LMFDB - Embedded newform 310.8.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,8,Mod(1,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("310.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	310.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:	$96.8393579001$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6454x^{4} + 26388x^{3} + 9833101x^{2} - 121319956x - 1373351770 $ x^6 - 2x^5 - 6454x^4 + 26388x^3 + 9833101x^2 - 121319956*x - 1373351770
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-56.7181$ of defining polynomial
Character	$\chi$	$=$	310.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} -70.7181 q^{3} +64.0000 q^{4} +125.000 q^{5} -565.745 q^{6} +432.491 q^{7} +512.000 q^{8} +2814.05 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -70.7181 q^{3} +64.0000 q^{4} +125.000 q^{5} -565.745 q^{6} +432.491 q^{7} +512.000 q^{8} +2814.05 q^{9} +1000.00 q^{10} +1753.60 q^{11} -4525.96 q^{12} -11272.6 q^{13} +3459.93 q^{14} -8839.76 q^{15} +4096.00 q^{16} -6597.84 q^{17} +22512.4 q^{18} -21681.2 q^{19} +8000.00 q^{20} -30585.0 q^{21} +14028.8 q^{22} +22425.8 q^{23} -36207.7 q^{24} +15625.0 q^{25} -90181.0 q^{26} -44343.9 q^{27} +27679.5 q^{28} +64604.3 q^{29} -70718.1 q^{30} +29791.0 q^{31} +32768.0 q^{32} -124011. q^{33} -52782.7 q^{34} +54061.4 q^{35} +180099. q^{36} +497756. q^{37} -173449. q^{38} +797179. q^{39} +64000.0 q^{40} +239913. q^{41} -244680. q^{42} -171081. q^{43} +112230. q^{44} +351757. q^{45} +179406. q^{46} -55126.7 q^{47} -289661. q^{48} -636494. q^{49} +125000. q^{50} +466587. q^{51} -721448. q^{52} +503947. q^{53} -354752. q^{54} +219200. q^{55} +221436. q^{56} +1.53325e6 q^{57} +516834. q^{58} -2.52552e6 q^{59} -565745. q^{60} -3.37557e6 q^{61} +238328. q^{62} +1.21705e6 q^{63} +262144. q^{64} -1.40908e6 q^{65} -992091. q^{66} +921540. q^{67} -422262. q^{68} -1.58591e6 q^{69} +432491. q^{70} -4.72808e6 q^{71} +1.44079e6 q^{72} -995778. q^{73} +3.98205e6 q^{74} -1.10497e6 q^{75} -1.38759e6 q^{76} +758418. q^{77} +6.37743e6 q^{78} +2.20866e6 q^{79} +512000. q^{80} -3.01841e6 q^{81} +1.91930e6 q^{82} +5.09596e6 q^{83} -1.95744e6 q^{84} -824730. q^{85} -1.36865e6 q^{86} -4.56869e6 q^{87} +897844. q^{88} +7.23105e6 q^{89} +2.81405e6 q^{90} -4.87532e6 q^{91} +1.43525e6 q^{92} -2.10676e6 q^{93} -441014. q^{94} -2.71015e6 q^{95} -2.31729e6 q^{96} -9.87194e6 q^{97} -5.09195e6 q^{98} +4.93473e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 82 q^{3} + 384 q^{4} + 750 q^{5} - 656 q^{6} - 1940 q^{7} + 3072 q^{8} + 910 q^{9}+O(q^{10}) $ 6 * q + 48 * q^2 - 82 * q^3 + 384 * q^4 + 750 * q^5 - 656 * q^6 - 1940 * q^7 + 3072 * q^8 + 910 * q^9	\( 6 q + 48 q^{2} - 82 q^{3} + 384 q^{4} + 750 q^{5} - 656 q^{6} - 1940 q^{7} + 3072 q^{8} + 910 q^{9} + 6000 q^{10} - 442 q^{11} - 5248 q^{12} - 4014 q^{13} - 15520 q^{14} - 10250 q^{15} + 24576 q^{16} - 37182 q^{17} + 7280 q^{18} - 68170 q^{19} + 48000 q^{20} - 16074 q^{21} - 3536 q^{22} - 71730 q^{23} - 41984 q^{24} + 93750 q^{25} - 32112 q^{26} - 239356 q^{27} - 124160 q^{28} - 300546 q^{29} - 82000 q^{30} + 178746 q^{31} + 196608 q^{32} + 233556 q^{33} - 297456 q^{34} - 242500 q^{35} + 58240 q^{36} - 4866 q^{37} - 545360 q^{38} - 413788 q^{39} + 384000 q^{40} - 38280 q^{41} - 128592 q^{42} - 289636 q^{43} - 28288 q^{44} + 113750 q^{45} - 573840 q^{46} - 1387980 q^{47} - 335872 q^{48} - 1665106 q^{49} + 750000 q^{50} - 1040966 q^{51} - 256896 q^{52} - 2061800 q^{53} - 1914848 q^{54} - 55250 q^{55} - 993280 q^{56} - 710586 q^{57} - 2404368 q^{58} - 5189426 q^{59} - 656000 q^{60} - 337160 q^{61} + 1429968 q^{62} - 1857360 q^{63} + 1572864 q^{64} - 501750 q^{65} + 1868448 q^{66} + 487628 q^{67} - 2379648 q^{68} + 240508 q^{69} - 1940000 q^{70} - 4767670 q^{71} + 465920 q^{72} - 2337232 q^{73} - 38928 q^{74} - 1281250 q^{75} - 4362880 q^{76} + 1773908 q^{77} - 3310304 q^{78} + 537410 q^{79} + 3072000 q^{80} - 1840886 q^{81} - 306240 q^{82} - 4608400 q^{83} - 1028736 q^{84} - 4647750 q^{85} - 2317088 q^{86} + 591248 q^{87} - 226304 q^{88} - 4507442 q^{89} + 910000 q^{90} + 1735616 q^{91} - 4590720 q^{92} - 2442862 q^{93} - 11103840 q^{94} - 8521250 q^{95} - 2686976 q^{96} + 1144396 q^{97} - 13320848 q^{98} - 4453908 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 82 * q^3 + 384 * q^4 + 750 * q^5 - 656 * q^6 - 1940 * q^7 + 3072 * q^8 + 910 * q^9 + 6000 * q^10 - 442 * q^11 - 5248 * q^12 - 4014 * q^13 - 15520 * q^14 - 10250 * q^15 + 24576 * q^16 - 37182 * q^17 + 7280 * q^18 - 68170 * q^19 + 48000 * q^20 - 16074 * q^21 - 3536 * q^22 - 71730 * q^23 - 41984 * q^24 + 93750 * q^25 - 32112 * q^26 - 239356 * q^27 - 124160 * q^28 - 300546 * q^29 - 82000 * q^30 + 178746 * q^31 + 196608 * q^32 + 233556 * q^33 - 297456 * q^34 - 242500 * q^35 + 58240 * q^36 - 4866 * q^37 - 545360 * q^38 - 413788 * q^39 + 384000 * q^40 - 38280 * q^41 - 128592 * q^42 - 289636 * q^43 - 28288 * q^44 + 113750 * q^45 - 573840 * q^46 - 1387980 * q^47 - 335872 * q^48 - 1665106 * q^49 + 750000 * q^50 - 1040966 * q^51 - 256896 * q^52 - 2061800 * q^53 - 1914848 * q^54 - 55250 * q^55 - 993280 * q^56 - 710586 * q^57 - 2404368 * q^58 - 5189426 * q^59 - 656000 * q^60 - 337160 * q^61 + 1429968 * q^62 - 1857360 * q^63 + 1572864 * q^64 - 501750 * q^65 + 1868448 * q^66 + 487628 * q^67 - 2379648 * q^68 + 240508 * q^69 - 1940000 * q^70 - 4767670 * q^71 + 465920 * q^72 - 2337232 * q^73 - 38928 * q^74 - 1281250 * q^75 - 4362880 * q^76 + 1773908 * q^77 - 3310304 * q^78 + 537410 * q^79 + 3072000 * q^80 - 1840886 * q^81 - 306240 * q^82 - 4608400 * q^83 - 1028736 * q^84 - 4647750 * q^85 - 2317088 * q^86 + 591248 * q^87 - 226304 * q^88 - 4507442 * q^89 + 910000 * q^90 + 1735616 * q^91 - 4590720 * q^92 - 2442862 * q^93 - 11103840 * q^94 - 8521250 * q^95 - 2686976 * q^96 + 1144396 * q^97 - 13320848 * q^98 - 4453908 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	−70.7181	−1.51219	−0.756095	−	0.654462i	$-0.772895\pi$
$3$	−70.7181	−1.51219	−0.756095	+	0.654462i	$0.772895\pi$
$4$	64.0000	0.500000
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	−565.745	−1.06928
$7$	432.491	0.476578	0.238289	−	0.971194i	$-0.423413\pi$
$7$	432.491	0.476578	0.238289	+	0.971194i	$0.423413\pi$
$8$	512.000	0.353553
$9$	2814.05	1.28672
$10$	1000.00	0.316228
$11$	1753.60	0.397243	0.198622	−	0.980076i	$-0.436354\pi$
$11$	1753.60	0.397243	0.198622	+	0.980076i	$0.436354\pi$
$12$	−4525.96	−0.756095
$13$	−11272.6	−1.42306	−0.711530	−	0.702655i	$-0.751998\pi$
$13$	−11272.6	−1.42306	−0.711530	+	0.702655i	$0.751998\pi$
$14$	3459.93	0.336992
$15$	−8839.76	−0.676272
$16$	4096.00	0.250000
$17$	−6597.84	−0.325710	−0.162855	−	0.986650i	$-0.552070\pi$
$17$	−6597.84	−0.325710	−0.162855	+	0.986650i	$0.552070\pi$
$18$	22512.4	0.909847
$19$	−21681.2	−0.725179	−0.362589	−	0.931949i	$-0.618107\pi$
$19$	−21681.2	−0.725179	−0.362589	+	0.931949i	$0.618107\pi$
$20$	8000.00	0.223607
$21$	−30585.0	−0.720677
$22$	14028.8	0.280893
$23$	22425.8	0.384326	0.192163	−	0.981363i	$-0.438450\pi$
$23$	22425.8	0.384326	0.192163	+	0.981363i	$0.438450\pi$
$24$	−36207.7	−0.534640
$25$	15625.0	0.200000
$26$	−90181.0	−1.00626
$27$	−44343.9	−0.433572
$28$	27679.5	0.238289
$29$	64604.3	0.491890	0.245945	−	0.969284i	$-0.420902\pi$
$29$	64604.3	0.491890	0.245945	+	0.969284i	$0.420902\pi$
$30$	−70718.1	−0.478196
$31$	29791.0	0.179605
$31$	29791.0	0.179605
$32$	32768.0	0.176777
$33$	−124011.	−0.600707
$34$	−52782.7	−0.230311
$35$	54061.4	0.213132
$36$	180099.	0.643359
$37$	497756.	1.61551	0.807757	−	0.589515i	$-0.200681\pi$
$37$	497756.	1.61551	0.807757	+	0.589515i	$0.200681\pi$
$38$	−173449.	−0.512779
$39$	797179.	2.15194
$40$	64000.0	0.158114
$41$	239913.	0.543639	0.271819	−	0.962348i	$-0.412375\pi$
$41$	239913.	0.543639	0.271819	+	0.962348i	$0.412375\pi$
$42$	−244680.	−0.509596
$43$	−171081.	−0.328143	−0.164071	−	0.986448i	$-0.552463\pi$
$43$	−171081.	−0.328143	−0.164071	+	0.986448i	$0.552463\pi$
$44$	112230.	0.198622
$45$	351757.	0.575438
$46$	179406.	0.271760
$47$	−55126.7	−0.0774497	−0.0387248	−	0.999250i	$-0.512330\pi$
$47$	−55126.7	−0.0774497	−0.0387248	+	0.999250i	$0.512330\pi$
$48$	−289661.	−0.378047
$49$	−636494.	−0.772873
$50$	125000.	0.141421
$51$	466587.	0.492535
$52$	−721448.	−0.711530
$53$	503947.	0.464964	0.232482	−	0.972601i	$-0.425315\pi$
$53$	503947.	0.464964	0.232482	+	0.972601i	$0.425315\pi$
$54$	−354752.	−0.306582
$55$	219200.	0.177653
$56$	221436.	0.168496
$57$	1.53325e6	1.09661
$58$	516834.	0.347819
$59$	−2.52552e6	−1.60091	−0.800457	−	0.599390i	$-0.795410\pi$
$59$	−2.52552e6	−1.60091	−0.800457	+	0.599390i	$0.795410\pi$
$60$	−565745.	−0.338136
$61$	−3.37557e6	−1.90411	−0.952057	−	0.305921i	$-0.901036\pi$
$61$	−3.37557e6	−1.90411	−0.952057	+	0.305921i	$0.901036\pi$
$62$	238328.	0.127000
$63$	1.21705e6	0.613222
$64$	262144.	0.125000
$65$	−1.40908e6	−0.636412
$66$	−992091.	−0.424764
$67$	921540.	0.374328	0.187164	−	0.982329i	$-0.440070\pi$
$67$	921540.	0.374328	0.187164	+	0.982329i	$0.440070\pi$
$68$	−422262.	−0.162855
$69$	−1.58591e6	−0.581174
$70$	432491.	0.150707
$71$	−4.72808e6	−1.56776	−0.783882	−	0.620910i	$-0.786763\pi$
$71$	−4.72808e6	−1.56776	−0.783882	+	0.620910i	$0.786763\pi$
$72$	1.44079e6	0.454923
$73$	−995778.	−0.299594	−0.149797	−	0.988717i	$-0.547862\pi$
$73$	−995778.	−0.299594	−0.149797	+	0.988717i	$0.547862\pi$
$74$	3.98205e6	1.14234
$75$	−1.10497e6	−0.302438
$76$	−1.38759e6	−0.362589
$77$	758418.	0.189318
$78$	6.37743e6	1.52165
$79$	2.20866e6	0.504004	0.252002	−	0.967727i	$-0.418911\pi$
$79$	2.20866e6	0.504004	0.252002	+	0.967727i	$0.418911\pi$
$80$	512000.	0.111803
$81$	−3.01841e6	−0.631075
$82$	1.91930e6	0.384411
$83$	5.09596e6	0.978257	0.489129	−	0.872212i	$-0.337315\pi$
$83$	5.09596e6	0.978257	0.489129	+	0.872212i	$0.337315\pi$
$84$	−1.95744e6	−0.360339
$85$	−824730.	−0.145662
$86$	−1.36865e6	−0.232032
$87$	−4.56869e6	−0.743832
$88$	897844.	0.140447
$89$	7.23105e6	1.08727	0.543634	−	0.839322i	$-0.317048\pi$
$89$	7.23105e6	1.08727	0.543634	+	0.839322i	$0.317048\pi$
$90$	2.81405e6	0.406896
$91$	−4.87532e6	−0.678200
$92$	1.43525e6	0.192163
$93$	−2.10676e6	−0.271597
$94$	−441014.	−0.0547652
$95$	−2.71015e6	−0.324310
$96$	−2.31729e6	−0.267320
$97$	−9.87194e6	−1.09825	−0.549125	−	0.835740i	$-0.685039\pi$
$97$	−9.87194e6	−1.09825	−0.549125	+	0.835740i	$0.685039\pi$
$98$	−5.09195e6	−0.546504
$99$	4.93473e6	0.511140
$100$	1.00000e6	0.100000
$101$	4.11558e6	0.397472	0.198736	−	0.980053i	$-0.436316\pi$
$101$	4.11558e6	0.397472	0.198736	+	0.980053i	$0.436316\pi$
$102$	3.73269e6	0.348275
$103$	−2.01308e7	−1.81522	−0.907612	−	0.419811i	$-0.862096\pi$
$103$	−2.01308e7	−1.81522	−0.907612	+	0.419811i	$0.862096\pi$
$104$	−5.77159e6	−0.503128
$105$	−3.82312e6	−0.322297
$106$	4.03158e6	0.328779
$107$	1.28209e7	1.01175	0.505877	−	0.862605i	$-0.331169\pi$
$107$	1.28209e7	1.01175	0.505877	+	0.862605i	$0.331169\pi$
$108$	−2.83801e6	−0.216786
$109$	−1.76262e7	−1.30367	−0.651833	−	0.758363i	$-0.726000\pi$
$109$	−1.76262e7	−1.30367	−0.651833	+	0.758363i	$0.726000\pi$
$110$	1.75360e6	0.125619
$111$	−3.52004e7	−2.44296
$112$	1.77148e6	0.119145
$113$	−1.16971e7	−0.762610	−0.381305	−	0.924449i	$-0.624525\pi$
$113$	−1.16971e7	−0.762610	−0.381305	+	0.924449i	$0.624525\pi$
$114$	1.22660e7	0.775419
$115$	2.80322e6	0.171876
$116$	4.13467e6	0.245945
$117$	−3.17218e7	−1.83108
$118$	−2.02041e7	−1.13202
$119$	−2.85351e6	−0.155226
$120$	−4.52596e6	−0.239098
$121$	−1.64121e7	−0.842198
$122$	−2.70046e7	−1.34641
$123$	−1.69662e7	−0.822085
$124$	1.90662e6	0.0898027
$125$	1.95312e6	0.0894427
$126$	9.73643e6	0.433613
$127$	1.64182e6	0.0711232	0.0355616	−	0.999367i	$-0.488678\pi$
$127$	1.64182e6	0.0711232	0.0355616	+	0.999367i	$0.488678\pi$
$128$	2.09715e6	0.0883883
$129$	1.20985e7	0.496214
$130$	−1.12726e7	−0.450011
$131$	−4.53463e7	−1.76235	−0.881175	−	0.472790i	$-0.843247\pi$
$131$	−4.53463e7	−1.76235	−0.881175	+	0.472790i	$0.843247\pi$
$132$	−7.93673e6	−0.300354
$133$	−9.37692e6	−0.345604
$134$	7.37232e6	0.264690
$135$	−5.54299e6	−0.193899
$136$	−3.37809e6	−0.115156
$137$	−5.69761e6	−0.189309	−0.0946544	−	0.995510i	$-0.530175\pi$
$137$	−5.69761e6	−0.189309	−0.0946544	+	0.995510i	$0.530175\pi$
$138$	−1.26873e7	−0.410952
$139$	2.43884e7	0.770251	0.385125	−	0.922864i	$-0.374158\pi$
$139$	2.43884e7	0.770251	0.385125	+	0.922864i	$0.374158\pi$
$140$	3.45993e6	0.106566
$141$	3.89846e6	0.117119
$142$	−3.78247e7	−1.10858
$143$	−1.97677e7	−0.565301
$144$	1.15264e7	0.321679
$145$	8.07553e6	0.219980
$146$	−7.96623e6	−0.211845
$147$	4.50117e7	1.16873
$148$	3.18564e7	0.807757
$149$	1.44012e7	0.356654	0.178327	−	0.983971i	$-0.442932\pi$
$149$	1.44012e7	0.356654	0.178327	+	0.983971i	$0.442932\pi$
$150$	−8.83976e6	−0.213856
$151$	−1.41944e7	−0.335504	−0.167752	−	0.985829i	$-0.553651\pi$
$151$	−1.41944e7	−0.335504	−0.167752	+	0.985829i	$0.553651\pi$
$152$	−1.11008e7	−0.256389
$153$	−1.85667e7	−0.419096
$154$	6.06734e6	0.133868
$155$	3.72388e6	0.0803219
$156$	5.10195e7	1.07597
$157$	−5.36435e7	−1.10629	−0.553145	−	0.833085i	$-0.686572\pi$
$157$	−5.36435e7	−1.10629	−0.553145	+	0.833085i	$0.686572\pi$
$158$	1.76693e7	0.356385
$159$	−3.56382e7	−0.703114
$160$	4.09600e6	0.0790569
$161$	9.69895e6	0.183161
$162$	−2.41473e7	−0.446237
$163$	−4.01558e7	−0.726259	−0.363130	−	0.931739i	$-0.618292\pi$
$163$	−4.01558e7	−0.726259	−0.363130	+	0.931739i	$0.618292\pi$
$164$	1.53544e7	0.271819
$165$	−1.55014e7	−0.268644
$166$	4.07677e7	0.691732
$167$	−8.32422e7	−1.38304	−0.691522	−	0.722355i	$-0.743060\pi$
$167$	−8.32422e7	−1.38304	−0.691522	+	0.722355i	$0.743060\pi$
$168$	−1.56595e7	−0.254798
$169$	6.43236e7	1.02510
$170$	−6.59784e6	−0.102998
$171$	−6.10119e7	−0.933100
$172$	−1.09492e7	−0.164071
$173$	5.26679e7	0.773365	0.386683	−	0.922213i	$-0.373621\pi$
$173$	5.26679e7	0.773365	0.386683	+	0.922213i	$0.373621\pi$
$174$	−3.65495e7	−0.525968
$175$	6.75768e6	0.0953157
$176$	7.18275e6	0.0993108
$177$	1.78600e8	2.42089
$178$	5.78484e7	0.768814
$179$	3.06028e7	0.398819	0.199410	−	0.979916i	$-0.436098\pi$
$179$	3.06028e7	0.398819	0.199410	+	0.979916i	$0.436098\pi$
$180$	2.25124e7	0.287719
$181$	−6.36501e6	−0.0797855	−0.0398927	−	0.999204i	$-0.512702\pi$
$181$	−6.36501e6	−0.0797855	−0.0398927	+	0.999204i	$0.512702\pi$
$182$	−3.90025e7	−0.479560
$183$	2.38714e8	2.87938
$184$	1.14820e7	0.135880
$185$	6.22195e7	0.722480
$186$	−1.68541e7	−0.192048
$187$	−1.15700e7	−0.129386
$188$	−3.52811e6	−0.0387248
$189$	−1.91784e7	−0.206631
$190$	−2.16812e7	−0.229322
$191$	−1.95013e7	−0.202510	−0.101255	−	0.994861i	$-0.532286\pi$
$191$	−1.95013e7	−0.202510	−0.101255	+	0.994861i	$0.532286\pi$
$192$	−1.85383e7	−0.189024
$193$	−8.50992e7	−0.852069	−0.426034	−	0.904707i	$-0.640090\pi$
$193$	−8.50992e7	−0.852069	−0.426034	+	0.904707i	$0.640090\pi$
$194$	−7.89755e7	−0.776580
$195$	9.96474e7	0.962376
$196$	−4.07356e7	−0.386437
$197$	3.67197e7	0.342190	0.171095	−	0.985255i	$-0.445270\pi$
$197$	3.67197e7	0.342190	0.171095	+	0.985255i	$0.445270\pi$
$198$	3.94778e7	0.361431
$199$	−6.60479e7	−0.594118	−0.297059	−	0.954859i	$-0.596006\pi$
$199$	−6.60479e7	−0.594118	−0.297059	+	0.954859i	$0.596006\pi$
$200$	8.00000e6	0.0707107
$201$	−6.51696e7	−0.566055
$202$	3.29247e7	0.281055
$203$	2.79408e7	0.234424
$204$	2.98616e7	0.246267
$205$	2.99891e7	0.243123
$206$	−1.61046e8	−1.28356
$207$	6.31073e7	0.494519
$208$	−4.61727e7	−0.355765
$209$	−3.80201e7	−0.288072
$210$	−3.05850e7	−0.227898
$211$	−9.71512e7	−0.711966	−0.355983	−	0.934492i	$-0.615854\pi$
$211$	−9.71512e7	−0.711966	−0.355983	+	0.934492i	$0.615854\pi$
$212$	3.22526e7	0.232482
$213$	3.34361e8	2.37076
$214$	1.02567e8	0.715418
$215$	−2.13852e7	−0.146750
$216$	−2.27041e7	−0.153291
$217$	1.28844e7	0.0855960
$218$	−1.41010e8	−0.921831
$219$	7.04196e7	0.453043
$220$	1.40288e7	0.0888263
$221$	7.43750e7	0.463505
$222$	−2.81603e8	−1.72744
$223$	−7.08992e7	−0.428129	−0.214064	−	0.976820i	$-0.568670\pi$
$223$	−7.08992e7	−0.428129	−0.214064	+	0.976820i	$0.568670\pi$
$224$	1.41719e7	0.0842480
$225$	4.39696e7	0.257344
$226$	−9.35765e7	−0.539247
$227$	−1.35749e8	−0.770273	−0.385136	−	0.922860i	$-0.625846\pi$
$227$	−1.35749e8	−0.770273	−0.385136	+	0.922860i	$0.625846\pi$
$228$	9.81281e7	0.548304
$229$	1.72199e8	0.947557	0.473778	−	0.880644i	$-0.342890\pi$
$229$	1.72199e8	0.947557	0.473778	+	0.880644i	$0.342890\pi$
$230$	2.24258e7	0.121535
$231$	−5.36339e7	−0.286284
$232$	3.30774e7	0.173909
$233$	3.19959e8	1.65710	0.828549	−	0.559916i	$-0.189167\pi$
$233$	3.19959e8	1.65710	0.828549	+	0.559916i	$0.189167\pi$
$234$	−2.53774e8	−1.29477
$235$	−6.89084e6	−0.0346366
$236$	−1.61633e8	−0.800457
$237$	−1.56192e8	−0.762150
$238$	−2.28281e7	−0.109761
$239$	−1.42762e8	−0.676427	−0.338213	−	0.941069i	$-0.609823\pi$
$239$	−1.42762e8	−0.676427	−0.338213	+	0.941069i	$0.609823\pi$
$240$	−3.62077e7	−0.169068
$241$	−1.75572e8	−0.807970	−0.403985	−	0.914766i	$-0.632375\pi$
$241$	−1.75572e8	−0.807970	−0.403985	+	0.914766i	$0.632375\pi$
$242$	−1.31296e8	−0.595524
$243$	3.10437e8	1.38788
$244$	−2.16037e8	−0.952057
$245$	−7.95618e7	−0.345639
$246$	−1.35730e8	−0.581302
$247$	2.44404e8	1.03197
$248$	1.52530e7	0.0635001
$249$	−3.60377e8	−1.47931
$250$	1.56250e7	0.0632456
$251$	−3.58348e8	−1.43037	−0.715183	−	0.698938i	$-0.753656\pi$
$251$	−3.58348e8	−1.43037	−0.715183	+	0.698938i	$0.753656\pi$
$252$	7.78914e7	0.306611
$253$	3.93258e7	0.152671
$254$	1.31345e7	0.0502917
$255$	5.83234e7	0.220268
$256$	1.67772e7	0.0625000
$257$	−2.34808e8	−0.862872	−0.431436	−	0.902144i	$-0.641993\pi$
$257$	−2.34808e8	−0.862872	−0.431436	+	0.902144i	$0.641993\pi$
$258$	9.67883e7	0.350876
$259$	2.15275e8	0.769919
$260$	−9.01810e7	−0.318206
$261$	1.81800e8	0.632924
$262$	−3.62770e8	−1.24617
$263$	−2.15810e8	−0.731521	−0.365761	−	0.930709i	$-0.619191\pi$
$263$	−2.15810e8	−0.731521	−0.365761	+	0.930709i	$0.619191\pi$
$264$	−6.34938e7	−0.212382
$265$	6.29934e7	0.207938
$266$	−7.50153e7	−0.244379
$267$	−5.11366e8	−1.64416
$268$	5.89786e7	0.187164
$269$	−2.59268e8	−0.812111	−0.406055	−	0.913849i	$-0.633096\pi$
$269$	−2.59268e8	−0.812111	−0.406055	+	0.913849i	$0.633096\pi$
$270$	−4.43439e7	−0.137107
$271$	−3.59960e8	−1.09866	−0.549329	−	0.835606i	$-0.685116\pi$
$271$	−3.59960e8	−1.09866	−0.549329	+	0.835606i	$0.685116\pi$
$272$	−2.70248e7	−0.0814274
$273$	3.44773e8	1.02557
$274$	−4.55809e7	−0.133862
$275$	2.74000e7	0.0794486
$276$	−1.01498e8	−0.290587
$277$	4.10419e8	1.16024	0.580120	−	0.814531i	$-0.303006\pi$
$277$	4.10419e8	1.16024	0.580120	+	0.814531i	$0.303006\pi$
$278$	1.95107e8	0.544649
$279$	8.38334e7	0.231101
$280$	2.76795e7	0.0753537
$281$	1.30115e8	0.349828	0.174914	−	0.984584i	$-0.444035\pi$
$281$	1.30115e8	0.349828	0.174914	+	0.984584i	$0.444035\pi$
$282$	3.11877e7	0.0828154
$283$	−3.01836e8	−0.791624	−0.395812	−	0.918332i	$-0.629537\pi$
$283$	−3.01836e8	−0.791624	−0.395812	+	0.918332i	$0.629537\pi$
$284$	−3.02597e8	−0.783882
$285$	1.91656e8	0.490418
$286$	−1.58142e8	−0.399728
$287$	1.03760e8	0.259086
$288$	9.22109e7	0.227462
$289$	−3.66807e8	−0.893913
$290$	6.46043e7	0.155549
$291$	6.98125e8	1.66076
$292$	−6.37298e7	−0.149797
$293$	5.99592e8	1.39258	0.696289	−	0.717762i	$-0.254833\pi$
$293$	5.99592e8	1.39258	0.696289	+	0.717762i	$0.254833\pi$
$294$	3.60093e8	0.826417
$295$	−3.15690e8	−0.715951
$296$	2.54851e8	0.571171
$297$	−7.77616e7	−0.172234
$298$	1.15210e8	0.252192
$299$	−2.52797e8	−0.546919
$300$	−7.07181e7	−0.151219
$301$	−7.39912e7	−0.156386
$302$	−1.13555e8	−0.237237
$303$	−2.91046e8	−0.601053
$304$	−8.88060e7	−0.181295
$305$	−4.21946e8	−0.851546
$306$	−1.48533e8	−0.296346
$307$	1.75963e8	0.347085	0.173543	−	0.984826i	$-0.444479\pi$
$307$	1.75963e8	0.347085	0.173543	+	0.984826i	$0.444479\pi$
$308$	4.85387e7	0.0946588
$309$	1.42361e9	2.74496
$310$	2.97910e7	0.0567962
$311$	4.30044e8	0.810683	0.405341	−	0.914165i	$-0.367153\pi$
$311$	4.30044e8	0.810683	0.405341	+	0.914165i	$0.367153\pi$
$312$	4.08156e8	0.760825
$313$	4.44539e8	0.819417	0.409709	−	0.912216i	$-0.365630\pi$
$313$	4.44539e8	0.819417	0.409709	+	0.912216i	$0.365630\pi$
$314$	−4.29148e8	−0.782265
$315$	1.52132e8	0.274241
$316$	1.41354e8	0.252002
$317$	−5.12029e7	−0.0902791	−0.0451395	−	0.998981i	$-0.514373\pi$
$317$	−5.12029e7	−0.0902791	−0.0451395	+	0.998981i	$0.514373\pi$
$318$	−2.85105e8	−0.497177
$319$	1.13290e8	0.195400
$320$	3.27680e7	0.0559017
$321$	−9.06670e8	−1.52996
$322$	7.75916e7	0.129515
$323$	1.43049e8	0.236198
$324$	−1.93178e8	−0.315537
$325$	−1.76135e8	−0.284612
$326$	−3.21246e8	−0.513543
$327$	1.24649e9	1.97139
$328$	1.22835e8	0.192205
$329$	−2.38418e7	−0.0369109
$330$	−1.24011e8	−0.189960
$331$	−3.81712e8	−0.578546	−0.289273	−	0.957247i	$-0.593413\pi$
$331$	−3.81712e8	−0.578546	−0.289273	+	0.957247i	$0.593413\pi$
$332$	3.26142e8	0.489129
$333$	1.40071e9	2.07871
$334$	−6.65938e8	−0.977960
$335$	1.15193e8	0.167405
$336$	−1.25276e8	−0.180169
$337$	−1.09759e8	−0.156219	−0.0781096	−	0.996945i	$-0.524888\pi$
$337$	−1.09759e8	−0.156219	−0.0781096	+	0.996945i	$0.524888\pi$
$338$	5.14589e8	0.724857
$339$	8.27194e8	1.15321
$340$	−5.27827e7	−0.0728309
$341$	5.22415e7	0.0713470
$342$	−4.88095e8	−0.659802
$343$	−6.31454e8	−0.844913
$344$	−8.75936e7	−0.116016
$345$	−1.98238e8	−0.259909
$346$	4.21343e8	0.546852
$347$	−1.22884e9	−1.57885	−0.789426	−	0.613846i	$-0.789622\pi$
$347$	−1.22884e9	−1.57885	−0.789426	+	0.613846i	$0.789622\pi$
$348$	−2.92396e8	−0.371916
$349$	5.47418e8	0.689334	0.344667	−	0.938725i	$-0.387992\pi$
$349$	5.47418e8	0.689334	0.344667	+	0.938725i	$0.387992\pi$
$350$	5.40614e7	0.0673984
$351$	4.99873e8	0.616999
$352$	5.74620e7	0.0702233
$353$	8.05222e8	0.974325	0.487163	−	0.873311i	$-0.338032\pi$
$353$	8.05222e8	0.974325	0.487163	+	0.873311i	$0.338032\pi$
$354$	1.42880e9	1.71183
$355$	−5.91010e8	−0.701125
$356$	4.62787e8	0.543634
$357$	2.01795e8	0.234731
$358$	2.44823e8	0.282008
$359$	5.56019e8	0.634248	0.317124	−	0.948384i	$-0.397283\pi$
$359$	5.56019e8	0.634248	0.317124	+	0.948384i	$0.397283\pi$
$360$	1.80099e8	0.203448
$361$	−4.23799e8	−0.474116
$362$	−5.09200e7	−0.0564168
$363$	1.16063e9	1.27356
$364$	−3.12020e8	−0.339100
$365$	−1.24472e8	−0.133982
$366$	1.90971e9	2.03603
$367$	1.43409e8	0.151441	0.0757206	−	0.997129i	$-0.475874\pi$
$367$	1.43409e8	0.151441	0.0757206	+	0.997129i	$0.475874\pi$
$368$	9.18559e7	0.0960815
$369$	6.75128e8	0.699510
$370$	4.97756e8	0.510870
$371$	2.17953e8	0.221592
$372$	−1.34833e8	−0.135799
$373$	1.39057e9	1.38743	0.693717	−	0.720248i	$-0.255972\pi$
$373$	1.39057e9	1.38743	0.693717	+	0.720248i	$0.255972\pi$
$374$	−9.25599e7	−0.0914897
$375$	−1.38121e8	−0.135254
$376$	−2.82249e7	−0.0273826
$377$	−7.28260e8	−0.699990
$378$	−1.53427e8	−0.146110
$379$	−4.29905e8	−0.405635	−0.202817	−	0.979217i	$-0.565010\pi$
$379$	−4.29905e8	−0.405635	−0.202817	+	0.979217i	$0.565010\pi$
$380$	−1.73449e8	−0.162155
$381$	−1.16106e8	−0.107552
$382$	−1.56010e8	−0.143196
$383$	4.89082e8	0.444821	0.222411	−	0.974953i	$-0.428607\pi$
$383$	4.89082e8	0.444821	0.222411	+	0.974953i	$0.428607\pi$
$384$	−1.48307e8	−0.133660
$385$	9.48022e7	0.0846654
$386$	−6.80793e8	−0.602504
$387$	−4.81431e8	−0.422227
$388$	−6.31804e8	−0.549125
$389$	1.08252e8	0.0932422	0.0466211	−	0.998913i	$-0.485155\pi$
$389$	1.08252e8	0.0932422	0.0466211	+	0.998913i	$0.485155\pi$
$390$	7.97179e8	0.680503
$391$	−1.47962e8	−0.125179
$392$	−3.25885e8	−0.273252
$393$	3.20681e9	2.66501
$394$	2.93757e8	0.241965
$395$	2.76082e8	0.225397
$396$	3.15822e8	0.255570
$397$	6.00116e8	0.481359	0.240679	−	0.970605i	$-0.422630\pi$
$397$	6.00116e8	0.481359	0.240679	+	0.970605i	$0.422630\pi$
$398$	−5.28383e8	−0.420105
$399$	6.63118e8	0.522620
$400$	6.40000e7	0.0500000
$401$	8.35161e8	0.646793	0.323396	−	0.946264i	$-0.395175\pi$
$401$	8.35161e8	0.646793	0.323396	+	0.946264i	$0.395175\pi$
$402$	−5.21357e8	−0.400262
$403$	−3.35823e8	−0.255589
$404$	2.63397e8	0.198736
$405$	−3.77301e8	−0.282225
$406$	2.23526e8	0.165763
$407$	8.72866e8	0.641752
$408$	2.38892e8	0.174137
$409$	3.82987e8	0.276791	0.138396	−	0.990377i	$-0.455805\pi$
$409$	3.82987e8	0.276791	0.138396	+	0.990377i	$0.455805\pi$
$410$	2.39913e8	0.171914
$411$	4.02924e8	0.286271
$412$	−1.28837e9	−0.907612
$413$	−1.09226e9	−0.762961
$414$	5.04858e8	0.349678
$415$	6.36996e8	0.437490
$416$	−3.69381e8	−0.251564
$417$	−1.72470e9	−1.16477
$418$	−3.04161e8	−0.203698
$419$	1.44488e9	0.959582	0.479791	−	0.877383i	$-0.340712\pi$
$419$	1.44488e9	0.959582	0.479791	+	0.877383i	$0.340712\pi$
$420$	−2.44680e8	−0.161148
$421$	4.27289e8	0.279083	0.139542	−	0.990216i	$-0.455437\pi$
$421$	4.27289e8	0.279083	0.139542	+	0.990216i	$0.455437\pi$
$422$	−7.77210e8	−0.503436
$423$	−1.55129e8	−0.0996559
$424$	2.58021e8	0.164390
$425$	−1.03091e8	−0.0651419
$426$	2.67489e9	1.67638
$427$	−1.45991e9	−0.907460
$428$	8.20537e8	0.505877
$429$	1.39793e9	0.854843
$430$	−1.71081e8	−0.103768
$431$	−8.97055e8	−0.539695	−0.269848	−	0.962903i	$-0.586973\pi$
$431$	−8.97055e8	−0.539695	−0.269848	+	0.962903i	$0.586973\pi$
$432$	−1.81633e8	−0.108393
$433$	1.19941e9	0.710005	0.355003	−	0.934865i	$-0.384480\pi$
$433$	1.19941e9	0.710005	0.355003	+	0.934865i	$0.384480\pi$
$434$	1.03075e8	0.0605255
$435$	−5.71087e8	−0.332652
$436$	−1.12808e9	−0.651833
$437$	−4.86217e8	−0.278705
$438$	5.63357e8	0.320349
$439$	−2.75938e9	−1.55663	−0.778316	−	0.627873i	$-0.783926\pi$
$439$	−2.75938e9	−1.55663	−0.778316	+	0.627873i	$0.783926\pi$
$440$	1.12230e8	0.0628097
$441$	−1.79113e9	−0.994470
$442$	5.95000e8	0.327747
$443$	4.47662e8	0.244646	0.122323	−	0.992490i	$-0.460966\pi$
$443$	4.47662e8	0.244646	0.122323	+	0.992490i	$0.460966\pi$
$444$	−2.25283e9	−1.22148
$445$	9.03882e8	0.486241
$446$	−5.67193e8	−0.302733
$447$	−1.01843e9	−0.539328
$448$	1.13375e8	0.0595723
$449$	3.76809e8	0.196453	0.0982267	−	0.995164i	$-0.468683\pi$
$449$	3.76809e8	0.196453	0.0982267	+	0.995164i	$0.468683\pi$
$450$	3.51757e8	0.181969
$451$	4.20712e8	0.215957
$452$	−7.48612e8	−0.381305
$453$	1.00380e9	0.507346
$454$	−1.08599e9	−0.544665
$455$	−6.09414e8	−0.303300
$456$	7.85025e8	0.387709
$457$	3.96799e9	1.94475	0.972375	−	0.233422i	$-0.0749924\pi$
$457$	3.96799e9	1.94475	0.972375	+	0.233422i	$0.0749924\pi$
$458$	1.37759e9	0.670024
$459$	2.92574e8	0.141219
$460$	1.79406e8	0.0859379
$461$	3.76127e8	0.178806	0.0894029	−	0.995996i	$-0.471504\pi$
$461$	3.76127e8	0.178806	0.0894029	+	0.995996i	$0.471504\pi$
$462$	−4.29071e8	−0.202433
$463$	−3.33475e9	−1.56146	−0.780728	−	0.624871i	$-0.785152\pi$
$463$	−3.33475e9	−1.56146	−0.780728	+	0.624871i	$0.785152\pi$
$464$	2.64619e8	0.122973
$465$	−2.63345e8	−0.121462
$466$	2.55967e9	1.17175
$467$	1.86992e9	0.849599	0.424800	−	0.905287i	$-0.360345\pi$
$467$	1.86992e9	0.849599	0.424800	+	0.905287i	$0.360345\pi$
$468$	−2.03019e9	−0.915539
$469$	3.98558e8	0.178397
$470$	−5.51267e7	−0.0244917
$471$	3.79357e9	1.67292
$472$	−1.29306e9	−0.566009
$473$	−3.00008e8	−0.130352
$474$	−1.24954e9	−0.538921
$475$	−3.38768e8	−0.145036
$476$	−1.82625e8	−0.0776131
$477$	1.41813e9	0.598278
$478$	−1.14210e9	−0.478306
$479$	−2.48781e9	−1.03429	−0.517146	−	0.855897i	$-0.673006\pi$
$479$	−2.48781e9	−1.03429	−0.517146	+	0.855897i	$0.673006\pi$
$480$	−2.89661e8	−0.119549
$481$	−5.61102e9	−2.29897
$482$	−1.40457e9	−0.571321
$483$	−6.85892e8	−0.276975
$484$	−1.05037e9	−0.421099
$485$	−1.23399e9	−0.491152
$486$	2.48349e9	0.981377
$487$	−1.30361e9	−0.511442	−0.255721	−	0.966751i	$-0.582313\pi$
$487$	−1.30361e9	−0.511442	−0.255721	+	0.966751i	$0.582313\pi$
$488$	−1.72829e9	−0.673206
$489$	2.83974e9	1.09824
$490$	−6.36494e8	−0.244404
$491$	−3.43268e9	−1.30872	−0.654362	−	0.756181i	$-0.727063\pi$
$491$	−3.43268e9	−1.30872	−0.654362	+	0.756181i	$0.727063\pi$
$492$	−1.08584e9	−0.411042
$493$	−4.26249e8	−0.160213
$494$	1.95523e9	0.729715
$495$	6.16841e8	0.228589
$496$	1.22024e8	0.0449013
$497$	−2.04485e9	−0.747163
$498$	−2.88302e9	−1.04603
$499$	−4.00306e8	−0.144225	−0.0721124	−	0.997397i	$-0.522974\pi$
$499$	−4.00306e8	−0.144225	−0.0721124	+	0.997397i	$0.522974\pi$
$500$	1.25000e8	0.0447214
$501$	5.88673e9	2.09143
$502$	−2.86678e9	−1.01142
$503$	−3.73792e9	−1.30961	−0.654806	−	0.755797i	$-0.727250\pi$
$503$	−3.73792e9	−1.30961	−0.654806	+	0.755797i	$0.727250\pi$
$504$	6.23131e8	0.216807
$505$	5.14448e8	0.177755
$506$	3.14607e8	0.107955
$507$	−4.54885e9	−1.55015
$508$	1.05076e8	0.0355616
$509$	2.25286e9	0.757220	0.378610	−	0.925556i	$-0.376402\pi$
$509$	2.25286e9	0.757220	0.378610	+	0.925556i	$0.376402\pi$
$510$	4.66587e8	0.155753
$511$	−4.30666e8	−0.142780
$512$	1.34218e8	0.0441942
$513$	9.61428e8	0.314417
$514$	−1.87846e9	−0.610143
$515$	−2.51635e9	−0.811793
$516$	7.74307e8	0.248107
$517$	−9.66703e7	−0.0307664
$518$	1.72220e9	0.544415
$519$	−3.72457e9	−1.16947
$520$	−7.21448e8	−0.225006
$521$	5.58554e9	1.73035	0.865174	−	0.501472i	$-0.167208\pi$
$521$	5.58554e9	1.73035	0.865174	+	0.501472i	$0.167208\pi$
$522$	1.45440e9	0.447545
$523$	−3.26750e9	−0.998756	−0.499378	−	0.866384i	$-0.666438\pi$
$523$	−3.26750e9	−0.998756	−0.499378	+	0.866384i	$0.666438\pi$
$524$	−2.90216e9	−0.881175
$525$	−4.77890e8	−0.144135
$526$	−1.72648e9	−0.517263
$527$	−1.96556e8	−0.0584992
$528$	−5.07951e8	−0.150177
$529$	−2.90191e9	−0.852294
$530$	5.03947e8	0.147035
$531$	−7.10693e9	−2.05993
$532$	−6.00123e8	−0.172802
$533$	−2.70445e9	−0.773631
$534$	−4.09093e9	−1.16259
$535$	1.60261e9	0.452470
$536$	4.71829e8	0.132345
$537$	−2.16417e9	−0.603090
$538$	−2.07414e9	−0.574249
$539$	−1.11616e9	−0.307019
$540$	−3.54752e8	−0.0969496
$541$	4.58141e9	1.24397	0.621983	−	0.783031i	$-0.286327\pi$
$541$	4.58141e9	1.24397	0.621983	+	0.783031i	$0.286327\pi$
$542$	−2.87968e9	−0.776868
$543$	4.50121e8	0.120651
$544$	−2.16198e8	−0.0575779
$545$	−2.20328e9	−0.583017
$546$	2.75818e9	0.725186
$547$	−1.61168e9	−0.421039	−0.210519	−	0.977590i	$-0.567515\pi$
$547$	−1.61168e9	−0.421039	−0.210519	+	0.977590i	$0.567515\pi$
$548$	−3.64647e8	−0.0946544
$549$	−9.49903e9	−2.45006
$550$	2.19200e8	0.0561787
$551$	−1.40070e9	−0.356708
$552$	−8.11985e8	−0.205476
$553$	9.55226e8	0.240197
$554$	3.28335e9	0.820414
$555$	−4.40005e9	−1.09253
$556$	1.56086e9	0.385125
$557$	7.32488e9	1.79600	0.898002	−	0.439992i	$-0.145019\pi$
$557$	7.32488e9	1.79600	0.898002	+	0.439992i	$0.145019\pi$
$558$	6.70667e8	0.163413
$559$	1.92854e9	0.466967
$560$	2.21436e8	0.0532831
$561$	8.18207e8	0.195656
$562$	1.04092e9	0.247366
$563$	−1.34971e9	−0.318758	−0.159379	−	0.987217i	$-0.550949\pi$
$563$	−1.34971e9	−0.318758	−0.159379	+	0.987217i	$0.550949\pi$
$564$	2.49501e8	0.0585593
$565$	−1.46213e9	−0.341049
$566$	−2.41469e9	−0.559763
$567$	−1.30544e9	−0.300757
$568$	−2.42078e9	−0.554288
$569$	−1.01242e9	−0.230392	−0.115196	−	0.993343i	$-0.536750\pi$
$569$	−1.01242e9	−0.230392	−0.115196	+	0.993343i	$0.536750\pi$
$570$	1.53325e9	0.346778
$571$	3.67593e9	0.826306	0.413153	−	0.910662i	$-0.364427\pi$
$571$	3.67593e9	0.826306	0.413153	+	0.910662i	$0.364427\pi$
$572$	−1.26513e9	−0.282651
$573$	1.37909e9	0.306233
$574$	8.30083e8	0.183202
$575$	3.50403e8	0.0768652
$576$	7.37687e8	0.160840
$577$	7.88739e9	1.70930	0.854649	−	0.519206i	$-0.173772\pi$
$577$	7.88739e9	1.70930	0.854649	+	0.519206i	$0.173772\pi$
$578$	−2.93446e9	−0.632092
$579$	6.01805e9	1.28849
$580$	5.16834e8	0.109990
$581$	2.20396e9	0.466216
$582$	5.58500e9	1.17434
$583$	8.83722e8	0.184704
$584$	−5.09839e8	−0.105922
$585$	−3.96522e9	−0.818883
$586$	4.79674e9	0.984701
$587$	2.56030e9	0.522464	0.261232	−	0.965276i	$-0.415871\pi$
$587$	2.56030e9	0.522464	0.261232	+	0.965276i	$0.415871\pi$
$588$	2.88075e9	0.584365
$589$	−6.45904e8	−0.130246
$590$	−2.52552e9	−0.506254
$591$	−2.59675e9	−0.517456
$592$	2.03881e9	0.403879
$593$	3.72506e9	0.733571	0.366785	−	0.930306i	$-0.380458\pi$
$593$	3.72506e9	0.733571	0.366785	+	0.930306i	$0.380458\pi$
$594$	−6.22093e8	−0.121787
$595$	−3.56689e8	−0.0694193
$596$	9.21677e8	0.178327
$597$	4.67078e9	0.898420
$598$	−2.02238e9	−0.386730
$599$	−1.02698e9	−0.195239	−0.0976196	−	0.995224i	$-0.531123\pi$
$599$	−1.02698e9	−0.195239	−0.0976196	+	0.995224i	$0.531123\pi$
$600$	−5.65745e8	−0.106928
$601$	−5.27085e9	−0.990422	−0.495211	−	0.868773i	$-0.664909\pi$
$601$	−5.27085e9	−0.990422	−0.495211	+	0.868773i	$0.664909\pi$
$602$	−5.91929e8	−0.110581
$603$	2.59326e9	0.481655
$604$	−9.08441e8	−0.167752
$605$	−2.05151e9	−0.376642
$606$	−2.32837e9	−0.425009
$607$	7.39071e9	1.34130	0.670650	−	0.741774i	$-0.266015\pi$
$607$	7.39071e9	1.34130	0.670650	+	0.741774i	$0.266015\pi$
$608$	−7.10448e8	−0.128195
$609$	−1.97592e9	−0.354494
$610$	−3.37557e9	−0.602134
$611$	6.21423e8	0.110216
$612$	−1.18827e9	−0.209548
$613$	−4.58842e9	−0.804546	−0.402273	−	0.915520i	$-0.631780\pi$
$613$	−4.58842e9	−0.804546	−0.402273	+	0.915520i	$0.631780\pi$
$614$	1.40770e9	0.245426
$615$	−2.12077e9	−0.367648
$616$	3.88310e8	0.0669339
$617$	−6.23031e9	−1.06785	−0.533926	−	0.845531i	$-0.679284\pi$
$617$	−6.23031e9	−1.06785	−0.533926	+	0.845531i	$0.679284\pi$
$618$	1.13889e10	1.94098
$619$	9.18726e9	1.55693	0.778465	−	0.627689i	$-0.215999\pi$
$619$	9.18726e9	1.55693	0.778465	+	0.627689i	$0.215999\pi$
$620$	2.38328e8	0.0401610
$621$	−9.94447e8	−0.166633
$622$	3.44035e9	0.573239
$623$	3.12737e9	0.518168
$624$	3.26525e9	0.537985
$625$	2.44141e8	0.0400000
$626$	3.55631e9	0.579415
$627$	2.68871e9	0.435620
$628$	−3.43319e9	−0.553145
$629$	−3.28412e9	−0.526188
$630$	1.21705e9	0.193918
$631$	3.21240e9	0.509011	0.254506	−	0.967071i	$-0.418087\pi$
$631$	3.21240e9	0.509011	0.254506	+	0.967071i	$0.418087\pi$
$632$	1.13083e9	0.178192
$633$	6.87035e9	1.07663
$634$	−4.09623e8	−0.0638369
$635$	2.05227e8	0.0318073
$636$	−2.28084e9	−0.351557
$637$	7.17496e9	1.09985
$638$	9.06321e8	0.138169
$639$	−1.33051e10	−2.01727
$640$	2.62144e8	0.0395285
$641$	−9.95731e9	−1.49327	−0.746636	−	0.665233i	$-0.768332\pi$
$641$	−9.95731e9	−1.49327	−0.746636	+	0.665233i	$0.768332\pi$
$642$	−7.25336e9	−1.08185
$643$	3.85110e9	0.571276	0.285638	−	0.958338i	$-0.407795\pi$
$643$	3.85110e9	0.571276	0.285638	+	0.958338i	$0.407795\pi$
$644$	6.20733e8	0.0915807
$645$	1.51232e9	0.221914
$646$	1.14439e9	0.167017
$647$	4.02520e9	0.584281	0.292141	−	0.956375i	$-0.405632\pi$
$647$	4.02520e9	0.584281	0.292141	+	0.956375i	$0.405632\pi$
$648$	−1.54543e9	−0.223119
$649$	−4.42875e9	−0.635952
$650$	−1.40908e9	−0.201251
$651$	−9.11157e8	−0.129437
$652$	−2.56997e9	−0.363130
$653$	5.00321e9	0.703157	0.351579	−	0.936158i	$-0.385645\pi$
$653$	5.00321e9	0.703157	0.351579	+	0.936158i	$0.385645\pi$
$654$	9.97194e9	1.39398
$655$	−5.66829e9	−0.788147
$656$	9.82684e8	0.135910
$657$	−2.80217e9	−0.385493
$658$	−1.90735e8	−0.0260999
$659$	−4.28498e9	−0.583244	−0.291622	−	0.956534i	$-0.594195\pi$
$659$	−4.28498e9	−0.583244	−0.291622	+	0.956534i	$0.594195\pi$
$660$	−9.92091e8	−0.134322
$661$	−6.82671e9	−0.919404	−0.459702	−	0.888073i	$-0.652044\pi$
$661$	−6.82671e9	−0.919404	−0.459702	+	0.888073i	$0.652044\pi$
$662$	−3.05370e9	−0.409094
$663$	−5.25966e9	−0.700907
$664$	2.60913e9	0.345866
$665$	−1.17211e9	−0.154559
$666$	1.12057e10	1.46987
$667$	1.44880e9	0.189046
$668$	−5.32750e9	−0.691522
$669$	5.01386e9	0.647412
$670$	9.21540e8	0.118373
$671$	−5.91941e9	−0.756396
$672$	−1.00221e9	−0.127399
$673$	−1.20915e10	−1.52907	−0.764534	−	0.644584i	$-0.777031\pi$
$673$	−1.20915e10	−1.52907	−0.764534	+	0.644584i	$0.777031\pi$
$674$	−8.78069e8	−0.110464
$675$	−6.92874e8	−0.0867144
$676$	4.11671e9	0.512551
$677$	−2.82248e9	−0.349599	−0.174800	−	0.984604i	$-0.555928\pi$
$677$	−2.82248e9	−0.349599	−0.174800	+	0.984604i	$0.555928\pi$
$678$	6.61756e9	0.815443
$679$	−4.26953e9	−0.523402
$680$	−4.22262e8	−0.0514992
$681$	9.59988e9	1.16480
$682$	4.17932e8	0.0504499
$683$	1.44331e9	0.173335	0.0866676	−	0.996237i	$-0.472378\pi$
$683$	1.44331e9	0.173335	0.0866676	+	0.996237i	$0.472378\pi$
$684$	−3.90476e9	−0.466550
$685$	−7.12201e8	−0.0846615
$686$	−5.05163e9	−0.597444
$687$	−1.21776e10	−1.43289
$688$	−7.00749e8	−0.0820357
$689$	−5.68081e9	−0.661672
$690$	−1.58591e9	−0.183783
$691$	3.51638e9	0.405436	0.202718	−	0.979237i	$-0.435022\pi$
$691$	3.51638e9	0.405436	0.202718	+	0.979237i	$0.435022\pi$
$692$	3.37075e9	0.386683
$693$	2.13423e9	0.243598
$694$	−9.83070e9	−1.11642
$695$	3.04855e9	0.344467
$696$	−2.33917e9	−0.262984
$697$	−1.58291e9	−0.177068
$698$	4.37934e9	0.487433
$699$	−2.26269e10	−2.50585
$700$	4.32491e8	0.0476578
$701$	−2.85377e9	−0.312900	−0.156450	−	0.987686i	$-0.550005\pi$
$701$	−2.85377e9	−0.312900	−0.156450	+	0.987686i	$0.550005\pi$
$702$	3.99898e9	0.436284
$703$	−1.07919e10	−1.17154
$704$	4.59696e8	0.0496554
$705$	4.87307e8	0.0523770
$706$	6.44177e9	0.688952
$707$	1.77995e9	0.189427
$708$	1.14304e10	1.21044
$709$	−1.77555e10	−1.87099	−0.935495	−	0.353339i	$-0.885046\pi$
$709$	−1.77555e10	−1.87099	−0.935495	+	0.353339i	$0.885046\pi$
$710$	−4.72808e9	−0.495771
$711$	6.21528e9	0.648511
$712$	3.70230e9	0.384407
$713$	6.68086e8	0.0690270
$714$	1.61436e9	0.165980
$715$	−2.47096e9	−0.252810
$716$	1.95858e9	0.199410
$717$	1.00959e10	1.02289
$718$	4.44815e9	0.448481
$719$	4.47382e9	0.448877	0.224438	−	0.974488i	$-0.427945\pi$
$719$	4.47382e9	0.448877	0.224438	+	0.974488i	$0.427945\pi$
$720$	1.44079e9	0.143859
$721$	−8.70638e9	−0.865096
$722$	−3.39039e9	−0.335251
$723$	1.24161e10	1.22180
$724$	−4.07360e8	−0.0398927
$725$	1.00944e9	0.0983781
$726$	9.28504e9	0.900545
$727$	4.83823e9	0.466999	0.233499	−	0.972357i	$-0.424982\pi$
$727$	4.83823e9	0.466999	0.233499	+	0.972357i	$0.424982\pi$
$728$	−2.49616e9	−0.239780
$729$	−1.53522e10	−1.46766
$730$	−9.95778e8	−0.0947399
$731$	1.12877e9	0.106879
$732$	1.52777e10	1.43969
$733$	−1.20497e10	−1.13009	−0.565043	−	0.825061i	$-0.691140\pi$
$733$	−1.20497e10	−1.13009	−0.565043	+	0.825061i	$0.691140\pi$
$734$	1.14727e9	0.107085
$735$	5.62646e9	0.522672
$736$	7.34847e8	0.0679399
$737$	1.61601e9	0.148699
$738$	5.40102e9	0.494628
$739$	5.43533e9	0.495417	0.247708	−	0.968835i	$-0.420323\pi$
$739$	5.43533e9	0.495417	0.247708	+	0.968835i	$0.420323\pi$
$740$	3.98205e9	0.361240
$741$	−1.72838e10	−1.56054
$742$	1.74362e9	0.156689
$743$	1.52597e9	0.136485	0.0682424	−	0.997669i	$-0.478261\pi$
$743$	1.52597e9	0.136485	0.0682424	+	0.997669i	$0.478261\pi$
$744$	−1.07866e9	−0.0960241
$745$	1.80015e9	0.159500
$746$	1.11246e10	0.981064
$747$	1.43403e10	1.25874
$748$	−7.40479e8	−0.0646930
$749$	5.54493e9	0.482180
$750$	−1.10497e9	−0.0956393
$751$	8.61502e9	0.742193	0.371096	−	0.928594i	$-0.378982\pi$
$751$	8.61502e9	0.742193	0.371096	+	0.928594i	$0.378982\pi$
$752$	−2.25799e8	−0.0193624
$753$	2.53417e10	2.16298
$754$	−5.82608e9	−0.494968
$755$	−1.77430e9	−0.150042
$756$	−1.22742e9	−0.103316
$757$	−8.10516e9	−0.679088	−0.339544	−	0.940590i	$-0.610273\pi$
$757$	−8.10516e9	−0.679088	−0.339544	+	0.940590i	$0.610273\pi$
$758$	−3.43924e9	−0.286827
$759$	−2.78105e9	−0.230867
$760$	−1.38759e9	−0.114661
$761$	4.68316e9	0.385206	0.192603	−	0.981277i	$-0.438307\pi$
$761$	4.68316e9	0.385206	0.192603	+	0.981277i	$0.438307\pi$
$762$	−9.28849e8	−0.0760506
$763$	−7.62319e9	−0.621299
$764$	−1.24808e9	−0.101255
$765$	−2.32083e9	−0.187426
$766$	3.91265e9	0.314536
$767$	2.84692e10	2.27820
$768$	−1.18645e9	−0.0945119
$769$	−2.20122e10	−1.74551	−0.872754	−	0.488160i	$-0.837668\pi$
$769$	−2.20122e10	−1.74551	−0.872754	+	0.488160i	$0.837668\pi$
$770$	7.58418e8	0.0598675
$771$	1.66052e10	1.30483
$772$	−5.44635e9	−0.426034
$773$	6.00413e8	0.0467544	0.0233772	−	0.999727i	$-0.492558\pi$
$773$	6.00413e8	0.0467544	0.0233772	+	0.999727i	$0.492558\pi$
$774$	−3.85145e9	−0.298560
$775$	4.65484e8	0.0359211
$776$	−5.05443e9	−0.388290
$777$	−1.52239e10	−1.16426
$778$	8.66017e8	0.0659322
$779$	−5.20159e9	−0.394235
$780$	6.37743e9	0.481188
$781$	−8.29117e9	−0.622784
$782$	−1.18369e9	−0.0885147
$783$	−2.86481e9	−0.213270
$784$	−2.60708e9	−0.193218
$785$	−6.70544e9	−0.494748
$786$	2.56544e10	1.88445
$787$	−2.25369e10	−1.64809	−0.824047	−	0.566521i	$-0.808289\pi$
$787$	−2.25369e10	−1.64809	−0.824047	+	0.566521i	$0.808289\pi$
$788$	2.35006e9	0.171095
$789$	1.52617e10	1.10620
$790$	2.20866e9	0.159380
$791$	−5.05888e9	−0.363443
$792$	2.52658e9	0.180715
$793$	3.80516e10	2.70967
$794$	4.80093e9	0.340372
$795$	−4.45477e9	−0.314442
$796$	−4.22706e9	−0.297059
$797$	−1.52054e10	−1.06388	−0.531940	−	0.846782i	$-0.678537\pi$
$797$	−1.52054e10	−1.06388	−0.531940	+	0.846782i	$0.678537\pi$
$798$	5.30494e9	0.369548
$799$	3.63717e8	0.0252261
$800$	5.12000e8	0.0353553
$801$	2.03486e10	1.39901
$802$	6.68129e9	0.457352
$803$	−1.74620e9	−0.119012
$804$	−4.17085e9	−0.283028
$805$	1.21237e9	0.0819123
$806$	−2.68658e9	−0.180729
$807$	1.83349e10	1.22807
$808$	2.10718e9	0.140528
$809$	2.16812e10	1.43967	0.719835	−	0.694145i	$-0.244217\pi$
$809$	2.16812e10	1.43967	0.719835	+	0.694145i	$0.244217\pi$
$810$	−3.01841e9	−0.199563
$811$	1.94434e10	1.27997	0.639985	−	0.768388i	$-0.278941\pi$
$811$	1.94434e10	1.27997	0.639985	+	0.768388i	$0.278941\pi$
$812$	1.78821e9	0.117212
$813$	2.54557e10	1.66138
$814$	6.98293e9	0.453787
$815$	−5.01947e9	−0.324793
$816$	1.91114e9	0.123134
$817$	3.70924e9	0.237962
$818$	3.06389e9	0.195721
$819$	−1.37194e10	−0.872652
$820$	1.91930e9	0.121561
$821$	1.76623e10	1.11390	0.556949	−	0.830547i	$-0.311972\pi$
$821$	1.76623e10	1.11390	0.556949	+	0.830547i	$0.311972\pi$
$822$	3.22339e9	0.202424
$823$	−7.00998e9	−0.438346	−0.219173	−	0.975686i	$-0.570336\pi$
$823$	−7.00998e9	−0.438346	−0.219173	+	0.975686i	$0.570336\pi$
$824$	−1.03070e10	−0.641778
$825$	−1.93768e9	−0.120141
$826$	−8.73811e9	−0.539495
$827$	9.10217e9	0.559597	0.279799	−	0.960059i	$-0.409732\pi$
$827$	9.10217e9	0.559597	0.279799	+	0.960059i	$0.409732\pi$
$828$	4.03886e9	0.247260
$829$	−1.38400e10	−0.843713	−0.421857	−	0.906663i	$-0.638621\pi$
$829$	−1.38400e10	−0.843713	−0.421857	+	0.906663i	$0.638621\pi$
$830$	5.09596e9	0.309352
$831$	−2.90240e10	−1.75450
$832$	−2.95505e9	−0.177883
$833$	4.19949e9	0.251732
$834$	−1.37976e10	−0.823613
$835$	−1.04053e10	−0.618516
$836$	−2.43329e9	−0.144036
$837$	−1.32105e9	−0.0778718
$838$	1.15590e10	0.678527
$839$	2.54394e7	0.00148710	0.000743549	−	1.00000i	$-0.499763\pi$
$839$	2.54394e7	0.00148710	0.000743549		1.00000i	$0.499763\pi$
$840$	−1.95744e9	−0.113949
$841$	−1.30762e10	−0.758044
$842$	3.41831e9	0.197342
$843$	−9.20146e9	−0.529006
$844$	−6.21768e9	−0.355983
$845$	8.04045e9	0.458440
$846$	−1.24104e9	−0.0704674
$847$	−7.09807e9	−0.401373
$848$	2.06417e9	0.116241
$849$	2.13453e10	1.19709
$850$	−8.24730e8	−0.0460623
$851$	1.11626e10	0.620884
$852$	2.13991e10	1.18538
$853$	3.44920e10	1.90282	0.951409	−	0.307931i	$-0.0996366\pi$
$853$	3.44920e10	1.90282	0.951409	+	0.307931i	$0.0996366\pi$
$854$	−1.16792e10	−0.641671
$855$	−7.62649e9	−0.417295
$856$	6.56430e9	0.357709
$857$	1.76082e10	0.955614	0.477807	−	0.878465i	$-0.341432\pi$
$857$	1.76082e10	0.955614	0.477807	+	0.878465i	$0.341432\pi$
$858$	1.11835e10	0.604465
$859$	2.52527e10	1.35935	0.679677	−	0.733512i	$-0.262120\pi$
$859$	2.52527e10	1.35935	0.679677	+	0.733512i	$0.262120\pi$
$860$	−1.36865e9	−0.0733749
$861$	−7.33774e9	−0.391788
$862$	−7.17644e9	−0.381622
$863$	1.26460e10	0.669755	0.334877	−	0.942262i	$-0.391305\pi$
$863$	1.26460e10	0.669755	0.334877	+	0.942262i	$0.391305\pi$
$864$	−1.45306e9	−0.0766454
$865$	6.58349e9	0.345859
$866$	9.59532e9	0.502050
$867$	2.59399e10	1.35177
$868$	8.24599e8	0.0427980
$869$	3.87311e9	0.200212
$870$	−4.56869e9	−0.235220
$871$	−1.03882e10	−0.532692
$872$	−9.02462e9	−0.460915
$873$	−2.77801e10	−1.41314
$874$	−3.88973e9	−0.197074
$875$	8.44710e8	0.0426265
$876$	4.50685e9	0.226521
$877$	−7.89544e9	−0.395255	−0.197628	−	0.980277i	$-0.563324\pi$
$877$	−7.89544e9	−0.395255	−0.197628	+	0.980277i	$0.563324\pi$
$878$	−2.20750e10	−1.10070
$879$	−4.24020e10	−2.10584
$880$	8.97844e8	0.0444131
$881$	−2.17979e10	−1.07398	−0.536992	−	0.843587i	$-0.680440\pi$
$881$	−2.17979e10	−1.07398	−0.536992	+	0.843587i	$0.680440\pi$
$882$	−1.43290e10	−0.703196
$883$	1.85783e10	0.908119	0.454060	−	0.890971i	$-0.349975\pi$
$883$	1.85783e10	0.908119	0.454060	+	0.890971i	$0.349975\pi$
$884$	4.76000e9	0.231752
$885$	2.23250e10	1.08265
$886$	3.58130e9	0.172991
$887$	−2.73097e10	−1.31397	−0.656983	−	0.753905i	$-0.728168\pi$
$887$	−2.73097e10	−1.31397	−0.656983	+	0.753905i	$0.728168\pi$
$888$	−1.80226e10	−0.863718
$889$	7.10071e8	0.0338958
$890$	7.23105e9	0.343824
$891$	−5.29309e9	−0.250690
$892$	−4.53755e9	−0.214064
$893$	1.19521e9	0.0561649
$894$	−8.14741e9	−0.381363
$895$	3.82535e9	0.178357
$896$	9.07000e8	0.0421240
$897$	1.78773e10	0.827046
$898$	3.01447e9	0.138914
$899$	1.92463e9	0.0883461
$900$	2.81405e9	0.128672
$901$	−3.32496e9	−0.151443
$902$	3.36569e9	0.152704
$903$	5.23252e9	0.236485
$904$	−5.98890e9	−0.269623
$905$	−7.95626e8	−0.0356811
$906$	8.03041e9	0.358748
$907$	2.70560e10	1.20403	0.602016	−	0.798484i	$-0.294364\pi$
$907$	2.70560e10	1.20403	0.602016	+	0.798484i	$0.294364\pi$
$908$	−8.68791e9	−0.385136
$909$	1.15815e10	0.511434
$910$	−4.87532e9	−0.214466
$911$	4.44829e8	0.0194930	0.00974650	−	0.999953i	$-0.496898\pi$
$911$	4.44829e8	0.0194930	0.00974650	+	0.999953i	$0.496898\pi$
$912$	6.28020e9	0.274152
$913$	8.93629e9	0.388606
$914$	3.17439e10	1.37515
$915$	2.98393e10	1.28770
$916$	1.10207e10	0.473778
$917$	−1.96119e10	−0.839898
$918$	2.34059e9	0.0998566
$919$	−2.72119e10	−1.15652	−0.578261	−	0.815852i	$-0.696269\pi$
$919$	−2.72119e10	−1.15652	−0.578261	+	0.815852i	$0.696269\pi$
$920$	1.43525e9	0.0607673
$921$	−1.24437e10	−0.524858
$922$	3.00902e9	0.126435
$923$	5.32979e10	2.23102
$924$	−3.43257e9	−0.143142
$925$	7.77744e9	0.323103
$926$	−2.66780e10	−1.10412
$927$	−5.66490e10	−2.33568
$928$	2.11695e9	0.0869547
$929$	−1.73348e10	−0.709357	−0.354678	−	0.934988i	$-0.615410\pi$
$929$	−1.73348e10	−0.709357	−0.354678	+	0.934988i	$0.615410\pi$
$930$	−2.10676e9	−0.0858866
$931$	1.37999e10	0.560471
$932$	2.04774e10	0.828549
$933$	−3.04119e10	−1.22591
$934$	1.49594e10	0.600757
$935$	−1.44625e9	−0.0578631
$936$	−1.62415e10	−0.647384
$937$	3.01989e9	0.119923	0.0599616	−	0.998201i	$-0.480902\pi$
$937$	3.01989e9	0.119923	0.0599616	+	0.998201i	$0.480902\pi$
$938$	3.18847e9	0.126146
$939$	−3.14370e10	−1.23911
$940$	−4.41014e8	−0.0173183
$941$	−1.98310e10	−0.775857	−0.387929	−	0.921689i	$-0.626809\pi$
$941$	−1.98310e10	−0.775857	−0.387929	+	0.921689i	$0.626809\pi$
$942$	3.03486e10	1.18293
$943$	5.38023e9	0.208934
$944$	−1.03445e10	−0.400229
$945$	−2.39730e9	−0.0924082
$946$	−2.40007e9	−0.0921731
$947$	−4.79886e10	−1.83617	−0.918085	−	0.396383i	$-0.870265\pi$
$947$	−4.79886e10	−1.83617	−0.918085	+	0.396383i	$0.870265\pi$
$948$	−9.99630e9	−0.381075
$949$	1.12250e10	0.426340
$950$	−2.71015e9	−0.102556
$951$	3.62097e9	0.136519
$952$	−1.46100e9	−0.0548807
$953$	3.35294e10	1.25488	0.627439	−	0.778666i	$-0.284103\pi$
$953$	3.35294e10	1.25488	0.627439	+	0.778666i	$0.284103\pi$
$954$	1.13451e10	0.423046
$955$	−2.43766e9	−0.0905651
$956$	−9.13679e9	−0.338213
$957$	−8.01167e9	−0.295482
$958$	−1.99025e10	−0.731355
$959$	−2.46417e9	−0.0902205
$960$	−2.31729e9	−0.0845340
$961$	8.87504e8	0.0322581
$962$	−4.48882e10	−1.62562
$963$	3.60787e10	1.30184
$964$	−1.12366e10	−0.403985
$965$	−1.06374e10	−0.381057
$966$	−5.48713e9	−0.195851
$967$	−4.32525e9	−0.153822	−0.0769110	−	0.997038i	$-0.524506\pi$
$967$	−4.32525e9	−0.153822	−0.0769110	+	0.997038i	$0.524506\pi$
$968$	−8.40297e9	−0.297762
$969$	−1.01161e10	−0.357176
$970$	−9.87194e9	−0.347297
$971$	−5.93860e9	−0.208169	−0.104085	−	0.994568i	$-0.533191\pi$
$971$	−5.93860e9	−0.208169	−0.104085	+	0.994568i	$0.533191\pi$
$972$	1.98679e10	0.693938
$973$	1.05478e10	0.367085
$974$	−1.04289e10	−0.361644
$975$	1.24559e10	0.430388
$976$	−1.38263e10	−0.476028
$977$	3.88401e10	1.33245	0.666223	−	0.745753i	$-0.267910\pi$
$977$	3.88401e10	1.33245	0.666223	+	0.745753i	$0.267910\pi$
$978$	2.27179e10	0.776574
$979$	1.26804e10	0.431910
$980$	−5.09195e9	−0.172820
$981$	−4.96011e10	−1.67745
$982$	−2.74614e10	−0.925408
$983$	−1.13494e10	−0.381099	−0.190549	−	0.981678i	$-0.561027\pi$
$983$	−1.13494e10	−0.381099	−0.190549	+	0.981678i	$0.561027\pi$
$984$	−8.68669e9	−0.290651
$985$	4.58996e9	0.153032
$986$	−3.40999e9	−0.113288
$987$	1.68605e9	0.0558162
$988$	1.56418e10	0.515987
$989$	−3.83663e9	−0.126114
$990$	4.93473e9	0.161637
$991$	6.57926e8	0.0214743	0.0107372	−	0.999942i	$-0.496582\pi$
$991$	6.57926e8	0.0214743	0.0107372	+	0.999942i	$0.496582\pi$
$992$	9.76191e8	0.0317500
$993$	2.69939e10	0.874871
$994$	−1.63588e10	−0.528324
$995$	−8.25598e9	−0.265698
$996$	−2.30641e10	−0.739655
$997$	5.97434e10	1.90922	0.954612	−	0.297853i	$-0.0962705\pi$
$997$	5.97434e10	1.90922	0.954612	+	0.297853i	$0.0962705\pi$
$998$	−3.20245e9	−0.101982
$999$	−2.20725e10	−0.700442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.8.a.a.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.8.a.a.1.2	✓	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	310.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -70.7181 q^{3} +64.0000 q^{4} +125.000 q^{5} -565.745 q^{6} +432.491 q^{7} +512.000 q^{8} +2814.05 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -70.7181 q^{3} +64.0000 q^{4} +125.000 q^{5} -565.745 q^{6} +432.491 q^{7} +512.000 q^{8} +2814.05 q^{9} +1000.00 q^{10} +1753.60 q^{11} -4525.96 q^{12} -11272.6 q^{13} +3459.93 q^{14} -8839.76 q^{15} +4096.00 q^{16} -6597.84 q^{17} +22512.4 q^{18} -21681.2 q^{19} +8000.00 q^{20} -30585.0 q^{21} +14028.8 q^{22} +22425.8 q^{23} -36207.7 q^{24} +15625.0 q^{25} -90181.0 q^{26} -44343.9 q^{27} +27679.5 q^{28} +64604.3 q^{29} -70718.1 q^{30} +29791.0 q^{31} +32768.0 q^{32} -124011. q^{33} -52782.7 q^{34} +54061.4 q^{35} +180099. q^{36} +497756. q^{37} -173449. q^{38} +797179. q^{39} +64000.0 q^{40} +239913. q^{41} -244680. q^{42} -171081. q^{43} +112230. q^{44} +351757. q^{45} +179406. q^{46} -55126.7 q^{47} -289661. q^{48} -636494. q^{49} +125000. q^{50} +466587. q^{51} -721448. q^{52} +503947. q^{53} -354752. q^{54} +219200. q^{55} +221436. q^{56} +1.53325e6 q^{57} +516834. q^{58} -2.52552e6 q^{59} -565745. q^{60} -3.37557e6 q^{61} +238328. q^{62} +1.21705e6 q^{63} +262144. q^{64} -1.40908e6 q^{65} -992091. q^{66} +921540. q^{67} -422262. q^{68} -1.58591e6 q^{69} +432491. q^{70} -4.72808e6 q^{71} +1.44079e6 q^{72} -995778. q^{73} +3.98205e6 q^{74} -1.10497e6 q^{75} -1.38759e6 q^{76} +758418. q^{77} +6.37743e6 q^{78} +2.20866e6 q^{79} +512000. q^{80} -3.01841e6 q^{81} +1.91930e6 q^{82} +5.09596e6 q^{83} -1.95744e6 q^{84} -824730. q^{85} -1.36865e6 q^{86} -4.56869e6 q^{87} +897844. q^{88} +7.23105e6 q^{89} +2.81405e6 q^{90} -4.87532e6 q^{91} +1.43525e6 q^{92} -2.10676e6 q^{93} -441014. q^{94} -2.71015e6 q^{95} -2.31729e6 q^{96} -9.87194e6 q^{97} -5.09195e6 q^{98} +4.93473e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 82 q^{3} + 384 q^{4} + 750 q^{5} - 656 q^{6} - 1940 q^{7} + 3072 q^{8} + 910 q^{9}+O(q^{10}) \) 6 * q + 48 * q^2 - 82 * q^3 + 384 * q^4 + 750 * q^5 - 656 * q^6 - 1940 * q^7 + 3072 * q^8 + 910 * q^9	\( 6 q + 48 q^{2} - 82 q^{3} + 384 q^{4} + 750 q^{5} - 656 q^{6} - 1940 q^{7} + 3072 q^{8} + 910 q^{9} + 6000 q^{10} - 442 q^{11} - 5248 q^{12} - 4014 q^{13} - 15520 q^{14} - 10250 q^{15} + 24576 q^{16} - 37182 q^{17} + 7280 q^{18} - 68170 q^{19} + 48000 q^{20} - 16074 q^{21} - 3536 q^{22} - 71730 q^{23} - 41984 q^{24} + 93750 q^{25} - 32112 q^{26} - 239356 q^{27} - 124160 q^{28} - 300546 q^{29} - 82000 q^{30} + 178746 q^{31} + 196608 q^{32} + 233556 q^{33} - 297456 q^{34} - 242500 q^{35} + 58240 q^{36} - 4866 q^{37} - 545360 q^{38} - 413788 q^{39} + 384000 q^{40} - 38280 q^{41} - 128592 q^{42} - 289636 q^{43} - 28288 q^{44} + 113750 q^{45} - 573840 q^{46} - 1387980 q^{47} - 335872 q^{48} - 1665106 q^{49} + 750000 q^{50} - 1040966 q^{51} - 256896 q^{52} - 2061800 q^{53} - 1914848 q^{54} - 55250 q^{55} - 993280 q^{56} - 710586 q^{57} - 2404368 q^{58} - 5189426 q^{59} - 656000 q^{60} - 337160 q^{61} + 1429968 q^{62} - 1857360 q^{63} + 1572864 q^{64} - 501750 q^{65} + 1868448 q^{66} + 487628 q^{67} - 2379648 q^{68} + 240508 q^{69} - 1940000 q^{70} - 4767670 q^{71} + 465920 q^{72} - 2337232 q^{73} - 38928 q^{74} - 1281250 q^{75} - 4362880 q^{76} + 1773908 q^{77} - 3310304 q^{78} + 537410 q^{79} + 3072000 q^{80} - 1840886 q^{81} - 306240 q^{82} - 4608400 q^{83} - 1028736 q^{84} - 4647750 q^{85} - 2317088 q^{86} + 591248 q^{87} - 226304 q^{88} - 4507442 q^{89} + 910000 q^{90} + 1735616 q^{91} - 4590720 q^{92} - 2442862 q^{93} - 11103840 q^{94} - 8521250 q^{95} - 2686976 q^{96} + 1144396 q^{97} - 13320848 q^{98} - 4453908 q^{99}+O(q^{100}) \) 6 * q + 48 * q^2 - 82 * q^3 + 384 * q^4 + 750 * q^5 - 656 * q^6 - 1940 * q^7 + 3072 * q^8 + 910 * q^9 + 6000 * q^10 - 442 * q^11 - 5248 * q^12 - 4014 * q^13 - 15520 * q^14 - 10250 * q^15 + 24576 * q^16 - 37182 * q^17 + 7280 * q^18 - 68170 * q^19 + 48000 * q^20 - 16074 * q^21 - 3536 * q^22 - 71730 * q^23 - 41984 * q^24 + 93750 * q^25 - 32112 * q^26 - 239356 * q^27 - 124160 * q^28 - 300546 * q^29 - 82000 * q^30 + 178746 * q^31 + 196608 * q^32 + 233556 * q^33 - 297456 * q^34 - 242500 * q^35 + 58240 * q^36 - 4866 * q^37 - 545360 * q^38 - 413788 * q^39 + 384000 * q^40 - 38280 * q^41 - 128592 * q^42 - 289636 * q^43 - 28288 * q^44 + 113750 * q^45 - 573840 * q^46 - 1387980 * q^47 - 335872 * q^48 - 1665106 * q^49 + 750000 * q^50 - 1040966 * q^51 - 256896 * q^52 - 2061800 * q^53 - 1914848 * q^54 - 55250 * q^55 - 993280 * q^56 - 710586 * q^57 - 2404368 * q^58 - 5189426 * q^59 - 656000 * q^60 - 337160 * q^61 + 1429968 * q^62 - 1857360 * q^63 + 1572864 * q^64 - 501750 * q^65 + 1868448 * q^66 + 487628 * q^67 - 2379648 * q^68 + 240508 * q^69 - 1940000 * q^70 - 4767670 * q^71 + 465920 * q^72 - 2337232 * q^73 - 38928 * q^74 - 1281250 * q^75 - 4362880 * q^76 + 1773908 * q^77 - 3310304 * q^78 + 537410 * q^79 + 3072000 * q^80 - 1840886 * q^81 - 306240 * q^82 - 4608400 * q^83 - 1028736 * q^84 - 4647750 * q^85 - 2317088 * q^86 + 591248 * q^87 - 226304 * q^88 - 4507442 * q^89 + 910000 * q^90 + 1735616 * q^91 - 4590720 * q^92 - 2442862 * q^93 - 11103840 * q^94 - 8521250 * q^95 - 2686976 * q^96 + 1144396 * q^97 - 13320848 * q^98 - 4453908 * q^99

Introduction

L-functions

Modular forms

Varieties

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