LMFDB - Embedded newform 25.7.c.b.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,7,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, 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:	$5.75135209050$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	25.18
Dual form			25.7.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00000 - 3.00000i) q^{2} +(-33.0000 - 33.0000i) q^{3} +46.0000i q^{4} -198.000 q^{6} +(-207.000 + 207.000i) q^{7} +(330.000 + 330.000i) q^{8} +1449.00i q^{9} +O(q^{10})$	\(q+(3.00000 - 3.00000i) q^{2} +(-33.0000 - 33.0000i) q^{3} +46.0000i q^{4} -198.000 q^{6} +(-207.000 + 207.000i) q^{7} +(330.000 + 330.000i) q^{8} +1449.00i q^{9} -1188.00 q^{11} +(1518.00 - 1518.00i) q^{12} +(-1548.00 - 1548.00i) q^{13} +1242.00i q^{14} -964.000 q^{16} +(-3252.00 + 3252.00i) q^{17} +(4347.00 + 4347.00i) q^{18} -5060.00i q^{19} +13662.0 q^{21} +(-3564.00 + 3564.00i) q^{22} +(-5313.00 - 5313.00i) q^{23} -21780.0i q^{24} -9288.00 q^{26} +(23760.0 - 23760.0i) q^{27} +(-9522.00 - 9522.00i) q^{28} +8910.00i q^{29} +25432.0 q^{31} +(-24012.0 + 24012.0i) q^{32} +(39204.0 + 39204.0i) q^{33} +19512.0i q^{34} -66654.0 q^{36} +(-20592.0 + 20592.0i) q^{37} +(-15180.0 - 15180.0i) q^{38} +102168. i q^{39} -19008.0 q^{41} +(40986.0 - 40986.0i) q^{42} +(-80343.0 - 80343.0i) q^{43} -54648.0i q^{44} -31878.0 q^{46} +(-16137.0 + 16137.0i) q^{47} +(31812.0 + 31812.0i) q^{48} +31951.0i q^{49} +214632. q^{51} +(71208.0 - 71208.0i) q^{52} +(155892. + 155892. i) q^{53} -142560. i q^{54} -136620. q^{56} +(-166980. + 166980. i) q^{57} +(26730.0 + 26730.0i) q^{58} -360180. i q^{59} +178112. q^{61} +(76296.0 - 76296.0i) q^{62} +(-299943. - 299943. i) q^{63} +82376.0i q^{64} +235224. q^{66} +(240273. - 240273. i) q^{67} +(-149592. - 149592. i) q^{68} +350658. i q^{69} -617328. q^{71} +(-478170. + 478170. i) q^{72} +(306612. + 306612. i) q^{73} +123552. i q^{74} +232760. q^{76} +(245916. - 245916. i) q^{77} +(306504. + 306504. i) q^{78} +232760. i q^{79} -511839. q^{81} +(-57024.0 + 57024.0i) q^{82} +(134097. + 134097. i) q^{83} +628452. i q^{84} -482058. q^{86} +(294030. - 294030. i) q^{87} +(-392040. - 392040. i) q^{88} -270270. i q^{89} +640872. q^{91} +(244398. - 244398. i) q^{92} +(-839256. - 839256. i) q^{93} +96822.0i q^{94} +1.58479e6 q^{96} +(-810612. + 810612. i) q^{97} +(95853.0 + 95853.0i) q^{98} -1.72141e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} - 66 q^{3} - 396 q^{6} - 414 q^{7} + 660 q^{8}+O(q^{10}) $ 2 * q + 6 * q^2 - 66 * q^3 - 396 * q^6 - 414 * q^7 + 660 * q^8	$ 2 q + 6 q^{2} - 66 q^{3} - 396 q^{6} - 414 q^{7} + 660 q^{8} - 2376 q^{11} + 3036 q^{12} - 3096 q^{13} - 1928 q^{16} - 6504 q^{17} + 8694 q^{18} + 27324 q^{21} - 7128 q^{22} - 10626 q^{23} - 18576 q^{26} + 47520 q^{27} - 19044 q^{28} + 50864 q^{31} - 48024 q^{32} + 78408 q^{33} - 133308 q^{36} - 41184 q^{37} - 30360 q^{38} - 38016 q^{41} + 81972 q^{42} - 160686 q^{43} - 63756 q^{46} - 32274 q^{47} + 63624 q^{48} + 429264 q^{51} + 142416 q^{52} + 311784 q^{53} - 273240 q^{56} - 333960 q^{57} + 53460 q^{58} + 356224 q^{61} + 152592 q^{62} - 599886 q^{63} + 470448 q^{66} + 480546 q^{67} - 299184 q^{68} - 1234656 q^{71} - 956340 q^{72} + 613224 q^{73} + 465520 q^{76} + 491832 q^{77} + 613008 q^{78} - 1023678 q^{81} - 114048 q^{82} + 268194 q^{83} - 964116 q^{86} + 588060 q^{87} - 784080 q^{88} + 1281744 q^{91} + 488796 q^{92} - 1678512 q^{93} + 3169584 q^{96} - 1621224 q^{97} + 191706 q^{98}+O(q^{100}) $ 2 * q + 6 * q^2 - 66 * q^3 - 396 * q^6 - 414 * q^7 + 660 * q^8 - 2376 * q^11 + 3036 * q^12 - 3096 * q^13 - 1928 * q^16 - 6504 * q^17 + 8694 * q^18 + 27324 * q^21 - 7128 * q^22 - 10626 * q^23 - 18576 * q^26 + 47520 * q^27 - 19044 * q^28 + 50864 * q^31 - 48024 * q^32 + 78408 * q^33 - 133308 * q^36 - 41184 * q^37 - 30360 * q^38 - 38016 * q^41 + 81972 * q^42 - 160686 * q^43 - 63756 * q^46 - 32274 * q^47 + 63624 * q^48 + 429264 * q^51 + 142416 * q^52 + 311784 * q^53 - 273240 * q^56 - 333960 * q^57 + 53460 * q^58 + 356224 * q^61 + 152592 * q^62 - 599886 * q^63 + 470448 * q^66 + 480546 * q^67 - 299184 * q^68 - 1234656 * q^71 - 956340 * q^72 + 613224 * q^73 + 465520 * q^76 + 491832 * q^77 + 613008 * q^78 - 1023678 * q^81 - 114048 * q^82 + 268194 * q^83 - 964116 * q^86 + 588060 * q^87 - 784080 * q^88 + 1281744 * q^91 + 488796 * q^92 - 1678512 * q^93 + 3169584 * q^96 - 1621224 * q^97 + 191706 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	3.00000	−	3.00000i	0.375000	−	0.375000i	−0.494295	−	0.869295i	$-0.664574\pi$
$2$	3.00000	−	3.00000i	0.375000	−	0.375000i	0.869295	+	0.494295i	$0.164574\pi$
$3$	−33.0000	−	33.0000i	−1.22222	−	1.22222i	−0.966840	−	0.255382i	$-0.917799\pi$
$3$	−33.0000	−	33.0000i	−1.22222	−	1.22222i	−0.255382	−	0.966840i	$-0.582201\pi$
$4$			46.0000i			0.718750i
$5$		0			0
$5$		0			0
$6$	−198.000			−0.916667
$7$	−207.000	+	207.000i	−0.603499	+	0.603499i	−0.941239	−	0.337741i	$-0.890337\pi$
$7$	−207.000	+	207.000i	−0.603499	+	0.603499i	0.337741	+	0.941239i	$0.390337\pi$
$8$	330.000	+	330.000i	0.644531	+	0.644531i
$9$			1449.00i			1.98765i
$10$		0			0
$11$	−1188.00			−0.892562			−0.446281	−	0.894893i	$-0.647252\pi$
$11$	−1188.00			−0.892562			−0.446281	+	0.894893i	$0.647252\pi$
$12$	1518.00	−	1518.00i	0.878472	−	0.878472i
$13$	−1548.00	−	1548.00i	−0.704597	−	0.704597i	0.260797	−	0.965394i	$-0.416015\pi$
$13$	−1548.00	−	1548.00i	−0.704597	−	0.704597i	−0.965394	+	0.260797i	$0.916015\pi$
$14$			1242.00i			0.452624i
$15$		0			0
$16$	−964.000			−0.235352
$17$	−3252.00	+	3252.00i	−0.661917	+	0.661917i	−0.955832	−	0.293914i	$-0.905042\pi$
$17$	−3252.00	+	3252.00i	−0.661917	+	0.661917i	0.293914	+	0.955832i	$0.405042\pi$
$18$	4347.00	+	4347.00i	0.745370	+	0.745370i
$19$		−	5060.00i		−	0.737717i	−0.929486	−	0.368858i	$-0.879749\pi$
$19$		−	5060.00i		−	0.737717i	0.929486	−	0.368858i	$-0.120251\pi$
$20$		0			0
$21$	13662.0			1.47522
$22$	−3564.00	+	3564.00i	−0.334711	+	0.334711i
$23$	−5313.00	−	5313.00i	−0.436673	−	0.436673i	0.454218	−	0.890891i	$-0.349919\pi$
$23$	−5313.00	−	5313.00i	−0.436673	−	0.436673i	−0.890891	+	0.454218i	$0.849919\pi$
$24$		−	21780.0i		−	1.57552i
$25$		0			0
$26$	−9288.00			−0.528448
$27$	23760.0	−	23760.0i	1.20713	−	1.20713i
$28$	−9522.00	−	9522.00i	−0.433765	−	0.433765i
$29$			8910.00i			0.365329i	0.983175	+	0.182664i	$0.0584722\pi$
$29$			8910.00i			0.365329i	−0.983175	+	0.182664i	$0.941528\pi$
$30$		0			0
$31$	25432.0			0.853681			0.426840	−	0.904327i	$-0.359627\pi$
$31$	25432.0			0.853681			0.426840	+	0.904327i	$0.359627\pi$
$32$	−24012.0	+	24012.0i	−0.732788	+	0.732788i
$33$	39204.0	+	39204.0i	1.09091	+	1.09091i
$34$			19512.0i			0.496438i
$35$		0			0
$36$	−66654.0			−1.42863
$37$	−20592.0	+	20592.0i	−0.406531	+	0.406531i	−0.880527	−	0.473996i	$-0.842811\pi$
$37$	−20592.0	+	20592.0i	−0.406531	+	0.406531i	0.473996	+	0.880527i	$0.342811\pi$
$38$	−15180.0	−	15180.0i	−0.276644	−	0.276644i
$39$			102168.i			1.72235i
$40$		0			0
$41$	−19008.0			−0.275794			−0.137897	−	0.990447i	$-0.544034\pi$
$41$	−19008.0			−0.275794			−0.137897	+	0.990447i	$0.544034\pi$
$42$	40986.0	−	40986.0i	0.553207	−	0.553207i
$43$	−80343.0	−	80343.0i	−1.01051	−	1.01051i	−0.999944	−	0.0105707i	$-0.996635\pi$
$43$	−80343.0	−	80343.0i	−1.01051	−	1.01051i	−0.0105707	−	0.999944i	$-0.503365\pi$
$44$		−	54648.0i		−	0.641529i
$45$		0			0
$46$	−31878.0			−0.327505
$47$	−16137.0	+	16137.0i	−0.155428	+	0.155428i	−0.780537	−	0.625109i	$-0.785054\pi$
$47$	−16137.0	+	16137.0i	−0.155428	+	0.155428i	0.625109	+	0.780537i	$0.285054\pi$
$48$	31812.0	+	31812.0i	0.287652	+	0.287652i
$49$			31951.0i			0.271579i
$50$		0			0
$51$	214632.			1.61802
$52$	71208.0	−	71208.0i	0.506429	−	0.506429i
$53$	155892.	+	155892.i	1.04712	+	1.04712i	0.998834	+	0.0482859i	$0.0153759\pi$
$53$	155892.	+	155892.i	1.04712	+	1.04712i	0.0482859	+	0.998834i	$0.484624\pi$
$54$		−	142560.i		−	0.905350i
$55$		0			0
$56$	−136620.			−0.777947
$57$	−166980.	+	166980.i	−0.901654	+	0.901654i
$58$	26730.0	+	26730.0i	0.136998	+	0.136998i
$59$		−	360180.i		−	1.75373i	−0.480734	−	0.876867i	$-0.659630\pi$
$59$		−	360180.i		−	1.75373i	0.480734	−	0.876867i	$-0.340370\pi$
$60$		0			0
$61$	178112.			0.784700			0.392350	−	0.919816i	$-0.371662\pi$
$61$	178112.			0.784700			0.392350	+	0.919816i	$0.371662\pi$
$62$	76296.0	−	76296.0i	0.320130	−	0.320130i
$63$	−299943.	−	299943.i	−1.19955	−	1.19955i
$64$			82376.0i			0.314240i
$65$		0			0
$66$	235224.			0.818182
$67$	240273.	−	240273.i	0.798878	−	0.798878i	−0.184040	−	0.982919i	$-0.558918\pi$
$67$	240273.	−	240273.i	0.798878	−	0.798878i	0.982919	+	0.184040i	$0.0589178\pi$
$68$	−149592.	−	149592.i	−0.475753	−	0.475753i
$69$			350658.i			1.06742i
$70$		0			0
$71$	−617328.			−1.72481			−0.862404	−	0.506220i	$-0.831042\pi$
$71$	−617328.			−1.72481			−0.862404	+	0.506220i	$0.831042\pi$
$72$	−478170.	+	478170.i	−1.28111	+	1.28111i
$73$	306612.	+	306612.i	0.788171	+	0.788171i	0.981194	−	0.193023i	$-0.0618292\pi$
$73$	306612.	+	306612.i	0.788171	+	0.788171i	−0.193023	+	0.981194i	$0.561829\pi$
$74$			123552.i			0.304898i
$75$		0			0
$76$	232760.			0.530234
$77$	245916.	−	245916.i	0.538660	−	0.538660i
$78$	306504.	+	306504.i	0.645881	+	0.645881i
$79$			232760.i			0.472092i	0.971742	+	0.236046i	$0.0758517\pi$
$79$			232760.i			0.472092i	−0.971742	+	0.236046i	$0.924148\pi$
$80$		0			0
$81$	−511839.			−0.963115
$82$	−57024.0	+	57024.0i	−0.103423	+	0.103423i
$83$	134097.	+	134097.i	0.234523	+	0.234523i	0.814577	−	0.580055i	$-0.196969\pi$
$83$	134097.	+	134097.i	0.234523	+	0.234523i	−0.580055	+	0.814577i	$0.696969\pi$
$84$			628452.i			1.06031i
$85$		0			0
$86$	−482058.			−0.757886
$87$	294030.	−	294030.i	0.446513	−	0.446513i
$88$	−392040.	−	392040.i	−0.575284	−	0.575284i
$89$		−	270270.i		−	0.383379i	−0.981456	−	0.191689i	$-0.938603\pi$
$89$		−	270270.i		−	0.383379i	0.981456	−	0.191689i	$-0.0613966\pi$
$90$		0			0
$91$	640872.			0.850447
$92$	244398.	−	244398.i	0.313859	−	0.313859i
$93$	−839256.	−	839256.i	−1.04339	−	1.04339i
$94$			96822.0i			0.116571i
$95$		0			0
$96$	1.58479e6			1.79126
$97$	−810612.	+	810612.i	−0.888174	+	0.888174i	−0.994348	−	0.106174i	$-0.966140\pi$
$97$	−810612.	+	810612.i	−0.888174	+	0.888174i	0.106174	+	0.994348i	$0.466140\pi$
$98$	95853.0	+	95853.0i	0.101842	+	0.101842i
$99$		−	1.72141e6i		−	1.77410i
$100$		0			0
$101$	−1.76240e6			−1.71057			−0.855283	−	0.518161i	$-0.826617\pi$
$101$	−1.76240e6			−1.71057			−0.855283	+	0.518161i	$0.826617\pi$
$102$	643896.	−	643896.i	0.606758	−	0.606758i
$103$	938817.	+	938817.i	0.859151	+	0.859151i	0.991238	−	0.132088i	$-0.0421680\pi$
$103$	938817.	+	938817.i	0.859151	+	0.859151i	−0.132088	+	0.991238i	$0.542168\pi$
$104$		−	1.02168e6i		−	0.908270i
$105$		0			0
$106$	935352.			0.785340
$107$	−1.52166e6	+	1.52166e6i	−1.24213	+	1.24213i	−0.283008	+	0.959118i	$0.591332\pi$
$107$	−1.52166e6	+	1.52166e6i	−1.24213	+	1.24213i	−0.959118	+	0.283008i	$0.908668\pi$
$108$	1.09296e6	+	1.09296e6i	0.867627	+	0.867627i
$109$			117920.i			0.0910559i	0.998963	+	0.0455279i	$0.0144970\pi$
$109$			117920.i			0.0910559i	−0.998963	+	0.0455279i	$0.985503\pi$
$110$		0			0
$111$	1.35907e6			0.993742
$112$	199548.	−	199548.i	0.142034	−	0.142034i
$113$	−965448.	−	965448.i	−0.669104	−	0.669104i	0.288405	−	0.957509i	$-0.406875\pi$
$113$	−965448.	−	965448.i	−0.669104	−	0.669104i	−0.957509	+	0.288405i	$0.906875\pi$
$114$			1.00188e6i			0.676240i
$115$		0			0
$116$	−409860.			−0.262580
$117$	2.24305e6	−	2.24305e6i	1.40050	−	1.40050i
$118$	−1.08054e6	−	1.08054e6i	−0.657650	−	0.657650i
$119$		−	1.34633e6i		−	0.798932i
$120$		0			0
$121$	−360217.			−0.203333
$122$	534336.	−	534336.i	0.294263	−	0.294263i
$123$	627264.	+	627264.i	0.337082	+	0.337082i
$124$			1.16987e6i			0.613583i
$125$		0			0
$126$	−1.79966e6			−0.899660
$127$	−716247.	+	716247.i	−0.349665	+	0.349665i	−0.859985	−	0.510320i	$-0.829527\pi$
$127$	−716247.	+	716247.i	−0.349665	+	0.349665i	0.510320	+	0.859985i	$0.329527\pi$
$128$	−1.28964e6	−	1.28964e6i	−0.614948	−	0.614948i
$129$			5.30264e6i			2.47015i
$130$		0			0
$131$	−963468.			−0.428572			−0.214286	−	0.976771i	$-0.568742\pi$
$131$	−963468.			−0.428572			−0.214286	+	0.976771i	$0.568742\pi$
$132$	−1.80338e6	+	1.80338e6i	−0.784091	+	0.784091i
$133$	1.04742e6	+	1.04742e6i	0.445211	+	0.445211i
$134$		−	1.44164e6i		−	0.599159i
$135$		0			0
$136$	−2.14632e6			−0.853253
$137$	−66792.0	+	66792.0i	−0.0259754	+	0.0259754i	−0.719975	−	0.694000i	$-0.755847\pi$
$137$	−66792.0	+	66792.0i	−0.0259754	+	0.0259754i	0.694000	+	0.719975i	$0.255847\pi$
$138$	1.05197e6	+	1.05197e6i	0.400284	+	0.400284i
$139$			426580.i			0.158839i	0.996841	+	0.0794193i	$0.0253066\pi$
$139$			426580.i			0.158839i	−0.996841	+	0.0794193i	$0.974693\pi$
$140$		0			0
$141$	1.06504e6			0.379935
$142$	−1.85198e6	+	1.85198e6i	−0.646803	+	0.646803i
$143$	1.83902e6	+	1.83902e6i	0.628897	+	0.628897i
$144$		−	1.39684e6i		−	0.467798i
$145$		0			0
$146$	1.83967e6			0.591128
$147$	1.05438e6	−	1.05438e6i	0.331930	−	0.331930i
$148$	−947232.	−	947232.i	−0.292194	−	0.292194i
$149$			3.08880e6i			0.933751i	0.884323	+	0.466875i	$0.154620\pi$
$149$			3.08880e6i			0.933751i	−0.884323	+	0.466875i	$0.845380\pi$
$150$		0			0
$151$	3.91415e6			1.13686			0.568430	−	0.822732i	$-0.307551\pi$
$151$	3.91415e6			1.13686			0.568430	+	0.822732i	$0.307551\pi$
$152$	1.66980e6	−	1.66980e6i	0.475482	−	0.475482i
$153$	−4.71215e6	−	4.71215e6i	−1.31566	−	1.31566i
$154$		−	1.47550e6i		−	0.403995i
$155$		0			0
$156$	−4.69973e6			−1.23794
$157$	3.94337e6	−	3.94337e6i	1.01899	−	1.01899i	0.0191701	−	0.999816i	$-0.493898\pi$
$157$	3.94337e6	−	3.94337e6i	1.01899	−	1.01899i	0.999816	−	0.0191701i	$-0.00610240\pi$
$158$	698280.	+	698280.i	0.177035	+	0.177035i
$159$		−	1.02889e7i		−	2.55963i
$160$		0			0
$161$	2.19958e6			0.527063
$162$	−1.53552e6	+	1.53552e6i	−0.361168	+	0.361168i
$163$	−661023.	−	661023.i	−0.152635	−	0.152635i	0.626659	−	0.779294i	$-0.284422\pi$
$163$	−661023.	−	661023.i	−0.152635	−	0.152635i	−0.779294	+	0.626659i	$0.784422\pi$
$164$		−	874368.i		−	0.198227i
$165$		0			0
$166$	804582.			0.175892
$167$	−1.71693e6	+	1.71693e6i	−0.368640	+	0.368640i	−0.866981	−	0.498341i	$-0.833943\pi$
$167$	−1.71693e6	+	1.71693e6i	−0.368640	+	0.368640i	0.498341	+	0.866981i	$0.333943\pi$
$168$	4.50846e6	+	4.50846e6i	0.950825	+	0.950825i
$169$		−	34201.0i		−	0.00708563i
$170$		0			0
$171$	7.33194e6			1.46633
$172$	3.69578e6	−	3.69578e6i	0.726308	−	0.726308i
$173$	3.90871e6	+	3.90871e6i	0.754910	+	0.754910i	0.975391	−	0.220481i	$-0.0707627\pi$
$173$	3.90871e6	+	3.90871e6i	0.754910	+	0.754910i	−0.220481	+	0.975391i	$0.570763\pi$
$174$		−	1.76418e6i		−	0.334885i
$175$		0			0
$176$	1.14523e6			0.210066
$177$	−1.18859e7	+	1.18859e7i	−2.14345	+	2.14345i
$178$	−810810.	−	810810.i	−0.143767	−	0.143767i
$179$			7.47846e6i			1.30393i	0.758251	+	0.651963i	$0.226054\pi$
$179$			7.47846e6i			1.30393i	−0.758251	+	0.651963i	$0.773946\pi$
$180$		0			0
$181$	−8.80042e6			−1.48412			−0.742058	−	0.670336i	$-0.766150\pi$
$181$	−8.80042e6			−1.48412			−0.742058	+	0.670336i	$0.766150\pi$
$182$	1.92262e6	−	1.92262e6i	0.318918	−	0.318918i
$183$	−5.87770e6	−	5.87770e6i	−0.959078	−	0.959078i
$184$		−	3.50658e6i		−	0.562899i
$185$		0			0
$186$	−5.03554e6			−0.782541
$187$	3.86338e6	−	3.86338e6i	0.590802	−	0.590802i
$188$	−742302.	−	742302.i	−0.111714	−	0.111714i
$189$			9.83664e6i			1.45701i
$190$		0			0
$191$	5.68339e6			0.815657			0.407828	−	0.913059i	$-0.366286\pi$
$191$	5.68339e6			0.815657			0.407828	+	0.913059i	$0.366286\pi$
$192$	2.71841e6	−	2.71841e6i	0.384071	−	0.384071i
$193$	1.25593e6	+	1.25593e6i	0.174701	+	0.174701i	0.789041	−	0.614341i	$-0.210578\pi$
$193$	1.25593e6	+	1.25593e6i	0.174701	+	0.174701i	−0.614341	+	0.789041i	$0.710578\pi$
$194$			4.86367e6i			0.666130i
$195$		0			0
$196$	−1.46975e6			−0.195197
$197$	3.97319e6	−	3.97319e6i	0.519685	−	0.519685i	−0.397791	−	0.917476i	$-0.630223\pi$
$197$	3.97319e6	−	3.97319e6i	0.519685	−	0.519685i	0.917476	+	0.397791i	$0.130223\pi$
$198$	−5.16424e6	−	5.16424e6i	−0.665289	−	0.665289i
$199$		−	7.74160e6i		−	0.982362i	−0.871058	−	0.491181i	$-0.836565\pi$
$199$		−	7.74160e6i		−	0.982362i	0.871058	−	0.491181i	$-0.163435\pi$
$200$		0			0
$201$	−1.58580e7			−1.95281
$202$	−5.28719e6	+	5.28719e6i	−0.641462	+	0.641462i
$203$	−1.84437e6	−	1.84437e6i	−0.220475	−	0.220475i
$204$			9.87307e6i			1.16295i
$205$		0			0
$206$	5.63290e6			0.644363
$207$	7.69854e6	−	7.69854e6i	0.867955	−	0.867955i
$208$	1.49227e6	+	1.49227e6i	0.165828	+	0.165828i
$209$			6.01128e6i			0.658458i
$210$		0			0
$211$	−5.05899e6			−0.538538			−0.269269	−	0.963065i	$-0.586782\pi$
$211$	−5.05899e6			−0.538538			−0.269269	+	0.963065i	$0.586782\pi$
$212$	−7.17103e6	+	7.17103e6i	−0.752617	+	0.752617i
$213$	2.03718e7	+	2.03718e7i	2.10810	+	2.10810i
$214$			9.12994e6i			0.931594i
$215$		0			0
$216$	1.56816e7			1.55607
$217$	−5.26442e6	+	5.26442e6i	−0.515195	+	0.515195i
$218$	353760.	+	353760.i	0.0341460	+	0.0341460i
$219$		−	2.02364e7i		−	1.92664i
$220$		0			0
$221$	1.00682e7			0.932770
$222$	4.07722e6	−	4.07722e6i	0.372653	−	0.372653i
$223$	−4.71111e6	−	4.71111e6i	−0.424824	−	0.424824i	0.462037	−	0.886861i	$-0.347119\pi$
$223$	−4.71111e6	−	4.71111e6i	−0.424824	−	0.424824i	−0.886861	+	0.462037i	$0.847119\pi$
$224$		−	9.94097e6i		−	0.884473i
$225$		0			0
$226$	−5.79269e6			−0.501828
$227$	−497697.	+	497697.i	−0.0425488	+	0.0425488i	−0.728061	−	0.685512i	$-0.759578\pi$
$227$	−497697.	+	497697.i	−0.0425488	+	0.0425488i	0.685512	+	0.728061i	$0.259578\pi$
$228$	−7.68108e6	−	7.68108e6i	−0.648064	−	0.648064i
$229$		−	8.23619e6i		−	0.685835i	−0.939365	−	0.342918i	$-0.888585\pi$
$229$		−	8.23619e6i		−	0.685835i	0.939365	−	0.342918i	$-0.111415\pi$
$230$		0			0
$231$	−1.62305e7			−1.31672
$232$	−2.94030e6	+	2.94030e6i	−0.235466	+	0.235466i
$233$	−1.29896e7	−	1.29896e7i	−1.02690	−	1.02690i	−0.999628	−	0.0272739i	$-0.991317\pi$
$233$	−1.29896e7	−	1.29896e7i	−1.02690	−	1.02690i	−0.0272739	−	0.999628i	$-0.508683\pi$
$234$		−	1.34583e7i		−	1.05037i
$235$		0			0
$236$	1.65683e7			1.26050
$237$	7.68108e6	−	7.68108e6i	0.577002	−	0.577002i
$238$	−4.03898e6	−	4.03898e6i	−0.299600	−	0.299600i
$239$			3.93228e6i			0.288039i	0.989575	+	0.144019i	$0.0460027\pi$
$239$			3.93228e6i			0.288039i	−0.989575	+	0.144019i	$0.953997\pi$
$240$		0			0
$241$	1.16542e7			0.832590			0.416295	−	0.909230i	$-0.363328\pi$
$241$	1.16542e7			0.832590			0.416295	+	0.909230i	$0.363328\pi$
$242$	−1.08065e6	+	1.08065e6i	−0.0762499	+	0.0762499i
$243$	−430353.	−	430353.i	−0.0299920	−	0.0299920i
$244$			8.19315e6i			0.564003i
$245$		0			0
$246$	3.76358e6			0.252811
$247$	−7.83288e6	+	7.83288e6i	−0.519793	+	0.519793i
$248$	8.39256e6	+	8.39256e6i	0.550224	+	0.550224i
$249$		−	8.85040e6i		−	0.573278i
$250$		0			0
$251$	3.69025e6			0.233365			0.116682	−	0.993169i	$-0.462774\pi$
$251$	3.69025e6			0.233365			0.116682	+	0.993169i	$0.462774\pi$
$252$	1.37974e7	−	1.37974e7i	0.862174	−	0.862174i
$253$	6.31184e6	+	6.31184e6i	0.389758	+	0.389758i
$254$			4.29748e6i			0.262248i
$255$		0			0
$256$	−1.30099e7			−0.775451
$257$	−7.78483e6	+	7.78483e6i	−0.458617	+	0.458617i	−0.898201	−	0.439585i	$-0.855126\pi$
$257$	−7.78483e6	+	7.78483e6i	−0.458617	+	0.458617i	0.439585	+	0.898201i	$0.355126\pi$
$258$	1.59079e7	+	1.59079e7i	0.926305	+	0.926305i
$259$		−	8.52509e6i		−	0.490681i
$260$		0			0
$261$	−1.29106e7			−0.726147
$262$	−2.89040e6	+	2.89040e6i	−0.160714	+	0.160714i
$263$	−1.46742e6	−	1.46742e6i	−0.0806655	−	0.0806655i	0.665623	−	0.746288i	$-0.268166\pi$
$263$	−1.46742e6	−	1.46742e6i	−0.0806655	−	0.0806655i	−0.746288	+	0.665623i	$0.768166\pi$
$264$			2.58746e7i			1.40625i
$265$		0			0
$266$	6.28452e6			0.333908
$267$	−8.91891e6	+	8.91891e6i	−0.468574	+	0.468574i
$268$	1.10526e7	+	1.10526e7i	0.574194	+	0.574194i
$269$			1.96214e7i			1.00803i	0.863695	+	0.504016i	$0.168145\pi$
$269$			1.96214e7i			1.00803i	−0.863695	+	0.504016i	$0.831855\pi$
$270$		0			0
$271$	−9.20313e6			−0.462410			−0.231205	−	0.972905i	$-0.574267\pi$
$271$	−9.20313e6			−0.462410			−0.231205	+	0.972905i	$0.574267\pi$
$272$	3.13493e6	−	3.13493e6i	0.155783	−	0.155783i
$273$	−2.11488e7	−	2.11488e7i	−1.03943	−	1.03943i
$274$			400752.i			0.0194816i
$275$		0			0
$276$	−1.61303e7			−0.767210
$277$	2.06153e7	−	2.06153e7i	0.969954	−	0.969954i	−0.0296080	−	0.999562i	$-0.509426\pi$
$277$	2.06153e7	−	2.06153e7i	0.969954	−	0.969954i	0.999562	+	0.0296080i	$0.00942590\pi$
$278$	1.27974e6	+	1.27974e6i	0.0595645	+	0.0595645i
$279$			3.68510e7i			1.69682i
$280$		0			0
$281$	−3.63956e7			−1.64032			−0.820162	−	0.572132i	$-0.806117\pi$
$281$	−3.63956e7			−1.64032			−0.820162	+	0.572132i	$0.806117\pi$
$282$	3.19513e6	−	3.19513e6i	0.142476	−	0.142476i
$283$	−1.63095e6	−	1.63095e6i	−0.0719585	−	0.0719585i	0.670212	−	0.742170i	$-0.266203\pi$
$283$	−1.63095e6	−	1.63095e6i	−0.0719585	−	0.0719585i	−0.742170	+	0.670212i	$0.766203\pi$
$284$		−	2.83971e7i		−	1.23971i
$285$		0			0
$286$	1.10341e7			0.471672
$287$	3.93466e6	−	3.93466e6i	0.166441	−	0.166441i
$288$	−3.47934e7	−	3.47934e7i	−1.45653	−	1.45653i
$289$			2.98656e6i			0.123731i
$290$		0			0
$291$	5.35004e7			2.17109
$292$	−1.41042e7	+	1.41042e7i	−0.566498	+	0.566498i
$293$	−1.31150e7	−	1.31150e7i	−0.521392	−	0.521392i	0.396600	−	0.917992i	$-0.370190\pi$
$293$	−1.31150e7	−	1.31150e7i	−0.521392	−	0.521392i	−0.917992	+	0.396600i	$0.870190\pi$
$294$		−	6.32630e6i		−	0.248947i
$295$		0			0
$296$	−1.35907e7			−0.524043
$297$	−2.82269e7	+	2.82269e7i	−1.07744	+	1.07744i
$298$	9.26640e6	+	9.26640e6i	0.350157	+	0.350157i
$299$			1.64490e7i			0.615357i
$300$		0			0
$301$	3.32620e7			1.21969
$302$	1.17425e7	−	1.17425e7i	0.426322	−	0.426322i
$303$	5.81591e7	+	5.81591e7i	2.09069	+	2.09069i
$304$			4.87784e6i			0.173623i
$305$		0			0
$306$	−2.82729e7			−0.986747
$307$	6.04419e6	−	6.04419e6i	0.208893	−	0.208893i	−0.594904	−	0.803797i	$-0.702810\pi$
$307$	6.04419e6	−	6.04419e6i	0.208893	−	0.208893i	0.803797	+	0.594904i	$0.202810\pi$
$308$	1.13121e7	+	1.13121e7i	0.387162	+	0.387162i
$309$		−	6.19619e7i		−	2.10015i
$310$		0			0
$311$	−2.97849e7			−0.990181			−0.495091	−	0.868841i	$-0.664865\pi$
$311$	−2.97849e7			−0.990181			−0.495091	+	0.868841i	$0.664865\pi$
$312$	−3.37154e7	+	3.37154e7i	−1.11011	+	1.11011i
$313$	400752.	+	400752.i	0.0130690	+	0.0130690i	0.713611	−	0.700542i	$-0.247058\pi$
$313$	400752.	+	400752.i	0.0130690	+	0.0130690i	−0.700542	+	0.713611i	$0.747058\pi$
$314$		−	2.36602e7i		−	0.764240i
$315$		0			0
$316$	−1.07070e7			−0.339316
$317$	4.06611e7	−	4.06611e7i	1.27644	−	1.27644i	0.333801	−	0.942644i	$-0.391669\pi$
$317$	4.06611e7	−	4.06611e7i	1.27644	−	1.27644i	0.942644	−	0.333801i	$-0.108331\pi$
$318$	−3.08666e7	−	3.08666e7i	−0.959859	−	0.959859i
$319$		−	1.05851e7i		−	0.326078i
$320$		0			0
$321$	1.00429e8			3.03631
$322$	6.59875e6	−	6.59875e6i	0.197649	−	0.197649i
$323$	1.64551e7	+	1.64551e7i	0.488308	+	0.488308i
$324$		−	2.35446e7i		−	0.692239i
$325$		0			0
$326$	−3.96614e6			−0.114476
$327$	3.89136e6	−	3.89136e6i	0.111291	−	0.111291i
$328$	−6.27264e6	−	6.27264e6i	−0.177758	−	0.177758i
$329$		−	6.68072e6i		−	0.187601i
$330$		0			0
$331$	9.62073e6			0.265292			0.132646	−	0.991163i	$-0.457653\pi$
$331$	9.62073e6			0.265292			0.132646	+	0.991163i	$0.457653\pi$
$332$	−6.16846e6	+	6.16846e6i	−0.168563	+	0.168563i
$333$	−2.98378e7	−	2.98378e7i	−0.808043	−	0.808043i
$334$			1.03016e7i			0.276480i
$335$		0			0
$336$	−1.31702e7			−0.347195
$337$	2.14318e7	−	2.14318e7i	0.559976	−	0.559976i	−0.369325	−	0.929300i	$-0.620411\pi$
$337$	2.14318e7	−	2.14318e7i	0.559976	−	0.559976i	0.929300	+	0.369325i	$0.120411\pi$
$338$	−102603.	−	102603.i	−0.00265711	−	0.00265711i
$339$			6.37196e7i			1.63559i
$340$		0			0
$341$	−3.02132e7			−0.761963
$342$	2.19958e7	−	2.19958e7i	0.549872	−	0.549872i
$343$	−3.09672e7	−	3.09672e7i	−0.767396	−	0.767396i
$344$		−	5.30264e7i		−	1.30262i
$345$		0			0
$346$	2.34523e7			0.566183
$347$	−5.13445e7	+	5.13445e7i	−1.22887	+	1.22887i	−0.264476	+	0.964392i	$0.585199\pi$
$347$	−5.13445e7	+	5.13445e7i	−1.22887	+	1.22887i	−0.964392	+	0.264476i	$0.914801\pi$
$348$	1.35254e7	+	1.35254e7i	0.320931	+	0.320931i
$349$			2.11304e7i			0.497087i	0.968621	+	0.248544i	$0.0799519\pi$
$349$			2.11304e7i			0.497087i	−0.968621	+	0.248544i	$0.920048\pi$
$350$		0			0
$351$	−7.35610e7			−1.70109
$352$	2.85263e7	−	2.85263e7i	0.654059	−	0.654059i
$353$	2.69882e7	+	2.69882e7i	0.613550	+	0.613550i	0.943869	−	0.330320i	$-0.107157\pi$
$353$	2.69882e7	+	2.69882e7i	0.613550	+	0.613550i	−0.330320	+	0.943869i	$0.607157\pi$
$354$			7.13156e7i			1.60759i
$355$		0			0
$356$	1.24324e7			0.275553
$357$	−4.44288e7	+	4.44288e7i	−0.976473	+	0.976473i
$358$	2.24354e7	+	2.24354e7i	0.488972	+	0.488972i
$359$			9.01692e6i			0.194883i	0.995241	+	0.0974417i	$0.0310660\pi$
$359$			9.01692e6i			0.194883i	−0.995241	+	0.0974417i	$0.968934\pi$
$360$		0			0
$361$	2.14423e7			0.455774
$362$	−2.64013e7	+	2.64013e7i	−0.556543	+	0.556543i
$363$	1.18872e7	+	1.18872e7i	0.248518	+	0.248518i
$364$			2.94801e7i			0.611259i
$365$		0			0
$366$	−3.52662e7			−0.719308
$367$	−4.10576e7	+	4.10576e7i	−0.830606	+	0.830606i	−0.987600	−	0.156994i	$-0.949820\pi$
$367$	−4.10576e7	+	4.10576e7i	−0.830606	+	0.830606i	0.156994	+	0.987600i	$0.449820\pi$
$368$	5.12173e6	+	5.12173e6i	0.102772	+	0.102772i
$369$		−	2.75426e7i		−	0.548183i
$370$		0			0
$371$	−6.45393e7			−1.26387
$372$	3.86058e7	−	3.86058e7i	0.749935	−	0.749935i
$373$	−9.56009e6	−	9.56009e6i	−0.184219	−	0.184219i	0.608972	−	0.793192i	$-0.291582\pi$
$373$	−9.56009e6	−	9.56009e6i	−0.184219	−	0.184219i	−0.793192	+	0.608972i	$0.791582\pi$
$374$		−	2.31803e7i		−	0.443102i
$375$		0			0
$376$	−1.06504e7			−0.200356
$377$	1.37927e7	−	1.37927e7i	0.257410	−	0.257410i
$378$	2.95099e7	+	2.95099e7i	0.546377	+	0.546377i
$379$			6.67649e7i			1.22639i	0.789930	+	0.613197i	$0.210117\pi$
$379$			6.67649e7i			1.22639i	−0.789930	+	0.613197i	$0.789883\pi$
$380$		0			0
$381$	4.72723e7			0.854736
$382$	1.70502e7	−	1.70502e7i	0.305871	−	0.305871i
$383$	−6.61994e7	−	6.61994e7i	−1.17830	−	1.17830i	−0.980176	−	0.198128i	$-0.936514\pi$
$383$	−6.61994e7	−	6.61994e7i	−1.17830	−	1.17830i	−0.198128	−	0.980176i	$-0.563486\pi$
$384$			8.51162e7i			1.50321i
$385$		0			0
$386$	7.53559e6			0.131025
$387$	1.16417e8	−	1.16417e8i	2.00855	−	2.00855i
$388$	−3.72882e7	−	3.72882e7i	−0.638375	−	0.638375i
$389$		−	3.44779e7i		−	0.585723i	−0.956155	−	0.292861i	$-0.905393\pi$
$389$		−	3.44779e7i		−	0.585723i	0.956155	−	0.292861i	$-0.0946075\pi$
$390$		0			0
$391$	3.45558e7			0.578083
$392$	−1.05438e7	+	1.05438e7i	−0.175041	+	0.175041i
$393$	3.17944e7	+	3.17944e7i	0.523810	+	0.523810i
$394$		−	2.38391e7i		−	0.389764i
$395$		0			0
$396$	7.91850e7			1.27514
$397$	−4.03512e7	+	4.03512e7i	−0.644889	+	0.644889i	−0.951753	−	0.306864i	$-0.900720\pi$
$397$	−4.03512e7	+	4.03512e7i	−0.644889	+	0.644889i	0.306864	+	0.951753i	$0.400720\pi$
$398$	−2.32248e7	−	2.32248e7i	−0.368386	−	0.368386i
$399$		−	6.91297e7i		−	1.08829i
$400$		0			0
$401$	−7.48541e7			−1.16087			−0.580433	−	0.814308i	$-0.697117\pi$
$401$	−7.48541e7			−1.16087			−0.580433	+	0.814308i	$0.697117\pi$
$402$	−4.75741e7	+	4.75741e7i	−0.732305	+	0.732305i
$403$	−3.93687e7	−	3.93687e7i	−0.601501	−	0.601501i
$404$		−	8.10703e7i		−	1.22947i
$405$		0			0
$406$	−1.10662e7			−0.165356
$407$	2.44633e7	−	2.44633e7i	0.362854	−	0.362854i
$408$	7.08286e7	+	7.08286e7i	1.04286	+	1.04286i
$409$		−	1.30148e8i		−	1.90226i	−0.308795	−	0.951128i	$-0.599926\pi$
$409$		−	1.30148e8i		−	1.90226i	0.308795	−	0.951128i	$-0.400074\pi$
$410$		0			0
$411$	4.40827e6			0.0634955
$412$	−4.31856e7	+	4.31856e7i	−0.617514	+	0.617514i
$413$	7.45573e7	+	7.45573e7i	1.05838	+	1.05838i
$414$		−	4.61912e7i		−	0.650966i
$415$		0			0
$416$	7.43412e7			1.03264
$417$	1.40771e7	−	1.40771e7i	0.194136	−	0.194136i
$418$	1.80338e7	+	1.80338e7i	0.246922	+	0.246922i
$419$			1.04966e8i			1.42694i	0.700686	+	0.713470i	$0.252877\pi$
$419$			1.04966e8i			1.42694i	−0.700686	+	0.713470i	$0.747123\pi$
$420$		0			0
$421$	−3.25297e7			−0.435947			−0.217974	−	0.975955i	$-0.569945\pi$
$421$	−3.25297e7			−0.435947			−0.217974	+	0.975955i	$0.569945\pi$
$422$	−1.51770e7	+	1.51770e7i	−0.201952	+	0.201952i
$423$	−2.33825e7	−	2.33825e7i	−0.308937	−	0.308937i
$424$			1.02889e8i			1.34980i
$425$		0			0
$426$	1.22231e8			1.58107
$427$	−3.68692e7	+	3.68692e7i	−0.473565	+	0.473565i
$428$	−6.99962e7	−	6.99962e7i	−0.892778	−	0.892778i
$429$		−	1.21376e8i		−	1.53730i
$430$		0			0
$431$	−1.97042e7			−0.246108			−0.123054	−	0.992400i	$-0.539269\pi$
$431$	−1.97042e7			−0.246108			−0.123054	+	0.992400i	$0.539269\pi$
$432$	−2.29046e7	+	2.29046e7i	−0.284101	+	0.284101i
$433$	7.02136e7	+	7.02136e7i	0.864883	+	0.864883i	0.991900	−	0.127017i	$-0.0405404\pi$
$433$	7.02136e7	+	7.02136e7i	0.864883	+	0.864883i	−0.127017	+	0.991900i	$0.540540\pi$
$434$			3.15865e7i			0.386396i
$435$		0			0
$436$	−5.42432e6			−0.0654464
$437$	−2.68838e7	+	2.68838e7i	−0.322141	+	0.322141i
$438$	−6.07092e7	−	6.07092e7i	−0.722490	−	0.722490i
$439$		−	1.09253e8i		−	1.29134i	−0.763616	−	0.645671i	$-0.776578\pi$
$439$		−	1.09253e8i		−	1.29134i	0.763616	−	0.645671i	$-0.223422\pi$
$440$		0			0
$441$	−4.62970e7			−0.539805
$442$	3.02046e7	−	3.02046e7i	0.349789	−	0.349789i
$443$	2.07006e6	+	2.07006e6i	0.0238106	+	0.0238106i	0.718912	−	0.695101i	$-0.244640\pi$
$443$	2.07006e6	+	2.07006e6i	0.0238106	+	0.0238106i	−0.695101	+	0.718912i	$0.744640\pi$
$444$			6.25173e7i			0.714252i
$445$		0			0
$446$	−2.82667e7			−0.318618
$447$	1.01930e8	−	1.01930e8i	1.14125	−	1.14125i
$448$	−1.70518e7	−	1.70518e7i	−0.189643	−	0.189643i
$449$			8.47044e7i			0.935765i	0.883791	+	0.467883i	$0.154983\pi$
$449$			8.47044e7i			0.935765i	−0.883791	+	0.467883i	$0.845017\pi$
$450$		0			0
$451$	2.25815e7			0.246163
$452$	4.44106e7	−	4.44106e7i	0.480918	−	0.480918i
$453$	−1.29167e8	−	1.29167e8i	−1.38950	−	1.38950i
$454$			2.98618e6i			0.0319116i
$455$		0			0
$456$	−1.10207e8			−1.16229
$457$	4.53668e7	−	4.53668e7i	0.475323	−	0.475323i	−0.428309	−	0.903632i	$-0.640890\pi$
$457$	4.53668e7	−	4.53668e7i	0.475323	−	0.475323i	0.903632	+	0.428309i	$0.140890\pi$
$458$	−2.47086e7	−	2.47086e7i	−0.257188	−	0.257188i
$459$			1.54535e8i			1.59804i
$460$		0			0
$461$	8.63813e7			0.881692			0.440846	−	0.897583i	$-0.354679\pi$
$461$	8.63813e7			0.881692			0.440846	+	0.897583i	$0.354679\pi$
$462$	−4.86914e7	+	4.86914e7i	−0.493772	+	0.493772i
$463$	9.36068e7	+	9.36068e7i	0.943114	+	0.943114i	0.998467	−	0.0553526i	$-0.0176283\pi$
$463$	9.36068e7	+	9.36068e7i	0.943114	+	0.943114i	−0.0553526	+	0.998467i	$0.517628\pi$
$464$		−	8.58924e6i		−	0.0859807i
$465$		0			0
$466$	−7.79378e7			−0.770176
$467$	−2.65425e7	+	2.65425e7i	−0.260610	+	0.260610i	−0.825302	−	0.564692i	$-0.808995\pi$
$467$	−2.65425e7	+	2.65425e7i	−0.260610	+	0.260610i	0.564692	+	0.825302i	$0.308995\pi$
$468$	1.03180e8	+	1.03180e8i	1.00661	+	1.00661i
$469$			9.94730e7i			0.964244i
$470$		0			0
$471$	−2.60262e8			−2.49086
$472$	1.18859e8	−	1.18859e8i	1.13034	−	1.13034i
$473$	9.54475e7	+	9.54475e7i	0.901947	+	0.901947i
$474$		−	4.60865e7i		−	0.432751i
$475$		0			0
$476$	6.19311e7			0.574233
$477$	−2.25888e8	+	2.25888e8i	−2.08131	+	2.08131i
$478$	1.17968e7	+	1.17968e7i	0.108014	+	0.108014i
$479$			6.72646e7i			0.612040i	0.952025	+	0.306020i	$0.0989974\pi$
$479$			6.72646e7i			0.612040i	−0.952025	+	0.306020i	$0.901003\pi$
$480$		0			0
$481$	6.37528e7			0.572881
$482$	3.49626e7	−	3.49626e7i	0.312221	−	0.312221i
$483$	−7.25862e7	−	7.25862e7i	−0.644188	−	0.644188i
$484$		−	1.65700e7i		−	0.146146i
$485$		0			0
$486$	−2.58212e6			−0.0224940
$487$	−8.32276e7	+	8.32276e7i	−0.720577	+	0.720577i	−0.968723	−	0.248145i	$-0.920179\pi$
$487$	−8.32276e7	+	8.32276e7i	−0.720577	+	0.720577i	0.248145	+	0.968723i	$0.420179\pi$
$488$	5.87770e7	+	5.87770e7i	0.505764	+	0.505764i
$489$			4.36275e7i			0.373107i
$490$		0			0
$491$	1.69895e8			1.43528			0.717638	−	0.696416i	$-0.245223\pi$
$491$	1.69895e8			1.43528			0.717638	+	0.696416i	$0.245223\pi$
$492$	−2.88541e7	+	2.88541e7i	−0.242277	+	0.242277i
$493$	−2.89753e7	−	2.89753e7i	−0.241817	−	0.241817i
$494$			4.69973e7i			0.389845i
$495$		0			0
$496$	−2.45164e7			−0.200915
$497$	1.27787e8	−	1.27787e8i	1.04092	−	1.04092i
$498$	−2.65512e7	−	2.65512e7i	−0.214979	−	0.214979i
$499$		−	1.12386e8i		−	0.904500i	−0.891891	−	0.452250i	$-0.850621\pi$
$499$		−	1.12386e8i		−	0.904500i	0.891891	−	0.452250i	$-0.149379\pi$
$500$		0			0
$501$	1.13317e8			0.901120
$502$	1.10708e7	−	1.10708e7i	0.0875117	−	0.0875117i
$503$	−8.49728e7	−	8.49728e7i	−0.667692	−	0.667692i	0.289490	−	0.957181i	$-0.406514\pi$
$503$	−8.49728e7	−	8.49728e7i	−0.667692	−	0.667692i	−0.957181	+	0.289490i	$0.906514\pi$
$504$		−	1.97962e8i		−	1.54629i
$505$		0			0
$506$	3.78711e7			0.292318
$507$	−1.12863e6	+	1.12863e6i	−0.00866022	+	0.00866022i
$508$	−3.29474e7	−	3.29474e7i	−0.251321	−	0.251321i
$509$			4.35675e7i			0.330376i	0.986262	+	0.165188i	$0.0528232\pi$
$509$			4.35675e7i			0.330376i	−0.986262	+	0.165188i	$0.947177\pi$
$510$		0			0
$511$	−1.26937e8			−0.951320
$512$	4.35072e7	−	4.35072e7i	0.324154	−	0.324154i
$513$	−1.20226e8	−	1.20226e8i	−0.890522	−	0.890522i
$514$			4.67090e7i			0.343963i
$515$		0			0
$516$	−2.43921e8			−1.77542
$517$	1.91708e7	−	1.91708e7i	0.138729	−	0.138729i
$518$	−2.55753e7	−	2.55753e7i	−0.184006	−	0.184006i
$519$		−	2.57975e8i		−	1.84534i
$520$		0			0
$521$	1.06987e8			0.756516			0.378258	−	0.925700i	$-0.376523\pi$
$521$	1.06987e8			0.756516			0.378258	+	0.925700i	$0.376523\pi$
$522$	−3.87318e7	+	3.87318e7i	−0.272305	+	0.272305i
$523$	9.22477e7	+	9.22477e7i	0.644838	+	0.644838i	0.951741	−	0.306903i	$-0.0992927\pi$
$523$	9.22477e7	+	9.22477e7i	0.644838	+	0.644838i	−0.306903	+	0.951741i	$0.599293\pi$
$524$		−	4.43195e7i		−	0.308036i
$525$		0			0
$526$	−8.80454e6			−0.0604992
$527$	−8.27049e7	+	8.27049e7i	−0.565066	+	0.565066i
$528$	−3.77927e7	−	3.77927e7i	−0.256747	−	0.256747i
$529$		−	9.15800e7i		−	0.618633i
$530$		0			0
$531$	5.21901e8			3.48582
$532$	−4.81813e7	+	4.81813e7i	−0.319995	+	0.319995i
$533$	2.94244e7	+	2.94244e7i	0.194324	+	0.194324i
$534$			5.35135e7i			0.351430i
$535$		0			0
$536$	1.58580e8			1.02980
$537$	2.46789e8	−	2.46789e8i	1.59369	−	1.59369i
$538$	5.88643e7	+	5.88643e7i	0.378012	+	0.378012i
$539$		−	3.79578e7i		−	0.242401i
$540$		0			0
$541$	−2.44414e8			−1.54360			−0.771800	−	0.635865i	$-0.780643\pi$
$541$	−2.44414e8			−1.54360			−0.771800	+	0.635865i	$0.780643\pi$
$542$	−2.76094e7	+	2.76094e7i	−0.173404	+	0.173404i
$543$	2.90414e8	+	2.90414e8i	1.81392	+	1.81392i
$544$		−	1.56174e8i		−	0.970090i
$545$		0			0
$546$	−1.26893e8			−0.779576
$547$	−3.23171e7	+	3.23171e7i	−0.197456	+	0.197456i	−0.798909	−	0.601452i	$-0.794589\pi$
$547$	−3.23171e7	+	3.23171e7i	−0.197456	+	0.197456i	0.601452	+	0.798909i	$0.294589\pi$
$548$	−3.07243e6	−	3.07243e6i	−0.0186698	−	0.0186698i
$549$			2.58084e8i			1.55971i
$550$		0			0
$551$	4.50846e7			0.269509
$552$	−1.15717e8	+	1.15717e8i	−0.687987	+	0.687987i
$553$	−4.81813e7	−	4.81813e7i	−0.284907	−	0.284907i
$554$		−	1.23692e8i		−	0.727465i
$555$		0			0
$556$	−1.96227e7			−0.114165
$557$	5.41757e6	−	5.41757e6i	0.0313501	−	0.0313501i	−0.691258	−	0.722608i	$-0.742943\pi$
$557$	5.41757e6	−	5.41757e6i	0.0313501	−	0.0313501i	0.722608	+	0.691258i	$0.242943\pi$
$558$	1.10553e8	+	1.10553e8i	0.636308	+	0.636308i
$559$			2.48742e8i			1.42401i
$560$		0			0
$561$	−2.54983e8			−1.44418
$562$	−1.09187e8	+	1.09187e8i	−0.615121	+	0.615121i
$563$	−3.71439e7	−	3.71439e7i	−0.208143	−	0.208143i	0.595335	−	0.803478i	$-0.297019\pi$
$563$	−3.71439e7	−	3.71439e7i	−0.208143	−	0.208143i	−0.803478	+	0.595335i	$0.797019\pi$
$564$			4.89919e7i			0.273078i
$565$		0			0
$566$	−9.78572e6			−0.0539689
$567$	1.05951e8	−	1.05951e8i	0.581239	−	0.581239i
$568$	−2.03718e8	−	2.03718e8i	−1.11169	−	1.11169i
$569$			2.17499e8i			1.18065i	0.807166	+	0.590324i	$0.201000\pi$
$569$			2.17499e8i			1.18065i	−0.807166	+	0.590324i	$0.799000\pi$
$570$		0			0
$571$	1.55107e8			0.833151			0.416575	−	0.909101i	$-0.363230\pi$
$571$	1.55107e8			0.833151			0.416575	+	0.909101i	$0.363230\pi$
$572$	−8.45951e7	+	8.45951e7i	−0.452019	+	0.452019i
$573$	−1.87552e8	−	1.87552e8i	−0.996914	−	0.996914i
$574$		−	2.36079e7i		−	0.124831i
$575$		0			0
$576$	−1.19363e8			−0.624600
$577$	2.22401e8	−	2.22401e8i	1.15773	−	1.15773i	0.172772	−	0.984962i	$-0.444728\pi$
$577$	2.22401e8	−	2.22401e8i	1.15773	−	1.15773i	0.984962	−	0.172772i	$-0.0552724\pi$
$578$	8.95968e6	+	8.95968e6i	0.0463991	+	0.0463991i
$579$		−	8.28915e7i		−	0.427046i
$580$		0			0
$581$	−5.55162e7			−0.283068
$582$	1.60501e8	−	1.60501e8i	0.814159	−	0.814159i
$583$	−1.85200e8	−	1.85200e8i	−0.934619	−	0.934619i
$584$			2.02364e8i			1.01600i
$585$		0			0
$586$	−7.86898e7			−0.391044
$587$	−1.72770e8	+	1.72770e8i	−0.854188	+	0.854188i	−0.990646	−	0.136458i	$-0.956428\pi$
$587$	−1.72770e8	+	1.72770e8i	−0.854188	+	0.854188i	0.136458	+	0.990646i	$0.456428\pi$
$588$	4.85016e7	+	4.85016e7i	0.238575	+	0.238575i
$589$		−	1.28686e8i		−	0.629775i
$590$		0			0
$591$	−2.62230e8			−1.27034
$592$	1.98507e7	−	1.98507e7i	0.0956776	−	0.0956776i
$593$	−6.50582e7	−	6.50582e7i	−0.311988	−	0.311988i	0.533691	−	0.845679i	$-0.320804\pi$
$593$	−6.50582e7	−	6.50582e7i	−0.311988	−	0.311988i	−0.845679	+	0.533691i	$0.820804\pi$
$594$			1.69361e8i			0.808081i
$595$		0			0
$596$	−1.42085e8			−0.671133
$597$	−2.55473e8	+	2.55473e8i	−1.20066	+	1.20066i
$598$	4.93471e7	+	4.93471e7i	0.230759	+	0.230759i
$599$			8.19720e6i			0.0381404i	0.999818	+	0.0190702i	$0.00607060\pi$
$599$			8.19720e6i			0.0381404i	−0.999818	+	0.0190702i	$0.993929\pi$
$600$		0			0
$601$	1.71402e8			0.789575			0.394787	−	0.918772i	$-0.370818\pi$
$601$	1.71402e8			0.789575			0.394787	+	0.918772i	$0.370818\pi$
$602$	9.97860e7	−	9.97860e7i	0.457383	−	0.457383i
$603$	3.48156e8	+	3.48156e8i	1.58789	+	1.58789i
$604$			1.80051e8i			0.817118i
$605$		0			0
$606$	3.48955e8			1.56802
$607$	−1.24642e8	+	1.24642e8i	−0.557310	+	0.557310i	−0.928541	−	0.371230i	$-0.878936\pi$
$607$	−1.24642e8	+	1.24642e8i	−0.557310	+	0.557310i	0.371230	+	0.928541i	$0.378936\pi$
$608$	1.21501e8	+	1.21501e8i	0.540590	+	0.540590i
$609$			1.21728e8i			0.538940i
$610$		0			0
$611$	4.99602e7			0.219028
$612$	2.16759e8	−	2.16759e8i	0.945633	−	0.945633i
$613$	3.56605e6	+	3.56605e6i	0.0154813	+	0.0154813i	0.714805	−	0.699324i	$-0.246515\pi$
$613$	3.56605e6	+	3.56605e6i	0.0154813	+	0.0154813i	−0.699324	+	0.714805i	$0.746515\pi$
$614$		−	3.62652e7i		−	0.156670i
$615$		0			0
$616$	1.62305e8			0.694366
$617$	−1.92655e8	+	1.92655e8i	−0.820211	+	0.820211i	−0.986138	−	0.165927i	$-0.946938\pi$
$617$	−1.92655e8	+	1.92655e8i	−0.820211	+	0.820211i	0.165927	+	0.986138i	$0.446938\pi$
$618$	−1.85886e8	−	1.85886e8i	−0.787555	−	0.787555i
$619$		−	1.66125e8i		−	0.700427i	−0.936670	−	0.350213i	$-0.886109\pi$
$619$		−	1.66125e8i		−	0.700427i	0.936670	−	0.350213i	$-0.113891\pi$
$620$		0			0
$621$	−2.52474e8			−1.05424
$622$	−8.93547e7	+	8.93547e7i	−0.371318	+	0.371318i
$623$	5.59459e7	+	5.59459e7i	0.231368	+	0.231368i
$624$		−	9.84900e7i		−	0.405357i
$625$		0			0
$626$	2.40451e6			0.00980176
$627$	1.98372e8	−	1.98372e8i	0.804782	−	0.804782i
$628$	1.81395e8	+	1.81395e8i	0.732396	+	0.732396i
$629$		−	1.33930e8i		−	0.538179i
$630$		0			0
$631$	−2.32977e8			−0.927310			−0.463655	−	0.886016i	$-0.653462\pi$
$631$	−2.32977e8			−0.927310			−0.463655	+	0.886016i	$0.653462\pi$
$632$	−7.68108e7	+	7.68108e7i	−0.304278	+	0.304278i
$633$	1.66947e8	+	1.66947e8i	0.658213	+	0.658213i
$634$		−	2.43967e8i		−	0.957333i
$635$		0			0
$636$	4.73288e8			1.83973
$637$	4.94601e7	−	4.94601e7i	0.191354	−	0.191354i
$638$	−3.17552e7	−	3.17552e7i	−0.122279	−	0.122279i
$639$		−	8.94508e8i		−	3.42832i
$640$		0			0
$641$	−1.98771e8			−0.754710			−0.377355	−	0.926069i	$-0.623166\pi$
$641$	−1.98771e8			−0.754710			−0.377355	+	0.926069i	$0.623166\pi$
$642$	3.01288e8	−	3.01288e8i	1.13861	−	1.13861i
$643$	−3.10831e8	−	3.10831e8i	−1.16921	−	1.16921i	−0.982396	−	0.186811i	$-0.940185\pi$
$643$	−3.10831e8	−	3.10831e8i	−1.16921	−	1.16921i	−0.186811	−	0.982396i	$-0.559815\pi$
$644$			1.01181e8i			0.378827i
$645$		0			0
$646$	9.87307e7			0.366231
$647$	1.85002e8	−	1.85002e8i	0.683066	−	0.683066i	−0.277624	−	0.960690i	$-0.589547\pi$
$647$	1.85002e8	−	1.85002e8i	0.683066	−	0.683066i	0.960690	+	0.277624i	$0.0895468\pi$
$648$	−1.68907e8	−	1.68907e8i	−0.620758	−	0.620758i
$649$			4.27894e8i			1.56532i
$650$		0			0
$651$	3.47452e8			1.25937
$652$	3.04071e7	−	3.04071e7i	0.109706	−	0.109706i
$653$	−5.38585e7	−	5.38585e7i	−0.193426	−	0.193426i	0.603749	−	0.797175i	$-0.293673\pi$
$653$	−5.38585e7	−	5.38585e7i	−0.193426	−	0.193426i	−0.797175	+	0.603749i	$0.793673\pi$
$654$		−	2.33482e7i		−	0.0834679i
$655$		0			0
$656$	1.83237e7			0.0649086
$657$	−4.44281e8	+	4.44281e8i	−1.56661	+	1.56661i
$658$	−2.00422e7	−	2.00422e7i	−0.0703504	−	0.0703504i
$659$		−	1.24841e8i		−	0.436215i	−0.975925	−	0.218108i	$-0.930012\pi$
$659$		−	1.24841e8i		−	0.436215i	0.975925	−	0.218108i	$-0.0699884\pi$
$660$		0			0
$661$	2.46400e8			0.853170			0.426585	−	0.904447i	$-0.359716\pi$
$661$	2.46400e8			0.853170			0.426585	+	0.904447i	$0.359716\pi$
$662$	2.88622e7	−	2.88622e7i	0.0994845	−	0.0994845i
$663$	−3.32250e8	−	3.32250e8i	−1.14005	−	1.14005i
$664$			8.85040e7i			0.302314i
$665$		0			0
$666$	−1.79027e8			−0.606032
$667$	4.73388e7	−	4.73388e7i	0.159529	−	0.159529i
$668$	−7.89786e7	−	7.89786e7i	−0.264960	−	0.264960i
$669$			3.10933e8i			1.03846i
$670$		0			0
$671$	−2.11597e8			−0.700393
$672$	−3.28052e8	+	3.28052e8i	−1.08102	+	1.08102i
$673$	3.32338e8	+	3.32338e8i	1.09027	+	1.09027i	0.995499	+	0.0947737i	$0.0302128\pi$
$673$	3.32338e8	+	3.32338e8i	1.09027	+	1.09027i	0.0947737	+	0.995499i	$0.469787\pi$
$674$		−	1.28591e8i		−	0.419982i
$675$		0			0
$676$	1.57325e6			0.00509280
$677$	3.92435e8	−	3.92435e8i	1.26474	−	1.26474i	0.315973	−	0.948768i	$-0.397669\pi$
$677$	3.92435e8	−	3.92435e8i	1.26474	−	1.26474i	0.948768	−	0.315973i	$-0.102331\pi$
$678$	1.91159e8	+	1.91159e8i	0.613345	+	0.613345i
$679$		−	3.35593e8i		−	1.07202i
$680$		0			0
$681$	3.28480e7			0.104008
$682$	−9.06396e7	+	9.06396e7i	−0.285736	+	0.285736i
$683$	8.00187e7	+	8.00187e7i	0.251148	+	0.251148i	0.821441	−	0.570293i	$-0.193170\pi$
$683$	8.00187e7	+	8.00187e7i	0.251148	+	0.251148i	−0.570293	+	0.821441i	$0.693170\pi$
$684$			3.37269e8i			1.05392i
$685$		0			0
$686$	−1.85803e8			−0.575547
$687$	−2.71794e8	+	2.71794e8i	−0.838243	+	0.838243i
$688$	7.74507e7	+	7.74507e7i	0.237826	+	0.237826i
$689$		−	4.82642e8i		−	1.47559i
$690$		0			0
$691$	1.24099e8			0.376126			0.188063	−	0.982157i	$-0.439779\pi$
$691$	1.24099e8			0.376126			0.188063	+	0.982157i	$0.439779\pi$
$692$	−1.79801e8	+	1.79801e8i	−0.542592	+	0.542592i
$693$	3.56332e8	+	3.56332e8i	1.07067	+	1.07067i
$694$			3.08067e8i			0.921651i
$695$		0			0
$696$	1.94060e8			0.575583
$697$	6.18140e7	−	6.18140e7i	0.182553	−	0.182553i
$698$	6.33914e7	+	6.33914e7i	0.186408	+	0.186408i
$699$			8.57315e8i			2.51020i
$700$		0			0
$701$	−6.65394e8			−1.93163			−0.965817	−	0.259225i	$-0.916533\pi$
$701$	−6.65394e8			−1.93163			−0.965817	+	0.259225i	$0.916533\pi$
$702$	−2.20683e8	+	2.20683e8i	−0.637907	+	0.637907i
$703$	1.04196e8	+	1.04196e8i	0.299905	+	0.299905i
$704$		−	9.78627e7i		−	0.280478i
$705$		0			0
$706$	1.61929e8			0.460162
$707$	3.64816e8	−	3.64816e8i	1.03232	−	1.03232i
$708$	−5.46753e8	−	5.46753e8i	−1.54061	−	1.54061i
$709$			4.10060e8i			1.15056i	0.817957	+	0.575279i	$0.195107\pi$
$709$			4.10060e8i			1.15056i	−0.817957	+	0.575279i	$0.804893\pi$
$710$		0			0
$711$	−3.37269e8			−0.938357
$712$	8.91891e7	−	8.91891e7i	0.247099	−	0.247099i
$713$	−1.35120e8	−	1.35120e8i	−0.372779	−	0.372779i
$714$			2.66573e8i			0.732355i
$715$		0			0
$716$	−3.44009e8			−0.937197
$717$	1.29765e8	−	1.29765e8i	0.352047	−	0.352047i
$718$	2.70508e7	+	2.70508e7i	0.0730813	+	0.0730813i
$719$		−	3.16685e8i		−	0.852003i	−0.904722	−	0.426001i	$-0.859922\pi$
$719$		−	3.16685e8i		−	0.852003i	0.904722	−	0.426001i	$-0.140078\pi$
$720$		0			0
$721$	−3.88670e8			−1.03699
$722$	6.43268e7	−	6.43268e7i	0.170915	−	0.170915i
$723$	−3.84588e8	−	3.84588e8i	−1.01761	−	1.01761i
$724$		−	4.04819e8i		−	1.06671i
$725$		0			0
$726$	7.13230e7			0.186389
$727$	4.32150e8	−	4.32150e8i	1.12468	−	1.12468i	0.133657	−	0.991028i	$-0.457328\pi$
$727$	4.32150e8	−	4.32150e8i	1.12468	−	1.12468i	0.991028	−	0.133657i	$-0.0426721\pi$
$728$	2.11488e8	+	2.11488e8i	0.548140	+	0.548140i
$729$			4.01534e8i			1.03643i
$730$		0			0
$731$	5.22551e8			1.33775
$732$	2.70374e8	−	2.70374e8i	0.689337	−	0.689337i
$733$	1.76123e8	+	1.76123e8i	0.447202	+	0.447202i	0.894423	−	0.447221i	$-0.147586\pi$
$733$	1.76123e8	+	1.76123e8i	0.447202	+	0.447202i	−0.447221	+	0.894423i	$0.647586\pi$
$734$			2.46345e8i			0.622955i
$735$		0			0
$736$	2.55152e8			0.639977
$737$	−2.85444e8	+	2.85444e8i	−0.713048	+	0.713048i
$738$	−8.26278e7	−	8.26278e7i	−0.205569	−	0.205569i
$739$			6.86279e8i			1.70046i	0.526409	+	0.850232i	$0.323538\pi$
$739$			6.86279e8i			1.70046i	−0.526409	+	0.850232i	$0.676462\pi$
$740$		0			0
$741$	5.16970e8			1.27061
$742$	−1.93618e8	+	1.93618e8i	−0.473951	+	0.473951i
$743$	−1.85043e8	−	1.85043e8i	−0.451136	−	0.451136i	0.444596	−	0.895731i	$-0.353347\pi$
$743$	−1.85043e8	−	1.85043e8i	−0.451136	−	0.451136i	−0.895731	+	0.444596i	$0.853347\pi$
$744$		−	5.53909e8i		−	1.34499i
$745$		0			0
$746$	−5.73605e7			−0.138165
$747$	−1.94307e8	+	1.94307e8i	−0.466150	+	0.466150i
$748$	1.77715e8	+	1.77715e8i	0.424639	+	0.424639i
$749$		−	6.29966e8i		−	1.49924i
$750$		0			0
$751$	1.85169e8			0.437168			0.218584	−	0.975818i	$-0.429856\pi$
$751$	1.85169e8			0.437168			0.218584	+	0.975818i	$0.429856\pi$
$752$	1.55561e7	−	1.55561e7i	0.0365802	−	0.0365802i
$753$	−1.21778e8	−	1.21778e8i	−0.285223	−	0.285223i
$754$		−	8.27561e7i		−	0.193057i
$755$		0			0
$756$	−4.52485e8			−1.04722
$757$	−1.39488e8	+	1.39488e8i	−0.321550	+	0.321550i	−0.849362	−	0.527811i	$-0.823013\pi$
$757$	−1.39488e8	+	1.39488e8i	−0.321550	+	0.321550i	0.527811	+	0.849362i	$0.323013\pi$
$758$	2.00295e8	+	2.00295e8i	0.459898	+	0.459898i
$759$		−	4.16582e8i		−	0.952741i
$760$		0			0
$761$	−3.92794e7			−0.0891274			−0.0445637	−	0.999007i	$-0.514190\pi$
$761$	−3.92794e7			−0.0891274			−0.0445637	+	0.999007i	$0.514190\pi$
$762$	1.41817e8	−	1.41817e8i	0.320526	−	0.320526i
$763$	−2.44094e7	−	2.44094e7i	−0.0549521	−	0.0549521i
$764$			2.61436e8i			0.586253i
$765$		0			0
$766$	−3.97196e8			−0.883728
$767$	−5.57559e8	+	5.57559e8i	−1.23568	+	1.23568i
$768$	4.29327e8	+	4.29327e8i	0.947773	+	0.947773i
$769$		−	4.31054e8i		−	0.947878i	−0.880558	−	0.473939i	$-0.842832\pi$
$769$		−	4.31054e8i		−	0.947878i	0.880558	−	0.473939i	$-0.157168\pi$
$770$		0			0
$771$	5.13799e8			1.12106
$772$	−5.77729e7	+	5.77729e7i	−0.125566	+	0.125566i
$773$	−5.53092e7	−	5.53092e7i	−0.119745	−	0.119745i	0.644695	−	0.764440i	$-0.276984\pi$
$773$	−5.53092e7	−	5.53092e7i	−0.119745	−	0.119745i	−0.764440	+	0.644695i	$0.776984\pi$
$774$		−	6.98502e8i		−	1.50642i
$775$		0			0
$776$	−5.35004e8			−1.14491
$777$	−2.81328e8	+	2.81328e8i	−0.599722	+	0.599722i
$778$	−1.03434e8	−	1.03434e8i	−0.219646	−	0.219646i
$779$			9.61805e7i			0.203458i
$780$		0			0
$781$	7.33386e8			1.53950
$782$	1.03667e8	−	1.03667e8i	0.216781	−	0.216781i
$783$	2.11702e8	+	2.11702e8i	0.441000	+	0.441000i
$784$		−	3.08008e7i		−	0.0639165i
$785$		0			0
$786$	1.90767e8			0.392857
$787$	−2.33171e8	+	2.33171e8i	−0.478355	+	0.478355i	−0.904605	−	0.426250i	$-0.859834\pi$
$787$	−2.33171e8	+	2.33171e8i	−0.478355	+	0.478355i	0.426250	+	0.904605i	$0.359834\pi$
$788$	1.82767e8	+	1.82767e8i	0.373524	+	0.373524i
$789$			9.68499e7i			0.197182i
$790$		0			0
$791$	3.99695e8			0.807606
$792$	5.68066e8	−	5.68066e8i	1.14347	−	1.14347i
$793$	−2.75717e8	−	2.75717e8i	−0.552897	−	0.552897i
$794$			2.42107e8i			0.483667i
$795$		0			0
$796$	3.56114e8			0.706073
$797$	5.73297e8	−	5.73297e8i	1.13241	−	1.13241i	0.142638	−	0.989775i	$-0.454442\pi$
$797$	5.73297e8	−	5.73297e8i	1.13241	−	1.13241i	0.989775	−	0.142638i	$-0.0455584\pi$
$798$	−2.07389e8	−	2.07389e8i	−0.408110	−	0.408110i
$799$		−	1.04955e8i		−	0.205761i
$800$		0			0
$801$	3.91621e8			0.762024
$802$	−2.24562e8	+	2.24562e8i	−0.435325	+	0.435325i
$803$	−3.64255e8	−	3.64255e8i	−0.703492	−	0.703492i
$804$		−	7.29469e8i		−	1.40358i
$805$		0			0
$806$	−2.36212e8			−0.451126
$807$	6.47508e8	−	6.47508e8i	1.23204	−	1.23204i
$808$	−5.81591e8	−	5.81591e8i	−1.10251	−	1.10251i
$809$		−	3.03739e8i		−	0.573660i	−0.957981	−	0.286830i	$-0.907398\pi$
$809$		−	3.03739e8i		−	0.573660i	0.957981	−	0.286830i	$-0.0926016\pi$
$810$		0			0
$811$	−7.53778e8			−1.41313			−0.706563	−	0.707650i	$-0.749755\pi$
$811$	−7.53778e8			−1.41313			−0.706563	+	0.707650i	$0.749755\pi$
$812$	8.48410e7	−	8.48410e7i	0.158467	−	0.158467i
$813$	3.03703e8	+	3.03703e8i	0.565168	+	0.565168i
$814$		−	1.46780e8i		−	0.272140i
$815$		0			0
$816$	−2.06905e8			−0.380804
$817$	−4.06536e8	+	4.06536e8i	−0.745474	+	0.745474i
$818$	−3.90445e8	−	3.90445e8i	−0.713346	−	0.713346i
$819$			9.28624e8i			1.69039i
$820$		0			0
$821$	1.61977e8			0.292700			0.146350	−	0.989233i	$-0.453247\pi$
$821$	1.61977e8			0.292700			0.146350	+	0.989233i	$0.453247\pi$
$822$	1.32248e7	−	1.32248e7i	0.0238108	−	0.0238108i
$823$	3.26681e8	+	3.26681e8i	0.586037	+	0.586037i	0.936556	−	0.350519i	$-0.113995\pi$
$823$	3.26681e8	+	3.26681e8i	0.586037	+	0.586037i	−0.350519	+	0.936556i	$0.613995\pi$
$824$			6.19619e8i			1.10750i
$825$		0			0
$826$	4.47344e8			0.793782
$827$	−4.04807e8	+	4.04807e8i	−0.715700	+	0.715700i	−0.967722	−	0.252021i	$-0.918905\pi$
$827$	−4.04807e8	+	4.04807e8i	−0.715700	+	0.715700i	0.252021	+	0.967722i	$0.418905\pi$
$828$	3.54133e8	+	3.54133e8i	0.623843	+	0.623843i
$829$			8.57650e8i			1.50538i	0.658375	+	0.752690i	$0.271244\pi$
$829$			8.57650e8i			1.50538i	−0.658375	+	0.752690i	$0.728756\pi$
$830$		0			0
$831$	−1.36061e9			−2.37100
$832$	1.27518e8	−	1.27518e8i	0.221412	−	0.221412i
$833$	−1.03905e8	−	1.03905e8i	−0.179763	−	0.179763i
$834$		−	8.44628e7i		−	0.145602i
$835$		0			0
$836$	−2.76519e8			−0.473267
$837$	6.04264e8	−	6.04264e8i	1.03051	−	1.03051i
$838$	3.14897e8	+	3.14897e8i	0.535102	+	0.535102i
$839$			3.20361e8i			0.542443i	0.962517	+	0.271222i	$0.0874277\pi$
$839$			3.20361e8i			0.542443i	−0.962517	+	0.271222i	$0.912572\pi$
$840$		0			0
$841$	5.15435e8			0.866535
$842$	−9.75892e7	+	9.75892e7i	−0.163480	+	0.163480i
$843$	1.20105e9	+	1.20105e9i	2.00484	+	2.00484i
$844$		−	2.32713e8i		−	0.387074i
$845$		0			0
$846$	−1.40295e8			−0.231703
$847$	7.45649e7	−	7.45649e7i	0.122711	−	0.122711i
$848$	−1.50280e8	−	1.50280e8i	−0.246441	−	0.246441i
$849$			1.07643e8i			0.175899i
$850$		0			0
$851$	2.18811e8			0.355042
$852$	−9.37104e8	+	9.37104e8i	−1.51520	+	1.51520i
$853$	−3.88384e8	−	3.88384e8i	−0.625770	−	0.625770i	0.321231	−	0.947001i	$-0.395903\pi$
$853$	−3.88384e8	−	3.88384e8i	−0.625770	−	0.625770i	−0.947001	+	0.321231i	$0.895903\pi$
$854$			2.21215e8i			0.355174i
$855$		0			0
$856$	−1.00429e9			−1.60118
$857$	−5.62507e8	+	5.62507e8i	−0.893687	+	0.893687i	−0.994868	−	0.101181i	$-0.967738\pi$
$857$	−5.62507e8	+	5.62507e8i	−0.893687	+	0.893687i	0.101181	+	0.994868i	$0.467738\pi$
$858$	−3.64127e8	−	3.64127e8i	−0.576489	−	0.576489i
$859$		−	8.47273e8i		−	1.33673i	−0.743834	−	0.668365i	$-0.766994\pi$
$859$		−	8.47273e8i		−	1.33673i	0.743834	−	0.668365i	$-0.233006\pi$
$860$		0			0
$861$	−2.59687e8			−0.406856
$862$	−5.91125e7	+	5.91125e7i	−0.0922906	+	0.0922906i
$863$	7.79332e8	+	7.79332e8i	1.21252	+	1.21252i	0.970194	+	0.242329i	$0.0779114\pi$
$863$	7.79332e8	+	7.79332e8i	1.21252	+	1.21252i	0.242329	+	0.970194i	$0.422089\pi$
$864$			1.14105e9i			1.76915i
$865$		0			0
$866$	4.21281e8			0.648662
$867$	9.85565e7	−	9.85565e7i	0.151227	−	0.151227i
$868$	−2.42164e8	−	2.42164e8i	−0.370296	−	0.370296i
$869$		−	2.76519e8i		−	0.421372i
$870$		0			0
$871$	−7.43885e8			−1.12577
$872$	−3.89136e7	+	3.89136e7i	−0.0586884	+	0.0586884i
$873$	−1.17458e9	−	1.17458e9i	−1.76538	−	1.76538i
$874$			1.61303e8i			0.241606i
$875$		0			0
$876$	9.30874e8			1.38477
$877$	7.41247e8	−	7.41247e8i	1.09892	−	1.09892i	0.104378	−	0.994538i	$-0.466715\pi$
$877$	7.41247e8	−	7.41247e8i	1.09892	−	1.09892i	0.994538	−	0.104378i	$-0.0332851\pi$
$878$	−3.27760e8	−	3.27760e8i	−0.484253	−	0.484253i
$879$			8.65588e8i			1.27451i
$880$		0			0
$881$	3.83908e8			0.561435			0.280717	−	0.959790i	$-0.409428\pi$
$881$	3.83908e8			0.561435			0.280717	+	0.959790i	$0.409428\pi$
$882$	−1.38891e8	+	1.38891e8i	−0.202427	+	0.202427i
$883$	−5.05244e7	−	5.05244e7i	−0.0733869	−	0.0733869i	0.669461	−	0.742848i	$-0.266525\pi$
$883$	−5.05244e7	−	5.05244e7i	−0.0733869	−	0.0733869i	−0.742848	+	0.669461i	$0.766525\pi$
$884$			4.63137e8i			0.670429i
$885$		0			0
$886$	1.24203e7			0.0178580
$887$	−1.31857e8	+	1.31857e8i	−0.188944	+	0.188944i	−0.795239	−	0.606296i	$-0.792655\pi$
$887$	−1.31857e8	+	1.31857e8i	−0.188944	+	0.188944i	0.606296	+	0.795239i	$0.292655\pi$
$888$	4.48494e8	+	4.48494e8i	0.640498	+	0.640498i
$889$		−	2.96526e8i		−	0.422044i
$890$		0			0
$891$	6.08065e8			0.859640
$892$	2.16711e8	−	2.16711e8i	0.305342	−	0.305342i
$893$	8.16532e7	+	8.16532e7i	0.114662	+	0.114662i
$894$		−	6.11582e8i		−	0.855938i
$895$		0			0
$896$	5.33911e8			0.742241
$897$	5.42819e8	−	5.42819e8i	0.752103	−	0.752103i
$898$	2.54113e8	+	2.54113e8i	0.350912	+	0.350912i
$899$			2.26599e8i			0.311874i
$900$		0			0
$901$	−1.01392e9			−1.38621
$902$	6.77445e7	−	6.77445e7i	0.0923112	−	0.0923112i
$903$	−1.09765e9	−	1.09765e9i	−1.49073	−	1.49073i
$904$		−	6.37196e8i		−	0.862517i
$905$		0			0
$906$	−7.75002e8			−1.04212
$907$	−7.39820e7	+	7.39820e7i	−0.0991526	+	0.0991526i	−0.754943	−	0.655790i	$-0.772336\pi$
$907$	−7.39820e7	+	7.39820e7i	−0.0991526	+	0.0991526i	0.655790	+	0.754943i	$0.272336\pi$
$908$	−2.28941e7	−	2.28941e7i	−0.0305820	−	0.0305820i
$909$		−	2.55371e9i		−	3.40001i
$910$		0			0
$911$	5.22927e8			0.691649			0.345824	−	0.938299i	$-0.387599\pi$
$911$	5.22927e8			0.691649			0.345824	+	0.938299i	$0.387599\pi$
$912$	1.60969e8	−	1.60969e8i	0.212206	−	0.212206i
$913$	−1.59307e8	−	1.59307e8i	−0.209326	−	0.209326i
$914$		−	2.72201e8i		−	0.356493i
$915$		0			0
$916$	3.78865e8			0.492944
$917$	1.99438e8	−	1.99438e8i	0.258642	−	0.258642i
$918$	4.63605e8	+	4.63605e8i	0.599267	+	0.599267i
$919$			8.71858e8i			1.12331i	0.827372	+	0.561655i	$0.189835\pi$
$919$			8.71858e8i			1.12331i	−0.827372	+	0.561655i	$0.810165\pi$
$920$		0			0
$921$	−3.98917e8			−0.510627
$922$	2.59144e8	−	2.59144e8i	0.330634	−	0.330634i
$923$	9.55624e8	+	9.55624e8i	1.21530	+	1.21530i
$924$		−	7.46601e8i		−	0.946395i
$925$		0			0
$926$	5.61641e8			0.707336
$927$	−1.36035e9	+	1.36035e9i	−1.70769	+	1.70769i
$928$	−2.13947e8	−	2.13947e8i	−0.267708	−	0.267708i
$929$		−	3.45641e8i		−	0.431100i	−0.976493	−	0.215550i	$-0.930846\pi$
$929$		−	3.45641e8i		−	0.431100i	0.976493	−	0.215550i	$-0.0691544\pi$
$930$		0			0
$931$	1.61672e8			0.200348
$932$	5.97523e8	−	5.97523e8i	0.738086	−	0.738086i
$933$	9.82901e8	+	9.82901e8i	1.21022	+	1.21022i
$934$			1.59255e8i			0.195458i
$935$		0			0
$936$	1.48041e9			1.80533
$937$	−4.65552e8	+	4.65552e8i	−0.565913	+	0.565913i	−0.930981	−	0.365068i	$-0.881046\pi$
$937$	−4.65552e8	+	4.65552e8i	−0.565913	+	0.565913i	0.365068	+	0.930981i	$0.381046\pi$
$938$	2.98419e8	+	2.98419e8i	0.361591	+	0.361591i
$939$		−	2.64496e7i		−	0.0319465i
$940$		0			0
$941$	1.13629e9			1.36370			0.681851	−	0.731491i	$-0.261175\pi$
$941$	1.13629e9			1.36370			0.681851	+	0.731491i	$0.261175\pi$
$942$	−7.80787e8	+	7.80787e8i	−0.934071	+	0.934071i
$943$	1.00990e8	+	1.00990e8i	0.120432	+	0.120432i
$944$			3.47214e8i			0.412744i
$945$		0			0
$946$	5.72685e8			0.676460
$947$	5.38433e8	−	5.38433e8i	0.633989	−	0.633989i	−0.315077	−	0.949066i	$-0.602030\pi$
$947$	5.38433e8	−	5.38433e8i	0.633989	−	0.633989i	0.949066	+	0.315077i	$0.102030\pi$
$948$	3.53330e8	+	3.53330e8i	0.414720	+	0.414720i
$949$		−	9.49271e8i		−	1.11069i
$950$		0			0
$951$	−2.68364e9			−3.12020
$952$	4.44288e8	−	4.44288e8i	0.514937	−	0.514937i
$953$	−1.36529e8	−	1.36529e8i	−0.157742	−	0.157742i	0.623823	−	0.781565i	$-0.285578\pi$
$953$	−1.36529e8	−	1.36529e8i	−0.157742	−	0.157742i	−0.781565	+	0.623823i	$0.785578\pi$
$954$			1.35533e9i			1.56098i
$955$		0			0
$956$	−1.80885e8			−0.207028
$957$	−3.49308e8	+	3.49308e8i	−0.398540	+	0.398540i
$958$	2.01794e8	+	2.01794e8i	0.229515	+	0.229515i
$959$		−	2.76519e7i		−	0.0313523i
$960$		0			0
$961$	−2.40717e8			−0.271229
$962$	1.91258e8	−	1.91258e8i	0.214830	−	0.214830i
$963$	−2.20488e9	−	2.20488e9i	−2.46892	−	2.46892i
$964$			5.36093e8i			0.598424i
$965$		0			0
$966$	−4.35517e8			−0.483141
$967$	3.28178e8	−	3.28178e8i	0.362936	−	0.362936i	−0.501957	−	0.864893i	$-0.667386\pi$
$967$	3.28178e8	−	3.28178e8i	0.362936	−	0.362936i	0.864893	+	0.501957i	$0.167386\pi$
$968$	−1.18872e8	−	1.18872e8i	−0.131055	−	0.131055i
$969$		−	1.08604e9i		−	1.19364i
$970$		0			0
$971$	1.35791e9			1.48324			0.741621	−	0.670819i	$-0.234057\pi$
$971$	1.35791e9			1.48324			0.741621	+	0.670819i	$0.234057\pi$
$972$	1.97962e7	−	1.97962e7i	0.0215568	−	0.0215568i
$973$	−8.83021e7	−	8.83021e7i	−0.0958589	−	0.0958589i
$974$			4.99366e8i			0.540433i
$975$		0			0
$976$	−1.71700e8			−0.184680
$977$	2.90834e7	−	2.90834e7i	0.0311862	−	0.0311862i	−0.691342	−	0.722528i	$-0.742980\pi$
$977$	2.90834e7	−	2.90834e7i	0.0311862	−	0.0311862i	0.722528	+	0.691342i	$0.242980\pi$
$978$	1.30883e8	+	1.30883e8i	0.139915	+	0.139915i
$979$			3.21081e8i			0.342189i
$980$		0			0
$981$	−1.70866e8			−0.180988
$982$	5.09684e8	−	5.09684e8i	0.538228	−	0.538228i
$983$	−5.98046e8	−	5.98046e8i	−0.629613	−	0.629613i	0.318358	−	0.947971i	$-0.396869\pi$
$983$	−5.98046e8	−	5.98046e8i	−0.629613	−	0.629613i	−0.947971	+	0.318358i	$0.896869\pi$
$984$			4.13994e8i			0.434519i
$985$		0			0
$986$	−1.73852e8			−0.181363
$987$	−2.20464e8	+	2.20464e8i	−0.229290	+	0.229290i
$988$	−3.60312e8	−	3.60312e8i	−0.373601	−	0.373601i
$989$			8.53725e8i			0.882529i
$990$		0			0
$991$	−1.00844e9			−1.03617			−0.518084	−	0.855330i	$-0.673354\pi$
$991$	−1.00844e9			−1.03617			−0.518084	+	0.855330i	$0.673354\pi$
$992$	−6.10673e8	+	6.10673e8i	−0.625567	+	0.625567i
$993$	−3.17484e8	−	3.17484e8i	−0.324246	−	0.324246i
$994$		−	7.66721e8i		−	0.780690i
$995$		0			0
$996$	4.07118e8			0.412043
$997$	−1.06301e9	+	1.06301e9i	−1.07264	+	1.07264i	−0.0754885	+	0.997147i	$0.524052\pi$
$997$	−1.06301e9	+	1.06301e9i	−1.07264	+	1.07264i	−0.997147	+	0.0754885i	$0.975948\pi$
$998$	−3.37156e8	−	3.37156e8i	−0.339188	−	0.339188i
$999$			9.78532e8i			0.981473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.7.c.b.18.1	yes	2
3.2	odd	2		225.7.g.a.118.1		2
5.2	odd	4	inner	25.7.c.b.7.1	yes	2
5.3	odd	4		25.7.c.a.7.1	✓	2
5.4	even	2		25.7.c.a.18.1	yes	2
15.2	even	4		225.7.g.a.82.1		2
15.8	even	4		225.7.g.b.82.1		2
15.14	odd	2		225.7.g.b.118.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.7.c.a.7.1	✓	2	5.3	odd	4
25.7.c.a.18.1	yes	2	5.4	even	2
25.7.c.b.7.1	yes	2	5.2	odd	4	inner
25.7.c.b.18.1	yes	2	1.1	even	1	trivial
225.7.g.a.82.1		2	15.2	even	4
225.7.g.a.118.1		2	3.2	odd	2
225.7.g.b.82.1		2	15.8	even	4
225.7.g.b.118.1		2	15.14	odd	2

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 - 3.00000i) q^{2} +(-33.0000 - 33.0000i) q^{3} +46.0000i q^{4} -198.000 q^{6} +(-207.000 + 207.000i) q^{7} +(330.000 + 330.000i) q^{8} +1449.00i q^{9} +O(q^{10})\)	\(q+(3.00000 - 3.00000i) q^{2} +(-33.0000 - 33.0000i) q^{3} +46.0000i q^{4} -198.000 q^{6} +(-207.000 + 207.000i) q^{7} +(330.000 + 330.000i) q^{8} +1449.00i q^{9} -1188.00 q^{11} +(1518.00 - 1518.00i) q^{12} +(-1548.00 - 1548.00i) q^{13} +1242.00i q^{14} -964.000 q^{16} +(-3252.00 + 3252.00i) q^{17} +(4347.00 + 4347.00i) q^{18} -5060.00i q^{19} +13662.0 q^{21} +(-3564.00 + 3564.00i) q^{22} +(-5313.00 - 5313.00i) q^{23} -21780.0i q^{24} -9288.00 q^{26} +(23760.0 - 23760.0i) q^{27} +(-9522.00 - 9522.00i) q^{28} +8910.00i q^{29} +25432.0 q^{31} +(-24012.0 + 24012.0i) q^{32} +(39204.0 + 39204.0i) q^{33} +19512.0i q^{34} -66654.0 q^{36} +(-20592.0 + 20592.0i) q^{37} +(-15180.0 - 15180.0i) q^{38} +102168. i q^{39} -19008.0 q^{41} +(40986.0 - 40986.0i) q^{42} +(-80343.0 - 80343.0i) q^{43} -54648.0i q^{44} -31878.0 q^{46} +(-16137.0 + 16137.0i) q^{47} +(31812.0 + 31812.0i) q^{48} +31951.0i q^{49} +214632. q^{51} +(71208.0 - 71208.0i) q^{52} +(155892. + 155892. i) q^{53} -142560. i q^{54} -136620. q^{56} +(-166980. + 166980. i) q^{57} +(26730.0 + 26730.0i) q^{58} -360180. i q^{59} +178112. q^{61} +(76296.0 - 76296.0i) q^{62} +(-299943. - 299943. i) q^{63} +82376.0i q^{64} +235224. q^{66} +(240273. - 240273. i) q^{67} +(-149592. - 149592. i) q^{68} +350658. i q^{69} -617328. q^{71} +(-478170. + 478170. i) q^{72} +(306612. + 306612. i) q^{73} +123552. i q^{74} +232760. q^{76} +(245916. - 245916. i) q^{77} +(306504. + 306504. i) q^{78} +232760. i q^{79} -511839. q^{81} +(-57024.0 + 57024.0i) q^{82} +(134097. + 134097. i) q^{83} +628452. i q^{84} -482058. q^{86} +(294030. - 294030. i) q^{87} +(-392040. - 392040. i) q^{88} -270270. i q^{89} +640872. q^{91} +(244398. - 244398. i) q^{92} +(-839256. - 839256. i) q^{93} +96822.0i q^{94} +1.58479e6 q^{96} +(-810612. + 810612. i) q^{97} +(95853.0 + 95853.0i) q^{98} -1.72141e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} - 66 q^{3} - 396 q^{6} - 414 q^{7} + 660 q^{8}+O(q^{10}) \) 2 * q + 6 * q^2 - 66 * q^3 - 396 * q^6 - 414 * q^7 + 660 * q^8	\( 2 q + 6 q^{2} - 66 q^{3} - 396 q^{6} - 414 q^{7} + 660 q^{8} - 2376 q^{11} + 3036 q^{12} - 3096 q^{13} - 1928 q^{16} - 6504 q^{17} + 8694 q^{18} + 27324 q^{21} - 7128 q^{22} - 10626 q^{23} - 18576 q^{26} + 47520 q^{27} - 19044 q^{28} + 50864 q^{31} - 48024 q^{32} + 78408 q^{33} - 133308 q^{36} - 41184 q^{37} - 30360 q^{38} - 38016 q^{41} + 81972 q^{42} - 160686 q^{43} - 63756 q^{46} - 32274 q^{47} + 63624 q^{48} + 429264 q^{51} + 142416 q^{52} + 311784 q^{53} - 273240 q^{56} - 333960 q^{57} + 53460 q^{58} + 356224 q^{61} + 152592 q^{62} - 599886 q^{63} + 470448 q^{66} + 480546 q^{67} - 299184 q^{68} - 1234656 q^{71} - 956340 q^{72} + 613224 q^{73} + 465520 q^{76} + 491832 q^{77} + 613008 q^{78} - 1023678 q^{81} - 114048 q^{82} + 268194 q^{83} - 964116 q^{86} + 588060 q^{87} - 784080 q^{88} + 1281744 q^{91} + 488796 q^{92} - 1678512 q^{93} + 3169584 q^{96} - 1621224 q^{97} + 191706 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 - 66 * q^3 - 396 * q^6 - 414 * q^7 + 660 * q^8 - 2376 * q^11 + 3036 * q^12 - 3096 * q^13 - 1928 * q^16 - 6504 * q^17 + 8694 * q^18 + 27324 * q^21 - 7128 * q^22 - 10626 * q^23 - 18576 * q^26 + 47520 * q^27 - 19044 * q^28 + 50864 * q^31 - 48024 * q^32 + 78408 * q^33 - 133308 * q^36 - 41184 * q^37 - 30360 * q^38 - 38016 * q^41 + 81972 * q^42 - 160686 * q^43 - 63756 * q^46 - 32274 * q^47 + 63624 * q^48 + 429264 * q^51 + 142416 * q^52 + 311784 * q^53 - 273240 * q^56 - 333960 * q^57 + 53460 * q^58 + 356224 * q^61 + 152592 * q^62 - 599886 * q^63 + 470448 * q^66 + 480546 * q^67 - 299184 * q^68 - 1234656 * q^71 - 956340 * q^72 + 613224 * q^73 + 465520 * q^76 + 491832 * q^77 + 613008 * q^78 - 1023678 * q^81 - 114048 * q^82 + 268194 * q^83 - 964116 * q^86 + 588060 * q^87 - 784080 * q^88 + 1281744 * q^91 + 488796 * q^92 - 1678512 * q^93 + 3169584 * q^96 - 1621224 * q^97 + 191706 * q^98

Introduction

L-functions

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