LMFDB - Embedded newform 175.5.d.e.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(76,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("175.76");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.d (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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.1
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	175.76
Dual form			175.5.d.e.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44949 q^{2} -5.00000i q^{3} -10.0000 q^{4} +12.2474i q^{6} +(-34.2929 + 35.0000i) q^{7} +63.6867 q^{8} +56.0000 q^{9} +O(q^{10})$	\(q-2.44949 q^{2} -5.00000i q^{3} -10.0000 q^{4} +12.2474i q^{6} +(-34.2929 + 35.0000i) q^{7} +63.6867 q^{8} +56.0000 q^{9} +89.0000 q^{11} +50.0000i q^{12} +5.00000i q^{13} +(84.0000 - 85.7321i) q^{14} +4.00000 q^{16} -485.000i q^{17} -137.171 q^{18} +220.454i q^{19} +(175.000 + 171.464i) q^{21} -218.005 q^{22} -700.554 q^{23} -318.434i q^{24} -12.2474i q^{26} -685.000i q^{27} +(342.929 - 350.000i) q^{28} -191.000 q^{29} +1053.28i q^{31} -1028.79 q^{32} -445.000i q^{33} +1188.00i q^{34} -560.000 q^{36} -1631.36 q^{37} -540.000i q^{38} +25.0000 q^{39} -2914.89i q^{41} +(-428.661 - 420.000i) q^{42} +377.221 q^{43} -890.000 q^{44} +1716.00 q^{46} -2195.00i q^{47} -20.0000i q^{48} +(-49.0000 - 2400.50i) q^{49} -2425.00 q^{51} -50.0000i q^{52} -1587.27 q^{53} +1677.90i q^{54} +(-2184.00 + 2229.04i) q^{56} +1102.27 q^{57} +467.853 q^{58} -3625.24i q^{59} -1935.10i q^{61} -2580.00i q^{62} +(-1920.40 + 1960.00i) q^{63} +2456.00 q^{64} +1090.02i q^{66} -2047.77 q^{67} +4850.00i q^{68} +3502.77i q^{69} +4454.00 q^{71} +3566.46 q^{72} -8650.00i q^{73} +3996.00 q^{74} -2204.54i q^{76} +(-3052.06 + 3115.00i) q^{77} -61.2372 q^{78} -5561.00 q^{79} +1111.00 q^{81} +7140.00i q^{82} -1990.00i q^{83} +(-1750.00 - 1714.64i) q^{84} -924.000 q^{86} +955.000i q^{87} +5668.12 q^{88} -808.332i q^{89} +(-175.000 - 171.464i) q^{91} +7005.54 q^{92} +5266.40 q^{93} +5376.63i q^{94} +5143.93i q^{96} +9235.00i q^{97} +(120.025 + 5880.00i) q^{98} +4984.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 40 q^{4} + 224 q^{9}+O(q^{10}) $ 4 * q - 40 * q^4 + 224 * q^9	$ 4 q - 40 q^{4} + 224 q^{9} + 356 q^{11} + 336 q^{14} + 16 q^{16} + 700 q^{21} - 764 q^{29} - 2240 q^{36} + 100 q^{39} - 3560 q^{44} + 6864 q^{46} - 196 q^{49} - 9700 q^{51} - 8736 q^{56} + 9824 q^{64} + 17816 q^{71} + 15984 q^{74} - 22244 q^{79} + 4444 q^{81} - 7000 q^{84} - 3696 q^{86} - 700 q^{91} + 19936 q^{99}+O(q^{100}) $ 4 * q - 40 * q^4 + 224 * q^9 + 356 * q^11 + 336 * q^14 + 16 * q^16 + 700 * q^21 - 764 * q^29 - 2240 * q^36 + 100 * q^39 - 3560 * q^44 + 6864 * q^46 - 196 * q^49 - 9700 * q^51 - 8736 * q^56 + 9824 * q^64 + 17816 * q^71 + 15984 * q^74 - 22244 * q^79 + 4444 * q^81 - 7000 * q^84 - 3696 * q^86 - 700 * q^91 + 19936 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.44949			−0.612372			−0.306186	−	0.951972i	$-0.599053\pi$
$2$	−2.44949			−0.612372			−0.306186	+	0.951972i	$0.599053\pi$
$3$		−	5.00000i		−	0.555556i	−0.960645	−	0.277778i	$-0.910402\pi$
$3$		−	5.00000i		−	0.555556i	0.960645	−	0.277778i	$-0.0895979\pi$
$4$	−10.0000			−0.625000
$5$		0			0
$5$		0			0
$6$			12.2474i			0.340207i
$7$	−34.2929	+	35.0000i	−0.699854	+	0.714286i
$7$	−34.2929	+	35.0000i	−0.699854	+	0.714286i
$8$	63.6867			0.995105
$9$	56.0000			0.691358
$10$		0			0
$11$	89.0000			0.735537			0.367769	−	0.929917i	$-0.380122\pi$
$11$	89.0000			0.735537			0.367769	+	0.929917i	$0.380122\pi$
$12$			50.0000i			0.347222i
$13$			5.00000i			0.0295858i	0.999891	+	0.0147929i	$0.00470890\pi$
$13$			5.00000i			0.0295858i	−0.999891	+	0.0147929i	$0.995291\pi$
$14$	84.0000	−	85.7321i	0.428571	−	0.437409i
$15$		0			0
$16$	4.00000			0.0156250
$17$		−	485.000i		−	1.67820i	−0.543977	−	0.839100i	$-0.683082\pi$
$17$		−	485.000i		−	1.67820i	0.543977	−	0.839100i	$-0.316918\pi$
$18$	−137.171			−0.423369
$19$			220.454i			0.610676i	0.952244	+	0.305338i	$0.0987695\pi$
$19$			220.454i			0.610676i	−0.952244	+	0.305338i	$0.901231\pi$
$20$		0			0
$21$	175.000	+	171.464i	0.396825	+	0.388808i
$22$	−218.005			−0.450423
$23$	−700.554			−1.32430			−0.662149	−	0.749372i	$-0.730356\pi$
$23$	−700.554			−1.32430			−0.662149	+	0.749372i	$0.730356\pi$
$24$		−	318.434i		−	0.552836i
$25$		0			0
$26$		−	12.2474i		−	0.0181175i
$27$		−	685.000i		−	0.939643i
$28$	342.929	−	350.000i	0.437409	−	0.446429i
$29$	−191.000			−0.227111			−0.113555	−	0.993532i	$-0.536224\pi$
$29$	−191.000			−0.227111			−0.113555	+	0.993532i	$0.536224\pi$
$30$		0			0
$31$			1053.28i			1.09603i	0.836470	+	0.548013i	$0.184615\pi$
$31$			1053.28i			1.09603i	−0.836470	+	0.548013i	$0.815385\pi$
$32$	−1028.79			−1.00467
$33$		−	445.000i		−	0.408632i
$34$			1188.00i			1.02768i
$35$		0			0
$36$	−560.000			−0.432099
$37$	−1631.36			−1.19164			−0.595822	−	0.803117i	$-0.703174\pi$
$37$	−1631.36			−1.19164			−0.595822	+	0.803117i	$0.703174\pi$
$38$		−	540.000i		−	0.373961i
$39$	25.0000			0.0164366
$40$		0			0
$41$		−	2914.89i		−	1.73402i	−0.498288	−	0.867012i	$-0.666038\pi$
$41$		−	2914.89i		−	1.73402i	0.498288	−	0.867012i	$-0.333962\pi$
$42$	−428.661	−	420.000i	−0.243005	−	0.238095i
$43$	377.221			0.204014			0.102007	−	0.994784i	$-0.467474\pi$
$43$	377.221			0.204014			0.102007	+	0.994784i	$0.467474\pi$
$44$	−890.000			−0.459711
$45$		0			0
$46$	1716.00			0.810964
$47$		−	2195.00i		−	0.993662i	−0.867847	−	0.496831i	$-0.834497\pi$
$47$		−	2195.00i		−	0.993662i	0.867847	−	0.496831i	$-0.165503\pi$
$48$		−	20.0000i		−	0.00868056i
$49$	−49.0000	−	2400.50i	−0.0204082	−	0.999792i
$50$		0			0
$51$	−2425.00			−0.932334
$52$		−	50.0000i		−	0.0184911i
$53$	−1587.27			−0.565066			−0.282533	−	0.959258i	$-0.591175\pi$
$53$	−1587.27			−0.565066			−0.282533	+	0.959258i	$0.591175\pi$
$54$			1677.90i			0.575412i
$55$		0			0
$56$	−2184.00	+	2229.04i	−0.696429	+	0.710789i
$57$	1102.27			0.339265
$58$	467.853			0.139076
$59$		−	3625.24i		−	1.04144i	−0.853728	−	0.520719i	$-0.825664\pi$
$59$		−	3625.24i		−	1.04144i	0.853728	−	0.520719i	$-0.174336\pi$
$60$		0			0
$61$		−	1935.10i		−	0.520048i	−0.965602	−	0.260024i	$-0.916270\pi$
$61$		−	1935.10i		−	0.520048i	0.965602	−	0.260024i	$-0.0837304\pi$
$62$		−	2580.00i		−	0.671176i
$63$	−1920.40	+	1960.00i	−0.483850	+	0.493827i
$64$	2456.00			0.599609
$65$		0			0
$66$			1090.02i			0.250235i
$67$	−2047.77			−0.456176			−0.228088	−	0.973641i	$-0.573247\pi$
$67$	−2047.77			−0.456176			−0.228088	+	0.973641i	$0.573247\pi$
$68$			4850.00i			1.04888i
$69$			3502.77i			0.735722i
$70$		0			0
$71$	4454.00			0.883555			0.441777	−	0.897125i	$-0.354348\pi$
$71$	4454.00			0.883555			0.441777	+	0.897125i	$0.354348\pi$
$72$	3566.46			0.687974
$73$		−	8650.00i		−	1.62319i	−0.584218	−	0.811597i	$-0.698599\pi$
$73$		−	8650.00i		−	1.62319i	0.584218	−	0.811597i	$-0.301401\pi$
$74$	3996.00			0.729730
$75$		0			0
$76$		−	2204.54i		−	0.381673i
$77$	−3052.06	+	3115.00i	−0.514769	+	0.525384i
$78$	−61.2372			−0.0100653
$79$	−5561.00			−0.891043			−0.445522	−	0.895271i	$-0.646982\pi$
$79$	−5561.00			−0.891043			−0.445522	+	0.895271i	$0.646982\pi$
$80$		0			0
$81$	1111.00			0.169334
$82$			7140.00i			1.06187i
$83$		−	1990.00i		−	0.288866i	−0.989515	−	0.144433i	$-0.953864\pi$
$83$		−	1990.00i		−	0.288866i	0.989515	−	0.144433i	$-0.0461359\pi$
$84$	−1750.00	−	1714.64i	−0.248016	−	0.243005i
$85$		0			0
$86$	−924.000			−0.124932
$87$			955.000i			0.126173i
$88$	5668.12			0.731937
$89$		−	808.332i		−	0.102049i	−0.998697	−	0.0510246i	$-0.983751\pi$
$89$		−	808.332i		−	0.102049i	0.998697	−	0.0510246i	$-0.0162487\pi$
$90$		0			0
$91$	−175.000	−	171.464i	−0.0211327	−	0.0207057i
$92$	7005.54			0.827687
$93$	5266.40			0.608903
$94$			5376.63i			0.608491i
$95$		0			0
$96$			5143.93i			0.558152i
$97$			9235.00i			0.981507i	0.871298	+	0.490754i	$0.163278\pi$
$97$			9235.00i			0.981507i	−0.871298	+	0.490754i	$0.836722\pi$
$98$	120.025	+	5880.00i	0.0124974	+	0.612245i
$99$	4984.00			0.508520
$100$		0			0
$101$			4825.49i			0.473041i	0.971626	+	0.236521i	$0.0760071\pi$
$101$			4825.49i			0.473041i	−0.971626	+	0.236521i	$0.923993\pi$
$102$	5940.01			0.570935
$103$			4715.00i			0.444434i	0.974997	+	0.222217i	$0.0713293\pi$
$103$			4715.00i			0.444434i	−0.974997	+	0.222217i	$0.928671\pi$
$104$			318.434i			0.0294410i
$105$		0			0
$106$	3888.00			0.346031
$107$	12668.8			1.10654			0.553269	−	0.833002i	$-0.313380\pi$
$107$	12668.8			1.10654			0.553269	+	0.833002i	$0.313380\pi$
$108$			6850.00i			0.587277i
$109$	−12311.0			−1.03619			−0.518096	−	0.855322i	$-0.673359\pi$
$109$	−12311.0			−1.03619			−0.518096	+	0.855322i	$0.673359\pi$
$110$		0			0
$111$			8156.80i			0.662024i
$112$	−137.171	+	140.000i	−0.0109352	+	0.0111607i
$113$	3120.65			0.244393			0.122196	−	0.992506i	$-0.461006\pi$
$113$	3120.65			0.244393			0.122196	+	0.992506i	$0.461006\pi$
$114$	−2700.00			−0.207756
$115$		0			0
$116$	1910.00			0.141944
$117$			280.000i			0.0204544i
$118$			8880.00i			0.637748i
$119$	16975.0	+	16632.0i	1.19871	+	1.17450i
$120$		0			0
$121$	−6720.00			−0.458985
$122$			4740.00i			0.318463i
$123$	−14574.5			−0.963346
$124$		−	10532.8i		−	0.685016i
$125$		0			0
$126$	4704.00	−	4801.00i	0.296296	−	0.302406i
$127$	23867.8			1.47981			0.739904	−	0.672712i	$-0.234871\pi$
$127$	23867.8			1.47981			0.739904	+	0.672712i	$0.234871\pi$
$128$	10444.6			0.637489
$129$		−	1886.11i		−	0.113341i
$130$		0			0
$131$		−	6736.10i		−	0.392524i	−0.980552	−	0.196262i	$-0.937120\pi$
$131$		−	6736.10i		−	0.392524i	0.980552	−	0.196262i	$-0.0628802\pi$
$132$			4450.00i			0.255395i
$133$	−7715.89	−	7560.00i	−0.436197	−	0.427384i
$134$	5016.00			0.279350
$135$		0			0
$136$		−	30888.1i		−	1.66999i
$137$	−23069.3			−1.22912			−0.614558	−	0.788871i	$-0.710666\pi$
$137$	−23069.3			−1.22912			−0.614558	+	0.788871i	$0.710666\pi$
$138$		−	8580.00i		−	0.450536i
$139$		−	29491.9i		−	1.52641i	−0.646154	−	0.763207i	$-0.723624\pi$
$139$		−	29491.9i		−	1.52641i	0.646154	−	0.763207i	$-0.276376\pi$
$140$		0			0
$141$	−10975.0			−0.552035
$142$	−10910.0			−0.541065
$143$			445.000i			0.0217615i
$144$	224.000			0.0108025
$145$		0			0
$146$			21188.1i			0.993999i
$147$	−12002.5	+	245.000i	−0.555440	+	0.0113379i
$148$	16313.6			0.744777
$149$	−28346.0			−1.27679			−0.638395	−	0.769709i	$-0.720401\pi$
$149$	−28346.0			−1.27679			−0.638395	+	0.769709i	$0.720401\pi$
$150$		0			0
$151$	−17551.0			−0.769747			−0.384873	−	0.922969i	$-0.625755\pi$
$151$	−17551.0			−0.769747			−0.384873	+	0.922969i	$0.625755\pi$
$152$			14040.0i			0.607687i
$153$		−	27160.0i		−	1.16024i
$154$	7476.00	−	7630.16i	0.315230	−	0.321731i
$155$		0			0
$156$	−250.000			−0.0102728
$157$		−	25790.0i		−	1.04629i	−0.852244	−	0.523145i	$-0.824759\pi$
$157$		−	25790.0i		−	1.04629i	0.852244	−	0.523145i	$-0.175241\pi$
$158$	13621.6			0.545650
$159$			7936.35i			0.313925i
$160$		0			0
$161$	24024.0	−	24519.4i	0.926816	−	0.945928i
$162$	−2721.38			−0.103695
$163$	−37153.9			−1.39839			−0.699196	−	0.714930i	$-0.746458\pi$
$163$	−37153.9			−1.39839			−0.699196	+	0.714930i	$0.746458\pi$
$164$			29148.9i			1.08376i
$165$		0			0
$166$			4874.48i			0.176894i
$167$		−	20795.0i		−	0.745634i	−0.927905	−	0.372817i	$-0.878392\pi$
$167$		−	20795.0i		−	0.745634i	0.927905	−	0.372817i	$-0.121608\pi$
$168$	11145.2	+	10920.0i	0.394883	+	0.386905i
$169$	28536.0			0.999125
$170$		0			0
$171$			12345.4i			0.422196i
$172$	−3772.21			−0.127509
$173$		−	115.000i		−	0.00384243i	−0.999998	−	0.00192121i	$-0.999388\pi$
$173$		−	115.000i		−	0.00384243i	0.999998	−	0.00192121i	$-0.000611542\pi$
$174$		−	2339.26i		−	0.0772646i
$175$		0			0
$176$	356.000			0.0114928
$177$	−18126.2			−0.578577
$178$			1980.00i			0.0624921i
$179$	−5318.00			−0.165975			−0.0829874	−	0.996551i	$-0.526446\pi$
$179$	−5318.00			−0.165975			−0.0829874	+	0.996551i	$0.526446\pi$
$180$		0			0
$181$			12345.4i			0.376833i	0.982089	+	0.188417i	$0.0603355\pi$
$181$			12345.4i			0.376833i	−0.982089	+	0.188417i	$0.939665\pi$
$182$	428.661	+	420.000i	0.0129411	+	0.0126796i
$183$	−9675.48			−0.288915
$184$	−44616.0			−1.31782
$185$		0			0
$186$	−12900.0			−0.372875
$187$		−	43165.0i		−	1.23438i
$188$			21950.0i			0.621039i
$189$	23975.0	+	23490.6i	0.671174	+	0.657613i
$190$		0			0
$191$	−14263.0			−0.390971			−0.195485	−	0.980707i	$-0.562628\pi$
$191$	−14263.0			−0.390971			−0.195485	+	0.980707i	$0.562628\pi$
$192$		−	12280.0i		−	0.333116i
$193$	−32005.0			−0.859219			−0.429609	−	0.903015i	$-0.641349\pi$
$193$	−32005.0			−0.859219			−0.429609	+	0.903015i	$0.641349\pi$
$194$		−	22621.0i		−	0.601048i
$195$		0			0
$196$	490.000	+	24005.0i	0.0127551	+	0.624870i
$197$	−3394.99			−0.0874795			−0.0437398	−	0.999043i	$-0.513927\pi$
$197$	−3394.99			−0.0874795			−0.0437398	+	0.999043i	$0.513927\pi$
$198$	−12208.3			−0.311403
$199$		−	19400.0i		−	0.489886i	−0.969538	−	0.244943i	$-0.921231\pi$
$199$		−	19400.0i		−	0.489886i	0.969538	−	0.244943i	$-0.0787692\pi$
$200$		0			0
$201$			10238.9i			0.253431i
$202$		−	11820.0i		−	0.289677i
$203$	6549.94	−	6685.00i	0.158944	−	0.162222i
$204$	24250.0			0.582709
$205$		0			0
$206$		−	11549.3i		−	0.272159i
$207$	−39231.0			−0.915565
$208$			20.0000i			0.000462278i
$209$			19620.4i			0.449175i
$210$		0			0
$211$	52817.0			1.18634			0.593170	−	0.805078i	$-0.297876\pi$
$211$	52817.0			1.18634			0.593170	+	0.805078i	$0.297876\pi$
$212$	15872.7			0.353166
$213$		−	22270.0i		−	0.490864i
$214$	−31032.0			−0.677614
$215$		0			0
$216$		−	43625.4i		−	0.935044i
$217$	−36864.8	−	36120.0i	−0.782875	−	0.767058i
$218$	30155.7			0.634536
$219$	−43250.0			−0.901774
$220$		0			0
$221$	2425.00			0.0496509
$222$		−	19980.0i		−	0.405405i
$223$		−	13645.0i		−	0.274387i	−0.990544	−	0.137194i	$-0.956192\pi$
$223$		−	13645.0i		−	0.274387i	0.990544	−	0.137194i	$-0.0438082\pi$
$224$	35280.0	−	36007.5i	0.703125	−	0.717624i
$225$		0			0
$226$	−7644.00			−0.149659
$227$			74485.0i			1.44550i	0.691111	+	0.722748i	$0.257121\pi$
$227$			74485.0i			1.44550i	−0.691111	+	0.722748i	$0.742879\pi$
$228$	−11022.7			−0.212040
$229$			68463.2i			1.30553i	0.757561	+	0.652764i	$0.226391\pi$
$229$			68463.2i			1.30553i	−0.757561	+	0.652764i	$0.773609\pi$
$230$		0			0
$231$	15575.0	+	15260.3i	0.291880	+	0.285983i
$232$	−12164.2			−0.225999
$233$	60169.3			1.10831			0.554157	−	0.832412i	$-0.313041\pi$
$233$	60169.3			1.10831			0.554157	+	0.832412i	$0.313041\pi$
$234$		−	685.857i		−	0.0125257i
$235$		0			0
$236$			36252.4i			0.650899i
$237$			27805.0i			0.495024i
$238$	−41580.1	−	40740.0i	−0.734060	−	0.719229i
$239$	75367.0			1.31943			0.659714	−	0.751517i	$-0.270678\pi$
$239$	75367.0			1.31943			0.659714	+	0.751517i	$0.270678\pi$
$240$		0			0
$241$			77869.3i			1.34070i	0.742044	+	0.670351i	$0.233856\pi$
$241$			77869.3i			1.34070i	−0.742044	+	0.670351i	$0.766144\pi$
$242$	16460.6			0.281070
$243$		−	61040.0i		−	1.03372i
$244$			19351.0i			0.325030i
$245$		0			0
$246$	35700.0			0.589927
$247$	−1102.27			−0.0180673
$248$			67080.0i			1.09066i
$249$	−9950.00			−0.160481
$250$		0			0
$251$		−	50410.5i		−	0.800154i	−0.916482	−	0.400077i	$-0.868983\pi$
$251$		−	50410.5i		−	0.800154i	0.916482	−	0.400077i	$-0.131017\pi$
$252$	19204.0	−	19600.0i	0.302406	−	0.308642i
$253$	−62349.3			−0.974071
$254$	−58464.0			−0.906194
$255$		0			0
$256$	−64880.0			−0.989990
$257$			3370.00i			0.0510227i	0.999675	+	0.0255114i	$0.00812140\pi$
$257$			3370.00i			0.0510227i	−0.999675	+	0.0255114i	$0.991879\pi$
$258$			4620.00i			0.0694069i
$259$	55944.0	−	57097.6i	0.833977	−	0.851174i
$260$		0			0
$261$	−10696.0			−0.157015
$262$			16500.0i			0.240371i
$263$	59385.4			0.858556			0.429278	−	0.903173i	$-0.358768\pi$
$263$	59385.4			0.858556			0.429278	+	0.903173i	$0.358768\pi$
$264$		−	28340.6i		−	0.406632i
$265$		0			0
$266$	18900.0	+	18518.1i	0.267115	+	0.261718i
$267$	−4041.66			−0.0566940
$268$	20477.7			0.285110
$269$		−	77012.0i		−	1.06427i	−0.846658	−	0.532137i	$-0.821389\pi$
$269$		−	77012.0i		−	1.06427i	0.846658	−	0.532137i	$-0.178611\pi$
$270$		0			0
$271$		−	143222.i		−	1.95016i	−0.221855	−	0.975080i	$-0.571211\pi$
$271$		−	143222.i		−	1.95016i	0.221855	−	0.975080i	$-0.428789\pi$
$272$		−	1940.00i		−	0.0262219i
$273$	−857.321	+	875.000i	−0.0115032	+	0.0117404i
$274$	56508.0			0.752677
$275$		0			0
$276$		−	35027.7i		−	0.459826i
$277$	101928.			1.32842			0.664209	−	0.747547i	$-0.268769\pi$
$277$	101928.			1.32842			0.664209	+	0.747547i	$0.268769\pi$
$278$			72240.0i			0.934734i
$279$			58983.7i			0.757746i
$280$		0			0
$281$	−47521.0			−0.601829			−0.300914	−	0.953651i	$-0.597292\pi$
$281$	−47521.0			−0.601829			−0.300914	+	0.953651i	$0.597292\pi$
$282$	26883.1			0.338051
$283$			43115.0i			0.538339i	0.963093	+	0.269169i	$0.0867491\pi$
$283$			43115.0i			0.538339i	−0.963093	+	0.269169i	$0.913251\pi$
$284$	−44540.0			−0.552222
$285$		0			0
$286$		−	1090.02i		−	0.0133261i
$287$	102021.	+	99960.0i	1.23859	+	1.21356i
$288$	−57612.0			−0.694589
$289$	−151704.			−1.81636
$290$		0			0
$291$	46175.0			0.545282
$292$			86500.0i			1.01450i
$293$			162125.i			1.88849i	0.329243	+	0.944245i	$0.393206\pi$
$293$			162125.i			1.88849i	−0.329243	+	0.944245i	$0.606794\pi$
$294$	29400.0	−	600.125i	0.340136	−	0.00694300i
$295$		0			0
$296$	−103896.			−1.18581
$297$		−	60965.0i		−	0.691143i
$298$	69433.2			0.781871
$299$		−	3502.77i		−	0.0391804i
$300$		0			0
$301$	−12936.0	+	13202.7i	−0.142780	+	0.145724i
$302$	42991.0			0.471372
$303$	24127.5			0.262801
$304$			881.816i			0.00954181i
$305$		0			0
$306$			66528.1i			0.710497i
$307$			33805.0i			0.358678i	0.983787	+	0.179339i	$0.0573958\pi$
$307$			33805.0i			0.358678i	−0.983787	+	0.179339i	$0.942604\pi$
$308$	30520.6	−	31150.0i	0.321731	−	0.328365i
$309$	23575.0			0.246908
$310$		0			0
$311$			50435.0i			0.521448i	0.965413	+	0.260724i	$0.0839613\pi$
$311$			50435.0i			0.521448i	−0.965413	+	0.260724i	$0.916039\pi$
$312$	1592.17			0.0163561
$313$		−	68155.0i		−	0.695679i	−0.937554	−	0.347840i	$-0.886915\pi$
$313$		−	68155.0i		−	0.695679i	0.937554	−	0.347840i	$-0.113085\pi$
$314$			63172.3i			0.640719i
$315$		0			0
$316$	55610.0			0.556902
$317$	42435.0			0.422285			0.211142	−	0.977455i	$-0.432282\pi$
$317$	42435.0			0.422285			0.211142	+	0.977455i	$0.432282\pi$
$318$		−	19440.0i		−	0.192239i
$319$	−16999.0			−0.167048
$320$		0			0
$321$		−	63343.8i		−	0.614744i
$322$	−58846.5	+	60060.0i	−0.567557	+	0.579260i
$323$	106920.			1.02484
$324$	−11110.0			−0.105834
$325$		0			0
$326$	91008.0			0.856336
$327$			61555.0i			0.575662i
$328$		−	185640.i		−	1.72554i
$329$	76825.0	+	75272.8i	0.709759	+	0.695419i
$330$		0			0
$331$	−114706.			−1.04696			−0.523480	−	0.852038i	$-0.675367\pi$
$331$	−114706.			−1.04696			−0.523480	+	0.852038i	$0.675367\pi$
$332$			19900.0i			0.180541i
$333$	−91356.2			−0.823852
$334$			50937.1i			0.456606i
$335$		0			0
$336$	700.000	+	685.857i	0.00620040	+	0.00607512i
$337$	−117007.			−1.03027			−0.515137	−	0.857108i	$-0.672259\pi$
$337$	−117007.			−1.03027			−0.515137	+	0.857108i	$0.672259\pi$
$338$	−69898.6			−0.611836
$339$		−	15603.2i		−	0.135774i
$340$		0			0
$341$			93742.0i			0.806168i
$342$		−	30240.0i		−	0.258541i
$343$	85697.8	+	80605.0i	0.728420	+	0.685131i
$344$	24024.0			0.203015
$345$		0			0
$346$			281.691i			0.00235300i
$347$	70481.6			0.585352			0.292676	−	0.956212i	$-0.405454\pi$
$347$	70481.6			0.585352			0.292676	+	0.956212i	$0.405454\pi$
$348$		−	9550.00i		−	0.0788578i
$349$		−	91390.5i		−	0.750326i	−0.926959	−	0.375163i	$-0.877587\pi$
$349$		−	91390.5i		−	0.750326i	0.926959	−	0.375163i	$-0.122413\pi$
$350$		0			0
$351$	3425.00			0.0278001
$352$	−91561.9			−0.738975
$353$			11405.0i			0.0915263i	0.998952	+	0.0457631i	$0.0145720\pi$
$353$			11405.0i			0.0915263i	−0.998952	+	0.0457631i	$0.985428\pi$
$354$	44400.0			0.354304
$355$		0			0
$356$			8083.32i			0.0637807i
$357$	83160.2	−	84875.0i	0.652498	−	0.665953i
$358$	13026.4			0.101638
$359$	−230366.			−1.78743			−0.893716	−	0.448633i	$-0.851911\pi$
$359$	−230366.			−1.78743			−0.893716	+	0.448633i	$0.851911\pi$
$360$		0			0
$361$	81721.0			0.627075
$362$		−	30240.0i		−	0.230762i
$363$			33600.0i			0.254992i
$364$	1750.00	+	1714.64i	0.0132079	+	0.0129411i
$365$		0			0
$366$	23700.0			0.176924
$367$			74485.0i			0.553015i	0.961012	+	0.276507i	$0.0891770\pi$
$367$			74485.0i			0.553015i	−0.961012	+	0.276507i	$0.910823\pi$
$368$	−2802.22			−0.0206922
$369$		−	163234.i		−	1.19883i
$370$		0			0
$371$	54432.0	−	55554.4i	0.395464	−	0.403618i
$372$	−52664.0			−0.380564
$373$	−102550.			−0.737088			−0.368544	−	0.929610i	$-0.620144\pi$
$373$	−102550.			−0.737088			−0.368544	+	0.929610i	$0.620144\pi$
$374$			105732.i			0.755900i
$375$		0			0
$376$		−	139792.i		−	0.988799i
$377$		−	955.000i		−	0.00671925i
$378$	−58726.5	−	57540.0i	−0.411008	−	0.402704i
$379$	172954.			1.20407			0.602036	−	0.798469i	$-0.294357\pi$
$379$	172954.			1.20407			0.602036	+	0.798469i	$0.294357\pi$
$380$		0			0
$381$		−	119339.i		−	0.822116i
$382$	34937.1			0.239420
$383$			144050.i			0.982010i	0.871157	+	0.491005i	$0.163370\pi$
$383$			144050.i			0.982010i	−0.871157	+	0.491005i	$0.836630\pi$
$384$		−	52223.1i		−	0.354161i
$385$		0			0
$386$	78396.0			0.526162
$387$	21124.4			0.141047
$388$		−	92350.0i		−	0.613442i
$389$	148969.			0.984457			0.492228	−	0.870466i	$-0.336182\pi$
$389$	148969.			0.984457			0.492228	+	0.870466i	$0.336182\pi$
$390$		0			0
$391$			339769.i			2.22244i
$392$	−3120.65	−	152880.i	−0.0203083	−	0.994898i
$393$	−33680.5			−0.218069
$394$	8316.00			0.0535700
$395$		0			0
$396$	−49840.0			−0.317825
$397$		−	256925.i		−	1.63014i	−0.579361	−	0.815071i	$-0.696698\pi$
$397$		−	256925.i		−	1.63014i	0.579361	−	0.815071i	$-0.303302\pi$
$398$			47520.0i			0.299992i
$399$	−37800.0	+	38579.5i	−0.237436	+	0.242332i
$400$		0			0
$401$	−35641.0			−0.221647			−0.110823	−	0.993840i	$-0.535349\pi$
$401$	−35641.0			−0.221647			−0.110823	+	0.993840i	$0.535349\pi$
$402$		−	25080.0i		−	0.155194i
$403$	−5266.40			−0.0324268
$404$		−	48254.9i		−	0.295651i
$405$		0			0
$406$	−16044.0	+	16374.8i	−0.0973331	+	0.0993402i
$407$	−145191.			−0.876498
$408$	−154440.			−0.927770
$409$			151721.i			0.906985i	0.891260	+	0.453493i	$0.149822\pi$
$409$			151721.i			0.906985i	−0.891260	+	0.453493i	$0.850178\pi$
$410$		0			0
$411$			115346.i			0.682843i
$412$		−	47150.0i		−	0.277771i
$413$	126884.	+	124320.i	0.743884	+	0.728855i
$414$	96096.0			0.560667
$415$		0			0
$416$		−	5143.93i		−	0.0297241i
$417$	−147459.			−0.848008
$418$		−	48060.0i		−	0.275062i
$419$		−	150889.i		−	0.859465i	−0.902956	−	0.429733i	$-0.858608\pi$
$419$		−	150889.i		−	0.859465i	0.902956	−	0.429733i	$-0.141392\pi$
$420$		0			0
$421$	−4681.00			−0.0264104			−0.0132052	−	0.999913i	$-0.504203\pi$
$421$	−4681.00			−0.0264104			−0.0132052	+	0.999913i	$0.504203\pi$
$422$	−129375.			−0.726481
$423$		−	122920.i		−	0.686976i
$424$	−101088.			−0.562300
$425$		0			0
$426$			54550.1i			0.300591i
$427$	67728.4	+	66360.0i	0.371463	+	0.363957i
$428$	−126688.			−0.691587
$429$	2225.00			0.0120897
$430$		0			0
$431$	−87103.0			−0.468898			−0.234449	−	0.972128i	$-0.575329\pi$
$431$	−87103.0			−0.468898			−0.234449	+	0.972128i	$0.575329\pi$
$432$		−	2740.00i		−	0.0146819i
$433$		−	231730.i		−	1.23597i	−0.786192	−	0.617983i	$-0.787950\pi$
$433$		−	231730.i		−	1.23597i	0.786192	−	0.617983i	$-0.212050\pi$
$434$	90300.0	+	88475.6i	0.479411	+	0.469725i
$435$		0			0
$436$	123110.			0.647620
$437$		−	154440.i		−	0.808718i
$438$	105940.			0.552222
$439$			246272.i			1.27787i	0.769262	+	0.638933i	$0.220624\pi$
$439$			246272.i			1.27787i	−0.769262	+	0.638933i	$0.779376\pi$
$440$		0			0
$441$	−2744.00	−	134428.i	−0.0141093	−	0.691214i
$442$	−5940.01			−0.0304048
$443$	349841.			1.78264			0.891319	−	0.453376i	$-0.149781\pi$
$443$	349841.			1.78264			0.891319	+	0.453376i	$0.149781\pi$
$444$		−	81568.0i		−	0.413765i
$445$		0			0
$446$			33423.3i			0.168027i
$447$			141730.i			0.709327i
$448$	−84223.3	+	85960.0i	−0.419639	+	0.428292i
$449$	−254711.			−1.26344			−0.631721	−	0.775196i	$-0.717651\pi$
$449$	−254711.			−1.26344			−0.631721	+	0.775196i	$0.717651\pi$
$450$		0			0
$451$		−	259425.i		−	1.27544i
$452$	−31206.5			−0.152745
$453$			87755.0i			0.427637i
$454$		−	182450.i		−	0.885182i
$455$		0			0
$456$	70200.0			0.337604
$457$	−263629.			−1.26229			−0.631147	−	0.775663i	$-0.717415\pi$
$457$	−263629.			−1.26229			−0.631147	+	0.775663i	$0.717415\pi$
$458$		−	167700.i		−	0.799470i
$459$	−332225.			−1.57691
$460$		0			0
$461$		−	128255.i		−	0.603495i	−0.953388	−	0.301747i	$-0.902430\pi$
$461$		−	128255.i		−	0.603495i	0.953388	−	0.301747i	$-0.0975699\pi$
$462$	−38150.8	−	37380.0i	−0.178739	−	0.175128i
$463$	−81857.0			−0.381851			−0.190926	−	0.981605i	$-0.561149\pi$
$463$	−81857.0			−0.381851			−0.190926	+	0.981605i	$0.561149\pi$
$464$	−764.000			−0.00354860
$465$		0			0
$466$	−147384.			−0.678701
$467$			204445.i			0.937438i	0.883347	+	0.468719i	$0.155284\pi$
$467$			204445.i			0.937438i	−0.883347	+	0.468719i	$0.844716\pi$
$468$		−	2800.00i		−	0.0127840i
$469$	70224.0	−	71672.1i	0.319257	−	0.325840i
$470$		0			0
$471$	−128950.			−0.581272
$472$		−	230880.i		−	1.03634i
$473$	33572.7			0.150060
$474$		−	68108.1i		−	0.303139i
$475$		0			0
$476$	−169750.	−	166320.i	−0.749197	−	0.734060i
$477$	−88887.1			−0.390663
$478$	−184611.			−0.807981
$479$			79534.9i			0.346647i	0.984865	+	0.173323i	$0.0554505\pi$
$479$			79534.9i			0.346647i	−0.984865	+	0.173323i	$0.944549\pi$
$480$		0			0
$481$		−	8156.80i		−	0.0352557i
$482$		−	190740.i		−	0.821009i
$483$	−122597.	−	120120.i	−0.525515	−	0.514898i
$484$	67200.0			0.286866
$485$		0			0
$486$			149517.i			0.633020i
$487$	164958.			0.695531			0.347766	−	0.937582i	$-0.386941\pi$
$487$	164958.			0.695531			0.347766	+	0.937582i	$0.386941\pi$
$488$		−	123240.i		−	0.517502i
$489$			185769.i			0.776884i
$490$		0			0
$491$	−74191.0			−0.307743			−0.153872	−	0.988091i	$-0.549174\pi$
$491$	−74191.0			−0.307743			−0.153872	+	0.988091i	$0.549174\pi$
$492$	145745.			0.602091
$493$			92635.0i			0.381137i
$494$	2700.00			0.0110639
$495$		0			0
$496$			4213.12i			0.0171254i
$497$	−152740.	+	155890.i	−0.618360	+	0.631111i
$498$	24372.4			0.0982743
$499$	278527.			1.11858			0.559289	−	0.828973i	$-0.311074\pi$
$499$	278527.			1.11858			0.559289	+	0.828973i	$0.311074\pi$
$500$		0			0
$501$	−103975.			−0.414241
$502$			123480.i			0.489992i
$503$			60275.0i			0.238233i	0.992880	+	0.119116i	$0.0380061\pi$
$503$			60275.0i			0.238233i	−0.992880	+	0.119116i	$0.961994\pi$
$504$	−122304.	+	124826.i	−0.481481	+	0.491410i
$505$		0			0
$506$	152724.			0.596494
$507$		−	142680.i		−	0.555069i
$508$	−238678.			−0.924880
$509$		−	348709.i		−	1.34595i	−0.739666	−	0.672974i	$-0.765017\pi$
$509$		−	348709.i		−	1.34595i	0.739666	−	0.672974i	$-0.234983\pi$
$510$		0			0
$511$	302750.	+	296633.i	1.15942	+	1.13600i
$512$	−8191.09			−0.0312465
$513$	151011.			0.573818
$514$		−	8254.78i		−	0.0312449i
$515$		0			0
$516$			18861.1i			0.0708381i
$517$		−	195355.i		−	0.730876i
$518$	−137034.	+	139860.i	−0.510704	+	0.521236i
$519$	−575.000			−0.00213468
$520$		0			0
$521$			84727.9i			0.312141i	0.987746	+	0.156070i	$0.0498827\pi$
$521$			84727.9i			0.312141i	−0.987746	+	0.156070i	$0.950117\pi$
$522$	26199.7			0.0961515
$523$			235610.i			0.861371i	0.902502	+	0.430686i	$0.141728\pi$
$523$			235610.i			0.861371i	−0.902502	+	0.430686i	$0.858272\pi$
$524$			67361.0i			0.245327i
$525$		0			0
$526$	−145464.			−0.525756
$527$	510841.			1.83935
$528$		−	1780.00i		−	0.00638487i
$529$	210935.			0.753767
$530$		0			0
$531$		−	203014.i		−	0.720006i
$532$	77158.9	+	75600.0i	0.272623	+	0.267115i
$533$	14574.5			0.0513025
$534$	9900.00			0.0347178
$535$		0			0
$536$	−130416.			−0.453943
$537$			26590.0i			0.0922082i
$538$			188640.i			0.651732i
$539$	−4361.00	−	213644.i	−0.0150110	−	0.735384i
$540$		0			0
$541$	259199.			0.885602			0.442801	−	0.896620i	$-0.353985\pi$
$541$	259199.			0.885602			0.442801	+	0.896620i	$0.353985\pi$
$542$			350820.i			1.19422i
$543$	61727.1			0.209352
$544$			498961.i			1.68604i
$545$		0			0
$546$	2100.00	−	2143.30i	0.00704424	−	0.00718950i
$547$	423894.			1.41672			0.708358	−	0.705854i	$-0.249436\pi$
$547$	423894.			1.41672			0.708358	+	0.705854i	$0.249436\pi$
$548$	230693.			0.768198
$549$		−	108365.i		−	0.359539i
$550$		0			0
$551$		−	42106.7i		−	0.138691i
$552$			223080.i			0.732120i
$553$	190703.	−	194635.i	0.623600	−	0.636459i
$554$	−249672.			−0.813486
$555$		0			0
$556$			294919.i			0.954009i
$557$	−133389.			−0.429943			−0.214972	−	0.976620i	$-0.568966\pi$
$557$	−133389.			−0.429943			−0.214972	+	0.976620i	$0.568966\pi$
$558$		−	144480.i		−	0.464023i
$559$			1886.11i			0.00603591i
$560$		0			0
$561$	−215825.			−0.685766
$562$	116402.			0.368543
$563$			369770.i			1.16658i	0.812264	+	0.583290i	$0.198235\pi$
$563$			369770.i			1.16658i	−0.812264	+	0.583290i	$0.801765\pi$
$564$	109750.			0.345022
$565$		0			0
$566$		−	105610.i		−	0.329664i
$567$	−38099.4	+	38885.0i	−0.118509	+	0.120953i
$568$	283661.			0.879230
$569$	326134.			1.00733			0.503665	−	0.863899i	$-0.331985\pi$
$569$	326134.			1.00733			0.503665	+	0.863899i	$0.331985\pi$
$570$		0			0
$571$	306374.			0.939679			0.469840	−	0.882752i	$-0.344312\pi$
$571$	306374.			0.939679			0.469840	+	0.882752i	$0.344312\pi$
$572$		−	4450.00i		−	0.0136009i
$573$			71315.0i			0.217206i
$574$	−249900.	−	244851.i	−0.758477	−	0.743153i
$575$		0			0
$576$	137536.			0.414545
$577$			387595.i			1.16420i	0.813118	+	0.582099i	$0.197768\pi$
$577$			387595.i			1.16420i	−0.813118	+	0.582099i	$0.802232\pi$
$578$	371597.			1.11229
$579$			160025.i			0.477344i
$580$		0			0
$581$	69650.0	+	68242.8i	0.206333	+	0.202164i
$582$	−113105.			−0.333915
$583$	−141267.			−0.415627
$584$		−	550890.i		−	1.61525i
$585$		0			0
$586$		−	397124.i		−	1.15646i
$587$			467350.i			1.35633i	0.734909	+	0.678166i	$0.237225\pi$
$587$			467350.i			1.35633i	−0.734909	+	0.678166i	$0.762775\pi$
$588$	120025.	−	2450.00i	0.347150	−	0.00708617i
$589$	−232200.			−0.669317
$590$		0			0
$591$			16975.0i			0.0485997i
$592$	−6525.44			−0.0186194
$593$		−	214315.i		−	0.609457i	−0.952439	−	0.304729i	$-0.901434\pi$
$593$		−	214315.i		−	0.609457i	0.952439	−	0.304729i	$-0.0985658\pi$
$594$			149333.i			0.423237i
$595$		0			0
$596$	283460.			0.797993
$597$	−96999.8			−0.272159
$598$			8580.00i			0.0239930i
$599$	283999.			0.791522			0.395761	−	0.918353i	$-0.370481\pi$
$599$	283999.			0.791522			0.395761	+	0.918353i	$0.370481\pi$
$600$		0			0
$601$		−	91219.0i		−	0.252544i	−0.991996	−	0.126272i	$-0.959699\pi$
$601$		−	91219.0i		−	0.252544i	0.991996	−	0.126272i	$-0.0403011\pi$
$602$	31686.6	−	32340.0i	0.0874345	−	0.0892374i
$603$	−114675.			−0.315381
$604$	175510.			0.481092
$605$		0			0
$606$	−59100.0			−0.160932
$607$		−	193715.i		−	0.525758i	−0.964829	−	0.262879i	$-0.915328\pi$
$607$		−	193715.i		−	0.525758i	0.964829	−	0.262879i	$-0.0846720\pi$
$608$		−	226800.i		−	0.613530i
$609$	−33425.0	−	32749.7i	−0.0901232	−	0.0883024i
$610$		0			0
$611$	10975.0			0.0293983
$612$			271600.i			0.725148i
$613$	−296231.			−0.788334			−0.394167	−	0.919039i	$-0.628967\pi$
$613$	−296231.			−0.788334			−0.394167	+	0.919039i	$0.628967\pi$
$614$		−	82805.0i		−	0.219644i
$615$		0			0
$616$	−194376.	+	198384.i	−0.512249	+	0.522812i
$617$	424751.			1.11574			0.557872	−	0.829927i	$-0.311618\pi$
$617$	424751.			1.11574			0.557872	+	0.829927i	$0.311618\pi$
$618$	−57746.7			−0.151200
$619$			375825.i			0.980855i	0.871482	+	0.490427i	$0.163159\pi$
$619$			375825.i			0.980855i	−0.871482	+	0.490427i	$0.836841\pi$
$620$		0			0
$621$			479880.i			1.24437i
$622$		−	123540.i		−	0.319321i
$623$	28291.6	+	27720.0i	0.0728923	+	0.0714196i
$624$	100.000			0.000256821
$625$		0			0
$626$			166945.i			0.426015i
$627$	98102.1			0.249542
$628$			257900.i			0.653931i
$629$			791210.i			1.99982i
$630$		0			0
$631$	−471511.			−1.18422			−0.592111	−	0.805856i	$-0.701705\pi$
$631$	−471511.			−1.18422			−0.592111	+	0.805856i	$0.701705\pi$
$632$	−354162.			−0.886682
$633$		−	264085.i		−	0.659077i
$634$	−103944.			−0.258595
$635$		0			0
$636$		−	79363.5i		−	0.196203i
$637$	12002.5	−	245.000i	0.0295796	−	0.000603792i
$638$	41638.9			0.102296
$639$	249424.			0.610853
$640$		0			0
$641$	558794.			1.35999			0.679995	−	0.733217i	$-0.261982\pi$
$641$	558794.			1.35999			0.679995	+	0.733217i	$0.261982\pi$
$642$			155160.i			0.376452i
$643$			454235.i			1.09865i	0.835609	+	0.549324i	$0.185115\pi$
$643$			454235.i			1.09865i	−0.835609	+	0.549324i	$0.814885\pi$
$644$	−240240.	+	245194.i	−0.579260	+	0.591205i
$645$		0			0
$646$	−261900.			−0.627582
$647$		−	129530.i		−	0.309430i	−0.987959	−	0.154715i	$-0.950554\pi$
$647$		−	129530.i		−	0.309430i	0.987959	−	0.154715i	$-0.0494459\pi$
$648$	70756.0			0.168505
$649$		−	322647.i		−	0.766016i
$650$		0			0
$651$	−180600.	+	184324.i	−0.426143	+	0.434931i
$652$	371539.			0.873995
$653$	−343903.			−0.806511			−0.403255	−	0.915087i	$-0.632121\pi$
$653$	−343903.			−0.806511			−0.403255	+	0.915087i	$0.632121\pi$
$654$		−	150778.i		−	0.352520i
$655$		0			0
$656$		−	11659.6i		−	0.0270941i
$657$		−	484400.i		−	1.12221i
$658$	−188182.	−	184380.i	−0.434637	−	0.425855i
$659$	−526913.			−1.21330			−0.606650	−	0.794969i	$-0.707487\pi$
$659$	−526913.			−1.21330			−0.606650	+	0.794969i	$0.707487\pi$
$660$		0			0
$661$		−	191844.i		−	0.439082i	−0.975603	−	0.219541i	$-0.929544\pi$
$661$		−	191844.i		−	0.439082i	0.975603	−	0.219541i	$-0.0704559\pi$
$662$	280971.			0.641130
$663$		−	12125.0i		−	0.0275838i
$664$		−	126737.i		−	0.287452i
$665$		0			0
$666$	223776.			0.504505
$667$	133806.			0.300762
$668$			207950.i			0.466022i
$669$	−68225.0			−0.152437
$670$		0			0
$671$		−	172224.i		−	0.382514i
$672$	−180037.	−	176400.i	−0.398680	−	0.390625i
$673$	429792.			0.948918			0.474459	−	0.880278i	$-0.342644\pi$
$673$	429792.			0.948918			0.474459	+	0.880278i	$0.342644\pi$
$674$	286608.			0.630912
$675$		0			0
$676$	−285360.			−0.624453
$677$		−	79685.0i		−	0.173860i	−0.996214	−	0.0869299i	$-0.972294\pi$
$677$		−	79685.0i		−	0.173860i	0.996214	−	0.0869299i	$-0.0277056\pi$
$678$			38220.0i			0.0831441i
$679$	−323225.	−	316695.i	−0.701076	−	0.686912i
$680$		0			0
$681$	372425.			0.803054
$682$		−	229620.i		−	0.493675i
$683$	−719577.			−1.54254			−0.771269	−	0.636510i	$-0.780378\pi$
$683$	−719577.			−1.54254			−0.771269	+	0.636510i	$0.780378\pi$
$684$		−	123454.i		−	0.263872i
$685$		0			0
$686$	−209916.	−	197441.i	−0.446064	−	0.419555i
$687$	342316.			0.725294
$688$	1508.89			0.00318771
$689$		−	7936.35i		−	0.0167179i
$690$		0			0
$691$		−	398532.i		−	0.834655i	−0.908756	−	0.417328i	$-0.862967\pi$
$691$		−	398532.i		−	0.834655i	0.908756	−	0.417328i	$-0.137033\pi$
$692$			1150.00i			0.00240152i
$693$	−170916.	+	174440.i	−0.355890	+	0.363228i
$694$	−172644.			−0.358453
$695$		0			0
$696$			60820.8i			0.125555i
$697$	−1.41372e6			−2.91004
$698$			223860.i			0.459479i
$699$		−	300846.i		−	0.615730i
$700$		0			0
$701$	−658873.			−1.34081			−0.670403	−	0.741998i	$-0.733879\pi$
$701$	−658873.			−1.34081			−0.670403	+	0.741998i	$0.733879\pi$
$702$	−8389.50			−0.0170240
$703$		−	359640.i		−	0.727708i
$704$	218584.			0.441035
$705$		0			0
$706$		−	27936.4i		−	0.0560482i
$707$	−168892.	−	165480.i	−0.337887	−	0.331060i
$708$	181262.			0.361610
$709$	593737.			1.18114			0.590570	−	0.806986i	$-0.298903\pi$
$709$	593737.			1.18114			0.590570	+	0.806986i	$0.298903\pi$
$710$		0			0
$711$	−311416.			−0.616030
$712$		−	51480.0i		−	0.101550i
$713$		−	737880.i		−	1.45147i
$714$	−203700.	+	207900.i	−0.399572	+	0.407811i
$715$		0			0
$716$	53180.0			0.103734
$717$		−	376835.i		−	0.733015i
$718$	564279.			1.09457
$719$			75321.8i			0.145701i	0.997343	+	0.0728506i	$0.0232096\pi$
$719$			75321.8i			0.145701i	−0.997343	+	0.0728506i	$0.976790\pi$
$720$		0			0
$721$	−165025.	−	161691.i	−0.317453	−	0.311039i
$722$	−200175.			−0.384003
$723$	389346.			0.744834
$724$		−	123454.i		−	0.235521i
$725$		0			0
$726$		−	82302.9i		−	0.156150i
$727$			342190.i			0.647438i	0.946153	+	0.323719i	$0.104933\pi$
$727$			342190.i			0.647438i	−0.946153	+	0.323719i	$0.895067\pi$
$728$	−11145.2	−	10920.0i	−0.0210293	−	0.0206044i
$729$	−215209.			−0.404954
$730$		0			0
$731$		−	182952.i		−	0.342376i
$732$	96754.8			0.180572
$733$		−	958555.i		−	1.78406i	−0.451978	−	0.892029i	$-0.649281\pi$
$733$		−	958555.i		−	1.78406i	0.451978	−	0.892029i	$-0.350719\pi$
$734$		−	182450.i		−	0.338651i
$735$		0			0
$736$	720720.			1.33049
$737$	−182252.			−0.335534
$738$			399840.i			0.734131i
$739$	229399.			0.420052			0.210026	−	0.977696i	$-0.432645\pi$
$739$	229399.			0.420052			0.210026	+	0.977696i	$0.432645\pi$
$740$		0			0
$741$			5511.35i			0.0100374i
$742$	−133331.	+	136080.i	−0.242171	+	0.247165i
$743$	−97803.2			−0.177164			−0.0885820	−	0.996069i	$-0.528234\pi$
$743$	−97803.2			−0.177164			−0.0885820	+	0.996069i	$0.528234\pi$
$744$	335400.			0.605923
$745$		0			0
$746$	251196.			0.451372
$747$		−	111440.i		−	0.199710i
$748$			431650.i			0.771487i
$749$	−434448.	+	443407.i	−0.774416	+	0.790385i
$750$		0			0
$751$	246977.			0.437902			0.218951	−	0.975736i	$-0.429737\pi$
$751$	246977.			0.437902			0.218951	+	0.975736i	$0.429737\pi$
$752$		−	8780.00i		−	0.0155260i
$753$	−252052.			−0.444530
$754$			2339.26i			0.00411468i
$755$		0			0
$756$	−239750.	−	234906.i	−0.419484	−	0.411008i
$757$	−1.05636e6			−1.84340			−0.921699	−	0.387906i	$-0.873198\pi$
$757$	−1.05636e6			−1.84340			−0.921699	+	0.387906i	$0.873198\pi$
$758$	−423649.			−0.737340
$759$			311747.i			0.541151i
$760$		0			0
$761$			406836.i			0.702506i	0.936281	+	0.351253i	$0.114244\pi$
$761$			406836.i			0.702506i	−0.936281	+	0.351253i	$0.885756\pi$
$762$			292320.i			0.503441i
$763$	422179.	−	430885.i	0.725184	−	0.740137i
$764$	142630.			0.244357
$765$		0			0
$766$		−	352849.i		−	0.601356i
$767$	18126.2			0.0308118
$768$			324400.i			0.549995i
$769$		−	592238.i		−	1.00148i	−0.865597	−	0.500741i	$-0.833061\pi$
$769$		−	592238.i		−	1.00148i	0.865597	−	0.500741i	$-0.166939\pi$
$770$		0			0
$771$	16850.0			0.0283460
$772$	320050.			0.537012
$773$			401165.i			0.671373i	0.941974	+	0.335687i	$0.108968\pi$
$773$			401165.i			0.671373i	−0.941974	+	0.335687i	$0.891032\pi$
$774$	−51744.0			−0.0863730
$775$		0			0
$776$			588147.i			0.976703i
$777$	−285488.	−	279720.i	−0.472874	−	0.463320i
$778$	−364898.			−0.602854
$779$	642600.			1.05893
$780$		0			0
$781$	396406.			0.649887
$782$		−	832260.i		−	1.36096i
$783$			130835.i			0.213403i
$784$	−196.000	−	9602.00i	−0.000318878	−	0.0156217i
$785$		0			0
$786$	82500.0			0.133539
$787$			357565.i			0.577305i	0.957434	+	0.288653i	$0.0932073\pi$
$787$			357565.i			0.577305i	−0.957434	+	0.288653i	$0.906793\pi$
$788$	33949.9			0.0546747
$789$		−	296927.i		−	0.476975i
$790$		0			0
$791$	−107016.	+	109223.i	−0.171039	+	0.174566i
$792$	317415.			0.506030
$793$	9675.48			0.0153860
$794$			629335.i			0.998254i
$795$		0			0
$796$			194000.i			0.306178i
$797$		−	1.18188e6i		−	1.86062i	−0.366769	−	0.930312i	$-0.619536\pi$
$797$		−	1.18188e6i		−	1.86062i	0.366769	−	0.930312i	$-0.380464\pi$
$798$	92590.7	−	94500.0i	0.145399	−	0.148397i
$799$	−1.06458e6			−1.66756
$800$		0			0
$801$		−	45266.6i		−	0.0705525i
$802$	87302.3			0.135730
$803$		−	769850.i		−	1.19392i
$804$		−	102389.i		−	0.158394i
$805$		0			0
$806$	12900.0			0.0198573
$807$	−385060.			−0.591264
$808$			307320.i			0.470726i
$809$	272449.			0.416283			0.208141	−	0.978099i	$-0.433259\pi$
$809$	272449.			0.416283			0.208141	+	0.978099i	$0.433259\pi$
$810$		0			0
$811$			1.22117e6i			1.85667i	0.371749	+	0.928333i	$0.378758\pi$
$811$			1.22117e6i			1.85667i	−0.371749	+	0.928333i	$0.621242\pi$
$812$	−65499.4	+	66850.0i	−0.0993402	+	0.101389i
$813$	−716108.			−1.08342
$814$	355644.			0.536743
$815$		0			0
$816$	−9700.00			−0.0145677
$817$			83160.0i			0.124586i
$818$		−	371640.i		−	0.555413i
$819$	−9800.00	−	9602.00i	−0.0146103	−	0.0143151i
$820$		0			0
$821$	−621793.			−0.922485			−0.461243	−	0.887274i	$-0.652596\pi$
$821$	−621793.			−0.922485			−0.461243	+	0.887274i	$0.652596\pi$
$822$		−	282540.i		−	0.418154i
$823$	−117394.			−0.173319			−0.0866597	−	0.996238i	$-0.527619\pi$
$823$	−117394.			−0.173319			−0.0866597	+	0.996238i	$0.527619\pi$
$824$			300283.i			0.442259i
$825$		0			0
$826$	−310800.	−	304521.i	−0.455534	−	0.446330i
$827$	199790.			0.292121			0.146061	−	0.989276i	$-0.453341\pi$
$827$	199790.			0.292121			0.146061	+	0.989276i	$0.453341\pi$
$828$	392310.			0.572228
$829$		−	197894.i		−	0.287955i	−0.989581	−	0.143977i	$-0.954011\pi$
$829$		−	197894.i		−	0.287955i	0.989581	−	0.143977i	$-0.0459892\pi$
$830$		0			0
$831$		−	509641.i		−	0.738010i
$832$			12280.0i			0.0177399i
$833$	−1.16424e6	+	23765.0i	−1.67785	+	0.0342490i
$834$	361200.			0.519297
$835$		0			0
$836$		−	196204.i		−	0.280734i
$837$	721497.			1.02987
$838$			369600.i			0.526313i
$839$		−	826972.i		−	1.17481i	−0.809294	−	0.587404i	$-0.800150\pi$
$839$		−	826972.i		−	1.17481i	0.809294	−	0.587404i	$-0.199850\pi$
$840$		0			0
$841$	−670800.			−0.948421
$842$	11466.1			0.0161730
$843$			237605.i			0.334349i
$844$	−528170.			−0.741462
$845$		0			0
$846$			301091.i			0.420685i
$847$	230448.	−	235200.i	0.321223	−	0.327846i
$848$	−6349.08			−0.00882915
$849$	215575.			0.299077
$850$		0			0
$851$	1.14286e6			1.57809
$852$			222700.i			0.306790i
$853$		−	385450.i		−	0.529749i	−0.964283	−	0.264874i	$-0.914670\pi$
$853$		−	385450.i		−	0.529749i	0.964283	−	0.264874i	$-0.0853305\pi$
$854$	−165900.	−	162548.i	−0.227473	−	0.222878i
$855$		0			0
$856$	806832.			1.10112
$857$		−	356750.i		−	0.485738i	−0.970059	−	0.242869i	$-0.921911\pi$
$857$		−	356750.i		−	0.485738i	0.970059	−	0.242869i	$-0.0780886\pi$
$858$	−5450.11			−0.00740340
$859$			578227.i			0.783631i	0.920044	+	0.391816i	$0.128153\pi$
$859$			578227.i			0.783631i	−0.920044	+	0.391816i	$0.871847\pi$
$860$		0			0
$861$	499800.	−	510106.i	0.674202	−	0.688104i
$862$	213358.			0.287140
$863$	151217.			0.203039			0.101519	−	0.994834i	$-0.467630\pi$
$863$	151217.			0.203039			0.101519	+	0.994834i	$0.467630\pi$
$864$			704718.i			0.944035i
$865$		0			0
$866$			567620.i			0.756871i
$867$			758520.i			1.00909i
$868$	368648.	+	361200.i	0.489297	+	0.479411i
$869$	−494929.			−0.655395
$870$		0			0
$871$		−	10238.9i		−	0.0134963i
$872$	−784047.			−1.03112
$873$			517160.i			0.678573i
$874$			378299.i			0.495236i
$875$		0			0
$876$	432500.			0.563609
$877$	553981.			0.720271			0.360136	−	0.932900i	$-0.382730\pi$
$877$	553981.			0.720271			0.360136	+	0.932900i	$0.382730\pi$
$878$		−	603240.i		−	0.782530i
$879$	810625.			1.04916
$880$		0			0
$881$		−	531882.i		−	0.685273i	−0.939468	−	0.342637i	$-0.888680\pi$
$881$		−	531882.i		−	0.685273i	0.939468	−	0.342637i	$-0.111320\pi$
$882$	6721.40	+	329280.i	0.00864018	+	0.423280i
$883$	606675.			0.778099			0.389049	−	0.921217i	$-0.372804\pi$
$883$	606675.			0.778099			0.389049	+	0.921217i	$0.372804\pi$
$884$	−24250.0			−0.0310318
$885$		0			0
$886$	−856932.			−1.09164
$887$			1.35703e6i			1.72481i	0.506216	+	0.862407i	$0.331044\pi$
$887$			1.35703e6i			1.72481i	−0.506216	+	0.862407i	$0.668956\pi$
$888$			519480.i			0.658784i
$889$	−818496.	+	835374.i	−1.03565	+	1.05701i
$890$		0			0
$891$	98879.0			0.124551
$892$			136450.i			0.171492i
$893$	483897.			0.606806
$894$		−	347166.i		−	0.434373i
$895$		0			0
$896$	−358176.	+	365562.i	−0.446150	+	0.455349i
$897$	−17513.9			−0.0217669
$898$	623912.			0.773697
$899$		−	201177.i		−	0.248919i
$900$		0			0
$901$			769826.i			0.948294i
$902$			635460.i			0.781043i
$903$	66013.7	+	64680.0i	0.0809578	+	0.0793222i
$904$	198744.			0.243196
$905$		0			0
$906$		−	214955.i		−	0.261873i
$907$	452230.			0.549724			0.274862	−	0.961484i	$-0.411368\pi$
$907$	452230.			0.549724			0.274862	+	0.961484i	$0.411368\pi$
$908$		−	744850.i		−	0.903435i
$909$			270228.i			0.327041i
$910$		0			0
$911$	−948106.			−1.14241			−0.571203	−	0.820809i	$-0.693523\pi$
$911$	−948106.			−1.14241			−0.571203	+	0.820809i	$0.693523\pi$
$912$	4409.08			0.00530101
$913$		−	177110.i		−	0.212472i
$914$	645756.			0.772994
$915$		0			0
$916$		−	684632.i		−	0.815956i
$917$	235763.	+	231000.i	0.280374	+	0.274709i
$918$	813782.			0.965656
$919$	−394481.			−0.467084			−0.233542	−	0.972347i	$-0.575032\pi$
$919$	−394481.			−0.467084			−0.233542	+	0.972347i	$0.575032\pi$
$920$		0			0
$921$	169025.			0.199265
$922$			314160.i			0.369563i
$923$			22270.0i			0.0261407i
$924$	−155750.	−	152603.i	−0.182425	−	0.178739i
$925$		0			0
$926$	200508.			0.233835
$927$			264040.i			0.307263i
$928$	196498.			0.228172
$929$		−	139523.i		−	0.161664i	−0.996728	−	0.0808322i	$-0.974242\pi$
$929$		−	139523.i		−	0.161664i	0.996728	−	0.0808322i	$-0.0257578\pi$
$930$		0			0
$931$	529200.	−	10802.2i	0.610549	−	0.0124628i
$932$	−601693.			−0.692696
$933$	252175.			0.289693
$934$		−	500786.i		−	0.574061i
$935$		0			0
$936$			17832.3i			0.0203543i
$937$		−	434285.i		−	0.494647i	−0.968933	−	0.247324i	$-0.920449\pi$
$937$		−	434285.i		−	0.494647i	0.968933	−	0.247324i	$-0.0795511\pi$
$938$	−172013.	+	175560.i	−0.195504	+	0.199535i
$939$	−340775.			−0.386488
$940$		0			0
$941$			539108.i			0.608831i	0.952539	+	0.304415i	$0.0984611\pi$
$941$			539108.i			0.608831i	−0.952539	+	0.304415i	$0.901539\pi$
$942$	315862.			0.355955
$943$			2.04204e6i			2.29636i
$944$		−	14501.0i		−	0.0162725i
$945$		0			0
$946$	−82236.0			−0.0918924
$947$	−167540.			−0.186818			−0.0934091	−	0.995628i	$-0.529776\pi$
$947$	−167540.			−0.186818			−0.0934091	+	0.995628i	$0.529776\pi$
$948$		−	278050.i		−	0.309390i
$949$	43250.0			0.0480235
$950$		0			0
$951$		−	212175.i		−	0.234603i
$952$	1.08108e6	+	1.05924e6i	1.19285	+	1.16875i
$953$	−1.31304e6			−1.44575			−0.722873	−	0.690981i	$-0.757179\pi$
$953$	−1.31304e6			−1.44575			−0.722873	+	0.690981i	$0.757179\pi$
$954$	217728.			0.239231
$955$		0			0
$956$	−753670.			−0.824642
$957$			84995.0i			0.0928046i
$958$		−	194820.i		−	0.212277i
$959$	791112.	−	807425.i	0.860203	−	0.877941i
$960$		0			0
$961$	−185879.			−0.201272
$962$			19980.0i			0.0215896i
$963$	709451.			0.765014
$964$		−	778693.i		−	0.837938i
$965$		0			0
$966$	300300.	+	294233.i	0.321811	+	0.315309i
$967$	338745.			0.362259			0.181130	−	0.983459i	$-0.442025\pi$
$967$	338745.			0.362259			0.181130	+	0.983459i	$0.442025\pi$
$968$	−427975.			−0.456738
$969$		−	534601.i		−	0.569354i
$970$		0			0
$971$		−	1.60718e6i		−	1.70462i	−0.523039	−	0.852309i	$-0.675202\pi$
$971$		−	1.60718e6i		−	1.70462i	0.523039	−	0.852309i	$-0.324798\pi$
$972$			610400.i			0.646074i
$973$	1.03221e6	+	1.01136e6i	1.09030	+	1.06827i
$974$	−404064.			−0.425924
$975$		0			0
$976$		−	7740.39i		−	0.00812574i
$977$	1.40070e6			1.46743			0.733713	−	0.679459i	$-0.237785\pi$
$977$	1.40070e6			1.46743			0.733713	+	0.679459i	$0.237785\pi$
$978$		−	455040.i		−	0.475742i
$979$		−	71941.5i		−	0.0750610i
$980$		0			0
$981$	−689416.			−0.716380
$982$	181730.			0.188453
$983$		−	1.73768e6i		−	1.79831i	−0.437633	−	0.899154i	$-0.644183\pi$
$983$		−	1.73768e6i		−	1.79831i	0.437633	−	0.899154i	$-0.355817\pi$
$984$	−928200.			−0.958631
$985$		0			0
$986$		−	226908.i		−	0.233398i
$987$	376364.	−	384125.i	0.386344	−	0.394310i
$988$	11022.7			0.0112921
$989$	−264264.			−0.270175
$990$		0			0
$991$	−423586.			−0.431315			−0.215657	−	0.976469i	$-0.569189\pi$
$991$	−423586.			−0.431315			−0.215657	+	0.976469i	$0.569189\pi$
$992$		−	1.08360e6i		−	1.10115i
$993$			573530.i			0.581645i
$994$	374136.	−	381851.i	0.378666	−	0.386475i
$995$		0			0
$996$	99500.0			0.100301
$997$			548035.i			0.551338i	0.961253	+	0.275669i	$0.0888994\pi$
$997$			548035.i			0.551338i	−0.961253	+	0.275669i	$0.911101\pi$
$998$	−682249.			−0.684986
$999$			1.11748e6i			1.11972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.d.e.76.1		4
5.2	odd	4		35.5.c.c.34.1	✓	2
5.3	odd	4		35.5.c.d.34.2	yes	2
5.4	even	2	inner	175.5.d.e.76.4		4
7.6	odd	2	inner	175.5.d.e.76.2		4
15.2	even	4		315.5.e.d.244.2		2
15.8	even	4		315.5.e.c.244.1		2
20.3	even	4		560.5.p.d.209.1		2
20.7	even	4		560.5.p.e.209.1		2
35.13	even	4		35.5.c.c.34.2	yes	2
35.27	even	4		35.5.c.d.34.1	yes	2
35.34	odd	2	inner	175.5.d.e.76.3		4
105.62	odd	4		315.5.e.c.244.2		2
105.83	odd	4		315.5.e.d.244.1		2
140.27	odd	4		560.5.p.d.209.2		2
140.83	odd	4		560.5.p.e.209.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.c.c.34.1	✓	2	5.2	odd	4
35.5.c.c.34.2	yes	2	35.13	even	4
35.5.c.d.34.1	yes	2	35.27	even	4
35.5.c.d.34.2	yes	2	5.3	odd	4
175.5.d.e.76.1		4	1.1	even	1	trivial
175.5.d.e.76.2		4	7.6	odd	2	inner
175.5.d.e.76.3		4	35.34	odd	2	inner
175.5.d.e.76.4		4	5.4	even	2	inner
315.5.e.c.244.1		2	15.8	even	4
315.5.e.c.244.2		2	105.62	odd	4
315.5.e.d.244.1		2	105.83	odd	4
315.5.e.d.244.2		2	15.2	even	4
560.5.p.d.209.1		2	20.3	even	4
560.5.p.d.209.2		2	140.27	odd	4
560.5.p.e.209.1		2	20.7	even	4
560.5.p.e.209.2		2	140.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.44949 q^{2} -5.00000i q^{3} -10.0000 q^{4} +12.2474i q^{6} +(-34.2929 + 35.0000i) q^{7} +63.6867 q^{8} +56.0000 q^{9} +O(q^{10})\)	\(q-2.44949 q^{2} -5.00000i q^{3} -10.0000 q^{4} +12.2474i q^{6} +(-34.2929 + 35.0000i) q^{7} +63.6867 q^{8} +56.0000 q^{9} +89.0000 q^{11} +50.0000i q^{12} +5.00000i q^{13} +(84.0000 - 85.7321i) q^{14} +4.00000 q^{16} -485.000i q^{17} -137.171 q^{18} +220.454i q^{19} +(175.000 + 171.464i) q^{21} -218.005 q^{22} -700.554 q^{23} -318.434i q^{24} -12.2474i q^{26} -685.000i q^{27} +(342.929 - 350.000i) q^{28} -191.000 q^{29} +1053.28i q^{31} -1028.79 q^{32} -445.000i q^{33} +1188.00i q^{34} -560.000 q^{36} -1631.36 q^{37} -540.000i q^{38} +25.0000 q^{39} -2914.89i q^{41} +(-428.661 - 420.000i) q^{42} +377.221 q^{43} -890.000 q^{44} +1716.00 q^{46} -2195.00i q^{47} -20.0000i q^{48} +(-49.0000 - 2400.50i) q^{49} -2425.00 q^{51} -50.0000i q^{52} -1587.27 q^{53} +1677.90i q^{54} +(-2184.00 + 2229.04i) q^{56} +1102.27 q^{57} +467.853 q^{58} -3625.24i q^{59} -1935.10i q^{61} -2580.00i q^{62} +(-1920.40 + 1960.00i) q^{63} +2456.00 q^{64} +1090.02i q^{66} -2047.77 q^{67} +4850.00i q^{68} +3502.77i q^{69} +4454.00 q^{71} +3566.46 q^{72} -8650.00i q^{73} +3996.00 q^{74} -2204.54i q^{76} +(-3052.06 + 3115.00i) q^{77} -61.2372 q^{78} -5561.00 q^{79} +1111.00 q^{81} +7140.00i q^{82} -1990.00i q^{83} +(-1750.00 - 1714.64i) q^{84} -924.000 q^{86} +955.000i q^{87} +5668.12 q^{88} -808.332i q^{89} +(-175.000 - 171.464i) q^{91} +7005.54 q^{92} +5266.40 q^{93} +5376.63i q^{94} +5143.93i q^{96} +9235.00i q^{97} +(120.025 + 5880.00i) q^{98} +4984.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 40 q^{4} + 224 q^{9}+O(q^{10}) \) 4 * q - 40 * q^4 + 224 * q^9	\( 4 q - 40 q^{4} + 224 q^{9} + 356 q^{11} + 336 q^{14} + 16 q^{16} + 700 q^{21} - 764 q^{29} - 2240 q^{36} + 100 q^{39} - 3560 q^{44} + 6864 q^{46} - 196 q^{49} - 9700 q^{51} - 8736 q^{56} + 9824 q^{64} + 17816 q^{71} + 15984 q^{74} - 22244 q^{79} + 4444 q^{81} - 7000 q^{84} - 3696 q^{86} - 700 q^{91} + 19936 q^{99}+O(q^{100}) \) 4 * q - 40 * q^4 + 224 * q^9 + 356 * q^11 + 336 * q^14 + 16 * q^16 + 700 * q^21 - 764 * q^29 - 2240 * q^36 + 100 * q^39 - 3560 * q^44 + 6864 * q^46 - 196 * q^49 - 9700 * q^51 - 8736 * q^56 + 9824 * q^64 + 17816 * q^71 + 15984 * q^74 - 22244 * q^79 + 4444 * q^81 - 7000 * q^84 - 3696 * q^86 - 700 * q^91 + 19936 * q^99

Introduction

L-functions

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