LMFDB - Embedded newform 43.8.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.a (trivial)

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:	yes
Analytic conductor:	$13.4325560958$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 $ x^11 - 2x^10 - 977x^9 + 2592x^8 + 344686x^7 - 1160956x^6 - 53409536x^5 + 209758592x^4 + 3410917248x^3 - 14180732672x^2 - 60918607872x + 238240894976
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-17.2185$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+15.2185 q^{2} -9.20709 q^{3} +103.603 q^{4} -537.911 q^{5} -140.118 q^{6} +1471.62 q^{7} -371.288 q^{8} -2102.23 q^{9} +O(q^{10})$	\(q+15.2185 q^{2} -9.20709 q^{3} +103.603 q^{4} -537.911 q^{5} -140.118 q^{6} +1471.62 q^{7} -371.288 q^{8} -2102.23 q^{9} -8186.21 q^{10} -3353.32 q^{11} -953.881 q^{12} -12401.8 q^{13} +22395.8 q^{14} +4952.60 q^{15} -18911.6 q^{16} +20775.2 q^{17} -31992.8 q^{18} -1067.31 q^{19} -55729.2 q^{20} -13549.3 q^{21} -51032.5 q^{22} -17801.1 q^{23} +3418.48 q^{24} +211224. q^{25} -188736. q^{26} +39491.3 q^{27} +152464. q^{28} +99935.2 q^{29} +75371.2 q^{30} -30140.3 q^{31} -240282. q^{32} +30874.3 q^{33} +316168. q^{34} -791601. q^{35} -217797. q^{36} -174672. q^{37} -16242.9 q^{38} +114184. q^{39} +199720. q^{40} -45042.7 q^{41} -206201. q^{42} +79507.0 q^{43} -347414. q^{44} +1.13081e6 q^{45} -270907. q^{46} -319582. q^{47} +174121. q^{48} +1.34212e6 q^{49} +3.21451e6 q^{50} -191279. q^{51} -1.28486e6 q^{52} +72727.4 q^{53} +600999. q^{54} +1.80379e6 q^{55} -546394. q^{56} +9826.85 q^{57} +1.52086e6 q^{58} -2.67444e6 q^{59} +513104. q^{60} -2.37204e6 q^{61} -458690. q^{62} -3.09368e6 q^{63} -1.23604e6 q^{64} +6.67106e6 q^{65} +469861. q^{66} +3.70267e6 q^{67} +2.15237e6 q^{68} +163897. q^{69} -1.20470e7 q^{70} -4.04493e6 q^{71} +780532. q^{72} +862213. q^{73} -2.65824e6 q^{74} -1.94476e6 q^{75} -110577. q^{76} -4.93481e6 q^{77} +1.73771e6 q^{78} -3.18079e6 q^{79} +1.01728e7 q^{80} +4.23398e6 q^{81} -685483. q^{82} -2.05380e6 q^{83} -1.40375e6 q^{84} -1.11752e7 q^{85} +1.20998e6 q^{86} -920113. q^{87} +1.24505e6 q^{88} -1.05466e7 q^{89} +1.72093e7 q^{90} -1.82507e7 q^{91} -1.84425e6 q^{92} +277505. q^{93} -4.86356e6 q^{94} +574120. q^{95} +2.21230e6 q^{96} +849791. q^{97} +2.04251e7 q^{98} +7.04945e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) $ 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9} - 1333 q^{10} + 1333 q^{11} + 5089 q^{12} - 17967 q^{13} - 22352 q^{14} - 49504 q^{15} - 34406 q^{16} - 63095 q^{17} - 165931 q^{18} - 54524 q^{19} - 280995 q^{20} - 139788 q^{21} - 289358 q^{22} - 138139 q^{23} - 429583 q^{24} + 3455 q^{25} - 132946 q^{26} - 240356 q^{27} - 12704 q^{28} - 308658 q^{29} + 421284 q^{30} - 209523 q^{31} - 644934 q^{32} + 96814 q^{33} + 762435 q^{34} - 578892 q^{35} + 426161 q^{36} - 298472 q^{37} - 369707 q^{38} + 292298 q^{39} + 2633173 q^{40} - 1346735 q^{41} + 1173266 q^{42} + 874577 q^{43} + 3134292 q^{44} + 1893784 q^{45} + 3588111 q^{46} + 499284 q^{47} + 5647533 q^{48} + 2544563 q^{49} + 3049745 q^{50} + 1258424 q^{51} + 983088 q^{52} - 2210495 q^{53} + 6789698 q^{54} - 1855072 q^{55} - 469976 q^{56} - 1238444 q^{57} + 4397067 q^{58} - 5824216 q^{59} - 2889372 q^{60} - 4453034 q^{61} + 1002789 q^{62} - 6240564 q^{63} + 4757538 q^{64} - 2162872 q^{65} - 258940 q^{66} - 6859513 q^{67} - 9397005 q^{68} - 10040030 q^{69} + 845078 q^{70} - 10726554 q^{71} + 1199517 q^{72} - 4456898 q^{73} + 1046637 q^{74} - 3349114 q^{75} + 5861267 q^{76} - 17019816 q^{77} + 1999122 q^{78} - 15541320 q^{79} - 15680911 q^{80} - 12976697 q^{81} + 20233655 q^{82} - 11146767 q^{83} + 12348278 q^{84} - 12471976 q^{85} - 1908168 q^{86} - 18648900 q^{87} - 24463544 q^{88} - 13531356 q^{89} + 20858990 q^{90} - 19746448 q^{91} - 26023161 q^{92} - 21903110 q^{93} + 20288857 q^{94} - 12291624 q^{95} - 13954503 q^{96} - 10999901 q^{97} + 29909168 q^{98} + 29396057 q^{99}+O(q^{100}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9 - 1333 * q^10 + 1333 * q^11 + 5089 * q^12 - 17967 * q^13 - 22352 * q^14 - 49504 * q^15 - 34406 * q^16 - 63095 * q^17 - 165931 * q^18 - 54524 * q^19 - 280995 * q^20 - 139788 * q^21 - 289358 * q^22 - 138139 * q^23 - 429583 * q^24 + 3455 * q^25 - 132946 * q^26 - 240356 * q^27 - 12704 * q^28 - 308658 * q^29 + 421284 * q^30 - 209523 * q^31 - 644934 * q^32 + 96814 * q^33 + 762435 * q^34 - 578892 * q^35 + 426161 * q^36 - 298472 * q^37 - 369707 * q^38 + 292298 * q^39 + 2633173 * q^40 - 1346735 * q^41 + 1173266 * q^42 + 874577 * q^43 + 3134292 * q^44 + 1893784 * q^45 + 3588111 * q^46 + 499284 * q^47 + 5647533 * q^48 + 2544563 * q^49 + 3049745 * q^50 + 1258424 * q^51 + 983088 * q^52 - 2210495 * q^53 + 6789698 * q^54 - 1855072 * q^55 - 469976 * q^56 - 1238444 * q^57 + 4397067 * q^58 - 5824216 * q^59 - 2889372 * q^60 - 4453034 * q^61 + 1002789 * q^62 - 6240564 * q^63 + 4757538 * q^64 - 2162872 * q^65 - 258940 * q^66 - 6859513 * q^67 - 9397005 * q^68 - 10040030 * q^69 + 845078 * q^70 - 10726554 * q^71 + 1199517 * q^72 - 4456898 * q^73 + 1046637 * q^74 - 3349114 * q^75 + 5861267 * q^76 - 17019816 * q^77 + 1999122 * q^78 - 15541320 * q^79 - 15680911 * q^80 - 12976697 * q^81 + 20233655 * q^82 - 11146767 * q^83 + 12348278 * q^84 - 12471976 * q^85 - 1908168 * q^86 - 18648900 * q^87 - 24463544 * q^88 - 13531356 * q^89 + 20858990 * q^90 - 19746448 * q^91 - 26023161 * q^92 - 21903110 * q^93 + 20288857 * q^94 - 12291624 * q^95 - 13954503 * q^96 - 10999901 * q^97 + 29909168 * q^98 + 29396057 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	15.2185	1.34514	0.672569	−	0.740034i	$-0.265191\pi$
$2$	15.2185	1.34514	0.672569	+	0.740034i	$0.265191\pi$
$3$	−9.20709	−0.196878	−0.0984392	−	0.995143i	$-0.531385\pi$
$3$	−9.20709	−0.196878	−0.0984392	+	0.995143i	$0.531385\pi$
$4$	103.603	0.809397
$5$	−537.911	−1.92449	−0.962245	−	0.272184i	$-0.912254\pi$
$5$	−537.911	−1.92449	−0.962245	+	0.272184i	$0.912254\pi$
$6$	−140.118	−0.264829
$7$	1471.62	1.62163	0.810816	−	0.585301i	$-0.199024\pi$
$7$	1471.62	1.62163	0.810816	+	0.585301i	$0.199024\pi$
$8$	−371.288	−0.256387
$9$	−2102.23	−0.961239
$10$	−8186.21	−2.58871
$11$	−3353.32	−0.759628	−0.379814	−	0.925063i	$-0.624012\pi$
$11$	−3353.32	−0.759628	−0.379814	+	0.925063i	$0.624012\pi$
$12$	−953.881	−0.159353
$13$	−12401.8	−1.56560	−0.782802	−	0.622270i	$-0.786210\pi$
$13$	−12401.8	−1.56560	−0.782802	+	0.622270i	$0.786210\pi$
$14$	22395.8	2.18132
$15$	4952.60	0.378891
$16$	−18911.6	−1.15427
$17$	20775.2	1.02559	0.512796	−	0.858511i	$-0.328610\pi$
$17$	20775.2	1.02559	0.512796	+	0.858511i	$0.328610\pi$
$18$	−31992.8	−1.29300
$19$	−1067.31	−0.0356988	−0.0178494	−	0.999841i	$-0.505682\pi$
$19$	−1067.31	−0.0356988	−0.0178494	+	0.999841i	$0.505682\pi$
$20$	−55729.2	−1.55768
$21$	−13549.3	−0.319264
$22$	−51032.5	−1.02180
$23$	−17801.1	−0.305071	−0.152535	−	0.988298i	$-0.548744\pi$
$23$	−17801.1	−0.305071	−0.152535	+	0.988298i	$0.548744\pi$
$24$	3418.48	0.0504771
$25$	211224.	2.70366
$26$	−188736.	−2.10596
$27$	39491.3	0.386126
$28$	152464.	1.31254
$29$	99935.2	0.760897	0.380448	−	0.924802i	$-0.375770\pi$
$29$	99935.2	0.760897	0.380448	+	0.924802i	$0.375770\pi$
$30$	75371.2	0.509660
$31$	−30140.3	−0.181711	−0.0908556	−	0.995864i	$-0.528960\pi$
$31$	−30140.3	−0.181711	−0.0908556	+	0.995864i	$0.528960\pi$
$32$	−240282.	−1.29627
$33$	30874.3	0.149554
$34$	316168.	1.37956
$35$	−791601.	−3.12081
$36$	−217797.	−0.778024
$37$	−174672.	−0.566913	−0.283457	−	0.958985i	$-0.591481\pi$
$37$	−174672.	−0.566913	−0.283457	+	0.958985i	$0.591481\pi$
$38$	−16242.9	−0.0480199
$39$	114184.	0.308234
$40$	199720.	0.493414
$41$	−45042.7	−0.102066	−0.0510330	−	0.998697i	$-0.516251\pi$
$41$	−45042.7	−0.102066	−0.0510330	+	0.998697i	$0.516251\pi$
$42$	−206201.	−0.429455
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	−347414.	−0.614841
$45$	1.13081e6	1.84989
$46$	−270907.	−0.410362
$47$	−319582.	−0.448993	−0.224497	−	0.974475i	$-0.572074\pi$
$47$	−319582.	−0.448993	−0.224497	+	0.974475i	$0.572074\pi$
$48$	174121.	0.227252
$49$	1.34212e6	1.62969
$50$	3.21451e6	3.63680
$51$	−191279.	−0.201917
$52$	−1.28486e6	−1.26720
$53$	72727.4	0.0671016	0.0335508	−	0.999437i	$-0.489318\pi$
$53$	72727.4	0.0671016	0.0335508	+	0.999437i	$0.489318\pi$
$54$	600999.	0.519392
$55$	1.80379e6	1.46190
$56$	−546394.	−0.415765
$57$	9826.85	0.00702833
$58$	1.52086e6	1.02351
$59$	−2.67444e6	−1.69531	−0.847657	−	0.530544i	$-0.821988\pi$
$59$	−2.67444e6	−1.69531	−0.847657	+	0.530544i	$0.821988\pi$
$60$	513104.	0.306673
$61$	−2.37204e6	−1.33804	−0.669019	−	0.743246i	$-0.733285\pi$
$61$	−2.37204e6	−1.33804	−0.669019	+	0.743246i	$0.733285\pi$
$62$	−458690.	−0.244427
$63$	−3.09368e6	−1.55878
$64$	−1.23604e6	−0.589390
$65$	6.67106e6	3.01299
$66$	469861.	0.201171
$67$	3.70267e6	1.50402	0.752009	−	0.659153i	$-0.229085\pi$
$67$	3.70267e6	1.50402	0.752009	+	0.659153i	$0.229085\pi$
$68$	2.15237e6	0.830111
$69$	163897.	0.0600618
$70$	−1.20470e7	−4.19793
$71$	−4.04493e6	−1.34124	−0.670620	−	0.741801i	$-0.733972\pi$
$71$	−4.04493e6	−1.34124	−0.670620	+	0.741801i	$0.733972\pi$
$72$	780532.	0.246449
$73$	862213.	0.259409	0.129704	−	0.991553i	$-0.458597\pi$
$73$	862213.	0.259409	0.129704	+	0.991553i	$0.458597\pi$
$74$	−2.65824e6	−0.762577
$75$	−1.94476e6	−0.532293
$76$	−110577.	−0.0288945
$77$	−4.93481e6	−1.23184
$78$	1.73771e6	0.414617
$79$	−3.18079e6	−0.725839	−0.362920	−	0.931820i	$-0.618220\pi$
$79$	−3.18079e6	−0.725839	−0.362920	+	0.931820i	$0.618220\pi$
$80$	1.01728e7	2.22139
$81$	4.23398e6	0.885219
$82$	−685483.	−0.137293
$83$	−2.05380e6	−0.394262	−0.197131	−	0.980377i	$-0.563162\pi$
$83$	−2.05380e6	−0.394262	−0.197131	+	0.980377i	$0.563162\pi$
$84$	−1.40375e6	−0.258412
$85$	−1.11752e7	−1.97374
$86$	1.20998e6	0.205132
$87$	−920113.	−0.149804
$88$	1.24505e6	0.194759
$89$	−1.05466e7	−1.58580	−0.792899	−	0.609353i	$-0.791429\pi$
$89$	−1.05466e7	−1.58580	−0.792899	+	0.609353i	$0.791429\pi$
$90$	1.72093e7	2.48836
$91$	−1.82507e7	−2.53883
$92$	−1.84425e6	−0.246923
$93$	277505.	0.0357750
$94$	−4.86356e6	−0.603958
$95$	574120.	0.0687021
$96$	2.21230e6	0.255208
$97$	849791.	0.0945390	0.0472695	−	0.998882i	$-0.484948\pi$
$97$	849791.	0.0945390	0.0472695	+	0.998882i	$0.484948\pi$
$98$	2.04251e7	2.19216
$99$	7.04945e6	0.730184
$100$	2.18834e7	2.18834
$101$	106287.	0.0102649	0.00513244	−	0.999987i	$-0.498366\pi$
$101$	106287.	0.0102649	0.00513244	+	0.999987i	$0.498366\pi$
$102$	−2.91099e6	−0.271606
$103$	9.84740e6	0.887956	0.443978	−	0.896038i	$-0.353567\pi$
$103$	9.84740e6	0.887956	0.443978	+	0.896038i	$0.353567\pi$
$104$	4.60463e6	0.401401
$105$	7.28834e6	0.614421
$106$	1.10680e6	0.0902609
$107$	−7.20095e6	−0.568260	−0.284130	−	0.958786i	$-0.591705\pi$
$107$	−7.20095e6	−0.568260	−0.284130	+	0.958786i	$0.591705\pi$
$108$	4.09142e6	0.312529
$109$	5.59758e6	0.414007	0.207003	−	0.978340i	$-0.433629\pi$
$109$	5.59758e6	0.414007	0.207003	+	0.978340i	$0.433629\pi$
$110$	2.74510e7	1.96645
$111$	1.60822e6	0.111613
$112$	−2.78307e7	−1.87181
$113$	−2.45481e7	−1.60046	−0.800229	−	0.599695i	$-0.795289\pi$
$113$	−2.45481e7	−1.60046	−0.800229	+	0.599695i	$0.795289\pi$
$114$	149550.	0.00945408
$115$	9.57543e6	0.587105
$116$	1.03536e7	0.615868
$117$	2.60714e7	1.50492
$118$	−4.07009e7	−2.28043
$119$	3.05732e7	1.66313
$120$	−1.83884e6	−0.0971426
$121$	−8.24241e6	−0.422966
$122$	−3.60990e7	−1.79985
$123$	414713.	0.0200946
$124$	−3.12262e6	−0.147077
$125$	−7.15953e7	−3.27868
$126$	−4.70812e7	−2.09677
$127$	3.30101e7	1.42999	0.714995	−	0.699129i	$-0.246429\pi$
$127$	3.30101e7	1.42999	0.714995	+	0.699129i	$0.246429\pi$
$128$	1.19454e7	0.503460
$129$	−732028.	−0.0300237
$130$	1.01524e8	4.05289
$131$	−2.31631e7	−0.900216	−0.450108	−	0.892974i	$-0.648615\pi$
$131$	−2.31631e7	−0.900216	−0.450108	+	0.892974i	$0.648615\pi$
$132$	3.19867e6	0.121049
$133$	−1.57068e6	−0.0578904
$134$	5.63490e7	2.02311
$135$	−2.12428e7	−0.743095
$136$	−7.71359e6	−0.262948
$137$	4.28026e7	1.42216	0.711079	−	0.703112i	$-0.248207\pi$
$137$	4.28026e7	1.42216	0.711079	+	0.703112i	$0.248207\pi$
$138$	2.49426e6	0.0807915
$139$	1.99694e6	0.0630688	0.0315344	−	0.999503i	$-0.489961\pi$
$139$	1.99694e6	0.0630688	0.0315344	+	0.999503i	$0.489961\pi$
$140$	−8.20121e7	−2.52598
$141$	2.94242e6	0.0883971
$142$	−6.15577e7	−1.80415
$143$	4.15871e7	1.18928
$144$	3.97566e7	1.10953
$145$	−5.37563e7	−1.46434
$146$	1.31216e7	0.348941
$147$	−1.23570e7	−0.320851
$148$	−1.80965e7	−0.458858
$149$	4.86799e7	1.20558	0.602792	−	0.797898i	$-0.294055\pi$
$149$	4.86799e7	1.20558	0.602792	+	0.797898i	$0.294055\pi$
$150$	−2.95963e7	−0.716008
$151$	2.21291e7	0.523051	0.261525	−	0.965197i	$-0.415775\pi$
$151$	2.21291e7	0.523051	0.261525	+	0.965197i	$0.415775\pi$
$152$	396280.	0.00915272
$153$	−4.36743e7	−0.985838
$154$	−7.51004e7	−1.65699
$155$	1.62128e7	0.349702
$156$	1.18298e7	0.249484
$157$	−1.06571e7	−0.219782	−0.109891	−	0.993944i	$-0.535050\pi$
$157$	−1.06571e7	−0.219782	−0.109891	+	0.993944i	$0.535050\pi$
$158$	−4.84069e7	−0.976354
$159$	−669608.	−0.0132109
$160$	1.29250e8	2.49466
$161$	−2.61965e7	−0.494712
$162$	6.44348e7	1.19074
$163$	1.16225e7	0.210205	0.105103	−	0.994461i	$-0.466483\pi$
$163$	1.16225e7	0.210205	0.105103	+	0.994461i	$0.466483\pi$
$164$	−4.66656e6	−0.0826120
$165$	−1.66077e7	−0.287816
$166$	−3.12557e7	−0.530336
$167$	−1.81744e7	−0.301962	−0.150981	−	0.988537i	$-0.548243\pi$
$167$	−1.81744e7	−0.301962	−0.150981	+	0.988537i	$0.548243\pi$
$168$	5.03071e6	0.0818552
$169$	9.10556e7	1.45112
$170$	−1.70070e8	−2.65495
$171$	2.24374e6	0.0343151
$172$	8.23715e6	0.123432
$173$	−8.49183e7	−1.24692	−0.623462	−	0.781854i	$-0.714274\pi$
$173$	−8.49183e7	−1.24692	−0.623462	+	0.781854i	$0.714274\pi$
$174$	−1.40027e7	−0.201507
$175$	3.10841e8	4.38435
$176$	6.34167e7	0.876818
$177$	2.46238e7	0.333771
$178$	−1.60504e8	−2.13312
$179$	−1.24796e8	−1.62636	−0.813179	−	0.582014i	$-0.802265\pi$
$179$	−1.24796e8	−1.62636	−0.813179	+	0.582014i	$0.802265\pi$
$180$	1.17155e8	1.49730
$181$	1.02160e7	0.128058	0.0640289	−	0.997948i	$-0.479605\pi$
$181$	1.02160e7	0.128058	0.0640289	+	0.997948i	$0.479605\pi$
$182$	−2.77748e8	−3.41508
$183$	2.18396e7	0.263431
$184$	6.60935e6	0.0782161
$185$	9.39579e7	1.09102
$186$	4.22321e6	0.0481224
$187$	−6.96660e7	−0.779067
$188$	−3.31096e7	−0.363414
$189$	5.81162e7	0.626154
$190$	8.73724e6	0.0924138
$191$	−1.39911e8	−1.45290	−0.726449	−	0.687221i	$-0.758831\pi$
$191$	−1.39911e8	−1.45290	−0.726449	+	0.687221i	$0.758831\pi$
$192$	1.13803e7	0.116038
$193$	7.00658e7	0.701545	0.350773	−	0.936461i	$-0.385919\pi$
$193$	7.00658e7	0.701545	0.350773	+	0.936461i	$0.385919\pi$
$194$	1.29325e7	0.127168
$195$	−6.14211e7	−0.593193
$196$	1.39047e8	1.31907
$197$	1.41757e8	1.32103	0.660513	−	0.750814i	$-0.270339\pi$
$197$	1.41757e8	1.32103	0.660513	+	0.750814i	$0.270339\pi$
$198$	1.07282e8	0.982198
$199$	−1.58549e8	−1.42620	−0.713098	−	0.701065i	$-0.752708\pi$
$199$	−1.58549e8	−1.42620	−0.713098	+	0.701065i	$0.752708\pi$
$200$	−7.84248e7	−0.693184
$201$	−3.40908e7	−0.296109
$202$	1.61752e6	0.0138077
$203$	1.47067e8	1.23389
$204$	−1.98171e7	−0.163431
$205$	2.42290e7	0.196425
$206$	1.49863e8	1.19442
$207$	3.74221e7	0.293246
$208$	2.34538e8	1.80714
$209$	3.57904e6	0.0271178
$210$	1.10918e8	0.826482
$211$	2.65269e8	1.94400	0.972002	−	0.234972i	$-0.0755000\pi$
$211$	2.65269e8	1.94400	0.972002	+	0.234972i	$0.0755000\pi$
$212$	7.53477e6	0.0543118
$213$	3.72420e7	0.264061
$214$	−1.09588e8	−0.764388
$215$	−4.27677e7	−0.293482
$216$	−1.46627e7	−0.0989976
$217$	−4.43551e7	−0.294669
$218$	8.51868e7	0.556897
$219$	−7.93848e6	−0.0510720
$220$	1.86878e8	1.18325
$221$	−2.57650e8	−1.60567
$222$	2.44747e7	0.150135
$223$	1.05872e8	0.639315	0.319658	−	0.947533i	$-0.396432\pi$
$223$	1.05872e8	0.639315	0.319658	+	0.947533i	$0.396432\pi$
$224$	−3.53603e8	−2.10207
$225$	−4.44041e8	−2.59887
$226$	−3.73586e8	−2.15284
$227$	1.29359e8	0.734014	0.367007	−	0.930218i	$-0.380382\pi$
$227$	1.29359e8	0.734014	0.367007	+	0.930218i	$0.380382\pi$
$228$	1.01809e6	0.00568871
$229$	−9.87515e7	−0.543400	−0.271700	−	0.962382i	$-0.587586\pi$
$229$	−9.87515e7	−0.543400	−0.271700	+	0.962382i	$0.587586\pi$
$230$	1.45724e8	0.789738
$231$	4.54353e7	0.242522
$232$	−3.71047e7	−0.195084
$233$	3.20820e8	1.66156	0.830779	−	0.556602i	$-0.187895\pi$
$233$	3.20820e8	1.66156	0.830779	+	0.556602i	$0.187895\pi$
$234$	3.96767e8	2.02433
$235$	1.71907e8	0.864083
$236$	−2.77079e8	−1.37218
$237$	2.92858e7	0.142902
$238$	4.65278e8	2.23714
$239$	1.03848e8	0.492045	0.246023	−	0.969264i	$-0.420876\pi$
$239$	1.03848e8	0.492045	0.246023	+	0.969264i	$0.420876\pi$
$240$	−9.36617e7	−0.437343
$241$	7.62277e7	0.350795	0.175397	−	0.984498i	$-0.443879\pi$
$241$	7.62277e7	0.350795	0.175397	+	0.984498i	$0.443879\pi$
$242$	−1.25437e8	−0.568948
$243$	−1.25350e8	−0.560406
$244$	−2.45751e8	−1.08300
$245$	−7.21942e8	−3.13632
$246$	6.31131e6	0.0270300
$247$	1.32366e7	0.0558903
$248$	1.11907e7	0.0465884
$249$	1.89095e7	0.0776216
$250$	−1.08957e9	−4.41028
$251$	−4.49350e8	−1.79360	−0.896802	−	0.442432i	$-0.854116\pi$
$251$	−4.49350e8	−1.79360	−0.896802	+	0.442432i	$0.854116\pi$
$252$	−3.20514e8	−1.26167
$253$	5.96929e7	0.231740
$254$	5.02364e8	1.92354
$255$	1.02891e8	0.388587
$256$	3.40004e8	1.26661
$257$	8.54500e7	0.314012	0.157006	−	0.987598i	$-0.449816\pi$
$257$	8.54500e7	0.314012	0.157006	+	0.987598i	$0.449816\pi$
$258$	−1.11404e7	−0.0403860
$259$	−2.57050e8	−0.919325
$260$	6.91141e8	2.43871
$261$	−2.10087e8	−0.731403
$262$	−3.52507e8	−1.21092
$263$	−1.42757e8	−0.483896	−0.241948	−	0.970289i	$-0.577786\pi$
$263$	−1.42757e8	−0.483896	−0.241948	+	0.970289i	$0.577786\pi$
$264$	−1.14633e7	−0.0383438
$265$	−3.91209e7	−0.129136
$266$	−2.39034e7	−0.0778706
$267$	9.71036e7	0.312209
$268$	3.83607e8	1.21735
$269$	1.00980e8	0.316302	0.158151	−	0.987415i	$-0.449447\pi$
$269$	1.00980e8	0.316302	0.158151	+	0.987415i	$0.449447\pi$
$270$	−3.23284e8	−0.999566
$271$	9.22392e7	0.281529	0.140765	−	0.990043i	$-0.455044\pi$
$271$	9.22392e7	0.281529	0.140765	+	0.990043i	$0.455044\pi$
$272$	−3.92893e8	−1.18381
$273$	1.68036e8	0.499842
$274$	6.51391e8	1.91300
$275$	−7.08301e8	−2.05378
$276$	1.69802e7	0.0486139
$277$	1.50780e8	0.426249	0.213125	−	0.977025i	$-0.431636\pi$
$277$	1.50780e8	0.426249	0.213125	+	0.977025i	$0.431636\pi$
$278$	3.03905e7	0.0848362
$279$	6.33618e7	0.174668
$280$	2.93912e8	0.800136
$281$	2.04352e8	0.549424	0.274712	−	0.961527i	$-0.411418\pi$
$281$	2.04352e8	0.549424	0.274712	+	0.961527i	$0.411418\pi$
$282$	4.47793e7	0.118906
$283$	−1.63381e8	−0.428499	−0.214250	−	0.976779i	$-0.568731\pi$
$283$	−1.63381e8	−0.428499	−0.214250	+	0.976779i	$0.568731\pi$
$284$	−4.19066e8	−1.08560
$285$	−5.28597e6	−0.0135260
$286$	6.32894e8	1.59974
$287$	−6.62858e7	−0.165514
$288$	5.05127e8	1.24603
$289$	2.12708e7	0.0518372
$290$	−8.18090e8	−1.96974
$291$	−7.82410e6	−0.0186127
$292$	8.93278e7	0.209965
$293$	4.41998e8	1.02656	0.513279	−	0.858222i	$-0.328431\pi$
$293$	4.41998e8	1.02656	0.513279	+	0.858222i	$0.328431\pi$
$294$	−1.88055e8	−0.431589
$295$	1.43861e9	3.26262
$296$	6.48535e7	0.145349
$297$	−1.32427e8	−0.293312
$298$	7.40835e8	1.62168
$299$	2.20766e8	0.477620
$300$	−2.01482e8	−0.430837
$301$	1.17004e8	0.247297
$302$	3.36771e8	0.703576
$303$	−978590.	−0.00202093
$304$	2.01846e7	0.0412062
$305$	1.27595e9	2.57504
$306$	−6.64657e8	−1.32609
$307$	−4.00924e8	−0.790820	−0.395410	−	0.918505i	$-0.629397\pi$
$307$	−4.00924e8	−0.790820	−0.395410	+	0.918505i	$0.629397\pi$
$308$	−5.11261e8	−0.997045
$309$	−9.06660e7	−0.174819
$310$	2.46735e8	0.470397
$311$	3.36264e8	0.633897	0.316948	−	0.948443i	$-0.397342\pi$
$311$	3.36264e8	0.633897	0.316948	+	0.948443i	$0.397342\pi$
$312$	−4.23953e7	−0.0790271
$313$	−1.24177e7	−0.0228895	−0.0114448	−	0.999935i	$-0.503643\pi$
$313$	−1.24177e7	−0.0228895	−0.0114448	+	0.999935i	$0.503643\pi$
$314$	−1.62186e8	−0.295637
$315$	1.66413e9	2.99985
$316$	−3.29539e8	−0.587492
$317$	−8.50201e8	−1.49904	−0.749521	−	0.661980i	$-0.769716\pi$
$317$	−8.50201e8	−1.49904	−0.749521	+	0.661980i	$0.769716\pi$
$318$	−1.01904e7	−0.0177704
$319$	−3.35115e8	−0.577998
$320$	6.64880e8	1.13427
$321$	6.62999e7	0.111878
$322$	−3.98671e8	−0.665456
$323$	−2.21736e7	−0.0366124
$324$	4.38652e8	0.716494
$325$	−2.61955e9	−4.23287
$326$	1.76877e8	0.282755
$327$	−5.15375e7	−0.0815090
$328$	1.67238e7	0.0261684
$329$	−4.70303e8	−0.728102
$330$	−2.52744e8	−0.387152
$331$	−4.63676e8	−0.702775	−0.351388	−	0.936230i	$-0.614290\pi$
$331$	−4.63676e8	−0.702775	−0.351388	+	0.936230i	$0.614290\pi$
$332$	−2.12779e8	−0.319114
$333$	3.67200e8	0.544939
$334$	−2.76587e8	−0.406180
$335$	−1.99171e9	−2.89447
$336$	2.56240e8	0.368518
$337$	−8.51629e8	−1.21212	−0.606060	−	0.795419i	$-0.707251\pi$
$337$	−8.51629e8	−1.21212	−0.606060	+	0.795419i	$0.707251\pi$
$338$	1.38573e9	1.95196
$339$	2.26017e8	0.315096
$340$	−1.15779e9	−1.59754
$341$	1.01070e8	0.138033
$342$	3.41463e7	0.0461586
$343$	7.63148e8	1.02113
$344$	−2.95200e7	−0.0390986
$345$	−8.81619e7	−0.115588
$346$	−1.29233e9	−1.67729
$347$	9.08191e8	1.16687	0.583437	−	0.812159i	$-0.301708\pi$
$347$	9.08191e8	1.16687	0.583437	+	0.812159i	$0.301708\pi$
$348$	−9.53263e7	−0.121251
$349$	−1.24649e9	−1.56963	−0.784817	−	0.619728i	$-0.787243\pi$
$349$	−1.24649e9	−1.56963	−0.784817	+	0.619728i	$0.787243\pi$
$350$	4.73053e9	5.89755
$351$	−4.89763e8	−0.604520
$352$	8.05741e8	0.984683
$353$	7.48315e8	0.905467	0.452734	−	0.891646i	$-0.350449\pi$
$353$	7.48315e8	0.905467	0.452734	+	0.891646i	$0.350449\pi$
$354$	3.74737e8	0.448968
$355$	2.17581e9	2.58120
$356$	−1.09266e9	−1.28354
$357$	−2.81490e8	−0.327435
$358$	−1.89921e9	−2.18768
$359$	−5.31954e8	−0.606798	−0.303399	−	0.952864i	$-0.598121\pi$
$359$	−5.31954e8	−0.606798	−0.303399	+	0.952864i	$0.598121\pi$
$360$	−4.19857e8	−0.474289
$361$	−8.92733e8	−0.998726
$362$	1.55472e8	0.172256
$363$	7.58887e7	0.0832729
$364$	−1.89082e9	−2.05493
$365$	−4.63794e8	−0.499230
$366$	3.32367e8	0.354351
$367$	1.07856e9	1.13897	0.569485	−	0.822001i	$-0.307142\pi$
$367$	1.07856e9	1.13897	0.569485	+	0.822001i	$0.307142\pi$
$368$	3.36648e8	0.352135
$369$	9.46902e7	0.0981098
$370$	1.42990e9	1.46757
$371$	1.07027e8	0.108814
$372$	2.87503e7	0.0289562
$373$	−1.07870e9	−1.07626	−0.538132	−	0.842860i	$-0.680870\pi$
$373$	−1.07870e9	−1.07626	−0.538132	+	0.842860i	$0.680870\pi$
$374$	−1.06021e9	−1.04795
$375$	6.59184e8	0.645502
$376$	1.18657e8	0.115116
$377$	−1.23937e9	−1.19126
$378$	8.84442e8	0.842263
$379$	−7.68170e8	−0.724803	−0.362401	−	0.932022i	$-0.618043\pi$
$379$	−7.68170e8	−0.724803	−0.362401	+	0.932022i	$0.618043\pi$
$380$	5.94804e7	0.0556073
$381$	−3.03927e8	−0.281534
$382$	−2.12924e9	−1.95435
$383$	2.81285e8	0.255829	0.127915	−	0.991785i	$-0.459172\pi$
$383$	2.81285e8	0.255829	0.127915	+	0.991785i	$0.459172\pi$
$384$	−1.09982e8	−0.0991203
$385$	2.65449e9	2.37066
$386$	1.06630e9	0.943675
$387$	−1.67142e8	−0.146588
$388$	8.80407e7	0.0765196
$389$	−1.52136e9	−1.31041	−0.655206	−	0.755450i	$-0.727418\pi$
$389$	−1.52136e9	−1.31041	−0.655206	+	0.755450i	$0.727418\pi$
$390$	−9.34736e8	−0.797927
$391$	−3.69822e8	−0.312878
$392$	−4.98313e8	−0.417831
$393$	2.13265e8	0.177233
$394$	2.15732e9	1.77696
$395$	1.71098e9	1.39687
$396$	7.30343e8	0.591009
$397$	9.64243e8	0.773428	0.386714	−	0.922200i	$-0.373610\pi$
$397$	9.64243e8	0.773428	0.386714	+	0.922200i	$0.373610\pi$
$398$	−2.41289e9	−1.91843
$399$	1.44614e7	0.0113974
$400$	−3.99458e9	−3.12077
$401$	1.46162e9	1.13195	0.565977	−	0.824421i	$-0.308499\pi$
$401$	1.46162e9	1.13195	0.565977	+	0.824421i	$0.308499\pi$
$402$	−5.18811e8	−0.398307
$403$	3.73793e8	0.284488
$404$	1.10116e7	0.00830836
$405$	−2.27750e9	−1.70360
$406$	2.23813e9	1.65976
$407$	5.85730e8	0.430643
$408$	7.10197e7	0.0517688
$409$	−1.40198e9	−1.01324	−0.506619	−	0.862170i	$-0.669105\pi$
$409$	−1.40198e9	−1.01324	−0.506619	+	0.862170i	$0.669105\pi$
$410$	3.68729e8	0.264219
$411$	−3.94087e8	−0.279992
$412$	1.02022e9	0.718709
$413$	−3.93575e9	−2.74918
$414$	5.69508e8	0.394456
$415$	1.10476e9	0.758753
$416$	2.97992e9	2.02945
$417$	−1.83861e7	−0.0124169
$418$	5.44677e7	0.0364772
$419$	2.20128e9	1.46193	0.730964	−	0.682416i	$-0.239071\pi$
$419$	2.20128e9	1.46193	0.730964	+	0.682416i	$0.239071\pi$
$420$	7.55093e8	0.497311
$421$	1.37650e9	0.899061	0.449530	−	0.893265i	$-0.351591\pi$
$421$	1.37650e9	0.899061	0.449530	+	0.893265i	$0.351591\pi$
$422$	4.03699e9	2.61495
$423$	6.71835e8	0.431590
$424$	−2.70028e7	−0.0172040
$425$	4.38822e9	2.77285
$426$	5.66768e8	0.355199
$427$	−3.49075e9	−2.16980
$428$	−7.46039e8	−0.459948
$429$	−3.82897e8	−0.234143
$430$	−6.50861e8	−0.394774
$431$	−1.13829e9	−0.684832	−0.342416	−	0.939548i	$-0.611245\pi$
$431$	−1.13829e9	−0.684832	−0.342416	+	0.939548i	$0.611245\pi$
$432$	−7.46845e8	−0.445695
$433$	−3.25059e8	−0.192422	−0.0962111	−	0.995361i	$-0.530672\pi$
$433$	−3.25059e8	−0.192422	−0.0962111	+	0.995361i	$0.530672\pi$
$434$	−6.75018e8	−0.396370
$435$	4.94939e8	0.288297
$436$	5.79925e8	0.335096
$437$	1.89994e7	0.0108907
$438$	−1.20812e8	−0.0686989
$439$	−2.09252e9	−1.18044	−0.590219	−	0.807243i	$-0.700959\pi$
$439$	−2.09252e9	−1.18044	−0.590219	+	0.807243i	$0.700959\pi$
$440$	−6.69725e8	−0.374811
$441$	−2.82144e9	−1.56652
$442$	−3.92104e9	−2.15985
$443$	−1.93713e9	−1.05863	−0.529316	−	0.848425i	$-0.677551\pi$
$443$	−1.93713e9	−1.05863	−0.529316	+	0.848425i	$0.677551\pi$
$444$	1.66616e8	0.0903393
$445$	5.67314e9	3.05185
$446$	1.61122e9	0.859968
$447$	−4.48200e8	−0.237354
$448$	−1.81898e9	−0.955773
$449$	−1.43342e9	−0.747329	−0.373665	−	0.927564i	$-0.621899\pi$
$449$	−1.43342e9	−0.747329	−0.373665	+	0.927564i	$0.621899\pi$
$450$	−6.75763e9	−3.49583
$451$	1.51043e8	0.0775322
$452$	−2.54326e9	−1.29541
$453$	−2.03744e8	−0.102977
$454$	1.96864e9	0.987351
$455$	9.81725e9	4.88596
$456$	−3.64859e6	−0.00180197
$457$	3.05243e8	0.149602	0.0748012	−	0.997198i	$-0.476168\pi$
$457$	3.05243e8	0.149602	0.0748012	+	0.997198i	$0.476168\pi$
$458$	−1.50285e9	−0.730948
$459$	8.20441e8	0.396007
$460$	9.92042e8	0.475202
$461$	−3.07533e9	−1.46197	−0.730986	−	0.682392i	$-0.760940\pi$
$461$	−3.07533e9	−1.46197	−0.730986	+	0.682392i	$0.760940\pi$
$462$	6.91457e8	0.326226
$463$	−6.71289e8	−0.314323	−0.157162	−	0.987573i	$-0.550234\pi$
$463$	−6.71289e8	−0.314323	−0.157162	+	0.987573i	$0.550234\pi$
$464$	−1.88994e9	−0.878283
$465$	−1.49273e8	−0.0688487
$466$	4.88240e9	2.23503
$467$	1.81833e9	0.826160	0.413080	−	0.910695i	$-0.364453\pi$
$467$	1.81833e9	0.826160	0.413080	+	0.910695i	$0.364453\pi$
$468$	2.70107e9	1.21808
$469$	5.44891e9	2.43896
$470$	2.61616e9	1.16231
$471$	9.81213e7	0.0432703
$472$	9.92986e8	0.434657
$473$	−2.66612e8	−0.115842
$474$	4.45687e8	0.192223
$475$	−2.25442e8	−0.0965176
$476$	3.16747e9	1.34613
$477$	−1.52890e8	−0.0645006
$478$	1.58041e9	0.661869
$479$	−2.05954e9	−0.856240	−0.428120	−	0.903722i	$-0.640824\pi$
$479$	−2.05954e9	−0.856240	−0.428120	+	0.903722i	$0.640824\pi$
$480$	−1.19002e9	−0.491145
$481$	2.16624e9	0.887562
$482$	1.16007e9	0.471867
$483$	2.41194e8	0.0973982
$484$	−8.53937e8	−0.342348
$485$	−4.57112e8	−0.181939
$486$	−1.90764e9	−0.753824
$487$	−2.54877e9	−0.999954	−0.499977	−	0.866039i	$-0.666658\pi$
$487$	−2.54877e9	−0.999954	−0.499977	+	0.866039i	$0.666658\pi$
$488$	8.80711e8	0.343055
$489$	−1.07010e8	−0.0413849
$490$	−1.09869e10	−4.21879
$491$	2.32288e9	0.885607	0.442804	−	0.896619i	$-0.353984\pi$
$491$	2.32288e9	0.885607	0.442804	+	0.896619i	$0.353984\pi$
$492$	4.29654e7	0.0162645
$493$	2.07618e9	0.780369
$494$	2.01441e8	0.0751802
$495$	−3.79198e9	−1.40523
$496$	5.70002e8	0.209744
$497$	−5.95259e9	−2.17500
$498$	2.87775e8	0.104412
$499$	5.35418e9	1.92904	0.964520	−	0.264009i	$-0.0850450\pi$
$499$	5.35418e9	1.92904	0.964520	+	0.264009i	$0.0850450\pi$
$500$	−7.41748e9	−2.65376
$501$	1.67333e8	0.0594497
$502$	−6.83843e9	−2.41265
$503$	−4.36661e9	−1.52988	−0.764938	−	0.644104i	$-0.777230\pi$
$503$	−4.36661e9	−1.52988	−0.764938	+	0.644104i	$0.777230\pi$
$504$	1.14865e9	0.399650
$505$	−5.71727e7	−0.0197546
$506$	9.08437e8	0.311722
$507$	−8.38357e8	−0.285694
$508$	3.41994e9	1.15743
$509$	3.03093e9	1.01874	0.509371	−	0.860547i	$-0.329878\pi$
$509$	3.03093e9	1.01874	0.509371	+	0.860547i	$0.329878\pi$
$510$	1.56585e9	0.522703
$511$	1.26885e9	0.420666
$512$	3.64534e9	1.20031
$513$	−4.21496e7	−0.0137842
$514$	1.30042e9	0.422389
$515$	−5.29703e9	−1.70886
$516$	−7.58402e7	−0.0243011
$517$	1.07166e9	0.341068
$518$	−3.91192e9	−1.23662
$519$	7.81851e8	0.245493
$520$	−2.47688e9	−0.772492
$521$	7.54943e8	0.233874	0.116937	−	0.993139i	$-0.462692\pi$
$521$	7.54943e8	0.233874	0.116937	+	0.993139i	$0.462692\pi$
$522$	−3.19721e9	−0.983839
$523$	1.20927e9	0.369630	0.184815	−	0.982773i	$-0.440831\pi$
$523$	1.20927e9	0.369630	0.184815	+	0.982773i	$0.440831\pi$
$524$	−2.39976e9	−0.728632
$525$	−2.86194e9	−0.863183
$526$	−2.17255e9	−0.650908
$527$	−6.26171e8	−0.186361
$528$	−5.83884e8	−0.172627
$529$	−3.08794e9	−0.906932
$530$	−5.95362e8	−0.173706
$531$	5.62228e9	1.62960
$532$	−1.62727e8	−0.0468563
$533$	5.58610e8	0.159795
$534$	1.47777e9	0.419965
$535$	3.87347e9	1.09361
$536$	−1.37476e9	−0.385610
$537$	1.14901e9	0.320195
$538$	1.53676e9	0.425470
$539$	−4.50056e9	−1.23796
$540$	−2.20082e9	−0.601459
$541$	3.74130e9	1.01586	0.507928	−	0.861400i	$-0.330412\pi$
$541$	3.74130e9	1.01586	0.507928	+	0.861400i	$0.330412\pi$
$542$	1.40374e9	0.378696
$543$	−9.40597e7	−0.0252118
$544$	−4.99190e9	−1.32944
$545$	−3.01100e9	−0.796752
$546$	2.55725e9	0.672357
$547$	1.07121e8	0.0279845	0.0139923	−	0.999902i	$-0.495546\pi$
$547$	1.07121e8	0.0279845	0.0139923	+	0.999902i	$0.495546\pi$
$548$	4.43447e9	1.15109
$549$	4.98658e9	1.28617
$550$	−1.07793e10	−2.76261
$551$	−1.06662e8	−0.0271631
$552$	−6.08529e7	−0.0153991
$553$	−4.68091e9	−1.17704
$554$	2.29464e9	0.573364
$555$	−8.65080e8	−0.214798
$556$	2.06889e8	0.0510477
$557$	−1.84003e9	−0.451160	−0.225580	−	0.974225i	$-0.572428\pi$
$557$	−1.84003e9	−0.451160	−0.225580	+	0.974225i	$0.572428\pi$
$558$	9.64273e8	0.234953
$559$	−9.86028e8	−0.238753
$560$	1.49704e10	3.60227
$561$	6.41421e8	0.153382
$562$	3.10994e9	0.739051
$563$	−2.91696e8	−0.0688892	−0.0344446	−	0.999407i	$-0.510966\pi$
$563$	−2.91696e8	−0.0688892	−0.0344446	+	0.999407i	$0.510966\pi$
$564$	3.04843e8	0.0715484
$565$	1.32047e10	3.08006
$566$	−2.48642e9	−0.576391
$567$	6.23080e9	1.43550
$568$	1.50183e9	0.343876
$569$	1.23531e9	0.281114	0.140557	−	0.990073i	$-0.455111\pi$
$569$	1.23531e9	0.281114	0.140557	+	0.990073i	$0.455111\pi$
$570$	−8.04446e7	−0.0181943
$571$	6.32334e9	1.42141	0.710706	−	0.703489i	$-0.248375\pi$
$571$	6.32334e9	1.42141	0.710706	+	0.703489i	$0.248375\pi$
$572$	4.30855e9	0.962597
$573$	1.28817e9	0.286044
$574$	−1.00877e9	−0.222639
$575$	−3.76002e9	−0.824808
$576$	2.59844e9	0.566544
$577$	−2.79809e9	−0.606381	−0.303191	−	0.952930i	$-0.598052\pi$
$577$	−2.79809e9	−0.606381	−0.303191	+	0.952930i	$0.598052\pi$
$578$	3.23710e8	0.0697282
$579$	−6.45103e8	−0.138119
$580$	−5.56931e9	−1.18523
$581$	−3.02241e9	−0.639347
$582$	−1.19071e8	−0.0250366
$583$	−2.43878e8	−0.0509722
$584$	−3.20129e8	−0.0665090
$585$	−1.40241e10	−2.89620
$586$	6.72654e9	1.38086
$587$	2.66505e9	0.543841	0.271921	−	0.962320i	$-0.412341\pi$
$587$	2.66505e9	0.543841	0.271921	+	0.962320i	$0.412341\pi$
$588$	−1.28022e9	−0.259696
$589$	3.21691e7	0.00648688
$590$	2.18935e10	4.38867
$591$	−1.30517e9	−0.260082
$592$	3.30332e9	0.654373
$593$	−2.31869e9	−0.456616	−0.228308	−	0.973589i	$-0.573319\pi$
$593$	−2.31869e9	−0.456616	−0.228308	+	0.973589i	$0.573319\pi$
$594$	−2.01534e9	−0.394545
$595$	−1.64457e10	−3.20068
$596$	5.04337e9	0.975797
$597$	1.45978e9	0.280787
$598$	3.35972e9	0.642465
$599$	−2.38951e9	−0.454271	−0.227135	−	0.973863i	$-0.572936\pi$
$599$	−2.38951e9	−0.454271	−0.227135	+	0.973863i	$0.572936\pi$
$600$	7.22065e8	0.136473
$601$	−5.85741e9	−1.10064	−0.550320	−	0.834954i	$-0.685494\pi$
$601$	−5.85741e9	−1.10064	−0.550320	+	0.834954i	$0.685494\pi$
$602$	1.78063e9	0.332648
$603$	−7.78385e9	−1.44572
$604$	2.29263e9	0.423356
$605$	4.43369e9	0.813994
$606$	−1.48927e7	−0.00271843
$607$	1.64112e8	0.0297838	0.0148919	−	0.999889i	$-0.495260\pi$
$607$	1.64112e8	0.0297838	0.0148919	+	0.999889i	$0.495260\pi$
$608$	2.56456e8	0.0462753
$609$	−1.35406e9	−0.242927
$610$	1.94180e10	3.46379
$611$	3.96339e9	0.702946
$612$	−4.52478e9	−0.797935
$613$	−6.13717e9	−1.07611	−0.538055	−	0.842910i	$-0.680841\pi$
$613$	−6.13717e9	−1.07611	−0.538055	+	0.842910i	$0.680841\pi$
$614$	−6.10146e9	−1.06376
$615$	−2.23079e8	−0.0386719
$616$	1.83224e9	0.315827
$617$	−1.73030e9	−0.296567	−0.148284	−	0.988945i	$-0.547375\pi$
$617$	−1.73030e9	−0.296567	−0.148284	+	0.988945i	$0.547375\pi$
$618$	−1.37980e9	−0.235156
$619$	3.65743e9	0.619811	0.309906	−	0.950767i	$-0.399703\pi$
$619$	3.65743e9	0.619811	0.309906	+	0.950767i	$0.399703\pi$
$620$	1.67969e9	0.283047
$621$	−7.02991e8	−0.117796
$622$	5.11743e9	0.852679
$623$	−1.55206e10	−2.57158
$624$	−2.15941e9	−0.355786
$625$	2.20101e10	3.60613
$626$	−1.88979e8	−0.0307896
$627$	−3.29526e7	−0.00533891
$628$	−1.10411e9	−0.177891
$629$	−3.62884e9	−0.581421
$630$	2.53255e10	4.03521
$631$	−8.67078e9	−1.37390	−0.686951	−	0.726704i	$-0.741051\pi$
$631$	−8.67078e9	−1.37390	−0.686951	+	0.726704i	$0.741051\pi$
$632$	1.18099e9	0.186096
$633$	−2.44235e9	−0.382733
$634$	−1.29388e10	−2.01642
$635$	−1.77565e10	−2.75200
$636$	−6.93733e7	−0.0106928
$637$	−1.66447e10	−2.55145
$638$	−5.09995e9	−0.777487
$639$	8.50336e9	1.28925
$640$	−6.42555e9	−0.968903
$641$	5.26409e9	0.789442	0.394721	−	0.918801i	$-0.370841\pi$
$641$	5.26409e9	0.789442	0.394721	+	0.918801i	$0.370841\pi$
$642$	1.00898e9	0.150491
$643$	−3.46768e9	−0.514399	−0.257200	−	0.966358i	$-0.582800\pi$
$643$	−3.46768e9	−0.514399	−0.257200	+	0.966358i	$0.582800\pi$
$644$	−2.71403e9	−0.400419
$645$	3.93766e8	0.0577803
$646$	−3.37450e8	−0.0492488
$647$	3.80535e9	0.552369	0.276185	−	0.961105i	$-0.410930\pi$
$647$	3.80535e9	0.552369	0.276185	+	0.961105i	$0.410930\pi$
$648$	−1.57202e9	−0.226959
$649$	8.96824e9	1.28781
$650$	−3.98656e10	−5.69379
$651$	4.08381e8	0.0580139
$652$	1.20413e9	0.170140
$653$	2.84050e9	0.399207	0.199603	−	0.979877i	$-0.436035\pi$
$653$	2.84050e9	0.399207	0.199603	+	0.979877i	$0.436035\pi$
$654$	−7.84323e8	−0.109641
$655$	1.24597e10	1.73246
$656$	8.51831e8	0.117812
$657$	−1.81257e9	−0.249354
$658$	−7.15731e9	−0.979398
$659$	3.52181e9	0.479365	0.239683	−	0.970851i	$-0.422957\pi$
$659$	3.52181e9	0.479365	0.239683	+	0.970851i	$0.422957\pi$
$660$	−1.72060e9	−0.232957
$661$	7.62689e9	1.02717	0.513585	−	0.858039i	$-0.328317\pi$
$661$	7.62689e9	1.02717	0.513585	+	0.858039i	$0.328317\pi$
$662$	−7.05645e9	−0.945330
$663$	2.37220e9	0.316122
$664$	7.62551e8	0.101084
$665$	8.44885e8	0.111409
$666$	5.58824e9	0.733019
$667$	−1.77896e9	−0.232127
$668$	−1.88292e9	−0.244407
$669$	−9.74776e8	−0.125867
$670$	−3.03108e10	−3.89346
$671$	7.95422e9	1.01641
$672$	3.25566e9	0.413853
$673$	1.76513e9	0.223216	0.111608	−	0.993752i	$-0.464400\pi$
$673$	1.76513e9	0.223216	0.111608	+	0.993752i	$0.464400\pi$
$674$	−1.29605e10	−1.63047
$675$	8.34150e9	1.04395
$676$	9.43362e9	1.17453
$677$	−1.21822e10	−1.50892	−0.754461	−	0.656345i	$-0.772102\pi$
$677$	−1.21822e10	−1.50892	−0.754461	+	0.656345i	$0.772102\pi$
$678$	3.43964e9	0.423847
$679$	1.25057e9	0.153307
$680$	4.14923e9	0.506041
$681$	−1.19102e9	−0.144512
$682$	1.53814e9	0.185673
$683$	9.06722e9	1.08893	0.544467	−	0.838782i	$-0.316732\pi$
$683$	9.06722e9	1.08893	0.544467	+	0.838782i	$0.316732\pi$
$684$	2.32457e8	0.0277746
$685$	−2.30240e10	−2.73693
$686$	1.16140e10	1.37356
$687$	9.09214e8	0.106984
$688$	−1.50361e9	−0.176025
$689$	−9.01949e8	−0.105055
$690$	−1.34169e9	−0.155482
$691$	1.27877e10	1.47441	0.737206	−	0.675668i	$-0.236145\pi$
$691$	1.27877e10	1.47441	0.737206	+	0.675668i	$0.236145\pi$
$692$	−8.79778e9	−1.00926
$693$	1.03741e10	1.18409
$694$	1.38213e10	1.56961
$695$	−1.07418e9	−0.121375
$696$	3.41627e8	0.0384078
$697$	−9.35772e8	−0.104678
$698$	−1.89696e10	−2.11137
$699$	−2.95382e9	−0.327125
$700$	3.22040e10	3.54868
$701$	1.61492e10	1.77068	0.885338	−	0.464948i	$-0.153927\pi$
$701$	1.61492e10	1.77068	0.885338	+	0.464948i	$0.153927\pi$
$702$	−7.45346e9	−0.813163
$703$	1.86429e8	0.0202381
$704$	4.14484e9	0.447717
$705$	−1.58276e9	−0.170119
$706$	1.13882e10	1.21798
$707$	1.56413e8	0.0166458
$708$	2.55110e9	0.270153
$709$	−4.31415e9	−0.454604	−0.227302	−	0.973824i	$-0.572991\pi$
$709$	−4.31415e9	−0.454604	−0.227302	+	0.973824i	$0.572991\pi$
$710$	3.31126e10	3.47207
$711$	6.68675e9	0.697705
$712$	3.91583e9	0.406578
$713$	5.36532e8	0.0554348
$714$	−4.28386e9	−0.440445
$715$	−2.23702e10	−2.28875
$716$	−1.29293e10	−1.31637
$717$	−9.56138e8	−0.0968731
$718$	−8.09555e9	−0.816227
$719$	8.62138e9	0.865019	0.432509	−	0.901629i	$-0.357628\pi$
$719$	8.62138e9	0.865019	0.432509	+	0.901629i	$0.357628\pi$
$720$	−2.13855e10	−2.13528
$721$	1.44916e10	1.43994
$722$	−1.35861e10	−1.34342
$723$	−7.01835e8	−0.0690639
$724$	1.05841e9	0.103650
$725$	2.11087e10	2.05721
$726$	1.15491e9	0.112014
$727$	−1.50745e10	−1.45503	−0.727517	−	0.686089i	$-0.759326\pi$
$727$	−1.50745e10	−1.45503	−0.727517	+	0.686089i	$0.759326\pi$
$728$	6.77626e9	0.650924
$729$	−8.10559e9	−0.774887
$730$	−7.05826e9	−0.671533
$731$	1.65177e9	0.156401
$732$	2.26265e9	0.213220
$733$	1.41082e10	1.32315	0.661574	−	0.749880i	$-0.269889\pi$
$733$	1.41082e10	1.32315	0.661574	+	0.749880i	$0.269889\pi$
$734$	1.64141e10	1.53207
$735$	6.64698e9	0.617474
$736$	4.27729e9	0.395454
$737$	−1.24162e10	−1.14249
$738$	1.44104e9	0.131971
$739$	−2.01127e10	−1.83322	−0.916611	−	0.399781i	$-0.869086\pi$
$739$	−2.01127e10	−1.83322	−0.916611	+	0.399781i	$0.869086\pi$
$740$	9.73431e9	0.883068
$741$	−1.21870e8	−0.0110036
$742$	1.62879e9	0.146370
$743$	7.77437e9	0.695352	0.347676	−	0.937615i	$-0.386971\pi$
$743$	7.77437e9	0.695352	0.347676	+	0.937615i	$0.386971\pi$
$744$	−1.03034e8	−0.00917225
$745$	−2.61855e10	−2.32014
$746$	−1.64162e10	−1.44772
$747$	4.31756e9	0.378980
$748$	−7.21759e9	−0.630575
$749$	−1.05971e10	−0.921508
$750$	1.00318e10	0.868289
$751$	−1.36165e10	−1.17307	−0.586536	−	0.809923i	$-0.699509\pi$
$751$	−1.36165e10	−1.17307	−0.586536	+	0.809923i	$0.699509\pi$
$752$	6.04381e9	0.518261
$753$	4.13721e9	0.353122
$754$	−1.88614e10	−1.60241
$755$	−1.19035e10	−1.00661
$756$	6.02101e9	0.506807
$757$	1.37437e10	1.15151	0.575756	−	0.817622i	$-0.304708\pi$
$757$	1.37437e10	1.15151	0.575756	+	0.817622i	$0.304708\pi$
$758$	−1.16904e10	−0.974960
$759$	−5.49598e8	−0.0456246
$760$	−2.13164e8	−0.0176143
$761$	9.87644e9	0.812370	0.406185	−	0.913791i	$-0.366859\pi$
$761$	9.87644e9	0.812370	0.406185	+	0.913791i	$0.366859\pi$
$762$	−4.62531e9	−0.378703
$763$	8.23751e9	0.671367
$764$	−1.44952e10	−1.17597
$765$	2.34929e10	1.89724
$766$	4.28073e9	0.344126
$767$	3.31678e10	2.65419
$768$	−3.13045e9	−0.249369
$769$	1.45345e10	1.15254	0.576272	−	0.817258i	$-0.304507\pi$
$769$	1.45345e10	1.15254	0.576272	+	0.817258i	$0.304507\pi$
$770$	4.03974e10	3.18886
$771$	−7.86746e8	−0.0618221
$772$	7.25902e9	0.567829
$773$	−1.27560e10	−0.993312	−0.496656	−	0.867947i	$-0.665439\pi$
$773$	−1.27560e10	−0.993312	−0.496656	+	0.867947i	$0.665439\pi$
$774$	−2.54365e9	−0.197181
$775$	−6.36635e9	−0.491286
$776$	−3.15517e8	−0.0242386
$777$	2.36669e9	0.180995
$778$	−2.31528e10	−1.76269
$779$	4.80747e7	0.00364364
$780$	−6.36340e9	−0.480129
$781$	1.35639e10	1.01884
$782$	−5.62814e9	−0.420864
$783$	3.94658e9	0.293802
$784$	−2.53817e10	−1.88111
$785$	5.73260e9	0.422968
$786$	3.24557e9	0.238403
$787$	−8.63446e9	−0.631428	−0.315714	−	0.948854i	$-0.602244\pi$
$787$	−8.63446e9	−0.631428	−0.315714	+	0.948854i	$0.602244\pi$
$788$	1.46864e10	1.06924
$789$	1.31438e9	0.0952688
$790$	2.60386e10	1.87898
$791$	−3.61255e10	−2.59535
$792$	−2.61738e9	−0.187210
$793$	2.94176e10	2.09484
$794$	1.46743e10	1.04037
$795$	3.60190e8	0.0254242
$796$	−1.64262e10	−1.15436
$797$	−2.05828e10	−1.44012	−0.720061	−	0.693911i	$-0.755886\pi$
$797$	−2.05828e10	−1.44012	−0.720061	+	0.693911i	$0.755886\pi$
$798$	2.20081e8	0.0153310
$799$	−6.63939e9	−0.460484
$800$	−5.07532e10	−3.50468
$801$	2.21714e10	1.52433
$802$	2.22436e10	1.52263
$803$	−2.89128e9	−0.197054
$804$	−3.53190e9	−0.239670
$805$	1.40914e10	0.952069
$806$	5.68858e9	0.382676
$807$	−9.29731e8	−0.0622730
$808$	−3.94629e7	−0.00263178
$809$	1.96518e9	0.130492	0.0652459	−	0.997869i	$-0.479217\pi$
$809$	1.96518e9	0.130492	0.0652459	+	0.997869i	$0.479217\pi$
$810$	−3.46602e10	−2.29157
$811$	−9.82285e9	−0.646643	−0.323321	−	0.946289i	$-0.604799\pi$
$811$	−9.82285e9	−0.646643	−0.323321	+	0.946289i	$0.604799\pi$
$812$	1.52365e10	0.998711
$813$	−8.49255e8	−0.0554270
$814$	8.91394e9	0.579274
$815$	−6.25189e9	−0.404538
$816$	3.61740e9	0.233067
$817$	−8.48588e7	−0.00544402
$818$	−2.13361e10	−1.36295
$819$	3.83671e10	2.44043
$820$	2.51019e9	0.158986
$821$	1.17346e10	0.740060	0.370030	−	0.929020i	$-0.379347\pi$
$821$	1.17346e10	0.740060	0.370030	+	0.929020i	$0.379347\pi$
$822$	−5.99742e9	−0.376628
$823$	−1.25381e10	−0.784029	−0.392015	−	0.919959i	$-0.628222\pi$
$823$	−1.25381e10	−0.784029	−0.392015	+	0.919959i	$0.628222\pi$
$824$	−3.65622e9	−0.227660
$825$	6.52139e9	0.404344
$826$	−5.98963e10	−3.69802
$827$	−7.60873e9	−0.467782	−0.233891	−	0.972263i	$-0.575146\pi$
$827$	−7.60873e9	−0.467782	−0.233891	+	0.972263i	$0.575146\pi$
$828$	3.87703e9	0.237352
$829$	−1.26864e10	−0.773388	−0.386694	−	0.922208i	$-0.626383\pi$
$829$	−1.26864e10	−0.773388	−0.386694	+	0.922208i	$0.626383\pi$
$830$	1.68128e10	1.02063
$831$	−1.38824e9	−0.0839193
$832$	1.53291e10	0.922752
$833$	2.78828e10	1.67140
$834$	−2.79808e8	−0.0167024
$835$	9.77620e9	0.581122
$836$	3.70799e8	0.0219491
$837$	−1.19028e9	−0.0701634
$838$	3.35002e10	1.96650
$839$	−1.25954e10	−0.736282	−0.368141	−	0.929770i	$-0.620006\pi$
$839$	−1.25954e10	−0.736282	−0.368141	+	0.929770i	$0.620006\pi$
$840$	−2.70607e9	−0.157530
$841$	−7.26283e9	−0.421036
$842$	2.09483e10	1.20936
$843$	−1.88149e9	−0.108170
$844$	2.74826e10	1.57347
$845$	−4.89798e10	−2.79266
$846$	1.02243e10	0.580548
$847$	−1.21297e10	−0.685895
$848$	−1.37539e9	−0.0774535
$849$	1.50427e9	0.0843623
$850$	6.67821e10	3.72987
$851$	3.10936e9	0.172949
$852$	3.85838e9	0.213730
$853$	−1.68559e10	−0.929890	−0.464945	−	0.885340i	$-0.653926\pi$
$853$	−1.68559e10	−0.929890	−0.464945	+	0.885340i	$0.653926\pi$
$854$	−5.31239e10	−2.91869
$855$	−1.20693e9	−0.0660391
$856$	2.67363e9	0.145694
$857$	3.15667e9	0.171315	0.0856577	−	0.996325i	$-0.472701\pi$
$857$	3.15667e9	0.171315	0.0856577	+	0.996325i	$0.472701\pi$
$858$	−5.82711e9	−0.314955
$859$	1.47310e10	0.792969	0.396484	−	0.918041i	$-0.370230\pi$
$859$	1.47310e10	0.792969	0.396484	+	0.918041i	$0.370230\pi$
$860$	−4.43086e9	−0.237544
$861$	6.10299e8	0.0325861
$862$	−1.73231e10	−0.921194
$863$	2.38879e10	1.26514	0.632571	−	0.774502i	$-0.282000\pi$
$863$	2.38879e10	1.26514	0.632571	+	0.774502i	$0.282000\pi$
$864$	−9.48904e9	−0.500523
$865$	4.56785e10	2.39969
$866$	−4.94692e9	−0.258834
$867$	−1.95842e8	−0.0102056
$868$	−4.59531e9	−0.238504
$869$	1.06662e10	0.551367
$870$	7.53224e9	0.387799
$871$	−4.59196e10	−2.35470
$872$	−2.07831e9	−0.106146
$873$	−1.78645e9	−0.0908745
$874$	2.89142e8	0.0146495
$875$	−1.05361e11	−5.31682
$876$	−8.22449e8	−0.0413375
$877$	2.26234e10	1.13255	0.566277	−	0.824215i	$-0.308383\pi$
$877$	2.26234e10	1.13255	0.566277	+	0.824215i	$0.308383\pi$
$878$	−3.18450e10	−1.58785
$879$	−4.06951e9	−0.202107
$880$	−3.41126e10	−1.68743
$881$	−1.42978e8	−0.00704454	−0.00352227	−	0.999994i	$-0.501121\pi$
$881$	−1.42978e8	−0.00704454	−0.00352227	+	0.999994i	$0.501121\pi$
$882$	−4.29382e10	−2.10719
$883$	−8.28063e9	−0.404763	−0.202381	−	0.979307i	$-0.564868\pi$
$883$	−8.28063e9	−0.404763	−0.202381	+	0.979307i	$0.564868\pi$
$884$	−2.66932e10	−1.29963
$885$	−1.32454e10	−0.642339
$886$	−2.94802e10	−1.42401
$887$	−3.14829e10	−1.51475	−0.757376	−	0.652979i	$-0.773519\pi$
$887$	−3.14829e10	−1.51475	−0.757376	+	0.652979i	$0.773519\pi$
$888$	−5.97112e8	−0.0286161
$889$	4.85782e10	2.31892
$890$	8.63367e10	4.10516
$891$	−1.41979e10	−0.672437
$892$	1.09687e10	0.517460
$893$	3.41094e8	0.0160285
$894$	−6.82094e9	−0.319273
$895$	6.71294e10	3.12991
$896$	1.75790e10	0.816426
$897$	−2.03261e9	−0.0940331
$898$	−2.18145e10	−1.00526
$899$	−3.01208e9	−0.138263
$900$	−4.60039e10	−2.10352
$901$	1.51093e9	0.0688188
$902$	2.29864e9	0.104292
$903$	−1.07727e9	−0.0486874
$904$	9.11443e9	0.410336
$905$	−5.49531e9	−0.246446
$906$	−3.10068e9	−0.138519
$907$	−2.58557e10	−1.15062	−0.575308	−	0.817937i	$-0.695118\pi$
$907$	−2.58557e10	−1.15062	−0.575308	+	0.817937i	$0.695118\pi$
$908$	1.34019e10	0.594109
$909$	−2.23439e8	−0.00986699
$910$	1.49404e11	6.57230
$911$	1.27853e10	0.560271	0.280136	−	0.959960i	$-0.409621\pi$
$911$	1.27853e10	0.560271	0.280136	+	0.959960i	$0.409621\pi$
$912$	−1.85842e8	−0.00811262
$913$	6.88704e9	0.299492
$914$	4.64534e9	0.201236
$915$	−1.17478e10	−0.506970
$916$	−1.02309e10	−0.439826
$917$	−3.40872e10	−1.45982
$918$	1.24859e10	0.532684
$919$	−2.07808e10	−0.883197	−0.441599	−	0.897213i	$-0.645588\pi$
$919$	−2.07808e10	−0.883197	−0.441599	+	0.897213i	$0.645588\pi$
$920$	−3.55524e9	−0.150526
$921$	3.69134e9	0.155695
$922$	−4.68020e10	−1.96656
$923$	5.01643e10	2.09985
$924$	4.70722e9	0.196297
$925$	−3.68948e10	−1.53274
$926$	−1.02160e10	−0.422808
$927$	−2.07015e10	−0.853538
$928$	−2.40126e10	−0.986328
$929$	3.30915e10	1.35414	0.677068	−	0.735921i	$-0.263250\pi$
$929$	3.30915e10	1.35414	0.677068	+	0.735921i	$0.263250\pi$
$930$	−2.27171e9	−0.0926110
$931$	−1.43246e9	−0.0581780
$932$	3.32379e10	1.34486
$933$	−3.09601e9	−0.124801
$934$	2.76723e10	1.11130
$935$	3.74741e10	1.49931
$936$	−9.67999e9	−0.385842
$937$	−2.83321e9	−0.112510	−0.0562548	−	0.998416i	$-0.517916\pi$
$937$	−2.83321e9	−0.112510	−0.0562548	+	0.998416i	$0.517916\pi$
$938$	8.29243e10	3.28074
$939$	1.14331e8	0.00450645
$940$	1.78100e10	0.699387
$941$	−4.17032e10	−1.63157	−0.815786	−	0.578354i	$-0.803695\pi$
$941$	−4.17032e10	−1.63157	−0.815786	+	0.578354i	$0.803695\pi$
$942$	1.49326e9	0.0582046
$943$	8.01812e8	0.0311373
$944$	5.05779e10	1.95686
$945$	−3.12614e10	−1.20503
$946$	−4.05744e9	−0.155824
$947$	1.58387e10	0.606032	0.303016	−	0.952985i	$-0.402006\pi$
$947$	1.58387e10	0.606032	0.303016	+	0.952985i	$0.402006\pi$
$948$	3.03410e9	0.115665
$949$	−1.06930e10	−0.406132
$950$	−3.43089e9	−0.129830
$951$	7.82788e9	0.295129
$952$	−1.13515e10	−0.426405
$953$	−2.37238e10	−0.887889	−0.443944	−	0.896054i	$-0.646421\pi$
$953$	−2.37238e10	−0.887889	−0.443944	+	0.896054i	$0.646421\pi$
$954$	−2.32675e9	−0.0867623
$955$	7.52597e10	2.79609
$956$	1.07589e10	0.398260
$957$	3.08543e9	0.113795
$958$	−3.13431e10	−1.15176
$959$	6.29891e10	2.30622
$960$	−6.12161e9	−0.223314
$961$	−2.66042e10	−0.966981
$962$	3.29669e10	1.19389
$963$	1.51381e10	0.546233
$964$	7.89740e9	0.283932
$965$	−3.76892e10	−1.35012
$966$	3.67061e9	0.131014
$967$	8.66320e9	0.308096	0.154048	−	0.988063i	$-0.450769\pi$
$967$	8.66320e9	0.308096	0.154048	+	0.988063i	$0.450769\pi$
$968$	3.06031e9	0.108443
$969$	2.04155e8	0.00720820
$970$	−6.95656e9	−0.244734
$971$	−2.16268e10	−0.758098	−0.379049	−	0.925377i	$-0.623749\pi$
$971$	−2.16268e10	−0.758098	−0.379049	+	0.925377i	$0.623749\pi$
$972$	−1.29866e10	−0.453591
$973$	2.93874e9	0.102274
$974$	−3.87885e10	−1.34508
$975$	2.41184e10	0.833360
$976$	4.48592e10	1.54446
$977$	3.39448e9	0.116451	0.0582255	−	0.998303i	$-0.481456\pi$
$977$	3.39448e9	0.116451	0.0582255	+	0.998303i	$0.481456\pi$
$978$	−1.62853e9	−0.0556684
$979$	3.53662e10	1.20462
$980$	−7.47952e10	−2.53853
$981$	−1.17674e10	−0.397960
$982$	3.53507e10	1.19126
$983$	1.20191e10	0.403585	0.201792	−	0.979428i	$-0.435323\pi$
$983$	1.20191e10	0.403585	0.201792	+	0.979428i	$0.435323\pi$
$984$	−1.53978e8	−0.00515199
$985$	−7.62525e10	−2.54230
$986$	3.15963e10	1.04970
$987$	4.33013e9	0.143348
$988$	1.37135e9	0.0452374
$989$	−1.41532e9	−0.0465228
$990$	−5.77082e10	−1.89023
$991$	−4.37960e10	−1.42948	−0.714738	−	0.699393i	$-0.753454\pi$
$991$	−4.37960e10	−1.42948	−0.714738	+	0.699393i	$0.753454\pi$
$992$	7.24216e9	0.235547
$993$	4.26911e9	0.138361
$994$	−9.05895e10	−2.92567
$995$	8.52855e10	2.74470
$996$	1.95908e9	0.0628267
$997$	−8.81226e9	−0.281614	−0.140807	−	0.990037i	$-0.544970\pi$
$997$	−8.81226e9	−0.281614	−0.140807	+	0.990037i	$0.544970\pi$
$998$	8.14827e10	2.59483
$999$	−6.89802e9	−0.218900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.10	✓	11
3.2	odd	2		387.8.a.b.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.10	✓	11	1.1	even	1	trivial
387.8.a.b.1.2		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+15.2185 q^{2} -9.20709 q^{3} +103.603 q^{4} -537.911 q^{5} -140.118 q^{6} +1471.62 q^{7} -371.288 q^{8} -2102.23 q^{9} +O(q^{10})\)	\(q+15.2185 q^{2} -9.20709 q^{3} +103.603 q^{4} -537.911 q^{5} -140.118 q^{6} +1471.62 q^{7} -371.288 q^{8} -2102.23 q^{9} -8186.21 q^{10} -3353.32 q^{11} -953.881 q^{12} -12401.8 q^{13} +22395.8 q^{14} +4952.60 q^{15} -18911.6 q^{16} +20775.2 q^{17} -31992.8 q^{18} -1067.31 q^{19} -55729.2 q^{20} -13549.3 q^{21} -51032.5 q^{22} -17801.1 q^{23} +3418.48 q^{24} +211224. q^{25} -188736. q^{26} +39491.3 q^{27} +152464. q^{28} +99935.2 q^{29} +75371.2 q^{30} -30140.3 q^{31} -240282. q^{32} +30874.3 q^{33} +316168. q^{34} -791601. q^{35} -217797. q^{36} -174672. q^{37} -16242.9 q^{38} +114184. q^{39} +199720. q^{40} -45042.7 q^{41} -206201. q^{42} +79507.0 q^{43} -347414. q^{44} +1.13081e6 q^{45} -270907. q^{46} -319582. q^{47} +174121. q^{48} +1.34212e6 q^{49} +3.21451e6 q^{50} -191279. q^{51} -1.28486e6 q^{52} +72727.4 q^{53} +600999. q^{54} +1.80379e6 q^{55} -546394. q^{56} +9826.85 q^{57} +1.52086e6 q^{58} -2.67444e6 q^{59} +513104. q^{60} -2.37204e6 q^{61} -458690. q^{62} -3.09368e6 q^{63} -1.23604e6 q^{64} +6.67106e6 q^{65} +469861. q^{66} +3.70267e6 q^{67} +2.15237e6 q^{68} +163897. q^{69} -1.20470e7 q^{70} -4.04493e6 q^{71} +780532. q^{72} +862213. q^{73} -2.65824e6 q^{74} -1.94476e6 q^{75} -110577. q^{76} -4.93481e6 q^{77} +1.73771e6 q^{78} -3.18079e6 q^{79} +1.01728e7 q^{80} +4.23398e6 q^{81} -685483. q^{82} -2.05380e6 q^{83} -1.40375e6 q^{84} -1.11752e7 q^{85} +1.20998e6 q^{86} -920113. q^{87} +1.24505e6 q^{88} -1.05466e7 q^{89} +1.72093e7 q^{90} -1.82507e7 q^{91} -1.84425e6 q^{92} +277505. q^{93} -4.86356e6 q^{94} +574120. q^{95} +2.21230e6 q^{96} +849791. q^{97} +2.04251e7 q^{98} +7.04945e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9} - 1333 q^{10} + 1333 q^{11} + 5089 q^{12} - 17967 q^{13} - 22352 q^{14} - 49504 q^{15} - 34406 q^{16} - 63095 q^{17} - 165931 q^{18} - 54524 q^{19} - 280995 q^{20} - 139788 q^{21} - 289358 q^{22} - 138139 q^{23} - 429583 q^{24} + 3455 q^{25} - 132946 q^{26} - 240356 q^{27} - 12704 q^{28} - 308658 q^{29} + 421284 q^{30} - 209523 q^{31} - 644934 q^{32} + 96814 q^{33} + 762435 q^{34} - 578892 q^{35} + 426161 q^{36} - 298472 q^{37} - 369707 q^{38} + 292298 q^{39} + 2633173 q^{40} - 1346735 q^{41} + 1173266 q^{42} + 874577 q^{43} + 3134292 q^{44} + 1893784 q^{45} + 3588111 q^{46} + 499284 q^{47} + 5647533 q^{48} + 2544563 q^{49} + 3049745 q^{50} + 1258424 q^{51} + 983088 q^{52} - 2210495 q^{53} + 6789698 q^{54} - 1855072 q^{55} - 469976 q^{56} - 1238444 q^{57} + 4397067 q^{58} - 5824216 q^{59} - 2889372 q^{60} - 4453034 q^{61} + 1002789 q^{62} - 6240564 q^{63} + 4757538 q^{64} - 2162872 q^{65} - 258940 q^{66} - 6859513 q^{67} - 9397005 q^{68} - 10040030 q^{69} + 845078 q^{70} - 10726554 q^{71} + 1199517 q^{72} - 4456898 q^{73} + 1046637 q^{74} - 3349114 q^{75} + 5861267 q^{76} - 17019816 q^{77} + 1999122 q^{78} - 15541320 q^{79} - 15680911 q^{80} - 12976697 q^{81} + 20233655 q^{82} - 11146767 q^{83} + 12348278 q^{84} - 12471976 q^{85} - 1908168 q^{86} - 18648900 q^{87} - 24463544 q^{88} - 13531356 q^{89} + 20858990 q^{90} - 19746448 q^{91} - 26023161 q^{92} - 21903110 q^{93} + 20288857 q^{94} - 12291624 q^{95} - 13954503 q^{96} - 10999901 q^{97} + 29909168 q^{98} + 29396057 q^{99}+O(q^{100}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9 - 1333 * q^10 + 1333 * q^11 + 5089 * q^12 - 17967 * q^13 - 22352 * q^14 - 49504 * q^15 - 34406 * q^16 - 63095 * q^17 - 165931 * q^18 - 54524 * q^19 - 280995 * q^20 - 139788 * q^21 - 289358 * q^22 - 138139 * q^23 - 429583 * q^24 + 3455 * q^25 - 132946 * q^26 - 240356 * q^27 - 12704 * q^28 - 308658 * q^29 + 421284 * q^30 - 209523 * q^31 - 644934 * q^32 + 96814 * q^33 + 762435 * q^34 - 578892 * q^35 + 426161 * q^36 - 298472 * q^37 - 369707 * q^38 + 292298 * q^39 + 2633173 * q^40 - 1346735 * q^41 + 1173266 * q^42 + 874577 * q^43 + 3134292 * q^44 + 1893784 * q^45 + 3588111 * q^46 + 499284 * q^47 + 5647533 * q^48 + 2544563 * q^49 + 3049745 * q^50 + 1258424 * q^51 + 983088 * q^52 - 2210495 * q^53 + 6789698 * q^54 - 1855072 * q^55 - 469976 * q^56 - 1238444 * q^57 + 4397067 * q^58 - 5824216 * q^59 - 2889372 * q^60 - 4453034 * q^61 + 1002789 * q^62 - 6240564 * q^63 + 4757538 * q^64 - 2162872 * q^65 - 258940 * q^66 - 6859513 * q^67 - 9397005 * q^68 - 10040030 * q^69 + 845078 * q^70 - 10726554 * q^71 + 1199517 * q^72 - 4456898 * q^73 + 1046637 * q^74 - 3349114 * q^75 + 5861267 * q^76 - 17019816 * q^77 + 1999122 * q^78 - 15541320 * q^79 - 15680911 * q^80 - 12976697 * q^81 + 20233655 * q^82 - 11146767 * q^83 + 12348278 * q^84 - 12471976 * q^85 - 1908168 * q^86 - 18648900 * q^87 - 24463544 * q^88 - 13531356 * q^89 + 20858990 * q^90 - 19746448 * q^91 - 26023161 * q^92 - 21903110 * q^93 + 20288857 * q^94 - 12291624 * q^95 - 13954503 * q^96 - 10999901 * q^97 + 29909168 * q^98 + 29396057 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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