LMFDB - Embedded newform 33.7.c.a.10.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(10,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("33.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.c (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:	$7.59178475946$
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} + 486x^{10} + 82401x^{8} + 6062364x^{6} + 204706260x^{4} + 2964086784x^{2} + 15081209856 $ x^12 + 486x^10 + 82401x^8 + 6062364x^6 + 204706260x^4 + 2964086784*x^2 + 15081209856
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.8
Root			$3.80817i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.7.c.a.10.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.80817i q^{2} -15.5885 q^{3} +49.4978 q^{4} -143.833 q^{5} -59.3636i q^{6} -413.864i q^{7} +432.219i q^{8} +243.000 q^{9} +O(q^{10})$	\(q+3.80817i q^{2} -15.5885 q^{3} +49.4978 q^{4} -143.833 q^{5} -59.3636i q^{6} -413.864i q^{7} +432.219i q^{8} +243.000 q^{9} -547.741i q^{10} +(-170.977 - 1319.97i) q^{11} -771.594 q^{12} -3337.89i q^{13} +1576.07 q^{14} +2242.14 q^{15} +1521.89 q^{16} -3629.60i q^{17} +925.386i q^{18} +3421.53i q^{19} -7119.42 q^{20} +6451.50i q^{21} +(5026.69 - 651.109i) q^{22} -11285.0 q^{23} -6737.63i q^{24} +5062.95 q^{25} +12711.3 q^{26} -3788.00 q^{27} -20485.4i q^{28} +26264.4i q^{29} +8538.44i q^{30} -47127.9 q^{31} +33457.7i q^{32} +(2665.26 + 20576.3i) q^{33} +13822.1 q^{34} +59527.3i q^{35} +12028.0 q^{36} +61704.4 q^{37} -13029.8 q^{38} +52032.5i q^{39} -62167.5i q^{40} -46068.4i q^{41} -24568.4 q^{42} -99085.7i q^{43} +(-8462.96 - 65335.8i) q^{44} -34951.4 q^{45} -42975.2i q^{46} +115212. q^{47} -23724.0 q^{48} -53634.4 q^{49} +19280.6i q^{50} +56579.9i q^{51} -165218. i q^{52} -86453.7 q^{53} -14425.3i q^{54} +(24592.1 + 189856. i) q^{55} +178880. q^{56} -53336.4i q^{57} -100019. q^{58} -221976. q^{59} +110981. q^{60} -196946. i q^{61} -179471. i q^{62} -100569. i q^{63} -30011.5 q^{64} +480099. i q^{65} +(-78358.3 + 10149.8i) q^{66} +421101. q^{67} -179657. i q^{68} +175916. q^{69} -226690. q^{70} +233869. q^{71} +105029. i q^{72} +555148. i q^{73} +234981. i q^{74} -78923.6 q^{75} +169358. i q^{76} +(-546289. + 70761.0i) q^{77} -198149. q^{78} +239919. i q^{79} -218898. q^{80} +59049.0 q^{81} +175437. q^{82} -724407. i q^{83} +319335. i q^{84} +522056. i q^{85} +377335. q^{86} -409421. i q^{87} +(570518. - 73899.4i) q^{88} +388350. q^{89} -133101. i q^{90} -1.38143e6 q^{91} -558582. q^{92} +734652. q^{93} +438749. i q^{94} -492129. i q^{95} -521554. i q^{96} -1.18719e6 q^{97} -204249. i q^{98} +(-41547.3 - 320753. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) $ 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9	$ 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9} - 3464 q^{11} + 1944 q^{12} - 6708 q^{14} + 1944 q^{15} + 5316 q^{16} - 44092 q^{20} + 60468 q^{22} - 15304 q^{23} + 95652 q^{25} - 76020 q^{26} - 58608 q^{31} + 4212 q^{33} + 117768 q^{34} - 49572 q^{36} - 202512 q^{37} + 29208 q^{38} - 264708 q^{42} + 434356 q^{44} + 54432 q^{45} + 516920 q^{47} - 377136 q^{48} + 157812 q^{49} - 1042192 q^{53} + 262656 q^{55} + 463020 q^{56} + 1029432 q^{58} - 461008 q^{59} - 417636 q^{60} - 725364 q^{64} + 200232 q^{66} + 364752 q^{67} + 504144 q^{69} - 1028400 q^{70} - 755176 q^{71} + 1364688 q^{75} - 102384 q^{77} + 1219212 q^{78} - 1220764 q^{80} + 708588 q^{81} - 158688 q^{82} + 248760 q^{86} - 2493252 q^{88} - 3513544 q^{89} - 702768 q^{91} + 6899300 q^{92} + 789264 q^{93} + 2370192 q^{97} - 841752 q^{99}+O(q^{100}) $ 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9 - 3464 * q^11 + 1944 * q^12 - 6708 * q^14 + 1944 * q^15 + 5316 * q^16 - 44092 * q^20 + 60468 * q^22 - 15304 * q^23 + 95652 * q^25 - 76020 * q^26 - 58608 * q^31 + 4212 * q^33 + 117768 * q^34 - 49572 * q^36 - 202512 * q^37 + 29208 * q^38 - 264708 * q^42 + 434356 * q^44 + 54432 * q^45 + 516920 * q^47 - 377136 * q^48 + 157812 * q^49 - 1042192 * q^53 + 262656 * q^55 + 463020 * q^56 + 1029432 * q^58 - 461008 * q^59 - 417636 * q^60 - 725364 * q^64 + 200232 * q^66 + 364752 * q^67 + 504144 * q^69 - 1028400 * q^70 - 755176 * q^71 + 1364688 * q^75 - 102384 * q^77 + 1219212 * q^78 - 1220764 * q^80 + 708588 * q^81 - 158688 * q^82 + 248760 * q^86 - 2493252 * q^88 - 3513544 * q^89 - 702768 * q^91 + 6899300 * q^92 + 789264 * q^93 + 2370192 * q^97 - 841752 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$1$

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 $

$2$			3.80817i			0.476022i	0.971262	+	0.238011i	$0.0764954\pi$
$2$			3.80817i			0.476022i	−0.971262	+	0.238011i	$0.923505\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	49.4978			0.773403
$5$	−143.833			−1.15066			−0.575332	−	0.817920i	$-0.695127\pi$
$5$	−143.833			−1.15066			−0.575332	+	0.817920i	$0.695127\pi$
$6$		−	59.3636i		−	0.274831i
$7$		−	413.864i		−	1.20660i	−0.797514	−	0.603300i	$-0.793852\pi$
$7$		−	413.864i		−	1.20660i	0.797514	−	0.603300i	$-0.206148\pi$
$8$			432.219i			0.844179i
$9$	243.000			0.333333
$10$		−	547.741i		−	0.547741i
$11$	−170.977	−	1319.97i	−0.128457	−	0.991715i
$11$	−170.977	−	1319.97i	−0.128457	−	0.991715i
$12$	−771.594			−0.446525
$13$		−	3337.89i		−	1.51929i	−0.650336	−	0.759647i	$-0.725372\pi$
$13$		−	3337.89i		−	1.51929i	0.650336	−	0.759647i	$-0.274628\pi$
$14$	1576.07			0.574368
$15$	2242.14			0.664337
$16$	1521.89			0.371556
$17$		−	3629.60i		−	0.738775i	−0.929276	−	0.369387i	$-0.879568\pi$
$17$		−	3629.60i		−	0.738775i	0.929276	−	0.369387i	$-0.120432\pi$
$18$			925.386i			0.158674i
$19$			3421.53i			0.498838i	0.968396	+	0.249419i	$0.0802397\pi$
$19$			3421.53i			0.498838i	−0.968396	+	0.249419i	$0.919760\pi$
$20$	−7119.42			−0.889928
$21$			6451.50i			0.696631i
$22$	5026.69	−	651.109i	0.472078	−	0.0611484i
$23$	−11285.0			−0.927508			−0.463754	−	0.885964i	$-0.653498\pi$
$23$	−11285.0			−0.927508			−0.463754	+	0.885964i	$0.653498\pi$
$24$		−	6737.63i		−	0.487387i
$25$	5062.95			0.324029
$26$	12711.3			0.723217
$27$	−3788.00			−0.192450
$28$		−	20485.4i		−	0.933189i
$29$			26264.4i			1.07689i	0.842660	+	0.538447i	$0.180989\pi$
$29$			26264.4i			1.07689i	−0.842660	+	0.538447i	$0.819011\pi$
$30$			8538.44i			0.316239i
$31$	−47127.9			−1.58195			−0.790976	−	0.611847i	$-0.790427\pi$
$31$	−47127.9			−1.58195			−0.790976	+	0.611847i	$0.790427\pi$
$32$			33457.7i			1.02105i
$33$	2665.26	+	20576.3i	0.0741648	+	0.572567i
$34$	13822.1			0.351673
$35$			59527.3i			1.38839i
$36$	12028.0			0.257801
$37$	61704.4			1.21818			0.609089	−	0.793102i	$-0.291535\pi$
$37$	61704.4			1.21818			0.609089	+	0.793102i	$0.291535\pi$
$38$	−13029.8			−0.237458
$39$			52032.5i			0.877164i
$40$		−	62167.5i		−	0.971366i
$41$		−	46068.4i		−	0.668423i	−0.942498	−	0.334212i	$-0.891530\pi$
$41$		−	46068.4i		−	0.668423i	0.942498	−	0.334212i	$-0.108470\pi$
$42$	−24568.4			−0.331612
$43$		−	99085.7i		−	1.24625i	−0.782122	−	0.623125i	$-0.785863\pi$
$43$		−	99085.7i		−	1.24625i	0.782122	−	0.623125i	$-0.214137\pi$
$44$	−8462.96	−	65335.8i	−0.0993492	−	0.766996i
$45$	−34951.4			−0.383555
$46$		−	42975.2i		−	0.441514i
$47$	115212.			1.10970			0.554850	−	0.831950i	$-0.312776\pi$
$47$	115212.			1.10970			0.554850	+	0.831950i	$0.312776\pi$
$48$	−23724.0			−0.214518
$49$	−53634.4			−0.455885
$50$			19280.6i			0.154245i
$51$			56579.9i			0.426532i
$52$		−	165218.i		−	1.17503i
$53$	−86453.7			−0.580705			−0.290353	−	0.956920i	$-0.593773\pi$
$53$	−86453.7			−0.580705			−0.290353	+	0.956920i	$0.593773\pi$
$54$		−	14425.3i		−	0.0916104i
$55$	24592.1	+	189856.i	0.147811	+	1.14113i
$56$	178880.			1.01859
$57$		−	53336.4i		−	0.288004i
$58$	−100019.			−0.512625
$59$	−221976.			−1.08081			−0.540405	−	0.841405i	$-0.681729\pi$
$59$	−221976.			−1.08081			−0.540405	+	0.841405i	$0.681729\pi$
$60$	110981.			0.513800
$61$		−	196946.i		−	0.867677i	−0.900991	−	0.433838i	$-0.857159\pi$
$61$		−	196946.i		−	0.867677i	0.900991	−	0.433838i	$-0.142841\pi$
$62$		−	179471.i		−	0.753044i
$63$		−	100569.i		−	0.402200i
$64$	−30011.5			−0.114485
$65$			480099.i			1.74820i
$66$	−78358.3	+	10149.8i	−0.272554	+	0.0353041i
$67$	421101.			1.40011			0.700055	−	0.714089i	$-0.253159\pi$
$67$	421101.			1.40011			0.700055	+	0.714089i	$0.253159\pi$
$68$		−	179657.i		−	0.571371i
$69$	175916.			0.535497
$70$	−226690.			−0.660905
$71$	233869.			0.653427			0.326713	−	0.945123i	$-0.394059\pi$
$71$	233869.			0.653427			0.326713	+	0.945123i	$0.394059\pi$
$72$			105029.i			0.281393i
$73$			555148.i			1.42705i	0.700628	+	0.713527i	$0.252903\pi$
$73$			555148.i			1.42705i	−0.700628	+	0.713527i	$0.747097\pi$
$74$			234981.i			0.579880i
$75$	−78923.6			−0.187078
$76$			169358.i			0.385803i
$77$	−546289.	+	70761.0i	−1.19660	+	0.154997i
$78$	−198149.			−0.417549
$79$			239919.i			0.486613i	0.969949	+	0.243307i	$0.0782322\pi$
$79$			239919.i			0.486613i	−0.969949	+	0.243307i	$0.921768\pi$
$80$	−218898.			−0.427536
$81$	59049.0			0.111111
$82$	175437.			0.318184
$83$		−	724407.i		−	1.26692i	−0.773777	−	0.633459i	$-0.781635\pi$
$83$		−	724407.i		−	1.26692i	0.773777	−	0.633459i	$-0.218365\pi$
$84$			319335.i			0.538777i
$85$			522056.i			0.850082i
$86$	377335.			0.593243
$87$		−	409421.i		−	0.621745i
$88$	570518.	−	73899.4i	0.837185	−	0.108441i
$89$	388350.			0.550875			0.275437	−	0.961319i	$-0.411177\pi$
$89$	388350.			0.550875			0.275437	+	0.961319i	$0.411177\pi$
$90$		−	133101.i		−	0.182580i
$91$	−1.38143e6			−1.83318
$92$	−558582.			−0.717338
$93$	734652.			0.913341
$94$			438749.i			0.528241i
$95$		−	492129.i		−	0.573995i
$96$		−	521554.i		−	0.589502i
$97$	−1.18719e6			−1.30078			−0.650390	−	0.759601i	$-0.725394\pi$
$97$	−1.18719e6			−1.30078			−0.650390	+	0.759601i	$0.725394\pi$
$98$		−	204249.i		−	0.217011i
$99$	−41547.3	−	320753.i	−0.0428191	−	0.330572i
$100$	250605.			0.250605
$101$			347062.i			0.336855i	0.985714	+	0.168427i	$0.0538689\pi$
$101$			347062.i			0.336855i	−0.985714	+	0.168427i	$0.946131\pi$
$102$	−215466.			−0.203038
$103$	1.81728e6			1.66307			0.831534	−	0.555473i	$-0.187463\pi$
$103$	1.81728e6			1.66307			0.831534	+	0.555473i	$0.187463\pi$
$104$	1.44270e6			1.28255
$105$		−	927939.i		−	0.801589i
$106$		−	329231.i		−	0.276428i
$107$		−	2.05551e6i		−	1.67791i	−0.544202	−	0.838955i	$-0.683167\pi$
$107$		−	2.05551e6i		−	1.67791i	0.544202	−	0.838955i	$-0.316833\pi$
$108$	−187497.			−0.148842
$109$			857964.i			0.662505i	0.943542	+	0.331253i	$0.107471\pi$
$109$			857964.i			0.662505i	−0.943542	+	0.331253i	$0.892529\pi$
$110$	−723004.	+	93650.9i	−0.543203	+	0.0703613i
$111$	−961877.			−0.703316
$112$		−	629857.i		−	0.448319i
$113$	597788.			0.414297			0.207148	−	0.978310i	$-0.433582\pi$
$113$	597788.			0.414297			0.207148	+	0.978310i	$0.433582\pi$
$114$	203114.			0.137096
$115$	1.62315e6			1.06725
$116$			1.30003e6i			0.832873i
$117$		−	811107.i		−	0.506431i
$118$		−	845322.i		−	0.514489i
$119$	−1.50216e6			−0.891406
$120$			969095.i			0.560819i
$121$	−1.71310e6	+	451369.i	−0.966997	+	0.254786i
$122$	750005.			0.413033
$123$			718135.i			0.385914i
$124$	−2.33273e6			−1.22349
$125$	1.51917e6			0.777816
$126$	382984.			0.191456
$127$			900156.i			0.439447i	0.975562	+	0.219724i	$0.0705155\pi$
$127$			900156.i			0.439447i	−0.975562	+	0.219724i	$0.929484\pi$
$128$			2.02700e6i			0.966550i
$129$			1.54459e6i			0.719523i
$130$	−1.82830e6			−0.832180
$131$		−	2.74570e6i		−	1.22135i	−0.791882	−	0.610674i	$-0.790899\pi$
$131$		−	2.74570e6i		−	1.22135i	0.791882	−	0.610674i	$-0.209101\pi$
$132$	131925.	+	1.01848e6i	0.0573593	+	0.442825i
$133$	1.41605e6			0.601898
$134$			1.60363e6i			0.666483i
$135$	544839.			0.221446
$136$	1.56878e6			0.623658
$137$	459151.			0.178564			0.0892820	−	0.996006i	$-0.471543\pi$
$137$	459151.			0.178564			0.0892820	+	0.996006i	$0.471543\pi$
$138$			669917.i			0.254908i
$139$		−	2.46768e6i		−	0.918848i	−0.888217	−	0.459424i	$-0.848056\pi$
$139$		−	2.46768e6i		−	0.918848i	0.888217	−	0.459424i	$-0.151944\pi$
$140$			2.94647e6i			1.07379i
$141$	−1.79598e6			−0.640686
$142$			890613.i			0.311045i
$143$	−4.40592e6	+	570700.i	−1.50671	+	0.195164i
$144$	369820.			0.123852
$145$		−	3.77768e6i		−	1.23914i
$146$	−2.11410e6			−0.679309
$147$	836078.			0.263205
$148$	3.05423e6			0.942144
$149$			1.71071e6i			0.517153i	0.965991	+	0.258576i	$0.0832533\pi$
$149$			1.71071e6i			0.517153i	−0.965991	+	0.258576i	$0.916747\pi$
$150$		−	300555.i		−	0.0890533i
$151$			4.09182e6i			1.18846i	0.804294	+	0.594231i	$0.202544\pi$
$151$			4.09182e6i			1.18846i	−0.804294	+	0.594231i	$0.797456\pi$
$152$	−1.47885e6			−0.421109
$153$		−	881993.i		−	0.246258i
$154$	−269470.	−	2.08036e6i	−0.0737817	−	0.569610i
$155$	6.77856e6			1.82030
$156$			2.57550e6i			0.678402i
$157$	3.24284e6			0.837965			0.418983	−	0.907994i	$-0.362387\pi$
$157$	3.24284e6			0.837965			0.418983	+	0.907994i	$0.362387\pi$
$158$	−913655.			−0.231639
$159$	1.34768e6			0.335270
$160$		−	4.81232e6i		−	1.17488i
$161$			4.67045e6i			1.11913i
$162$			224869.i			0.0528913i
$163$	−2.55609e6			−0.590220			−0.295110	−	0.955463i	$-0.595356\pi$
$163$	−2.55609e6			−0.590220			−0.295110	+	0.955463i	$0.595356\pi$
$164$		−	2.28028e6i		−	0.516961i
$165$	−383353.	−	2.95956e6i	−0.0853388	−	0.658833i
$166$	2.75867e6			0.603080
$167$		−	3.70245e6i		−	0.794949i	−0.917613	−	0.397475i	$-0.869887\pi$
$167$		−	3.70245e6i		−	0.794949i	0.917613	−	0.397475i	$-0.130113\pi$
$168$	−2.78846e6			−0.588081
$169$	−6.31468e6			−1.30825
$170$	−1.98808e6			−0.404657
$171$			831432.i			0.166279i
$172$		−	4.90452e6i		−	0.963854i
$173$		−	861133.i		−	0.166315i	−0.996536	−	0.0831576i	$-0.973500\pi$
$173$		−	861133.i		−	0.166315i	0.996536	−	0.0831576i	$-0.0265005\pi$
$174$	1.55915e6			0.295964
$175$		−	2.09537e6i		−	0.390974i
$176$	−260208.	−	2.00886e6i	−0.0477290	−	0.368477i
$177$	3.46026e6			0.624006
$178$			1.47890e6i			0.262228i
$179$	948442.			0.165368			0.0826840	−	0.996576i	$-0.473651\pi$
$179$	948442.			0.165368			0.0826840	+	0.996576i	$0.473651\pi$
$180$	−1.73002e6			−0.296643
$181$	6.45363e6			1.08835			0.544175	−	0.838972i	$-0.316843\pi$
$181$	6.45363e6			1.08835			0.544175	+	0.838972i	$0.316843\pi$
$182$		−	5.26073e6i		−	0.872634i
$183$			3.07009e6i			0.500953i
$184$		−	4.87759e6i		−	0.782982i
$185$	−8.87514e6			−1.40172
$186$			2.79768e6i			0.434770i
$187$	−4.79097e6	+	620576.i	−0.732654	+	0.0949009i
$188$	5.70276e6			0.858245
$189$			1.56771e6i			0.232210i
$190$	1.87411e6			0.273234
$191$	2.06663e6			0.296594			0.148297	−	0.988943i	$-0.452621\pi$
$191$	2.06663e6			0.296594			0.148297	+	0.988943i	$0.452621\pi$
$192$	467834.			0.0660979
$193$			6.46744e6i			0.899623i	0.893123	+	0.449812i	$0.148509\pi$
$193$			6.46744e6i			0.899623i	−0.893123	+	0.449812i	$0.851491\pi$
$194$		−	4.52101e6i		−	0.619200i
$195$		−	7.48400e6i		−	1.00932i
$196$	−2.65479e6			−0.352583
$197$			4.12967e6i			0.540152i	0.962839	+	0.270076i	$0.0870489\pi$
$197$			4.12967e6i			0.540152i	−0.962839	+	0.270076i	$0.912951\pi$
$198$	1.22148e6	−	158219.i	0.157359	−	0.0203828i
$199$	−2.88027e6			−0.365489			−0.182744	−	0.983160i	$-0.558498\pi$
$199$	−2.88027e6			−0.365489			−0.182744	+	0.983160i	$0.558498\pi$
$200$			2.18831e6i			0.273538i
$201$	−6.56432e6			−0.808354
$202$	−1.32167e6			−0.160350
$203$	1.08699e7			1.29938
$204$			2.80058e6i			0.329881i
$205$			6.62616e6i			0.769131i
$206$			6.92052e6i			0.791657i
$207$	−2.74225e6			−0.309169
$208$		−	5.07991e6i		−	0.564502i
$209$	4.51633e6	−	585002.i	0.494705	−	0.0640794i
$210$	3.53375e6			0.381574
$211$			5.93306e6i			0.631584i	0.948828	+	0.315792i	$0.102270\pi$
$211$			5.93306e6i			0.631584i	−0.948828	+	0.315792i	$0.897730\pi$
$212$	−4.27927e6			−0.449119
$213$	−3.64565e6			−0.377256
$214$	7.82774e6			0.798721
$215$			1.42518e7i			1.43402i
$216$		−	1.63725e6i		−	0.162462i
$217$			1.95046e7i			1.90878i
$218$	−3.26728e6			−0.315367
$219$		−	8.65391e6i		−	0.823910i
$220$	1.21725e6	+	9.39744e6i	0.114318	+	0.882555i
$221$	−1.21152e7			−1.12242
$222$		−	3.66299e6i		−	0.334794i
$223$	−529880.			−0.0477819			−0.0238909	−	0.999715i	$-0.507605\pi$
$223$	−529880.			−0.0477819			−0.0238909	+	0.999715i	$0.507605\pi$
$224$	1.38469e7			1.23200
$225$	1.23030e6			0.108010
$226$			2.27648e6i			0.197214i
$227$		−	1.75869e7i		−	1.50353i	−0.659431	−	0.751765i	$-0.729203\pi$
$227$		−	1.75869e7i		−	1.50353i	0.659431	−	0.751765i	$-0.270797\pi$
$228$		−	2.64003e6i		−	0.222743i
$229$	3.74744e6			0.312053			0.156026	−	0.987753i	$-0.450132\pi$
$229$	3.74744e6			0.312053			0.156026	+	0.987753i	$0.450132\pi$
$230$			6.18126e6i			0.508034i
$231$	8.51581e6	−	1.10306e6i	0.690860	−	0.0894873i
$232$	−1.13520e7			−0.909091
$233$			5.84195e6i			0.461838i	0.972973	+	0.230919i	$0.0741733\pi$
$233$			5.84195e6i			0.461838i	−0.972973	+	0.230919i	$0.925827\pi$
$234$	3.08884e6			0.241072
$235$	−1.65713e7			−1.27689
$236$	−1.09873e7			−0.835902
$237$		−	3.73997e6i		−	0.280946i
$238$		−	5.72049e6i		−	0.424329i
$239$		−	2.58601e7i		−	1.89425i	−0.320867	−	0.947124i	$-0.603974\pi$
$239$		−	2.58601e7i		−	1.89425i	0.320867	−	0.947124i	$-0.396026\pi$
$240$	3.41229e6			0.246838
$241$			1.41287e7i			1.00937i	0.863302	+	0.504687i	$0.168392\pi$
$241$			1.41287e7i			1.00937i	−0.863302	+	0.504687i	$0.831608\pi$
$242$	−1.71889e6	−	6.52376e6i	−0.121284	−	0.460312i
$243$	−920483.			−0.0641500
$244$		−	9.74840e6i		−	0.671064i
$245$	7.71440e6			0.524571
$246$	−2.73478e6			−0.183704
$247$	1.14207e7			0.757881
$248$		−	2.03696e7i		−	1.33545i
$249$			1.12924e7i			0.731455i
$250$			5.78527e6i			0.370257i
$251$	−1.01697e7			−0.643111			−0.321556	−	0.946891i	$-0.604206\pi$
$251$	−1.01697e7			−0.643111			−0.321556	+	0.946891i	$0.604206\pi$
$252$		−	4.97794e6i		−	0.311063i
$253$	1.92947e6	+	1.48959e7i	0.119145	+	0.919823i
$254$	−3.42795e6			−0.209186
$255$		−	8.13805e6i		−	0.490795i
$256$	−9.63992e6			−0.574584
$257$	2.60279e7			1.53335			0.766673	−	0.642038i	$-0.221911\pi$
$257$	2.60279e7			1.53335			0.766673	+	0.642038i	$0.221911\pi$
$258$	−5.88208e6			−0.342509
$259$		−	2.55372e7i		−	1.46986i
$260$			2.37638e7i			1.35206i
$261$			6.38224e6i			0.358965i
$262$	1.04561e7			0.581388
$263$		−	7.30787e6i		−	0.401720i	−0.979620	−	0.200860i	$-0.935626\pi$
$263$		−	7.30787e6i		−	0.401720i	0.979620	−	0.200860i	$-0.0643736\pi$
$264$	−8.89349e6	+	1.15198e6i	−0.483349	+	0.0626083i
$265$	1.24349e7			0.668197
$266$			5.39256e6i			0.286517i
$267$	−6.05377e6			−0.318048
$268$	2.08436e7			1.08285
$269$	−3.32174e7			−1.70651			−0.853255	−	0.521494i	$-0.825375\pi$
$269$	−3.32174e7			−1.70651			−0.853255	+	0.521494i	$0.825375\pi$
$270$			2.07484e6i			0.105413i
$271$			8.36847e6i			0.420473i	0.977651	+	0.210237i	$0.0674234\pi$
$271$			8.36847e6i			0.420473i	−0.977651	+	0.210237i	$0.932577\pi$
$272$		−	5.52386e6i		−	0.274496i
$273$	2.15344e7			1.05839
$274$			1.74853e6i			0.0850004i
$275$	−865646.	−	6.68296e6i	−0.0416239	−	0.321344i
$276$	8.70743e6			0.414155
$277$		−	4.04156e7i		−	1.90156i	−0.309869	−	0.950779i	$-0.600285\pi$
$277$		−	4.04156e7i		−	1.90156i	0.309869	−	0.950779i	$-0.399715\pi$
$278$	9.39734e6			0.437392
$279$	−1.14521e7			−0.527317
$280$	−2.57289e7			−1.17205
$281$		−	254744.i		−	0.0114812i	−0.999984	−	0.00574058i	$-0.998173\pi$
$281$		−	254744.i		−	0.0114812i	0.999984	−	0.00574058i	$-0.00182729\pi$
$282$		−	6.83942e6i		−	0.304980i
$283$		−	3.09753e7i		−	1.36664i	−0.730117	−	0.683322i	$-0.760534\pi$
$283$		−	3.09753e7i		−	1.36664i	0.730117	−	0.683322i	$-0.239466\pi$
$284$	1.15760e7			0.505362
$285$			7.67154e6i			0.331396i
$286$	−2.17333e6	−	1.67785e7i	−0.0929024	−	0.717225i
$287$	−1.90661e7			−0.806520
$288$			8.13022e6i			0.340349i
$289$	1.09636e7			0.454212
$290$	1.43861e7			0.589859
$291$	1.85064e7			0.751006
$292$			2.74786e7i			1.10369i
$293$			4.36299e6i			0.173453i	0.996232	+	0.0867264i	$0.0276406\pi$
$293$			4.36299e6i			0.173453i	−0.996232	+	0.0867264i	$0.972359\pi$
$294$			3.18393e6i			0.125292i
$295$	3.19274e7			1.24365
$296$			2.66698e7i			1.02836i
$297$	647658.	+	5.00005e6i	0.0247216	+	0.190856i
$298$	−6.51470e6			−0.246176
$299$			3.76680e7i			1.40916i
$300$	−3.90655e6			−0.144687
$301$	−4.10080e7			−1.50373
$302$	−1.55824e7			−0.565734
$303$		−	5.41016e6i		−	0.194483i
$304$			5.20720e6i			0.185346i
$305$			2.83274e7i			0.998405i
$306$	3.35878e6			0.117224
$307$		−	983200.i		−	0.0339803i	−0.999856	−	0.0169901i	$-0.994592\pi$
$307$		−	983200.i		−	0.0339803i	0.999856	−	0.0169901i	$-0.00540839\pi$
$308$	−2.70401e7	+	3.50252e6i	−0.925457	+	0.119875i
$309$	−2.83286e7			−0.960173
$310$			2.58139e7i			0.866501i
$311$	3.83821e7			1.27599			0.637996	−	0.770040i	$-0.279764\pi$
$311$	3.83821e7			1.27599			0.637996	+	0.770040i	$0.279764\pi$
$312$	−2.24895e7			−0.740483
$313$	−4.92166e7			−1.60501			−0.802507	−	0.596643i	$-0.796501\pi$
$313$	−4.92166e7			−1.60501			−0.802507	+	0.596643i	$0.796501\pi$
$314$			1.23493e7i			0.398890i
$315$			1.44651e7i			0.462798i
$316$			1.18755e7i			0.376348i
$317$	2.40649e7			0.755451			0.377726	−	0.925918i	$-0.376706\pi$
$317$	2.40649e7			0.755451			0.377726	+	0.925918i	$0.376706\pi$
$318$			5.13220e6i			0.159596i
$319$	3.46682e7	−	4.49059e6i	1.06797	−	0.138335i
$320$	4.31665e6			0.131734
$321$			3.20422e7i			0.968741i
$322$	−1.77859e7			−0.532731
$323$	1.24188e7			0.368529
$324$	2.92280e6			0.0859337
$325$		−	1.68996e7i		−	0.492295i
$326$		−	9.73405e6i		−	0.280958i
$327$		−	1.33743e7i		−	0.382498i
$328$	1.99117e7			0.564269
$329$		−	4.76823e7i		−	1.33896i
$330$	1.12705e7	−	1.45987e6i	0.313619	−	0.0406231i
$331$	2.41539e7			0.666043			0.333022	−	0.942919i	$-0.391932\pi$
$331$	2.41539e7			0.666043			0.333022	+	0.942919i	$0.391932\pi$
$332$		−	3.58565e7i		−	0.979838i
$333$	1.49942e7			0.406060
$334$	1.40996e7			0.378413
$335$	−6.05683e7			−1.61106
$336$			9.81849e6i			0.258837i
$337$		−	6.07545e7i		−	1.58741i	−0.608303	−	0.793705i	$-0.708150\pi$
$337$		−	6.07545e7i		−	1.58741i	0.608303	−	0.793705i	$-0.291850\pi$
$338$		−	2.40474e7i		−	0.622756i
$339$	−9.31859e6			−0.239194
$340$			2.58407e7i			0.657456i
$341$	8.05777e6	+	6.22076e7i	0.203213	+	1.56885i
$342$	−3.16624e6			−0.0791526
$343$		−	2.64933e7i		−	0.656529i
$344$	4.28267e7			1.05206
$345$	−2.53025e7			−0.616177
$346$	3.27934e6			0.0791697
$347$		−	6.00467e6i		−	0.143715i	−0.997415	−	0.0718573i	$-0.977107\pi$
$347$		−	6.00467e6i		−	0.143715i	0.997415	−	0.0718573i	$-0.0228926\pi$
$348$		−	2.02654e7i		−	0.480859i
$349$		−	2.38935e7i		−	0.562086i	−0.959695	−	0.281043i	$-0.909320\pi$
$349$		−	2.38935e7i		−	0.562086i	0.959695	−	0.281043i	$-0.0906804\pi$
$350$	7.97955e6			0.186112
$351$			1.26439e7i			0.292388i
$352$	4.41632e7	−	5.72048e6i	1.01259	−	0.131161i
$353$	−3.49936e7			−0.795544			−0.397772	−	0.917484i	$-0.630217\pi$
$353$	−3.49936e7			−0.795544			−0.397772	+	0.917484i	$0.630217\pi$
$354$			1.31773e7i			0.297040i
$355$	−3.36380e7			−0.751875
$356$	1.92225e7			0.426048
$357$	2.34164e7			0.514653
$358$			3.61183e6i			0.0787188i
$359$			4.37813e7i			0.946249i	0.880996	+	0.473124i	$0.156874\pi$
$359$			4.37813e7i			0.946249i	−0.880996	+	0.473124i	$0.843126\pi$
$360$		−	1.51067e7i		−	0.323789i
$361$	3.53390e7			0.751160
$362$			2.45766e7i			0.518078i
$363$	2.67045e7	−	7.03614e6i	0.558296	−	0.147101i
$364$	−6.83778e7			−1.41779
$365$		−	7.98487e7i		−	1.64206i
$366$	−1.16914e7			−0.238465
$367$	−4.07533e7			−0.824451			−0.412226	−	0.911082i	$-0.635248\pi$
$367$	−4.07533e7			−0.824451			−0.412226	+	0.911082i	$0.635248\pi$
$368$	−1.71745e7			−0.344621
$369$		−	1.11946e7i		−	0.222808i
$370$		−	3.37981e7i		−	0.667247i
$371$			3.57801e7i			0.700679i
$372$	3.63637e7			0.706381
$373$		−	4.63812e7i		−	0.893748i	−0.894597	−	0.446874i	$-0.852537\pi$
$373$		−	4.63812e7i		−	0.893748i	0.894597	−	0.446874i	$-0.147463\pi$
$374$	−2.36326e6	−	1.82449e7i	−0.0451749	−	0.348759i
$375$	−2.36815e7			−0.449072
$376$			4.97970e7i			0.936785i
$377$	8.76675e7			1.63612
$378$	−5.97013e6			−0.110537
$379$	1.47151e7			0.270299			0.135150	−	0.990825i	$-0.456848\pi$
$379$	1.47151e7			0.270299			0.135150	+	0.990825i	$0.456848\pi$
$380$		−	2.43593e7i		−	0.443930i
$381$		−	1.40320e7i		−	0.253715i
$382$			7.87008e6i			0.141185i
$383$	−8.90918e7			−1.58577			−0.792887	−	0.609369i	$-0.791423\pi$
$383$	−8.90918e7			−1.58577			−0.792887	+	0.609369i	$0.791423\pi$
$384$		−	3.15978e7i		−	0.558038i
$385$	7.85745e7	−	1.01778e7i	1.37689	−	0.178349i
$386$	−2.46291e7			−0.428240
$387$		−	2.40778e7i		−	0.415417i
$388$	−5.87631e7			−1.00603
$389$	2.11827e7			0.359860			0.179930	−	0.983679i	$-0.442413\pi$
$389$	2.11827e7			0.359860			0.179930	+	0.983679i	$0.442413\pi$
$390$	2.85004e7			0.480459
$391$			4.09600e7i			0.685219i
$392$		−	2.31818e7i		−	0.384848i
$393$			4.28012e7i			0.705145i
$394$	−1.57265e7			−0.257124
$395$		−	3.45083e7i		−	0.559929i
$396$	−2.05650e6	−	1.58766e7i	−0.0331164	−	0.255665i
$397$	5.54702e6			0.0886520			0.0443260	−	0.999017i	$-0.485886\pi$
$397$	5.54702e6			0.0886520			0.0443260	+	0.999017i	$0.485886\pi$
$398$		−	1.09686e7i		−	0.173981i
$399$	−2.20740e7			−0.347506
$400$	7.70527e6			0.120395
$401$	−1.05269e8			−1.63256			−0.816279	−	0.577658i	$-0.803967\pi$
$401$	−1.05269e8			−1.63256			−0.816279	+	0.577658i	$0.803967\pi$
$402$		−	2.49981e7i		−	0.384794i
$403$			1.57308e8i			2.40345i
$404$			1.71788e7i			0.260525i
$405$	−8.49320e6			−0.127852
$406$			4.13944e7i			0.618533i
$407$	−1.05500e7	−	8.14481e7i	−0.156484	−	1.20809i
$408$	−2.44549e7			−0.360069
$409$			8.16321e7i			1.19314i	0.802561	+	0.596569i	$0.203470\pi$
$409$			8.16321e7i			1.19314i	−0.802561	+	0.596569i	$0.796530\pi$
$410$	−2.52336e7			−0.366123
$411$	−7.15746e6			−0.103094
$412$	8.99514e7			1.28622
$413$			9.18678e7i			1.30411i
$414$		−	1.04430e7i		−	0.147171i
$415$			1.04194e8i			1.45780i
$416$	1.11678e8			1.55127
$417$			3.84673e7i			0.530497i
$418$	2.22779e6	+	1.71990e7i	0.0305032	+	0.235491i
$419$	9.99417e7			1.35864			0.679320	−	0.733842i	$-0.262275\pi$
$419$	9.99417e7			1.35864			0.679320	+	0.733842i	$0.262275\pi$
$420$		−	4.59310e7i		−	0.619951i
$421$	4.88968e7			0.655291			0.327646	−	0.944801i	$-0.393745\pi$
$421$	4.88968e7			0.655291			0.327646	+	0.944801i	$0.393745\pi$
$422$	−2.25941e7			−0.300648
$423$	2.79966e7			0.369900
$424$		−	3.73670e7i		−	0.490219i
$425$		−	1.83765e7i		−	0.239384i
$426$		−	1.38833e7i		−	0.179582i
$427$	−8.15089e7			−1.04694
$428$		−	1.01743e8i		−	1.29770i
$429$	6.86815e7	−	8.89634e6i	0.869897	−	0.112678i
$430$	−5.42733e7			−0.682623
$431$			1.15659e8i			1.44460i	0.691581	+	0.722299i	$0.256914\pi$
$431$			1.15659e8i			1.44460i	−0.691581	+	0.722299i	$0.743086\pi$
$432$	−5.76492e6			−0.0715059
$433$	−7.32830e7			−0.902691			−0.451346	−	0.892349i	$-0.649056\pi$
$433$	−7.32830e7			−0.902691			−0.451346	+	0.892349i	$0.649056\pi$
$434$	−7.42768e7			−0.908623
$435$			5.88883e7i			0.715420i
$436$			4.24673e7i			0.512384i
$437$		−	3.86119e7i		−	0.462676i
$438$	3.29556e7			0.392199
$439$		−	1.56264e7i		−	0.184699i	−0.995727	−	0.0923497i	$-0.970562\pi$
$439$		−	1.56264e7i		−	0.184699i	0.995727	−	0.0923497i	$-0.0294378\pi$
$440$	−8.20593e7	+	1.06292e7i	−0.963319	+	0.124779i
$441$	−1.30332e7			−0.151962
$442$		−	4.61368e7i		−	0.534294i
$443$	1.11245e8			1.27958			0.639790	−	0.768550i	$-0.279021\pi$
$443$	1.11245e8			1.27958			0.639790	+	0.768550i	$0.279021\pi$
$444$	−4.76108e7			−0.543947
$445$	−5.58575e7			−0.633872
$446$		−	2.01788e6i		−	0.0227452i
$447$		−	2.66674e7i		−	0.298578i
$448$			1.24207e7i			0.138138i
$449$	−2.90875e7			−0.321341			−0.160671	−	0.987008i	$-0.551366\pi$
$449$	−2.90875e7			−0.321341			−0.160671	+	0.987008i	$0.551366\pi$
$450$			4.68519e6i			0.0514150i
$451$	−6.08090e7	+	7.87662e6i	−0.662885	+	0.0858638i
$452$	2.95892e7			0.320419
$453$		−	6.37851e7i		−	0.686159i
$454$	6.69741e7			0.715713
$455$	1.98696e8			2.10938
$456$	2.30530e7			0.243127
$457$		−	3.84390e7i		−	0.402739i	−0.979515	−	0.201369i	$-0.935461\pi$
$457$		−	3.84390e7i		−	0.402739i	0.979515	−	0.201369i	$-0.0645391\pi$
$458$			1.42709e7i			0.148544i
$459$			1.37489e7i			0.142177i
$460$	8.03426e7			0.825415
$461$			1.47266e8i			1.50315i	0.659650	+	0.751573i	$0.270704\pi$
$461$			1.47266e8i			1.50315i	−0.659650	+	0.751573i	$0.729296\pi$
$462$	4.20063e6	+	3.24297e7i	0.0425979	+	0.328864i
$463$	4.76859e7			0.480449			0.240225	−	0.970717i	$-0.422779\pi$
$463$	4.76859e7			0.480449			0.240225	+	0.970717i	$0.422779\pi$
$464$			3.99715e7i			0.400126i
$465$	−1.05667e8			−1.05095
$466$	−2.22472e7			−0.219845
$467$	−1.15589e8			−1.13493			−0.567463	−	0.823399i	$-0.692075\pi$
$467$	−1.15589e8			−1.13493			−0.567463	+	0.823399i	$0.692075\pi$
$468$		−	4.01480e7i		−	0.391675i
$469$		−	1.74279e8i		−	1.68937i
$470$		−	6.31066e7i		−	0.607829i
$471$	−5.05508e7			−0.483799
$472$		−	9.59422e7i		−	0.912397i
$473$	−1.30790e8	+	1.69413e7i	−1.23593	+	0.160090i
$474$	1.42425e7			0.133737
$475$			1.73230e7i			0.161638i
$476$	−7.43537e7			−0.689416
$477$	−2.10082e7			−0.193568
$478$	9.84799e7			0.901704
$479$		−	1.03379e8i		−	0.940643i	−0.882495	−	0.470321i	$-0.844138\pi$
$479$		−	1.03379e8i		−	0.940643i	0.882495	−	0.470321i	$-0.155862\pi$
$480$			7.50167e7i			0.678319i
$481$		−	2.05962e8i		−	1.85077i
$482$	−5.38047e7			−0.480484
$483$		−	7.28051e7i		−	0.646131i
$484$	−8.47944e7	+	2.23418e7i	−0.747879	+	0.197052i
$485$	1.70757e8			1.49676
$486$		−	3.50536e6i		−	0.0305368i
$487$	−2.42743e7			−0.210165			−0.105082	−	0.994464i	$-0.533511\pi$
$487$	−2.42743e7			−0.210165			−0.105082	+	0.994464i	$0.533511\pi$
$488$	8.51239e7			0.732474
$489$	3.98456e7			0.340764
$490$			2.93778e7i			0.249707i
$491$		−	1.75638e8i		−	1.48379i	−0.670515	−	0.741896i	$-0.733927\pi$
$491$		−	1.75638e8i		−	1.48379i	0.670515	−	0.741896i	$-0.266073\pi$
$492$			3.55461e7i			0.298467i
$493$	9.53291e7			0.795582
$494$			4.34920e7i			0.360768i
$495$	5.97588e6	+	4.61349e7i	0.0492704	+	0.380377i
$496$	−7.17237e7			−0.587784
$497$		−	9.67898e7i		−	0.788425i
$498$	−4.30034e7			−0.348189
$499$	−6.15096e7			−0.495041			−0.247521	−	0.968883i	$-0.579616\pi$
$499$	−6.15096e7			−0.495041			−0.247521	+	0.968883i	$0.579616\pi$
$500$	7.51957e7			0.601565
$501$			5.77154e7i			0.458964i
$502$		−	3.87279e7i		−	0.306135i
$503$			8.55183e7i			0.671978i	0.941866	+	0.335989i	$0.109070\pi$
$503$			8.55183e7i			0.671978i	−0.941866	+	0.335989i	$0.890930\pi$
$504$	4.34679e7			0.339529
$505$		−	4.99190e7i		−	0.387607i
$506$	−5.67261e7	+	7.34775e6i	−0.437856	+	0.0567157i
$507$	9.84362e7			0.755320
$508$			4.45557e7i			0.339870i
$509$	7.08572e7			0.537317			0.268659	−	0.963235i	$-0.413420\pi$
$509$	7.08572e7			0.537317			0.268659	+	0.963235i	$0.413420\pi$
$510$	3.09911e7			0.233629
$511$	2.29756e8			1.72188
$512$			9.30177e7i			0.693036i
$513$		−	1.29607e7i		−	0.0960015i
$514$			9.91189e7i			0.729906i
$515$	−2.61385e8			−1.91363
$516$			7.64539e7i			0.556482i
$517$	−1.96986e7	−	1.52077e8i	−0.142549	−	1.10051i
$518$	9.72503e7			0.699683
$519$			1.34237e7i			0.0960221i
$520$	−2.07508e8			−1.47579
$521$	7.11136e7			0.502851			0.251426	−	0.967877i	$-0.419101\pi$
$521$	7.11136e7			0.502851			0.251426	+	0.967877i	$0.419101\pi$
$522$	−2.43047e7			−0.170875
$523$			1.45854e8i			1.01956i	0.860304	+	0.509781i	$0.170274\pi$
$523$			1.45854e8i			1.01956i	−0.860304	+	0.509781i	$0.829726\pi$
$524$		−	1.35906e8i		−	0.944594i
$525$			3.26636e7i			0.225729i
$526$	2.78296e7			0.191227
$527$			1.71056e8i			1.16871i
$528$	4.05624e6	+	3.13150e7i	0.0275564	+	0.212741i
$529$	−2.06849e7			−0.139729
$530$			4.73542e7i			0.318076i
$531$	−5.39401e7			−0.360270
$532$	7.00913e7			0.465510
$533$	−1.53771e8			−1.01553
$534$		−	2.30538e7i		−	0.151398i
$535$			2.95650e8i			1.93071i
$536$			1.82008e8i			1.18194i
$537$	−1.47847e7			−0.0954753
$538$		−	1.26498e8i		−	0.812336i
$539$	9.17023e6	+	7.07960e7i	0.0585617	+	0.452108i
$540$	2.69683e7			0.171267
$541$		−	9.25860e7i		−	0.584727i	−0.956307	−	0.292364i	$-0.905558\pi$
$541$		−	9.25860e7i		−	0.584727i	0.956307	−	0.292364i	$-0.0944418\pi$
$542$	−3.18686e7			−0.200154
$543$	−1.00602e8			−0.628359
$544$	1.21438e8			0.754324
$545$		−	1.23404e8i		−	0.762322i
$546$			8.20067e7i			0.503815i
$547$		−	2.41415e8i		−	1.47503i	−0.675329	−	0.737517i	$-0.735998\pi$
$547$		−	2.41415e8i		−	1.47503i	0.675329	−	0.737517i	$-0.264002\pi$
$548$	2.27270e7			0.138102
$549$		−	4.78579e7i		−	0.289226i
$550$	2.54499e7	−	3.29653e6i	0.152967	−	0.0198139i
$551$	−8.98643e7			−0.537196
$552$			7.60341e7i			0.452055i
$553$	9.92940e7			0.587148
$554$	1.53910e8			0.905183
$555$	1.38350e8			0.809281
$556$		−	1.22145e8i		−	0.710640i
$557$			3.26608e8i			1.89000i	0.327078	+	0.944998i	$0.393936\pi$
$557$			3.26608e8i			1.89000i	−0.327078	+	0.944998i	$0.606064\pi$
$558$		−	4.36116e7i		−	0.251015i
$559$	−3.30737e8			−1.89342
$560$			9.05942e7i			0.515865i
$561$	7.46839e7	−	9.67383e6i	0.422998	−	0.0547911i
$562$	970111.			0.00546528
$563$		−	1.53779e8i		−	0.861731i	−0.902416	−	0.430865i	$-0.858208\pi$
$563$		−	1.53779e8i		−	0.861731i	0.902416	−	0.430865i	$-0.141792\pi$
$564$	−8.88972e7			−0.495508
$565$	−8.59817e7			−0.476717
$566$	1.17959e8			0.650553
$567$		−	2.44383e7i		−	0.134067i
$568$			1.01083e8i			0.551609i
$569$			2.70551e7i			0.146863i	0.997300	+	0.0734314i	$0.0233950\pi$
$569$			2.70551e7i			0.146863i	−0.997300	+	0.0734314i	$0.976605\pi$
$570$	−2.92146e7			−0.157752
$571$			1.96339e8i			1.05463i	0.849671	+	0.527314i	$0.176801\pi$
$571$			1.96339e8i			1.05463i	−0.849671	+	0.527314i	$0.823199\pi$
$572$	−2.18083e8	+	2.82484e7i	−1.16529	+	0.150941i
$573$	−3.22155e7			−0.171239
$574$		−	7.26069e7i		−	0.383921i
$575$	−5.71354e7			−0.300539
$576$	−7.29281e6			−0.0381617
$577$	2.92653e8			1.52344			0.761721	−	0.647906i	$-0.224355\pi$
$577$	2.92653e8			1.52344			0.761721	+	0.647906i	$0.224355\pi$
$578$			4.17512e7i			0.216215i
$579$		−	1.00817e8i		−	0.519398i
$580$		−	1.86987e8i		−	0.958357i
$581$	−2.99806e8			−1.52866
$582$			7.04756e7i			0.357495i
$583$	1.47815e7	+	1.14116e8i	0.0745958	+	0.575894i
$584$	−2.39946e8			−1.20469
$585$			1.16664e8i			0.582732i
$586$	−1.66150e7			−0.0825673
$587$	1.54222e8			0.762484			0.381242	−	0.924475i	$-0.375496\pi$
$587$	1.54222e8			0.762484			0.381242	+	0.924475i	$0.375496\pi$
$588$	4.13840e7			0.203564
$589$		−	1.61250e8i		−	0.789138i
$590$			1.21585e8i			0.592005i
$591$		−	6.43751e7i		−	0.311857i
$592$	9.39075e7			0.452621
$593$		−	3.01658e8i		−	1.44661i	−0.690530	−	0.723304i	$-0.742623\pi$
$593$		−	3.01658e8i		−	1.44661i	0.690530	−	0.723304i	$-0.257377\pi$
$594$	−1.90411e7	+	2.46640e6i	−0.0908515	+	0.0117680i
$595$	2.16060e8			1.02571
$596$			8.46766e7i			0.399967i
$597$	4.48990e7			0.211015
$598$	−1.43446e8			−0.670789
$599$	4.00049e8			1.86137			0.930685	−	0.365821i	$-0.119212\pi$
$599$	4.00049e8			1.86137			0.930685	+	0.365821i	$0.119212\pi$
$600$		−	3.41123e7i		−	0.157927i
$601$		−	1.91805e8i		−	0.883559i	−0.897124	−	0.441779i	$-0.854347\pi$
$601$		−	1.91805e8i		−	0.883559i	0.897124	−	0.441779i	$-0.145653\pi$
$602$		−	1.56166e8i		−	0.715807i
$603$	1.02328e8			0.466703
$604$			2.02536e8i			0.919161i
$605$	2.46400e8	−	6.49218e7i	1.11269	−	0.293173i
$606$	2.06028e7			0.0925783
$607$			3.65271e8i			1.63324i	0.577177	+	0.816619i	$0.304154\pi$
$607$			3.65271e8i			1.63324i	−0.577177	+	0.816619i	$0.695846\pi$
$608$	−1.14476e8			−0.509337
$609$	−1.69445e8			−0.750198
$610$	−1.07876e8			−0.475262
$611$		−	3.84566e8i		−	1.68596i
$612$		−	4.36567e7i		−	0.190457i
$613$			1.21047e8i			0.525501i	0.964864	+	0.262750i	$0.0846296\pi$
$613$			1.21047e8i			0.525501i	−0.964864	+	0.262750i	$0.915370\pi$
$614$	3.74420e6			0.0161754
$615$		−	1.03292e8i		−	0.444058i
$616$	−3.05843e7	−	2.36117e8i	−0.130845	−	1.01015i
$617$	1.98674e8			0.845833			0.422917	−	0.906169i	$-0.361006\pi$
$617$	1.98674e8			0.845833			0.422917	+	0.906169i	$0.361006\pi$
$618$		−	1.07880e8i		−	0.457063i
$619$	−2.11047e8			−0.889832			−0.444916	−	0.895572i	$-0.646767\pi$
$619$	−2.11047e8			−0.889832			−0.444916	+	0.895572i	$0.646767\pi$
$620$	3.35524e8			1.40782
$621$	4.27475e7			0.178499
$622$			1.46166e8i			0.607400i
$623$		−	1.60724e8i		−	0.664686i
$624$			7.91879e7i			0.325916i
$625$	−2.97616e8			−1.21903
$626$		−	1.87425e8i		−	0.764021i
$627$	−7.04026e7	+	9.11927e6i	−0.285618	+	0.0369962i
$628$	1.60513e8			0.648085
$629$		−	2.23962e8i		−	0.899960i
$630$	−5.50858e7			−0.220302
$631$	−2.67113e8			−1.06318			−0.531591	−	0.847001i	$-0.678405\pi$
$631$	−2.67113e8			−1.06318			−0.531591	+	0.847001i	$0.678405\pi$
$632$	−1.03698e8			−0.410789
$633$		−	9.24872e7i		−	0.364645i
$634$			9.16434e7i			0.359611i
$635$		−	1.29472e8i		−	0.505656i
$636$	6.67072e7			0.259299
$637$			1.79026e8i			0.692623i
$638$	1.71009e7	+	1.32023e8i	0.0658504	+	0.508378i
$639$	5.68301e7			0.217809
$640$		−	2.91550e8i		−	1.11217i
$641$	3.34838e8			1.27134			0.635669	−	0.771962i	$-0.280724\pi$
$641$	3.34838e8			1.27134			0.635669	+	0.771962i	$0.280724\pi$
$642$	−1.22022e8			−0.461142
$643$	1.03629e8			0.389805			0.194903	−	0.980823i	$-0.437561\pi$
$643$	1.03629e8			0.389805			0.194903	+	0.980823i	$0.437561\pi$
$644$			2.31177e8i			0.865540i
$645$		−	2.22163e8i		−	0.827930i
$646$			4.72929e7i			0.175428i
$647$	−2.26601e8			−0.836661			−0.418331	−	0.908295i	$-0.637385\pi$
$647$	−2.26601e8			−0.836661			−0.418331	+	0.908295i	$0.637385\pi$
$648$			2.55221e7i			0.0937976i
$649$	3.79526e7	+	2.93002e8i	0.138838	+	1.07186i
$650$	6.43565e7			0.234343
$651$		−	3.04046e8i		−	1.10204i
$652$	−1.26521e8			−0.456478
$653$	−4.76849e8			−1.71254			−0.856271	−	0.516526i	$-0.827225\pi$
$653$	−4.76849e8			−1.71254			−0.856271	+	0.516526i	$0.827225\pi$
$654$	5.09318e7			0.182077
$655$			3.94923e8i			1.40536i
$656$		−	7.01112e7i		−	0.248357i
$657$			1.34901e8i			0.475685i
$658$	1.81582e8			0.637376
$659$		−	2.50328e7i		−	0.0874688i	−0.999043	−	0.0437344i	$-0.986074\pi$
$659$		−	2.50328e7i		−	0.0874688i	0.999043	−	0.0437344i	$-0.0139255\pi$
$660$	−1.89751e7	−	1.46492e8i	−0.0660013	−	0.509543i
$661$	3.78940e8			1.31210			0.656048	−	0.754719i	$-0.272227\pi$
$661$	3.78940e8			1.31210			0.656048	+	0.754719i	$0.272227\pi$
$662$			9.19821e7i			0.317051i
$663$	1.88857e8			0.648027
$664$	3.13103e8			1.06950
$665$	−2.03675e8			−0.692583
$666$			5.71004e7i			0.193293i
$667$		−	2.96393e8i		−	0.998827i
$668$		−	1.83263e8i		−	0.614816i
$669$	8.26002e6			0.0275869
$670$		−	2.30655e8i		−	0.766898i
$671$	−2.59964e8	+	3.36732e7i	−0.860488	+	0.111459i
$672$	−2.15852e8			−0.711293
$673$			4.58524e8i			1.50424i	0.659027	+	0.752119i	$0.270968\pi$
$673$			4.58524e8i			1.50424i	−0.659027	+	0.752119i	$0.729032\pi$
$674$	2.31364e8			0.755641
$675$	−1.91784e7			−0.0623594
$676$	−3.12563e8			−1.01181
$677$			5.53725e8i			1.78455i	0.451495	+	0.892274i	$0.350891\pi$
$677$			5.53725e8i			1.78455i	−0.451495	+	0.892274i	$0.649109\pi$
$678$		−	3.54868e7i		−	0.113862i
$679$			4.91334e8i			1.56952i
$680$	−2.25643e8			−0.717621
$681$			2.74153e8i			0.868064i
$682$	−2.36897e8	+	3.06854e7i	−0.746805	+	0.0967339i
$683$	−1.53935e7			−0.0483141			−0.0241571	−	0.999708i	$-0.507690\pi$
$683$	−1.53935e7			−0.0483141			−0.0241571	+	0.999708i	$0.507690\pi$
$684$			4.11541e7i			0.128601i
$685$	−6.60411e7			−0.205467
$686$	1.00891e8			0.312522
$687$	−5.84167e7			−0.180164
$688$		−	1.50798e8i		−	0.463052i
$689$			2.88573e8i			0.882262i
$690$		−	9.63562e7i		−	0.293314i
$691$	3.77442e7			0.114397			0.0571987	−	0.998363i	$-0.481783\pi$
$691$	3.77442e7			0.114397			0.0571987	+	0.998363i	$0.481783\pi$
$692$		−	4.26242e7i		−	0.128629i
$693$	−1.32748e8	+	1.71949e7i	−0.398868	+	0.0516655i
$694$	2.28668e7			0.0684113
$695$			3.54933e8i			1.05729i
$696$	1.76960e8			0.524864
$697$	−1.67210e8			−0.493814
$698$	9.09905e7			0.267565
$699$		−	9.10669e7i		−	0.266642i
$700$		−	1.03716e8i		−	0.302380i
$701$			1.85021e7i			0.0537115i	0.999639	+	0.0268558i	$0.00854948\pi$
$701$			1.85021e7i			0.0537115i	−0.999639	+	0.0268558i	$0.991451\pi$
$702$	−4.81502e7			−0.139183
$703$			2.11124e8i			0.607674i
$704$	5.13127e6	+	3.96144e7i	0.0147064	+	0.113536i
$705$	2.58322e8			0.737214
$706$		−	1.33262e8i		−	0.378696i
$707$	1.43636e8			0.406449
$708$	1.71275e8			0.482608
$709$	−4.14236e8			−1.16228			−0.581138	−	0.813805i	$-0.697392\pi$
$709$	−4.14236e8			−1.16228			−0.581138	+	0.813805i	$0.697392\pi$
$710$		−	1.28100e8i		−	0.357909i
$711$			5.83004e7i			0.162204i
$712$			1.67852e8i			0.465037i
$713$	5.31838e8			1.46727
$714$			8.91736e7i			0.244986i
$715$	6.33717e8	−	8.20856e7i	1.73371	−	0.224569i
$716$	4.69458e7			0.127896
$717$			4.03119e8i			1.09364i
$718$	−1.66727e8			−0.450435
$719$	5.27426e7			0.141898			0.0709488	−	0.997480i	$-0.477397\pi$
$719$	5.27426e7			0.141898			0.0709488	+	0.997480i	$0.477397\pi$
$720$	−5.31923e7			−0.142512
$721$		−	7.52107e8i		−	2.00666i
$722$			1.34577e8i			0.357569i
$723$		−	2.20245e8i		−	0.582763i
$724$	3.19441e8			0.841733
$725$			1.32975e8i			0.348945i
$726$	2.67949e7	+	1.01695e8i	0.0700231	+	0.265761i
$727$	−2.95940e8			−0.770194			−0.385097	−	0.922876i	$-0.625832\pi$
$727$	−2.95940e8			−0.770194			−0.385097	+	0.922876i	$0.625832\pi$
$728$		−	5.97082e8i		−	1.54753i
$729$	1.43489e7			0.0370370
$730$	3.04078e8			0.781657
$731$	−3.59641e8			−0.920698
$732$			1.51963e8i			0.387439i
$733$			5.16234e8i			1.31080i	0.755284	+	0.655398i	$0.227499\pi$
$733$			5.16234e8i			1.31080i	−0.755284	+	0.655398i	$0.772501\pi$
$734$		−	1.55196e8i		−	0.392457i
$735$	−1.20256e8			−0.302861
$736$		−	3.77569e8i		−	0.947029i
$737$	−7.19985e7	−	5.55842e8i	−0.179854	−	1.38851i
$738$	4.26311e7			0.106061
$739$		−	4.13265e8i		−	1.02399i	−0.858989	−	0.511995i	$-0.828907\pi$
$739$		−	4.13265e8i		−	1.02399i	0.858989	−	0.511995i	$-0.171093\pi$
$740$	−4.39300e8			−1.08409
$741$	−1.78031e8			−0.437563
$742$	−1.36257e8			−0.333539
$743$			1.45121e8i			0.353804i	0.984228	+	0.176902i	$0.0566076\pi$
$743$			1.45121e8i			0.353804i	−0.984228	+	0.176902i	$0.943392\pi$
$744$			3.17531e8i			0.771023i
$745$		−	2.46057e8i		−	0.595069i
$746$	1.76628e8			0.425444
$747$		−	1.76031e8i		−	0.422306i
$748$	−2.37143e8	+	3.07172e7i	−0.566637	+	0.0733967i
$749$	−8.50702e8			−2.02457
$750$		−	9.01834e7i		−	0.213768i
$751$	4.40685e8			1.04042			0.520210	−	0.854039i	$-0.325854\pi$
$751$	4.40685e8			1.04042			0.520210	+	0.854039i	$0.325854\pi$
$752$	1.75341e8			0.412315
$753$	1.58530e8			0.371301
$754$			3.33853e8i			0.778827i
$755$		−	5.88539e8i		−	1.36752i
$756$			7.75984e7i			0.179592i
$757$	4.28690e7			0.0988226			0.0494113	−	0.998779i	$-0.484265\pi$
$757$	4.28690e7			0.0988226			0.0494113	+	0.998779i	$0.484265\pi$
$758$			5.60376e7i			0.128668i
$759$	−3.00774e7	−	2.32204e8i	−0.0687884	−	0.531060i
$760$	2.12708e8			0.484555
$761$			4.40711e8i			0.999999i	0.866026	+	0.500000i	$0.166667\pi$
$761$			4.40711e8i			0.999999i	−0.866026	+	0.500000i	$0.833333\pi$
$762$	5.34365e7			0.120774
$763$	3.55080e8			0.799380
$764$	1.02294e8			0.229387
$765$			1.26860e8i			0.283361i
$766$		−	3.39277e8i		−	0.754863i
$767$			7.40930e8i			1.64207i
$768$	1.50271e8			0.331736
$769$		−	4.99724e8i		−	1.09888i	−0.835532	−	0.549441i	$-0.814841\pi$
$769$		−	4.99724e8i		−	1.09888i	0.835532	−	0.549441i	$-0.185159\pi$
$770$	3.87588e7	+	2.99225e8i	0.0848980	+	0.655430i
$771$	−4.05735e8			−0.885278
$772$			3.20124e8i			0.695772i
$773$	3.85200e8			0.833964			0.416982	−	0.908915i	$-0.363088\pi$
$773$	3.85200e8			0.833964			0.416982	+	0.908915i	$0.363088\pi$
$774$	9.16925e7			0.197748
$775$	−2.38607e8			−0.512598
$776$		−	5.13125e8i		−	1.09809i
$777$			3.98086e8i			0.848621i
$778$			8.06675e7i			0.171301i
$779$	1.57624e8			0.333435
$780$		−	3.70441e8i		−	0.780613i
$781$	−3.99861e7	−	3.08700e8i	−0.0839374	−	0.648013i
$782$	−1.55983e8			−0.326179
$783$		−	9.94893e7i		−	0.207248i
$784$	−8.16258e7			−0.169387
$785$	−4.66427e8			−0.964217
$786$	−1.62995e8			−0.335665
$787$		−	3.09625e8i		−	0.635202i	−0.948224	−	0.317601i	$-0.897123\pi$
$787$		−	3.09625e8i		−	0.635202i	0.948224	−	0.317601i	$-0.102877\pi$
$788$			2.04409e8i			0.417756i
$789$			1.13918e8i			0.231933i
$790$	1.31414e8			0.266538
$791$		−	2.47403e8i		−	0.499891i
$792$	1.38636e8	−	1.79576e7i	0.279062	−	0.0361469i
$793$	−6.57384e8			−1.31826
$794$			2.11240e7i			0.0422003i
$795$	−1.93841e8			−0.385784
$796$	−1.42567e8			−0.282670
$797$	5.44519e8			1.07557			0.537784	−	0.843082i	$-0.319261\pi$
$797$	5.44519e8			1.07557			0.537784	+	0.843082i	$0.319261\pi$
$798$		−	8.40617e7i		−	0.165421i
$799$		−	4.18175e8i		−	0.819818i
$800$			1.69395e8i			0.330849i
$801$	9.43690e7			0.183625
$802$		−	4.00884e8i		−	0.777133i
$803$	7.32781e8	−	9.49173e7i	1.41523	−	0.183315i
$804$	−3.24919e8			−0.625184
$805$		−	6.71765e8i		−	1.28774i
$806$	−5.99055e8			−1.14409
$807$	5.17808e8			0.985254
$808$	−1.50007e8			−0.284366
$809$			3.29687e8i			0.622668i	0.950301	+	0.311334i	$0.100776\pi$
$809$			3.29687e8i			0.622668i	−0.950301	+	0.311334i	$0.899224\pi$
$810$		−	3.23436e7i		−	0.0608602i
$811$		−	3.57075e8i		−	0.669417i	−0.942322	−	0.334709i	$-0.891362\pi$
$811$		−	3.57075e8i		−	0.669417i	0.942322	−	0.334709i	$-0.108638\pi$
$812$	5.38035e8			1.00495
$813$		−	1.30452e8i		−	0.242760i
$814$	3.10169e8	−	4.01763e7i	0.575075	−	0.0744897i
$815$	3.67651e8			0.679146
$816$			8.61085e7i			0.158480i
$817$	3.39025e8			0.621677
$818$	−3.10869e8			−0.567960
$819$	−3.35688e8			−0.611060
$820$			3.27980e8i			0.594848i
$821$		−	1.39268e8i		−	0.251664i	−0.992052	−	0.125832i	$-0.959840\pi$
$821$		−	1.39268e8i		−	0.251664i	0.992052	−	0.125832i	$-0.0401601\pi$
$822$		−	2.72569e7i		−	0.0490750i
$823$	−4.43171e8			−0.795008			−0.397504	−	0.917600i	$-0.630124\pi$
$823$	−4.43171e8			−0.795008			−0.397504	+	0.917600i	$0.630124\pi$
$824$			7.85464e8i			1.40393i
$825$	1.34941e7	+	1.04177e8i	0.0240315	+	0.185528i
$826$	−3.49848e8			−0.620783
$827$		−	1.15772e8i		−	0.204685i	−0.994749	−	0.102343i	$-0.967366\pi$
$827$		−	1.15772e8i		−	0.204685i	0.994749	−	0.102343i	$-0.0326338\pi$
$828$	−1.35735e8			−0.239113
$829$	5.83413e8			1.02403			0.512015	−	0.858977i	$-0.328899\pi$
$829$	5.83413e8			1.02403			0.512015	+	0.858977i	$0.328899\pi$
$830$	−3.96788e8			−0.693943
$831$			6.30017e8i			1.09787i
$832$			1.00175e8i			0.173936i
$833$			1.94671e8i			0.336796i
$834$	−1.46490e8			−0.252528
$835$			5.32534e8i			0.914720i
$836$	2.23548e8	−	2.89563e7i	0.382607	−	0.0495592i
$837$	1.78520e8			0.304447
$838$			3.80595e8i			0.646743i
$839$	1.11980e8			0.189607			0.0948033	−	0.995496i	$-0.469778\pi$
$839$	1.11980e8			0.189607			0.0948033	+	0.995496i	$0.469778\pi$
$840$	4.01073e8			0.676684
$841$	−9.49932e7			−0.159700
$842$			1.86208e8i			0.311933i
$843$			3.97107e6i			0.00662865i
$844$			2.93673e8i			0.488469i
$845$	9.08260e8			1.50536
$846$			1.06616e8i			0.176080i
$847$	1.86805e8	+	7.08988e8i	0.307425	+	1.16678i
$848$	−1.31573e8			−0.215764
$849$			4.82856e8i			0.789033i
$850$	6.99809e7			0.113952
$851$	−6.96334e8			−1.12987
$852$	−1.80452e8			−0.291771
$853$			4.52825e8i			0.729597i	0.931087	+	0.364798i	$0.118862\pi$
$853$			4.52825e8i			0.729597i	−0.931087	+	0.364798i	$0.881138\pi$
$854$		−	3.10400e8i		−	0.498366i
$855$		−	1.19587e8i		−	0.191332i
$856$	8.88432e8			1.41645
$857$			2.58493e8i			0.410683i	0.978690	+	0.205341i	$0.0658305\pi$
$857$			2.58493e8i			0.410683i	−0.978690	+	0.205341i	$0.934170\pi$
$858$	3.38788e7	+	2.61551e8i	0.0536372	+	0.414090i
$859$	−1.08422e9			−1.71056			−0.855282	−	0.518163i	$-0.826616\pi$
$859$	−1.08422e9			−1.71056			−0.855282	+	0.518163i	$0.826616\pi$
$860$			7.05433e8i			1.10907i
$861$	2.97210e8			0.465645
$862$	−4.40449e8			−0.687660
$863$	−1.01522e9			−1.57954			−0.789768	−	0.613405i	$-0.789799\pi$
$863$	−1.01522e9			−1.57954			−0.789768	+	0.613405i	$0.789799\pi$
$864$		−	1.26738e8i		−	0.196501i
$865$			1.23859e8i			0.191373i
$866$		−	2.79074e8i		−	0.429701i
$867$	−1.70905e8			−0.262239
$868$			9.65433e8i			1.47626i
$869$	3.16687e8	−	4.10206e7i	0.482582	−	0.0625090i
$870$	−2.24257e8			−0.340555
$871$		−	1.40559e9i		−	2.12718i
$872$	−3.70829e8			−0.559273
$873$	−2.88486e8			−0.433593
$874$	1.47041e8			0.220244
$875$		−	6.28731e8i		−	0.938513i
$876$		−	4.28349e8i		−	0.637215i
$877$		−	2.37232e8i		−	0.351702i	−0.984417	−	0.175851i	$-0.943732\pi$
$877$		−	2.37232e8i		−	0.351702i	0.984417	−	0.175851i	$-0.0562676\pi$
$878$	5.95081e7			0.0879209
$879$		−	6.80123e7i		−	0.100143i
$880$	3.74265e7	+	2.88940e8i	0.0549201	+	0.423994i
$881$	4.84940e8			0.709186			0.354593	−	0.935021i	$-0.384619\pi$
$881$	4.84940e8			0.709186			0.354593	+	0.935021i	$0.384619\pi$
$882$		−	4.96326e7i		−	0.0723371i
$883$	4.73109e8			0.687193			0.343597	−	0.939117i	$-0.388355\pi$
$883$	4.73109e8			0.687193			0.343597	+	0.939117i	$0.388355\pi$
$884$	−5.99676e8			−0.868080
$885$	−4.97700e8			−0.718022
$886$			4.23638e8i			0.609108i
$887$		−	6.28412e7i		−	0.0900480i	−0.998986	−	0.0450240i	$-0.985664\pi$
$887$		−	6.28412e7i		−	0.0900480i	0.998986	−	0.0450240i	$-0.0143364\pi$
$888$		−	4.15742e8i		−	0.593724i
$889$	3.72542e8			0.530237
$890$		−	2.12715e8i		−	0.301737i
$891$	−1.00960e7	−	7.79431e7i	−0.0142730	−	0.110191i
$892$	−2.62279e7			−0.0369547
$893$			3.94203e8i			0.553561i
$894$	1.01554e8			0.142130
$895$	−1.36417e8			−0.190283
$896$	8.38903e8			1.16624
$897$		−	5.87186e8i		−	0.813577i
$898$		−	1.10770e8i		−	0.152966i
$899$		−	1.23779e9i		−	1.70359i
$900$	6.08970e7			0.0835350
$901$			3.13792e8i			0.429010i
$902$	−2.99955e7	−	2.31571e8i	−0.0408730	−	0.315548i
$903$	6.39251e8			0.868177
$904$			2.58376e8i			0.349741i
$905$	−9.28246e8			−1.25233
$906$	2.42905e8			0.326627
$907$	3.28080e8			0.439702			0.219851	−	0.975534i	$-0.429443\pi$
$907$	3.28080e8			0.439702			0.219851	+	0.975534i	$0.429443\pi$
$908$		−	8.70514e8i		−	1.16284i
$909$			8.43361e7i			0.112285i
$910$			7.56667e8i			1.00411i
$911$	1.22039e9			1.61415			0.807074	−	0.590450i	$-0.201050\pi$
$911$	1.22039e9			1.61415			0.807074	+	0.590450i	$0.201050\pi$
$912$		−	8.11723e7i		−	0.107010i
$913$	−9.56197e8	+	1.23857e8i	−1.25642	+	0.162745i
$914$	1.46382e8			0.191712
$915$		−	4.41580e8i		−	0.576429i
$916$	1.85490e8			0.241342
$917$	−1.13635e9			−1.47368
$918$	−5.23582e7			−0.0676795
$919$			1.49855e8i			0.193075i	0.995329	+	0.0965373i	$0.0307767\pi$
$919$			1.49855e8i			0.193075i	−0.995329	+	0.0965373i	$0.969223\pi$
$920$			7.01559e8i			0.900950i
$921$			1.53266e7i			0.0196185i
$922$	−5.60816e8			−0.715530
$923$		−	7.80627e8i		−	0.992747i
$924$	4.21514e8	−	5.45988e7i	0.534313	−	0.0692098i
$925$	3.12407e8			0.394725
$926$			1.81596e8i			0.228704i
$927$	4.41599e8			0.554356
$928$	−8.78744e8			−1.09956
$929$	−4.94460e8			−0.616715			−0.308357	−	0.951271i	$-0.599779\pi$
$929$	−4.94460e8			−0.616715			−0.308357	+	0.951271i	$0.599779\pi$
$930$		−	4.02399e8i		−	0.500274i
$931$		−	1.83512e8i		−	0.227413i
$932$			2.89164e8i			0.357187i
$933$	−5.98318e8			−0.736694
$934$		−	4.40184e8i		−	0.540249i
$935$	6.89100e8	−	8.92594e7i	0.843039	−	0.109199i
$936$	3.50576e8			0.427518
$937$			1.63904e8i			0.199238i	0.995026	+	0.0996189i	$0.0317624\pi$
$937$			1.63904e8i			0.199238i	−0.995026	+	0.0996189i	$0.968238\pi$
$938$	6.63684e8			0.804179
$939$	7.67211e8			0.926655
$940$	−8.20245e8			−0.987553
$941$			8.56917e8i			1.02842i	0.857665	+	0.514209i	$0.171914\pi$
$941$			8.56917e8i			1.02842i	−0.857665	+	0.514209i	$0.828086\pi$
$942$		−	1.92506e8i		−	0.230299i
$943$			5.19881e8i			0.619968i
$944$	−3.37823e8			−0.401581
$945$		−	2.25489e8i		−	0.267196i
$946$	−6.45155e7	−	4.98073e8i	−0.0762063	−	0.588328i
$947$	−7.64105e7			−0.0899711			−0.0449856	−	0.998988i	$-0.514324\pi$
$947$	−7.64105e7			−0.0899711			−0.0449856	+	0.998988i	$0.514324\pi$
$948$		−	1.85120e8i		−	0.217285i
$949$	1.85302e9			2.16811
$950$	−6.59692e7			−0.0769432
$951$	−3.75135e8			−0.436160
$952$		−	6.49263e8i		−	0.752506i
$953$			3.45937e8i			0.399686i	0.979828	+	0.199843i	$0.0640432\pi$
$953$			3.45937e8i			0.399686i	−0.979828	+	0.199843i	$0.935957\pi$
$954$		−	8.00030e7i		−	0.0921428i
$955$	−2.97249e8			−0.341280
$956$		−	1.28002e9i		−	1.46502i
$957$	−5.40424e8	+	7.00014e7i	−0.616594	+	0.0798676i
$958$	3.93684e8			0.447767
$959$		−	1.90026e8i		−	0.215456i
$960$	−6.72900e7			−0.0760565
$961$	1.33354e9			1.50257
$962$	7.84341e8			0.881007
$963$		−	4.99489e8i		−	0.559303i
$964$			6.99342e8i			0.780653i
$965$		−	9.30232e8i		−	1.03516i
$966$	2.77255e8			0.307572
$967$			3.59209e8i			0.397254i	0.980075	+	0.198627i	$0.0636482\pi$
$967$			3.59209e8i			0.397254i	−0.980075	+	0.198627i	$0.936352\pi$
$968$	−1.95090e8	−	7.40433e8i	−0.215085	−	0.816319i
$969$	−1.93590e8			−0.212770
$970$			6.50271e8i			0.712491i
$971$	−5.52963e7			−0.0604001			−0.0302001	−	0.999544i	$-0.509614\pi$
$971$	−5.52963e7			−0.0604001			−0.0302001	+	0.999544i	$0.509614\pi$
$972$	−4.55619e7			−0.0496138
$973$	−1.02128e9			−1.10868
$974$		−	9.24408e7i		−	0.100043i
$975$			2.63438e8i			0.284227i
$976$		−	2.99731e8i		−	0.322390i
$977$	−1.12505e9			−1.20639			−0.603197	−	0.797592i	$-0.706107\pi$
$977$	−1.12505e9			−1.20639			−0.603197	+	0.797592i	$0.706107\pi$
$978$			1.51739e8i			0.162211i
$979$	−6.63987e7	−	5.12611e8i	−0.0707639	−	0.546311i
$980$	3.81846e8			0.405705
$981$			2.08485e8i			0.220835i
$982$	6.68859e8			0.706318
$983$	−7.26410e8			−0.764753			−0.382377	−	0.924007i	$-0.624894\pi$
$983$	−7.26410e8			−0.764753			−0.382377	+	0.924007i	$0.624894\pi$
$984$	−3.10392e8			−0.325781
$985$		−	5.93983e8i		−	0.621534i
$986$			3.63030e8i			0.378714i
$987$			7.43293e8i			0.773052i
$988$	5.65299e8			0.586148
$989$			1.11818e9i			1.15591i
$990$	−1.75690e8	+	2.27572e7i	−0.181068	+	0.0234538i
$991$	−3.55671e6			−0.00365450			−0.00182725	−	0.999998i	$-0.500582\pi$
$991$	−3.55671e6			−0.00365450			−0.00182725	+	0.999998i	$0.500582\pi$
$992$		−	1.57679e9i		−	1.61525i
$993$	−3.76521e8			−0.384540
$994$	3.68593e8			0.375308
$995$	4.14278e8			0.420555
$996$			5.58948e8i			0.565710i
$997$			1.50471e7i			0.0151833i	0.999971	+	0.00759167i	$0.00241653\pi$
$997$			1.50471e7i			0.0151833i	−0.999971	+	0.00759167i	$0.997583\pi$
$998$		−	2.34239e8i		−	0.235651i
$999$	−2.33736e8			−0.234439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.c.a.10.8	yes	12
3.2	odd	2		99.7.c.d.10.5		12
4.3	odd	2		528.7.j.c.241.8		12
11.10	odd	2	inner	33.7.c.a.10.5	✓	12
33.32	even	2		99.7.c.d.10.8		12
44.43	even	2		528.7.j.c.241.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.c.a.10.5	✓	12	11.10	odd	2	inner
33.7.c.a.10.8	yes	12	1.1	even	1	trivial
99.7.c.d.10.5		12	3.2	odd	2
99.7.c.d.10.8		12	33.32	even	2
528.7.j.c.241.7		12	44.43	even	2
528.7.j.c.241.8		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.80817i q^{2} -15.5885 q^{3} +49.4978 q^{4} -143.833 q^{5} -59.3636i q^{6} -413.864i q^{7} +432.219i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+3.80817i q^{2} -15.5885 q^{3} +49.4978 q^{4} -143.833 q^{5} -59.3636i q^{6} -413.864i q^{7} +432.219i q^{8} +243.000 q^{9} -547.741i q^{10} +(-170.977 - 1319.97i) q^{11} -771.594 q^{12} -3337.89i q^{13} +1576.07 q^{14} +2242.14 q^{15} +1521.89 q^{16} -3629.60i q^{17} +925.386i q^{18} +3421.53i q^{19} -7119.42 q^{20} +6451.50i q^{21} +(5026.69 - 651.109i) q^{22} -11285.0 q^{23} -6737.63i q^{24} +5062.95 q^{25} +12711.3 q^{26} -3788.00 q^{27} -20485.4i q^{28} +26264.4i q^{29} +8538.44i q^{30} -47127.9 q^{31} +33457.7i q^{32} +(2665.26 + 20576.3i) q^{33} +13822.1 q^{34} +59527.3i q^{35} +12028.0 q^{36} +61704.4 q^{37} -13029.8 q^{38} +52032.5i q^{39} -62167.5i q^{40} -46068.4i q^{41} -24568.4 q^{42} -99085.7i q^{43} +(-8462.96 - 65335.8i) q^{44} -34951.4 q^{45} -42975.2i q^{46} +115212. q^{47} -23724.0 q^{48} -53634.4 q^{49} +19280.6i q^{50} +56579.9i q^{51} -165218. i q^{52} -86453.7 q^{53} -14425.3i q^{54} +(24592.1 + 189856. i) q^{55} +178880. q^{56} -53336.4i q^{57} -100019. q^{58} -221976. q^{59} +110981. q^{60} -196946. i q^{61} -179471. i q^{62} -100569. i q^{63} -30011.5 q^{64} +480099. i q^{65} +(-78358.3 + 10149.8i) q^{66} +421101. q^{67} -179657. i q^{68} +175916. q^{69} -226690. q^{70} +233869. q^{71} +105029. i q^{72} +555148. i q^{73} +234981. i q^{74} -78923.6 q^{75} +169358. i q^{76} +(-546289. + 70761.0i) q^{77} -198149. q^{78} +239919. i q^{79} -218898. q^{80} +59049.0 q^{81} +175437. q^{82} -724407. i q^{83} +319335. i q^{84} +522056. i q^{85} +377335. q^{86} -409421. i q^{87} +(570518. - 73899.4i) q^{88} +388350. q^{89} -133101. i q^{90} -1.38143e6 q^{91} -558582. q^{92} +734652. q^{93} +438749. i q^{94} -492129. i q^{95} -521554. i q^{96} -1.18719e6 q^{97} -204249. i q^{98} +(-41547.3 - 320753. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) \) 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9} - 3464 q^{11} + 1944 q^{12} - 6708 q^{14} + 1944 q^{15} + 5316 q^{16} - 44092 q^{20} + 60468 q^{22} - 15304 q^{23} + 95652 q^{25} - 76020 q^{26} - 58608 q^{31} + 4212 q^{33} + 117768 q^{34} - 49572 q^{36} - 202512 q^{37} + 29208 q^{38} - 264708 q^{42} + 434356 q^{44} + 54432 q^{45} + 516920 q^{47} - 377136 q^{48} + 157812 q^{49} - 1042192 q^{53} + 262656 q^{55} + 463020 q^{56} + 1029432 q^{58} - 461008 q^{59} - 417636 q^{60} - 725364 q^{64} + 200232 q^{66} + 364752 q^{67} + 504144 q^{69} - 1028400 q^{70} - 755176 q^{71} + 1364688 q^{75} - 102384 q^{77} + 1219212 q^{78} - 1220764 q^{80} + 708588 q^{81} - 158688 q^{82} + 248760 q^{86} - 2493252 q^{88} - 3513544 q^{89} - 702768 q^{91} + 6899300 q^{92} + 789264 q^{93} + 2370192 q^{97} - 841752 q^{99}+O(q^{100}) \) 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9 - 3464 * q^11 + 1944 * q^12 - 6708 * q^14 + 1944 * q^15 + 5316 * q^16 - 44092 * q^20 + 60468 * q^22 - 15304 * q^23 + 95652 * q^25 - 76020 * q^26 - 58608 * q^31 + 4212 * q^33 + 117768 * q^34 - 49572 * q^36 - 202512 * q^37 + 29208 * q^38 - 264708 * q^42 + 434356 * q^44 + 54432 * q^45 + 516920 * q^47 - 377136 * q^48 + 157812 * q^49 - 1042192 * q^53 + 262656 * q^55 + 463020 * q^56 + 1029432 * q^58 - 461008 * q^59 - 417636 * q^60 - 725364 * q^64 + 200232 * q^66 + 364752 * q^67 + 504144 * q^69 - 1028400 * q^70 - 755176 * q^71 + 1364688 * q^75 - 102384 * q^77 + 1219212 * q^78 - 1220764 * q^80 + 708588 * q^81 - 158688 * q^82 + 248760 * q^86 - 2493252 * q^88 - 3513544 * q^89 - 702768 * q^91 + 6899300 * q^92 + 789264 * q^93 + 2370192 * q^97 - 841752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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