LMFDB - Embedded newform 7.17.b.b.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,17,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("7.6");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	7.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:	$11.3627180700$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5365384x^{6} + 10449491370210x^{4} + 8743024230718881600x^{2} + 2655236149032650377194000 $ x^8 + 5365384x^6 + 10449491370210x^4 + 8743024230718881600*x^2 + 2655236149032650377194000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{5}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.1
Root			$-1246.39i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.17.b.b.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-408.297 q^{2} -7478.36i q^{3} +101171. q^{4} +25884.6i q^{5} +3.05340e6i q^{6} +(879246. + 5.69736e6i) q^{7} -1.45496e7 q^{8} -1.28792e7 q^{9} +O(q^{10})$	\(q-408.297 q^{2} -7478.36i q^{3} +101171. q^{4} +25884.6i q^{5} +3.05340e6i q^{6} +(879246. + 5.69736e6i) q^{7} -1.45496e7 q^{8} -1.28792e7 q^{9} -1.05686e7i q^{10} +2.58740e8 q^{11} -7.56592e8i q^{12} -7.88399e8i q^{13} +(-3.58994e8 - 2.32622e9i) q^{14} +1.93574e8 q^{15} -6.89767e8 q^{16} +8.43625e9i q^{17} +5.25853e9 q^{18} -2.52026e10i q^{19} +2.61876e9i q^{20} +(4.26069e10 - 6.57532e9i) q^{21} -1.05643e11 q^{22} -9.65568e9 q^{23} +1.08807e11i q^{24} +1.51918e11 q^{25} +3.21901e11i q^{26} -2.25604e11i q^{27} +(8.89540e10 + 5.76406e11i) q^{28} -6.70946e11 q^{29} -7.90358e10 q^{30} -7.88414e11i q^{31} +1.23515e12 q^{32} -1.93495e12i q^{33} -3.44450e12i q^{34} +(-1.47474e11 + 2.27589e10i) q^{35} -1.30300e12 q^{36} +4.88762e12 q^{37} +1.02902e13i q^{38} -5.89594e12 q^{39} -3.76610e11i q^{40} +2.16776e11i q^{41} +(-1.73963e13 + 2.68469e12i) q^{42} +5.58592e12 q^{43} +2.61769e13 q^{44} -3.33372e11i q^{45} +3.94239e12 q^{46} -4.97420e11i q^{47} +5.15833e12i q^{48} +(-3.16868e13 + 1.00188e13i) q^{49} -6.20277e13 q^{50} +6.30893e13 q^{51} -7.97630e13i q^{52} +4.55472e13 q^{53} +9.21135e13i q^{54} +6.69738e12i q^{55} +(-1.27927e13 - 8.28942e13i) q^{56} -1.88474e14 q^{57} +2.73946e14 q^{58} -1.09329e14i q^{59} +1.95841e13 q^{60} -3.61273e14i q^{61} +3.21907e14i q^{62} +(-1.13240e13 - 7.33772e13i) q^{63} -4.59105e14 q^{64} +2.04074e13 q^{65} +7.90036e14i q^{66} +2.27208e14 q^{67} +8.53502e14i q^{68} +7.22087e13i q^{69} +(6.02131e13 - 9.29240e12i) q^{70} +6.95480e14 q^{71} +1.87387e14 q^{72} -1.27766e15i q^{73} -1.99560e15 q^{74} -1.13610e15i q^{75} -2.54977e15i q^{76} +(2.27496e14 + 1.47413e15i) q^{77} +2.40730e15 q^{78} -1.01425e14 q^{79} -1.78543e13i q^{80} -2.24155e15 q^{81} -8.85089e13i q^{82} +9.27081e14i q^{83} +(4.31057e15 - 6.65230e14i) q^{84} -2.18369e14 q^{85} -2.28072e15 q^{86} +5.01758e15i q^{87} -3.76456e15 q^{88} +2.66921e15i q^{89} +1.36115e14i q^{90} +(4.49179e15 - 6.93197e14i) q^{91} -9.76873e14 q^{92} -5.89604e15 q^{93} +2.03095e14i q^{94} +6.52359e14 q^{95} -9.23692e15i q^{96} +6.68122e15i q^{97} +(1.29376e16 - 4.09063e15i) q^{98} -3.33236e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) $ 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9	$ 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) $ 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9 + 430398704 * q^11 - 2080234240 * q^14 + 83393280 * q^15 - 4357080832 * q^16 - 7232400864 * q^18 + 45847234944 * q^21 - 34275403968 * q^22 + 89765082416 * q^23 + 61966251080 * q^25 - 376785722656 * q^28 - 22437591664 * q^29 - 192018300480 * q^30 + 941689387008 * q^32 + 371925382080 * q^35 - 4527659399328 * q^36 + 5737866534416 * q^37 - 7975804007808 * q^39 - 13160568536640 * q^42 - 3976952110864 * q^43 + 45337613120448 * q^44 + 35817469755072 * q^46 - 27450534789496 * q^49 - 96564765668320 * q^50 + 58670380591488 * q^51 - 108679841507824 * q^53 - 15117119134208 * q^56 - 196163055495360 * q^57 + 650847682404672 * q^58 - 335782392744960 * q^60 + 223739049782808 * q^63 - 460533940742144 * q^64 + 573279455461440 * q^65 - 722120065643024 * q^67 + 1268642086877760 * q^70 - 289095246669136 * q^71 + 1560006716205312 * q^72 - 5411665863643328 * q^74 + 4485628262682896 * q^77 + 192459573633600 * q^78 + 5832776866563376 * q^79 - 14617034931574584 * q^81 + 12924747561148416 * q^84 - 5815379514337920 * q^85 + 7508453217752512 * q^86 - 24665635192321536 * q^88 + 23929798963272384 * q^91 + 1197288221450688 * q^92 + 27012151562451840 * q^93 - 53204702857107840 * q^95 + 43278421367298656 * q^98 - 15738606124789392 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−408.297			−1.59491			−0.797456	−	0.603377i	$-0.793821\pi$
$2$	−408.297			−1.59491			−0.797456	+	0.603377i	$0.793821\pi$
$3$		−	7478.36i		−	1.13982i	−0.821707	−	0.569910i	$-0.806978\pi$
$3$		−	7478.36i		−	1.13982i	0.821707	−	0.569910i	$-0.193022\pi$
$4$	101171.			1.54374
$5$			25884.6i			0.0662645i	0.999451	+	0.0331322i	$0.0105483\pi$
$5$			25884.6i			0.0662645i	−0.999451	+	0.0331322i	$0.989452\pi$
$6$			3.05340e6i			1.81791i
$7$	879246.	+	5.69736e6i	0.152520	+	0.988300i
$7$	879246.	+	5.69736e6i	0.152520	+	0.988300i
$8$	−1.45496e7			−0.867223
$9$	−1.28792e7			−0.299191
$10$		−	1.05686e7i		−	0.105686i
$11$	2.58740e8			1.20704			0.603521	−	0.797347i	$-0.293764\pi$
$11$	2.58740e8			1.20704			0.603521	+	0.797347i	$0.293764\pi$
$12$		−	7.56592e8i		−	1.75959i
$13$		−	7.88399e8i		−	0.966495i	−0.875484	−	0.483247i	$-0.839457\pi$
$13$		−	7.88399e8i		−	0.966495i	0.875484	−	0.483247i	$-0.160543\pi$
$14$	−3.58994e8	−	2.32622e9i	−0.243256	−	1.57625i
$15$	1.93574e8			0.0755296
$16$	−6.89767e8			−0.160599
$17$			8.43625e9i			1.20937i	0.796466	+	0.604683i	$0.206700\pi$
$17$			8.43625e9i			1.20937i	−0.796466	+	0.604683i	$0.793300\pi$
$18$	5.25853e9			0.477183
$19$		−	2.52026e10i		−	1.48394i	−0.670432	−	0.741971i	$-0.733891\pi$
$19$		−	2.52026e10i		−	1.48394i	0.670432	−	0.741971i	$-0.266109\pi$
$20$			2.61876e9i			0.102295i
$21$	4.26069e10	−	6.57532e9i	1.12649	−	0.173845i
$22$	−1.05643e11			−1.92512
$23$	−9.65568e9			−0.123299			−0.0616496	−	0.998098i	$-0.519636\pi$
$23$	−9.65568e9			−0.123299			−0.0616496	+	0.998098i	$0.519636\pi$
$24$			1.08807e11i			0.988479i
$25$	1.51918e11			0.995609
$26$			3.21901e11i			1.54147i
$27$		−	2.25604e11i		−	0.798797i
$28$	8.89540e10	+	5.76406e11i	0.235451	+	1.52568i
$29$	−6.70946e11			−1.34123			−0.670616	−	0.741805i	$-0.733970\pi$
$29$	−6.70946e11			−1.34123			−0.670616	+	0.741805i	$0.733970\pi$
$30$	−7.90358e10			−0.120463
$31$		−	7.88414e11i		−	0.924401i	−0.886775	−	0.462201i	$-0.847060\pi$
$31$		−	7.88414e11i		−	0.924401i	0.886775	−	0.462201i	$-0.152940\pi$
$32$	1.23515e12			1.12336
$33$		−	1.93495e12i		−	1.37581i
$34$		−	3.44450e12i		−	1.92883i
$35$	−1.47474e11	+	2.27589e10i	−0.0654892	+	0.0101066i
$36$	−1.30300e12			−0.461874
$37$	4.88762e12			1.39150			0.695750	−	0.718284i	$-0.255072\pi$
$37$	4.88762e12			1.39150			0.695750	+	0.718284i	$0.255072\pi$
$38$			1.02902e13i			2.36676i
$39$	−5.89594e12			−1.10163
$40$		−	3.76610e11i		−	0.0574661i
$41$			2.16776e11i			0.0271481i	0.999908	+	0.0135740i	$0.00432089\pi$
$41$			2.16776e11i			0.0271481i	−0.999908	+	0.0135740i	$0.995679\pi$
$42$	−1.73963e13	+	2.68469e12i	−1.79664	+	0.277268i
$43$	5.58592e12			0.477911			0.238956	−	0.971030i	$-0.423195\pi$
$43$	5.58592e12			0.477911			0.238956	+	0.971030i	$0.423195\pi$
$44$	2.61769e13			1.86336
$45$		−	3.33372e11i		−	0.0198257i
$46$	3.94239e12			0.196651
$47$		−	4.97420e11i		−	0.0208901i	−0.999945	−	0.0104450i	$-0.996675\pi$
$47$		−	4.97420e11i		−	0.0208901i	0.999945	−	0.0104450i	$-0.00332482\pi$
$48$			5.15833e12i			0.183054i
$49$	−3.16868e13	+	1.00188e13i	−0.953475	+	0.301471i
$50$	−6.20277e13			−1.58791
$51$	6.30893e13			1.37846
$52$		−	7.97630e13i		−	1.49202i
$53$	4.55472e13			0.731569			0.365784	−	0.930700i	$-0.380801\pi$
$53$	4.55472e13			0.731569			0.365784	+	0.930700i	$0.380801\pi$
$54$			9.21135e13i			1.27401i
$55$			6.69738e12i			0.0799840i
$56$	−1.27927e13	−	8.28942e13i	−0.132269	−	0.857077i
$57$	−1.88474e14			−1.69143
$58$	2.73946e14			2.13915
$59$		−	1.09329e14i		−	0.744594i	−0.928114	−	0.372297i	$-0.878570\pi$
$59$		−	1.09329e14i		−	0.744594i	0.928114	−	0.372297i	$-0.121430\pi$
$60$	1.95841e13			0.116598
$61$		−	3.61273e14i		−	1.88450i	−0.334907	−	0.942251i	$-0.608705\pi$
$61$		−	3.61273e14i		−	1.88450i	0.334907	−	0.942251i	$-0.391295\pi$
$62$			3.21907e14i			1.47434i
$63$	−1.13240e13	−	7.33772e13i	−0.0456325	−	0.295690i
$64$	−4.59105e14			−1.63107
$65$	2.04074e13			0.0640443
$66$			7.90036e14i			2.19430i
$67$	2.27208e14			0.559531			0.279766	−	0.960068i	$-0.409743\pi$
$67$	2.27208e14			0.559531			0.279766	+	0.960068i	$0.409743\pi$
$68$			8.53502e14i			1.86695i
$69$			7.22087e13i			0.140539i
$70$	6.02131e13	−	9.29240e12i	0.104450	−	0.0161192i
$71$	6.95480e14			1.07700			0.538502	−	0.842624i	$-0.318990\pi$
$71$	6.95480e14			1.07700			0.538502	+	0.842624i	$0.318990\pi$
$72$	1.87387e14			0.259465
$73$		−	1.27766e15i		−	1.58428i	−0.610338	−	0.792141i	$-0.708967\pi$
$73$		−	1.27766e15i		−	1.58428i	0.610338	−	0.792141i	$-0.291033\pi$
$74$	−1.99560e15			−2.21932
$75$		−	1.13610e15i		−	1.13482i
$76$		−	2.54977e15i		−	2.29082i
$77$	2.27496e14	+	1.47413e15i	0.184098	+	1.19292i
$78$	2.40730e15			1.75700
$79$	−1.01425e14			−0.0668544			−0.0334272	−	0.999441i	$-0.510642\pi$
$79$	−1.01425e14			−0.0668544			−0.0334272	+	0.999441i	$0.510642\pi$
$80$		−	1.78543e13i		−	0.0106420i
$81$	−2.24155e15			−1.20968
$82$		−	8.85089e13i		−	0.0432988i
$83$			9.27081e14i			0.411617i	0.978592	+	0.205808i	$0.0659823\pi$
$83$			9.27081e14i			0.411617i	−0.978592	+	0.205808i	$0.934018\pi$
$84$	4.31057e15	−	6.65230e14i	1.73900	−	0.268372i
$85$	−2.18369e14			−0.0801381
$86$	−2.28072e15			−0.762227
$87$			5.01758e15i			1.52876i
$88$	−3.76456e15			−1.04677
$89$			2.66921e15i			0.678051i	0.940777	+	0.339026i	$0.110097\pi$
$89$			2.66921e15i			0.678051i	−0.940777	+	0.339026i	$0.889903\pi$
$90$			1.36115e14i			0.0316203i
$91$	4.49179e15	−	6.93197e14i	0.955187	−	0.147410i
$92$	−9.76873e14			−0.190342
$93$	−5.89604e15			−1.05365
$94$			2.03095e14i			0.0333178i
$95$	6.52359e14			0.0983326
$96$		−	9.23692e15i		−	1.28043i
$97$			6.68122e15i			0.852476i	0.904611	+	0.426238i	$0.140161\pi$
$97$			6.68122e15i			0.852476i	−0.904611	+	0.426238i	$0.859839\pi$
$98$	1.29376e16	−	4.09063e15i	1.52071	−	0.480819i
$99$	−3.33236e15			−0.361136
$100$	1.53697e16			1.53697
$101$		−	1.23999e16i		−	1.14511i	−0.819865	−	0.572557i	$-0.805952\pi$
$101$		−	1.23999e16i		−	1.14511i	0.819865	−	0.572557i	$-0.194048\pi$
$102$	−2.57592e16			−2.19852
$103$			1.67784e16i			1.32450i	0.749283	+	0.662250i	$0.230399\pi$
$103$			1.67784e16i			1.32450i	−0.749283	+	0.662250i	$0.769601\pi$
$104$			1.14709e16i			0.838167i
$105$	1.70199e14	+	1.10286e15i	0.0115198	+	0.0746460i
$106$	−1.85968e16			−1.16679
$107$	1.80063e16			1.04799			0.523993	−	0.851723i	$-0.324442\pi$
$107$	1.80063e16			1.04799			0.523993	+	0.851723i	$0.324442\pi$
$108$		−	2.28245e16i		−	1.23314i
$109$	−9.07598e14			−0.0455493			−0.0227746	−	0.999741i	$-0.507250\pi$
$109$	−9.07598e14			−0.0455493			−0.0227746	+	0.999741i	$0.507250\pi$
$110$		−	2.73452e15i		−	0.127567i
$111$		−	3.65514e16i		−	1.58606i
$112$	−6.06475e14	−	3.92985e15i	−0.0244945	−	0.158720i
$113$	7.26810e15			0.273397			0.136698	−	0.990613i	$-0.456351\pi$
$113$	7.26810e15			0.273397			0.136698	+	0.990613i	$0.456351\pi$
$114$	7.69535e16			2.69768
$115$		−	2.49933e14i		−	0.00817036i
$116$	−6.78802e16			−2.07052
$117$			1.01539e16i			0.289166i
$118$			4.46388e16i			1.18756i
$119$	−4.80643e16	+	7.41754e15i	−1.19522	+	0.184452i
$120$	−2.81643e15			−0.0655011
$121$	2.09967e16			0.456949
$122$			1.47507e17i			3.00562i
$123$	1.62113e15			0.0309440
$124$		−	7.97644e16i		−	1.42704i
$125$			7.88200e15i			0.132238i
$126$	4.62355e15	+	2.99597e16i	0.0727798	+	0.471600i
$127$	−9.59192e16			−1.41735			−0.708673	−	0.705537i	$-0.750706\pi$
$127$	−9.59192e16			−1.41735			−0.708673	+	0.705537i	$0.750706\pi$
$128$	1.06504e17			1.47805
$129$		−	4.17736e16i		−	0.544733i
$130$	−8.33228e15			−0.102145
$131$			7.13773e16i			0.822981i	0.911414	+	0.411490i	$0.134992\pi$
$131$			7.13773e16i			0.822981i	−0.911414	+	0.411490i	$0.865008\pi$
$132$		−	1.95761e17i		−	2.12390i
$133$	1.43588e17	−	2.21593e16i	1.46658	−	0.226330i
$134$	−9.27683e16			−0.892403
$135$	5.83966e15			0.0529319
$136$		−	1.22744e17i		−	1.04879i
$137$	5.85495e16			0.471801			0.235900	−	0.971777i	$-0.424196\pi$
$137$	5.85495e16			0.471801			0.235900	+	0.971777i	$0.424196\pi$
$138$		−	2.94826e16i		−	0.224147i
$139$		−	6.49021e16i		−	0.465737i	−0.972508	−	0.232868i	$-0.925189\pi$
$139$		−	6.49021e16i		−	0.465737i	0.972508	−	0.232868i	$-0.0748111\pi$
$140$	−1.49200e16	+	2.30254e15i	−0.101099	+	0.0156021i
$141$	−3.71989e15			−0.0238109
$142$	−2.83963e17			−1.71773
$143$		−	2.03990e17i		−	1.16660i
$144$	8.88363e15			0.0480497
$145$		−	1.73672e16i		−	0.0888760i
$146$			5.21665e17i			2.52679i
$147$	7.49239e16	+	2.36965e17i	0.343622	+	1.08679i
$148$	4.94484e17			2.14812
$149$	−2.20489e17			−0.907605			−0.453802	−	0.891102i	$-0.649933\pi$
$149$	−2.20489e17			−0.907605			−0.453802	+	0.891102i	$0.649933\pi$
$150$			4.63865e17i			1.80993i
$151$	4.42629e16			0.163766			0.0818831	−	0.996642i	$-0.473907\pi$
$151$	4.42629e16			0.163766			0.0818831	+	0.996642i	$0.473907\pi$
$152$			3.66688e17i			1.28691i
$153$		−	1.08652e17i		−	0.361831i
$154$	−9.28861e16	−	6.01885e17i	−0.293620	−	1.90260i
$155$	2.04077e16			0.0612550
$156$	−5.96496e17			−1.70063
$157$		−	3.29112e17i		−	0.891550i	−0.895145	−	0.445775i	$-0.852928\pi$
$157$		−	3.29112e17i		−	0.891550i	0.895145	−	0.445775i	$-0.147072\pi$
$158$	4.14117e16			0.106627
$159$		−	3.40619e17i		−	0.833857i
$160$			3.19714e16i			0.0744392i
$161$	−8.48972e15	−	5.50119e16i	−0.0188056	−	0.121857i
$162$	9.15220e17			1.92933
$163$	−2.26747e17			−0.455030			−0.227515	−	0.973775i	$-0.573060\pi$
$163$	−2.26747e17			−0.455030			−0.227515	+	0.973775i	$0.573060\pi$
$164$			2.19314e16i			0.0419097i
$165$	5.00854e16			0.0911674
$166$		−	3.78525e17i		−	0.656492i
$167$			7.85584e17i			1.29856i	0.760551	+	0.649278i	$0.224929\pi$
$167$			7.85584e17i			1.29856i	−0.760551	+	0.649278i	$0.775071\pi$
$168$	−6.19913e17	+	9.56682e16i	−0.976914	+	0.150763i
$169$	4.38432e16			0.0658883
$170$	8.91594e16			0.127813
$171$			3.24589e17i			0.443981i
$172$	5.65132e17			0.737773
$173$			2.44552e17i			0.304791i	0.988320	+	0.152395i	$0.0486987\pi$
$173$			2.44552e17i			0.304791i	−0.988320	+	0.152395i	$0.951301\pi$
$174$		−	2.04866e18i		−	2.43824i
$175$	1.33573e17	+	8.65530e17i	0.151850	+	0.983961i
$176$	−1.78470e17			−0.193850
$177$	−8.17603e17			−0.848704
$178$		−	1.08983e18i		−	1.08143i
$179$	2.04826e18			1.94340			0.971698	−	0.236227i	$-0.0759110\pi$
$179$	2.04826e18			1.94340			0.971698	+	0.236227i	$0.0759110\pi$
$180$		−	3.37275e16i		−	0.0306058i
$181$		−	2.67477e16i		−	0.0232198i	−0.999933	−	0.0116099i	$-0.996304\pi$
$181$		−	2.67477e16i		−	0.0232198i	0.999933	−	0.0116099i	$-0.00369563\pi$
$182$	−1.83399e18	+	2.83031e17i	−1.52344	+	0.235105i
$183$	−2.70173e18			−2.14799
$184$	1.40486e17			0.106928
$185$			1.26514e17i			0.0922071i
$186$	2.40734e18			1.68048
$187$			2.18280e18i			1.45976i
$188$		−	5.03244e16i		−	0.0322489i
$189$	1.28535e18	−	1.98361e17i	0.789451	−	0.121832i
$190$	−2.66356e17			−0.156832
$191$	2.28035e18			1.28746			0.643731	−	0.765252i	$-0.277386\pi$
$191$	2.28035e18			1.28746			0.643731	+	0.765252i	$0.277386\pi$
$192$			3.43335e18i			1.85913i
$193$	1.10363e17			0.0573278			0.0286639	−	0.999589i	$-0.490875\pi$
$193$	1.10363e17			0.0573278			0.0286639	+	0.999589i	$0.490875\pi$
$194$		−	2.72793e18i		−	1.35962i
$195$		−	1.52614e17i		−	0.0729990i
$196$	−3.20578e18	+	1.01361e18i	−1.47192	+	0.465394i
$197$	−3.51439e18			−1.54925			−0.774624	−	0.632422i	$-0.782061\pi$
$197$	−3.51439e18			−1.54925			−0.774624	+	0.632422i	$0.782061\pi$
$198$	1.36059e18			0.575979
$199$			2.37297e18i			0.964868i	0.875932	+	0.482434i	$0.160247\pi$
$199$			2.37297e18i			0.964868i	−0.875932	+	0.482434i	$0.839753\pi$
$200$	−2.21034e18			−0.863415
$201$		−	1.69914e18i		−	0.637765i
$202$			5.06286e18i			1.82636i
$203$	−5.89927e17	−	3.82262e18i	−0.204564	−	1.32554i
$204$	6.38280e18			2.12799
$205$	−5.61114e15			−0.00179895
$206$		−	6.85057e18i		−	2.11246i
$207$	1.24357e17			0.0368900
$208$			5.43812e17i			0.155218i
$209$		−	6.52092e18i		−	1.79118i
$210$	−6.94920e16	−	4.50295e17i	−0.0183730	−	0.119054i
$211$	1.78169e18			0.453494			0.226747	−	0.973954i	$-0.427191\pi$
$211$	1.78169e18			0.453494			0.226747	+	0.973954i	$0.427191\pi$
$212$	4.60805e18			1.12935
$213$		−	5.20105e18i		−	1.22759i
$214$	−7.35194e18			−1.67144
$215$			1.44589e17i			0.0316686i
$216$			3.28244e18i			0.692735i
$217$	4.49187e18	−	6.93210e17i	0.913586	−	0.140989i
$218$	3.70570e17			0.0726471
$219$	−9.55480e18			−1.80580
$220$			6.77579e17i			0.123475i
$221$	6.65113e18			1.16885
$222$			1.49238e19i			2.52963i
$223$			7.19769e18i			1.17694i	0.808519	+	0.588470i	$0.200269\pi$
$223$			7.19769e18i			1.17694i	−0.808519	+	0.588470i	$0.799731\pi$
$224$	1.08600e18	+	7.03710e18i	0.171335	+	1.11022i
$225$	−1.95658e18			−0.297877
$226$	−2.96755e18			−0.436044
$227$			6.89000e18i			0.977265i	0.872490	+	0.488633i	$0.162504\pi$
$227$			6.89000e18i			0.977265i	−0.872490	+	0.488633i	$0.837496\pi$
$228$	−1.90681e19			−2.61113
$229$		−	1.04660e19i		−	1.38387i	−0.721960	−	0.691934i	$-0.756759\pi$
$229$		−	1.04660e19i		−	1.38387i	0.721960	−	0.691934i	$-0.243241\pi$
$230$			1.02047e17i			0.0130310i
$231$	1.10241e19	−	1.70130e18i	1.35971	−	0.209838i
$232$	9.76200e18			1.16315
$233$	5.39492e18			0.621066			0.310533	−	0.950563i	$-0.399492\pi$
$233$	5.39492e18			0.621066			0.310533	+	0.950563i	$0.399492\pi$
$234$		−	4.14583e18i		−	0.461195i
$235$	1.28755e16			0.00138427
$236$		−	1.10609e19i		−	1.14946i
$237$			7.58495e17i			0.0762020i
$238$	1.96245e19	−	3.02856e18i	1.90627	−	0.294185i
$239$	−1.56767e19			−1.47256			−0.736279	−	0.676678i	$-0.763419\pi$
$239$	−1.56767e19			−1.47256			−0.736279	+	0.676678i	$0.763419\pi$
$240$	−1.33521e17			−0.0121300
$241$			1.10188e19i			0.968270i	0.874993	+	0.484135i	$0.160866\pi$
$241$			1.10188e19i			0.968270i	−0.874993	+	0.484135i	$0.839134\pi$
$242$	−8.57290e18			−0.728794
$243$			7.05164e18i			0.580016i
$244$		−	3.65503e19i		−	2.90919i
$245$	−2.59331e17	−	8.20199e17i	−0.0199768	−	0.0631816i
$246$	−6.61902e17			−0.0493529
$247$	−1.98697e19			−1.43422
$248$			1.14711e19i			0.801662i
$249$	6.93305e18			0.469169
$250$		−	3.21820e18i		−	0.210908i
$251$			8.64238e18i			0.548584i	0.961646	+	0.274292i	$0.0884435\pi$
$251$			8.64238e18i			0.548584i	−0.961646	+	0.274292i	$0.911556\pi$
$252$	−1.14565e18	−	7.42363e18i	−0.0704449	−	0.456470i
$253$	−2.49831e18			−0.148827
$254$	3.91636e19			2.26054
$255$			1.63304e18i			0.0913430i
$256$	−1.33976e19			−0.726284
$257$		−	2.02542e19i		−	1.06427i	−0.846661	−	0.532133i	$-0.821391\pi$
$257$		−	2.02542e19i		−	1.06427i	0.846661	−	0.532133i	$-0.178609\pi$
$258$			1.70560e19i			0.868801i
$259$	4.29742e18	+	2.78465e19i	0.212231	+	1.37522i
$260$	2.06463e18			0.0988680
$261$	8.64124e18			0.401284
$262$		−	2.91432e19i		−	1.31258i
$263$	−1.07807e19			−0.470977			−0.235488	−	0.971877i	$-0.575669\pi$
$263$	−1.07807e19			−0.470977			−0.235488	+	0.971877i	$0.575669\pi$
$264$			2.81528e19i			1.19314i
$265$			1.17897e18i			0.0484770i
$266$	−5.86267e19	+	9.04758e18i	−2.33907	+	0.360977i
$267$	1.99613e19			0.772856
$268$	2.29868e19			0.863773
$269$		−	2.06012e19i		−	0.751404i	−0.926741	−	0.375702i	$-0.877402\pi$
$269$		−	2.06012e19i		−	0.751404i	0.926741	−	0.375702i	$-0.122598\pi$
$270$	−2.38432e18			−0.0844217
$271$			1.74826e19i			0.600970i	0.953787	+	0.300485i	$0.0971485\pi$
$271$			1.74826e19i			0.600970i	−0.953787	+	0.300485i	$0.902852\pi$
$272$		−	5.81904e18i		−	0.194223i
$273$	−5.18398e18	−	3.35912e19i	−0.168020	−	1.08874i
$274$	−2.39056e19			−0.752481
$275$	3.93072e19			1.20174
$276$			7.30541e18i			0.216956i
$277$	−1.37674e19			−0.397204			−0.198602	−	0.980080i	$-0.563640\pi$
$277$	−1.37674e19			−0.397204			−0.198602	+	0.980080i	$0.563640\pi$
$278$			2.64994e19i			0.742809i
$279$			1.01541e19i			0.276572i
$280$	2.14568e18	−	3.31133e17i	0.0567938	−	0.00876472i
$281$	−3.60798e19			−0.928141			−0.464071	−	0.885798i	$-0.653612\pi$
$281$	−3.60798e19			−0.928141			−0.464071	+	0.885798i	$0.653612\pi$
$282$	1.51882e18			0.0379764
$283$			3.17753e19i			0.772323i	0.922431	+	0.386161i	$0.126199\pi$
$283$			3.17753e19i			0.772323i	−0.922431	+	0.386161i	$0.873801\pi$
$284$	7.03622e19			1.66262
$285$		−	4.87857e18i		−	0.112082i
$286$			8.32888e19i			1.86062i
$287$	−1.23505e18	+	1.90599e17i	−0.0268305	+	0.00414062i
$288$	−1.59077e19			−0.336100
$289$	−2.25091e19			−0.462567
$290$			7.09097e18i			0.141749i
$291$	4.99646e19			0.971669
$292$		−	1.29262e20i		−	2.44572i
$293$		−	6.40161e18i		−	0.117855i	−0.998262	−	0.0589275i	$-0.981232\pi$
$293$		−	6.40161e18i		−	0.117855i	0.998262	−	0.0589275i	$-0.0187681\pi$
$294$	−3.05912e19	−	9.67523e19i	−0.548048	−	1.73334i
$295$	2.82994e18			0.0493402
$296$	−7.11129e19			−1.20674
$297$		−	5.83727e19i		−	0.964181i
$298$	9.00251e19			1.44755
$299$			7.61253e18i			0.119168i
$300$		−	1.14940e20i		−	1.75186i
$301$	4.91140e18	+	3.18250e19i	0.0728909	+	0.472320i
$302$	−1.80724e19			−0.261193
$303$	−9.27312e19			−1.30522
$304$			1.73839e19i			0.238319i
$305$	9.35139e18			0.124876
$306$			4.43623e19i			0.577089i
$307$		−	5.38516e19i		−	0.682483i	−0.939976	−	0.341241i	$-0.889153\pi$
$307$		−	5.38516e19i		−	0.682483i	0.939976	−	0.341241i	$-0.110847\pi$
$308$	2.30160e19	+	1.49139e20i	0.284200	+	1.84156i
$309$	1.25475e20			1.50969
$310$	−8.33243e18			−0.0976963
$311$			2.58213e18i			0.0295049i	0.999891	+	0.0147525i	$0.00469603\pi$
$311$			2.58213e18i			0.0295049i	−0.999891	+	0.0147525i	$0.995304\pi$
$312$	8.57835e19			0.955360
$313$			1.59989e20i			1.73674i	0.495916	+	0.868371i	$0.334832\pi$
$313$			1.59989e20i			1.73674i	−0.495916	+	0.868371i	$0.665168\pi$
$314$			1.34375e20i			1.42194i
$315$	1.89934e18	−	2.93116e17i	0.0195938	−	0.00302381i
$316$	−1.02613e19			−0.103206
$317$	−1.54925e20			−1.51931			−0.759654	−	0.650327i	$-0.774632\pi$
$317$	−1.54925e20			−1.51931			−0.759654	+	0.650327i	$0.774632\pi$
$318$			1.39074e20i			1.32993i
$319$	−1.73601e20			−1.61892
$320$		−	1.18837e19i		−	0.108082i
$321$		−	1.34658e20i		−	1.19452i
$322$	3.46633e18	+	2.24612e19i	0.0299932	+	0.194351i
$323$	2.12615e20			1.79463
$324$	−2.26780e20			−1.86743
$325$		−	1.19772e20i		−	0.962251i
$326$	9.25801e19			0.725733
$327$			6.78734e18i			0.0519180i
$328$		−	3.15400e18i		−	0.0235435i
$329$	2.83398e18	−	4.37354e17i	0.0206457	−	0.00318615i
$330$	−2.04497e19			−0.145404
$331$	1.34757e20			0.935250			0.467625	−	0.883927i	$-0.345110\pi$
$331$	1.34757e20			0.935250			0.467625	+	0.883927i	$0.345110\pi$
$332$			9.37935e19i			0.635431i
$333$	−6.29485e19			−0.416324
$334$		−	3.20752e20i		−	2.07108i
$335$			5.88117e18i			0.0370771i
$336$	−2.93888e19	+	4.53544e18i	−0.180912	+	0.0279193i
$337$	3.14834e20			1.89253			0.946263	−	0.323397i	$-0.104825\pi$
$337$	3.14834e20			1.89253			0.946263	+	0.323397i	$0.104825\pi$
$338$	−1.79011e19			−0.105086
$339$		−	5.43535e19i		−	0.311623i
$340$	−2.20925e19			−0.123713
$341$		−	2.03994e20i		−	1.11579i
$342$		−	1.32529e20i		−	0.708111i
$343$	−8.49409e19	−	1.71722e20i	−0.443367	−	0.896340i
$344$	−8.12729e19			−0.414456
$345$	−1.86909e18			−0.00931275
$346$		−	9.98499e19i		−	0.486115i
$347$	−5.16019e19			−0.245488			−0.122744	−	0.992438i	$-0.539169\pi$
$347$	−5.16019e19			−0.245488			−0.122744	+	0.992438i	$0.539169\pi$
$348$			5.07633e20i			2.36002i
$349$			3.15723e20i			1.43451i	0.696813	+	0.717253i	$0.254601\pi$
$349$			3.15723e20i			1.43451i	−0.696813	+	0.717253i	$0.745399\pi$
$350$	−5.45376e19	−	3.53394e20i	−0.242187	−	1.56933i
$351$	−1.77866e20			−0.772033
$352$	3.19583e20			1.35595
$353$			1.58851e20i			0.658859i	0.944180	+	0.329430i	$0.106856\pi$
$353$			1.58851e20i			0.658859i	−0.944180	+	0.329430i	$0.893144\pi$
$354$	3.33825e20			1.35361
$355$			1.80022e19i			0.0713672i
$356$			2.70046e20i			1.04674i
$357$	5.54710e19	+	3.59442e20i	0.210242	+	1.36233i
$358$	−8.36300e20			−3.09954
$359$	−2.20331e20			−0.798584			−0.399292	−	0.916824i	$-0.630744\pi$
$359$	−2.20331e20			−0.798584			−0.399292	+	0.916824i	$0.630744\pi$
$360$			4.85043e18i			0.0171933i
$361$	−3.46730e20			−1.20208
$362$			1.09210e19i			0.0370335i
$363$		−	1.57021e20i		−	0.520840i
$364$	4.54438e20	−	7.01313e19i	1.47456	−	0.227563i
$365$	3.30717e19			0.104982
$366$	1.10311e21			3.42586
$367$		−	2.42153e20i		−	0.735804i	−0.929865	−	0.367902i	$-0.880076\pi$
$367$		−	2.42153e20i		−	0.735804i	0.929865	−	0.367902i	$-0.119924\pi$
$368$	6.66017e18			0.0198017
$369$		−	2.79189e18i		−	0.00812246i
$370$		−	5.16553e19i		−	0.147062i
$371$	4.00472e19	+	2.59499e20i	0.111579	+	0.723010i
$372$	−5.96507e20			−1.62657
$373$	1.57395e20			0.420070			0.210035	−	0.977694i	$-0.432642\pi$
$373$	1.57395e20			0.420070			0.210035	+	0.977694i	$0.432642\pi$
$374$		−	8.91230e20i		−	2.32818i
$375$	5.89445e19			0.150728
$376$			7.23726e18i			0.0181164i
$377$			5.28974e20i			1.29629i
$378$	−5.24803e20	+	8.09904e19i	−1.25911	+	0.194312i
$379$	3.11365e20			0.731402			0.365701	−	0.930732i	$-0.380829\pi$
$379$	3.11365e20			0.731402			0.365701	+	0.930732i	$0.380829\pi$
$380$	6.59996e19			0.151800
$381$			7.17319e20i			1.61552i
$382$	−9.31061e20			−2.05339
$383$			1.87875e20i			0.405770i	0.979203	+	0.202885i	$0.0650318\pi$
$383$			1.87875e20i			0.405770i	−0.979203	+	0.202885i	$0.934968\pi$
$384$		−	7.96479e20i		−	1.68471i
$385$	−3.81573e19	+	5.88864e18i	−0.0790482	+	0.0121991i
$386$	−4.50610e19			−0.0914328
$387$	−7.19421e19			−0.142987
$388$			6.75945e20i			1.31600i
$389$	1.12070e20			0.213744			0.106872	−	0.994273i	$-0.465917\pi$
$389$	1.12070e20			0.213744			0.106872	+	0.994273i	$0.465917\pi$
$390$			6.23118e19i			0.116427i
$391$		−	8.14577e19i		−	0.149114i
$392$	4.61030e20	−	1.45769e20i	0.826876	−	0.261442i
$393$	5.33785e20			0.938050
$394$	1.43492e21			2.47091
$395$		−	2.62535e18i		−	0.00443007i
$396$	−3.37137e20			−0.557501
$397$		−	6.53675e20i		−	1.05935i	−0.848202	−	0.529673i	$-0.822315\pi$
$397$		−	6.53675e20i		−	1.05935i	0.848202	−	0.529673i	$-0.177685\pi$
$398$		−	9.68878e20i		−	1.53888i
$399$	−1.65715e20	−	1.07380e21i	−0.257976	−	1.67164i
$400$	−1.04788e20			−0.159894
$401$	−1.04007e21			−1.55564			−0.777818	−	0.628489i	$-0.783674\pi$
$401$	−1.04007e21			−1.55564			−0.777818	+	0.628489i	$0.783674\pi$
$402$			6.93755e20i			1.01718i
$403$	−6.21585e20			−0.893429
$404$		−	1.25451e21i		−	1.76776i
$405$		−	5.80216e19i		−	0.0801585i
$406$	2.40866e20	+	1.56077e21i	0.326262	+	2.11412i
$407$	1.26462e21			1.67960
$408$	−9.17924e20			−1.19543
$409$		−	6.01406e19i		−	0.0768036i	−0.999262	−	0.0384018i	$-0.987773\pi$
$409$		−	6.01406e19i		−	0.0768036i	0.999262	−	0.0384018i	$-0.0122267\pi$
$410$	2.29101e18			0.00286917
$411$		−	4.37855e20i		−	0.537768i
$412$			1.69748e21i			2.04469i
$413$	6.22887e20	−	9.61272e19i	0.735883	−	0.113565i
$414$	−5.07748e19			−0.0588363
$415$	−2.39971e19			−0.0272756
$416$		−	9.73793e20i		−	1.08573i
$417$	−4.85361e20			−0.530856
$418$			2.66248e21i			2.85677i
$419$		−	1.48142e21i		−	1.55943i	−0.626132	−	0.779717i	$-0.715363\pi$
$419$		−	1.48142e21i		−	1.55943i	0.626132	−	0.779717i	$-0.284637\pi$
$420$	1.72192e19	+	1.11577e20i	0.0177836	+	0.115234i
$421$	−8.00717e20			−0.811377			−0.405688	−	0.914011i	$-0.632968\pi$
$421$	−8.00717e20			−0.811377			−0.405688	+	0.914011i	$0.632968\pi$
$422$	−7.27458e20			−0.723283
$423$			6.40636e18i			0.00625012i
$424$	−6.62694e20			−0.634433
$425$			1.28162e21i			1.20406i
$426$			2.12358e21i			1.95790i
$427$	2.05830e21	−	3.17648e20i	1.86245	−	0.287424i
$428$	1.82172e21			1.61782
$429$	−1.52551e21			−1.32971
$430$		−	5.90354e19i		−	0.0505086i
$431$	9.39265e20			0.788805			0.394403	−	0.918938i	$-0.370952\pi$
$431$	9.39265e20			0.788805			0.394403	+	0.918938i	$0.370952\pi$
$432$			1.55614e20i			0.128286i
$433$		−	8.56977e20i		−	0.693531i	−0.937952	−	0.346766i	$-0.887280\pi$
$433$		−	8.56977e20i		−	0.693531i	0.937952	−	0.346766i	$-0.112720\pi$
$434$	−1.83402e21	+	2.83036e20i	−1.45709	+	0.224866i
$435$	−1.29878e20			−0.101303
$436$	−9.18224e19			−0.0703164
$437$			2.43348e20i			0.182969i
$438$	3.90120e21			2.88009
$439$		−	9.40472e20i		−	0.681757i	−0.940107	−	0.340879i	$-0.889275\pi$
$439$		−	9.40472e20i		−	0.681757i	0.940107	−	0.340879i	$-0.110725\pi$
$440$		−	9.74441e19i		−	0.0693640i
$441$	4.08100e20	−	1.29033e20i	0.285271	−	0.0901972i
$442$	−2.71564e21			−1.86421
$443$	−2.61949e21			−1.76598			−0.882991	−	0.469390i	$-0.844474\pi$
$443$	−2.61949e21			−1.76598			−0.882991	+	0.469390i	$0.844474\pi$
$444$		−	3.69793e21i		−	2.44847i
$445$	−6.90913e19			−0.0449307
$446$		−	2.93880e21i		−	1.87712i
$447$			1.64890e21i			1.03451i
$448$	−4.03666e20	−	2.61568e21i	−0.248770	−	1.61199i
$449$	−2.75819e20			−0.166976			−0.0834879	−	0.996509i	$-0.526606\pi$
$449$	−2.75819e20			−0.166976			−0.0834879	+	0.996509i	$0.526606\pi$
$450$	7.98865e20			0.475087
$451$			5.60885e19i			0.0327689i
$452$	7.35319e20			0.422054
$453$		−	3.31014e20i		−	0.186664i
$454$		−	2.81317e21i		−	1.55865i
$455$	1.79431e19	+	1.16268e20i	0.00976802	+	0.0632950i
$456$	2.74222e21			1.46684
$457$	2.49048e21			1.30904			0.654520	−	0.756044i	$-0.272871\pi$
$457$	2.49048e21			1.30904			0.654520	+	0.756044i	$0.272871\pi$
$458$			4.27322e21i			2.20715i
$459$	1.90325e21			0.966038
$460$		−	2.52859e19i		−	0.0126129i
$461$			3.69003e21i			1.80893i	0.426545	+	0.904466i	$0.359730\pi$
$461$			3.69003e21i			1.80893i	−0.426545	+	0.904466i	$0.640270\pi$
$462$	−4.50112e21	+	6.94636e20i	−2.16862	+	0.334674i
$463$	−3.06537e20			−0.145156			−0.0725780	−	0.997363i	$-0.523123\pi$
$463$	−3.06537e20			−0.145156			−0.0725780	+	0.997363i	$0.523123\pi$
$464$	4.62797e20			0.215400
$465$		−	1.52617e20i		−	0.0698197i
$466$	−2.20273e21			−0.990546
$467$			3.86462e21i			1.70833i	0.520002	+	0.854165i	$0.325931\pi$
$467$			3.86462e21i			1.70833i	−0.520002	+	0.854165i	$0.674069\pi$
$468$			1.02728e21i			0.446398i
$469$	1.99771e20	+	1.29448e21i	0.0853396	+	0.552985i
$470$	−5.25703e18			−0.00220779
$471$	−2.46122e21			−1.01621
$472$			1.59069e21i			0.645730i
$473$	1.44530e21			0.576859
$474$		−	3.09692e20i		−	0.121535i
$475$		−	3.82873e21i		−	1.47743i
$476$	−4.86270e21	+	7.50438e20i	−1.84511	+	0.284747i
$477$	−5.86611e20			−0.218879
$478$	6.40077e21			2.34860
$479$			2.80191e21i			1.01105i	0.862813	+	0.505523i	$0.168700\pi$
$479$			2.80191e21i			1.01105i	−0.862813	+	0.505523i	$0.831300\pi$
$480$	2.39094e20			0.0848473
$481$		−	3.85339e21i		−	1.34488i
$482$		−	4.49893e21i		−	1.54431i
$483$	−4.11399e20	+	6.34892e19i	−0.138895	+	0.0214350i
$484$	2.12425e21			0.705413
$485$	−1.72941e20			−0.0564889
$486$		−	2.87917e21i		−	0.925075i
$487$	−2.42694e21			−0.767058			−0.383529	−	0.923529i	$-0.625291\pi$
$487$	−2.42694e21			−0.767058			−0.383529	+	0.923529i	$0.625291\pi$
$488$			5.25637e21i			1.63428i
$489$			1.69569e21i			0.518652i
$490$	1.05884e20	+	3.34885e20i	0.0318612	+	0.100769i
$491$	−3.73522e21			−1.10577			−0.552884	−	0.833258i	$-0.686473\pi$
$491$	−3.73522e21			−1.10577			−0.552884	+	0.833258i	$0.686473\pi$
$492$	1.64011e20			0.0477695
$493$		−	5.66027e21i		−	1.62204i
$494$	8.11275e21			2.28746
$495$		−	8.62567e19i		−	0.0239305i
$496$			5.43822e20i			0.148458i
$497$	6.11498e20	+	3.96240e21i	0.164265	+	1.06440i
$498$	−2.83074e21			−0.748283
$499$	−2.75957e21			−0.717855			−0.358928	−	0.933365i	$-0.616857\pi$
$499$	−2.75957e21			−0.717855			−0.358928	+	0.933365i	$0.616857\pi$
$500$			7.97428e20i			0.204142i
$501$	5.87488e21			1.48012
$502$		−	3.52866e21i		−	0.874944i
$503$		−	1.16453e21i		−	0.284190i	−0.989853	−	0.142095i	$-0.954616\pi$
$503$		−	1.16453e21i		−	0.284190i	0.989853	−	0.142095i	$-0.0453838\pi$
$504$	1.64759e20	+	1.06761e21i	0.0395736	+	0.256430i
$505$	3.20967e20			0.0758804
$506$	1.02005e21			0.237366
$507$		−	3.27875e20i		−	0.0751008i
$508$	−9.70422e21			−2.18802
$509$		−	1.91798e21i		−	0.425697i	−0.977085	−	0.212849i	$-0.931726\pi$
$509$		−	1.91798e21i		−	0.425697i	0.977085	−	0.212849i	$-0.0682742\pi$
$510$		−	6.66766e20i		−	0.145684i
$511$	7.27928e21	−	1.12338e21i	1.56575	−	0.241634i
$512$	−1.50968e21			−0.319686
$513$	−5.68580e21			−1.18537
$514$			8.26974e21i			1.69741i
$515$	−4.34301e20			−0.0877674
$516$		−	4.22626e21i		−	0.840928i
$517$		−	1.28702e20i		−	0.0252152i
$518$	−1.75463e21	−	1.13697e22i	−0.338490	−	2.19336i
$519$	1.82885e21			0.347407
$520$	−2.96919e20			−0.0555407
$521$		−	4.45565e21i		−	0.820747i	−0.911918	−	0.410373i	$-0.865398\pi$
$521$		−	4.45565e21i		−	0.820747i	0.911918	−	0.410373i	$-0.134602\pi$
$522$	−3.52819e21			−0.640013
$523$			1.08881e22i			1.94509i	0.232708	+	0.972547i	$0.425241\pi$
$523$			1.08881e22i			1.94509i	−0.232708	+	0.972547i	$0.574759\pi$
$524$			7.22130e21i			1.27047i
$525$	6.47275e21	−	9.98909e20i	1.12154	−	0.173082i
$526$	4.40172e21			0.751166
$527$	6.65125e21			1.11794
$528$			1.33467e21i			0.220954i
$529$	−6.03938e21			−0.984797
$530$		−	4.81371e20i		−	0.0773166i
$531$			1.40807e21i			0.222776i
$532$	1.45269e22	−	2.24187e21i	2.26402	−	0.349396i
$533$	1.70906e20			0.0262385
$534$	−8.15015e21			−1.23264
$535$			4.66086e20i			0.0694442i
$536$	−3.30578e21			−0.485239
$537$		−	1.53176e22i		−	2.21512i
$538$			8.41140e21i			1.19842i
$539$	−8.19864e21	+	2.59225e21i	−1.15088	+	0.363888i
$540$	5.90803e20			0.0817132
$541$	−7.31461e21			−0.996812			−0.498406	−	0.866944i	$-0.666081\pi$
$541$	−7.31461e21			−0.996812			−0.498406	+	0.866944i	$0.666081\pi$
$542$		−	7.13811e21i		−	0.958494i
$543$	−2.00029e20			−0.0264664
$544$			1.04201e22i			1.35856i
$545$		−	2.34928e19i		−	0.00301830i
$546$	2.11660e21	+	1.37152e22i	0.267978	+	1.73645i
$547$	2.34362e21			0.292408			0.146204	−	0.989254i	$-0.453294\pi$
$547$	2.34362e21			0.292408			0.146204	+	0.989254i	$0.453294\pi$
$548$	5.92350e21			0.728340
$549$			4.65290e21i			0.563826i
$550$	−1.60490e22			−1.91667
$551$			1.69096e22i			1.99031i
$552$		−	1.05061e21i		−	0.121879i
$553$	−8.91778e19	−	5.77856e20i	−0.0101966	−	0.0660722i
$554$	5.62120e21			0.633506
$555$	9.46117e20			0.105100
$556$		−	6.56620e21i		−	0.718978i
$557$	−6.84087e21			−0.738362			−0.369181	−	0.929357i	$-0.620362\pi$
$557$	−6.84087e21			−0.738362			−0.369181	+	0.929357i	$0.620362\pi$
$558$		−	4.14590e21i		−	0.441108i
$559$		−	4.40394e21i		−	0.461899i
$560$	1.01722e20	−	1.56983e19i	0.0105175	−	0.00162312i
$561$	1.63237e22			1.66386
$562$	1.47313e22			1.48030
$563$		−	7.20778e21i		−	0.714059i	−0.934093	−	0.357030i	$-0.883789\pi$
$563$		−	7.20778e21i		−	0.714059i	0.934093	−	0.357030i	$-0.116211\pi$
$564$	−3.76344e20			−0.0367580
$565$			1.88132e20i			0.0181165i
$566$		−	1.29738e22i		−	1.23179i
$567$	−1.97088e21	−	1.27709e22i	−0.184499	−	1.19552i
$568$	−1.01189e22			−0.934004
$569$	6.81288e20			0.0620058			0.0310029	−	0.999519i	$-0.490130\pi$
$569$	6.81288e20			0.0620058			0.0310029	+	0.999519i	$0.490130\pi$
$570$			1.99191e21i			0.178760i
$571$	−2.77732e21			−0.245774			−0.122887	−	0.992421i	$-0.539215\pi$
$571$	−2.77732e21			−0.245774			−0.122887	+	0.992421i	$0.539215\pi$
$572$		−	2.06379e22i		−	1.80093i
$573$		−	1.70533e22i		−	1.46748i
$574$	5.04267e20	−	7.78211e19i	0.0427922	−	0.00660393i
$575$	−1.46687e21			−0.122758
$576$	5.91289e21			0.488000
$577$		−	1.80819e20i		−	0.0147176i	−0.999973	−	0.00735880i	$-0.997658\pi$
$577$		−	1.80819e20i		−	0.0147176i	0.999973	−	0.00735880i	$-0.00234240\pi$
$578$	9.19040e21			0.737754
$579$		−	8.25335e20i		−	0.0653434i
$580$		−	1.75705e21i		−	0.137202i
$581$	−5.28191e21	+	8.15132e20i	−0.406801	+	0.0627797i
$582$	−2.04004e22			−1.54973
$583$	1.17849e22			0.883034
$584$			1.85894e22i			1.37393i
$585$	−2.62830e20			−0.0191614
$586$			2.61376e21i			0.187968i
$587$			6.30905e21i			0.447568i	0.974639	+	0.223784i	$0.0718410\pi$
$587$			6.30905e21i			0.447568i	−0.974639	+	0.223784i	$0.928159\pi$
$588$	7.58011e21	+	2.39740e22i	0.530465	+	1.67773i
$589$	−1.98701e22			−1.37176
$590$	−1.15546e21			−0.0786932
$591$			2.62819e22i			1.76586i
$592$	−3.37132e21			−0.223473
$593$		−	1.60991e22i		−	1.05284i	−0.850224	−	0.526421i	$-0.823534\pi$
$593$		−	1.60991e22i		−	1.05284i	0.850224	−	0.526421i	$-0.176466\pi$
$594$			2.38334e22i			1.53778i
$595$	−1.92000e20	−	1.24412e21i	−0.0122226	−	0.0792005i
$596$	−2.23070e22			−1.40111
$597$	1.77459e22			1.09978
$598$		−	3.10818e21i		−	0.190063i
$599$	1.71308e22			1.03362			0.516812	−	0.856099i	$-0.327119\pi$
$599$	1.71308e22			1.03362			0.516812	+	0.856099i	$0.327119\pi$
$600$			1.65297e22i			0.984139i
$601$			1.53192e22i			0.899993i	0.893030	+	0.449997i	$0.148575\pi$
$601$			1.53192e22i			0.899993i	−0.893030	+	0.449997i	$0.851425\pi$
$602$	−2.00531e21	−	1.29941e22i	−0.116255	−	0.753309i
$603$	−2.92625e21			−0.167407
$604$	4.47811e21			0.252813
$605$			5.43490e20i			0.0302795i
$606$	3.78619e22			2.08172
$607$			5.15548e21i			0.279743i	0.990170	+	0.139872i	$0.0446690\pi$
$607$			5.15548e21i			0.279743i	−0.990170	+	0.139872i	$0.955331\pi$
$608$		−	3.11291e22i		−	1.66701i
$609$	−2.85869e22	+	4.41169e21i	−1.51088	+	0.233167i
$610$	−3.81815e21			−0.199166
$611$	−3.92165e20			−0.0201902
$612$		−	1.09924e22i		−	0.558575i
$613$	1.13034e22			0.566923			0.283462	−	0.958984i	$-0.408517\pi$
$613$	1.13034e22			0.566923			0.283462	+	0.958984i	$0.408517\pi$
$614$			2.19875e22i			1.08850i
$615$			4.19621e19i			0.00205049i
$616$	−3.30998e21	−	2.14481e22i	−0.159654	−	1.03453i
$617$	2.39769e22			1.14159			0.570797	−	0.821091i	$-0.306634\pi$
$617$	2.39769e22			1.14159			0.570797	+	0.821091i	$0.306634\pi$
$618$	−5.12310e22			−2.40783
$619$		−	3.21184e21i		−	0.149015i	−0.997220	−	0.0745073i	$-0.976262\pi$
$619$		−	3.21184e21i		−	0.149015i	0.997220	−	0.0745073i	$-0.0237384\pi$
$620$	2.06467e21			0.0945620
$621$			2.17836e21i			0.0984910i
$622$		−	1.05428e21i		−	0.0470578i
$623$	−1.52074e22	+	2.34689e21i	−0.670118	+	0.103416i
$624$	4.06682e21			0.176921
$625$	2.29768e22			0.986846
$626$		−	6.53230e22i		−	2.76995i
$627$	−4.87658e22			−2.04162
$628$		−	3.32965e22i		−	1.37633i
$629$			4.12332e22i			1.68283i
$630$	−7.75495e20	+	1.19679e20i	−0.0312503	+	0.00482272i
$631$	9.93900e21			0.395465			0.197732	−	0.980256i	$-0.436642\pi$
$631$	9.93900e21			0.395465			0.197732	+	0.980256i	$0.436642\pi$
$632$	1.47570e21			0.0579777
$633$		−	1.33241e22i		−	0.516902i
$634$	6.32553e22			2.42316
$635$		−	2.48283e21i		−	0.0939197i
$636$		−	3.44607e22i		−	1.28726i
$637$	7.89878e21	+	2.49818e22i	0.291370	+	0.921529i
$638$	7.08807e22			2.58204
$639$	−8.95721e21			−0.322230
$640$			2.75682e21i			0.0979420i
$641$	−3.43710e22			−1.20594			−0.602972	−	0.797762i	$-0.706017\pi$
$641$	−3.43710e22			−1.20594			−0.602972	+	0.797762i	$0.706017\pi$
$642$			5.49805e22i			1.90515i
$643$			3.40151e20i			0.0116408i	0.999983	+	0.00582042i	$0.00185271\pi$
$643$			3.40151e20i			0.0116408i	−0.999983	+	0.00582042i	$0.998147\pi$
$644$	−8.58912e20	−	5.56559e21i	−0.0290310	−	0.188115i
$645$	1.08129e21			0.0360965
$646$	−8.68103e22			−2.86227
$647$			3.80798e22i			1.24011i	0.784558	+	0.620055i	$0.212890\pi$
$647$			3.80798e22i			1.24011i	−0.784558	+	0.620055i	$0.787110\pi$
$648$	3.26137e22			1.04906
$649$		−	2.82878e22i		−	0.898756i
$650$			4.89026e22i			1.53471i
$651$	−5.18407e21	−	3.35918e22i	−0.160703	−	1.04132i
$652$	−2.29401e22			−0.702450
$653$	−1.17440e22			−0.355230			−0.177615	−	0.984100i	$-0.556838\pi$
$653$	−1.17440e22			−0.355230			−0.177615	+	0.984100i	$0.556838\pi$
$654$		−	2.77126e21i		−	0.0828046i
$655$	−1.84757e21			−0.0545344
$656$		−	1.49525e20i		−	0.00435995i
$657$			1.64552e22i			0.474002i
$658$	−1.15711e21	+	1.78571e20i	−0.0329280	+	0.00508163i
$659$	4.51030e22			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$659$	4.51030e22			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$660$	5.06718e21			0.140739
$661$			1.43753e22i			0.394463i	0.980357	+	0.197231i	$0.0631950\pi$
$661$			1.43753e22i			0.394463i	−0.980357	+	0.197231i	$0.936805\pi$
$662$	−5.50210e22			−1.49164
$663$		−	4.97396e22i		−	1.33227i
$664$		−	1.34887e22i		−	0.356964i
$665$	5.73584e20	+	3.71672e21i	0.0149977	+	0.0971822i
$666$	2.57017e22			0.664000
$667$	6.47845e21			0.165373
$668$			7.94782e22i			2.00464i
$669$	5.38269e22			1.34150
$670$		−	2.40127e21i		−	0.0591346i
$671$		−	9.34758e22i		−	2.27467i
$672$	5.26260e22	−	8.12152e21i	1.26545	−	0.195291i
$673$	−4.89270e21			−0.116259			−0.0581297	−	0.998309i	$-0.518514\pi$
$673$	−4.89270e21			−0.116259			−0.0581297	+	0.998309i	$0.518514\pi$
$674$	−1.28546e23			−3.01841
$675$		−	3.42733e22i		−	0.795289i
$676$	4.43565e21			0.101715
$677$			1.54232e22i			0.349514i	0.984612	+	0.174757i	$0.0559139\pi$
$677$			1.54232e22i			0.349514i	−0.984612	+	0.174757i	$0.944086\pi$
$678$			2.21924e22i			0.497011i
$679$	−3.80653e22	+	5.87444e21i	−0.842502	+	0.130019i
$680$	3.17718e21			0.0694976
$681$	5.15259e22			1.11391
$682$			8.32903e22i			1.77959i
$683$	6.61604e22			1.39712			0.698558	−	0.715554i	$-0.253826\pi$
$683$	6.61604e22			1.39712			0.698558	+	0.715554i	$0.253826\pi$
$684$			3.28389e22i			0.685393i
$685$			1.51553e21i			0.0312637i
$686$	3.46811e22	+	7.01136e22i	0.707132	+	1.42958i
$687$	−7.82682e22			−1.57736
$688$	−3.85299e21			−0.0767520
$689$		−	3.59094e22i		−	0.707057i
$690$	7.63145e20			0.0148530
$691$			8.37600e22i			1.61143i	0.592302	+	0.805716i	$0.298219\pi$
$691$			8.37600e22i			1.61143i	−0.592302	+	0.805716i	$0.701781\pi$
$692$			2.47415e22i			0.470519i
$693$	−2.92996e21	−	1.89856e22i	−0.0550803	−	0.356910i
$694$	2.10689e22			0.391531
$695$	1.67996e21			0.0308618
$696$		−	7.30038e22i		−	1.32578i
$697$	−1.82877e21			−0.0328320
$698$		−	1.28909e23i		−	2.28791i
$699$		−	4.03452e22i		−	0.707904i
$700$	1.35137e22	+	8.75664e22i	0.234418	+	1.51898i
$701$	−8.86161e22			−1.51974			−0.759869	−	0.650077i	$-0.774737\pi$
$701$	−8.86161e22			−1.51974			−0.759869	+	0.650077i	$0.774737\pi$
$702$	7.26222e22			1.23132
$703$		−	1.23181e23i		−	2.06491i
$704$	−1.18789e23			−1.96877
$705$		−	9.62876e19i		−	0.00157782i
$706$		−	6.48585e22i		−	1.05082i
$707$	7.06469e22	−	1.09026e22i	1.13172	−	0.174652i
$708$	−8.27175e22			−1.31018
$709$	7.77992e21			0.121844			0.0609221	−	0.998143i	$-0.480596\pi$
$709$	7.77992e21			0.121844			0.0609221	+	0.998143i	$0.480596\pi$
$710$		−	7.35025e21i		−	0.113824i
$711$	1.30627e21			0.0200022
$712$		−	3.88359e22i		−	0.588022i
$713$			7.61267e21i			0.113978i
$714$	−2.26487e22	−	1.46759e23i	−0.335318	−	2.17280i
$715$	5.28021e21			0.0773041
$716$	2.07224e23			3.00010
$717$			1.17236e23i			1.67845i
$718$	8.99607e22			1.27367
$719$			6.60721e22i			0.925097i	0.886594	+	0.462548i	$0.153065\pi$
$719$			6.60721e22i			0.925097i	−0.886594	+	0.462548i	$0.846935\pi$
$720$			2.29949e20i			0.00318399i
$721$	−9.55924e22	+	1.47523e22i	−1.30900	+	0.202013i
$722$	1.41569e23			1.91721
$723$	8.24023e22			1.10365
$724$		−	2.70609e21i		−	0.0358454i
$725$	−1.01929e23			−1.33534
$726$			6.41112e22i			0.830694i
$727$			3.85624e21i			0.0494184i	0.999695	+	0.0247092i	$0.00786599\pi$
$727$			3.85624e21i			0.0494184i	−0.999695	+	0.0247092i	$0.992134\pi$
$728$	−6.53537e22	+	1.00857e22i	−0.828361	+	0.127837i
$729$	−4.37568e22			−0.548561
$730$	−1.35031e22			−0.167436
$731$			4.71242e22i			0.577970i
$732$	−2.73336e23			−3.31595
$733$		−	2.57776e20i		−	0.00309322i	−0.999999	−	0.00154661i	$-0.999508\pi$
$733$		−	2.57776e20i		−	0.00309322i	0.999999	−	0.00154661i	$-0.000492302\pi$
$734$			9.88706e22i			1.17354i
$735$	−6.13374e21	+	1.93937e21i	−0.0720156	+	0.0227700i
$736$	−1.19262e22			−0.138510
$737$	5.87877e22			0.675377
$738$			1.13992e21i			0.0129546i
$739$	1.11396e23			1.25232			0.626160	−	0.779695i	$-0.284626\pi$
$739$	1.11396e23			1.25232			0.626160	+	0.779695i	$0.284626\pi$
$740$			1.27995e22i			0.142344i
$741$			1.48593e23i			1.63475i
$742$	−1.63512e22	−	1.05953e23i	−0.177958	−	1.15314i
$743$	−6.66485e22			−0.717596			−0.358798	−	0.933415i	$-0.616813\pi$
$743$	−6.66485e22			−0.717596			−0.358798	+	0.933415i	$0.616813\pi$
$744$	8.57850e22			0.913751
$745$		−	5.70726e21i		−	0.0601420i
$746$	−6.42641e22			−0.669974
$747$		−	1.19400e22i		−	0.123152i
$748$			2.20835e23i			2.25349i
$749$	1.58320e22	+	1.02589e23i	0.159838	+	1.03572i
$750$	−2.40669e22			−0.240397
$751$	5.43412e22			0.537044			0.268522	−	0.963274i	$-0.413465\pi$
$751$	5.43412e22			0.537044			0.268522	+	0.963274i	$0.413465\pi$
$752$			3.43104e20i			0.00335492i
$753$	6.46308e22			0.625288
$754$		−	2.15979e23i		−	2.06747i
$755$			1.14573e21i			0.0108519i
$756$	1.30039e23	−	2.00684e22i	1.21871	−	0.188078i
$757$	−7.67803e22			−0.712004			−0.356002	−	0.934485i	$-0.615860\pi$
$757$	−7.67803e22			−0.712004			−0.356002	+	0.934485i	$0.615860\pi$
$758$	−1.27130e23			−1.16652
$759$			1.86833e22i			0.169636i
$760$	−9.49155e21			−0.0852763
$761$			1.23846e23i			1.10104i	0.834822	+	0.550520i	$0.185571\pi$
$761$			1.23846e23i			1.10104i	−0.834822	+	0.550520i	$0.814429\pi$
$762$		−	2.92879e23i		−	2.57661i
$763$	−7.98002e20	−	5.17091e21i	−0.00694716	−	0.0450164i
$764$	2.30705e23			1.98751
$765$	2.81241e21			0.0239766
$766$		−	7.67091e22i		−	0.647167i
$767$	−8.61950e22			−0.719646
$768$			1.00192e23i			0.827834i
$769$		−	2.33391e23i		−	1.90841i	−0.299148	−	0.954207i	$-0.596702\pi$
$769$		−	2.33391e23i		−	1.90841i	0.299148	−	0.954207i	$-0.403298\pi$
$770$	1.55795e22	−	2.40432e21i	0.126075	−	0.0194566i
$771$	−1.51468e23			−1.21307
$772$	1.11655e22			0.0884994
$773$		−	1.65084e23i		−	1.29500i	−0.762067	−	0.647498i	$-0.775816\pi$
$773$		−	1.65084e23i		−	1.29500i	0.762067	−	0.647498i	$-0.224184\pi$
$774$	2.93738e22			0.228051
$775$		−	1.19774e23i		−	0.920342i
$776$		−	9.72091e22i		−	0.739287i
$777$	2.08246e23	−	3.21377e22i	1.56750	−	0.241906i
$778$	−4.57579e22			−0.340902
$779$	5.46331e21			0.0402862
$780$		−	1.54401e22i		−	0.112692i
$781$	1.79948e23			1.29999
$782$			3.32590e22i			0.237824i
$783$			1.51368e23i			1.07137i
$784$	2.18565e22	−	6.91061e21i	0.153127	−	0.0484159i
$785$	8.51891e21			0.0590781
$786$	−2.17943e23			−1.49611
$787$		−	3.33541e22i		−	0.226648i	−0.993558	−	0.113324i	$-0.963850\pi$
$787$		−	3.33541e22i		−	0.226648i	0.993558	−	0.113324i	$-0.0361498\pi$
$788$	−3.55554e23			−2.39164
$789$			8.06217e22i			0.536829i
$790$			1.07192e21i			0.00706557i
$791$	6.39045e21	+	4.14089e22i	0.0416984	+	0.270198i
$792$	4.84845e22			0.313185
$793$	−2.84827e23			−1.82136
$794$			2.66894e23i			1.68956i
$795$	8.81677e21			0.0552551
$796$			2.40075e23i			1.48951i
$797$			5.63199e22i			0.345936i	0.984927	+	0.172968i	$0.0553357\pi$
$797$			5.63199e22i			0.345936i	−0.984927	+	0.172968i	$0.944664\pi$
$798$	6.76611e22	+	4.38432e23i	0.411449	+	2.66611i
$799$	4.19636e21			0.0252638
$800$	1.87642e23			1.11843
$801$		−	3.43772e22i		−	0.202867i
$802$	4.24658e23			2.48110
$803$		−	3.30582e23i		−	1.91229i
$804$		−	1.71903e23i		−	0.984546i
$805$	1.42396e21	−	2.19753e20i	0.00807477	−	0.00124614i
$806$	2.53791e23			1.42494
$807$	−1.54063e23			−0.856465
$808$			1.80414e23i			0.993069i
$809$	5.47445e22			0.298368			0.149184	−	0.988809i	$-0.452335\pi$
$809$	5.47445e22			0.298368			0.149184	+	0.988809i	$0.452335\pi$
$810$			2.36901e22i			0.127846i
$811$			1.44446e23i			0.771863i	0.922528	+	0.385931i	$0.126120\pi$
$811$			1.44446e23i			0.771863i	−0.922528	+	0.385931i	$0.873880\pi$
$812$	−5.96834e22	−	3.86737e23i	−0.315795	−	2.04629i
$813$	1.30741e23			0.684998
$814$	−5.16342e23			−2.67881
$815$		−	5.86924e21i		−	0.0301523i
$816$	−4.35169e22			−0.221379
$817$		−	1.40780e23i		−	0.709192i
$818$			2.45553e22i			0.122495i
$819$	−5.78506e22	+	8.92781e21i	−0.285783	+	0.0441036i
$820$	−5.67684e20			−0.00277713
$821$	7.11622e22			0.344750			0.172375	−	0.985031i	$-0.444856\pi$
$821$	7.11622e22			0.344750			0.172375	+	0.985031i	$0.444856\pi$
$822$			1.78775e23i			0.857693i
$823$	8.58942e22			0.408098			0.204049	−	0.978961i	$-0.434590\pi$
$823$	8.58942e22			0.408098			0.204049	+	0.978961i	$0.434590\pi$
$824$		−	2.44119e23i		−	1.14864i
$825$		−	2.93954e23i		−	1.36977i
$826$	−2.54323e23	+	3.92485e22i	−1.17367	+	0.181127i
$827$	−4.41577e22			−0.201819			−0.100910	−	0.994896i	$-0.532175\pi$
$827$	−4.41577e22			−0.201819			−0.100910	+	0.994896i	$0.532175\pi$
$828$	1.25813e22			0.0569487
$829$			3.71226e23i			1.66419i	0.554635	+	0.832094i	$0.312858\pi$
$829$			3.71226e23i			1.66419i	−0.554635	+	0.832094i	$0.687142\pi$
$830$	9.79795e21			0.0435021
$831$			1.02958e23i			0.452742i
$832$			3.61958e23i			1.57642i
$833$	−8.45207e22	−	2.67318e23i	−0.364589	−	1.15310i
$834$	1.98172e23			0.846669
$835$	−2.03345e22			−0.0860482
$836$		−	6.59727e23i		−	2.76512i
$837$	−1.77869e23			−0.738409
$838$			6.04861e23i			2.48716i
$839$			8.56516e22i			0.348851i	0.984670	+	0.174425i	$0.0558068\pi$
$839$			8.56516e22i			0.348851i	−0.984670	+	0.174425i	$0.944193\pi$
$840$	−2.47633e21	−	1.60462e22i	−0.00999021	−	0.0647347i
$841$	1.99923e23			0.798903
$842$	3.26931e23			1.29407
$843$			2.69818e23i			1.05791i
$844$	1.80255e23			0.700079
$845$			1.13486e21i			0.00436605i
$846$		−	2.61570e21i		−	0.00996839i
$847$	1.84613e22	+	1.19626e23i	0.0696938	+	0.451603i
$848$	−3.14170e22			−0.117489
$849$	2.37628e23			0.880309
$850$		−	5.23281e23i		−	1.92036i
$851$	−4.71933e22			−0.171571
$852$		−	5.26194e23i		−	1.89509i
$853$			4.29816e21i			0.0153352i	0.999971	+	0.00766761i	$0.00244070\pi$
$853$			4.29816e21i			0.0153352i	−0.999971	+	0.00766761i	$0.997559\pi$
$854$	−8.40399e23	+	1.29695e23i	−2.97045	+	0.458416i
$855$	−8.40184e21			−0.0294202
$856$	−2.61985e23			−0.908837
$857$		−	2.97073e23i		−	1.02098i	−0.859884	−	0.510490i	$-0.829464\pi$
$857$		−	2.97073e23i		−	1.02098i	0.859884	−	0.510490i	$-0.170536\pi$
$858$	6.22864e23			2.12078
$859$			6.90793e22i			0.233025i	0.993189	+	0.116513i	$0.0371715\pi$
$859$			6.90793e22i			0.233025i	−0.993189	+	0.116513i	$0.962828\pi$
$860$			1.46282e22i			0.0488881i
$861$	1.42537e21	+	9.23613e21i	0.00471956	+	0.0305819i
$862$	−3.83499e23			−1.25807
$863$	3.93816e23			1.27999			0.639995	−	0.768379i	$-0.278936\pi$
$863$	3.93816e23			1.27999			0.639995	+	0.768379i	$0.278936\pi$
$864$		−	2.78655e23i		−	0.897340i
$865$	−6.33012e21			−0.0201968
$866$			3.49902e23i			1.10612i
$867$			1.68331e23i			0.527244i
$868$	4.54446e23	−	7.01326e22i	1.41034	−	0.217652i
$869$	−2.62428e22			−0.0806960
$870$	5.30288e22			0.161569
$871$		−	1.79130e23i		−	0.540784i
$872$	1.32052e22			0.0395014
$873$		−	8.60486e22i		−	0.255053i
$874$		−	9.93585e22i		−	0.291819i
$875$	−4.49066e22	+	6.93022e21i	−0.130691	+	0.0201689i
$876$	−9.66667e23			−2.78769
$877$	−2.92693e23			−0.836403			−0.418201	−	0.908354i	$-0.637339\pi$
$877$	−2.92693e23			−0.836403			−0.418201	+	0.908354i	$0.637339\pi$
$878$			3.83992e23i			1.08734i
$879$	−4.78735e22			−0.134334
$880$		−	4.61963e21i		−	0.0128453i
$881$		−	3.48409e23i		−	0.960024i	−0.877262	−	0.480012i	$-0.840632\pi$
$881$		−	3.48409e23i		−	0.960024i	0.877262	−	0.480012i	$-0.159368\pi$
$882$	−1.66626e23	+	5.26840e22i	−0.454982	+	0.143857i
$883$	−1.09594e23			−0.296552			−0.148276	−	0.988946i	$-0.547372\pi$
$883$	−1.09594e23			−0.296552			−0.148276	+	0.988946i	$0.547372\pi$
$884$	6.72900e23			1.80440
$885$		−	2.11633e22i		−	0.0562389i
$886$	1.06953e24			2.81659
$887$			2.59226e23i			0.676534i	0.941050	+	0.338267i	$0.109841\pi$
$887$			2.59226e23i			0.676534i	−0.941050	+	0.338267i	$0.890159\pi$
$888$			5.31808e23i			1.37547i
$889$	−8.43366e22	−	5.46486e23i	−0.216173	−	1.40076i
$890$	2.82098e22			0.0716605
$891$	−5.79980e23			−1.46013
$892$			7.28196e23i			1.81689i
$893$	−1.25363e22			−0.0309997
$894$		−	6.73240e23i		−	1.64995i
$895$			5.30184e22i			0.128778i
$896$	9.36436e22	+	6.06794e23i	0.225431	+	1.46075i
$897$	5.69293e22			0.135830
$898$	1.12616e23			0.266312
$899$			5.28983e23i			1.23984i
$900$	−1.97948e23			−0.459846
$901$			3.84248e23i			0.884735i
$902$		−	2.29008e22i		−	0.0522635i
$903$	2.37999e23	−	3.67292e22i	0.538360	−	0.0830826i
$904$	−1.05748e23			−0.237096
$905$	6.92353e20			0.00153865
$906$			1.35152e23i			0.297713i
$907$	−2.87326e23			−0.627360			−0.313680	−	0.949529i	$-0.601562\pi$
$907$	−2.87326e23			−0.627360			−0.313680	+	0.949529i	$0.601562\pi$
$908$			6.97067e23i			1.50865i
$909$			1.59701e23i			0.342607i
$910$	−7.32612e21	−	4.74720e22i	−0.0155791	−	0.100950i
$911$	7.32222e23			1.54346			0.771731	−	0.635949i	$-0.219391\pi$
$911$	7.32222e23			1.54346			0.771731	+	0.635949i	$0.219391\pi$
$912$	1.30003e23			0.271641
$913$			2.39873e23i			0.496838i
$914$	−1.01686e24			−2.08780
$915$		−	6.99331e22i		−	0.142336i
$916$		−	1.05885e24i		−	2.13634i
$917$	−4.06662e23	+	6.27582e22i	−0.813352	+	0.125521i
$918$	−7.77092e23			−1.54075
$919$	1.29155e23			0.253856			0.126928	−	0.991912i	$-0.459488\pi$
$919$	1.29155e23			0.253856			0.126928	+	0.991912i	$0.459488\pi$
$920$			3.63643e21i			0.00708553i
$921$	−4.02722e23			−0.777908
$922$		−	1.50663e24i		−	2.88509i
$923$		−	5.48316e23i		−	1.04092i
$924$	1.11532e24	−	1.72122e23i	2.09905	−	0.323937i
$925$	7.42517e23			1.38539
$926$	1.25158e23			0.231511
$927$		−	2.16092e23i		−	0.396278i
$928$	−8.28721e23			−1.50669
$929$		−	5.12792e23i		−	0.924306i	−0.886800	−	0.462153i	$-0.847077\pi$
$929$		−	5.12792e23i		−	0.924306i	0.886800	−	0.462153i	$-0.152923\pi$
$930$			6.23129e22i			0.111356i
$931$	2.52499e23	+	7.98590e23i	0.447365	+	1.41490i
$932$	5.45809e23			0.958767
$933$	1.93101e22			0.0336303
$934$		−	1.57792e24i		−	2.72464i
$935$	−5.65007e22			−0.0967300
$936$		−	1.47736e23i		−	0.250772i
$937$			8.68179e22i			0.146114i	0.997328	+	0.0730571i	$0.0232755\pi$
$937$			8.68179e22i			0.146114i	−0.997328	+	0.0730571i	$0.976724\pi$
$938$	−8.15661e22	−	5.28534e23i	−0.136109	−	0.881962i
$939$	1.19645e24			1.97957
$940$	1.30262e21			0.00213696
$941$			1.04223e23i			0.169531i	0.996401	+	0.0847653i	$0.0270140\pi$
$941$			1.04223e23i			0.169531i	−0.996401	+	0.0847653i	$0.972986\pi$
$942$	1.00491e24			1.62076
$943$		−	2.09312e21i		−	0.00334734i
$944$			7.54116e22i			0.119581i
$945$	5.13450e21	+	3.32706e22i	0.00807316	+	0.0523126i
$946$	−5.90113e23			−0.920039
$947$	−1.05845e24			−1.63633			−0.818166	−	0.574982i	$-0.805009\pi$
$947$	−1.05845e24			−1.63633			−0.818166	+	0.574982i	$0.805009\pi$
$948$			7.67376e22i			0.117636i
$949$	−1.00731e24			−1.53120
$950$			1.56326e24i			2.35636i
$951$			1.15858e24i			1.73174i
$952$	6.99316e23	−	1.07922e23i	1.03652	−	0.159961i
$953$	1.95863e23			0.287878			0.143939	−	0.989587i	$-0.454023\pi$
$953$	1.95863e23			0.287878			0.143939	+	0.989587i	$0.454023\pi$
$954$	2.39512e23			0.349092
$955$			5.90258e22i			0.0853130i
$956$	−1.58603e24			−2.27325
$957$			1.29825e24i			1.84528i
$958$		−	1.14401e24i		−	1.61253i
$959$	5.14794e22	+	3.33577e23i	0.0719590	+	0.466281i
$960$	−8.88709e22			−0.123194
$961$	1.05827e23			0.145482
$962$			1.57333e24i			2.14496i
$963$	−2.31907e23			−0.313547
$964$			1.11478e24i			1.49476i
$965$			2.85670e21i			0.00379880i
$966$	1.67973e23	−	2.59225e22i	0.221525	−	0.0341869i
$967$	−1.73315e23			−0.226685			−0.113343	−	0.993556i	$-0.536156\pi$
$967$	−1.73315e23			−0.226685			−0.113343	+	0.993556i	$0.536156\pi$
$968$	−3.05493e23			−0.396277
$969$		−	1.59002e24i		−	2.04555i
$970$	7.06112e22			0.0900948
$971$		−	1.48269e24i		−	1.87627i	−0.346268	−	0.938136i	$-0.612551\pi$
$971$		−	1.48269e24i		−	1.87627i	0.346268	−	0.938136i	$-0.387449\pi$
$972$			7.13420e23i			0.895396i
$973$	3.69770e23	−	5.70649e22i	0.460288	−	0.0710340i
$974$	9.90915e23			1.22339
$975$	−8.95698e23			−1.09679
$976$			2.49194e23i			0.302649i
$977$	4.94529e23			0.595710			0.297855	−	0.954611i	$-0.403729\pi$
$977$	4.94529e23			0.595710			0.297855	+	0.954611i	$0.403729\pi$
$978$		−	6.92347e23i		−	0.827205i
$979$			6.90631e23i			0.818436i
$980$	−2.62367e22	−	8.29802e22i	−0.0308391	−	0.0975362i
$981$	1.16891e22			0.0136279
$982$	1.52508e24			1.76360
$983$		−	6.39086e23i		−	0.733046i	−0.930409	−	0.366523i	$-0.880548\pi$
$983$		−	6.39086e23i		−	0.733046i	0.930409	−	0.366523i	$-0.119452\pi$
$984$	−2.35867e22			−0.0268353
$985$		−	9.09686e22i		−	0.102660i
$986$			2.31107e24i			2.58701i
$987$	−3.27069e21	−	2.11935e22i	−0.00363164	−	0.0235324i
$988$	−2.01024e24			−2.21407
$989$	−5.39359e22			−0.0589261
$990$			3.52184e22i			0.0381670i
$991$	3.14566e23			0.338160			0.169080	−	0.985602i	$-0.445920\pi$
$991$	3.14566e23			0.338160			0.169080	+	0.985602i	$0.445920\pi$
$992$		−	9.73811e23i		−	1.03844i
$993$		−	1.00776e24i		−	1.06602i
$994$	−2.49673e23	−	1.61784e24i	−0.261987	−	1.69763i
$995$	−6.14233e22			−0.0639365
$996$	7.01422e23			0.724277
$997$			1.42667e24i			1.46138i	0.682711	+	0.730688i	$0.260801\pi$
$997$			1.42667e24i			1.46138i	−0.682711	+	0.730688i	$0.739199\pi$
$998$	1.12672e24			1.14492
$999$		−	1.10267e24i		−	1.11153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.17.b.b.6.1	✓	8
3.2	odd	2		63.17.d.c.55.7		8
4.3	odd	2		112.17.c.b.97.7		8
7.6	odd	2	inner	7.17.b.b.6.2	yes	8
21.20	even	2		63.17.d.c.55.8		8
28.27	even	2		112.17.c.b.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.17.b.b.6.1	✓	8	1.1	even	1	trivial
7.17.b.b.6.2	yes	8	7.6	odd	2	inner
63.17.d.c.55.7		8	3.2	odd	2
63.17.d.c.55.8		8	21.20	even	2
112.17.c.b.97.2		8	28.27	even	2
112.17.c.b.97.7		8	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-408.297 q^{2} -7478.36i q^{3} +101171. q^{4} +25884.6i q^{5} +3.05340e6i q^{6} +(879246. + 5.69736e6i) q^{7} -1.45496e7 q^{8} -1.28792e7 q^{9} +O(q^{10})\)	\(q-408.297 q^{2} -7478.36i q^{3} +101171. q^{4} +25884.6i q^{5} +3.05340e6i q^{6} +(879246. + 5.69736e6i) q^{7} -1.45496e7 q^{8} -1.28792e7 q^{9} -1.05686e7i q^{10} +2.58740e8 q^{11} -7.56592e8i q^{12} -7.88399e8i q^{13} +(-3.58994e8 - 2.32622e9i) q^{14} +1.93574e8 q^{15} -6.89767e8 q^{16} +8.43625e9i q^{17} +5.25853e9 q^{18} -2.52026e10i q^{19} +2.61876e9i q^{20} +(4.26069e10 - 6.57532e9i) q^{21} -1.05643e11 q^{22} -9.65568e9 q^{23} +1.08807e11i q^{24} +1.51918e11 q^{25} +3.21901e11i q^{26} -2.25604e11i q^{27} +(8.89540e10 + 5.76406e11i) q^{28} -6.70946e11 q^{29} -7.90358e10 q^{30} -7.88414e11i q^{31} +1.23515e12 q^{32} -1.93495e12i q^{33} -3.44450e12i q^{34} +(-1.47474e11 + 2.27589e10i) q^{35} -1.30300e12 q^{36} +4.88762e12 q^{37} +1.02902e13i q^{38} -5.89594e12 q^{39} -3.76610e11i q^{40} +2.16776e11i q^{41} +(-1.73963e13 + 2.68469e12i) q^{42} +5.58592e12 q^{43} +2.61769e13 q^{44} -3.33372e11i q^{45} +3.94239e12 q^{46} -4.97420e11i q^{47} +5.15833e12i q^{48} +(-3.16868e13 + 1.00188e13i) q^{49} -6.20277e13 q^{50} +6.30893e13 q^{51} -7.97630e13i q^{52} +4.55472e13 q^{53} +9.21135e13i q^{54} +6.69738e12i q^{55} +(-1.27927e13 - 8.28942e13i) q^{56} -1.88474e14 q^{57} +2.73946e14 q^{58} -1.09329e14i q^{59} +1.95841e13 q^{60} -3.61273e14i q^{61} +3.21907e14i q^{62} +(-1.13240e13 - 7.33772e13i) q^{63} -4.59105e14 q^{64} +2.04074e13 q^{65} +7.90036e14i q^{66} +2.27208e14 q^{67} +8.53502e14i q^{68} +7.22087e13i q^{69} +(6.02131e13 - 9.29240e12i) q^{70} +6.95480e14 q^{71} +1.87387e14 q^{72} -1.27766e15i q^{73} -1.99560e15 q^{74} -1.13610e15i q^{75} -2.54977e15i q^{76} +(2.27496e14 + 1.47413e15i) q^{77} +2.40730e15 q^{78} -1.01425e14 q^{79} -1.78543e13i q^{80} -2.24155e15 q^{81} -8.85089e13i q^{82} +9.27081e14i q^{83} +(4.31057e15 - 6.65230e14i) q^{84} -2.18369e14 q^{85} -2.28072e15 q^{86} +5.01758e15i q^{87} -3.76456e15 q^{88} +2.66921e15i q^{89} +1.36115e14i q^{90} +(4.49179e15 - 6.93197e14i) q^{91} -9.76873e14 q^{92} -5.89604e15 q^{93} +2.03095e14i q^{94} +6.52359e14 q^{95} -9.23692e15i q^{96} +6.68122e15i q^{97} +(1.29376e16 - 4.09063e15i) q^{98} -3.33236e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) \) 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9	\( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) \) 8 * q - 544 * q^2 + 18784 * q^4 - 3034472 * q^7 - 35863808 * q^8 - 41933880 * q^9 + 430398704 * q^11 - 2080234240 * q^14 + 83393280 * q^15 - 4357080832 * q^16 - 7232400864 * q^18 + 45847234944 * q^21 - 34275403968 * q^22 + 89765082416 * q^23 + 61966251080 * q^25 - 376785722656 * q^28 - 22437591664 * q^29 - 192018300480 * q^30 + 941689387008 * q^32 + 371925382080 * q^35 - 4527659399328 * q^36 + 5737866534416 * q^37 - 7975804007808 * q^39 - 13160568536640 * q^42 - 3976952110864 * q^43 + 45337613120448 * q^44 + 35817469755072 * q^46 - 27450534789496 * q^49 - 96564765668320 * q^50 + 58670380591488 * q^51 - 108679841507824 * q^53 - 15117119134208 * q^56 - 196163055495360 * q^57 + 650847682404672 * q^58 - 335782392744960 * q^60 + 223739049782808 * q^63 - 460533940742144 * q^64 + 573279455461440 * q^65 - 722120065643024 * q^67 + 1268642086877760 * q^70 - 289095246669136 * q^71 + 1560006716205312 * q^72 - 5411665863643328 * q^74 + 4485628262682896 * q^77 + 192459573633600 * q^78 + 5832776866563376 * q^79 - 14617034931574584 * q^81 + 12924747561148416 * q^84 - 5815379514337920 * q^85 + 7508453217752512 * q^86 - 24665635192321536 * q^88 + 23929798963272384 * q^91 + 1197288221450688 * q^92 + 27012151562451840 * q^93 - 53204702857107840 * q^95 + 43278421367298656 * q^98 - 15738606124789392 * q^99

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