LMFDB - Embedded newform 22.15.b.a.21.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,15,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	22.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$27.3523729934$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 38299509 x^{12} + 1255603312 x^{11} + 548839279225666 x^{10} + \cdots + 61\!\cdots\!00 $ x^14 - 2x^13 - 38299509x^12 + 1255603312x^11 + 548839279225666x^10 - 62614853719962708x^9 - 3647746096331338780406x^8 + 909709401522475794317032x^7 + 11341528896592004854718535645x^6 - 4608641836922062401823748151666x^5 - 14199433672677462467950659880576257x^4 + 7648786246750765008517429480227297240x^3 + 5468207905418692926727112276614665574080x^2 - 3973529610997293170696151713639263984312200*x + 613220922939245616829253347741252697812260300
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{6}\cdot 11^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.9
Root			$2199.62 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.15.b.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+90.5097i q^{2} -1885.62 q^{3} -8192.00 q^{4} +124487. q^{5} -170667. i q^{6} -166636. i q^{7} -741455. i q^{8} -1.22739e6 q^{9} +O(q^{10})$	\(q+90.5097i q^{2} -1885.62 q^{3} -8192.00 q^{4} +124487. q^{5} -170667. i q^{6} -166636. i q^{7} -741455. i q^{8} -1.22739e6 q^{9} +1.12672e7i q^{10} +(-1.92714e7 + 2.89160e6i) q^{11} +1.54470e7 q^{12} +1.04219e8i q^{13} +1.50821e7 q^{14} -2.34735e8 q^{15} +6.71089e7 q^{16} -6.64437e8i q^{17} -1.11091e8i q^{18} -3.30004e8i q^{19} -1.01979e9 q^{20} +3.14212e8i q^{21} +(-2.61717e8 - 1.74425e9i) q^{22} -2.67783e9 q^{23} +1.39811e9i q^{24} +9.39342e9 q^{25} -9.43278e9 q^{26} +1.13333e10 q^{27} +1.36508e9i q^{28} -2.62721e10i q^{29} -2.12458e10i q^{30} -1.16205e10 q^{31} +6.07400e9i q^{32} +(3.63387e10 - 5.45246e9i) q^{33} +6.01379e10 q^{34} -2.07439e10i q^{35} +1.00548e10 q^{36} -9.20022e10 q^{37} +2.98685e10 q^{38} -1.96517e11i q^{39} -9.23013e10i q^{40} -1.38594e11i q^{41} -2.84393e10 q^{42} -3.30567e11i q^{43} +(1.57872e11 - 2.36880e10i) q^{44} -1.52794e11 q^{45} -2.42369e11i q^{46} -6.93012e11 q^{47} -1.26542e11 q^{48} +6.50456e11 q^{49} +8.50195e11i q^{50} +1.25288e12i q^{51} -8.53758e11i q^{52} +1.16505e12 q^{53} +1.02577e12i q^{54} +(-2.39904e12 + 3.59965e11i) q^{55} -1.23553e11 q^{56} +6.22263e11i q^{57} +2.37788e12 q^{58} -1.87331e10 q^{59} +1.92295e12 q^{60} -4.90504e12i q^{61} -1.05177e12i q^{62} +2.04527e11i q^{63} -5.49756e11 q^{64} +1.29738e13i q^{65} +(4.93501e11 + 3.28900e12i) q^{66} -4.98130e12 q^{67} +5.44307e12i q^{68} +5.04938e12 q^{69} +1.87753e12 q^{70} -1.21737e13 q^{71} +9.10055e11i q^{72} +7.76078e12i q^{73} -8.32709e12i q^{74} -1.77125e13 q^{75} +2.70339e12i q^{76} +(4.81843e11 + 3.21131e12i) q^{77} +1.77867e13 q^{78} -2.28669e13i q^{79} +8.35416e12 q^{80} -1.54997e13 q^{81} +1.25441e13 q^{82} -1.80711e13i q^{83} -2.57403e12i q^{84} -8.27135e13i q^{85} +2.99195e13 q^{86} +4.95392e13i q^{87} +(2.14399e12 + 1.42889e13i) q^{88} -3.47798e13 q^{89} -1.38293e13i q^{90} +1.73665e13 q^{91} +2.19368e13 q^{92} +2.19120e13 q^{93} -6.27243e13i q^{94} -4.10811e13i q^{95} -1.14533e13i q^{96} +6.06667e13 q^{97} +5.88725e13i q^{98} +(2.36536e13 - 3.54911e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) $ 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

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

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 $

$2$			90.5097i			0.707107i
$2$			90.5097i			0.707107i
$3$	−1885.62			−0.862197			−0.431098	−	0.902305i	$-0.641874\pi$
$3$	−1885.62			−0.862197			−0.431098	+	0.902305i	$0.641874\pi$
$4$	−8192.00			−0.500000
$5$	124487.			1.59343			0.796715	−	0.604355i	$-0.206569\pi$
$5$	124487.			1.59343			0.796715	+	0.604355i	$0.206569\pi$
$6$		−	170667.i		−	0.609665i
$7$		−	166636.i		−	0.202340i	−0.994869	−	0.101170i	$-0.967741\pi$
$7$		−	166636.i		−	0.202340i	0.994869	−	0.101170i	$-0.0322586\pi$
$8$		−	741455.i		−	0.353553i
$9$	−1.22739e6			−0.256617
$10$			1.12672e7i			1.12672i
$11$	−1.92714e7	+	2.89160e6i	−0.988930	+	0.148385i
$11$	−1.92714e7	+	2.89160e6i	−0.988930	+	0.148385i
$12$	1.54470e7			0.431098
$13$			1.04219e8i			1.66089i	0.557099	+	0.830446i	$0.311914\pi$
$13$			1.04219e8i			1.66089i	−0.557099	+	0.830446i	$0.688086\pi$
$14$	1.50821e7			0.143076
$15$	−2.34735e8			−1.37385
$16$	6.71089e7			0.250000
$17$		−	6.64437e8i		−	1.61924i	−0.586955	−	0.809620i	$-0.699673\pi$
$17$		−	6.64437e8i		−	1.61924i	0.586955	−	0.809620i	$-0.300327\pi$
$18$		−	1.11091e8i		−	0.181455i
$19$		−	3.30004e8i		−	0.369185i	−0.982815	−	0.184592i	$-0.940903\pi$
$19$		−	3.30004e8i		−	0.369185i	0.982815	−	0.184592i	$-0.0590965\pi$
$20$	−1.01979e9			−0.796715
$21$			3.14212e8i			0.174457i
$22$	−2.61717e8	−	1.74425e9i	−0.104924	−	0.699279i
$23$	−2.67783e9			−0.786480			−0.393240	−	0.919436i	$-0.628646\pi$
$23$	−2.67783e9			−0.786480			−0.393240	+	0.919436i	$0.628646\pi$
$24$			1.39811e9i			0.304833i
$25$	9.39342e9			1.53902
$26$	−9.43278e9			−1.17443
$27$	1.13333e10			1.08345
$28$			1.36508e9i			0.101170i
$29$		−	2.62721e10i		−	1.52303i	−0.648148	−	0.761515i	$-0.724456\pi$
$29$		−	2.62721e10i		−	1.52303i	0.648148	−	0.761515i	$-0.275544\pi$
$30$		−	2.12458e10i		−	0.971459i
$31$	−1.16205e10			−0.422371			−0.211186	−	0.977446i	$-0.567732\pi$
$31$	−1.16205e10			−0.422371			−0.211186	+	0.977446i	$0.567732\pi$
$32$			6.07400e9i			0.176777i
$33$	3.63387e10	−	5.45246e9i	0.852652	−	0.127937i
$34$	6.01379e10			1.14498
$35$		−	2.07439e10i		−	0.322415i
$36$	1.00548e10			0.128308
$37$	−9.20022e10			−0.969140			−0.484570	−	0.874753i	$-0.661024\pi$
$37$	−9.20022e10			−0.969140			−0.484570	+	0.874753i	$0.661024\pi$
$38$	2.98685e10			0.261053
$39$		−	1.96517e11i		−	1.43202i
$40$		−	9.23013e10i		−	0.563362i
$41$		−	1.38594e11i		−	0.711633i	−0.934556	−	0.355817i	$-0.884203\pi$
$41$		−	1.38594e11i		−	0.711633i	0.934556	−	0.355817i	$-0.115797\pi$
$42$	−2.84393e10			−0.123360
$43$		−	3.30567e11i		−	1.21613i	−0.793886	−	0.608066i	$-0.791946\pi$
$43$		−	3.30567e11i		−	1.21613i	0.793886	−	0.608066i	$-0.208054\pi$
$44$	1.57872e11	−	2.36880e10i	0.494465	−	0.0741923i
$45$	−1.52794e11			−0.408901
$46$		−	2.42369e11i		−	0.556125i
$47$	−6.93012e11			−1.36790			−0.683952	−	0.729527i	$-0.739740\pi$
$47$	−6.93012e11			−1.36790			−0.683952	+	0.729527i	$0.739740\pi$
$48$	−1.26542e11			−0.215549
$49$	6.50456e11			0.959058
$50$			8.50195e11i			1.08825i
$51$			1.25288e12i			1.39610i
$52$		−	8.53758e11i		−	0.830446i
$53$	1.16505e12			0.991777			0.495889	−	0.868386i	$-0.334842\pi$
$53$	1.16505e12			0.991777			0.495889	+	0.868386i	$0.334842\pi$
$54$			1.02577e12i			0.766115i
$55$	−2.39904e12	+	3.59965e11i	−1.57579	+	0.236440i
$56$	−1.23553e11			−0.0715380
$57$			6.22263e11i			0.318310i
$58$	2.37788e12			1.07694
$59$	−1.87331e10			−0.00752741			−0.00376371	−	0.999993i	$-0.501198\pi$
$59$	−1.87331e10			−0.00752741			−0.00376371	+	0.999993i	$0.501198\pi$
$60$	1.92295e12			0.686925
$61$		−	4.90504e12i		−	1.56075i	−0.625311	−	0.780376i	$-0.715028\pi$
$61$		−	4.90504e12i		−	1.56075i	0.625311	−	0.780376i	$-0.284972\pi$
$62$		−	1.05177e12i		−	0.298662i
$63$			2.04527e11i			0.0519239i
$64$	−5.49756e11			−0.125000
$65$			1.29738e13i			2.64651i
$66$	4.93501e11	+	3.28900e12i	0.0904649	+	0.602916i
$67$	−4.98130e12			−0.821901			−0.410950	−	0.911658i	$-0.634803\pi$
$67$	−4.98130e12			−0.821901			−0.410950	+	0.911658i	$0.634803\pi$
$68$			5.44307e12i			0.809620i
$69$	5.04938e12			0.678100
$70$	1.87753e12			0.227982
$71$	−1.21737e13			−1.33849			−0.669243	−	0.743044i	$-0.733381\pi$
$71$	−1.21737e13			−1.33849			−0.669243	+	0.743044i	$0.733381\pi$
$72$			9.10055e11i			0.0907277i
$73$			7.76078e12i			0.702498i	0.936282	+	0.351249i	$0.114243\pi$
$73$			7.76078e12i			0.702498i	−0.936282	+	0.351249i	$0.885757\pi$
$74$		−	8.32709e12i		−	0.685285i
$75$	−1.77125e13			−1.32694
$76$			2.70339e12i			0.184592i
$77$	4.81843e11	+	3.21131e12i	0.0300242	+	0.200100i
$78$	1.77867e13			1.01259
$79$		−	2.28669e13i		−	1.19074i	−0.803451	−	0.595371i	$-0.797005\pi$
$79$		−	2.28669e13i		−	1.19074i	0.803451	−	0.595371i	$-0.202995\pi$
$80$	8.35416e12			0.398357
$81$	−1.54997e13			−0.677531
$82$	1.25441e13			0.503201
$83$		−	1.80711e13i		−	0.665944i	−0.942937	−	0.332972i	$-0.891948\pi$
$83$		−	1.80711e13i		−	0.665944i	0.942937	−	0.332972i	$-0.108052\pi$
$84$		−	2.57403e12i		−	0.0872285i
$85$		−	8.27135e13i		−	2.58014i
$86$	2.99195e13			0.859935
$87$			4.95392e13i			1.31315i
$88$	2.14399e12	+	1.42889e13i	0.0524619	+	0.349639i
$89$	−3.47798e13			−0.786315			−0.393158	−	0.919471i	$-0.628617\pi$
$89$	−3.47798e13			−0.786315			−0.393158	+	0.919471i	$0.628617\pi$
$90$		−	1.38293e13i		−	0.289136i
$91$	1.73665e13			0.336065
$92$	2.19368e13			0.393240
$93$	2.19120e13			0.364167
$94$		−	6.27243e13i		−	0.967255i
$95$		−	4.10811e13i		−	0.588270i
$96$		−	1.14533e13i		−	0.152416i
$97$	6.06667e13			0.750841			0.375421	−	0.926855i	$-0.377498\pi$
$97$	6.06667e13			0.750841			0.375421	+	0.926855i	$0.377498\pi$
$98$			5.88725e13i			0.678157i
$99$	2.36536e13	−	3.54911e12i	0.253776	−	0.0380780i
$100$	−7.69509e13			−0.769509
$101$		−	1.52333e13i		−	0.142083i	−0.997473	−	0.0710417i	$-0.977368\pi$
$101$		−	1.52333e13i		−	0.142083i	0.997473	−	0.0710417i	$-0.0226323\pi$
$102$	−1.13398e14			−0.987194
$103$	−3.45051e13			−0.280558			−0.140279	−	0.990112i	$-0.544800\pi$
$103$	−3.45051e13			−0.280558			−0.140279	+	0.990112i	$0.544800\pi$
$104$	7.72734e13			0.587214
$105$			3.91153e13i			0.277985i
$106$			1.05448e14i			0.701292i
$107$		−	2.25481e13i		−	0.140418i	−0.997532	−	0.0702092i	$-0.977633\pi$
$107$		−	2.25481e13i		−	0.140418i	0.997532	−	0.0702092i	$-0.0223667\pi$
$108$	−9.28422e13			−0.541725
$109$			2.93923e14i			1.60786i	0.594724	+	0.803930i	$0.297261\pi$
$109$			2.93923e14i			1.60786i	−0.594724	+	0.803930i	$0.702739\pi$
$110$	−3.25803e13	−	2.17136e14i	−0.167189	−	1.11425i
$111$	1.73482e14			0.835589
$112$		−	1.11827e13i		−	0.0505850i
$113$	−1.09613e14			−0.465921			−0.232961	−	0.972486i	$-0.574841\pi$
$113$	−1.09613e14			−0.465921			−0.232961	+	0.972486i	$0.574841\pi$
$114$	−5.63208e13			−0.225079
$115$	−3.33354e14			−1.25320
$116$			2.15221e14i			0.761515i
$117$		−	1.27917e14i		−	0.426213i
$118$		−	1.69553e12i		−	0.00532268i
$119$	−1.10719e14			−0.327637
$120$			1.74046e14i			0.485729i
$121$	3.63027e14	−	1.11450e14i	0.955964	−	0.293484i
$122$	4.43954e14			1.10362
$123$			2.61336e14i			0.613568i
$124$	9.51955e13			0.211186
$125$	4.09549e14			0.858887
$126$	−1.85117e13			−0.0367157
$127$			9.88479e14i			1.85499i	0.373836	+	0.927495i	$0.378042\pi$
$127$			9.88479e14i			1.85499i	−0.373836	+	0.927495i	$0.621958\pi$
$128$		−	4.97582e13i		−	0.0883883i
$129$			6.23326e14i			1.04855i
$130$	−1.17426e15			−1.87137
$131$		−	5.83135e14i		−	0.880785i	−0.897805	−	0.440393i	$-0.854839\pi$
$131$		−	5.83135e14i		−	0.880785i	0.897805	−	0.440393i	$-0.145161\pi$
$132$	−2.97687e14	+	4.46666e13i	−0.426326	+	0.0639684i
$133$	−5.49905e13			−0.0747009
$134$		−	4.50856e14i		−	0.581172i
$135$	1.41084e15			1.72640
$136$	−4.92650e14			−0.572488
$137$	−4.15195e13			−0.0458361			−0.0229181	−	0.999737i	$-0.507296\pi$
$137$	−4.15195e13			−0.0458361			−0.0229181	+	0.999737i	$0.507296\pi$
$138$			4.57017e14i			0.479489i
$139$		−	2.39351e14i		−	0.238744i	−0.992850	−	0.119372i	$-0.961912\pi$
$139$		−	2.39351e14i		−	0.238744i	0.992850	−	0.119372i	$-0.0380881\pi$
$140$			1.69934e14i			0.161207i
$141$	1.30676e15			1.17940
$142$		−	1.10184e15i		−	0.946452i
$143$	−3.01358e14	−	2.00844e15i	−0.246451	−	1.64251i
$144$	−8.23687e13			−0.0641542
$145$		−	3.27052e15i		−	2.42684i
$146$	−7.02426e14			−0.496741
$147$	−1.22651e15			−0.826897
$148$	7.53682e14			0.484570
$149$			1.60095e15i			0.981917i	0.871183	+	0.490959i	$0.163353\pi$
$149$			1.60095e15i			0.981917i	−0.871183	+	0.490959i	$0.836647\pi$
$150$		−	1.60315e15i		−	0.938286i
$151$		−	9.06471e13i		−	0.0506425i	−0.999679	−	0.0253213i	$-0.991939\pi$
$151$		−	9.06471e13i		−	0.0506425i	0.999679	−	0.0253213i	$-0.00806087\pi$
$152$	−2.44683e14			−0.130527
$153$			8.15523e14i			0.415524i
$154$	−2.90655e14	+	4.36115e13i	−0.141492	+	0.0212303i
$155$	−1.44660e15			−0.673019
$156$			1.60987e15i			0.716008i
$157$	−2.69665e14			−0.114690			−0.0573451	−	0.998354i	$-0.518264\pi$
$157$	−2.69665e14			−0.114690			−0.0573451	+	0.998354i	$0.518264\pi$
$158$	2.06968e15			0.841982
$159$	−2.19685e15			−0.855107
$160$			7.56132e14i			0.281681i
$161$			4.46222e14i			0.159136i
$162$		−	1.40288e15i		−	0.479087i
$163$	1.04441e15			0.341632			0.170816	−	0.985303i	$-0.445360\pi$
$163$	1.04441e15			0.341632			0.170816	+	0.985303i	$0.445360\pi$
$164$			1.13536e15i			0.355817i
$165$	4.52368e15	−	6.78759e14i	1.35864	−	0.203858i
$166$	1.63561e15			0.470894
$167$			1.12290e15i			0.309976i	0.987916	+	0.154988i	$0.0495338\pi$
$167$			1.12290e15i			0.309976i	−0.987916	+	0.154988i	$0.950466\pi$
$168$	2.32974e14			0.0616799
$169$	−6.92412e15			−1.75856
$170$	7.48637e15			1.82444
$171$			4.05043e14i			0.0947390i
$172$			2.70801e15i			0.608066i
$173$			9.12620e14i			0.196774i	0.995148	+	0.0983869i	$0.0313683\pi$
$173$			9.12620e14i			0.196774i	−0.995148	+	0.0983869i	$0.968632\pi$
$174$	−4.48378e15			−0.928538
$175$		−	1.56528e15i		−	0.311405i
$176$	−1.29328e15	+	1.94052e14i	−0.247232	+	0.0370961i
$177$	3.53236e13			0.00649011
$178$		−	3.14791e15i		−	0.556009i
$179$	1.03136e16			1.75161			0.875807	−	0.482661i	$-0.160330\pi$
$179$	1.03136e16			1.75161			0.875807	+	0.482661i	$0.160330\pi$
$180$	1.25169e15			0.204450
$181$	−8.98419e15			−1.41166			−0.705828	−	0.708384i	$-0.749425\pi$
$181$	−8.98419e15			−1.41166			−0.705828	+	0.708384i	$0.749425\pi$
$182$			1.57184e15i			0.237634i
$183$			9.24907e15i			1.34568i
$184$			1.98549e15i			0.278063i
$185$	−1.14531e16			−1.54426
$186$			1.98325e15i			0.257505i
$187$	1.92128e15	+	1.28047e16i	0.240270	+	1.60131i
$188$	5.67716e15			0.683952
$189$		−	1.88853e15i		−	0.219226i
$190$	3.71824e15			0.415970
$191$	−8.32303e15			−0.897528			−0.448764	−	0.893650i	$-0.648136\pi$
$191$	−8.32303e15			−0.897528			−0.448764	+	0.893650i	$0.648136\pi$
$192$	1.03663e15			0.107775
$193$			2.03873e15i			0.204390i	0.994764	+	0.102195i	$0.0325865\pi$
$193$			2.03873e15i			0.204390i	−0.994764	+	0.102195i	$0.967413\pi$
$194$			5.49092e15i			0.530925i
$195$		−	2.44637e16i		−	2.28182i
$196$	−5.32853e15			−0.479529
$197$			7.92927e15i			0.688605i	0.938859	+	0.344302i	$0.111884\pi$
$197$			7.92927e15i			0.688605i	−0.938859	+	0.344302i	$0.888116\pi$
$198$	3.21229e14	+	2.14088e15i	0.0269252	+	0.179447i
$199$	−5.90781e15			−0.478030			−0.239015	−	0.971016i	$-0.576825\pi$
$199$	−5.90781e15			−0.478030			−0.239015	+	0.971016i	$0.576825\pi$
$200$		−	6.96480e15i		−	0.544125i
$201$	9.39287e15			0.708640
$202$	1.37876e15			0.100468
$203$	−4.37787e15			−0.308170
$204$		−	1.02636e16i		−	0.698052i
$205$		−	1.72531e16i		−	1.13394i
$206$		−	3.12305e15i		−	0.198385i
$207$	3.28674e15			0.201824
$208$			6.99399e15i			0.415223i
$209$	9.54238e14	+	6.35965e15i	0.0547813	+	0.365098i
$210$	−3.54031e15			−0.196565
$211$			2.97179e16i			1.59603i	0.602639	+	0.798014i	$0.294116\pi$
$211$			2.97179e16i			1.59603i	−0.602639	+	0.798014i	$0.705884\pi$
$212$	−9.54411e15			−0.495889
$213$	2.29550e16			1.15404
$214$	2.04082e15			0.0992907
$215$		−	4.11512e16i		−	1.93782i
$216$		−	8.40312e15i		−	0.383058i
$217$			1.93640e15i			0.0854627i
$218$	−2.66029e16			−1.13693
$219$		−	1.46339e16i		−	0.605692i
$220$	1.96529e16	−	2.94883e15i	0.787895	−	0.118220i
$221$	6.92466e16			2.68938
$222$			1.57018e16i			0.590851i
$223$	−2.07626e16			−0.757092			−0.378546	−	0.925583i	$-0.623576\pi$
$223$	−2.07626e16			−0.757092			−0.378546	+	0.925583i	$0.623576\pi$
$224$	1.01215e15			0.0357690
$225$	−1.15294e16			−0.394938
$226$		−	9.92103e15i		−	0.329456i
$227$		−	2.78540e16i		−	0.896824i	−0.893827	−	0.448412i	$-0.851990\pi$
$227$		−	2.78540e16i		−	0.896824i	0.893827	−	0.448412i	$-0.148010\pi$
$228$		−	5.09758e15i		−	0.159155i
$229$	2.83051e16			0.857069			0.428534	−	0.903525i	$-0.359030\pi$
$229$	2.83051e16			0.857069			0.428534	+	0.903525i	$0.359030\pi$
$230$		−	3.01717e16i		−	0.886146i
$231$	−9.08575e14	−	6.05533e15i	−0.0258867	−	0.172526i
$232$	−1.94796e16			−0.538472
$233$		−	3.75050e16i		−	1.00600i	−0.864287	−	0.503000i	$-0.832230\pi$
$233$		−	3.75050e16i		−	1.00600i	0.864287	−	0.503000i	$-0.167770\pi$
$234$	1.15777e16			0.301378
$235$	−8.62708e16			−2.17966
$236$	1.53462e14			0.00376371
$237$			4.31184e16i			1.02665i
$238$		−	1.00211e16i		−	0.231674i
$239$			6.23113e16i			1.39888i	0.714690	+	0.699442i	$0.246568\pi$
$239$			6.23113e16i			1.39888i	−0.714690	+	0.699442i	$0.753432\pi$
$240$	−1.57528e16			−0.343462
$241$			1.07519e16i			0.227702i	0.993498	+	0.113851i	$0.0363187\pi$
$241$			1.07519e16i			0.227702i	−0.993498	+	0.113851i	$0.963681\pi$
$242$	1.00873e16	+	3.28575e16i	0.207524	+	0.675969i
$243$	−2.49800e16			−0.499286
$244$			4.01821e16i			0.780376i
$245$	8.09731e16			1.52819
$246$	−2.36534e16			−0.433858
$247$	3.43925e16			0.613176
$248$			8.61611e15i			0.149331i
$249$			3.40753e16i			0.574175i
$250$			3.70682e16i			0.607325i
$251$	−9.47898e16			−1.51024			−0.755119	−	0.655587i	$-0.772421\pi$
$251$	−9.47898e16			−1.51024			−0.755119	+	0.655587i	$0.772421\pi$
$252$		−	1.67549e15i		−	0.0259619i
$253$	5.16056e16	−	7.74319e15i	0.777773	−	0.116701i
$254$	−8.94669e16			−1.31168
$255$			1.55967e17i			2.22459i
$256$	4.50360e15			0.0625000
$257$	−1.66999e16			−0.225519			−0.112759	−	0.993622i	$-0.535969\pi$
$257$	−1.66999e16			−0.225519			−0.112759	+	0.993622i	$0.535969\pi$
$258$	−5.64170e16			−0.741433
$259$			1.53309e16i			0.196096i
$260$		−	1.06282e17i		−	1.32326i
$261$			3.22461e16i			0.390835i
$262$	5.27794e16			0.622809
$263$		−	1.45655e17i		−	1.67353i	−0.547560	−	0.836767i	$-0.684443\pi$
$263$		−	1.45655e17i		−	1.67353i	0.547560	−	0.836767i	$-0.315557\pi$
$264$	−4.04276e15	−	2.69435e16i	−0.0452325	−	0.301458i
$265$	1.45033e17			1.58033
$266$		−	4.97717e15i		−	0.0528215i
$267$	6.55816e16			0.677959
$268$	4.08068e16			0.410950
$269$	6.45305e16			0.633139			0.316570	−	0.948569i	$-0.397469\pi$
$269$	6.45305e16			0.633139			0.316570	+	0.948569i	$0.397469\pi$
$270$			1.27695e17i			1.22075i
$271$		−	1.40774e17i		−	1.31141i	−0.755018	−	0.655704i	$-0.772372\pi$
$271$		−	1.40774e17i		−	1.31141i	0.755018	−	0.655704i	$-0.227628\pi$
$272$		−	4.45896e16i		−	0.404810i
$273$	−3.27468e16			−0.289754
$274$		−	3.75791e15i		−	0.0324110i
$275$	−1.81025e17	+	2.71620e16i	−1.52198	+	0.228366i
$276$	−4.13645e16			−0.339050
$277$			4.18922e16i			0.334792i	0.985890	+	0.167396i	$0.0535358\pi$
$277$			4.18922e16i			0.334792i	−0.985890	+	0.167396i	$0.946464\pi$
$278$	2.16636e16			0.168817
$279$	1.42629e16			0.108388
$280$	−1.53807e16			−0.113991
$281$			9.46066e16i			0.683876i	0.939723	+	0.341938i	$0.111083\pi$
$281$			9.46066e16i			0.683876i	−0.939723	+	0.341938i	$0.888917\pi$
$282$			1.18274e17i			0.833964i
$283$			2.54488e16i			0.175050i	0.996162	+	0.0875252i	$0.0278958\pi$
$283$			2.54488e16i			0.175050i	−0.996162	+	0.0875252i	$0.972104\pi$
$284$	9.97268e16			0.669243
$285$			7.74635e16i			0.507205i
$286$	1.81783e17	−	2.72758e16i	1.16143	−	0.174267i
$287$	−2.30947e16			−0.143992
$288$		−	7.45517e15i		−	0.0453639i
$289$	−2.73098e17			−1.62194
$290$	2.96014e17			1.71603
$291$	−1.14395e17			−0.647373
$292$		−	6.35763e16i		−	0.351249i
$293$		−	3.18695e17i		−	1.71911i	−0.511047	−	0.859553i	$-0.670742\pi$
$293$		−	3.18695e17i		−	1.71911i	0.511047	−	0.859553i	$-0.329258\pi$
$294$		−	1.11011e17i		−	0.584705i
$295$	−2.33202e15			−0.0119944
$296$			6.82155e16i			0.342643i
$297$	−2.18409e17	+	3.27713e16i	−1.07146	+	0.160767i
$298$	−1.44902e17			−0.694321
$299$		−	2.79079e17i		−	1.30626i
$300$	1.45100e17			0.663468
$301$	−5.50843e16			−0.246072
$302$	8.20444e15			0.0358097
$303$			2.87242e16i			0.122504i
$304$		−	2.21462e16i		−	0.0922962i
$305$		−	6.10612e17i		−	2.48695i
$306$	−7.38127e16			−0.293820
$307$			5.67968e16i			0.220981i	0.993877	+	0.110491i	$0.0352422\pi$
$307$			5.67968e16i			0.220981i	−0.993877	+	0.110491i	$0.964758\pi$
$308$	−3.94726e15	−	2.63071e16i	−0.0150121	−	0.100050i
$309$	6.50637e16			0.241896
$310$		−	1.30932e17i		−	0.475896i
$311$	−1.84712e17			−0.656407			−0.328204	−	0.944607i	$-0.606443\pi$
$311$	−1.84712e17			−0.656407			−0.328204	+	0.944607i	$0.606443\pi$
$312$	−1.45709e17			−0.506294
$313$	4.03054e17			1.36947			0.684736	−	0.728791i	$-0.259917\pi$
$313$	4.03054e17			1.36947			0.684736	+	0.728791i	$0.259917\pi$
$314$		−	2.44072e16i		−	0.0810982i
$315$			2.54609e16i			0.0827370i
$316$			1.87326e17i			0.595371i
$317$	3.42160e17			1.06369			0.531844	−	0.846842i	$-0.321499\pi$
$317$	3.42160e17			1.06369			0.531844	+	0.846842i	$0.321499\pi$
$318$		−	1.98836e17i		−	0.604652i
$319$	7.59682e16	+	5.06301e17i	0.225994	+	1.50617i
$320$	−6.84373e16			−0.199179
$321$			4.25173e16i			0.121068i
$322$	−4.03874e16			−0.112526
$323$	−2.19267e17			−0.597799
$324$	1.26974e17			0.338766
$325$			9.78968e17i			2.55614i
$326$			9.45295e16i			0.241571i
$327$		−	5.54229e17i		−	1.38629i
$328$	−1.02761e17			−0.251600
$329$			1.15481e17i			0.276782i
$330$	6.14343e16	+	4.09437e17i	0.144149	+	0.960704i
$331$	2.77834e17			0.638248			0.319124	−	0.947713i	$-0.396611\pi$
$331$	2.77834e17			0.638248			0.319124	+	0.947713i	$0.396611\pi$
$332$			1.48038e17i			0.332972i
$333$	1.12923e17			0.248697
$334$	−1.01634e17			−0.219186
$335$	−6.20106e17			−1.30964
$336$			2.10864e16i			0.0436142i
$337$			5.13728e17i			1.04070i	0.853955	+	0.520348i	$0.174198\pi$
$337$			5.13728e17i			1.04070i	−0.853955	+	0.520348i	$0.825802\pi$
$338$		−	6.26700e17i		−	1.24349i
$339$	2.06689e17			0.401716
$340$			6.77589e17i			1.29007i
$341$	2.23945e17	−	3.36019e16i	0.417696	−	0.0626734i
$342$	−3.66603e16			−0.0669906
$343$		−	2.21405e17i		−	0.396396i
$344$	−2.45101e17			−0.429968
$345$	6.28580e17			1.08051
$346$	−8.26010e16			−0.139140
$347$			4.28496e17i			0.707359i	0.935367	+	0.353680i	$0.115070\pi$
$347$			4.28496e17i			0.707359i	−0.935367	+	0.353680i	$0.884930\pi$
$348$		−	4.05825e17i		−	0.656575i
$349$		−	4.90107e17i		−	0.777164i	−0.921414	−	0.388582i	$-0.872965\pi$
$349$		−	4.90107e17i		−	0.777164i	0.921414	−	0.388582i	$-0.127035\pi$
$350$	1.41673e17			0.220197
$351$			1.18114e18i			1.79950i
$352$	−1.75636e16	−	1.17055e17i	−0.0262309	−	0.174820i
$353$	−1.08883e17			−0.159418			−0.0797089	−	0.996818i	$-0.525399\pi$
$353$	−1.08883e17			−0.159418			−0.0797089	+	0.996818i	$0.525399\pi$
$354$			3.19713e15i			0.00458920i
$355$	−1.51546e18			−2.13278
$356$	2.84916e17			0.393158
$357$	2.08774e17			0.282488
$358$			9.33479e17i			1.23858i
$359$		−	1.50572e18i		−	1.95922i	−0.200897	−	0.979612i	$-0.564386\pi$
$359$		−	1.50572e18i		−	1.95922i	0.200897	−	0.979612i	$-0.435614\pi$
$360$			1.13290e17i			0.144568i
$361$	6.90104e17			0.863703
$362$		−	8.13156e17i		−	0.998191i
$363$	−6.84533e17	+	2.10154e17i	−0.824229	+	0.253041i
$364$	−1.42267e17			−0.168033
$365$			9.66114e17i			1.11938i
$366$	−8.37130e17			−0.951536
$367$	8.39157e17			0.935795			0.467897	−	0.883783i	$-0.345012\pi$
$367$	8.39157e17			0.935795			0.467897	+	0.883783i	$0.345012\pi$
$368$	−1.79706e17			−0.196620
$369$			1.70108e17i			0.182617i
$370$		−	1.03661e18i		−	1.09195i
$371$		−	1.94139e17i		−	0.200676i
$372$	−1.79503e17			−0.182084
$373$		−	1.60474e18i		−	1.59751i	−0.601655	−	0.798756i	$-0.705492\pi$
$373$		−	1.60474e18i		−	1.59751i	0.601655	−	0.798756i	$-0.294508\pi$
$374$	−1.15895e18	+	1.73895e17i	−1.13230	+	0.169897i
$375$	−7.72256e17			−0.740529
$376$			5.13837e17i			0.483627i
$377$	2.73804e18			2.52959
$378$	1.70930e17			0.155016
$379$	−9.81553e17			−0.873855			−0.436927	−	0.899497i	$-0.643933\pi$
$379$	−9.81553e17			−0.873855			−0.436927	+	0.899497i	$0.643933\pi$
$380$			3.36536e17i			0.294135i
$381$		−	1.86390e18i		−	1.59937i
$382$		−	7.53315e17i		−	0.634648i
$383$	2.05205e18			1.69745			0.848724	−	0.528837i	$-0.177372\pi$
$383$	2.05205e18			1.69745			0.848724	+	0.528837i	$0.177372\pi$
$384$			9.38253e16i			0.0762081i
$385$	5.99831e16	+	3.99766e17i	0.0478414	+	0.318845i
$386$	−1.84525e17			−0.144525
$387$			4.05735e17i			0.312080i
$388$	−4.96981e17			−0.375421
$389$	−6.17128e17			−0.457855			−0.228927	−	0.973444i	$-0.573522\pi$
$389$	−6.17128e17			−0.457855			−0.228927	+	0.973444i	$0.573522\pi$
$390$	2.21421e18			1.61349
$391$			1.77925e18i			1.27350i
$392$		−	4.82284e17i		−	0.339078i
$393$			1.09957e18i			0.759410i
$394$	−7.17676e17			−0.486917
$395$		−	2.84663e18i		−	1.89737i
$396$	−1.93770e17	+	2.90743e16i	−0.126888	+	0.0190390i
$397$	−5.87673e17			−0.378096			−0.189048	−	0.981968i	$-0.560540\pi$
$397$	−5.87673e17			−0.378096			−0.189048	+	0.981968i	$0.560540\pi$
$398$		−	5.34714e17i		−	0.338018i
$399$	1.03691e17			0.0644069
$400$	6.30382e17			0.384754
$401$	1.52468e17			0.0914469			0.0457235	−	0.998954i	$-0.485441\pi$
$401$	1.52468e17			0.0914469			0.0457235	+	0.998954i	$0.485441\pi$
$402$			8.50145e17i			0.501084i
$403$		−	1.21108e18i		−	0.701513i
$404$			1.24791e17i			0.0710417i
$405$	−1.92951e18			−1.07960
$406$		−	3.96239e17i		−	0.217909i
$407$	1.77302e18	−	2.66033e17i	0.958411	−	0.143805i
$408$	9.28953e17			0.493597
$409$			2.36186e18i			1.23365i	0.787101	+	0.616824i	$0.211581\pi$
$409$			2.36186e18i			1.23365i	−0.787101	+	0.616824i	$0.788419\pi$
$410$	1.56157e18			0.801815
$411$	7.82902e16			0.0395198
$412$	2.82666e17			0.140279
$413$			3.12161e15i			0.00152310i
$414$			2.97482e17i			0.142711i
$415$		−	2.24961e18i		−	1.06114i
$416$	−6.33023e17			−0.293607
$417$			4.51326e17i			0.205844i
$418$	−5.75610e17	+	8.63677e16i	−0.258163	+	0.0387363i
$419$	−1.70787e18			−0.753278			−0.376639	−	0.926360i	$-0.622920\pi$
$419$	−1.70787e18			−0.753278			−0.376639	+	0.926360i	$0.622920\pi$
$420$		−	3.20432e17i		−	0.138992i
$421$	−2.76585e18			−1.17992			−0.589962	−	0.807431i	$-0.700857\pi$
$421$	−2.76585e18			−1.17992			−0.589962	+	0.807431i	$0.700857\pi$
$422$	−2.68975e18			−1.12856
$423$	8.50596e17			0.351027
$424$		−	8.63834e17i		−	0.350646i
$425$		−	6.24133e18i		−	2.49204i
$426$			2.07765e18i			0.816028i
$427$	−8.17355e17			−0.315803
$428$			1.84714e17i			0.0702092i
$429$	5.68248e17	+	3.78717e18i	0.212489	+	1.41616i
$430$	3.72458e18			1.37025
$431$			4.41041e18i			1.59639i	0.602402	+	0.798193i	$0.294210\pi$
$431$			4.41041e18i			1.59639i	−0.602402	+	0.798193i	$0.705790\pi$
$432$	7.60563e17			0.270863
$433$	−7.74580e17			−0.271426			−0.135713	−	0.990748i	$-0.543332\pi$
$433$	−7.74580e17			−0.271426			−0.135713	+	0.990748i	$0.543332\pi$
$434$	−1.75263e17			−0.0604312
$435$			6.16698e18i			2.09241i
$436$		−	2.40782e18i		−	0.803930i
$437$			8.83693e17i			0.290356i
$438$	1.32451e18			0.428289
$439$			2.74489e18i			0.873522i	0.899578	+	0.436761i	$0.143874\pi$
$439$			2.74489e18i			0.873522i	−0.899578	+	0.436761i	$0.856126\pi$
$440$	2.66898e17	+	1.77878e18i	0.0835943	+	0.557126i
$441$	−7.98363e17			−0.246110
$442$			6.26749e18i			1.90168i
$443$	−3.47473e18			−1.03776			−0.518878	−	0.854848i	$-0.673650\pi$
$443$	−3.47473e18			−1.03776			−0.518878	+	0.854848i	$0.673650\pi$
$444$	−1.42116e18			−0.417795
$445$	−4.32962e18			−1.25294
$446$		−	1.87922e18i		−	0.535345i
$447$		−	3.01880e18i		−	0.846606i
$448$			9.16090e16i			0.0252925i
$449$	−7.15817e17			−0.194571			−0.0972853	−	0.995257i	$-0.531016\pi$
$449$	−7.15817e17			−0.194571			−0.0972853	+	0.995257i	$0.531016\pi$
$450$		−	1.04352e18i		−	0.279263i
$451$	4.00757e17	+	2.67090e18i	0.105595	+	0.703755i
$452$	8.97949e17			0.232961
$453$			1.70926e17i			0.0436638i
$454$	2.52106e18			0.634150
$455$	2.16190e18			0.535496
$456$	4.61380e17			0.112540
$457$		−	6.58439e17i		−	0.158162i	−0.996868	−	0.0790810i	$-0.974801\pi$
$457$		−	6.58439e17i		−	0.158162i	0.996868	−	0.0790810i	$-0.0251986\pi$
$458$			2.56188e18i			0.606039i
$459$		−	7.53025e18i		−	1.75437i
$460$	2.73083e18			0.626600
$461$		−	2.19268e18i		−	0.495529i	−0.968820	−	0.247764i	$-0.920304\pi$
$461$		−	2.19268e18i		−	0.495529i	0.968820	−	0.247764i	$-0.0796959\pi$
$462$	5.48066e17	−	8.22349e16i	0.121994	−	0.0183047i
$463$	−8.72445e17			−0.191281			−0.0956403	−	0.995416i	$-0.530490\pi$
$463$	−8.72445e17			−0.191281			−0.0956403	+	0.995416i	$0.530490\pi$
$464$		−	1.76309e18i		−	0.380757i
$465$	2.72775e18			0.580275
$466$	3.39457e18			0.711349
$467$	4.20301e18			0.867645			0.433822	−	0.900998i	$-0.357165\pi$
$467$	4.20301e18			0.867645			0.433822	+	0.900998i	$0.357165\pi$
$468$			1.04789e18i			0.213106i
$469$			8.30063e17i			0.166303i
$470$		−	7.80834e18i		−	1.54125i
$471$	5.08486e17			0.0988855
$472$			1.38898e16i			0.00266134i
$473$	9.55867e17	+	6.37051e18i	0.180455	+	1.20267i
$474$	−3.90263e18			−0.725955
$475$		−	3.09986e18i		−	0.568182i
$476$	9.07009e17			0.163819
$477$	−1.42997e18			−0.254507
$478$	−5.63978e18			−0.989160
$479$		−	3.31857e18i		−	0.573591i	−0.957992	−	0.286795i	$-0.907410\pi$
$479$		−	3.31857e18i		−	0.573591i	0.957992	−	0.286795i	$-0.0925900\pi$
$480$		−	1.42578e18i		−	0.242865i
$481$		−	9.58834e18i		−	1.60964i
$482$	−9.73153e17			−0.161010
$483$		−	8.41407e17i		−	0.137207i
$484$	−2.97392e18	+	9.13002e17i	−0.477982	+	0.146742i
$485$	7.55219e18			1.19641
$486$		−	2.26093e18i		−	0.353048i
$487$	1.01665e19			1.56483			0.782415	−	0.622758i	$-0.213988\pi$
$487$	1.01665e19			1.56483			0.782415	+	0.622758i	$0.213988\pi$
$488$	−3.63687e18			−0.551809
$489$	−1.96937e18			−0.294554
$490$			7.32884e18i			1.08060i
$491$			2.73840e18i			0.398040i	0.979995	+	0.199020i	$0.0637758\pi$
$491$			2.73840e18i			0.398040i	−0.979995	+	0.199020i	$0.936224\pi$
$492$		−	2.14086e18i		−	0.306784i
$493$	−1.74561e19			−2.46615
$494$			3.11286e18i			0.433581i
$495$	2.94455e18	−	4.41818e17i	0.404374	−	0.0606745i
$496$	−7.79841e17			−0.105593
$497$			2.02857e18i			0.270829i
$498$	−3.08414e18			−0.406003
$499$	8.38402e18			1.08830			0.544150	−	0.838988i	$-0.316852\pi$
$499$	8.38402e18			1.08830			0.544150	+	0.838988i	$0.316852\pi$
$500$	−3.35503e18			−0.429443
$501$		−	2.11738e18i		−	0.267260i
$502$		−	8.57939e18i		−	1.06790i
$503$			1.41464e18i			0.173648i	0.996224	+	0.0868241i	$0.0276718\pi$
$503$			1.41464e18i			0.173648i	−0.996224	+	0.0868241i	$0.972328\pi$
$504$	1.51648e17			0.0183579
$505$		−	1.89634e18i		−	0.226400i
$506$	7.00834e17	+	4.67080e18i	0.0825204	+	0.549969i
$507$	1.30563e19			1.51623
$508$		−	8.09762e18i		−	0.927495i
$509$	−7.47965e18			−0.845001			−0.422500	−	0.906363i	$-0.638847\pi$
$509$	−7.47965e18			−0.845001			−0.422500	+	0.906363i	$0.638847\pi$
$510$	−1.41165e19			−1.57302
$511$	1.29322e18			0.142144
$512$			4.07619e17i			0.0441942i
$513$		−	3.74003e18i		−	0.399994i
$514$		−	1.51150e18i		−	0.159466i
$515$	−4.29543e18			−0.447050
$516$		−	5.10628e18i		−	0.524273i
$517$	1.33553e19	−	2.00391e18i	1.35276	−	0.202976i
$518$	−1.38759e18			−0.138661
$519$		−	1.72086e18i		−	0.169658i
$520$	9.61950e18			0.935684
$521$	−1.30155e19			−1.24910			−0.624549	−	0.780986i	$-0.714717\pi$
$521$	−1.30155e19			−1.24910			−0.624549	+	0.780986i	$0.714717\pi$
$522$	−2.91858e18			−0.276362
$523$			1.07519e19i			1.00456i	0.864706	+	0.502279i	$0.167505\pi$
$523$			1.07519e19i			1.00456i	−0.864706	+	0.502279i	$0.832495\pi$
$524$			4.77704e18i			0.440393i
$525$			2.95153e18i			0.268492i
$526$	1.31832e19			1.18337
$527$			7.72112e18i			0.683921i
$528$	2.43865e18	−	3.65909e17i	0.213163	−	0.0319842i
$529$	−4.42208e18			−0.381449
$530$			1.31269e19i			1.11746i
$531$	2.29928e16			0.00193166
$532$	4.50482e17			0.0373504
$533$	1.44440e19			1.18195
$534$			5.93577e18i			0.479389i
$535$		−	2.80694e18i		−	0.223747i
$536$			3.69341e18i			0.290586i
$537$	−1.94475e19			−1.51024
$538$			5.84064e18i			0.447697i
$539$	−1.25352e19	+	1.88085e18i	−0.948441	+	0.142309i
$540$	−1.15576e19			−0.863201
$541$		−	1.14628e19i		−	0.845107i	−0.906338	−	0.422553i	$-0.861134\pi$
$541$		−	1.14628e19i		−	0.845107i	0.906338	−	0.422553i	$-0.138866\pi$
$542$	1.27414e19			0.927306
$543$	1.69408e19			1.21712
$544$	4.03579e18			0.286244
$545$			3.65895e19i			2.56201i
$546$		−	2.96390e18i		−	0.204887i
$547$			2.13002e18i			0.145369i	0.997355	+	0.0726846i	$0.0231566\pi$
$547$			2.13002e18i			0.145369i	−0.997355	+	0.0726846i	$0.976843\pi$
$548$	3.40128e17			0.0229181
$549$			6.02040e18i			0.400515i
$550$	−2.45842e18	−	1.63845e19i	−0.161479	−	1.07620i
$551$	−8.66988e18			−0.562279
$552$		−	3.74389e18i		−	0.239745i
$553$	−3.81045e18			−0.240935
$554$	−3.79165e18			−0.236734
$555$	2.15962e19			1.33145
$556$			1.96076e18i			0.119372i
$557$		−	7.39340e18i		−	0.444486i	−0.974991	−	0.222243i	$-0.928662\pi$
$557$		−	7.39340e18i		−	0.444486i	0.974991	−	0.222243i	$-0.0713378\pi$
$558$			1.29093e18i			0.0766416i
$559$	3.44512e19			2.01986
$560$		−	1.39210e18i		−	0.0806037i
$561$	−3.62282e18	−	2.41448e19i	−0.207160	−	1.38065i
$562$	−8.56281e18			−0.483573
$563$			1.72745e19i			0.963486i	0.876312	+	0.481743i	$0.159996\pi$
$563$			1.72745e19i			0.963486i	−0.876312	+	0.481743i	$0.840004\pi$
$564$	−1.07050e19			−0.589702
$565$	−1.36453e19			−0.742413
$566$	−2.30337e18			−0.123779
$567$			2.58281e18i			0.137092i
$568$			9.02624e18i			0.473226i
$569$			2.13943e19i			1.10793i	0.832541	+	0.553964i	$0.186885\pi$
$569$			2.13943e19i			1.10793i	−0.832541	+	0.553964i	$0.813115\pi$
$570$	−7.01120e18			−0.358648
$571$		−	1.67691e19i		−	0.847339i	−0.905817	−	0.423669i	$-0.860742\pi$
$571$		−	1.67691e19i		−	0.847339i	0.905817	−	0.423669i	$-0.139258\pi$
$572$	2.46872e18	+	1.64532e19i	0.123225	+	0.821253i
$573$	1.56941e19			0.773845
$574$		−	2.09029e18i		−	0.101818i
$575$	−2.51539e19			−1.21041
$576$	6.74765e17			0.0320771
$577$	−3.53900e19			−1.66207			−0.831036	−	0.556218i	$-0.812252\pi$
$577$	−3.53900e19			−1.66207			−0.831036	+	0.556218i	$0.812252\pi$
$578$		−	2.47180e19i		−	1.14688i
$579$		−	3.84428e18i		−	0.176224i
$580$			2.67921e19i			1.21342i
$581$	−3.01129e18			−0.134747
$582$		−	1.03538e19i		−	0.457762i
$583$	−2.24522e19	+	3.36886e18i	−0.980798	+	0.147164i
$584$	5.75427e18			0.248371
$585$		−	1.59239e19i		−	0.679140i
$586$	2.88450e19			1.21559
$587$	1.49056e19			0.620701			0.310351	−	0.950622i	$-0.399554\pi$
$587$	1.49056e19			0.620701			0.310351	+	0.950622i	$0.399554\pi$
$588$	1.00476e19			0.413449
$589$			3.83482e18i			0.155933i
$590$		−	2.11071e17i		−	0.00848132i
$591$		−	1.49516e19i		−	0.593713i
$592$	−6.17417e18			−0.242285
$593$		−	2.10046e19i		−	0.814577i	−0.913300	−	0.407289i	$-0.866474\pi$
$593$		−	2.10046e19i		−	0.814577i	0.913300	−	0.407289i	$-0.133526\pi$
$594$	−2.96612e18	−	1.97681e19i	−0.113680	−	0.757634i
$595$	−1.37830e19			−0.522067
$596$		−	1.31150e19i		−	0.490959i
$597$	1.11399e19			0.412156
$598$	2.52594e19			0.923664
$599$	−5.44258e19			−1.96706			−0.983528	−	0.180754i	$-0.942146\pi$
$599$	−5.44258e19			−1.96706			−0.983528	+	0.180754i	$0.942146\pi$
$600$			1.31330e19i			0.469143i
$601$			9.25151e18i			0.326656i	0.986572	+	0.163328i	$0.0522229\pi$
$601$			9.25151e18i			0.326656i	−0.986572	+	0.163328i	$0.947777\pi$
$602$		−	4.98567e18i		−	0.173999i
$603$	6.11400e18			0.210913
$604$			7.42581e17i			0.0253213i
$605$	4.51921e19	−	1.38741e19i	1.52326	−	0.467646i
$606$	−2.59982e18			−0.0866233
$607$		−	2.59379e19i		−	0.854307i	−0.904179	−	0.427153i	$-0.859516\pi$
$607$		−	2.59379e19i		−	0.854307i	0.904179	−	0.427153i	$-0.140484\pi$
$608$	2.00444e18			0.0652633
$609$	8.25501e18			0.265703
$610$	5.52663e19			1.75854
$611$		−	7.22247e19i		−	2.27194i
$612$		−	6.68076e18i		−	0.207762i
$613$		−	4.45571e19i		−	1.36991i	−0.728583	−	0.684957i	$-0.759821\pi$
$613$		−	4.45571e19i		−	1.36991i	0.728583	−	0.684957i	$-0.240179\pi$
$614$	−5.14066e18			−0.156257
$615$			3.25328e19i			0.977677i
$616$	2.38104e18	−	3.57265e17i	0.0707461	−	0.0106151i
$617$	5.35917e19			1.57435			0.787175	−	0.616730i	$-0.211543\pi$
$617$	5.35917e19			1.57435			0.787175	+	0.616730i	$0.211543\pi$
$618$			5.88889e18i			0.171047i
$619$	−6.45279e19			−1.85316			−0.926580	−	0.376099i	$-0.877265\pi$
$619$	−6.45279e19			−1.85316			−0.926580	+	0.376099i	$0.877265\pi$
$620$	1.18506e19			0.336510
$621$	−3.03486e19			−0.852112
$622$		−	1.67183e19i		−	0.464150i
$623$			5.79556e18i			0.159103i
$624$		−	1.31880e19i		−	0.358004i
$625$	−6.34946e18			−0.170442
$626$			3.64803e19i			0.968363i
$627$	−1.79933e18	−	1.19919e19i	−0.0472323	−	0.314786i
$628$	2.20909e18			0.0573451
$629$			6.11297e19i			1.56927i
$630$	−2.30446e18			−0.0585039
$631$	−2.57079e19			−0.645448			−0.322724	−	0.946493i	$-0.604599\pi$
$631$	−2.57079e19			−0.645448			−0.322724	+	0.946493i	$0.604599\pi$
$632$	−1.69548e19			−0.420991
$633$		−	5.60367e19i		−	1.37609i
$634$			3.09688e19i			0.752141i
$635$			1.23052e20i			2.95580i
$636$	1.79966e19			0.427554
$637$			6.77895e19i			1.59289i
$638$	−4.58251e19	+	6.87585e18i	−1.06502	+	0.159802i
$639$	1.49419e19			0.343478
$640$		−	6.19424e18i		−	0.140841i
$641$	5.36833e19			1.20735			0.603674	−	0.797231i	$-0.293703\pi$
$641$	5.36833e19			1.20735			0.603674	+	0.797231i	$0.293703\pi$
$642$	−3.84822e18			−0.0856082
$643$	2.59588e19			0.571226			0.285613	−	0.958345i	$-0.407803\pi$
$643$	2.59588e19			0.571226			0.285613	+	0.958345i	$0.407803\pi$
$644$		−	3.65545e18i		−	0.0795682i
$645$			7.75958e19i			1.67078i
$646$		−	1.98458e19i		−	0.422708i
$647$	8.60195e19			1.81245			0.906227	−	0.422791i	$-0.138949\pi$
$647$	8.60195e19			1.81245			0.906227	+	0.422791i	$0.138949\pi$
$648$			1.14924e19i			0.239543i
$649$	3.61014e17	−	5.41686e16i	0.00744408	−	0.00111695i
$650$	−8.86061e19			−1.80747
$651$		−	3.65132e18i		−	0.0736857i
$652$	−8.55583e18			−0.170816
$653$	−5.06557e18			−0.100054			−0.0500272	−	0.998748i	$-0.515931\pi$
$653$	−5.06557e18			−0.100054			−0.0500272	+	0.998748i	$0.515931\pi$
$654$	5.01630e19			0.980256
$655$		−	7.25926e19i		−	1.40347i
$656$		−	9.30086e18i		−	0.177908i
$657$		−	9.52550e18i		−	0.180273i
$658$	−1.04521e19			−0.195714
$659$		−	7.23028e19i		−	1.33955i	−0.742566	−	0.669773i	$-0.766392\pi$
$659$		−	7.23028e19i		−	1.33955i	0.742566	−	0.669773i	$-0.233608\pi$
$660$	−3.70580e19	+	5.56039e18i	−0.679320	+	0.101929i
$661$	−6.12063e19			−1.11016			−0.555080	−	0.831797i	$-0.687312\pi$
$661$	−6.12063e19			−1.11016			−0.555080	+	0.831797i	$0.687312\pi$
$662$			2.51467e19i			0.451309i
$663$	−1.30573e20			−2.31878
$664$	−1.33989e19			−0.235447
$665$	−6.84558e18			−0.119031
$666$			1.02206e19i			0.175856i
$667$			7.03520e19i			1.19783i
$668$		−	9.19883e18i		−	0.154988i
$669$	3.91505e19			0.652762
$670$		−	5.61256e19i		−	0.926056i
$671$	1.41834e19	+	9.45272e19i	0.231591	+	1.54347i
$672$	−1.90853e18			−0.0308399
$673$		−	6.21336e19i		−	0.993622i	−0.867859	−	0.496811i	$-0.834504\pi$
$673$		−	6.21336e19i		−	0.993622i	0.867859	−	0.496811i	$-0.165496\pi$
$674$	−4.64973e19			−0.735883
$675$	1.06458e20			1.66745
$676$	5.67224e19			0.879281
$677$		−	1.12818e20i		−	1.73084i	−0.501043	−	0.865422i	$-0.667050\pi$
$677$		−	1.12818e20i		−	1.73084i	0.501043	−	0.865422i	$-0.332950\pi$
$678$			1.87073e19i			0.284056i
$679$		−	1.01092e19i		−	0.151925i
$680$	−6.13284e19			−0.912219
$681$			5.25222e19i			0.773238i
$682$	3.04130e18	+	2.02692e19i	0.0443168	+	0.295355i
$683$	4.24795e19			0.612681			0.306340	−	0.951922i	$-0.400895\pi$
$683$	4.24795e19			0.612681			0.306340	+	0.951922i	$0.400895\pi$
$684$		−	3.31812e18i		−	0.0473695i
$685$	−5.16862e18			−0.0730367
$686$	2.00393e19			0.280294
$687$	−5.33727e19			−0.738962
$688$		−	2.21840e19i		−	0.304033i
$689$			1.21420e20i			1.64724i
$690$			5.68926e19i			0.764033i
$691$	8.52411e19			1.13319			0.566595	−	0.823997i	$-0.308261\pi$
$691$	8.52411e19			1.13319			0.566595	+	0.823997i	$0.308261\pi$
$692$		−	7.47619e18i		−	0.0983869i
$693$	−5.91410e17	−	3.94153e18i	−0.00770470	−	0.0513490i
$694$	−3.87830e19			−0.500178
$695$		−	2.97960e19i		−	0.380421i
$696$	3.67311e19			0.464269
$697$	−9.20867e19			−1.15231
$698$	4.43594e19			0.549538
$699$			7.07203e19i			0.867369i
$700$			1.28228e19i			0.155703i
$701$			8.91790e19i			1.07210i	0.844185	+	0.536052i	$0.180085\pi$
$701$			8.91790e19i			1.07210i	−0.844185	+	0.536052i	$0.819915\pi$
$702$	−1.06904e20			−1.27244
$703$			3.03611e19i			0.357792i
$704$	1.05946e19	−	1.58967e18i	0.123616	−	0.0185481i
$705$	1.62674e20			1.87930
$706$		−	9.85496e18i		−	0.112725i
$707$	−2.53841e18			−0.0287492
$708$	−2.89371e17			−0.00324505
$709$	4.95798e18			0.0550531			0.0275265	−	0.999621i	$-0.491237\pi$
$709$	4.95798e18			0.0550531			0.0275265	+	0.999621i	$0.491237\pi$
$710$		−	1.37164e20i		−	1.50810i
$711$			2.80666e19i			0.305565i
$712$			2.57876e19i			0.278004i
$713$	3.11178e19			0.332187
$714$			1.88961e19i			0.199749i
$715$	−3.75150e19	−	2.50024e20i	−0.392702	−	2.61722i
$716$	−8.44889e19			−0.875807
$717$		−	1.17496e20i		−	1.20611i
$718$	1.36283e20			1.38538
$719$	1.36747e20			1.37662			0.688312	−	0.725415i	$-0.258352\pi$
$719$	1.36747e20			1.37662			0.688312	+	0.725415i	$0.258352\pi$
$720$	−1.02538e19			−0.102225
$721$			5.74979e18i			0.0567682i
$722$			6.24611e19i			0.610730i
$723$		−	2.02741e19i		−	0.196324i
$724$	7.35985e19			0.705828
$725$		−	2.46784e20i		−	2.34397i
$726$	−1.90209e19	−	6.19568e19i	−0.178927	−	0.582818i
$727$	−3.97776e19			−0.370594			−0.185297	−	0.982683i	$-0.559325\pi$
$727$	−3.97776e19			−0.370594			−0.185297	+	0.982683i	$0.559325\pi$
$728$		−	1.28765e19i		−	0.118817i
$729$	1.21238e20			1.10801
$730$	−8.74426e19			−0.791522
$731$	−2.19641e20			−1.96921
$732$		−	7.57683e19i		−	0.672838i
$733$		−	6.50728e19i		−	0.572363i	−0.958175	−	0.286182i	$-0.907614\pi$
$733$		−	6.50728e19i		−	0.572363i	0.958175	−	0.286182i	$-0.0923861\pi$
$734$			7.59518e19i			0.661707i
$735$	−1.52685e20			−1.31760
$736$		−	1.62651e19i		−	0.139031i
$737$	9.59969e19	−	1.44039e19i	0.812802	−	0.121957i
$738$	−1.53965e19			−0.129130
$739$			1.08437e20i			0.900883i	0.892806	+	0.450441i	$0.148733\pi$
$739$			1.08437e20i			0.900883i	−0.892806	+	0.450441i	$0.851267\pi$
$740$	9.38234e19			0.772128
$741$	−6.48514e19			−0.528679
$742$	1.75715e19			0.141900
$743$		−	1.54849e20i		−	1.23876i	−0.785092	−	0.619380i	$-0.787384\pi$
$743$		−	1.54849e20i		−	1.23876i	0.785092	−	0.619380i	$-0.212616\pi$
$744$		−	1.62468e19i		−	0.128753i
$745$			1.99297e20i			1.56462i
$746$	1.45245e20			1.12961
$747$			2.21803e19i			0.170892i
$748$	−1.57391e19	−	1.04896e20i	−0.120135	−	0.800657i
$749$	−3.75732e18			−0.0284123
$750$		−	6.98966e19i		−	0.523633i
$751$	−1.71524e20			−1.27305			−0.636523	−	0.771258i	$-0.719628\pi$
$751$	−1.71524e20			−1.27305			−0.636523	+	0.771258i	$0.719628\pi$
$752$	−4.65073e19			−0.341976
$753$	1.78738e20			1.30212
$754$			2.47819e20i			1.78869i
$755$		−	1.12844e19i		−	0.0806953i
$756$			1.54708e19i			0.109613i
$757$	−2.36340e20			−1.65908			−0.829539	−	0.558449i	$-0.811396\pi$
$757$	−2.36340e20			−1.65908			−0.829539	+	0.558449i	$0.811396\pi$
$758$		−	8.88400e19i		−	0.617908i
$759$	−9.73088e19	+	1.46008e19i	−0.670594	+	0.100620i
$760$	−3.04598e19			−0.207985
$761$			4.32720e19i			0.292762i	0.989228	+	0.146381i	$0.0467625\pi$
$761$			4.32720e19i			0.292762i	−0.989228	+	0.146381i	$0.953237\pi$
$762$	1.68701e20			1.13092
$763$	4.89781e19			0.325335
$764$	6.81823e19			0.448764
$765$			1.01522e20i			0.662108i
$766$			1.85730e20i			1.20028i
$767$		−	1.95234e18i		−	0.0125022i
$768$	−8.49210e18			−0.0538873
$769$			1.25822e20i			0.791172i	0.918429	+	0.395586i	$0.129459\pi$
$769$			1.25822e20i			0.791172i	−0.918429	+	0.395586i	$0.870541\pi$
$770$	−3.61826e19	+	5.42905e18i	−0.225458	+	0.0338290i
$771$	3.14898e19			0.194442
$772$		−	1.67013e19i		−	0.102195i
$773$	−1.83236e20			−1.11110			−0.555551	−	0.831483i	$-0.687493\pi$
$773$	−1.83236e20			−1.11110			−0.555551	+	0.831483i	$0.687493\pi$
$774$	−3.67229e19			−0.220674
$775$	−1.09157e20			−0.650037
$776$		−	4.49816e19i		−	0.265462i
$777$		−	2.89083e19i		−	0.169073i
$778$		−	5.58560e19i		−	0.323752i
$779$	−4.57364e19			−0.262724
$780$			2.00407e20i			1.14091i
$781$	2.34604e20	−	3.52014e19i	1.32367	−	0.198611i
$782$	−1.61039e20			−0.900500
$783$		−	2.97749e20i		−	1.65013i
$784$	4.36513e19			0.239765
$785$	−3.35696e19			−0.182751
$786$	−9.95221e19			−0.536984
$787$			3.19548e20i			1.70889i	0.519544	+	0.854443i	$0.326102\pi$
$787$			3.19548e20i			1.70889i	−0.519544	+	0.854443i	$0.673898\pi$
$788$		−	6.49566e19i		−	0.344302i
$789$			2.74650e20i			1.44291i
$790$	2.57647e20			1.34164
$791$			1.82654e19i			0.0942746i
$792$	−2.63151e18	−	1.75381e19i	−0.0134626	−	0.0897233i
$793$	5.11196e20			2.59224
$794$		−	5.31901e19i		−	0.267354i
$795$	−2.73479e20			−1.36255
$796$	4.83968e19			0.239015
$797$	7.48582e19			0.366464			0.183232	−	0.983070i	$-0.441344\pi$
$797$	7.48582e19			0.366464			0.183232	+	0.983070i	$0.441344\pi$
$798$			9.38507e18i			0.0455425i
$799$			4.60463e20i			2.21497i
$800$			5.70556e19i			0.272062i
$801$	4.26883e19			0.201782
$802$			1.37999e19i			0.0646627i
$803$	−2.24410e19	−	1.49561e20i	−0.104240	−	0.694722i
$804$	−7.69464e19			−0.354320
$805$			5.55487e19i			0.253573i
$806$	1.09614e20			0.496045
$807$	−1.21680e20			−0.545891
$808$	−1.12948e19			−0.0502341
$809$		−	3.54440e20i		−	1.56280i	−0.624031	−	0.781400i	$-0.714506\pi$
$809$		−	3.54440e20i		−	1.56280i	0.624031	−	0.781400i	$-0.285494\pi$
$810$		−	1.74639e20i		−	0.763391i
$811$		−	2.29141e20i		−	0.993015i	−0.868032	−	0.496508i	$-0.834615\pi$
$811$		−	2.29141e20i		−	0.993015i	0.868032	−	0.496508i	$-0.165385\pi$
$812$	3.58635e19			0.154085
$813$			2.65447e20i			1.13069i
$814$	2.40786e19	+	1.60475e20i	0.101686	+	0.677699i
$815$	1.30015e20			0.544367
$816$			8.40792e19i			0.349026i
$817$	−1.09088e20			−0.448977
$818$	−2.13771e20			−0.872321
$819$	−2.13155e19			−0.0862399
$820$			1.41337e20i			0.566969i
$821$		−	5.63959e19i		−	0.224308i	−0.993691	−	0.112154i	$-0.964225\pi$
$821$		−	5.63959e19i		−	0.224308i	0.993691	−	0.112154i	$-0.0357750\pi$
$822$			7.08602e18i			0.0279447i
$823$	−3.34815e20			−1.30920			−0.654601	−	0.755975i	$-0.727163\pi$
$823$	−3.34815e20			−1.30920			−0.654601	+	0.755975i	$0.727163\pi$
$824$			2.55840e19i			0.0991923i
$825$	3.41345e20	−	5.12173e19i	1.31225	−	0.196897i
$826$	−2.82535e17			−0.00107699
$827$			9.33316e19i			0.352769i	0.984321	+	0.176384i	$0.0564402\pi$
$827$			9.33316e19i			0.352769i	−0.984321	+	0.176384i	$0.943560\pi$
$828$	−2.69250e19			−0.100912
$829$	1.01506e20			0.377232			0.188616	−	0.982051i	$-0.439600\pi$
$829$	1.01506e20			0.377232			0.188616	+	0.982051i	$0.439600\pi$
$830$	2.03612e20			0.750336
$831$		−	7.89930e19i		−	0.288656i
$832$		−	5.72947e19i		−	0.207612i
$833$		−	4.32187e20i		−	1.55295i
$834$	−4.08494e19			−0.145554
$835$			1.39787e20i			0.493924i
$836$	−7.81712e18	−	5.20983e19i	−0.0273907	−	0.182549i
$837$	−1.31699e20			−0.457619
$838$		−	1.54578e20i		−	0.532648i
$839$	2.93410e20			1.00263			0.501316	−	0.865264i	$-0.332849\pi$
$839$	2.93410e20			1.00263			0.501316	+	0.865264i	$0.332849\pi$
$840$	2.90022e19			0.0982825
$841$	−3.92663e20			−1.31962
$842$		−	2.50336e20i		−	0.834332i
$843$		−	1.78392e20i		−	0.589635i
$844$		−	2.43449e20i		−	0.798014i
$845$	−8.61961e20			−2.80215
$846$			7.69872e19i			0.248214i
$847$	−1.85716e19	−	6.04933e19i	−0.0593836	−	0.193430i
$848$	7.81853e19			0.247944
$849$		−	4.79870e19i		−	0.150928i
$850$	5.64901e20			1.76214
$851$	2.46366e20			0.762209
$852$	−1.88047e20			−0.577019
$853$		−	1.63239e20i		−	0.496798i	−0.968658	−	0.248399i	$-0.920096\pi$
$853$		−	1.63239e20i		−	0.496798i	0.968658	−	0.248399i	$-0.0799045\pi$
$854$		−	7.39786e19i		−	0.223306i
$855$			5.04225e19i			0.150960i
$856$	−1.67184e19			−0.0496454
$857$			6.80282e19i			0.200366i	0.994969	+	0.100183i	$0.0319428\pi$
$857$			6.80282e19i			0.200366i	−0.994969	+	0.100183i	$0.968057\pi$
$858$	−3.42775e20	+	5.14319e19i	−1.00138	+	0.150252i
$859$	7.48806e19			0.216979			0.108489	−	0.994098i	$-0.465399\pi$
$859$	7.48806e19			0.216979			0.108489	+	0.994098i	$0.465399\pi$
$860$			3.37111e20i			0.968910i
$861$	4.35479e19			0.124149
$862$	−3.99184e20			−1.12881
$863$	6.32975e20			1.77546			0.887731	−	0.460363i	$-0.152281\pi$
$863$	6.32975e20			1.77546			0.887731	+	0.460363i	$0.152281\pi$
$864$			6.88383e19i			0.191529i
$865$			1.13609e20i			0.313545i
$866$		−	7.01069e19i		−	0.191927i
$867$	5.14961e20			1.39843
$868$		−	1.58630e19i		−	0.0427313i
$869$	6.61219e19	+	4.40679e20i	0.176688	+	1.17756i
$870$	−5.58171e20			−1.47956
$871$		−	5.19144e20i		−	1.36509i
$872$	2.17931e20			0.568464
$873$	−7.44617e19			−0.192678
$874$	−7.99828e19			−0.205313
$875$		−	6.82455e19i		−	0.173787i
$876$			1.19881e20i			0.302846i
$877$		−	5.98486e20i		−	1.49988i	−0.661506	−	0.749940i	$-0.730082\pi$
$877$		−	5.98486e20i		−	1.49988i	0.661506	−	0.749940i	$-0.269918\pi$
$878$	−2.48439e20			−0.617673
$879$			6.00940e20i			1.48221i
$880$	−1.60997e20	+	2.41569e19i	−0.393947	+	0.0591101i
$881$	2.57533e20			0.625175			0.312588	−	0.949889i	$-0.398804\pi$
$881$	2.57533e20			0.625175			0.312588	+	0.949889i	$0.398804\pi$
$882$		−	7.22595e19i		−	0.174026i
$883$	1.66633e20			0.398140			0.199070	−	0.979985i	$-0.436208\pi$
$883$	1.66633e20			0.398140			0.199070	+	0.979985i	$0.436208\pi$
$884$	−5.67268e20			−1.34469
$885$	4.39732e18			0.0103415
$886$		−	3.14497e20i		−	0.733804i
$887$		−	6.34376e20i		−	1.46853i	−0.678865	−	0.734263i	$-0.737528\pi$
$887$		−	6.34376e20i		−	1.46853i	0.678865	−	0.734263i	$-0.262472\pi$
$888$		−	1.28629e20i		−	0.295425i
$889$	1.64716e20			0.375339
$890$		−	3.91872e20i		−	0.885961i
$891$	2.98702e20	−	4.48190e19i	0.670031	−	0.100535i
$892$	1.70087e20			0.378546
$893$			2.28697e20i			0.505010i
$894$	2.73230e20			0.598641
$895$	1.28390e21			2.79107
$896$	−8.29150e18			−0.0178845
$897$			5.26238e20i			1.12625i
$898$		−	6.47883e19i		−	0.137582i
$899$			3.05296e20i			0.643284i
$900$	9.44487e19			0.197469
$901$		−	7.74103e20i		−	1.60593i
$902$	−2.41742e20	+	3.62724e19i	−0.497630	+	0.0746672i
$903$	1.03868e20			0.212163
$904$			8.12731e19i			0.164728i
$905$	−1.11841e21			−2.24937
$906$	−1.54705e19			−0.0308750
$907$	−8.39504e20			−1.66254			−0.831270	−	0.555870i	$-0.812385\pi$
$907$	−8.39504e20			−1.66254			−0.831270	+	0.555870i	$0.812385\pi$
$908$			2.28180e20i			0.448412i
$909$			1.86971e19i			0.0364610i
$910$			1.95673e20i			0.378653i
$911$	6.90687e20			1.32633			0.663166	−	0.748472i	$-0.269212\pi$
$911$	6.90687e20			1.32633			0.663166	+	0.748472i	$0.269212\pi$
$912$			4.17594e19i			0.0795775i
$913$	5.22543e19	+	3.48256e20i	0.0988159	+	0.658572i
$914$	5.95951e19			0.111837
$915$			1.15139e21i			2.14424i
$916$	−2.31875e20			−0.428534
$917$	−9.71712e19			−0.178218
$918$	6.81560e20			1.24052
$919$			5.89114e20i			1.06412i	0.846707	+	0.532060i	$0.178582\pi$
$919$			5.89114e20i			1.06412i	−0.846707	+	0.532060i	$0.821418\pi$
$920$			2.47167e20i			0.443073i
$921$		−	1.07097e20i		−	0.190529i
$922$	1.98459e20			0.350392
$923$		−	1.26872e21i		−	2.22308i
$924$	7.44305e18	+	4.96052e19i	0.0129434	+	0.0862629i
$925$	−8.64216e20			−1.49152
$926$		−	7.89647e19i		−	0.135256i
$927$	4.23512e19			0.0719959
$928$	1.59577e20			0.269236
$929$	−2.79476e20			−0.467987			−0.233994	−	0.972238i	$-0.575179\pi$
$929$	−2.79476e20			−0.467987			−0.233994	+	0.972238i	$0.575179\pi$
$930$			2.46888e20i			0.410316i
$931$		−	2.14653e20i		−	0.354070i
$932$			3.07241e20i			0.503000i
$933$	3.48298e20			0.565952
$934$			3.80413e20i			0.613517i
$935$	2.39174e20	+	1.59401e21i	0.382854	+	2.55158i
$936$	−9.48445e19			−0.150689
$937$			8.75954e20i			1.38135i	0.723165	+	0.690676i	$0.242687\pi$
$937$			8.75954e20i			1.38135i	−0.723165	+	0.690676i	$0.757313\pi$
$938$	−7.51288e19			−0.117594
$939$	−7.60009e20			−1.18075
$940$	7.06730e20			1.08983
$941$			3.17910e20i			0.486605i	0.969950	+	0.243303i	$0.0782308\pi$
$941$			3.17910e20i			0.486605i	−0.969950	+	0.243303i	$0.921769\pi$
$942$			4.60229e19i			0.0699226i
$943$			3.71130e20i			0.559685i
$944$	−1.25716e18			−0.00188185
$945$		−	2.35097e20i		−	0.349321i
$946$	−5.76593e20	+	8.65152e19i	−0.850415	+	0.127601i
$947$	−8.74322e19			−0.128003			−0.0640017	−	0.997950i	$-0.520386\pi$
$947$	−8.74322e19			−0.128003			−0.0640017	+	0.997950i	$0.520386\pi$
$948$		−	3.53226e20i		−	0.513327i
$949$	−8.08817e20			−1.16677
$950$	2.80568e20			0.401765
$951$	−6.45185e20			−0.917108
$952$			8.20931e19i			0.115837i
$953$		−	7.66379e20i		−	1.07348i	−0.843748	−	0.536739i	$-0.819656\pi$
$953$		−	7.66379e20i		−	1.07348i	0.843748	−	0.536739i	$-0.180344\pi$
$954$		−	1.29426e20i		−	0.179963i
$955$	−1.03611e21			−1.43015
$956$		−	5.10454e20i		−	0.699442i
$957$	−1.43247e20	−	9.54693e20i	−0.194851	−	1.29861i
$958$	3.00363e20			0.405590
$959$			6.91863e18i			0.00927449i
$960$	1.29047e20			0.171731
$961$	−6.21907e20			−0.821602
$962$	8.67837e20			1.13818
$963$			2.76753e19i			0.0360337i
$964$		−	8.80798e19i		−	0.113851i
$965$			2.53795e20i			0.325680i
$966$	7.61554e19			0.0970199
$967$		−	5.43498e20i		−	0.687405i	−0.939079	−	0.343702i	$-0.888319\pi$
$967$		−	5.43498e20i		−	0.687405i	0.939079	−	0.343702i	$-0.111681\pi$
$968$	−8.26355e19	−	2.69168e20i	−0.103762	−	0.337984i
$969$	4.13455e20			0.515420
$970$			6.83546e20i			0.845991i
$971$	7.85690e20			0.965420			0.482710	−	0.875780i	$-0.339652\pi$
$971$	7.85690e20			0.965420			0.482710	+	0.875780i	$0.339652\pi$
$972$	2.04636e20			0.249643
$973$	−3.98845e19			−0.0483074
$974$			9.20163e20i			1.10650i
$975$		−	1.84597e21i		−	2.20390i
$976$		−	3.29172e20i		−	0.390188i
$977$	1.61165e21			1.89674			0.948370	−	0.317167i	$-0.102731\pi$
$977$	1.61165e21			1.89674			0.948370	+	0.317167i	$0.102731\pi$
$978$		−	1.78247e20i		−	0.208281i
$979$	6.70257e20	−	1.00569e20i	0.777611	−	0.116677i
$980$	−6.63331e20			−0.764096
$981$		−	3.60758e20i		−	0.412604i
$982$	−2.47852e20			−0.281457
$983$	8.51195e19			0.0959742			0.0479871	−	0.998848i	$-0.484719\pi$
$983$	8.51195e19			0.0959742			0.0479871	+	0.998848i	$0.484719\pi$
$984$	1.93769e20			0.216929
$985$			9.87089e20i			1.09724i
$986$		−	1.57995e21i		−	1.74383i
$987$		−	2.17753e20i		−	0.238641i
$988$	−2.81743e20			−0.306588
$989$			8.85202e20i			0.956463i
$990$	3.99888e19	+	2.66511e20i	0.0429034	+	0.285936i
$991$	1.08162e21			1.15229			0.576144	−	0.817348i	$-0.304557\pi$
$991$	1.08162e21			1.15229			0.576144	+	0.817348i	$0.304557\pi$
$992$		−	7.05832e19i		−	0.0746654i
$993$	−5.23891e20			−0.550295
$994$	−1.83605e20			−0.191505
$995$	−7.35444e20			−0.761707
$996$		−	2.79145e20i		−	0.287087i
$997$		−	6.59778e20i		−	0.673801i	−0.941540	−	0.336901i	$-0.890621\pi$
$997$		−	6.59778e20i		−	0.673801i	0.941540	−	0.336901i	$-0.109379\pi$
$998$			7.58835e20i			0.769544i
$999$	−1.04269e21			−1.05002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.15.b.a.21.9	yes	14
4.3	odd	2		176.15.h.e.65.12		14
11.10	odd	2	inner	22.15.b.a.21.2	✓	14
44.43	even	2		176.15.h.e.65.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.15.b.a.21.2	✓	14	11.10	odd	2	inner
22.15.b.a.21.9	yes	14	1.1	even	1	trivial
176.15.h.e.65.11		14	44.43	even	2
176.15.h.e.65.12		14	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+90.5097i q^{2} -1885.62 q^{3} -8192.00 q^{4} +124487. q^{5} -170667. i q^{6} -166636. i q^{7} -741455. i q^{8} -1.22739e6 q^{9} +O(q^{10})\)	\(q+90.5097i q^{2} -1885.62 q^{3} -8192.00 q^{4} +124487. q^{5} -170667. i q^{6} -166636. i q^{7} -741455. i q^{8} -1.22739e6 q^{9} +1.12672e7i q^{10} +(-1.92714e7 + 2.89160e6i) q^{11} +1.54470e7 q^{12} +1.04219e8i q^{13} +1.50821e7 q^{14} -2.34735e8 q^{15} +6.71089e7 q^{16} -6.64437e8i q^{17} -1.11091e8i q^{18} -3.30004e8i q^{19} -1.01979e9 q^{20} +3.14212e8i q^{21} +(-2.61717e8 - 1.74425e9i) q^{22} -2.67783e9 q^{23} +1.39811e9i q^{24} +9.39342e9 q^{25} -9.43278e9 q^{26} +1.13333e10 q^{27} +1.36508e9i q^{28} -2.62721e10i q^{29} -2.12458e10i q^{30} -1.16205e10 q^{31} +6.07400e9i q^{32} +(3.63387e10 - 5.45246e9i) q^{33} +6.01379e10 q^{34} -2.07439e10i q^{35} +1.00548e10 q^{36} -9.20022e10 q^{37} +2.98685e10 q^{38} -1.96517e11i q^{39} -9.23013e10i q^{40} -1.38594e11i q^{41} -2.84393e10 q^{42} -3.30567e11i q^{43} +(1.57872e11 - 2.36880e10i) q^{44} -1.52794e11 q^{45} -2.42369e11i q^{46} -6.93012e11 q^{47} -1.26542e11 q^{48} +6.50456e11 q^{49} +8.50195e11i q^{50} +1.25288e12i q^{51} -8.53758e11i q^{52} +1.16505e12 q^{53} +1.02577e12i q^{54} +(-2.39904e12 + 3.59965e11i) q^{55} -1.23553e11 q^{56} +6.22263e11i q^{57} +2.37788e12 q^{58} -1.87331e10 q^{59} +1.92295e12 q^{60} -4.90504e12i q^{61} -1.05177e12i q^{62} +2.04527e11i q^{63} -5.49756e11 q^{64} +1.29738e13i q^{65} +(4.93501e11 + 3.28900e12i) q^{66} -4.98130e12 q^{67} +5.44307e12i q^{68} +5.04938e12 q^{69} +1.87753e12 q^{70} -1.21737e13 q^{71} +9.10055e11i q^{72} +7.76078e12i q^{73} -8.32709e12i q^{74} -1.77125e13 q^{75} +2.70339e12i q^{76} +(4.81843e11 + 3.21131e12i) q^{77} +1.77867e13 q^{78} -2.28669e13i q^{79} +8.35416e12 q^{80} -1.54997e13 q^{81} +1.25441e13 q^{82} -1.80711e13i q^{83} -2.57403e12i q^{84} -8.27135e13i q^{85} +2.99195e13 q^{86} +4.95392e13i q^{87} +(2.14399e12 + 1.42889e13i) q^{88} -3.47798e13 q^{89} -1.38293e13i q^{90} +1.73665e13 q^{91} +2.19368e13 q^{92} +2.19120e13 q^{93} -6.27243e13i q^{94} -4.10811e13i q^{95} -1.14533e13i q^{96} +6.06667e13 q^{97} +5.88725e13i q^{98} +(2.36536e13 - 3.54911e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

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