LMFDB - Embedded newform 33.7.c.a.10.3

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			10.3
Root			$-7.49503i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.7.c.a.10.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.49503i q^{2} +15.5885 q^{3} +7.82458 q^{4} -189.722 q^{5} -116.836i q^{6} -392.912i q^{7} -538.327i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-7.49503i q^{2} +15.5885 q^{3} +7.82458 q^{4} -189.722 q^{5} -116.836i q^{6} -392.912i q^{7} -538.327i q^{8} +243.000 q^{9} +1421.97i q^{10} +(-1248.26 + 461.970i) q^{11} +121.973 q^{12} -3165.60i q^{13} -2944.89 q^{14} -2957.47 q^{15} -3534.00 q^{16} +7694.83i q^{17} -1821.29i q^{18} -4208.75i q^{19} -1484.50 q^{20} -6124.89i q^{21} +(3462.48 + 9355.72i) q^{22} +15309.9 q^{23} -8391.69i q^{24} +20369.5 q^{25} -23726.3 q^{26} +3788.00 q^{27} -3074.37i q^{28} -17803.4i q^{29} +22166.3i q^{30} +42452.2 q^{31} -7965.50i q^{32} +(-19458.4 + 7201.40i) q^{33} +57673.0 q^{34} +74544.1i q^{35} +1901.37 q^{36} -21910.6 q^{37} -31544.7 q^{38} -49346.8i q^{39} +102133. i q^{40} -123658. i q^{41} -45906.2 q^{42} +95655.3i q^{43} +(-9767.09 + 3614.72i) q^{44} -46102.5 q^{45} -114748. i q^{46} +82110.6 q^{47} -55089.6 q^{48} -36730.8 q^{49} -152670. i q^{50} +119951. i q^{51} -24769.5i q^{52} -61306.3 q^{53} -28391.1i q^{54} +(236822. - 87645.9i) q^{55} -211515. q^{56} -65607.9i q^{57} -133437. q^{58} -78276.8 q^{59} -23141.0 q^{60} +132377. i q^{61} -318180. i q^{62} -95477.6i q^{63} -285878. q^{64} +600584. i q^{65} +(53974.7 + 145841. i) q^{66} +90877.1 q^{67} +60208.9i q^{68} +238658. q^{69} +558710. q^{70} +170923. q^{71} -130813. i q^{72} +169852. i q^{73} +164221. i q^{74} +317528. q^{75} -32931.7i q^{76} +(181513. + 490455. i) q^{77} -369856. q^{78} -14851.1i q^{79} +670478. q^{80} +59049.0 q^{81} -926823. q^{82} -438889. i q^{83} -47924.7i q^{84} -1.45988e6i q^{85} +716939. q^{86} -277528. i q^{87} +(248691. + 671970. i) q^{88} -727603. q^{89} +345539. i q^{90} -1.24380e6 q^{91} +119794. q^{92} +661764. q^{93} -615421. i q^{94} +798493. i q^{95} -124170. i q^{96} +761993. q^{97} +275299. i q^{98} +(-303326. + 112259. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	7.49503i		−	0.936878i	−0.883496	−	0.468439i	$-0.844817\pi$
$2$		−	7.49503i		−	0.936878i	0.883496	−	0.468439i	$-0.155183\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	7.82458			0.122259
$5$	−189.722			−1.51778			−0.758888	−	0.651221i	$-0.774257\pi$
$5$	−189.722			−1.51778			−0.758888	+	0.651221i	$0.774257\pi$
$6$		−	116.836i		−	0.540907i
$7$		−	392.912i		−	1.14552i	−0.819724	−	0.572758i	$-0.805873\pi$
$7$		−	392.912i		−	1.14552i	0.819724	−	0.572758i	$-0.194127\pi$
$8$		−	538.327i		−	1.05142i
$9$	243.000			0.333333
$10$			1421.97i			1.42197i
$11$	−1248.26	+	461.970i	−0.937834	+	0.347085i
$11$	−1248.26	+	461.970i	−0.937834	+	0.347085i
$12$	121.973			0.0705863
$13$		−	3165.60i		−	1.44087i	−0.693520	−	0.720437i	$-0.743941\pi$
$13$		−	3165.60i		−	1.44087i	0.693520	−	0.720437i	$-0.256059\pi$
$14$	−2944.89			−1.07321
$15$	−2957.47			−0.876289
$16$	−3534.00			−0.862794
$17$			7694.83i			1.56622i	0.621884	+	0.783109i	$0.286368\pi$
$17$			7694.83i			1.56622i	−0.621884	+	0.783109i	$0.713632\pi$
$18$		−	1821.29i		−	0.312293i
$19$		−	4208.75i		−	0.613610i	−0.951772	−	0.306805i	$-0.900740\pi$
$19$		−	4208.75i		−	0.613610i	0.951772	−	0.306805i	$-0.0992599\pi$
$20$	−1484.50			−0.185562
$21$		−	6124.89i		−	0.661364i
$22$	3462.48	+	9355.72i	0.325176	+	0.878636i
$23$	15309.9			1.25831			0.629157	−	0.777278i	$-0.283400\pi$
$23$	15309.9			1.25831			0.629157	+	0.777278i	$0.283400\pi$
$24$		−	8391.69i		−	0.607038i
$25$	20369.5			1.30364
$26$	−23726.3			−1.34992
$27$	3788.00			0.192450
$28$		−	3074.37i		−	0.140050i
$29$		−	17803.4i		−	0.729977i	−0.931012	−	0.364989i	$-0.881073\pi$
$29$		−	17803.4i		−	0.729977i	0.931012	−	0.364989i	$-0.118927\pi$
$30$			22166.3i			0.820976i
$31$	42452.2			1.42500			0.712500	−	0.701672i	$-0.247563\pi$
$31$	42452.2			1.42500			0.712500	+	0.701672i	$0.247563\pi$
$32$		−	7965.50i		−	0.243088i
$33$	−19458.4	+	7201.40i	−0.541459	+	0.200389i
$34$	57673.0			1.46736
$35$			74544.1i			1.73864i
$36$	1901.37			0.0407530
$37$	−21910.6			−0.432563			−0.216282	−	0.976331i	$-0.569393\pi$
$37$	−21910.6			−0.432563			−0.216282	+	0.976331i	$0.569393\pi$
$38$	−31544.7			−0.574878
$39$		−	49346.8i		−	0.831889i
$40$			102133.i			1.59582i
$41$		−	123658.i		−	1.79420i	−0.441823	−	0.897102i	$-0.645668\pi$
$41$		−	123658.i		−	1.79420i	0.441823	−	0.897102i	$-0.354332\pi$
$42$	−45906.2			−0.619618
$43$			95655.3i			1.20310i	0.798833	+	0.601552i	$0.205451\pi$
$43$			95655.3i			1.20310i	−0.798833	+	0.601552i	$0.794549\pi$
$44$	−9767.09	+	3614.72i	−0.114659	+	0.0424343i
$45$	−46102.5			−0.505925
$46$		−	114748.i		−	1.17889i
$47$	82110.6			0.790871			0.395435	−	0.918494i	$-0.370594\pi$
$47$	82110.6			0.790871			0.395435	+	0.918494i	$0.370594\pi$
$48$	−55089.6			−0.498134
$49$	−36730.8			−0.312207
$50$		−	152670.i		−	1.22136i
$51$			119951.i			0.904257i
$52$		−	24769.5i		−	0.176160i
$53$	−61306.3			−0.411792			−0.205896	−	0.978574i	$-0.566011\pi$
$53$	−61306.3			−0.411792			−0.205896	+	0.978574i	$0.566011\pi$
$54$		−	28391.1i		−	0.180302i
$55$	236822.	−	87645.9i	1.42342	−	0.526797i
$56$	−211515.			−1.20442
$57$		−	65607.9i		−	0.354268i
$58$	−133437.			−0.683900
$59$	−78276.8			−0.381133			−0.190567	−	0.981674i	$-0.561033\pi$
$59$	−78276.8			−0.381133			−0.190567	+	0.981674i	$0.561033\pi$
$60$	−23141.0			−0.107134
$61$			132377.i			0.583205i	0.956540	+	0.291603i	$0.0941885\pi$
$61$			132377.i			0.583205i	−0.956540	+	0.291603i	$0.905811\pi$
$62$		−	318180.i		−	1.33505i
$63$		−	95477.6i		−	0.381839i
$64$	−285878.			−1.09054
$65$			600584.i			2.18692i
$66$	53974.7	+	145841.i	0.187741	+	0.507281i
$67$	90877.1			0.302155			0.151078	−	0.988522i	$-0.451726\pi$
$67$	90877.1			0.302155			0.151078	+	0.988522i	$0.451726\pi$
$68$			60208.9i			0.191485i
$69$	238658.			0.726488
$70$	558710.			1.62889
$71$	170923.			0.477558			0.238779	−	0.971074i	$-0.423253\pi$
$71$	170923.			0.477558			0.238779	+	0.971074i	$0.423253\pi$
$72$		−	130813.i		−	0.350473i
$73$			169852.i			0.436618i	0.975880	+	0.218309i	$0.0700541\pi$
$73$			169852.i			0.436618i	−0.975880	+	0.218309i	$0.929946\pi$
$74$			164221.i			0.405259i
$75$	317528.			0.752660
$76$		−	32931.7i		−	0.0750194i
$77$	181513.	+	490455.i	0.397591	+	1.07430i
$78$	−369856.			−0.779379
$79$		−	14851.1i		−	0.0301216i	−0.999887	−	0.0150608i	$-0.995206\pi$
$79$		−	14851.1i		−	0.0301216i	0.999887	−	0.0150608i	$-0.00479418\pi$
$80$	670478.			1.30953
$81$	59049.0			0.111111
$82$	−926823.			−1.68095
$83$		−	438889.i		−	0.767574i	−0.923422	−	0.383787i	$-0.874620\pi$
$83$		−	438889.i		−	0.767574i	0.923422	−	0.383787i	$-0.125380\pi$
$84$		−	47924.7i		−	0.0808578i
$85$		−	1.45988e6i		−	2.37717i
$86$	716939.			1.12716
$87$		−	277528.i		−	0.421453i
$88$	248691.	+	671970.i	0.364932	+	0.986057i
$89$	−727603.			−1.03211			−0.516053	−	0.856557i	$-0.672599\pi$
$89$	−727603.			−1.03211			−0.516053	+	0.856557i	$0.672599\pi$
$90$			345539.i			0.473991i
$91$	−1.24380e6			−1.65054
$92$	119794.			0.153840
$93$	661764.			0.822724
$94$		−	615421.i		−	0.740950i
$95$			798493.i			0.931322i
$96$		−	124170.i		−	0.140347i
$97$	761993.			0.834903			0.417451	−	0.908699i	$-0.362923\pi$
$97$	761993.			0.834903			0.417451	+	0.908699i	$0.362923\pi$
$98$			275299.i			0.292500i
$99$	−303326.	+	112259.i	−0.312611	+	0.115695i
$100$	159382.			0.159382
$101$		−	967199.i		−	0.938754i	−0.882998	−	0.469377i	$-0.844479\pi$
$101$		−	967199.i		−	0.938754i	0.882998	−	0.469377i	$-0.155521\pi$
$102$	899033.			0.847179
$103$	−1.76161e6			−1.61212			−0.806062	−	0.591831i	$-0.798405\pi$
$103$	−1.76161e6			−1.61212			−0.806062	+	0.591831i	$0.798405\pi$
$104$	−1.70413e6			−1.51496
$105$			1.16203e6i			1.00380i
$106$			459493.i			0.385799i
$107$		−	70472.7i		−	0.0575267i	−0.999586	−	0.0287634i	$-0.990843\pi$
$107$		−	70472.7i		−	0.0575267i	0.999586	−	0.0287634i	$-0.00915693\pi$
$108$	29639.5			0.0235288
$109$			36969.9i			0.0285475i	0.999898	+	0.0142738i	$0.00454363\pi$
$109$			36969.9i			0.0285475i	−0.999898	+	0.0142738i	$0.995456\pi$
$110$	−656908.	−	1.77499e6i	−0.493545	−	1.33357i
$111$	−341553.			−0.249740
$112$			1.38855e6i			0.988344i
$113$	434149.			0.300887			0.150444	−	0.988619i	$-0.451930\pi$
$113$	434149.			0.300887			0.150444	+	0.988619i	$0.451930\pi$
$114$	−491733.			−0.331906
$115$	−2.90463e6			−1.90984
$116$		−	139304.i		−	0.0892464i
$117$		−	769241.i		−	0.480291i
$118$			586687.i			0.357076i
$119$	3.02339e6			1.79413
$120$			1.59209e6i			0.921347i
$121$	1.34473e6	−	1.15331e6i	0.759064	−	0.651016i
$122$	992166.			0.546392
$123$		−	1.92764e6i		−	1.03588i
$124$	332171.			0.174219
$125$	−900127.			−0.460865
$126$	−715607.			−0.357736
$127$		−	357170.i		−	0.174367i	−0.996192	−	0.0871834i	$-0.972213\pi$
$127$		−	357170.i		−	0.174367i	0.996192	−	0.0871834i	$-0.0277866\pi$
$128$			1.63287e6i			0.778613i
$129$			1.49112e6i			0.694613i
$130$	4.50139e6			2.04888
$131$		−	2.03648e6i		−	0.905872i	−0.891543	−	0.452936i	$-0.850377\pi$
$131$		−	2.03648e6i		−	0.905872i	0.891543	−	0.452936i	$-0.149623\pi$
$132$	−152254.	+	56347.9i	−0.0661983	+	0.0244994i
$133$	−1.65367e6			−0.702900
$134$		−	681126.i		−	0.283083i
$135$	−718666.			−0.292096
$136$	4.14234e6			1.64675
$137$	−357512.			−0.139037			−0.0695183	−	0.997581i	$-0.522146\pi$
$137$	−357512.			−0.139037			−0.0695183	+	0.997581i	$0.522146\pi$
$138$		−	1.78875e6i		−	0.680630i
$139$		−	1.33871e6i		−	0.498475i	−0.968442	−	0.249237i	$-0.919820\pi$
$139$		−	1.33871e6i		−	0.498475i	0.968442	−	0.249237i	$-0.0801800\pi$
$140$			583276.i			0.212564i
$141$	1.27998e6			0.456610
$142$		−	1.28108e6i		−	0.447414i
$143$	1.46241e6	+	3.95148e6i	0.500105	+	1.35130i
$144$	−858763.			−0.287598
$145$			3.37770e6i			1.10794i
$146$	1.27304e6			0.409058
$147$	−572577.			−0.180253
$148$	−171442.			−0.0528848
$149$			2.85163e6i			0.862054i	0.902339	+	0.431027i	$0.141849\pi$
$149$			2.85163e6i			0.862054i	−0.902339	+	0.431027i	$0.858151\pi$
$150$		−	2.37988e6i		−	0.705151i
$151$			3.96095e6i			1.15045i	0.817994	+	0.575226i	$0.195086\pi$
$151$			3.96095e6i			1.15045i	−0.817994	+	0.575226i	$0.804914\pi$
$152$	−2.26568e6			−0.645162
$153$			1.86984e6i			0.522073i
$154$	3.67597e6	−	1.36045e6i	1.00649	−	0.372495i
$155$	−8.05411e6			−2.16283
$156$		−	386118.i		−	0.101706i
$157$	4.88282e6			1.26175			0.630873	−	0.775886i	$-0.282697\pi$
$157$	4.88282e6			1.26175			0.630873	+	0.775886i	$0.282697\pi$
$158$	−111309.			−0.0282202
$159$	−955671.			−0.237748
$160$			1.51123e6i			0.368953i
$161$		−	6.01544e6i		−	1.44142i
$162$		−	442574.i		−	0.104098i
$163$	−539421.			−0.124556			−0.0622780	−	0.998059i	$-0.519837\pi$
$163$	−539421.			−0.124556			−0.0622780	+	0.998059i	$0.519837\pi$
$164$		−	967575.i		−	0.219358i
$165$	3.69169e6	−	1.36626e6i	0.821813	−	0.304146i
$166$	−3.28948e6			−0.719123
$167$		−	204862.i		−	0.0439858i	−0.999758	−	0.0219929i	$-0.992999\pi$
$167$		−	204862.i		−	0.0439858i	0.999758	−	0.0219929i	$-0.00700112\pi$
$168$	−3.29720e6			−0.695371
$169$	−5.19421e6			−1.07612
$170$	−1.09418e7			−2.22712
$171$		−	1.02273e6i		−	0.204537i
$172$			748463.i			0.147091i
$173$			1.84068e6i			0.355500i	0.984076	+	0.177750i	$0.0568818\pi$
$173$			1.84068e6i			0.355500i	−0.984076	+	0.177750i	$0.943118\pi$
$174$	−2.08008e6			−0.394850
$175$		−	8.00340e6i		−	1.49335i
$176$	4.41134e6	−	1.63260e6i	0.809157	−	0.299462i
$177$	−1.22021e6			−0.220048
$178$			5.45340e6i			0.966958i
$179$	2.95303e6			0.514883			0.257441	−	0.966294i	$-0.417121\pi$
$179$	2.95303e6			0.514883			0.257441	+	0.966294i	$0.417121\pi$
$180$	−360733.			−0.0618540
$181$	4.71761e6			0.795584			0.397792	−	0.917476i	$-0.369776\pi$
$181$	4.71761e6			0.795584			0.397792	+	0.917476i	$0.369776\pi$
$182$			9.32233e6i			1.54636i
$183$			2.06355e6i			0.336714i
$184$		−	8.24173e6i		−	1.32302i
$185$	4.15693e6			0.656534
$186$		−	4.95994e6i		−	0.770792i
$187$	−3.55478e6	−	9.60513e6i	−0.543611	−	1.46885i
$188$	642481.			0.0966912
$189$		−	1.48835e6i		−	0.220455i
$190$	5.98472e6			0.872536
$191$	8.90080e6			1.27741			0.638703	−	0.769453i	$-0.279471\pi$
$191$	8.90080e6			1.27741			0.638703	+	0.769453i	$0.279471\pi$
$192$	−4.45639e6			−0.629622
$193$			6.85119e6i			0.953003i	0.879174	+	0.476502i	$0.158095\pi$
$193$			6.85119e6i			0.953003i	−0.879174	+	0.476502i	$0.841905\pi$
$194$		−	5.71116e6i		−	0.782202i
$195$			9.36218e6i			1.26262i
$196$	−287404.			−0.0381702
$197$		−	7.04029e6i		−	0.920856i	−0.887697	−	0.460428i	$-0.847696\pi$
$197$		−	7.04029e6i		−	0.920856i	0.887697	−	0.460428i	$-0.152304\pi$
$198$	841382.	+	2.27344e6i	0.108392	+	0.292879i
$199$	−9.23926e6			−1.17241			−0.586203	−	0.810164i	$-0.699378\pi$
$199$	−9.23926e6			−1.17241			−0.586203	+	0.810164i	$0.699378\pi$
$200$		−	1.09654e7i		−	1.37068i
$201$	1.41663e6			0.174449
$202$	−7.24918e6			−0.879498
$203$	−6.99518e6			−0.836201
$204$			938563.i			0.110554i
$205$			2.34607e7i			2.72320i
$206$			1.32033e7i			1.51036i
$207$	3.72031e6			0.419438
$208$			1.11872e7i			1.24318i
$209$	1.94432e6	+	5.25360e6i	0.212975	+	0.575464i
$210$	8.70942e6			0.940441
$211$			578650.i			0.0615983i	0.999526	+	0.0307992i	$0.00980523\pi$
$211$			578650.i			0.0615983i	−0.999526	+	0.0307992i	$0.990195\pi$
$212$	−479697.			−0.0503453
$213$	2.66443e6			0.275718
$214$	−528195.			−0.0538955
$215$		−	1.81479e7i		−	1.82604i
$216$		−	2.03918e6i		−	0.202346i
$217$		−	1.66800e7i		−	1.63236i
$218$	277090.			0.0267456
$219$			2.64773e6i			0.252081i
$220$	1.85303e6	−	685792.i	0.174026	−	0.0644057i
$221$	2.43588e7			2.25672
$222$			2.55995e6i			0.233976i
$223$	4.34553e6			0.391858			0.195929	−	0.980618i	$-0.437228\pi$
$223$	4.34553e6			0.391858			0.195929	+	0.980618i	$0.437228\pi$
$224$	−3.12974e6			−0.278461
$225$	4.94978e6			0.434548
$226$		−	3.25396e6i		−	0.281895i
$227$			177192.i			0.0151484i	0.999971	+	0.00757420i	$0.00241097\pi$
$227$			177192.i			0.0151484i	−0.999971	+	0.00757420i	$0.997589\pi$
$228$		−	513355.i		−	0.0433125i
$229$	1.53988e7			1.28227			0.641137	−	0.767427i	$-0.278463\pi$
$229$	1.53988e7			1.28227			0.641137	+	0.767427i	$0.278463\pi$
$230$			2.17702e7i			1.78929i
$231$	2.82952e6	+	7.64544e6i	0.229549	+	0.620250i
$232$	−9.58406e6			−0.767513
$233$			1.10734e7i			0.875416i	0.899117	+	0.437708i	$0.144210\pi$
$233$			1.10734e7i			0.875416i	−0.899117	+	0.437708i	$0.855790\pi$
$234$	−5.76548e6			−0.449974
$235$	−1.55782e7			−1.20037
$236$	−612483.			−0.0465970
$237$		−	231506.i		−	0.0173907i
$238$		−	2.26604e7i		−	1.68088i
$239$			8.32346e6i			0.609692i	0.952402	+	0.304846i	$0.0986050\pi$
$239$			8.32346e6i			0.609692i	−0.952402	+	0.304846i	$0.901395\pi$
$240$	1.04517e7			0.756056
$241$		−	2.10193e7i		−	1.50165i	−0.660502	−	0.750824i	$-0.729657\pi$
$241$		−	2.10193e7i		−	1.50165i	0.660502	−	0.750824i	$-0.270343\pi$
$242$	−8.64412e6	−	1.00788e7i	−0.609922	−	0.711151i
$243$	920483.			0.0641500
$244$			1.03579e6i			0.0713022i
$245$	6.96865e6			0.473860
$246$	−1.44477e7			−0.970498
$247$	−1.33232e7			−0.884134
$248$		−	2.28532e7i		−	1.49827i
$249$		−	6.84160e6i		−	0.443159i
$250$			6.74648e6i			0.431775i
$251$	−1.36672e7			−0.864291			−0.432145	−	0.901804i	$-0.642243\pi$
$251$	−1.36672e7			−0.864291			−0.432145	+	0.901804i	$0.642243\pi$
$252$		−	747073.i		−	0.0466833i
$253$	−1.91107e7	+	7.07271e6i	−1.18009	+	0.436741i
$254$	−2.67700e6			−0.163360
$255$		−	2.27573e7i		−	1.37246i
$256$	−6.05778e6			−0.361072
$257$	2.04897e7			1.20708			0.603539	−	0.797334i	$-0.293757\pi$
$257$	2.04897e7			1.20708			0.603539	+	0.797334i	$0.293757\pi$
$258$	1.11760e7			0.650768
$259$			8.60895e6i			0.495508i
$260$			4.69932e6i			0.267371i
$261$		−	4.32623e6i		−	0.243326i
$262$	−1.52635e7			−0.848692
$263$			1.50639e7i			0.828076i	0.910260	+	0.414038i	$0.135882\pi$
$263$			1.50639e7i			0.828076i	−0.910260	+	0.414038i	$0.864118\pi$
$264$	3.87671e6	+	1.04750e7i	0.210694	+	0.569300i
$265$	1.16312e7			0.625008
$266$			1.23943e7i			0.658532i
$267$	−1.13422e7			−0.595887
$268$	711076.			0.0369412
$269$	−8.01963e6			−0.412000			−0.206000	−	0.978552i	$-0.566045\pi$
$269$	−8.01963e6			−0.412000			−0.206000	+	0.978552i	$0.566045\pi$
$270$			5.38642e6i			0.273659i
$271$			1.91654e7i			0.962962i	0.876457	+	0.481481i	$0.159901\pi$
$271$			1.91654e7i			0.962962i	−0.876457	+	0.481481i	$0.840099\pi$
$272$		−	2.71936e7i		−	1.35132i
$273$	−1.93890e7			−0.952942
$274$			2.67956e6i			0.130260i
$275$	−2.54263e7	+	9.41007e6i	−1.22260	+	0.452475i
$276$	1.86740e6			0.0888197
$277$			9.78348e6i			0.460314i	0.973154	+	0.230157i	$0.0739239\pi$
$277$			9.78348e6i			0.460314i	−0.973154	+	0.230157i	$0.926076\pi$
$278$	−1.00337e7			−0.467010
$279$	1.03159e7			0.475000
$280$	4.01291e7			1.82804
$281$			3.45664e7i			1.55789i	0.627095	+	0.778943i	$0.284244\pi$
$281$			3.45664e7i			1.55789i	−0.627095	+	0.778943i	$0.715756\pi$
$282$		−	9.59346e6i		−	0.427788i
$283$		−	4.31606e7i		−	1.90427i	−0.305679	−	0.952135i	$-0.598883\pi$
$283$		−	4.31606e7i		−	1.90427i	0.305679	−	0.952135i	$-0.401117\pi$
$284$	1.33740e6			0.0583859
$285$			1.24473e7i			0.537699i
$286$	2.96165e7	−	1.09608e7i	1.26600	−	0.468538i
$287$	−4.85869e7			−2.05529
$288$		−	1.93562e6i		−	0.0810292i
$289$	−3.50729e7			−1.45304
$290$	2.53160e7			1.03801
$291$	1.18783e7			0.482031
$292$			1.32902e6i			0.0533805i
$293$			4.58466e6i			0.182266i	0.995839	+	0.0911328i	$0.0290488\pi$
$293$			4.58466e6i			0.182266i	−0.995839	+	0.0911328i	$0.970951\pi$
$294$			4.29148e6i			0.168875i
$295$	1.48508e7			0.578475
$296$			1.17951e7i			0.454806i
$297$	−4.72839e6	+	1.74994e6i	−0.180486	+	0.0667965i
$298$	2.13730e7			0.807640
$299$		−	4.84650e7i		−	1.81307i
$300$	2.48453e6			0.0920195
$301$	3.75841e7			1.37818
$302$	2.96874e7			1.07783
$303$		−	1.50771e7i		−	0.541990i
$304$			1.48737e7i			0.529419i
$305$		−	2.51147e7i		−	0.885175i
$306$	1.40145e7			0.489119
$307$			1.97706e7i			0.683289i	0.939829	+	0.341645i	$0.110984\pi$
$307$			1.97706e7i			0.683289i	−0.939829	+	0.341645i	$0.889016\pi$
$308$	1.42027e6	+	3.83761e6i	0.0486091	+	0.131343i
$309$	−2.74608e7			−0.930760
$310$			6.03658e7i			2.02631i
$311$	2.78255e7			0.925044			0.462522	−	0.886608i	$-0.346945\pi$
$311$	2.78255e7			0.925044			0.462522	+	0.886608i	$0.346945\pi$
$312$	−2.65647e7			−0.874665
$313$	4.83630e7			1.57718			0.788589	−	0.614921i	$-0.210812\pi$
$313$	4.83630e7			1.57718			0.788589	+	0.614921i	$0.210812\pi$
$314$		−	3.65969e7i		−	1.18210i
$315$			1.81142e7i			0.579546i
$316$		−	116204.i		−	0.00368264i
$317$	−5.26062e7			−1.65143			−0.825714	−	0.564089i	$-0.809227\pi$
$317$	−5.26062e7			−1.65143			−0.825714	+	0.564089i	$0.809227\pi$
$318$			7.16278e6i			0.222741i
$319$	8.22464e6	+	2.22232e7i	0.253364	+	0.684597i
$320$	5.42373e7			1.65519
$321$		−	1.09856e6i		−	0.0332131i
$322$	−4.50859e7			−1.35043
$323$	3.23856e7			0.961047
$324$	462034.			0.0135843
$325$		−	6.44815e7i		−	1.87839i
$326$			4.04297e6i			0.116694i
$327$			576303.i			0.0164819i
$328$	−6.65686e7			−1.88646
$329$		−	3.22622e7i		−	0.905955i
$330$	−1.02402e7	−	2.76693e7i	−0.284948	−	0.769939i
$331$	6.25572e7			1.72502			0.862509	−	0.506042i	$-0.168892\pi$
$331$	6.25572e7			1.72502			0.862509	+	0.506042i	$0.168892\pi$
$332$		−	3.43412e6i		−	0.0938429i
$333$	−5.32428e6			−0.144188
$334$	−1.53545e6			−0.0412093
$335$	−1.72414e7			−0.458604
$336$			2.16454e7i			0.570621i
$337$			3.91359e7i			1.02255i	0.859416	+	0.511277i	$0.170827\pi$
$337$			3.91359e7i			1.02255i	−0.859416	+	0.511277i	$0.829173\pi$
$338$			3.89308e7i			1.00819i
$339$	6.76772e6			0.173717
$340$		−	1.14229e7i		−	0.290631i
$341$	−5.29912e7	+	1.96116e7i	−1.33641	+	0.494596i
$342$	−7.66536e6			−0.191626
$343$		−	3.17937e7i		−	0.787878i
$344$	5.14938e7			1.26497
$345$	−4.52786e7			−1.10265
$346$	1.37959e7			0.333060
$347$			6.04019e7i			1.44565i	0.691033	+	0.722824i	$0.257156\pi$
$347$			6.04019e7i			1.44565i	−0.691033	+	0.722824i	$0.742844\pi$
$348$		−	2.17154e6i		−	0.0515264i
$349$			6.91884e7i			1.62763i	0.581121	+	0.813817i	$0.302614\pi$
$349$			6.91884e7i			1.62763i	−0.581121	+	0.813817i	$0.697386\pi$
$350$	−5.99857e7			−1.39908
$351$		−	1.19913e7i		−	0.277296i
$352$	3.67982e6	+	9.94298e6i	0.0843720	+	0.227976i
$353$	1.15642e7			0.262900			0.131450	−	0.991323i	$-0.458037\pi$
$353$	1.15642e7			0.262900			0.131450	+	0.991323i	$0.458037\pi$
$354$			9.14554e6i			0.206158i
$355$	−3.24279e7			−0.724827
$356$	−5.69319e6			−0.126184
$357$	4.71300e7			1.03584
$358$		−	2.21330e7i		−	0.482383i
$359$		−	5.94327e7i		−	1.28452i	−0.766485	−	0.642262i	$-0.777996\pi$
$359$		−	5.94327e7i		−	1.28452i	0.766485	−	0.642262i	$-0.222004\pi$
$360$			2.48182e7i			0.531940i
$361$	2.93323e7			0.623483
$362$		−	3.53586e7i		−	0.745366i
$363$	2.09622e7	−	1.79784e7i	0.438246	−	0.375864i
$364$	−9.73223e6			−0.201794
$365$		−	3.22246e7i		−	0.662688i
$366$	1.54663e7			0.315460
$367$	−4.75829e7			−0.962615			−0.481308	−	0.876552i	$-0.659838\pi$
$367$	−4.75829e7			−0.962615			−0.481308	+	0.876552i	$0.659838\pi$
$368$	−5.41052e7			−1.08566
$369$		−	3.00490e7i		−	0.598068i
$370$		−	3.11563e7i		−	0.615093i
$371$			2.40880e7i			0.471714i
$372$	5.17803e6			0.100586
$373$		−	1.59677e6i		−	0.0307691i	−0.999882	−	0.0153846i	$-0.995103\pi$
$373$		−	1.59677e6i		−	0.0307691i	0.999882	−	0.0153846i	$-0.00489725\pi$
$374$	−7.19907e7	+	2.66432e7i	−1.37614	+	0.509297i
$375$	−1.40316e7			−0.266081
$376$		−	4.42024e7i		−	0.831538i
$377$	−5.63585e7			−1.05181
$378$	−1.11552e7			−0.206539
$379$	−2.76386e7			−0.507689			−0.253845	−	0.967245i	$-0.581695\pi$
$379$	−2.76386e7			−0.507689			−0.253845	+	0.967245i	$0.581695\pi$
$380$			6.24787e6i			0.113863i
$381$		−	5.56773e6i		−	0.100671i
$382$		−	6.67117e7i		−	1.19677i
$383$	1.35465e7			0.241118			0.120559	−	0.992706i	$-0.461531\pi$
$383$	1.35465e7			0.241118			0.120559	+	0.992706i	$0.461531\pi$
$384$			2.54539e7i			0.449532i
$385$	−3.44371e7	−	9.30501e7i	−0.603454	−	1.63055i
$386$	5.13499e7			0.892848
$387$			2.32442e7i			0.401035i
$388$	5.96228e6			0.102074
$389$	6.43032e7			1.09241			0.546203	−	0.837653i	$-0.316073\pi$
$389$	6.43032e7			1.09241			0.546203	+	0.837653i	$0.316073\pi$
$390$	7.01698e7			1.18292
$391$			1.17807e8i			1.97079i
$392$			1.97732e7i			0.328261i
$393$		−	3.17456e7i		−	0.523005i
$394$	−5.27671e7			−0.862730
$395$			2.81758e6i			0.0457178i
$396$	−2.37340e6	+	878377.i	−0.0382196	+	0.0141448i
$397$	1.12860e8			1.80371			0.901856	−	0.432036i	$-0.142205\pi$
$397$	1.12860e8			1.80371			0.901856	+	0.432036i	$0.142205\pi$
$398$			6.92485e7i			1.09840i
$399$	−2.57781e7			−0.405819
$400$	−7.19857e7			−1.12478
$401$	6.66212e7			1.03319			0.516594	−	0.856231i	$-0.327200\pi$
$401$	6.66212e7			1.03319			0.516594	+	0.856231i	$0.327200\pi$
$402$		−	1.06177e7i		−	0.163438i
$403$		−	1.34387e8i		−	2.05325i
$404$		−	7.56793e6i		−	0.114771i
$405$	−1.12029e7			−0.168642
$406$			5.24290e7i			0.783418i
$407$	2.73501e7	−	1.01220e7i	0.405672	−	0.150136i
$408$	6.45726e7			0.950754
$409$			6.64913e7i			0.971840i	0.874003	+	0.485920i	$0.161515\pi$
$409$			6.64913e7i			0.971840i	−0.874003	+	0.485920i	$0.838485\pi$
$410$	1.75839e8			2.55131
$411$	−5.57306e6			−0.0802728
$412$	−1.37839e7			−0.197097
$413$			3.07559e7i			0.436594i
$414$		−	2.78838e7i		−	0.392962i
$415$			8.32669e7i			1.16501i
$416$	−2.52156e7			−0.350259
$417$		−	2.08685e7i		−	0.287795i
$418$	3.93759e7	−	1.45727e7i	0.539140	−	0.199531i
$419$	4.24264e7			0.576759			0.288380	−	0.957516i	$-0.406883\pi$
$419$	4.24264e7			0.576759			0.288380	+	0.957516i	$0.406883\pi$
$420$			9.09238e6i			0.122724i
$421$	−5.27665e7			−0.707151			−0.353575	−	0.935406i	$-0.615034\pi$
$421$	−5.27665e7			−0.707151			−0.353575	+	0.935406i	$0.615034\pi$
$422$	4.33700e6			0.0577101
$423$	1.99529e7			0.263624
$424$			3.30029e7i			0.432966i
$425$			1.56740e8i			2.04179i
$426$		−	1.99700e7i		−	0.258315i
$427$	5.20123e7			0.668071
$428$		−	551420.i		−	0.00703317i
$429$	2.27967e7	+	6.15975e7i	0.288736	+	0.780173i
$430$	−1.36019e8			−1.71078
$431$			8.08728e7i			1.01011i	0.863086	+	0.505057i	$0.168529\pi$
$431$			8.08728e7i			1.01011i	−0.863086	+	0.505057i	$0.831471\pi$
$432$	−1.33868e7			−0.166045
$433$	−7.28610e7			−0.897493			−0.448747	−	0.893659i	$-0.648129\pi$
$433$	−7.28610e7			−0.897493			−0.448747	+	0.893659i	$0.648129\pi$
$434$	−1.25017e8			−1.52932
$435$			5.26531e7i			0.639671i
$436$			289274.i			0.00349019i
$437$		−	6.44355e7i		−	0.772113i
$438$	1.98448e7			0.236170
$439$		−	1.37100e8i		−	1.62048i	−0.586098	−	0.810240i	$-0.699337\pi$
$439$		−	1.37100e8i		−	1.62048i	0.586098	−	0.810240i	$-0.300663\pi$
$440$	−4.71821e7	−	1.27488e8i	−0.553885	−	1.49661i
$441$	−8.92560e6			−0.104069
$442$		−	1.82570e8i		−	2.11428i
$443$	6.44268e6			0.0741064			0.0370532	−	0.999313i	$-0.488203\pi$
$443$	6.44268e6			0.0741064			0.0370532	+	0.999313i	$0.488203\pi$
$444$	−2.67251e6			−0.0305331
$445$	1.38042e8			1.56651
$446$		−	3.25699e7i		−	0.367123i
$447$			4.44525e7i			0.497707i
$448$			1.12325e8i			1.24923i
$449$	−3.45704e7			−0.381914			−0.190957	−	0.981598i	$-0.561159\pi$
$449$	−3.45704e7			−0.381914			−0.190957	+	0.981598i	$0.561159\pi$
$450$		−	3.70987e7i		−	0.407119i
$451$	5.71264e7	+	1.54357e8i	0.622741	+	1.68267i
$452$	3.39704e6			0.0367862
$453$			6.17451e7i			0.664214i
$454$	1.32806e6			0.0141922
$455$	2.35977e8			2.50516
$456$	−3.53185e7			−0.372484
$457$			3.71576e7i			0.389313i	0.980871	+	0.194656i	$0.0623592\pi$
$457$			3.71576e7i			0.389313i	−0.980871	+	0.194656i	$0.937641\pi$
$458$		−	1.15414e8i		−	1.20133i
$459$			2.91480e7i			0.301419i
$460$	−2.27275e7			−0.233495
$461$		−	1.52668e8i		−	1.55828i	−0.626851	−	0.779139i	$-0.715657\pi$
$461$		−	1.52668e8i		−	1.55828i	0.626851	−	0.779139i	$-0.284343\pi$
$462$	5.73028e7	−	2.12073e7i	0.581098	−	0.215060i
$463$	−1.68834e8			−1.70104			−0.850522	−	0.525939i	$-0.823714\pi$
$463$	−1.68834e8			−1.70104			−0.850522	+	0.525939i	$0.823714\pi$
$464$			6.29173e7i			0.629820i
$465$	−1.25551e8			−1.24871
$466$	8.29956e7			0.820158
$467$	−1.53962e8			−1.51169			−0.755843	−	0.654753i	$-0.772773\pi$
$467$	−1.53962e8			−1.51169			−0.755843	+	0.654753i	$0.772773\pi$
$468$		−	6.01899e6i		−	0.0587200i
$469$		−	3.57067e7i		−	0.346124i
$470$			1.16759e8i			1.12460i
$471$	7.61157e7			0.728469
$472$			4.21385e7i			0.400731i
$473$	−4.41898e7	−	1.19402e8i	−0.417579	−	1.12831i
$474$	−1.73514e6			−0.0162930
$475$		−	8.57299e7i		−	0.799929i
$476$	2.36568e7			0.219349
$477$	−1.48974e7			−0.137264
$478$	6.23846e7			0.571207
$479$		−	2.05003e8i		−	1.86532i	−0.360758	−	0.932660i	$-0.617482\pi$
$479$		−	2.05003e8i		−	1.86532i	0.360758	−	0.932660i	$-0.382518\pi$
$480$			2.35577e7i			0.213015i
$481$			6.93603e7i			0.623269i
$482$	−1.57541e8			−1.40686
$483$		−	9.37715e7i		−	0.832203i
$484$	1.05219e7	−	9.02420e6i	0.0928025	−	0.0795926i
$485$	−1.44567e8			−1.26720
$486$		−	6.89904e6i		−	0.0601008i
$487$	−1.75661e7			−0.152086			−0.0760429	−	0.997105i	$-0.524229\pi$
$487$	−1.75661e7			−0.152086			−0.0760429	+	0.997105i	$0.524229\pi$
$488$	7.12619e7			0.613194
$489$	−8.40874e6			−0.0719125
$490$		−	5.22302e7i		−	0.443950i
$491$			4.51111e7i			0.381100i	0.981677	+	0.190550i	$0.0610272\pi$
$491$			4.51111e7i			0.381100i	−0.981677	+	0.190550i	$0.938973\pi$
$492$		−	1.50830e7i		−	0.126646i
$493$	1.36994e8			1.14330
$494$			9.98578e7i			0.828326i
$495$	5.75477e7	−	2.12979e7i	0.474474	−	0.175599i
$496$	−1.50026e8			−1.22948
$497$		−	6.71579e7i		−	0.547051i
$498$	−5.12779e7			−0.415186
$499$	−1.02233e8			−0.822788			−0.411394	−	0.911458i	$-0.634958\pi$
$499$	−1.02233e8			−0.822788			−0.411394	+	0.911458i	$0.634958\pi$
$500$	−7.04312e6			−0.0563450
$501$		−	3.19348e6i		−	0.0253952i
$502$			1.02436e8i			0.809735i
$503$		−	3.02022e7i		−	0.237320i	−0.992935	−	0.118660i	$-0.962140\pi$
$503$		−	3.02022e7i		−	0.237320i	0.992935	−	0.118660i	$-0.0378598\pi$
$504$	−5.13982e7			−0.401473
$505$			1.83499e8i			1.42482i
$506$	5.30102e7	+	1.43235e8i	0.409174	+	1.10560i
$507$	−8.09698e7			−0.621297
$508$		−	2.79471e6i		−	0.0213179i
$509$	−1.67946e8			−1.27355			−0.636777	−	0.771048i	$-0.719733\pi$
$509$	−1.67946e8			−1.27355			−0.636777	+	0.771048i	$0.719733\pi$
$510$	−1.70566e8			−1.28583
$511$	6.67368e7			0.500153
$512$			1.49907e8i			1.11689i
$513$		−	1.59427e7i		−	0.118089i
$514$		−	1.53570e8i		−	1.13088i
$515$	3.34216e8			2.44684
$516$			1.16674e7i			0.0849228i
$517$	−1.02495e8	+	3.79326e7i	−0.741705	+	0.274499i
$518$	6.45243e7			0.464231
$519$			2.86933e7i			0.205248i
$520$	3.23311e8			2.29938
$521$	8.18675e6			0.0578893			0.0289447	−	0.999581i	$-0.490785\pi$
$521$	8.18675e6			0.0578893			0.0289447	+	0.999581i	$0.490785\pi$
$522$	−3.24252e7			−0.227967
$523$		−	1.24984e8i		−	0.873674i	−0.899541	−	0.436837i	$-0.856099\pi$
$523$		−	1.24984e8i		−	0.873674i	0.899541	−	0.436837i	$-0.143901\pi$
$524$		−	1.59346e7i		−	0.110751i
$525$		−	1.24761e8i		−	0.862184i
$526$	1.12904e8			0.775806
$527$			3.26662e8i			2.23186i
$528$	6.87660e7	−	2.54498e7i	0.467167	−	0.172895i
$529$	8.63572e7			0.583353
$530$		−	8.71759e7i		−	0.585556i
$531$	−1.90213e7			−0.127044
$532$	−1.29393e7			−0.0859359
$533$	−3.91453e8			−2.58522
$534$			8.50101e7i			0.558273i
$535$			1.33702e7i			0.0873127i
$536$		−	4.89216e7i		−	0.317692i
$537$	4.60332e7			0.297268
$538$			6.01074e7i			0.385994i
$539$	4.58495e7	−	1.69685e7i	0.292798	−	0.108362i
$540$	−5.62326e6			−0.0357114
$541$		−	1.72410e8i		−	1.08885i	−0.838808	−	0.544427i	$-0.816747\pi$
$541$		−	1.72410e8i		−	1.08885i	0.838808	−	0.544427i	$-0.183253\pi$
$542$	1.43645e8			0.902178
$543$	7.35403e7			0.459331
$544$	6.12932e7			0.380728
$545$		−	7.01400e6i		−	0.0433288i
$546$			1.45321e8i			0.892791i
$547$			5.98303e7i			0.365561i	0.983154	+	0.182780i	$0.0585097\pi$
$547$			5.98303e7i			0.365561i	−0.983154	+	0.182780i	$0.941490\pi$
$548$	−2.79738e6			−0.0169985
$549$			3.21675e7i			0.194402i
$550$	7.05287e7	+	1.90571e8i	0.423914	+	1.14543i
$551$	−7.49301e7			−0.447921
$552$		−	1.28476e8i		−	0.763844i
$553$	−5.83518e6			−0.0345047
$554$	7.33274e7			0.431258
$555$	6.48001e7			0.379050
$556$		−	1.04749e7i		−	0.0609431i
$557$		−	1.01671e8i		−	0.588347i	−0.955752	−	0.294173i	$-0.904956\pi$
$557$		−	1.01671e8i		−	0.588347i	0.955752	−	0.294173i	$-0.0950443\pi$
$558$		−	7.73178e7i		−	0.445017i
$559$	3.02806e8			1.73352
$560$		−	2.63439e8i		−	1.50009i
$561$	−5.54135e7	−	1.49729e8i	−0.313854	−	0.848043i
$562$	2.59076e8			1.45955
$563$			2.72011e8i			1.52427i	0.647419	+	0.762135i	$0.275849\pi$
$563$			2.72011e8i			1.52427i	−0.647419	+	0.762135i	$0.724151\pi$
$564$	1.00153e7			0.0558247
$565$	−8.23677e7			−0.456679
$566$	−3.23490e8			−1.78407
$567$		−	2.32011e7i		−	0.127280i
$568$		−	9.20127e7i		−	0.502114i
$569$		−	2.72888e8i		−	1.48132i	−0.671883	−	0.740658i	$-0.734514\pi$
$569$		−	2.72888e8i		−	1.48132i	0.671883	−	0.740658i	$-0.265486\pi$
$570$	9.32926e7			0.503759
$571$		−	1.27343e8i		−	0.684016i	−0.939697	−	0.342008i	$-0.888893\pi$
$571$		−	1.27343e8i		−	0.684016i	0.939697	−	0.342008i	$-0.111107\pi$
$572$	1.14428e7	+	3.09187e7i	0.0611424	+	0.165209i
$573$	1.38750e8			0.737511
$574$			3.64160e8i			1.92556i
$575$	3.11854e8			1.64039
$576$	−6.94683e7			−0.363512
$577$	−2.21263e8			−1.15181			−0.575906	−	0.817516i	$-0.695351\pi$
$577$	−2.21263e8			−1.15181			−0.575906	+	0.817516i	$0.695351\pi$
$578$			2.62872e8i			1.36132i
$579$			1.06800e8i			0.550217i
$580$			2.64291e7i			0.135456i
$581$	−1.72445e8			−0.879268
$582$		−	8.90282e7i		−	0.451605i
$583$	7.65260e7	−	2.83217e7i	0.386192	−	0.142927i
$584$	9.14358e7			0.459069
$585$			1.45942e8i			0.728975i
$586$	3.43622e7			0.170761
$587$	5.35495e7			0.264753			0.132376	−	0.991200i	$-0.457739\pi$
$587$	5.35495e7			0.264753			0.132376	+	0.991200i	$0.457739\pi$
$588$	−4.48018e6			−0.0220376
$589$		−	1.78671e8i		−	0.874394i
$590$		−	1.11307e8i		−	0.541961i
$591$		−	1.09747e8i		−	0.531656i
$592$	7.74322e7			0.373213
$593$			3.07963e8i			1.47684i	0.674339	+	0.738422i	$0.264429\pi$
$593$			3.07963e8i			1.47684i	−0.674339	+	0.738422i	$0.735571\pi$
$594$	1.31158e7	+	3.54394e7i	0.0625802	+	0.169094i
$595$	−5.73604e8			−2.72309
$596$			2.23128e7i			0.105394i
$597$	−1.44026e8			−0.676889
$598$	−3.63247e8			−1.69863
$599$	4.83610e7			0.225017			0.112508	−	0.993651i	$-0.464111\pi$
$599$	4.83610e7			0.225017			0.112508	+	0.993651i	$0.464111\pi$
$600$		−	1.70934e8i		−	0.791362i
$601$		−	2.73748e8i		−	1.26104i	−0.776174	−	0.630519i	$-0.782842\pi$
$601$		−	2.73748e8i		−	1.26104i	0.776174	−	0.630519i	$-0.217158\pi$
$602$		−	2.81694e8i		−	1.29118i
$603$	2.20831e7			0.100718
$604$			3.09928e7i			0.140653i
$605$	−2.55125e8	+	2.18809e8i	−1.15209	+	0.988096i
$606$	−1.13004e8			−0.507778
$607$		−	1.08031e8i		−	0.483039i	−0.970396	−	0.241520i	$-0.922354\pi$
$607$		−	1.08031e8i		−	0.483039i	0.970396	−	0.241520i	$-0.0776458\pi$
$608$	−3.35248e7			−0.149161
$609$	−1.09044e8			−0.482781
$610$	−1.88236e8			−0.829302
$611$		−	2.59929e8i		−	1.13955i
$612$			1.46308e7i			0.0638282i
$613$			3.49825e8i			1.51869i	0.650687	+	0.759346i	$0.274481\pi$
$613$			3.49825e8i			1.51869i	−0.650687	+	0.759346i	$0.725519\pi$
$614$	1.48181e8			0.640159
$615$			3.65716e8i			1.57224i
$616$	2.64025e8	−	9.77136e7i	1.12954	−	0.418035i
$617$	1.68402e8			0.716957			0.358478	−	0.933538i	$-0.383296\pi$
$617$	1.68402e8			0.716957			0.358478	+	0.933538i	$0.383296\pi$
$618$			2.05819e8i			0.872009i
$619$	−4.24119e8			−1.78820			−0.894100	−	0.447868i	$-0.852184\pi$
$619$	−4.24119e8			−1.78820			−0.894100	+	0.447868i	$0.852184\pi$
$620$	−6.30201e7			−0.264426
$621$	5.79938e7			0.242163
$622$		−	2.08553e8i		−	0.866654i
$623$			2.85884e8i			1.18229i
$624$			1.74392e8i			0.717748i
$625$	−1.47499e8			−0.604155
$626$		−	3.62482e8i		−	1.47762i
$627$	3.03089e7	+	8.18955e7i	0.122961	+	0.332244i
$628$	3.82060e7			0.154260
$629$		−	1.68599e8i		−	0.677489i
$630$	1.35766e8			0.542964
$631$	1.47309e8			0.586330			0.293165	−	0.956062i	$-0.405291\pi$
$631$	1.47309e8			0.586330			0.293165	+	0.956062i	$0.405291\pi$
$632$	−7.99475e6			−0.0316704
$633$			9.02027e6i			0.0355638i
$634$			3.94285e8i			1.54719i
$635$			6.77630e7i			0.264650i
$636$	−7.47773e6			−0.0290669
$637$			1.16275e8i			0.449851i
$638$	1.66564e8	−	6.16439e7i	0.641384	−	0.237371i
$639$	4.15344e7			0.159186
$640$		−	3.09791e8i		−	1.18176i
$641$	3.13995e8			1.19220			0.596099	−	0.802911i	$-0.296717\pi$
$641$	3.13995e8			1.19220			0.596099	+	0.802911i	$0.296717\pi$
$642$	−8.23374e6			−0.0311166
$643$	−3.79094e8			−1.42598			−0.712990	−	0.701174i	$-0.752660\pi$
$643$	−3.79094e8			−1.42598			−0.712990	+	0.701174i	$0.752660\pi$
$644$		−	4.70683e7i		−	0.176227i
$645$		−	2.82898e8i		−	1.05427i
$646$		−	2.42731e8i		−	0.900384i
$647$	1.99854e8			0.737904			0.368952	−	0.929448i	$-0.379717\pi$
$647$	1.99854e8			0.737904			0.368952	+	0.929448i	$0.379717\pi$
$648$		−	3.17877e7i		−	0.116824i
$649$	9.77096e7	−	3.61615e7i	0.357440	−	0.132286i
$650$	−4.83291e8			−1.75982
$651$		−	2.60015e8i		−	0.942444i
$652$	−4.22074e6			−0.0152281
$653$	2.81558e8			1.01118			0.505589	−	0.862774i	$-0.331275\pi$
$653$	2.81558e8			1.01118			0.505589	+	0.862774i	$0.331275\pi$
$654$	4.31941e6			0.0154416
$655$			3.86366e8i			1.37491i
$656$			4.37009e8i			1.54803i
$657$			4.12740e7i			0.145539i
$658$	−2.41806e8			−0.848770
$659$		−	1.27397e8i		−	0.445148i	−0.974916	−	0.222574i	$-0.928554\pi$
$659$		−	1.27397e8i		−	0.445148i	0.974916	−	0.222574i	$-0.0714458\pi$
$660$	2.88859e7	−	1.06904e7i	0.100474	−	0.0371847i
$661$	1.80970e8			0.626617			0.313308	−	0.949651i	$-0.398563\pi$
$661$	1.80970e8			0.626617			0.313308	+	0.949651i	$0.398563\pi$
$662$		−	4.68868e8i		−	1.61613i
$663$	3.79715e8			1.30292
$664$	−2.36266e8			−0.807042
$665$	3.13737e8			1.06684
$666$			3.99056e7i			0.135086i
$667$		−	2.72569e8i		−	0.918540i
$668$		−	1.60296e6i		−	0.00537766i
$669$	6.77402e7			0.226239
$670$			1.29225e8i			0.429656i
$671$	−6.11540e7	−	1.65240e8i	−0.202422	−	0.546950i
$672$	−4.87878e7			−0.160769
$673$		−	5.71849e6i		−	0.0187601i	−0.999956	−	0.00938007i	$-0.997014\pi$
$673$		−	5.71849e6i		−	0.0187601i	0.999956	−	0.00938007i	$-0.00298581\pi$
$674$	2.93325e8			0.958008
$675$	7.71594e7			0.250887
$676$	−4.06426e7			−0.131565
$677$			1.06666e8i			0.343762i	0.985118	+	0.171881i	$0.0549845\pi$
$677$			1.06666e8i			0.343762i	−0.985118	+	0.171881i	$0.945016\pi$
$678$		−	5.07242e7i		−	0.162752i
$679$		−	2.99396e8i		−	0.956395i
$680$	−7.85893e8			−2.49940
$681$			2.76215e6i			0.00874593i
$682$	1.46990e8	+	3.97171e8i	0.463376	+	1.25206i
$683$	−2.34039e8			−0.734558			−0.367279	−	0.930111i	$-0.619711\pi$
$683$	−2.34039e8			−0.734558			−0.367279	+	0.930111i	$0.619711\pi$
$684$		−	8.00241e6i		−	0.0250065i
$685$	6.78279e7			0.211026
$686$	−2.38295e8			−0.738146
$687$	2.40044e8			0.740321
$688$		−	3.38046e8i		−	1.03803i
$689$			1.94071e8i			0.593340i
$690$			3.39365e8i			1.03304i
$691$	−2.00294e8			−0.607062			−0.303531	−	0.952822i	$-0.598166\pi$
$691$	−2.00294e8			−0.607062			−0.303531	+	0.952822i	$0.598166\pi$
$692$			1.44025e7i			0.0434631i
$693$	4.41078e7	+	1.19181e8i	0.132530	+	0.358101i
$694$	4.52714e8			1.35440
$695$			2.53984e8i			0.756574i
$696$	−1.49401e8			−0.443124
$697$	9.51530e8			2.81012
$698$	5.18569e8			1.52490
$699$			1.72618e8i			0.505422i
$700$		−	6.26233e7i		−	0.182575i
$701$			6.54620e8i			1.90036i	0.311706	+	0.950179i	$0.399100\pi$
$701$			6.54620e8i			1.90036i	−0.311706	+	0.950179i	$0.600900\pi$
$702$	−8.98749e7			−0.259793
$703$			9.22163e7i			0.265425i
$704$	3.56849e8	−	1.32067e8i	1.02274	−	0.378509i
$705$	−2.42840e8			−0.693031
$706$		−	8.66737e7i		−	0.246305i
$707$	−3.80024e8			−1.07536
$708$	−9.54767e6			−0.0269028
$709$	2.56170e8			0.718770			0.359385	−	0.933189i	$-0.382986\pi$
$709$	2.56170e8			0.718770			0.359385	+	0.933189i	$0.382986\pi$
$710$			2.43048e8i			0.679074i
$711$		−	3.60882e6i		−	0.0100405i
$712$			3.91688e8i			1.08518i
$713$	6.49939e8			1.79310
$714$		−	3.53241e8i		−	0.970457i
$715$	−2.77452e8	−	7.49683e8i	−0.759048	−	2.05097i
$716$	2.31062e7			0.0629491
$717$			1.29750e8i			0.352006i
$718$	−4.45450e8			−1.20344
$719$	3.13234e8			0.842718			0.421359	−	0.906894i	$-0.361553\pi$
$719$	3.13234e8			0.842718			0.421359	+	0.906894i	$0.361553\pi$
$720$	1.62926e8			0.436509
$721$			6.92158e8i			1.84671i
$722$		−	2.19846e8i		−	0.584128i
$723$		−	3.27659e8i		−	0.866977i
$724$	3.69133e7			0.0972675
$725$		−	3.62646e8i		−	0.951631i
$726$	−1.34748e8	−	1.57113e8i	−0.352139	−	0.410583i
$727$	−1.02043e8			−0.265570			−0.132785	−	0.991145i	$-0.542392\pi$
$727$	−1.02043e8			−0.265570			−0.132785	+	0.991145i	$0.542392\pi$
$728$			6.69572e8i			1.73542i
$729$	1.43489e7			0.0370370
$730$	−2.41524e8			−0.620858
$731$	−7.36051e8			−1.88433
$732$			1.61464e7i			0.0411663i
$733$			3.03024e7i			0.0769424i	0.999260	+	0.0384712i	$0.0122488\pi$
$733$			3.03024e7i			0.0769424i	−0.999260	+	0.0384712i	$0.987751\pi$
$734$			3.56635e8i			0.901853i
$735$	1.08631e8			0.273583
$736$		−	1.21951e8i		−	0.305880i
$737$	−1.13438e8	+	4.19825e7i	−0.283371	+	0.104873i
$738$	−2.25218e8			−0.560317
$739$			5.31715e8i			1.31749i	0.752368	+	0.658743i	$0.228912\pi$
$739$			5.31715e8i			1.31749i	−0.752368	+	0.658743i	$0.771088\pi$
$740$	3.25262e7			0.0802673
$741$	−2.07688e8			−0.510455
$742$	1.80540e8			0.441939
$743$		−	3.39376e8i		−	0.827397i	−0.910414	−	0.413699i	$-0.864237\pi$
$743$		−	3.39376e8i		−	0.827397i	0.910414	−	0.413699i	$-0.135763\pi$
$744$		−	3.56246e8i		−	0.865029i
$745$		−	5.41017e8i		−	1.30841i
$746$	−1.19678e7			−0.0288269
$747$		−	1.06650e8i		−	0.255858i
$748$	−2.78147e7	−	7.51561e7i	−0.0664614	−	0.179581i
$749$	−2.76896e7			−0.0658978
$750$			1.05167e8i			0.249285i
$751$	−3.64901e8			−0.861500			−0.430750	−	0.902471i	$-0.641751\pi$
$751$	−3.64901e8			−0.861500			−0.430750	+	0.902471i	$0.641751\pi$
$752$	−2.90179e8			−0.682358
$753$	−2.13051e8			−0.498999
$754$			4.22408e8i			0.985413i
$755$		−	7.51480e8i		−	1.74613i
$756$		−	1.16457e7i		−	0.0269526i
$757$	4.27946e7			0.0986511			0.0493255	−	0.998783i	$-0.484293\pi$
$757$	4.27946e7			0.0986511			0.0493255	+	0.998783i	$0.484293\pi$
$758$			2.07152e8i			0.475643i
$759$	−2.97906e8	+	1.10253e8i	−0.681325	+	0.252153i
$760$	4.29850e8			0.979211
$761$		−	2.37195e8i		−	0.538210i	−0.963111	−	0.269105i	$-0.913272\pi$
$761$		−	2.37195e8i		−	0.538210i	0.963111	−	0.269105i	$-0.0867278\pi$
$762$	−4.17303e7			−0.0943162
$763$	1.45259e7			0.0327016
$764$	6.96451e7			0.156175
$765$		−	3.54751e8i		−	0.792390i
$766$		−	1.01531e8i		−	0.225899i
$767$			2.47793e8i			0.549165i
$768$	−9.44314e7			−0.208465
$769$		−	6.28413e8i		−	1.38187i	−0.722919	−	0.690933i	$-0.757200\pi$
$769$		−	6.28413e8i		−	1.38187i	0.722919	−	0.690933i	$-0.242800\pi$
$770$	−6.97413e8	+	2.58107e8i	−1.52763	+	0.565363i
$771$	3.19402e8			0.696907
$772$			5.36077e7i			0.116513i
$773$	−3.36864e8			−0.729316			−0.364658	−	0.931142i	$-0.618814\pi$
$773$	−3.36864e8			−0.729316			−0.364658	+	0.931142i	$0.618814\pi$
$774$	1.74216e8			0.375721
$775$	8.64728e8			1.85769
$776$		−	4.10202e8i		−	0.877834i
$777$			1.34200e8i			0.286082i
$778$		−	4.81954e8i		−	1.02345i
$779$	−5.20447e8			−1.10094
$780$			7.32552e7i			0.154367i
$781$	−2.13356e8	+	7.89614e7i	−0.447870	+	0.165753i
$782$	8.82967e8			1.84639
$783$		−	6.74393e7i		−	0.140484i
$784$	1.29807e8			0.269370
$785$	−9.26379e8			−1.91505
$786$	−2.37934e8			−0.489992
$787$		−	7.97315e6i		−	0.0163571i	−0.999967	−	0.00817854i	$-0.997397\pi$
$787$		−	7.97315e6i		−	0.0163571i	0.999967	−	0.00817854i	$-0.00260334\pi$
$788$		−	5.50873e7i		−	0.112583i
$789$			2.34823e8i			0.478090i
$790$	2.11178e7			0.0428320
$791$		−	1.70582e8i		−	0.344671i
$792$	6.04319e7	+	1.63289e8i	0.121644	+	0.328686i
$793$	4.19051e8			0.840325
$794$		−	8.45886e8i		−	1.68986i
$795$	1.81312e8			0.360848
$796$	−7.22934e7			−0.143337
$797$	7.75045e8			1.53092			0.765459	−	0.643485i	$-0.222512\pi$
$797$	7.75045e8			1.53092			0.765459	+	0.643485i	$0.222512\pi$
$798$			1.93208e8i			0.380203i
$799$			6.31827e8i			1.23868i
$800$		−	1.62253e8i		−	0.316900i
$801$	−1.76807e8			−0.344035
$802$		−	4.99327e8i		−	0.967971i
$803$	−7.84664e7	−	2.12019e8i	−0.151543	−	0.409475i
$804$	1.10846e7			0.0213280
$805$			1.14126e9i			2.18775i
$806$	−1.00723e9			−1.92364
$807$	−1.25014e8			−0.237869
$808$	−5.20669e8			−0.987024
$809$			2.58198e8i			0.487648i	0.969819	+	0.243824i	$0.0784020\pi$
$809$			2.58198e8i			0.487648i	−0.969819	+	0.243824i	$0.921598\pi$
$810$			8.39660e7i			0.157997i
$811$			7.46227e8i			1.39897i	0.714648	+	0.699485i	$0.246587\pi$
$811$			7.46227e8i			1.39897i	−0.714648	+	0.699485i	$0.753413\pi$
$812$	−5.47343e7			−0.102233
$813$			2.98758e8i			0.555966i
$814$	−7.58650e7	−	2.04990e8i	−0.140659	−	0.380066i
$815$	1.02340e8			0.189048
$816$		−	4.23906e8i		−	0.780187i
$817$	4.02589e8			0.738237
$818$	4.98354e8			0.910496
$819$	−3.02244e8			−0.550181
$820$			1.83570e8i			0.332936i
$821$		−	8.45423e8i		−	1.52772i	−0.645380	−	0.763862i	$-0.723301\pi$
$821$		−	8.45423e8i		−	1.52772i	0.645380	−	0.763862i	$-0.276699\pi$
$822$			4.17702e7i			0.0752058i
$823$	−1.66846e8			−0.299307			−0.149654	−	0.988738i	$-0.547816\pi$
$823$	−1.66846e8			−0.299307			−0.149654	+	0.988738i	$0.547816\pi$
$824$			9.48323e8i			1.69502i
$825$	−3.96357e8	+	1.46689e8i	−0.705870	+	0.261237i
$826$	2.30516e8			0.409036
$827$			1.30992e8i			0.231594i	0.993273	+	0.115797i	$0.0369422\pi$
$827$			1.30992e8i			0.231594i	−0.993273	+	0.115797i	$0.963058\pi$
$828$	2.91098e7			0.0512801
$829$	2.68469e8			0.471228			0.235614	−	0.971847i	$-0.424290\pi$
$829$	2.68469e8			0.471228			0.235614	+	0.971847i	$0.424290\pi$
$830$	6.24087e8			1.09147
$831$			1.52509e8i			0.265762i
$832$			9.04975e8i			1.57133i
$833$		−	2.82638e8i		−	0.488985i
$834$	−1.56410e8			−0.269629
$835$			3.88668e7i			0.0667605i
$836$	1.52135e7	+	4.11072e7i	0.0260381	+	0.0703557i
$837$	1.60809e8			0.274241
$838$		−	3.17987e8i		−	0.540353i
$839$	8.26802e7			0.139996			0.0699980	−	0.997547i	$-0.477701\pi$
$839$	8.26802e7			0.139996			0.0699980	+	0.997547i	$0.477701\pi$
$840$	6.25551e8			1.05542
$841$	2.77862e8			0.467133
$842$			3.95486e8i			0.662514i
$843$			5.38838e8i			0.899446i
$844$			4.52770e6i			0.00753096i
$845$	9.85457e8			1.63331
$846$		−	1.49547e8i		−	0.246983i
$847$	−4.53151e8	−	5.28360e8i	−0.745749	−	0.869520i
$848$	2.16657e8			0.355291
$849$		−	6.72807e8i		−	1.09943i
$850$	1.17477e9			1.91291
$851$	−3.35449e8			−0.544300
$852$	2.08481e7			0.0337091
$853$		−	7.22695e8i		−	1.16442i	−0.813040	−	0.582208i	$-0.802189\pi$
$853$		−	7.22695e8i		−	1.16442i	0.813040	−	0.582208i	$-0.197811\pi$
$854$		−	3.89834e8i		−	0.625901i
$855$			1.94034e8i			0.310441i
$856$	−3.79374e7			−0.0604848
$857$			1.05821e9i			1.68123i	0.541632	+	0.840616i	$0.317807\pi$
$857$			1.05821e9i			1.68123i	−0.541632	+	0.840616i	$0.682193\pi$
$858$	4.61675e8	−	1.70862e8i	0.730928	−	0.270510i
$859$	−9.02566e8			−1.42397			−0.711983	−	0.702197i	$-0.752203\pi$
$859$	−9.02566e8			−1.42397			−0.711983	+	0.702197i	$0.752203\pi$
$860$		−	1.42000e8i		−	0.223251i
$861$	−7.57394e8			−1.18662
$862$	6.06144e8			0.946354
$863$	1.13650e9			1.76822			0.884111	−	0.467277i	$-0.154765\pi$
$863$	1.13650e9			1.76822			0.884111	+	0.467277i	$0.154765\pi$
$864$		−	3.01733e7i		−	0.0467822i
$865$		−	3.49217e8i		−	0.539569i
$866$			5.46095e8i			0.840842i
$867$	−5.46732e8			−0.838914
$868$		−	1.30514e8i		−	0.199571i
$869$	6.86076e6	+	1.85380e7i	0.0104547	+	0.0282490i
$870$	3.94637e8			0.599294
$871$		−	2.87681e8i		−	0.435368i
$872$	1.99019e7			0.0300154
$873$	1.85164e8			0.278301
$874$	−4.82946e8			−0.723376
$875$			3.53671e8i			0.527928i
$876$			2.07174e7i			0.0308193i
$877$			8.41294e8i			1.24724i	0.781729	+	0.623619i	$0.214338\pi$
$877$			8.41294e8i			1.24724i	−0.781729	+	0.623619i	$0.785662\pi$
$878$	−1.02757e9			−1.51819
$879$			7.14679e7i			0.105231i
$880$	−8.36929e8	+	3.09741e8i	−1.22812	+	0.454517i
$881$	−9.12634e6			−0.0133466			−0.00667328	−	0.999978i	$-0.502124\pi$
$881$	−9.12634e6			−0.0133466			−0.00667328	+	0.999978i	$0.502124\pi$
$882$			6.68976e7i			0.0975000i
$883$	−6.38007e8			−0.926709			−0.463354	−	0.886173i	$-0.653354\pi$
$883$	−6.38007e8			−0.926709			−0.463354	+	0.886173i	$0.653354\pi$
$884$	1.90597e8			0.275905
$885$	2.31502e8			0.333983
$886$		−	4.82881e7i		−	0.0694286i
$887$			7.18002e7i			0.102886i	0.998676	+	0.0514428i	$0.0163820\pi$
$887$			7.18002e7i			0.102886i	−0.998676	+	0.0514428i	$0.983618\pi$
$888$			1.83867e8i			0.262582i
$889$	−1.40336e8			−0.199740
$890$		−	1.03463e9i		−	1.46763i
$891$	−7.37083e7	+	2.72789e7i	−0.104204	+	0.0385650i
$892$	3.40020e7			0.0479082
$893$		−	3.45583e8i		−	0.485286i
$894$	3.33173e8			0.466291
$895$	−5.60255e8			−0.781477
$896$	6.41574e8			0.891914
$897$		−	7.55495e8i		−	1.04678i
$898$			2.59106e8i			0.357807i
$899$		−	7.55794e8i		−	1.04022i
$900$	3.87299e7			0.0531275
$901$		−	4.71742e8i		−	0.644956i
$902$	1.15691e9	−	4.28164e8i	1.57645	−	0.583432i
$903$	5.85878e8			0.795690
$904$		−	2.33714e8i		−	0.316359i
$905$	−8.95035e8			−1.20752
$906$	4.62781e8			0.622288
$907$	1.25100e9			1.67662			0.838310	−	0.545194i	$-0.183544\pi$
$907$	1.25100e9			1.67662			0.838310	+	0.545194i	$0.183544\pi$
$908$			1.38645e6i			0.00185203i
$909$		−	2.35029e8i		−	0.312918i
$910$		−	1.76865e9i		−	2.34703i
$911$	−6.41885e8			−0.848988			−0.424494	−	0.905431i	$-0.639548\pi$
$911$	−6.41885e8			−0.848988			−0.424494	+	0.905431i	$0.639548\pi$
$912$			2.31859e8i			0.305660i
$913$	2.02753e8	+	5.47846e8i	0.266413	+	0.719857i
$914$	2.78497e8			0.364739
$915$		−	3.91500e8i		−	0.511056i
$916$	1.20489e8			0.156770
$917$	−8.00158e8			−1.03769
$918$	2.18465e8			0.282393
$919$		−	7.46566e8i		−	0.961881i	−0.876753	−	0.480941i	$-0.840295\pi$
$919$		−	7.46566e8i		−	0.961881i	0.876753	−	0.480941i	$-0.159705\pi$
$920$			1.56364e9i			2.00804i
$921$			3.08193e8i			0.394497i
$922$	−1.14425e9			−1.45992
$923$		−	5.41075e8i		−	0.688101i
$924$	2.21398e7	+	5.98224e7i	0.0280645	+	0.0758312i
$925$	−4.46307e8			−0.563909
$926$			1.26541e9i			1.59367i
$927$	−4.28072e8			−0.537375
$928$	−1.41813e8			−0.177448
$929$	−1.30758e9			−1.63088			−0.815440	−	0.578842i	$-0.803505\pi$
$929$	−1.30758e9			−1.63088			−0.815440	+	0.578842i	$0.803505\pi$
$930$			9.41010e8i			1.16989i
$931$			1.54591e8i			0.191573i
$932$			8.66450e7i			0.107028i
$933$	4.33757e8			0.534074
$934$			1.15395e9i			1.41627i
$935$	6.74420e8	+	1.82230e9i	0.825079	+	2.22939i
$936$	−4.14103e8			−0.504988
$937$			9.43205e8i			1.14653i	0.819368	+	0.573267i	$0.194324\pi$
$937$			9.43205e8i			1.14653i	−0.819368	+	0.573267i	$0.805676\pi$
$938$	−2.67623e8			−0.324276
$939$	7.53905e8			0.910584
$940$	−1.21893e8			−0.146756
$941$		−	6.78047e8i		−	0.813750i	−0.913484	−	0.406875i	$-0.866619\pi$
$941$		−	6.78047e8i		−	0.813750i	0.913484	−	0.406875i	$-0.133381\pi$
$942$		−	5.70489e8i		−	0.682487i
$943$		−	1.89320e9i		−	2.25767i
$944$	2.76630e8			0.328840
$945$			2.82373e8i			0.334601i
$946$	−8.94923e8	+	3.31204e8i	−1.05709	+	0.391221i
$947$	−5.12929e8			−0.603959			−0.301980	−	0.953314i	$-0.597647\pi$
$947$	−5.12929e8			−0.603959			−0.301980	+	0.953314i	$0.597647\pi$
$948$		−	1.81144e6i		−	0.00212617i
$949$	5.37683e8			0.629111
$950$	−6.42548e8			−0.749436
$951$	−8.20050e8			−0.953452
$952$		−	1.62757e9i		−	1.88638i
$953$			6.46534e8i			0.746986i	0.927633	+	0.373493i	$0.121840\pi$
$953$			6.46534e8i			0.746986i	−0.927633	+	0.373493i	$0.878160\pi$
$954$			1.11657e8i			0.128600i
$955$	−1.68868e9			−1.93882
$956$			6.51276e7i			0.0745404i
$957$	1.28209e8	+	3.46426e8i	0.146280	+	0.395252i
$958$	−1.53650e9			−1.74758
$959$			1.40471e8i			0.159269i
$960$	8.45476e8			0.955625
$961$	9.14684e8			1.03063
$962$	5.19857e8			0.583927
$963$		−	1.71249e7i		−	0.0191756i
$964$		−	1.64468e8i		−	0.183590i
$965$		−	1.29982e9i		−	1.44645i
$966$	−7.02820e8			−0.779673
$967$		−	8.39502e7i		−	0.0928415i	−0.998922	−	0.0464207i	$-0.985219\pi$
$967$		−	8.39502e7i		−	0.0928415i	0.998922	−	0.0464207i	$-0.0147815\pi$
$968$	−6.20860e8	−	7.23904e8i	−0.684491	−	0.798096i
$969$	5.04842e8			0.554861
$970$			1.08353e9i			1.18721i
$971$	−4.03954e8			−0.441239			−0.220619	−	0.975360i	$-0.570808\pi$
$971$	−4.03954e8			−0.441239			−0.220619	+	0.975360i	$0.570808\pi$
$972$	7.20239e6			0.00784293
$973$	−5.25997e8			−0.571011
$974$			1.31658e8i			0.142486i
$975$		−	1.00517e9i		−	1.08449i
$976$		−	4.67819e8i		−	0.503186i
$977$	2.95938e8			0.317334			0.158667	−	0.987332i	$-0.449280\pi$
$977$	2.95938e8			0.317334			0.158667	+	0.987332i	$0.449280\pi$
$978$			6.30237e7i			0.0673732i
$979$	9.08235e8	−	3.36130e8i	0.967944	−	0.358228i
$980$	5.45268e7			0.0579338
$981$			8.98368e6i			0.00951584i
$982$	3.38109e8			0.357045
$983$	6.57801e7			0.0692522			0.0346261	−	0.999400i	$-0.488976\pi$
$983$	6.57801e7			0.0692522			0.0346261	+	0.999400i	$0.488976\pi$
$984$	−1.03770e9			−1.08915
$985$			1.33570e9i			1.39765i
$986$		−	1.02678e9i		−	1.07114i
$987$		−	5.02918e8i		−	0.523054i
$988$	−1.04249e8			−0.108093
$989$			1.46447e9i			1.51388i
$990$	−1.59629e8	−	4.31322e8i	−0.164515	−	0.444524i
$991$	7.89075e8			0.810769			0.405384	−	0.914146i	$-0.367138\pi$
$991$	7.89075e8			0.810769			0.405384	+	0.914146i	$0.367138\pi$
$992$		−	3.38153e8i		−	0.346400i
$993$	9.75171e8			0.995939
$994$	−5.03350e8			−0.512520
$995$	1.75289e9			1.77945
$996$		−	5.35326e7i		−	0.0541802i
$997$			5.45410e8i			0.550348i	0.961394	+	0.275174i	$0.0887355\pi$
$997$			5.45410e8i			0.550348i	−0.961394	+	0.275174i	$0.911264\pi$
$998$			7.66236e8i			0.770852i
$999$	−8.29973e7			−0.0832468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.c.a.10.3	✓	12
3.2	odd	2		99.7.c.d.10.10		12
4.3	odd	2		528.7.j.c.241.2		12
11.10	odd	2	inner	33.7.c.a.10.10	yes	12
33.32	even	2		99.7.c.d.10.3		12
44.43	even	2		528.7.j.c.241.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.c.a.10.3	✓	12	1.1	even	1	trivial
33.7.c.a.10.10	yes	12	11.10	odd	2	inner
99.7.c.d.10.3		12	33.32	even	2
99.7.c.d.10.10		12	3.2	odd	2
528.7.j.c.241.1		12	44.43	even	2
528.7.j.c.241.2		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)

\(f(q)\)	\(=\)	\(q-7.49503i q^{2} +15.5885 q^{3} +7.82458 q^{4} -189.722 q^{5} -116.836i q^{6} -392.912i q^{7} -538.327i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-7.49503i q^{2} +15.5885 q^{3} +7.82458 q^{4} -189.722 q^{5} -116.836i q^{6} -392.912i q^{7} -538.327i q^{8} +243.000 q^{9} +1421.97i q^{10} +(-1248.26 + 461.970i) q^{11} +121.973 q^{12} -3165.60i q^{13} -2944.89 q^{14} -2957.47 q^{15} -3534.00 q^{16} +7694.83i q^{17} -1821.29i q^{18} -4208.75i q^{19} -1484.50 q^{20} -6124.89i q^{21} +(3462.48 + 9355.72i) q^{22} +15309.9 q^{23} -8391.69i q^{24} +20369.5 q^{25} -23726.3 q^{26} +3788.00 q^{27} -3074.37i q^{28} -17803.4i q^{29} +22166.3i q^{30} +42452.2 q^{31} -7965.50i q^{32} +(-19458.4 + 7201.40i) q^{33} +57673.0 q^{34} +74544.1i q^{35} +1901.37 q^{36} -21910.6 q^{37} -31544.7 q^{38} -49346.8i q^{39} +102133. i q^{40} -123658. i q^{41} -45906.2 q^{42} +95655.3i q^{43} +(-9767.09 + 3614.72i) q^{44} -46102.5 q^{45} -114748. i q^{46} +82110.6 q^{47} -55089.6 q^{48} -36730.8 q^{49} -152670. i q^{50} +119951. i q^{51} -24769.5i q^{52} -61306.3 q^{53} -28391.1i q^{54} +(236822. - 87645.9i) q^{55} -211515. q^{56} -65607.9i q^{57} -133437. q^{58} -78276.8 q^{59} -23141.0 q^{60} +132377. i q^{61} -318180. i q^{62} -95477.6i q^{63} -285878. q^{64} +600584. i q^{65} +(53974.7 + 145841. i) q^{66} +90877.1 q^{67} +60208.9i q^{68} +238658. q^{69} +558710. q^{70} +170923. q^{71} -130813. i q^{72} +169852. i q^{73} +164221. i q^{74} +317528. q^{75} -32931.7i q^{76} +(181513. + 490455. i) q^{77} -369856. q^{78} -14851.1i q^{79} +670478. q^{80} +59049.0 q^{81} -926823. q^{82} -438889. i q^{83} -47924.7i q^{84} -1.45988e6i q^{85} +716939. q^{86} -277528. i q^{87} +(248691. + 671970. i) q^{88} -727603. q^{89} +345539. i q^{90} -1.24380e6 q^{91} +119794. q^{92} +661764. q^{93} -615421. i q^{94} +798493. i q^{95} -124170. i q^{96} +761993. q^{97} +275299. i q^{98} +(-303326. + 112259. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) \) 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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