LMFDB - Embedded newform 5.10.b.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,10,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	5.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:	$2.57517918082$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.49740556.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 45x^{2} + 304 $ x^4 + 45*x^2 + 304
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.4
Root			$2.87724i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.10.b.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+41.3193i q^{2} -37.6407i q^{3} -1195.29 q^{4} +(1138.29 + 810.818i) q^{5} +1555.29 q^{6} +5315.22i q^{7} -28233.0i q^{8} +18266.2 q^{9} +O(q^{10})$	\(q+41.3193i q^{2} -37.6407i q^{3} -1195.29 q^{4} +(1138.29 + 810.818i) q^{5} +1555.29 q^{6} +5315.22i q^{7} -28233.0i q^{8} +18266.2 q^{9} +(-33502.5 + 47033.3i) q^{10} +10426.2 q^{11} +44991.4i q^{12} -79655.1i q^{13} -219621. q^{14} +(30519.7 - 42845.9i) q^{15} +554581. q^{16} -313750. i q^{17} +754746. i q^{18} +246945. q^{19} +(-1.36058e6 - 969161. i) q^{20} +200068. q^{21} +430806. i q^{22} +721761. i q^{23} -1.06271e6 q^{24} +(638273. + 1.84589e6i) q^{25} +3.29130e6 q^{26} -1.42843e6i q^{27} -6.35321e6i q^{28} -2.56903e6 q^{29} +(1.77037e6 + 1.26106e6i) q^{30} -3.29543e6 q^{31} +8.45965e6i q^{32} -392451. i q^{33} +1.29639e7 q^{34} +(-4.30967e6 + 6.05025e6i) q^{35} -2.18333e7 q^{36} -1.40463e7i q^{37} +1.02036e7i q^{38} -2.99827e6 q^{39} +(2.28918e7 - 3.21373e7i) q^{40} +1.70412e7 q^{41} +8.26669e6i q^{42} +2.92261e7i q^{43} -1.24624e7 q^{44} +(2.07922e7 + 1.48105e7i) q^{45} -2.98227e7 q^{46} -4.10316e7i q^{47} -2.08748e7i q^{48} +1.21021e7 q^{49} +(-7.62709e7 + 2.63730e7i) q^{50} -1.18098e7 q^{51} +9.52108e7i q^{52} -5.67230e7i q^{53} +5.90219e7 q^{54} +(1.18681e7 + 8.45379e6i) q^{55} +1.50065e8 q^{56} -9.29518e6i q^{57} -1.06150e8i q^{58} -1.60408e8 q^{59} +(-3.64799e7 + 5.12132e7i) q^{60} +5.33033e7 q^{61} -1.36165e8i q^{62} +9.70887e7i q^{63} -6.56012e7 q^{64} +(6.45858e7 - 9.06705e7i) q^{65} +1.62158e7 q^{66} +2.80916e8i q^{67} +3.75022e8i q^{68} +2.71676e7 q^{69} +(-2.49992e8 - 1.78073e8i) q^{70} -8.97228e7 q^{71} -5.15709e8i q^{72} -7.60225e7i q^{73} +5.80383e8 q^{74} +(6.94805e7 - 2.40250e7i) q^{75} -2.95170e8 q^{76} +5.54178e7i q^{77} -1.23887e8i q^{78} -4.10672e8 q^{79} +(6.31273e8 + 4.49665e8i) q^{80} +3.05766e8 q^{81} +7.04131e8i q^{82} -5.21969e8i q^{83} -2.39139e8 q^{84} +(2.54394e8 - 3.57138e8i) q^{85} -1.20760e9 q^{86} +9.66999e7i q^{87} -2.94364e8i q^{88} -2.37312e8 q^{89} +(-6.11962e8 + 8.59119e8i) q^{90} +4.23384e8 q^{91} -8.62712e8i q^{92} +1.24042e8i q^{93} +1.69540e9 q^{94} +(2.81094e8 + 2.00227e8i) q^{95} +3.18427e8 q^{96} +6.03778e8i q^{97} +5.00050e8i q^{98} +1.90448e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9}+O(q^{10}) $ 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9	\( 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9} - 69160 q^{10} + 109968 q^{11} - 424536 q^{14} - 396720 q^{15} + 1631264 q^{16} - 636880 q^{19} - 3302280 q^{20} + 3523968 q^{21} - 2435040 q^{24} - 1337900 q^{25} + 6618768 q^{26} - 3531720 q^{29} + 3712680 q^{30} - 10587712 q^{31} + 26434624 q^{34} + 13629840 q^{35} - 56399976 q^{36} + 1686816 q^{39} + 43578400 q^{40} - 16788552 q^{41} + 20638944 q^{44} + 55737180 q^{45} - 61250072 q^{46} - 46921028 q^{49} - 150092400 q^{50} + 84017088 q^{51} + 115855920 q^{54} - 26907120 q^{55} + 315178080 q^{56} - 460829040 q^{59} - 307006560 q^{60} + 360490568 q^{61} + 134995072 q^{64} + 183895680 q^{65} + 18949536 q^{66} - 286524864 q^{69} - 508341960 q^{70} - 47611872 q^{71} + 1176861744 q^{74} + 659239200 q^{75} - 1168489440 q^{76} - 728043520 q^{79} + 965843040 q^{80} - 343387836 q^{81} + 1118898144 q^{84} + 1275419840 q^{85} - 2375904552 q^{86} - 1582700760 q^{89} - 1197088920 q^{90} + 473322528 q^{91} + 3327101704 q^{94} + 1204791600 q^{95} + 399339648 q^{96} - 728787024 q^{99}+O(q^{100}) \) 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9 - 69160 * q^10 + 109968 * q^11 - 424536 * q^14 - 396720 * q^15 + 1631264 * q^16 - 636880 * q^19 - 3302280 * q^20 + 3523968 * q^21 - 2435040 * q^24 - 1337900 * q^25 + 6618768 * q^26 - 3531720 * q^29 + 3712680 * q^30 - 10587712 * q^31 + 26434624 * q^34 + 13629840 * q^35 - 56399976 * q^36 + 1686816 * q^39 + 43578400 * q^40 - 16788552 * q^41 + 20638944 * q^44 + 55737180 * q^45 - 61250072 * q^46 - 46921028 * q^49 - 150092400 * q^50 + 84017088 * q^51 + 115855920 * q^54 - 26907120 * q^55 + 315178080 * q^56 - 460829040 * q^59 - 307006560 * q^60 + 360490568 * q^61 + 134995072 * q^64 + 183895680 * q^65 + 18949536 * q^66 - 286524864 * q^69 - 508341960 * q^70 - 47611872 * q^71 + 1176861744 * q^74 + 659239200 * q^75 - 1168489440 * q^76 - 728043520 * q^79 + 965843040 * q^80 - 343387836 * q^81 + 1118898144 * q^84 + 1275419840 * q^85 - 2375904552 * q^86 - 1582700760 * q^89 - 1197088920 * q^90 + 473322528 * q^91 + 3327101704 * q^94 + 1204791600 * q^95 + 399339648 * q^96 - 728787024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			41.3193i			1.82607i	0.407877	+	0.913037i	$0.366269\pi$
$2$			41.3193i			1.82607i	−0.407877	+	0.913037i	$0.633731\pi$
$3$		−	37.6407i		−	0.268294i	−0.990961	−	0.134147i	$-0.957170\pi$
$3$		−	37.6407i		−	0.268294i	0.990961	−	0.134147i	$-0.0428295\pi$
$4$	−1195.29			−2.33455
$5$	1138.29	+	810.818i	0.814492	+	0.580174i
$5$	1138.29	+	810.818i	0.814492	+	0.580174i
$6$	1555.29			0.489926
$7$			5315.22i			0.836719i	0.908281	+	0.418360i	$0.137395\pi$
$7$			5315.22i			0.836719i	−0.908281	+	0.418360i	$0.862605\pi$
$8$		−	28233.0i		−	2.43698i
$9$	18266.2			0.928018
$10$	−33502.5	+	47033.3i	−1.05944	+	1.48732i
$11$	10426.2			0.214714			0.107357	−	0.994221i	$-0.465761\pi$
$11$	10426.2			0.214714			0.107357	+	0.994221i	$0.465761\pi$
$12$			44991.4i			0.626346i
$13$		−	79655.1i		−	0.773515i	−0.922181	−	0.386758i	$-0.873595\pi$
$13$		−	79655.1i		−	0.773515i	0.922181	−	0.386758i	$-0.126405\pi$
$14$	−219621.			−1.52791
$15$	30519.7	−	42845.9i	0.155658	−	0.218524i
$16$	554581.			2.11556
$17$		−	313750.i		−	0.911095i	−0.890212	−	0.455547i	$-0.849444\pi$
$17$		−	313750.i		−	0.911095i	0.890212	−	0.455547i	$-0.150556\pi$
$18$			754746.i			1.69463i
$19$	246945.			0.434719			0.217360	−	0.976092i	$-0.430256\pi$
$19$	246945.			0.434719			0.217360	+	0.976092i	$0.430256\pi$
$20$	−1.36058e6	−	969161.i	−1.90147	−	1.35444i
$21$	200068.			0.224487
$22$			430806.i			0.392084i
$23$			721761.i			0.537797i	0.963169	+	0.268898i	$0.0866595\pi$
$23$			721761.i			0.537797i	−0.963169	+	0.268898i	$0.913340\pi$
$24$	−1.06271e6			−0.653828
$25$	638273.	+	1.84589e6i	0.326796	+	0.945095i
$26$	3.29130e6			1.41250
$27$		−	1.42843e6i		−	0.517277i
$28$		−	6.35321e6i		−	1.95336i
$29$	−2.56903e6			−0.674493			−0.337247	−	0.941416i	$-0.609496\pi$
$29$	−2.56903e6			−0.674493			−0.337247	+	0.941416i	$0.609496\pi$
$30$	1.77037e6	+	1.26106e6i	0.399041	+	0.284242i
$31$	−3.29543e6			−0.640891			−0.320445	−	0.947267i	$-0.603833\pi$
$31$	−3.29543e6			−0.640891			−0.320445	+	0.947267i	$0.603833\pi$
$32$			8.45965e6i			1.42619i
$33$		−	392451.i		−	0.0576066i
$34$	1.29639e7			1.66373
$35$	−4.30967e6	+	6.05025e6i	−0.485443	+	0.681502i
$36$	−2.18333e7			−2.16650
$37$		−	1.40463e7i		−	1.23212i	−0.787699	−	0.616060i	$-0.788728\pi$
$37$		−	1.40463e7i		−	1.23212i	0.787699	−	0.616060i	$-0.211272\pi$
$38$			1.02036e7i			0.793830i
$39$	−2.99827e6			−0.207530
$40$	2.28918e7	−	3.21373e7i	1.41387	−	1.98490i
$41$	1.70412e7			0.941830			0.470915	−	0.882178i	$-0.343924\pi$
$41$	1.70412e7			0.941830			0.470915	+	0.882178i	$0.343924\pi$
$42$			8.26669e6i			0.409930i
$43$			2.92261e7i			1.30365i	0.758368	+	0.651827i	$0.225997\pi$
$43$			2.92261e7i			1.30365i	−0.758368	+	0.651827i	$0.774003\pi$
$44$	−1.24624e7			−0.501260
$45$	2.07922e7	+	1.48105e7i	0.755864	+	0.538412i
$46$	−2.98227e7			−0.982056
$47$		−	4.10316e7i		−	1.22653i	−0.789878	−	0.613264i	$-0.789856\pi$
$47$		−	4.10316e7i		−	1.22653i	0.789878	−	0.613264i	$-0.210144\pi$
$48$		−	2.08748e7i		−	0.567593i
$49$	1.21021e7			0.299901
$50$	−7.62709e7	+	2.63730e7i	−1.72581	+	0.596753i
$51$	−1.18098e7			−0.244442
$52$			9.52108e7i			1.80581i
$53$		−	5.67230e7i		−	0.987456i	−0.869616	−	0.493728i	$-0.835634\pi$
$53$		−	5.67230e7i		−	0.987456i	0.869616	−	0.493728i	$-0.164366\pi$
$54$	5.90219e7			0.944585
$55$	1.18681e7	+	8.45379e6i	0.174883	+	0.124572i
$56$	1.50065e8			2.03907
$57$		−	9.29518e6i		−	0.116633i
$58$		−	1.06150e8i		−	1.23167i
$59$	−1.60408e8			−1.72342			−0.861710	−	0.507402i	$-0.830606\pi$
$59$	−1.60408e8			−1.72342			−0.861710	+	0.507402i	$0.830606\pi$
$60$	−3.64799e7	+	5.12132e7i	−0.363390	+	0.510154i
$61$	5.33033e7			0.492912			0.246456	−	0.969154i	$-0.420734\pi$
$61$	5.33033e7			0.492912			0.246456	+	0.969154i	$0.420734\pi$
$62$		−	1.36165e8i		−	1.17031i
$63$			9.70887e7i			0.776491i
$64$	−6.56012e7			−0.488767
$65$	6.45858e7	−	9.06705e7i	0.448773	−	0.630022i
$66$	1.62158e7			0.105194
$67$			2.80916e8i			1.70310i	0.524276	+	0.851548i	$0.324336\pi$
$67$			2.80916e8i			1.70310i	−0.524276	+	0.851548i	$0.675664\pi$
$68$			3.75022e8i			2.12699i
$69$	2.71676e7			0.144288
$70$	−2.49992e8	−	1.78073e8i	−1.24447	−	0.886455i
$71$	−8.97228e7			−0.419025			−0.209513	−	0.977806i	$-0.567188\pi$
$71$	−8.97228e7			−0.419025			−0.209513	+	0.977806i	$0.567188\pi$
$72$		−	5.15709e8i		−	2.26156i
$73$		−	7.60225e7i		−	0.313321i	−0.987653	−	0.156660i	$-0.949927\pi$
$73$		−	7.60225e7i		−	0.313321i	0.987653	−	0.156660i	$-0.0500728\pi$
$74$	5.80383e8			2.24994
$75$	6.94805e7	−	2.40250e7i	0.253564	−	0.0876775i
$76$	−2.95170e8			−1.01487
$77$			5.54178e7i			0.179656i
$78$		−	1.23887e8i		−	0.378965i
$79$	−4.10672e8			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$79$	−4.10672e8			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$80$	6.31273e8	+	4.49665e8i	1.72311	+	1.22739i
$81$	3.05766e8			0.789236
$82$			7.04131e8i			1.71985i
$83$		−	5.21969e8i		−	1.20724i	−0.797272	−	0.603620i	$-0.793724\pi$
$83$		−	5.21969e8i		−	1.20724i	0.797272	−	0.603620i	$-0.206276\pi$
$84$	−2.39139e8			−0.524076
$85$	2.54394e8	−	3.57138e8i	0.528594	−	0.742080i
$86$	−1.20760e9			−2.38057
$87$			9.66999e7i			0.180963i
$88$		−	2.94364e8i		−	0.523254i
$89$	−2.37312e8			−0.400926			−0.200463	−	0.979701i	$-0.564245\pi$
$89$	−2.37312e8			−0.400926			−0.200463	+	0.979701i	$0.564245\pi$
$90$	−6.11962e8	+	8.59119e8i	−0.983180	+	1.38026i
$91$	4.23384e8			0.647215
$92$		−	8.62712e8i		−	1.25551i
$93$			1.24042e8i			0.171947i
$94$	1.69540e9			2.23973
$95$	2.81094e8	+	2.00227e8i	0.354076	+	0.252213i
$96$	3.18427e8			0.382639
$97$			6.03778e8i			0.692476i	0.938147	+	0.346238i	$0.112541\pi$
$97$			6.03778e8i			0.692476i	−0.938147	+	0.346238i	$0.887459\pi$
$98$			5.00050e8i			0.547641i
$99$	1.90448e8			0.199259
$100$	−7.62920e8	−	2.20637e9i	−0.762920	−	2.20637i
$101$	−2.03606e8			−0.194690			−0.0973451	−	0.995251i	$-0.531035\pi$
$101$	−2.03606e8			−0.194690			−0.0973451	+	0.995251i	$0.531035\pi$
$102$		−	4.87972e8i		−	0.446369i
$103$			9.15893e8i			0.801821i	0.916117	+	0.400910i	$0.131306\pi$
$103$			9.15893e8i			0.801821i	−0.916117	+	0.400910i	$0.868694\pi$
$104$	−2.24890e9			−1.88504
$105$	2.27735e8	+	1.62219e8i	0.182843	+	0.130242i
$106$	2.34376e9			1.80317
$107$		−	1.66237e9i		−	1.22603i	−0.790072	−	0.613014i	$-0.789957\pi$
$107$		−	1.66237e9i		−	1.22603i	0.790072	−	0.613014i	$-0.210043\pi$
$108$			1.70739e9i			1.20761i
$109$	−1.73161e9			−1.17498			−0.587491	−	0.809231i	$-0.699884\pi$
$109$	−1.73161e9			−1.17498			−0.587491	+	0.809231i	$0.699884\pi$
$110$	−3.49305e8	+	4.90381e8i	−0.227477	+	0.319350i
$111$	−5.28711e8			−0.330571
$112$			2.94772e9i			1.77013i
$113$			6.30956e8i			0.364038i	0.983295	+	0.182019i	$0.0582632\pi$
$113$			6.30956e8i			0.364038i	−0.983295	+	0.182019i	$0.941737\pi$
$114$	3.84070e8			0.212980
$115$	−5.85217e8	+	8.21571e8i	−0.312016	+	0.438031i
$116$	3.07073e9			1.57464
$117$		−	1.45500e9i		−	0.717836i
$118$		−	6.62794e9i		−	3.14709i
$119$	1.66765e9			0.762331
$120$	−1.20967e9	−	8.61664e8i	−0.532538	−	0.379334i
$121$	−2.24924e9			−0.953898
$122$			2.20246e9i			0.900094i
$123$		−	6.41442e8i		−	0.252688i
$124$	3.93898e9			1.49619
$125$	−7.70141e8	+	2.61868e9i	−0.282147	+	0.959371i
$126$	−4.01164e9			−1.41793
$127$		−	2.12104e9i		−	0.723490i	−0.932277	−	0.361745i	$-0.882181\pi$
$127$		−	2.12104e9i		−	0.723490i	0.932277	−	0.361745i	$-0.117819\pi$
$128$			1.62074e9i			0.533664i
$129$	1.10009e9			0.349763
$130$	3.74644e9	+	2.66864e9i	1.15047	+	0.819494i
$131$	5.57686e9			1.65451			0.827254	−	0.561828i	$-0.189902\pi$
$131$	5.57686e9			1.65451			0.827254	+	0.561828i	$0.189902\pi$
$132$			4.69092e8i			0.134485i
$133$			1.31257e9i			0.363738i
$134$	−1.16072e10			−3.10998
$135$	1.15820e9	−	1.62597e9i	0.300111	−	0.421318i
$136$	−8.85810e9			−2.22032
$137$			2.57317e9i			0.624059i	0.950072	+	0.312029i	$0.101009\pi$
$137$			2.57317e9i			0.624059i	−0.950072	+	0.312029i	$0.898991\pi$
$138$			1.12255e9i			0.263480i
$139$	1.62297e9			0.368761			0.184380	−	0.982855i	$-0.440972\pi$
$139$	1.62297e9			0.368761			0.184380	+	0.982855i	$0.440972\pi$
$140$	5.15130e9	−	7.23179e9i	1.13329	−	1.59100i
$141$	−1.54446e9			−0.329071
$142$		−	3.70729e9i		−	0.765171i
$143$		−	8.30504e8i		−	0.166085i
$144$	1.01301e10			1.96328
$145$	−2.92429e9	−	2.08301e9i	−0.549370	−	0.391324i
$146$	3.14120e9			0.572147
$147$		−	4.55530e8i		−	0.0804617i
$148$			1.67893e10i			2.87644i
$149$	5.98422e9			0.994647			0.497324	−	0.867565i	$-0.334316\pi$
$149$	5.98422e9			0.994647			0.497324	+	0.867565i	$0.334316\pi$
$150$	9.92698e8	+	2.87089e9i	0.160106	+	0.463026i
$151$	−5.95089e9			−0.931505			−0.465753	−	0.884915i	$-0.654216\pi$
$151$	−5.95089e9			−0.931505			−0.465753	+	0.884915i	$0.654216\pi$
$152$		−	6.97200e9i		−	1.05940i
$153$		−	5.73101e9i		−	0.845513i
$154$	−2.28983e9			−0.328064
$155$	−3.75114e9	−	2.67199e9i	−0.522001	−	0.371828i
$156$	3.58380e9			0.484488
$157$			2.94325e9i			0.386615i	0.981138	+	0.193308i	$0.0619215\pi$
$157$			2.94325e9i			0.386615i	−0.981138	+	0.193308i	$0.938078\pi$
$158$		−	1.69687e10i		−	2.16616i
$159$	−2.13509e9			−0.264929
$160$	−6.85923e9	+	9.62951e9i	−0.827438	+	1.16162i
$161$	−3.83632e9			−0.449985
$162$			1.26341e10i			1.44120i
$163$			2.69823e9i			0.299389i	0.988732	+	0.149694i	$0.0478290\pi$
$163$			2.69823e9i			0.299389i	−0.988732	+	0.149694i	$0.952171\pi$
$164$	−2.03691e10			−2.19875
$165$	3.18206e8	−	4.46722e8i	0.0334219	−	0.0469202i
$166$	2.15674e10			2.20451
$167$			1.47132e10i			1.46380i	0.681410	+	0.731902i	$0.261367\pi$
$167$			1.47132e10i			1.46380i	−0.681410	+	0.731902i	$0.738633\pi$
$168$		−	5.64853e9i		−	0.547071i
$169$	4.25956e9			0.401675
$170$	1.47567e10	+	1.05114e10i	1.35509	+	0.965251i
$171$	4.51074e9			0.403427
$172$		−	3.49336e10i		−	3.04344i
$173$		−	1.56605e8i		−	0.0132923i	−0.999978	−	0.00664613i	$-0.997884\pi$
$173$		−	1.56605e8i		−	0.0132923i	0.999978	−	0.00664613i	$-0.00211555\pi$
$174$	−3.99558e9			−0.330452
$175$	−9.81130e9	+	3.39256e9i	−0.790779	+	0.273436i
$176$	5.78220e9			0.454241
$177$			6.03785e9i			0.462384i
$178$		−	9.80557e9i		−	0.732121i
$179$	5.35516e9			0.389883			0.194941	−	0.980815i	$-0.437548\pi$
$179$	5.35516e9			0.389883			0.194941	+	0.980815i	$0.437548\pi$
$180$	−2.48526e10	−	1.77029e10i	−1.76460	−	1.25695i
$181$	−1.52107e9			−0.105341			−0.0526704	−	0.998612i	$-0.516773\pi$
$181$	−1.52107e9			−0.105341			−0.0526704	+	0.998612i	$0.516773\pi$
$182$			1.74940e10i			1.18186i
$183$		−	2.00637e9i		−	0.132246i
$184$	2.03775e10			1.31060
$185$	1.13890e10	−	1.59887e10i	0.714845	−	1.00355i
$186$	−5.12534e9			−0.313989
$187$		−	3.27123e9i		−	0.195625i
$188$			4.90445e10i			2.86339i
$189$	7.59243e9			0.432815
$190$	−8.27327e9	+	1.16146e10i	−0.460560	+	0.646568i
$191$	−9.28266e9			−0.504687			−0.252344	−	0.967638i	$-0.581201\pi$
$191$	−9.28266e9			−0.504687			−0.252344	+	0.967638i	$0.581201\pi$
$192$			2.46927e9i			0.131134i
$193$			6.94351e9i			0.360223i	0.983646	+	0.180111i	$0.0576458\pi$
$193$			6.94351e9i			0.360223i	−0.983646	+	0.180111i	$0.942354\pi$
$194$	−2.49477e10			−1.26451
$195$	−3.41290e9	−	2.43105e9i	−0.169031	−	0.120403i
$196$	−1.44655e10			−0.700132
$197$		−	3.60722e10i		−	1.70637i	−0.521606	−	0.853187i	$-0.674667\pi$
$197$		−	3.60722e10i		−	1.70637i	0.521606	−	0.853187i	$-0.325333\pi$
$198$			7.86917e9i			0.363861i
$199$	−2.25173e10			−1.01784			−0.508918	−	0.860815i	$-0.669955\pi$
$199$	−2.25173e10			−1.01784			−0.508918	+	0.860815i	$0.669955\pi$
$200$	5.21150e10	−	1.80204e10i	2.30318	−	0.796395i
$201$	1.05739e10			0.456931
$202$		−	8.41286e9i		−	0.355519i
$203$		−	1.36549e10i		−	0.564362i
$204$	1.41161e10			0.570661
$205$	1.93978e10	+	1.38173e10i	0.767114	+	0.546426i
$206$	−3.78441e10			−1.46418
$207$			1.31838e10i			0.499085i
$208$		−	4.41753e10i		−	1.63642i
$209$	2.57471e9			0.0933404
$210$	−6.70278e9	+	9.40988e9i	−0.237831	+	0.333885i
$211$	3.62300e10			1.25834			0.629169	−	0.777268i	$-0.283395\pi$
$211$	3.62300e10			1.25834			0.629169	+	0.777268i	$0.283395\pi$
$212$			6.78003e10i			2.30526i
$213$			3.37723e9i			0.112422i
$214$	6.86879e10			2.23882
$215$	−2.36970e10	+	3.32677e10i	−0.756346	+	1.06182i
$216$	−4.03289e10			−1.26059
$217$		−	1.75159e10i		−	0.536246i
$218$		−	7.15490e10i		−	2.14560i
$219$	−2.86154e9			−0.0840623
$220$	−1.41858e10	−	1.01047e10i	−0.408273	−	0.290818i
$221$	−2.49918e10			−0.704746
$222$		−	2.18460e10i		−	0.603647i
$223$			4.93834e10i			1.33724i	0.743605	+	0.668619i	$0.233114\pi$
$223$			4.93834e10i			1.33724i	−0.743605	+	0.668619i	$0.766886\pi$
$224$	−4.49649e10			−1.19332
$225$	1.16588e10	+	3.37173e10i	0.303272	+	0.877065i
$226$	−2.60707e10			−0.664760
$227$		−	3.27710e10i		−	0.819169i	−0.912272	−	0.409585i	$-0.865674\pi$
$227$		−	3.27710e10i		−	0.819169i	0.912272	−	0.409585i	$-0.134326\pi$
$228$			1.11104e10i			0.272285i
$229$	−1.35586e10			−0.325803			−0.162902	−	0.986642i	$-0.552085\pi$
$229$	−1.35586e10			−0.325803			−0.162902	+	0.986642i	$0.552085\pi$
$230$	−3.39468e10	−	2.41808e10i	−0.799877	−	0.569764i
$231$	2.08596e9			0.0482006
$232$			7.25313e10i			1.64373i
$233$		−	7.99837e9i		−	0.177787i	−0.996041	−	0.0888935i	$-0.971667\pi$
$233$		−	7.99837e9i		−	0.177787i	0.996041	−	0.0888935i	$-0.0283331\pi$
$234$	6.01194e10			1.31082
$235$	3.32691e10	−	4.67057e10i	0.711600	−	0.998998i
$236$	1.91733e11			4.02340
$237$			1.54580e10i			0.318262i
$238$			6.89062e10i			1.39207i
$239$	−8.30208e10			−1.64587			−0.822937	−	0.568133i	$-0.807666\pi$
$239$	−8.30208e10			−1.64587			−0.822937	+	0.568133i	$0.807666\pi$
$240$	1.69257e10	−	2.37616e10i	0.329303	−	0.462300i
$241$	−6.04789e10			−1.15485			−0.577427	−	0.816442i	$-0.695943\pi$
$241$	−6.04789e10			−1.15485			−0.577427	+	0.816442i	$0.695943\pi$
$242$		−	9.29372e10i		−	1.74189i
$243$		−	3.96251e10i		−	0.729024i
$244$	−6.37128e10			−1.15073
$245$	1.37756e10	+	9.81258e9i	0.244267	+	0.173995i
$246$	2.65040e10			0.461427
$247$		−	1.96704e10i		−	0.336262i
$248$			9.30398e10i			1.56184i
$249$	−1.96473e10			−0.323896
$250$	−1.08202e11	−	3.18217e10i	−1.75188	−	0.515221i
$251$	1.04682e11			1.66471			0.832354	−	0.554244i	$-0.186993\pi$
$251$	1.04682e11			1.66471			0.832354	+	0.554244i	$0.186993\pi$
$252$		−	1.16049e11i		−	1.81275i
$253$			7.52525e9i			0.115473i
$254$	8.76400e10			1.32115
$255$	−1.34429e10	−	9.57557e9i	−0.199096	−	0.141819i
$256$	−1.00556e11			−1.46328
$257$			7.92751e10i			1.13354i	0.823875	+	0.566771i	$0.191808\pi$
$257$			7.92751e10i			1.13354i	−0.823875	+	0.566771i	$0.808192\pi$
$258$			4.54549e10i			0.638693i
$259$	7.46590e10			1.03094
$260$	−7.71987e10	+	1.08377e11i	−1.04768	+	1.47082i
$261$	−4.69263e10			−0.625942
$262$			2.30432e11i			3.02126i
$263$		−	1.04629e8i		−	0.00134850i	−1.00000		0.000674250i	$-0.999785\pi$
$263$		−	1.04629e8i		−	0.00134850i	1.00000		0.000674250i	$-0.000214620\pi$
$264$	−1.10801e10			−0.140386
$265$	4.59920e10	−	6.45671e10i	0.572897	−	0.804275i
$266$	−5.42344e10			−0.664213
$267$			8.93258e9i			0.107566i
$268$		−	3.35775e11i		−	3.97596i
$269$	7.38735e9			0.0860208			0.0430104	−	0.999075i	$-0.486305\pi$
$269$	7.38735e9			0.0860208			0.0430104	+	0.999075i	$0.486305\pi$
$270$	6.71839e10	+	4.78560e10i	0.769358	+	0.548024i
$271$	1.27706e11			1.43831			0.719153	−	0.694852i	$-0.244530\pi$
$271$	1.27706e11			1.43831			0.719153	+	0.694852i	$0.244530\pi$
$272$		−	1.74000e11i		−	1.92748i
$273$		−	1.59365e10i		−	0.173644i
$274$	−1.06322e11			−1.13958
$275$	6.65479e9	+	1.92457e10i	0.0701677	+	0.202925i
$276$	−3.24731e10			−0.336847
$277$			3.16563e10i			0.323074i	0.986867	+	0.161537i	$0.0516451\pi$
$277$			3.16563e10i			0.323074i	−0.986867	+	0.161537i	$0.948355\pi$
$278$			6.70602e10i			0.673385i
$279$	−6.01949e10			−0.594758
$280$	1.70817e11	+	1.21675e11i	1.66081	+	1.18302i
$281$	−9.50309e10			−0.909257			−0.454628	−	0.890681i	$-0.650228\pi$
$281$	−9.50309e10			−0.909257			−0.454628	+	0.890681i	$0.650228\pi$
$282$		−	6.38159e10i		−	0.600908i
$283$		−	4.91862e10i		−	0.455832i	−0.973681	−	0.227916i	$-0.926809\pi$
$283$		−	4.91862e10i		−	0.455832i	0.973681	−	0.227916i	$-0.0731911\pi$
$284$	1.07245e11			0.978234
$285$	7.53670e9	−	1.05806e10i	0.0676673	−	0.0949965i
$286$	3.43159e10			0.303283
$287$			9.05777e10i			0.788048i
$288$			1.54525e11i			1.32353i
$289$	2.01488e10			0.169906
$290$	8.60687e10	−	1.20830e11i	0.714586	−	1.00319i
$291$	2.27266e10			0.185787
$292$			9.08688e10i			0.731462i
$293$		−	3.53889e10i		−	0.280519i	−0.990115	−	0.140260i	$-0.955206\pi$
$293$		−	3.53889e10i		−	0.280519i	0.990115	−	0.140260i	$-0.0447937\pi$
$294$	1.88222e10			0.146929
$295$	−1.82590e11	−	1.30061e11i	−1.40371	−	0.999883i
$296$	−3.96568e11			−3.00265
$297$		−	1.48932e10i		−	0.111067i
$298$			2.47264e11i			1.81630i
$299$	5.74920e10			0.415994
$300$	−8.30492e10	+	2.87168e10i	−0.591956	+	0.204687i
$301$	−1.55343e11			−1.09079
$302$		−	2.45887e11i		−	1.70100i
$303$			7.66386e9i			0.0522343i
$304$	1.36951e11			0.919675
$305$	6.06745e10	+	4.32193e10i	0.401473	+	0.285975i
$306$	2.36802e11			1.54397
$307$		−	8.30301e10i		−	0.533474i	−0.963769	−	0.266737i	$-0.914055\pi$
$307$		−	8.30301e10i		−	0.533474i	0.963769	−	0.266737i	$-0.0859455\pi$
$308$		−	6.62402e10i		−	0.419414i
$309$	3.44748e10			0.215124
$310$	1.10405e11	−	1.54995e11i	0.678986	−	0.953212i
$311$	2.13935e10			0.129676			0.0648382	−	0.997896i	$-0.479347\pi$
$311$	2.13935e10			0.129676			0.0648382	+	0.997896i	$0.479347\pi$
$312$			8.46502e10i			0.505746i
$313$			2.56558e11i			1.51090i	0.655204	+	0.755452i	$0.272582\pi$
$313$			2.56558e11i			1.51090i	−0.655204	+	0.755452i	$0.727418\pi$
$314$	−1.21613e11			−0.705988
$315$	−7.87213e10	+	1.10515e11i	−0.450500	+	0.632446i
$316$	4.90871e11			2.76933
$317$			1.26112e11i			0.701436i	0.936481	+	0.350718i	$0.114062\pi$
$317$			1.26112e11i			0.701436i	−0.936481	+	0.350718i	$0.885938\pi$
$318$		−	8.82206e10i		−	0.483780i
$319$	−2.67853e10			−0.144823
$320$	−7.46731e10	−	5.31907e10i	−0.398097	−	0.283570i
$321$	−6.25727e10			−0.328936
$322$		−	1.58514e11i		−	0.821706i
$323$		−	7.74790e10i		−	0.396071i
$324$	−3.65478e11			−1.84251
$325$	1.47035e11	−	5.08417e10i	0.731045	−	0.252781i
$326$	−1.11489e11			−0.546706
$327$			6.51790e10i			0.315241i
$328$		−	4.81124e11i		−	2.29522i
$329$	2.18092e11			1.02626
$330$	1.84583e10	+	1.31481e10i	0.0856797	+	0.0610308i
$331$	1.71300e11			0.784389			0.392194	−	0.919882i	$-0.371716\pi$
$331$	1.71300e11			0.784389			0.392194	+	0.919882i	$0.371716\pi$
$332$			6.23904e11i			2.81836i
$333$		−	2.56572e11i		−	1.14343i
$334$	−6.07939e11			−2.67301
$335$	−2.27771e11	+	3.19763e11i	−0.988093	+	1.38716i
$336$	1.10954e11			0.474916
$337$		−	4.70320e11i		−	1.98637i	−0.116569	−	0.993183i	$-0.537190\pi$
$337$		−	4.70320e11i		−	1.98637i	0.116569	−	0.993183i	$-0.462810\pi$
$338$			1.76002e11i			0.733487i
$339$	2.37496e10			0.0976693
$340$	−3.04074e11	+	4.26882e11i	−1.23403	+	1.73242i
$341$	−3.43589e10			−0.137608
$342$			1.86381e11i			0.736688i
$343$			2.78813e11i			1.08765i
$344$	8.25140e11			3.17698
$345$	3.09245e10	+	2.20279e10i	0.117521	+	0.0837121i
$346$	6.47083e9			0.0242727
$347$		−	2.86642e11i		−	1.06135i	−0.847576	−	0.530674i	$-0.821939\pi$
$347$		−	2.86642e11i		−	1.06135i	0.847576	−	0.530674i	$-0.178061\pi$
$348$		−	1.15584e11i		−	0.422466i
$349$	3.54310e11			1.27841			0.639203	−	0.769038i	$-0.279264\pi$
$349$	3.54310e11			1.27841			0.639203	+	0.769038i	$0.279264\pi$
$350$	−1.40178e11	−	4.05396e11i	−0.499315	−	1.44402i
$351$	−1.13782e11			−0.400121
$352$			8.82023e10i			0.306223i
$353$		−	2.09491e11i		−	0.718092i	−0.933320	−	0.359046i	$-0.883102\pi$
$353$		−	2.09491e11i		−	0.718092i	0.933320	−	0.359046i	$-0.116898\pi$
$354$	−2.49480e11			−0.844347
$355$	−1.02130e11	−	7.27489e10i	−0.341293	−	0.243108i
$356$	2.83656e11			0.935981
$357$		−	6.27715e10i		−	0.204529i
$358$			2.21272e11i			0.711955i
$359$	−2.88081e11			−0.915355			−0.457678	−	0.889118i	$-0.651319\pi$
$359$	−2.88081e11			−0.915355			−0.457678	+	0.889118i	$0.651319\pi$
$360$	4.18146e11	−	5.87025e11i	1.31210	−	1.84203i
$361$	−2.61706e11			−0.811019
$362$		−	6.28498e10i		−	0.192360i
$363$			8.46630e10i			0.255926i
$364$	−5.06066e11			−1.51095
$365$	6.16404e10	−	8.65355e10i	0.181781	−	0.255197i
$366$	8.29019e10			0.241490
$367$		−	1.33587e10i		−	0.0384387i	−0.999815	−	0.0192193i	$-0.993882\pi$
$367$		−	1.33587e10i		−	0.0384387i	0.999815	−	0.0192193i	$-0.00611808\pi$
$368$			4.00275e11i			1.13774i
$369$	3.11278e11			0.874036
$370$	6.60642e11	+	4.70585e11i	1.83256	+	1.30536i
$371$	3.01495e11			0.826224
$372$		−	1.48266e11i		−	0.401419i
$373$			4.17763e11i			1.11748i	0.829342	+	0.558741i	$0.188716\pi$
$373$			4.17763e11i			1.11748i	−0.829342	+	0.558741i	$0.811284\pi$
$374$	1.35165e11			0.357226
$375$	9.85687e10	+	2.89886e10i	0.257394	+	0.0756985i
$376$	−1.15844e12			−2.98903
$377$			2.04636e11i			0.521731i
$378$			3.13714e11i			0.790353i
$379$	−2.63110e11			−0.655031			−0.327515	−	0.944846i	$-0.606211\pi$
$379$	−2.63110e11			−0.655031			−0.327515	+	0.944846i	$0.606211\pi$
$380$	−3.35989e11	−	2.39329e11i	−0.826606	−	0.588803i
$381$	−7.98374e10			−0.194108
$382$		−	3.83553e11i		−	0.921596i
$383$		−	7.84146e10i		−	0.186210i	−0.995656	−	0.0931049i	$-0.970321\pi$
$383$		−	7.84146e10i		−	0.186210i	0.995656	−	0.0931049i	$-0.0296792\pi$
$384$	6.10057e10			0.143179
$385$	−4.49337e10	+	6.30814e10i	−0.104232	+	0.146328i
$386$	−2.86901e11			−0.657793
$387$			5.33849e11i			1.20981i
$388$		−	7.21688e11i		−	1.61662i
$389$	−1.66007e11			−0.367581			−0.183791	−	0.982965i	$-0.558837\pi$
$389$	−1.66007e11			−0.367581			−0.183791	+	0.982965i	$0.558837\pi$
$390$	1.00450e11	−	1.41019e11i	0.219866	−	0.308664i
$391$	2.26452e11			0.489984
$392$		−	3.41678e11i		−	0.730852i
$393$		−	2.09917e11i		−	0.443896i
$394$	1.49048e12			3.11596
$395$	−4.67462e11	−	3.32980e11i	−0.966184	−	0.688226i
$396$	−2.27640e11			−0.465179
$397$			4.09536e11i			0.827437i	0.910405	+	0.413719i	$0.135770\pi$
$397$			4.09536e11i			0.827437i	−0.910405	+	0.413719i	$0.864230\pi$
$398$		−	9.30402e11i		−	1.85865i
$399$	4.94059e10			0.0975889
$400$	3.53974e11	+	1.02370e12i	0.691356	+	1.99941i
$401$	−7.92645e10			−0.153084			−0.0765419	−	0.997066i	$-0.524388\pi$
$401$	−7.92645e10			−0.153084			−0.0765419	+	0.997066i	$0.524388\pi$
$402$			4.36905e11i			0.834391i
$403$			2.62498e11i			0.495739i
$404$	2.43367e11			0.454513
$405$	3.48050e11	+	2.47921e11i	0.642826	+	0.457894i
$406$	5.64213e11			1.03057
$407$		−	1.46450e11i		−	0.264554i
$408$			3.33425e11i			0.595700i
$409$	−6.85827e11			−1.21188			−0.605940	−	0.795510i	$-0.707203\pi$
$409$	−6.85827e11			−1.21188			−0.605940	+	0.795510i	$0.707203\pi$
$410$	−5.70922e11	+	8.01504e11i	−0.997814	+	1.40081i
$411$	9.68557e10			0.167431
$412$		−	1.09476e12i		−	1.87189i
$413$		−	8.52601e11i		−	1.44202i
$414$	−5.44746e11			−0.911366
$415$	4.23222e11	−	5.94151e11i	0.700410	−	0.983288i
$416$	6.73854e11			1.10318
$417$		−	6.10898e10i		−	0.0989365i
$418$			1.06385e11i			0.170447i
$419$	−3.31879e11			−0.526037			−0.263018	−	0.964791i	$-0.584718\pi$
$419$	−3.31879e11			−0.526037			−0.263018	+	0.964791i	$0.584718\pi$
$420$	−2.72209e11	−	1.93898e11i	−0.426856	−	0.304055i
$421$	−6.30694e11			−0.978475			−0.489237	−	0.872151i	$-0.662725\pi$
$421$	−6.30694e11			−0.978475			−0.489237	+	0.872151i	$0.662725\pi$
$422$			1.49700e12i			2.29782i
$423$		−	7.49490e11i		−	1.13824i
$424$	−1.60146e12			−2.40641
$425$	5.79148e11	−	2.00258e11i	0.861071	−	0.297742i
$426$	−1.39545e11			−0.205291
$427$			2.83319e11i			0.412429i
$428$			1.98701e12i			2.86222i
$429$	−3.12607e10			−0.0445596
$430$	−1.37460e12	−	9.79145e11i	−1.93896	−	1.38114i
$431$	7.70903e11			1.07610			0.538049	−	0.842913i	$-0.319161\pi$
$431$	7.70903e11			1.07610			0.538049	+	0.842913i	$0.319161\pi$
$432$		−	7.92182e11i		−	1.09433i
$433$			1.07829e12i			1.47415i	0.675811	+	0.737075i	$0.263794\pi$
$433$			1.07829e12i			1.47415i	−0.675811	+	0.737075i	$0.736206\pi$
$434$	7.23746e11			0.979225
$435$	−7.84060e10	+	1.10072e11i	−0.104990	+	0.147393i
$436$	2.06977e12			2.74305
$437$			1.78235e11i			0.233791i
$438$		−	1.18237e11i		−	0.153504i
$439$	9.56419e11			1.22902			0.614508	−	0.788910i	$-0.289354\pi$
$439$	9.56419e11			1.22902			0.614508	+	0.788910i	$0.289354\pi$
$440$	2.38676e11	−	3.35071e11i	0.303579	−	0.426187i
$441$	2.21059e11			0.278313
$442$		−	1.03264e12i		−	1.28692i
$443$			2.06392e11i			0.254611i	0.991864	+	0.127305i	$0.0406328\pi$
$443$			2.06392e11i			0.254611i	−0.991864	+	0.127305i	$0.959367\pi$
$444$	6.31962e11			0.771734
$445$	−2.70129e11	−	1.92417e11i	−0.326551	−	0.232607i
$446$	−2.04049e12			−2.44190
$447$		−	2.25250e11i		−	0.266858i
$448$		−	3.48685e11i		−	0.408961i
$449$	−1.75939e11			−0.204293			−0.102147	−	0.994769i	$-0.532571\pi$
$449$	−1.75939e11			−0.204293			−0.102147	+	0.994769i	$0.532571\pi$
$450$	−1.39318e12	+	4.81734e11i	−1.60159	+	0.553798i
$451$	1.77676e11			0.202224
$452$		−	7.54174e11i		−	0.849863i
$453$			2.23995e11i			0.249918i
$454$	1.35408e12			1.49586
$455$	4.81933e11	+	3.43288e11i	0.527152	+	0.375497i
$456$	−2.62431e11			−0.284232
$457$			2.98819e11i			0.320469i	0.987079	+	0.160234i	$0.0512250\pi$
$457$			2.98819e11i			0.320469i	−0.987079	+	0.160234i	$0.948775\pi$
$458$		−	5.60233e11i		−	0.594941i
$459$	−4.48171e11			−0.471288
$460$	6.99502e11	−	9.82014e11i	0.728415	−	1.02260i
$461$	4.39422e11			0.453135			0.226567	−	0.973995i	$-0.427250\pi$
$461$	4.39422e11			0.453135			0.226567	+	0.973995i	$0.427250\pi$
$462$			8.61906e10i			0.0880179i
$463$		−	1.16254e12i		−	1.17569i	−0.808973	−	0.587846i	$-0.799976\pi$
$463$		−	1.16254e12i		−	1.17569i	0.808973	−	0.587846i	$-0.200024\pi$
$464$	−1.42473e12			−1.42693
$465$	−1.00576e11	+	1.41196e11i	−0.0997595	+	0.140050i
$466$	3.30487e11			0.324652
$467$			1.65923e11i			0.161429i	0.996737	+	0.0807144i	$0.0257202\pi$
$467$			1.65923e11i			0.161429i	−0.996737	+	0.0807144i	$0.974280\pi$
$468$			1.73914e12i			1.67582i
$469$	−1.49313e12			−1.42501
$470$	1.92985e12	+	1.37466e12i	1.82425	+	1.29944i
$471$	1.10786e11			0.103727
$472$			4.52879e12i			4.19994i
$473$			3.04718e11i			0.279913i
$474$	−6.38712e11			−0.581169
$475$	1.57618e11	+	4.55833e11i	0.142064	+	0.410851i
$476$	−1.99332e12			−1.77970
$477$		−	1.03611e12i		−	0.916377i
$478$		−	3.43036e12i		−	3.00549i
$479$	−1.33180e11			−0.115592			−0.0577960	−	0.998328i	$-0.518407\pi$
$479$	−1.33180e11			−0.115592			−0.0577960	+	0.998328i	$0.518407\pi$
$480$	3.62461e11	+	2.58186e11i	0.311656	+	0.221997i
$481$	−1.11886e12			−0.953064
$482$		−	2.49895e12i		−	2.10885i
$483$			1.44401e11i			0.120728i
$484$	2.68849e12			2.22692
$485$	−4.89554e11	+	6.87273e11i	−0.401756	+	0.564016i
$486$	1.63728e12			1.33125
$487$		−	1.43276e12i		−	1.15423i	−0.816662	−	0.577116i	$-0.804178\pi$
$487$		−	1.43276e12i		−	1.15423i	0.816662	−	0.577116i	$-0.195822\pi$
$488$		−	1.50491e12i		−	1.20122i
$489$	1.01563e11			0.0803243
$490$	−4.05449e11	+	5.69200e11i	−0.317727	+	0.446049i
$491$	−1.05688e12			−0.820655			−0.410327	−	0.911938i	$-0.634586\pi$
$491$	−1.05688e12			−0.820655			−0.410327	+	0.911938i	$0.634586\pi$
$492$			7.66708e11i			0.589912i
$493$			8.06032e11i			0.614527i
$494$	8.12769e11			0.614039
$495$	2.16784e11	+	1.54418e11i	0.162295	+	0.115605i
$496$	−1.82758e12			−1.35584
$497$		−	4.76896e11i		−	0.350607i
$498$		−	8.11813e11i		−	0.591458i
$499$	−1.77897e11			−0.128445			−0.0642223	−	0.997936i	$-0.520457\pi$
$499$	−1.77897e11			−0.128445			−0.0642223	+	0.997936i	$0.520457\pi$
$500$	9.20541e11	−	3.13007e12i	0.658685	−	2.23970i
$501$	5.53814e11			0.392730
$502$			4.32537e12i			3.03988i
$503$			1.58467e12i			1.10378i	0.833917	+	0.551889i	$0.186093\pi$
$503$			1.58467e12i			1.10378i	−0.833917	+	0.551889i	$0.813907\pi$
$504$	2.74111e12			1.89229
$505$	−2.31762e11	−	1.65087e11i	−0.158574	−	0.112954i
$506$	−3.10939e11			−0.210861
$507$		−	1.60333e11i		−	0.107767i
$508$			2.53525e12i			1.68902i
$509$	1.93674e12			1.27891			0.639456	−	0.768827i	$-0.279159\pi$
$509$	1.93674e12			1.27891			0.639456	+	0.768827i	$0.279159\pi$
$510$	3.95656e11	−	5.55452e11i	0.258972	−	0.363564i
$511$	4.04076e11			0.262162
$512$		−	3.32508e12i		−	2.13839i
$513$		−	3.52744e11i		−	0.224870i
$514$	−3.27560e12			−2.06993
$515$	−7.42623e11	+	1.04255e12i	−0.465196	+	0.653077i
$516$	−1.31492e12			−0.816538
$517$		−	4.27805e11i		−	0.263353i
$518$			3.08486e12i			1.88257i
$519$	−5.89473e9			−0.00356624
$520$	−2.55990e12	−	1.82345e12i	−1.53535	−	1.09365i
$521$	2.72419e12			1.61982			0.809912	−	0.586552i	$-0.199515\pi$
$521$	2.72419e12			1.61982			0.809912	+	0.586552i	$0.199515\pi$
$522$		−	1.93896e12i		−	1.14302i
$523$			4.86784e11i			0.284497i	0.989831	+	0.142249i	$0.0454333\pi$
$523$			4.86784e11i			0.284497i	−0.989831	+	0.142249i	$0.954567\pi$
$524$	−6.66596e12			−3.86253
$525$	1.27698e11	+	3.69304e11i	0.0733615	+	0.212162i
$526$	4.32320e9			0.00246246
$527$			1.03394e12i			0.583912i
$528$		−	2.17646e11i		−	0.121870i
$529$	1.28021e12			0.710775
$530$	2.66787e12	+	1.90036e12i	1.46867	+	1.04615i
$531$	−2.93003e12			−1.59936
$532$		−	1.56889e12i		−	0.849164i
$533$		−	1.35742e12i		−	0.728520i
$534$	−3.69088e11			−0.196424
$535$	1.34788e12	−	1.89225e12i	0.711309	−	0.998590i
$536$	7.93109e12			4.15041
$537$		−	2.01572e11i		−	0.104603i
$538$			3.05240e11i			0.157080i
$539$	1.26179e11			0.0643929
$540$	−1.38438e12	+	1.94350e12i	−0.700622	+	0.983586i
$541$	1.98233e11			0.0994920			0.0497460	−	0.998762i	$-0.484159\pi$
$541$	1.98233e11			0.0994920			0.0497460	+	0.998762i	$0.484159\pi$
$542$			5.27675e12i			2.62645i
$543$			5.72543e10i			0.0282624i
$544$	2.65421e12			1.29939
$545$	−1.97107e12	−	1.40402e12i	−0.957014	−	0.681694i
$546$	6.58485e11			0.317087
$547$			4.79532e11i			0.229021i	0.993422	+	0.114510i	$0.0365299\pi$
$547$			4.79532e11i			0.229021i	−0.993422	+	0.114510i	$0.963470\pi$
$548$		−	3.07567e12i		−	1.45689i
$549$	9.73647e11			0.457432
$550$	−7.95219e11	+	2.74972e11i	−0.370557	+	0.128131i
$551$	−6.34408e11			−0.293215
$552$		−	7.67022e11i		−	0.351627i
$553$		−	2.18281e12i		−	0.992550i
$554$	−1.30802e12			−0.589957
$555$	−6.01825e11	−	4.28688e11i	−0.269248	−	0.191789i
$556$	−1.93992e12			−0.860889
$557$		−	1.20856e11i		−	0.0532011i	−0.999646	−	0.0266006i	$-0.991532\pi$
$557$		−	1.20856e11i		−	0.0532011i	0.999646	−	0.0266006i	$-0.00846822\pi$
$558$		−	2.48721e12i		−	1.08607i
$559$	2.32801e12			1.00840
$560$	−2.39007e12	+	3.35536e12i	−1.02698	+	1.44176i
$561$	−1.23131e11			−0.0524851
$562$		−	3.92662e12i		−	1.66037i
$563$		−	1.01468e12i		−	0.425637i	−0.977092	−	0.212818i	$-0.931736\pi$
$563$		−	1.01468e12i		−	0.425637i	0.977092	−	0.212818i	$-0.0682643\pi$
$564$	1.84607e12			0.768231
$565$	−5.11591e11	+	7.18210e11i	−0.211205	+	0.296506i
$566$	2.03234e12			0.832382
$567$			1.62521e12i			0.660369i
$568$			2.53314e12i			1.02116i
$569$	−1.12630e12			−0.450454			−0.225227	−	0.974306i	$-0.572312\pi$
$569$	−1.12630e12			−0.450454			−0.225227	+	0.974306i	$0.572312\pi$
$570$	4.37183e11	+	3.11411e11i	0.173471	+	0.123566i
$571$	−2.75478e12			−1.08449			−0.542243	−	0.840221i	$-0.682425\pi$
$571$	−2.75478e12			−1.08449			−0.542243	+	0.840221i	$0.682425\pi$
$572$			9.92691e11i			0.387732i
$573$			3.49405e11i			0.135405i
$574$	−3.74261e12			−1.43903
$575$	−1.33229e12	+	4.60680e11i	−0.508269	+	0.175750i
$576$	−1.19828e12			−0.453585
$577$			4.14763e12i			1.55779i	0.627155	+	0.778895i	$0.284219\pi$
$577$			4.14763e12i			1.55779i	−0.627155	+	0.778895i	$0.715781\pi$
$578$			8.32535e11i			0.310261i
$579$	2.61358e11			0.0966458
$580$	3.49537e12	+	2.48980e12i	1.28253	+	0.913563i
$581$	2.77438e12			1.01012
$582$			9.39049e11i			0.339262i
$583$		−	5.91408e11i		−	0.212021i
$584$	−2.14634e12			−0.763557
$585$	1.17974e12	−	1.65620e12i	0.416470	−	0.584672i
$586$	1.46224e12			0.512248
$587$			1.38017e12i			0.479800i	0.970798	+	0.239900i	$0.0771147\pi$
$587$			1.38017e12i			0.479800i	−0.970798	+	0.239900i	$0.922885\pi$
$588$			5.44490e11i			0.187842i
$589$	−8.13789e11			−0.278608
$590$	5.37405e12	−	7.54450e12i	1.82586	−	2.56328i
$591$	−1.35778e12			−0.457811
$592$		−	7.78980e12i		−	2.60663i
$593$			6.90406e11i			0.229276i	0.993407	+	0.114638i	$0.0365708\pi$
$593$			6.90406e11i			0.229276i	−0.993407	+	0.114638i	$0.963429\pi$
$594$	6.15377e11			0.202816
$595$	1.89827e12	+	1.35216e12i	0.620913	+	0.442285i
$596$	−7.15286e12			−2.32205
$597$			8.47568e11i			0.273080i
$598$			2.37553e12i			0.759635i
$599$	−1.24239e12			−0.394309			−0.197155	−	0.980372i	$-0.563170\pi$
$599$	−1.24239e12			−0.394309			−0.197155	+	0.980372i	$0.563170\pi$
$600$	−6.78299e11	−	1.96164e12i	−0.213668	−	0.617930i
$601$	2.01140e12			0.628873			0.314437	−	0.949278i	$-0.398184\pi$
$601$	2.01140e12			0.628873			0.314437	+	0.949278i	$0.398184\pi$
$602$		−	6.41867e12i		−	1.99187i
$603$			5.13126e12i			1.58050i
$604$	7.11302e12			2.17464
$605$	−2.56028e12	−	1.82373e12i	−0.776943	−	0.553427i
$606$	−3.16666e11			−0.0953837
$607$		−	2.73579e12i		−	0.817963i	−0.912543	−	0.408981i	$-0.865884\pi$
$607$		−	2.73579e12i		−	0.817963i	0.912543	−	0.408981i	$-0.134116\pi$
$608$			2.08907e12i			0.619992i
$609$	−5.13981e11			−0.151415
$610$	−1.78579e12	+	2.50703e12i	−0.522211	+	0.733120i
$611$	−3.26838e12			−0.948738
$612$			6.85021e12i			1.97389i
$613$		−	1.63707e12i		−	0.468269i	−0.972204	−	0.234135i	$-0.924774\pi$
$613$		−	1.63707e12i		−	0.468269i	0.972204	−	0.234135i	$-0.0752257\pi$
$614$	3.43075e12			0.974162
$615$	5.20093e11	−	7.30146e11i	0.146603	−	0.205812i
$616$	1.56461e12			0.437817
$617$		−	1.22267e12i		−	0.339646i	−0.985475	−	0.169823i	$-0.945680\pi$
$617$		−	1.22267e12i		−	0.339646i	0.985475	−	0.169823i	$-0.0543197\pi$
$618$			1.42448e12i			0.392832i
$619$	5.78784e12			1.58456			0.792280	−	0.610158i	$-0.208894\pi$
$619$	5.78784e12			1.58456			0.792280	+	0.610158i	$0.208894\pi$
$620$	4.48370e12	+	3.19380e12i	1.21863	+	0.868050i
$621$	1.03099e12			0.278190
$622$			8.83967e11i			0.236799i
$623$		−	1.26136e12i		−	0.335463i
$624$	−1.66279e12			−0.439042
$625$	−2.99991e12	+	2.35636e12i	−0.786409	+	0.617706i
$626$	−1.06008e13			−2.75902
$627$		−	9.69138e10i		−	0.0250427i
$628$		−	3.51803e12i		−	0.902571i
$629$	−4.40702e12			−1.12258
$630$	−4.56640e12	−	3.25271e12i	−1.15489	−	0.822646i
$631$	2.00341e12			0.503081			0.251540	−	0.967847i	$-0.419063\pi$
$631$	2.00341e12			0.503081			0.251540	+	0.967847i	$0.419063\pi$
$632$			1.15945e13i			2.89084i
$633$		−	1.36372e12i		−	0.337605i
$634$	−5.21084e12			−1.28087
$635$	1.71978e12	−	2.41435e12i	0.419750	−	0.589277i
$636$	2.55205e12			0.618489
$637$		−	9.63992e11i		−	0.231978i
$638$		−	1.10675e12i		−	0.264458i
$639$	−1.63889e12			−0.388863
$640$	−1.31412e12	+	1.84487e12i	−0.309618	+	0.434666i
$641$	2.75478e12			0.644505			0.322253	−	0.946654i	$-0.395560\pi$
$641$	2.75478e12			0.644505			0.322253	+	0.946654i	$0.395560\pi$
$642$		−	2.58546e12i		−	0.600662i
$643$		−	7.38857e12i		−	1.70455i	−0.523091	−	0.852277i	$-0.675221\pi$
$643$		−	7.38857e12i		−	1.70455i	0.523091	−	0.852277i	$-0.324779\pi$
$644$	4.58550e12			1.05051
$645$	1.25222e12	+	8.91972e11i	0.284879	+	0.202924i
$646$	3.20138e12			0.723254
$647$		−	4.12045e12i		−	0.924432i	−0.886767	−	0.462216i	$-0.847054\pi$
$647$		−	4.12045e12i		−	0.924432i	0.886767	−	0.462216i	$-0.152946\pi$
$648$		−	8.63269e12i		−	1.92335i
$649$	−1.67245e12			−0.370043
$650$	2.10075e12	+	6.07537e12i	0.461598	+	1.33494i
$651$	−6.59311e11			−0.143872
$652$		−	3.22517e12i		−	0.698937i
$653$			6.51407e12i			1.40198i	0.713170	+	0.700992i	$0.247259\pi$
$653$			6.51407e12i			1.40198i	−0.713170	+	0.700992i	$0.752741\pi$
$654$	−2.69315e12			−0.575654
$655$	6.34807e12	+	4.52182e12i	1.34758	+	0.959903i
$656$	9.45073e12			1.99250
$657$		−	1.38864e12i		−	0.290767i
$658$			9.01141e12i			1.87403i
$659$	1.74145e12			0.359688			0.179844	−	0.983695i	$-0.442441\pi$
$659$	1.74145e12			0.359688			0.179844	+	0.983695i	$0.442441\pi$
$660$	−3.80348e11	+	5.33961e11i	−0.0780250	+	0.109537i
$661$	−1.39849e12			−0.284939			−0.142469	−	0.989799i	$-0.545504\pi$
$661$	−1.39849e12			−0.284939			−0.142469	+	0.989799i	$0.545504\pi$
$662$			7.07800e12i			1.43235i
$663$			9.40708e11i			0.189079i
$664$	−1.47368e13			−2.94202
$665$	−1.06425e12	+	1.49408e12i	−0.211031	+	0.296262i
$666$	1.06014e13			2.08799
$667$		−	1.85422e12i		−	0.362740i
$668$		−	1.75865e13i		−	3.41732i
$669$	1.85882e12			0.358774
$670$	−1.32124e13	−	9.41137e12i	−2.53306	−	1.80433i
$671$	5.55753e11			0.105835
$672$			1.69251e12i			0.320161i
$673$			7.23077e12i			1.35868i	0.733824	+	0.679340i	$0.237734\pi$
$673$			7.23077e12i			1.35868i	−0.733824	+	0.679340i	$0.762266\pi$
$674$	1.94333e13			3.62725
$675$	2.63673e12	−	9.11730e11i	0.488876	−	0.169044i
$676$	−5.09140e12			−0.937728
$677$		−	1.09854e12i		−	0.200986i	−0.994938	−	0.100493i	$-0.967958\pi$
$677$		−	1.09854e12i		−	0.200986i	0.994938	−	0.100493i	$-0.0320419\pi$
$678$			9.81319e11i			0.178351i
$679$	−3.20921e12			−0.579408
$680$	−1.00831e13	−	7.18231e12i	−1.80843	−	1.28817i
$681$	−1.23352e12			−0.219779
$682$		−	1.41969e12i		−	0.251283i
$683$			1.51781e12i			0.266885i	0.991057	+	0.133442i	$0.0426031\pi$
$683$			1.51781e12i			0.266885i	−0.991057	+	0.133442i	$0.957397\pi$
$684$	−5.39163e12			−0.941820
$685$	−2.08637e12	+	2.92900e12i	−0.362063	+	0.508291i
$686$	−1.15204e13			−1.98613
$687$			5.10355e11i			0.0874112i
$688$			1.62082e13i			2.75796i
$689$	−4.51828e12			−0.763812
$690$	−9.10180e11	+	1.27778e12i	−0.152864	+	0.214603i
$691$	1.51489e12			0.252772			0.126386	−	0.991981i	$-0.459662\pi$
$691$	1.51489e12			0.252772			0.126386	+	0.991981i	$0.459662\pi$
$692$			1.87188e11i			0.0310314i
$693$			1.01227e12i			0.166724i
$694$	1.18439e13			1.93810
$695$	1.84741e12	+	1.31594e12i	0.300353	+	0.213946i
$696$	2.73013e12			0.441003
$697$		−	5.34668e12i		−	0.858097i
$698$			1.46398e13i			2.33446i
$699$	−3.01064e11			−0.0476993
$700$	1.17273e13	−	4.05509e12i	1.84611	−	0.638350i
$701$	7.62368e12			1.19243			0.596216	−	0.802824i	$-0.296670\pi$
$701$	7.62368e12			1.19243			0.596216	+	0.802824i	$0.296670\pi$
$702$		−	4.70140e12i		−	0.730651i
$703$		−	3.46866e12i		−	0.535627i
$704$	−6.83975e11			−0.104945
$705$	−1.75804e12	−	1.25227e12i	−0.268026	−	0.190918i
$706$	8.65605e12			1.31129
$707$		−	1.08221e12i		−	0.162901i
$708$		−	7.21697e12i		−	1.07946i
$709$	−1.00657e13			−1.49602			−0.748010	−	0.663687i	$-0.768991\pi$
$709$	−1.00657e13			−1.49602			−0.748010	+	0.663687i	$0.768991\pi$
$710$	3.00594e12	−	4.21996e12i	0.443933	−	0.623226i
$711$	−7.50140e12			−1.10085
$712$			6.70002e12i			0.977049i
$713$		−	2.37851e12i		−	0.344669i
$714$	2.59367e12			0.373485
$715$	6.73388e11	−	9.45353e11i	0.0963580	−	0.135275i
$716$	−6.40096e12			−0.910199
$717$			3.12496e12i			0.441579i
$718$		−	1.19033e13i		−	1.67151i
$719$	−8.94464e12			−1.24820			−0.624098	−	0.781346i	$-0.714534\pi$
$719$	−8.94464e12			−1.24820			−0.624098	+	0.781346i	$0.714534\pi$
$720$	1.15310e13	+	8.21366e12i	1.59908	+	1.13904i
$721$	−4.86817e12			−0.670899
$722$		−	1.08135e13i		−	1.48098i
$723$			2.27647e12i			0.309841i
$724$	1.81812e12			0.245923
$725$	−1.63974e12	−	4.74214e12i	−0.220422	−	0.637460i
$726$	−3.49822e12			−0.467339
$727$			1.22168e13i			1.62201i	0.585038	+	0.811006i	$0.301079\pi$
$727$			1.22168e13i			1.62201i	−0.585038	+	0.811006i	$0.698921\pi$
$728$		−	1.19534e13i		−	1.57725i
$729$	4.52688e12			0.593642
$730$	3.57559e12	+	2.54694e12i	0.466009	+	0.331945i
$731$	9.16968e12			1.18775
$732$			2.39819e12i			0.308734i
$733$		−	1.44452e13i		−	1.84823i	−0.382118	−	0.924114i	$-0.624805\pi$
$733$		−	1.44452e13i		−	1.84823i	0.382118	−	0.924114i	$-0.375195\pi$
$734$	5.51974e11			0.0701919
$735$	3.69352e11	−	5.18524e11i	0.0466818	−	0.0655354i
$736$	−6.10584e12			−0.767000
$737$			2.92889e12i			0.365679i
$738$			1.28618e13i			1.59605i
$739$	1.11591e13			1.37635			0.688175	−	0.725545i	$-0.258412\pi$
$739$	1.11591e13			1.37635			0.688175	+	0.725545i	$0.258412\pi$
$740$	−1.36131e13	+	1.91111e13i	−1.66884	+	2.34284i
$741$	−7.40409e11			−0.0902172
$742$			1.24576e13i			1.50875i
$743$			9.35882e12i			1.12660i	0.826251	+	0.563302i	$0.190469\pi$
$743$			9.35882e12i			1.12660i	−0.826251	+	0.563302i	$0.809531\pi$
$744$	3.50208e12			0.419033
$745$	6.81176e12	+	4.85211e12i	0.810133	+	0.577069i
$746$	−1.72617e13			−2.04061
$747$		−	9.53439e12i		−	1.12034i
$748$			3.91007e12i			0.456696i
$749$	8.83585e12			1.02584
$750$	−1.19779e12	+	4.07279e12i	−0.138231	+	0.470020i
$751$	−1.28609e13			−1.47533			−0.737667	−	0.675165i	$-0.764072\pi$
$751$	−1.28609e13			−1.47533			−0.737667	+	0.675165i	$0.764072\pi$
$752$		−	2.27553e13i		−	2.59480i
$753$		−	3.94028e12i		−	0.446632i
$754$	−8.45543e12			−0.952719
$755$	−6.77382e12	−	4.82509e12i	−0.758704	−	0.540435i
$756$	−9.07514e12			−1.01043
$757$			1.42250e13i			1.57442i	0.616684	+	0.787211i	$0.288476\pi$
$757$			1.42250e13i			1.57442i	−0.616684	+	0.787211i	$0.711524\pi$
$758$		−	1.08716e13i		−	1.19613i
$759$	2.83256e11			0.0309807
$760$	5.65302e12	−	7.93614e12i	0.614638	−	0.862875i
$761$	1.65722e13			1.79122			0.895610	−	0.444841i	$-0.146740\pi$
$761$	1.65722e13			1.79122			0.895610	+	0.444841i	$0.146740\pi$
$762$		−	3.29883e12i		−	0.354456i
$763$		−	9.20389e12i		−	0.983130i
$764$	1.10954e13			1.17822
$765$	4.64681e12	−	6.52354e12i	0.490545	−	0.688664i
$766$	3.24004e12			0.340033
$767$			1.27773e13i			1.33309i
$768$			3.78498e12i			0.392589i
$769$	−2.81269e12			−0.290037			−0.145019	−	0.989429i	$-0.546324\pi$
$769$	−2.81269e12			−0.290037			−0.145019	+	0.989429i	$0.546324\pi$
$770$	−2.60648e12	−	1.85663e12i	−0.267206	−	0.190334i
$771$	2.98397e12			0.304123
$772$		−	8.29949e12i		−	0.840957i
$773$			8.57982e12i			0.864311i	0.901799	+	0.432156i	$0.142247\pi$
$773$			8.57982e12i			0.864311i	−0.901799	+	0.432156i	$0.857753\pi$
$774$	−2.20583e13			−2.20921
$775$	−2.10338e12	−	6.08299e12i	−0.209440	−	0.605703i
$776$	1.70465e13			1.68755
$777$		−	2.81021e12i		−	0.276595i
$778$		−	6.85930e12i		−	0.671230i
$779$	4.20824e12			0.409432
$780$	4.07940e12	+	2.90581e12i	0.394612	+	0.281087i
$781$	−9.35472e11			−0.0899707
$782$			9.35687e12i			0.894746i
$783$			3.66968e12i			0.348900i
$784$	6.71158e12			0.634458
$785$	−2.38644e12	+	3.35027e12i	−0.224304	+	0.314895i
$786$	8.67363e12			0.810586
$787$		−	1.75771e12i		−	0.163328i	−0.996660	−	0.0816642i	$-0.973976\pi$
$787$		−	1.75771e12i		−	0.163328i	0.996660	−	0.0816642i	$-0.0260235\pi$
$788$			4.31166e13i			3.98361i
$789$	−3.93830e9			−0.000361795
$790$	1.37585e13	−	1.93152e13i	1.25675	−	1.76432i
$791$	−3.35367e12			−0.304597
$792$		−	5.37691e12i		−	0.485590i
$793$		−	4.24588e12i		−	0.381275i
$794$	−1.69218e13			−1.51096
$795$	−2.43035e12	−	1.73117e12i	−0.215783	−	0.153705i
$796$	2.69147e13			2.37619
$797$		−	2.27115e13i		−	1.99381i	−0.0786130	−	0.996905i	$-0.525049\pi$
$797$		−	2.27115e13i		−	1.99381i	0.0786130	−	0.996905i	$-0.474951\pi$
$798$			2.04142e12i			0.178205i
$799$	−1.28737e13			−1.11748
$800$	−1.56156e13	+	5.39956e12i	−1.34788	+	0.466073i
$801$	−4.33478e12			−0.372067
$802$		−	3.27516e12i		−	0.279542i
$803$		−	7.92629e11i		−	0.0672744i
$804$	−1.26388e13			−1.06673
$805$	−4.36683e12	−	3.11055e12i	−0.366509	−	0.261070i
$806$	−1.08462e13			−0.905255
$807$		−	2.78065e11i		−	0.0230789i
$808$			5.74840e12i			0.474456i
$809$	9.95176e12			0.816829			0.408415	−	0.912796i	$-0.366082\pi$
$809$	9.95176e12			0.816829			0.408415	+	0.912796i	$0.366082\pi$
$810$	−1.02439e13	+	1.43812e13i	−0.836149	+	1.17385i
$811$	−7.01292e12			−0.569253			−0.284626	−	0.958639i	$-0.591870\pi$
$811$	−7.01292e12			−0.569253			−0.284626	+	0.958639i	$0.591870\pi$
$812$			1.63216e13i			1.31753i
$813$		−	4.80696e12i		−	0.385889i
$814$	6.05121e12			0.483095
$815$	−2.18778e12	+	3.07137e12i	−0.173698	+	0.243850i
$816$	−6.54948e12			−0.517131
$817$			7.21723e12i			0.566724i
$818$		−	2.83379e13i		−	2.21298i
$819$	7.73362e12			0.600627
$820$	−2.31859e13	−	1.65157e13i	−1.79086	−	1.27566i
$821$	−1.20992e13			−0.929420			−0.464710	−	0.885463i	$-0.653841\pi$
$821$	−1.20992e13			−0.929420			−0.464710	+	0.885463i	$0.653841\pi$
$822$			4.00202e12i			0.305742i
$823$			1.21261e13i			0.921346i	0.887570	+	0.460673i	$0.152392\pi$
$823$			1.21261e13i			0.921346i	−0.887570	+	0.460673i	$0.847608\pi$
$824$	2.58584e13			1.95402
$825$	7.24421e11	−	2.50491e11i	0.0544438	−	0.0188256i
$826$	3.52289e13			2.63323
$827$			1.32495e13i			0.984973i	0.870320	+	0.492486i	$0.163912\pi$
$827$			1.32495e13i			0.984973i	−0.870320	+	0.492486i	$0.836088\pi$
$828$		−	1.57584e13i		−	1.16514i
$829$	1.87106e13			1.37592			0.687960	−	0.725749i	$-0.258507\pi$
$829$	1.87106e13			1.37592			0.687960	+	0.725749i	$0.258507\pi$
$830$	2.45499e13	+	1.74873e13i	1.79556	+	1.27900i
$831$	1.19157e12			0.0866789
$832$			5.22548e12i			0.378069i
$833$		−	3.79702e12i		−	0.273238i
$834$	2.52419e12			0.180665
$835$	−1.19297e13	+	1.67478e13i	−0.849261	+	1.19226i
$836$	−3.07752e12			−0.217908
$837$			4.70730e12i			0.331518i
$838$		−	1.37130e13i		−	0.960582i
$839$	−1.21346e13			−0.845469			−0.422734	−	0.906254i	$-0.638930\pi$
$839$	−1.21346e13			−0.845469			−0.422734	+	0.906254i	$0.638930\pi$
$840$	4.57993e12	−	6.42965e12i	0.317396	−	0.445585i
$841$	−7.90725e12			−0.545059
$842$		−	2.60599e13i		−	1.78677i
$843$			3.57703e12i			0.243949i
$844$	−4.33053e13			−2.93765
$845$	4.84860e12	+	3.45373e12i	0.327161	+	0.233041i
$846$	3.09684e13			2.07851
$847$		−	1.19552e13i		−	0.798145i
$848$		−	3.14575e13i		−	2.08902i
$849$	−1.85140e12			−0.122297
$850$	8.27454e12	+	2.39300e13i	0.543699	+	1.57238i
$851$	1.01380e13			0.662630
$852$		−	4.03676e12i		−	0.262455i
$853$			2.34098e13i			1.51401i	0.653411	+	0.757004i	$0.273337\pi$
$853$			2.34098e13i			1.51401i	−0.653411	+	0.757004i	$0.726663\pi$
$854$	−1.17065e13			−0.753126
$855$	5.13452e12	+	3.65739e12i	0.328589	+	0.234058i
$856$	−4.69336e13			−2.98780
$857$		−	1.61008e13i		−	1.01961i	−0.860290	−	0.509805i	$-0.829718\pi$
$857$		−	1.61008e13i		−	1.01961i	0.860290	−	0.509805i	$-0.170282\pi$
$858$		−	1.29167e12i		−	0.0813691i
$859$	1.34163e13			0.840745			0.420373	−	0.907352i	$-0.361899\pi$
$859$	1.34163e13			0.840745			0.420373	+	0.907352i	$0.361899\pi$
$860$	2.83248e13	−	3.97644e13i	1.76573	−	2.47886i
$861$	3.40940e12			0.211429
$862$			3.18532e13i			1.96504i
$863$		−	2.03784e13i		−	1.25061i	−0.780381	−	0.625304i	$-0.784975\pi$
$863$		−	2.03784e13i		−	1.25061i	0.780381	−	0.625304i	$-0.215025\pi$
$864$	1.20840e13			0.737735
$865$	1.26978e11	−	1.78262e11i	0.00771183	−	0.0108264i
$866$	−4.45544e13			−2.69191
$867$		−	7.58415e11i		−	0.0455849i
$868$			2.09366e13i			1.25189i
$869$	−4.28176e12			−0.254703
$870$	−4.54811e12	−	3.23969e12i	−0.269150	−	0.191719i
$871$	2.23764e13			1.31737
$872$			4.88886e13i			2.86341i
$873$			1.10287e13i			0.642630i
$874$	−7.36456e12			−0.426919
$875$	−1.39188e13	−	4.09347e12i	−0.802725	−	0.236078i
$876$	3.42036e12			0.196247
$877$		−	3.55027e12i		−	0.202658i	−0.994853	−	0.101329i	$-0.967691\pi$
$877$		−	3.55027e12i		−	0.202658i	0.994853	−	0.101329i	$-0.0323094\pi$
$878$			3.95186e13i			2.24428i
$879$	−1.33206e12			−0.0752617
$880$	6.58181e12	+	4.68831e12i	0.369976	+	0.263539i
$881$	−2.33443e13			−1.30554			−0.652769	−	0.757557i	$-0.726393\pi$
$881$	−2.33443e13			−1.30554			−0.652769	+	0.757557i	$0.726393\pi$
$882$			9.13399e12i			0.508220i
$883$		−	8.70030e12i		−	0.481627i	−0.970571	−	0.240814i	$-0.922586\pi$
$883$		−	8.70030e12i		−	0.481627i	0.970571	−	0.240814i	$-0.0774142\pi$
$884$	2.98724e13			1.64526
$885$	−4.89560e12	+	6.87281e12i	−0.268263	+	0.376608i
$886$	−8.52799e12			−0.464938
$887$		−	2.98568e13i		−	1.61952i	−0.586760	−	0.809761i	$-0.699597\pi$
$887$		−	2.98568e13i		−	1.61952i	0.586760	−	0.809761i	$-0.300403\pi$
$888$			1.49271e13i			0.805596i
$889$	1.12738e13			0.605358
$890$	7.95053e12	−	1.11616e13i	0.424758	−	0.596307i
$891$	3.18799e12			0.169460
$892$		−	5.90273e13i		−	3.12184i
$893$		−	1.01325e13i		−	0.533196i
$894$	9.30718e12			0.487303
$895$	6.09572e12	+	4.34206e12i	0.317557	+	0.226200i
$896$	−8.61458e12			−0.446527
$897$		−	2.16404e12i		−	0.111609i
$898$		−	7.26969e12i		−	0.373055i
$899$	8.46604e12			0.432277
$900$	−1.39356e13	−	4.03019e13i	−0.708004	−	2.04755i
$901$	−1.77968e13			−0.899666
$902$			7.34144e12i			0.369277i
$903$			5.84721e12i			0.292654i
$904$	1.78138e13			0.887153
$905$	−1.73142e12	−	1.23331e12i	−0.0857993	−	0.0611160i
$906$	−9.25534e12			−0.456368
$907$		−	2.14293e13i		−	1.05142i	−0.850664	−	0.525709i	$-0.823800\pi$
$907$		−	2.14293e13i		−	1.05142i	0.850664	−	0.525709i	$-0.176200\pi$
$908$			3.91708e13i			1.91239i
$909$	−3.71910e12			−0.180676
$910$	−1.41844e13	+	1.99132e13i	−0.685686	+	0.962618i
$911$	3.43474e13			1.65219			0.826097	−	0.563529i	$-0.190557\pi$
$911$	3.43474e13			1.65219			0.826097	+	0.563529i	$0.190557\pi$
$912$		−	5.15493e12i		−	0.246744i
$913$		−	5.44218e12i		−	0.259212i
$914$	−1.23470e13			−0.585200
$915$	1.62680e12	−	2.28383e12i	0.0767255	−	0.107713i
$916$	1.62064e13			0.760603
$917$			2.96422e13i			1.38436i
$918$		−	1.85181e13i		−	0.860607i
$919$	−2.05847e13			−0.951975			−0.475987	−	0.879452i	$-0.657909\pi$
$919$	−2.05847e13			−0.951975			−0.475987	+	0.879452i	$0.657909\pi$
$920$	2.31954e13	+	1.65224e13i	1.06747	+	0.760376i
$921$	−3.12531e12			−0.143128
$922$			1.81566e13i			0.827458i
$923$			7.14688e12i			0.324122i
$924$	−2.49332e12			−0.112527
$925$	2.59278e13	−	8.96535e12i	1.16447	−	0.402652i
$926$	4.80354e13			2.14690
$927$			1.67299e13i			0.744104i
$928$		−	2.17331e13i		−	0.961955i
$929$	−1.78605e13			−0.786726			−0.393363	−	0.919383i	$-0.628688\pi$
$929$	−1.78605e13			−0.786726			−0.393363	+	0.919383i	$0.628688\pi$
$930$	−5.83411e12	−	4.15572e12i	−0.255741	−	0.182168i
$931$	2.98855e12			0.130373
$932$			9.56035e12i			0.415052i
$933$		−	8.05267e11i		−	0.0347915i
$934$	−6.85583e12			−0.294781
$935$	2.65238e12	−	3.72361e12i	0.113497	−	0.159335i
$936$	−4.10789e13			−1.74935
$937$			1.00969e13i			0.427917i	0.976843	+	0.213959i	$0.0686358\pi$
$937$			1.00969e13i			0.427917i	−0.976843	+	0.213959i	$0.931364\pi$
$938$		−	6.16950e13i		−	2.60218i
$939$	9.65703e12			0.405367
$940$	−3.97662e13	+	5.58268e13i	−1.66126	+	2.33221i
$941$	−2.40159e12			−0.0998496			−0.0499248	−	0.998753i	$-0.515898\pi$
$941$	−2.40159e12			−0.0998496			−0.0499248	+	0.998753i	$0.515898\pi$
$942$			4.57760e12i			0.189413i
$943$			1.22997e13i			0.506513i
$944$	−8.89591e13			−3.64600
$945$	8.64237e12	+	6.15608e12i	0.352525	+	0.251108i
$946$	−1.25908e13			−0.511142
$947$			2.09609e13i			0.846907i	0.905918	+	0.423453i	$0.139182\pi$
$947$			2.09609e13i			0.846907i	−0.905918	+	0.423453i	$0.860818\pi$
$948$		−	1.84767e13i		−	0.742997i
$949$	−6.05558e12			−0.242358
$950$	−1.88347e13	+	6.51268e12i	−0.750245	+	0.259420i
$951$	4.74692e12			0.188191
$952$		−	4.70827e13i		−	1.85779i
$953$		−	1.23636e12i		−	0.0485543i	−0.999705	−	0.0242771i	$-0.992272\pi$
$953$		−	1.23636e12i		−	0.0485543i	0.999705	−	0.0242771i	$-0.00772841\pi$
$954$	4.28115e13			1.67337
$955$	−1.05663e13	−	7.52655e12i	−0.411064	−	0.292806i
$956$	9.92338e13			3.84237
$957$			1.00822e12i			0.0388553i
$958$		−	5.50289e12i		−	0.211080i
$959$	−1.36769e13			−0.522162
$960$	−2.00213e12	+	2.81075e12i	−0.0760803	+	0.106807i
$961$	−1.55798e13			−0.589259
$962$		−	4.62305e13i		−	1.74037i
$963$		−	3.03651e13i		−	1.13778i
$964$	7.22897e13			2.69606
$965$	−5.62992e12	+	7.90371e12i	−0.208992	+	0.293399i
$966$	−5.96657e12			−0.220459
$967$			1.93044e13i			0.709966i	0.934873	+	0.354983i	$0.115513\pi$
$967$			1.93044e13i			0.709966i	−0.934873	+	0.354983i	$0.884487\pi$
$968$			6.35028e13i			2.32463i
$969$	−2.91636e12			−0.106264
$970$	−2.83977e13	−	2.02281e13i	−1.02994	−	0.733637i
$971$	−2.95198e12			−0.106568			−0.0532840	−	0.998579i	$-0.516969\pi$
$971$	−2.95198e12			−0.106568			−0.0532840	+	0.998579i	$0.516969\pi$
$972$			4.73634e13i			1.70194i
$973$			8.62646e12i			0.308549i
$974$	5.92007e13			2.10771
$975$	−1.91372e12	−	5.53448e12i	−0.0678199	−	0.196135i
$976$	2.95610e13			1.04279
$977$			5.39705e13i			1.89509i	0.319617	+	0.947547i	$0.396446\pi$
$977$			5.39705e13i			1.89509i	−0.319617	+	0.947547i	$0.603554\pi$
$978$			4.19653e12i			0.146678i
$979$	−2.47427e12			−0.0860845
$980$	−1.64659e13	−	1.17289e13i	−0.570252	−	0.406198i
$981$	−3.16299e13			−1.09040
$982$		−	4.36697e13i		−	1.49858i
$983$		−	2.52782e13i		−	0.863487i	−0.901996	−	0.431743i	$-0.857899\pi$
$983$		−	2.52782e13i		−	0.863487i	0.901996	−	0.431743i	$-0.142101\pi$
$984$	−1.81098e13			−0.615795
$985$	2.92480e13	−	4.10605e13i	0.989994	−	1.38983i
$986$	−3.33047e13			−1.12217
$987$		−	8.20912e12i		−	0.275340i
$988$			2.35118e13i			0.785019i
$989$	−2.10942e13			−0.701101
$990$	−6.38047e12	+	8.95738e12i	−0.211103	+	0.296362i
$991$	3.62973e13			1.19548			0.597741	−	0.801689i	$-0.296065\pi$
$991$	3.62973e13			1.19548			0.597741	+	0.801689i	$0.296065\pi$
$992$		−	2.78781e13i		−	0.914032i
$993$		−	6.44785e12i		−	0.210447i
$994$	1.97050e13			0.640234
$995$	−2.56312e13	−	1.82575e13i	−0.829020	−	0.590523i
$996$	2.34842e13			0.756150
$997$		−	5.75313e13i		−	1.84406i	−0.387114	−	0.922032i	$-0.626528\pi$
$997$		−	5.75313e13i		−	1.84406i	0.387114	−	0.922032i	$-0.373472\pi$
$998$		−	7.35058e12i		−	0.234549i
$999$	−2.00642e13			−0.637347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.10.b.a.4.4	yes	4
3.2	odd	2		45.10.b.b.19.1		4
4.3	odd	2		80.10.c.c.49.3		4
5.2	odd	4		25.10.a.e.1.1		4
5.3	odd	4		25.10.a.e.1.4		4
5.4	even	2	inner	5.10.b.a.4.1	✓	4
15.2	even	4		225.10.a.s.1.4		4
15.8	even	4		225.10.a.s.1.1		4
15.14	odd	2		45.10.b.b.19.4		4
20.3	even	4		400.10.a.ba.1.2		4
20.7	even	4		400.10.a.ba.1.3		4
20.19	odd	2		80.10.c.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.b.a.4.1	✓	4	5.4	even	2	inner
5.10.b.a.4.4	yes	4	1.1	even	1	trivial
25.10.a.e.1.1		4	5.2	odd	4
25.10.a.e.1.4		4	5.3	odd	4
45.10.b.b.19.1		4	3.2	odd	2
45.10.b.b.19.4		4	15.14	odd	2
80.10.c.c.49.2		4	20.19	odd	2
80.10.c.c.49.3		4	4.3	odd	2
225.10.a.s.1.1		4	15.8	even	4
225.10.a.s.1.4		4	15.2	even	4
400.10.a.ba.1.2		4	20.3	even	4
400.10.a.ba.1.3		4	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+41.3193i q^{2} -37.6407i q^{3} -1195.29 q^{4} +(1138.29 + 810.818i) q^{5} +1555.29 q^{6} +5315.22i q^{7} -28233.0i q^{8} +18266.2 q^{9} +O(q^{10})\)	\(q+41.3193i q^{2} -37.6407i q^{3} -1195.29 q^{4} +(1138.29 + 810.818i) q^{5} +1555.29 q^{6} +5315.22i q^{7} -28233.0i q^{8} +18266.2 q^{9} +(-33502.5 + 47033.3i) q^{10} +10426.2 q^{11} +44991.4i q^{12} -79655.1i q^{13} -219621. q^{14} +(30519.7 - 42845.9i) q^{15} +554581. q^{16} -313750. i q^{17} +754746. i q^{18} +246945. q^{19} +(-1.36058e6 - 969161. i) q^{20} +200068. q^{21} +430806. i q^{22} +721761. i q^{23} -1.06271e6 q^{24} +(638273. + 1.84589e6i) q^{25} +3.29130e6 q^{26} -1.42843e6i q^{27} -6.35321e6i q^{28} -2.56903e6 q^{29} +(1.77037e6 + 1.26106e6i) q^{30} -3.29543e6 q^{31} +8.45965e6i q^{32} -392451. i q^{33} +1.29639e7 q^{34} +(-4.30967e6 + 6.05025e6i) q^{35} -2.18333e7 q^{36} -1.40463e7i q^{37} +1.02036e7i q^{38} -2.99827e6 q^{39} +(2.28918e7 - 3.21373e7i) q^{40} +1.70412e7 q^{41} +8.26669e6i q^{42} +2.92261e7i q^{43} -1.24624e7 q^{44} +(2.07922e7 + 1.48105e7i) q^{45} -2.98227e7 q^{46} -4.10316e7i q^{47} -2.08748e7i q^{48} +1.21021e7 q^{49} +(-7.62709e7 + 2.63730e7i) q^{50} -1.18098e7 q^{51} +9.52108e7i q^{52} -5.67230e7i q^{53} +5.90219e7 q^{54} +(1.18681e7 + 8.45379e6i) q^{55} +1.50065e8 q^{56} -9.29518e6i q^{57} -1.06150e8i q^{58} -1.60408e8 q^{59} +(-3.64799e7 + 5.12132e7i) q^{60} +5.33033e7 q^{61} -1.36165e8i q^{62} +9.70887e7i q^{63} -6.56012e7 q^{64} +(6.45858e7 - 9.06705e7i) q^{65} +1.62158e7 q^{66} +2.80916e8i q^{67} +3.75022e8i q^{68} +2.71676e7 q^{69} +(-2.49992e8 - 1.78073e8i) q^{70} -8.97228e7 q^{71} -5.15709e8i q^{72} -7.60225e7i q^{73} +5.80383e8 q^{74} +(6.94805e7 - 2.40250e7i) q^{75} -2.95170e8 q^{76} +5.54178e7i q^{77} -1.23887e8i q^{78} -4.10672e8 q^{79} +(6.31273e8 + 4.49665e8i) q^{80} +3.05766e8 q^{81} +7.04131e8i q^{82} -5.21969e8i q^{83} -2.39139e8 q^{84} +(2.54394e8 - 3.57138e8i) q^{85} -1.20760e9 q^{86} +9.66999e7i q^{87} -2.94364e8i q^{88} -2.37312e8 q^{89} +(-6.11962e8 + 8.59119e8i) q^{90} +4.23384e8 q^{91} -8.62712e8i q^{92} +1.24042e8i q^{93} +1.69540e9 q^{94} +(2.81094e8 + 2.00227e8i) q^{95} +3.18427e8 q^{96} +6.03778e8i q^{97} +5.00050e8i q^{98} +1.90448e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9}+O(q^{10}) \) 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9	\( 4 q - 1368 q^{4} + 1140 q^{5} + 2808 q^{6} + 11628 q^{9} - 69160 q^{10} + 109968 q^{11} - 424536 q^{14} - 396720 q^{15} + 1631264 q^{16} - 636880 q^{19} - 3302280 q^{20} + 3523968 q^{21} - 2435040 q^{24} - 1337900 q^{25} + 6618768 q^{26} - 3531720 q^{29} + 3712680 q^{30} - 10587712 q^{31} + 26434624 q^{34} + 13629840 q^{35} - 56399976 q^{36} + 1686816 q^{39} + 43578400 q^{40} - 16788552 q^{41} + 20638944 q^{44} + 55737180 q^{45} - 61250072 q^{46} - 46921028 q^{49} - 150092400 q^{50} + 84017088 q^{51} + 115855920 q^{54} - 26907120 q^{55} + 315178080 q^{56} - 460829040 q^{59} - 307006560 q^{60} + 360490568 q^{61} + 134995072 q^{64} + 183895680 q^{65} + 18949536 q^{66} - 286524864 q^{69} - 508341960 q^{70} - 47611872 q^{71} + 1176861744 q^{74} + 659239200 q^{75} - 1168489440 q^{76} - 728043520 q^{79} + 965843040 q^{80} - 343387836 q^{81} + 1118898144 q^{84} + 1275419840 q^{85} - 2375904552 q^{86} - 1582700760 q^{89} - 1197088920 q^{90} + 473322528 q^{91} + 3327101704 q^{94} + 1204791600 q^{95} + 399339648 q^{96} - 728787024 q^{99}+O(q^{100}) \) 4 * q - 1368 * q^4 + 1140 * q^5 + 2808 * q^6 + 11628 * q^9 - 69160 * q^10 + 109968 * q^11 - 424536 * q^14 - 396720 * q^15 + 1631264 * q^16 - 636880 * q^19 - 3302280 * q^20 + 3523968 * q^21 - 2435040 * q^24 - 1337900 * q^25 + 6618768 * q^26 - 3531720 * q^29 + 3712680 * q^30 - 10587712 * q^31 + 26434624 * q^34 + 13629840 * q^35 - 56399976 * q^36 + 1686816 * q^39 + 43578400 * q^40 - 16788552 * q^41 + 20638944 * q^44 + 55737180 * q^45 - 61250072 * q^46 - 46921028 * q^49 - 150092400 * q^50 + 84017088 * q^51 + 115855920 * q^54 - 26907120 * q^55 + 315178080 * q^56 - 460829040 * q^59 - 307006560 * q^60 + 360490568 * q^61 + 134995072 * q^64 + 183895680 * q^65 + 18949536 * q^66 - 286524864 * q^69 - 508341960 * q^70 - 47611872 * q^71 + 1176861744 * q^74 + 659239200 * q^75 - 1168489440 * q^76 - 728043520 * q^79 + 965843040 * q^80 - 343387836 * q^81 + 1118898144 * q^84 + 1275419840 * q^85 - 2375904552 * q^86 - 1582700760 * q^89 - 1197088920 * q^90 + 473322528 * q^91 + 3327101704 * q^94 + 1204791600 * q^95 + 399339648 * q^96 - 728787024 * q^99

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