LMFDB - Embedded newform 92.5.c.a.47.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(47,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("92.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.c (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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.22
Character	$\chi$	$=$	92.47
Dual form			92.5.c.a.47.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0192498 + 3.99995i) q^{2} +15.0928i q^{3} +(-15.9993 + 0.153996i) q^{4} -8.67002 q^{5} +(-60.3703 + 0.290532i) q^{6} -26.8452i q^{7} +(-0.923961 - 63.9933i) q^{8} -146.791 q^{9} +(-0.166896 - 34.6797i) q^{10} +98.3454i q^{11} +(-2.32423 - 241.473i) q^{12} +12.0738 q^{13} +(107.379 - 0.516763i) q^{14} -130.855i q^{15} +(255.953 - 4.92766i) q^{16} -66.5536 q^{17} +(-2.82570 - 587.159i) q^{18} +385.008i q^{19} +(138.714 - 1.33515i) q^{20} +405.168 q^{21} +(-393.377 + 1.89313i) q^{22} -110.304i q^{23} +(965.836 - 13.9451i) q^{24} -549.831 q^{25} +(0.232419 + 48.2948i) q^{26} -992.974i q^{27} +(4.13406 + 429.503i) q^{28} +200.733 q^{29} +(523.412 - 2.51892i) q^{30} -1720.44i q^{31} +(24.6374 + 1023.70i) q^{32} -1484.30 q^{33} +(-1.28114 - 266.211i) q^{34} +232.748i q^{35} +(2348.55 - 22.6053i) q^{36} -2035.02 q^{37} +(-1540.02 + 7.41132i) q^{38} +182.227i q^{39} +(8.01076 + 554.824i) q^{40} -2014.14 q^{41} +(7.79938 + 1620.65i) q^{42} +539.916i q^{43} +(-15.1448 - 1573.45i) q^{44} +1272.69 q^{45} +(441.211 - 2.12333i) q^{46} +1913.98i q^{47} +(74.3719 + 3863.03i) q^{48} +1680.34 q^{49} +(-10.5841 - 2199.30i) q^{50} -1004.48i q^{51} +(-193.172 + 1.85933i) q^{52} +2581.83 q^{53} +(3971.85 - 19.1145i) q^{54} -852.657i q^{55} +(-1717.91 + 24.8039i) q^{56} -5810.84 q^{57} +(3.86407 + 802.924i) q^{58} +4108.44i q^{59} +(20.1511 + 2093.58i) q^{60} -4282.80 q^{61} +(6881.68 - 33.1181i) q^{62} +3940.64i q^{63} +(-4094.29 + 118.255i) q^{64} -104.680 q^{65} +(-28.5725 - 5937.15i) q^{66} +8140.75i q^{67} +(1064.81 - 10.2490i) q^{68} +1664.79 q^{69} +(-930.982 + 4.48035i) q^{70} +4364.82i q^{71} +(135.629 + 9393.67i) q^{72} -2120.81 q^{73} +(-39.1737 - 8139.99i) q^{74} -8298.46i q^{75} +(-59.2899 - 6159.85i) q^{76} +2640.10 q^{77} +(-728.901 + 3.50784i) q^{78} -2996.86i q^{79} +(-2219.12 + 42.7229i) q^{80} +3096.61 q^{81} +(-38.7717 - 8056.45i) q^{82} -9844.45i q^{83} +(-6482.38 + 62.3943i) q^{84} +577.021 q^{85} +(-2159.64 + 10.3933i) q^{86} +3029.62i q^{87} +(6293.45 - 90.8673i) q^{88} +5764.95 q^{89} +(24.4989 + 5090.68i) q^{90} -324.124i q^{91} +(16.9864 + 1764.78i) q^{92} +25966.2 q^{93} +(-7655.82 + 36.8436i) q^{94} -3338.03i q^{95} +(-15450.5 + 371.847i) q^{96} -9929.30 q^{97} +(32.3461 + 6721.27i) q^{98} -14436.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) $ 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$	0.0192498	+	3.99995i	0.00481244	+	0.999988i
$2$	0.0192498	+	3.99995i	0.00481244	+	0.999988i
$3$			15.0928i			1.67697i	0.544922	+	0.838487i	$0.316559\pi$
$3$			15.0928i			1.67697i	−0.544922	+	0.838487i	$0.683441\pi$
$4$	−15.9993	+	0.153996i	−0.999954	+	0.00962477i
$5$	−8.67002			−0.346801			−0.173400	−	0.984851i	$-0.555476\pi$
$5$	−8.67002			−0.346801			−0.173400	+	0.984851i	$0.555476\pi$
$6$	−60.3703	+	0.290532i	−1.67695	+	0.00807034i
$7$		−	26.8452i		−	0.547860i	−0.961750	−	0.273930i	$-0.911676\pi$
$7$		−	26.8452i		−	0.547860i	0.961750	−	0.273930i	$-0.0883237\pi$
$8$	−0.923961	−	63.9933i	−0.0144369	−	0.999896i
$9$	−146.791			−1.81224
$10$	−0.166896	−	34.6797i	−0.00166896	−	0.346797i
$11$			98.3454i			0.812772i	0.913702	+	0.406386i	$0.133211\pi$
$11$			98.3454i			0.812772i	−0.913702	+	0.406386i	$0.866789\pi$
$12$	−2.32423	−	241.473i	−0.0161405	−	1.67690i
$13$	12.0738			0.0714428			0.0357214	−	0.999362i	$-0.488627\pi$
$13$	12.0738			0.0714428			0.0357214	+	0.999362i	$0.488627\pi$
$14$	107.379	−	0.516763i	0.547854	−	0.00263655i
$15$		−	130.855i		−	0.581576i
$16$	255.953	−	4.92766i	0.999815	−	0.0192487i
$17$	−66.5536			−0.230289			−0.115145	−	0.993349i	$-0.536733\pi$
$17$	−66.5536			−0.230289			−0.115145	+	0.993349i	$0.536733\pi$
$18$	−2.82570	−	587.159i	−0.00872130	−	1.81222i
$19$			385.008i			1.06651i	0.845956	+	0.533253i	$0.179030\pi$
$19$			385.008i			1.06651i	−0.845956	+	0.533253i	$0.820970\pi$
$20$	138.714	−	1.33515i	0.346785	−	0.00333788i
$21$	405.168			0.918747
$22$	−393.377	+	1.89313i	−0.812763	+	0.00391142i
$23$		−	110.304i		−	0.208514i
$23$		−	110.304i		−	0.208514i
$24$	965.836	−	13.9451i	1.67680	−	0.0242103i
$25$	−549.831			−0.879729
$26$	0.232419	+	48.2948i	0.000343814	+	0.0714420i
$27$		−	992.974i		−	1.36210i
$28$	4.13406	+	429.503i	0.00527303	+	0.547835i
$29$	200.733			0.238684			0.119342	−	0.992853i	$-0.461921\pi$
$29$	200.733			0.238684			0.119342	+	0.992853i	$0.461921\pi$
$30$	523.412	−	2.51892i	0.581569	−	0.00279880i
$31$		−	1720.44i		−	1.79026i	−0.445805	−	0.895130i	$-0.647083\pi$
$31$		−	1720.44i		−	1.79026i	0.445805	−	0.895130i	$-0.352917\pi$
$32$	24.6374	+	1023.70i	0.0240600	+	0.999711i
$33$	−1484.30			−1.36300
$34$	−1.28114	−	266.211i	−0.00110825	−	0.230287i
$35$			232.748i			0.189999i
$36$	2348.55	−	22.6053i	1.81216	−	0.0174424i
$37$	−2035.02			−1.48650			−0.743251	−	0.669013i	$-0.766717\pi$
$37$	−2035.02			−1.48650			−0.743251	+	0.669013i	$0.766717\pi$
$38$	−1540.02	+	7.41132i	−1.06649	+	0.00513250i
$39$			182.227i			0.119808i
$40$	8.01076	+	554.824i	0.00500673	+	0.346765i
$41$	−2014.14			−1.19818			−0.599089	−	0.800683i	$-0.704470\pi$
$41$	−2014.14			−1.19818			−0.599089	+	0.800683i	$0.704470\pi$
$42$	7.79938	+	1620.65i	0.00442142	+	0.918737i
$43$			539.916i			0.292004i	0.989284	+	0.146002i	$0.0466407\pi$
$43$			539.916i			0.292004i	−0.989284	+	0.146002i	$0.953359\pi$
$44$	−15.1448	−	1573.45i	−0.00782275	−	0.812734i
$45$	1272.69			0.628486
$46$	441.211	−	2.12333i	0.208512	−	0.00100346i
$47$			1913.98i			0.866445i	0.901287	+	0.433222i	$0.142624\pi$
$47$			1913.98i			0.866445i	−0.901287	+	0.433222i	$0.857376\pi$
$48$	74.3719	+	3863.03i	0.0322795	+	1.67666i
$49$	1680.34			0.699849
$50$	−10.5841	−	2199.30i	−0.00423365	−	0.879719i
$51$		−	1004.48i		−	0.386189i
$52$	−193.172	+	1.85933i	−0.0714395	+	0.000687621i
$53$	2581.83			0.919129			0.459565	−	0.888144i	$-0.348005\pi$
$53$	2581.83			0.919129			0.459565	+	0.888144i	$0.348005\pi$
$54$	3971.85	−	19.1145i	1.36209	−	0.00655505i
$55$		−	852.657i		−	0.281870i
$56$	−1717.91	+	24.8039i	−0.547803	+	0.00790940i
$57$	−5810.84			−1.78850
$58$	3.86407	+	802.924i	0.00114865	+	0.238681i
$59$			4108.44i			1.18025i	0.807313	+	0.590123i	$0.200921\pi$
$59$			4108.44i			1.18025i	−0.807313	+	0.590123i	$0.799079\pi$
$60$	20.1511	+	2093.58i	0.00559754	+	0.581549i
$61$	−4282.80			−1.15098			−0.575490	−	0.817809i	$-0.695189\pi$
$61$	−4282.80			−1.15098			−0.575490	+	0.817809i	$0.695189\pi$
$62$	6881.68	−	33.1181i	1.79024	−	0.00861552i
$63$			3940.64i			0.992854i
$64$	−4094.29	+	118.255i	−0.999583	+	0.0288708i
$65$	−104.680			−0.0247764
$66$	−28.5725	−	5937.15i	−0.00655934	−	1.36298i
$67$			8140.75i			1.81349i	0.421681	+	0.906744i	$0.361440\pi$
$67$			8140.75i			1.81349i	−0.421681	+	0.906744i	$0.638560\pi$
$68$	1064.81	−	10.2490i	0.230279	−	0.00221648i
$69$	1664.79			0.349673
$70$	−930.982	+	4.48035i	−0.189996	+	0.000914357i
$71$			4364.82i			0.865864i	0.901427	+	0.432932i	$0.142521\pi$
$71$			4364.82i			0.865864i	−0.901427	+	0.432932i	$0.857479\pi$
$72$	135.629	+	9393.67i	0.0261631	+	1.81205i
$73$	−2120.81			−0.397975			−0.198987	−	0.980002i	$-0.563765\pi$
$73$	−2120.81			−0.397975			−0.198987	+	0.980002i	$0.563765\pi$
$74$	−39.1737	−	8139.99i	−0.00715371	−	1.48648i
$75$		−	8298.46i		−	1.47528i
$76$	−59.2899	−	6159.85i	−0.0102649	−	1.06646i
$77$	2640.10			0.445286
$78$	−728.901	+	3.50784i	−0.119806	+	0.000576568i
$79$		−	2996.86i		−	0.480189i	−0.970750	−	0.240095i	$-0.922822\pi$
$79$		−	2996.86i		−	0.480189i	0.970750	−	0.240095i	$-0.0771785\pi$
$80$	−2219.12	+	42.7229i	−0.346737	+	0.00667545i
$81$	3096.61			0.471972
$82$	−38.7717	−	8056.45i	−0.00576616	−	1.19816i
$83$		−	9844.45i		−	1.42901i	−0.699631	−	0.714505i	$-0.746652\pi$
$83$		−	9844.45i		−	1.42901i	0.699631	−	0.714505i	$-0.253348\pi$
$84$	−6482.38	+	62.3943i	−0.918705	+	0.00884273i
$85$	577.021			0.0798645
$86$	−2159.64	+	10.3933i	−0.292001	+	0.00140525i
$87$			3029.62i			0.400267i
$88$	6293.45	−	90.8673i	0.812687	−	0.0117339i
$89$	5764.95			0.727805			0.363903	−	0.931437i	$-0.381444\pi$
$89$	5764.95			0.727805			0.363903	+	0.931437i	$0.381444\pi$
$90$	24.4989	+	5090.68i	0.00302456	+	0.628479i
$91$		−	324.124i		−	0.0391407i
$92$	16.9864	+	1764.78i	0.00200690	+	0.208505i
$93$	25966.2			3.00222
$94$	−7655.82	+	36.8436i	−0.866435	+	0.00416972i
$95$		−	3338.03i		−	0.369865i
$96$	−15450.5	+	371.847i	−1.67649	+	0.0403480i
$97$	−9929.30			−1.05530			−0.527649	−	0.849462i	$-0.676926\pi$
$97$	−9929.30			−1.05530			−0.527649	+	0.849462i	$0.676926\pi$
$98$	32.3461	+	6721.27i	0.00336798	+	0.699841i
$99$		−	14436.3i		−	1.47294i
$100$	8796.88	−	84.6719i	0.879688	−	0.00846719i
$101$	9369.14			0.918453			0.459227	−	0.888319i	$-0.348127\pi$
$101$	9369.14			0.918453			0.459227	+	0.888319i	$0.348127\pi$
$102$	4017.86	−	19.3360i	0.386184	−	0.00185851i
$103$			19588.7i			1.84643i	0.384287	+	0.923214i	$0.374447\pi$
$103$			19588.7i			1.84643i	−0.384287	+	0.923214i	$0.625553\pi$
$104$	−11.1557	−	772.645i	−0.00103141	−	0.0714354i
$105$	−3512.81			−0.318622
$106$	49.6997	+	10327.2i	0.00442326	+	0.919119i
$107$		−	11414.4i		−	0.996981i	−0.866895	−	0.498490i	$-0.833888\pi$
$107$		−	11414.4i		−	0.996981i	0.866895	−	0.498490i	$-0.166112\pi$
$108$	152.914	+	15886.8i	0.0131099	+	1.36204i
$109$	−1964.51			−0.165349			−0.0826745	−	0.996577i	$-0.526346\pi$
$109$	−1964.51			−0.165349			−0.0826745	+	0.996577i	$0.526346\pi$
$110$	3410.59	−	16.4135i	0.281867	−	0.00135648i
$111$		−	30714.1i		−	2.49282i
$112$	−132.284	−	6871.09i	−0.0105456	−	0.547759i
$113$	−10996.5			−0.861191			−0.430595	−	0.902545i	$-0.641696\pi$
$113$	−10996.5			−0.861191			−0.430595	+	0.902545i	$0.641696\pi$
$114$	−111.857	−	23243.1i	−0.00860706	−	1.78848i
$115$			956.340i			0.0723130i
$116$	−3211.58	+	30.9122i	−0.238673	+	0.00229728i
$117$	−1772.33			−0.129471
$118$	−16433.6	+	79.0865i	−1.18023	+	0.00567987i
$119$			1786.64i			0.126166i
$120$	−8373.82	+	120.904i	−0.581515	+	0.00839615i
$121$	4969.18			0.339402
$122$	−82.4429	−	17131.0i	−0.00553903	−	1.15097i
$123$		−	30398.9i		−	2.00931i
$124$	264.942	+	27525.8i	0.0172308	+	1.79018i
$125$	10185.8			0.651892
$126$	−15762.4	+	75.8564i	−0.992843	+	0.00477805i
$127$			21897.1i			1.35762i	0.734313	+	0.678811i	$0.237505\pi$
$127$			21897.1i			1.35762i	−0.734313	+	0.678811i	$0.762495\pi$
$128$	−551.827	−	16374.7i	−0.0336809	−	0.999433i
$129$	−8148.83			−0.489684
$130$	−2.01507	−	418.717i	−0.000119235	−	0.0247761i
$131$			24705.1i			1.43961i	0.694177	+	0.719804i	$0.255768\pi$
$131$			24705.1i			1.43961i	−0.694177	+	0.719804i	$0.744232\pi$
$132$	23747.8	−	228.577i	1.36293	−	0.0131185i
$133$	10335.6			0.584296
$134$	−32562.6	+	156.708i	−1.81347	+	0.00872731i
$135$			8609.11i			0.472379i
$136$	61.4929	+	4258.99i	0.00332466	+	0.230265i
$137$	18904.2			1.00720			0.503602	−	0.863936i	$-0.332008\pi$
$137$	18904.2			1.00720			0.503602	+	0.863936i	$0.332008\pi$
$138$	32.0469	+	6659.10i	0.00168278	+	0.349669i
$139$			17872.5i			0.925030i	0.886611	+	0.462515i	$0.153053\pi$
$139$			17872.5i			0.925030i	−0.886611	+	0.462515i	$0.846947\pi$
$140$	−35.8424	−	3723.80i	−0.00182869	−	0.189990i
$141$	−28887.2			−1.45300
$142$	−17459.1	+	84.0218i	−0.865854	+	0.00416692i
$143$			1187.41i			0.0580667i
$144$	−37571.6	+	723.338i	−1.81190	+	0.0348832i
$145$	−1740.36			−0.0827759
$146$	−40.8251	−	8483.14i	−0.00191523	−	0.397970i
$147$			25360.9i			1.17363i
$148$	32558.8	−	313.386i	1.48643	−	0.0143072i
$149$	20610.4			0.928355			0.464177	−	0.885742i	$-0.346350\pi$
$149$	20610.4			0.928355			0.464177	+	0.885742i	$0.346350\pi$
$150$	33193.5	−	159.744i	1.47527	−	0.00709971i
$151$			4962.01i			0.217622i	0.994062	+	0.108811i	$0.0347044\pi$
$151$			4962.01i			0.217622i	−0.994062	+	0.108811i	$0.965296\pi$
$152$	24638.0	−	355.733i	1.06639	−	0.0153970i
$153$	9769.50			0.417339
$154$	50.8213	+	10560.3i	0.00214291	+	0.445280i
$155$			14916.3i			0.620864i
$156$	−28.0624	−	2915.50i	−0.00115312	−	0.119802i
$157$	19704.6			0.799407			0.399703	−	0.916645i	$-0.369113\pi$
$157$	19704.6			0.799407			0.399703	+	0.916645i	$0.369113\pi$
$158$	11987.3	−	57.6889i	0.480184	−	0.00231088i
$159$			38967.0i			1.54136i
$160$	−213.607	−	8875.54i	−0.00834403	−	0.346701i
$161$	−2961.13			−0.114237
$162$	59.6090	+	12386.3i	0.00227134	+	0.471967i
$163$			29177.1i			1.09816i	0.835769	+	0.549081i	$0.185022\pi$
$163$			29177.1i			1.09816i	−0.835769	+	0.549081i	$0.814978\pi$
$164$	32224.7	−	310.170i	1.19812	−	0.0115322i
$165$	12868.9			0.472689
$166$	39377.3	−	189.503i	1.42899	−	0.00687703i
$167$		−	6116.08i		−	0.219301i	−0.993970	−	0.109650i	$-0.965027\pi$
$167$		−	6116.08i		−	0.219301i	0.993970	−	0.109650i	$-0.0349731\pi$
$168$	−374.359	−	25928.0i	−0.0132638	−	0.918651i
$169$	−28415.2			−0.994896
$170$	11.1075	+	2308.06i	0.000384344	+	0.0798636i
$171$		−	56515.9i		−	1.93276i
$172$	−83.1452	−	8638.26i	−0.00281048	−	0.291991i
$173$	12701.3			0.424380			0.212190	−	0.977228i	$-0.431940\pi$
$173$	12701.3			0.424380			0.212190	+	0.977228i	$0.431940\pi$
$174$	−12118.3	+	58.3195i	−0.400262	+	0.00192626i
$175$			14760.3i			0.481969i
$176$	484.612	+	25171.8i	0.0156448	+	0.812621i
$177$	−62007.6			−1.97924
$178$	110.974	+	23059.5i	0.00350252	+	0.727797i
$179$			13435.6i			0.419327i	0.977774	+	0.209663i	$0.0672368\pi$
$179$			13435.6i			0.419327i	−0.977774	+	0.209663i	$0.932763\pi$
$180$	−20362.0	+	195.989i	−0.628457	+	0.00604904i
$181$	−36457.6			−1.11284			−0.556418	−	0.830903i	$-0.687825\pi$
$181$	−36457.6			−1.11284			−0.556418	+	0.830903i	$0.687825\pi$
$182$	1296.48	−	6.23931i	0.0391402	−	0.000188362i
$183$		−	64639.2i		−	1.93016i
$184$	−7058.73	+	101.917i	−0.208493	+	0.00301030i
$185$	17643.7			0.515520
$186$	499.843	+	103864.i	0.0144480	+	3.00218i
$187$		−	6545.24i		−	0.187173i
$188$	−294.745	−	30622.2i	−0.00833934	−	0.866405i
$189$	−26656.5			−0.746243
$190$	13352.0	−	64.2564i	0.369861	−	0.00177995i
$191$		−	63923.6i		−	1.75224i	−0.482090	−	0.876122i	$-0.660122\pi$
$191$		−	63923.6i		−	1.75224i	0.482090	−	0.876122i	$-0.339878\pi$
$192$	−1784.79	−	61794.2i	−0.0484155	−	1.67627i
$193$	74040.7			1.98772			0.993861	−	0.110634i	$-0.0352883\pi$
$193$	74040.7			1.98772			0.993861	+	0.110634i	$0.0352883\pi$
$194$	−191.137	−	39716.8i	−0.00507856	−	1.05529i
$195$		−	1579.92i		−	0.0415494i
$196$	−26884.2	+	258.766i	−0.699817	+	0.00673589i
$197$	−14781.2			−0.380869			−0.190435	−	0.981700i	$-0.560990\pi$
$197$	−14781.2			−0.380869			−0.190435	+	0.981700i	$0.560990\pi$
$198$	57744.4	−	277.895i	1.47292	−	0.00708843i
$199$			42170.8i			1.06489i	0.846464	+	0.532446i	$0.178727\pi$
$199$			42170.8i			1.06489i	−0.846464	+	0.532446i	$0.821273\pi$
$200$	508.022	+	35185.5i	0.0127005	+	0.879637i
$201$	−122866.			−3.04117
$202$	180.354	+	37476.1i	0.00442000	+	0.918443i
$203$		−	5388.72i		−	0.130766i
$204$	154.686	+	16070.9i	0.00371698	+	0.386171i
$205$	17462.6			0.415529
$206$	−78354.1	+	377.079i	−1.84641	+	0.00888583i
$207$			16191.7i			0.377878i
$208$	3090.33	−	59.4957i	0.0714296	−	0.00137518i
$209$	−37863.8			−0.866826
$210$	−67.6208	−	14051.1i	−0.00153335	−	0.318619i
$211$		−	59442.3i		−	1.33515i	−0.744541	−	0.667576i	$-0.767332\pi$
$211$		−	59442.3i		−	1.33515i	0.744541	−	0.667576i	$-0.232668\pi$
$212$	−41307.4	+	397.593i	−0.919087	+	0.00884641i
$213$	−65877.2			−1.45203
$214$	45657.2	−	219.725i	0.996969	−	0.00479791i
$215$		−	4681.09i		−	0.101267i
$216$	−63543.7	+	917.468i	−1.36196	+	0.0196645i
$217$	−46185.5			−0.980812
$218$	−37.8164	−	7857.95i	−0.000795732	−	0.165347i
$219$		−	32008.9i		−	0.667393i
$220$	131.306	+	13641.9i	0.00271294	+	0.281857i
$221$	−803.557			−0.0164525
$222$	122855.	−	591.239i	2.49279	−	0.0119966i
$223$		−	15263.3i		−	0.306930i	−0.988154	−	0.153465i	$-0.950957\pi$
$223$		−	15263.3i		−	0.306930i	0.988154	−	0.153465i	$-0.0490433\pi$
$224$	27481.5	−	661.396i	0.547702	−	0.0131815i
$225$	80710.4			1.59428
$226$	−211.681	−	43985.7i	−0.00414443	−	0.861181i
$227$		−	25948.9i		−	0.503579i	−0.967782	−	0.251789i	$-0.918981\pi$
$227$		−	25948.9i		−	0.503579i	0.967782	−	0.251789i	$-0.0810190\pi$
$228$	92969.1	−	894.848i	1.78842	−	0.0172139i
$229$	−66572.7			−1.26948			−0.634739	−	0.772727i	$-0.718892\pi$
$229$	−66572.7			−1.26948			−0.634739	+	0.772727i	$0.718892\pi$
$230$	−3825.31	+	18.4093i	−0.0723122	+	0.000348002i
$231$			39846.4i			0.746732i
$232$	−185.470	−	12845.6i	−0.00344585	−	0.238659i
$233$	35100.3			0.646545			0.323272	−	0.946306i	$-0.395217\pi$
$233$	35100.3			0.646545			0.323272	+	0.946306i	$0.395217\pi$
$234$	−34.1170	−	7089.26i	−0.000623074	−	0.129470i
$235$		−	16594.2i		−	0.300484i
$236$	−632.684	−	65731.9i	−0.0113596	−	1.18019i
$237$	45230.9			0.805264
$238$	−7146.48	+	34.3924i	−0.126165	+	0.000607168i
$239$			34649.9i			0.606606i	0.952894	+	0.303303i	$0.0980894\pi$
$239$			34649.9i			0.606606i	−0.952894	+	0.303303i	$0.901911\pi$
$240$	−644.807	−	33492.6i	−0.0111946	−	0.581468i
$241$	40329.9			0.694374			0.347187	−	0.937796i	$-0.387137\pi$
$241$	40329.9			0.694374			0.347187	+	0.937796i	$0.387137\pi$
$242$	95.6556	+	19876.5i	0.00163335	+	0.339398i
$243$		−	33694.5i		−	0.570619i
$244$	68521.6	−	659.536i	1.15093	−	0.0110779i
$245$	−14568.6			−0.242708
$246$	121594.	−	585.171i	2.00929	−	0.00966970i
$247$			4648.53i			0.0761941i
$248$	−110097.	+	1589.62i	−1.79007	+	0.0258458i
$249$	148580.			2.39641
$250$	196.075	+	40742.8i	0.00313719	+	0.651884i
$251$		−	65425.7i		−	1.03849i	−0.854627	−	0.519243i	$-0.826214\pi$
$251$		−	65425.7i		−	1.03849i	0.854627	−	0.519243i	$-0.173786\pi$
$252$	−606.844	−	63047.3i	−0.00955600	−	0.992808i
$253$	10847.9			0.169475
$254$	−87587.4	+	421.514i	−1.35761	+	0.00653348i
$255$			8708.84i			0.133931i
$256$	65487.4	−	2522.49i	0.999259	−	0.0384902i
$257$	69755.6			1.05612			0.528060	−	0.849207i	$-0.322920\pi$
$257$	69755.6			1.05612			0.528060	+	0.849207i	$0.322920\pi$
$258$	−156.863	−	32594.9i	−0.00235657	−	0.489678i
$259$			54630.5i			0.814395i
$260$	1674.81	−	16.1204i	0.0247753	−	0.000238468i
$261$	−29465.9			−0.432553
$262$	−98819.4	+	475.568i	−1.43959	+	0.00692803i
$263$			89499.2i			1.29392i	0.762524	+	0.646960i	$0.223960\pi$
$263$			89499.2i			1.29392i	−0.762524	+	0.646960i	$0.776040\pi$
$264$	1371.44	+	94985.5i	0.0196774	+	1.36285i
$265$	−22384.6			−0.318755
$266$	198.958	+	41342.0i	0.00281189	+	0.584289i
$267$			87008.9i			1.22051i
$268$	−1253.65	−	130246.i	−0.0174544	−	1.81340i
$269$	−54205.7			−0.749101			−0.374551	−	0.927206i	$-0.622203\pi$
$269$	−54205.7			−0.749101			−0.374551	+	0.927206i	$0.622203\pi$
$270$	−34436.0	+	165.723i	−0.472373	+	0.00227330i
$271$			6644.04i			0.0904677i	0.998976	+	0.0452338i	$0.0144033\pi$
$271$			6644.04i			0.0904677i	−0.998976	+	0.0452338i	$0.985597\pi$
$272$	−17034.6	+	327.953i	−0.230247	+	0.00443276i
$273$	4891.92			0.0656379
$274$	363.902	+	75616.0i	0.00484711	+	1.00719i
$275$		−	54073.3i		−	0.715019i
$276$	−26635.5	+	256.372i	−0.349657	+	0.00336552i
$277$	78534.5			1.02353			0.511765	−	0.859125i	$-0.328992\pi$
$277$	78534.5			1.02353			0.511765	+	0.859125i	$0.328992\pi$
$278$	−71489.2	+	344.042i	−0.925019	+	0.00445165i
$279$			252546.i			3.24438i
$280$	14894.3	−	215.050i	0.189979	−	0.00274299i
$281$	−4096.80			−0.0518838			−0.0259419	−	0.999663i	$-0.508258\pi$
$281$	−4096.80			−0.0518838			−0.0259419	+	0.999663i	$0.508258\pi$
$282$	−556.072	−	115547.i	−0.00699250	−	1.45299i
$283$		−	108571.i		−	1.35563i	−0.735231	−	0.677817i	$-0.762926\pi$
$283$		−	108571.i		−	1.35563i	0.735231	−	0.677817i	$-0.237074\pi$
$284$	−672.166	−	69833.9i	−0.00833374	−	0.865823i
$285$	50380.1			0.620254
$286$	−4749.57	+	22.8573i	−0.0580660	+	0.000279443i
$287$			54069.8i			0.656434i
$288$	−3616.56	−	150271.i	−0.0436025	−	1.81171i
$289$	−79091.6			−0.946967
$290$	−33.5016	−	6961.37i	−0.000398354	−	0.0827749i
$291$		−	149861.i		−	1.76971i
$292$	33931.4	−	326.597i	0.397957	−	0.00383042i
$293$	−128178.			−1.49307			−0.746534	−	0.665347i	$-0.768284\pi$
$293$	−128178.			−1.49307			−0.746534	+	0.665347i	$0.768284\pi$
$294$	−101443.	+	488.192i	−1.17361	+	0.00564802i
$295$		−	35620.2i		−	0.409310i
$296$	1880.28	+	130228.i	0.0214605	+	1.48635i
$297$	97654.4			1.10708
$298$	396.746	+	82440.6i	0.00446765	+	0.928344i
$299$		−	1331.79i		−	0.0148969i
$300$	1277.93	+	132769.i	0.0141993	+	1.47521i
$301$	14494.1			0.159978
$302$	−19847.8	+	95.5175i	−0.217620	+	0.00104729i
$303$			141406.i			1.54022i
$304$	1897.19	+	98543.9i	0.0205288	+	1.06631i
$305$	37132.0			0.399161
$306$	188.061	+	39077.5i	0.00200842	+	0.417334i
$307$			166440.i			1.76596i	0.469406	+	0.882982i	$0.344468\pi$
$307$			166440.i			1.76596i	−0.469406	+	0.882982i	$0.655532\pi$
$308$	−42239.6	+	406.566i	−0.445265	+	0.00428577i
$309$	−295648.			−3.09641
$310$	−59664.3	+	287.135i	−0.620857	+	0.00298787i
$311$		−	79055.7i		−	0.817358i	−0.912678	−	0.408679i	$-0.865989\pi$
$311$		−	79055.7i		−	0.817358i	0.912678	−	0.408679i	$-0.134011\pi$
$312$	11661.3	−	168.371i	0.119795	−	0.00172965i
$313$	−177145.			−1.80817			−0.904087	−	0.427348i	$-0.859448\pi$
$313$	−177145.			−1.80817			−0.904087	+	0.427348i	$0.859448\pi$
$314$	379.309	+	78817.4i	0.00384710	+	0.799397i
$315$		−	34165.4i		−	0.344323i
$316$	461.506	+	47947.5i	0.00462171	+	0.480167i
$317$	194022.			1.93078			0.965390	−	0.260811i	$-0.0839900\pi$
$317$	194022.			1.93078			0.965390	+	0.260811i	$0.0839900\pi$
$318$	−155866.	+	750.106i	−1.54134	+	0.00741769i
$319$			19741.2i			0.193996i
$320$	35497.6	−	1025.27i	0.346656	−	0.0100124i
$321$	172275.			1.67191
$322$	−57.0011	−	11844.4i	−0.000549758	−	0.114235i
$323$		−	25623.7i		−	0.245605i
$324$	−49543.5	+	476.867i	−0.471950	+	0.00454263i
$325$	−6638.56			−0.0628503
$326$	−116707.	+	561.652i	−1.09815	+	0.00528484i
$327$		−	29649.9i		−	0.277286i
$328$	1860.98	+	128891.i	0.0172979	+	1.19805i
$329$	51381.0			0.474691
$330$	247.724	+	51475.2i	0.00227479	+	0.472683i
$331$		−	72539.5i		−	0.662093i	−0.943615	−	0.331046i	$-0.892598\pi$
$331$		−	72539.5i		−	0.662093i	0.943615	−	0.331046i	$-0.107402\pi$
$332$	1516.01	+	157504.i	0.0137539	+	1.42894i
$333$	298724.			2.69390
$334$	24464.0	−	117.733i	0.219298	−	0.00105537i
$335$		−	70580.5i		−	0.628920i
$336$	103704.	−	1996.53i	0.918577	−	0.0176847i
$337$	107960.			0.950608			0.475304	−	0.879822i	$-0.342338\pi$
$337$	107960.			0.950608			0.475304	+	0.879822i	$0.342338\pi$
$338$	−546.987	−	113660.i	−0.00478788	−	0.994884i
$339$		−	165968.i		−	1.44419i
$340$	−9231.91	+	88.8592i	−0.0798608	+	0.000768678i
$341$	169197.			1.45507
$342$	226061.	−	1087.92i	1.93274	−	0.00930131i
$343$		−	109564.i		−	0.931280i
$344$	34551.0	−	498.861i	0.291974	−	0.00421563i
$345$	−14433.8			−0.121267
$346$	244.497	+	50804.5i	0.00204231	+	0.424376i
$347$		−	34604.8i		−	0.287393i	−0.989622	−	0.143697i	$-0.954101\pi$
$347$		−	34604.8i		−	0.287393i	0.989622	−	0.143697i	$-0.0458990\pi$
$348$	−466.550	−	48471.7i	−0.00385248	−	0.400248i
$349$	−142889.			−1.17314			−0.586568	−	0.809900i	$-0.699521\pi$
$349$	−142889.			−1.17314			−0.586568	+	0.809900i	$0.699521\pi$
$350$	−59040.5	+	284.132i	−0.481963	+	0.00231945i
$351$		−	11989.0i		−	0.0973125i
$352$	−100677.	+	2422.98i	−0.812537	+	0.0195553i
$353$	150543.			1.20812			0.604060	−	0.796939i	$-0.293549\pi$
$353$	150543.			1.20812			0.604060	+	0.796939i	$0.293549\pi$
$354$	−1193.63	−	248028.i	−0.00952498	−	1.97922i
$355$		−	37843.1i		−	0.300282i
$356$	−92234.9	+	887.781i	−0.727772	+	0.00700496i
$357$	−26965.4			−0.211578
$358$	−53742.0	+	258.633i	−0.419322	+	0.00201799i
$359$			39625.5i			0.307458i	0.988113	+	0.153729i	$0.0491282\pi$
$359$			39625.5i			0.307458i	−0.988113	+	0.153729i	$0.950872\pi$
$360$	−1175.91	−	81443.4i	−0.00907339	−	0.628421i
$361$	−17910.5			−0.137434
$362$	−701.800	−	145829.i	−0.00535546	−	1.11282i
$363$			74998.7i			0.569168i
$364$	49.9139	+	5185.74i	0.000376720	+	0.0391389i
$365$	18387.5			0.138018
$366$	258554.	−	1244.29i	1.93014	−	0.00928880i
$367$			59595.5i			0.442467i	0.975221	+	0.221234i	$0.0710083\pi$
$367$			59595.5i			0.442467i	−0.975221	+	0.221234i	$0.928992\pi$
$368$	−543.541	−	28232.6i	−0.00401362	−	0.208476i
$369$	295658.			2.17138
$370$	339.637	+	70573.9i	0.00248091	+	0.515514i
$371$		−	69309.8i		−	0.503555i
$372$	−415440.	+	3998.70i	−3.00208	+	0.0288957i
$373$	−217062.			−1.56015			−0.780075	−	0.625687i	$-0.784819\pi$
$373$	−217062.			−1.56015			−0.780075	+	0.625687i	$0.784819\pi$
$374$	26180.7	−	125.994i	0.187170	−	0.000900758i
$375$			153732.i			1.09321i
$376$	122482.	−	1768.44i	0.866354	−	0.0125088i
$377$	2423.62			0.0170523
$378$	−513.132	−	106625.i	−0.00359125	−	0.746234i
$379$		−	109100.i		−	0.759531i	−0.925083	−	0.379765i	$-0.876005\pi$
$379$		−	109100.i		−	0.759531i	0.925083	−	0.379765i	$-0.123995\pi$
$380$	514.045	+	53406.0i	0.00355987	+	0.369848i
$381$	−330488.			−2.27670
$382$	255691.	−	1230.51i	1.75222	−	0.00843257i
$383$			153795.i			1.04844i	0.851582	+	0.524221i	$0.175643\pi$
$383$			153795.i			1.04844i	−0.851582	+	0.524221i	$0.824357\pi$
$384$	247139.	−	8328.60i	1.67602	−	0.0564819i
$385$	−22889.7			−0.154425
$386$	1425.27	+	296159.i	0.00956580	+	1.98770i
$387$		−	79255.1i		−	0.529182i
$388$	158862.	−	1529.08i	1.05525	−	0.0101570i
$389$	−65375.8			−0.432034			−0.216017	−	0.976390i	$-0.569307\pi$
$389$	−65375.8			−0.432034			−0.216017	+	0.976390i	$0.569307\pi$
$390$	6319.59	−	30.4130i	0.0415489	−	0.000199954i
$391$			7341.14i			0.0480186i
$392$	−1552.57	−	107530.i	−0.0101036	−	0.699776i
$393$	−372869.			−2.41419
$394$	−284.534	−	59123.9i	−0.00183291	−	0.380865i
$395$			25982.9i			0.166530i
$396$	2223.13	+	230969.i	0.0141767	+	1.47287i
$397$	77069.3			0.488990			0.244495	−	0.969650i	$-0.421378\pi$
$397$	77069.3			0.488990			0.244495	+	0.969650i	$0.421378\pi$
$398$	−168681.	+	811.778i	−1.06488	+	0.00512473i
$399$			155993.i			0.979849i
$400$	−140731.	+	2709.38i	−0.879566	+	0.0169336i
$401$	−5569.30			−0.0346347			−0.0173174	−	0.999850i	$-0.505513\pi$
$401$	−5569.30			−0.0346347			−0.0173174	+	0.999850i	$0.505513\pi$
$402$	−2365.15	−	491460.i	−0.0146355	−	3.04114i
$403$		−	20772.3i		−	0.127901i
$404$	−149899.	+	1442.81i	−0.918411	+	0.00883991i
$405$	−26847.7			−0.163680
$406$	21554.6	−	103.732i	0.130764	−	0.000629302i
$407$		−	200135.i		−	1.20819i
$408$	−64279.9	+	928.098i	−0.386149	+	0.00557536i
$409$	47028.9			0.281137			0.140568	−	0.990071i	$-0.455107\pi$
$409$	47028.9			0.281137			0.140568	+	0.990071i	$0.455107\pi$
$410$	336.151	+	69849.6i	0.00199971	+	0.415524i
$411$			285317.i			1.68905i
$412$	−3016.60	−	313405.i	−0.0177714	−	1.84634i
$413$	110292.			0.646610
$414$	−64766.0	+	311.686i	−0.377874	+	0.00181852i
$415$			85351.6i			0.495582i
$416$	297.468	+	12360.0i	0.00171891	+	0.0714221i
$417$	−269745.			−1.55125
$418$	−728.870	−	151453.i	−0.00417155	−	0.866816i
$419$			85422.2i			0.486567i	0.969955	+	0.243283i	$0.0782245\pi$
$419$			85422.2i			0.486567i	−0.969955	+	0.243283i	$0.921775\pi$
$420$	56202.4	−	540.960i	0.318608	−	0.00306667i
$421$	−6485.60			−0.0365920			−0.0182960	−	0.999833i	$-0.505824\pi$
$421$	−6485.60			−0.0365920			−0.0182960	+	0.999833i	$0.505824\pi$
$422$	237767.	−	1144.25i	1.33514	−	0.00642535i
$423$		−	280955.i		−	1.57021i
$424$	−2385.51	−	165220.i	−0.0132694	−	0.919034i
$425$	36593.2			0.202592
$426$	−1268.12	−	263506.i	−0.00698781	−	1.45201i
$427$			114972.i			0.630577i
$428$	1757.78	+	182622.i	0.00959572	+	0.996935i
$429$	−17921.2			−0.0973763
$430$	18724.1	−	90.1099i	0.101266	−	0.000487344i
$431$		−	131497.i		−	0.707885i	−0.935267	−	0.353942i	$-0.884841\pi$
$431$		−	131497.i		−	0.707885i	0.935267	−	0.353942i	$-0.115159\pi$
$432$	−4893.03	−	254154.i	−0.0262187	−	1.36185i
$433$	109324.			0.583098			0.291549	−	0.956556i	$-0.405829\pi$
$433$	109324.			0.583098			0.291549	+	0.956556i	$0.405829\pi$
$434$	−889.060	−	184740.i	−0.00472010	−	0.980801i
$435$		−	26266.9i		−	0.138813i
$436$	31430.7	−	302.528i	0.165341	−	0.00159145i
$437$	42468.0			0.222382
$438$	128034.	−	616.163i	0.667386	−	0.00321179i
$439$		−	202782.i		−	1.05220i	−0.850421	−	0.526102i	$-0.823653\pi$
$439$		−	202782.i		−	1.05220i	0.850421	−	0.526102i	$-0.176347\pi$
$440$	−54564.4	+	787.822i	−0.281841	+	0.00406933i
$441$	−246659.			−1.26829
$442$	−15.4683	−	3214.19i	−7.91768e−5	−	0.0164523i
$443$		−	118804.i		−	0.605373i	−0.953090	−	0.302686i	$-0.902117\pi$
$443$		−	118804.i		−	0.605373i	0.953090	−	0.302686i	$-0.0978835\pi$
$444$	4729.86	+	491403.i	0.0239929	+	2.49271i
$445$	−49982.2			−0.252404
$446$	61052.6	−	293.816i	0.306927	−	0.00147708i
$447$			311068.i			1.55683i
$448$	3174.56	+	109912.i	0.0158171	+	0.547632i
$449$	58661.9			0.290980			0.145490	−	0.989360i	$-0.453524\pi$
$449$	58661.9			0.290980			0.145490	+	0.989360i	$0.453524\pi$
$450$	1553.66	+	322838.i	0.00767238	+	1.59426i
$451$		−	198081.i		−	0.973845i
$452$	175937.	−	1693.43i	0.861151	−	0.00828877i
$453$	−74890.4			−0.364947
$454$	103794.	−	499.511i	0.503573	−	0.00242344i
$455$			2810.16i			0.0135740i
$456$	5368.99	+	371855.i	0.0258204	+	1.78831i
$457$	−223451.			−1.06992			−0.534959	−	0.844878i	$-0.679673\pi$
$457$	−223451.			−1.06992			−0.534959	+	0.844878i	$0.679673\pi$
$458$	−1281.51	−	266288.i	−0.00610929	−	1.26946i
$459$			66086.0i			0.313678i
$460$	−147.273	−	15300.7i	−0.000695996	−	0.0723097i
$461$	377443.			1.77603			0.888013	−	0.459819i	$-0.152086\pi$
$461$	377443.			1.77603			0.888013	+	0.459819i	$0.152086\pi$
$462$	−159384.	+	767.033i	−0.746723	+	0.00359360i
$463$		−	272861.i		−	1.27286i	−0.771336	−	0.636428i	$-0.780411\pi$
$463$		−	272861.i		−	1.27286i	0.771336	−	0.636428i	$-0.219589\pi$
$464$	51378.2	−	989.145i	0.238640	−	0.00459435i
$465$	−225127.			−1.04117
$466$	675.672	+	140399.i	0.00311146	+	0.646537i
$467$			267888.i			1.22834i	0.789173	+	0.614171i	$0.210510\pi$
$467$			267888.i			1.22834i	−0.789173	+	0.614171i	$0.789490\pi$
$468$	28356.0	−	272.933i	0.129465	−	0.00124613i
$469$	218540.			0.993539
$470$	66376.1	−	319.435i	0.300480	−	0.00144606i
$471$			297396.i			1.34058i
$472$	262912.	−	3796.03i	1.18012	−	0.0170391i
$473$	−53098.3			−0.237333
$474$	870.684	+	180921.i	0.00387529	+	0.805255i
$475$		−	211689.i		−	0.938236i
$476$	−275.136	−	28584.9i	−0.00121432	−	0.126161i
$477$	−378991.			−1.66568
$478$	−138598.	+	667.003i	−0.606599	+	0.00291926i
$479$			34754.2i			0.151474i	0.997128	+	0.0757368i	$0.0241309\pi$
$479$			34754.2i			0.151474i	−0.997128	+	0.0757368i	$0.975869\pi$
$480$	133956.	−	3223.92i	0.581408	−	0.0139927i
$481$	−24570.5			−0.106200
$482$	776.342	+	161318.i	0.00334163	+	0.694366i
$483$		−	44691.6i		−	0.191572i
$484$	−79503.2	+	765.236i	−0.339386	+	0.00326667i
$485$	86087.3			0.365979
$486$	134776.	−	648.611i	0.570612	−	0.00274607i
$487$			43208.8i			0.182186i	0.995842	+	0.0910928i	$0.0290360\pi$
$487$			43208.8i			0.182186i	−0.995842	+	0.0910928i	$0.970964\pi$
$488$	3957.14	+	274071.i	0.0166166	+	1.15086i
$489$	−440362.			−1.84159
$490$	−280.442	−	58273.6i	−0.00116802	−	0.242706i
$491$		−	8589.30i		−	0.0356283i	−0.999841	−	0.0178141i	$-0.994329\pi$
$491$		−	8589.30i		−	0.0356283i	0.999841	−	0.0178141i	$-0.00567072\pi$
$492$	4681.32	+	486359.i	0.0193392	+	2.00922i
$493$	−13359.5			−0.0549664
$494$	−18593.9	+	89.4831i	−0.0761932	+	0.000366680i
$495$			125163.i			0.510816i
$496$	−8477.74	−	440351.i	−0.0344601	−	1.78993i
$497$	117174.			0.474372
$498$	2860.13	+	594313.i	0.0115326	+	2.39638i
$499$			60266.8i			0.242034i	0.992650	+	0.121017i	$0.0386156\pi$
$499$			60266.8i			0.242034i	−0.992650	+	0.121017i	$0.961384\pi$
$500$	−162965.	+	1568.58i	−0.651862	+	0.00627431i
$501$	92308.5			0.367761
$502$	261700.	−	1259.43i	1.03847	−	0.00499766i
$503$			355156.i			1.40373i	0.712310	+	0.701865i	$0.247649\pi$
$503$			355156.i			1.40373i	−0.712310	+	0.701865i	$0.752351\pi$
$504$	252175.	−	3640.99i	0.992751	−	0.0143337i
$505$	−81230.7			−0.318521
$506$	208.820	+	43391.1i	0.000815587	+	0.169473i
$507$		−	428864.i		−	1.66841i
$508$	−3372.07	−	350337.i	−0.0130668	−	1.35756i
$509$	343577.			1.32614			0.663070	−	0.748558i	$-0.269253\pi$
$509$	343577.			1.32614			0.663070	+	0.748558i	$0.269253\pi$
$510$	−34835.0	+	167.643i	−0.133929	+	0.000644534i
$511$			56933.4i			0.218035i
$512$	11350.5	+	261898.i	0.0432986	+	0.999062i
$513$	382303.			1.45269
$514$	1342.78	+	279019.i	0.00508251	+	1.05611i
$515$		−	169835.i		−	0.640343i
$516$	130375.	−	1254.89i	0.489661	−	0.00471310i
$517$	−188231.			−0.704222
$518$	−218519.	+	1051.62i	−0.814386	+	0.00391923i
$519$			191697.i			0.711675i
$520$	96.7206	+	6698.85i	0.000357694	+	0.0247739i
$521$	108928.			0.401297			0.200649	−	0.979663i	$-0.435695\pi$
$521$	108928.			0.401297			0.200649	+	0.979663i	$0.435695\pi$
$522$	−567.212	−	117862.i	−0.00208164	−	0.432548i
$523$			13496.1i			0.0493406i	0.999696	+	0.0246703i	$0.00785360\pi$
$523$			13496.1i			0.0493406i	−0.999696	+	0.0246703i	$0.992146\pi$
$524$	−3804.50	−	395264.i	−0.0138559	−	1.43954i
$525$	−222774.			−0.808249
$526$	−357993.	+	1722.84i	−1.29391	+	0.00622692i
$527$			114501.i			0.412278i
$528$	−379911.	+	7314.14i	−1.36274	+	0.0262359i
$529$	−12167.0			−0.0434783
$530$	−430.898	−	89537.2i	−0.00153399	−	0.318751i
$531$		−	603083.i		−	2.13889i
$532$	−165362.	+	1591.65i	−0.584269	+	0.00562372i
$533$	−24318.3			−0.0856012
$534$	−348032.	+	1674.90i	−1.22050	+	0.00587363i
$535$			98963.4i			0.345754i
$536$	520954.	−	7521.73i	1.81330	−	0.0261811i
$537$	−202781.			−0.703200
$538$	−1043.45	−	216820.i	−0.00360501	−	0.749092i
$539$			165253.i			0.568818i
$540$	−1325.77	−	137739.i	−0.00454654	−	0.472357i
$541$	−125339.			−0.428245			−0.214122	−	0.976807i	$-0.568689\pi$
$541$	−125339.			−0.428245			−0.214122	+	0.976807i	$0.568689\pi$
$542$	−26575.8	+	127.896i	−0.0904667	+	0.000435371i
$543$		−	550246.i		−	1.86619i
$544$	−1639.71	−	68131.2i	−0.00554076	−	0.230223i
$545$	17032.4			0.0573432
$546$	94.1684	+	19567.5i	0.000315879	+	0.0656371i
$547$			92377.0i			0.308737i	0.988013	+	0.154369i	$0.0493343\pi$
$547$			92377.0i			0.308737i	−0.988013	+	0.154369i	$0.950666\pi$
$548$	−302453.	+	2911.18i	−1.00716	+	0.00969411i
$549$	628678.			2.08585
$550$	216291.	−	1040.90i	0.715011	−	0.00344099i
$551$			77284.0i			0.254558i
$552$	−1538.20	−	106536.i	−0.00504819	−	0.349637i
$553$	−80451.2			−0.263077
$554$	1511.77	+	314134.i	0.00492568	+	1.02352i
$555$			266292.i			0.864514i
$556$	−2752.30	−	285947.i	−0.00890321	−	0.924987i
$557$	323942.			1.04414			0.522068	−	0.852904i	$-0.325161\pi$
$557$	323942.			1.04414			0.522068	+	0.852904i	$0.325161\pi$
$558$	−1.01017e6	+	4861.45i	−3.24434	+	0.0156134i
$559$			6518.86i			0.0208616i
$560$	1146.90	+	59572.5i	0.00365722	+	0.189963i
$561$	98785.7			0.313884
$562$	−78.8625	−	16387.0i	−0.000249688	−	0.0518832i
$563$			436042.i			1.37566i	0.725871	+	0.687831i	$0.241437\pi$
$563$			436042.i			1.37566i	−0.725871	+	0.687831i	$0.758563\pi$
$564$	462174.	−	4448.52i	1.45294	−	0.0139848i
$565$	95340.3			0.298662
$566$	434280.	−	2089.97i	1.35562	−	0.00652391i
$567$		−	83129.0i		−	0.258575i
$568$	279319.	−	4032.92i	0.865773	−	0.0125004i
$569$	−387367.			−1.19646			−0.598231	−	0.801324i	$-0.704129\pi$
$569$	−387367.			−1.19646			−0.598231	+	0.801324i	$0.704129\pi$
$570$	969.806	+	201518.i	0.00298494	+	0.620247i
$571$		−	583498.i		−	1.78965i	−0.446420	−	0.894824i	$-0.647301\pi$
$571$		−	583498.i		−	1.78965i	0.446420	−	0.894824i	$-0.352699\pi$
$572$	−182.856	−	18997.6i	−0.000558879	−	0.0580640i
$573$	964783.			2.93846
$574$	−216277.	+	1040.83i	−0.656426	+	0.00315905i
$575$			60648.6i			0.183436i
$576$	601007.	−	17358.8i	1.81148	−	0.0523207i
$577$	−366826.			−1.10182			−0.550908	−	0.834566i	$-0.685718\pi$
$577$	−366826.			−1.10182			−0.550908	+	0.834566i	$0.685718\pi$
$578$	−1522.50	−	316363.i	−0.00455722	−	0.946956i
$579$			1.11748e6i			3.33336i
$580$	27844.5	−	268.010i	0.0827720	−	0.000796699i
$581$	−264276.			−0.782898
$582$	599435.	−	2884.78i	1.76969	−	0.00851662i
$583$			253912.i			0.747043i
$584$	1959.54	+	135718.i	0.00574552	+	0.397933i
$585$	15366.2			0.0449008
$586$	−2467.41	−	512708.i	−0.00718531	−	1.49305i
$587$			514906.i			1.49435i	0.664628	+	0.747175i	$0.268590\pi$
$587$			514906.i			1.49435i	−0.664628	+	0.747175i	$0.731410\pi$
$588$	−3905.49	−	405756.i	−0.0112959	−	1.17357i
$589$	662384.			1.90932
$590$	142479.	−	685.682i	0.409306	−	0.00196978i
$591$		−	223088.i		−	0.638708i
$592$	−520869.	+	10027.9i	−1.48623	+	0.0286132i
$593$	−313256.			−0.890819			−0.445409	−	0.895327i	$-0.646942\pi$
$593$	−313256.			−0.890819			−0.445409	+	0.895327i	$0.646942\pi$
$594$	1879.82	+	390613.i	0.00532776	+	1.10707i
$595$		−	15490.2i		−	0.0437546i
$596$	−329751.	+	3173.93i	−0.928312	+	0.00893520i
$597$	−636474.			−1.78580
$598$	5327.11	−	25.6367i	0.0148967	−	7.16903e-5i
$599$		−	129271.i		−	0.360286i	−0.983640	−	0.180143i	$-0.942344\pi$
$599$		−	129271.i		−	0.360286i	0.983640	−	0.180143i	$-0.0576561\pi$
$600$	−531046.	+	7667.45i	−1.47513	+	0.0212985i
$601$	107075.			0.296442			0.148221	−	0.988954i	$-0.452645\pi$
$601$	107075.			0.296442			0.148221	+	0.988954i	$0.452645\pi$
$602$	279.009	+	57975.9i	0.000769883	+	0.159976i
$603$		−	1.19499e6i		−	3.28648i
$604$	−764.131	−	79388.4i	−0.00209457	−	0.217612i
$605$	−43082.9			−0.117705
$606$	−565618.	+	2722.04i	−1.54020	+	0.00741223i
$607$			85001.9i			0.230702i	0.993325	+	0.115351i	$0.0367993\pi$
$607$			85001.9i			0.230702i	−0.993325	+	0.115351i	$0.963201\pi$
$608$	−394134.	+	9485.62i	−1.06620	+	0.0256601i
$609$	81330.6			0.219290
$610$	714.782	+	148526.i	0.00192094	+	0.399157i
$611$			23109.0i			0.0619012i
$612$	−156305.	+	1504.47i	−0.417320	+	0.00401680i
$613$	224732.			0.598058			0.299029	−	0.954244i	$-0.403337\pi$
$613$	224732.			0.598058			0.299029	+	0.954244i	$0.403337\pi$
$614$	−665754.	+	3203.94i	−1.76594	+	0.00849861i
$615$			263559.i			0.696831i
$616$	−2439.35	−	168949.i	−0.00642854	−	0.445239i
$617$	328259.			0.862275			0.431138	−	0.902286i	$-0.358112\pi$
$617$	328259.			0.862275			0.431138	+	0.902286i	$0.358112\pi$
$618$	−5691.16	−	1.18258e6i	−0.0149013	−	3.09637i
$619$			425665.i			1.11093i	0.831540	+	0.555465i	$0.187460\pi$
$619$			425665.i			1.11093i	−0.831540	+	0.555465i	$0.812540\pi$
$620$	−2297.05	−	238649.i	−0.00597568	−	0.620835i
$621$	−109529.			−0.284018
$622$	316219.	−	1521.80i	0.817349	−	0.00393349i
$623$		−	154761.i		−	0.398736i
$624$	897.954	+	46641.6i	0.00230614	+	0.119785i
$625$	255333.			0.653652
$626$	−3410.00	−	708572.i	−0.00870174	−	1.80815i
$627$		−	571469.i		−	1.45364i
$628$	−315259.	+	3034.43i	−0.799370	+	0.00769411i
$629$	135438.			0.342325
$630$	136660.	−	657.677i	0.344319	−	0.00165703i
$631$			156911.i			0.394090i	0.980394	+	0.197045i	$0.0631345\pi$
$631$			156911.i			0.394090i	−0.980394	+	0.197045i	$0.936866\pi$
$632$	−191779.	+	2768.98i	−0.480139	+	0.00693243i
$633$	897149.			2.23902
$634$	3734.88	+	776080.i	0.00929177	+	1.93076i
$635$		−	189848.i		−	0.470825i
$636$	−6000.78	−	623443.i	−0.0148352	−	1.54128i
$637$	20288.1			0.0499992
$638$	−78963.9	+	380.014i	−0.193993	+	0.000933593i
$639$		−	640718.i		−	1.56915i
$640$	4784.36	+	141969.i	0.0116806	+	0.346604i
$641$	−645391.			−1.57075			−0.785374	−	0.619022i	$-0.787529\pi$
$641$	−645391.			−1.57075			−0.785374	+	0.619022i	$0.787529\pi$
$642$	3316.26	+	689093.i	0.00804597	+	1.67189i
$643$			384517.i			0.930023i	0.885305	+	0.465012i	$0.153950\pi$
$643$			384517.i			0.930023i	−0.885305	+	0.465012i	$0.846050\pi$
$644$	47375.9	−	456.004i	0.114231	−	0.00109950i
$645$	70650.5			0.169823
$646$	102494.	−	493.250i	0.245602	−	0.00118196i
$647$			112828.i			0.269530i	0.990878	+	0.134765i	$0.0430280\pi$
$647$			112828.i			0.269530i	−0.990878	+	0.134765i	$0.956972\pi$
$648$	−2861.15	−	198162.i	−0.00681381	−	0.471923i
$649$	−404046.			−0.959271
$650$	−127.791	−	26553.9i	−0.000302464	−	0.0628496i
$651$		−	697066.i		−	1.64480i
$652$	−4493.16	−	466811.i	−0.0105696	−	1.09811i
$653$	−269520.			−0.632069			−0.316034	−	0.948748i	$-0.602352\pi$
$653$	−269520.			−0.632069			−0.316034	+	0.948748i	$0.602352\pi$
$654$	118598.	−	570.754i	0.277283	−	0.00133442i
$655$		−	214194.i		−	0.499258i
$656$	−515523.	+	9924.97i	−1.19796	+	0.0230633i
$657$	311316.			0.721226
$658$	989.073	+	205522.i	0.00228442	+	0.474685i
$659$			165385.i			0.380824i	0.981704	+	0.190412i	$0.0609824\pi$
$659$			165385.i			0.380824i	−0.981704	+	0.190412i	$0.939018\pi$
$660$	−205894.	+	1981.77i	−0.472667	+	0.00454952i
$661$	55446.3			0.126902			0.0634512	−	0.997985i	$-0.479789\pi$
$661$	55446.3			0.126902			0.0634512	+	0.997985i	$0.479789\pi$
$662$	290155.	−	1396.37i	0.662085	−	0.00318628i
$663$		−	12127.9i		−	0.0275904i
$664$	−629979.	+	9095.88i	−1.42886	+	0.0206304i
$665$	−89610.0			−0.202634
$666$	5750.36	+	1.19488e6i	0.0129642	+	2.69387i
$667$		−	22141.7i		−	0.0497691i
$668$	941.854	+	97852.7i	0.00211072	+	0.219290i
$669$	230366.			0.514714
$670$	282319.	−	1358.66i	0.628912	−	0.00302664i
$671$		−	421194.i		−	0.935485i
$672$	9982.28	+	414771.i	0.0221050	+	0.918481i
$673$	123942.			0.273645			0.136822	−	0.990596i	$-0.456311\pi$
$673$	123942.			0.273645			0.136822	+	0.990596i	$0.456311\pi$
$674$	2078.20	+	431833.i	0.00457475	+	0.950597i
$675$			545967.i			1.19828i
$676$	454623.	−	4375.84i	0.994850	−	0.00957565i
$677$	642026.			1.40080			0.700399	−	0.713752i	$-0.253005\pi$
$677$	642026.			1.40080			0.700399	+	0.713752i	$0.253005\pi$
$678$	663865.	−	3194.85i	1.44418	−	0.00695010i
$679$			266554.i			0.578156i
$680$	−533.145	−	36925.5i	−0.00115300	−	0.0798562i
$681$	391641.			0.844488
$682$	3257.01	+	676782.i	0.00700246	+	1.45506i
$683$			262866.i			0.563499i	0.959488	+	0.281750i	$0.0909148\pi$
$683$			262866.i			0.563499i	−0.959488	+	0.281750i	$0.909085\pi$
$684$	8703.25	+	904213.i	0.0186024	+	1.93267i
$685$	−163900.			−0.349299
$686$	438252.	−	2109.08i	0.931269	−	0.00448173i
$687$		−	1.00477e6i		−	2.12888i
$688$	2660.52	+	138193.i	0.00562069	+	0.291950i
$689$	31172.6			0.0656652
$690$	−277.847	−	57734.5i	−0.000583590	−	0.121266i
$691$		−	265572.i		−	0.556194i	−0.960553	−	0.278097i	$-0.910296\pi$
$691$		−	265572.i		−	0.556194i	0.960553	−	0.278097i	$-0.0897037\pi$
$692$	−203211.	+	1955.95i	−0.424361	+	0.00408457i
$693$	−387544.			−0.806964
$694$	138417.	−	666.134i	0.287390	−	0.00138306i
$695$		−	154955.i		−	0.320801i
$696$	193875.	−	2799.25i	0.400225	−	0.00577861i
$697$	134048.			0.275927
$698$	−2750.59	−	571550.i	−0.00564565	−	1.17312i
$699$			529760.i			1.08424i
$700$	−2273.03	−	236154.i	−0.00463884	−	0.481946i
$701$	−915607.			−1.86326			−0.931629	−	0.363411i	$-0.881612\pi$
$701$	−915607.			−1.86326			−0.931629	+	0.363411i	$0.881612\pi$
$702$	47955.4	−	230.785i	0.0973114	−	0.000468311i
$703$		−	783500.i		−	1.58536i
$704$	−11629.8	−	402655.i	−0.0234653	−	0.812433i
$705$	250453.			0.503903
$706$	2897.91	+	602164.i	0.00581401	+	1.20811i
$707$		−	251516.i		−	0.503184i
$708$	992076.	−	9548.95i	1.97915	−	0.0190497i
$709$	−630772.			−1.25482			−0.627408	−	0.778691i	$-0.715884\pi$
$709$	−630772.			−1.25482			−0.627408	+	0.778691i	$0.715884\pi$
$710$	151371.	−	728.471i	0.300279	−	0.00144509i
$711$			439913.i			0.870218i
$712$	−5326.58	−	368918.i	−0.0105072	−	0.727729i
$713$	−189772.			−0.373295
$714$	−519.077	−	107860.i	−0.00101821	−	0.211575i
$715$		−	10294.8i		−	0.0201376i
$716$	−2069.04	−	214960.i	−0.00403593	−	0.419307i
$717$	−522963.			−1.01726
$718$	−158500.	+	762.781i	−0.307454	+	0.00147962i
$719$			529083.i			1.02345i	0.859150	+	0.511724i	$0.170993\pi$
$719$			529083.i			1.02345i	−0.859150	+	0.511724i	$0.829007\pi$
$720$	325747.	−	6271.35i	0.628370	−	0.0120975i
$721$	525863.			1.01158
$722$	−344.773	−	71641.1i	−0.000661391	−	0.137432i
$723$			608690.i			1.16445i
$724$	583294.	−	5614.34i	1.11278	−	0.0107108i
$725$	−110369.			−0.209977
$726$	−299991.	+	1443.71i	−0.569161	+	0.00273909i
$727$			110867.i			0.209765i	0.994485	+	0.104883i	$0.0334467\pi$
$727$			110867.i			0.209765i	−0.994485	+	0.104883i	$0.966553\pi$
$728$	−20741.8	+	299.478i	−0.0391366	+	0.000565069i
$729$	759368.			1.42888
$730$	353.954	+	73549.0i	0.000664204	+	0.138017i
$731$		−	35933.4i		−	0.0672455i
$732$	9954.21	+	1.03418e6i	0.0185774	+	1.93007i
$733$	782648.			1.45666			0.728330	−	0.685226i	$-0.240297\pi$
$733$	782648.			1.45666			0.728330	+	0.685226i	$0.240297\pi$
$734$	−238379.	+	1147.20i	−0.442462	+	0.00212935i
$735$		−	219880.i		−	0.407015i
$736$	112919.	−	2717.61i	0.208454	−	0.00501685i
$737$	−800605.			−1.47395
$738$	5691.35	+	1.18262e6i	0.0104497	+	2.17136i
$739$			720072.i			1.31852i	0.751914	+	0.659261i	$0.229131\pi$
$739$			720072.i			1.31852i	−0.751914	+	0.659261i	$0.770869\pi$
$740$	−282286.	+	2717.06i	−0.515496	+	0.00496177i
$741$	−70159.1			−0.127776
$742$	277236.	−	1334.20i	0.503549	−	0.00242333i
$743$		−	602226.i		−	1.09089i	−0.838146	−	0.545447i	$-0.816360\pi$
$743$		−	602226.i		−	1.09089i	0.838146	−	0.545447i	$-0.183640\pi$
$744$	−23991.7	−	1.66166e6i	−0.0433427	−	3.00191i
$745$	−178693.			−0.321954
$746$	−4178.39	−	868238.i	−0.00750813	−	1.56013i
$747$			1.44508e6i			2.58971i
$748$	1007.94	+	104719.i	0.00180149	+	0.187164i
$749$	−306422.			−0.546206
$750$	−614921.	+	2959.31i	−1.09319	+	0.00526099i
$751$			101175.i			0.179389i	0.995969	+	0.0896943i	$0.0285890\pi$
$751$			101175.i			0.179389i	−0.995969	+	0.0896943i	$0.971411\pi$
$752$	9431.42	+	489887.i	0.0166779	+	0.866284i
$753$	987454.			1.74151
$754$	46.6541	+	9694.37i	8.20630e−5	+	0.0170521i
$755$		−	43020.7i		−	0.0754716i
$756$	426485.	−	4105.01i	0.746208	−	0.00718242i
$757$	−922318.			−1.60949			−0.804746	−	0.593619i	$-0.797699\pi$
$757$	−922318.			−1.60949			−0.804746	+	0.593619i	$0.797699\pi$
$758$	436394.	−	2100.15i	0.759522	−	0.00365520i
$759$			163725.i			0.284204i
$760$	−213612.	+	3084.21i	−0.369827	+	0.00533970i
$761$	−232213.			−0.400974			−0.200487	−	0.979696i	$-0.564253\pi$
$761$	−232213.			−0.400974			−0.200487	+	0.979696i	$0.564253\pi$
$762$	−6361.81	−	1.32193e6i	−0.0109565	−	2.27667i
$763$			52737.6i			0.0905881i
$764$	9844.00	+	1.02273e6i	0.0168649	+	1.75216i
$765$	−84701.8			−0.144734
$766$	−615172.	+	2960.52i	−1.04843	+	0.00504557i
$767$			49604.6i			0.0843201i
$768$	38071.4	+	988386.i	0.0645470	+	1.67573i
$769$	286510.			0.484492			0.242246	−	0.970215i	$-0.422116\pi$
$769$	286510.			0.484492			0.242246	+	0.970215i	$0.422116\pi$
$770$	−440.622	−	91557.8i	−0.000743164	−	0.154424i
$771$			1.05281e6i			1.77108i
$772$	−1.18460e6	+	11402.0i	−1.98763	+	0.0191314i
$773$	715722.			1.19780			0.598902	−	0.800822i	$-0.295604\pi$
$773$	715722.			1.19780			0.598902	+	0.800822i	$0.295604\pi$
$774$	317017.	−	1525.64i	0.529176	−	0.00254666i
$775$			945951.i			1.57494i
$776$	9174.29	+	635409.i	0.0152352	+	1.05519i
$777$	−824524.			−1.36572
$778$	−1258.47	−	261500.i	−0.00207914	−	0.432029i
$779$		−	775459.i		−	1.27786i
$780$	243.301	+	25277.5i	0.000399904	+	0.0415475i
$781$	−429260.			−0.703750
$782$	−29364.2	+	141.315i	−0.0480181	+	0.000231087i
$783$		−	199323.i		−	0.325112i
$784$	430087.	−	8280.13i	0.699719	−	0.0134712i
$785$	−170839.			−0.277235
$786$	−7177.63	−	1.49146e6i	−0.0116181	−	2.41416i
$787$		−	58952.2i		−	0.0951811i	−0.998867	−	0.0475905i	$-0.984846\pi$
$787$		−	58952.2i		−	0.0951811i	0.998867	−	0.0475905i	$-0.0151543\pi$
$788$	236488.	−	2276.24i	0.380852	−	0.00366578i
$789$	−1.35079e6			−2.16987
$790$	−103930.	+	500.164i	−0.166528	+	0.000801417i
$791$			295204.i			0.471812i
$792$	−923824.	+	13338.5i	−1.47278	+	0.0212646i
$793$	−51709.8			−0.0822293
$794$	1483.57	+	308274.i	0.00235324	+	0.488985i
$795$		−	337845.i		−	0.534544i
$796$	−6494.15	−	674701.i	−0.0102493	−	1.06484i
$797$	−520467.			−0.819364			−0.409682	−	0.912228i	$-0.634360\pi$
$797$	−520467.			−0.819364			−0.409682	+	0.912228i	$0.634360\pi$
$798$	−623964.	+	3002.83i	−0.979837	+	0.00471547i
$799$		−	127382.i		−	0.199533i
$800$	−13546.4	−	562864.i	−0.0211663	−	0.879474i
$801$	−846244.			−1.31896
$802$	−107.208	−	22276.9i	−0.000166678	−	0.0346343i
$803$		−	208572.i		−	0.323463i
$804$	1.96577e6	−	18921.0i	3.04103	−	0.0292706i
$805$	25673.1			0.0396174
$806$	83088.2	−	399.862i	0.127900	−	0.000615517i
$807$		−	818114.i		−	1.25622i
$808$	−8656.72	−	599563.i	−0.0132596	−	0.918358i
$809$	−1.21393e6			−1.85479			−0.927396	−	0.374081i	$-0.877958\pi$
$809$	−1.21393e6			−1.85479			−0.927396	+	0.374081i	$0.877958\pi$
$810$	−516.812	−	107390.i	−0.000787703	−	0.163679i
$811$			890630.i			1.35412i	0.735930	+	0.677058i	$0.236745\pi$
$811$			890630.i			1.35412i	−0.735930	+	0.677058i	$0.763255\pi$
$812$	829.843	+	86215.5i	0.00125859	+	0.130759i
$813$	−100277.			−0.151712
$814$	800531.	−	3852.55i	1.20817	−	0.00581433i
$815$		−	252966.i		−	0.380844i
$816$	−4949.72	−	257099.i	−0.00743362	−	0.386117i
$817$	−207872.			−0.311424
$818$	905.295	+	188113.i	0.00135296	+	0.281134i
$819$			47578.6i			0.0709323i
$820$	−279389.	+	2689.18i	−0.415510	+	0.00399937i
$821$	570780.			0.846804			0.423402	−	0.905942i	$-0.360836\pi$
$821$	570780.			0.846804			0.423402	+	0.905942i	$0.360836\pi$
$822$	−1.14125e6	+	5492.28i	−1.68903	+	0.00812848i
$823$		−	512644.i		−	0.756861i	−0.925630	−	0.378431i	$-0.876464\pi$
$823$		−	512644.i		−	0.756861i	0.925630	−	0.378431i	$-0.123536\pi$
$824$	1.25355e6	−	18099.2i	1.84623	−	0.0266567i
$825$	816116.			1.19907
$826$	2123.09	+	441161.i	0.00311177	+	0.646602i
$827$		−	887671.i		−	1.29790i	−0.760831	−	0.648950i	$-0.775208\pi$
$827$		−	887671.i		−	1.29790i	0.760831	−	0.648950i	$-0.224792\pi$
$828$	−2493.46	−	259055.i	−0.00363699	−	0.377861i
$829$	573777.			0.834899			0.417450	−	0.908700i	$-0.362924\pi$
$829$	573777.			0.834899			0.417450	+	0.908700i	$0.362924\pi$
$830$	−341402.	+	1643.00i	−0.495576	+	0.00238496i
$831$			1.18530e6i			1.71643i
$832$	−49433.8	+	1427.79i	−0.0714130	+	0.00206261i
$833$	−111833.			−0.161168
$834$	−5192.54	−	1.07897e6i	−0.00746531	−	1.55123i
$835$			53026.5i			0.0760537i
$836$	605793.	−	5830.89i	0.866785	−	0.00834300i
$837$	−1.70835e6			−2.43852
$838$	−341685.	+	1644.36i	−0.486561	+	0.00234158i
$839$		−	543571.i		−	0.772204i	−0.922456	−	0.386102i	$-0.873821\pi$
$839$		−	543571.i		−	0.772204i	0.922456	−	0.386102i	$-0.126179\pi$
$840$	3245.70	+	224797.i	0.00459992	+	0.318589i
$841$	−666987.			−0.943030
$842$	−124.846	−	25942.1i	−0.000176097	−	0.0365915i
$843$		−	61832.0i		−	0.0870078i
$844$	9153.90	+	951033.i	0.0128505	+	1.33509i
$845$	246361.			0.345031
$846$	1.12381e6	−	5408.32i	1.57019	−	0.00755652i
$847$		−	133398.i		−	0.185945i
$848$	660827.	−	12722.4i	0.918959	−	0.0176920i
$849$	1.63864e6			2.27336
$850$	704.411	+	146371.i	0.000974963	+	0.202590i
$851$			224471.i			0.309957i
$852$	1.05399e6	−	10144.8i	1.45196	−	0.0139755i
$853$	231144.			0.317676			0.158838	−	0.987305i	$-0.449225\pi$
$853$	231144.			0.317676			0.158838	+	0.987305i	$0.449225\pi$
$854$	−459884.	+	2213.19i	−0.630569	+	0.00303461i
$855$			489994.i			0.670284i
$856$	−730448.	+	10546.5i	−0.996877	+	0.0143933i
$857$	1.24547e6			1.69579			0.847894	−	0.530165i	$-0.177870\pi$
$857$	1.24547e6			1.69579			0.847894	+	0.530165i	$0.177870\pi$
$858$	−344.980	−	71684.1i	−0.000468618	−	0.0973752i
$859$		−	229570.i		−	0.311120i	−0.987826	−	0.155560i	$-0.950282\pi$
$859$		−	229570.i		−	0.311120i	0.987826	−	0.155560i	$-0.0497182\pi$
$860$	720.871	+	74893.9i	0.000974676	+	0.101263i
$861$	−816063.			−1.10082
$862$	525983.	−	2531.29i	0.707877	−	0.00340666i
$863$			616334.i			0.827551i	0.910379	+	0.413775i	$0.135790\pi$
$863$			616334.i			0.827551i	−0.910379	+	0.413775i	$0.864210\pi$
$864$	1.01651e6	−	24464.3i	1.36171	−	0.0327722i
$865$	−110120.			−0.147176
$866$	2104.47	+	437293.i	0.00280613	+	0.583091i
$867$		−	1.19371e6i		−	1.58804i
$868$	738933.	−	7112.40i	0.980767	−	0.00944010i
$869$	294727.			0.390284
$870$	105066.	−	505.631i	0.138811	−	0.000668029i
$871$			98290.1i			0.129561i
$872$	1815.13	+	125716.i	0.00238712	+	0.165332i
$873$	1.45754e6			1.91245
$874$	817.500	+	169870.i	0.00107020	+	0.222379i
$875$		−	273440.i		−	0.357146i
$876$	4929.25	+	512118.i	0.00642351	+	0.667362i
$877$	968470.			1.25918			0.629589	−	0.776929i	$-0.283224\pi$
$877$	968470.			1.25918			0.629589	+	0.776929i	$0.283224\pi$
$878$	811118.	−	3903.50i	1.05219	−	0.00506367i
$879$		−	1.93457e6i		−	2.50384i
$880$	−4201.60	−	218240.i	−0.00542562	−	0.281818i
$881$	195988.			0.252509			0.126254	−	0.991998i	$-0.459704\pi$
$881$	195988.			0.252509			0.126254	+	0.991998i	$0.459704\pi$
$882$	−4748.13	−	986625.i	−0.00610359	−	1.26828i
$883$		−	67516.7i		−	0.0865943i	−0.999062	−	0.0432972i	$-0.986214\pi$
$883$		−	67516.7i		−	0.0865943i	0.999062	−	0.0432972i	$-0.0137862\pi$
$884$	12856.3	−	123.745i	0.0164517	−	0.000158352i
$885$	537608.			0.686403
$886$	475210.	−	2286.95i	0.605366	−	0.00291332i
$887$			169572.i			0.215529i	0.994176	+	0.107765i	$0.0343693\pi$
$887$			169572.i			0.215529i	−0.994176	+	0.107765i	$0.965631\pi$
$888$	−1.96550e6	+	28378.6i	−2.49256	+	0.0359886i
$889$	587831.			0.743788
$890$	−962.146	−	199927.i	−0.00121468	−	0.252401i
$891$			304537.i			0.383606i
$892$	2350.50	+	244202.i	0.00295413	+	0.306916i
$893$	−736897.			−0.924068
$894$	−1.24426e6	+	5987.98i	−1.55681	+	0.00749214i
$895$		−	116487.i		−	0.145423i
$896$	−439582.	+	14813.9i	−0.547550	+	0.0184524i
$897$	20100.4			0.0249816
$898$	1129.23	+	234645.i	0.00140033	+	0.290977i
$899$		−	345350.i		−	0.427307i
$900$	−1.29131e6	+	12429.1i	−1.59421	+	0.0153446i
$901$	−171830.			−0.211666
$902$	792315.	−	3813.02i	0.973834	−	0.00468657i
$903$			218757.i			0.268278i
$904$	10160.4	+	703705.i	0.0124329	+	0.861101i
$905$	316088.			0.385932
$906$	−1441.62	−	299558.i	−0.00175629	−	0.364943i
$907$		−	102703.i		−	0.124844i	−0.998050	−	0.0624220i	$-0.980118\pi$
$907$		−	102703.i		−	0.124844i	0.998050	−	0.0624220i	$-0.0198825\pi$
$908$	3996.04	+	415163.i	0.00484683	+	0.503555i
$909$	−1.37531e6			−1.66446
$910$	−11240.5	+	54.0950i	−0.0135739	+	6.53242e-5i
$911$		−	459170.i		−	0.553270i	−0.960975	−	0.276635i	$-0.910781\pi$
$911$		−	459170.i		−	0.553270i	0.960975	−	0.276635i	$-0.0892193\pi$
$912$	−1.48730e6	+	28633.8i	−1.78817	+	0.0344262i
$913$	968156.			1.16146
$914$	−4301.39	−	893795.i	−0.00514892	−	1.06991i
$915$			560424.i			0.669383i
$916$	1.06511e6	−	10252.0i	1.26942	−	0.0122184i
$917$	663213.			0.788705
$918$	−264341.	+	1272.14i	−0.313674	+	0.00150956i
$919$		−	1.41323e6i		−	1.67333i	−0.547717	−	0.836664i	$-0.684503\pi$
$919$		−	1.41323e6i		−	1.67333i	0.547717	−	0.836664i	$-0.315497\pi$
$920$	61199.4	−	883.620i	0.0723055	−	0.00104397i
$921$	−2.51205e6			−2.96148
$922$	7265.69	+	1.50975e6i	0.00854702	+	1.77600i
$923$			52700.1i			0.0618597i
$924$	−6136.20	−	637512.i	−0.00718713	−	0.746697i
$925$	1.11892e6			1.30772
$926$	1.09143e6	−	5252.51i	1.27284	−	0.00612555i
$927$		−	2.87546e6i		−	3.34617i
$928$	4945.55	+	205491.i	0.00574274	+	0.238615i
$929$	−1.04495e6			−1.21077			−0.605387	−	0.795931i	$-0.706982\pi$
$929$	−1.04495e6			−1.21077			−0.605387	+	0.795931i	$0.706982\pi$
$930$	−4333.65	−	900499.i	−0.00501058	−	1.04116i
$931$			646944.i			0.746393i
$932$	−561578.	+	5405.31i	−0.646515	+	0.00622285i
$933$	1.19317e6			1.37069
$934$	−1.07154e6	+	5156.78i	−1.22833	+	0.00591133i
$935$			56747.4i			0.0649117i
$936$	1637.57	+	113418.i	0.00186916	+	0.129458i
$937$	1.13447e6			1.29215			0.646075	−	0.763274i	$-0.276409\pi$
$937$	1.13447e6			1.29215			0.646075	+	0.763274i	$0.276409\pi$
$938$	4206.84	+	874149.i	0.00478135	+	0.993527i
$939$		−	2.67361e6i		−	3.03226i
$940$	2555.45	+	265495.i	0.00289209	+	0.300470i
$941$	−721077.			−0.814334			−0.407167	−	0.913354i	$-0.633483\pi$
$941$	−721077.			−0.814334			−0.407167	+	0.913354i	$0.633483\pi$
$942$	−1.18957e6	+	5724.81i	−1.34057	+	0.00645148i
$943$			222168.i			0.249837i
$944$	20245.0	+	1.05156e6i	0.0227181	+	1.18003i
$945$	231113.			0.258798
$946$	−1022.13	−	212391.i	−0.00114215	−	0.237330i
$947$			1.47121e6i			1.64049i	0.572012	+	0.820245i	$0.306163\pi$
$947$			1.47121e6i			1.64049i	−0.572012	+	0.820245i	$0.693837\pi$
$948$	−723661.	+	6965.39i	−0.805227	+	0.00775049i
$949$	−25606.3			−0.0284324
$950$	846748.	−	4074.97i	0.938225	−	0.00451521i
$951$			2.92833e6i			3.23787i
$952$	114333.	−	1650.79i	0.126153	−	0.00182145i
$953$	444730.			0.489678			0.244839	−	0.969564i	$-0.421265\pi$
$953$	444730.			0.489678			0.244839	+	0.969564i	$0.421265\pi$
$954$	−7295.49	−	1.51595e6i	−0.00801600	−	1.66566i
$955$			554219.i			0.607680i
$956$	−5335.97	−	554373.i	−0.00583845	−	0.606578i
$957$	−297949.			−0.325326
$958$	−139015.	+	669.011i	−0.151472	+	0.000728958i
$959$		−	507487.i		−	0.551807i
$960$	15474.2	+	535757.i	0.0167905	+	0.581334i
$961$	−2.03639e6			−2.20503
$962$	−472.977	−	98280.9i	−0.000511081	−	0.106199i
$963$			1.67554e6i			1.80677i
$964$	−645249.	+	6210.66i	−0.694342	+	0.00668319i
$965$	−641934.			−0.689344
$966$	178765.	−	860.304i	0.191570	−	0.000921930i
$967$		−	736685.i		−	0.787823i	−0.919148	−	0.393911i	$-0.871122\pi$
$967$		−	736685.i		−	0.787823i	0.919148	−	0.393911i	$-0.128878\pi$
$968$	−4591.33	−	317994.i	−0.00489990	−	0.339366i
$969$	386732.			0.411873
$970$	1657.16	+	344345.i	0.00176125	+	0.365974i
$971$			520873.i			0.552450i	0.961093	+	0.276225i	$0.0890835\pi$
$971$			520873.i			0.552450i	−0.961093	+	0.276225i	$0.910916\pi$
$972$	5188.83	+	539087.i	0.00549208	+	0.570592i
$973$	479790.			0.506787
$974$	−172833.	+	831.759i	−0.182184	+	0.000876758i
$975$		−	100194.i		−	0.105398i
$976$	−1.09619e6	+	21104.2i	−1.15077	+	0.0221548i
$977$	−914224.			−0.957775			−0.478887	−	0.877876i	$-0.658960\pi$
$977$	−914224.			−0.957775			−0.478887	+	0.877876i	$0.658960\pi$
$978$	−8476.88	−	1.76143e6i	−0.00886254	−	1.84157i
$979$			566956.i			0.591540i
$980$	233086.	−	2243.51i	0.242697	−	0.00233601i
$981$	288373.			0.299652
$982$	34356.8	−	165.342i	0.0356279	−	0.000171459i
$983$		−	996679.i		−	1.03145i	−0.856754	−	0.515725i	$-0.827523\pi$
$983$		−	996679.i		−	1.03145i	0.856754	−	0.515725i	$-0.172477\pi$
$984$	−1.94533e6	+	28087.4i	−2.00910	+	0.0290082i
$985$	128153.			0.132086
$986$	−257.168	−	53437.5i	−0.000264523	−	0.0549657i
$987$			775481.i			0.796044i
$988$	−715.856	−	74373.0i	−0.000733351	−	0.0761906i
$989$	59555.0			0.0608871
$990$	−500645.	+	2409.35i	−0.510810	+	0.00245827i
$991$		−	905919.i		−	0.922448i	−0.887284	−	0.461224i	$-0.847410\pi$
$991$		−	905919.i		−	0.922448i	0.887284	−	0.461224i	$-0.152590\pi$
$992$	1.76122e6	−	42387.2i	1.78974	−	0.0430736i
$993$	1.09482e6			1.11031
$994$	2255.58	+	468692.i	0.00228289	+	0.474367i
$995$		−	365622.i		−	0.369306i
$996$	−2.37717e6	+	22880.8i	−2.39630	+	0.0230649i
$997$	160611.			0.161579			0.0807895	−	0.996731i	$-0.474256\pi$
$997$	160611.			0.161579			0.0807895	+	0.996731i	$0.474256\pi$
$998$	−241064.	+	1160.12i	−0.242031	+	0.00116478i
$999$			2.02072e6i			2.02477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.c.a.47.22	yes	44
4.3	odd	2	inner	92.5.c.a.47.21	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.c.a.47.21	✓	44	4.3	odd	2	inner
92.5.c.a.47.22	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0192498 + 3.99995i) q^{2} +15.0928i q^{3} +(-15.9993 + 0.153996i) q^{4} -8.67002 q^{5} +(-60.3703 + 0.290532i) q^{6} -26.8452i q^{7} +(-0.923961 - 63.9933i) q^{8} -146.791 q^{9} +(-0.166896 - 34.6797i) q^{10} +98.3454i q^{11} +(-2.32423 - 241.473i) q^{12} +12.0738 q^{13} +(107.379 - 0.516763i) q^{14} -130.855i q^{15} +(255.953 - 4.92766i) q^{16} -66.5536 q^{17} +(-2.82570 - 587.159i) q^{18} +385.008i q^{19} +(138.714 - 1.33515i) q^{20} +405.168 q^{21} +(-393.377 + 1.89313i) q^{22} -110.304i q^{23} +(965.836 - 13.9451i) q^{24} -549.831 q^{25} +(0.232419 + 48.2948i) q^{26} -992.974i q^{27} +(4.13406 + 429.503i) q^{28} +200.733 q^{29} +(523.412 - 2.51892i) q^{30} -1720.44i q^{31} +(24.6374 + 1023.70i) q^{32} -1484.30 q^{33} +(-1.28114 - 266.211i) q^{34} +232.748i q^{35} +(2348.55 - 22.6053i) q^{36} -2035.02 q^{37} +(-1540.02 + 7.41132i) q^{38} +182.227i q^{39} +(8.01076 + 554.824i) q^{40} -2014.14 q^{41} +(7.79938 + 1620.65i) q^{42} +539.916i q^{43} +(-15.1448 - 1573.45i) q^{44} +1272.69 q^{45} +(441.211 - 2.12333i) q^{46} +1913.98i q^{47} +(74.3719 + 3863.03i) q^{48} +1680.34 q^{49} +(-10.5841 - 2199.30i) q^{50} -1004.48i q^{51} +(-193.172 + 1.85933i) q^{52} +2581.83 q^{53} +(3971.85 - 19.1145i) q^{54} -852.657i q^{55} +(-1717.91 + 24.8039i) q^{56} -5810.84 q^{57} +(3.86407 + 802.924i) q^{58} +4108.44i q^{59} +(20.1511 + 2093.58i) q^{60} -4282.80 q^{61} +(6881.68 - 33.1181i) q^{62} +3940.64i q^{63} +(-4094.29 + 118.255i) q^{64} -104.680 q^{65} +(-28.5725 - 5937.15i) q^{66} +8140.75i q^{67} +(1064.81 - 10.2490i) q^{68} +1664.79 q^{69} +(-930.982 + 4.48035i) q^{70} +4364.82i q^{71} +(135.629 + 9393.67i) q^{72} -2120.81 q^{73} +(-39.1737 - 8139.99i) q^{74} -8298.46i q^{75} +(-59.2899 - 6159.85i) q^{76} +2640.10 q^{77} +(-728.901 + 3.50784i) q^{78} -2996.86i q^{79} +(-2219.12 + 42.7229i) q^{80} +3096.61 q^{81} +(-38.7717 - 8056.45i) q^{82} -9844.45i q^{83} +(-6482.38 + 62.3943i) q^{84} +577.021 q^{85} +(-2159.64 + 10.3933i) q^{86} +3029.62i q^{87} +(6293.45 - 90.8673i) q^{88} +5764.95 q^{89} +(24.4989 + 5090.68i) q^{90} -324.124i q^{91} +(16.9864 + 1764.78i) q^{92} +25966.2 q^{93} +(-7655.82 + 36.8436i) q^{94} -3338.03i q^{95} +(-15450.5 + 371.847i) q^{96} -9929.30 q^{97} +(32.3461 + 6721.27i) q^{98} -14436.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) \) 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more