LMFDB - Embedded newform 91.8.q.a.36.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$50$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.42
Character	$\chi$	$=$	91.36
Dual form			91.8.q.a.43.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.8892 - 7.44160i) q^{2} +(-21.6312 - 37.4664i) q^{3} +(46.7547 - 80.9816i) q^{4} -26.3028i q^{5} +(-557.619 - 321.942i) q^{6} +(-297.047 - 171.500i) q^{7} +513.329i q^{8} +(157.681 - 273.111i) q^{9} +O(q^{10})$	\(q+(12.8892 - 7.44160i) q^{2} +(-21.6312 - 37.4664i) q^{3} +(46.7547 - 80.9816i) q^{4} -26.3028i q^{5} +(-557.619 - 321.942i) q^{6} +(-297.047 - 171.500i) q^{7} +513.329i q^{8} +(157.681 - 273.111i) q^{9} +(-195.735 - 339.022i) q^{10} +(-6710.27 + 3874.18i) q^{11} -4045.45 q^{12} +(-1062.38 - 7849.83i) q^{13} -5104.94 q^{14} +(-985.469 + 568.961i) q^{15} +(9804.60 + 16982.1i) q^{16} +(-13556.9 + 23481.2i) q^{17} -4693.58i q^{18} +(-16567.1 - 9565.03i) q^{19} +(-2130.04 - 1229.78i) q^{20} +14839.0i q^{21} +(-57660.1 + 99870.2i) q^{22} +(16313.3 + 28255.5i) q^{23} +(19232.6 - 11103.9i) q^{24} +77433.2 q^{25} +(-72108.5 - 93272.4i) q^{26} -108258. q^{27} +(-27776.7 + 16036.9i) q^{28} +(-36606.8 - 63404.9i) q^{29} +(-8467.96 + 14666.9i) q^{30} +188597. i q^{31} +(195844. + 113071. i) q^{32} +(290303. + 167606. i) q^{33} +403539. i q^{34} +(-4510.92 + 7813.15i) q^{35} +(-14744.6 - 25538.5i) q^{36} +(-186320. + 107572. i) q^{37} -284716. q^{38} +(-271124. + 209605. i) q^{39} +13502.0 q^{40} +(216753. - 125142. i) q^{41} +(110426. + 191263. i) q^{42} +(-123008. + 213056. i) q^{43} +724544. i q^{44} +(-7183.57 - 4147.44i) q^{45} +(420533. + 242795. i) q^{46} -1.03061e6i q^{47} +(424171. - 734685. i) q^{48} +(58824.5 + 101887. i) q^{49} +(998053. - 576226. i) q^{50} +1.17301e6 q^{51} +(-685363. - 280984. i) q^{52} -1.80039e6 q^{53} +(-1.39536e6 + 805614. i) q^{54} +(101902. + 176499. i) q^{55} +(88036.0 - 152483. i) q^{56} +827613. i q^{57} +(-943667. - 544826. i) q^{58} +(-741757. - 428254. i) q^{59} +106406. i q^{60} +(1.29373e6 - 2.24081e6i) q^{61} +(1.40346e6 + 2.43087e6i) q^{62} +(-93677.1 + 54084.5i) q^{63} +855727. q^{64} +(-206472. + 27943.5i) q^{65} +4.98903e6 q^{66} +(-3.51228e6 + 2.02782e6i) q^{67} +(1.26770e6 + 2.19572e6i) q^{68} +(705755. - 1.22240e6i) q^{69} +134274. i q^{70} +(-1.36982e6 - 790866. i) q^{71} +(140196. + 80942.1i) q^{72} +2.39836e6i q^{73} +(-1.60101e6 + 2.77303e6i) q^{74} +(-1.67497e6 - 2.90114e6i) q^{75} +(-1.54918e6 + 894420. i) q^{76} +2.65768e6 q^{77} +(-1.93478e6 + 4.71924e6i) q^{78} -6.38508e6 q^{79} +(446675. - 257888. i) q^{80} +(1.99691e6 + 3.45875e6i) q^{81} +(1.86252e6 - 3.22597e6i) q^{82} -6.27233e6i q^{83} +(1.20169e6 + 693794. i) q^{84} +(617621. + 356584. i) q^{85} +3.66150e6i q^{86} +(-1.58370e6 + 2.74305e6i) q^{87} +(-1.98873e6 - 3.44458e6i) q^{88} +(-8.86921e6 + 5.12064e6i) q^{89} -123454. q^{90} +(-1.03067e6 + 2.51396e6i) q^{91} +3.05090e6 q^{92} +(7.06605e6 - 4.07958e6i) q^{93} +(-7.66939e6 - 1.32838e7i) q^{94} +(-251587. + 435761. i) q^{95} -9.78342e6i q^{96} +(1.12701e7 + 6.50682e6i) q^{97} +(1.51640e6 + 875496. i) q^{98} +2.44353e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) $ 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9 - 2728 * q^10 - 3954 * q^11 - 54708 * q^12 - 32008 * q^13 + 21952 * q^14 + 46398 * q^15 - 228808 * q^16 + 16832 * q^17 - 203520 * q^20 + 148982 * q^22 + 154164 * q^23 - 436560 * q^24 - 1918852 * q^25 - 624246 * q^26 + 661404 * q^27 - 451396 * q^29 + 313736 * q^30 + 1854432 * q^32 + 315450 * q^33 - 372498 * q^35 + 2704174 * q^36 + 1777146 * q^37 - 338468 * q^38 + 189708 * q^39 - 2875580 * q^40 - 2158998 * q^41 - 296352 * q^42 + 1876346 * q^43 + 7252980 * q^45 + 234336 * q^46 + 1316674 * q^48 + 5882450 * q^49 + 6432894 * q^50 - 3602684 * q^51 - 14093326 * q^52 + 1719628 * q^53 - 14915976 * q^54 - 1225470 * q^55 + 2107392 * q^56 + 18792564 * q^58 + 5131962 * q^59 + 886858 * q^61 + 3663272 * q^62 - 1848084 * q^63 - 38282980 * q^64 - 17072760 * q^65 + 54390948 * q^66 - 15529368 * q^67 + 2633716 * q^68 + 12342620 * q^69 + 20194104 * q^71 + 12742440 * q^72 - 23243862 * q^74 - 12055866 * q^75 - 7828698 * q^76 - 11143384 * q^77 - 32361130 * q^78 + 38408264 * q^79 - 38368944 * q^80 - 55140914 * q^81 + 27439818 * q^82 + 46422306 * q^84 + 16353300 * q^85 - 15866954 * q^87 - 39468942 * q^88 + 11465844 * q^89 - 22072424 * q^90 - 3481450 * q^91 + 67780968 * q^92 - 71319114 * q^93 - 6119236 * q^94 + 60860930 * q^95 + 45060702 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	12.8892	−	7.44160i	1.13926	−	0.657750i	0.193011	−	0.981197i	$-0.438175\pi$
$2$	12.8892	−	7.44160i	1.13926	−	0.657750i	0.946247	+	0.323446i	$0.104841\pi$
$3$	−21.6312	−	37.4664i	−0.462548	−	0.801156i	0.536539	−	0.843875i	$-0.319731\pi$
$3$	−21.6312	−	37.4664i	−0.462548	−	0.801156i	−0.999087	+	0.0427190i	$0.986398\pi$
$4$	46.7547	−	80.9816i	0.365271	−	0.632668i
$5$		−	26.3028i		−	0.0941036i	−0.998892	−	0.0470518i	$-0.985017\pi$
$5$		−	26.3028i		−	0.0941036i	0.998892	−	0.0470518i	$-0.0149826\pi$
$6$	−557.619	−	321.942i	−1.05392	−	0.608482i
$7$	−297.047	−	171.500i	−0.327327	−	0.188982i
$7$	−297.047	−	171.500i	−0.327327	−	0.188982i
$8$			513.329i			0.354471i
$9$	157.681	−	273.111i	0.0720991	−	0.124879i
$10$	−195.735	−	339.022i	−0.0618967	−	0.107208i
$11$	−6710.27	+	3874.18i	−1.52008	+	0.877617i	−0.520357	+	0.853949i	$0.674201\pi$
$11$	−6710.27	+	3874.18i	−1.52008	+	0.877617i	−0.999720	+	0.0236679i	$0.992466\pi$
$12$	−4045.45			−0.675822
$13$	−1062.38	−	7849.83i	−0.134115	−	0.990966i
$13$	−1062.38	−	7849.83i	−0.134115	−	0.990966i
$14$	−5104.94			−0.497213
$15$	−985.469	+	568.961i	−0.0753917	+	0.0435274i
$16$	9804.60	+	16982.1i	0.598425	+	1.03650i
$17$	−13556.9	+	23481.2i	−0.669250	+	1.15918i	0.308864	+	0.951106i	$0.400051\pi$
$17$	−13556.9	+	23481.2i	−0.669250	+	1.15918i	−0.978114	+	0.208069i	$0.933282\pi$
$18$		−	4693.58i		−	0.189693i
$19$	−16567.1	−	9565.03i	−0.554127	−	0.319925i	0.196658	−	0.980472i	$-0.436991\pi$
$19$	−16567.1	−	9565.03i	−0.554127	−	0.319925i	−0.750785	+	0.660547i	$0.770324\pi$
$20$	−2130.04	−	1229.78i	−0.0595364	−	0.0343734i
$21$			14839.0i			0.349653i
$22$	−57660.1	+	99870.2i	−1.15451	+	1.99966i
$23$	16313.3	+	28255.5i	0.279573	+	0.484235i	0.971279	−	0.237945i	$-0.0764737\pi$
$23$	16313.3	+	28255.5i	0.279573	+	0.484235i	−0.691705	+	0.722180i	$0.743140\pi$
$24$	19232.6	−	11103.9i	0.283987	−	0.163960i
$25$	77433.2			0.991145
$26$	−72108.5	−	93272.4i	−0.804600	−	1.04075i
$27$	−108258.			−1.05849
$28$	−27776.7	+	16036.9i	−0.239126	+	0.138060i
$29$	−36606.8	−	63404.9i	−0.278721	−	0.482758i	0.692346	−	0.721565i	$-0.256577\pi$
$29$	−36606.8	−	63404.9i	−0.278721	−	0.482758i	−0.971067	+	0.238807i	$0.923244\pi$
$30$	−8467.96	+	14666.9i	−0.0572604	+	0.0991779i
$31$			188597.i			1.13702i	0.822676	+	0.568511i	$0.192480\pi$
$31$			188597.i			1.13702i	−0.822676	+	0.568511i	$0.807520\pi$
$32$	195844.	+	113071.i	1.05654	+	0.609993i
$33$	290303.	+	167606.i	1.40622	+	0.811879i
$34$			403539.i			1.76080i
$35$	−4510.92	+	7813.15i	−0.0177839	+	0.0308026i
$36$	−14744.6	−	25538.5i	−0.0526714	−	0.0912296i
$37$	−186320.	+	107572.i	−0.604717	+	0.349134i	−0.770895	−	0.636962i	$-0.780191\pi$
$37$	−186320.	+	107572.i	−0.604717	+	0.349134i	0.166178	+	0.986096i	$0.446857\pi$
$38$	−284716.			−0.841724
$39$	−271124.	+	209605.i	−0.731884	+	0.565816i
$40$	13502.0			0.0333570
$41$	216753.	−	125142.i	0.491158	−	0.283570i	−0.233897	−	0.972261i	$-0.575148\pi$
$41$	216753.	−	125142.i	0.491158	−	0.283570i	0.725055	+	0.688691i	$0.241814\pi$
$42$	110426.	+	191263.i	0.229985	+	0.398345i
$43$	−123008.	+	213056.i	−0.235936	+	0.408652i	−0.959544	−	0.281558i	$-0.909149\pi$
$43$	−123008.	+	213056.i	−0.235936	+	0.408652i	0.723609	+	0.690211i	$0.242482\pi$
$44$			724544.i			1.28227i
$45$	−7183.57	−	4147.44i	−0.0117516	−	0.00678479i
$46$	420533.	+	242795.i	0.637012	+	0.367779i
$47$		−	1.03061e6i		−	1.44794i	−0.689829	−	0.723972i	$-0.742314\pi$
$47$		−	1.03061e6i		−	1.44794i	0.689829	−	0.723972i	$-0.257686\pi$
$48$	424171.	−	734685.i	0.553600	−	0.958864i
$49$	58824.5	+	101887.i	0.0714286	+	0.123718i
$50$	998053.	−	576226.i	1.12917	−	0.651926i
$51$	1.17301e6			1.23824
$52$	−685363.	−	280984.i	−0.675941	−	0.277121i
$53$	−1.80039e6			−1.66112			−0.830560	−	0.556929i	$-0.811979\pi$
$53$	−1.80039e6			−1.66112			−0.830560	+	0.556929i	$0.811979\pi$
$54$	−1.39536e6	+	805614.i	−1.20590	+	0.696224i
$55$	101902.	+	176499.i	0.0825869	+	0.143045i
$56$	88036.0	−	152483.i	0.0669888	−	0.116028i
$57$			827613.i			0.591923i
$58$	−943667.	−	544826.i	−0.635069	−	0.366657i
$59$	−741757.	−	428254.i	−0.470197	−	0.271468i	0.246125	−	0.969238i	$-0.420843\pi$
$59$	−741757.	−	428254.i	−0.470197	−	0.271468i	−0.716322	+	0.697770i	$0.754176\pi$
$60$			106406.i			0.0635973i
$61$	1.29373e6	−	2.24081e6i	0.729775	−	1.26401i	−0.227203	−	0.973847i	$-0.572958\pi$
$61$	1.29373e6	−	2.24081e6i	0.729775	−	1.26401i	0.956978	−	0.290160i	$-0.0937086\pi$
$62$	1.40346e6	+	2.43087e6i	0.747877	+	1.29536i
$63$	−93677.1	+	54084.5i	−0.0471999	+	0.0272509i
$64$	855727.			0.408043
$65$	−206472.	+	27943.5i	−0.0932535	+	0.0126207i
$66$	4.98903e6			2.13606
$67$	−3.51228e6	+	2.02782e6i	−1.42668	+	0.823696i	−0.996858	−	0.0792151i	$-0.974759\pi$
$67$	−3.51228e6	+	2.02782e6i	−1.42668	+	0.823696i	−0.429826	+	0.902912i	$0.641425\pi$
$68$	1.26770e6	+	2.19572e6i	0.488916	+	0.846827i
$69$	705755.	−	1.22240e6i	0.258632	−	0.447964i
$70$			134274.i			0.0467895i
$71$	−1.36982e6	−	790866.i	−0.454213	−	0.262240i	0.255395	−	0.966837i	$-0.417795\pi$
$71$	−1.36982e6	−	790866.i	−0.454213	−	0.262240i	−0.709608	+	0.704597i	$0.751128\pi$
$72$	140196.	+	80942.1i	0.0442661	+	0.0255571i
$73$			2.39836e6i			0.721580i	0.932647	+	0.360790i	$0.117493\pi$
$73$			2.39836e6i			0.721580i	−0.932647	+	0.360790i	$0.882507\pi$
$74$	−1.60101e6	+	2.77303e6i	−0.459286	+	0.795506i
$75$	−1.67497e6	−	2.90114e6i	−0.458452	−	0.794062i
$76$	−1.54918e6	+	894420.i	−0.404813	+	0.233719i
$77$	2.65768e6			0.663416
$78$	−1.93478e6	+	4.71924e6i	−0.461638	+	1.12601i
$79$	−6.38508e6			−1.45704			−0.728520	−	0.685024i	$-0.759791\pi$
$79$	−6.38508e6			−1.45704			−0.728520	+	0.685024i	$0.759791\pi$
$80$	446675.	−	257888.i	0.0975387	−	0.0563140i
$81$	1.99691e6	+	3.45875e6i	0.417504	+	0.723139i
$82$	1.86252e6	−	3.22597e6i	0.373037	−	0.646119i
$83$		−	6.27233e6i		−	1.20408i	−0.798465	−	0.602041i	$-0.794354\pi$
$83$		−	6.27233e6i		−	1.20408i	0.798465	−	0.602041i	$-0.205646\pi$
$84$	1.20169e6	+	693794.i	0.221215	+	0.127718i
$85$	617621.	+	356584.i	0.109083	+	0.0629789i
$86$			3.66150e6i			0.620747i
$87$	−1.58370e6	+	2.74305e6i	−0.257843	+	0.446597i
$88$	−1.98873e6	−	3.44458e6i	−0.311090	−	0.538824i
$89$	−8.86921e6	+	5.12064e6i	−1.33358	+	0.769944i	−0.985847	−	0.167649i	$-0.946383\pi$
$89$	−8.86921e6	+	5.12064e6i	−1.33358	+	0.769944i	−0.347735	+	0.937593i	$0.613049\pi$
$90$	−123454.			−0.0178508
$91$	−1.03067e6	+	2.51396e6i	−0.143375	+	0.349715i
$92$	3.05090e6			0.408480
$93$	7.06605e6	−	4.07958e6i	0.910932	−	0.525927i
$94$	−7.66939e6	−	1.32838e7i	−0.952386	−	1.64958i
$95$	−251587.	+	435761.i	−0.0301061	+	0.0521454i
$96$		−	9.78342e6i		−	1.12860i
$97$	1.12701e7	+	6.50682e6i	1.25380	+	0.723881i	0.971862	−	0.235551i	$-0.0756896\pi$
$97$	1.12701e7	+	6.50682e6i	1.25380	+	0.723881i	0.281937	+	0.959433i	$0.409023\pi$
$98$	1.51640e6	+	875496.i	0.162751	+	0.0939644i
$99$			2.44353e6i			0.253101i
$100$	3.62037e6	−	6.27066e6i	0.362037	−	0.627066i
$101$	−9.29664e6	−	1.61023e7i	−0.897845	−	1.55511i	−0.830244	−	0.557400i	$-0.811799\pi$
$101$	−9.29664e6	−	1.61023e7i	−0.897845	−	1.55511i	−0.0676009	−	0.997712i	$-0.521534\pi$
$102$	1.51192e7	−	8.72905e6i	1.41068	−	0.814454i
$103$	1.28690e7			1.16041			0.580207	−	0.814469i	$-0.302972\pi$
$103$	1.28690e7			1.16041			0.580207	+	0.814469i	$0.302972\pi$
$104$	4.02955e6	−	545351.i	0.351269	−	0.0475400i
$105$	390307.			0.0329036
$106$	−2.32056e7	+	1.33978e7i	−1.89244	+	1.09260i
$107$	−1.05760e7	−	1.83181e7i	−0.834598	−	1.44557i	−0.894357	−	0.447354i	$-0.852366\pi$
$107$	−1.05760e7	−	1.83181e7i	−0.834598	−	1.44557i	0.0597587	−	0.998213i	$-0.480967\pi$
$108$	−5.06159e6	+	8.76692e6i	−0.386637	+	0.669675i
$109$		−	9.16654e6i		−	0.677974i	−0.940791	−	0.338987i	$-0.889916\pi$
$109$		−	9.16654e6i		−	0.677974i	0.940791	−	0.338987i	$-0.110084\pi$
$110$	2.62686e6	+	1.51662e6i	0.188176	+	0.108643i
$111$	8.06064e6	+	4.65381e6i	0.559421	+	0.322982i
$112$		−	6.72595e6i		−	0.452367i
$113$	5.81556e6	−	1.00728e7i	0.379155	−	0.656716i	−0.611785	−	0.791024i	$-0.709548\pi$
$113$	5.81556e6	−	1.00728e7i	0.379155	−	0.656716i	0.990940	+	0.134309i	$0.0428814\pi$
$114$	6.15876e6	+	1.06673e7i	0.389338	+	0.674353i
$115$	743199.	−	429086.i	0.0455683	−	0.0263089i
$116$	−6.84617e6			−0.407234
$117$	−2.31139e6	−	947619.i	−0.133421	−	0.0546995i
$118$	−1.27476e7			−0.714234
$119$	8.05406e6	−	4.65001e6i	0.438127	−	0.252953i
$120$	−292064.	−	505870.i	−0.0154292	−	0.0267242i
$121$	2.02749e7	−	3.51171e7i	1.04042	−	1.80206i
$122$		−	3.85097e7i		−	1.92004i
$123$	−9.37726e6	−	5.41396e6i	−0.454368	−	0.262330i
$124$	1.52729e7	+	8.81780e6i	0.719358	+	0.415322i
$125$		−	4.09161e6i		−	0.187374i
$126$	−804950.	+	1.39421e6i	−0.0358486	+	0.0620915i
$127$	975237.	+	1.68916e6i	0.0422471	+	0.0731742i	0.886376	−	0.462967i	$-0.153215\pi$
$127$	975237.	+	1.68916e6i	0.0422471	+	0.0731742i	−0.844129	+	0.536141i	$0.819882\pi$
$128$	−1.40384e7	+	8.10506e6i	−0.591673	+	0.341603i
$129$	1.06432e7			0.436526
$130$	−2.45332e6	+	1.89665e6i	−0.0979384	+	0.0757158i
$131$	2.88636e7			1.12176			0.560882	−	0.827896i	$-0.310462\pi$
$131$	2.88636e7			1.12176			0.560882	+	0.827896i	$0.310462\pi$
$132$	2.71460e7	−	1.56728e7i	1.02730	−	0.593113i
$133$	3.28080e6	+	5.68252e6i	0.120920	+	0.209440i
$134$	−3.01804e7	+	5.22740e7i	−1.08357	+	1.87680i
$135$			2.84749e6i			0.0996080i
$136$	−1.20536e7	−	6.95915e6i	−0.410895	−	0.237230i
$137$	3.30999e6	+	1.91102e6i	0.109978	+	0.0634956i	0.553980	−	0.832530i	$-0.313108\pi$
$137$	3.30999e6	+	1.91102e6i	0.109978	+	0.0634956i	−0.444002	+	0.896026i	$0.646442\pi$
$138$		−	2.10078e7i		−	0.680461i
$139$	−6.18047e6	+	1.07049e7i	−0.195195	+	0.338089i	−0.946965	−	0.321338i	$-0.895867\pi$
$139$	−6.18047e6	+	1.07049e7i	−0.195195	+	0.338089i	0.751769	+	0.659426i	$0.229201\pi$
$140$	421814.	+	730603.i	0.0129919	+	0.0225026i
$141$	−3.86132e7	+	2.22934e7i	−1.16003	+	0.669744i
$142$	−2.35412e7			−0.689954
$143$	3.75405e7	+	4.85586e7i	1.07355	+	1.38864i
$144$	6.18398e6			0.172584
$145$	−1.66772e6	+	962861.i	−0.0454293	+	0.0262286i
$146$	1.78476e7	+	3.09130e7i	0.474619	+	0.822065i
$147$	2.54489e6	−	4.40788e6i	0.0660783	−	0.114451i
$148$			2.01179e7i			0.510114i
$149$	1.00018e7	+	5.77455e6i	0.247701	+	0.143010i	0.618711	−	0.785619i	$-0.287655\pi$
$149$	1.00018e7	+	5.77455e6i	0.247701	+	0.143010i	−0.371010	+	0.928629i	$0.620989\pi$
$150$	−4.31782e7	−	2.49290e7i	−1.04459	−	0.603094i
$151$			5.95023e7i			1.40642i	0.710983	+	0.703209i	$0.248250\pi$
$151$			5.95023e7i			1.40642i	−0.710983	+	0.703209i	$0.751750\pi$
$152$	4.91001e6	−	8.50439e6i	0.113404	−	0.196422i
$153$	4.27532e6	+	7.40507e6i	0.0965047	+	0.167151i
$154$	3.42555e7	−	1.97774e7i	0.755801	−	0.436362i
$155$	4.96062e6			0.106998
$156$	4.29780e6	+	3.17561e7i	0.0906380	+	0.669716i
$157$	−6.36255e7			−1.31215			−0.656073	−	0.754697i	$-0.727784\pi$
$157$	−6.36255e7			−1.31215			−0.656073	+	0.754697i	$0.727784\pi$
$158$	−8.22987e7	+	4.75152e7i	−1.65994	+	0.958369i
$159$	3.89446e7	+	6.74541e7i	0.768347	+	1.33082i
$160$	2.97407e6	−	5.15124e6i	0.0574026	−	0.0994242i
$161$		−	1.11910e7i		−	0.211338i
$162$	5.14773e7	+	2.97204e7i	0.951290	+	0.549227i
$163$	4.85135e7	+	2.80093e7i	0.877417	+	0.506577i	0.869806	−	0.493394i	$-0.164244\pi$
$163$	4.85135e7	+	2.80093e7i	0.877417	+	0.506577i	0.00761103	+	0.999971i	$0.497577\pi$
$164$		−	2.34040e7i		−	0.414320i
$165$	4.40851e6	−	7.63576e6i	0.0764008	−	0.132330i
$166$	−4.66762e7	−	8.08455e7i	−0.791985	−	1.37176i
$167$	1.79675e7	−	1.03735e7i	0.298524	−	0.172353i	−0.343256	−	0.939242i	$-0.611530\pi$
$167$	1.79675e7	−	1.03735e7i	0.298524	−	0.172353i	0.641779	+	0.766889i	$0.278196\pi$
$168$	−7.61730e6			−0.123942
$169$	−6.04912e7	+	1.66790e7i	−0.964026	+	0.265807i
$170$	1.06142e7			0.165698
$171$	−5.22463e6	+	3.01644e6i	−0.0799041	+	0.0461326i
$172$	1.15024e7	+	1.99227e7i	0.172361	+	0.298538i
$173$	−8.23301e6	+	1.42600e7i	−0.120892	+	0.209391i	−0.920120	−	0.391637i	$-0.871909\pi$
$173$	−8.23301e6	+	1.42600e7i	−0.120892	+	0.209391i	0.799228	+	0.601028i	$0.205242\pi$
$174$			4.71410e7i			0.678386i
$175$	−2.30013e7	−	1.32798e7i	−0.324428	−	0.187309i
$176$	−1.31583e8	−	7.59695e7i	−1.81930	−	1.05038i
$177$			3.70546e7i			0.502268i
$178$	−7.62115e7	+	1.32002e8i	−1.01286	+	1.75433i
$179$	4.42218e7	+	7.65945e7i	0.576303	+	0.998187i	0.995899	+	0.0904753i	$0.0288386\pi$
$179$	4.42218e7	+	7.65945e7i	0.576303	+	0.998187i	−0.419595	+	0.907711i	$0.637828\pi$
$180$	−671732.	+	387825.i	−0.00858504	+	0.00495658i
$181$	8.68290e7			1.08840			0.544202	−	0.838954i	$-0.316833\pi$
$181$	8.68290e7			1.08840			0.544202	+	0.838954i	$0.316833\pi$
$182$	5.42338e6	+	4.00729e7i	0.0666838	+	0.492721i
$183$	−1.11940e8			−1.35022
$184$	−1.45044e7	+	8.37412e6i	−0.171647	+	0.0991007i
$185$	2.82943e6	+	4.90072e6i	0.0328548	+	0.0569061i
$186$	6.07172e7	−	1.05165e8i	0.691858	−	1.19833i
$187$		−	2.10087e8i		−	2.34938i
$188$	−8.34604e7	−	4.81859e7i	−0.916069	−	0.528893i
$189$	3.21578e7	+	1.85663e7i	0.346473	+	0.200036i
$190$			7.48883e6i			0.0792093i
$191$	−6.20488e7	+	1.07472e8i	−0.644342	+	1.11603i	0.340111	+	0.940385i	$0.389535\pi$
$191$	−6.20488e7	+	1.07472e8i	−0.644342	+	1.11603i	−0.984453	+	0.175648i	$0.943798\pi$
$192$	−1.85104e7	−	3.20610e7i	−0.188739	−	0.326906i
$193$	1.58930e8	−	9.17580e7i	1.59131	−	0.918741i	0.598224	−	0.801329i	$-0.295873\pi$
$193$	1.58930e8	−	9.17580e7i	1.59131	−	0.918741i	0.993083	−	0.117412i	$-0.0374599\pi$
$194$	1.93684e8			1.90453
$195$	5.51319e6	+	7.13132e6i	0.0532454	+	0.0688729i
$196$	1.10013e7			0.104363
$197$	−1.73253e8	+	1.00028e8i	−1.61454	+	0.932155i	−0.626240	+	0.779630i	$0.715407\pi$
$197$	−1.73253e8	+	1.00028e8i	−1.61454	+	0.932155i	−0.988300	+	0.152525i	$0.951260\pi$
$198$	1.81838e7	+	3.14952e7i	0.166478	+	0.288348i
$199$	−1.06503e7	+	1.84469e7i	−0.0958024	+	0.165935i	−0.909943	−	0.414733i	$-0.863875\pi$
$199$	−1.06503e7	+	1.84469e7i	−0.0958024	+	0.165935i	0.814141	+	0.580667i	$0.197208\pi$
$200$			3.97487e7i			0.351332i
$201$	1.51950e8	+	8.77284e7i	1.31982	+	0.761998i
$202$	−2.39653e8	−	1.38364e8i	−2.04575	−	1.18112i
$203$			2.51123e7i			0.210693i
$204$	5.48437e7	−	9.49920e7i	0.452294	−	0.783396i
$205$	−3.29159e6	−	5.70120e6i	−0.0266850	−	0.0462198i
$206$	1.65871e8	−	9.57656e7i	1.32201	−	0.763263i
$207$	1.02892e7			0.0806279
$208$	1.22890e8	−	9.50058e7i	0.946881	−	0.732029i
$209$	1.48226e8			1.12309
$210$	5.03076e6	−	2.90451e6i	0.0374857	−	0.0216424i
$211$	6.45705e7	+	1.11839e8i	0.473201	+	0.819608i	0.999529	−	0.0306736i	$-0.00976524\pi$
$211$	6.45705e7	+	1.11839e8i	0.473201	+	0.819608i	−0.526329	+	0.850281i	$0.676432\pi$
$212$	−8.41767e7	+	1.45798e8i	−0.606759	+	1.05094i
$213$			6.84296e7i			0.485194i
$214$	−2.72632e8	−	1.57404e8i	−1.90164	−	1.09791i
$215$	5.60396e6	+	3.23545e6i	0.0384557	+	0.0222024i
$216$		−	5.55721e7i		−	0.375205i
$217$	3.23444e7	−	5.60221e7i	0.214877	−	0.372178i
$218$	−6.82137e7	−	1.18150e8i	−0.445938	−	0.772386i
$219$	8.98578e7	−	5.18794e7i	0.578098	−	0.333765i
$220$	1.90575e7			0.120667
$221$	1.98726e8	+	8.14733e7i	1.23846	+	0.507741i
$222$	1.38527e8			0.849766
$223$	1.63507e7	−	9.44010e6i	0.0987348	−	0.0570046i	−0.449820	−	0.893119i	$-0.648512\pi$
$223$	1.63507e7	−	9.44010e6i	0.0987348	−	0.0570046i	0.548554	+	0.836115i	$0.315178\pi$
$224$	−3.87832e7	−	6.71745e7i	−0.230556	−	0.399334i
$225$	1.22097e7	−	2.11478e7i	0.0714606	−	0.123773i
$226$		−	1.73108e8i		−	0.997558i
$227$	9.54331e7	+	5.50983e7i	0.541513	+	0.312642i	0.745692	−	0.666291i	$-0.232119\pi$
$227$	9.54331e7	+	5.50983e7i	0.541513	+	0.312642i	−0.204179	+	0.978934i	$0.565452\pi$
$228$	6.70214e7	+	3.86948e7i	0.374491	+	0.216212i
$229$		−	2.56185e8i		−	1.40971i	−0.709353	−	0.704853i	$-0.751013\pi$
$229$		−	2.56185e8i		−	1.40971i	0.709353	−	0.704853i	$-0.248987\pi$
$230$	6.38617e6	−	1.10612e7i	0.0346093	−	0.0599451i
$231$	−5.74890e7	−	9.95738e7i	−0.306862	−	0.531500i
$232$	3.25476e7	−	1.87914e7i	0.171124	−	0.0987985i
$233$	4.59235e7			0.237842			0.118921	−	0.992904i	$-0.462056\pi$
$233$	4.59235e7			0.237842			0.118921	+	0.992904i	$0.462056\pi$
$234$	−3.68438e7	+	4.98637e6i	−0.187979	+	0.0254407i
$235$	−2.71079e7			−0.136257
$236$	−6.93613e7	+	4.00458e7i	−0.343499	+	0.198319i
$237$	1.38117e8	+	2.39226e8i	0.673951	+	1.16732i
$238$	6.92070e7	−	1.19870e8i	0.332760	−	0.576357i
$239$			5.52981e7i			0.262010i	0.991382	+	0.131005i	$0.0418204\pi$
$239$			5.52981e7i			0.262010i	−0.991382	+	0.131005i	$0.958180\pi$
$240$	−1.93243e7	−	1.11569e7i	−0.0902326	−	0.0520958i
$241$	1.24500e6	+	718801.i	0.00572941	+	0.00330788i	0.502862	−	0.864367i	$-0.332280\pi$
$241$	1.24500e6	+	718801.i	0.00572941	+	0.00330788i	−0.497133	+	0.867675i	$0.665614\pi$
$242$		−	6.03510e8i		−	2.73735i
$243$	−3.19892e7	+	5.54069e7i	−0.143015	+	0.247709i
$244$	−1.20976e8	−	2.09536e8i	−0.533132	−	0.923411i
$245$	2.67991e6	−	1.54725e6i	0.0116423	−	0.00672169i
$246$	−1.61154e8			−0.690190
$247$	−5.74833e7	+	1.40211e8i	−0.242718	+	0.592028i
$248$	−9.68124e7			−0.403042
$249$	−2.35002e8	+	1.35678e8i	−0.964657	+	0.556945i
$250$	−3.04481e7	−	5.27377e7i	−0.123245	−	0.213467i
$251$	−1.44912e8	+	2.50995e8i	−0.578425	+	1.00186i	0.417235	+	0.908798i	$0.362999\pi$
$251$	−1.44912e8	+	2.50995e8i	−0.578425	+	1.00186i	−0.995660	+	0.0930627i	$0.970334\pi$
$252$			1.01148e7i			0.0398159i
$253$	−2.18934e8	−	1.26402e8i	−0.849946	−	0.490716i
$254$	2.51401e7	+	1.45146e7i	0.0962607	+	0.0555761i
$255$		−	3.08533e7i		−	0.116523i
$256$	−1.75396e8	+	3.03794e8i	−0.653400	+	1.13172i
$257$	−7.08181e7	−	1.22661e8i	−0.260243	−	0.450753i	0.706064	−	0.708148i	$-0.250469\pi$
$257$	−7.08181e7	−	1.22661e8i	−0.260243	−	0.450753i	−0.966306	+	0.257395i	$0.917136\pi$
$258$	1.37183e8	−	7.92027e7i	0.497315	−	0.287125i
$259$	7.37941e7			0.263920
$260$	−7.39065e6	+	1.80269e7i	−0.0260781	+	0.0636085i
$261$	−2.30888e7			−0.0803820
$262$	3.72030e8	−	2.14791e8i	1.27798	−	0.737840i
$263$	−1.56587e8	−	2.71217e8i	−0.530775	−	0.919329i	−0.999355	−	0.0359084i	$-0.988568\pi$
$263$	−1.56587e8	−	2.71217e8i	−0.530775	−	0.919329i	0.468580	−	0.883421i	$-0.344766\pi$
$264$	−8.60372e7	+	1.49021e8i	−0.287788	+	0.498463i
$265$			4.73552e7i			0.156317i
$266$	8.45740e7	+	4.88288e7i	0.275519	+	0.159071i
$267$	3.83704e8	+	2.21531e8i	1.23369	+	0.712272i
$268$			3.79240e8i			1.20349i
$269$	1.00864e7	−	1.74701e7i	0.0315938	−	0.0547221i	−0.849796	−	0.527111i	$-0.823275\pi$
$269$	1.00864e7	−	1.74701e7i	0.0315938	−	0.0547221i	0.881390	+	0.472389i	$0.156608\pi$
$270$	2.11899e7	+	3.67020e7i	0.0655172	+	0.113479i
$271$	−3.76697e8	+	2.17486e8i	−1.14974	+	0.663802i	−0.948824	−	0.315806i	$-0.897725\pi$
$271$	−3.76697e8	+	2.17486e8i	−1.14974	+	0.663802i	−0.200916	+	0.979609i	$0.564392\pi$
$272$	−5.31679e8			−1.60198
$273$	1.16484e8	−	1.57647e7i	0.346494	−	0.0468938i
$274$	5.68843e7			0.167057
$275$	−5.19597e8	+	2.99990e8i	−1.50662	+	0.869845i
$276$	−6.59948e7	−	1.14306e8i	−0.188942	−	0.327257i
$277$	7.55038e7	−	1.30776e8i	0.213447	−	0.369701i	−0.739344	−	0.673328i	$-0.764864\pi$
$277$	7.55038e7	−	1.30776e8i	0.213447	−	0.369701i	0.952791	+	0.303627i	$0.0981977\pi$
$278$			1.83970e8i			0.513560i
$279$	5.15079e7	+	2.97381e7i	0.141990	+	0.0819782i
$280$	−4.01072e6	−	2.31559e6i	−0.0109187	−	0.00630389i
$281$		−	3.83756e8i		−	1.03177i	−0.856658	−	0.515885i	$-0.827463\pi$
$281$		−	3.83756e8i		−	1.03177i	0.856658	−	0.515885i	$-0.172537\pi$
$282$	−3.31796e8	+	5.74688e8i	−0.881048	+	1.52602i
$283$	5.82127e7	+	1.00827e8i	0.152674	+	0.264439i	0.932210	−	0.361919i	$-0.117878\pi$
$283$	5.82127e7	+	1.00827e8i	0.152674	+	0.264439i	−0.779536	+	0.626358i	$0.784545\pi$
$284$	−1.28091e8	+	7.39535e7i	−0.331822	+	0.191578i
$285$	2.17685e7			0.0557021
$286$	8.45222e8	+	3.46522e8i	2.13643	+	0.875890i
$287$	−8.58476e7			−0.214359
$288$	6.17616e7	−	3.56581e7i	0.152351	−	0.0879599i
$289$	−1.62409e8	−	2.81300e8i	−0.395792	−	0.685532i
$290$	−1.43304e7	+	2.48211e7i	−0.0345038	+	0.0597623i
$291$		−	5.63001e8i		−	1.33932i
$292$	1.94223e8	+	1.12135e8i	0.456521	+	0.263572i
$293$	7.28257e7	+	4.20459e7i	0.169141	+	0.0976533i	0.582181	−	0.813060i	$-0.302200\pi$
$293$	7.28257e7	+	4.20459e7i	0.169141	+	0.0976533i	−0.413040	+	0.910713i	$0.635533\pi$
$294$		−	7.57522e7i		−	0.173852i
$295$	−1.12643e7	+	1.95103e7i	−0.0255462	+	0.0442472i
$296$	−5.52197e7	−	9.56433e7i	−0.123758	−	0.214355i
$297$	7.26442e8	−	4.19412e8i	1.60899	−	0.928951i
$298$	1.71888e8			0.376260
$299$	2.04470e8	−	1.58075e8i	0.442365	−	0.341991i
$300$	−3.13252e8			−0.669837
$301$	7.30782e7	−	4.21917e7i	0.154456	−	0.0891753i
$302$	4.42792e8	+	7.66938e8i	0.925072	+	1.60227i
$303$	−4.02195e8	+	6.96623e8i	−0.830592	+	1.43863i
$304$		−	3.75125e8i		−	0.765805i
$305$	−5.89394e7	−	3.40287e7i	−0.118948	−	0.0686745i
$306$	1.10211e8	+	6.36304e7i	0.219887	+	0.126952i
$307$		−	4.46416e8i		−	0.880553i	−0.897862	−	0.440276i	$-0.854881\pi$
$307$		−	4.46416e8i		−	0.880553i	0.897862	−	0.440276i	$-0.145119\pi$
$308$	1.24259e8	−	2.15223e8i	0.242327	−	0.419722i
$309$	−2.78371e8	−	4.82153e8i	−0.536747	−	0.929673i
$310$	6.39386e7	−	3.69150e7i	0.121898	−	0.0703779i
$311$	6.49304e8			1.22401			0.612007	−	0.790852i	$-0.290362\pi$
$311$	6.49304e8			1.22401			0.612007	+	0.790852i	$0.290362\pi$
$312$	−1.07596e8	−	1.39176e8i	−0.200566	−	0.259432i
$313$	−1.77269e8			−0.326760			−0.163380	−	0.986563i	$-0.552240\pi$
$313$	−1.77269e8			−0.326760			−0.163380	+	0.986563i	$0.552240\pi$
$314$	−8.20083e8	+	4.73475e8i	−1.49487	+	0.863065i
$315$	1.42257e6	+	2.46397e6i	0.00256441	+	0.00444168i
$316$	−2.98533e8	+	5.17074e8i	−0.532215	+	0.921823i
$317$		−	1.42893e7i		−	0.0251945i	−0.999921	−	0.0125972i	$-0.995990\pi$
$317$		−	1.42893e7i		−	0.0251945i	0.999921	−	0.0125972i	$-0.00400993\pi$
$318$	1.00393e9	+	5.79620e8i	1.75069	+	1.01076i
$319$	4.91283e8	+	2.83642e8i	0.847353	+	0.489220i
$320$		−	2.25080e7i		−	0.0383983i
$321$	−4.57543e8	+	7.92487e8i	−0.772083	+	1.33729i
$322$	−8.32786e7	−	1.44243e8i	−0.139007	−	0.240768i
$323$	4.49197e8	−	2.59344e8i	0.741699	−	0.428220i
$324$	3.73460e8			0.610009
$325$	−8.22634e7	−	6.07837e8i	−0.132928	−	0.982190i
$326$	8.33735e8			1.33280
$327$	−3.43437e8	+	1.98284e8i	−0.543163	+	0.313595i
$328$	6.42392e7	+	1.11266e8i	0.100518	+	0.174102i
$329$	−1.76750e8	+	3.06139e8i	−0.273636	+	0.473951i
$330$		−	1.31225e8i		−	0.201011i
$331$	5.49042e8	+	3.16990e8i	0.832162	+	0.480449i	0.854592	−	0.519299i	$-0.173807\pi$
$331$	5.49042e8	+	3.16990e8i	0.832162	+	0.480449i	−0.0224303	+	0.999748i	$0.507140\pi$
$332$	−5.07943e8	−	2.93261e8i	−0.761784	−	0.439816i
$333$			6.78479e7i			0.100689i
$334$	1.54391e8	−	2.67413e8i	0.226730	−	0.392708i
$335$	5.33372e7	+	9.23828e7i	0.0775128	+	0.134256i
$336$	−2.51997e8	+	1.45491e8i	−0.362417	+	0.209241i
$337$	1.10196e9			1.56842			0.784210	−	0.620495i	$-0.213068\pi$
$337$	1.10196e9			1.56842			0.784210	+	0.620495i	$0.213068\pi$
$338$	−6.55566e8	+	6.65131e8i	−0.923439	+	0.936911i
$339$	−5.03190e8			−0.701509
$340$	5.77534e7	−	3.33439e7i	0.0796895	−	0.0460088i
$341$	−7.30658e8	−	1.26554e9i	−0.997870	−	1.72836i
$342$	−4.48943e7	+	7.77591e7i	−0.0606875	+	0.105114i
$343$		−	4.03536e7i		−	0.0539949i
$344$	−1.09368e8	−	6.31436e7i	−0.144856	−	0.0836324i
$345$	−3.21526e7	−	1.85633e7i	−0.0421550	−	0.0243382i
$346$			2.45067e8i			0.318067i
$347$	5.09787e8	−	8.82976e8i	0.654991	−	1.13448i	−0.326905	−	0.945057i	$-0.606006\pi$
$347$	5.09787e8	−	8.82976e8i	0.654991	−	1.13448i	0.981896	−	0.189420i	$-0.0606608\pi$
$348$	1.48091e8	+	2.56501e8i	0.188365	+	0.326258i
$349$	−7.48080e7	+	4.31904e7i	−0.0942018	+	0.0543874i	−0.546361	−	0.837550i	$-0.683987\pi$
$349$	−7.48080e7	+	4.31904e7i	−0.0942018	+	0.0543874i	0.452159	+	0.891937i	$0.350654\pi$
$350$	−3.95291e8			−0.492810
$351$	1.15011e8	+	8.49809e8i	0.141960	+	1.04893i
$352$	−1.75222e9			−2.14136
$353$	1.33352e8	−	7.69906e7i	0.161357	−	0.0931594i	−0.417147	−	0.908839i	$-0.636970\pi$
$353$	1.33352e8	−	7.69906e7i	0.161357	−	0.0931594i	0.578504	+	0.815680i	$0.303637\pi$
$354$	2.75745e8	+	4.77605e8i	0.330367	+	0.572213i
$355$	−2.08020e7	+	3.60301e7i	−0.0246777	+	0.0427431i
$356$			9.57656e8i			1.12495i
$357$	−3.48438e8	−	2.01171e8i	−0.405310	−	0.234006i
$358$	1.13997e9	+	6.58162e8i	1.31312	+	0.758127i
$359$		−	7.02209e8i		−	0.801007i	−0.916295	−	0.400503i	$-0.868835\pi$
$359$		−	7.02209e8i		−	0.801007i	0.916295	−	0.400503i	$-0.131165\pi$
$360$	2.12900e6	−	3.68754e6i	0.00240501	−	0.00416560i
$361$	−2.63956e8	−	4.57186e8i	−0.295296	−	0.511467i
$362$	1.11916e9	−	6.46147e8i	1.23997	−	0.715898i
$363$	−1.75428e9			−1.92498
$364$	1.55396e8	+	2.01005e8i	0.168883	+	0.218450i
$365$	6.30835e7			0.0679033
$366$	−1.44282e9	+	8.33011e8i	−1.53825	+	0.888110i
$367$	2.59694e7	+	4.49803e7i	0.0274240	+	0.0474998i	0.879412	−	0.476062i	$-0.157936\pi$
$367$	2.59694e7	+	4.49803e7i	0.0274240	+	0.0474998i	−0.851988	+	0.523562i	$0.824603\pi$
$368$	−3.19892e8	+	5.54068e8i	−0.334607	+	0.579557i
$369$		−	7.89301e7i		−	0.0817806i
$370$	7.29384e7	+	4.21110e7i	0.0748600	+	0.0432205i
$371$	5.34800e8	+	3.08767e8i	0.543729	+	0.313922i
$372$		−	7.62959e8i		−	0.768424i
$373$	−7.33246e7	+	1.27002e8i	−0.0731592	+	0.126715i	−0.900284	−	0.435302i	$-0.856641\pi$
$373$	−7.33246e7	+	1.27002e8i	−0.0731592	+	0.126715i	0.827125	+	0.562018i	$0.189975\pi$
$374$	−1.56338e9	−	2.70786e9i	−1.54531	−	2.67655i
$375$	−1.53298e8	+	8.85065e7i	−0.150116	+	0.0866694i
$376$	5.29043e8			0.513255
$377$	−4.58827e8	+	3.54717e8i	−0.441016	+	0.340948i
$378$	5.52651e8			0.526296
$379$	−1.07403e9	+	6.20094e8i	−1.01340	+	0.585087i	−0.912186	−	0.409777i	$-0.865606\pi$
$379$	−1.07403e9	+	6.20094e8i	−1.01340	+	0.585087i	−0.101215	+	0.994865i	$0.532273\pi$
$380$	2.35257e7	+	4.07478e7i	0.0219938	+	0.0380944i
$381$	4.21911e7	−	7.30772e7i	0.0390826	−	0.0676931i
$382$			1.84697e9i			1.69527i
$383$	−1.34272e9	−	7.75221e8i	−1.22121	−	0.705066i	−0.256034	−	0.966668i	$-0.582416\pi$
$383$	−1.34272e9	−	7.75221e8i	−1.22121	−	0.705066i	−0.965176	+	0.261602i	$0.915749\pi$
$384$	6.07334e8	+	3.50645e8i	0.547354	+	0.316015i
$385$		−	6.99045e7i		−	0.0624299i
$386$	1.36565e9	−	2.36538e9i	1.20861	−	2.09337i
$387$	3.87919e7	+	6.71896e7i	0.0340215	+	0.0589269i
$388$	1.05386e9	−	6.08449e8i	0.915954	−	0.528826i
$389$	8.50737e8			0.732777			0.366388	−	0.930462i	$-0.380594\pi$
$389$	8.50737e8			0.732777			0.366388	+	0.930462i	$0.380594\pi$
$390$	1.24129e8	+	5.08902e7i	0.105961	+	0.0434418i
$391$	−8.84632e8			−0.748418
$392$	−5.23016e7	+	3.01963e7i	−0.0438545	+	0.0253194i
$393$	−6.24355e8	−	1.08141e9i	−0.518869	−	0.898708i
$394$	−1.48873e9	+	2.57856e9i	−1.22625	+	2.12393i
$395$			1.67945e8i			0.137113i
$396$	1.97881e8	+	1.14247e8i	0.160129	+	0.0924507i
$397$	8.28461e8	+	4.78312e8i	0.664516	+	0.383658i	0.793995	−	0.607924i	$-0.207997\pi$
$397$	8.28461e8	+	4.78312e8i	0.664516	+	0.383658i	−0.129480	+	0.991582i	$0.541331\pi$
$398$			3.17021e8i			0.252056i
$399$	1.41936e8	−	2.45840e8i	0.111863	−	0.193752i
$400$	7.59201e8	+	1.31497e9i	0.593126	+	1.02732i
$401$	−4.93553e8	+	2.84953e8i	−0.382233	+	0.220682i	−0.678789	−	0.734333i	$-0.737495\pi$
$401$	−4.93553e8	+	2.84953e8i	−0.382233	+	0.220682i	0.296556	+	0.955015i	$0.404162\pi$
$402$	2.61136e9			2.00482
$403$	1.48046e9	−	2.00362e8i	1.12675	−	0.152492i
$404$	−1.73865e9			−1.31183
$405$	9.09747e7	−	5.25243e7i	0.0680500	−	0.0392887i
$406$	1.86875e8	+	3.23678e8i	0.138583	+	0.240033i
$407$	8.33503e8	−	1.44367e9i	0.612811	−	1.06142i
$408$			6.02139e8i			0.438921i
$409$	−2.37535e7	−	1.37141e7i	−0.0171671	−	0.00991141i	0.491392	−	0.870939i	$-0.336488\pi$
$409$	−2.37535e7	−	1.37141e7i	−0.0171671	−	0.00991141i	−0.508559	+	0.861027i	$0.669822\pi$
$410$	−8.48521e7	−	4.89894e7i	−0.0608022	−	0.0351041i
$411$		−	1.65351e8i		−	0.117479i
$412$	6.01685e8	−	1.04215e9i	0.423866	−	0.734157i
$413$	1.46891e8	+	2.54423e8i	0.102605	+	0.177718i
$414$	1.32620e8	−	7.65681e7i	0.0918559	−	0.0530330i
$415$	−1.64980e8			−0.113308
$416$	6.79525e8	−	1.65747e9i	0.462784	−	1.12880i
$417$	5.34765e8			0.361149
$418$	1.91052e9	−	1.10304e9i	1.27949	−	0.738711i
$419$	−8.55947e8	−	1.48254e9i	−0.568457	−	0.984597i	−0.996719	−	0.0809419i	$-0.974207\pi$
$419$	−8.55947e8	−	1.48254e9i	−0.568457	−	0.984597i	0.428262	−	0.903655i	$-0.359126\pi$
$420$	1.82487e7	−	3.16077e7i	0.0120188	−	0.0208171i
$421$			2.44205e9i			1.59503i	0.603302	+	0.797513i	$0.293851\pi$
$421$			2.44205e9i			1.59503i	−0.603302	+	0.797513i	$0.706149\pi$
$422$	1.66453e9	+	9.61015e8i	1.07819	+	0.622496i
$423$	−2.81471e8	−	1.62507e8i	−0.180818	−	0.104395i
$424$		−	9.24193e8i		−	0.588819i
$425$	−1.04975e9	+	1.81822e9i	−0.663324	+	1.14891i
$426$	5.09226e8	+	8.82005e8i	0.319137	+	0.552761i
$427$	−7.68596e8	+	4.43749e8i	−0.477750	+	0.275829i
$428$	−1.97791e9			−1.21942
$429$	1.00727e9	−	2.45689e9i	0.615950	−	1.50240i
$430$	9.63076e7			0.0584146
$431$	−1.86079e9	+	1.07433e9i	−1.11950	+	0.646346i	−0.941274	−	0.337642i	$-0.890371\pi$
$431$	−1.86079e9	+	1.07433e9i	−1.11950	+	0.646346i	−0.178230	+	0.983989i	$0.557037\pi$
$432$	−1.06143e9	−	1.83845e9i	−0.633429	−	1.09713i
$433$	−9.92920e8	+	1.71979e9i	−0.587769	+	1.01805i	0.406755	+	0.913537i	$0.366660\pi$
$433$	−9.92920e8	+	1.71979e9i	−0.587769	+	1.01805i	−0.994524	+	0.104508i	$0.966673\pi$
$434$		−	9.62776e8i		−	0.565342i
$435$	7.21498e7	+	4.16557e7i	0.0420264	+	0.0242640i
$436$	−7.42321e8	−	4.28579e8i	−0.428933	−	0.247644i
$437$		−	6.24150e8i		−	0.357770i
$438$	7.72132e8	−	1.33737e9i	0.439068	−	0.760488i
$439$	−9.09072e8	−	1.57456e9i	−0.512829	−	0.888246i	−0.999889	−	0.0148774i	$-0.995264\pi$
$439$	−9.09072e8	−	1.57456e9i	−0.512829	−	0.888246i	0.487060	−	0.873368i	$-0.338069\pi$
$440$	−9.06019e7	+	5.23091e7i	−0.0507053	+	0.0292747i
$441$	3.71019e7			0.0205997
$442$	3.16772e9	−	4.28712e8i	1.74489	−	0.236150i
$443$	−1.67763e9			−0.916816			−0.458408	−	0.888742i	$-0.651580\pi$
$443$	−1.67763e9			−0.916816			−0.458408	+	0.888742i	$0.651580\pi$
$444$	7.53746e8	−	4.35175e8i	0.408681	−	0.235952i
$445$	1.34687e8	+	2.33285e8i	0.0724545	+	0.125495i
$446$	1.40499e8	−	2.43351e8i	0.0749895	−	0.129886i
$447$		−	4.99642e8i		−	0.264596i
$448$	−2.54191e8	−	1.46757e8i	−0.133563	−	0.0771128i
$449$	−1.82548e9	−	1.05394e9i	−0.951733	−	0.549483i	−0.0581138	−	0.998310i	$-0.518509\pi$
$449$	−1.82548e9	−	1.05394e9i	−0.951733	−	0.549483i	−0.893619	+	0.448827i	$0.851842\pi$
$450$		−	3.63439e8i		−	0.188013i
$451$	−9.69647e8	+	1.67948e9i	−0.497732	+	0.862097i
$452$	−5.43810e8	−	9.41906e8i	−0.276989	−	0.479759i
$453$	2.22934e9	−	1.28711e9i	1.12676	−	0.650536i
$454$	1.64008e9			0.822563
$455$	6.61242e7	+	2.71095e7i	0.0329095	+	0.0134921i
$456$	−4.24838e8			−0.209820
$457$	1.00084e9	−	5.77835e8i	0.490521	−	0.283203i	−0.234269	−	0.972172i	$-0.575270\pi$
$457$	1.00084e9	−	5.77835e8i	0.490521	−	0.283203i	0.724791	+	0.688969i	$0.241936\pi$
$458$	−1.90642e9	−	3.30202e9i	−0.927235	−	1.60602i
$459$	1.46764e9	−	2.54203e9i	0.708397	−	1.22698i
$460$		−	8.02472e7i		−	0.0384395i
$461$	−4.64341e7	−	2.68087e7i	−0.0220741	−	0.0127445i	0.488922	−	0.872327i	$-0.337390\pi$
$461$	−4.64341e7	−	2.68087e7i	−0.0220741	−	0.0127445i	−0.510996	+	0.859583i	$0.670723\pi$
$462$	−1.48198e9	−	8.55619e8i	−0.699189	−	0.403677i
$463$			1.55744e9i			0.729253i	0.931154	+	0.364627i	$0.118803\pi$
$463$			1.55744e9i			0.729253i	−0.931154	+	0.364627i	$0.881197\pi$
$464$	7.17830e8	−	1.24332e9i	0.333587	−	0.577789i
$465$	−1.07304e8	−	1.85857e8i	−0.0494917	−	0.0857221i
$466$	5.91918e8	−	3.41744e8i	0.270964	−	0.156441i
$467$	−2.06111e9			−0.936468			−0.468234	−	0.883604i	$-0.655110\pi$
$467$	−2.06111e9			−0.936468			−0.468234	+	0.883604i	$0.655110\pi$
$468$	−1.84808e8	+	1.42874e8i	−0.0833414	+	0.0644309i
$469$	1.39108e9			0.622656
$470$	−3.49400e8	+	2.01726e8i	−0.155232	+	0.0896230i
$471$	1.37630e9	+	2.38382e9i	0.606930	+	1.05123i
$472$	2.19835e8	−	3.80766e8i	0.0962278	−	0.166671i
$473$		−	1.90622e9i		−	0.828244i
$474$	3.56044e9	+	2.05562e9i	1.53561	+	0.886583i
$475$	−1.28284e9	−	7.40650e8i	−0.549220	−	0.317092i
$476$		−	8.69640e8i		−	0.369586i
$477$	−2.83887e8	+	4.91706e8i	−0.119765	+	0.207439i
$478$	4.11506e8	+	7.12750e8i	0.172337	+	0.298497i
$479$	−2.08914e9	+	1.20617e9i	−0.868547	+	0.501456i	−0.866865	−	0.498543i	$-0.833869\pi$
$479$	−2.08914e9	+	1.20617e9i	−0.868547	+	0.501456i	−0.00168168	+	0.999999i	$0.500535\pi$
$480$	−2.57331e8			−0.106206
$481$	1.04236e9	+	1.34830e9i	0.427081	+	0.552430i
$482$	2.13961e7			0.00870303
$483$	−4.19284e8	+	2.42074e8i	−0.169314	+	0.0977537i
$484$	−1.89589e9	−	3.28378e9i	−0.760073	−	1.31648i
$485$	1.71147e8	−	2.96436e8i	0.0681199	−	0.117987i
$486$			9.52202e8i			0.376272i
$487$	1.52483e9	+	8.80359e8i	0.598231	+	0.345389i	0.768345	−	0.640035i	$-0.221080\pi$
$487$	1.52483e9	+	8.80359e8i	0.598231	+	0.345389i	−0.170114	+	0.985424i	$0.554414\pi$
$488$	1.15027e9	+	6.64109e8i	0.448055	+	0.258684i
$489$		−	2.42350e9i		−	0.937264i
$490$	2.30280e7	−	3.98856e7i	0.00884239	−	0.0153155i
$491$	1.88643e9	+	3.26739e9i	0.719209	+	1.24571i	0.961314	+	0.275456i	$0.0888290\pi$
$491$	1.88643e9	+	3.26739e9i	0.719209	+	1.24571i	−0.242105	+	0.970250i	$0.577838\pi$
$492$	−8.76862e8	+	5.06257e8i	−0.331935	+	0.191643i
$493$	1.98510e9			0.746135
$494$	3.02477e8	+	2.23498e9i	0.112888	+	0.834120i
$495$	6.42716e7			0.0238178
$496$	−3.20277e9	+	1.84912e9i	−1.17853	+	0.680423i
$497$	2.71267e8	+	4.69849e8i	0.0991174	+	0.171676i
$498$	−2.01933e9	+	3.49757e9i	−0.732662	+	1.26901i
$499$		−	6.82719e8i		−	0.245975i	−0.992408	−	0.122987i	$-0.960753\pi$
$499$		−	6.82719e8i		−	0.245975i	0.992408	−	0.122987i	$-0.0392474\pi$
$500$	−3.31345e8	−	1.91302e8i	−0.118546	−	0.0684423i
$501$	−7.77316e8	−	4.48783e8i	−0.276163	−	0.159443i
$502$			4.31351e9i			1.52184i
$503$	4.51733e8	−	7.82425e8i	0.158268	−	0.274129i	−0.775976	−	0.630762i	$-0.782742\pi$
$503$	4.51733e8	−	7.82425e8i	0.158268	−	0.274129i	0.934244	+	0.356634i	$0.116076\pi$
$504$	−2.77632e7	−	4.80872e7i	−0.00965966	−	0.0167310i
$505$	−4.23534e8	+	2.44527e8i	−0.146342	+	0.0844905i
$506$	−3.76252e9			−1.29108
$507$	1.93340e9	+	1.90560e9i	0.658861	+	0.649387i
$508$	1.82388e8			0.0617266
$509$	−7.86769e8	+	4.54241e8i	−0.264445	+	0.152677i	−0.626360	−	0.779534i	$-0.715456\pi$
$509$	−7.86769e8	+	4.54241e8i	−0.264445	+	0.152677i	0.361916	+	0.932211i	$0.382123\pi$
$510$	−2.29598e8	−	3.97676e8i	−0.0766431	−	0.132750i
$511$	4.11319e8	−	7.12425e8i	0.136366	−	0.236192i
$512$			3.14600e9i			1.03589i
$513$	1.79353e9	+	1.03549e9i	0.586539	+	0.338639i
$514$	−1.82558e9	−	1.05400e9i	−0.592967	−	0.342349i
$515$		−	3.38489e8i		−	0.109199i
$516$	4.97622e8	−	8.61907e8i	0.159450	−	0.276176i
$517$	3.99277e9	+	6.91567e9i	1.27074	+	2.20099i
$518$	9.51149e8	−	5.49146e8i	0.300673	−	0.173594i
$519$	7.12360e8			0.223673
$520$	−1.43442e7	−	1.05988e8i	−0.00447369	−	0.0330557i
$521$	3.04175e8			0.0942305			0.0471153	−	0.998889i	$-0.484997\pi$
$521$	3.04175e8			0.0942305			0.0471153	+	0.998889i	$0.484997\pi$
$522$	−2.97596e8	+	1.71817e8i	−0.0915757	+	0.0528713i
$523$	1.17947e9	+	2.04291e9i	0.360523	+	0.624444i	0.988047	−	0.154153i	$-0.0492649\pi$
$523$	1.17947e9	+	2.04291e9i	0.360523	+	0.624444i	−0.627524	+	0.778597i	$0.715932\pi$
$524$	1.34951e9	−	2.33742e9i	0.409748	−	0.709704i
$525$			1.14903e9i			0.346557i
$526$	−4.03657e9	−	2.33051e9i	−1.20938	−	0.698235i
$527$	−4.42849e9	−	2.55679e9i	−1.31801	−	0.760952i
$528$			6.57325e9i			1.94340i
$529$	1.17016e9	−	2.02678e9i	0.343678	−	0.595267i
$530$	3.52398e8	+	6.10372e8i	0.102818	+	0.178086i
$531$	−2.33922e8	+	1.35055e8i	−0.0678015	+	0.0391452i
$532$	6.13572e8			0.176675
$533$	−1.21262e9	−	1.56853e9i	−0.346880	−	0.448690i
$534$	6.59419e9			1.87399
$535$	−4.81818e8	+	2.78178e8i	−0.136033	+	0.0785387i
$536$	−1.04094e9	−	1.80296e9i	−0.291977	−	0.505719i
$537$	1.91314e9	−	3.31366e9i	0.533136	−	0.923418i
$538$		−	3.00235e8i		−	0.0831234i
$539$	−7.89456e8	−	4.55793e8i	−0.217154	−	0.125374i
$540$	2.30594e8	+	1.33134e8i	0.0630189	+	0.0363840i
$541$			4.25954e9i			1.15657i	0.815835	+	0.578285i	$0.196278\pi$
$541$			4.25954e9i			1.15657i	−0.815835	+	0.578285i	$0.803722\pi$
$542$	−3.23689e9	+	5.60645e9i	−0.873233	+	1.51248i
$543$	−1.87822e9	−	3.25317e9i	−0.503439	−	0.871981i
$544$	−5.31007e9	+	3.06577e9i	−1.41418	+	0.816476i
$545$	−2.41105e8			−0.0637998
$546$	1.38407e9	−	1.07002e9i	0.363902	−	0.281331i
$547$	1.83247e8			0.0478719			0.0239360	−	0.999713i	$-0.492380\pi$
$547$	1.83247e8			0.0478719			0.0239360	+	0.999713i	$0.492380\pi$
$548$	3.09515e8	−	1.78699e8i	0.0803434	−	0.0463863i
$549$	−4.07992e8	−	7.06663e8i	−0.105232	−	0.182268i
$550$	−4.46480e9	+	7.73327e9i	−1.14428	+	1.98195i
$551$			1.40058e9i			0.356679i
$552$	6.27496e8	+	3.62285e8i	0.158790	+	0.0916776i
$553$	1.89667e9	+	1.09504e9i	0.476928	+	0.275355i
$554$		−	2.24748e9i		−	0.561579i
$555$	1.22408e8	−	2.12017e8i	0.0303938	−	0.0526436i
$556$	5.77932e8	+	1.00101e9i	0.142599	+	0.246988i
$557$	−3.88055e9	+	2.24044e9i	−0.951481	+	0.549338i	−0.893541	−	0.448982i	$-0.851787\pi$
$557$	−3.88055e9	+	2.24044e9i	−0.951481	+	0.549338i	−0.0579400	+	0.998320i	$0.518453\pi$
$558$	8.85196e8			0.215685
$559$	1.80313e9	+	7.39245e8i	0.436603	+	0.178998i
$560$	−1.76911e8			−0.0425694
$561$	−7.87120e9	+	4.54444e9i	−1.88222	+	1.08670i
$562$	−2.85576e9	−	4.94632e9i	−0.678647	−	1.17545i
$563$	−5.01186e8	+	8.68080e8i	−0.118364	+	0.205013i	−0.919120	−	0.393979i	$-0.871098\pi$
$563$	−5.01186e8	+	8.68080e8i	−0.118364	+	0.205013i	0.800755	+	0.598991i	$0.204432\pi$
$564$			4.16928e9i			0.978553i
$565$	−2.64944e8	−	1.52965e8i	−0.0617993	−	0.0356799i
$566$	1.50063e9	+	8.66390e8i	0.347870	+	0.200843i
$567$		−	1.36988e9i		−	0.315604i
$568$	4.05975e8	−	7.03169e8i	0.0929566	−	0.161006i
$569$	3.80497e9	+	6.59041e9i	0.865882	+	1.49975i	0.866169	+	0.499751i	$0.166575\pi$
$569$	3.80497e9	+	6.59041e9i	0.865882	+	1.49975i	−0.000287396		1.00000i	$0.500091\pi$
$570$	2.80579e8	−	1.61992e8i	0.0634590	−	0.0366381i
$571$	−4.95959e9			−1.11486			−0.557428	−	0.830225i	$-0.688212\pi$
$571$	−4.95959e9			−1.11486			−0.557428	+	0.830225i	$0.688212\pi$
$572$	5.68755e9	−	7.69741e8i	1.27069	−	0.171972i
$573$	5.36877e9			1.19216
$574$	−1.10651e9	+	6.38844e8i	−0.244210	+	0.140995i
$575$	1.26319e9	+	2.18792e9i	0.277097	+	0.479947i
$576$	1.34932e8	−	2.33708e8i	0.0294195	−	0.0509561i
$577$			3.08698e9i			0.668988i	0.942398	+	0.334494i	$0.108565\pi$
$577$			3.08698e9i			0.668988i	−0.942398	+	0.334494i	$0.891435\pi$
$578$	−4.18665e9	−	2.41716e9i	−0.901818	−	0.520665i
$579$	−6.87568e9	−	3.96967e9i	−1.47211	−	0.849924i
$580$			1.80073e8i			0.0383222i
$581$	−1.07571e9	+	1.86318e9i	−0.227550	+	0.394128i
$582$	−4.18963e9	−	7.25665e9i	−0.880938	−	1.52583i
$583$	1.20811e10	−	6.97502e9i	2.52503	−	1.45783i
$584$	−1.23115e9			−0.255779
$585$	−2.49250e7	+	6.07960e7i	−0.00514742	+	0.0125554i
$586$	1.25155e9			0.256926
$587$	1.05973e8	−	6.11836e7i	0.0216253	−	0.0124854i	−0.489148	−	0.872201i	$-0.662692\pi$
$587$	1.05973e8	−	6.11836e7i	0.0216253	−	0.0124854i	0.510774	+	0.859715i	$0.329359\pi$
$588$	−2.37971e8	−	4.12179e8i	−0.0482730	−	0.0836113i
$589$	1.80394e9	−	3.12451e9i	0.363762	−	0.630055i
$590$			3.35296e8i			0.0672120i
$591$	7.49534e9	+	4.32744e9i	1.49360	+	0.862332i
$592$	−3.65358e9	−	2.10939e9i	−0.723756	−	0.417861i
$593$		−	1.93483e9i		−	0.381023i	−0.981685	−	0.190512i	$-0.938985\pi$
$593$		−	1.93483e9i		−	0.381023i	0.981685	−	0.190512i	$-0.0610147\pi$
$594$	6.24218e9	−	1.08118e10i	1.22204	−	2.11663i
$595$	−1.22308e8	−	2.11844e8i	−0.0238038	−	0.0412294i
$596$	9.35265e8	−	5.39975e8i	0.180956	−	0.104475i
$597$	9.21516e8			0.177253
$598$	1.45913e9	−	3.55905e9i	0.279023	−	0.680581i
$599$	5.88705e8			0.111919			0.0559595	−	0.998433i	$-0.482178\pi$
$599$	5.88705e8			0.111919			0.0559595	+	0.998433i	$0.482178\pi$
$600$	1.48924e9	−	8.59813e8i	0.281472	−	0.162508i
$601$	−3.68270e9	−	6.37862e9i	−0.691999	−	1.19858i	−0.971182	−	0.238340i	$-0.923397\pi$
$601$	−3.68270e9	−	6.37862e9i	−0.691999	−	1.19858i	0.279183	−	0.960238i	$-0.409937\pi$
$602$	6.27948e8	−	1.08764e9i	0.117310	−	0.203187i
$603$			1.27899e9i			0.237551i
$604$	4.81859e9	+	2.78201e9i	0.889796	+	0.513724i
$605$	−9.23678e8	−	5.33286e8i	−0.169581	−	0.0979075i
$606$			1.19719e10i			2.18529i
$607$	4.97200e9	−	8.61175e9i	0.902340	−	1.56290i	0.0778924	−	0.996962i	$-0.475181\pi$
$607$	4.97200e9	−	8.61175e9i	0.902340	−	1.56290i	0.824448	−	0.565938i	$-0.191486\pi$
$608$	−2.16305e9	−	3.74651e9i	−0.390304	−	0.676027i
$609$	9.40866e8	−	5.43209e8i	0.168798	−	0.0974555i
$610$	−1.01291e9			−0.180683
$611$	−8.09012e9	+	1.09490e9i	−1.43486	+	0.194191i
$612$	7.99565e8			0.141002
$613$	2.51713e9	−	1.45327e9i	0.441361	−	0.254820i	−0.262814	−	0.964847i	$-0.584650\pi$
$613$	2.51713e9	−	1.45327e9i	0.441361	−	0.254820i	0.704175	+	0.710027i	$0.251317\pi$
$614$	−3.32205e9	−	5.75395e9i	−0.579184	−	1.00318i
$615$	−1.42402e8	+	2.46648e8i	−0.0246862	+	0.0427577i
$616$			1.36427e9i			0.235162i
$617$	1.56675e9	+	9.04562e8i	0.268535	+	0.155039i	0.628222	−	0.778034i	$-0.283783\pi$
$617$	1.56675e9	+	9.04562e8i	0.268535	+	0.155039i	−0.359687	+	0.933073i	$0.617116\pi$
$618$	−7.17598e9	−	4.14305e9i	−1.22299	−	0.706091i
$619$			5.46906e9i			0.926820i	0.886144	+	0.463410i	$0.153374\pi$
$619$			5.46906e9i			0.926820i	−0.886144	+	0.463410i	$0.846626\pi$
$620$	2.31933e8	−	4.01719e8i	0.0390833	−	0.0676942i
$621$	−1.76605e9	−	3.05890e9i	−0.295926	−	0.512559i
$622$	8.36902e9	−	4.83186e9i	1.39447	−	0.805096i
$623$	3.51276e9			0.582023
$624$	−6.21779e9	−	2.54915e9i	−1.02445	−	0.420001i
$625$	5.94185e9			0.973512
$626$	−2.28487e9	+	1.31917e9i	−0.372264	+	0.214926i
$627$	−3.20632e9	−	5.55350e9i	−0.519482	−	0.899768i
$628$	−2.97479e9	+	5.15249e9i	−0.479289	+	0.830154i
$629$		−	5.83334e9i		−	0.934631i
$630$	3.66717e7	+	2.11724e7i	0.00584304	+	0.00337348i
$631$	−7.69284e9	−	4.44146e9i	−1.21894	−	0.703758i	−0.254252	−	0.967138i	$-0.581829\pi$
$631$	−7.69284e9	−	4.44146e9i	−1.21894	−	0.703758i	−0.964692	+	0.263380i	$0.915163\pi$
$632$		−	3.27765e9i		−	0.516479i
$633$	2.79348e9	−	4.83844e9i	0.437756	−	0.758215i
$634$	−1.06336e8	−	1.84179e8i	−0.0165717	−	0.0287030i
$635$	4.44296e7	−	2.56514e7i	0.00688596	−	0.00397561i
$636$	7.28338e9			1.12262
$637$	7.37302e8	−	5.70005e8i	0.113021	−	0.0873757i
$638$	8.44301e9			1.28714
$639$	−4.31989e8	+	2.49409e8i	−0.0654967	+	0.0378145i
$640$	2.13186e8	+	3.69248e8i	0.0321461	+	0.0556786i
$641$	5.92890e9	−	1.02692e10i	0.889142	−	1.54004i	0.0482508	−	0.998835i	$-0.484635\pi$
$641$	5.92890e9	−	1.02692e10i	0.889142	−	1.54004i	0.840891	−	0.541204i	$-0.182031\pi$
$642$			1.36194e10i			2.03135i
$643$	6.62835e8	+	3.82688e8i	0.0983257	+	0.0567684i	0.548357	−	0.836245i	$-0.315254\pi$
$643$	6.62835e8	+	3.82688e8i	0.0983257	+	0.0567684i	−0.450031	+	0.893013i	$0.648587\pi$
$644$	−9.06261e8	−	5.23230e8i	−0.133707	−	0.0771955i
$645$		−	2.79947e8i		−	0.0410787i
$646$	3.85987e9	−	6.68548e9i	0.563324	−	0.975706i
$647$	−2.61361e9	−	4.52690e9i	−0.379381	−	0.657107i	0.611592	−	0.791174i	$-0.290530\pi$
$647$	−2.61361e9	−	4.52690e9i	−0.379381	−	0.657107i	−0.990972	+	0.134067i	$0.957196\pi$
$648$	−1.77548e9	+	1.02507e9i	−0.256332	+	0.147993i
$649$	6.63652e9			0.952981
$650$	−5.58359e9	−	7.22238e9i	−0.797475	−	1.03153i
$651$	−2.79859e9			−0.397563
$652$	4.53647e9	−	2.61913e9i	0.640990	−	0.370076i
$653$	−3.51332e9	−	6.08525e9i	−0.493766	−	0.855228i	0.506208	−	0.862412i	$-0.331047\pi$
$653$	−3.51332e9	−	6.08525e9i	−0.493766	−	0.855228i	−0.999974	+	0.00718305i	$0.997714\pi$
$654$	−2.95109e9	+	5.11144e9i	−0.412535	+	0.714531i
$655$		−	7.59193e8i		−	0.105562i
$656$	4.25035e9	+	2.45394e9i	0.587843	+	0.339391i
$657$	6.55018e8	+	3.78175e8i	0.0901103	+	0.0520252i
$658$			5.26120e9i			0.719936i
$659$	−2.97256e9	+	5.14863e9i	−0.404605	+	0.700797i	−0.994275	−	0.106847i	$-0.965924\pi$
$659$	−2.97256e9	+	5.14863e9i	−0.404605	+	0.700797i	0.589670	+	0.807644i	$0.299258\pi$
$660$	−4.12237e8	−	7.14016e8i	−0.0558140	−	0.0966728i
$661$	−1.25068e10	+	7.22079e9i	−1.68438	+	0.972478i	−0.725692	+	0.688020i	$0.758480\pi$
$661$	−1.25068e10	+	7.22079e9i	−1.68438	+	0.972478i	−0.958689	+	0.284458i	$0.908186\pi$
$662$	9.43564e9			1.26406
$663$	−1.24618e9	−	9.20791e9i	−0.166067	−	1.22705i
$664$	3.21977e9			0.426812
$665$	1.49466e8	−	8.62942e7i	0.0197091	−	0.0113790i
$666$	5.04897e8	+	8.74506e8i	0.0662281	+	0.114711i
$667$	1.19436e9	−	2.06869e9i	0.155846	−	0.269933i
$668$		−	1.94004e9i		−	0.251822i
$669$	−7.07373e8	−	4.08402e8i	−0.0913391	−	0.0527347i
$670$	1.37495e9	+	7.93828e8i	0.176614	+	0.101968i
$671$			2.00485e10i			2.56185i
$672$	−1.67786e9	+	2.90613e9i	−0.213286	+	0.369422i
$673$	6.35388e9	+	1.10052e10i	0.803501	+	1.39170i	0.917299	+	0.398200i	$0.130365\pi$
$673$	6.35388e9	+	1.10052e10i	0.803501	+	1.39170i	−0.113798	+	0.993504i	$0.536302\pi$
$674$	1.42034e10	−	8.20037e9i	1.78683	−	1.03163i
$675$	−8.38278e9			−1.04912
$676$	−1.47756e9	+	5.67850e9i	−0.183963	+	0.707001i
$677$	7.29817e9			0.903969			0.451985	−	0.892026i	$-0.350716\pi$
$677$	7.29817e9			0.903969			0.451985	+	0.892026i	$0.350716\pi$
$678$	−6.48573e9	+	3.74454e9i	−0.799199	+	0.461418i
$679$	−2.23184e9	−	3.86566e9i	−0.273601	−	0.473892i
$680$	−1.83045e8	+	3.17043e8i	−0.0223242	+	0.0386667i
$681$		−	4.76738e9i		−	0.578448i
$682$	−1.88352e10	−	1.08745e10i	−2.27366	−	1.31270i
$683$	1.09895e10	+	6.34480e9i	1.31979	+	0.761984i	0.983695	−	0.179843i	$-0.0575590\pi$
$683$	1.09895e10	+	6.34480e9i	1.31979	+	0.761984i	0.336099	+	0.941827i	$0.390892\pi$
$684$			5.64131e8i			0.0674037i
$685$	5.02652e7	−	8.70619e7i	0.00597517	−	0.0103493i
$686$	−3.00295e8	−	5.20127e8i	−0.0355152	−	0.0615141i
$687$	−9.59830e9	+	5.54158e9i	−1.12940	+	0.652057i
$688$	−4.82417e9			−0.564759
$689$	1.91270e9	+	1.41328e10i	0.222781	+	1.64611i
$690$	−5.52563e8			−0.0640339
$691$	−3.54747e9	+	2.04813e9i	−0.409021	+	0.236148i	−0.690369	−	0.723458i	$-0.742552\pi$
$691$	−3.54747e9	+	2.04813e9i	−0.409021	+	0.236148i	0.281348	+	0.959606i	$0.409218\pi$
$692$	7.69864e8	+	1.33344e9i	0.0883167	+	0.152969i
$693$	4.19065e8	−	7.25843e8i	0.0478317	−	0.0828469i
$694$		−	1.51745e10i		−	1.72328i
$695$	2.81568e8	+	1.62563e8i	0.0318154	+	0.0183686i
$696$	−1.40809e9	−	8.12960e8i	−0.158306	−	0.0913980i
$697$			6.78616e9i			0.759118i
$698$	−6.42811e8	+	1.11338e9i	−0.0715467	+	0.123923i
$699$	−9.93381e8	−	1.72059e9i	−0.110013	−	0.190549i
$700$	−2.15084e9	+	1.24179e9i	−0.237009	+	0.136837i
$701$	1.96440e9			0.215386			0.107693	−	0.994184i	$-0.465654\pi$
$701$	1.96440e9			0.215386			0.107693	+	0.994184i	$0.465654\pi$
$702$	7.80634e9	+	1.00975e10i	0.851663	+	1.10163i
$703$	4.11570e9			0.446787
$704$	−5.74216e9	+	3.31524e9i	−0.620256	+	0.358105i
$705$	5.86377e8	+	1.01563e9i	0.0630253	+	0.109163i
$706$	1.14587e9	−	1.98470e9i	0.122551	−	0.212265i
$707$			6.37750e9i			0.678707i
$708$	3.00074e9	+	1.73248e9i	0.317769	+	0.183464i
$709$	2.32405e9	+	1.34179e9i	0.244897	+	0.141391i	0.617425	−	0.786630i	$-0.288176\pi$
$709$	2.32405e9	+	1.34179e9i	0.244897	+	0.141391i	−0.372528	+	0.928021i	$0.621509\pi$
$710$			6.19200e8i			0.0649272i
$711$	−1.00680e9	+	1.74384e9i	−0.105051	+	0.181954i
$712$	−2.62857e9	−	4.55282e9i	−0.272923	−	0.472717i
$713$	−5.32891e9	+	3.07665e9i	−0.550586	+	0.317881i
$714$	−5.98813e9			−0.615669
$715$	1.27723e9	−	9.87419e8i	0.130676	−	0.101025i
$716$	8.27032e9			0.842028
$717$	2.07182e9	−	1.19617e9i	0.209911	−	0.121192i
$718$	−5.22556e9	−	9.05093e9i	−0.526862	−	0.912553i
$719$	−7.87713e9	+	1.36436e10i	−0.790345	+	1.36892i	0.135408	+	0.990790i	$0.456765\pi$
$719$	−7.87713e9	+	1.36436e10i	−0.790345	+	1.36892i	−0.925753	+	0.378128i	$0.876568\pi$
$720$		−	1.62656e8i		−	0.0162407i
$721$	−3.82268e9	−	2.20703e9i	−0.379835	−	0.219298i
$722$	−6.80439e9	−	3.92851e9i	−0.672835	−	0.388462i
$723$		−	6.21942e7i		−	0.00612020i
$724$	4.05967e9	−	7.03155e9i	0.397563	−	0.688599i
$725$	−2.83458e9	−	4.90964e9i	−0.276252	−	0.478483i
$726$	−2.26113e10	+	1.30547e10i	−2.19305	+	1.26616i
$727$	−4.78270e9			−0.461639			−0.230820	−	0.972997i	$-0.574141\pi$
$727$	−4.78270e9			−0.461639			−0.230820	+	0.972997i	$0.574141\pi$
$728$	−1.29049e9	−	5.29073e8i	−0.123964	−	0.0508225i
$729$	1.15023e10			1.09961
$730$	8.13097e8	−	4.69442e8i	0.0773593	−	0.0446634i
$731$	−3.33521e9	−	5.77675e9i	−0.315800	−	0.546982i
$732$	−5.23371e9	+	9.06506e9i	−0.493198	+	0.854244i
$733$			2.40096e6i			0.000225175i	1.00000		0.000112588i	$3.58377e-5\pi$
$733$			2.40096e6i			0.000225175i	−1.00000		0.000112588i	$0.999964\pi$
$734$	6.69451e8	+	3.86508e8i	0.0624860	+	0.0360763i
$735$	−1.15939e8	−	6.69377e7i	−0.0107702	−	0.00621820i
$736$			7.37824e9i			0.682151i
$737$	1.57122e10	−	2.72144e10i	1.44578	−	2.50416i
$738$	−5.87366e8	−	1.01735e9i	−0.0537912	−	0.0931692i
$739$	3.10167e9	−	1.79075e9i	0.282709	−	0.163222i	−0.351940	−	0.936022i	$-0.614478\pi$
$739$	3.10167e9	−	1.79075e9i	0.282709	−	0.163222i	0.634649	+	0.772800i	$0.281145\pi$
$740$	5.29157e8			0.0480036
$741$	6.49662e9	−	8.79239e8i	0.586575	−	0.0793859i
$742$	9.19087e9			0.825930
$743$	3.81002e9	−	2.19972e9i	0.340774	−	0.196746i	−0.319840	−	0.947471i	$-0.603629\pi$
$743$	3.81002e9	−	2.19972e9i	0.340774	−	0.196746i	0.660614	+	0.750725i	$0.270296\pi$
$744$	2.09417e9	+	3.62721e9i	0.186426	+	0.322899i
$745$	1.51887e8	−	2.63075e8i	0.0134578	−	0.0233095i
$746$			2.18261e9i			0.192482i
$747$	−1.71304e9	−	9.89026e8i	−0.150365	−	0.0868132i
$748$	−1.70132e10	−	9.82256e9i	−1.48638	−	0.858162i
$749$			7.25512e9i			0.630897i
$750$	−1.31726e9	+	2.28156e9i	−0.114014	+	0.197477i
$751$	−5.72465e9	−	9.91538e9i	−0.493184	−	0.854219i	0.506785	−	0.862072i	$-0.330834\pi$
$751$	−5.72465e9	−	9.91538e9i	−0.493184	−	0.854219i	−0.999969	+	0.00785289i	$0.997500\pi$
$752$	1.75019e10	−	1.01047e10i	1.50080	−	0.866486i
$753$	1.25385e10			1.07020
$754$	−3.27426e9	+	7.98644e9i	−0.278172	+	0.678506i
$755$	1.56508e9			0.132349
$756$	3.00705e9	−	1.73612e9i	0.253113	−	0.146135i
$757$	−4.01657e9	−	6.95691e9i	−0.336527	−	0.582882i	0.647250	−	0.762278i	$-0.275919\pi$
$757$	−4.01657e9	−	6.95691e9i	−0.336527	−	0.582882i	−0.983777	+	0.179396i	$0.942586\pi$
$758$	−9.22898e9	+	1.59851e10i	−0.769683	+	1.33313i
$759$			1.09369e10i			0.907919i
$760$	−2.23689e8	−	1.29147e8i	−0.0184840	−	0.0106718i
$761$	−1.37104e9	−	7.91569e8i	−0.112772	−	0.0651092i	0.442553	−	0.896742i	$-0.354073\pi$
$761$	−1.37104e9	−	7.91569e8i	−0.112772	−	0.0651092i	−0.555325	+	0.831633i	$0.687406\pi$
$762$		−	1.25588e9i		−	0.102826i
$763$	−1.57206e9	+	2.72289e9i	−0.128125	+	0.221919i
$764$	5.80215e9	+	1.00496e10i	0.470720	+	0.815310i
$765$	1.94774e8	−	1.12453e8i	0.0157295	−	0.00908144i
$766$	−2.30755e10			−1.85503
$767$	−2.57369e9	+	6.27764e9i	−0.205955	+	0.502357i
$768$	1.51761e10			1.20892
$769$	5.57295e7	−	3.21754e7i	0.00441919	−	0.00255142i	−0.497789	−	0.867298i	$-0.665855\pi$
$769$	5.57295e7	−	3.21754e7i	0.00441919	−	0.00255142i	0.502208	+	0.864747i	$0.332521\pi$
$770$	−5.20201e8	−	9.01014e8i	−0.0410633	−	0.0711237i
$771$	−3.06376e9	+	5.30660e9i	−0.240749	+	0.416990i
$772$		−	1.71605e10i		−	1.34236i
$773$	7.29186e9	+	4.20996e9i	0.567820	+	0.327831i	0.756278	−	0.654250i	$-0.227016\pi$
$773$	7.29186e9	+	4.20996e9i	0.567820	+	0.327831i	−0.188458	+	0.982081i	$0.560349\pi$
$774$	9.99996e8	+	5.77348e8i	0.0775184	+	0.0447553i
$775$			1.46037e10i			1.12695i
$776$	−3.34014e9	+	5.78529e9i	−0.256595	+	0.444436i
$777$	−1.59626e9	−	2.76480e9i	−0.122076	−	0.211441i
$778$	1.09653e10	−	6.33084e9i	0.834821	−	0.481984i
$779$	−4.78796e9			−0.362885
$780$	8.35273e8	−	1.13044e8i	0.0630227	−	0.00852936i
$781$	1.22558e10			0.920585
$782$	−1.14022e10	+	6.58308e9i	−0.852641	+	0.492272i
$783$	3.96299e9	+	6.86410e9i	0.295024	+	0.510996i
$784$	−1.15350e9	+	1.99792e9i	−0.0854893	+	0.148072i
$785$			1.67353e9i			0.123478i
$786$	−1.60949e10	−	9.29240e9i	−1.18225	−	0.682573i
$787$	4.50638e8	+	2.60176e8i	0.0329546	+	0.0190263i	0.516387	−	0.856355i	$-0.327277\pi$
$787$	4.50638e8	+	2.60176e8i	0.0329546	+	0.0190263i	−0.483432	+	0.875382i	$0.660610\pi$
$788$			1.87071e10i			1.36196i
$789$	−6.77433e9	+	1.17335e10i	−0.491018	+	0.850468i
$790$	1.24978e9	+	2.16468e9i	0.0901860	+	0.156207i
$791$	−3.45498e9	+	1.99474e9i	−0.248215	+	0.143307i
$792$	−1.25434e9			−0.0897172
$793$	−1.89644e10	−	7.77497e9i	−1.35046	−	0.553660i
$794$	1.42376e10			1.00941
$795$	1.77423e9	−	1.02435e9i	0.125235	−	0.0723043i
$796$	9.95904e8	+	1.72496e9i	0.0699877	+	0.121222i
$797$	−4.35316e9	+	7.53989e9i	−0.304579	+	0.527546i	−0.977168	−	0.212470i	$-0.931849\pi$
$797$	−4.35316e9	+	7.53989e9i	−0.304579	+	0.527546i	0.672588	+	0.740017i	$0.265182\pi$
$798$		−	4.22491e9i		−	0.294312i
$799$	2.42000e10	+	1.39719e10i	1.67842	+	0.969037i
$800$	1.51648e10	+	8.75542e9i	1.04718	+	0.604591i
$801$			3.22970e9i			0.222049i
$802$	−4.24101e9	+	7.34564e9i	−0.290308	+	0.502828i
$803$	−9.29166e9	−	1.60936e10i	−0.633270	−	1.09686i
$804$	1.42088e10	−	8.20343e9i	0.964184	−	0.556672i
$805$	−2.94353e8			−0.0198876
$806$	1.75909e10	−	1.35995e10i	1.18336	−	0.914848i
$807$	−8.72723e8			−0.0584546
$808$	8.26576e9	−	4.77224e9i	0.551243	−	0.318260i
$809$	−6.71996e9	−	1.16393e10i	−0.446218	−	0.772872i	0.551918	−	0.833898i	$-0.313896\pi$
$809$	−6.71996e9	−	1.16393e10i	−0.446218	−	0.772872i	−0.998136	+	0.0610264i	$0.980563\pi$
$810$	7.81729e8	−	1.35399e9i	0.0516843	−	0.0895198i
$811$		−	1.49475e9i		−	0.0984003i	−0.998789	−	0.0492001i	$-0.984333\pi$
$811$		−	1.49475e9i		−	0.0984003i	0.998789	−	0.0492001i	$-0.0156672\pi$
$812$	2.03363e9	+	1.17412e9i	0.133299	+	0.0769601i
$813$	1.62968e10	+	9.40898e9i	1.06362	+	0.614081i
$814$		−	2.48104e10i		−	1.61231i
$815$	7.36722e8	−	1.27604e9i	0.0476707	−	0.0825681i
$816$	1.15009e10	+	1.99201e10i	0.740995	+	1.28344i
$817$	4.07577e9	−	2.35315e9i	0.261477	−	0.150964i
$818$	−4.08219e8			−0.0260769
$819$	5.24075e8	+	6.77891e8i	0.0333349	+	0.0431187i
$820$	−6.15590e8			−0.0389891
$821$	−8.54243e9	+	4.93198e9i	−0.538742	+	0.311043i	−0.744569	−	0.667546i	$-0.767345\pi$
$821$	−8.54243e9	+	4.93198e9i	−0.538742	+	0.311043i	0.205827	+	0.978588i	$0.434012\pi$
$822$	−1.23048e9	−	2.13125e9i	−0.0772719	−	0.133839i
$823$	−4.38544e9	+	7.59581e9i	−0.274229	+	0.474979i	−0.969940	−	0.243342i	$-0.921756\pi$
$823$	−4.38544e9	+	7.59581e9i	−0.274229	+	0.474979i	0.695711	+	0.718322i	$0.255089\pi$
$824$			6.60601e9i			0.411334i
$825$	2.24790e10	+	1.29783e10i	1.39376	+	0.804690i
$826$	3.78662e9	+	2.18621e9i	0.233788	+	0.134977i
$827$			1.30834e9i			0.0804359i	0.999191	+	0.0402180i	$0.0128052\pi$
$827$			1.30834e9i			0.0804359i	−0.999191	+	0.0402180i	$0.987195\pi$
$828$	4.81069e8	−	8.33235e8i	0.0294511	−	0.0510107i
$829$	−1.00769e10	−	1.74537e10i	−0.614306	−	1.06401i	−0.990506	−	0.137471i	$-0.956103\pi$
$829$	−1.00769e10	−	1.74537e10i	−0.614306	−	1.06401i	0.376199	−	0.926539i	$-0.377231\pi$
$830$	−2.12646e9	+	1.22771e9i	−0.129087	+	0.0745287i
$831$	−6.53296e9			−0.394917
$832$	−9.09107e8	−	6.71732e9i	−0.0547247	−	0.404356i
$833$	−3.18991e9			−0.191214
$834$	6.89270e9	−	3.97950e9i	0.411442	−	0.237546i
$835$	−2.72852e8	−	4.72594e8i	−0.0162190	−	0.0280922i
$836$	6.93028e9	−	1.20036e10i	0.410232	−	0.710542i
$837$		−	2.04172e10i		−	1.20353i
$838$	−2.20650e10	−	1.27392e10i	−1.29524	−	0.747806i
$839$	−2.07398e10	−	1.19741e10i	−1.21238	−	0.699966i	−0.249101	−	0.968478i	$-0.580135\pi$
$839$	−2.07398e10	−	1.19741e10i	−1.21238	−	0.699966i	−0.963276	+	0.268511i	$0.913468\pi$
$840$			2.00356e8i			0.0116634i
$841$	5.94482e9	−	1.02967e10i	0.344630	−	0.596916i
$842$	1.81728e10	+	3.14762e10i	1.04913	+	1.81714i
$843$	−1.43779e10	+	8.30111e9i	−0.826609	+	0.477243i
$844$	1.20759e10			0.691386
$845$	4.38704e8	+	1.59109e9i	0.0250134	+	0.0907184i
$846$	−4.83726e9			−0.274665
$847$	−1.20452e10	+	6.95429e9i	−0.681116	+	0.393243i
$848$	−1.76521e10	−	3.05743e10i	−0.994056	−	1.72175i
$849$	2.51842e9	−	4.36204e9i	0.141238	−	0.244631i
$850$			3.12473e10i			1.74521i
$851$	−6.07899e9	−	3.50971e9i	−0.338126	−	0.195217i
$852$	5.54154e9	+	3.19941e9i	0.306967	+	0.177228i
$853$		−	3.35934e10i		−	1.85324i	−0.375997	−	0.926621i	$-0.622700\pi$
$853$		−	3.35934e10i		−	1.85324i	0.375997	−	0.926621i	$-0.377300\pi$
$854$	−6.60441e9	+	1.14392e10i	−0.362853	+	0.628481i
$855$	7.93407e7	+	1.37422e8i	0.00434125	+	0.00751926i
$856$	9.40324e9	−	5.42896e9i	0.512412	−	0.295841i
$857$	9.83481e9			0.533744			0.266872	−	0.963732i	$-0.414010\pi$
$857$	9.83481e9			0.533744			0.266872	+	0.963732i	$0.414010\pi$
$858$	−5.30025e9	−	3.91631e10i	−0.286478	−	2.11676i
$859$	−1.43054e10			−0.770060			−0.385030	−	0.922904i	$-0.625809\pi$
$859$	−1.43054e10			−0.770060			−0.385030	+	0.922904i	$0.625809\pi$
$860$	5.24023e8	−	3.02545e8i	0.0280935	−	0.0162198i
$861$	1.85699e9	+	3.21640e9i	0.0991513	+	0.171735i
$862$	−1.59894e10	+	2.76944e10i	−0.850269	+	1.47271i
$863$			3.03497e10i			1.60737i	0.595053	+	0.803687i	$0.297131\pi$
$863$			3.03497e10i			1.60737i	−0.595053	+	0.803687i	$0.702869\pi$
$864$	−2.12017e10	−	1.22408e10i	−1.11834	−	0.645673i
$865$	3.75077e8	+	2.16551e8i	0.0197044	+	0.0113764i
$866$			2.95556e10i			1.54642i
$867$	−7.02620e9	+	1.21697e10i	−0.366146	+	0.634183i
$868$	−3.02451e9	−	5.23860e9i	−0.156977	−	0.271892i
$869$	4.28456e10	−	2.47369e10i	2.21481	−	1.27872i
$870$	1.23994e9			0.0638386
$871$	1.96494e10	+	2.54165e10i	1.00759	+	1.30332i
$872$	4.70546e9			0.240322
$873$	3.55417e9	−	2.05200e9i	0.180796	−	0.104382i
$874$	−4.64468e9	−	8.04481e9i	−0.235324	−	0.407592i
$875$	−7.01711e8	+	1.21540e9i	−0.0354103	+	0.0613325i
$876$		−	9.70244e9i		−	0.487659i
$877$	1.65026e10	+	9.52777e9i	0.826139	+	0.476972i	0.852529	−	0.522680i	$-0.175068\pi$
$877$	1.65026e10	+	9.52777e9i	0.826139	+	0.476972i	−0.0263898	+	0.999652i	$0.508401\pi$
$878$	−2.34345e10	−	1.35299e10i	−1.16849	−	0.674627i
$879$		−	3.63802e9i		−	0.180677i
$880$	−1.99821e9	+	3.46100e9i	−0.0988442	+	0.171203i
$881$	1.36045e10	+	2.35636e10i	0.670295	+	1.16098i	0.977820	+	0.209445i	$0.0671657\pi$
$881$	1.36045e10	+	2.35636e10i	0.670295	+	1.16098i	−0.307525	+	0.951540i	$0.599501\pi$
$882$	4.78215e8	−	2.76098e8i	0.0234684	−	0.0135495i
$883$	−8.35378e9			−0.408339			−0.204169	−	0.978936i	$-0.565449\pi$
$883$	−8.35378e9			−0.408339			−0.204169	+	0.978936i	$0.565449\pi$
$884$	1.58892e10	−	1.22839e10i	0.773606	−	0.598071i
$885$	9.74639e8			0.0472653
$886$	−2.16233e10	+	1.24842e10i	−1.04449	+	0.603036i
$887$	3.71520e9	+	6.43491e9i	0.178751	+	0.309607i	0.941453	−	0.337144i	$-0.109461\pi$
$887$	3.71520e9	+	6.43491e9i	0.178751	+	0.309607i	−0.762702	+	0.646750i	$0.776128\pi$
$888$	−2.38894e9	+	4.13776e9i	−0.114488	+	0.198299i
$889$		−	6.69013e8i		−	0.0319358i
$890$	3.47202e9	+	2.00457e9i	0.165089	+	0.0953140i
$891$	−2.67996e10	−	1.54728e10i	−1.26928	−	0.732818i
$892$		−	1.76548e9i		−	0.0832885i
$893$	−9.85781e9	+	1.70742e10i	−0.463234	+	0.802345i
$894$	−3.71814e9	−	6.44000e9i	−0.174038	−	0.301443i
$895$	2.01465e9	−	1.16316e9i	0.0939330	−	0.0542322i
$896$	5.56007e9			0.258227
$897$	−1.03454e10	−	4.24140e9i	−0.478603	−	0.196217i
$898$	−3.13720e10			−1.44569
$899$	1.19580e10	−	6.90394e9i	0.548907	−	0.316911i
$900$	−1.14172e9	−	1.97752e9i	−0.0522050	−	0.0904217i
$901$	2.44077e10	−	4.22753e10i	1.11170	−	1.92553i
$902$			2.88629e10i			1.30953i
$903$	−3.16154e9	−	1.82532e9i	−0.142887	−	0.0824957i
$904$	5.17069e9	+	2.98530e9i	0.232787	+	0.134400i
$905$		−	2.28384e9i		−	0.102423i
$906$	1.91563e10	−	3.31796e10i	0.855780	−	1.48225i
$907$	−2.59942e9	−	4.50233e9i	−0.115678	−	0.200360i	0.802373	−	0.596824i	$-0.203571\pi$
$907$	−2.59942e9	−	4.50233e9i	−0.115678	−	0.200360i	−0.918051	+	0.396463i	$0.870237\pi$
$908$	8.92390e9	−	5.15222e9i	0.395598	−	0.228399i
$909$	−5.86360e9			−0.258935
$910$	1.05403e9	−	1.42650e8i	0.0463668	−	0.00627519i
$911$	6.81056e8			0.0298448			0.0149224	−	0.999889i	$-0.495250\pi$
$911$	6.81056e8			0.0298448			0.0149224	+	0.999889i	$0.495250\pi$
$912$	−1.40546e10	+	8.11441e9i	−0.613530	+	0.354222i
$913$	2.43001e10	+	4.20890e10i	1.05672	+	1.83030i
$914$	8.60003e9	−	1.48957e10i	0.372553	−	0.645281i
$915$			2.94433e9i			0.127061i
$916$	−2.07462e10	−	1.19778e10i	−0.891877	−	0.514925i
$917$	−8.57384e9	−	4.95011e9i	−0.367183	−	0.211993i
$918$		−	4.36865e10i		−	1.86379i
$919$	1.24859e10	−	2.16263e10i	0.530661	−	0.919131i	−0.468699	−	0.883358i	$-0.655277\pi$
$919$	1.24859e10	−	2.16263e10i	0.530661	−	0.919131i	0.999360	−	0.0357734i	$-0.0113895\pi$
$920$	2.20263e8	+	3.81506e8i	0.00932574	+	0.0161527i
$921$	−1.67256e10	+	9.65652e9i	−0.705460	+	0.407298i
$922$	−7.97999e8			−0.0335308
$923$	−4.75290e9	+	1.15931e10i	−0.198954	+	0.485280i
$924$	−1.07515e10			−0.448351
$925$	−1.44273e10	+	8.32961e9i	−0.599362	+	0.346042i
$926$	1.15899e10	+	2.00742e10i	0.479667	+	0.830807i
$927$	2.02919e9	−	3.51465e9i	0.0836648	−	0.144912i
$928$		−	1.65566e10i		−	0.680070i
$929$	−2.68778e10	−	1.55179e10i	−1.09986	−	0.635007i	−0.163679	−	0.986514i	$-0.552336\pi$
$929$	−2.68778e10	−	1.55179e10i	−1.09986	−	0.635007i	−0.936185	+	0.351506i	$0.885670\pi$
$930$	−2.76614e9	−	1.59703e9i	−0.112767	−	0.0651063i
$931$		−	2.25063e9i		−	0.0914072i
$932$	2.14714e9	−	3.71896e9i	0.0868770	−	0.150475i
$933$	−1.40452e10	−	2.43271e10i	−0.566165	−	0.980627i
$934$	−2.65662e10	+	1.53380e10i	−1.06688	+	0.615962i
$935$	−5.52587e9			−0.221085
$936$	4.86441e8	−	1.18651e9i	0.0193894	−	0.0472938i
$937$	−2.15800e10			−0.856966			−0.428483	−	0.903550i	$-0.640952\pi$
$937$	−2.15800e10			−0.856966			−0.428483	+	0.903550i	$0.640952\pi$
$938$	1.79300e10	−	1.03519e10i	0.709365	−	0.409552i
$939$	3.83456e9	+	6.64164e9i	0.151142	+	0.261786i
$940$	−1.26742e9	+	2.19524e9i	−0.0497707	+	0.0862054i
$941$			2.80734e10i			1.09833i	0.835715	+	0.549164i	$0.185054\pi$
$941$			2.80734e10i			1.09833i	−0.835715	+	0.549164i	$0.814946\pi$
$942$	3.54788e10	+	2.04837e10i	1.38290	+	0.798417i
$943$	7.07193e9	+	4.08298e9i	0.274629	+	0.158557i
$944$		−	1.67954e10i		−	0.649814i
$945$	4.88345e8	−	8.45838e8i	0.0188241	−	0.0326044i
$946$	−1.41853e10	−	2.45697e10i	−0.544778	−	0.943583i
$947$	−1.92619e10	+	1.11209e10i	−0.737013	+	0.425515i	−0.820982	−	0.570954i	$-0.806574\pi$
$947$	−1.92619e10	+	1.11209e10i	−0.737013	+	0.425515i	0.0839692	+	0.996468i	$0.473240\pi$
$948$	2.58305e10			0.984699
$949$	1.88267e10	−	2.54797e9i	0.715061	−	0.0967748i
$950$	−2.20465e10			−0.834270
$951$	−5.35370e8	+	3.09096e8i	−0.0201847	+	0.0116536i
$952$	2.38699e9	+	4.13438e9i	0.0896646	+	0.155304i
$953$	9.89265e9	−	1.71346e10i	0.370243	−	0.641280i	−0.619359	−	0.785108i	$-0.712608\pi$
$953$	9.89265e9	−	1.71346e10i	0.370243	−	0.641280i	0.989603	+	0.143827i	$0.0459410\pi$
$954$			8.45028e9i			0.315102i
$955$	2.82680e9	+	1.63206e9i	0.105023	+	0.0606350i
$956$	4.47813e9	+	2.58545e9i	0.165765	+	0.0957047i
$957$		−	2.45421e10i		−	0.905150i
$958$	−1.79516e10	+	3.10931e10i	−0.659665	+	1.14257i
$959$	−6.55481e8	−	1.13533e9i	−0.0239991	−	0.0415677i
$960$	−8.43293e8	+	4.86875e8i	−0.0307630	+	0.0177610i
$961$	−8.05622e9			−0.292819
$962$	2.34687e10	+	9.62165e9i	0.849916	+	0.348447i
$963$	−6.67051e9			−0.240695
$964$	1.16419e8	−	6.72147e7i	0.00418558	−	0.00241654i
$965$	−2.41349e9	−	4.18029e9i	−0.0864569	−	0.149748i
$966$	−3.60283e9	+	6.24029e9i	−0.128595	+	0.222733i
$967$			1.36339e10i			0.484873i	0.970167	+	0.242437i	$0.0779466\pi$
$967$			1.36339e10i			0.484873i	−0.970167	+	0.242437i	$0.922053\pi$
$968$	1.80267e10	+	1.04077e10i	0.638780	+	0.368800i
$969$	−1.94333e10	−	1.12198e10i	−0.686143	−	0.396145i
$970$		−	5.09444e9i		−	0.179224i
$971$	1.68497e10	−	2.91845e10i	0.590642	−	1.02302i	−0.403504	−	0.914978i	$-0.632208\pi$
$971$	1.68497e10	−	2.91845e10i	0.590642	−	1.02302i	0.994146	−	0.108044i	$-0.0344587\pi$
$972$	2.99129e9	+	5.18107e9i	0.104478	+	0.180962i
$973$	3.67178e9	−	2.11990e9i	0.127785	−	0.0737770i
$974$	2.62051e10			0.908719
$975$	−2.09940e10	+	1.62304e10i	−0.725403	+	0.560806i
$976$	5.07380e10			1.74686
$977$	−3.48488e10	+	2.01200e10i	−1.19552	+	0.690235i	−0.959553	−	0.281526i	$-0.909159\pi$
$977$	−3.48488e10	+	2.01200e10i	−1.19552	+	0.690235i	−0.235968	+	0.971761i	$0.575826\pi$
$978$	−1.80347e10	−	3.12370e10i	−0.616486	−	1.06778i
$979$	3.96765e10	−	6.87217e10i	1.35143	−	2.34075i
$980$		−	2.89364e8i		−	0.00982096i
$981$	−2.50348e9	−	1.44539e9i	−0.0846649	−	0.0488813i
$982$	4.86292e10	+	2.80761e10i	1.63873	+	0.946120i
$983$		−	2.77190e10i		−	0.930766i	−0.885109	−	0.465383i	$-0.845917\pi$
$983$		−	2.77190e10i		−	0.930766i	0.885109	−	0.465383i	$-0.154083\pi$
$984$	2.77915e9	−	4.81362e9i	0.0929883	−	0.161061i
$985$	2.63100e9	+	4.55703e9i	0.0877192	+	0.151934i
$986$	2.55864e10	−	1.47723e10i	0.850040	−	0.490771i
$987$	1.52932e10			0.506279
$988$	8.66687e9	+	1.12106e10i	0.285899	+	0.369811i
$989$	−8.02668e9			−0.263845
$990$	8.28411e8	−	4.78283e8i	0.0271346	−	0.0156661i
$991$	−1.47699e10	−	2.55823e10i	−0.482082	−	0.834990i	0.517707	−	0.855558i	$-0.326786\pi$
$991$	−1.47699e10	−	2.55823e10i	−0.482082	−	0.834990i	−0.999788	+	0.0205681i	$0.993453\pi$
$992$	−2.13248e10	+	3.69356e10i	−0.693576	+	1.20131i
$993$		−	2.74275e10i		−	0.888923i
$994$	6.99285e9	+	4.03732e9i	0.225840	+	0.130389i
$995$	4.85204e8	+	2.80132e8i	0.0156150	+	0.00901535i
$996$			2.53744e10i			0.813744i
$997$	−1.06622e10	+	1.84675e10i	−0.340733	+	0.590167i	−0.984569	−	0.174996i	$-0.944009\pi$
$997$	−1.06622e10	+	1.84675e10i	−0.340733	+	0.590167i	0.643836	+	0.765164i	$0.277342\pi$
$998$	−5.08052e9	−	8.79972e9i	−0.161790	−	0.280228i
$999$	2.01706e10	−	1.16455e10i	0.640089	−	0.369555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.q.a.36.42	✓	100
13.4	even	6	inner	91.8.q.a.43.42	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.q.a.36.42	✓	100	1.1	even	1	trivial
91.8.q.a.43.42	yes	100	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.8892 - 7.44160i) q^{2} +(-21.6312 - 37.4664i) q^{3} +(46.7547 - 80.9816i) q^{4} -26.3028i q^{5} +(-557.619 - 321.942i) q^{6} +(-297.047 - 171.500i) q^{7} +513.329i q^{8} +(157.681 - 273.111i) q^{9} +O(q^{10})\)	\(q+(12.8892 - 7.44160i) q^{2} +(-21.6312 - 37.4664i) q^{3} +(46.7547 - 80.9816i) q^{4} -26.3028i q^{5} +(-557.619 - 321.942i) q^{6} +(-297.047 - 171.500i) q^{7} +513.329i q^{8} +(157.681 - 273.111i) q^{9} +(-195.735 - 339.022i) q^{10} +(-6710.27 + 3874.18i) q^{11} -4045.45 q^{12} +(-1062.38 - 7849.83i) q^{13} -5104.94 q^{14} +(-985.469 + 568.961i) q^{15} +(9804.60 + 16982.1i) q^{16} +(-13556.9 + 23481.2i) q^{17} -4693.58i q^{18} +(-16567.1 - 9565.03i) q^{19} +(-2130.04 - 1229.78i) q^{20} +14839.0i q^{21} +(-57660.1 + 99870.2i) q^{22} +(16313.3 + 28255.5i) q^{23} +(19232.6 - 11103.9i) q^{24} +77433.2 q^{25} +(-72108.5 - 93272.4i) q^{26} -108258. q^{27} +(-27776.7 + 16036.9i) q^{28} +(-36606.8 - 63404.9i) q^{29} +(-8467.96 + 14666.9i) q^{30} +188597. i q^{31} +(195844. + 113071. i) q^{32} +(290303. + 167606. i) q^{33} +403539. i q^{34} +(-4510.92 + 7813.15i) q^{35} +(-14744.6 - 25538.5i) q^{36} +(-186320. + 107572. i) q^{37} -284716. q^{38} +(-271124. + 209605. i) q^{39} +13502.0 q^{40} +(216753. - 125142. i) q^{41} +(110426. + 191263. i) q^{42} +(-123008. + 213056. i) q^{43} +724544. i q^{44} +(-7183.57 - 4147.44i) q^{45} +(420533. + 242795. i) q^{46} -1.03061e6i q^{47} +(424171. - 734685. i) q^{48} +(58824.5 + 101887. i) q^{49} +(998053. - 576226. i) q^{50} +1.17301e6 q^{51} +(-685363. - 280984. i) q^{52} -1.80039e6 q^{53} +(-1.39536e6 + 805614. i) q^{54} +(101902. + 176499. i) q^{55} +(88036.0 - 152483. i) q^{56} +827613. i q^{57} +(-943667. - 544826. i) q^{58} +(-741757. - 428254. i) q^{59} +106406. i q^{60} +(1.29373e6 - 2.24081e6i) q^{61} +(1.40346e6 + 2.43087e6i) q^{62} +(-93677.1 + 54084.5i) q^{63} +855727. q^{64} +(-206472. + 27943.5i) q^{65} +4.98903e6 q^{66} +(-3.51228e6 + 2.02782e6i) q^{67} +(1.26770e6 + 2.19572e6i) q^{68} +(705755. - 1.22240e6i) q^{69} +134274. i q^{70} +(-1.36982e6 - 790866. i) q^{71} +(140196. + 80942.1i) q^{72} +2.39836e6i q^{73} +(-1.60101e6 + 2.77303e6i) q^{74} +(-1.67497e6 - 2.90114e6i) q^{75} +(-1.54918e6 + 894420. i) q^{76} +2.65768e6 q^{77} +(-1.93478e6 + 4.71924e6i) q^{78} -6.38508e6 q^{79} +(446675. - 257888. i) q^{80} +(1.99691e6 + 3.45875e6i) q^{81} +(1.86252e6 - 3.22597e6i) q^{82} -6.27233e6i q^{83} +(1.20169e6 + 693794. i) q^{84} +(617621. + 356584. i) q^{85} +3.66150e6i q^{86} +(-1.58370e6 + 2.74305e6i) q^{87} +(-1.98873e6 - 3.44458e6i) q^{88} +(-8.86921e6 + 5.12064e6i) q^{89} -123454. q^{90} +(-1.03067e6 + 2.51396e6i) q^{91} +3.05090e6 q^{92} +(7.06605e6 - 4.07958e6i) q^{93} +(-7.66939e6 - 1.32838e7i) q^{94} +(-251587. + 435761. i) q^{95} -9.78342e6i q^{96} +(1.12701e7 + 6.50682e6i) q^{97} +(1.51640e6 + 875496. i) q^{98} +2.44353e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9}+O(q^{10}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9	\( 100 q + 3328 q^{4} + 522 q^{6} - 38792 q^{9} - 2728 q^{10} - 3954 q^{11} - 54708 q^{12} - 32008 q^{13} + 21952 q^{14} + 46398 q^{15} - 228808 q^{16} + 16832 q^{17} - 203520 q^{20} + 148982 q^{22} + 154164 q^{23} - 436560 q^{24} - 1918852 q^{25} - 624246 q^{26} + 661404 q^{27} - 451396 q^{29} + 313736 q^{30} + 1854432 q^{32} + 315450 q^{33} - 372498 q^{35} + 2704174 q^{36} + 1777146 q^{37} - 338468 q^{38} + 189708 q^{39} - 2875580 q^{40} - 2158998 q^{41} - 296352 q^{42} + 1876346 q^{43} + 7252980 q^{45} + 234336 q^{46} + 1316674 q^{48} + 5882450 q^{49} + 6432894 q^{50} - 3602684 q^{51} - 14093326 q^{52} + 1719628 q^{53} - 14915976 q^{54} - 1225470 q^{55} + 2107392 q^{56} + 18792564 q^{58} + 5131962 q^{59} + 886858 q^{61} + 3663272 q^{62} - 1848084 q^{63} - 38282980 q^{64} - 17072760 q^{65} + 54390948 q^{66} - 15529368 q^{67} + 2633716 q^{68} + 12342620 q^{69} + 20194104 q^{71} + 12742440 q^{72} - 23243862 q^{74} - 12055866 q^{75} - 7828698 q^{76} - 11143384 q^{77} - 32361130 q^{78} + 38408264 q^{79} - 38368944 q^{80} - 55140914 q^{81} + 27439818 q^{82} + 46422306 q^{84} + 16353300 q^{85} - 15866954 q^{87} - 39468942 q^{88} + 11465844 q^{89} - 22072424 q^{90} - 3481450 q^{91} + 67780968 q^{92} - 71319114 q^{93} - 6119236 q^{94} + 60860930 q^{95} + 45060702 q^{97}+O(q^{100}) \) 100 * q + 3328 * q^4 + 522 * q^6 - 38792 * q^9 - 2728 * q^10 - 3954 * q^11 - 54708 * q^12 - 32008 * q^13 + 21952 * q^14 + 46398 * q^15 - 228808 * q^16 + 16832 * q^17 - 203520 * q^20 + 148982 * q^22 + 154164 * q^23 - 436560 * q^24 - 1918852 * q^25 - 624246 * q^26 + 661404 * q^27 - 451396 * q^29 + 313736 * q^30 + 1854432 * q^32 + 315450 * q^33 - 372498 * q^35 + 2704174 * q^36 + 1777146 * q^37 - 338468 * q^38 + 189708 * q^39 - 2875580 * q^40 - 2158998 * q^41 - 296352 * q^42 + 1876346 * q^43 + 7252980 * q^45 + 234336 * q^46 + 1316674 * q^48 + 5882450 * q^49 + 6432894 * q^50 - 3602684 * q^51 - 14093326 * q^52 + 1719628 * q^53 - 14915976 * q^54 - 1225470 * q^55 + 2107392 * q^56 + 18792564 * q^58 + 5131962 * q^59 + 886858 * q^61 + 3663272 * q^62 - 1848084 * q^63 - 38282980 * q^64 - 17072760 * q^65 + 54390948 * q^66 - 15529368 * q^67 + 2633716 * q^68 + 12342620 * q^69 + 20194104 * q^71 + 12742440 * q^72 - 23243862 * q^74 - 12055866 * q^75 - 7828698 * q^76 - 11143384 * q^77 - 32361130 * q^78 + 38408264 * q^79 - 38368944 * q^80 - 55140914 * q^81 + 27439818 * q^82 + 46422306 * q^84 + 16353300 * q^85 - 15866954 * q^87 - 39468942 * q^88 + 11465844 * q^89 - 22072424 * q^90 - 3481450 * q^91 + 67780968 * q^92 - 71319114 * q^93 - 6119236 * q^94 + 60860930 * q^95 + 45060702 * q^97

Introduction

L-functions

Modular forms

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Database

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