.251i q^{39} +(-7973.90 + 3243.37i) q^{40} +1848.03i q^{41} +3423.76i q^{43} +(-10013.2 + 9928.26i) q^{44} -11401.2i q^{45} +(-4966.75 + 11918.9i) q^{46} +15907.9 q^{47} +(15.7219 - 1845.68i) q^{48} +(4509.23 + 1879.04i) q^{50} +2689.79i q^{51} +(6445.23 - 6390.56i) q^{52} -32107.3 q^{53} +(4543.62 + 1893.37i) q^{54} -20955.0 q^{55} +3825.12 q^{57} +(9629.72 + 4012.81i) q^{58} -8022.27 q^{59} +(1947.78 - 1931.26i) q^{60} +46698.1i q^{61} +(-40872.9 - 17032.2i) q^{62} +(-23464.6 + 22872.5i) q^{64} +13488.2 q^{65} +(1728.26 - 4147.38i) q^{66} +53887.8i q^{67} +(33909.6 - 33622.0i) q^{68} -4114.38i q^{69} -16295.5i q^{71} +(-16351.8 - 40201.3i) q^{72} -20384.0i q^{73} +(-21071.5 - 8780.71i) q^{74} -1556.57 q^{75} +(-47813.4 - 48222.4i) q^{76} +(-1112.43 + 2669.56i) q^{78} -44562.4i q^{79} +(-48694.1 - 414.787i) q^{80} +56691.1 q^{81} +(-4021.15 + 9649.73i) q^{82} +44256.0 q^{83} +70963.9 q^{85} +(-7449.80 + 17877.6i) q^{86} -3324.14 q^{87} +(-73888.1 + 30053.9i) q^{88} +39941.0i q^{89} +(24808.1 - 59533.1i) q^{90} +(-51869.1 + 51429.1i) q^{92} +14109.2 q^{93} +(83065.3 + 34614.2i) q^{94} -100917. i q^{95} +(4098.13 - 9603.25i) q^{96} +131224. i q^{97} -105647. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50}+ \cdots + 330324 q^{93}+O(q^{100}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

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