LMFDB - Embedded newform 175.10.b.b.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(99,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 97x^{2} + 2304 $ x^4 + 97*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$-6.44622i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.b.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.8924i q^{2} -195.817i q^{3} +393.355 q^{4} -2132.92 q^{6} +2401.00i q^{7} -9861.52i q^{8} -18661.3 q^{9} +O(q^{10})$	\(q-10.8924i q^{2} -195.817i q^{3} +393.355 q^{4} -2132.92 q^{6} +2401.00i q^{7} -9861.52i q^{8} -18661.3 q^{9} +63864.3 q^{11} -77025.5i q^{12} -164679. i q^{13} +26152.8 q^{14} +93981.5 q^{16} +362910. i q^{17} +203267. i q^{18} +436498. q^{19} +470156. q^{21} -695638. i q^{22} +918199. i q^{23} -1.93105e6 q^{24} -1.79375e6 q^{26} -200076. i q^{27} +944445. i q^{28} +3.68643e6 q^{29} +3.47629e6 q^{31} -6.07279e6i q^{32} -1.25057e7i q^{33} +3.95298e6 q^{34} -7.34049e6 q^{36} -1.88149e7i q^{37} -4.75453e6i q^{38} -3.22469e7 q^{39} +2.40714e6 q^{41} -5.12115e6i q^{42} -1.25306e7i q^{43} +2.51213e7 q^{44} +1.00014e7 q^{46} +5.54509e7i q^{47} -1.84032e7i q^{48} -5.76480e6 q^{49} +7.10639e7 q^{51} -6.47772e7i q^{52} -9.26889e7i q^{53} -2.17931e6 q^{54} +2.36775e7 q^{56} -8.54737e7i q^{57} -4.01542e7i q^{58} +2.52600e7 q^{59} +6.93275e7 q^{61} -3.78653e7i q^{62} -4.48057e7i q^{63} -1.80290e7 q^{64} -1.36218e8 q^{66} +2.33494e7i q^{67} +1.42752e8i q^{68} +1.79799e8 q^{69} -1.06194e8 q^{71} +1.84028e8i q^{72} -2.10115e8i q^{73} -2.04940e8 q^{74} +1.71699e8 q^{76} +1.53338e8i q^{77} +3.51247e8i q^{78} +149606. q^{79} -4.06488e8 q^{81} -2.62197e7i q^{82} +5.21565e8i q^{83} +1.84938e8 q^{84} -1.36489e8 q^{86} -7.21865e8i q^{87} -6.29799e8i q^{88} -2.98587e8 q^{89} +3.95394e8 q^{91} +3.61178e8i q^{92} -6.80716e8i q^{93} +6.03996e8 q^{94} -1.18915e9 q^{96} +8.95983e8i q^{97} +6.27928e7i q^{98} -1.19179e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9}+O(q^{10}) $ 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9	$ 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9} + 70632 q^{11} - 28812 q^{14} - 1504 q^{16} + 1850852 q^{19} + 412972 q^{21} - 6602592 q^{24} - 8254848 q^{26} + 20007168 q^{29} + 4934520 q^{31} + 4493352 q^{34} - 11225432 q^{36} - 94835888 q^{39} - 38206896 q^{41} + 37301952 q^{44} + 24735168 q^{46} - 23059204 q^{49} + 119942712 q^{51} - 105668944 q^{54} - 12562032 q^{56} + 14138436 q^{59} + 88632772 q^{61} - 294834304 q^{64} - 166516928 q^{66} + 390362304 q^{69} + 412987632 q^{71} - 7143048 q^{74} + 565023536 q^{76} - 937070192 q^{79} - 1171491268 q^{81} + 250357072 q^{84} - 833661216 q^{86} - 1272534792 q^{89} + 127397060 q^{91} + 304446384 q^{94} - 3429962368 q^{96} - 2818835720 q^{99}+O(q^{100}) $ 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9 + 70632 * q^11 - 28812 * q^14 - 1504 * q^16 + 1850852 * q^19 + 412972 * q^21 - 6602592 * q^24 - 8254848 * q^26 + 20007168 * q^29 + 4934520 * q^31 + 4493352 * q^34 - 11225432 * q^36 - 94835888 * q^39 - 38206896 * q^41 + 37301952 * q^44 + 24735168 * q^46 - 23059204 * q^49 + 119942712 * q^51 - 105668944 * q^54 - 12562032 * q^56 + 14138436 * q^59 + 88632772 * q^61 - 294834304 * q^64 - 166516928 * q^66 + 390362304 * q^69 + 412987632 * q^71 - 7143048 * q^74 + 565023536 * q^76 - 937070192 * q^79 - 1171491268 * q^81 + 250357072 * q^84 - 833661216 * q^86 - 1272534792 * q^89 + 127397060 * q^91 + 304446384 * q^94 - 3429962368 * q^96 - 2818835720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 10.8924i	− 0.481383i	−0.970602	−	0.240691i	$-0.922626\pi$
$2$	− 10.8924i	− 0.481383i	0.970602	−	0.240691i	$-0.0773741\pi$
$3$	− 195.817i	− 1.39574i	−0.716225	−	0.697870i	$-0.754131\pi$
$3$	− 195.817i	− 1.39574i	0.716225	−	0.697870i	$-0.245869\pi$
$4$	393.355	0.768271
$5$	0	0
$5$	0	0
$6$	−2132.92	−0.671885
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	− 9861.52i	− 0.851215i
$9$	−18661.3	−0.948090
$10$	0	0
$11$	63864.3	1.31520	0.657599	−	0.753369i	$-0.271572\pi$
$11$	63864.3	1.31520	0.657599	+	0.753369i	$0.271572\pi$
$12$	− 77025.5i	− 1.07231i
$13$	− 164679.i	− 1.59916i	−0.600558	−	0.799581i	$-0.705055\pi$
$13$	− 164679.i	− 1.59916i	0.600558	−	0.799581i	$-0.294945\pi$
$14$	26152.8	0.181946
$15$	0	0
$16$	93981.5	0.358511
$17$	362910.i	1.05385i	0.849912	+	0.526925i	$0.176655\pi$
$17$	362910.i	1.05385i	−0.849912	+	0.526925i	$0.823345\pi$
$18$	203267.i	0.456394i
$19$	436498.	0.768406	0.384203	−	0.923249i	$-0.374476\pi$
$19$	436498.	0.768406	0.384203	+	0.923249i	$0.374476\pi$
$20$	0	0
$21$	470156.	0.527540
$22$	− 695638.i	− 0.633113i
$23$	918199.i	0.684166i	0.939670	+	0.342083i	$0.111132\pi$
$23$	918199.i	0.684166i	−0.939670	+	0.342083i	$0.888868\pi$
$24$	−1.93105e6	−1.18807
$25$	0	0
$26$	−1.79375e6	−0.769809
$27$	− 200076.i	− 0.0724531i
$28$	944445.i	0.290379i
$29$	3.68643e6	0.967865	0.483932	−	0.875105i	$-0.339208\pi$
$29$	3.68643e6	0.967865	0.483932	+	0.875105i	$0.339208\pi$
$30$	0	0
$31$	3.47629e6	0.676064	0.338032	−	0.941135i	$-0.390239\pi$
$31$	3.47629e6	0.676064	0.338032	+	0.941135i	$0.390239\pi$
$32$	− 6.07279e6i	− 1.02380i
$33$	− 1.25057e7i	− 1.83567i
$34$	3.95298e6	0.507305
$35$	0	0
$36$	−7.34049e6	−0.728390
$37$	− 1.88149e7i	− 1.65042i	−0.564826	−	0.825210i	$-0.691057\pi$
$37$	− 1.88149e7i	− 1.65042i	0.564826	−	0.825210i	$-0.308943\pi$
$38$	− 4.75453e6i	− 0.369897i
$39$	−3.22469e7	−2.23201
$40$	0	0
$41$	2.40714e6	0.133038	0.0665188	−	0.997785i	$-0.478811\pi$
$41$	2.40714e6	0.133038	0.0665188	+	0.997785i	$0.478811\pi$
$42$	− 5.12115e6i	− 0.253949i
$43$	− 1.25306e7i	− 0.558938i	−0.960155	−	0.279469i	$-0.909842\pi$
$43$	− 1.25306e7i	− 0.558938i	0.960155	−	0.279469i	$-0.0901584\pi$
$44$	2.51213e7	1.01043
$45$	0	0
$46$	1.00014e7	0.329346
$47$	5.54509e7i	1.65756i	0.559577	+	0.828779i	$0.310964\pi$
$47$	5.54509e7i	1.65756i	−0.559577	+	0.828779i	$0.689036\pi$
$48$	− 1.84032e7i	− 0.500388i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	7.10639e7	1.47090
$52$	− 6.47772e7i	− 1.22859i
$53$	− 9.26889e7i	− 1.61356i	−0.590849	−	0.806782i	$-0.701207\pi$
$53$	− 9.26889e7i	− 1.61356i	0.590849	−	0.806782i	$-0.298793\pi$
$54$	−2.17931e6	−0.0348777
$55$	0	0
$56$	2.36775e7	0.321729
$57$	− 8.54737e7i	− 1.07250i
$58$	− 4.01542e7i	− 0.465913i
$59$	2.52600e7	0.271393	0.135696	−	0.990750i	$-0.456673\pi$
$59$	2.52600e7	0.271393	0.135696	+	0.990750i	$0.456673\pi$
$60$	0	0
$61$	6.93275e7	0.641093	0.320547	−	0.947233i	$-0.396133\pi$
$61$	6.93275e7	0.641093	0.320547	+	0.947233i	$0.396133\pi$
$62$	− 3.78653e7i	− 0.325446i
$63$	− 4.48057e7i	− 0.358344i
$64$	−1.80290e7	−0.134326
$65$	0	0
$66$	−1.36218e8	−0.883661
$67$	2.33494e7i	0.141559i	0.997492	+	0.0707796i	$0.0225487\pi$
$67$	2.33494e7i	0.141559i	−0.997492	+	0.0707796i	$0.977451\pi$
$68$	1.42752e8i	0.809643i
$69$	1.79799e8	0.954918
$70$	0	0
$71$	−1.06194e8	−0.495950	−0.247975	−	0.968766i	$-0.579765\pi$
$71$	−1.06194e8	−0.495950	−0.247975	+	0.968766i	$0.579765\pi$
$72$	1.84028e8i	0.807028i
$73$	− 2.10115e8i	− 0.865974i	−0.901400	−	0.432987i	$-0.857460\pi$
$73$	− 2.10115e8i	− 0.865974i	0.901400	−	0.432987i	$-0.142540\pi$
$74$	−2.04940e8	−0.794483
$75$	0	0
$76$	1.71699e8	0.590344
$77$	1.53338e8i	0.497098i
$78$	3.51247e8i	1.07445i
$79$	149606.	0.000432144 0	0.000216072	−	1.00000i	$-0.499931\pi$
$79$	149606.	0.000432144 0	0.000216072		1.00000i	$0.499931\pi$
$80$	0	0
$81$	−4.06488e8	−1.04922
$82$	− 2.62197e7i	− 0.0640420i
$83$	5.21565e8i	1.20630i	0.797626	+	0.603152i	$0.206089\pi$
$83$	5.21565e8i	1.20630i	−0.797626	+	0.603152i	$0.793911\pi$
$84$	1.84938e8	0.405294
$85$	0	0
$86$	−1.36489e8	−0.269063
$87$	− 7.21865e8i	− 1.35089i
$88$	− 6.29799e8i	− 1.11952i
$89$	−2.98587e8	−0.504448	−0.252224	−	0.967669i	$-0.581162\pi$
$89$	−2.98587e8	−0.504448	−0.252224	+	0.967669i	$0.581162\pi$
$90$	0	0
$91$	3.95394e8	0.604426
$92$	3.61178e8i	0.525625i
$93$	− 6.80716e8i	− 0.943610i
$94$	6.03996e8	0.797919
$95$	0	0
$96$	−1.18915e9	−1.42895
$97$	8.95983e8i	1.02761i	0.857908	+	0.513803i	$0.171764\pi$
$97$	8.95983e8i	1.02761i	−0.857908	+	0.513803i	$0.828236\pi$
$98$	6.27928e7i	0.0687689i
$99$	−1.19179e9	−1.24693
$100$	0	0
$101$	−4.13043e7	−0.0394956	−0.0197478	−	0.999805i	$-0.506286\pi$
$101$	−4.13043e7	−0.0394956	−0.0197478	+	0.999805i	$0.506286\pi$
$102$	− 7.74060e8i	− 0.708066i
$103$	4.29472e8i	0.375982i	0.982171	+	0.187991i	$0.0601976\pi$
$103$	4.29472e8i	0.375982i	−0.982171	+	0.187991i	$0.939802\pi$
$104$	−1.62398e9	−1.36123
$105$	0	0
$106$	−1.00961e9	−0.776742
$107$	− 1.23287e9i	− 0.909265i	−0.890679	−	0.454632i	$-0.849771\pi$
$107$	− 1.23287e9i	− 0.909265i	0.890679	−	0.454632i	$-0.150229\pi$
$108$	− 7.87006e7i	− 0.0556636i
$109$	−1.69619e9	−1.15095	−0.575475	−	0.817820i	$-0.695183\pi$
$109$	−1.69619e9	−1.15095	−0.575475	+	0.817820i	$0.695183\pi$
$110$	0	0
$111$	−3.68428e9	−2.30356
$112$	2.25650e8i	0.135504i
$113$	− 1.42449e9i	− 0.821878i	−0.911663	−	0.410939i	$-0.865201\pi$
$113$	− 1.42449e9i	− 0.821878i	0.911663	−	0.410939i	$-0.134799\pi$
$114$	−9.31017e8	−0.516281
$115$	0	0
$116$	1.45007e9	0.743582
$117$	3.07311e9i	1.51615i
$118$	− 2.75143e8i	− 0.130644i
$119$	−8.71347e8	−0.398318
$120$	0	0
$121$	1.72070e9	0.729744
$122$	− 7.55146e8i	− 0.308611i
$123$	− 4.71359e8i	− 0.185686i
$124$	1.36741e9	0.519401
$125$	0	0
$126$	−4.88043e8	−0.172501
$127$	3.12858e9i	1.06716i	0.845749	+	0.533581i	$0.179154\pi$
$127$	3.12858e9i	1.06716i	−0.845749	+	0.533581i	$0.820846\pi$
$128$	− 2.91289e9i	− 0.959133i
$129$	−2.45370e9	−0.780132
$130$	0	0
$131$	7.03123e8	0.208598	0.104299	−	0.994546i	$-0.466740\pi$
$131$	7.03123e8	0.208598	0.104299	+	0.994546i	$0.466740\pi$
$132$	− 4.91918e9i	− 1.41029i
$133$	1.04803e9i	0.290430i
$134$	2.54332e8	0.0681442
$135$	0	0
$136$	3.57885e9	0.897053
$137$	3.07310e9i	0.745306i	0.927971	+	0.372653i	$0.121552\pi$
$137$	3.07310e9i	0.745306i	−0.927971	+	0.372653i	$0.878448\pi$
$138$	− 1.95845e9i	− 0.459681i
$139$	−5.07806e9	−1.15380	−0.576901	−	0.816814i	$-0.695738\pi$
$139$	−5.07806e9	−1.15380	−0.576901	+	0.816814i	$0.695738\pi$
$140$	0	0
$141$	1.08582e10	2.31352
$142$	1.15671e9i	0.238742i
$143$	− 1.05171e10i	− 2.10321i
$144$	−1.75381e9	−0.339901
$145$	0	0
$146$	−2.28867e9	−0.416865
$147$	1.12885e9i	0.199391i
$148$	− 7.40093e9i	− 1.26797i
$149$	−2.13455e9	−0.354788	−0.177394	−	0.984140i	$-0.556767\pi$
$149$	−2.13455e9	−0.354788	−0.177394	+	0.984140i	$0.556767\pi$
$150$	0	0
$151$	−2.35298e9	−0.368318	−0.184159	−	0.982897i	$-0.558956\pi$
$151$	−2.35298e9	−0.368318	−0.184159	+	0.982897i	$0.558956\pi$
$152$	− 4.30454e9i	− 0.654079i
$153$	− 6.77236e9i	− 0.999145i
$154$	1.67023e9	0.239294
$155$	0	0
$156$	−1.26845e10	−1.71479
$157$	2.98482e9i	0.392075i	0.980596	+	0.196038i	$0.0628075\pi$
$157$	2.98482e9i	0.392075i	−0.980596	+	0.196038i	$0.937193\pi$
$158$	− 1.62958e6i	0 0.000208027i
$159$	−1.81501e10	−2.25212
$160$	0	0
$161$	−2.20460e9	−0.258591
$162$	4.42764e9i	0.505074i
$163$	9.20745e9i	1.02163i	0.859690	+	0.510817i	$0.170657\pi$
$163$	9.20745e9i	1.02163i	−0.859690	+	0.510817i	$0.829343\pi$
$164$	9.46860e8	0.102209
$165$	0	0
$166$	5.68111e9	0.580694
$167$	4.95501e9i	0.492970i	0.969147	+	0.246485i	$0.0792756\pi$
$167$	4.95501e9i	0.492970i	−0.969147	+	0.246485i	$0.920724\pi$
$168$	− 4.63646e9i	− 0.449050i
$169$	−1.65146e10	−1.55732
$170$	0	0
$171$	−8.14560e9	−0.728518
$172$	− 4.92897e9i	− 0.429416i
$173$	3.77546e9i	0.320452i	0.987080	+	0.160226i	$0.0512223\pi$
$173$	3.77546e9i	0.320452i	−0.987080	+	0.160226i	$0.948778\pi$
$174$	−7.86287e9	−0.650294
$175$	0	0
$176$	6.00206e9	0.471513
$177$	− 4.94633e9i	− 0.378794i
$178$	3.25235e9i	0.242833i
$179$	1.94362e10	1.41505	0.707526	−	0.706687i	$-0.249811\pi$
$179$	1.94362e10	1.41505	0.707526	+	0.706687i	$0.249811\pi$
$180$	0	0
$181$	−9.81530e9	−0.679751	−0.339875	−	0.940470i	$-0.610385\pi$
$181$	−9.81530e9	−0.679751	−0.339875	+	0.940470i	$0.610385\pi$
$182$	− 4.30680e9i	− 0.290960i
$183$	− 1.35755e10i	− 0.894799i
$184$	9.05485e9	0.582373
$185$	0	0
$186$	−7.41466e9	−0.454237
$187$	2.31770e10i	1.38602i
$188$	2.18119e10i	1.27345i
$189$	4.80381e8	0.0273847
$190$	0	0
$191$	−1.84579e10	−1.00354	−0.501768	−	0.865002i	$-0.667317\pi$
$191$	−1.84579e10	−1.00354	−0.501768	+	0.865002i	$0.667317\pi$
$192$	3.53038e9i	0.187485i
$193$	4.83605e9i	0.250890i	0.992101	+	0.125445i	$0.0400358\pi$
$193$	4.83605e9i	0.250890i	−0.992101	+	0.125445i	$0.959964\pi$
$194$	9.75944e9	0.494672
$195$	0	0
$196$	−2.26761e9	−0.109753
$197$	− 2.70242e10i	− 1.27836i	−0.769056	−	0.639182i	$-0.779273\pi$
$197$	− 2.70242e10i	− 1.27836i	0.769056	−	0.639182i	$-0.220727\pi$
$198$	1.29815e10i	0.600248i
$199$	−1.65772e10	−0.749330	−0.374665	−	0.927160i	$-0.622242\pi$
$199$	−1.65772e10	−0.749330	−0.374665	+	0.927160i	$0.622242\pi$
$200$	0	0
$201$	4.57220e9	0.197580
$202$	4.49904e8i	0.0190125i
$203$	8.85111e9i	0.365819i
$204$	2.79533e10	1.13005
$205$	0	0
$206$	4.67800e9	0.180991
$207$	− 1.71348e10i	− 0.648651i
$208$	− 1.54768e10i	− 0.573317i
$209$	2.78766e10	1.01061
$210$	0	0
$211$	−5.44866e10	−1.89243	−0.946213	−	0.323544i	$-0.895126\pi$
$211$	−5.44866e10	−1.89243	−0.946213	+	0.323544i	$0.895126\pi$
$212$	− 3.64596e10i	− 1.23965i
$213$	2.07946e10i	0.692218i
$214$	−1.34290e10	−0.437704
$215$	0	0
$216$	−1.97305e9	−0.0616731
$217$	8.34657e9i	0.255528i
$218$	1.84757e10i	0.554047i
$219$	−4.11441e10	−1.20867
$220$	0	0
$221$	5.97636e10	1.68528
$222$	4.01308e10i	1.10889i
$223$	− 2.05500e10i	− 0.556468i	−0.960513	−	0.278234i	$-0.910251\pi$
$223$	− 2.05500e10i	− 0.556468i	0.960513	−	0.278234i	$-0.0897491\pi$
$224$	1.45808e10	0.386958
$225$	0	0
$226$	−1.55162e10	−0.395638
$227$	3.94058e10i	0.985017i	0.870307	+	0.492509i	$0.163920\pi$
$227$	3.94058e10i	0.985017i	−0.870307	+	0.492509i	$0.836080\pi$
$228$	− 3.36215e10i	− 0.823967i
$229$	1.82516e10	0.438572	0.219286	−	0.975661i	$-0.429627\pi$
$229$	1.82516e10	0.438572	0.219286	+	0.975661i	$0.429627\pi$
$230$	0	0
$231$	3.00262e10	0.693819
$232$	− 3.63538e10i	− 0.823861i
$233$	− 5.08161e10i	− 1.12953i	−0.825250	−	0.564767i	$-0.808966\pi$
$233$	− 5.08161e10i	− 1.12953i	0.825250	−	0.564767i	$-0.191034\pi$
$234$	3.34737e10	0.729848
$235$	0	0
$236$	9.93612e9	0.208503
$237$	− 2.92955e7i	0 0.000603160i
$238$	9.49110e9i	0.191743i
$239$	−3.80447e10	−0.754230	−0.377115	−	0.926166i	$-0.623084\pi$
$239$	−3.80447e10	−0.754230	−0.377115	+	0.926166i	$0.623084\pi$
$240$	0	0
$241$	9.80077e10	1.87147	0.935737	−	0.352699i	$-0.114736\pi$
$241$	9.80077e10	1.87147	0.935737	+	0.352699i	$0.114736\pi$
$242$	− 1.87426e10i	− 0.351286i
$243$	7.56590e10i	1.39198i
$244$	2.72703e10	0.492533
$245$	0	0
$246$	−5.13425e9	−0.0893859
$247$	− 7.18819e10i	− 1.22881i
$248$	− 3.42815e10i	− 0.575476i
$249$	1.02131e11	1.68369
$250$	0	0
$251$	7.75125e10	1.23265	0.616325	−	0.787492i	$-0.288621\pi$
$251$	7.75125e10	1.23265	0.616325	+	0.787492i	$0.288621\pi$
$252$	− 1.76245e10i	− 0.275305i
$253$	5.86401e10i	0.899814i
$254$	3.40778e10	0.513713
$255$	0	0
$256$	−4.09593e10	−0.596036
$257$	1.07589e11i	1.53840i	0.639009	+	0.769199i	$0.279345\pi$
$257$	1.07589e11i	1.53840i	−0.639009	+	0.769199i	$0.720655\pi$
$258$	2.67268e10i	0.375542i
$259$	4.51746e10	0.623800
$260$	0	0
$261$	−6.87934e10	−0.917623
$262$	− 7.65873e9i	− 0.100416i
$263$	− 1.21615e10i	− 0.156742i	−0.996924	−	0.0783708i	$-0.975028\pi$
$263$	− 1.21615e10i	− 0.156742i	0.996924	−	0.0783708i	$-0.0249718\pi$
$264$	−1.23325e11	−1.56255
$265$	0	0
$266$	1.14156e10	0.139808
$267$	5.84685e10i	0.704078i
$268$	9.18458e9i	0.108756i
$269$	1.23517e11	1.43827	0.719134	−	0.694872i	$-0.244539\pi$
$269$	1.23517e11	1.43827	0.719134	+	0.694872i	$0.244539\pi$
$270$	0	0
$271$	1.34305e11	1.51263	0.756313	−	0.654210i	$-0.226999\pi$
$271$	1.34305e11	1.51263	0.756313	+	0.654210i	$0.226999\pi$
$272$	3.41068e10i	0.377817i
$273$	− 7.74248e10i	− 0.843622i
$274$	3.34736e10	0.358777
$275$	0	0
$276$	7.07248e10	0.733636
$277$	2.16684e10i	0.221140i	0.993868	+	0.110570i	$0.0352677\pi$
$277$	2.16684e10i	0.221140i	−0.993868	+	0.110570i	$0.964732\pi$
$278$	5.53125e10i	0.555420i
$279$	−6.48719e10	−0.640970
$280$	0	0
$281$	7.73283e9	0.0739878	0.0369939	−	0.999315i	$-0.488222\pi$
$281$	7.73283e9	0.0739878	0.0369939	+	0.999315i	$0.488222\pi$
$282$	− 1.18273e11i	− 1.11369i
$283$	− 7.19601e10i	− 0.666888i	−0.942770	−	0.333444i	$-0.891789\pi$
$283$	− 7.19601e10i	− 0.666888i	0.942770	−	0.333444i	$-0.108211\pi$
$284$	−4.17720e10	−0.381024
$285$	0	0
$286$	−1.14557e11	−1.01245
$287$	5.77955e9i	0.0502835i
$288$	1.13326e11i	0.970650i
$289$	−1.31159e10	−0.110601
$290$	0	0
$291$	1.75449e11	1.43427
$292$	− 8.26498e10i	− 0.665303i
$293$	1.73674e11i	1.37667i	0.725393	+	0.688335i	$0.241658\pi$
$293$	1.73674e11i	1.37667i	−0.725393	+	0.688335i	$0.758342\pi$
$294$	1.22959e10	0.0959835
$295$	0	0
$296$	−1.85544e11	−1.40486
$297$	− 1.27777e10i	− 0.0952901i
$298$	2.32505e10i	0.170789i
$299$	1.51208e11	1.09409
$300$	0	0
$301$	3.00860e10	0.211259
$302$	2.56297e10i	0.177302i
$303$	8.08807e9i	0.0551256i
$304$	4.10227e10	0.275482
$305$	0	0
$306$	−7.37675e10	−0.480971
$307$	− 2.27108e11i	− 1.45918i	−0.683884	−	0.729591i	$-0.739710\pi$
$307$	− 2.27108e11i	− 1.45918i	0.683884	−	0.729591i	$-0.260290\pi$
$308$	6.03163e10i	0.381906i
$309$	8.40978e10	0.524773
$310$	0	0
$311$	−8.68962e10	−0.526719	−0.263360	−	0.964698i	$-0.584831\pi$
$311$	−8.68962e10	−0.526719	−0.263360	+	0.964698i	$0.584831\pi$
$312$	3.18003e11i	1.89992i
$313$	− 5.25289e10i	− 0.309349i	−0.987965	−	0.154674i	$-0.950567\pi$
$313$	− 5.25289e10i	− 0.309349i	0.987965	−	0.154674i	$-0.0494329\pi$
$314$	3.25120e10	0.188738
$315$	0	0
$316$	5.88484e7	0.000332004 0
$317$	− 2.63784e11i	− 1.46718i	−0.679595	−	0.733588i	$-0.737844\pi$
$317$	− 2.63784e11i	− 1.46718i	0.679595	−	0.733588i	$-0.262156\pi$
$318$	1.97698e11i	1.08413i
$319$	2.35431e11	1.27293
$320$	0	0
$321$	−2.41417e11	−1.26910
$322$	2.40134e10i	0.124481i
$323$	1.58410e11i	0.809786i
$324$	−1.59894e11	−0.806082
$325$	0	0
$326$	1.00292e11	0.491797
$327$	3.32143e11i	1.60643i
$328$	− 2.37381e10i	− 0.113244i
$329$	−1.33138e11	−0.626498
$330$	0	0
$331$	−2.11350e11	−0.967780	−0.483890	−	0.875129i	$-0.660776\pi$
$331$	−2.11350e11	−0.967780	−0.483890	+	0.875129i	$0.660776\pi$
$332$	2.05160e11i	0.926768i
$333$	3.51110e11i	1.56475i
$334$	5.39722e10	0.237307
$335$	0	0
$336$	4.41860e10	0.189129
$337$	3.67482e11i	1.55203i	0.630712	+	0.776017i	$0.282763\pi$
$337$	3.67482e11i	1.55203i	−0.630712	+	0.776017i	$0.717237\pi$
$338$	1.79884e11i	0.749666i
$339$	−2.78940e11	−1.14713
$340$	0	0
$341$	2.22011e11	0.889158
$342$	8.87255e10i	0.350696i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−1.23571e11	−0.475776
$345$	0	0
$346$	4.11240e10	0.154260
$347$	− 4.33866e11i	− 1.60647i	−0.595662	−	0.803235i	$-0.703110\pi$
$347$	− 4.33866e11i	− 1.60647i	0.595662	−	0.803235i	$-0.296890\pi$
$348$	− 2.83949e11i	− 1.03785i
$349$	−1.04086e11	−0.375559	−0.187780	−	0.982211i	$-0.560129\pi$
$349$	−1.04086e11	−0.375559	−0.187780	+	0.982211i	$0.560129\pi$
$350$	0	0
$351$	−3.29482e10	−0.115864
$352$	− 3.87834e11i	− 1.34649i
$353$	− 4.46890e11i	− 1.53184i	−0.642934	−	0.765922i	$-0.722283\pi$
$353$	− 4.46890e11i	− 1.53184i	0.642934	−	0.765922i	$-0.277717\pi$
$354$	−5.38776e10	−0.182345
$355$	0	0
$356$	−1.17451e11	−0.387553
$357$	1.70625e11i	0.555948i
$358$	− 2.11708e11i	− 0.681182i
$359$	1.96551e11	0.624526	0.312263	−	0.949996i	$-0.398913\pi$
$359$	1.96551e11	0.624526	0.312263	+	0.949996i	$0.398913\pi$
$360$	0	0
$361$	−1.32157e11	−0.409551
$362$	1.06913e11i	0.327220i
$363$	− 3.36942e11i	− 1.01853i
$364$	1.55530e11	0.464363
$365$	0	0
$366$	−1.47870e11	−0.430741
$367$	2.25518e11i	0.648908i	0.945901	+	0.324454i	$0.105181\pi$
$367$	2.25518e11i	0.648908i	−0.945901	+	0.324454i	$0.894819\pi$
$368$	8.62937e10i	0.245281i
$369$	−4.49203e10	−0.126132
$370$	0	0
$371$	2.22546e11	0.609870
$372$	− 2.67763e11i	− 0.724948i
$373$	− 2.04414e11i	− 0.546791i	−0.961902	−	0.273395i	$-0.911853\pi$
$373$	− 2.04414e11i	− 0.546791i	0.961902	−	0.273395i	$-0.0881467\pi$
$374$	2.52454e11	0.667206
$375$	0	0
$376$	5.46831e11	1.41094
$377$	− 6.07076e11i	− 1.54777i
$378$	− 5.23253e9i	− 0.0131825i
$379$	−4.03306e10	−0.100406	−0.0502029	−	0.998739i	$-0.515987\pi$
$379$	−4.03306e10	−0.100406	−0.0502029	+	0.998739i	$0.515987\pi$
$380$	0	0
$381$	6.12628e11	1.48948
$382$	2.01052e11i	0.483084i
$383$	− 3.98325e11i	− 0.945895i	−0.881091	−	0.472947i	$-0.843190\pi$
$383$	− 3.98325e11i	− 0.945895i	0.881091	−	0.472947i	$-0.156810\pi$
$384$	−5.70393e11	−1.33870
$385$	0	0
$386$	5.26764e10	0.120774
$387$	2.33837e11i	0.529923i
$388$	3.52439e11i	0.789480i
$389$	4.22504e11	0.935531	0.467765	−	0.883853i	$-0.345059\pi$
$389$	4.22504e11	0.935531	0.467765	+	0.883853i	$0.345059\pi$
$390$	0	0
$391$	−3.33224e11	−0.721009
$392$	5.68497e10i	0.121602i
$393$	− 1.37683e11i	− 0.291149i
$394$	−2.94359e11	−0.615382
$395$	0	0
$396$	−4.68795e11	−0.957976
$397$	− 6.50999e11i	− 1.31529i	−0.753326	−	0.657647i	$-0.771552\pi$
$397$	− 6.50999e11i	− 1.31529i	0.753326	−	0.657647i	$-0.228448\pi$
$398$	1.80567e11i	0.360714i
$399$	2.05222e11	0.405365
$400$	0	0
$401$	−3.10509e11	−0.599687	−0.299843	−	0.953988i	$-0.596934\pi$
$401$	−3.10509e11	−0.599687	−0.299843	+	0.953988i	$0.596934\pi$
$402$	− 4.98024e10i	− 0.0951115i
$403$	− 5.72471e11i	− 1.08114i
$404$	−1.62472e10	−0.0303433
$405$	0	0
$406$	9.64102e10	0.176099
$407$	− 1.20160e12i	− 2.17063i
$408$	− 7.00799e11i	− 1.25205i
$409$	−2.99519e11	−0.529261	−0.264630	−	0.964350i	$-0.585250\pi$
$409$	−2.99519e11	−0.529261	−0.264630	+	0.964350i	$0.585250\pi$
$410$	0	0
$411$	6.01766e11	1.04025
$412$	1.68935e11i	0.288856i
$413$	6.06492e10i	0.102577i
$414$	−1.86639e11	−0.312249
$415$	0	0
$416$	−1.00006e12	−1.63722
$417$	9.94370e11i	1.61041i
$418$	− 3.03645e11i	− 0.486488i
$419$	4.35217e11	0.689832	0.344916	−	0.938634i	$-0.387907\pi$
$419$	4.35217e11	0.689832	0.344916	+	0.938634i	$0.387907\pi$
$420$	0	0
$421$	−2.07600e11	−0.322076	−0.161038	−	0.986948i	$-0.551484\pi$
$421$	−2.07600e11	−0.322076	−0.161038	+	0.986948i	$0.551484\pi$
$422$	5.93493e11i	0.910981i
$423$	− 1.03478e12i	− 1.57151i
$424$	−9.14054e11	−1.37349
$425$	0	0
$426$	2.26504e11	0.333222
$427$	1.66455e11i	0.242310i
$428$	− 4.84955e11i	− 0.698562i
$429$	−2.05942e12	−2.93554
$430$	0	0
$431$	8.61584e11	1.20268	0.601340	−	0.798993i	$-0.294634\pi$
$431$	8.61584e11	1.20268	0.601340	+	0.798993i	$0.294634\pi$
$432$	− 1.88034e10i	− 0.0259752i
$433$	1.45840e11i	0.199379i	0.995019	+	0.0996896i	$0.0317850\pi$
$433$	1.45840e11i	0.199379i	−0.995019	+	0.0996896i	$0.968215\pi$
$434$	9.09145e10	0.123007
$435$	0	0
$436$	−6.67206e11	−0.884241
$437$	4.00792e11i	0.525718i
$438$	4.48160e11i	0.581835i
$439$	1.07131e11	0.137665	0.0688324	−	0.997628i	$-0.478073\pi$
$439$	1.07131e11	0.137665	0.0688324	+	0.997628i	$0.478073\pi$
$440$	0	0
$441$	1.07578e11	0.135441
$442$	− 6.50972e11i	− 0.811263i
$443$	− 1.36838e11i	− 0.168806i	−0.996432	−	0.0844031i	$-0.973102\pi$
$443$	− 1.36838e11i	− 0.168806i	0.996432	−	0.0844031i	$-0.0268984\pi$
$444$	−1.44923e12	−1.76976
$445$	0	0
$446$	−2.23840e11	−0.267874
$447$	4.17981e11i	0.495191i
$448$	− 4.32876e10i	− 0.0507706i
$449$	7.65671e11	0.889065	0.444532	−	0.895763i	$-0.353370\pi$
$449$	7.65671e11	0.889065	0.444532	+	0.895763i	$0.353370\pi$
$450$	0	0
$451$	1.53730e11	0.174971
$452$	− 5.60331e11i	− 0.631425i
$453$	4.60754e11i	0.514076i
$454$	4.29226e11	0.474170
$455$	0	0
$456$	−8.42901e11	−0.912924
$457$	− 5.41842e11i	− 0.581099i	−0.956860	−	0.290549i	$-0.906162\pi$
$457$	− 5.41842e11i	− 0.581099i	0.956860	−	0.290549i	$-0.0938381\pi$
$458$	− 1.98805e11i	− 0.211121i
$459$	7.26094e10	0.0763547
$460$	0	0
$461$	−7.10838e11	−0.733021	−0.366510	−	0.930414i	$-0.619448\pi$
$461$	−7.10838e11	−0.733021	−0.366510	+	0.930414i	$0.619448\pi$
$462$	− 3.27059e11i	− 0.333992i
$463$	7.96272e11i	0.805280i	0.915358	+	0.402640i	$0.131907\pi$
$463$	7.96272e11i	0.805280i	−0.915358	+	0.402640i	$0.868093\pi$
$464$	3.46456e11	0.346990
$465$	0	0
$466$	−5.53511e11	−0.543738
$467$	1.67673e12i	1.63132i	0.578535	+	0.815658i	$0.303625\pi$
$467$	1.67673e12i	1.63132i	−0.578535	+	0.815658i	$0.696375\pi$
$468$	1.20882e12i	1.16481i
$469$	−5.60618e10	−0.0535044
$470$	0	0
$471$	5.84478e11	0.547235
$472$	− 2.49102e11i	− 0.231014i
$473$	− 8.00257e11i	− 0.735114i
$474$	−3.19099e8	−0.000290351 0
$475$	0	0
$476$	−3.42749e11	−0.306016
$477$	1.72969e12i	1.52980i
$478$	4.14400e11i	0.363073i
$479$	−1.17129e12	−1.01661	−0.508305	−	0.861177i	$-0.669728\pi$
$479$	−1.17129e12	−1.01661	−0.508305	+	0.861177i	$0.669728\pi$
$480$	0	0
$481$	−3.09842e12	−2.63929
$482$	− 1.06754e12i	− 0.900895i
$483$	4.31697e11i	0.360925i
$484$	6.76844e11	0.560641
$485$	0	0
$486$	8.24112e11	0.670074
$487$	− 4.49797e11i	− 0.362357i	−0.983450	−	0.181178i	$-0.942009\pi$
$487$	− 4.49797e11i	− 0.362357i	0.983450	−	0.181178i	$-0.0579911\pi$
$488$	− 6.83675e11i	− 0.545708i
$489$	1.80297e12	1.42594
$490$	0	0
$491$	2.25034e12	1.74735	0.873677	−	0.486506i	$-0.161729\pi$
$491$	2.25034e12	1.74735	0.873677	+	0.486506i	$0.161729\pi$
$492$	− 1.85411e11i	− 0.142657i
$493$	1.33784e12i	1.01998i
$494$	−7.82970e11	−0.591526
$495$	0	0
$496$	3.26707e11	0.242376
$497$	− 2.54972e11i	− 0.187452i
$498$	− 1.11246e12i	− 0.810497i
$499$	−1.59712e10	−0.0115315	−0.00576574	−	0.999983i	$-0.501835\pi$
$499$	−1.59712e10	−0.0115315	−0.00576574	+	0.999983i	$0.501835\pi$
$500$	0	0
$501$	9.70275e11	0.688058
$502$	− 8.44300e11i	− 0.593376i
$503$	1.73375e12i	1.20762i	0.797127	+	0.603811i	$0.206352\pi$
$503$	1.73375e12i	1.20762i	−0.797127	+	0.603811i	$0.793648\pi$
$504$	−4.41852e11	−0.305028
$505$	0	0
$506$	6.38734e11	0.433155
$507$	3.23384e12i	2.17361i
$508$	1.23064e12i	0.819869i
$509$	−9.77460e11	−0.645460	−0.322730	−	0.946491i	$-0.604601\pi$
$509$	−9.77460e11	−0.645460	−0.322730	+	0.946491i	$0.604601\pi$
$510$	0	0
$511$	5.04487e11	0.327307
$512$	− 1.04525e12i	− 0.672212i
$513$	− 8.73326e10i	− 0.0556734i
$514$	1.17191e12	0.740558
$515$	0	0
$516$	−9.65175e11	−0.599353
$517$	3.54133e12i	2.18001i
$518$	− 4.92062e11i	− 0.300286i
$519$	7.39300e11	0.447268
$520$	0	0
$521$	5.89223e11	0.350356	0.175178	−	0.984537i	$-0.443950\pi$
$521$	5.89223e11	0.350356	0.175178	+	0.984537i	$0.443950\pi$
$522$	7.49328e11i	0.441728i
$523$	1.43218e12i	0.837027i	0.908211	+	0.418513i	$0.137449\pi$
$523$	1.43218e12i	0.837027i	−0.908211	+	0.418513i	$0.862551\pi$
$524$	2.76577e11	0.160260
$525$	0	0
$526$	−1.32468e11	−0.0754527
$527$	1.26158e12i	0.712471i
$528$	− 1.17530e12i	− 0.658109i
$529$	9.58063e11	0.531916
$530$	0	0
$531$	−4.71382e11	−0.257305
$532$	4.12248e11i	0.223129i
$533$	− 3.96405e11i	− 0.212749i
$534$	6.36865e11	0.338931
$535$	0	0
$536$	2.30260e11	0.120497
$537$	− 3.80594e12i	− 1.97505i
$538$	− 1.34540e12i	− 0.692357i
$539$	−3.68165e11	−0.187885
$540$	0	0
$541$	1.17323e12	0.588839	0.294419	−	0.955676i	$-0.404874\pi$
$541$	1.17323e12	0.588839	0.294419	+	0.955676i	$0.404874\pi$
$542$	− 1.46291e12i	− 0.728152i
$543$	1.92200e12i	0.948755i
$544$	2.20388e12	1.07893
$545$	0	0
$546$	−8.43345e11	−0.406105
$547$	− 2.59515e11i	− 0.123942i	−0.998078	−	0.0619712i	$-0.980261\pi$
$547$	− 2.59515e11i	− 0.123942i	0.998078	−	0.0619712i	$-0.0197387\pi$
$548$	1.20882e12i	0.572597i
$549$	−1.29374e12	−0.607814
$550$	0	0
$551$	1.60912e12	0.743714
$552$	− 1.77309e12i	− 0.812841i
$553$	3.59205e8i	0 0.000163335i
$554$	2.36022e11	0.106453
$555$	0	0
$556$	−1.99748e12	−0.886432
$557$	2.36651e12i	1.04174i	0.853635	+	0.520871i	$0.174393\pi$
$557$	2.36651e12i	1.04174i	−0.853635	+	0.520871i	$0.825607\pi$
$558$	7.06613e11i	0.308552i
$559$	−2.06352e12	−0.893832
$560$	0	0
$561$	4.53845e12	1.93453
$562$	− 8.42294e10i	− 0.0356164i
$563$	− 2.42400e12i	− 1.01682i	−0.861115	−	0.508410i	$-0.830233\pi$
$563$	− 2.42400e12i	− 1.01682i	0.861115	−	0.508410i	$-0.169767\pi$
$564$	4.27113e12	1.77741
$565$	0	0
$566$	−7.83821e11	−0.321028
$567$	− 9.75977e11i	− 0.396566i
$568$	1.04724e12i	0.422160i
$569$	2.11854e12	0.847290	0.423645	−	0.905828i	$-0.360750\pi$
$569$	2.11854e12	0.847290	0.423645	+	0.905828i	$0.360750\pi$
$570$	0	0
$571$	−7.50992e11	−0.295646	−0.147823	−	0.989014i	$-0.547227\pi$
$571$	−7.50992e11	−0.295646	−0.147823	+	0.989014i	$0.547227\pi$
$572$	− 4.13695e12i	− 1.61584i
$573$	3.61437e12i	1.40067i
$574$	6.29534e10	0.0242056
$575$	0	0
$576$	3.36444e11	0.127354
$577$	− 4.35951e12i	− 1.63737i	−0.574243	−	0.818685i	$-0.694704\pi$
$577$	− 4.35951e12i	− 1.63737i	0.574243	−	0.818685i	$-0.305296\pi$
$578$	1.42864e11i	0.0532413i
$579$	9.46981e11	0.350177
$580$	0	0
$581$	−1.25228e12	−0.455940
$582$	− 1.91106e12i	− 0.690433i
$583$	− 5.91951e12i	− 2.12216i
$584$	−2.07206e12	−0.737130
$585$	0	0
$586$	1.89173e12	0.662704
$587$	2.20056e12i	0.765002i	0.923955	+	0.382501i	$0.124937\pi$
$587$	2.20056e12i	0.765002i	−0.923955	+	0.382501i	$0.875063\pi$
$588$	4.44037e11i	0.153187i
$589$	1.51739e12	0.519492
$590$	0	0
$591$	−5.29179e12	−1.78426
$592$	− 1.76825e12i	− 0.591693i
$593$	− 2.83604e12i	− 0.941815i	−0.882183	−	0.470907i	$-0.843927\pi$
$593$	− 2.83604e12i	− 0.941815i	0.882183	−	0.470907i	$-0.156073\pi$
$594$	−1.39180e11	−0.0458710
$595$	0	0
$596$	−8.39636e11	−0.272573
$597$	3.24610e12i	1.04587i
$598$	− 1.64702e12i	− 0.526677i
$599$	8.29286e11	0.263199	0.131599	−	0.991303i	$-0.457989\pi$
$599$	8.29286e11	0.263199	0.131599	+	0.991303i	$0.457989\pi$
$600$	0	0
$601$	5.62459e12	1.75855	0.879277	−	0.476311i	$-0.158026\pi$
$601$	5.62459e12	1.75855	0.879277	+	0.476311i	$0.158026\pi$
$602$	− 3.27710e11i	− 0.101696i
$603$	− 4.35728e11i	− 0.134211i
$604$	−9.25557e11	−0.282968
$605$	0	0
$606$	8.80989e10	0.0265365
$607$	4.68777e11i	0.140158i	0.997541	+	0.0700789i	$0.0223251\pi$
$607$	4.68777e11i	0.140158i	−0.997541	+	0.0700789i	$0.977675\pi$
$608$	− 2.65076e12i	− 0.786691i
$609$	1.73320e12	0.510588
$610$	0	0
$611$	9.13159e12	2.65070
$612$	− 2.66394e12i	− 0.767614i
$613$	5.58394e12i	1.59723i	0.601840	+	0.798617i	$0.294434\pi$
$613$	5.58394e12i	1.59723i	−0.601840	+	0.798617i	$0.705566\pi$
$614$	−2.47376e12	−0.702425
$615$	0	0
$616$	1.51215e12	0.423137
$617$	3.36717e12i	0.935367i	0.883896	+	0.467683i	$0.154911\pi$
$617$	3.36717e12i	0.935367i	−0.883896	+	0.467683i	$0.845089\pi$
$618$	− 9.16031e11i	− 0.252617i
$619$	5.66928e12	1.55210	0.776051	−	0.630671i	$-0.217220\pi$
$619$	5.66928e12	1.55210	0.776051	+	0.630671i	$0.217220\pi$
$620$	0	0
$621$	1.83709e11	0.0495700
$622$	9.46512e11i	0.253553i
$623$	− 7.16909e11i	− 0.190663i
$624$	−3.03061e12	−0.800201
$625$	0	0
$626$	−5.72168e11	−0.148915
$627$	− 5.45871e12i	− 1.41054i
$628$	1.17409e12i	0.301220i
$629$	6.82812e12	1.73930
$630$	0	0
$631$	−1.06685e12	−0.267899	−0.133950	−	0.990988i	$-0.542766\pi$
$631$	−1.06685e12	−0.267899	−0.133950	+	0.990988i	$0.542766\pi$
$632$	− 1.47535e9i	0 0.000367847i
$633$	1.06694e13i	2.64133i
$634$	−2.87325e12	−0.706273
$635$	0	0
$636$	−7.13941e12	−1.73024
$637$	9.49340e11i	0.228452i
$638$	− 2.56442e12i	− 0.612768i
$639$	1.98172e12	0.470205
$640$	0	0
$641$	−7.83632e12	−1.83337	−0.916686	−	0.399607i	$-0.869147\pi$
$641$	−7.83632e12	−1.83337	−0.916686	+	0.399607i	$0.869147\pi$
$642$	2.62962e12i	0.610921i
$643$	7.05971e12i	1.62869i	0.580383	+	0.814343i	$0.302903\pi$
$643$	7.05971e12i	1.62869i	−0.580383	+	0.814343i	$0.697097\pi$
$644$	−8.67188e11	−0.198668
$645$	0	0
$646$	1.72547e12	0.389817
$647$	− 2.77314e12i	− 0.622161i	−0.950384	−	0.311081i	$-0.899309\pi$
$647$	− 2.77314e12i	− 0.622161i	0.950384	−	0.311081i	$-0.100691\pi$
$648$	4.00859e12i	0.893108i
$649$	1.61321e12	0.356935
$650$	0	0
$651$	1.63440e12	0.356651
$652$	3.62179e12i	0.784891i
$653$	3.09564e12i	0.666257i	0.942882	+	0.333128i	$0.108104\pi$
$653$	3.09564e12i	0.666257i	−0.942882	+	0.333128i	$0.891896\pi$
$654$	3.61785e12	0.773305
$655$	0	0
$656$	2.26227e11	0.0476954
$657$	3.92102e12i	0.821021i
$658$	1.45019e12i	0.301585i
$659$	4.80261e12	0.991958	0.495979	−	0.868335i	$-0.334809\pi$
$659$	4.80261e12	0.991958	0.495979	+	0.868335i	$0.334809\pi$
$660$	0	0
$661$	−5.13389e12	−1.04602	−0.523010	−	0.852327i	$-0.675191\pi$
$661$	−5.13389e12	−1.04602	−0.523010	+	0.852327i	$0.675191\pi$
$662$	2.30212e12i	0.465872i
$663$	− 1.17027e13i	− 2.35221i
$664$	5.14342e12	1.02682
$665$	0	0
$666$	3.82444e12	0.753241
$667$	3.38488e12i	0.662181i
$668$	1.94908e12i	0.378735i
$669$	−4.02404e12	−0.776685
$670$	0	0
$671$	4.42755e12	0.843164
$672$	− 2.85516e12i	− 0.540093i
$673$	4.43802e12i	0.833915i	0.908926	+	0.416957i	$0.136904\pi$
$673$	4.43802e12i	0.833915i	−0.908926	+	0.416957i	$0.863096\pi$
$674$	4.00277e12	0.747122
$675$	0	0
$676$	−6.49609e12	−1.19644
$677$	4.70675e12i	0.861136i	0.902558	+	0.430568i	$0.141687\pi$
$677$	4.70675e12i	0.861136i	−0.902558	+	0.430568i	$0.858313\pi$
$678$	3.03834e12i	0.552207i
$679$	−2.15126e12	−0.388399
$680$	0	0
$681$	7.71632e12	1.37483
$682$	− 2.41824e12i	− 0.428025i
$683$	6.12667e11i	0.107729i	0.998548	+	0.0538644i	$0.0171539\pi$
$683$	6.12667e11i	0.107729i	−0.998548	+	0.0538644i	$0.982846\pi$
$684$	−3.20411e12	−0.559699
$685$	0	0
$686$	−1.50765e11	−0.0259922
$687$	− 3.57397e12i	− 0.612133i
$688$	− 1.17764e12i	− 0.200385i
$689$	−1.52639e13	−2.58035
$690$	0	0
$691$	2.69919e12	0.450383	0.225191	−	0.974315i	$-0.427699\pi$
$691$	2.69919e12	0.450383	0.225191	+	0.974315i	$0.427699\pi$
$692$	1.48510e12i	0.246194i
$693$	− 2.86148e12i	− 0.471293i
$694$	−4.72586e12	−0.773327
$695$	0	0
$696$	−7.11869e12	−1.14990
$697$	8.73576e11i	0.140202i
$698$	1.13375e12i	0.180788i
$699$	−9.95064e12	−1.57654
$700$	0	0
$701$	−5.78506e12	−0.904850	−0.452425	−	0.891802i	$-0.649441\pi$
$701$	−5.78506e12	−0.904850	−0.452425	+	0.891802i	$0.649441\pi$
$702$	3.58886e11i	0.0557750i
$703$	− 8.21267e12i	− 1.26819i
$704$	−1.15141e12	−0.176666
$705$	0	0
$706$	−4.86772e12	−0.737403
$707$	− 9.91715e10i	− 0.0149279i
$708$	− 1.94566e12i	− 0.291016i
$709$	3.72656e12	0.553860	0.276930	−	0.960890i	$-0.410683\pi$
$709$	3.72656e12	0.553860	0.276930	+	0.960890i	$0.410683\pi$
$710$	0	0
$711$	−2.79184e9	−0.000409711 0
$712$	2.94453e12i	0.429394i
$713$	3.19192e12i	0.462541i
$714$	1.85852e12	0.267624
$715$	0	0
$716$	7.64532e12	1.08714
$717$	7.44980e12i	1.05271i
$718$	− 2.14092e12i	− 0.300636i
$719$	−1.33255e13	−1.85953	−0.929765	−	0.368154i	$-0.879990\pi$
$719$	−1.33255e13	−1.85953	−0.929765	+	0.368154i	$0.879990\pi$
$720$	0	0
$721$	−1.03116e12	−0.142108
$722$	1.43952e12i	0.197151i
$723$	− 1.91916e13i	− 2.61209i
$724$	−3.86089e12	−0.522233
$725$	0	0
$726$	−3.67012e12	−0.490304
$727$	2.39852e12i	0.318448i	0.987242	+	0.159224i	$0.0508992\pi$
$727$	2.39852e12i	0.318448i	−0.987242	+	0.159224i	$0.949101\pi$
$728$	− 3.89918e12i	− 0.514497i
$729$	6.81442e12	0.893625
$730$	0	0
$731$	4.54748e12	0.589037
$732$	− 5.33998e12i	− 0.687448i
$733$	7.93815e12i	1.01567i	0.861455	+	0.507834i	$0.169554\pi$
$733$	7.93815e12i	1.01567i	−0.861455	+	0.507834i	$0.830446\pi$
$734$	2.45644e12	0.312373
$735$	0	0
$736$	5.57603e12	0.700447
$737$	1.49119e12i	0.186178i
$738$	4.89292e11i	0.0607175i
$739$	2.20371e12	0.271803	0.135902	−	0.990722i	$-0.456607\pi$
$739$	2.20371e12	0.271803	0.135902	+	0.990722i	$0.456607\pi$
$740$	0	0
$741$	−1.40757e13	−1.71509
$742$	− 2.42407e12i	− 0.293581i
$743$	− 1.09079e12i	− 0.131308i	−0.997842	−	0.0656540i	$-0.979087\pi$
$743$	− 1.09079e12i	− 0.131308i	0.997842	−	0.0656540i	$-0.0209133\pi$
$744$	−6.71290e12	−0.803215
$745$	0	0
$746$	−2.22657e12	−0.263215
$747$	− 9.73305e12i	− 1.14368i
$748$	9.11678e12i	1.06484i
$749$	2.96012e12	0.343670
$750$	0	0
$751$	−3.09647e11	−0.0355212	−0.0177606	−	0.999842i	$-0.505654\pi$
$751$	−3.09647e11	−0.0355212	−0.0177606	+	0.999842i	$0.505654\pi$
$752$	5.21136e12i	0.594252i
$753$	− 1.51783e13i	− 1.72046i
$754$	−6.61254e12	−0.745071
$755$	0	0
$756$	1.88960e11	0.0210389
$757$	− 1.44340e12i	− 0.159755i	−0.996805	−	0.0798777i	$-0.974547\pi$
$757$	− 1.44340e12i	− 0.159755i	0.996805	−	0.0798777i	$-0.0254530\pi$
$758$	4.39299e11i	0.0483336i
$759$	1.14827e13	1.25591
$760$	0	0
$761$	−2.27862e12	−0.246287	−0.123143	−	0.992389i	$-0.539297\pi$
$761$	−2.27862e12	−0.246287	−0.123143	+	0.992389i	$0.539297\pi$
$762$	− 6.67302e12i	− 0.717010i
$763$	− 4.07256e12i	− 0.435018i
$764$	−7.26051e12	−0.770987
$765$	0	0
$766$	−4.33873e12	−0.455337
$767$	− 4.15978e12i	− 0.434001i
$768$	8.02053e12i	0.831912i
$769$	−1.09547e13	−1.12962	−0.564809	−	0.825221i	$-0.691050\pi$
$769$	−1.09547e13	−1.12962	−0.564809	+	0.825221i	$0.691050\pi$
$770$	0	0
$771$	2.10677e13	2.14720
$772$	1.90228e12i	0.192751i
$773$	7.52114e12i	0.757663i	0.925466	+	0.378831i	$0.123674\pi$
$773$	7.52114e12i	0.757663i	−0.925466	+	0.378831i	$0.876326\pi$
$774$	2.54705e12	0.255096
$775$	0	0
$776$	8.83576e12	0.874714
$777$	− 8.84595e12i	− 0.870662i
$778$	− 4.60211e12i	− 0.450348i
$779$	1.05071e12	0.102227
$780$	0	0
$781$	−6.78201e12	−0.652272
$782$	3.62962e12i	0.347081i
$783$	− 7.37564e11i	− 0.0701248i
$784$	−5.41785e11	−0.0512158
$785$	0	0
$786$	−1.49971e12	−0.140154
$787$	− 1.85303e12i	− 0.172185i	−0.996287	−	0.0860926i	$-0.972562\pi$
$787$	− 1.85303e12i	− 0.172185i	0.996287	−	0.0860926i	$-0.0274381\pi$
$788$	− 1.06301e13i	− 0.982129i
$789$	−2.38142e12	−0.218771
$790$	0	0
$791$	3.42021e12	0.310641
$792$	1.17528e13i	1.06140i
$793$	− 1.14168e13i	− 1.02521i
$794$	−7.09097e12	−0.633159
$795$	0	0
$796$	−6.52073e12	−0.575688
$797$	1.84378e13i	1.61863i	0.587377	+	0.809314i	$0.300161\pi$
$797$	1.84378e13i	1.61863i	−0.587377	+	0.809314i	$0.699839\pi$
$798$	− 2.23537e12i	− 0.195136i
$799$	−2.01237e13	−1.74682
$800$	0	0
$801$	5.57202e12	0.478262
$802$	3.38220e12i	0.288679i
$803$	− 1.34189e13i	− 1.13893i
$804$	1.79850e12	0.151795
$805$	0	0
$806$	−6.23560e12	−0.520440
$807$	− 2.41866e13i	− 2.00745i
$808$	4.07323e11i	0.0336192i
$809$	1.03419e13	0.848856	0.424428	−	0.905462i	$-0.360475\pi$
$809$	1.03419e13	0.848856	0.424428	+	0.905462i	$0.360475\pi$
$810$	0	0
$811$	−2.31795e13	−1.88153	−0.940764	−	0.339062i	$-0.889890\pi$
$811$	−2.31795e13	−1.88153	−0.940764	+	0.339062i	$0.889890\pi$
$812$	3.48163e12i	0.281048i
$813$	− 2.62993e13i	− 2.11123i
$814$	−1.30884e13	−1.04490
$815$	0	0
$816$	6.67869e12	0.527334
$817$	− 5.46958e12i	− 0.429492i
$818$	3.26250e12i	0.254777i
$819$	−7.37854e12	−0.573051
$820$	0	0
$821$	1.10059e13	0.845436	0.422718	−	0.906261i	$-0.361076\pi$
$821$	1.10059e13	0.845436	0.422718	+	0.906261i	$0.361076\pi$
$822$	− 6.55470e12i	− 0.500760i
$823$	2.30119e13i	1.74845i	0.485523	+	0.874224i	$0.338629\pi$
$823$	2.30119e13i	1.74845i	−0.485523	+	0.874224i	$0.661371\pi$
$824$	4.23525e12	0.320041
$825$	0	0
$826$	6.60618e11	0.0493787
$827$	− 6.58898e12i	− 0.489827i	−0.969545	−	0.244914i	$-0.921240\pi$
$827$	− 6.58898e12i	− 0.489827i	0.969545	−	0.244914i	$-0.0787596\pi$
$828$	− 6.74003e12i	− 0.498340i
$829$	1.32427e13	0.973829	0.486915	−	0.873450i	$-0.338122\pi$
$829$	1.32427e13	0.973829	0.486915	+	0.873450i	$0.338122\pi$
$830$	0	0
$831$	4.24304e12	0.308654
$832$	2.96899e12i	0.214810i
$833$	− 2.09210e12i	− 0.150550i
$834$	1.08311e13	0.775222
$835$	0	0
$836$	1.09654e13	0.776419
$837$	− 6.95520e11i	− 0.0489830i
$838$	− 4.74058e12i	− 0.332073i
$839$	5.05558e12	0.352243	0.176122	−	0.984368i	$-0.443645\pi$
$839$	5.05558e12	0.352243	0.176122	+	0.984368i	$0.443645\pi$
$840$	0	0
$841$	−9.17397e11	−0.0632376
$842$	2.26127e12i	0.155042i
$843$	− 1.51422e12i	− 0.103268i
$844$	−2.14326e13	−1.45390
$845$	0	0
$846$	−1.12713e13	−0.756499
$847$	4.13139e12i	0.275817i
$848$	− 8.71104e12i	− 0.578480i
$849$	−1.40910e13	−0.930802
$850$	0	0
$851$	1.72758e13	1.12916
$852$	8.17966e12i	0.531811i
$853$	1.03049e13i	0.666456i	0.942846	+	0.333228i	$0.108138\pi$
$853$	1.03049e13i	0.666456i	−0.942846	+	0.333228i	$0.891862\pi$
$854$	1.81310e12	0.116644
$855$	0	0
$856$	−1.21580e13	−0.773979
$857$	1.66788e13i	1.05621i	0.849179	+	0.528105i	$0.177097\pi$
$857$	1.66788e13i	1.05621i	−0.849179	+	0.528105i	$0.822903\pi$
$858$	2.24322e13i	1.41312i
$859$	2.36677e13	1.48316	0.741579	−	0.670865i	$-0.234077\pi$
$859$	2.36677e13	1.48316	0.741579	+	0.670865i	$0.234077\pi$
$860$	0	0
$861$	1.13173e12	0.0701827
$862$	− 9.38476e12i	− 0.578949i
$863$	1.26428e13i	0.775880i	0.921685	+	0.387940i	$0.126813\pi$
$863$	1.26428e13i	0.775880i	−0.921685	+	0.387940i	$0.873187\pi$
$864$	−1.21502e12	−0.0741772
$865$	0	0
$866$	1.58855e12	0.0959776
$867$	2.56832e12i	0.154370i
$868$	3.28316e12i	0.196315i
$869$	9.55450e9	0.000568354 0
$870$	0	0
$871$	3.84514e12	0.226376
$872$	1.67271e13i	0.979705i
$873$	− 1.67202e13i	− 0.974264i
$874$	4.36561e12	0.253071
$875$	0	0
$876$	−1.61842e13	−0.928589
$877$	− 2.21629e13i	− 1.26511i	−0.774515	−	0.632555i	$-0.782006\pi$
$877$	− 2.21629e13i	− 1.26511i	0.774515	−	0.632555i	$-0.217994\pi$
$878$	− 1.16691e12i	− 0.0662695i
$879$	3.40082e13	1.92147
$880$	0	0
$881$	−1.87132e13	−1.04654	−0.523272	−	0.852166i	$-0.675289\pi$
$881$	−1.87132e13	−1.04654	−0.523272	+	0.852166i	$0.675289\pi$
$882$	− 1.17179e12i	− 0.0651991i
$883$	− 1.66483e13i	− 0.921611i	−0.887501	−	0.460805i	$-0.847561\pi$
$883$	− 1.66483e13i	− 0.921611i	0.887501	−	0.460805i	$-0.152439\pi$
$884$	2.35083e13	1.29475
$885$	0	0
$886$	−1.49050e12	−0.0812604
$887$	1.58859e13i	0.861698i	0.902424	+	0.430849i	$0.141786\pi$
$887$	1.58859e13i	0.861698i	−0.902424	+	0.430849i	$0.858214\pi$
$888$	3.63326e13i	1.96082i
$889$	−7.51171e12	−0.403349
$890$	0	0
$891$	−2.59600e13	−1.37993
$892$	− 8.08344e12i	− 0.427518i
$893$	2.42042e13i	1.27368i
$894$	4.55284e12	0.238376
$895$	0	0
$896$	6.99384e12	0.362518
$897$	− 2.96091e13i	− 1.52707i
$898$	− 8.34003e12i	− 0.427980i
$899$	1.28151e13	0.654339
$900$	0	0
$901$	3.36377e13	1.70046
$902$	− 1.67450e12i	− 0.0842278i
$903$	− 5.89134e12i	− 0.294862i
$904$	−1.40477e13	−0.699595
$905$	0	0
$906$	5.01873e12	0.247467
$907$	3.65370e13i	1.79267i	0.443381	+	0.896333i	$0.353779\pi$
$907$	3.65370e13i	1.79267i	−0.443381	+	0.896333i	$0.646221\pi$
$908$	1.55005e13i	0.756760i
$909$	7.70789e11	0.0374454
$910$	0	0
$911$	2.09138e13	1.00600	0.503002	−	0.864286i	$-0.332229\pi$
$911$	2.09138e13	1.00600	0.503002	+	0.864286i	$0.332229\pi$
$912$	− 8.03294e12i	− 0.384501i
$913$	3.33093e13i	1.58653i
$914$	−5.90199e12	−0.279731
$915$	0	0
$916$	7.17935e12	0.336942
$917$	1.68820e12i	0.0788427i
$918$	− 7.90894e11i	− 0.0367558i
$919$	1.22511e12	0.0566571	0.0283286	−	0.999599i	$-0.490982\pi$
$919$	1.22511e12	0.0566571	0.0283286	+	0.999599i	$0.490982\pi$
$920$	0	0
$921$	−4.44716e13	−2.03664
$922$	7.74276e12i	0.352863i
$923$	1.74879e13i	0.793105i
$924$	1.18109e13	0.533041
$925$	0	0
$926$	8.67335e12	0.387648
$927$	− 8.01448e12i	− 0.356465i
$928$	− 2.23869e13i	− 0.990896i
$929$	−9.53162e12	−0.419852	−0.209926	−	0.977717i	$-0.567322\pi$
$929$	−9.53162e12	−0.419852	−0.209926	+	0.977717i	$0.567322\pi$
$930$	0	0
$931$	−2.51632e12	−0.109772
$932$	− 1.99887e13i	− 0.867788i
$933$	1.70157e13i	0.735163i
$934$	1.82637e13	0.785287
$935$	0	0
$936$	3.03056e13	1.29057
$937$	9.70345e12i	0.411242i	0.978632	+	0.205621i	$0.0659215\pi$
$937$	9.70345e12i	0.411242i	−0.978632	+	0.205621i	$0.934079\pi$
$938$	6.10650e11i	0.0257561i
$939$	−1.02860e13	−0.431770
$940$	0	0
$941$	−2.29625e13	−0.954698	−0.477349	−	0.878714i	$-0.658402\pi$
$941$	−2.29625e13	−0.954698	−0.477349	+	0.878714i	$0.658402\pi$
$942$	− 6.36639e12i	− 0.263429i
$943$	2.21024e12i	0.0910198i
$944$	2.37397e12	0.0972973
$945$	0	0
$946$	−8.71676e12	−0.353871
$947$	− 1.40763e13i	− 0.568738i	−0.958715	−	0.284369i	$-0.908216\pi$
$947$	− 1.40763e13i	− 0.568738i	0.958715	−	0.284369i	$-0.0917841\pi$
$948$	− 1.15235e10i	0 0.000463391i
$949$	−3.46015e13	−1.38483
$950$	0	0
$951$	−5.16534e13	−2.04780
$952$	8.59281e12i	0.339054i
$953$	9.86435e12i	0.387392i	0.981062	+	0.193696i	$0.0620475\pi$
$953$	9.86435e12i	0.387392i	−0.981062	+	0.193696i	$0.937953\pi$
$954$	1.88406e13	0.736421
$955$	0	0
$956$	−1.49651e13	−0.579453
$957$	− 4.61014e13i	− 1.77668i
$958$	1.27582e13i	0.489378i
$959$	−7.37852e12	−0.281699
$960$	0	0
$961$	−1.43550e13	−0.542937
$962$	3.37493e13i	1.27051i
$963$	2.30069e13i	0.862065i
$964$	3.85518e13	1.43780
$965$	0	0
$966$	4.70224e12	0.173743
$967$	2.37375e12i	0.0873002i	0.999047	+	0.0436501i	$0.0138987\pi$
$967$	2.37375e12i	0.0873002i	−0.999047	+	0.0436501i	$0.986101\pi$
$968$	− 1.69687e13i	− 0.621168i
$969$	3.10193e13	1.13025
$970$	0	0
$971$	4.45895e13	1.60970	0.804852	−	0.593476i	$-0.202245\pi$
$971$	4.45895e13	1.60970	0.804852	+	0.593476i	$0.202245\pi$
$972$	2.97608e13i	1.06942i
$973$	− 1.21924e13i	− 0.436096i
$974$	−4.89939e12	−0.174432
$975$	0	0
$976$	6.51550e12	0.229839
$977$	− 8.90599e11i	− 0.0312721i	−0.999878	−	0.0156360i	$-0.995023\pi$
$977$	− 8.90599e11i	− 0.0312721i	0.999878	−	0.0156360i	$-0.00497731\pi$
$978$	− 1.96388e13i	− 0.686420i
$979$	−1.90691e13	−0.663449
$980$	0	0
$981$	3.16531e13	1.09120
$982$	− 2.45117e13i	− 0.841146i
$983$	8.23794e12i	0.281402i	0.990052	+	0.140701i	$0.0449357\pi$
$983$	8.23794e12i	0.281402i	−0.990052	+	0.140701i	$0.955064\pi$
$984$	−4.64832e12	−0.158059
$985$	0	0
$986$	1.45724e13	0.491003
$987$	2.60706e13i	0.874428i
$988$	− 2.82751e13i	− 0.944056i
$989$	1.15056e13	0.382407
$990$	0	0
$991$	8.90224e12	0.293203	0.146601	−	0.989196i	$-0.453167\pi$
$991$	8.90224e12	0.293203	0.146601	+	0.989196i	$0.453167\pi$
$992$	− 2.11108e13i	− 0.692152i
$993$	4.13859e13i	1.35077i
$994$	−2.77727e12	−0.0902359
$995$	0	0
$996$	4.01738e13	1.29353
$997$	− 1.45450e13i	− 0.466216i	−0.972451	−	0.233108i	$-0.925110\pi$
$997$	− 1.45450e13i	− 0.466216i	0.972451	−	0.233108i	$-0.0748895\pi$
$998$	1.73965e11i	0.00555106i
$999$	−3.76440e12	−0.119578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.b.99.2		4
5.2	odd	4		7.10.a.a.1.2	✓	2
5.3	odd	4		175.10.a.b.1.1		2
5.4	even	2	inner	175.10.b.b.99.3		4
15.2	even	4		63.10.a.d.1.1		2
20.7	even	4		112.10.a.e.1.2		2
35.2	odd	12		49.10.c.c.18.1		4
35.12	even	12		49.10.c.b.18.1		4
35.17	even	12		49.10.c.b.30.1		4
35.27	even	4		49.10.a.b.1.2		2
35.32	odd	12		49.10.c.c.30.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.2	✓	2	5.2	odd	4
49.10.a.b.1.2		2	35.27	even	4
49.10.c.b.18.1		4	35.12	even	12
49.10.c.b.30.1		4	35.17	even	12
49.10.c.c.18.1		4	35.2	odd	12
49.10.c.c.30.1		4	35.32	odd	12
63.10.a.d.1.1		2	15.2	even	4
112.10.a.e.1.2		2	20.7	even	4
175.10.a.b.1.1		2	5.3	odd	4
175.10.b.b.99.2		4	1.1	even	1	trivial
175.10.b.b.99.3		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-10.8924i q^{2} -195.817i q^{3} +393.355 q^{4} -2132.92 q^{6} +2401.00i q^{7} -9861.52i q^{8} -18661.3 q^{9} +O(q^{10})\)	\(q-10.8924i q^{2} -195.817i q^{3} +393.355 q^{4} -2132.92 q^{6} +2401.00i q^{7} -9861.52i q^{8} -18661.3 q^{9} +63864.3 q^{11} -77025.5i q^{12} -164679. i q^{13} +26152.8 q^{14} +93981.5 q^{16} +362910. i q^{17} +203267. i q^{18} +436498. q^{19} +470156. q^{21} -695638. i q^{22} +918199. i q^{23} -1.93105e6 q^{24} -1.79375e6 q^{26} -200076. i q^{27} +944445. i q^{28} +3.68643e6 q^{29} +3.47629e6 q^{31} -6.07279e6i q^{32} -1.25057e7i q^{33} +3.95298e6 q^{34} -7.34049e6 q^{36} -1.88149e7i q^{37} -4.75453e6i q^{38} -3.22469e7 q^{39} +2.40714e6 q^{41} -5.12115e6i q^{42} -1.25306e7i q^{43} +2.51213e7 q^{44} +1.00014e7 q^{46} +5.54509e7i q^{47} -1.84032e7i q^{48} -5.76480e6 q^{49} +7.10639e7 q^{51} -6.47772e7i q^{52} -9.26889e7i q^{53} -2.17931e6 q^{54} +2.36775e7 q^{56} -8.54737e7i q^{57} -4.01542e7i q^{58} +2.52600e7 q^{59} +6.93275e7 q^{61} -3.78653e7i q^{62} -4.48057e7i q^{63} -1.80290e7 q^{64} -1.36218e8 q^{66} +2.33494e7i q^{67} +1.42752e8i q^{68} +1.79799e8 q^{69} -1.06194e8 q^{71} +1.84028e8i q^{72} -2.10115e8i q^{73} -2.04940e8 q^{74} +1.71699e8 q^{76} +1.53338e8i q^{77} +3.51247e8i q^{78} +149606. q^{79} -4.06488e8 q^{81} -2.62197e7i q^{82} +5.21565e8i q^{83} +1.84938e8 q^{84} -1.36489e8 q^{86} -7.21865e8i q^{87} -6.29799e8i q^{88} -2.98587e8 q^{89} +3.95394e8 q^{91} +3.61178e8i q^{92} -6.80716e8i q^{93} +6.03996e8 q^{94} -1.18915e9 q^{96} +8.95983e8i q^{97} +6.27928e7i q^{98} -1.19179e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9}+O(q^{10}) \) 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9	\( 4 q + 1240 q^{4} - 7976 q^{6} - 22076 q^{9} + 70632 q^{11} - 28812 q^{14} - 1504 q^{16} + 1850852 q^{19} + 412972 q^{21} - 6602592 q^{24} - 8254848 q^{26} + 20007168 q^{29} + 4934520 q^{31} + 4493352 q^{34} - 11225432 q^{36} - 94835888 q^{39} - 38206896 q^{41} + 37301952 q^{44} + 24735168 q^{46} - 23059204 q^{49} + 119942712 q^{51} - 105668944 q^{54} - 12562032 q^{56} + 14138436 q^{59} + 88632772 q^{61} - 294834304 q^{64} - 166516928 q^{66} + 390362304 q^{69} + 412987632 q^{71} - 7143048 q^{74} + 565023536 q^{76} - 937070192 q^{79} - 1171491268 q^{81} + 250357072 q^{84} - 833661216 q^{86} - 1272534792 q^{89} + 127397060 q^{91} + 304446384 q^{94} - 3429962368 q^{96} - 2818835720 q^{99}+O(q^{100}) \) 4 * q + 1240 * q^4 - 7976 * q^6 - 22076 * q^9 + 70632 * q^11 - 28812 * q^14 - 1504 * q^16 + 1850852 * q^19 + 412972 * q^21 - 6602592 * q^24 - 8254848 * q^26 + 20007168 * q^29 + 4934520 * q^31 + 4493352 * q^34 - 11225432 * q^36 - 94835888 * q^39 - 38206896 * q^41 + 37301952 * q^44 + 24735168 * q^46 - 23059204 * q^49 + 119942712 * q^51 - 105668944 * q^54 - 12562032 * q^56 + 14138436 * q^59 + 88632772 * q^61 - 294834304 * q^64 - 166516928 * q^66 + 390362304 * q^69 + 412987632 * q^71 - 7143048 * q^74 + 565023536 * q^76 - 937070192 * q^79 - 1171491268 * q^81 + 250357072 * q^84 - 833661216 * q^86 - 1272534792 * q^89 + 127397060 * q^91 + 304446384 * q^94 - 3429962368 * q^96 - 2818835720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more