LMFDB - Embedded newform 115.4.b.a.24.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.b (of order $2$, degree $1$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.18
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.231361i q^{2} -2.18914i q^{3} +7.94647 q^{4} +(-10.8138 + 2.83950i) q^{5} +0.506482 q^{6} -29.8467i q^{7} +3.68940i q^{8} +22.2077 q^{9} +O(q^{10})$	\(q+0.231361i q^{2} -2.18914i q^{3} +7.94647 q^{4} +(-10.8138 + 2.83950i) q^{5} +0.506482 q^{6} -29.8467i q^{7} +3.68940i q^{8} +22.2077 q^{9} +(-0.656949 - 2.50188i) q^{10} -17.9942 q^{11} -17.3959i q^{12} -35.4826i q^{13} +6.90538 q^{14} +(6.21605 + 23.6728i) q^{15} +62.7182 q^{16} -68.5478i q^{17} +5.13799i q^{18} -3.31172 q^{19} +(-85.9312 + 22.5640i) q^{20} -65.3387 q^{21} -4.16316i q^{22} -23.0000i q^{23} +8.07660 q^{24} +(108.875 - 61.4112i) q^{25} +8.20929 q^{26} -107.722i q^{27} -237.176i q^{28} -96.3930 q^{29} +(-5.47697 + 1.43815i) q^{30} +191.898 q^{31} +44.0257i q^{32} +39.3918i q^{33} +15.8593 q^{34} +(84.7497 + 322.755i) q^{35} +176.473 q^{36} +250.817i q^{37} -0.766204i q^{38} -77.6763 q^{39} +(-10.4760 - 39.8962i) q^{40} -96.7284 q^{41} -15.1168i q^{42} +84.4844i q^{43} -142.990 q^{44} +(-240.148 + 63.0586i) q^{45} +5.32131 q^{46} +587.542i q^{47} -137.299i q^{48} -547.828 q^{49} +(14.2082 + 25.1893i) q^{50} -150.061 q^{51} -281.961i q^{52} +429.652i q^{53} +24.9228 q^{54} +(194.585 - 51.0945i) q^{55} +110.116 q^{56} +7.24981i q^{57} -22.3016i q^{58} +587.627 q^{59} +(49.3957 + 188.115i) q^{60} -613.935 q^{61} +44.3977i q^{62} -662.827i q^{63} +491.560 q^{64} +(100.753 + 383.700i) q^{65} -9.11374 q^{66} +800.098i q^{67} -544.713i q^{68} -50.3502 q^{69} +(-74.6731 + 19.6078i) q^{70} -79.4669 q^{71} +81.9329i q^{72} -957.564i q^{73} -58.0293 q^{74} +(-134.438 - 238.341i) q^{75} -26.3165 q^{76} +537.068i q^{77} -17.9713i q^{78} +938.245 q^{79} +(-678.219 + 178.088i) q^{80} +363.788 q^{81} -22.3792i q^{82} -396.624i q^{83} -519.212 q^{84} +(194.641 + 741.259i) q^{85} -19.5464 q^{86} +211.018i q^{87} -66.3877i q^{88} +292.699 q^{89} +(-14.5893 - 55.5610i) q^{90} -1059.04 q^{91} -182.769i q^{92} -420.091i q^{93} -135.935 q^{94} +(35.8121 - 9.40362i) q^{95} +96.3784 q^{96} +82.7907i q^{97} -126.746i q^{98} -399.609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.231361i			0.0817986i	0.999163	+	0.0408993i	$0.0130223\pi$
$2$			0.231361i			0.0817986i	−0.999163	+	0.0408993i	$0.986978\pi$
$3$		−	2.18914i		−	0.421300i	−0.977562	−	0.210650i	$-0.932442\pi$
$3$		−	2.18914i		−	0.421300i	0.977562	−	0.210650i	$-0.0675580\pi$
$4$	7.94647			0.993309
$5$	−10.8138	+	2.83950i	−0.967211	+	0.253972i
$5$	−10.8138	+	2.83950i	−0.967211	+	0.253972i
$6$	0.506482			0.0344617
$7$		−	29.8467i		−	1.61157i	−0.592206	−	0.805786i	$-0.701743\pi$
$7$		−	29.8467i		−	1.61157i	0.592206	−	0.805786i	$-0.298257\pi$
$8$			3.68940i			0.163050i
$9$	22.2077			0.822506
$10$	−0.656949	−	2.50188i	−0.0207746	−	0.0791165i
$11$	−17.9942			−0.493223			−0.246612	−	0.969114i	$-0.579317\pi$
$11$	−17.9942			−0.493223			−0.246612	+	0.969114i	$0.579317\pi$
$12$		−	17.3959i		−	0.418481i
$13$		−	35.4826i		−	0.757007i	−0.925600	−	0.378504i	$-0.876439\pi$
$13$		−	35.4826i		−	0.757007i	0.925600	−	0.378504i	$-0.123561\pi$
$14$	6.90538			0.131824
$15$	6.21605	+	23.6728i	0.106999	+	0.407486i
$16$	62.7182			0.979972
$17$		−	68.5478i		−	0.977957i	−0.872296	−	0.488979i	$-0.837370\pi$
$17$		−	68.5478i		−	0.977957i	0.872296	−	0.488979i	$-0.162630\pi$
$18$			5.13799i			0.0672798i
$19$	−3.31172			−0.0399874			−0.0199937	−	0.999800i	$-0.506365\pi$
$19$	−3.31172			−0.0399874			−0.0199937	+	0.999800i	$0.506365\pi$
$20$	−85.9312	+	22.5640i	−0.960740	+	0.252273i
$21$	−65.3387			−0.678956
$22$		−	4.16316i		−	0.0403449i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	8.07660			0.0686929
$25$	108.875	−	61.4112i	0.870996	−	0.491290i
$26$	8.20929			0.0619221
$27$		−	107.722i		−	0.767822i
$28$		−	237.176i		−	1.60079i
$29$	−96.3930			−0.617232			−0.308616	−	0.951187i	$-0.599866\pi$
$29$	−96.3930			−0.617232			−0.308616	+	0.951187i	$0.599866\pi$
$30$	−5.47697	+	1.43815i	−0.0333318	+	0.00875232i
$31$	191.898			1.11180			0.555901	−	0.831249i	$-0.312373\pi$
$31$	191.898			1.11180			0.555901	+	0.831249i	$0.312373\pi$
$32$			44.0257i			0.243210i
$33$			39.3918i			0.207795i
$34$	15.8593			0.0799955
$35$	84.7497	+	322.755i	0.409295	+	1.55873i
$36$	176.473			0.817003
$37$			250.817i			1.11443i	0.830367	+	0.557217i	$0.188131\pi$
$37$			250.817i			1.11443i	−0.830367	+	0.557217i	$0.811869\pi$
$38$		−	0.766204i		−	0.00327091i
$39$	−77.6763			−0.318927
$40$	−10.4760	−	39.8962i	−0.0414101	−	0.157704i
$41$	−96.7284			−0.368450			−0.184225	−	0.982884i	$-0.558977\pi$
$41$	−96.7284			−0.368450			−0.184225	+	0.982884i	$0.558977\pi$
$42$		−	15.1168i		−	0.0555376i
$43$			84.4844i			0.299622i	0.988715	+	0.149811i	$0.0478666\pi$
$43$			84.4844i			0.299622i	−0.988715	+	0.149811i	$0.952133\pi$
$44$	−142.990			−0.489923
$45$	−240.148	+	63.0586i	−0.795538	+	0.208894i
$46$	5.32131			0.0170562
$47$			587.542i			1.82344i	0.410808	+	0.911722i	$0.365247\pi$
$47$			587.542i			1.82344i	−0.410808	+	0.911722i	$0.634753\pi$
$48$		−	137.299i		−	0.412862i
$49$	−547.828			−1.59717
$50$	14.2082	+	25.1893i	0.0401868	+	0.0712462i
$51$	−150.061			−0.412013
$52$		−	281.961i		−	0.751942i
$53$			429.652i			1.11353i	0.830669	+	0.556766i	$0.187958\pi$
$53$			429.652i			1.11353i	−0.830669	+	0.556766i	$0.812042\pi$
$54$	24.9228			0.0628067
$55$	194.585	−	51.0945i	0.477051	−	0.125265i
$56$	110.116			0.262767
$57$			7.24981i			0.0168467i
$58$		−	22.3016i		−	0.0504887i
$59$	587.627			1.29665			0.648327	−	0.761362i	$-0.275469\pi$
$59$	587.627			1.29665			0.648327	+	0.761362i	$0.275469\pi$
$60$	49.3957	+	188.115i	0.106283	+	0.404760i
$61$	−613.935			−1.28863			−0.644314	−	0.764761i	$-0.722857\pi$
$61$	−613.935			−1.28863			−0.644314	+	0.764761i	$0.722857\pi$
$62$			44.3977i			0.0909438i
$63$		−	662.827i		−	1.32553i
$64$	491.560			0.960078
$65$	100.753	+	383.700i	0.192259	+	0.732186i
$66$	−9.11374			−0.0169973
$67$			800.098i			1.45892i	0.684024	+	0.729460i	$0.260228\pi$
$67$			800.098i			1.45892i	−0.684024	+	0.729460i	$0.739772\pi$
$68$		−	544.713i		−	0.971414i
$69$	−50.3502			−0.0878471
$70$	−74.6731	+	19.6078i	−0.127502	+	0.0334797i
$71$	−79.4669			−0.132831			−0.0664154	−	0.997792i	$-0.521156\pi$
$71$	−79.4669			−0.132831			−0.0664154	+	0.997792i	$0.521156\pi$
$72$			81.9329i			0.134109i
$73$		−	957.564i		−	1.53526i	−0.640890	−	0.767632i	$-0.721435\pi$
$73$		−	957.564i		−	1.53526i	0.640890	−	0.767632i	$-0.278565\pi$
$74$	−58.0293			−0.0911590
$75$	−134.438	−	238.341i	−0.206980	−	0.366951i
$76$	−26.3165			−0.0397198
$77$			537.068i			0.794865i
$78$		−	17.9713i		−	0.0260878i
$79$	938.245			1.33621			0.668106	−	0.744066i	$-0.267105\pi$
$79$	938.245			1.33621			0.668106	+	0.744066i	$0.267105\pi$
$80$	−678.219	+	178.088i	−0.947840	+	0.248886i
$81$	363.788			0.499023
$82$		−	22.3792i		−	0.0301386i
$83$		−	396.624i		−	0.524519i	−0.964997	−	0.262260i	$-0.915532\pi$
$83$		−	396.624i		−	0.524519i	0.964997	−	0.262260i	$-0.0844677\pi$
$84$	−519.212			−0.674413
$85$	194.641	+	741.259i	0.248374	+	0.945892i
$86$	−19.5464			−0.0245087
$87$			211.018i			0.260040i
$88$		−	66.3877i		−	0.0804200i
$89$	292.699			0.348607			0.174303	−	0.984692i	$-0.444233\pi$
$89$	292.699			0.348607			0.174303	+	0.984692i	$0.444233\pi$
$90$	−14.5893	−	55.5610i	−0.0170872	−	0.0650738i
$91$	−1059.04			−1.21997
$92$		−	182.769i		−	0.207119i
$93$		−	420.091i		−	0.468402i
$94$	−135.935			−0.149155
$95$	35.8121	−	9.40362i	0.0386763	−	0.0101557i
$96$	96.3784			0.102464
$97$			82.7907i			0.0866610i	0.999061	+	0.0433305i	$0.0137969\pi$
$97$			82.7907i			0.0866610i	−0.999061	+	0.0433305i	$0.986203\pi$
$98$		−	126.746i		−	0.130646i
$99$	−399.609			−0.405679
$100$	865.168	−	488.003i	0.865168	−	0.488003i
$101$	1777.99			1.75165			0.875823	−	0.482633i	$-0.160320\pi$
$101$	1777.99			1.75165			0.875823	+	0.482633i	$0.160320\pi$
$102$		−	34.7182i		−	0.0337021i
$103$		−	397.698i		−	0.380450i	−0.981741	−	0.190225i	$-0.939078\pi$
$103$		−	397.698i		−	0.380450i	0.981741	−	0.190225i	$-0.0609218\pi$
$104$	130.909			0.123430
$105$	706.556	−	185.529i	0.656694	−	0.172436i
$106$	−99.4048			−0.0910854
$107$		−	959.394i		−	0.866805i	−0.901200	−	0.433402i	$-0.857313\pi$
$107$		−	959.394i		−	0.866805i	0.901200	−	0.433402i	$-0.142687\pi$
$108$		−	856.013i		−	0.762684i
$109$	−319.904			−0.281112			−0.140556	−	0.990073i	$-0.544889\pi$
$109$	−319.904			−0.281112			−0.140556	+	0.990073i	$0.544889\pi$
$110$	11.8213	+	45.0194i	0.0102465	+	0.0390221i
$111$	549.073			0.469511
$112$		−	1871.93i		−	1.57930i
$113$		−	1401.54i		−	1.16677i	−0.812194	−	0.583387i	$-0.801727\pi$
$113$		−	1401.54i		−	1.16677i	0.812194	−	0.583387i	$-0.198273\pi$
$114$	−1.67733			−0.00137803
$115$	65.3084	+	248.716i	0.0529569	+	0.201678i
$116$	−765.984			−0.613102
$117$		−	787.985i		−	0.622643i
$118$			135.954i			0.106064i
$119$	−2045.93			−1.57605
$120$	−87.3384	+	22.9335i	−0.0664405	+	0.0174461i
$121$	−1007.21			−0.756731
$122$		−	142.041i		−	0.105408i
$123$			211.752i			0.155228i
$124$	1524.91			1.10436
$125$	−1002.97	+	973.235i	−0.717664	+	0.696390i
$126$	153.352			0.108426
$127$			985.066i			0.688272i	0.938920	+	0.344136i	$0.111828\pi$
$127$			985.066i			0.688272i	−0.938920	+	0.344136i	$0.888172\pi$
$128$			465.934i			0.321743i
$129$	184.948			0.126231
$130$	−88.7733	+	23.3103i	−0.0598918	+	0.0157265i
$131$	−511.288			−0.341003			−0.170502	−	0.985357i	$-0.554539\pi$
$131$	−511.288			−0.341003			−0.170502	+	0.985357i	$0.554539\pi$
$132$			313.026i			0.206405i
$133$			98.8441i			0.0644426i
$134$	−185.112			−0.119337
$135$	305.877	+	1164.88i	0.195005	+	0.742646i
$136$	252.900			0.159456
$137$			764.986i			0.477060i	0.971135	+	0.238530i	$0.0766655\pi$
$137$			764.986i			0.477060i	−0.971135	+	0.238530i	$0.923334\pi$
$138$		−	11.6491i		−	0.00718577i
$139$	−1336.27			−0.815402			−0.407701	−	0.913115i	$-0.633669\pi$
$139$	−1336.27			−0.815402			−0.407701	+	0.913115i	$0.633669\pi$
$140$	673.461	+	2564.77i	0.406556	+	1.54830i
$141$	1286.21			0.768217
$142$		−	18.3856i		−	0.0108654i
$143$			638.481i			0.373374i
$144$	1392.83			0.806033
$145$	1042.37	−	273.708i	0.596994	−	0.156760i
$146$	221.543			0.125582
$147$			1199.27i			0.672886i
$148$			1993.11i			1.10698i
$149$	−255.507			−0.140483			−0.0702415	−	0.997530i	$-0.522377\pi$
$149$	−255.507			−0.140483			−0.0702415	+	0.997530i	$0.522377\pi$
$150$	55.1430	−	31.1037i	0.0300160	−	0.0169307i
$151$	264.687			0.142649			0.0713244	−	0.997453i	$-0.477277\pi$
$151$	264.687			0.142649			0.0713244	+	0.997453i	$0.477277\pi$
$152$		−	12.2182i		−	0.00651994i
$153$		−	1522.29i		−	0.804376i
$154$	−124.257			−0.0650188
$155$	−2075.13	+	544.893i	−1.07535	+	0.282367i
$156$	−617.252			−0.316793
$157$		−	2795.74i		−	1.42118i	−0.703609	−	0.710588i	$-0.748429\pi$
$157$		−	2795.74i		−	1.42118i	0.703609	−	0.710588i	$-0.251571\pi$
$158$			217.074i			0.109300i
$159$	940.568			0.469131
$160$	−125.011	−	476.083i	−0.0617686	−	0.235236i
$161$	−686.475			−0.336036
$162$			84.1664i			0.0408194i
$163$			2202.45i			1.05834i	0.848516	+	0.529169i	$0.177496\pi$
$163$			2202.45i			1.05834i	−0.848516	+	0.529169i	$0.822504\pi$
$164$	−768.649			−0.365984
$165$	−111.853	−	425.973i	−0.0527742	−	0.200982i
$166$	91.7634			0.0429049
$167$			4079.63i			1.89037i	0.326541	+	0.945183i	$0.394117\pi$
$167$			4079.63i			1.89037i	−0.326541	+	0.945183i	$0.605883\pi$
$168$		−	241.060i		−	0.110704i
$169$	937.987			0.426940
$170$	−171.499	+	45.0324i	−0.0773726	+	0.0203166i
$171$	−73.5456			−0.0328899
$172$			671.353i			0.297617i
$173$		−	1600.93i		−	0.703563i	−0.936082	−	0.351781i	$-0.885576\pi$
$173$		−	1600.93i		−	0.703563i	0.936082	−	0.351781i	$-0.114424\pi$
$174$	−48.8213			−0.0212709
$175$	−1832.93	−	3249.55i	−0.791749	−	1.40367i
$176$	−1128.56			−0.483345
$177$		−	1286.40i		−	0.546280i
$178$			67.7191i			0.0285155i
$179$	1883.80			0.786601			0.393301	−	0.919410i	$-0.371333\pi$
$179$	1883.80			0.786601			0.393301	+	0.919410i	$0.371333\pi$
$180$	−1908.33	+	501.093i	−0.790215	+	0.207496i
$181$	2427.54			0.996891			0.498446	−	0.866921i	$-0.333904\pi$
$181$	2427.54			0.996891			0.498446	+	0.866921i	$0.333904\pi$
$182$		−	245.021i		−	0.0997920i
$183$			1343.99i			0.542899i
$184$	84.8561			0.0339982
$185$	−712.193	−	2712.27i	−0.283035	−	1.07789i
$186$	97.1927			0.0383146
$187$			1233.46i			0.482351i
$188$			4668.89i			1.81124i
$189$	−3215.16			−1.23740
$190$	2.17563	+	8.28554i	0.000830721	+	0.00316366i
$191$	2657.82			1.00687			0.503437	−	0.864032i	$-0.332069\pi$
$191$	2657.82			1.00687			0.503437	+	0.864032i	$0.332069\pi$
$192$		−	1076.09i		−	0.404481i
$193$		−	2728.68i		−	1.01769i	−0.860857	−	0.508847i	$-0.830072\pi$
$193$		−	2728.68i		−	1.01769i	0.860857	−	0.508847i	$-0.169928\pi$
$194$	−19.1546			−0.00708875
$195$	839.972	−	220.562i	0.308470	−	0.0809987i
$196$	−4353.30			−1.58648
$197$			4454.85i			1.61114i	0.592499	+	0.805572i	$0.298142\pi$
$197$			4454.85i			1.61114i	−0.592499	+	0.805572i	$0.701858\pi$
$198$		−	92.4541i		−	0.0331840i
$199$	4838.81			1.72369			0.861845	−	0.507171i	$-0.169309\pi$
$199$	4838.81			1.72369			0.861845	+	0.507171i	$0.169309\pi$
$200$	226.570	+	401.681i	0.0801047	+	0.142016i
$201$	1751.53			0.614643
$202$			411.357i			0.143282i
$203$			2877.02i			0.994714i
$204$	−1192.45			−0.409257
$205$	1046.00	−	274.660i	0.356369	−	0.0935760i
$206$	92.0119			0.0311203
$207$		−	510.776i		−	0.171504i
$208$		−	2225.40i		−	0.741846i
$209$	59.5917			0.0197227
$210$	42.9242	+	163.470i	0.0141050	+	0.0537166i
$211$	−3697.01			−1.20622			−0.603111	−	0.797657i	$-0.706072\pi$
$211$	−3697.01			−1.20622			−0.603111	+	0.797657i	$0.706072\pi$
$212$			3414.22i			1.10608i
$213$			173.964i			0.0559616i
$214$	221.967			0.0709034
$215$	−239.893	−	913.594i	−0.0760957	−	0.289798i
$216$	397.431			0.125193
$217$		−	5727.52i		−	1.79175i
$218$		−	74.0134i		−	0.0229946i
$219$	−2096.24			−0.646807
$220$	1546.26	−	406.021i	0.473859	−	0.124427i
$221$	−2432.25			−0.740321
$222$			127.034i			0.0384053i
$223$			1829.35i			0.549337i	0.961539	+	0.274669i	$0.0885682\pi$
$223$			1829.35i			0.549337i	−0.961539	+	0.274669i	$0.911432\pi$
$224$	1314.02			0.391951
$225$	2417.85	−	1363.80i	0.716400	−	0.404089i
$226$	324.261			0.0954405
$227$		−	1947.98i		−	0.569567i	−0.958592	−	0.284783i	$-0.908078\pi$
$227$		−	1947.98i		−	0.569567i	0.958592	−	0.284783i	$-0.0919217\pi$
$228$			57.6104i			0.0167340i
$229$	−4105.64			−1.18475			−0.592376	−	0.805662i	$-0.701810\pi$
$229$	−4105.64			−1.18475			−0.592376	+	0.805662i	$0.701810\pi$
$230$	−57.5433	+	15.1098i	−0.0164969	+	0.00433180i
$231$	1175.72			0.334877
$232$		−	355.632i		−	0.100640i
$233$			748.718i			0.210516i	0.994445	+	0.105258i	$0.0335668\pi$
$233$			748.718i			0.210516i	−0.994445	+	0.105258i	$0.966433\pi$
$234$	182.309			0.0509313
$235$	−1668.32	−	6353.54i	−0.463104	−	1.76366i
$236$	4669.56			1.28798
$237$		−	2053.95i		−	0.562946i
$238$		−	473.348i		−	0.128919i
$239$	−1389.15			−0.375968			−0.187984	−	0.982172i	$-0.560195\pi$
$239$	−1389.15			−0.375968			−0.187984	+	0.982172i	$0.560195\pi$
$240$	389.860	+	1484.72i	0.104856	+	0.399325i
$241$	4753.91			1.27065			0.635324	−	0.772246i	$-0.280867\pi$
$241$	4753.91			1.27065			0.635324	+	0.772246i	$0.280867\pi$
$242$		−	233.029i		−	0.0618995i
$243$		−	3704.89i		−	0.978060i
$244$	−4878.62			−1.28001
$245$	5924.08	−	1555.56i	1.54480	−	0.405636i
$246$	−48.9912			−0.0126974
$247$			117.508i			0.0302708i
$248$			707.987i			0.181279i
$249$	−868.264			−0.220980
$250$	−225.169	−	232.047i	−0.0569637	−	0.0587038i
$251$	−261.930			−0.0658679			−0.0329340	−	0.999458i	$-0.510485\pi$
$251$	−261.930			−0.0658679			−0.0329340	+	0.999458i	$0.510485\pi$
$252$		−	5267.13i		−	1.31666i
$253$			413.867i			0.102844i
$254$	−227.906			−0.0562996
$255$	1622.72	−	426.096i	0.398504	−	0.104640i
$256$	3824.68			0.933759
$257$		−	7297.93i		−	1.77133i	−0.464324	−	0.885666i	$-0.653703\pi$
$257$		−	7297.93i		−	1.77133i	0.464324	−	0.885666i	$-0.346297\pi$
$258$			42.7898i			0.0103255i
$259$	7486.07			1.79599
$260$	800.628	+	3049.06i	0.190972	+	0.727287i
$261$	−2140.66			−0.507677
$262$		−	118.292i		−	0.0278936i
$263$			1815.23i			0.425597i	0.977096	+	0.212799i	$0.0682578\pi$
$263$			1815.23i			0.425597i	−0.977096	+	0.212799i	$0.931742\pi$
$264$	−145.332			−0.0338809
$265$	−1220.00	−	4646.15i	−0.282806	−	1.07702i
$266$	−22.8687			−0.00527131
$267$		−	640.758i		−	0.146868i
$268$			6357.96i			1.44916i
$269$	−1481.03			−0.335688			−0.167844	−	0.985814i	$-0.553681\pi$
$269$	−1481.03			−0.335688			−0.167844	+	0.985814i	$0.553681\pi$
$270$	−269.509	+	70.7682i	−0.0607474	+	0.0159512i
$271$	−4310.66			−0.966251			−0.483125	−	0.875551i	$-0.660499\pi$
$271$	−4310.66			−0.966251			−0.483125	+	0.875551i	$0.660499\pi$
$272$		−	4299.19i		−	0.958371i
$273$			2318.38i			0.513974i
$274$	−176.988			−0.0390228
$275$	−1959.11	+	1105.05i	−0.429596	+	0.242316i
$276$	−400.106			−0.0872593
$277$			7827.17i			1.69780i	0.528557	+	0.848898i	$0.322733\pi$
$277$			7827.17i			1.69780i	−0.528557	+	0.848898i	$0.677267\pi$
$278$		−	309.161i		−	0.0666987i
$279$	4261.60			0.914464
$280$	−1190.77	+	312.675i	−0.254151	+	0.0667354i
$281$	−8367.74			−1.77643			−0.888217	−	0.459425i	$-0.848056\pi$
$281$	−8367.74			−1.77643			−0.888217	+	0.459425i	$0.848056\pi$
$282$			297.580i			0.0628390i
$283$			5370.37i			1.12804i	0.825761	+	0.564021i	$0.190746\pi$
$283$			5370.37i			1.12804i	−0.825761	+	0.564021i	$0.809254\pi$
$284$	−631.482			−0.131942
$285$	−20.5858	−	78.3977i	−0.00427859	−	0.0162943i
$286$	−147.720			−0.0305414
$287$			2887.03i			0.593783i
$288$			977.709i			0.200042i
$289$	214.204			0.0435994
$290$	63.3253	+	241.164i	0.0128227	+	0.0488332i
$291$	181.240			0.0365103
$292$		−	7609.25i		−	1.52499i
$293$		−	345.504i		−	0.0688892i	−0.999407	−	0.0344446i	$-0.989034\pi$
$293$		−	345.504i		−	0.0688892i	0.999407	−	0.0344446i	$-0.0109662\pi$
$294$	−277.465			−0.0550411
$295$	−6354.46	+	1668.57i	−1.25414	+	0.329314i
$296$	−925.362			−0.181708
$297$			1938.38i			0.378708i
$298$		−	59.1145i		−	0.0114913i
$299$	−816.099			−0.157847
$300$	−1068.31	−	1893.97i	−0.205595	−	0.364495i
$301$	2521.59			0.482863
$302$			61.2384i			0.0116685i
$303$		−	3892.26i		−	0.737968i
$304$	−207.705			−0.0391865
$305$	6638.94	−	1743.27i	1.24638	−	0.327276i
$306$	352.198			0.0657968
$307$			7071.81i			1.31469i	0.753590	+	0.657345i	$0.228320\pi$
$307$			7071.81i			1.31469i	−0.753590	+	0.657345i	$0.771680\pi$
$308$			4267.80i			0.789547i
$309$	−870.616			−0.160284
$310$	−126.067	−	480.106i	−0.0230972	−	0.0879619i
$311$	−9492.89			−1.73084			−0.865421	−	0.501045i	$-0.832949\pi$
$311$	−9492.89			−1.73084			−0.865421	+	0.501045i	$0.832949\pi$
$312$		−	286.579i		−	0.0520010i
$313$			4717.54i			0.851921i	0.904742	+	0.425961i	$0.140064\pi$
$313$			4717.54i			0.851921i	−0.904742	+	0.425961i	$0.859936\pi$
$314$	646.826			0.116250
$315$	1882.09	+	7167.64i	0.336648	+	1.28207i
$316$	7455.74			1.32727
$317$		−	4143.12i		−	0.734072i	−0.930207	−	0.367036i	$-0.880373\pi$
$317$		−	4143.12i		−	0.734072i	0.930207	−	0.367036i	$-0.119627\pi$
$318$			217.611i			0.0383743i
$319$	1734.51			0.304433
$320$	−5315.61	+	1395.78i	−0.928598	+	0.243833i
$321$	−2100.25			−0.365185
$322$		−	158.824i		−	0.0274873i
$323$			227.011i			0.0391060i
$324$	2890.83			0.495684
$325$	−2179.03	−	3863.15i	−0.371910	−	0.659351i
$326$	−509.562			−0.0865706
$327$			700.314i			0.118433i
$328$		−	356.869i		−	0.0600756i
$329$	17536.2			2.93861
$330$	98.5537	−	25.8784i	0.0164400	−	0.00431685i
$331$	10794.8			1.79256			0.896281	−	0.443488i	$-0.146259\pi$
$331$	10794.8			1.79256			0.896281	+	0.443488i	$0.146259\pi$
$332$		−	3151.76i		−	0.521010i
$333$			5570.06i			0.916628i
$334$	−943.868			−0.154629
$335$	−2271.88	−	8652.07i	−0.370525	−	1.41108i
$336$	−4097.92			−0.665357
$337$			9284.49i			1.50077i	0.661003	+	0.750384i	$0.270131\pi$
$337$			9284.49i			1.50077i	−0.661003	+	0.750384i	$0.729869\pi$
$338$			217.014i			0.0349231i
$339$	−3068.16			−0.491562
$340$	1546.71	+	5890.39i	0.246712	+	0.939563i
$341$	−3453.05			−0.548366
$342$		−	17.0156i		−	0.00269035i
$343$			6113.46i			0.962378i
$344$	−311.697			−0.0488534
$345$	544.475	−	142.969i	0.0849667	−	0.0223107i
$346$	370.393			0.0575504
$347$		−	9820.77i		−	1.51933i	−0.650317	−	0.759663i	$-0.725364\pi$
$347$		−	9820.77i		−	1.51933i	0.650317	−	0.759663i	$-0.274636\pi$
$348$			1676.85i			0.258300i
$349$	−4126.17			−0.632862			−0.316431	−	0.948615i	$-0.602485\pi$
$349$	−4126.17			−0.632862			−0.316431	+	0.948615i	$0.602485\pi$
$350$	751.820	−	424.068i	0.114818	−	0.0647640i
$351$	−3822.27			−0.581247
$352$		−	792.208i		−	0.119957i
$353$		−	1306.28i		−	0.196958i	−0.995139	−	0.0984789i	$-0.968602\pi$
$353$		−	1306.28i		−	0.196958i	0.995139	−	0.0984789i	$-0.0313977\pi$
$354$	297.623			0.0446849
$355$	859.336	−	225.646i	0.128475	−	0.0337353i
$356$	2325.92			0.346274
$357$			4478.82i			0.663990i
$358$			435.838i			0.0643428i
$359$	−12360.8			−1.81721			−0.908607	−	0.417653i	$-0.862853\pi$
$359$	−12360.8			−1.81721			−0.908607	+	0.417653i	$0.862853\pi$
$360$	−232.648	−	886.002i	−0.0340601	−	0.129712i
$361$	−6848.03			−0.998401
$362$			561.638i			0.0815443i
$363$			2204.92i			0.318811i
$364$	−8415.63			−1.21181
$365$	2719.00	+	10354.9i	0.389915	+	1.48493i
$366$	−310.947			−0.0444083
$367$			6974.82i			0.992051i	0.868308	+	0.496025i	$0.165208\pi$
$367$			6974.82i			0.992051i	−0.868308	+	0.496025i	$0.834792\pi$
$368$		−	1442.52i		−	0.204338i
$369$	−2148.11			−0.303052
$370$	627.514	−	164.774i	0.0881701	−	0.0231519i
$371$	12823.7			1.79454
$372$		−	3338.24i		−	0.465268i
$373$		−	11235.4i		−	1.55965i	−0.625999	−	0.779823i	$-0.715309\pi$
$373$		−	11235.4i		−	1.55965i	0.625999	−	0.779823i	$-0.284691\pi$
$374$	−285.375			−0.0394556
$375$	2130.55	+	2195.63i	0.293389	+	0.302352i
$376$	−2167.68			−0.297312
$377$			3420.27i			0.467249i
$378$		−	743.864i		−	0.101218i
$379$	−4293.68			−0.581930			−0.290965	−	0.956734i	$-0.593976\pi$
$379$	−4293.68			−0.581930			−0.290965	+	0.956734i	$0.593976\pi$
$380$	284.580	−	74.7256i	0.0384175	−	0.0100877i
$381$	2156.45			0.289969
$382$			614.916i			0.0823608i
$383$			186.199i			0.0248416i	0.999923	+	0.0124208i	$0.00395376\pi$
$383$			186.199i			0.0248416i	−0.999923	+	0.0124208i	$0.996046\pi$
$384$	1019.99			0.135550
$385$	−1525.00	−	5807.72i	−0.201874	−	0.768803i
$386$	631.312			0.0832459
$387$			1876.20i			0.246441i
$388$			657.894i			0.0860812i
$389$	640.962			0.0835426			0.0417713	−	0.999127i	$-0.486700\pi$
$389$	640.962			0.0835426			0.0417713	+	0.999127i	$0.486700\pi$
$390$	51.0294	+	194.337i	0.00662557	+	0.0252324i
$391$	−1576.60			−0.203918
$392$		−	2021.16i		−	0.260418i
$393$			1119.28i			0.143665i
$394$	−1030.68			−0.131789
$395$	−10146.0	+	2664.14i	−1.29240	+	0.339361i
$396$	−3175.48			−0.402965
$397$			1707.89i			0.215910i	0.994156	+	0.107955i	$0.0344303\pi$
$397$			1707.89i			0.215910i	−0.994156	+	0.107955i	$0.965570\pi$
$398$			1119.51i			0.140995i
$399$	216.383			0.0271497
$400$	6828.41	−	3851.60i	0.853552	−	0.481450i
$401$	14078.5			1.75323			0.876614	−	0.481194i	$-0.159797\pi$
$401$	14078.5			1.75323			0.876614	+	0.481194i	$0.159797\pi$
$402$			405.235i			0.0502769i
$403$		−	6809.03i		−	0.841642i
$404$	14128.7			1.73992
$405$	−3933.91	+	1032.97i	−0.482661	+	0.126738i
$406$	−665.630			−0.0813662
$407$		−	4513.25i		−	0.549664i
$408$		−	553.633i		−	0.0671787i
$409$	−1406.85			−0.170084			−0.0850418	−	0.996377i	$-0.527102\pi$
$409$	−1406.85			−0.170084			−0.0850418	+	0.996377i	$0.527102\pi$
$410$	63.5457	+	242.003i	0.00765438	+	0.0291504i
$411$	1674.66			0.200985
$412$		−	3160.30i		−	0.377905i
$413$		−	17538.8i		−	2.08965i
$414$	118.174			0.0140288
$415$	1126.21	+	4288.99i	0.133213	+	0.507321i
$416$	1562.15			0.184112
$417$			2925.28i			0.343529i
$418$			13.7872i			0.00161329i
$419$	−6372.79			−0.743034			−0.371517	−	0.928426i	$-0.621162\pi$
$419$	−6372.79			−0.743034			−0.371517	+	0.928426i	$0.621162\pi$
$420$	5614.63	−	1474.30i	0.652300	−	0.171282i
$421$	5072.75			0.587246			0.293623	−	0.955921i	$-0.405139\pi$
$421$	5072.75			0.587246			0.293623	+	0.955921i	$0.405139\pi$
$422$		−	855.346i		−	0.0986672i
$423$			13048.0i			1.49979i
$424$	−1585.16			−0.181561
$425$	−4209.60	−	7463.11i	−0.480460	−	0.851797i
$426$	−40.2486			−0.00457758
$427$			18324.0i			2.07672i
$428$		−	7623.80i		−	0.861005i
$429$	1397.72			0.157302
$430$	211.370	−	55.5020i	0.0237051	−	0.00622452i
$431$	2838.66			0.317247			0.158624	−	0.987339i	$-0.449294\pi$
$431$	2838.66			0.317247			0.158624	+	0.987339i	$0.449294\pi$
$432$		−	6756.16i		−	0.752444i
$433$		−	12359.8i		−	1.37176i	−0.727714	−	0.685881i	$-0.759417\pi$
$433$		−	12359.8i		−	1.37176i	0.727714	−	0.685881i	$-0.240583\pi$
$434$	1325.13			0.146562
$435$	−599.184	−	2281.89i	−0.0660429	−	0.251514i
$436$	−2542.11			−0.279232
$437$			76.1695i			0.00833795i
$438$		−	484.989i		−	0.0529079i
$439$	−3708.94			−0.403230			−0.201615	−	0.979465i	$-0.564619\pi$
$439$	−3708.94			−0.403230			−0.201615	+	0.979465i	$0.564619\pi$
$440$	188.508	+	717.901i	0.0204244	+	0.0777831i
$441$	−12166.0			−1.31368
$442$		−	562.729i		−	0.0605572i
$443$		−	2948.32i		−	0.316205i	−0.987423	−	0.158103i	$-0.949462\pi$
$443$		−	2948.32i		−	0.316205i	0.987423	−	0.158103i	$-0.0505377\pi$
$444$	4363.19			0.466369
$445$	−3165.17	+	831.117i	−0.337176	+	0.0885364i
$446$	−423.240			−0.0449350
$447$			559.341i			0.0591855i
$448$		−	14671.5i		−	1.54723i
$449$	2712.01			0.285050			0.142525	−	0.989791i	$-0.454478\pi$
$449$	2712.01			0.285050			0.142525	+	0.989791i	$0.454478\pi$
$450$	315.531	+	559.397i	0.0330539	+	0.0586005i
$451$	1740.55			0.181728
$452$		−	11137.3i		−	1.15897i
$453$		−	579.438i		−	0.0600979i
$454$	450.686			0.0465897
$455$	11452.2	−	3007.14i	1.17997	−	0.309839i
$456$	−26.7474			−0.00274685
$457$		−	2043.37i		−	0.209157i	−0.994517	−	0.104579i	$-0.966651\pi$
$457$		−	2043.37i		−	0.209157i	0.994517	−	0.104579i	$-0.0333494\pi$
$458$		−	949.886i		−	0.0969110i
$459$	−7384.13			−0.750897
$460$	518.971	+	1976.42i	0.0526025	+	0.200328i
$461$	−1974.86			−0.199519			−0.0997597	−	0.995012i	$-0.531807\pi$
$461$	−1974.86			−0.199519			−0.0997597	+	0.995012i	$0.531807\pi$
$462$			272.015i			0.0273924i
$463$		−	6523.98i		−	0.654849i	−0.944877	−	0.327424i	$-0.893819\pi$
$463$		−	6523.98i		−	0.654849i	0.944877	−	0.327424i	$-0.106181\pi$
$464$	−6045.59			−0.604870
$465$	1192.85	+	4542.76i	0.118961	+	0.453044i
$466$	−173.224			−0.0172199
$467$			1656.59i			0.164150i	0.996626	+	0.0820749i	$0.0261547\pi$
$467$			1656.59i			0.164150i	−0.996626	+	0.0820749i	$0.973845\pi$
$468$		−	6261.70i		−	0.618477i
$469$	23880.3			2.35115
$470$	1469.96	−	385.986i	0.144265	−	0.0378813i
$471$	−6120.27			−0.598741
$472$			2167.99i			0.211419i
$473$		−	1520.23i		−	0.147781i
$474$	475.204			0.0460482
$475$	−360.562	+	203.377i	−0.0348289	+	0.0196454i
$476$	−16257.9			−1.56550
$477$			9541.57i			0.915888i
$478$		−	321.395i		−	0.0307537i
$479$	210.175			0.0200483			0.0100241	−	0.999950i	$-0.496809\pi$
$479$	210.175			0.0200483			0.0100241	+	0.999950i	$0.496809\pi$
$480$	−1042.21	+	273.666i	−0.0991047	+	0.0260231i
$481$	8899.63			0.843634
$482$			1099.87i			0.103937i
$483$			1502.79i			0.141572i
$484$	−8003.76			−0.751668
$485$	−235.084	−	895.278i	−0.0220095	−	0.0838195i
$486$	857.167			0.0800039
$487$			8539.58i			0.794590i	0.917691	+	0.397295i	$0.130051\pi$
$487$			8539.58i			0.794590i	−0.917691	+	0.397295i	$0.869949\pi$
$488$		−	2265.05i		−	0.210110i
$489$	4821.47			0.445878
$490$	359.895	+	1370.60i	0.0331804	+	0.126362i
$491$	18614.3			1.71090			0.855449	−	0.517887i	$-0.173281\pi$
$491$	18614.3			1.71090			0.855449	+	0.517887i	$0.173281\pi$
$492$			1682.68i			0.154189i
$493$			6607.52i			0.603627i
$494$	−27.1869			−0.00247610
$495$	4321.28	−	1134.69i	0.392378	−	0.103031i
$496$	12035.5			1.08953
$497$			2371.83i			0.214066i
$498$		−	200.883i		−	0.0180758i
$499$	10948.7			0.982223			0.491111	−	0.871097i	$-0.336591\pi$
$499$	10948.7			0.982223			0.491111	+	0.871097i	$0.336591\pi$
$500$	−7970.04	+	7733.78i	−0.712862	+	0.691730i
$501$	8930.87			0.796411
$502$		−	60.6004i		−	0.00538790i
$503$		−	10198.0i		−	0.903993i	−0.892020	−	0.451997i	$-0.850712\pi$
$503$		−	10198.0i		−	0.903993i	0.892020	−	0.451997i	$-0.149288\pi$
$504$	2445.43			0.216127
$505$	−19226.7	+	5048.58i	−1.69421	+	0.444869i
$506$	−95.7527			−0.00841250
$507$		−	2053.38i		−	0.179870i
$508$			7827.80i			0.683666i
$509$	−2725.11			−0.237305			−0.118653	−	0.992936i	$-0.537858\pi$
$509$	−2725.11			−0.237305			−0.118653	+	0.992936i	$0.537858\pi$
$510$	98.5822	+	375.434i	0.00855940	+	0.0325971i
$511$	−28580.2			−2.47419
$512$			4612.35i			0.398123i
$513$			356.746i			0.0307032i
$514$	1688.46			0.144892
$515$	1129.26	+	4300.61i	0.0966238	+	0.367976i
$516$	1469.69			0.125386
$517$		−	10572.4i		−	0.899365i
$518$			1731.99i			0.146909i
$519$	−3504.66			−0.296411
$520$	−1415.62	+	371.716i	−0.119383	+	0.0313478i
$521$	−15150.1			−1.27397			−0.636984	−	0.770877i	$-0.719818\pi$
$521$	−15150.1			−1.27397			−0.636984	+	0.770877i	$0.719818\pi$
$522$		−	495.267i		−	0.0415273i
$523$			211.059i			0.0176462i	0.999961	+	0.00882312i	$0.00280852\pi$
$523$			211.059i			0.0176462i	−0.999961	+	0.00882312i	$0.997191\pi$
$524$	−4062.93			−0.338722
$525$	−7113.72	+	4012.53i	−0.591368	+	0.333564i
$526$	−419.975			−0.0348132
$527$		−	13154.2i		−	1.08729i
$528$			2470.58i			0.203633i
$529$	−529.000			−0.0434783
$530$	1074.94	−	282.260i	0.0880988	−	0.0231332i
$531$	13049.8			1.06651
$532$			785.461i			0.0640114i
$533$			3432.17i			0.278919i
$534$	148.247			0.0120136
$535$	2724.20	+	10374.7i	0.220144	+	0.838384i
$536$	−2951.88			−0.237876
$537$		−	4123.89i		−	0.331395i
$538$		−	342.654i		−	0.0274588i
$539$	9857.73			0.787760
$540$	2430.65	+	9256.72i	0.193701	+	0.737677i
$541$	−17057.1			−1.35553			−0.677767	−	0.735277i	$-0.737052\pi$
$541$	−17057.1			−1.35553			−0.677767	+	0.735277i	$0.737052\pi$
$542$		−	997.320i		−	0.0790379i
$543$		−	5314.21i		−	0.419990i
$544$	3017.87			0.237849
$545$	3459.36	−	908.367i	0.271895	−	0.0713948i
$546$	−536.384			−0.0420424
$547$			19175.8i			1.49890i	0.662062	+	0.749449i	$0.269682\pi$
$547$			19175.8i			1.49890i	−0.662062	+	0.749449i	$0.730318\pi$
$548$			6078.94i			0.473868i
$549$	−13634.1			−1.05990
$550$	−255.665	−	453.262i	−0.0198211	−	0.0351403i
$551$	319.227			0.0246815
$552$		−	185.762i		−	0.0143235i
$553$		−	28003.6i		−	2.15340i
$554$	−1810.90			−0.138877
$555$	−5937.54	+	1559.09i	−0.454116	+	0.119243i
$556$	−10618.6			−0.809946
$557$			2511.65i			0.191063i	0.995426	+	0.0955314i	$0.0304550\pi$
$557$			2511.65i			0.191063i	−0.995426	+	0.0955314i	$0.969545\pi$
$558$			985.969i			0.0748018i
$559$	2997.73			0.226816
$560$	5315.35	+	20242.6i	0.401097	+	1.52751i
$561$	2700.22			0.203215
$562$		−	1935.97i		−	0.145310i
$563$			16742.0i			1.25327i	0.779313	+	0.626635i	$0.215568\pi$
$563$			16742.0i			1.25327i	−0.779313	+	0.626635i	$0.784432\pi$
$564$	10220.8			0.763077
$565$	3979.66	+	15155.9i	0.296328	+	1.12852i
$566$	−1242.50			−0.0922721
$567$		−	10857.9i		−	0.804212i
$568$		−	293.185i		−	0.0216580i
$569$	−18107.8			−1.33413			−0.667063	−	0.745001i	$-0.732449\pi$
$569$	−18107.8			−1.33413			−0.667063	+	0.745001i	$0.732449\pi$
$570$	18.1382	−	4.76276i	0.00133285	−	0.000349983i
$571$	14057.9			1.03030			0.515152	−	0.857099i	$-0.327735\pi$
$571$	14057.9			1.03030			0.515152	+	0.857099i	$0.327735\pi$
$572$			5073.67i			0.370875i
$573$		−	5818.33i		−	0.424196i
$574$	−667.946			−0.0485706
$575$	−1412.46	−	2504.11i	−0.102441	−	0.181615i
$576$	10916.4			0.789670
$577$			24894.9i			1.79617i	0.439824	+	0.898084i	$0.355041\pi$
$577$			24894.9i			1.79617i	−0.439824	+	0.898084i	$0.644959\pi$
$578$			49.5585i			0.00356637i
$579$	−5973.47			−0.428755
$580$	8283.16	−	2175.01i	0.592999	−	0.155711i
$581$	−11837.9			−0.845301
$582$			41.9320i			0.00298649i
$583$		−	7731.24i		−	0.549220i
$584$	3532.83			0.250325
$585$	2237.48	+	8521.08i	0.158134	+	0.602228i
$586$	79.9361			0.00563504
$587$		−	18303.1i		−	1.28697i	−0.765459	−	0.643485i	$-0.777488\pi$
$587$		−	18303.1i		−	1.28697i	0.765459	−	0.643485i	$-0.222512\pi$
$588$			9529.98i			0.668384i
$589$	−635.511			−0.0444581
$590$	−386.041	−	1470.18i	−0.0269374	−	0.102587i
$591$	9752.29			0.678774
$592$			15730.8i			1.09211i
$593$		−	998.486i		−	0.0691449i	−0.999402	−	0.0345724i	$-0.988993\pi$
$593$		−	998.486i		−	0.0691449i	0.999402	−	0.0345724i	$-0.0110069\pi$
$594$	−448.466			−0.0309777
$595$	22124.2	−	5809.40i	1.52437	−	0.400273i
$596$	−2030.38			−0.139543
$597$		−	10592.8i		−	0.726191i
$598$		−	188.814i		−	0.0129117i
$599$	−15981.0			−1.09009			−0.545046	−	0.838406i	$-0.683488\pi$
$599$	−15981.0			−1.09009			−0.545046	+	0.838406i	$0.683488\pi$
$600$	879.336	−	495.994i	0.0598312	−	0.0337481i
$601$	−4484.14			−0.304346			−0.152173	−	0.988354i	$-0.548627\pi$
$601$	−4484.14			−0.304346			−0.152173	+	0.988354i	$0.548627\pi$
$602$			583.397i			0.0394975i
$603$			17768.3i			1.19997i
$604$	2103.33			0.141694
$605$	10891.7	−	2859.97i	0.731919	−	0.192189i
$606$	900.517			0.0603647
$607$			4545.05i			0.303917i	0.988387	+	0.151959i	$0.0485580\pi$
$607$			4545.05i			0.303917i	−0.988387	+	0.151959i	$0.951442\pi$
$608$		−	145.801i		−	0.00972534i
$609$	6298.19			0.419073
$610$	403.324	+	1535.99i	0.0267707	+	0.101952i
$611$	20847.5			1.38036
$612$		−	12096.8i		−	0.798994i
$613$			11055.0i			0.728399i	0.931321	+	0.364199i	$0.118657\pi$
$613$			11055.0i			0.728399i	−0.931321	+	0.364199i	$0.881343\pi$
$614$	−1636.14			−0.107540
$615$	−601.269	−	2289.83i	−0.0394236	−	0.150138i
$616$	−1981.46			−0.129603
$617$		−	8197.75i		−	0.534893i	−0.963573	−	0.267447i	$-0.913820\pi$
$617$		−	8197.75i		−	0.534893i	0.963573	−	0.267447i	$-0.0861799\pi$
$618$		−	201.427i		−	0.0131110i
$619$	−15296.1			−0.993219			−0.496609	−	0.867974i	$-0.665422\pi$
$619$	−15296.1			−0.993219			−0.496609	+	0.867974i	$0.665422\pi$
$620$	−16490.0	+	4329.98i	−1.06815	+	0.280477i
$621$	−2477.62			−0.160102
$622$		−	2196.29i		−	0.141580i
$623$		−	8736.10i		−	0.561805i
$624$	−4871.72			−0.312540
$625$	8082.32	−	13372.2i	0.517269	−	0.855823i
$626$	−1091.46			−0.0696859
$627$		−	130.455i		−	0.00830918i
$628$		−	22216.3i		−	1.41167i
$629$	17192.9			1.08987
$630$	−1658.32	+	435.444i	−0.104871	+	0.0275373i
$631$	−20580.5			−1.29841			−0.649204	−	0.760614i	$-0.724898\pi$
$631$	−20580.5			−1.29841			−0.649204	+	0.760614i	$0.724898\pi$
$632$			3461.56i			0.217869i
$633$			8093.27i			0.508181i
$634$	958.558			0.0600461
$635$	−2797.09	−	10652.3i	−0.174802	−	0.665704i
$636$	7474.20			0.465992
$637$			19438.4i			1.20907i
$638$			401.300i			0.0249022i
$639$	−1764.77			−0.109254
$640$	−1323.02	−	5038.49i	−0.0817138	−	0.311194i
$641$	6994.55			0.430995			0.215498	−	0.976504i	$-0.430863\pi$
$641$	6994.55			0.430995			0.215498	+	0.976504i	$0.430863\pi$
$642$		−	485.916i		−	0.0298716i
$643$			2966.12i			0.181917i	0.995855	+	0.0909583i	$0.0289930\pi$
$643$			2966.12i			0.181917i	−0.995855	+	0.0909583i	$0.971007\pi$
$644$	−5455.06			−0.333788
$645$	−1999.98	+	525.160i	−0.122092	+	0.0320591i
$646$	−52.5215			−0.00319881
$647$		−	8546.86i		−	0.519338i	−0.965698	−	0.259669i	$-0.916387\pi$
$647$		−	8546.86i		−	0.519338i	0.965698	−	0.259669i	$-0.0836135\pi$
$648$			1342.16i			0.0813656i
$649$	−10573.9			−0.639540
$650$	893.783	−	504.143i	0.0539339	−	0.0304217i
$651$	−12538.3			−0.754864
$652$			17501.7i			1.05126i
$653$		−	15603.2i		−	0.935067i	−0.883975	−	0.467534i	$-0.845143\pi$
$653$		−	15603.2i		−	0.935067i	0.883975	−	0.467534i	$-0.154857\pi$
$654$	−162.026			−0.00968762
$655$	5528.94	−	1451.80i	0.329822	−	0.0866054i
$656$	−6066.63			−0.361070
$657$		−	21265.3i		−	1.26277i
$658$			4057.20i			0.240374i
$659$	5103.40			0.301670			0.150835	−	0.988559i	$-0.451804\pi$
$659$	5103.40			0.301670			0.150835	+	0.988559i	$0.451804\pi$
$660$	−888.836	−	3384.98i	−0.0524210	−	0.199637i
$661$	7344.53			0.432177			0.216088	−	0.976374i	$-0.430670\pi$
$661$	7344.53			0.432177			0.216088	+	0.976374i	$0.430670\pi$
$662$			2497.51i			0.146629i
$663$			5324.54i			0.311897i
$664$	1463.30			0.0855228
$665$	−280.667	−	1068.88i	−0.0163666	−	0.0623296i
$666$	−1288.70			−0.0749789
$667$			2217.04i			0.128702i
$668$			32418.7i			1.87772i
$669$	4004.70			0.231436
$670$	2001.75	−	525.624i	0.115425	−	0.0303084i
$671$	11047.3			0.635581
$672$		−	2876.58i		−	0.165129i
$673$		−	28042.1i		−	1.60615i	−0.595875	−	0.803077i	$-0.703195\pi$
$673$		−	28042.1i		−	1.60615i	0.595875	−	0.803077i	$-0.296805\pi$
$674$	−2148.07			−0.122761
$675$	−6615.37	−	11728.2i	−0.377223	−	0.668770i
$676$	7453.68			0.424083
$677$			29440.9i			1.67135i	0.549221	+	0.835677i	$0.314925\pi$
$677$			29440.9i			1.67135i	−0.549221	+	0.835677i	$0.685075\pi$
$678$		−	709.853i		−	0.0402091i
$679$	2471.03			0.139661
$680$	−2734.80	+	718.108i	−0.154227	+	0.0404973i
$681$	−4264.39			−0.239958
$682$		−	798.901i		−	0.0448556i
$683$		−	22928.9i		−	1.28455i	−0.766472	−	0.642277i	$-0.777990\pi$
$683$		−	22928.9i		−	1.28455i	0.766472	−	0.642277i	$-0.222010\pi$
$684$	−584.428			−0.0326698
$685$	−2172.18	−	8272.37i	−0.121160	−	0.461418i
$686$	−1414.42			−0.0787211
$687$			8987.81i			0.499136i
$688$			5298.71i			0.293621i
$689$	15245.2			0.842953
$690$	33.0775	+	125.970i	0.00182499	+	0.00695016i
$691$	−15653.2			−0.861760			−0.430880	−	0.902409i	$-0.641797\pi$
$691$	−15653.2			−0.861760			−0.430880	+	0.902409i	$0.641797\pi$
$692$		−	12721.7i		−	0.698855i
$693$			11927.0i			0.653782i
$694$	2272.14			0.124279
$695$	14450.1	−	3794.33i	0.788666	−	0.207090i
$696$	−778.528			−0.0423994
$697$			6630.51i			0.360328i
$698$		−	954.637i		−	0.0517672i
$699$	1639.05			0.0886902
$700$	−14565.3	−	25822.5i	−0.786452	−	1.39428i
$701$	7593.43			0.409130			0.204565	−	0.978853i	$-0.434422\pi$
$701$	7593.43			0.409130			0.204565	+	0.978853i	$0.434422\pi$
$702$		−	884.325i		−	0.0475452i
$703$		−	830.635i		−	0.0445633i
$704$	−8845.22			−0.473533
$705$	−13908.8	+	3652.19i	−0.743028	+	0.195106i
$706$	302.222			0.0161109
$707$		−	53067.1i		−	2.82290i
$708$		−	10222.3i		−	0.542625i
$709$	12701.1			0.672778			0.336389	−	0.941723i	$-0.390794\pi$
$709$	12701.1			0.672778			0.336389	+	0.941723i	$0.390794\pi$
$710$	52.2057	+	198.817i	0.00275950	+	0.0105091i
$711$	20836.2			1.09904
$712$			1079.88i			0.0568403i
$713$		−	4413.65i		−	0.231827i
$714$	−1036.23			−0.0543134
$715$	−1812.96	−	6904.37i	−0.0948266	−	0.361131i
$716$	14969.5			0.781338
$717$			3041.03i			0.158395i
$718$		−	2859.82i		−	0.148645i
$719$	26304.6			1.36439			0.682196	−	0.731170i	$-0.261025\pi$
$719$	26304.6			1.36439			0.682196	+	0.731170i	$0.261025\pi$
$720$	−15061.7	+	3954.92i	−0.779604	+	0.204710i
$721$	−11870.0			−0.613123
$722$		−	1584.37i		−	0.0816678i
$723$		−	10407.0i		−	0.535324i
$724$	19290.3			0.990221
$725$	−10494.7	+	5919.61i	−0.537607	+	0.303240i
$726$	−510.133			−0.0260783
$727$		−	9229.67i		−	0.470852i	−0.971892	−	0.235426i	$-0.924351\pi$
$727$		−	9229.67i		−	0.470852i	0.971892	−	0.235426i	$-0.0756485\pi$
$728$		−	3907.22i		−	0.198916i
$729$	1711.76			0.0869663
$730$	−2395.71	+	629.071i	−0.121465	+	0.0318945i
$731$	5791.22			0.293018
$732$			10680.0i			0.539266i
$733$		−	15537.8i		−	0.782951i	−0.920188	−	0.391476i	$-0.871965\pi$
$733$		−	15537.8i		−	0.782951i	0.920188	−	0.391476i	$-0.128035\pi$
$734$	−1613.70			−0.0811483
$735$	−3405.33	−	12968.6i	−0.170894	−	0.650823i
$736$	1012.59			0.0507128
$737$		−	14397.1i		−	0.719573i
$738$		−	496.990i		−	0.0247892i
$739$	−22475.8			−1.11879			−0.559396	−	0.828901i	$-0.688967\pi$
$739$	−22475.8			−1.11879			−0.559396	+	0.828901i	$0.688967\pi$
$740$	−5659.42	−	21553.0i	−0.281141	−	1.07068i
$741$	257.242			0.0127531
$742$			2966.91i			0.146791i
$743$			17908.6i			0.884257i	0.896952	+	0.442129i	$0.145776\pi$
$743$			17908.6i			0.884257i	−0.896952	+	0.442129i	$0.854224\pi$
$744$	1549.88			0.0763728
$745$	2762.99	−	725.512i	0.135877	−	0.0356788i
$746$	2599.44			0.127577
$747$		−	8808.09i		−	0.431420i
$748$			9801.67i			0.479124i
$749$	−28634.8			−1.39692
$750$	−507.984	+	492.926i	−0.0247319	+	0.0239988i
$751$	5921.85			0.287738			0.143869	−	0.989597i	$-0.454046\pi$
$751$	5921.85			0.287738			0.143869	+	0.989597i	$0.454046\pi$
$752$			36849.6i			1.78692i
$753$			573.400i			0.0277502i
$754$	−791.318			−0.0382203
$755$	−2862.27	+	751.579i	−0.137972	+	0.0362288i
$756$	−25549.2			−1.22912
$757$			34839.6i			1.67274i	0.548164	+	0.836371i	$0.315327\pi$
$757$			34839.6i			1.67274i	−0.548164	+	0.836371i	$0.684673\pi$
$758$		−	993.392i		−	0.0476011i
$759$	906.011			0.0433282
$760$	34.6937	+	132.125i	0.00165588	+	0.00630616i
$761$	31403.6			1.49590			0.747950	−	0.663755i	$-0.231038\pi$
$761$	31403.6			1.49590			0.747950	+	0.663755i	$0.231038\pi$
$762$			498.918i			0.0237190i
$763$			9548.10i			0.453033i
$764$	21120.3			1.00014
$765$	4322.53	+	16461.6i	0.204289	+	0.778002i
$766$	−43.0792			−0.00203200
$767$		−	20850.5i		−	0.981576i
$768$		−	8372.75i		−	0.393393i
$769$	12357.6			0.579486			0.289743	−	0.957104i	$-0.406430\pi$
$769$	12357.6			0.579486			0.289743	+	0.957104i	$0.406430\pi$
$770$	1343.68	−	352.827i	0.0628870	−	0.0165130i
$771$	−15976.2			−0.746262
$772$		−	21683.4i		−	1.01089i
$773$			33770.7i			1.57134i	0.618644	+	0.785672i	$0.287683\pi$
$773$			33770.7i			1.57134i	−0.618644	+	0.785672i	$0.712317\pi$
$774$	−434.081			−0.0201585
$775$	20892.8	−	11784.7i	0.968375	−	0.546217i
$776$	−305.448			−0.0141301
$777$		−	16388.0i		−	0.756651i
$778$			148.294i			0.00683366i
$779$	320.337			0.0147333
$780$	6674.82	−	1752.69i	0.306406	−	0.0804567i
$781$	1429.94			0.0655152
$782$		−	364.764i		−	0.0166802i
$783$			10383.7i			0.473924i
$784$	−34358.8			−1.56518
$785$	7938.50	+	30232.5i	0.360939	+	1.37458i
$786$	−258.958			−0.0117516
$787$		−	42918.6i		−	1.94394i	−0.235101	−	0.971971i	$-0.575542\pi$
$787$		−	42918.6i		−	1.94394i	0.235101	−	0.971971i	$-0.424458\pi$
$788$			35400.4i			1.60036i
$789$	3973.80			0.179304
$790$	−616.380	−	2347.38i	−0.0277592	−	0.105716i
$791$	−41831.3			−1.88034
$792$		−	1474.32i		−	0.0661459i
$793$			21784.0i			0.975501i
$794$	−395.139			−0.0176611
$795$	−10171.1	+	2670.74i	−0.453749	+	0.119146i
$796$	38451.5			1.71216
$797$			14345.5i			0.637568i	0.947827	+	0.318784i	$0.103275\pi$
$797$			14345.5i			0.637568i	−0.947827	+	0.318784i	$0.896725\pi$
$798$			50.0627i			0.00222080i
$799$	40274.7			1.78325
$800$	2703.67	+	4793.28i	0.119487	+	0.211835i
$801$	6500.16			0.286731
$802$			3257.21i			0.143412i
$803$			17230.6i			0.757228i
$804$	13918.5			0.610530
$805$	7423.37	−	1949.24i	0.325018	−	0.0853439i
$806$	1575.34			0.0688451
$807$			3242.19i			0.141425i
$808$			6559.69i			0.285605i
$809$	12561.6			0.545912			0.272956	−	0.962027i	$-0.411999\pi$
$809$	12561.6			0.545912			0.272956	+	0.962027i	$0.411999\pi$
$810$	−238.990	−	910.155i	−0.0103670	−	0.0394810i
$811$	−7400.12			−0.320411			−0.160206	−	0.987084i	$-0.551216\pi$
$811$	−7400.12			−0.320411			−0.160206	+	0.987084i	$0.551216\pi$
$812$			22862.1i			0.988059i
$813$			9436.64i			0.407081i
$814$	1044.19			0.0449618
$815$	−6253.85	−	23816.8i	−0.268789	−	1.02364i
$816$	−9411.53			−0.403761
$817$		−	279.789i		−	0.0119811i
$818$		−	325.490i		−	0.0139126i
$819$	−23518.8			−1.00344
$820$	8311.98	−	2182.58i	0.353984	−	0.0929499i
$821$	−27083.9			−1.15132			−0.575661	−	0.817688i	$-0.695255\pi$
$821$	−27083.9			−1.15132			−0.575661	+	0.817688i	$0.695255\pi$
$822$			387.452i			0.0164403i
$823$			27819.6i			1.17829i	0.808029	+	0.589143i	$0.200535\pi$
$823$			27819.6i			1.17829i	−0.808029	+	0.589143i	$0.799465\pi$
$824$	1467.27			0.0620323
$825$	2419.10	+	4288.76i	0.102088	+	0.180989i
$826$	4057.79			0.170931
$827$			21998.3i			0.924976i	0.886626	+	0.462488i	$0.153043\pi$
$827$			21998.3i			0.924976i	−0.886626	+	0.462488i	$0.846957\pi$
$828$		−	4058.87i		−	0.170357i
$829$	−35730.6			−1.49696			−0.748478	−	0.663160i	$-0.769215\pi$
$829$	−35730.6			−1.49696			−0.748478	+	0.663160i	$0.769215\pi$
$830$	−992.306	+	260.562i	−0.0414981	+	0.0108967i
$831$	17134.8			0.715281
$832$		−	17441.8i		−	0.726786i
$833$			37552.4i			1.56196i
$834$	−676.796			−0.0281002
$835$	−11584.1	−	44116.1i	−0.480101	−	1.82838i
$836$	473.544			0.0195907
$837$		−	20671.7i		−	0.853666i
$838$		−	1474.42i		−	0.0607791i
$839$	−29929.6			−1.23157			−0.615783	−	0.787916i	$-0.711160\pi$
$839$	−29929.6			−1.23157			−0.615783	+	0.787916i	$0.711160\pi$
$840$	684.490	+	2606.77i	0.0281156	+	0.107074i
$841$	−15097.4			−0.619025
$842$			1173.64i			0.0480359i
$843$			18318.2i			0.748411i
$844$	−29378.2			−1.19815
$845$	−10143.2	+	2663.41i	−0.412941	+	0.108431i
$846$	−3018.79			−0.122681
$847$			30061.9i			1.21953i
$848$			26947.0i			1.09123i
$849$	11756.5			0.475244
$850$	1726.67	−	973.939i	0.0696758	−	0.0393010i
$851$	5768.79			0.232375
$852$			1382.40i			0.0555872i
$853$		−	2871.31i		−	0.115254i	−0.998338	−	0.0576271i	$-0.981647\pi$
$853$		−	2871.31i		−	0.115254i	0.998338	−	0.0576271i	$-0.0183534\pi$
$854$	−4239.45			−0.169872
$855$	795.304	−	208.832i	0.0318115	−	0.00835312i
$856$	3539.58			0.141332
$857$		−	29553.3i		−	1.17797i	−0.808144	−	0.588986i	$-0.799527\pi$
$857$		−	29553.3i		−	1.17797i	0.808144	−	0.588986i	$-0.200473\pi$
$858$			323.379i			0.0128671i
$859$	−19794.9			−0.786253			−0.393127	−	0.919484i	$-0.628607\pi$
$859$	−19794.9			−0.786253			−0.393127	+	0.919484i	$0.628607\pi$
$860$	−1906.31	−	7259.85i	−0.0755866	−	0.287859i
$861$	6320.10			0.250161
$862$			656.756i			0.0259504i
$863$		−	6600.80i		−	0.260364i	−0.991490	−	0.130182i	$-0.958444\pi$
$863$		−	6600.80i		−	0.260364i	0.991490	−	0.130182i	$-0.0415561\pi$
$864$	4742.56			0.186742
$865$	4545.83	+	17312.0i	0.178685	+	0.680494i
$866$	2859.57			0.112208
$867$		−	468.922i		−	0.0183684i
$868$		−	45513.6i		−	1.77976i
$869$	−16883.0			−0.659051
$870$	527.942	−	138.628i	0.0205734	−	0.00540221i
$871$	28389.6			1.10441
$872$		−	1180.25i		−	0.0458353i
$873$			1838.59i			0.0712793i
$874$	−17.6227			−0.000682032
$875$	29047.9	+	29935.2i	1.12228	+	1.15657i
$876$	−16657.7			−0.642479
$877$		−	12262.9i		−	0.472166i	−0.971733	−	0.236083i	$-0.924136\pi$
$877$		−	12262.9i		−	0.472166i	0.971733	−	0.236083i	$-0.0758637\pi$
$878$		−	858.105i		−	0.0329837i
$879$	−756.355			−0.0290230
$880$	12204.0	−	3204.55i	0.467497	−	0.122756i
$881$	−10918.6			−0.417546			−0.208773	−	0.977964i	$-0.566947\pi$
$881$	−10918.6			−0.417546			−0.208773	+	0.977964i	$0.566947\pi$
$882$		−	2814.74i		−	0.107457i
$883$			11939.0i			0.455017i	0.973776	+	0.227508i	$0.0730579\pi$
$883$			11939.0i			0.455017i	−0.973776	+	0.227508i	$0.926942\pi$
$884$	−19327.8			−0.735367
$885$	3652.72	+	13910.8i	0.138740	+	0.528368i
$886$	682.127			0.0258651
$887$		−	40102.6i		−	1.51805i	−0.651059	−	0.759027i	$-0.725675\pi$
$887$		−	40102.6i		−	1.51805i	0.651059	−	0.759027i	$-0.274325\pi$
$888$			2025.75i			0.0765536i
$889$	29401.0			1.10920
$890$	−192.288	−	732.298i	−0.00724215	−	0.0275805i
$891$	−6546.07			−0.246130
$892$			14536.9i			0.545662i
$893$		−	1945.78i		−	0.0729148i
$894$	−129.410			−0.00484129
$895$	−20370.9	+	5349.03i	−0.760810	+	0.199775i
$896$	13906.6			0.518512
$897$			1786.55i			0.0665009i
$898$			627.453i			0.0233167i
$899$	−18497.6			−0.686240
$900$	19213.4	−	10837.4i	0.711606	−	0.401385i
$901$	29451.7			1.08899
$902$			402.696i			0.0148651i
$903$		−	5520.10i		−	0.203430i
$904$	5170.83			0.190242
$905$	−26250.8	+	6892.98i	−0.964205	+	0.253183i
$906$	134.059			0.00491592
$907$			14805.0i			0.541998i	0.962580	+	0.270999i	$0.0873540\pi$
$907$			14805.0i			0.541998i	−0.962580	+	0.270999i	$0.912646\pi$
$908$		−	15479.5i		−	0.565756i
$909$	39484.9			1.44074
$910$	695.735	+	2649.59i	0.0253444	+	0.0965200i
$911$	−11369.7			−0.413496			−0.206748	−	0.978394i	$-0.566288\pi$
$911$	−11369.7			−0.413496			−0.206748	+	0.978394i	$0.566288\pi$
$912$			454.695i			0.0165093i
$913$			7136.93i			0.258705i
$914$	472.757			0.0171088
$915$	−3816.25	−	14533.6i	−0.137881	−	0.525098i
$916$	−32625.3			−1.17682
$917$			15260.3i			0.549551i
$918$		−	1708.40i		−	0.0614223i
$919$	50555.8			1.81467			0.907336	−	0.420407i	$-0.138113\pi$
$919$	50555.8			1.81467			0.907336	+	0.420407i	$0.138113\pi$
$920$	−917.613	+	240.949i	−0.0328835	+	0.00863461i
$921$	15481.2			0.553879
$922$		−	456.906i		−	0.0163204i
$923$			2819.69i			0.100554i
$924$	9342.80			0.332636
$925$	15403.0	+	27307.6i	0.547510	+	0.970667i
$926$	1509.40			0.0535657
$927$		−	8831.95i		−	0.312923i
$928$		−	4243.77i		−	0.150117i
$929$	−52215.8			−1.84407			−0.922037	−	0.387101i	$-0.873476\pi$
$929$	−52215.8			−1.84407			−0.922037	+	0.387101i	$0.873476\pi$
$930$	−1051.02	+	275.978i	−0.0370583	+	0.00973085i
$931$	1814.25			0.0638665
$932$			5949.67i			0.209107i
$933$			20781.2i			0.729204i
$934$	−383.271			−0.0134272
$935$	−3502.41	−	13338.4i	−0.122504	−	0.466536i
$936$	2907.19			0.101522
$937$			21484.8i			0.749069i	0.927213	+	0.374535i	$0.122198\pi$
$937$			21484.8i			0.749069i	−0.927213	+	0.374535i	$0.877802\pi$
$938$			5524.98i			0.192321i
$939$	10327.4			0.358914
$940$	−13257.3	−	50488.2i	−0.460006	−	1.75186i
$941$	−43503.9			−1.50711			−0.753554	−	0.657386i	$-0.771662\pi$
$941$	−43503.9			−1.50711			−0.753554	+	0.657386i	$0.771662\pi$
$942$		−	1415.99i		−	0.0489762i
$943$			2224.75i			0.0768271i
$944$	36854.9			1.27068
$945$	34768.0	−	9129.45i	1.19683	−	0.314265i
$946$	351.722			0.0120882
$947$			18488.5i			0.634420i	0.948355	+	0.317210i	$0.102746\pi$
$947$			18488.5i			0.634420i	−0.948355	+	0.317210i	$0.897254\pi$
$948$		−	16321.6i		−	0.559180i
$949$	−33976.8			−1.16221
$950$	−47.0535	−	83.4201i	−0.00160697	−	0.00284895i
$951$	−9069.87			−0.309265
$952$		−	7548.24i		−	0.256975i
$953$			31777.8i			1.08015i	0.841616	+	0.540076i	$0.181604\pi$
$953$			31777.8i			1.08015i	−0.841616	+	0.540076i	$0.818396\pi$
$954$	−2207.55			−0.0749183
$955$	−28741.0	+	7546.86i	−0.973859	+	0.255718i
$956$	−11038.8			−0.373453
$957$		−	3797.09i		−	0.128258i
$958$			48.6263i			0.00163992i
$959$	22832.4			0.768817
$960$	3055.56	+	11636.6i	0.102727	+	0.391218i
$961$	7033.74			0.236103
$962$			2059.03i			0.0690081i
$963$		−	21305.9i		−	0.712953i
$964$	37776.8			1.26215
$965$	7748.09	+	29507.3i	0.258466	+	0.984326i
$966$	−347.687			−0.0115804
$967$			1305.15i			0.0434029i	0.999764	+	0.0217015i	$0.00690834\pi$
$967$			1305.15i			0.0434029i	−0.999764	+	0.0217015i	$0.993092\pi$
$968$		−	3715.99i		−	0.123385i
$969$	496.959			0.0164753
$970$	207.133	−	54.3893i	0.00685632	−	0.00180035i
$971$	28301.8			0.935373			0.467686	−	0.883894i	$-0.345088\pi$
$971$	28301.8			0.935373			0.467686	+	0.883894i	$0.345088\pi$
$972$		−	29440.8i		−	0.971516i
$973$			39883.3i			1.31408i
$974$	−1975.73			−0.0649963
$975$	−8456.97	+	4770.20i	−0.277784	+	0.156686i
$976$	−38504.9			−1.26282
$977$		−	20836.1i		−	0.682299i	−0.940009	−	0.341150i	$-0.889184\pi$
$977$		−	20836.1i		−	0.682299i	0.940009	−	0.341150i	$-0.110816\pi$
$978$			1115.50i			0.0364722i
$979$	−5266.88			−0.171941
$980$	47075.5	−	12361.2i	1.53446	−	0.402922i
$981$	−7104.33			−0.231217
$982$			4306.63i			0.139949i
$983$			52785.9i			1.71272i	0.516376	+	0.856362i	$0.327281\pi$
$983$			52785.9i			1.71272i	−0.516376	+	0.856362i	$0.672719\pi$
$984$	−781.236			−0.0253099
$985$	−12649.5	−	48173.7i	−0.409186	−	1.55832i
$986$	−1528.73			−0.0493758
$987$		−	38389.2i		−	1.23804i
$988$			933.777i			0.0300682i
$989$	1943.14			0.0624756
$990$	262.523	+	999.776i	0.00842781	+	0.0320959i
$991$	−25400.6			−0.814205			−0.407103	−	0.913382i	$-0.633461\pi$
$991$	−25400.6			−0.814205			−0.407103	+	0.913382i	$0.633461\pi$
$992$			8448.44i			0.270401i
$993$		−	23631.4i		−	0.755206i
$994$	−548.749			−0.0175103
$995$	−52325.7	+	13739.8i	−1.66717	+	0.437770i
$996$	−6899.64			−0.219501
$997$		−	17764.8i		−	0.564308i	−0.959369	−	0.282154i	$-0.908951\pi$
$997$		−	17764.8i		−	0.564308i	0.959369	−	0.282154i	$-0.0910490\pi$
$998$			2533.09i			0.0803444i
$999$	27018.6			0.855686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.18	yes	34
5.2	odd	4		575.4.a.q.1.9		17
5.3	odd	4		575.4.a.r.1.9		17
5.4	even	2	inner	115.4.b.a.24.17	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.17	✓	34	5.4	even	2	inner
115.4.b.a.24.18	yes	34	1.1	even	1	trivial
575.4.a.q.1.9		17	5.2	odd	4
575.4.a.r.1.9		17	5.3	odd	4

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.231361i q^{2} -2.18914i q^{3} +7.94647 q^{4} +(-10.8138 + 2.83950i) q^{5} +0.506482 q^{6} -29.8467i q^{7} +3.68940i q^{8} +22.2077 q^{9} +O(q^{10})\)	\(q+0.231361i q^{2} -2.18914i q^{3} +7.94647 q^{4} +(-10.8138 + 2.83950i) q^{5} +0.506482 q^{6} -29.8467i q^{7} +3.68940i q^{8} +22.2077 q^{9} +(-0.656949 - 2.50188i) q^{10} -17.9942 q^{11} -17.3959i q^{12} -35.4826i q^{13} +6.90538 q^{14} +(6.21605 + 23.6728i) q^{15} +62.7182 q^{16} -68.5478i q^{17} +5.13799i q^{18} -3.31172 q^{19} +(-85.9312 + 22.5640i) q^{20} -65.3387 q^{21} -4.16316i q^{22} -23.0000i q^{23} +8.07660 q^{24} +(108.875 - 61.4112i) q^{25} +8.20929 q^{26} -107.722i q^{27} -237.176i q^{28} -96.3930 q^{29} +(-5.47697 + 1.43815i) q^{30} +191.898 q^{31} +44.0257i q^{32} +39.3918i q^{33} +15.8593 q^{34} +(84.7497 + 322.755i) q^{35} +176.473 q^{36} +250.817i q^{37} -0.766204i q^{38} -77.6763 q^{39} +(-10.4760 - 39.8962i) q^{40} -96.7284 q^{41} -15.1168i q^{42} +84.4844i q^{43} -142.990 q^{44} +(-240.148 + 63.0586i) q^{45} +5.32131 q^{46} +587.542i q^{47} -137.299i q^{48} -547.828 q^{49} +(14.2082 + 25.1893i) q^{50} -150.061 q^{51} -281.961i q^{52} +429.652i q^{53} +24.9228 q^{54} +(194.585 - 51.0945i) q^{55} +110.116 q^{56} +7.24981i q^{57} -22.3016i q^{58} +587.627 q^{59} +(49.3957 + 188.115i) q^{60} -613.935 q^{61} +44.3977i q^{62} -662.827i q^{63} +491.560 q^{64} +(100.753 + 383.700i) q^{65} -9.11374 q^{66} +800.098i q^{67} -544.713i q^{68} -50.3502 q^{69} +(-74.6731 + 19.6078i) q^{70} -79.4669 q^{71} +81.9329i q^{72} -957.564i q^{73} -58.0293 q^{74} +(-134.438 - 238.341i) q^{75} -26.3165 q^{76} +537.068i q^{77} -17.9713i q^{78} +938.245 q^{79} +(-678.219 + 178.088i) q^{80} +363.788 q^{81} -22.3792i q^{82} -396.624i q^{83} -519.212 q^{84} +(194.641 + 741.259i) q^{85} -19.5464 q^{86} +211.018i q^{87} -66.3877i q^{88} +292.699 q^{89} +(-14.5893 - 55.5610i) q^{90} -1059.04 q^{91} -182.769i q^{92} -420.091i q^{93} -135.935 q^{94} +(35.8121 - 9.40362i) q^{95} +96.3784 q^{96} +82.7907i q^{97} -126.746i q^{98} -399.609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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