LMFDB - Embedded newform 91.8.f.a.22.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(22,91)]

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, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.6
Character	$\chi$	$=$	91.22
Dual form			91.8.f.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.42253 + 11.1242i) q^{2} +(-13.9142 + 24.1002i) q^{3} +(-18.4978 - 32.0392i) q^{4} -93.0462 q^{5} +(-178.729 - 309.568i) q^{6} +(171.500 + 297.047i) q^{7} -1168.96 q^{8} +(706.288 + 1223.33i) q^{9} +O(q^{10})$	\(q+(-6.42253 + 11.1242i) q^{2} +(-13.9142 + 24.1002i) q^{3} +(-18.4978 - 32.0392i) q^{4} -93.0462 q^{5} +(-178.729 - 309.568i) q^{6} +(171.500 + 297.047i) q^{7} -1168.96 q^{8} +(706.288 + 1223.33i) q^{9} +(597.592 - 1035.06i) q^{10} +(-1790.98 + 3102.07i) q^{11} +1029.53 q^{12} +(-7751.98 - 1629.51i) q^{13} -4405.86 q^{14} +(1294.67 - 2242.43i) q^{15} +(9875.38 - 17104.7i) q^{16} +(-19090.0 - 33064.8i) q^{17} -18144.6 q^{18} +(16931.7 + 29326.5i) q^{19} +(1721.15 + 2981.13i) q^{20} -9545.17 q^{21} +(-23005.3 - 39846.3i) q^{22} +(1813.85 - 3141.68i) q^{23} +(16265.1 - 28172.0i) q^{24} -69467.4 q^{25} +(67914.3 - 75768.6i) q^{26} -100171. q^{27} +(6344.76 - 10989.5i) q^{28} +(433.752 - 751.281i) q^{29} +(16630.1 + 28804.2i) q^{30} +112498. q^{31} +(52036.8 + 90130.3i) q^{32} +(-49840.3 - 86325.9i) q^{33} +490424. q^{34} +(-15957.4 - 27639.1i) q^{35} +(26129.6 - 45257.8i) q^{36} +(-45934.4 + 79560.8i) q^{37} -434976. q^{38} +(147135. - 164151. i) q^{39} +108767. q^{40} +(332426. - 575778. i) q^{41} +(61304.2 - 106182. i) q^{42} +(442115. + 765766. i) q^{43} +132517. q^{44} +(-65717.4 - 113826. i) q^{45} +(23299.0 + 40355.1i) q^{46} +628343. q^{47} +(274817. + 475997. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(446157. - 772766. i) q^{50} +1.06249e6 q^{51} +(91186.6 + 278510. i) q^{52} +796645. q^{53} +(643350. - 1.11431e6i) q^{54} +(166644. - 288636. i) q^{55} +(-200476. - 347235. i) q^{56} -942365. q^{57} +(5571.58 + 9650.26i) q^{58} +(912659. + 1.58077e6i) q^{59} -95794.3 q^{60} +(-900836. - 1.56029e6i) q^{61} +(-722522. + 1.25145e6i) q^{62} +(-242257. + 419601. i) q^{63} +1.19127e6 q^{64} +(721292. + 151620. i) q^{65} +1.28040e6 q^{66} +(374686. - 648974. i) q^{67} +(-706247. + 1.22325e6i) q^{68} +(50476.7 + 87428.2i) q^{69} +409948. q^{70} +(-2.44354e6 - 4.23234e6i) q^{71} +(-825619. - 1.43001e6i) q^{72} -404443. q^{73} +(-590031. - 1.02196e6i) q^{74} +(966586. - 1.67418e6i) q^{75} +(626398. - 1.08495e6i) q^{76} -1.22861e6 q^{77} +(881060. + 2.69101e6i) q^{78} -2.52580e6 q^{79} +(-918867. + 1.59152e6i) q^{80} +(-150852. + 261283. i) q^{81} +(4.27003e6 + 7.39591e6i) q^{82} -3.41727e6 q^{83} +(176565. + 305820. i) q^{84} +(1.77625e6 + 3.07655e6i) q^{85} -1.13580e7 q^{86} +(12070.7 + 20907.0i) q^{87} +(2.09358e6 - 3.62618e6i) q^{88} +(2.60120e6 - 4.50542e6i) q^{89} +1.68829e6 q^{90} +(-845423. - 2.58216e6i) q^{91} -134209. q^{92} +(-1.56532e6 + 2.71122e6i) q^{93} +(-4.03555e6 + 6.98978e6i) q^{94} +(-1.57543e6 - 2.72872e6i) q^{95} -2.89621e6 q^{96} +(-8.25704e6 - 1.43016e7i) q^{97} +(-755605. - 1.30875e6i) q^{98} -5.05979e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−6.42253	+	11.1242i	−0.567677	+	0.983245i	0.429118	+	0.903248i	$0.358824\pi$
$2$	−6.42253	+	11.1242i	−0.567677	+	0.983245i	−0.996795	+	0.0799971i	$0.974509\pi$
$3$	−13.9142	+	24.1002i	−0.297533	+	0.515342i	−0.975571	−	0.219685i	$-0.929497\pi$
$3$	−13.9142	+	24.1002i	−0.297533	+	0.515342i	0.678038	+	0.735027i	$0.262831\pi$
$4$	−18.4978	−	32.0392i	−0.144514	−	0.250306i
$5$	−93.0462			−0.332892			−0.166446	−	0.986051i	$-0.553229\pi$
$5$	−93.0462			−0.332892			−0.166446	+	0.986051i	$0.553229\pi$
$6$	−178.729	−	309.568i	−0.337805	−	0.585096i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$	−1168.96			−0.807204
$9$	706.288	+	1223.33i	0.322948	+	0.559363i
$10$	597.592	−	1035.06i	0.188975	−	0.327315i
$11$	−1790.98	+	3102.07i	−0.405711	+	0.702711i	−0.994404	−	0.105645i	$-0.966309\pi$
$11$	−1790.98	+	3102.07i	−0.405711	+	0.702711i	0.588693	+	0.808356i	$0.299643\pi$
$12$	1029.53			0.171991
$13$	−7751.98	−	1629.51i	−0.978613	−	0.205711i
$13$	−7751.98	−	1629.51i	−0.978613	−	0.205711i
$14$	−4405.86			−0.429124
$15$	1294.67	−	2242.43i	0.0990464	−	0.171553i
$16$	9875.38	−	17104.7i	0.602746	−	1.04399i
$17$	−19090.0	−	33064.8i	−0.942397	−	1.63228i	−0.760881	−	0.648891i	$-0.775233\pi$
$17$	−19090.0	−	33064.8i	−0.942397	−	1.63228i	−0.181516	−	0.983388i	$-0.558100\pi$
$18$	−18144.6			−0.733321
$19$	16931.7	+	29326.5i	0.566320	+	0.980895i	0.996926	+	0.0783546i	$0.0249666\pi$
$19$	16931.7	+	29326.5i	0.566320	+	0.980895i	−0.430606	+	0.902540i	$0.641700\pi$
$20$	1721.15	+	2981.13i	0.0481077	+	0.0833251i
$21$	−9545.17			−0.224914
$22$	−23005.3	−	39846.3i	−0.460625	−	0.797826i
$23$	1813.85	−	3141.68i	0.0310852	−	0.0538412i	−0.850064	−	0.526679i	$-0.823437\pi$
$23$	1813.85	−	3141.68i	0.0310852	−	0.0538412i	0.881150	+	0.472838i	$0.156770\pi$
$24$	16265.1	−	28172.0i	0.240170	−	0.415986i
$25$	−69467.4			−0.889183
$26$	67914.3	−	75768.6i	0.757800	−	0.845440i
$27$	−100171.			−0.979417
$28$	6344.76	−	10989.5i	0.0546213	−	0.0946069i
$29$	433.752	−	751.281i	0.00330255	−	0.00572018i	−0.864369	−	0.502857i	$-0.832282\pi$
$29$	433.752	−	751.281i	0.00330255	−	0.00572018i	0.867672	+	0.497137i	$0.165615\pi$
$30$	16630.1	+	28804.2i	0.112453	+	0.194774i
$31$	112498.			0.678233			0.339116	−	0.940744i	$-0.389872\pi$
$31$	112498.			0.678233			0.339116	+	0.940744i	$0.389872\pi$
$32$	52036.8	+	90130.3i	0.280728	+	0.486235i
$33$	−49840.3	−	86325.9i	−0.241425	−	0.418160i
$34$	490424.			2.13991
$35$	−15957.4	−	27639.1i	−0.0629107	−	0.108965i
$36$	26129.6	−	45257.8i	0.0933414	−	0.161672i
$37$	−45934.4	+	79560.8i	−0.149084	+	0.258222i	−0.930889	−	0.365301i	$-0.880966\pi$
$37$	−45934.4	+	79560.8i	−0.149084	+	0.258222i	0.781805	+	0.623523i	$0.214299\pi$
$38$	−434976.			−1.28595
$39$	147135.	−	164151.i	0.397181	−	0.443115i
$40$	108767.			0.268712
$41$	332426.	−	575778.i	0.753271	−	1.30470i	−0.192959	−	0.981207i	$-0.561808\pi$
$41$	332426.	−	575778.i	0.753271	−	1.30470i	0.946230	−	0.323496i	$-0.104858\pi$
$42$	61304.2	−	106182.i	0.127678	−	0.221145i
$43$	442115.	+	765766.i	0.848000	+	1.46878i	0.882990	+	0.469392i	$0.155527\pi$
$43$	442115.	+	765766.i	0.848000	+	1.46878i	−0.0349895	+	0.999388i	$0.511140\pi$
$44$	132517.			0.234524
$45$	−65717.4	−	113826.i	−0.107507	−	0.186208i
$46$	23299.0	+	40355.1i	0.0352927	+	0.0611288i
$47$	628343.			0.882784			0.441392	−	0.897314i	$-0.354485\pi$
$47$	628343.			0.882784			0.441392	+	0.897314i	$0.354485\pi$
$48$	274817.	+	475997.i	0.358673	+	0.621241i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	446157.	−	772766.i	0.504769	−	0.874285i
$51$	1.06249e6			1.12158
$52$	91186.6	+	278510.i	0.0899330	+	0.274681i
$53$	796645.			0.735020			0.367510	−	0.930019i	$-0.380210\pi$
$53$	796645.			0.735020			0.367510	+	0.930019i	$0.380210\pi$
$54$	643350.	−	1.11431e6i	0.555993	−	0.963007i
$55$	166644.	−	288636.i	0.135058	−	0.233927i
$56$	−200476.	−	347235.i	−0.152547	−	0.264220i
$57$	−942365.			−0.673995
$58$	5571.58	+	9650.26i	0.00374956	+	0.00649443i
$59$	912659.	+	1.58077e6i	0.578531	+	1.00205i	0.995648	+	0.0931925i	$0.0297072\pi$
$59$	912659.	+	1.58077e6i	0.578531	+	1.00205i	−0.417117	+	0.908853i	$0.636959\pi$
$60$	−95794.3			−0.0572546
$61$	−900836.	−	1.56029e6i	−0.508149	−	0.880140i	−0.999955	−	0.00943565i	$-0.996996\pi$
$61$	−900836.	−	1.56029e6i	−0.508149	−	0.880140i	0.491806	−	0.870705i	$-0.336337\pi$
$62$	−722522.	+	1.25145e6i	−0.385017	+	0.666870i
$63$	−242257.	+	419601.i	−0.122063	+	0.211419i
$64$	1.19127e6			0.568041
$65$	721292.	+	151620.i	0.325773	+	0.0684795i
$66$	1.28040e6			0.548205
$67$	374686.	−	648974.i	0.152197	−	0.263612i	−0.779838	−	0.625981i	$-0.784699\pi$
$67$	374686.	−	648974.i	0.152197	−	0.263612i	0.932035	+	0.362369i	$0.118032\pi$
$68$	−706247.	+	1.22325e6i	−0.272380	+	0.471776i
$69$	50476.7	+	87428.2i	0.0184978	+	0.0320391i
$70$	409948.			0.142852
$71$	−2.44354e6	−	4.23234e6i	−0.810245	−	1.40338i	−0.912693	−	0.408646i	$-0.866001\pi$
$71$	−2.44354e6	−	4.23234e6i	−0.810245	−	1.40338i	0.102448	−	0.994738i	$-0.467332\pi$
$72$	−825619.	−	1.43001e6i	−0.260685	−	0.451520i
$73$	−404443.			−0.121682			−0.0608411	−	0.998147i	$-0.519378\pi$
$73$	−404443.			−0.121682			−0.0608411	+	0.998147i	$0.519378\pi$
$74$	−590031.	−	1.02196e6i	−0.169264	−	0.293173i
$75$	966586.	−	1.67418e6i	0.264561	−	0.458233i
$76$	626398.	−	1.08495e6i	0.163683	−	0.283507i
$77$	−1.22861e6			−0.306688
$78$	881060.	+	2.69101e6i	0.210220	+	0.642073i
$79$	−2.52580e6			−0.576373			−0.288186	−	0.957574i	$-0.593052\pi$
$79$	−2.52580e6			−0.576373			−0.288186	+	0.957574i	$0.593052\pi$
$80$	−918867.	+	1.59152e6i	−0.200649	+	0.347535i
$81$	−150852.	+	261283.i	−0.0315393	+	0.0546277i
$82$	4.27003e6	+	7.39591e6i	0.855229	+	1.48130i
$83$	−3.41727e6			−0.656004			−0.328002	−	0.944677i	$-0.606375\pi$
$83$	−3.41727e6			−0.656004			−0.328002	+	0.944677i	$0.606375\pi$
$84$	176565.	+	305820.i	0.0325033	+	0.0562974i
$85$	1.77625e6	+	3.07655e6i	0.313717	+	0.543373i
$86$	−1.13580e7			−1.92556
$87$	12070.7	+	20907.0i	0.00196523	+	0.00340388i
$88$	2.09358e6	−	3.62618e6i	0.327491	−	0.567231i
$89$	2.60120e6	−	4.50542e6i	0.391119	−	0.677439i	−0.601478	−	0.798889i	$-0.705421\pi$
$89$	2.60120e6	−	4.50542e6i	0.391119	−	0.677439i	0.992597	+	0.121451i	$0.0387546\pi$
$90$	1.68829e6			0.244117
$91$	−845423.	−	2.58216e6i	−0.117606	−	0.359202i
$92$	−134209.			−0.0179691
$93$	−1.56532e6	+	2.71122e6i	−0.201797	+	0.349522i
$94$	−4.03555e6	+	6.98978e6i	−0.501136	+	0.867993i
$95$	−1.57543e6	−	2.72872e6i	−0.188524	−	0.326532i
$96$	−2.89621e6			−0.334103
$97$	−8.25704e6	−	1.43016e7i	−0.918594	−	1.59105i	−0.801553	−	0.597924i	$-0.795992\pi$
$97$	−8.25704e6	−	1.43016e7i	−0.918594	−	1.59105i	−0.117041	−	0.993127i	$-0.537341\pi$
$98$	−755605.	−	1.30875e6i	−0.0810967	−	0.140464i
$99$	−5.05979e6			−0.524094
$100$	1.28500e6	+	2.22568e6i	0.128500	+	0.222568i
$101$	−7.74607e6	+	1.34166e7i	−0.748095	+	1.29574i	0.200640	+	0.979665i	$0.435698\pi$
$101$	−7.74607e6	+	1.34166e7i	−0.748095	+	1.29574i	−0.948735	+	0.316074i	$0.897635\pi$
$102$	−6.82387e6	+	1.18193e7i	−0.636693	+	1.10279i
$103$	−1.79441e7			−1.61805			−0.809025	−	0.587775i	$-0.800004\pi$
$103$	−1.79441e7			−1.61805			−0.809025	+	0.587775i	$0.800004\pi$
$104$	9.06173e6	+	1.90483e6i	0.789940	+	0.166050i
$105$	888142.			0.0748721
$106$	−5.11648e6	+	8.86200e6i	−0.417254	+	0.722706i
$107$	7.00752e6	−	1.21374e7i	0.552995	−	0.957816i	−0.445061	−	0.895500i	$-0.646818\pi$
$107$	7.00752e6	−	1.21374e7i	0.552995	−	0.957816i	0.998056	−	0.0623158i	$-0.0198486\pi$
$108$	1.85294e6	+	3.20939e6i	0.141540	+	0.245154i
$109$	1.32295e7			0.978478			0.489239	−	0.872150i	$-0.337275\pi$
$109$	1.32295e7			0.978478			0.489239	+	0.872150i	$0.337275\pi$
$110$	2.14055e6	+	3.70754e6i	0.153339	+	0.265590i
$111$	−1.27829e6	−	2.21406e6i	−0.0887151	−	0.153659i
$112$	6.77451e6			0.455633
$113$	2.07028e6	+	3.58582e6i	0.134975	+	0.233784i	0.925588	−	0.378533i	$-0.123571\pi$
$113$	2.07028e6	+	3.58582e6i	0.134975	+	0.233784i	−0.790613	+	0.612316i	$0.790238\pi$
$114$	6.05237e6	−	1.04830e7i	0.382612	−	0.662703i
$115$	−168772.	+	292322.i	−0.0103480	+	0.0179233i
$116$	−32093.9			−0.00190906
$117$	−3.48170e6	−	1.06341e7i	−0.200974	−	0.613833i
$118$	−2.34463e7			−1.31368
$119$	6.54786e6	−	1.13412e7i	0.356193	−	0.616944i
$120$	−1.51341e6	+	2.62130e6i	−0.0799507	+	0.138479i
$121$	3.32837e6	+	5.76490e6i	0.170798	+	0.295831i
$122$	2.31426e7			1.15386
$123$	9.25090e6	+	1.60230e7i	0.448246	+	0.776384i
$124$	−2.08097e6	−	3.60435e6i	−0.0980145	−	0.169766i
$125$	1.37329e7			0.628894
$126$	−3.11180e6	−	5.38980e6i	−0.138585	−	0.240036i
$127$	−1.46768e7	+	2.54209e7i	−0.635796	+	1.10123i	0.350550	+	0.936544i	$0.385995\pi$
$127$	−1.46768e7	+	2.54209e7i	−0.635796	+	1.10123i	−0.986346	+	0.164687i	$0.947338\pi$
$128$	−1.43117e7	+	2.47885e7i	−0.603191	+	1.04476i
$129$	−2.46068e7			−1.00923
$130$	−6.31917e6	+	7.04998e6i	−0.252266	+	0.281440i
$131$	3.63760e7			1.41372			0.706862	−	0.707351i	$-0.250110\pi$
$131$	3.63760e7			1.41372			0.706862	+	0.707351i	$0.250110\pi$
$132$	−1.84388e6	+	3.19369e6i	−0.0697787	+	0.120860i
$133$	−5.80756e6	+	1.00590e7i	−0.214049	+	0.370743i
$134$	4.81286e6	+	8.33612e6i	0.172797	+	0.299293i
$135$	9.32051e6			0.326040
$136$	2.23153e7	+	3.86513e7i	0.760707	+	1.31758i
$137$	−2.07140e7	−	3.58776e7i	−0.688242	−	1.19207i	−0.972406	−	0.233294i	$-0.925049\pi$
$137$	−2.07140e7	−	3.58776e7i	−0.688242	−	1.19207i	0.284164	−	0.958776i	$-0.408284\pi$
$138$	−1.29675e6			−0.0420030
$139$	−1.14720e7	−	1.98700e7i	−0.362315	−	0.627547i	0.626027	−	0.779802i	$-0.284680\pi$
$139$	−1.14720e7	−	1.98700e7i	−0.362315	−	0.627547i	−0.988341	+	0.152254i	$0.951347\pi$
$140$	−590356.	+	1.02253e6i	−0.0181830	+	0.0314939i
$141$	−8.74292e6	+	1.51432e7i	−0.262657	+	0.454936i
$142$	6.27750e7			1.83983
$143$	1.89385e7	−	2.11287e7i	0.541589	−	0.604223i
$144$	2.78995e7			0.778622
$145$	−40359.0	+	69903.9i	−0.00109939	+	0.00190420i
$146$	2.59755e6	−	4.49908e6i	0.0690762	−	0.119643i
$147$	−1.63700e6	−	2.83536e6i	−0.0425047	−	0.0736203i
$148$	3.39875e6			0.0861794
$149$	−3.17343e7	−	5.49653e7i	−0.785916	−	1.36125i	−0.928450	−	0.371457i	$-0.878858\pi$
$149$	−3.17343e7	−	5.49653e7i	−0.785916	−	1.36125i	0.142534	−	0.989790i	$-0.454475\pi$
$150$	1.24159e7	+	2.15049e7i	0.300371	+	0.520257i
$151$	−1.65584e7			−0.391382			−0.195691	−	0.980666i	$-0.562695\pi$
$151$	−1.65584e7			−0.391382			−0.195691	+	0.980666i	$0.562695\pi$
$152$	−1.97924e7	−	3.42814e7i	−0.457136	−	0.791782i
$153$	2.69660e7	−	4.67065e7i	0.608691	−	1.05428i
$154$	7.89080e6	−	1.36673e7i	0.174100	−	0.301550i
$155$	−1.04675e7			−0.225779
$156$	−7.98093e6	−	1.67764e6i	−0.168313	−	0.0353804i
$157$	−2.18353e7			−0.450309			−0.225154	−	0.974323i	$-0.572289\pi$
$157$	−2.18353e7			−0.450309			−0.225154	+	0.974323i	$0.572289\pi$
$158$	1.62220e7	−	2.80973e7i	0.327193	−	0.566716i
$159$	−1.10847e7	+	1.91993e7i	−0.218693	+	0.378787i
$160$	−4.84182e6	−	8.38628e6i	−0.0934521	−	0.161864i
$161$	1.24430e6			0.0234982
$162$	−1.93770e6	−	3.35619e6i	−0.0358083	−	0.0620218i
$163$	−1.19388e7	−	2.06786e7i	−0.215926	−	0.373994i	0.737633	−	0.675202i	$-0.235944\pi$
$163$	−1.19388e7	−	2.06786e7i	−0.215926	−	0.373994i	−0.953559	+	0.301208i	$0.902610\pi$
$164$	−2.45966e7			−0.435434
$165$	4.63745e6	+	8.03229e6i	0.0803684	+	0.139202i
$166$	2.19475e7	−	3.80143e7i	0.372398	−	0.645013i
$167$	3.04399e7	−	5.27235e7i	0.505750	−	0.875985i	−0.494228	−	0.869333i	$-0.664549\pi$
$167$	3.04399e7	−	5.27235e7i	0.505750	−	0.875985i	0.999978	−	0.00665267i	$-0.00211763\pi$
$168$	1.11579e7			0.181551
$169$	5.74379e7	+	2.52639e7i	0.915366	+	0.402622i
$170$	−4.56321e7			−0.712359
$171$	−2.39172e7	+	4.14259e7i	−0.365784	+	0.633556i
$172$	1.63564e7	−	2.83301e7i	0.245097	−	0.424520i
$173$	−5.03019e7	−	8.71255e7i	−0.738624	−	1.27933i	−0.953115	−	0.302608i	$-0.902143\pi$
$173$	−5.03019e7	−	8.71255e7i	−0.738624	−	1.27933i	0.214491	−	0.976726i	$-0.431191\pi$
$174$	−310097.			−0.00446247
$175$	−1.19137e7	−	2.06351e7i	−0.168040	−	0.291053i
$176$	3.53732e7	+	6.12682e7i	0.489081	+	0.847112i
$177$	−5.07959e7			−0.688528
$178$	3.34126e7	+	5.78724e7i	0.444059	+	0.769133i
$179$	−5.85436e7	+	1.01400e8i	−0.762946	+	1.32146i	0.178380	+	0.983962i	$0.442914\pi$
$179$	−5.85436e7	+	1.01400e8i	−0.762946	+	1.32146i	−0.941326	+	0.337499i	$0.890419\pi$
$180$	−2.43126e6	+	4.21107e6i	−0.0310726	+	0.0538194i
$181$	1.23236e7			0.154477			0.0772385	−	0.997013i	$-0.475390\pi$
$181$	1.23236e7			0.154477			0.0772385	+	0.997013i	$0.475390\pi$
$182$	3.41541e7	+	7.17941e6i	0.419946	+	0.0882752i
$183$	5.01378e7			0.604765
$184$	−2.12031e6	+	3.67249e6i	−0.0250921	+	0.0434608i
$185$	4.27403e6	−	7.40283e6i	0.0496291	−	0.0859601i
$186$	−2.01067e7	−	3.48258e7i	−0.229111	−	0.396831i
$187$	1.36759e8			1.52936
$188$	−1.16230e7	−	2.01316e7i	−0.127575	−	0.220966i
$189$	−1.71793e7	−	2.97554e7i	−0.185092	−	0.320589i
$190$	4.04729e7			0.428082
$191$	−8.34573e7	−	1.44552e8i	−0.866658	−	1.50110i	−0.865391	−	0.501097i	$-0.832930\pi$
$191$	−8.34573e7	−	1.44552e8i	−0.866658	−	1.50110i	−0.00126670	−	0.999999i	$-0.500403\pi$
$192$	−1.65756e7	+	2.87097e7i	−0.169011	+	0.292735i
$193$	−4.47620e7	+	7.75300e7i	−0.448186	+	0.776281i	−0.998268	−	0.0588295i	$-0.981263\pi$
$193$	−4.47620e7	+	7.75300e7i	−0.448186	+	0.776281i	0.550082	+	0.835111i	$0.314596\pi$
$194$	2.12125e8			2.08586
$195$	−1.36903e7	+	1.52736e7i	−0.132218	+	0.147510i
$196$	4.35251e6			0.0412898
$197$	−5.00978e7	+	8.67720e7i	−0.466861	+	0.808626i	−0.999283	−	0.0378523i	$-0.987948\pi$
$197$	−5.00978e7	+	8.67720e7i	−0.466861	+	0.808626i	0.532423	+	0.846479i	$0.321282\pi$
$198$	3.24967e7	−	5.62859e7i	0.297516	−	0.515313i
$199$	7.32261e7	+	1.26831e8i	0.658689	+	1.14088i	0.980955	+	0.194233i	$0.0622218\pi$
$199$	7.32261e7	+	1.26831e8i	0.658689	+	1.14088i	−0.322267	+	0.946649i	$0.604445\pi$
$200$	8.12043e7			0.717752
$201$	1.04269e7	+	1.80600e7i	0.0905671	+	0.156867i
$202$	−9.94988e7	−	1.72337e8i	−0.849353	−	1.47112i
$203$	297554.			0.00249649
$204$	−1.96538e7	−	3.40413e7i	−0.162084	−	0.280738i
$205$	−3.09309e7	+	5.35740e7i	−0.250758	+	0.434326i
$206$	1.15247e8	−	1.99613e8i	0.918529	−	1.59094i
$207$	5.12440e6			0.0401557
$208$	−1.04426e8	+	1.16503e8i	−0.804614	+	0.897667i
$209$	−1.21297e8			−0.919048
$210$	−5.70412e6	+	9.87983e6i	−0.0425032	+	0.0736176i
$211$	−6.10739e7	+	1.05783e8i	−0.447576	+	0.775225i	−0.998228	−	0.0595104i	$-0.981046\pi$
$211$	−6.10739e7	+	1.05783e8i	−0.447576	+	0.775225i	0.550651	+	0.834735i	$0.314379\pi$
$212$	−1.47362e7	−	2.55239e7i	−0.106221	−	0.183980i
$213$	1.36000e8			0.964298
$214$	9.00121e7	+	1.55906e8i	0.627845	+	1.08746i
$215$	−4.11372e7	−	7.12517e7i	−0.282293	−	0.488945i
$216$	1.17095e8			0.790589
$217$	1.92934e7	+	3.34172e7i	0.128174	+	0.222004i
$218$	−8.49670e7	+	1.47167e8i	−0.555460	+	0.962084i
$219$	5.62751e6	−	9.74714e6i	0.0362045	−	0.0627080i
$220$	−1.23302e7			−0.0780713
$221$	9.41055e7	+	2.87425e8i	0.586465	+	1.79123i
$222$	3.28393e7			0.201446
$223$	−8.22373e7	+	1.42439e8i	−0.496594	+	0.860126i	−0.999992	−	0.00392818i	$-0.998750\pi$
$223$	−8.22373e7	+	1.42439e8i	−0.496594	+	0.860126i	0.503398	+	0.864055i	$0.332083\pi$
$224$	−1.78486e7	+	3.09147e7i	−0.106105	+	0.183779i
$225$	−4.90640e7	−	8.49813e7i	−0.287160	−	0.497376i
$226$	−5.31856e7			−0.306489
$227$	−2.57563e7	−	4.46111e7i	−0.146148	−	0.253135i	0.783653	−	0.621199i	$-0.213354\pi$
$227$	−2.57563e7	−	4.46111e7i	−0.146148	−	0.253135i	−0.929801	+	0.368064i	$0.880021\pi$
$228$	1.74317e7	+	3.01926e7i	0.0974021	+	0.168705i
$229$	−7.82967e6			−0.0430843			−0.0215422	−	0.999768i	$-0.506858\pi$
$229$	−7.82967e6			−0.0430843			−0.0215422	+	0.999768i	$0.506858\pi$
$230$	−2.16789e6	−	3.75489e6i	−0.0117487	−	0.0203493i
$231$	1.70952e7	−	2.96098e7i	0.0912499	−	0.158049i
$232$	−507038.	+	878215.i	−0.00266583	+	0.00461735i
$233$	−2.80970e8			−1.45517			−0.727587	−	0.686016i	$-0.759358\pi$
$233$	−2.80970e8			−1.45517			−0.727587	+	0.686016i	$0.759358\pi$
$234$	1.40657e8	+	2.95669e7i	0.717638	+	0.150852i
$235$	−5.84649e7			−0.293872
$236$	3.37645e7	−	5.84818e7i	0.167212	−	0.289620i
$237$	3.51445e7	−	6.08721e7i	0.171490	−	0.297029i
$238$	8.41077e7	+	1.45679e8i	0.404405	+	0.700449i
$239$	−1.76984e8			−0.838572			−0.419286	−	0.907854i	$-0.637720\pi$
$239$	−1.76984e8			−0.838572			−0.419286	+	0.907854i	$0.637720\pi$
$240$	−2.55707e7	−	4.42897e7i	−0.119400	−	0.206806i
$241$	1.46644e7	+	2.53995e7i	0.0674847	+	0.116887i	0.897793	−	0.440417i	$-0.145169\pi$
$241$	1.46644e7	+	2.53995e7i	0.0674847	+	0.116887i	−0.830309	+	0.557304i	$0.811836\pi$
$242$	−8.55062e7			−0.387832
$243$	−1.13735e8	−	1.96994e8i	−0.508476	−	0.880707i
$244$	−3.33271e7	+	5.77242e7i	−0.146870	+	0.254386i
$245$	5.47340e6	−	9.48020e6i	0.0237780	−	0.0411847i
$246$	−2.37657e8			−1.01784
$247$	−8.34659e7	−	2.54929e8i	−0.352427	−	1.07641i
$248$	−1.31505e8			−0.547472
$249$	4.75488e7	−	8.23569e7i	0.195183	−	0.338067i
$250$	−8.82001e7	+	1.52767e8i	−0.357009	+	0.618358i
$251$	1.19802e8	+	2.07503e8i	0.478196	+	0.828260i	0.999688	−	0.0249967i	$-0.00795753\pi$
$251$	1.19802e8	+	2.07503e8i	0.478196	+	0.828260i	−0.521492	+	0.853256i	$0.674624\pi$
$252$	1.79249e7			0.0705594
$253$	6.49714e6	+	1.12534e7i	0.0252232	+	0.0436879i
$254$	−1.88524e8	−	3.26534e8i	−0.721854	−	1.25029i
$255$	−9.88606e7			−0.373364
$256$	−1.07593e8	−	1.86357e8i	−0.400815	−	0.694233i
$257$	−1.02239e8	+	1.77082e8i	−0.375707	+	0.650743i	−0.990433	−	0.137998i	$-0.955933\pi$
$257$	−1.02239e8	+	1.77082e8i	−0.375707	+	0.650743i	0.614726	+	0.788741i	$0.289267\pi$
$258$	1.58038e8	−	2.73730e8i	0.572918	−	0.992323i
$259$	−3.15110e7			−0.112697
$260$	−8.48457e6	−	2.59143e7i	−0.0299380	−	0.0914392i
$261$	1.22542e6			0.00426621
$262$	−2.33626e8	+	4.04652e8i	−0.802539	+	1.39004i
$263$	1.32261e8	−	2.29082e8i	0.448317	−	0.776508i	−0.549960	−	0.835191i	$-0.685357\pi$
$263$	1.32261e8	−	2.29082e8i	0.448317	−	0.776508i	0.998277	+	0.0586833i	$0.0186902\pi$
$264$	5.82611e7	+	1.00911e8i	0.194879	+	0.337540i
$265$	−7.41248e7			−0.244683
$266$	−7.45985e7	−	1.29208e8i	−0.243021	−	0.420925i
$267$	7.23875e7	+	1.25379e8i	0.232742	+	0.403121i
$268$	−2.77235e7			−0.0879785
$269$	838334.	+	1.45204e6i	0.00262594	+	0.00454826i	0.867335	−	0.497724i	$-0.165831\pi$
$269$	838334.	+	1.45204e6i	0.00262594	+	0.00454826i	−0.864709	+	0.502272i	$0.832497\pi$
$270$	−5.98613e7	+	1.03683e8i	−0.185086	+	0.320578i
$271$	4.48130e7	−	7.76185e7i	0.136777	−	0.236904i	−0.789498	−	0.613753i	$-0.789659\pi$
$271$	4.48130e7	−	7.76185e7i	0.136777	−	0.236904i	0.926275	+	0.376849i	$0.122992\pi$
$272$	−7.54083e8			−2.27210
$273$	7.39940e7	+	1.55540e7i	0.220104	+	0.0462672i
$274$	5.32144e8			1.56280
$275$	1.24415e8	−	2.15493e8i	0.360751	−	0.624839i
$276$	1.86742e6	−	3.23447e6i	0.00534639	−	0.00926022i
$277$	−1.32934e8	−	2.30248e8i	−0.375799	−	0.650903i	0.614647	−	0.788802i	$-0.289298\pi$
$277$	−1.32934e8	−	2.30248e8i	−0.375799	−	0.650903i	−0.990446	+	0.137899i	$0.955965\pi$
$278$	2.94716e8			0.822711
$279$	7.94560e7	+	1.37622e8i	0.219034	+	0.379378i
$280$	1.86535e7	+	3.23089e7i	0.0507818	+	0.0879566i
$281$	−5.99901e8			−1.61290			−0.806450	−	0.591303i	$-0.798614\pi$
$281$	−5.99901e8			−1.61290			−0.806450	+	0.591303i	$0.798614\pi$
$282$	−1.12303e8	−	1.94515e8i	−0.298209	−	0.516513i
$283$	8.21272e7	−	1.42249e8i	0.215395	−	0.373074i	−0.738000	−	0.674801i	$-0.764230\pi$
$283$	8.21272e7	−	1.42249e8i	0.215395	−	0.373074i	0.953395	+	0.301726i	$0.0975629\pi$
$284$	−9.04007e7	+	1.56579e8i	−0.234184	+	0.405619i
$285$	8.76835e7			0.224368
$286$	1.13406e8	+	3.46375e8i	0.286652	+	0.875518i
$287$	2.28044e8			0.569419
$288$	−7.35058e7	+	1.27316e8i	−0.181321	+	0.314057i
$289$	−5.23684e8	+	9.07047e8i	−1.27622	+	2.21049i
$290$	−518414.	−	897920.i	−0.00124820	−	0.00216194i
$291$	4.59562e8			1.09325
$292$	7.48132e6	+	1.29580e7i	0.0175848	+	0.0304578i
$293$	−3.34455e8	−	5.79293e8i	−0.776785	−	1.34543i	−0.933786	−	0.357832i	$-0.883516\pi$
$293$	−3.34455e8	−	5.79293e8i	−0.776785	−	1.34543i	0.157001	−	0.987598i	$-0.449817\pi$
$294$	4.20547e7			0.0965158
$295$	−8.49195e7	−	1.47085e8i	−0.192589	−	0.333573i
$296$	5.36953e7	−	9.30031e7i	0.120342	−	0.208438i
$297$	1.79404e8	−	3.10736e8i	0.397360	−	0.688247i
$298$	8.15257e8			1.78459
$299$	−1.91804e7	+	2.13986e7i	−0.0414961	+	0.0462951i
$300$	−7.15191e7			−0.152932
$301$	−1.51646e8	+	2.62658e8i	−0.320514	+	0.555147i
$302$	1.06347e8	−	1.84199e8i	0.222178	−	0.384824i
$303$	−2.15561e8	−	3.73363e8i	−0.445166	−	0.771050i
$304$	6.68826e8			1.36539
$305$	8.38194e7	+	1.45179e8i	0.169159	+	0.292992i
$306$	3.46380e8	+	5.99948e8i	0.691080	+	1.19699i
$307$	4.67939e7			0.0923008			0.0461504	−	0.998935i	$-0.485305\pi$
$307$	4.67939e7			0.0923008			0.0461504	+	0.998935i	$0.485305\pi$
$308$	2.27267e7	+	3.93638e7i	0.0443209	+	0.0767661i
$309$	2.49679e8	−	4.32456e8i	0.481423	−	0.833849i
$310$	6.72280e7	−	1.16442e8i	0.128169	−	0.221996i
$311$	4.32722e8			0.815733			0.407866	−	0.913042i	$-0.366273\pi$
$311$	4.32722e8			0.815733			0.407866	+	0.913042i	$0.366273\pi$
$312$	−1.71994e8	+	1.91885e8i	−0.320606	+	0.357684i
$313$	7.01386e8			1.29286			0.646430	−	0.762973i	$-0.276261\pi$
$313$	7.01386e8			1.29286			0.646430	+	0.762973i	$0.276261\pi$
$314$	1.40238e8	−	2.42899e8i	0.255630	−	0.442764i
$315$	2.25411e7	−	3.90423e7i	0.0406338	−	0.0703798i
$316$	4.67218e7	+	8.09245e7i	0.0832942	+	0.144270i
$317$	1.02387e9			1.80525			0.902625	−	0.430428i	$-0.141637\pi$
$317$	1.02387e9			1.80525			0.902625	+	0.430428i	$0.141637\pi$
$318$	−1.42384e8	−	2.46616e8i	−0.248294	−	0.430058i
$319$	1.55368e6	+	2.69106e6i	0.00267976	+	0.00464147i
$320$	−1.10843e8			−0.189096
$321$	1.95009e8	+	3.37765e8i	0.329069	+	0.569964i
$322$	−7.99157e6	+	1.38418e7i	−0.0133394	+	0.0231045i
$323$	6.46449e8	−	1.11968e9i	1.06740	−	1.84878i
$324$	1.11617e7			0.0182315
$325$	5.38510e8	+	1.13198e8i	0.870166	+	0.182914i
$326$	3.06710e8			0.490304
$327$	−1.84079e8	+	3.18834e8i	−0.291130	+	0.504251i
$328$	−3.88591e8	+	6.73059e8i	−0.608043	+	1.05316i
$329$	1.07761e8	+	1.86647e8i	0.166830	+	0.288959i
$330$	−1.19137e8			−0.182493
$331$	−3.82818e8	−	6.63061e8i	−0.580223	−	1.00497i	−0.995453	−	0.0952585i	$-0.969632\pi$
$331$	−3.82818e8	−	6.63061e8i	−0.580223	−	1.00497i	0.415230	−	0.909716i	$-0.363701\pi$
$332$	6.32122e7	+	1.09487e8i	0.0948020	+	0.164202i
$333$	−1.29772e8			−0.192586
$334$	3.91003e8	+	6.77237e8i	0.574206	+	0.994553i
$335$	−3.48631e7	+	6.03846e7i	−0.0506651	+	0.0877545i
$336$	−9.42622e7	+	1.63267e8i	−0.135566	+	0.234807i
$337$	−2.79433e8			−0.397716			−0.198858	−	0.980028i	$-0.563723\pi$
$337$	−2.79433e8			−0.397716			−0.198858	+	0.980028i	$0.563723\pi$
$338$	−6.49937e8	+	4.76689e8i	−0.915509	+	0.671470i
$339$	−1.15225e8			−0.160638
$340$	6.57136e7	−	1.13819e8i	0.0906732	−	0.157051i
$341$	−2.01482e8	+	3.48977e8i	−0.275166	+	0.476602i
$342$	−3.07219e8	−	5.32118e8i	−0.415294	−	0.719311i
$343$	−4.03536e7			−0.0539949
$344$	−5.16814e8	−	8.95147e8i	−0.684509	−	1.18560i
$345$	−4.69667e6	−	8.13487e6i	−0.00615776	−	0.0106656i
$346$	1.29226e9			1.67720
$347$	−4.81438e7	−	8.33875e7i	−0.0618567	−	0.107139i	0.833439	−	0.552612i	$-0.186369\pi$
$347$	−4.81438e7	−	8.33875e7i	−0.0618567	−	0.107139i	−0.895295	+	0.445473i	$0.853036\pi$
$348$	446563.	−	773470.i	0.000568009	−	0.000983821i
$349$	2.40029e8	−	4.15743e8i	0.302256	−	0.523523i	−0.674390	−	0.738375i	$-0.735593\pi$
$349$	2.40029e8	−	4.15743e8i	0.302256	−	0.523523i	0.976647	+	0.214852i	$0.0689268\pi$
$350$	3.06063e8			0.381569
$351$	7.76522e8	+	1.63230e8i	0.958470	+	0.201476i
$352$	−3.72787e8			−0.455577
$353$	1.31146e8	−	2.27152e8i	0.158688	−	0.274856i	−0.775708	−	0.631093i	$-0.782607\pi$
$353$	1.31146e8	−	2.27152e8i	0.158688	−	0.274856i	0.934396	+	0.356236i	$0.115940\pi$
$354$	3.26238e8	−	5.65061e8i	0.390862	−	0.676992i
$355$	2.27363e8	+	3.93804e8i	0.269724	+	0.467176i
$356$	−1.92467e8			−0.226090
$357$	1.82217e8	+	3.15609e8i	0.211958	+	0.367122i
$358$	−7.51996e8	−	1.30250e9i	−0.866214	−	1.50033i
$359$	−1.57407e9			−1.79553			−0.897767	−	0.440472i	$-0.854811\pi$
$359$	−1.57407e9			−1.79553			−0.897767	+	0.440472i	$0.854811\pi$
$360$	7.68208e7	+	1.33057e8i	0.0867801	+	0.150307i
$361$	−1.26426e8	+	2.18976e8i	−0.141436	+	0.244975i
$362$	−7.91490e7	+	1.37090e8i	−0.0876931	+	0.151889i
$363$	−1.85247e8			−0.203272
$364$	−6.70919e7	+	7.48511e7i	−0.0729148	+	0.0813474i
$365$	3.76319e7			0.0405070
$366$	−3.22012e8	+	5.57741e8i	−0.343311	+	0.594632i
$367$	−2.10461e8	+	3.64530e8i	−0.222250	+	0.384948i	−0.955491	−	0.295021i	$-0.904673\pi$
$367$	−2.10461e8	+	3.64530e8i	−0.222250	+	0.384948i	0.733241	+	0.679969i	$0.238007\pi$
$368$	−3.58249e7	−	6.20506e7i	−0.0374730	−	0.0649051i
$369$	9.39153e8			0.973069
$370$	5.49001e7	+	9.50898e7i	0.0563466	+	0.0975951i
$371$	1.36625e8	+	2.36641e8i	0.138906	+	0.240592i
$372$	1.15821e8			0.116650
$373$	−6.37739e8	−	1.10460e9i	−0.636301	−	1.10211i	−0.986238	−	0.165332i	$-0.947130\pi$
$373$	−6.37739e8	−	1.10460e9i	−0.636301	−	1.10211i	0.349937	−	0.936773i	$-0.386203\pi$
$374$	−8.78339e8	+	1.52133e9i	−0.868184	+	1.50374i
$375$	−1.91083e8	+	3.30966e8i	−0.187117	+	0.324096i
$376$	−7.34505e8			−0.712586
$377$	−4.58666e6	+	5.11711e6i	−0.00440862	+	0.00491847i
$378$	4.41338e8			0.420291
$379$	8.82438e8	−	1.52843e9i	0.832620	−	1.44214i	−0.0633337	−	0.997992i	$-0.520173\pi$
$379$	8.82438e8	−	1.52843e9i	0.832620	−	1.44214i	0.895954	−	0.444148i	$-0.146493\pi$
$380$	−5.82840e7	+	1.00951e8i	−0.0544887	+	0.0943773i
$381$	−4.08433e8	−	7.07426e8i	−0.378341	−	0.655305i
$382$	2.14403e9			1.96793
$383$	4.51033e8	+	7.81211e8i	0.410216	+	0.710514i	0.994913	−	0.100737i	$-0.0321201\pi$
$383$	4.51033e8	+	7.81211e8i	0.410216	+	0.710514i	−0.584697	+	0.811251i	$0.698787\pi$
$384$	−3.98272e8	−	6.89827e8i	−0.358939	−	0.621700i
$385$	1.14318e8			0.102094
$386$	−5.74970e8	−	9.95878e8i	−0.508850	−	0.881354i
$387$	−6.24521e8	+	1.08170e9i	−0.547720	+	0.948680i
$388$	−3.05475e8	+	5.29098e8i	−0.265500	+	0.459860i
$389$	−1.89905e9			−1.63573			−0.817866	−	0.575409i	$-0.804843\pi$
$389$	−1.89905e9			−1.63573			−0.817866	+	0.575409i	$0.804843\pi$
$390$	−8.19793e7	−	2.50388e8i	−0.0699807	−	0.213741i
$391$	−1.38505e8			−0.117179
$392$	6.87633e7	−	1.19101e8i	0.0576574	−	0.0998656i
$393$	−5.06144e8	+	8.76667e8i	−0.420630	+	0.728552i
$394$	−6.43510e8	−	1.11459e9i	−0.530052	−	0.918077i
$395$	2.35016e8			0.191870
$396$	9.35952e7	+	1.62112e8i	0.0757392	+	0.131184i
$397$	−7.58733e7	−	1.31416e8i	−0.0608586	−	0.105410i	0.833991	−	0.551778i	$-0.186051\pi$
$397$	−7.58733e7	−	1.31416e8i	−0.0608586	−	0.105410i	−0.894849	+	0.446368i	$0.852717\pi$
$398$	−1.88119e9			−1.49569
$399$	−1.61616e8	−	2.79926e8i	−0.127373	−	0.220617i
$400$	−6.86017e8	+	1.18822e9i	−0.535951	+	0.928294i
$401$	1.21421e7	−	2.10308e7i	0.00940350	−	0.0162873i	−0.861285	−	0.508122i	$-0.830340\pi$
$401$	1.21421e7	−	2.10308e7i	0.00940350	−	0.0162873i	0.870689	+	0.491834i	$0.163673\pi$
$402$	−2.67869e8			−0.205651
$403$	−8.72082e8	−	1.83317e8i	−0.663728	−	0.139520i
$404$	5.73143e8			0.432442
$405$	1.40362e7	−	2.43114e7i	0.0104992	−	0.0181851i
$406$	−1.91105e6	+	3.31004e6i	−0.00141720	+	0.00245466i
$407$	−1.64535e8	−	2.84984e8i	−0.120970	−	0.209527i
$408$	−1.24200e9			−0.905341
$409$	3.56201e8	+	6.16959e8i	0.257433	+	0.445887i	0.965553	−	0.260205i	$-0.0837901\pi$
$409$	3.56201e8	+	6.16959e8i	0.257433	+	0.445887i	−0.708121	+	0.706091i	$0.750457\pi$
$410$	−3.97310e8	−	6.88161e8i	−0.284699	−	0.493113i
$411$	1.15288e9			0.819099
$412$	3.31927e8	+	5.74915e8i	0.233831	+	0.405008i
$413$	−3.13042e8	+	5.42205e8i	−0.218664	+	0.378738i
$414$	−3.29116e7	+	5.70046e7i	−0.0227955	+	0.0394829i
$415$	3.17964e8			0.218379
$416$	−2.56519e8	−	7.83483e8i	−0.174700	−	0.533584i
$417$	6.38494e8			0.431202
$418$	7.79034e8	−	1.34933e9i	0.521722	−	0.903650i
$419$	6.20528e8	−	1.07479e9i	0.412109	−	0.713794i	−0.583011	−	0.812464i	$-0.698126\pi$
$419$	6.20528e8	−	1.07479e9i	0.412109	−	0.713794i	0.995120	+	0.0986704i	$0.0314590\pi$
$420$	−1.64287e7	−	2.84554e7i	−0.0108201	−	0.0187410i
$421$	9.73971e8			0.636149			0.318074	−	0.948066i	$-0.396964\pi$
$421$	9.73971e8			0.636149			0.318074	+	0.948066i	$0.396964\pi$
$422$	−7.84498e8	−	1.35879e9i	−0.508158	−	0.880155i
$423$	4.43791e8	+	7.68669e8i	0.285093	+	0.493796i
$424$	−9.31243e8			−0.593311
$425$	1.32613e9	+	2.29692e9i	0.837963	+	1.45139i
$426$	−8.73466e8	+	1.51289e9i	−0.547410	+	0.948142i
$427$	3.08987e8	−	5.35181e8i	0.192062	−	0.332662i
$428$	−5.18497e8			−0.319663
$429$	2.45691e8	+	7.50412e8i	0.150241	+	0.458880i
$430$	1.05682e9			0.641005
$431$	−2.60064e8	+	4.50443e8i	−0.156462	+	0.271000i	−0.933590	−	0.358342i	$-0.883342\pi$
$431$	−2.60064e8	+	4.50443e8i	−0.156462	+	0.271000i	0.777128	+	0.629342i	$0.216676\pi$
$432$	−9.89224e8	+	1.71339e9i	−0.590339	+	1.02250i
$433$	8.11817e8	+	1.40611e9i	0.480563	+	0.832360i	0.999751	−	0.0223000i	$-0.00709891\pi$
$433$	8.11817e8	+	1.40611e9i	0.480563	+	0.832360i	−0.519188	+	0.854660i	$0.673766\pi$
$434$	−4.95650e8			−0.291046
$435$	−1.12313e6	−	1.94532e6i	−0.000654211	−	0.00113313i
$436$	−2.44718e8	−	4.23863e8i	−0.141404	−	0.244919i
$437$	1.22846e8			0.0704167
$438$	7.22858e7	+	1.25203e8i	0.0411049	+	0.0711957i
$439$	−5.79946e8	+	1.00450e9i	−0.327161	+	0.566660i	−0.981947	−	0.189154i	$-0.939425\pi$
$439$	−5.79946e8	+	1.00450e9i	−0.327161	+	0.566660i	0.654786	+	0.755814i	$0.272759\pi$
$440$	−1.94799e8	+	3.37403e8i	−0.109019	+	0.188827i
$441$	−1.66188e8			−0.0922709
$442$	−3.80175e9	−	7.99153e8i	−2.09414	−	0.440202i
$443$	7.14540e8			0.390493			0.195247	−	0.980754i	$-0.437449\pi$
$443$	7.14540e8			0.390493			0.195247	+	0.980754i	$0.437449\pi$
$444$	−4.72911e7	+	8.19105e7i	−0.0256412	+	0.0444119i
$445$	−2.42032e8	+	4.19212e8i	−0.130201	+	0.225514i
$446$	−1.05634e9	−	1.82964e9i	−0.563810	−	0.976548i
$447$	1.76623e9			0.935344
$448$	2.04302e8	+	3.53862e8i	0.107350	+	0.185935i
$449$	−2.58286e8	−	4.47364e8i	−0.134660	−	0.233238i	0.790808	−	0.612065i	$-0.209661\pi$
$449$	−2.58286e8	−	4.47364e8i	−0.134660	−	0.233238i	−0.925467	+	0.378827i	$0.876327\pi$
$450$	1.26046e9			0.652057
$451$	1.19074e9	+	2.06241e9i	0.611220	+	1.05866i
$452$	7.65913e7	−	1.32660e8i	0.0390117	−	0.0675702i
$453$	2.30398e8	−	3.99061e8i	0.116449	−	0.201695i
$454$	6.61682e8			0.331859
$455$	7.86634e7	+	2.40260e8i	0.0391501	+	0.119576i
$456$	1.10158e9			0.544052
$457$	−1.86979e9	+	3.23857e9i	−0.916401	+	1.58725i	−0.111565	+	0.993757i	$0.535586\pi$
$457$	−1.86979e9	+	3.23857e9i	−0.916401	+	1.58725i	−0.804837	+	0.593497i	$0.797747\pi$
$458$	5.02863e7	−	8.70985e7i	0.0244580	−	0.0423625i
$459$	1.91226e9	+	3.31212e9i	0.923000	+	1.59868i
$460$	1.24877e7			0.00598176
$461$	−3.61449e8	−	6.26049e8i	−0.171828	−	0.297615i	0.767231	−	0.641371i	$-0.221634\pi$
$461$	−3.61449e8	−	6.26049e8i	−0.171828	−	0.297615i	−0.939059	+	0.343756i	$0.888301\pi$
$462$	2.19589e8	+	3.80339e8i	0.103601	+	0.179442i
$463$	1.67276e9			0.783250			0.391625	−	0.920125i	$-0.371913\pi$
$463$	1.67276e9			0.783250			0.391625	+	0.920125i	$0.371913\pi$
$464$	−8.56694e6	−	1.48384e7i	−0.00398119	−	0.00689562i
$465$	1.45648e8	−	2.52269e8i	0.0671766	−	0.116353i
$466$	1.80454e9	−	3.12556e9i	0.826069	−	1.43079i
$467$	−4.39813e9			−1.99829			−0.999147	−	0.0412980i	$-0.986851\pi$
$467$	−4.39813e9			−1.99829			−0.999147	+	0.0412980i	$0.986851\pi$
$468$	−2.76304e8	+	3.08259e8i	−0.124603	+	0.139013i
$469$	2.57034e8			0.115050
$470$	3.75493e8	−	6.50373e8i	0.166824	−	0.288948i
$471$	3.03822e8	−	5.26235e8i	0.133982	−	0.232063i
$472$	−1.06686e9	−	1.84785e9i	−0.466993	−	0.808855i
$473$	−3.16728e9			−1.37617
$474$	4.51434e8	+	7.81906e8i	0.194702	+	0.337233i
$475$	−1.17620e9	−	2.03723e9i	−0.503562	−	0.872195i
$476$	−4.84485e8			−0.205900
$477$	5.62661e8	+	9.74557e8i	0.237374	+	0.411143i
$478$	1.13668e9	−	1.96879e9i	0.476038	−	0.824522i
$479$	3.57892e8	−	6.19888e8i	0.148792	−	0.257715i	−0.781990	−	0.623292i	$-0.785795\pi$
$479$	3.57892e8	−	6.19888e8i	0.148792	−	0.257715i	0.930781	+	0.365577i	$0.119128\pi$
$480$	2.69481e8			0.111220
$481$	4.85728e8	−	5.41903e8i	0.199015	−	0.222031i
$482$	−3.76731e8			−0.153238
$483$	−1.73135e7	+	2.99879e7i	−0.00699150	+	0.0121096i
$484$	1.23135e8	−	2.13277e8i	0.0493655	−	0.0855036i
$485$	7.68287e8	+	1.33071e9i	0.305793	+	0.529649i
$486$	2.92186e9			1.15460
$487$	−1.28223e9	−	2.22089e9i	−0.503055	−	0.871316i	−0.999994	−	0.00353096i	$-0.998876\pi$
$487$	−1.28223e9	−	2.22089e9i	−0.503055	−	0.871316i	0.496939	−	0.867785i	$-0.334457\pi$
$488$	1.05304e9	+	1.82391e9i	0.410180	+	0.710453i
$489$	6.64478e8			0.256980
$490$	7.03061e7	+	1.21774e8i	0.0269965	+	0.0467593i
$491$	−4.97875e8	+	8.62345e8i	−0.189817	+	0.328773i	−0.945189	−	0.326523i	$-0.894123\pi$
$491$	−4.97875e8	+	8.62345e8i	−0.189817	+	0.328773i	0.755372	+	0.655296i	$0.227456\pi$
$492$	3.42244e8	−	5.92783e8i	0.129556	−	0.224397i
$493$	−3.31213e7			−0.0124492
$494$	3.37193e9	+	7.08801e8i	1.25844	+	0.264533i
$495$	4.70794e8			0.174467
$496$	1.11096e9	−	1.92424e9i	0.408802	−	0.708066i
$497$	8.38136e8	−	1.45169e9i	0.306244	−	0.530430i
$498$	6.10767e8	+	1.05788e9i	0.221602	+	0.383825i
$499$	1.24987e9			0.450312			0.225156	−	0.974323i	$-0.427711\pi$
$499$	1.24987e9			0.450312			0.225156	+	0.974323i	$0.427711\pi$
$500$	−2.54029e8	−	4.39992e8i	−0.0908843	−	0.157416i
$501$	8.47097e8	+	1.46722e9i	0.300955	+	0.521269i
$502$	−3.07773e9			−1.08584
$503$	−5.65432e7	−	9.79357e7i	−0.0198104	−	0.0343126i	0.855950	−	0.517058i	$-0.172973\pi$
$503$	−5.65432e7	−	9.79357e7i	−0.0198104	−	0.0343126i	−0.875761	+	0.482746i	$0.839640\pi$
$504$	2.83187e8	−	4.90495e8i	0.0985297	−	0.170658i
$505$	7.20743e8	−	1.24836e9i	0.249035	−	0.431341i
$506$	−1.66912e8			−0.0572746
$507$	−1.40807e9	+	1.03273e9i	−0.479840	+	0.351934i
$508$	1.08596e9			0.367527
$509$	3.60587e8	−	6.24556e8i	0.121199	−	0.209923i	−0.799042	−	0.601275i	$-0.794659\pi$
$509$	3.60587e8	−	6.24556e8i	0.121199	−	0.209923i	0.920241	+	0.391353i	$0.127993\pi$
$510$	6.34936e8	−	1.09974e9i	0.211950	−	0.367109i
$511$	−6.93619e7	−	1.20138e8i	−0.0229958	−	0.0398298i
$512$	−8.99704e8			−0.296248
$513$	−1.69606e9	−	2.93766e9i	−0.554663	−	0.960705i
$514$	−1.31326e9	−	2.27464e9i	−0.426560	−	0.738824i
$515$	1.66963e9			0.538636
$516$	4.55173e8	+	7.88383e8i	0.145849	+	0.252617i
$517$	−1.12535e9	+	1.94916e9i	−0.358155	+	0.620342i
$518$	2.02381e8	−	3.50533e8i	0.0639756	−	0.110809i
$519$	2.79965e9			0.879060
$520$	−8.43159e8	−	1.77237e8i	−0.262965	−	0.0552769i
$521$	1.33546e9			0.413713			0.206857	−	0.978371i	$-0.433677\pi$
$521$	1.33546e9			0.413713			0.206857	+	0.978371i	$0.433677\pi$
$522$	−7.87027e6	+	1.36317e7i	−0.00242183	+	0.00419473i
$523$	2.98461e9	−	5.16949e9i	0.912286	−	1.58013i	0.101460	−	0.994840i	$-0.467649\pi$
$523$	2.98461e9	−	5.16949e9i	0.912286	−	1.58013i	0.810826	−	0.585287i	$-0.199018\pi$
$524$	−6.72877e8	−	1.16546e9i	−0.204304	−	0.353864i
$525$	6.63078e8			0.199989
$526$	1.69890e9	+	2.94257e9i	0.508999	+	0.881612i
$527$	−2.14758e9	−	3.71972e9i	−0.639165	−	1.10707i
$528$	−1.96877e9			−0.582070
$529$	1.69583e9	+	2.93727e9i	0.498067	+	0.862678i
$530$	4.76069e8	−	8.24576e8i	0.138901	−	0.240583i
$531$	−1.28920e9	+	2.23296e9i	−0.373671	+	0.647217i
$532$	4.29709e8			0.123733
$533$	−3.51520e9	+	3.92173e9i	−1.00555	+	1.12184i
$534$	−1.85965e9			−0.528489
$535$	−6.52024e8	+	1.12934e9i	−0.184088	+	0.318850i
$536$	−4.37991e8	+	7.58623e8i	−0.122854	+	0.212789i
$537$	−1.62918e9	−	2.82182e9i	−0.454003	−	0.786357i
$538$	−2.15369e7			−0.00596274
$539$	−2.10707e8	−	3.64955e8i	−0.0579587	−	0.100387i
$540$	−1.72409e8	−	2.98622e8i	−0.0471175	−	0.0816100i
$541$	7.03424e9			1.90997			0.954986	−	0.296652i	$-0.0958702\pi$
$541$	7.03424e9			1.90997			0.954986	+	0.296652i	$0.0958702\pi$
$542$	5.75626e8	+	9.97014e8i	0.155290	+	0.268970i
$543$	−1.71474e8	+	2.97002e8i	−0.0459620	+	0.0796086i
$544$	1.98676e9	−	3.44117e9i	0.529114	−	0.916452i
$545$	−1.23096e9			−0.325728
$546$	−6.48254e8	+	7.23224e8i	−0.170440	+	0.190151i
$547$	−3.23091e9			−0.844051			−0.422026	−	0.906584i	$-0.638681\pi$
$547$	−3.23091e9			−0.844051			−0.422026	+	0.906584i	$0.638681\pi$
$548$	−7.66327e8	+	1.32732e9i	−0.198922	+	0.344543i
$549$	1.27250e9	−	2.20403e9i	0.328212	−	0.568479i
$550$	1.59812e9	+	2.76802e9i	0.409580	+	0.709413i
$551$	2.93766e7			0.00748119
$552$	−5.90051e7	−	1.02200e8i	−0.0149315	−	0.0258621i
$553$	−4.33174e8	−	7.50279e8i	−0.108924	−	0.188662i
$554$	3.41508e9			0.853330
$555$	1.18940e8	+	2.06010e8i	0.0295326	+	0.0511519i
$556$	−4.24413e8	+	7.35105e8i	−0.104719	+	0.181379i
$557$	−5.73327e8	+	9.93031e8i	−0.140575	+	0.243484i	−0.927713	−	0.373293i	$-0.878229\pi$
$557$	−5.73327e8	+	9.93031e8i	−0.140575	+	0.243484i	0.787138	+	0.616777i	$0.211562\pi$
$558$	−2.04123e9			−0.497363
$559$	−2.17944e9	−	6.65664e9i	−0.527721	−	1.61181i
$560$	−6.30343e8			−0.151677
$561$	−1.90290e9	+	3.29592e9i	−0.455036	+	0.788145i
$562$	3.85288e9	−	6.67339e9i	0.915606	−	1.58588i
$563$	−1.52400e7	−	2.63965e7i	−0.00359920	−	0.00623400i	0.864220	−	0.503114i	$-0.167812\pi$
$563$	−1.52400e7	−	2.63965e7i	−0.00359920	−	0.00623400i	−0.867819	+	0.496880i	$0.834479\pi$
$564$	6.46901e8			0.151831
$565$	−1.92631e8	−	3.33647e8i	−0.0449322	−	0.0778248i
$566$	1.05493e9	+	1.82719e9i	0.244549	+	0.423571i
$567$	−1.03484e8			−0.0238415
$568$	2.85640e9	+	4.94742e9i	0.654033	+	1.13282i
$569$	3.31390e8	−	5.73985e8i	0.0754131	−	0.130619i	−0.825853	−	0.563886i	$-0.809306\pi$
$569$	3.31390e8	−	5.73985e8i	0.0754131	−	0.130619i	0.901266	+	0.433266i	$0.142639\pi$
$570$	−5.63150e8	+	9.75404e8i	−0.127368	+	0.220609i
$571$	−5.52956e9			−1.24298			−0.621490	−	0.783422i	$-0.713473\pi$
$571$	−5.52956e9			−1.24298			−0.621490	+	0.783422i	$0.713473\pi$
$572$	−1.02727e9	−	2.15939e8i	−0.229508	−	0.0482441i
$573$	4.64498e9			1.03144
$574$	−1.46462e9	+	2.53680e9i	−0.323246	+	0.559879i
$575$	−1.26003e8	+	2.18244e8i	−0.0276405	+	0.0478747i
$576$	8.41378e8	+	1.45731e9i	0.183448	+	0.317741i
$577$	2.66624e9			0.577807			0.288904	−	0.957358i	$-0.406709\pi$
$577$	2.66624e9			0.577807			0.288904	+	0.957358i	$0.406709\pi$
$578$	−6.72676e9	−	1.16511e10i	−1.44897	−	2.50968i
$579$	−1.24566e9	−	2.15754e9i	−0.266700	−	0.461939i
$580$	2.98622e6			0.000635512
$581$	−5.86062e8	−	1.01509e9i	−0.123973	−	0.214728i
$582$	−2.95155e9	+	5.11224e9i	−0.620612	+	1.07493i
$583$	−1.42678e9	+	2.47125e9i	−0.298206	+	0.516507i
$584$	4.72776e8			0.0982223
$585$	3.23959e8	+	9.89464e8i	0.0669028	+	0.204340i
$586$	8.59219e9			1.76385
$587$	2.65958e9	−	4.60653e9i	0.542725	−	0.940027i	−0.456021	−	0.889969i	$-0.650726\pi$
$587$	2.65958e9	−	4.60653e9i	0.542725	−	0.940027i	0.998746	−	0.0500584i	$-0.0159407\pi$
$588$	−6.05618e7	+	1.04896e8i	−0.0122851	+	0.0212784i
$589$	1.90478e9	+	3.29917e9i	0.384097	+	0.665275i
$590$	2.18159e9			0.437312
$591$	−1.39415e9	−	2.41473e9i	−0.277813	−	0.481186i
$592$	9.07240e8	+	1.57139e9i	0.179720	+	0.311284i
$593$	6.84428e9			1.34783			0.673917	−	0.738807i	$-0.264611\pi$
$593$	6.84428e9			1.34783			0.673917	+	0.738807i	$0.264611\pi$
$594$	2.30445e9	+	3.99143e9i	0.451144	+	0.781405i
$595$	−6.09253e8	+	1.05526e9i	−0.118574	+	0.205376i
$596$	−1.17403e9	+	2.03348e9i	−0.227153	+	0.393440i
$597$	−4.07554e9			−0.783926
$598$	−1.14854e8	−	3.50798e8i	−0.0219631	−	0.0670816i
$599$	−4.76045e9			−0.905011			−0.452506	−	0.891762i	$-0.649470\pi$
$599$	−4.76045e9			−0.905011			−0.452506	+	0.891762i	$0.649470\pi$
$600$	−1.12990e9	+	1.95704e9i	−0.213555	+	0.369888i
$601$	8.17153e8	−	1.41535e9i	0.153548	−	0.265952i	−0.778982	−	0.627047i	$-0.784264\pi$
$601$	8.17153e8	−	1.41535e9i	0.153548	−	0.265952i	0.932529	+	0.361095i	$0.117597\pi$
$602$	−1.94790e9	−	3.37386e9i	−0.363897	−	0.630288i
$603$	1.05854e9			0.196607
$604$	3.06296e8	+	5.30520e8i	0.0565603	+	0.0979653i
$605$	−3.09692e8	−	5.36402e8i	−0.0568573	−	0.0984797i
$606$	5.53780e9			1.01084
$607$	−2.01362e9	−	3.48769e9i	−0.365441	−	0.632962i	0.623406	−	0.781898i	$-0.285748\pi$
$607$	−2.01362e9	−	3.48769e9i	−0.365441	−	0.632962i	−0.988847	+	0.148936i	$0.952415\pi$
$608$	−1.76214e9	+	3.05211e9i	−0.317963	+	0.550729i
$609$	−4.14024e6	+	7.17111e6i	−0.000742788	+	0.00128655i
$610$	−2.15333e9			−0.384111
$611$	−4.87090e9	−	1.02389e9i	−0.863903	−	0.181598i
$612$	−1.99525e9			−0.351858
$613$	−7.13768e8	+	1.23628e9i	−0.125154	+	0.216774i	−0.921793	−	0.387682i	$-0.873276\pi$
$613$	−7.13768e8	+	1.23628e9i	−0.125154	+	0.216774i	0.796639	+	0.604455i	$0.206609\pi$
$614$	−3.00536e8	+	5.20543e8i	−0.0523970	+	0.0907543i
$615$	−8.60761e8	−	1.49088e9i	−0.149218	−	0.258452i
$616$	1.43619e9			0.247560
$617$	−8.84353e8	−	1.53174e9i	−0.151575	−	0.262536i	0.780232	−	0.625491i	$-0.215101\pi$
$617$	−8.84353e8	−	1.53174e9i	−0.151575	−	0.262536i	−0.931807	+	0.362955i	$0.881768\pi$
$618$	3.20714e9	+	5.55493e9i	0.546586	+	0.946714i
$619$	−5.85600e9			−0.992393			−0.496196	−	0.868210i	$-0.665270\pi$
$619$	−5.85600e9			−0.992393			−0.496196	+	0.868210i	$0.665270\pi$
$620$	1.93627e8	+	3.35371e8i	0.0326283	+	0.0565138i
$621$	−1.81695e8	+	3.14705e8i	−0.0304454	+	0.0527330i
$622$	−2.77917e9	+	4.81367e9i	−0.463073	+	0.802065i
$623$	1.78443e9			0.295658
$624$	−1.35473e9	−	4.13774e9i	−0.223207	−	0.681737i
$625$	4.14934e9			0.679829
$626$	−4.50467e9	+	7.80232e9i	−0.733927	+	1.27120i
$627$	1.68776e9	−	2.92328e9i	0.273447	−	0.473624i
$628$	4.03906e8	+	6.99586e8i	0.0650762	+	0.112715i
$629$	3.50755e9			0.561987
$630$	2.89542e8	+	5.01501e8i	0.0461338	+	0.0799060i
$631$	4.84081e9	+	8.38454e9i	0.767036	+	1.32855i	0.939163	+	0.343471i	$0.111603\pi$
$631$	4.84081e9	+	8.38454e9i	0.767036	+	1.32855i	−0.172128	+	0.985075i	$0.555064\pi$
$632$	2.95254e9			0.465250
$633$	−1.69959e9	−	2.94378e9i	−0.266337	−	0.461310i
$634$	−6.57584e9	+	1.13897e10i	−1.02480	+	1.77500i
$635$	1.36562e9	−	2.36532e9i	0.211652	−	0.366591i
$636$	8.20174e8			0.126417
$637$	6.22033e8	−	6.93971e8i	0.0953510	−	0.106378i
$638$	−3.99143e7			−0.00608494
$639$	3.45169e9	−	5.97851e9i	0.523334	−	0.906441i
$640$	1.33165e9	−	2.30648e9i	0.200798	−	0.347792i
$641$	4.49202e8	+	7.78040e8i	0.0673656	+	0.116681i	0.897741	−	0.440524i	$-0.145207\pi$
$641$	4.49202e8	+	7.78040e8i	0.0673656	+	0.116681i	−0.830375	+	0.557205i	$0.811874\pi$
$642$	−5.00980e9			−0.747219
$643$	−3.48981e9	−	6.04453e9i	−0.517682	−	0.896652i	−0.999789	−	0.0205395i	$-0.993462\pi$
$643$	−3.48981e9	−	6.04453e9i	−0.517682	−	0.896652i	0.482107	−	0.876112i	$-0.339872\pi$
$644$	−2.30169e7	−	3.98664e7i	−0.00339583	−	0.00588176i
$645$	2.28957e9			0.335966
$646$	8.30368e9	+	1.43824e10i	1.21187	+	2.09903i
$647$	−8.45999e8	+	1.46531e9i	−0.122802	+	0.212699i	−0.920872	−	0.389866i	$-0.872521\pi$
$647$	−8.45999e8	+	1.46531e9i	−0.122802	+	0.212699i	0.798070	+	0.602565i	$0.205855\pi$
$648$	1.76339e8	−	3.05428e8i	0.0254587	−	0.0440957i
$649$	−6.53822e9			−0.938865
$650$	−4.71783e9	+	5.26345e9i	−0.673823	+	0.751750i
$651$	−1.07381e9			−0.152544
$652$	−4.41685e8	+	7.65020e8i	−0.0624088	+	0.108095i
$653$	−5.27127e9	+	9.13011e9i	−0.740831	+	1.28316i	0.211287	+	0.977424i	$0.432235\pi$
$653$	−5.27127e9	+	9.13011e9i	−0.740831	+	1.28316i	−0.952117	+	0.305733i	$0.901099\pi$
$654$	−2.36450e9	−	4.09544e9i	−0.330535	−	0.572504i
$655$	−3.38464e9			−0.470618
$656$	−6.56566e9	−	1.13721e10i	−0.908061	−	1.57281i
$657$	−2.85653e8	−	4.94765e8i	−0.0392970	−	0.0680645i
$658$	−2.76839e9			−0.378823
$659$	1.29089e9	+	2.23589e9i	0.175708	+	0.304335i	0.940406	−	0.340054i	$-0.110445\pi$
$659$	1.29089e9	+	2.23589e9i	0.175708	+	0.304335i	−0.764698	+	0.644389i	$0.777112\pi$
$660$	1.71566e8	−	2.97160e8i	0.0232288	−	0.0402334i
$661$	−7.35063e9	+	1.27317e10i	−0.989965	+	1.71467i	−0.372600	+	0.927992i	$0.621534\pi$
$661$	−7.35063e9	+	1.27317e10i	−0.989965	+	1.71467i	−0.617365	+	0.786677i	$0.711800\pi$
$662$	9.83465e9			1.31752
$663$	−8.23640e9	−	1.73134e9i	−1.09759	−	0.230720i
$664$	3.99464e9			0.529529
$665$	5.40371e8	−	9.35951e8i	0.0712552	−	0.123418i
$666$	8.33463e8	−	1.44360e9i	0.109327	−	0.189360i
$667$	−1.57352e6	−	2.72542e6i	−0.000205321	−	0.000355626i
$668$	−2.25229e9			−0.292353
$669$	−2.28854e9	−	3.96387e9i	−0.295506	−	0.511832i
$670$	−4.47818e8	−	7.75644e8i	−0.0575228	−	0.0996325i
$671$	6.45352e9			0.824646
$672$	−4.96700e8	−	8.60309e8i	−0.0631395	−	0.109361i
$673$	2.80736e9	−	4.86249e9i	0.355014	−	0.614902i	−0.632107	−	0.774881i	$-0.717810\pi$
$673$	2.80736e9	−	4.86249e9i	0.355014	−	0.614902i	0.987120	+	0.159980i	$0.0511428\pi$
$674$	1.79467e9	−	3.10845e9i	0.225774	−	0.391052i
$675$	6.95860e9			0.870881
$676$	−2.53041e8	−	2.30759e9i	−0.0315048	−	0.287307i
$677$	−4.97590e9			−0.616327			−0.308163	−	0.951333i	$-0.599714\pi$
$677$	−4.97590e9			−0.616327			−0.308163	+	0.951333i	$0.599714\pi$
$678$	7.40038e8	−	1.28178e9i	0.0911906	−	0.157947i
$679$	2.83217e9	−	4.90546e9i	0.347196	−	0.601361i
$680$	−2.07636e9	−	3.59636e9i	−0.253233	−	0.438613i
$681$	1.43352e9			0.173935
$682$	−2.58805e9	−	4.48263e9i	−0.312411	−	0.541112i
$683$	2.36846e9	+	4.10229e9i	0.284442	+	0.492667i	0.972474	−	0.233013i	$-0.0748585\pi$
$683$	2.36846e9	+	4.10229e9i	0.284442	+	0.492667i	−0.688032	+	0.725680i	$0.741525\pi$
$684$	1.76967e9			0.211444
$685$	1.92736e9	+	3.33828e9i	0.229110	+	0.396831i
$686$	2.59172e8	−	4.48900e8i	0.0306517	−	0.0530903i
$687$	1.08944e8	−	1.88697e8i	0.0128190	−	0.0222032i
$688$	1.74642e10			2.04451
$689$	−6.17558e9	−	1.29815e9i	−0.719301	−	0.151201i
$690$	1.20658e8			0.0139825
$691$	−3.07607e9	+	5.32791e9i	−0.354669	+	0.614305i	−0.987061	−	0.160343i	$-0.948740\pi$
$691$	−3.07607e9	+	5.32791e9i	−0.354669	+	0.614305i	0.632392	+	0.774648i	$0.282073\pi$
$692$	−1.86096e9	+	3.22327e9i	−0.213484	+	0.369765i
$693$	−8.67754e8	−	1.50299e9i	−0.0990445	−	0.171550i
$694$	1.23682e9			0.140459
$695$	1.06742e9	+	1.84883e9i	0.120612	+	0.208906i
$696$	−1.41101e7	−	2.44394e7i	−0.00158634	−	0.00274763i
$697$	−2.53840e10			−2.83952
$698$	3.08319e9	+	5.34025e9i	0.343168	+	0.594384i
$699$	3.90949e9	−	6.77143e9i	0.432962	−	0.749912i
$700$	−4.40754e8	+	7.63409e8i	−0.0485683	+	0.0841228i
$701$	−2.12270e9			−0.232742			−0.116371	−	0.993206i	$-0.537126\pi$
$701$	−2.12270e9			−0.232742			−0.116371	+	0.993206i	$0.537126\pi$
$702$	−6.80303e9	+	7.58980e9i	−0.742202	+	0.828038i
$703$	−3.11098e9			−0.337718
$704$	−2.13354e9	+	3.69539e9i	−0.230460	+	0.399169i
$705$	8.13495e8	−	1.40902e9i	0.0874366	−	0.151445i
$706$	1.68459e9	+	2.91779e9i	0.180168	+	0.312059i
$707$	−5.31381e9			−0.565507
$708$	9.39614e8	+	1.62746e9i	0.0995023	+	0.172343i
$709$	−2.82655e9	−	4.89572e9i	−0.297848	−	0.515888i	0.677796	−	0.735250i	$-0.262935\pi$
$709$	−2.82655e9	−	4.89572e9i	−0.297848	−	0.515888i	−0.975643	+	0.219363i	$0.929602\pi$
$710$	−5.84098e9			−0.612465
$711$	−1.78394e9	−	3.08987e9i	−0.186138	−	0.322401i
$712$	−3.04069e9	+	5.26663e9i	−0.315713	+	0.546831i
$713$	2.04055e8	−	3.53433e8i	0.0210830	−	0.0365169i
$714$	−4.68118e9			−0.481295
$715$	−1.76216e9	+	1.96595e9i	−0.180291	+	0.201141i
$716$	4.33172e9			0.441027
$717$	2.46259e9	−	4.26534e9i	0.249503	−	0.432152i
$718$	1.01095e10	−	1.75102e10i	1.01928	−	1.76545i
$719$	−1.03614e9	−	1.79465e9i	−0.103960	−	0.180065i	0.809353	−	0.587323i	$-0.199818\pi$
$719$	−1.03614e9	−	1.79465e9i	−0.103960	−	0.180065i	−0.913313	+	0.407258i	$0.866485\pi$
$720$	−2.59594e9			−0.259197
$721$	−3.07742e9	−	5.33024e9i	−0.305783	−	0.529631i
$722$	−1.62395e9	−	2.81276e9i	−0.160580	−	0.278133i
$723$	−8.16177e8			−0.0803157
$724$	−2.27961e8	−	3.94840e8i	−0.0223242	−	0.0386666i
$725$	−3.01317e7	+	5.21896e7i	−0.00293657	+	0.00508628i
$726$	1.18975e9	−	2.06071e9i	0.115393	−	0.199866i
$727$	6.01611e9			0.580691			0.290346	−	0.956922i	$-0.406230\pi$
$727$	6.01611e9			0.580691			0.290346	+	0.956922i	$0.406230\pi$
$728$	9.88262e8	+	3.01843e9i	0.0949319	+	0.289949i
$729$	5.67030e9			0.542076
$730$	−2.41692e8	+	4.18623e8i	−0.0229949	+	0.0398284i
$731$	1.68799e10	−	2.92369e10i	1.59831	−	2.76835i
$732$	−9.27441e8	−	1.60638e9i	−0.0873972	−	0.151376i
$733$	−1.16913e10			−1.09647			−0.548237	−	0.836323i	$-0.684701\pi$
$733$	−1.16913e10			−1.09647			−0.548237	+	0.836323i	$0.684701\pi$
$734$	−2.70339e9	−	4.68241e9i	−0.252332	−	0.437052i
$735$	1.52316e8	+	2.63820e8i	0.0141495	+	0.0245076i
$736$	3.77548e8			0.0349059
$737$	1.34211e9	+	2.32460e9i	0.123496	+	0.213901i
$738$	−6.03174e9	+	1.04473e10i	−0.552389	+	0.956766i
$739$	−4.15883e9	+	7.20331e9i	−0.379067	+	0.656563i	−0.990927	−	0.134403i	$-0.957088\pi$
$739$	−4.15883e9	+	7.20331e9i	−0.379067	+	0.656563i	0.611860	+	0.790966i	$0.290422\pi$
$740$	−3.16241e8			−0.0286885
$741$	7.30519e9	+	1.53560e9i	0.659581	+	0.138648i
$742$	−3.50991e9			−0.315415
$743$	−2.39489e7	+	4.14807e7i	−0.00214203	+	0.00371010i	−0.867094	−	0.498144i	$-0.834015\pi$
$743$	−2.39489e7	+	4.14807e7i	−0.00214203	+	0.00371010i	0.864952	+	0.501854i	$0.167348\pi$
$744$	1.82980e9	−	3.16930e9i	0.162891	−	0.282136i
$745$	2.95275e9	+	5.11432e9i	0.261626	+	0.453149i
$746$	1.63836e10			1.44485
$747$	−2.41358e9	−	4.18044e9i	−0.211855	−	0.366944i
$748$	−2.52975e9	−	4.38165e9i	−0.221015	−	0.382809i
$749$	4.80716e9			0.418025
$750$	−2.45447e9	−	4.25128e9i	−0.212444	−	0.367964i
$751$	−2.91007e8	+	5.04039e8i	−0.0250706	+	0.0434235i	−0.878288	−	0.478131i	$-0.841314\pi$
$751$	−2.91007e8	+	5.04039e8i	−0.0250706	+	0.0434235i	0.853218	+	0.521555i	$0.174648\pi$
$752$	6.20513e9	−	1.07476e10i	0.532094	−	0.921614i
$753$	−6.66781e9			−0.569116
$754$	−2.74655e7	−	8.38876e7i	−0.00233339	−	0.00712685i
$755$	1.54070e9			0.130288
$756$	−6.35559e8	+	1.10082e9i	−0.0534971	+	0.0926596i
$757$	2.78728e9	−	4.82770e9i	0.233531	−	0.404488i	−0.725314	−	0.688418i	$-0.758305\pi$
$757$	2.78728e9	−	4.82770e9i	0.233531	−	0.404488i	0.958845	+	0.283931i	$0.0916386\pi$
$758$	1.13350e10	+	1.96327e10i	0.945318	+	1.63734i
$759$	−3.61611e8			−0.0300190
$760$	1.84160e9	+	3.18975e9i	0.152177	+	0.263578i
$761$	3.71827e9	+	6.44023e9i	0.305840	+	0.529730i	0.977448	−	0.211176i	$-0.0677294\pi$
$761$	3.71827e9	+	6.44023e9i	0.305840	+	0.529730i	−0.671608	+	0.740907i	$0.734396\pi$
$762$	1.04927e10			0.859101
$763$	2.26886e9	+	3.92978e9i	0.184915	+	0.320282i
$764$	−3.08756e9	+	5.34782e9i	−0.250489	+	0.433860i
$765$	−2.50909e9	+	4.34586e9i	−0.202628	+	0.350963i
$766$	−1.15871e10			−0.931480
$767$	−4.49903e9	−	1.37413e10i	−0.360027	−	1.09962i
$768$	5.98830e9			0.477023
$769$	−1.04159e10	+	1.80410e10i	−0.825955	+	1.43060i	0.0752315	+	0.997166i	$0.476030\pi$
$769$	−1.04159e10	+	1.80410e10i	−0.825955	+	1.43060i	−0.901187	+	0.433431i	$0.857303\pi$
$770$	−7.34209e8	+	1.27169e9i	−0.0579565	+	0.100384i
$771$	−2.84515e9	−	4.92794e9i	−0.223570	−	0.387235i
$772$	3.31200e9			0.259077
$773$	7.40099e8	+	1.28189e9i	0.0576318	+	0.0998211i	0.893402	−	0.449258i	$-0.148312\pi$
$773$	7.40099e8	+	1.28189e9i	0.0576318	+	0.0998211i	−0.835770	+	0.549080i	$0.814978\pi$
$774$	−8.02202e9	−	1.38945e10i	−0.621857	−	1.07709i
$775$	−7.81494e9			−0.603073
$776$	9.65212e9	+	1.67180e10i	0.741493	+	1.28430i
$777$	4.38452e8	−	7.59421e8i	0.0335312	−	0.0580777i
$778$	1.21967e10	−	2.11253e10i	0.928567	−	1.60833i
$779$	2.25141e10			1.70637
$780$	7.42595e8	+	1.56098e8i	0.0560301	+	0.0117779i
$781$	1.75054e10			1.31490
$782$	8.89555e8	−	1.54076e9i	0.0665196	−	0.115215i
$783$	−4.34493e7	+	7.52564e7i	−0.00323457	+	0.00560244i
$784$	1.16183e9	+	2.01235e9i	0.0861065	+	0.149141i
$785$	2.03169e9			0.149904
$786$	−6.50145e9	−	1.12608e10i	−0.477564	−	0.827165i
$787$	6.02082e9	+	1.04284e10i	0.440295	+	0.762614i	0.997711	−	0.0676194i	$-0.0215404\pi$
$787$	6.02082e9	+	1.04284e10i	0.440295	+	0.762614i	−0.557416	+	0.830234i	$0.688207\pi$
$788$	3.70681e9			0.269872
$789$	3.68061e9	+	6.37501e9i	0.266778	+	0.462074i
$790$	−1.50940e9	+	2.61435e9i	−0.108920	+	0.188655i
$791$	−7.10104e8	+	1.22994e9i	−0.0510158	+	0.0883619i
$792$	5.91467e9			0.423051
$793$	4.44074e9	+	1.35633e10i	0.316227	+	0.965848i
$794$	1.94919e9			0.138192
$795$	1.03139e9	−	1.78642e9i	0.0728012	−	0.126095i
$796$	2.70905e9	−	4.69221e9i	0.190380	−	0.329748i
$797$	6.59359e9	+	1.14204e10i	0.461337	+	0.799059i	0.999028	−	0.0440833i	$-0.0140367\pi$
$797$	6.59359e9	+	1.14204e10i	0.461337	+	0.799059i	−0.537691	+	0.843142i	$0.680703\pi$
$798$	4.15192e9			0.289227
$799$	−1.19950e10	−	2.07760e10i	−0.831933	−	1.44095i
$800$	−3.61486e9	−	6.26112e9i	−0.249618	−	0.432351i
$801$	7.34879e9			0.505245
$802$	1.55966e8	+	2.70142e8i	0.0106763	+	0.0184919i
$803$	7.24349e8	−	1.25461e9i	0.0493677	−	0.0855074i
$804$	3.85752e8	−	6.68141e8i	0.0261765	−	0.0453390i
$805$	−1.15778e8			−0.00782238
$806$	7.64023e9	−	8.52382e9i	0.513965	−	0.573405i
$807$	−4.66591e7			−0.00312521
$808$	9.05482e9	−	1.56834e10i	0.603865	−	1.04593i
$809$	−4.94038e9	+	8.55699e9i	−0.328050	+	0.568200i	−0.982125	−	0.188230i	$-0.939725\pi$
$809$	−4.94038e9	+	8.55699e9i	−0.328050	+	0.568200i	0.654075	+	0.756430i	$0.273058\pi$
$810$	1.80296e8	+	3.12281e8i	0.0119203	+	0.0206466i
$811$	2.25578e10			1.48499			0.742494	−	0.669852i	$-0.233643\pi$
$811$	2.25578e10			1.48499			0.742494	+	0.669852i	$0.233643\pi$
$812$	−5.50411e6	−	9.53340e6i	−0.000360779	−	0.000624887i
$813$	1.24708e9	+	2.16000e9i	0.0813911	+	0.140974i
$814$	4.22693e9			0.274688
$815$	1.11086e9	+	1.92407e9i	0.0718800	+	0.124500i
$816$	1.04925e10	−	1.81735e10i	0.676025	−	1.17091i
$817$	−1.49715e10	+	2.59314e10i	−0.960479	+	1.66360i
$818$	−9.15086e9			−0.584555
$819$	2.56172e9	−	2.85798e9i	0.162944	−	0.181788i
$820$	2.28862e9			0.144953
$821$	−4.54905e8	+	7.87918e8i	−0.0286893	+	0.0496913i	−0.880014	−	0.474949i	$-0.842467\pi$
$821$	−4.54905e8	+	7.87918e8i	−0.0286893	+	0.0496913i	0.851324	+	0.524640i	$0.175800\pi$
$822$	−7.40438e9	+	1.28248e10i	−0.464984	+	0.805375i
$823$	−3.27919e9	−	5.67973e9i	−0.205054	−	0.355163i	0.745096	−	0.666957i	$-0.232404\pi$
$823$	−3.27919e9	−	5.67973e9i	−0.205054	−	0.355163i	−0.950150	+	0.311794i	$0.899070\pi$
$824$	2.09759e10			1.30610
$825$	3.46227e9	+	5.99683e9i	0.214671	+	0.371820i
$826$	−4.02105e9	−	6.96466e9i	−0.248261	−	0.430001i
$827$	6.55505e9			0.403002			0.201501	−	0.979488i	$-0.435418\pi$
$827$	6.55505e9			0.403002			0.201501	+	0.979488i	$0.435418\pi$
$828$	−9.47904e7	−	1.64182e8i	−0.00580308	−	0.0100512i
$829$	−7.12947e9	+	1.23486e10i	−0.434627	+	0.752795i	−0.997265	−	0.0739077i	$-0.976453\pi$
$829$	−7.12947e9	+	1.23486e10i	−0.434627	+	0.752795i	0.562638	+	0.826703i	$0.309786\pi$
$830$	−2.04214e9	+	3.53708e9i	−0.123969	+	0.214720i
$831$	7.39868e9			0.447251
$832$	−9.23468e9	−	1.94119e9i	−0.555892	−	0.116852i
$833$	4.49183e9			0.269256
$834$	−4.10075e9	+	7.10271e9i	−0.244784	+	0.423978i
$835$	−2.83232e9	+	4.90572e9i	−0.168360	+	0.291609i
$836$	2.24373e9	+	3.88626e9i	0.132816	+	0.230044i
$837$	−1.12690e10			−0.664273
$838$	7.97072e9	+	1.38057e10i	0.467890	+	0.810409i
$839$	−4.34350e9	−	7.52317e9i	−0.253906	−	0.439778i	0.710692	−	0.703504i	$-0.248382\pi$
$839$	−4.34350e9	−	7.52317e9i	−0.253906	−	0.439778i	−0.964598	+	0.263725i	$0.915049\pi$
$840$	−1.03820e9			−0.0604370
$841$	8.62456e9	+	1.49382e10i	0.499978	+	0.865988i
$842$	−6.25536e9	+	1.08346e10i	−0.361127	+	0.625491i
$843$	8.34716e9	−	1.44577e10i	0.479891	−	0.831195i
$844$	4.51894e9			0.258725
$845$	−5.34438e9	−	2.35071e9i	−0.304718	−	0.134030i
$846$	−1.14010e10			−0.647364
$847$	−1.14163e9	+	1.97736e9i	−0.0645555	+	0.111813i
$848$	7.86718e9	−	1.36264e10i	0.443030	−	0.767351i
$849$	2.28548e9	+	3.95856e9i	0.128174	+	0.222004i
$850$	−3.40685e10			−1.90277
$851$	1.66636e8	+	2.88623e8i	0.00926865	+	0.0160538i
$852$	−2.51571e9	−	4.35734e9i	−0.139355	−	0.241370i
$853$	2.04833e10			1.13000			0.565001	−	0.825090i	$-0.308876\pi$
$853$	2.04833e10			1.13000			0.565001	+	0.825090i	$0.308876\pi$
$854$	3.96895e9	+	6.87443e9i	0.218059	+	0.377689i
$855$	2.22541e9	−	3.85452e9i	0.121767	−	0.210906i
$856$	−8.19149e9	+	1.41881e10i	−0.446380	+	0.773153i
$857$	−2.46261e10			−1.33648			−0.668241	−	0.743945i	$-0.732953\pi$
$857$	−2.46261e10			−1.33648			−0.668241	+	0.743945i	$0.732953\pi$
$858$	−9.92566e9	−	2.08644e9i	−0.536480	−	0.112772i
$859$	−2.92171e9			−0.157276			−0.0786378	−	0.996903i	$-0.525057\pi$
$859$	−2.92171e9			−0.157276			−0.0786378	+	0.996903i	$0.525057\pi$
$860$	−1.52190e9	+	2.63601e9i	−0.0815908	+	0.141319i
$861$	−3.17306e9	+	5.49590e9i	−0.169421	+	0.293446i
$862$	−3.34053e9	−	5.78597e9i	−0.177640	−	0.307681i
$863$	2.05754e10			1.08971			0.544854	−	0.838531i	$-0.316585\pi$
$863$	2.05754e10			1.08971			0.544854	+	0.838531i	$0.316585\pi$
$864$	−5.21256e9	−	9.02842e9i	−0.274949	−	0.476226i
$865$	4.68041e9	+	8.10670e9i	0.245882	+	0.425880i
$866$	−2.08557e10			−1.09122
$867$	−1.45733e10	−	2.52418e10i	−0.759438	−	1.31538i
$868$	7.13773e8	−	1.23629e9i	0.0370460	−	0.0641655i
$869$	4.52365e9	−	7.83519e9i	0.233840	−	0.405024i
$870$	2.88534e7			0.00148552
$871$	−3.96207e9	+	4.42028e9i	−0.203169	+	0.226666i
$872$	−1.54647e10			−0.789832
$873$	1.16637e10	−	2.02021e10i	0.593316	−	1.02765i
$874$	−7.88982e8	+	1.36656e9i	−0.0399740	+	0.0692369i
$875$	2.35519e9	+	4.07932e9i	0.118850	+	0.205854i
$876$	−4.16387e8			−0.0209283
$877$	1.45470e9	+	2.51961e9i	0.0728239	+	0.126135i	0.900138	−	0.435605i	$-0.143466\pi$
$877$	1.45470e9	+	2.51961e9i	0.0728239	+	0.126135i	−0.827314	+	0.561740i	$0.810132\pi$
$878$	−7.44945e9	−	1.29028e10i	−0.371444	−	0.643360i
$879$	1.86147e10			0.924477
$880$	−3.29135e9	−	5.70078e9i	−0.162811	−	0.281997i
$881$	1.15834e9	−	2.00631e9i	0.0570718	−	0.0988513i	−0.836078	−	0.548611i	$-0.815157\pi$
$881$	1.15834e9	−	2.00631e9i	0.0570718	−	0.0988513i	0.893150	+	0.449759i	$0.148490\pi$
$882$	1.06735e9	−	1.84870e9i	0.0523801	−	0.0907250i
$883$	−2.85382e10			−1.39497			−0.697484	−	0.716600i	$-0.745697\pi$
$883$	−2.85382e10			−1.39497			−0.697484	+	0.716600i	$0.745697\pi$
$884$	7.46812e9	−	8.33181e9i	0.363604	−	0.405655i
$885$	4.72636e9			0.229206
$886$	−4.58915e9	+	7.94865e9i	−0.221674	+	0.383951i
$887$	−4.80546e9	+	8.32331e9i	−0.231208	+	0.400464i	−0.958164	−	0.286220i	$-0.907601\pi$
$887$	−4.80546e9	+	8.32331e9i	−0.231208	+	0.400464i	0.726956	+	0.686684i	$0.240934\pi$
$888$	1.49426e9	+	2.58813e9i	0.0716112	+	0.124034i
$889$	−1.00683e10			−0.480617
$890$	−3.10892e9	−	5.38480e9i	−0.147824	−	0.256038i
$891$	−5.40344e8	−	9.35904e8i	−0.0255917	−	0.0443261i
$892$	6.08485e9			0.287060
$893$	1.06389e10	+	1.84271e10i	0.499938	+	0.865918i
$894$	−1.13437e10	+	1.96478e10i	−0.530973	+	0.919673i
$895$	5.44726e9	−	9.43493e9i	0.253979	−	0.439904i
$896$	−9.81780e9			−0.455970
$897$	−2.48829e8	−	7.59995e8i	−0.0115114	−	0.0351590i
$898$	6.63539e9			0.305773
$899$	4.87963e7	−	8.45176e7i	0.00223990	−	0.00387961i
$900$	−1.81516e9	+	3.14394e9i	−0.0829975	+	0.143756i
$901$	−1.52079e10	−	2.63409e10i	−0.692681	−	1.19976i
$902$	−3.05901e10			−1.38790
$903$	−4.22007e9	−	7.30937e9i	−0.190727	−	0.330349i
$904$	−2.42006e9	−	4.19167e9i	−0.108952	−	0.188711i
$905$	−1.14667e9			−0.0514242
$906$	2.95948e9	+	5.12597e9i	0.132211	+	0.228996i
$907$	−1.21279e10	+	2.10061e10i	−0.539709	+	0.934803i	0.459211	+	0.888327i	$0.348132\pi$
$907$	−1.21279e10	+	2.10061e10i	−0.539709	+	0.934803i	−0.998919	+	0.0464755i	$0.985201\pi$
$908$	−9.52871e8	+	1.65042e9i	−0.0422409	+	0.0731634i
$909$	−2.18838e10			−0.966384
$910$	−3.17791e9	−	6.68017e8i	−0.139797	−	0.0293861i
$911$	−1.79177e10			−0.785176			−0.392588	−	0.919714i	$-0.628420\pi$
$911$	−1.79177e10			−0.785176			−0.392588	+	0.919714i	$0.628420\pi$
$912$	−9.30621e9	+	1.61188e10i	−0.406248	+	0.703642i
$913$	6.12027e9	−	1.06006e10i	0.266148	−	0.460981i
$914$	−2.40176e10	−	4.15996e10i	−1.04044	−	1.80210i
$915$	−4.66513e9			−0.201322
$916$	1.44832e8	+	2.50857e8i	0.00622631	+	0.0107843i
$917$	6.23848e9	+	1.08054e10i	0.267169	+	0.462750i
$918$	−4.91261e10			−2.09586
$919$	−1.36926e10	−	2.37163e10i	−0.581945	−	1.00796i	−0.995249	−	0.0973645i	$-0.968959\pi$
$919$	−1.36926e10	−	2.37163e10i	−0.581945	−	1.00796i	0.413304	−	0.910593i	$-0.364375\pi$
$920$	1.97287e8	−	3.41711e8i	0.00835297	−	0.0144678i
$921$	−6.51102e8	+	1.12774e9i	−0.0274625	+	0.0475665i
$922$	9.28568e9			0.390171
$923$	1.20456e10	+	3.67908e10i	0.504225	+	1.54005i
$924$	−1.26490e9			−0.0527477
$925$	3.19095e9	−	5.52688e9i	0.132563	−	0.229606i
$926$	−1.07434e10	+	1.86081e10i	−0.444633	+	0.770127i
$927$	−1.26737e10	−	2.19515e10i	−0.522546	−	0.905076i
$928$	9.02843e7			0.00370846
$929$	6.68162e8	+	1.15729e9i	0.0273418	+	0.0473574i	0.879373	−	0.476134i	$-0.157962\pi$
$929$	6.68162e8	+	1.15729e9i	0.0273418	+	0.0473574i	−0.852031	+	0.523492i	$0.824629\pi$
$930$	1.87085e9	+	3.24041e9i	0.0762692	+	0.132102i
$931$	−3.98398e9			−0.161806
$932$	5.19735e9	+	9.00207e9i	0.210294	+	0.364239i
$933$	−6.02100e9	+	1.04287e10i	−0.242707	+	0.420382i
$934$	2.82472e10	−	4.89255e10i	1.13439	−	1.96481i
$935$	−1.27249e10			−0.509113
$936$	4.06995e9	+	1.24308e10i	0.162227	+	0.495489i
$937$	−3.13419e10			−1.24462			−0.622309	−	0.782771i	$-0.713805\pi$
$937$	−3.13419e10			−1.24462			−0.622309	+	0.782771i	$0.713805\pi$
$938$	−1.65081e9	+	2.85929e9i	−0.0653112	+	0.113122i
$939$	−9.75925e9	+	1.69035e10i	−0.384669	+	0.666266i
$940$	1.08148e9	+	1.87317e9i	0.0424687	+	0.0735580i
$941$	1.91364e10			0.748679			0.374339	−	0.927292i	$-0.377870\pi$
$941$	1.91364e10			0.748679			0.374339	+	0.927292i	$0.377870\pi$
$942$	3.90261e9	+	6.75952e9i	0.152117	+	0.263474i
$943$	−1.20594e9	−	2.08875e9i	−0.0468312	−	0.0811140i
$944$	3.60515e10			1.39483
$945$	1.59847e9	+	2.76863e9i	0.0616158	+	0.106722i
$946$	2.03420e10	−	3.52333e10i	0.781221	−	1.35311i
$947$	4.80551e9	−	8.32339e9i	0.183872	−	0.318475i	−0.759324	−	0.650713i	$-0.774470\pi$
$947$	4.80551e9	−	8.32339e9i	0.183872	−	0.318475i	0.943196	+	0.332238i	$0.107804\pi$
$948$	−2.60039e9			−0.0991310
$949$	3.13523e9	+	6.59045e8i	0.119080	+	0.0250313i
$950$	3.02167e10			1.14344
$951$	−1.42464e10	+	2.46754e10i	−0.537121	+	0.930322i
$952$	−7.65416e9	+	1.32574e10i	−0.287520	+	0.497999i
$953$	2.34017e10	+	4.05329e10i	0.875834	+	1.51699i	0.855871	+	0.517189i	$0.173021\pi$
$953$	2.34017e10	+	4.05329e10i	0.875834	+	1.51699i	0.0199627	+	0.999801i	$0.493645\pi$
$954$	−1.44548e10			−0.539006
$955$	7.76539e9	+	1.34501e10i	0.288504	+	0.499703i
$956$	3.27382e9	+	5.67042e9i	0.121186	+	0.209900i
$957$	−8.64733e7			−0.00318926
$958$	4.59715e9	+	7.96250e9i	0.168931	+	0.292597i
$959$	7.10489e9	−	1.23060e10i	0.260131	−	0.450560i
$960$	1.54230e9	−	2.67133e9i	0.0562624	−	0.0974493i
$961$	−1.48568e10			−0.540000
$962$	2.90860e9	+	8.88370e9i	0.105335	+	0.321722i
$963$	1.97973e10			0.714355
$964$	5.42521e8	−	9.39673e8i	0.0195050	−	0.0337837i
$965$	4.16493e9	−	7.21387e9i	0.149198	−	0.258418i
$966$	−2.22393e8	−	3.85196e8i	−0.00793783	−	0.0137487i
$967$	5.26647e10			1.87295			0.936476	−	0.350731i	$-0.114067\pi$
$967$	5.26647e10			1.87295			0.936476	+	0.350731i	$0.114067\pi$
$968$	−3.89072e9	−	6.73892e9i	−0.137869	−	0.238796i
$969$	1.79897e10	+	3.11591e10i	0.635171	+	1.10015i
$970$	−1.97374e10			−0.694366
$971$	1.24062e10	+	2.14882e10i	0.434884	+	0.753241i	0.997286	−	0.0736230i	$-0.0234562\pi$
$971$	1.24062e10	+	2.14882e10i	0.434884	+	0.753241i	−0.562402	+	0.826864i	$0.690123\pi$
$972$	−4.20769e9	+	7.28794e9i	−0.146964	+	0.254550i
$973$	3.93488e9	−	6.81542e9i	0.136942	−	0.237191i
$974$	3.29407e10			1.14229
$975$	−1.02211e10	+	1.14031e10i	−0.353166	+	0.394010i
$976$	−3.55844e10			−1.22514
$977$	−3.10732e9	+	5.38203e9i	−0.106599	+	0.184635i	−0.914390	−	0.404833i	$-0.867330\pi$
$977$	−3.10732e9	+	5.38203e9i	−0.106599	+	0.184635i	0.807791	+	0.589469i	$0.200663\pi$
$978$	−4.26763e9	+	7.39176e9i	−0.145882	+	0.252675i
$979$	9.31741e9	+	1.61382e10i	0.317362	+	0.549688i
$980$	−4.04984e8			−0.0137451
$981$	9.34385e9	+	1.61840e10i	0.315998	+	0.547324i
$982$	−6.39524e9	−	1.10769e10i	−0.215509	−	0.373273i
$983$	−2.58238e10			−0.867128			−0.433564	−	0.901123i	$-0.642744\pi$
$983$	−2.58238e10			−0.867128			−0.433564	+	0.901123i	$0.642744\pi$
$984$	−1.08139e10	−	1.87302e10i	−0.361826	−	0.626700i
$985$	4.66141e9	−	8.07381e9i	0.155414	−	0.269185i
$986$	2.12722e8	−	3.68446e8i	0.00706715	−	0.0122407i
$987$	−5.99764e9			−0.198550
$988$	−6.62378e9	+	7.38981e9i	−0.218502	+	0.243772i
$989$	3.20773e9			0.105441
$990$	−3.02369e9	+	5.23719e9i	−0.0990408	+	0.171544i
$991$	−2.49317e9	+	4.31830e9i	−0.0813756	+	0.140947i	−0.903841	−	0.427868i	$-0.859265\pi$
$991$	−2.49317e9	+	4.31830e9i	−0.0813756	+	0.140947i	0.822465	+	0.568815i	$0.192598\pi$
$992$	5.85403e9	+	1.01395e10i	0.190399	+	0.329780i
$993$	2.13065e10			0.690541
$994$	1.07659e10	+	1.86471e10i	0.347695	+	0.602225i
$995$	−6.81341e9	−	1.18012e10i	−0.219272	−	0.379791i
$996$	−3.51820e9			−0.112827
$997$	−1.80555e10	−	3.12730e10i	−0.577000	−	0.999394i	−0.995821	−	0.0913248i	$-0.970890\pi$
$997$	−1.80555e10	−	3.12730e10i	−0.577000	−	0.999394i	0.418821	−	0.908069i	$-0.362443\pi$
$998$	−8.02735e9	+	1.39038e10i	−0.255632	+	0.442768i
$999$	4.60129e9	−	7.96966e9i	0.146016	−	0.252907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.f.a.22.6	✓	48
13.3	even	3	inner	91.8.f.a.29.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.f.a.22.6	✓	48	1.1	even	1	trivial
91.8.f.a.29.6	yes	48	13.3	even	3	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.42253 + 11.1242i) q^{2} +(-13.9142 + 24.1002i) q^{3} +(-18.4978 - 32.0392i) q^{4} -93.0462 q^{5} +(-178.729 - 309.568i) q^{6} +(171.500 + 297.047i) q^{7} -1168.96 q^{8} +(706.288 + 1223.33i) q^{9} +O(q^{10})\)	\(q+(-6.42253 + 11.1242i) q^{2} +(-13.9142 + 24.1002i) q^{3} +(-18.4978 - 32.0392i) q^{4} -93.0462 q^{5} +(-178.729 - 309.568i) q^{6} +(171.500 + 297.047i) q^{7} -1168.96 q^{8} +(706.288 + 1223.33i) q^{9} +(597.592 - 1035.06i) q^{10} +(-1790.98 + 3102.07i) q^{11} +1029.53 q^{12} +(-7751.98 - 1629.51i) q^{13} -4405.86 q^{14} +(1294.67 - 2242.43i) q^{15} +(9875.38 - 17104.7i) q^{16} +(-19090.0 - 33064.8i) q^{17} -18144.6 q^{18} +(16931.7 + 29326.5i) q^{19} +(1721.15 + 2981.13i) q^{20} -9545.17 q^{21} +(-23005.3 - 39846.3i) q^{22} +(1813.85 - 3141.68i) q^{23} +(16265.1 - 28172.0i) q^{24} -69467.4 q^{25} +(67914.3 - 75768.6i) q^{26} -100171. q^{27} +(6344.76 - 10989.5i) q^{28} +(433.752 - 751.281i) q^{29} +(16630.1 + 28804.2i) q^{30} +112498. q^{31} +(52036.8 + 90130.3i) q^{32} +(-49840.3 - 86325.9i) q^{33} +490424. q^{34} +(-15957.4 - 27639.1i) q^{35} +(26129.6 - 45257.8i) q^{36} +(-45934.4 + 79560.8i) q^{37} -434976. q^{38} +(147135. - 164151. i) q^{39} +108767. q^{40} +(332426. - 575778. i) q^{41} +(61304.2 - 106182. i) q^{42} +(442115. + 765766. i) q^{43} +132517. q^{44} +(-65717.4 - 113826. i) q^{45} +(23299.0 + 40355.1i) q^{46} +628343. q^{47} +(274817. + 475997. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(446157. - 772766. i) q^{50} +1.06249e6 q^{51} +(91186.6 + 278510. i) q^{52} +796645. q^{53} +(643350. - 1.11431e6i) q^{54} +(166644. - 288636. i) q^{55} +(-200476. - 347235. i) q^{56} -942365. q^{57} +(5571.58 + 9650.26i) q^{58} +(912659. + 1.58077e6i) q^{59} -95794.3 q^{60} +(-900836. - 1.56029e6i) q^{61} +(-722522. + 1.25145e6i) q^{62} +(-242257. + 419601. i) q^{63} +1.19127e6 q^{64} +(721292. + 151620. i) q^{65} +1.28040e6 q^{66} +(374686. - 648974. i) q^{67} +(-706247. + 1.22325e6i) q^{68} +(50476.7 + 87428.2i) q^{69} +409948. q^{70} +(-2.44354e6 - 4.23234e6i) q^{71} +(-825619. - 1.43001e6i) q^{72} -404443. q^{73} +(-590031. - 1.02196e6i) q^{74} +(966586. - 1.67418e6i) q^{75} +(626398. - 1.08495e6i) q^{76} -1.22861e6 q^{77} +(881060. + 2.69101e6i) q^{78} -2.52580e6 q^{79} +(-918867. + 1.59152e6i) q^{80} +(-150852. + 261283. i) q^{81} +(4.27003e6 + 7.39591e6i) q^{82} -3.41727e6 q^{83} +(176565. + 305820. i) q^{84} +(1.77625e6 + 3.07655e6i) q^{85} -1.13580e7 q^{86} +(12070.7 + 20907.0i) q^{87} +(2.09358e6 - 3.62618e6i) q^{88} +(2.60120e6 - 4.50542e6i) q^{89} +1.68829e6 q^{90} +(-845423. - 2.58216e6i) q^{91} -134209. q^{92} +(-1.56532e6 + 2.71122e6i) q^{93} +(-4.03555e6 + 6.98978e6i) q^{94} +(-1.57543e6 - 2.72872e6i) q^{95} -2.89621e6 q^{96} +(-8.25704e6 - 1.43016e7i) q^{97} +(-755605. - 1.30875e6i) q^{98} -5.05979e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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