LMFDB - Embedded newform 76.7.j.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.1
Character	$\chi$	$=$	76.21
Dual form			76.7.j.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-31.3285 + 37.3358i) q^{3} +(37.0498 - 13.4850i) q^{5} +(-148.463 - 257.146i) q^{7} +(-285.900 - 1621.42i) q^{9} +O(q^{10})$	\(q+(-31.3285 + 37.3358i) q^{3} +(37.0498 - 13.4850i) q^{5} +(-148.463 - 257.146i) q^{7} +(-285.900 - 1621.42i) q^{9} +(-242.144 + 419.405i) q^{11} +(-423.045 - 504.165i) q^{13} +(-657.238 + 1805.75i) q^{15} +(332.340 - 1884.79i) q^{17} +(6811.05 + 809.605i) q^{19} +(14251.9 + 2512.99i) q^{21} +(13274.6 + 4831.54i) q^{23} +(-10778.6 + 9044.32i) q^{25} +(38723.8 + 22357.2i) q^{27} +(18843.2 - 3322.57i) q^{29} +(2078.65 - 1200.11i) q^{31} +(-8072.85 - 22180.0i) q^{33} +(-8968.13 - 7525.15i) q^{35} -78184.4i q^{37} +32076.7 q^{39} +(7742.49 - 9227.15i) q^{41} +(-17391.5 + 6329.98i) q^{43} +(-32457.4 - 56217.9i) q^{45} +(31825.7 + 180493. i) q^{47} +(14742.0 - 25533.8i) q^{49} +(59958.6 + 71455.9i) q^{51} +(91075.1 - 250227. i) q^{53} +(-3315.68 + 18804.2i) q^{55} +(-243607. + 228932. i) q^{57} +(18413.6 + 3246.82i) q^{59} +(210217. + 76512.6i) q^{61} +(-374496. + 314239. i) q^{63} +(-22472.4 - 12974.4i) q^{65} +(320356. - 56487.3i) q^{67} +(-596261. + 344252. i) q^{69} +(-91899.1 - 252491. i) q^{71} +(-532504. - 446824. i) q^{73} -685773. i q^{75} +143798. q^{77} +(329216. - 392344. i) q^{79} +(-920012. + 334857. i) q^{81} +(-337004. - 583709. i) q^{83} +(-13103.3 - 74312.8i) q^{85} +(-466278. + 807617. i) q^{87} +(254809. + 303669. i) q^{89} +(-66837.3 + 183634. i) q^{91} +(-20313.9 + 115206. i) q^{93} +(263265. - 61851.4i) q^{95} +(925946. + 163269. i) q^{97} +(749262. + 272709. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−31.3285	+	37.3358i	−1.16031	+	1.38281i	−0.250331	+	0.968160i	$0.580540\pi$
$3$	−31.3285	+	37.3358i	−1.16031	+	1.38281i	−0.909982	+	0.414647i	$0.863905\pi$
$4$		0			0
$5$	37.0498	−	13.4850i	0.296398	−	0.107880i	−0.189541	−	0.981873i	$-0.560700\pi$
$5$	37.0498	−	13.4850i	0.296398	−	0.107880i	0.485939	+	0.873993i	$0.338478\pi$
$6$		0			0
$7$	−148.463	−	257.146i	−0.432837	−	0.749695i	0.564279	−	0.825584i	$-0.309154\pi$
$7$	−148.463	−	257.146i	−0.432837	−	0.749695i	−0.997116	+	0.0758885i	$0.975821\pi$
$8$		0			0
$9$	−285.900	−	1621.42i	−0.392182	−	2.22417i
$10$		0			0
$11$	−242.144	+	419.405i	−0.181926	+	0.315105i	−0.942536	−	0.334103i	$-0.891567\pi$
$11$	−242.144	+	419.405i	−0.181926	+	0.315105i	0.760610	+	0.649209i	$0.224900\pi$
$12$		0			0
$13$	−423.045	−	504.165i	−0.192556	−	0.229479i	0.661125	−	0.750276i	$-0.270079\pi$
$13$	−423.045	−	504.165i	−0.192556	−	0.229479i	−0.853681	+	0.520797i	$0.825635\pi$
$14$		0			0
$15$	−657.238	+	1805.75i	−0.194737	+	0.535036i
$16$		0			0
$17$	332.340	−	1884.79i	0.0676450	−	0.383634i	−0.932124	−	0.362139i	$-0.882046\pi$
$17$	332.340	−	1884.79i	0.0676450	−	0.383634i	0.999769	−	0.0214946i	$-0.00684248\pi$
$18$		0			0
$19$	6811.05	+	809.605i	0.993009	+	0.118035i
$19$	6811.05	+	809.605i	0.993009	+	0.118035i
$20$		0			0
$21$	14251.9	+	2512.99i	1.53891	+	0.271352i
$22$		0			0
$23$	13274.6	+	4831.54i	1.09103	+	0.397102i	0.824002	−	0.566587i	$-0.191736\pi$
$23$	13274.6	+	4831.54i	1.09103	+	0.397102i	0.267028	+	0.963689i	$0.413959\pi$
$24$		0			0
$25$	−10778.6	+	9044.32i	−0.689831	+	0.578837i
$26$		0			0
$27$	38723.8	+	22357.2i	1.96737	+	1.13586i
$28$		0			0
$29$	18843.2	−	3322.57i	0.772611	−	0.136232i	0.226575	−	0.973994i	$-0.427247\pi$
$29$	18843.2	−	3322.57i	0.772611	−	0.136232i	0.546036	+	0.837762i	$0.316136\pi$
$30$		0			0
$31$	2078.65	−	1200.11i	0.0697745	−	0.0402843i	−0.464707	−	0.885465i	$-0.653840\pi$
$31$	2078.65	−	1200.11i	0.0697745	−	0.0402843i	0.534481	+	0.845180i	$0.320507\pi$
$32$		0			0
$33$	−8072.85	−	22180.0i	−0.224639	−	0.617190i
$34$		0			0
$35$	−8968.13	−	7525.15i	−0.209169	−	0.175514i
$36$		0			0
$37$		−	78184.4i		−	1.54353i	−0.635908	−	0.771765i	$-0.719374\pi$
$37$		−	78184.4i		−	1.54353i	0.635908	−	0.771765i	$-0.280626\pi$
$38$		0			0
$39$	32076.7			0.540750
$40$		0			0
$41$	7742.49	−	9227.15i	0.112339	−	0.133880i	−0.706945	−	0.707269i	$-0.749927\pi$
$41$	7742.49	−	9227.15i	0.112339	−	0.133880i	0.819283	+	0.573389i	$0.194372\pi$
$42$		0			0
$43$	−17391.5	+	6329.98i	−0.218742	+	0.0796154i	−0.449066	−	0.893498i	$-0.648243\pi$
$43$	−17391.5	+	6329.98i	−0.218742	+	0.0796154i	0.230325	+	0.973114i	$0.426021\pi$
$44$		0			0
$45$	−32457.4	−	56217.9i	−0.356186	−	0.616932i
$46$		0			0
$47$	31825.7	+	180493.i	0.306538	+	1.73847i	0.616173	+	0.787611i	$0.288682\pi$
$47$	31825.7	+	180493.i	0.306538	+	1.73847i	−0.309635	+	0.950856i	$0.600207\pi$
$48$		0			0
$49$	14742.0	−	25533.8i	0.125305	−	0.217034i
$50$		0			0
$51$	59958.6	+	71455.9i	0.452003	+	0.538676i
$52$		0			0
$53$	91075.1	−	250227.i	0.611748	−	1.68076i	−0.114580	−	0.993414i	$-0.536552\pi$
$53$	91075.1	−	250227.i	0.611748	−	1.68076i	0.726328	−	0.687349i	$-0.241226\pi$
$54$		0			0
$55$	−3315.68	+	18804.2i	−0.0199290	+	0.113023i
$56$		0			0
$57$	−243607.	+	228932.i	−1.31542	+	1.23618i
$58$		0			0
$59$	18413.6	+	3246.82i	0.0896567	+	0.0158089i	0.218297	−	0.975882i	$-0.429950\pi$
$59$	18413.6	+	3246.82i	0.0896567	+	0.0158089i	−0.128640	+	0.991691i	$0.541061\pi$
$60$		0			0
$61$	210217.	+	76512.6i	0.926142	+	0.337088i	0.760679	−	0.649128i	$-0.224866\pi$
$61$	210217.	+	76512.6i	0.926142	+	0.337088i	0.165462	+	0.986216i	$0.447088\pi$
$62$		0			0
$63$	−374496.	+	314239.i	−1.49770	+	1.25672i
$64$		0			0
$65$	−22472.4	−	12974.4i	−0.0818293	−	0.0472442i
$66$		0			0
$67$	320356.	−	56487.3i	1.06514	−	0.187813i	0.386506	−	0.922287i	$-0.373682\pi$
$67$	320356.	−	56487.3i	1.06514	−	0.187813i	0.678637	+	0.734474i	$0.262571\pi$
$68$		0			0
$69$	−596261.	+	344252.i	−1.81505	+	1.04792i
$70$		0			0
$71$	−91899.1	−	252491.i	−0.256765	−	0.705456i	−0.999362	−	0.0357177i	$-0.988628\pi$
$71$	−91899.1	−	252491.i	−0.256765	−	0.705456i	0.742597	−	0.669739i	$-0.233594\pi$
$72$		0			0
$73$	−532504.	−	446824.i	−1.36885	−	1.14860i	−0.973139	−	0.230220i	$-0.926055\pi$
$73$	−532504.	−	446824.i	−1.36885	−	1.14860i	−0.395706	−	0.918377i	$-0.629500\pi$
$74$		0			0
$75$		−	685773.i		−	1.62554i
$76$		0			0
$77$	143798.			0.314977
$78$		0			0
$79$	329216.	−	392344.i	0.667728	−	0.795767i	−0.320745	−	0.947166i	$-0.603933\pi$
$79$	329216.	−	392344.i	0.667728	−	0.795767i	0.988473	+	0.151399i	$0.0483778\pi$
$80$		0			0
$81$	−920012.	+	334857.i	−1.73117	+	0.630093i
$82$		0			0
$83$	−337004.	−	583709.i	−0.589388	−	1.02085i	−0.994313	−	0.106500i	$-0.966036\pi$
$83$	−337004.	−	583709.i	−0.589388	−	1.02085i	0.404925	−	0.914350i	$-0.367298\pi$
$84$		0			0
$85$	−13103.3	−	74312.8i	−0.0213366	−	0.121006i
$86$		0			0
$87$	−466278.	+	807617.i	−0.708088	+	1.22644i
$88$		0			0
$89$	254809.	+	303669.i	0.361447	+	0.430756i	0.915867	−	0.401481i	$-0.131504\pi$
$89$	254809.	+	303669.i	0.361447	+	0.430756i	−0.554420	+	0.832237i	$0.687060\pi$
$90$		0			0
$91$	−66837.3	+	183634.i	−0.0886941	+	0.243685i
$92$		0			0
$93$	−20313.9	+	115206.i	−0.0252548	+	0.143227i
$94$		0			0
$95$	263265.	−	61851.4i	0.307060	−	0.0721404i
$96$		0			0
$97$	925946.	+	163269.i	1.01454	+	0.178891i	0.656111	−	0.754665i	$-0.272200\pi$
$97$	925946.	+	163269.i	1.01454	+	0.178891i	0.358432	+	0.933556i	$0.383311\pi$
$98$		0			0
$99$	749262.	+	272709.i	0.772197	+	0.281057i
$100$		0			0
$101$	91299.9	−	76609.7i	0.0886148	−	0.0743566i	−0.597404	−	0.801940i	$-0.703801\pi$
$101$	91299.9	−	76609.7i	0.0886148	−	0.0743566i	0.686019	+	0.727584i	$0.259357\pi$
$102$		0			0
$103$	−188214.	−	108666.i	−0.172243	−	0.0994443i	0.411400	−	0.911455i	$-0.365040\pi$
$103$	−188214.	−	108666.i	−0.172243	−	0.0994443i	−0.583643	+	0.812010i	$0.698373\pi$
$104$		0			0
$105$	561915.	−	99080.8i	0.485404	−	0.0855898i
$106$		0			0
$107$	877446.	−	506594.i	0.716258	−	0.413532i	−0.0971161	−	0.995273i	$-0.530962\pi$
$107$	877446.	−	506594.i	0.716258	−	0.413532i	0.813374	+	0.581742i	$0.197628\pi$
$108$		0			0
$109$	281569.	+	773604.i	0.217423	+	0.597364i	0.999672	−	0.0256010i	$-0.00814993\pi$
$109$	281569.	+	773604.i	0.217423	+	0.597364i	−0.782249	+	0.622965i	$0.785928\pi$
$110$		0			0
$111$	2.91908e6	+	2.44940e6i	2.13441	+	1.79098i
$112$		0			0
$113$		−	2.54223e6i		−	1.76189i	−0.473216	−	0.880947i	$-0.656907\pi$
$113$		−	2.54223e6i		−	1.76189i	0.473216	−	0.880947i	$-0.343093\pi$
$114$		0			0
$115$	556973.			0.366219
$116$		0			0
$117$	−696516.	+	830075.i	−0.434884	+	0.518274i
$118$		0			0
$119$	−534007.	+	194363.i	−0.316888	+	0.115338i
$120$		0			0
$121$	768513.	+	1.33110e6i	0.433806	+	0.751373i
$122$		0			0
$123$	101942.	+	578145.i	0.0547823	+	0.310686i
$124$		0			0
$125$	−585409.	+	1.01396e6i	−0.299730	+	0.519147i
$126$		0			0
$127$	−543606.	−	647845.i	−0.265383	−	0.316271i	0.616853	−	0.787078i	$-0.288407\pi$
$127$	−543606.	−	647845.i	−0.265383	−	0.316271i	−0.882236	+	0.470807i	$0.843963\pi$
$128$		0			0
$129$	308513.	−	847634.i	0.143716	−	0.394856i
$130$		0			0
$131$	615006.	−	3.48787e6i	0.273568	−	1.55148i	−0.469906	−	0.882717i	$-0.655712\pi$
$131$	615006.	−	3.48787e6i	0.273568	−	1.55148i	0.743474	−	0.668765i	$-0.233177\pi$
$132$		0			0
$133$	−803003.	−	1.87163e6i	−0.341320	−	0.795545i
$134$		0			0
$135$	1.73619e6	+	306138.i	0.705662	+	0.124427i
$136$		0			0
$137$	−288469.	−	104994.i	−0.112186	−	0.0408322i	0.285317	−	0.958433i	$-0.407901\pi$
$137$	−288469.	−	104994.i	−0.112186	−	0.0408322i	−0.397503	+	0.917601i	$0.630123\pi$
$138$		0			0
$139$	2.55077e6	−	2.14035e6i	0.949788	−	0.796966i	−0.0294742	−	0.999566i	$-0.509383\pi$
$139$	2.55077e6	−	2.14035e6i	0.949788	−	0.796966i	0.979262	+	0.202599i	$0.0649388\pi$
$140$		0			0
$141$	−7.73589e6	−	4.46632e6i	−2.75965	−	1.59328i
$142$		0			0
$143$	313887.	−	55346.8i	0.107341	−	0.0189271i
$144$		0			0
$145$	653332.	−	377201.i	0.214304	−	0.123728i
$146$		0			0
$147$	491483.	+	1.35034e6i	0.154724	+	0.425099i
$148$		0			0
$149$	3.43614e6	+	2.88327e6i	1.03875	+	0.871617i	0.991866	−	0.127283i	$-0.0406257\pi$
$149$	3.43614e6	+	2.88327e6i	1.03875	+	0.871617i	0.0468864	+	0.998900i	$0.485070\pi$
$150$		0			0
$151$			2.00834e6i			0.583320i	0.956522	+	0.291660i	$0.0942076\pi$
$151$			2.00834e6i			0.583320i	−0.956522	+	0.291660i	$0.905792\pi$
$152$		0			0
$153$	−3.15106e6			−0.879798
$154$		0			0
$155$	60830.0	−	72494.4i	0.0163351	−	0.0194675i
$156$		0			0
$157$	−5.47202e6	+	1.99165e6i	−1.41400	+	0.514653i	−0.932300	−	0.361685i	$-0.882201\pi$
$157$	−5.47202e6	+	1.99165e6i	−1.41400	+	0.514653i	−0.481697	+	0.876338i	$0.659979\pi$
$158$		0			0
$159$	6.48918e6	+	1.12396e7i	1.61435	+	2.79614i
$160$		0			0
$161$	−728371.	−	4.13080e6i	−0.174532	−	0.989821i
$162$		0			0
$163$	−4.02772e6	+	6.97621e6i	−0.930028	+	1.61086i	−0.146759	+	0.989172i	$0.546884\pi$
$163$	−4.02772e6	+	6.97621e6i	−0.930028	+	1.61086i	−0.783269	+	0.621683i	$0.786449\pi$
$164$		0			0
$165$	−598194.	−	712900.i	−0.133165	−	0.158700i
$166$		0			0
$167$	−1.69694e6	+	4.66229e6i	−0.364348	+	1.00104i	0.613127	+	0.789984i	$0.289911\pi$
$167$	−1.69694e6	+	4.66229e6i	−0.364348	+	1.00104i	−0.977475	+	0.211053i	$0.932311\pi$
$168$		0			0
$169$	762951.	−	4.32691e6i	0.158065	−	0.896433i
$170$		0			0
$171$	−634571.	−	1.12751e7i	−0.126909	−	2.25492i
$172$		0			0
$173$	5.05633e6	+	891567.i	0.976555	+	0.172193i	0.639079	−	0.769141i	$-0.279316\pi$
$173$	5.05633e6	+	891567.i	0.976555	+	0.172193i	0.337476	+	0.941334i	$0.390427\pi$
$174$		0			0
$175$	3.92593e6	+	1.42892e6i	0.732535	+	0.266621i
$176$		0			0
$177$	−698092.	+	585769.i	−0.125891	+	0.105635i
$178$		0			0
$179$	−6.76948e6	−	3.90836e6i	−1.18031	−	0.681453i	−0.224224	−	0.974538i	$-0.571985\pi$
$179$	−6.76948e6	−	3.90836e6i	−1.18031	−	0.681453i	−0.956086	+	0.293085i	$0.905318\pi$
$180$		0			0
$181$	347793.	−	61325.3i	0.0586523	−	0.0103420i	−0.144245	−	0.989542i	$-0.546075\pi$
$181$	347793.	−	61325.3i	0.0586523	−	0.0103420i	0.202897	+	0.979200i	$0.434964\pi$
$182$		0			0
$183$	−9.44242e6	+	5.45158e6i	−1.54074	+	0.889548i
$184$		0			0
$185$	−1.05432e6	−	2.89671e6i	−0.166516	−	0.457499i
$186$		0			0
$187$	710019.	+	595776.i	0.108579	+	0.0911084i
$188$		0			0
$189$		−	1.32769e7i		−	1.96657i
$190$		0			0
$191$	−2.98900e6			−0.428968			−0.214484	−	0.976727i	$-0.568807\pi$
$191$	−2.98900e6			−0.428968			−0.214484	+	0.976727i	$0.568807\pi$
$192$		0			0
$193$	−5.61399e6	+	6.69050e6i	−0.780908	+	0.930650i	−0.998974	−	0.0452839i	$-0.985581\pi$
$193$	−5.61399e6	+	6.69050e6i	−0.780908	+	0.930650i	0.218066	+	0.975934i	$0.430025\pi$
$194$		0			0
$195$	1.18844e6	−	432555.i	0.160277	−	0.0583361i
$196$		0			0
$197$	−5.00190e6	−	8.66355e6i	−0.654239	−	1.13318i	−0.982084	−	0.188444i	$-0.939656\pi$
$197$	−5.00190e6	−	8.66355e6i	−0.654239	−	1.13318i	0.327845	−	0.944732i	$-0.393678\pi$
$198$		0			0
$199$	1.67114e6	+	9.47750e6i	0.212057	+	1.20264i	0.885940	+	0.463799i	$0.153514\pi$
$199$	1.67114e6	+	9.47750e6i	0.212057	+	1.20264i	−0.673883	+	0.738838i	$0.735375\pi$
$200$		0			0
$201$	−7.92725e6	+	1.37304e7i	−0.976190	+	1.69081i
$202$		0			0
$203$	−3.65190e6	−	4.35217e6i	−0.436547	−	0.520257i
$204$		0			0
$205$	162429.	−	446271.i	0.0188540	−	0.0518009i
$206$		0			0
$207$	4.03877e6	−	2.29050e7i	0.455342	−	2.58238i
$208$		0			0
$209$	−1.98881e6	+	2.66055e6i	−0.217848	+	0.291429i
$210$		0			0
$211$	−1.13327e7	−	1.99826e6i	−1.20639	−	0.212719i	−0.465930	−	0.884822i	$-0.654280\pi$
$211$	−1.13327e7	−	1.99826e6i	−1.20639	−	0.212719i	−0.740458	+	0.672103i	$0.765391\pi$
$212$		0			0
$213$	1.23060e7	+	4.47902e6i	1.27344	+	0.463494i
$214$		0			0
$215$	−558990.	+	469049.i	−0.0562456	+	0.0471957i
$216$		0			0
$217$	−617206.	−	356344.i	−0.0604019	−	0.0348731i
$218$		0			0
$219$	3.33651e7	−	5.88316e6i	3.17658	−	0.560117i
$220$		0			0
$221$	−1.09084e6	+	629798.i	−0.101061	+	0.0583478i
$222$		0			0
$223$	−1.09700e6	−	3.01399e6i	−0.0989220	−	0.271786i	0.880354	−	0.474318i	$-0.157305\pi$
$223$	−1.09700e6	−	3.01399e6i	−0.0989220	−	0.271786i	−0.979276	+	0.202532i	$0.935083\pi$
$224$		0			0
$225$	1.77463e7	+	1.48909e7i	1.55797	+	1.30729i
$226$		0			0
$227$		−	1.41155e7i		−	1.20675i	−0.797456	−	0.603377i	$-0.793821\pi$
$227$		−	1.41155e7i		−	1.20675i	0.797456	−	0.603377i	$-0.206179\pi$
$228$		0			0
$229$	1.53287e7			1.27644			0.638219	−	0.769855i	$-0.279671\pi$
$229$	1.53287e7			1.27644			0.638219	+	0.769855i	$0.279671\pi$
$230$		0			0
$231$	−4.50496e6	+	5.36880e6i	−0.365473	+	0.435553i
$232$		0			0
$233$	−1.16397e7	+	4.23650e6i	−0.920181	+	0.334918i	−0.758310	−	0.651894i	$-0.773975\pi$
$233$	−1.16397e7	+	4.23650e6i	−0.920181	+	0.334918i	−0.161870	+	0.986812i	$0.551753\pi$
$234$		0			0
$235$	3.61308e6	+	6.25804e6i	0.278403	+	0.482209i
$236$		0			0
$237$	4.33466e6	+	2.45831e7i	0.325619	+	1.84668i
$238$		0			0
$239$	−5.15357e6	+	8.92625e6i	−0.377498	+	0.653846i	−0.990698	−	0.136082i	$-0.956549\pi$
$239$	−5.15357e6	+	8.92625e6i	−0.377498	+	0.653846i	0.613200	+	0.789928i	$0.289882\pi$
$240$		0			0
$241$	1.50153e7	+	1.78946e7i	1.07271	+	1.27841i	0.958543	+	0.284949i	$0.0919765\pi$
$241$	1.50153e7	+	1.78946e7i	1.07271	+	1.27841i	0.114170	+	0.993461i	$0.463579\pi$
$242$		0			0
$243$	5.17166e6	−	1.42090e7i	0.360422	−	0.990251i
$244$		0			0
$245$	201862.	−	1.14482e6i	0.0137264	−	0.0778463i
$246$		0			0
$247$	−2.47320e6	−	3.77639e6i	−0.164123	−	0.250603i
$248$		0			0
$249$	3.23511e7	+	5.70437e6i	2.09551	+	0.369496i
$250$		0			0
$251$	3.58690e6	+	1.30552e6i	0.226828	+	0.0825588i	0.452934	−	0.891544i	$-0.350377\pi$
$251$	3.58690e6	+	1.30552e6i	0.226828	+	0.0825588i	−0.226106	+	0.974103i	$0.572599\pi$
$252$		0			0
$253$	−5.24073e6	+	4.39749e6i	−0.323616	+	0.271546i
$254$		0			0
$255$	3.18504e6	+	1.83888e6i	0.192085	+	0.110900i
$256$		0			0
$257$	1.73607e7	−	3.06117e6i	1.02275	−	0.180338i	0.362972	−	0.931800i	$-0.381762\pi$
$257$	1.73607e7	−	3.06117e6i	1.02275	−	0.180338i	0.659776	+	0.751462i	$0.270651\pi$
$258$		0			0
$259$	−2.01048e7	+	1.16075e7i	−1.15718	+	0.668097i
$260$		0			0
$261$	−1.07746e7	−	2.96029e7i	−0.606008	−	1.66499i
$262$		0			0
$263$	−1.79371e7	−	1.50510e7i	−0.986018	−	0.827367i	−0.00103122	−	0.999999i	$-0.500328\pi$
$263$	−1.79371e7	−	1.50510e7i	−0.986018	−	0.827367i	−0.984986	+	0.172633i	$0.944773\pi$
$264$		0			0
$265$		−	1.04990e7i		−	0.564170i
$266$		0			0
$267$	−1.93205e7			−1.01504
$268$		0			0
$269$	1.92310e7	−	2.29186e7i	0.987973	−	1.17742i	0.00383938	−	0.999993i	$-0.498778\pi$
$269$	1.92310e7	−	2.29186e7i	0.987973	−	1.17742i	0.984134	−	0.177428i	$-0.0567777\pi$
$270$		0			0
$271$	6.83558e6	−	2.48795e6i	0.343453	−	0.125007i	−0.164534	−	0.986371i	$-0.552612\pi$
$271$	6.83558e6	−	2.48795e6i	0.343453	−	0.125007i	0.507987	+	0.861365i	$0.330390\pi$
$272$		0			0
$273$	−4.76221e6	−	8.24839e6i	−0.234056	−	0.405398i
$274$		0			0
$275$	−1.18327e6	−	6.71063e6i	−0.0568963	−	0.322675i
$276$		0			0
$277$	−1.49464e7	+	2.58879e7i	−0.703229	+	1.21803i	0.264098	+	0.964496i	$0.414926\pi$
$277$	−1.49464e7	+	2.58879e7i	−0.703229	+	1.21803i	−0.967327	+	0.253532i	$0.918408\pi$
$278$		0			0
$279$	−2.54017e6	−	3.02726e6i	−0.116964	−	0.139392i
$280$		0			0
$281$	7.82841e6	−	2.15084e7i	0.352821	−	0.969368i	−0.628638	−	0.777698i	$-0.716387\pi$
$281$	7.82841e6	−	2.15084e7i	0.352821	−	0.969368i	0.981459	−	0.191670i	$-0.0613904\pi$
$282$		0			0
$283$	1.08510e6	−	6.15389e6i	0.0478750	−	0.271513i	−0.951468	−	0.307747i	$-0.900425\pi$
$283$	1.08510e6	−	6.15389e6i	0.0478750	−	0.271513i	0.999343	+	0.0362340i	$0.0115362\pi$
$284$		0			0
$285$	−5.93843e6	+	1.17669e7i	−0.256529	+	0.508310i
$286$		0			0
$287$	−3.52219e6	−	621058.i	−0.148994	−	0.0262716i
$288$		0			0
$289$	1.92399e7	+	7.00275e6i	0.797093	+	0.290118i
$290$		0			0
$291$	−3.51043e7	+	2.94560e7i	−1.42456	+	1.19535i
$292$		0			0
$293$	−3.61623e7	−	2.08783e7i	−1.43765	−	0.830028i	−0.439965	−	0.898015i	$-0.645009\pi$
$293$	−3.61623e7	−	2.08783e7i	−1.43765	−	0.830028i	−0.997686	+	0.0679867i	$0.978342\pi$
$294$		0			0
$295$	726003.	−	128014.i	0.0282795	−	0.00498645i
$296$		0			0
$297$	−1.87534e7	+	1.08273e7i	−0.715833	+	0.413286i
$298$		0			0
$299$	−3.17984e6	−	8.73653e6i	−0.118957	−	0.326833i
$300$		0			0
$301$	4.20972e6	+	3.53237e6i	0.154367	+	0.129529i
$302$		0			0
$303$			5.80882e6i			0.208814i
$304$		0			0
$305$	8.82024e6			0.310872
$306$		0			0
$307$	−8.89427e6	+	1.05998e7i	−0.307394	+	0.366338i	−0.897520	−	0.440973i	$-0.854633\pi$
$307$	−8.89427e6	+	1.05998e7i	−0.307394	+	0.366338i	0.590126	+	0.807311i	$0.299078\pi$
$308$		0			0
$309$	9.95358e6	−	3.62281e6i	0.337368	−	0.122792i
$310$		0			0
$311$	−199423.	−	345411.i	−0.00662971	−	0.0114830i	0.862692	−	0.505731i	$-0.168777\pi$
$311$	−199423.	−	345411.i	−0.00662971	−	0.0114830i	−0.869321	+	0.494248i	$0.835444\pi$
$312$		0			0
$313$	−5.99701e6	−	3.40107e7i	−0.195570	−	1.10913i	−0.911605	−	0.411067i	$-0.865156\pi$
$313$	−5.99701e6	−	3.40107e7i	−0.195570	−	1.10913i	0.716035	−	0.698064i	$-0.245955\pi$
$314$		0			0
$315$	−9.63746e6	+	1.66926e7i	−0.308341	+	0.534062i
$316$		0			0
$317$	1.08407e7	+	1.29195e7i	0.340314	+	0.405571i	0.908874	−	0.417071i	$-0.136943\pi$
$317$	1.08407e7	+	1.29195e7i	0.340314	+	0.405571i	−0.568559	+	0.822642i	$0.692499\pi$
$318$		0			0
$319$	−3.16927e6	+	8.70748e6i	−0.0976307	+	0.268238i
$320$		0			0
$321$	−8.57495e6	+	4.86310e7i	−0.259249	+	1.47027i
$322$		0			0
$323$	3.78953e6	−	1.25684e7i	0.112455	−	0.372968i
$324$		0			0
$325$	9.11966e6	+	1.60804e6i	0.265662	+	0.0468433i
$326$		0			0
$327$	−3.77043e7	−	1.37232e7i	−1.07832	−	0.392476i
$328$		0			0
$329$	4.16880e7	−	3.49803e7i	1.17064	−	0.982283i
$330$		0			0
$331$	2.65634e7	+	1.53364e7i	0.732487	+	0.422902i	0.819331	−	0.573320i	$-0.194345\pi$
$331$	2.65634e7	+	1.53364e7i	0.732487	+	0.422902i	−0.0868442	+	0.996222i	$0.527678\pi$
$332$		0			0
$333$	−1.26770e8	+	2.23530e7i	−3.43308	+	0.605344i
$334$		0			0
$335$	1.11074e7	−	6.41284e6i	0.295445	−	0.170575i
$336$		0			0
$337$	5.72206e6	+	1.57212e7i	0.149507	+	0.410768i	0.991727	−	0.128367i	$-0.0409735\pi$
$337$	5.72206e6	+	1.57212e7i	0.149507	+	0.410768i	−0.842219	+	0.539135i	$0.818751\pi$
$338$		0			0
$339$	9.49162e7	+	7.96442e7i	2.43636	+	2.04435i
$340$		0			0
$341$			1.16240e6i			0.0293151i
$342$		0			0
$343$	−4.36876e7			−1.08262
$344$		0			0
$345$	−1.74491e7	+	2.07950e7i	−0.424928	+	0.506410i
$346$		0			0
$347$	2.45510e7	−	8.93584e6i	0.587599	−	0.213869i	−0.0310739	−	0.999517i	$-0.509893\pi$
$347$	2.45510e7	−	8.93584e6i	0.587599	−	0.213869i	0.618673	+	0.785648i	$0.287670\pi$
$348$		0			0
$349$	−1.62613e7	−	2.81654e7i	−0.382541	−	0.662581i	0.608883	−	0.793260i	$-0.291618\pi$
$349$	−1.62613e7	−	2.81654e7i	−0.382541	−	0.662581i	−0.991425	+	0.130679i	$0.958284\pi$
$350$		0			0
$351$	−5.11018e6	−	2.89813e7i	−0.118172	−	0.670187i
$352$		0			0
$353$	2.53382e7	−	4.38871e7i	0.576039	−	0.997729i	−0.419889	−	0.907576i	$-0.637931\pi$
$353$	2.53382e7	−	4.38871e7i	0.576039	−	0.997729i	0.995928	−	0.0901536i	$-0.0287358\pi$
$354$		0			0
$355$	−6.80968e6	−	8.11546e6i	−0.152209	−	0.181396i
$356$		0			0
$357$	9.47292e6	−	2.60266e7i	0.208199	−	0.572023i
$358$		0			0
$359$	6.37275e6	−	3.61417e7i	0.137735	−	0.781133i	−0.835181	−	0.549975i	$-0.814637\pi$
$359$	6.37275e6	−	3.61417e7i	0.137735	−	0.781133i	0.972916	−	0.231158i	$-0.0742515\pi$
$360$		0			0
$361$	4.57350e7	+	1.10285e7i	0.972135	+	0.234421i
$362$		0			0
$363$	−7.37742e7	−	1.30084e7i	−1.54236	−	0.271959i
$364$		0			0
$365$	−2.57546e7	−	9.37390e6i	−0.529634	−	0.192771i
$366$		0			0
$367$	1.12674e7	−	9.45447e6i	0.227942	−	0.191266i	−0.521662	−	0.853152i	$-0.674688\pi$
$367$	1.12674e7	−	9.45447e6i	0.227942	−	0.191266i	0.749605	+	0.661886i	$0.230244\pi$
$368$		0			0
$369$	−1.71747e7	−	9.91581e6i	−0.341830	−	0.197355i
$370$		0			0
$371$	−7.78660e7	+	1.37299e7i	−1.52485	+	0.268872i
$372$		0			0
$373$	7.79023e7	−	4.49769e7i	1.50115	−	0.866689i	0.501150	−	0.865360i	$-0.332910\pi$
$373$	7.79023e7	−	4.49769e7i	1.50115	−	0.866689i	0.999999	−	0.00132863i	$-0.000422915\pi$
$374$		0			0
$375$	−1.95170e7	−	5.36225e7i	−0.370100	−	1.01684i
$376$		0			0
$377$	−9.64664e6	−	8.09449e6i	−0.180033	−	0.151066i
$378$		0			0
$379$			9.20053e7i			1.69003i	0.534741	+	0.845016i	$0.320409\pi$
$379$			9.20053e7i			1.69003i	−0.534741	+	0.845016i	$0.679591\pi$
$380$		0			0
$381$	4.12182e7			0.745270
$382$		0			0
$383$	2.27927e7	−	2.71632e7i	0.405694	−	0.483487i	−0.524053	−	0.851685i	$-0.675581\pi$
$383$	2.27927e7	−	2.71632e7i	0.405694	−	0.483487i	0.929747	+	0.368198i	$0.120025\pi$
$384$		0			0
$385$	5.32767e6	−	1.93911e6i	0.0933587	−	0.0339798i
$386$		0			0
$387$	1.52358e7	+	2.63892e7i	0.262865	+	0.455295i
$388$		0			0
$389$	−1.02493e7	−	5.81268e7i	−0.174119	−	0.987479i	−0.939156	−	0.343492i	$-0.888390\pi$
$389$	−1.02493e7	−	5.81268e7i	−0.174119	−	0.987479i	0.765036	−	0.643987i	$-0.222721\pi$
$390$		0			0
$391$	1.35181e7	−	2.34141e7i	0.226145	−	0.391694i
$392$		0			0
$393$	1.10955e8	+	1.32231e8i	1.82798	+	2.17850i
$394$		0			0
$395$	6.90660e6	−	1.89757e7i	0.112066	−	0.307898i
$396$		0			0
$397$	−2.77126e6	+	1.57166e7i	−0.0442901	+	0.251181i	−0.998912	−	0.0466396i	$-0.985149\pi$
$397$	−2.77126e6	+	1.57166e7i	−0.0442901	+	0.251181i	0.954622	+	0.297821i	$0.0962599\pi$
$398$		0			0
$399$	9.50356e7	+	2.86545e7i	1.49612	+	0.451101i
$400$		0			0
$401$	−4.15766e7	−	7.33108e6i	−0.644787	−	0.113693i	−0.158314	−	0.987389i	$-0.550606\pi$
$401$	−4.15766e7	−	7.33108e6i	−0.644787	−	0.113693i	−0.486473	+	0.873696i	$0.661717\pi$
$402$		0			0
$403$	−1.48442e6	−	540283.i	−0.0226799	−	0.00825479i
$404$		0			0
$405$	−2.95707e7	+	2.48127e7i	−0.445140	+	0.373516i
$406$		0			0
$407$	3.27910e7	+	1.89319e7i	0.486375	+	0.280809i
$408$		0			0
$409$	−6.29540e6	+	1.11005e6i	−0.0920140	+	0.0162245i	−0.219466	−	0.975620i	$-0.570431\pi$
$409$	−6.29540e6	+	1.11005e6i	−0.0920140	+	0.0162245i	0.127452	+	0.991845i	$0.459320\pi$
$410$		0			0
$411$	1.29573e7	−	7.48091e6i	0.186633	−	0.107753i
$412$		0			0
$413$	−1.89884e6	−	5.21701e6i	−0.0269549	−	0.0740579i
$414$		0			0
$415$	−2.03573e7	−	1.70818e7i	−0.284823	−	0.238995i
$416$		0			0
$417$			1.62289e8i			2.23810i
$418$		0			0
$419$	5.69646e7			0.774396			0.387198	−	0.921997i	$-0.373443\pi$
$419$	5.69646e7			0.774396			0.387198	+	0.921997i	$0.373443\pi$
$420$		0			0
$421$	2.76699e7	−	3.29757e7i	0.370818	−	0.441924i	−0.548076	−	0.836429i	$-0.684639\pi$
$421$	2.76699e7	−	3.29757e7i	0.370818	−	0.441924i	0.918894	+	0.394505i	$0.129084\pi$
$422$		0			0
$423$	2.83556e8	−	1.03206e8i	3.74643	−	1.36359i
$424$		0			0
$425$	1.34645e7	+	2.33212e7i	0.175398	+	0.303798i
$426$		0			0
$427$	−1.15345e7	−	6.54155e7i	−0.148155	−	0.840228i
$428$		0			0
$429$	−7.76719e6	+	1.34532e7i	−0.0983766	+	0.170393i
$430$		0			0
$431$	−2.28026e7	−	2.71751e7i	−0.284809	−	0.339422i	0.604605	−	0.796526i	$-0.293331\pi$
$431$	−2.28026e7	−	2.71751e7i	−0.284809	−	0.339422i	−0.889413	+	0.457104i	$0.848887\pi$
$432$		0			0
$433$	−1.18105e7	+	3.24490e7i	−0.145480	+	0.399703i	−0.990935	−	0.134344i	$-0.957107\pi$
$433$	−1.18105e7	+	3.24490e7i	−0.145480	+	0.399703i	0.845455	+	0.534047i	$0.179330\pi$
$434$		0			0
$435$	−6.38476e6	+	3.62098e7i	−0.0775670	+	0.439904i
$436$		0			0
$437$	8.65021e7	+	4.36551e7i	1.03653	+	0.523107i
$438$		0			0
$439$	2.74048e7	+	4.83221e6i	0.323917	+	0.0571153i	0.333242	−	0.942841i	$-0.391857\pi$
$439$	2.74048e7	+	4.83221e6i	0.323917	+	0.0571153i	−0.00932544	+	0.999957i	$0.502968\pi$
$440$		0			0
$441$	−4.56158e7	−	1.66028e7i	−0.531863	−	0.193582i
$442$		0			0
$443$	−1.19328e8	+	1.00128e8i	−1.37256	+	1.15172i	−0.400687	+	0.916215i	$0.631228\pi$
$443$	−1.19328e8	+	1.00128e8i	−1.37256	+	1.15172i	−0.971874	+	0.235501i	$0.924327\pi$
$444$		0			0
$445$	1.35356e7	+	7.81478e6i	0.153602	+	0.0886822i
$446$		0			0
$447$	−2.15298e8	+	3.79629e7i	−2.41056	+	0.425046i
$448$		0			0
$449$	−9.30509e7	+	5.37229e7i	−1.02797	+	0.593500i	−0.916403	−	0.400257i	$-0.868921\pi$
$449$	−9.30509e7	+	5.37229e7i	−1.02797	+	0.593500i	−0.111569	+	0.993757i	$0.535588\pi$
$450$		0			0
$451$	1.99512e6	+	5.48154e6i	0.0217490	+	0.0597548i
$452$		0			0
$453$	−7.49831e7	−	6.29183e7i	−0.806620	−	0.676834i
$454$		0			0
$455$			7.70489e6i			0.0817961i
$456$		0			0
$457$	3.31597e7			0.347426			0.173713	−	0.984796i	$-0.444423\pi$
$457$	3.31597e7			0.347426			0.173713	+	0.984796i	$0.444423\pi$
$458$		0			0
$459$	5.50081e7	−	6.55562e7i	0.568838	−	0.677915i
$460$		0			0
$461$	6.53129e7	−	2.37719e7i	0.666647	−	0.242640i	0.0135436	−	0.999908i	$-0.495689\pi$
$461$	6.53129e7	−	2.37719e7i	0.666647	−	0.242640i	0.653104	+	0.757269i	$0.273467\pi$
$462$		0			0
$463$	2.49634e6	+	4.32380e6i	0.0251514	+	0.0435634i	0.878327	−	0.478060i	$-0.158660\pi$
$463$	2.49634e6	+	4.32380e6i	0.0251514	+	0.0435634i	−0.853176	+	0.521624i	$0.825327\pi$
$464$		0			0
$465$	800926.	+	4.54228e6i	0.00796587	+	0.0451767i
$466$		0			0
$467$	1.73978e7	−	3.01338e7i	0.170822	−	0.295872i	−0.767886	−	0.640587i	$-0.778691\pi$
$467$	1.73978e7	−	3.01338e7i	0.170822	−	0.295872i	0.938707	+	0.344715i	$0.112024\pi$
$468$		0			0
$469$	−6.20864e7	−	7.39917e7i	−0.601836	−	0.717240i
$470$		0			0
$471$	9.70700e7	−	2.66698e8i	0.929014	−	2.55244i
$472$		0			0
$473$	1.55641e6	−	8.82685e6i	0.0147076	−	0.0834108i
$474$		0			0
$475$	−8.07360e7	+	5.28749e7i	−0.753332	+	0.493366i
$476$		0			0
$477$	−4.31762e8	−	7.61313e7i	−3.97822	−	0.701468i
$478$		0			0
$479$	−8.88966e7	−	3.23557e7i	−0.808870	−	0.294405i	−0.0957129	−	0.995409i	$-0.530513\pi$
$479$	−8.88966e7	−	3.23557e7i	−0.808870	−	0.294405i	−0.713157	+	0.701004i	$0.752735\pi$
$480$		0			0
$481$	−3.94179e7	+	3.30755e7i	−0.354208	+	0.297215i
$482$		0			0
$483$	1.77045e8	+	1.02217e8i	1.57124	+	0.907158i
$484$		0			0
$485$	3.65078e7	−	6.43730e6i	0.320007	−	0.0564259i
$486$		0			0
$487$	−1.27625e8	+	7.36844e7i	−1.10497	+	0.637953i	−0.937521	−	0.347929i	$-0.886885\pi$
$487$	−1.27625e8	+	7.36844e7i	−1.10497	+	0.637953i	−0.167445	+	0.985881i	$0.553552\pi$
$488$		0			0
$489$	−1.34280e8	−	3.68932e8i	−1.14838	−	3.15515i
$490$		0			0
$491$	−9.92074e6	−	8.32449e6i	−0.0838108	−	0.0703256i	0.599920	−	0.800060i	$-0.295199\pi$
$491$	−9.92074e6	−	8.32449e6i	−0.0838108	−	0.0703256i	−0.683731	+	0.729735i	$0.739644\pi$
$492$		0			0
$493$		−	3.66198e7i		−	0.305615i
$494$		0			0
$495$	3.14375e7			0.259198
$496$		0			0
$497$	−5.12832e7	+	6.11170e7i	−0.417740	+	0.497843i
$498$		0			0
$499$	5.82069e7	−	2.11856e7i	0.468461	−	0.170506i	−0.0969943	−	0.995285i	$-0.530923\pi$
$499$	5.82069e7	−	2.11856e7i	0.468461	−	0.170506i	0.565455	+	0.824779i	$0.308701\pi$
$500$		0			0
$501$	−1.20908e8	−	2.09419e8i	−0.961484	−	1.66534i
$502$		0			0
$503$	4.01352e7	+	2.27618e8i	0.315371	+	1.78856i	0.570130	+	0.821554i	$0.306893\pi$
$503$	4.01352e7	+	2.27618e8i	0.315371	+	1.78856i	−0.254759	+	0.967004i	$0.581996\pi$
$504$		0			0
$505$	2.34956e6	−	4.06955e6i	0.0182436	−	0.0315989i
$506$		0			0
$507$	1.37647e8	+	1.64041e8i	1.05619	+	1.25872i
$508$		0			0
$509$	−2.91735e7	+	8.01535e7i	−0.221225	+	0.607812i	−0.999805	−	0.0197338i	$-0.993718\pi$
$509$	−2.91735e7	+	8.01535e7i	−0.221225	+	0.607812i	0.778580	+	0.627545i	$0.215940\pi$
$510$		0			0
$511$	−3.58416e7	+	2.03268e8i	−0.268612	+	1.52337i
$512$		0			0
$513$	2.45649e8	+	1.83627e8i	1.81955	+	1.36014i
$514$		0			0
$515$	−8.43865e6	−	1.48796e6i	−0.0617805	−	0.0108936i
$516$		0			0
$517$	−8.34060e7	−	3.03573e7i	−0.603568	−	0.219681i
$518$		0			0
$519$	−1.91694e8	+	1.60851e8i	−1.37122	+	1.15059i
$520$		0			0
$521$	9.89390e7	+	5.71225e7i	0.699608	+	0.403919i	0.807201	−	0.590276i	$-0.200981\pi$
$521$	9.89390e7	+	5.71225e7i	0.699608	+	0.403919i	−0.107594	+	0.994195i	$0.534315\pi$
$522$		0			0
$523$	−8.37047e6	+	1.47594e6i	−0.0585120	+	0.0103172i	−0.202828	−	0.979214i	$-0.565013\pi$
$523$	−8.37047e6	+	1.47594e6i	−0.0585120	+	0.0103172i	0.144316	+	0.989532i	$0.453902\pi$
$524$		0			0
$525$	−1.76343e8	+	1.01812e8i	−1.21866	+	0.703592i
$526$		0			0
$527$	−1.57114e6	−	4.31667e6i	−0.0107345	−	0.0294929i
$528$		0			0
$529$	3.94681e7	+	3.31176e7i	0.266611	+	0.223713i
$530$		0			0
$531$		−	3.07845e7i		−	0.205612i
$532$		0			0
$533$	−7.92742e6			−0.0523541
$534$		0			0
$535$	2.56778e7	−	3.06016e7i	0.167686	−	0.199840i
$536$		0			0
$537$	3.57999e8	−	1.30301e8i	2.31185	−	0.841444i
$538$		0			0
$539$	7.13935e6	+	1.23657e7i	0.0455924	+	0.0789683i
$540$		0			0
$541$	7.78962e6	+	4.41771e7i	0.0491954	+	0.279001i	0.999475	−	0.0323967i	$-0.0103140\pi$
$541$	7.78962e6	+	4.41771e7i	0.0491954	+	0.279001i	−0.950280	+	0.311398i	$0.899203\pi$
$542$		0			0
$543$	−8.60619e6	+	1.49064e7i	−0.0537541	+	0.0931048i
$544$		0			0
$545$	2.08641e7	+	2.48649e7i	0.128887	+	0.153602i
$546$		0			0
$547$	8.27564e7	−	2.27371e8i	0.505638	−	1.38923i	−0.380058	−	0.924963i	$-0.624096\pi$
$547$	8.27564e7	−	2.27371e8i	0.505638	−	1.38923i	0.885696	−	0.464266i	$-0.153682\pi$
$548$		0			0
$549$	6.39582e7	−	3.62725e8i	0.386526	−	2.19210i
$550$		0			0
$551$	1.31032e8	−	7.37460e6i	0.783290	−	0.0440843i
$552$		0			0
$553$	−1.49766e8	−	2.64078e7i	−0.885600	−	0.156155i
$554$		0			0
$555$	1.41181e8	+	5.13858e7i	0.825845	+	0.300583i
$556$		0			0
$557$	−1.59350e8	+	1.33711e8i	−0.922121	+	0.773751i	−0.974386	−	0.224882i	$-0.927800\pi$
$557$	−1.59350e8	+	1.33711e8i	−0.922121	+	0.773751i	0.0522654	+	0.998633i	$0.483356\pi$
$558$		0			0
$559$	1.05487e7	+	6.09031e6i	0.0603900	+	0.0348662i
$560$		0			0
$561$	−4.44876e7	+	7.84436e6i	−0.251971	+	0.0444293i
$562$		0			0
$563$	1.15625e8	−	6.67559e7i	0.647925	−	0.374080i	−0.139736	−	0.990189i	$-0.544625\pi$
$563$	1.15625e8	−	6.67559e7i	0.647925	−	0.374080i	0.787661	+	0.616109i	$0.211292\pi$
$564$		0			0
$565$	−3.42820e7	−	9.41890e7i	−0.190073	−	0.522222i
$566$		0			0
$567$	2.22695e8	+	1.86863e8i	1.22169	+	1.02512i
$568$		0			0
$569$			1.51450e8i			0.822117i	0.911609	+	0.411058i	$0.134841\pi$
$569$			1.51450e8i			0.822117i	−0.911609	+	0.411058i	$0.865159\pi$
$570$		0			0
$571$	−2.68042e8			−1.43977			−0.719887	−	0.694091i	$-0.755806\pi$
$571$	−2.68042e8			−1.43977			−0.719887	+	0.694091i	$0.755806\pi$
$572$		0			0
$573$	9.36406e7	−	1.11597e8i	0.497738	−	0.593181i
$574$		0			0
$575$	−1.86779e8	+	6.79821e7i	−0.982483	+	0.357595i
$576$		0			0
$577$	1.11743e6	+	1.93544e6i	0.00581690	+	0.0100752i	0.868919	−	0.494954i	$-0.164815\pi$
$577$	1.11743e6	+	1.93544e6i	0.00581690	+	0.0100752i	−0.863102	+	0.505029i	$0.831482\pi$
$578$		0			0
$579$	−7.39173e7	−	4.19206e8i	−0.380812	−	2.15969i
$580$		0			0
$581$	−1.00065e8	+	1.73318e8i	−0.510218	+	0.883723i
$582$		0			0
$583$	8.28932e7	+	9.87883e7i	0.418325	+	0.498540i
$584$		0			0
$585$	−1.46122e7	+	4.01466e7i	−0.0729872	+	0.200531i
$586$		0			0
$587$	−1.84878e7	+	1.04850e8i	−0.0914054	+	0.518386i	0.904384	+	0.426719i	$0.140331\pi$
$587$	−1.84878e7	+	1.04850e8i	−0.0914054	+	0.518386i	−0.995790	+	0.0916670i	$0.970780\pi$
$588$		0			0
$589$	1.51294e7	−	6.49112e6i	0.0740417	−	0.0317668i
$590$		0			0
$591$	4.80162e8	+	8.46656e7i	2.32609	+	0.410152i
$592$		0			0
$593$	2.23843e8	+	8.14722e7i	1.07344	+	0.390702i	0.817463	−	0.575981i	$-0.195380\pi$
$593$	2.23843e8	+	8.14722e7i	1.07344	+	0.390702i	0.255980	+	0.966682i	$0.417602\pi$
$594$		0			0
$595$	−1.71638e7	+	1.44022e7i	−0.0814823	+	0.0683718i
$596$		0			0
$597$	−4.06204e8	−	2.34522e8i	−1.90907	−	1.10220i
$598$		0			0
$599$	−2.22493e8	+	3.92316e7i	−1.03523	+	0.182539i	−0.665342	−	0.746538i	$-0.731714\pi$
$599$	−2.22493e8	+	3.92316e7i	−1.03523	+	0.182539i	−0.369886	+	0.929077i	$0.620603\pi$
$600$		0			0
$601$	1.43439e8	−	8.28145e7i	0.660760	−	0.381490i	−0.131807	−	0.991275i	$-0.542078\pi$
$601$	1.43439e8	−	8.28145e7i	0.660760	−	0.381490i	0.792566	+	0.609786i	$0.208744\pi$
$602$		0			0
$603$	−1.83180e8	−	5.03282e8i	−0.835459	−	2.29541i
$604$		0			0
$605$	4.64232e7	+	3.89537e7i	0.209637	+	0.175907i
$606$		0			0
$607$			7.62124e7i			0.340768i	0.985378	+	0.170384i	$0.0545009\pi$
$607$			7.62124e7i			0.340768i	−0.985378	+	0.170384i	$0.945499\pi$
$608$		0			0
$609$	2.76900e8			1.22595
$610$		0			0
$611$	7.75344e7	−	9.24019e7i	0.339915	−	0.405095i
$612$		0			0
$613$	2.89383e8	−	1.05327e8i	1.25629	−	0.457254i	0.373770	−	0.927521i	$-0.378065\pi$
$613$	2.89383e8	−	1.05327e8i	1.25629	−	0.457254i	0.882524	+	0.470268i	$0.155843\pi$
$614$		0			0
$615$	1.15732e7	+	2.00454e7i	0.0497541	+	0.0861767i
$616$		0			0
$617$	−983517.	−	5.57780e6i	−0.00418723	−	0.0237469i	0.982643	−	0.185509i	$-0.0593934\pi$
$617$	−983517.	−	5.57780e6i	−0.00418723	−	0.0237469i	−0.986830	+	0.161762i	$0.948282\pi$
$618$		0			0
$619$	−4.24041e7	+	7.34461e7i	−0.178787	+	0.309668i	−0.941465	−	0.337110i	$-0.890551\pi$
$619$	−4.24041e7	+	7.34461e7i	−0.178787	+	0.309668i	0.762678	+	0.646778i	$0.223884\pi$
$620$		0			0
$621$	4.06021e8	+	4.83877e8i	1.69541	+	2.02051i
$622$		0			0
$623$	4.02575e7	−	1.10607e8i	0.166488	−	0.457422i
$624$		0			0
$625$	3.01607e7	−	1.71050e8i	0.123538	−	0.700620i
$626$		0			0
$627$	−3.70275e7	−	1.57605e8i	−0.150218	−	0.639391i
$628$		0			0
$629$	−1.47362e8	−	2.59838e7i	−0.592151	−	0.104412i
$630$		0			0
$631$	−2.30870e8	−	8.40299e7i	−0.918924	−	0.334461i	−0.161114	−	0.986936i	$-0.551509\pi$
$631$	−2.30870e8	−	8.40299e7i	−0.918924	−	0.334461i	−0.757810	+	0.652475i	$0.773731\pi$
$632$		0			0
$633$	4.29644e8	−	3.60514e8i	1.69394	−	1.42138i
$634$		0			0
$635$	−2.88767e7	−	1.66720e7i	−0.112778	−	0.0651126i
$636$		0			0
$637$	−1.91098e7	+	3.36957e6i	−0.0739328	+	0.0130363i
$638$		0			0
$639$	−3.83120e8	+	2.21194e8i	−1.46836	+	0.847757i
$640$		0			0
$641$	1.58495e8	+	4.35463e8i	0.601787	+	1.65340i	0.747651	+	0.664091i	$0.231181\pi$
$641$	1.58495e8	+	4.35463e8i	0.601787	+	1.65340i	−0.145864	+	0.989305i	$0.546596\pi$
$642$		0			0
$643$	4.05342e8	+	3.40122e8i	1.52471	+	1.27939i	0.825353	+	0.564616i	$0.190976\pi$
$643$	4.05342e8	+	3.40122e8i	1.52471	+	1.27939i	0.699360	+	0.714770i	$0.253469\pi$
$644$		0			0
$645$		−	3.55649e7i		−	0.132539i
$646$		0			0
$647$	1.61848e8			0.597576			0.298788	−	0.954319i	$-0.403418\pi$
$647$	1.61848e8			0.597576			0.298788	+	0.954319i	$0.403418\pi$
$648$		0			0
$649$	−5.82047e6	+	6.93657e6i	−0.0212924	+	0.0253753i
$650$		0			0
$651$	3.26405e7	−	1.18802e7i	0.118308	−	0.0430605i
$652$		0			0
$653$	1.90607e8	+	3.30142e8i	0.684542	+	1.18566i	0.973581	+	0.228344i	$0.0733310\pi$
$653$	1.90607e8	+	3.30142e8i	0.684542	+	1.18566i	−0.289039	+	0.957317i	$0.593336\pi$
$654$		0			0
$655$	−2.42482e7	−	1.37518e8i	−0.0862889	−	0.489369i
$656$		0			0
$657$	−5.72247e8	+	9.91161e8i	−2.01784	+	3.49501i
$658$		0			0
$659$	−8.27563e7	−	9.86251e7i	−0.289164	−	0.344613i	0.601832	−	0.798622i	$-0.294438\pi$
$659$	−8.27563e7	−	9.86251e7i	−0.289164	−	0.344613i	−0.890997	+	0.454010i	$0.849993\pi$
$660$		0			0
$661$	6.16305e7	−	1.69328e8i	0.213398	−	0.586308i	−0.786096	−	0.618105i	$-0.787901\pi$
$661$	6.16305e7	−	1.69328e8i	0.213398	−	0.586308i	0.999494	+	0.0317971i	$0.0101230\pi$
$662$		0			0
$663$	1.06604e7	−	6.04581e7i	0.0365791	−	0.207450i
$664$		0			0
$665$	−5.49900e7	−	5.85149e7i	−0.186990	−	0.198976i
$666$		0			0
$667$	2.66188e8	+	4.69362e7i	0.897040	+	0.158172i
$668$		0			0
$669$	1.46897e8	+	5.34662e7i	0.490608	+	0.178567i
$670$		0			0
$671$	−8.29924e7	+	6.96389e7i	−0.274708	+	0.230507i
$672$		0			0
$673$	−3.90836e8	−	2.25649e8i	−1.28218	−	0.740267i	−0.304934	−	0.952373i	$-0.598634\pi$
$673$	−3.90836e8	−	2.25649e8i	−1.28218	−	0.740267i	−0.977247	+	0.212106i	$0.931968\pi$
$674$		0			0
$675$	−6.19594e8	+	1.09251e8i	−2.01463	+	0.355234i
$676$		0			0
$677$	−1.75557e7	+	1.01358e7i	−0.0565787	+	0.0326658i	−0.528023	−	0.849230i	$-0.677066\pi$
$677$	−1.75557e7	+	1.01358e7i	−0.0565787	+	0.0326658i	0.471444	+	0.881896i	$0.343733\pi$
$678$		0			0
$679$	−9.54848e7	−	2.62342e8i	−0.305018	−	0.838029i
$680$		0			0
$681$	5.27014e8	+	4.42217e8i	1.66871	+	1.40021i
$682$		0			0
$683$		−	4.87646e8i		−	1.53053i	−0.643713	−	0.765267i	$-0.722607\pi$
$683$		−	4.87646e8i		−	1.53053i	0.643713	−	0.765267i	$-0.277393\pi$
$684$		0			0
$685$	−1.21035e7			−0.0376566
$686$		0			0
$687$	−4.80225e8	+	5.72310e8i	−1.48107	+	1.76507i
$688$		0			0
$689$	−1.64684e8	+	5.99403e7i	−0.503495	+	0.183257i
$690$		0			0
$691$	−5.46020e7	−	9.45734e7i	−0.165491	−	0.286639i	0.771339	−	0.636425i	$-0.219588\pi$
$691$	−5.46020e7	−	9.45734e7i	−0.165491	−	0.286639i	−0.936830	+	0.349786i	$0.886254\pi$
$692$		0			0
$693$	−4.11118e7	−	2.33157e8i	−0.123528	−	0.700564i
$694$		0			0
$695$	6.56427e7	−	1.13697e8i	0.195538	−	0.338682i
$696$		0			0
$697$	−1.48181e7	−	1.76596e7i	−0.0437618	−	0.0521533i
$698$		0			0
$699$	2.06480e8	−	5.67300e8i	0.604570	−	1.66104i
$700$		0			0
$701$	2.65171e7	−	1.50386e8i	0.0769789	−	0.436569i	−0.921822	−	0.387613i	$-0.873300\pi$
$701$	2.65171e7	−	1.50386e8i	0.0769789	−	0.436569i	0.998801	−	0.0489557i	$-0.0155893\pi$
$702$		0			0
$703$	6.32986e7	−	5.32518e8i	0.182191	−	1.53274i
$704$		0			0
$705$	−3.46841e8	−	6.11575e7i	−0.989837	−	0.174535i
$706$		0			0
$707$	−3.32545e7	−	1.21036e7i	−0.0941005	−	0.0342498i
$708$		0			0
$709$	2.99162e8	−	2.51027e8i	0.839399	−	0.704339i	−0.118030	−	0.993010i	$-0.537658\pi$
$709$	2.99162e8	−	2.51027e8i	0.839399	−	0.704339i	0.957428	+	0.288671i	$0.0932133\pi$
$710$		0			0
$711$	−7.30278e8	−	4.21626e8i	−2.03179	−	1.17306i
$712$		0			0
$713$	3.33916e7	−	5.88783e6i	0.0921230	−	0.0162438i
$714$		0			0
$715$	1.08831e7	−	6.28336e6i	0.0297738	−	0.0171899i
$716$		0			0
$717$	−1.71815e8	−	4.72058e8i	−0.466127	−	1.28067i
$718$		0			0
$719$	4.83850e8	+	4.05998e8i	1.30174	+	1.09229i	0.989842	+	0.142173i	$0.0454090\pi$
$719$	4.83850e8	+	4.05998e8i	1.30174	+	1.09229i	0.311897	+	0.950116i	$0.399035\pi$
$720$		0			0
$721$			6.45313e7i			0.172173i
$722$		0			0
$723$	−1.13852e9			−3.01248
$724$		0			0
$725$	−1.73053e8	+	2.06237e8i	−0.454115	+	0.541193i
$726$		0			0
$727$	−4.10281e8	+	1.49330e8i	−1.06777	+	0.388637i	−0.815342	−	0.578979i	$-0.803451\pi$
$727$	−4.10281e8	+	1.49330e8i	−1.06777	+	0.388637i	−0.252428	+	0.967616i	$0.581229\pi$
$728$		0			0
$729$	1.16189e7	+	2.01245e7i	0.0299904	+	0.0519450i
$730$		0			0
$731$	6.15083e6	+	3.48831e7i	0.0157464	+	0.0893023i
$732$		0			0
$733$	−2.46781e8	+	4.27437e8i	−0.626613	+	1.08533i	0.361614	+	0.932328i	$0.382226\pi$
$733$	−2.46781e8	+	4.27437e8i	−0.626613	+	1.08533i	−0.988227	+	0.152997i	$0.951107\pi$
$734$		0			0
$735$	3.64186e7	+	4.34020e7i	0.0917195	+	0.109307i
$736$		0			0
$737$	−5.38810e7	+	1.48037e8i	−0.134596	+	0.369801i
$738$		0			0
$739$	7.98200e7	−	4.52682e8i	0.197778	−	1.12166i	−0.710628	−	0.703568i	$-0.751589\pi$
$739$	7.98200e7	−	4.52682e8i	0.197778	−	1.12166i	0.908407	−	0.418088i	$-0.137300\pi$
$740$		0			0
$741$	2.18476e8	+	2.59695e7i	0.536970	+	0.0638277i
$742$		0			0
$743$	5.93848e8	+	1.04711e8i	1.44780	+	0.255286i	0.841633	−	0.540050i	$-0.181595\pi$
$743$	5.93848e8	+	1.04711e8i	1.44780	+	0.255286i	0.606168	+	0.795337i	$0.292706\pi$
$744$		0			0
$745$	1.66189e8	+	6.04879e7i	0.401914	+	0.146285i
$746$		0			0
$747$	−8.50089e8	+	7.13309e8i	−2.03940	+	1.71126i
$748$		0			0
$749$	−2.60537e8	−	1.50421e8i	−0.620045	−	0.357983i
$750$		0			0
$751$	3.09537e8	−	5.45798e7i	0.730791	−	0.128858i	0.204142	−	0.978941i	$-0.434559\pi$
$751$	3.09537e8	−	5.45798e7i	0.730791	−	0.128858i	0.526649	+	0.850083i	$0.323448\pi$
$752$		0			0
$753$	−1.61115e8	+	9.30196e7i	−0.377355	+	0.217866i
$754$		0			0
$755$	2.70825e7	+	7.44086e7i	0.0629286	+	0.172895i
$756$		0			0
$757$	−2.55469e8	−	2.14364e8i	−0.588911	−	0.494155i	0.298948	−	0.954269i	$-0.403364\pi$
$757$	−2.55469e8	−	2.14364e8i	−0.588911	−	0.494155i	−0.887860	+	0.460114i	$0.847809\pi$
$758$		0			0
$759$		−	3.33434e8i		−	0.762577i
$760$		0			0
$761$	5.39991e8			1.22527			0.612636	−	0.790365i	$-0.290109\pi$
$761$	5.39991e8			1.22527			0.612636	+	0.790365i	$0.290109\pi$
$762$		0			0
$763$	1.57126e8	−	1.87256e8i	0.353733	−	0.421562i
$764$		0			0
$765$	−1.16746e8	+	4.24921e7i	−0.260770	+	0.0949126i
$766$		0			0
$767$	−6.15285e6	−	1.06570e7i	−0.0136361	−	0.0236184i
$768$		0			0
$769$	−7.39665e6	−	4.19485e7i	−0.0162651	−	0.0922438i	0.975595	−	0.219580i	$-0.0704685\pi$
$769$	−7.39665e6	−	4.19485e7i	−0.0162651	−	0.0922438i	−0.991860	+	0.127336i	$0.959357\pi$
$770$		0			0
$771$	−4.29594e8	+	7.44079e8i	−0.937335	+	1.62351i
$772$		0			0
$773$	3.05370e8	+	3.63926e8i	0.661133	+	0.787907i	0.987548	−	0.157319i	$-0.0502852\pi$
$773$	3.05370e8	+	3.63926e8i	0.661133	+	0.787907i	−0.326415	+	0.945226i	$0.605841\pi$
$774$		0			0
$775$	−1.15508e7	+	3.17355e7i	−0.0248145	+	0.0681774i
$776$		0			0
$777$	1.96476e8	−	1.11427e9i	0.418839	−	2.37536i
$778$		0			0
$779$	6.02049e7	−	5.65782e7i	0.127356	−	0.119684i
$780$		0			0
$781$	1.28149e8	+	2.25961e7i	0.269006	+	0.0474329i
$782$		0			0
$783$	8.03963e8	+	2.92619e8i	1.67475	+	0.609561i
$784$		0			0
$785$	−1.75879e8	+	1.47580e8i	−0.363585	+	0.305084i
$786$		0			0
$787$	5.31342e8	+	3.06770e8i	1.09006	+	0.629346i	0.933592	−	0.358337i	$-0.116656\pi$
$787$	5.31342e8	+	3.06770e8i	1.09006	+	0.629346i	0.156467	+	0.987683i	$0.449990\pi$
$788$		0			0
$789$	1.12388e9	−	1.98171e8i	2.28818	−	0.403468i
$790$		0			0
$791$	−6.53723e8	+	3.77427e8i	−1.32088	+	0.762612i
$792$		0			0
$793$	−5.03560e7	−	1.38352e8i	−0.100979	−	0.277438i
$794$		0			0
$795$	3.91988e8	+	3.28917e8i	0.780139	+	0.654614i
$796$		0			0
$797$		−	3.68440e8i		−	0.727766i	−0.931445	−	0.363883i	$-0.881451\pi$
$797$		−	3.68440e8i		−	0.727766i	0.931445	−	0.363883i	$-0.118549\pi$
$798$		0			0
$799$	3.50769e8			0.687671
$800$		0			0
$801$	4.19526e8	−	4.99972e8i	0.816322	−	0.972855i
$802$		0			0
$803$	3.16343e8	−	1.15139e8i	0.610958	−	0.222371i
$804$		0			0
$805$	−8.26898e7	−	1.43223e8i	−0.158513	−	0.274552i
$806$		0			0
$807$	2.53207e8	+	1.43601e9i	0.481788	+	2.73235i
$808$		0			0
$809$	−2.13340e8	+	3.69516e8i	−0.402928	+	0.697891i	−0.994078	−	0.108670i	$-0.965341\pi$
$809$	−2.13340e8	+	3.69516e8i	−0.402928	+	0.697891i	0.591150	+	0.806561i	$0.298674\pi$
$810$		0			0
$811$	−1.42491e8	−	1.69815e8i	−0.267132	−	0.318356i	0.615758	−	0.787935i	$-0.288850\pi$
$811$	−1.42491e8	−	1.69815e8i	−0.267132	−	0.318356i	−0.882890	+	0.469580i	$0.844406\pi$
$812$		0			0
$813$	−1.21259e8	+	3.33155e8i	−0.225653	+	0.619976i
$814$		0			0
$815$	−5.51517e7	+	3.12781e8i	−0.101879	+	0.577786i
$816$		0			0
$817$	−1.23579e8	+	2.90336e7i	−0.226610	+	0.0532396i
$818$		0			0
$819$	3.16857e8	+	5.58704e7i	0.576782	+	0.101702i
$820$		0			0
$821$	−7.79901e7	−	2.83861e7i	−0.140932	−	0.0512951i	0.270591	−	0.962694i	$-0.412781\pi$
$821$	−7.79901e7	−	2.83861e7i	−0.140932	−	0.0512951i	−0.411523	+	0.911399i	$0.635003\pi$
$822$		0			0
$823$	−2.65109e8	+	2.22453e8i	−0.475581	+	0.399060i	−0.848826	−	0.528673i	$-0.822690\pi$
$823$	−2.65109e8	+	2.22453e8i	−0.475581	+	0.399060i	0.373244	+	0.927733i	$0.378245\pi$
$824$		0			0
$825$	2.87617e8	+	1.66056e8i	0.512215	+	0.295728i
$826$		0			0
$827$	6.93359e8	−	1.22258e8i	1.22586	−	0.216153i	0.477015	−	0.878895i	$-0.341719\pi$
$827$	6.93359e8	−	1.22258e8i	1.22586	−	0.216153i	0.748847	+	0.662743i	$0.230608\pi$
$828$		0			0
$829$	−1.61595e8	+	9.32966e7i	−0.283637	+	0.163758i	−0.635069	−	0.772456i	$-0.719028\pi$
$829$	−1.61595e8	+	9.32966e7i	−0.283637	+	0.163758i	0.351432	+	0.936214i	$0.385695\pi$
$830$		0			0
$831$	−4.98298e8	−	1.36906e9i	−0.868333	−	2.38572i
$832$		0			0
$833$	−4.32267e7	−	3.62715e7i	−0.0747854	−	0.0627524i
$834$		0			0
$835$			1.95620e8i			0.336011i
$836$		0			0
$837$	1.07324e8			0.183030
$838$		0			0
$839$	4.78229e8	−	5.69931e8i	0.809748	−	0.965020i	−0.190112	−	0.981763i	$-0.560885\pi$
$839$	4.78229e8	−	5.69931e8i	0.809748	−	0.965020i	0.999860	+	0.0167420i	$0.00532940\pi$
$840$		0			0
$841$	−2.14924e8	+	7.82259e7i	−0.361324	+	0.131511i
$842$		0			0
$843$	5.57781e8	+	9.66104e8i	0.931066	+	1.61265i
$844$		0			0
$845$	−3.00813e7	−	1.70599e8i	−0.0498570	−	0.282753i
$846$		0			0
$847$	2.28192e8	−	3.95239e8i	0.375534	−	0.650444i
$848$		0			0
$849$	1.95766e8	+	2.33305e8i	0.319900	+	0.381242i
$850$		0			0
$851$	3.77752e8	−	1.03786e9i	0.612940	−	1.68404i
$852$		0			0
$853$	3.99579e7	−	2.26613e8i	0.0643807	−	0.365121i	−0.935548	−	0.353199i	$-0.885094\pi$
$853$	3.99579e7	−	2.26613e8i	0.0643807	−	0.365121i	0.999929	−	0.0119221i	$-0.00379502\pi$
$854$		0			0
$855$	−1.75555e8	−	4.09181e8i	−0.280876	−	0.654662i
$856$		0			0
$857$	−1.05743e9	−	1.86454e8i	−1.68000	−	0.296230i	−0.749362	−	0.662160i	$-0.769640\pi$
$857$	−1.05743e9	−	1.86454e8i	−1.68000	−	0.296230i	−0.930642	+	0.365930i	$0.880751\pi$
$858$		0			0
$859$	−1.18363e8	−	4.30804e7i	−0.186739	−	0.0679674i	0.246958	−	0.969026i	$-0.420569\pi$
$859$	−1.18363e8	−	4.30804e7i	−0.186739	−	0.0679674i	−0.433697	+	0.901059i	$0.642791\pi$
$860$		0			0
$861$	1.33533e8	−	1.12047e8i	0.209208	−	0.175546i
$862$		0			0
$863$	−7.08595e8	−	4.09107e8i	−1.10247	−	0.636509i	−0.165599	−	0.986193i	$-0.552956\pi$
$863$	−7.08595e8	−	4.09107e8i	−1.10247	−	0.636509i	−0.936868	+	0.349684i	$0.886289\pi$
$864$		0			0
$865$	1.99359e8	−	3.51523e7i	0.308025	−	0.0543132i
$866$		0			0
$867$	−8.64210e8	+	4.98952e8i	−1.32606	+	0.765599i
$868$		0			0
$869$	8.48336e7	+	2.33079e8i	0.129273	+	0.355175i
$870$		0			0
$871$	−1.64004e8	−	1.37615e8i	−0.248198	−	0.208263i
$872$		0			0
$873$		−	1.54803e9i		−	2.32668i
$874$		0			0
$875$	3.47647e8			0.518936
$876$		0			0
$877$	−6.71112e8	+	7.99801e8i	−0.994939	+	1.18572i	−0.0123511	+	0.999924i	$0.503932\pi$
$877$	−6.71112e8	+	7.99801e8i	−0.994939	+	1.18572i	−0.982588	+	0.185798i	$0.940513\pi$
$878$		0			0
$879$	1.91242e9	−	6.96064e8i	2.81590	−	1.02490i
$880$		0			0
$881$	−2.07303e8	−	3.59059e8i	−0.303164	−	0.525095i	0.673687	−	0.739017i	$-0.264710\pi$
$881$	−2.07303e8	−	3.59059e8i	−0.303164	−	0.525095i	−0.976851	+	0.213922i	$0.931376\pi$
$882$		0			0
$883$	1.23567e8	+	7.00781e8i	0.179481	+	1.01789i	0.932843	+	0.360283i	$0.117320\pi$
$883$	1.23567e8	+	7.00781e8i	0.179481	+	1.01789i	−0.753362	+	0.657606i	$0.771569\pi$
$884$		0			0
$885$	−1.79651e7	+	3.11164e7i	−0.0259178	+	0.0448910i
$886$		0			0
$887$	−4.28434e8	−	5.10588e8i	−0.613922	−	0.731644i	0.366090	−	0.930579i	$-0.380696\pi$
$887$	−4.28434e8	−	5.10588e8i	−0.613922	−	0.731644i	−0.980013	+	0.198935i	$0.936252\pi$
$888$		0			0
$889$	−8.58849e7	+	2.35967e8i	−0.122240	+	0.335850i
$890$		0			0
$891$	8.23344e7	−	4.66942e8i	0.116399	−	0.660130i
$892$		0			0
$893$	7.06388e7	+	1.25511e9i	0.0991949	+	1.76250i
$894$		0			0
$895$	−3.03512e8	−	5.35173e7i	−0.423357	−	0.0746492i
$896$		0			0
$897$	4.25805e8	+	1.54980e8i	0.589974	+	0.214733i
$898$		0			0
$899$	3.51810e7	−	2.95204e7i	0.0484205	−	0.0406296i
$900$		0			0
$901$	−4.41358e8	−	2.54818e8i	−0.603416	−	0.348382i
$902$		0			0
$903$	−2.63768e8	+	4.65094e7i	−0.358227	+	0.0631652i
$904$		0			0
$905$	1.20587e7	−	6.96208e6i	0.0162687	−	0.00939276i
$906$		0			0
$907$	4.84740e8	+	1.33181e9i	0.649661	+	1.78493i	0.618989	+	0.785400i	$0.287543\pi$
$907$	4.84740e8	+	1.33181e9i	0.649661	+	1.78493i	0.0306727	+	0.999529i	$0.490235\pi$
$908$		0			0
$909$	−1.50319e8	−	1.26133e8i	−0.200135	−	0.167933i
$910$		0			0
$911$		−	7.65924e7i		−	0.101305i	−0.998716	−	0.0506525i	$-0.983870\pi$
$911$		−	7.65924e7i		−	0.101305i	0.998716	−	0.0506525i	$-0.0161301\pi$
$912$		0			0
$913$	3.26414e8			0.428901
$914$		0			0
$915$	−2.76325e8	+	3.29311e8i	−0.360709	+	0.429876i
$916$		0			0
$917$	−9.88196e8	+	3.59674e8i	−1.28155	+	0.466446i
$918$		0			0
$919$	1.04560e7	+	1.81104e7i	0.0134717	+	0.0233336i	0.872683	−	0.488288i	$-0.162378\pi$
$919$	1.04560e7	+	1.81104e7i	0.0134717	+	0.0233336i	−0.859211	+	0.511621i	$0.829045\pi$
$920$		0			0
$921$	−1.17107e8	−	6.64150e8i	−0.149901	−	0.850133i
$922$		0			0
$923$	−8.84195e7	+	1.53147e8i	−0.112446	+	0.194762i
$924$		0			0
$925$	7.07125e8	+	8.42719e8i	0.893452	+	1.06477i
$926$		0			0
$927$	−1.22382e8	+	3.36242e8i	−0.153631	+	0.422098i
$928$		0			0
$929$	−1.56266e8	+	8.86227e8i	−0.194902	+	1.10535i	0.717656	+	0.696398i	$0.245215\pi$
$929$	−1.56266e8	+	8.86227e8i	−0.194902	+	1.10535i	−0.912558	+	0.408947i	$0.865896\pi$
$930$		0			0
$931$	1.21081e8	−	1.61977e8i	0.150046	−	0.200726i
$932$		0			0
$933$	1.91438e7	+	3.37557e6i	0.0235713	+	0.00415626i
$934$		0			0
$935$	3.43401e7	+	1.24988e7i	0.0420113	+	0.0152909i
$936$		0			0
$937$	3.12276e8	−	2.62030e8i	0.379594	−	0.318517i	−0.432949	−	0.901418i	$-0.642527\pi$
$937$	3.12276e8	−	2.62030e8i	0.379594	−	0.318517i	0.812543	+	0.582901i	$0.198083\pi$
$938$		0			0
$939$	1.45770e9	+	8.41601e8i	1.76064	+	1.01650i
$940$		0			0
$941$	−8.62158e7	+	1.52022e7i	−0.103471	+	0.0182447i	−0.225144	−	0.974326i	$-0.572285\pi$
$941$	−8.62158e7	+	1.52022e7i	−0.103471	+	0.0182447i	0.121673	+	0.992570i	$0.461174\pi$
$942$		0			0
$943$	1.47360e8	−	8.50781e7i	0.175729	−	0.101457i
$944$		0			0
$945$	−1.79039e8	−	4.91904e8i	−0.212154	−	0.582888i
$946$		0			0
$947$	−5.83606e8	−	4.89704e8i	−0.687179	−	0.576612i	0.230915	−	0.972974i	$-0.425828\pi$
$947$	−5.83606e8	−	4.89704e8i	−0.687179	−	0.576612i	−0.918094	+	0.396362i	$0.870272\pi$
$948$		0			0
$949$			4.57496e8i			0.535290i
$950$		0			0
$951$	−8.21982e8			−0.955698
$952$		0			0
$953$	5.75248e8	−	6.85554e8i	0.664625	−	0.792069i	−0.323417	−	0.946257i	$-0.604832\pi$
$953$	5.75248e8	−	6.85554e8i	0.664625	−	0.792069i	0.988042	+	0.154187i	$0.0492760\pi$
$954$		0			0
$955$	−1.10742e8	+	4.03066e7i	−0.127145	+	0.0462771i
$956$		0			0
$957$	−2.25813e8	−	3.91119e8i	−0.257640	−	0.446245i
$958$		0			0
$959$	1.58282e7	+	8.97661e7i	0.0179463	+	0.101779i
$960$		0			0
$961$	−4.40871e8	+	7.63612e8i	−0.496754	+	0.860404i
$962$		0			0
$963$	−1.07227e9	−	1.27788e9i	−1.20067	−	1.43090i
$964$		0			0
$965$	−1.17776e8	+	3.23586e8i	−0.131061	+	0.360087i
$966$		0			0
$967$	−7.89459e7	+	4.47724e8i	−0.0873072	+	0.495144i	0.909528	+	0.415643i	$0.136444\pi$
$967$	−7.89459e7	+	4.47724e8i	−0.0873072	+	0.495144i	−0.996835	+	0.0795002i	$0.974668\pi$
$968$		0			0
$969$	3.50530e8	+	5.35233e8i	0.385260	+	0.588263i
$970$		0			0
$971$	−9.39767e8	−	1.65706e8i	−1.02651	−	0.181001i	−0.365054	−	0.930986i	$-0.618950\pi$
$971$	−9.39767e8	−	1.65706e8i	−1.02651	−	0.181001i	−0.661455	+	0.749985i	$0.730061\pi$
$972$		0			0
$973$	−9.29076e8	−	3.38156e8i	−1.00859	−	0.367095i
$974$		0			0
$975$	−3.45743e8	+	2.90112e8i	−0.373026	+	0.313006i
$976$		0			0
$977$	−3.37948e8	−	1.95114e8i	−0.362382	−	0.209221i	0.307743	−	0.951469i	$-0.400426\pi$
$977$	−3.37948e8	−	1.95114e8i	−0.362382	−	0.209221i	−0.670125	+	0.742248i	$0.733760\pi$
$978$		0			0
$979$	−1.89061e8	+	3.33365e7i	−0.201490	+	0.0355281i
$980$		0			0
$981$	1.17384e9	−	6.77716e8i	1.24337	−	0.717862i
$982$		0			0
$983$	−2.97563e8	−	8.17549e8i	−0.313270	−	0.860702i	−0.991991	−	0.126306i	$-0.959688\pi$
$983$	−2.97563e8	−	8.17549e8i	−0.313270	−	0.860702i	0.678721	−	0.734396i	$-0.262534\pi$
$984$		0			0
$985$	−3.02147e8	−	2.53532e8i	−0.316162	−	0.265292i
$986$		0			0
$987$			2.65233e9i			2.75852i
$988$		0			0
$989$	−2.61448e8			−0.270269
$990$		0			0
$991$	−8.96383e8	+	1.06827e9i	−0.921027	+	1.09764i	0.0739223	+	0.997264i	$0.476448\pi$
$991$	−8.96383e8	+	1.06827e9i	−0.921027	+	1.09764i	−0.994950	+	0.100374i	$0.967996\pi$
$992$		0			0
$993$	−1.40479e9	+	5.11301e8i	−1.43471	+	0.522190i
$994$		0			0
$995$	1.89720e8	+	3.28604e8i	0.192594	+	0.333583i
$996$		0			0
$997$	−2.27026e8	−	1.28753e9i	−0.229081	−	1.29918i	−0.854727	−	0.519077i	$-0.826276\pi$
$997$	−2.27026e8	−	1.28753e9i	−0.229081	−	1.29918i	0.625646	−	0.780107i	$-0.284835\pi$
$998$		0			0
$999$	1.74798e9	−	3.02760e9i	1.75324	−	3.03670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.21.1	✓	60
19.10	odd	18	inner	76.7.j.a.29.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.1	✓	60	1.1	even	1	trivial
76.7.j.a.29.1	yes	60	19.10	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-31.3285 + 37.3358i) q^{3} +(37.0498 - 13.4850i) q^{5} +(-148.463 - 257.146i) q^{7} +(-285.900 - 1621.42i) q^{9} +O(q^{10})\)	\(q+(-31.3285 + 37.3358i) q^{3} +(37.0498 - 13.4850i) q^{5} +(-148.463 - 257.146i) q^{7} +(-285.900 - 1621.42i) q^{9} +(-242.144 + 419.405i) q^{11} +(-423.045 - 504.165i) q^{13} +(-657.238 + 1805.75i) q^{15} +(332.340 - 1884.79i) q^{17} +(6811.05 + 809.605i) q^{19} +(14251.9 + 2512.99i) q^{21} +(13274.6 + 4831.54i) q^{23} +(-10778.6 + 9044.32i) q^{25} +(38723.8 + 22357.2i) q^{27} +(18843.2 - 3322.57i) q^{29} +(2078.65 - 1200.11i) q^{31} +(-8072.85 - 22180.0i) q^{33} +(-8968.13 - 7525.15i) q^{35} -78184.4i q^{37} +32076.7 q^{39} +(7742.49 - 9227.15i) q^{41} +(-17391.5 + 6329.98i) q^{43} +(-32457.4 - 56217.9i) q^{45} +(31825.7 + 180493. i) q^{47} +(14742.0 - 25533.8i) q^{49} +(59958.6 + 71455.9i) q^{51} +(91075.1 - 250227. i) q^{53} +(-3315.68 + 18804.2i) q^{55} +(-243607. + 228932. i) q^{57} +(18413.6 + 3246.82i) q^{59} +(210217. + 76512.6i) q^{61} +(-374496. + 314239. i) q^{63} +(-22472.4 - 12974.4i) q^{65} +(320356. - 56487.3i) q^{67} +(-596261. + 344252. i) q^{69} +(-91899.1 - 252491. i) q^{71} +(-532504. - 446824. i) q^{73} -685773. i q^{75} +143798. q^{77} +(329216. - 392344. i) q^{79} +(-920012. + 334857. i) q^{81} +(-337004. - 583709. i) q^{83} +(-13103.3 - 74312.8i) q^{85} +(-466278. + 807617. i) q^{87} +(254809. + 303669. i) q^{89} +(-66837.3 + 183634. i) q^{91} +(-20313.9 + 115206. i) q^{93} +(263265. - 61851.4i) q^{95} +(925946. + 163269. i) q^{97} +(749262. + 272709. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more