LMFDB - Embedded newform 100.7.d.b.99.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,7,Mod(99,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("100.99");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.0054083620$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.6
Character	$\chi$	$=$	100.99
Dual form			100.7.d.b.99.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.75771 + 6.43150i) q^{2} +20.5795 q^{3} +(-18.7284 - 61.1984i) q^{4} +(-97.9113 + 132.357i) q^{6} -24.2619 q^{7} +(482.702 + 170.712i) q^{8} -305.483 q^{9} +O(q^{10})$	\(q+(-4.75771 + 6.43150i) q^{2} +20.5795 q^{3} +(-18.7284 - 61.1984i) q^{4} +(-97.9113 + 132.357i) q^{6} -24.2619 q^{7} +(482.702 + 170.712i) q^{8} -305.483 q^{9} +40.6577i q^{11} +(-385.422 - 1259.43i) q^{12} -1938.91i q^{13} +(115.431 - 156.041i) q^{14} +(-3394.49 + 2292.30i) q^{16} +5830.75i q^{17} +(1453.40 - 1964.72i) q^{18} +12002.0i q^{19} -499.299 q^{21} +(-261.490 - 193.437i) q^{22} -8569.95 q^{23} +(9933.78 + 3513.17i) q^{24} +(12470.1 + 9224.76i) q^{26} -21289.2 q^{27} +(454.388 + 1484.79i) q^{28} +19067.7 q^{29} +48329.0i q^{31} +(1407.05 - 32737.8i) q^{32} +836.716i q^{33} +(-37500.5 - 27741.0i) q^{34} +(5721.23 + 18695.1i) q^{36} -9465.63i q^{37} +(-77190.7 - 57101.9i) q^{38} -39901.8i q^{39} -100314. q^{41} +(2375.52 - 3211.24i) q^{42} -137824. q^{43} +(2488.19 - 761.455i) q^{44} +(40773.3 - 55117.7i) q^{46} +35806.2 q^{47} +(-69857.0 + 47174.5i) q^{48} -117060. q^{49} +119994. i q^{51} +(-118658. + 36312.7i) q^{52} -60878.2i q^{53} +(101288. - 136921. i) q^{54} +(-11711.3 - 4141.80i) q^{56} +246995. i q^{57} +(-90718.4 + 122634. i) q^{58} -5727.78i q^{59} -189058. q^{61} +(-310828. - 229935. i) q^{62} +7411.61 q^{63} +(203859. + 164806. i) q^{64} +(-5381.34 - 3980.85i) q^{66} +435857. q^{67} +(356833. - 109201. i) q^{68} -176366. q^{69} +281476. i q^{71} +(-147457. - 52149.7i) q^{72} -246850. i q^{73} +(60878.2 + 45034.7i) q^{74} +(734502. - 224778. i) q^{76} -986.434i q^{77} +(256629. + 189841. i) q^{78} +568574. i q^{79} -215424. q^{81} +(477264. - 645168. i) q^{82} +877394. q^{83} +(9351.09 + 30556.3i) q^{84} +(655728. - 886418. i) q^{86} +392403. q^{87} +(-6940.76 + 19625.6i) q^{88} +49386.0 q^{89} +47041.7i q^{91} +(160502. + 524468. i) q^{92} +994587. i q^{93} +(-170355. + 230288. i) q^{94} +(28956.4 - 673728. i) q^{96} +1.50441e6i q^{97} +(556939. - 752874. i) q^{98} -12420.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 312 q^{4} - 1344 q^{6} + 3992 q^{9}+O(q^{10}) $ 24 * q - 312 * q^4 - 1344 * q^6 + 3992 * q^9	$ 24 q - 312 q^{4} - 1344 q^{6} + 3992 q^{9} - 12496 q^{14} + 6624 q^{16} - 54928 q^{21} - 57056 q^{24} - 37368 q^{26} + 149936 q^{29} - 96408 q^{34} - 257160 q^{36} - 33952 q^{41} + 444320 q^{44} - 289584 q^{46} - 145128 q^{49} - 300832 q^{54} - 493024 q^{56} + 92928 q^{61} + 1085568 q^{64} - 130400 q^{66} - 82512 q^{69} - 3163848 q^{74} + 416640 q^{76} + 4574856 q^{81} + 4512448 q^{84} - 125024 q^{86} - 556784 q^{89} - 9413136 q^{94} - 5282304 q^{96}+O(q^{100}) $ 24 * q - 312 * q^4 - 1344 * q^6 + 3992 * q^9 - 12496 * q^14 + 6624 * q^16 - 54928 * q^21 - 57056 * q^24 - 37368 * q^26 + 149936 * q^29 - 96408 * q^34 - 257160 * q^36 - 33952 * q^41 + 444320 * q^44 - 289584 * q^46 - 145128 * q^49 - 300832 * q^54 - 493024 * q^56 + 92928 * q^61 + 1085568 * q^64 - 130400 * q^66 - 82512 * q^69 - 3163848 * q^74 + 416640 * q^76 + 4574856 * q^81 + 4512448 * q^84 - 125024 * q^86 - 556784 * q^89 - 9413136 * q^94 - 5282304 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.75771	+	6.43150i	−0.594713	+	0.803938i
$2$	−4.75771	+	6.43150i	−0.594713	+	0.803938i
$3$	20.5795			0.762204			0.381102	−	0.924533i	$-0.375545\pi$
$3$	20.5795			0.762204			0.381102	+	0.924533i	$0.375545\pi$
$4$	−18.7284	−	61.1984i	−0.292632	−	0.956225i
$5$		0			0
$5$		0			0
$6$	−97.9113	+	132.357i	−0.453293	+	0.612765i
$7$	−24.2619			−0.0707345			−0.0353672	−	0.999374i	$-0.511260\pi$
$7$	−24.2619			−0.0707345			−0.0353672	+	0.999374i	$0.511260\pi$
$8$	482.702	+	170.712i	0.942778	+	0.333422i
$9$	−305.483			−0.419044
$10$		0			0
$11$			40.6577i			0.0305467i	0.999883	+	0.0152734i	$0.00486185\pi$
$11$			40.6577i			0.0305467i	−0.999883	+	0.0152734i	$0.995138\pi$
$12$	−385.422	−	1259.43i	−0.223045	−	0.728839i
$13$		−	1938.91i		−	0.882525i	−0.897378	−	0.441263i	$-0.854531\pi$
$13$		−	1938.91i		−	0.882525i	0.897378	−	0.441263i	$-0.145469\pi$
$14$	115.431	−	156.041i	0.0420667	−	0.0568661i
$15$		0			0
$16$	−3394.49	+	2292.30i	−0.828733	+	0.559644i
$17$			5830.75i			1.18680i	0.804907	+	0.593401i	$0.202215\pi$
$17$			5830.75i			1.18680i	−0.804907	+	0.593401i	$0.797785\pi$
$18$	1453.40	−	1964.72i	0.249211	−	0.336886i
$19$			12002.0i			1.74981i	0.484291	+	0.874907i	$0.339078\pi$
$19$			12002.0i			1.74981i	−0.484291	+	0.874907i	$0.660922\pi$
$20$		0			0
$21$	−499.299			−0.0539141
$22$	−261.490	−	193.437i	−0.0245577	−	0.0181665i
$23$	−8569.95			−0.704361			−0.352180	−	0.935932i	$-0.614560\pi$
$23$	−8569.95			−0.704361			−0.352180	+	0.935932i	$0.614560\pi$
$24$	9933.78	+	3513.17i	0.718589	+	0.254136i
$25$		0			0
$26$	12470.1	+	9224.76i	0.709496	+	0.524850i
$27$	−21289.2			−1.08160
$28$	454.388	+	1484.79i	0.0206992	+	0.0676381i
$29$	19067.7			0.781814			0.390907	−	0.920430i	$-0.372161\pi$
$29$	19067.7			0.781814			0.390907	+	0.920430i	$0.372161\pi$
$30$		0			0
$31$			48329.0i			1.62227i	0.584861	+	0.811134i	$0.301149\pi$
$31$			48329.0i			1.62227i	−0.584861	+	0.811134i	$0.698851\pi$
$32$	1407.05	−	32737.8i	0.0429397	−	0.999078i
$33$			836.716i			0.0232828i
$34$	−37500.5	−	27741.0i	−0.954114	−	0.705807i
$35$		0			0
$36$	5721.23	+	18695.1i	0.122626	+	0.400701i
$37$		−	9465.63i		−	0.186872i	−0.995625	−	0.0934360i	$-0.970215\pi$
$37$		−	9465.63i		−	0.186872i	0.995625	−	0.0934360i	$-0.0297851\pi$
$38$	−77190.7	−	57101.9i	−1.40674	−	1.04064i
$39$		−	39901.8i		−	0.672665i
$40$		0			0
$41$	−100314.			−1.45549			−0.727745	−	0.685848i	$-0.759431\pi$
$41$	−100314.			−1.45549			−0.727745	+	0.685848i	$0.759431\pi$
$42$	2375.52	−	3211.24i	0.0320635	−	0.0433436i
$43$	−137824.			−1.73349			−0.866744	−	0.498754i	$-0.833791\pi$
$43$	−137824.			−1.73349			−0.866744	+	0.498754i	$0.833791\pi$
$44$	2488.19	−	761.455i	0.0292095	−	0.00893895i
$45$		0			0
$46$	40773.3	−	55117.7i	0.418893	−	0.566262i
$47$	35806.2			0.344877			0.172439	−	0.985020i	$-0.444835\pi$
$47$	35806.2			0.344877			0.172439	+	0.985020i	$0.444835\pi$
$48$	−69857.0	+	47174.5i	−0.631664	+	0.426563i
$49$	−117060.			−0.994997
$50$		0			0
$51$			119994.i			0.904585i
$52$	−118658.	+	36312.7i	−0.843893	+	0.258255i
$53$		−	60878.2i		−	0.408916i	−0.978875	−	0.204458i	$-0.934457\pi$
$53$		−	60878.2i		−	0.408916i	0.978875	−	0.204458i	$-0.0655432\pi$
$54$	101288.	−	136921.i	0.643243	−	0.869541i
$55$		0			0
$56$	−11711.3	−	4141.80i	−0.0666869	−	0.0235844i
$57$			246995.i			1.33372i
$58$	−90718.4	+	122634.i	−0.464955	+	0.628530i
$59$		−	5727.78i		−	0.0278888i	−0.999903	−	0.0139444i	$-0.995561\pi$
$59$		−	5727.78i		−	0.0278888i	0.999903	−	0.0139444i	$-0.00443879\pi$
$60$		0			0
$61$	−189058.			−0.832924			−0.416462	−	0.909153i	$-0.636730\pi$
$61$	−189058.			−0.832924			−0.416462	+	0.909153i	$0.636730\pi$
$62$	−310828.	−	229935.i	−1.30420	−	0.964784i
$63$	7411.61			0.0296409
$64$	203859.	+	164806.i	0.777659	+	0.628686i
$65$		0			0
$66$	−5381.34	−	3980.85i	−0.0187180	−	0.0138466i
$67$	435857.			1.44917			0.724585	−	0.689185i	$-0.242031\pi$
$67$	435857.			1.44917			0.724585	+	0.689185i	$0.242031\pi$
$68$	356833.	−	109201.i	1.13485	−	0.347296i
$69$	−176366.			−0.536867
$70$		0			0
$71$			281476.i			0.786441i	0.919444	+	0.393221i	$0.128639\pi$
$71$			281476.i			0.786441i	−0.919444	+	0.393221i	$0.871361\pi$
$72$	−147457.	−	52149.7i	−0.395066	−	0.139719i
$73$		−	246850.i		−	0.634548i	−0.948334	−	0.317274i	$-0.897232\pi$
$73$		−	246850.i		−	0.634548i	0.948334	−	0.317274i	$-0.102768\pi$
$74$	60878.2	+	45034.7i	0.150234	+	0.111135i
$75$		0			0
$76$	734502.	−	224778.i	1.67322	−	0.512052i
$77$		−	986.434i		−	0.00216071i
$78$	256629.	+	189841.i	0.540781	+	0.400043i
$79$			568574.i			1.15320i	0.817026	+	0.576601i	$0.195621\pi$
$79$			568574.i			1.15320i	−0.817026	+	0.576601i	$0.804379\pi$
$80$		0			0
$81$	−215424.			−0.405357
$82$	477264.	−	645168.i	0.865599	−	1.17012i
$83$	877394.			1.53448			0.767238	−	0.641362i	$-0.221630\pi$
$83$	877394.			1.53448			0.767238	+	0.641362i	$0.221630\pi$
$84$	9351.09	+	30556.3i	0.0157770	+	0.0515540i
$85$		0			0
$86$	655728.	−	886418.i	1.03093	−	1.39362i
$87$	392403.			0.595902
$88$	−6940.76	+	19625.6i	−0.0101850	+	0.0287988i
$89$	49386.0			0.0700541			0.0350271	−	0.999386i	$-0.488848\pi$
$89$	49386.0			0.0700541			0.0350271	+	0.999386i	$0.488848\pi$
$90$		0			0
$91$			47041.7i			0.0624250i
$92$	160502.	+	524468.i	0.206118	+	0.673527i
$93$			994587.i			1.23650i
$94$	−170355.	+	230288.i	−0.205103	+	0.277260i
$95$		0			0
$96$	28956.4	−	673728.i	0.0327288	−	0.761501i
$97$			1.50441e6i			1.64835i	0.566334	+	0.824176i	$0.308361\pi$
$97$			1.50441e6i			1.64835i	−0.566334	+	0.824176i	$0.691639\pi$
$98$	556939.	−	752874.i	0.591738	−	0.799915i
$99$		−	12420.2i		−	0.0128004i
$100$		0			0
$101$	−1.94071e6			−1.88363			−0.941815	−	0.336132i	$-0.890881\pi$
$101$	−1.94071e6			−1.88363			−0.941815	+	0.336132i	$0.890881\pi$
$102$	−771742.	−	570897.i	−0.727230	−	0.537969i
$103$	41692.0			0.0381541			0.0190770	−	0.999818i	$-0.493927\pi$
$103$	41692.0			0.0381541			0.0190770	+	0.999818i	$0.493927\pi$
$104$	330995.	−	935915.i	0.294253	−	0.832025i
$105$		0			0
$106$	391539.	+	289641.i	0.328743	+	0.243188i
$107$	−721600.			−0.589040			−0.294520	−	0.955645i	$-0.595160\pi$
$107$	−721600.			−0.589040			−0.294520	+	0.955645i	$0.595160\pi$
$108$	398713.	+	1.30286e6i	0.316511	+	1.03425i
$109$	221610.			0.171123			0.0855617	−	0.996333i	$-0.472732\pi$
$109$	221610.			0.171123			0.0855617	+	0.996333i	$0.472732\pi$
$110$		0			0
$111$		−	194798.i		−	0.142435i
$112$	82356.9	−	55615.7i	0.0586200	−	0.0395861i
$113$		−	742683.i		−	0.514717i	−0.966316	−	0.257358i	$-0.917148\pi$
$113$		−	742683.i		−	0.514717i	0.966316	−	0.257358i	$-0.0828521\pi$
$114$	−1.58855e6	−	1.17513e6i	−1.07222	−	0.793179i
$115$		0			0
$116$	−357108.	−	1.16691e6i	−0.228784	−	0.747591i
$117$			592304.i			0.369817i
$118$	36838.2	+	27251.1i	0.0224209	+	0.0165858i
$119$		−	141465.i		−	0.0839478i
$120$		0			0
$121$	1.76991e6			0.999067
$122$	899482.	−	1.21593e6i	0.495351	−	0.669619i
$123$	−2.06441e6			−1.10938
$124$	2.95766e6	−	905126.i	1.55125	−	0.474727i
$125$		0			0
$126$	−35262.3	+	47667.8i	−0.0176278	+	0.0238294i
$127$	2.45824e6			1.20009			0.600044	−	0.799967i	$-0.295150\pi$
$127$	2.45824e6			1.20009			0.600044	+	0.799967i	$0.295150\pi$
$128$	−2.02985e6	+	527018.i	−0.967909	+	0.251302i
$129$	−2.83636e6			−1.32127
$130$		0			0
$131$		−	875075.i		−	0.389252i	−0.980877	−	0.194626i	$-0.937651\pi$
$131$		−	875075.i		−	0.389252i	0.980877	−	0.194626i	$-0.0623494\pi$
$132$	51205.7	−	15670.4i	0.0222636	−	0.00681330i
$133$		−	291191.i		−	0.123772i
$134$	−2.07368e6	+	2.80321e6i	−0.861841	+	1.16504i
$135$		0			0
$136$	−995380.	+	2.81452e6i	−0.395706	+	1.11889i
$137$		−	1.79826e6i		−	0.699345i	−0.936872	−	0.349673i	$-0.886293\pi$
$137$		−	1.79826e6i		−	0.699345i	0.936872	−	0.349673i	$-0.113707\pi$
$138$	839096.	−	1.13430e6i	0.319282	−	0.431607i
$139$		−	130543.i		−	0.0486083i	−0.999705	−	0.0243042i	$-0.992263\pi$
$139$		−	130543.i		−	0.0486083i	0.999705	−	0.0243042i	$-0.00773702\pi$
$140$		0			0
$141$	736875.			0.262867
$142$	−1.81031e6	−	1.33918e6i	−0.632250	−	0.467707i
$143$	78831.5			0.0269583
$144$	1.03696e6	−	700260.i	0.347276	−	0.234516i
$145$		0			0
$146$	1.58762e6	+	1.17444e6i	0.510137	+	0.377374i
$147$	−2.40905e6			−0.758391
$148$	−579282.	+	177277.i	−0.178692	+	0.0546847i
$149$	4.46107e6			1.34859			0.674296	−	0.738461i	$-0.264447\pi$
$149$	4.46107e6			1.34859			0.674296	+	0.738461i	$0.264447\pi$
$150$		0			0
$151$			5.31949e6i			1.54504i	0.634992	+	0.772519i	$0.281004\pi$
$151$			5.31949e6i			1.54504i	−0.634992	+	0.772519i	$0.718996\pi$
$152$	−2.04888e6	+	5.79338e6i	−0.583427	+	1.64969i
$153$		−	1.78120e6i		−	0.497322i
$154$	6344.25	+	4693.16i	0.00173707	+	0.00128500i
$155$		0			0
$156$	−2.44193e6	+	747299.i	−0.643219	+	0.196843i
$157$		−	5.17889e6i		−	1.33825i	−0.743149	−	0.669125i	$-0.766669\pi$
$157$		−	5.17889e6i		−	1.33825i	0.743149	−	0.669125i	$-0.233331\pi$
$158$	−3.65678e6	−	2.70511e6i	−0.927103	−	0.685825i
$159$		−	1.25285e6i		−	0.311678i
$160$		0			0
$161$	207924.			0.0498226
$162$	1.02492e6	−	1.38550e6i	0.241071	−	0.325882i
$163$	1.67288e6			0.386279			0.193139	−	0.981171i	$-0.438133\pi$
$163$	1.67288e6			0.386279			0.193139	+	0.981171i	$0.438133\pi$
$164$	1.87872e6	+	6.13904e6i	0.425923	+	1.39178i
$165$		0			0
$166$	−4.17438e6	+	5.64296e6i	−0.912574	+	1.23362i
$167$	−5.82015e6			−1.24964			−0.624820	−	0.780769i	$-0.714828\pi$
$167$	−5.82015e6			−1.24964			−0.624820	+	0.780769i	$0.714828\pi$
$168$	−241013.	−	85236.3i	−0.0508290	−	0.0179762i
$169$	1.06744e6			0.221149
$170$		0			0
$171$		−	3.66640e6i		−	0.733250i
$172$	2.58124e6	+	8.43463e6i	0.507274	+	1.65760i
$173$			3.31004e6i			0.639285i	0.947538	+	0.319642i	$0.103563\pi$
$173$			3.31004e6i			0.639285i	−0.947538	+	0.319642i	$0.896437\pi$
$174$	−1.86694e6	+	2.52374e6i	−0.354391	+	0.479068i
$175$		0			0
$176$	−93199.7	−	138012.i	−0.0170953	−	0.0253151i
$177$		−	117875.i		−	0.0212570i
$178$	−234964.	+	317626.i	−0.0416621	+	0.0563192i
$179$		−	2.57688e6i		−	0.449299i	−0.974440	−	0.224650i	$-0.927876\pi$
$179$		−	2.57688e6i		−	0.449299i	0.974440	−	0.224650i	$-0.0721238\pi$
$180$		0			0
$181$	3.49422e6			0.589270			0.294635	−	0.955610i	$-0.404802\pi$
$181$	3.49422e6			0.589270			0.294635	+	0.955610i	$0.404802\pi$
$182$	−302548.	−	223810.i	−0.0501858	−	0.0371250i
$183$	−3.89072e6			−0.634858
$184$	−4.13674e6	−	1.46299e6i	−0.664055	−	0.234849i
$185$		0			0
$186$	−6.39669e6	−	4.73195e6i	−0.994069	−	0.735363i
$187$	−237065.			−0.0362529
$188$	−670594.	−	2.19128e6i	−0.100922	−	0.329780i
$189$	516516.			0.0765065
$190$		0			0
$191$		−	6.14107e6i		−	0.881341i	−0.897669	−	0.440670i	$-0.854741\pi$
$191$		−	6.14107e6i		−	0.881341i	0.897669	−	0.440670i	$-0.145259\pi$
$192$	4.19532e6	+	3.39163e6i	0.592735	+	0.479187i
$193$		−	2.81628e6i		−	0.391746i	−0.980629	−	0.195873i	$-0.937246\pi$
$193$		−	2.81628e6i		−	0.391746i	0.980629	−	0.195873i	$-0.0627540\pi$
$194$	−9.67559e6	−	7.15752e6i	−1.32517	−	0.980297i
$195$		0			0
$196$	2.19236e6	+	7.16391e6i	0.291168	+	0.951441i
$197$		−	4.26385e6i		−	0.557703i	−0.960334	−	0.278851i	$-0.910046\pi$
$197$		−	4.26385e6i		−	0.557703i	0.960334	−	0.278851i	$-0.0899537\pi$
$198$	79880.9	+	59091.9i	0.0102908	+	0.00761259i
$199$			1.52923e6i			0.194049i	0.995282	+	0.0970247i	$0.0309326\pi$
$199$			1.52923e6i			0.194049i	−0.995282	+	0.0970247i	$0.969067\pi$
$200$		0			0
$201$	8.96972e6			1.10456
$202$	9.23331e6	−	1.24817e7i	1.12022	−	1.51432i
$203$	−462618.			−0.0553012
$204$	7.34345e6	−	2.24730e6i	0.864987	−	0.264710i
$205$		0			0
$206$	−198358.	+	268142.i	−0.0226907	+	0.0306735i
$207$	2.61798e6			0.295158
$208$	4.44456e6	+	6.58161e6i	0.493900	+	0.731378i
$209$	−487973.			−0.0534511
$210$		0			0
$211$		−	1.29980e7i		−	1.38366i	−0.722058	−	0.691832i	$-0.756804\pi$
$211$		−	1.29980e7i		−	1.38366i	0.722058	−	0.691832i	$-0.243196\pi$
$212$	−3.72565e6	+	1.14015e6i	−0.391016	+	0.119662i
$213$			5.79264e6i			0.599429i
$214$	3.43316e6	−	4.64097e6i	0.350310	−	0.473552i
$215$		0			0
$216$	−1.02763e7	−	3.63432e6i	−1.01971	−	0.360630i
$217$		−	1.17255e6i		−	0.114750i
$218$	−1.05435e6	+	1.42528e6i	−0.101769	+	0.137573i
$219$		−	5.08006e6i		−	0.483656i
$220$		0			0
$221$	1.13053e7			1.04738
$222$	1.25284e6	+	926793.i	0.114509	+	0.0847078i
$223$	6.60113e6			0.595256			0.297628	−	0.954682i	$-0.403804\pi$
$223$	6.60113e6			0.595256			0.297628	+	0.954682i	$0.403804\pi$
$224$	−34137.7	+	794281.i	−0.00303732	+	0.0706692i
$225$		0			0
$226$	4.77657e6	+	3.53347e6i	0.413800	+	0.306109i
$227$	−1.56180e7			−1.33521			−0.667604	−	0.744517i	$-0.732680\pi$
$227$	−1.56180e7			−1.33521			−0.667604	+	0.744517i	$0.732680\pi$
$228$	1.51157e7	−	4.62583e6i	1.27533	−	0.390288i
$229$	−552000.			−0.0459656			−0.0229828	−	0.999736i	$-0.507316\pi$
$229$	−552000.			−0.0459656			−0.0229828	+	0.999736i	$0.507316\pi$
$230$		0			0
$231$		−	20300.3i		−	0.00164690i
$232$	9.20401e6	+	3.25508e6i	0.737077	+	0.260674i
$233$			2.63489e6i			0.208302i	0.994561	+	0.104151i	$0.0332126\pi$
$233$			2.63489e6i			0.208302i	−0.994561	+	0.104151i	$0.966787\pi$
$234$	−3.80941e6	−	2.81801e6i	−0.297310	−	0.219935i
$235$		0			0
$236$	−350531.	+	107272.i	−0.0266680	+	0.00816116i
$237$			1.17010e7i			0.878976i
$238$	909834.	+	673051.i	0.0674888	+	0.0499249i
$239$			1.22694e7i			0.898734i	0.893347	+	0.449367i	$0.148350\pi$
$239$			1.22694e7i			0.898734i	−0.893347	+	0.449367i	$0.851650\pi$
$240$		0			0
$241$	−1.12114e7			−0.800959			−0.400480	−	0.916306i	$-0.631156\pi$
$241$	−1.12114e7			−0.800959			−0.400480	+	0.916306i	$0.631156\pi$
$242$	−8.42070e6	+	1.13832e7i	−0.594158	+	0.803188i
$243$	1.10865e7			0.772637
$244$	3.54076e6	+	1.15700e7i	0.243740	+	0.796462i
$245$		0			0
$246$	9.82185e6	−	1.32773e7i	0.659763	−	0.891873i
$247$	2.32707e7			1.54426
$248$	−8.25034e6	+	2.33285e7i	−0.540900	+	1.52944i
$249$	1.80563e7			1.16958
$250$		0			0
$251$		−	7.65449e6i		−	0.484055i	−0.970269	−	0.242028i	$-0.922188\pi$
$251$		−	7.65449e6i		−	0.484055i	0.970269	−	0.242028i	$-0.0778125\pi$
$252$	−138808.	−	453579.i	−0.00867387	−	0.0283434i
$253$		−	348435.i		−	0.0215159i
$254$	−1.16956e7	+	1.58102e7i	−0.713708	+	0.964796i
$255$		0			0
$256$	6.26792e6	−	1.55624e7i	0.373597	−	0.927591i
$257$		−	1.09187e7i		−	0.643236i	−0.946870	−	0.321618i	$-0.895773\pi$
$257$		−	1.09187e7i		−	0.643236i	0.946870	−	0.321618i	$-0.104227\pi$
$258$	1.34946e7	−	1.82421e7i	0.785778	−	1.06222i
$259$			229654.i			0.0132183i
$260$		0			0
$261$	−5.82486e6			−0.327615
$262$	5.62805e6	+	4.16335e6i	0.312935	+	0.231494i
$263$	8.91372e6			0.489995			0.244998	−	0.969524i	$-0.421213\pi$
$263$	8.91372e6			0.489995			0.244998	+	0.969524i	$0.421213\pi$
$264$	−142837.	+	403884.i	−0.00776301	+	0.0219505i
$265$		0			0
$266$	1.87280e6	+	1.38540e6i	0.0995051	+	0.0736090i
$267$	1.01634e6			0.0533956
$268$	−8.16292e6	−	2.66737e7i	−0.424073	−	1.38573i
$269$	−2.68537e7			−1.37958			−0.689792	−	0.724008i	$-0.742298\pi$
$269$	−2.68537e7			−1.37958			−0.689792	+	0.724008i	$0.742298\pi$
$270$		0			0
$271$			2.83005e7i			1.42196i	0.703215	+	0.710978i	$0.251747\pi$
$271$			2.83005e7i			1.42196i	−0.703215	+	0.710978i	$0.748253\pi$
$272$	−1.33658e7	−	1.97924e7i	−0.664186	−	0.983541i
$273$			968095.i			0.0475806i
$274$	1.15655e7	+	8.55561e6i	0.562230	+	0.415910i
$275$		0			0
$276$	3.30305e6	+	1.07933e7i	0.157104	+	0.513365i
$277$			6.22973e6i			0.293109i	0.989203	+	0.146555i	$0.0468185\pi$
$277$			6.22973e6i			0.293109i	−0.989203	+	0.146555i	$0.953182\pi$
$278$	839590.	+	621087.i	0.0390781	+	0.0289080i
$279$		−	1.47637e7i		−	0.679802i
$280$		0			0
$281$	−3.17788e7			−1.43225			−0.716124	−	0.697973i	$-0.754085\pi$
$281$	−3.17788e7			−1.43225			−0.716124	+	0.697973i	$0.754085\pi$
$282$	−3.50583e6	+	4.73921e6i	−0.156331	+	0.211329i
$283$	6.72478e6			0.296701			0.148350	−	0.988935i	$-0.452604\pi$
$283$	6.72478e6			0.296701			0.148350	+	0.988935i	$0.452604\pi$
$284$	1.72259e7	−	5.27161e6i	0.752015	−	0.230138i
$285$		0			0
$286$	−375057.	+	507005.i	−0.0160324	+	0.0216728i
$287$	2.43380e6			0.102953
$288$	−429830.	+	1.00008e7i	−0.0179936	+	0.418658i
$289$	−9.86012e6			−0.408497
$290$		0			0
$291$			3.09600e7i			1.25638i
$292$	−1.51068e7	+	4.62312e6i	−0.606771	+	0.185689i
$293$		−	2.92187e7i		−	1.16161i	−0.814044	−	0.580803i	$-0.802739\pi$
$293$		−	2.92187e7i		−	1.16161i	0.814044	−	0.580803i	$-0.197261\pi$
$294$	1.14615e7	−	1.54938e7i	0.451025	−	0.609699i
$295$		0			0
$296$	1.61590e6	−	4.56908e6i	0.0623073	−	0.176179i
$297$		−	865568.i		−	0.0330394i
$298$	−2.12245e7	+	2.86914e7i	−0.802025	+	1.08418i
$299$			1.66164e7i			0.621616i
$300$		0			0
$301$	3.34388e6			0.122617
$302$	−3.42123e7	−	2.53086e7i	−1.24211	−	0.918855i
$303$	−3.99388e7			−1.43571
$304$	−2.75122e7	−	4.07406e7i	−0.979273	−	1.45013i
$305$		0			0
$306$	1.14558e7	+	8.47442e6i	0.399816	+	0.295764i
$307$	2.28641e7			0.790205			0.395103	−	0.918637i	$-0.370709\pi$
$307$	2.28641e7			0.790205			0.395103	+	0.918637i	$0.370709\pi$
$308$	−60368.2	+	18474.4i	−0.00206612	+	0.000632292i
$309$	858001.			0.0290812
$310$		0			0
$311$			5.60021e6i			0.186176i	0.995658	+	0.0930879i	$0.0296738\pi$
$311$			5.60021e6i			0.186176i	−0.995658	+	0.0930879i	$0.970326\pi$
$312$	6.81172e6	−	1.92607e7i	0.224281	−	0.634173i
$313$			1.38055e7i			0.450213i	0.974334	+	0.225107i	$0.0722731\pi$
$313$			1.38055e7i			0.450213i	−0.974334	+	0.225107i	$0.927727\pi$
$314$	3.33080e7	+	2.46396e7i	1.07587	+	0.795876i
$315$		0			0
$316$	3.47958e7	−	1.06485e7i	1.10272	−	0.337464i
$317$			5.24913e7i			1.64782i	0.566721	+	0.823910i	$0.308212\pi$
$317$			5.24913e7i			1.64782i	−0.566721	+	0.823910i	$0.691788\pi$
$318$	8.05768e6	+	5.96067e6i	0.250570	+	0.185359i
$319$			775247.i			0.0238819i
$320$		0			0
$321$	−1.48502e7			−0.448969
$322$	−989240.	+	1.33726e6i	−0.0296302	+	0.0400542i
$323$	−6.99806e7			−2.07668
$324$	4.03455e6	+	1.31836e7i	0.118621	+	0.387613i
$325$		0			0
$326$	−7.95906e6	+	1.07591e7i	−0.229725	+	0.310544i
$327$	4.56062e6			0.130431
$328$	−4.84217e7	−	1.71248e7i	−1.37220	−	0.485292i
$329$	−868727.			−0.0243947
$330$		0			0
$331$		−	1.16408e6i		−	0.0320996i	−0.999871	−	0.0160498i	$-0.994891\pi$
$331$		−	1.16408e6i		−	0.0320996i	0.999871	−	0.0160498i	$-0.00510903\pi$
$332$	−1.64322e7	−	5.36951e7i	−0.449037	−	1.46730i
$333$			2.89159e6i			0.0783077i
$334$	2.76906e7	−	3.74323e7i	0.743178	−	1.00463i
$335$		0			0
$336$	1.69487e6	−	1.14454e6i	0.0446804	−	0.0301727i
$337$			1.47881e7i			0.386387i	0.981161	+	0.193194i	$0.0618846\pi$
$337$			1.47881e7i			0.386387i	−0.981161	+	0.193194i	$0.938115\pi$
$338$	−5.07858e6	+	6.86526e6i	−0.131520	+	0.177790i
$339$		−	1.52841e7i		−	0.392319i
$340$		0			0
$341$	−1.96494e6			−0.0495550
$342$	2.35805e7	+	1.74437e7i	0.589487	+	0.436074i
$343$	5.69450e6			0.141115
$344$	−6.65281e7	−	2.35283e7i	−1.63429	−	0.577983i
$345$		0			0
$346$	−2.12885e7	−	1.57482e7i	−0.513945	−	0.380191i
$347$	−1.67575e7			−0.401072			−0.200536	−	0.979686i	$-0.564268\pi$
$347$	−1.67575e7			−0.401072			−0.200536	+	0.979686i	$0.564268\pi$
$348$	−7.34911e6	−	2.40145e7i	−0.174380	−	0.569817i
$349$	−2.65359e7			−0.624248			−0.312124	−	0.950041i	$-0.601041\pi$
$349$	−2.65359e7			−0.624248			−0.312124	+	0.950041i	$0.601041\pi$
$350$		0			0
$351$			4.12778e7i			0.954541i
$352$	1.33104e6	+	57207.3i	0.0305185	+	0.00131167i
$353$		−	5.51050e7i		−	1.25276i	−0.779519	−	0.626379i	$-0.784536\pi$
$353$		−	5.51050e7i		−	1.25276i	0.779519	−	0.626379i	$-0.215464\pi$
$354$	758112.	+	560814.i	0.0170893	+	0.0126418i
$355$		0			0
$356$	−924923.	−	3.02234e6i	−0.0205001	−	0.0669875i
$357$		−	2.91129e6i		−	0.0639853i
$358$	1.65732e7	+	1.22601e7i	0.361209	+	0.267204i
$359$			4.29022e7i			0.927249i	0.886032	+	0.463625i	$0.153451\pi$
$359$			4.29022e7i			0.927249i	−0.886032	+	0.463625i	$0.846549\pi$
$360$		0			0
$361$	−9.70016e7			−2.06185
$362$	−1.66245e7	+	2.24731e7i	−0.350447	+	0.473737i
$363$	3.64239e7			0.761493
$364$	2.87887e6	−	881017.i	0.0596923	−	0.0182675i
$365$		0			0
$366$	1.85109e7	−	2.50232e7i	0.377559	−	0.510386i
$367$	−4.92753e7			−0.996853			−0.498427	−	0.866932i	$-0.666089\pi$
$367$	−4.92753e7			−0.996853			−0.498427	+	0.866932i	$0.666089\pi$
$368$	2.90906e7	−	1.96449e7i	0.583727	−	0.394191i
$369$	3.06442e7			0.609915
$370$		0			0
$371$			1.47702e6i			0.0289245i
$372$	6.08671e7	−	1.86271e7i	1.18237	−	0.361839i
$373$			1.02492e8i			1.97498i	0.157685	+	0.987489i	$0.449597\pi$
$373$			1.02492e8i			1.97498i	−0.157685	+	0.987489i	$0.550403\pi$
$374$	1.12789e6	−	1.52468e6i	0.0215601	−	0.0291451i
$375$		0			0
$376$	1.72837e7	+	6.11255e6i	0.325143	+	0.114990i
$377$		−	3.69705e7i		−	0.689971i
$378$	−2.45743e6	+	3.32198e6i	−0.0454995	+	0.0615065i
$379$		−	2.40144e7i		−	0.441117i	−0.975374	−	0.220559i	$-0.929212\pi$
$379$		−	2.40144e7i		−	0.441117i	0.975374	−	0.220559i	$-0.0707881\pi$
$380$		0			0
$381$	5.05894e7			0.914712
$382$	3.94963e7	+	2.92174e7i	0.708543	+	0.524145i
$383$	5.08955e7			0.905906			0.452953	−	0.891534i	$-0.350371\pi$
$383$	5.08955e7			0.905906			0.452953	+	0.891534i	$0.350371\pi$
$384$	−4.17734e7	+	1.08458e7i	−0.737744	+	0.191543i
$385$		0			0
$386$	1.81129e7	+	1.33990e7i	0.314939	+	0.232976i
$387$	4.21031e7			0.726408
$388$	9.20673e7	−	2.81752e7i	1.57620	−	0.482360i
$389$	3.54629e7			0.602457			0.301228	−	0.953552i	$-0.402603\pi$
$389$	3.54629e7			0.602457			0.301228	+	0.953552i	$0.402603\pi$
$390$		0			0
$391$		−	4.99693e7i		−	0.835936i
$392$	−5.65053e7	−	1.99836e7i	−0.938061	−	0.331754i
$393$		−	1.80086e7i		−	0.296690i
$394$	2.74229e7	+	2.02861e7i	0.448358	+	0.331673i
$395$		0			0
$396$	−760099.	+	232612.i	−0.0122401	+	0.00374582i
$397$			1.41021e7i			0.225379i	0.993630	+	0.112690i	$0.0359465\pi$
$397$			1.41021e7i			0.225379i	−0.993630	+	0.112690i	$0.964053\pi$
$398$	−9.83522e6	−	7.27561e6i	−0.156004	−	0.115404i
$399$		−	5.99257e6i		−	0.0943397i
$400$		0			0
$401$	7.63677e7			1.18434			0.592170	−	0.805813i	$-0.298271\pi$
$401$	7.63677e7			1.18434			0.592170	+	0.805813i	$0.298271\pi$
$402$	−4.26753e7	+	5.76888e7i	−0.656899	+	0.888001i
$403$	9.37054e7			1.43169
$404$	3.63464e7	+	1.18768e8i	0.551210	+	1.80117i
$405$		0			0
$406$	2.20100e6	−	2.97533e6i	0.0328884	−	0.0444587i
$407$	384851.			0.00570833
$408$	−2.04844e7	+	5.79214e7i	−0.301609	+	0.852823i
$409$	4.76292e6			0.0696150			0.0348075	−	0.999394i	$-0.488918\pi$
$409$	4.76292e6			0.0696150			0.0348075	+	0.999394i	$0.488918\pi$
$410$		0			0
$411$		−	3.70074e7i		−	0.533044i
$412$	−780826.	−	2.55148e6i	−0.0111651	−	0.0364839i
$413$			138967.i			0.00197270i
$414$	−1.24556e7	+	1.68375e7i	−0.175535	+	0.237289i
$415$		0			0
$416$	−6.34756e7	−	2.72814e6i	−0.881711	−	0.0378954i
$417$		−	2.68652e6i		−	0.0370495i
$418$	2.32163e6	−	3.13840e6i	0.0317881	−	0.0429714i
$419$			9.51171e7i			1.29305i	0.762891	+	0.646527i	$0.223779\pi$
$419$			9.51171e7i			1.29305i	−0.762891	+	0.646527i	$0.776221\pi$
$420$		0			0
$421$	7.92057e7			1.06148			0.530738	−	0.847536i	$-0.321915\pi$
$421$	7.92057e7			1.06148			0.530738	+	0.847536i	$0.321915\pi$
$422$	8.35970e7	+	6.18409e7i	1.11238	+	0.822884i
$423$	−1.09382e7			−0.144519
$424$	1.03927e7	−	2.93861e7i	0.136342	−	0.385517i
$425$		0			0
$426$	−3.72554e7	−	2.75597e7i	−0.481904	−	0.356489i
$427$	4.58691e6			0.0589164
$428$	1.35144e7	+	4.41608e7i	0.172372	+	0.563255i
$429$	1.62232e6			0.0205477
$430$		0			0
$431$		−	1.24667e8i		−	1.55711i	−0.627576	−	0.778555i	$-0.715953\pi$
$431$		−	1.24667e8i		−	1.55711i	0.627576	−	0.778555i	$-0.284047\pi$
$432$	7.22659e7	−	4.88012e7i	0.896359	−	0.605312i
$433$		−	9.68564e7i		−	1.19307i	−0.802588	−	0.596533i	$-0.796544\pi$
$433$		−	9.68564e7i		−	1.19307i	0.802588	−	0.596533i	$-0.203456\pi$
$434$	7.54128e6	+	5.57867e6i	0.0922520	+	0.0682435i
$435$		0			0
$436$	−4.15041e6	−	1.35622e7i	−0.0500762	−	0.163633i
$437$		−	1.02856e8i		−	1.23250i
$438$	3.26724e7	+	2.41694e7i	0.388829	+	0.287636i
$439$		−	8.52847e7i		−	1.00804i	−0.863692	−	0.504020i	$-0.831854\pi$
$439$		−	8.52847e7i		−	1.00804i	0.863692	−	0.504020i	$-0.168146\pi$
$440$		0			0
$441$	3.57600e7			0.416948
$442$	−5.37873e7	+	7.27100e7i	−0.622892	+	0.842030i
$443$	−6.98986e7			−0.804002			−0.402001	−	0.915639i	$-0.631685\pi$
$443$	−6.98986e7			−0.804002			−0.402001	+	0.915639i	$0.631685\pi$
$444$	−1.19213e7	+	3.64827e6i	−0.136200	+	0.0416810i
$445$		0			0
$446$	−3.14063e7	+	4.24552e7i	−0.354007	+	0.478549i
$447$	9.18067e7			1.02790
$448$	−4.94601e6	−	3.99852e6i	−0.0550073	−	0.0444698i
$449$	−7.16693e7			−0.791762			−0.395881	−	0.918302i	$-0.629561\pi$
$449$	−7.16693e7			−0.791762			−0.395881	+	0.918302i	$0.629561\pi$
$450$		0			0
$451$		−	4.07853e6i		−	0.0444604i
$452$	−4.54510e7	+	1.39093e7i	−0.492185	+	0.150623i
$453$			1.09473e8i			1.17763i
$454$	7.43060e7	−	1.00447e8i	0.794066	−	1.07342i
$455$		0			0
$456$	−4.21650e7	+	1.19225e8i	−0.444690	+	1.25740i
$457$		−	8.06623e7i		−	0.845127i	−0.906333	−	0.422563i	$-0.861130\pi$
$457$		−	8.06623e7i		−	0.845127i	0.906333	−	0.422563i	$-0.138870\pi$
$458$	2.62626e6	−	3.55019e6i	0.0273364	−	0.0369535i
$459$		−	1.24132e8i		−	1.28365i
$460$		0			0
$461$	1.09917e8			1.12192			0.560961	−	0.827843i	$-0.310432\pi$
$461$	1.09917e8			1.12192			0.560961	+	0.827843i	$0.310432\pi$
$462$	130562.	+	96583.0i	0.00132401	+	0.000979434i
$463$	7.14847e7			0.720229			0.360114	−	0.932908i	$-0.382738\pi$
$463$	7.14847e7			0.720229			0.360114	+	0.932908i	$0.382738\pi$
$464$	−6.47250e7	+	4.37089e7i	−0.647915	+	0.437538i
$465$		0			0
$466$	−1.69463e7	−	1.25360e7i	−0.167462	−	0.123880i
$467$	−1.00414e8			−0.985929			−0.492964	−	0.870050i	$-0.664087\pi$
$467$	−1.00414e8			−0.985929			−0.492964	+	0.870050i	$0.664087\pi$
$468$	3.62481e7	−	1.10929e7i	0.353629	−	0.108220i
$469$	−1.05747e7			−0.102506
$470$		0			0
$471$		−	1.06579e8i		−	1.02002i
$472$	977800.	−	2.76481e6i	0.00929874	−	0.0262929i
$473$		−	5.60362e6i		−	0.0529524i
$474$	−7.52549e7	−	5.56698e7i	−0.706642	−	0.522739i
$475$		0			0
$476$	−8.65745e6	+	2.64943e6i	−0.0802730	+	0.0245658i
$477$			1.85973e7i			0.171354i
$478$	−7.89109e7	−	5.83744e7i	−0.722526	−	0.534489i
$479$		−	9.67106e7i		−	0.879969i	−0.898005	−	0.439984i	$-0.854984\pi$
$479$		−	9.67106e7i		−	0.879969i	0.898005	−	0.439984i	$-0.145016\pi$
$480$		0			0
$481$	−1.83530e7			−0.164919
$482$	5.33408e7	−	7.21064e7i	0.476341	−	0.643921i
$483$	4.27897e6			0.0379750
$484$	−3.31476e7	−	1.08316e8i	−0.292359	−	0.955333i
$485$		0			0
$486$	−5.27463e7	+	7.13028e7i	−0.459497	+	0.621152i
$487$	−1.33542e8			−1.15619			−0.578096	−	0.815969i	$-0.696204\pi$
$487$	−1.33542e8			−1.15619			−0.578096	+	0.815969i	$0.696204\pi$
$488$	−9.12586e7	−	3.22745e7i	−0.785262	−	0.277715i
$489$	3.44270e7			0.294423
$490$		0			0
$491$			1.33885e8i			1.13107i	0.824725	+	0.565534i	$0.191330\pi$
$491$			1.33885e8i			1.13107i	−0.824725	+	0.565534i	$0.808670\pi$
$492$	3.86632e7	+	1.26339e8i	0.324640	+	1.06082i
$493$			1.11179e8i			0.927858i
$494$	−1.10715e8	+	1.49666e8i	−0.918390	+	1.24149i
$495$		0			0
$496$	−1.10785e8	−	1.64052e8i	−0.907892	−	1.34443i
$497$		−	6.82915e6i		−	0.0556285i
$498$	−8.59068e7	+	1.16129e8i	−0.695568	+	0.940273i
$499$			1.04600e8i			0.841842i	0.907097	+	0.420921i	$0.138293\pi$
$499$			1.04600e8i			0.841842i	−0.907097	+	0.420921i	$0.861707\pi$
$500$		0			0
$501$	−1.19776e8			−0.952481
$502$	4.92299e7	+	3.64178e7i	0.389150	+	0.287874i
$503$	−1.83299e8			−1.44031			−0.720155	−	0.693813i	$-0.755930\pi$
$503$	−1.83299e8			−1.44031			−0.720155	+	0.693813i	$0.755930\pi$
$504$	3.57760e6	+	1.26525e6i	0.0279448	+	0.00988293i
$505$		0			0
$506$	2.24096e6	+	1.65775e6i	0.0172975	+	0.0127958i
$507$	2.19675e7			0.168561
$508$	−4.60390e7	−	1.50440e8i	−0.351184	−	1.14755i
$509$	2.27028e8			1.72158			0.860789	−	0.508961i	$-0.169970\pi$
$509$	2.27028e8			1.72158			0.860789	+	0.508961i	$0.169970\pi$
$510$		0			0
$511$			5.98906e6i			0.0448845i
$512$	7.02687e7	+	1.14353e8i	0.523542	+	0.852000i
$513$		−	2.55512e8i		−	1.89260i
$514$	7.02234e7	+	5.19478e7i	0.517122	+	0.382541i
$515$		0			0
$516$	5.31206e7	+	1.73581e8i	0.386646	+	1.26343i
$517$			1.45580e6i			0.0105349i
$518$	−1.47702e6	−	1.09263e6i	−0.0106267	−	0.00786110i
$519$			6.81190e7i			0.487266i
$520$		0			0
$521$	−3.90610e7			−0.276204			−0.138102	−	0.990418i	$-0.544100\pi$
$521$	−3.90610e7			−0.276204			−0.138102	+	0.990418i	$0.544100\pi$
$522$	2.77130e7	−	3.74626e7i	0.194837	−	0.263382i
$523$	−1.21695e8			−0.850686			−0.425343	−	0.905032i	$-0.639846\pi$
$523$	−1.21695e8			−0.850686			−0.425343	+	0.905032i	$0.639846\pi$
$524$	−5.35532e7	+	1.63888e7i	−0.372213	+	0.113908i
$525$		0			0
$526$	−4.24089e7	+	5.73286e7i	−0.291407	+	0.393926i
$527$	−2.81794e8			−1.92531
$528$	−1.91800e6	−	2.84022e6i	−0.0130301	−	0.0192953i
$529$	−7.45918e7			−0.503876
$530$		0			0
$531$			1.74974e6i			0.0116866i
$532$	−1.78204e7	+	5.45356e6i	−0.118354	+	0.0362197i
$533$			1.94499e8i			1.28451i
$534$	−4.83545e6	+	6.53659e6i	−0.0317551	+	0.0429267i
$535$		0			0
$536$	2.10389e8	+	7.44060e7i	1.36625	+	0.483185i
$537$		−	5.30310e7i		−	0.342458i
$538$	1.27762e8	−	1.72710e8i	0.820457	−	1.10910i
$539$		−	4.75940e6i		−	0.0303939i
$540$		0			0
$541$	1.30798e8			0.826053			0.413027	−	0.910719i	$-0.364472\pi$
$541$	1.30798e8			0.826053			0.413027	+	0.910719i	$0.364472\pi$
$542$	−1.82015e8	−	1.34645e8i	−1.14316	−	0.845656i
$543$	7.19094e7			0.449145
$544$	1.90886e8	+	8.20415e6i	1.18571	+	0.0509609i
$545$		0			0
$546$	−6.22630e6	−	4.60591e6i	−0.0382518	−	0.0282968i
$547$	1.53703e8			0.939120			0.469560	−	0.882901i	$-0.344413\pi$
$547$	1.53703e8			0.939120			0.469560	+	0.882901i	$0.344413\pi$
$548$	−1.10051e8	+	3.36787e7i	−0.668731	+	0.204651i
$549$	5.77540e7			0.349032
$550$		0			0
$551$			2.28850e8i			1.36803i
$552$	−8.51320e7	−	3.01077e7i	−0.506146	−	0.179003i
$553$		−	1.37947e7i		−	0.0815712i
$554$	−4.00665e7	−	2.96392e7i	−0.235642	−	0.174316i
$555$		0			0
$556$	−7.98905e6	+	2.44488e6i	−0.0464805	+	0.0142243i
$557$			6.91251e7i			0.400009i	0.979795	+	0.200005i	$0.0640957\pi$
$557$			6.91251e7i			0.400009i	−0.979795	+	0.200005i	$0.935904\pi$
$558$	9.49527e7	+	7.02413e7i	0.546519	+	0.404287i
$559$			2.67229e8i			1.52985i
$560$		0			0
$561$	−4.87868e6			−0.0276321
$562$	1.51194e8	−	2.04385e8i	0.851777	−	1.15144i
$563$	1.01350e8			0.567937			0.283969	−	0.958834i	$-0.408349\pi$
$563$	1.01350e8			0.567937			0.283969	+	0.958834i	$0.408349\pi$
$564$	−1.38005e7	−	4.50955e7i	−0.0769233	−	0.251360i
$565$		0			0
$566$	−3.19945e7	+	4.32505e7i	−0.176452	+	0.238529i
$567$	5.22659e6			0.0286727
$568$	−4.80514e7	+	1.35869e8i	−0.262217	+	0.741439i
$569$	1.24684e8			0.676820			0.338410	−	0.940999i	$-0.390111\pi$
$569$	1.24684e8			0.676820			0.338410	+	0.940999i	$0.390111\pi$
$570$		0			0
$571$			1.02626e8i			0.551252i	0.961265	+	0.275626i	$0.0888851\pi$
$571$			1.02626e8i			0.551252i	−0.961265	+	0.275626i	$0.911115\pi$
$572$	−1.47639e6	−	4.82436e6i	−0.00788885	−	0.0257782i
$573$		−	1.26380e8i		−	0.671762i
$574$	−1.15793e7	+	1.56530e7i	−0.0612277	+	0.0827680i
$575$		0			0
$576$	−6.22755e7	−	5.03456e7i	−0.325874	−	0.263447i
$577$			1.73246e8i			0.901853i	0.892561	+	0.450926i	$0.148906\pi$
$577$			1.73246e8i			0.901853i	−0.892561	+	0.450926i	$0.851094\pi$
$578$	4.69116e7	−	6.34154e7i	0.242939	−	0.328406i
$579$		−	5.79577e7i		−	0.298590i
$580$		0			0
$581$	−2.12873e7			−0.108540
$582$	−1.99119e8	−	1.47298e8i	−1.01005	−	0.747187i
$583$	2.47517e6			0.0124911
$584$	4.21403e7	−	1.19155e8i	0.211572	−	0.598238i
$585$		0			0
$586$	1.87920e8	+	1.39014e8i	0.933859	+	0.690822i
$587$	1.99472e8			0.986204			0.493102	−	0.869971i	$-0.335863\pi$
$587$	1.99472e8			0.986204			0.493102	+	0.869971i	$0.335863\pi$
$588$	4.51177e7	+	1.47430e8i	0.221929	+	0.725192i
$589$	−5.80043e8			−2.83867
$590$		0			0
$591$		−	8.77479e7i		−	0.425084i
$592$	2.16981e7	+	3.21310e7i	0.104582	+	0.154867i
$593$		−	2.74305e8i		−	1.31543i	−0.753265	−	0.657717i	$-0.771522\pi$
$593$		−	2.74305e8i		−	1.31543i	0.753265	−	0.657717i	$-0.228478\pi$
$594$	5.56691e6	+	4.11812e6i	0.0265616	+	0.0196490i
$595$		0			0
$596$	−8.35489e7	−	2.73011e8i	−0.394641	−	1.28956i
$597$			3.14707e7i			0.147905i
$598$	−1.06868e8	−	7.90558e7i	−0.499741	−	0.369683i
$599$		−	3.19919e8i		−	1.48854i	−0.667881	−	0.744268i	$-0.732798\pi$
$599$		−	3.19919e8i		−	1.48854i	0.667881	−	0.744268i	$-0.267202\pi$
$600$		0			0
$601$	−3.87120e8			−1.78329			−0.891646	−	0.452733i	$-0.850449\pi$
$601$	−3.87120e8			−1.78329			−0.891646	+	0.452733i	$0.850449\pi$
$602$	−1.59092e7	+	2.15062e7i	−0.0729222	+	0.0985767i
$603$	−1.33147e8			−0.607267
$604$	3.25544e8	−	9.96258e7i	1.47740	−	0.452128i
$605$		0			0
$606$	1.90017e8	−	2.56866e8i	0.853836	−	1.15422i
$607$	3.02210e8			1.35127			0.675635	−	0.737236i	$-0.263869\pi$
$607$	3.02210e8			1.35127			0.675635	+	0.737236i	$0.263869\pi$
$608$	3.92918e8	+	1.68874e7i	1.74820	+	0.0751365i
$609$	−9.52046e6			−0.0421508
$610$		0			0
$611$		−	6.94250e7i		−	0.304363i
$612$	−1.09007e8	+	3.33591e7i	−0.475552	+	0.145532i
$613$			4.00237e8i			1.73754i	0.495213	+	0.868771i	$0.335090\pi$
$613$			4.00237e8i			1.73754i	−0.495213	+	0.868771i	$0.664910\pi$
$614$	−1.08781e8	+	1.47051e8i	−0.469946	+	0.635276i
$615$		0			0
$616$	168396.	−	476154.i	0.000720427	−	0.00203707i
$617$		−	6.04515e6i		−	0.0257366i	−0.999917	−	0.0128683i	$-0.995904\pi$
$617$		−	6.04515e6i		−	0.0257366i	0.999917	−	0.0128683i	$-0.00409623\pi$
$618$	−4.08212e6	+	5.51823e6i	−0.0172950	+	0.0233795i
$619$			2.61775e8i			1.10371i	0.833939	+	0.551857i	$0.186081\pi$
$619$			2.61775e8i			1.10371i	−0.833939	+	0.551857i	$0.813919\pi$
$620$		0			0
$621$	1.82447e8			0.761838
$622$	−3.60178e7	−	2.66442e7i	−0.149674	−	0.110721i
$623$	−1.19820e6			−0.00495524
$624$	9.14670e7	+	1.35446e8i	0.376453	+	0.557460i
$625$		0			0
$626$	−8.87900e7	−	6.56824e7i	−0.361944	−	0.267748i
$627$	−1.00422e7			−0.0407407
$628$	−3.16940e8	+	9.69925e7i	−1.27967	+	0.391615i
$629$	5.51918e7			0.221780
$630$		0			0
$631$		−	6.02284e7i		−	0.239725i	−0.992791	−	0.119862i	$-0.961755\pi$
$631$		−	6.02284e7i		−	0.239725i	0.992791	−	0.119862i	$-0.0382454\pi$
$632$	−9.70624e7	+	2.74452e8i	−0.384503	+	1.08721i
$633$		−	2.67494e8i		−	1.05464i
$634$	−3.37598e8	−	2.49738e8i	−1.32474	−	0.979981i
$635$		0			0
$636$	−7.66721e7	+	2.34638e7i	−0.298034	+	0.0912069i
$637$			2.26969e8i			0.878110i
$638$	−4.98601e6	−	3.68840e6i	−0.0191995	−	0.0142029i
$639$		−	8.59862e7i		−	0.329554i
$640$		0			0
$641$	−4.36896e8			−1.65884			−0.829419	−	0.558627i	$-0.811328\pi$
$641$	−4.36896e8			−1.65884			−0.829419	+	0.558627i	$0.811328\pi$
$642$	7.06528e7	−	9.55089e7i	0.267008	−	0.360943i
$643$	2.07486e8			0.780468			0.390234	−	0.920716i	$-0.372394\pi$
$643$	2.07486e8			0.780468			0.390234	+	0.920716i	$0.372394\pi$
$644$	−3.89409e6	−	1.27246e7i	−0.0145797	−	0.0476416i
$645$		0			0
$646$	3.32947e8	−	4.50080e8i	1.23503	−	1.66952i
$647$	2.85482e8			1.05406			0.527030	−	0.849847i	$-0.323306\pi$
$647$	2.85482e8			1.05406			0.527030	+	0.849847i	$0.323306\pi$
$648$	−1.03985e8	−	3.67754e7i	−0.382162	−	0.135155i
$649$	232878.			0.000851912
$650$		0			0
$651$		−	2.41306e7i		−	0.0874631i
$652$	−3.13304e7	−	1.02377e8i	−0.113038	−	0.369370i
$653$			2.64397e8i			0.949550i	0.880107	+	0.474775i	$0.157470\pi$
$653$			2.64397e8i			0.949550i	−0.880107	+	0.474775i	$0.842530\pi$
$654$	−2.16981e7	+	2.93317e7i	−0.0775691	+	0.104858i
$655$		0			0
$656$	3.40514e8	−	2.29949e8i	1.20621	−	0.814556i
$657$			7.54086e7i			0.265904i
$658$	4.13315e6	−	5.58722e6i	0.0145079	−	0.0196118i
$659$		−	2.24450e8i		−	0.784267i	−0.919908	−	0.392133i	$-0.871737\pi$
$659$		−	2.24450e8i		−	0.784267i	0.919908	−	0.392133i	$-0.128263\pi$
$660$		0			0
$661$	5.36714e7			0.185840			0.0929199	−	0.995674i	$-0.470380\pi$
$661$	5.36714e7			0.185840			0.0929199	+	0.995674i	$0.470380\pi$
$662$	7.48679e6	+	5.53836e6i	0.0258061	+	0.0190901i
$663$	2.32658e8			0.798319
$664$	4.23520e8	+	1.49782e8i	1.44667	+	0.511628i
$665$		0			0
$666$	−1.85973e7	−	1.37574e7i	−0.0629545	−	0.0465706i
$667$	−1.63409e8			−0.550679
$668$	1.09002e8	+	3.56184e8i	0.365685	+	1.19494i
$669$	1.35848e8			0.453707
$670$		0			0
$671$		−	7.68665e6i		−	0.0254431i
$672$	−702538.	+	1.63459e7i	−0.00231506	+	0.0538644i
$673$			2.66858e8i			0.875457i	0.899107	+	0.437729i	$0.144217\pi$
$673$			2.66858e8i			0.875457i	−0.899107	+	0.437729i	$0.855783\pi$
$674$	−9.51098e7	−	7.03575e7i	−0.310631	−	0.229790i
$675$		0			0
$676$	−1.99916e7	−	6.53258e7i	−0.0647152	−	0.211468i
$677$			1.94003e8i			0.625234i	0.949879	+	0.312617i	$0.101206\pi$
$677$			1.94003e8i			0.625234i	−0.949879	+	0.312617i	$0.898794\pi$
$678$	9.82995e7	+	7.27171e7i	0.315400	+	0.233318i
$679$		−	3.64998e7i		−	0.116595i
$680$		0			0
$681$	−3.21412e8			−1.01770
$682$	9.34863e6	−	1.26375e7i	0.0294710	−	0.0398391i
$683$	1.59493e8			0.500586			0.250293	−	0.968170i	$-0.419473\pi$
$683$	1.59493e8			0.500586			0.250293	+	0.968170i	$0.419473\pi$
$684$	−2.24378e8	+	6.86660e7i	−0.701152	+	0.214572i
$685$		0			0
$686$	−2.70928e7	+	3.66242e7i	−0.0839230	+	0.113448i
$687$	−1.13599e7			−0.0350352
$688$	4.67844e8	−	3.15935e8i	1.43660	−	0.970136i
$689$	−1.18037e8			−0.360879
$690$		0			0
$691$			6.04045e8i			1.83078i	0.402573	+	0.915388i	$0.368116\pi$
$691$			6.04045e8i			1.83078i	−0.402573	+	0.915388i	$0.631884\pi$
$692$	2.02569e8	−	6.19918e7i	0.611300	−	0.187075i
$693$			301339.i			0.000905432i
$694$	7.97275e7	−	1.07776e8i	0.238523	−	0.322437i
$695$		0			0
$696$	1.89414e8	+	6.69880e7i	0.561803	+	0.198687i
$697$		−	5.84905e8i		−	1.72738i
$698$	1.26250e8	−	1.70666e8i	0.371249	−	0.501857i
$699$			5.42247e7i			0.158769i
$700$		0			0
$701$	3.93380e8			1.14198			0.570990	−	0.820957i	$-0.306559\pi$
$701$	3.93380e8			1.14198			0.570990	+	0.820957i	$0.306559\pi$
$702$	−2.65478e8	−	1.96387e8i	−0.767392	−	0.567678i
$703$	1.13606e8			0.326991
$704$	−6.70064e6	+	8.28843e6i	−0.0192043	+	0.0237549i
$705$		0			0
$706$	3.54408e8	+	2.62174e8i	1.00714	+	0.745032i
$707$	4.70852e7			0.133238
$708$	−7.21375e6	+	2.20761e6i	−0.0203265	+	0.00622047i
$709$	−1.36855e8			−0.383992			−0.191996	−	0.981396i	$-0.561496\pi$
$709$	−1.36855e8			−0.383992			−0.191996	+	0.981396i	$0.561496\pi$
$710$		0			0
$711$		−	1.73690e8i		−	0.483243i
$712$	2.38387e7	+	8.43079e6i	0.0660455	+	0.0233576i
$713$		−	4.14177e8i		−	1.14266i
$714$	1.87240e7	+	1.38511e7i	0.0514402	+	0.0380529i
$715$		0			0
$716$	−1.57701e8	+	4.82610e7i	−0.429631	+	0.131479i
$717$			2.52499e8i			0.685019i
$718$	−2.75926e8	−	2.04116e8i	−0.745451	−	0.551448i
$719$			6.36997e8i			1.71376i	0.515513	+	0.856881i	$0.327601\pi$
$719$			6.36997e8i			1.71376i	−0.515513	+	0.856881i	$0.672399\pi$
$720$		0			0
$721$	−1.01153e6			−0.00269881
$722$	4.61505e8	−	6.23866e8i	1.22621	−	1.65760i
$723$	−2.30726e8			−0.610495
$724$	−6.54413e7	−	2.13841e8i	−0.172439	−	0.563475i
$725$		0			0
$726$	−1.73294e8	+	2.34260e8i	−0.452870	+	0.612193i
$727$	−5.89955e7			−0.153538			−0.0767689	−	0.997049i	$-0.524460\pi$
$727$	−5.89955e7			−0.153538			−0.0767689	+	0.997049i	$0.524460\pi$
$728$	−8.03058e6	+	2.27071e7i	−0.0208139	+	0.0588529i
$729$	3.85198e8			0.994265
$730$		0			0
$731$		−	8.03620e8i		−	2.05730i
$732$	7.28671e7	+	2.38106e8i	0.185780	+	0.607067i
$733$		−	1.27557e7i		−	0.0323886i	−0.999869	−	0.0161943i	$-0.994845\pi$
$733$		−	1.27557e7i		−	0.0323886i	0.999869	−	0.0161943i	$-0.00515504\pi$
$734$	2.34438e8	−	3.16914e8i	0.592842	−	0.801408i
$735$		0			0
$736$	−1.20583e7	+	2.80561e8i	−0.0302450	+	0.703711i
$737$			1.77209e7i			0.0442674i
$738$	−1.45796e8	+	1.97088e8i	−0.362724	+	0.490333i
$739$			5.13652e8i			1.27273i	0.771389	+	0.636364i	$0.219562\pi$
$739$			5.13652e8i			1.27273i	−0.771389	+	0.636364i	$0.780438\pi$
$740$		0			0
$741$	4.78901e8			1.17704
$742$	−9.49948e6	−	7.02725e6i	−0.0232535	−	0.0172018i
$743$	−4.82260e8			−1.17575			−0.587874	−	0.808952i	$-0.700035\pi$
$743$	−4.82260e8			−1.17575			−0.587874	+	0.808952i	$0.700035\pi$
$744$	−1.69788e8	+	4.80089e8i	−0.412276	+	1.16574i
$745$		0			0
$746$	−6.59176e8	−	4.87626e8i	−1.58776	−	1.17455i
$747$	−2.68029e8			−0.643014
$748$	4.43986e6	+	1.45080e7i	0.0106088	+	0.0346659i
$749$	1.75074e7			0.0416655
$750$		0			0
$751$			8.05235e8i			1.90109i	0.310585	+	0.950546i	$0.399475\pi$
$751$			8.05235e8i			1.90109i	−0.310585	+	0.950546i	$0.600525\pi$
$752$	−1.21544e8	+	8.20786e7i	−0.285811	+	0.193009i
$753$		−	1.57526e8i		−	0.368949i
$754$	2.37776e8	+	1.75895e8i	0.554694	+	0.410335i
$755$		0			0
$756$	−9.67355e6	−	3.16100e7i	−0.0223883	−	0.0731575i
$757$			4.01651e8i			0.925894i	0.886386	+	0.462947i	$0.153208\pi$
$757$			4.01651e8i			0.925894i	−0.886386	+	0.462947i	$0.846792\pi$
$758$	1.54449e8	+	1.14253e8i	0.354631	+	0.262338i
$759$		−	7.17062e6i		−	0.0163995i
$760$		0			0
$761$	−2.41523e8			−0.548029			−0.274015	−	0.961726i	$-0.588352\pi$
$761$	−2.41523e8			−0.548029			−0.274015	+	0.961726i	$0.588352\pi$
$762$	−2.40690e8	+	3.25366e8i	−0.543992	+	0.735372i
$763$	−5.37668e6			−0.0121043
$764$	−3.75824e8	+	1.15013e8i	−0.842760	+	0.257908i
$765$		0			0
$766$	−2.42146e8	+	3.27335e8i	−0.538754	+	0.728292i
$767$	−1.11056e7			−0.0246126
$768$	1.28991e8	−	3.20267e8i	0.284757	−	0.707014i
$769$	−2.03639e8			−0.447799			−0.223899	−	0.974612i	$-0.571879\pi$
$769$	−2.03639e8			−0.447799			−0.223899	+	0.974612i	$0.571879\pi$
$770$		0			0
$771$		−	2.24701e8i		−	0.490277i
$772$	−1.72352e8	+	5.27446e7i	−0.374597	+	0.114637i
$773$		−	2.34074e8i		−	0.506774i	−0.967365	−	0.253387i	$-0.918455\pi$
$773$		−	2.34074e8i		−	0.506774i	0.967365	−	0.253387i	$-0.0815446\pi$
$774$	−2.00314e8	+	2.70786e8i	−0.432005	+	0.583987i
$775$		0			0
$776$	−2.56820e8	+	7.26180e8i	−0.549597	+	1.55403i
$777$			4.72618e6i			0.0100750i
$778$	−1.68722e8	+	2.28080e8i	−0.358289	+	0.484338i
$779$		−	1.20396e9i		−	2.54684i
$780$		0			0
$781$	−1.14442e7			−0.0240232
$782$	3.21378e8	+	2.37739e8i	0.672040	+	0.497142i
$783$	−4.05935e8			−0.845612
$784$	3.97360e8	−	2.68338e8i	0.824587	−	0.556844i
$785$		0			0
$786$	1.15822e8	+	8.56798e7i	0.238520	+	0.176445i
$787$	−6.41938e8			−1.31695			−0.658474	−	0.752603i	$-0.728798\pi$
$787$	−6.41938e8			−1.31695			−0.658474	+	0.752603i	$0.728798\pi$
$788$	−2.60941e8	+	7.98552e7i	−0.533290	+	0.163202i
$789$	1.83440e8			0.373476
$790$		0			0
$791$			1.80189e7i			0.0364082i
$792$	2.12029e6	−	5.99528e6i	0.00426795	−	0.0120680i
$793$			3.66566e8i			0.735076i
$794$	−9.06979e7	−	6.70938e7i	−0.181191	−	0.134036i
$795$		0			0
$796$	9.35862e7	−	2.86400e7i	0.185555	−	0.0567851i
$797$			1.82268e8i			0.360027i	0.983664	+	0.180013i	$0.0576141\pi$
$797$			1.82268e8i			0.360027i	−0.983664	+	0.180013i	$0.942386\pi$
$798$	3.85412e7	+	2.85109e7i	0.0758433	+	0.0561051i
$799$			2.08777e8i			0.409301i
$800$		0			0
$801$	−1.50866e7			−0.0293558
$802$	−3.63335e8	+	4.91159e8i	−0.704343	+	0.952136i
$803$	1.00364e7			0.0193834
$804$	−1.67989e8	−	5.48933e8i	−0.323231	−	1.05621i
$805$		0			0
$806$	−4.45823e8	+	6.02667e8i	−0.851447	+	1.15099i
$807$	−5.52637e8			−1.05152
$808$	−9.36783e8	−	3.31302e8i	−1.77584	−	0.628044i
$809$	6.12560e8			1.15692			0.578460	−	0.815711i	$-0.303654\pi$
$809$	6.12560e8			1.15692			0.578460	+	0.815711i	$0.303654\pi$
$810$		0			0
$811$		−	2.59393e8i		−	0.486291i	−0.969990	−	0.243146i	$-0.921821\pi$
$811$		−	2.59393e8i		−	0.486291i	0.969990	−	0.243146i	$-0.0781793\pi$
$812$	8.66412e6	+	2.83115e7i	0.0161829	+	0.0528804i
$813$			5.82410e8i			1.08382i
$814$	−1.83101e6	+	2.47517e6i	−0.00339482	+	0.00458914i
$815$		0			0
$816$	−2.75063e8	−	4.07319e8i	−0.506246	−	0.749660i
$817$		−	1.65416e9i		−	3.03328i
$818$	−2.26606e7	+	3.06327e7i	−0.0414010	+	0.0559662i
$819$		−	1.43704e7i		−	0.0261588i
$820$		0			0
$821$	7.94760e8			1.43617			0.718086	−	0.695954i	$-0.245018\pi$
$821$	7.94760e8			1.43617			0.718086	+	0.695954i	$0.245018\pi$
$822$	2.38013e8	+	1.76070e8i	0.428534	+	0.317008i
$823$	2.70019e8			0.484390			0.242195	−	0.970228i	$-0.422133\pi$
$823$	2.70019e8			0.484390			0.242195	+	0.970228i	$0.422133\pi$
$824$	2.01248e7	+	7.11732e6i	0.0359708	+	0.0127214i
$825$		0			0
$826$	−893766.	−	661164.i	−0.00158593	−	0.00117319i
$827$	6.56468e8			1.16064			0.580320	−	0.814389i	$-0.302928\pi$
$827$	6.56468e8			1.16064			0.580320	+	0.814389i	$0.302928\pi$
$828$	−4.90307e7	−	1.60216e8i	−0.0863728	−	0.282238i
$829$	−6.40196e8			−1.12370			−0.561849	−	0.827240i	$-0.689910\pi$
$829$	−6.40196e8			−1.12370			−0.561849	+	0.827240i	$0.689910\pi$
$830$		0			0
$831$			1.28205e8i			0.223409i
$832$	3.19544e8	−	3.95263e8i	0.554831	−	0.686304i
$833$		−	6.82550e8i		−	1.18086i
$834$	1.72784e7	+	1.27817e7i	0.0297855	+	0.0220338i
$835$		0			0
$836$	9.13897e6	+	2.98631e7i	0.0156415	+	0.0511113i
$837$		−	1.02888e9i		−	1.75465i
$838$	−6.11746e8	−	4.52540e8i	−1.03954	−	0.768997i
$839$		−	9.87826e8i		−	1.67261i	−0.548265	−	0.836305i	$-0.684711\pi$
$839$		−	9.87826e8i		−	1.67261i	0.548265	−	0.836305i	$-0.315289\pi$
$840$		0			0
$841$	−2.31247e8			−0.388766
$842$	−3.76838e8	+	5.09412e8i	−0.631274	+	0.853361i
$843$	−6.53992e8			−1.09167
$844$	−7.95460e8	+	2.43433e8i	−1.32309	+	0.404904i
$845$		0			0
$846$	5.20408e7	−	7.03491e7i	0.0859474	−	0.116184i
$847$	−4.29414e7			−0.0706685
$848$	1.39551e8	+	2.06651e8i	0.228848	+	0.338883i
$849$	1.38393e8			0.226147
$850$		0			0
$851$			8.11200e7i			0.131625i
$852$	3.54500e8	−	1.08487e8i	0.573189	−	0.175412i
$853$			4.88523e8i			0.787114i	0.919300	+	0.393557i	$0.128756\pi$
$853$			4.88523e8i			0.787114i	−0.919300	+	0.393557i	$0.871244\pi$
$854$	−2.18232e7	+	2.95007e7i	−0.0350384	+	0.0473651i
$855$		0			0
$856$	−3.48318e8	−	1.23186e8i	−0.555334	−	0.196399i
$857$			1.42078e8i			0.225728i	0.993610	+	0.112864i	$0.0360024\pi$
$857$			1.42078e8i			0.225728i	−0.993610	+	0.112864i	$0.963998\pi$
$858$	−7.71850e6	+	1.04339e7i	−0.0122200	+	0.0165191i
$859$		−	1.67240e8i		−	0.263852i	−0.991260	−	0.131926i	$-0.957884\pi$
$859$		−	1.67240e8i		−	0.263852i	0.991260	−	0.131926i	$-0.0421161\pi$
$860$		0			0
$861$	5.00865e7			0.0784714
$862$	8.01796e8	+	5.93129e8i	1.25182	+	0.926035i
$863$	3.61010e8			0.561678			0.280839	−	0.959755i	$-0.409387\pi$
$863$	3.61010e8			0.561678			0.280839	+	0.959755i	$0.409387\pi$
$864$	−2.99549e7	+	6.96960e8i	−0.0464437	+	1.08060i
$865$		0			0
$866$	6.22932e8	+	4.60814e8i	0.959151	+	0.709533i
$867$	−2.02917e8			−0.311358
$868$	−7.17584e7	+	2.19601e7i	−0.109727	+	0.0335796i
$869$	−2.31169e7			−0.0352266
$870$		0			0
$871$		−	8.45086e8i		−	1.27893i
$872$	1.06972e8	+	3.78315e7i	0.161331	+	0.0570563i
$873$		−	4.59571e8i		−	0.690733i
$874$	6.61521e8	+	4.89361e8i	0.990853	+	0.732984i
$875$		0			0
$876$	−3.10891e8	+	9.51416e7i	−0.462484	+	0.141533i
$877$			1.29370e8i			0.191794i	0.995391	+	0.0958970i	$0.0305719\pi$
$877$			1.29370e8i			0.191794i	−0.995391	+	0.0958970i	$0.969428\pi$
$878$	5.48509e8	+	4.05760e8i	0.810401	+	0.599495i
$879$		−	6.01308e8i		−	0.885381i
$880$		0			0
$881$	8.24185e8			1.20531			0.602653	−	0.798004i	$-0.294111\pi$
$881$	8.24185e8			1.20531			0.602653	+	0.798004i	$0.294111\pi$
$882$	−1.70136e8	+	2.29990e8i	−0.247964	+	0.335200i
$883$	6.17488e8			0.896906			0.448453	−	0.893807i	$-0.351975\pi$
$883$	6.17488e8			0.896906			0.448453	+	0.893807i	$0.351975\pi$
$884$	−2.11731e8	−	6.91866e8i	−0.306497	−	1.00153i
$885$		0			0
$886$	3.32557e8	−	4.49553e8i	0.478151	−	0.646367i
$887$	9.48736e8			1.35948			0.679742	−	0.733451i	$-0.262092\pi$
$887$	9.48736e8			1.35948			0.679742	+	0.733451i	$0.262092\pi$
$888$	3.32544e7	−	9.40295e7i	0.0474909	−	0.134284i
$889$	−5.96416e7			−0.0848876
$890$		0			0
$891$		−	8.75862e6i		−	0.0123823i
$892$	−1.23629e8	−	4.03979e8i	−0.174191	−	0.569199i
$893$			4.29745e8i			0.603471i
$894$	−4.36789e8	+	5.90455e8i	−0.611307	+	0.826370i
$895$		0			0
$896$	4.92481e7	−	1.27865e7i	0.0684645	−	0.0177757i
$897$			3.41957e8i			0.473799i
$898$	3.40982e8	−	4.60942e8i	0.470871	−	0.636527i
$899$			9.21521e8i			1.26831i
$900$		0			0
$901$	3.54966e8			0.485302
$902$	2.62310e7	+	1.94044e7i	0.0357434	+	0.0264412i
$903$	6.88155e7			0.0934595
$904$	1.26785e8	−	3.58495e8i	0.171618	−	0.485263i
$905$		0			0
$906$	−7.04073e8	−	5.20838e8i	−0.946745	−	0.700355i
$907$	−6.41528e8			−0.859793			−0.429896	−	0.902878i	$-0.641450\pi$
$907$	−6.41528e8			−0.859793			−0.429896	+	0.902878i	$0.641450\pi$
$908$	2.92501e8	+	9.55799e8i	0.390724	+	1.27676i
$909$	5.92853e8			0.789324
$910$		0			0
$911$		−	1.42626e8i		−	0.188645i	−0.995542	−	0.0943223i	$-0.969932\pi$
$911$		−	1.42626e8i		−	0.188645i	0.995542	−	0.0943223i	$-0.0300684\pi$
$912$	−5.66187e8	−	8.38422e8i	−0.746406	−	1.10529i
$913$			3.56728e7i			0.0468732i
$914$	5.18780e8	+	3.83768e8i	0.679429	+	0.502608i
$915$		0			0
$916$	1.03381e7	+	3.37816e7i	0.0134510	+	0.0439535i
$917$			2.12310e7i			0.0275336i
$918$	7.98355e8	+	5.90583e8i	1.03197	+	0.763402i
$919$			1.37495e9i			1.77149i	0.464171	+	0.885745i	$0.346352\pi$
$919$			1.37495e9i			1.77149i	−0.464171	+	0.885745i	$0.653648\pi$
$920$		0			0
$921$	4.70533e8			0.602298
$922$	−5.22953e8	+	7.06932e8i	−0.667222	+	0.901955i
$923$	5.45756e8			0.694055
$924$	−1.24235e6	+	380194.i	−0.00157481	+	0.000481936i
$925$		0			0
$926$	−3.40103e8	+	4.59754e8i	−0.428330	+	0.579019i
$927$	−1.27362e7			−0.0159882
$928$	2.68291e7	−	6.24233e8i	0.0335709	−	0.781093i
$929$	3.34030e8			0.416618			0.208309	−	0.978063i	$-0.433204\pi$
$929$	3.34030e8			0.416618			0.208309	+	0.978063i	$0.433204\pi$
$930$		0			0
$931$		−	1.40496e9i		−	1.74106i
$932$	1.61251e8	−	4.93473e7i	0.199184	−	0.0609559i
$933$			1.15250e8i			0.141904i
$934$	4.77742e8	−	6.45816e8i	0.586345	−	0.792625i
$935$		0			0
$936$	−1.01114e8	+	2.85907e8i	−0.123305	+	0.348656i
$937$			1.21360e9i			1.47522i	0.675229	+	0.737608i	$0.264045\pi$
$937$			1.21360e9i			1.47522i	−0.675229	+	0.737608i	$0.735955\pi$
$938$	5.03114e7	−	6.80114e7i	0.0609619	−	0.0824087i
$939$			2.84110e8i			0.343155i
$940$		0			0
$941$	−4.33889e8			−0.520727			−0.260364	−	0.965511i	$-0.583842\pi$
$941$	−4.33889e8			−0.520727			−0.260364	+	0.965511i	$0.583842\pi$
$942$	6.85463e8	+	5.07072e8i	0.820033	+	0.606620i
$943$	8.59684e8			1.02519
$944$	1.31298e7	+	1.94429e7i	0.0156078	+	0.0231124i
$945$		0			0
$946$	3.60397e7	+	2.66604e7i	0.0425704	+	0.0314915i
$947$	−3.55184e8			−0.418218			−0.209109	−	0.977892i	$-0.567056\pi$
$947$	−3.55184e8			−0.418218			−0.209109	+	0.977892i	$0.567056\pi$
$948$	7.16081e8	−	2.19141e8i	0.840499	−	0.257216i
$949$	−4.78620e8			−0.560005
$950$		0			0
$951$			1.08025e9i			1.25598i
$952$	2.41498e7	−	6.82856e7i	0.0279900	−	0.0791441i
$953$		−	5.71323e8i		−	0.660089i	−0.943965	−	0.330045i	$-0.892936\pi$
$953$		−	5.71323e8i		−	0.660089i	0.943965	−	0.330045i	$-0.107064\pi$
$954$	−1.19609e8	−	8.84805e7i	−0.137758	−	0.101907i
$955$		0			0
$956$	7.50870e8	−	2.29787e8i	0.859392	−	0.262998i
$957$			1.59542e7i			0.0182029i
$958$	6.21994e8	+	4.60120e8i	0.707440	+	0.523329i
$959$			4.36293e7i			0.0494678i
$960$		0			0
$961$	−1.44819e9			−1.63175
$962$	8.73182e7	−	1.18037e8i	0.0980798	−	0.132585i
$963$	2.20437e8			0.246834
$964$	2.09973e8	+	6.86123e8i	0.234386	+	0.765897i
$965$		0			0
$966$	−2.03581e7	+	2.75202e7i	−0.0225842	+	0.0305295i
$967$	2.99131e8			0.330812			0.165406	−	0.986226i	$-0.447107\pi$
$967$	2.99131e8			0.330812			0.165406	+	0.986226i	$0.447107\pi$
$968$	8.54338e8	+	3.02145e8i	0.941898	+	0.333111i
$969$	−1.44017e9			−1.58286
$970$		0			0
$971$			1.83579e8i			0.200524i	0.994961	+	0.100262i	$0.0319680\pi$
$971$			1.83579e8i			0.200524i	−0.994961	+	0.100262i	$0.968032\pi$
$972$	−2.07633e8	−	6.78476e8i	−0.226098	−	0.738815i
$973$			3.16724e6i			0.00343828i
$974$	6.35352e8	−	8.58873e8i	0.687602	−	0.929506i
$975$		0			0
$976$	6.41755e8	−	4.33378e8i	0.690271	−	0.466141i
$977$			7.32043e8i			0.784970i	0.919758	+	0.392485i	$0.128385\pi$
$977$			7.32043e8i			0.784970i	−0.919758	+	0.392485i	$0.871615\pi$
$978$	−1.63794e8	+	2.21417e8i	−0.175098	+	0.236698i
$979$			2.00792e6i			0.00213992i
$980$		0			0
$981$	−6.76981e7			−0.0717083
$982$	−8.61084e8	−	6.36987e8i	−0.909308	−	0.672661i
$983$	−9.20691e8			−0.969289			−0.484644	−	0.874711i	$-0.661051\pi$
$983$	−9.20691e8			−0.969289			−0.484644	+	0.874711i	$0.661051\pi$
$984$	−9.96495e8	−	3.52420e8i	−1.04590	−	0.369892i
$985$		0			0
$986$	−7.15047e8	−	5.28957e8i	−0.745940	−	0.551810i
$987$	−1.78780e7			−0.0185938
$988$	−4.35825e8	−	1.42413e9i	−0.451899	−	1.47666i
$989$	1.18115e9			1.22100
$990$		0			0
$991$		−	1.09773e8i		−	0.112792i	−0.998408	−	0.0563958i	$-0.982039\pi$
$991$		−	1.09773e8i		−	0.112792i	0.998408	−	0.0563958i	$-0.0179609\pi$
$992$	1.58218e9	+	6.80012e7i	1.62077	+	0.0696597i
$993$		−	2.39562e7i		−	0.0244664i
$994$	4.39217e7	+	3.24911e7i	0.0447219	+	0.0330830i
$995$		0			0
$996$	−3.38167e8	−	1.10502e9i	−0.342258	−	1.11839i
$997$			9.84752e7i			0.0993668i	0.998765	+	0.0496834i	$0.0158212\pi$
$997$			9.84752e7i			0.0993668i	−0.998765	+	0.0496834i	$0.984179\pi$
$998$	−6.72736e8	−	4.97657e8i	−0.676789	−	0.500655i
$999$			2.01515e8i			0.202121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.7.d.b.99.6		24
4.3	odd	2	inner	100.7.d.b.99.20		24
5.2	odd	4		100.7.b.h.51.3		12
5.3	odd	4		20.7.b.a.11.10	yes	12
5.4	even	2	inner	100.7.d.b.99.19		24
15.8	even	4		180.7.c.a.91.3		12
20.3	even	4		20.7.b.a.11.9	✓	12
20.7	even	4		100.7.b.h.51.4		12
20.19	odd	2	inner	100.7.d.b.99.5		24
40.3	even	4		320.7.b.d.191.9		12
40.13	odd	4		320.7.b.d.191.4		12
60.23	odd	4		180.7.c.a.91.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.7.b.a.11.9	✓	12	20.3	even	4
20.7.b.a.11.10	yes	12	5.3	odd	4
100.7.b.h.51.3		12	5.2	odd	4
100.7.b.h.51.4		12	20.7	even	4
100.7.d.b.99.5		24	20.19	odd	2	inner
100.7.d.b.99.6		24	1.1	even	1	trivial
100.7.d.b.99.19		24	5.4	even	2	inner
100.7.d.b.99.20		24	4.3	odd	2	inner
180.7.c.a.91.3		12	15.8	even	4
180.7.c.a.91.4		12	60.23	odd	4
320.7.b.d.191.4		12	40.13	odd	4
320.7.b.d.191.9		12	40.3	even	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.75771 + 6.43150i) q^{2} +20.5795 q^{3} +(-18.7284 - 61.1984i) q^{4} +(-97.9113 + 132.357i) q^{6} -24.2619 q^{7} +(482.702 + 170.712i) q^{8} -305.483 q^{9} +O(q^{10})\)	\(q+(-4.75771 + 6.43150i) q^{2} +20.5795 q^{3} +(-18.7284 - 61.1984i) q^{4} +(-97.9113 + 132.357i) q^{6} -24.2619 q^{7} +(482.702 + 170.712i) q^{8} -305.483 q^{9} +40.6577i q^{11} +(-385.422 - 1259.43i) q^{12} -1938.91i q^{13} +(115.431 - 156.041i) q^{14} +(-3394.49 + 2292.30i) q^{16} +5830.75i q^{17} +(1453.40 - 1964.72i) q^{18} +12002.0i q^{19} -499.299 q^{21} +(-261.490 - 193.437i) q^{22} -8569.95 q^{23} +(9933.78 + 3513.17i) q^{24} +(12470.1 + 9224.76i) q^{26} -21289.2 q^{27} +(454.388 + 1484.79i) q^{28} +19067.7 q^{29} +48329.0i q^{31} +(1407.05 - 32737.8i) q^{32} +836.716i q^{33} +(-37500.5 - 27741.0i) q^{34} +(5721.23 + 18695.1i) q^{36} -9465.63i q^{37} +(-77190.7 - 57101.9i) q^{38} -39901.8i q^{39} -100314. q^{41} +(2375.52 - 3211.24i) q^{42} -137824. q^{43} +(2488.19 - 761.455i) q^{44} +(40773.3 - 55117.7i) q^{46} +35806.2 q^{47} +(-69857.0 + 47174.5i) q^{48} -117060. q^{49} +119994. i q^{51} +(-118658. + 36312.7i) q^{52} -60878.2i q^{53} +(101288. - 136921. i) q^{54} +(-11711.3 - 4141.80i) q^{56} +246995. i q^{57} +(-90718.4 + 122634. i) q^{58} -5727.78i q^{59} -189058. q^{61} +(-310828. - 229935. i) q^{62} +7411.61 q^{63} +(203859. + 164806. i) q^{64} +(-5381.34 - 3980.85i) q^{66} +435857. q^{67} +(356833. - 109201. i) q^{68} -176366. q^{69} +281476. i q^{71} +(-147457. - 52149.7i) q^{72} -246850. i q^{73} +(60878.2 + 45034.7i) q^{74} +(734502. - 224778. i) q^{76} -986.434i q^{77} +(256629. + 189841. i) q^{78} +568574. i q^{79} -215424. q^{81} +(477264. - 645168. i) q^{82} +877394. q^{83} +(9351.09 + 30556.3i) q^{84} +(655728. - 886418. i) q^{86} +392403. q^{87} +(-6940.76 + 19625.6i) q^{88} +49386.0 q^{89} +47041.7i q^{91} +(160502. + 524468. i) q^{92} +994587. i q^{93} +(-170355. + 230288. i) q^{94} +(28956.4 - 673728. i) q^{96} +1.50441e6i q^{97} +(556939. - 752874. i) q^{98} -12420.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 312 q^{4} - 1344 q^{6} + 3992 q^{9}+O(q^{10}) \) 24 * q - 312 * q^4 - 1344 * q^6 + 3992 * q^9	\( 24 q - 312 q^{4} - 1344 q^{6} + 3992 q^{9} - 12496 q^{14} + 6624 q^{16} - 54928 q^{21} - 57056 q^{24} - 37368 q^{26} + 149936 q^{29} - 96408 q^{34} - 257160 q^{36} - 33952 q^{41} + 444320 q^{44} - 289584 q^{46} - 145128 q^{49} - 300832 q^{54} - 493024 q^{56} + 92928 q^{61} + 1085568 q^{64} - 130400 q^{66} - 82512 q^{69} - 3163848 q^{74} + 416640 q^{76} + 4574856 q^{81} + 4512448 q^{84} - 125024 q^{86} - 556784 q^{89} - 9413136 q^{94} - 5282304 q^{96}+O(q^{100}) \) 24 * q - 312 * q^4 - 1344 * q^6 + 3992 * q^9 - 12496 * q^14 + 6624 * q^16 - 54928 * q^21 - 57056 * q^24 - 37368 * q^26 + 149936 * q^29 - 96408 * q^34 - 257160 * q^36 - 33952 * q^41 + 444320 * q^44 - 289584 * q^46 - 145128 * q^49 - 300832 * q^54 - 493024 * q^56 + 92928 * q^61 + 1085568 * q^64 - 130400 * q^66 - 82512 * q^69 - 3163848 * q^74 + 416640 * q^76 + 4574856 * q^81 + 4512448 * q^84 - 125024 * q^86 - 556784 * q^89 - 9413136 * q^94 - 5282304 * q^96

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