LMFDB - Embedded newform 100.7.b.f.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,7,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	100.b (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:	$23.0054083620$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} - 10x^{8} + 1775x^{6} - 1000x^{4} - 160000x^{2} + 1000000 $ x^12 - 16x^10 - 10x^8 + 1775x^6 - 1000x^4 - 160000*x^2 + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.4
Root			$3.01463 - 0.954985i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.7.b.f.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.35482 + 5.94356i) q^{2} +40.3729i q^{3} +(-6.65182 - 63.6534i) q^{4} +(-239.959 - 216.189i) q^{6} -450.705i q^{7} +(413.947 + 301.317i) q^{8} -900.969 q^{9} +O(q^{10})$	\(q+(-5.35482 + 5.94356i) q^{2} +40.3729i q^{3} +(-6.65182 - 63.6534i) q^{4} +(-239.959 - 216.189i) q^{6} -450.705i q^{7} +(413.947 + 301.317i) q^{8} -900.969 q^{9} +390.888i q^{11} +(2569.87 - 268.553i) q^{12} +3234.51 q^{13} +(2678.79 + 2413.44i) q^{14} +(-4007.51 + 846.821i) q^{16} +4937.20 q^{17} +(4824.53 - 5354.96i) q^{18} -1980.00i q^{19} +18196.2 q^{21} +(-2323.27 - 2093.14i) q^{22} +1077.32i q^{23} +(-12165.0 + 16712.2i) q^{24} +(-17320.2 + 19224.5i) q^{26} -6942.88i q^{27} +(-28688.9 + 2998.00i) q^{28} +21158.1 q^{29} -33221.4i q^{31} +(16426.3 - 28353.4i) q^{32} -15781.3 q^{33} +(-26437.8 + 29344.6i) q^{34} +(5993.08 + 57349.7i) q^{36} -14159.5 q^{37} +(11768.3 + 10602.6i) q^{38} +130586. i q^{39} -42870.4 q^{41} +(-97437.6 + 108150. i) q^{42} +57775.6i q^{43} +(24881.4 - 2600.12i) q^{44} +(-6403.13 - 5768.87i) q^{46} +138151. i q^{47} +(-34188.6 - 161795. i) q^{48} -85485.6 q^{49} +199329. i q^{51} +(-21515.4 - 205887. i) q^{52} +277123. q^{53} +(41265.4 + 37177.9i) q^{54} +(135805. - 186568. i) q^{56} +79938.4 q^{57} +(-113298. + 125755. i) q^{58} -28176.1i q^{59} -34082.0 q^{61} +(197453. + 177894. i) q^{62} +406071. i q^{63} +(80560.3 + 249458. i) q^{64} +(84506.0 - 93797.1i) q^{66} -230002. i q^{67} +(-32841.4 - 314270. i) q^{68} -43494.6 q^{69} +214659. i q^{71} +(-372953. - 271477. i) q^{72} +21193.6 q^{73} +(75821.5 - 84157.8i) q^{74} +(-126034. + 13170.6i) q^{76} +176175. q^{77} +(-776148. - 699267. i) q^{78} -365752. i q^{79} -376502. q^{81} +(229563. - 254803. i) q^{82} +50231.1i q^{83} +(-121038. - 1.15825e6i) q^{84} +(-343393. - 309378. i) q^{86} +854215. i q^{87} +(-117781. + 161807. i) q^{88} +177274. q^{89} -1.45781e6i q^{91} +(68575.2 - 7166.15i) q^{92} +1.34124e6 q^{93} +(-821109. - 739774. i) q^{94} +(1.14471e6 + 663179. i) q^{96} +1.15267e6 q^{97} +(457760. - 508089. i) q^{98} -352178. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9}+O(q^{10}) $ 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9	$ 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9} - 512 q^{14} - 20928 q^{16} + 51216 q^{21} + 20928 q^{24} + 14496 q^{26} + 16072 q^{29} - 257216 q^{34} - 144960 q^{36} - 192136 q^{41} + 165120 q^{44} - 49472 q^{46} - 145796 q^{49} + 118656 q^{54} + 1078208 q^{56} + 215384 q^{61} + 6656 q^{64} - 1403520 q^{66} - 1015824 q^{69} + 1020384 q^{74} + 2515200 q^{76} - 2327652 q^{81} - 424704 q^{84} - 5268832 q^{86} + 4346152 q^{89} - 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) $ 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9 - 512 * q^14 - 20928 * q^16 + 51216 * q^21 + 20928 * q^24 + 14496 * q^26 + 16072 * q^29 - 257216 * q^34 - 144960 * q^36 - 192136 * q^41 + 165120 * q^44 - 49472 * q^46 - 145796 * q^49 + 118656 * q^54 + 1078208 * q^56 + 215384 * q^61 + 6656 * q^64 - 1403520 * q^66 - 1015824 * q^69 + 1020384 * q^74 + 2515200 * q^76 - 2327652 * q^81 - 424704 * q^84 - 5268832 * q^86 + 4346152 * q^89 - 4292992 * q^94 + 7673088 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−5.35482	+	5.94356i	−0.669352	+	0.742945i
$2$	−5.35482	+	5.94356i	−0.669352	+	0.742945i
$3$			40.3729i			1.49529i	0.664098	+	0.747646i	$0.268816\pi$
$3$			40.3729i			1.49529i	−0.664098	+	0.747646i	$0.731184\pi$
$4$	−6.65182	−	63.6534i	−0.103935	−	0.994584i
$5$		0			0
$5$		0			0
$6$	−239.959	−	216.189i	−1.11092	−	1.00088i
$7$		−	450.705i		−	1.31401i	−0.753887	−	0.657004i	$-0.771824\pi$
$7$		−	450.705i		−	1.31401i	0.753887	−	0.657004i	$-0.228176\pi$
$8$	413.947	+	301.317i	0.808490	+	0.588510i
$9$	−900.969			−1.23590
$10$		0			0
$11$			390.888i			0.293680i	0.989160	+	0.146840i	$0.0469103\pi$
$11$			390.888i			0.293680i	−0.989160	+	0.146840i	$0.953090\pi$
$12$	2569.87	−	268.553i	1.48719	−	0.155413i
$13$	3234.51			1.47224			0.736119	−	0.676852i	$-0.236656\pi$
$13$	3234.51			1.47224			0.736119	+	0.676852i	$0.236656\pi$
$14$	2678.79	+	2413.44i	0.976235	+	0.879534i
$15$		0			0
$16$	−4007.51	+	846.821i	−0.978395	+	0.206744i
$17$	4937.20			1.00493			0.502463	−	0.864599i	$-0.332427\pi$
$17$	4937.20			1.00493			0.502463	+	0.864599i	$0.332427\pi$
$18$	4824.53	−	5354.96i	0.827251	−	0.918204i
$19$		−	1980.00i		−	0.288672i	−0.989529	−	0.144336i	$-0.953895\pi$
$19$		−	1980.00i		−	0.288672i	0.989529	−	0.144336i	$-0.0461047\pi$
$20$		0			0
$21$	18196.2			1.96482
$22$	−2323.27	−	2093.14i	−0.218188	−	0.196576i
$23$			1077.32i			0.0885446i	0.999020	+	0.0442723i	$0.0140969\pi$
$23$			1077.32i			0.0885446i	−0.999020	+	0.0442723i	$0.985903\pi$
$24$	−12165.0	+	16712.2i	−0.879993	+	1.20893i
$25$		0			0
$26$	−17320.2	+	19224.5i	−0.985447	+	1.09379i
$27$		−	6942.88i		−	0.352735i
$28$	−28688.9	+	2998.00i	−1.30689	+	0.136571i
$29$	21158.1			0.867528			0.433764	−	0.901027i	$-0.357185\pi$
$29$	21158.1			0.867528			0.433764	+	0.901027i	$0.357185\pi$
$30$		0			0
$31$		−	33221.4i		−	1.11515i	−0.830127	−	0.557574i	$-0.811732\pi$
$31$		−	33221.4i		−	1.11515i	0.830127	−	0.557574i	$-0.188268\pi$
$32$	16426.3	−	28353.4i	0.501292	−	0.865278i
$33$	−15781.3			−0.439138
$34$	−26437.8	+	29344.6i	−0.672650	+	0.746605i
$35$		0			0
$36$	5993.08	+	57349.7i	0.128453	+	1.22920i
$37$	−14159.5			−0.279539			−0.139769	−	0.990184i	$-0.544636\pi$
$37$	−14159.5			−0.279539			−0.139769	+	0.990184i	$0.544636\pi$
$38$	11768.3	+	10602.6i	0.214468	+	0.193223i
$39$			130586.i			2.20143i
$40$		0			0
$41$	−42870.4			−0.622023			−0.311011	−	0.950406i	$-0.600668\pi$
$41$	−42870.4			−0.622023			−0.311011	+	0.950406i	$0.600668\pi$
$42$	−97437.6	+	108150.i	−1.31516	+	1.45976i
$43$			57775.6i			0.726673i	0.931658	+	0.363337i	$0.118363\pi$
$43$			57775.6i			0.726673i	−0.931658	+	0.363337i	$0.881637\pi$
$44$	24881.4	−	2600.12i	0.292090	−	0.0305236i
$45$		0			0
$46$	−6403.13	−	5768.87i	−0.0657838	−	0.0592676i
$47$			138151.i			1.33064i	0.746558	+	0.665320i	$0.231705\pi$
$47$			138151.i			1.33064i	−0.746558	+	0.665320i	$0.768295\pi$
$48$	−34188.6	−	161795.i	−0.309142	−	1.46299i
$49$	−85485.6			−0.726616
$50$		0			0
$51$			199329.i			1.50266i
$52$	−21515.4	−	205887.i	−0.153017	−	1.46427i
$53$	277123.			1.86142			0.930711	−	0.365756i	$-0.119189\pi$
$53$	277123.			1.86142			0.930711	+	0.365756i	$0.119189\pi$
$54$	41265.4	+	37177.9i	0.262063	+	0.236104i
$55$		0			0
$56$	135805.	−	186568.i	0.773306	−	1.06236i
$57$	79938.4			0.431649
$58$	−113298.	+	125755.i	−0.580682	+	0.644525i
$59$		−	28176.1i		−	0.137191i	−0.997645	−	0.0685954i	$-0.978148\pi$
$59$		−	28176.1i		−	0.137191i	0.997645	−	0.0685954i	$-0.0218518\pi$
$60$		0			0
$61$	−34082.0			−0.150154			−0.0750769	−	0.997178i	$-0.523920\pi$
$61$	−34082.0			−0.150154			−0.0750769	+	0.997178i	$0.523920\pi$
$62$	197453.	+	177894.i	0.828494	+	0.746427i
$63$			406071.i			1.62398i
$64$	80560.3	+	249458.i	0.307313	+	0.951608i
$65$		0			0
$66$	84506.0	−	93797.1i	0.293938	−	0.326255i
$67$		−	230002.i		−	0.764730i	−0.924011	−	0.382365i	$-0.875110\pi$
$67$		−	230002.i		−	0.764730i	0.924011	−	0.382365i	$-0.124890\pi$
$68$	−32841.4	−	314270.i	−0.104447	−	0.999484i
$69$	−43494.6			−0.132400
$70$		0			0
$71$			214659.i			0.599757i	0.953977	+	0.299878i	$0.0969461\pi$
$71$			214659.i			0.599757i	−0.953977	+	0.299878i	$0.903054\pi$
$72$	−372953.	−	271477.i	−0.999211	−	0.727337i
$73$	21193.6			0.0544800			0.0272400	−	0.999629i	$-0.491328\pi$
$73$	21193.6			0.0544800			0.0272400	+	0.999629i	$0.491328\pi$
$74$	75821.5	−	84157.8i	0.187110	−	0.207682i
$75$		0			0
$76$	−126034.	+	13170.6i	−0.287109	+	0.0300030i
$77$	176175.			0.385898
$78$	−776148.	−	699267.i	−1.63554	−	1.47353i
$79$		−	365752.i		−	0.741832i	−0.928666	−	0.370916i	$-0.879044\pi$
$79$		−	365752.i		−	0.741832i	0.928666	−	0.370916i	$-0.120956\pi$
$80$		0			0
$81$	−376502.			−0.708456
$82$	229563.	−	254803.i	0.416352	−	0.462129i
$83$			50231.1i			0.0878493i	0.999035	+	0.0439247i	$0.0139862\pi$
$83$			50231.1i			0.0878493i	−0.999035	+	0.0439247i	$0.986014\pi$
$84$	−121038.	−	1.15825e6i	−0.204213	−	1.95418i
$85$		0			0
$86$	−343393.	−	309378.i	−0.539878	−	0.486401i
$87$			854215.i			1.29721i
$88$	−117781.	+	161807.i	−0.172834	+	0.237438i
$89$	177274.			0.251463			0.125731	−	0.992064i	$-0.459872\pi$
$89$	177274.			0.251463			0.125731	+	0.992064i	$0.459872\pi$
$90$		0			0
$91$		−	1.45781e6i		−	1.93453i
$92$	68575.2	−	7166.15i	0.0880651	−	0.00920286i
$93$	1.34124e6			1.66747
$94$	−821109.	−	739774.i	−0.988592	−	0.890667i
$95$		0			0
$96$	1.14471e6	+	663179.i	1.29384	+	0.749578i
$97$	1.15267e6			1.26296			0.631479	−	0.775393i	$-0.282448\pi$
$97$	1.15267e6			1.26296			0.631479	+	0.775393i	$0.282448\pi$
$98$	457760.	−	508089.i	0.486362	−	0.539836i
$99$		−	352178.i		−	0.362959i
$100$		0			0
$101$	1.27960e6			1.24197			0.620985	−	0.783822i	$-0.286733\pi$
$101$	1.27960e6			1.24197			0.620985	+	0.783822i	$0.286733\pi$
$102$	−1.18472e6	−	1.06737e6i	−1.11639	−	1.00581i
$103$			2.08267e6i			1.90593i	0.303074	+	0.952967i	$0.401987\pi$
$103$			2.08267e6i			1.90593i	−0.303074	+	0.952967i	$0.598013\pi$
$104$	1.33892e6	+	974612.i	1.19029	+	0.866427i
$105$		0			0
$106$	−1.48394e6	+	1.64710e6i	−1.24595	+	1.38293i
$107$		−	512122.i		−	0.418044i	−0.977911	−	0.209022i	$-0.932972\pi$
$107$		−	512122.i		−	0.418044i	0.977911	−	0.209022i	$-0.0670281\pi$
$108$	−441938.	+	46182.8i	−0.350824	+	0.0366614i
$109$	1.32906e6			1.02628			0.513141	−	0.858305i	$-0.328482\pi$
$109$	1.32906e6			1.02628			0.513141	+	0.858305i	$0.328482\pi$
$110$		0			0
$111$		−	571659.i		−	0.417992i
$112$	381666.	+	1.80620e6i	0.271663	+	1.28562i
$113$	160172.			0.111007			0.0555035	−	0.998458i	$-0.482324\pi$
$113$	160172.			0.111007			0.0555035	+	0.998458i	$0.482324\pi$
$114$	−428056.	+	475119.i	−0.288925	+	0.320692i
$115$		0			0
$116$	−140740.	−	1.34679e6i	−0.0901662	−	0.862829i
$117$	−2.91419e6			−1.81954
$118$	167466.	+	150878.i	0.101925	+	0.0918290i
$119$		−	2.22522e6i		−	1.32048i
$120$		0			0
$121$	1.61877e6			0.913752
$122$	182503.	−	202569.i	0.100506	−	0.111556i
$123$		−	1.73080e6i		−	0.930105i
$124$	−2.11465e6	+	220982.i	−1.10911	+	0.115903i
$125$		0			0
$126$	−2.41351e6	−	2.17444e6i	−1.20653	−	1.08701i
$127$			1.90105e6i			0.928071i	0.885816	+	0.464036i	$0.153599\pi$
$127$			1.90105e6i			0.928071i	−0.885816	+	0.464036i	$0.846401\pi$
$128$	−1.91406e6	−	856990.i	−0.912693	−	0.408645i
$129$	−2.33257e6			−1.08659
$130$		0			0
$131$			2.76248e6i			1.22881i	0.788990	+	0.614407i	$0.210605\pi$
$131$			2.76248e6i			1.22881i	−0.788990	+	0.614407i	$0.789395\pi$
$132$	104974.	+	1.00453e6i	0.0456416	+	0.436759i
$133$	−892396.			−0.379317
$134$	1.36703e6	+	1.23162e6i	0.568152	+	0.511874i
$135$		0			0
$136$	2.04374e6	+	1.48766e6i	0.812473	+	0.591409i
$137$	2.60078e6			1.01144			0.505722	−	0.862696i	$-0.331226\pi$
$137$	2.60078e6			1.01144			0.505722	+	0.862696i	$0.331226\pi$
$138$	232906.	−	258513.i	0.0886223	−	0.0983660i
$139$			3.07350e6i			1.14443i	0.820104	+	0.572214i	$0.193915\pi$
$139$			3.07350e6i			1.14443i	−0.820104	+	0.572214i	$0.806085\pi$
$140$		0			0
$141$	−5.57755e6			−1.98969
$142$	−1.27584e6	−	1.14946e6i	−0.445586	−	0.401448i
$143$			1.26433e6i			0.432368i
$144$	3.61064e6	−	762960.i	1.20920	−	0.255514i
$145$		0			0
$146$	−113488.	+	125966.i	−0.0364663	+	0.0404756i
$147$		−	3.45130e6i		−	1.08650i
$148$	94186.3	+	901299.i	0.0290538	+	0.278025i
$149$	−2.10750e6			−0.637102			−0.318551	−	0.947906i	$-0.603196\pi$
$149$	−2.10750e6			−0.637102			−0.318551	+	0.947906i	$0.603196\pi$
$150$		0			0
$151$			2.20804e6i			0.641323i	0.947194	+	0.320662i	$0.103905\pi$
$151$			2.20804e6i			0.641323i	−0.947194	+	0.320662i	$0.896095\pi$
$152$	596608.	−	819616.i	0.169886	−	0.233389i
$153$	−4.44827e6			−1.24199
$154$	−943387.	+	1.04711e6i	−0.258302	+	0.286701i
$155$		0			0
$156$	8.31227e6	−	868637.i	2.18950	−	0.228805i
$157$	−821139.			−0.212187			−0.106093	−	0.994356i	$-0.533834\pi$
$157$	−821139.			−0.212187			−0.106093	+	0.994356i	$0.533834\pi$
$158$	2.17387e6	+	1.95854e6i	0.551140	+	0.496547i
$159$			1.11882e7i			2.78337i
$160$		0			0
$161$	485554.			0.116348
$162$	2.01610e6	−	2.23776e6i	0.474206	−	0.526344i
$163$		−	7.70810e6i		−	1.77985i	−0.456103	−	0.889927i	$-0.650755\pi$
$163$		−	7.70810e6i		−	1.77985i	0.456103	−	0.889927i	$-0.349245\pi$
$164$	285166.	+	2.72885e6i	0.0646497	+	0.618654i
$165$		0			0
$166$	−298552.	−	268979.i	−0.0652672	−	0.0588022i
$167$		−	2.37157e6i		−	0.509197i	−0.967047	−	0.254599i	$-0.918057\pi$
$167$		−	2.37157e6i		−	0.509197i	0.967047	−	0.254599i	$-0.0819433\pi$
$168$	7.53228e6	+	5.48283e6i	1.58854	+	1.15632i
$169$	5.63524e6			1.16749
$170$		0			0
$171$			1.78392e6i			0.356769i
$172$	3.67761e6	−	384313.i	0.722738	−	0.0755266i
$173$	5.22589e6			1.00930			0.504652	−	0.863323i	$-0.331621\pi$
$173$	5.22589e6			1.00930			0.504652	+	0.863323i	$0.331621\pi$
$174$	−5.07708e6	−	4.57417e6i	−0.963753	−	0.868289i
$175$		0			0
$176$	−331013.	−	1.56649e6i	−0.0607165	−	0.287335i
$177$	1.13755e6			0.205140
$178$	−949268.	+	1.05364e6i	−0.168317	+	0.186823i
$179$		−	6.41696e6i		−	1.11885i	−0.828882	−	0.559423i	$-0.811023\pi$
$179$		−	6.41696e6i		−	1.11885i	0.828882	−	0.559423i	$-0.188977\pi$
$180$		0			0
$181$	−2.74959e6			−0.463694			−0.231847	−	0.972752i	$-0.574477\pi$
$181$	−2.74959e6			−0.463694			−0.231847	+	0.972752i	$0.574477\pi$
$182$	8.66457e6	+	7.80630e6i	1.43725	+	1.29488i
$183$		−	1.37599e6i		−	0.224524i
$184$	−324615.	+	445954.i	−0.0521094	+	0.0715875i
$185$		0			0
$186$	−7.18211e6	+	7.97175e6i	−1.11613	+	1.23884i
$187$			1.92990e6i			0.295127i
$188$	8.79378e6	−	918955.i	1.32343	−	0.138300i
$189$	−3.12919e6			−0.463496
$190$		0			0
$191$		−	7.97496e6i		−	1.14453i	−0.820068	−	0.572267i	$-0.806064\pi$
$191$		−	7.97496e6i		−	1.14453i	0.820068	−	0.572267i	$-0.193936\pi$
$192$	−1.00714e7	+	3.25245e6i	−1.42293	+	0.459523i
$193$	−1.21860e7			−1.69508			−0.847539	−	0.530734i	$-0.821916\pi$
$193$	−1.21860e7			−1.69508			−0.847539	+	0.530734i	$0.821916\pi$
$194$	−6.17233e6	+	6.85095e6i	−0.845364	+	0.938308i
$195$		0			0
$196$	568635.	+	5.44145e6i	0.0755206	+	0.722681i
$197$	−5.27192e6			−0.689557			−0.344778	−	0.938684i	$-0.612046\pi$
$197$	−5.27192e6			−0.689557			−0.344778	+	0.938684i	$0.612046\pi$
$198$	2.09319e6	+	1.88585e6i	0.269658	+	0.242947i
$199$		−	1.14435e7i		−	1.45210i	−0.687639	−	0.726052i	$-0.741353\pi$
$199$		−	1.14435e7i		−	1.45210i	0.687639	−	0.726052i	$-0.258647\pi$
$200$		0			0
$201$	9.28586e6			1.14349
$202$	−6.85205e6	+	7.60540e6i	−0.831316	+	0.922716i
$203$		−	9.53607e6i		−	1.13994i
$204$	1.26880e7	−	1.32590e6i	1.49452	−	0.156178i
$205$		0			0
$206$	−1.23785e7	−	1.11523e7i	−1.41600	−	1.27574i
$207$		−	970634.i		−	0.109432i
$208$	−1.29623e7	+	2.73905e6i	−1.44043	+	0.304376i
$209$	773960.			0.0847773
$210$		0			0
$211$		−	3.30342e6i		−	0.351655i	−0.984421	−	0.175828i	$-0.943740\pi$
$211$		−	3.30342e6i		−	0.351655i	0.984421	−	0.175828i	$-0.0562601\pi$
$212$	−1.84337e6	−	1.76398e7i	−0.193466	−	1.85134i
$213$	−8.66642e6			−0.896811
$214$	3.04383e6	+	2.74232e6i	0.310584	+	0.279819i
$215$		0			0
$216$	2.09201e6	−	2.87398e6i	0.207588	−	0.285183i
$217$	−1.49730e7			−1.46531
$218$	−7.11690e6	+	7.89937e6i	−0.686944	+	0.762471i
$219$			855648.i			0.0814634i
$220$		0			0
$221$	1.59694e7			1.47949
$222$	3.39769e6	+	3.06113e6i	0.310545	+	0.279784i
$223$			1.43034e7i			1.28981i	0.764265	+	0.644903i	$0.223102\pi$
$223$			1.43034e7i			1.28981i	−0.764265	+	0.644903i	$0.776898\pi$
$224$	−1.27790e7	−	7.40343e6i	−1.13698	−	0.658702i
$225$		0			0
$226$	−857690.	+	951990.i	−0.0743028	+	0.0824721i
$227$		−	879277.i		−	0.0751706i	−0.999293	−	0.0375853i	$-0.988033\pi$
$227$		−	879277.i		−	0.0751706i	0.999293	−	0.0375853i	$-0.0119666\pi$
$228$	−531736.	−	5.08835e6i	−0.0448633	−	0.429311i
$229$	363899.			0.0303022			0.0151511	−	0.999885i	$-0.495177\pi$
$229$	363899.			0.0303022			0.0151511	+	0.999885i	$0.495177\pi$
$230$		0			0
$231$			7.11270e6i			0.577030i
$232$	8.75835e6	+	6.37530e6i	0.701388	+	0.510548i
$233$	3.19027e6			0.252208			0.126104	−	0.992017i	$-0.459753\pi$
$233$	3.19027e6			0.252208			0.126104	+	0.992017i	$0.459753\pi$
$234$	1.56050e7	−	1.73207e7i	1.21791	−	1.35182i
$235$		0			0
$236$	−1.79350e6	+	187422.i	−0.136448	+	0.0142589i
$237$	1.47665e7			1.10926
$238$	1.32257e7	+	1.19157e7i	0.981045	+	0.883867i
$239$		−	1.72090e7i		−	1.26056i	−0.776368	−	0.630279i	$-0.782940\pi$
$239$		−	1.72090e7i		−	1.26056i	0.776368	−	0.630279i	$-0.217060\pi$
$240$		0			0
$241$	−1.26609e7			−0.904508			−0.452254	−	0.891889i	$-0.649380\pi$
$241$	−1.26609e7			−0.904508			−0.452254	+	0.891889i	$0.649380\pi$
$242$	−8.66821e6	+	9.62124e6i	−0.611622	+	0.678867i
$243$		−	2.02618e7i		−	1.41208i
$244$	226708.	+	2.16944e6i	0.0156062	+	0.149341i
$245$		0			0
$246$	1.02871e7	+	9.26813e6i	0.691017	+	0.622568i
$247$		−	6.40434e6i		−	0.424995i
$248$	1.00102e7	−	1.37519e7i	0.656275	−	0.901586i
$249$	−2.02797e6			−0.131360
$250$		0			0
$251$		−	2.69052e7i		−	1.70143i	−0.525625	−	0.850716i	$-0.676168\pi$
$251$		−	2.69052e7i		−	1.70143i	0.525625	−	0.850716i	$-0.323832\pi$
$252$	2.58478e7	−	2.70111e6i	1.61518	−	0.168788i
$253$	−421113.			−0.0260038
$254$	−1.12990e7	−	1.01798e7i	−0.689506	−	0.621207i
$255$		0			0
$256$	1.53430e7	−	6.78729e6i	0.914514	−	0.404554i
$257$	7.81210e6			0.460223			0.230112	−	0.973164i	$-0.426091\pi$
$257$	7.81210e6			0.460223			0.230112	+	0.973164i	$0.426091\pi$
$258$	1.24905e7	−	1.38638e7i	0.727311	−	0.807276i
$259$			6.38175e6i			0.367316i
$260$		0			0
$261$	−1.90628e7			−1.07217
$262$	−1.64190e7	−	1.47926e7i	−0.912941	−	0.822509i
$263$			1.33139e7i			0.731877i	0.930639	+	0.365938i	$0.119252\pi$
$263$			1.33139e7i			0.731877i	−0.930639	+	0.365938i	$0.880748\pi$
$264$	−6.53262e6	−	4.75517e6i	−0.355039	−	0.258437i
$265$		0			0
$266$	4.77862e6	−	5.30401e6i	0.253897	−	0.281812i
$267$			7.15704e6i			0.376010i
$268$	−1.46404e7	+	1.52993e6i	−0.760588	+	0.0794819i
$269$	1.73876e7			0.893271			0.446635	−	0.894716i	$-0.352622\pi$
$269$	1.73876e7			0.893271			0.446635	+	0.894716i	$0.352622\pi$
$270$		0			0
$271$			2.13357e7i			1.07201i	0.844215	+	0.536005i	$0.180067\pi$
$271$			2.13357e7i			1.07201i	−0.844215	+	0.536005i	$0.819933\pi$
$272$	−1.97859e7	+	4.18093e6i	−0.983215	+	0.207762i
$273$	5.88559e7			2.89269
$274$	−1.39267e7	+	1.54579e7i	−0.677013	+	0.751447i
$275$		0			0
$276$	289318.	+	2.76858e6i	0.0137610	+	0.131683i
$277$	1.72036e7			0.809431			0.404716	−	0.914443i	$-0.367371\pi$
$277$	1.72036e7			0.809431			0.404716	+	0.914443i	$0.367371\pi$
$278$	−1.82675e7	−	1.64580e7i	−0.850247	−	0.766025i
$279$			2.99314e7i			1.37821i
$280$		0			0
$281$	−2.56886e7			−1.15777			−0.578883	−	0.815411i	$-0.696511\pi$
$281$	−2.56886e7			−1.15777			−0.578883	+	0.815411i	$0.696511\pi$
$282$	2.98668e7	−	3.31505e7i	1.33181	−	1.47823i
$283$			1.39377e7i			0.614937i	0.951558	+	0.307469i	$0.0994819\pi$
$283$			1.39377e7i			0.614937i	−0.951558	+	0.307469i	$0.900518\pi$
$284$	1.36638e7	−	1.42788e6i	0.596508	−	0.0623355i
$285$		0			0
$286$	−7.51464e6	−	6.77027e6i	−0.321225	−	0.289406i
$287$			1.93219e7i			0.817342i
$288$	−1.47996e7	+	2.55456e7i	−0.619545	+	1.06939i
$289$	238417.			0.00987743
$290$		0			0
$291$			4.65365e7i			1.88849i
$292$	−140976.	−	1.34905e6i	−0.00566235	−	0.0541849i
$293$	−3.28329e7			−1.30529			−0.652644	−	0.757665i	$-0.726340\pi$
$293$	−3.28329e7			−1.30529			−0.652644	+	0.757665i	$0.726340\pi$
$294$	2.05130e7	+	1.84811e7i	0.807212	+	0.727253i
$295$		0			0
$296$	−5.86128e6	−	4.26649e6i	−0.226005	−	0.164511i
$297$	2.71389e6			0.103591
$298$	1.12853e7	−	1.25261e7i	0.426446	−	0.473332i
$299$			3.48461e6i			0.130359i
$300$		0			0
$301$	2.60397e7			0.954854
$302$	−1.31236e7	−	1.18237e7i	−0.476468	−	0.429271i
$303$			5.16613e7i			1.85711i
$304$	1.67671e6	+	7.93487e6i	0.0596811	+	0.282436i
$305$		0			0
$306$	2.38197e7	−	2.64385e7i	0.831326	−	0.922727i
$307$		−	3.20799e7i		−	1.10871i	−0.832280	−	0.554356i	$-0.812965\pi$
$307$		−	3.20799e7i		−	1.10871i	0.832280	−	0.554356i	$-0.187035\pi$
$308$	−1.17189e6	−	1.12141e7i	−0.0401082	−	0.383808i
$309$	−8.40832e7			−2.84993
$310$		0			0
$311$		−	3.21955e7i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$311$		−	3.21955e7i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$312$	−3.93479e7	+	5.40559e7i	−1.29556	+	1.77983i
$313$	3.62694e6			0.118279			0.0591394	−	0.998250i	$-0.481164\pi$
$313$	3.62694e6			0.118279			0.0591394	+	0.998250i	$0.481164\pi$
$314$	4.39705e6	−	4.88049e6i	0.142028	−	0.157643i
$315$		0			0
$316$	−2.32814e7	+	2.43292e6i	−0.737814	+	0.0771020i
$317$	−2.70689e7			−0.849754			−0.424877	−	0.905251i	$-0.639683\pi$
$317$	−2.70689e7			−0.849754			−0.424877	+	0.905251i	$0.639683\pi$
$318$	−6.64980e7	−	5.99110e7i	−2.06789	−	1.86305i
$319$			8.27047e6i			0.254776i
$320$		0			0
$321$	2.06758e7			0.625098
$322$	−2.60006e6	+	2.88592e6i	−0.0778780	+	0.0864404i
$323$		−	9.77568e6i		−	0.290094i
$324$	2.50443e6	+	2.39656e7i	0.0736331	+	0.704619i
$325$		0			0
$326$	4.58135e7	+	4.12755e7i	1.32233	+	1.19135i
$327$			5.36581e7i			1.53459i
$328$	−1.77461e7	−	1.29176e7i	−0.502899	−	0.366066i
$329$	6.22653e7			1.74847
$330$		0			0
$331$			3.35438e7i			0.924972i	0.886627	+	0.462486i	$0.153042\pi$
$331$			3.35438e7i			0.924972i	−0.886627	+	0.462486i	$0.846958\pi$
$332$	3.19738e6	−	334128.i	0.0873736	−	0.00913059i
$333$	1.27573e7			0.345481
$334$	1.40955e7	+	1.26993e7i	0.378305	+	0.340832i
$335$		0			0
$336$	−7.29215e7	+	1.54090e7i	−1.92237	+	0.406215i
$337$	−5.29894e7			−1.38452			−0.692260	−	0.721648i	$-0.743385\pi$
$337$	−5.29894e7			−1.38452			−0.692260	+	0.721648i	$0.743385\pi$
$338$	−3.01757e7	+	3.34934e7i	−0.781461	+	0.867379i
$339$			6.46659e6i			0.165988i
$340$		0			0
$341$	1.29859e7			0.327497
$342$	−1.06028e7	−	9.55257e6i	−0.265060	−	0.238804i
$343$		−	1.44962e7i		−	0.359229i
$344$	−1.74088e7	+	2.39160e7i	−0.427654	+	0.587508i
$345$		0			0
$346$	−2.79837e7	+	3.10604e7i	−0.675580	+	0.749858i
$347$			1.30197e7i			0.311611i	0.987788	+	0.155805i	$0.0497973\pi$
$347$			1.30197e7i			0.311611i	−0.987788	+	0.155805i	$0.950203\pi$
$348$	5.43737e7	−	5.68208e6i	1.29018	−	0.134825i
$349$	1.95421e7			0.459721			0.229860	−	0.973224i	$-0.426173\pi$
$349$	1.95421e7			0.459721			0.229860	+	0.973224i	$0.426173\pi$
$350$		0			0
$351$		−	2.24568e7i		−	0.519310i
$352$	1.10830e7	+	6.42087e6i	0.254115	+	0.147220i
$353$	4.20948e7			0.956984			0.478492	−	0.878092i	$-0.341184\pi$
$353$	4.20948e7			0.956984			0.478492	+	0.878092i	$0.341184\pi$
$354$	−6.09138e6	+	6.76110e6i	−0.137311	+	0.152408i
$355$		0			0
$356$	−1.17919e6	−	1.12841e7i	−0.0261357	−	0.250101i
$357$	8.98386e7			1.97450
$358$	3.81396e7	+	3.43617e7i	0.831241	+	0.748902i
$359$			6.88488e6i			0.148803i	0.997228	+	0.0744017i	$0.0237047\pi$
$359$			6.88488e6i			0.148803i	−0.997228	+	0.0744017i	$0.976295\pi$
$360$		0			0
$361$	4.31255e7			0.916668
$362$	1.47235e7	−	1.63423e7i	0.310375	−	0.344499i
$363$			6.53543e7i			1.36633i
$364$	−9.27944e7	+	9.69707e6i	−1.92406	+	0.201065i
$365$		0			0
$366$	8.17828e6	+	7.36818e6i	0.166809	+	0.150285i
$367$		−	1.25791e7i		−	0.254480i	−0.991872	−	0.127240i	$-0.959388\pi$
$367$		−	1.25791e7i		−	0.254480i	0.991872	−	0.127240i	$-0.0406118\pi$
$368$	−912300.	−	4.31738e6i	−0.0183060	−	0.0866316i
$369$	3.86249e7			0.768756
$370$		0			0
$371$		−	1.24901e8i		−	2.44592i
$372$	−8.92170e6	−	8.53746e7i	−0.173308	−	1.65844i
$373$	5.80469e7			1.11854			0.559272	−	0.828984i	$-0.311081\pi$
$373$	5.80469e7			1.11854			0.559272	+	0.828984i	$0.311081\pi$
$374$	−1.14705e7	−	1.03342e7i	−0.219263	−	0.197544i
$375$		0			0
$376$	−4.16272e7	+	5.71872e7i	−0.783094	+	1.07581i
$377$	6.84362e7			1.27721
$378$	1.67562e7	−	1.85985e7i	0.310242	−	0.344352i
$379$		−	4.35438e7i		−	0.799850i	−0.916548	−	0.399925i	$-0.869036\pi$
$379$		−	4.35438e7i		−	0.799850i	0.916548	−	0.399925i	$-0.130964\pi$
$380$		0			0
$381$	−7.67507e7			−1.38774
$382$	4.73997e7	+	4.27045e7i	0.850325	+	0.766096i
$383$		−	2.94725e6i		−	0.0524591i	−0.999656	−	0.0262296i	$-0.991650\pi$
$383$		−	2.94725e6i		−	0.0524591i	0.999656	−	0.0262296i	$-0.00835009\pi$
$384$	3.45992e7	−	7.72760e7i	0.611043	−	1.36474i
$385$		0			0
$386$	6.52539e7	−	7.24283e7i	1.13460	−	1.25935i
$387$		−	5.20540e7i		−	0.898094i
$388$	−7.66733e6	−	7.33712e7i	−0.131265	−	1.25612i
$389$	−1.87700e7			−0.318871			−0.159436	−	0.987208i	$-0.550967\pi$
$389$	−1.87700e7			−0.318871			−0.159436	+	0.987208i	$0.550967\pi$
$390$		0			0
$391$			5.31896e6i			0.0889809i
$392$	−3.53865e7	−	2.57583e7i	−0.587462	−	0.427620i
$393$	−1.11529e8			−1.83743
$394$	2.82302e7	−	3.13340e7i	0.461556	−	0.512303i
$395$		0			0
$396$	−2.24173e7	+	2.34263e6i	−0.360993	+	0.0377240i
$397$	−3.99848e7			−0.639033			−0.319517	−	0.947581i	$-0.603521\pi$
$397$	−3.99848e7			−0.639033			−0.319517	+	0.947581i	$0.603521\pi$
$398$	6.80149e7	+	6.12776e7i	1.07883	+	0.971970i
$399$		−	3.60286e7i		−	0.567190i
$400$		0			0
$401$	6.49364e6			0.100706			0.0503530	−	0.998731i	$-0.483965\pi$
$401$	6.49364e6			0.100706			0.0503530	+	0.998731i	$0.483965\pi$
$402$	−4.97241e7	+	5.51911e7i	−0.765401	+	0.849553i
$403$		−	1.07455e8i		−	1.64176i
$404$	−8.51169e6	−	8.14511e7i	−0.129084	−	1.23524i
$405$		0			0
$406$	5.66782e7	+	5.10639e7i	0.846911	+	0.763020i
$407$		−	5.53478e6i		−	0.0820951i
$408$	−6.00612e7	+	8.25117e7i	−0.884329	+	1.21488i
$409$	−2.76062e7			−0.403494			−0.201747	−	0.979438i	$-0.564662\pi$
$409$	−2.76062e7			−0.403494			−0.201747	+	0.979438i	$0.564662\pi$
$410$		0			0
$411$			1.05001e8i			1.51240i
$412$	1.32569e8	−	1.38535e7i	1.89561	−	0.198093i
$413$	−1.26991e7			−0.180270
$414$	5.76902e6	+	5.19757e6i	0.0813020	+	0.0732486i
$415$		0			0
$416$	5.31311e7	−	9.17094e7i	0.738022	−	1.27390i
$417$	−1.24086e8			−1.71125
$418$	−4.14442e6	+	4.60008e6i	−0.0567459	+	0.0629849i
$419$			1.47995e7i			0.201190i	0.994927	+	0.100595i	$0.0320746\pi$
$419$			1.47995e7i			0.201190i	−0.994927	+	0.100595i	$0.967925\pi$
$420$		0			0
$421$	−3.29248e7			−0.441242			−0.220621	−	0.975360i	$-0.570808\pi$
$421$	−3.29248e7			−0.441242			−0.220621	+	0.975360i	$0.570808\pi$
$422$	1.96341e7	+	1.76892e7i	0.261260	+	0.235381i
$423$		−	1.24470e8i		−	1.64453i
$424$	1.14714e8	+	8.35018e7i	1.50494	+	1.09546i
$425$		0			0
$426$	4.64071e7	−	5.15094e7i	0.600283	−	0.666281i
$427$			1.53609e7i			0.197303i
$428$	−3.25983e7	+	3.40654e6i	−0.415780	+	0.0434493i
$429$	−5.10447e7			−0.646516
$430$		0			0
$431$			9.46095e7i			1.18169i	0.806786	+	0.590844i	$0.201205\pi$
$431$			9.46095e7i			1.18169i	−0.806786	+	0.590844i	$0.798795\pi$
$432$	5.87938e6	+	2.78236e7i	0.0729256	+	0.345114i
$433$	−6.50578e7			−0.801375			−0.400687	−	0.916215i	$-0.631229\pi$
$433$	−6.50578e7			−0.801375			−0.400687	+	0.916215i	$0.631229\pi$
$434$	8.01778e7	−	8.89931e7i	0.980811	−	1.08865i
$435$		0			0
$436$	−8.84069e6	−	8.45994e7i	−0.106666	−	1.02072i
$437$	2.13310e6			0.0255604
$438$	−5.08559e6	−	4.58184e6i	−0.0605228	−	0.0545277i
$439$		−	5.30694e7i		−	0.627264i	−0.949545	−	0.313632i	$-0.898454\pi$
$439$		−	5.30694e7i		−	0.627264i	0.949545	−	0.313632i	$-0.101546\pi$
$440$		0			0
$441$	7.70199e7			0.898022
$442$	−8.55134e7	+	9.49153e7i	−0.990302	+	1.09918i
$443$			1.37420e8i			1.58066i	0.612684	+	0.790328i	$0.290090\pi$
$443$			1.37420e8i			1.58066i	−0.612684	+	0.790328i	$0.709910\pi$
$444$	−3.63880e7	+	3.80257e6i	−0.415729	+	0.0434439i
$445$		0			0
$446$	−8.50130e7	−	7.65921e7i	−0.958255	−	0.863335i
$447$		−	8.50859e7i		−	0.952654i
$448$	1.12432e8	−	3.63089e7i	1.25042	−	0.403812i
$449$	−1.37603e6			−0.0152016			−0.00760078	−	0.999971i	$-0.502419\pi$
$449$	−1.37603e6			−0.0152016			−0.00760078	+	0.999971i	$0.502419\pi$
$450$		0			0
$451$		−	1.67576e7i		−	0.182676i
$452$	−1.06543e6	−	1.01955e7i	−0.0115375	−	0.110406i
$453$	−8.91451e7			−0.958965
$454$	5.22603e6	+	4.70837e6i	0.0558476	+	0.0503156i
$455$		0			0
$456$	3.30903e7	+	2.40868e7i	0.348984	+	0.254030i
$457$	1.19484e8			1.25187			0.625937	−	0.779873i	$-0.284717\pi$
$457$	1.19484e8			1.25187			0.625937	+	0.779873i	$0.284717\pi$
$458$	−1.94861e6	+	2.16285e6i	−0.0202828	+	0.0225129i
$459$		−	3.42784e7i		−	0.354473i
$460$		0			0
$461$	−1.26030e8			−1.28639			−0.643194	−	0.765703i	$-0.722391\pi$
$461$	−1.26030e8			−1.28639			−0.643194	+	0.765703i	$0.722391\pi$
$462$	−4.22748e7	−	3.80872e7i	−0.428702	−	0.386237i
$463$		−	1.01206e8i		−	1.01968i	−0.860270	−	0.509839i	$-0.829705\pi$
$463$		−	1.01206e8i		−	1.01968i	0.860270	−	0.509839i	$-0.170295\pi$
$464$	−8.47914e7	+	1.79172e7i	−0.848785	+	0.179356i
$465$		0			0
$466$	−1.70833e7	+	1.89616e7i	−0.168816	+	0.187377i
$467$			9.72528e7i			0.954886i	0.878663	+	0.477443i	$0.158436\pi$
$467$			9.72528e7i			0.954886i	−0.878663	+	0.477443i	$0.841564\pi$
$468$	1.93847e7	+	1.85498e8i	0.189113	+	1.80968i
$469$	−1.03663e8			−1.00486
$470$		0			0
$471$		−	3.31517e7i		−	0.317281i
$472$	8.48994e6	−	1.16634e7i	0.0807381	−	0.110917i
$473$	−2.25838e7			−0.213410
$474$	−7.90717e7	+	8.77654e7i	−0.742483	+	0.824116i
$475$		0			0
$476$	−1.41643e8	+	1.48018e7i	−1.31333	+	0.137244i
$477$	−2.49679e8			−2.30053
$478$	1.02283e8	+	9.21513e7i	0.936526	+	0.843758i
$479$		−	6.06291e7i		−	0.551664i	−0.961206	−	0.275832i	$-0.911047\pi$
$479$		−	6.06291e7i		−	0.551664i	0.961206	−	0.275832i	$-0.0889533\pi$
$480$		0			0
$481$	−4.57990e7			−0.411548
$482$	6.77967e7	−	7.52506e7i	0.605435	−	0.672000i
$483$			1.96032e7i			0.173975i
$484$	−1.07677e7	−	1.03040e8i	−0.0949705	−	0.908803i
$485$		0			0
$486$	1.20427e8	+	1.08498e8i	1.04910	+	0.945181i
$487$		−	1.20117e8i		−	1.03996i	−0.854179	−	0.519979i	$-0.825940\pi$
$487$		−	1.20117e8i		−	1.03996i	0.854179	−	0.519979i	$-0.174060\pi$
$488$	−1.41082e7	−	1.02695e7i	−0.121398	−	0.0883669i
$489$	3.11198e8			2.66140
$490$		0			0
$491$		−	1.17425e8i		−	0.992011i	−0.868319	−	0.496005i	$-0.834800\pi$
$491$		−	1.17425e8i		−	0.992011i	0.868319	−	0.496005i	$-0.165200\pi$
$492$	−1.10171e8	+	1.15130e7i	−0.925068	+	0.0966701i
$493$	1.04462e8			0.871802
$494$	3.80646e7	+	3.42941e7i	0.315748	+	0.284471i
$495$		0			0
$496$	2.81326e7	+	1.33135e8i	0.230550	+	1.09106i
$497$	9.67480e7			0.788085
$498$	1.08594e7	−	1.20534e7i	0.0879264	−	0.0975935i
$499$			2.08663e8i			1.67936i	0.543083	+	0.839679i	$0.317257\pi$
$499$			2.08663e8i			1.67936i	−0.543083	+	0.839679i	$0.682743\pi$
$500$		0			0
$501$	9.57470e7			0.761398
$502$	1.59913e8	+	1.44072e8i	1.26407	+	1.13886i
$503$		−	2.10295e8i		−	1.65244i	−0.563348	−	0.826220i	$-0.690487\pi$
$503$		−	2.10295e8i		−	1.65244i	0.563348	−	0.826220i	$-0.309513\pi$
$504$	−1.22356e8	+	1.68092e8i	−0.955727	+	1.31297i
$505$		0			0
$506$	2.25498e6	−	2.50291e6i	0.0174057	−	0.0193194i
$507$			2.27511e8i			1.74573i
$508$	1.21008e8	−	1.26454e7i	0.923045	−	0.0964588i
$509$	−1.78286e8			−1.35196			−0.675980	−	0.736920i	$-0.736279\pi$
$509$	−1.78286e8			−1.35196			−0.675980	+	0.736920i	$0.736279\pi$
$510$		0			0
$511$		−	9.55206e6i		−	0.0715871i
$512$	−4.18184e7	+	1.27537e8i	−0.311571	+	0.950223i
$513$	−1.37469e7			−0.101825
$514$	−4.18324e7	+	4.64317e7i	−0.308052	+	0.341921i
$515$		0			0
$516$	1.55158e7	+	1.48476e8i	0.112934	+	1.08070i
$517$	−5.40016e7			−0.390783
$518$	−3.79303e7	−	3.41731e7i	−0.272896	−	0.245864i
$519$			2.10984e8i			1.50920i
$520$		0			0
$521$	2.05210e8			1.45106			0.725531	−	0.688189i	$-0.241594\pi$
$521$	2.05210e8			1.45106			0.725531	+	0.688189i	$0.241594\pi$
$522$	1.02078e8	−	1.13301e8i	0.717663	−	0.796567i
$523$			7.21180e7i			0.504125i	0.967711	+	0.252063i	$0.0811089\pi$
$523$			7.21180e7i			0.504125i	−0.967711	+	0.252063i	$0.918891\pi$
$524$	1.75841e8	−	1.83755e7i	1.22216	−	0.127716i
$525$		0			0
$526$	−7.91320e7	−	7.12935e7i	−0.543744	−	0.489884i
$527$		−	1.64021e8i		−	1.12064i
$528$	6.32436e7	−	1.33639e7i	0.429650	−	0.0907889i
$529$	1.46875e8			0.992160
$530$		0			0
$531$			2.53858e7i			0.169554i
$532$	5.93606e6	+	5.68040e7i	0.0394242	+	0.377263i
$533$	−1.38665e8			−0.915766
$534$	−4.25383e7	−	3.83247e7i	−0.279355	−	0.251683i
$535$		0			0
$536$	6.93036e7	−	9.52088e7i	0.450051	−	0.618277i
$537$	2.59071e8			1.67300
$538$	−9.31075e7	+	1.03344e8i	−0.597913	+	0.663651i
$539$		−	3.34153e7i		−	0.213393i
$540$		0			0
$541$	−1.48242e7			−0.0936225			−0.0468112	−	0.998904i	$-0.514906\pi$
$541$	−1.48242e7			−0.0936225			−0.0468112	+	0.998904i	$0.514906\pi$
$542$	−1.26810e8	−	1.14249e8i	−0.796444	−	0.717552i
$543$		−	1.11009e8i		−	0.693358i
$544$	8.11002e7	−	1.39987e8i	0.503762	−	0.869541i
$545$		0			0
$546$	−3.15163e8	+	3.49814e8i	−1.93623	+	2.14911i
$547$		−	2.59533e8i		−	1.58574i	−0.609392	−	0.792869i	$-0.708587\pi$
$547$		−	2.59533e8i		−	1.58574i	0.609392	−	0.792869i	$-0.291413\pi$
$548$	−1.72999e7	−	1.65548e8i	−0.105124	−	1.00597i
$549$	3.07069e7			0.185575
$550$		0			0
$551$		−	4.18932e7i		−	0.250431i
$552$	−1.80045e7	−	1.31057e7i	−0.107044	−	0.0779187i
$553$	−1.64846e8			−0.974773
$554$	−9.21221e7	+	1.02251e8i	−0.541795	+	0.601363i
$555$		0			0
$556$	1.95638e8	−	2.04443e7i	1.13823	−	0.118946i
$557$	−3.21717e7			−0.186169			−0.0930847	−	0.995658i	$-0.529673\pi$
$557$	−3.21717e7			−0.186169			−0.0930847	+	0.995658i	$0.529673\pi$
$558$	−1.77899e8	−	1.60277e8i	−1.02393	−	0.922507i
$559$			1.86876e8i			1.06984i
$560$		0			0
$561$	−7.79155e7			−0.441301
$562$	1.37558e8	−	1.52681e8i	0.774953	−	0.860156i
$563$			2.80885e8i			1.57400i	0.616955	+	0.786999i	$0.288366\pi$
$563$			2.80885e8i			1.57400i	−0.616955	+	0.786999i	$0.711634\pi$
$564$	3.71009e7	+	3.55030e8i	0.206798	+	1.97892i
$565$		0			0
$566$	−8.28394e7	−	7.46337e7i	−0.456865	−	0.411610i
$567$			1.69691e8i			0.930916i
$568$	−6.46805e7	+	8.88576e7i	−0.352962	+	0.484897i
$569$	−3.50834e8			−1.90443			−0.952216	−	0.305426i	$-0.901201\pi$
$569$	−3.50834e8			−1.90443			−0.952216	+	0.305426i	$0.901201\pi$
$570$		0			0
$571$			1.49375e8i			0.802360i	0.915999	+	0.401180i	$0.131400\pi$
$571$			1.49375e8i			0.802360i	−0.915999	+	0.401180i	$0.868600\pi$
$572$	8.04790e7	−	8.41011e6i	0.430026	−	0.0449380i
$573$	3.21972e8			1.71141
$574$	−1.14841e8	−	1.03465e8i	−0.607240	−	0.547090i
$575$		0			0
$576$	−7.25823e7	−	2.24754e8i	−0.379807	−	1.17609i
$577$	−3.18308e8			−1.65699			−0.828496	−	0.559996i	$-0.810803\pi$
$577$	−3.18308e8			−1.65699			−0.828496	+	0.559996i	$0.810803\pi$
$578$	−1.27668e6	+	1.41705e6i	−0.00661148	+	0.00733839i
$579$		−	4.91984e8i		−	2.53463i
$580$		0			0
$581$	2.26394e7			0.115435
$582$	−2.76592e8	−	2.49195e8i	−1.40304	−	1.26407i
$583$			1.08324e8i			0.546663i
$584$	8.77304e6	+	6.38600e6i	0.0440465	+	0.0320620i
$585$		0			0
$586$	1.75814e8	−	1.95144e8i	0.873697	−	0.969757i
$587$			3.05295e8i			1.50940i	0.656068	+	0.754702i	$0.272218\pi$
$587$			3.05295e8i			1.50940i	−0.656068	+	0.754702i	$0.727782\pi$
$588$	−2.19687e8	+	2.29574e7i	−1.08062	+	0.112925i
$589$	−6.57784e7			−0.321912
$590$		0			0
$591$		−	2.12842e8i		−	1.03109i
$592$	5.67442e7	−	1.19906e7i	0.273500	−	0.0577929i
$593$	3.16115e8			1.51594			0.757968	−	0.652292i	$-0.226192\pi$
$593$	3.16115e8			1.51594			0.757968	+	0.652292i	$0.226192\pi$
$594$	−1.45324e7	+	1.61302e7i	−0.0693391	+	0.0769626i
$595$		0			0
$596$	1.40187e7	+	1.34150e8i	0.0662170	+	0.633652i
$597$	4.62005e8			2.17132
$598$	−2.07110e7	−	1.86595e7i	−0.0968495	−	0.0872560i
$599$		−	1.45523e8i		−	0.677097i	−0.940949	−	0.338549i	$-0.890064\pi$
$599$		−	1.45523e8i		−	0.677097i	0.940949	−	0.338549i	$-0.109936\pi$
$600$		0			0
$601$	−1.38073e8			−0.636040			−0.318020	−	0.948084i	$-0.603018\pi$
$601$	−1.38073e8			−0.636040			−0.318020	+	0.948084i	$0.603018\pi$
$602$	−1.39438e8	+	1.54769e8i	−0.639134	+	0.709404i
$603$			2.07225e8i			0.945128i
$604$	1.40550e8	−	1.46875e7i	0.637850	−	0.0666557i
$605$		0			0
$606$	−3.07052e8	−	2.76637e8i	−1.37973	−	1.24306i
$607$		−	2.20855e8i		−	0.987510i	−0.869601	−	0.493755i	$-0.835624\pi$
$607$		−	2.20855e8i		−	0.987510i	0.869601	−	0.493755i	$-0.164376\pi$
$608$	−5.61399e7	−	3.25242e7i	−0.249782	−	0.144709i
$609$	3.84998e8			1.70454
$610$		0			0
$611$			4.46851e8i			1.95902i
$612$	2.95891e7	+	2.83147e8i	0.129085	+	1.23526i
$613$	−6.60483e7			−0.286735			−0.143367	−	0.989670i	$-0.545793\pi$
$613$	−6.60483e7			−0.286735			−0.143367	+	0.989670i	$0.545793\pi$
$614$	1.90669e8	+	1.71782e8i	0.823712	+	0.742119i
$615$		0			0
$616$	7.29272e7	+	5.30846e7i	0.311995	+	0.227105i
$617$	−9.38189e6			−0.0399425			−0.0199712	−	0.999801i	$-0.506357\pi$
$617$	−9.38189e6			−0.0399425			−0.0199712	+	0.999801i	$0.506357\pi$
$618$	4.50250e8	−	4.99754e8i	1.90761	−	2.11734i
$619$			3.27827e8i			1.38221i	0.722756	+	0.691103i	$0.242875\pi$
$619$			3.27827e8i			1.38221i	−0.722756	+	0.691103i	$0.757125\pi$
$620$		0			0
$621$	7.47972e6			0.0312328
$622$	1.91356e8	+	1.72401e8i	0.795188	+	0.716421i
$623$		−	7.98980e7i		−	0.330424i
$624$	−1.10583e8	−	5.23326e8i	−0.455131	−	2.15387i
$625$		0			0
$626$	−1.94216e7	+	2.15569e7i	−0.0791702	+	0.0878747i
$627$			3.12470e7i			0.126767i
$628$	5.46207e6	+	5.22683e7i	0.0220535	+	0.211037i
$629$	−6.99083e7			−0.280916
$630$		0			0
$631$			2.66189e8i			1.05950i	0.848153	+	0.529751i	$0.177715\pi$
$631$			2.66189e8i			1.05950i	−0.848153	+	0.529751i	$0.822285\pi$
$632$	1.10207e8	−	1.51402e8i	0.436575	−	0.599764i
$633$	1.33369e8			0.525827
$634$	1.44949e8	−	1.60886e8i	0.568785	−	0.631320i
$635$		0			0
$636$	7.12170e8	−	7.44222e7i	2.76829	−	0.289288i
$637$	−2.76504e8			−1.06975
$638$	−4.91560e7	−	4.42869e7i	−0.189284	−	0.170535i
$639$		−	1.93401e8i		−	0.741237i
$640$		0			0
$641$	4.00719e7			0.152148			0.0760739	−	0.997102i	$-0.475762\pi$
$641$	4.00719e7			0.152148			0.0760739	+	0.997102i	$0.475762\pi$
$642$	−1.10715e8	+	1.22888e8i	−0.418411	+	0.464413i
$643$		−	7.15926e7i		−	0.269299i	−0.990893	−	0.134650i	$-0.957009\pi$
$643$		−	7.15926e7i		−	0.269299i	0.990893	−	0.134650i	$-0.0429909\pi$
$644$	−3.22982e6	−	3.09072e7i	−0.0120926	−	0.115718i
$645$		0			0
$646$	5.81023e7	+	5.23470e7i	0.215524	+	0.194175i
$647$			4.24659e8i			1.56793i	0.620803	+	0.783966i	$0.286807\pi$
$647$			4.24659e8i			1.56793i	−0.620803	+	0.783966i	$0.713193\pi$
$648$	−1.55852e8	−	1.13447e8i	−0.572779	−	0.416933i
$649$	1.10137e7			0.0402902
$650$		0			0
$651$		−	6.04504e8i		−	2.19107i
$652$	−4.90646e8	+	5.12728e7i	−1.77021	+	0.184988i
$653$	3.37874e8			1.21343			0.606716	−	0.794918i	$-0.292486\pi$
$653$	3.37874e8			1.21343			0.606716	+	0.794918i	$0.292486\pi$
$654$	−3.18920e8	−	2.87330e8i	−1.14012	−	1.02718i
$655$		0			0
$656$	1.71803e8	−	3.63036e7i	0.608584	−	0.128599i
$657$	−1.90948e7			−0.0673316
$658$	−3.33419e8	+	3.70077e8i	−1.17034	+	1.29902i
$659$			2.03482e8i			0.711001i	0.934676	+	0.355501i	$0.115690\pi$
$659$			2.03482e8i			0.711001i	−0.934676	+	0.355501i	$0.884310\pi$
$660$		0			0
$661$	−5.04157e8			−1.74567			−0.872833	−	0.488019i	$-0.837720\pi$
$661$	−5.04157e8			−1.74567			−0.872833	+	0.488019i	$0.837720\pi$
$662$	−1.99370e8	−	1.79621e8i	−0.687203	−	0.619132i
$663$			6.44732e8i			2.21227i
$664$	−1.51355e7	+	2.07930e7i	−0.0517002	+	0.0710253i
$665$		0			0
$666$	−6.83128e7	+	7.58235e7i	−0.231249	+	0.256674i
$667$			2.27941e7i			0.0768149i
$668$	−1.50958e8	+	1.57752e7i	−0.506439	+	0.0529232i
$669$	−5.77469e8			−1.92864
$670$		0			0
$671$		−	1.33223e7i		−	0.0440972i
$672$	2.98898e8	−	5.15926e8i	0.984951	−	1.70012i
$673$	−2.63250e8			−0.863621			−0.431810	−	0.901964i	$-0.642125\pi$
$673$	−2.63250e8			−0.863621			−0.431810	+	0.901964i	$0.642125\pi$
$674$	2.83749e8	−	3.14946e8i	0.926732	−	1.02862i
$675$		0			0
$676$	−3.74846e7	−	3.58702e8i	−0.121342	−	1.16116i
$677$	2.04498e8			0.659056			0.329528	−	0.944146i	$-0.393110\pi$
$677$	2.04498e8			0.659056			0.329528	+	0.944146i	$0.393110\pi$
$678$	−3.84346e7	−	3.46274e7i	−0.123320	−	0.111104i
$679$		−	5.19513e8i		−	1.65954i
$680$		0			0
$681$	3.54989e7			0.112402
$682$	−6.95369e7	+	7.71822e7i	−0.219211	+	0.243312i
$683$		−	9.73212e7i		−	0.305454i	−0.988268	−	0.152727i	$-0.951195\pi$
$683$		−	9.73212e7i		−	0.305454i	0.988268	−	0.152727i	$-0.0488054\pi$
$684$	1.13553e8	−	1.18663e7i	0.354837	−	0.0370807i
$685$		0			0
$686$	8.61589e7	+	7.76244e7i	0.266887	+	0.240451i
$687$			1.46916e7i			0.0453106i
$688$	−4.89256e7	−	2.31536e8i	−0.150235	−	0.710974i
$689$	8.96356e8			2.74046
$690$		0			0
$691$		−	4.93368e8i		−	1.49533i	−0.664076	−	0.747665i	$-0.731175\pi$
$691$		−	4.93368e8i		−	1.49533i	0.664076	−	0.747665i	$-0.268825\pi$
$692$	−3.47617e7	−	3.32646e8i	−0.104902	−	1.00384i
$693$	−1.58728e8			−0.476930
$694$	−7.73833e7	−	6.97181e7i	−0.231510	−	0.208577i
$695$		0			0
$696$	−2.57389e8	+	3.53600e8i	−0.763419	+	1.04878i
$697$	−2.11660e8			−0.625087
$698$	−1.04644e8	+	1.16149e8i	−0.307715	+	0.341547i
$699$			1.28800e8i			0.377125i
$700$		0			0
$701$	−1.60818e6			−0.00466855			−0.00233427	−	0.999997i	$-0.500743\pi$
$701$	−1.60818e6			−0.00466855			−0.00233427	+	0.999997i	$0.500743\pi$
$702$	1.33473e8	+	1.20252e8i	0.385819	+	0.347601i
$703$			2.80358e7i			0.0806951i
$704$	−9.75104e7	+	3.14901e7i	−0.279469	+	0.0902518i
$705$		0			0
$706$	−2.25410e8	+	2.50193e8i	−0.640559	+	0.710986i
$707$		−	5.76723e8i		−	1.63196i
$708$	−7.56678e6	−	7.24089e7i	−0.0213212	−	0.204029i
$709$	−5.27495e8			−1.48006			−0.740031	−	0.672573i	$-0.765189\pi$
$709$	−5.27495e8			−1.48006			−0.740031	+	0.672573i	$0.765189\pi$
$710$		0			0
$711$			3.29531e8i			0.916828i
$712$	7.33819e7	+	5.34155e7i	0.203305	+	0.147988i
$713$	3.57901e7			0.0987404
$714$	−4.81069e8	+	5.33961e8i	−1.32164	+	1.46695i
$715$		0			0
$716$	−4.08461e8	+	4.26845e7i	−1.11279	+	0.116287i
$717$	6.94779e8			1.88490
$718$	−4.09207e7	−	3.68673e7i	−0.110553	−	0.0996020i
$719$			3.85369e8i			1.03679i	0.855142	+	0.518394i	$0.173470\pi$
$719$			3.85369e8i			1.03679i	−0.855142	+	0.518394i	$0.826530\pi$
$720$		0			0
$721$	9.38667e8			2.50441
$722$	−2.30929e8	+	2.56319e8i	−0.613574	+	0.681034i
$723$		−	5.11156e8i		−	1.35250i
$724$	1.82898e7	+	1.75021e8i	0.0481939	+	0.461183i
$725$		0			0
$726$	−3.88437e8	−	3.49960e8i	−1.01510	−	0.914553i
$727$			2.91515e8i			0.758679i	0.925258	+	0.379339i	$0.123849\pi$
$727$			2.91515e8i			0.758679i	−0.925258	+	0.379339i	$0.876151\pi$
$728$	4.39262e8	−	6.03455e8i	1.13849	−	1.56405i
$729$	5.43559e8			1.40302
$730$		0			0
$731$			2.85250e8i			0.730254i
$732$	−8.75864e7	+	9.15283e6i	−0.223308	+	0.0233358i
$733$	−4.31296e8			−1.09512			−0.547562	−	0.836765i	$-0.684444\pi$
$733$	−4.31296e8			−1.09512			−0.547562	+	0.836765i	$0.684444\pi$
$734$	7.47649e7	+	6.73591e7i	0.189064	+	0.170337i
$735$		0			0
$736$	3.05458e7	+	1.76965e7i	0.0766157	+	0.0443867i
$737$	8.99053e7			0.224586
$738$	−2.06829e8	+	2.29569e8i	−0.514569	+	0.571143i
$739$		−	6.53807e8i		−	1.62000i	−0.586427	−	0.810002i	$-0.699466\pi$
$739$		−	6.53807e8i		−	1.62000i	0.586427	−	0.810002i	$-0.300534\pi$
$740$		0			0
$741$	2.58561e8			0.635491
$742$	7.42354e8	+	6.68820e8i	1.81719	+	1.63718i
$743$			3.07461e8i			0.749589i	0.927108	+	0.374794i	$0.122287\pi$
$743$			3.07461e8i			0.749589i	−0.927108	+	0.374794i	$0.877713\pi$
$744$	5.55203e8	+	4.04139e8i	1.34813	+	0.981323i
$745$		0			0
$746$	−3.10831e8	+	3.45005e8i	−0.748700	+	0.831016i
$747$		−	4.52567e7i		−	0.108573i
$748$	1.22844e8	−	1.28373e7i	0.293529	−	0.0306739i
$749$	−2.30816e8			−0.549313
$750$		0			0
$751$		−	4.94845e8i		−	1.16829i	−0.811650	−	0.584143i	$-0.801431\pi$
$751$		−	4.94845e8i		−	1.16829i	0.811650	−	0.584143i	$-0.198569\pi$
$752$	−1.16989e8	−	5.53641e8i	−0.275101	−	1.30189i
$753$	1.08624e9			2.54414
$754$	−3.66463e8	+	4.06755e8i	−0.854902	+	0.948895i
$755$		0			0
$756$	2.08148e7	+	1.99183e8i	0.0481733	+	0.460986i
$757$	−8.18948e8			−1.88786			−0.943928	−	0.330152i	$-0.892900\pi$
$757$	−8.18948e8			−1.88786			−0.943928	+	0.330152i	$0.892900\pi$
$758$	2.58805e8	+	2.33169e8i	0.594245	+	0.535382i
$759$		−	1.70015e7i		−	0.0388833i
$760$		0			0
$761$	−4.68400e7			−0.106283			−0.0531414	−	0.998587i	$-0.516923\pi$
$761$	−4.68400e7			−0.106283			−0.0531414	+	0.998587i	$0.516923\pi$
$762$	4.10986e8	−	4.56172e8i	0.928885	−	1.03101i
$763$		−	5.99015e8i		−	1.34854i
$764$	−5.07633e8	+	5.30480e7i	−1.13833	+	0.118957i
$765$		0			0
$766$	1.75172e7	+	1.57820e7i	0.0389742	+	0.0351136i
$767$		−	9.11359e7i		−	0.201978i
$768$	2.74022e8	+	6.19441e8i	0.604926	+	1.36747i
$769$	5.79761e6			0.0127488			0.00637441	−	0.999980i	$-0.497971\pi$
$769$	5.79761e6			0.0127488			0.00637441	+	0.999980i	$0.497971\pi$
$770$		0			0
$771$			3.15397e8i			0.688168i
$772$	8.10591e7	+	7.75681e8i	0.176177	+	1.68590i
$773$	−4.58350e8			−0.992335			−0.496168	−	0.868227i	$-0.665260\pi$
$773$	−4.58350e8			−0.992335			−0.496168	+	0.868227i	$0.665260\pi$
$774$	3.09386e8	+	2.78740e8i	0.667234	+	0.601141i
$775$		0			0
$776$	4.77143e8	+	3.47318e8i	1.02109	+	0.743263i
$777$	−2.57649e8			−0.549245
$778$	1.00510e8	−	1.11561e8i	0.213437	−	0.236904i
$779$			8.48835e7i			0.179561i
$780$		0			0
$781$	−8.39079e7			−0.176137
$782$	−3.16136e7	−	2.84821e7i	−0.0661079	−	0.0595595i
$783$		−	1.46898e8i		−	0.306007i
$784$	3.42584e8	−	7.23911e7i	0.710917	−	0.150223i
$785$		0			0
$786$	5.97220e8	−	6.62882e8i	1.22989	−	1.36511i
$787$		−	8.86461e8i		−	1.81859i	−0.416149	−	0.909297i	$-0.636620\pi$
$787$		−	8.86461e8i		−	1.81859i	0.416149	−	0.909297i	$-0.363380\pi$
$788$	3.50678e7	+	3.35575e8i	0.0716688	+	0.685822i
$789$	−5.37520e8			−1.09437
$790$		0			0
$791$		−	7.21901e7i		−	0.145864i
$792$	1.06117e8	−	1.45783e8i	0.213605	−	0.293448i
$793$	−1.10239e8			−0.221062
$794$	2.14111e8	−	2.37652e8i	0.427739	−	0.474767i
$795$		0			0
$796$	−7.28415e8	+	7.61198e7i	−1.44424	+	0.150924i
$797$	5.08284e8			1.00400			0.501998	−	0.864869i	$-0.332599\pi$
$797$	5.08284e8			1.00400			0.501998	+	0.864869i	$0.332599\pi$
$798$	2.14138e8	+	1.92927e8i	0.421391	+	0.379650i
$799$			6.82080e8i			1.33720i
$800$		0			0
$801$	−1.59718e8			−0.310782
$802$	−3.47723e7	+	3.85954e7i	−0.0674078	+	0.0748190i
$803$			8.28434e6i			0.0159997i
$804$	−6.17679e7	−	5.91077e8i	−0.118849	−	1.13730i
$805$		0			0
$806$	6.38664e8	+	5.75401e8i	1.21974	+	1.09892i
$807$			7.01988e8i			1.33570i
$808$	5.29688e8	+	3.85566e8i	1.00412	+	0.730912i
$809$	3.14322e6			0.00593648			0.00296824	−	0.999996i	$-0.499055\pi$
$809$	3.14322e6			0.00593648			0.00296824	+	0.999996i	$0.499055\pi$
$810$		0			0
$811$			3.62482e8i			0.679553i	0.940506	+	0.339777i	$0.110352\pi$
$811$			3.62482e8i			0.679553i	−0.940506	+	0.339777i	$0.889648\pi$
$812$	−6.07003e8	+	6.34322e7i	−1.13376	+	0.118479i
$813$	−8.61382e8			−1.60297
$814$	3.28963e7	+	2.96378e7i	0.0609921	+	0.0549506i
$815$		0			0
$816$	−1.68796e8	−	7.98813e8i	−0.310665	−	1.47019i
$817$	1.14396e8			0.209770
$818$	1.47826e8	−	1.64079e8i	0.270080	−	0.299774i
$819$			1.31344e9i			2.39088i
$820$		0			0
$821$	−7.24735e8			−1.30963			−0.654816	−	0.755788i	$-0.727254\pi$
$821$	−7.24735e8			−1.30963			−0.654816	+	0.755788i	$0.727254\pi$
$822$	−6.24080e8	−	5.62261e8i	−1.12363	−	1.01233i
$823$			5.63218e8i			1.01036i	0.863013	+	0.505181i	$0.168574\pi$
$823$			5.63218e8i			1.01036i	−0.863013	+	0.505181i	$0.831426\pi$
$824$	−6.27542e8	+	8.62113e8i	−1.12166	+	1.54093i
$825$		0			0
$826$	6.80014e7	−	7.54779e7i	0.120664	−	0.133930i
$827$			6.66821e8i			1.17894i	0.807789	+	0.589471i	$0.200664\pi$
$827$			6.66821e8i			1.17894i	−0.807789	+	0.589471i	$0.799336\pi$
$828$	−6.17841e7	+	6.45648e6i	−0.108839	+	0.0113738i
$829$	5.69391e8			0.999418			0.499709	−	0.866193i	$-0.333440\pi$
$829$	5.69391e8			0.999418			0.499709	+	0.866193i	$0.333440\pi$
$830$		0			0
$831$			6.94558e8i			1.21034i
$832$	2.60573e8	+	8.06876e8i	0.452438	+	1.40100i
$833$	−4.22060e8			−0.730196
$834$	6.64458e8	−	7.37512e8i	1.14543	−	1.27137i
$835$		0			0
$836$	−5.14824e6	−	4.92652e7i	−0.00881130	−	0.0843182i
$837$	−2.30652e8			−0.393351
$838$	−8.79619e7	−	7.92488e7i	−0.149473	−	0.134667i
$839$			9.23641e8i			1.56393i	0.623322	+	0.781965i	$0.285783\pi$
$839$			9.23641e8i			1.56393i	−0.623322	+	0.781965i	$0.714217\pi$
$840$		0			0
$841$	−1.47157e8			−0.247396
$842$	1.76306e8	−	1.95691e8i	0.295346	−	0.327819i
$843$		−	1.03712e9i		−	1.73120i
$844$	−2.10274e8	+	2.19738e7i	−0.349751	+	0.0365492i
$845$		0			0
$846$	7.39793e8	+	6.66513e8i	1.22180	+	1.10077i
$847$		−	7.29586e8i		−	1.20068i
$848$	−1.11057e9	+	2.34674e8i	−1.82121	+	0.384837i
$849$	−5.62704e8			−0.919511
$850$		0			0
$851$		−	1.52543e7i		−	0.0247517i
$852$	5.76474e7	+	5.51647e8i	0.0932097	+	0.891954i
$853$	−7.92638e7			−0.127711			−0.0638555	−	0.997959i	$-0.520340\pi$
$853$	−7.92638e7			−0.127711			−0.0638555	+	0.997959i	$0.520340\pi$
$854$	−9.12986e7	−	8.22550e7i	−0.146585	−	0.132065i
$855$		0			0
$856$	1.54311e8	−	2.11991e8i	0.246023	−	0.337985i
$857$	−8.08687e8			−1.28481			−0.642404	−	0.766366i	$-0.722063\pi$
$857$	−8.08687e8			−1.28481			−0.642404	+	0.766366i	$0.722063\pi$
$858$	2.73335e8	−	3.03387e8i	0.432747	−	0.480326i
$859$		−	1.08418e9i		−	1.71049i	−0.518225	−	0.855244i	$-0.673407\pi$
$859$		−	1.08418e9i		−	1.71049i	0.518225	−	0.855244i	$-0.326593\pi$
$860$		0			0
$861$	−7.80080e8			−1.22217
$862$	−5.62317e8	−	5.06617e8i	−0.877929	−	0.790966i
$863$		−	8.65764e8i		−	1.34700i	−0.739188	−	0.673499i	$-0.764790\pi$
$863$		−	8.65764e8i		−	1.34700i	0.739188	−	0.673499i	$-0.235210\pi$
$864$	−1.96854e8	−	1.14046e8i	−0.305214	−	0.176823i
$865$		0			0
$866$	3.48373e8	−	3.86675e8i	0.536402	−	0.595377i
$867$			9.62558e6i			0.0147696i
$868$	9.95978e7	+	9.53084e8i	0.152297	+	1.45738i
$869$	1.42968e8			0.217861
$870$		0			0
$871$		−	7.43945e8i		−	1.12587i
$872$	5.50162e8	+	4.00469e8i	0.829738	+	0.603976i
$873$	−1.03852e9			−1.56089
$874$	−1.14224e7	+	1.26782e7i	−0.0171089	+	0.0189900i
$875$		0			0
$876$	5.44649e7	−	5.69161e6i	0.0810222	−	0.00846687i
$877$	−6.80856e8			−1.00938			−0.504692	−	0.863299i	$-0.668394\pi$
$877$	−6.80856e8			−1.00938			−0.504692	+	0.863299i	$0.668394\pi$
$878$	3.15421e8	+	2.84177e8i	0.466023	+	0.419861i
$879$		−	1.32556e9i		−	1.95179i
$880$		0			0
$881$	−1.01305e9			−1.48150			−0.740750	−	0.671780i	$-0.765530\pi$
$881$	−1.01305e9			−1.48150			−0.740750	+	0.671780i	$0.765530\pi$
$882$	−4.12428e8	+	4.57772e8i	−0.601093	+	0.667181i
$883$		−	7.97017e8i		−	1.15767i	−0.815444	−	0.578836i	$-0.803507\pi$
$883$		−	7.97017e8i		−	1.15767i	0.815444	−	0.578836i	$-0.196493\pi$
$884$	−1.06226e8	−	1.01651e9i	−0.153770	−	1.47148i
$885$		0			0
$886$	−8.16761e8	−	7.35857e8i	−1.17434	−	1.05802i
$887$			8.37782e8i			1.20049i	0.799815	+	0.600247i	$0.204931\pi$
$887$			8.37782e8i			1.20049i	−0.799815	+	0.600247i	$0.795069\pi$
$888$	1.72251e8	−	2.36637e8i	0.245992	−	0.337943i
$889$	8.56810e8			1.21949
$890$		0			0
$891$		−	1.47170e8i		−	0.208059i
$892$	9.10459e8	−	9.51435e7i	1.28282	−	0.134056i
$893$	2.73539e8			0.384119
$894$	5.05713e8	+	4.55620e8i	0.707769	+	0.637661i
$895$		0			0
$896$	−3.86249e8	+	8.62674e8i	−0.536962	+	1.19929i
$897$	−1.40684e8			−0.194924
$898$	7.36838e6	−	8.17851e6i	0.0101752	−	0.0112939i
$899$		−	7.02902e8i		−	0.967422i
$900$		0			0
$901$	1.36821e9			1.87059
$902$	9.95995e7	+	8.97337e7i	0.135718	+	0.122274i
$903$			1.05130e9i			1.42779i
$904$	6.63026e7	+	4.82624e7i	0.0897481	+	0.0653287i
$905$		0			0
$906$	4.77356e8	−	5.29839e8i	0.641886	−	0.712458i
$907$		−	8.35297e8i		−	1.11949i	−0.828666	−	0.559743i	$-0.810900\pi$
$907$		−	8.35297e8i		−	1.11949i	0.828666	−	0.559743i	$-0.189100\pi$
$908$	−5.59689e7	+	5.84879e6i	−0.0747635	+	0.00781283i
$909$	−1.15288e9			−1.53495
$910$		0			0
$911$			5.22073e8i			0.690519i	0.938507	+	0.345260i	$0.112209\pi$
$911$			5.22073e8i			0.690519i	−0.938507	+	0.345260i	$0.887791\pi$
$912$	−3.20354e8	+	6.76936e7i	−0.422323	+	0.0892407i
$913$	−1.96348e7			−0.0257996
$914$	−6.39815e8	+	7.10160e8i	−0.837945	+	0.930074i
$915$		0			0
$916$	−2.42059e6	−	2.31634e7i	−0.00314945	−	0.0301381i
$917$	1.24506e9			1.61467
$918$	2.03736e8	+	1.83555e8i	0.263354	+	0.237267i
$919$		−	7.05912e7i		−	0.0909502i	−0.998965	−	0.0454751i	$-0.985520\pi$
$919$		−	7.05912e7i		−	0.0909502i	0.998965	−	0.0454751i	$-0.0144802\pi$
$920$		0			0
$921$	1.29516e9			1.65785
$922$	6.74870e8	−	7.49069e8i	0.861047	−	0.955716i
$923$			6.94318e8i			0.882985i
$924$	4.52747e8	−	4.73124e7i	0.573905	−	0.0599734i
$925$		0			0
$926$	6.01523e8	+	5.41939e8i	0.757564	+	0.682524i
$927$		−	1.87642e9i		−	2.35554i
$928$	3.47551e8	−	5.99906e8i	0.434885	−	0.750653i
$929$	3.30334e8			0.412008			0.206004	−	0.978551i	$-0.433954\pi$
$929$	3.30334e8			0.412008			0.206004	+	0.978551i	$0.433954\pi$
$930$		0			0
$931$			1.69262e8i			0.209754i
$932$	−2.12211e7	−	2.03071e8i	−0.0262132	−	0.250843i
$933$	1.29982e9			1.60044
$934$	−5.78028e8	−	5.20771e8i	−0.709428	−	0.639155i
$935$		0			0
$936$	−1.20632e9	−	8.78095e8i	−1.47108	−	1.07081i
$937$	1.37475e9			1.67111			0.835556	−	0.549406i	$-0.185146\pi$
$937$	1.37475e9			1.67111			0.835556	+	0.549406i	$0.185146\pi$
$938$	5.55098e8	−	6.16128e8i	0.672606	−	0.746557i
$939$			1.46430e8i			0.176861i
$940$		0			0
$941$	1.35847e9			1.63035			0.815177	−	0.579211i	$-0.196639\pi$
$941$	1.35847e9			1.63035			0.815177	+	0.579211i	$0.196639\pi$
$942$	1.97039e8	+	1.77522e8i	0.235722	+	0.212373i
$943$		−	4.61853e7i		−	0.0550768i
$944$	2.38601e7	+	1.12916e8i	0.0283633	+	0.134227i
$945$		0			0
$946$	1.20932e8	−	1.34228e8i	0.142846	−	0.158552i
$947$			3.76294e8i			0.443075i	0.975152	+	0.221537i	$0.0711075\pi$
$947$			3.76294e8i			0.443075i	−0.975152	+	0.221537i	$0.928892\pi$
$948$	−9.82238e7	−	9.39935e8i	−0.115290	−	1.10325i
$949$	6.85510e7			0.0802075
$950$		0			0
$951$		−	1.09285e9i		−	1.27063i
$952$	6.70497e8	−	9.21123e8i	0.777116	−	1.06760i
$953$	6.28773e8			0.726465			0.363233	−	0.931698i	$-0.381673\pi$
$953$	6.28773e8			0.726465			0.363233	+	0.931698i	$0.381673\pi$
$954$	1.33699e9	−	1.48398e9i	1.53986	−	1.70916i
$955$		0			0
$956$	−1.09541e9	+	1.14471e8i	−1.25373	+	0.131016i
$957$	−3.33903e8			−0.380964
$958$	3.60353e8	+	3.24658e8i	0.409856	+	0.369258i
$959$		−	1.17218e9i		−	1.32905i
$960$		0			0
$961$	−2.16156e8			−0.243555
$962$	2.45245e8	−	2.72209e8i	0.275471	−	0.305758i
$963$			4.61406e8i			0.516660i
$964$	8.42178e7	+	8.05907e8i	0.0940097	+	0.899609i
$965$		0			0
$966$	−1.16513e8	−	1.04972e8i	−0.129254	−	0.116450i
$967$			6.61713e8i			0.731796i	0.930655	+	0.365898i	$0.119238\pi$
$967$			6.61713e8i			0.731796i	−0.930655	+	0.365898i	$0.880762\pi$
$968$	6.70084e8	+	4.87762e8i	0.738759	+	0.537752i
$969$	3.94672e8			0.433776
$970$		0			0
$971$			8.80062e7i			0.0961292i	0.998844	+	0.0480646i	$0.0153053\pi$
$971$			8.80062e7i			0.0961292i	−0.998844	+	0.0480646i	$0.984695\pi$
$972$	−1.28973e9	+	1.34778e8i	−1.40443	+	0.146764i
$973$	1.38524e9			1.50379
$974$	7.13920e8	+	6.43202e8i	0.772632	+	0.696099i
$975$		0			0
$976$	1.36584e8	−	2.88614e7i	0.146910	−	0.0310433i
$977$	7.15460e8			0.767188			0.383594	−	0.923502i	$-0.374686\pi$
$977$	7.15460e8			0.767188			0.383594	+	0.923502i	$0.374686\pi$
$978$	−1.66641e9	+	1.84962e9i	−1.78141	+	1.97727i
$979$			6.92942e7i			0.0738497i
$980$		0			0
$981$	−1.19745e9			−1.26838
$982$	6.97923e8	+	6.28790e8i	0.737010	+	0.664005i
$983$		−	1.11848e8i		−	0.117752i	−0.998265	−	0.0588760i	$-0.981248\pi$
$983$		−	1.11848e8i		−	0.117752i	0.998265	−	0.0588760i	$-0.0187517\pi$
$984$	5.21520e8	−	7.16460e8i	0.547376	−	0.751981i
$985$		0			0
$986$	−5.59375e8	+	6.20876e8i	−0.583543	+	0.647701i
$987$			2.51383e9i			2.61447i
$988$	−4.07658e8	+	4.26005e7i	−0.422693	+	0.0441717i
$989$	−6.22430e7			−0.0643430
$990$		0			0
$991$		−	1.31906e8i		−	0.135532i	−0.997701	−	0.0677661i	$-0.978413\pi$
$991$		−	1.31906e8i		−	0.135532i	0.997701	−	0.0677661i	$-0.0215872\pi$
$992$	−9.41940e8	−	5.45706e8i	−0.964913	−	0.559015i
$993$	−1.35426e9			−1.38310
$994$	−5.18068e8	+	5.75028e8i	−0.527506	+	0.585504i
$995$		0			0
$996$	1.34897e7	+	1.29087e8i	0.0136529	+	0.130649i
$997$	−1.67136e9			−1.68649			−0.843246	−	0.537527i	$-0.819359\pi$
$997$	−1.67136e9			−1.68649			−0.843246	+	0.537527i	$0.819359\pi$
$998$	−1.24020e9	−	1.11735e9i	−1.24767	−	1.12408i
$999$			9.83076e7i			0.0986031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.7.b.f.51.4		12
4.3	odd	2	inner	100.7.b.f.51.3		12
5.2	odd	4		20.7.d.d.19.3	✓	12
5.3	odd	4		20.7.d.d.19.10	yes	12
5.4	even	2	inner	100.7.b.f.51.9		12
15.2	even	4		180.7.f.e.19.10		12
15.8	even	4		180.7.f.e.19.3		12
20.3	even	4		20.7.d.d.19.4	yes	12
20.7	even	4		20.7.d.d.19.9	yes	12
20.19	odd	2	inner	100.7.b.f.51.10		12
40.3	even	4		320.7.h.f.319.2		12
40.13	odd	4		320.7.h.f.319.12		12
40.27	even	4		320.7.h.f.319.11		12
40.37	odd	4		320.7.h.f.319.1		12
60.23	odd	4		180.7.f.e.19.9		12
60.47	odd	4		180.7.f.e.19.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.d.d.19.3	✓	12	5.2	odd	4
20.7.d.d.19.4	yes	12	20.3	even	4
20.7.d.d.19.9	yes	12	20.7	even	4
20.7.d.d.19.10	yes	12	5.3	odd	4
100.7.b.f.51.3		12	4.3	odd	2	inner
100.7.b.f.51.4		12	1.1	even	1	trivial
100.7.b.f.51.9		12	5.4	even	2	inner
100.7.b.f.51.10		12	20.19	odd	2	inner
180.7.f.e.19.3		12	15.8	even	4
180.7.f.e.19.4		12	60.47	odd	4
180.7.f.e.19.9		12	60.23	odd	4
180.7.f.e.19.10		12	15.2	even	4
320.7.h.f.319.1		12	40.37	odd	4
320.7.h.f.319.2		12	40.3	even	4
320.7.h.f.319.11		12	40.27	even	4
320.7.h.f.319.12		12	40.13	odd	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.35482 + 5.94356i) q^{2} +40.3729i q^{3} +(-6.65182 - 63.6534i) q^{4} +(-239.959 - 216.189i) q^{6} -450.705i q^{7} +(413.947 + 301.317i) q^{8} -900.969 q^{9} +O(q^{10})\)	\(q+(-5.35482 + 5.94356i) q^{2} +40.3729i q^{3} +(-6.65182 - 63.6534i) q^{4} +(-239.959 - 216.189i) q^{6} -450.705i q^{7} +(413.947 + 301.317i) q^{8} -900.969 q^{9} +390.888i q^{11} +(2569.87 - 268.553i) q^{12} +3234.51 q^{13} +(2678.79 + 2413.44i) q^{14} +(-4007.51 + 846.821i) q^{16} +4937.20 q^{17} +(4824.53 - 5354.96i) q^{18} -1980.00i q^{19} +18196.2 q^{21} +(-2323.27 - 2093.14i) q^{22} +1077.32i q^{23} +(-12165.0 + 16712.2i) q^{24} +(-17320.2 + 19224.5i) q^{26} -6942.88i q^{27} +(-28688.9 + 2998.00i) q^{28} +21158.1 q^{29} -33221.4i q^{31} +(16426.3 - 28353.4i) q^{32} -15781.3 q^{33} +(-26437.8 + 29344.6i) q^{34} +(5993.08 + 57349.7i) q^{36} -14159.5 q^{37} +(11768.3 + 10602.6i) q^{38} +130586. i q^{39} -42870.4 q^{41} +(-97437.6 + 108150. i) q^{42} +57775.6i q^{43} +(24881.4 - 2600.12i) q^{44} +(-6403.13 - 5768.87i) q^{46} +138151. i q^{47} +(-34188.6 - 161795. i) q^{48} -85485.6 q^{49} +199329. i q^{51} +(-21515.4 - 205887. i) q^{52} +277123. q^{53} +(41265.4 + 37177.9i) q^{54} +(135805. - 186568. i) q^{56} +79938.4 q^{57} +(-113298. + 125755. i) q^{58} -28176.1i q^{59} -34082.0 q^{61} +(197453. + 177894. i) q^{62} +406071. i q^{63} +(80560.3 + 249458. i) q^{64} +(84506.0 - 93797.1i) q^{66} -230002. i q^{67} +(-32841.4 - 314270. i) q^{68} -43494.6 q^{69} +214659. i q^{71} +(-372953. - 271477. i) q^{72} +21193.6 q^{73} +(75821.5 - 84157.8i) q^{74} +(-126034. + 13170.6i) q^{76} +176175. q^{77} +(-776148. - 699267. i) q^{78} -365752. i q^{79} -376502. q^{81} +(229563. - 254803. i) q^{82} +50231.1i q^{83} +(-121038. - 1.15825e6i) q^{84} +(-343393. - 309378. i) q^{86} +854215. i q^{87} +(-117781. + 161807. i) q^{88} +177274. q^{89} -1.45781e6i q^{91} +(68575.2 - 7166.15i) q^{92} +1.34124e6 q^{93} +(-821109. - 739774. i) q^{94} +(1.14471e6 + 663179. i) q^{96} +1.15267e6 q^{97} +(457760. - 508089. i) q^{98} -352178. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9}+O(q^{10}) \) 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9	\( 12 q - 64 q^{4} - 672 q^{6} - 1956 q^{9} - 512 q^{14} - 20928 q^{16} + 51216 q^{21} + 20928 q^{24} + 14496 q^{26} + 16072 q^{29} - 257216 q^{34} - 144960 q^{36} - 192136 q^{41} + 165120 q^{44} - 49472 q^{46} - 145796 q^{49} + 118656 q^{54} + 1078208 q^{56} + 215384 q^{61} + 6656 q^{64} - 1403520 q^{66} - 1015824 q^{69} + 1020384 q^{74} + 2515200 q^{76} - 2327652 q^{81} - 424704 q^{84} - 5268832 q^{86} + 4346152 q^{89} - 4292992 q^{94} + 7673088 q^{96}+O(q^{100}) \) 12 * q - 64 * q^4 - 672 * q^6 - 1956 * q^9 - 512 * q^14 - 20928 * q^16 + 51216 * q^21 + 20928 * q^24 + 14496 * q^26 + 16072 * q^29 - 257216 * q^34 - 144960 * q^36 - 192136 * q^41 + 165120 * q^44 - 49472 * q^46 - 145796 * q^49 + 118656 * q^54 + 1078208 * q^56 + 215384 * q^61 + 6656 * q^64 - 1403520 * q^66 - 1015824 * q^69 + 1020384 * q^74 + 2515200 * q^76 - 2327652 * q^81 - 424704 * q^84 - 5268832 * q^86 + 4346152 * q^89 - 4292992 * q^94 + 7673088 * q^96

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