LMFDB - Embedded newform 72.7.b.c.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 31 x^{10} - 1286 x^{9} + 7702 x^{8} - 174032 x^{7} + 1952056 x^{6} + \cdots + 767595744 $ x^12 - 2x^11 + 31x^10 - 1286x^9 + 7702x^8 - 174032x^7 + 1952056x^6 - 6345392x^5 + 7695616x^4 - 6850848x^3 - 19274256x^2 - 69390432*x + 767595744
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{11} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.8
Root			$0.630233 - 2.92643i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.c.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.278171 + 7.99516i) q^{2} +(-63.8452 - 4.44805i) q^{4} -111.403i q^{5} +106.838i q^{7} +(53.3228 - 509.216i) q^{8} +O(q^{10})$	\(q+(-0.278171 + 7.99516i) q^{2} +(-63.8452 - 4.44805i) q^{4} -111.403i q^{5} +106.838i q^{7} +(53.3228 - 509.216i) q^{8} +(890.684 + 30.9891i) q^{10} +948.811 q^{11} +2793.04i q^{13} +(-854.185 - 29.7192i) q^{14} +(4056.43 + 567.973i) q^{16} +8802.70 q^{17} -5267.46 q^{19} +(-495.525 + 7112.54i) q^{20} +(-263.932 + 7585.89i) q^{22} +14142.6i q^{23} +3214.40 q^{25} +(-22330.8 - 776.943i) q^{26} +(475.219 - 6821.08i) q^{28} -16132.9i q^{29} -893.982i q^{31} +(-5669.42 + 32273.8i) q^{32} +(-2448.66 + 70379.0i) q^{34} +11902.0 q^{35} +76362.9i q^{37} +(1465.26 - 42114.2i) q^{38} +(-56728.1 - 5940.31i) q^{40} +8443.58 q^{41} +93797.7 q^{43} +(-60577.0 - 4220.35i) q^{44} +(-113073. - 3934.07i) q^{46} +128416. i q^{47} +106235. q^{49} +(-894.153 + 25699.6i) q^{50} +(12423.6 - 178322. i) q^{52} -170026. i q^{53} -105700. i q^{55} +(54403.4 + 5696.88i) q^{56} +(128985. + 4487.72i) q^{58} +365818. q^{59} -364256. i q^{61} +(7147.53 + 248.680i) q^{62} +(-256457. - 54305.6i) q^{64} +311153. q^{65} +4749.56 q^{67} +(-562010. - 39154.8i) q^{68} +(-3310.80 + 95158.6i) q^{70} -369703. i q^{71} -205508. q^{73} +(-610534. - 21242.0i) q^{74} +(336302. + 23429.9i) q^{76} +101369. i q^{77} +928499. i q^{79} +(63273.9 - 451898. i) q^{80} +(-2348.76 + 67507.8i) q^{82} -228408. q^{83} -980646. i q^{85} +(-26091.8 + 749927. i) q^{86} +(50593.2 - 483149. i) q^{88} +305878. q^{89} -298402. q^{91} +(62907.0 - 902939. i) q^{92} +(-1.02671e6 - 35721.8i) q^{94} +586810. i q^{95} +574256. q^{97} +(-29551.4 + 849364. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) $ 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8	$ 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8} + 2172 q^{10} - 2720 q^{11} + 6444 q^{14} + 11640 q^{16} + 4888 q^{17} + 3936 q^{19} + 31608 q^{20} - 60432 q^{22} - 27204 q^{25} - 53952 q^{26} - 57072 q^{28} - 109480 q^{32} + 47388 q^{34} - 162336 q^{35} + 89080 q^{38} + 72120 q^{40} + 54280 q^{41} - 49824 q^{43} - 229184 q^{44} + 171864 q^{46} - 304644 q^{49} + 500078 q^{50} + 256848 q^{52} + 699816 q^{56} - 409524 q^{58} + 886144 q^{59} - 691356 q^{62} - 500640 q^{64} - 473376 q^{65} + 1565952 q^{67} - 669104 q^{68} + 473784 q^{70} + 555480 q^{73} + 753720 q^{74} - 293136 q^{76} + 251616 q^{80} + 2317716 q^{82} - 2497760 q^{83} - 476024 q^{86} + 971424 q^{88} - 367400 q^{89} - 4475808 q^{91} + 377376 q^{92} - 2642568 q^{94} - 1165656 q^{97} - 182674 q^{98}+O(q^{100}) $ 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8 + 2172 * q^10 - 2720 * q^11 + 6444 * q^14 + 11640 * q^16 + 4888 * q^17 + 3936 * q^19 + 31608 * q^20 - 60432 * q^22 - 27204 * q^25 - 53952 * q^26 - 57072 * q^28 - 109480 * q^32 + 47388 * q^34 - 162336 * q^35 + 89080 * q^38 + 72120 * q^40 + 54280 * q^41 - 49824 * q^43 - 229184 * q^44 + 171864 * q^46 - 304644 * q^49 + 500078 * q^50 + 256848 * q^52 + 699816 * q^56 - 409524 * q^58 + 886144 * q^59 - 691356 * q^62 - 500640 * q^64 - 473376 * q^65 + 1565952 * q^67 - 669104 * q^68 + 473784 * q^70 + 555480 * q^73 + 753720 * q^74 - 293136 * q^76 + 251616 * q^80 + 2317716 * q^82 - 2497760 * q^83 - 476024 * q^86 + 971424 * q^88 - 367400 * q^89 - 4475808 * q^91 + 377376 * q^92 - 2642568 * q^94 - 1165656 * q^97 - 182674 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.278171	+	7.99516i	−0.0347714	+	0.999395i
$2$	−0.278171	+	7.99516i	−0.0347714	+	0.999395i
$3$		0			0
$3$		0			0
$4$	−63.8452	−	4.44805i	−0.997582	−	0.0695007i
$5$		−	111.403i		−	0.891223i	−0.895226	−	0.445612i	$-0.852986\pi$
$5$		−	111.403i		−	0.891223i	0.895226	−	0.445612i	$-0.147014\pi$
$6$		0			0
$7$			106.838i			0.311480i	0.987798	+	0.155740i	$0.0497762\pi$
$7$			106.838i			0.311480i	−0.987798	+	0.155740i	$0.950224\pi$
$8$	53.3228	−	509.216i	0.104146	−	0.994562i
$9$		0			0
$10$	890.684	+	30.9891i	0.890684	+	0.0309891i
$11$	948.811			0.712855			0.356428	−	0.934323i	$-0.383995\pi$
$11$	948.811			0.712855			0.356428	+	0.934323i	$0.383995\pi$
$12$		0			0
$13$			2793.04i			1.27130i	0.771979	+	0.635648i	$0.219267\pi$
$13$			2793.04i			1.27130i	−0.771979	+	0.635648i	$0.780733\pi$
$14$	−854.185	−	29.7192i	−0.311292	−	0.0108306i
$15$		0			0
$16$	4056.43	+	567.973i	0.990339	+	0.138665i
$17$	8802.70			1.79172			0.895858	−	0.444341i	$-0.146562\pi$
$17$	8802.70			1.79172			0.895858	+	0.444341i	$0.146562\pi$
$18$		0			0
$19$	−5267.46			−0.767963			−0.383982	−	0.923341i	$-0.625447\pi$
$19$	−5267.46			−0.767963			−0.383982	+	0.923341i	$0.625447\pi$
$20$	−495.525	+	7112.54i	−0.0619407	+	0.889068i
$21$		0			0
$22$	−263.932	+	7585.89i	−0.0247870	+	0.712424i
$23$			14142.6i			1.16238i	0.813770	+	0.581188i	$0.197412\pi$
$23$			14142.6i			1.16238i	−0.813770	+	0.581188i	$0.802588\pi$
$24$		0			0
$25$	3214.40			0.205722
$26$	−22330.8	−	776.943i	−1.27053	−	0.0442048i
$27$		0			0
$28$	475.219	−	6821.08i	0.0216481	−	0.310727i
$29$		−	16132.9i		−	0.661484i	−0.943721	−	0.330742i	$-0.892701\pi$
$29$		−	16132.9i		−	0.661484i	0.943721	−	0.330742i	$-0.107299\pi$
$30$		0			0
$31$		−	893.982i		−	0.0300085i	−0.999887	−	0.0150042i	$-0.995224\pi$
$31$		−	893.982i		−	0.0300085i	0.999887	−	0.0150042i	$-0.00477617\pi$
$32$	−5669.42	+	32273.8i	−0.173017	+	0.984919i
$33$		0			0
$34$	−2448.66	+	70379.0i	−0.0623005	+	1.79063i
$35$	11902.0			0.277598
$36$		0			0
$37$			76362.9i			1.50757i	0.657121	+	0.753785i	$0.271774\pi$
$37$			76362.9i			1.50757i	−0.657121	+	0.753785i	$0.728226\pi$
$38$	1465.26	−	42114.2i	0.0267032	−	0.767499i
$39$		0			0
$40$	−56728.1	−	5940.31i	−0.886377	−	0.0928173i
$41$	8443.58			0.122511			0.0612555	−	0.998122i	$-0.480490\pi$
$41$	8443.58			0.122511			0.0612555	+	0.998122i	$0.480490\pi$
$42$		0			0
$43$	93797.7			1.17974			0.589870	−	0.807498i	$-0.299179\pi$
$43$	93797.7			1.17974			0.589870	+	0.807498i	$0.299179\pi$
$44$	−60577.0	−	4220.35i	−0.711132	−	0.0495440i
$45$		0			0
$46$	−113073.	−	3934.07i	−1.16167	−	0.0404174i
$47$			128416.i			1.23688i	0.785832	+	0.618439i	$0.212235\pi$
$47$			128416.i			1.23688i	−0.785832	+	0.618439i	$0.787765\pi$
$48$		0			0
$49$	106235.			0.902980
$50$	−894.153	+	25699.6i	−0.00715322	+	0.205597i
$51$		0			0
$52$	12423.6	−	178322.i	0.0883561	−	1.26822i
$53$		−	170026.i		−	1.14206i	−0.820929	−	0.571030i	$-0.806544\pi$
$53$		−	170026.i		−	1.14206i	0.820929	−	0.571030i	$-0.193456\pi$
$54$		0			0
$55$		−	105700.i		−	0.635313i
$56$	54403.4	+	5696.88i	0.309786	+	0.0324394i
$57$		0			0
$58$	128985.	+	4487.72i	0.661084	+	0.0230007i
$59$	365818.			1.78119			0.890593	−	0.454802i	$-0.150290\pi$
$59$	365818.			1.78119			0.890593	+	0.454802i	$0.150290\pi$
$60$		0			0
$61$		−	364256.i		−	1.60478i	−0.596797	−	0.802392i	$-0.703560\pi$
$61$		−	364256.i		−	1.60478i	0.596797	−	0.802392i	$-0.296440\pi$
$62$	7147.53	+	248.680i	0.0299903	+	0.00104344i
$63$		0			0
$64$	−256457.	−	54305.6i	−0.978307	−	0.207159i
$65$	311153.			1.13301
$66$		0			0
$67$	4749.56			0.0157917			0.00789585	−	0.999969i	$-0.497487\pi$
$67$	4749.56			0.0157917			0.00789585	+	0.999969i	$0.497487\pi$
$68$	−562010.	−	39154.8i	−1.78738	−	0.124526i
$69$		0			0
$70$	−3310.80	+	95158.6i	−0.00965248	+	0.277430i
$71$		−	369703.i		−	1.03295i	−0.856303	−	0.516474i	$-0.827244\pi$
$71$		−	369703.i		−	1.03295i	0.856303	−	0.516474i	$-0.172756\pi$
$72$		0			0
$73$	−205508.			−0.528275			−0.264138	−	0.964485i	$-0.585087\pi$
$73$	−205508.			−0.528275			−0.264138	+	0.964485i	$0.585087\pi$
$74$	−610534.	−	21242.0i	−1.50666	−	0.0524203i
$75$		0			0
$76$	336302.	+	23429.9i	0.766106	+	0.0533740i
$77$			101369.i			0.222040i
$78$		0			0
$79$			928499.i			1.88322i	0.336711	+	0.941608i	$0.390685\pi$
$79$			928499.i			1.88322i	−0.336711	+	0.941608i	$0.609315\pi$
$80$	63273.9	−	451898.i	0.123582	−	0.882613i
$81$		0			0
$82$	−2348.76	+	67507.8i	−0.00425988	+	0.122437i
$83$	−228408.			−0.399463			−0.199731	−	0.979851i	$-0.564007\pi$
$83$	−228408.			−0.399463			−0.199731	+	0.979851i	$0.564007\pi$
$84$		0			0
$85$		−	980646.i		−	1.59682i
$86$	−26091.8	+	749927.i	−0.0410212	+	1.17903i
$87$		0			0
$88$	50593.2	−	483149.i	0.0742411	−	0.708979i
$89$	305878.			0.433888			0.216944	−	0.976184i	$-0.430391\pi$
$89$	305878.			0.433888			0.216944	+	0.976184i	$0.430391\pi$
$90$		0			0
$91$	−298402.			−0.395984
$92$	62907.0	−	902939.i	0.0807859	−	1.15956i
$93$		0			0
$94$	−1.02671e6	−	35721.8i	−1.23613	−	0.0430080i
$95$			586810.i			0.684427i
$96$		0			0
$97$	574256.			0.629202			0.314601	−	0.949224i	$-0.398129\pi$
$97$	574256.			0.629202			0.314601	+	0.949224i	$0.398129\pi$
$98$	−29551.4	+	849364.i	−0.0313979	+	0.902434i
$99$		0			0
$100$	−205224.	−	14297.8i	−0.205224	−	0.0142978i
$101$			280982.i			0.272719i	0.990659	+	0.136359i	$0.0435402\pi$
$101$			280982.i			0.272719i	−0.990659	+	0.136359i	$0.956460\pi$
$102$		0			0
$103$			1.62014e6i			1.48266i	0.671140	+	0.741331i	$0.265805\pi$
$103$			1.62014e6i			1.48266i	−0.671140	+	0.741331i	$0.734195\pi$
$104$	1.42226e6	+	148933.i	1.26438	+	0.132401i
$105$		0			0
$106$	1.35939e6	+	47296.4i	1.14137	+	0.0397110i
$107$	−611322.			−0.499021			−0.249510	−	0.968372i	$-0.580270\pi$
$107$	−611322.			−0.499021			−0.249510	+	0.968372i	$0.580270\pi$
$108$		0			0
$109$		−	895534.i		−	0.691517i	−0.938324	−	0.345758i	$-0.887622\pi$
$109$		−	895534.i		−	0.691517i	0.938324	−	0.345758i	$-0.112378\pi$
$110$	845090.	+	29402.8i	0.634929	+	0.0220907i
$111$		0			0
$112$	−60681.0	+	433380.i	−0.0431915	+	0.308471i
$113$	−1.79641e6			−1.24500			−0.622499	−	0.782620i	$-0.713883\pi$
$113$	−1.79641e6			−1.24500			−0.622499	+	0.782620i	$0.713883\pi$
$114$		0			0
$115$	1.57553e6			1.03594
$116$	−71760.1	+	1.03001e6i	−0.0459736	+	0.659885i
$117$		0			0
$118$	−101760.	+	2.92477e6i	−0.0619343	+	1.78011i
$119$			940460.i			0.558084i
$120$		0			0
$121$	−871320.			−0.491837
$122$	2.91228e6	+	101325.i	1.60381	+	0.0558006i
$123$		0			0
$124$	−3976.47	+	57076.5i	−0.00208561	+	0.0299359i
$125$		−	2.09876e6i		−	1.07457i
$126$		0			0
$127$			2.38759e6i			1.16560i	0.812616	+	0.582799i	$0.198043\pi$
$127$			2.38759e6i			1.16560i	−0.812616	+	0.582799i	$0.801957\pi$
$128$	505521.	−	2.03531e6i	0.241051	−	0.970512i
$129$		0			0
$130$	−86553.7	+	2.48772e6i	−0.0393963	+	1.13232i
$131$	−825660.			−0.367272			−0.183636	−	0.982994i	$-0.558787\pi$
$131$	−825660.			−0.367272			−0.183636	+	0.982994i	$0.558787\pi$
$132$		0			0
$133$		−	562763.i		−	0.239205i
$134$	−1321.19	+	37973.5i	−0.000549100	+	0.0157822i
$135$		0			0
$136$	469384.	−	4.48247e6i	0.186600	−	1.78197i
$137$	−1.37153e6			−0.533387			−0.266693	−	0.963781i	$-0.585931\pi$
$137$	−1.37153e6			−0.533387			−0.266693	+	0.963781i	$0.585931\pi$
$138$		0			0
$139$	−3.81225e6			−1.41951			−0.709753	−	0.704451i	$-0.751193\pi$
$139$	−3.81225e6			−1.41951			−0.709753	+	0.704451i	$0.751193\pi$
$140$	−759888.	−	52940.8i	−0.276927	−	0.0192933i
$141$		0			0
$142$	2.95584e6	+	102841.i	1.03232	+	0.0359170i
$143$			2.65006e6i			0.906251i
$144$		0			0
$145$	−1.79726e6			−0.589530
$146$	57166.4	−	1.64307e6i	0.0183689	−	0.527956i
$147$		0			0
$148$	339666.	−	4.87541e6i	0.104777	−	1.50392i
$149$		−	1.37138e6i		−	0.414572i	−0.978280	−	0.207286i	$-0.933537\pi$
$149$		−	1.37138e6i		−	0.414572i	0.978280	−	0.207286i	$-0.0664631\pi$
$150$		0			0
$151$		−	3.59066e6i		−	1.04290i	−0.853282	−	0.521450i	$-0.825391\pi$
$151$		−	3.59066e6i		−	1.04290i	0.853282	−	0.521450i	$-0.174609\pi$
$152$	−280876.	+	2.68227e6i	−0.0799803	+	0.763787i
$153$		0			0
$154$	−810459.	−	28197.9i	−0.221906	−	0.00772065i
$155$	−99592.2			−0.0267442
$156$		0			0
$157$		−	852222.i		−	0.220218i	−0.993919	−	0.110109i	$-0.964880\pi$
$157$		−	852222.i		−	0.220218i	0.993919	−	0.110109i	$-0.0351201\pi$
$158$	−7.42350e6	−	258282.i	−1.88208	−	0.0654820i
$159$		0			0
$160$	3.59540e6	+	631590.i	0.877782	+	0.154197i
$161$	−1.51096e6			−0.362057
$162$		0			0
$163$	−1.19776e6			−0.276572			−0.138286	−	0.990392i	$-0.544159\pi$
$163$	−1.19776e6			−0.276572			−0.138286	+	0.990392i	$0.544159\pi$
$164$	−539082.	−	37557.4i	−0.122215	−	0.00851460i
$165$		0			0
$166$	63536.4	−	1.82616e6i	0.0138899	−	0.399221i
$167$			3.36180e6i			0.721809i	0.932603	+	0.360904i	$0.117532\pi$
$167$			3.36180e6i			0.721809i	−0.932603	+	0.360904i	$0.882468\pi$
$168$		0			0
$169$	−2.97426e6			−0.616196
$170$	7.84042e6	+	272787.i	1.59585	+	0.0555236i
$171$		0			0
$172$	−5.98853e6	−	417216.i	−1.17689	−	0.0819929i
$173$		−	6.41173e6i		−	1.23833i	−0.785261	−	0.619165i	$-0.787471\pi$
$173$		−	6.41173e6i		−	1.23833i	0.785261	−	0.619165i	$-0.212529\pi$
$174$		0			0
$175$			343419.i			0.0640782i
$176$	3.84878e6	+	538899.i	0.705969	+	0.0988483i
$177$		0			0
$178$	−85086.3	+	2.44554e6i	−0.0150869	+	0.433626i
$179$	−1.55551e6			−0.271216			−0.135608	−	0.990763i	$-0.543299\pi$
$179$	−1.55551e6			−0.271216			−0.135608	+	0.990763i	$0.543299\pi$
$180$		0			0
$181$		−	2.59979e6i		−	0.438432i	−0.975676	−	0.219216i	$-0.929650\pi$
$181$		−	2.59979e6i		−	0.438432i	0.975676	−	0.219216i	$-0.0703499\pi$
$182$	83006.8	−	2.38577e6i	0.0137689	−	0.395744i
$183$		0			0
$184$	7.20164e6	+	754124.i	1.15605	+	0.121057i
$185$	8.50705e6			1.34358
$186$		0			0
$187$	8.35209e6			1.27723
$188$	571203.	−	8.19878e6i	0.0859640	−	1.23389i
$189$		0			0
$190$	−4.69164e6	−	163234.i	−0.684013	−	0.0237985i
$191$		−	7.34227e6i		−	1.05373i	−0.849948	−	0.526866i	$-0.823367\pi$
$191$		−	7.34227e6i		−	1.05373i	0.849948	−	0.526866i	$-0.176633\pi$
$192$		0			0
$193$	1.22552e7			1.70470			0.852348	−	0.522976i	$-0.175178\pi$
$193$	1.22552e7			1.70470			0.852348	+	0.522976i	$0.175178\pi$
$194$	−159741.	+	4.59127e6i	−0.0218782	+	0.628821i
$195$		0			0
$196$	−6.78258e6	−	472537.i	−0.900797	−	0.0627578i
$197$			6.44715e6i			0.843274i	0.906765	+	0.421637i	$0.138544\pi$
$197$			6.44715e6i			0.843274i	−0.906765	+	0.421637i	$0.861456\pi$
$198$		0			0
$199$		−	23184.8i		−	0.00294201i	−0.999999	−	0.00147101i	$-0.999532\pi$
$199$		−	23184.8i		−	0.00294201i	0.999999	−	0.00147101i	$-0.000468236\pi$
$200$	171401.	−	1.63682e6i	0.0214251	−	0.204603i
$201$		0			0
$202$	−2.24650e6	−	78161.2i	−0.272554	−	0.00948281i
$203$	1.72361e6			0.206039
$204$		0			0
$205$		−	940639.i		−	0.109185i
$206$	−1.29533e7	−	450677.i	−1.48176	−	0.0515542i
$207$		0			0
$208$	−1.58637e6	+	1.13298e7i	−0.176285	+	1.25902i
$209$	−4.99782e6			−0.547447
$210$		0			0
$211$	−6.47878e6			−0.689677			−0.344838	−	0.938662i	$-0.612066\pi$
$211$	−6.47878e6			−0.689677			−0.344838	+	0.938662i	$0.612066\pi$
$212$	−756285.	+	1.08554e7i	−0.0793740	+	1.13930i
$213$		0			0
$214$	170052.	−	4.88762e6i	0.0173516	−	0.498719i
$215$		−	1.04493e7i		−	1.05141i
$216$		0			0
$217$	95511.0			0.00934704
$218$	7.15994e6	+	249112.i	0.691098	+	0.0240450i
$219$		0			0
$220$	−470160.	+	6.74846e6i	−0.0441547	+	0.633777i
$221$			2.45863e7i			2.27780i
$222$		0			0
$223$			1.22334e7i			1.10315i	0.834125	+	0.551575i	$0.185973\pi$
$223$			1.22334e7i			1.10315i	−0.834125	+	0.551575i	$0.814027\pi$
$224$	−3.44806e6	−	605708.i	−0.306783	−	0.0538914i
$225$		0			0
$226$	499708.	−	1.43626e7i	0.0432903	−	1.24425i
$227$	9.98241e6			0.853410			0.426705	−	0.904391i	$-0.359674\pi$
$227$	9.98241e6			0.853410			0.426705	+	0.904391i	$0.359674\pi$
$228$		0			0
$229$			1.09419e7i			0.911144i	0.890199	+	0.455572i	$0.150565\pi$
$229$			1.09419e7i			0.911144i	−0.890199	+	0.455572i	$0.849435\pi$
$230$	−438267.	+	1.25966e7i	−0.0360209	+	1.03531i
$231$		0			0
$232$	−8.21515e6	−	860253.i	−0.657887	−	0.0688910i
$233$	1.29052e7			1.02023			0.510115	−	0.860106i	$-0.329603\pi$
$233$	1.29052e7			1.02023			0.510115	+	0.860106i	$0.329603\pi$
$234$		0			0
$235$	1.43060e7			1.10233
$236$	−2.33557e7	−	1.62718e6i	−1.77688	−	0.123794i
$237$		0			0
$238$	−7.51913e6	−	261609.i	−0.557746	−	0.0194054i
$239$			1.13200e7i			0.829187i	0.910007	+	0.414594i	$0.136076\pi$
$239$			1.13200e7i			0.829187i	−0.910007	+	0.414594i	$0.863924\pi$
$240$		0			0
$241$	−6.17444e6			−0.441110			−0.220555	−	0.975375i	$-0.570787\pi$
$241$	−6.17444e6			−0.441110			−0.220555	+	0.975375i	$0.570787\pi$
$242$	242376.	−	6.96634e6i	0.0171019	−	0.491540i
$243$		0			0
$244$	−1.62023e6	+	2.32560e7i	−0.111534	+	1.60090i
$245$		−	1.18349e7i		−	0.804757i
$246$		0			0
$247$		−	1.47122e7i		−	0.976309i
$248$	−455230.	−	47669.6i	−0.0298453	−	0.00312526i
$249$		0			0
$250$	1.67800e7	+	583815.i	1.07392	+	0.0373642i
$251$	1.29225e7			0.817197			0.408599	−	0.912714i	$-0.366018\pi$
$251$	1.29225e7			0.817197			0.408599	+	0.912714i	$0.366018\pi$
$252$		0			0
$253$			1.34187e7i			0.828605i
$254$	−1.90892e7	−	664159.i	−1.16489	−	0.0405295i
$255$		0			0
$256$	1.61320e7	+	4.60789e6i	0.961544	+	0.274651i
$257$	−8.33091e6			−0.490787			−0.245394	−	0.969424i	$-0.578917\pi$
$257$	−8.33091e6			−0.490787			−0.245394	+	0.969424i	$0.578917\pi$
$258$		0			0
$259$	−8.15844e6			−0.469578
$260$	−1.98656e7	−	1.38402e6i	−1.13027	−	0.0787450i
$261$		0			0
$262$	229675.	−	6.60129e6i	0.0127706	−	0.367050i
$263$		−	2.53621e7i		−	1.39418i	−0.716986	−	0.697088i	$-0.754479\pi$
$263$		−	2.53621e7i		−	1.39418i	0.716986	−	0.697088i	$-0.245521\pi$
$264$		0			0
$265$	−1.89414e7			−1.01783
$266$	4.49938e6	+	156545.i	0.239061	+	0.00831750i
$267$		0			0
$268$	−303237.	−	21126.3i	−0.0157535	−	0.00109754i
$269$		−	1.73137e6i		−	0.0889473i	−0.999011	−	0.0444736i	$-0.985839\pi$
$269$		−	1.73137e6i		−	0.0889473i	0.999011	−	0.0444736i	$-0.0141611\pi$
$270$		0			0
$271$		−	2.69849e7i		−	1.35586i	−0.735128	−	0.677928i	$-0.762878\pi$
$271$		−	2.69849e7i		−	1.35586i	0.735128	−	0.677928i	$-0.237122\pi$
$272$	3.57075e7	+	4.99970e6i	1.77441	+	0.248449i
$273$		0			0
$274$	381519.	−	1.09656e7i	0.0185466	−	0.533064i
$275$	3.04986e6			0.146650
$276$		0			0
$277$			1.50256e7i			0.706956i	0.935443	+	0.353478i	$0.115001\pi$
$277$			1.50256e7i			0.706956i	−0.935443	+	0.353478i	$0.884999\pi$
$278$	1.06046e6	−	3.04796e7i	0.0493582	−	1.41865i
$279$		0			0
$280$	634649.	−	6.06070e6i	0.0289108	−	0.276089i
$281$	2.42725e7			1.09394			0.546972	−	0.837151i	$-0.315781\pi$
$281$	2.42725e7			1.09394			0.546972	+	0.837151i	$0.315781\pi$
$282$		0			0
$283$	−2.06960e7			−0.913121			−0.456560	−	0.889692i	$-0.650919\pi$
$283$	−2.06960e7			−0.913121			−0.456560	+	0.889692i	$0.650919\pi$
$284$	−1.64446e6	+	2.36038e7i	−0.0717906	+	1.03045i
$285$		0			0
$286$	−2.11877e7	−	737172.i	−0.905703	−	0.0315116i
$287$			902092.i			0.0381597i
$288$		0			0
$289$	5.33499e7			2.21024
$290$	499945.	−	1.43694e7i	0.0204988	−	0.589173i
$291$		0			0
$292$	1.31207e7	+	914110.i	0.526998	+	0.0367155i
$293$			1.17991e7i			0.469080i	0.972106	+	0.234540i	$0.0753584\pi$
$293$			1.17991e7i			0.469080i	−0.972106	+	0.234540i	$0.924642\pi$
$294$		0			0
$295$		−	4.07532e7i		−	1.58743i
$296$	3.88852e7	+	4.07188e6i	1.49937	+	0.157007i
$297$		0			0
$298$	1.09644e7	+	381479.i	0.414321	+	0.0144152i
$299$	−3.95009e7			−1.47772
$300$		0			0
$301$			1.00211e7i			0.367466i
$302$	2.87079e7	+	998817.i	1.04227	+	0.0362631i
$303$		0			0
$304$	−2.13671e7	−	2.99178e6i	−0.760544	−	0.106490i
$305$	−4.05791e7			−1.43022
$306$		0			0
$307$	3.39456e7			1.17319			0.586595	−	0.809881i	$-0.300468\pi$
$307$	3.39456e7			1.17319			0.586595	+	0.809881i	$0.300468\pi$
$308$	450893.	−	6.47191e6i	0.0154320	−	0.221503i
$309$		0			0
$310$	27703.7	−	796256.i	0.000929934	−	0.0267281i
$311$			2.82481e7i			0.939092i	0.882908	+	0.469546i	$0.155582\pi$
$311$			2.82481e7i			0.939092i	−0.882908	+	0.469546i	$0.844418\pi$
$312$		0			0
$313$	−4.43593e7			−1.44661			−0.723306	−	0.690528i	$-0.757378\pi$
$313$	−4.43593e7			−1.44661			−0.723306	+	0.690528i	$0.757378\pi$
$314$	6.81365e6	+	237063.i	0.220085	+	0.00765730i
$315$		0			0
$316$	4.13001e6	−	5.92802e7i	0.130885	−	1.87866i
$317$		−	2.81173e7i		−	0.882666i	−0.897343	−	0.441333i	$-0.854506\pi$
$317$		−	2.81173e7i		−	0.882666i	0.897343	−	0.441333i	$-0.145494\pi$
$318$		0			0
$319$		−	1.53071e7i		−	0.471543i
$320$	−6.04980e6	+	2.85701e7i	−0.184625	+	0.871890i
$321$		0			0
$322$	420307.	−	1.20804e7i	0.0125892	−	0.361838i
$323$	−4.63679e7			−1.37597
$324$		0			0
$325$			8.97794e6i			0.261533i
$326$	333184.	−	9.57632e6i	0.00961681	−	0.276405i
$327$		0			0
$328$	450235.	−	4.29960e6i	0.0127590	−	0.121845i
$329$	−1.37197e7			−0.385263
$330$		0			0
$331$	−3.09974e7			−0.854755			−0.427377	−	0.904073i	$-0.640562\pi$
$331$	−3.09974e7			−0.854755			−0.427377	+	0.904073i	$0.640562\pi$
$332$	1.45827e7	+	1.01597e6i	0.398497	+	0.0277630i
$333$		0			0
$334$	−2.68781e7	−	935155.i	−0.721372	−	0.0250983i
$335$		−	529115.i		−	0.0140739i
$336$		0			0
$337$	4.41594e6			0.115381			0.0576905	−	0.998335i	$-0.481626\pi$
$337$	4.41594e6			0.115381			0.0576905	+	0.998335i	$0.481626\pi$
$338$	827353.	−	2.37797e7i	0.0214260	−	0.615823i
$339$		0			0
$340$	−4.36196e6	+	6.26096e7i	−0.110980	+	1.59296i
$341$		−	848220.i		−	0.0213917i
$342$		0			0
$343$			2.39192e7i			0.592741i
$344$	5.00155e6	−	4.77632e7i	0.122865	−	1.17333i
$345$		0			0
$346$	5.12628e7	+	1.78356e6i	1.23758	+	0.0430585i
$347$	1.41629e7			0.338972			0.169486	−	0.985533i	$-0.445789\pi$
$347$	1.41629e7			0.338972			0.169486	+	0.985533i	$0.445789\pi$
$348$		0			0
$349$			2.94783e7i			0.693468i	0.937963	+	0.346734i	$0.112709\pi$
$349$			2.94783e7i			0.693468i	−0.937963	+	0.346734i	$0.887291\pi$
$350$	−2.74569e6	−	95529.2i	−0.0640394	−	0.00222809i
$351$		0			0
$352$	−5.37921e6	+	3.06217e7i	−0.123336	+	0.702105i
$353$	−4.50728e7			−1.02469			−0.512343	−	0.858781i	$-0.671222\pi$
$353$	−4.50728e7			−1.02469			−0.512343	+	0.858781i	$0.671222\pi$
$354$		0			0
$355$	−4.11860e7			−0.920587
$356$	−1.95288e7	−	1.36056e6i	−0.432839	−	0.0301555i
$357$		0			0
$358$	432699.	−	1.24366e7i	0.00943054	−	0.271052i
$359$		−	6.86999e6i		−	0.148482i	−0.997240	−	0.0742408i	$-0.976347\pi$
$359$		−	6.86999e6i		−	0.148482i	0.997240	−	0.0742408i	$-0.0236534\pi$
$360$		0			0
$361$	−1.92997e7			−0.410232
$362$	2.07857e7	+	723185.i	0.438167	+	0.0152449i
$363$		0			0
$364$	1.90515e7	+	1.32731e6i	0.395026	+	0.0275212i
$365$			2.28942e7i			0.470811i
$366$		0			0
$367$			2.07872e7i			0.420530i	0.977644	+	0.210265i	$0.0674327\pi$
$367$			2.07872e7i			0.420530i	−0.977644	+	0.210265i	$0.932567\pi$
$368$	−8.03263e6	+	5.73685e7i	−0.161181	+	1.15115i
$369$		0			0
$370$	−2.36642e6	+	6.80152e7i	−0.0467182	+	1.34277i
$371$	1.81652e7			0.355729
$372$		0			0
$373$		−	4.43619e7i		−	0.854838i	−0.904054	−	0.427419i	$-0.859423\pi$
$373$		−	4.43619e7i		−	0.854838i	0.904054	−	0.427419i	$-0.140577\pi$
$374$	−2.32331e6	+	6.67763e7i	−0.0444112	+	1.27646i
$375$		0			0
$376$	6.53917e7	+	6.84752e6i	1.23015	+	0.128816i
$377$	4.50599e7			0.840943
$378$		0			0
$379$	4.90435e7			0.900874			0.450437	−	0.892808i	$-0.351268\pi$
$379$	4.90435e7			0.900874			0.450437	+	0.892808i	$0.351268\pi$
$380$	2.61016e6	−	3.74650e7i	0.0475681	−	0.682772i
$381$		0			0
$382$	5.87026e7	+	2.04241e6i	1.05309	+	0.0366397i
$383$		−	4.14018e7i		−	0.736925i	−0.929643	−	0.368463i	$-0.879884\pi$
$383$		−	4.14018e7i		−	0.736925i	0.929643	−	0.368463i	$-0.120116\pi$
$384$		0			0
$385$	1.12928e7			0.197887
$386$	−3.40903e6	+	9.79819e7i	−0.0592746	+	1.70366i
$387$		0			0
$388$	−3.66635e7	−	2.55432e6i	−0.627680	−	0.0437300i
$389$			3.28418e7i			0.557928i	0.960302	+	0.278964i	$0.0899910\pi$
$389$			3.28418e7i			0.557928i	−0.960302	+	0.278964i	$0.910009\pi$
$390$		0			0
$391$			1.24493e8i			2.08265i
$392$	5.66473e6	−	5.40964e7i	0.0940418	−	0.898070i
$393$		0			0
$394$	−5.15460e7	−	1.79341e6i	−0.842764	−	0.0293218i
$395$	1.03437e8			1.67837
$396$		0			0
$397$		−	6.86949e7i		−	1.09787i	−0.835863	−	0.548937i	$-0.815033\pi$
$397$		−	6.86949e7i		−	1.09787i	0.835863	−	0.548937i	$-0.184967\pi$
$398$	185366.	+	6449.35i	0.00294023	+	0.000102298i
$399$		0			0
$400$	1.30390e7	+	1.82569e6i	0.203734	+	0.0285264i
$401$	3.25031e7			0.504072			0.252036	−	0.967718i	$-0.418900\pi$
$401$	3.25031e7			0.504072			0.252036	+	0.967718i	$0.418900\pi$
$402$		0			0
$403$	2.49693e6			0.0381497
$404$	1.24982e6	−	1.79394e7i	0.0189542	−	0.272059i
$405$		0			0
$406$	−479457.	+	1.37805e7i	−0.00716427	+	0.205915i
$407$			7.24540e7i			1.07468i
$408$		0			0
$409$	−1.01765e8			−1.48740			−0.743698	−	0.668516i	$-0.766930\pi$
$409$	−1.01765e8			−1.48740			−0.743698	+	0.668516i	$0.766930\pi$
$410$	7.52056e6	+	261659.i	0.109119	+	0.00379650i
$411$		0			0
$412$	7.20648e6	−	1.03438e8i	0.103046	−	1.47908i
$413$			3.90832e7i			0.554804i
$414$		0			0
$415$			2.54453e7i			0.356011i
$416$	−9.01420e7	−	1.58349e7i	−1.25212	−	0.219956i
$417$		0			0
$418$	1.39025e6	−	3.99584e7i	0.0190355	−	0.547116i
$419$	−7.19503e7			−0.978117			−0.489058	−	0.872251i	$-0.662660\pi$
$419$	−7.19503e7			−0.978117			−0.489058	+	0.872251i	$0.662660\pi$
$420$		0			0
$421$		−	8.70973e7i		−	1.16724i	−0.812029	−	0.583618i	$-0.801637\pi$
$421$		−	8.70973e7i		−	1.16724i	0.812029	−	0.583618i	$-0.198363\pi$
$422$	1.80221e6	−	5.17989e7i	0.0239810	−	0.689260i
$423$		0			0
$424$	−8.65801e7	−	9.06628e6i	−1.13585	−	0.118941i
$425$	2.82954e7			0.368594
$426$		0			0
$427$	3.89162e7			0.499858
$428$	3.90300e7	+	2.71919e6i	0.497814	+	0.0346823i
$429$		0			0
$430$	8.35441e7	+	2.90670e6i	1.05078	+	0.0365591i
$431$		−	7.13375e7i		−	0.891017i	−0.895278	−	0.445509i	$-0.853023\pi$
$431$		−	7.13375e7i		−	0.891017i	0.895278	−	0.445509i	$-0.146977\pi$
$432$		0			0
$433$	1.54528e8			1.90346			0.951728	−	0.306944i	$-0.0993064\pi$
$433$	1.54528e8			1.90346			0.951728	+	0.306944i	$0.0993064\pi$
$434$	−26568.4	+	763626.i	−0.000325010	+	0.00934139i
$435$		0			0
$436$	−3.98338e6	+	5.71756e7i	−0.0480609	+	0.689844i
$437$		−	7.44957e7i		−	0.892661i
$438$		0			0
$439$			1.04908e8i			1.23998i	0.784609	+	0.619991i	$0.212864\pi$
$439$			1.04908e8i			1.23998i	−0.784609	+	0.619991i	$0.787136\pi$
$440$	−5.38242e7	−	5.63623e6i	−0.631858	−	0.0661653i
$441$		0			0
$442$	−1.96571e8	−	6.83919e6i	−2.27643	−	0.0792024i
$443$	2.92340e7			0.336262			0.168131	−	0.985765i	$-0.446227\pi$
$443$	2.92340e7			0.336262			0.168131	+	0.985765i	$0.446227\pi$
$444$		0			0
$445$		−	3.40756e7i		−	0.386691i
$446$	−9.78084e7	−	3.40299e6i	−1.10248	−	0.0383580i
$447$		0			0
$448$	5.80188e6	−	2.73993e7i	0.0645260	−	0.304723i
$449$	−3.58409e7			−0.395949			−0.197975	−	0.980207i	$-0.563436\pi$
$449$	−3.58409e7			−0.395949			−0.197975	+	0.980207i	$0.563436\pi$
$450$		0			0
$451$	8.01136e6			0.0873326
$452$	1.14692e8	+	7.99049e6i	1.24199	+	0.0865283i
$453$		0			0
$454$	−2.77682e6	+	7.98110e7i	−0.0296743	+	0.852894i
$455$			3.32428e7i			0.352910i
$456$		0			0
$457$	1.69388e8			1.77474			0.887370	−	0.461058i	$-0.152530\pi$
$457$	1.69388e8			1.77474			0.887370	+	0.461058i	$0.152530\pi$
$458$	−8.74824e7	−	3.04373e6i	−0.910593	−	0.0316817i
$459$		0			0
$460$	−1.00590e8	−	7.00802e6i	−1.03343	−	0.0719983i
$461$		−	1.31708e8i		−	1.34434i	−0.740396	−	0.672171i	$-0.765362\pi$
$461$		−	1.31708e8i		−	1.34434i	0.740396	−	0.672171i	$-0.234638\pi$
$462$		0			0
$463$		−	9.70927e7i		−	0.978236i	−0.872218	−	0.489118i	$-0.837319\pi$
$463$		−	9.70927e7i		−	0.978236i	0.872218	−	0.489118i	$-0.162681\pi$
$464$	9.16308e6	−	6.54421e7i	0.0917249	−	0.655094i
$465$		0			0
$466$	−3.58986e6	+	1.03179e8i	−0.0354748	+	1.01961i
$467$	−1.01509e8			−0.996675			−0.498337	−	0.866983i	$-0.666056\pi$
$467$	−1.01509e8			−0.996675			−0.498337	+	0.866983i	$0.666056\pi$
$468$		0			0
$469$			507432.i			0.00491880i
$470$	−3.97951e6	+	1.14379e8i	−0.0383297	+	1.10167i
$471$		0			0
$472$	1.95064e7	−	1.86280e8i	0.185503	−	1.77150i
$473$	8.89962e7			0.840985
$474$		0			0
$475$	−1.69317e7			−0.157987
$476$	4.18321e6	−	6.00439e7i	0.0387872	−	0.556734i
$477$		0			0
$478$	−9.05052e7	−	3.14890e6i	−0.828686	−	0.0288320i
$479$			1.53877e8i			1.40013i	0.714081	+	0.700064i	$0.246845\pi$
$479$			1.53877e8i			1.40013i	−0.714081	+	0.700064i	$0.753155\pi$
$480$		0			0
$481$	−2.13285e8			−1.91657
$482$	1.71755e6	−	4.93657e7i	0.0153380	−	0.440843i
$483$		0			0
$484$	5.56296e7	+	3.87567e6i	0.490648	+	0.0341830i
$485$		−	6.39737e7i		−	0.560759i
$486$		0			0
$487$		−	9.18051e7i		−	0.794840i	−0.917637	−	0.397420i	$-0.869906\pi$
$487$		−	9.18051e7i		−	0.794840i	0.917637	−	0.397420i	$-0.130094\pi$
$488$	−1.85485e8	−	1.94231e7i	−1.59606	−	0.167132i
$489$		0			0
$490$	9.46216e7	+	3.29211e6i	0.804270	+	0.0279825i
$491$	8.69921e7			0.734912			0.367456	−	0.930041i	$-0.380229\pi$
$491$	8.69921e7			0.734912			0.367456	+	0.930041i	$0.380229\pi$
$492$		0			0
$493$		−	1.42013e8i		−	1.18519i
$494$	1.17627e8	+	4.09252e6i	0.975719	+	0.0339476i
$495$		0			0
$496$	507758.	−	3.62638e6i	0.00416113	−	0.0297186i
$497$	3.94982e7			0.321743
$498$		0			0
$499$	−3.62466e7			−0.291720			−0.145860	−	0.989305i	$-0.546595\pi$
$499$	−3.62466e7			−0.291720			−0.145860	+	0.989305i	$0.546595\pi$
$500$	−9.33540e6	+	1.33996e8i	−0.0746832	+	1.07197i
$501$		0			0
$502$	−3.59468e6	+	1.03318e8i	−0.0284151	+	0.816703i
$503$		−	3.70870e6i		−	0.0291419i	−0.999894	−	0.0145709i	$-0.995362\pi$
$503$		−	3.70870e6i		−	0.0291419i	0.999894	−	0.0145709i	$-0.00463824\pi$
$504$		0			0
$505$	3.13023e7			0.243053
$506$	−1.07284e8	−	3.73269e6i	−0.828104	−	0.0288118i
$507$		0			0
$508$	1.06201e7	−	1.52436e8i	0.0810099	−	1.16278i
$509$		−	2.40377e7i		−	0.182280i	−0.995838	−	0.0911400i	$-0.970949\pi$
$509$		−	2.40377e7i		−	0.182280i	0.995838	−	0.0911400i	$-0.0290511\pi$
$510$		0			0
$511$		−	2.19560e7i		−	0.164547i
$512$	−4.13283e7	+	1.27696e8i	−0.307920	+	0.951412i
$513$		0			0
$514$	2.31742e6	−	6.66070e7i	0.0170653	−	0.490490i
$515$	1.80489e8			1.32138
$516$		0			0
$517$			1.21843e8i			0.881716i
$518$	2.26944e6	−	6.52280e7i	0.0163279	−	0.469294i
$519$		0			0
$520$	1.65915e7	−	1.58444e8i	0.117998	−	1.12685i
$521$	2.29641e7			0.162382			0.0811908	−	0.996699i	$-0.474128\pi$
$521$	2.29641e7			0.162382			0.0811908	+	0.996699i	$0.474128\pi$
$522$		0			0
$523$	1.59549e8			1.11529			0.557646	−	0.830079i	$-0.311705\pi$
$523$	1.59549e8			1.11529			0.557646	+	0.830079i	$0.311705\pi$
$524$	5.27145e7	+	3.67258e6i	0.366384	+	0.0255257i
$525$		0			0
$526$	2.02774e8	+	7.05500e6i	1.39333	+	0.0484774i
$527$		−	7.86946e6i		−	0.0537666i
$528$		0			0
$529$	−5.19778e7			−0.351116
$530$	5.26896e6	−	1.51440e8i	0.0353914	−	1.01721i
$531$		0			0
$532$	−2.50320e6	+	3.59298e7i	−0.0166249	+	0.238627i
$533$			2.35832e7i			0.155748i
$534$		0			0
$535$			6.81030e7i			0.444739i
$536$	253260.	−	2.41855e6i	0.00164464	−	0.0157058i
$537$		0			0
$538$	1.38426e7	+	481617.i	0.0888935	+	0.00309282i
$539$	1.00797e8			0.643694
$540$		0			0
$541$			1.15088e8i			0.726840i	0.931625	+	0.363420i	$0.118391\pi$
$541$			1.15088e8i			0.726840i	−0.931625	+	0.363420i	$0.881609\pi$
$542$	2.15749e8	+	7.50643e6i	1.35504	+	0.0471450i
$543$		0			0
$544$	−4.99062e7	+	2.84097e8i	−0.309997	+	1.76469i
$545$	−9.97651e7			−0.616295
$546$		0			0
$547$	−1.08641e8			−0.663791			−0.331896	−	0.943316i	$-0.607688\pi$
$547$	−1.08641e8			−0.663791			−0.331896	+	0.943316i	$0.607688\pi$
$548$	8.75654e7	+	6.10061e6i	0.532097	+	0.0370708i
$549$		0			0
$550$	−848382.	+	2.43841e7i	−0.00509921	+	0.146561i
$551$			8.49796e7i			0.507996i
$552$		0			0
$553$	−9.91987e7			−0.586584
$554$	−1.20132e8	−	4.17968e6i	−0.706528	−	0.0245818i
$555$		0			0
$556$	2.43394e8	+	1.69571e7i	1.41607	+	0.0986567i
$557$			8.05257e7i			0.465982i	0.972479	+	0.232991i	$0.0748512\pi$
$557$			8.05257e7i			0.465982i	−0.972479	+	0.232991i	$0.925149\pi$
$558$		0			0
$559$			2.61981e8i			1.49980i
$560$	4.82797e7	+	6.76003e6i	0.274916	+	0.0384933i
$561$		0			0
$562$	−6.75190e6	+	1.94062e8i	−0.0380379	+	1.09328i
$563$	−1.37953e8			−0.773047			−0.386523	−	0.922280i	$-0.626324\pi$
$563$	−1.37953e8			−0.773047			−0.386523	+	0.922280i	$0.626324\pi$
$564$		0			0
$565$			2.00125e8i			1.10957i
$566$	5.75704e6	−	1.65468e8i	0.0317505	−	0.912568i
$567$		0			0
$568$	−1.88259e8	−	1.97136e7i	−1.02733	−	0.107577i
$569$	−1.98224e8			−1.07602			−0.538010	−	0.842939i	$-0.680824\pi$
$569$	−1.98224e8			−1.07602			−0.538010	+	0.842939i	$0.680824\pi$
$570$		0			0
$571$	−2.12119e8			−1.13939			−0.569695	−	0.821857i	$-0.692938\pi$
$571$	−2.12119e8			−1.13939			−0.569695	+	0.821857i	$0.692938\pi$
$572$	1.17876e7	−	1.69194e8i	0.0629851	−	0.904059i
$573$		0			0
$574$	−7.21238e6	−	250936.i	−0.0381367	−	0.00132687i
$575$			4.54600e7i			0.239126i
$576$		0			0
$577$	1.15697e8			0.602273			0.301136	−	0.953581i	$-0.402634\pi$
$577$	1.15697e8			0.602273			0.301136	+	0.953581i	$0.402634\pi$
$578$	−1.48404e7	+	4.26541e8i	−0.0768533	+	2.20891i
$579$		0			0
$580$	1.14746e8	+	7.99428e6i	0.588104	+	0.0409728i
$581$		−	2.44025e7i		−	0.124425i
$582$		0			0
$583$		−	1.61323e8i		−	0.814123i
$584$	−1.09583e7	+	1.04648e8i	−0.0550178	+	0.525403i
$585$		0			0
$586$	−9.43359e7	−	3.28218e6i	−0.468796	−	0.0163106i
$587$	−3.57884e8			−1.76941			−0.884704	−	0.466153i	$-0.845640\pi$
$587$	−3.57884e8			−1.76941			−0.884704	+	0.466153i	$0.845640\pi$
$588$		0			0
$589$			4.70902e6i			0.0230454i
$590$	3.25828e8	+	1.13364e7i	1.58647	+	0.0551973i
$591$		0			0
$592$	−4.33721e7	+	3.09761e8i	−0.209048	+	1.49301i
$593$	8.27994e7			0.397066			0.198533	−	0.980094i	$-0.436382\pi$
$593$	8.27994e7			0.397066			0.198533	+	0.980094i	$0.436382\pi$
$594$		0			0
$595$	1.04770e8			0.497377
$596$	−6.09998e6	+	8.75563e7i	−0.0288131	+	0.413569i
$597$		0			0
$598$	1.09880e7	−	3.15816e8i	0.0513825	−	1.47683i
$599$		−	3.62837e8i		−	1.68823i	−0.536164	−	0.844114i	$-0.680127\pi$
$599$		−	3.62837e8i		−	1.68823i	0.536164	−	0.844114i	$-0.319873\pi$
$600$		0			0
$601$	1.65470e7			0.0762245			0.0381123	−	0.999273i	$-0.487866\pi$
$601$	1.65470e7			0.0762245			0.0381123	+	0.999273i	$0.487866\pi$
$602$	−8.01205e7	−	2.78759e6i	−0.367244	−	0.0127773i
$603$		0			0
$604$	−1.59714e7	+	2.29246e8i	−0.0724824	+	1.04038i
$605$			9.70675e7i			0.438337i
$606$		0			0
$607$		−	1.76869e8i		−	0.790832i	−0.918502	−	0.395416i	$-0.870600\pi$
$607$		−	1.76869e8i		−	0.790832i	0.918502	−	0.395416i	$-0.129400\pi$
$608$	2.98634e7	−	1.70001e8i	0.132871	−	0.756381i
$609$		0			0
$610$	1.12879e7	−	3.24437e8i	0.0497308	−	1.42936i
$611$	−3.58672e8			−1.57244
$612$		0			0
$613$		−	3.25145e8i		−	1.41155i	−0.708437	−	0.705774i	$-0.750600\pi$
$613$		−	3.25145e8i		−	1.41155i	0.708437	−	0.705774i	$-0.249400\pi$
$614$	−9.44268e6	+	2.71400e8i	−0.0407934	+	1.17248i
$615$		0			0
$616$	5.16185e7	+	5.40526e6i	0.220833	+	0.0231246i
$617$	−4.08079e8			−1.73736			−0.868679	−	0.495376i	$-0.835030\pi$
$617$	−4.08079e8			−1.73736			−0.868679	+	0.495376i	$0.835030\pi$
$618$		0			0
$619$	1.72430e8			0.727012			0.363506	−	0.931592i	$-0.381580\pi$
$619$	1.72430e8			0.727012			0.363506	+	0.931592i	$0.381580\pi$
$620$	6.35849e6	+	442991.i	0.0266796	+	0.00185874i
$621$		0			0
$622$	−2.25848e8	−	7.85781e6i	−0.938524	−	0.0326535i
$623$			3.26793e7i			0.135147i
$624$		0			0
$625$	−1.83583e8			−0.751957
$626$	1.23395e7	−	3.54660e8i	0.0503007	−	1.44574i
$627$		0			0
$628$	−3.79072e6	+	5.44103e7i	−0.0153053	+	0.219686i
$629$			6.72200e8i			2.70114i
$630$		0			0
$631$		−	1.98104e8i		−	0.788507i	−0.919002	−	0.394254i	$-0.871003\pi$
$631$		−	1.98104e8i		−	0.788507i	0.919002	−	0.394254i	$-0.128997\pi$
$632$	4.72806e8	+	4.95101e7i	1.87297	+	0.196129i
$633$		0			0
$634$	2.24803e8	+	7.82143e6i	0.882133	+	0.0306915i
$635$	2.65985e8			1.03881
$636$		0			0
$637$			2.96718e8i			1.14796i
$638$	1.22383e8	+	4.25799e6i	0.471257	+	0.0163962i
$639$		0			0
$640$	−2.26740e8	−	5.63165e7i	−0.864943	−	0.214830i
$641$	2.82397e8			1.07222			0.536112	−	0.844147i	$-0.319893\pi$
$641$	2.82397e8			1.07222			0.536112	+	0.844147i	$0.319893\pi$
$642$		0			0
$643$	−3.25467e8			−1.22426			−0.612131	−	0.790757i	$-0.709687\pi$
$643$	−3.25467e8			−1.22426			−0.612131	+	0.790757i	$0.709687\pi$
$644$	9.64679e7	+	6.72084e6i	0.361181	+	0.0251632i
$645$		0			0
$646$	1.28982e7	−	3.70719e8i	0.0478445	−	1.37514i
$647$		−	2.67526e8i		−	0.987762i	−0.869529	−	0.493881i	$-0.835578\pi$
$647$		−	2.67526e8i		−	0.987762i	0.869529	−	0.493881i	$-0.164422\pi$
$648$		0			0
$649$	3.47092e8			1.26973
$650$	−7.17801e7	−	2.49740e6i	−0.261375	−	0.00909387i
$651$		0			0
$652$	7.64716e7	+	5.32771e6i	0.275904	+	0.0192220i
$653$		−	1.06717e8i		−	0.383259i	−0.981467	−	0.191630i	$-0.938623\pi$
$653$		−	1.06717e8i		−	0.383259i	0.981467	−	0.191630i	$-0.0613773\pi$
$654$		0			0
$655$			9.19809e7i			0.327321i
$656$	3.42508e7	+	4.79573e6i	0.121327	+	0.0169880i
$657$		0			0
$658$	3.81643e6	−	1.09691e8i	0.0133961	−	0.385030i
$659$	−1.93350e8			−0.675598			−0.337799	−	0.941218i	$-0.609682\pi$
$659$	−1.93350e8			−0.675598			−0.337799	+	0.941218i	$0.609682\pi$
$660$		0			0
$661$		−	2.70769e7i		−	0.0937550i	−0.998901	−	0.0468775i	$-0.985073\pi$
$661$		−	2.70769e7i		−	0.0937550i	0.998901	−	0.0468775i	$-0.0149270\pi$
$662$	8.62259e6	−	2.47829e8i	0.0297210	−	0.854238i
$663$		0			0
$664$	−1.21793e7	+	1.16309e8i	−0.0416025	+	0.397291i
$665$	−6.26934e7			−0.213185
$666$		0			0
$667$	2.28162e8			0.768893
$668$	1.49534e7	−	2.14635e8i	0.0501662	−	0.720063i
$669$		0			0
$670$	4.23036e6	+	147184.i	0.0140654	+	0.000489370i
$671$		−	3.45609e8i		−	1.14398i
$672$		0			0
$673$	−2.68785e8			−0.881779			−0.440890	−	0.897561i	$-0.645337\pi$
$673$	−2.68785e8			−0.881779			−0.440890	+	0.897561i	$0.645337\pi$
$674$	−1.22839e6	+	3.53062e7i	−0.00401195	+	0.115311i
$675$		0			0
$676$	1.89892e8	+	1.32296e7i	0.614706	+	0.0428260i
$677$		−	4.66230e8i		−	1.50257i	−0.659980	−	0.751283i	$-0.729435\pi$
$677$		−	4.66230e8i		−	1.50257i	0.659980	−	0.751283i	$-0.270565\pi$
$678$		0			0
$679$			6.13521e7i			0.195984i
$680$	−4.99360e8	−	5.22908e7i	−1.58813	−	0.166302i
$681$		0			0
$682$	6.78165e6	+	235950.i	0.0213788	+	0.000743819i
$683$	4.47811e8			1.40551			0.702753	−	0.711434i	$-0.251954\pi$
$683$	4.47811e8			1.40551			0.702753	+	0.711434i	$0.251954\pi$
$684$		0			0
$685$			1.52792e8i			0.475366i
$686$	−1.91238e8	−	6.65364e6i	−0.592382	−	0.0206104i
$687$		0			0
$688$	3.80484e8	+	5.32746e7i	1.16834	+	0.163589i
$689$	4.74890e8			1.45190
$690$		0			0
$691$	−3.86187e8			−1.17048			−0.585239	−	0.810860i	$-0.699000\pi$
$691$	−3.86187e8			−1.17048			−0.585239	+	0.810860i	$0.699000\pi$
$692$	−2.85197e7	+	4.09358e8i	−0.0860649	+	1.23534i
$693$		0			0
$694$	−3.93972e6	+	1.13235e8i	−0.0117865	+	0.338767i
$695$			4.24696e8i			1.26510i
$696$		0			0
$697$	7.43263e7			0.219505
$698$	−2.35684e8	−	8.20002e6i	−0.693049	−	0.0241129i
$699$		0			0
$700$	1.52754e6	−	2.19257e7i	0.00445348	−	0.0639232i
$701$			2.07974e8i			0.603747i	0.953348	+	0.301874i	$0.0976121\pi$
$701$			2.07974e8i			0.603747i	−0.953348	+	0.301874i	$0.902388\pi$
$702$		0			0
$703$		−	4.02239e8i		−	1.15776i
$704$	−2.43329e8	−	5.15257e7i	−0.697392	−	0.147675i
$705$		0			0
$706$	1.25380e7	−	3.60365e8i	0.0356297	−	1.02407i
$707$	−3.00195e7			−0.0849465
$708$		0			0
$709$			3.33724e7i			0.0936373i	0.998903	+	0.0468187i	$0.0149083\pi$
$709$			3.33724e7i			0.0936373i	−0.998903	+	0.0468187i	$0.985092\pi$
$710$	1.14568e7	−	3.29289e8i	0.0320101	−	0.920030i
$711$		0			0
$712$	1.63102e7	−	1.55758e8i	0.0451877	−	0.431529i
$713$	1.26432e7			0.0348811
$714$		0			0
$715$	2.95225e8			0.807672
$716$	9.93121e7	+	6.91900e6i	0.270560	+	0.0188497i
$717$		0			0
$718$	5.49267e7	+	1.91103e6i	0.148392	+	0.00516291i
$719$		−	3.41255e8i		−	0.918105i	−0.888409	−	0.459053i	$-0.848189\pi$
$719$		−	3.41255e8i		−	0.918105i	0.888409	−	0.459053i	$-0.151811\pi$
$720$		0			0
$721$	−1.73092e8			−0.461819
$722$	5.36863e6	−	1.54305e8i	0.0142644	−	0.409984i
$723$		0			0
$724$	−1.15640e7	+	1.65984e8i	−0.0304713	+	0.437371i
$725$		−	5.18577e7i		−	0.136082i
$726$		0			0
$727$		−	6.82590e8i		−	1.77646i	−0.459394	−	0.888232i	$-0.651934\pi$
$727$		−	6.82590e8i		−	1.77646i	0.459394	−	0.888232i	$-0.348066\pi$
$728$	−1.59116e7	+	1.51951e8i	−0.0412401	+	0.393830i
$729$		0			0
$730$	−1.83043e8	−	6.36850e6i	−0.470526	−	0.0163708i
$731$	8.25672e8			2.11376
$732$		0			0
$733$			1.82234e8i			0.462718i	0.972868	+	0.231359i	$0.0743173\pi$
$733$			1.82234e8i			0.462718i	−0.972868	+	0.231359i	$0.925683\pi$
$734$	−1.66197e8	−	5.78239e6i	−0.420276	−	0.0146224i
$735$		0			0
$736$	−4.56436e8	−	8.01805e7i	−1.14485	−	0.201111i
$737$	4.50643e6			0.0112572
$738$		0			0
$739$	2.03535e8			0.504319			0.252159	−	0.967686i	$-0.418859\pi$
$739$	2.03535e8			0.504319			0.252159	+	0.967686i	$0.418859\pi$
$740$	−5.43135e8	−	3.78398e7i	−1.34033	−	0.0933799i
$741$		0			0
$742$	−5.05304e6	+	1.45234e8i	−0.0123692	+	0.355514i
$743$			7.10372e7i			0.173189i	0.996244	+	0.0865943i	$0.0275984\pi$
$743$			7.10372e7i			0.173189i	−0.996244	+	0.0865943i	$0.972402\pi$
$744$		0			0
$745$	−1.52776e8			−0.369476
$746$	3.54681e8	+	1.23402e7i	0.854321	+	0.0297239i
$747$		0			0
$748$	−5.33241e8	−	3.71505e7i	−1.27415	−	0.0887687i
$749$		−	6.53122e7i		−	0.155435i
$750$		0			0
$751$		−	1.99498e8i		−	0.470998i	−0.971875	−	0.235499i	$-0.924328\pi$
$751$		−	1.99498e8i		−	0.470998i	0.971875	−	0.235499i	$-0.0756724\pi$
$752$	−7.29371e7	+	5.20912e8i	−0.171512	+	1.22493i
$753$		0			0
$754$	−1.25344e7	+	3.60261e8i	−0.0292408	+	0.840434i
$755$	−4.00009e8			−0.929457
$756$		0			0
$757$			8.43054e8i			1.94343i	0.236166	+	0.971713i	$0.424109\pi$
$757$			8.43054e8i			1.94343i	−0.236166	+	0.971713i	$0.575891\pi$
$758$	−1.36425e7	+	3.92111e8i	−0.0313246	+	0.900329i
$759$		0			0
$760$	2.98813e8	+	3.12903e7i	0.680705	+	0.0712803i
$761$	−3.01360e8			−0.683804			−0.341902	−	0.939736i	$-0.611071\pi$
$761$	−3.01360e8			−0.683804			−0.341902	+	0.939736i	$0.611071\pi$
$762$		0			0
$763$	9.56768e7			0.215394
$764$	−3.26588e7	+	4.68769e8i	−0.0732351	+	1.05118i
$765$		0			0
$766$	3.31014e8	+	1.15168e7i	0.736479	+	0.0256239i
$767$			1.02174e9i			2.26442i
$768$		0			0
$769$	3.06970e8			0.675020			0.337510	−	0.941322i	$-0.390415\pi$
$769$	3.06970e8			0.675020			0.337510	+	0.941322i	$0.390415\pi$
$770$	−3.14132e6	+	9.02875e7i	−0.00688082	+	0.197768i
$771$		0			0
$772$	−7.82433e8	−	5.45115e7i	−1.70057	−	0.118478i
$773$		−	1.51375e8i		−	0.327729i	−0.986483	−	0.163865i	$-0.947604\pi$
$773$		−	1.51375e8i		−	0.327729i	0.986483	−	0.163865i	$-0.0523960\pi$
$774$		0			0
$775$		−	2.87362e6i		−	0.00617339i
$776$	3.06209e7	−	2.92420e8i	0.0655289	−	0.625780i
$777$		0			0
$778$	−2.62576e8	−	9.13564e6i	−0.557591	−	0.0193999i
$779$	−4.44762e7			−0.0940839
$780$		0			0
$781$		−	3.50778e8i		−	0.736342i
$782$	−9.95343e8	−	3.46304e7i	−2.08139	−	0.0724165i
$783$		0			0
$784$	4.30934e8	+	6.03385e7i	0.894257	+	0.125212i
$785$	−9.49399e7			−0.196264
$786$		0			0
$787$	−2.14155e8			−0.439344			−0.219672	−	0.975574i	$-0.570499\pi$
$787$	−2.14155e8			−0.439344			−0.219672	+	0.975574i	$0.570499\pi$
$788$	2.86772e7	−	4.11620e8i	0.0586082	−	0.841235i
$789$		0			0
$790$	−2.87733e7	+	8.26999e8i	−0.0583591	+	1.67735i
$791$		−	1.91924e8i		−	0.387792i
$792$		0			0
$793$	1.01738e9			2.04016
$794$	5.49227e8	+	1.91089e7i	1.09721	+	0.0381746i
$795$		0			0
$796$	−103127.	+	1.48024e6i	−0.000204472	+	0.00293490i
$797$			2.71436e7i			0.0536157i	0.999641	+	0.0268079i	$0.00853423\pi$
$797$			2.71436e7i			0.0536157i	−0.999641	+	0.0268079i	$0.991466\pi$
$798$		0			0
$799$			1.13041e9i			2.21614i
$800$	−1.82238e7	+	1.03741e8i	−0.0355933	+	0.202619i
$801$		0			0
$802$	−9.04144e6	+	2.59868e8i	−0.0175273	+	0.503767i
$803$	−1.94988e8			−0.376584
$804$		0			0
$805$			1.68326e8i			0.322673i
$806$	−694573.	+	1.99633e7i	−0.00132652	+	0.0381266i
$807$		0			0
$808$	1.43081e8	+	1.49828e7i	0.271236	+	0.0284026i
$809$	3.65026e8			0.689411			0.344705	−	0.938711i	$-0.387979\pi$
$809$	3.65026e8			0.689411			0.344705	+	0.938711i	$0.387979\pi$
$810$		0			0
$811$	5.16038e8			0.967429			0.483714	−	0.875226i	$-0.339287\pi$
$811$	5.16038e8			0.967429			0.483714	+	0.875226i	$0.339287\pi$
$812$	−1.10044e8	−	7.66668e6i	−0.205541	−	0.0143199i
$813$		0			0
$814$	−5.79281e8	−	2.01546e7i	−1.07403	−	0.0373681i
$815$			1.33434e8i			0.246488i
$816$		0			0
$817$	−4.94075e8			−0.905998
$818$	2.83080e7	−	8.13624e8i	0.0517188	−	1.48650i
$819$		0			0
$820$	−4.18401e6	+	6.00553e7i	−0.00758841	+	0.108921i
$821$		−	5.88169e8i		−	1.06285i	−0.847105	−	0.531426i	$-0.821656\pi$
$821$		−	5.88169e8i		−	1.06285i	0.847105	−	0.531426i	$-0.178344\pi$
$822$		0			0
$823$			5.86037e8i			1.05130i	0.850702	+	0.525649i	$0.176177\pi$
$823$			5.86037e8i			1.05130i	−0.850702	+	0.525649i	$0.823823\pi$
$824$	8.25003e8	+	8.63905e7i	1.47460	+	0.154413i
$825$		0			0
$826$	−3.12476e8	−	1.08718e7i	−0.554468	−	0.0192913i
$827$	6.70313e8			1.18512			0.592558	−	0.805528i	$-0.298118\pi$
$827$	6.70313e8			1.18512			0.592558	+	0.805528i	$0.298118\pi$
$828$		0			0
$829$		−	2.28039e8i		−	0.400262i	−0.979769	−	0.200131i	$-0.935863\pi$
$829$		−	2.28039e8i		−	0.400262i	0.979769	−	0.200131i	$-0.0641368\pi$
$830$	−2.03439e8	−	7.07814e6i	−0.355795	−	0.0123790i
$831$		0			0
$832$	1.51678e8	−	7.16295e8i	0.263361	−	1.24372i
$833$	9.35152e8			1.61788
$834$		0			0
$835$	3.74514e8			0.643293
$836$	3.19087e8	+	2.22305e7i	0.546123	+	0.0380480i
$837$		0			0
$838$	2.00145e7	−	5.75255e8i	0.0340105	−	0.977525i
$839$		−	539319.i		−	0.000913187i	−1.00000		0.000456593i	$-0.999855\pi$
$839$		−	539319.i		−	0.000913187i	1.00000		0.000456593i	$-0.000145338\pi$
$840$		0			0
$841$	3.34552e8			0.562439
$842$	6.96357e8	+	2.42280e7i	1.16653	+	0.0405864i
$843$		0			0
$844$	4.13639e8	+	2.88179e7i	0.688009	+	0.0479330i
$845$			3.31341e8i			0.549168i
$846$		0			0
$847$		−	9.30898e7i		−	0.153198i
$848$	9.65704e7	−	6.89700e8i	0.158364	−	1.13103i
$849$		0			0
$850$	−7.87096e6	+	2.26226e8i	−0.0128165	+	0.368372i
$851$	−1.07997e9			−1.75236
$852$		0			0
$853$		−	7.14484e8i		−	1.15119i	−0.817737	−	0.575593i	$-0.804771\pi$
$853$		−	7.14484e8i		−	1.15119i	0.817737	−	0.575593i	$-0.195229\pi$
$854$	−1.08254e7	+	3.11141e8i	−0.0173808	+	0.499556i
$855$		0			0
$856$	−3.25974e7	+	3.11295e8i	−0.0519710	+	0.496307i
$857$	−2.30104e8			−0.365579			−0.182789	−	0.983152i	$-0.558513\pi$
$857$	−2.30104e8			−0.365579			−0.182789	+	0.983152i	$0.558513\pi$
$858$		0			0
$859$	−9.52885e8			−1.50335			−0.751677	−	0.659532i	$-0.770755\pi$
$859$	−9.52885e8			−1.50335			−0.751677	+	0.659532i	$0.770755\pi$
$860$	−4.64791e7	+	6.67140e8i	−0.0730739	+	1.04887i
$861$		0			0
$862$	5.70355e8	+	1.98440e7i	0.890479	+	0.0309819i
$863$		−	1.14673e9i		−	1.78413i	−0.451904	−	0.892067i	$-0.649255\pi$
$863$		−	1.14673e9i		−	1.78413i	0.451904	−	0.892067i	$-0.350745\pi$
$864$		0			0
$865$	−7.14285e8			−1.10363
$866$	−4.29852e7	+	1.23547e9i	−0.0661858	+	1.90230i
$867$		0			0
$868$	−6.09792e6	−	424837.i	−0.00932444	−	0.000649626i
$869$			8.80969e8i			1.34246i
$870$		0			0
$871$			1.32657e7i			0.0200759i
$872$	−4.56020e8	−	4.77523e7i	−0.687756	−	0.0720187i
$873$		0			0
$874$	5.95605e8	+	2.07225e7i	0.892122	+	0.0310391i
$875$	2.24227e8			0.334706
$876$		0			0
$877$		−	8.56646e8i		−	1.27000i	−0.772513	−	0.634999i	$-0.781001\pi$
$877$		−	8.56646e8i		−	1.27000i	0.772513	−	0.634999i	$-0.218999\pi$
$878$	−8.38757e8	−	2.91824e7i	−1.23923	−	0.0431159i
$879$		0			0
$880$	6.00349e7	−	4.28766e8i	0.0880959	−	0.629176i
$881$	−7.23838e8			−1.05856			−0.529278	−	0.848449i	$-0.677537\pi$
$881$	−7.23838e8			−1.05856			−0.529278	+	0.848449i	$0.677537\pi$
$882$		0			0
$883$	−2.02781e8			−0.294541			−0.147270	−	0.989096i	$-0.547049\pi$
$883$	−2.02781e8			−0.294541			−0.147270	+	0.989096i	$0.547049\pi$
$884$	1.09361e8	−	1.56972e9i	0.158309	−	2.27229i
$885$		0			0
$886$	−8.13207e6	+	2.33731e8i	−0.0116923	+	0.336059i
$887$			5.63272e8i			0.807137i	0.914950	+	0.403568i	$0.132230\pi$
$887$			5.63272e8i			0.807137i	−0.914950	+	0.403568i	$0.867770\pi$
$888$		0			0
$889$	−2.55085e8			−0.363061
$890$	2.72440e8	+	9.47886e6i	0.386457	+	0.0134458i
$891$		0			0
$892$	5.44150e7	−	7.81048e8i	0.0766697	−	1.10048i
$893$		−	6.76429e8i		−	0.949878i
$894$		0			0
$895$			1.73289e8i			0.241714i
$896$	2.17448e8	+	5.40087e7i	0.302295	+	0.0750827i
$897$		0			0
$898$	9.96990e6	−	2.86554e8i	0.0137677	−	0.395710i
$899$	−1.44226e7			−0.0198501
$900$		0			0
$901$		−	1.49669e9i		−	2.04625i
$902$	−2.22853e6	+	6.40521e7i	−0.00303668	+	0.0872798i
$903$		0			0
$904$	−9.57893e7	+	9.14758e8i	−0.129662	+	1.23823i
$905$	−2.89624e8			−0.390740
$906$		0			0
$907$	2.50169e8			0.335282			0.167641	−	0.985848i	$-0.446385\pi$
$907$	2.50169e8			0.335282			0.167641	+	0.985848i	$0.446385\pi$
$908$	−6.37329e8	−	4.44022e7i	−0.851346	−	0.0593126i
$909$		0			0
$910$	−2.65782e8	−	9.24719e6i	−0.352696	−	0.0122712i
$911$			8.98125e8i			1.18790i	0.804500	+	0.593952i	$0.202433\pi$
$911$			8.98125e8i			1.18790i	−0.804500	+	0.593952i	$0.797567\pi$
$912$		0			0
$913$	−2.16716e8			−0.284759
$914$	−4.71189e7	+	1.35429e9i	−0.0617102	+	1.77367i
$915$		0			0
$916$	4.86702e7	−	6.98589e8i	0.0633252	−	0.908941i
$917$		−	8.82116e7i		−	0.114398i
$918$		0			0
$919$			1.07862e9i			1.38971i	0.719152	+	0.694853i	$0.244530\pi$
$919$			1.07862e9i			1.38971i	−0.719152	+	0.694853i	$0.755470\pi$
$920$	8.40115e7	−	8.02284e8i	0.107889	−	1.03030i
$921$		0			0
$922$	1.05303e9	+	3.66374e7i	1.34353	+	0.0467446i
$923$	1.03260e9			1.31318
$924$		0			0
$925$			2.45461e8i			0.310140i
$926$	7.76272e8	+	2.70084e7i	0.977644	+	0.0340146i
$927$		0			0
$928$	5.20672e8	+	9.14644e7i	0.651508	+	0.114448i
$929$	−3.07935e8			−0.384071			−0.192035	−	0.981388i	$-0.561509\pi$
$929$	−3.07935e8			−0.384071			−0.192035	+	0.981388i	$0.561509\pi$
$930$		0			0
$931$	−5.59587e8			−0.693456
$932$	−8.23938e8	−	5.74031e7i	−1.01776	−	0.0709067i
$933$		0			0
$934$	2.82369e7	−	8.11580e8i	0.0346558	−	0.996072i
$935$		−	9.30447e8i		−	1.13830i
$936$		0			0
$937$	−1.35456e9			−1.64657			−0.823283	−	0.567632i	$-0.807860\pi$
$937$	−1.35456e9			−1.64657			−0.823283	+	0.567632i	$0.807860\pi$
$938$	−4.05700e6	−	141153.i	−0.00491583	−	0.000171034i
$939$		0			0
$940$	−9.13368e8	−	6.36336e7i	−1.09967	−	0.0766131i
$941$		−	6.47945e7i		−	0.0777624i	−0.999244	−	0.0388812i	$-0.987621\pi$
$941$		−	6.47945e7i		−	0.0777624i	0.999244	−	0.0388812i	$-0.0123794\pi$
$942$		0			0
$943$			1.19414e8i			0.142404i
$944$	1.48392e9	+	2.07775e8i	1.76398	+	0.246989i
$945$		0			0
$946$	−2.47562e7	+	7.11539e8i	−0.0292422	+	0.840476i
$947$	−1.49171e9			−1.75644			−0.878222	−	0.478252i	$-0.841270\pi$
$947$	−1.49171e9			−1.75644			−0.878222	+	0.478252i	$0.841270\pi$
$948$		0			0
$949$		−	5.73992e8i		−	0.671595i
$950$	4.70992e6	−	1.35372e8i	0.00549341	−	0.157891i
$951$		0			0
$952$	4.78897e8	+	5.01479e7i	0.555049	+	0.0581222i
$953$	−3.76409e8			−0.434892			−0.217446	−	0.976072i	$-0.569773\pi$
$953$	−3.76409e8			−0.434892			−0.217446	+	0.976072i	$0.569773\pi$
$954$		0			0
$955$	−8.17950e8			−0.939110
$956$	5.03519e7	−	7.22728e8i	0.0576291	−	0.827182i
$957$		0			0
$958$	−1.23027e9	−	4.28042e7i	−1.39928	−	0.0486844i
$959$		−	1.46531e8i		−	0.166139i
$960$		0			0
$961$	8.86704e8			0.999099
$962$	5.93296e7	−	1.70525e9i	0.0666418	−	1.91541i
$963$		0			0
$964$	3.94209e8	+	2.74642e7i	0.440043	+	0.0306575i
$965$		−	1.36526e9i		−	1.51926i
$966$		0			0
$967$		−	2.25279e7i		−	0.0249139i	−0.999922	−	0.0124569i	$-0.996035\pi$
$967$		−	2.25279e7i		−	0.0249139i	0.999922	−	0.0124569i	$-0.00396527\pi$
$968$	−4.64612e7	+	4.43690e8i	−0.0512229	+	0.489163i
$969$		0			0
$970$	5.11480e8	+	1.77956e7i	0.560420	+	0.0194984i
$971$	−1.28142e9			−1.39970			−0.699849	−	0.714291i	$-0.746749\pi$
$971$	−1.28142e9			−1.39970			−0.699849	+	0.714291i	$0.746749\pi$
$972$		0			0
$973$		−	4.07292e8i		−	0.442148i
$974$	7.33996e8	+	2.55375e7i	0.794359	+	0.0276377i
$975$		0			0
$976$	2.06887e8	−	1.47758e9i	0.222528	−	1.58928i
$977$	−7.05116e8			−0.756096			−0.378048	−	0.925786i	$-0.623405\pi$
$977$	−7.05116e8			−0.756096			−0.378048	+	0.925786i	$0.623405\pi$
$978$		0			0
$979$	2.90220e8			0.309299
$980$	−5.26420e7	+	7.55599e8i	−0.0559312	+	0.802811i
$981$		0			0
$982$	−2.41987e7	+	6.95516e8i	−0.0255539	+	0.734467i
$983$		−	7.74258e7i		−	0.0815126i	−0.999169	−	0.0407563i	$-0.987023\pi$
$983$		−	7.74258e7i		−	0.0815126i	0.999169	−	0.0407563i	$-0.0129767\pi$
$984$		0			0
$985$	7.18231e8			0.751546
$986$	1.13542e9	+	3.95040e7i	1.18447	+	0.0412108i
$987$		0			0
$988$	−6.54407e7	+	9.39305e8i	−0.0678542	+	0.973948i
$989$			1.32654e9i			1.37130i
$990$		0			0
$991$			8.16099e8i			0.838537i	0.907862	+	0.419268i	$0.137713\pi$
$991$			8.16099e8i			0.838537i	−0.907862	+	0.419268i	$0.862287\pi$
$992$	2.88522e7	+	5.06836e6i	0.0295559	+	0.00519197i
$993$		0			0
$994$	−1.09873e7	+	3.15795e8i	−0.0111874	+	0.321548i
$995$	−2.58286e6			−0.00262199
$996$		0			0
$997$			9.27018e8i			0.935412i	0.883884	+	0.467706i	$0.154919\pi$
$997$			9.27018e8i			0.935412i	−0.883884	+	0.467706i	$0.845081\pi$
$998$	1.00828e7	−	2.89797e8i	0.0101435	−	0.291543i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.c.19.8		12
3.2	odd	2		24.7.b.a.19.5	✓	12
4.3	odd	2		288.7.b.d.271.3		12
8.3	odd	2	inner	72.7.b.c.19.7		12
8.5	even	2		288.7.b.d.271.10		12
12.11	even	2		96.7.b.a.79.11		12
24.5	odd	2		96.7.b.a.79.8		12
24.11	even	2		24.7.b.a.19.6	yes	12
48.5	odd	4		768.7.g.l.511.11		24
48.11	even	4		768.7.g.l.511.9		24
48.29	odd	4		768.7.g.l.511.10		24
48.35	even	4		768.7.g.l.511.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.b.a.19.5	✓	12	3.2	odd	2
24.7.b.a.19.6	yes	12	24.11	even	2
72.7.b.c.19.7		12	8.3	odd	2	inner
72.7.b.c.19.8		12	1.1	even	1	trivial
96.7.b.a.79.8		12	24.5	odd	2
96.7.b.a.79.11		12	12.11	even	2
288.7.b.d.271.3		12	4.3	odd	2
288.7.b.d.271.10		12	8.5	even	2
768.7.g.l.511.9		24	48.11	even	4
768.7.g.l.511.10		24	48.29	odd	4
768.7.g.l.511.11		24	48.5	odd	4
768.7.g.l.511.12		24	48.35	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.278171 + 7.99516i) q^{2} +(-63.8452 - 4.44805i) q^{4} -111.403i q^{5} +106.838i q^{7} +(53.3228 - 509.216i) q^{8} +O(q^{10})\)	\(q+(-0.278171 + 7.99516i) q^{2} +(-63.8452 - 4.44805i) q^{4} -111.403i q^{5} +106.838i q^{7} +(53.3228 - 509.216i) q^{8} +(890.684 + 30.9891i) q^{10} +948.811 q^{11} +2793.04i q^{13} +(-854.185 - 29.7192i) q^{14} +(4056.43 + 567.973i) q^{16} +8802.70 q^{17} -5267.46 q^{19} +(-495.525 + 7112.54i) q^{20} +(-263.932 + 7585.89i) q^{22} +14142.6i q^{23} +3214.40 q^{25} +(-22330.8 - 776.943i) q^{26} +(475.219 - 6821.08i) q^{28} -16132.9i q^{29} -893.982i q^{31} +(-5669.42 + 32273.8i) q^{32} +(-2448.66 + 70379.0i) q^{34} +11902.0 q^{35} +76362.9i q^{37} +(1465.26 - 42114.2i) q^{38} +(-56728.1 - 5940.31i) q^{40} +8443.58 q^{41} +93797.7 q^{43} +(-60577.0 - 4220.35i) q^{44} +(-113073. - 3934.07i) q^{46} +128416. i q^{47} +106235. q^{49} +(-894.153 + 25699.6i) q^{50} +(12423.6 - 178322. i) q^{52} -170026. i q^{53} -105700. i q^{55} +(54403.4 + 5696.88i) q^{56} +(128985. + 4487.72i) q^{58} +365818. q^{59} -364256. i q^{61} +(7147.53 + 248.680i) q^{62} +(-256457. - 54305.6i) q^{64} +311153. q^{65} +4749.56 q^{67} +(-562010. - 39154.8i) q^{68} +(-3310.80 + 95158.6i) q^{70} -369703. i q^{71} -205508. q^{73} +(-610534. - 21242.0i) q^{74} +(336302. + 23429.9i) q^{76} +101369. i q^{77} +928499. i q^{79} +(63273.9 - 451898. i) q^{80} +(-2348.76 + 67507.8i) q^{82} -228408. q^{83} -980646. i q^{85} +(-26091.8 + 749927. i) q^{86} +(50593.2 - 483149. i) q^{88} +305878. q^{89} -298402. q^{91} +(62907.0 - 902939. i) q^{92} +(-1.02671e6 - 35721.8i) q^{94} +586810. i q^{95} +574256. q^{97} +(-29551.4 + 849364. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) \) 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8} + 2172 q^{10} - 2720 q^{11} + 6444 q^{14} + 11640 q^{16} + 4888 q^{17} + 3936 q^{19} + 31608 q^{20} - 60432 q^{22} - 27204 q^{25} - 53952 q^{26} - 57072 q^{28} - 109480 q^{32} + 47388 q^{34} - 162336 q^{35} + 89080 q^{38} + 72120 q^{40} + 54280 q^{41} - 49824 q^{43} - 229184 q^{44} + 171864 q^{46} - 304644 q^{49} + 500078 q^{50} + 256848 q^{52} + 699816 q^{56} - 409524 q^{58} + 886144 q^{59} - 691356 q^{62} - 500640 q^{64} - 473376 q^{65} + 1565952 q^{67} - 669104 q^{68} + 473784 q^{70} + 555480 q^{73} + 753720 q^{74} - 293136 q^{76} + 251616 q^{80} + 2317716 q^{82} - 2497760 q^{83} - 476024 q^{86} + 971424 q^{88} - 367400 q^{89} - 4475808 q^{91} + 377376 q^{92} - 2642568 q^{94} - 1165656 q^{97} - 182674 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8 + 2172 * q^10 - 2720 * q^11 + 6444 * q^14 + 11640 * q^16 + 4888 * q^17 + 3936 * q^19 + 31608 * q^20 - 60432 * q^22 - 27204 * q^25 - 53952 * q^26 - 57072 * q^28 - 109480 * q^32 + 47388 * q^34 - 162336 * q^35 + 89080 * q^38 + 72120 * q^40 + 54280 * q^41 - 49824 * q^43 - 229184 * q^44 + 171864 * q^46 - 304644 * q^49 + 500078 * q^50 + 256848 * q^52 + 699816 * q^56 - 409524 * q^58 + 886144 * q^59 - 691356 * q^62 - 500640 * q^64 - 473376 * q^65 + 1565952 * q^67 - 669104 * q^68 + 473784 * q^70 + 555480 * q^73 + 753720 * q^74 - 293136 * q^76 + 251616 * q^80 + 2317716 * q^82 - 2497760 * q^83 - 476024 * q^86 + 971424 * q^88 - 367400 * q^89 - 4475808 * q^91 + 377376 * q^92 - 2642568 * q^94 - 1165656 * q^97 - 182674 * q^98

Introduction

L-functions

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