LMFDB - Embedded newform 91.8.f.a.22.13

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			22.13
Character	$\chi$	$=$	91.22
Dual form			91.8.f.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.408038 + 0.706743i) q^{2} +(34.4693 - 59.7025i) q^{3} +(63.6670 + 110.274i) q^{4} -447.050 q^{5} +(28.1296 + 48.7218i) q^{6} +(171.500 + 297.047i) q^{7} -208.372 q^{8} +(-1282.76 - 2221.80i) q^{9} +O(q^{10})$	\(q+(-0.408038 + 0.706743i) q^{2} +(34.4693 - 59.7025i) q^{3} +(63.6670 + 110.274i) q^{4} -447.050 q^{5} +(28.1296 + 48.7218i) q^{6} +(171.500 + 297.047i) q^{7} -208.372 q^{8} +(-1282.76 - 2221.80i) q^{9} +(182.414 - 315.950i) q^{10} +(2653.00 - 4595.14i) q^{11} +8778.22 q^{12} +(-2741.01 + 7432.05i) q^{13} -279.914 q^{14} +(-15409.5 + 26690.0i) q^{15} +(-8064.35 + 13967.9i) q^{16} +(2529.55 + 4381.31i) q^{17} +2093.66 q^{18} +(20074.8 + 34770.5i) q^{19} +(-28462.4 - 49298.2i) q^{20} +23645.9 q^{21} +(2165.05 + 3749.98i) q^{22} +(-22758.0 + 39418.0i) q^{23} +(-7182.43 + 12440.3i) q^{24} +121729. q^{25} +(-4134.11 - 4969.75i) q^{26} -26094.5 q^{27} +(-21837.8 + 37824.2i) q^{28} +(-75631.4 + 130997. i) q^{29} +(-12575.3 - 21781.1i) q^{30} +229538. q^{31} +(-19916.9 - 34497.2i) q^{32} +(-182894. - 316782. i) q^{33} -4128.62 q^{34} +(-76669.1 - 132795. i) q^{35} +(163339. - 282911. i) q^{36} +(99285.9 - 171968. i) q^{37} -32765.1 q^{38} +(349231. + 419823. i) q^{39} +93152.8 q^{40} +(-143662. + 248830. i) q^{41} +(-9648.44 + 16711.6i) q^{42} +(344946. + 597464. i) q^{43} +675635. q^{44} +(573458. + 993258. i) q^{45} +(-18572.3 - 32168.1i) q^{46} +306240. q^{47} +(555945. + 962924. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(-49670.1 + 86031.1i) q^{50} +348767. q^{51} +(-994078. + 170913. i) q^{52} -1.22672e6 q^{53} +(10647.5 - 18442.1i) q^{54} +(-1.18603e6 + 2.05426e6i) q^{55} +(-35735.8 - 61896.3i) q^{56} +2.76785e6 q^{57} +(-61721.0 - 106904. i) q^{58} +(582887. + 1.00959e6i) q^{59} -3.92430e6 q^{60} +(364010. + 630484. i) q^{61} +(-93660.4 + 162225. i) q^{62} +(439986. - 762079. i) q^{63} -2.03197e6 q^{64} +(1.22537e6 - 3.32250e6i) q^{65} +298511. q^{66} +(-1.13519e6 + 1.96621e6i) q^{67} +(-322098. + 557890. i) q^{68} +(1.56890e6 + 2.71742e6i) q^{69} +125136. q^{70} +(-2.60139e6 - 4.50574e6i) q^{71} +(267291. + 462962. i) q^{72} +6.17622e6 q^{73} +(81024.9 + 140339. i) q^{74} +(4.19590e6 - 7.26752e6i) q^{75} +(-2.55620e6 + 4.42747e6i) q^{76} +1.81996e6 q^{77} +(-439206. + 75513.1i) q^{78} -2.48904e6 q^{79} +(3.60517e6 - 6.24434e6i) q^{80} +(1.90594e6 - 3.30118e6i) q^{81} +(-117239. - 203064. i) q^{82} -1.53386e6 q^{83} +(1.50546e6 + 2.60754e6i) q^{84} +(-1.13084e6 - 1.95867e6i) q^{85} -563005. q^{86} +(5.21392e6 + 9.03077e6i) q^{87} +(-552812. + 957498. i) q^{88} +(-557262. + 965206. i) q^{89} -935971. q^{90} +(-2.67775e6 + 460388. i) q^{91} -5.79573e6 q^{92} +(7.91202e6 - 1.37040e7i) q^{93} +(-124958. + 216433. i) q^{94} +(-8.97443e6 - 1.55442e7i) q^{95} -2.74609e6 q^{96} +(-175631. - 304202. i) q^{97} +(-48005.3 - 83147.6i) q^{98} -1.36127e7 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 $

$2$	−0.408038	+	0.706743i	−0.0360658	+	0.0624679i	−0.883495	−	0.468441i	$-0.844816\pi$
$2$	−0.408038	+	0.706743i	−0.0360658	+	0.0624679i	0.847429	+	0.530909i	$0.178149\pi$
$3$	34.4693	−	59.7025i	0.737068	−	1.27664i	−0.216742	−	0.976229i	$-0.569543\pi$
$3$	34.4693	−	59.7025i	0.737068	−	1.27664i	0.953810	−	0.300410i	$-0.0971236\pi$
$4$	63.6670	+	110.274i	0.497399	+	0.861519i
$5$	−447.050			−1.59942			−0.799708	−	0.600389i	$-0.795012\pi$
$5$	−447.050			−1.59942			−0.799708	+	0.600389i	$0.795012\pi$
$6$	28.1296	+	48.7218i	0.0531659	+	0.0920861i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$	−208.372			−0.143888
$9$	−1282.76	−	2221.80i	−0.586538	−	1.01591i
$10$	182.414	−	315.950i	0.0576843	−	0.0999121i
$11$	2653.00	−	4595.14i	0.600985	−	1.04094i	−0.391688	−	0.920098i	$-0.628109\pi$
$11$	2653.00	−	4595.14i	0.600985	−	1.04094i	0.992672	−	0.120838i	$-0.0385580\pi$
$12$	8778.22			1.46647
$13$	−2741.01	+	7432.05i	−0.346026	+	0.938225i
$13$	−2741.01	+	7432.05i	−0.346026	+	0.938225i
$14$	−279.914			−0.0272632
$15$	−15409.5	+	26690.0i	−1.17888	+	2.04188i
$16$	−8064.35	+	13967.9i	−0.492209	+	0.852531i
$17$	2529.55	+	4381.31i	0.124874	+	0.216288i	0.921684	−	0.387942i	$-0.126814\pi$
$17$	2529.55	+	4381.31i	0.124874	+	0.216288i	−0.796810	+	0.604230i	$0.793481\pi$
$18$	2093.66			0.0846160
$19$	20074.8	+	34770.5i	0.671449	+	1.16298i	0.977493	+	0.210966i	$0.0676610\pi$
$19$	20074.8	+	34770.5i	0.671449	+	1.16298i	−0.306045	+	0.952017i	$0.599006\pi$
$20$	−28462.4	−	49298.2i	−0.795547	−	1.37793i
$21$	23645.9			0.557171
$22$	2165.05	+	3749.98i	0.0433500	+	0.0750844i
$23$	−22758.0	+	39418.0i	−0.390020	+	0.675534i	−0.992452	−	0.122636i	$-0.960865\pi$
$23$	−22758.0	+	39418.0i	−0.390020	+	0.675534i	0.602432	+	0.798170i	$0.294198\pi$
$24$	−7182.43	+	12440.3i	−0.106055	+	0.183693i
$25$	121729.			1.55813
$26$	−4134.11	−	4969.75i	−0.0461292	−	0.0554534i
$27$	−26094.5			−0.255138
$28$	−21837.8	+	37824.2i	−0.187999	+	0.325624i
$29$	−75631.4	+	130997.i	−0.575850	+	0.997401i	0.420099	+	0.907478i	$0.361995\pi$
$29$	−75631.4	+	130997.i	−0.575850	+	0.997401i	−0.995949	+	0.0899226i	$0.971338\pi$
$30$	−12575.3	−	21781.1i	−0.0850344	−	0.147284i
$31$	229538.			1.38385			0.691925	−	0.721969i	$-0.256763\pi$
$31$	229538.			1.38385			0.691925	+	0.721969i	$0.256763\pi$
$32$	−19916.9	−	34497.2i	−0.107448	−	0.186105i
$33$	−182894.	−	316782.i	−0.885933	−	1.53448i
$34$	−4128.62			−0.0180148
$35$	−76669.1	−	132795.i	−0.302261	−	0.523532i
$36$	163339.	−	282911.i	0.583486	−	1.01063i
$37$	99285.9	−	171968.i	0.322241	−	0.558139i	−0.658709	−	0.752398i	$-0.728897\pi$
$37$	99285.9	−	171968.i	0.322241	−	0.558139i	0.980950	+	0.194260i	$0.0622304\pi$
$38$	−32765.1			−0.0968654
$39$	349231.	+	419823.i	0.942729	+	1.13329i
$40$	93152.8			0.230137
$41$	−143662.	+	248830.i	−0.325535	+	0.563844i	−0.981621	−	0.190843i	$-0.938878\pi$
$41$	−143662.	+	248830.i	−0.325535	+	0.563844i	0.656085	+	0.754687i	$0.272211\pi$
$42$	−9648.44	+	16711.6i	−0.0200948	+	0.0348053i
$43$	344946.	+	597464.i	0.661624	+	1.14597i	0.980189	+	0.198066i	$0.0634660\pi$
$43$	344946.	+	597464.i	0.661624	+	1.14597i	−0.318564	+	0.947901i	$0.603201\pi$
$44$	675635.			1.19572
$45$	573458.	+	993258.i	0.938118	+	1.62487i
$46$	−18572.3	−	32168.1i	−0.0281328	−	0.0487274i
$47$	306240.			0.430249			0.215124	−	0.976587i	$-0.430984\pi$
$47$	306240.			0.430249			0.215124	+	0.976587i	$0.430984\pi$
$48$	555945.	+	962924.i	0.725583	+	1.25675i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	−49670.1	+	86031.1i	−0.0561953	+	0.0973330i
$51$	348767.			0.368163
$52$	−994078.	+	170913.i	−0.980412	+	0.168563i
$53$	−1.22672e6			−1.13183			−0.565914	−	0.824464i	$-0.691477\pi$
$53$	−1.22672e6			−1.13183			−0.565914	+	0.824464i	$0.691477\pi$
$54$	10647.5	−	18442.1i	0.00920177	−	0.0159379i
$55$	−1.18603e6	+	2.05426e6i	−0.961224	+	1.66489i
$56$	−35735.8	−	61896.3i	−0.0271923	−	0.0470984i
$57$	2.76785e6			1.97961
$58$	−61721.0	−	106904.i	−0.0415370	−	0.0719442i
$59$	582887.	+	1.00959e6i	0.369489	+	0.639975i	0.989486	−	0.144630i	$-0.0461992\pi$
$59$	582887.	+	1.00959e6i	0.369489	+	0.639975i	−0.619996	+	0.784605i	$0.712866\pi$
$60$	−3.92430e6			−2.34549
$61$	364010.	+	630484.i	0.205333	+	0.355647i	0.950239	−	0.311522i	$-0.100839\pi$
$61$	364010.	+	630484.i	0.205333	+	0.355647i	−0.744906	+	0.667170i	$0.767506\pi$
$62$	−93660.4	+	162225.i	−0.0499097	+	0.0864462i
$63$	439986.	−	762079.i	0.221691	−	0.383979i
$64$	−2.03197e6			−0.968917
$65$	1.22537e6	−	3.32250e6i	0.553440	−	1.50061i
$66$	298511.			0.127808
$67$	−1.13519e6	+	1.96621e6i	−0.461112	+	0.798670i	−0.999017	−	0.0443358i	$-0.985883\pi$
$67$	−1.13519e6	+	1.96621e6i	−0.461112	+	0.798670i	0.537904	+	0.843006i	$0.319216\pi$
$68$	−322098.	+	557890.i	−0.124224	+	0.215163i
$69$	1.56890e6	+	2.71742e6i	0.574942	+	0.995828i
$70$	125136.			0.0436052
$71$	−2.60139e6	−	4.50574e6i	−0.862584	−	1.49404i	−0.869426	−	0.494063i	$-0.835511\pi$
$71$	−2.60139e6	−	4.50574e6i	−0.862584	−	1.49404i	0.00684205	−	0.999977i	$-0.497822\pi$
$72$	267291.	+	462962.i	0.0843958	+	0.146178i
$73$	6.17622e6			1.85820			0.929100	−	0.369828i	$-0.120583\pi$
$73$	6.17622e6			1.85820			0.929100	+	0.369828i	$0.120583\pi$
$74$	81024.9	+	140339.i	0.0232438	+	0.0402595i
$75$	4.19590e6	−	7.26752e6i	1.14845	−	1.98917i
$76$	−2.55620e6	+	4.42747e6i	−0.667955	+	1.15693i
$77$	1.81996e6			0.454302
$78$	−439206.	+	75513.1i	−0.104794	+	0.0180174i
$79$	−2.48904e6			−0.567985			−0.283993	−	0.958826i	$-0.591659\pi$
$79$	−2.48904e6			−0.567985			−0.283993	+	0.958826i	$0.591659\pi$
$80$	3.60517e6	−	6.24434e6i	0.787247	−	1.36355i
$81$	1.90594e6	−	3.30118e6i	0.398484	−	0.690195i
$82$	−117239.	−	203064.i	−0.0234814	−	0.0406710i
$83$	−1.53386e6			−0.294451			−0.147225	−	0.989103i	$-0.547034\pi$
$83$	−1.53386e6			−0.294451			−0.147225	+	0.989103i	$0.547034\pi$
$84$	1.50546e6	+	2.60754e6i	0.277136	+	0.480014i
$85$	−1.13084e6	−	1.95867e6i	−0.199726	−	0.345935i
$86$	−563005.			−0.0954481
$87$	5.21392e6	+	9.03077e6i	0.848881	+	1.47030i
$88$	−552812.	+	957498.i	−0.0864745	+	0.149778i
$89$	−557262.	+	965206.i	−0.0837904	+	0.145129i	−0.904875	−	0.425677i	$-0.860036\pi$
$89$	−557262.	+	965206.i	−0.0837904	+	0.145129i	0.821085	+	0.570806i	$0.193369\pi$
$90$	−935971.			−0.135336
$91$	−2.67775e6	+	460388.i	−0.372499	+	0.0640441i
$92$	−5.79573e6			−0.775981
$93$	7.91202e6	−	1.37040e7i	1.01999	−	1.76668i
$94$	−124958.	+	216433.i	−0.0155173	+	0.0268767i
$95$	−8.97443e6	−	1.55442e7i	−1.07393	−	1.86009i
$96$	−2.74609e6			−0.316786
$97$	−175631.	−	304202.i	−0.0195389	−	0.0338423i	0.856091	−	0.516826i	$-0.172886\pi$
$97$	−175631.	−	304202.i	−0.0195389	−	0.0338423i	−0.875630	+	0.482983i	$0.839553\pi$
$98$	−48005.3	−	83147.6i	−0.00515226	−	0.00892398i
$99$	−1.36127e7			−1.41000
$100$	7.75012e6	+	1.34236e7i	0.775012	+	1.34236i
$101$	−2.81878e6	+	4.88227e6i	−0.272230	+	0.471517i	−0.969433	−	0.245358i	$-0.921095\pi$
$101$	−2.81878e6	+	4.88227e6i	−0.272230	+	0.471517i	0.697202	+	0.716874i	$0.254428\pi$
$102$	−142310.	+	246489.i	−0.0132781	+	0.0229983i
$103$	−1.58278e7			−1.42722			−0.713609	−	0.700544i	$-0.752941\pi$
$103$	−1.58278e7			−1.42722			−0.713609	+	0.700544i	$0.752941\pi$
$104$	571151.	−	1.54863e6i	0.0497891	−	0.134999i
$105$	−1.05709e7			−0.891148
$106$	500550.	−	866978.i	0.0408204	−	0.0707029i
$107$	3.90962e6	−	6.77166e6i	0.308526	−	0.534382i	−0.669514	−	0.742799i	$-0.733498\pi$
$107$	3.90962e6	−	6.77166e6i	0.308526	−	0.534382i	0.978040	+	0.208417i	$0.0668310\pi$
$108$	−1.66136e6	−	2.87756e6i	−0.126905	−	0.219807i
$109$	−1.35617e7			−1.00304			−0.501522	−	0.865145i	$-0.667226\pi$
$109$	−1.35617e7			−1.00304			−0.501522	+	0.865145i	$0.667226\pi$
$110$	−967888.	−	1.67643e6i	−0.0693347	−	0.120091i
$111$	−6.84462e6	−	1.18552e7i	−0.475028	−	0.822772i
$112$	−5.53215e6			−0.372075
$113$	9.27459e6	+	1.60641e7i	0.604673	+	1.04732i	0.992103	+	0.125425i	$0.0400294\pi$
$113$	9.27459e6	+	1.60641e7i	0.604673	+	1.04732i	−0.387430	+	0.921899i	$0.626637\pi$
$114$	−1.12939e6	+	1.95616e6i	−0.0713964	+	0.123662i
$115$	1.01740e7	−	1.76218e7i	0.623803	−	1.08046i
$116$	−1.92609e7			−1.14571
$117$	2.00286e7	−	3.44354e6i	1.15611	−	0.198772i
$118$	−951360.			−0.0533038
$119$	−867637.	+	1.50279e6i	−0.0471980	+	0.0817493i
$120$	3.21091e6	−	5.56146e6i	0.169626	−	0.293802i
$121$	−4.33326e6	−	7.50543e6i	−0.222365	−	0.385147i
$122$	−594120.			−0.0296220
$123$	9.90384e6	+	1.71540e7i	0.479883	+	0.831183i
$124$	1.46140e7	+	2.53122e7i	0.688325	+	1.19221i
$125$	−1.94931e7			−0.892682
$126$	359063.	+	621915.i	0.0159909	+	0.0276971i
$127$	−2.02107e7	+	3.50059e7i	−0.875524	+	1.51645i	−0.0193203	+	0.999813i	$0.506150\pi$
$127$	−2.02107e7	+	3.50059e7i	−0.875524	+	1.51645i	−0.856204	+	0.516639i	$0.827183\pi$
$128$	3.37849e6	−	5.85172e6i	0.142393	−	0.246631i
$129$	4.75601e7			1.95065
$130$	1.84816e6	+	2.22173e6i	0.0737797	+	0.0886930i
$131$	−8.73065e6			−0.339310			−0.169655	−	0.985503i	$-0.554265\pi$
$131$	−8.73065e6			−0.339310			−0.169655	+	0.985503i	$0.554265\pi$
$132$	2.32886e7	−	4.03371e7i	0.881323	−	1.52650i
$133$	−6.88564e6	+	1.19263e7i	−0.253784	+	0.439566i
$134$	−926402.	−	1.60458e6i	−0.0332608	−	0.0576094i
$135$	1.16655e7			0.408072
$136$	−527088.	−	912944.i	−0.0179679	−	0.0311213i
$137$	−2.02142e7	−	3.50121e7i	−0.671638	−	1.16331i	−0.977440	−	0.211216i	$-0.932258\pi$
$137$	−2.02142e7	−	3.50121e7i	−0.671638	−	1.16331i	0.305802	−	0.952095i	$-0.401076\pi$
$138$	−2.56069e6			−0.0829430
$139$	2.16362e6	+	3.74750e6i	0.0683328	+	0.118356i	0.898168	−	0.439653i	$-0.144899\pi$
$139$	2.16362e6	+	3.74750e6i	0.0683328	+	0.118356i	−0.829835	+	0.558009i	$0.811565\pi$
$140$	9.76259e6	−	1.69093e7i	0.300688	−	0.520808i
$141$	1.05559e7	−	1.82833e7i	0.317123	−	0.549272i
$142$	4.24587e6			0.124439
$143$	2.68794e7	+	3.23126e7i	0.768675	+	0.924050i
$144$	4.13785e7			1.15480
$145$	3.38110e7	−	5.85624e7i	0.921023	−	1.59526i
$146$	−2.52013e6	+	4.36500e6i	−0.0670175	+	0.116078i
$147$	4.05527e6	+	7.02394e6i	0.105295	+	0.182377i
$148$	2.52849e7			0.641130
$149$	4.14200e6	+	7.17415e6i	0.102579	+	0.177672i	0.912746	−	0.408527i	$-0.133957\pi$
$149$	4.14200e6	+	7.17415e6i	0.102579	+	0.177672i	−0.810168	+	0.586198i	$0.800624\pi$
$150$	3.42418e6	+	5.93085e6i	0.0828394	+	0.143482i
$151$	−4.49207e7			−1.06176			−0.530881	−	0.847446i	$-0.678139\pi$
$151$	−4.49207e7			−1.06176			−0.530881	+	0.847446i	$0.678139\pi$
$152$	−4.18302e6	−	7.24521e6i	−0.0966134	−	0.167339i
$153$	6.48961e6	−	1.12403e7i	0.146487	−	0.253723i
$154$	−742613.	+	1.28624e6i	−0.0163848	+	0.0283792i
$155$	−1.02615e8			−2.21335
$156$	−2.40612e7	+	6.52402e7i	−0.507436	+	1.37587i
$157$	−1.37636e6			−0.0283846			−0.0141923	−	0.999899i	$-0.504518\pi$
$157$	−1.37636e6			−0.0283846			−0.0141923	+	0.999899i	$0.504518\pi$
$158$	1.01562e6	−	1.75911e6i	0.0204849	−	0.0354808i
$159$	−4.22842e7	+	7.32384e7i	−0.834235	+	1.44494i
$160$	8.90388e6	+	1.54220e7i	0.171854	+	0.297660i
$161$	−1.56120e7			−0.294827
$162$	1.55539e6	+	2.69402e6i	0.0287433	+	0.0497849i
$163$	−3.24350e7	−	5.61790e7i	−0.586620	−	1.01606i	−0.994671	−	0.103096i	$-0.967125\pi$
$163$	−3.24350e7	−	5.61790e7i	−0.586620	−	1.01606i	0.408052	−	0.912959i	$-0.366208\pi$
$164$	−3.65861e7			−0.647683
$165$	8.17628e7	+	1.41617e8i	1.41697	+	2.45427i
$166$	625874.	−	1.08405e6i	0.0106196	−	0.0183937i
$167$	3.05607e7	−	5.29327e7i	0.507757	−	0.879460i	−0.492203	−	0.870480i	$-0.663808\pi$
$167$	3.05607e7	−	5.29327e7i	0.507757	−	0.879460i	0.999960	−	0.00897986i	$-0.00285842\pi$
$168$	−4.92715e6			−0.0801702
$169$	−4.77222e7	−	4.07427e7i	−0.760531	−	0.649301i
$170$	1.84570e6			0.0288131
$171$	5.15022e7	−	8.92044e7i	0.787661	−	1.36427i
$172$	−4.39234e7	+	7.60775e7i	−0.658182	+	1.14000i
$173$	5.15683e7	+	8.93190e7i	0.757219	+	1.31154i	0.944263	+	0.329191i	$0.106776\pi$
$173$	5.15683e7	+	8.93190e7i	0.757219	+	1.31154i	−0.187044	+	0.982352i	$0.559891\pi$
$174$	−8.50991e6			−0.122462
$175$	2.08765e7	+	3.61592e7i	0.294459	+	0.510018i
$176$	4.27895e7	+	7.41136e7i	0.591620	+	1.02472i
$177$	8.03667e7			1.08936
$178$	−454768.	−	787682.i	−0.00604394	−	0.0104684i
$179$	5.28702e7	−	9.15739e7i	0.689010	−	1.19340i	−0.283148	−	0.959076i	$-0.591379\pi$
$179$	5.28702e7	−	9.15739e7i	0.689010	−	1.19340i	0.972158	−	0.234325i	$-0.0752878\pi$
$180$	−7.30207e7	+	1.26476e8i	−0.933237	+	1.61641i
$181$	4.58322e7			0.574508			0.287254	−	0.957854i	$-0.407258\pi$
$181$	4.58322e7			0.574508			0.287254	+	0.957854i	$0.407258\pi$
$182$	767249.	−	2.08034e6i	0.00943379	−	0.0255790i
$183$	5.01886e7			0.605378
$184$	4.74213e6	−	8.21361e6i	0.0561191	−	0.0972012i
$185$	−4.43858e7	+	7.68784e7i	−0.515398	+	0.892695i
$186$	6.45681e6	+	1.11835e7i	0.0735737	+	0.127433i
$187$	2.68436e7			0.300190
$188$	1.94974e7	+	3.37705e7i	0.214005	+	0.370668i
$189$	−4.47520e6	−	7.75128e6i	−0.0482166	−	0.0835136i
$190$	1.46476e7			0.154928
$191$	9.21766e7	+	1.59655e8i	0.957203	+	1.65792i	0.729245	+	0.684253i	$0.239872\pi$
$191$	9.21766e7	+	1.59655e8i	0.957203	+	1.65792i	0.227958	+	0.973671i	$0.426795\pi$
$192$	−7.00404e7	+	1.21314e8i	−0.714158	+	1.23696i
$193$	2.12747e7	−	3.68489e7i	0.213017	−	0.368956i	−0.739640	−	0.673002i	$-0.765004\pi$
$193$	2.12747e7	−	3.68489e7i	0.213017	−	0.368956i	0.952657	+	0.304046i	$0.0983378\pi$
$194$	286656.			0.00281874
$195$	−1.56124e8	−	1.87682e8i	−1.50782	−	1.81260i
$196$	−1.49807e7			−0.142114
$197$	5.04231e7	−	8.73354e7i	0.469892	−	0.813876i	−0.529516	−	0.848300i	$-0.677626\pi$
$197$	5.04231e7	−	8.73354e7i	0.469892	−	0.813876i	0.999407	+	0.0344240i	$0.0109596\pi$
$198$	5.55448e6	−	9.62065e6i	0.0508529	−	0.0880798i
$199$	−6.84482e7	−	1.18556e8i	−0.615710	−	1.06644i	−0.990259	−	0.139234i	$-0.955536\pi$
$199$	−6.84482e7	−	1.18556e8i	−0.615710	−	1.06644i	0.374549	−	0.927207i	$-0.377797\pi$
$200$	−2.53649e7			−0.224196
$201$	7.82583e7	+	1.35547e8i	0.679742	+	1.17735i
$202$	−2.30034e6	−	3.98431e6i	−0.0196364	−	0.0340113i
$203$	−5.18831e7			−0.435301
$204$	2.22050e7	+	3.84601e7i	0.183124	+	0.317179i
$205$	6.42241e7	−	1.11239e8i	0.520666	−	0.901821i
$206$	6.45835e6	−	1.11862e7i	0.0514738	−	0.0891553i
$207$	1.16772e8			0.915045
$208$	−8.17054e7	−	9.82208e7i	−0.629548	−	0.756801i
$209$	2.13034e8			1.61412
$210$	4.31334e6	−	7.47092e6i	0.0321400	−	0.0556681i
$211$	9.13919e7	−	1.58295e8i	0.669760	−	1.16006i	−0.308212	−	0.951318i	$-0.599730\pi$
$211$	9.13919e7	−	1.58295e8i	0.669760	−	1.16006i	0.977971	−	0.208740i	$-0.0669362\pi$
$212$	−7.81018e7	−	1.35276e8i	−0.562970	−	0.975093i
$213$	−3.58672e8			−2.54313
$214$	3.19055e6	+	5.52620e6i	0.0222545	+	0.0385459i
$215$	−1.54208e8	−	2.67096e8i	−1.05821	−	1.83288i
$216$	5.43736e6			0.0367113
$217$	3.93658e7	+	6.81836e7i	0.261523	+	0.452972i
$218$	5.53368e6	−	9.58461e6i	0.0361756	−	0.0626580i
$219$	2.12890e8	−	3.68736e8i	1.36962	−	2.37225i
$220$	−3.02043e8			−1.91245
$221$	−3.94957e7	+	6.79052e6i	−0.246137	+	0.0423185i
$222$	1.11715e7			0.0685291
$223$	−1.08005e8	+	1.87071e8i	−0.652195	+	1.12964i	0.330394	+	0.943843i	$0.392819\pi$
$223$	−1.08005e8	+	1.87071e8i	−0.652195	+	1.12964i	−0.982589	+	0.185792i	$0.940515\pi$
$224$	6.83151e6	−	1.18325e7i	0.0406115	−	0.0703411i
$225$	−1.56149e8	−	2.70458e8i	−0.913903	−	1.58293i
$226$	−1.51376e7			−0.0872321
$227$	7.76195e7	+	1.34441e8i	0.440433	+	0.762853i	0.997722	−	0.0674663i	$-0.0214915\pi$
$227$	7.76195e7	+	1.34441e8i	0.440433	+	0.762853i	−0.557288	+	0.830319i	$0.688158\pi$
$228$	1.76221e8	+	3.05223e8i	0.984657	+	1.70548i
$229$	2.90096e8			1.59631			0.798156	−	0.602451i	$-0.205809\pi$
$229$	2.90096e8			1.59631			0.798156	+	0.602451i	$0.205809\pi$
$230$	8.30273e6	+	1.43808e7i	0.0449960	+	0.0779353i
$231$	6.27327e7	−	1.08656e8i	0.334851	−	0.579979i
$232$	1.57595e7	−	2.72962e7i	0.0828579	−	0.143514i
$233$	−1.97504e8			−1.02289			−0.511447	−	0.859315i	$-0.670891\pi$
$233$	−1.97504e8			−1.02289			−0.511447	+	0.859315i	$0.670891\pi$
$234$	−5.73875e6	+	1.55602e7i	−0.0292794	+	0.0793888i
$235$	−1.36905e8			−0.688147
$236$	−7.42213e7	+	1.28555e8i	−0.367567	+	0.636645i
$237$	−8.57954e7	+	1.48602e8i	−0.418644	+	0.725112i
$238$	−708058.	−	1.22639e6i	−0.00340447	−	0.00589671i
$239$	9.46754e7			0.448585			0.224292	−	0.974522i	$-0.427993\pi$
$239$	9.46754e7			0.448585			0.224292	+	0.974522i	$0.427993\pi$
$240$	−2.48535e8	−	4.30475e8i	−1.16051	−	2.01006i
$241$	2.10447e8	+	3.64505e8i	0.968463	+	1.67743i	0.700009	+	0.714134i	$0.253180\pi$
$241$	2.10447e8	+	3.64505e8i	0.968463	+	1.67743i	0.268454	+	0.963292i	$0.413487\pi$
$242$	7.07255e6			0.0320791
$243$	−1.59927e8	−	2.77001e8i	−0.714989	−	1.23840i
$244$	−4.63509e7	+	8.02821e7i	−0.204265	+	0.353797i
$245$	2.62975e7	−	4.55486e7i	0.114244	−	0.197876i
$246$	−1.61646e7			−0.0692296
$247$	−3.13441e8	+	5.38902e7i	−1.32348	+	0.227547i
$248$	−4.78294e7			−0.199120
$249$	−5.28710e7	+	9.15753e7i	−0.217030	+	0.375907i
$250$	7.95395e6	−	1.37766e7i	0.0321953	−	0.0557639i
$251$	−4.73436e7	−	8.20016e7i	−0.188975	−	0.327314i	0.755934	−	0.654648i	$-0.227183\pi$
$251$	−4.73436e7	−	8.20016e7i	−0.188975	−	0.327314i	−0.944909	+	0.327334i	$0.893850\pi$
$252$	1.12050e8			0.441074
$253$	1.20754e8	+	2.09152e8i	0.468791	+	0.811971i
$254$	−1.64935e7	−	2.85675e7i	−0.0631530	−	0.109384i
$255$	−1.55916e8			−0.588845
$256$	−1.27289e8	−	2.20471e8i	−0.474188	−	0.821317i
$257$	−5.01821e7	+	8.69180e7i	−0.184409	+	0.319406i	−0.943377	−	0.331722i	$-0.892371\pi$
$257$	−5.01821e7	+	8.69180e7i	−0.184409	+	0.319406i	0.758968	+	0.651128i	$0.225704\pi$
$258$	−1.94064e7	+	3.36128e7i	−0.0703518	+	0.121853i
$259$	6.81101e7			0.243592
$260$	4.44403e8	−	7.64065e7i	1.56809	−	0.269602i
$261$	3.88067e8			1.35103
$262$	3.56244e6	−	6.17033e6i	0.0122375	−	0.0211960i
$263$	−2.28847e8	+	3.96374e8i	−0.775710	+	1.34357i	0.158684	+	0.987329i	$0.449275\pi$
$263$	−2.28847e8	+	3.96374e8i	−0.775710	+	1.34357i	−0.934394	+	0.356240i	$0.884059\pi$
$264$	3.81100e7	+	6.60085e7i	0.127475	+	0.220793i
$265$	5.48407e8			1.81026
$266$	−5.61921e6	−	9.73276e6i	−0.0183058	−	0.0317067i
$267$	3.84168e7	+	6.65398e7i	0.123518	+	0.213940i
$268$	−2.89097e8			−0.917427
$269$	−4.25999e6	−	7.37851e6i	−0.0133437	−	0.0231119i	0.859276	−	0.511511i	$-0.170914\pi$
$269$	−4.25999e6	−	7.37851e6i	−0.0133437	−	0.0231119i	−0.872620	+	0.488400i	$0.837581\pi$
$270$	−4.75999e6	+	8.24454e6i	−0.0147175	+	0.0254914i
$271$	−1.56699e8	+	2.71410e8i	−0.478269	+	0.828386i	−0.999690	−	0.0249134i	$-0.992069\pi$
$271$	−1.56699e8	+	2.71410e8i	−0.478269	+	0.828386i	0.521420	+	0.853300i	$0.325402\pi$
$272$	−8.15968e7			−0.245857
$273$	−6.48137e7	+	1.75738e8i	−0.192796	+	0.522752i
$274$	3.29927e7			0.0968927
$275$	3.22947e8	−	5.59361e8i	0.936412	−	1.62191i
$276$	−1.99775e8	+	3.46020e8i	−0.571950	+	0.990647i
$277$	−1.60875e8	−	2.78644e8i	−0.454788	−	0.787716i	0.543888	−	0.839158i	$-0.316952\pi$
$277$	−1.60875e8	−	2.78644e8i	−0.454788	−	0.787716i	−0.998676	+	0.0514416i	$0.983618\pi$
$278$	−3.53136e6			−0.00985791
$279$	−2.94442e8	−	5.09989e8i	−0.811682	−	1.40587i
$280$	1.59757e7	+	2.76707e7i	0.0434918	+	0.0753299i
$281$	7.22559e8			1.94268			0.971340	−	0.237694i	$-0.0763915\pi$
$281$	7.22559e8			1.94268			0.971340	+	0.237694i	$0.0763915\pi$
$282$	8.61440e6	+	1.49206e7i	0.0228746	+	0.0396199i
$283$	−3.52878e7	+	6.11203e7i	−0.0925491	+	0.160300i	−0.908583	−	0.417704i	$-0.862835\pi$
$283$	−3.52878e7	+	6.11203e7i	−0.0925491	+	0.160300i	0.816034	+	0.578004i	$0.196168\pi$
$284$	3.31246e8	−	5.73734e8i	0.858096	−	1.48627i
$285$	−1.23737e9			−3.16622
$286$	−3.38045e7	+	5.81203e6i	−0.0854463	+	0.0146909i
$287$	−9.85521e7			−0.246082
$288$	−5.10973e7	+	8.85031e7i	−0.126045	+	0.218316i
$289$	1.92372e8	−	3.33198e8i	0.468813	−	0.812008i
$290$	2.75924e7	+	4.77914e7i	0.0664349	+	0.115069i
$291$	−2.42155e7			−0.0576059
$292$	3.93221e8	+	6.81079e8i	0.924266	+	1.60088i
$293$	−1.18844e8	−	2.05844e8i	−0.276020	−	0.478081i	0.694372	−	0.719616i	$-0.255682\pi$
$293$	−1.18844e8	−	2.05844e8i	−0.276020	−	0.478081i	−0.970392	+	0.241535i	$0.922349\pi$
$294$	−6.61883e6			−0.0151903
$295$	−2.60580e8	−	4.51337e8i	−0.590967	−	1.02359i
$296$	−2.06884e7	+	3.58334e7i	−0.0463667	+	0.0803095i
$297$	−6.92287e7	+	1.19908e8i	−0.153334	+	0.265582i
$298$	−6.76037e6			−0.0147984
$299$	−2.30576e8	−	2.77184e8i	−0.498845	−	0.599679i
$300$	1.06856e9			2.28494
$301$	−1.18316e8	+	2.04930e8i	−0.250071	+	0.433135i
$302$	1.83294e7	−	3.17474e7i	0.0382933	−	0.0663260i
$303$	1.94322e8	+	3.36576e8i	0.401304	+	0.695079i
$304$	−6.47560e8			−1.32197
$305$	−1.62731e8	−	2.81858e8i	−0.328413	−	0.568828i
$306$	5.29602e6	+	9.17298e6i	0.0105663	+	0.0183014i
$307$	7.14736e8			1.40981			0.704906	−	0.709300i	$-0.250989\pi$
$307$	7.14736e8			1.40981			0.704906	+	0.709300i	$0.250989\pi$
$308$	1.15871e8	+	2.00695e8i	0.225969	+	0.391390i
$309$	−5.45573e8	+	9.44960e8i	−1.05196	+	1.82204i
$310$	4.18709e7	−	7.25226e7i	0.0798264	−	0.138263i
$311$	7.51084e8			1.41588			0.707941	−	0.706272i	$-0.249624\pi$
$311$	7.51084e8			1.41588			0.707941	+	0.706272i	$0.249624\pi$
$312$	−7.27701e7	−	8.74793e7i	−0.135647	−	0.163066i
$313$	2.21683e7			0.0408627			0.0204314	−	0.999791i	$-0.493496\pi$
$313$	2.21683e7			0.0408627			0.0204314	+	0.999791i	$0.493496\pi$
$314$	561606.	−	972730.i	0.00102371	−	0.00177312i
$315$	−1.96696e8	+	3.40687e8i	−0.354575	+	0.614143i
$316$	−1.58470e8	−	2.74478e8i	−0.282515	−	0.489330i
$317$	7.19587e8			1.26875			0.634375	−	0.773026i	$-0.281258\pi$
$317$	7.19587e8			1.26875			0.634375	+	0.773026i	$0.281258\pi$
$318$	−3.45072e7	−	5.97682e7i	−0.0601747	−	0.104226i
$319$	4.01301e8	+	6.95073e8i	0.692153	+	1.19884i
$320$	9.08391e8			1.54970
$321$	−2.69524e8	−	4.66828e8i	−0.454809	−	0.787752i
$322$	6.37028e6	−	1.10337e7i	0.0106332	−	0.0184172i
$323$	−1.01560e8	+	1.75908e8i	−0.167693	+	0.290453i
$324$	4.85381e8			0.792821
$325$	−3.33660e8	+	9.04695e8i	−0.539154	+	1.46188i
$326$	5.29388e7			0.0846277
$327$	−4.67460e8	+	8.09665e8i	−0.739312	+	1.28053i
$328$	2.99351e7	−	5.18492e7i	0.0468407	−	0.0811304i
$329$	5.25202e7	+	9.09676e7i	0.0813094	+	0.140832i
$330$	−1.33449e8			−0.204417
$331$	2.47692e8	+	4.29015e8i	0.375417	+	0.650242i	0.990389	−	0.138307i	$-0.0441661\pi$
$331$	2.47692e8	+	4.29015e8i	0.375417	+	0.650242i	−0.614972	+	0.788549i	$0.710833\pi$
$332$	−9.76563e7	−	1.69146e8i	−0.146459	−	0.253675i
$333$	−5.09439e8			−0.756028
$334$	2.49399e7	+	4.31971e7i	0.0366253	+	0.0634369i
$335$	5.07487e8	−	8.78993e8i	0.737510	−	1.27741i
$336$	−1.90689e8	+	3.30283e8i	−0.274245	+	0.475006i
$337$	−2.77964e8			−0.395625			−0.197813	−	0.980240i	$-0.563384\pi$
$337$	−2.77964e8			−0.395625			−0.197813	+	0.980240i	$0.563384\pi$
$338$	4.82671e7	−	1.71028e7i	0.0679897	−	0.0240912i
$339$	1.27875e9			1.78274
$340$	1.43994e8	−	2.49405e8i	0.198686	−	0.344135i
$341$	6.08966e8	−	1.05476e9i	0.831673	−	1.44050i
$342$	4.20297e7	+	7.27976e7i	0.0568153	+	0.0984070i
$343$	−4.03536e7			−0.0539949
$344$	−7.18771e7	−	1.24495e8i	−0.0951998	−	0.164891i
$345$	−7.01378e8	−	1.21482e9i	−0.919571	−	1.59274i
$346$	−8.41674e7			−0.109239
$347$	3.64432e8	+	6.31215e8i	0.468234	+	0.811006i	0.999341	−	0.0362994i	$-0.0115570\pi$
$347$	3.64432e8	+	6.31215e8i	0.468234	+	0.811006i	−0.531107	+	0.847305i	$0.678224\pi$
$348$	−6.63909e8	+	1.14992e9i	−0.844464	+	1.46265i
$349$	−2.56914e8	+	4.44987e8i	−0.323518	+	0.560349i	−0.981211	−	0.192936i	$-0.938199\pi$
$349$	−2.56914e8	+	4.44987e8i	−0.323518	+	0.560349i	0.657694	+	0.753286i	$0.271532\pi$
$350$	−3.40737e7			−0.0424796
$351$	7.15253e7	−	1.93935e8i	0.0882846	−	0.239377i
$352$	−2.11359e8			−0.258298
$353$	−2.40749e8	+	4.16990e8i	−0.291309	+	0.504562i	−0.974120	−	0.226034i	$-0.927424\pi$
$353$	−2.40749e8	+	4.16990e8i	−0.291309	+	0.504562i	0.682811	+	0.730595i	$0.260757\pi$
$354$	−3.27927e7	+	5.67986e7i	−0.0392885	+	0.0680497i
$355$	1.16295e9	+	2.01429e9i	1.37963	+	2.38959i
$356$	−1.41917e8			−0.166709
$357$	5.98136e7	+	1.03600e8i	0.0695762	+	0.120510i
$358$	4.31462e7	+	7.47314e7i	0.0496995	+	0.0860820i
$359$	−9.63827e8			−1.09943			−0.549716	−	0.835351i	$-0.685264\pi$
$359$	−9.63827e8			−1.09943			−0.549716	+	0.835351i	$0.685264\pi$
$360$	−1.19493e8	−	2.06967e8i	−0.134984	−	0.233799i
$361$	−3.59057e8	+	6.21904e8i	−0.401687	+	0.695742i
$362$	−1.87013e7	+	3.23916e7i	−0.0207201	+	0.0358883i
$363$	−5.97457e8			−0.655592
$364$	−2.21253e8	−	2.65976e8i	−0.240456	−	0.289060i
$365$	−2.76108e9			−2.97203
$366$	−2.04789e7	+	3.54705e7i	−0.0218335	+	0.0378167i
$367$	5.54913e8	−	9.61138e8i	0.585995	−	1.01497i	−0.408756	−	0.912644i	$-0.634037\pi$
$367$	5.54913e8	−	9.61138e8i	0.585995	−	1.01497i	0.994751	−	0.102329i	$-0.0326294\pi$
$368$	−3.67057e8	−	6.35761e8i	−0.383942	−	0.665008i
$369$	7.37135e8			0.763756
$370$	−3.62222e7	−	6.27387e7i	−0.0371765	−	0.0643916i
$371$	−2.10383e8	−	3.64394e8i	−0.213896	−	0.370478i
$372$	2.01494e9			2.02937
$373$	5.03814e8	+	8.72631e8i	0.502677	+	0.870663i	0.999995	+	0.00309433i	$0.000984957\pi$
$373$	5.03814e8	+	8.72631e8i	0.502677	+	0.870663i	−0.497318	+	0.867568i	$0.665682\pi$
$374$	−1.09532e7	+	1.89716e7i	−0.0108266	+	0.0187522i
$375$	−6.71914e8	+	1.16379e9i	−0.657967	+	1.13963i
$376$	−6.38119e7			−0.0619076
$377$	−7.66273e8	−	9.21162e8i	−0.736527	−	0.885403i
$378$	7.30422e6			0.00695589
$379$	8.79176e8	−	1.52278e9i	0.829542	−	1.43681i	−0.0688554	−	0.997627i	$-0.521935\pi$
$379$	8.79176e8	−	1.52278e9i	0.829542	−	1.43681i	0.898398	−	0.439183i	$-0.144732\pi$
$380$	1.14275e9	−	1.97930e9i	1.06834	−	1.85042i
$381$	1.39329e9	+	2.41326e9i	1.29064	+	2.23546i
$382$	−1.50446e8			−0.138089
$383$	−2.40721e8	−	4.16940e8i	−0.218936	−	0.379209i	0.735547	−	0.677474i	$-0.236925\pi$
$383$	−2.40721e8	−	4.16940e8i	−0.218936	−	0.379209i	−0.954483	+	0.298265i	$0.903592\pi$
$384$	−2.32908e8	−	4.03409e8i	−0.209906	−	0.363568i
$385$	−8.13613e8			−0.726617
$386$	1.73618e7	+	3.00716e7i	0.0153653	+	0.0266134i
$387$	8.84965e8	−	1.53280e9i	0.776136	−	1.34431i
$388$	2.23638e7	−	3.87352e7i	0.0194372	−	0.0336663i
$389$	5.02755e8			0.433045			0.216523	−	0.976278i	$-0.430529\pi$
$389$	5.02755e8			0.433045			0.216523	+	0.976278i	$0.430529\pi$
$390$	1.96347e8	−	3.37582e7i	0.167610	−	0.0288173i
$391$	−2.30270e8			−0.194813
$392$	1.22574e7	−	2.12304e7i	0.0102777	−	0.0178015i
$393$	−3.00939e8	+	5.21242e8i	−0.250095	+	0.433177i
$394$	4.11491e7	+	7.12724e7i	0.0338941	+	0.0587062i
$395$	1.11273e9			0.908444
$396$	−8.66677e8	−	1.50113e9i	−0.701333	−	1.21474i
$397$	−8.35980e8	−	1.44796e9i	−0.670547	−	1.16142i	−0.977749	−	0.209777i	$-0.932726\pi$
$397$	−8.35980e8	−	1.44796e9i	−0.670547	−	1.16142i	0.307202	−	0.951644i	$-0.400607\pi$
$398$	1.11718e8			0.0888244
$399$	4.74686e8	+	8.22180e8i	0.374112	+	0.647981i
$400$	−9.81665e8	+	1.70029e9i	−0.766926	+	1.32835i
$401$	7.86969e8	−	1.36307e9i	0.609470	−	1.05563i	−0.381858	−	0.924221i	$-0.624716\pi$
$401$	7.86969e8	−	1.36307e9i	0.609470	−	1.05563i	0.991328	−	0.131412i	$-0.0419511\pi$
$402$	−1.27730e8			−0.0980619
$403$	−6.29168e8	+	1.70594e9i	−0.478849	+	1.29836i
$404$	−7.17853e8			−0.541628
$405$	−8.52049e8	+	1.47579e9i	−0.637342	+	1.10391i
$406$	2.11703e7	−	3.66680e7i	0.0156995	−	0.0271923i
$407$	−5.26811e8	−	9.12464e8i	−0.387324	−	0.670865i
$408$	−7.26734e7			−0.0529742
$409$	−6.85232e8	−	1.18686e9i	−0.495229	−	0.857762i	0.504756	−	0.863262i	$-0.331583\pi$
$409$	−6.85232e8	−	1.18686e9i	−0.495229	−	0.857762i	−0.999985	+	0.00550026i	$0.998249\pi$
$410$	5.24118e7	+	9.07799e7i	0.0375565	+	0.0650498i
$411$	−2.78708e9			−1.98017
$412$	−1.00771e9	−	1.74540e9i	−0.709896	−	1.22958i
$413$	−1.99930e8	+	3.46289e8i	−0.139654	+	0.241888i
$414$	−4.76475e7	+	8.25278e7i	−0.0330019	+	0.0571609i
$415$	6.85713e8			0.470949
$416$	3.10977e8	−	5.34666e7i	0.211788	−	0.0364129i
$417$	2.98313e8			0.201464
$418$	−8.69259e7	+	1.50560e8i	−0.0582146	+	0.100831i
$419$	5.97854e8	−	1.03551e9i	0.397051	−	0.687712i	−0.596310	−	0.802754i	$-0.703367\pi$
$419$	5.97854e8	−	1.03551e9i	0.397051	−	0.687712i	0.993361	+	0.115042i	$0.0367004\pi$
$420$	−6.73018e8	−	1.16570e9i	−0.443256	−	0.767741i
$421$	2.77548e9			1.81280			0.906401	−	0.422419i	$-0.138819\pi$
$421$	2.77548e9			1.81280			0.906401	+	0.422419i	$0.138819\pi$
$422$	7.45828e7	+	1.29181e8i	0.0483109	+	0.0836769i
$423$	−3.92832e8	−	6.80406e8i	−0.252357	−	0.437096i
$424$	2.55615e8			0.162857
$425$	3.07920e8	+	5.33332e8i	0.194570	+	0.337005i
$426$	1.46352e8	−	2.53489e8i	0.0917202	−	0.158864i
$427$	−1.24855e8	+	2.16256e8i	−0.0776086	+	0.134422i
$428$	9.95656e8			0.613841
$429$	2.85565e9	−	4.90975e8i	1.74624	−	0.300233i
$430$	2.51691e8			0.152661
$431$	−1.57667e9	+	2.73088e9i	−0.948574	+	1.64298i	−0.200141	+	0.979767i	$0.564140\pi$
$431$	−1.57667e9	+	2.73088e9i	−0.948574	+	1.64298i	−0.748433	+	0.663211i	$0.769193\pi$
$432$	2.10435e8	−	3.64484e8i	0.125581	−	0.217513i
$433$	−7.07662e8	−	1.22571e9i	−0.418908	−	0.725569i	0.576922	−	0.816799i	$-0.304254\pi$
$433$	−7.07662e8	−	1.22571e9i	−0.418908	−	0.725569i	−0.995830	+	0.0912297i	$0.970920\pi$
$434$	−6.42511e7			−0.0377282
$435$	−2.33088e9	−	4.03721e9i	−1.35771	−	2.35163i
$436$	−8.63431e8	−	1.49551e9i	−0.498913	−	0.864142i
$437$	−1.82744e9			−1.04751
$438$	1.73734e8	+	3.00917e8i	0.0987930	+	0.171114i
$439$	8.39142e8	−	1.45344e9i	0.473380	−	0.819918i	−0.526156	−	0.850388i	$-0.676367\pi$
$439$	8.39142e8	−	1.45344e9i	0.473380	−	0.819918i	0.999536	+	0.0304701i	$0.00970044\pi$
$440$	2.47135e8	−	4.28050e8i	0.138309	−	0.239558i
$441$	3.01831e8			0.167582
$442$	1.13166e7	−	3.06841e7i	0.00623358	−	0.0169019i
$443$	5.91551e8			0.323280			0.161640	−	0.986850i	$-0.448322\pi$
$443$	5.91551e8			0.323280			0.161640	+	0.986850i	$0.448322\pi$
$444$	8.71553e8	−	1.50957e9i	0.472556	−	0.818491i
$445$	2.49124e8	−	4.31495e8i	0.134016	−	0.232122i
$446$	−8.81405e7	−	1.52664e8i	−0.0470439	−	0.0814825i
$447$	5.71086e8			0.302430
$448$	−3.48482e8	−	6.03589e8i	−0.183108	−	0.317153i
$449$	−5.73180e8	−	9.92776e8i	−0.298833	−	0.517594i	0.677036	−	0.735950i	$-0.263264\pi$
$449$	−5.73180e8	−	9.92776e8i	−0.298833	−	0.517594i	−0.975869	+	0.218356i	$0.929931\pi$
$450$	2.54859e8			0.131843
$451$	7.62271e8	+	1.32029e9i	0.391284	+	0.677723i
$452$	−1.18097e9	+	2.04550e9i	−0.601527	+	1.04187i
$453$	−1.54838e9	+	2.68188e9i	−0.782591	+	1.35549i
$454$	−1.26687e8			−0.0635384
$455$	1.19709e9	−	2.05816e8i	0.595781	−	0.102433i
$456$	−5.76743e8			−0.284843
$457$	−2.32133e8	+	4.02066e8i	−0.113770	+	0.197056i	−0.917288	−	0.398225i	$-0.869626\pi$
$457$	−2.32133e8	+	4.02066e8i	−0.113770	+	0.197056i	0.803517	+	0.595282i	$0.202960\pi$
$458$	−1.18370e8	+	2.05023e8i	−0.0575723	+	0.0997181i
$459$	−6.60074e7	−	1.14328e8i	−0.0318602	−	0.0551834i
$460$	2.59098e9			1.24112
$461$	−1.00395e8	−	1.73890e8i	−0.0477266	−	0.0826649i	0.841175	−	0.540763i	$-0.181864\pi$
$461$	−1.00395e8	−	1.73890e8i	−0.0477266	−	0.0826649i	−0.888902	+	0.458098i	$0.848531\pi$
$462$	5.11947e7	+	8.86718e7i	0.0241534	+	0.0418349i
$463$	−2.55134e9			−1.19463			−0.597317	−	0.802005i	$-0.703767\pi$
$463$	−2.55134e9			−1.19463			−0.597317	+	0.802005i	$0.703767\pi$
$464$	−1.21984e9	−	2.11282e9i	−0.566877	−	0.981859i
$465$	−3.53707e9	+	6.12638e9i	−1.63139	+	2.82565i
$466$	8.05894e7	−	1.39585e8i	0.0368916	−	0.0638981i
$467$	−1.33292e9			−0.605611			−0.302805	−	0.953052i	$-0.597923\pi$
$467$	−1.33292e9			−0.605611			−0.302805	+	0.953052i	$0.597923\pi$
$468$	1.65490e9	+	1.98941e9i	0.746295	+	0.897146i
$469$	−7.78741e8			−0.348568
$470$	5.58624e7	−	9.67565e7i	0.0248186	−	0.0429870i
$471$	−4.74420e7	+	8.21719e7i	−0.0209213	+	0.0362368i
$472$	−1.21457e8	−	2.10370e8i	−0.0531651	−	0.0920847i
$473$	3.66057e9			1.59050
$474$	−7.00156e7	−	1.21271e8i	−0.0301975	−	0.0523036i
$475$	2.44368e9	+	4.23258e9i	1.04620	+	1.81208i
$476$	−2.20959e8			−0.0939048
$477$	1.57359e9	+	2.72554e9i	0.663861	+	1.14984i
$478$	−3.86312e7	+	6.69112e7i	−0.0161786	+	0.0280221i
$479$	2.06194e9	−	3.57138e9i	0.857239	−	1.48478i	−0.0173141	−	0.999850i	$-0.505512\pi$
$479$	2.06194e9	−	3.57138e9i	0.857239	−	1.48478i	0.874553	−	0.484931i	$-0.161155\pi$
$480$	1.22764e9			0.506672
$481$	1.00593e9	+	1.20926e9i	0.412155	+	0.495466i
$482$	−3.43482e8			−0.139714
$483$	−5.38133e8	+	9.32074e8i	−0.217308	+	0.376388i
$484$	5.51772e8	−	9.55696e8i	0.221208	−	0.383143i
$485$	7.85158e7	+	1.35993e8i	0.0312508	+	0.0541280i
$486$	2.61025e8			0.103147
$487$	−2.04857e6	−	3.54822e6i	−0.000803709	−	0.00139206i	0.865623	−	0.500696i	$-0.166922\pi$
$487$	−2.04857e6	−	3.54822e6i	−0.000803709	−	0.00139206i	−0.866427	+	0.499304i	$0.833589\pi$
$488$	−7.58496e7	−	1.31375e8i	−0.0295450	−	0.0511734i
$489$	−4.47204e9			−1.72951
$490$	2.14608e7	+	3.71712e7i	0.00824061	+	0.0142732i
$491$	−1.39007e9	+	2.40767e9i	−0.529970	+	0.917935i	0.469419	+	0.882976i	$0.344464\pi$
$491$	−1.39007e9	+	2.40767e9i	−0.529970	+	0.917935i	−0.999389	+	0.0349595i	$0.988870\pi$
$492$	−1.26110e9	+	2.18428e9i	−0.477387	+	0.826858i
$493$	−7.65254e8			−0.287635
$494$	8.98096e7	−	2.43512e8i	0.0335180	−	0.0908816i
$495$	6.08554e9			2.25518
$496$	−1.85108e9	+	3.20616e9i	−0.681144	+	1.17978i
$497$	8.92277e8	−	1.54547e9i	0.326026	−	0.564694i
$498$	−4.31468e7	−	7.47325e7i	−0.0156548	−	0.0271148i
$499$	−2.56384e9			−0.923718			−0.461859	−	0.886953i	$-0.652817\pi$
$499$	−2.56384e9			−0.923718			−0.461859	+	0.886953i	$0.652817\pi$
$500$	−1.24107e9	−	2.14960e9i	−0.444019	−	0.769063i
$501$	−2.10681e9	−	3.64910e9i	−0.748502	−	1.29644i
$502$	7.72720e7			0.0272621
$503$	7.46811e8	+	1.29351e9i	0.261651	+	0.453193i	0.966681	−	0.255985i	$-0.0823997\pi$
$503$	7.46811e8	+	1.29351e9i	0.261651	+	0.453193i	−0.705030	+	0.709178i	$0.749066\pi$
$504$	−9.16809e7	+	1.58796e8i	−0.0318986	+	0.0552500i
$505$	1.26014e9	−	2.18262e9i	0.435409	−	0.754151i
$506$	−1.97089e8			−0.0676294
$507$	−4.07739e9	+	1.44477e9i	−1.38949	+	0.492345i
$508$	−5.14702e9			−1.74194
$509$	3.24786e8	−	5.62545e8i	0.109165	−	0.189080i	−0.806267	−	0.591552i	$-0.798516\pi$
$509$	3.24786e8	−	5.62545e8i	0.109165	−	0.189080i	0.915432	+	0.402472i	$0.131849\pi$
$510$	6.36199e7	−	1.10193e8i	0.0212372	−	0.0367839i
$511$	1.05922e9	+	1.83463e9i	0.351167	+	0.608239i
$512$	1.07265e9			0.353193
$513$	−5.23841e8	−	9.07319e8i	−0.171312	−	0.296722i
$514$	−4.09525e7	−	7.09317e7i	−0.0133018	−	0.0230393i
$515$	7.07582e9			2.28272
$516$	3.02801e9	+	5.24467e9i	0.970250	+	1.68052i
$517$	8.12456e8	−	1.40721e9i	0.258573	−	0.447861i
$518$	−2.77915e7	+	4.81363e7i	−0.00878533	+	0.0152166i
$519$	7.11009e9			2.23249
$520$	−2.55333e8	+	6.92316e8i	−0.0796334	+	0.215920i
$521$	−3.54004e9			−1.09667			−0.548335	−	0.836259i	$-0.684738\pi$
$521$	−3.54004e9			−1.09667			−0.548335	+	0.836259i	$0.684738\pi$
$522$	−1.58346e8	+	2.74264e8i	−0.0487261	+	0.0843960i
$523$	−4.91516e6	+	8.51331e6i	−0.00150239	+	0.00260221i	−0.866776	−	0.498698i	$-0.833812\pi$
$523$	−4.91516e6	+	8.51331e6i	−0.00150239	+	0.00260221i	0.865273	+	0.501301i	$0.167145\pi$
$524$	−5.55854e8	−	9.62768e8i	−0.168772	−	0.292322i
$525$	2.87839e9			0.868145
$526$	−1.86756e8	−	3.23472e8i	−0.0559533	−	0.0969139i
$527$	5.80629e8	+	1.00568e9i	0.172807	+	0.299311i
$528$	5.89969e9			1.74426
$529$	6.66561e8	+	1.15452e9i	0.195770	+	0.339083i
$530$	−2.23771e8	+	3.87583e8i	−0.0652887	+	0.113083i
$531$	1.49541e9	−	2.59012e9i	0.433439	−	0.750739i
$532$	−1.75355e9			−0.504927
$533$	−1.45554e9	−	1.74975e9i	−0.416368	−	0.500530i
$534$	−6.27021e7			−0.0178192
$535$	−1.74780e9	+	3.02727e9i	−0.493461	+	0.854700i
$536$	2.36542e8	−	4.09703e8i	0.0663486	−	0.114919i
$537$	−3.64480e9	−	6.31297e9i	−1.01569	−	1.75923i
$538$	6.95295e6			0.00192500
$539$	3.12123e8	+	5.40613e8i	0.0858549	+	0.148705i
$540$	7.42710e8	+	1.28641e9i	0.202974	+	0.351562i
$541$	−2.59597e9			−0.704870			−0.352435	−	0.935836i	$-0.614646\pi$
$541$	−2.59597e9			−0.704870			−0.352435	+	0.935836i	$0.614646\pi$
$542$	−1.27878e8	−	2.21491e8i	−0.0344984	−	0.0597529i
$543$	1.57980e9	−	2.73630e9i	0.423451	−	0.733439i
$544$	1.00762e8	−	1.74525e8i	0.0268349	−	0.0464794i
$545$	6.06274e9			1.60428
$546$	−9.77548e7	−	1.17514e8i	−0.0257018	−	0.0308970i
$547$	−4.84335e7			−0.0126529			−0.00632646	−	0.999980i	$-0.502014\pi$
$547$	−4.84335e7			−0.0126529			−0.00632646	+	0.999980i	$0.502014\pi$
$548$	2.57396e9	−	4.45823e9i	0.668143	−	1.15726i
$549$	9.33874e8	−	1.61752e9i	0.240871	−	0.417202i
$550$	2.63550e8	+	4.56481e8i	0.0675450	+	0.116991i
$551$	−6.07313e9			−1.54661
$552$	−3.26915e8	−	5.66234e8i	−0.0827272	−	0.143288i
$553$	−4.26870e8	−	7.39361e8i	−0.107339	−	0.185917i
$554$	2.62573e8			0.0656093
$555$	3.05989e9	+	5.29988e9i	0.759767	+	1.31595i
$556$	−2.75502e8	+	4.77184e8i	−0.0679772	+	0.117740i
$557$	2.22619e9	−	3.85587e9i	0.545844	−	0.945429i	−0.452710	−	0.891658i	$-0.649543\pi$
$557$	2.22619e9	−	3.85587e9i	0.545844	−	0.945429i	0.998553	−	0.0537711i	$-0.0171241\pi$
$558$	4.80575e8			0.117096
$559$	−5.38588e9	+	9.25999e8i	−1.30411	+	0.224217i
$560$	2.47315e9			0.595103
$561$	9.25280e8	−	1.60263e9i	0.221260	−	0.383234i
$562$	−2.94832e8	+	5.10664e8i	−0.0700644	+	0.121355i
$563$	2.69263e9	+	4.66378e9i	0.635913	+	1.10143i	0.986321	+	0.164837i	$0.0527097\pi$
$563$	2.69263e9	+	4.66378e9i	0.635913	+	1.10143i	−0.350408	+	0.936597i	$0.613957\pi$
$564$	2.68824e9			0.630945
$565$	−4.14621e9	−	7.18144e9i	−0.967123	−	1.67511i
$566$	−2.87976e7	−	4.98788e7i	−0.00667572	−	0.0115627i
$567$	1.30747e9			0.301226
$568$	5.42057e8	+	9.38871e8i	0.124116	+	0.214974i
$569$	−7.03158e8	+	1.21791e9i	−0.160015	+	0.277154i	−0.934874	−	0.354980i	$-0.884488\pi$
$569$	−7.03158e8	+	1.21791e9i	−0.160015	+	0.277154i	0.774859	+	0.632134i	$0.217821\pi$
$570$	5.04893e8	−	8.74501e8i	0.114193	−	0.197787i
$571$	−4.58024e9			−1.02958			−0.514792	−	0.857315i	$-0.672131\pi$
$571$	−4.58024e9			−1.02958			−0.514792	+	0.857315i	$0.672131\pi$
$572$	−1.85192e9	+	5.02135e9i	−0.413749	+	1.12185i
$573$	1.27090e10			2.82209
$574$	4.02130e7	−	6.96510e7i	0.00887514	−	0.0153722i
$575$	−2.77030e9	+	4.79831e9i	−0.607701	+	1.05257i
$576$	2.60652e9	+	4.51463e9i	0.568307	+	0.984337i
$577$	−6.69187e9			−1.45021			−0.725107	−	0.688636i	$-0.758210\pi$
$577$	−6.69187e9			−1.45021			−0.725107	+	0.688636i	$0.758210\pi$
$578$	1.56990e8	+	2.71915e8i	0.0338163	+	0.0585715i
$579$	−1.46665e9	−	2.54031e9i	−0.314016	−	0.543891i
$580$	8.61059e9			1.83246
$581$	−2.63057e8	−	4.55628e8i	−0.0556460	−	0.0963816i
$582$	9.88083e6	−	1.71141e7i	0.00207761	−	0.00359852i
$583$	−3.25450e9	+	5.63696e9i	−0.680212	+	1.17816i
$584$	−1.28695e9			−0.267373
$585$	−8.95380e9	+	1.53943e9i	−1.84911	+	0.317918i
$586$	1.93972e8			0.0398196
$587$	−1.93789e9	+	3.35653e9i	−0.395455	+	0.684948i	−0.993159	−	0.116769i	$-0.962746\pi$
$587$	−1.93789e9	+	3.35653e9i	−0.395455	+	0.684948i	0.597704	+	0.801717i	$0.296080\pi$
$588$	−5.16374e8	+	8.94386e8i	−0.104748	+	0.181428i
$589$	4.60793e9	+	7.98117e9i	0.929185	+	1.60940i
$590$	4.25306e8			0.0852549
$591$	−3.47609e9	−	6.02077e9i	−0.692684	−	1.19976i
$592$	1.60135e9	+	2.77362e9i	0.317220	+	0.549442i
$593$	−9.46942e9			−1.86480			−0.932400	−	0.361429i	$-0.882289\pi$
$593$	−9.46942e9			−1.86480			−0.932400	+	0.361429i	$0.882289\pi$
$594$	−5.64960e7	−	9.78539e7i	−0.0110602	−	0.0191569i
$595$	3.87877e8	−	6.71823e8i	0.0754892	−	0.130751i
$596$	−5.27417e8	+	9.13513e8i	−0.102045	+	0.176747i
$597$	−9.43743e9			−1.81528
$598$	2.89982e8	−	4.98568e7i	0.0554519	−	0.00953389i
$599$	8.22571e9			1.56379			0.781897	−	0.623407i	$-0.214252\pi$
$599$	8.22571e9			1.56379			0.781897	+	0.623407i	$0.214252\pi$
$600$	−8.74310e8	+	1.51435e9i	−0.165248	+	0.286218i
$601$	7.39311e8	−	1.28052e9i	0.138921	−	0.240617i	−0.788168	−	0.615460i	$-0.788970\pi$
$601$	7.39311e8	−	1.28052e9i	0.138921	−	0.240617i	0.927088	+	0.374843i	$0.122303\pi$
$602$	−9.65553e7	−	1.67239e8i	−0.0180380	−	0.0312427i
$603$	5.82470e9			1.08184
$604$	−2.85997e9	−	4.95361e9i	−0.528119	−	0.914729i
$605$	1.93719e9	+	3.35530e9i	0.355654	+	0.616010i
$606$	−3.17164e8			−0.0578935
$607$	4.10001e9	+	7.10143e9i	0.744089	+	1.28880i	0.950619	+	0.310359i	$0.100449\pi$
$607$	4.10001e9	+	7.10143e9i	0.744089	+	1.28880i	−0.206531	+	0.978440i	$0.566217\pi$
$608$	7.99656e8	−	1.38505e9i	0.144291	−	0.249920i
$609$	−1.78837e9	+	3.09755e9i	−0.320847	+	0.555723i
$610$	2.65602e8			0.0473779
$611$	−8.39408e8	+	2.27599e9i	−0.148877	+	0.403670i
$612$	1.65270e9			0.291449
$613$	−6.42592e8	+	1.11300e9i	−0.112674	+	0.195157i	−0.916848	−	0.399237i	$-0.869275\pi$
$613$	−6.42592e8	+	1.11300e9i	−0.112674	+	0.195157i	0.804174	+	0.594395i	$0.202608\pi$
$614$	−2.91640e8	+	5.05135e8i	−0.0508461	+	0.0880680i
$615$	−4.42751e9	−	7.66868e9i	−0.767533	−	1.32941i
$616$	−3.79229e8			−0.0653686
$617$	1.27516e9	+	2.20864e9i	0.218558	+	0.378553i	0.954367	−	0.298636i	$-0.0965315\pi$
$617$	1.27516e9	+	2.20864e9i	0.218558	+	0.378553i	−0.735810	+	0.677188i	$0.763198\pi$
$618$	−4.45229e8	−	7.71160e8i	−0.0758794	−	0.131427i
$619$	3.77843e9			0.640316			0.320158	−	0.947364i	$-0.396264\pi$
$619$	3.77843e9			0.640316			0.320158	+	0.947364i	$0.396264\pi$
$620$	−6.53320e9	−	1.13158e10i	−1.10092	−	1.90685i
$621$	5.93858e8	−	1.02859e9i	0.0995089	−	0.172354i
$622$	−3.06471e8	+	5.30823e8i	−0.0510650	+	0.0884471i
$623$	−3.82282e8			−0.0633396
$624$	−8.68035e9	+	1.49242e9i	−1.43018	+	0.245892i
$625$	−7.95661e8			−0.130361
$626$	−9.04552e6	+	1.56673e7i	−0.00147375	+	0.00255261i
$627$	7.34311e9	−	1.27186e10i	1.18972	−	2.06065i
$628$	−8.76285e7	−	1.51777e8i	−0.0141184	−	0.0244538i
$629$	1.00460e9			0.160958
$630$	−1.60519e8	−	2.78027e8i	−0.0255761	−	0.0442991i
$631$	4.62020e9	+	8.00241e9i	0.732078	+	1.26800i	0.955993	+	0.293388i	$0.0947828\pi$
$631$	4.62020e9	+	8.00241e9i	0.732078	+	1.26800i	−0.223915	+	0.974609i	$0.571884\pi$
$632$	5.18647e8			0.0817263
$633$	−6.30042e9	−	1.09126e10i	−0.987317	−	1.71008i
$634$	−2.93619e8	+	5.08563e8i	−0.0457585	+	0.0792561i
$635$	9.03519e9	−	1.56494e10i	1.40033	−	2.42544i
$636$	−1.07684e10			−1.65979
$637$	−5.95991e8	−	7.16460e8i	−0.0913590	−	0.109826i
$638$	−6.54984e8			−0.0998524
$639$	−6.67392e9	+	1.15596e10i	−1.01188	+	1.75262i
$640$	−1.51035e9	+	2.61601e9i	−0.227745	+	0.394466i
$641$	−3.80044e9	−	6.58255e9i	−0.569942	−	0.987168i	−0.996571	−	0.0827412i	$-0.973633\pi$
$641$	−3.80044e9	−	6.58255e9i	−0.569942	−	0.987168i	0.426630	−	0.904426i	$-0.359701\pi$
$642$	4.39904e8			0.0656123
$643$	−1.03273e9	−	1.78875e9i	−0.153197	−	0.265345i	0.779204	−	0.626770i	$-0.215624\pi$
$643$	−1.03273e9	−	1.78875e9i	−0.153197	−	0.265345i	−0.932401	+	0.361425i	$0.882290\pi$
$644$	−9.93968e8	−	1.72160e9i	−0.146647	−	0.253999i
$645$	−2.12618e10			−3.11990
$646$	−8.28810e7	−	1.43554e8i	−0.0120960	−	0.0209509i
$647$	1.88801e9	−	3.27013e9i	0.274056	−	0.474680i	−0.695840	−	0.718197i	$-0.744968\pi$
$647$	1.88801e9	−	3.27013e9i	0.274056	−	0.474680i	0.969897	+	0.243517i	$0.0783012\pi$
$648$	−3.97144e8	+	6.87874e8i	−0.0573371	+	0.0993107i
$649$	6.18560e9			0.888230
$650$	−5.03241e8	−	6.04963e8i	−0.0718752	−	0.0864036i
$651$	5.42764e9			0.771042
$652$	4.13007e9	−	7.15350e9i	0.583568	−	1.01077i
$653$	1.89437e9	−	3.28115e9i	0.266237	−	0.461136i	−0.701650	−	0.712522i	$-0.747553\pi$
$653$	1.89437e9	−	3.28115e9i	0.266237	−	0.461136i	0.967887	+	0.251386i	$0.0808862\pi$
$654$	−3.81484e8	−	6.60749e8i	−0.0533278	−	0.0923665i
$655$	3.90304e9			0.542698
$656$	−2.31708e9	−	4.01330e9i	−0.320463	−	0.555058i
$657$	−7.92260e9	−	1.37223e10i	−1.08991	−	1.88777i
$658$	−8.57210e7			−0.0117300
$659$	−1.39989e8	−	2.42468e8i	−0.0190544	−	0.0330031i	0.856341	−	0.516411i	$-0.172732\pi$
$659$	−1.39989e8	−	2.42468e8i	−0.0190544	−	0.0330031i	−0.875395	+	0.483408i	$0.839399\pi$
$660$	−1.04112e10	+	1.80327e10i	−1.40960	+	2.44150i
$661$	4.54648e9	−	7.87473e9i	0.612308	−	1.06055i	−0.378543	−	0.925584i	$-0.623575\pi$
$661$	4.54648e9	−	7.87473e9i	0.612308	−	1.06055i	0.990850	−	0.134965i	$-0.0430920\pi$
$662$	−4.04271e8			−0.0541589
$663$	−9.55975e8	+	2.59205e9i	−0.127394	+	0.345419i
$664$	3.19614e8			0.0423679
$665$	3.07823e9	−	5.33165e9i	0.405906	−	0.703049i
$666$	2.07871e8	−	3.60043e8i	0.0272668	−	0.0472274i
$667$	−3.44244e9	−	5.96247e9i	−0.449185	−	0.778012i
$668$	7.78283e9			1.01023
$669$	7.44572e9	+	1.28964e10i	0.961425	+	1.66524i
$670$	4.14148e8	+	7.17326e8i	0.0531979	+	0.0921414i
$671$	3.86288e9			0.493608
$672$	−4.70954e8	−	8.15717e8i	−0.0598668	−	0.103692i
$673$	1.95235e9	−	3.38158e9i	0.246891	−	0.427628i	−0.715770	−	0.698336i	$-0.753924\pi$
$673$	1.95235e9	−	3.38158e9i	0.246891	−	0.427628i	0.962662	+	0.270707i	$0.0872576\pi$
$674$	1.13420e8	−	1.96449e8i	0.0142685	−	0.0247138i
$675$	−3.17645e9			−0.397538
$676$	1.45455e9	−	7.85651e9i	0.181099	−	0.978174i
$677$	8.76534e9			1.08570			0.542848	−	0.839831i	$-0.317346\pi$
$677$	8.76534e9			1.08570			0.542848	+	0.839831i	$0.317346\pi$
$678$	−5.21780e8	+	9.03750e8i	−0.0642960	+	0.111364i
$679$	6.02414e7	−	1.04341e8i	0.00738500	−	0.0127912i
$680$	2.35635e8	+	4.08132e8i	0.0287381	+	0.0497759i
$681$	1.07019e10			1.29852
$682$	4.96963e8	+	8.60765e8i	0.0599900	+	0.103906i
$683$	6.88777e8	+	1.19300e9i	0.0827192	+	0.143274i	0.904417	−	0.426650i	$-0.140306\pi$
$683$	6.88777e8	+	1.19300e9i	0.0827192	+	0.143274i	−0.821698	+	0.569923i	$0.806973\pi$
$684$	1.31160e10			1.56713
$685$	9.03677e9	+	1.56522e10i	1.07423	+	1.86062i
$686$	1.64658e7	−	2.85196e7i	0.00194737	−	0.00337295i
$687$	9.99939e9	−	1.73195e10i	1.17659	−	2.03791i
$688$	−1.11271e10			−1.30263
$689$	3.36246e9	−	9.11706e9i	0.391643	−	1.06191i
$690$	1.14476e9			0.132660
$691$	5.27175e9	−	9.13094e9i	0.607829	−	1.05279i	−0.383768	−	0.923429i	$-0.625374\pi$
$691$	5.27175e9	−	9.13094e9i	0.607829	−	1.05279i	0.991598	−	0.129361i	$-0.0412927\pi$
$692$	−6.56640e9	+	1.13733e10i	−0.753280	+	1.30472i
$693$	−2.33457e9	−	4.04359e9i	−0.266465	−	0.461531i
$694$	−5.94809e8			−0.0675490
$695$	−9.67246e8	−	1.67532e9i	−0.109292	−	0.189300i
$696$	−1.08643e9	−	1.88176e9i	−0.122144	−	0.211559i
$697$	−1.45360e9			−0.162604
$698$	−2.09661e8	−	3.63144e8i	−0.0233359	−	0.0404189i
$699$	−6.80783e9	+	1.17915e10i	−0.753943	+	1.30587i
$700$	−2.65829e9	+	4.60429e9i	−0.292927	+	0.507364i
$701$	−7.10207e9			−0.778704			−0.389352	−	0.921089i	$-0.627301\pi$
$701$	−7.10207e9			−0.778704			−0.389352	+	0.921089i	$0.627301\pi$
$702$	1.07878e8	+	1.29683e8i	0.0117693	+	0.0141483i
$703$	7.97256e9			0.865474
$704$	−5.39081e9	+	9.33716e9i	−0.582304	+	1.00858i
$705$	−4.71900e9	+	8.17355e9i	−0.507211	+	0.878515i
$706$	−1.96470e8	−	3.40296e8i	−0.0210126	−	0.0363949i
$707$	−1.93368e9			−0.205787
$708$	5.11671e9	+	8.86239e9i	0.541844	+	0.938501i
$709$	5.60664e8	+	9.71099e8i	0.0590801	+	0.102330i	0.894053	−	0.447962i	$-0.147850\pi$
$709$	5.60664e8	+	9.71099e8i	0.0590801	+	0.102330i	−0.834973	+	0.550291i	$0.814517\pi$
$710$	−1.89812e9			−0.199030
$711$	3.19284e9	+	5.53016e9i	0.333145	+	0.577024i
$712$	1.16118e8	−	2.01122e8i	0.0120564	−	0.0208824i
$713$	−5.22383e9	+	9.04794e9i	−0.539729	+	0.934838i
$714$	−9.76249e7			−0.0100373
$715$	−1.20164e10	−	1.44453e10i	−1.22943	−	1.47794i
$716$	1.34644e10			1.37085
$717$	3.26339e9	−	5.65236e9i	0.330637	−	0.572681i
$718$	3.93278e8	−	6.81178e8i	0.0396520	−	0.0686792i
$719$	−6.66793e9	−	1.15492e10i	−0.669022	−	1.15878i	−0.978178	−	0.207768i	$-0.933380\pi$
$719$	−6.66793e9	−	1.15492e10i	−0.669022	−	1.15878i	0.309157	−	0.951011i	$-0.399953\pi$
$720$	−1.84983e10			−1.84700
$721$	−2.71447e9	−	4.70160e9i	−0.269719	−	0.467167i
$722$	−2.93018e8	−	5.07522e8i	−0.0289744	−	0.0501850i
$723$	2.90158e10			2.85529
$724$	2.91800e9	+	5.05413e9i	0.285759	+	0.494950i
$725$	−9.20653e9	+	1.59462e10i	−0.897249	+	1.55408i
$726$	2.43785e8	−	4.22249e8i	0.0236445	−	0.0409534i
$727$	−6.61234e9			−0.638241			−0.319120	−	0.947714i	$-0.603387\pi$
$727$	−6.61234e9			−0.638241			−0.319120	+	0.947714i	$0.603387\pi$
$728$	5.57968e8	−	9.59320e7i	0.0535981	−	0.00921517i
$729$	−1.37137e10			−1.31101
$730$	1.12663e9	−	1.95137e9i	0.107189	−	0.185657i
$731$	−1.74512e9	+	3.02263e9i	−0.165240	+	0.286203i
$732$	3.19536e9	+	5.53453e9i	0.301114	+	0.521545i
$733$	2.10331e9			0.197260			0.0986301	−	0.995124i	$-0.468554\pi$
$733$	2.10331e9			0.197260			0.0986301	+	0.995124i	$0.468554\pi$
$734$	4.52852e8	+	7.84362e8i	0.0422688	+	0.0732117i
$735$	−1.81291e9	−	3.14005e9i	−0.168411	−	0.291697i
$736$	1.81308e9			0.167627
$737$	6.02333e9	+	1.04327e10i	0.554243	+	0.959977i
$738$	−3.00779e8	+	5.20965e8i	−0.0275455	+	0.0477102i
$739$	1.69009e9	−	2.92732e9i	0.154047	−	0.266817i	−0.778665	−	0.627440i	$-0.784103\pi$
$739$	1.69009e9	−	2.92732e9i	0.154047	−	0.266817i	0.932712	+	0.360623i	$0.117436\pi$
$740$	−1.13036e10			−1.02543
$741$	−7.58671e9	+	2.05708e10i	−0.684999	+	1.85732i
$742$	3.43377e8			0.0308573
$743$	−3.12103e9	+	5.40579e9i	−0.279150	+	0.483502i	−0.971174	−	0.238373i	$-0.923386\pi$
$743$	−3.12103e9	+	5.40579e9i	−0.279150	+	0.483502i	0.692024	+	0.721875i	$0.256719\pi$
$744$	−1.64864e9	+	2.85553e9i	−0.146765	+	0.254204i
$745$	−1.85168e9	−	3.20720e9i	−0.164066	−	0.284171i
$746$	−8.22302e8			−0.0725179
$747$	1.96757e9	+	3.40794e9i	0.172707	+	0.299137i
$748$	1.70905e9	+	2.96017e9i	0.149314	+	0.258619i
$749$	2.68200e9			0.233224
$750$	−5.48333e8	−	9.49741e8i	−0.0474603	−	0.0822036i
$751$	−1.38703e9	+	2.40241e9i	−0.119494	+	0.206970i	−0.919567	−	0.392932i	$-0.871461\pi$
$751$	−1.38703e9	+	2.40241e9i	−0.119494	+	0.206970i	0.800073	+	0.599903i	$0.204794\pi$
$752$	−2.46963e9	+	4.27752e9i	−0.211772	+	0.366800i
$753$	−6.52760e9			−0.557148
$754$	9.63693e8	−	1.65689e8i	0.0818727	−	0.0140764i
$755$	2.00818e10			1.69820
$756$	5.69846e8	−	9.87002e8i	0.0479657	−	0.0830791i
$757$	8.32613e9	−	1.44213e10i	0.697602	−	1.20828i	−0.271694	−	0.962384i	$-0.587584\pi$
$757$	8.32613e9	−	1.44213e10i	0.697602	−	1.20828i	0.969296	−	0.245898i	$-0.0790827\pi$
$758$	7.17475e8	+	1.24270e9i	0.0598363	+	0.103639i
$759$	1.66492e10			1.38212
$760$	1.87002e9	+	3.23897e9i	0.154525	+	0.267645i
$761$	−9.47824e8	−	1.64168e9i	−0.0779618	−	0.135034i	0.824409	−	0.565995i	$-0.191508\pi$
$761$	−9.47824e8	−	1.64168e9i	−0.0779618	−	0.135034i	−0.902370	+	0.430961i	$0.858175\pi$
$762$	−2.27407e9			−0.186192
$763$	−2.32583e9	−	4.02845e9i	−0.189558	−	0.328323i
$764$	−1.17372e10	+	2.03295e10i	−0.952223	+	1.64930i
$765$	−2.90118e9	+	5.02500e9i	−0.234293	+	0.405808i
$766$	3.92893e8			0.0315845
$767$	−9.10102e9	+	1.56475e9i	−0.728293	+	0.125216i
$768$	−1.75502e10			−1.39803
$769$	−2.07651e9	+	3.59662e9i	−0.164661	+	0.285201i	−0.936535	−	0.350574i	$-0.885986\pi$
$769$	−2.07651e9	+	3.59662e9i	−0.164661	+	0.285201i	0.771874	+	0.635776i	$0.219320\pi$
$770$	3.31985e8	−	5.75016e8i	0.0262060	−	0.0453902i
$771$	3.45948e9	+	5.99200e9i	0.271845	+	0.470849i
$772$	5.41800e9			0.423817
$773$	−1.70075e9	−	2.94579e9i	−0.132438	−	0.229390i	0.792178	−	0.610291i	$-0.208947\pi$
$773$	−1.70075e9	−	2.94579e9i	−0.132438	−	0.229390i	−0.924616	+	0.380901i	$0.875614\pi$
$774$	7.22199e8	+	1.25089e9i	0.0559840	+	0.0969671i
$775$	2.79415e10			2.15622
$776$	3.65966e7	+	6.33871e7i	0.00281141	+	0.00486951i
$777$	2.34770e9	−	4.06634e9i	0.179544	−	0.310979i
$778$	−2.05143e8	+	3.55319e8i	−0.0156181	+	0.0270514i
$779$	−1.15359e10			−0.874322
$780$	1.07566e10	−	2.91656e10i	0.811601	−	2.20060i
$781$	−2.76060e10			−2.07360
$782$	9.39590e7	−	1.62742e8i	0.00702611	−	0.0121696i
$783$	1.97356e9	−	3.41831e9i	0.146921	−	0.254475i
$784$	−9.48763e8	−	1.64331e9i	−0.0703156	−	0.121790i
$785$	6.15300e8			0.0453987
$786$	−2.45589e8	−	4.25373e8i	−0.0180398	−	0.0312458i
$787$	6.47540e9	+	1.12157e10i	0.473539	+	0.820193i	0.999541	−	0.0302901i	$-0.00964312\pi$
$787$	6.47540e9	+	1.12157e10i	0.473539	+	0.820193i	−0.526003	+	0.850483i	$0.676310\pi$
$788$	1.28412e10			0.934894
$789$	1.57763e10	+	2.73254e10i	1.14350	+	1.98060i
$790$	−4.54035e8	+	7.86411e8i	−0.0327638	+	0.0567486i
$791$	−3.18119e9	+	5.50998e9i	−0.228545	+	0.395851i
$792$	2.83650e9			0.202882
$793$	−5.68354e9	+	9.77176e8i	−0.404728	+	0.0695852i
$794$	1.36445e9			0.0967354
$795$	1.89032e10	−	3.27412e10i	1.33429	−	2.31105i
$796$	8.71579e9	−	1.50962e10i	0.612507	−	1.06089i
$797$	−1.28283e9	−	2.22193e9i	−0.0897565	−	0.155463i	0.817652	−	0.575713i	$-0.195276\pi$
$797$	−1.28283e9	−	2.22193e9i	−0.0897565	−	0.155463i	−0.907408	+	0.420250i	$0.861942\pi$
$798$	−7.74760e8			−0.0539706
$799$	7.74651e8	+	1.34173e9i	0.0537269	+	0.0930578i
$800$	−2.42447e9	−	4.19930e9i	−0.167418	−	0.289976i
$801$	2.85933e9			0.196585
$802$	6.42227e8	+	1.11237e9i	0.0439621	+	0.0761446i
$803$	1.63855e10	−	2.83806e10i	1.11675	−	1.93427i
$804$	−9.96495e9	+	1.72598e10i	−0.676206	+	1.17122i
$805$	6.97934e9			0.471551
$806$	−9.48937e8	−	1.14075e9i	−0.0638359	−	0.0767392i
$807$	−5.87354e8			−0.0393408
$808$	5.87355e8	−	1.01733e9i	0.0391707	−	0.0678456i
$809$	−2.80299e9	+	4.85492e9i	−0.186124	+	0.322376i	−0.943955	−	0.330075i	$-0.892926\pi$
$809$	−2.80299e9	+	4.85492e9i	−0.186124	+	0.322376i	0.757831	+	0.652451i	$0.226259\pi$
$810$	−6.95338e8	−	1.20436e9i	−0.0459725	−	0.0796267i
$811$	2.18388e10			1.43766			0.718830	−	0.695186i	$-0.244678\pi$
$811$	2.18388e10			1.43766			0.718830	+	0.695186i	$0.244678\pi$
$812$	−3.30324e9	−	5.72139e9i	−0.216518	−	0.375021i
$813$	1.08026e10	+	1.87106e10i	0.705034	+	1.22115i
$814$	8.59837e8			0.0558767
$815$	1.45001e10	+	2.51148e10i	0.938249	+	1.62509i
$816$	−2.81258e9	+	4.87153e9i	−0.181213	+	0.313870i
$817$	−1.38494e10	+	2.39879e10i	−0.888494	+	1.53892i
$818$	1.11840e9			0.0714434
$819$	4.45780e9	+	5.35887e9i	0.283548	+	0.340863i
$820$	1.63558e10			1.03591
$821$	−4.92076e9	+	8.52301e9i	−0.310336	+	0.537517i	−0.978435	−	0.206555i	$-0.933775\pi$
$821$	−4.92076e9	+	8.52301e9i	−0.310336	+	0.537517i	0.668099	+	0.744072i	$0.267108\pi$
$822$	1.13723e9	−	1.96975e9i	0.0714165	−	0.123697i
$823$	5.22130e9	+	9.04355e9i	0.326497	+	0.565509i	0.981814	−	0.189845i	$-0.0607984\pi$
$823$	5.22130e9	+	9.04355e9i	0.326497	+	0.565509i	−0.655317	+	0.755354i	$0.727465\pi$
$824$	3.29807e9			0.205360
$825$	−2.22635e10	−	3.85615e10i	−1.38040	−	2.39092i
$826$	−1.63158e8	−	2.82598e8i	−0.0100735	−	0.0174478i
$827$	−2.99536e10			−1.84153			−0.920767	−	0.390112i	$-0.872436\pi$
$827$	−2.99536e10			−1.84153			−0.920767	+	0.390112i	$0.872436\pi$
$828$	7.43453e9	+	1.28770e10i	0.455142	+	0.788330i
$829$	7.99714e9	−	1.38514e10i	0.487521	−	0.844412i	−0.512376	−	0.858761i	$-0.671234\pi$
$829$	7.99714e9	−	1.38514e10i	0.487521	−	0.844412i	0.999897	+	0.0143496i	$0.00456778\pi$
$830$	−2.79797e8	+	4.84623e8i	−0.0169852	+	0.0294192i
$831$	−2.21810e10			−1.34084
$832$	5.56965e9	−	1.51017e10i	0.335271	−	0.909062i
$833$	−5.95199e8			−0.0356783
$834$	−1.21723e8	+	2.10831e8i	−0.00726595	+	0.0125850i
$835$	−1.36622e10	+	2.36636e10i	−0.812114	+	1.40662i
$836$	1.35632e10	+	2.34922e10i	0.802862	+	1.39060i
$837$	−5.98968e9			−0.353073
$838$	4.87895e8	+	8.45058e8i	0.0286399	+	0.0496058i
$839$	−2.49609e8	−	4.32335e8i	−0.0145913	−	0.0252728i	0.858638	−	0.512583i	$-0.171311\pi$
$839$	−2.49609e8	−	4.32335e8i	−0.0145913	−	0.0252728i	−0.873229	+	0.487310i	$0.837978\pi$
$840$	2.20268e9			0.128226
$841$	−2.81528e9	−	4.87620e9i	−0.163206	−	0.282680i
$842$	−1.13250e9	+	1.96155e9i	−0.0653802	+	0.113242i
$843$	2.49061e10	−	4.31386e10i	1.43189	−	2.48010i
$844$	2.32746e10			1.33255
$845$	2.13342e10	+	1.82140e10i	1.21641	+	1.03850i
$846$	6.41163e8			0.0364059
$847$	1.48631e9	−	2.57436e9i	0.0840460	−	0.145572i
$848$	9.89272e9	−	1.71347e10i	0.557096	−	0.964919i
$849$	2.43269e9	+	4.21354e9i	0.136430	+	0.236304i
$850$	−5.02572e8			−0.0280693
$851$	4.51909e9	+	7.82730e9i	0.251361	+	0.435370i
$852$	−2.28356e10	−	3.95524e10i	−1.26495	−	2.19096i
$853$	−5.11719e9			−0.282299			−0.141150	−	0.989988i	$-0.545080\pi$
$853$	−5.11719e9			−0.282299			−0.141150	+	0.989988i	$0.545080\pi$
$854$	−1.01892e8	−	1.76481e8i	−0.00559804	−	0.00969609i
$855$	−2.30241e10	+	3.98788e10i	−1.25980	+	2.18203i
$856$	−8.14656e8	+	1.41103e9i	−0.0443932	+	0.0768912i
$857$	−1.12203e10			−0.608936			−0.304468	−	0.952523i	$-0.598479\pi$
$857$	−1.12203e10			−0.608936			−0.304468	+	0.952523i	$0.598479\pi$
$858$	−8.18223e8	+	2.21855e9i	−0.0442248	+	0.119912i
$859$	1.32776e10			0.714733			0.357366	−	0.933964i	$-0.383675\pi$
$859$	1.32776e10			0.714733			0.357366	+	0.933964i	$0.383675\pi$
$860$	1.96359e10	−	3.40105e10i	1.05271	−	1.82334i
$861$	−3.39702e9	+	5.88381e9i	−0.181379	+	0.314157i
$862$	−1.28669e9	−	2.22860e9i	−0.0684222	−	0.118511i
$863$	−2.16885e10			−1.14866			−0.574331	−	0.818623i	$-0.694738\pi$
$863$	−2.16885e10			−1.14866			−0.574331	+	0.818623i	$0.694738\pi$
$864$	5.19722e8	+	9.00186e8i	0.0274141	+	0.0474825i
$865$	−2.30536e10	−	3.99301e10i	−1.21111	−	2.09770i
$866$	1.15501e9			0.0604330
$867$	−1.32618e10	−	2.29702e10i	−0.691094	−	1.19701i
$868$	−5.01261e9	+	8.68209e9i	−0.260163	+	0.450615i
$869$	−6.60343e9	+	1.14375e10i	−0.341350	+	0.591236i
$870$	3.80436e9			0.195868
$871$	−1.15014e10	−	1.38262e10i	−0.589775	−	0.708988i
$872$	2.82587e9			0.144326
$873$	−4.50584e8	+	7.80434e8i	−0.0229206	+	0.0396996i
$874$	7.45668e8	−	1.29153e9i	0.0377794	−	0.0654359i
$875$	−3.34307e9	−	5.79037e9i	−0.168701	−	0.292199i
$876$	5.42162e10			2.72499
$877$	−8.36696e9	−	1.44920e10i	−0.418860	−	0.725487i	0.576965	−	0.816769i	$-0.304237\pi$
$877$	−8.36696e9	−	1.44920e10i	−0.418860	−	0.725487i	−0.995825	+	0.0912820i	$0.970904\pi$
$878$	6.84805e8	+	1.18612e9i	0.0341457	+	0.0591421i
$879$	−1.63859e10			−0.813782
$880$	−1.91291e10	−	3.31325e10i	−0.946246	−	1.63895i
$881$	−1.80556e10	+	3.12732e10i	−0.889602	+	1.54084i	−0.0492554	+	0.998786i	$0.515685\pi$
$881$	−1.80556e10	+	3.12732e10i	−0.889602	+	1.54084i	−0.840347	+	0.542050i	$0.817649\pi$
$882$	−1.23158e8	+	2.13317e8i	−0.00604400	+	0.0104685i
$883$	9.37920e9			0.458462			0.229231	−	0.973372i	$-0.426379\pi$
$883$	9.37920e9			0.458462			0.229231	+	0.973372i	$0.426379\pi$
$884$	−3.26339e9	−	3.92303e9i	−0.158886	−	0.191003i
$885$	−3.59279e10			−1.74233
$886$	−2.41376e8	+	4.18075e8i	−0.0116594	+	0.0201946i
$887$	−4.53044e9	+	7.84696e9i	−0.217976	+	0.377545i	−0.954189	−	0.299205i	$-0.903279\pi$
$887$	−4.53044e9	+	7.84696e9i	−0.217976	+	0.377545i	0.736213	+	0.676750i	$0.236612\pi$
$888$	1.42623e9	+	2.47030e9i	0.0683508	+	0.118387i
$889$	−1.38645e10			−0.661834
$890$	2.03304e8	+	3.52133e8i	0.00966677	+	0.0167433i
$891$	−1.01129e10	−	1.75161e10i	−0.478965	−	0.829593i
$892$	−2.75055e10			−1.29760
$893$	6.14770e9	+	1.06481e10i	0.288890	+	0.500372i
$894$	−2.33025e8	+	4.03611e8i	−0.0109074	+	0.0188922i
$895$	−2.36357e10	+	4.09382e10i	−1.10201	+	1.90874i
$896$	2.31764e9			0.107639
$897$	−2.44964e10	+	4.21168e9i	−1.13326	+	0.194842i
$898$	9.35517e8			0.0431106
$899$	−1.73603e10	+	3.00689e10i	−0.796890	+	1.38025i
$900$	1.98831e10	−	3.44385e10i	0.909148	−	1.57469i
$901$	−3.10306e9	−	5.37466e9i	−0.141336	−	0.244801i
$902$	−1.24414e9			−0.0564479
$903$	8.15656e9	+	1.41276e10i	0.368638	+	0.638500i
$904$	−1.93257e9	−	3.34730e9i	−0.0870052	−	0.150697i
$905$	−2.04893e10			−0.918877
$906$	−1.26360e9	−	2.18862e9i	−0.0564496	−	0.0977735i
$907$	8.94212e9	−	1.54882e10i	0.397938	−	0.689248i	−0.595534	−	0.803330i	$-0.703059\pi$
$907$	8.94212e9	−	1.54882e10i	0.397938	−	0.689248i	0.993471	+	0.114082i	$0.0363927\pi$
$908$	−9.88360e9	+	1.71189e10i	−0.438142	+	0.758884i
$909$	1.44633e10			0.638694
$910$	−3.42999e8	+	9.30015e8i	−0.0150886	+	0.0409115i
$911$	−7.55371e9			−0.331014			−0.165507	−	0.986209i	$-0.552926\pi$
$911$	−7.55371e9			−0.331014			−0.165507	+	0.986209i	$0.552926\pi$
$912$	−2.23209e10	+	3.86610e10i	−0.974384	+	1.68768i
$913$	−4.06934e9	+	7.04830e9i	−0.176960	+	0.306504i
$914$	−1.89438e8	−	3.28116e8i	−0.00820645	−	0.0142140i
$915$	−2.24368e10			−0.968251
$916$	1.84695e10	+	3.19902e10i	0.794003	+	1.37525i
$917$	−1.49731e9	−	2.59341e9i	−0.0641236	−	0.111065i
$918$	1.07734e8			0.00459625
$919$	1.01124e10	+	1.75151e10i	0.429782	+	0.744405i	0.996854	−	0.0792637i	$-0.0252569\pi$
$919$	1.01124e10	+	1.75151e10i	0.429782	+	0.744405i	−0.567071	+	0.823669i	$0.691924\pi$
$920$	−2.11997e9	+	3.67190e9i	−0.0897578	+	0.155465i
$921$	2.46364e10	−	4.26715e10i	1.03913	−	1.79982i
$922$	1.63861e8			0.00688520
$923$	4.06173e10	−	6.98337e9i	1.70022	−	0.292321i
$924$	1.59760e10			0.666218
$925$	1.20860e10	−	2.09335e10i	0.502094	−	0.869652i
$926$	1.04105e9	−	1.80314e9i	0.0430855	−	0.0746263i
$927$	2.03033e10	+	3.51663e10i	0.837118	+	1.44993i
$928$	6.02539e9			0.247495
$929$	7.32674e9	+	1.26903e10i	0.299817	+	0.519298i	0.976094	−	0.217350i	$-0.0697411\pi$
$929$	7.32674e9	+	1.26903e10i	0.299817	+	0.519298i	−0.676277	+	0.736647i	$0.736408\pi$
$930$	−2.88652e9	−	4.99960e9i	−0.117675	−	0.203819i
$931$	−4.72355e9			−0.191843
$932$	−1.25745e10	−	2.17797e10i	−0.508786	−	0.881244i
$933$	2.58893e10	−	4.48416e10i	1.04360	−	1.80757i
$934$	5.43881e8	−	9.42029e8i	0.0218419	−	0.0378312i
$935$	−1.20005e10			−0.480128
$936$	−4.17341e9	+	7.17537e8i	−0.166351	+	0.0286008i
$937$	2.82015e10			1.11991			0.559956	−	0.828523i	$-0.310818\pi$
$937$	2.82015e10			1.11991			0.559956	+	0.828523i	$0.310818\pi$
$938$	3.17756e8	−	5.50369e8i	0.0125714	−	0.0217743i
$939$	7.64125e8	−	1.32350e9i	0.0301186	−	0.0521669i
$940$	−8.71631e9	−	1.50971e10i	−0.342283	−	0.592852i
$941$	1.53401e10			0.600158			0.300079	−	0.953914i	$-0.402987\pi$
$941$	1.53401e10			0.600158			0.300079	+	0.953914i	$0.402987\pi$
$942$	−3.87163e7	−	6.70586e7i	−0.00150909	−	0.00261382i
$943$	−6.53891e9	−	1.13257e10i	−0.253930	−	0.439820i
$944$	−1.88024e10			−0.727464
$945$	2.00064e9	+	3.46521e9i	0.0771184	+	0.133573i
$946$	−1.49365e9	+	2.58708e9i	−0.0573629	+	0.0993554i
$947$	2.01894e10	−	3.49691e10i	0.772501	−	1.33801i	−0.163687	−	0.986512i	$-0.552339\pi$
$947$	2.01894e10	−	3.49691e10i	0.772501	−	1.33801i	0.936188	−	0.351499i	$-0.114328\pi$
$948$	−2.18493e10			−0.832931
$949$	−1.69291e10	+	4.59020e10i	−0.642987	+	1.74341i
$950$	−3.98846e9			−0.150929
$951$	2.48036e10	−	4.29611e10i	0.935155	−	1.61974i
$952$	1.80791e8	−	3.13140e8i	0.00679123	−	0.0117627i
$953$	1.45121e10	+	2.51357e10i	0.543132	+	0.940732i	0.998722	+	0.0505421i	$0.0160949\pi$
$953$	1.45121e10	+	2.51357e10i	0.543132	+	0.940732i	−0.455590	+	0.890190i	$0.650572\pi$
$954$	−2.56834e9			−0.0957708
$955$	−4.12076e10	−	7.13736e10i	−1.53097	−	2.65171i
$956$	6.02770e9	+	1.04403e10i	0.223125	+	0.386464i
$957$	5.53301e10			2.04066
$958$	1.68270e9	+	2.91452e9i	0.0618340	+	0.107100i
$959$	6.93348e9	−	1.20091e10i	0.253855	−	0.439690i
$960$	3.13116e10	−	5.42332e10i	1.14224	−	1.97841i
$961$	2.51752e10			0.915044
$962$	−1.26510e9	+	2.17509e8i	−0.0458154	+	0.00787708i
$963$	−2.00604e10			−0.723849
$964$	−2.67971e10	+	4.64139e10i	−0.963424	+	1.66870i
$965$	−9.51088e9	+	1.64733e10i	−0.340702	+	0.590114i
$966$	−4.39158e8	−	7.60644e8i	−0.0156748	−	0.0271495i
$967$	−1.78761e10			−0.635742			−0.317871	−	0.948134i	$-0.602968\pi$
$967$	−1.78761e10			−0.635742			−0.317871	+	0.948134i	$0.602968\pi$
$968$	9.02931e8	+	1.56392e9i	0.0319956	+	0.0554181i
$969$	7.00142e9	+	1.21268e10i	0.247203	+	0.428167i
$970$	−1.28150e8			−0.00450834
$971$	−1.67633e10	−	2.90350e10i	−0.587616	−	1.01778i	−0.994544	−	0.104320i	$-0.966733\pi$
$971$	−1.67633e10	−	2.90350e10i	−0.587616	−	1.01778i	0.406928	−	0.913460i	$-0.366600\pi$
$972$	2.03641e10	−	3.52717e10i	0.711269	−	1.23195i
$973$	−7.42121e8	+	1.28539e9i	−0.0258274	+	0.0447343i
$974$	3.34358e6			0.000115946
$975$	4.25115e10	+	5.11045e10i	1.46889	+	1.76581i
$976$	−1.17420e10			−0.404267
$977$	−8.25570e9	+	1.42993e10i	−0.283219	+	0.490550i	−0.972176	−	0.234252i	$-0.924736\pi$
$977$	−8.25570e9	+	1.42993e10i	−0.283219	+	0.490550i	0.688957	+	0.724803i	$0.258069\pi$
$978$	1.82476e9	−	3.16058e9i	0.0623764	−	0.108039i
$979$	2.95683e9	+	5.12139e9i	0.100713	+	0.174441i
$980$	6.69713e9			0.227299
$981$	1.73963e10	+	3.01314e10i	0.588324	+	1.01901i
$982$	−1.13440e9	−	1.96484e9i	−0.0382276	−	0.0662122i
$983$	−4.47443e10			−1.50245			−0.751225	−	0.660046i	$-0.770537\pi$
$983$	−4.47443e10			−1.50245			−0.751225	+	0.660046i	$0.770537\pi$
$984$	−2.06368e9	−	3.57441e9i	−0.0690495	−	0.119597i
$985$	−2.25417e10	+	3.90433e10i	−0.751552	+	1.30173i
$986$	3.12253e8	−	5.40838e8i	0.0103738	−	0.0179679i
$987$	7.24133e9			0.239722
$988$	−2.58986e10	−	3.11336e10i	−0.854332	−	1.02702i
$989$	−3.14011e10			−1.03219
$990$	−2.48313e9	+	4.30091e9i	−0.0813349	+	0.140876i
$991$	1.81731e10	−	3.14768e10i	0.593160	−	1.02738i	−0.400643	−	0.916234i	$-0.631213\pi$
$991$	1.81731e10	−	3.14768e10i	0.593160	−	1.02738i	0.993804	−	0.111150i	$-0.0354533\pi$
$992$	−4.57170e9	−	7.91842e9i	−0.148692	−	0.257542i
$993$	3.41510e10			1.10683
$994$	7.28167e8	+	1.26122e9i	0.0235168	+	0.0407323i
$995$	3.05998e10	+	5.30004e10i	0.984776	+	1.70568i
$996$	−1.34646e10			−0.431802
$997$	−1.18882e9	−	2.05909e9i	−0.0379911	−	0.0658024i	0.846405	−	0.532540i	$-0.178763\pi$
$997$	−1.18882e9	−	2.05909e9i	−0.0379911	−	0.0658024i	−0.884396	+	0.466738i	$0.845429\pi$
$998$	1.04615e9	−	1.81198e9i	0.0333147	−	0.0577027i
$999$	−2.59081e9	+	4.48742e9i	−0.0822161	+	0.142402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.f.a.22.13	✓	48
13.3	even	3	inner	91.8.f.a.29.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.f.a.22.13	✓	48	1.1	even	1	trivial
91.8.f.a.29.13	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)

\(f(q)\)	\(=\)	\(q+(-0.408038 + 0.706743i) q^{2} +(34.4693 - 59.7025i) q^{3} +(63.6670 + 110.274i) q^{4} -447.050 q^{5} +(28.1296 + 48.7218i) q^{6} +(171.500 + 297.047i) q^{7} -208.372 q^{8} +(-1282.76 - 2221.80i) q^{9} +O(q^{10})\)	\(q+(-0.408038 + 0.706743i) q^{2} +(34.4693 - 59.7025i) q^{3} +(63.6670 + 110.274i) q^{4} -447.050 q^{5} +(28.1296 + 48.7218i) q^{6} +(171.500 + 297.047i) q^{7} -208.372 q^{8} +(-1282.76 - 2221.80i) q^{9} +(182.414 - 315.950i) q^{10} +(2653.00 - 4595.14i) q^{11} +8778.22 q^{12} +(-2741.01 + 7432.05i) q^{13} -279.914 q^{14} +(-15409.5 + 26690.0i) q^{15} +(-8064.35 + 13967.9i) q^{16} +(2529.55 + 4381.31i) q^{17} +2093.66 q^{18} +(20074.8 + 34770.5i) q^{19} +(-28462.4 - 49298.2i) q^{20} +23645.9 q^{21} +(2165.05 + 3749.98i) q^{22} +(-22758.0 + 39418.0i) q^{23} +(-7182.43 + 12440.3i) q^{24} +121729. q^{25} +(-4134.11 - 4969.75i) q^{26} -26094.5 q^{27} +(-21837.8 + 37824.2i) q^{28} +(-75631.4 + 130997. i) q^{29} +(-12575.3 - 21781.1i) q^{30} +229538. q^{31} +(-19916.9 - 34497.2i) q^{32} +(-182894. - 316782. i) q^{33} -4128.62 q^{34} +(-76669.1 - 132795. i) q^{35} +(163339. - 282911. i) q^{36} +(99285.9 - 171968. i) q^{37} -32765.1 q^{38} +(349231. + 419823. i) q^{39} +93152.8 q^{40} +(-143662. + 248830. i) q^{41} +(-9648.44 + 16711.6i) q^{42} +(344946. + 597464. i) q^{43} +675635. q^{44} +(573458. + 993258. i) q^{45} +(-18572.3 - 32168.1i) q^{46} +306240. q^{47} +(555945. + 962924. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(-49670.1 + 86031.1i) q^{50} +348767. q^{51} +(-994078. + 170913. i) q^{52} -1.22672e6 q^{53} +(10647.5 - 18442.1i) q^{54} +(-1.18603e6 + 2.05426e6i) q^{55} +(-35735.8 - 61896.3i) q^{56} +2.76785e6 q^{57} +(-61721.0 - 106904. i) q^{58} +(582887. + 1.00959e6i) q^{59} -3.92430e6 q^{60} +(364010. + 630484. i) q^{61} +(-93660.4 + 162225. i) q^{62} +(439986. - 762079. i) q^{63} -2.03197e6 q^{64} +(1.22537e6 - 3.32250e6i) q^{65} +298511. q^{66} +(-1.13519e6 + 1.96621e6i) q^{67} +(-322098. + 557890. i) q^{68} +(1.56890e6 + 2.71742e6i) q^{69} +125136. q^{70} +(-2.60139e6 - 4.50574e6i) q^{71} +(267291. + 462962. i) q^{72} +6.17622e6 q^{73} +(81024.9 + 140339. i) q^{74} +(4.19590e6 - 7.26752e6i) q^{75} +(-2.55620e6 + 4.42747e6i) q^{76} +1.81996e6 q^{77} +(-439206. + 75513.1i) q^{78} -2.48904e6 q^{79} +(3.60517e6 - 6.24434e6i) q^{80} +(1.90594e6 - 3.30118e6i) q^{81} +(-117239. - 203064. i) q^{82} -1.53386e6 q^{83} +(1.50546e6 + 2.60754e6i) q^{84} +(-1.13084e6 - 1.95867e6i) q^{85} -563005. q^{86} +(5.21392e6 + 9.03077e6i) q^{87} +(-552812. + 957498. i) q^{88} +(-557262. + 965206. i) q^{89} -935971. q^{90} +(-2.67775e6 + 460388. i) q^{91} -5.79573e6 q^{92} +(7.91202e6 - 1.37040e7i) q^{93} +(-124958. + 216433. i) q^{94} +(-8.97443e6 - 1.55442e7i) q^{95} -2.74609e6 q^{96} +(-175631. - 304202. i) q^{97} +(-48005.3 - 83147.6i) q^{98} -1.36127e7 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

Fields

Representations

Groups

Database

Properties

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